Properties

Label 177.10.a.b.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

\(f(q)\) \(=\) \(q+11.8993 q^{2} -81.0000 q^{3} -370.407 q^{4} -236.774 q^{5} -963.842 q^{6} +4185.56 q^{7} -10500.0 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+11.8993 q^{2} -81.0000 q^{3} -370.407 q^{4} -236.774 q^{5} -963.842 q^{6} +4185.56 q^{7} -10500.0 q^{8} +6561.00 q^{9} -2817.44 q^{10} -25832.4 q^{11} +30003.0 q^{12} +10977.2 q^{13} +49805.2 q^{14} +19178.7 q^{15} +64705.7 q^{16} -74869.7 q^{17} +78071.2 q^{18} +575877. q^{19} +87702.6 q^{20} -339030. q^{21} -307387. q^{22} +1.18652e6 q^{23} +850501. q^{24} -1.89706e6 q^{25} +130621. q^{26} -531441. q^{27} -1.55036e6 q^{28} +971729. q^{29} +228213. q^{30} +7.66093e6 q^{31} +6.14596e6 q^{32} +2.09243e6 q^{33} -890896. q^{34} -991030. q^{35} -2.43024e6 q^{36} -1.34632e7 q^{37} +6.85252e6 q^{38} -889153. q^{39} +2.48613e6 q^{40} +3.71716e6 q^{41} -4.03422e6 q^{42} +1.42413e7 q^{43} +9.56851e6 q^{44} -1.55347e6 q^{45} +1.41188e7 q^{46} +5.03480e7 q^{47} -5.24116e6 q^{48} -2.28347e7 q^{49} -2.25737e7 q^{50} +6.06445e6 q^{51} -4.06603e6 q^{52} -4.53012e7 q^{53} -6.32377e6 q^{54} +6.11644e6 q^{55} -4.39484e7 q^{56} -4.66460e7 q^{57} +1.15629e7 q^{58} -1.21174e7 q^{59} -7.10391e6 q^{60} -1.39439e8 q^{61} +9.11596e7 q^{62} +2.74614e7 q^{63} +4.00032e7 q^{64} -2.59911e6 q^{65} +2.48984e7 q^{66} -1.76510e8 q^{67} +2.77323e7 q^{68} -9.61083e7 q^{69} -1.17926e7 q^{70} -4.76874e7 q^{71} -6.88906e7 q^{72} -1.70848e8 q^{73} -1.60202e8 q^{74} +1.53662e8 q^{75} -2.13309e8 q^{76} -1.08123e8 q^{77} -1.05803e7 q^{78} -7.11694e7 q^{79} -1.53206e7 q^{80} +4.30467e7 q^{81} +4.42315e7 q^{82} -3.04121e8 q^{83} +1.25579e8 q^{84} +1.77272e7 q^{85} +1.69462e8 q^{86} -7.87100e7 q^{87} +2.71241e8 q^{88} -6.08801e8 q^{89} -1.84852e7 q^{90} +4.59457e7 q^{91} -4.39496e8 q^{92} -6.20535e8 q^{93} +5.99106e8 q^{94} -1.36353e8 q^{95} -4.97823e8 q^{96} -5.99259e8 q^{97} -2.71717e8 q^{98} -1.69487e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} + O(q^{10}) \) \( 21q + 20q^{2} - 1701q^{3} + 4950q^{4} + 2058q^{5} - 1620q^{6} - 17167q^{7} - 2853q^{8} + 137781q^{9} - 31559q^{10} - 38751q^{11} - 400950q^{12} - 58915q^{13} + 3453q^{14} - 166698q^{15} + 1655714q^{16} - 64233q^{17} + 131220q^{18} - 1937236q^{19} - 1065507q^{20} + 1390527q^{21} - 5386882q^{22} - 1838574q^{23} + 231093q^{24} + 4565755q^{25} - 839702q^{26} - 11160261q^{27} - 4471034q^{28} + 15658544q^{29} + 2556279q^{30} - 14282802q^{31} - 2205286q^{32} + 3138831q^{33} + 19005532q^{34} - 8633300q^{35} + 32476950q^{36} + 7531195q^{37} + 26649773q^{38} + 4772115q^{39} + 17775672q^{40} + 18338245q^{41} - 279693q^{42} - 22480305q^{43} - 80230922q^{44} + 13502538q^{45} - 83894107q^{46} - 110397260q^{47} - 134112834q^{48} + 130653638q^{49} + 65575693q^{50} + 5202873q^{51} + 177908014q^{52} + 145498338q^{53} - 10628820q^{54} + 86448944q^{55} + 354387888q^{56} + 156916116q^{57} + 115508368q^{58} - 254464581q^{59} + 86306067q^{60} + 287595506q^{61} + 819899030q^{62} - 112632687q^{63} + 822446413q^{64} + 77238206q^{65} + 436337442q^{66} - 392860610q^{67} + 167325073q^{68} + 148924494q^{69} - 424902116q^{70} - 248960491q^{71} - 18718533q^{72} - 758406074q^{73} - 923266846q^{74} - 369826155q^{75} - 2312747568q^{76} - 878126795q^{77} + 68015862q^{78} - 1925801029q^{79} - 1898919861q^{80} + 903981141q^{81} - 3249102191q^{82} - 1650336307q^{83} + 362153754q^{84} - 2342480762q^{85} - 3609864952q^{86} - 1268342064q^{87} - 5987792887q^{88} - 574997526q^{89} - 207058599q^{90} - 4481387117q^{91} - 5317166770q^{92} + 1156906962q^{93} - 5360726568q^{94} - 2789231462q^{95} + 178628166q^{96} - 4651540898q^{97} - 5566652976q^{98} - 254245311q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 11.8993 0.525879 0.262940 0.964812i \(-0.415308\pi\)
0.262940 + 0.964812i \(0.415308\pi\)
\(3\) −81.0000 −0.577350
\(4\) −370.407 −0.723451
\(5\) −236.774 −0.169422 −0.0847108 0.996406i \(-0.526997\pi\)
−0.0847108 + 0.996406i \(0.526997\pi\)
\(6\) −963.842 −0.303617
\(7\) 4185.56 0.658889 0.329444 0.944175i \(-0.393139\pi\)
0.329444 + 0.944175i \(0.393139\pi\)
\(8\) −10500.0 −0.906327
\(9\) 6561.00 0.333333
\(10\) −2817.44 −0.0890952
\(11\) −25832.4 −0.531983 −0.265992 0.963975i \(-0.585699\pi\)
−0.265992 + 0.963975i \(0.585699\pi\)
\(12\) 30003.0 0.417685
\(13\) 10977.2 0.106597 0.0532987 0.998579i \(-0.483026\pi\)
0.0532987 + 0.998579i \(0.483026\pi\)
\(14\) 49805.2 0.346496
\(15\) 19178.7 0.0978156
\(16\) 64705.7 0.246832
\(17\) −74869.7 −0.217413 −0.108707 0.994074i \(-0.534671\pi\)
−0.108707 + 0.994074i \(0.534671\pi\)
\(18\) 78071.2 0.175293
\(19\) 575877. 1.01377 0.506884 0.862014i \(-0.330797\pi\)
0.506884 + 0.862014i \(0.330797\pi\)
\(20\) 87702.6 0.122568
\(21\) −339030. −0.380410
\(22\) −307387. −0.279759
\(23\) 1.18652e6 0.884098 0.442049 0.896991i \(-0.354252\pi\)
0.442049 + 0.896991i \(0.354252\pi\)
\(24\) 850501. 0.523268
\(25\) −1.89706e6 −0.971296
\(26\) 130621. 0.0560573
\(27\) −531441. −0.192450
\(28\) −1.55036e6 −0.476674
\(29\) 971729. 0.255126 0.127563 0.991830i \(-0.459285\pi\)
0.127563 + 0.991830i \(0.459285\pi\)
\(30\) 228213. 0.0514392
\(31\) 7.66093e6 1.48989 0.744944 0.667127i \(-0.232476\pi\)
0.744944 + 0.667127i \(0.232476\pi\)
\(32\) 6.14596e6 1.03613
\(33\) 2.09243e6 0.307141
\(34\) −890896. −0.114333
\(35\) −991030. −0.111630
\(36\) −2.43024e6 −0.241150
\(37\) −1.34632e7 −1.18097 −0.590487 0.807047i \(-0.701064\pi\)
−0.590487 + 0.807047i \(0.701064\pi\)
\(38\) 6.85252e6 0.533119
\(39\) −889153. −0.0615440
\(40\) 2.48613e6 0.153551
\(41\) 3.71716e6 0.205439 0.102720 0.994710i \(-0.467246\pi\)
0.102720 + 0.994710i \(0.467246\pi\)
