Properties

Label 289.10.a.g.1.6
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 1.6
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-33.0540 q^{2} +199.787 q^{3} +580.568 q^{4} -108.765 q^{5} -6603.77 q^{6} +1478.44 q^{7} -2266.45 q^{8} +20231.9 q^{9} +O(q^{10})\) \(q-33.0540 q^{2} +199.787 q^{3} +580.568 q^{4} -108.765 q^{5} -6603.77 q^{6} +1478.44 q^{7} -2266.45 q^{8} +20231.9 q^{9} +3595.11 q^{10} +82128.1 q^{11} +115990. q^{12} +23617.4 q^{13} -48868.3 q^{14} -21729.8 q^{15} -222336. q^{16} -668745. q^{18} -539058. q^{19} -63145.3 q^{20} +295373. q^{21} -2.71466e6 q^{22} -960277. q^{23} -452808. q^{24} -1.94130e6 q^{25} -780651. q^{26} +109662. q^{27} +858334. q^{28} +6.36845e6 q^{29} +718256. q^{30} -5.33710e6 q^{31} +8.50951e6 q^{32} +1.64081e7 q^{33} -160802. q^{35} +1.17460e7 q^{36} -2.03822e7 q^{37} +1.78180e7 q^{38} +4.71846e6 q^{39} +246510. q^{40} -3.70567e6 q^{41} -9.76326e6 q^{42} -3.16986e7 q^{43} +4.76809e7 q^{44} -2.20051e6 q^{45} +3.17410e7 q^{46} +3.24736e7 q^{47} -4.44198e7 q^{48} -3.81678e7 q^{49} +6.41676e7 q^{50} +1.37115e7 q^{52} -3.44852e7 q^{53} -3.62476e6 q^{54} -8.93263e6 q^{55} -3.35081e6 q^{56} -1.07697e8 q^{57} -2.10503e8 q^{58} -8.66911e7 q^{59} -1.26156e7 q^{60} -2.76467e7 q^{61} +1.76413e8 q^{62} +2.99116e7 q^{63} -1.67438e8 q^{64} -2.56874e6 q^{65} -5.42355e8 q^{66} -8.41005e7 q^{67} -1.91851e8 q^{69} +5.31514e6 q^{70} -1.01356e8 q^{71} -4.58546e7 q^{72} +3.67214e8 q^{73} +6.73712e8 q^{74} -3.87846e8 q^{75} -3.12960e8 q^{76} +1.21421e8 q^{77} -1.55964e8 q^{78} -1.40097e8 q^{79} +2.41822e7 q^{80} -3.76315e8 q^{81} +1.22487e8 q^{82} -7.40629e8 q^{83} +1.71484e8 q^{84} +1.04777e9 q^{86} +1.27233e9 q^{87} -1.86139e8 q^{88} -2.04859e8 q^{89} +7.27358e7 q^{90} +3.49169e7 q^{91} -5.57506e8 q^{92} -1.06628e9 q^{93} -1.07338e9 q^{94} +5.86304e7 q^{95} +1.70009e9 q^{96} +7.98484e8 q^{97} +1.26160e9 q^{98} +1.66161e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} - 60000q^{10} - 76902q^{11} - 373248q^{12} + 54216q^{13} - 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} - 6439479q^{20} - 138102q^{21} - 267324q^{22} - 4041462q^{23} - 7653888q^{24} + 16582356q^{25} + 15822744q^{26} - 13281612q^{27} - 18614784q^{28} - 4005936q^{29} + 22471686q^{30} - 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} - 22076682q^{37} - 27401376q^{38} - 62736162q^{39} + 12231630q^{40} - 59641782q^{41} + 150001536q^{42} - 47951586q^{43} + 49578936q^{44} - 129308238q^{45} - 140524827q^{46} - 118557912q^{47} - 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} - 209848575q^{54} - 365439924q^{55} - 203095059q^{56} + 4614108q^{57} + 179071413q^{58} + 343015128q^{59} + 427179186q^{60} - 175597116q^{61} - 720602571q^{62} - 587415936q^{63} + 853082511q^{64} - 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} - 1308709542q^{71} - 275337849q^{72} - 494841342q^{73} - 1545361890q^{74} - 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} - 2270624538q^{78} - 1980107868q^{79} - 2897000199q^{80} + 1598298840q^{81} - 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} + 2705904618q^{88} + 148394658q^{89} - 117916215q^{90} - 636340896q^{91} + 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} - 4878626298q^{95} + 8390096634q^{96} + 891786822q^{97} + 4285627647q^{98} + 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −33.0540 −1.46080 −0.730398 0.683022i \(-0.760665\pi\)
−0.730398 + 0.683022i \(0.760665\pi\)
\(3\) 199.787 1.42404 0.712019 0.702160i \(-0.247781\pi\)
0.712019 + 0.702160i \(0.247781\pi\)
\(4\) 580.568 1.13392
\(5\) −108.765 −0.0778256 −0.0389128 0.999243i \(-0.512389\pi\)
−0.0389128 + 0.999243i \(0.512389\pi\)
\(6\) −6603.77 −2.08023
\(7\) 1478.44 0.232735 0.116368 0.993206i \(-0.462875\pi\)
0.116368 + 0.993206i \(0.462875\pi\)
\(8\) −2266.45 −0.195633
\(9\) 20231.9 1.02789
\(10\) 3595.11 0.113687
\(11\) 82128.1 1.69131 0.845657 0.533726i \(-0.179209\pi\)
0.845657 + 0.533726i \(0.179209\pi\)
\(12\) 115990. 1.61475
\(13\) 23617.4 0.229344 0.114672 0.993403i \(-0.463418\pi\)
0.114672 + 0.993403i \(0.463418\pi\)
\(14\) −48868.3 −0.339978
\(15\) −21729.8 −0.110827
\(16\) −222336. −0.848143
\(17\) 0 0
\(18\) −668745. −1.50153
\(19\) −539058. −0.948952 −0.474476 0.880268i \(-0.657362\pi\)
−0.474476 + 0.880268i \(0.657362\pi\)
\(20\) −63145.3 −0.0882482
\(21\) 295373. 0.331424
\(22\) −2.71466e6 −2.47066
\(23\) −960277. −0.715519 −0.357760 0.933814i \(-0.616459\pi\)
−0.357760 + 0.933814i \(0.616459\pi\)
\(24\) −452808. −0.278589
\(25\) −1.94130e6 −0.993943
\(26\) −780651. −0.335025
\(27\) 109662. 0.0397116
\(28\) 858334. 0.263903
\(29\) 6.36845e6 1.67203 0.836013 0.548710i \(-0.184881\pi\)
0.836013 + 0.548710i \(0.184881\pi\)
\(30\) 718256. 0.161895
\(31\) −5.33710e6 −1.03795 −0.518977 0.854788i \(-0.673687\pi\)
−0.518977 + 0.854788i \(0.673687\pi\)
\(32\) 8.50951e6 1.43460
\(33\) 1.64081e7 2.40850
\(34\) 0 0
\(35\) −160802. −0.0181127
\(36\) 1.17460e7 1.16554
\(37\) −2.03822e7 −1.78790 −0.893948 0.448171i \(-0.852076\pi\)
−0.893948 + 0.448171i \(0.852076\pi\)
\(38\) 1.78180e7 1.38622
\(39\) 4.71846e6 0.326595
\(40\) 246510. 0.0152252
\(41\) −3.70567e6 −0.204804 −0.102402 0.994743i \(-0.532653\pi\)
−0.102402 + 0.994743i \(0.532653\pi\)
\(42\) −9.76326e6 −0.484142
\(43\) −3.16986e7 −1.41394 −0.706972 0.707242i \(-0.749939\pi\)
−0.706972 + 0.707242i \(0.749939\pi\)
\(44\) 4.76809e7 1.91782
\(45\) −2.20051e6 −0.0799959
\(46\) 3.17410e7 1.04523
\(47\) 3.24736e7 0.970711 0.485356 0.874317i \(-0.338690\pi\)
