Properties

Label 289.10.a.i.1.11
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 289.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(148.845356651\)
Analytic rank: \(0\)
Dimension: \(52\)
Twist minimal: no (minimal twist has level 17)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-26.9890 q^{2} -111.659 q^{3} +216.409 q^{4} -2126.40 q^{5} +3013.56 q^{6} -8475.21 q^{7} +7977.73 q^{8} -7215.34 q^{9} +O(q^{10})\) \(q-26.9890 q^{2} -111.659 q^{3} +216.409 q^{4} -2126.40 q^{5} +3013.56 q^{6} -8475.21 q^{7} +7977.73 q^{8} -7215.34 q^{9} +57389.5 q^{10} -7768.93 q^{11} -24163.9 q^{12} +188698. q^{13} +228738. q^{14} +237431. q^{15} -326113. q^{16} +194735. q^{18} +117938. q^{19} -460172. q^{20} +946331. q^{21} +209676. q^{22} +1.84165e6 q^{23} -890782. q^{24} +2.56845e6 q^{25} -5.09279e6 q^{26} +3.00343e6 q^{27} -1.83411e6 q^{28} -5.18387e6 q^{29} -6.40804e6 q^{30} -4.70232e6 q^{31} +4.71687e6 q^{32} +867468. q^{33} +1.80217e7 q^{35} -1.56146e6 q^{36} +337590. q^{37} -3.18303e6 q^{38} -2.10698e7 q^{39} -1.69638e7 q^{40} -1.68128e7 q^{41} -2.55406e7 q^{42} -1.06248e7 q^{43} -1.68126e6 q^{44} +1.53427e7 q^{45} -4.97043e7 q^{46} +9.90984e6 q^{47} +3.64133e7 q^{48} +3.14756e7 q^{49} -6.93202e7 q^{50} +4.08360e7 q^{52} +8.09197e7 q^{53} -8.10598e7 q^{54} +1.65199e7 q^{55} -6.76129e7 q^{56} -1.31688e7 q^{57} +1.39908e8 q^{58} +3.54248e7 q^{59} +5.13822e7 q^{60} +1.51754e7 q^{61} +1.26911e8 q^{62} +6.11516e7 q^{63} +3.96658e7 q^{64} -4.01248e8 q^{65} -2.34121e7 q^{66} -1.17520e8 q^{67} -2.05636e8 q^{69} -4.86388e8 q^{70} -3.17626e8 q^{71} -5.75620e7 q^{72} +1.04290e8 q^{73} -9.11124e6 q^{74} -2.86790e8 q^{75} +2.55228e7 q^{76} +6.58433e7 q^{77} +5.68654e8 q^{78} -1.97824e8 q^{79} +6.93446e8 q^{80} -1.93340e8 q^{81} +4.53760e8 q^{82} +1.02741e7 q^{83} +2.04794e8 q^{84} +2.86754e8 q^{86} +5.78823e8 q^{87} -6.19784e7 q^{88} -9.95387e8 q^{89} -4.14085e8 q^{90} -1.59926e9 q^{91} +3.98549e8 q^{92} +5.25054e8 q^{93} -2.67457e8 q^{94} -2.50783e8 q^{95} -5.26679e8 q^{96} +2.90283e8 q^{97} -8.49497e8 q^{98} +5.60555e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 64q^{2} + 13312q^{4} + 49152q^{8} + 341172q^{9} + O(q^{10}) \) \( 52q + 64q^{2} + 13312q^{4} + 49152q^{8} + 341172q^{9} + 156200q^{13} + 1207872q^{15} + 3407880q^{16} + 2193336q^{18} + 1185568q^{19} + 5198336q^{21} + 13827692q^{25} + 3618944q^{26} - 9167544q^{30} + 61884888q^{32} + 1635208q^{33} + 46992776q^{35} + 156027320q^{36} + 84813952q^{38} - 4635776q^{42} + 125448912q^{43} + 164193176q^{47} + 270850284q^{49} - 226223888q^{50} + 103553016q^{52} + 426167208q^{53} + 677761520q^{55} + 375214512q^{59} + 336918024q^{60} + 190014416q^{64} + 1377178928q^{66} + 311910088q^{67} + 533688136q^{69} + 1477690280q^{70} + 2757942680q^{72} + 4047975520q^{76} + 3440336432q^{77} + 3266558756q^{81} + 2072890608q^{83} + 2630025952q^{84} + 1538547296q^{86} - 1010436256q^{87} + 1873849184q^{89} - 1998451624q^{93} - 6880776704q^{94} - 4667454128q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −26.9890 −1.19276 −0.596379 0.802703i \(-0.703395\pi\)
−0.596379 + 0.802703i \(0.703395\pi\)
\(3\) −111.659 −0.795878 −0.397939 0.917412i \(-0.630275\pi\)
−0.397939 + 0.917412i \(0.630275\pi\)
\(4\) 216.409 0.422673
\(5\) −2126.40 −1.52153 −0.760764 0.649028i \(-0.775176\pi\)
−0.760764 + 0.649028i \(0.775176\pi\)
\(6\) 3013.56 0.949291
\(7\) −8475.21 −1.33416 −0.667082 0.744984i \(-0.732457\pi\)
−0.667082 + 0.744984i \(0.732457\pi\)
\(8\) 7977.73 0.688611
\(9\) −7215.34 −0.366577
\(10\) 57389.5 1.81482
\(11\) −7768.93 −0.159990 −0.0799952 0.996795i \(-0.525491\pi\)
−0.0799952 + 0.996795i \(0.525491\pi\)
\(12\) −24163.9 −0.336397
\(13\) 188698. 1.83241 0.916205 0.400709i \(-0.131236\pi\)
0.916205 + 0.400709i \(0.131236\pi\)
\(14\) 228738. 1.59134
\(15\) 237431. 1.21095
\(16\) −326113. −1.24402
\(17\) 0 0
\(18\) 194735. 0.437238
\(19\) 117938. 0.207616 0.103808 0.994597i \(-0.466897\pi\)
0.103808 + 0.994597i \(0.466897\pi\)
\(20\) −460172. −0.643109
\(21\) 946331. 1.06183
\(22\) 209676. 0.190830
\(23\) 1.84165e6 1.37224 0.686122 0.727486i \(-0.259311\pi\)
0.686122 + 0.727486i \(0.259311\pi\)
\(24\) −890782. −0.548051
\(25\) 2.56845e6 1.31505
\(26\) −5.09279e6 −2.18562
\(27\) 3.00343e6 1.08763
\(28\) −1.83411e6 −0.563916
\(29\) −5.18387e6 −1.36101 −0.680507 0.732741i \(-0.738240\pi\)
−0.680507 + 0.732741i \(0.738240\pi\)
\(30\) −6.40804e6 −1.44437
\(31\) −4.70232e6 −0.914501 −0.457250 0.889338i \(-0.651166\pi\)
−0.457250 + 0.889338i \(0.651166\pi\)
\(32\) 4.71687e6 0.795205
\(33\) 867468. 0.127333
\(34\) 0 0
\(35\) 1.80217e7 2.02997
\(36\) −1.56146e6 −0.154942
\(37\) 337590. 0.0296130 0.0148065 0.999890i \(-0.495287\pi\)
0.0148065 + 0.999890i \(0.495287\pi\)
\(38\) −3.18303e6 −0.247636
\(39\) −2.10698e7 −1.45838
\(40\) −1.69638e7 −1.04774
\(41\) −1.68128e7 −0.929205 −0.464603 0.885519i \(-0.653803\pi\)
−0.464603 + 0.885519i \(0.653803\pi\)
\(42\) −2.55406e7 −1.26651
\(43\) −1.06248e7 −0.473929 −0.236965 0.971518i \(-0.576153\pi\)
−0.236965 + 0.971518i \(0.576153\pi\)
\(44\) −1.68126e6 −0.0676237
\(45\) 1.53427e7 0.557758
\(46\) −4.97043e7 −1.63676
\(47\) 9.90984e6 0.296228 0.148114 0.988970i \(-0.452680\pi\)
0.148114 + 0.988970i \(0.452680\pi\)
\(48\) 3.64133e7 0.990089
\(49\) 3.14756e7 0.779995
\(50\) −6.93202e7 −1.56854
\(51\) 0 0
\(52\) 4.08360e7 0.774511
\(53\) 8.09197e7 1.40868 0.704341 0.709862i \(-0.251243\pi\)
0.704341 + 0.709862i \(0.251243\pi\)