\(42\) −4.03422e6 −0.200050
\(43\) 1.42413e7 0.635248 0.317624 0.948217i \(-0.397115\pi\)
0.317624 + 0.948217i \(0.397115\pi\)
\(44\) 9.56851e6 0.384864
\(45\) −1.55347e6 −0.0564738
\(46\) 1.41188e7 0.464929
\(47\) 5.03480e7 1.50502 0.752510 0.658581i \(-0.228843\pi\)
0.752510 + 0.658581i \(0.228843\pi\)
\(48\) −5.24116e6 −0.142509
\(49\) −2.28347e7 −0.565866
\(50\) −2.25737e7 −0.510785
\(51\) 6.06445e6 0.125524
\(52\) −4.06603e6 −0.0771180
\(53\) −4.53012e7 −0.788622 −0.394311 0.918977i \(-0.629017\pi\)
−0.394311 + 0.918977i \(0.629017\pi\)
\(54\) −6.32377e6 −0.101206
\(55\) 6.11644e6 0.0901294
\(56\) −4.39484e7 −0.597169
\(57\) −4.66460e7 −0.585299
\(58\) 1.15629e7 0.134165
\(59\) −1.21174e7 −0.130189
\(60\) −7.10391e6 −0.0707648
\(61\) −1.39439e8 −1.28944 −0.644718 0.764421i \(-0.723025\pi\)
−0.644718 + 0.764421i \(0.723025\pi\)
\(62\) 9.11596e7 0.783501
\(63\) 2.74614e7 0.219630
\(64\) 4.00032e7 0.298047
\(65\) −2.59911e6 −0.0180599
\(66\) 2.48984e7 0.161519
\(67\) −1.76510e8 −1.07012 −0.535060 0.844814i \(-0.679711\pi\)
−0.535060 + 0.844814i \(0.679711\pi\)
\(68\) 2.77323e7 0.157288
\(69\) −9.61083e7 −0.510434
\(70\) −1.17926e7 −0.0587039
\(71\) −4.76874e7 −0.222711 −0.111355 0.993781i \(-0.535519\pi\)
−0.111355 + 0.993781i \(0.535519\pi\)
\(72\) −6.88906e7 −0.302109
\(73\) −1.70848e8 −0.704136 −0.352068 0.935974i \(-0.614521\pi\)
−0.352068 + 0.935974i \(0.614521\pi\)
\(74\) −1.60202e8 −0.621049
\(75\) 1.53662e8 0.560778
\(76\) −2.13309e8 −0.733411
\(77\) −1.08123e8 −0.350518
\(78\) −1.05803e7 −0.0323647
\(79\) −7.11694e7 −0.205576 −0.102788 0.994703i \(-0.532776\pi\)
−0.102788 + 0.994703i \(0.532776\pi\)
\(80\) −1.53206e7 −0.0418187
\(81\) 4.30467e7 0.111111
\(82\) 4.42315e7 0.108036
\(83\) −3.04121e8 −0.703388 −0.351694 0.936115i \(-0.614394\pi\)
−0.351694 + 0.936115i \(0.614394\pi\)
\(84\) 1.25579e8 0.275208
\(85\) 1.77272e7 0.0368345
\(86\) 1.69462e8 0.334064
\(87\) −7.87100e7 −0.147297
\(88\) 2.71241e8 0.482151
\(89\) −6.08801e8 −1.02854 −0.514269 0.857629i \(-0.671937\pi\)
−0.514269 + 0.857629i \(0.671937\pi\)
\(90\) −1.84852e7 −0.0296984
\(91\) 4.59457e7 0.0702358
\(92\) −4.39496e8 −0.639602
\(93\) −6.20535e8 −0.860187
\(94\) 5.99106e8 0.791459
\(95\) −1.36353e8 −0.171754
\(96\) −4.97823e8 −0.598211
\(97\) −5.99259e8 −0.687293 −0.343646 0.939099i \(-0.611662\pi\)
−0.343646 + 0.939099i \(0.611662\pi\)
\(98\) −2.71717e8 −0.297577
\(99\) −1.69487e8 −0.177328
\(100\) 7.02685e8 0.702685
\(101\) −1.03425e9 −0.988965 −0.494483 0.869188i \(-0.664642\pi\)
−0.494483 + 0.869188i \(0.664642\pi\)
\(102\) 7.21626e7 0.0660102
\(103\) 1.11407e8 0.0975318 0.0487659 0.998810i \(-0.484471\pi\)
0.0487659 + 0.998810i \(0.484471\pi\)
\(104\) −1.15261e8 −0.0966121
\(105\) 8.02734e7 0.0644496
\(106\) −5.39053e8 −0.414720
\(107\) −4.84503e8 −0.357330 −0.178665 0.983910i \(-0.557178\pi\)
−0.178665 + 0.983910i \(0.557178\pi\)
\(108\) 1.96849e8 0.139228
\(109\) 1.80758e9 1.22653 0.613264 0.789878i \(-0.289856\pi\)
0.613264 + 0.789878i \(0.289856\pi\)
\(110\) 7.27813e7 0.0473972
\(111\) 1.09052e9 0.681835
\(112\) 2.70829e8 0.162635
\(113\) −5.89242e8 −0.339970 −0.169985 0.985447i \(-0.554372\pi\)
−0.169985 + 0.985447i \(0.554372\pi\)
\(114\) −5.55054e8 −0.307797
\(115\) −2.80937e8 −0.149785
\(116\) −3.59935e8 −0.184571
\(117\) 7.20214e7 0.0355324
\(118\) −1.44188e8 −0.0684636
\(119\) −3.13371e8 −0.143251
\(120\) −2.01376e8 −0.0886529
\(121\) −1.69063e9 −0.716994
\(122\) −1.65922e9 −0.678087
\(123\) −3.01090e8 −0.118610
\(124\) −2.83766e9 −1.07786
\(125\) 9.11624e8 0.333980
\(126\) 3.26772e8 0.115499
\(127\) −2.92506e9 −0.997743 −0.498871 0.866676i \(-0.666252\pi\)
−0.498871 + 0.866676i \(0.666252\pi\)
\(128\) −2.67072e9 −0.879394
\(129\) −1.15355e9 −0.366760
\(130\) −3.09276e7 −0.00949732
\(131\) 6.59454e9 1.95643 0.978214 0.207599i \(-0.0665650\pi\)
0.978214 + 0.207599i \(0.0665650\pi\)
\(132\) −7.75049e8 −0.222201
\(133\) 2.41037e9 0.667960
\(134\) −2.10034e9 −0.562754
\(135\) 1.25831e8 0.0326052
\(136\) 7.86133e8 0.197047
\(137\) −3.35904e9 −0.814652 −0.407326 0.913283i \(-0.633539\pi\)
−0.407326 + 0.913283i \(0.633539\pi\)
\(138\) −1.14362e9 −0.268427
\(139\) 6.25873e9 1.42207 0.711033 0.703159i \(-0.248228\pi\)
0.711033 + 0.703159i \(0.248228\pi\)
\(140\) 3.67084e8 0.0807588
\(141\) −4.07819e9 −0.868924
\(142\) −5.67447e8 −0.117119
\(143\) −2.83568e8 −0.0567080
\(144\) 4.24534e8 0.0822775
\(145\) −2.30080e8 −0.0432238
\(146\) −2.03297e9 −0.370290
\(147\) 1.84961e9 0.326703
\(148\) 4.98686e9 0.854376
\(149\) −1.91528e8 −0.0318341 −0.0159171 0.999873i \(-0.505067\pi\)
−0.0159171 + 0.999873i \(0.505067\pi\)
\(150\) 1.82847e9 0.294902
\(151\) −5.18282e9 −0.811279 −0.405639 0.914033i \(-0.632951\pi\)
−0.405639 + 0.914033i \(0.632951\pi\)
\(152\) −6.04672e9 −0.918805
\(153\) −4.91220e8 −0.0724711
\(154\) −1.28659e9 −0.184330
\(155\) −1.81391e9 −0.252419
\(156\) 3.29348e8 0.0445241
\(157\) 6.75931e9 0.887879 0.443940 0.896057i \(-0.353580\pi\)
0.443940 + 0.896057i \(0.353580\pi\)
\(158\) −8.46865e8 −0.108108
\(159\) 3.66940e9 0.455311
\(160\) −1.45520e9 −0.175543
\(161\) 4.96626e9 0.582522
\(162\) 5.12225e8 0.0584310
\(163\) −1.32321e10 −1.46819 −0.734097 0.679045i \(-0.762394\pi\)
−0.734097 + 0.679045i \(0.762394\pi\)
\(164\) −1.37686e9 −0.148625
\(165\) −4.95432e8 −0.0520362
\(166\) −3.61882e9 −0.369897
\(167\) −1.29087e10 −1.28427 −0.642137 0.766590i \(-0.721952\pi\)
−0.642137 + 0.766590i \(0.721952\pi\)
\(168\) 3.55982e9 0.344776
\(169\) −1.04840e10 −0.988637
\(170\) 2.10941e8 0.0193705
\(171\) 3.77833e9 0.337923
\(172\) −5.27509e9 −0.459571
\(173\) 1.16986e10 0.992948 0.496474 0.868051i \(-0.334628\pi\)
0.496474 + 0.868051i \(0.334628\pi\)
