Properties

Label 177.12.a.c.1.1
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 1.1
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-83.3973 q^{2} -243.000 q^{3} +4907.11 q^{4} -4959.60 q^{5} +20265.5 q^{6} +14303.6 q^{7} -238442. q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-83.3973 q^{2} -243.000 q^{3} +4907.11 q^{4} -4959.60 q^{5} +20265.5 q^{6} +14303.6 q^{7} -238442. q^{8} +59049.0 q^{9} +413617. q^{10} -546385. q^{11} -1.19243e6 q^{12} +349555. q^{13} -1.19288e6 q^{14} +1.20518e6 q^{15} +9.83569e6 q^{16} -7.20582e6 q^{17} -4.92453e6 q^{18} -6.45289e6 q^{19} -2.43373e7 q^{20} -3.47578e6 q^{21} +4.55670e7 q^{22} -3.67315e7 q^{23} +5.79415e7 q^{24} -2.42305e7 q^{25} -2.91520e7 q^{26} -1.43489e7 q^{27} +7.01895e7 q^{28} +1.87043e6 q^{29} -1.00509e8 q^{30} +4.50654e7 q^{31} -3.31940e8 q^{32} +1.32771e8 q^{33} +6.00946e8 q^{34} -7.09402e7 q^{35} +2.89760e8 q^{36} +2.68624e8 q^{37} +5.38154e8 q^{38} -8.49419e7 q^{39} +1.18258e9 q^{40} +5.73687e6 q^{41} +2.89871e8 q^{42} +5.13220e7 q^{43} -2.68117e9 q^{44} -2.92859e8 q^{45} +3.06331e9 q^{46} -9.01445e8 q^{47} -2.39007e9 q^{48} -1.77273e9 q^{49} +2.02076e9 q^{50} +1.75102e9 q^{51} +1.71531e9 q^{52} +1.88074e9 q^{53} +1.19666e9 q^{54} +2.70985e9 q^{55} -3.41059e9 q^{56} +1.56805e9 q^{57} -1.55989e8 q^{58} -7.14924e8 q^{59} +5.91396e9 q^{60} -5.74971e8 q^{61} -3.75833e9 q^{62} +8.44615e8 q^{63} +7.53942e9 q^{64} -1.73365e9 q^{65} -1.10728e10 q^{66} +5.65779e9 q^{67} -3.53598e10 q^{68} +8.92576e9 q^{69} +5.91623e9 q^{70} -1.97306e10 q^{71} -1.40798e10 q^{72} -2.79361e10 q^{73} -2.24025e10 q^{74} +5.88802e9 q^{75} -3.16651e10 q^{76} -7.81528e9 q^{77} +7.08393e9 q^{78} -2.92512e10 q^{79} -4.87810e10 q^{80} +3.48678e9 q^{81} -4.78440e8 q^{82} -5.40192e9 q^{83} -1.70561e10 q^{84} +3.57380e10 q^{85} -4.28012e9 q^{86} -4.54516e8 q^{87} +1.30281e11 q^{88} -6.94302e10 q^{89} +2.44237e10 q^{90} +4.99991e9 q^{91} -1.80246e11 q^{92} -1.09509e10 q^{93} +7.51781e10 q^{94} +3.20037e10 q^{95} +8.06614e10 q^{96} -4.27544e10 q^{97} +1.47841e11 q^{98} -3.22635e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −83.3973 −1.84284 −0.921419 0.388571i \(-0.872969\pi\)
−0.921419 + 0.388571i \(0.872969\pi\)
\(3\) −243.000 −0.577350
\(4\) 4907.11 2.39605
\(5\) −4959.60 −0.709760 −0.354880 0.934912i \(-0.615478\pi\)
−0.354880 + 0.934912i \(0.615478\pi\)
\(6\) 20265.5 1.06396
\(7\) 14303.6 0.321667 0.160834 0.986982i \(-0.448582\pi\)
0.160834 + 0.986982i \(0.448582\pi\)
\(8\) −238442. −2.57270
\(9\) 59049.0 0.333333
\(10\) 413617. 1.30797
\(11\) −546385. −1.02291 −0.511456 0.859309i \(-0.670894\pi\)
−0.511456 + 0.859309i \(0.670894\pi\)
\(12\) −1.19243e6 −1.38336
\(13\) 349555. 0.261112 0.130556 0.991441i \(-0.458324\pi\)
0.130556 + 0.991441i \(0.458324\pi\)
\(14\) −1.19288e6 −0.592781
\(15\) 1.20518e6 0.409780
\(16\) 9.83569e6 2.34501
\(17\) −7.20582e6 −1.23088 −0.615438 0.788185i \(-0.711021\pi\)
−0.615438 + 0.788185i \(0.711021\pi\)
\(18\) −4.92453e6 −0.614279
\(19\) −6.45289e6 −0.597874 −0.298937 0.954273i \(-0.596632\pi\)
−0.298937 + 0.954273i \(0.596632\pi\)
\(20\) −2.43373e7 −1.70062
\(21\) −3.47578e6 −0.185715
\(22\) 4.55670e7 1.88506
\(23\) −3.67315e7 −1.18997 −0.594985 0.803737i \(-0.702842\pi\)
−0.594985 + 0.803737i \(0.702842\pi\)
\(24\) 5.79415e7 1.48535
\(25\) −2.42305e7 −0.496241
\(26\) −2.91520e7 −0.481188
\(27\) −1.43489e7 −0.192450
\(28\) 7.01895e7 0.770732
\(29\) 1.87043e6 0.0169338 0.00846688 0.999964i \(-0.497305\pi\)
0.00846688 + 0.999964i \(0.497305\pi\)
\(30\) −1.00509e8 −0.755158
\(31\) 4.50654e7 0.282718 0.141359 0.989958i \(-0.454853\pi\)
0.141359 + 0.989958i \(0.454853\pi\)
\(32\) −3.31940e8 −1.74878
\(33\) 1.32771e8 0.590579
\(34\) 6.00946e8 2.26831
\(35\) −7.09402e7 −0.228307
\(36\) 2.89760e8 0.798684
\(37\) 2.68624e8 0.636848 0.318424 0.947948i \(-0.396846\pi\)
0.318424 + 0.947948i \(0.396846\pi\)
\(38\) 5.38154e8 1.10178
\(39\) −8.49419e7 −0.150753
\(40\) 1.18258e9 1.82600
\(41\) 5.73687e6 0.00773329 0.00386664 0.999993i \(-0.498769\pi\)
0.00386664 + 0.999993i \(0.498769\pi\)
\(42\) 2.89871e8 0.342242
\(43\) 5.13220e7 0.0532386 0.0266193 0.999646i \(-0.491526\pi\)
0.0266193 + 0.999646i \(0.491526\pi\)
\(44\) −2.68117e9 −2.45095
\(45\) −2.92859e8 −0.236587
\(46\) 3.06331e9 2.19292
\(47\) −9.01445e8 −0.573325 −0.286663 0.958032i \(-0.592546\pi\)
−0.286663 + 0.958032i \(0.592546\pi\)
\(48\) −2.39007e9 −1.35389
\(49\) −1.77273e9 −0.896530
\(50\) 2.02076e9 0.914492
\(51\) 1.75102e9 0.710647
\(52\) 1.71531e9 0.625638
\(53\) 1.88074e9 0.617748 0.308874 0.951103i \(-0.400048\pi\)
0.308874 + 0.951103i \(0.400048\pi\)
\(54\) 1.19666e9 0.354654
\(55\) 2.70985e9 0.726022
\(56\) −3.41059e9 −0.827553
\(57\) 1.56805e9 0.345183
\(58\) −1.55989e8 −0.0312062
\(59\) −7.14924e8 −0.130189
\(60\) 5.91396e9 0.981854
\(61\) −5.74971e8 −0.0871630 −0.0435815 0.999050i \(-0.513877\pi\)
−0.0435815 + 0.999050i \(0.513877\pi\)
\(62\) −3.75833e9 −0.521004
\(63\) 8.44615e8 0.107222
\(64\) 7.53942e9 0.877704
\(65\) −1.73365e9 −0.185327
\(66\) −1.10728e10 −1.08834
\(67\) 5.65779e9 0.511960 0.255980 0.966682i \(-0.417602\pi\)
0.255980 + 0.966682i \(0.417602\pi\)
\(68\) −3.53598e10 −2.94924
\(69\) 8.92576e9 0.687029
\(70\) 5.91623e9 0.420732
\(71\) −1.97306e10 −1.29784 −0.648918 0.760859i \(-0.724778\pi\)
−0.648918 + 0.760859i \(0.724778\pi\)
\(72\) −1.40798e10 −0.857565
\(73\) −2.79361e10 −1.57721 −0.788606 0.614899i \(-0.789197\pi\)
−0.788606 + 0.614899i \(0.789197\pi\)
