Properties

Label 289.10.a.g.1.18
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 1.18
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.07469 q^{2} +18.6108 q^{3} -502.546 q^{4} -2540.06 q^{5} -57.2223 q^{6} -10949.3 q^{7} +3119.41 q^{8} -19336.6 q^{9} +O(q^{10})\) \(q-3.07469 q^{2} +18.6108 q^{3} -502.546 q^{4} -2540.06 q^{5} -57.2223 q^{6} -10949.3 q^{7} +3119.41 q^{8} -19336.6 q^{9} +7809.90 q^{10} +55022.0 q^{11} -9352.77 q^{12} -101901. q^{13} +33665.8 q^{14} -47272.5 q^{15} +247712. q^{16} +59454.1 q^{18} -243294. q^{19} +1.27650e6 q^{20} -203776. q^{21} -169176. q^{22} -799065. q^{23} +58054.7 q^{24} +4.49879e6 q^{25} +313313. q^{26} -726185. q^{27} +5.50255e6 q^{28} +1.08920e6 q^{29} +145348. q^{30} -6.11921e6 q^{31} -2.35878e6 q^{32} +1.02400e6 q^{33} +2.78120e7 q^{35} +9.71756e6 q^{36} +1.09051e7 q^{37} +748053. q^{38} -1.89645e6 q^{39} -7.92350e6 q^{40} +2.74132e6 q^{41} +626547. q^{42} +3.55746e7 q^{43} -2.76511e7 q^{44} +4.91163e7 q^{45} +2.45687e6 q^{46} -1.19501e7 q^{47} +4.61012e6 q^{48} +7.95346e7 q^{49} -1.38324e7 q^{50} +5.12099e7 q^{52} +6.12587e7 q^{53} +2.23279e6 q^{54} -1.39759e8 q^{55} -3.41555e7 q^{56} -4.52789e6 q^{57} -3.34895e6 q^{58} -7.89274e7 q^{59} +2.37566e7 q^{60} +5.32867e7 q^{61} +1.88147e7 q^{62} +2.11724e8 q^{63} -1.19576e8 q^{64} +2.58835e8 q^{65} -3.14849e6 q^{66} -1.84553e8 q^{67} -1.48712e7 q^{69} -8.55133e7 q^{70} -1.25020e8 q^{71} -6.03190e7 q^{72} +9.89488e6 q^{73} -3.35297e7 q^{74} +8.37259e7 q^{75} +1.22267e8 q^{76} -6.02455e8 q^{77} +5.83100e6 q^{78} -3.48965e8 q^{79} -6.29205e8 q^{80} +3.67088e8 q^{81} -8.42870e6 q^{82} -1.63123e8 q^{83} +1.02407e8 q^{84} -1.09381e8 q^{86} +2.02708e7 q^{87} +1.71636e8 q^{88} +1.08465e9 q^{89} -1.51017e8 q^{90} +1.11575e9 q^{91} +4.01567e8 q^{92} -1.13883e8 q^{93} +3.67427e7 q^{94} +6.17982e8 q^{95} -4.38987e7 q^{96} -1.20151e8 q^{97} -2.44544e8 q^{98} -1.06394e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} - 60000q^{10} - 76902q^{11} - 373248q^{12} + 54216q^{13} - 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} - 6439479q^{20} - 138102q^{21} - 267324q^{22} - 4041462q^{23} - 7653888q^{24} + 16582356q^{25} + 15822744q^{26} - 13281612q^{27} - 18614784q^{28} - 4005936q^{29} + 22471686q^{30} - 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} - 22076682q^{37} - 27401376q^{38} - 62736162q^{39} + 12231630q^{40} - 59641782q^{41} + 150001536q^{42} - 47951586q^{43} + 49578936q^{44} - 129308238q^{45} - 140524827q^{46} - 118557912q^{47} - 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} - 209848575q^{54} - 365439924q^{55} - 203095059q^{56} + 4614108q^{57} + 179071413q^{58} + 343015128q^{59} + 427179186q^{60} - 175597116q^{61} - 720602571q^{62} - 587415936q^{63} + 853082511q^{64} - 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} - 1308709542q^{71} - 275337849q^{72} - 494841342q^{73} - 1545361890q^{74} - 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} - 2270624538q^{78} - 1980107868q^{79} - 2897000199q^{80} + 1598298840q^{81} - 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} + 2705904618q^{88} + 148394658q^{89} - 117916215q^{90} - 636340896q^{91} + 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} - 4878626298q^{95} + 8390096634q^{96} + 891786822q^{97} + 4285627647q^{98} + 1476187998q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.07469 −0.135883 −0.0679416 0.997689i \(-0.521643\pi\)
−0.0679416 + 0.997689i \(0.521643\pi\)
\(3\) 18.6108 0.132653 0.0663267 0.997798i \(-0.478872\pi\)
0.0663267 + 0.997798i \(0.478872\pi\)
\(4\) −502.546 −0.981536
\(5\) −2540.06 −1.81752 −0.908760 0.417319i \(-0.862970\pi\)
−0.908760 + 0.417319i \(0.862970\pi\)
\(6\) −57.2223 −0.0180254
\(7\) −10949.3 −1.72364 −0.861821 0.507213i \(-0.830676\pi\)
−0.861821 + 0.507213i \(0.830676\pi\)
\(8\) 3119.41 0.269258
\(9\) −19336.6 −0.982403
\(10\) 7809.90 0.246971
\(11\) 55022.0 1.13310 0.566552 0.824026i \(-0.308277\pi\)
0.566552 + 0.824026i \(0.308277\pi\)
