Properties

Label 289.10.a.g.1.26
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $1$
Dimension $36$
CM no
Inner twists $1$

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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: \(1\)
Dimension: \(36\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.26
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q+19.5847 q^{2} -220.079 q^{3} -128.440 q^{4} +130.049 q^{5} -4310.17 q^{6} -9771.35 q^{7} -12542.8 q^{8} +28751.6 q^{9} +O(q^{10})\) \(q+19.5847 q^{2} -220.079 q^{3} -128.440 q^{4} +130.049 q^{5} -4310.17 q^{6} -9771.35 q^{7} -12542.8 q^{8} +28751.6 q^{9} +2546.96 q^{10} -71260.2 q^{11} +28266.9 q^{12} +126726. q^{13} -191369. q^{14} -28621.0 q^{15} -179886. q^{16} +563092. q^{18} +604683. q^{19} -16703.5 q^{20} +2.15047e6 q^{21} -1.39561e6 q^{22} +1.07633e6 q^{23} +2.76041e6 q^{24} -1.93621e6 q^{25} +2.48189e6 q^{26} -1.99582e6 q^{27} +1.25503e6 q^{28} +1.91386e6 q^{29} -560533. q^{30} -7.71934e6 q^{31} +2.89892e6 q^{32} +1.56829e7 q^{33} -1.27075e6 q^{35} -3.69287e6 q^{36} +1.53482e7 q^{37} +1.18425e7 q^{38} -2.78897e7 q^{39} -1.63118e6 q^{40} +1.94717e7 q^{41} +4.21162e7 q^{42} -1.95272e7 q^{43} +9.15267e6 q^{44} +3.73912e6 q^{45} +2.10796e7 q^{46} +4.08642e7 q^{47} +3.95890e7 q^{48} +5.51256e7 q^{49} -3.79201e7 q^{50} -1.62767e7 q^{52} -489443. q^{53} -3.90874e7 q^{54} -9.26730e6 q^{55} +1.22560e8 q^{56} -1.33078e8 q^{57} +3.74824e7 q^{58} +1.93634e7 q^{59} +3.67608e6 q^{60} -9.43914e7 q^{61} -1.51181e8 q^{62} -2.80942e8 q^{63} +1.48876e8 q^{64} +1.64806e7 q^{65} +3.07144e8 q^{66} -1.30119e8 q^{67} -2.36878e8 q^{69} -2.48873e7 q^{70} +1.90225e8 q^{71} -3.60627e8 q^{72} -8.01389e7 q^{73} +3.00589e8 q^{74} +4.26119e8 q^{75} -7.76656e7 q^{76} +6.96308e8 q^{77} -5.46211e8 q^{78} -4.53181e8 q^{79} -2.33939e7 q^{80} -1.26682e8 q^{81} +3.81348e8 q^{82} +2.97054e8 q^{83} -2.76206e8 q^{84} -3.82434e8 q^{86} -4.21200e8 q^{87} +8.93804e8 q^{88} +7.19298e8 q^{89} +7.32294e7 q^{90} -1.23828e9 q^{91} -1.38244e8 q^{92} +1.69886e9 q^{93} +8.00312e8 q^{94} +7.86383e7 q^{95} -6.37990e8 q^{96} -2.68261e8 q^{97} +1.07962e9 q^{98} -2.04885e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} - 60000q^{10} - 76902q^{11} - 373248q^{12} + 54216q^{13} - 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} - 6439479q^{20} - 138102q^{21} - 267324q^{22} - 4041462q^{23} - 7653888q^{24} + 16582356q^{25} + 15822744q^{26} - 13281612q^{27} - 18614784q^{28} - 4005936q^{29} + 22471686q^{30} - 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} - 22076682q^{37} - 27401376q^{38} - 62736162q^{39} + 12231630q^{40} - 59641782q^{41} + 150001536q^{42} - 47951586q^{43} + 49578936q^{44} - 129308238q^{45} - 140524827q^{46} - 118557912q^{47} - 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} - 209848575q^{54} - 365439924q^{55} - 203095059q^{56} + 4614108q^{57} + 179071413q^{58} + 343015128q^{59} + 427179186q^{60} - 175597116q^{61} - 720602571q^{62} - 587415936q^{63} + 853082511q^{64} - 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} - 1308709542q^{71} - 275337849q^{72} - 494841342q^{73} - 1545361890q^{74} - 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} - 2270624538q^{78} - 1980107868q^{79} - 2897000199q^{80} + 1598298840q^{81} - 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} + 2705904618q^{88} + 148394658q^{89} - 117916215q^{90} - 636340896q^{91} + 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} - 4878626298q^{95} + 8390096634q^{96} + 891786822q^{97} + 4285627647q^{98} + 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 19.5847 0.865529 0.432764 0.901507i \(-0.357538\pi\)
0.432764 + 0.901507i \(0.357538\pi\)
\(3\) −220.079 −1.56867 −0.784337 0.620336i \(-0.786996\pi\)
−0.784337 + 0.620336i \(0.786996\pi\)
\(4\) −128.440 −0.250860
\(5\) 130.049 0.0930553 0.0465277 0.998917i \(-0.485184\pi\)
0.0465277 + 0.998917i \(0.485184\pi\)
\(6\) −4310.17 −1.35773
\(7\) −9771.35 −1.53820 −0.769101 0.639127i \(-0.779296\pi\)
−0.769101 + 0.639127i \(0.779296\pi\)
\(8\) −12542.8 −1.08266
\(9\) 28751.6 1.46074
\(10\) 2546.96 0.0805421
\(11\) −71260.2 −1.46751 −0.733753 0.679416i \(-0.762233\pi\)
−0.733753 + 0.679416i \(0.762233\pi\)
\(12\) 28266.9 0.393517
\(13\) 126726. 1.23061 0.615306 0.788289i \(-0.289033\pi\)
0.615306 + 0.788289i \(0.289033\pi\)
\(14\) −191369. −1.33136
\(15\) −28621.0 −0.145973
\(16\) −179886. −0.686210
\(17\) 0 0
\(18\) 563092. 1.26431
\(19\) 604683. 1.06448 0.532239 0.846594i \(-0.321351\pi\)
0.532239 + 0.846594i \(0.321351\pi\)
\(20\) −16703.5 −0.0233438
\(21\) 2.15047e6 2.41294
\(22\) −1.39561e6 −1.27017
\(23\) 1.07633e6 0.801994 0.400997 0.916079i \(-0.368664\pi\)
0.400997 + 0.916079i \(0.368664\pi\)
\(24\) 2.76041e6 1.69833
\(25\) −1.93621e6 −0.991341
\(26\) 2.48189e6 1.06513
\(27\) −1.99582e6 −0.722743
\(28\) 1.25503e6 0.385873
\(29\) 1.91386e6 0.502481 0.251240 0.967925i \(-0.419162\pi\)
0.251240 + 0.967925i \(0.419162\pi\)
\(30\) −560533. −0.126344
\(31\) −7.71934e6 −1.50125 −0.750624 0.660729i \(-0.770247\pi\)
−0.750624 + 0.660729i \(0.770247\pi\)
\(32\) 2.89892e6 0.488721
\(33\) 1.56829e7 2.30204
\(34\) 0 0
\(35\) −1.27075e6 −0.143138
\(36\) −3.69287e6 −0.366439
\(37\) 1.53482e7 1.34632 0.673161 0.739496i \(-0.264936\pi\)
0.673161 + 0.739496i \(0.264936\pi\)
\(38\) 1.18425e7 0.921337
\(39\) −2.78897e7 −1.93043
\(40\) −1.63118e6 −0.100747
\(41\) 1.94717e7 1.07616 0.538081 0.842893i \(-0.319150\pi\)
0.538081 + 0.842893i \(0.319150\pi\)
\(42\) 4.21162e7 2.08847
