Properties

Label 177.10.a.b.1.11
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $1$
Dimension $21$
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: \(1\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.64725 q^{2} -81.0000 q^{3} -504.992 q^{4} +1268.04 q^{5} -214.427 q^{6} +7400.58 q^{7} -2692.23 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+2.64725 q^{2} -81.0000 q^{3} -504.992 q^{4} +1268.04 q^{5} -214.427 q^{6} +7400.58 q^{7} -2692.23 q^{8} +6561.00 q^{9} +3356.80 q^{10} -83963.0 q^{11} +40904.4 q^{12} -20968.8 q^{13} +19591.2 q^{14} -102711. q^{15} +251429. q^{16} +236460. q^{17} +17368.6 q^{18} -382997. q^{19} -640348. q^{20} -599447. q^{21} -222271. q^{22} +605458. q^{23} +218071. q^{24} -345212. q^{25} -55509.5 q^{26} -531441. q^{27} -3.73724e6 q^{28} +1.75753e6 q^{29} -271901. q^{30} -2.07730e6 q^{31} +2.04402e6 q^{32} +6.80100e6 q^{33} +625969. q^{34} +9.38420e6 q^{35} -3.31325e6 q^{36} +1.60852e7 q^{37} -1.01389e6 q^{38} +1.69847e6 q^{39} -3.41384e6 q^{40} +3.00304e7 q^{41} -1.58688e6 q^{42} -2.29946e6 q^{43} +4.24007e7 q^{44} +8.31958e6 q^{45} +1.60280e6 q^{46} -6.22537e7 q^{47} -2.03657e7 q^{48} +1.44150e7 q^{49} -913861. q^{50} -1.91533e7 q^{51} +1.05891e7 q^{52} +5.08411e7 q^{53} -1.40686e6 q^{54} -1.06468e8 q^{55} -1.99241e7 q^{56} +3.10228e7 q^{57} +4.65261e6 q^{58} -1.21174e7 q^{59} +5.18682e7 q^{60} +1.27624e8 q^{61} -5.49914e6 q^{62} +4.85552e7 q^{63} -1.23321e8 q^{64} -2.65891e7 q^{65} +1.80039e7 q^{66} +1.93722e7 q^{67} -1.19411e8 q^{68} -4.90421e7 q^{69} +2.48423e7 q^{70} -2.57271e8 q^{71} -1.76637e7 q^{72} -4.11266e8 q^{73} +4.25816e7 q^{74} +2.79622e7 q^{75} +1.93411e8 q^{76} -6.21375e8 q^{77} +4.49627e6 q^{78} +3.74382e7 q^{79} +3.18821e8 q^{80} +4.30467e7 q^{81} +7.94978e7 q^{82} -4.85239e8 q^{83} +3.02716e8 q^{84} +2.99840e8 q^{85} -6.08724e6 q^{86} -1.42360e8 q^{87} +2.26048e8 q^{88} -1.10415e9 q^{89} +2.20240e7 q^{90} -1.55181e8 q^{91} -3.05751e8 q^{92} +1.68262e8 q^{93} -1.64801e8 q^{94} -4.85654e8 q^{95} -1.65565e8 q^{96} -1.73000e8 q^{97} +3.81601e7 q^{98} -5.50881e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} - 31559q^{10} - 38751q^{11} - 400950q^{12} - 58915q^{13} + 3453q^{14} - 166698q^{15} + 1655714q^{16} - 64233q^{17} + 131220q^{18} - 1937236q^{19} - 1065507q^{20} + 1390527q^{21} - 5386882q^{22} - 1838574q^{23} + 231093q^{24} + 4565755q^{25} - 839702q^{26} - 11160261q^{27} - 4471034q^{28} + 15658544q^{29} + 2556279q^{30} - 14282802q^{31} - 2205286q^{32} + 3138831q^{33} + 19005532q^{34} - 8633300q^{35} + 32476950q^{36} + 7531195q^{37} + 26649773q^{38} + 4772115q^{39} + 17775672q^{40} + 18338245q^{41} - 279693q^{42} - 22480305q^{43} - 80230922q^{44} + 13502538q^{45} - 83894107q^{46} - 110397260q^{47} - 134112834q^{48} + 130653638q^{49} + 65575693q^{50} + 5202873q^{51} + 177908014q^{52} + 145498338q^{53} - 10628820q^{54} + 86448944q^{55} + 354387888q^{56} + 156916116q^{57} + 115508368q^{58} - 254464581q^{59} + 86306067q^{60} + 287595506q^{61} + 819899030q^{62} - 112632687q^{63} + 822446413q^{64} + 77238206q^{65} + 436337442q^{66} - 392860610q^{67} + 167325073q^{68} + 148924494q^{69} - 424902116q^{70} - 248960491q^{71} - 18718533q^{72} - 758406074q^{73} - 923266846q^{74} - 369826155q^{75} - 2312747568q^{76} - 878126795q^{77} + 68015862q^{78} - 1925801029q^{79} - 1898919861q^{80} + 903981141q^{81} - 3249102191q^{82} - 1650336307q^{83} + 362153754q^{84} - 2342480762q^{85} - 3609864952q^{86} - 1268342064q^{87} - 5987792887q^{88} - 574997526q^{89} - 207058599q^{90} - 4481387117q^{91} - 5317166770q^{92} + 1156906962q^{93} - 5360726568q^{94} - 2789231462q^{95} + 178628166q^{96} - 4651540898q^{97} - 5566652976q^{98} - 254245311q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.64725 0.116993 0.0584964 0.998288i \(-0.481369\pi\)
0.0584964 + 0.998288i \(0.481369\pi\)
\(3\) −81.0000 −0.577350
\(4\) −504.992 −0.986313
\(5\) 1268.04 0.907332 0.453666 0.891172i \(-0.350116\pi\)
0.453666 + 0.891172i \(0.350116\pi\)
\(6\) −214.427 −0.0675459
\(7\) 7400.58 1.16500 0.582498 0.812832i \(-0.302075\pi\)
0.582498 + 0.812832i \(0.302075\pi\)
\(8\) −2692.23 −0.232384
\(9\) 6561.00 0.333333
\(10\) 3356.80 0.106151
\(11\) −83963.0 −1.72910 −0.864552 0.502544i \(-0.832398\pi\)
−0.864552 + 0.502544i \(0.832398\pi\)
\(12\) 40904.4 0.569448
\(13\) −20968.8 −0.203623 −0.101812 0.994804i \(-0.532464\pi\)
−0.101812 + 0.994804i \(0.532464\pi\)
\(14\) 19591.2 0.136296
\(15\) −102711. −0.523848
\(16\) 251429. 0.959125
\(17\) 236460. 0.686655 0.343327 0.939216i \(-0.388446\pi\)
0.343327 + 0.939216i \(0.388446\pi\)
\(18\) 17368.6 0.0389976
\(19\) −382997. −0.674225 −0.337112 0.941464i \(-0.609450\pi\)
−0.337112 + 0.941464i \(0.609450\pi\)
\(20\) −640348. −0.894913
\(21\) −599447. −0.672611
\(22\) −222271. −0.202293
\(23\) 605458. 0.451137 0.225568 0.974227i \(-0.427576\pi\)
0.225568 + 0.974227i \(0.427576\pi\)
\(24\) 218071. 0.134167
\(25\) −345212. −0.176749
\(26\) −55509.5 −0.0238225
\(27\) −531441. −0.192450
\(28\) −3.73724e6 −1.14905
\(29\) 1.75753e6 0.461436 0.230718 0.973021i \(-0.425892\pi\)
0.230718 + 0.973021i \(0.425892\pi\)
\(30\) −271901. −0.0612865
\(31\) −2.07730e6 −0.403992 −0.201996 0.979386i \(-0.564743\pi\)
−0.201996 + 0.979386i \(0.564743\pi\)
\(32\) 2.04402e6 0.344595
\(33\) 6.80100e6 0.998298
\(34\) 625969. 0.0803337
\(35\) 9.38420e6 1.05704
\(36\) −3.31325e6 −0.328771
\(37\) 1.60852e7 1.41098 0.705488 0.708722i \(-0.250728\pi\)
0.705488 + 0.708722i \(0.250728\pi\)
\(38\) −1.01389e6 −0.0788795
\(39\) 1.69847e6 0.117562
\(40\) −3.41384e6 −0.210850
\(41\) 3.00304e7 1.65971 0.829857 0.557976i \(-0.188422\pi\)
0.829857 + 0.557976i \(0.188422\pi\)