\(54\) −8.10598e7 −1.29728
\(55\) 1.65199e7 0.243430
\(56\) −6.76129e7 −0.918721
\(57\) −1.31688e7 −0.165237
\(58\) 1.39908e8 1.62336
\(59\) 3.54248e7 0.380604 0.190302 0.981726i \(-0.439053\pi\)
0.190302 + 0.981726i \(0.439053\pi\)
\(60\) 5.13822e7 0.511837
\(61\) 1.51754e7 0.140331 0.0701657 0.997535i \(-0.477647\pi\)
0.0701657 + 0.997535i \(0.477647\pi\)
\(62\) 1.26911e8 1.09078
\(63\) 6.11516e7 0.489075
\(64\) 3.96658e7 0.295533
\(65\) −4.01248e8 −2.78806
\(66\) −2.34121e7 −0.151878
\(67\) −1.17520e8 −0.712486 −0.356243 0.934393i \(-0.615943\pi\)
−0.356243 + 0.934393i \(0.615943\pi\)
\(68\) 0 0
\(69\) −2.05636e8 −1.09214
\(70\) −4.86388e8 −2.42126
\(71\) −3.17626e8 −1.48338 −0.741692 0.670740i \(-0.765976\pi\)
−0.741692 + 0.670740i \(0.765976\pi\)
\(72\) −5.75620e7 −0.252429
\(73\) 1.04290e8 0.429824 0.214912 0.976633i \(-0.431053\pi\)
0.214912 + 0.976633i \(0.431053\pi\)
\(74\) −9.11124e6 −0.0353211
\(75\) −2.86790e8 −1.04662
\(76\) 2.55228e7 0.0877539
\(77\) 6.58433e7 0.213454
\(78\) 5.68654e8 1.73949
\(79\) −1.97824e8 −0.571423 −0.285712 0.958316i \(-0.592230\pi\)
−0.285712 + 0.958316i \(0.592230\pi\)
\(80\) 6.93446e8 1.89281
\(81\) −1.93340e8 −0.499044
\(82\) 4.53760e8 1.10832
\(83\) 1.02741e7 0.0237626 0.0118813 0.999929i \(-0.496218\pi\)
0.0118813 + 0.999929i \(0.496218\pi\)
\(84\) 2.04794e8 0.448808
\(85\) 0 0
\(86\) 2.86754e8 0.565283
\(87\) 5.78823e8 1.08320
\(88\) −6.19784e7 −0.110171
\(89\) −9.95387e8 −1.68166 −0.840828 0.541303i \(-0.817931\pi\)
−0.840828 + 0.541303i \(0.817931\pi\)
\(90\) −4.14085e8 −0.665271
\(91\) −1.59926e9 −2.44474
\(92\) 3.98549e8 0.580011
\(93\) 5.25054e8 0.727832
\(94\) −2.67457e8 −0.353329
\(95\) −2.50783e8 −0.315894
\(96\) −5.26679e8 −0.632887
\(97\) 2.90283e8 0.332926 0.166463 0.986048i \(-0.446765\pi\)
0.166463 + 0.986048i \(0.446765\pi\)
\(98\) −8.49497e8 −0.930346
\(99\) 5.60555e7 0.0586489
\(100\) 5.55836e8 0.555836
\(101\) −1.04616e8 −0.100035 −0.0500176 0.998748i \(-0.515928\pi\)
−0.0500176 + 0.998748i \(0.515928\pi\)
\(102\) 0 0
\(103\) −2.89721e8 −0.253637 −0.126818 0.991926i \(-0.540477\pi\)
−0.126818 + 0.991926i \(0.540477\pi\)
\(104\) 1.50538e9 1.26182
\(105\) −2.01228e9 −1.61561
\(106\) −2.18395e9 −1.68022
\(107\) 2.59660e8 0.191504 0.0957520 0.995405i \(-0.469474\pi\)
0.0957520 + 0.995405i \(0.469474\pi\)
\(108\) 6.49969e8 0.459712
\(109\) −8.72678e8 −0.592154 −0.296077 0.955164i \(-0.595679\pi\)
−0.296077 + 0.955164i \(0.595679\pi\)
\(110\) −4.45855e8 −0.290353
\(111\) −3.76949e7 −0.0235683
\(112\) 2.76387e9 1.65973
\(113\) 1.61677e9 0.932815 0.466408 0.884570i \(-0.345548\pi\)
0.466408 + 0.884570i \(0.345548\pi\)
\(114\) 3.55413e8 0.197088
\(115\) −3.91608e9 −2.08791
\(116\) −1.12183e9 −0.575264
\(117\) −1.36152e9 −0.671720
\(118\) −9.56082e8 −0.453969
\(119\) 0 0
\(120\) 1.89416e9 0.833875
\(121\) −2.29759e9 −0.974403
\(122\) −4.09569e8 −0.167382
\(123\) 1.87729e9 0.739535
\(124\) −1.01762e9 −0.386535
\(125\) −1.30844e9 −0.479356
\(126\) −1.65042e9 −0.583348
\(127\) −4.64829e9 −1.58554 −0.792769 0.609522i \(-0.791361\pi\)
−0.792769 + 0.609522i \(0.791361\pi\)
\(128\) −3.48558e9 −1.14770
\(129\) 1.18635e9 0.377190
\(130\) 1.08293e10 3.32549
\(131\) 3.87389e9 1.14928 0.574641 0.818405i \(-0.305142\pi\)
0.574641 + 0.818405i \(0.305142\pi\)
\(132\) 1.87728e8 0.0538203
\(133\) −9.99547e8 −0.276994
\(134\) 3.17176e9 0.849824
\(135\) −6.38650e9 −1.65486
\(136\) 0 0
\(137\) −2.81827e9 −0.683502 −0.341751 0.939790i \(-0.611020\pi\)
−0.341751 + 0.939790i \(0.611020\pi\)
\(138\) 5.54992e9 1.30266
\(139\) −6.78367e9 −1.54134 −0.770670 0.637235i \(-0.780078\pi\)
−0.770670 + 0.637235i \(0.780078\pi\)
\(140\) 3.90005e9 0.858014
\(141\) −1.10652e9 −0.235762
\(142\) 8.57243e9 1.76932
\(143\) −1.46598e9 −0.293168
\(144\) 2.35301e9 0.456030
\(145\) 1.10230e10 2.07082
\(146\) −2.81469e9 −0.512677
\(147\) −3.51453e9 −0.620781
\(148\) 7.30575e7 0.0125166
\(149\) −8.91855e9 −1.48237 −0.741184 0.671302i \(-0.765736\pi\)
−0.741184 + 0.671302i \(0.765736\pi\)
\(150\) 7.74020e9 1.24836
\(151\) 9.82516e9 1.53795 0.768977 0.639276i \(-0.220766\pi\)
0.768977 + 0.639276i \(0.220766\pi\)
\(152\) 9.40875e8 0.142967
\(153\) 0 0
\(154\) −1.77705e9 −0.254599
\(155\) 9.99901e9 1.39144
\(156\) −4.55969e9 −0.616417
\(157\) −3.59938e8 −0.0472802 −0.0236401 0.999721i \(-0.507526\pi\)
−0.0236401 + 0.999721i \(0.507526\pi\)
\(158\) 5.33909e9 0.681570
\(159\) −9.03539e9 −1.12114
\(160\) −1.00300e10 −1.20993
\(161\) −1.56084e10 −1.83080
\(162\) 5.21805e9 0.595239
\(163\) −2.33468e9 −0.259050 −0.129525 0.991576i \(-0.541345\pi\)
−0.129525 + 0.991576i \(0.541345\pi\)
\(164\) −3.63843e9 −0.392750
\(165\) −1.84459e9 −0.193741
\(166\) −2.77289e8 −0.0283431
\(167\) −1.41903e10 −1.41178 −0.705891 0.708321i \(-0.749453\pi\)
−0.705891 + 0.708321i \(0.749453\pi\)
\(168\) 7.54957e9 0.731190
\(169\) 2.50025e10 2.35773
\(170\) 0 0
\(171\) −8.50961e8 −0.0761075
\(172\) −2.29930e9 −0.200317
\(173\) 1.14445e10 0.971380 0.485690 0.874131i \(-0.338568\pi\)
0.485690 + 0.874131i \(0.338568\pi\)
\(174\) −1.56219e10 −1.29200
\(175\) −2.17682e10 −1.75449
\(176\) 2.53355e9 0.199031
\(177\) −3.95549e9 −0.302915
\(178\) 2.68645e10 2.00581
\(179\) 1.03273e10 0.751883 0.375941 0.926643i \(-0.377319\pi\)
0.375941 + 0.926643i \(0.377319\pi\)
\(180\) 3.32030e9 0.235749
\(181\) −7.53319e9 −0.521706 −0.260853 0.965379i \(-0.584004\pi\)
−0.260853 + 0.965379i \(0.584004\pi\)
\(182\) 4.31624e10 2.91598
\(183\) −1.69446e9 −0.111687
