Properties

Label 177.12.a.c.1.5
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 1.5
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-66.1318 q^{2} -243.000 q^{3} +2325.41 q^{4} +6882.52 q^{5} +16070.0 q^{6} +7668.92 q^{7} -18345.7 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q-66.1318 q^{2} -243.000 q^{3} +2325.41 q^{4} +6882.52 q^{5} +16070.0 q^{6} +7668.92 q^{7} -18345.7 q^{8} +59049.0 q^{9} -455153. q^{10} +265231. q^{11} -565075. q^{12} -2.03008e6 q^{13} -507159. q^{14} -1.67245e6 q^{15} -3.54921e6 q^{16} -2.19078e6 q^{17} -3.90502e6 q^{18} +1.39158e7 q^{19} +1.60047e7 q^{20} -1.86355e6 q^{21} -1.75402e7 q^{22} -1.47893e7 q^{23} +4.45802e6 q^{24} -1.45904e6 q^{25} +1.34253e8 q^{26} -1.43489e7 q^{27} +1.78334e7 q^{28} +1.32726e8 q^{29} +1.10602e8 q^{30} -6.41414e7 q^{31} +2.72287e8 q^{32} -6.44512e7 q^{33} +1.44880e8 q^{34} +5.27815e7 q^{35} +1.37313e8 q^{36} +2.46731e8 q^{37} -9.20275e8 q^{38} +4.93310e8 q^{39} -1.26265e8 q^{40} -1.45972e7 q^{41} +1.23240e8 q^{42} +6.41487e7 q^{43} +6.16772e8 q^{44} +4.06406e8 q^{45} +9.78041e8 q^{46} +1.68292e9 q^{47} +8.62457e8 q^{48} -1.91851e9 q^{49} +9.64887e7 q^{50} +5.32358e8 q^{51} -4.72078e9 q^{52} +5.02137e9 q^{53} +9.48919e8 q^{54} +1.82546e9 q^{55} -1.40692e8 q^{56} -3.38153e9 q^{57} -8.77743e9 q^{58} -7.14924e8 q^{59} -3.88914e9 q^{60} +1.12753e9 q^{61} +4.24178e9 q^{62} +4.52842e8 q^{63} -1.07381e10 q^{64} -1.39721e10 q^{65} +4.26227e9 q^{66} -1.51714e10 q^{67} -5.09446e9 q^{68} +3.59379e9 q^{69} -3.49053e9 q^{70} -5.00236e9 q^{71} -1.08330e9 q^{72} +2.20994e10 q^{73} -1.63167e10 q^{74} +3.54546e8 q^{75} +3.23599e10 q^{76} +2.03404e9 q^{77} -3.26235e10 q^{78} -4.29957e10 q^{79} -2.44275e10 q^{80} +3.48678e9 q^{81} +9.65342e8 q^{82} -1.16822e10 q^{83} -4.33351e9 q^{84} -1.50781e10 q^{85} -4.24227e9 q^{86} -3.22525e10 q^{87} -4.86587e9 q^{88} -8.90945e10 q^{89} -2.68763e10 q^{90} -1.55685e10 q^{91} -3.43911e10 q^{92} +1.55864e10 q^{93} -1.11294e11 q^{94} +9.57757e10 q^{95} -6.61659e10 q^{96} +1.57286e11 q^{97} +1.26875e11 q^{98} +1.56616e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + O(q^{10}) \) \( 27q - 46q^{2} - 6561q^{3} + 26142q^{4} - 2442q^{5} + 11178q^{6} + 170093q^{7} - 19341q^{8} + 1594323q^{9} + 140249q^{10} + 256992q^{11} - 6352506q^{12} + 2436978q^{13} + 5233061q^{14} + 593406q^{15} + 28295194q^{16} - 4565351q^{17} - 2716254q^{18} + 33607699q^{19} - 19208463q^{20} - 41332599q^{21} + 79735622q^{22} + 43966161q^{23} + 4699863q^{24} + 406675819q^{25} + 42605404q^{26} - 387420489q^{27} + 635747682q^{28} - 107217773q^{29} - 34080507q^{30} + 570926627q^{31} + 526569236q^{32} - 62449056q^{33} + 129790240q^{34} + 134356079q^{35} + 1543658958q^{36} - 107121371q^{37} + 208302581q^{38} - 592185654q^{39} - 958762162q^{40} - 1935967559q^{41} - 1271633823q^{42} + 1725943824q^{43} + 196885756q^{44} - 144197658q^{45} - 13265966407q^{46} + 1801256065q^{47} - 6875732142q^{48} + 10484289252q^{49} - 10067682271q^{50} + 1109380293q^{51} - 882697024q^{52} - 6214238922q^{53} + 660049722q^{54} + 4460552366q^{55} + 28328012310q^{56} - 8166670857q^{57} + 12220116750q^{58} - 19302956073q^{59} + 4667656509q^{60} + 13167821039q^{61} - 1162130230q^{62} + 10043821557q^{63} - 5337557395q^{64} - 16849896006q^{65} - 19375756146q^{66} - 16856763152q^{67} - 36171071977q^{68} - 10683777123q^{69} - 120177261588q^{70} - 5198545690q^{71} - 1142066709q^{72} - 25075321857q^{73} - 182979651978q^{74} - 98822224017q^{75} - 3501293988q^{76} - 42787697701q^{77} - 10353113172q^{78} + 6850314702q^{79} - 261464428159q^{80} + 94143178827q^{81} - 148881516273q^{82} + 30908370899q^{83} - 154486686726q^{84} - 49419624969q^{85} - 220725475224q^{86} + 26053918839q^{87} - 53091280787q^{88} + 28988060121q^{89} + 8281563201q^{90} + 97120614047q^{91} + 45374597708q^{92} - 138735170361q^{93} + 208966927220q^{94} - 125253904969q^{95} - 127956324348q^{96} + 367722840268q^{97} - 48265639912q^{98} + 15175120608q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −66.1318 −1.46132 −0.730660 0.682742i \(-0.760787\pi\)
−0.730660 + 0.682742i \(0.760787\pi\)
\(3\) −243.000 −0.577350
\(4\) 2325.41 1.13546
\(5\) 6882.52 0.984946 0.492473 0.870328i \(-0.336093\pi\)
0.492473 + 0.870328i \(0.336093\pi\)
\(6\) 16070.0 0.843693
\(7\) 7668.92 0.172463 0.0862313 0.996275i \(-0.472518\pi\)
0.0862313 + 0.996275i \(0.472518\pi\)
\(8\) −18345.7 −0.197943
\(9\) 59049.0 0.333333
\(10\) −455153. −1.43932
\(11\) 265231. 0.496552 0.248276 0.968689i \(-0.420136\pi\)
0.248276 + 0.968689i \(0.420136\pi\)
\(12\) −565075. −0.655555
\(13\) −2.03008e6 −1.51644 −0.758220 0.651999i \(-0.773931\pi\)
−0.758220 + 0.651999i \(0.773931\pi\)
\(14\) −507159. −0.252023
\(15\) −1.67245e6 −0.568659
\(16\) −3.54921e6 −0.846197
\(17\) −2.19078e6 −0.374222 −0.187111 0.982339i \(-0.559912\pi\)
−0.187111 + 0.982339i \(0.559912\pi\)
\(18\) −3.90502e6 −0.487107
\(19\) 1.39158e7 1.28933 0.644663 0.764467i \(-0.276998\pi\)
0.644663 + 0.764467i \(0.276998\pi\)
\(20\) 1.60047e7 1.11836
\(21\) −1.86355e6 −0.0995713
\(22\) −1.75402e7 −0.725622
\(23\) −1.47893e7 −0.479119 −0.239560 0.970882i \(-0.577003\pi\)
−0.239560 + 0.970882i \(0.577003\pi\)
\(24\) 4.45802e6 0.114282
\(25\) −1.45904e6 −0.0298811
\(26\) 1.34253e8 2.21600
\(27\) −1.43489e7 −0.192450
\(28\) 1.78334e7 0.195823
\(29\) 1.32726e8 1.20162 0.600811 0.799391i \(-0.294844\pi\)
0.600811 + 0.799391i \(0.294844\pi\)
\(30\) 1.10602e8 0.830992
\(31\) −6.41414e7 −0.402392 −0.201196 0.979551i \(-0.564483\pi\)
−0.201196 + 0.979551i \(0.564483\pi\)
\(32\) 2.72287e8 1.43451
\(33\) −6.44512e7 −0.286685
\(34\) 1.44880e8 0.546857
\(35\) 5.27815e7 0.169866
\(36\) 1.37313e8 0.378485
\(37\) 2.46731e8 0.584943 0.292471 0.956274i \(-0.405522\pi\)
