Properties

Label 289.10.a.g.1.2
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $1$
Dimension $36$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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 1.2
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-43.7427 q^{2} -83.5916 q^{3} +1401.42 q^{4} +712.522 q^{5} +3656.52 q^{6} -5542.36 q^{7} -38905.7 q^{8} -12695.4 q^{9} +O(q^{10})\) \(q-43.7427 q^{2} -83.5916 q^{3} +1401.42 q^{4} +712.522 q^{5} +3656.52 q^{6} -5542.36 q^{7} -38905.7 q^{8} -12695.4 q^{9} -31167.6 q^{10} -36089.6 q^{11} -117147. q^{12} -175561. q^{13} +242438. q^{14} -59560.8 q^{15} +984313. q^{16} +555333. q^{18} -512948. q^{19} +998544. q^{20} +463295. q^{21} +1.57866e6 q^{22} +1.41122e6 q^{23} +3.25219e6 q^{24} -1.44544e6 q^{25} +7.67951e6 q^{26} +2.70657e6 q^{27} -7.76719e6 q^{28} +6.23829e6 q^{29} +2.60535e6 q^{30} +100038. q^{31} -2.31367e7 q^{32} +3.01679e6 q^{33} -3.94906e6 q^{35} -1.77917e7 q^{36} +1.77417e7 q^{37} +2.24377e7 q^{38} +1.46754e7 q^{39} -2.77212e7 q^{40} -2.70173e7 q^{41} -2.02658e7 q^{42} +778967. q^{43} -5.05768e7 q^{44} -9.04578e6 q^{45} -6.17308e7 q^{46} +1.03172e7 q^{47} -8.22803e7 q^{48} -9.63580e6 q^{49} +6.32273e7 q^{50} -2.46035e8 q^{52} +3.35090e7 q^{53} -1.18392e8 q^{54} -2.57146e7 q^{55} +2.15630e8 q^{56} +4.28782e7 q^{57} -2.72880e8 q^{58} +1.32523e8 q^{59} -8.34699e7 q^{60} +4.00552e7 q^{61} -4.37595e6 q^{62} +7.03628e7 q^{63} +5.08095e8 q^{64} -1.25091e8 q^{65} -1.31962e8 q^{66} +2.73645e8 q^{67} -1.17967e8 q^{69} +1.72742e8 q^{70} -1.50488e8 q^{71} +4.93925e8 q^{72} -1.55653e7 q^{73} -7.76071e8 q^{74} +1.20826e8 q^{75} -7.18857e8 q^{76} +2.00022e8 q^{77} -6.41943e8 q^{78} +4.95165e7 q^{79} +7.01344e8 q^{80} +2.36382e7 q^{81} +1.18181e9 q^{82} -2.23284e8 q^{83} +6.49272e8 q^{84} -3.40741e7 q^{86} -5.21469e8 q^{87} +1.40409e9 q^{88} +3.53228e7 q^{89} +3.95687e8 q^{90} +9.73023e8 q^{91} +1.97772e9 q^{92} -8.36237e6 q^{93} -4.51304e8 q^{94} -3.65487e8 q^{95} +1.93404e9 q^{96} +1.41983e9 q^{97} +4.21496e8 q^{98} +4.58174e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} - 60000q^{10} - 76902q^{11} - 373248q^{12} + 54216q^{13} - 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} - 6439479q^{20} - 138102q^{21} - 267324q^{22} - 4041462q^{23} - 7653888q^{24} + 16582356q^{25} + 15822744q^{26} - 13281612q^{27} - 18614784q^{28} - 4005936q^{29} + 22471686q^{30} - 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} - 22076682q^{37} - 27401376q^{38} - 62736162q^{39} + 12231630q^{40} - 59641782q^{41} + 150001536q^{42} - 47951586q^{43} + 49578936q^{44} - 129308238q^{45} - 140524827q^{46} - 118557912q^{47} - 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} - 209848575q^{54} - 365439924q^{55} - 203095059q^{56} + 4614108q^{57} + 179071413q^{58} + 343015128q^{59} + 427179186q^{60} - 175597116q^{61} - 720602571q^{62} - 587415936q^{63} + 853082511q^{64} - 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} - 1308709542q^{71} - 275337849q^{72} - 494841342q^{73} - 1545361890q^{74} - 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} - 2270624538q^{78} - 1980107868q^{79} - 2897000199q^{80} + 1598298840q^{81} - 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} + 2705904618q^{88} + 148394658q^{89} - 117916215q^{90} - 636340896q^{91} + 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} - 4878626298q^{95} + 8390096634q^{96} + 891786822q^{97} + 4285627647q^{98} + 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −43.7427 −1.93317 −0.966586 0.256343i \(-0.917482\pi\)
−0.966586 + 0.256343i \(0.917482\pi\)
\(3\) −83.5916 −0.595823 −0.297911 0.954594i \(-0.596290\pi\)
−0.297911 + 0.954594i \(0.596290\pi\)
\(4\) 1401.42 2.73715
\(5\) 712.522 0.509839 0.254920 0.966962i \(-0.417951\pi\)
0.254920 + 0.966962i \(0.417951\pi\)
\(6\) 3656.52 1.15183
\(7\) −5542.36 −0.872477 −0.436238 0.899831i \(-0.643690\pi\)
−0.436238 + 0.899831i \(0.643690\pi\)
\(8\) −38905.7 −3.35822
\(9\) −12695.4 −0.644995
\(10\) −31167.6 −0.985607
\(11\) −36089.6 −0.743216 −0.371608 0.928390i \(-0.621193\pi\)
−0.371608 + 0.928390i \(0.621193\pi\)
\(12\) −117147. −1.63086
\(13\) −175561. −1.70484 −0.852419 0.522859i \(-0.824865\pi\)
−0.852419 + 0.522859i \(0.824865\pi\)
\(14\) 242438. 1.68665
\(15\) −59560.8 −0.303774
\(16\) 984313. 3.75486
\(17\) 0 0
\(18\) 555333. 1.24689
\(19\) −512948. −0.902988 −0.451494 0.892274i \(-0.649109\pi\)
−0.451494 + 0.892274i \(0.649109\pi\)
\(20\) 998544. 1.39551
\(21\) 463295. 0.519841
\(22\) 1.57866e6 1.43676
\(23\) 1.41122e6 1.05153 0.525764 0.850630i \(-0.323779\pi\)
0.525764 + 0.850630i \(0.323779\pi\)
\(24\) 3.25219e6 2.00090
\(25\) −1.44544e6 −0.740064
\(26\) 7.67951e6 3.29574
\(27\) 2.70657e6 0.980126
\(28\) −7.76719e6 −2.38810
\(29\) 6.23829e6 1.63785 0.818926 0.573899i \(-0.194570\pi\)
0.818926 + 0.573899i \(0.194570\pi\)
\(30\) 2.60535e6 0.587247
\(31\) 100038. 0.0194553 0.00972767 0.999953i \(-0.496904\pi\)
0.00972767 + 0.999953i \(0.496904\pi\)
\(32\) −2.31367e7 −3.90056
\(33\) 3.01679e6 0.442825
\(34\) 0 0
\(35\) −3.94906e6 −0.444823
\(36\) −1.77917e7 −1.76545
\(37\) 1.77417e7 1.55628 0.778141 0.628090i \(-0.216163\pi\)
0.778141 + 0.628090i \(0.216163\pi\)
\(38\) 2.24377e7 1.74563
\(39\) 1.46754e7 1.01578
\(40\) −2.77212e7 −1.71215
\(41\) −2.70173e7 −1.49319 −0.746594 0.665280i \(-0.768312\pi\)
−0.746594 + 0.665280i \(0.768312\pi\)
\(42\) −2.02658e7 −1.00494
\(43\) 778967. 0.0347465 0.0173733 0.999849i \(-0.494470\pi\)
0.0173733 + 0.999849i \(0.494470\pi\)