0.485356 + 0.874317i \(0.338690\pi\)
\(48\) −4.44198e7 −1.20779
\(49\) −3.81678e7 −0.945834
\(50\) 6.41676e7 1.45195
\(51\) 0 0
\(52\) 1.37115e7 0.260058
\(53\) −3.44852e7 −0.600332 −0.300166 0.953887i \(-0.597042\pi\)
−0.300166 + 0.953887i \(0.597042\pi\)
\(54\) −3.62476e6 −0.0580106
\(55\) −8.93263e6 −0.131628
\(56\) −3.35081e6 −0.0455306
\(57\) −1.07697e8 −1.35134
\(58\) −2.10503e8 −2.44249
\(59\) −8.66911e7 −0.931409 −0.465704 0.884940i \(-0.654199\pi\)
−0.465704 + 0.884940i \(0.654199\pi\)
\(60\) −1.26156e7 −0.125669
\(61\) −2.76467e7 −0.255658 −0.127829 0.991796i \(-0.540801\pi\)
−0.127829 + 0.991796i \(0.540801\pi\)
\(62\) 1.76413e8 1.51624
\(63\) 2.99116e7 0.239225
\(64\) −1.67438e8 −1.24751
\(65\) −2.56874e6 −0.0178488
\(66\) −5.42355e8 −3.51832
\(67\) −8.41005e7 −0.509873 −0.254936 0.966958i \(-0.582055\pi\)
−0.254936 + 0.966958i \(0.582055\pi\)
\(68\) 0 0
\(69\) −1.91851e8 −1.01893
\(70\) 5.31514e6 0.0264590
\(71\) −1.01356e8 −0.473354 −0.236677 0.971588i \(-0.576058\pi\)
−0.236677 + 0.971588i \(0.576058\pi\)
\(72\) −4.58546e7 −0.201088
\(73\) 3.67214e8 1.51345 0.756723 0.653736i \(-0.226799\pi\)
0.756723 + 0.653736i \(0.226799\pi\)
\(74\) 6.73712e8 2.61175
\(75\) −3.87846e8 −1.41541
\(76\) −3.12960e8 −1.07604
\(77\) 1.21421e8 0.393628
\(78\) −1.55964e8 −0.477088
\(79\) −1.40097e8 −0.404676 −0.202338 0.979316i \(-0.564854\pi\)
−0.202338 + 0.979316i \(0.564854\pi\)
\(80\) 2.41822e7 0.0660072
\(81\) −3.76315e8 −0.971336
\(82\) 1.22487e8 0.299177
\(83\) −7.40629e8 −1.71297 −0.856484 0.516173i \(-0.827356\pi\)
−0.856484 + 0.516173i \(0.827356\pi\)
\(84\) 1.71484e8 0.375809
\(85\) 0 0
\(86\) 1.04777e9 2.06548
\(87\) 1.27233e9 2.38103
\(88\) −1.86139e8 −0.330877
\(89\) −2.04859e8 −0.346099 −0.173049 0.984913i \(-0.555362\pi\)
−0.173049 + 0.984913i \(0.555362\pi\)
\(90\) 7.27358e7 0.116858
\(91\) 3.49169e7 0.0533764
\(92\) −5.57506e8 −0.811343
\(93\) −1.06628e9 −1.47809
\(94\) −1.07338e9 −1.41801
\(95\) 5.86304e7 0.0738528
\(96\) 1.70009e9 2.04292
\(97\) 7.98484e8 0.915784 0.457892 0.889008i \(-0.348605\pi\)
0.457892 + 0.889008i \(0.348605\pi\)
\(98\) 1.26160e9 1.38167
\(99\) 1.66161e9 1.73848
\(100\) −1.12705e9 −1.12705
\(101\) −3.07991e8 −0.294504 −0.147252 0.989099i \(-0.547043\pi\)
−0.147252 + 0.989099i \(0.547043\pi\)
\(102\) 0 0
\(103\) −6.64656e8 −0.581875 −0.290937 0.956742i \(-0.593967\pi\)
−0.290937 + 0.956742i \(0.593967\pi\)
\(104\) −5.35278e7 −0.0448672
\(105\) −3.21261e7 −0.0257933
\(106\) 1.13987e9 0.876961
\(107\) −1.44876e9 −1.06849 −0.534245 0.845330i \(-0.679404\pi\)
−0.534245 + 0.845330i \(0.679404\pi\)
\(108\) 6.36661e7 0.0450299
\(109\) 2.45299e9 1.66447 0.832235 0.554423i \(-0.187061\pi\)
0.832235 + 0.554423i \(0.187061\pi\)
\(110\) 2.95259e8 0.192281
\(111\) −4.07209e9 −2.54603
\(112\) −3.28709e8 −0.197393
\(113\) 3.00054e9 1.73120 0.865598 0.500740i \(-0.166939\pi\)
0.865598 + 0.500740i \(0.166939\pi\)
\(114\) 3.55981e9 1.97404
\(115\) 1.04444e8 0.0556857
\(116\) 3.69732e9 1.89595
\(117\) 4.77825e8 0.235740
\(118\) 2.86549e9 1.36060
\(119\) 0 0
\(120\) 4.92495e7 0.0216813
\(121\) 4.38707e9 1.86055
\(122\) 9.13835e8 0.373464
\(123\) −7.40345e8 −0.291649
\(124\) −3.09855e9 −1.17696
\(125\) 4.23575e8 0.155180
\(126\) −9.88698e8 −0.349459
\(127\) 1.22338e9 0.417297 0.208649 0.977991i \(-0.433094\pi\)
0.208649 + 0.977991i \(0.433094\pi\)
\(128\) 1.17762e9 0.387757
\(129\) −6.33297e9 −2.01351
\(130\) 8.49072e7 0.0260735
\(131\) 1.89291e9 0.561576 0.280788 0.959770i \(-0.409404\pi\)
0.280788 + 0.959770i \(0.409404\pi\)
\(132\) 9.52604e9 2.73105
\(133\) −7.96964e8 −0.220854
\(134\) 2.77986e9 0.744820
\(135\) −1.19273e7 −0.00309058
\(136\) 0 0
\(137\) −1.42855e9 −0.346461 −0.173230 0.984881i \(-0.555421\pi\)
−0.173230 + 0.984881i \(0.555421\pi\)
\(138\) 6.34145e9 1.48844
\(139\) 4.86338e9 1.10502 0.552512 0.833505i \(-0.313669\pi\)
0.552512 + 0.833505i \(0.313669\pi\)
\(140\) −9.33563e7 −0.0205384
\(141\) 6.48781e9 1.38233
\(142\) 3.35021e9 0.691473
\(143\) 1.93965e9 0.387893
\(144\) −4.49827e9 −0.871795
\(145\) −6.92662e8 −0.130126
\(146\) −1.21379e10 −2.21083
\(147\) −7.62544e9 −1.34690
\(148\) −1.18332e10 −2.02734
\(149\) 3.73603e8 0.0620972 0.0310486 0.999518i \(-0.490115\pi\)
0.0310486 + 0.999518i \(0.490115\pi\)
\(150\) 1.28199e10 2.06763
\(151\) −1.22330e10 −1.91486 −0.957429 0.288670i \(-0.906787\pi\)
−0.957429 + 0.288670i \(0.906787\pi\)
\(152\) 1.22175e9 0.185646
\(153\) 0 0
\(154\) −4.01346e9 −0.575010
\(155\) 5.80488e8 0.0807794
\(156\) 2.73939e9 0.370333
\(157\) 7.26890e9 0.954818 0.477409 0.878681i \(-0.341576\pi\)
0.477409 + 0.878681i \(0.341576\pi\)
\(158\) 4.63078e9 0.591149
\(159\) −6.88970e9 −0.854895
\(160\) −9.25533e8 −0.111648
\(161\) −1.41971e9 −0.166526
\(162\) 1.24387e10 1.41892
\(163\) −3.62816e9 −0.402571 −0.201285 0.979533i \(-0.564512\pi\)
−0.201285 + 0.979533i \(0.564512\pi\)
\(164\) −2.15139e9 −0.232232
\(165\) −1.78462e9 −0.187443
\(166\) 2.44808e10 2.50230
\(167\) −1.50076e10 −1.49309 −0.746546 0.665334i \(-0.768289\pi\)
−0.746546 + 0.665334i \(0.768289\pi\)
\(168\) −6.69448e8 −0.0648374
\(169\) −1.00467e10 −0.947401
\(170\) 0 0
\(171\) −1.09062e10 −0.975415
\(172\) −1.84032e10 −1.60330
\(173\) 2.29866e10 1.95105 0.975523 0.219899i \(-0.0705728\pi\)
0.975523 + 0.219899i \(0.0705728\pi\)
\(174\) −4.20558e10 −3.47820
\(175\) −2.87008e9 −0.231325
\(176\) −1.82600e10 −1.43448
\(177\) −1.73198e10 −1.32636
\(178\) 6.77141e9 0.505579