\(43\) −1.95272e7 −0.871027 −0.435513 0.900182i \(-0.643433\pi\)
−0.435513 + 0.900182i \(0.643433\pi\)
\(44\) 9.15267e6 0.368138
\(45\) 3.73912e6 0.135929
\(46\) 2.10796e7 0.694149
\(47\) 4.08642e7 1.22152 0.610762 0.791814i \(-0.290863\pi\)
0.610762 + 0.791814i \(0.290863\pi\)
\(48\) 3.95890e7 1.07644
\(49\) 5.51256e7 1.36606
\(50\) −3.79201e7 −0.858034
\(51\) 0 0
\(52\) −1.62767e7 −0.308711
\(53\) −489443. −0.00852041 −0.00426021 0.999991i \(-0.501356\pi\)
−0.00426021 + 0.999991i \(0.501356\pi\)
\(54\) −3.90874e7 −0.625555
\(55\) −9.26730e6 −0.136559
\(56\) 1.22560e8 1.66534
\(57\) −1.33078e8 −1.66982
\(58\) 3.74824e7 0.434912
\(59\) 1.93634e7 0.208040 0.104020 0.994575i \(-0.466829\pi\)
0.104020 + 0.994575i \(0.466829\pi\)
\(60\) 3.67608e6 0.0366188
\(61\) −9.43914e7 −0.872867 −0.436433 0.899737i \(-0.643759\pi\)
−0.436433 + 0.899737i \(0.643759\pi\)
\(62\) −1.51181e8 −1.29937
\(63\) −2.80942e8 −2.24691
\(64\) 1.48876e8 1.10921
\(65\) 1.64806e7 0.114515
\(66\) 3.07144e8 1.99248
\(67\) −1.30119e8 −0.788870 −0.394435 0.918924i \(-0.629060\pi\)
−0.394435 + 0.918924i \(0.629060\pi\)
\(68\) 0 0
\(69\) −2.36878e8 −1.25807
\(70\) −2.48873e7 −0.123890
\(71\) 1.90225e8 0.888395 0.444197 0.895929i \(-0.353489\pi\)
0.444197 + 0.895929i \(0.353489\pi\)
\(72\) −3.60627e8 −1.58147
\(73\) −8.01389e7 −0.330286 −0.165143 0.986270i \(-0.552809\pi\)
−0.165143 + 0.986270i \(0.552809\pi\)
\(74\) 3.00589e8 1.16528
\(75\) 4.26119e8 1.55509
\(76\) −7.76656e7 −0.267035
\(77\) 6.96308e8 2.25732
\(78\) −5.46211e8 −1.67084
\(79\) −4.53181e8 −1.30903 −0.654516 0.756049i \(-0.727127\pi\)
−0.654516 + 0.756049i \(0.727127\pi\)
\(80\) −2.33939e7 −0.0638555
\(81\) −1.26682e8 −0.326988
\(82\) 3.81348e8 0.931449
\(83\) 2.97054e8 0.687042 0.343521 0.939145i \(-0.388380\pi\)
0.343521 + 0.939145i \(0.388380\pi\)
\(84\) −2.76206e8 −0.605308
\(85\) 0 0
\(86\) −3.82434e8 −0.753899
\(87\) −4.21200e8 −0.788228
\(88\) 8.93804e8 1.58880
\(89\) 7.19298e8 1.21522 0.607608 0.794237i \(-0.292129\pi\)
0.607608 + 0.794237i \(0.292129\pi\)
\(90\) 7.32294e7 0.117651
\(91\) −1.23828e9 −1.89293
\(92\) −1.38244e8 −0.201188
\(93\) 1.69886e9 2.35497
\(94\) 8.00312e8 1.05727
\(95\) 7.86383e7 0.0990554
\(96\) −6.37990e8 −0.766643
\(97\) −2.68261e8 −0.307670 −0.153835 0.988097i \(-0.549162\pi\)
−0.153835 + 0.988097i \(0.549162\pi\)
\(98\) 1.07962e9 1.18237
\(99\) −2.04885e9 −2.14364
\(100\) 2.48687e8 0.248687
\(101\) 1.18587e9 1.13394 0.566972 0.823737i \(-0.308115\pi\)
0.566972 + 0.823737i \(0.308115\pi\)
\(102\) 0 0
\(103\) 1.67664e9 1.46782 0.733908 0.679249i \(-0.237694\pi\)
0.733908 + 0.679249i \(0.237694\pi\)
\(104\) −1.58950e9 −1.33233
\(105\) 2.79665e8 0.224537
\(106\) −9.58558e6 −0.00737466
\(107\) −2.00739e9 −1.48049 −0.740245 0.672337i \(-0.765290\pi\)
−0.740245 + 0.672337i \(0.765290\pi\)
\(108\) 2.56343e8 0.181307
\(109\) 1.92164e9 1.30393 0.651963 0.758251i \(-0.273946\pi\)
0.651963 + 0.758251i \(0.273946\pi\)
\(110\) −1.81497e8 −0.118196
\(111\) −3.37780e9 −2.11194
\(112\) 1.75773e9 1.05553
\(113\) −1.42093e9 −0.819820 −0.409910 0.912126i \(-0.634440\pi\)
−0.409910 + 0.912126i \(0.634440\pi\)
\(114\) −2.60629e9 −1.44528
\(115\) 1.39976e8 0.0746298
\(116\) −2.45817e8 −0.126052
\(117\) 3.64358e9 1.79760
\(118\) 3.79225e8 0.180065
\(119\) 0 0
\(120\) 3.58988e8 0.158039
\(121\) 2.72007e9 1.15357
\(122\) −1.84863e9 −0.755492
\(123\) −4.28531e9 −1.68814
\(124\) 9.91473e8 0.376603
\(125\) −5.05804e8 −0.185305
\(126\) −5.50217e9 −1.94476
\(127\) −2.22693e9 −0.759609 −0.379805 0.925067i \(-0.624009\pi\)
−0.379805 + 0.925067i \(0.624009\pi\)
\(128\) 1.43144e9 0.471334
\(129\) 4.29752e9 1.36636
\(130\) 3.22767e8 0.0991160
\(131\) 3.56937e9 1.05894 0.529469 0.848329i \(-0.322391\pi\)
0.529469 + 0.848329i \(0.322391\pi\)
\(132\) −2.01431e9 −0.577488
\(133\) −5.90857e9 −1.63738
\(134\) −2.54835e9 −0.682790
\(135\) −2.59553e8 −0.0672551
\(136\) 0 0
\(137\) −1.99937e9 −0.484899 −0.242449 0.970164i \(-0.577951\pi\)
−0.242449 + 0.970164i \(0.577951\pi\)
\(138\) −4.63918e9 −1.08889
\(139\) −2.89838e9 −0.658549 −0.329275 0.944234i \(-0.606804\pi\)
−0.329275 + 0.944234i \(0.606804\pi\)
\(140\) 1.63216e8 0.0359075
\(141\) −8.99333e9 −1.91617
\(142\) 3.72550e9 0.768931
\(143\) −9.03053e9 −1.80593
\(144\) −5.17201e9 −1.00237
\(145\) 2.48895e8 0.0467585
\(146\) −1.56949e9 −0.285872
\(147\) −1.21320e10 −2.14291
\(148\) −1.97132e9 −0.337738
\(149\) −1.02281e10 −1.70003 −0.850014 0.526760i \(-0.823407\pi\)
−0.850014 + 0.526760i \(0.823407\pi\)
\(150\) 8.34541e9 1.34597
\(151\) −3.39052e9 −0.530726 −0.265363 0.964149i \(-0.585492\pi\)
−0.265363 + 0.964149i \(0.585492\pi\)
\(152\) −7.58443e9 −1.15246
\(153\) 0 0
\(154\) 1.36370e10 1.95378
\(155\) −1.00389e9 −0.139699
\(156\) 3.58216e9 0.484266
\(157\) −1.49487e10 −1.96360 −0.981802 0.189909i \(-0.939181\pi\)
−0.981802 + 0.189909i \(0.939181\pi\)
\(158\) −8.87541e9 −1.13300
\(159\) 1.07716e8 0.0133657
\(160\) 3.77001e8 0.0454781
\(161\) −1.05172e10 −1.23363
\(162\) −2.48103e9 −0.283018
\(163\) 2.58066e9 0.286343 0.143171 0.989698i \(-0.454270\pi\)
0.143171 + 0.989698i \(0.454270\pi\)
\(164\) −2.50095e9 −0.269965
\(165\) 2.03954e9 0.214217
\(166\) 5.81770e9 0.594655
\(167\) −5.21438e9 −0.518774 −0.259387 0.965773i \(-0.583521\pi\)
−0.259387 + 0.965773i \(0.583521\pi\)
\(168\) −2.69729e10 −2.61238
\(169\) 5.45500e9 0.514404
\(170\) 0 0
\(171\) 1.73856e10 1.55492
\(172\) 2.50807e9 0.218506
\(173\) 2.07537e10 1.76152 0.880760 0.473562i \(-0.157032\pi\)