\(12\) −9352.77 −0.130204
\(13\) −101901. −0.989539 −0.494770 0.869024i \(-0.664748\pi\)
−0.494770 + 0.869024i \(0.664748\pi\)
\(14\) 33665.8 0.234214
\(15\) −47272.5 −0.241100
\(16\) 247712. 0.944948
\(17\) 0 0
\(18\) 59454.1 0.133492
\(19\) −243294. −0.428292 −0.214146 0.976802i \(-0.568697\pi\)
−0.214146 + 0.976802i \(0.568697\pi\)
\(20\) 1.27650e6 1.78396
\(21\) −203776. −0.228647
\(22\) −169176. −0.153970
\(23\) −799065. −0.595397 −0.297699 0.954660i \(-0.596219\pi\)
−0.297699 + 0.954660i \(0.596219\pi\)
\(24\) 58054.7 0.0357180
\(25\) 4.49879e6 2.30338
\(26\) 313313. 0.134462
\(27\) −726185. −0.262973
\(28\) 5.50255e6 1.69182
\(29\) 1.08920e6 0.285967 0.142984 0.989725i \(-0.454330\pi\)
0.142984 + 0.989725i \(0.454330\pi\)
\(30\) 145348. 0.0327615
\(31\) −6.11921e6 −1.19006 −0.595028 0.803705i \(-0.702859\pi\)
−0.595028 + 0.803705i \(0.702859\pi\)
\(32\) −2.35878e6 −0.397660
\(33\) 1.02400e6 0.150310
\(34\) 0 0
\(35\) 2.78120e7 3.13275
\(36\) 9.71756e6 0.964264
\(37\) 1.09051e7 0.956578 0.478289 0.878203i \(-0.341257\pi\)
0.478289 + 0.878203i \(0.341257\pi\)
\(38\) 748053. 0.0581978
\(39\) −1.89645e6 −0.131266
\(40\) −7.92350e6 −0.489381
\(41\) 2.74132e6 0.151507 0.0757534 0.997127i \(-0.475864\pi\)
0.0757534 + 0.997127i \(0.475864\pi\)
\(42\) 626547. 0.0310693
\(43\) 3.55746e7 1.58684 0.793419 0.608676i \(-0.208299\pi\)
0.793419 + 0.608676i \(0.208299\pi\)
\(44\) −2.76511e7 −1.11218
\(45\) 4.91163e7 1.78554
\(46\) 2.45687e6 0.0809045
\(47\) −1.19501e7 −0.357215 −0.178607 0.983920i \(-0.557159\pi\)
−0.178607 + 0.983920i \(0.557159\pi\)
\(48\) 4.61012e6 0.125351
\(49\) 7.95346e7 1.97094
\(50\) −1.38324e7 −0.312991
\(51\) 0 0
\(52\) 5.12099e7 0.971268
\(53\) 6.12587e7 1.06641 0.533207 0.845985i \(-0.320987\pi\)
0.533207 + 0.845985i \(0.320987\pi\)
\(54\) 2.23279e6 0.0357336
\(55\) −1.39759e8 −2.05944
\(56\) −3.41555e7 −0.464104
\(57\) −4.52789e6 −0.0568144
\(58\) −3.34895e6 −0.0388582
\(59\) −7.89274e7 −0.847996 −0.423998 0.905663i \(-0.639374\pi\)
−0.423998 + 0.905663i \(0.639374\pi\)
\(60\) 2.37566e7 0.236649
\(61\) 5.32867e7 0.492759 0.246379 0.969173i \(-0.420759\pi\)
0.246379 + 0.969173i \(0.420759\pi\)
\(62\) 1.88147e7 0.161709
\(63\) 2.11724e8 1.69331
\(64\) −1.19576e8 −0.890913
\(65\) 2.58835e8 1.79851
\(66\) −3.14849e6 −0.0204246
\(67\) −1.84553e8 −1.11888 −0.559441 0.828870i \(-0.688984\pi\)
−0.559441 + 0.828870i \(0.688984\pi\)
\(68\) 0 0
\(69\) −1.48712e7 −0.0789815
\(70\) −8.55133e7 −0.425689
\(71\) −1.25020e8 −0.583871 −0.291935 0.956438i \(-0.594299\pi\)
−0.291935 + 0.956438i \(0.594299\pi\)
\(72\) −6.03190e7 −0.264520
\(73\) 9.89488e6 0.0407810 0.0203905 0.999792i \(-0.493509\pi\)
0.0203905 + 0.999792i \(0.493509\pi\)
\(74\) −3.35297e7 −0.129983
\(75\) 8.37259e7 0.305551
\(76\) 1.22267e8 0.420384
\(77\) −6.02455e8 −1.95306
\(78\) 5.83100e6 0.0178368
\(79\) −3.48965e8 −1.00800 −0.504000 0.863704i \(-0.668139\pi\)
−0.504000 + 0.863704i \(0.668139\pi\)
\(80\) −6.29205e8 −1.71746
\(81\) 3.67088e8 0.947519
\(82\) −8.42870e6 −0.0205872
\(83\) −1.63123e8 −0.377281 −0.188641 0.982046i \(-0.560408\pi\)
−0.188641 + 0.982046i \(0.560408\pi\)
\(84\) 1.02407e8 0.224425
\(85\) 0 0
\(86\) −1.09381e8 −0.215625
\(87\) 2.02708e7 0.0379346
\(88\) 1.71636e8 0.305097
\(89\) 1.08465e9 1.83246 0.916229 0.400656i \(-0.131218\pi\)
0.916229 + 0.400656i \(0.131218\pi\)
\(90\) −1.51017e8 −0.242625
\(91\) 1.11575e9 1.70561
\(92\) 4.01567e8 0.584404
\(93\) −1.13883e8 −0.157865
\(94\) 3.67427e7 0.0485395
\(95\) 6.17982e8 0.778430
\(96\) −4.38987e7 −0.0527510
\(97\) −1.20151e8 −0.137802 −0.0689009 0.997624i \(-0.521949\pi\)
−0.0689009 + 0.997624i \(0.521949\pi\)
\(98\) −2.44544e8 −0.267818
\(99\) −1.06394e9 −1.11316
\(100\) −2.26085e9 −2.26085
\(101\) 1.08867e9 1.04100 0.520498 0.853863i \(-0.325746\pi\)
0.520498 + 0.853863i \(0.325746\pi\)
\(102\) 0 0
\(103\) −1.18252e9 −1.03524 −0.517622 0.855610i \(-0.673183\pi\)
−0.517622 + 0.855610i \(0.673183\pi\)
