Properties

Label 177.10.a.c.1.3
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.1613430010\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-36.7798 q^{2} -81.0000 q^{3} +840.750 q^{4} +2305.05 q^{5} +2979.16 q^{6} -1509.72 q^{7} -12091.4 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q-36.7798 q^{2} -81.0000 q^{3} +840.750 q^{4} +2305.05 q^{5} +2979.16 q^{6} -1509.72 q^{7} -12091.4 q^{8} +6561.00 q^{9} -84779.2 q^{10} +35450.7 q^{11} -68100.8 q^{12} -117653. q^{13} +55527.1 q^{14} -186709. q^{15} +14252.9 q^{16} +466502. q^{17} -241312. q^{18} -91326.6 q^{19} +1.93797e6 q^{20} +122287. q^{21} -1.30387e6 q^{22} +507220. q^{23} +979400. q^{24} +3.36014e6 q^{25} +4.32724e6 q^{26} -531441. q^{27} -1.26930e6 q^{28} +4.06202e6 q^{29} +6.86712e6 q^{30} +3.34831e6 q^{31} +5.66656e6 q^{32} -2.87151e6 q^{33} -1.71578e7 q^{34} -3.47998e6 q^{35} +5.51616e6 q^{36} +1.50859e7 q^{37} +3.35897e6 q^{38} +9.52989e6 q^{39} -2.78712e7 q^{40} -1.13871e7 q^{41} -4.49769e6 q^{42} +5.74084e6 q^{43} +2.98052e7 q^{44} +1.51234e7 q^{45} -1.86554e7 q^{46} -3.17720e7 q^{47} -1.15449e6 q^{48} -3.80744e7 q^{49} -1.23585e8 q^{50} -3.77867e7 q^{51} -9.89167e7 q^{52} -6.11272e6 q^{53} +1.95463e7 q^{54} +8.17158e7 q^{55} +1.82545e7 q^{56} +7.39745e6 q^{57} -1.49400e8 q^{58} +1.21174e7 q^{59} -1.56976e8 q^{60} -2.97629e7 q^{61} -1.23150e8 q^{62} -9.90526e6 q^{63} -2.15712e8 q^{64} -2.71196e8 q^{65} +1.05613e8 q^{66} +2.83881e8 q^{67} +3.92212e8 q^{68} -4.10848e7 q^{69} +1.27993e8 q^{70} +2.32533e7 q^{71} -7.93314e7 q^{72} -2.01972e8 q^{73} -5.54856e8 q^{74} -2.72171e8 q^{75} -7.67828e7 q^{76} -5.35206e7 q^{77} -3.50507e8 q^{78} +1.98003e8 q^{79} +3.28537e7 q^{80} +4.30467e7 q^{81} +4.18816e8 q^{82} +6.95648e8 q^{83} +1.02813e8 q^{84} +1.07531e9 q^{85} -2.11147e8 q^{86} -3.29024e8 q^{87} -4.28647e8 q^{88} -3.82476e8 q^{89} -5.56236e8 q^{90} +1.77623e8 q^{91} +4.26445e8 q^{92} -2.71213e8 q^{93} +1.16857e9 q^{94} -2.10512e8 q^{95} -4.58991e8 q^{96} -1.05403e9 q^{97} +1.40037e9 q^{98} +2.32592e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 36q^{2} - 1782q^{3} + 5718q^{4} + 808q^{5} - 2916q^{6} + 21249q^{7} + 9435q^{8} + 144342q^{9} + 68441q^{10} - 68033q^{11} - 463158q^{12} + 283817q^{13} + 80285q^{14} - 65448q^{15} + 1067674q^{16} + 436893q^{17} + 236196q^{18} + 1207580q^{19} + 4209677q^{20} - 1721169q^{21} + 5460442q^{22} + 2421966q^{23} - 764235q^{24} + 7441842q^{25} - 2736526q^{26} - 11691702q^{27} + 4095246q^{28} - 2320594q^{29} - 5543721q^{30} - 3178024q^{31} - 20786874q^{32} + 5510673q^{33} - 13809336q^{34} - 2630800q^{35} + 37515798q^{36} + 3981807q^{37} - 24156377q^{38} - 22989177q^{39} - 29544450q^{40} - 885225q^{41} - 6503085q^{42} + 12360835q^{43} - 117711882q^{44} + 5301288q^{45} + 161066949q^{46} + 75901252q^{47} - 86481594q^{48} + 170907951q^{49} - 61318927q^{50} - 35388333q^{51} - 100762q^{52} - 34790192q^{53} - 19131876q^{54} + 151773316q^{55} - 417630344q^{56} - 97813980q^{57} - 432929294q^{58} + 266581942q^{59} - 340983837q^{60} - 290555332q^{61} + 158267098q^{62} + 139414689q^{63} - 131794443q^{64} - 650690086q^{65} - 442295802q^{66} + 86645184q^{67} + 62738541q^{68} - 196179246q^{69} + 429714610q^{70} - 36567631q^{71} + 61903035q^{72} + 907807228q^{73} - 171827242q^{74} - 602789202q^{75} + 1744504396q^{76} - 310688725q^{77} + 221658606q^{78} + 2508604687q^{79} + 3509441927q^{80} + 947027862q^{81} + 1759214793q^{82} + 2185672083q^{83} - 331714926q^{84} + 2868860198q^{85} + 2397001564q^{86} + 187968114q^{87} + 7683735877q^{88} + 1320145942q^{89} + 449041401q^{90} + 3894639897q^{91} + 3505964640q^{92} + 257419944q^{93} + 5406355552q^{94} + 3093659122q^{95} + 1683736794q^{96} + 3904552980q^{97} + 6137683116q^{98} - 446364513q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −36.7798 −1.62545 −0.812725 0.582647i \(-0.802017\pi\)
−0.812725 + 0.582647i \(0.802017\pi\)
\(3\) −81.0000 −0.577350
\(4\) 840.750 1.64209
\(5\) 2305.05 1.64936 0.824680 0.565599i \(-0.191355\pi\)
0.824680 + 0.565599i \(0.191355\pi\)
\(6\) 2979.16 0.938454
\(7\) −1509.72 −0.237659 −0.118830 0.992915i \(-0.537914\pi\)
−0.118830 + 0.992915i \(0.537914\pi\)
\(8\) −12091.4 −1.04369
\(9\) 6561.00 0.333333
\(10\) −84779.2 −2.68095
\(11\) 35450.7 0.730059 0.365030 0.930996i \(-0.381059\pi\)
0.365030 + 0.930996i \(0.381059\pi\)
\(12\) −68100.8 −0.948061
\(13\) −117653. −1.14250 −0.571252 0.820775i \(-0.693542\pi\)
−0.571252 + 0.820775i \(0.693542\pi\)
\(14\) 55527.1 0.386303
\(15\) −186709. −0.952259
\(16\) 14252.9 0.0543705
\(17\) 466502. 1.35467 0.677335 0.735675i \(-0.263135\pi\)
0.677335 + 0.735675i \(0.263135\pi\)
\(18\) −241312. −0.541817
\(19\) −91326.6 −0.160770 −0.0803852 0.996764i \(-0.525615\pi\)
−0.0803852 + 0.996764i \(0.525615\pi\)
\(20\) 1.93797e6 2.70840
\(21\) 122287. 0.137213
\(22\) −1.30387e6 −1.18668
\(23\) 507220. 0.377939 0.188969 0.981983i \(-0.439485\pi\)
0.188969 + 0.981983i \(0.439485\pi\)
\(24\) 979400. 0.602573
\(25\) 3.36014e6 1.72039
\(26\) 4.32724e6 1.85708
\(27\) −531441. −0.192450
\(28\) −1.26930e6 −0.390258
\(29\) 4.06202e6 1.06648 0.533239 0.845965i \(-0.320975\pi\)
0.533239 + 0.845965i \(0.320975\pi\)
\(30\) 6.86712e6 1.54785
\(31\) 3.34831e6 0.651176 0.325588 0.945512i \(-0.394438\pi\)
0.325588 + 0.945512i \(0.394438\pi\)
\(32\) 5.66656e6 0.955310
\(33\) −2.87151e6 −0.421500
\(34\) −1.71578e7 −2.20195
\(35\) −3.47998e6 −0.391986
\(36\) 5.51616e6 0.547363
\(37\) 1.50859e7 1.32332 0.661658 0.749806i \(-0.269853\pi\)
0.661658 + 0.749806i \(0.269853\pi\)
\(38\) 3.35897e6 0.261324
\(39\) 9.52989e6 0.659625
\(40\) −2.78712e7 −1.72142
\(41\) −1.13871e7 −0.629342 −0.314671 0.949201i \(-0.601894\pi\)