\(44\) −5.05768e7 −2.03430
\(45\) −9.04578e6 −0.328844
\(46\) −6.17308e7 −2.03278
\(47\) 1.03172e7 0.308406 0.154203 0.988039i \(-0.450719\pi\)
0.154203 + 0.988039i \(0.450719\pi\)
\(48\) −8.22803e7 −2.23723
\(49\) −9.63580e6 −0.238784
\(50\) 6.32273e7 1.43067
\(51\) 0 0
\(52\) −2.46035e8 −4.66640
\(53\) 3.35090e7 0.583338 0.291669 0.956519i \(-0.405789\pi\)
0.291669 + 0.956519i \(0.405789\pi\)
\(54\) −1.18392e8 −1.89475
\(55\) −2.57146e7 −0.378921
\(56\) 2.15630e8 2.92997
\(57\) 4.28782e7 0.538021
\(58\) −2.72880e8 −3.16625
\(59\) 1.32523e8 1.42383 0.711915 0.702265i \(-0.247828\pi\)
0.711915 + 0.702265i \(0.247828\pi\)
\(60\) −8.34699e7 −0.831475
\(61\) 4.00552e7 0.370403 0.185202 0.982701i \(-0.440706\pi\)
0.185202 + 0.982701i \(0.440706\pi\)
\(62\) −4.37595e6 −0.0376105
\(63\) 7.03628e7 0.562744
\(64\) 5.08095e8 3.78561
\(65\) −1.25091e8 −0.869193
\(66\) −1.31962e8 −0.856057
\(67\) 2.73645e8 1.65902 0.829509 0.558494i \(-0.188621\pi\)
0.829509 + 0.558494i \(0.188621\pi\)
\(68\) 0 0
\(69\) −1.17967e8 −0.626524
\(70\) 1.72742e8 0.859919
\(71\) −1.50488e8 −0.702813 −0.351406 0.936223i \(-0.614296\pi\)
−0.351406 + 0.936223i \(0.614296\pi\)
\(72\) 4.93925e8 2.16603
\(73\) −1.55653e7 −0.0641511 −0.0320755 0.999485i \(-0.510212\pi\)
−0.0320755 + 0.999485i \(0.510212\pi\)
\(74\) −7.76071e8 −3.00856
\(75\) 1.20826e8 0.440947
\(76\) −7.18857e8 −2.47162
\(77\) 2.00022e8 0.648439
\(78\) −6.41943e8 −1.96368
\(79\) 4.95165e7 0.143030 0.0715152 0.997440i \(-0.477217\pi\)
0.0715152 + 0.997440i \(0.477217\pi\)
\(80\) 7.01344e8 1.91437
\(81\) 2.36382e7 0.0610143
\(82\) 1.18181e9 2.88659
\(83\) −2.23284e8 −0.516423 −0.258211 0.966088i \(-0.583133\pi\)
−0.258211 + 0.966088i \(0.583133\pi\)
\(84\) 6.49272e8 1.42289
\(85\) 0 0
\(86\) −3.40741e7 −0.0671710
\(87\) −5.21469e8 −0.975869
\(88\) 1.40409e9 2.49588
\(89\) 3.53228e7 0.0596761 0.0298380 0.999555i \(-0.490501\pi\)
0.0298380 + 0.999555i \(0.490501\pi\)
\(90\) 3.95687e8 0.635712
\(91\) 9.73023e8 1.48743
\(92\) 1.97772e9 2.87819
\(93\) −8.36237e6 −0.0115919
\(94\) −4.51304e8 −0.596203
\(95\) −3.65487e8 −0.460379
\(96\) 1.93404e9 2.32404
\(97\) 1.41983e9 1.62841 0.814207 0.580575i \(-0.197172\pi\)
0.814207 + 0.580575i \(0.197172\pi\)
\(98\) 4.21496e8 0.461611
\(99\) 4.58174e8 0.479371
\(100\) −2.02567e9 −2.02567
\(101\) −6.69672e8 −0.640348 −0.320174 0.947359i \(-0.603741\pi\)
−0.320174 + 0.947359i \(0.603741\pi\)
\(102\) 0 0
\(103\) 8.49559e8 0.743748 0.371874 0.928283i \(-0.378715\pi\)
0.371874 + 0.928283i \(0.378715\pi\)
\(104\) 6.83033e9 5.72521
\(105\) 3.30108e8 0.265036
\(106\) −1.46577e9 −1.12769
\(107\) −1.20391e9 −0.887905 −0.443952 0.896050i \(-0.646424\pi\)
−0.443952 + 0.896050i \(0.646424\pi\)
\(108\) 3.79304e9 2.68275
\(109\) −1.20826e9 −0.819861 −0.409930 0.912117i \(-0.634447\pi\)
−0.409930 + 0.912117i \(0.634447\pi\)
\(110\) 1.12483e9 0.732519
\(111\) −1.48306e9 −0.927268
\(112\) −5.45542e9 −3.27602
\(113\) 2.90740e9 1.67746 0.838729 0.544549i \(-0.183299\pi\)
0.838729 + 0.544549i \(0.183299\pi\)
\(114\) −1.87561e9 −1.04009
\(115\) 1.00553e9 0.536110
\(116\) 8.74248e9 4.48305
\(117\) 2.22883e9 1.09961
\(118\) −5.79693e9 −2.75251
\(119\) 0 0
\(120\) 2.31726e9 1.02014
\(121\) −1.05549e9 −0.447630
\(122\) −1.75212e9 −0.716053
\(123\) 2.25842e9 0.889675
\(124\) 1.40196e8 0.0532523
\(125\) −2.42155e9 −0.887153
\(126\) −3.07786e9 −1.08788
\(127\) −1.75281e8 −0.0597884 −0.0298942 0.999553i \(-0.509517\pi\)
−0.0298942 + 0.999553i \(0.509517\pi\)
\(128\) −1.03794e10 −3.41766
\(129\) −6.51151e7 −0.0207028
\(130\) 5.47182e9 1.68030
\(131\) −4.29446e9 −1.27405 −0.637027 0.770841i \(-0.719836\pi\)
−0.637027 + 0.770841i \(0.719836\pi\)
\(132\) 4.22779e9 1.21208
\(133\) 2.84295e9 0.787837
\(134\) −1.19700e10 −3.20717
\(135\) 1.92849e9 0.499706
\(136\) 0 0
\(137\) −1.83424e9 −0.444850 −0.222425 0.974950i \(-0.571397\pi\)
−0.222425 + 0.974950i \(0.571397\pi\)
\(138\) 5.16017e9 1.21118
\(139\) −3.09950e9 −0.704247 −0.352123 0.935954i \(-0.614540\pi\)
−0.352123 + 0.935954i \(0.614540\pi\)
\(140\) −5.53430e9 −1.21755
\(141\) −8.62435e8 −0.183756
\(142\) 6.58275e9 1.35866
\(143\) 6.33593e9 1.26706
\(144\) −1.24963e10 −2.42186
\(145\) 4.44492e9 0.835041
\(146\) 6.80867e8 0.124015
\(147\) 8.05472e8 0.142273
\(148\) 2.48637e10 4.25978
\(149\) 2.53473e9 0.421302 0.210651 0.977561i \(-0.432442\pi\)
0.210651 + 0.977561i \(0.432442\pi\)
\(150\) −5.28527e9 −0.852426
\(151\) −1.10620e9 −0.173156 −0.0865780 0.996245i \(-0.527593\pi\)
−0.0865780 + 0.996245i \(0.527593\pi\)
\(152\) 1.99566e10 3.03243
\(153\) 0 0
\(154\) −8.74949e9 −1.25354
\(155\) 7.12795e7 0.00991909
\(156\) 2.05665e10 2.78035
\(157\) −1.70941e9 −0.224542 −0.112271 0.993678i \(-0.535813\pi\)
−0.112271 + 0.993678i \(0.535813\pi\)
\(158\) −2.16599e9 −0.276502
\(159\) −2.80107e9 −0.347566
\(160\) −1.64854e10 −1.98866
\(161\) −7.82152e9 −0.917434
\(162\) −1.03400e9 −0.117951
\(163\) 4.74641e9 0.526649 0.263324 0.964707i \(-0.415181\pi\)
0.263324 + 0.964707i \(0.415181\pi\)
\(164\) −3.78626e10 −4.08708
\(165\) 2.14953e9 0.225769
\(166\) 9.76703e9 0.998334
\(167\) −2.19497e8 −0.0218376 −0.0109188 0.999940i \(-0.503476\pi\)
−0.0109188 + 0.999940i \(0.503476\pi\)
\(168\) −1.80248e10 −1.74574
\(169\) 2.02172e10 1.90647
\(170\) 0 0
\(171\) 6.51210e9 0.582423
\(172\) 1.09166e9 0.0951065
\(173\) −1.63408e10 −1.38697 −0.693485 0.720471i \(-0.743926\pi\)
−0.693485 + 0.720471i \(0.743926\pi\)
\(174\) 2.28104e10 1.88652
\(175\) 8.01114e9 0.645689
