# Properties

 Label 720.6.a.a.1.1 Level $720$ Weight $6$ Character 720.1 Self dual yes Analytic conductor $115.476$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$720 = 2^{4} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 720.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$115.476350265$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 5) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 720.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-25.0000 q^{5} -192.000 q^{7} +O(q^{10})$$ $$q-25.0000 q^{5} -192.000 q^{7} -148.000 q^{11} +286.000 q^{13} +1678.00 q^{17} -1060.00 q^{19} +2976.00 q^{23} +625.000 q^{25} +3410.00 q^{29} +2448.00 q^{31} +4800.00 q^{35} +182.000 q^{37} +9398.00 q^{41} +1244.00 q^{43} -12088.0 q^{47} +20057.0 q^{49} -23846.0 q^{53} +3700.00 q^{55} -20020.0 q^{59} +32302.0 q^{61} -7150.00 q^{65} -60972.0 q^{67} -32648.0 q^{71} -38774.0 q^{73} +28416.0 q^{77} +33360.0 q^{79} +16716.0 q^{83} -41950.0 q^{85} -101370. q^{89} -54912.0 q^{91} +26500.0 q^{95} -119038. q^{97} +O(q^{100})$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −25.0000 −0.447214
$$6$$ 0 0
$$7$$ −192.000 −1.48100 −0.740502 0.672054i $$-0.765412\pi$$
−0.740502 + 0.672054i $$0.765412\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −148.000 −0.368791 −0.184395 0.982852i $$-0.559033\pi$$
−0.184395 + 0.982852i $$0.559033\pi$$
$$12$$ 0 0
$$13$$ 286.000 0.469362 0.234681 0.972072i $$-0.424595\pi$$
0.234681 + 0.972072i $$0.424595\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 1678.00 1.40822 0.704109 0.710092i $$-0.251347\pi$$
0.704109 + 0.710092i $$0.251347\pi$$
$$18$$ 0 0
$$19$$ −1060.00 −0.673631 −0.336815 0.941571i $$-0.609350\pi$$
−0.336815 + 0.941571i $$0.609350\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 2976.00 1.17304 0.586521 0.809934i $$-0.300497\pi$$
0.586521 + 0.809934i $$0.300497\pi$$
$$24$$ 0 0
$$25$$ 625.000 0.200000
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 3410.00 0.752938 0.376469 0.926429i $$-0.377138\pi$$
0.376469 + 0.926429i $$0.377138\pi$$
$$30$$ 0 0
$$31$$ 2448.00 0.457517 0.228758 0.973483i $$-0.426533\pi$$
0.228758 + 0.973483i $$0.426533\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 4800.00 0.662325
$$36$$ 0 0
$$37$$ 182.000 0.0218558 0.0109279 0.999940i $$-0.496521\pi$$
0.0109279 + 0.999940i $$0.496521\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 9398.00 0.873124 0.436562 0.899674i $$-0.356196\pi$$
0.436562 + 0.899674i $$0.356196\pi$$
$$42$$ 0 0
$$43$$ 1244.00 0.102600 0.0513002 0.998683i $$-0.483663\pi$$
0.0513002 + 0.998683i $$0.483663\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −12088.0 −0.798196 −0.399098 0.916908i $$-0.630677\pi$$
−0.399098 + 0.916908i $$0.630677\pi$$
$$48$$ 0 0
$$49$$ 20057.0 1.19337
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −23846.0 −1.16607 −0.583037 0.812446i $$-0.698136\pi$$
−0.583037 + 0.812446i $$0.698136\pi$$
$$54$$ 0 0
$$55$$ 3700.00 0.164928
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −20020.0 −0.748745 −0.374373 0.927278i $$-0.622142\pi$$
−0.374373 + 0.927278i $$0.622142\pi$$
$$60$$ 0 0
$$61$$ 32302.0 1.11149 0.555744 0.831353i $$-0.312433\pi$$
0.555744 + 0.831353i $$0.312433\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −7150.00 −0.209905
$$66$$ 0 0
$$67$$ −60972.0 −1.65937 −0.829685 0.558231i $$-0.811480\pi$$
−0.829685 + 0.558231i $$0.811480\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −32648.0 −0.768618 −0.384309 0.923204i $$-0.625560\pi$$
−0.384309 + 0.923204i $$0.625560\pi$$
$$72$$ 0 0
$$73$$ −38774.0 −0.851596 −0.425798 0.904818i $$-0.640007\pi$$
−0.425798 + 0.904818i $$0.640007\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 28416.0 0.546180
$$78$$ 0 0
$$79$$ 33360.0 0.601393 0.300696 0.953720i $$-0.402781\pi$$
0.300696 + 0.953720i $$0.402781\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 16716.0 0.266340 0.133170 0.991093i $$-0.457484\pi$$
0.133170 + 0.991093i $$0.457484\pi$$
$$84$$ 0 0
$$85$$ −41950.0 −0.629774
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −101370. −1.35655 −0.678273 0.734810i $$-0.737271\pi$$