−0.314671 + 0.949201i \(0.601894\pi\)
\(42\) −4.49769e6 −0.223032
\(43\) 5.74084e6 0.256075 0.128038 0.991769i \(-0.459132\pi\)
0.128038 + 0.991769i \(0.459132\pi\)
\(44\) 2.98052e7 1.19882
\(45\) 1.51234e7 0.549787
\(46\) −1.86554e7 −0.614320
\(47\) −3.17720e7 −0.949738 −0.474869 0.880056i \(-0.657505\pi\)
−0.474869 + 0.880056i \(0.657505\pi\)
\(48\) −1.15449e6 −0.0313908
\(49\) −3.80744e7 −0.943518
\(50\) −1.23585e8 −2.79641
\(51\) −3.77867e7 −0.782119
\(52\) −9.89167e7 −1.87609
\(53\) −6.11272e6 −0.106413 −0.0532063 0.998584i \(-0.516944\pi\)
−0.0532063 + 0.998584i \(0.516944\pi\)
\(54\) 1.95463e7 0.312818
\(55\) 8.17158e7 1.20413
\(56\) 1.82545e7 0.248042
\(57\) 7.39745e6 0.0928208
\(58\) −1.49400e8 −1.73351
\(59\) 1.21174e7 0.130189
\(60\) −1.56976e8 −1.56369
\(61\) −2.97629e7 −0.275227 −0.137614 0.990486i \(-0.543943\pi\)
−0.137614 + 0.990486i \(0.543943\pi\)
\(62\) −1.23150e8 −1.05845
\(63\) −9.90526e6 −0.0792198
\(64\) −2.15712e8 −1.60718
\(65\) −2.71196e8 −1.88440
\(66\) 1.05613e8 0.685127
\(67\) 2.83881e8 1.72107 0.860537 0.509388i \(-0.170128\pi\)
0.860537 + 0.509388i \(0.170128\pi\)
\(68\) 3.92212e8 2.22449
\(69\) −4.10848e7 −0.218203
\(70\) 1.27993e8 0.637154
\(71\) 2.32533e7 0.108598 0.0542990 0.998525i \(-0.482708\pi\)
0.0542990 + 0.998525i \(0.482708\pi\)
\(72\) −7.93314e7 −0.347895
\(73\) −2.01972e8 −0.832411 −0.416205 0.909271i \(-0.636640\pi\)
−0.416205 + 0.909271i \(0.636640\pi\)
\(74\) −5.54856e8 −2.15098
\(75\) −2.72171e8 −0.993268
\(76\) −7.67828e7 −0.263999
\(77\) −5.35206e7 −0.173505
\(78\) −3.50507e8 −1.07219
\(79\) 1.98003e8 0.571939 0.285969 0.958239i \(-0.407684\pi\)
0.285969 + 0.958239i \(0.407684\pi\)
\(80\) 3.28537e7 0.0896766
\(81\) 4.30467e7 0.111111
\(82\) 4.18816e8 1.02296
\(83\) 6.95648e8 1.60893 0.804467 0.593997i \(-0.202451\pi\)
0.804467 + 0.593997i \(0.202451\pi\)
\(84\) 1.02813e8 0.225316
\(85\) 1.07531e9 2.23434
\(86\) −2.11147e8 −0.416237
\(87\) −3.29024e8 −0.615731
\(88\) −4.28647e8 −0.761953
\(89\) −3.82476e8 −0.646173 −0.323086 0.946369i \(-0.604720\pi\)
−0.323086 + 0.946369i \(0.604720\pi\)
\(90\) −5.56236e8 −0.893651
\(91\) 1.77623e8 0.271527
\(92\) 4.26445e8 0.620609
\(93\) −2.71213e8 −0.375956
\(94\) 1.16857e9 1.54375
\(95\) −2.10512e8 −0.265168
\(96\) −4.58991e8 −0.551548
\(97\) −1.05403e9 −1.20888 −0.604438 0.796652i \(-0.706602\pi\)
−0.604438 + 0.796652i \(0.706602\pi\)
\(98\) 1.40037e9 1.53364
\(99\) 2.32592e8 0.243353
\(100\) 2.82504e9 2.82504
\(101\) −8.05218e8 −0.769959 −0.384979 0.922925i \(-0.625791\pi\)
−0.384979 + 0.922925i \(0.625791\pi\)
\(102\) 1.38978e9 1.27130
\(103\) −1.12043e8 −0.0980880 −0.0490440 0.998797i \(-0.515617\pi\)
−0.0490440 + 0.998797i \(0.515617\pi\)
\(104\) 1.42258e9 1.19242
\(105\) 2.81878e8 0.226313
\(106\) 2.24824e8 0.172968
\(107\) 6.59567e8 0.486443 0.243221 0.969971i \(-0.421796\pi\)
0.243221 + 0.969971i \(0.421796\pi\)
\(108\) −4.46809e8 −0.316020
\(109\) −1.38910e9 −0.942572 −0.471286 0.881980i \(-0.656210\pi\)
−0.471286 + 0.881980i \(0.656210\pi\)
\(110\) −3.00549e9 −1.95726
\(111\) −1.22196e9 −0.764017
\(112\) −2.15179e7 −0.0129217
\(113\) 2.63289e9 1.51908 0.759539 0.650462i \(-0.225425\pi\)
0.759539 + 0.650462i \(0.225425\pi\)
\(114\) −2.72076e8 −0.150876
\(115\) 1.16917e9 0.623357
\(116\) 3.41515e9 1.75125
\(117\) −7.71921e8 −0.380835
\(118\) −4.45674e8 −0.211616
\(119\) −7.04287e8 −0.321950
\(120\) 2.25757e9 0.993860
\(121\) −1.10119e9 −0.467014
\(122\) 1.09467e9 0.447369
\(123\) 9.22357e8 0.363351
\(124\) 2.81509e9 1.06929
\(125\) 3.24324e9 1.18818
\(126\) 3.64313e8 0.128768
\(127\) −5.10549e8 −0.174149 −0.0870745 0.996202i \(-0.527752\pi\)
−0.0870745 + 0.996202i \(0.527752\pi\)
\(128\) 5.03256e9 1.65708
\(129\) −4.65008e8 −0.147845
\(130\) 9.97452e9 3.06300
\(131\) 1.13916e9 0.337960 0.168980 0.985619i \(-0.445953\pi\)
0.168980 + 0.985619i \(0.445953\pi\)
\(132\) −2.41422e9 −0.692141
\(133\) 1.37877e8 0.0382086
\(134\) −1.04411e10 −2.79752
\(135\) −1.22500e9 −0.317420
\(136\) −5.64064e9 −1.41385
\(137\) −4.66620e9 −1.13167 −0.565837 0.824517i \(-0.691447\pi\)
−0.565837 + 0.824517i \(0.691447\pi\)
\(138\) 1.51109e9 0.354678
\(139\) 5.88666e9 1.33753 0.668763 0.743476i \(-0.266824\pi\)
0.668763 + 0.743476i \(0.266824\pi\)
\(140\) −2.92579e9 −0.643676
\(141\) 2.57353e9 0.548332
\(142\) −8.55250e8 −0.176521
\(143\) −4.17088e9 −0.834095
\(144\) 9.35133e7 0.0181235
\(145\) 9.36317e9 1.75901
\(146\) 7.42847e9 1.35304
\(147\) 3.08402e9 0.544740
\(148\) 1.26835e10 2.17300
\(149\) −9.79197e9 −1.62754 −0.813770 0.581187i \(-0.802589\pi\)
−0.813770 + 0.581187i \(0.802589\pi\)
\(150\) 1.00104e10 1.61451
\(151\) 9.09556e9 1.42375 0.711874 0.702307i \(-0.247847\pi\)
0.711874 + 0.702307i \(0.247847\pi\)
\(152\) 1.10426e9 0.167794
\(153\) 3.06072e9 0.451557
\(154\) 1.96848e9 0.282024
\(155\) 7.71803e9 1.07402
\(156\) 8.01225e9 1.08316
\(157\) 1.46356e9 0.192248 0.0961240 0.995369i \(-0.469355\pi\)
0.0961240 + 0.995369i \(0.469355\pi\)
\(158\) −7.28250e9 −0.929658
\(159\) 4.95130e8 0.0614373
\(160\) 1.30617e10 1.57565
\(161\) −7.65760e8 −0.0898206
\(162\) −1.58325e9 −0.180606
\(163\) 3.32269e9 0.368677 0.184339 0.982863i \(-0.440986\pi\)
0.184339 + 0.982863i \(0.440986\pi\)
\(164\) −9.57373e9 −1.03344
\(165\) −6.61898e9 −0.695205
\(166\) −2.55858e10 −2.61524
\(167\) −1.00560e8 −0.0100046 −0.00500231 0.999987i \(-0.501592\pi\)
−0.00500231 + 0.999987i \(0.501592\pi\)
\(168\) −1.47862e9 −0.143207
\(169\) 3.23771e9 0.305314
\(170\) −3.95497e10 −3.63181
\(171\) −5.99193e8 −0.0535901
\(172\) 4.82661e9 0.420498
\(173\) 1.68475e10 1.42997 0.714986 0.699138i \(-0.246433\pi\)
