Properties

Label 177.12.a.c.1.10
Level $177$
Weight $12$
Character 177.1
Self dual yes
Analytic conductor $135.997$
Analytic rank $0$
Dimension $27$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(135.996742959\)
Analytic rank: \(0\)
Dimension: \(27\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-38.5064 q^{2} -243.000 q^{3} -565.255 q^{4} -13229.8 q^{5} +9357.06 q^{6} -8923.95 q^{7} +100627. q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-38.5064 q^{2} -243.000 q^{3} -565.255 q^{4} -13229.8 q^{5} +9357.06 q^{6} -8923.95 q^{7} +100627. q^{8} +59049.0 q^{9} +509431. q^{10} -548740. q^{11} +137357. q^{12} +1.36786e6 q^{13} +343630. q^{14} +3.21483e6 q^{15} -2.71715e6 q^{16} +5.04723e6 q^{17} -2.27377e6 q^{18} -5.16583e6 q^{19} +7.47818e6 q^{20} +2.16852e6 q^{21} +2.11300e7 q^{22} -9.48085e6 q^{23} -2.44524e7 q^{24} +1.26198e8 q^{25} -5.26712e7 q^{26} -1.43489e7 q^{27} +5.04431e6 q^{28} -1.29431e8 q^{29} -1.23792e8 q^{30} -9.27006e7 q^{31} -1.01457e8 q^{32} +1.33344e8 q^{33} -1.94351e8 q^{34} +1.18062e8 q^{35} -3.33777e7 q^{36} -3.97993e7 q^{37} +1.98918e8 q^{38} -3.32389e8 q^{39} -1.33127e9 q^{40} +9.65170e7 q^{41} -8.35020e7 q^{42} -6.50542e8 q^{43} +3.10178e8 q^{44} -7.81204e8 q^{45} +3.65074e8 q^{46} -1.60481e9 q^{47} +6.60267e8 q^{48} -1.89769e9 q^{49} -4.85945e9 q^{50} -1.22648e9 q^{51} -7.73187e8 q^{52} -3.48155e9 q^{53} +5.52525e8 q^{54} +7.25970e9 q^{55} -8.97992e8 q^{56} +1.25530e9 q^{57} +4.98393e9 q^{58} -7.14924e8 q^{59} -1.81720e9 q^{60} +5.15750e9 q^{61} +3.56957e9 q^{62} -5.26950e8 q^{63} +9.47145e9 q^{64} -1.80964e10 q^{65} -5.13460e9 q^{66} -5.22349e9 q^{67} -2.85297e9 q^{68} +2.30385e9 q^{69} -4.54614e9 q^{70} +1.67408e10 q^{71} +5.94193e9 q^{72} +2.13806e10 q^{73} +1.53253e9 q^{74} -3.06662e10 q^{75} +2.92001e9 q^{76} +4.89693e9 q^{77} +1.27991e10 q^{78} -3.48354e10 q^{79} +3.59472e10 q^{80} +3.48678e9 q^{81} -3.71653e9 q^{82} -6.02784e10 q^{83} -1.22577e9 q^{84} -6.67736e10 q^{85} +2.50500e10 q^{86} +3.14518e10 q^{87} -5.52181e10 q^{88} -5.21245e10 q^{89} +3.00814e10 q^{90} -1.22067e10 q^{91} +5.35910e9 q^{92} +2.25262e10 q^{93} +6.17956e10 q^{94} +6.83426e10 q^{95} +2.46540e10 q^{96} -1.33295e11 q^{97} +7.30733e10 q^{98} -3.24026e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

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 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −38.5064 −0.850880 −0.425440 0.904987i \(-0.639881\pi\)
−0.425440 + 0.904987i \(0.639881\pi\)
\(3\) −243.000 −0.577350
\(4\) −565.255 −0.276003
\(5\) −13229.8 −1.89329 −0.946644 0.322280i \(-0.895551\pi\)
−0.946644 + 0.322280i \(0.895551\pi\)
\(6\) 9357.06 0.491256
\(7\) −8923.95 −0.200686 −0.100343 0.994953i \(-0.531994\pi\)
−0.100343 + 0.994953i \(0.531994\pi\)
\(8\) 100627. 1.08573
\(9\) 59049.0 0.333333
\(10\) 509431. 1.61096
\(11\) −548740. −1.02732 −0.513662 0.857993i \(-0.671711\pi\)
−0.513662 + 0.857993i \(0.671711\pi\)
\(12\) 137357. 0.159351
\(13\) 1.36786e6 1.02177 0.510884 0.859650i \(-0.329318\pi\)
0.510884 + 0.859650i \(0.329318\pi\)
\(14\) 343630. 0.170760
\(15\) 3.21483e6 1.09309
\(16\) −2.71715e6 −0.647819
\(17\) 5.04723e6 0.862152 0.431076 0.902316i \(-0.358134\pi\)
0.431076 + 0.902316i \(0.358134\pi\)
\(18\) −2.27377e6 −0.283627
\(19\) −5.16583e6 −0.478625 −0.239312 0.970943i \(-0.576922\pi\)
−0.239312 + 0.970943i \(0.576922\pi\)
\(20\) 7.47818e6 0.522554
\(21\) 2.16852e6 0.115866
\(22\) 2.11300e7 0.874129
\(23\) −9.48085e6 −0.307146 −0.153573 0.988137i \(-0.549078\pi\)
−0.153573 + 0.988137i \(0.549078\pi\)
\(24\) −2.44524e7 −0.626844
\(25\) 1.26198e8 2.58454
\(26\) −5.26712e7 −0.869401
\(27\) −1.43489e7 −0.192450
\(28\) 5.04431e6 0.0553901
\(29\) −1.29431e8 −1.17179 −0.585895 0.810387i \(-0.699257\pi\)
−0.585895 + 0.810387i \(0.699257\pi\)
\(30\) −1.23792e8 −0.930089
\(31\) −9.27006e7 −0.581558 −0.290779 0.956790i \(-0.593914\pi\)
−0.290779 + 0.956790i \(0.593914\pi\)
\(32\) −1.01457e8 −0.534510
\(33\) 1.33344e8 0.593125
\(34\) −1.94351e8 −0.733588
\(35\) 1.18062e8 0.379957
\(36\) −3.33777e7 −0.0920011
\(37\) −3.97993e7 −0.0943552 −0.0471776 0.998887i \(-0.515023\pi\)
−0.0471776 + 0.998887i \(0.515023\pi\)
\(38\) 1.98918e8 0.407252
\(39\) −3.32389e8 −0.589918
\(40\) −1.33127e9 −2.05559
\(41\) 9.65170e7 0.130105 0.0650523 0.997882i \(-0.479279\pi\)
0.0650523 + 0.997882i \(0.479279\pi\)
\(42\) −8.35020e7 −0.0985884
\(43\) −6.50542e8 −0.674837 −0.337418 0.941355i \(-0.609554\pi\)
−0.337418 + 0.941355i \(0.609554\pi\)
\(44\) 3.10178e8 0.283545
\(45\) −7.81204e8 −0.631096
\(46\) 3.65074e8 0.261344
\(47\) −1.60481e9 −1.02067 −0.510336 0.859975i \(-0.670479\pi\)
−0.510336 + 0.859975i \(0.670479\pi\)
\(48\) 6.60267e8 0.374018
\(49\) −1.89769e9 −0.959725
\(50\) −4.85945e9 −2.19914
\(51\) −1.22648e9 −0.497763
\(52\) −7.73187e8 −0.282011
\(53\) −3.48155e9 −1.14355 −0.571775 0.820411i \(-0.693745\pi\)
−0.571775 + 0.820411i \(0.693745\pi\)
\(54\) 5.52525e8 0.163752
\(55\) 7.25970e9 1.94502
\(56\) −8.97992e8 −0.217890
\(57\) 1.25530e9 0.276334
\(58\) 4.98393e9 0.997053
\(59\) −7.14924e8 −0.130189
\(60\) −1.81720e9 −0.301697
\(61\) 5.15750e9 0.781853 0.390927 0.920422i \(-0.372155\pi\)
0.390927 + 0.920422i \(0.372155\pi\)
\(62\) 3.56957e9 0.494836
\(63\) −5.26950e8 −0.0668955
\(64\) 9.47145e9 1.10262
\(65\) −1.80964e10 −1.93450
\(66\) −5.13460e9 −0.504678
\(67\) −5.22349e9 −0.472661 −0.236330 0.971673i \(-0.575945\pi\)
−0.236330 + 0.971673i \(0.575945\pi\)
\(68\) −2.85297e9 −0.237957
\(69\) 2.30385e9 0.177331