\(176\) −3.55235e10 −2.79067
\(177\) −1.10778e10 −0.848351
\(178\) −1.54512e9 −0.115364
\(179\) 8.32078e9 0.605795 0.302897 0.953023i \(-0.402046\pi\)
0.302897 + 0.953023i \(0.402046\pi\)
\(180\) −1.26770e10 −0.900096
\(181\) 5.65108e9 0.391361 0.195681 0.980668i \(-0.437308\pi\)
0.195681 + 0.980668i \(0.437308\pi\)
\(182\) −4.25627e10 −2.87546
\(183\) −3.34828e9 −0.220695
\(184\) −5.49047e10 −3.53126
\(185\) 1.26414e10 0.793453
\(186\) 3.65792e8 0.0224092
\(187\) 0 0
\(188\) 1.44588e10 0.844156
\(189\) −1.50008e10 −0.855137
\(190\) 1.59874e10 0.889991
\(191\) −4.52797e9 −0.246180 −0.123090 0.992395i \(-0.539280\pi\)
−0.123090 + 0.992395i \(0.539280\pi\)
\(192\) −4.24725e10 −2.25555
\(193\) 2.74959e10 1.42646 0.713230 0.700931i \(-0.247232\pi\)
0.713230 + 0.700931i \(0.247232\pi\)
\(194\) −6.21073e10 −3.14800
\(195\) 1.04566e10 0.517885
\(196\) −1.35038e10 −0.653589
\(197\) −1.50301e10 −0.710991 −0.355495 0.934678i \(-0.615688\pi\)
−0.355495 + 0.934678i \(0.615688\pi\)
\(198\) −2.00417e10 −0.926706
\(199\) 5.79615e9 0.262000 0.131000 0.991382i \(-0.458181\pi\)
0.131000 + 0.991382i \(0.458181\pi\)
\(200\) 5.62358e10 2.48529
\(201\) −2.28744e10 −0.988480
\(202\) 2.92932e10 1.23790
\(203\) −3.45749e10 −1.42899
\(204\) 0 0
\(205\) −1.92504e10 −0.761286
\(206\) −3.71620e10 −1.43779
\(207\) −1.79161e10 −0.678231
\(208\) −1.72807e11 −6.40142
\(209\) 1.85121e10 0.671115
\(210\) −1.44398e10 −0.512359
\(211\) 3.03732e10 1.05492 0.527460 0.849580i \(-0.323144\pi\)
0.527460 + 0.849580i \(0.323144\pi\)
\(212\) 4.69603e10 1.59669
\(213\) 1.25795e10 0.418752
\(214\) 5.26622e10 1.71647
\(215\) 5.55031e8 0.0177151
\(216\) −1.05301e11 −3.29147
\(217\) −5.54449e8 −0.0169743
\(218\) 5.28524e10 1.58493
\(219\) 1.30113e9 0.0382227
\(220\) −3.60371e10 −1.03716
\(221\) 0 0
\(222\) 6.48730e10 1.79257
\(223\) 4.61309e10 1.24916 0.624582 0.780959i \(-0.285269\pi\)
0.624582 + 0.780959i \(0.285269\pi\)
\(224\) 1.28232e11 3.40315
\(225\) 1.83505e10 0.477338
\(226\) −1.27177e11 −3.24282
\(227\) 1.32854e9 0.0332092 0.0166046 0.999862i \(-0.494714\pi\)
0.0166046 + 0.999862i \(0.494714\pi\)
\(228\) 6.00904e10 1.47265
\(229\) 1.58431e10 0.380699 0.190349 0.981716i \(-0.439038\pi\)
0.190349 + 0.981716i \(0.439038\pi\)
\(230\) −4.39845e10 −1.03639
\(231\) −1.67201e10 −0.386355
\(232\) −2.42705e11 −5.50026
\(233\) 4.53578e8 0.0100821 0.00504104 0.999987i \(-0.498395\pi\)
0.00504104 + 0.999987i \(0.498395\pi\)
\(234\) −9.74948e10 −2.12574
\(235\) 7.35126e9 0.157238
\(236\) 1.85721e11 3.89724
\(237\) −4.13917e9 −0.0852208
\(238\) 0 0
\(239\) 6.02131e10 1.19371 0.596857 0.802348i \(-0.296416\pi\)
0.596857 + 0.802348i \(0.296416\pi\)
\(240\) −5.86265e10 −1.14063
\(241\) 1.95681e10 0.373656 0.186828 0.982393i \(-0.440179\pi\)
0.186828 + 0.982393i \(0.440179\pi\)
\(242\) 4.61699e10 0.865346
\(243\) −5.52493e10 −1.01648
\(244\) 5.61343e10 1.01385
\(245\) −6.86572e9 −0.121741
\(246\) −9.87893e10 −1.71989
\(247\) 9.00537e10 1.53945
\(248\) −3.89206e9 −0.0653352
\(249\) 1.86646e10 0.307696
\(250\) 1.05925e11 1.71502
\(251\) −1.06749e11 −1.69759 −0.848794 0.528724i \(-0.822671\pi\)
−0.848794 + 0.528724i \(0.822671\pi\)
\(252\) 9.86080e10 1.54032
\(253\) −5.09305e10 −0.781513
\(254\) 7.66724e9 0.115581
\(255\) 0 0
\(256\) 1.93880e11 2.82132
\(257\) −1.35700e10 −0.194035 −0.0970176 0.995283i \(-0.530930\pi\)
−0.0970176 + 0.995283i \(0.530930\pi\)
\(258\) 2.84831e9 0.0400220
\(259\) −9.83311e10 −1.35782
\(260\) −1.75305e11 −2.37911
\(261\) −7.91979e10 −1.05641
\(262\) 1.87851e11 2.46297
\(263\) −4.47087e10 −0.576224 −0.288112 0.957597i \(-0.593027\pi\)
−0.288112 + 0.957597i \(0.593027\pi\)
\(264\) −1.17370e11 −1.48710
\(265\) 2.38759e10 0.297409
\(266\) −1.24358e11 −1.52302
\(267\) −2.95269e9 −0.0355564
\(268\) 3.83492e11 4.54098
\(269\) −9.73705e10 −1.13381 −0.566907 0.823782i \(-0.691860\pi\)
−0.566907 + 0.823782i \(0.691860\pi\)
\(270\) −8.43572e10 −0.966018
\(271\) −8.62013e10 −0.970850 −0.485425 0.874278i \(-0.661335\pi\)
−0.485425 + 0.874278i \(0.661335\pi\)
\(272\) 0 0
\(273\) −8.13366e10 −0.886245
\(274\) 8.02346e10 0.859971
\(275\) 5.21653e10 0.550027
\(276\) −1.65321e11 −1.71489
\(277\) 1.81712e10 0.185449 0.0927243 0.995692i \(-0.470442\pi\)
0.0927243 + 0.995692i \(0.470442\pi\)
\(278\) 1.35580e11 1.36143
\(279\) −1.27003e9 −0.0125486
\(280\) 1.53641e11 1.49381
\(281\) −3.90556e10 −0.373684 −0.186842 0.982390i \(-0.559825\pi\)
−0.186842 + 0.982390i \(0.559825\pi\)
\(282\) 3.77252e10 0.355231
\(283\) 1.56085e11 1.44651 0.723255 0.690581i \(-0.242645\pi\)
0.723255 + 0.690581i \(0.242645\pi\)
\(284\) −2.10897e11 −1.92371
\(285\) 3.05516e10 0.274304
\(286\) −2.77151e11 −2.44945
\(287\) 1.49740e11 1.30277
\(288\) 2.93731e11 2.51585
\(289\) 0 0
\(290\) −1.94433e11 −1.61428
\(291\) −1.18686e11 −0.970246
\(292\) −2.18135e10 −0.175591
\(293\) 1.99350e11 1.58020 0.790099 0.612980i \(-0.210029\pi\)
0.790099 + 0.612980i \(0.210029\pi\)
\(294\) −3.52335e10 −0.275038
\(295\) 9.44258e10 0.725925
\(296\) −6.90255e11 −5.22633
\(297\) −9.76789e10 −0.728445
\(298\) −1.10876e11 −0.814449
\(299\) −2.47756e11 −1.79269
\(300\) 1.69329e11 1.20694
\(301\) −4.31732e9 −0.0303155
\(302\) 4.83882e10 0.334740
\(303\) 5.59789e10 0.381534
\(304\) −5.04901e11 −3.39059
\(305\) 2.85402e10 0.188846
\(306\) 0 0
\(307\) −1.45882e11 −0.937298 −0.468649 0.883384i \(-0.655259\pi\)
−0.468649 + 0.883384i \(0.655259\pi\)
\(308\) 2.80315e11 1.77488
\(309\) −7.10160e10 −0.443142
\(310\) −3.11796e9 −0.0191753