\(104\) −3.17871e8 −0.266441
\(105\) 5.17603e8 0.415571
\(106\) −1.88351e8 −0.144908
\(107\) −1.49518e9 −1.10272 −0.551361 0.834267i \(-0.685891\pi\)
−0.551361 + 0.834267i \(0.685891\pi\)
\(108\) 3.64942e8 0.258117
\(109\) −2.08481e9 −1.41464 −0.707321 0.706892i \(-0.750097\pi\)
−0.707321 + 0.706892i \(0.750097\pi\)
\(110\) 4.29716e8 0.279843
\(111\) 2.02952e8 0.126893
\(112\) −2.71229e9 −1.62875
\(113\) −7.38570e8 −0.426126 −0.213063 0.977038i \(-0.568344\pi\)
−0.213063 + 0.977038i \(0.568344\pi\)
\(114\) 1.39218e7 0.00772013
\(115\) 2.02967e9 1.08215
\(116\) −5.47373e8 −0.280687
\(117\) 1.97042e9 0.972126
\(118\) 2.42677e8 0.115229
\(119\) 0 0
\(120\) −1.47462e8 −0.0649181
\(121\) 6.69477e8 0.283924
\(122\) −1.63840e8 −0.0669577
\(123\) 5.10180e7 0.0200979
\(124\) 3.07519e9 1.16808
\(125\) −6.46614e9 −2.36892
\(126\) −6.50984e8 −0.230093
\(127\) −2.74828e9 −0.937441 −0.468721 0.883346i \(-0.655285\pi\)
−0.468721 + 0.883346i \(0.655285\pi\)
\(128\) 1.57535e9 0.518720
\(129\) 6.62071e8 0.210499
\(130\) −7.95836e8 −0.244387
\(131\) 5.20552e9 1.54434 0.772170 0.635416i \(-0.219171\pi\)
0.772170 + 0.635416i \(0.219171\pi\)
\(132\) −5.14609e8 −0.147535
\(133\) 2.66391e9 0.738223
\(134\) 5.67442e8 0.152037
\(135\) 1.84456e9 0.477958
\(136\) 0 0
\(137\) 6.18810e9 1.50077 0.750386 0.661000i \(-0.229868\pi\)
0.750386 + 0.661000i \(0.229868\pi\)
\(138\) 4.57243e7 0.0107323
\(139\) 1.88233e9 0.427690 0.213845 0.976868i \(-0.431401\pi\)
0.213845 + 0.976868i \(0.431401\pi\)
\(140\) −1.39768e10 −3.07491
\(141\) −2.22400e8 −0.0473858
\(142\) 3.84397e8 0.0793383
\(143\) −5.60680e9 −1.12125
\(144\) −4.78993e9 −0.928320
\(145\) −2.76663e9 −0.519751
\(146\) −3.04237e7 −0.00554146
\(147\) 1.48020e9 0.261452
\(148\) −5.48030e9 −0.938915
\(149\) 8.74040e9 1.45276 0.726378 0.687295i \(-0.241202\pi\)
0.726378 + 0.687295i \(0.241202\pi\)
\(150\) −2.57431e8 −0.0415193
\(151\) 4.41501e9 0.691091 0.345546 0.938402i \(-0.387694\pi\)
0.345546 + 0.938402i \(0.387694\pi\)
\(152\) −7.58935e8 −0.115321
\(153\) 0 0
\(154\) 1.85236e9 0.265389
\(155\) 1.55432e10 2.16295
\(156\) 9.53056e8 0.128842
\(157\) 1.83214e9 0.240664 0.120332 0.992734i \(-0.461604\pi\)
0.120332 + 0.992734i \(0.461604\pi\)
\(158\) 1.07296e9 0.136970
\(159\) 1.14007e9 0.141464
\(160\) 5.99144e9 0.722756
\(161\) 8.74924e9 1.02625
\(162\) −1.12868e9 −0.128752
\(163\) −3.05664e9 −0.339156 −0.169578 0.985517i \(-0.554241\pi\)
−0.169578 + 0.985517i \(0.554241\pi\)
\(164\) −1.37764e9 −0.148709
\(165\) −2.60103e9 −0.273192
\(166\) 5.01554e8 0.0512662
\(167\) 5.54078e9 0.551248 0.275624 0.961266i \(-0.411116\pi\)
0.275624 + 0.961266i \(0.411116\pi\)
\(168\) −6.35661e8 −0.0615650
\(169\) −2.20706e8 −0.0208124
\(170\) 0 0
\(171\) 4.70449e9 0.420756
\(172\) −1.78779e10 −1.55754
\(173\) 2.19119e10 1.85983 0.929914 0.367778i \(-0.119881\pi\)
0.929914 + 0.367778i \(0.119881\pi\)
\(174\) −6.23265e7 −0.00515467
\(175\) −4.92588e10 −3.97020
\(176\) 1.36296e10 1.07072
\(177\) −1.46890e9 −0.112490
\(178\) −3.33495e9 −0.249000
\(179\) −7.29594e9 −0.531181 −0.265591 0.964086i \(-0.585567\pi\)
−0.265591 + 0.964086i \(0.585567\pi\)
\(180\) −2.46832e10 −1.75257
\(181\) −2.75510e10 −1.90802 −0.954011 0.299770i \(-0.903090\pi\)
−0.954011 + 0.299770i \(0.903090\pi\)
\(182\) −3.43058e9 −0.231764
\(183\) 9.91705e8 0.0653661
\(184\) −2.49261e9 −0.160315
\(185\) −2.76995e10 −1.73860
\(186\) 3.50155e8 0.0214512
\(187\) 0 0
\(188\) 6.00545e9 0.350619
\(189\) 7.95126e9 0.453271
\(190\) −1.90010e9 −0.105776
\(191\) 8.40002e9 0.456699 0.228350 0.973579i \(-0.426667\pi\)
0.228350 + 0.973579i \(0.426667\pi\)
\(192\) −2.22541e9 −0.118183
\(193\) 2.32479e10 1.20608 0.603040 0.797711i \(-0.293956\pi\)
0.603040 + 0.797711i \(0.293956\pi\)
\(194\) 3.69427e8 0.0187250
\(195\) 4.81711e9 0.238578
\(196\) −3.99698e10 −1.93455
\(197\) 2.22594e10 1.05297 0.526485 0.850185i \(-0.323510\pi\)
0.526485 + 0.850185i \(0.323510\pi\)
\(198\) 3.27129e9 0.151260
