Properties

Label 289.10.a.h.1.33
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $0$
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: \(0\)
Dimension: \(36\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.33
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q+38.8851 q^{2} -39.5980 q^{3} +1000.05 q^{4} -1326.61 q^{5} -1539.77 q^{6} +2031.17 q^{7} +18977.8 q^{8} -18115.0 q^{9} +O(q^{10})\) \(q+38.8851 q^{2} -39.5980 q^{3} +1000.05 q^{4} -1326.61 q^{5} -1539.77 q^{6} +2031.17 q^{7} +18977.8 q^{8} -18115.0 q^{9} -51585.4 q^{10} +79765.4 q^{11} -39600.0 q^{12} +19866.3 q^{13} +78982.0 q^{14} +52531.2 q^{15} +225928. q^{16} -704403. q^{18} -430239. q^{19} -1.32668e6 q^{20} -80430.2 q^{21} +3.10168e6 q^{22} +1.47745e6 q^{23} -751484. q^{24} -193226. q^{25} +772501. q^{26} +1.49673e6 q^{27} +2.03126e6 q^{28} -5.01398e6 q^{29} +2.04268e6 q^{30} +8.00000e6 q^{31} -931397. q^{32} -3.15856e6 q^{33} -2.69457e6 q^{35} -1.81159e7 q^{36} +688170. q^{37} -1.67299e7 q^{38} -786665. q^{39} -2.51762e7 q^{40} +8.23001e6 q^{41} -3.12753e6 q^{42} +4.37889e7 q^{43} +7.97693e7 q^{44} +2.40316e7 q^{45} +5.74509e7 q^{46} -3.64741e7 q^{47} -8.94632e6 q^{48} -3.62280e7 q^{49} -7.51362e6 q^{50} +1.98672e7 q^{52} +5.12196e7 q^{53} +5.82003e7 q^{54} -1.05818e8 q^{55} +3.85471e7 q^{56} +1.70366e7 q^{57} -1.94969e8 q^{58} +1.34598e8 q^{59} +5.25338e7 q^{60} +9.39211e7 q^{61} +3.11081e8 q^{62} -3.67946e7 q^{63} -1.51893e8 q^{64} -2.63548e7 q^{65} -1.22821e8 q^{66} +1.29800e8 q^{67} -5.85043e7 q^{69} -1.04778e8 q^{70} +2.39269e7 q^{71} -3.43783e8 q^{72} +4.14566e8 q^{73} +2.67595e7 q^{74} +7.65139e6 q^{75} -4.30260e8 q^{76} +1.62017e8 q^{77} -3.05895e7 q^{78} +3.87393e8 q^{79} -2.99719e8 q^{80} +2.97290e8 q^{81} +3.20024e8 q^{82} +2.80744e8 q^{83} -8.04341e7 q^{84} +1.70274e9 q^{86} +1.98544e8 q^{87} +1.51377e9 q^{88} +9.07508e8 q^{89} +9.34469e8 q^{90} +4.03516e7 q^{91} +1.47753e9 q^{92} -3.16784e8 q^{93} -1.41830e9 q^{94} +5.70760e8 q^{95} +3.68815e7 q^{96} -1.62096e9 q^{97} -1.40873e9 q^{98} -1.44495e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q + 486q^{3} + 9216q^{4} + 3750q^{5} + 11061q^{6} + 29040q^{7} + 24837q^{8} + 236196q^{9} + 60000q^{10} + 76902q^{11} + 373248q^{12} + 54216q^{13} + 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} + 6439479q^{20} - 138102q^{21} + 267324q^{22} + 4041462q^{23} + 7653888q^{24} + 16582356q^{25} + 15822744q^{26} + 13281612q^{27} + 18614784q^{28} + 4005936q^{29} + 22471686q^{30} + 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} + 22076682q^{37} - 27401376q^{38} + 62736162q^{39} - 12231630q^{40} + 59641782q^{41} + 150001536q^{42} - 47951586q^{43} - 49578936q^{44} + 129308238q^{45} + 140524827q^{46} - 118557912q^{47} + 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} + 209848575q^{54} - 365439924q^{55} + 203095059q^{56} - 4614108q^{57} - 179071413q^{58} + 343015128q^{59} + 427179186q^{60} + 175597116q^{61} + 720602571q^{62} + 587415936q^{63} + 853082511q^{64} + 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} + 1308709542q^{71} - 275337849q^{72} + 494841342q^{73} + 1545361890q^{74} + 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} + 2270624538q^{78} + 1980107868q^{79} + 2897000199q^{80} + 1598298840q^{81} + 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} - 2705904618q^{88} + 148394658q^{89} + 117916215q^{90} + 636340896q^{91} - 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} + 4878626298q^{95} - 8390096634q^{96} - 891786822q^{97} + 4285627647q^{98} - 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 38.8851 1.71849 0.859247 0.511561i \(-0.170933\pi\)
0.859247 + 0.511561i \(0.170933\pi\)
\(3\) −39.5980 −0.282246 −0.141123 0.989992i \(-0.545071\pi\)
−0.141123 + 0.989992i \(0.545071\pi\)
\(4\) 1000.05 1.95322
\(5\) −1326.61 −0.949246 −0.474623 0.880189i \(-0.657416\pi\)
−0.474623 + 0.880189i \(0.657416\pi\)
\(6\) −1539.77 −0.485038
\(7\) 2031.17 0.319745 0.159873 0.987138i \(-0.448892\pi\)
0.159873 + 0.987138i \(0.448892\pi\)
\(8\) 18977.8 1.63810
\(9\) −18115.0 −0.920337
\(10\) −51585.4 −1.63127
\(11\) 79765.4 1.64266 0.821330 0.570453i \(-0.193233\pi\)
0.821330 + 0.570453i \(0.193233\pi\)
\(12\) −39600.0 −0.551289
\(13\) 19866.3 0.192917 0.0964586 0.995337i \(-0.469248\pi\)
0.0964586 + 0.995337i \(0.469248\pi\)
\(14\) 78982.0 0.549480
\(15\) 52531.2 0.267921
\(16\) 225928. 0.861848
\(17\) 0 0
\(18\) −704403. −1.58159
\(19\) −430239. −0.757388 −0.378694 0.925522i \(-0.623627\pi\)
−0.378694 + 0.925522i \(0.623627\pi\)
\(20\) −1.32668e6 −1.85409
\(21\) −80430.2 −0.0902469
\(22\) 3.10168e6 2.82290
\(23\) 1.47745e6 1.10088 0.550438 0.834876i \(-0.314461\pi\)
0.550438 + 0.834876i \(0.314461\pi\)
\(24\) −751484. −0.462348
\(25\) −193226. −0.0989319
\(26\) 772501. 0.331527
\(27\) 1.49673e6 0.542008
\(28\) 2.03126e6 0.624533
\(29\) −5.01398e6 −1.31641 −0.658206 0.752838i \(-0.728684\pi\)
−0.658206 + 0.752838i \(0.728684\pi\)
\(30\) 2.04268e6 0.460421
\(31\) 8.00000e6 1.55583 0.777915 0.628369i \(-0.216277\pi\)
0.777915 + 0.628369i \(0.216277\pi\)
\(32\) −931397. −0.157022
\(33\) −3.15856e6 −0.463635
\(34\) 0 0
\(35\) −2.69457e6 −0.303517
\(36\) −1.81159e7 −1.79762
\(37\) 688170. 0.0603653 0.0301827 0.999544i \(-0.490391\pi\)
0.0301827 + 0.999544i \(0.490391\pi\)
\(38\) −1.67299e7 −1.30157
\(39\) −786665. −0.0544501
\(40\) −2.51762e7 −1.55496
\(41\) 8.23001e6 0.454855 0.227427 0.973795i \(-0.426969\pi\)
0.227427 + 0.973795i \(0.426969\pi\)
\(42\) −3.12753e6 −0.155089