\(179\) −1.02963e10 −0.749625 −0.374812 0.927101i \(-0.622293\pi\)
−0.374812 + 0.927101i \(0.622293\pi\)
\(180\) −1.27755e9 −0.0907091
\(181\) −1.97780e10 −1.36971 −0.684857 0.728678i \(-0.740135\pi\)
−0.684857 + 0.728678i \(0.740135\pi\)
\(182\) −1.15414e9 −0.0779720
\(183\) −5.52346e9 −0.364067
\(184\) 2.17642e9 0.139979
\(185\) 2.21686e9 0.139144
\(186\) 3.52450e10 2.15918
\(187\) 0 0
\(188\) 1.88531e10 1.10071
\(189\) 1.62128e8 0.00924229
\(190\) −1.93797e9 −0.107884
\(191\) 1.03563e10 0.563057 0.281529 0.959553i \(-0.409159\pi\)
0.281529 + 0.959553i \(0.409159\pi\)
\(192\) −3.34519e10 −1.77650
\(193\) 1.76983e10 0.918173 0.459086 0.888392i \(-0.348177\pi\)
0.459086 + 0.888392i \(0.348177\pi\)
\(194\) −2.63931e10 −1.33777
\(195\) −5.13201e8 −0.0254174
\(196\) −2.21590e10 −1.07250
\(197\) 1.40731e10 0.665721 0.332860 0.942976i \(-0.391986\pi\)
0.332860 + 0.942976i \(0.391986\pi\)
\(198\) −5.49228e10 −2.53956
\(199\) −9.51240e8 −0.0429983 −0.0214992 0.999769i \(-0.506844\pi\)
−0.0214992 + 0.999769i \(0.506844\pi\)
\(200\) 4.39985e9 0.194448
\(201\) −1.68022e10 −0.726079
\(202\) 1.01803e10 0.430211
\(203\) 9.41536e9 0.389139
\(204\) 0 0
\(205\) 4.03046e8 0.0159390
\(206\) 2.19696e10 0.850000
\(207\) −1.94282e10 −0.735473
\(208\) −5.25099e9 −0.194516
\(209\) −4.42718e10 −1.60498
\(210\) 1.06190e9 0.0376787
\(211\) 2.33273e10 0.810201 0.405101 0.914272i \(-0.367236\pi\)
0.405101 + 0.914272i \(0.367236\pi\)
\(212\) −2.00210e10 −0.680729
\(213\) −2.02496e10 −0.674074
\(214\) 4.78875e10 1.56085
\(215\) 3.44769e9 0.110041
\(216\) −2.48543e8 −0.00776890
\(217\) −7.89057e9 −0.241568
\(218\) −8.10811e10 −2.43145
\(219\) 7.33647e10 2.15520
\(220\) −5.18600e9 −0.149255
\(221\) 0 0
\(222\) 1.34599e11 3.71923
\(223\) −2.38061e10 −0.644638 −0.322319 0.946631i \(-0.604462\pi\)
−0.322319 + 0.946631i \(0.604462\pi\)
\(224\) 1.25808e10 0.333881
\(225\) −3.92761e10 −1.02166
\(226\) −9.91799e10 −2.52892
\(227\) 1.43719e10 0.359251 0.179626 0.983735i \(-0.442511\pi\)
0.179626 + 0.983735i \(0.442511\pi\)
\(228\) −6.25254e10 −1.53232
\(229\) −5.55766e10 −1.33546 −0.667732 0.744402i \(-0.732735\pi\)
−0.667732 + 0.744402i \(0.732735\pi\)
\(230\) −3.45230e9 −0.0813454
\(231\) 2.42584e10 0.560542
\(232\) −1.44338e10 −0.327103
\(233\) −4.77598e10 −1.06160 −0.530800 0.847497i \(-0.678108\pi\)
−0.530800 + 0.847497i \(0.678108\pi\)
\(234\) −1.57940e10 −0.344367
\(235\) −3.53198e9 −0.0755462
\(236\) −5.03301e10 −1.05614
\(237\) −2.79896e10 −0.576274
\(238\) 0 0
\(239\) 8.16620e9 0.161894 0.0809468 0.996718i \(-0.474206\pi\)
0.0809468 + 0.996718i \(0.474206\pi\)
\(240\) 4.83130e9 0.0939969
\(241\) 1.30949e10 0.250049 0.125025 0.992154i \(-0.460099\pi\)
0.125025 + 0.992154i \(0.460099\pi\)
\(242\) −1.45010e11 −2.71788
\(243\) −7.73414e10 −1.42293
\(244\) −1.60508e10 −0.289896
\(245\) 4.15131e9 0.0736101
\(246\) 2.44714e10 0.426040
\(247\) −1.27312e10 −0.217637
\(248\) 1.20963e10 0.203058
\(249\) −1.47968e11 −2.43933
\(250\) −1.40009e10 −0.226686
\(251\) 4.05239e9 0.0644435 0.0322217 0.999481i \(-0.489742\pi\)
0.0322217 + 0.999481i \(0.489742\pi\)
\(252\) 1.73657e10 0.271263
\(253\) −7.88657e10 −1.21017
\(254\) −4.04377e10 −0.609586
\(255\) 0 0
\(256\) 4.68030e10 0.681074
\(257\) −1.03270e11 −1.47664 −0.738322 0.674448i \(-0.764382\pi\)
−0.738322 + 0.674448i \(0.764382\pi\)
\(258\) 2.09330e11 2.94133
\(259\) −3.01337e10 −0.416106
\(260\) −1.49133e9 −0.0202392
\(261\) 1.28846e11 1.71865
\(262\) −6.25682e10 −0.820348
\(263\) 4.00733e10 0.516480 0.258240 0.966081i \(-0.416857\pi\)
0.258240 + 0.966081i \(0.416857\pi\)
\(264\) −3.71882e10 −0.471181
\(265\) 3.75077e9 0.0467212
\(266\) 2.63429e10 0.322623
\(267\) −4.09282e10 −0.492858
\(268\) −4.88260e10 −0.578156
\(269\) 1.37028e11 1.59560 0.797799 0.602924i \(-0.205998\pi\)
0.797799 + 0.602924i \(0.205998\pi\)
\(270\) 3.94245e8 0.00451471
\(271\) −4.28730e10 −0.482861 −0.241431 0.970418i \(-0.577617\pi\)
−0.241431 + 0.970418i \(0.577617\pi\)
\(272\) 0 0
\(273\) 6.97594e9 0.0760100
\(274\) 4.72195e10 0.506108
\(275\) −1.59435e11 −1.68107
\(276\) −1.11383e11 −1.15538
\(277\) 3.59363e10 0.366753 0.183377 0.983043i \(-0.441297\pi\)
0.183377 + 0.983043i \(0.441297\pi\)
\(278\) −1.60754e11 −1.61421
\(279\) −1.07980e11 −1.06690
\(280\) 3.64449e8 0.00354345
\(281\) 6.81885e10 0.652429 0.326214 0.945296i \(-0.394227\pi\)
0.326214 + 0.945296i \(0.394227\pi\)
\(282\) −2.14448e11 −2.01930
\(283\) −5.87965e10 −0.544895 −0.272448 0.962171i \(-0.587833\pi\)
−0.272448 + 0.962171i \(0.587833\pi\)
\(284\) −5.88439e10 −0.536746
\(285\) 1.17136e10 0.105169
\(286\) −6.41133e10 −0.566632
\(287\) −5.47860e9 −0.0476652
\(288\) 1.72163e11 1.47460
\(289\) 0 0
\(290\) 2.28953e10 0.190088
\(291\) 1.59527e11 1.30411
\(292\) 2.13193e11 1.71613
\(293\) 9.24412e10 0.732760 0.366380 0.930465i \(-0.380597\pi\)
0.366380 + 0.930465i \(0.380597\pi\)
\(294\) 2.52051e11 1.96755
\(295\) 9.42892e9 0.0724875
\(296\) 4.61952e10 0.349771
\(297\) 9.00630e9 0.0671649
\(298\) −1.23491e10 −0.0907112
\(299\) −2.26793e10 −0.164100
\(300\) −2.25171e11 −1.60497
\(301\) −4.68644e10 −0.329074
\(302\) 4.04350e11 2.79721
\(303\) −6.15326e10 −0.419386
\(304\) 1.19852e11 0.804847
\(305\) 3.00698e9 0.0198967
\(306\) 0 0
\(307\) −2.31914e11 −1.49006 −0.745032 0.667029i \(-0.767566\pi\)
−0.745032 + 0.667029i \(0.767566\pi\)
\(308\) 7.04933e10 0.446344
\(309\) −1.32790e11 −0.828612
\(310\) −1.91875e10 −0.118002
\(311\) −3.18428e11 −1.93014 −0.965071 0.261989i \(-0.915622\pi\)
−0.965071 + 0.261989i \(0.915622\pi\)
