Properties

Label 177.10.a.d.1.21
Level $177$
Weight $10$
Character 177.1
Self dual yes
Analytic conductor $91.161$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $1$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.21
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+42.2698 q^{2} +81.0000 q^{3} +1274.73 q^{4} -60.0153 q^{5} +3423.85 q^{6} +8826.78 q^{7} +32240.5 q^{8} +6561.00 q^{9} +O(q^{10})\) \(q+42.2698 q^{2} +81.0000 q^{3} +1274.73 q^{4} -60.0153 q^{5} +3423.85 q^{6} +8826.78 q^{7} +32240.5 q^{8} +6561.00 q^{9} -2536.83 q^{10} +16200.8 q^{11} +103253. q^{12} +123272. q^{13} +373106. q^{14} -4861.24 q^{15} +710136. q^{16} -165876. q^{17} +277332. q^{18} -692496. q^{19} -76503.4 q^{20} +714969. q^{21} +684803. q^{22} -387376. q^{23} +2.61148e6 q^{24} -1.94952e6 q^{25} +5.21069e6 q^{26} +531441. q^{27} +1.12518e7 q^{28} -1.66452e6 q^{29} -205483. q^{30} -1.05783e6 q^{31} +1.35101e7 q^{32} +1.31226e6 q^{33} -7.01153e6 q^{34} -529742. q^{35} +8.36352e6 q^{36} +5.42244e6 q^{37} -2.92717e7 q^{38} +9.98505e6 q^{39} -1.93492e6 q^{40} -2.48157e7 q^{41} +3.02216e7 q^{42} +1.30273e7 q^{43} +2.06516e7 q^{44} -393760. q^{45} -1.63743e7 q^{46} +2.22102e7 q^{47} +5.75210e7 q^{48} +3.75584e7 q^{49} -8.24059e7 q^{50} -1.34359e7 q^{51} +1.57139e8 q^{52} +9.05128e7 q^{53} +2.24639e7 q^{54} -972293. q^{55} +2.84580e8 q^{56} -5.60922e7 q^{57} -7.03589e7 q^{58} -1.21174e7 q^{59} -6.19678e6 q^{60} +5.78319e7 q^{61} -4.47143e7 q^{62} +5.79125e7 q^{63} +2.07481e8 q^{64} -7.39822e6 q^{65} +5.54690e7 q^{66} -2.31519e8 q^{67} -2.11447e8 q^{68} -3.13775e7 q^{69} -2.23920e7 q^{70} +1.74344e7 q^{71} +2.11530e8 q^{72} +1.14788e8 q^{73} +2.29205e8 q^{74} -1.57911e8 q^{75} -8.82748e8 q^{76} +1.43001e8 q^{77} +4.22066e8 q^{78} -1.84489e8 q^{79} -4.26190e7 q^{80} +4.30467e7 q^{81} -1.04895e9 q^{82} +5.49192e8 q^{83} +9.11394e8 q^{84} +9.95509e6 q^{85} +5.50661e8 q^{86} -1.34826e8 q^{87} +5.22321e8 q^{88} +1.64838e8 q^{89} -1.66442e7 q^{90} +1.08810e9 q^{91} -4.93801e8 q^{92} -8.56843e7 q^{93} +9.38821e8 q^{94} +4.15604e7 q^{95} +1.09432e9 q^{96} -1.37978e9 q^{97} +1.58758e9 q^{98} +1.06293e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + O(q^{10}) \) \( 22q + 46q^{2} + 1782q^{3} + 5974q^{4} + 5786q^{5} + 3726q^{6} + 7641q^{7} + 61395q^{8} + 144342q^{9} + 45337q^{10} + 111769q^{11} + 483894q^{12} + 189121q^{13} + 251053q^{14} + 468666q^{15} + 2311074q^{16} + 1113841q^{17} + 301806q^{18} + 476068q^{19} - 42495q^{20} + 618921q^{21} - 2252022q^{22} + 7103062q^{23} + 4972995q^{24} + 10628442q^{25} + 6871048q^{26} + 11691702q^{27} + 8112650q^{28} + 15279316q^{29} + 3672297q^{30} + 17610338q^{31} + 32378276q^{32} + 9053289q^{33} + 29339436q^{34} + 7134904q^{35} + 39195414q^{36} + 21961411q^{37} + 65195131q^{38} + 15318801q^{39} + 75185084q^{40} + 52781575q^{41} + 20335293q^{42} + 76191313q^{43} + 61127768q^{44} + 37961946q^{45} + 290208769q^{46} + 160572396q^{47} + 187196994q^{48} + 156292703q^{49} + 169504821q^{50} + 90221121q^{51} + 65465920q^{52} - 8762038q^{53} + 24446286q^{54} + 147125140q^{55} + 9671794q^{56} + 38561508q^{57} - 37665424q^{58} - 266581942q^{59} - 3442095q^{60} + 120750754q^{61} - 152465186q^{62} + 50132601q^{63} - 40658803q^{64} + 331055798q^{65} - 182413782q^{66} + 41371828q^{67} + 145606631q^{68} + 575348022q^{69} - 920887614q^{70} + 261018751q^{71} + 402812595q^{72} + 178388q^{73} - 303908734q^{74} + 860903802q^{75} - 94541144q^{76} + 299640561q^{77} + 556554888q^{78} - 905381353q^{79} + 939128289q^{80} + 947027862q^{81} - 551739753q^{82} + 1173257869q^{83} + 657124650q^{84} - 1546633210q^{85} + 1384869460q^{86} + 1237624596q^{87} + 189740713q^{88} + 898004974q^{89} + 297456057q^{90} + 591272339q^{91} + 4328210270q^{92} + 1426437378q^{93} + 122568068q^{94} + 2487967134q^{95} + 2622640356q^{96} + 3175709684q^{97} + 5095778404q^{98} + 733316409q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 42.2698 1.86808 0.934039 0.357172i \(-0.116259\pi\)
0.934039 + 0.357172i \(0.116259\pi\)
\(3\) 81.0000 0.577350
\(4\) 1274.73 2.48971
\(5\) −60.0153 −0.0429434 −0.0214717 0.999769i \(-0.506835\pi\)
−0.0214717 + 0.999769i \(0.506835\pi\)
\(6\) 3423.85 1.07853
\(7\) 8826.78 1.38951 0.694754 0.719247i \(-0.255513\pi\)
0.694754 + 0.719247i \(0.255513\pi\)
\(8\) 32240.5 2.78290
\(9\) 6561.00 0.333333
\(10\) −2536.83 −0.0802217
\(11\) 16200.8 0.333633 0.166816 0.985988i \(-0.446651\pi\)
0.166816 + 0.985988i \(0.446651\pi\)
\(12\) 103253. 1.43744
\(13\) 123272. 1.19707 0.598536 0.801096i \(-0.295749\pi\)
0.598536 + 0.801096i \(0.295749\pi\)
\(14\) 373106. 2.59571
\(15\) −4861.24 −0.0247934
\(16\) 710136. 2.70896
\(17\) −165876. −0.481685 −0.240842 0.970564i \(-0.577424\pi\)
−0.240842 + 0.970564i \(0.577424\pi\)
\(18\) 277332. 0.622692
\(19\) −692496. −1.21906 −0.609532 0.792762i \(-0.708643\pi\)
−0.609532 + 0.792762i \(0.708643\pi\)
\(20\) −76503.4 −0.106917
\(21\) 714969. 0.802233
\(22\) 684803. 0.623251
\(23\) −387376. −0.288641 −0.144320 0.989531i \(-0.546100\pi\)
−0.144320 + 0.989531i \(0.546100\pi\)
\(24\) 2.61148e6 1.60671
\(25\) −1.94952e6 −0.998156
\(26\) 5.21069e6 2.23622
\(27\) 531441. 0.192450
\(28\) 1.12518e7 3.45947
\(29\) −1.66452e6 −0.437017 −0.218509 0.975835i \(-0.570119\pi\)
−0.218509 + 0.975835i \(0.570119\pi\)
\(30\) −205483. −0.0463160
\(31\) −1.05783e6 −0.205726 −0.102863 0.994696i \(-0.532800\pi\)
−0.102863 + 0.994696i \(0.532800\pi\)
\(32\) 1.35101e7 2.27764
\(33\) 1.31226e6 0.192623
\(34\) −7.01153e6 −0.899825
\(35\) −529742. −0.0596702
\(36\) 8.36352e6 0.829904
\(37\) 5.42244e6 0.475650 0.237825 0.971308i \(-0.423566\pi\)
0.237825 + 0.971308i \(0.423566\pi\)
\(38\) −2.92717e7 −2.27730