0.714986 + 0.699138i \(0.246433\pi\)
\(174\) 1.21014e10 1.00084
\(175\) −5.07286e9 −0.408867
\(176\) 5.05276e8 0.0396937
\(177\) −9.81506e8 −0.0751646
\(178\) 1.40674e10 1.05032
\(179\) −1.84958e10 −1.34659 −0.673294 0.739375i \(-0.735121\pi\)
−0.673294 + 0.739375i \(0.735121\pi\)
\(180\) 1.27150e10 0.902800
\(181\) 9.26293e9 0.641497 0.320749 0.947164i \(-0.396066\pi\)
0.320749 + 0.947164i \(0.396066\pi\)
\(182\) −6.53292e9 −0.441353
\(183\) 2.41080e9 0.158903
\(184\) −6.13298e9 −0.394449
\(185\) 3.47738e10 2.18262
\(186\) 9.97515e9 0.611099
\(187\) 1.65378e10 0.988989
\(188\) −2.67123e10 −1.55956
\(189\) 8.02326e8 0.0457376
\(190\) 7.74259e9 0.431018
\(191\) −2.03676e10 −1.10736 −0.553681 0.832729i \(-0.686777\pi\)
−0.553681 + 0.832729i \(0.686777\pi\)
\(192\) 1.74727e10 0.927906
\(193\) 2.26136e10 1.17317 0.586587 0.809886i \(-0.300471\pi\)
0.586587 + 0.809886i \(0.300471\pi\)
\(194\) 3.87671e10 1.96497
\(195\) 2.19669e10 1.08796
\(196\) −3.20110e10 −1.54934
\(197\) 1.67147e10 0.790679 0.395339 0.918535i \(-0.370627\pi\)
0.395339 + 0.918535i \(0.370627\pi\)
\(198\) −8.55469e9 −0.395558
\(199\) −1.64044e10 −0.741516 −0.370758 0.928730i \(-0.620902\pi\)
−0.370758 + 0.928730i \(0.620902\pi\)
\(200\) −4.06286e10 −1.79555
\(201\) −2.29944e10 −0.993663
\(202\) 2.96157e10 1.25153
\(203\) −6.13251e9 −0.253458
\(204\) −3.17691e10 −1.28431
\(205\) −2.62479e10 −1.03801
\(206\) 4.12090e9 0.159437
\(207\) 3.32787e9 0.125980
\(208\) −1.67690e9 −0.0621185
\(209\) −3.23759e9 −0.117372
\(210\) −1.03674e10 −0.367861
\(211\) −7.46581e8 −0.0259302 −0.0129651 0.999916i \(-0.504127\pi\)
−0.0129651 + 0.999916i \(0.504127\pi\)
\(212\) −5.13927e9 −0.174739
\(213\) −1.88352e9 −0.0626991
\(214\) −2.42587e10 −0.790689
\(215\) 1.32329e10 0.422360
\(216\) 6.42584e9 0.200858
\(217\) −5.05501e9 −0.154758
\(218\) 5.10908e10 1.53210
\(219\) 1.63597e10 0.480593
\(220\) 6.87025e10 1.97729
\(221\) −5.48853e10 −1.54771
\(222\) 4.49433e10 1.24187
\(223\) −4.62018e10 −1.25108 −0.625542 0.780190i \(-0.715122\pi\)
−0.625542 + 0.780190i \(0.715122\pi\)
\(224\) −8.55490e9 −0.227038
\(225\) 2.20459e10 0.573463
\(226\) −9.68371e10 −2.46919
\(227\) −5.67272e10 −1.41800 −0.708998 0.705210i \(-0.750853\pi\)
−0.708998 + 0.705210i \(0.750853\pi\)
\(228\) 6.21941e9 0.152420
\(229\) 9.38022e9 0.225400 0.112700 0.993629i \(-0.464050\pi\)
0.112700 + 0.993629i \(0.464050\pi\)
\(230\) −4.30017e10 −1.01324
\(231\) 4.33517e9 0.100173
\(232\) −4.91154e10 −1.11307
\(233\) −8.40758e10 −1.86883 −0.934414 0.356190i \(-0.884076\pi\)
−0.934414 + 0.356190i \(0.884076\pi\)
\(234\) 2.83911e10 0.619028
\(235\) −7.32361e10 −1.56646
\(236\) 1.01877e10 0.213782
\(237\) −1.60382e10 −0.330209
\(238\) 2.59035e10 0.523314
\(239\) 3.89690e10 0.772555 0.386277 0.922383i \(-0.373761\pi\)
0.386277 + 0.922383i \(0.373761\pi\)
\(240\) −2.66115e9 −0.0517748
\(241\) 4.12574e10 0.787817 0.393908 0.919150i \(-0.371123\pi\)
0.393908 + 0.919150i \(0.371123\pi\)
\(242\) 4.05016e10 0.759107
\(243\) −3.48678e9 −0.0641500
\(244\) −2.50232e10 −0.451948
\(245\) −8.77634e10 −1.55620
\(246\) −3.39241e10 −0.590609
\(247\) 1.07448e10 0.183681
\(248\) −4.04856e10 −0.679623
\(249\) −5.63475e10 −0.928919
\(250\) −1.19285e11 −1.93133
\(251\) 6.27279e10 0.997537 0.498768 0.866735i \(-0.333786\pi\)
0.498768 + 0.866735i \(0.333786\pi\)
\(252\) −8.32785e9 −0.130086
\(253\) 1.79813e10 0.275918
\(254\) 1.87779e10 0.283071
\(255\) −8.71002e10 −1.29000
\(256\) −7.46517e10 −1.08633
\(257\) 1.69603e10 0.242512 0.121256 0.992621i \(-0.461308\pi\)
0.121256 + 0.992621i \(0.461308\pi\)
\(258\) 1.71029e10 0.240315
\(259\) −2.27755e10 −0.314498
\(260\) −2.28008e11 −3.09436
\(261\) 2.66509e10 0.355492
\(262\) −4.18982e10 −0.549338
\(263\) 7.27475e10 0.937599 0.468800 0.883305i \(-0.344687\pi\)
0.468800 + 0.883305i \(0.344687\pi\)
\(264\) 3.47204e10 0.439914
\(265\) −1.40901e10 −0.175513
\(266\) −5.07110e9 −0.0621061
\(267\) 3.09805e10 0.373068
\(268\) 2.38673e11 2.82616
\(269\) 5.34079e10 0.621900 0.310950 0.950426i \(-0.399353\pi\)
0.310950 + 0.950426i \(0.399353\pi\)
\(270\) 4.50552e10 0.515950
\(271\) 7.94110e10 0.894373 0.447187 0.894441i \(-0.352426\pi\)
0.447187 + 0.894441i \(0.352426\pi\)
\(272\) 6.64901e9 0.0736541
\(273\) −1.43874e10 −0.156766
\(274\) 1.71622e11 1.83948
\(275\) 1.19119e11 1.25599
\(276\) −3.45421e10 −0.358309
\(277\) 1.11912e10 0.114214 0.0571068 0.998368i \(-0.481812\pi\)
0.0571068 + 0.998368i \(0.481812\pi\)
\(278\) −2.16510e11 −2.17408
\(279\) 2.19683e10 0.217059
\(280\) 4.20777e10 0.409110
\(281\) 2.08069e11 1.99081 0.995404 0.0957622i \(-0.0305288\pi\)
0.995404 + 0.0957622i \(0.0305288\pi\)
\(282\) −9.46538e10 −0.891286
\(283\) 7.63522e10 0.707591 0.353796 0.935323i \(-0.384891\pi\)
0.353796 + 0.935323i \(0.384891\pi\)
\(284\) 1.95502e10 0.178328
\(285\) 1.70515e10 0.153095
\(286\) 1.53404e11 1.35578
\(287\) 1.71914e10 0.149569
\(288\) 3.71783e10 0.318437
\(289\) 9.90362e10 0.835130
\(290\) −3.44375e11 −2.85918
\(291\) 8.53767e10 0.697945
\(292\) −1.69808e11 −1.36689
\(293\) 1.56322e11 1.23913 0.619563 0.784947i \(-0.287310\pi\)
0.619563 + 0.784947i \(0.287310\pi\)
\(294\) −1.13430e11 −0.885449
\(295\) 2.79311e10 0.214728
\(296\) −1.82409e11 −1.38113
\(297\) −1.88400e10 −0.140500
\(298\) 3.60146e11 2.64549
\(299\) −5.96759e10 −0.431796
\(300\) −2.28828e11 −1.63104
\(301\) −8.66705e9 −0.0608586
\(302\) −3.34532e11 −2.31423
\(303\) 6.52227e10 0.444536
\(304\) −1.30167e9 −0.00874117
\(305\) −6.86051e10 −0.453949
\(306\) −1.12573e11 −0.733983
\(307\) 2.12661e11 1.36636 0.683180 0.730250i \(-0.260596\pi\)
0.683180 + 0.730250i \(0.260596\pi\)