−0.678273 + 0.734810i $$0.737271\pi$$
$$90$$ 0 0
$$91$$ −54912.0 −0.695126
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 26500.0 0.301257
$$96$$ 0 0
$$97$$ −119038. −1.28457 −0.642283 0.766468i $$-0.722013\pi$$
−0.642283 + 0.766468i $$0.722013\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 89898.0 0.876893 0.438446 0.898757i $$-0.355529\pi$$
0.438446 + 0.898757i $$0.355529\pi$$
$$102$$ 0 0
$$103$$ 19504.0 0.181147 0.0905734 0.995890i $$-0.471130\pi$$
0.0905734 + 0.995890i $$0.471130\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 158292. 1.33659 0.668297 0.743895i $$-0.267024\pi$$
0.668297 + 0.743895i $$0.267024\pi$$
$$108$$ 0 0
$$109$$ 36830.0 0.296917 0.148459 0.988919i $$-0.452569\pi$$
0.148459 + 0.988919i $$0.452569\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −11186.0 −0.0824098 −0.0412049 0.999151i $$-0.513120\pi$$
−0.0412049 + 0.999151i $$0.513120\pi$$
$$114$$ 0 0
$$115$$ −74400.0 −0.524600
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ −322176. −2.08557
$$120$$ 0 0
$$121$$ −139147. −0.863993
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −15625.0 −0.0894427
$$126$$ 0 0
$$127$$ −70552.0 −0.388150 −0.194075 0.980987i $$-0.562171\pi$$
−0.194075 + 0.980987i $$0.562171\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 76452.0 0.389234 0.194617 0.980879i $$-0.437654\pi$$
0.194617 + 0.980879i $$0.437654\pi$$
$$132$$ 0 0
$$133$$ 203520. 0.997650
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 144918. 0.659661 0.329831 0.944040i $$-0.393008\pi$$
0.329831 + 0.944040i $$0.393008\pi$$
$$138$$ 0 0
$$139$$ −112220. −0.492644 −0.246322 0.969188i $$-0.579222\pi$$
−0.246322 + 0.969188i $$0.579222\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −42328.0 −0.173096
$$144$$ 0 0
$$145$$ −85250.0 −0.336724
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −403750. −1.48986 −0.744932 0.667140i $$-0.767518\pi$$
−0.744932 + 0.667140i $$0.767518\pi$$
$$150$$ 0 0
$$151$$ 446648. 1.59413 0.797064 0.603895i $$-0.206385\pi$$
0.797064 + 0.603895i $$0.206385\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −61200.0 −0.204608
$$156$$ 0 0
$$157$$ −262258. −0.849141 −0.424570 0.905395i $$-0.639575\pi$$
−0.424570 + 0.905395i $$0.639575\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −571392. −1.73728
$$162$$ 0 0
$$163$$ 154564. 0.455658 0.227829 0.973701i $$-0.426837\pi$$
0.227829 + 0.973701i $$0.426837\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 396672. 1.10063 0.550314 0.834958i $$-0.314508\pi$$
0.550314 + 0.834958i $$0.314508\pi$$
$$168$$ 0 0
$$169$$ −289497. −0.779700
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 573474. 1.45680 0.728398 0.685155i $$-0.240265\pi$$
0.728398 + 0.685155i $$0.240265\pi$$
$$174$$ 0 0
$$175$$ −120000. −0.296201
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −594460. −1.38672 −0.693362 0.720589i $$-0.743871\pi$$
−0.693362 + 0.720589i $$0.743871\pi$$
$$180$$ 0 0
$$181$$ −107098. −0.242988 −0.121494 0.992592i $$-0.538769\pi$$
−0.121494 + 0.992592i $$0.538769\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −4550.00 −0.00977422
$$186$$ 0 0
$$187$$ −248344. −0.519337
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 469552. 0.931323 0.465661 0.884963i $$-0.345816\pi$$
0.465661 + 0.884963i $$0.345816\pi$$
$$192$$ 0 0
$$193$$ 52706.0 0.101851 0.0509257 0.998702i $$-0.483783\pi$$
0.0509257 + 0.998702i $$0.483783\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −455862. −0.836889 −0.418444 0.908242i $$-0.637425\pi$$
−0.418444 + 0.908242i $$0.637425\pi$$
$$198$$ 0 0
$$199$$ −865000. −1.54840 −0.774200 0.632940i $$-0.781848\pi$$
−0.774200 + 0.632940i $$0.781848\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −654720. −1.11510
$$204$$ 0 0
$$205$$ −234950. −0.390473
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 156880. 0.248429
$$210$$ 0 0
$$211$$ −1.10565e6 −1.70967 −0.854835 0.518900i $$-0.826342\pi$$
−0.854835 + 0.518900i $$0.826342\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −31100.0 −0.0458843
$$216$$ 0 0
$$217$$ −470016. −0.677584
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 479908. 0.660963