\(39\) 9.98505e6 0.691130
\(40\) −1.93492e6 −0.119507
\(41\) −2.48157e7 −1.37151 −0.685755 0.727832i \(-0.740528\pi\)
−0.685755 + 0.727832i \(0.740528\pi\)
\(42\) 3.02216e7 1.49863
\(43\) 1.30273e7 0.581094 0.290547 0.956861i \(-0.406163\pi\)
0.290547 + 0.956861i \(0.406163\pi\)
\(44\) 2.06516e7 0.830649
\(45\) −393760. −0.0143145
\(46\) −1.63743e7 −0.539203
\(47\) 2.22102e7 0.663915 0.331958 0.943294i \(-0.392291\pi\)
0.331958 + 0.943294i \(0.392291\pi\)
\(48\) 5.75210e7 1.56402
\(49\) 3.75584e7 0.930732
\(50\) −8.24059e7 −1.86463
\(51\) −1.34359e7 −0.278101
\(52\) 1.57139e8 2.98036
\(53\) 9.05128e7 1.57568 0.787841 0.615879i \(-0.211199\pi\)
0.787841 + 0.615879i \(0.211199\pi\)
\(54\) 2.24639e7 0.359512
\(55\) −972293. −0.0143273
\(56\) 2.84580e8 3.86686
\(57\) −5.60922e7 −0.703827
\(58\) −7.03589e7 −0.816382
\(59\) −1.21174e7 −0.130189
\(60\) −6.19678e6 −0.0617284
\(61\) 5.78319e7 0.534790 0.267395 0.963587i \(-0.413837\pi\)
0.267395 + 0.963587i \(0.413837\pi\)
\(62\) −4.47143e7 −0.384312
\(63\) 5.79125e7 0.463169
\(64\) 2.07481e8 1.54585
\(65\) −7.39822e6 −0.0514064
\(66\) 5.54690e7 0.359834
\(67\) −2.31519e8 −1.40362 −0.701810 0.712364i \(-0.747624\pi\)
−0.701810 + 0.712364i \(0.747624\pi\)
\(68\) −2.11447e8 −1.19926
\(69\) −3.13775e7 −0.166647
\(70\) −2.23920e7 −0.111469
\(71\) 1.74344e7 0.0814227 0.0407114 0.999171i \(-0.487038\pi\)
0.0407114 + 0.999171i \(0.487038\pi\)
\(72\) 2.11530e8 0.927633
\(73\) 1.14788e8 0.473092 0.236546 0.971620i \(-0.423985\pi\)
0.236546 + 0.971620i \(0.423985\pi\)
\(74\) 2.29205e8 0.888551
\(75\) −1.57911e8 −0.576286
\(76\) −8.82748e8 −3.03512
\(77\) 1.43001e8 0.463585
\(78\) 4.22066e8 1.29108
\(79\) −1.84489e8 −0.532905 −0.266452 0.963848i \(-0.585852\pi\)
−0.266452 + 0.963848i \(0.585852\pi\)
\(80\) −4.26190e7 −0.116332
\(81\) 4.30467e7 0.111111
\(82\) −1.04895e9 −2.56209
\(83\) 5.49192e8 1.27020 0.635101 0.772429i \(-0.280959\pi\)
0.635101 + 0.772429i \(0.280959\pi\)
\(84\) 9.11394e8 1.99733
\(85\) 9.95509e6 0.0206852
\(86\) 5.50661e8 1.08553
\(87\) −1.34826e8 −0.252312
\(88\) 5.22321e8 0.928465
\(89\) 1.64838e8 0.278485 0.139242 0.990258i \(-0.455533\pi\)
0.139242 + 0.990258i \(0.455533\pi\)
\(90\) −1.66442e7 −0.0267406
\(91\) 1.08810e9 1.66334
\(92\) −4.93801e8 −0.718632
\(93\) −8.56843e7 −0.118776
\(94\) 9.38821e8 1.24025
\(95\) 4.15604e7 0.0523508
\(96\) 1.09432e9 1.31500
\(97\) −1.37978e9 −1.58248 −0.791239 0.611507i \(-0.790564\pi\)
−0.791239 + 0.611507i \(0.790564\pi\)
\(98\) 1.58758e9 1.73868
\(99\) 1.06293e8 0.111211
\(100\) −2.48512e9 −2.48512
\(101\) 7.27601e8 0.695740 0.347870 0.937543i \(-0.386905\pi\)
0.347870 + 0.937543i \(0.386905\pi\)
\(102\) −5.67934e8 −0.519514
\(103\) 2.84037e8 0.248661 0.124330 0.992241i \(-0.460322\pi\)
0.124330 + 0.992241i \(0.460322\pi\)
\(104\) 3.97436e9 3.33133
\(105\) −4.29091e7 −0.0344506
\(106\) 3.82595e9 2.94350
\(107\) 7.20470e8 0.531360 0.265680 0.964061i \(-0.414404\pi\)
0.265680 + 0.964061i \(0.414404\pi\)
\(108\) 6.77445e8 0.479145
\(109\) −2.76564e9 −1.87662 −0.938312 0.345790i \(-0.887611\pi\)
−0.938312 + 0.345790i \(0.887611\pi\)
\(110\) −4.10986e7 −0.0267646
\(111\) 4.39218e8 0.274617
\(112\) 6.26822e9 3.76411
\(113\) −1.41911e9 −0.818773 −0.409386 0.912361i \(-0.634257\pi\)
−0.409386 + 0.912361i \(0.634257\pi\)
\(114\) −2.37100e9 −1.31480
\(115\) 2.32485e7 0.0123952
\(116\) −2.12182e9 −1.08805
\(117\) 8.08789e8 0.399024
\(118\) −5.12198e8 −0.243203
\(119\) −1.46415e9 −0.669305
\(120\) −1.56729e8 −0.0689975
\(121\) −2.09548e9 −0.888689
\(122\) 2.44454e9 0.999029
\(123\) −2.01007e9 −0.791842
\(124\) −1.34845e9 −0.512198
\(125\) 2.34219e8 0.0858077
\(126\) 2.44795e9 0.865236
\(127\) −4.50001e9 −1.53496 −0.767479 0.641074i \(-0.778489\pi\)
−0.767479 + 0.641074i \(0.778489\pi\)
\(128\) 1.85297e9 0.610130
\(129\) 1.05521e9 0.335495
\(130\) −3.12721e8 −0.0960311
\(131\) −2.56225e8 −0.0760151 −0.0380076 0.999277i \(-0.512101\pi\)
−0.0380076 + 0.999277i \(0.512101\pi\)
\(132\) 1.67278e9 0.479576
\(133\) −6.11251e9 −1.69390
\(134\) −9.78624e9 −2.62207
\(135\) −3.18946e7 −0.00826447
\(136\) −5.34793e9 −1.34048
\(137\) 7.23263e9 1.75410 0.877048 0.480402i \(-0.159509\pi\)
0.877048 + 0.480402i \(0.159509\pi\)
\(138\) −1.32632e9 −0.311309
\(139\) 6.75360e9 1.53451 0.767253 0.641344i \(-0.221623\pi\)
0.767253 + 0.641344i \(0.221623\pi\)
\(140\) −6.75279e8 −0.148562
\(141\) 1.79903e9 0.383312
\(142\) 7.36950e8 0.152104
\(143\) 1.99710e9 0.399382
\(144\) 4.65920e9 0.902985
\(145\) 9.98967e7 0.0187670
\(146\) 4.85208e9 0.883772
\(147\) 3.04223e9 0.537359
\(148\) 6.91217e9 1.18423
\(149\) −8.62282e9 −1.43321 −0.716607 0.697477i \(-0.754306\pi\)
−0.716607 + 0.697477i \(0.754306\pi\)
\(150\) −6.67488e9 −1.07655
\(151\) −4.09088e9 −0.640355 −0.320178 0.947358i \(-0.603743\pi\)
−0.320178 + 0.947358i \(0.603743\pi\)
\(152\) −2.23265e10 −3.39253
\(153\) −1.08831e9 −0.160562
\(154\) 6.04460e9 0.866013
\(155\) 6.34860e7 0.00883457
\(156\) 1.27283e10 1.72071
\(157\) −3.74731e9 −0.492234 −0.246117 0.969240i \(-0.579155\pi\)
−0.246117 + 0.969240i \(0.579155\pi\)
\(158\) −7.79833e9 −0.995507
\(159\) 7.33154e9 0.909720
\(160\) −8.10815e8 −0.0978097
\(161\) −3.41928e9 −0.401068
\(162\) 1.81957e9 0.207564
\(163\) 1.62523e9 0.180332 0.0901658 0.995927i \(-0.471260\pi\)
0.0901658 + 0.995927i \(0.471260\pi\)
\(164\) −3.16334e10 −3.41467
\(165\) −7.87558e7 −0.00827189
\(166\) 2.32142e10 2.37283
\(167\) −8.68516e9 −0.864080 −0.432040 0.901854i \(-0.642206\pi\)
−0.432040 + 0.901854i \(0.642206\pi\)
\(168\) 2.30510e10 2.23253
\(169\) 4.59154e9 0.432980
\(170\) 4.20799e8 0.0386416
\(171\) −4.54347e9 −0.406355
\(172\) 1.66063e10 1.44676