\(311\) 5.10899e10 0.309680 0.154840 0.987940i \(-0.450514\pi\)
0.154840 + 0.987940i \(0.450514\pi\)
\(312\) −5.70958e11 −3.41121
\(313\) −2.60411e11 −1.53359 −0.766797 0.641890i \(-0.778151\pi\)
−0.766797 + 0.641890i \(0.778151\pi\)
\(314\) 7.47742e10 0.434079
\(315\) 5.01350e10 0.286909
\(316\) 6.93936e10 0.391496
\(317\) −6.41873e8 −0.00357012 −0.00178506 0.999998i \(-0.500568\pi\)
−0.00178506 + 0.999998i \(0.500568\pi\)
\(318\) 1.22526e11 0.671905
\(319\) −2.25137e11 −1.21728
\(320\) 3.62029e11 1.93005
\(321\) 1.00637e11 0.529034
\(322\) 3.42134e11 1.77356
\(323\) 0 0
\(324\) 3.31271e10 0.167006
\(325\) 2.53763e11 1.26169
\(326\) −2.07621e11 −1.01810
\(327\) 1.01000e11 0.488492
\(328\) 1.05113e12 5.01445
\(329\) −5.71819e10 −0.269077
\(330\) −9.40261e10 −0.436451
\(331\) −2.52438e11 −1.15592 −0.577962 0.816063i \(-0.696152\pi\)
−0.577962 + 0.816063i \(0.696152\pi\)
\(332\) −3.12915e11 −1.41353
\(333\) −2.25239e11 −1.00379
\(334\) 9.60139e9 0.0422158
\(335\) 1.94978e11 0.845832
\(336\) 4.56027e11 1.95193
\(337\) −2.71455e11 −1.14647 −0.573235 0.819391i \(-0.694312\pi\)
−0.573235 + 0.819391i \(0.694312\pi\)
\(338\) −8.84354e11 −3.68554
\(339\) −2.43034e11 −0.999468
\(340\) 0 0
\(341\) −3.61034e9 −0.0144595
\(342\) −2.84857e11 −1.12592
\(343\) 2.77060e11 1.08081
\(344\) −3.03063e10 −0.116686
\(345\) −8.40537e10 −0.319427
\(346\) 7.14792e11 2.68125
\(347\) 1.21278e11 0.449053 0.224527 0.974468i \(-0.427916\pi\)
0.224527 + 0.974468i \(0.427916\pi\)
\(348\) −7.30798e11 −2.67110
\(349\) 4.94486e11 1.78418 0.892092 0.451854i \(-0.149237\pi\)
0.892092 + 0.451854i \(0.149237\pi\)
\(350\) −3.50429e11 −1.24823
\(351\) −4.75168e11 −1.67096
\(352\) 8.34996e11 2.89896
\(353\) 2.59580e11 0.889785 0.444893 0.895584i \(-0.353242\pi\)
0.444893 + 0.895584i \(0.353242\pi\)
\(354\) 4.84574e11 1.64001
\(355\) −1.07226e11 −0.358321
\(356\) 4.95022e10 0.163343
\(357\) 0 0
\(358\) −3.63973e11 −1.17111
\(359\) 5.64703e11 1.79430 0.897150 0.441725i \(-0.145633\pi\)
0.897150 + 0.441725i \(0.145633\pi\)
\(360\) 3.51933e11 1.10433
\(361\) −5.95720e10 −0.184612
\(362\) −2.47193e11 −0.756569
\(363\) 8.82299e10 0.266708
\(364\) 1.36362e12 4.07133
\(365\) −1.10906e10 −0.0327067
\(366\) 1.46463e11 0.426641
\(367\) −5.01887e10 −0.144414 −0.0722069 0.997390i \(-0.523004\pi\)
−0.0722069 + 0.997390i \(0.523004\pi\)
\(368\) 1.38909e12 3.94834
\(369\) 3.42996e11 0.963099
\(370\) −5.52967e11 −1.53388
\(371\) −1.85719e11 −0.508949
\(372\) −1.17192e10 −0.0317289
\(373\) 2.42202e11 0.647870 0.323935 0.946079i \(-0.394994\pi\)
0.323935 + 0.946079i \(0.394994\pi\)
\(374\) 0 0
\(375\) 2.02421e11 0.528586
\(376\) −4.01400e11 −1.03570
\(377\) −1.09520e12 −2.79227
\(378\) 6.56174e11 1.65313
\(379\) −6.36704e11 −1.58512 −0.792559 0.609796i \(-0.791251\pi\)
−0.792559 + 0.609796i \(0.791251\pi\)
\(380\) −5.12201e11 −1.26013
\(381\) 1.46520e10 0.0356233
\(382\) 1.98066e11 0.475909
\(383\) 4.29691e10 0.102038 0.0510190 0.998698i \(-0.483753\pi\)
0.0510190 + 0.998698i \(0.483753\pi\)
\(384\) 8.67634e11 2.03632
\(385\) 1.42520e11 0.330599
\(386\) −1.20274e12 −2.75759
\(387\) −9.88934e9 −0.0224113
\(388\) 1.98979e12 4.45722
\(389\) 5.97037e11 1.32199 0.660995 0.750391i \(-0.270135\pi\)
0.660995 + 0.750391i \(0.270135\pi\)
\(390\) −4.57398e11 −1.00116
\(391\) 0 0
\(392\) 3.74888e11 0.801889
\(393\) 3.58981e11 0.759110
\(394\) 6.57457e11 1.37447
\(395\) 3.52816e10 0.0729225
\(396\) 6.42095e11 1.31211
\(397\) 4.91474e11 0.992986 0.496493 0.868041i \(-0.334621\pi\)
0.496493 + 0.868041i \(0.334621\pi\)
\(398\) −2.53539e11 −0.506491
\(399\) −2.37646e11 −0.469411
\(400\) −1.42276e12 −2.77883
\(401\) −2.34902e11 −0.453668 −0.226834 0.973933i \(-0.572837\pi\)
−0.226834 + 0.973933i \(0.572837\pi\)
\(402\) 1.00059e12 1.91090
\(403\) −1.75628e10 −0.0331682
\(404\) −9.38493e11 −1.75273
\(405\) 1.68427e10 0.0311075
\(406\) 1.51240e12 2.76248
\(407\) −6.40292e11 −1.15665
\(408\) 0 0
\(409\) 1.31401e11 0.232191 0.116095 0.993238i \(-0.462962\pi\)
0.116095 + 0.993238i \(0.462962\pi\)
\(410\) 8.42065e11 1.47170
\(411\) 1.53327e11 0.265052
\(412\) 1.19059e12 2.03575
\(413\) −7.34493e11 −1.24226
\(414\) 7.83699e11 1.31114
\(415\) −1.59094e11 −0.263293
\(416\) 4.06191e12 6.64983
\(417\) 2.59092e11 0.419606
\(418\) −8.09769e11 −1.29738
\(419\) 6.01297e11 0.953072 0.476536 0.879155i \(-0.341892\pi\)
0.476536 + 0.879155i \(0.341892\pi\)
\(420\) 4.62621e11 0.725443
\(421\) 1.16288e11 0.180412 0.0902062 0.995923i \(-0.471247\pi\)
0.0902062 + 0.995923i \(0.471247\pi\)
\(422\) −1.32861e12 −2.03934
\(423\) −1.30982e11 −0.198921
\(424\) −1.30369e12 −1.95898
\(425\) 0 0
\(426\) −5.50263e11 −0.809519
\(427\) −2.22001e11 −0.323168
\(428\) −1.68718e12 −2.43033
\(429\) −5.29630e11 −0.754945
\(430\) −2.42786e10 −0.0342464
\(431\) 9.23955e11 1.28974 0.644871 0.764291i \(-0.276911\pi\)
0.644871 + 0.764291i \(0.276911\pi\)
\(432\) 2.66411e12 3.68023
\(433\) −3.64410e11 −0.498189 −0.249095 0.968479i \(-0.580133\pi\)
−0.249095 + 0.968479i \(0.580133\pi\)
\(434\) 2.42531e10 0.0328143
\(435\) −3.71558e11 −0.497536
\(436\) −1.69328e12 −2.24408
\(437\) −7.23885e11 −0.949518
\(438\) −5.69148e10 −0.0738910
\(439\) −6.78960e11 −0.872476 −0.436238 0.899831i \(-0.643689\pi\)
−0.436238 + 0.899831i \(0.643689\pi\)
\(440\) 1.00045e12 1.27250
\(441\) 1.22331e11 0.154015
\(442\) 0 0
\(443\) −5.20909e11 −0.642607 −0.321303 0.946976i \(-0.604121\pi\)
−0.321303 + 0.946976i \(0.604121\pi\)
\(444\) −2.07839e12 −2.53807