$$222$$ 0 0
$$223$$ −1.12158e6 −1.51031 −0.755156 0.655545i $$-0.772439\pi$$
−0.755156 + 0.655545i $$0.772439\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −23348.0 −0.0300736 −0.0150368 0.999887i $$-0.504787\pi$$
−0.0150368 + 0.999887i $$0.504787\pi$$
$$228$$ 0 0
$$229$$ −596010. −0.751043 −0.375522 0.926814i $$-0.622536\pi$$
−0.375522 + 0.926814i $$0.622536\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 485334. 0.585667 0.292834 0.956163i $$-0.405402\pi$$
0.292834 + 0.956163i $$0.405402\pi$$
$$234$$ 0 0
$$235$$ 302200. 0.356964
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −48880.0 −0.0553524 −0.0276762 0.999617i $$-0.508811\pi$$
−0.0276762 + 0.999617i $$0.508811\pi$$
$$240$$ 0 0
$$241$$ −110798. −0.122882 −0.0614411 0.998111i $$-0.519570\pi$$
−0.0614411 + 0.998111i $$0.519570\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −501425. −0.533692
$$246$$ 0 0
$$247$$ −303160. −0.316176
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −1.64375e6 −1.64684 −0.823419 0.567434i $$-0.807936\pi$$
−0.823419 + 0.567434i $$0.807936\pi$$
$$252$$ 0 0
$$253$$ −440448. −0.432607
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −1.30624e6 −1.23365 −0.616823 0.787102i $$-0.711581\pi$$
−0.616823 + 0.787102i $$0.711581\pi$$
$$258$$ 0 0
$$259$$ −34944.0 −0.0323685
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 2.12834e6 1.89736 0.948682 0.316231i $$-0.102417\pi$$
0.948682 + 0.316231i $$0.102417\pi$$
$$264$$ 0 0
$$265$$ 596150. 0.521484
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 1.44109e6 1.21426 0.607128 0.794604i $$-0.292321\pi$$
0.607128 + 0.794604i $$0.292321\pi$$
$$270$$ 0 0
$$271$$ 93248.0 0.0771288 0.0385644 0.999256i $$-0.487722\pi$$
0.0385644 + 0.999256i $$0.487722\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −92500.0 −0.0737581
$$276$$ 0 0
$$277$$ −110298. −0.0863711 −0.0431855 0.999067i $$-0.513751\pi$$
−0.0431855 + 0.999067i $$0.513751\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 192198. 0.145205 0.0726027 0.997361i $$-0.476869\pi$$
0.0726027 + 0.997361i $$0.476869\pi$$
$$282$$ 0 0
$$283$$ 331884. 0.246332 0.123166 0.992386i $$-0.460695\pi$$
0.123166 + 0.992386i $$0.460695\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −1.80442e6 −1.29310
$$288$$ 0 0
$$289$$ 1.39583e6 0.983076
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −2.19481e6 −1.49358 −0.746788 0.665063i $$-0.768405\pi$$
−0.746788 + 0.665063i $$0.768405\pi$$
$$294$$ 0 0
$$295$$ 500500. 0.334849
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 851136. 0.550581
$$300$$ 0 0
$$301$$ −238848. −0.151952
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −807550. −0.497073
$$306$$ 0 0
$$307$$ 2.37751e6 1.43971 0.719857 0.694123i $$-0.244207\pi$$
0.719857 + 0.694123i $$0.244207\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −2.37305e6 −1.39125 −0.695626 0.718405i $$-0.744873\pi$$
−0.695626 + 0.718405i $$0.744873\pi$$
$$312$$ 0 0
$$313$$ −1.42941e6 −0.824702 −0.412351 0.911025i $$-0.635292\pi$$
−0.412351 + 0.911025i $$0.635292\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −2.12462e6 −1.18750 −0.593750 0.804650i $$-0.702353\pi$$
−0.593750 + 0.804650i $$0.702353\pi$$
$$318$$ 0 0
$$319$$ −504680. −0.277677
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −1.77868e6 −0.948618
$$324$$ 0 0
$$325$$ 178750. 0.0938723
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 2.32090e6 1.18213
$$330$$ 0 0
$$331$$ −3.09985e6 −1.55515 −0.777573 0.628793i $$-0.783549\pi$$
−0.777573 + 0.628793i $$0.783549\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 1.52430e6 0.742093
$$336$$ 0 0
$$337$$ 2.40008e6 1.15120 0.575601 0.817731i $$-0.304768\pi$$
0.575601 + 0.817731i $$0.304768\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −362304. −0.168728
$$342$$ 0 0
$$343$$ −624000. −0.286384
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 1.77741e6 0.792436 0.396218 0.918156i $$-0.370322\pi$$
0.396218 + 0.918156i $$0.370322\pi$$
$$348$$ 0 0
$$349$$ −2.14805e6 −0.944019 −0.472010 0.881593i $$-0.656471\pi$$