\(173\) −5.57213e9 −0.472948 −0.236474 0.971638i \(-0.575992\pi\)
−0.236474 + 0.971638i \(0.575992\pi\)
\(174\) −5.69907e9 −0.471338
\(175\) −1.72080e10 −1.38695
\(176\) 1.15048e10 0.903796
\(177\) −9.81506e8 −0.0751646
\(178\) 6.96765e9 0.520231
\(179\) 2.83494e9 0.206398 0.103199 0.994661i \(-0.467092\pi\)
0.103199 + 0.994661i \(0.467092\pi\)
\(180\) −5.01939e8 −0.0356389
\(181\) −6.81693e8 −0.0472101 −0.0236051 0.999721i \(-0.507514\pi\)
−0.0236051 + 0.999721i \(0.507514\pi\)
\(182\) 4.59936e10 3.10725
\(183\) 4.68439e9 0.308761
\(184\) −1.24892e10 −0.803257
\(185\) −3.25430e8 −0.0204260
\(186\) −3.62186e9 −0.221882
\(187\) −2.68732e9 −0.160706
\(188\) 2.83121e10 1.65296
\(189\) 4.69091e9 0.267411
\(190\) 1.75675e9 0.0977953
\(191\) 3.50450e9 0.190535 0.0952676 0.995452i \(-0.469629\pi\)
0.0952676 + 0.995452i \(0.469629\pi\)
\(192\) 1.68059e10 0.892498
\(193\) 3.04202e10 1.57817 0.789085 0.614285i \(-0.210555\pi\)
0.789085 + 0.614285i \(0.210555\pi\)
\(194\) −5.83231e10 −2.95619
\(195\) −5.99256e8 −0.0296795
\(196\) 4.78769e10 2.31726
\(197\) 2.76245e10 1.30676 0.653380 0.757030i \(-0.273350\pi\)
0.653380 + 0.757030i \(0.273350\pi\)
\(198\) 4.49299e9 0.207750
\(199\) 1.23928e10 0.560185 0.280093 0.959973i \(-0.409635\pi\)
0.280093 + 0.959973i \(0.409635\pi\)
\(200\) −6.28537e10 −2.77777
\(201\) −1.87530e10 −0.810380
\(202\) 3.07555e10 1.29970
\(203\) −1.46924e10 −0.607239
\(204\) −1.71272e10 −0.692391
\(205\) 1.48932e9 0.0588974
\(206\) 1.20062e10 0.464517
\(207\) −2.54157e9 −0.0962135
\(208\) 8.75401e10 3.24281
\(209\) −1.12190e10 −0.406719
\(210\) −1.81376e9 −0.0643564
\(211\) 2.58153e10 0.896615 0.448308 0.893879i \(-0.352027\pi\)
0.448308 + 0.893879i \(0.352027\pi\)
\(212\) 1.15380e11 3.92299
\(213\) 1.41219e9 0.0470094
\(214\) 3.04541e10 0.992621
\(215\) −7.81837e8 −0.0249542
\(216\) 1.71339e10 0.535569
\(217\) −9.33724e9 −0.285858
\(218\) −1.16903e11 −3.50568
\(219\) 9.29786e9 0.273140
\(220\) −1.23941e9 −0.0356709
\(221\) −2.04479e10 −0.576611
\(222\) 1.85656e10 0.513005
\(223\) −2.78289e9 −0.0753572 −0.0376786 0.999290i \(-0.511996\pi\)
−0.0376786 + 0.999290i \(0.511996\pi\)
\(224\) 1.19251e11 3.16480
\(225\) −1.27908e10 −0.332719
\(226\) −5.99855e10 −1.52953
\(227\) −2.66911e10 −0.667191 −0.333595 0.942716i \(-0.608262\pi\)
−0.333595 + 0.942716i \(0.608262\pi\)
\(228\) −7.15026e10 −1.75233
\(229\) −2.17020e10 −0.521482 −0.260741 0.965409i \(-0.583967\pi\)
−0.260741 + 0.965409i \(0.583967\pi\)
\(230\) 9.82707e8 0.0231552
\(231\) 1.15830e10 0.267651
\(232\) −5.36650e10 −1.21617
\(233\) 8.26830e10 1.83787 0.918935 0.394409i \(-0.129051\pi\)
0.918935 + 0.394409i \(0.129051\pi\)
\(234\) 3.41873e10 0.745407
\(235\) −1.33295e9 −0.0285108
\(236\) −1.54464e10 −0.324133
\(237\) −1.49436e10 −0.307673
\(238\) −6.18892e10 −1.25031
\(239\) −4.38699e10 −0.869713 −0.434857 0.900500i \(-0.643201\pi\)
−0.434857 + 0.900500i \(0.643201\pi\)
\(240\) −3.45214e9 −0.0671642
\(241\) 2.06071e10 0.393495 0.196748 0.980454i \(-0.436962\pi\)
0.196748 + 0.980454i \(0.436962\pi\)
\(242\) −8.85756e10 −1.66014
\(243\) 3.48678e9 0.0641500
\(244\) 7.37202e10 1.33147
\(245\) −2.25408e9 −0.0399688
\(246\) −8.49652e10 −1.47922
\(247\) −8.53656e10 −1.45931
\(248\) −3.41050e10 −0.572514
\(249\) 4.44845e10 0.733351
\(250\) 9.90036e9 0.160295
\(251\) 4.19417e10 0.666983 0.333492 0.942753i \(-0.391773\pi\)
0.333492 + 0.942753i \(0.391773\pi\)
\(252\) 7.38229e10 1.15316
\(253\) −6.27579e9 −0.0962999
\(254\) −1.90214e11 −2.86742
\(255\) 8.06362e8 0.0119426
\(256\) −2.79057e10 −0.406081
\(257\) −1.08931e11 −1.55759 −0.778796 0.627277i \(-0.784169\pi\)
−0.778796 + 0.627277i \(0.784169\pi\)
\(258\) 4.46035e10 0.626730
\(259\) 4.78627e10 0.660919
\(260\) −9.43075e9 −0.127987
\(261\) −1.09209e10 −0.145672
\(262\) −1.08306e10 −0.142002
\(263\) −1.51234e11 −1.94916 −0.974581 0.224037i \(-0.928076\pi\)
−0.974581 + 0.224037i \(0.928076\pi\)
\(264\) 4.23080e10 0.536050
\(265\) −5.43215e9 −0.0676652
\(266\) −2.58374e11 −3.16433
\(267\) 1.33518e10 0.160783
\(268\) −2.95124e11 −3.49461
\(269\) −4.01575e10 −0.467607 −0.233804 0.972284i \(-0.575117\pi\)
−0.233804 + 0.972284i \(0.575117\pi\)
\(270\) −1.34818e9 −0.0154387
\(271\) −3.70127e10 −0.416859 −0.208429 0.978037i \(-0.566835\pi\)
−0.208429 + 0.978037i \(0.566835\pi\)
\(272\) −1.17794e11 −1.30486
\(273\) 8.81358e10 0.960330
\(274\) 3.05721e11 3.27679
\(275\) −3.15838e10 −0.333017
\(276\) −3.99979e10 −0.414902
\(277\) 8.72178e10 0.890115 0.445057 0.895502i \(-0.353183\pi\)
0.445057 + 0.895502i \(0.353183\pi\)
\(278\) 2.85473e11 2.86658
\(279\) −6.94043e9 −0.0685753
\(280\) −1.70791e10 −0.166056
\(281\) −8.67326e10 −0.829859 −0.414929 0.909854i \(-0.636194\pi\)
−0.414929 + 0.909854i \(0.636194\pi\)
\(282\) 7.60445e10 0.716056
\(283\) 3.51750e10 0.325983 0.162992 0.986627i \(-0.447886\pi\)
0.162992 + 0.986627i \(0.447886\pi\)
\(284\) 2.22243e10 0.202719
\(285\) 3.36639e9 0.0302247
\(286\) 8.44171e10 0.746077
\(287\) −2.19043e11 −1.90572
\(288\) 8.86400e10 0.759213
\(289\) −9.10731e10 −0.767980
\(290\) 4.22261e9 0.0350582
\(291\) −1.11762e11 −0.913644
\(292\) 1.46325e11 1.17786
\(293\) 1.83113e11 1.45149 0.725746 0.687963i \(-0.241495\pi\)
0.725746 + 0.687963i \(0.241495\pi\)
\(294\) 1.28594e11 1.00383
\(295\) 7.27227e8 0.00559076
\(296\) 1.74822e11 1.32368
\(297\) 8.60975e9 0.0642076
\(298\) −3.64484e11 −2.67735
\(299\) −4.77527e10 −0.345523
\(300\) −2.01295e11 −1.43479
\(301\) 1.14989e11 0.807434
\(302\) −1.72921e11 −1.19623
\(303\) 5.89357e10 0.401686
\(304\) −4.91767e11 −3.30239
\(305\) −3.47080e9 −0.0229657
\(306\) −4.60027e10 −0.299942
\(307\) −1.30126e11 −0.836068 −0.418034 0.908431i \(-0.637281\pi\)