\(70\) −4.54614e9 −0.323298
\(71\) 1.67408e10 1.10117 0.550586 0.834779i \(-0.314404\pi\)
0.550586 + 0.834779i \(0.314404\pi\)
\(72\) 5.94193e9 0.361909
\(73\) 2.13806e10 1.20710 0.603552 0.797323i \(-0.293751\pi\)
0.603552 + 0.797323i \(0.293751\pi\)
\(74\) 1.53253e9 0.0802850
\(75\) −3.06662e10 −1.49219
\(76\) 2.92001e9 0.132102
\(77\) 4.89693e9 0.206170
\(78\) 1.27991e10 0.501949
\(79\) −3.48354e10 −1.27371 −0.636857 0.770982i \(-0.719766\pi\)
−0.636857 + 0.770982i \(0.719766\pi\)
\(80\) 3.59472e10 1.22651
\(81\) 3.48678e9 0.111111
\(82\) −3.71653e9 −0.110703
\(83\) −6.02784e10 −1.67970 −0.839850 0.542818i \(-0.817357\pi\)
−0.839850 + 0.542818i \(0.817357\pi\)
\(84\) −1.22577e9 −0.0319795
\(85\) −6.67736e10 −1.63230
\(86\) 2.50500e10 0.574205
\(87\) 3.14518e10 0.676533
\(88\) −5.52181e10 −1.11539
\(89\) −5.21245e10 −0.989458 −0.494729 0.869047i \(-0.664733\pi\)
−0.494729 + 0.869047i \(0.664733\pi\)
\(90\) 3.00814e10 0.536987
\(91\) −1.22067e10 −0.205055
\(92\) 5.35910e9 0.0847732
\(93\) 2.25262e10 0.335763
\(94\) 6.17956e10 0.868469
\(95\) 6.83426e10 0.906175
\(96\) 2.46540e10 0.308599
\(97\) −1.33295e11 −1.57605 −0.788024 0.615644i \(-0.788896\pi\)
−0.788024 + 0.615644i \(0.788896\pi\)
\(98\) 7.30733e10 0.816611
\(99\) −3.24026e10 −0.342441
\(100\) −7.13342e10 −0.713342
\(101\) −1.75528e11 −1.66180 −0.830902 0.556419i \(-0.812175\pi\)
−0.830902 + 0.556419i \(0.812175\pi\)
\(102\) 4.72272e10 0.423537
\(103\) 7.57783e10 0.644080 0.322040 0.946726i \(-0.395631\pi\)
0.322040 + 0.946726i \(0.395631\pi\)
\(104\) 1.37643e11 1.10936
\(105\) −2.86890e10 −0.219369
\(106\) 1.34062e11 0.973023
\(107\) 2.53729e10 0.174887 0.0874437 0.996169i \(-0.472130\pi\)
0.0874437 + 0.996169i \(0.472130\pi\)
\(108\) 8.11079e9 0.0531169
\(109\) −1.49235e11 −0.929018 −0.464509 0.885568i \(-0.653769\pi\)
−0.464509 + 0.885568i \(0.653769\pi\)
\(110\) −2.79545e11 −1.65498
\(111\) 9.67123e9 0.0544760
\(112\) 2.42477e10 0.130008
\(113\) −2.95296e11 −1.50774 −0.753869 0.657025i \(-0.771815\pi\)
−0.753869 + 0.657025i \(0.771815\pi\)
\(114\) −4.83370e10 −0.235127
\(115\) 1.25429e11 0.581515
\(116\) 7.31616e10 0.323418
\(117\) 8.07705e10 0.340589
\(118\) 2.75292e10 0.110775
\(119\) −4.50412e10 −0.173022
\(120\) 3.23499e11 1.18680
\(121\) 1.58041e10 0.0553926
\(122\) −1.98597e11 −0.665263
\(123\) −2.34536e10 −0.0751159
\(124\) 5.23994e10 0.160512
\(125\) −1.02359e12 −3.00000
\(126\) 2.02910e10 0.0569200
\(127\) −7.67775e10 −0.206212 −0.103106 0.994670i \(-0.532878\pi\)
−0.103106 + 0.994670i \(0.532878\pi\)
\(128\) −1.56929e11 −0.403690
\(129\) 1.58082e11 0.389617
\(130\) 6.96828e11 1.64603
\(131\) 3.86066e11 0.874317 0.437159 0.899384i \(-0.355985\pi\)
0.437159 + 0.899384i \(0.355985\pi\)
\(132\) −7.53733e10 −0.163705
\(133\) 4.60996e10 0.0960534
\(134\) 2.01138e11 0.402178
\(135\) 1.89833e11 0.364364
\(136\) 5.07888e11 0.936060
\(137\) 8.37523e11 1.48263 0.741317 0.671155i \(-0.234202\pi\)
0.741317 + 0.671155i \(0.234202\pi\)
\(138\) −8.87129e10 −0.150887
\(139\) 7.87009e10 0.128647 0.0643233 0.997929i \(-0.479511\pi\)
0.0643233 + 0.997929i \(0.479511\pi\)
\(140\) −6.67350e10 −0.104870
\(141\) 3.89969e11 0.589285
\(142\) −6.44628e11 −0.936965
\(143\) −7.50598e11 −1.04968
\(144\) −1.60445e11 −0.215940
\(145\) 1.71234e12 2.21854
\(146\) −8.23292e11 −1.02710
\(147\) 4.61139e11 0.554097
\(148\) 2.24968e10 0.0260424
\(149\) 4.99227e11 0.556896 0.278448 0.960451i \(-0.410180\pi\)
0.278448 + 0.960451i \(0.410180\pi\)
\(150\) 1.18085e12 1.26967
\(151\) 1.27434e12 1.32103 0.660514 0.750814i \(-0.270338\pi\)
0.660514 + 0.750814i \(0.270338\pi\)
\(152\) −5.19822e11 −0.519655
\(153\) 2.98034e11 0.287384
\(154\) −1.88563e11 −0.175426
\(155\) 1.22641e12 1.10106
\(156\) 1.87884e11 0.162819
\(157\) −5.95494e11 −0.498229 −0.249115 0.968474i \(-0.580140\pi\)
−0.249115 + 0.968474i \(0.580140\pi\)
\(158\) 1.34139e12 1.08378
\(159\) 8.46016e11 0.660228
\(160\) 1.34225e12 1.01198
\(161\) 8.46067e10 0.0616400
\(162\) −1.34264e11 −0.0945422
\(163\) 6.18612e11 0.421101 0.210551 0.977583i \(-0.432474\pi\)
0.210551 + 0.977583i \(0.432474\pi\)
\(164\) −5.45567e10 −0.0359093
\(165\) −1.76411e12 −1.12296
\(166\) 2.32110e12 1.42922
\(167\) −1.69328e12 −1.00876 −0.504381 0.863481i \(-0.668279\pi\)
−0.504381 + 0.863481i \(0.668279\pi\)
\(168\) 2.18212e11 0.125799
\(169\) 7.88694e10 0.0440080
\(170\) 2.57121e12 1.38889
\(171\) −3.05037e11 −0.159542
\(172\) 3.67722e11 0.186257
\(173\) −2.92929e12 −1.43717 −0.718587 0.695438i \(-0.755211\pi\)
−0.718587 + 0.695438i \(0.755211\pi\)
\(174\) −1.21110e12 −0.575649
\(175\) −1.12619e12 −0.518683
\(176\) 1.49101e12 0.665519
\(177\) 1.73727e11 0.0751646
\(178\) 2.00713e12 0.841910
\(179\) 1.28881e12 0.524199 0.262099 0.965041i \(-0.415585\pi\)
0.262099 + 0.965041i \(0.415585\pi\)
\(180\) 4.41579e11 0.174185
\(181\) −1.05813e12 −0.404860 −0.202430 0.979297i \(-0.564884\pi\)
−0.202430 + 0.979297i \(0.564884\pi\)
\(182\) 4.70036e11 0.174477
\(183\) −1.25327e12 −0.451403
\(184\) −9.54031e11 −0.333476
\(185\) 5.26535e11 0.178642
\(186\) −8.67405e11 −0.285694
\(187\) −2.76962e12 −0.885708
\(188\) 9.07128e11 0.281709
\(189\) 1.28049e11 0.0386221
\(190\) −2.63163e12 −0.771046
\(191\) 2.32669e12 0.662301 0.331150 0.943578i \(-0.392563\pi\)
0.331150 + 0.943578i \(0.392563\pi\)
\(192\) −2.30156e12 −0.636599
\(193\) −2.14235e12 −0.575872 −0.287936 0.957650i \(-0.592969\pi\)
−0.287936 + 0.957650i \(0.592969\pi\)
\(194\) 5.13272e12 1.34103
\(195\) 4.39743e12 1.11688