−0.472010 + 0.881593i $$0.656471\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 661854. 0.282700 0.141350 0.989960i $$-0.454856\pi$$
0.141350 + 0.989960i $$0.454856\pi$$
$$354$$ 0 0
$$355$$ 816200. 0.343737
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −259320. −0.106194 −0.0530970 0.998589i $$-0.516909\pi$$
−0.0530970 + 0.998589i $$0.516909\pi$$
$$360$$ 0 0
$$361$$ −1.35250e6 −0.546222
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 969350. 0.380845
$$366$$ 0 0
$$367$$ 1.49993e6 0.581307 0.290653 0.956828i $$-0.406127\pi$$
0.290653 + 0.956828i $$0.406127\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 4.57843e6 1.72696
$$372$$ 0 0
$$373$$ −2.23807e6 −0.832918 −0.416459 0.909154i $$-0.636729\pi$$
−0.416459 + 0.909154i $$0.636729\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 975260. 0.353400
$$378$$ 0 0
$$379$$ −3.15934e6 −1.12979 −0.564896 0.825162i $$-0.691084\pi$$
−0.564896 + 0.825162i $$0.691084\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 342216. 0.119207 0.0596037 0.998222i $$-0.481016\pi$$
0.0596037 + 0.998222i $$0.481016\pi$$
$$384$$ 0 0
$$385$$ −710400. −0.244259
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −88470.0 −0.0296430 −0.0148215 0.999890i $$-0.504718\pi$$
−0.0148215 + 0.999890i $$0.504718\pi$$
$$390$$ 0 0
$$391$$ 4.99373e6 1.65190
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ −834000. −0.268951
$$396$$ 0 0
$$397$$ −5.45674e6 −1.73763 −0.868814 0.495138i $$-0.835117\pi$$
−0.868814 + 0.495138i $$0.835117\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −4.04680e6 −1.25676 −0.628378 0.777908i $$-0.716281\pi$$
−0.628378 + 0.777908i $$0.716281\pi$$
$$402$$ 0 0
$$403$$ 700128. 0.214741
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −26936.0 −0.00806022
$$408$$ 0 0
$$409$$ −2.71207e6 −0.801664 −0.400832 0.916151i $$-0.631279\pi$$
−0.400832 + 0.916151i $$0.631279\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 3.84384e6 1.10889
$$414$$ 0 0
$$415$$ −417900. −0.119111
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 3.71746e6 1.03445 0.517227 0.855848i $$-0.326964\pi$$
0.517227 + 0.855848i $$0.326964\pi$$
$$420$$ 0 0
$$421$$ 3.55250e6 0.976853 0.488426 0.872605i $$-0.337571\pi$$
0.488426 + 0.872605i $$0.337571\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 1.04875e6 0.281643
$$426$$ 0 0
$$427$$ −6.20198e6 −1.64612
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −4.06205e6 −1.05330 −0.526650 0.850082i $$-0.676552\pi$$
−0.526650 + 0.850082i $$0.676552\pi$$
$$432$$ 0 0
$$433$$ 7.26287e6 1.86161 0.930804 0.365518i $$-0.119108\pi$$
0.930804 + 0.365518i $$0.119108\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −3.15456e6 −0.790197
$$438$$ 0 0
$$439$$ 5.41028e6 1.33986 0.669928 0.742426i $$-0.266325\pi$$
0.669928 + 0.742426i $$0.266325\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −6.51524e6 −1.57733 −0.788663 0.614826i $$-0.789226\pi$$
−0.788663 + 0.614826i $$0.789226\pi$$
$$444$$ 0 0
$$445$$ 2.53425e6 0.606666
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 509950. 0.119375 0.0596873 0.998217i $$-0.480990\pi$$
0.0596873 + 0.998217i $$0.480990\pi$$
$$450$$ 0 0
$$451$$ −1.39090e6 −0.322000
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 1.37280e6 0.310870
$$456$$ 0 0
$$457$$ 1.22084e6 0.273444 0.136722 0.990609i $$-0.456343\pi$$
0.136722 + 0.990609i $$0.456343\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 4.07210e6 0.892413 0.446207 0.894930i $$-0.352775\pi$$
0.446207 + 0.894930i $$0.352775\pi$$
$$462$$ 0 0
$$463$$ −2.02294e6 −0.438561 −0.219280 0.975662i $$-0.570371\pi$$
−0.219280 + 0.975662i $$0.570371\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 3.25097e6 0.689797 0.344898 0.938640i $$-0.387913\pi$$
0.344898 + 0.938640i $$0.387913\pi$$
$$468$$ 0 0
$$469$$ 1.17066e7 2.45753
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −184112. −0.0378381
$$474$$ 0 0
$$475$$ −662500. −0.134726
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −3.27936e6 −0.653056 −0.326528 0.945188i $$-0.605879\pi$$
−0.326528 + 0.945188i $$0.605879\pi$$
$$480$$ 0 0
$$481$$ 52052.0 0.0102583
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 2.97595e6 0.574475