\(43\) 4.37889e7 1.95324 0.976621 0.214967i \(-0.0689644\pi\)
0.976621 + 0.214967i \(0.0689644\pi\)
\(44\) 7.97693e7 3.20848
\(45\) 2.40316e7 0.873626
\(46\) 5.74509e7 1.89185
\(47\) −3.64741e7 −1.09030 −0.545148 0.838340i \(-0.683526\pi\)
−0.545148 + 0.838340i \(0.683526\pi\)
\(48\) −8.94632e6 −0.243253
\(49\) −3.62280e7 −0.897763
\(50\) −7.51362e6 −0.170014
\(51\) 0 0
\(52\) 1.98672e7 0.376810
\(53\) 5.12196e7 0.891651 0.445826 0.895120i \(-0.352910\pi\)
0.445826 + 0.895120i \(0.352910\pi\)
\(54\) 5.82003e7 0.931437
\(55\) −1.05818e8 −1.55929
\(56\) 3.85471e7 0.523775
\(57\) 1.70366e7 0.213770
\(58\) −1.94969e8 −2.26225
\(59\) 1.34598e8 1.44612 0.723060 0.690785i \(-0.242735\pi\)
0.723060 + 0.690785i \(0.242735\pi\)
\(60\) 5.25338e7 0.523309
\(61\) 9.39211e7 0.868518 0.434259 0.900788i \(-0.357010\pi\)
0.434259 + 0.900788i \(0.357010\pi\)
\(62\) 3.11081e8 2.67369
\(63\) −3.67946e7 −0.294273
\(64\) −1.51893e8 −1.13169
\(65\) −2.63548e7 −0.183126
\(66\) −1.22821e8 −0.796753
\(67\) 1.29800e8 0.786934 0.393467 0.919339i \(-0.371276\pi\)
0.393467 + 0.919339i \(0.371276\pi\)
\(68\) 0 0
\(69\) −5.85043e7 −0.310718
\(70\) −1.04778e8 −0.521592
\(71\) 2.39269e7 0.111744 0.0558720 0.998438i \(-0.482206\pi\)
0.0558720 + 0.998438i \(0.482206\pi\)
\(72\) −3.43783e8 −1.50761
\(73\) 4.14566e8 1.70860 0.854301 0.519779i \(-0.173986\pi\)
0.854301 + 0.519779i \(0.173986\pi\)
\(74\) 2.67595e7 0.103737
\(75\) 7.65139e6 0.0279232
\(76\) −4.30260e8 −1.47935
\(77\) 1.62017e8 0.525233
\(78\) −3.05895e7 −0.0935722
\(79\) 3.87393e8 1.11900 0.559500 0.828830i \(-0.310993\pi\)
0.559500 + 0.828830i \(0.310993\pi\)
\(80\) −2.99719e8 −0.818106
\(81\) 2.97290e8 0.767357
\(82\) 3.20024e8 0.781665
\(83\) 2.80744e8 0.649319 0.324660 0.945831i \(-0.394750\pi\)
0.324660 + 0.945831i \(0.394750\pi\)
\(84\) −8.04341e7 −0.176272
\(85\) 0 0
\(86\) 1.70274e9 3.35663
\(87\) 1.98544e8 0.371552
\(88\) 1.51377e9 2.69084
\(89\) 9.07508e8 1.53319 0.766594 0.642132i \(-0.221950\pi\)
0.766594 + 0.642132i \(0.221950\pi\)
\(90\) 9.34469e8 1.50132
\(91\) 4.03516e7 0.0616843
\(92\) 1.47753e9 2.15025
\(93\) −3.16784e8 −0.439127
\(94\) −1.41830e9 −1.87367
\(95\) 5.70760e8 0.718948
\(96\) 3.68815e7 0.0443188
\(97\) −1.62096e9 −1.85908 −0.929542 0.368716i \(-0.879798\pi\)
−0.929542 + 0.368716i \(0.879798\pi\)
\(98\) −1.40873e9 −1.54280
\(99\) −1.44495e9 −1.51180
\(100\) −1.93236e8 −0.193236
\(101\) 1.25201e9 1.19719 0.598593 0.801053i \(-0.295727\pi\)
0.598593 + 0.801053i \(0.295727\pi\)
\(102\) 0 0
\(103\) −1.74839e8 −0.153063 −0.0765315 0.997067i \(-0.524385\pi\)
−0.0765315 + 0.997067i \(0.524385\pi\)
\(104\) 3.77018e8 0.316018
\(105\) 1.06700e8 0.0856665
\(106\) 1.99168e9 1.53230
\(107\) −1.01435e9 −0.748105 −0.374053 0.927407i \(-0.622032\pi\)
−0.374053 + 0.927407i \(0.622032\pi\)
\(108\) 1.49680e9 1.05866
\(109\) 6.13770e8 0.416472 0.208236 0.978079i \(-0.433228\pi\)
0.208236 + 0.978079i \(0.433228\pi\)
\(110\) −4.11473e9 −2.67963
\(111\) −2.72502e7 −0.0170379
\(112\) 4.58898e8 0.275572
\(113\) −5.73250e7 −0.0330743 −0.0165372 0.999863i \(-0.505264\pi\)
−0.0165372 + 0.999863i \(0.505264\pi\)
\(114\) 6.62470e8 0.367362
\(115\) −1.96001e9 −1.04500
\(116\) −5.01423e9 −2.57124
\(117\) −3.59877e8 −0.177549
\(118\) 5.23385e9 2.48515
\(119\) 0 0
\(120\) 9.96927e8 0.438882
\(121\) 4.00458e9 1.69833
\(122\) 3.65213e9 1.49254
\(123\) −3.25892e8 −0.128381
\(124\) 8.00039e9 3.03888
\(125\) 2.84737e9 1.04316
\(126\) −1.43076e9 −0.505707
\(127\) −5.54930e9 −1.89287 −0.946436 0.322892i \(-0.895345\pi\)
−0.946436 + 0.322892i \(0.895345\pi\)
\(128\) −5.42948e9 −1.78778
\(129\) −1.73396e9 −0.551295
\(130\) −1.02481e9 −0.314701
\(131\) −1.26351e9 −0.374851 −0.187425 0.982279i \(-0.560014\pi\)
−0.187425 + 0.982279i \(0.560014\pi\)
\(132\) −3.15871e9 −0.905580
\(133\) −8.73886e8 −0.242171
\(134\) 5.04728e9 1.35234
\(135\) −1.98558e9 −0.514499
\(136\) 0 0
\(137\) 3.64045e9 0.882903 0.441452 0.897285i \(-0.354464\pi\)
0.441452 + 0.897285i \(0.354464\pi\)
\(138\) −2.27494e9 −0.533967
\(139\) 2.14697e9 0.487820 0.243910 0.969798i \(-0.421570\pi\)
0.243910 + 0.969798i \(0.421570\pi\)
\(140\) −2.69470e9 −0.592835
\(141\) 1.44430e9 0.307732
\(142\) 9.30400e8 0.192031
\(143\) 1.58464e9 0.316897
\(144\) −4.09269e9 −0.793191
\(145\) 6.65161e9 1.24960
\(146\) 1.61204e10 2.93622
\(147\) 1.43456e9 0.253390
\(148\) 6.88203e8 0.117907
\(149\) −2.29251e9 −0.381041 −0.190521 0.981683i \(-0.561018\pi\)
−0.190521 + 0.981683i \(0.561018\pi\)
\(150\) 2.97525e8 0.0479858
\(151\) −2.31951e9 −0.363079 −0.181539 0.983384i \(-0.558108\pi\)
−0.181539 + 0.983384i \(0.558108\pi\)
\(152\) −8.16499e9 −1.24068
\(153\) 0 0
\(154\) 6.30003e9 0.902609
\(155\) −1.06129e10 −1.47687
\(156\) −7.86703e8 −0.106353
\(157\) −2.99512e9 −0.393429 −0.196714 0.980461i \(-0.563027\pi\)
−0.196714 + 0.980461i \(0.563027\pi\)
\(158\) 1.50638e10 1.92299
\(159\) −2.02820e9 −0.251665
\(160\) 1.23560e9 0.149052
\(161\) 3.00095e9 0.352000
\(162\) 1.15601e10 1.31870
\(163\) 2.18156e9 0.242060 0.121030 0.992649i \(-0.461380\pi\)
0.121030 + 0.992649i \(0.461380\pi\)
\(164\) 8.23041e9 0.888432
\(165\) 4.19018e9 0.440103
\(166\) 1.09167e10 1.11585
\(167\) 1.30714e10 1.30046 0.650232 0.759736i \(-0.274672\pi\)
0.650232 + 0.759736i \(0.274672\pi\)
\(168\) −1.52639e9 −0.147834
\(169\) −1.02098e10 −0.962783
\(170\) 0 0
\(171\) 7.79378e9 0.697052
\(172\) 4.37911e10 3.81511
\(173\) 2.58955e9 0.219794 0.109897 0.993943i \(-0.464948\pi\)
0.109897 + 0.993943i \(0.464948\pi\)