\(445\) 2.51683e10 0.0304252
\(446\) −2.01789e12 −2.41485
\(447\) −2.11882e11 −0.251021
\(448\) −2.81605e12 −3.30285
\(449\) −8.95134e11 −1.03939 −0.519696 0.854351i \(-0.673955\pi\)
−0.519696 + 0.854351i \(0.673955\pi\)
\(450\) −8.02699e11 −0.922776
\(451\) 9.75043e11 1.10976
\(452\) 4.07450e12 4.59146
\(453\) 9.24690e10 0.103170
\(454\) −5.81139e10 −0.0641991
\(455\) 6.93300e11 0.758351
\(456\) −1.66821e12 −1.80679
\(457\) 1.95511e11 0.209675 0.104838 0.994489i \(-0.466568\pi\)
0.104838 + 0.994489i \(0.466568\pi\)
\(458\) −6.93021e11 −0.735956
\(459\) 0 0
\(460\) 1.40917e12 1.46742
\(461\) −6.94628e11 −0.716305 −0.358153 0.933663i \(-0.616593\pi\)
−0.358153 + 0.933663i \(0.616593\pi\)
\(462\) 7.31384e11 0.746890
\(463\) 1.44310e12 1.45943 0.729713 0.683753i \(-0.239654\pi\)
0.729713 + 0.683753i \(0.239654\pi\)
\(464\) 6.14043e12 6.14990
\(465\) −5.95837e9 −0.00591002
\(466\) −1.98407e10 −0.0194904
\(467\) −1.73333e12 −1.68637 −0.843187 0.537620i \(-0.819324\pi\)
−0.843187 + 0.537620i \(0.819324\pi\)
\(468\) 3.12353e12 3.00981
\(469\) −1.51664e12 −1.44745
\(470\) −3.21564e11 −0.303967
\(471\) 1.42892e11 0.133787
\(472\) −5.15592e12 −4.78153
\(473\) −2.81126e10 −0.0258242
\(474\) 1.81058e11 0.164746
\(475\) 7.41434e11 0.668269
\(476\) 0 0
\(477\) −4.25412e11 −0.376250
\(478\) −2.63388e12 −2.30765
\(479\) −4.61090e11 −0.400199 −0.200100 0.979776i \(-0.564127\pi\)
−0.200100 + 0.979776i \(0.564127\pi\)
\(480\) 1.37804e12 1.18489
\(481\) −3.11476e12 −2.65321
\(482\) −8.55961e11 −0.722341
\(483\) 6.53814e11 0.546628
\(484\) −1.47918e12 −1.22523
\(485\) 1.01166e12 0.830229
\(486\) 2.41675e12 1.96503
\(487\) −1.31130e12 −1.05638 −0.528191 0.849126i \(-0.677129\pi\)
−0.528191 + 0.849126i \(0.677129\pi\)
\(488\) −1.55838e12 −1.24389
\(489\) −3.96760e11 −0.313789
\(490\) 3.00325e11 0.235347
\(491\) −2.42631e11 −0.188399 −0.0941997 0.995553i \(-0.530029\pi\)
−0.0941997 + 0.995553i \(0.530029\pi\)
\(492\) 3.16500e12 2.43518
\(493\) 0 0
\(494\) −3.93919e12 −2.97602
\(495\) 3.26459e11 0.244402
\(496\) 9.84690e10 0.0730520
\(497\) 8.34060e11 0.613188
\(498\) −8.16441e11 −0.594830
\(499\) −1.85899e12 −1.34223 −0.671113 0.741355i \(-0.734184\pi\)
−0.671113 + 0.741355i \(0.734184\pi\)
\(500\) −3.39361e12 −2.42827
\(501\) 1.83481e10 0.0130113
\(502\) 4.66949e12 3.28173
\(503\) −1.96267e12 −1.36707 −0.683537 0.729916i \(-0.739559\pi\)
−0.683537 + 0.729916i \(0.739559\pi\)
\(504\) −2.73752e12 −1.88981
\(505\) −4.77156e11 −0.326474
\(506\) 2.22784e12 1.51080
\(507\) −1.68999e12 −1.13592
\(508\) −2.45642e11 −0.163650
\(509\) −1.96893e12 −1.30017 −0.650085 0.759861i \(-0.725267\pi\)
−0.650085 + 0.759861i \(0.725267\pi\)
\(510\) 0 0
\(511\) 8.62684e10 0.0559703
\(512\) −3.16655e12 −2.03644
\(513\) −1.38833e12 −0.885042
\(514\) 5.93588e11 0.375103
\(515\) 6.05329e11 0.379192
\(516\) −9.12538e10 −0.0566666
\(517\) −3.72345e11 −0.229213
\(518\) 4.30127e12 2.62490
\(519\) 1.36596e12 0.826388
\(520\) 4.86676e12 2.91894
\(521\) −7.98293e11 −0.474671 −0.237335 0.971428i \(-0.576274\pi\)
−0.237335 + 0.971428i \(0.576274\pi\)
\(522\) 3.46433e12 2.04222
\(523\) −1.48202e12 −0.866158 −0.433079 0.901356i \(-0.642573\pi\)
−0.433079 + 0.901356i \(0.642573\pi\)
\(524\) −6.01835e12 −3.48728
\(525\) −6.69664e11 −0.384716
\(526\) 1.95568e12 1.11394
\(527\) 0 0
\(528\) 2.96946e12 1.66274
\(529\) 1.90403e11 0.105712
\(530\) −1.04440e12 −0.574942
\(531\) −1.68244e12 −0.918364
\(532\) 3.98417e12 2.15643
\(533\) 4.74318e12 2.54564
\(534\) 1.29159e11 0.0687366
\(535\) −8.57811e11 −0.452689
\(536\) −1.06464e13 −5.57134
\(537\) −6.95547e11 −0.360946
\(538\) 4.25925e12 2.19186
\(539\) 3.47752e11 0.177468
\(540\) 2.70263e12 1.36777
\(541\) 1.28357e12 0.644219 0.322109 0.946702i \(-0.395608\pi\)
0.322109 + 0.946702i \(0.395608\pi\)
\(542\) 3.77068e12 1.87682
\(543\) −4.72383e11 −0.233182
\(544\) 0 0
\(545\) −8.60909e11 −0.417997
\(546\) 3.55788e12 1.71326
\(547\) −2.44820e12 −1.16924 −0.584619 0.811308i \(-0.698756\pi\)
−0.584619 + 0.811308i \(0.698756\pi\)
\(548\) −2.57054e12 −1.21762
\(549\) −5.08519e11 −0.238908
\(550\) −2.28185e12 −1.06330
\(551\) −3.19992e12 −1.47896
\(552\) 4.58957e12 2.10400
\(553\) −2.74439e11 −0.124791
\(554\) −7.94855e11 −0.358504
\(555\) −1.05671e12 −0.472757
\(556\) −4.34371e12 −1.92763
\(557\) −2.37115e11 −0.104378 −0.0521892 0.998637i \(-0.516620\pi\)
−0.0521892 + 0.998637i \(0.516620\pi\)
\(558\) 5.55546e10 0.0242586
\(559\) −1.36756e11 −0.0592372
\(560\) −3.88711e12 −1.67025
\(561\) 0 0
\(562\) 1.70840e12 0.722396
\(563\) −1.25277e12 −0.525512 −0.262756 0.964862i \(-0.584631\pi\)
−0.262756 + 0.964862i \(0.584631\pi\)
\(564\) −1.20864e12 −0.502967
\(565\) 2.07159e12 0.855234
\(566\) −6.82756e12 −2.79635
\(567\) −1.31012e11 −0.0532336
\(568\) 5.85485e12 2.36020
\(569\) 9.49810e11 0.379867 0.189933 0.981797i \(-0.439173\pi\)
0.189933 + 0.981797i \(0.439173\pi\)
\(570\) −1.33641e12 −0.530277
\(571\) −4.03177e12 −1.58721 −0.793604 0.608435i \(-0.791798\pi\)
−0.793604 + 0.608435i \(0.791798\pi\)
\(572\) 8.87931e12 3.46815
\(573\) 3.78500e11 0.146680
\(574\) −6.55002e12 −2.51848
\(575\) −2.03984e12 −0.778198
\(576\) −6.45050e12 −2.44170
\(577\) −2.32183e12 −0.872045 −0.436023 0.899936i \(-0.643613\pi\)
−0.436023 + 0.899936i \(0.643613\pi\)
\(578\) 0 0
\(579\) −2.29842e12 −0.849917
\(580\) 6.22921e12 2.28564
\(581\) 1.23752e12 0.450567
\(582\) 5.19165e12 1.87565
\(583\) −1.20933e12 −0.433546
\(584\) 6.05578e11 0.215433
\(585\) 1.58809e12 0.560625