0.880760 + 0.473562i \(0.157032\pi\)
\(174\) −8.24907e9 −0.682234
\(175\) 1.89194e10 1.52488
\(176\) 1.28187e10 1.00702
\(177\) −4.26147e9 −0.326347
\(178\) 1.40872e10 1.05181
\(179\) −1.53399e10 −1.11682 −0.558411 0.829564i \(-0.688589\pi\)
−0.558411 + 0.829564i \(0.688589\pi\)
\(180\) −4.80253e8 −0.0340991
\(181\) 2.17045e10 1.50313 0.751564 0.659660i \(-0.229300\pi\)
0.751564 + 0.659660i \(0.229300\pi\)
\(182\) −2.42514e10 −1.63838
\(183\) 2.07735e10 1.36924
\(184\) −1.35002e10 −0.868283
\(185\) 1.99601e9 0.125282
\(186\) 3.32717e10 2.03829
\(187\) 0 0
\(188\) −5.24860e9 −0.306431
\(189\) 1.95018e10 1.11172
\(190\) 1.54011e9 0.0857353
\(191\) 1.93832e10 1.05384 0.526921 0.849914i \(-0.323346\pi\)
0.526921 + 0.849914i \(0.323346\pi\)
\(192\) −3.27644e10 −1.73999
\(193\) −1.51098e10 −0.783884 −0.391942 0.919990i \(-0.628197\pi\)
−0.391942 + 0.919990i \(0.628197\pi\)
\(194\) −5.25381e9 −0.266297
\(195\) −3.62702e9 −0.179637
\(196\) −7.08034e9 −0.342691
\(197\) −1.89475e10 −0.896303 −0.448152 0.893958i \(-0.647917\pi\)
−0.448152 + 0.893958i \(0.647917\pi\)
\(198\) −4.01260e10 −1.85538
\(199\) 1.87541e10 0.847730 0.423865 0.905725i \(-0.360673\pi\)
0.423865 + 0.905725i \(0.360673\pi\)
\(200\) 2.42856e10 1.07328
\(201\) 2.86365e10 1.23748
\(202\) 2.32249e10 0.981461
\(203\) −1.87010e10 −0.772917
\(204\) 0 0
\(205\) 2.53228e9 0.100143
\(206\) 3.28364e10 1.27044
\(207\) 3.09463e10 1.17150
\(208\) −2.27962e10 −0.844458
\(209\) −4.30898e10 −1.56213
\(210\) 5.47716e9 0.194343
\(211\) −2.18570e10 −0.759137 −0.379568 0.925164i \(-0.623927\pi\)
−0.379568 + 0.925164i \(0.623927\pi\)
\(212\) 6.28641e7 0.00213743
\(213\) −4.18646e10 −1.39360
\(214\) −3.93142e10 −1.28141
\(215\) −2.53949e9 −0.0810537
\(216\) 2.50332e10 0.782481
\(217\) 7.54284e10 2.30922
\(218\) 3.76347e10 1.12859
\(219\) 1.76369e10 0.518111
\(220\) 1.19029e9 0.0342572
\(221\) 0 0
\(222\) −6.61532e10 −1.82794
\(223\) 3.02105e9 0.0818061 0.0409030 0.999163i \(-0.486977\pi\)
0.0409030 + 0.999163i \(0.486977\pi\)
\(224\) −2.83263e10 −0.751751
\(225\) −5.56693e10 −1.44809
\(226\) −2.78284e10 −0.709578
\(227\) −4.81313e10 −1.20313 −0.601563 0.798825i \(-0.705455\pi\)
−0.601563 + 0.798825i \(0.705455\pi\)
\(228\) 1.70925e10 0.418890
\(229\) −4.00686e10 −0.962817 −0.481409 0.876496i \(-0.659875\pi\)
−0.481409 + 0.876496i \(0.659875\pi\)
\(230\) 2.74138e9 0.0645943
\(231\) −1.53243e11 −3.54100
\(232\) −2.40052e10 −0.544014
\(233\) 8.39788e9 0.186667 0.0933336 0.995635i \(-0.470248\pi\)
0.0933336 + 0.995635i \(0.470248\pi\)
\(234\) 7.13584e10 1.55587
\(235\) 5.31434e9 0.113669
\(236\) −2.48703e9 −0.0521888
\(237\) 9.97355e10 2.05344
\(238\) 0 0
\(239\) 6.01533e9 0.119253 0.0596264 0.998221i \(-0.481009\pi\)
0.0596264 + 0.998221i \(0.481009\pi\)
\(240\) 5.14851e9 0.100168
\(241\) 7.51031e10 1.43411 0.717053 0.697018i \(-0.245490\pi\)
0.717053 + 0.697018i \(0.245490\pi\)
\(242\) 5.32717e10 0.998452
\(243\) 6.71637e10 1.23568
\(244\) 1.21236e10 0.218967
\(245\) 7.16902e9 0.127120
\(246\) −8.39265e10 −1.46114
\(247\) 7.66291e10 1.30996
\(248\) 9.68223e10 1.62533
\(249\) −6.53752e10 −1.07774
\(250\) −9.90600e9 −0.160387
\(251\) 6.51989e10 1.03683 0.518416 0.855129i \(-0.326522\pi\)
0.518416 + 0.855129i \(0.326522\pi\)
\(252\) 3.60843e10 0.563658
\(253\) −7.66997e10 −1.17693
\(254\) −4.36138e10 −0.657464
\(255\) 0 0
\(256\) −4.81901e10 −0.701258
\(257\) 7.68717e10 1.09918 0.549589 0.835435i \(-0.314785\pi\)
0.549589 + 0.835435i \(0.314785\pi\)
\(258\) 8.41655e10 1.18262
\(259\) −1.49972e11 −2.07091
\(260\) −2.11677e9 −0.0287272
\(261\) 5.50267e10 0.733992
\(262\) 6.99050e10 0.916542
\(263\) 8.56612e10 1.10404 0.552018 0.833832i \(-0.313858\pi\)
0.552018 + 0.833832i \(0.313858\pi\)
\(264\) −1.96707e11 −2.49231
\(265\) −6.36514e7 −0.000792870 0
\(266\) −1.15717e11 −1.41720
\(267\) −1.58302e11 −1.90628
\(268\) 1.67126e10 0.197896
\(269\) 1.22894e11 1.43102 0.715510 0.698602i \(-0.246194\pi\)
0.715510 + 0.698602i \(0.246194\pi\)
\(270\) −5.08327e9 −0.0582112
\(271\) −2.64893e10 −0.298338 −0.149169 0.988812i \(-0.547660\pi\)
−0.149169 + 0.988812i \(0.547660\pi\)
\(272\) 0 0
\(273\) 2.72520e11 2.96939
\(274\) −3.91571e10 −0.419694
\(275\) 1.37975e11 1.45480
\(276\) 3.04246e10 0.315598
\(277\) −3.08003e10 −0.314337 −0.157169 0.987572i \(-0.550237\pi\)
−0.157169 + 0.987572i \(0.550237\pi\)
\(278\) −5.67638e10 −0.569993
\(279\) −2.21944e11 −2.19293
\(280\) 1.59388e10 0.154969
\(281\) 1.69421e11 1.62102 0.810512 0.585722i \(-0.199189\pi\)
0.810512 + 0.585722i \(0.199189\pi\)
\(282\) −1.76132e11 −1.65850
\(283\) 1.15304e11 1.06857 0.534286 0.845304i \(-0.320581\pi\)
0.534286 + 0.845304i \(0.320581\pi\)
\(284\) −2.44326e10 −0.222862
\(285\) −1.73066e10 −0.155385
\(286\) −1.76860e11 −1.56308
\(287\) −1.90265e11 −1.65535
\(288\) 8.33486e10 0.713892
\(289\) 0 0
\(290\) 4.87454e9 0.0404709
\(291\) 5.90386e10 0.482634
\(292\) 1.02931e10 0.0828555
\(293\) −1.05539e10 −0.0836581 −0.0418290 0.999125i \(-0.513318\pi\)
−0.0418290 + 0.999125i \(0.513318\pi\)
\(294\) −2.37601e11 −1.85475
\(295\) 2.51818e9 0.0193592
\(296\) −1.92509e11 −1.45760
\(297\) 1.42222e11 1.06063
\(298\) −2.00314e11 −1.47142
\(299\) 1.36399e11 0.986943
\(300\) −5.47308e10 −0.390109
\(301\) 1.90807e11 1.33982
\(302\) −6.64023e10 −0.459358
\(303\) −2.60985e11 −1.77879
\(304\) −1.08774e11 −0.730455
\(305\) −1.22755e10 −0.0812249
\(306\) 0 0
\(307\) −7.23530e10 −0.464872 −0.232436 0.972612i \(-0.574670\pi\)
−0.232436 + 0.972612i \(0.574670\pi\)
\(308\) −8.94339e10 −0.566271