\(74\) −2.24025e10 −1.17361
\(75\) 5.88802e9 0.286505
\(76\) −3.16651e10 −1.43254
\(77\) −7.81528e9 −0.329038
\(78\) 7.08393e9 0.277814
\(79\) −2.92512e10 −1.06953 −0.534767 0.845000i \(-0.679600\pi\)
−0.534767 + 0.845000i \(0.679600\pi\)
\(80\) −4.87810e10 −1.66439
\(81\) 3.48678e9 0.111111
\(82\) −4.78440e8 −0.0142512
\(83\) −5.40192e9 −0.150528 −0.0752642 0.997164i \(-0.523980\pi\)
−0.0752642 + 0.997164i \(0.523980\pi\)
\(84\) −1.70561e10 −0.444982
\(85\) 3.57380e10 0.873627
\(86\) −4.28012e9 −0.0981102
\(87\) −4.54516e8 −0.00977671
\(88\) 1.30281e11 2.63164
\(89\) −6.94302e10 −1.31796 −0.658982 0.752159i \(-0.729013\pi\)
−0.658982 + 0.752159i \(0.729013\pi\)
\(90\) 2.44237e10 0.435991
\(91\) 4.99991e9 0.0839913
\(92\) −1.80246e11 −2.85123
\(93\) −1.09509e10 −0.163228
\(94\) 7.51781e10 1.05655
\(95\) 3.20037e10 0.424347
\(96\) 8.06614e10 1.00966
\(97\) −4.27544e10 −0.505518 −0.252759 0.967529i \(-0.581338\pi\)
−0.252759 + 0.967529i \(0.581338\pi\)
\(98\) 1.47841e11 1.65216
\(99\) −3.22635e10 −0.340971
\(100\) −1.18902e11 −1.18902
\(101\) −1.00886e11 −0.955133 −0.477566 0.878596i \(-0.658481\pi\)
−0.477566 + 0.878596i \(0.658481\pi\)
\(102\) −1.46030e11 −1.30961
\(103\) −6.70494e10 −0.569889 −0.284945 0.958544i \(-0.591975\pi\)
−0.284945 + 0.958544i \(0.591975\pi\)
\(104\) −8.33488e10 −0.671762
\(105\) 1.72385e10 0.131813
\(106\) −1.56849e11 −1.13841
\(107\) −8.21881e10 −0.566498 −0.283249 0.959046i \(-0.591412\pi\)
−0.283249 + 0.959046i \(0.591412\pi\)
\(108\) −7.04117e10 −0.461120
\(109\) −2.65324e11 −1.65170 −0.825849 0.563891i \(-0.809304\pi\)
−0.825849 + 0.563891i \(0.809304\pi\)
\(110\) −2.25994e11 −1.33794
\(111\) −6.52757e10 −0.367684
\(112\) 1.40686e11 0.754314
\(113\) −1.45626e11 −0.743546 −0.371773 0.928324i \(-0.621250\pi\)
−0.371773 + 0.928324i \(0.621250\pi\)
\(114\) −1.30771e11 −0.636115
\(115\) 1.82174e11 0.844593
\(116\) 9.17843e9 0.0405742
\(117\) 2.06409e10 0.0870374
\(118\) 5.96228e10 0.239917
\(119\) −1.03069e11 −0.395933
\(120\) −2.87366e11 −1.05424
\(121\) 1.32244e10 0.0463507
\(122\) 4.79511e10 0.160627
\(123\) −1.39406e9 −0.00446481
\(124\) 2.21141e11 0.677408
\(125\) 3.62341e11 1.06197
\(126\) −7.04386e10 −0.197594
\(127\) 1.24646e11 0.334778 0.167389 0.985891i \(-0.446466\pi\)
0.167389 + 0.985891i \(0.446466\pi\)
\(128\) 5.10457e10 0.131312
\(129\) −1.24712e10 −0.0307373
\(130\) 1.44582e11 0.341527
\(131\) 1.97858e11 0.448087 0.224043 0.974579i \(-0.428074\pi\)
0.224043 + 0.974579i \(0.428074\pi\)
\(132\) 6.51525e11 1.41506
\(133\) −9.22998e10 −0.192316
\(134\) −4.71845e11 −0.943458
\(135\) 7.11648e10 0.136593
\(136\) 1.71817e12 3.16667
\(137\) 2.57583e11 0.455989 0.227995 0.973662i \(-0.426783\pi\)
0.227995 + 0.973662i \(0.426783\pi\)
\(138\) −7.44385e11 −1.26608
\(139\) 1.25005e11 0.204337 0.102168 0.994767i \(-0.467422\pi\)
0.102168 + 0.994767i \(0.467422\pi\)
\(140\) −3.48112e11 −0.547034
\(141\) 2.19051e11 0.331009
\(142\) 1.64548e12 2.39170
\(143\) −1.90992e11 −0.267095
\(144\) 5.80788e11 0.781670
\(145\) −9.27660e9 −0.0120189
\(146\) 2.32980e12 2.90655
\(147\) 4.30774e11 0.517612
\(148\) 1.31817e12 1.52592
\(149\) 3.95190e11 0.440840 0.220420 0.975405i \(-0.429257\pi\)
0.220420 + 0.975405i \(0.429257\pi\)
\(150\) −4.91045e11 −0.527982
\(151\) 1.39688e11 0.144806 0.0724031 0.997375i \(-0.476933\pi\)
0.0724031 + 0.997375i \(0.476933\pi\)
\(152\) 1.53864e12 1.53815
\(153\) −4.25497e11 −0.410292
\(154\) 6.51774e11 0.606363
\(155\) −2.23506e11 −0.200662
\(156\) −4.16819e11 −0.361212
\(157\) 1.62174e12 1.35685 0.678426 0.734669i \(-0.262662\pi\)
0.678426 + 0.734669i \(0.262662\pi\)
\(158\) 2.43947e12 1.97098
\(159\) −4.57019e11 −0.356657
\(160\) 1.64629e12 1.24121
\(161\) −5.25394e11 −0.382775
\(162\) −2.90788e11 −0.204760
\(163\) −5.54768e11 −0.377641 −0.188821 0.982012i \(-0.560466\pi\)
−0.188821 + 0.982012i \(0.560466\pi\)
\(164\) 2.81515e10 0.0185294
\(165\) −6.58493e11 −0.419169
\(166\) 4.50506e11 0.277400
\(167\) −2.41302e12 −1.43754 −0.718771 0.695246i \(-0.755295\pi\)
−0.718771 + 0.695246i \(0.755295\pi\)
\(168\) 8.28774e11 0.477788
\(169\) −1.66997e12 −0.931820
\(170\) −2.98045e12 −1.60995
\(171\) −3.81037e11 −0.199291
\(172\) 2.51843e11 0.127562
\(173\) −9.30942e11 −0.456740 −0.228370 0.973574i \(-0.573340\pi\)
−0.228370 + 0.973574i \(0.573340\pi\)
\(174\) 3.79054e10 0.0180169
\(175\) −3.46585e11 −0.159625
\(176\) −5.37407e12 −2.39874
\(177\) 1.73727e11 0.0751646
\(178\) 5.79029e12 2.42879
\(179\) −1.69178e12 −0.688100 −0.344050 0.938951i \(-0.611799\pi\)
−0.344050 + 0.938951i \(0.611799\pi\)
\(180\) −1.43709e12 −0.566873
\(181\) −2.85686e11 −0.109309 −0.0546545 0.998505i \(-0.517406\pi\)
−0.0546545 + 0.998505i \(0.517406\pi\)
\(182\) −4.16979e11 −0.154782
\(183\) 1.39718e11 0.0503236
\(184\) 8.75836e12 3.06143
\(185\) −1.33227e12 −0.452009
\(186\) 9.13275e11 0.300802
\(187\) 3.93715e12 1.25908
\(188\) −4.42349e12 −1.37372
\(189\) −2.05241e11 −0.0619049
\(190\) −2.66902e12 −0.782002
\(191\) −5.28943e12 −1.50565 −0.752827 0.658219i \(-0.771310\pi\)
−0.752827 + 0.658219i \(0.771310\pi\)
\(192\) −1.83208e12 −0.506743
\(193\) −5.24928e11 −0.141103 −0.0705513 0.997508i \(-0.522476\pi\)
−0.0705513 + 0.997508i \(0.522476\pi\)
\(194\) 3.56560e12 0.931587
\(195\) 4.21277e11 0.106999
\(196\) −8.69900e12 −2.14813
\(197\) 1.71957e12 0.412911 0.206456 0.978456i \(-0.433807\pi\)
0.206456 + 0.978456i \(0.433807\pi\)
\(198\) 2.69069e12 0.628354