\(196\) 1.07268e12 0.264887
\(197\) −5.43248e12 −1.30447 −0.652235 0.758017i \(-0.726168\pi\)
−0.652235 + 0.758017i \(0.726168\pi\)
\(198\) 1.24771e12 0.291376
\(199\) 4.38801e12 0.996726 0.498363 0.866968i \(-0.333935\pi\)
0.498363 + 0.866968i \(0.333935\pi\)
\(200\) 1.26990e13 2.80610
\(201\) 1.26931e12 0.272891
\(202\) 6.75897e12 1.41399
\(203\) 1.15504e12 0.235162
\(204\) 6.93271e11 0.137384
\(205\) −1.27690e12 −0.246326
\(206\) −2.91795e12 −0.548035
\(207\) −5.59835e11 −0.102382
\(208\) −3.71667e12 −0.661920
\(209\) 2.83470e12 0.491702
\(210\) 1.10471e12 0.186656
\(211\) −2.77223e12 −0.456327 −0.228163 0.973623i \(-0.573272\pi\)
−0.228163 + 0.973623i \(0.573272\pi\)
\(212\) 1.96796e12 0.315623
\(213\) −4.06801e12 −0.635762
\(214\) −9.77018e11 −0.148808
\(215\) 8.60651e12 1.27766
\(216\) −1.44389e12 −0.208948
\(217\) 8.27255e11 0.116711
\(218\) 5.74650e12 0.790483
\(219\) −5.19549e12 −0.696922
\(220\) −4.10358e12 −0.536832
\(221\) 6.90388e12 0.880918
\(222\) −3.72405e11 −0.0463526
\(223\) 1.79436e12 0.217887 0.108944 0.994048i \(-0.465253\pi\)
0.108944 + 0.994048i \(0.465253\pi\)
\(224\) 9.05394e11 0.107269
\(225\) 7.45189e12 0.861514
\(226\) 1.13708e13 1.28290
\(227\) −1.07806e12 −0.118713 −0.0593567 0.998237i \(-0.518905\pi\)
−0.0593567 + 0.998237i \(0.518905\pi\)
\(228\) −7.09562e11 −0.0762691
\(229\) 9.89002e12 1.03777 0.518886 0.854843i \(-0.326347\pi\)
0.518886 + 0.854843i \(0.326347\pi\)
\(230\) −4.82984e12 −0.494800
\(231\) −1.18995e12 −0.119032
\(232\) −1.30243e13 −1.27224
\(233\) −1.08290e13 −1.03307 −0.516534 0.856267i \(-0.672778\pi\)
−0.516534 + 0.856267i \(0.672778\pi\)
\(234\) −3.11018e12 −0.289800
\(235\) 2.12313e13 1.93243
\(236\) 4.04114e11 0.0359326
\(237\) 8.46501e12 0.735380
\(238\) 1.73438e12 0.147221
\(239\) 1.53403e13 1.27247 0.636233 0.771497i \(-0.280492\pi\)
0.636233 + 0.771497i \(0.280492\pi\)
\(240\) −8.73518e12 −0.708125
\(241\) −5.27094e12 −0.417633 −0.208816 0.977955i \(-0.566961\pi\)
−0.208816 + 0.977955i \(0.566961\pi\)
\(242\) −6.08561e11 −0.0471324
\(243\) −8.47289e11 −0.0641500
\(244\) −2.91530e12 −0.215794
\(245\) 2.51060e13 1.81704
\(246\) 9.03116e11 0.0639146
\(247\) −7.06611e12 −0.489043
\(248\) −9.32819e12 −0.631412
\(249\) 1.46476e13 0.969776
\(250\) 3.94148e13 2.55264
\(251\) −2.06077e13 −1.30564 −0.652820 0.757513i \(-0.726414\pi\)
−0.652820 + 0.757513i \(0.726414\pi\)
\(252\) 2.97861e11 0.0184634
\(253\) 5.20253e12 0.315538
\(254\) 2.95643e12 0.175462
\(255\) 1.62260e13 0.942410
\(256\) −1.33548e13 −0.759131
\(257\) −2.21773e13 −1.23389 −0.616946 0.787006i \(-0.711630\pi\)
−0.616946 + 0.787006i \(0.711630\pi\)
\(258\) −6.08716e12 −0.331517
\(259\) 3.55167e11 0.0189358
\(260\) 1.02291e13 0.533929
\(261\) −7.64278e12 −0.390597
\(262\) −1.48660e13 −0.743939
\(263\) −1.25777e12 −0.0616375 −0.0308188 0.999525i \(-0.509811\pi\)
−0.0308188 + 0.999525i \(0.509811\pi\)
\(264\) 1.34180e13 0.643971
\(265\) 4.60600e13 2.16507
\(266\) −1.77513e12 −0.0817300
\(267\) 1.26663e13 0.571264
\(268\) 2.95260e12 0.130456
\(269\) −9.80514e12 −0.424440 −0.212220 0.977222i \(-0.568069\pi\)
−0.212220 + 0.977222i \(0.568069\pi\)
\(270\) −7.30978e12 −0.310030
\(271\) −2.77249e13 −1.15223 −0.576114 0.817369i \(-0.695432\pi\)
−0.576114 + 0.817369i \(0.695432\pi\)
\(272\) −1.37141e13 −0.558518
\(273\) 2.96622e12 0.118388
\(274\) −3.22500e13 −1.26154
\(275\) −6.92501e13 −2.65516
\(276\) −1.30226e12 −0.0489438
\(277\) −1.02150e13 −0.376358 −0.188179 0.982135i \(-0.560259\pi\)
−0.188179 + 0.982135i \(0.560259\pi\)
\(278\) −3.03049e12 −0.109463
\(279\) −5.47388e12 −0.193853
\(280\) 1.18802e13 0.412529
\(281\) −2.51699e13 −0.857031 −0.428516 0.903534i \(-0.640963\pi\)
−0.428516 + 0.903534i \(0.640963\pi\)
\(282\) −1.50163e13 −0.501411
\(283\) 4.75093e13 1.55580 0.777900 0.628388i \(-0.216285\pi\)
0.777900 + 0.628388i \(0.216285\pi\)
\(284\) −9.46281e12 −0.303927
\(285\) −1.66073e13 −0.523180
\(286\) 2.89028e13 0.893156
\(287\) −8.61313e11 −0.0261102
\(288\) −5.99091e12 −0.178170
\(289\) −8.79741e12 −0.256695
\(290\) −6.59362e13 −1.88771
\(291\) 3.23907e13 0.909932
\(292\) −1.20855e13 −0.333165
\(293\) −2.75677e13 −0.745811 −0.372906 0.927869i \(-0.621639\pi\)
−0.372906 + 0.927869i \(0.621639\pi\)
\(294\) −1.77568e13 −0.471470
\(295\) 9.45828e12 0.246485
\(296\) −4.00489e12 −0.102444
\(297\) 7.87382e12 0.197708
\(298\) −1.92235e13 −0.473851
\(299\) −1.29684e13 −0.313831
\(300\) 1.73342e13 0.411848
\(301\) 5.80540e12 0.135431
\(302\) −4.90703e13 −1.12404
\(303\) 4.26534e13 0.959442
\(304\) 1.40363e13 0.310062
\(305\) −6.82325e13 −1.48027
\(306\) −1.14762e13 −0.244529
\(307\) −2.04562e13 −0.428118 −0.214059 0.976821i \(-0.568669\pi\)
−0.214059 + 0.976821i \(0.568669\pi\)
\(308\) −2.76801e12 −0.0569035
\(309\) −1.84141e13 −0.371860
\(310\) −4.72245e13 −0.936868
\(311\) 3.95899e13 0.771617 0.385809 0.922579i \(-0.373923\pi\)
0.385809 + 0.922579i \(0.373923\pi\)
\(312\) −3.34473e13 −0.640489
\(313\) −7.17027e13 −1.34909 −0.674546 0.738233i \(-0.735661\pi\)
−0.674546 + 0.738233i \(0.735661\pi\)
\(314\) 2.29303e13 0.423933
\(315\) 6.97143e12 0.126652
\(316\) 1.96909e13 0.351550
\(317\) 5.35317e10 0.000939258 0 0.000469629 1.00000i \(-0.499851\pi\)
0.000469629 1.00000i \(0.499851\pi\)
\(318\) −3.25770e13 −0.561775
\(319\) 7.10241e13 1.20381
\(320\) −1.25305e14 −2.08758
\(321\) −6.16560e12 −0.100971
\(322\) −3.25790e12 −0.0524482
\(323\) −2.60731e13 −0.412647
\(324\) −1.97092e12 −0.0306670
\(325\) 1.72621e14 2.64080
\(326\) −2.38205e13 −0.358306