0.292471 + 0.956274i \(0.405522\pi\)
\(38\) −9.20275e8 −1.88412
\(39\) 4.93310e8 0.875517
\(40\) −1.26265e8 −0.194963
\(41\) −1.45972e7 −0.0196770 −0.00983852 0.999952i \(-0.503132\pi\)
−0.00983852 + 0.999952i \(0.503132\pi\)
\(42\) 1.23240e8 0.145505
\(43\) 6.41487e7 0.0665444 0.0332722 0.999446i \(-0.489407\pi\)
0.0332722 + 0.999446i \(0.489407\pi\)
\(44\) 6.16772e8 0.563813
\(45\) 4.06406e8 0.328315
\(46\) 9.78041e8 0.700146
\(47\) 1.68292e9 1.07035 0.535174 0.844742i \(-0.320246\pi\)
0.535174 + 0.844742i \(0.320246\pi\)
\(48\) 8.62457e8 0.488552
\(49\) −1.91851e9 −0.970257
\(50\) 9.64887e7 0.0436658
\(51\) 5.32358e8 0.216057
\(52\) −4.72078e9 −1.72185
\(53\) 5.02137e9 1.64932 0.824660 0.565629i \(-0.191367\pi\)
0.824660 + 0.565629i \(0.191367\pi\)
\(54\) 9.48919e8 0.281231
\(55\) 1.82546e9 0.489077
\(56\) −1.40692e8 −0.0341378
\(57\) −3.38153e9 −0.744393
\(58\) −8.77743e9 −1.75595
\(59\) −7.14924e8 −0.130189
\(60\) −3.88914e9 −0.645687
\(61\) 1.12753e9 0.170928 0.0854642 0.996341i \(-0.472763\pi\)
0.0854642 + 0.996341i \(0.472763\pi\)
\(62\) 4.24178e9 0.588023
\(63\) 4.52842e8 0.0574875
\(64\) −1.07381e10 −1.25008
\(65\) −1.39721e10 −1.49361
\(66\) 4.26227e9 0.418938
\(67\) −1.51714e10 −1.37282 −0.686412 0.727213i \(-0.740815\pi\)
−0.686412 + 0.727213i \(0.740815\pi\)
\(68\) −5.09446e9 −0.424912
\(69\) 3.59379e9 0.276620
\(70\) −3.49053e9 −0.248229
\(71\) −5.00236e9 −0.329044 −0.164522 0.986373i \(-0.552608\pi\)
−0.164522 + 0.986373i \(0.552608\pi\)
\(72\) −1.08330e9 −0.0659810
\(73\) 2.20994e10 1.24768 0.623841 0.781551i \(-0.285571\pi\)
0.623841 + 0.781551i \(0.285571\pi\)
\(74\) −1.63167e10 −0.854788
\(75\) 3.54546e8 0.0172518
\(76\) 3.23599e10 1.46397
\(77\) 2.03404e9 0.0856367
\(78\) −3.26235e10 −1.27941
\(79\) −4.29957e10 −1.57209 −0.786043 0.618172i \(-0.787873\pi\)
−0.786043 + 0.618172i \(0.787873\pi\)
\(80\) −2.44275e10 −0.833458
\(81\) 3.48678e9 0.111111
\(82\) 9.65342e8 0.0287544
\(83\) −1.16822e10 −0.325533 −0.162767 0.986665i \(-0.552042\pi\)
−0.162767 + 0.986665i \(0.552042\pi\)
\(84\) −4.33351e9 −0.113059
\(85\) −1.50781e10 −0.368588
\(86\) −4.24227e9 −0.0972426
\(87\) −3.22525e10 −0.693757
\(88\) −4.86587e9 −0.0982891
\(89\) −8.90945e10 −1.69124 −0.845621 0.533783i \(-0.820770\pi\)
−0.845621 + 0.533783i \(0.820770\pi\)
\(90\) −2.68763e10 −0.479774
\(91\) −1.55685e10 −0.261529
\(92\) −3.43911e10 −0.544018
\(93\) 1.55864e10 0.232321
\(94\) −1.11294e11 −1.56412
\(95\) 9.57757e10 1.26992
\(96\) −6.61659e10 −0.828213
\(97\) 1.57286e11 1.85971 0.929853 0.367932i \(-0.119934\pi\)
0.929853 + 0.367932i \(0.119934\pi\)
\(98\) 1.26875e11 1.41786
\(99\) 1.56616e10 0.165517
\(100\) −3.39286e9 −0.0339286
\(101\) −2.07070e11 −1.96042 −0.980212 0.197951i \(-0.936571\pi\)
−0.980212 + 0.197951i \(0.936571\pi\)
\(102\) −3.52058e10 −0.315728
\(103\) 2.11248e11 1.79551 0.897757 0.440491i \(-0.145196\pi\)
0.897757 + 0.440491i \(0.145196\pi\)
\(104\) 3.72434e10 0.300169
\(105\) −1.28259e10 −0.0980724
\(106\) −3.32072e11 −2.41018
\(107\) −1.72110e9 −0.0118630 −0.00593150 0.999982i \(-0.501888\pi\)
−0.00593150 + 0.999982i \(0.501888\pi\)
\(108\) −3.33671e10 −0.218518
\(109\) 2.58436e11 1.60882 0.804411 0.594074i \(-0.202481\pi\)
0.804411 + 0.594074i \(0.202481\pi\)
\(110\) −1.20721e11 −0.714698
\(111\) −5.99555e10 −0.337717
\(112\) −2.72186e10 −0.145937
\(113\) −1.78825e11 −0.913054 −0.456527 0.889710i \(-0.650907\pi\)
−0.456527 + 0.889710i \(0.650907\pi\)
\(114\) 2.23627e11 1.08780
\(115\) −1.01787e11 −0.471907
\(116\) 3.08643e11 1.36439
\(117\) −1.19874e11 −0.505480
\(118\) 4.72792e10 0.190248
\(119\) −1.68009e10 −0.0645392
\(120\) 3.06824e10 0.112562
\(121\) −2.14964e11 −0.753436
\(122\) −7.45656e10 −0.249781
\(123\) 3.54713e9 0.0113605
\(124\) −1.49155e11 −0.456898
\(125\) −3.46102e11 −1.01438
\(126\) −2.99472e10 −0.0840076
\(127\) 1.23462e11 0.331599 0.165800 0.986159i \(-0.446980\pi\)
0.165800 + 0.986159i \(0.446980\pi\)
\(128\) 1.52483e11 0.392254
\(129\) −1.55881e10 −0.0384194
\(130\) 9.23999e11 2.18264
\(131\) 4.74686e11 1.07502 0.537508 0.843259i \(-0.319366\pi\)
0.537508 + 0.843259i \(0.319366\pi\)
\(132\) −1.49876e11 −0.325518
\(133\) 1.06719e11 0.222360
\(134\) 1.00331e12 2.00613
\(135\) −9.87566e10 −0.189553
\(136\) 4.01914e10 0.0740746
\(137\) 8.43562e11 1.49332 0.746661 0.665204i \(-0.231656\pi\)
0.746661 + 0.665204i \(0.231656\pi\)
\(138\) −2.37664e11 −0.404230
\(139\) −3.30930e11 −0.540948 −0.270474 0.962727i \(-0.587180\pi\)
−0.270474 + 0.962727i \(0.587180\pi\)
\(140\) 1.22739e11 0.192876
\(141\) −4.08949e11 −0.617966
\(142\) 3.30815e11 0.480839
\(143\) −5.38442e11 −0.752992
\(144\) −2.09577e11 −0.282066
\(145\) 9.13492e11 1.18353
\(146\) −1.46147e12 −1.82326
\(147\) 4.66199e11 0.560178
\(148\) 5.73750e11 0.664176
\(149\) 7.63172e11 0.851330 0.425665 0.904881i \(-0.360040\pi\)
0.425665 + 0.904881i \(0.360040\pi\)
\(150\) −2.34468e10 −0.0252105
\(151\) −8.84524e11 −0.916930 −0.458465 0.888712i \(-0.651601\pi\)
−0.458465 + 0.888712i \(0.651601\pi\)
\(152\) −2.55295e11 −0.255213
\(153\) −1.29363e11 −0.124741
\(154\) −1.34515e11 −0.125143
\(155\) −4.41454e11 −0.396334
\(156\) 1.14715e12 0.994110
\(157\) −1.22177e12 −1.02221 −0.511106 0.859518i \(-0.670764\pi\)
−0.511106 + 0.859518i \(0.670764\pi\)
\(158\) 2.84338e12 2.29732
\(159\) −1.22019e12 −0.952235
\(160\) 1.87402e12 1.41291
\(161\) −1.13418e11 −0.0826301
\(162\) −2.30587e11 −0.162369
\(163\) 1.93527e12 1.31737 0.658687 0.752417i \(-0.271112\pi\)
0.658687 + 0.752417i \(0.271112\pi\)
\(164\) −3.39446e10 −0.0223424
\(165\) −4.43587e11 −0.282369
\(166\) 7.72565e11 0.475708
\(167\) −1.66922e12 −0.994426 −0.497213 0.867628i \(-0.665643\pi\)