\(308\) −4.49975e10 −0.284911
\(309\) 9.07546e9 0.0566311
\(310\) −2.83867e11 −1.74577
\(311\) −3.72002e10 −0.225488 −0.112744 0.993624i \(-0.535964\pi\)
−0.112744 + 0.993624i \(0.535964\pi\)
\(312\) −1.15229e11 −0.688441
\(313\) 2.77044e11 1.63155 0.815774 0.578371i \(-0.196312\pi\)
0.815774 + 0.578371i \(0.196312\pi\)
\(314\) −5.38293e10 −0.312490
\(315\) −2.28321e10 −0.130662
\(316\) 1.66471e11 0.939175
\(317\) 2.39309e11 1.33104 0.665521 0.746379i \(-0.268209\pi\)
0.665521 + 0.746379i \(0.268209\pi\)
\(318\) −1.82108e10 −0.0998634
\(319\) 1.44002e11 0.778591
\(320\) −4.97227e11 −2.65082
\(321\) −5.34249e10 −0.280848
\(322\) 2.81644e10 0.145999
\(323\) −4.26040e10 −0.217791
\(324\) 3.61915e10 0.182454
\(325\) −3.95330e11 −1.96555
\(326\) −1.22208e11 −0.599266
\(327\) 1.12517e11 0.544194
\(328\) 1.37686e11 0.656836
\(329\) 4.79668e10 0.225714
\(330\) 2.43444e11 1.13002
\(331\) 3.48803e11 1.59718 0.798592 0.601873i \(-0.205579\pi\)
0.798592 + 0.601873i \(0.205579\pi\)
\(332\) 5.84866e11 2.64202
\(333\) 9.89786e10 0.441105
\(334\) 3.69857e9 0.0162620
\(335\) 6.54360e11 2.83867
\(336\) 1.74295e9 0.00746032
\(337\) −8.65430e10 −0.365508 −0.182754 0.983159i \(-0.558501\pi\)
−0.182754 + 0.983159i \(0.558501\pi\)
\(338\) −1.19082e11 −0.496274
\(339\) −2.13264e11 −0.877040
\(340\) 9.04068e11 3.66899
\(341\) 1.18700e11 0.475397
\(342\) 2.20382e10 0.0871081
\(343\) 1.18404e11 0.461895
\(344\) −6.94145e10 −0.267262
\(345\) −9.47026e10 −0.359895
\(346\) −6.19647e11 −2.32435
\(347\) 2.19430e11 0.812482 0.406241 0.913766i \(-0.366839\pi\)
0.406241 + 0.913766i \(0.366839\pi\)
\(348\) −2.76627e11 −1.01109
\(349\) −4.39980e11 −1.58752 −0.793759 0.608232i \(-0.791879\pi\)
−0.793759 + 0.608232i \(0.791879\pi\)
\(350\) 1.86579e11 0.664593
\(351\) 6.25256e10 0.219875
\(352\) 2.00884e11 0.697433
\(353\) 4.16655e11 1.42821 0.714103 0.700041i \(-0.246835\pi\)
0.714103 + 0.700041i \(0.246835\pi\)
\(354\) 3.60996e10 0.122176
\(355\) 5.36000e10 0.179117
\(356\) −3.21566e11 −1.06107
\(357\) 5.70472e10 0.185878
\(358\) 6.80271e11 2.18881
\(359\) −2.97015e10 −0.0943743 −0.0471871 0.998886i \(-0.515026\pi\)
−0.0471871 + 0.998886i \(0.515026\pi\)
\(360\) −1.82863e11 −0.573805
\(361\) −3.14347e11 −0.974153
\(362\) −3.40688e11 −1.04272
\(363\) 8.91967e10 0.269630
\(364\) 1.49336e11 0.445871
\(365\) −4.65555e11 −1.37295
\(366\) −8.86686e10 −0.258288
\(367\) −3.18328e11 −0.915961 −0.457980 0.888962i \(-0.651427\pi\)
−0.457980 + 0.888962i \(0.651427\pi\)
\(368\) 7.22936e9 0.0205487
\(369\) −7.47109e10 −0.209781
\(370\) −1.27897e12 −3.54775
\(371\) 9.22848e9 0.0252899
\(372\) −2.28023e11 −0.617354
\(373\) −8.06333e10 −0.215687 −0.107844 0.994168i \(-0.534395\pi\)
−0.107844 + 0.994168i \(0.534395\pi\)
\(374\) −6.08258e11 −1.60755
\(375\) −2.62702e11 −0.685998
\(376\) 3.84166e11 0.991229
\(377\) −4.77909e11 −1.21845
\(378\) −2.95094e10 −0.0743441
\(379\) −2.59164e11 −0.645206 −0.322603 0.946534i \(-0.604558\pi\)
−0.322603 + 0.946534i \(0.604558\pi\)
\(380\) −1.76988e11 −0.435430
\(381\) 4.13545e10 0.100545
\(382\) 7.49115e11 1.79996
\(383\) 3.47447e11 0.825076 0.412538 0.910940i \(-0.364642\pi\)
0.412538 + 0.910940i \(0.364642\pi\)
\(384\) −4.07637e11 −0.956717
\(385\) −1.23368e11 −0.286173
\(386\) −8.31724e11 −1.90694
\(387\) 3.76656e10 0.0853584
\(388\) −8.86179e11 −1.98508
\(389\) 4.61381e11 1.02161 0.510806 0.859696i \(-0.329347\pi\)
0.510806 + 0.859696i \(0.329347\pi\)
\(390\) −8.07936e11 −1.76842
\(391\) 2.36619e11 0.511982
\(392\) 4.60371e11 0.984737
\(393\) −9.22723e10 −0.195121
\(394\) −6.14762e11 −1.28521
\(395\) 4.56407e11 0.943333
\(396\) 1.95552e11 0.399608
\(397\) 4.04008e11 0.816268 0.408134 0.912922i \(-0.366180\pi\)
0.408134 + 0.912922i \(0.366180\pi\)
\(398\) 6.03348e11 1.20530
\(399\) −1.11681e10 −0.0220597
\(400\) 4.78917e10 0.0935385
\(401\) −7.47106e11 −1.44289 −0.721444 0.692473i \(-0.756521\pi\)
−0.721444 + 0.692473i \(0.756521\pi\)
\(402\) 8.45727e11 1.61515
\(403\) −3.93938e11 −0.743970
\(404\) −6.76987e11 −1.26434
\(405\) 9.92249e10 0.183262
\(406\) 2.25552e11 0.411984
\(407\) 5.34806e11 0.966099
\(408\) 4.56892e11 0.816287
\(409\) −6.34261e11 −1.12076 −0.560380 0.828235i \(-0.689345\pi\)
−0.560380 + 0.828235i \(0.689345\pi\)
\(410\) 9.65392e11 1.68724
\(411\) 3.77963e11 0.653372
\(412\) −9.41999e10 −0.161069
\(413\) −1.82938e10 −0.0309406
\(414\) −1.22398e11 −0.204773
\(415\) 1.60351e12 2.65371
\(416\) −6.66687e11 −1.09144
\(417\) −4.76819e11 −0.772221
\(418\) 1.19078e11 0.190782
\(419\) −8.64658e10 −0.137051 −0.0685254 0.997649i \(-0.521829\pi\)
−0.0685254 + 0.997649i \(0.521829\pi\)
\(420\) 2.36989e11 0.371627
\(421\) −5.16689e11 −0.801605 −0.400802 0.916165i \(-0.631269\pi\)
−0.400802 + 0.916165i \(0.631269\pi\)
\(422\) 2.74591e10 0.0421482
\(423\) −2.08456e11 −0.316579
\(424\) 7.39110e10 0.111061
\(425\) 1.56751e12 2.33056
\(426\) 6.92753e10 0.101914
\(427\) 4.49337e10 0.0654104
\(428\) 5.54531e11 0.798783
\(429\) 3.37841e11 0.481565
\(430\) −4.86704e11 −0.686526
\(431\) 9.04621e11 1.26275 0.631377 0.775476i \(-0.282490\pi\)
0.631377 + 0.775476i \(0.282490\pi\)
\(432\) −7.57458e9 −0.0104636
\(433\) 1.92088e10 0.0262607 0.0131303 0.999914i \(-0.495820\pi\)
0.0131303 + 0.999914i \(0.495820\pi\)
\(434\) 1.85922e11 0.251551
\(435\) −7.58417e11 −1.01556
\(436\) −1.16789e12 −1.54779
\(437\) −4.63227e10 −0.0607613
\(438\) −6.01706e11 −0.781180
\(439\) 1.38256e12 1.77661 0.888307 0.459249i \(-0.151882\pi\)
0.888307 + 0.459249i \(0.151882\pi\)
\(440\) −9.88054e11 −1.25674
\(441\) −2.49806e11 −0.314506
\(442\) 2.01867e12 2.51573
\(443\) 4.48443e11 0.553211 0.276605 0.960984i \(-0.410791\pi\)