\(174\) −9.36593e8 −0.0774603
\(175\) −7.94027e9 −0.639976
\(176\) −1.67150e9 −0.131311
\(177\) 9.81506e8 0.0751646
\(178\) −7.24430e9 −0.540887
\(179\) −1.47861e10 −1.07650 −0.538252 0.842784i \(-0.680915\pi\)
−0.538252 + 0.842784i \(0.680915\pi\)
\(180\) 5.75417e8 0.0408561
\(181\) 1.06044e10 0.734398 0.367199 0.930142i \(-0.380317\pi\)
0.367199 + 0.930142i \(0.380317\pi\)
\(182\) 5.46721e8 0.0369355
\(183\) 1.12945e10 0.744456
\(184\) −1.24585e10 −0.801282
\(185\) 3.18773e9 0.200082
\(186\) −7.38393e9 −0.452355
\(187\) 1.93407e9 0.115660
\(188\) −1.86493e10 −1.08881
\(189\) −2.22438e9 −0.126803
\(190\) −1.62250e9 −0.0903219
\(191\) 1.74635e10 0.949471 0.474735 0.880129i \(-0.342544\pi\)
0.474735 + 0.880129i \(0.342544\pi\)
\(192\) −3.24026e9 −0.172078
\(193\) 3.68522e9 0.191186 0.0955929 0.995421i \(-0.469525\pi\)
0.0955929 + 0.995421i \(0.469525\pi\)
\(194\) −7.13075e9 −0.361433
\(195\) 2.10528e8 0.0104269
\(196\) 8.45814e9 0.409376
\(197\) −2.92499e10 −1.38365 −0.691826 0.722064i \(-0.743194\pi\)
−0.691826 + 0.722064i \(0.743194\pi\)
\(198\) −2.01677e9 −0.0932530
\(199\) −3.10443e10 −1.40328 −0.701639 0.712533i \(-0.747548\pi\)
−0.701639 + 0.712533i \(0.747548\pi\)
\(200\) 1.99192e10 0.880312
\(201\) 1.42973e10 0.617834
\(202\) −1.23069e10 −0.520076
\(203\) 4.06723e9 0.168099
\(204\) −2.24631e9 −0.0908102
\(205\) −8.80125e8 −0.0348058
\(206\) 1.32567e9 0.0512900
\(207\) 7.78477e9 0.294699
\(208\) 7.10287e8 0.0263117
\(209\) −1.48763e10 −0.539308
\(210\) 9.55197e8 0.0338927
\(211\) −7.45417e9 −0.258898 −0.129449 0.991586i \(-0.541321\pi\)
−0.129449 + 0.991586i \(0.541321\pi\)
\(212\) 1.67799e10 0.570529
\(213\) 3.86268e9 0.128582
\(214\) −5.76524e9 −0.187912
\(215\) −3.37198e9 −0.107625
\(216\) 5.58014e9 0.174423
\(217\) 3.20652e10 0.981671
\(218\) 2.15089e10 0.645005
\(219\) 1.38387e10 0.406533
\(220\) −2.26557e9 −0.0652042
\(221\) −8.21859e8 −0.0231757
\(222\) 1.29764e10 0.358563
\(223\) −1.40269e10 −0.379831 −0.189915 0.981800i \(-0.560821\pi\)
−0.189915 + 0.981800i \(0.560821\pi\)
\(224\) 2.57243e10 0.682695
\(225\) −1.24466e10 −0.323765
\(226\) −7.01156e9 −0.178783
\(227\) −2.64313e9 −0.0660696 −0.0330348 0.999454i \(-0.510517\pi\)
−0.0330348 + 0.999454i \(0.510517\pi\)
\(228\) 1.72780e10 0.423435
\(229\) 7.05707e10 1.69576 0.847881 0.530187i \(-0.177878\pi\)
0.847881 + 0.530187i \(0.177878\pi\)
\(230\) −3.34295e9 −0.0787690
\(231\) 8.75797e9 0.202372
\(232\) −1.02032e10 −0.231227
\(233\) −4.79787e9 −0.106647 −0.0533233 0.998577i \(-0.516981\pi\)
−0.0533233 + 0.998577i \(0.516981\pi\)
\(234\) 8.57003e8 0.0186858
\(235\) −1.19211e10 −0.254983
\(236\) 4.48835e9 0.0941853
\(237\) 5.76472e9 0.118689
\(238\) −3.72890e9 −0.0753328
\(239\) −6.36448e10 −1.26175 −0.630874 0.775885i \(-0.717303\pi\)
−0.630874 + 0.775885i \(0.717303\pi\)
\(240\) 1.24097e9 0.0241441
\(241\) −3.20440e10 −0.611885 −0.305942 0.952050i \(-0.598971\pi\)
−0.305942 + 0.952050i \(0.598971\pi\)
\(242\) −2.01173e10 −0.377052
\(243\) −3.48678e9 −0.0641500
\(244\) 5.16491e10 0.932843
\(245\) 5.40666e9 0.0958698
\(246\) −3.58275e9 −0.0623748
\(247\) 6.32151e9 0.108065
\(248\) −8.04398e10 −1.35033
\(249\) 2.46338e10 0.406101
\(250\) 1.08477e10 0.175633
\(251\) 6.51872e10 1.03665 0.518323 0.855185i \(-0.326557\pi\)
0.518323 + 0.855185i \(0.326557\pi\)
\(252\) −1.01719e10 −0.158891
\(253\) −3.06507e10 −0.470326
\(254\) −3.48062e10 −0.524692
\(255\) −1.43590e9 −0.0212664
\(256\) −5.22613e10 −0.760503
\(257\) −4.28183e10 −0.612252 −0.306126 0.951991i \(-0.599033\pi\)
−0.306126 + 0.951991i \(0.599033\pi\)
\(258\) −1.37264e10 −0.192872
\(259\) −5.63509e10 −0.778130
\(260\) 9.62729e8 0.0130654
\(261\) 6.37551e9 0.0850419
\(262\) 7.84704e10 1.02884
\(263\) 1.34491e11 1.73338 0.866689 0.498849i \(-0.166244\pi\)
0.866689 + 0.498849i \(0.166244\pi\)
\(264\) −2.19705e10 −0.278370
\(265\) 1.07261e10 0.133609
\(266\) 2.86816e10 0.351266
\(267\) 4.93129e10 0.593827
\(268\) 6.53805e10 0.774179
\(269\) 1.08095e11 1.25869 0.629346 0.777126i \(-0.283323\pi\)
0.629346 + 0.777126i \(0.283323\pi\)
\(270\) 1.49730e9 0.0171464
\(271\) 4.11140e10 0.463050 0.231525 0.972829i \(-0.425628\pi\)
0.231525 + 0.972829i \(0.425628\pi\)
\(272\) −4.84449e9 −0.0536646
\(273\) −3.72160e9 −0.0405507
\(274\) −3.99701e10 −0.428408
\(275\) 4.90057e10 0.516714
\(276\) 3.55992e10 0.369274
\(277\) 1.37905e11 1.40741 0.703703 0.710494i \(-0.251528\pi\)
0.703703 + 0.710494i \(0.251528\pi\)
\(278\) 7.44745e10 0.747835
\(279\) 5.02633e10 0.496629
\(280\) 1.04058e10 0.101173
\(281\) 3.43222e10 0.328395 0.164197 0.986427i \(-0.447497\pi\)
0.164197 + 0.986427i \(0.447497\pi\)
\(282\) −4.85276e10 −0.456949
\(283\) 2.76964e10 0.256675 0.128338 0.991731i \(-0.459036\pi\)
0.128338 + 0.991731i \(0.459036\pi\)
\(284\) 1.76638e10 0.161120
\(285\) 1.10446e10 0.0991622
\(286\) −3.37425e9 −0.0298216
\(287\) 1.55584e10 0.135362
\(288\) 4.03236e10 0.345377
\(289\) −1.12982e11 −0.952731
\(290\) −2.73779e9 −0.0227305
\(291\) 4.85400e10 0.396809
\(292\) 6.32832e10 0.509408
\(293\) 4.86080e10 0.385304 0.192652 0.981267i \(-0.438291\pi\)
0.192652 + 0.981267i \(0.438291\pi\)
\(294\) 2.20091e10 0.171806
\(295\) 2.86907e9 0.0220568
\(296\) 1.41364e11 1.07035
\(297\) 1.37284e10 0.102380
\(298\) −2.27904e9 −0.0167409
\(299\) 1.30247e10 0.0942425
\(300\) −5.69175e10 −0.405696
\(301\) 5.96080e10 0.418558
\(302\) −6.16719e10 −0.426635
\(303\) 8.37746e10 0.570979
\(304\) 3.72625e10 0.250231
\(305\) 3.30155e10 0.218458
\(306\) −5.84517e9 −0.0381110
\(307\) 7.92006e10 0.508869 0.254434 0.967090i \(-0.418111\pi\)
0.254434 + 0.967090i \(0.418111\pi\)
\(308\) 4.00495e10 0.253583
\(309\) −9.02399e9 −0.0563100