\(42\) −1.58688e6 −0.0786907
\(43\) −2.29946e6 −0.102570 −0.0512848 0.998684i \(-0.516332\pi\)
−0.0512848 + 0.998684i \(0.516332\pi\)
\(44\) 4.24007e7 1.70544
\(45\) 8.31958e6 0.302444
\(46\) 1.60280e6 0.0527798
\(47\) −6.22537e7 −1.86091 −0.930454 0.366408i \(-0.880587\pi\)
−0.930454 + 0.366408i \(0.880587\pi\)
\(48\) −2.03657e7 −0.553751
\(49\) 1.44150e7 0.357218
\(50\) −913861. −0.0206783
\(51\) −1.91533e7 −0.396440
\(52\) 1.05891e7 0.200836
\(53\) 5.08411e7 0.885062 0.442531 0.896753i \(-0.354081\pi\)
0.442531 + 0.896753i \(0.354081\pi\)
\(54\) −1.40686e6 −0.0225153
\(55\) −1.06468e8 −1.56887
\(56\) −1.99241e7 −0.270727
\(57\) 3.10228e7 0.389264
\(58\) 4.65261e6 0.0539847
\(59\) −1.21174e7 −0.130189
\(60\) 5.18682e7 0.516678
\(61\) 1.27624e8 1.18018 0.590088 0.807339i \(-0.299093\pi\)
0.590088 + 0.807339i \(0.299093\pi\)
\(62\) −5.49914e6 −0.0472642
\(63\) 4.85552e7 0.388332
\(64\) −1.23321e8 −0.918810
\(65\) −2.65891e7 −0.184754
\(66\) 1.80039e7 0.116794
\(67\) 1.93722e7 0.117447 0.0587235 0.998274i \(-0.481297\pi\)
0.0587235 + 0.998274i \(0.481297\pi\)
\(68\) −1.19411e8 −0.677256
\(69\) −4.90421e7 −0.260464
\(70\) 2.48423e7 0.123666
\(71\) −2.57271e8 −1.20151 −0.600756 0.799432i \(-0.705134\pi\)
−0.600756 + 0.799432i \(0.705134\pi\)
\(72\) −1.76637e7 −0.0774615
\(73\) −4.11266e8 −1.69500 −0.847500 0.530796i \(-0.821893\pi\)
−0.847500 + 0.530796i \(0.821893\pi\)
\(74\) 4.25816e7 0.165074
\(75\) 2.79622e7 0.102046
\(76\) 1.93411e8 0.664996
\(77\) −6.21375e8 −2.01440
\(78\) 4.49627e6 0.0137539
\(79\) 3.74382e7 0.108142 0.0540708 0.998537i \(-0.482780\pi\)
0.0540708 + 0.998537i \(0.482780\pi\)
\(80\) 3.18821e8 0.870245
\(81\) 4.30467e7 0.111111
\(82\) 7.94978e7 0.194175
\(83\) −4.85239e8 −1.12229 −0.561144 0.827718i \(-0.689639\pi\)
−0.561144 + 0.827718i \(0.689639\pi\)
\(84\) 3.02716e8 0.663405
\(85\) 2.99840e8 0.623024
\(86\) −6.08724e6 −0.0119999
\(87\) −1.42360e8 −0.266410
\(88\) 2.26048e8 0.401817
\(89\) −1.10415e9 −1.86540 −0.932701 0.360650i \(-0.882555\pi\)
−0.932701 + 0.360650i \(0.882555\pi\)
\(90\) 2.20240e7 0.0353838
\(91\) −1.55181e8 −0.237221
\(92\) −3.05751e8 −0.444962
\(93\) 1.68262e8 0.233245
\(94\) −1.64801e8 −0.217713
\(95\) −4.85654e8 −0.611746
\(96\) −1.65565e8 −0.198952
\(97\) −1.73000e8 −0.198415 −0.0992073 0.995067i \(-0.531631\pi\)
−0.0992073 + 0.995067i \(0.531631\pi\)
\(98\) 3.81601e7 0.0417919
\(99\) −5.50881e8 −0.576368
\(100\) 1.74329e8 0.174329
\(101\) −1.52660e8 −0.145975 −0.0729877 0.997333i \(-0.523253\pi\)
−0.0729877 + 0.997333i \(0.523253\pi\)
\(102\) −5.07035e7 −0.0463807
\(103\) 6.75584e8 0.591441 0.295721 0.955274i \(-0.404440\pi\)
0.295721 + 0.955274i \(0.404440\pi\)
\(104\) 5.64527e7 0.0473189
\(105\) −7.60120e8 −0.610282
\(106\) 1.34589e8 0.103546
\(107\) 1.71946e8 0.126813 0.0634067 0.997988i \(-0.479803\pi\)
0.0634067 + 0.997988i \(0.479803\pi\)
\(108\) 2.68373e8 0.189816
\(109\) −2.23617e9 −1.51735 −0.758675 0.651469i \(-0.774153\pi\)
−0.758675 + 0.651469i \(0.774153\pi\)
\(110\) −2.81847e8 −0.183547
\(111\) −1.30290e9 −0.814628
\(112\) 1.86072e9 1.11738
\(113\) 1.03949e9 0.599746 0.299873 0.953979i \(-0.403056\pi\)
0.299873 + 0.953979i \(0.403056\pi\)
\(114\) 8.21250e7 0.0455411
\(115\) 7.67741e8 0.409331
\(116\) −8.87539e8 −0.455120
\(117\) −1.37576e8 −0.0678745
\(118\) −3.20776e7 −0.0152312
\(119\) 1.74995e9 0.799950
\(120\) 2.76521e8 0.121734
\(121\) 4.69184e9 1.98980
\(122\) 3.37851e8 0.138072
\(123\) −2.43246e9 −0.958236
\(124\) 1.04902e9 0.398462
\(125\) −2.91437e9 −1.06770
\(126\) 1.28538e8 0.0454321
\(127\) −5.55509e8 −0.189485 −0.0947424 0.995502i \(-0.530203\pi\)
−0.0947424 + 0.995502i \(0.530203\pi\)
\(128\) −1.37300e9 −0.452089
\(129\) 1.86256e8 0.0592185
\(130\) −7.03880e7 −0.0216149
\(131\) −5.56674e9 −1.65151 −0.825753 0.564032i \(-0.809250\pi\)
−0.825753 + 0.564032i \(0.809250\pi\)
\(132\) −3.43445e9 −0.984634
\(133\) −2.83440e9 −0.785470
\(134\) 5.12829e7 0.0137405
\(135\) −6.73886e8 −0.174616
\(136\) −6.36606e8 −0.159568
\(137\) 4.06140e9 0.984994 0.492497 0.870314i \(-0.336084\pi\)
0.492497 + 0.870314i \(0.336084\pi\)
\(138\) −1.29826e8 −0.0304724
\(139\) −6.88552e9 −1.56448 −0.782240 0.622977i \(-0.785923\pi\)
−0.782240 + 0.622977i \(0.785923\pi\)
\(140\) −4.73895e9 −1.04257
\(141\) 5.04255e9 1.07440
\(142\) −6.81060e8 −0.140568
\(143\) 1.76060e9 0.352086
\(144\) 1.64963e9 0.319708
\(145\) 2.22861e9 0.418676
\(146\) −1.08872e9 −0.198303
\(147\) −1.16762e9 −0.206240
\(148\) −8.12292e9 −1.39166
\(149\) 4.91341e8 0.0816667 0.0408333 0.999166i \(-0.486999\pi\)
0.0408333 + 0.999166i \(0.486999\pi\)
\(150\) 7.40228e7 0.0119386
\(151\) −2.31149e9 −0.361822 −0.180911 0.983499i \(-0.557905\pi\)
−0.180911 + 0.983499i \(0.557905\pi\)
\(152\) 1.03112e9 0.156679
\(153\) 1.55142e9 0.228885
\(154\) −1.64493e9 −0.235670
\(155\) −2.63410e9 −0.366555
\(156\) −8.57714e8 −0.115953
\(157\) −3.56376e9 −0.468123 −0.234061 0.972222i \(-0.575202\pi\)
−0.234061 + 0.972222i \(0.575202\pi\)
\(158\) 9.91081e7 0.0126518
\(159\) −4.11813e9 −0.510991
\(160\) 2.59188e9 0.312662
\(161\) 4.48074e9 0.525573
\(162\) 1.13955e8 0.0129992
\(163\) 5.02224e9 0.557254 0.278627 0.960399i \(-0.410121\pi\)
0.278627 + 0.960399i \(0.410121\pi\)
\(164\) −1.51651e10 −1.63700
\(165\) 8.62391e9 0.905788
\(166\) −1.28455e9 −0.131300
\(167\) 9.65049e9 0.960120 0.480060 0.877236i \(-0.340615\pi\)
0.480060 + 0.877236i \(0.340615\pi\)
\(168\) 1.61385e9 0.156304
\(169\) −1.01648e10 −0.958537
\(170\) 7.93751e8 0.0728893
\(171\) −2.51285e9 −0.224742
\(172\) 1.16121e9 0.101166
\(173\) −1.56297e10 −1.32661 −0.663305 0.748349i \(-0.730847\pi\)
−0.663305 + 0.748349i \(0.730847\pi\)
\(174\) −3.76862e8 −0.0311681