−0.497213 + 0.867628i \(0.665643\pi\)
\(168\) 3.41881e10 0.0197094
\(169\) 2.32907e12 1.29959
\(170\) 9.97139e11 0.538625
\(171\) 8.21713e11 0.429775
\(172\) 1.49172e11 0.0755581
\(173\) 1.28276e12 0.629347 0.314674 0.949200i \(-0.398105\pi\)
0.314674 + 0.949200i \(0.398105\pi\)
\(174\) 2.13291e12 1.01380
\(175\) −1.11892e10 −0.00515337
\(176\) −9.41361e11 −0.420181
\(177\) 1.73727e11 0.0751646
\(178\) 5.89198e12 2.47145
\(179\) −1.09968e12 −0.447276 −0.223638 0.974672i \(-0.571793\pi\)
−0.223638 + 0.974672i \(0.571793\pi\)
\(180\) 9.45061e11 0.372787
\(181\) 2.45767e12 0.940353 0.470177 0.882572i \(-0.344190\pi\)
0.470177 + 0.882572i \(0.344190\pi\)
\(182\) 1.02957e12 0.382178
\(183\) −2.73990e11 −0.0986855
\(184\) 2.71320e11 0.0948383
\(185\) 1.69813e12 0.576137
\(186\) −1.03075e12 −0.339495
\(187\) −5.81062e11 −0.185821
\(188\) 3.91348e12 1.21533
\(189\) −1.10041e11 −0.0331904
\(190\) −6.33381e12 −1.85575
\(191\) −1.69206e12 −0.481650 −0.240825 0.970569i \(-0.577418\pi\)
−0.240825 + 0.970569i \(0.577418\pi\)
\(192\) 2.60935e12 0.721732
\(193\) 4.25498e11 0.114375 0.0571876 0.998363i \(-0.481787\pi\)
0.0571876 + 0.998363i \(0.481787\pi\)
\(194\) −1.04016e13 −2.71762
\(195\) 3.39522e12 0.862337
\(196\) −4.46134e12 −1.10168
\(197\) 3.94792e12 0.947990 0.473995 0.880527i \(-0.342811\pi\)
0.473995 + 0.880527i \(0.342811\pi\)
\(198\) −1.03573e12 −0.241874
\(199\) 1.31854e12 0.299502 0.149751 0.988724i \(-0.452153\pi\)
0.149751 + 0.988724i \(0.452153\pi\)
\(200\) 2.67671e10 0.00591475
\(201\) 3.68666e12 0.792600
\(202\) 1.36939e13 2.86481
\(203\) 1.01787e12 0.207235
\(204\) 1.23795e12 0.245323
\(205\) −1.00466e11 −0.0193808
\(206\) −1.39702e13 −2.62382
\(207\) −8.73292e11 −0.159706
\(208\) 7.20518e12 1.28321
\(209\) 3.69090e12 0.640218
\(210\) 8.48199e11 0.143315
\(211\) 5.99993e12 0.987626 0.493813 0.869568i \(-0.335603\pi\)
0.493813 + 0.869568i \(0.335603\pi\)
\(212\) 1.16767e13 1.87273
\(213\) 1.21557e12 0.189974
\(214\) 1.13819e11 0.0173356
\(215\) 4.41505e11 0.0655426
\(216\) 2.63241e11 0.0380942
\(217\) −4.91895e11 −0.0693975
\(218\) −1.70909e13 −2.35100
\(219\) −5.37015e12 −0.720350
\(220\) 4.24495e12 0.555325
\(221\) 4.44745e12 0.567485
\(222\) 3.96496e12 0.493512
\(223\) 2.51473e12 0.305362 0.152681 0.988276i \(-0.451209\pi\)
0.152681 + 0.988276i \(0.451209\pi\)
\(224\) 2.08815e12 0.247399
\(225\) −8.61547e10 −0.00996036
\(226\) 1.18260e13 1.33426
\(227\) 1.57568e12 0.173510 0.0867552 0.996230i \(-0.472350\pi\)
0.0867552 + 0.996230i \(0.472350\pi\)
\(228\) −7.86346e12 −0.845225
\(229\) 1.54637e13 1.62262 0.811310 0.584616i \(-0.198755\pi\)
0.811310 + 0.584616i \(0.198755\pi\)
\(230\) 6.73138e12 0.689606
\(231\) −4.94271e11 −0.0494424
\(232\) −2.43496e12 −0.237853
\(233\) 7.69781e12 0.734361 0.367181 0.930150i \(-0.380323\pi\)
0.367181 + 0.930150i \(0.380323\pi\)
\(234\) 7.92750e12 0.738668
\(235\) 1.15827e13 1.05424
\(236\) −1.66249e12 −0.147824
\(237\) 1.04480e13 0.907644
\(238\) 1.11107e12 0.0943124
\(239\) −9.02876e12 −0.748927 −0.374464 0.927242i \(-0.622173\pi\)
−0.374464 + 0.927242i \(0.622173\pi\)
\(240\) 5.93588e12 0.481197
\(241\) −1.40911e13 −1.11648 −0.558238 0.829681i \(-0.688523\pi\)
−0.558238 + 0.829681i \(0.688523\pi\)
\(242\) 1.42159e13 1.10101
\(243\) −8.47289e11 −0.0641500
\(244\) 2.62197e12 0.194081
\(245\) −1.32042e13 −0.955651
\(246\) −2.34578e11 −0.0166014
\(247\) −2.82502e13 −1.95519
\(248\) 1.17672e12 0.0796507
\(249\) 2.83878e12 0.187947
\(250\) 2.28884e13 1.48233
\(251\) −1.89090e12 −0.119802 −0.0599010 0.998204i \(-0.519078\pi\)
−0.0599010 + 0.998204i \(0.519078\pi\)
\(252\) 1.05304e12 0.0652745
\(253\) −3.92258e12 −0.237908
\(254\) −8.16477e12 −0.484573
\(255\) 3.66397e12 0.212804
\(256\) 1.19076e13 0.676868
\(257\) −1.60395e12 −0.0892398 −0.0446199 0.999004i \(-0.514208\pi\)
−0.0446199 + 0.999004i \(0.514208\pi\)
\(258\) 1.03087e12 0.0561430
\(259\) 1.89216e12 0.100881
\(260\) −3.24908e13 −1.69593
\(261\) 7.83736e12 0.400541
\(262\) −3.13918e13 −1.57094
\(263\) −2.83907e13 −1.39130 −0.695648 0.718383i \(-0.744883\pi\)
−0.695648 + 0.718383i \(0.744883\pi\)
\(264\) 1.18241e12 0.0567473
\(265\) 3.45597e13 1.62449
\(266\) −7.05751e12 −0.324940
\(267\) 2.16500e13 0.976439
\(268\) −3.52798e13 −1.55878
\(269\) −2.14423e13 −0.928185 −0.464093 0.885787i \(-0.653620\pi\)
−0.464093 + 0.885787i \(0.653620\pi\)
\(270\) 6.53095e12 0.276997
\(271\) −2.63137e13 −1.09358 −0.546791 0.837269i \(-0.684151\pi\)
−0.546791 + 0.837269i \(0.684151\pi\)
\(272\) 7.77552e12 0.316665
\(273\) 3.78315e12 0.150994
\(274\) −5.57862e13 −2.18222
\(275\) −3.86982e11 −0.0148375
\(276\) 8.35705e12 0.314089
\(277\) −3.69721e13 −1.36218 −0.681091 0.732199i \(-0.738494\pi\)
−0.681091 + 0.732199i \(0.738494\pi\)
\(278\) 2.18850e13 0.790498
\(279\) −3.78748e12 −0.134131
\(280\) −9.68315e11 −0.0336239
\(281\) −1.62031e13 −0.551712 −0.275856 0.961199i \(-0.588961\pi\)
−0.275856 + 0.961199i \(0.588961\pi\)
\(282\) 2.70446e13 0.903046
\(283\) 5.24493e13 1.71757 0.858784 0.512338i \(-0.171220\pi\)
0.858784 + 0.512338i \(0.171220\pi\)
\(284\) −1.16326e13 −0.373615
\(285\) −2.32735e13 −0.733187
\(286\) 3.56081e13 1.10036
\(287\) −1.11945e11 −0.00339355
\(288\) 1.60783e13 0.478169
\(289\) −2.94724e13 −0.859958
\(290\) −6.04108e13 −1.72952
\(291\) −3.82204e13 −1.07370
\(292\) 5.13901e13 1.41669
\(293\) −1.90369e13 −0.515019 −0.257510 0.966276i \(-0.582902\pi\)
−0.257510 + 0.966276i \(0.582902\pi\)
\(294\) −3.08306e13 −0.818599
\(295\) −4.92048e12 −0.128229
\(296\) −4.52645e12 −0.115785
\(297\) −3.80578e12 −0.0955616
\(298\) −5.04699e13 −1.24406
\(299\) 3.00234e13 0.726556
\(300\) 8.24465e11 0.0195887
\(301\) 4.91951e11 0.0114764
\(302\) 5.84951e13 1.33993