\(312\) −1.06942e10 −0.0638927
\(313\) 1.68213e11 0.990629 0.495315 0.868714i \(-0.335053\pi\)
0.495315 + 0.868714i \(0.335053\pi\)
\(314\) −2.40266e11 −1.39479
\(315\) −3.25332e9 −0.0186179
\(316\) −8.13360e10 −0.458871
\(317\) 1.71014e11 0.951187 0.475594 0.879665i \(-0.342233\pi\)
0.475594 + 0.879665i \(0.342233\pi\)
\(318\) 2.27732e11 1.24883
\(319\) 5.23029e11 2.82792
\(320\) 1.82113e10 0.0970880
\(321\) −2.89444e11 −1.52157
\(322\) 4.69271e10 0.243261
\(323\) 0 0
\(324\) −2.18477e11 −1.10142
\(325\) −4.58484e10 −0.227955
\(326\) 1.19925e11 0.588073
\(327\) 4.90075e11 2.37027
\(328\) 8.39873e9 0.0400665
\(329\) 4.80102e10 0.225919
\(330\) 5.89890e10 0.273816
\(331\) −2.35952e11 −1.08043 −0.540215 0.841527i \(-0.681657\pi\)
−0.540215 + 0.841527i \(0.681657\pi\)
\(332\) −4.29986e11 −1.94237
\(333\) −4.12370e11 −1.83775
\(334\) 4.96061e11 2.18110
\(335\) 9.14715e9 0.0396812
\(336\) −6.56719e10 −0.281095
\(337\) 1.03556e11 0.437364 0.218682 0.975796i \(-0.429824\pi\)
0.218682 + 0.975796i \(0.429824\pi\)
\(338\) 3.32084e11 1.38396
\(339\) 5.99469e11 2.46529
\(340\) 0 0
\(341\) −4.38326e11 −1.75551
\(342\) 3.60493e11 1.42488
\(343\) −1.16089e11 −0.452864
\(344\) 7.18434e10 0.276614
\(345\) 2.08666e10 0.0792986
\(346\) −7.59800e11 −2.85008
\(347\) −4.83654e10 −0.179082 −0.0895411 0.995983i \(-0.528540\pi\)
−0.0895411 + 0.995983i \(0.528540\pi\)
\(348\) 7.38677e11 2.69990
\(349\) 3.17902e11 1.14704 0.573520 0.819191i \(-0.305577\pi\)
0.573520 + 0.819191i \(0.305577\pi\)
\(350\) 9.48678e10 0.337919
\(351\) 2.58993e9 0.00910763
\(352\) 6.98869e11 2.42635
\(353\) −1.59102e11 −0.545368 −0.272684 0.962104i \(-0.587911\pi\)
−0.272684 + 0.962104i \(0.587911\pi\)
\(354\) 5.72488e11 1.93754
\(355\) 1.10239e10 0.0368390
\(356\) −1.18935e11 −0.392449
\(357\) 0 0
\(358\) 3.40335e11 1.09505
\(359\) −6.73256e10 −0.213922 −0.106961 0.994263i \(-0.534112\pi\)
−0.106961 + 0.994263i \(0.534112\pi\)
\(360\) 4.98736e9 0.0156498
\(361\) −3.21040e10 −0.0994895
\(362\) 6.53744e11 2.00087
\(363\) 8.76480e11 2.64949
\(364\) 2.02716e10 0.0605247
\(365\) −3.99399e10 −0.117785
\(366\) 1.82572e11 0.531827
\(367\) −8.98916e10 −0.258655 −0.129328 0.991602i \(-0.541282\pi\)
−0.129328 + 0.991602i \(0.541282\pi\)
\(368\) 2.13504e11 0.606862
\(369\) −7.49727e10 −0.210516
\(370\) −7.32760e10 −0.203261
\(371\) −5.09842e10 −0.139718
\(372\) −6.19051e11 −1.67603
\(373\) −4.15763e11 −1.11213 −0.556065 0.831139i \(-0.687690\pi\)
−0.556065 + 0.831139i \(0.687690\pi\)
\(374\) 0 0
\(375\) 8.46248e10 0.220982
\(376\) −7.35999e10 −0.189903
\(377\) 1.50406e11 0.383469
\(378\) −5.35898e9 −0.0135011
\(379\) −2.18793e11 −0.544699 −0.272350 0.962198i \(-0.587801\pi\)
−0.272350 + 0.962198i \(0.587801\pi\)
\(380\) 3.40390e10 0.0837433
\(381\) 2.44416e11 0.594247
\(382\) −3.42316e11 −0.822511
\(383\) −7.68723e11 −1.82547 −0.912736 0.408549i \(-0.866035\pi\)
−0.912736 + 0.408549i \(0.866035\pi\)
\(384\) 2.35273e11 0.552181
\(385\) −1.32063e10 −0.0306344
\(386\) −5.85001e11 −1.34126
\(387\) −6.41323e11 −1.45337
\(388\) 4.63574e11 1.03843
\(389\) −3.53345e11 −0.782394 −0.391197 0.920307i \(-0.627939\pi\)
−0.391197 + 0.920307i \(0.627939\pi\)
\(390\) 1.69634e10 0.0371297
\(391\) 0 0
\(392\) 8.65056e10 0.185036
\(393\) 3.78179e11 0.799706
\(394\) −4.65173e11 −0.972481
\(395\) 1.52376e10 0.0314942
\(396\) 9.64676e11 1.97130
\(397\) 3.01014e11 0.608176 0.304088 0.952644i \(-0.401648\pi\)
0.304088 + 0.952644i \(0.401648\pi\)
\(398\) 3.14423e10 0.0628117
\(399\) −1.59223e11 −0.314505
\(400\) 4.31619e11 0.843006
\(401\) −2.94871e11 −0.569486 −0.284743 0.958604i \(-0.591908\pi\)
−0.284743 + 0.958604i \(0.591908\pi\)
\(402\) 5.55380e11 1.06065
\(403\) −1.26049e11 −0.238048
\(404\) −1.78810e11 −0.333945
\(405\) 4.09298e10 0.0755948
\(406\) −3.11215e11 −0.568452
\(407\) −1.67395e12 −3.02390
\(408\) 0 0
\(409\) 5.44264e11 0.961733 0.480867 0.876794i \(-0.340322\pi\)
0.480867 + 0.876794i \(0.340322\pi\)
\(410\) −1.33223e10 −0.0232837
\(411\) −2.85407e11 −0.493374
\(412\) −3.85878e11 −0.659801
\(413\) −1.28167e11 −0.216771
\(414\) 6.42181e11 1.07437
\(415\) 8.05543e10 0.133313
\(416\) 2.00973e11 0.329016
\(417\) 9.71641e11 1.57360
\(418\) 1.46336e12 2.34454
\(419\) 7.83707e11 1.24220 0.621099 0.783732i \(-0.286686\pi\)
0.621099 + 0.783732i \(0.286686\pi\)
\(420\) −1.86514e10 −0.0292475
\(421\) −8.34641e11 −1.29488 −0.647441 0.762115i \(-0.724161\pi\)
−0.647441 + 0.762115i \(0.724161\pi\)
\(422\) −7.71060e11 −1.18354
\(423\) 6.57002e11 0.997781
\(424\) 7.81590e10 0.117445
\(425\) 0 0
\(426\) 6.69330e11 0.984684
\(427\) −4.08739e10 −0.0595005
\(428\) −8.41106e11 −1.21159
\(429\) 3.87518e11 0.552375
\(430\) −1.13960e11 −0.160747
\(431\) −5.21428e11 −0.727858 −0.363929 0.931427i \(-0.618565\pi\)
−0.363929 + 0.931427i \(0.618565\pi\)
\(432\) −2.43817e10 −0.0336811
\(433\) −1.09566e12 −1.49790 −0.748948 0.662629i \(-0.769441\pi\)
−0.748948 + 0.662629i \(0.769441\pi\)
\(434\) 2.60815e11 0.352882
\(435\) −1.38385e11 −0.185305
\(436\) 1.42413e12 1.88738
\(437\) 5.17645e11 0.678994
\(438\) −2.42500e12 −3.14831
\(439\) −5.78364e11 −0.743208 −0.371604 0.928391i \(-0.621192\pi\)
−0.371604 + 0.928391i \(0.621192\pi\)
\(440\) 2.02454e10 0.0257507
\(441\) −7.72207e11 −0.972211
\(442\) 0 0
\(443\) −1.28456e12 −1.58466 −0.792332 0.610091i \(-0.791133\pi\)
−0.792332 + 0.610091i \(0.791133\pi\)
\(444\) −2.36413e12 −2.88700
\(445\) 2.22814e10 0.0269354
\(446\) 7.86886e11 0.941684
\(447\) 7.46410e10 0.0884288