\(184\) 1.46922e10 0.944943
\(185\) −7.17852e8 −0.0450570
\(186\) −1.41707e10 −0.868127
\(187\) 0 0
\(188\) 2.14458e9 0.125208
\(189\) −2.54547e10 −1.45108
\(190\) 6.76839e9 0.376786
\(191\) 1.86443e10 1.01367 0.506834 0.862044i \(-0.330816\pi\)
0.506834 + 0.862044i \(0.330816\pi\)
\(192\) −4.42903e9 −0.235208
\(193\) 2.71011e10 1.40598 0.702989 0.711200i \(-0.251848\pi\)
0.702989 + 0.711200i \(0.251848\pi\)
\(194\) −7.83445e9 −0.397101
\(195\) 4.48028e10 2.21896
\(196\) 6.81160e9 0.329683
\(197\) −1.57089e9 −0.0743101 −0.0371551 0.999310i \(-0.511830\pi\)
−0.0371551 + 0.999310i \(0.511830\pi\)
\(198\) −1.51288e9 −0.0699540
\(199\) −1.15986e10 −0.524285 −0.262143 0.965029i \(-0.584429\pi\)
−0.262143 + 0.965029i \(0.584429\pi\)
\(200\) 2.04904e10 0.905558
\(201\) 1.31222e10 0.567052
\(202\) 2.82349e9 0.119318
\(203\) 4.39344e10 1.81582
\(204\) 0 0
\(205\) 3.57507e10 1.41381
\(206\) 7.81928e9 0.302527
\(207\) −1.32881e10 −0.503034
\(208\) −6.15369e10 −2.27956
\(209\) −9.16250e8 −0.0332166
\(210\) 5.43095e10 1.92703
\(211\) 3.17418e10 1.10246 0.551228 0.834355i \(-0.314160\pi\)
0.551228 + 0.834355i \(0.314160\pi\)
\(212\) 1.75117e10 0.595412
\(213\) 3.54657e10 1.18059
\(214\) −7.00797e9 −0.228418
\(215\) 2.25926e10 0.721097
\(216\) 2.39606e10 0.748954
\(217\) 3.98531e10 1.22009
\(218\) 2.35527e10 0.706297
\(219\) −1.16449e10 −0.342088
\(220\) 3.57504e9 0.102891
\(221\) 0 0
\(222\) 1.01735e9 0.0281113
\(223\) 4.39482e10 1.19006 0.595030 0.803704i \(-0.297140\pi\)
0.595030 + 0.803704i \(0.297140\pi\)
\(224\) −3.99765e10 −1.06093
\(225\) −1.85323e10 −0.482067
\(226\) −4.36351e10 −1.11262
\(227\) 3.84258e10 0.960520 0.480260 0.877126i \(-0.340542\pi\)
0.480260 + 0.877126i \(0.340542\pi\)
\(228\) −2.84984e9 −0.0698414
\(229\) −1.92884e10 −0.463487 −0.231744 0.972777i \(-0.574443\pi\)
−0.231744 + 0.972777i \(0.574443\pi\)
\(230\) 1.05691e11 2.49037
\(231\) −7.35198e9 −0.169883
\(232\) −4.13555e10 −0.937210
\(233\) −7.60123e10 −1.68959 −0.844797 0.535087i \(-0.820279\pi\)
−0.844797 + 0.535087i \(0.820279\pi\)
\(234\) 3.67462e10 0.801200
\(235\) −2.10723e10 −0.450720
\(236\) 7.66624e9 0.160871
\(237\) 2.20888e10 0.454784
\(238\) 0 0
\(239\) 2.69458e10 0.534196 0.267098 0.963669i \(-0.413935\pi\)
0.267098 + 0.963669i \(0.413935\pi\)
\(240\) −7.74292e10 −1.50645
\(241\) −7.71206e10 −1.47263 −0.736315 0.676639i \(-0.763436\pi\)
−0.736315 + 0.676639i \(0.763436\pi\)
\(242\) 6.20098e10 1.16223
\(243\) −3.75285e10 −0.690452
\(244\) 3.28408e9 0.0593144
\(245\) −6.69298e10 −1.18678
\(246\) −5.06663e10 −0.882086
\(247\) 2.22546e10 0.380438
\(248\) −3.75138e10 −0.629736
\(249\) −1.14720e9 −0.0189122
\(250\) 3.53135e10 0.571756
\(251\) −2.37776e10 −0.378125 −0.189063 0.981965i \(-0.560545\pi\)
−0.189063 + 0.981965i \(0.560545\pi\)
\(252\) 1.32337e10 0.206719
\(253\) −1.43076e10 −0.219546
\(254\) 1.25453e11 1.89116
\(255\) 0 0
\(256\) 7.37636e10 1.07340
\(257\) −4.21200e10 −0.602267 −0.301134 0.953582i \(-0.597365\pi\)
−0.301134 + 0.953582i \(0.597365\pi\)
\(258\) −3.20185e10 −0.449897
\(259\) −2.86115e9 −0.0395086
\(260\) −8.68336e10 −1.17844
\(261\) 3.74034e10 0.498917
\(262\) −1.04553e11 −1.37082
\(263\) 4.71166e10 0.607257 0.303629 0.952790i \(-0.401802\pi\)
0.303629 + 0.952790i \(0.401802\pi\)
\(264\) 6.92043e9 0.0876829
\(265\) −1.72068e11 −2.14335
\(266\) 2.69768e10 0.330388
\(267\) 1.11144e11 1.33839
\(268\) −2.54324e10 −0.301149
\(269\) −5.69389e9 −0.0663015 −0.0331508 0.999450i \(-0.510554\pi\)
−0.0331508 + 0.999450i \(0.510554\pi\)
\(270\) 1.72366e11 1.97385
\(271\) −1.51533e11 −1.70666 −0.853328 0.521375i \(-0.825419\pi\)
−0.853328 + 0.521375i \(0.825419\pi\)
\(272\) 0 0
\(273\) 1.78571e11 1.94571
\(274\) 7.60624e10 0.815253
\(275\) −1.99541e10 −0.210395
\(276\) −4.45014e10 −0.461618
\(277\) 5.65276e10 0.576901 0.288451 0.957495i \(-0.406860\pi\)
0.288451 + 0.957495i \(0.406860\pi\)
\(278\) 1.83085e11 1.83845
\(279\) 3.39288e10 0.335235
\(280\) 1.43772e11 1.39786
\(281\) −3.63183e10 −0.347493 −0.173747 0.984790i \(-0.555587\pi\)
−0.173747 + 0.984790i \(0.555587\pi\)
\(282\) 2.98639e10 0.281207
\(283\) 2.29141e10 0.212355 0.106178 0.994347i \(-0.466139\pi\)
0.106178 + 0.994347i \(0.466139\pi\)
\(284\) −6.87371e10 −0.626987
\(285\) 2.80021e10 0.251413
\(286\) 3.95655e10 0.349679
\(287\) 1.42492e11 1.23971
\(288\) −3.40338e10 −0.291504
\(289\) 0 0
\(290\) −2.97500e11 −2.46999
\(291\) −3.24126e10 −0.264969
\(292\) 2.25693e10 0.181675
\(293\) 7.83040e10 0.620697 0.310348 0.950623i \(-0.399554\pi\)
0.310348 + 0.950623i \(0.399554\pi\)
\(294\) 9.48537e10 0.740442
\(295\) −7.53273e10 −0.579100
\(296\) 2.69320e9 0.0203918
\(297\) −2.33335e10 −0.174010
\(298\) 2.40703e11 1.76811
\(299\) 3.47516e11 2.51452
\(300\) −6.20639e10 −0.442378
\(301\) 9.00476e10 0.632300
\(302\) −2.65172e11 −1.83441
\(303\) 1.16813e10 0.0796158
\(304\) −3.84610e10 −0.258279
\(305\) −3.22689e10 −0.213518
\(306\) 0 0
\(307\) −9.62528e10 −0.618430 −0.309215 0.950992i \(-0.600066\pi\)
−0.309215 + 0.950992i \(0.600066\pi\)
\(308\) 1.42491e10 0.0902212
\(309\) 3.23498e10 0.201864
\(310\) −2.69864e11 −1.65965
\(311\) −2.06836e11 −1.25373 −0.626865 0.779128i \(-0.715662\pi\)
−0.626865 + 0.779128i \(0.715662\pi\)
\(312\) −1.68089e11 −1.00425
\(313\) −4.43872e10 −0.261402 −0.130701 0.991422i \(-0.541723\pi\)
−0.130701 + 0.991422i \(0.541723\pi\)
\(314\) 9.71439e9 0.0563939
\(315\) −1.30033e11 −0.744141
\(316\) −4.28109e10 −0.241525