\(586\) −8.72009e12 −3.05479
\(587\) −3.45750e12 −1.20196 −0.600982 0.799263i \(-0.705224\pi\)
−0.600982 + 0.799263i \(0.705224\pi\)
\(588\) 1.12881e12 0.389423
\(589\) −5.13145e10 −0.0175679
\(590\) −4.13044e12 −1.40334
\(591\) 1.25639e12 0.423624
\(592\) 1.74634e13 5.84361
\(593\) 4.64446e12 1.54237 0.771186 0.636610i \(-0.219664\pi\)
0.771186 + 0.636610i \(0.219664\pi\)
\(594\) 4.27274e12 1.40821
\(595\) 0 0
\(596\) 3.55223e12 1.15317
\(597\) −4.84510e11 −0.156105
\(598\) 1.08375e13 3.46557
\(599\) −2.82740e10 −0.00897358 −0.00448679 0.999990i \(-0.501428\pi\)
−0.00448679 + 0.999990i \(0.501428\pi\)
\(600\) −4.70084e12 −1.48080
\(601\) 4.13809e12 1.29379 0.646896 0.762578i \(-0.276067\pi\)
0.646896 + 0.762578i \(0.276067\pi\)
\(602\) 1.88851e11 0.0586051
\(603\) −3.47404e12 −1.07006
\(604\) −1.55025e12 −0.473954
\(605\) −7.52058e11 −0.228219
\(606\) −2.44867e12 −0.737570
\(607\) 4.30595e12 1.28742 0.643709 0.765270i \(-0.277395\pi\)
0.643709 + 0.765270i \(0.277395\pi\)
\(608\) 1.18680e13 3.52216
\(609\) 2.89017e12 0.851423
\(610\) −1.24843e12 −0.365072
\(611\) −1.81131e12 −0.525783
\(612\) 0 0
\(613\) 6.41377e12 1.83460 0.917300 0.398197i \(-0.130364\pi\)
0.917300 + 0.398197i \(0.130364\pi\)
\(614\) 6.38125e12 1.81196
\(615\) 1.60917e12 0.453591
\(616\) −7.78199e12 −2.17760
\(617\) 5.16320e12 1.43429 0.717143 0.696926i \(-0.245449\pi\)
0.717143 + 0.696926i \(0.245449\pi\)
\(618\) 3.10643e12 0.856670
\(619\) 6.94645e12 1.90176 0.950878 0.309566i \(-0.100184\pi\)
0.950878 + 0.309566i \(0.100184\pi\)
\(620\) 9.98927e10 0.0271501
\(621\) 3.81957e12 1.03063
\(622\) −2.23481e12 −0.598665
\(623\) −1.95772e11 −0.0520660
\(624\) 1.44452e13 3.81411
\(625\) 1.09771e12 0.287759
\(626\) 1.13911e13 2.96470
\(627\) −1.54746e12 −0.399866
\(628\) −2.39561e12 −0.614607
\(629\) 0 0
\(630\) −2.19304e12 −0.554644
\(631\) 2.70305e12 0.678770 0.339385 0.940648i \(-0.389781\pi\)
0.339385 + 0.940648i \(0.389781\pi\)
\(632\) −1.92648e12 −0.480327
\(633\) −2.53895e12 −0.628545
\(634\) 2.80772e10 0.00690165
\(635\) −1.24891e11 −0.0304825
\(636\) −3.92549e12 −0.951342
\(637\) 1.69167e12 0.407088
\(638\) 9.84812e12 2.35321
\(639\) 1.91051e12 0.453311
\(640\) −7.39558e12 −1.74246
\(641\) −2.11271e10 −0.00494286 −0.00247143 0.999997i \(-0.500787\pi\)
−0.00247143 + 0.999997i \(0.500787\pi\)
\(642\) −4.40212e12 −1.02271
\(643\) −6.38463e12 −1.47294 −0.736472 0.676468i \(-0.763510\pi\)
−0.736472 + 0.676468i \(0.763510\pi\)
\(644\) −1.09613e13 −2.51116
\(645\) −4.63960e10 −0.0105551
\(646\) 0 0
\(647\) −6.90284e12 −1.54867 −0.774334 0.632777i \(-0.781915\pi\)
−0.774334 + 0.632777i \(0.781915\pi\)
\(648\) −9.19662e11 −0.204899
\(649\) −4.78271e12 −1.05821
\(650\) −1.11003e13 −2.43906
\(651\) 4.63473e10 0.0101137
\(652\) 6.65172e12 1.44152
\(653\) 6.56358e11 0.141264 0.0706319 0.997502i \(-0.477498\pi\)
0.0706319 + 0.997502i \(0.477498\pi\)
\(654\) −4.41802e12 −0.944338
\(655\) −3.05990e12 −0.649563
\(656\) −2.65935e13 −5.60670
\(657\) 1.97608e11 0.0413771
\(658\) 2.50129e12 0.520173
\(659\) −4.39856e12 −0.908503 −0.454251 0.890874i \(-0.650093\pi\)
−0.454251 + 0.890874i \(0.650093\pi\)
\(660\) 3.01240e12 0.617966
\(661\) −8.91098e12 −1.81559 −0.907797 0.419410i \(-0.862237\pi\)
−0.907797 + 0.419410i \(0.862237\pi\)
\(662\) 1.10423e13 2.23460
\(663\) 0 0
\(664\) 8.68701e12 1.73426
\(665\) 2.02566e12 0.401670
\(666\) 9.85256e12 1.94051
\(667\) 8.80363e12 1.72225
\(668\) −3.07608e11 −0.0597728
\(669\) −3.85615e12 −0.744281
\(670\) −8.52886e12 −1.63514
\(671\) −1.44558e12 −0.275290
\(672\) −1.07191e13 −2.02768
\(673\) −1.29085e11 −0.0242554 −0.0121277 0.999926i \(-0.503860\pi\)
−0.0121277 + 0.999926i \(0.503860\pi\)
\(674\) 1.18742e13 2.21632
\(675\) −3.91217e12 −0.725356
\(676\) 2.83328e13 5.21831
\(677\) −2.61666e12 −0.478738 −0.239369 0.970929i \(-0.576941\pi\)
−0.239369 + 0.970929i \(0.576941\pi\)
\(678\) 1.06310e13 1.93214
\(679\) −7.86924e12 −1.42075
\(680\) 0 0
\(681\) −1.11055e11 −0.0197868
\(682\) 1.57926e11 0.0279527
\(683\) −5.88812e12 −1.03534 −0.517671 0.855580i \(-0.673201\pi\)
−0.517671 + 0.855580i \(0.673201\pi\)
\(684\) 9.12621e12 1.59418
\(685\) −1.30694e12 −0.226802
\(686\) −1.21193e13 −2.08939
\(687\) −1.32435e12 −0.226829
\(688\) 7.66748e11 0.130468
\(689\) −5.88288e12 −0.994497
\(690\) 3.67674e12 0.617507
\(691\) 1.46603e12 0.244620 0.122310 0.992492i \(-0.460970\pi\)
0.122310 + 0.992492i \(0.460970\pi\)
\(692\) −2.29004e13 −3.79635
\(693\) −2.53936e12 −0.418240
\(694\) −5.30500e12 −0.868097
\(695\) −2.20846e12 −0.359053
\(696\) 2.02881e13 3.27718
\(697\) 0 0
\(698\) −2.16302e13 −3.44913
\(699\) −3.79153e10 −0.00600713
\(700\) 1.12270e13 1.76735
\(701\) 6.32038e12 0.988580 0.494290 0.869297i \(-0.335428\pi\)
0.494290 + 0.869297i \(0.335428\pi\)
\(702\) 2.07851e13 3.23024
\(703\) −9.10058e12 −1.40530
\(704\) −1.83370e13 −2.81352
\(705\) −6.14504e11 −0.0936858
\(706\) −1.13547e13 −1.72011
\(707\) 3.71156e12 0.558688
\(708\) −1.55247e13 −2.32207
\(709\) 3.78053e12 0.561882 0.280941 0.959725i \(-0.409354\pi\)
0.280941 + 0.959725i \(0.409354\pi\)
\(710\) 4.69036e12 0.692697
\(711\) −6.28634e11 −0.0922539
\(712\) −1.37426e12 −0.200405
\(713\) 1.41177e11 0.0204578
\(714\) 0 0
\(715\) 4.51449e12 0.645998
\(716\) 1.16609e13 1.65815
\(717\) −5.03331e12 −0.711242
\(718\) −2.47016e13 −3.46869
\(719\) −9.62888e12 −1.34368 −0.671840 0.740696i \(-0.734496\pi\)
−0.671840 + 0.740696i \(0.734496\pi\)
\(720\) −8.90388e12 −1.23476
\(721\) −4.70857e12 −0.648903