\(448\) −2.47546e11 −0.290339
\(449\) −8.37005e11 −0.971895 −0.485948 0.873988i \(-0.661525\pi\)
−0.485948 + 0.873988i \(0.661525\pi\)
\(450\) 1.29823e12 1.49244
\(451\) −3.04339e11 −0.346389
\(452\) 1.74202e12 1.96304
\(453\) −2.44399e12 −2.72683
\(454\) −4.75049e11 −0.524792
\(455\) −3.79772e9 −0.00415405
\(456\) 2.44090e11 0.264367
\(457\) 1.06355e12 1.14061 0.570304 0.821434i \(-0.306825\pi\)
0.570304 + 0.821434i \(0.306825\pi\)
\(458\) 1.83703e12 1.95084
\(459\) 0 0
\(460\) 6.06369e10 0.0631433
\(461\) 2.92562e10 0.0301691 0.0150846 0.999886i \(-0.495198\pi\)
0.0150846 + 0.999886i \(0.495198\pi\)
\(462\) −8.01837e11 −0.818837
\(463\) 8.91918e11 0.902008 0.451004 0.892522i \(-0.351066\pi\)
0.451004 + 0.892522i \(0.351066\pi\)
\(464\) −1.41593e12 −1.41812
\(465\) 1.15974e11 0.115033
\(466\) 1.57865e12 1.55078
\(467\) 1.16802e12 1.13638 0.568190 0.822898i \(-0.307644\pi\)
0.568190 + 0.822898i \(0.307644\pi\)
\(468\) 2.77410e11 0.267310
\(469\) −1.24337e11 −0.118665
\(470\) 1.16746e11 0.110358
\(471\) 1.45223e12 1.35970
\(472\) 1.96481e11 0.182214
\(473\) −2.60334e12 −2.39142
\(474\) 9.25169e11 0.841819
\(475\) 1.04647e12 0.943205
\(476\) 0 0
\(477\) −6.97701e11 −0.617073
\(478\) −2.69926e11 −0.236493
\(479\) −1.54953e12 −1.34490 −0.672452 0.740141i \(-0.734759\pi\)
−0.672452 + 0.740141i \(0.734759\pi\)
\(480\) −1.84910e11 −0.158991
\(481\) −4.81374e11 −0.410043
\(482\) −4.32839e11 −0.365271
\(483\) −2.83640e11 −0.237140
\(484\) 2.54699e12 2.10971
\(485\) −8.68468e10 −0.0712715
\(486\) 2.55645e12 2.07861
\(487\) −5.43663e11 −0.437975 −0.218988 0.975728i \(-0.570275\pi\)
−0.218988 + 0.975728i \(0.570275\pi\)
\(488\) 6.26600e10 0.0500151
\(489\) −7.24859e11 −0.573276
\(490\) −1.37217e11 −0.107529
\(491\) 1.97444e12 1.53312 0.766561 0.642171i \(-0.221966\pi\)
0.766561 + 0.642171i \(0.221966\pi\)
\(492\) −4.29821e11 −0.330708
\(493\) 0 0
\(494\) 4.20816e11 0.317922
\(495\) −1.80724e11 −0.135298
\(496\) 1.18663e12 0.880333
\(497\) −1.49848e11 −0.110166
\(498\) 4.89094e12 3.56337
\(499\) −7.59393e11 −0.548295 −0.274147 0.961688i \(-0.588396\pi\)
−0.274147 + 0.961688i \(0.588396\pi\)
\(500\) 2.45914e11 0.175962
\(501\) −2.99832e12 −2.12622
\(502\) −1.33948e11 −0.0941387
\(503\) −6.63986e11 −0.462490 −0.231245 0.972895i \(-0.574280\pi\)
−0.231245 + 0.972895i \(0.574280\pi\)
\(504\) −6.77932e10 −0.0468003
\(505\) 3.34985e10 0.0229200
\(506\) 2.60683e12 1.76781
\(507\) −2.00720e12 −1.34914
\(508\) 7.10257e11 0.473182
\(509\) 3.72373e11 0.245894 0.122947 0.992413i \(-0.460765\pi\)
0.122947 + 0.992413i \(0.460765\pi\)
\(510\) 0 0
\(511\) 5.42903e11 0.352232
\(512\) −2.14997e12 −1.38267
\(513\) −5.91140e10 −0.0376845
\(514\) 3.41349e12 2.15707
\(515\) 7.22911e10 0.0452848
\(516\) −3.67672e12 −2.28316
\(517\) 2.66699e12 1.64178
\(518\) 9.96041e11 0.607846
\(519\) 4.59243e12 2.77836
\(520\) 5.82193e9 0.00349182
\(521\) 1.83776e12 1.09275 0.546374 0.837541i \(-0.316008\pi\)
0.546374 + 0.837541i \(0.316008\pi\)
\(522\) −4.25887e12 −2.51060
\(523\) −1.35808e12 −0.793720 −0.396860 0.917879i \(-0.629900\pi\)
−0.396860 + 0.917879i \(0.629900\pi\)
\(524\) 1.09896e12 0.636784
\(525\) −5.73406e11 −0.329416
\(526\) −1.32458e12 −0.754472
\(527\) 0 0
\(528\) −3.64811e12 −2.04275
\(529\) −8.79021e11 −0.488032
\(530\) −1.23978e11 −0.0682501
\(531\) −1.75392e12 −0.957383
\(532\) −4.62692e11 −0.250432
\(533\) −8.75184e10 −0.0469707
\(534\) 1.35284e12 0.719965
\(535\) 1.57574e11 0.0831559
\(536\) 1.90610e11 0.0997478
\(537\) −2.05708e12 −1.06750
\(538\) −4.52932e12 −2.33084
\(539\) −3.13465e12 −1.59970
\(540\) −6.92461e9 −0.00350448
\(541\) −3.20356e11 −0.160785 −0.0803925 0.996763i \(-0.525617\pi\)
−0.0803925 + 0.996763i \(0.525617\pi\)
\(542\) 1.41713e12 0.705362
\(543\) −3.95140e12 −1.95053
\(544\) 0 0
\(545\) −2.66798e11 −0.129538
\(546\) −2.30583e11 −0.111035
\(547\) 6.22782e11 0.297436 0.148718 0.988880i \(-0.452485\pi\)
0.148718 + 0.988880i \(0.452485\pi\)
\(548\) −8.29373e11 −0.392860
\(549\) −5.59345e11 −0.262787
\(550\) 5.26996e12 2.45570
\(551\) −3.43297e12 −1.58667
\(552\) 4.34821e11 0.199336
\(553\) −2.07125e11 −0.0941823
\(554\) −1.18784e12 −0.535751
\(555\) 4.42899e11 0.198147
\(556\) 2.82353e12 1.25301
\(557\) 6.56343e11 0.288923 0.144462 0.989510i \(-0.453855\pi\)
0.144462 + 0.989510i \(0.453855\pi\)
\(558\) 3.56916e12 1.55852
\(559\) −7.48639e11 −0.324279
\(560\) 3.57519e10 0.0153622
\(561\) 0 0
\(562\) −2.25391e12 −0.953064
\(563\) 4.16855e12 1.74863 0.874313 0.485362i \(-0.161312\pi\)
0.874313 + 0.485362i \(0.161312\pi\)
\(564\) 3.76661e12 1.56746
\(565\) −3.26352e11 −0.134731
\(566\) 1.94346e12 0.795980
\(567\) −5.56359e11 −0.226064
\(568\) 2.29718e11 0.0926035
\(569\) 3.85025e12 1.53987 0.769935 0.638122i \(-0.220289\pi\)
0.769935 + 0.638122i \(0.220289\pi\)
\(570\) −3.87182e11 −0.153631
\(571\) −3.98793e12 −1.56995 −0.784973 0.619530i \(-0.787323\pi\)
−0.784973 + 0.619530i \(0.787323\pi\)
\(572\) 1.12610e12 0.439840
\(573\) 2.06905e12 0.801815
\(574\) 1.81090e11 0.0696290
\(575\) 1.86418e12 0.711185
\(576\) −3.38758e12 −1.28230
\(577\) 1.61359e12 0.606042 0.303021 0.952984i \(-0.402005\pi\)
0.303021 + 0.952984i \(0.402005\pi\)
\(578\) 0 0
\(579\) 3.53590e12 1.30751
\(580\) −4.02138e11 −0.147553
\(581\) −1.09497e12 −0.398668
\(582\) −5.27300e12 −1.90504
\(583\) −2.83220e12 −1.01535
\(584\) −8.32274e11 −0.296080
\(585\) −5.19705e10 −0.0183466
\(586\) −3.05555e12 −1.07041
\(587\) 2.68902e12 0.934809 0.467405 0.884043i \(-0.345189\pi\)