\(317\) 1.67214e10 0.0930052 0.0465026 0.998918i \(-0.485192\pi\)
0.0465026 + 0.998918i \(0.485192\pi\)
\(318\) 2.43857e11 1.33725
\(319\) 4.02731e10 0.217749
\(320\) −8.43453e10 −0.449662
\(321\) −2.89933e10 −0.152414
\(322\) 4.21255e11 2.18370
\(323\) 0 0
\(324\) −4.18404e10 −0.210932
\(325\) 4.84663e11 2.40971
\(326\) 6.30107e10 0.308984
\(327\) 9.74420e10 0.471283
\(328\) −1.34128e11 −0.639861
\(329\) −8.39880e10 −0.395217
\(330\) 4.97836e10 0.231086
\(331\) −2.85648e11 −1.30799 −0.653995 0.756499i \(-0.726908\pi\)
−0.653995 + 0.756499i \(0.726908\pi\)
\(332\) 2.22341e9 0.0100438
\(333\) −2.43583e9 −0.0108554
\(334\) 3.82983e11 1.68391
\(335\) 2.49895e11 1.08407
\(336\) −3.08610e11 −1.32094
\(337\) 1.51192e11 0.638549 0.319274 0.947662i \(-0.396561\pi\)
0.319274 + 0.947662i \(0.396561\pi\)
\(338\) −6.74795e11 −2.81220
\(339\) −1.80526e11 −0.742407
\(340\) 0 0
\(341\) 3.65320e10 0.146311
\(342\) 2.29666e10 0.0907779
\(343\) 7.52429e10 0.293523
\(344\) −8.47619e10 −0.326353
\(345\) 4.37265e11 1.66172
\(346\) −3.08876e11 −1.15862
\(347\) 3.16975e9 0.0117366 0.00586830 0.999983i \(-0.498132\pi\)
0.00586830 + 0.999983i \(0.498132\pi\)
\(348\) 1.25262e11 0.457841
\(349\) −1.16871e11 −0.421689 −0.210844 0.977520i \(-0.567621\pi\)
−0.210844 + 0.977520i \(0.567621\pi\)
\(350\) 5.87503e11 2.09269
\(351\) 5.66743e11 1.99298
\(352\) −3.66450e10 −0.127225
\(353\) 6.42891e9 0.0220369 0.0110185 0.999939i \(-0.496493\pi\)
0.0110185 + 0.999939i \(0.496493\pi\)
\(354\) 1.06755e11 0.361304
\(355\) 6.75401e11 2.25701
\(356\) −2.15410e11 −0.710791
\(357\) 0 0
\(358\) −2.78725e11 −0.896815
\(359\) −4.93384e10 −0.156769 −0.0783846 0.996923i \(-0.524976\pi\)
−0.0783846 + 0.996923i \(0.524976\pi\)
\(360\) 1.22400e11 0.384079
\(361\) −3.08778e11 −0.956895
\(362\) 2.03314e11 0.622269
\(363\) 2.56546e11 0.775506
\(364\) −3.46093e11 −1.03333
\(365\) −2.21763e11 −0.653990
\(366\) 4.57319e10 0.133215
\(367\) −4.03374e11 −1.16068 −0.580338 0.814376i \(-0.697079\pi\)
−0.580338 + 0.814376i \(0.697079\pi\)
\(368\) −6.00585e11 −1.70710
\(369\) 1.21310e11 0.340626
\(370\) 1.93741e10 0.0537421
\(371\) −6.85812e11 −1.87941
\(372\) 1.13626e11 0.307635
\(373\) −4.66959e10 −0.124908 −0.0624538 0.998048i \(-0.519893\pi\)
−0.0624538 + 0.998048i \(0.519893\pi\)
\(374\) 0 0
\(375\) 1.46098e11 0.381509
\(376\) 7.90580e10 0.203986
\(377\) −9.78186e11 −2.49394
\(378\) 6.86999e11 1.73078
\(379\) 4.32289e10 0.107621 0.0538106 0.998551i \(-0.482863\pi\)
0.0538106 + 0.998551i \(0.482863\pi\)
\(380\) −5.42716e10 −0.133520
\(381\) 5.19022e11 1.26190
\(382\) −5.03192e11 −1.20906
\(383\) −6.63545e11 −1.57571 −0.787854 0.615862i \(-0.788808\pi\)
−0.787854 + 0.615862i \(0.788808\pi\)
\(384\) 3.89195e11 0.913433
\(385\) −1.40009e11 −0.324776
\(386\) −7.31432e11 −1.67699
\(387\) 7.66617e10 0.173732
\(388\) 6.28197e10 0.140719
\(389\) 3.77536e11 0.835959 0.417979 0.908456i \(-0.362738\pi\)
0.417979 + 0.908456i \(0.362738\pi\)
\(390\) −1.20919e12 −2.64668
\(391\) 0 0
\(392\) 2.51104e11 0.537114
\(393\) −4.32554e11 −0.914690
\(394\) 4.23969e10 0.0886341
\(395\) 4.20654e11 0.869437
\(396\) 1.21309e10 0.0247893
\(397\) −8.10743e11 −1.63805 −0.819023 0.573760i \(-0.805484\pi\)
−0.819023 + 0.573760i \(0.805484\pi\)
\(398\) 3.13036e11 0.625346
\(399\) 1.11608e11 0.220454
\(400\) −8.37605e11 −1.63595
\(401\) −7.54539e11 −1.45724 −0.728622 0.684916i \(-0.759839\pi\)
−0.728622 + 0.684916i \(0.759839\pi\)
\(402\) −3.54155e11 −0.676357
\(403\) −8.87319e11 −1.67574
\(404\) −2.26398e10 −0.0422822
\(405\) 4.11118e11 0.759309
\(406\) −1.18575e12 −2.16583
\(407\) −2.62271e9 −0.00473779
\(408\) 0 0
\(409\) 4.84207e11 0.855611 0.427805 0.903871i \(-0.359287\pi\)
0.427805 + 0.903871i \(0.359287\pi\)
\(410\) −9.64877e11 −1.68634
\(411\) 3.14684e11 0.543985
\(412\) −6.26981e10 −0.107205
\(413\) −3.00233e11 −0.507788
\(414\) 3.58634e11 0.599998
\(415\) −2.18469e10 −0.0361555
\(416\) 8.90065e11 1.45714
\(417\) 7.57456e11 1.22672
\(418\) 2.47287e10 0.0396194
\(419\) 7.47691e10 0.118511 0.0592555 0.998243i \(-0.481127\pi\)
0.0592555 + 0.998243i \(0.481127\pi\)
\(420\) −4.35475e11 −0.682875
\(421\) −5.91134e11 −0.917100 −0.458550 0.888669i \(-0.651631\pi\)
−0.458550 + 0.888669i \(0.651631\pi\)
\(422\) −8.56682e11 −1.31496
\(423\) −7.15029e10 −0.108591
\(424\) 6.45556e11 0.970035
\(425\) 0 0
\(426\) −9.57186e11 −1.40816
\(427\) −1.28614e11 −0.187225
\(428\) 5.61927e10 0.0809436
\(429\) 1.63690e11 0.233326
\(430\) −6.09753e11 −0.860094
\(431\) −4.74524e11 −0.662386 −0.331193 0.943563i \(-0.607451\pi\)
−0.331193 + 0.943563i \(0.607451\pi\)
\(432\) −9.79457e11 −1.35303
\(433\) −1.35727e12 −1.85554 −0.927770 0.373153i \(-0.878277\pi\)
−0.927770 + 0.373153i \(0.878277\pi\)
\(434\) −1.07560e12 −1.45528
\(435\) −1.23081e12 −1.64812
\(436\) −1.88855e11 −0.250288
\(437\) 2.17200e11 0.284900
\(438\) 3.14285e11 0.408028
\(439\) 5.54359e11 0.712362 0.356181 0.934417i \(-0.384079\pi\)
0.356181 + 0.934417i \(0.384079\pi\)
\(440\) 1.31791e11 0.167629
\(441\) −2.27107e11 −0.285929
\(442\) 0 0
\(443\) 1.17232e12 1.44621 0.723103 0.690740i \(-0.242715\pi\)
0.723103 + 0.690740i \(0.242715\pi\)
\(444\) −8.15750e9 −0.00996170
\(445\) 2.11659e12 2.55869
\(446\) −1.18612e12 −1.41945
\(447\) 9.95834e11 1.17979
\(448\) −3.36176e11 −0.394290
\(449\) 9.38348e11 1.08957 0.544786 0.838575i \(-0.316611\pi\)
0.544786 + 0.838575i \(0.316611\pi\)
\(450\) 5.00169e11 0.574990
\(451\) 1.30617e11 0.148664
\(452\) 3.49883e11 0.394276
