Properties

Label 177.10.a.a.1.13
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 1.13
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.31191 q^{2} +81.0000 q^{3} -506.655 q^{4} -66.4563 q^{5} +187.265 q^{6} -1904.69 q^{7} -2355.04 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+2.31191 q^{2} +81.0000 q^{3} -506.655 q^{4} -66.4563 q^{5} +187.265 q^{6} -1904.69 q^{7} -2355.04 q^{8} +6561.00 q^{9} -153.641 q^{10} -51285.5 q^{11} -41039.1 q^{12} +118285. q^{13} -4403.48 q^{14} -5382.96 q^{15} +253963. q^{16} +412063. q^{17} +15168.4 q^{18} +216219. q^{19} +33670.4 q^{20} -154280. q^{21} -118567. q^{22} -730788. q^{23} -190758. q^{24} -1.94871e6 q^{25} +273464. q^{26} +531441. q^{27} +965023. q^{28} -2.16650e6 q^{29} -12444.9 q^{30} +7.53898e6 q^{31} +1.79292e6 q^{32} -4.15413e6 q^{33} +952652. q^{34} +126579. q^{35} -3.32416e6 q^{36} +2.06192e7 q^{37} +499880. q^{38} +9.58108e6 q^{39} +156507. q^{40} -3.10914e7 q^{41} -356682. q^{42} -1.98819e7 q^{43} +2.59841e7 q^{44} -436020. q^{45} -1.68951e6 q^{46} -2.28396e7 q^{47} +2.05710e7 q^{48} -3.67257e7 q^{49} -4.50524e6 q^{50} +3.33771e7 q^{51} -5.99297e7 q^{52} -3.27629e7 q^{53} +1.22864e6 q^{54} +3.40825e6 q^{55} +4.48562e6 q^{56} +1.75138e7 q^{57} -5.00874e6 q^{58} +1.21174e7 q^{59} +2.72731e6 q^{60} -8.93784e7 q^{61} +1.74294e7 q^{62} -1.24967e7 q^{63} -1.25884e8 q^{64} -7.86078e6 q^{65} -9.60396e6 q^{66} +7.39877e7 q^{67} -2.08774e8 q^{68} -5.91938e7 q^{69} +292639. q^{70} +3.75295e8 q^{71} -1.54514e7 q^{72} -3.48461e7 q^{73} +4.76697e7 q^{74} -1.57845e8 q^{75} -1.09549e8 q^{76} +9.76832e7 q^{77} +2.21506e7 q^{78} -4.51823e8 q^{79} -1.68774e7 q^{80} +4.30467e7 q^{81} -7.18804e7 q^{82} -4.70214e8 q^{83} +7.81668e7 q^{84} -2.73842e7 q^{85} -4.59651e7 q^{86} -1.75486e8 q^{87} +1.20779e8 q^{88} +2.05108e8 q^{89} -1.00804e6 q^{90} -2.25297e8 q^{91} +3.70257e8 q^{92} +6.10657e8 q^{93} -5.28032e7 q^{94} -1.43692e7 q^{95} +1.45226e8 q^{96} -9.28232e8 q^{97} -8.49066e7 q^{98} -3.36484e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q - 66q^{2} + 1701q^{3} + 5206q^{4} - 2964q^{5} - 5346q^{6} - 30775q^{7} - 24621q^{8} + 137781q^{9} - 54663q^{10} - 151769q^{11} + 421686q^{12} - 153611q^{13} - 286771q^{14} - 240084q^{15} + 805530q^{16} - 723621q^{17} - 433026q^{18} - 549388q^{19} - 527311q^{20} - 2492775q^{21} + 2973158q^{22} + 169962q^{23} - 1994301q^{24} + 8035779q^{25} - 2337392q^{26} + 11160261q^{27} - 22659054q^{28} - 16845442q^{29} - 4427703q^{30} - 19307976q^{31} - 44923568q^{32} - 12293289q^{33} - 35547496q^{34} - 34882596q^{35} + 34156566q^{36} - 41561129q^{37} - 52335371q^{38} - 12442491q^{39} - 125735038q^{40} - 68169291q^{41} - 23228451q^{42} - 25719587q^{43} - 126277032q^{44} - 19446804q^{45} - 292814271q^{46} - 174095332q^{47} + 65247930q^{48} + 7479350q^{49} - 227877439q^{50} - 58613301q^{51} - 232397708q^{52} - 228390500q^{53} - 35075106q^{54} - 29426208q^{55} + 326778474q^{56} - 44500428q^{57} + 480343762q^{58} + 254464581q^{59} - 42712191q^{60} - 183928964q^{61} - 21753862q^{62} - 201914775q^{63} + 310571245q^{64} + 5308466q^{65} + 240825798q^{66} - 82724114q^{67} - 138336205q^{68} + 13766922q^{69} + 1030274876q^{70} - 404721965q^{71} - 161538381q^{72} + 154162574q^{73} + 36352054q^{74} + 650898099q^{75} + 1068940636q^{76} - 448535481q^{77} - 189328752q^{78} + 272529635q^{79} - 345587859q^{80} + 903981141q^{81} - 38412637q^{82} + 432518643q^{83} - 1835383374q^{84} - 126211490q^{85} - 3699273072q^{86} - 1364480802q^{87} + 170111045q^{88} - 1255621070q^{89} - 358643943q^{90} + 1448885849q^{91} + 1568933320q^{92} - 1563946056q^{93} - 1908445164q^{94} - 2896546490q^{95} - 3638809008q^{96} + 1007235486q^{97} - 9506868248q^{98} - 995756409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.31191 0.102173 0.0510864 0.998694i \(-0.483732\pi\)
0.0510864 + 0.998694i \(0.483732\pi\)
\(3\) 81.0000 0.577350
\(4\) −506.655 −0.989561
\(5\) −66.4563 −0.0475523 −0.0237761 0.999717i \(-0.507569\pi\)
−0.0237761 + 0.999717i \(0.507569\pi\)
\(6\) 187.265 0.0589895
\(7\) −1904.69 −0.299836 −0.149918 0.988698i \(-0.547901\pi\)
−0.149918 + 0.988698i \(0.547901\pi\)
\(8\) −2355.04 −0.203279
\(9\) 6561.00 0.333333
\(10\) −153.641 −0.00485855
\(11\) −51285.5 −1.05615 −0.528077 0.849196i \(-0.677087\pi\)
−0.528077 + 0.849196i \(0.677087\pi\)
\(12\) −41039.1 −0.571323
\(13\) 118285. 1.14864 0.574320 0.818631i \(-0.305266\pi\)
0.574320 + 0.818631i \(0.305266\pi\)
\(14\) −4403.48 −0.0306351
\(15\) −5382.96 −0.0274543
\(16\) 253963. 0.968791
\(17\) 412063. 1.19658 0.598292 0.801278i \(-0.295846\pi\)
0.598292 + 0.801278i \(0.295846\pi\)
\(18\) 15168.4 0.0340576
\(19\) 216219. 0.380631 0.190315 0.981723i \(-0.439049\pi\)
0.190315 + 0.981723i \(0.439049\pi\)
\(20\) 33670.4 0.0470559
\(21\) −154280. −0.173110
\(22\) −118567. −0.107910
\(23\) −730788. −0.544523 −0.272261 0.962223i \(-0.587772\pi\)
−0.272261 + 0.962223i \(0.587772\pi\)
\(24\) −190758. −0.117363
\(25\) −1.94871e6 −0.997739
\(26\) 273464. 0.117360
\(27\) 531441. 0.192450
\(28\) 965023. 0.296706
\(29\) −2.16650e6 −0.568810 −0.284405 0.958704i \(-0.591796\pi\)
−0.284405 + 0.958704i \(0.591796\pi\)
\(30\) −12444.9 −0.00280509
\(31\) 7.53898e6 1.46617 0.733086 0.680136i \(-0.238079\pi\)
0.733086 + 0.680136i \(0.238079\pi\)
\(32\) 1.79292e6 0.302263
\(33\) −4.15413e6 −0.609771
\(34\) 952652. 0.122258
\(35\) 126579. 0.0142579
\(36\) −3.32416e6 −0.329854
\(37\) 2.06192e7 1.80869 0.904345 0.426802i \(-0.140360\pi\)
0.904345 + 0.426802i \(0.140360\pi\)
\(38\) 499880. 0.0388901
\(39\) 9.58108e6 0.663168
\(40\) 156507. 0.00966639
\(41\) −3.10914e7 −1.71835 −0.859177 0.511678i \(-0.829024\pi\)
−0.859177 + 0.511678i \(0.829024\pi\)