0.276605 + 0.960984i \(0.410791\pi\)
\(444\) −1.02736e12 −1.25458
\(445\) −8.81626e11 −1.06577
\(446\) 1.69929e12 2.03358
\(447\) 7.93149e11 0.939661
\(448\) 3.25664e11 0.381961
\(449\) −2.49011e11 −0.289141 −0.144571 0.989494i \(-0.546180\pi\)
−0.144571 + 0.989494i \(0.546180\pi\)
\(450\) −8.10841e11 −0.932137
\(451\) −4.03682e11 −0.459457
\(452\) 2.21361e12 2.49446
\(453\) −7.36740e11 −0.822001
\(454\) 2.08641e12 2.30488
\(455\) 4.09430e11 0.447845
\(456\) −8.94452e10 −0.0968758
\(457\) 1.08090e12 1.15921 0.579604 0.814898i \(-0.303207\pi\)
0.579604 + 0.814898i \(0.303207\pi\)
\(458\) −3.45002e11 −0.366376
\(459\) −2.47918e11 −0.260706
\(460\) 9.82979e11 1.02361
\(461\) 1.37122e11 0.141401 0.0707006 0.997498i \(-0.477477\pi\)
0.0707006 + 0.997498i \(0.477477\pi\)
\(462\) −1.59447e11 −0.162827
\(463\) −3.53202e10 −0.0357198 −0.0178599 0.999840i \(-0.505685\pi\)
−0.0178599 + 0.999840i \(0.505685\pi\)
\(464\) 5.78957e10 0.0579849
\(465\) −6.25160e11 −0.620088
\(466\) 3.09229e12 3.03769
\(467\) −5.12926e11 −0.499032 −0.249516 0.968371i \(-0.580272\pi\)
−0.249516 + 0.968371i \(0.580272\pi\)
\(468\) −6.48993e11 −0.625365
\(469\) −4.28580e11 −0.409029
\(470\) 2.69360e12 2.54621
\(471\) −1.18548e11 −0.110994
\(472\) −1.46515e11 −0.135876
\(473\) 2.03517e11 0.186950
\(474\) 5.89882e11 0.536738
\(475\) −3.06870e11 −0.276588
\(476\) −5.92129e11 −0.528671
\(477\) −4.01055e10 −0.0354709
\(478\) −1.43327e12 −1.25575
\(479\) 4.90437e11 0.425671 0.212835 0.977088i \(-0.431730\pi\)
0.212835 + 0.977088i \(0.431730\pi\)
\(480\) −1.05800e12 −0.909702
\(481\) −1.77490e12 −1.51189
\(482\) −1.51744e12 −1.28056
\(483\) 6.20265e10 0.0518579
\(484\) −9.25829e11 −0.766878
\(485\) −2.42960e12 −1.99387
\(486\) 1.28243e11 0.104273
\(487\) 5.75614e11 0.463715 0.231858 0.972750i \(-0.425520\pi\)
0.231858 + 0.972750i \(0.425520\pi\)
\(488\) 3.59874e11 0.287251
\(489\) −2.69138e11 −0.212856
\(490\) 3.22791e12 2.52953
\(491\) −1.50968e12 −1.17225 −0.586123 0.810222i \(-0.699346\pi\)
−0.586123 + 0.810222i \(0.699346\pi\)
\(492\) 7.75472e11 0.596655
\(493\) 1.89494e12 1.44472
\(494\) −3.95192e11 −0.298564
\(495\) 5.36137e11 0.401377
\(496\) 4.77232e10 0.0354048
\(497\) −3.51059e10 −0.0258093
\(498\) 2.07245e12 1.50991
\(499\) −1.49662e12 −1.08059 −0.540293 0.841477i \(-0.681687\pi\)
−0.540293 + 0.841477i \(0.681687\pi\)
\(500\) 2.72675e12 1.95110
\(501\) 8.14534e9 0.00577617
\(502\) −2.30712e12 −1.62145
\(503\) 1.77267e12 1.23473 0.617365 0.786677i \(-0.288200\pi\)
0.617365 + 0.786677i \(0.288200\pi\)
\(504\) 1.19768e11 0.0826806
\(505\) −1.85607e12 −1.26994
\(506\) −6.61349e11 −0.448490
\(507\) −2.62254e11 −0.176273
\(508\) −4.29245e11 −0.285968
\(509\) 1.93992e12 1.28102 0.640508 0.767952i \(-0.278724\pi\)
0.640508 + 0.767952i \(0.278724\pi\)
\(510\) 3.20352e12 2.09682
\(511\) 3.04920e11 0.197830
\(512\) 1.69001e11 0.108686
\(513\) 4.85347e10 0.0309403
\(514\) −6.23795e11 −0.394192
\(515\) −2.58264e11 −0.161782
\(516\) −3.90956e11 −0.242775
\(517\) −1.12634e12 −0.693365
\(518\) 8.37676e11 0.511201
\(519\) −1.36465e12 −0.825595
\(520\) 3.27913e12 1.96672
\(521\) 2.67538e12 1.59080 0.795401 0.606083i \(-0.207260\pi\)
0.795401 + 0.606083i \(0.207260\pi\)
\(522\) −9.80215e11 −0.577835
\(523\) 1.58808e12 0.928141 0.464071 0.885798i \(-0.346388\pi\)
0.464071 + 0.885798i \(0.346388\pi\)
\(524\) 9.57753e11 0.554961
\(525\) 4.10902e11 0.236059
\(526\) −2.67564e12 −1.52402
\(527\) 1.56199e12 0.882128
\(528\) −4.09274e10 −0.0229172
\(529\) −1.54388e12 −0.857162
\(530\) 5.18231e11 0.285287
\(531\) 7.95020e10 0.0433963
\(532\) 1.15920e11 0.0627419
\(533\) 1.33973e12 0.719025
\(534\) −1.13946e12 −0.606404
\(535\) 1.52034e12 0.802319
\(536\) −3.43251e12 −1.79626
\(537\) 1.49816e12 0.777453
\(538\) −1.96433e12 −1.01087
\(539\) −1.34976e12 −0.688824
\(540\) −1.02992e12 −0.521232
\(541\) −3.35888e11 −0.168580 −0.0842901 0.996441i \(-0.526862\pi\)
−0.0842901 + 0.996441i \(0.526862\pi\)
\(542\) −2.92072e12 −1.45376
\(543\) −7.50297e11 −0.370369
\(544\) 2.64346e12 1.29413
\(545\) −3.20195e12 −1.55464
\(546\) 5.29167e11 0.254815
\(547\) 1.21188e12 0.578782 0.289391 0.957211i \(-0.406547\pi\)
0.289391 + 0.957211i \(0.406547\pi\)
\(548\) −3.92311e12 −1.85831
\(549\) −1.95275e11 −0.0917425
\(550\) −4.38118e12 −2.04154
\(551\) −3.70971e11 −0.171458
\(552\) 4.96771e11 0.227735
\(553\) −2.98929e11 −0.135927
\(554\) −4.11610e11 −0.185649
\(555\) −2.81668e12 −1.26014
\(556\) 4.94921e12 2.19634
\(557\) −1.57543e12 −0.693509 −0.346754 0.937956i \(-0.612716\pi\)
−0.346754 + 0.937956i \(0.612716\pi\)
\(558\) −8.07987e11 −0.352818
\(559\) −6.75426e11 −0.292567
\(560\) −4.95998e10 −0.0213125
\(561\) −1.33956e12 −0.570993
\(562\) −7.65274e12 −3.23596
\(563\) −3.96521e12 −1.66333 −0.831664 0.555279i \(-0.812612\pi\)
−0.831664 + 0.555279i \(0.812612\pi\)
\(564\) 2.16370e12 0.900410
\(565\) 6.06895e12 2.50551
\(566\) −2.80821e12 −1.15015
\(567\) −6.49884e10 −0.0264066
\(568\) −2.81164e11 −0.113342
\(569\) −2.86059e12 −1.14407 −0.572033 0.820231i \(-0.693845\pi\)
−0.572033 + 0.820231i \(0.693845\pi\)
\(570\) −6.27150e11 −0.248848
\(571\) 3.50661e12 1.38046 0.690232 0.723589i \(-0.257509\pi\)
0.690232 + 0.723589i \(0.257509\pi\)
\(572\) −3.50667e12 −1.36966
\(573\) 1.64977e12 0.639335
\(574\) −6.32294e11 −0.243117
\(575\) 1.70433e12 0.650202
\(576\) −1.41529e12 −0.535727
\(577\) −2.00934e12 −0.754678 −0.377339 0.926075i \(-0.623161\pi\)
−0.377339 + 0.926075i \(0.623161\pi\)
\(578\) −3.64253e12 −1.35746
\(579\) −1.83170e12 −0.677332
\(580\) 7.87209e12 2.88845
\(581\) −1.05023e12 −0.382378
\(582\) −3.14014e12 −1.13447
\(583\) −2.16700e11 −0.0776875