\(327\) 3.62640e13 0.536369
\(328\) 9.71223e12 0.141258
\(329\) 1.43213e13 0.204835
\(330\) 6.79295e13 0.955502
\(331\) −1.17536e14 −1.62599 −0.812996 0.582269i \(-0.802165\pi\)
−0.812996 + 0.582269i \(0.802165\pi\)
\(332\) 3.40726e13 0.463603
\(333\) −2.35011e12 −0.0314517
\(334\) 6.52022e13 0.858335
\(335\) 6.91055e13 0.894883
\(336\) −5.89219e12 −0.0750604
\(337\) 1.37448e14 1.72256 0.861279 0.508133i \(-0.169664\pi\)
0.861279 + 0.508133i \(0.169664\pi\)
\(338\) −3.03698e12 −0.0374455
\(339\) 7.17569e13 0.870493
\(340\) 3.77441e13 0.450521
\(341\) 5.08685e13 0.597448
\(342\) 1.17459e13 0.135751
\(343\) 3.45805e13 0.393290
\(344\) −6.54621e13 −0.732688
\(345\) −3.04793e13 −0.335738
\(346\) 1.12797e14 1.22286
\(347\) 1.18508e14 1.26455 0.632276 0.774744i \(-0.282121\pi\)
0.632276 + 0.774744i \(0.282121\pi\)
\(348\) −1.77783e13 −0.186725
\(349\) 5.65533e13 0.584680 0.292340 0.956314i \(-0.405566\pi\)
0.292340 + 0.956314i \(0.405566\pi\)
\(350\) 4.33655e13 0.441337
\(351\) −1.96272e13 −0.196639
\(352\) 5.56733e13 0.549114
\(353\) −8.08290e13 −0.784886 −0.392443 0.919776i \(-0.628370\pi\)
−0.392443 + 0.919776i \(0.628370\pi\)
\(354\) −6.68959e12 −0.0639561
\(355\) −2.21477e14 −2.08484
\(356\) 2.94636e13 0.273094
\(357\) 1.09450e13 0.0998944
\(358\) −4.96273e13 −0.446030
\(359\) 3.39630e13 0.300598 0.150299 0.988641i \(-0.451976\pi\)
0.150299 + 0.988641i \(0.451976\pi\)
\(360\) −7.86103e13 −0.685197
\(361\) −8.98045e13 −0.770919
\(362\) 4.07446e13 0.344487
\(363\) −3.84041e12 −0.0319809
\(364\) 6.89988e12 0.0565958
\(365\) −2.82861e14 −2.28540
\(366\) 4.82590e13 0.384090
\(367\) −7.35188e13 −0.576415 −0.288207 0.957568i \(-0.593059\pi\)
−0.288207 + 0.957568i \(0.593059\pi\)
\(368\) 2.57609e13 0.198975
\(369\) 5.69923e12 0.0433682
\(370\) −2.02750e13 −0.152003
\(371\) 3.10691e13 0.229495
\(372\) −1.27331e13 −0.0926716
\(373\) −1.36850e14 −0.981398 −0.490699 0.871329i \(-0.663258\pi\)
−0.490699 + 0.871329i \(0.663258\pi\)
\(374\) 1.06648e14 0.753631
\(375\) 2.48732e14 1.73205
\(376\) −1.61488e14 −1.10817
\(377\) −1.77043e14 −1.19730
\(378\) −4.93071e12 −0.0328628
\(379\) −1.56486e14 −1.02792 −0.513960 0.857814i \(-0.671822\pi\)
−0.513960 + 0.857814i \(0.671822\pi\)
\(380\) −3.86310e13 −0.250107
\(381\) 1.86569e13 0.119056
\(382\) −8.95926e13 −0.563538
\(383\) −2.72767e14 −1.69121 −0.845607 0.533806i \(-0.820761\pi\)
−0.845607 + 0.533806i \(0.820761\pi\)
\(384\) 3.81337e13 0.233070
\(385\) −6.47852e13 −0.390339
\(386\) 8.24944e13 0.489998
\(387\) −3.84138e13 −0.224946
\(388\) 7.53457e13 0.434995
\(389\) −3.21230e14 −1.82849 −0.914247 0.405157i \(-0.867217\pi\)
−0.914247 + 0.405157i \(0.867217\pi\)
\(390\) −1.69329e14 −0.950334
\(391\) −4.78520e13 −0.264806
\(392\) −1.90959e14 −1.04200
\(393\) −9.38139e13 −0.504787
\(394\) 2.09185e14 1.10995
\(395\) 4.60864e14 2.41151
\(396\) 1.83157e13 0.0945149
\(397\) 3.76608e14 1.91664 0.958322 0.285690i \(-0.0922227\pi\)
0.958322 + 0.285690i \(0.0922227\pi\)
\(398\) −1.68967e14 −0.848094
\(399\) −1.12022e13 −0.0554565
\(400\) −3.42900e14 −1.67432
\(401\) −6.97557e13 −0.335958 −0.167979 0.985791i \(-0.553724\pi\)
−0.167979 + 0.985791i \(0.553724\pi\)
\(402\) −4.88765e13 −0.232197
\(403\) −1.26801e14 −0.594217
\(404\) 9.92182e13 0.458663
\(405\) −4.61293e13 −0.210365
\(406\) −4.44764e13 −0.200095
\(407\) 2.18395e13 0.0969333
\(408\) −1.23417e14 −0.540435
\(409\) 3.30559e14 1.42814 0.714069 0.700075i \(-0.246850\pi\)
0.714069 + 0.700075i \(0.246850\pi\)
\(410\) 4.91687e13 0.209594
\(411\) −2.03518e14 −0.855999
\(412\) −4.28340e13 −0.177768
\(413\) 6.37995e12 0.0261271
\(414\) 2.15572e13 0.0871147
\(415\) 7.97468e14 3.18016
\(416\) −1.38778e14 −0.546144
\(417\) −1.91243e13 −0.0742742
\(418\) −1.09154e14 −0.418379
\(419\) −3.91370e14 −1.48051 −0.740254 0.672327i \(-0.765295\pi\)
−0.740254 + 0.672327i \(0.765295\pi\)
\(420\) 1.62166e13 0.0605464
\(421\) 2.19574e14 0.809150 0.404575 0.914505i \(-0.367419\pi\)
0.404575 + 0.914505i \(0.367419\pi\)
\(422\) 1.06749e14 0.388279
\(423\) −9.47625e13 −0.340224
\(424\) −3.50338e14 −1.24158
\(425\) 6.36952e14 2.22827
\(426\) 1.56645e14 0.540957
\(427\) −4.60253e13 −0.156907
\(428\) −1.43421e13 −0.0482695
\(429\) 1.82395e14 0.606036
\(430\) −3.31406e14 −1.08714
\(431\) 1.17139e14 0.379382 0.189691 0.981844i \(-0.439251\pi\)
0.189691 + 0.981844i \(0.439251\pi\)
\(432\) 3.89881e13 0.124673
\(433\) 1.68180e14 0.530995 0.265497 0.964112i \(-0.414464\pi\)
0.265497 + 0.964112i \(0.414464\pi\)
\(434\) −3.18546e13 −0.0993069
\(435\) −4.16099e14 −1.28087
\(436\) 8.43556e13 0.256412
\(437\) 4.89764e13 0.147007
\(438\) 2.00060e14 0.592997
\(439\) 4.29459e14 1.25709 0.628546 0.777772i \(-0.283650\pi\)
0.628546 + 0.777772i \(0.283650\pi\)
\(440\) 7.30523e14 2.11176
\(441\) −1.12057e14 −0.319908
\(442\) −2.65844e14 −0.749556
\(443\) −4.46499e14 −1.24337 −0.621684 0.783268i \(-0.713551\pi\)
−0.621684 + 0.783268i \(0.713551\pi\)
\(444\) −5.46671e12 −0.0150356
\(445\) 6.89595e14 1.87333
\(446\) −6.90942e13 −0.185396
\(447\) −1.21312e14 −0.321524
\(448\) −8.45228e13 −0.221281
\(449\) −2.27812e14 −0.589145 −0.294573 0.955629i \(-0.595177\pi\)
−0.294573 + 0.955629i \(0.595177\pi\)
\(450\) −2.86946e14 −0.733045
\(451\) −5.29628e13 −0.133659
\(452\) 1.66917e14 0.416141
\(453\) −3.09665e14 −0.762696
\(454\) 4.15122e13 0.101011
\(455\) 1.61491e14 0.388228
\(456\) 1.26317e14 0.300023
\(457\) 4.70956e13 0.110520 0.0552600 0.998472i \(-0.482401\pi\)
0.0552600 + 0.998472i \(0.482401\pi\)