\(42\) −356682. −0.0176872
\(43\) −1.98819e7 −0.886848 −0.443424 0.896312i \(-0.646236\pi\)
−0.443424 + 0.896312i \(0.646236\pi\)
\(44\) 2.59841e7 1.04513
\(45\) −436020. −0.0158508
\(46\) −1.68951e6 −0.0556354
\(47\) −2.28396e7 −0.682730 −0.341365 0.939931i \(-0.610889\pi\)
−0.341365 + 0.939931i \(0.610889\pi\)
\(48\) 2.05710e7 0.559332
\(49\) −3.67257e7 −0.910098
\(50\) −4.50524e6 −0.101942
\(51\) 3.33771e7 0.690849
\(52\) −5.99297e7 −1.13665
\(53\) −3.27629e7 −0.570350 −0.285175 0.958475i \(-0.592052\pi\)
−0.285175 + 0.958475i \(0.592052\pi\)
\(54\) 1.22864e6 0.0196632
\(55\) 3.40825e6 0.0502226
\(56\) 4.48562e6 0.0609504
\(57\) 1.75138e7 0.219757
\(58\) −5.00874e6 −0.0581169
\(59\) 1.21174e7 0.130189
\(60\) 2.72731e6 0.0271677
\(61\) −8.93784e7 −0.826510 −0.413255 0.910615i \(-0.635608\pi\)
−0.413255 + 0.910615i \(0.635608\pi\)
\(62\) 1.74294e7 0.149803
\(63\) −1.24967e7 −0.0999454
\(64\) −1.25884e8 −0.937908
\(65\) −7.86078e6 −0.0546205
\(66\) −9.60396e6 −0.0623021
\(67\) 7.39877e7 0.448563 0.224281 0.974524i \(-0.427997\pi\)
0.224281 + 0.974524i \(0.427997\pi\)
\(68\) −2.08774e8 −1.18409
\(69\) −5.91938e7 −0.314380
\(70\) 292639. 0.00145677
\(71\) 3.75295e8 1.75271 0.876355 0.481665i \(-0.159968\pi\)
0.876355 + 0.481665i \(0.159968\pi\)
\(72\) −1.54514e7 −0.0677597
\(73\) −3.48461e7 −0.143616 −0.0718078 0.997418i \(-0.522877\pi\)
−0.0718078 + 0.997418i \(0.522877\pi\)
\(74\) 4.76697e7 0.184799
\(75\) −1.57845e8 −0.576045
\(76\) −1.09549e8 −0.376657
\(77\) 9.76832e7 0.316673
\(78\) 2.21506e7 0.0677578
\(79\) −4.51823e8 −1.30511 −0.652554 0.757742i \(-0.726303\pi\)
−0.652554 + 0.757742i \(0.726303\pi\)
\(80\) −1.68774e7 −0.0460682
\(81\) 4.30467e7 0.111111
\(82\) −7.18804e7 −0.175569
\(83\) −4.70214e8 −1.08754 −0.543768 0.839235i \(-0.683003\pi\)
−0.543768 + 0.839235i \(0.683003\pi\)
\(84\) 7.81668e7 0.171303
\(85\) −2.73842e7 −0.0569003
\(86\) −4.59651e7 −0.0906118
\(87\) −1.75486e8 −0.328402
\(88\) 1.20779e8 0.214694
\(89\) 2.05108e8 0.346519 0.173259 0.984876i \(-0.444570\pi\)
0.173259 + 0.984876i \(0.444570\pi\)
\(90\) −1.00804e6 −0.00161952
\(91\) −2.25297e8 −0.344404
\(92\) 3.70257e8 0.538838
\(93\) 6.10657e8 0.846495
\(94\) −5.28032e7 −0.0697565
\(95\) −1.43692e7 −0.0180998
\(96\) 1.45226e8 0.174512
\(97\) −9.28232e8 −1.06459 −0.532297 0.846558i \(-0.678671\pi\)
−0.532297 + 0.846558i \(0.678671\pi\)
\(98\) −8.49066e7 −0.0929874
\(99\) −3.36484e8 −0.352052
\(100\) 9.87323e8 0.987323
\(101\) −1.09966e9 −1.05150 −0.525752 0.850638i \(-0.676216\pi\)
−0.525752 + 0.850638i \(0.676216\pi\)
\(102\) 7.71648e7 0.0705860
\(103\) 1.31181e8 0.114843 0.0574215 0.998350i \(-0.481712\pi\)
0.0574215 + 0.998350i \(0.481712\pi\)
\(104\) −2.78565e8 −0.233495
\(105\) 1.02529e7 0.00823180
\(106\) −7.57449e7 −0.0582743
\(107\) 1.41720e9 1.04521 0.522607 0.852574i \(-0.324960\pi\)
0.522607 + 0.852574i \(0.324960\pi\)
\(108\) −2.69257e8 −0.190441
\(109\) 2.15601e8 0.146296 0.0731478 0.997321i \(-0.476696\pi\)
0.0731478 + 0.997321i \(0.476696\pi\)
\(110\) 7.87955e6 0.00513138
\(111\) 1.67016e9 1.04425
\(112\) −4.83721e8 −0.290479
\(113\) −9.24420e8 −0.533355 −0.266678 0.963786i \(-0.585926\pi\)
−0.266678 + 0.963786i \(0.585926\pi\)
\(114\) 4.04902e7 0.0224532
\(115\) 4.85655e7 0.0258933
\(116\) 1.09767e9 0.562872
\(117\) 7.76067e8 0.382880
\(118\) 2.80142e7 0.0133018
\(119\) −7.84854e8 −0.358779
\(120\) 1.26771e7 0.00558089
\(121\) 2.72256e8 0.115463
\(122\) −2.06635e8 −0.0844469
\(123\) −2.51840e9 −0.992092
\(124\) −3.81966e9 −1.45087
\(125\) 2.59302e8 0.0949970
\(126\) −2.88912e7 −0.0102117
\(127\) −3.33077e9 −1.13613 −0.568065 0.822984i \(-0.692308\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(128\) −1.20901e9 −0.398092
\(129\) −1.61043e9 −0.512022
\(130\) −1.81734e7 −0.00558073
\(131\) −5.99263e9 −1.77786 −0.888929 0.458046i \(-0.848550\pi\)
−0.888929 + 0.458046i \(0.848550\pi\)
\(132\) 2.10471e9 0.603406
\(133\) −4.11832e8 −0.114127
\(134\) 1.71053e8 0.0458309
\(135\) −3.53176e7 −0.00915144
\(136\) −9.70424e8 −0.243241
\(137\) −9.77396e8 −0.237044 −0.118522 0.992951i \(-0.537816\pi\)
−0.118522 + 0.992951i \(0.537816\pi\)
\(138\) −1.36851e8 −0.0321211
\(139\) −6.15322e9 −1.39809 −0.699046 0.715077i \(-0.746392\pi\)
−0.699046 + 0.715077i \(0.746392\pi\)
\(140\) −6.41319e7 −0.0141090
\(141\) −1.85001e9 −0.394174
\(142\) 8.67647e8 0.179079
\(143\) −6.06630e9 −1.21314
\(144\) 1.66625e9 0.322930
\(145\) 1.43977e8 0.0270482
\(146\) −8.05611e7 −0.0146736
\(147\) −2.97479e9 −0.525445
\(148\) −1.04468e10 −1.78981
\(149\) 6.61664e9 1.09976 0.549882 0.835242i \(-0.314673\pi\)
0.549882 + 0.835242i \(0.314673\pi\)
\(150\) −3.64924e8 −0.0588561
\(151\) −9.46985e9 −1.48234 −0.741169 0.671319i \(-0.765728\pi\)
−0.741169 + 0.671319i \(0.765728\pi\)
\(152\) −5.09205e8 −0.0773742
\(153\) 2.70355e9 0.398862
\(154\) 2.25835e8 0.0323554
\(155\) −5.01013e8 −0.0697198
\(156\) −4.85430e9 −0.656245
\(157\) 1.10136e10 1.44671 0.723355 0.690477i \(-0.242599\pi\)
0.723355 + 0.690477i \(0.242599\pi\)
\(158\) −1.04457e9 −0.133347
\(159\) −2.65380e9 −0.329292
\(160\) −1.19151e8 −0.0143733
\(161\) 1.39193e9 0.163268
\(162\) 9.95201e7 0.0113525
\(163\) 3.97578e9 0.441142 0.220571 0.975371i \(-0.429208\pi\)
0.220571 + 0.975371i \(0.429208\pi\)
\(164\) 1.57526e10 1.70042
\(165\) 2.76068e8 0.0289960
\(166\) −1.08709e9 −0.111117
\(167\) −1.18492e10 −1.17887 −0.589434 0.807817i \(-0.700649\pi\)
−0.589434 + 0.807817i \(0.700649\pi\)
\(168\) 3.63336e8 0.0351897
\(169\) 3.38682e9 0.319376
\(170\) −6.33097e7 −0.00581367
\(171\) 1.41862e9 0.126877
\(172\) 1.00732e10 0.877590
\(173\) −1.55109e10 −1.31653 −0.658264 0.752787i \(-0.728709\pi\)
−0.658264 + 0.752787i \(0.728709\pi\)