\(453\) −1.09706e12 −1.22402
\(454\) −1.03708e12 −1.14567
\(455\) 3.40066e12 3.71974
\(456\) −1.05057e11 −0.113784
\(457\) −1.33793e12 −1.43487 −0.717433 0.696628i \(-0.754683\pi\)
−0.717433 + 0.696628i \(0.754683\pi\)
\(458\) 5.20577e11 0.552828
\(459\) 0 0
\(460\) −8.47475e11 −0.882504
\(461\) 8.45027e11 0.871398 0.435699 0.900092i \(-0.356501\pi\)
0.435699 + 0.900092i \(0.356501\pi\)
\(462\) 1.98423e11 0.202630
\(463\) −3.24656e11 −0.328328 −0.164164 0.986433i \(-0.552493\pi\)
−0.164164 + 0.986433i \(0.552493\pi\)
\(464\) 1.69052e12 1.69313
\(465\) −1.11648e12 −1.10742
\(466\) 2.05150e12 2.01528
\(467\) 7.41373e11 0.721292 0.360646 0.932703i \(-0.382556\pi\)
0.360646 + 0.932703i \(0.382556\pi\)
\(468\) −2.94645e11 −0.283918
\(469\) 9.96010e11 0.950574
\(470\) 5.68721e11 0.537600
\(471\) 4.01902e10 0.0376293
\(472\) 2.82609e11 0.262088
\(473\) 8.25435e10 0.0758242
\(474\) −5.96156e11 −0.542447
\(475\) 3.02918e11 0.273026
\(476\) 0 0
\(477\) −5.83864e11 −0.516391
\(478\) −7.27242e11 −0.637167
\(479\) 3.31368e11 0.287608 0.143804 0.989606i \(-0.454067\pi\)
0.143804 + 0.989606i \(0.454067\pi\)
\(480\) 1.11993e12 0.962955
\(481\) 6.37027e10 0.0542631
\(482\) 2.08141e12 1.75649
\(483\) 1.74281e12 1.45709
\(484\) −4.97219e11 −0.411854
\(485\) −6.17257e11 −0.506557
\(486\) 1.01286e12 0.823542
\(487\) −1.84180e12 −1.48375 −0.741877 0.670536i \(-0.766064\pi\)
−0.741877 + 0.670536i \(0.766064\pi\)
\(488\) 1.21065e11 0.0966338
\(489\) 2.60687e11 0.206172
\(490\) 1.80637e12 1.41555
\(491\) −1.63755e12 −1.27153 −0.635767 0.771881i \(-0.719316\pi\)
−0.635767 + 0.771881i \(0.719316\pi\)
\(492\) 4.06262e11 0.312582
\(493\) 0 0
\(494\) −6.00632e11 −0.453771
\(495\) −1.19196e11 −0.0892360
\(496\) 1.53348e12 1.13766
\(497\) 2.69195e12 1.97908
\(498\) 3.09618e10 0.0225576
\(499\) 8.40100e11 0.606567 0.303283 0.952900i \(-0.401917\pi\)
0.303283 + 0.952900i \(0.401917\pi\)
\(500\) −2.83157e11 −0.202611
\(501\) 1.58447e12 1.12361
\(502\) 6.41734e11 0.451012
\(503\) 8.41199e11 0.585926 0.292963 0.956124i \(-0.405359\pi\)
0.292963 + 0.956124i \(0.405359\pi\)
\(504\) 4.87850e11 0.336782
\(505\) 2.22456e11 0.152206
\(506\) 3.86150e11 0.261865
\(507\) −2.79175e12 −1.87647
\(508\) −1.00593e12 −0.670165
\(509\) 1.64594e12 1.08688 0.543442 0.839447i \(-0.317121\pi\)
0.543442 + 0.839447i \(0.317121\pi\)
\(510\) 0 0
\(511\) −8.83882e11 −0.573456
\(512\) −2.06193e11 −0.132605
\(513\) 3.54218e11 0.225810
\(514\) 1.13678e12 0.718359
\(515\) 6.16062e11 0.385915
\(516\) 2.56737e11 0.159428
\(517\) −7.69889e10 −0.0473937
\(518\) 7.72197e10 0.0471242
\(519\) −1.27788e12 −0.773101
\(520\) −3.20105e12 −1.91989
\(521\) 3.51701e11 0.209124 0.104562 0.994518i \(-0.466656\pi\)
0.104562 + 0.994518i \(0.466656\pi\)
\(522\) −1.00948e12 −0.595088
\(523\) 5.05119e11 0.295213 0.147607 0.989046i \(-0.452843\pi\)
0.147607 + 0.989046i \(0.452843\pi\)
\(524\) 8.38345e11 0.485771
\(525\) 2.43061e12 1.39636
\(526\) −1.27163e12 −0.724311
\(527\) 0 0
\(528\) −2.82892e11 −0.158405
\(529\) 1.59052e12 0.883055
\(530\) 4.64395e12 2.55650
\(531\) −2.55602e11 −0.139521
\(532\) −2.16311e11 −0.117078
\(533\) −3.17254e12 −1.70269
\(534\) −2.99966e12 −1.59638
\(535\) −5.52141e11 −0.291379
\(536\) −9.37545e11 −0.490626
\(537\) −1.15314e12 −0.598407
\(538\) 1.53673e11 0.0790817
\(539\) −2.44532e11 −0.124792
\(540\) −1.38209e12 −0.699465
\(541\) −2.41525e11 −0.121220 −0.0606099 0.998162i \(-0.519305\pi\)
−0.0606099 + 0.998162i \(0.519305\pi\)
\(542\) 4.08974e12 2.03563
\(543\) 8.41146e11 0.415214
\(544\) 0 0
\(545\) 1.85566e12 0.900979
\(546\) −4.81946e12 −2.32077
\(547\) −2.61893e12 −1.25078 −0.625389 0.780313i \(-0.715060\pi\)
−0.625389 + 0.780313i \(0.715060\pi\)
\(548\) −6.09898e11 −0.288898
\(549\) −1.09495e11 −0.0514423
\(550\) 5.38543e11 0.250951
\(551\) −6.11373e11 −0.282569
\(552\) −1.64051e12 −0.752060
\(553\) 1.67660e12 0.762373
\(554\) −1.52563e12 −0.688104
\(555\) 8.01544e10 0.0358599
\(556\) −1.46805e12 −0.651483
\(557\) −1.90268e12 −0.837565 −0.418782 0.908087i \(-0.637543\pi\)
−0.418782 + 0.908087i \(0.637543\pi\)
\(558\) −9.15707e11 −0.399855
\(559\) −2.00488e12 −0.868433
\(560\) −5.87710e12 −2.52532
\(561\) 0 0
\(562\) 9.80195e11 0.414476
\(563\) 2.77945e12 1.16593 0.582964 0.812498i \(-0.301893\pi\)
0.582964 + 0.812498i \(0.301893\pi\)
\(564\) −2.39460e11 −0.0996501
\(565\) −3.43790e12 −1.41930
\(566\) −6.18429e11 −0.253289
\(567\) 1.63860e12 0.665806
\(568\) −2.53394e12 −1.02148
\(569\) −2.91719e12 −1.16670 −0.583350 0.812221i \(-0.698258\pi\)
−0.583350 + 0.812221i \(0.698258\pi\)
\(570\) −7.55750e11 −0.299876
\(571\) −1.08718e12 −0.427994 −0.213997 0.976834i \(-0.568648\pi\)
−0.213997 + 0.976834i \(0.568648\pi\)
\(572\) −3.17252e11 −0.123914
\(573\) −2.08180e12 −0.806756
\(574\) −3.84572e12 −1.47868
\(575\) 4.73019e12 1.80457
\(576\) −2.86202e11 −0.108336
\(577\) 7.13293e11 0.267902 0.133951 0.990988i \(-0.457233\pi\)
0.133951 + 0.990988i \(0.457233\pi\)
\(578\) 0 0
\(579\) −3.02607e12 −1.11899
\(580\) 2.38547e12 0.875281
\(581\) −8.70755e10 −0.0317032
\(582\) 8.74784e11 0.316044
\(583\) −6.28660e11 −0.225376
\(584\) 8.31999e11 0.295982
\(585\) 2.89514e12 1.02204
\(586\) −2.11335e12 −0.740341
\(587\) −6.12219e11 −0.212831 −0.106416 0.994322i \(-0.533937\pi\)
−0.106416 + 0.994322i \(0.533937\pi\)
\(588\) −7.60574e11 −0.262388
\(589\) −5.54580e11 −0.189865
\(590\) 2.03301e12 0.690726
\(591\) 1.75404e11 0.0591418
\(592\) −1.10092e11 −0.0368391