\(199\) 5.23104e12 1.18822 0.594109 0.804385i \(-0.297505\pi\)
0.594109 + 0.804385i \(0.297505\pi\)
\(200\) 5.77759e12 1.27668
\(201\) −1.37484e12 −0.295580
\(202\) 8.41363e12 1.76016
\(203\) 2.67540e10 0.00544704
\(204\) 8.59243e12 1.70275
\(205\) −2.84526e10 −0.00548877
\(206\) 5.59174e12 1.05021
\(207\) −2.16896e12 −0.396657
\(208\) 3.43812e12 0.612311
\(209\) 3.52576e12 0.611573
\(210\) −1.43764e12 −0.242910
\(211\) 2.35748e12 0.388057 0.194028 0.980996i \(-0.437845\pi\)
0.194028 + 0.980996i \(0.437845\pi\)
\(212\) 9.22900e12 1.48016
\(213\) 4.79454e12 0.749306
\(214\) 6.85427e12 1.04396
\(215\) −2.54536e11 −0.0377866
\(216\) 3.42139e12 0.495116
\(217\) 6.44599e11 0.0909413
\(218\) 2.21273e13 3.04381
\(219\) 6.78847e12 0.910604
\(220\) 1.32975e13 1.73959
\(221\) −2.51883e12 −0.321397
\(222\) 5.44382e12 0.677583
\(223\) −1.27662e13 −1.55019 −0.775094 0.631846i \(-0.782297\pi\)
−0.775094 + 0.631846i \(0.782297\pi\)
\(224\) −4.74795e12 −0.562525
\(225\) −1.43079e12 −0.165414
\(226\) 1.21448e13 1.37023
\(227\) −2.04201e12 −0.224862 −0.112431 0.993660i \(-0.535864\pi\)
−0.112431 + 0.993660i \(0.535864\pi\)
\(228\) 7.69461e12 0.827075
\(229\) −1.70733e13 −1.79152 −0.895762 0.444534i \(-0.853369\pi\)
−0.895762 + 0.444534i \(0.853369\pi\)
\(230\) −1.51928e13 −1.55645
\(231\) 1.89911e12 0.189970
\(232\) −4.45991e11 −0.0435654
\(233\) −2.27402e12 −0.216938 −0.108469 0.994100i \(-0.534595\pi\)
−0.108469 + 0.994100i \(0.534595\pi\)
\(234\) −1.72139e12 −0.160396
\(235\) 4.47080e12 0.406923
\(236\) −3.50821e12 −0.311939
\(237\) 7.10804e12 0.617495
\(238\) 8.59572e12 0.729640
\(239\) 4.41334e12 0.366083 0.183041 0.983105i \(-0.441406\pi\)
0.183041 + 0.983105i \(0.441406\pi\)
\(240\) 1.18538e13 0.960938
\(241\) −2.82488e12 −0.223824 −0.111912 0.993718i \(-0.535697\pi\)
−0.111912 + 0.993718i \(0.535697\pi\)
\(242\) −1.10288e12 −0.0854169
\(243\) −8.47289e11 −0.0641500
\(244\) −2.82145e12 −0.208847
\(245\) 8.79204e12 0.636321
\(246\) 1.16261e11 0.00822793
\(247\) −2.25564e12 −0.156112
\(248\) −1.07455e13 −0.727349
\(249\) 1.31267e12 0.0869076
\(250\) −3.02183e13 −1.95704
\(251\) 4.62012e12 0.292717 0.146359 0.989232i \(-0.453245\pi\)
0.146359 + 0.989232i \(0.453245\pi\)
\(252\) 4.14462e12 0.256911
\(253\) 2.00695e13 1.21724
\(254\) −1.03951e13 −0.616941
\(255\) −8.68433e12 −0.504389
\(256\) −1.96978e13 −1.11969
\(257\) 2.49949e12 0.139065 0.0695327 0.997580i \(-0.477849\pi\)
0.0695327 + 0.997580i \(0.477849\pi\)
\(258\) 1.04007e12 0.0566439
\(259\) 3.84230e12 0.204853
\(260\) −8.50723e12 −0.444053
\(261\) 1.10447e11 0.00564459
\(262\) −1.65008e13 −0.825751
\(263\) 2.24755e13 1.10142 0.550711 0.834696i \(-0.314357\pi\)
0.550711 + 0.834696i \(0.314357\pi\)
\(264\) −3.16583e13 −1.51938
\(265\) −9.32770e12 −0.438452
\(266\) 7.69755e12 0.354408
\(267\) 1.68715e13 0.760927
\(268\) 2.77634e13 1.22668
\(269\) −1.31913e13 −0.571018 −0.285509 0.958376i \(-0.592163\pi\)
−0.285509 + 0.958376i \(0.592163\pi\)
\(270\) −5.93495e12 −0.251719
\(271\) 2.51249e13 1.04418 0.522088 0.852892i \(-0.325153\pi\)
0.522088 + 0.852892i \(0.325153\pi\)
\(272\) −7.08742e13 −2.88642
\(273\) −1.21498e12 −0.0484924
\(274\) −2.14818e13 −0.840314
\(275\) 1.32392e13 0.507612
\(276\) 4.37997e13 1.64616
\(277\) 1.34055e13 0.493906 0.246953 0.969027i \(-0.420571\pi\)
0.246953 + 0.969027i \(0.420571\pi\)
\(278\) −1.04251e13 −0.376560
\(279\) 2.66107e12 0.0942395
\(280\) 1.69152e13 0.587363
\(281\) −1.83577e12 −0.0625078 −0.0312539 0.999511i \(-0.509950\pi\)
−0.0312539 + 0.999511i \(0.509950\pi\)
\(282\) −1.82683e13 −0.609997
\(283\) −3.14105e13 −1.02861 −0.514304 0.857608i \(-0.671950\pi\)
−0.514304 + 0.857608i \(0.671950\pi\)
\(284\) −9.68203e13 −3.10968
\(285\) −7.77690e12 −0.244997
\(286\) 1.59282e13 0.492213
\(287\) 8.20581e10 0.00248755
\(288\) −1.96007e13 −0.582926
\(289\) 1.76520e13 0.515058
\(290\) 7.73644e11 0.0221489
\(291\) 1.03893e13 0.291861
\(292\) −1.37086e14 −3.77908
\(293\) 1.20608e13 0.326291 0.163146 0.986602i \(-0.447836\pi\)
0.163146 + 0.986602i \(0.447836\pi\)
\(294\) −3.59254e13 −0.953875
\(295\) 3.54574e12 0.0924028
\(296\) −6.40514e13 −1.63842
\(297\) 7.84002e12 0.196860
\(298\) −3.29578e13 −0.812397
\(299\) −1.28397e13 −0.310716
\(300\) 2.88932e13 0.686481
\(301\) 7.34091e11 0.0171251
\(302\) −1.16496e13 −0.266854
\(303\) 2.45153e13 0.551446
\(304\) −6.34686e13 −1.40202
\(305\) 2.85163e12 0.0618648
\(306\) 3.54853e13 0.756102
\(307\) −6.18345e13 −1.29410 −0.647052 0.762445i \(-0.723999\pi\)
−0.647052 + 0.762445i \(0.723999\pi\)
\(308\) −3.83505e13 −0.788391
\(309\) 1.62930e13 0.329026
\(310\) 1.86398e13 0.369788
\(311\) 4.95094e13 0.964952 0.482476 0.875909i \(-0.339737\pi\)
0.482476 + 0.875909i \(0.339737\pi\)
\(312\) 2.02537e13 0.387842
\(313\) 5.33269e13 1.00335 0.501675 0.865056i \(-0.332717\pi\)
0.501675 + 0.865056i \(0.332717\pi\)
\(314\) −1.35249e14 −2.50046
\(315\) −4.18895e12 −0.0761022
\(316\) −1.43539e14 −2.56266
\(317\) −6.16876e13 −1.08236 −0.541180 0.840907i \(-0.682022\pi\)
−0.541180 + 0.840907i \(0.682022\pi\)
\(318\) 3.81142e13 0.657261
\(319\) −1.02198e12 −0.0173218
\(320\) −3.73925e13 −0.622959
\(321\) 1.99717e13 0.327068
\(322\) 4.38165e13 0.705392
\(323\) 4.64984e13 0.735909
\(324\) 1.71100e13 0.266228
\(325\) −8.46991e12 −0.129575
\(326\) 4.62662e13 0.695932
\(327\) 6.44737e13 0.953609
\(328\) −1.36791e12 −0.0198954
\(329\) −1.28939e13 −0.184420
\(330\) 5.49165e13 0.772461
\(331\) 8.79575e13 1.21680 0.608400 0.793631i \(-0.291812\pi\)