\(174\) −4.05708e8 −0.0335538
\(175\) 3.71169e9 0.299158
\(176\) −1.30246e10 −1.02319
\(177\) 9.81506e8 0.0751646
\(178\) 4.74190e8 0.0354048
\(179\) −2.04589e10 −1.48951 −0.744755 0.667338i \(-0.767434\pi\)
−0.744755 + 0.667338i \(0.767434\pi\)
\(180\) 2.20912e8 0.0156853
\(181\) −1.25668e10 −0.870305 −0.435152 0.900357i \(-0.643306\pi\)
−0.435152 + 0.900357i \(0.643306\pi\)
\(182\) −5.20865e8 −0.0351888
\(183\) −7.23965e9 −0.477186
\(184\) 1.72103e9 0.110690
\(185\) −1.37028e9 −0.0860073
\(186\) 1.41178e9 0.0864888
\(187\) −2.11329e10 −1.26378
\(188\) 1.15718e10 0.675603
\(189\) −1.01223e9 −0.0577035
\(190\) −3.32202e7 −0.00184931
\(191\) 2.61909e10 1.42397 0.711985 0.702195i \(-0.247796\pi\)
0.711985 + 0.702195i \(0.247796\pi\)
\(192\) −1.01966e10 −0.541501
\(193\) 2.59647e10 1.34702 0.673512 0.739177i \(-0.264785\pi\)
0.673512 + 0.739177i \(0.264785\pi\)
\(194\) −2.14599e9 −0.108773
\(195\) −6.36723e8 −0.0315352
\(196\) 1.86073e10 0.900598
\(197\) −1.11591e9 −0.0527877 −0.0263938 0.999652i \(-0.508402\pi\)
−0.0263938 + 0.999652i \(0.508402\pi\)
\(198\) −7.77921e8 −0.0359701
\(199\) 2.98397e10 1.34882 0.674412 0.738356i \(-0.264397\pi\)
0.674412 + 0.738356i \(0.264397\pi\)
\(200\) 4.58928e9 0.202819
\(201\) 5.99301e9 0.258978
\(202\) −2.54231e9 −0.107435
\(203\) 4.12651e9 0.170550
\(204\) −1.69107e10 −0.683637
\(205\) 2.06622e9 0.0817117
\(206\) 3.03279e8 0.0117338
\(207\) −4.79470e9 −0.181508
\(208\) 3.00400e10 1.11279
\(209\) −1.10889e10 −0.402005
\(210\) 2.37038e7 0.000841066 0
\(211\) −4.53349e10 −1.57457 −0.787284 0.616590i \(-0.788514\pi\)
−0.787284 + 0.616590i \(0.788514\pi\)
\(212\) 1.65995e10 0.564396
\(213\) 3.03989e10 1.01193
\(214\) 3.27644e9 0.106792
\(215\) 1.32128e9 0.0421716
\(216\) −1.25156e9 −0.0391211
\(217\) −1.43594e10 −0.439611
\(218\) 4.98449e8 0.0149474
\(219\) −2.82254e9 −0.0829165
\(220\) −1.72681e9 −0.0496983
\(221\) 4.87408e10 1.37445
\(222\) 3.86125e9 0.106694
\(223\) 4.29880e10 1.16406 0.582030 0.813167i \(-0.302258\pi\)
0.582030 + 0.813167i \(0.302258\pi\)
\(224\) −3.41496e9 −0.0906295
\(225\) −1.27855e10 −0.332580
\(226\) −2.13717e9 −0.0544944
\(227\) −4.70552e10 −1.17623 −0.588113 0.808779i \(-0.700129\pi\)
−0.588113 + 0.808779i \(0.700129\pi\)
\(228\) −8.87345e9 −0.217463
\(229\) 2.65931e10 0.639012 0.319506 0.947584i \(-0.396483\pi\)
0.319506 + 0.947584i \(0.396483\pi\)
\(230\) 1.12279e8 0.00264559
\(231\) 7.91234e9 0.182831
\(232\) 5.10218e9 0.115627
\(233\) −2.79305e10 −0.620837 −0.310418 0.950600i \(-0.600469\pi\)
−0.310418 + 0.950600i \(0.600469\pi\)
\(234\) 1.79420e9 0.0391200
\(235\) 1.51784e9 0.0324654
\(236\) −6.13932e9 −0.128830
\(237\) −3.65977e10 −0.753505
\(238\) −1.81451e9 −0.0366575
\(239\) −6.43052e10 −1.27484 −0.637420 0.770516i \(-0.719998\pi\)
−0.637420 + 0.770516i \(0.719998\pi\)
\(240\) −1.36707e9 −0.0265975
\(241\) −2.46077e10 −0.469889 −0.234944 0.972009i \(-0.575491\pi\)
−0.234944 + 0.972009i \(0.575491\pi\)
\(242\) 6.29430e8 0.0117972
\(243\) 3.48678e9 0.0641500
\(244\) 4.52840e10 0.817882
\(245\) 2.44066e9 0.0432772
\(246\) −5.82232e9 −0.101365
\(247\) 2.55755e10 0.437208
\(248\) −1.77546e10 −0.298042
\(249\) −3.80873e10 −0.627890
\(250\) 5.99481e8 0.00970612
\(251\) −2.02230e10 −0.321599 −0.160799 0.986987i \(-0.551407\pi\)
−0.160799 + 0.986987i \(0.551407\pi\)
\(252\) 6.33151e9 0.0989020
\(253\) 3.74788e10 0.575100
\(254\) −7.70043e9 −0.116082
\(255\) −2.21812e9 −0.0328514
\(256\) 6.16574e10 0.897234
\(257\) 6.69980e10 0.957995 0.478997 0.877816i \(-0.341000\pi\)
0.478997 + 0.877816i \(0.341000\pi\)
\(258\) −3.72317e9 −0.0523147
\(259\) −3.92733e10 −0.542311
\(260\) 3.98270e9 0.0540503
\(261\) −1.42144e10 −0.189603
\(262\) −1.38544e10 −0.181649
\(263\) 5.85641e10 0.754798 0.377399 0.926051i \(-0.376819\pi\)
0.377399 + 0.926051i \(0.376819\pi\)
\(264\) 9.78312e9 0.123954
\(265\) 2.17730e9 0.0271214
\(266\) −9.52118e8 −0.0116607
\(267\) 1.66137e10 0.200063
\(268\) −3.74863e10 −0.443880
\(269\) 4.85172e9 0.0564951 0.0282476 0.999601i \(-0.491007\pi\)
0.0282476 + 0.999601i \(0.491007\pi\)
\(270\) −8.16511e7 −0.000935029 0
\(271\) 1.61545e11 1.81942 0.909708 0.415248i \(-0.136305\pi\)
0.909708 + 0.415248i \(0.136305\pi\)
\(272\) 1.04649e11 1.15924
\(273\) −1.82490e10 −0.198842
\(274\) −2.25965e9 −0.0242194
\(275\) 9.99405e10 1.05377
\(276\) 2.99908e10 0.311098
\(277\) −9.49694e10 −0.969225 −0.484613 0.874729i \(-0.661039\pi\)
−0.484613 + 0.874729i \(0.661039\pi\)
\(278\) −1.42257e10 −0.142847
\(279\) 4.94632e10 0.488724
\(280\) −2.98098e8 −0.00289833
\(281\) 1.41795e10 0.135670 0.0678349 0.997697i \(-0.478391\pi\)
0.0678349 + 0.997697i \(0.478391\pi\)
\(282\) −4.27706e9 −0.0402739
\(283\) 5.25711e10 0.487201 0.243601 0.969876i \(-0.421671\pi\)
0.243601 + 0.969876i \(0.421671\pi\)
\(284\) −1.90145e11 −1.73441
\(285\) −1.16390e9 −0.0104500
\(286\) −1.40247e10 −0.123950
\(287\) 5.92196e10 0.515225
\(288\) 1.17633e10 0.100754
\(289\) 5.12080e10 0.431815
\(290\) 3.32862e8 0.00276359
\(291\) −7.51868e10 −0.614643
\(292\) 1.76550e10 0.142116
\(293\) 2.09217e11 1.65841 0.829207 0.558941i \(-0.188792\pi\)
0.829207 + 0.558941i \(0.188792\pi\)
\(294\) −6.87743e9 −0.0536863
\(295\) −8.05275e8 −0.00619078
\(296\) −4.85590e10 −0.367669
\(297\) −2.72552e10 −0.203257
\(298\) 1.52971e10 0.112366
\(299\) −8.64412e10 −0.625461
\(300\) 7.99732e10 0.570031
\(301\) 3.78689e10 0.265909
\(302\) −2.18934e10 −0.151455
\(303\) −8.90722e10 −0.607086
\(304\) 5.49117e10 0.368751
\(305\) 5.93976e9 0.0393024
\(306\) 6.25035e9 0.0407528
\(307\) 1.53968e11 0.989251 0.494626 0.869106i \(-0.335305\pi\)
0.494626 + 0.869106i \(0.335305\pi\)
\(308\) −4.94917e10 −0.313368
\(309\) 1.06257e10 0.0663046