\(593\) 1.86289e12 0.618643 0.309322 0.950957i \(-0.399898\pi\)
0.309322 + 0.950957i \(0.399898\pi\)
\(594\) 6.29748e11 0.207552
\(595\) 0 0
\(596\) −1.93005e12 −0.626558
\(597\) 1.29509e12 0.417267
\(598\) −9.37912e12 −2.99921
\(599\) 5.47380e12 1.73727 0.868637 0.495449i \(-0.164996\pi\)
0.868637 + 0.495449i \(0.164996\pi\)
\(600\) −2.28793e12 −0.720714
\(601\) −4.44329e12 −1.38921 −0.694607 0.719389i \(-0.744422\pi\)
−0.694607 + 0.719389i \(0.744422\pi\)
\(602\) −2.43030e12 −0.754181
\(603\) 8.47950e11 0.261181
\(604\) 2.12625e12 0.650052
\(605\) 4.88560e12 1.48258
\(606\) −3.15267e11 −0.0949624
\(607\) 1.25061e12 0.373916 0.186958 0.982368i \(-0.440137\pi\)
0.186958 + 0.982368i \(0.440137\pi\)
\(608\) 5.56297e11 0.165098
\(609\) −4.90565e12 −1.44517
\(610\) 8.70907e11 0.254676
\(611\) 1.86997e12 0.542812
\(612\) 0 0
\(613\) 6.34599e12 1.81521 0.907606 0.419823i \(-0.137908\pi\)
0.907606 + 0.419823i \(0.137908\pi\)
\(614\) 2.59777e12 0.737638
\(615\) −3.99187e12 −1.12522
\(616\) 5.25280e11 0.146987
\(617\) 3.48028e12 0.966786 0.483393 0.875403i \(-0.339404\pi\)
0.483393 + 0.875403i \(0.339404\pi\)
\(618\) −8.73091e11 −0.240775
\(619\) 2.75090e12 0.753125 0.376563 0.926391i \(-0.377106\pi\)
0.376563 + 0.926391i \(0.377106\pi\)
\(620\) 2.16387e12 0.588124
\(621\) 5.53127e12 1.49249
\(622\) 5.58230e12 1.49540
\(623\) 8.43612e12 2.24360
\(624\) 6.87112e12 1.81425
\(625\) −2.23425e12 −0.585695
\(626\) 1.19797e12 0.311789
\(627\) 1.02307e11 0.0264364
\(628\) −7.78938e10 −0.0199841
\(629\) 0 0
\(630\) 3.50946e12 0.887581
\(631\) −3.13630e12 −0.787563 −0.393782 0.919204i \(-0.628833\pi\)
−0.393782 + 0.919204i \(0.628833\pi\)
\(632\) −1.57819e12 −0.393489
\(633\) −3.54425e12 −0.877421
\(634\) −4.51296e11 −0.110933
\(635\) 9.88413e12 2.41244
\(636\) −1.95534e12 −0.473876
\(637\) 5.93939e12 1.42927
\(638\) −1.08693e12 −0.259722
\(639\) 2.29178e12 0.543775
\(640\) 7.41174e12 1.74627
\(641\) 3.99573e12 0.934836 0.467418 0.884036i \(-0.345184\pi\)
0.467418 + 0.884036i \(0.345184\pi\)
\(642\) 7.82501e11 0.181793
\(643\) −4.46811e12 −1.03080 −0.515400 0.856950i \(-0.672357\pi\)
−0.515400 + 0.856950i \(0.672357\pi\)
\(644\) −3.37779e12 −0.773830
\(645\) −2.52266e12 −0.573905
\(646\) 0 0
\(647\) −2.65786e12 −0.596297 −0.298148 0.954520i \(-0.596369\pi\)
−0.298148 + 0.954520i \(0.596369\pi\)
\(648\) −1.54241e12 −0.343647
\(649\) −2.75213e11 −0.0608930
\(650\) −1.30806e13 −2.87420
\(651\) −4.44995e12 −0.971047
\(652\) −5.05245e11 −0.109493
\(653\) 1.39817e12 0.300919 0.150459 0.988616i \(-0.451925\pi\)
0.150459 + 0.988616i \(0.451925\pi\)
\(654\) −2.62987e12 −0.562126
\(655\) −8.23745e12 −1.74867
\(656\) 5.48285e12 1.15595
\(657\) −7.52490e11 −0.157564
\(658\) 2.26676e12 0.471399
\(659\) −3.25916e12 −0.673165 −0.336582 0.941654i \(-0.609271\pi\)
−0.336582 + 0.941654i \(0.609271\pi\)
\(660\) −3.99184e11 −0.0818890
\(661\) −3.38834e12 −0.690368 −0.345184 0.938535i \(-0.612183\pi\)
−0.345184 + 0.938535i \(0.612183\pi\)
\(662\) 7.70936e12 1.56012
\(663\) 0 0
\(664\) 8.19643e10 0.0163632
\(665\) 2.12544e12 0.421455
\(666\) 6.57407e10 0.0129479
\(667\) −9.54686e12 −1.86764
\(668\) −3.07090e12 −0.596722
\(669\) −4.90719e12 −0.947143
\(670\) −6.74444e12 −1.29303
\(671\) −1.17896e11 −0.0224517
\(672\) 4.46372e12 0.844375
\(673\) 3.81702e12 0.717228 0.358614 0.933486i \(-0.383250\pi\)
0.358614 + 0.933486i \(0.383250\pi\)
\(674\) −4.08052e12 −0.761634
\(675\) 7.71418e12 1.43029
\(676\) 5.41077e12 0.996549
\(677\) 9.52051e12 1.74185 0.870926 0.491414i \(-0.163520\pi\)
0.870926 + 0.491414i \(0.163520\pi\)
\(678\) 4.87224e12 0.885513
\(679\) −2.46021e12 −0.444178
\(680\) 0 0
\(681\) −4.29057e12 −0.764457
\(682\) −9.85963e11 −0.174514
\(683\) −3.65262e12 −0.642260 −0.321130 0.947035i \(-0.604063\pi\)
−0.321130 + 0.947035i \(0.604063\pi\)
\(684\) −1.84155e11 −0.0321686
\(685\) 5.99277e12 1.03997
\(686\) −2.03073e12 −0.350102
\(687\) 2.15372e12 0.368879
\(688\) 3.46489e12 0.589578
\(689\) 1.52694e13 2.58128
\(690\) −1.18014e13 −1.98203
\(691\) −7.17157e12 −1.19664 −0.598320 0.801258i \(-0.704165\pi\)
−0.598320 + 0.801258i \(0.704165\pi\)
\(692\) 2.47669e12 0.410577
\(693\) −4.75082e11 −0.0782473
\(694\) −8.55485e10 −0.0139989
\(695\) 1.44248e13 2.34519
\(696\) 4.61770e12 0.745905
\(697\) 0 0
\(698\) 3.15424e12 0.502973
\(699\) 8.48743e12 1.34471
\(700\) −4.71083e12 −0.741577
\(701\) 2.77953e12 0.434750 0.217375 0.976088i \(-0.430251\pi\)
0.217375 + 0.976088i \(0.430251\pi\)
\(702\) −1.52958e13 −2.37715
\(703\) 3.98146e10 0.00614814
\(704\) −3.08161e11 −0.0472825
\(705\) 2.35290e12 0.358718
\(706\) −1.73510e11 −0.0262847
\(707\) 8.86644e11 0.133463
\(708\) −8.56002e11 −0.128034
\(709\) 2.42496e12 0.360410 0.180205 0.983629i \(-0.442324\pi\)
0.180205 + 0.983629i \(0.442324\pi\)
\(710\) −1.82284e13 −2.69207
\(711\) 1.42737e12 0.209471
\(712\) −7.94093e12 −1.15801
\(713\) −8.66001e12 −1.25492
\(714\) 0 0
\(715\) 3.11727e12 0.446064
\(716\) 2.23493e12 0.317801
\(717\) −3.00874e12 −0.425155
\(718\) 1.33160e12 0.186988
\(719\) −1.26802e13 −1.76948 −0.884742 0.466081i \(-0.845666\pi\)
−0.884742 + 0.466081i \(0.845666\pi\)
\(720\) −5.00345e12 −0.693862
\(721\) 2.45544e12 0.338393
\(722\) 8.33363e12 1.14135
\(723\) 8.61118e12 1.17203
\(724\) −1.63025e12 −0.220511
\(725\) −1.33145e13 −1.78980
\(726\) −6.92393e12 −0.924992
\(727\) 3.80482e12 0.505160 0.252580 0.967576i \(-0.418721\pi\)
0.252580 + 0.967576i \(0.418721\pi\)
\(728\) −1.27584e13 −1.68347