\(303\) 5.03181e13 1.13185
\(304\) −4.93900e13 −1.09102
\(305\) 7.76025e12 0.168355
\(306\) 8.55501e12 0.182286
\(307\) −1.69753e13 −0.355268 −0.177634 0.984097i \(-0.556844\pi\)
−0.177634 + 0.984097i \(0.556844\pi\)
\(308\) 4.72997e12 0.0972366
\(309\) −5.13334e13 −1.03664
\(310\) 2.91942e13 0.579171
\(311\) −2.69573e13 −0.525406 −0.262703 0.964877i \(-0.584614\pi\)
−0.262703 + 0.964877i \(0.584614\pi\)
\(312\) −9.05014e12 −0.173303
\(313\) 3.07747e13 0.579029 0.289514 0.957174i \(-0.406506\pi\)
0.289514 + 0.957174i \(0.406506\pi\)
\(314\) 8.07977e13 1.49378
\(315\) 3.11669e12 0.0566221
\(316\) −9.99827e13 −1.78503
\(317\) −2.86706e13 −0.503050 −0.251525 0.967851i \(-0.580932\pi\)
−0.251525 + 0.967851i \(0.580932\pi\)
\(318\) 8.06935e13 1.39152
\(319\) 3.52032e13 0.596669
\(320\) −7.39050e13 −1.23126
\(321\) 4.18227e11 0.00684911
\(322\) 7.50051e12 0.120749
\(323\) −3.04864e13 −0.482494
\(324\) 8.10821e12 0.126162
\(325\) 2.96196e12 0.0453129
\(326\) −1.27983e14 −1.92510
\(327\) −6.28000e13 −0.928853
\(328\) 2.67797e11 0.00389493
\(329\) 1.29062e13 0.184595
\(330\) 2.93352e13 0.412631
\(331\) 8.39875e13 1.16188 0.580939 0.813947i \(-0.302686\pi\)
0.580939 + 0.813947i \(0.302686\pi\)
\(332\) −2.71660e13 −0.369629
\(333\) 1.45692e13 0.194981
\(334\) 1.10388e14 1.45317
\(335\) −1.04418e14 −1.35216
\(336\) 6.61411e12 0.0842569
\(337\) 7.95960e12 0.0997532 0.0498766 0.998755i \(-0.484117\pi\)
0.0498766 + 0.998755i \(0.484117\pi\)
\(338\) −1.54026e14 −1.89912
\(339\) 4.34544e13 0.527152
\(340\) −3.50627e13 −0.418515
\(341\) −1.70123e13 −0.199809
\(342\) −5.43413e13 −0.628039
\(343\) −2.98769e13 −0.339795
\(344\) −1.17686e12 −0.0131720
\(345\) 2.47343e13 0.272455
\(346\) −8.48309e13 −0.919677
\(347\) 1.70126e13 0.181534 0.0907669 0.995872i \(-0.471068\pi\)
0.0907669 + 0.995872i \(0.471068\pi\)
\(348\) −7.50003e13 −0.787730
\(349\) 1.55596e14 1.60864 0.804318 0.594200i \(-0.202531\pi\)
0.804318 + 0.594200i \(0.202531\pi\)
\(350\) 7.39964e11 0.00753071
\(351\) 2.91295e13 0.291839
\(352\) 7.22192e13 0.712308
\(353\) 9.94759e13 0.965955 0.482978 0.875633i \(-0.339555\pi\)
0.482978 + 0.875633i \(0.339555\pi\)
\(354\) −1.14888e13 −0.109840
\(355\) −3.44289e13 −0.324091
\(356\) −2.07181e14 −1.92033
\(357\) 4.08261e12 0.0372617
\(358\) 7.27239e13 0.653613
\(359\) 1.64530e14 1.45622 0.728109 0.685462i \(-0.240400\pi\)
0.728109 + 0.685462i \(0.240400\pi\)
\(360\) −7.45582e12 −0.0649878
\(361\) 7.71587e13 0.662362
\(362\) −1.62530e14 −1.37416
\(363\) 5.22362e13 0.434996
\(364\) −3.62032e13 −0.296955
\(365\) 1.52099e14 1.22890
\(366\) 1.81194e13 0.144211
\(367\) 1.37417e14 1.07740 0.538701 0.842497i \(-0.318915\pi\)
0.538701 + 0.842497i \(0.318915\pi\)
\(368\) 5.24902e13 0.405429
\(369\) −8.61953e11 −0.00655901
\(370\) −1.12300e14 −0.841920
\(371\) 3.85084e13 0.284446
\(372\) 3.62447e13 0.263790
\(373\) 1.09871e14 0.787925 0.393962 0.919127i \(-0.371104\pi\)
0.393962 + 0.919127i \(0.371104\pi\)
\(374\) 3.84267e13 0.271543
\(375\) 8.41029e13 0.585651
\(376\) −3.08744e13 −0.211868
\(377\) −2.69445e14 −1.82219
\(378\) 7.27718e12 0.0485018
\(379\) 2.48057e14 1.62943 0.814716 0.579860i \(-0.196893\pi\)
0.814716 + 0.579860i \(0.196893\pi\)
\(380\) 2.22718e14 1.44193
\(381\) −3.00013e13 −0.191449
\(382\) 1.11899e14 0.703845
\(383\) 1.35785e14 0.841894 0.420947 0.907085i \(-0.361698\pi\)
0.420947 + 0.907085i \(0.361698\pi\)
\(384\) −3.70535e13 −0.226468
\(385\) 1.39993e13 0.0843475
\(386\) −2.81389e13 −0.167139
\(387\) 3.78792e12 0.0221815
\(388\) 3.65754e14 2.11161
\(389\) 7.94373e13 0.452170 0.226085 0.974108i \(-0.427407\pi\)
0.226085 + 0.974108i \(0.427407\pi\)
\(390\) −2.24532e14 −1.26015
\(391\) 3.24000e13 0.179297
\(392\) 3.51966e13 0.192056
\(393\) −1.15349e14 −0.620660
\(394\) −2.61083e14 −1.38532
\(395\) −2.95919e14 −1.54842
\(396\) 3.64198e13 0.187938
\(397\) 1.52289e13 0.0775035 0.0387518 0.999249i \(-0.487662\pi\)
0.0387518 + 0.999249i \(0.487662\pi\)
\(398\) −8.71971e13 −0.437668
\(399\) −2.59327e13 −0.128380
\(400\) 5.17842e12 0.0252853
\(401\) 2.68365e14 1.29250 0.646252 0.763124i \(-0.276335\pi\)
0.646252 + 0.763124i \(0.276335\pi\)
\(402\) −2.43805e14 −1.15824
\(403\) 1.30212e14 0.610203
\(404\) −4.81523e14 −2.22597
\(405\) 2.39979e13 0.109438
\(406\) −6.73134e13 −0.302836
\(407\) 6.54407e13 0.290455
\(408\) −9.76651e12 −0.0427670
\(409\) −3.75994e14 −1.62444 −0.812218 0.583355i \(-0.801740\pi\)
−0.812218 + 0.583355i \(0.801740\pi\)
\(410\) 6.64398e12 0.0283216
\(411\) −2.04985e14 −0.862170
\(412\) 4.91240e14 2.03873
\(413\) −5.48269e12 −0.0224527
\(414\) 5.77523e13 0.233382
\(415\) −8.04031e13 −0.320633
\(416\) −5.52766e14 −2.17534
\(417\) 8.04161e13 0.312316
\(418\) −2.44086e14 −0.935563
\(419\) 5.07594e13 0.192017 0.0960083 0.995381i \(-0.469392\pi\)
0.0960083 + 0.995381i \(0.469392\pi\)
\(420\) −2.98255e13 −0.111357
\(421\) 3.23595e14 1.19248 0.596238 0.802808i \(-0.296661\pi\)
0.596238 + 0.802808i \(0.296661\pi\)
\(422\) −3.96786e14 −1.44324
\(423\) 9.93747e13 0.356783
\(424\) −9.21207e13 −0.326471
\(425\) 3.19642e12 0.0111821
\(426\) −8.03881e13 −0.277612
\(427\) 8.64693e12 0.0294787
\(428\) −4.00226e12 −0.0134699
\(429\) 1.30841e14 0.434740
\(430\) −2.91975e13 −0.0957787
\(431\) −2.28987e14 −0.741628 −0.370814 0.928707i \(-0.620921\pi\)
−0.370814 + 0.928707i \(0.620921\pi\)
\(432\) 5.09272e13 0.162851
\(433\) −2.16476e14 −0.683482 −0.341741 0.939794i \(-0.611017\pi\)
−0.341741 + 0.939794i \(0.611017\pi\)
\(434\) 3.25299e13 0.101412
\(435\) −2.21978e14 −0.683313
\(436\) 6.00971e14 1.82674
\(437\) −2.05804e14 −0.617741
\(438\) 3.55137e14 1.05266
\(439\) 3.66508e14 1.07283 0.536413 0.843956i \(-0.319779\pi\)
0.536413 + 0.843956i \(0.319779\pi\)