\(199\) −1.96549e10 −0.888447 −0.444223 0.895916i \(-0.646520\pi\)
−0.444223 + 0.895916i \(0.646520\pi\)
\(200\) 1.40336e10 0.620202
\(201\) −3.43467e9 −0.148423
\(202\) −3.34731e9 −0.141454
\(203\) −1.19260e10 −0.492905
\(204\) 0 0
\(205\) −6.96312e9 −0.275367
\(206\) 3.63589e9 0.140672
\(207\) 1.54512e10 0.584920
\(208\) −2.52421e10 −0.935063
\(209\) −1.33865e10 −0.485299
\(210\) −1.59147e9 −0.0564691
\(211\) −2.13271e10 −0.740730 −0.370365 0.928886i \(-0.620767\pi\)
−0.370365 + 0.928886i \(0.620767\pi\)
\(212\) −3.07853e10 −1.04672
\(213\) −2.32672e9 −0.0774525
\(214\) 4.59721e9 0.149842
\(215\) −9.03618e10 −2.88411
\(216\) −2.26527e9 −0.0708074
\(217\) 6.70013e10 2.05123
\(218\) 6.41013e9 0.192226
\(219\) 1.84151e8 0.00540974
\(220\) 7.02356e10 2.02141
\(221\) 0 0
\(222\) −6.24013e8 −0.0172427
\(223\) 1.60477e10 0.434552 0.217276 0.976110i \(-0.430283\pi\)
0.217276 + 0.976110i \(0.430283\pi\)
\(224\) 2.58271e10 0.685424
\(225\) −8.69914e10 −2.26285
\(226\) 2.27087e9 0.0579035
\(227\) −6.61656e10 −1.65393 −0.826963 0.562257i \(-0.809933\pi\)
−0.826963 + 0.562257i \(0.809933\pi\)
\(228\) 2.27547e9 0.0557654
\(229\) −4.43447e10 −1.06557 −0.532786 0.846250i \(-0.678855\pi\)
−0.532786 + 0.846250i \(0.678855\pi\)
\(230\) −6.24061e9 −0.147046
\(231\) −1.12122e10 −0.259081
\(232\) 3.39766e9 0.0769989
\(233\) 5.39484e9 0.119916 0.0599579 0.998201i \(-0.480903\pi\)
0.0599579 + 0.998201i \(0.480903\pi\)
\(234\) −6.05843e9 −0.132096
\(235\) 3.03539e10 0.649245
\(236\) 3.96647e10 0.832339
\(237\) −6.49451e9 −0.133715
\(238\) 0 0
\(239\) 4.13971e10 0.820690 0.410345 0.911930i \(-0.365408\pi\)
0.410345 + 0.911930i \(0.365408\pi\)
\(240\) −1.17100e10 −0.227827
\(241\) −1.66107e10 −0.317183 −0.158592 0.987344i \(-0.550695\pi\)
−0.158592 + 0.987344i \(0.550695\pi\)
\(242\) −2.05843e9 −0.0385805
\(243\) 2.11253e10 0.388664
\(244\) −2.67790e10 −0.483660
\(245\) −2.02023e11 −3.58223
\(246\) −1.56865e8 −0.00273097
\(247\) 2.47919e10 0.423812
\(248\) −1.90883e10 −0.320432
\(249\) −3.03585e9 −0.0500476
\(250\) 1.98814e10 0.321896
\(251\) 3.10377e10 0.493581 0.246790 0.969069i \(-0.420624\pi\)
0.246790 + 0.969069i \(0.420624\pi\)
\(252\) −1.06401e11 −1.66205
\(253\) −4.39662e10 −0.674647
\(254\) 8.45010e9 0.127383
\(255\) 0 0
\(256\) 5.63793e10 0.820427
\(257\) 5.97981e10 0.855044 0.427522 0.904005i \(-0.359387\pi\)
0.427522 + 0.904005i \(0.359387\pi\)
\(258\) −2.03566e9 −0.0286034
\(259\) −1.19403e11 −1.64880
\(260\) −1.30076e11 −1.76530
\(261\) −2.10615e10 −0.280935
\(262\) −1.60053e10 −0.209850
\(263\) −3.18665e10 −0.410709 −0.205354 0.978688i \(-0.565835\pi\)
−0.205354 + 0.978688i \(0.565835\pi\)
\(264\) 3.19429e9 0.0404721
\(265\) −1.55601e11 −1.93823
\(266\) −8.19069e9 −0.100312
\(267\) 2.01861e10 0.243082
\(268\) 9.27463e10 1.09822
\(269\) −3.97001e10 −0.462281 −0.231141 0.972920i \(-0.574246\pi\)
−0.231141 + 0.972920i \(0.574246\pi\)
\(270\) −5.67143e9 −0.0649465
\(271\) 7.58840e10 0.854650 0.427325 0.904098i \(-0.359456\pi\)
0.427325 + 0.904098i \(0.359456\pi\)
\(272\) 0 0
\(273\) 2.07649e10 0.226255
\(274\) −1.90265e10 −0.203930
\(275\) 2.47532e11 2.60997
\(276\) 7.47347e9 0.0775231
\(277\) −7.03115e10 −0.717575 −0.358788 0.933419i \(-0.616810\pi\)
−0.358788 + 0.933419i \(0.616810\pi\)
\(278\) −5.78758e9 −0.0581160
\(279\) 1.18325e11 1.16912
\(280\) 8.67572e10 0.843518
\(281\) 4.27010e10 0.408563 0.204282 0.978912i \(-0.434514\pi\)
0.204282 + 0.978912i \(0.434514\pi\)
\(282\) 6.83809e8 0.00643894
\(283\) −1.99849e10 −0.185209 −0.0926047 0.995703i \(-0.529519\pi\)
−0.0926047 + 0.995703i \(0.529519\pi\)
\(284\) 6.28283e10 0.573090
\(285\) 1.15011e10 0.103261
\(286\) 1.72391e10 0.152359
\(287\) −3.00156e10 −0.261143
\(288\) 4.56108e10 0.390663
\(289\) 0 0
\(290\) 8.50653e9 0.0706255
\(291\) −2.23610e9 −0.0182799
\(292\) −4.97264e9 −0.0400280
\(293\) 1.04039e11 0.824695 0.412347 0.911027i \(-0.364709\pi\)
0.412347 + 0.911027i \(0.364709\pi\)
