Theta_p can be defined in terms of the tau coefficients by the formula
with Theta_p in the interval [0,Pi]. The angles Theta_p are supposed to be distributed according to the Sato-Tate distribution. Here is a numerical list of Theta_p:
{2, 1.839171415409252}
{3, 1.266767370974077}
{5, 1.217911114048765}
{7, 1.760200592888874}
{11, 1.046693503300122}
{13, 1.788287572158221}
{17, 2.201638749720374}
{19, 1.054225415325547}
{23, 1.264019467241492}
{29, 0.950523288737463}
{31, 1.737321000403601}
{37, 1.78850553404388}
{41, 1.361601191428082}
{43, 1.579679083041952}
{47, 0.5460432176599398}
{53, 1.836015065829757}
{59, 2.062900404041979}
{61, 1.015394298049476}
{67, 2.346832407971304}
{71, 1.242922354102152}
{73, 1.529463309640569}
{79, 0.79980324867815}
{83, 1.991849696225951}
{89, 1.810294212518243}
{97, 1.111328634635751}
{101, 1.173476681894353}
{103, 2.855688404990901}
{107, 1.254548298320956}
{109, 1.34003094836512}
{113, 1.789919461844269}
{127, 1.931366387463395}
{131, 0.7740192017504763}
{137, 1.836988272625491}
{139, 1.061265906583865}
{149, 2.242271551878075}
{151, 2.012329792669862}
{157, 0.988244722078683}
{163, 1.692891313691184}
{167, 0.608358326841798}
{173, 1.806101933160705}
{179, 1.221819620080869}
{181, 1.762664383366978}
{191, 1.16672630202497}
{193, 0.7503265670948139}
{197, 1.923364820654254}
{199, 1.487975511722744}
{211, 2.16409526950679}
{223, 1.109249741741686}
{227, 1.645737770404376}
{229, 2.240017230464492}
{233, 2.563965188447506}
{239, 1.871414455891192}
{241, 1.579960028720735}
{251, 1.146934502715512}
{257, 0.841197342528927}
{263, 2.207777239463872}
{269, 0.977345902093985}
{271, 1.649172983073249}
{277, 1.87807482506664}
{281, 1.20453029796193}
{283, 1.293605140420732}
{293, 1.900387347356086}
{307, 1.409883396054847}
{311, 1.063243330485097}
{313, 2.781516725304158}
{317, 0.7504360565780624}
{331, 2.026182227335814}
{337, 0.7102154587171291}
{347, 2.550799803751562}
{349, 1.703743613000095}
{353, 1.449556836178938}
{359, 0.7990753723264199}
{367, 2.342567704202878}
{373, 1.76990152002047}
{379, 1.068953925819901}
{383, 0.7705631276036473}
{389, 2.01146745612642}
{397, 1.012712516334753}
{401, 1.897856802460628}
{409, 2.032373742594574}
{419, 1.431507924948365}
{421, 1.250042840826021}
{431, 1.687290977929717}
{433, 1.412457740968632}
{439, 1.613298506724037}
{443, 1.09594423625328}
{449, 2.48458325157144}
{457, 1.206711196162149}
{461, 2.524719627953313}
{463, 1.436951633769512}
{467, 2.269339159984439}
{479, 0.3109232976479444}
{487, 1.753703144307067}
{491, 1.963404494054447}
{499, 1.649647134361179}
{503, 1.212421349232917}
{509, 1.515142153599665}
{521, 1.01300736946206}
{523, 1.582987608762306}
{541, 2.475695550858549}
{547, 1.236236839209952}
{557, 1.496641333310439}
{563, 1.479407370683485}
{569, 1.075493592661858}
{571, 1.054430103546671}
{577, 1.860477360597678}
{587, 2.375778307596555}
{593, 1.65583004756025}
{599, 2.038567152829934}
{601, 0.916680030482427}
{607, 2.23284888116845}
{613, 0.955766233884562}
{617, 1.565317761524143}
{619, 0.3641549265592105}
{631, 2.583566503786621}
{641, 1.385732865889046}
{643, 1.516236421978009}
{647, 0.932658891654574}
{653, 1.767408029980983}
{659, 1.93367516444379}
{661, 2.534804868760154}
{673, 0.847480406309101}
{677, 1.762915818407543}
{683, 1.971623066035651}
{691, 1.908904174142938}
{701, 0.877632230532398}
{709, 1.497537029602451}
{719, 0.341479832030592}
{727, 1.343794804249119}
{733, 0.80846780862808}
{739, 2.348377260398369}
{743, 1.460166523134542}
{751, 1.023167660861861}
{757, 1.619579793513977}
{761, 2.153102215629794}
{769, 1.400745499930612}
{773, 2.383616117031935}
{787, 0.674753384517691}
{797, 1.443646573347738}
{809, 1.282499610295966}
{811, 1.828110306721855}
{821, 1.557738479580651}
{823, 2.245148486128435}
{827, 1.558546298924528}
{829, 0.6428588119320614}
{839, 1.907727131929766}
{853, 2.174854925799265}
{857, 2.536220268397258}
{859, 1.370952850993427}
{863, 1.176245613298162}
{877, 2.725236006902816}
{881, 1.436384205045668}
{883, 1.554618052172685}
{887, 1.395022809938955}
{907, 1.573078551590131}
{911, 1.865701564430041}
{919, 1.693476612708028}
{929, 1.48593245881352}
{937, 0.5078446972871125}
{941, 2.451191586182668}
{947, 2.224641700859286}
{953, 0.6008362537031032}
{967, 1.211398133323816}
{971, 1.981704175894451}
{977, 1.72848592472509}
{983, 1.362665624689936}
{991, 1.170677537001703}
{997, 1.921978685386645}