\(309\) −3.68992e11 −2.30252
\(310\) −1.96609e10 −0.120914
\(311\) −8.82988e10 −0.535221 −0.267610 0.963527i \(-0.586234\pi\)
−0.267610 + 0.963527i \(0.586234\pi\)
\(312\) 3.49816e11 2.08999
\(313\) 8.39412e10 0.494340 0.247170 0.968972i \(-0.420499\pi\)
0.247170 + 0.968972i \(0.420499\pi\)
\(314\) −2.92765e11 −1.69956
\(315\) −3.65362e10 −0.209087
\(316\) 5.82067e10 0.328383
\(317\) 8.95945e10 0.498327 0.249164 0.968461i \(-0.419844\pi\)
0.249164 + 0.968461i \(0.419844\pi\)
\(318\) 2.10958e9 0.0115684
\(319\) −1.36382e11 −0.737394
\(320\) 1.93611e10 0.103218
\(321\) 4.41785e11 2.32240
\(322\) −2.05976e11 −1.06774
\(323\) 0 0
\(324\) 1.62710e10 0.0820281
\(325\) −2.45369e11 −1.21996
\(326\) 5.05414e10 0.247838
\(327\) −4.22912e11 −2.04543
\(328\) −2.44230e11 −1.16511
\(329\) −3.99298e11 −1.87895
\(330\) 3.99437e10 0.185411
\(331\) −2.83756e11 −1.29933 −0.649664 0.760222i \(-0.725090\pi\)
−0.649664 + 0.760222i \(0.725090\pi\)
\(332\) −3.81536e10 −0.172351
\(333\) 4.41285e11 1.96662
\(334\) −1.02122e11 −0.449014
\(335\) −1.69219e10 −0.0734086
\(336\) −3.86838e11 −1.65578
\(337\) 3.79770e10 0.160393 0.0801965 0.996779i \(-0.474445\pi\)
0.0801965 + 0.996779i \(0.474445\pi\)
\(338\) 1.06834e11 0.445232
\(339\) 3.12716e11 1.28603
\(340\) 0 0
\(341\) 5.50082e11 2.20309
\(342\) 3.40492e11 1.34583
\(343\) −1.44343e11 −0.563081
\(344\) 2.44926e11 0.943022
\(345\) −3.08057e10 −0.117070
\(346\) 4.06454e11 1.52465
\(347\) −2.53157e11 −0.937364 −0.468682 0.883367i \(-0.655271\pi\)
−0.468682 + 0.883367i \(0.655271\pi\)
\(348\) 5.40990e10 0.197735
\(349\) 1.41590e10 0.0510880 0.0255440 0.999674i \(-0.491868\pi\)
0.0255440 + 0.999674i \(0.491868\pi\)
\(350\) 3.70531e11 1.31983
\(351\) −2.52922e11 −0.889415
\(352\) −2.06577e11 −0.717201
\(353\) 2.27285e11 0.779085 0.389542 0.921009i \(-0.372633\pi\)
0.389542 + 0.921009i \(0.372633\pi\)
\(354\) −8.34595e10 −0.282463
\(355\) 2.47386e10 0.0826699
\(356\) −9.23867e10 −0.304849
\(357\) 0 0
\(358\) −3.00427e11 −0.966642
\(359\) −2.15607e10 −0.0685076 −0.0342538 0.999413i \(-0.510905\pi\)
−0.0342538 + 0.999413i \(0.510905\pi\)
\(360\) −4.68991e10 −0.147164
\(361\) 4.29542e10 0.133114
\(362\) 4.25076e11 1.30100
\(363\) −5.98629e11 −1.80958
\(364\) 1.59045e11 0.474859
\(365\) −1.04220e10 −0.0307349
\(366\) 4.06843e11 1.18512
\(367\) 1.34746e11 0.387720 0.193860 0.981029i \(-0.437899\pi\)
0.193860 + 0.981029i \(0.437899\pi\)
\(368\) −1.93617e11 −0.550336
\(369\) 5.59844e11 1.57199
\(370\) 3.90912e10 0.108436
\(371\) 4.78252e9 0.0131061
\(372\) −2.18202e11 −0.590766
\(373\) −6.32594e10 −0.169214 −0.0846068 0.996414i \(-0.526963\pi\)
−0.0846068 + 0.996414i \(0.526963\pi\)
\(374\) 0 0
\(375\) 1.11317e11 0.290683
\(376\) −5.12552e11 −1.32249
\(377\) 2.42536e11 0.618359
\(378\) 3.81937e11 0.962229
\(379\) 5.65418e11 1.40764 0.703822 0.710376i \(-0.251475\pi\)
0.703822 + 0.710376i \(0.251475\pi\)
\(380\) −1.01003e10 −0.0248490
\(381\) 4.90100e11 1.19158
\(382\) 3.79614e11 0.912130
\(383\) −1.03757e11 −0.246391 −0.123196 0.992382i \(-0.539314\pi\)
−0.123196 + 0.992382i \(0.539314\pi\)
\(384\) −3.15030e11 −0.739369
\(385\) 9.05540e10 0.210056
\(386\) −2.95921e11 −0.678474
\(387\) −5.61439e11 −1.27234
\(388\) 3.44555e10 0.0771820
\(389\) 2.18349e11 0.483479 0.241739 0.970341i \(-0.422282\pi\)
0.241739 + 0.970341i \(0.422282\pi\)
\(390\) −7.10341e10 −0.155481
\(391\) 0 0
\(392\) −6.91431e11 −1.47898
\(393\) −7.85542e11 −1.66113
\(394\) −3.71082e11 −0.775776
\(395\) −5.89357e10 −0.121812
\(396\) 2.63154e11 0.537752
\(397\) 2.66965e9 0.00539383 0.00269691 0.999996i \(-0.499142\pi\)
0.00269691 + 0.999996i \(0.499142\pi\)
\(398\) 3.67293e11 0.733734
\(399\) 1.30035e12 2.56852
\(400\) 3.48297e11 0.680268
\(401\) −6.04105e11 −1.16671 −0.583355 0.812217i \(-0.698260\pi\)
−0.583355 + 0.812217i \(0.698260\pi\)
\(402\) 5.60837e11 1.07107
\(403\) −9.78242e11 −1.84745
\(404\) −1.52314e11 −0.284461
\(405\) −1.64748e10 −0.0304280
\(406\) −3.66253e11 −0.668982
\(407\) −1.09371e12 −1.97573
\(408\) 0 0
\(409\) −1.23512e11 −0.218250 −0.109125 0.994028i \(-0.534805\pi\)
−0.109125 + 0.994028i \(0.534805\pi\)
\(410\) 4.95938e10 0.0866763
\(411\) 4.40019e11 0.760648
\(412\) −2.15348e11 −0.368216
\(413\) −1.89206e11 −0.320008
\(414\) 6.06074e11 1.01397
\(415\) 3.86315e10 0.0639329
\(416\) 3.67368e11 0.601425
\(417\) 6.37871e11 1.03305
\(418\) −8.43901e11 −1.35207
\(419\) 1.05297e12 1.66899 0.834496 0.551014i \(-0.185759\pi\)
0.834496 + 0.551014i \(0.185759\pi\)
\(420\) −3.59203e10 −0.0563272
\(421\) 5.01032e11 0.777313 0.388656 0.921383i \(-0.372939\pi\)
0.388656 + 0.921383i \(0.372939\pi\)
\(422\) −4.28063e11 −0.657055
\(423\) 1.17491e12 1.78432
\(424\) 6.13899e9 0.00922467
\(425\) 0 0
\(426\) −8.19904e11 −1.20620
\(427\) 9.22331e11 1.34265
\(428\) 2.57830e11 0.371395
\(429\) 1.98743e12 2.83291
\(430\) −4.97350e10 −0.0701543
\(431\) 1.29815e10 0.0181208 0.00906041 0.999959i \(-0.497116\pi\)
0.00906041 + 0.999959i \(0.497116\pi\)
\(432\) 3.59019e11 0.495953
\(433\) −4.46092e11 −0.609859 −0.304929 0.952375i \(-0.598633\pi\)
−0.304929 + 0.952375i \(0.598633\pi\)
\(434\) 1.47724e12 1.99870
\(435\) −5.47766e10 −0.0733488
\(436\) −2.46816e11 −0.327102
\(437\) 6.50840e11 0.853705
\(438\) 3.45412e11 0.448440
\(439\) −1.26258e11 −0.162244 −0.0811218 0.996704i \(-0.525850\pi\)
−0.0811218 + 0.996704i \(0.525850\pi\)
\(440\) 1.16238e11 0.147847
\(441\) 1.58495e12 1.99546
\(442\) 0 0
\(443\) −1.10374e12 −1.36160 −0.680801 0.732468i \(-0.738368\pi\)