\(729\) 7.99589e12 1.04856
\(730\) 5.98517e12 0.780052
\(731\) 0 0
\(732\) −3.66696e11 −0.0472070
\(733\) −1.10980e13 −1.41996 −0.709979 0.704223i \(-0.751296\pi\)
−0.709979 + 0.704223i \(0.751296\pi\)
\(734\) 1.08867e13 1.38441
\(735\) 7.47329e12 0.944537
\(736\) 8.68682e12 1.09122
\(737\) 9.13007e11 0.113991
\(738\) −3.27404e12 −0.406284
\(739\) 2.33123e12 0.287531 0.143765 0.989612i \(-0.454079\pi\)
0.143765 + 0.989612i \(0.454079\pi\)
\(740\) −1.55349e11 −0.0190444
\(741\) −2.48492e12 −0.302783
\(742\) 1.85094e13 2.24169
\(743\) −1.09510e13 −1.31827 −0.659136 0.752024i \(-0.729078\pi\)
−0.659136 + 0.752024i \(0.729078\pi\)
\(744\) 4.18874e12 0.501193
\(745\) 1.89644e13 2.25547
\(746\) 1.26028e12 0.148985
\(747\) −7.41315e10 −0.00871084
\(748\) 0 0
\(749\) −2.20067e12 −0.255498
\(750\) −3.94306e12 −0.455048
\(751\) −4.36338e12 −0.500545 −0.250272 0.968175i \(-0.580520\pi\)
−0.250272 + 0.968175i \(0.580520\pi\)
\(752\) −3.23172e12 −0.368514
\(753\) 2.65497e12 0.300942
\(754\) 2.64003e13 2.97467
\(755\) −2.08922e13 −2.34004
\(756\) −5.50863e12 −0.613331
\(757\) 5.31168e12 0.587896 0.293948 0.955821i \(-0.405031\pi\)
0.293948 + 0.955821i \(0.405031\pi\)
\(758\) −1.16671e12 −0.128366
\(759\) 1.59757e12 0.174732
\(760\) −2.00068e12 −0.217528
\(761\) 1.63902e13 1.77155 0.885777 0.464111i \(-0.153626\pi\)
0.885777 + 0.464111i \(0.153626\pi\)
\(762\) −1.40079e13 −1.50514
\(763\) 7.39613e12 0.790031
\(764\) 4.03479e12 0.428450
\(765\) 0 0
\(766\) 1.79084e13 1.87944
\(767\) 6.68460e12 0.697423
\(768\) −8.23634e12 −0.854297
\(769\) 1.34189e13 1.38372 0.691859 0.722033i \(-0.256792\pi\)
0.691859 + 0.722033i \(0.256792\pi\)
\(770\) 3.77872e12 0.387379
\(771\) 4.70306e12 0.479331
\(772\) 5.86491e12 0.594270
\(773\) −5.22917e12 −0.526775 −0.263387 0.964690i \(-0.584840\pi\)
−0.263387 + 0.964690i \(0.584840\pi\)
\(774\) −2.06903e12 −0.207220
\(775\) −1.20777e13 −1.20261
\(776\) 2.31579e12 0.229257
\(777\) 3.19472e11 0.0314440
\(778\) −1.01893e13 −0.997097
\(779\) −1.98286e12 −0.192918
\(780\) 9.69572e12 0.937896
\(781\) 2.46762e12 0.237327
\(782\) 0 0
\(783\) −1.55694e13 −1.48028
\(784\) −1.02646e13 −0.970330
\(785\) 7.65373e11 0.0719382
\(786\) 1.16742e13 1.09100
\(787\) 6.84661e12 0.636194 0.318097 0.948058i \(-0.396956\pi\)
0.318097 + 0.948058i \(0.396956\pi\)
\(788\) −3.39955e11 −0.0314089
\(789\) −5.26097e12 −0.483303
\(790\) −1.13531e13 −1.03703
\(791\) −1.37025e13 −1.24453
\(792\) 4.47195e11 0.0403863
\(793\) 2.86357e12 0.257145
\(794\) 2.18812e13 1.95379
\(795\) 1.92129e13 1.70585
\(796\) −2.51004e12 −0.221601
\(797\) −1.71243e13 −1.50332 −0.751658 0.659553i \(-0.770745\pi\)
−0.751658 + 0.659553i \(0.770745\pi\)
\(798\) −3.01220e12 −0.262948
\(799\) 0 0
\(800\) 1.21151e13 1.04573
\(801\) 7.18206e12 0.616457
\(802\) 2.03643e13 1.73814
\(803\) −8.10224e11 −0.0687678
\(804\) 2.83975e12 0.239678
\(805\) 3.31896e13 2.78561
\(806\) 2.39479e13 1.99875
\(807\) 6.35772e11 0.0527680
\(808\) −8.34599e11 −0.0688853
\(809\) −1.37472e13 −1.12836 −0.564178 0.825653i \(-0.690807\pi\)
−0.564178 + 0.825653i \(0.690807\pi\)
\(810\) −1.10957e13 −0.905672
\(811\) −4.44088e12 −0.360475 −0.180237 0.983623i \(-0.557687\pi\)
−0.180237 + 0.983623i \(0.557687\pi\)
\(812\) 9.50778e12 0.767497
\(813\) 1.69200e13 1.35829
\(814\) 7.07846e10 0.00565104
\(815\) 4.96446e12 0.394151
\(816\) 0 0
\(817\) −1.25307e12 −0.0983955
\(818\) −1.30683e13 −1.02054
\(819\) 1.15392e13 0.896185
\(820\) 7.73676e12 0.597581
\(821\) −3.20955e12 −0.246547 −0.123274 0.992373i \(-0.539339\pi\)
−0.123274 + 0.992373i \(0.539339\pi\)
\(822\) −8.49303e12 −0.648843
\(823\) 1.82964e12 0.139016 0.0695081 0.997581i \(-0.477857\pi\)
0.0695081 + 0.997581i \(0.477857\pi\)
\(824\) −2.31131e12 −0.174657
\(825\) 2.22805e12 0.167449
\(826\) 8.10299e12 0.605669
\(827\) 4.67524e12 0.347560 0.173780 0.984785i \(-0.444402\pi\)
0.173780 + 0.984785i \(0.444402\pi\)
\(828\) −2.87567e12 −0.212619
\(829\) −2.09218e13 −1.53852 −0.769260 0.638936i \(-0.779375\pi\)
−0.769260 + 0.638936i \(0.779375\pi\)
\(830\) 5.89628e11 0.0431248
\(831\) −6.31179e12 −0.459143
\(832\) 7.48486e12 0.541538
\(833\) 0 0
\(834\) −2.04430e13 −1.46318
\(835\) 3.01743e13 2.14807
\(836\) −1.98285e11 −0.0140398
\(837\) −1.41231e13 −0.994638
\(838\) −2.01795e12 −0.141355
\(839\) −2.22899e13 −1.55303 −0.776515 0.630098i \(-0.783015\pi\)
−0.776515 + 0.630098i \(0.783015\pi\)
\(840\) −1.60534e13 −1.11253
\(841\) 1.23653e13 0.852360
\(842\) 1.59541e13 1.09388
\(843\) 4.05525e12 0.276563
\(844\) 6.86921e12 0.465979
\(845\) −5.31654e13 −3.58735
\(846\) 1.92980e12 0.129522
\(847\) 1.94726e13 1.30001
\(848\) −2.63889e13 −1.75243
\(849\) −2.55855e12 −0.169009
\(850\) 0 0
\(851\) 6.21722e11 0.0406362
\(852\) 7.67509e12 0.499006
\(853\) −1.82969e13 −1.18333 −0.591666 0.806183i \(-0.701530\pi\)
−0.591666 + 0.806183i \(0.701530\pi\)
\(854\) 3.47118e12 0.223315
\(855\) 1.80948e12 0.115800
\(856\) 2.07150e12 0.131872
\(857\) 2.46088e13 1.55839 0.779197 0.626780i \(-0.215627\pi\)
0.779197 + 0.626780i \(0.215627\pi\)
\(858\) −4.41783e12 −0.278302
\(859\) 9.01006e12 0.564623 0.282311 0.959323i \(-0.408899\pi\)
0.282311 + 0.959323i \(0.408899\pi\)
\(860\) 4.88924e12 0.304788
\(861\) −1.59104e13 −0.986661
\(862\) 1.28070e13 0.790066
\(863\) 2.76290e13 1.69557 0.847785 0.530339i \(-0.177935\pi\)
0.847785 + 0.530339i \(0.177935\pi\)
\(864\) 1.41668e13 0.864888
\(865\) −2.43356e13 −1.47798
\(866\) 3.66314e13 2.21321