\(294\) −4.55115e9 −0.0355270
\(295\) 2.00481e11 1.54125
\(296\) 3.40174e10 0.257566
\(297\) −3.99562e10 −0.297975
\(298\) −2.68740e10 −0.197405
\(299\) 8.14254e10 0.589169
\(300\) −4.20761e10 −0.299909
\(301\) −3.89519e11 −2.73514
\(302\) −1.35748e10 −0.0939077
\(303\) 2.02609e10 0.138092
\(304\) −6.02670e10 −0.404714
\(305\) −1.35351e11 −0.895599
\(306\) 0 0
\(307\) 1.84431e11 1.18498 0.592490 0.805578i \(-0.298145\pi\)
0.592490 + 0.805578i \(0.298145\pi\)
\(308\) 3.02762e11 1.91700
\(309\) −2.20077e10 −0.137329
\(310\) −4.77904e10 −0.293909
\(311\) −1.22863e11 −0.744731 −0.372365 0.928086i \(-0.621453\pi\)
−0.372365 + 0.928086i \(0.621453\pi\)
\(312\) −5.91582e9 −0.0353443
\(313\) 4.77009e10 0.280916 0.140458 0.990087i \(-0.455142\pi\)
0.140458 + 0.990087i \(0.455142\pi\)
\(314\) −5.63327e9 −0.0327022
\(315\) −5.37791e11 −3.07763
\(316\) 1.75371e11 0.989388
\(317\) −2.10729e11 −1.17208 −0.586041 0.810281i \(-0.699314\pi\)
−0.586041 + 0.810281i \(0.699314\pi\)
\(318\) −3.50536e9 −0.0192225
\(319\) 5.99300e10 0.324031
\(320\) 3.03731e11 1.61925
\(321\) −2.78264e10 −0.146280
\(322\) −2.69012e10 −0.139450
\(323\) 0 0
\(324\) −1.84479e11 −0.930024
\(325\) −4.58431e11 −2.27928
\(326\) 9.39821e9 0.0460857
\(327\) −3.87999e10 −0.187657
\(328\) 8.55130e9 0.0407944
\(329\) 1.30845e11 0.615710
\(330\) 7.99735e9 0.0371222
\(331\) −3.32123e10 −0.152080 −0.0760400 0.997105i \(-0.524228\pi\)
−0.0760400 + 0.997105i \(0.524228\pi\)
\(332\) 8.19771e10 0.370315
\(333\) −2.10867e11 −0.939745
\(334\) −1.70362e10 −0.0749054
\(335\) 4.68775e11 2.03359
\(336\) −5.04778e10 −0.216060
\(337\) 3.00476e11 1.26904 0.634519 0.772907i \(-0.281198\pi\)
0.634519 + 0.772907i \(0.281198\pi\)
\(338\) 6.78601e8 0.00282806
\(339\) −1.37453e10 −0.0565271
\(340\) 0 0
\(341\) −3.36691e11 −1.34846
\(342\) −1.44648e10 −0.0571737
\(343\) −4.29006e11 −1.67356
\(344\) 1.10972e11 0.427268
\(345\) 3.77738e10 0.143550
\(346\) −6.73723e10 −0.252719
\(347\) 3.76252e11 1.39314 0.696571 0.717487i \(-0.254708\pi\)
0.696571 + 0.717487i \(0.254708\pi\)
\(348\) −1.01870e10 −0.0372341
\(349\) 2.25550e11 0.813819 0.406909 0.913469i \(-0.366607\pi\)
0.406909 + 0.913469i \(0.366607\pi\)
\(350\) 1.51455e11 0.539484
\(351\) 7.39989e10 0.260222
\(352\) −1.29785e11 −0.450590
\(353\) 7.61898e9 0.0261162 0.0130581 0.999915i \(-0.495843\pi\)
0.0130581 + 0.999915i \(0.495843\pi\)
\(354\) 4.51641e9 0.0152855
\(355\) 3.17558e11 1.06120
\(356\) −5.45086e11 −1.79862
\(357\) 0 0
\(358\) 2.24328e10 0.0721787
\(359\) 2.66775e11 0.847656 0.423828 0.905743i \(-0.360686\pi\)
0.423828 + 0.905743i \(0.360686\pi\)
\(360\) 1.53214e11 0.480770
\(361\) −2.63496e11 −0.816566
\(362\) 8.47107e10 0.259268
\(363\) 1.24595e10 0.0376634
\(364\) −5.60715e11 −1.67412
\(365\) −2.51336e10 −0.0741203
\(366\) −3.04918e9 −0.00888217
\(367\) −2.28618e11 −0.657829 −0.328914 0.944360i \(-0.606683\pi\)
−0.328914 + 0.944360i \(0.606683\pi\)
\(368\) −1.97938e11 −0.562619
\(369\) −5.30079e10 −0.148841
\(370\) 8.51674e10 0.236247
\(371\) −6.70743e11 −1.83812
\(372\) 5.72316e10 0.154950
\(373\) 6.18391e11 1.65415 0.827073 0.562095i \(-0.190005\pi\)
0.827073 + 0.562095i \(0.190005\pi\)
\(374\) 0 0
\(375\) −1.20340e11 −0.314245
\(376\) −3.72771e10 −0.0961828
\(377\) −1.10990e11 −0.282976
\(378\) −2.44476e10 −0.0615919
\(379\) 2.10741e11 0.524654 0.262327 0.964979i \(-0.415510\pi\)
0.262327 + 0.964979i \(0.415510\pi\)
\(380\) −3.10564e11 −0.764057
\(381\) −5.11476e10 −0.124355
\(382\) −2.58274e10 −0.0620578
\(383\) 3.03050e11 0.719648 0.359824 0.933020i \(-0.382837\pi\)
0.359824 + 0.933020i \(0.382837\pi\)
\(384\) 2.93185e10 0.0688101
\(385\) 1.53027e12 3.54973
\(386\) −7.14800e10 −0.163886
\(387\) −6.87894e11 −1.55891
\(388\) 6.03815e10 0.135257
\(389\) −3.07324e11 −0.680491 −0.340246 0.940337i \(-0.610510\pi\)
−0.340246 + 0.940337i \(0.610510\pi\)
\(390\) −1.48111e10 −0.0324188
\(391\) 0 0
\(392\) 2.48101e11 0.530691
\(393\) 9.68787e10 0.204862
\(394\) −6.84408e10 −0.143081