$$486$$ 0 0
$$487$$ 8.53197e6 1.63015 0.815074 0.579357i $$-0.196696\pi$$
0.815074 + 0.579357i $$0.196696\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 1.51265e6 0.283162 0.141581 0.989927i $$-0.454781\pi$$
0.141581 + 0.989927i $$0.454781\pi$$
$$492$$ 0 0
$$493$$ 5.72198e6 1.06030
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 6.26842e6 1.13833
$$498$$ 0 0
$$499$$ 6.49190e6 1.16713 0.583567 0.812065i $$-0.301657\pi$$
0.583567 + 0.812065i $$0.301657\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 8.61770e6 1.51870 0.759349 0.650684i $$-0.225518\pi$$
0.759349 + 0.650684i $$0.225518\pi$$
$$504$$ 0 0
$$505$$ −2.24745e6 −0.392158
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −2.67323e6 −0.457343 −0.228671 0.973504i $$-0.573438\pi$$
−0.228671 + 0.973504i $$0.573438\pi$$
$$510$$ 0 0
$$511$$ 7.44461e6 1.26122
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −487600. −0.0810113
$$516$$ 0 0
$$517$$ 1.78902e6 0.294367
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −6.18500e6 −0.998264 −0.499132 0.866526i $$-0.666348\pi$$
−0.499132 + 0.866526i $$0.666348\pi$$
$$522$$ 0 0
$$523$$ 6.89452e6 1.10217 0.551087 0.834448i $$-0.314213\pi$$
0.551087 + 0.834448i $$0.314213\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 4.10774e6 0.644283
$$528$$ 0 0
$$529$$ 2.42023e6 0.376026
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 2.68783e6 0.409811
$$534$$ 0 0
$$535$$ −3.95730e6 −0.597743
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −2.96844e6 −0.440104
$$540$$ 0 0
$$541$$ 155502. 0.0228425 0.0114212 0.999935i $$-0.496364\pi$$
0.0114212 + 0.999935i $$0.496364\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −920750. −0.132785
$$546$$ 0 0
$$547$$ −1.26544e7 −1.80831 −0.904157 0.427201i $$-0.859500\pi$$
−0.904157 + 0.427201i $$0.859500\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −3.61460e6 −0.507202
$$552$$ 0 0
$$553$$ −6.40512e6 −0.890665
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 7.07786e6 0.966638 0.483319 0.875444i $$-0.339431\pi$$
0.483319 + 0.875444i $$0.339431\pi$$
$$558$$ 0 0
$$559$$ 355784. 0.0481567
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 846636. 0.112571 0.0562854 0.998415i $$-0.482074\pi$$
0.0562854 + 0.998415i $$0.482074\pi$$
$$564$$ 0 0
$$565$$ 279650. 0.0368548
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −4.96041e6 −0.642299 −0.321149 0.947029i $$-0.604069\pi$$
−0.321149 + 0.947029i $$0.604069\pi$$
$$570$$ 0 0
$$571$$ −8.96505e6 −1.15070 −0.575351 0.817907i $$-0.695134\pi$$
−0.575351 + 0.817907i $$0.695134\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 1.86000e6 0.234608
$$576$$ 0 0
$$577$$ −2.86080e6 −0.357724 −0.178862 0.983874i $$-0.557242\pi$$
−0.178862 + 0.983874i $$0.557242\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −3.20947e6 −0.394451
$$582$$ 0 0
$$583$$ 3.52921e6 0.430037
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −6.74027e6 −0.807387 −0.403694 0.914894i $$-0.632274\pi$$
−0.403694 + 0.914894i $$0.632274\pi$$
$$588$$ 0 0
$$589$$ −2.59488e6 −0.308197
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 1.78609e6 0.208578 0.104289 0.994547i $$-0.466743\pi$$
0.104289 + 0.994547i $$0.466743\pi$$
$$594$$ 0 0
$$595$$ 8.05440e6 0.932697
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 4.94620e6 0.563254 0.281627 0.959524i $$-0.409126\pi$$
0.281627 + 0.959524i $$0.409126\pi$$
$$600$$ 0 0
$$601$$ −4.58100e6 −0.517337 −0.258669 0.965966i $$-0.583284\pi$$
−0.258669 + 0.965966i $$0.583284\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 3.47868e6 0.386390
$$606$$ 0 0
$$607$$ −7.07999e6 −0.779940 −0.389970 0.920828i $$-0.627515\pi$$
−0.389970 + 0.920828i $$0.627515\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −3.45717e6 −0.374643
$$612$$ 0 0
$$613$$ 5.09609e6 0.547754 0.273877 0.961765i $$-0.411694\pi$$
0.273877 + 0.961765i $$0.411694\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 1.30003e7 1.37480 0.687400 0.726279i $$-0.258752\pi$$
0.687400 + 0.726279i $$0.258752\pi$$
$$618$$ 0 0
$$619$$ −4.84406e6 −0.508139 −0.254070 0.967186i $$-0.581769\pi$$