\(175\) −2.55477e9 −0.205912
\(176\) −2.11107e10 −1.65843
\(177\) 9.81506e8 0.0751646
\(178\) −2.92295e9 −0.218239
\(179\) 8.44559e9 0.614881 0.307441 0.951567i \(-0.400527\pi\)
0.307441 + 0.951567i \(0.400527\pi\)
\(180\) −4.20132e9 −0.298304
\(181\) −2.04552e10 −1.41661 −0.708304 0.705907i \(-0.750539\pi\)
−0.708304 + 0.705907i \(0.750539\pi\)
\(182\) −4.10803e8 −0.0277531
\(183\) −1.03375e10 −0.681375
\(184\) −1.63003e9 −0.104837
\(185\) 2.03966e10 1.28022
\(186\) 4.45430e8 0.0272880
\(187\) −1.98539e10 −1.18730
\(188\) 3.14376e10 1.83544
\(189\) −3.93297e9 −0.224204
\(190\) −1.28565e9 −0.0715699
\(191\) −1.10483e10 −0.600681 −0.300341 0.953832i \(-0.597100\pi\)
−0.300341 + 0.953832i \(0.597100\pi\)
\(192\) 9.98897e9 0.530475
\(193\) 3.46522e9 0.179772 0.0898862 0.995952i \(-0.471350\pi\)
0.0898862 + 0.995952i \(0.471350\pi\)
\(194\) −4.57974e8 −0.0232131
\(195\) 2.15372e9 0.106668
\(196\) −7.27947e9 −0.352328
\(197\) 2.42596e10 1.14759 0.573795 0.818999i \(-0.305471\pi\)
0.573795 + 0.818999i \(0.305471\pi\)
\(198\) −1.45832e9 −0.0674309
\(199\) −3.35206e10 −1.51521 −0.757605 0.652713i \(-0.773631\pi\)
−0.757605 + 0.652713i \(0.773631\pi\)
\(200\) 9.29390e8 0.0410736
\(201\) −1.56915e9 −0.0678080
\(202\) −4.04129e8 −0.0170781
\(203\) 1.30067e10 0.537572
\(204\) 9.67226e9 0.391014
\(205\) 3.80795e10 1.50591
\(206\) 1.78844e9 0.0691944
\(207\) 3.97241e9 0.150379
\(208\) −5.27216e9 −0.195300
\(209\) 3.21576e10 1.16580
\(210\) −2.01223e9 −0.0713986
\(211\) 2.65185e10 0.921039 0.460520 0.887650i \(-0.347663\pi\)
0.460520 + 0.887650i \(0.347663\pi\)
\(212\) −2.56744e10 −0.872948
\(213\) 2.08389e10 0.693693
\(214\) 4.55183e8 0.0148363
\(215\) −2.91580e9 −0.0930646
\(216\) 1.43076e9 0.0447224
\(217\) −1.53733e10 −0.470649
\(218\) −5.91970e9 −0.177519
\(219\) 3.33125e10 0.978609
\(220\) 5.37655e10 1.54740
\(221\) −4.95828e9 −0.139819
\(222\) −3.44911e9 −0.0953056
\(223\) −2.56391e10 −0.694273 −0.347137 0.937815i \(-0.612846\pi\)
−0.347137 + 0.937815i \(0.612846\pi\)
\(224\) 1.51269e10 0.401452
\(225\) −2.26494e9 −0.0589162
\(226\) 2.75179e9 0.0701660
\(227\) 3.49072e8 0.00872567 0.00436283 0.999990i \(-0.498611\pi\)
0.00436283 + 0.999990i \(0.498611\pi\)
\(228\) −1.56663e10 −0.383936
\(229\) −4.41360e10 −1.06055 −0.530277 0.847824i \(-0.677912\pi\)
−0.530277 + 0.847824i \(0.677912\pi\)
\(230\) 2.03240e9 0.0478888
\(231\) 5.03314e10 1.16301
\(232\) −4.73167e9 −0.107231
\(233\) −7.72944e9 −0.171809 −0.0859046 0.996303i \(-0.527378\pi\)
−0.0859046 + 0.996303i \(0.527378\pi\)
\(234\) −3.64198e8 −0.00794083
\(235\) −7.89399e10 −1.68846
\(236\) 6.11917e9 0.128407
\(237\) −3.03249e9 −0.0624356
\(238\) 4.63254e9 0.0935885
\(239\) −5.40150e10 −1.07084 −0.535419 0.844587i \(-0.679846\pi\)
−0.535419 + 0.844587i \(0.679846\pi\)
\(240\) −2.58245e10 −0.502436
\(241\) 3.72961e10 0.712174 0.356087 0.934453i \(-0.384111\pi\)
0.356087 + 0.934453i \(0.384111\pi\)
\(242\) 1.24205e10 0.232792
\(243\) −3.48678e9 −0.0641500
\(244\) −6.44489e10 −1.16402
\(245\) 1.82788e10 0.324115
\(246\) −6.43932e9 −0.112107
\(247\) 8.03099e9 0.137288
\(248\) 5.59258e9 0.0938814
\(249\) 3.93043e10 0.647953
\(250\) −7.71506e9 −0.124913
\(251\) −3.71733e10 −0.591153 −0.295576 0.955319i \(-0.595512\pi\)
−0.295576 + 0.955319i \(0.595512\pi\)
\(252\) −2.45200e10 −0.383017
\(253\) −5.08360e10 −0.780063
\(254\) −1.47057e9 −0.0221684
\(255\) −2.42870e10 −0.359703
\(256\) 5.95055e10 0.865919
\(257\) −2.50707e10 −0.358481 −0.179241 0.983805i \(-0.557364\pi\)
−0.179241 + 0.983805i \(0.557364\pi\)
\(258\) 4.93067e8 0.00692815
\(259\) 1.19040e11 1.64378
\(260\) 1.34273e10 0.182225
\(261\) 1.15312e10 0.153812
\(262\) −1.47365e10 −0.193214
\(263\) −3.73057e10 −0.480811 −0.240405 0.970673i \(-0.577280\pi\)
−0.240405 + 0.970673i \(0.577280\pi\)
\(264\) −1.83099e10 −0.231989
\(265\) 6.44683e10 0.803045
\(266\) −7.50337e9 −0.0918944
\(267\) 8.94361e10 1.07699
\(268\) −9.78279e9 −0.115839
\(269\) −9.05863e10 −1.05482 −0.527409 0.849612i \(-0.676836\pi\)
−0.527409 + 0.849612i \(0.676836\pi\)
\(270\) −1.78394e9 −0.0204288
\(271\) 1.37795e11 1.55193 0.775963 0.630778i \(-0.217264\pi\)
0.775963 + 0.630778i \(0.217264\pi\)
\(272\) 5.94530e10 0.658588
\(273\) 1.25697e10 0.136959
\(274\) 1.07515e10 0.115237
\(275\) 2.89850e10 0.305617
\(276\) 2.47659e10 0.256899
\(277\) 1.13941e11 1.16284 0.581420 0.813603i \(-0.302497\pi\)
0.581420 + 0.813603i \(0.302497\pi\)
\(278\) −1.82277e10 −0.183033
\(279\) −1.36292e10 −0.134664
\(280\) −2.52644e10 −0.245639
\(281\) −7.38986e9 −0.0707062 −0.0353531 0.999375i \(-0.511256\pi\)
−0.0353531 + 0.999375i \(0.511256\pi\)
\(282\) 1.33489e10 0.125697
\(283\) 1.41655e11 1.31278 0.656392 0.754420i \(-0.272082\pi\)
0.656392 + 0.754420i \(0.272082\pi\)
\(284\) 1.29920e11 1.18507
\(285\) 3.93380e10 0.353192
\(286\) 4.66075e9 0.0411916
\(287\) 2.22242e11 1.93356
\(288\) 1.34108e10 0.114865
\(289\) −6.26743e10 −0.528505
\(290\) 5.89968e9 0.0489821
\(291\) 1.40130e10 0.114555
\(292\) 2.07686e11 1.67180
\(293\) 4.52982e10 0.359068 0.179534 0.983752i \(-0.442541\pi\)
0.179534 + 0.983752i \(0.442541\pi\)
\(294\) −3.09097e9 −0.0241286
\(295\) −1.53652e10 −0.118125
\(296\) −4.33051e10 −0.327889
\(297\) 4.46214e10 0.332766
\(298\) 1.30070e9 0.00955442
\(299\) −1.26957e10 −0.0918621
\(300\) −1.41207e10 −0.100649
\(301\) −1.70174e10 −0.119493
\(302\) −6.11908e9 −0.0423306
\(303\) 1.23655e10 0.0842789
\(304\) −9.62967e10 −0.646666
\(305\) 1.61831e11 1.07081
\(306\) 4.10698e9 0.0267779
\(307\) −1.00284e11 −0.644332 −0.322166 0.946683i \(-0.604411\pi\)
−0.322166 + 0.946683i \(0.604411\pi\)
\(308\) 3.13790e11 1.98683
\(309\) −5.47223e10 −0.341469
\(310\) −6.97310e9 −0.0428843