\(310\) −1.15830e9 −0.00712347
\(311\) −2.79730e10 −0.169558 −0.0847789 0.996400i \(-0.527018\pi\)
−0.0847789 + 0.996400i \(0.527018\pi\)
\(312\) −2.25638e10 −0.134808
\(313\) 2.14977e11 1.26603 0.633014 0.774141i \(-0.281818\pi\)
0.633014 + 0.774141i \(0.281818\pi\)
\(314\) 2.54625e10 0.147814
\(315\) 8.30484e8 0.00475263
\(316\) 2.28918e11 1.29148
\(317\) 2.33306e11 1.29766 0.648828 0.760935i \(-0.275259\pi\)
0.648828 + 0.760935i \(0.275259\pi\)
\(318\) −6.13534e9 −0.0336447
\(319\) 1.11110e11 0.600751
\(320\) 8.36578e9 0.0445997
\(321\) 1.14793e11 0.603454
\(322\) 3.21801e9 0.0166815
\(323\) 8.90961e10 0.455457
\(324\) −2.18098e10 −0.109951
\(325\) −2.30503e11 −1.14604
\(326\) 9.19164e9 0.0450727
\(327\) 1.74637e10 0.0844638
\(328\) 7.32214e10 0.349306
\(329\) 4.35025e10 0.204707
\(330\) 6.38244e8 0.00296261
\(331\) −1.32503e11 −0.606738 −0.303369 0.952873i \(-0.598111\pi\)
−0.303369 + 0.952873i \(0.598111\pi\)
\(332\) 2.38236e11 1.07618
\(333\) 1.35283e11 0.602897
\(334\) −2.73943e10 −0.120448
\(335\) −4.91695e9 −0.0213302
\(336\) −3.91814e10 −0.167708
\(337\) −3.77882e11 −1.59596 −0.797979 0.602685i \(-0.794097\pi\)
−0.797979 + 0.602685i \(0.794097\pi\)
\(338\) 7.83002e9 0.0326316
\(339\) −7.48780e10 −0.307933
\(340\) 1.38743e10 0.0563063
\(341\) −3.86640e11 −1.54850
\(342\) 3.27971e9 0.0129634
\(343\) 1.46813e11 0.572717
\(344\) 4.68225e10 0.180278
\(345\) 3.93380e9 0.0149495
\(346\) −3.58598e10 −0.134513
\(347\) −5.13729e11 −1.90218 −0.951090 0.308914i \(-0.900034\pi\)
−0.951090 + 0.308914i \(0.900034\pi\)
\(348\) 8.89110e10 0.324974
\(349\) 4.77122e11 1.72153 0.860765 0.509002i \(-0.169985\pi\)
0.860765 + 0.509002i \(0.169985\pi\)
\(350\) 8.58109e9 0.0305658
\(351\) 6.28615e10 0.221056
\(352\) −9.19507e10 −0.319237
\(353\) 1.57630e11 0.540323 0.270162 0.962815i \(-0.412923\pi\)
0.270162 + 0.962815i \(0.412923\pi\)
\(354\) 2.26915e9 0.00767978
\(355\) −2.49407e10 −0.0833454
\(356\) −1.03919e11 −0.342902
\(357\) −6.35732e10 −0.207141
\(358\) −4.72991e10 −0.152187
\(359\) −1.17398e11 −0.373022 −0.186511 0.982453i \(-0.559718\pi\)
−0.186511 + 0.982453i \(0.559718\pi\)
\(360\) 1.02684e9 0.00322213
\(361\) −2.75937e11 −0.855120
\(362\) −2.90533e10 −0.0889215
\(363\) 2.20527e10 0.0666626
\(364\) 1.14148e11 0.340809
\(365\) 2.31575e9 0.00682925
\(366\) −1.67374e10 −0.0487555
\(367\) 3.08329e11 0.887192 0.443596 0.896227i \(-0.353703\pi\)
0.443596 + 0.896227i \(0.353703\pi\)
\(368\) −1.85593e11 −0.527529
\(369\) −2.03991e11 −0.572785
\(370\) −3.16795e9 −0.00878762
\(371\) 6.24034e10 0.171012
\(372\) −3.09393e11 −0.837658
\(373\) −5.75361e11 −1.53904 −0.769522 0.638620i \(-0.779505\pi\)
−0.769522 + 0.638620i \(0.779505\pi\)
\(374\) −4.88572e10 −0.129124
\(375\) 2.10034e10 0.0548466
\(376\) 5.37882e10 0.138785
\(377\) −2.56264e11 −0.653358
\(378\) −2.34019e9 −0.00589573
\(379\) 2.91299e11 0.725207 0.362604 0.931943i \(-0.381888\pi\)
0.362604 + 0.931943i \(0.381888\pi\)
\(380\) 7.28020e9 0.0179109
\(381\) −2.69792e11 −0.655945
\(382\) 6.05510e10 0.145491
\(383\) −6.52162e11 −1.54868 −0.774338 0.632772i \(-0.781917\pi\)
−0.774338 + 0.632772i \(0.781917\pi\)
\(384\) −9.79295e10 −0.229839
\(385\) −6.49167e9 −0.0150585
\(386\) 6.00280e10 0.137629
\(387\) −1.30445e11 −0.295616
\(388\) 4.70293e11 1.05348
\(389\) 2.32127e10 0.0513987 0.0256993 0.999670i \(-0.491819\pi\)
0.0256993 + 0.999670i \(0.491819\pi\)
\(390\) −1.47205e9 −0.00322204
\(391\) −3.01131e11 −0.651568
\(392\) 8.64905e10 0.185004
\(393\) −4.85403e11 −1.02645
\(394\) −2.57989e9 −0.00539347
\(395\) 3.00265e10 0.0620609
\(396\) 1.70481e11 0.348376
\(397\) −2.94489e11 −0.594993 −0.297496 0.954723i \(-0.596152\pi\)
−0.297496 + 0.954723i \(0.596152\pi\)
\(398\) 6.89865e10 0.137813
\(399\) −3.33584e10 −0.0658911
\(400\) −4.94899e11 −0.966600
\(401\) −6.28022e11 −1.21290 −0.606451 0.795121i \(-0.707407\pi\)
−0.606451 + 0.795121i \(0.707407\pi\)
\(402\) 1.38553e10 0.0264605
\(403\) 8.91748e11 1.68411
\(404\) 5.57147e11 1.04053
\(405\) −2.86073e9 −0.00528359
\(406\) 9.54012e9 0.0174256
\(407\) −1.05747e12 −1.91026
\(408\) −7.86043e10 −0.140435
\(409\) 3.47418e11 0.613900 0.306950 0.951726i \(-0.400692\pi\)
0.306950 + 0.951726i \(0.400692\pi\)
\(410\) 4.77691e9 0.00834872
\(411\) −7.91691e10 −0.136857
\(412\) −6.64637e10 −0.113644
\(413\) −2.30799e10 −0.0390353
\(414\) −1.10849e10 −0.0185451
\(415\) 3.12487e10 0.0517148
\(416\) 2.12075e11 0.347192
\(417\) −4.98411e11 −0.807189
\(418\) −2.56366e10 −0.0410740
\(419\) 1.58933e11 0.251913 0.125956 0.992036i \(-0.459800\pi\)
0.125956 + 0.992036i \(0.459800\pi\)
\(420\) −5.19468e9 −0.00814586
\(421\) 9.69796e11 1.50456 0.752282 0.658841i \(-0.228953\pi\)
0.752282 + 0.658841i \(0.228953\pi\)
\(422\) −1.04810e11 −0.160878
\(423\) −1.49851e11 −0.227577
\(424\) 7.71579e10 0.115940
\(425\) −8.02991e11 −1.19388
\(426\) 7.02794e10 0.103392
\(427\) 1.70238e11 0.247818
\(428\) −7.18033e11 −1.03430
\(429\) −4.91370e11 −0.700408
\(430\) 3.05467e9 0.00430880
\(431\) −5.04058e11 −0.703611 −0.351805 0.936073i \(-0.614432\pi\)
−0.351805 + 0.936073i \(0.614432\pi\)
\(432\) 1.34966e11 0.186444
\(433\) 5.44129e11 0.743886 0.371943 0.928256i \(-0.378692\pi\)
0.371943 + 0.928256i \(0.378692\pi\)
\(434\) −3.31977e10 −0.0449164
\(435\) 1.16622e10 0.0156163
\(436\) −1.09235e11 −0.144768
\(437\) −1.58011e11 −0.207262
\(438\) −6.52545e9 −0.00847182
\(439\) −1.07969e12 −1.38743 −0.693713 0.720252i \(-0.744026\pi\)
−0.693713 + 0.720252i \(0.744026\pi\)
\(440\) −8.02655e9 −0.0102092
\(441\) −2.40958e11 −0.303366
\(442\) 1.12684e11 0.140431
\(443\) 7.29394e11 0.899798 0.449899 0.893079i \(-0.351460\pi\)
0.449899 + 0.893079i \(0.351460\pi\)