−0.680801 + 0.732468i \(0.738368\pi\)
\(444\) 4.33846e11 0.529800
\(445\) 9.35438e10 0.113082
\(446\) 5.91662e10 0.0708055
\(447\) 2.25098e12 2.66679
\(448\) −1.45472e12 −1.70619
\(449\) 7.22088e11 0.838459 0.419229 0.907880i \(-0.362300\pi\)
0.419229 + 0.907880i \(0.362300\pi\)
\(450\) −1.09027e12 −1.25336
\(451\) −1.38756e12 −1.57927
\(452\) 1.82504e11 0.205660
\(453\) 7.46181e11 0.832535
\(454\) −9.42636e11 −1.04134
\(455\) −1.61037e11 −0.176147
\(456\) 1.66917e12 1.80784
\(457\) −2.66380e11 −0.285679 −0.142840 0.989746i \(-0.545623\pi\)
−0.142840 + 0.989746i \(0.545623\pi\)
\(458\) −7.84730e11 −0.833346
\(459\) 0 0
\(460\) −1.79785e10 −0.0187216
\(461\) 1.13987e11 0.117544 0.0587718 0.998271i \(-0.481282\pi\)
0.0587718 + 0.998271i \(0.481282\pi\)
\(462\) −3.00121e12 −3.06484
\(463\) 1.41507e12 1.43108 0.715538 0.698574i \(-0.246182\pi\)
0.715538 + 0.698574i \(0.246182\pi\)
\(464\) −3.44277e11 −0.344807
\(465\) 2.20935e11 0.219142
\(466\) 1.64470e11 0.161566
\(467\) 7.79171e11 0.758066 0.379033 0.925383i \(-0.376257\pi\)
0.379033 + 0.925383i \(0.376257\pi\)
\(468\) −4.67982e11 −0.450945
\(469\) 1.27144e12 1.21344
\(470\) 1.04080e11 0.0983842
\(471\) 3.28988e12 3.08025
\(472\) −2.42871e11 −0.225236
\(473\) 1.39151e12 1.27824
\(474\) 1.95329e12 1.77731
\(475\) −1.17080e12 −1.05526
\(476\) 0 0
\(477\) −1.40723e10 −0.0124461
\(478\) 1.17808e11 0.103217
\(479\) −6.94378e11 −0.602679 −0.301339 0.953517i \(-0.597434\pi\)
−0.301339 + 0.953517i \(0.597434\pi\)
\(480\) −8.29698e10 −0.0713402
\(481\) 1.94501e12 1.65680
\(482\) 1.47087e12 1.24126
\(483\) 2.31462e12 1.93516
\(484\) −3.49366e11 −0.289385
\(485\) −3.48870e10 −0.0286303
\(486\) 1.31538e12 1.06952
\(487\) 4.59496e11 0.370171 0.185085 0.982722i \(-0.440744\pi\)
0.185085 + 0.982722i \(0.440744\pi\)
\(488\) 1.18393e12 0.945014
\(489\) −5.67948e11 −0.449178
\(490\) 1.40403e11 0.110026
\(491\) −2.13503e12 −1.65782 −0.828911 0.559381i \(-0.811039\pi\)
−0.828911 + 0.559381i \(0.811039\pi\)
\(492\) 5.50406e11 0.423487
\(493\) 0 0
\(494\) 1.50076e12 1.13381
\(495\) −2.66450e11 −0.199477
\(496\) 1.38860e12 1.03017
\(497\) −1.85876e12 −1.36653
\(498\) −1.28035e12 −0.932819
\(499\) −1.50477e12 −1.08647 −0.543234 0.839581i \(-0.682801\pi\)
−0.543234 + 0.839581i \(0.682801\pi\)
\(500\) 6.49655e10 0.0464855
\(501\) 1.14757e12 0.813787
\(502\) 1.27690e12 0.897408
\(503\) −1.44460e12 −1.00622 −0.503109 0.864223i \(-0.667811\pi\)
−0.503109 + 0.864223i \(0.667811\pi\)
\(504\) 3.52381e12 2.43262
\(505\) 1.54221e11 0.105519
\(506\) −1.50214e12 −1.01867
\(507\) −1.20053e12 −0.806932
\(508\) 2.86027e11 0.190555
\(509\) 1.23179e12 0.813404 0.406702 0.913561i \(-0.366679\pi\)
0.406702 + 0.913561i \(0.366679\pi\)
\(510\) 0 0
\(511\) 7.83065e11 0.508047
\(512\) −1.67669e12 −1.07829
\(513\) −1.20684e12 −0.769344
\(514\) 1.50551e12 0.951370
\(515\) 2.18045e11 0.136588
\(516\) −5.51974e11 −0.342764
\(517\) −2.91199e12 −1.79260
\(518\) −2.93716e12 −1.79244
\(519\) −4.56745e12 −2.76325
\(520\) −2.06713e11 −0.123980
\(521\) −1.08435e12 −0.644761 −0.322380 0.946610i \(-0.604483\pi\)
−0.322380 + 0.946610i \(0.604483\pi\)
\(522\) 1.07768e12 0.635291
\(523\) −1.91259e12 −1.11780 −0.558899 0.829236i \(-0.688776\pi\)
−0.558899 + 0.829236i \(0.688776\pi\)
\(524\) −4.58450e11 −0.265645
\(525\) −4.16376e12 −2.39204
\(526\) 1.67765e12 0.955576
\(527\) 0 0
\(528\) −2.82112e12 −1.57968
\(529\) −6.42661e11 −0.356806
\(530\) −1.24659e9 −0.000686252 0
\(531\) 5.56729e11 0.303891
\(532\) 7.58898e11 0.410753
\(533\) 2.46758e12 1.32434
\(534\) −3.10030e12 −1.64994
\(535\) −2.61059e11 −0.137767
\(536\) 1.63206e12 0.854074
\(537\) 3.37599e12 1.75193
\(538\) 2.40684e12 1.23859
\(539\) −3.92826e12 −2.00471
\(540\) 3.33371e10 0.0168716
\(541\) 2.15523e12 1.08170 0.540850 0.841119i \(-0.318103\pi\)
0.540850 + 0.841119i \(0.318103\pi\)
\(542\) −5.18784e11 −0.258220
\(543\) −4.77670e12 −2.35792
\(544\) 0 0
\(545\) 2.49907e11 0.121337
\(546\) 5.33722e12 2.57009
\(547\) −7.09837e10 −0.0339013 −0.0169506 0.999856i \(-0.505396\pi\)
−0.0169506 + 0.999856i \(0.505396\pi\)
\(548\) 2.56800e11 0.121642
\(549\) −2.71391e12 −1.27503
\(550\) 2.70219e12 1.25917
\(551\) 1.15728e12 0.534880
\(552\) 2.97112e12 1.36205
\(553\) 4.42819e12 2.01355
\(554\) −6.03214e11 −0.272068
\(555\) −4.39279e11 −0.196527
\(556\) 3.72268e11 0.165203
\(557\) −6.52747e11 −0.287340 −0.143670 0.989626i \(-0.545890\pi\)
−0.143670 + 0.989626i \(0.545890\pi\)
\(558\) −4.34670e12 −1.89804
\(559\) −2.47460e12 −1.07190
\(560\) 2.28590e11 0.0982226
\(561\) 0 0
\(562\) 3.31806e12 1.40304
\(563\) −1.22765e12 −0.514977 −0.257488 0.966281i \(-0.582895\pi\)
−0.257488 + 0.966281i \(0.582895\pi\)
\(564\) 1.15511e12 0.480691
\(565\) −1.84790e11 −0.0762886
\(566\) 2.25818e12 0.924880
\(567\) 1.23785e12 0.502974
\(568\) −2.38596e12 −0.961825
\(569\) −6.00953e11 −0.240345 −0.120173 0.992753i \(-0.538345\pi\)
−0.120173 + 0.992753i \(0.538345\pi\)
\(570\) −3.38945e11 −0.134491
\(571\) −2.49531e12 −0.982339 −0.491170 0.871064i \(-0.663430\pi\)
−0.491170 + 0.871064i \(0.663430\pi\)
\(572\) 1.15988e12 0.453035
\(573\) −4.26583e12 −1.65313
\(574\) −3.72628e12 −1.43276
\(575\) −2.08401e12 −0.795049
\(576\) 4.28043e12 1.62026
\(577\) −2.87670e12 −1.08045 −0.540223 0.841522i \(-0.681660\pi\)
−0.540223 + 0.841522i \(0.681660\pi\)
\(578\) 0 0
\(579\) 3.32535e12 1.22966
\(580\) −3.19682e10 −0.0117298
\(581\) −2.90261e12 −1.05681
\(582\) 1.15625e12 0.417733
\(583\) 3.48778e10 0.0125038
\(584\) 1.00517e12 0.357586
\(585\) 4.73844e11 0.167276