\(867\) 0 0
\(868\) 8.62456e12 0.515701
\(869\) 1.53688e12 0.0914223
\(870\) 3.32184e13 1.96581
\(871\) −2.21759e13 −1.30557
\(872\) −6.96198e12 −0.407764
\(873\) −2.09449e12 −0.122043
\(874\) −5.86202e12 −0.339817
\(875\) 1.10893e13 0.639540
\(876\) −2.52006e12 −0.144591
\(877\) 1.67098e12 0.0953833 0.0476916 0.998862i \(-0.484814\pi\)
0.0476916 + 0.998862i \(0.484814\pi\)
\(878\) −1.49616e13 −0.849677
\(879\) −8.74332e12 −0.493999
\(880\) −5.38733e12 −0.302832
\(881\) −2.17946e13 −1.21887 −0.609434 0.792837i \(-0.708603\pi\)
−0.609434 + 0.792837i \(0.708603\pi\)
\(882\) 6.12941e12 0.341044
\(883\) −2.01668e13 −1.11639 −0.558193 0.829711i \(-0.688505\pi\)
−0.558193 + 0.829711i \(0.688505\pi\)
\(884\) 0 0
\(885\) 8.41095e12 0.460893
\(886\) −3.16399e13 −1.72497
\(887\) 1.66457e13 0.902914 0.451457 0.892293i \(-0.350904\pi\)
0.451457 + 0.892293i \(0.350904\pi\)
\(888\) −3.00719e11 −0.0162294
\(889\) 3.93953e13 2.11537
\(890\) −5.71248e13 −3.05190
\(891\) 1.50204e12 0.0798422
\(892\) 9.51077e12 0.503007
\(893\) 1.16874e12 0.0615018
\(894\) −2.68766e13 −1.40720
\(895\) −2.19601e13 −1.14401
\(896\) 2.95410e13 1.53123
\(897\) −3.88032e13 −2.00125
\(898\) −2.53251e13 −1.29960
\(899\) 2.43762e13 1.24465
\(900\) −4.01055e12 −0.203757
\(901\) 0 0
\(902\) −3.52523e12 −0.177320
\(903\) −1.00546e13 −0.503234
\(904\) 1.28982e13 0.642347
\(905\) 1.60186e13 0.793790
\(906\) 2.96087e13 1.45997
\(907\) 2.83791e13 1.39241 0.696204 0.717844i \(-0.254871\pi\)
0.696204 + 0.717844i \(0.254871\pi\)
\(908\) 8.31568e12 0.405986
\(909\) 7.54841e11 0.0366706
\(910\) −9.17807e13 −4.43675
\(911\) 2.64888e13 1.27418 0.637088 0.770791i \(-0.280139\pi\)
0.637088 + 0.770791i \(0.280139\pi\)
\(912\) 4.29450e12 0.205559
\(913\) −7.98191e10 −0.00380179
\(914\) 3.61095e13 1.71145
\(915\) 3.60310e12 0.169935
\(916\) −4.17419e12 −0.195904
\(917\) −3.28321e13 −1.53333
\(918\) 0 0
\(919\) −3.71751e13 −1.71922 −0.859612 0.510947i \(-0.829295\pi\)
−0.859612 + 0.510947i \(0.829295\pi\)
\(920\) −3.12414e13 −1.43776
\(921\) 1.07475e13 0.492195
\(922\) −2.28065e13 −1.03937
\(923\) −5.99355e13 −2.71817
\(924\) −1.59103e12 −0.0718051
\(925\) 8.67085e11 0.0389425
\(926\) 8.76214e12 0.391616
\(927\) 2.09043e12 0.0929774
\(928\) −2.44516e13 −1.08229
\(929\) 1.56182e13 0.687953 0.343977 0.938978i \(-0.388226\pi\)
0.343977 + 0.938978i \(0.388226\pi\)
\(930\) 3.01326e13 1.32088
\(931\) 3.71216e12 0.161940
\(932\) −1.64497e13 −0.714146
\(933\) 2.30950e13 0.997816
\(934\) −2.00090e13 −0.860327
\(935\) 0 0
\(936\) −1.08619e13 −0.462554
\(937\) −1.17488e13 −0.497927 −0.248964 0.968513i \(-0.580090\pi\)
−0.248964 + 0.968513i \(0.580090\pi\)
\(938\) −2.68814e13 −1.13381
\(939\) 4.95621e12 0.208044
\(940\) −4.56023e12 −0.190507
\(941\) −6.72829e12 −0.279738 −0.139869 0.990170i \(-0.544668\pi\)
−0.139869 + 0.990170i \(0.544668\pi\)
\(942\) −1.08470e12 −0.0448827
\(943\) −3.09632e13 −1.27510
\(944\) −1.15525e13 −0.473479
\(945\) 5.41270e13 2.20785
\(946\) −2.22777e12 −0.0904399
\(947\) −3.08477e13 −1.24637 −0.623186 0.782074i \(-0.714162\pi\)
−0.623186 + 0.782074i \(0.714162\pi\)
\(948\) 4.78021e12 0.192225
\(949\) 1.96794e13 0.787614
\(950\) −8.17546e12 −0.325654
\(951\) −1.86709e12 −0.0740208
\(952\) 0 0
\(953\) 1.93554e13 0.760123 0.380062 0.924961i \(-0.375903\pi\)
0.380062 + 0.924961i \(0.375903\pi\)
\(954\) 1.57579e13 0.615930
\(955\) −3.96452e13 −1.54232
\(956\) 5.83131e12 0.225791
\(957\) −4.49684e12 −0.173302
\(958\) −8.94330e12 −0.343047
\(959\) 2.38854e13 0.911905
\(960\) 9.41788e12 0.357876
\(961\) −4.32785e12 −0.163688
\(962\) −1.71927e12 −0.0647228
\(963\) −1.87354e12 −0.0702010
\(964\) −1.66896e13 −0.622441
\(965\) −5.76278e13 −2.13924
\(966\) −4.70368e13 −1.73796
\(967\) −3.72066e13 −1.36836 −0.684181 0.729312i \(-0.739840\pi\)
−0.684181 + 0.729312i \(0.739840\pi\)
\(968\) −1.83296e13 −0.670985
\(969\) 0 0
\(970\) 1.66592e13 0.604200
\(971\) 4.17404e13 1.50685 0.753426 0.657533i \(-0.228400\pi\)
0.753426 + 0.657533i \(0.228400\pi\)
\(972\) −8.12150e12 −0.291835
\(973\) 5.74931e13 2.05640
\(974\) 4.97084e13 1.76976
\(975\) −5.41168e13 −1.91784
\(976\) −4.94888e12 −0.174575
\(977\) −3.20906e12 −0.112681 −0.0563407 0.998412i \(-0.517943\pi\)
−0.0563407 + 0.998412i \(0.517943\pi\)
\(978\) −7.03569e12 −0.245913
\(979\) 7.73309e12 0.269049
\(980\) −1.44842e13 −0.501622
\(981\) 6.29667e12 0.217070
\(982\) 4.41959e13 1.51663
\(983\) −7.14967e12 −0.244228 −0.122114 0.992516i \(-0.538967\pi\)
−0.122114 + 0.992516i \(0.538967\pi\)
\(984\) 1.49765e13 0.509252
\(985\) 3.34034e12 0.113065
\(986\) 0 0
\(987\) 9.37799e12 0.314545
\(988\) 4.81610e12 0.160801
\(989\) −1.95672e13 −0.650347
\(990\) 3.21700e12 0.106437
\(991\) 4.53035e13 1.49211 0.746053 0.665886i \(-0.231946\pi\)
0.746053 + 0.665886i \(0.231946\pi\)
\(992\) −2.21802e13 −0.727216
\(993\) 3.18950e13 1.04100
\(994\) −7.26532e13 −2.36056
\(995\) 2.46633e13 0.797715
\(996\) −2.48263e11 −0.00799366
\(997\) 1.60620e13 0.514838 0.257419 0.966300i \(-0.417128\pi\)
0.257419 + 0.966300i \(0.417128\pi\)
\(998\) −2.26735e13 −0.723488
\(999\) 1.01393e12 0.0322079
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 289.10.a.i.1.11 52
17.3 odd 16 17.10.d.a.9.4 yes 52
17.6 odd 16 17.10.d.a.2.4 52
17.16 even 2 inner 289.10.a.i.1.12 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.d.a.2.4 52 17.6 odd 16
17.10.d.a.9.4 yes 52 17.3 odd 16
289.10.a.i.1.11 52 1.1 even 1 trivial
289.10.a.i.1.12 52 17.16 even 2 inner