\(722\) 2.60584e12 0.356886
\(723\) −1.63573e12 −0.222633
\(724\) 7.91955e12 1.07122
\(725\) −9.01706e12 −1.21212
\(726\) −3.85941e12 −0.515593
\(727\) 9.26284e12 1.22981 0.614907 0.788600i \(-0.289194\pi\)
0.614907 + 0.788600i \(0.289194\pi\)
\(728\) −3.78562e13 −4.99512
\(729\) 4.15311e12 0.544627
\(730\) 4.85133e11 0.0632277
\(731\) 0 0
\(732\) −4.69236e12 −0.604075
\(733\) −3.26111e12 −0.417251 −0.208625 0.977996i \(-0.566899\pi\)
−0.208625 + 0.977996i \(0.566899\pi\)
\(734\) 2.19539e12 0.279177
\(735\) 5.73916e11 0.0725363
\(736\) −3.26512e13 −4.10155
\(737\) −9.87574e12 −1.23301
\(738\) −1.50036e13 −1.86184
\(739\) 1.43463e13 1.76946 0.884731 0.466101i \(-0.154342\pi\)
0.884731 + 0.466101i \(0.154342\pi\)
\(740\) 1.77159e13 2.17180
\(741\) −7.52773e12 −0.917239
\(742\) 8.12386e12 0.983886
\(743\) 5.86395e12 0.705896 0.352948 0.935643i \(-0.385179\pi\)
0.352948 + 0.935643i \(0.385179\pi\)
\(744\) 3.25344e11 0.0389282
\(745\) 1.80605e12 0.214796
\(746\) −1.05946e13 −1.25244
\(747\) 2.83468e12 0.333090
\(748\) 0 0
\(749\) 6.67250e12 0.774676
\(750\) −8.85445e12 −1.02185
\(751\) 7.70810e12 0.884234 0.442117 0.896957i \(-0.354228\pi\)
0.442117 + 0.896957i \(0.354228\pi\)
\(752\) 1.01554e13 1.15802
\(753\) 8.92332e12 1.01146
\(754\) 4.79070e13 5.39794
\(755\) −7.88192e11 −0.0882817
\(756\) −2.10224e13 −2.34064
\(757\) 9.90551e12 1.09634 0.548170 0.836367i \(-0.315325\pi\)
0.548170 + 0.836367i \(0.315325\pi\)
\(758\) 2.78512e13 3.06430
\(759\) 4.25737e12 0.465643
\(760\) 1.42195e13 1.54605
\(761\) 2.67093e12 0.288690 0.144345 0.989527i \(-0.453893\pi\)
0.144345 + 0.989527i \(0.453893\pi\)
\(762\) −6.40917e11 −0.0688659
\(763\) 6.69660e12 0.715309
\(764\) −6.34560e12 −0.673834
\(765\) 0 0
\(766\) −1.87959e12 −0.197257
\(767\) −2.32659e13 −2.42740
\(768\) −1.62067e13 −1.68101
\(769\) 2.81525e12 0.290301 0.145151 0.989410i \(-0.453633\pi\)
0.145151 + 0.989410i \(0.453633\pi\)
\(770\) −6.23420e12 −0.639106
\(771\) 1.13434e12 0.115611
\(772\) 3.85333e13 3.90444
\(773\) 1.90214e12 0.191617 0.0958085 0.995400i \(-0.469456\pi\)
0.0958085 + 0.995400i \(0.469456\pi\)
\(774\) 4.32586e11 0.0433250
\(775\) −1.44599e11 −0.0143982
\(776\) −5.52397e13 −5.46856
\(777\) 8.21966e12 0.809020
\(778\) −2.61160e13 −2.55563
\(779\) 1.38585e13 1.34833
\(780\) 1.46541e13 1.41753
\(781\) 5.43106e12 0.522342
\(782\) 0 0
\(783\) 1.68843e13 1.60530
\(784\) −9.48464e12 −0.896600
\(785\) −1.21799e12 −0.114480
\(786\) −1.57028e13 −1.46749
\(787\) 1.30989e13 1.21716 0.608580 0.793493i \(-0.291740\pi\)
0.608580 + 0.793493i \(0.291740\pi\)
\(788\) −2.10635e13 −1.94609
\(789\) 3.73727e12 0.343327
\(790\) −1.54331e12 −0.140972
\(791\) −1.61139e13 −1.46354
\(792\) −1.78256e13 −1.60983
\(793\) −7.03214e12 −0.631478
\(794\) −2.14984e13 −1.91961
\(795\) −1.99583e12 −0.177203
\(796\) 8.12286e12 0.717134
\(797\) −9.57855e12 −0.840886 −0.420443 0.907319i \(-0.638125\pi\)
−0.420443 + 0.907319i \(0.638125\pi\)
\(798\) 1.03953e13 0.907452
\(799\) 0 0
\(800\) 3.34427e13 2.88667
\(801\) −4.48439e11 −0.0384908
\(802\) 1.02753e13 0.877017
\(803\) 5.61745e11 0.0476781
\(804\) −3.20567e13 −2.70562
\(805\) −5.57301e12 −0.467744
\(806\) 7.68246e11 0.0641198
\(807\) 8.13935e12 0.675552
\(808\) 2.60541e13 2.15043
\(809\) 2.70995e12 0.222430 0.111215 0.993796i \(-0.464526\pi\)
0.111215 + 0.993796i \(0.464526\pi\)
\(810\) −7.36747e11 −0.0601361
\(811\) −8.05231e11 −0.0653622 −0.0326811 0.999466i \(-0.510405\pi\)
−0.0326811 + 0.999466i \(0.510405\pi\)
\(812\) −4.84540e13 −3.91136
\(813\) 7.20571e12 0.578455
\(814\) 2.80081e13 2.23601
\(815\) 3.38192e12 0.268506
\(816\) 0 0
\(817\) −3.99570e11 −0.0313757
\(818\) −5.74785e12 −0.448865
\(819\) −1.23530e13 −0.959386
\(820\) −2.69780e13 −2.08376
\(821\) 3.07077e12 0.235886 0.117943 0.993020i \(-0.462370\pi\)
0.117943 + 0.993020i \(0.462370\pi\)
\(822\) −6.70694e12 −0.512390
\(823\) 1.09157e13 0.829375 0.414688 0.909964i \(-0.363891\pi\)
0.414688 + 0.909964i \(0.363891\pi\)
\(824\) −3.30527e13 −2.49767
\(825\) −4.36058e12 −0.327719
\(826\) 3.21287e13 2.40150
\(827\) 4.38102e12 0.325687 0.162844 0.986652i \(-0.447933\pi\)
0.162844 + 0.986652i \(0.447933\pi\)
\(828\) −2.51081e13 −1.85642
\(829\) −9.43248e11 −0.0693634 −0.0346817 0.999398i \(-0.511042\pi\)
−0.0346817 + 0.999398i \(0.511042\pi\)
\(830\) 6.95922e12 0.508990
\(831\) −1.51896e12 −0.110494
\(832\) −8.92018e13 −6.45384
\(833\) 0 0
\(834\) −1.13334e13 −0.811171
\(835\) −1.56396e11 −0.0111336
\(836\) 2.59433e13 1.83695
\(837\) 2.70760e11 0.0190687
\(838\) −2.63023e13 −1.84245
\(839\) 1.06739e13 0.743695 0.371847 0.928294i \(-0.378724\pi\)
0.371847 + 0.928294i \(0.378724\pi\)
\(840\) −1.28431e13 −0.890047
\(841\) 2.44091e13 1.68256
\(842\) −5.08676e12 −0.348768
\(843\) 3.26472e12 0.222650
\(844\) 4.25657e13 2.88748
\(845\) 1.44052e13 0.971994
\(846\) 5.72950e12 0.384548
\(847\) 5.84990e12 0.390547
\(848\) 3.29834e13 2.19035
\(849\) −1.30474e13 −0.861863
\(850\) 0 0
\(851\) 2.50376e13 1.63647
\(852\) 1.76293e13 1.14619
\(853\) −1.66067e11 −0.0107402 −0.00537012 0.999986i \(-0.501709\pi\)
−0.00537012 + 0.999986i \(0.501709\pi\)
\(854\) 9.71091e12 0.624740
\(855\) 4.64002e12 0.296942
\(856\) 4.68389e13 2.98178
\(857\) −1.03151e13 −0.653223 −0.326611 0.945159i \(-0.605907\pi\)
−0.326611 + 0.945159i \(0.605907\pi\)
\(858\) 2.31675e13 1.45944
\(859\) 1.10331e12 0.0691398 0.0345699 0.999402i \(-0.488994\pi\)
0.0345699 + 0.999402i \(0.488994\pi\)
\(860\) 7.77833e11 0.0484890
\(861\) −1.25170e13 −0.776221