\(584\) 2.44211e12 0.868776
\(585\) −1.77932e12 −0.628133
\(586\) −5.74948e12 −2.01414
\(587\) −1.63446e12 −0.568201 −0.284101 0.958794i \(-0.591695\pi\)
−0.284101 + 0.958794i \(0.591695\pi\)
\(588\) 2.59289e12 0.894513
\(589\) −3.05790e11 −0.104690
\(590\) −1.02730e12 −0.349031
\(591\) −1.35389e12 −0.456498
\(592\) 2.15018e11 0.0719494
\(593\) 1.82250e12 0.605231 0.302615 0.953113i \(-0.402140\pi\)
0.302615 + 0.953113i \(0.402140\pi\)
\(594\) 6.92930e11 0.228376
\(595\) −1.62342e12 −0.531011
\(596\) −8.23260e12 −2.67257
\(597\) 1.32875e12 0.428114
\(598\) 2.19487e12 0.701863
\(599\) −5.77039e12 −1.83141 −0.915703 0.401856i \(-0.868365\pi\)
−0.915703 + 0.401856i \(0.868365\pi\)
\(600\) 3.29092e12 1.03666
\(601\) 4.99973e12 1.56319 0.781594 0.623787i \(-0.214407\pi\)
0.781594 + 0.623787i \(0.214407\pi\)
\(602\) 3.18772e11 0.0989227
\(603\) 1.86254e12 0.573691
\(604\) 7.64709e12 2.33792
\(605\) −2.53831e12 −0.770274
\(606\) −2.39887e12 −0.722571
\(607\) −4.28668e12 −1.28166 −0.640829 0.767683i \(-0.721409\pi\)
−0.640829 + 0.767683i \(0.721409\pi\)
\(608\) −5.17507e11 −0.153585
\(609\) 4.96734e11 0.146334
\(610\) 2.52328e12 0.737872
\(611\) 3.73807e12 1.08508
\(612\) 2.57330e12 0.741497
\(613\) −2.98840e12 −0.854804 −0.427402 0.904062i \(-0.640571\pi\)
−0.427402 + 0.904062i \(0.640571\pi\)
\(614\) −7.82162e12 −2.22095
\(615\) 2.12608e12 0.599296
\(616\) 6.47137e11 0.181085
\(617\) 3.29595e11 0.0915583 0.0457791 0.998952i \(-0.485423\pi\)
0.0457791 + 0.998952i \(0.485423\pi\)
\(618\) −3.33793e11 −0.0920511
\(619\) 2.70477e12 0.740495 0.370247 0.928933i \(-0.379273\pi\)
0.370247 + 0.928933i \(0.379273\pi\)
\(620\) 6.48893e12 1.76364
\(621\) −2.69558e11 −0.0727343
\(622\) 1.36822e12 0.366520
\(623\) 5.77430e11 0.153569
\(624\) 1.35829e11 0.0358641
\(625\) 9.13056e11 0.239352
\(626\) −1.01896e13 −2.65200
\(627\) 2.62245e11 0.0677647
\(628\) 1.23049e12 0.315688
\(629\) 7.03760e12 1.79266
\(630\) 8.39761e11 0.212385
\(631\) 4.58604e12 1.15161 0.575806 0.817587i \(-0.304689\pi\)
0.575806 + 0.817587i \(0.304689\pi\)
\(632\) −2.39412e12 −0.596925
\(633\) 6.04730e10 0.0149708
\(634\) −8.80172e12 −2.16354
\(635\) −1.17684e12 −0.287235
\(636\) 4.16281e11 0.100886
\(637\) 4.47956e12 1.07797
\(638\) −5.29635e12 −1.26556
\(639\) 1.52565e11 0.0361993
\(640\) 1.16003e13 2.73313
\(641\) −3.90799e12 −0.914308 −0.457154 0.889388i \(-0.651131\pi\)
−0.457154 + 0.889388i \(0.651131\pi\)
\(642\) 1.96495e12 0.456504
\(643\) 2.37716e12 0.548414 0.274207 0.961671i \(-0.411585\pi\)
0.274207 + 0.961671i \(0.411585\pi\)
\(644\) −6.43813e11 −0.147494
\(645\) −1.07187e12 −0.243850
\(646\) 1.56697e12 0.354008
\(647\) −6.73230e12 −1.51041 −0.755204 0.655490i \(-0.772462\pi\)
−0.755204 + 0.655490i \(0.772462\pi\)
\(648\) −5.20493e11 −0.115965
\(649\) 4.29569e11 0.0950456
\(650\) 1.45401e13 3.19491
\(651\) 4.09456e11 0.0893495
\(652\) 2.79356e12 0.605401
\(653\) −7.63732e12 −1.64373 −0.821867 0.569679i \(-0.807068\pi\)
−0.821867 + 0.569679i \(0.807068\pi\)
\(654\) −4.13835e12 −0.884561
\(655\) 2.62583e12 0.557418
\(656\) −1.62300e11 −0.0342177
\(657\) −1.32514e12 −0.277470
\(658\) −1.76421e12 −0.366887
\(659\) 4.30843e11 0.0889887 0.0444943 0.999010i \(-0.485832\pi\)
0.0444943 + 0.999010i \(0.485832\pi\)
\(660\) −5.56491e12 −1.14159
\(661\) 7.63300e12 1.55521 0.777605 0.628753i \(-0.216435\pi\)
0.777605 + 0.628753i \(0.216435\pi\)
\(662\) −1.28289e13 −2.59614
\(663\) 4.44571e12 0.893574
\(664\) −8.41133e12 −1.67922
\(665\) 3.17814e11 0.0630197
\(666\) −3.64041e12 −0.716995
\(667\) 2.06034e12 0.403063
\(668\) −8.45457e10 −0.0164285
\(669\) 3.74234e12 0.722314
\(670\) −2.40672e13 −4.61412
\(671\) −1.05512e12 −0.200932
\(672\) 6.92947e11 0.131081
\(673\) −7.50409e12 −1.41004 −0.705018 0.709189i \(-0.749061\pi\)
−0.705018 + 0.709189i \(0.749061\pi\)
\(674\) 3.18303e12 0.594116
\(675\) −1.78571e12 −0.331089
\(676\) 2.72210e12 0.501354
\(677\) 8.82974e12 1.61547 0.807735 0.589546i \(-0.200693\pi\)
0.807735 + 0.589546i \(0.200693\pi\)
\(678\) 7.84381e12 1.42559
\(679\) 1.59129e12 0.287301
\(680\) −1.30020e13 −2.33195
\(681\) 4.59491e12 0.818681
\(682\) −4.36576e12 −0.772734
\(683\) 2.73826e12 0.481483 0.240741 0.970589i \(-0.422609\pi\)
0.240741 + 0.970589i \(0.422609\pi\)
\(684\) −5.03772e11 −0.0879998
\(685\) −1.07558e13 −1.86654
\(686\) −4.35488e12 −0.750788
\(687\) −7.59798e11 −0.130135
\(688\) 8.18236e10 0.0139229
\(689\) 7.19179e11 0.121577
\(690\) 3.48314e12 0.584992
\(691\) −1.05692e13 −1.76357 −0.881785 0.471651i \(-0.843658\pi\)
−0.881785 + 0.471651i \(0.843658\pi\)
\(692\) 1.41645e13 2.34814
\(693\) −3.51149e11 −0.0578351
\(694\) −8.07059e12 −1.32065
\(695\) 1.35691e13 2.20606
\(696\) 3.97835e12 0.642630
\(697\) −5.31212e12 −0.852550
\(698\) 1.61824e13 2.58043
\(699\) 6.81014e12 1.07897
\(700\) −4.26501e12 −0.671396
\(701\) −4.23002e12 −0.661625 −0.330812 0.943697i \(-0.607323\pi\)
−0.330812 + 0.943697i \(0.607323\pi\)
\(702\) −2.29968e12 −0.357396
\(703\) −1.37774e12 −0.212750
\(704\) −7.64715e12 −1.17334
\(705\) 5.93212e12 0.904397
\(706\) −1.53245e13 −2.32148
\(707\) 1.21565e12 0.182988
\(708\) −8.25202e11 −0.123427
\(709\) 3.88781e12 0.577826 0.288913 0.957355i \(-0.406706\pi\)
0.288913 + 0.957355i \(0.406706\pi\)
\(710\) −1.97140e12 −0.291146
\(711\) 1.29910e12 0.190646
\(712\) 4.62465e12 0.674402
\(713\) 1.69833e12 0.246104
\(714\) −2.09818e12 −0.302135
\(715\) −9.61410e12 −1.37572
\(716\) −1.55504e13 −2.21122
\(717\) −3.15649e12 −0.446035
\(718\) 1.09241e12 0.153401
\(719\) 9.21625e12 1.28610 0.643049 0.765825i \(-0.277669\pi\)
0.643049 + 0.765825i \(0.277669\pi\)
\(720\) 2.15553e11 0.0298922