\(311\) −6.47700e10 −0.392602 −0.196301 0.980544i \(-0.562893\pi\)
−0.196301 + 0.980544i \(0.562893\pi\)
\(312\) −4.57267e9 −0.0273196
\(313\) −3.40302e10 −0.200408 −0.100204 0.994967i \(-0.531950\pi\)
−0.100204 + 0.994967i \(0.531950\pi\)
\(314\) −9.43415e9 −0.0547670
\(315\) 6.15697e10 0.352346
\(316\) −1.89060e10 −0.106661
\(317\) 1.62420e11 0.903383 0.451692 0.892174i \(-0.350821\pi\)
0.451692 + 0.892174i \(0.350821\pi\)
\(318\) −1.09017e10 −0.0597823
\(319\) −1.47567e11 −0.797871
\(320\) −1.56375e11 −0.833666
\(321\) −1.39276e10 −0.0732157
\(322\) 1.18616e10 0.0614883
\(323\) −9.05637e10 −0.462960
\(324\) −2.17383e10 −0.109590
\(325\) 7.23867e9 0.0359902
\(326\) 1.32951e10 0.0651948
\(327\) 1.81130e11 0.876043
\(328\) −8.08486e10 −0.385692
\(329\) −4.60714e11 −2.16795
\(330\) 2.28296e10 0.105971
\(331\) −1.18427e11 −0.542281 −0.271141 0.962540i \(-0.587401\pi\)
−0.271141 + 0.962540i \(0.587401\pi\)
\(332\) 2.45042e11 1.10693
\(333\) 1.05535e11 0.470325
\(334\) 2.55472e10 0.112327
\(335\) 2.45646e10 0.106563
\(336\) −1.50718e11 −0.645118
\(337\) −3.82790e11 −1.61669 −0.808343 0.588712i \(-0.799635\pi\)
−0.808343 + 0.588712i \(0.799635\pi\)
\(338\) −2.69088e10 −0.112142
\(339\) −8.41987e10 −0.346264
\(340\) −1.51417e11 −0.614496
\(341\) 1.74417e11 0.698544
\(342\) −6.65212e9 −0.0262932
\(343\) −1.91961e11 −0.748839
\(344\) 6.19068e9 0.0238356
\(345\) −6.21871e10 −0.236327
\(346\) −4.13757e10 −0.155204
\(347\) 3.70788e11 1.37291 0.686457 0.727170i \(-0.259165\pi\)
0.686457 + 0.727170i \(0.259165\pi\)
\(348\) 7.18906e10 0.262764
\(349\) −2.96796e11 −1.07089 −0.535444 0.844571i \(-0.679856\pi\)
−0.535444 + 0.844571i \(0.679856\pi\)
\(350\) −6.76311e9 −0.0240902
\(351\) 1.11437e10 0.0391874
\(352\) −1.71622e11 −0.595841
\(353\) −6.71934e8 −0.00230325 −0.00115162 0.999999i \(-0.500367\pi\)
−0.00115162 + 0.999999i \(0.500367\pi\)
\(354\) 2.59829e9 0.00879372
\(355\) −3.26229e11 −1.09017
\(356\) 5.57586e11 1.83987
\(357\) −1.41746e11 −0.461852
\(358\) 2.23576e10 0.0719367
\(359\) −1.03830e11 −0.329912 −0.164956 0.986301i \(-0.552748\pi\)
−0.164956 + 0.986301i \(0.552748\pi\)
\(360\) −2.23982e10 −0.0702833
\(361\) −1.76001e11 −0.545421
\(362\) −5.41499e10 −0.165733
\(363\) −3.80039e11 −1.14881
\(364\) 7.83652e10 0.233974
\(365\) −5.21499e11 −1.53793
\(366\) −2.73659e10 −0.0797160
\(367\) −1.97639e11 −0.568689 −0.284344 0.958722i \(-0.591776\pi\)
−0.284344 + 0.958722i \(0.591776\pi\)
\(368\) 1.52230e11 0.432697
\(369\) 1.97029e11 0.553238
\(370\) 5.39950e10 0.149777
\(371\) 3.76254e11 1.03109
\(372\) −8.49708e10 −0.230052
\(373\) 5.84644e11 1.56387 0.781937 0.623358i \(-0.214232\pi\)
0.781937 + 0.623358i \(0.214232\pi\)
\(374\) −5.25583e10 −0.138905
\(375\) 2.36064e11 0.616438
\(376\) 1.67601e11 0.432446
\(377\) −3.68532e10 −0.0939592
\(378\) −1.04115e10 −0.0262302
\(379\) −3.90824e11 −0.972982 −0.486491 0.873686i \(-0.661723\pi\)
−0.486491 + 0.873686i \(0.661723\pi\)
\(380\) 2.45252e11 0.603373
\(381\) 4.49962e10 0.109399
\(382\) −2.92475e10 −0.0702754
\(383\) −3.50848e11 −0.833152 −0.416576 0.909101i \(-0.636770\pi\)
−0.416576 + 0.909101i \(0.636770\pi\)
\(384\) 1.11213e11 0.261014
\(385\) −7.87926e11 −1.82773
\(386\) 9.17329e9 0.0210321
\(387\) −1.50868e10 −0.0341898
\(388\) 8.73637e10 0.195699
\(389\) −4.73630e11 −1.04874 −0.524368 0.851492i \(-0.675698\pi\)
−0.524368 + 0.851492i \(0.675698\pi\)
\(390\) 5.70143e9 0.0124794
\(391\) 1.43167e11 0.309775
\(392\) −3.88085e10 −0.0830118
\(393\) 4.50906e11 0.953498
\(394\) 6.42213e10 0.134260
\(395\) 4.74729e10 0.0981204
\(396\) 2.78191e11 0.568479
\(397\) 4.00573e11 0.809327 0.404664 0.914466i \(-0.367389\pi\)
0.404664 + 0.914466i \(0.367389\pi\)
\(398\) −8.87373e10 −0.177269
\(399\) 2.29587e11 0.453491
\(400\) −8.67963e10 −0.169524
\(401\) −5.08723e10 −0.0982497 −0.0491249 0.998793i \(-0.515643\pi\)
−0.0491249 + 0.998793i \(0.515643\pi\)
\(402\) −4.15392e9 −0.00793305
\(403\) 4.35585e10 0.0822622
\(404\) 7.70922e10 0.143977
\(405\) 5.45848e10 0.100815
\(406\) 3.44321e10 0.0628921
\(407\) −1.35057e12 −2.43972
\(408\) 5.15650e10 0.0921265
\(409\) −1.01888e12 −1.80040 −0.900201 0.435475i \(-0.856581\pi\)
−0.900201 + 0.435475i \(0.856581\pi\)
\(410\) 1.00806e11 0.176181
\(411\) −3.28974e11 −0.568687
\(412\) −3.41164e11 −0.583346
\(413\) −8.96755e10 −0.151670
\(414\) 1.05159e10 0.0175933
\(415\) −6.15300e11 −1.01829
\(416\) −4.28605e10 −0.0701677
\(417\) 5.57727e11 0.903253
\(418\) 8.51292e10 0.136391
\(419\) 6.31480e11 1.00091 0.500457 0.865762i \(-0.333166\pi\)
0.500457 + 0.865762i \(0.333166\pi\)
\(420\) 3.83855e11 0.601929
\(421\) 1.07466e12 1.66725 0.833627 0.552328i \(-0.186260\pi\)
0.833627 + 0.552328i \(0.186260\pi\)
\(422\) 7.02010e10 0.107755
\(423\) −4.08447e11 −0.620303
\(424\) −1.36876e11 −0.205675
\(425\) −8.16290e10 −0.121365
\(426\) 5.51658e10 0.0811572
\(427\) 9.44489e11 1.37490
\(428\) −8.68313e10 −0.125078
\(429\) −1.42609e11 −0.203277
\(430\) −7.71884e9 −0.0108879
\(431\) 8.34208e11 1.16446 0.582232 0.813022i \(-0.302179\pi\)
0.582232 + 0.813022i \(0.302179\pi\)
\(432\) −1.33620e11 −0.184584
\(433\) −2.77552e11 −0.379445 −0.189722 0.981838i \(-0.560759\pi\)
−0.189722 + 0.981838i \(0.560759\pi\)
\(434\) −4.06968e10 −0.0550626
\(435\) −1.80517e11 −0.241723
\(436\) 1.12925e12 1.49658
\(437\) −2.31889e11 −0.304168
\(438\) 8.81865e10 0.114490
\(439\) −1.24198e12 −1.59597 −0.797985 0.602677i \(-0.794101\pi\)
−0.797985 + 0.602677i \(0.794101\pi\)
\(440\) 2.86636e11 0.364581
\(441\) 9.45769e10 0.119073
\(442\) −1.31258e10 −0.0163578
\(443\) 1.30548e12 1.61048 0.805238 0.592952i \(-0.202038\pi\)
0.805238 + 0.592952i \(0.202038\pi\)