\(444\) −8.46193e11 −1.03335
\(445\) −1.36307e10 −0.0164778
\(446\) 9.93844e10 0.118935
\(447\) 5.35948e11 0.634949
\(448\) 2.39770e11 0.281219
\(449\) 4.06817e11 0.472379 0.236190 0.971707i \(-0.424101\pi\)
0.236190 + 0.971707i \(0.424101\pi\)
\(450\) −2.95588e10 −0.0339806
\(451\) 1.59454e12 1.81485
\(452\) 4.68362e11 0.527787
\(453\) −7.67058e11 −0.855828
\(454\) −1.08787e11 −0.120178
\(455\) 1.49724e10 0.0163772
\(456\) −4.12456e10 −0.0446720
\(457\) 8.28426e11 0.888445 0.444223 0.895916i \(-0.353480\pi\)
0.444223 + 0.895916i \(0.353480\pi\)
\(458\) 6.14808e10 0.0652897
\(459\) 2.18987e11 0.230283
\(460\) −2.46059e10 −0.0256230
\(461\) −1.71341e12 −1.76688 −0.883442 0.468540i \(-0.844780\pi\)
−0.883442 + 0.468540i \(0.844780\pi\)
\(462\) 1.82926e10 0.0186804
\(463\) 1.18389e12 1.19728 0.598641 0.801017i \(-0.295708\pi\)
0.598641 + 0.801017i \(0.295708\pi\)
\(464\) −5.50209e11 −0.551058
\(465\) −4.05820e10 −0.0402528
\(466\) −6.45728e10 −0.0634327
\(467\) −1.00024e12 −0.973143 −0.486571 0.873641i \(-0.661753\pi\)
−0.486571 + 0.873641i \(0.661753\pi\)
\(468\) −3.93198e11 −0.378883
\(469\) −1.40924e11 −0.134495
\(470\) 3.50910e9 0.00331708
\(471\) 8.92102e11 0.835258
\(472\) −2.85368e10 −0.0264647
\(473\) 1.01965e12 0.936649
\(474\) −8.46105e10 −0.0769877
\(475\) −4.21349e11 −0.379770
\(476\) 3.97650e11 0.355034
\(477\) −2.14958e11 −0.190117
\(478\) −1.48668e11 −0.130254
\(479\) −1.87270e12 −1.62540 −0.812698 0.582685i \(-0.802002\pi\)
−0.812698 + 0.582685i \(0.802002\pi\)
\(480\) −9.65121e9 −0.00829843
\(481\) 2.43894e12 2.07754
\(482\) −5.68908e10 −0.0480099
\(483\) 1.12746e11 0.0942626
\(484\) −1.37940e11 −0.114258
\(485\) 6.16869e10 0.0506238
\(486\) 8.06113e9 0.00655439
\(487\) −1.59310e12 −1.28340 −0.641701 0.766955i \(-0.721771\pi\)
−0.641701 + 0.766955i \(0.721771\pi\)
\(488\) 2.10489e11 0.168012
\(489\) 3.22038e11 0.254693
\(490\) 5.64258e9 0.00442176
\(491\) −7.08110e11 −0.549837 −0.274919 0.961468i \(-0.588651\pi\)
−0.274919 + 0.961468i \(0.588651\pi\)
\(492\) 1.27596e12 0.981736
\(493\) −8.92733e11 −0.680629
\(494\) 5.91282e10 0.0446708
\(495\) 2.23615e10 0.0167409
\(496\) 1.91462e12 1.42041
\(497\) −7.14822e11 −0.525526
\(498\) −8.80544e10 −0.0641533
\(499\) −9.15454e11 −0.660974 −0.330487 0.943811i \(-0.607213\pi\)
−0.330487 + 0.943811i \(0.607213\pi\)
\(500\) −1.31376e11 −0.0940053
\(501\) −9.59786e11 −0.680620
\(502\) −4.67538e10 −0.0328587
\(503\) −5.42714e11 −0.378021 −0.189010 0.981975i \(-0.560528\pi\)
−0.189010 + 0.981975i \(0.560528\pi\)
\(504\) 2.94302e10 0.0203168
\(505\) 7.30792e10 0.0500014
\(506\) 8.66476e10 0.0587596
\(507\) 2.74333e11 0.184392
\(508\) 1.68755e12 1.12427
\(509\) −1.26506e12 −0.835376 −0.417688 0.908591i \(-0.637159\pi\)
−0.417688 + 0.908591i \(0.637159\pi\)
\(510\) −5.12809e9 −0.00335652
\(511\) 6.63712e10 0.0430612
\(512\) 7.61557e11 0.489765
\(513\) 1.14908e11 0.0732524
\(514\) 1.54893e11 0.0978811
\(515\) −8.71783e9 −0.00546105
\(516\) 8.15933e11 0.506677
\(517\) 1.17134e12 0.721069
\(518\) −9.07962e10 −0.0554094
\(519\) −1.25638e12 −0.760098
\(520\) 1.85124e10 0.0111032
\(521\) 7.82364e10 0.0465199 0.0232600 0.999729i \(-0.492595\pi\)
0.0232600 + 0.999729i \(0.492595\pi\)
\(522\) −3.28623e10 −0.0193723
\(523\) −2.77023e12 −1.61904 −0.809521 0.587092i \(-0.800273\pi\)
−0.809521 + 0.587092i \(0.800273\pi\)
\(524\) 3.03620e12 1.75930
\(525\) 3.00647e11 0.172719
\(526\) 1.35395e11 0.0771198
\(527\) 3.10653e12 1.75440
\(528\) −1.05499e12 −0.590741
\(529\) −1.26710e12 −0.703495
\(530\) 5.03373e9 0.00277108
\(531\) 7.95020e10 0.0433963
\(532\) 2.08657e11 0.112935
\(533\) −3.67764e12 −1.97377
\(534\) 3.84094e10 0.0204410
\(535\) −9.41821e10 −0.0497023
\(536\) −1.74244e11 −0.0911834
\(537\) −1.65717e12 −0.859969
\(538\) 1.12167e10 0.00577227
\(539\) 1.88350e12 0.961205
\(540\) 1.78938e10 0.00905590
\(541\) 4.11901e11 0.206731 0.103366 0.994643i \(-0.467039\pi\)
0.103366 + 0.994643i \(0.467039\pi\)
\(542\) 3.73478e11 0.185895
\(543\) −1.01791e12 −0.502471
\(544\) 7.38795e11 0.361684
\(545\) −1.43280e10 −0.00695668
\(546\) −4.21901e10 −0.0203162
\(547\) 1.13699e12 0.543019 0.271509 0.962436i \(-0.412477\pi\)
0.271509 + 0.962436i \(0.412477\pi\)
\(548\) 4.95203e11 0.234569
\(549\) −5.86412e11 −0.275503
\(550\) 2.31053e11 0.107666
\(551\) −4.68439e11 −0.216506
\(552\) 1.39404e11 0.0639070
\(553\) 8.60585e11 0.391319
\(554\) −2.19561e11 −0.0990285
\(555\) −1.10992e11 −0.0496564
\(556\) 3.11756e12 1.38350
\(557\) 1.99820e12 0.879612 0.439806 0.898093i \(-0.355047\pi\)
0.439806 + 0.898093i \(0.355047\pi\)
\(558\) 1.14354e11 0.0499343
\(559\) −2.35173e12 −1.01867
\(560\) 3.21463e10 0.0138129
\(561\) −1.71176e12 −0.729643
\(562\) 3.27818e10 0.0138618
\(563\) 2.68941e12 1.12815 0.564077 0.825722i \(-0.309232\pi\)
0.564077 + 0.825722i \(0.309232\pi\)
\(564\) 9.37318e11 0.390059
\(565\) 6.14336e10 0.0253623
\(566\) 1.21540e11 0.0497787
\(567\) −8.19908e10 −0.0333151
\(568\) −8.83833e11 −0.356289
\(569\) 1.26023e12 0.504017 0.252009 0.967725i \(-0.418909\pi\)
0.252009 + 0.967725i \(0.418909\pi\)
\(570\) −2.69083e9 −0.00106770
\(571\) −2.08633e12 −0.821336 −0.410668 0.911785i \(-0.634704\pi\)
−0.410668 + 0.911785i \(0.634704\pi\)
\(572\) 3.07352e12 1.20048
\(573\) 2.12147e12 0.822130
\(574\) 1.36910e11 0.0526420
\(575\) 1.42409e12 0.543291
\(576\) −8.25924e11 −0.312636
\(577\) 9.10416e11 0.341939 0.170970 0.985276i \(-0.445310\pi\)
0.170970 + 0.985276i \(0.445310\pi\)
\(578\) 1.18388e11 0.0441198
\(579\) 2.10314e12 0.777704
\(580\) −7.29469e10 −0.0267658
\(581\) 8.95613e11 0.326083
\(582\) −1.73825e11 −0.0627999
\(583\) 1.68026e12 0.602378
\(584\) 8.20639e10 0.0291941
\(585\) −5.15746e10 −0.0182068