−0.254070 + 0.967186i $$0.581769\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 1.94630e7 2.00905
$$624$$ 0 0
$$625$$ 390625. 0.0400000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 305396. 0.0307777
$$630$$ 0 0
$$631$$ −6.22775e6 −0.622670 −0.311335 0.950300i $$-0.600776\pi$$
−0.311335 + 0.950300i $$0.600776\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 1.76380e6 0.173586
$$636$$ 0 0
$$637$$ 5.73630e6 0.560123
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −1.53280e6 −0.147347 −0.0736734 0.997282i $$-0.523472\pi$$
−0.0736734 + 0.997282i $$0.523472\pi$$
$$642$$ 0 0
$$643$$ 1.74382e7 1.66332 0.831659 0.555287i $$-0.187391\pi$$
0.831659 + 0.555287i $$0.187391\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −4.25469e6 −0.399583 −0.199792 0.979838i $$-0.564026\pi$$
−0.199792 + 0.979838i $$0.564026\pi$$
$$648$$ 0 0
$$649$$ 2.96296e6 0.276130
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −3.01085e6 −0.276316 −0.138158 0.990410i $$-0.544118\pi$$
−0.138158 + 0.990410i $$0.544118\pi$$
$$654$$ 0 0
$$655$$ −1.91130e6 −0.174071
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −8.11462e6 −0.727871 −0.363936 0.931424i $$-0.618567\pi$$
−0.363936 + 0.931424i $$0.618567\pi$$
$$660$$ 0 0
$$661$$ 2.47370e6 0.220213 0.110107 0.993920i $$-0.464881\pi$$
0.110107 + 0.993920i $$0.464881\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −5.08800e6 −0.446162
$$666$$ 0 0
$$667$$ 1.01482e7 0.883228
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −4.78070e6 −0.409907
$$672$$ 0 0
$$673$$ 5.77063e6 0.491117 0.245559 0.969382i $$-0.421029\pi$$
0.245559 + 0.969382i $$0.421029\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −1.67197e7 −1.40203 −0.701014 0.713147i $$-0.747269\pi$$
−0.701014 + 0.713147i $$0.747269\pi$$
$$678$$ 0 0
$$679$$ 2.28553e7 1.90245
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 7.14532e6 0.586097 0.293049 0.956098i $$-0.405330\pi$$
0.293049 + 0.956098i $$0.405330\pi$$
$$684$$ 0 0
$$685$$ −3.62295e6 −0.295009
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −6.81996e6 −0.547310
$$690$$ 0 0
$$691$$ 8.78395e6 0.699833 0.349917 0.936781i $$-0.386210\pi$$
0.349917 + 0.936781i $$0.386210\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 2.80550e6 0.220317
$$696$$ 0 0
$$697$$ 1.57698e7 1.22955
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 1.60141e7 1.23086 0.615428 0.788193i $$-0.288983\pi$$
0.615428 + 0.788193i $$0.288983\pi$$
$$702$$ 0 0
$$703$$ −192920. −0.0147228
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −1.72604e7 −1.29868
$$708$$ 0 0
$$709$$ −1.91354e7 −1.42962 −0.714811 0.699318i $$-0.753487\pi$$
−0.714811 + 0.699318i $$0.753487\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 7.28525e6 0.536686
$$714$$ 0 0
$$715$$ 1.05820e6 0.0774110
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 1.02934e7 0.742566 0.371283 0.928520i $$-0.378918\pi$$
0.371283 + 0.928520i $$0.378918\pi$$
$$720$$ 0 0
$$721$$ −3.74477e6 −0.268279
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 2.13125e6 0.150588
$$726$$ 0 0
$$727$$ 1.93264e7 1.35618 0.678088 0.734981i $$-0.262809\pi$$
0.678088 + 0.734981i $$0.262809\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 2.08743e6 0.144484
$$732$$ 0 0
$$733$$ 5.26197e6 0.361733 0.180866 0.983508i $$-0.442110\pi$$
0.180866 + 0.983508i $$0.442110\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 9.02386e6 0.611961
$$738$$ 0 0
$$739$$ −2.82944e7 −1.90585 −0.952927 0.303199i $$-0.901945\pi$$
−0.952927 + 0.303199i $$0.901945\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 2.09863e7 1.39464 0.697321 0.716759i $$-0.254375\pi$$
0.697321 + 0.716759i $$0.254375\pi$$
$$744$$ 0 0
$$745$$ 1.00938e7 0.666288
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −3.03921e7 −1.97950
$$750$$ 0 0
$$751$$ 1.89668e7 1.22714 0.613572 0.789639i $$-0.289732\pi$$
0.613572 + 0.789639i $$0.289732\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −1.11662e7 −0.712915
$$756$$ 0 0
$$757$$ −1.08257e7 −0.686617 −0.343309 0.939223i $$-0.611548\pi$$