\(444\) 6.57956e11 0.803478
\(445\) −1.40010e12 −1.69254
\(446\) −6.78729e10 −0.0812250
\(447\) −3.97986e10 −0.0471503
\(448\) −9.12644e11 −1.07041
\(449\) 1.24776e11 0.144885 0.0724423 0.997373i \(-0.476921\pi\)
0.0724423 + 0.997373i \(0.476921\pi\)
\(450\) −5.99584e9 −0.00689277
\(451\) −2.52144e12 −2.86982
\(452\) −5.24934e11 −0.591537
\(453\) 1.87230e11 0.208898
\(454\) 9.24079e8 0.00102084
\(455\) −1.96775e11 −0.215238
\(456\) −8.35205e10 −0.0904589
\(457\) −2.00971e11 −0.215532 −0.107766 0.994176i \(-0.534370\pi\)
−0.107766 + 0.994176i \(0.534370\pi\)
\(458\) −1.16839e11 −0.124077
\(459\) −1.25665e11 −0.132147
\(460\) −3.87703e11 −0.403728
\(461\) 5.94860e11 0.613424 0.306712 0.951802i \(-0.400771\pi\)
0.306712 + 0.951802i \(0.400771\pi\)
\(462\) 1.33240e11 0.136064
\(463\) −1.77212e12 −1.79217 −0.896086 0.443880i \(-0.853602\pi\)
−0.896086 + 0.443880i \(0.853602\pi\)
\(464\) 4.41894e11 0.442575
\(465\) 2.13362e11 0.211630
\(466\) −2.04617e10 −0.0201004
\(467\) −3.70502e11 −0.360466 −0.180233 0.983624i \(-0.557685\pi\)
−0.180233 + 0.983624i \(0.557685\pi\)
\(468\) 6.94748e10 0.0669455
\(469\) 1.43365e11 0.136825
\(470\) −2.08973e11 −0.197538
\(471\) 2.88664e11 0.270271
\(472\) 3.26227e10 0.0302539
\(473\) 1.93070e11 0.177353
\(474\) −8.02776e9 −0.00730452
\(475\) 1.32215e11 0.119168
\(476\) −8.83708e11 −0.789001
\(477\) 3.33568e11 0.295021
\(478\) −1.42991e11 −0.125280
\(479\) 1.99610e12 1.73249 0.866247 0.499616i \(-0.166526\pi\)
0.866247 + 0.499616i \(0.166526\pi\)
\(480\) −2.09943e11 −0.180516
\(481\) −3.37288e11 −0.287308
\(482\) 9.87319e10 0.0833193
\(483\) −3.62940e11 −0.303440
\(484\) −2.36934e12 −1.96256
\(485\) −2.19370e11 −0.180028
\(486\) −9.23038e9 −0.00750510
\(487\) 1.94904e12 1.57015 0.785074 0.619402i \(-0.212625\pi\)
0.785074 + 0.619402i \(0.212625\pi\)
\(488\) −3.43592e11 −0.274254
\(489\) −4.06801e11 −0.321731
\(490\) 4.83884e10 0.0379191
\(491\) −1.65894e12 −1.28814 −0.644071 0.764966i \(-0.722756\pi\)
−0.644071 + 0.764966i \(0.722756\pi\)
\(492\) 1.22837e12 0.945120
\(493\) 4.15586e11 0.316847
\(494\) 2.12600e10 0.0160617
\(495\) −6.98537e11 −0.522957
\(496\) −5.22295e11 −0.387479
\(497\) −1.90395e12 −1.39976
\(498\) 1.04048e11 0.0758059
\(499\) 2.60326e11 0.187960 0.0939800 0.995574i \(-0.470041\pi\)
0.0939800 + 0.995574i \(0.470041\pi\)
\(500\) 1.47173e12 1.05309
\(501\) −7.81690e11 −0.554325
\(502\) −9.84070e10 −0.0691607
\(503\) 5.42560e10 0.0377913 0.0188956 0.999821i \(-0.493985\pi\)
0.0188956 + 0.999821i \(0.493985\pi\)
\(504\) −1.30722e11 −0.0902424
\(505\) −1.93579e11 −0.132448
\(506\) −1.34576e11 −0.0912617
\(507\) 8.23350e11 0.553412
\(508\) 2.80528e11 0.186891
\(509\) −1.84767e12 −1.22009 −0.610047 0.792365i \(-0.708849\pi\)
−0.610047 + 0.792365i \(0.708849\pi\)
\(510\) −6.42938e10 −0.0420827
\(511\) −3.04361e12 −1.97467
\(512\) 8.60500e11 0.553396
\(513\) 2.03541e11 0.129755
\(514\) −6.63682e10 −0.0419398
\(515\) 8.56664e11 0.536634
\(516\) −9.40581e10 −0.0584080
\(517\) 5.22701e12 3.21770
\(518\) 3.15129e11 0.192311
\(519\) 1.26601e12 0.765918
\(520\) 7.15840e10 0.0429340
\(521\) 2.95733e12 1.75845 0.879224 0.476408i \(-0.158062\pi\)
0.879224 + 0.476408i \(0.158062\pi\)
\(522\) 3.05258e10 0.0179949
\(523\) −7.77640e11 −0.454486 −0.227243 0.973838i \(-0.572971\pi\)
−0.227243 + 0.973838i \(0.572971\pi\)
\(524\) 2.81116e12 1.62890
\(525\) 2.06936e11 0.118883
\(526\) −9.87574e10 −0.0562514
\(527\) −4.91200e11 −0.277403
\(528\) 1.70997e12 0.957493
\(529\) −1.43457e12 −0.796475
\(530\) 1.70663e11 0.0939505
\(531\) −7.95020e10 −0.0433963
\(532\) 1.43135e12 0.774719
\(533\) −6.29700e11 −0.337957
\(534\) 2.36759e11 0.126000
\(535\) 2.18033e11 0.115062
\(536\) −5.21543e10 −0.0272928
\(537\) −6.84093e11 −0.355002
\(538\) −2.39804e11 −0.123406
\(539\) −1.21033e12 −0.617666
\(540\) 3.40307e11 0.172226
\(541\) −2.42887e12 −1.21904 −0.609518 0.792772i \(-0.708637\pi\)
−0.609518 + 0.792772i \(0.708637\pi\)
\(542\) 3.64777e11 0.181564
\(543\) 1.65687e12 0.817879
\(544\) 4.83329e11 0.236618
\(545\) −2.83554e12 −1.37674
\(546\) 3.32750e10 0.0160233
\(547\) −1.71049e12 −0.816915 −0.408458 0.912777i \(-0.633933\pi\)
−0.408458 + 0.912777i \(0.633933\pi\)
\(548\) −2.05098e12 −0.971512
\(549\) 8.37338e11 0.393392
\(550\) 7.67306e10 0.0357550
\(551\) −6.73129e11 −0.311112
\(552\) 1.32032e11 0.0605278
\(553\) 2.77064e11 0.125985
\(554\) 3.01629e11 0.136044
\(555\) −1.65213e12 −0.739138
\(556\) 3.47713e12 1.54307
\(557\) 2.43566e12 1.07218 0.536090 0.844161i \(-0.319901\pi\)
0.536090 + 0.844161i \(0.319901\pi\)
\(558\) −3.60798e10 −0.0157547
\(559\) 4.82169e10 0.0208856
\(560\) 2.35946e12 1.01383
\(561\) 1.60817e12 0.685486
\(562\) −1.95628e10 −0.00827212
\(563\) 3.00333e12 1.25984 0.629920 0.776660i \(-0.283088\pi\)
0.629920 + 0.776660i \(0.283088\pi\)
\(564\) −2.54645e12 −1.05969
\(565\) 1.31811e12 0.544169
\(566\) 3.74996e11 0.153586
\(567\) 3.18571e11 0.129444
\(568\) 6.92632e11 0.279213
\(569\) −1.16306e12 −0.465154 −0.232577 0.972578i \(-0.574716\pi\)
−0.232577 + 0.972578i \(0.574716\pi\)
\(570\) 1.04137e11 0.0413209
\(571\) −1.84040e12 −0.724520 −0.362260 0.932077i \(-0.617995\pi\)
−0.362260 + 0.932077i \(0.617995\pi\)
\(572\) −8.89090e11 −0.347267
\(573\) 8.94910e11 0.346803
\(574\) 5.88330e11 0.226213
\(575\) −2.09011e11 −0.0797378
\(576\) −8.09107e11 −0.306270
\(577\) 1.75431e12 0.658893 0.329447 0.944174i \(-0.393138\pi\)
0.329447 + 0.944174i \(0.393138\pi\)
\(578\) −1.65914e11 −0.0618314
\(579\) −2.80683e11 −0.103792
\(580\) −1.12543e12 −0.412945
\(581\) −3.59105e12 −1.30746
\(582\) 3.70959e10 0.0134021
\(583\) −4.26877e12 −1.53036
\(584\) 1.10722e12 0.393892
\(585\) −1.74451e11 −0.0615847