\(586\) 4.83691e11 0.169445
\(587\) −4.36065e12 −1.51593 −0.757966 0.652294i \(-0.773807\pi\)
−0.757966 + 0.652294i \(0.773807\pi\)
\(588\) 1.50719e12 0.519960
\(589\) 1.63007e12 0.558070
\(590\) −1.86172e9 −0.000632530 0
\(591\) −9.03890e10 −0.0304770
\(592\) 5.23651e12 1.75224
\(593\) −4.56249e12 −1.51515 −0.757575 0.652748i \(-0.773616\pi\)
−0.757575 + 0.652748i \(0.773616\pi\)
\(594\) −6.30116e10 −0.0207674
\(595\) 5.21585e10 0.0170608
\(596\) −3.35236e12 −1.08828
\(597\) 2.41701e12 0.778743
\(598\) −1.99844e11 −0.0639052
\(599\) 4.09645e12 1.30013 0.650066 0.759878i \(-0.274741\pi\)
0.650066 + 0.759878i \(0.274741\pi\)
\(600\) 3.71732e11 0.117098
\(601\) −2.16427e12 −0.676670 −0.338335 0.941026i \(-0.609864\pi\)
−0.338335 + 0.941026i \(0.609864\pi\)
\(602\) 8.75494e10 0.0271687
\(603\) 4.85434e11 0.149521
\(604\) 4.79795e12 1.46686
\(605\) −1.80931e10 −0.00549053
\(606\) −2.05927e11 −0.0620278
\(607\) −5.62833e12 −1.68279 −0.841397 0.540418i \(-0.818266\pi\)
−0.841397 + 0.540418i \(0.818266\pi\)
\(608\) 3.87664e11 0.115051
\(609\) 3.34247e11 0.0984669
\(610\) 1.37322e10 0.00401564
\(611\) −2.70159e12 −0.784212
\(612\) −1.36976e12 −0.394698
\(613\) −5.37170e12 −1.53653 −0.768263 0.640135i \(-0.778878\pi\)
−0.768263 + 0.640135i \(0.778878\pi\)
\(614\) 3.55959e11 0.101075
\(615\) 1.67364e11 0.0471763
\(616\) −2.30048e11 −0.0643731
\(617\) 5.20100e12 1.44479 0.722393 0.691482i \(-0.243042\pi\)
0.722393 + 0.691482i \(0.243042\pi\)
\(618\) 2.45656e10 0.00677453
\(619\) 3.02993e12 0.829515 0.414757 0.909932i \(-0.363866\pi\)
0.414757 + 0.909932i \(0.363866\pi\)
\(620\) 2.53841e11 0.0689920
\(621\) −3.88371e11 −0.104793
\(622\) −6.46711e10 −0.0173242
\(623\) −3.90667e11 −0.103899
\(624\) 2.43324e12 0.642471
\(625\) 3.78884e12 0.993221
\(626\) 4.97008e11 0.129354
\(627\) −8.98203e11 −0.232098
\(628\) −5.58010e12 −1.43161
\(629\) 8.49641e12 2.16425
\(630\) 1.92000e9 0.000485590 0
\(631\) −7.43674e11 −0.186746 −0.0933728 0.995631i \(-0.529765\pi\)
−0.0933728 + 0.995631i \(0.529765\pi\)
\(632\) 1.06406e12 0.265301
\(633\) −3.67213e12 −0.909077
\(634\) 5.39383e11 0.132585
\(635\) 2.21351e11 0.0540255
\(636\) 1.34456e12 0.325854
\(637\) −4.34410e12 −1.04538
\(638\) 2.56876e11 0.0613805
\(639\) 2.46231e12 0.584237
\(640\) 8.03461e10 0.0189302
\(641\) −2.70635e12 −0.633175 −0.316587 0.948563i \(-0.602537\pi\)
−0.316587 + 0.948563i \(0.602537\pi\)
\(642\) 2.65392e11 0.0616566
\(643\) 7.61624e12 1.75708 0.878540 0.477670i \(-0.158518\pi\)
0.878540 + 0.477670i \(0.158518\pi\)
\(644\) −7.05227e11 −0.161563
\(645\) 1.07023e11 0.0243478
\(646\) 2.05982e11 0.0465353
\(647\) 3.39864e12 0.762492 0.381246 0.924474i \(-0.375495\pi\)
0.381246 + 0.924474i \(0.375495\pi\)
\(648\) −1.01377e11 −0.0225866
\(649\) −6.21445e11 −0.137500
\(650\) −5.32901e11 −0.117095
\(651\) −1.16312e12 −0.253810
\(652\) −2.01435e12 −0.436537
\(653\) −7.24539e12 −1.55938 −0.779690 0.626165i \(-0.784624\pi\)
−0.779690 + 0.626165i \(0.784624\pi\)
\(654\) 4.03744e10 0.00862990
\(655\) 3.98248e11 0.0845412
\(656\) −7.89606e12 −1.66473
\(657\) −2.28625e11 −0.0478719
\(658\) 1.00574e11 0.0209155
\(659\) −5.42798e12 −1.12113 −0.560563 0.828112i \(-0.689415\pi\)
−0.560563 + 0.828112i \(0.689415\pi\)
\(660\) −1.39871e11 −0.0286933
\(661\) −1.19116e12 −0.242697 −0.121349 0.992610i \(-0.538722\pi\)
−0.121349 + 0.992610i \(0.538722\pi\)
\(662\) −3.06336e11 −0.0619921
\(663\) 3.94801e12 0.793537
\(664\) 1.10737e12 0.221074
\(665\) 2.73688e10 0.00542699
\(666\) 3.12761e11 0.0615997
\(667\) 1.58325e12 0.309730
\(668\) 6.00346e12 1.16656
\(669\) 3.48203e12 0.672071
\(670\) −1.13675e10 −0.00217937
\(671\) 4.58382e12 0.872923
\(672\) −2.76612e11 −0.0523249
\(673\) 3.67244e12 0.690060 0.345030 0.938592i \(-0.387869\pi\)
0.345030 + 0.938592i \(0.387869\pi\)
\(674\) −8.73628e11 −0.163064
\(675\) −1.03562e12 −0.192015
\(676\) −1.71595e12 −0.316042
\(677\) 1.04927e13 1.91972 0.959860 0.280479i \(-0.0904932\pi\)
0.959860 + 0.280479i \(0.0904932\pi\)
\(678\) −1.73111e11 −0.0314624
\(679\) 1.76800e12 0.319203
\(680\) 6.44908e10 0.0115666
\(681\) −3.81147e12 −0.679094
\(682\) −8.93877e11 −0.158215
\(683\) −8.23433e12 −1.44789 −0.723944 0.689858i \(-0.757673\pi\)
−0.723944 + 0.689858i \(0.757673\pi\)
\(684\) −7.18749e11 −0.125552
\(685\) 6.49542e10 0.0112720
\(686\) 3.39417e11 0.0585161
\(687\) 2.15404e12 0.368934
\(688\) −5.04925e12 −0.859170
\(689\) −3.87536e12 −0.655127
\(690\) 9.09459e9 0.00152743
\(691\) −6.64111e11 −0.110813 −0.0554063 0.998464i \(-0.517645\pi\)
−0.0554063 + 0.998464i \(0.517645\pi\)
\(692\) 7.85869e12 1.30278
\(693\) 6.40899e11 0.105558
\(694\) −1.18769e12 −0.194351
\(695\) 4.08920e11 0.0664825
\(696\) 4.13277e11 0.0667574
\(697\) −1.28116e13 −2.05616
\(698\) 1.10306e12 0.175894
\(699\) −2.26237e12 −0.358440
\(700\) −1.88055e12 −0.296035
\(701\) −1.00530e13 −1.57241 −0.786205 0.617966i \(-0.787957\pi\)
−0.786205 + 0.617966i \(0.787957\pi\)
\(702\) 1.45330e11 0.0225859
\(703\) 4.45827e12 0.688443
\(704\) 6.45602e12 0.990576
\(705\) 1.22945e11 0.0187439
\(706\) 3.64427e11 0.0552064
\(707\) 2.09451e12 0.315279
\(708\) −4.97285e11 −0.0743799
\(709\) −8.17137e12 −1.21447 −0.607235 0.794522i \(-0.707721\pi\)
−0.607235 + 0.794522i \(0.707721\pi\)
\(710\) −5.76607e10 −0.00851564
\(711\) −2.96441e12 −0.435036
\(712\) −4.83036e11 −0.0704401
\(713\) −5.50939e12 −0.798364
\(714\) −1.46975e11 −0.0211642
\(715\) 4.03144e11 0.0576877
\(716\) 1.03656e13 1.47396
\(717\) −5.20872e12 −0.736029
\(718\) −2.71412e11 −0.0381127
\(719\) −3.94171e12 −0.550054 −0.275027 0.961437i \(-0.588687\pi\)
−0.275027 + 0.961437i \(0.588687\pi\)
\(720\) −1.10733e11 −0.0153561
\(721\) −2.49860e11 −0.0344341