\(310\) −2.15842e10 −0.132742
\(311\) 1.37118e11 0.831140 0.415570 0.909561i \(-0.363582\pi\)
0.415570 + 0.909561i \(0.363582\pi\)
\(312\) 9.33612e9 0.0557790
\(313\) −1.44336e11 −0.850010 −0.425005 0.905191i \(-0.639728\pi\)
−0.425005 + 0.905191i \(0.639728\pi\)
\(314\) 8.04310e10 0.466917
\(315\) −6.50215e9 −0.0372100
\(316\) 2.63616e10 0.148724
\(317\) 6.54419e9 0.0363990 0.0181995 0.999834i \(-0.494207\pi\)
0.0181995 + 0.999834i \(0.494207\pi\)
\(318\) 4.36633e10 0.239439
\(319\) −2.51021e10 −0.135723
\(320\) −9.47172e9 −0.0504956
\(321\) 3.92447e10 0.206305
\(322\) 5.90949e10 0.306336
\(323\) −4.31157e10 −0.220406
\(324\) −1.59448e10 −0.0803835
\(325\) −2.08244e10 −0.103538
\(326\) −1.57452e11 −0.772092
\(327\) −1.46414e11 −0.708136
\(328\) −3.90302e10 −0.186195
\(329\) 2.10735e11 0.991641
\(330\) −5.89528e9 −0.0273648
\(331\) −2.27735e11 −1.04281 −0.521403 0.853310i \(-0.674591\pi\)
−0.521403 + 0.853310i \(0.674591\pi\)
\(332\) 1.12648e11 0.508866
\(333\) −8.83320e10 −0.393658
\(334\) −1.53604e11 −0.675373
\(335\) 4.17929e10 0.181301
\(336\) −2.19372e10 −0.0938974
\(337\) 4.60566e10 0.194517 0.0972585 0.995259i \(-0.468993\pi\)
0.0972585 + 0.995259i \(0.468993\pi\)
\(338\) −1.24752e11 −0.519904
\(339\) 4.77286e10 0.196282
\(340\) −6.56627e9 −0.0266479
\(341\) −1.97900e11 −0.792596
\(342\) 4.49594e10 0.177706
\(343\) −2.64478e11 −1.03173
\(344\) −1.49534e11 −0.575742
\(345\) 2.27559e10 0.0864786
\(346\) 1.39205e11 0.522171
\(347\) 1.44580e11 0.535335 0.267668 0.963511i \(-0.413747\pi\)
0.267668 + 0.963511i \(0.413747\pi\)
\(348\) 2.91547e10 0.106562
\(349\) −4.92873e11 −1.77836 −0.889182 0.457553i \(-0.848726\pi\)
−0.889182 + 0.457553i \(0.848726\pi\)
\(350\) −9.44835e10 −0.336550
\(351\) −5.83373e9 −0.0205147
\(352\) −1.58765e11 −0.551205
\(353\) −5.00845e11 −1.71679 −0.858395 0.512989i \(-0.828538\pi\)
−0.858395 + 0.512989i \(0.828538\pi\)
\(354\) 1.16792e10 0.0395275
\(355\) 1.12911e10 0.0377320
\(356\) 2.25504e11 0.744097
\(357\) 2.53831e10 0.0827061
\(358\) −1.75944e11 −0.566111
\(359\) 1.96532e11 0.624466 0.312233 0.950006i \(-0.398923\pi\)
0.312233 + 0.950006i \(0.398923\pi\)
\(360\) 1.63115e10 0.0511838
\(361\) 8.94644e9 0.0277247
\(362\) 1.26185e11 0.386205
\(363\) 1.36941e11 0.413956
\(364\) −1.70186e10 −0.0508122
\(365\) 4.04523e10 0.119296
\(366\) 1.34397e11 0.391494
\(367\) 4.01737e11 1.15596 0.577982 0.816050i \(-0.303840\pi\)
0.577982 + 0.816050i \(0.303840\pi\)
\(368\) 7.67747e10 0.218224
\(369\) 2.43883e10 0.0684798
\(370\) 3.79317e10 0.105219
\(371\) −1.89611e11 −0.519614
\(372\) 2.29851e11 0.622303
\(373\) −2.55522e11 −0.683500 −0.341750 0.939791i \(-0.611020\pi\)
−0.341750 + 0.939791i \(0.611020\pi\)
\(374\) 2.30140e10 0.0608233
\(375\) −7.38415e10 −0.192823
\(376\) −5.28655e11 −1.36404
\(377\) 1.06669e10 0.0271957
\(378\) −2.64685e10 −0.0666832
\(379\) −4.55440e11 −1.13385 −0.566924 0.823770i \(-0.691867\pi\)
−0.566924 + 0.823770i \(0.691867\pi\)
\(380\) 5.05059e10 0.124256
\(381\) 2.36930e11 0.576047
\(382\) 2.07803e11 0.499307
\(383\) −4.42583e11 −1.05099 −0.525497 0.850795i \(-0.676121\pi\)
−0.525497 + 0.850795i \(0.676121\pi\)
\(384\) 2.16328e11 0.507719
\(385\) 2.56007e10 0.0593853
\(386\) 4.38515e10 0.100541
\(387\) 9.34375e10 0.211749
\(388\) 2.21970e11 0.497223
\(389\) −1.20591e11 −0.267018 −0.133509 0.991048i \(-0.542625\pi\)
−0.133509 + 0.991048i \(0.542625\pi\)
\(390\) 2.50513e9 0.00548328
\(391\) −8.88346e10 −0.192215
\(392\) 2.39765e11 0.512859
\(393\) −5.34158e11 −1.12954
\(394\) −3.48053e11 −0.727634
\(395\) 1.68510e10 0.0348289
\(396\) 6.27790e10 0.128288
\(397\) −4.20019e11 −0.848617 −0.424308 0.905518i \(-0.639483\pi\)
−0.424308 + 0.905518i \(0.639483\pi\)
\(398\) −3.69406e11 −0.737954
\(399\) −1.95240e11 −0.385647
\(400\) −1.22751e11 −0.239747
\(401\) 4.58107e11 0.884743 0.442372 0.896832i \(-0.354137\pi\)
0.442372 + 0.896832i \(0.354137\pi\)
\(402\) 1.70128e11 0.324906
\(403\) 8.40955e10 0.158818
\(404\) 3.83095e11 0.715468
\(405\) −1.01923e10 −0.0188246
\(406\) 4.83971e10 0.0884000
\(407\) 3.47787e11 0.628258
\(408\) −6.36768e10 −0.113765
\(409\) −6.42534e11 −1.13538 −0.567690 0.823243i \(-0.692163\pi\)
−0.567690 + 0.823243i \(0.692163\pi\)
\(410\) −1.04729e10 −0.0183037
\(411\) 2.72082e11 0.470339
\(412\) −4.12661e10 −0.0705595
\(413\) −5.07179e10 −0.0857800
\(414\) 9.26332e10 0.154976
\(415\) 7.20078e10 0.119169
\(416\) 6.74654e10 0.110449
\(417\) −5.06957e11 −0.821030
\(418\) −1.77017e11 −0.283611
\(419\) −1.02142e12 −1.61898 −0.809488 0.587136i \(-0.800255\pi\)
−0.809488 + 0.587136i \(0.800255\pi\)
\(420\) −2.97338e10 −0.0466261
\(421\) −4.44401e11 −0.689454 −0.344727 0.938703i \(-0.612028\pi\)
−0.344727 + 0.938703i \(0.612028\pi\)
\(422\) −8.86993e10 −0.136149
\(423\) 3.30334e11 0.501673
\(424\) 4.75664e11 0.714749
\(425\) 1.42033e11 0.211173
\(426\) 4.59632e10 0.0676187
\(427\) −5.83629e11 −0.849594
\(428\) 1.79463e11 0.258511
\(429\) 2.29690e10 0.0327404
\(430\) −4.01241e10 −0.0565976
\(431\) 1.51261e11 0.211144 0.105572 0.994412i \(-0.466333\pi\)
0.105572 + 0.994412i \(0.466333\pi\)
\(432\) −3.43872e10 −0.0475029
\(433\) −5.86010e11 −0.801142 −0.400571 0.916266i \(-0.631188\pi\)
−0.400571 + 0.916266i \(0.631188\pi\)
\(434\) 3.81554e11 0.516240
\(435\) 1.86365e10 0.0249552
\(436\) −6.69539e11 −0.887332
\(437\) 6.83291e11 0.896270
\(438\) 1.64670e11 0.213787
\(439\) −1.29798e12 −1.66793 −0.833963 0.551820i \(-0.813933\pi\)
−0.833963 + 0.551820i \(0.813933\pi\)
\(440\) −6.42227e10 −0.0816867
\(441\) −1.49819e11 −0.188622
\(442\) −9.77954e9 −0.0121876
\(443\) −4.17677e10 −0.0515257 −0.0257628 0.999668i \(-0.508201\pi\)
−0.0257628 + 0.999668i \(0.508201\pi\)