\(174\) 7.72039e9 0.638510
\(175\) −3.92475e8 −0.0316330
\(176\) 1.80213e10 1.41572
\(177\) −5.32982e9 −0.408162
\(178\) 3.52885e10 2.63477
\(179\) −6.20782e9 −0.451960 −0.225980 0.974132i \(-0.572558\pi\)
−0.225980 + 0.974132i \(0.572558\pi\)
\(180\) 2.40327e10 1.70638
\(181\) 1.12580e10 0.779664 0.389832 0.920886i \(-0.372533\pi\)
0.389832 + 0.920886i \(0.372533\pi\)
\(182\) 1.56908e9 0.106004
\(183\) −3.71909e9 −0.245136
\(184\) 2.80388e10 1.80335
\(185\) −9.12934e8 −0.0573016
\(186\) −1.23182e10 −0.754638
\(187\) 0 0
\(188\) −3.64759e10 −2.12959
\(189\) 3.04010e9 0.173304
\(190\) 2.21940e10 1.23551
\(191\) −2.49016e10 −1.35387 −0.676936 0.736042i \(-0.736693\pi\)
−0.676936 + 0.736042i \(0.736693\pi\)
\(192\) 6.01466e9 0.319415
\(193\) −2.70015e9 −0.140081 −0.0700407 0.997544i \(-0.522313\pi\)
−0.0700407 + 0.997544i \(0.522313\pi\)
\(194\) −6.30311e10 −3.19482
\(195\) 1.04360e9 0.0516866
\(196\) −3.62297e10 −1.75353
\(197\) 6.99326e8 0.0330813 0.0165406 0.999863i \(-0.494735\pi\)
0.0165406 + 0.999863i \(0.494735\pi\)
\(198\) −5.61870e10 −2.59802
\(199\) 1.79474e10 0.811267 0.405634 0.914036i \(-0.367051\pi\)
0.405634 + 0.914036i \(0.367051\pi\)
\(200\) −3.66701e9 −0.162061
\(201\) −5.13983e9 −0.222109
\(202\) 4.86845e10 2.05736
\(203\) −1.01842e10 −0.420916
\(204\) 0 0
\(205\) −1.09180e10 −0.431769
\(206\) −6.79861e9 −0.263038
\(207\) −2.67641e10 −1.01318
\(208\) 4.48835e9 0.166265
\(209\) −3.43182e10 −1.24413
\(210\) 4.14902e9 0.147217
\(211\) 1.27607e10 0.443202 0.221601 0.975137i \(-0.428872\pi\)
0.221601 + 0.975137i \(0.428872\pi\)
\(212\) 5.12221e10 1.74159
\(213\) −9.47459e8 −0.0315393
\(214\) −3.94432e10 −1.28561
\(215\) −5.80909e10 −1.85411
\(216\) 2.84046e10 0.887864
\(217\) 1.62493e10 0.497470
\(218\) 2.38665e10 0.715705
\(219\) −1.64160e10 −0.482246
\(220\) −1.05823e11 −3.04563
\(221\) 0 0
\(222\) −1.05962e9 −0.0292795
\(223\) 4.40038e10 1.19157 0.595783 0.803145i \(-0.296842\pi\)
0.595783 + 0.803145i \(0.296842\pi\)
\(224\) −1.89182e9 −0.0502070
\(225\) 3.50030e9 0.0910507
\(226\) −2.22909e9 −0.0568381
\(227\) 5.01424e9 0.125340 0.0626698 0.998034i \(-0.480038\pi\)
0.0626698 + 0.998034i \(0.480038\pi\)
\(228\) 1.70374e10 0.417540
\(229\) −4.24718e10 −1.02057 −0.510283 0.860007i \(-0.670459\pi\)
−0.510283 + 0.860007i \(0.670459\pi\)
\(230\) −7.62150e10 −1.79583
\(231\) −6.41555e9 −0.148245
\(232\) −9.51544e10 −2.15642
\(233\) −7.54306e10 −1.67666 −0.838332 0.545160i \(-0.816469\pi\)
−0.838332 + 0.545160i \(0.816469\pi\)
\(234\) −1.39938e10 −0.305116
\(235\) 4.83870e10 1.03496
\(236\) 1.34605e11 2.82459
\(237\) −1.53400e10 −0.315834
\(238\) 0 0
\(239\) −4.07962e10 −0.808778 −0.404389 0.914587i \(-0.632516\pi\)
−0.404389 + 0.914587i \(0.632516\pi\)
\(240\) 1.18683e10 0.230907
\(241\) −5.72156e10 −1.09254 −0.546271 0.837609i \(-0.683953\pi\)
−0.546271 + 0.837609i \(0.683953\pi\)
\(242\) 1.55718e11 2.91857
\(243\) −4.12322e10 −0.758592
\(244\) 9.39257e10 1.69641
\(245\) 4.80605e10 0.852198
\(246\) −1.26723e10 −0.220622
\(247\) −8.54723e9 −0.146113
\(248\) 1.51822e11 2.54861
\(249\) −1.11169e10 −0.183268
\(250\) 1.10720e11 1.79266
\(251\) −2.21629e10 −0.352448 −0.176224 0.984350i \(-0.556388\pi\)
−0.176224 + 0.984350i \(0.556388\pi\)
\(252\) −3.67963e10 −0.574781
\(253\) 1.17850e11 1.80837
\(254\) −2.15785e11 −3.25289
\(255\) 0 0
\(256\) −1.33357e11 −1.94060
\(257\) −8.84957e10 −1.26539 −0.632693 0.774402i \(-0.718051\pi\)
−0.632693 + 0.774402i \(0.718051\pi\)
\(258\) −6.74250e10 −0.947398
\(259\) 1.39779e9 0.0193015
\(260\) −2.63561e10 −0.357685
\(261\) 9.08283e10 1.21154
\(262\) −4.91317e10 −0.644179
\(263\) 6.15949e10 0.793860 0.396930 0.917849i \(-0.370076\pi\)
0.396930 + 0.917849i \(0.370076\pi\)
\(264\) −5.99424e10 −0.759481
\(265\) −6.79485e10 −0.846396
\(266\) −3.39811e10 −0.416170
\(267\) −3.59355e10 −0.432736
\(268\) 1.29806e11 1.53705
\(269\) −4.19152e10 −0.488075 −0.244037 0.969766i \(-0.578472\pi\)
−0.244037 + 0.969766i \(0.578472\pi\)
\(270\) −7.72092e10 −0.884163
\(271\) 1.56140e11 1.75854 0.879272 0.476319i \(-0.158029\pi\)
0.879272 + 0.476319i \(0.158029\pi\)
\(272\) 0 0
\(273\) −1.59785e9 −0.0174102
\(274\) 1.41559e11 1.51726
\(275\) −1.54128e10 −0.162511
\(276\) −5.85071e10 −0.606901
\(277\) 1.43796e11 1.46753 0.733765 0.679404i \(-0.237762\pi\)
0.733765 + 0.679404i \(0.237762\pi\)
\(278\) 8.34851e10 0.838316
\(279\) −1.44920e11 −1.43189
\(280\) −5.11370e10 −0.497192
\(281\) 8.85329e10 0.847083 0.423542 0.905877i \(-0.360787\pi\)
0.423542 + 0.905877i \(0.360787\pi\)
\(282\) 5.61618e10 0.528835
\(283\) −1.83307e10 −0.169879 −0.0849394 0.996386i \(-0.527070\pi\)
−0.0849394 + 0.996386i \(0.527070\pi\)
\(284\) 2.39281e10 0.218261
\(285\) −2.26010e10 −0.202920
\(286\) 6.16188e10 0.544586
\(287\) 1.67165e10 0.145438
\(288\) 1.68722e10 0.144513
\(289\) 0 0
\(290\) 2.58648e11 2.14743
\(291\) 6.41868e10 0.524720
\(292\) 4.14586e11 3.33727
\(293\) −8.61025e10 −0.682514 −0.341257 0.939970i \(-0.610853\pi\)
−0.341257 + 0.939970i \(0.610853\pi\)
\(294\) 5.57829e10 0.435449
\(295\) −1.78559e11 −1.37272
\(296\) 1.30599e10 0.0988846
\(297\) 1.19387e11 0.890335
\(298\) −8.91442e10 −0.654817
\(299\) 2.93515e10 0.212378
\(300\) 7.65176e9 0.0545401
\(301\) 8.89426e10 0.624540
\(302\) −9.01945e10 −0.623949
\(303\) −4.95772e10 −0.337901
\(304\) −9.72032e10 −0.652754
\(305\) −1.24597e11 −0.824438
\(306\) 0 0
\(307\) −1.18874e11 −0.763775 −0.381887 0.924209i \(-0.624726\pi\)
−0.381887 + 0.924209i \(0.624726\pi\)
\(308\) 1.62025e11 1.02590