\(458\) −3.80830e14 −0.883020
\(459\) −7.24222e13 −0.165921
\(460\) −7.08996e13 −0.160500
\(461\) −7.29447e13 −0.163169 −0.0815847 0.996666i \(-0.525998\pi\)
−0.0815847 + 0.996666i \(0.525998\pi\)
\(462\) 4.58209e13 0.101282
\(463\) −3.70200e14 −0.808613 −0.404306 0.914624i \(-0.632487\pi\)
−0.404306 + 0.914624i \(0.632487\pi\)
\(464\) 3.51684e14 0.759108
\(465\) −2.98017e14 −0.635696
\(466\) 4.16984e14 0.879017
\(467\) −3.41187e14 −0.710803 −0.355402 0.934714i \(-0.615656\pi\)
−0.355402 + 0.934714i \(0.615656\pi\)
\(468\) −4.56559e13 −0.0940037
\(469\) 4.66142e13 0.0948566
\(470\) −8.17541e14 −1.64426
\(471\) 1.44705e14 0.287653
\(472\) −7.19408e13 −0.141349
\(473\) 3.56978e14 0.693275
\(474\) −3.25957e14 −0.625720
\(475\) −6.51919e14 −1.23703
\(476\) 2.54598e13 0.0477547
\(477\) −2.05582e14 −0.381183
\(478\) −5.90701e14 −1.08272
\(479\) −3.09598e14 −0.560986 −0.280493 0.959856i \(-0.590498\pi\)
−0.280493 + 0.959856i \(0.590498\pi\)
\(480\) −3.26166e14 −0.584268
\(481\) −5.44397e13 −0.0964091
\(482\) 2.02965e14 0.355355
\(483\) −2.05594e13 −0.0355878
\(484\) −8.93337e12 −0.0152885
\(485\) 1.76346e15 2.98392
\(486\) 3.26261e13 0.0545840
\(487\) 9.11010e14 1.50700 0.753501 0.657447i \(-0.228364\pi\)
0.753501 + 0.657447i \(0.228364\pi\)
\(488\) 5.18984e14 0.848878
\(489\) −1.50323e14 −0.243123
\(490\) −9.66742e14 −1.54608
\(491\) −4.54520e14 −0.718795 −0.359398 0.933185i \(-0.617018\pi\)
−0.359398 + 0.933185i \(0.617018\pi\)
\(492\) 1.32573e13 0.0207322
\(493\) −6.53268e14 −1.01026
\(494\) 2.72091e14 0.416117
\(495\) 4.28678e14 0.648340
\(496\) 2.51881e14 0.376744
\(497\) −1.49394e14 −0.220990
\(498\) −5.64028e14 −0.825163
\(499\) 4.96092e14 0.717809 0.358904 0.933374i \(-0.383150\pi\)
0.358904 + 0.933374i \(0.383150\pi\)
\(500\) 5.78589e14 0.828009
\(501\) 4.11467e14 0.582409
\(502\) 7.93528e14 1.11094
\(503\) −7.22327e14 −1.00025 −0.500126 0.865952i \(-0.666713\pi\)
−0.500126 + 0.865952i \(0.666713\pi\)
\(504\) −5.30255e13 −0.0726301
\(505\) 2.32220e15 3.14627
\(506\) −2.00331e14 −0.268485
\(507\) −1.91653e13 −0.0254080
\(508\) 4.33989e13 0.0569152
\(509\) −5.21265e14 −0.676256 −0.338128 0.941100i \(-0.609794\pi\)
−0.338128 + 0.941100i \(0.609794\pi\)
\(510\) −6.24805e14 −0.801878
\(511\) −1.90800e14 −0.242249
\(512\) 8.35635e14 1.04962
\(513\) 7.41240e13 0.0921113
\(514\) 8.53970e14 1.04989
\(515\) −1.00253e15 −1.21943
\(516\) −8.93564e13 −0.107536
\(517\) 8.80625e14 1.04856
\(518\) −1.36762e13 −0.0161121
\(519\) 7.11818e14 0.829752
\(520\) −1.82099e15 −2.10034
\(521\) 9.18931e14 1.04876 0.524379 0.851485i \(-0.324297\pi\)
0.524379 + 0.851485i \(0.324297\pi\)
\(522\) 2.94296e14 0.332351
\(523\) 6.36992e13 0.0711827 0.0355913 0.999366i \(-0.488669\pi\)
0.0355913 + 0.999366i \(0.488669\pi\)
\(524\) −2.18225e14 −0.241314
\(525\) 2.73664e14 0.299462
\(526\) 4.84323e13 0.0524461
\(527\) −4.67881e14 −0.501391
\(528\) −3.62315e14 −0.384238
\(529\) −8.62923e14 −0.905662
\(530\) −1.77361e15 −1.84221
\(531\) −4.22156e13 −0.0433963
\(532\) −2.60580e13 −0.0265111
\(533\) 1.32021e14 0.132937
\(534\) −4.87733e14 −0.486077
\(535\) −3.35677e14 −0.331112
\(536\) −5.25625e14 −0.513180
\(537\) −3.13180e14 −0.302646
\(538\) 3.77561e14 0.361147
\(539\) 1.04134e15 0.985948
\(540\) −1.07304e14 −0.100566
\(541\) −1.62321e15 −1.50588 −0.752939 0.658090i \(-0.771365\pi\)
−0.752939 + 0.658090i \(0.771365\pi\)
\(542\) 1.06759e15 0.980408
\(543\) 2.57124e14 0.233746
\(544\) −5.12074e14 −0.460828
\(545\) 1.97434e15 1.75890
\(546\) −1.14219e14 −0.100734
\(547\) 1.15177e15 1.00562 0.502810 0.864397i \(-0.332299\pi\)
0.502810 + 0.864397i \(0.332299\pi\)
\(548\) −4.73414e14 −0.409212
\(549\) 3.04545e14 0.260618
\(550\) 2.66658e15 2.25922
\(551\) 6.68619e14 0.560847
\(552\) 2.31830e14 0.192532
\(553\) 3.10870e14 0.255617
\(554\) 3.93345e14 0.320236
\(555\) −1.27948e14 −0.103139
\(556\) −4.44861e13 −0.0355069
\(557\) −3.76631e14 −0.297654 −0.148827 0.988863i \(-0.547550\pi\)
−0.148827 + 0.988863i \(0.547550\pi\)
\(558\) 2.10779e14 0.164945
\(559\) −8.89847e14 −0.689526
\(560\) −3.20791e14 −0.246144
\(561\) 6.73017e14 0.511364
\(562\) 9.69203e14 0.729231
\(563\) 5.16229e14 0.384632 0.192316 0.981333i \(-0.438400\pi\)
0.192316 + 0.981333i \(0.438400\pi\)
\(564\) −2.20432e14 −0.162645
\(565\) 3.90669e15 2.85458
\(566\) −1.82942e15 −1.32380
\(567\) −3.11159e13 −0.0222985
\(568\) 1.68458e15 1.19557
\(569\) 1.67695e14 0.117870 0.0589349 0.998262i \(-0.481230\pi\)
0.0589349 + 0.998262i \(0.481230\pi\)
\(570\) 6.39486e14 0.445163
\(571\) 2.56075e15 1.76550 0.882752 0.469839i \(-0.155688\pi\)
0.882752 + 0.469839i \(0.155688\pi\)
\(572\) 4.24279e14 0.289717
\(573\) −5.65386e14 −0.382379
\(574\) 3.31661e13 0.0222167
\(575\) −1.19647e15 −0.793831
\(576\) 5.59280e14 0.367541
\(577\) 1.11755e15 0.727442 0.363721 0.931508i \(-0.381506\pi\)
0.363721 + 0.931508i \(0.381506\pi\)
\(578\) 3.38757e14 0.218416
\(579\) 5.20592e14 0.332480
\(580\) −9.67910e14 −0.612324
\(581\) 5.37921e14 0.337093
\(582\) −1.24725e15 −0.774243
\(583\) 1.91046e15 1.17479
\(584\) 2.15147e15 1.31058
\(585\) −1.06857e15 −0.644833
\(586\) 1.06153e15 0.634596
\(587\) −3.26597e15 −1.93420 −0.967102 0.254390i \(-0.918125\pi\)
−0.967102 + 0.254390i \(0.918125\pi\)
\(588\) −2.60661e14 −0.152933
\(589\) 4.78875e14 0.278348
\(590\) −3.64204e14 −0.209729
\(591\) 1.32009e15 0.753136
\(592\) 1.08141e14 0.0611251
\(593\) 1.98254e15 1.11025 0.555125 0.831767i \(-0.312671\pi\)
0.555125 + 0.831767i \(0.312671\pi\)
\(594\) −3.03193e14 −0.168226