\(440\) −3.34894e13 −0.0968095
\(441\) −1.13286e14 −0.323419
\(442\) −2.94118e14 −0.829276
\(443\) 3.26305e14 0.908664 0.454332 0.890832i \(-0.349878\pi\)
0.454332 + 0.890832i \(0.349878\pi\)
\(444\) −1.39421e14 −0.383462
\(445\) −6.13195e14 −1.66578
\(446\) −1.66304e14 −0.446231
\(447\) −1.85451e14 −0.491515
\(448\) −8.23494e13 −0.215591
\(449\) 4.19927e13 0.108597 0.0542986 0.998525i \(-0.482708\pi\)
0.0542986 + 0.998525i \(0.482708\pi\)
\(450\) 5.69756e12 0.0145553
\(451\) −3.87165e12 −0.00977068
\(452\) −4.15841e14 −1.03673
\(453\) 2.14939e14 0.529390
\(454\) −1.04202e14 −0.253554
\(455\) −1.07151e14 −0.257592
\(456\) 6.20368e13 0.147347
\(457\) 1.76811e14 0.414926 0.207463 0.978243i \(-0.433479\pi\)
0.207463 + 0.978243i \(0.433479\pi\)
\(458\) −1.02264e15 −2.37117
\(459\) 3.14352e13 0.0720190
\(460\) −2.36698e14 −0.535829
\(461\) 6.73921e14 1.50749 0.753744 0.657168i \(-0.228246\pi\)
0.753744 + 0.657168i \(0.228246\pi\)
\(462\) 3.26870e13 0.0722511
\(463\) 5.54820e14 1.21187 0.605936 0.795514i \(-0.292799\pi\)
0.605936 + 0.795514i \(0.292799\pi\)
\(464\) −4.71073e14 −1.01681
\(465\) 1.07273e14 0.228824
\(466\) −5.09070e14 −1.07314
\(467\) 6.39614e14 1.33252 0.666262 0.745717i \(-0.267893\pi\)
0.666262 + 0.745717i \(0.267893\pi\)
\(468\) −2.78757e14 −0.573950
\(469\) −1.16348e14 −0.236761
\(470\) −7.65986e14 −1.54058
\(471\) 2.96890e14 0.590174
\(472\) 1.31158e13 0.0257700
\(473\) 1.70142e13 0.0330428
\(474\) −6.90942e14 −1.32636
\(475\) −2.03036e13 −0.0385264
\(476\) −3.90690e13 −0.0732814
\(477\) 2.96507e14 0.549773
\(478\) 5.97088e14 1.09442
\(479\) 4.30598e14 0.780238 0.390119 0.920764i \(-0.372434\pi\)
0.390119 + 0.920764i \(0.372434\pi\)
\(480\) −4.55388e14 −0.815745
\(481\) −5.00883e14 −0.887031
\(482\) 9.31866e14 1.63153
\(483\) 2.75605e13 0.0477065
\(484\) −4.99880e14 −0.855492
\(485\) 1.08252e15 1.83171
\(486\) 5.60327e13 0.0937437
\(487\) 1.84161e14 0.304641 0.152321 0.988331i \(-0.451325\pi\)
0.152321 + 0.988331i \(0.451325\pi\)
\(488\) −2.06854e13 −0.0338341
\(489\) −4.70270e14 −0.760586
\(490\) 8.73218e14 1.39651
\(491\) 4.53217e13 0.0716734 0.0358367 0.999358i \(-0.488590\pi\)
0.0358367 + 0.999358i \(0.488590\pi\)
\(492\) 8.24854e12 0.0128994
\(493\) −2.90774e14 −0.449673
\(494\) 1.86823e15 2.85715
\(495\) 1.07792e14 0.163026
\(496\) 2.27651e14 0.340503
\(497\) −3.83627e13 −0.0567478
\(498\) −1.87733e14 −0.274650
\(499\) −4.58426e14 −0.663310 −0.331655 0.943401i \(-0.607607\pi\)
−0.331655 + 0.943401i \(0.607607\pi\)
\(500\) −8.04831e14 −1.15178
\(501\) 4.05620e14 0.574132
\(502\) 1.25049e14 0.175069
\(503\) −5.06253e14 −0.701042 −0.350521 0.936555i \(-0.613995\pi\)
−0.350521 + 0.936555i \(0.613995\pi\)
\(504\) −8.30772e12 −0.0113793
\(505\) −1.42516e15 −1.93091
\(506\) 2.59407e14 0.347659
\(507\) −5.65965e14 −0.750319
\(508\) 2.87100e14 0.376516
\(509\) −7.38876e14 −0.958570 −0.479285 0.877659i \(-0.659104\pi\)
−0.479285 + 0.877659i \(0.659104\pi\)
\(510\) −2.42305e14 −0.310975
\(511\) 1.69478e14 0.215178
\(512\) −1.09976e15 −1.38137
\(513\) −1.99676e14 −0.248131
\(514\) 1.06072e14 0.130408
\(515\) 1.45392e15 1.76848
\(516\) −3.62488e13 −0.0436235
\(517\) 4.46363e14 0.531484
\(518\) −1.25132e14 −0.147419
\(519\) −3.11710e14 −0.363354
\(520\) 2.56328e14 0.295650
\(521\) 1.57532e15 1.79789 0.898943 0.438066i \(-0.144336\pi\)
0.898943 + 0.438066i \(0.144336\pi\)
\(522\) −5.18298e14 −0.585318
\(523\) 1.23678e15 1.38208 0.691039 0.722818i \(-0.257153\pi\)
0.691039 + 0.722818i \(0.257153\pi\)
\(524\) 1.10384e15 1.22063
\(525\) 2.71898e12 0.00297530
\(526\) 1.87753e15 2.03313
\(527\) 1.40519e14 0.150584
\(528\) 2.28751e14 0.242592
\(529\) −7.34087e14 −0.770445
\(530\) −2.28549e15 −2.37390
\(531\) −4.22156e13 −0.0433963
\(532\) 2.48166e14 0.252480
\(533\) 2.96336e13 0.0298390
\(534\) −1.43175e15 −1.42689
\(535\) −1.18455e13 −0.0116844
\(536\) 2.78331e14 0.271741
\(537\) 2.67223e14 0.258235
\(538\) 1.41802e15 1.35638
\(539\) −5.08850e14 −0.481783
\(540\) −2.29650e14 −0.215229
\(541\) 1.52839e15 1.41791 0.708957 0.705251i \(-0.249166\pi\)
0.708957 + 0.705251i \(0.249166\pi\)
\(542\) 1.74017e15 1.59807
\(543\) −5.97213e14 −0.542913
\(544\) −5.96521e14 −0.536824
\(545\) 1.77869e15 1.58460
\(546\) −2.50187e14 −0.220650
\(547\) 2.00393e15 1.74965 0.874827 0.484436i \(-0.160975\pi\)
0.874827 + 0.484436i \(0.160975\pi\)
\(548\) 1.96163e15 1.69560
\(549\) 6.65795e13 0.0569761
\(550\) 2.55918e13 0.0216824
\(551\) 1.84699e15 1.54928
\(552\) −6.59308e13 −0.0547549
\(553\) −3.29730e14 −0.271126
\(554\) 2.44503e15 1.99058
\(555\) −4.12645e14 −0.332633
\(556\) −7.69550e14 −0.614222
\(557\) −8.50142e14 −0.671874 −0.335937 0.941884i \(-0.609053\pi\)
−0.335937 + 0.941884i \(0.609053\pi\)
\(558\) 2.50473e14 0.196008
\(559\) −1.30227e14 −0.100911
\(560\) −1.87332e14 −0.143740
\(561\) 1.41198e14 0.107284
\(562\) 1.07154e15 0.806228
\(563\) 1.76992e15 1.31873 0.659367 0.751821i \(-0.270824\pi\)
0.659367 + 0.751821i \(0.270824\pi\)
\(564\) −9.50976e14 −0.701673
\(565\) −1.23077e15 −0.899309
\(566\) −3.46856e15 −2.50992
\(567\) 2.67399e13 0.0191625
\(568\) 9.17721e13 0.0651320
\(569\) −7.42644e14 −0.521991 −0.260996 0.965340i \(-0.584051\pi\)
−0.260996 + 0.965340i \(0.584051\pi\)
\(570\) 1.53912e15 1.07142
\(571\) 1.42799e15 0.984527 0.492263 0.870446i \(-0.336170\pi\)
0.492263 + 0.870446i \(0.336170\pi\)
\(572\) −1.25210e15 −0.854989
\(573\) 4.11170e14 0.278081
\(574\) 7.40312e12 0.00495906
\(575\) 2.15781e13 0.0143166
\(576\) −6.34073e14 −0.416692
\(577\) −5.49111e14 −0.357432 −0.178716 0.983901i \(-0.557194\pi\)
−0.178716 + 0.983901i \(0.557194\pi\)
\(578\) 1.94906e15 1.25667
\(579\) −1.03396e14 −0.0660346
\(580\) 2.12424e15 1.34385
\(581\) −8.95899e13 −0.0561423