\(444\) −4.03935e11 −0.493274
\(445\) 1.44148e11 0.174257
\(446\) −1.66910e11 −0.199745
\(447\) 1.55137e10 0.0183795
\(448\) 1.67436e11 0.196380
\(449\) 2.60197e11 0.302130 0.151065 0.988524i \(-0.451730\pi\)
0.151065 + 0.988524i \(0.451730\pi\)
\(450\) −1.48106e11 −0.170262
\(451\) −9.60232e10 −0.109290
\(452\) 2.18259e11 0.245952
\(453\) 4.19809e11 0.468392
\(454\) −3.14513e10 −0.0347446
\(455\) −1.08787e10 −0.0118995
\(456\) 4.89784e11 0.530472
\(457\) −9.53046e11 −1.02209 −0.511047 0.859553i \(-0.670742\pi\)
−0.511047 + 0.859553i \(0.670742\pi\)
\(458\) 8.39741e11 0.891766
\(459\) 3.97888e10 0.0418412
\(460\) 1.04061e11 0.108362
\(461\) 4.57852e11 0.472140 0.236070 0.971736i \(-0.424141\pi\)
0.236070 + 0.971736i \(0.424141\pi\)
\(462\) 1.04214e11 0.106423
\(463\) −3.51961e11 −0.355943 −0.177971 0.984036i \(-0.556953\pi\)
−0.177971 + 0.984036i \(0.556953\pi\)
\(464\) 6.28763e10 0.0629733
\(465\) 1.46926e11 0.145734
\(466\) −5.70912e10 −0.0560832
\(467\) 1.19947e11 0.116698 0.0583492 0.998296i \(-0.481416\pi\)
0.0583492 + 0.998296i \(0.481416\pi\)
\(468\) −2.66772e10 −0.0257060
\(469\) −7.38792e11 −0.705090
\(470\) −1.41853e11 −0.134090
\(471\) −5.47504e11 −0.512617
\(472\) 1.27232e11 0.117994
\(473\) −3.67889e11 −0.337941
\(474\) 6.85961e10 0.0624161
\(475\) −1.09247e12 −0.984669
\(476\) 1.16075e11 0.103635
\(477\) −2.97221e11 −0.262874
\(478\) −7.57328e11 −0.663527
\(479\) 1.99573e12 1.73218 0.866088 0.499892i \(-0.166627\pi\)
0.866088 + 0.499892i \(0.166627\pi\)
\(480\) 1.17871e11 0.101350
\(481\) −1.47788e11 −0.125889
\(482\) −3.81300e11 −0.321777
\(483\) −4.02267e11 −0.336319
\(484\) 6.26222e11 0.518710
\(485\) 1.41889e11 0.116442
\(486\) −4.14903e10 −0.0337352
\(487\) −6.44151e11 −0.518929 −0.259464 0.965753i \(-0.583546\pi\)
−0.259464 + 0.965753i \(0.583546\pi\)
\(488\) 1.46411e12 1.16865
\(489\) 1.07180e12 0.847662
\(490\) 6.43354e10 0.0504159
\(491\) 1.01386e11 0.0787244 0.0393622 0.999225i \(-0.487467\pi\)
0.0393622 + 0.999225i \(0.487467\pi\)
\(492\) 1.11526e11 0.0858088
\(493\) −7.27530e10 −0.0554677
\(494\) 7.52215e10 0.0568291
\(495\) 4.01300e10 0.0300431
\(496\) 4.95705e11 0.367753
\(497\) −1.99599e11 −0.146742
\(498\) 2.93124e11 0.213560
\(499\) −1.90534e12 −1.37569 −0.687845 0.725857i \(-0.741443\pi\)
−0.687845 + 0.725857i \(0.741443\pi\)
\(500\) −3.37672e11 −0.241618
\(501\) 1.04560e12 0.741476
\(502\) 7.75681e11 0.545150
\(503\) 4.69546e11 0.327056 0.163528 0.986539i \(-0.447713\pi\)
0.163528 + 0.986539i \(0.447713\pi\)
\(504\) −2.88346e11 −0.199056
\(505\) 2.44884e11 0.167552
\(506\) −3.64722e11 −0.247334
\(507\) 8.49204e11 0.570790
\(508\) 1.08346e12 0.721818
\(509\) −9.05674e11 −0.598056 −0.299028 0.954244i \(-0.596662\pi\)
−0.299028 + 0.954244i \(0.596662\pi\)
\(510\) −1.70862e10 −0.0111836
\(511\) −7.15093e11 −0.463947
\(512\) 7.45536e11 0.479462
\(513\) −3.06045e11 −0.195100
\(514\) −5.09507e11 −0.321971
\(515\) −2.63783e10 −0.0165240
\(516\) 4.27283e11 0.265333
\(517\) −1.30061e12 −0.800646
\(518\) −6.70536e11 −0.409202
\(519\) −9.47587e11 −0.573279
\(520\) 2.72907e10 0.0163682
\(521\) −4.04998e11 −0.240815 −0.120407 0.992725i \(-0.538420\pi\)
−0.120407 + 0.992725i \(0.538420\pi\)
\(522\) 7.58640e10 0.0447217
\(523\) 1.73293e12 1.01280 0.506399 0.862299i \(-0.330976\pi\)
0.506399 + 0.862299i \(0.330976\pi\)
\(524\) −2.44266e12 −1.41538
\(525\) 6.43162e11 0.369490
\(526\) 1.60035e12 0.911547
\(527\) −5.73571e11 −0.323921
\(528\) 1.35392e11 0.0758123
\(529\) −3.93318e11 −0.218370
\(530\) 1.27634e11 0.0702624
\(531\) −7.95020e10 −0.0433963
\(532\) −8.92816e11 −0.483236
\(533\) 4.08040e10 0.0218993
\(534\) 5.86789e11 0.312281
\(535\) 1.14718e11 0.0605394
\(536\) 1.85336e12 0.969879
\(537\) 1.19767e12 0.621519
\(538\) 1.28625e12 0.661920
\(539\) 5.89876e11 0.301031
\(540\) −4.66088e10 −0.0235883
\(541\) 2.03592e11 0.102182 0.0510909 0.998694i \(-0.483730\pi\)
0.0510909 + 0.998694i \(0.483730\pi\)
\(542\) 4.89227e11 0.243508
\(543\) −8.58955e11 −0.424005
\(544\) −4.60146e11 −0.225269
\(545\) −4.27986e11 −0.207800
\(546\) −4.42844e10 −0.0213247
\(547\) −1.51327e11 −0.0722727 −0.0361363 0.999347i \(-0.511505\pi\)
−0.0361363 + 0.999347i \(0.511505\pi\)
\(548\) 1.24421e12 0.589361
\(549\) −9.14858e11 −0.429812
\(550\) 5.83133e11 0.271729
\(551\) 5.59596e11 0.258638
\(552\) 1.00914e12 0.462621
\(553\) −2.97884e11 −0.135451
\(554\) 1.64097e12 0.740126
\(555\) −2.58206e11 −0.115518
\(556\) −2.31828e12 −1.02880
\(557\) −2.02940e12 −0.893344 −0.446672 0.894698i \(-0.647391\pi\)
−0.446672 + 0.894698i \(0.647391\pi\)
\(558\) 5.98098e11 0.261167
\(559\) 1.56330e11 0.0677157
\(560\) −6.41252e10 −0.0275539
\(561\) −1.56659e11 −0.0667765
\(562\) 4.08409e11 0.172696
\(563\) −3.83974e12 −1.61070 −0.805348 0.592802i \(-0.798022\pi\)
−0.805348 + 0.592802i \(0.798022\pi\)
\(564\) 1.51059e12 0.628624
\(565\) 1.39517e11 0.0575982
\(566\) 3.29567e11 0.134980
\(567\) 1.80175e11 0.0732099
\(568\) 5.00719e11 0.201849
\(569\) 2.59199e12 1.03664 0.518319 0.855187i \(-0.326558\pi\)
0.518319 + 0.855187i \(0.326558\pi\)
\(570\) 1.31422e11 0.0521474
\(571\) 2.26611e11 0.0892110 0.0446055 0.999005i \(-0.485797\pi\)
0.0446055 + 0.999005i \(0.485797\pi\)
\(572\) 1.05035e11 0.0410255
\(573\) −1.41455e12 −0.548177
\(574\) 1.85134e11 0.0711839
\(575\) −2.25091e12 −0.858722
\(576\) 2.62461e11 0.0993491
\(577\) 4.33956e12 1.62988 0.814938 0.579548i \(-0.196771\pi\)
0.814938 + 0.579548i \(0.196771\pi\)
\(578\) −1.34441e12 −0.501022
\(579\) −2.98503e11 −0.110381
\(580\) 8.52232e10 0.0312703
\(581\) −1.27291e12 −0.463454
\(582\) 5.77591e11 0.208673
\(583\) 1.17024e12 0.419534
\(584\) 1.79390e12 0.638177
\(585\) −1.70528e10 −0.00601996