\(586\) 1.19915e11 0.0420084
\(587\) 3.10713e12 1.08016 0.540079 0.841614i \(-0.318394\pi\)
0.540079 + 0.841614i \(0.318394\pi\)
\(588\) 5.89637e11 0.203417
\(589\) 7.95603e11 0.272381
\(590\) −4.06756e10 −0.0138197
\(591\) −1.96503e12 −0.662561
\(592\) 4.04430e12 1.35330
\(593\) 5.13068e12 1.70384 0.851919 0.523673i \(-0.175439\pi\)
0.851919 + 0.523673i \(0.175439\pi\)
\(594\) 1.18124e11 0.0389313
\(595\) 2.21899e12 0.725821
\(596\) −2.48123e11 −0.0805489
\(597\) 2.71517e12 0.874807
\(598\) −3.36086e10 −0.0107472
\(599\) 3.74232e12 1.18774 0.593869 0.804562i \(-0.297600\pi\)
0.593869 + 0.804562i \(0.297600\pi\)
\(600\) −7.52806e10 −0.0237139
\(601\) 2.89651e12 0.905606 0.452803 0.891611i \(-0.350424\pi\)
0.452803 + 0.891611i \(0.350424\pi\)
\(602\) −4.50492e10 −0.0139798
\(603\) 1.27101e11 0.0391490
\(604\) 1.16728e12 0.356870
\(605\) 5.94942e12 1.80541
\(606\) 3.27345e10 0.00986003
\(607\) 4.39157e12 1.31302 0.656509 0.754318i \(-0.272033\pi\)
0.656509 + 0.754318i \(0.272033\pi\)
\(608\) −7.82853e11 −0.232335
\(609\) −1.05355e12 −0.310367
\(610\) 4.28407e11 0.125277
\(611\) 1.30538e12 0.378925
\(612\) −7.83453e11 −0.225752
\(613\) 4.73516e12 1.35445 0.677225 0.735776i \(-0.263182\pi\)
0.677225 + 0.735776i \(0.263182\pi\)
\(614\) −2.65477e11 −0.0753823
\(615\) −3.08444e12 −0.869438
\(616\) 1.67288e12 0.468115
\(617\) −1.27730e12 −0.354822 −0.177411 0.984137i \(-0.556772\pi\)
−0.177411 + 0.984137i \(0.556772\pi\)
\(618\) −1.44863e11 −0.0399494
\(619\) 6.62813e12 1.81461 0.907304 0.420475i \(-0.138137\pi\)
0.907304 + 0.420475i \(0.138137\pi\)
\(620\) 1.33020e12 0.361538
\(621\) −3.21765e11 −0.0868213
\(622\) −1.71462e11 −0.0459316
\(623\) −8.17135e12 −2.17319
\(624\) 4.27045e11 0.112757
\(625\) −3.02128e12 −0.792011
\(626\) −9.00863e10 −0.0234463
\(627\) −2.60477e12 −0.673077
\(628\) 1.79967e12 0.461716
\(629\) 3.80352e12 0.968853
\(630\) 1.62990e11 0.0412220
\(631\) −2.91085e12 −0.730949 −0.365474 0.930821i \(-0.619093\pi\)
−0.365474 + 0.930821i \(0.619093\pi\)
\(632\) −1.00792e11 −0.0251304
\(633\) −2.14800e12 −0.531762
\(634\) 4.29965e11 0.105689
\(635\) −7.04405e11 −0.171926
\(636\) 2.07962e12 0.503997
\(637\) −3.02265e11 −0.0727379
\(638\) −3.90648e11 −0.0933452
\(639\) −1.68795e12 −0.400504
\(640\) −1.74101e12 −0.410195
\(641\) 1.50835e12 0.352892 0.176446 0.984310i \(-0.443540\pi\)
0.176446 + 0.984310i \(0.443540\pi\)
\(642\) −3.68698e10 −0.00856572
\(643\) −4.67324e12 −1.07812 −0.539062 0.842266i \(-0.681221\pi\)
−0.539062 + 0.842266i \(0.681221\pi\)
\(644\) −2.26274e12 −0.518379
\(645\) 2.36180e11 0.0537309
\(646\) −2.39745e11 −0.0541630
\(647\) −3.96680e12 −0.889960 −0.444980 0.895540i \(-0.646789\pi\)
−0.444980 + 0.895540i \(0.646789\pi\)
\(648\) −1.15892e11 −0.0258205
\(649\) 1.01741e12 0.225110
\(650\) 1.91625e10 0.00421059
\(651\) 1.24523e12 0.271729
\(652\) −2.53619e12 −0.549627
\(653\) 6.89985e11 0.148501 0.0742507 0.997240i \(-0.476344\pi\)
0.0742507 + 0.997240i \(0.476344\pi\)
\(654\) 4.79495e11 0.102491
\(655\) −7.05882e12 −1.49846
\(656\) 7.55050e12 1.59187
\(657\) −2.69831e12 −0.565000
\(658\) −1.21962e12 −0.253635
\(659\) 1.30340e12 0.269212 0.134606 0.990899i \(-0.457023\pi\)
0.134606 + 0.990899i \(0.457023\pi\)
\(660\) −4.35501e12 −0.893390
\(661\) −7.17732e11 −0.146237 −0.0731183 0.997323i \(-0.523295\pi\)
−0.0731183 + 0.997323i \(0.523295\pi\)
\(662\) −3.13505e11 −0.0634430
\(663\) 4.01621e11 0.0807245
\(664\) 1.30637e12 0.260802
\(665\) −3.59412e12 −0.712682
\(666\) 2.79378e11 0.0550247
\(667\) 1.06411e12 0.208171
\(668\) −4.87342e12 −0.946978
\(669\) 2.07676e12 0.400839
\(670\) 6.50285e10 0.0124672
\(671\) −1.07157e13 −2.04065
\(672\) −1.22528e12 −0.231779
\(673\) −2.07991e12 −0.390819 −0.195410 0.980722i \(-0.562604\pi\)
−0.195410 + 0.980722i \(0.562604\pi\)
\(674\) −1.01334e12 −0.189141
\(675\) 1.83460e11 0.0340153
\(676\) 5.13315e12 0.945418
\(677\) −2.75692e11 −0.0504400 −0.0252200 0.999682i \(-0.508029\pi\)
−0.0252200 + 0.999682i \(0.508029\pi\)
\(678\) −2.22895e11 −0.0405104
\(679\) −1.28030e12 −0.231152
\(680\) −8.07238e11 −0.144781
\(681\) −2.82748e10 −0.00503777
\(682\) 4.61724e11 0.0817246
\(683\) −2.66370e12 −0.468374 −0.234187 0.972192i \(-0.575243\pi\)
−0.234187 + 0.972192i \(0.575243\pi\)
\(684\) 1.26897e12 0.221665
\(685\) 5.15000e12 0.893717
\(686\) −5.08167e11 −0.0876089
\(687\) 3.57502e12 0.612312
\(688\) −5.78152e11 −0.0983770
\(689\) −1.06608e12 −0.180219
\(690\) −1.64624e11 −0.0276486
\(691\) −1.07739e13 −1.79772 −0.898861 0.438234i \(-0.855604\pi\)
−0.898861 + 0.438234i \(0.855604\pi\)
\(692\) 7.89287e12 1.30845
\(693\) −4.07684e12 −0.671467
\(694\) 9.81568e11 0.160621
\(695\) −8.73108e12 −1.41950
\(696\) 3.83265e11 0.0619096
\(697\) 7.10099e12 1.13965
\(698\) −7.85693e11 −0.125286
\(699\) 6.26084e11 0.0991940
\(700\) 1.29014e12 0.203093
\(701\) −4.43000e12 −0.692903 −0.346452 0.938068i \(-0.612614\pi\)
−0.346452 + 0.938068i \(0.612614\pi\)
\(702\) 2.95000e10 0.00458464
\(703\) −6.16061e12 −0.951315
\(704\) 1.03544e13 1.58872
\(705\) 6.39413e12 0.974834
\(706\) −1.77877e9 −0.000269463 0
\(707\) −1.12977e12 −0.170061
\(708\) −4.95653e11 −0.0741358
\(709\) −2.47005e12 −0.367112 −0.183556 0.983009i \(-0.558761\pi\)
−0.183556 + 0.983009i \(0.558761\pi\)
\(710\) −8.63607e11 −0.127542
\(711\) 2.45632e11 0.0360472
\(712\) 2.97262e12 0.433491
\(713\) −1.25772e12 −0.182256
\(714\) −3.75235e11 −0.0540333
\(715\) 2.23250e12 0.319459
\(716\) −4.26496e12 −0.606465
\(717\) 4.37521e12 0.618248
\(718\) −2.74864e11 −0.0385973
\(719\) 1.20822e13 1.68604 0.843019 0.537884i \(-0.180776\pi\)
0.843019 + 0.537884i \(0.180776\pi\)
\(720\) 2.09178e12 0.290082
\(721\) 4.99971e12 0.689027