−0.418034 + 0.908431i \(0.637281\pi\)
\(308\) 1.82287e11 1.15419
\(309\) 2.30070e10 0.143564
\(310\) 2.68354e9 0.0165037
\(311\) 2.36559e11 1.43390 0.716948 0.697127i \(-0.245538\pi\)
0.716948 + 0.697127i \(0.245538\pi\)
\(312\) 3.21923e11 1.92334
\(313\) −2.09703e11 −1.23497 −0.617483 0.786584i \(-0.711848\pi\)
−0.617483 + 0.786584i \(0.711848\pi\)
\(314\) −1.58398e11 −0.919531
\(315\) −3.47563e9 −0.0198901
\(316\) −2.35175e11 −1.32678
\(317\) 2.01816e11 1.12251 0.561253 0.827645i \(-0.310320\pi\)
0.561253 + 0.827645i \(0.310320\pi\)
\(318\) 3.09902e11 1.69943
\(319\) −2.69665e10 −0.145803
\(320\) −1.24520e10 −0.0663842
\(321\) 5.83581e10 0.306781
\(322\) −1.44532e11 −0.749227
\(323\) 1.14868e11 0.587205
\(324\) 5.48731e10 0.276635
\(325\) −2.40322e11 −1.19486
\(326\) 6.86983e10 0.336873
\(327\) −2.24017e11 −1.08347
\(328\) −8.00071e11 −3.81677
\(329\) 1.96045e11 0.922516
\(330\) −3.32899e9 −0.0154525
\(331\) −3.32010e11 −1.52029 −0.760144 0.649755i \(-0.774871\pi\)
−0.760144 + 0.649755i \(0.774871\pi\)
\(332\) 7.00073e11 3.16244
\(333\) 3.55767e10 0.158550
\(334\) −3.67120e11 −1.61417
\(335\) 1.38947e10 0.0602763
\(336\) 5.07725e11 2.17321
\(337\) −5.50980e10 −0.232703 −0.116351 0.993208i \(-0.537120\pi\)
−0.116351 + 0.993208i \(0.537120\pi\)
\(338\) 1.94083e11 0.808841
\(339\) −1.14948e11 −0.472719
\(340\) 1.26901e10 0.0515002
\(341\) −1.71377e10 −0.0686368
\(342\) −1.92051e11 −0.759102
\(343\) −2.46726e10 −0.0962481
\(344\) 4.20007e11 1.61712
\(345\) 1.88313e9 0.00715638
\(346\) −2.35533e11 −0.883504
\(347\) −3.11529e11 −1.15349 −0.576747 0.816923i \(-0.695678\pi\)
−0.576747 + 0.816923i \(0.695678\pi\)
\(348\) −1.71867e11 −0.628184
\(349\) −3.19139e11 −1.15150 −0.575751 0.817625i \(-0.695290\pi\)
−0.575751 + 0.817625i \(0.695290\pi\)
\(350\) −7.27378e11 −2.59092
\(351\) 6.55119e10 0.230377
\(352\) 2.18875e11 0.759895
\(353\) −1.33725e11 −0.458382 −0.229191 0.973382i \(-0.573608\pi\)
−0.229191 + 0.973382i \(0.573608\pi\)
\(354\) −4.14880e10 −0.140413
\(355\) −1.04633e9 −0.00349657
\(356\) 2.10124e11 0.693347
\(357\) −1.18596e11 −0.386423
\(358\) 1.19832e11 0.385567
\(359\) −1.61952e11 −0.514590 −0.257295 0.966333i \(-0.582831\pi\)
−0.257295 + 0.966333i \(0.582831\pi\)
\(360\) −1.26950e10 −0.0398357
\(361\) 1.56864e11 0.486116
\(362\) −2.88150e10 −0.0881921
\(363\) −1.69734e11 −0.513085
\(364\) 1.38703e12 4.14124
\(365\) −6.88906e9 −0.0203162
\(366\) 1.98008e11 0.576790
\(367\) −2.17085e11 −0.624643 −0.312322 0.949976i \(-0.601107\pi\)
−0.312322 + 0.949976i \(0.601107\pi\)
\(368\) −2.75090e11 −0.781914
\(369\) −1.62816e11 −0.457170
\(370\) −1.37558e10 −0.0381574
\(371\) 7.98936e11 2.18942
\(372\) −1.09225e11 −0.295718
\(373\) −3.00669e11 −0.804265 −0.402132 0.915581i \(-0.631731\pi\)
−0.402132 + 0.915581i \(0.631731\pi\)
\(374\) −1.13592e11 −0.300211
\(375\) 1.89717e10 0.0495411
\(376\) 7.16070e11 1.84761
\(377\) −2.05189e11 −0.523141
\(378\) 1.98284e11 0.499544
\(379\) 3.67439e11 0.914763 0.457381 0.889271i \(-0.348787\pi\)
0.457381 + 0.889271i \(0.348787\pi\)
\(380\) 5.29784e10 0.130338
\(381\) −3.64501e11 −0.886209
\(382\) 1.48134e11 0.355935
\(383\) 3.85840e11 0.916247 0.458124 0.888888i \(-0.348522\pi\)
0.458124 + 0.888888i \(0.348522\pi\)
\(384\) 1.50090e11 0.352259
\(385\) −8.58222e9 −0.0199079
\(386\) 1.28585e12 2.94814
\(387\) 8.54721e10 0.193698
\(388\) −1.75885e12 −3.93992
\(389\) 4.01764e11 0.889606 0.444803 0.895628i \(-0.353274\pi\)
0.444803 + 0.895628i \(0.353274\pi\)
\(390\) −2.53304e10 −0.0554436
\(391\) 6.42563e10 0.139034
\(392\) 1.21090e12 2.59013
\(393\) −2.07542e10 −0.0438874
\(394\) 1.16768e12 2.44113
\(395\) 1.10722e10 0.0228848
\(396\) 1.35495e11 0.276883
\(397\) 1.01154e11 0.204374 0.102187 0.994765i \(-0.467416\pi\)
0.102187 + 0.994765i \(0.467416\pi\)
\(398\) 5.23842e11 1.04647
\(399\) −4.95113e11 −0.977973
\(400\) −1.38443e12 −2.70396
\(401\) 2.50446e11 0.483687 0.241844 0.970315i \(-0.422248\pi\)
0.241844 + 0.970315i \(0.422248\pi\)
\(402\) −7.92685e11 −1.51385
\(403\) −1.30401e11 −0.246269
\(404\) 9.27497e11 1.73219
\(405\) −2.58346e9 −0.00477149
\(406\) −6.21043e11 −1.13437
\(407\) 8.78478e10 0.158692
\(408\) −4.33182e11 −0.773926
\(409\) 1.11159e12 1.96421 0.982106 0.188329i \(-0.0603070\pi\)
0.982106 + 0.188329i \(0.0603070\pi\)
\(410\) 6.29532e10 0.110025
\(411\) 5.85843e11 1.01273
\(412\) 3.62071e11 0.619094
\(413\) −1.06957e11 −0.180899
\(414\) −1.07432e11 −0.179734
\(415\) −3.29599e10 −0.0545468
\(416\) 1.66543e12 2.72650
\(417\) 5.47042e11 0.885948
\(418\) −4.74223e11 −0.759783
\(419\) 1.33843e11 0.212145 0.106072 0.994358i \(-0.466173\pi\)
0.106072 + 0.994358i \(0.466173\pi\)
\(420\) −5.46976e10 −0.0857722
\(421\) 1.05335e12 1.63419 0.817095 0.576504i \(-0.195583\pi\)
0.817095 + 0.576504i \(0.195583\pi\)
\(422\) 1.09121e12 1.67495
\(423\) 1.45721e11 0.221305
\(424\) 2.91818e12 4.38496
\(425\) 3.23379e11 0.480797
\(426\) 5.96929e10 0.0878172
\(427\) 5.10470e11 0.743095
\(428\) 9.18406e11 1.32293
\(429\) 1.61765e11 0.230583
\(430\) −3.30481e10 −0.0466163
\(431\) −1.21469e12 −1.69558 −0.847792 0.530330i \(-0.822068\pi\)
−0.847792 + 0.530330i \(0.822068\pi\)
\(432\) 3.77396e11 0.521339
\(433\) −4.80989e11 −0.657567 −0.328783 0.944405i \(-0.606639\pi\)
−0.328783 + 0.944405i \(0.606639\pi\)
\(434\) −3.94683e11 −0.534004
\(435\) 8.09163e9 0.0108351
\(436\) −3.52546e12 −4.67225
\(437\) 2.68256e11 0.351871
\(438\) 3.93018e11 0.510246
\(439\) 6.73221e11 0.865101 0.432551 0.901610i \(-0.357614\pi\)
0.432551 + 0.901610i \(0.357614\pi\)
\(440\) −3.13473e10 −0.0398715
\(441\) 2.46421e11 0.310244
\(442\) −8.64327e11 −1.07715