\(309\) 6.92327e9 0.0432014
\(310\) −4.12683e11 −2.53798
\(311\) 2.72867e11 1.65397 0.826987 0.562220i \(-0.190053\pi\)
0.826987 + 0.562220i \(0.190053\pi\)
\(312\) −1.49292e10 −0.0891949
\(313\) −1.05123e11 −0.619080 −0.309540 0.950886i \(-0.600175\pi\)
−0.309540 + 0.950886i \(0.600175\pi\)
\(314\) −1.16466e11 −0.676105
\(315\) 4.88121e10 0.279338
\(316\) 3.87412e11 2.18565
\(317\) 1.75077e11 0.973781 0.486891 0.873463i \(-0.338131\pi\)
0.486891 + 0.873463i \(0.338131\pi\)
\(318\) −7.88666e10 −0.432485
\(319\) −3.99942e11 −2.16242
\(320\) 2.01503e11 1.07425
\(321\) 4.01664e10 0.211150
\(322\) 1.16692e11 0.604910
\(323\) 0 0
\(324\) 2.97304e11 1.49882
\(325\) −3.83868e9 −0.0190857
\(326\) 8.48300e10 0.415978
\(327\) −2.43041e10 −0.117548
\(328\) 1.56187e11 0.745099
\(329\) −7.40849e10 −0.348617
\(330\) 1.62935e11 0.756315
\(331\) −1.62608e11 −0.744588 −0.372294 0.928115i \(-0.621429\pi\)
−0.372294 + 0.928115i \(0.621429\pi\)
\(332\) 2.80757e11 1.26826
\(333\) −1.24662e10 −0.0555565
\(334\) 5.08282e11 2.23484
\(335\) −1.72194e11 −0.746994
\(336\) −1.81715e10 −0.0777791
\(337\) 5.36814e10 0.226720 0.113360 0.993554i \(-0.463839\pi\)
0.113360 + 0.993554i \(0.463839\pi\)
\(338\) −3.97010e11 −1.65454
\(339\) 2.26996e9 0.00933511
\(340\) 0 0
\(341\) 6.38123e11 2.55570
\(342\) 3.03061e11 1.19788
\(343\) −1.55550e11 −0.606801
\(344\) 8.31018e11 3.19961
\(345\) 7.76124e10 0.294948
\(346\) 1.00695e11 0.377715
\(347\) 1.15461e11 0.427517 0.213758 0.976887i \(-0.431430\pi\)
0.213758 + 0.976887i \(0.431430\pi\)
\(348\) 1.98554e11 0.725723
\(349\) 1.42013e11 0.512404 0.256202 0.966623i \(-0.417529\pi\)
0.256202 + 0.966623i \(0.417529\pi\)
\(350\) −1.52614e10 −0.0543611
\(351\) 2.97344e10 0.104563
\(352\) −7.42933e10 −0.257933
\(353\) 3.90958e11 1.34012 0.670060 0.742307i \(-0.266268\pi\)
0.670060 + 0.742307i \(0.266268\pi\)
\(354\) −2.07250e11 −0.701424
\(355\) −3.17417e10 −0.106073
\(356\) 9.07552e11 2.99465
\(357\) 0 0
\(358\) −2.41391e11 −0.776691
\(359\) −4.03346e11 −1.28160 −0.640800 0.767708i \(-0.721397\pi\)
−0.640800 + 0.767708i \(0.721397\pi\)
\(360\) 4.56066e11 1.43109
\(361\) −1.37582e11 −0.426363
\(362\) 4.37768e11 1.33985
\(363\) −1.58573e11 −0.479348
\(364\) 4.03536e10 0.120483
\(365\) −5.49968e11 −1.62188
\(366\) −1.44617e11 −0.421265
\(367\) −1.76479e11 −0.507803 −0.253901 0.967230i \(-0.581714\pi\)
−0.253901 + 0.967230i \(0.581714\pi\)
\(368\) 3.33799e11 0.948788
\(369\) −1.49087e11 −0.418620
\(370\) −3.54995e10 −0.0984724
\(371\) 1.04036e11 0.285101
\(372\) −3.16800e11 −0.857712
\(373\) −1.09830e11 −0.293786 −0.146893 0.989152i \(-0.546927\pi\)
−0.146893 + 0.989152i \(0.546927\pi\)
\(374\) 0 0
\(375\) −1.12750e11 −0.294427
\(376\) −6.92198e11 −1.78601
\(377\) −9.96090e10 −0.253958
\(378\) 1.18215e11 0.297823
\(379\) 2.01826e11 0.502459 0.251230 0.967928i \(-0.419165\pi\)
0.251230 + 0.967928i \(0.419165\pi\)
\(380\) 5.70788e11 1.40426
\(381\) 2.19741e11 0.534256
\(382\) −9.68302e11 −2.32662
\(383\) −4.10697e11 −0.975275 −0.487638 0.873046i \(-0.662141\pi\)
−0.487638 + 0.873046i \(0.662141\pi\)
\(384\) 2.14997e11 0.504594
\(385\) −2.14933e11 −0.498575
\(386\) −1.04996e11 −0.240729
\(387\) −7.93236e11 −1.79764
\(388\) −1.62104e12 −3.63120
\(389\) 8.47825e11 1.87730 0.938649 0.344875i \(-0.112079\pi\)
0.938649 + 0.344875i \(0.112079\pi\)
\(390\) 4.05804e10 0.0888230
\(391\) 0 0
\(392\) −6.87527e11 −1.47063
\(393\) 5.00326e10 0.105800
\(394\) 2.71934e10 0.0568499
\(395\) −5.13921e11 −1.06221
\(396\) −1.44502e12 −2.95288
\(397\) 1.38204e11 0.279231 0.139615 0.990206i \(-0.455413\pi\)
0.139615 + 0.990206i \(0.455413\pi\)
\(398\) 6.97888e11 1.39416
\(399\) 3.46042e10 0.0683519
\(400\) −4.36553e10 −0.0852643
\(401\) −8.10829e11 −1.56596 −0.782978 0.622050i \(-0.786300\pi\)
−0.782978 + 0.622050i \(0.786300\pi\)
\(402\) −1.99863e11 −0.381693
\(403\) 1.58930e11 0.300146
\(404\) 1.25207e12 2.33837
\(405\) −3.94388e11 −0.728411
\(406\) −3.96014e11 −0.723342
\(407\) 5.48921e10 0.0991597
\(408\) 0 0
\(409\) 5.60175e11 0.989849 0.494924 0.868936i \(-0.335196\pi\)
0.494924 + 0.868936i \(0.335196\pi\)
\(410\) −4.24548e11 −0.741993
\(411\) −1.44155e11 −0.249196
\(412\) −1.74847e11 −0.298966
\(413\) 2.73391e11 0.462390
\(414\) −1.04072e12 −1.74114
\(415\) −3.72438e11 −0.616364
\(416\) −1.85034e10 −0.0302922
\(417\) −8.50159e10 −0.137685
\(418\) −1.33447e12 −2.13803
\(419\) −9.94635e11 −1.57652 −0.788262 0.615340i \(-0.789019\pi\)
−0.788262 + 0.615340i \(0.789019\pi\)
\(420\) 1.06705e11 0.167326
\(421\) −4.43656e11 −0.688299 −0.344149 0.938915i \(-0.611833\pi\)
−0.344149 + 0.938915i \(0.611833\pi\)
\(422\) 4.96199e11 0.761640
\(423\) 6.60728e11 1.00344
\(424\) 9.72036e11 1.46062
\(425\) 0 0
\(426\) −3.68420e10 −0.0542001
\(427\) 1.90769e11 0.277705
\(428\) −1.01440e12 −1.46121
\(429\) −6.27487e10 −0.0894430
\(430\) −2.25887e12 −3.18627
\(431\) −7.58706e11 −1.05907 −0.529536 0.848287i \(-0.677634\pi\)
−0.529536 + 0.848287i \(0.677634\pi\)
\(432\) 3.38153e11 0.467129
\(433\) 1.31991e12 1.80447 0.902234 0.431246i \(-0.141926\pi\)
0.902234 + 0.431246i \(0.141926\pi\)
\(434\) 6.31856e11 0.854898
\(435\) −2.63391e11 −0.352695
\(436\) 6.13800e11 0.813462
\(437\) −6.35658e11 −0.833790
\(438\) −6.38337e11 −0.828737
\(439\) −3.84672e11 −0.494312 −0.247156 0.968976i \(-0.579496\pi\)
−0.247156 + 0.968976i \(0.579496\pi\)
\(440\) −2.00819e12 −2.55427
\(441\) 6.56270e11 0.826245
\(442\) 0 0
\(443\) 3.34971e11 0.413228 0.206614 0.978423i \(-0.433756\pi\)
0.206614 + 0.978423i \(0.433756\pi\)