\(722\) −4.65917e11 −0.0638104
\(723\) −3.02098e12 −0.411174
\(724\) 1.03297e13 1.39722
\(725\) −6.06720e11 −0.0815582
\(726\) −1.00606e12 −0.134403
\(727\) 5.60118e11 0.0743660 0.0371830 0.999308i \(-0.488162\pi\)
0.0371830 + 0.999308i \(0.488162\pi\)
\(728\) 4.17783e11 0.0551264
\(729\) 2.82430e11 0.0370370
\(730\) −1.38054e12 −0.179927
\(731\) −5.43732e11 −0.0704298
\(732\) 5.22036e12 0.672049
\(733\) −1.15065e13 −1.47223 −0.736116 0.676855i \(-0.763342\pi\)
−0.736116 + 0.676855i \(0.763342\pi\)
\(734\) −5.23198e11 −0.0665325
\(735\) −1.48058e12 −0.187128
\(736\) 1.23756e12 0.155460
\(737\) −1.62655e12 −0.203078
\(738\) 5.21585e11 0.0647249
\(739\) −5.25102e12 −0.647654 −0.323827 0.946116i \(-0.604970\pi\)
−0.323827 + 0.946116i \(0.604970\pi\)
\(740\) −1.03001e13 −1.26270
\(741\) −6.50510e11 −0.0792633
\(742\) 9.96036e11 0.120631
\(743\) 7.30377e12 0.879219 0.439610 0.898189i \(-0.355117\pi\)
0.439610 + 0.898189i \(0.355117\pi\)
\(744\) −4.52999e11 −0.0542025
\(745\) 6.23038e11 0.0740988
\(746\) 1.54770e12 0.182962
\(747\) −3.18365e12 −0.374096
\(748\) 1.00261e13 1.17105
\(749\) 1.27250e12 0.147737
\(750\) 6.24920e11 0.0721188
\(751\) −8.33892e12 −0.956599 −0.478300 0.878197i \(-0.658747\pi\)
−0.478300 + 0.878197i \(0.658747\pi\)
\(752\) −1.56524e13 −1.78484
\(753\) 3.01104e12 0.341302
\(754\) −9.75596e10 −0.0109926
\(755\) −2.93105e12 −0.328293
\(756\) 1.98612e12 0.221135
\(757\) −3.39837e12 −0.376131 −0.188065 0.982157i \(-0.560222\pi\)
−0.188065 + 0.982157i \(0.560222\pi\)
\(758\) −1.03461e12 −0.113832
\(759\) 4.11772e12 0.450369
\(760\) 1.30749e12 0.142160
\(761\) −1.02566e13 −1.10860 −0.554298 0.832319i \(-0.687013\pi\)
−0.554298 + 0.832319i \(0.687013\pi\)
\(762\) 1.19116e11 0.0127989
\(763\) −1.65490e13 −1.76771
\(764\) 5.57929e12 0.592460
\(765\) 1.96725e12 0.207675
\(766\) −9.28780e11 −0.0974728
\(767\) 2.54086e11 0.0265095
\(768\) −4.81995e12 −0.499939
\(769\) 3.84432e12 0.396416 0.198208 0.980160i \(-0.436488\pi\)
0.198208 + 0.980160i \(0.436488\pi\)
\(770\) −2.08583e12 −0.213831
\(771\) 2.03072e12 0.206969
\(772\) −1.74991e12 −0.177312
\(773\) −5.47346e12 −0.551384 −0.275692 0.961246i \(-0.588907\pi\)
−0.275692 + 0.961246i \(0.588907\pi\)
\(774\) −3.99384e10 −0.00399997
\(775\) 7.17111e11 0.0714050
\(776\) 4.65756e11 0.0461085
\(777\) −9.64225e12 −0.949039
\(778\) −1.25382e12 −0.122695
\(779\) −1.15016e13 −1.11902
\(780\) −1.08761e12 −0.105208
\(781\) 2.16012e13 2.07754
\(782\) 3.78998e11 0.0362415
\(783\) −9.34023e11 −0.0888034
\(784\) 3.62435e12 0.342616
\(785\) −4.51897e12 −0.424743
\(786\) 1.19366e12 0.111552
\(787\) −1.00323e12 −0.0932208 −0.0466104 0.998913i \(-0.514842\pi\)
−0.0466104 + 0.998913i \(0.514842\pi\)
\(788\) −1.22509e13 −1.13188
\(789\) 3.02176e12 0.277596
\(790\) 1.25673e11 0.0114794
\(791\) 7.69283e12 0.698702
\(792\) 1.48310e12 0.133939
\(793\) −2.67611e12 −0.240312
\(794\) 1.06041e12 0.0946855
\(795\) −5.22193e12 −0.463638
\(796\) 1.69276e13 1.49447
\(797\) 7.85435e12 0.689522 0.344761 0.938691i \(-0.387960\pi\)
0.344761 + 0.938691i \(0.387960\pi\)
\(798\) 6.07773e11 0.0530552
\(799\) −1.47205e13 −1.27780
\(800\) −7.05619e11 −0.0609067
\(801\) −7.24432e12 −0.621801
\(802\) −1.34671e11 −0.0114945
\(803\) 3.45311e13 2.93083
\(804\) 7.92406e11 0.0668799
\(805\) 5.68173e12 0.476869
\(806\) 1.15310e11 0.00962409
\(807\) 7.33749e12 0.608999
\(808\) 4.10996e11 0.0339224
\(809\) −2.34330e13 −1.92335 −0.961676 0.274188i \(-0.911591\pi\)
−0.961676 + 0.274188i \(0.911591\pi\)
\(810\) 1.44499e11 0.0117946
\(811\) −5.12210e12 −0.415771 −0.207885 0.978153i \(-0.566658\pi\)
−0.207885 + 0.978153i \(0.566658\pi\)
\(812\) −6.56830e12 −0.530214
\(813\) −1.11614e13 −0.896005
\(814\) −3.57528e12 −0.285430
\(815\) 6.36838e12 0.505614
\(816\) −4.81569e12 −0.380236
\(817\) 8.80688e11 0.0691549
\(818\) −2.69723e12 −0.210634
\(819\) −1.01814e12 −0.0790736
\(820\) −1.92299e13 −1.48530
\(821\) −1.89983e13 −1.45939 −0.729693 0.683775i \(-0.760337\pi\)
−0.729693 + 0.683775i \(0.760337\pi\)
\(822\) −8.70875e11 −0.0665323
\(823\) 4.77442e12 0.362762 0.181381 0.983413i \(-0.441943\pi\)
0.181381 + 0.983413i \(0.441943\pi\)
\(824\) −1.81883e12 −0.137442
\(825\) −2.34779e12 −0.176448
\(826\) −2.37393e11 −0.0177443
\(827\) 1.54874e13 1.15134 0.575669 0.817683i \(-0.304742\pi\)
0.575669 + 0.817683i \(0.304742\pi\)
\(828\) −2.00603e12 −0.148321
\(829\) 2.20968e13 1.62493 0.812465 0.583010i \(-0.198125\pi\)
0.812465 + 0.583010i \(0.198125\pi\)
\(830\) −1.62885e12 −0.119132
\(831\) −9.22920e12 −0.671366
\(832\) 2.58588e12 0.187091
\(833\) 3.40858e12 0.245285
\(834\) 1.47644e12 0.105674
\(835\) 1.22372e13 0.871147
\(836\) −1.62393e13 −1.14985
\(837\) 1.10396e12 0.0777483
\(838\) 1.67168e12 0.117100
\(839\) 6.56319e12 0.457284 0.228642 0.973511i \(-0.426571\pi\)
0.228642 + 0.973511i \(0.426571\pi\)
\(840\) 2.04642e12 0.141820
\(841\) −1.14182e13 −0.787077
\(842\) 2.84489e12 0.195057
\(843\) 5.98579e11 0.0408223
\(844\) −1.33916e13 −0.908433
\(845\) −1.28893e13 −0.869712
\(846\) −1.08126e12 −0.0725710
\(847\) 3.47224e13 2.31811
\(848\) 1.27829e13 0.848885
\(849\) −1.14741e13 −0.757937
\(850\) −2.16092e11 −0.0141989
\(851\) 9.73893e12 0.636544
\(852\) −1.05235e13 −0.684199
\(853\) 1.02788e13 0.664773 0.332386 0.943143i \(-0.392146\pi\)
0.332386 + 0.943143i \(0.392146\pi\)
\(854\) 2.50029e12 0.160854
\(855\) −3.18638e12 −0.203915
\(856\) −4.62918e11 −0.0294694
\(857\) 1.06746e13 0.675983 0.337992 0.941149i \(-0.390252\pi\)
0.337992 + 0.941149i \(0.390252\pi\)
\(858\) −3.77520e11 −0.0237820
\(859\) −2.46494e13 −1.54468 −0.772339 0.635211i \(-0.780913\pi\)
−0.772339 + 0.635211i \(0.780913\pi\)
\(860\) 1.47246e12 0.0917908