\(722\) −6.37941e11 −0.0873701
\(723\) −1.99323e12 −0.271290
\(724\) 6.36704e12 0.861219
\(725\) 4.22187e12 0.567523
\(726\) 5.09838e10 0.00681111
\(727\) 3.78831e12 0.502968 0.251484 0.967861i \(-0.419081\pi\)
0.251484 + 0.967861i \(0.419081\pi\)
\(728\) 5.30582e11 0.0700102
\(729\) 2.82430e11 0.0370370
\(730\) 5.35379e9 0.000697764 0
\(731\) −8.19258e12 −1.06119
\(732\) 3.66800e12 0.472204
\(733\) 1.11628e13 1.42825 0.714126 0.700017i \(-0.246824\pi\)
0.714126 + 0.700017i \(0.246824\pi\)
\(734\) 7.12829e11 0.0906469
\(735\) 1.97693e11 0.0249861
\(736\) −1.31024e12 −0.164589
\(737\) −3.79450e12 −0.473752
\(738\) −4.71608e11 −0.0585231
\(739\) −5.41764e12 −0.668205 −0.334103 0.942537i \(-0.608433\pi\)
−0.334103 + 0.942537i \(0.608433\pi\)
\(740\) 6.94258e11 0.0851095
\(741\) 2.07162e12 0.252422
\(742\) 1.44271e11 0.0174727
\(743\) 7.35609e12 0.885518 0.442759 0.896641i \(-0.354000\pi\)
0.442759 + 0.896641i \(0.354000\pi\)
\(744\) −1.43812e12 −0.172075
\(745\) −4.39718e11 −0.0522963
\(746\) −1.33018e12 −0.157249
\(747\) −3.08507e12 −0.362512
\(748\) 1.07071e13 1.25059
\(749\) −2.69934e12 −0.313393
\(750\) 4.85580e10 0.00560383
\(751\) −1.05347e13 −1.20849 −0.604245 0.796798i \(-0.706525\pi\)
−0.604245 + 0.796798i \(0.706525\pi\)
\(752\) −5.80042e12 −0.661423
\(753\) −1.63806e12 −0.185675
\(754\) −5.92458e11 −0.0667555
\(755\) 6.29332e11 0.0704885
\(756\) 5.12853e11 0.0571011
\(757\) 9.67726e12 1.07108 0.535539 0.844511i \(-0.320109\pi\)
0.535539 + 0.844511i \(0.320109\pi\)
\(758\) 6.73456e11 0.0740965
\(759\) 3.03578e12 0.332034
\(760\) 3.38399e10 0.00367932
\(761\) −8.20057e12 −0.886366 −0.443183 0.896431i \(-0.646151\pi\)
−0.443183 + 0.896431i \(0.646151\pi\)
\(762\) −6.23735e11 −0.0670197
\(763\) −4.10653e11 −0.0438647
\(764\) −1.32698e13 −1.40910
\(765\) −1.79668e11 −0.0189668
\(766\) −1.50774e12 −0.158233
\(767\) 1.43330e12 0.149540
\(768\) 4.99425e12 0.518018
\(769\) 3.67559e12 0.379016 0.189508 0.981879i \(-0.439311\pi\)
0.189508 + 0.981879i \(0.439311\pi\)
\(770\) −1.50081e10 −0.00153857
\(771\) 5.42684e12 0.553098
\(772\) −1.31551e13 −1.33296
\(773\) 9.52868e12 0.959898 0.479949 0.877297i \(-0.340655\pi\)
0.479949 + 0.877297i \(0.340655\pi\)
\(774\) −3.01577e11 −0.0302039
\(775\) −1.46913e13 −1.46286
\(776\) 2.18602e12 0.216410
\(777\) −3.18114e12 −0.313103
\(778\) 5.36656e10 0.00525155
\(779\) −6.72256e12 −0.654058
\(780\) 3.22599e11 0.0312059
\(781\) −1.92472e13 −1.85113
\(782\) −6.96186e11 −0.0665725
\(783\) −1.15137e12 −0.109467
\(784\) −9.32697e12 −0.881695
\(785\) −7.31924e11 −0.0687943
\(786\) −1.12221e12 −0.104875
\(787\) 1.32251e13 1.22889 0.614444 0.788961i \(-0.289380\pi\)
0.614444 + 0.788961i \(0.289380\pi\)
\(788\) 5.65383e11 0.0522366
\(789\) 4.74369e12 0.435783
\(790\) 6.94185e10 0.00634094
\(791\) 1.76074e12 0.159919
\(792\) 7.92433e11 0.0715647
\(793\) −1.05721e13 −0.949363
\(794\) −6.80832e11 −0.0607921
\(795\) 1.76362e11 0.0156586
\(796\) −1.51184e13 −1.33474
\(797\) 6.09773e12 0.535311 0.267655 0.963515i \(-0.413751\pi\)
0.267655 + 0.963515i \(0.413751\pi\)
\(798\) −7.71215e10 −0.00673229
\(799\) −9.41137e12 −0.816944
\(800\) −3.49387e12 −0.301580
\(801\) 1.34571e12 0.115506
\(802\) −1.45193e12 −0.123926
\(803\) 1.78710e12 0.151680
\(804\) −3.03639e12 −0.256274
\(805\) −9.25023e10 −0.00776375
\(806\) 2.06164e12 0.172070
\(807\) 3.92990e11 0.0326175
\(808\) 2.58973e12 0.213749
\(809\) 1.66134e13 1.36361 0.681806 0.731533i \(-0.261195\pi\)
0.681806 + 0.731533i \(0.261195\pi\)
\(810\) −6.61374e9 −0.000539839 0
\(811\) −9.14648e12 −0.742438 −0.371219 0.928545i \(-0.621060\pi\)
−0.371219 + 0.928545i \(0.621060\pi\)
\(812\) −2.09072e12 −0.168769
\(813\) 1.30852e13 1.05044
\(814\) −2.44477e12 −0.195176
\(815\) −2.64216e11 −0.0209773
\(816\) 8.47654e12 0.669288
\(817\) −4.29885e12 −0.337561
\(818\) 8.03199e11 0.0627239
\(819\) −1.47817e12 −0.114801
\(820\) −1.04686e12 −0.0808587
\(821\) 1.42232e12 0.109258 0.0546289 0.998507i \(-0.482602\pi\)
0.0546289 + 0.998507i \(0.482602\pi\)
\(822\) −1.83032e11 −0.0139831
\(823\) −6.31868e12 −0.480095 −0.240048 0.970761i \(-0.577163\pi\)
−0.240048 + 0.970761i \(0.577163\pi\)
\(824\) −3.08937e11 −0.0233452
\(825\) 8.09518e12 0.608392
\(826\) −5.33585e10 −0.00398835
\(827\) 1.17040e13 0.870081 0.435040 0.900411i \(-0.356734\pi\)
0.435040 + 0.900411i \(0.356734\pi\)
\(828\) 2.42926e12 0.179613
\(829\) −6.67758e12 −0.491048 −0.245524 0.969391i \(-0.578960\pi\)
−0.245524 + 0.969391i \(0.578960\pi\)
\(830\) 7.22441e10 0.00528385
\(831\) −7.69252e12 −0.559582
\(832\) −1.48902e13 −1.07732
\(833\) −1.51333e13 −1.08901
\(834\) −1.15228e12 −0.0824728
\(835\) 7.87455e11 0.0560579
\(836\) 5.61826e12 0.397808
\(837\) 4.00652e12 0.282165
\(838\) 3.67438e11 0.0257386
\(839\) −2.68487e11 −0.0187066 −0.00935330 0.999956i \(-0.502977\pi\)
−0.00935330 + 0.999956i \(0.502977\pi\)
\(840\) −2.41459e10 −0.00167335
\(841\) −9.81344e12 −0.676456
\(842\) 2.24208e12 0.153726
\(843\) 1.14854e12 0.0783290
\(844\) 2.29692e13 1.55813
\(845\) −2.25076e11 −0.0151871
\(846\) −3.46442e11 −0.0232522
\(847\) −5.18564e11 −0.0346200
\(848\) −8.32057e12 −0.552550
\(849\) 4.25826e12 0.281286
\(850\) −1.85644e12 −0.121982
\(851\) −1.50683e13 −0.984873
\(852\) −1.54018e13 −1.00136
\(853\) −8.26573e12 −0.534577 −0.267289 0.963617i \(-0.586128\pi\)
−0.267289 + 0.963617i \(0.586128\pi\)
\(854\) 3.93576e11 0.0253202
\(855\) −9.42760e10 −0.00603328
\(856\) −3.33756e12 −0.212470
\(857\) −2.19334e13 −1.38897 −0.694484 0.719508i \(-0.744367\pi\)
−0.694484 + 0.719508i \(0.744367\pi\)
\(858\) −1.13600e12 −0.0715627
\(859\) 3.54754e12 0.222309 0.111155 0.993803i \(-0.464545\pi\)
0.111155 + 0.993803i \(0.464545\pi\)