\(444\) −2.72515e10 −0.0332788
\(445\) −1.20391e12 −1.45537
\(446\) 1.71109e12 2.04770
\(447\) 9.07787e10 0.107547
\(448\) −3.08519e11 −0.361852
\(449\) 1.09901e12 1.27612 0.638060 0.769986i \(-0.279737\pi\)
0.638060 + 0.769986i \(0.279737\pi\)
\(450\) 1.36109e11 0.156470
\(451\) 6.56470e11 0.747172
\(452\) −5.73278e10 −0.0646015
\(453\) 9.18483e10 0.102478
\(454\) 1.94979e11 0.215395
\(455\) −5.35310e10 −0.0585536
\(456\) 3.23318e11 0.350177
\(457\) 1.31545e12 1.41075 0.705376 0.708833i \(-0.250778\pi\)
0.705376 + 0.708833i \(0.250778\pi\)
\(458\) −1.65152e12 −1.75384
\(459\) 0 0
\(460\) −1.96010e12 −2.04112
\(461\) −1.21831e12 −1.25633 −0.628163 0.778082i \(-0.716193\pi\)
−0.628163 + 0.778082i \(0.716193\pi\)
\(462\) −2.49469e11 −0.254758
\(463\) −1.04671e12 −1.05856 −0.529278 0.848449i \(-0.677537\pi\)
−0.529278 + 0.848449i \(0.677537\pi\)
\(464\) −1.13280e12 −1.13455
\(465\) 4.20250e11 0.416840
\(466\) −2.93312e12 −2.88134
\(467\) 5.48990e11 0.534119 0.267060 0.963680i \(-0.413948\pi\)
0.267060 + 0.963680i \(0.413948\pi\)
\(468\) −3.59895e11 −0.346792
\(469\) 2.63645e11 0.251618
\(470\) 1.88153e12 1.77857
\(471\) 1.18601e11 0.111044
\(472\) 2.55437e12 2.36889
\(473\) 3.49284e12 3.20851
\(474\) −5.96498e11 −0.542758
\(475\) 8.31335e10 0.0749299
\(476\) 0 0
\(477\) −9.27843e11 −0.820619
\(478\) −1.58636e12 −1.38988
\(479\) −8.94844e11 −0.776672 −0.388336 0.921518i \(-0.626950\pi\)
−0.388336 + 0.921518i \(0.626950\pi\)
\(480\) −4.89274e10 −0.0420694
\(481\) 1.36713e10 0.0116455
\(482\) −2.22483e12 −1.87753
\(483\) −1.18832e11 −0.0993507
\(484\) 4.00477e12 3.31721
\(485\) 2.15038e12 1.76473
\(486\) −1.60332e12 −1.30363
\(487\) −4.43593e11 −0.357359 −0.178679 0.983907i \(-0.557182\pi\)
−0.178679 + 0.983907i \(0.557182\pi\)
\(488\) 1.78242e12 1.42272
\(489\) −8.63854e10 −0.0683204
\(490\) 1.86883e12 1.46450
\(491\) −7.29563e11 −0.566495 −0.283247 0.959047i \(-0.591412\pi\)
−0.283247 + 0.959047i \(0.591412\pi\)
\(492\) −3.25908e11 −0.250757
\(493\) 0 0
\(494\) −3.32360e11 −0.251094
\(495\) 1.91689e12 1.43507
\(496\) 1.80743e12 1.34089
\(497\) 4.85995e10 0.0357296
\(498\) −4.32281e11 −0.314945
\(499\) 3.28866e11 0.237447 0.118723 0.992927i \(-0.462120\pi\)
0.118723 + 0.992927i \(0.462120\pi\)
\(500\) 2.84751e12 2.03751
\(501\) −5.17602e11 −0.367051
\(502\) −8.61808e11 −0.605680
\(503\) −1.15730e12 −0.806099 −0.403049 0.915178i \(-0.632050\pi\)
−0.403049 + 0.915178i \(0.632050\pi\)
\(504\) −6.98280e11 −0.482050
\(505\) −1.66093e12 −1.13642
\(506\) 4.58259e12 3.10766
\(507\) 4.04289e11 0.271742
\(508\) −5.54957e12 −3.69719
\(509\) −1.53067e12 −1.01077 −0.505384 0.862895i \(-0.668649\pi\)
−0.505384 + 0.862895i \(0.668649\pi\)
\(510\) 0 0
\(511\) 8.42052e11 0.546317
\(512\) −2.40569e12 −1.54712
\(513\) −6.43950e11 −0.410510
\(514\) −3.44116e12 −2.17456
\(515\) 2.31943e11 0.145294
\(516\) −1.73404e12 −1.07680
\(517\) −2.90937e12 −1.79098
\(518\) 5.43530e10 0.0331696
\(519\) −1.02541e11 −0.0620361
\(520\) −5.00156e11 −0.299979
\(521\) 8.28369e11 0.492554 0.246277 0.969199i \(-0.420793\pi\)
0.246277 + 0.969199i \(0.420793\pi\)
\(522\) 3.53186e12 2.08203
\(523\) −1.93852e12 −1.13295 −0.566476 0.824078i \(-0.691694\pi\)
−0.566476 + 0.824078i \(0.691694\pi\)
\(524\) −1.26357e12 −0.732166
\(525\) 1.55412e10 0.00892830
\(526\) 2.39512e12 1.36424
\(527\) 0 0
\(528\) −7.13607e11 −0.399583
\(529\) 3.81715e11 0.211928
\(530\) −2.64218e12 −1.45453
\(531\) −2.43824e12 −1.33092
\(532\) −8.73929e11 −0.473014
\(533\) 1.63499e11 0.0877493
\(534\) −1.39736e12 −0.743655
\(535\) 1.34565e12 0.710136
\(536\) 2.46332e12 1.28908
\(537\) 2.45818e11 0.127564
\(538\) −1.62988e12 −0.838753
\(539\) −2.88974e12 −1.47472
\(540\) −1.98567e12 −1.00493
\(541\) −8.12932e11 −0.408006 −0.204003 0.978970i \(-0.565395\pi\)
−0.204003 + 0.978970i \(0.565395\pi\)
\(542\) 6.07153e12 3.02205
\(543\) −4.45795e11 −0.220057
\(544\) 0 0
\(545\) −8.14234e11 −0.395335
\(546\) −6.21324e10 −0.0299193
\(547\) −1.04434e12 −0.498768 −0.249384 0.968405i \(-0.580228\pi\)
−0.249384 + 0.968405i \(0.580228\pi\)
\(548\) 3.64063e12 1.72450
\(549\) −1.70138e12 −0.799330
\(550\) −5.99327e11 −0.279275
\(551\) 2.15721e12 0.997035
\(552\) −1.11028e12 −0.508988
\(553\) 7.86860e11 0.357795
\(554\) 5.59150e12 2.52194
\(555\) 3.61504e10 0.0161732
\(556\) 2.14708e12 0.952820
\(557\) −3.24890e12 −1.43017 −0.715086 0.699036i \(-0.753613\pi\)
−0.715086 + 0.699036i \(0.753613\pi\)
\(558\) −5.63522e12 −2.46069
\(559\) 8.69922e11 0.376814
\(560\) −6.08779e11 −0.261586
\(561\) 0 0
\(562\) 3.44261e12 1.45571
\(563\) 4.37456e11 0.183504 0.0917522 0.995782i \(-0.470753\pi\)
0.0917522 + 0.995782i \(0.470753\pi\)
\(564\) 1.44437e12 0.601068
\(565\) 7.60481e10 0.0313957
\(566\) −7.12789e11 −0.291936
\(567\) 6.03845e11 0.245359
\(568\) 4.54080e11 0.183048
\(569\) −2.44467e12 −0.977720 −0.488860 0.872362i \(-0.662587\pi\)
−0.488860 + 0.872362i \(0.662587\pi\)
\(570\) −8.78841e11 −0.348717
\(571\) −4.30219e12 −1.69366 −0.846832 0.531860i \(-0.821493\pi\)
−0.846832 + 0.531860i \(0.821493\pi\)
\(572\) 1.58472e12 0.618970
\(573\) 9.86056e11 0.382125
\(574\) 6.50023e11 0.249934
\(575\) −2.85483e11 −0.108912
\(576\) 2.75154e12 1.04154
\(577\) 1.04390e12 0.392075 0.196037 0.980596i \(-0.437193\pi\)
0.196037 + 0.980596i \(0.437193\pi\)
\(578\) 0 0
\(579\) 1.06921e11 0.0395374
\(580\) 6.65193e12 2.44074
\(581\) 5.70237e11 0.207617
\(582\) 2.49591e12 0.901727
\(583\) 4.08555e12 1.46468
\(584\) 7.86755e12 2.79886
\(585\) 4.77417e11 0.168537