\(443\) −1.33274e12 −1.64411 −0.822054 0.569410i \(-0.807172\pi\)
−0.822054 + 0.569410i \(0.807172\pi\)
\(444\) 5.59886e11 0.683716
\(445\) −9.89278e9 −0.0119591
\(446\) −1.17632e11 −0.140773
\(447\) −6.98448e11 −0.827466
\(448\) 1.83139e12 2.14797
\(449\) 9.05955e11 1.05196 0.525979 0.850498i \(-0.323699\pi\)
0.525979 + 0.850498i \(0.323699\pi\)
\(450\) −5.40665e11 −0.621544
\(451\) −4.02033e11 −0.457581
\(452\) −1.80899e12 −2.03851
\(453\) −3.31362e11 −0.369709
\(454\) −1.12823e12 −1.24636
\(455\) −6.53024e10 −0.0714296
\(456\) −1.80844e12 −1.95868
\(457\) 1.69512e12 1.81793 0.908965 0.416872i \(-0.136874\pi\)
0.908965 + 0.416872i \(0.136874\pi\)
\(458\) −9.17337e11 −0.974168
\(459\) −8.81532e10 −0.0927003
\(460\) 2.96356e10 0.0308605
\(461\) 1.26008e12 1.29940 0.649702 0.760189i \(-0.274894\pi\)
0.649702 + 0.760189i \(0.274894\pi\)
\(462\) 4.89613e11 0.499993
\(463\) 5.71530e11 0.577996 0.288998 0.957330i \(-0.406678\pi\)
0.288998 + 0.957330i \(0.406678\pi\)
\(464\) −1.18204e12 −1.18386
\(465\) 5.14237e9 0.00510064
\(466\) 3.49499e12 3.43328
\(467\) 1.03056e12 1.00264 0.501322 0.865261i \(-0.332847\pi\)
0.501322 + 0.865261i \(0.332847\pi\)
\(468\) 1.03099e12 0.993455
\(469\) −2.04356e12 −1.95034
\(470\) −5.63436e10 −0.0532604
\(471\) −3.03532e11 −0.284191
\(472\) −3.90670e11 −0.362302
\(473\) 2.11052e11 0.193872
\(474\) −6.31664e11 −0.574756
\(475\) 1.35004e12 1.21682
\(476\) −1.86640e12 −1.66638
\(477\) 5.93854e11 0.525227
\(478\) −1.85437e12 −1.62469
\(479\) −1.20661e12 −1.04727 −0.523634 0.851943i \(-0.675424\pi\)
−0.523634 + 0.851943i \(0.675424\pi\)
\(480\) −6.56760e10 −0.0564704
\(481\) 6.68437e11 0.569387
\(482\) 8.71056e11 0.735079
\(483\) −2.76962e11 −0.231557
\(484\) −2.67118e12 −2.21258
\(485\) 8.28080e10 0.0679571
\(486\) 1.47386e11 0.119837
\(487\) −1.26332e12 −1.01773 −0.508867 0.860845i \(-0.669935\pi\)
−0.508867 + 0.860845i \(0.669935\pi\)
\(488\) 1.86453e12 1.48827
\(489\) 1.31644e11 0.104115
\(490\) −9.52793e10 −0.0746649
\(491\) −7.81392e11 −0.606740 −0.303370 0.952873i \(-0.598112\pi\)
−0.303370 + 0.952873i \(0.598112\pi\)
\(492\) −2.56230e12 −1.97146
\(493\) 2.76104e11 0.210505
\(494\) −3.60838e12 −2.72610
\(495\) −6.37922e9 −0.00477578
\(496\) −7.51205e11 −0.557302
\(497\) 1.53890e11 0.113137
\(498\) 1.88035e12 1.36996
\(499\) 2.09499e12 1.51262 0.756309 0.654215i \(-0.227001\pi\)
0.756309 + 0.654215i \(0.227001\pi\)
\(500\) 2.98566e11 0.213636
\(501\) −7.03498e11 −0.498877
\(502\) 1.77287e12 1.24598
\(503\) −7.43670e11 −0.517993 −0.258997 0.965878i \(-0.583392\pi\)
−0.258997 + 0.965878i \(0.583392\pi\)
\(504\) 1.86713e12 1.28895
\(505\) −4.36672e10 −0.0298775
\(506\) −2.65276e11 −0.179896
\(507\) 3.71915e11 0.249981
\(508\) −5.73631e12 −3.82161
\(509\) 2.21983e12 1.46585 0.732926 0.680308i \(-0.238154\pi\)
0.732926 + 0.680308i \(0.238154\pi\)
\(510\) 3.40847e10 0.0223097
\(511\) 1.01321e12 0.657364
\(512\) −2.12829e12 −1.36872
\(513\) −3.68021e11 −0.234609
\(514\) −4.60450e12 −2.90970
\(515\) −1.70465e10 −0.0106783
\(516\) 1.34511e12 0.835285
\(517\) 3.59823e11 0.221504
\(518\) 2.02315e12 1.23465
\(519\) −4.51343e11 −0.273057
\(520\) −2.38522e11 −0.143059
\(521\) 8.40218e9 0.00499600 0.00249800 0.999997i \(-0.499205\pi\)
0.00249800 + 0.999997i \(0.499205\pi\)
\(522\) −4.61625e11 −0.272127
\(523\) 2.60435e12 1.52209 0.761047 0.648697i \(-0.224686\pi\)
0.761047 + 0.648697i \(0.224686\pi\)
\(524\) −3.26618e11 −0.189256
\(525\) −1.39385e12 −0.800753
\(526\) −6.39261e12 −3.64118
\(527\) 1.75469e11 0.0990950
\(528\) 9.31885e11 0.521807
\(529\) −1.65109e12 −0.916687
\(530\) −2.29616e11 −0.126404
\(531\) −7.95020e10 −0.0433963
\(532\) −7.79182e12 −4.21732
\(533\) −3.05909e12 −1.64180
\(534\) 5.64379e11 0.300355
\(535\) −4.32392e10 −0.0228184
\(536\) −7.46429e12 −3.90613
\(537\) 2.29630e11 0.119164
\(538\) −1.69745e12 −0.873526
\(539\) 6.08475e11 0.310523
\(540\) −4.06571e10 −0.0205761
\(541\) 8.34995e11 0.419079 0.209540 0.977800i \(-0.432803\pi\)
0.209540 + 0.977800i \(0.432803\pi\)
\(542\) −1.56452e12 −0.778724
\(543\) −5.52171e10 −0.0272568
\(544\) −2.24101e12 −1.09710
\(545\) 1.65981e11 0.0805887
\(546\) 3.72548e12 1.79397
\(547\) −6.95891e11 −0.332352 −0.166176 0.986096i \(-0.553142\pi\)
−0.166176 + 0.986096i \(0.553142\pi\)
\(548\) 9.21967e12 4.36720
\(549\) 3.79435e11 0.178263
\(550\) −1.33504e12 −0.622102
\(551\) 1.15268e12 0.532752
\(552\) −1.01163e12 −0.463761
\(553\) −1.62845e12 −0.740476
\(554\) 3.68667e12 1.66280
\(555\) −2.63598e10 −0.0117930
\(556\) 8.60904e12 3.82048
\(557\) 1.76865e12 0.778562 0.389281 0.921119i \(-0.372724\pi\)
0.389281 + 0.921119i \(0.372724\pi\)
\(558\) −2.93370e11 −0.128104
\(559\) 1.60590e12 0.695611
\(560\) −3.76189e11 −0.161644
\(561\) −2.17673e11 −0.0927835
\(562\) −3.66617e12 −1.55024
\(563\) 2.10069e12 0.881201 0.440600 0.897703i \(-0.354766\pi\)
0.440600 + 0.897703i \(0.354766\pi\)
\(564\) 2.29328e12 0.954336
\(565\) 8.51683e10 0.0351609
\(566\) 1.48684e12 0.608962
\(567\) 3.79964e11 0.154390
\(568\) 5.62096e11 0.226591
\(569\) 1.35737e12 0.542867 0.271434 0.962457i \(-0.412502\pi\)
0.271434 + 0.962457i \(0.412502\pi\)
\(570\) 1.42296e11 0.0564621
\(571\) 3.13960e12 1.23598 0.617991 0.786185i \(-0.287947\pi\)
0.617991 + 0.786185i \(0.287947\pi\)
\(572\) 2.54577e12 0.994347
\(573\) 2.83864e11 0.110006
\(574\) −9.25888e12 −3.56004
\(575\) 7.55198e11 0.288108
\(576\) 1.36128e12 0.515284
\(577\) 2.09516e12 0.786913 0.393456 0.919343i \(-0.371279\pi\)
0.393456 + 0.919343i \(0.371279\pi\)
\(578\) −3.84964e12 −1.43465
\(579\) 2.46403e12 0.911156
\(580\) 1.27342e11 0.0467245
\(581\) 4.84759e12 1.76496
\(582\) −4.72417e12 −1.70676
\(583\) 1.46638e12 0.525699