\(860\) −6.69431e11 −0.0417314
\(861\) 4.79679e12 0.297465
\(862\) −1.16534e12 −0.0718900
\(863\) 1.86855e13 1.14672 0.573359 0.819304i \(-0.305640\pi\)
0.573359 + 0.819304i \(0.305640\pi\)
\(864\) 9.52830e11 0.0581706
\(865\) 1.03080e12 0.0626039
\(866\) 1.25798e12 0.0760050
\(867\) 4.14785e12 0.249309
\(868\) 7.27529e12 0.435022
\(869\) 2.31720e13 1.37840
\(870\) 2.69619e10 0.00159556
\(871\) 8.75163e12 0.515237
\(872\) −5.07748e11 −0.0297388
\(873\) −6.09013e12 −0.354864
\(874\) −3.65306e11 −0.0211766
\(875\) −4.93890e11 −0.0284835
\(876\) 1.43005e12 0.0820509
\(877\) 7.73856e12 0.441735 0.220868 0.975304i \(-0.429111\pi\)
0.220868 + 0.975304i \(0.429111\pi\)
\(878\) −2.49615e12 −0.141757
\(879\) 1.69466e13 0.957486
\(880\) 8.65568e11 0.0486552
\(881\) −2.62226e13 −1.46651 −0.733254 0.679954i \(-0.762000\pi\)
−0.733254 + 0.679954i \(0.762000\pi\)
\(882\) −5.57072e11 −0.0309958
\(883\) 1.14258e13 0.632503 0.316251 0.948675i \(-0.397576\pi\)
0.316251 + 0.948675i \(0.397576\pi\)
\(884\) −2.46948e13 −1.36010
\(885\) −6.52273e10 −0.00357425
\(886\) 1.68629e12 0.0919350
\(887\) 2.65841e13 1.44200 0.721001 0.692934i \(-0.243682\pi\)
0.721001 + 0.692934i \(0.243682\pi\)
\(888\) −3.93328e12 −0.212274
\(889\) 6.34409e12 0.340653
\(890\) −3.15129e10 −0.00168358
\(891\) −2.20767e12 −0.117351
\(892\) −2.17801e13 −1.15191
\(893\) −4.93838e12 −0.259868
\(894\) 1.23906e12 0.0648746
\(895\) 1.35962e12 0.0708296
\(896\) 2.30279e12 0.119362
\(897\) −7.00173e12 −0.361110
\(898\) 9.40524e11 0.0482643
\(899\) −1.63332e13 −0.833973
\(900\) 6.47783e12 0.329108
\(901\) −1.35004e13 −0.682472
\(902\) 3.68642e12 0.185428
\(903\) 3.06738e12 0.153523
\(904\) 2.17704e12 0.108420
\(905\) 8.35144e11 0.0413850
\(906\) −1.77337e12 −0.0874424
\(907\) 5.90778e12 0.289862 0.144931 0.989442i \(-0.453704\pi\)
0.144931 + 0.989442i \(0.453704\pi\)
\(908\) 2.38407e13 1.16395
\(909\) −7.21485e12 −0.350502
\(910\) 3.46148e10 0.00167331
\(911\) −2.75232e13 −1.32393 −0.661967 0.749533i \(-0.730278\pi\)
−0.661967 + 0.749533i \(0.730278\pi\)
\(912\) 4.44785e12 0.212899
\(913\) 2.41152e13 1.14861
\(914\) 1.91524e12 0.0907750
\(915\) 4.81120e11 0.0226913
\(916\) −1.34735e13 −0.632341
\(917\) 1.14141e13 0.533066
\(918\) 5.06278e11 0.0235287
\(919\) −2.28256e13 −1.05561 −0.527804 0.849366i \(-0.676984\pi\)
−0.527804 + 0.849366i \(0.676984\pi\)
\(920\) −1.14373e11 −0.00526357
\(921\) 1.24714e13 0.571144
\(922\) −3.96126e12 −0.180528
\(923\) 4.43917e13 2.01323
\(924\) −4.00883e12 −0.180923
\(925\) −4.01808e13 −1.80460
\(926\) 2.73704e12 0.122330
\(927\) 8.60681e11 0.0382810
\(928\) −3.88435e12 −0.171930
\(929\) 1.55548e13 0.685161 0.342580 0.939489i \(-0.388699\pi\)
0.342580 + 0.939489i \(0.388699\pi\)
\(930\) −9.38220e10 −0.00411274
\(931\) −7.94082e12 −0.346411
\(932\) 1.41511e13 0.614356
\(933\) −2.26581e12 −0.0978942
\(934\) −2.31245e12 −0.0994288
\(935\) 1.40441e12 0.0600956
\(936\) −1.82767e12 −0.0778316
\(937\) 1.18680e13 0.502980 0.251490 0.967860i \(-0.419079\pi\)
0.251490 + 0.967860i \(0.419079\pi\)
\(938\) −3.25803e11 −0.0137418
\(939\) 1.74132e13 0.730941
\(940\) −7.69021e11 −0.0321264
\(941\) 1.60605e13 0.667736 0.333868 0.942620i \(-0.391646\pi\)
0.333868 + 0.942620i \(0.391646\pi\)
\(942\) 2.06246e12 0.0853407
\(943\) 2.27212e13 0.935683
\(944\) 3.07736e12 0.126126
\(945\) 6.72692e10 0.00274393
\(946\) 2.35734e12 0.0957001
\(947\) 4.70957e13 1.90286 0.951430 0.307866i \(-0.0996149\pi\)
0.951430 + 0.307866i \(0.0996149\pi\)
\(948\) 1.85424e13 0.745639
\(949\) −4.12177e12 −0.164963
\(950\) −9.74120e11 −0.0388022
\(951\) 1.88978e13 0.749202
\(952\) 1.84836e12 0.0729324
\(953\) −8.41327e12 −0.330405 −0.165203 0.986260i \(-0.552828\pi\)
−0.165203 + 0.986260i \(0.552828\pi\)
\(954\) −4.96962e11 −0.0194248
\(955\) −1.74055e12 −0.0677130
\(956\) 3.25806e13 1.26153
\(957\) 8.99990e12 0.346844
\(958\) −4.32952e12 −0.166071
\(959\) 1.86164e12 0.0710742
\(960\) 6.77628e11 0.0257496
\(961\) 3.03966e13 1.14966
\(962\) 5.63861e12 0.212268
\(963\) 9.29827e12 0.348404
\(964\) 1.24676e13 0.464983
\(965\) −1.72552e12 −0.0640540
\(966\) 2.60659e11 0.00963108
\(967\) −4.14309e12 −0.152372 −0.0761861 0.997094i \(-0.524274\pi\)
−0.0761861 + 0.997094i \(0.524274\pi\)
\(968\) −6.41172e11 −0.0234712
\(969\) 7.21678e12 0.262958
\(970\) 1.42614e11 0.00517238
\(971\) −1.40316e13 −0.506546 −0.253273 0.967395i \(-0.581507\pi\)
−0.253273 + 0.967395i \(0.581507\pi\)
\(972\) −1.76660e12 −0.0634803
\(973\) 1.17200e13 0.419199
\(974\) −3.68310e12 −0.131129
\(975\) −1.86707e13 −0.661669
\(976\) −2.26988e13 −0.800716
\(977\) −1.55480e13 −0.545945 −0.272972 0.962022i \(-0.588007\pi\)
−0.272972 + 0.962022i \(0.588007\pi\)
\(978\) 7.44523e11 0.0260227
\(979\) −1.05191e13 −0.365978
\(980\) −1.23657e12 −0.0428255
\(981\) 1.41456e12 0.0487652
\(982\) −1.63709e12 −0.0561784
\(983\) 4.09312e13 1.39818 0.699090 0.715033i \(-0.253589\pi\)
0.699090 + 0.715033i \(0.253589\pi\)
\(984\) 5.93093e12 0.201672
\(985\) 7.41595e10 0.00251017
\(986\) −2.06392e12 −0.0695418
\(987\) 3.52370e12 0.118188
\(988\) −1.29580e13 −0.432644
\(989\) 1.45294e13 0.482909
\(990\) 5.16977e10 0.00171046
\(991\) 3.33333e13 1.09786 0.548930 0.835868i \(-0.315035\pi\)
0.548930 + 0.835868i \(0.315035\pi\)
\(992\) 1.35168e13 0.443170
\(993\) −1.07328e13 −0.350300
\(994\) −1.65260e12 −0.0536945
\(995\) −1.98303e12 −0.0641396
\(996\) 1.92971e13 0.621335
\(997\) 1.23092e13 0.394548 0.197274 0.980348i \(-0.436791\pi\)
0.197274 + 0.980348i \(0.436791\pi\)
\(998\) −2.11645e12 −0.0675336
\(999\) 1.09579e13 0.348083
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.a.1.13 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.a.1.13 21 1.1 even 1 trivial