\(395\) 8.86394e11 1.83206
\(396\) 5.34680e11 1.09261
\(397\) −2.80841e11 −0.567418 −0.283709 0.958910i \(-0.591565\pi\)
−0.283709 + 0.958910i \(0.591565\pi\)
\(398\) 6.04326e10 0.120725
\(399\) 4.95774e10 0.0979278
\(400\) 1.11441e12 2.17657
\(401\) 3.13411e11 0.605291 0.302645 0.953103i \(-0.402130\pi\)
0.302645 + 0.953103i \(0.402130\pi\)
\(402\) 1.05605e10 0.0201683
\(403\) 6.23553e11 1.17761
\(404\) −5.47106e11 −1.02177
\(405\) −9.32427e11 −1.72213
\(406\) 3.66688e10 0.0669776
\(407\) 6.00019e11 1.08390
\(408\) 0 0
\(409\) 5.95263e11 1.05185 0.525926 0.850531i \(-0.323719\pi\)
0.525926 + 0.850531i \(0.323719\pi\)
\(410\) 2.14094e10 0.0374177
\(411\) 1.15165e11 0.199082
\(412\) 5.94273e11 1.01613
\(413\) 8.64204e11 1.46164
\(414\) −4.75077e10 −0.0794808
\(415\) 4.14344e11 0.685716
\(416\) 2.40362e11 0.393500
\(417\) 3.50316e10 0.0567346
\(418\) 4.11594e10 0.0659441
\(419\) −3.62055e11 −0.573867 −0.286934 0.957950i \(-0.592636\pi\)
−0.286934 + 0.957950i \(0.592636\pi\)
\(420\) −2.60119e11 −0.407897
\(421\) 1.01670e12 1.57734 0.788668 0.614819i \(-0.210771\pi\)
0.788668 + 0.614819i \(0.210771\pi\)
\(422\) 6.55740e10 0.100653
\(423\) 2.31074e11 0.350929
\(424\) 1.91091e11 0.287140
\(425\) 0 0
\(426\) 7.15393e9 0.0105245
\(427\) −5.83454e11 −0.849339
\(428\) 7.51397e11 1.08236
\(429\) −1.04347e11 −0.148738
\(430\) 2.77834e11 0.391902
\(431\) −8.42323e11 −1.17579 −0.587897 0.808936i \(-0.700044\pi\)
−0.587897 + 0.808936i \(0.700044\pi\)
\(432\) −1.79885e11 −0.248495
\(433\) 1.18575e12 1.62106 0.810529 0.585698i \(-0.199180\pi\)
0.810529 + 0.585698i \(0.199180\pi\)
\(434\) −2.06008e11 −0.278728
\(435\) −5.14892e10 −0.0689468
\(436\) 1.04771e12 1.38852
\(437\) 1.94408e11 0.255004
\(438\) −5.66208e8 −0.000735093 0
\(439\) 2.80153e11 0.360002 0.180001 0.983666i \(-0.442390\pi\)
0.180001 + 0.983666i \(0.442390\pi\)
\(440\) −4.35967e11 −0.554519
\(441\) −1.53793e12 −1.93626
\(442\) 0 0
\(443\) −1.03647e12 −1.27861 −0.639307 0.768951i \(-0.720779\pi\)
−0.639307 + 0.768951i \(0.720779\pi\)
\(444\) −1.01993e11 −0.124550
\(445\) −2.75507e12 −3.33053
\(446\) −4.93418e10 −0.0590484
\(447\) 1.62665e11 0.192713
\(448\) 1.30928e12 1.53561
\(449\) 9.51471e11 1.10481 0.552404 0.833576i \(-0.313710\pi\)
0.552404 + 0.833576i \(0.313710\pi\)
\(450\) 2.67472e11 0.307483
\(451\) 1.50833e11 0.171673
\(452\) 3.71165e11 0.418258
\(453\) 8.21667e10 0.0916756
\(454\) 2.03439e11 0.224741
\(455\) −2.83407e12 −3.09998
\(456\) −1.41244e10 −0.0152977
\(457\) 5.23939e11 0.561899 0.280949 0.959723i \(-0.409351\pi\)
0.280949 + 0.959723i \(0.409351\pi\)
\(458\) 1.36346e11 0.144793
\(459\) 0 0
\(460\) −1.02000e12 −1.06217
\(461\) −1.57356e12 −1.62267 −0.811333 0.584585i \(-0.801257\pi\)
−0.811333 + 0.584585i \(0.801257\pi\)
\(462\) 3.44739e10 0.0352048
\(463\) 8.11193e11 0.820370 0.410185 0.912002i \(-0.365464\pi\)
0.410185 + 0.912002i \(0.365464\pi\)
\(464\) 2.69808e11 0.270224
\(465\) 2.89270e11 0.286923
\(466\) −1.65874e10 −0.0162946
\(467\) −1.43619e12 −1.39729 −0.698646 0.715467i \(-0.746214\pi\)
−0.698646 + 0.715467i \(0.746214\pi\)
\(468\) −9.90228e11 −0.954177
\(469\) 2.02073e12 1.92855
\(470\) −9.33287e10 −0.0882216
\(471\) 3.40976e10 0.0319249
\(472\) −2.46207e11 −0.228329
\(473\) 1.95739e12 1.79805
\(474\) 1.99686e10 0.0181696
\(475\) −1.09453e12 −0.986520
\(476\) 0 0
\(477\) −1.18454e12 −1.04765
\(478\) −1.27283e11 −0.111518
\(479\) −1.19894e11 −0.104061 −0.0520304 0.998646i \(-0.516569\pi\)
−0.0520304 + 0.998646i \(0.516569\pi\)
\(480\) 1.11505e11 0.0958760
\(481\) −1.11124e12 −0.946571
\(482\) 5.10726e10 0.0430999
\(483\) 1.62830e11 0.136136
\(484\) −3.36443e11 −0.278681
\(485\) 3.05191e11 0.250458
\(486\) −6.49537e10 −0.0528130
\(487\) −1.21696e12 −0.980386 −0.490193 0.871614i \(-0.663074\pi\)
−0.490193 + 0.871614i \(0.663074\pi\)
\(488\) 1.66223e11 0.132679
\(489\) −5.68864e10 −0.0449902
\(490\) 6.21157e11 0.486765
\(491\) 1.10228e12 0.855904 0.427952 0.903802i \(-0.359235\pi\)