\(582\) 2.52758e15 1.56902
\(583\) 1.33182e15 0.818973
\(584\) −4.05429e14 −0.246970
\(585\) −8.25038e14 −0.497871
\(586\) 1.25894e15 0.752608
\(587\) 1.98082e15 1.17310 0.586550 0.809913i \(-0.300486\pi\)
0.586550 + 0.809913i \(0.300486\pi\)
\(588\) 1.08410e15 0.636057
\(589\) −8.92578e14 −0.518814
\(590\) 3.25400e14 0.187384
\(591\) −9.59344e14 −0.547322
\(592\) −8.75698e14 −0.494977
\(593\) 3.24270e15 1.81596 0.907981 0.419012i \(-0.137624\pi\)
0.907981 + 0.419012i \(0.137624\pi\)
\(594\) 2.51683e14 0.139646
\(595\) −1.15632e14 −0.0635676
\(596\) 1.77469e15 0.966646
\(597\) −3.20404e14 −0.172918
\(598\) −1.98550e15 −1.06173
\(599\) 3.16947e15 1.67934 0.839670 0.543098i \(-0.182749\pi\)
0.839670 + 0.543098i \(0.182749\pi\)
\(600\) −6.50441e12 −0.00341488
\(601\) −3.20242e15 −1.66598 −0.832989 0.553290i \(-0.813372\pi\)
−0.832989 + 0.553290i \(0.813372\pi\)
\(602\) −3.25336e13 −0.0167707
\(603\) −8.95857e14 −0.457608
\(604\) −2.05688e15 −1.04113
\(605\) −1.47949e15 −0.742094
\(606\) −3.32762e15 −1.65400
\(607\) −3.31168e14 −0.163121 −0.0815606 0.996668i \(-0.525990\pi\)
−0.0815606 + 0.996668i \(0.525990\pi\)
\(608\) 3.78909e15 1.84955
\(609\) −2.47342e14 −0.119647
\(610\) −5.13199e14 −0.246021
\(611\) −3.41647e15 −1.62312
\(612\) −3.00823e14 −0.141637
\(613\) 1.67829e15 0.783131 0.391566 0.920150i \(-0.371934\pi\)
0.391566 + 0.920150i \(0.371934\pi\)
\(614\) 1.12261e15 0.519160
\(615\) 2.44132e13 0.0111895
\(616\) −3.73159e13 −0.0169512
\(617\) −2.13368e15 −0.960640 −0.480320 0.877093i \(-0.659480\pi\)
−0.480320 + 0.877093i \(0.659480\pi\)
\(618\) 3.39477e15 1.51486
\(619\) −1.97750e14 −0.0874617 −0.0437309 0.999043i \(-0.513924\pi\)
−0.0437309 + 0.999043i \(0.513924\pi\)
\(620\) −1.02656e15 −0.450020
\(621\) 2.12210e14 0.0922065
\(622\) 1.78274e15 0.767786
\(623\) −6.83258e14 −0.291676
\(624\) −1.75086e15 −0.740860
\(625\) −2.31081e15 −0.969226
\(626\) −2.03519e15 −0.846146
\(627\) −8.96889e14 −0.369630
\(628\) −2.84111e15 −1.16068
\(629\) −5.40531e14 −0.218898
\(630\) −2.06112e14 −0.0827430
\(631\) −5.35469e13 −0.0213095 −0.0106547 0.999943i \(-0.503392\pi\)
−0.0106547 + 0.999943i \(0.503392\pi\)
\(632\) 7.88788e14 0.311183
\(633\) −1.45798e15 −0.570206
\(634\) 1.89604e15 0.735116
\(635\) 8.49731e14 0.326607
\(636\) −2.83745e15 −1.08122
\(637\) 3.89474e15 1.47134
\(638\) −2.32805e15 −0.871924
\(639\) −2.95385e14 −0.109681
\(640\) 1.04947e15 0.386349
\(641\) 1.18003e14 0.0430699 0.0215350 0.999768i \(-0.493145\pi\)
0.0215350 + 0.999768i \(0.493145\pi\)
\(642\) −2.76581e13 −0.0100087
\(643\) −5.38608e15 −1.93247 −0.966234 0.257666i \(-0.917047\pi\)
−0.966234 + 0.257666i \(0.917047\pi\)
\(644\) −2.63743e14 −0.0938228
\(645\) −1.07286e14 −0.0378411
\(646\) 2.01612e15 0.705077
\(647\) −2.44963e15 −0.849429 −0.424714 0.905327i \(-0.639625\pi\)
−0.424714 + 0.905327i \(0.639625\pi\)
\(648\) −6.39676e13 −0.0219937
\(649\) −1.89620e14 −0.0646456
\(650\) −1.95880e14 −0.0662166
\(651\) 1.19530e14 0.0400667
\(652\) 4.50029e15 1.49582
\(653\) −1.91375e15 −0.630758 −0.315379 0.948966i \(-0.602132\pi\)
−0.315379 + 0.948966i \(0.602132\pi\)
\(654\) 4.15308e15 1.35735
\(655\) 3.26704e15 1.05883
\(656\) 5.18086e13 0.0166506
\(657\) 1.30495e15 0.415894
\(658\) −8.53508e14 −0.269752
\(659\) 5.66582e14 0.177580 0.0887898 0.996050i \(-0.471700\pi\)
0.0887898 + 0.996050i \(0.471700\pi\)
\(660\) −1.03152e15 −0.320617
\(661\) 1.39801e15 0.430924 0.215462 0.976512i \(-0.430874\pi\)
0.215462 + 0.976512i \(0.430874\pi\)
\(662\) −5.55424e15 −1.69787
\(663\) −1.08073e15 −0.327637
\(664\) 2.14319e14 0.0644371
\(665\) 7.34495e14 0.219013
\(666\) −9.63486e14 −0.284929
\(667\) −1.96293e15 −0.575721
\(668\) −3.88162e15 −1.12913
\(669\) −6.11079e14 −0.176301
\(670\) 6.90532e15 1.97593
\(671\) 2.99056e14 0.0848749
\(672\) −5.07420e14 −0.142836
\(673\) 2.62224e15 0.732133 0.366067 0.930589i \(-0.380704\pi\)
0.366067 + 0.930589i \(0.380704\pi\)
\(674\) −5.26383e14 −0.145771
\(675\) 2.09356e13 0.00575062
\(676\) 5.41606e15 1.47563
\(677\) −1.68017e15 −0.454062 −0.227031 0.973888i \(-0.572902\pi\)
−0.227031 + 0.973888i \(0.572902\pi\)
\(678\) −2.87372e15 −0.770338
\(679\) 1.20621e15 0.320730
\(680\) 2.76618e14 0.0729595
\(681\) −3.82890e14 −0.100176
\(682\) 1.12505e15 0.291984
\(683\) 6.60997e14 0.170171 0.0850855 0.996374i \(-0.472884\pi\)
0.0850855 + 0.996374i \(0.472884\pi\)
\(684\) 1.91082e15 0.487991
\(685\) 5.80583e15 1.47084
\(686\) 1.97581e15 0.496550
\(687\) −3.75767e15 −0.936821
\(688\) −2.27677e14 −0.0563096
\(689\) −1.01938e16 −2.50109
\(690\) −1.63573e15 −0.398144
\(691\) 3.54965e15 0.857149 0.428574 0.903507i \(-0.359016\pi\)
0.428574 + 0.903507i \(0.359016\pi\)
\(692\) 2.98293e15 0.714595
\(693\) 1.20108e14 0.0285456
\(694\) −1.12507e15 −0.265279
\(695\) −2.27764e15 −0.532804
\(696\) 5.91696e14 0.137324
\(697\) 3.19793e13 0.00736357
\(698\) −1.02898e16 −2.35073
\(699\) −1.87057e15 −0.423984
\(700\) −2.60196e13 −0.00585142
\(701\) −3.81648e15 −0.851558 −0.425779 0.904827i \(-0.640000\pi\)
−0.425779 + 0.904827i \(0.640000\pi\)
\(702\) −1.92638e15 −0.426470
\(703\) 3.43345e15 0.754182
\(704\) −2.84808e15 −0.620729
\(705\) −2.81460e15 −0.608663
\(706\) −6.57852e15 −1.41157
\(707\) −1.58800e15 −0.338100
\(708\) 4.03986e14 0.0853460
\(709\) 4.42457e15 0.927507 0.463753 0.885964i \(-0.346502\pi\)
0.463753 + 0.885964i \(0.346502\pi\)
\(710\) 2.27684e15 0.473600
\(711\) −2.53885e15 −0.524028
\(712\) 1.63450e15 0.334770
\(713\) 9.48604e14 0.192794
\(714\) −2.69990e14 −0.0544513
\(715\) −3.70584e15 −0.741657
\(716\) −2.55721e15 −0.507861
\(717\) 2.19399e15 0.432393
\(718\) −1.08807e16 −2.12800
\(719\) −3.23176e15 −0.627235 −0.313617 0.949549i \(-0.601541\pi\)