\(586\) −3.34810e12 −1.17290
\(587\) −2.53007e12 −0.879552 −0.439776 0.898107i \(-0.644942\pi\)
−0.439776 + 0.898107i \(0.644942\pi\)
\(588\) 1.43463e12 0.494927
\(589\) −3.44191e12 −1.17837
\(590\) −6.94329e12 −2.35902
\(591\) −2.76920e10 −0.00933706
\(592\) 1.55477e11 0.0520258
\(593\) 2.29492e11 0.0762117 0.0381058 0.999274i \(-0.487868\pi\)
0.0381058 + 0.999274i \(0.487868\pi\)
\(594\) 4.64237e12 1.53003
\(595\) 0 0
\(596\) −2.29262e12 −0.744258
\(597\) −7.10684e11 −0.228977
\(598\) 1.14133e12 0.364970
\(599\) 2.96044e12 0.939583 0.469792 0.882777i \(-0.344329\pi\)
0.469792 + 0.882777i \(0.344329\pi\)
\(600\) 1.45207e11 0.0457410
\(601\) −2.71047e12 −0.847443 −0.423721 0.905793i \(-0.639276\pi\)
−0.423721 + 0.905793i \(0.639276\pi\)
\(602\) 3.45854e12 1.07327
\(603\) −2.35133e12 −0.724244
\(604\) −2.31963e12 −0.709173
\(605\) −5.31252e12 −1.61213
\(606\) −1.92781e12 −0.580681
\(607\) 2.72636e12 0.815142 0.407571 0.913173i \(-0.366376\pi\)
0.407571 + 0.913173i \(0.366376\pi\)
\(608\) 4.00723e11 0.118926
\(609\) 4.03276e11 0.118802
\(610\) −4.84496e12 −1.41679
\(611\) −7.24603e11 −0.210337
\(612\) 0 0
\(613\) 3.18239e12 0.910294 0.455147 0.890416i \(-0.349587\pi\)
0.455147 + 0.890416i \(0.349587\pi\)
\(614\) −4.62243e12 −1.31254
\(615\) 4.32332e11 0.121865
\(616\) 3.07472e12 0.860385
\(617\) 5.80402e12 1.61230 0.806150 0.591712i \(-0.201548\pi\)
0.806150 + 0.591712i \(0.201548\pi\)
\(618\) 2.69212e11 0.0742414
\(619\) 2.54189e12 0.695903 0.347952 0.937512i \(-0.386877\pi\)
0.347952 + 0.937512i \(0.386877\pi\)
\(620\) −1.06134e13 −2.88464
\(621\) 2.21134e12 0.596684
\(622\) 1.06104e13 2.84234
\(623\) 1.84330e12 0.490230
\(624\) −1.77730e11 −0.0469278
\(625\) −3.39997e12 −0.891281
\(626\) −4.08770e12 −1.06388
\(627\) 1.35893e12 0.351151
\(628\) −2.99527e12 −0.768453
\(629\) 0 0
\(630\) 1.89806e12 0.480040
\(631\) −6.29472e12 −1.58068 −0.790340 0.612668i \(-0.790096\pi\)
−0.790340 + 0.612668i \(0.790096\pi\)
\(632\) 7.35187e12 1.83304
\(633\) −5.05297e11 −0.125092
\(634\) 6.80787e12 1.67344
\(635\) 7.36176e12 1.79680
\(636\) −2.02830e12 −0.491557
\(637\) −7.19714e11 −0.173194
\(638\) −1.55518e13 −3.71610
\(639\) −4.33436e11 −0.102842
\(640\) 7.20282e12 1.69704
\(641\) −4.27476e12 −1.00012 −0.500058 0.865992i \(-0.666688\pi\)
−0.500058 + 0.865992i \(0.666688\pi\)
\(642\) 1.56188e12 0.362860
\(643\) −3.30486e12 −0.762437 −0.381218 0.924485i \(-0.624495\pi\)
−0.381218 + 0.924485i \(0.624495\pi\)
\(644\) 3.00110e12 0.687533
\(645\) 2.30029e12 0.523315
\(646\) 0 0
\(647\) 1.81390e12 0.406952 0.203476 0.979080i \(-0.434776\pi\)
0.203476 + 0.979080i \(0.434776\pi\)
\(648\) 5.64191e12 1.25701
\(649\) 1.07363e13 2.37548
\(650\) −1.49268e11 −0.0327986
\(651\) −6.43442e11 −0.140409
\(652\) 2.18166e12 0.472796
\(653\) 1.96397e12 0.422694 0.211347 0.977411i \(-0.432215\pi\)
0.211347 + 0.977411i \(0.432215\pi\)
\(654\) −9.45066e11 −0.202005
\(655\) 1.67619e12 0.355826
\(656\) 1.85939e12 0.392016
\(657\) −7.50986e12 −1.57249
\(658\) −2.88080e12 −0.599096
\(659\) 1.93103e11 0.0398845 0.0199422 0.999801i \(-0.493652\pi\)
0.0199422 + 0.999801i \(0.493652\pi\)
\(660\) 4.19038e12 0.859618
\(661\) 1.01510e10 0.00206825 0.00103413 0.999999i \(-0.499671\pi\)
0.00103413 + 0.999999i \(0.499671\pi\)
\(662\) −6.32302e12 −1.27957
\(663\) 0 0
\(664\) 5.32790e12 1.06365
\(665\) 1.15931e12 0.229880
\(666\) −4.84749e11 −0.0954734
\(667\) −7.40792e12 −1.44921
\(668\) 1.30720e13 2.54009
\(669\) −1.74246e12 −0.336315
\(670\) −6.69578e12 −1.28370
\(671\) 7.49166e12 1.42668
\(672\) 7.49124e10 0.0141707
\(673\) 6.50508e12 1.22232 0.611160 0.791507i \(-0.290703\pi\)
0.611160 + 0.791507i \(0.290703\pi\)
\(674\) 2.08741e12 0.389617
\(675\) −2.89207e11 −0.0536219
\(676\) −1.02103e13 −1.88053
\(677\) 9.60958e12 1.75815 0.879074 0.476685i \(-0.158162\pi\)
0.879074 + 0.476685i \(0.158162\pi\)
\(678\) 8.82675e10 0.0160423
\(679\) −3.29244e12 −0.594433
\(680\) 0 0
\(681\) −1.98554e11 −0.0353766
\(682\) 2.48135e13 4.39196
\(683\) 5.49684e11 0.0966541 0.0483271 0.998832i \(-0.484611\pi\)
0.0483271 + 0.998832i \(0.484611\pi\)
\(684\) 7.79415e12 1.36150
\(685\) −4.82947e12 −0.838092
\(686\) −6.04857e12 −1.04278
\(687\) 1.68180e12 0.288051
\(688\) 9.89316e12 1.68340
\(689\) 1.01754e12 0.172015
\(690\) 3.01797e12 0.506866
\(691\) 1.00783e13 1.68166 0.840828 0.541302i \(-0.182068\pi\)
0.840828 + 0.541302i \(0.182068\pi\)
\(692\) 2.58967e12 0.429306
\(693\) −2.93493e12 −0.483391
\(694\) 4.48971e12 0.734684
\(695\) −2.84820e12 −0.463061
\(696\) 3.76793e12 0.608641
\(697\) 0 0
\(698\) 5.52217e12 0.880562
\(699\) 2.98691e12 0.473232
\(700\) −3.92494e11 −0.0617862
\(701\) −9.77792e11 −0.152938 −0.0764690 0.997072i \(-0.524365\pi\)
−0.0764690 + 0.997072i \(0.524365\pi\)
\(702\) 1.15622e12 0.179690
\(703\) −2.96077e11 −0.0457200
\(704\) −1.21158e13 −1.85898
\(705\) −1.91603e12 −0.292113
\(706\) 1.52024e13 2.30299
\(707\) 2.54304e12 0.382795
\(708\) −5.33008e12 −0.797230
\(709\) 1.08153e13 1.60743 0.803714 0.595016i \(-0.202854\pi\)
0.803714 + 0.595016i \(0.202854\pi\)
\(710\) −1.23428e12 −0.182285
\(711\) −7.01763e12 −1.02986
\(712\) 1.72225e13 2.51152
\(713\) 1.18196e13 1.71278
\(714\) 0 0
\(715\) −2.10220e12 −0.300813
\(716\) −6.20812e12 −0.882778
\(717\) 1.61545e12 0.228274
\(718\) −1.56841e13 −2.20242
\(719\) −1.62784e12 −0.227161 −0.113580 0.993529i \(-0.536232\pi\)
−0.113580 + 0.993529i \(0.536232\pi\)
\(720\) 5.42941e12 0.752933
\(721\) −3.55126e11 −0.0489411
\(722\) −5.34989e12 −0.732703