\(586\) −2.06694e11 −0.0724085
\(587\) −2.45305e12 −0.852777 −0.426388 0.904540i \(-0.640214\pi\)
−0.426388 + 0.904540i \(0.640214\pi\)
\(588\) 1.55823e12 0.537569
\(589\) −4.66776e12 −1.59805
\(590\) 4.93178e10 0.0167560
\(591\) 4.16995e12 1.40601
\(592\) −2.76092e12 −0.923859
\(593\) −2.15859e12 −0.716841 −0.358421 0.933560i \(-0.616685\pi\)
−0.358421 + 0.933560i \(0.616685\pi\)
\(594\) 2.78538e12 0.918005
\(595\) 0 0
\(596\) 1.31370e12 0.426469
\(597\) −4.12738e12 −1.32981
\(598\) 2.67134e12 0.854228
\(599\) −3.31263e12 −1.05136 −0.525680 0.850682i \(-0.676189\pi\)
−0.525680 + 0.850682i \(0.676189\pi\)
\(600\) −5.34473e12 −1.68363
\(601\) −4.10617e12 −1.28381 −0.641906 0.766783i \(-0.721856\pi\)
−0.641906 + 0.766783i \(0.721856\pi\)
\(602\) 3.73689e12 1.15965
\(603\) −3.74115e12 −1.15233
\(604\) 4.35479e11 0.133138
\(605\) 3.53742e11 0.107346
\(606\) −5.11131e12 −1.53959
\(607\) 3.99884e12 1.19560 0.597799 0.801646i \(-0.296042\pi\)
0.597799 + 0.801646i \(0.296042\pi\)
\(608\) 1.75293e12 0.520233
\(609\) 4.11569e12 1.21245
\(610\) −2.40411e11 −0.0703025
\(611\) 5.17856e12 1.50322
\(612\) 0 0
\(613\) −5.51148e12 −1.57651 −0.788254 0.615350i \(-0.789015\pi\)
−0.788254 + 0.615350i \(0.789015\pi\)
\(614\) −1.41701e12 −0.402360
\(615\) −5.57300e11 −0.157091
\(616\) −8.73367e12 −2.44390
\(617\) 4.10732e12 1.14097 0.570486 0.821307i \(-0.306755\pi\)
0.570486 + 0.821307i \(0.306755\pi\)
\(618\) −7.22660e12 −1.99290
\(619\) −2.66297e12 −0.729052 −0.364526 0.931193i \(-0.618769\pi\)
−0.364526 + 0.931193i \(0.618769\pi\)
\(620\) 1.28940e11 0.0350449
\(621\) −2.14816e12 −0.579635
\(622\) −1.72930e12 −0.463249
\(623\) −7.02851e12 −1.86925
\(624\) 5.01696e12 1.32468
\(625\) 3.71589e12 0.974097
\(626\) 1.64396e12 0.427866
\(627\) 9.48316e12 2.45047
\(628\) 1.92001e12 0.492589
\(629\) 0 0
\(630\) −7.15550e11 −0.180970
\(631\) −2.98865e12 −0.750486 −0.375243 0.926927i \(-0.622441\pi\)
−0.375243 + 0.926927i \(0.622441\pi\)
\(632\) 5.68417e12 1.41723
\(633\) 4.81027e12 1.19084
\(634\) 1.75468e12 0.431317
\(635\) −2.89610e11 −0.0706857
\(636\) −1.38351e10 −0.00335292
\(637\) 6.98586e12 1.68109
\(638\) −2.67100e12 −0.638236
\(639\) 5.46929e12 1.29771
\(640\) 1.86157e11 0.0438601
\(641\) −4.15467e12 −0.972020 −0.486010 0.873953i \(-0.661548\pi\)
−0.486010 + 0.873953i \(0.661548\pi\)
\(642\) 8.65221e12 2.01011
\(643\) 4.20371e12 0.969802 0.484901 0.874569i \(-0.338856\pi\)
0.484901 + 0.874569i \(0.338856\pi\)
\(644\) 1.35083e12 0.309468
\(645\) 5.58887e11 0.127147
\(646\) 0 0
\(647\) −1.62658e12 −0.364927 −0.182463 0.983213i \(-0.558407\pi\)
−0.182463 + 0.983213i \(0.558407\pi\)
\(648\) 1.58895e12 0.354015
\(649\) −1.37984e12 −0.305300
\(650\) −4.80547e12 −1.05591
\(651\) −1.66002e13 −3.62242
\(652\) −3.31460e11 −0.0718318
\(653\) 3.12868e12 0.673366 0.336683 0.941618i \(-0.390695\pi\)
0.336683 + 0.941618i \(0.390695\pi\)
\(654\) −8.28260e12 −1.77038
\(655\) 4.64192e11 0.0985398
\(656\) −3.50269e12 −0.738472
\(657\) −2.30413e12 −0.482461
\(658\) −7.82013e12 −1.62629
\(659\) −6.29602e12 −1.30041 −0.650207 0.759757i \(-0.725318\pi\)
−0.650207 + 0.759757i \(0.725318\pi\)
\(660\) −2.61958e11 −0.0537384
\(661\) 5.35726e12 1.09153 0.545766 0.837938i \(-0.316239\pi\)
0.545766 + 0.837938i \(0.316239\pi\)
\(662\) −5.55727e12 −1.12461
\(663\) 0 0
\(664\) −3.72589e12 −0.743830
\(665\) −7.68402e11 −0.152367
\(666\) 8.64243e12 1.70217
\(667\) 2.05995e12 0.402987
\(668\) 6.69736e11 0.130140
\(669\) −6.64868e11 −0.128327
\(670\) −3.31410e11 −0.0635372
\(671\) 6.72635e12 1.28094
\(672\) 6.23402e12 1.17925
\(673\) −4.82131e12 −0.905935 −0.452968 0.891527i \(-0.649635\pi\)
−0.452968 + 0.891527i \(0.649635\pi\)
\(674\) 7.43767e11 0.138825
\(675\) 3.86432e12 0.716484
\(676\) −7.00641e11 −0.129043
\(677\) −3.90335e12 −0.714149 −0.357074 0.934076i \(-0.616226\pi\)
−0.357074 + 0.934076i \(0.616226\pi\)
\(678\) 6.12444e12 1.11310
\(679\) 2.62127e12 0.473258
\(680\) 0 0
\(681\) 1.05927e13 1.88731
\(682\) 1.07732e13 1.90684
\(683\) 4.33110e12 0.761561 0.380781 0.924665i \(-0.375655\pi\)
0.380781 + 0.924665i \(0.375655\pi\)
\(684\) −2.23301e12 −0.390067
\(685\) −2.60016e11 −0.0451224
\(686\) −2.82691e12 −0.487363
\(687\) 8.81824e12 1.51035
\(688\) 3.51266e12 0.597707
\(689\) −6.20252e10 −0.0104853
\(690\) −6.03319e11 −0.101327
\(691\) −1.03878e13 −1.73329 −0.866646 0.498923i \(-0.833729\pi\)
−0.866646 + 0.498923i \(0.833729\pi\)
\(692\) −2.66561e12 −0.441895
\(693\) 2.00200e13 3.29735
\(694\) −4.95801e12 −0.811315
\(695\) −3.76930e11 −0.0612815
\(696\) 5.28304e12 0.853379
\(697\) 0 0
\(698\) 2.77300e11 0.0442181
\(699\) −1.84819e12 −0.292820
\(700\) −2.43001e12 −0.382531
\(701\) −2.88822e12 −0.451752 −0.225876 0.974156i \(-0.572524\pi\)
−0.225876 + 0.974156i \(0.572524\pi\)
\(702\) −4.95340e12 −0.769815
\(703\) 9.28078e12 1.43313
\(704\) −1.06089e13 −1.62778
\(705\) −1.16957e12 −0.178310
\(706\) 4.45131e12 0.674320
\(707\) −1.15876e13 −1.74423
\(708\) 5.47343e11 0.0818672
\(709\) −6.02354e12 −0.895249 −0.447624 0.894222i \(-0.647730\pi\)
−0.447624 + 0.894222i \(0.647730\pi\)
\(710\) 4.84497e11 0.0715532
\(711\) −1.30297e13 −1.91215
\(712\) −9.02202e12 −1.31566
\(713\) −8.30857e12 −1.20399
\(714\) 0 0
\(715\) −1.17441e12 −0.168051
\(716\) 1.97026e12 0.280166
\(717\) −1.32385e12 −0.187069
\(718\) −4.22260e11 −0.0592953
\(719\) 3.75893e12 0.524547 0.262274 0.964994i \(-0.415528\pi\)
0.262274 + 0.964994i \(0.415528\pi\)
\(720\) −6.72614e11 −0.0932759
\(721\) −1.63830e13 −2.25780