\(586\) 5.78401e11 0.202624
\(587\) 5.17738e12 1.79986 0.899931 0.436033i \(-0.143617\pi\)
0.899931 + 0.436033i \(0.143617\pi\)
\(588\) −6.85109e11 −0.236353
\(589\) 4.41175e12 1.51040
\(590\) 3.41399e10 0.0115992
\(591\) 2.36924e12 0.798852
\(592\) −8.71144e11 −0.291503
\(593\) 7.39550e11 0.245596 0.122798 0.992432i \(-0.460813\pi\)
0.122798 + 0.992432i \(0.460813\pi\)
\(594\) 1.63358e11 0.0538396
\(595\) 7.41981e10 0.0242698
\(596\) 7.09432e10 0.0230304
\(597\) 2.51459e12 0.810183
\(598\) 1.54985e11 0.0495602
\(599\) −8.86839e11 −0.281465 −0.140732 0.990048i \(-0.544946\pi\)
−0.140732 + 0.990048i \(0.544946\pi\)
\(600\) −1.61345e12 −0.508248
\(601\) 3.84620e12 1.20253 0.601266 0.799049i \(-0.294663\pi\)
0.601266 + 0.799049i \(0.294663\pi\)
\(602\) 7.09293e11 0.220111
\(603\) −1.15808e12 −0.356707
\(604\) 1.91975e12 0.586921
\(605\) 4.00298e11 0.121474
\(606\) 9.96858e11 0.300266
\(607\) −6.84903e11 −0.204776 −0.102388 0.994745i \(-0.532648\pi\)
−0.102388 + 0.994745i \(0.532648\pi\)
\(608\) 3.53932e12 1.05040
\(609\) −3.29445e11 −0.0970522
\(610\) 3.92860e11 0.114883
\(611\) 5.52680e11 0.160431
\(612\) 1.81951e11 0.0524293
\(613\) −1.76600e12 −0.505149 −0.252574 0.967578i \(-0.581277\pi\)
−0.252574 + 0.967578i \(0.581277\pi\)
\(614\) 9.42431e11 0.267604
\(615\) 7.12901e10 0.0200952
\(616\) 1.13529e12 0.317684
\(617\) −1.34640e12 −0.374018 −0.187009 0.982358i \(-0.559879\pi\)
−0.187009 + 0.982358i \(0.559879\pi\)
\(618\) −1.07379e11 −0.0296123
\(619\) 9.78641e11 0.267926 0.133963 0.990986i \(-0.457230\pi\)
0.133963 + 0.990986i \(0.457230\pi\)
\(620\) 6.71884e11 0.182613
\(621\) −6.30567e11 −0.170145
\(622\) 1.63161e12 0.437079
\(623\) −2.54817e12 −0.677693
\(624\) −5.75332e10 −0.0151911
\(625\) 3.48935e12 0.914713
\(626\) −1.71749e12 −0.447003
\(627\) 1.20498e12 0.311369
\(628\) −2.50370e12 −0.642337
\(629\) 1.00798e12 0.256759
\(630\) −7.73709e10 −0.0195680
\(631\) 1.69265e11 0.0425046 0.0212523 0.999774i \(-0.493235\pi\)
0.0212523 + 0.999774i \(0.493235\pi\)
\(632\) 7.47280e11 0.186319
\(633\) 6.03788e11 0.149475
\(634\) 7.78713e10 0.0191415
\(635\) 6.92578e11 0.169039
\(636\) −1.35917e12 −0.329395
\(637\) −2.50661e11 −0.0603198
\(638\) −2.98697e11 −0.0713737
\(639\) −3.12877e11 −0.0742370
\(640\) 6.32357e11 0.148988
\(641\) −5.73879e12 −1.34264 −0.671319 0.741169i \(-0.734272\pi\)
−0.671319 + 0.741169i \(0.734272\pi\)
\(642\) 4.66984e11 0.108491
\(643\) −7.62978e12 −1.76020 −0.880101 0.474787i \(-0.842525\pi\)
−0.880101 + 0.474787i \(0.842525\pi\)
\(644\) −1.83954e12 −0.421426
\(645\) 2.73130e11 0.0621371
\(646\) −5.13046e11 −0.115907
\(647\) 3.78174e12 0.848442 0.424221 0.905559i \(-0.360548\pi\)
0.424221 + 0.905559i \(0.360548\pi\)
\(648\) −4.51991e11 −0.100703
\(649\) 3.13021e11 0.0692583
\(650\) −2.47796e11 −0.0544483
\(651\) −2.59729e12 −0.566768
\(652\) 4.90125e12 1.06217
\(653\) −6.52719e12 −1.40481 −0.702404 0.711779i \(-0.747890\pi\)
−0.702404 + 0.711779i \(0.747890\pi\)
\(654\) −1.74222e12 −0.372394
\(655\) −1.56141e12 −0.331461
\(656\) 2.40521e11 0.0507091
\(657\) −1.12093e12 −0.234712
\(658\) 2.50759e12 0.521483
\(659\) −8.14077e12 −1.68144 −0.840719 0.541471i \(-0.817868\pi\)
−0.840719 + 0.541471i \(0.817868\pi\)
\(660\) 1.83511e11 0.0376457
\(661\) −6.28394e12 −1.28034 −0.640170 0.768233i \(-0.721136\pi\)
−0.640170 + 0.768233i \(0.721136\pi\)
\(662\) −2.70988e12 −0.548390
\(663\) 6.65706e10 0.0133805
\(664\) 3.19327e12 0.637499
\(665\) −5.70711e11 −0.113167
\(666\) −1.05109e12 −0.207016
\(667\) 1.15298e12 0.225556
\(668\) 4.78147e12 0.929110
\(669\) 1.13618e12 0.219295
\(670\) 4.97306e11 0.0953426
\(671\) 3.60204e12 0.685958
\(672\) −2.08367e12 −0.394154
\(673\) −4.54764e12 −0.854512 −0.427256 0.904131i \(-0.640520\pi\)
−0.427256 + 0.904131i \(0.640520\pi\)
\(674\) 5.48041e11 0.102292
\(675\) 1.00818e12 0.186926
\(676\) 3.88335e12 0.715230
\(677\) 9.68222e12 1.77144 0.885719 0.464221i \(-0.153666\pi\)
0.885719 + 0.464221i \(0.153666\pi\)
\(678\) 5.67936e11 0.103220
\(679\) −2.50823e12 −0.452849
\(680\) −1.86136e11 −0.0333841
\(681\) 2.14093e11 0.0381453
\(682\) −2.35487e12 −0.416810
\(683\) 1.20065e12 0.211117 0.105559 0.994413i \(-0.466337\pi\)
0.105559 + 0.994413i \(0.466337\pi\)
\(684\) −1.39952e12 −0.244470
\(685\) 7.95331e11 0.138020
\(686\) −3.14710e12 −0.542566
\(687\) −5.71623e12 −0.979049
\(688\) 9.21496e11 0.156800
\(689\) −4.97281e11 −0.0840650
\(690\) 2.70779e11 0.0454773
\(691\) −2.62792e12 −0.438491 −0.219245 0.975670i \(-0.570360\pi\)
−0.219245 + 0.975670i \(0.570360\pi\)
\(692\) −4.33325e12 −0.718350
\(693\) −7.09396e11 −0.116839
\(694\) 1.72040e12 0.281522
\(695\) −1.48190e12 −0.240929
\(696\) 8.26456e11 0.133499
\(697\) −2.78302e11 −0.0446652
\(698\) −5.86484e12 −0.935205
\(699\) 3.88628e11 0.0615724
\(700\) 2.94113e12 0.462991
\(701\) −2.63768e12 −0.412563 −0.206282 0.978493i \(-0.566136\pi\)
−0.206282 + 0.978493i \(0.566136\pi\)
\(702\) −6.94173e10 −0.0107882
\(703\) −7.75314e12 −1.19723
\(704\) −1.03338e12 −0.158556
\(705\) 9.65609e11 0.147214
\(706\) −5.95970e12 −0.902824
\(707\) −4.32893e12 −0.651618
\(708\) −3.63557e11 −0.0543779
\(709\) 6.76875e12 1.00601 0.503003 0.864285i \(-0.332229\pi\)
0.503003 + 0.864285i \(0.332229\pi\)
\(710\) 1.34356e11 0.0198425
\(711\) −4.66942e11 −0.0685252
\(712\) 6.39242e12 0.932193
\(713\) 9.08986e12 1.31721
\(714\) 3.02041e11 0.0434934
\(715\) 6.71414e10 0.00960756
\(716\) 5.47688e12 0.778797
\(717\) 5.15523e12 0.728470
\(718\) 2.33859e12 0.328394
\(719\) −5.03693e12 −0.702887 −0.351444 0.936209i \(-0.614309\pi\)
−0.351444 + 0.936209i \(0.614309\pi\)
\(720\) −1.00518e11 −0.0139396
\(721\) 4.66302e11 0.0642626