−0.313617 + 0.949549i \(0.601541\pi\)
\(720\) −1.44242e15 −0.277819
\(721\) 1.62005e15 0.309659
\(722\) −5.10264e15 −0.967923
\(723\) 3.42413e15 0.644598
\(724\) 5.71509e15 1.06773
\(725\) −1.93653e14 −0.0359058
\(726\) −3.45448e15 −0.635669
\(727\) 4.85991e15 0.887543 0.443771 0.896140i \(-0.353640\pi\)
0.443771 + 0.896140i \(0.353640\pi\)
\(728\) 2.85616e14 0.0517679
\(729\) 2.05891e14 0.0370370
\(730\) −1.00586e16 −1.79582
\(731\) −1.40535e14 −0.0249023
\(732\) −6.37139e14 −0.112053
\(733\) −7.63492e15 −1.33270 −0.666350 0.745639i \(-0.732144\pi\)
−0.666350 + 0.745639i \(0.732144\pi\)
\(734\) −9.08765e15 −1.57443
\(735\) 3.20862e15 0.551745
\(736\) −4.02693e15 −0.687300
\(737\) −4.02394e15 −0.681679
\(738\) 5.70025e13 0.00958481
\(739\) 5.02289e15 0.838319 0.419159 0.907913i \(-0.362325\pi\)
0.419159 + 0.907913i \(0.362325\pi\)
\(740\) 3.94885e15 0.654178
\(741\) 6.86479e15 1.12883
\(742\) −2.54663e15 −0.415666
\(743\) 4.65787e15 0.754655 0.377328 0.926080i \(-0.376843\pi\)
0.377328 + 0.926080i \(0.376843\pi\)
\(744\) −2.85943e14 −0.0459863
\(745\) 5.25254e15 0.838514
\(746\) −7.26597e15 −1.15141
\(747\) −6.89823e14 −0.108511
\(748\) −1.35121e15 −0.210991
\(749\) −1.31990e13 −0.00204592
\(750\) −5.56187e15 −0.855823
\(751\) −3.09246e15 −0.472373 −0.236186 0.971708i \(-0.575898\pi\)
−0.236186 + 0.971708i \(0.575898\pi\)
\(752\) −5.97303e15 −0.905726
\(753\) 4.59489e14 0.0691677
\(754\) 1.78189e16 2.66280
\(755\) −6.08775e15 −0.903127
\(756\) −2.55890e14 −0.0376862
\(757\) −7.13211e15 −1.04278 −0.521388 0.853320i \(-0.674585\pi\)
−0.521388 + 0.853320i \(0.674585\pi\)
\(758\) −1.64045e16 −2.38112
\(759\) 9.53187e14 0.137356
\(760\) −1.75708e15 −0.251371
\(761\) −2.50666e15 −0.356024 −0.178012 0.984028i \(-0.556967\pi\)
−0.178012 + 0.984028i \(0.556967\pi\)
\(762\) 1.98404e15 0.279768
\(763\) 1.98193e15 0.277461
\(764\) −3.93473e15 −0.546892
\(765\) −8.90344e14 −0.122863
\(766\) −8.97968e15 −1.23028
\(767\) 1.45136e15 0.197424
\(768\) −2.89354e15 −0.390790
\(769\) −1.13780e16 −1.52571 −0.762856 0.646569i \(-0.776203\pi\)
−0.762856 + 0.646569i \(0.776203\pi\)
\(770\) −9.25799e14 −0.123259
\(771\) 3.89760e14 0.0515226
\(772\) 9.89457e14 0.129868
\(773\) 5.28918e15 0.689288 0.344644 0.938733i \(-0.388000\pi\)
0.344644 + 0.938733i \(0.388000\pi\)
\(774\) −2.50502e14 −0.0324142
\(775\) 9.35846e13 0.0120239
\(776\) −2.88552e15 −0.368116
\(777\) −4.59794e14 −0.0582435
\(778\) −5.25333e15 −0.660765
\(779\) −2.03132e14 −0.0253701
\(780\) 7.89528e15 0.979145
\(781\) −1.32678e15 −0.163388
\(782\) −2.14267e15 −0.262010
\(783\) −1.90448e15 −0.231252
\(784\) 6.80921e15 0.821028
\(785\) −8.40885e15 −1.00682
\(786\) 7.62822e15 0.906983
\(787\) 5.05298e15 0.596605 0.298302 0.954471i \(-0.403580\pi\)
0.298302 + 0.954471i \(0.403580\pi\)
\(788\) 9.18053e15 1.07640
\(789\) 6.89894e15 0.803265
\(790\) 1.95696e16 2.26274
\(791\) −1.37139e15 −0.157468
\(792\) −2.87325e14 −0.0327630
\(793\) −2.28898e15 −0.259203
\(794\) −1.00712e15 −0.113257
\(795\) −8.39800e15 −0.937900
\(796\) 3.06614e15 0.340071
\(797\) 1.24735e16 1.37394 0.686970 0.726686i \(-0.258940\pi\)
0.686970 + 0.726686i \(0.258940\pi\)
\(798\) 1.71498e15 0.187604
\(799\) −3.68690e15 −0.400547
\(800\) −3.97277e14 −0.0428646
\(801\) −5.26094e15 −0.563748
\(802\) −1.77475e16 −1.88876
\(803\) 5.86144e15 0.619540
\(804\) 8.57299e15 0.899962
\(805\) −7.80599e14 −0.0813862
\(806\) −8.61117e15 −0.891701
\(807\) 5.21049e15 0.535888
\(808\) 3.79886e15 0.388052
\(809\) 5.04702e15 0.512057 0.256029 0.966669i \(-0.417586\pi\)
0.256029 + 0.966669i \(0.417586\pi\)
\(810\) −1.58702e15 −0.159925
\(811\) 1.93186e15 0.193358 0.0966789 0.995316i \(-0.469178\pi\)
0.0966789 + 0.995316i \(0.469178\pi\)
\(812\) 2.36696e15 0.235306
\(813\) 6.39424e15 0.631380
\(814\) −4.32771e15 −0.424447
\(815\) 1.33195e16 1.29754
\(816\) −1.88945e15 −0.182827
\(817\) 8.92679e14 0.0857974
\(818\) 2.48651e16 2.37382
\(819\) −9.19306e14 −0.0871764
\(820\) −2.33624e14 −0.0220060
\(821\) 4.37286e15 0.409146 0.204573 0.978851i \(-0.434419\pi\)
0.204573 + 0.978851i \(0.434419\pi\)
\(822\) 1.35561e16 1.25991
\(823\) 7.49452e15 0.691902 0.345951 0.938253i \(-0.387556\pi\)
0.345951 + 0.938253i \(0.387556\pi\)
\(824\) −3.87551e15 −0.355410
\(825\) 9.40367e13 0.00856645
\(826\) 3.62580e14 0.0328106
\(827\) −1.90369e16 −1.71126 −0.855629 0.517590i \(-0.826829\pi\)
−0.855629 + 0.517590i \(0.826829\pi\)
\(828\) −2.03076e15 −0.181339
\(829\) −7.72884e15 −0.685590 −0.342795 0.939410i \(-0.611374\pi\)
−0.342795 + 0.939410i \(0.611374\pi\)
\(830\) 5.31720e15 0.468547
\(831\) 8.98421e15 0.786456
\(832\) 2.17992e16 1.89567
\(833\) 4.20303e15 0.363091
\(834\) −5.31806e15 −0.456394
\(835\) −1.14884e16 −0.979457
\(836\) 8.58287e15 0.726939
\(837\) 9.20359e14 0.0774403
\(838\) −3.35681e15 −0.280598
\(839\) 1.44536e16 1.20029 0.600145 0.799891i \(-0.295110\pi\)
0.600145 + 0.799891i \(0.295110\pi\)
\(840\) 2.35301e14 0.0194127
\(841\) 5.41577e15 0.443897
\(842\) −2.13999e16 −1.74259
\(843\) 3.93734e15 0.318531
\(844\) 1.39523e16 1.12141
\(845\) 1.60299e16 1.28003
\(846\) −6.57183e15 −0.521374
\(847\) −1.64854e15 −0.129939
\(848\) −1.78219e16 −1.39565
\(849\) −1.27452e16 −0.991638
\(850\) −2.11385e14 −0.0163407
\(851\) −3.64896e15 −0.280257
\(852\) 2.82671e15 0.215707
\(853\) −8.00796e15 −0.607159 −0.303579 0.952806i \(-0.598182\pi\)
−0.303579 + 0.952806i \(0.598182\pi\)
\(854\) −5.71837e14 −0.0430779
\(855\) 5.65546e15 0.423306
\(856\) 3.15748e13 0.00234820
\(857\) 1.37390e16 1.01522 0.507610 0.861587i \(-0.330529\pi\)
0.507610 + 0.861587i \(0.330529\pi\)
\(858\) −8.65277e15 −0.635294
\(859\) 1.35946e16 0.991755 0.495878 0.868392i \(-0.334846\pi\)
0.495878 + 0.868392i \(0.334846\pi\)