0.427952 + 0.903802i \(0.359235\pi\)
\(492\) −2.56389e10 −0.0197268
\(493\) 0 0
\(494\) −7.62273e10 −0.0575890
\(495\) 2.70248e12 2.02320
\(496\) −1.51580e12 −1.12454
\(497\) 1.36889e12 1.00638
\(498\) 9.33430e9 0.00680064
\(499\) 1.83821e12 1.32722 0.663610 0.748078i \(-0.269023\pi\)
0.663610 + 0.748078i \(0.269023\pi\)
\(500\) 3.24953e12 2.32518
\(501\) 1.03118e11 0.0731250
\(502\) −9.54314e10 −0.0670694
\(503\) −1.35686e12 −0.945104 −0.472552 0.881303i \(-0.656667\pi\)
−0.472552 + 0.881303i \(0.656667\pi\)
\(504\) 6.60453e11 0.455937
\(505\) −2.76528e12 −1.89203
\(506\) 1.35182e11 0.0916732
\(507\) −4.10750e9 −0.00276084
\(508\) 1.38114e12 0.920132
\(509\) −1.97514e12 −1.30427 −0.652137 0.758101i \(-0.726127\pi\)
−0.652137 + 0.758101i \(0.726127\pi\)
\(510\) 0 0
\(511\) −1.08342e11 −0.0702918
\(512\) −9.79930e11 −0.630203
\(513\) 1.76677e11 0.112629
\(514\) −1.83861e11 −0.116186
\(515\) 3.00368e12 1.88158
\(516\) −3.32721e11 −0.206613
\(517\) −6.57516e11 −0.404761
\(518\) 3.67128e11 0.224044
\(519\) 4.07797e11 0.246713
\(520\) 8.07412e11 0.484262
\(521\) 1.99095e12 1.18383 0.591917 0.805999i \(-0.298371\pi\)
0.591917 + 0.805999i \(0.298371\pi\)
\(522\) 6.47574e10 0.0381744
\(523\) −3.10464e11 −0.181448 −0.0907242 0.995876i \(-0.528918\pi\)
−0.0907242 + 0.995876i \(0.528918\pi\)
\(524\) −2.61601e12 −1.51583
\(525\) −9.16744e11 −0.526661
\(526\) 9.79796e10 0.0558084
\(527\) 0 0
\(528\) 2.53658e11 0.142035
\(529\) −1.16265e12 −0.645502
\(530\) 4.78424e11 0.263373
\(531\) 1.52619e12 0.833074
\(532\) −1.33874e12 −0.724592
\(533\) −2.79343e11 −0.149922
\(534\) −6.20661e10 −0.0330308
\(535\) 3.79785e12 2.00422
\(536\) −5.75696e11 −0.301267
\(537\) −1.35783e11 −0.0704630
\(538\) 1.22065e11 0.0628163
\(539\) 4.37616e12 2.23328
\(540\) −9.26975e11 −0.469133
\(541\) 8.59585e11 0.431421 0.215711 0.976457i \(-0.430793\pi\)
0.215711 + 0.976457i \(0.430793\pi\)
\(542\) −2.33320e11 −0.116133
\(543\) −5.12745e11 −0.253106
\(544\) 0 0
\(545\) 5.29554e12 2.57114
\(546\) −6.38457e10 −0.0307443
\(547\) 2.41617e12 1.15394 0.576971 0.816765i \(-0.304235\pi\)
0.576971 + 0.816765i \(0.304235\pi\)
\(548\) −3.10980e12 −1.47306
\(549\) −1.03038e12 −0.484088
\(550\) −7.61085e11 −0.354651
\(551\) −2.64996e11 −0.122478
\(552\) −4.63894e10 −0.0212664
\(553\) 3.82094e12 1.73743
\(554\) 2.16186e11 0.0975065
\(555\) −5.15509e11 −0.230631
\(556\) −9.45958e11 −0.419793
\(557\) 1.61258e12 0.709859 0.354929 0.934893i \(-0.384505\pi\)
0.354929 + 0.934893i \(0.384505\pi\)
\(558\) −3.63812e11 −0.158863
\(559\) −3.62509e12 −1.57024
\(560\) 6.88938e12 2.96029
\(561\) 0 0
\(562\) −1.31292e11 −0.0555169
\(563\) 4.85659e10 0.0203725 0.0101862 0.999948i \(-0.496758\pi\)
0.0101862 + 0.999948i \(0.496758\pi\)
\(564\) 1.11766e11 0.0465108
\(565\) 1.87601e12 0.774493
\(566\) 6.14473e10 0.0251669
\(567\) −4.01938e12 −1.63318
\(568\) −3.89989e11 −0.157212
\(569\) −2.08971e12 −0.835758 −0.417879 0.908503i \(-0.637226\pi\)
−0.417879 + 0.908503i \(0.637226\pi\)
\(570\) −3.53623e10 −0.0140315
\(571\) −1.98387e12 −0.780999 −0.390500 0.920603i \(-0.627698\pi\)
−0.390500 + 0.920603i \(0.627698\pi\)
\(572\) 2.81767e12 1.10055
\(573\) 1.56331e11 0.0605827
\(574\) 9.22887e10 0.0354850
\(575\) −3.59482e12 −1.37143
\(576\) 2.31220e12 0.875235
\(577\) −1.30195e12 −0.488992 −0.244496 0.969650i \(-0.578623\pi\)
−0.244496 + 0.969650i \(0.578623\pi\)
\(578\) 0 0
\(579\) 4.32661e11 0.159991
\(580\) 1.39036e12 0.510155
\(581\) 1.78610e12 0.650297
\(582\) 6.87532e9 0.00248393
\(583\) 3.37058e12 1.20836
\(584\) 3.08662e10 0.0109806
\(585\) −5.00499e12 −1.76686
\(586\) −3.19888e11 −0.112062
\(587\) 8.77295e11 0.304982 0.152491 0.988305i \(-0.451270\pi\)
0.152491 + 0.988305i \(0.451270\pi\)
\(588\) −7.43869e11 −0.256625
\(589\) 1.48877e12 0.509692
\(590\) −6.16415e11 −0.209430
\(591\) 4.14265e11 0.139680
\(592\) 2.70132e12 0.903917
\(593\) 1.76865e12 0.587348 0.293674 0.955906i \(-0.405122\pi\)