−0.343309 + 0.939223i $$0.611548\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −1.90534e7 −1.19264 −0.596322 0.802745i $$-0.703372\pi$$
−0.596322 + 0.802745i $$0.703372\pi$$
$$762$$ 0 0
$$763$$ −7.07136e6 −0.439736
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −5.72572e6 −0.351432
$$768$$ 0 0
$$769$$ −1.57826e7 −0.962415 −0.481208 0.876607i $$-0.659802\pi$$
−0.481208 + 0.876607i $$0.659802\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 2.44049e7 1.46902 0.734510 0.678598i $$-0.237412\pi$$
0.734510 + 0.678598i $$0.237412\pi$$
$$774$$ 0 0
$$775$$ 1.53000e6 0.0915034
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −9.96188e6 −0.588163
$$780$$ 0 0
$$781$$ 4.83190e6 0.283459
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 6.55645e6 0.379747
$$786$$ 0 0
$$787$$ −3.37607e7 −1.94301 −0.971505 0.237019i $$-0.923830\pi$$
−0.971505 + 0.237019i $$0.923830\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 2.14771e6 0.122049
$$792$$ 0 0
$$793$$ 9.23837e6 0.521690
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −2.19885e7 −1.22617 −0.613083 0.790019i $$-0.710071\pi$$
−0.613083 + 0.790019i $$0.710071\pi$$
$$798$$ 0 0
$$799$$ −2.02837e7 −1.12403
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 5.73855e6 0.314061
$$804$$ 0 0
$$805$$ 1.42848e7 0.776935
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 2.93597e7 1.57717 0.788587 0.614923i $$-0.210813\pi$$
0.788587 + 0.614923i $$0.210813\pi$$
$$810$$ 0 0
$$811$$ −3.17703e7 −1.69617 −0.848083 0.529863i $$-0.822243\pi$$
−0.848083 + 0.529863i $$0.822243\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −3.86410e6 −0.203777
$$816$$ 0 0
$$817$$ −1.31864e6 −0.0691148
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 2.71430e6 0.140540 0.0702699 0.997528i $$-0.477614\pi$$
0.0702699 + 0.997528i $$0.477614\pi$$
$$822$$ 0 0
$$823$$ 1.25866e7 0.647753 0.323877 0.946099i $$-0.395014\pi$$
0.323877 + 0.946099i $$0.395014\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −8.72355e6 −0.443537 −0.221768 0.975099i $$-0.571183\pi$$
−0.221768 + 0.975099i $$0.571183\pi$$
$$828$$ 0 0
$$829$$ −1.06178e7 −0.536597 −0.268299 0.963336i $$-0.586461\pi$$
−0.268299 + 0.963336i $$0.586461\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 3.36556e7 1.68053
$$834$$ 0 0
$$835$$ −9.91680e6 −0.492216
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 1.67765e7 0.822805 0.411403 0.911454i $$-0.365039\pi$$
0.411403 + 0.911454i $$0.365039\pi$$
$$840$$ 0 0
$$841$$ −8.88305e6 −0.433084
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 7.23742e6 0.348692
$$846$$ 0 0
$$847$$ 2.67162e7 1.27958
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 541632. 0.0256378
$$852$$ 0 0
$$853$$ −2.20186e7 −1.03613 −0.518067 0.855340i $$-0.673348\pi$$
−0.518067 + 0.855340i $$0.673348\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ −3.16676e7 −1.47287 −0.736434 0.676510i $$-0.763492\pi$$
−0.736434 + 0.676510i $$0.763492\pi$$
$$858$$ 0 0
$$859$$ −1.58064e7 −0.730886 −0.365443 0.930834i $$-0.619082\pi$$
−0.365443 + 0.930834i $$0.619082\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ −1.44287e7 −0.659476 −0.329738 0.944072i $$-0.606960\pi$$
−0.329738 + 0.944072i $$0.606960\pi$$
$$864$$ 0 0
$$865$$ −1.43368e7 −0.651499
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ −4.93728e6 −0.221788
$$870$$ 0 0
$$871$$ −1.74380e7 −0.778845
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 3.00000e6 0.132465
$$876$$ 0 0
$$877$$ 247902. 0.0108838 0.00544191 0.999985i $$-0.498268\pi$$
0.00544191 + 0.999985i $$0.498268\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ −4.10268e7 −1.78085 −0.890426 0.455128i $$-0.849594\pi$$
−0.890426 + 0.455128i $$0.849594\pi$$
$$882$$ 0 0
$$883$$ −4.18015e7 −1.80422 −0.902112 0.431503i $$-0.857984\pi$$
−0.902112 + 0.431503i $$0.857984\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0 0
$$887$$ −2.10476e7 −0.898241 −0.449120 0.893471i $$-0.648263\pi$$
−0.449120 + 0.893471i $$0.648263\pi$$
$$888$$ 0 0
$$889$$ 1.35460e7 0.574852
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 1.28133e7 0.537690
$$894$$ 0 0
$$895$$ 1.48615e7 0.620162