\(722\) 8.41244e11 0.115214
\(723\) −1.65286e13 −2.24964
\(724\) −2.78773e12 −0.377074
\(725\) −3.70564e12 −0.498130
\(726\) −1.17240e13 −1.56624
\(727\) 9.68647e12 1.28606 0.643029 0.765841i \(-0.277677\pi\)
0.643029 + 0.765841i \(0.277677\pi\)
\(728\) 1.55316e13 2.04939
\(729\) −1.22878e13 −1.61139
\(730\) −2.04111e11 −0.0266019
\(731\) 0 0
\(732\) −2.66816e12 −0.343488
\(733\) −2.52987e12 −0.323691 −0.161845 0.986816i \(-0.551745\pi\)
−0.161845 + 0.986816i \(0.551745\pi\)
\(734\) 2.63896e12 0.335583
\(735\) −1.57775e12 −0.199409
\(736\) 3.12020e12 0.391951
\(737\) 9.27234e12 1.15767
\(738\) 1.09644e13 1.36060
\(739\) −1.04522e13 −1.28916 −0.644579 0.764538i \(-0.722967\pi\)
−0.644579 + 0.764538i \(0.722967\pi\)
\(740\) −2.56368e11 −0.0314283
\(741\) −1.68644e13 −2.05490
\(742\) 9.36641e10 0.0113437
\(743\) 2.07330e12 0.249582 0.124791 0.992183i \(-0.460174\pi\)
0.124791 + 0.992183i \(0.460174\pi\)
\(744\) −2.13085e13 −2.54962
\(745\) −1.33015e12 −0.158197
\(746\) −1.23892e12 −0.146459
\(747\) 8.54078e12 1.00359
\(748\) 0 0
\(749\) 1.96149e13 2.27729
\(750\) 2.18010e12 0.251594
\(751\) 7.54749e12 0.865811 0.432905 0.901439i \(-0.357488\pi\)
0.432905 + 0.901439i \(0.357488\pi\)
\(752\) −7.35088e12 −0.838222
\(753\) −1.43489e13 −1.62645
\(754\) 4.75000e12 0.535207
\(755\) −4.40933e11 −0.0493869
\(756\) −2.50482e12 −0.278887
\(757\) 3.67976e12 0.407276 0.203638 0.979046i \(-0.434723\pi\)
0.203638 + 0.979046i \(0.434723\pi\)
\(758\) 1.10735e13 1.21836
\(759\) 1.68800e13 1.84622
\(760\) −9.86346e11 −0.107243
\(761\) −5.86789e12 −0.634236 −0.317118 0.948386i \(-0.602715\pi\)
−0.317118 + 0.948386i \(0.602715\pi\)
\(762\) 9.59846e12 1.03135
\(763\) −1.87770e13 −2.00570
\(764\) −2.48958e12 −0.264366
\(765\) 0 0
\(766\) −2.03206e12 −0.213259
\(767\) 2.45384e12 0.256016
\(768\) 1.06056e13 1.10005
\(769\) 3.89763e12 0.401913 0.200956 0.979600i \(-0.435595\pi\)
0.200956 + 0.979600i \(0.435595\pi\)
\(770\) 1.77347e12 0.181809
\(771\) −1.69178e13 −1.72425
\(772\) 1.94071e12 0.196645
\(773\) 7.44642e12 0.750135 0.375068 0.926997i \(-0.377619\pi\)
0.375068 + 0.926997i \(0.377619\pi\)
\(774\) −1.09956e13 −1.10125
\(775\) 1.49463e13 1.48825
\(776\) 3.36475e12 0.333100
\(777\) 3.30057e13 3.24859
\(778\) 4.27629e12 0.418465
\(779\) 1.17742e13 1.14555
\(780\) 4.65855e11 0.0450636
\(781\) −1.35555e13 −1.30372
\(782\) 0 0
\(783\) −3.81972e12 −0.363164
\(784\) −9.91632e12 −0.937407
\(785\) −1.94405e12 −0.182724
\(786\) −1.53846e13 −1.43775
\(787\) 1.57052e13 1.45935 0.729673 0.683796i \(-0.239672\pi\)
0.729673 + 0.683796i \(0.239672\pi\)
\(788\) 2.43363e12 0.224846
\(789\) −1.88522e13 −1.73187
\(790\) −1.15424e12 −0.105432
\(791\) 1.38844e13 1.26105
\(792\) 2.56983e13 2.32082
\(793\) −1.19618e13 −1.07416
\(794\) 5.22843e10 0.00466851
\(795\) 1.40083e10 0.00124375
\(796\) −2.40878e12 −0.212661
\(797\) 7.79223e12 0.684068 0.342034 0.939688i \(-0.388884\pi\)
0.342034 + 0.939688i \(0.388884\pi\)
\(798\) 2.54670e13 2.22313
\(799\) 0 0
\(800\) −5.61292e12 −0.484489
\(801\) 2.06810e13 1.77511
\(802\) −1.18312e13 −1.00982
\(803\) 5.71071e12 0.484697
\(804\) −3.67808e12 −0.310434
\(805\) −1.36775e12 −0.114796
\(806\) −1.91586e13 −1.59902
\(807\) −2.70464e13 −2.24480
\(808\) −1.48742e13 −1.22767
\(809\) 6.21234e12 0.509902 0.254951 0.966954i \(-0.417941\pi\)
0.254951 + 0.966954i \(0.417941\pi\)
\(810\) −3.22654e11 −0.0263363
\(811\) 1.28983e13 1.04698 0.523488 0.852033i \(-0.324630\pi\)
0.523488 + 0.852033i \(0.324630\pi\)
\(812\) 2.40196e12 0.193894
\(813\) 5.82972e12 0.467994
\(814\) −2.14200e13 −1.71006
\(815\) 3.35611e11 0.0266457
\(816\) 0 0
\(817\) −1.18078e13 −0.927189
\(818\) −2.41894e12 −0.188901
\(819\) −3.56027e13 −2.76507
\(820\) −3.25246e11 −0.0251217
\(821\) −1.48692e13 −1.14221 −0.571103 0.820878i \(-0.693484\pi\)
−0.571103 + 0.820878i \(0.693484\pi\)
\(822\) 8.61764e12 0.658363
\(823\) 1.65419e13 1.25686 0.628429 0.777867i \(-0.283698\pi\)
0.628429 + 0.777867i \(0.283698\pi\)
\(824\) −2.10298e13 −1.58914
\(825\) −3.03653e13 −2.28210
\(826\) −3.70554e12 −0.276976
\(827\) 6.35336e12 0.472312 0.236156 0.971715i \(-0.424112\pi\)
0.236156 + 0.971715i \(0.424112\pi\)
\(828\) −3.97475e12 −0.293882
\(829\) −9.20903e12 −0.677203 −0.338601 0.940930i \(-0.609954\pi\)
−0.338601 + 0.940930i \(0.609954\pi\)
\(830\) 7.56585e11 0.0553358
\(831\) 6.77849e12 0.493093
\(832\) 1.88665e13 1.36501
\(833\) 0 0
\(834\) 1.24925e13 0.894133
\(835\) −6.78124e11 −0.0482747
\(836\) 5.53447e12 0.391875
\(837\) 1.54064e13 1.08502
\(838\) 2.06222e13 1.44456
\(839\) −4.07347e12 −0.283815 −0.141907 0.989880i \(-0.545324\pi\)
−0.141907 + 0.989880i \(0.545324\pi\)
\(840\) −3.50779e12 −0.243096
\(841\) −1.08443e13 −0.747513
\(842\) 9.81255e12 0.672787
\(843\) −3.72860e13 −2.54286
\(844\) 2.80732e12 0.190437
\(845\) 7.09416e11 0.0478681
\(846\) 2.30103e13 1.54438
\(847\) −2.65787e13 −1.77443
\(848\) 8.80438e10 0.00584679
\(849\) −2.53759e13 −1.67624
\(850\) 0 0
\(851\) 1.65197e13 1.07974
\(852\) 5.37709e12 0.349598
\(853\) −9.92297e12 −0.641758 −0.320879 0.947120i \(-0.603978\pi\)
−0.320879 + 0.947120i \(0.603978\pi\)
\(854\) 1.80636e13 1.16210
\(855\) 2.26098e12 0.144694
\(856\) 2.51784e13 1.60286
\(857\) 7.30125e12 0.462363 0.231182 0.972911i \(-0.425741\pi\)
0.231182 + 0.972911i \(0.425741\pi\)
\(858\) 3.89231e13 2.45197
\(859\) 1.34564e13 0.843254 0.421627 0.906769i \(-0.361459\pi\)
0.421627 + 0.906769i \(0.361459\pi\)
\(860\) 3.26172e11 0.0203331
\(861\) 4.18733e13 2.59671
\(862\) 2.54239e11 0.0156841