\(860\) 1.02668e15 0.0744207
\(861\) 2.72026e13 0.00195927
\(862\) 1.51433e16 1.08375
\(863\) 1.57105e16 1.11720 0.558601 0.829437i \(-0.311338\pi\)
0.558601 + 0.829437i \(0.311338\pi\)
\(864\) −3.90703e15 −0.276071
\(865\) 8.82859e15 0.619873
\(866\) 1.43160e16 0.998785
\(867\) 7.16179e15 0.496497
\(868\) −1.14386e15 −0.0787977
\(869\) −1.14038e16 −0.780623
\(870\) 1.46798e16 0.998539
\(871\) 3.07992e16 2.08181
\(872\) −4.74121e15 −0.318455
\(873\) 9.28755e15 0.619902
\(874\) 1.36102e16 0.902717
\(875\) −2.65423e15 −0.174942
\(876\) −1.24878e16 −0.817925
\(877\) −7.13883e15 −0.464654 −0.232327 0.972638i \(-0.574634\pi\)
−0.232327 + 0.972638i \(0.574634\pi\)
\(878\) −2.42378e16 −1.56774
\(879\) 4.62596e15 0.297346
\(880\) −6.47894e15 −0.413856
\(881\) −2.56583e15 −0.162877 −0.0814387 0.996678i \(-0.525951\pi\)
−0.0814387 + 0.996678i \(0.525951\pi\)
\(882\) 7.49183e15 0.472618
\(883\) 1.85749e16 1.16451 0.582254 0.813007i \(-0.302171\pi\)
0.582254 + 0.813007i \(0.302171\pi\)
\(884\) 1.03422e16 0.644353
\(885\) 1.19568e15 0.0740331
\(886\) −2.15791e16 −1.32785
\(887\) −5.83734e15 −0.356973 −0.178486 0.983942i \(-0.557120\pi\)
−0.178486 + 0.983942i \(0.557120\pi\)
\(888\) 1.09993e15 0.0668487
\(889\) 9.46821e14 0.0571885
\(890\) 4.05517e16 2.43424
\(891\) 9.24805e14 0.0551725
\(892\) 5.84778e15 0.346725
\(893\) 2.34191e16 1.38003
\(894\) 1.22642e16 0.718261
\(895\) −7.56858e15 −0.440543
\(896\) 1.16938e15 0.0676492
\(897\) −7.29569e15 −0.419477
\(898\) −2.77705e15 −0.158695
\(899\) −8.51325e15 −0.483523
\(900\) −2.00345e14 −0.0113095
\(901\) −1.10007e16 −0.617211
\(902\) 2.56039e14 0.0142781
\(903\) −1.19544e14 −0.00662591
\(904\) 3.28067e15 0.180733
\(905\) 1.69149e16 0.926197
\(906\) −1.42143e16 −0.773608
\(907\) −6.91706e15 −0.374181 −0.187090 0.982343i \(-0.559906\pi\)
−0.187090 + 0.982343i \(0.559906\pi\)
\(908\) 3.66410e15 0.197013
\(909\) −1.22273e16 −0.653475
\(910\) 7.08607e15 0.376424
\(911\) 1.08098e16 0.570778 0.285389 0.958412i \(-0.407877\pi\)
0.285389 + 0.958412i \(0.407877\pi\)
\(912\) 1.20018e16 0.629903
\(913\) −3.09849e15 −0.161644
\(914\) −1.16928e16 −0.606339
\(915\) −1.88574e15 −0.0971999
\(916\) 3.59594e16 1.84241
\(917\) 3.64033e15 0.185400
\(918\) −2.07887e15 −0.105243
\(919\) −8.23865e15 −0.414592 −0.207296 0.978278i \(-0.566466\pi\)
−0.207296 + 0.978278i \(0.566466\pi\)
\(920\) 1.86737e15 0.0934107
\(921\) 4.12500e15 0.205114
\(922\) −4.45676e16 −2.20292
\(923\) 1.01552e16 0.498976
\(924\) −1.14938e15 −0.0561396
\(925\) −3.59989e14 −0.0174787
\(926\) −3.66912e16 −1.77093
\(927\) 1.24740e16 0.598505
\(928\) 3.61397e16 1.72374
\(929\) −2.99868e16 −1.42182 −0.710909 0.703284i \(-0.751716\pi\)
−0.710909 + 0.703284i \(0.751716\pi\)
\(930\) −7.09418e15 −0.334384
\(931\) −2.66976e16 −1.25098
\(932\) 1.79006e16 0.833834
\(933\) 6.55063e15 0.303343
\(934\) −4.22988e16 −1.94724
\(935\) −3.99917e15 −0.183023
\(936\) 2.19918e15 0.100056
\(937\) 2.94975e16 1.33419 0.667095 0.744973i \(-0.267538\pi\)
0.667095 + 0.744973i \(0.267538\pi\)
\(938\) 7.69432e15 0.345983
\(939\) −7.47826e15 −0.334302
\(940\) 2.69346e16 1.19704
\(941\) −3.09688e16 −1.36830 −0.684150 0.729341i \(-0.739827\pi\)
−0.684150 + 0.729341i \(0.739827\pi\)
\(942\) −1.96338e16 −0.862433
\(943\) 2.15883e14 0.00942765
\(944\) 2.53741e15 0.110165
\(945\) −7.57356e14 −0.0326908
\(946\) −1.12518e15 −0.0482861
\(947\) −1.68641e15 −0.0719514 −0.0359757 0.999353i \(-0.511454\pi\)
−0.0359757 + 0.999353i \(0.511454\pi\)
\(948\) 2.42958e16 1.03059
\(949\) −4.48635e16 −1.89204
\(950\) 1.34272e15 0.0562995
\(951\) 6.96696e15 0.290436
\(952\) 3.08224e14 0.0127751
\(953\) 1.59140e14 0.00655794 0.00327897 0.999995i \(-0.498956\pi\)
0.00327897 + 0.999995i \(0.498956\pi\)
\(954\) −1.96085e16 −0.803394
\(955\) −1.16456e16 −0.474399
\(956\) −2.09956e16 −0.850373
\(957\) −8.55437e15 −0.344487
\(958\) −2.84762e16 −1.14018
\(959\) 6.46920e15 0.257542
\(960\) 1.79589e16 0.710867
\(961\) −2.12944e16 −0.838081
\(962\) 3.31243e16 1.29624
\(963\) −1.01629e14 −0.00395434
\(964\) −3.27675e16 −1.26771
\(965\) 2.92850e15 0.112653
\(966\) −1.82262e15 −0.0697145
\(967\) 2.51928e16 0.958146 0.479073 0.877775i \(-0.340973\pi\)
0.479073 + 0.877775i \(0.340973\pi\)
\(968\) 3.94367e15 0.149137
\(969\) 7.40818e15 0.278568
\(970\) −7.15890e16 −2.67671
\(971\) 3.97901e16 1.47934 0.739672 0.672967i \(-0.234981\pi\)
0.739672 + 0.672967i \(0.234981\pi\)
\(972\) −1.97030e15 −0.0728395
\(973\) −2.53788e15 −0.0932932
\(974\) −1.21789e16 −0.445178
\(975\) −7.19757e14 −0.0261614
\(976\) −4.00184e15 −0.144639
\(977\) −1.75457e16 −0.630594 −0.315297 0.948993i \(-0.602104\pi\)
−0.315297 + 0.948993i \(0.602104\pi\)
\(978\) 3.10998e16 1.11146
\(979\) −2.36307e16 −0.839791
\(980\) −3.07052e16 −1.08510
\(981\) 1.52604e16 0.536274
\(982\) −2.99721e15 −0.104738
\(983\) −4.06557e16 −1.41279 −0.706395 0.707818i \(-0.749680\pi\)
−0.706395 + 0.707818i \(0.749680\pi\)
\(984\) −6.50747e13 −0.00224874
\(985\) 2.71716e16 0.933719
\(986\) 1.92294e16 0.657116
\(987\) −3.13620e15 −0.106576
\(988\) −6.56933e16 −2.22003
\(989\) −9.48712e14 −0.0318827
\(990\) −7.12845e15 −0.238233
\(991\) 3.73863e15 0.124253 0.0621266 0.998068i \(-0.480212\pi\)
0.0621266 + 0.998068i \(0.480212\pi\)
\(992\) −1.74649e16 −0.577234
\(993\) −2.04090e16 −0.670810
\(994\) 2.53699e15 0.0829267
\(995\) 9.07485e15 0.294993
\(996\) 6.60133e15 0.213405
\(997\) 3.08638e16 0.992261 0.496131 0.868248i \(-0.334754\pi\)
0.496131 + 0.868248i \(0.334754\pi\)
\(998\) 3.03165e16 0.969307
\(999\) −3.54031e15 −0.112572
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.1.5 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.12.a.c.1.5 27 1.1 even 1 trivial