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 8.34768e6 0.344482
$$900$$ 0 0
$$901$$ −4.00136e7 −1.64208
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 2.67745e6 0.108668
$$906$$ 0 0
$$907$$ −7.48309e6 −0.302039 −0.151019 0.988531i $$-0.548256\pi$$
−0.151019 + 0.988531i $$0.548256\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ −6.63165e6 −0.264744 −0.132372 0.991200i $$-0.542259\pi$$
−0.132372 + 0.991200i $$0.542259\pi$$
$$912$$ 0 0
$$913$$ −2.47397e6 −0.0982239
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0 0
$$917$$ −1.46788e7 −0.576457
$$918$$ 0 0
$$919$$ 1.68976e7 0.659990 0.329995 0.943983i $$-0.392953\pi$$
0.329995 + 0.943983i $$0.392953\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −9.33733e6 −0.360760
$$924$$ 0 0
$$925$$ 113750. 0.00437116
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0 0
$$929$$ 1.28653e7 0.489081 0.244541 0.969639i $$-0.421363\pi$$
0.244541 + 0.969639i $$0.421363\pi$$
$$930$$ 0 0
$$931$$ −2.12604e7 −0.803892
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 6.20860e6 0.232255
$$936$$ 0 0
$$937$$ 1.06887e7 0.397718 0.198859 0.980028i $$-0.436276\pi$$
0.198859 + 0.980028i $$0.436276\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ −2.82455e7 −1.03986 −0.519930 0.854209i $$-0.674042\pi$$
−0.519930 + 0.854209i $$0.674042\pi$$
$$942$$ 0 0
$$943$$ 2.79684e7 1.02421
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ −1.70892e7 −0.619222 −0.309611 0.950863i $$-0.600199\pi$$
−0.309611 + 0.950863i $$0.600199\pi$$
$$948$$ 0 0
$$949$$ −1.10894e7 −0.399706
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ −2.22259e7 −0.792735 −0.396367 0.918092i $$-0.629729\pi$$
−0.396367 + 0.918092i $$0.629729\pi$$
$$954$$ 0 0
$$955$$ −1.17388e7 −0.416500
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ −2.78243e7 −0.976961
$$960$$ 0 0
$$961$$ −2.26364e7 −0.790678
$$962$$ 0 0
$$963$$ 0 0
$$964$$ 0 0
$$965$$ −1.31765e6 −0.0455493
$$966$$ 0 0
$$967$$ −2.41551e7 −0.830696 −0.415348 0.909663i $$-0.636340\pi$$
−0.415348 + 0.909663i $$0.636340\pi$$
$$968$$ 0 0
$$969$$ 0 0
$$970$$ 0 0
$$971$$ −5.48313e7 −1.86630 −0.933149 0.359491i $$-0.882950\pi$$
−0.933149 + 0.359491i $$0.882950\pi$$
$$972$$ 0 0
$$973$$ 2.15462e7 0.729608
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 1.56612e7 0.524915 0.262457 0.964944i $$-0.415467\pi$$
0.262457 + 0.964944i $$0.415467\pi$$
$$978$$ 0 0
$$979$$ 1.50028e7 0.500281
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ −1.63420e7 −0.539412 −0.269706 0.962943i $$-0.586927\pi$$
−0.269706 + 0.962943i $$0.586927\pi$$
$$984$$ 0 0
$$985$$ 1.13966e7 0.374268
$$986$$ 0 0
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 3.70214e6 0.120355
$$990$$ 0 0
$$991$$ −1.37576e7 −0.444997 −0.222498 0.974933i $$-0.571421\pi$$
−0.222498 + 0.974933i $$0.571421\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 2.16250e7 0.692466
$$996$$ 0 0
$$997$$ −1.29097e7 −0.411320 −0.205660 0.978624i $$-0.565934\pi$$
−0.205660 + 0.978624i $$0.565934\pi$$
$$998$$ 0 0
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 720.6.a.a.1.1 1
3.2 odd 2 80.6.a.e.1.1 1
4.3 odd 2 45.6.a.b.1.1 1
12.11 even 2 5.6.a.a.1.1 1
15.2 even 4 400.6.c.j.49.1 2
15.8 even 4 400.6.c.j.49.2 2
15.14 odd 2 400.6.a.g.1.1 1
20.3 even 4 225.6.b.e.199.2 2
20.7 even 4 225.6.b.e.199.1 2
20.19 odd 2 225.6.a.f.1.1 1
24.5 odd 2 320.6.a.g.1.1 1
24.11 even 2 320.6.a.j.1.1 1
60.23 odd 4 25.6.b.a.24.1 2
60.47 odd 4 25.6.b.a.24.2 2
60.59 even 2 25.6.a.a.1.1 1
84.83 odd 2 245.6.a.b.1.1 1
132.131 odd 2 605.6.a.a.1.1 1
156.155 even 2 845.6.a.b.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
5.6.a.a.1.1 1 12.11 even 2
25.6.a.a.1.1 1 60.59 even 2
25.6.b.a.24.1 2 60.23 odd 4
25.6.b.a.24.2 2 60.47 odd 4
45.6.a.b.1.1 1 4.3 odd 2
80.6.a.e.1.1 1 3.2 odd 2
225.6.a.f.1.1 1 20.19 odd 2
225.6.b.e.199.1 2 20.7 even 4
225.6.b.e.199.2 2 20.3 even 4
245.6.a.b.1.1 1 84.83 odd 2
320.6.a.g.1.1 1 24.5 odd 2
320.6.a.j.1.1 1 24.11 even 2
400.6.a.g.1.1 1 15.14 odd 2
400.6.c.j.49.1 2 15.2 even 4
400.6.c.j.49.2 2 15.8 even 4
605.6.a.a.1.1 1 132.131 odd 2
720.6.a.a.1.1 1 1.1 even 1 trivial
845.6.a.b.1.1 1 156.155 even 2