\(595\) 5.95884e14 0.327581
\(596\) −2.82191e14 −0.153705
\(597\) −1.06629e15 −0.575460
\(598\) 4.99368e14 0.267033
\(599\) −3.00851e14 −0.159406 −0.0797028 0.996819i \(-0.525397\pi\)
−0.0797028 + 0.996819i \(0.525397\pi\)
\(600\) −3.08585e15 −1.62011
\(601\) −4.02711e14 −0.209500 −0.104750 0.994499i \(-0.533404\pi\)
−0.104750 + 0.994499i \(0.533404\pi\)
\(602\) −2.23545e14 −0.115235
\(603\) −3.08442e14 −0.157554
\(604\) −7.20327e14 −0.364608
\(605\) −2.09085e14 −0.104874
\(606\) −1.64243e15 −0.816370
\(607\) 1.62300e14 0.0799431 0.0399715 0.999201i \(-0.487273\pi\)
0.0399715 + 0.999201i \(0.487273\pi\)
\(608\) 5.24107e14 0.255829
\(609\) −2.80674e14 −0.135771
\(610\) 2.62739e15 1.25954
\(611\) −2.19515e15 −1.04289
\(612\) −1.68465e14 −0.0793189
\(613\) 2.80499e15 1.30888 0.654439 0.756114i \(-0.272905\pi\)
0.654439 + 0.756114i \(0.272905\pi\)
\(614\) 7.87695e14 0.364277
\(615\) 3.10286e14 0.142216
\(616\) 4.92764e14 0.223844
\(617\) 2.73536e15 1.23153 0.615766 0.787929i \(-0.288847\pi\)
0.615766 + 0.787929i \(0.288847\pi\)
\(618\) 7.09062e14 0.316408
\(619\) −3.03415e14 −0.134196 −0.0670979 0.997746i \(-0.521374\pi\)
−0.0670979 + 0.997746i \(0.521374\pi\)
\(620\) −6.93232e14 −0.303895
\(621\) 1.36040e14 0.0591102
\(622\) −1.52446e15 −0.656554
\(623\) 4.65157e14 0.198571
\(624\) 9.03150e14 0.382160
\(625\) 7.37982e15 3.09532
\(626\) 2.76101e15 1.14792
\(627\) −6.88831e14 −0.283884
\(628\) 3.36606e14 0.137513
\(629\) −2.00876e14 −0.0813485
\(630\) −2.68445e14 −0.107766
\(631\) 1.28691e15 0.512137 0.256068 0.966659i \(-0.417573\pi\)
0.256068 + 0.966659i \(0.417573\pi\)
\(632\) −3.50539e15 −1.38290
\(633\) 6.73652e14 0.263460
\(634\) −2.06131e12 −0.000799196 0
\(635\) 1.01575e15 0.390419
\(636\) −4.78214e14 −0.182225
\(637\) −2.59577e15 −0.980615
\(638\) −2.73488e15 −1.02430
\(639\) 9.88527e14 0.367057
\(640\) 2.07613e15 0.764301
\(641\) 2.70651e15 0.987848 0.493924 0.869505i \(-0.335562\pi\)
0.493924 + 0.869505i \(0.335562\pi\)
\(642\) 2.37415e14 0.0859145
\(643\) −5.18247e15 −1.85942 −0.929708 0.368298i \(-0.879941\pi\)
−0.929708 + 0.368298i \(0.879941\pi\)
\(644\) −4.78243e13 −0.0170128
\(645\) −2.09138e15 −0.737658
\(646\) 1.00398e15 0.351113
\(647\) 3.11247e15 1.07927 0.539637 0.841898i \(-0.318561\pi\)
0.539637 + 0.841898i \(0.318561\pi\)
\(648\) 3.50865e14 0.120636
\(649\) 3.92308e14 0.133746
\(650\) −6.64703e15 −2.24700
\(651\) −2.01023e14 −0.0673830
\(652\) −3.49673e14 −0.116225
\(653\) −1.22125e15 −0.402516 −0.201258 0.979538i \(-0.564503\pi\)
−0.201258 + 0.979538i \(0.564503\pi\)
\(654\) −1.39640e15 −0.456385
\(655\) −5.10755e15 −1.65533
\(656\) −2.62251e14 −0.0842842
\(657\) 1.26251e15 0.402368
\(658\) −5.51461e14 −0.174290
\(659\) 4.37350e14 0.137075 0.0685377 0.997649i \(-0.478167\pi\)
0.0685377 + 0.997649i \(0.478167\pi\)
\(660\) 9.97170e14 0.309940
\(661\) −1.38090e15 −0.425650 −0.212825 0.977090i \(-0.568266\pi\)
−0.212825 + 0.977090i \(0.568266\pi\)
\(662\) 4.52591e15 1.38352
\(663\) −1.67764e15 −0.508598
\(664\) −6.06564e15 −1.82369
\(665\) −6.09886e14 −0.181857
\(666\) 9.04943e13 0.0267617
\(667\) 1.22712e15 0.359910
\(668\) 9.57135e14 0.278422
\(669\) −4.36028e14 −0.125797
\(670\) −2.66101e15 −0.761438
\(671\) −2.83013e15 −0.803216
\(672\) −2.20011e14 −0.0619317
\(673\) −4.15651e15 −1.16050 −0.580252 0.814437i \(-0.697046\pi\)
−0.580252 + 0.814437i \(0.697046\pi\)
\(674\) −5.29263e15 −1.46569
\(675\) −1.81081e15 −0.497396
\(676\) −4.45813e13 −0.0121464
\(677\) 1.94680e15 0.526119 0.263060 0.964780i \(-0.415268\pi\)
0.263060 + 0.964780i \(0.415268\pi\)
\(678\) −2.76310e15 −0.740685
\(679\) 1.18952e15 0.316292
\(680\) −6.71923e15 −1.77223
\(681\) 2.61968e14 0.0685393
\(682\) −1.95877e15 −0.508356
\(683\) −3.57495e15 −0.920358 −0.460179 0.887826i \(-0.652215\pi\)
−0.460179 + 0.887826i \(0.652215\pi\)
\(684\) 1.72424e14 0.0440340
\(685\) −1.10802e16 −2.80705
\(686\) −1.33157e15 −0.334643
\(687\) −2.40328e15 −0.599158
\(688\) 1.76762e15 0.437172
\(689\) −4.76225e15 −1.16844
\(690\) 1.17365e15 0.285673
\(691\) −2.73596e15 −0.660663 −0.330331 0.943865i \(-0.607160\pi\)
−0.330331 + 0.943865i \(0.607160\pi\)
\(692\) 1.65580e15 0.396665
\(693\) 2.89159e14 0.0687233
\(694\) −4.56333e15 −1.07598
\(695\) −1.04119e15 −0.243565
\(696\) 3.16490e15 0.734529
\(697\) 4.87143e14 0.112170
\(698\) −2.17767e15 −0.497492
\(699\) 2.63144e15 0.596442
\(700\) 6.36583e14 0.143158
\(701\) 3.17495e15 0.708415 0.354208 0.935167i \(-0.384751\pi\)
0.354208 + 0.935167i \(0.384751\pi\)
\(702\) 7.55775e14 0.167316
\(703\) 2.05596e14 0.0451607
\(704\) −5.19737e15 −1.13275
\(705\) −5.15920e15 −1.11569
\(706\) 3.11244e15 0.667844
\(707\) 1.56641e15 0.333501
\(708\) −9.81998e13 −0.0207457
\(709\) 4.33573e15 0.908883 0.454441 0.890777i \(-0.349839\pi\)
0.454441 + 0.890777i \(0.349839\pi\)
\(710\) 8.52827e15 1.77395
\(711\) −2.05700e15 −0.424572
\(712\) −5.24514e15 −1.07428
\(713\) 8.78880e14 0.178623
\(714\) −4.21453e14 −0.0849981
\(715\) 9.93022e15 1.98736
\(716\) −7.28504e14 −0.144681
\(717\) −3.72770e15 −0.734659
\(718\) −1.30779e15 −0.255773
\(719\) 5.63989e15 1.09462 0.547308 0.836931i \(-0.315653\pi\)
0.547308 + 0.836931i \(0.315653\pi\)
\(720\) 2.12265e15 0.408836
\(721\) −6.76242e14 −0.129258
\(722\) 3.45805e15 0.655959
\(723\) 1.28084e15 0.241120
\(724\) 5.98110e14 0.111743
\(725\) −1.63340e16 −3.02854
\(726\) 1.47880e14 0.0272119
\(727\) −5.36267e15 −0.979358 −0.489679 0.871903i \(-0.662886\pi\)
−0.489679 + 0.871903i \(0.662886\pi\)