\(862\) −4.04163e13 −2.49329
\(863\) 1.58469e13 0.972514 0.486257 0.873816i \(-0.338362\pi\)
0.486257 + 0.873816i \(0.338362\pi\)
\(864\) −6.26211e13 −3.82304
\(865\) −1.16432e13 −0.707131
\(866\) 1.59403e13 0.963086
\(867\) 0 0
\(868\) −7.77017e11 −0.0464614
\(869\) −1.78703e12 −0.106302
\(870\) 1.62529e13 0.961823
\(871\) −4.80414e13 −2.82836
\(872\) 4.70081e13 2.75327
\(873\) −1.80254e13 −1.05032
\(874\) 3.16647e13 1.83558
\(875\) 1.34211e13 0.774020
\(876\) 1.82343e12 0.104621
\(877\) 3.07621e13 1.75597 0.877987 0.478684i \(-0.158886\pi\)
0.877987 + 0.478684i \(0.158886\pi\)
\(878\) 2.96995e13 1.68665
\(879\) −1.66640e13 −0.941517
\(880\) −2.53112e13 −1.42279
\(881\) 7.14002e10 0.00399308 0.00199654 0.999998i \(-0.499364\pi\)
0.00199654 + 0.999998i \(0.499364\pi\)
\(882\) −5.35108e12 −0.297737
\(883\) −2.91216e13 −1.61210 −0.806050 0.591847i \(-0.798399\pi\)
−0.806050 + 0.591847i \(0.798399\pi\)
\(884\) 0 0
\(885\) −7.89320e12 −0.432522
\(886\) 2.27860e13 1.24227
\(887\) −5.81157e12 −0.315237 −0.157618 0.987500i \(-0.550382\pi\)
−0.157618 + 0.987500i \(0.550382\pi\)
\(888\) 5.76995e13 3.11397
\(889\) 9.71469e11 0.0521640
\(890\) −1.10093e12 −0.0588171
\(891\) −8.53094e11 −0.0453468
\(892\) 6.46488e13 3.41916
\(893\) −5.29221e12 −0.278487
\(894\) 9.26829e12 0.485267
\(895\) 5.92874e12 0.308858
\(896\) 5.75267e13 2.98183
\(897\) 2.07103e13 1.06812
\(898\) 3.91555e13 2.00932
\(899\) 6.24068e11 0.0318650
\(900\) 2.57168e13 1.30655
\(901\) 0 0
\(902\) −4.26510e13 −2.14536
\(903\) 3.60892e11 0.0180627
\(904\) −1.13115e14 −5.63327
\(905\) 4.02652e12 0.199531
\(906\) −4.04484e12 −0.199446
\(907\) −2.77171e13 −1.35993 −0.679963 0.733246i \(-0.738004\pi\)
−0.679963 + 0.733246i \(0.738004\pi\)
\(908\) 1.86185e12 0.0908987
\(909\) 8.50178e12 0.413021
\(910\) −3.03268e13 −1.46602
\(911\) −2.12590e13 −1.02261 −0.511305 0.859399i \(-0.670838\pi\)
−0.511305 + 0.859399i \(0.670838\pi\)
\(912\) 4.22055e13 2.02019
\(913\) 8.05822e12 0.383814
\(914\) −8.55216e12 −0.405339
\(915\) −2.38572e12 −0.112519
\(916\) 2.22029e13 1.04203
\(917\) 2.38015e13 1.11158
\(918\) 0 0
\(919\) 3.16408e13 1.46328 0.731641 0.681690i \(-0.238755\pi\)
0.731641 + 0.681690i \(0.238755\pi\)
\(920\) −3.91208e13 −1.80037
\(921\) 1.21945e13 0.558464
\(922\) 3.03849e13 1.38474
\(923\) 2.64198e13 1.19818
\(924\) −2.34320e13 −1.05751
\(925\) −2.56446e13 −1.15175
\(926\) −6.31251e13 −2.82132
\(927\) −1.07855e13 −0.479714
\(928\) −1.44334e14 −6.38855
\(929\) −2.81954e13 −1.24196 −0.620980 0.783827i \(-0.713265\pi\)
−0.620980 + 0.783827i \(0.713265\pi\)
\(930\) 2.60635e11 0.0114251
\(931\) 4.94267e12 0.215619
\(932\) 6.35654e11 0.0275962
\(933\) −4.27069e12 −0.184515
\(934\) 7.58203e13 3.26005
\(935\) 0 0
\(936\) −8.67141e13 −3.69274
\(937\) −1.91653e13 −0.812244 −0.406122 0.913819i \(-0.633119\pi\)
−0.406122 + 0.913819i \(0.633119\pi\)
\(938\) 6.63419e13 2.79818
\(939\) 2.17682e13 0.913750
\(940\) 1.03022e13 0.430384
\(941\) −5.92110e11 −0.0246178 −0.0123089 0.999924i \(-0.503918\pi\)
−0.0123089 + 0.999924i \(0.503918\pi\)
\(942\) −6.25050e12 −0.258634
\(943\) −3.81275e13 −1.57013
\(944\) 1.30444e14 5.34628
\(945\) −1.06884e13 −0.435982
\(946\) 1.22972e12 0.0499226
\(947\) 2.32692e13 0.940171 0.470085 0.882621i \(-0.344223\pi\)
0.470085 + 0.882621i \(0.344223\pi\)
\(948\) −5.80072e12 −0.233262
\(949\) 2.73266e12 0.109367
\(950\) −3.24323e13 −1.29188
\(951\) 5.36552e10 0.00212716
\(952\) 0 0
\(953\) 3.58962e13 1.40971 0.704856 0.709351i \(-0.251012\pi\)
0.704856 + 0.709351i \(0.251012\pi\)
\(954\) 1.86087e13 0.727357
\(955\) −3.22628e12 −0.125512
\(956\) 8.43840e13 3.26738
\(957\) 1.88196e13 0.725282
\(958\) 2.01693e13 0.773654
\(959\) 1.01660e13 0.388121
\(960\) −3.02626e13 −1.14997
\(961\) −2.64296e13 −0.999621
\(962\) 1.36248e14 5.12911
\(963\) 1.52841e13 0.572694
\(964\) 2.74232e13 1.02275
\(965\) 1.95914e13 0.727265
\(966\) −2.85996e13 −1.05673
\(967\) −2.74118e13 −1.00813 −0.504067 0.863664i \(-0.668164\pi\)
−0.504067 + 0.863664i \(0.668164\pi\)
\(968\) 4.10645e13 1.50324
\(969\) 0 0
\(970\) −4.42528e13 −1.60497
\(971\) −4.52819e13 −1.63470 −0.817350 0.576141i \(-0.804558\pi\)
−0.817350 + 0.576141i \(0.804558\pi\)
\(972\) −7.74276e13 −2.78226
\(973\) 1.71786e13 0.614439
\(974\) 5.73596e13 2.04217
\(975\) −2.12124e13 −0.751743
\(976\) 3.94269e13 1.39081
\(977\) 9.97230e12 0.350163 0.175081 0.984554i \(-0.443981\pi\)
0.175081 + 0.984554i \(0.443981\pi\)
\(978\) 1.73553e13 0.606608
\(979\) −1.27479e12 −0.0443522
\(980\) −9.62177e12 −0.333225
\(981\) 1.53394e13 0.528806
\(982\) 1.06133e13 0.364208
\(983\) 1.25146e13 0.427491 0.213745 0.976889i \(-0.431434\pi\)
0.213745 + 0.976889i \(0.431434\pi\)
\(984\) −8.78654e13 −2.98772
\(985\) −1.07093e13 −0.362491
\(986\) 0 0
\(987\) 4.77993e12 0.160322
\(988\) 1.26203e14 4.21371
\(989\) 1.09930e12 0.0365369
\(990\) −1.42802e13 −0.472471
\(991\) 2.64145e12 0.0869982 0.0434991 0.999053i \(-0.486149\pi\)
0.0434991 + 0.999053i \(0.486149\pi\)
\(992\) −2.31456e12 −0.0758868
\(993\) 2.11017e13 0.688726
\(994\) −3.64840e13 −1.18540
\(995\) 4.12989e12 0.133578
\(996\) 2.61570e13 0.842212
\(997\) 1.22459e13 0.392520 0.196260 0.980552i \(-0.437120\pi\)
0.196260 + 0.980552i \(0.437120\pi\)
\(998\) 8.13174e13 2.59475
\(999\) 4.80192e13 1.52535
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.1.2 36
17.16 even 2 289.10.a.h.1.2 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.2 36 1.1 even 1 trivial
289.10.a.h.1.2 yes 36 17.16 even 2