\(721\) 1.69153e11 0.0233115
\(722\) 1.15616e13 1.58344
\(723\) −3.34185e12 −0.454846
\(724\) 7.78781e12 1.05340
\(725\) 1.36490e13 1.83476
\(726\) −3.28063e12 −0.438271
\(727\) 1.25499e13 1.66623 0.833117 0.553097i \(-0.186554\pi\)
0.833117 + 0.553097i \(0.186554\pi\)
\(728\) −2.14770e12 −0.283389
\(729\) 2.82430e11 0.0370370
\(730\) 1.71230e13 2.23166
\(731\) 2.67811e12 0.346897
\(732\) 2.02688e12 0.260932
\(733\) −2.84612e12 −0.364154 −0.182077 0.983284i \(-0.558282\pi\)
−0.182077 + 0.983284i \(0.558282\pi\)
\(734\) 1.17080e13 1.48885
\(735\) 7.10883e12 0.898473
\(736\) 2.87419e12 0.361048
\(737\) 1.00638e13 1.25649
\(738\) 2.74785e12 0.340988
\(739\) 6.83170e12 0.842615 0.421307 0.906918i \(-0.361571\pi\)
0.421307 + 0.906918i \(0.361571\pi\)
\(740\) 2.92361e13 3.58407
\(741\) −8.70332e11 −0.106048
\(742\) −3.39421e11 −0.0411075
\(743\) 4.95226e12 0.596148 0.298074 0.954543i \(-0.403656\pi\)
0.298074 + 0.954543i \(0.403656\pi\)
\(744\) 3.27933e12 0.392381
\(745\) −2.25710e13 −2.68440
\(746\) 2.96567e12 0.350589
\(747\) 4.56415e12 0.536311
\(748\) 1.39042e13 1.62401
\(749\) −9.95760e11 −0.115608
\(750\) 9.66212e12 1.11506
\(751\) −1.37451e13 −1.57677 −0.788387 0.615180i \(-0.789084\pi\)
−0.788387 + 0.615180i \(0.789084\pi\)
\(752\) −4.52843e11 −0.0516378
\(753\) −5.08096e12 −0.575928
\(754\) 1.75774e13 1.98054
\(755\) 2.09657e13 2.34827
\(756\) 6.74556e11 0.0751052
\(757\) 3.83996e12 0.425006 0.212503 0.977160i \(-0.431838\pi\)
0.212503 + 0.977160i \(0.431838\pi\)
\(758\) 9.53200e12 1.04875
\(759\) −1.45649e12 −0.159301
\(760\) 2.54538e12 0.276752
\(761\) −5.55937e12 −0.600890 −0.300445 0.953799i \(-0.597135\pi\)
−0.300445 + 0.953799i \(0.597135\pi\)
\(762\) −1.52101e12 −0.163431
\(763\) 2.09715e12 0.224011
\(764\) −1.71241e13 −1.81839
\(765\) 7.05512e12 0.744779
\(766\) −1.27790e13 −1.34112
\(767\) −1.42564e12 −0.148741
\(768\) 6.04679e12 0.627190
\(769\) −1.89732e12 −0.195646 −0.0978230 0.995204i \(-0.531188\pi\)
−0.0978230 + 0.995204i \(0.531188\pi\)
\(770\) 4.53744e12 0.465160
\(771\) −1.37378e12 −0.140015
\(772\) 1.90124e13 1.92646
\(773\) −5.99602e12 −0.604026 −0.302013 0.953304i \(-0.597659\pi\)
−0.302013 + 0.953304i \(0.597659\pi\)
\(774\) −1.38533e12 −0.138746
\(775\) 1.12508e13 1.12028
\(776\) 1.27447e13 1.26169
\(777\) 1.84481e12 0.181576
\(778\) −1.69695e13 −1.66058
\(779\) 1.03995e12 0.101180
\(780\) 1.84687e13 1.78653
\(781\) 8.24346e11 0.0792830
\(782\) −8.70280e12 −0.832201
\(783\) −2.15873e12 −0.205244
\(784\) −5.42670e11 −0.0512996
\(785\) 3.37358e12 0.317086
\(786\) 3.39375e12 0.317160
\(787\) 6.16958e10 0.00573283 0.00286642 0.999996i \(-0.499088\pi\)
0.00286642 + 0.999996i \(0.499088\pi\)
\(788\) 1.40529e13 1.29837
\(789\) −5.89255e12 −0.541323
\(790\) −1.67865e13 −1.53334
\(791\) −3.97493e12 −0.361023
\(792\) −2.81236e12 −0.253984
\(793\) 3.50170e12 0.314448
\(794\) −1.48593e13 −1.32680
\(795\) 1.14130e12 0.101332
\(796\) −1.37920e13 −1.21764
\(797\) 2.19638e13 1.92817 0.964086 0.265590i \(-0.0855668\pi\)
0.964086 + 0.265590i \(0.0855668\pi\)
\(798\) 4.10759e11 0.0358570
\(799\) −1.48217e13 −1.28658
\(800\) 1.90404e13 1.64351
\(801\) −2.50942e12 −0.215391
\(802\) 2.74784e13 2.34534
\(803\) −7.16004e12 −0.607709
\(804\) −1.93325e13 −1.63168
\(805\) −1.76512e12 −0.148147
\(806\) 1.44890e13 1.20929
\(807\) −4.32604e12 −0.359054
\(808\) 9.73618e12 0.803595
\(809\) −8.35367e12 −0.685660 −0.342830 0.939397i \(-0.611386\pi\)
−0.342830 + 0.939397i \(0.611386\pi\)
\(810\) −3.64947e12 −0.297884
\(811\) 8.75828e12 0.710927 0.355464 0.934690i \(-0.384323\pi\)
0.355464 + 0.934690i \(0.384323\pi\)
\(812\) −5.15591e12 −0.416201
\(813\) −6.43229e12 −0.516367
\(814\) −1.96700e13 −1.57035
\(815\) 7.65898e12 0.608081
\(816\) −5.38570e11 −0.0425242
\(817\) −5.24291e11 −0.0411693
\(818\) 2.33280e13 1.82174
\(819\) 1.16538e12 0.0905089
\(820\) −2.20679e13 −1.70451
\(821\) −1.34448e13 −1.03278 −0.516392 0.856352i \(-0.672725\pi\)
−0.516392 + 0.856352i \(0.672725\pi\)
\(822\) −1.39014e13 −1.06202
\(823\) 1.50431e13 1.14298 0.571490 0.820609i \(-0.306366\pi\)
0.571490 + 0.820609i \(0.306366\pi\)
\(824\) 1.35475e12 0.102373
\(825\) −9.64866e12 −0.725144
\(826\) 6.72842e11 0.0502924
\(827\) 1.70601e12 0.126825 0.0634126 0.997987i \(-0.479802\pi\)
0.0634126 + 0.997987i \(0.479802\pi\)
\(828\) 2.79791e12 0.206870
\(829\) −2.01122e12 −0.147899 −0.0739493 0.997262i \(-0.523560\pi\)
−0.0739493 + 0.997262i \(0.523560\pi\)
\(830\) −5.89765e13 −4.31348
\(831\) −9.06488e11 −0.0659413
\(832\) 2.53791e13 1.83621
\(833\) −1.77618e13 −1.27816
\(834\) 1.75373e13 1.25521
\(835\) −2.31796e11 −0.0165012
\(836\) −2.72201e12 −0.192735
\(837\) −1.77943e12 −0.125319
\(838\) 3.18019e12 0.222769
\(839\) 1.58548e13 1.10467 0.552336 0.833622i \(-0.313737\pi\)
0.552336 + 0.833622i \(0.313737\pi\)
\(840\) −3.40829e12 −0.236200
\(841\) 1.99289e12 0.137373
\(842\) 1.90037e13 1.30297
\(843\) −1.68536e13 −1.14939
\(844\) −6.27688e11 −0.0425797
\(845\) 7.46308e12 0.503574
\(846\) 7.66696e12 0.514584
\(847\) 1.66249e12 0.110990
\(848\) −8.71240e10 −0.00578571
\(849\) −6.18453e12 −0.408528
\(850\) −5.76527e13 −3.78821
\(851\) 7.65187e12 0.500132
\(852\) −1.58357e12 −0.102958
\(853\) −1.26290e13 −0.816768 −0.408384 0.912810i \(-0.633907\pi\)
−0.408384 + 0.912810i \(0.633907\pi\)
\(854\) −1.65265e12 −0.106321
\(855\) −1.38117e12 −0.0883894
\(856\) −7.97506e12 −0.507694
\(857\) −3.23239e12 −0.204697 −0.102348 0.994749i \(-0.532636\pi\)
−0.102348 + 0.994749i \(0.532636\pi\)
\(858\) −1.24257e13 −0.782760
\(859\) 2.02618e13 1.26972 0.634860 0.772627i \(-0.281058\pi\)
0.634860 + 0.772627i \(0.281058\pi\)