\(722\) 1.06456e11 0.0145799
\(723\) 2.59556e12 0.353272
\(724\) −3.92794e12 −0.531301
\(725\) −1.84343e12 −0.247803
\(726\) 1.62950e12 0.217691
\(727\) −7.13148e12 −0.946836 −0.473418 0.880838i \(-0.656980\pi\)
−0.473418 + 0.880838i \(0.656980\pi\)
\(728\) −4.82430e11 −0.0636566
\(729\) 2.82430e11 0.0370370
\(730\) 4.81353e11 0.0627352
\(731\) −1.06625e12 −0.138111
\(732\) −4.18358e12 −0.538577
\(733\) 6.89412e12 0.882086 0.441043 0.897486i \(-0.354609\pi\)
0.441043 + 0.897486i \(0.354609\pi\)
\(734\) 4.78038e12 0.607897
\(735\) −4.37940e11 −0.0553505
\(736\) 7.29232e12 0.916042
\(737\) 4.55968e12 0.569286
\(738\) 2.90203e11 0.0360121
\(739\) 9.41890e12 1.16172 0.580858 0.814005i \(-0.302717\pi\)
0.580858 + 0.814005i \(0.302717\pi\)
\(740\) −1.18076e12 −0.144750
\(741\) −5.12043e11 −0.0623913
\(742\) −2.25624e12 −0.273254
\(743\) −9.53131e12 −1.14737 −0.573684 0.819076i \(-0.694486\pi\)
−0.573684 + 0.819076i \(0.694486\pi\)
\(744\) 6.51563e12 0.779611
\(745\) 4.53487e10 0.00539339
\(746\) −3.04053e12 −0.359439
\(747\) −1.99534e12 −0.234463
\(748\) −7.16391e11 −0.0836745
\(749\) −2.02791e12 −0.235441
\(750\) −8.78661e11 −0.101402
\(751\) −2.76101e12 −0.316729 −0.158364 0.987381i \(-0.550622\pi\)
−0.158364 + 0.987381i \(0.550622\pi\)
\(752\) 3.25780e12 0.371488
\(753\) −5.28016e12 −0.598508
\(754\) 1.26928e11 0.0143017
\(755\) 1.22716e12 0.137448
\(756\) 8.23925e11 0.0917359
\(757\) −1.15173e12 −0.127473 −0.0637366 0.997967i \(-0.520302\pi\)
−0.0637366 + 0.997967i \(0.520302\pi\)
\(758\) −5.41941e12 −0.596267
\(759\) 2.48271e12 0.271543
\(760\) 1.43170e12 0.155665
\(761\) −1.51598e13 −1.63856 −0.819278 0.573396i \(-0.805626\pi\)
−0.819278 + 0.573396i \(0.805626\pi\)
\(762\) 2.81930e12 0.302931
\(763\) 7.56571e12 0.808145
\(764\) −6.46861e12 −0.686896
\(765\) 1.16308e11 0.0122782
\(766\) −5.26643e12 −0.552696
\(767\) −1.33015e11 −0.0138778
\(768\) 4.23317e12 0.439076
\(769\) −1.24406e13 −1.28284 −0.641419 0.767191i \(-0.721654\pi\)
−0.641419 + 0.767191i \(0.721654\pi\)
\(770\) 3.04630e11 0.0312295
\(771\) 3.46828e12 0.353484
\(772\) −1.36503e12 −0.138314
\(773\) 1.80557e13 1.81890 0.909448 0.415818i \(-0.136505\pi\)
0.909448 + 0.415818i \(0.136505\pi\)
\(774\) 1.11184e12 0.111355
\(775\) −1.45333e13 −1.44712
\(776\) 6.29223e12 0.622912
\(777\) 4.56443e12 0.449254
\(778\) −1.43494e12 −0.140419
\(779\) 2.14062e12 0.208268
\(780\) −7.79811e10 −0.00754334
\(781\) 1.23188e12 0.118479
\(782\) −1.05707e12 −0.101082
\(783\) −5.16416e11 −0.0490989
\(784\) −1.47754e12 −0.139674
\(785\) −1.60043e12 −0.150426
\(786\) −6.35610e12 −0.594004
\(787\) 4.66959e12 0.433903 0.216951 0.976182i \(-0.430389\pi\)
0.216951 + 0.976182i \(0.430389\pi\)
\(788\) 1.08344e13 1.00100
\(789\) −1.08938e13 −1.00077
\(790\) 2.00515e11 0.0183158
\(791\) −2.46630e12 −0.224002
\(792\) 1.77961e12 0.160717
\(793\) −1.53065e12 −0.137450
\(794\) −4.99793e12 −0.446270
\(795\) −8.68818e11 −0.0771395
\(796\) 1.14990e13 1.01520
\(797\) −6.81590e12 −0.598358 −0.299179 0.954197i \(-0.596713\pi\)
−0.299179 + 0.954197i \(0.596713\pi\)
\(798\) −2.32321e12 −0.202804
\(799\) −3.76954e12 −0.327211
\(800\) −1.16593e13 −1.00639
\(801\) −3.99435e12 −0.342846
\(802\) 5.45115e12 0.465268
\(803\) 4.41341e12 0.374589
\(804\) −5.29582e12 −0.446973
\(805\) −1.17588e12 −0.0986918
\(806\) 1.00068e12 0.0835192
\(807\) −8.75567e12 −0.726706
\(808\) 1.08597e13 0.896326
\(809\) 1.08706e13 0.892244 0.446122 0.894972i \(-0.352805\pi\)
0.446122 + 0.894972i \(0.352805\pi\)
\(810\) −1.21282e11 −0.00989947
\(811\) −2.22237e12 −0.180395 −0.0901973 0.995924i \(-0.528750\pi\)
−0.0901973 + 0.995924i \(0.528750\pi\)
\(812\) −1.50653e12 −0.121612
\(813\) −3.33023e12 −0.267342
\(814\) 4.13841e12 0.330388
\(815\) 3.13300e12 0.248743
\(816\) 3.92404e11 0.0309833
\(817\) 8.20126e12 0.643994
\(818\) −7.64569e12 −0.597072
\(819\) 3.01450e11 0.0234119
\(820\) 3.26004e11 0.0251803
\(821\) −1.89934e13 −1.45901 −0.729505 0.683975i \(-0.760250\pi\)
−0.729505 + 0.683975i \(0.760250\pi\)
\(822\) 3.23758e12 0.247342
\(823\) 2.41144e13 1.83222 0.916111 0.400925i \(-0.131311\pi\)
0.916111 + 0.400925i \(0.131311\pi\)
\(824\) −1.16978e12 −0.0883957
\(825\) −3.96946e12 −0.298325
\(826\) −6.03507e11 −0.0451099
\(827\) −1.28933e13 −0.958497 −0.479249 0.877679i \(-0.659091\pi\)
−0.479249 + 0.877679i \(0.659091\pi\)
\(828\) −2.88353e12 −0.213201
\(829\) 1.20665e13 0.887334 0.443667 0.896192i \(-0.353677\pi\)
0.443667 + 0.896192i \(0.353677\pi\)
\(830\) 8.56842e11 0.0626685
\(831\) −1.11703e13 −0.812567
\(832\) 4.39123e11 0.0317711
\(833\) 1.70963e12 0.123027
\(834\) −6.03243e12 −0.431763
\(835\) 3.05644e12 0.217584
\(836\) 5.51028e12 0.390163
\(837\) −4.07133e12 −0.286729
\(838\) −1.21541e13 −0.851386
\(839\) 1.09334e13 0.761771 0.380886 0.924622i \(-0.375619\pi\)
0.380886 + 0.924622i \(0.375619\pi\)
\(840\) −8.42872e11 −0.0584124
\(841\) −1.35629e13 −0.934911
\(842\) −5.28805e12 −0.362569
\(843\) −2.78010e12 −0.189599
\(844\) 2.76108e12 0.187300
\(845\) 2.48234e12 0.167496
\(846\) 3.93073e12 0.263820
\(847\) −7.07624e12 −0.472419
\(848\) −2.93125e12 −0.194657
\(849\) −2.24341e12 −0.148191
\(850\) 1.69009e12 0.111051
\(851\) −1.59744e13 −1.04410
\(852\) −1.43076e12 −0.0930229
\(853\) 6.39450e12 0.413557 0.206779 0.978388i \(-0.433702\pi\)
0.206779 + 0.978388i \(0.433702\pi\)
\(854\) −6.94477e12 −0.446784
\(855\) −8.94609e11 −0.0572513
\(856\) 5.08729e12 0.323858
\(857\) −4.53813e12 −0.287384 −0.143692 0.989622i \(-0.545898\pi\)
−0.143692 + 0.989622i \(0.545898\pi\)
\(858\) 2.73314e11 0.0172175
\(859\) −4.99842e12 −0.313230 −0.156615 0.987660i \(-0.550058\pi\)
−0.156615 + 0.987660i \(0.550058\pi\)
\(860\) 1.24900e12 0.0778611