0.608400 + 0.793631i \(0.291812\pi\)
\(332\) −2.65078e13 −0.360674
\(333\) 1.58620e13 0.212283
\(334\) 2.01240e14 2.64916
\(335\) −2.80604e13 −0.363368
\(336\) −3.41867e13 −0.435503
\(337\) −1.26756e11 −0.00158856 −0.000794281 1.00000i \(-0.500253\pi\)
−0.000794281 1.00000i \(0.500253\pi\)
\(338\) 1.39271e14 1.71719
\(339\) 3.53871e13 0.429286
\(340\) 1.75370e14 2.09325
\(341\) −2.46230e13 −0.289196
\(342\) 3.17774e13 0.367261
\(343\) −5.36395e13 −0.610052
\(344\) −1.22373e13 −0.136967
\(345\) −4.42682e13 −0.487626
\(346\) 7.76380e13 0.841698
\(347\) −7.12641e13 −0.760429 −0.380215 0.924898i \(-0.624150\pi\)
−0.380215 + 0.924898i \(0.624150\pi\)
\(348\) −2.23036e12 −0.0234255
\(349\) −1.04720e14 −1.08266 −0.541328 0.840811i \(-0.682078\pi\)
−0.541328 + 0.840811i \(0.682078\pi\)
\(350\) 2.89042e13 0.294162
\(351\) −5.01573e12 −0.0502511
\(352\) 1.81367e14 1.78885
\(353\) 7.30297e13 0.709150 0.354575 0.935028i \(-0.384625\pi\)
0.354575 + 0.935028i \(0.384625\pi\)
\(354\) −1.44883e13 −0.138516
\(355\) 9.78558e13 0.921151
\(356\) −3.40702e14 −3.15791
\(357\) 2.50459e13 0.228592
\(358\) 1.41090e14 1.26806
\(359\) −1.41878e14 −1.25573 −0.627865 0.778322i \(-0.716071\pi\)
−0.627865 + 0.778322i \(0.716071\pi\)
\(360\) 6.98300e13 0.608665
\(361\) −7.48505e13 −0.642547
\(362\) 2.38254e13 0.201439
\(363\) −3.21353e12 −0.0267606
\(364\) 2.45351e13 0.201247
\(365\) 1.38552e14 1.11944
\(366\) −1.16521e13 −0.0927382
\(367\) 2.14692e14 1.68327 0.841633 0.540049i \(-0.181594\pi\)
0.841633 + 0.540049i \(0.181594\pi\)
\(368\) −3.61280e14 −2.79049
\(369\) 3.38757e11 0.00257776
\(370\) 1.11108e14 0.832979
\(371\) 2.69014e13 0.198709
\(372\) −5.37373e13 −0.391102
\(373\) 1.11879e14 0.802322 0.401161 0.916008i \(-0.368607\pi\)
0.401161 + 0.916008i \(0.368607\pi\)
\(374\) −3.28348e14 −2.32028
\(375\) −8.80490e13 −0.613130
\(376\) 2.14943e14 1.47499
\(377\) 6.53820e11 0.00442161
\(378\) 1.71166e13 0.114081
\(379\) 1.46426e14 0.961836 0.480918 0.876766i \(-0.340303\pi\)
0.480918 + 0.876766i \(0.340303\pi\)
\(380\) 1.57046e14 1.01676
\(381\) −3.02889e13 −0.193284
\(382\) 4.41124e14 2.77467
\(383\) 1.52508e14 0.945580 0.472790 0.881175i \(-0.343247\pi\)
0.472790 + 0.881175i \(0.343247\pi\)
\(384\) −1.24041e13 −0.0758130
\(385\) 3.87606e13 0.233538
\(386\) 4.37776e13 0.260029
\(387\) 3.03051e12 0.0177462
\(388\) −2.09801e14 −1.21125
\(389\) −2.17674e14 −1.23903 −0.619516 0.784984i \(-0.712671\pi\)
−0.619516 + 0.784984i \(0.712671\pi\)
\(390\) −3.51334e13 −0.197181
\(391\) 2.64681e14 1.46471
\(392\) 4.22695e14 2.30650
\(393\) −4.80796e13 −0.258703
\(394\) −1.43408e14 −0.760928
\(395\) 1.45074e14 0.759111
\(396\) −1.58320e14 −0.816984
\(397\) 1.53503e14 0.781214 0.390607 0.920558i \(-0.372265\pi\)
0.390607 + 0.920558i \(0.372265\pi\)
\(398\) −4.36254e14 −2.18969
\(399\) 2.24288e13 0.111034
\(400\) −2.38324e14 −1.16369
\(401\) −1.06802e13 −0.0514382 −0.0257191 0.999669i \(-0.508188\pi\)
−0.0257191 + 0.999669i \(0.508188\pi\)
\(402\) 1.14658e14 0.544706
\(403\) 1.57528e13 0.0738212
\(404\) −4.95060e14 −2.28855
\(405\) −1.72930e13 −0.0788622
\(406\) −2.23121e12 −0.0100380
\(407\) −1.46772e14 −0.651440
\(408\) −4.17516e14 −1.82828
\(409\) 2.31463e14 1.00001 0.500004 0.866023i \(-0.333332\pi\)
0.500004 + 0.866023i \(0.333332\pi\)
\(410\) 2.37287e12 0.0101149
\(411\) −6.25927e13 −0.263266
\(412\) −3.29019e14 −1.36548
\(413\) −1.02260e13 −0.0418775
\(414\) 1.80885e14 0.730974
\(415\) 2.67913e13 0.106839
\(416\) −1.16031e14 −0.456627
\(417\) −3.03763e13 −0.117974
\(418\) −2.94039e14 −1.12703
\(419\) 1.65430e14 0.625801 0.312901 0.949786i \(-0.398699\pi\)
0.312901 + 0.949786i \(0.398699\pi\)
\(420\) 8.45912e13 0.315830
\(421\) −8.85315e13 −0.326247 −0.163123 0.986606i \(-0.552157\pi\)
−0.163123 + 0.986606i \(0.552157\pi\)
\(422\) −1.96608e14 −0.715126
\(423\) −5.32294e13 −0.191108
\(424\) −4.48448e14 −1.58928
\(425\) 1.74601e14 0.610812
\(426\) −3.99852e14 −1.38085
\(427\) −8.22418e12 −0.0280375
\(428\) −4.03306e14 −1.35736
\(429\) 4.64109e13 0.154207
\(430\) 2.12276e13 0.0696346
\(431\) −9.36415e13 −0.303280 −0.151640 0.988436i \(-0.548455\pi\)
−0.151640 + 0.988436i \(0.548455\pi\)
\(432\) −1.41131e14 −0.451298
\(433\) −2.54820e14 −0.804544 −0.402272 0.915520i \(-0.631779\pi\)
−0.402272 + 0.915520i \(0.631779\pi\)
\(434\) −5.37578e13 −0.167590
\(435\) 2.25421e12 0.00693912
\(436\) −1.30197e15 −3.95755
\(437\) 2.37025e14 0.711452
\(438\) −5.66140e14 −1.67810
\(439\) −1.35184e14 −0.395704 −0.197852 0.980232i \(-0.563397\pi\)
−0.197852 + 0.980232i \(0.563397\pi\)
\(440\) −6.46142e14 −1.86783
\(441\) −1.04678e14 −0.298843
\(442\) 2.10064e14 0.592283
\(443\) 3.09237e14 0.861134 0.430567 0.902559i \(-0.358314\pi\)
0.430567 + 0.902559i \(0.358314\pi\)
\(444\) −3.20315e14 −0.880991
\(445\) 3.44346e14 0.935437
\(446\) 1.06467e15 2.85674
\(447\) −9.60311e13 −0.254519
\(448\) 1.07841e14 0.282329
\(449\) 1.96122e14 0.507191 0.253595 0.967310i \(-0.418387\pi\)
0.253595 + 0.967310i \(0.418387\pi\)
\(450\) 1.19324e14 0.304831
\(451\) −3.13454e12 −0.00791048
\(452\) −7.14604e14 −1.78157
\(453\) −3.39443e13 −0.0836039
\(454\) 1.70298e14 0.414384
\(455\) −2.47975e13 −0.0596136
\(456\) −3.73890e14 −0.888050
\(457\) 7.06198e14 1.65725 0.828623 0.559807i \(-0.189125\pi\)
0.828623 + 0.559807i \(0.189125\pi\)
\(458\) 1.42387e15 3.30149
\(459\) 1.03396e14 0.236882
\(460\) 8.93946e14 2.02369
\(461\) 4.63516e14 1.03684 0.518418 0.855127i \(-0.326521\pi\)