\(584\) 3.70084e12 1.31657
\(585\) −4.85397e10 −0.0171355
\(586\) 7.74014e12 2.71150
\(587\) 4.64609e12 1.61516 0.807581 0.589757i \(-0.200776\pi\)
0.807581 + 0.589757i \(0.200776\pi\)
\(588\) 3.87803e12 1.33787
\(589\) 7.32545e11 0.250793
\(590\) 3.07397e10 0.0104440
\(591\) 2.23758e12 0.754458
\(592\) 3.85067e12 1.28851
\(593\) 4.34209e12 1.44196 0.720979 0.692957i \(-0.243693\pi\)
0.720979 + 0.692957i \(0.243693\pi\)
\(594\) 3.63932e11 0.119945
\(595\) 8.78713e10 0.0287423
\(596\) −1.09918e13 −3.56829
\(597\) 1.00382e12 0.323423
\(598\) −2.01849e12 −0.645464
\(599\) 4.84567e12 1.53792 0.768958 0.639299i \(-0.220775\pi\)
0.768958 + 0.639299i \(0.220775\pi\)
\(600\) −5.09115e12 −1.60374
\(601\) −2.85729e12 −0.893344 −0.446672 0.894698i \(-0.647391\pi\)
−0.446672 + 0.894698i \(0.647391\pi\)
\(602\) 4.86056e12 1.50835
\(603\) −1.51899e12 −0.467873
\(604\) −5.21478e12 −1.59430
\(605\) 1.25761e11 0.0381634
\(606\) 2.49120e12 0.750380
\(607\) −6.02059e11 −0.180007 −0.0900036 0.995941i \(-0.528688\pi\)
−0.0900036 + 0.995941i \(0.528688\pi\)
\(608\) −9.35572e12 −2.77659
\(609\) −1.19008e12 −0.350589
\(610\) −1.46710e11 −0.0429017
\(611\) 2.73790e12 0.794754
\(612\) −1.38731e12 −0.399752
\(613\) −3.72672e12 −1.06599 −0.532997 0.846117i \(-0.678934\pi\)
−0.532997 + 0.846117i \(0.678934\pi\)
\(614\) −5.50040e12 −1.56184
\(615\) 1.20635e11 0.0340044
\(616\) 4.61041e12 1.29011
\(617\) −5.71905e12 −1.58869 −0.794347 0.607464i \(-0.792187\pi\)
−0.794347 + 0.607464i \(0.792187\pi\)
\(618\) 9.72500e11 0.268189
\(619\) −2.32367e12 −0.636159 −0.318080 0.948064i \(-0.603038\pi\)
−0.318080 + 0.948064i \(0.603038\pi\)
\(620\) 8.09277e10 0.0219955
\(621\) −2.05867e11 −0.0555489
\(622\) 9.99929e12 2.67863
\(623\) 1.45499e12 0.386957
\(624\) 7.09075e12 1.87224
\(625\) 3.79361e12 0.994471
\(626\) −8.86410e12 −2.30701
\(627\) −9.08737e11 −0.234820
\(628\) −4.77682e12 −1.22552
\(629\) −8.99453e11 −0.229113
\(630\) −1.46914e11 −0.0371562
\(631\) −4.04352e12 −1.01538 −0.507689 0.861541i \(-0.669500\pi\)
−0.507689 + 0.861541i \(0.669500\pi\)
\(632\) −5.94804e12 −1.48302
\(633\) 2.09104e12 0.517661
\(634\) 8.53070e12 2.09693
\(635\) 2.70069e11 0.0659164
\(636\) 9.34575e12 2.26494
\(637\) 4.62991e12 1.11415
\(638\) −1.13987e12 −0.272371
\(639\) 1.14387e11 0.0271409
\(640\) −1.11206e11 −0.0262011
\(641\) 8.23067e11 0.192563 0.0962817 0.995354i \(-0.469305\pi\)
0.0962817 + 0.995354i \(0.469305\pi\)
\(642\) 2.46678e12 0.573090
\(643\) 2.70737e12 0.624594 0.312297 0.949985i \(-0.398902\pi\)
0.312297 + 0.949985i \(0.398902\pi\)
\(644\) −4.35867e12 −0.998545
\(645\) −6.33288e10 −0.0144073
\(646\) 4.85546e12 1.09694
\(647\) 5.65228e12 1.26810 0.634051 0.773291i \(-0.281391\pi\)
0.634051 + 0.773291i \(0.281391\pi\)
\(648\) 1.38785e12 0.309211
\(649\) −1.96311e11 −0.0434353
\(650\) −1.01584e13 −2.23210
\(651\) −7.56317e11 −0.165040
\(652\) 2.07174e12 0.448974
\(653\) −5.64503e11 −0.121495 −0.0607473 0.998153i \(-0.519348\pi\)
−0.0607473 + 0.998153i \(0.519348\pi\)
\(654\) −9.46915e12 −2.02400
\(655\) 1.53774e10 0.00326435
\(656\) −1.76225e13 −3.71536
\(657\) 7.53127e11 0.157697
\(658\) 8.28677e12 1.72333
\(659\) 8.34085e11 0.172276 0.0861382 0.996283i \(-0.472547\pi\)
0.0861382 + 0.996283i \(0.472547\pi\)
\(660\) −1.00393e11 −0.0205946
\(661\) −4.09602e12 −0.834555 −0.417278 0.908779i \(-0.637016\pi\)
−0.417278 + 0.908779i \(0.637016\pi\)
\(662\) −1.40340e13 −2.84001
\(663\) −1.65628e12 −0.332907
\(664\) 1.77062e13 3.53484
\(665\) 3.66844e11 0.0727418
\(666\) 1.50382e12 0.296184
\(667\) 6.44796e11 0.126141
\(668\) −1.10713e13 −2.15131
\(669\) −2.25414e11 −0.0435075
\(670\) 5.87324e11 0.112601
\(671\) 9.36921e11 0.178423
\(672\) 9.65933e12 1.82720
\(673\) 6.26288e12 1.17681 0.588405 0.808566i \(-0.299756\pi\)
0.588405 + 0.808566i \(0.299756\pi\)
\(674\) −2.32898e12 −0.434707
\(675\) −1.03606e12 −0.192095
\(676\) 5.85299e12 1.07800
\(677\) 5.43978e11 0.0995250 0.0497625 0.998761i \(-0.484154\pi\)
0.0497625 + 0.998761i \(0.484154\pi\)
\(678\) −4.85882e12 −0.883075
\(679\) −1.21790e13 −2.19887
\(680\) 3.20957e11 0.0575648
\(681\) −2.16198e12 −0.385203
\(682\) −7.24406e11 −0.128219
\(683\) −7.39909e12 −1.30102 −0.650512 0.759496i \(-0.725446\pi\)
−0.650512 + 0.759496i \(0.725446\pi\)
\(684\) −5.79171e12 −1.01171
\(685\) −4.34068e11 −0.0753269
\(686\) −1.04291e12 −0.179799
\(687\) −1.75786e12 −0.301078
\(688\) 9.25116e12 1.57416
\(689\) 1.11577e13 1.88620
\(690\) 7.95993e10 0.0133687
\(691\) −4.12021e12 −0.687493 −0.343746 0.939063i \(-0.611696\pi\)
−0.343746 + 0.939063i \(0.611696\pi\)
\(692\) −7.10298e12 −1.17751
\(693\) 9.38227e11 0.154528
\(694\) −1.31682e13 −2.15482
\(695\) −4.05319e11 −0.0658970
\(696\) −4.34687e12 −0.702158
\(697\) 4.11632e12 0.660636
\(698\) −1.34899e13 −2.15110
\(699\) 6.69733e12 1.06109
\(700\) −2.19356e13 −3.45310
\(701\) −1.38815e12 −0.217123 −0.108561 0.994090i \(-0.534624\pi\)
−0.108561 + 0.994090i \(0.534624\pi\)
\(702\) 2.76917e12 0.430361
\(703\) −3.75502e12 −0.579847
\(704\) 3.36135e12 0.515746
\(705\) −1.07969e11 −0.0164607
\(706\) −5.65253e12 −0.856292
\(707\) 6.42237e12 0.966737
\(708\) −1.25116e12 −0.187138
\(709\) −6.66867e12 −0.991131 −0.495565 0.868571i \(-0.665039\pi\)
−0.495565 + 0.868571i \(0.665039\pi\)
\(710\) −4.42282e10 −0.00653186
\(711\) −1.21044e12 −0.177635
\(712\) 5.31445e12 0.774994
\(713\) 4.09778e11 0.0593808
\(714\) −5.01303e12 −0.721869
\(715\) −1.19857e11 −0.0171508
\(716\) 3.61379e12 0.513871
\(717\) −3.55346e12 −0.502129
\(718\) −6.84568e12 −0.961294
\(719\) −1.00413e12 −0.140123 −0.0700616 0.997543i \(-0.522320\pi\)
−0.0700616 + 0.997543i \(0.522320\pi\)
\(720\) −2.79623e11 −0.0387773