\(723\) 2.26563e12 0.308366
\(724\) 1.12585e13 1.52286
\(725\) 9.68834e11 0.130235
\(726\) −6.16614e12 −0.823756
\(727\) 2.04920e12 0.272069 0.136035 0.990704i \(-0.456564\pi\)
0.136035 + 0.990704i \(0.456564\pi\)
\(728\) 7.65786e11 0.101045
\(729\) −4.21884e12 −0.553248
\(730\) −2.13855e13 −2.78720
\(731\) 0 0
\(732\) −3.71927e12 −0.478805
\(733\) −2.62355e12 −0.335677 −0.167839 0.985814i \(-0.553679\pi\)
−0.167839 + 0.985814i \(0.553679\pi\)
\(734\) −6.86239e12 −0.872656
\(735\) −1.90310e12 −0.240530
\(736\) −1.37610e12 −0.172862
\(737\) 1.03536e13 1.29266
\(738\) −5.79724e12 −0.719396
\(739\) 1.33151e13 1.64227 0.821133 0.570737i \(-0.193342\pi\)
0.821133 + 0.570737i \(0.193342\pi\)
\(740\) −9.12978e11 −0.111923
\(741\) 3.38454e11 0.0412399
\(742\) 4.04543e12 0.489945
\(743\) 6.67750e11 0.0803830 0.0401915 0.999192i \(-0.487203\pi\)
0.0401915 + 0.999192i \(0.487203\pi\)
\(744\) −6.01187e12 −0.719336
\(745\) 3.04126e12 0.361702
\(746\) −4.27074e12 −0.504869
\(747\) −5.08567e12 −0.597593
\(748\) 0 0
\(749\) −2.06032e12 −0.239203
\(750\) −4.38431e12 −0.505971
\(751\) −4.40301e12 −0.505092 −0.252546 0.967585i \(-0.581268\pi\)
−0.252546 + 0.967585i \(0.581268\pi\)
\(752\) −8.24053e12 −0.939669
\(753\) 8.77609e11 0.0994773
\(754\) −3.87330e12 −0.436426
\(755\) 3.07710e12 0.344651
\(756\) 3.04025e12 0.338502
\(757\) 1.43998e12 0.159376 0.0796882 0.996820i \(-0.474608\pi\)
0.0796882 + 0.996820i \(0.474608\pi\)
\(758\) 7.84802e12 0.863473
\(759\) −4.66662e12 −0.510404
\(760\) 1.08318e13 1.17771
\(761\) 1.23305e13 1.33276 0.666379 0.745613i \(-0.267843\pi\)
0.666379 + 0.745613i \(0.267843\pi\)
\(762\) 8.54465e12 0.918115
\(763\) 1.24667e12 0.133165
\(764\) −2.49028e13 −2.64441
\(765\) 0 0
\(766\) −1.59700e13 −1.67600
\(767\) 2.67396e12 0.278982
\(768\) 5.28067e12 0.547726
\(769\) 7.33617e12 0.756486 0.378243 0.925706i \(-0.376528\pi\)
0.378243 + 0.925706i \(0.376528\pi\)
\(770\) −8.35770e12 −0.856798
\(771\) 3.50426e12 0.357151
\(772\) −2.70028e12 −0.273610
\(773\) 1.30977e13 1.31944 0.659718 0.751513i \(-0.270676\pi\)
0.659718 + 0.751513i \(0.270676\pi\)
\(774\) −3.08450e13 −3.08924
\(775\) −1.54581e12 −0.153921
\(776\) −3.07622e13 −3.04537
\(777\) −5.53496e10 −0.00544779
\(778\) 3.29677e13 3.22612
\(779\) −3.54087e12 −0.344502
\(780\) 1.04365e12 0.100955
\(781\) 1.90854e12 0.183557
\(782\) 0 0
\(783\) −7.50456e12 −0.713506
\(784\) −8.18493e12 −0.773735
\(785\) 3.97337e12 0.373461
\(786\) 1.94552e12 0.181817
\(787\) 1.90562e13 1.77072 0.885358 0.464910i \(-0.153913\pi\)
0.885358 + 0.464910i \(0.153913\pi\)
\(788\) 6.99360e11 0.0646150
\(789\) −2.43904e12 −0.224064
\(790\) −1.99838e13 −1.82540
\(791\) −1.16437e11 −0.0105754
\(792\) −2.74220e13 −2.47648
\(793\) 1.86586e12 0.167552
\(794\) 5.37407e12 0.479856
\(795\) 2.69063e12 0.238892
\(796\) 1.79483e13 1.58458
\(797\) 1.05555e13 0.926652 0.463326 0.886188i \(-0.346656\pi\)
0.463326 + 0.886188i \(0.346656\pi\)
\(798\) 1.34559e12 0.117462
\(799\) 0 0
\(800\) 1.79970e11 0.0155345
\(801\) −1.64395e13 −1.41105
\(802\) −3.15291e13 −2.69108
\(803\) 3.30680e13 2.80665
\(804\) −5.14008e12 −0.433828
\(805\) −3.98110e12 −0.334135
\(806\) 6.18000e12 0.515800
\(807\) 1.65976e12 0.137757
\(808\) 2.37604e13 1.96111
\(809\) −7.11754e12 −0.584200 −0.292100 0.956388i \(-0.594354\pi\)
−0.292100 + 0.956388i \(0.594354\pi\)
\(810\) −1.53358e13 −1.25177
\(811\) 1.96032e13 1.59123 0.795616 0.605802i \(-0.207148\pi\)
0.795616 + 0.605802i \(0.207148\pi\)
\(812\) −1.01847e13 −0.822142
\(813\) −6.18285e12 −0.496343
\(814\) 2.13448e12 0.170405
\(815\) −2.89408e12 −0.229774
\(816\) 0 0
\(817\) −1.88397e13 −1.47936
\(818\) 2.17824e13 1.70105
\(819\) −7.30970e11 −0.0567704
\(820\) −1.09186e13 −0.843340
\(821\) −2.57782e13 −1.98020 −0.990099 0.140370i \(-0.955171\pi\)
−0.990099 + 0.140370i \(0.955171\pi\)
\(822\) −5.60547e12 −0.428242
\(823\) 1.81960e13 1.38254 0.691270 0.722597i \(-0.257052\pi\)
0.691270 + 0.722597i \(0.257052\pi\)
\(824\) −3.31805e12 −0.250733
\(825\) 6.10316e11 0.0458683
\(826\) 1.06308e13 0.794615
\(827\) −1.68619e13 −1.25352 −0.626760 0.779213i \(-0.715619\pi\)
−0.626760 + 0.779213i \(0.715619\pi\)
\(828\) −2.67654e13 −1.97896
\(829\) −2.04363e13 −1.50282 −0.751411 0.659834i \(-0.770626\pi\)
−0.751411 + 0.659834i \(0.770626\pi\)
\(830\) −1.44823e13 −1.05922
\(831\) −5.69403e12 −0.414205
\(832\) −3.01754e12 −0.218322
\(833\) 0 0
\(834\) −3.30585e12 −0.236611
\(835\) −1.73407e13 −1.23446
\(836\) −3.43199e13 −2.43006
\(837\) 1.19738e13 0.843273
\(838\) −3.86765e13 −2.70925
\(839\) 1.01784e13 0.709167 0.354584 0.935024i \(-0.384623\pi\)
0.354584 + 0.935024i \(0.384623\pi\)
\(840\) 2.02492e12 0.140331
\(841\) 1.06329e13 0.732940
\(842\) −1.72516e13 −1.18284
\(843\) −3.50573e12 −0.239086
\(844\) 1.27613e13 0.865671
\(845\) 1.35445e13 0.913918
\(846\) 2.56924e13 1.72440
\(847\) 8.13396e12 0.543033
\(848\) 1.15720e13 0.768468
\(849\) 7.25859e11 0.0479477
\(850\) 0 0
\(851\) 1.01674e12 0.0664548
\(852\) −9.47505e11 −0.0616032
\(853\) 1.86820e13 1.20824 0.604119 0.796894i \(-0.293525\pi\)
0.604119 + 0.796894i \(0.293525\pi\)
\(854\) 7.41808e12 0.477234
\(855\) −1.03393e13 −0.661674
\(856\) −1.92502e13 −1.22547
\(857\) −7.29110e12 −0.461721 −0.230860 0.972987i \(-0.574154\pi\)
−0.230860 + 0.972987i \(0.574154\pi\)
\(858\) −2.43999e12 −0.153707
\(859\) 4.02170e12 0.252023 0.126011 0.992029i \(-0.459782\pi\)
0.126011 + 0.992029i \(0.459782\pi\)
\(860\) −5.80937e13 −3.62148
\(861\) −6.61941e11 −0.0410492
\(862\) −2.95023e13 −1.82001