0.467405 + 0.884043i \(0.345189\pi\)
\(588\) −4.42709e12 −1.52729
\(589\) 2.87701e12 0.984969
\(590\) −3.11664e11 −0.105889
\(591\) 2.81163e12 0.948012
\(592\) 4.53168e12 1.51639
\(593\) 1.62650e12 0.540141 0.270071 0.962840i \(-0.412953\pi\)
0.270071 + 0.962840i \(0.412953\pi\)
\(594\) −2.97694e11 −0.0981141
\(595\) 0 0
\(596\) 2.16902e11 0.0704134
\(597\) −1.90046e11 −0.0612313
\(598\) 7.49641e11 0.239717
\(599\) 2.52469e12 0.801286 0.400643 0.916234i \(-0.368787\pi\)
0.400643 + 0.916234i \(0.368787\pi\)
\(600\) 8.79034e11 0.276901
\(601\) 5.30235e11 0.165781 0.0828903 0.996559i \(-0.473585\pi\)
0.0828903 + 0.996559i \(0.473585\pi\)
\(602\) 1.54906e12 0.480710
\(603\) −1.70151e12 −0.524091
\(604\) −7.10209e12 −2.17130
\(605\) −4.77158e11 −0.144798
\(606\) 2.03390e12 0.612637
\(607\) 4.14892e12 1.24047 0.620234 0.784416i \(-0.287037\pi\)
0.620234 + 0.784416i \(0.287037\pi\)
\(608\) −4.58712e12 −1.36136
\(609\) 1.88107e12 0.554149
\(610\) −9.93929e10 −0.0290651
\(611\) 7.66943e11 0.222627
\(612\) 0 0
\(613\) 4.35661e12 1.24617 0.623084 0.782155i \(-0.285879\pi\)
0.623084 + 0.782155i \(0.285879\pi\)
\(614\) 7.66570e12 2.17668
\(615\) 8.05233e10 0.0226978
\(616\) −2.75195e11 −0.0770066
\(617\) −6.33871e11 −0.176083 −0.0880416 0.996117i \(-0.528061\pi\)
−0.0880416 + 0.996117i \(0.528061\pi\)
\(618\) 4.38923e12 1.21043
\(619\) 2.92858e12 0.801770 0.400885 0.916128i \(-0.368703\pi\)
0.400885 + 0.916128i \(0.368703\pi\)
\(620\) 3.37013e11 0.0915975
\(621\) −1.05306e11 −0.0284144
\(622\) 1.05253e13 2.81954
\(623\) −3.02871e11 −0.0805493
\(624\) −1.04908e12 −0.276999
\(625\) 3.74552e12 0.981866
\(626\) −5.56013e12 −1.44711
\(627\) −8.84493e12 −2.28555
\(628\) 4.22009e12 1.08269
\(629\) 0 0
\(630\) 1.07535e11 0.0271969
\(631\) 1.86510e12 0.468348 0.234174 0.972195i \(-0.424761\pi\)
0.234174 + 0.972195i \(0.424761\pi\)
\(632\) 3.17524e11 0.0791679
\(633\) 4.66049e12 1.15376
\(634\) −5.65271e12 −1.38949
\(635\) −1.33061e11 −0.0324764
\(636\) −3.99994e12 −0.969385
\(637\) −9.01426e11 −0.216921
\(638\) −1.72882e13 −4.13101
\(639\) −2.05062e12 −0.486554
\(640\) −1.28083e11 −0.0301774
\(641\) 4.47273e12 1.04643 0.523216 0.852200i \(-0.324732\pi\)
0.523216 + 0.852200i \(0.324732\pi\)
\(642\) 9.56730e12 2.22270
\(643\) 6.50740e12 1.50127 0.750634 0.660718i \(-0.229748\pi\)
0.750634 + 0.660718i \(0.229748\pi\)
\(644\) −8.24238e11 −0.188828
\(645\) 6.88803e11 0.156703
\(646\) 0 0
\(647\) 4.43814e12 0.995708 0.497854 0.867261i \(-0.334121\pi\)
0.497854 + 0.867261i \(0.334121\pi\)
\(648\) 8.52901e11 0.190025
\(649\) −7.11977e12 −1.57531
\(650\) 1.51547e12 0.332995
\(651\) −1.57643e12 −0.344002
\(652\) −2.10639e12 −0.456484
\(653\) −4.32967e12 −0.931848 −0.465924 0.884825i \(-0.654278\pi\)
−0.465924 + 0.884825i \(0.654278\pi\)
\(654\) −1.61990e13 −3.46248
\(655\) −2.05881e11 −0.0437050
\(656\) 8.23902e11 0.173703
\(657\) 7.42944e12 1.55565
\(658\) −1.58693e12 −0.330021
\(659\) 4.54367e12 0.938475 0.469238 0.883072i \(-0.344529\pi\)
0.469238 + 0.883072i \(0.344529\pi\)
\(660\) −1.03610e12 −0.212546
\(661\) 6.91408e12 1.40873 0.704365 0.709838i \(-0.251232\pi\)
0.704365 + 0.709838i \(0.251232\pi\)
\(662\) 7.79915e12 1.57829
\(663\) 0 0
\(664\) 1.67860e12 0.335113
\(665\) 8.66814e10 0.0171881
\(666\) 1.36305e13 2.68458
\(667\) −6.11548e12 −1.19637
\(668\) −8.71292e12 −1.69305
\(669\) −4.75615e12 −0.917990
\(670\) −3.02350e11 −0.0579660
\(671\) −2.27057e12 −0.432398
\(672\) 2.51348e12 0.475459
\(673\) −5.42906e12 −1.02013 −0.510066 0.860135i \(-0.670379\pi\)
−0.510066 + 0.860135i \(0.670379\pi\)
\(674\) −3.42296e12 −0.638898
\(675\) −2.12886e11 −0.0394711
\(676\) −5.83280e12 −1.07428
\(677\) −4.96708e12 −0.908766 −0.454383 0.890806i \(-0.650140\pi\)
−0.454383 + 0.890806i \(0.650140\pi\)
\(678\) −1.98149e13 −3.60128
\(679\) 1.18051e12 0.213135
\(680\) 0 0
\(681\) 2.87132e12 0.511587
\(682\) 1.44884e13 2.56444
\(683\) −5.99267e12 −1.05372 −0.526862 0.849951i \(-0.676632\pi\)
−0.526862 + 0.849951i \(0.676632\pi\)
\(684\) −6.33177e12 −1.10605
\(685\) 1.55376e11 0.0269635
\(686\) 3.83721e12 0.661541
\(687\) −1.11035e13 −1.90175
\(688\) 7.04772e12 1.19923
\(689\) −8.14451e11 −0.137682
\(690\) −6.89725e11 −0.115839
\(691\) −1.36510e12 −0.227778 −0.113889 0.993493i \(-0.536331\pi\)
−0.113889 + 0.993493i \(0.536331\pi\)
\(692\) 1.33453e13 2.21233
\(693\) 2.45658e12 0.404605
\(694\) 1.59867e12 0.261602
\(695\) −5.28964e11 −0.0859992
\(696\) −2.88369e12 −0.465807
\(697\) 0 0
\(698\) −1.05079e13 −1.67559
\(699\) −9.54179e12 −1.51176
\(700\) −1.66628e12 −0.262305
\(701\) −6.05370e12 −0.946869 −0.473435 0.880829i \(-0.656986\pi\)
−0.473435 + 0.880829i \(0.656986\pi\)
\(702\) −8.56075e10 −0.0133044
\(703\) 1.09872e13 1.69663
\(704\) −1.37513e13 −2.10993
\(705\) −7.05644e11 −0.107581
\(706\) 5.25896e12 0.796671
\(707\) −4.55345e11 −0.0685415
\(708\) −1.00553e13 −1.50399
\(709\) 4.47272e12 0.664758 0.332379 0.943146i \(-0.392149\pi\)
0.332379 + 0.943146i \(0.392149\pi\)
\(710\) −3.64385e11 −0.0538143
\(711\) −2.83443e12 −0.415961
\(712\) 4.64303e11 0.0677083
\(713\) 5.12510e12 0.742676
\(714\) 0 0
\(715\) −2.10966e11 −0.0301880
\(716\) −5.97772e12 −0.850016
\(717\) 1.63150e12 0.230543
\(718\) 2.22538e12 0.312496
\(719\) 1.23980e13 1.73010 0.865050 0.501686i \(-0.167287\pi\)
0.865050 + 0.501686i \(0.167287\pi\)
\(720\) 4.89252e11 0.0678479
\(721\) −9.82652e11 −0.135423
\(722\) 1.06117e12 0.145334
\(723\) 2.61619e12 0.356080
\(724\) −1.14825e13 −1.55315