\(721\) 2.50713e12 0.345516
\(722\) 6.63059e12 0.908102
\(723\) 1.66917e12 0.227185
\(724\) −8.68976e11 −0.117540
\(725\) 3.24502e12 0.436211
\(726\) −7.17462e12 −0.958482
\(727\) 1.41169e13 1.87428 0.937139 0.348958i \(-0.113464\pi\)
0.937139 + 0.348958i \(0.113464\pi\)
\(728\) 3.50808e13 4.62891
\(729\) 2.82430e11 0.0370370
\(730\) −2.91199e11 −0.0379522
\(731\) −2.16091e12 −0.279904
\(732\) 5.97134e12 0.768727
\(733\) 7.89551e12 1.01021 0.505106 0.863057i \(-0.331453\pi\)
0.505106 + 0.863057i \(0.331453\pi\)
\(734\) −9.17612e12 −1.16688
\(735\) −1.82580e11 −0.0230760
\(736\) −5.23350e12 −0.657419
\(737\) −3.75078e12 −0.468293
\(738\) −6.88218e12 −0.854029
\(739\) 5.28001e12 0.651231 0.325615 0.945502i \(-0.394429\pi\)
0.325615 + 0.945502i \(0.394429\pi\)
\(740\) −4.14836e11 −0.0508550
\(741\) −6.91461e12 −0.842531
\(742\) 3.37708e13 4.09001
\(743\) 7.69938e12 0.926843 0.463422 0.886138i \(-0.346622\pi\)
0.463422 + 0.886138i \(0.346622\pi\)
\(744\) −2.76251e12 −0.330541
\(745\) 5.17501e11 0.0615471
\(746\) −1.27092e13 −1.50243
\(747\) 3.60325e12 0.423401
\(748\) −3.42561e12 −0.400111
\(749\) 6.35943e12 0.738329
\(750\) 8.01929e11 0.0925466
\(751\) −1.35739e13 −1.55713 −0.778563 0.627566i \(-0.784051\pi\)
−0.778563 + 0.627566i \(0.784051\pi\)
\(752\) 1.57723e13 1.79852
\(753\) 3.39728e12 0.385083
\(754\) −8.67330e12 −0.977267
\(755\) 2.45516e11 0.0274991
\(756\) 5.97966e12 0.665776
\(757\) −9.32404e12 −1.03198 −0.515992 0.856594i \(-0.672577\pi\)
−0.515992 + 0.856594i \(0.672577\pi\)
\(758\) 1.55315e13 1.70885
\(759\) −5.08339e11 −0.0555988
\(760\) 1.33993e12 0.145687
\(761\) −6.42108e12 −0.694028 −0.347014 0.937860i \(-0.612804\pi\)
−0.347014 + 0.937860i \(0.612804\pi\)
\(762\) −1.54074e13 −1.65551
\(763\) −2.44117e13 −2.60758
\(764\) 4.46729e12 0.474378
\(765\) 6.53153e10 0.00689507
\(766\) 1.63094e13 1.71162
\(767\) −1.49373e12 −0.155845
\(768\) −2.26036e12 −0.234451
\(769\) −5.58942e12 −0.576366 −0.288183 0.957575i \(-0.593051\pi\)
−0.288183 + 0.957575i \(0.593051\pi\)
\(770\) −3.62768e11 −0.0371896
\(771\) −8.82344e12 −0.899276
\(772\) 3.87776e13 3.92919
\(773\) 8.17454e12 0.823485 0.411742 0.911300i \(-0.364920\pi\)
0.411742 + 0.911300i \(0.364920\pi\)
\(774\) 3.61288e12 0.361843
\(775\) 2.06227e12 0.205346
\(776\) −4.44849e13 −4.40388
\(777\) 3.87688e12 0.381582
\(778\) 1.69825e13 1.66185
\(779\) 1.71848e13 1.67196
\(780\) −7.63891e11 −0.0738934
\(781\) 2.82451e11 0.0271653
\(782\) 2.71610e12 0.259726
\(783\) −8.84595e11 −0.0841040
\(784\) 2.66716e13 2.52131
\(785\) 2.24896e11 0.0211382
\(786\) −8.77275e11 −0.0819850
\(787\) −3.35172e12 −0.311445 −0.155723 0.987801i \(-0.549771\pi\)
−0.155723 + 0.987801i \(0.549771\pi\)
\(788\) 3.52138e13 3.25346
\(789\) −1.22499e13 −1.12535
\(790\) 4.68019e11 0.0427505
\(791\) −1.25262e13 −1.13769
\(792\) 3.42695e12 0.309488
\(793\) 7.12907e12 0.640182
\(794\) 4.27575e12 0.381786
\(795\) −4.40004e11 −0.0390665
\(796\) 1.57975e13 1.39470
\(797\) −1.48041e13 −1.29963 −0.649817 0.760091i \(-0.725154\pi\)
−0.649817 + 0.760091i \(0.725154\pi\)
\(798\) −2.09283e13 −1.82693
\(799\) −3.68414e12 −0.319798
\(800\) −2.63383e13 −2.27344
\(801\) 1.08150e12 0.0928282
\(802\) 1.05863e13 0.903565
\(803\) 1.85966e12 0.157839
\(804\) −2.39051e13 −2.01761
\(805\) 2.05209e11 0.0172233
\(806\) −5.51203e12 −0.460049
\(807\) −3.25276e12 −0.269973
\(808\) 2.34582e13 1.93617
\(809\) 1.05150e13 0.863058 0.431529 0.902099i \(-0.357974\pi\)
0.431529 + 0.902099i \(0.357974\pi\)
\(810\) −1.09202e11 −0.00891352
\(811\) −2.07754e13 −1.68638 −0.843191 0.537615i \(-0.819326\pi\)
−0.843191 + 0.537615i \(0.819326\pi\)
\(812\) −1.87288e13 −1.51185
\(813\) −2.99803e12 −0.240673
\(814\) 3.71330e12 0.296449
\(815\) −9.75389e10 −0.00774406
\(816\) −9.54135e12 −0.753363
\(817\) −9.02136e12 −0.708390
\(818\) 4.69865e13 3.66930
\(819\) 7.13900e12 0.554447
\(820\) 1.89849e12 0.146637
\(821\) 7.67497e12 0.589566 0.294783 0.955564i \(-0.404753\pi\)
0.294783 + 0.955564i \(0.404753\pi\)
\(822\) 2.47634e13 1.89185
\(823\) −9.08768e12 −0.690484 −0.345242 0.938514i \(-0.612203\pi\)
−0.345242 + 0.938514i \(0.612203\pi\)
\(824\) 9.15750e12 0.691997
\(825\) −2.55829e12 −0.192268
\(826\) −4.52106e12 −0.337932
\(827\) −1.56022e13 −1.15988 −0.579938 0.814660i \(-0.696923\pi\)
−0.579938 + 0.814660i \(0.696923\pi\)
\(828\) −3.23983e12 −0.239544
\(829\) 2.64563e13 1.94551 0.972754 0.231840i \(-0.0744747\pi\)
0.972754 + 0.231840i \(0.0744747\pi\)
\(830\) −1.39321e12 −0.101898
\(831\) 7.06464e12 0.513908
\(832\) 2.55766e13 1.85049
\(833\) −6.23003e12 −0.448320
\(834\) 2.31233e13 1.65502
\(835\) 5.21243e11 0.0371066
\(836\) −1.43012e13 −1.01261
\(837\) −5.62175e11 −0.0395920
\(838\) 5.65750e12 0.396302
\(839\) 8.86025e12 0.617329 0.308665 0.951171i \(-0.400118\pi\)
0.308665 + 0.951171i \(0.400118\pi\)
\(840\) −1.38341e12 −0.0958726
\(841\) −1.17365e13 −0.809016
\(842\) 4.45248e13 3.05279
\(843\) −7.02534e12 −0.479119
\(844\) 3.29076e13 2.23231
\(845\) −2.75563e11 −0.0185937
\(846\) 6.15961e12 0.413415
\(847\) −1.84964e13 −1.23484
\(848\) 6.42764e13 4.26845
\(849\) 2.84918e12 0.188207
\(850\) 1.36691e13 0.898165
\(851\) −2.10052e12 −0.137292
\(852\) 1.80016e12 0.117040
\(853\) −1.33799e13 −0.865332 −0.432666 0.901554i \(-0.642427\pi\)
−0.432666 + 0.901554i \(0.642427\pi\)
\(854\) 2.15774e13 1.38816
\(855\) 2.72678e11 0.0174503
\(856\) 2.32283e13 1.47872
\(857\) −7.75808e12 −0.491293 −0.245646 0.969360i \(-0.579000\pi\)
−0.245646 + 0.969360i \(0.579000\pi\)
\(858\) 6.83779e12 0.430748
\(859\) −1.43176e13 −0.897222 −0.448611 0.893727i \(-0.648081\pi\)
−0.448611 + 0.893727i \(0.648081\pi\)
\(860\) −9.96633e11 −0.0621287