\(863\) −1.68689e13 −1.03523 −0.517617 0.855613i \(-0.673181\pi\)
−0.517617 + 0.855613i \(0.673181\pi\)
\(864\) −1.39405e12 −0.0851070
\(865\) −3.43532e12 −0.208639
\(866\) 5.13249e13 3.10097
\(867\) 0 0
\(868\) 1.62501e13 0.971667
\(869\) 3.09006e13 1.83814
\(870\) −1.02420e13 −0.606103
\(871\) 2.57864e12 0.151813
\(872\) 1.16480e13 0.682224
\(873\) 2.93637e13 1.71098
\(874\) −2.47176e13 −1.43286
\(875\) 5.78349e12 0.333544
\(876\) −1.64168e13 −0.941933
\(877\) 9.39568e12 0.536328 0.268164 0.963373i \(-0.413583\pi\)
0.268164 + 0.963373i \(0.413583\pi\)
\(878\) −1.49580e13 −0.849471
\(879\) 3.40949e12 0.192637
\(880\) −2.39072e13 −1.34387
\(881\) −2.49688e13 −1.39639 −0.698194 0.715909i \(-0.746013\pi\)
−0.698194 + 0.715909i \(0.746013\pi\)
\(882\) 2.55191e13 1.41990
\(883\) −1.24749e13 −0.690578 −0.345289 0.938496i \(-0.612219\pi\)
−0.345289 + 0.938496i \(0.612219\pi\)
\(884\) 0 0
\(885\) 7.07060e12 0.387446
\(886\) 1.30254e13 0.710130
\(887\) 2.86371e13 1.55336 0.776682 0.629893i \(-0.216901\pi\)
0.776682 + 0.629893i \(0.216901\pi\)
\(888\) −5.17148e11 −0.0279098
\(889\) −1.12715e13 −0.605237
\(890\) −4.68141e13 −2.50105
\(891\) 2.37135e13 1.26051
\(892\) 4.40059e13 2.32739
\(893\) 1.56926e13 0.825777
\(894\) 3.52994e12 0.184820
\(895\) 8.23537e12 0.429022
\(896\) −1.10282e13 −0.571634
\(897\) −1.16226e12 −0.0599429
\(898\) 4.27349e13 2.19301
\(899\) −4.01119e13 −2.04811
\(900\) 3.50047e12 0.177842
\(901\) 0 0
\(902\) 2.55269e13 1.28401
\(903\) −3.52195e12 −0.176274
\(904\) −1.08790e12 −0.0541792
\(905\) −1.49350e13 −0.740093
\(906\) 3.57153e12 0.176107
\(907\) −1.51352e13 −0.742599 −0.371300 0.928513i \(-0.621088\pi\)
−0.371300 + 0.928513i \(0.621088\pi\)
\(908\) 5.01448e12 0.244816
\(909\) −2.26802e13 −1.10182
\(910\) −2.08156e12 −0.100624
\(911\) −7.50977e12 −0.361238 −0.180619 0.983553i \(-0.557810\pi\)
−0.180619 + 0.983553i \(0.557810\pi\)
\(912\) 3.84906e12 0.184237
\(913\) 2.23936e13 1.06661
\(914\) 5.11513e13 2.42437
\(915\) 4.93379e12 0.232694
\(916\) −4.24739e13 −1.99339
\(917\) −2.56640e12 −0.119857
\(918\) 0 0
\(919\) −2.29909e13 −1.06325 −0.531626 0.846979i \(-0.678419\pi\)
−0.531626 + 0.846979i \(0.678419\pi\)
\(920\) −3.71966e13 −1.71182
\(921\) 4.70719e12 0.215572
\(922\) −4.73739e13 −2.15899
\(923\) 4.75338e11 0.0215573
\(924\) −6.41586e12 −0.289555
\(925\) −1.32973e11 −0.00597206
\(926\) −4.07016e13 −1.81912
\(927\) 3.16720e12 0.140869
\(928\) 4.67001e12 0.206705
\(929\) 4.46802e12 0.196809 0.0984044 0.995147i \(-0.468626\pi\)
0.0984044 + 0.995147i \(0.468626\pi\)
\(930\) 1.63414e13 0.716337
\(931\) 1.55867e13 0.679955
\(932\) −7.54343e13 −3.27489
\(933\) −1.08050e13 −0.466828
\(934\) 2.13475e13 0.917881
\(935\) 0 0
\(936\) −6.82968e12 −0.290843
\(937\) −3.69266e13 −1.56499 −0.782494 0.622658i \(-0.786053\pi\)
−0.782494 + 0.622658i \(0.786053\pi\)
\(938\) 1.02519e13 0.432404
\(939\) 4.16265e12 0.174733
\(940\) 4.83893e13 2.02150
\(941\) 2.73922e13 1.13887 0.569434 0.822037i \(-0.307162\pi\)
0.569434 + 0.822037i \(0.307162\pi\)
\(942\) 4.61181e12 0.190828
\(943\) 1.21595e13 0.500739
\(944\) 3.04095e13 1.24634
\(945\) −4.03303e12 −0.164509
\(946\) 1.35819e14 5.51381
\(947\) −4.08999e12 −0.165252 −0.0826261 0.996581i \(-0.526331\pi\)
−0.0826261 + 0.996581i \(0.526331\pi\)
\(948\) −1.53408e13 −0.616893
\(949\) 8.23587e12 0.329618
\(950\) 3.23265e12 0.128766
\(951\) −6.93269e12 −0.274846
\(952\) 0 0
\(953\) −1.68559e13 −0.661964 −0.330982 0.943637i \(-0.607380\pi\)
−0.330982 + 0.943637i \(0.607380\pi\)
\(954\) −3.60792e13 −1.41023
\(955\) 3.30348e13 1.28516
\(956\) −4.07982e13 −1.57972
\(957\) 1.58369e13 0.610334
\(958\) −3.47961e13 −1.33471
\(959\) 7.39437e12 0.282304
\(960\) −7.97911e12 −0.303203
\(961\) 3.75604e13 1.42061
\(962\) 5.31611e11 0.0200127
\(963\) 1.83750e13 0.688509
\(964\) −5.72184e13 −2.13397
\(965\) 3.58205e12 0.132972
\(966\) −4.62078e12 −0.170733
\(967\) −3.07043e13 −1.12922 −0.564611 0.825357i \(-0.690974\pi\)
−0.564611 + 0.825357i \(0.690974\pi\)
\(968\) 7.59981e13 2.78204
\(969\) 0 0
\(970\) 8.36178e13 3.03267
\(971\) −6.39625e12 −0.230908 −0.115454 0.993313i \(-0.536832\pi\)
−0.115454 + 0.993313i \(0.536832\pi\)
\(972\) −4.12342e13 −1.48170
\(973\) 4.36086e12 0.155978
\(974\) −1.72492e13 −0.614119
\(975\) 1.52004e11 0.00538686
\(976\) 2.12194e13 0.748531
\(977\) −1.10943e13 −0.389559 −0.194780 0.980847i \(-0.562399\pi\)
−0.194780 + 0.980847i \(0.562399\pi\)
\(978\) −3.35910e12 −0.117408
\(979\) 7.23877e13 2.51851
\(980\) 4.80628e13 1.66453
\(981\) −1.11184e13 −0.383295
\(982\) −2.83691e13 −0.973518
\(983\) 1.58231e13 0.540506 0.270253 0.962789i \(-0.412893\pi\)
0.270253 + 0.962789i \(0.412893\pi\)
\(984\) −6.18472e12 −0.210301
\(985\) −9.27735e11 −0.0314022
\(986\) 0 0
\(987\) 2.93362e12 0.0983958
\(988\) −8.54765e12 −0.285391
\(989\) 6.46961e13 2.15028
\(990\) 7.45383e13 2.46616
\(991\) 2.00594e13 0.660672 0.330336 0.943863i \(-0.392838\pi\)
0.330336 + 0.943863i \(0.392838\pi\)
\(992\) −7.45117e12 −0.244299
\(993\) 6.43896e12 0.210157
\(994\) 1.88980e12 0.0614011
\(995\) −2.38093e13 −0.770092
\(996\) −1.11174e13 −0.357963
\(997\) −2.94028e12 −0.0942455 −0.0471228 0.998889i \(-0.515005\pi\)
−0.0471228 + 0.998889i \(0.515005\pi\)
\(998\) 1.27880e13 0.408051
\(999\) 1.03000e12 0.0327185
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.h.1.33 yes 36
17.16 even 2 289.10.a.g.1.33 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.33 36 17.16 even 2
289.10.a.h.1.33 yes 36 1.1 even 1 trivial