\(725\) −1.23630e13 −1.66190
\(726\) −2.89712e13 −3.87036
\(727\) −6.14698e12 −0.816125 −0.408063 0.912954i \(-0.633795\pi\)
−0.408063 + 0.912954i \(0.633795\pi\)
\(728\) −7.91375e10 −0.0104422
\(729\) −8.04481e12 −1.05497
\(730\) 1.32017e12 0.172059
\(731\) 0 0
\(732\) −3.20674e12 −0.412823
\(733\) −5.25486e12 −0.672347 −0.336173 0.941800i \(-0.609133\pi\)
−0.336173 + 0.941800i \(0.609133\pi\)
\(734\) 2.97128e12 0.377843
\(735\) 8.29378e11 0.104824
\(736\) −8.17148e12 −1.02648
\(737\) −6.90701e12 −0.862355
\(738\) 2.47815e12 0.307520
\(739\) −1.24520e12 −0.153581 −0.0767907 0.997047i \(-0.524467\pi\)
−0.0767907 + 0.997047i \(0.524467\pi\)
\(740\) 1.28704e12 0.157779
\(741\) −2.54352e12 −0.309923
\(742\) 1.68523e12 0.204100
\(743\) −8.09895e12 −0.974943 −0.487471 0.873139i \(-0.662081\pi\)
−0.487471 + 0.873139i \(0.662081\pi\)
\(744\) 2.41668e12 0.289162
\(745\) −4.06348e10 −0.00483275
\(746\) 1.37426e13 1.62459
\(747\) −1.49843e13 −1.76074
\(748\) 0 0
\(749\) −2.14191e12 −0.248675
\(750\) −2.79719e12 −0.322810
\(751\) 1.09947e13 1.26125 0.630627 0.776086i \(-0.282798\pi\)
0.630627 + 0.776086i \(0.282798\pi\)
\(752\) −7.22004e12 −0.823302
\(753\) 8.09615e11 0.0917700
\(754\) −4.97154e12 −0.560170
\(755\) 1.33052e12 0.149025
\(756\) 9.41263e10 0.0104800
\(757\) −9.44013e12 −1.04483 −0.522416 0.852691i \(-0.674969\pi\)
−0.522416 + 0.852691i \(0.674969\pi\)
\(758\) 7.23199e12 0.795694
\(759\) −1.57563e13 −1.72333
\(760\) −1.32883e11 −0.0144480
\(761\) 1.19815e13 1.29504 0.647518 0.762050i \(-0.275807\pi\)
0.647518 + 0.762050i \(0.275807\pi\)
\(762\) −8.07893e12 −0.868073
\(763\) 3.62659e12 0.387380
\(764\) 6.01251e12 0.638463
\(765\) 0 0
\(766\) 2.54094e13 2.66664
\(767\) −2.04742e12 −0.213613
\(768\) 9.35064e12 0.969876
\(769\) −1.26588e13 −1.30535 −0.652673 0.757640i \(-0.726352\pi\)
−0.652673 + 0.757640i \(0.726352\pi\)
\(770\) 4.36522e11 0.0447505
\(771\) −2.06321e13 −2.10280
\(772\) 1.02751e13 1.04114
\(773\) −1.64501e12 −0.165715 −0.0828574 0.996561i \(-0.526405\pi\)
−0.0828574 + 0.996561i \(0.526405\pi\)
\(774\) 2.11983e13 2.12308
\(775\) 1.03609e13 1.03167
\(776\) −1.80973e12 −0.179157
\(777\) −6.02033e12 −0.592551
\(778\) 1.16795e13 1.14292
\(779\) 1.99757e12 0.194350
\(780\) −2.97948e11 −0.0288214
\(781\) −8.32415e12 −0.800590
\(782\) 0 0
\(783\) 6.98375e11 0.0663989
\(784\) 8.48606e12 0.802203
\(785\) −7.90599e11 −0.0743093
\(786\) −1.25003e13 −1.16821
\(787\) 2.05349e12 0.190812 0.0954060 0.995438i \(-0.469585\pi\)
0.0954060 + 0.995438i \(0.469585\pi\)
\(788\) 8.17040e12 0.754875
\(789\) 8.00612e12 0.735488
\(790\) −5.03664e11 −0.0460065
\(791\) 4.43611e12 0.402910
\(792\) −3.76595e12 −0.340104
\(793\) −6.52944e11 −0.0586336
\(794\) −9.94971e12 −0.888420
\(795\) 7.49355e11 0.0665328
\(796\) −5.52260e11 −0.0487567
\(797\) 3.95127e12 0.346876 0.173438 0.984845i \(-0.444512\pi\)
0.173438 + 0.984845i \(0.444512\pi\)
\(798\) 5.26296e12 0.459428
\(799\) 0 0
\(800\) −1.65195e13 −1.42591
\(801\) −4.14469e12 −0.355750
\(802\) 9.74669e12 0.831902
\(803\) 3.01586e13 2.55971
\(804\) −9.75482e12 −0.823317
\(805\) 1.54414e11 0.0129600
\(806\) 4.16641e12 0.347740
\(807\) 2.73764e13 2.27219
\(808\) 6.98047e11 0.0576147
\(809\) −5.18664e11 −0.0425714 −0.0212857 0.999773i \(-0.506776\pi\)
−0.0212857 + 0.999773i \(0.506776\pi\)
\(810\) −1.35289e12 −0.110429
\(811\) 2.06846e13 1.67901 0.839506 0.543350i \(-0.182844\pi\)
0.839506 + 0.543350i \(0.182844\pi\)
\(812\) 5.46626e12 0.441253
\(813\) −8.56548e12 −0.687613
\(814\) 5.53307e13 4.41729
\(815\) 3.94615e11 0.0313303
\(816\) 0 0
\(817\) 1.70874e13 1.34176
\(818\) −1.79901e13 −1.40489
\(819\) 7.06435e11 0.0548649
\(820\) 2.33996e11 0.0180736
\(821\) −1.09345e13 −0.839952 −0.419976 0.907535i \(-0.637962\pi\)
−0.419976 + 0.907535i \(0.637962\pi\)
\(822\) 9.43384e12 0.720718
\(823\) 2.58366e13 1.96307 0.981537 0.191270i \(-0.0612606\pi\)
0.981537 + 0.191270i \(0.0612606\pi\)
\(824\) 1.50641e12 0.113834
\(825\) −3.18530e13 −2.39391
\(826\) 4.23644e12 0.316659
\(827\) −1.70530e13 −1.26773 −0.633866 0.773443i \(-0.718533\pi\)
−0.633866 + 0.773443i \(0.718533\pi\)
\(828\) −1.12794e13 −0.833969
\(829\) −2.05890e13 −1.51405 −0.757023 0.653388i \(-0.773347\pi\)
−0.757023 + 0.653388i \(0.773347\pi\)
\(830\) −2.66264e12 −0.194743
\(831\) 7.17960e12 0.522271
\(832\) −3.95444e12 −0.286108
\(833\) 0 0
\(834\) −3.21167e13 −2.29870
\(835\) 1.63229e12 0.116201
\(836\) −2.57028e13 −1.81992
\(837\) −5.85276e11 −0.0412188
\(838\) −2.59047e13 −1.81460
\(839\) −1.36702e13 −0.952459 −0.476230 0.879321i \(-0.657997\pi\)
−0.476230 + 0.879321i \(0.657997\pi\)
\(840\) 7.28123e10 0.00504601
\(841\) 2.60500e13 1.79567
\(842\) 2.75882e13 1.89156
\(843\) 1.36232e13 0.929084
\(844\) 1.35431e13 0.918705
\(845\) 1.09273e12 0.0737321
\(846\) −2.17166e13 −1.45755
\(847\) 6.48601e12 0.433014
\(848\) 7.66728e12 0.509167
\(849\) −1.17468e13 −0.775952
\(850\) 0 0
\(851\) 1.95725e13 1.27927
\(852\) −1.17563e13 −0.764347
\(853\) −1.37513e13 −0.889348 −0.444674 0.895692i \(-0.646680\pi\)
−0.444674 + 0.895692i \(0.646680\pi\)
\(854\) 1.35105e12 0.0869181
\(855\) 1.18620e12 0.0759123
\(856\) 3.28356e12 0.209032
\(857\) 1.76873e13 1.12008 0.560038 0.828467i \(-0.310787\pi\)
0.560038 + 0.828467i \(0.310787\pi\)
\(858\) −1.28090e13 −0.806906
\(859\) −1.77011e13 −1.10925 −0.554627 0.832099i \(-0.687139\pi\)
−0.554627 + 0.832099i \(0.687139\pi\)
\(860\) 2.00162e12 0.124778
\(861\) −1.09455e12 −0.0678770
\(862\) 1.72353e13 1.06325