\(861\) −1.77425e13 −1.10027
\(862\) −5.13448e13 −3.16748
\(863\) 6.99759e12 0.429437 0.214719 0.976676i \(-0.431117\pi\)
0.214719 + 0.976676i \(0.431117\pi\)
\(864\) 7.17984e12 0.438332
\(865\) 3.34413e11 0.0203100
\(866\) −2.03313e13 −1.22839
\(867\) −7.37692e12 −0.443393
\(868\) −1.19025e13 −0.711703
\(869\) −2.98887e12 −0.177794
\(870\) 3.42031e11 0.0202409
\(871\) −2.85398e13 −1.68023
\(872\) −8.91659e13 −5.22245
\(873\) −9.05275e12 −0.527493
\(874\) 1.13391e13 0.657323
\(875\) 2.06739e12 0.119230
\(876\) 1.18523e13 0.680039
\(877\) 3.15194e13 1.79920 0.899600 0.436714i \(-0.143858\pi\)
0.899600 + 0.436714i \(0.143858\pi\)
\(878\) 2.84569e13 1.61608
\(879\) 1.48321e13 0.838019
\(880\) −6.90461e11 −0.0388121
\(881\) −1.72449e13 −0.964424 −0.482212 0.876055i \(-0.660166\pi\)
−0.482212 + 0.876055i \(0.660166\pi\)
\(882\) 1.04161e13 0.579560
\(883\) −1.01246e13 −0.560472 −0.280236 0.959931i \(-0.590413\pi\)
−0.280236 + 0.959931i \(0.590413\pi\)
\(884\) −2.60656e13 −1.43560
\(885\) 5.89054e10 0.00322783
\(886\) −5.63348e13 −3.07132
\(887\) −1.50249e12 −0.0814995 −0.0407497 0.999169i \(-0.512975\pi\)
−0.0407497 + 0.999169i \(0.512975\pi\)
\(888\) 1.41606e13 0.764230
\(889\) −3.97206e13 −2.13284
\(890\) −4.18165e11 −0.0223405
\(891\) 6.97390e11 0.0370703
\(892\) −3.54745e12 −0.187618
\(893\) −1.53805e13 −0.809355
\(894\) −2.95232e13 −1.54577
\(895\) −1.70140e11 −0.00886343
\(896\) 1.63557e13 0.847781
\(897\) −3.86797e12 −0.199488
\(898\) 3.82945e13 1.96514
\(899\) 1.76078e12 0.0899057
\(900\) −1.63049e13 −0.828374
\(901\) −1.50139e13 −0.758982
\(902\) −1.69938e13 −0.854796
\(903\) 9.31411e12 0.466172
\(904\) −4.57529e13 −2.27856
\(905\) 4.09120e10 0.00202736
\(906\) −1.40066e13 −0.690645
\(907\) 2.46747e13 1.21065 0.605326 0.795977i \(-0.293043\pi\)
0.605326 + 0.795977i \(0.293043\pi\)
\(908\) −3.40240e13 −1.66111
\(909\) 4.77379e12 0.231913
\(910\) −2.76032e12 −0.133436
\(911\) −2.96700e13 −1.42720 −0.713599 0.700554i \(-0.752936\pi\)
−0.713599 + 0.700554i \(0.752936\pi\)
\(912\) −3.98331e13 −1.90663
\(913\) 8.89733e12 0.423781
\(914\) 7.16523e13 3.39603
\(915\) −2.81135e11 −0.0132593
\(916\) −2.76642e13 −1.29834
\(917\) −2.26164e12 −0.105624
\(918\) −3.72622e12 −0.173171
\(919\) −6.41468e11 −0.0296658 −0.0148329 0.999890i \(-0.504722\pi\)
−0.0148329 + 0.999890i \(0.504722\pi\)
\(920\) 7.49543e11 0.0344946
\(921\) −1.05402e13 −0.482704
\(922\) 5.32633e13 2.42739
\(923\) 2.14918e12 0.0974688
\(924\) 1.47653e13 0.666374
\(925\) −1.05712e13 −0.474773
\(926\) 2.41584e13 1.07974
\(927\) 1.86357e12 0.0828869
\(928\) −2.24879e13 −0.995367
\(929\) 2.78508e13 1.22678 0.613391 0.789779i \(-0.289805\pi\)
0.613391 + 0.789779i \(0.289805\pi\)
\(930\) 2.17367e11 0.00952840
\(931\) −2.60091e13 −1.13462
\(932\) 1.05399e14 4.57577
\(933\) 1.91613e13 0.827860
\(934\) 4.35614e13 1.87302
\(935\) 1.61280e11 0.00690126
\(936\) 2.60758e13 1.11044
\(937\) 2.19926e13 0.932071 0.466035 0.884766i \(-0.345682\pi\)
0.466035 + 0.884766i \(0.345682\pi\)
\(938\) −8.63810e13 −3.64339
\(939\) −1.69859e13 −0.713008
\(940\) −1.69916e12 −0.0709837
\(941\) 3.39798e13 1.41276 0.706378 0.707835i \(-0.250328\pi\)
0.706378 + 0.707835i \(0.250328\pi\)
\(942\) −1.28302e13 −0.530892
\(943\) 9.61300e12 0.395874
\(944\) −8.60498e12 −0.352676
\(945\) −2.81526e11 −0.0114835
\(946\) 8.92113e12 0.362168
\(947\) 3.01777e13 1.21930 0.609650 0.792671i \(-0.291310\pi\)
0.609650 + 0.792671i \(0.291310\pi\)
\(948\) −1.90492e13 −0.766017
\(949\) 1.41502e13 0.566324
\(950\) 5.70658e13 2.27311
\(951\) 1.63471e13 0.648079
\(952\) −4.72050e13 −1.86261
\(953\) 8.09006e12 0.317712 0.158856 0.987302i \(-0.449219\pi\)
0.158856 + 0.987302i \(0.449219\pi\)
\(954\) 2.51021e13 0.981165
\(955\) −2.10323e11 −0.00818224
\(956\) −5.59224e13 −2.16534
\(957\) −2.18429e12 −0.0841795
\(958\) −5.10032e13 −1.95638
\(959\) 6.38408e13 2.43733
\(960\) −1.00861e12 −0.0383269
\(961\) −2.53206e13 −0.957677
\(962\) 2.82547e13 1.06366
\(963\) 4.72700e12 0.177120
\(964\) 2.62685e13 0.979690
\(965\) −1.82567e12 −0.0677720
\(966\) −1.17071e13 −0.432566
\(967\) 1.06043e13 0.389998 0.194999 0.980803i \(-0.437530\pi\)
0.194999 + 0.980803i \(0.437530\pi\)
\(968\) −6.75595e13 −2.47313
\(969\) 9.30434e12 0.339023
\(970\) 3.50028e12 0.126949
\(971\) 3.83413e13 1.38414 0.692071 0.721830i \(-0.256699\pi\)
0.692071 + 0.721830i \(0.256699\pi\)
\(972\) 4.44472e12 0.159715
\(973\) 5.96125e13 2.13221
\(974\) −5.34003e13 −1.90120
\(975\) −1.94661e13 −0.689855
\(976\) 4.10685e13 1.44872
\(977\) 1.97686e12 0.0694145 0.0347073 0.999398i \(-0.488950\pi\)
0.0347073 + 0.999398i \(0.488950\pi\)
\(978\) 5.56456e12 0.194494
\(979\) 2.67050e12 0.0929116
\(980\) −2.87335e12 −0.0995109
\(981\) −1.81454e13 −0.625541
\(982\) −3.30293e13 −1.13344
\(983\) 5.58570e12 0.190804 0.0954019 0.995439i \(-0.469586\pi\)
0.0954019 + 0.995439i \(0.469586\pi\)
\(984\) −6.48058e13 −2.20361
\(985\) −1.65789e12 −0.0561168
\(986\) 1.16708e13 0.393239
\(987\) 1.58796e13 0.532615
\(988\) −1.08818e14 −3.63325
\(989\) −5.04646e12 −0.167727
\(990\) −2.69648e11 −0.00892152
\(991\) −4.45379e10 −0.00146689 −0.000733447 1.00000i \(-0.500233\pi\)
−0.000733447 1.00000i \(0.500233\pi\)
\(992\) −1.42915e13 −0.468569
\(993\) −2.68928e13 −0.877738
\(994\) 6.50489e12 0.211350
\(995\) −7.43759e11 −0.0240563
\(996\) 5.67059e13 1.82583
\(997\) −5.30115e13 −1.69919 −0.849595 0.527436i \(-0.823154\pi\)
−0.849595 + 0.527436i \(0.823154\pi\)
\(998\) 8.85547e13 2.82569
\(999\) 2.88171e12 0.0915389
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.d.1.21 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.10.a.d.1.21 22 1.1 even 1 trivial