0.518418 + 0.855127i \(0.326521\pi\)
\(462\) −1.58381e14 −0.350084
\(463\) 6.93967e14 1.51581 0.757903 0.652368i \(-0.226224\pi\)
0.757903 + 0.652368i \(0.226224\pi\)
\(464\) 1.83970e13 0.0397099
\(465\) 5.43120e13 0.115852
\(466\) 1.89647e14 0.399782
\(467\) −2.33325e14 −0.486093 −0.243046 0.970015i \(-0.578147\pi\)
−0.243046 + 0.970015i \(0.578147\pi\)
\(468\) 1.01287e14 0.208546
\(469\) 8.09270e13 0.164681
\(470\) −3.72853e14 −0.749893
\(471\) −3.94082e14 −0.783379
\(472\) 1.70468e14 0.334937
\(473\) −2.80415e13 −0.0544585
\(474\) −5.92791e14 −1.13794
\(475\) 1.56357e14 0.296690
\(476\) −5.05774e14 −0.948676
\(477\) 1.11056e14 0.205916
\(478\) −3.68061e14 −0.674631
\(479\) −1.48153e14 −0.268452 −0.134226 0.990951i \(-0.542855\pi\)
−0.134226 + 0.990951i \(0.542855\pi\)
\(480\) −4.00048e14 −0.716614
\(481\) 9.38990e13 0.166289
\(482\) 2.35587e14 0.412471
\(483\) 1.27671e14 0.220995
\(484\) 6.48937e13 0.111059
\(485\) 2.12045e14 0.358796
\(486\) 7.06616e13 0.118218
\(487\) −1.13233e15 −1.87311 −0.936555 0.350520i \(-0.886005\pi\)
−0.936555 + 0.350520i \(0.886005\pi\)
\(488\) 1.37098e14 0.224244
\(489\) 1.34809e14 0.218031
\(490\) −7.33232e14 −1.17264
\(491\) −2.89335e14 −0.457566 −0.228783 0.973477i \(-0.573475\pi\)
−0.228783 + 0.973477i \(0.573475\pi\)
\(492\) −6.84081e12 −0.0106979
\(493\) −1.34780e13 −0.0208434
\(494\) 1.88114e14 0.287689
\(495\) 1.60014e14 0.242007
\(496\) 4.43249e14 0.662978
\(497\) −2.82219e14 −0.417471
\(498\) −1.09473e14 −0.160157
\(499\) −3.44746e14 −0.498822 −0.249411 0.968398i \(-0.580237\pi\)
−0.249411 + 0.968398i \(0.580237\pi\)
\(500\) 1.77805e15 2.54454
\(501\) 5.86364e14 0.829966
\(502\) −3.85306e14 −0.539430
\(503\) 5.58932e14 0.773989 0.386994 0.922082i \(-0.373513\pi\)
0.386994 + 0.922082i \(0.373513\pi\)
\(504\) −2.01392e14 −0.275851
\(505\) 5.00354e14 0.677915
\(506\) −1.67375e15 −2.24317
\(507\) 4.05803e14 0.537987
\(508\) 6.11650e14 0.802145
\(509\) 9.71059e14 1.25979 0.629895 0.776680i \(-0.283098\pi\)
0.629895 + 0.776680i \(0.283098\pi\)
\(510\) 7.24250e14 0.929506
\(511\) −3.99588e14 −0.507338
\(512\) 1.53820e15 1.93210
\(513\) 9.25919e13 0.115061
\(514\) −2.08451e14 −0.256275
\(515\) 3.32538e14 0.404484
\(516\) −6.11978e13 −0.0736482
\(517\) 4.92536e14 0.586462
\(518\) −3.20438e14 −0.377511
\(519\) 2.26219e14 0.263699
\(520\) 4.13376e14 0.476790
\(521\) −1.48106e14 −0.169030 −0.0845151 0.996422i \(-0.526934\pi\)
−0.0845151 + 0.996422i \(0.526934\pi\)
\(522\) −9.21101e12 −0.0104021
\(523\) −1.31977e15 −1.47482 −0.737412 0.675443i \(-0.763952\pi\)
−0.737412 + 0.675443i \(0.763952\pi\)
\(524\) 9.70913e14 1.07364
\(525\) 8.42201e13 0.0921594
\(526\) −1.87440e15 −2.02974
\(527\) −3.24733e14 −0.347992
\(528\) 1.30590e15 1.38491
\(529\) 3.96396e14 0.416029
\(530\) 7.77906e14 0.807997
\(531\) −4.22156e13 −0.0433963
\(532\) −4.52925e14 −0.460800
\(533\) 2.00535e12 0.00201926
\(534\) −1.40704e15 −1.40226
\(535\) 4.07620e14 0.402077
\(536\) −1.34906e15 −1.31712
\(537\) 4.11102e14 0.397275
\(538\) 1.10012e15 1.05229
\(539\) 9.68594e14 0.917072
\(540\) 3.49214e14 0.327285
\(541\) −1.13130e15 −1.04953 −0.524765 0.851247i \(-0.675847\pi\)
−0.524765 + 0.851247i \(0.675847\pi\)
\(542\) −2.09535e15 −1.92425
\(543\) 6.94216e13 0.0631096
\(544\) 2.39190e15 2.15253
\(545\) 1.31590e15 1.17231
\(546\) 1.01326e14 0.0893636
\(547\) 5.68051e14 0.495972 0.247986 0.968764i \(-0.420231\pi\)
0.247986 + 0.968764i \(0.420231\pi\)
\(548\) 1.26399e15 1.09257
\(549\) −3.39515e13 −0.0290543
\(550\) −1.10411e15 −0.935446
\(551\) −1.20697e13 −0.0101243
\(552\) −2.12828e15 −1.76752
\(553\) −4.18398e14 −0.344034
\(554\) −1.11798e15 −0.910189
\(555\) 3.23741e14 0.260968
\(556\) 6.13415e14 0.489602
\(557\) 2.50975e14 0.198348 0.0991738 0.995070i \(-0.468380\pi\)
0.0991738 + 0.995070i \(0.468380\pi\)
\(558\) −2.21926e14 −0.173668
\(559\) 1.79399e13 0.0139013
\(560\) −6.97746e14 −0.535381
\(561\) −9.56728e14 −0.726930
\(562\) 1.53098e14 0.115192
\(563\) −1.54239e15 −1.14921 −0.574604 0.818432i \(-0.694844\pi\)
−0.574604 + 0.818432i \(0.694844\pi\)
\(564\) 1.07491e15 0.793116
\(565\) 7.22246e14 0.527739
\(566\) 2.61955e15 1.89556
\(567\) 4.98737e13 0.0357408
\(568\) 4.70461e15 3.33894
\(569\) 1.95135e15 1.37157 0.685786 0.727803i \(-0.259459\pi\)
0.685786 + 0.727803i \(0.259459\pi\)
\(570\) 6.48573e14 0.451489
\(571\) −1.97176e15 −1.35942 −0.679711 0.733480i \(-0.737895\pi\)
−0.679711 + 0.733480i \(0.737895\pi\)
\(572\) −9.37217e14 −0.639973
\(573\) 1.28533e15 0.869289
\(574\) −6.84343e12 −0.00458414
\(575\) 8.90025e14 0.590512
\(576\) 4.45195e14 0.292568
\(577\) 1.64414e15 1.07021 0.535107 0.844784i \(-0.320271\pi\)
0.535107 + 0.844784i \(0.320271\pi\)
\(578\) −1.47213e15 −0.949168
\(579\) 1.27558e14 0.0814656
\(580\) −4.55213e13 −0.0287979
\(581\) −7.72671e13 −0.0484201
\(582\) −8.66441e14 −0.537852
\(583\) −1.02761e15 −0.631902
\(584\) 6.66115e15 4.05769
\(585\) −1.02370e14 −0.0617756
\(586\) −1.00584e15 −0.601302
\(587\) −5.18026e14 −0.306791 −0.153395 0.988165i \(-0.549021\pi\)
−0.153395 + 0.988165i \(0.549021\pi\)
\(588\) 2.11386e15 1.24022
\(589\) −2.90802e14 −0.169030
\(590\) −2.95705e14 −0.170283
\(591\) −4.17856e14 −0.238394
\(592\) 2.64210e15 1.49342
\(593\) 3.68206e14 0.206201 0.103100 0.994671i \(-0.467124\pi\)
0.103100 + 0.994671i \(0.467124\pi\)
\(594\) −6.53837e14 −0.362780
\(595\) 5.11183e14 0.281017
\(596\) 1.93924e15 1.05628
\(597\) −1.27114e15 −0.686017
\(598\) 1.07080e15 0.572599