\(861\) −1.80016e13 −1.11634
\(862\) 2.20835e12 0.136234
\(863\) 1.62899e13 0.999699 0.499850 0.866112i \(-0.333389\pi\)
0.499850 + 0.866112i \(0.333389\pi\)
\(864\) −1.08627e12 −0.0663174
\(865\) −1.98190e13 −1.20368
\(866\) −7.34748e11 −0.0443923
\(867\) 5.07662e12 0.305133
\(868\) 7.76338e12 0.464207
\(869\) −3.14342e12 −0.186988
\(870\) −4.77874e11 −0.0282798
\(871\) −4.06211e11 −0.0239150
\(872\) 6.02028e12 0.352609
\(873\) −1.13505e12 −0.0661382
\(874\) −6.13867e11 −0.0355855
\(875\) −2.15681e13 −1.24387
\(876\) −1.68226e13 −0.965214
\(877\) 2.73486e13 1.56112 0.780562 0.625078i \(-0.214933\pi\)
0.780562 + 0.625078i \(0.214933\pi\)
\(878\) −3.28783e12 −0.186717
\(879\) −3.66915e12 −0.207308
\(880\) −2.67692e13 −1.50474
\(881\) −8.62622e12 −0.482424 −0.241212 0.970472i \(-0.577545\pi\)
−0.241212 + 0.970472i \(0.577545\pi\)
\(882\) 2.50368e11 0.0139306
\(883\) 2.05976e13 1.14023 0.570116 0.821564i \(-0.306898\pi\)
0.570116 + 0.821564i \(0.306898\pi\)
\(884\) 2.50389e12 0.137905
\(885\) 1.24458e12 0.0681993
\(886\) 3.45593e12 0.188414
\(887\) −2.61466e13 −1.41827 −0.709134 0.705073i \(-0.750914\pi\)
−0.709134 + 0.705073i \(0.750914\pi\)
\(888\) 3.50772e12 0.189307
\(889\) −4.11109e12 −0.220749
\(890\) −3.70641e12 −0.198015
\(891\) −3.61433e12 −0.192123
\(892\) 1.29475e13 0.684770
\(893\) 2.38430e13 1.25467
\(894\) −1.05357e11 −0.00551625
\(895\) 1.07093e13 0.557902
\(896\) −1.01610e13 −0.526683
\(897\) 1.02835e12 0.0530366
\(898\) 3.30313e11 0.0169505
\(899\) −3.65092e12 −0.186416
\(900\) 1.14377e12 0.0581098
\(901\) 1.20219e13 0.607732
\(902\) −6.67487e12 −0.335748
\(903\) 1.37841e12 0.0689894
\(904\) −2.79855e12 −0.139372
\(905\) −2.59379e13 −1.28533
\(906\) 4.95645e11 0.0244396
\(907\) −9.64696e12 −0.473323 −0.236662 0.971592i \(-0.576053\pi\)
−0.236662 + 0.971592i \(0.576053\pi\)
\(908\) −1.76279e11 −0.00860624
\(909\) −1.00160e12 −0.0486585
\(910\) −5.20912e11 −0.0251813
\(911\) 3.40085e13 1.63589 0.817947 0.575294i \(-0.195112\pi\)
0.817947 + 0.575294i \(0.195112\pi\)
\(912\) 7.80003e12 0.373353
\(913\) 4.07421e13 1.94055
\(914\) −5.32020e11 −0.0252157
\(915\) −1.31083e13 −0.618233
\(916\) 2.22883e13 1.04604
\(917\) −4.11971e13 −1.92400
\(918\) −3.32666e11 −0.0154602
\(919\) 2.17503e13 1.00588 0.502939 0.864322i \(-0.332252\pi\)
0.502939 + 0.864322i \(0.332252\pi\)
\(920\) −2.06694e12 −0.0951221
\(921\) 8.12302e12 0.372005
\(922\) 1.57474e12 0.0717662
\(923\) 5.39465e12 0.244656
\(924\) −2.54170e13 −1.14710
\(925\) −5.55282e12 −0.249388
\(926\) −4.69125e12 −0.209671
\(927\) 4.43250e12 0.197147
\(928\) 3.59242e12 0.159009
\(929\) 1.64442e13 0.724338 0.362169 0.932112i \(-0.382036\pi\)
0.362169 + 0.932112i \(0.382036\pi\)
\(930\) 5.64821e11 0.0247593
\(931\) −5.52092e12 −0.240845
\(932\) 3.90330e12 0.169458
\(933\) 5.24637e12 0.226669
\(934\) −9.80811e11 −0.0421720
\(935\) −2.51755e13 −1.07727
\(936\) 3.70386e11 0.0157730
\(937\) −3.48954e13 −1.47890 −0.739452 0.673209i \(-0.764916\pi\)
−0.739452 + 0.673209i \(0.764916\pi\)
\(938\) 3.79523e11 0.0160076
\(939\) 2.75645e12 0.115706
\(940\) 3.98640e13 1.66535
\(941\) 3.27535e13 1.36177 0.680886 0.732389i \(-0.261595\pi\)
0.680886 + 0.732389i \(0.261595\pi\)
\(942\) 7.64166e11 0.0316198
\(943\) 1.81821e13 0.748758
\(944\) −3.04666e12 −0.124867
\(945\) −4.98715e12 −0.203427
\(946\) 5.11103e11 0.0207491
\(947\) 3.21396e12 0.129857 0.0649285 0.997890i \(-0.479318\pi\)
0.0649285 + 0.997890i \(0.479318\pi\)
\(948\) 1.53138e12 0.0615810
\(949\) 8.62374e12 0.345142
\(950\) 3.50007e11 0.0139418
\(951\) −1.31560e13 −0.521569
\(952\) −4.71125e12 −0.185896
\(953\) 1.10804e13 0.435150 0.217575 0.976044i \(-0.430185\pi\)
0.217575 + 0.976044i \(0.430185\pi\)
\(954\) 8.83038e11 0.0345153
\(955\) −1.40096e13 −0.545017
\(956\) 2.72771e13 1.05618
\(957\) 1.19530e13 0.460651
\(958\) 5.28416e12 0.202689
\(959\) 3.00568e13 1.14752
\(960\) 1.26664e13 0.481317
\(961\) −2.21244e13 −0.836791
\(962\) −8.92884e11 −0.0336130
\(963\) 1.12814e12 0.0422711
\(964\) −1.88342e13 −0.702427
\(965\) 4.39402e12 0.163113
\(966\) −9.60791e11 −0.0355003
\(967\) 1.09145e13 0.401408 0.200704 0.979652i \(-0.435677\pi\)
0.200704 + 0.979652i \(0.435677\pi\)
\(968\) −1.26315e13 −0.462398
\(969\) 7.33566e12 0.267290
\(970\) −5.80727e11 −0.0210620
\(971\) 6.96329e11 0.0251379 0.0125689 0.999921i \(-0.495999\pi\)
0.0125689 + 0.999921i \(0.495999\pi\)
\(972\) 1.76080e12 0.0632720
\(973\) −5.09569e13 −1.82262
\(974\) 5.15959e12 0.183696
\(975\) −5.86332e11 −0.0207789
\(976\) 3.20883e13 1.13194
\(977\) −1.37974e13 −0.484476 −0.242238 0.970217i \(-0.577881\pi\)
−0.242238 + 0.970217i \(0.577881\pi\)
\(978\) −1.07690e12 −0.0376402
\(979\) 9.27077e13 3.22547
\(980\) −9.23062e12 −0.319679
\(981\) −1.46715e13 −0.505783
\(982\) −4.39162e12 −0.150703
\(983\) −1.76354e13 −0.602415 −0.301207 0.953559i \(-0.597390\pi\)
−0.301207 + 0.953559i \(0.597390\pi\)
\(984\) 6.54874e12 0.222679
\(985\) 3.07621e13 1.04124
\(986\) 1.10016e12 0.0370689
\(987\) 3.73178e13 1.25167
\(988\) −4.05558e12 −0.135409
\(989\) −1.39223e12 −0.0462729
\(990\) −1.84920e12 −0.0611822
\(991\) 2.80655e13 0.924362 0.462181 0.886786i \(-0.347067\pi\)
0.462181 + 0.886786i \(0.347067\pi\)
\(992\) −4.24604e12 −0.139214
\(993\) 9.59258e12 0.313086
\(994\) −5.04024e12 −0.163762
\(995\) −4.25053e13 −1.37480
\(996\) −1.98484e13 −0.639084
\(997\) −1.61831e12 −0.0518720 −0.0259360 0.999664i \(-0.508257\pi\)
−0.0259360 + 0.999664i \(0.508257\pi\)
\(998\) 6.89148e11 0.0219900
\(999\) −8.54836e12 −0.271543
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.b.1.11 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.b.1.11 21 1.1 even 1 trivial