\(863\) −2.00180e13 −1.22849 −0.614247 0.789114i \(-0.710540\pi\)
−0.614247 + 0.789114i \(0.710540\pi\)
\(864\) −5.78571e12 −0.353219
\(865\) 2.69899e12 0.163919
\(866\) −8.73658e12 −0.527850
\(867\) 0 0
\(868\) −9.68803e12 −0.579291
\(869\) 3.22938e13 1.92101
\(870\) −1.07278e12 −0.0634855
\(871\) −1.64895e13 −0.970793
\(872\) −2.41028e13 −1.41170
\(873\) −7.71295e12 −0.449424
\(874\) 1.27465e13 0.738906
\(875\) 4.94238e12 0.285036
\(876\) −2.26528e12 −0.129973
\(877\) −5.42206e12 −0.309504 −0.154752 0.987953i \(-0.549458\pi\)
−0.154752 + 0.987953i \(0.549458\pi\)
\(878\) −2.47272e12 −0.140426
\(879\) 2.32269e12 0.131232
\(880\) 1.66706e12 0.0937083
\(881\) −5.00837e12 −0.280095 −0.140047 0.990145i \(-0.544725\pi\)
−0.140047 + 0.990145i \(0.544725\pi\)
\(882\) 3.10408e13 1.72713
\(883\) 9.14629e12 0.506316 0.253158 0.967425i \(-0.418531\pi\)
0.253158 + 0.967425i \(0.418531\pi\)
\(884\) 0 0
\(885\) −5.54198e11 −0.0303683
\(886\) −2.16164e13 −1.17851
\(887\) −6.90655e12 −0.374632 −0.187316 0.982300i \(-0.559979\pi\)
−0.187316 + 0.982300i \(0.559979\pi\)
\(888\) 4.23672e13 2.28650
\(889\) 2.17601e13 1.16843
\(890\) 1.83203e12 0.0978761
\(891\) 9.02738e12 0.479857
\(892\) −3.88024e11 −0.0205218
\(893\) 2.47099e13 1.30029
\(894\) 4.40848e13 2.30818
\(895\) −1.99494e12 −0.103926
\(896\) −1.39871e13 −0.725007
\(897\) −3.00186e13 −1.54819
\(898\) 1.41419e13 0.725710
\(899\) −1.47737e13 −0.754349
\(900\) 7.15017e12 0.363266
\(901\) 0 0
\(902\) −2.71749e13 −1.36691
\(903\) −4.19925e13 −2.10173
\(904\) 1.78224e13 0.887583
\(905\) 2.82264e12 0.139874
\(906\) 1.46137e13 0.720583
\(907\) −3.23902e13 −1.58921 −0.794604 0.607128i \(-0.792321\pi\)
−0.794604 + 0.607128i \(0.792321\pi\)
\(908\) 6.18199e12 0.301816
\(909\) 3.40958e13 1.65639
\(910\) −3.15387e12 −0.152460
\(911\) −3.75724e13 −1.80732 −0.903662 0.428246i \(-0.859132\pi\)
−0.903662 + 0.428246i \(0.859132\pi\)
\(912\) 2.39388e13 1.14585
\(913\) −2.11681e13 −1.00824
\(914\) −5.21697e12 −0.247264
\(915\) 2.70157e12 0.127415
\(916\) 5.14641e12 0.241532
\(917\) −3.48775e13 −1.62886
\(918\) 0 0
\(919\) 1.23759e12 0.0572343 0.0286172 0.999590i \(-0.490890\pi\)
0.0286172 + 0.999590i \(0.490890\pi\)
\(920\) −1.75569e12 −0.0807984
\(921\) 1.59233e13 0.729232
\(922\) 2.23239e12 0.101737
\(923\) 2.41065e13 1.09327
\(924\) 1.96825e13 0.888294
\(925\) −2.97173e13 −1.33466
\(926\) 2.77136e13 1.23864
\(927\) 4.82061e13 2.14409
\(928\) 5.54813e12 0.245573
\(929\) −3.05199e13 −1.34435 −0.672175 0.740393i \(-0.734640\pi\)
−0.672175 + 0.740393i \(0.734640\pi\)
\(930\) 4.32694e12 0.189674
\(931\) 3.33336e13 1.45415
\(932\) −1.07862e12 −0.0468273
\(933\) 1.94327e13 0.839586
\(934\) 1.52598e13 0.656128
\(935\) 0 0
\(936\) −4.57008e13 −1.94618
\(937\) 3.94116e12 0.167030 0.0835152 0.996507i \(-0.473385\pi\)
0.0835152 + 0.996507i \(0.473385\pi\)
\(938\) 2.49008e13 1.05027
\(939\) −1.84737e13 −0.775458
\(940\) −6.82574e11 −0.0285151
\(941\) −3.24583e13 −1.34950 −0.674750 0.738046i \(-0.735749\pi\)
−0.674750 + 0.738046i \(0.735749\pi\)
\(942\) 6.44313e13 2.66605
\(943\) 2.09581e13 0.863075
\(944\) −3.48319e12 −0.142759
\(945\) 2.53619e12 0.103452
\(946\) 2.72523e13 1.10635
\(947\) −1.58799e13 −0.641611 −0.320806 0.947145i \(-0.603954\pi\)
−0.320806 + 0.947145i \(0.603954\pi\)
\(948\) −1.28100e13 −0.515126
\(949\) −1.01557e13 −0.406454
\(950\) −2.29297e13 −0.913359
\(951\) −1.97178e13 −0.781713
\(952\) 0 0
\(953\) −1.20490e13 −0.473188 −0.236594 0.971609i \(-0.576031\pi\)
−0.236594 + 0.971609i \(0.576031\pi\)
\(954\) −2.75601e11 −0.0107724
\(955\) 2.52076e12 0.0980656
\(956\) −7.72609e11 −0.0299157
\(957\) 3.00148e13 1.15673
\(958\) −1.35992e13 −0.521636
\(959\) 1.95366e13 0.745872
\(960\) −4.26097e12 −0.161915
\(961\) 3.31486e13 1.25375
\(962\) 3.80925e13 1.43401
\(963\) −5.77159e13 −2.16260
\(964\) −9.64626e12 −0.359759
\(965\) −1.96502e12 −0.0729446
\(966\) 4.53310e13 1.67494
\(967\) −2.33579e12 −0.0859044 −0.0429522 0.999077i \(-0.513676\pi\)
−0.0429522 + 0.999077i \(0.513676\pi\)
\(968\) −3.41173e13 −1.24892
\(969\) 0 0
\(970\) −6.83252e11 −0.0247804
\(971\) −4.77817e13 −1.72494 −0.862471 0.506106i \(-0.831085\pi\)
−0.862471 + 0.506106i \(0.831085\pi\)
\(972\) −8.62651e12 −0.309982
\(973\) 2.83210e13 1.01298
\(974\) 8.99909e12 0.320393
\(975\) 5.40004e13 1.91371
\(976\) 1.69797e13 0.598970
\(977\) 1.26420e13 0.443905 0.221952 0.975057i \(-0.428757\pi\)
0.221952 + 0.975057i \(0.428757\pi\)
\(978\) −1.11231e13 −0.388777
\(979\) −5.12573e13 −1.78334
\(980\) −9.20790e11 −0.0318892
\(981\) 5.52503e13 1.90469
\(982\) −4.18139e13 −1.43489
\(983\) 1.21089e13 0.413633 0.206817 0.978380i \(-0.433690\pi\)
0.206817 + 0.978380i \(0.433690\pi\)
\(984\) 5.37499e13 1.82768
\(985\) −2.46410e12 −0.0834058
\(986\) 0 0
\(987\) 8.78770e13 2.94746
\(988\) −9.84226e12 −0.328616
\(989\) −2.10177e13 −0.698558
\(990\) −5.21834e12 −0.172653
\(991\) 1.14838e13 0.378228 0.189114 0.981955i \(-0.439438\pi\)
0.189114 + 0.981955i \(0.439438\pi\)
\(992\) −2.23777e13 −0.733691
\(993\) 6.24486e13 2.03822
\(994\) −3.64032e13 −1.18277
\(995\) 2.43895e12 0.0788858
\(996\) 8.39680e12 0.270363
\(997\) 1.48822e13 0.477021 0.238511 0.971140i \(-0.423341\pi\)
0.238511 + 0.971140i \(0.423341\pi\)
\(998\) −2.94704e13 −0.940370
\(999\) −3.06321e13 −0.973044
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.g.1.26 36
17.16 even 2 289.10.a.h.1.26 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.26 36 1.1 even 1 trivial
289.10.a.h.1.26 yes 36 17.16 even 2