\(599\) −1.69876e14 −0.0900085 −0.0450043 0.998987i \(-0.514330\pi\)
−0.0450043 + 0.998987i \(0.514330\pi\)
\(600\) −1.40395e15 −0.737091
\(601\) 2.59770e15 1.35139 0.675694 0.737182i \(-0.263844\pi\)
0.675694 + 0.737182i \(0.263844\pi\)
\(602\) −6.12212e13 −0.0315588
\(603\) 3.34087e14 0.170653
\(604\) 6.85467e14 0.346963
\(605\) −6.55877e13 −0.0328979
\(606\) −2.04451e15 −1.01623
\(607\) −1.62707e15 −0.801435 −0.400718 0.916202i \(-0.631239\pi\)
−0.400718 + 0.916202i \(0.631239\pi\)
\(608\) 2.14197e15 1.04555
\(609\) −6.50122e12 −0.00314485
\(610\) −2.37818e14 −0.114007
\(611\) −3.15105e14 −0.149702
\(612\) −2.08796e15 −0.983081
\(613\) −1.33812e15 −0.624401 −0.312200 0.950016i \(-0.601066\pi\)
−0.312200 + 0.950016i \(0.601066\pi\)
\(614\) 5.15683e15 2.38483
\(615\) 6.91398e12 0.00316895
\(616\) 1.86349e15 0.846514
\(617\) −2.37894e15 −1.07106 −0.535532 0.844515i \(-0.679889\pi\)
−0.535532 + 0.844515i \(0.679889\pi\)
\(618\) −1.35879e15 −0.606341
\(619\) 2.40624e15 1.06424 0.532121 0.846668i \(-0.321395\pi\)
0.532121 + 0.846668i \(0.321395\pi\)
\(620\) −1.09677e15 −0.480797
\(621\) 5.27057e14 0.229010
\(622\) −4.12895e15 −1.77825
\(623\) −9.93104e14 −0.423946
\(624\) −8.35462e14 −0.353518
\(625\) −6.13936e14 −0.257503
\(626\) −4.44732e15 −1.84901
\(627\) −8.56759e14 −0.353092
\(628\) 7.95805e15 3.25109
\(629\) −1.93566e15 −0.783882
\(630\) 3.49347e14 0.140244
\(631\) −2.72622e15 −1.08492 −0.542462 0.840080i \(-0.682508\pi\)
−0.542462 + 0.840080i \(0.682508\pi\)
\(632\) 6.97472e15 2.75158
\(633\) −5.72869e14 −0.224045
\(634\) 5.14458e15 1.99461
\(635\) −6.18192e14 −0.237612
\(636\) −2.24265e15 −0.854568
\(637\) −6.19668e14 −0.234095
\(638\) 8.52301e13 0.0319212
\(639\) −1.16507e15 −0.432612
\(640\) −2.53166e14 −0.0931999
\(641\) −2.10085e15 −0.766789 −0.383394 0.923585i \(-0.625245\pi\)
−0.383394 + 0.923585i \(0.625245\pi\)
\(642\) −1.66559e15 −0.602733
\(643\) 3.29789e15 1.18325 0.591625 0.806213i \(-0.298487\pi\)
0.591625 + 0.806213i \(0.298487\pi\)
\(644\) −2.57817e15 −0.917148
\(645\) 6.18523e13 0.0218161
\(646\) −3.87784e15 −1.35616
\(647\) 4.71365e15 1.63450 0.817248 0.576286i \(-0.195499\pi\)
0.817248 + 0.576286i \(0.195499\pi\)
\(648\) −8.31397e14 −0.285855
\(649\) 3.90624e14 0.133172
\(650\) 7.06368e14 0.238785
\(651\) −1.56638e14 −0.0525050
\(652\) −2.72231e15 −0.904848
\(653\) 3.44656e15 1.13596 0.567981 0.823042i \(-0.307725\pi\)
0.567981 + 0.823042i \(0.307725\pi\)
\(654\) −5.37694e15 −1.75735
\(655\) −9.81297e14 −0.318034
\(656\) 5.64261e13 0.0181346
\(657\) −1.64960e15 −0.525737
\(658\) 1.07532e15 0.339856
\(659\) −2.78457e14 −0.0872746 −0.0436373 0.999047i \(-0.513895\pi\)
−0.0436373 + 0.999047i \(0.513895\pi\)
\(660\) −3.23130e15 −1.00435
\(661\) −5.09253e15 −1.56973 −0.784867 0.619665i \(-0.787269\pi\)
−0.784867 + 0.619665i \(0.787269\pi\)
\(662\) −7.33542e15 −2.24236
\(663\) 6.12076e14 0.185559
\(664\) 1.28805e15 0.387264
\(665\) 4.57770e14 0.136498
\(666\) −1.32285e15 −0.391203
\(667\) −6.87039e13 −0.0201507
\(668\) −1.18410e16 −3.44443
\(669\) 3.10218e15 0.895001
\(670\) 2.34016e15 0.669629
\(671\) 3.14155e14 0.0891601
\(672\) 1.15375e15 0.324774
\(673\) 5.21673e15 1.45652 0.728259 0.685302i \(-0.240330\pi\)
0.728259 + 0.685302i \(0.240330\pi\)
\(674\) 1.05711e13 0.00292746
\(675\) 3.47682e14 0.0955017
\(676\) −8.19474e15 −2.23269
\(677\) 1.15157e15 0.311210 0.155605 0.987819i \(-0.450267\pi\)
0.155605 + 0.987819i \(0.450267\pi\)
\(678\) −2.95119e15 −0.791105
\(679\) −6.11543e14 −0.162609
\(680\) −8.52145e15 −2.24758
\(681\) 4.96209e14 0.129824
\(682\) 2.05350e15 0.532942
\(683\) 6.55543e15 1.68767 0.843835 0.536603i \(-0.180293\pi\)
0.843835 + 0.536603i \(0.180293\pi\)
\(684\) −1.86979e15 −0.477512
\(685\) −1.27751e15 −0.323643
\(686\) 4.47339e15 1.12423
\(687\) 4.14881e15 1.03434
\(688\) 5.04787e14 0.124845
\(689\) 6.57422e14 0.161301
\(690\) 3.69185e15 0.898615
\(691\) −3.38267e13 −0.00816829 −0.00408414 0.999992i \(-0.501300\pi\)
−0.00408414 + 0.999992i \(0.501300\pi\)
\(692\) −4.56824e15 −1.09437
\(693\) −4.61485e14 −0.109679
\(694\) 5.94324e15 1.40135
\(695\) −6.19975e14 −0.145030
\(696\) 1.08376e14 0.0251525
\(697\) −4.13389e13 −0.00951872
\(698\) 8.73339e15 1.99516
\(699\) 5.52586e14 0.125249
\(700\) −1.70073e15 −0.382469
\(701\) −4.68184e15 −1.04464 −0.522321 0.852749i \(-0.674934\pi\)
−0.522321 + 0.852749i \(0.674934\pi\)
\(702\) 4.18299e14 0.0926046
\(703\) −1.73340e15 −0.380755
\(704\) −4.11942e15 −0.897815
\(705\) −1.08641e15 −0.234937
\(706\) −6.09048e15 −1.30685
\(707\) −1.44304e15 −0.307235
\(708\) 8.52496e14 0.180098
\(709\) −8.27809e15 −1.73530 −0.867652 0.497171i \(-0.834372\pi\)
−0.867652 + 0.497171i \(0.834372\pi\)
\(710\) −8.16092e15 −1.69753
\(711\) −1.72725e15 −0.356511
\(712\) 1.65551e16 3.39072
\(713\) −1.65532e15 −0.336426
\(714\) −2.08876e15 −0.421258
\(715\) 9.47241e14 0.189573
\(716\) −8.30174e15 −1.64872
\(717\) −1.07244e15 −0.211358
\(718\) 1.18323e16 2.31411
\(719\) −5.73761e15 −1.11358 −0.556791 0.830653i \(-0.687967\pi\)
−0.556791 + 0.830653i \(0.687967\pi\)
\(720\) −2.88047e15 −0.554798
\(721\) −9.59051e14 −0.183315
\(722\) 6.24233e15 1.18411
\(723\) 6.86445e14 0.129225
\(724\) −1.40189e15 −0.261910
\(725\) −4.53216e13 −0.00840323
\(726\) 2.68000e14 0.0493155
\(727\) −5.22763e15 −0.954697 −0.477349 0.878714i \(-0.658402\pi\)
−0.477349 + 0.878714i \(0.658402\pi\)
\(728\) −1.19219e15 −0.216084
\(729\) 2.05891e14 0.0370370
\(730\) −1.15548e16 −2.06295