\(860\) 1.11256e13 0.693554
\(861\) −1.39250e12 −0.0863537
\(862\) −3.32717e13 −2.05255
\(863\) −2.78672e13 −1.71019 −0.855096 0.518470i \(-0.826502\pi\)
−0.855096 + 0.518470i \(0.826502\pi\)
\(864\) −3.01144e12 −0.183849
\(865\) 3.88343e13 2.35854
\(866\) −7.06496e11 −0.0426854
\(867\) −8.02194e12 −0.482162
\(868\) −4.25000e12 −0.254127
\(869\) 7.01935e12 0.417549
\(870\) 2.78944e13 1.65075
\(871\) −3.33994e13 −1.96633
\(872\) 1.67961e13 0.983750
\(873\) −6.91552e12 −0.402959
\(874\) 1.70374e12 0.0987645
\(875\) −4.89637e12 −0.282383
\(876\) 1.37544e13 0.789176
\(877\) −2.46269e12 −0.140576 −0.0702879 0.997527i \(-0.522392\pi\)
−0.0702879 + 0.997527i \(0.522392\pi\)
\(878\) −5.08502e13 −2.88780
\(879\) −1.26621e13 −0.715410
\(880\) 1.16469e12 0.0654692
\(881\) 7.45957e12 0.417179 0.208589 0.978003i \(-0.433113\pi\)
0.208589 + 0.978003i \(0.433113\pi\)
\(882\) 9.18780e12 0.511214
\(883\) −1.66555e13 −0.922006 −0.461003 0.887398i \(-0.652510\pi\)
−0.461003 + 0.887398i \(0.652510\pi\)
\(884\) −4.61448e13 −2.54149
\(885\) −2.26242e12 −0.123974
\(886\) −1.64936e13 −0.899217
\(887\) 3.51781e12 0.190817 0.0954084 0.995438i \(-0.469584\pi\)
0.0954084 + 0.995438i \(0.469584\pi\)
\(888\) 1.47751e13 0.797394
\(889\) 7.70786e11 0.0413881
\(890\) 3.24260e13 1.73236
\(891\) 1.52604e12 0.0811177
\(892\) −3.88441e13 −2.05439
\(893\) 2.90163e12 0.152690
\(894\) −2.91718e13 −1.52737
\(895\) −4.26338e13 −2.22101
\(896\) −7.59775e12 −0.393821
\(897\) 4.83375e12 0.249298
\(898\) 9.15857e12 0.469985
\(899\) 1.36009e13 0.694464
\(900\) 1.85351e13 0.941679
\(901\) −2.85160e12 −0.144154
\(902\) 1.48473e13 0.746825
\(903\) 7.02031e11 0.0351367
\(904\) −3.18352e13 −1.58544
\(905\) 2.13515e13 1.05806
\(906\) 2.70971e13 1.33612
\(907\) 1.64544e13 0.807329 0.403664 0.914907i \(-0.367736\pi\)
0.403664 + 0.914907i \(0.367736\pi\)
\(908\) −4.76934e13 −2.32848
\(909\) −5.28304e12 −0.256653
\(910\) −1.50587e13 −0.727950
\(911\) −5.40184e12 −0.259842 −0.129921 0.991524i \(-0.541472\pi\)
−0.129921 + 0.991524i \(0.541472\pi\)
\(912\) 1.05435e11 0.00504671
\(913\) 2.46612e13 1.17462
\(914\) −3.97551e13 −1.88424
\(915\) 5.55702e12 0.262088
\(916\) 7.88642e12 0.370127
\(917\) −1.71982e12 −0.0803194
\(918\) 9.11837e12 0.423765
\(919\) 1.42308e11 0.00658126 0.00329063 0.999995i \(-0.498953\pi\)
0.00329063 + 0.999995i \(0.498953\pi\)
\(920\) −1.41368e13 −0.650589
\(921\) −1.72255e13 −0.788868
\(922\) −5.04331e12 −0.229841
\(923\) −2.73582e12 −0.124074
\(924\) 3.64480e12 0.164494
\(925\) 5.06907e13 2.27662
\(926\) 1.29907e12 0.0580608
\(927\) −7.35112e11 −0.0326960
\(928\) 2.30177e13 1.01882
\(929\) 4.07512e13 1.79502 0.897511 0.440993i \(-0.145374\pi\)
0.897511 + 0.440993i \(0.145374\pi\)
\(930\) 2.29932e13 1.00792
\(931\) 3.47720e12 0.151690
\(932\) −7.06867e13 −3.06878
\(933\) 3.01322e12 0.130186
\(934\) 1.88653e13 0.811152
\(935\) 3.81206e13 1.63120
\(936\) 9.33357e12 0.397472
\(937\) 3.27907e13 1.38970 0.694852 0.719153i \(-0.255470\pi\)
0.694852 + 0.719153i \(0.255470\pi\)
\(938\) 1.57631e13 0.664857
\(939\) −2.24406e13 −0.941974
\(940\) −6.15732e13 −2.57227
\(941\) 1.88488e13 0.783665 0.391833 0.920037i \(-0.371841\pi\)
0.391833 + 0.920037i \(0.371841\pi\)
\(942\) 4.36017e12 0.180416
\(943\) −5.77578e12 −0.237853
\(944\) 1.72708e11 0.00707844
\(945\) 1.84940e12 0.0754377
\(946\) −7.48530e12 −0.303878
\(947\) 4.28640e13 1.73188 0.865939 0.500149i \(-0.166721\pi\)
0.865939 + 0.500149i \(0.166721\pi\)
\(948\) −1.34841e13 −0.542233
\(949\) 2.37626e13 0.951032
\(950\) 1.12866e13 0.449580
\(951\) −1.93840e13 −0.768478
\(952\) 8.51578e12 0.336015
\(953\) 4.54717e12 0.178576 0.0892880 0.996006i \(-0.471541\pi\)
0.0892880 + 0.996006i \(0.471541\pi\)
\(954\) 1.47507e12 0.0576561
\(955\) −4.69483e13 −1.82644
\(956\) 3.27632e13 1.26860
\(957\) −1.16641e13 −0.449520
\(958\) −1.80382e13 −0.691907
\(959\) 7.04465e12 0.268953
\(960\) 4.02754e13 1.53045
\(961\) −1.52284e13 −0.575970
\(962\) 6.52804e13 2.45751
\(963\) 4.32742e12 0.162148
\(964\) 3.46872e13 1.29367
\(965\) 5.21256e13 1.93499
\(966\) −2.28132e12 −0.0842925
\(967\) 4.06541e12 0.149515 0.0747576 0.997202i \(-0.476182\pi\)
0.0747576 + 0.997202i \(0.476182\pi\)
\(968\) 1.33149e13 0.487416
\(969\) 3.45093e12 0.125741
\(970\) 8.93602e13 3.24094
\(971\) −3.27148e13 −1.18102 −0.590511 0.807030i \(-0.701074\pi\)
−0.590511 + 0.807030i \(0.701074\pi\)
\(972\) −2.93152e12 −0.105340
\(973\) −8.88720e12 −0.317876
\(974\) −2.11710e13 −0.753746
\(975\) 3.20217e13 1.13481
\(976\) −4.24209e11 −0.0149643
\(977\) −2.51558e13 −0.883310 −0.441655 0.897185i \(-0.645609\pi\)
−0.441655 + 0.897185i \(0.645609\pi\)
\(978\) 9.89884e12 0.345987
\(979\) −1.35590e13 −0.471744
\(980\) −7.37871e13 −2.55542
\(981\) −9.11389e12 −0.314191
\(982\) 5.55257e13 1.90543
\(983\) 2.66468e13 0.910236 0.455118 0.890431i \(-0.349597\pi\)
0.455118 + 0.890431i \(0.349597\pi\)
\(984\) −1.11525e13 −0.379224
\(985\) 3.85282e13 1.30411
\(986\) −6.96955e13 −2.34833
\(987\) −3.88531e12 −0.130316
\(988\) 9.03372e12 0.301620
\(989\) 2.91187e12 0.0967806
\(990\) −1.97190e13 −0.652419
\(991\) 1.86088e13 0.612896 0.306448 0.951887i \(-0.400859\pi\)
0.306448 + 0.951887i \(0.400859\pi\)
\(992\) 1.89734e13 0.622074
\(993\) −2.82531e13 −0.922134
\(994\) 1.29119e12 0.0419518
\(995\) −3.78129e13 −1.22303
\(996\) −4.73742e13 −1.52537
\(997\) 4.95421e13 1.58799 0.793993 0.607927i \(-0.207999\pi\)
0.793993 + 0.607927i \(0.207999\pi\)
\(998\) 5.50454e13 1.75644
\(999\) −8.01726e12 −0.254672
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 177.10.a.c.1.3 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.c.1.3 22 1.1 even 1 trivial