\(728\) −1.22832e15 −0.222633
\(729\) 2.05891e14 0.0370370
\(730\) 1.08920e16 1.94460
\(731\) −3.28343e15 −0.581812
\(732\) 7.08418e14 0.124589
\(733\) 4.25039e15 0.741920 0.370960 0.928649i \(-0.379029\pi\)
0.370960 + 0.928649i \(0.379029\pi\)
\(734\) 2.83095e15 0.490460
\(735\) −6.10075e15 −1.04907
\(736\) 9.61895e14 0.164172
\(737\) 2.86634e15 0.485575
\(738\) −2.19457e14 −0.0369011
\(739\) −1.19448e16 −1.99358 −0.996790 0.0800612i \(-0.974488\pi\)
−0.996790 + 0.0800612i \(0.974488\pi\)
\(740\) −2.97627e14 −0.0493057
\(741\) 1.71706e15 0.282349
\(742\) −1.19636e15 −0.195273
\(743\) 6.10708e15 0.989453 0.494727 0.869049i \(-0.335268\pi\)
0.494727 + 0.869049i \(0.335268\pi\)
\(744\) 2.26675e15 0.364546
\(745\) −6.60466e15 −1.05436
\(746\) 5.26959e15 0.835052
\(747\) −3.55938e15 −0.559900
\(748\) 1.56554e15 0.244458
\(749\) −2.26426e14 −0.0350975
\(750\) −9.57780e15 −1.47377
\(751\) 1.08674e15 0.165999 0.0829996 0.996550i \(-0.473550\pi\)
0.0829996 + 0.996550i \(0.473550\pi\)
\(752\) 4.36051e15 0.661210
\(753\) 5.00766e15 0.753811
\(754\) 6.81730e15 1.01876
\(755\) −1.68592e16 −2.50109
\(756\) −7.23803e13 −0.0106598
\(757\) 8.46368e15 1.23746 0.618731 0.785603i \(-0.287647\pi\)
0.618731 + 0.785603i \(0.287647\pi\)
\(758\) 6.02570e15 0.874636
\(759\) −1.26421e15 −0.182176
\(760\) 6.87712e15 0.983857
\(761\) −2.19644e15 −0.311963 −0.155982 0.987760i \(-0.549854\pi\)
−0.155982 + 0.987760i \(0.549854\pi\)
\(762\) −7.18412e14 −0.101303
\(763\) 1.33176e15 0.186441
\(764\) −1.31517e15 −0.182797
\(765\) −3.94291e15 −0.544101
\(766\) 1.05033e16 1.43902
\(767\) −9.77913e14 −0.133023
\(768\) 3.24521e15 0.438284
\(769\) 5.08350e15 0.681661 0.340830 0.940125i \(-0.389292\pi\)
0.340830 + 0.940125i \(0.389292\pi\)
\(770\) 2.49465e15 0.332132
\(771\) 5.38909e15 0.712388
\(772\) 1.21098e15 0.158943
\(773\) 1.19595e16 1.55856 0.779282 0.626674i \(-0.215584\pi\)
0.779282 + 0.626674i \(0.215584\pi\)
\(774\) 1.47918e15 0.191402
\(775\) −1.16987e16 −1.50306
\(776\) −1.34131e16 −1.71116
\(777\) −8.63056e13 −0.0109326
\(778\) 1.23694e16 1.55583
\(779\) −4.98590e14 −0.0622713
\(780\) −2.48567e15 −0.308264
\(781\) −9.18634e15 −1.13126
\(782\) 1.84261e15 0.225318
\(783\) 1.85720e15 0.225511
\(784\) 5.15631e15 0.621728
\(785\) 7.87824e15 0.943292
\(786\) 3.61244e15 0.429513
\(787\) 1.14735e16 1.35467 0.677335 0.735675i \(-0.263135\pi\)
0.677335 + 0.735675i \(0.263135\pi\)
\(788\) 3.07074e15 0.360038
\(789\) 3.05639e14 0.0355864
\(790\) −1.77462e16 −2.05191
\(791\) 2.63520e15 0.302582
\(792\) −3.26058e15 −0.371797
\(793\) 7.05472e15 0.798872
\(794\) −1.45018e16 −1.63083
\(795\) −1.11926e16 −1.25000
\(796\) −2.48034e15 −0.275100
\(797\) −1.37704e16 −1.51679 −0.758393 0.651798i \(-0.774015\pi\)
−0.758393 + 0.651798i \(0.774015\pi\)
\(798\) 4.31357e14 0.0471868
\(799\) −8.09985e15 −0.879973
\(800\) −1.28037e16 −1.38146
\(801\) −3.07790e15 −0.329819
\(802\) 2.68604e15 0.285860
\(803\) −1.17324e16 −1.24009
\(804\) −7.17483e14 −0.0753188
\(805\) −1.11933e15 −0.116702
\(806\) 4.88265e15 0.505607
\(807\) 2.38265e15 0.245050
\(808\) −1.76629e16 −1.80426
\(809\) 4.97789e15 0.505043 0.252521 0.967591i \(-0.418740\pi\)
0.252521 + 0.967591i \(0.418740\pi\)
\(810\) 1.77628e15 0.178996
\(811\) 9.30004e15 0.930830 0.465415 0.885093i \(-0.345905\pi\)
0.465415 + 0.885093i \(0.345905\pi\)
\(812\) −6.52890e14 −0.0649056
\(813\) 6.73715e15 0.665240
\(814\) −8.40960e14 −0.0824786
\(815\) −8.18408e15 −0.797266
\(816\) 3.33252e15 0.322461
\(817\) 3.36059e15 0.322993
\(818\) −1.27286e16 −1.21517
\(819\) −7.20792e14 −0.0683516
\(820\) 7.21772e14 0.0679867
\(821\) 1.83634e16 1.71817 0.859085 0.511834i \(-0.171034\pi\)
0.859085 + 0.511834i \(0.171034\pi\)
\(822\) 7.83676e15 0.728352
\(823\) 1.65501e16 1.52793 0.763964 0.645259i \(-0.223251\pi\)
0.763964 + 0.645259i \(0.223251\pi\)
\(824\) 7.62535e15 0.699294
\(825\) 1.68278e16 1.53296
\(826\) −2.45669e14 −0.0222311
\(827\) 1.94784e16 1.75094 0.875471 0.483270i \(-0.160551\pi\)
0.875471 + 0.483270i \(0.160551\pi\)
\(828\) 3.16449e14 0.0282577
\(829\) −9.00331e15 −0.798643 −0.399321 0.916811i \(-0.630754\pi\)
−0.399321 + 0.916811i \(0.630754\pi\)
\(830\) −3.07077e16 −2.70593
\(831\) 2.48226e15 0.217291
\(832\) 1.29556e16 1.12662
\(833\) −9.57807e15 −0.827428
\(834\) 7.36409e14 0.0631984
\(835\) 2.24017e16 1.90988
\(836\) −1.60233e15 −0.135711
\(837\) 1.33015e15 0.111921
\(838\) 1.50703e16 1.25973
\(839\) 8.51024e15 0.706726 0.353363 0.935486i \(-0.385038\pi\)
0.353363 + 0.935486i \(0.385038\pi\)
\(840\) −2.88689e15 −0.238174
\(841\) 4.55191e15 0.373092
\(842\) −8.45500e15 −0.688489
\(843\) 6.11628e15 0.494807
\(844\) 1.56702e15 0.125948
\(845\) −1.04342e15 −0.0833199
\(846\) 3.64897e15 0.289490
\(847\) −1.41035e14 −0.0111165
\(848\) 9.45988e15 0.740813
\(849\) −1.15448e16 −0.898241
\(850\) −2.45267e16 −1.89599
\(851\) 3.77331e14 0.0289808
\(852\) 2.29946e15 0.175472
\(853\) −1.47084e16 −1.11519 −0.557593 0.830115i \(-0.688275\pi\)
−0.557593 + 0.830115i \(0.688275\pi\)
\(854\) 1.77227e15 0.133509
\(855\) 4.03556e15 0.302058
\(856\) 2.55320e15 0.189880
\(857\) −5.31834e15 −0.392990 −0.196495 0.980505i \(-0.562956\pi\)
−0.196495 + 0.980505i \(0.562956\pi\)
\(858\) −7.02339e15 −0.515664
\(859\) 1.44436e16 1.05369 0.526845 0.849962i \(-0.323375\pi\)
0.526845 + 0.849962i \(0.323375\pi\)
\(860\) −4.86487e15 −0.352639
\(861\) 2.09299e14 0.0150747
\(862\) −4.51061e15 −0.322809
\(863\) −1.88206e16 −1.33836 −0.669180 0.743100i \(-0.733355\pi\)