\(731\) −3.69817e14 −0.0655302
\(732\) 6.85612e14 0.120578
\(733\) 7.96294e15 1.38996 0.694979 0.719030i \(-0.255414\pi\)
0.694979 + 0.719030i \(0.255414\pi\)
\(734\) −1.79048e16 −3.10199
\(735\) −2.13647e15 −0.367380
\(736\) 1.21927e16 2.08099
\(737\) −3.09133e15 −0.523690
\(738\) −2.82514e13 −0.00475040
\(739\) 4.61683e15 0.770548 0.385274 0.922802i \(-0.374107\pi\)
0.385274 + 0.922802i \(0.374107\pi\)
\(740\) −6.53759e15 −1.08304
\(741\) 5.48121e14 0.0901314
\(742\) −2.24350e15 −0.366189
\(743\) 7.98858e15 1.29429 0.647144 0.762368i \(-0.275963\pi\)
0.647144 + 0.762368i \(0.275963\pi\)
\(744\) 2.61116e15 0.419935
\(745\) −1.95998e15 −0.312890
\(746\) −9.33038e15 −1.47855
\(747\) −3.18978e14 −0.0501761
\(748\) 1.93200e16 3.01682
\(749\) −1.17559e15 −0.182224
\(750\) 7.34305e15 1.12990
\(751\) −6.84251e15 −1.04519 −0.522596 0.852581i \(-0.675036\pi\)
−0.522596 + 0.852581i \(0.675036\pi\)
\(752\) −8.86633e15 −1.34445
\(753\) −1.12269e15 −0.169000
\(754\) −5.45268e13 −0.00814832
\(755\) −6.92798e14 −0.102778
\(756\) −1.00714e15 −0.148327
\(757\) 2.52303e15 0.368888 0.184444 0.982843i \(-0.440952\pi\)
0.184444 + 0.982843i \(0.440952\pi\)
\(758\) −1.22115e16 −1.77251
\(759\) −4.87690e15 −0.702771
\(760\) −7.63104e15 −1.09171
\(761\) −1.05894e15 −0.150402 −0.0752011 0.997168i \(-0.523960\pi\)
−0.0752011 + 0.997168i \(0.523960\pi\)
\(762\) 2.52601e15 0.356191
\(763\) −3.79510e15 −0.531298
\(764\) −2.59558e16 −3.60762
\(765\) 2.11029e15 0.291209
\(766\) −1.27187e16 −1.74255
\(767\) −2.49905e14 −0.0339939
\(768\) 4.78657e15 0.646454
\(769\) −7.85928e15 −1.05387 −0.526936 0.849905i \(-0.676659\pi\)
−0.526936 + 0.849905i \(0.676659\pi\)
\(770\) −3.23253e15 −0.430372
\(771\) −6.07376e14 −0.0802895
\(772\) −2.57588e15 −0.338089
\(773\) −1.45099e16 −1.89094 −0.945471 0.325706i \(-0.894398\pi\)
−0.945471 + 0.325706i \(0.894398\pi\)
\(774\) −2.52737e14 −0.0327034
\(775\) −1.09196e15 −0.140297
\(776\) 1.01945e16 1.30054
\(777\) −9.33680e14 −0.118272
\(778\) 1.81534e16 2.28334
\(779\) −3.70194e13 −0.00462353
\(780\) 2.06726e15 0.256374
\(781\) 1.07805e16 1.32757
\(782\) −2.20737e16 −2.69922
\(783\) −2.68387e13 −0.00325890
\(784\) −1.74360e16 −2.10237
\(785\) −8.04316e15 −0.963039
\(786\) 4.00971e15 0.476748
\(787\) −3.21154e15 −0.379186 −0.189593 0.981863i \(-0.560717\pi\)
−0.189593 + 0.981863i \(0.560717\pi\)
\(788\) 8.43814e15 0.989356
\(789\) −5.46156e15 −0.635906
\(790\) −1.20988e16 −1.39892
\(791\) −2.08298e15 −0.239174
\(792\) 7.69298e15 0.877215
\(793\) −2.00984e14 −0.0227593
\(794\) −1.28018e16 −1.43965
\(795\) 2.26663e15 0.253141
\(796\) 2.56693e16 2.84703
\(797\) 1.01522e16 1.11825 0.559125 0.829083i \(-0.311137\pi\)
0.559125 + 0.829083i \(0.311137\pi\)
\(798\) −1.87051e15 −0.204618
\(799\) 6.49565e15 0.705693
\(800\) 8.04308e15 0.867816
\(801\) −4.09978e15 −0.439321
\(802\) 8.90701e14 0.0947923
\(803\) 1.52639e16 1.61335
\(804\) −6.74651e15 −0.708225
\(805\) 2.60574e15 0.271678
\(806\) −1.31375e15 −0.136041
\(807\) 3.20548e15 0.329677
\(808\) 2.40555e16 2.45727
\(809\) 1.33199e16 1.35140 0.675701 0.737176i \(-0.263841\pi\)
0.675701 + 0.737176i \(0.263841\pi\)
\(810\) 1.44219e15 0.145330
\(811\) 1.37708e15 0.137830 0.0689152 0.997623i \(-0.478046\pi\)
0.0689152 + 0.997623i \(0.478046\pi\)
\(812\) 1.31285e14 0.0130514
\(813\) −6.10535e15 −0.602855
\(814\) 1.22404e16 1.20050
\(815\) 2.75143e15 0.268035
\(816\) 1.72224e16 1.66648
\(817\) −3.31175e14 −0.0318300
\(818\) −1.93034e16 −1.84285
\(819\) 2.95240e14 0.0279971
\(820\) −1.39620e14 −0.0131514
\(821\) −1.78359e15 −0.166881 −0.0834405 0.996513i \(-0.526591\pi\)
−0.0834405 + 0.996513i \(0.526591\pi\)
\(822\) 5.22007e15 0.485156
\(823\) 9.86243e15 0.910510 0.455255 0.890361i \(-0.349548\pi\)
0.455255 + 0.890361i \(0.349548\pi\)
\(824\) 1.59874e16 1.46615
\(825\) −3.21712e15 −0.293070
\(826\) 8.52822e14 0.0771735
\(827\) 1.02941e16 0.925352 0.462676 0.886528i \(-0.346889\pi\)
0.462676 + 0.886528i \(0.346889\pi\)
\(828\) −1.06433e16 −0.950410
\(829\) −1.38018e16 −1.22429 −0.612145 0.790746i \(-0.709693\pi\)
−0.612145 + 0.790746i \(0.709693\pi\)
\(830\) −2.23433e15 −0.196887
\(831\) −3.25754e15 −0.285157
\(832\) 2.63544e15 0.229179
\(833\) 1.27740e16 1.10352
\(834\) 2.53330e15 0.217407
\(835\) 1.19676e16 1.02031
\(836\) 1.73013e16 1.46536
\(837\) −6.46639e14 −0.0544092
\(838\) −1.37964e16 −1.15325
\(839\) −3.33414e15 −0.276881 −0.138441 0.990371i \(-0.544209\pi\)
−0.138441 + 0.990371i \(0.544209\pi\)
\(840\) −4.11038e15 −0.339114
\(841\) −1.21970e16 −0.999713
\(842\) 7.38329e15 0.601220
\(843\) 4.46093e14 0.0360889
\(844\) 1.15684e16 0.929804
\(845\) 8.28238e15 0.661368
\(846\) 4.43919e15 0.352182
\(847\) 1.89157e14 0.0149095
\(848\) 1.84984e16 1.44863
\(849\) 7.63275e15 0.593867
\(850\) −1.45613e16 −1.12563
\(851\) −9.86698e15 −0.757830
\(852\) 2.35273e16 1.79537
\(853\) 1.93774e16 1.46919 0.734593 0.678508i \(-0.237373\pi\)
0.734593 + 0.678508i \(0.237373\pi\)
\(854\) 6.85874e14 0.0516686
\(855\) 1.88979e15 0.141449
\(856\) 1.95971e16 1.45743
\(857\) 2.15218e16 1.59032 0.795158 0.606402i \(-0.207388\pi\)
0.795158 + 0.606402i \(0.207388\pi\)
\(858\) −3.87055e15 −0.284179
\(859\) 5.38738e15 0.393020 0.196510 0.980502i \(-0.437039\pi\)
0.196510 + 0.980502i \(0.437039\pi\)
\(860\) −1.24904e15 −0.0905387
\(861\) −1.99401e13 −0.00143619
\(862\) 7.80945e15 0.558895
\(863\) 4.24392e15 0.301792 0.150896 0.988550i \(-0.451784\pi\)
0.150896 + 0.988550i \(0.451784\pi\)