\(861\) −1.26023e12 −0.0781511
\(862\) 1.79990e12 0.111036
\(863\) 4.53292e12 0.278182 0.139091 0.990280i \(-0.455582\pi\)
0.139091 + 0.990280i \(0.455582\pi\)
\(864\) −3.26621e12 −0.199404
\(865\) −2.76992e12 −0.168227
\(866\) −6.97310e12 −0.421304
\(867\) 9.15157e12 0.550060
\(868\) −1.18772e13 −0.710191
\(869\) 1.83848e12 0.109363
\(870\) 2.21761e11 0.0131234
\(871\) −1.93758e12 −0.114072
\(872\) −1.89796e13 −1.11163
\(873\) −3.93174e12 −0.229098
\(874\) 8.13067e12 0.471330
\(875\) 3.81565e12 0.220056
\(876\) −5.12594e12 −0.294107
\(877\) 4.25995e12 0.243168 0.121584 0.992581i \(-0.461203\pi\)
0.121584 + 0.992581i \(0.461203\pi\)
\(878\) −1.54450e13 −0.877128
\(879\) −3.93725e12 −0.222456
\(880\) 3.95768e11 0.0222469
\(881\) 1.07615e13 0.601841 0.300920 0.953649i \(-0.402706\pi\)
0.300920 + 0.953649i \(0.402706\pi\)
\(882\) −1.78273e12 −0.0991923
\(883\) −2.51265e13 −1.39094 −0.695471 0.718554i \(-0.744804\pi\)
−0.695471 + 0.718554i \(0.744804\pi\)
\(884\) 3.04422e11 0.0167665
\(885\) −2.32395e11 −0.0127345
\(886\) −4.97006e11 −0.0270963
\(887\) 1.29291e13 0.701311 0.350655 0.936505i \(-0.385959\pi\)
0.350655 + 0.936505i \(0.385959\pi\)
\(888\) −1.14505e13 −0.617966
\(889\) −1.22430e13 −0.657401
\(890\) 1.71526e12 0.0916379
\(891\) −1.11200e12 −0.0591093
\(892\) 5.19567e12 0.274789
\(893\) 2.89943e13 1.52574
\(894\) 1.84602e11 0.00966537
\(895\) 3.50096e12 0.182383
\(896\) −1.11785e13 −0.579423
\(897\) −1.05500e12 −0.0544110
\(898\) 3.09616e12 0.158884
\(899\) 7.44434e12 0.380109
\(900\) 4.61032e12 0.234228
\(901\) 3.39169e12 0.171457
\(902\) −1.14261e12 −0.0574735
\(903\) −4.82825e12 −0.241654
\(904\) 6.18704e12 0.308124
\(905\) −2.51084e12 −0.124423
\(906\) 4.99542e12 0.246318
\(907\) 1.13077e13 0.554806 0.277403 0.960754i \(-0.410526\pi\)
0.277403 + 0.960754i \(0.410526\pi\)
\(908\) 9.79033e11 0.0477981
\(909\) −6.78574e12 −0.329655
\(910\) −1.29449e11 −0.00625768
\(911\) −8.95975e12 −0.430986 −0.215493 0.976505i \(-0.569136\pi\)
−0.215493 + 0.976505i \(0.569136\pi\)
\(912\) −3.01826e12 −0.144471
\(913\) 7.85618e12 0.374191
\(914\) −1.13406e13 −0.537498
\(915\) −2.67425e12 −0.126127
\(916\) −2.61399e13 −1.22680
\(917\) 2.76018e13 1.28907
\(918\) 4.73459e11 0.0220034
\(919\) 1.85630e13 0.858477 0.429239 0.903191i \(-0.358782\pi\)
0.429239 + 0.903191i \(0.358782\pi\)
\(920\) 2.94985e12 0.135754
\(921\) −6.41525e12 −0.293796
\(922\) 5.44811e12 0.248289
\(923\) −5.23475e11 −0.0237404
\(924\) −3.24401e12 −0.146406
\(925\) 2.55405e13 1.14708
\(926\) −4.18808e12 −0.187183
\(927\) 7.30944e11 0.0325106
\(928\) 5.97220e12 0.264344
\(929\) −3.05904e13 −1.34746 −0.673728 0.738980i \(-0.735308\pi\)
−0.673728 + 0.738980i \(0.735308\pi\)
\(930\) 1.74832e12 0.0766386
\(931\) −1.31500e13 −0.573656
\(932\) 1.77716e12 0.0771536
\(933\) −1.11066e13 −0.479859
\(934\) 1.42729e12 0.0613693
\(935\) −4.57936e11 −0.0195953
\(936\) −7.56226e11 −0.0322040
\(937\) 3.38827e13 1.43599 0.717993 0.696050i \(-0.245061\pi\)
0.717993 + 0.696050i \(0.245061\pi\)
\(938\) −8.79110e12 −0.370792
\(939\) 1.16912e13 0.490754
\(940\) 4.41566e12 0.184468
\(941\) 3.41437e13 1.41957 0.709785 0.704418i \(-0.248792\pi\)
0.709785 + 0.704418i \(0.248792\pi\)
\(942\) −6.51491e12 −0.269575
\(943\) 4.41049e12 0.181629
\(944\) −7.84062e11 −0.0321349
\(945\) 5.26674e11 0.0214832
\(946\) −4.37761e12 −0.177716
\(947\) 3.30474e13 1.33525 0.667624 0.744499i \(-0.267311\pi\)
0.667624 + 0.744499i \(0.267311\pi\)
\(948\) −2.13529e12 −0.0858657
\(949\) −1.87543e12 −0.0750590
\(950\) −1.29997e13 −0.517817
\(951\) −5.30080e11 −0.0210150
\(952\) 3.29040e12 0.129832
\(953\) −3.77689e12 −0.148326 −0.0741628 0.997246i \(-0.523628\pi\)
−0.0741628 + 0.997246i \(0.523628\pi\)
\(954\) −3.53672e12 −0.138240
\(955\) −4.13490e12 −0.160861
\(956\) 2.35745e13 0.912813
\(957\) 2.03327e12 0.0783595
\(958\) 2.37478e13 0.910915
\(959\) −1.40594e13 −0.536765
\(960\) 7.67209e11 0.0291537
\(961\) 3.22502e13 1.21977
\(962\) −1.75857e12 −0.0662022
\(963\) −3.17882e12 −0.119110
\(964\) 1.18693e13 0.442669
\(965\) −8.72563e11 −0.0323910
\(966\) −4.78669e12 −0.176863
\(967\) 4.64428e13 1.70804 0.854022 0.520237i \(-0.174156\pi\)
0.854022 + 0.520237i \(0.174156\pi\)
\(968\) 1.77517e13 0.649831
\(969\) 3.49237e12 0.127252
\(970\) 1.68838e12 0.0612345
\(971\) −9.18432e12 −0.331559 −0.165779 0.986163i \(-0.553014\pi\)
−0.165779 + 0.986163i \(0.553014\pi\)
\(972\) 1.29153e12 0.0464094
\(973\) 2.61963e13 0.936983
\(974\) −7.66494e12 −0.272894
\(975\) 1.68678e12 0.0597775
\(976\) −9.02248e12 −0.318274
\(977\) −3.16019e13 −1.10965 −0.554826 0.831966i \(-0.687215\pi\)
−0.554826 + 0.831966i \(0.687215\pi\)
\(978\) 1.27536e13 0.445768
\(979\) 1.57268e13 0.547166
\(980\) −2.00267e12 −0.0693571
\(981\) 1.18595e13 0.408842
\(982\) 1.20642e12 0.0413995
\(983\) 3.93532e13 1.34428 0.672139 0.740425i \(-0.265376\pi\)
0.672139 + 0.740425i \(0.265376\pi\)
\(984\) 3.16145e12 0.107500
\(985\) 6.92562e12 0.234420
\(986\) −8.65709e11 −0.0291693
\(987\) −1.70695e13 −0.572524
\(988\) −2.34153e12 −0.0781797
\(989\) 1.68977e13 0.561621
\(990\) 4.77518e11 0.0157991
\(991\) −3.64226e12 −0.119961 −0.0599805 0.998200i \(-0.519104\pi\)
−0.0599805 + 0.998200i \(0.519104\pi\)
\(992\) 4.70837e13 1.54372
\(993\) 1.84465e13 0.602065
\(994\) −2.37508e12 −0.0771684
\(995\) 7.35048e12 0.237745
\(996\) −9.12452e12 −0.293794
\(997\) −4.88557e11 −0.0156598 −0.00782991 0.999969i \(-0.502492\pi\)
−0.00782991 + 0.999969i \(0.502492\pi\)
\(998\) −2.26722e13 −0.723447
\(999\) 7.15489e12 0.227278
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.1.13 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.b.1.13 21 1.1 even 1 trivial