−0.669180 + 0.743100i \(0.733355\pi\)
\(864\) 1.45579e15 0.102866
\(865\) 3.87538e16 2.72098
\(866\) −6.47600e15 −0.451813
\(867\) 2.13777e15 0.148203
\(868\) −4.67610e14 −0.0322126
\(869\) 1.91156e16 1.30852
\(870\) 1.60225e16 1.08987
\(871\) −7.14498e15 −0.482949
\(872\) −1.50171e16 −1.00866
\(873\) −7.87094e15 −0.525350
\(874\) −1.88591e15 −0.125086
\(875\) 9.13447e15 0.602059
\(876\) 2.93678e15 0.192353
\(877\) −1.11677e16 −0.726885 −0.363443 0.931617i \(-0.618399\pi\)
−0.363443 + 0.931617i \(0.618399\pi\)
\(878\) −1.65370e16 −1.06964
\(879\) 6.69896e15 0.430594
\(880\) −1.97257e16 −1.26002
\(881\) −2.25647e16 −1.43239 −0.716195 0.697900i \(-0.754118\pi\)
−0.716195 + 0.697900i \(0.754118\pi\)
\(882\) 4.31490e15 0.272204
\(883\) 1.02568e16 0.643026 0.321513 0.946905i \(-0.395809\pi\)
0.321513 + 0.946905i \(0.395809\pi\)
\(884\) −3.90245e15 −0.243136
\(885\) −2.29836e15 −0.142308
\(886\) 1.71931e16 1.05796
\(887\) −4.84262e15 −0.296143 −0.148071 0.988977i \(-0.547307\pi\)
−0.148071 + 0.988977i \(0.547307\pi\)
\(888\) 9.73188e14 0.0591460
\(889\) 6.85159e14 0.0413839
\(890\) −2.65538e16 −1.59398
\(891\) −1.91334e15 −0.114147
\(892\) −1.01427e15 −0.0601376
\(893\) 8.29018e15 0.488518
\(894\) 4.67130e15 0.273578
\(895\) −1.70506e16 −0.992460
\(896\) 1.40042e15 0.0810150
\(897\) 3.15133e15 0.181191
\(898\) 8.77224e15 0.501292
\(899\) 1.19983e16 0.681464
\(900\) −4.21222e15 −0.237781
\(901\) −1.75721e16 −0.985913
\(902\) 2.03941e15 0.113728
\(903\) −1.41071e15 −0.0781909
\(904\) −2.97148e16 −1.63699
\(905\) 1.39987e16 0.766517
\(906\) 1.19241e16 0.648963
\(907\) 2.75849e16 1.49222 0.746108 0.665825i \(-0.231920\pi\)
0.746108 + 0.665825i \(0.231920\pi\)
\(908\) 6.09378e14 0.0327653
\(909\) −1.03648e16 −0.553934
\(910\) −6.21846e15 −0.330335
\(911\) 3.00066e16 1.58440 0.792202 0.610259i \(-0.208934\pi\)
0.792202 + 0.610259i \(0.208934\pi\)
\(912\) −3.41083e15 −0.179014
\(913\) 3.30772e16 1.72560
\(914\) −1.81348e15 −0.0940392
\(915\) 1.65805e16 0.854636
\(916\) −5.59038e15 −0.286429
\(917\) −3.44523e15 −0.175464
\(918\) 2.78872e15 0.141179
\(919\) −1.72784e16 −0.869495 −0.434748 0.900552i \(-0.643162\pi\)
−0.434748 + 0.900552i \(0.643162\pi\)
\(920\) 1.26216e16 0.631366
\(921\) 4.97086e15 0.247174
\(922\) 2.80884e15 0.138838
\(923\) 2.28990e16 1.12514
\(924\) 6.72627e14 0.0328533
\(925\) −5.02261e15 −0.243865
\(926\) 1.42551e16 0.688032
\(927\) 4.47463e15 0.214693
\(928\) 1.31316e16 0.626333
\(929\) −2.08626e16 −0.989194 −0.494597 0.869122i \(-0.664684\pi\)
−0.494597 + 0.869122i \(0.664684\pi\)
\(930\) 1.14756e16 0.540901
\(931\) 9.80314e15 0.459348
\(932\) 6.12112e15 0.285130
\(933\) −9.62034e15 −0.445493
\(934\) 1.31379e16 0.604808
\(935\) 3.66413e16 1.67690
\(936\) 8.12770e15 0.369786
\(937\) −1.02457e16 −0.463418 −0.231709 0.972785i \(-0.574432\pi\)
−0.231709 + 0.972785i \(0.574432\pi\)
\(938\) −1.79495e15 −0.0807116
\(939\) 1.74238e16 0.778899
\(940\) −1.20011e16 −0.533356
\(941\) 2.75473e16 1.21713 0.608565 0.793504i \(-0.291746\pi\)
0.608565 + 0.793504i \(0.291746\pi\)
\(942\) −5.57207e15 −0.244758
\(943\) −9.15064e14 −0.0399611
\(944\) 1.94256e15 0.0843388
\(945\) −1.69406e15 −0.0731228
\(946\) −1.37460e16 −0.589894
\(947\) 4.25827e16 1.81681 0.908403 0.418095i \(-0.137302\pi\)
0.908403 + 0.418095i \(0.137302\pi\)
\(948\) −4.78489e15 −0.202967
\(949\) 2.92456e16 1.23338
\(950\) 2.51031e16 1.05256
\(951\) −1.30082e13 −0.000542281 0
\(952\) −4.53237e15 −0.187855
\(953\) 2.07111e16 0.853476 0.426738 0.904375i \(-0.359663\pi\)
0.426738 + 0.904375i \(0.359663\pi\)
\(954\) 7.91622e15 0.324341
\(955\) −3.07816e16 −1.25393
\(956\) −8.67120e15 −0.351205
\(957\) −1.72588e16 −0.695018
\(958\) 1.19215e16 0.477332
\(959\) −7.47402e15 −0.297544
\(960\) 3.04491e16 1.20527
\(961\) −1.68151e16 −0.661790
\(962\) 2.09628e15 0.0820326
\(963\) 1.49824e15 0.0582958
\(964\) 2.97942e15 0.115268
\(965\) 2.83428e16 1.09029
\(966\) 7.91670e14 0.0302810
\(967\) −5.37393e14 −0.0204384 −0.0102192 0.999948i \(-0.503253\pi\)
−0.0102192 + 0.999948i \(0.503253\pi\)
\(968\) 1.59033e15 0.0601411
\(969\) 6.33576e15 0.238242
\(970\) −6.79046e16 −2.53895
\(971\) 1.89251e16 0.703612 0.351806 0.936073i \(-0.385568\pi\)
0.351806 + 0.936073i \(0.385568\pi\)
\(972\) 4.78934e14 0.0177056
\(973\) −7.02323e14 −0.0258176
\(974\) −3.50797e16 −1.28228
\(975\) −4.19470e16 −1.52467
\(976\) −1.40137e16 −0.506499
\(977\) −5.54836e15 −0.199409 −0.0997044 0.995017i \(-0.531790\pi\)
−0.0997044 + 0.995017i \(0.531790\pi\)
\(978\) 5.78839e15 0.206868
\(979\) 2.86028e16 1.01649
\(980\) −1.41913e16 −0.501508
\(981\) −8.81216e15 −0.309673
\(982\) 1.75020e16 0.611608
\(983\) 4.72330e16 1.64135 0.820675 0.571396i \(-0.193598\pi\)
0.820675 + 0.571396i \(0.193598\pi\)
\(984\) −2.36007e15 −0.0815553
\(985\) 7.18704e16 2.46974
\(986\) 2.51550e16 0.859610
\(987\) −3.48007e15 −0.118261
\(988\) 3.99415e15 0.134977
\(989\) 6.16769e15 0.207273
\(990\) −1.65069e16 −0.551659
\(991\) −6.68696e15 −0.222241 −0.111120 0.993807i \(-0.535444\pi\)
−0.111120 + 0.993807i \(0.535444\pi\)
\(992\) 9.40508e15 0.310848
\(993\) 2.85614e16 0.938767
\(994\) 5.75263e15 0.188036
\(995\) −5.80523e16 −1.88709
\(996\) −8.27965e15 −0.267661
\(997\) 8.23312e15 0.264692 0.132346 0.991204i \(-0.457749\pi\)
0.132346 + 0.991204i \(0.457749\pi\)
\(998\) −1.91027e16 −0.610769
\(999\) 5.71077e14 0.0181587
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.12.a.c.1.10 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.c.1.10 27 1.1 even 1 trivial