\(864\) 4.76298e15 0.336553
\(865\) 4.61709e15 0.324176
\(866\) 2.12513e16 1.48264
\(867\) −4.28944e15 −0.297369
\(868\) 3.16312e15 0.217900
\(869\) 1.59824e16 1.09404
\(870\) −1.87995e14 −0.0127877
\(871\) 1.97771e15 0.133679
\(872\) 6.32645e16 4.24932
\(873\) −2.52460e15 −0.168506
\(874\) −1.97672e16 −1.31109
\(875\) 5.18280e15 0.341602
\(876\) 3.33118e16 2.18185
\(877\) −2.28429e16 −1.48680 −0.743400 0.668847i \(-0.766788\pi\)
−0.743400 + 0.668847i \(0.766788\pi\)
\(878\) 1.12740e16 0.729219
\(879\) −2.93078e15 −0.188384
\(880\) 2.66532e16 1.70253
\(881\) 1.29626e16 0.822855 0.411428 0.911442i \(-0.365030\pi\)
0.411428 + 0.911442i \(0.365030\pi\)
\(882\) 8.72987e15 0.550720
\(883\) −1.18413e16 −0.742363 −0.371182 0.928560i \(-0.621047\pi\)
−0.371182 + 0.928560i \(0.621047\pi\)
\(884\) −1.23602e16 −0.770084
\(885\) −8.61614e14 −0.0533488
\(886\) −2.57895e16 −1.58693
\(887\) 4.09002e14 0.0250118 0.0125059 0.999922i \(-0.496019\pi\)
0.0125059 + 0.999922i \(0.496019\pi\)
\(888\) 1.55645e16 0.945940
\(889\) 1.78289e15 0.107687
\(890\) −2.87175e16 −1.72386
\(891\) −1.90513e15 −0.113657
\(892\) −6.26451e16 −3.71433
\(893\) 5.81692e15 0.342776
\(894\) 8.00873e15 0.469037
\(895\) 8.39053e15 0.488385
\(896\) 7.30139e14 0.0422388
\(897\) 3.12005e15 0.179392
\(898\) −1.63561e16 −0.934671
\(899\) 8.42919e13 0.00478749
\(900\) −7.02104e15 −0.396340
\(901\) −1.35523e16 −0.760371
\(902\) 2.61412e14 0.0145777
\(903\) −1.78384e14 −0.00988720
\(904\) 3.47234e16 1.91292
\(905\) 1.41689e15 0.0775832
\(906\) 2.83086e15 0.154069
\(907\) 1.49683e16 0.809715 0.404858 0.914380i \(-0.367321\pi\)
0.404858 + 0.914380i \(0.367321\pi\)
\(908\) −1.00204e16 −0.538781
\(909\) −5.95722e15 −0.318378
\(910\) 2.06805e15 0.109858
\(911\) 3.05019e16 1.61056 0.805278 0.592898i \(-0.202016\pi\)
0.805278 + 0.592898i \(0.202016\pi\)
\(912\) 1.54229e16 0.809457
\(913\) 2.95153e15 0.153977
\(914\) −5.88950e16 −3.05404
\(915\) −6.92945e14 −0.0357176
\(916\) −8.37807e16 −4.29258
\(917\) 2.83009e15 0.144135
\(918\) −8.62292e15 −0.436536
\(919\) −1.93002e16 −0.971240 −0.485620 0.874170i \(-0.661406\pi\)
−0.485620 + 0.874170i \(0.661406\pi\)
\(920\) −4.34379e16 −2.17288
\(921\) 1.50258e16 0.747152
\(922\) −3.86560e16 −1.91072
\(923\) −6.89693e15 −0.338881
\(924\) 9.31917e15 0.455178
\(925\) −6.50891e15 −0.316030
\(926\) −5.78750e16 −2.79338
\(927\) −3.95920e15 −0.189963
\(928\) −6.20872e14 −0.0296134
\(929\) 7.83924e15 0.371696 0.185848 0.982579i \(-0.440497\pi\)
0.185848 + 0.982579i \(0.440497\pi\)
\(930\) −4.52948e15 −0.213497
\(931\) 1.14392e16 0.536012
\(932\) −1.11589e16 −0.519795
\(933\) −1.20308e16 −0.557116
\(934\) 1.94587e16 0.895790
\(935\) −1.95267e16 −0.893644
\(936\) −4.92166e15 −0.223921
\(937\) 2.29388e15 0.103754 0.0518768 0.998653i \(-0.483480\pi\)
0.0518768 + 0.998653i \(0.483480\pi\)
\(938\) −6.74909e15 −0.303480
\(939\) −1.29584e16 −0.579285
\(940\) 2.19387e16 0.975008
\(941\) −2.06121e16 −0.910710 −0.455355 0.890310i \(-0.650488\pi\)
−0.455355 + 0.890310i \(0.650488\pi\)
\(942\) 3.28654e16 1.44364
\(943\) −2.10724e14 −0.00920238
\(944\) −7.03177e15 −0.305294
\(945\) 1.01791e15 0.0439376
\(946\) 2.33859e15 0.100358
\(947\) 2.22170e15 0.0947894 0.0473947 0.998876i \(-0.484908\pi\)
0.0473947 + 0.998876i \(0.484908\pi\)
\(948\) 3.48799e16 1.47955
\(949\) −9.76521e15 −0.411829
\(950\) −1.30398e16 −0.546751
\(951\) 1.49901e16 0.624901
\(952\) 2.45761e16 1.01862
\(953\) 2.83465e16 1.16812 0.584061 0.811710i \(-0.301463\pi\)
0.584061 + 0.811710i \(0.301463\pi\)
\(954\) −9.26175e15 −0.379470
\(955\) 2.62334e16 1.06865
\(956\) 2.16568e16 0.877153
\(957\) 2.48340e14 0.0100007
\(958\) 1.23556e16 0.494713
\(959\) 3.68438e15 0.146677
\(960\) 9.08637e15 0.359666
\(961\) −2.33776e16 −0.920070
\(962\) −7.83093e15 −0.306443
\(963\) −4.85312e15 −0.188833
\(964\) −1.38620e16 −0.536293
\(965\) 2.60343e15 0.100149
\(966\) −1.06474e16 −0.407258
\(967\) 1.51061e16 0.574521 0.287260 0.957853i \(-0.407255\pi\)
0.287260 + 0.957853i \(0.407255\pi\)
\(968\) −3.15326e15 −0.119246
\(969\) −1.12991e16 −0.424877
\(970\) −1.76839e16 −0.661203
\(971\) −3.85944e16 −1.43489 −0.717444 0.696616i \(-0.754688\pi\)
−0.717444 + 0.696616i \(0.754688\pi\)
\(972\) −4.15774e15 −0.153707
\(973\) 1.78803e15 0.0657285
\(974\) 9.44332e16 3.45184
\(975\) 2.05819e15 0.0748100
\(976\) −5.65524e15 −0.204398
\(977\) 2.44688e16 0.879411 0.439706 0.898142i \(-0.355083\pi\)
0.439706 + 0.898142i \(0.355083\pi\)
\(978\) −1.12427e16 −0.401796
\(979\) 3.79356e16 1.34816
\(980\) 4.31435e16 1.52466
\(981\) −1.56671e16 −0.550566
\(982\) 2.41298e16 0.843219
\(983\) 4.87784e16 1.69505 0.847526 0.530754i \(-0.178091\pi\)
0.847526 + 0.530754i \(0.178091\pi\)
\(984\) 3.32403e14 0.0114866
\(985\) −8.52839e15 −0.293068
\(986\) 1.12403e15 0.0384110
\(987\) 3.13323e15 0.106475
\(988\) −1.10687e16 −0.374053
\(989\) −1.88514e15 −0.0633524
\(990\) −1.33447e16 −0.445980
\(991\) 4.13941e16 1.37573 0.687866 0.725838i \(-0.258548\pi\)
0.687866 + 0.725838i \(0.258548\pi\)
\(992\) −1.49590e16 −0.494412
\(993\) −2.13737e16 −0.702519
\(994\) 2.35363e16 0.769332
\(995\) −2.59438e16 −0.843348
\(996\) 6.44140e15 0.208235
\(997\) −2.58983e16 −0.832621 −0.416310 0.909223i \(-0.636677\pi\)
−0.416310 + 0.909223i \(0.636677\pi\)
\(998\) 2.87509e16 0.919249
\(999\) −3.85447e15 −0.122561
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.1.1 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.c.1.1 27 1.1 even 1 trivial