\(863\) −1.00533e12 −0.0616965 −0.0308483 0.999524i \(-0.509821\pi\)
−0.0308483 + 0.999524i \(0.509821\pi\)
\(864\) 9.33167e11 0.0569701
\(865\) −2.50013e12 −0.151841
\(866\) 3.62161e13 2.18812
\(867\) 0 0
\(868\) −4.58101e12 −0.273919
\(869\) −1.15059e13 −0.684435
\(870\) 4.57418e12 0.270693
\(871\) −1.98624e12 −0.116936
\(872\) −5.55958e12 −0.325625
\(873\) 1.61548e13 0.941323
\(874\) −1.71103e13 −0.991870
\(875\) 6.26229e11 0.0361158
\(876\) 4.25932e13 2.44383
\(877\) −1.95904e13 −1.11827 −0.559134 0.829077i \(-0.688866\pi\)
−0.559134 + 0.829077i \(0.688866\pi\)
\(878\) 1.91172e13 1.08568
\(879\) 1.84686e13 1.04348
\(880\) 1.98604e12 0.111639
\(881\) −1.82837e13 −1.02252 −0.511260 0.859426i \(-0.670821\pi\)
−0.511260 + 0.859426i \(0.670821\pi\)
\(882\) 2.55246e13 1.42020
\(883\) −2.47667e13 −1.37102 −0.685512 0.728061i \(-0.740422\pi\)
−0.685512 + 0.728061i \(0.740422\pi\)
\(884\) 0 0
\(885\) 1.88378e12 0.103225
\(886\) 4.24598e13 2.31487
\(887\) 1.60579e13 0.871030 0.435515 0.900181i \(-0.356566\pi\)
0.435515 + 0.900181i \(0.356566\pi\)
\(888\) 9.22920e12 0.498088
\(889\) 1.80869e12 0.0971196
\(890\) −7.36490e11 −0.0393470
\(891\) −3.09060e13 −1.64283
\(892\) −1.38210e13 −0.730969
\(893\) −1.75052e13 −0.921159
\(894\) −2.46719e12 −0.129176
\(895\) 1.11988e12 0.0583400
\(896\) 1.74103e12 0.0902446
\(897\) −4.53103e12 −0.233685
\(898\) 2.76664e13 1.41974
\(899\) −3.39891e13 −1.73548
\(900\) −2.28024e13 −1.15848
\(901\) 0 0
\(902\) 1.00596e13 0.506003
\(903\) −9.36290e12 −0.468614
\(904\) −6.80058e12 −0.338679
\(905\) 2.15115e12 0.106599
\(906\) 8.07838e13 3.98334
\(907\) −1.25253e13 −0.614547 −0.307273 0.951621i \(-0.599417\pi\)
−0.307273 + 0.951621i \(0.599417\pi\)
\(908\) 8.34387e12 0.407363
\(909\) −6.23124e12 −0.302717
\(910\) 1.25530e11 0.00606822
\(911\) 1.02944e13 0.495185 0.247593 0.968864i \(-0.420361\pi\)
0.247593 + 0.968864i \(0.420361\pi\)
\(912\) 2.39448e13 1.14613
\(913\) −6.08264e13 −2.89717
\(914\) −3.51547e13 −1.66619
\(915\) 6.00757e11 0.0283337
\(916\) −3.22660e13 −1.51431
\(917\) 2.79855e12 0.130698
\(918\) 0 0
\(919\) −7.39445e12 −0.341968 −0.170984 0.985274i \(-0.554695\pi\)
−0.170984 + 0.985274i \(0.554695\pi\)
\(920\) −2.36718e11 −0.0108940
\(921\) −4.63335e13 −2.12191
\(922\) −9.67033e11 −0.0440709
\(923\) −2.39376e12 −0.108561
\(924\) 1.40836e13 0.635611
\(925\) 3.95678e13 1.77707
\(926\) −2.94815e13 −1.31765
\(927\) −1.34472e13 −0.598101
\(928\) 5.41924e13 2.39868
\(929\) −9.16655e12 −0.403771 −0.201886 0.979409i \(-0.564707\pi\)
−0.201886 + 0.979409i \(0.564707\pi\)
\(930\) −3.83341e12 −0.168040
\(931\) 2.05747e13 0.897552
\(932\) −2.77278e13 −1.20377
\(933\) −6.36178e13 −2.74860
\(934\) −3.86077e13 −1.66002
\(935\) 0 0
\(936\) −1.08297e12 −0.0461184
\(937\) −4.03344e13 −1.70941 −0.854706 0.519112i \(-0.826263\pi\)
−0.854706 + 0.519112i \(0.826263\pi\)
\(938\) 4.10985e12 0.173346
\(939\) 3.36069e13 1.41069
\(940\) −2.05055e12 −0.0856635
\(941\) −1.80297e13 −0.749609 −0.374804 0.927104i \(-0.622290\pi\)
−0.374804 + 0.927104i \(0.622290\pi\)
\(942\) −4.80021e13 −1.98624
\(943\) 3.55847e12 0.146541
\(944\) 1.92745e13 0.789967
\(945\) −1.76338e10 −0.000719287 0
\(946\) 8.60510e13 3.49338
\(947\) 3.85278e13 1.55668 0.778339 0.627844i \(-0.216062\pi\)
0.778339 + 0.627844i \(0.216062\pi\)
\(948\) −1.62499e13 −0.653450
\(949\) 8.67266e12 0.347100
\(950\) −3.45901e13 −1.37783
\(951\) 3.41665e13 1.35453
\(952\) 0 0
\(953\) −4.24042e13 −1.66530 −0.832648 0.553803i \(-0.813176\pi\)
−0.832648 + 0.553803i \(0.813176\pi\)
\(954\) 2.30618e13 0.901417
\(955\) −1.12639e12 −0.0438203
\(956\) 4.74104e12 0.183575
\(957\) 1.04494e14 4.02707
\(958\) 5.12183e13 1.96463
\(959\) −2.11203e12 −0.0806336
\(960\) 3.63838e12 0.138257
\(961\) 2.04505e12 0.0773477
\(962\) 1.59113e13 0.598989
\(963\) −2.93112e13 −1.09829
\(964\) 7.60249e12 0.283536
\(965\) −1.92495e12 −0.0714573
\(966\) 9.37543e12 0.346413
\(967\) −3.95530e12 −0.145466 −0.0727328 0.997351i \(-0.523172\pi\)
−0.0727328 + 0.997351i \(0.523172\pi\)
\(968\) −9.94309e12 −0.363984
\(969\) 0 0
\(970\) 2.87063e12 0.104113
\(971\) 2.88879e13 1.04287 0.521434 0.853292i \(-0.325397\pi\)
0.521434 + 0.853292i \(0.325397\pi\)
\(972\) −4.49020e13 −1.61349
\(973\) 7.19021e12 0.257178
\(974\) 1.79702e13 0.639792
\(975\) −9.15992e12 −0.324617
\(976\) 6.14685e12 0.216834
\(977\) 6.86810e12 0.241163 0.120582 0.992703i \(-0.461524\pi\)
0.120582 + 0.992703i \(0.461524\pi\)
\(978\) 2.39595e13 0.837439
\(979\) −1.68247e13 −0.585362
\(980\) 2.41012e12 0.0834682
\(981\) 4.96286e13 1.71089
\(982\) −6.52631e13 −2.23958
\(983\) 2.43295e13 0.831079 0.415539 0.909575i \(-0.363593\pi\)
0.415539 + 0.909575i \(0.363593\pi\)
\(984\) 1.67796e12 0.0570562
\(985\) −1.53066e12 −0.0518101
\(986\) 0 0
\(987\) 9.59182e12 0.321717
\(988\) −7.39131e12 −0.246783
\(989\) 3.04394e13 1.01170
\(990\) 5.97365e12 0.197643
\(991\) −2.94849e13 −0.971109 −0.485554 0.874206i \(-0.661382\pi\)
−0.485554 + 0.874206i \(0.661382\pi\)
\(992\) −4.54161e13 −1.48904
\(993\) −4.71401e13 −1.53858
\(994\) 4.95308e12 0.160930
\(995\) 1.03461e11 0.00334637
\(996\) −8.59056e13 −2.76602
\(997\) 3.59823e13 1.15335 0.576674 0.816974i \(-0.304350\pi\)
0.576674 + 0.816974i \(0.304350\pi\)
\(998\) 2.51010e13 0.800946
\(999\) −2.23514e12 −0.0710003
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.1.6 36
17.16 even 2 289.10.a.h.1.6 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.6 36 1.1 even 1 trivial
289.10.a.h.1.6 yes 36 17.16 even 2