0.293674 + 0.955906i \(0.405122\pi\)
\(594\) 1.22853e11 0.0404899
\(595\) 0 0
\(596\) −4.39245e12 −1.42593
\(597\) −3.65792e11 −0.117856
\(598\) −2.50358e11 −0.0800582
\(599\) −4.78571e12 −1.51889 −0.759444 0.650573i \(-0.774529\pi\)
−0.759444 + 0.650573i \(0.774529\pi\)
\(600\) 2.61176e11 0.0822720
\(601\) −2.40341e12 −0.751439 −0.375719 0.926734i \(-0.622604\pi\)
−0.375719 + 0.926734i \(0.622604\pi\)
\(602\) 1.19765e12 0.371660
\(603\) 3.56863e12 1.09919
\(604\) −2.21875e12 −0.678331
\(605\) −1.70051e12 −0.516037
\(606\) −6.22960e10 −0.0187644
\(607\) −3.97836e11 −0.118947 −0.0594737 0.998230i \(-0.518942\pi\)
−0.0594737 + 0.998230i \(0.518942\pi\)
\(608\) 5.73877e11 0.170315
\(609\) −2.21952e11 −0.0653856
\(610\) 4.16163e11 0.121697
\(611\) 1.21772e12 0.353478
\(612\) 0 0
\(613\) −2.43845e12 −0.697497 −0.348748 0.937216i \(-0.613393\pi\)
−0.348748 + 0.937216i \(0.613393\pi\)
\(614\) −5.67068e11 −0.161019
\(615\) −1.29589e11 −0.0365283
\(616\) −1.87931e12 −0.525878
\(617\) −5.95149e12 −1.65326 −0.826632 0.562743i \(-0.809746\pi\)
−0.826632 + 0.562743i \(0.809746\pi\)
\(618\) 6.76667e10 0.0186607
\(619\) −5.90632e12 −1.61700 −0.808499 0.588498i \(-0.799720\pi\)
−0.808499 + 0.588498i \(0.799720\pi\)
\(620\) −7.81116e12 −2.12301
\(621\) 5.80269e11 0.156573
\(622\) 3.77765e11 0.101196
\(623\) −1.18762e13 −3.15850
\(624\) −4.69775e11 −0.124039
\(625\) 7.63770e12 2.00218
\(626\) −1.46665e11 −0.0381718
\(627\) −2.49134e11 −0.0643767
\(628\) −9.20737e11 −0.236220
\(629\) 0 0
\(630\) 1.65354e12 0.418198
\(631\) 5.67619e12 1.42536 0.712680 0.701489i \(-0.247481\pi\)
0.712680 + 0.701489i \(0.247481\pi\)
\(632\) −1.08857e12 −0.271412
\(633\) −3.96913e11 −0.0982604
\(634\) 6.47926e11 0.159266
\(635\) 6.98080e12 1.70382
\(636\) −5.72938e11 −0.138852
\(637\) −8.10465e12 −1.95032
\(638\) −1.84266e11 −0.0440303
\(639\) 2.41747e12 0.573597
\(640\) −4.00150e12 −0.942785
\(641\) 1.49036e12 0.348681 0.174341 0.984685i \(-0.444221\pi\)
0.174341 + 0.984685i \(0.444221\pi\)
\(642\) 8.55576e10 0.0198770
\(643\) −8.89423e11 −0.205191 −0.102596 0.994723i \(-0.532715\pi\)
−0.102596 + 0.994723i \(0.532715\pi\)
\(644\) −4.39690e12 −1.00730
\(645\) −1.68170e12 −0.382587
\(646\) 0 0
\(647\) 1.62659e12 0.364929 0.182465 0.983212i \(-0.441593\pi\)
0.182465 + 0.983212i \(0.441593\pi\)
\(648\) 1.14510e12 0.255127
\(649\) −4.34275e12 −0.960867
\(650\) 1.40953e12 0.309717
\(651\) 1.24695e12 0.272103
\(652\) 1.53610e12 0.332894
\(653\) 5.76853e12 1.24153 0.620763 0.783998i \(-0.286823\pi\)
0.620763 + 0.783998i \(0.286823\pi\)
\(654\) 1.19297e11 0.0254995
\(655\) −1.32223e13 −2.80687
\(656\) 6.79059e11 0.143166
\(657\) −1.91334e11 −0.0400634
\(658\) −4.02308e11 −0.0836648
\(659\) −2.19347e12 −0.453050 −0.226525 0.974005i \(-0.572737\pi\)
−0.226525 + 0.974005i \(0.572737\pi\)
\(660\) 1.30714e12 0.268147
\(661\) −3.13563e12 −0.638879 −0.319439 0.947607i \(-0.603495\pi\)
−0.319439 + 0.947607i \(0.603495\pi\)
\(662\) 1.02117e11 0.0206651
\(663\) 0 0
\(664\) −5.08850e11 −0.101586
\(665\) −6.76650e12 −1.34173
\(666\) 6.48351e11 0.127696
\(667\) −8.70341e11 −0.170264
\(668\) −2.78450e12 −0.541070
\(669\) 2.98661e11 0.0576449
\(670\) −1.44134e12 −0.276331
\(671\) 2.93194e12 0.558346
\(672\) 4.80662e11 0.0909239
\(673\) −3.23212e12 −0.607323 −0.303662 0.952780i \(-0.598209\pi\)
−0.303662 + 0.952780i \(0.598209\pi\)
\(674\) −9.23869e11 −0.172441
\(675\) −3.26695e12 −0.605726
\(676\) 1.10915e11 0.0204282
\(677\) 6.52077e12 1.19303 0.596513 0.802603i \(-0.296552\pi\)
0.596513 + 0.802603i \(0.296552\pi\)
\(678\) 4.22626e10 0.00768109
\(679\) 1.31558e12 0.237521
\(680\) 0 0
\(681\) −1.23139e12 −0.219399
\(682\) 1.03522e12 0.183233
\(683\) 2.88073e11 0.0506534 0.0253267 0.999679i \(-0.491937\pi\)
0.0253267 + 0.999679i \(0.491937\pi\)
\(684\) −2.36422e12 −0.412987
\(685\) −1.57181e13 −2.72768
\(686\) 1.31906e12 0.227408
\(687\) −8.25290e11 −0.141352
\(688\) 8.81228e12 1.49948
\(689\) −6.24231e12 −1.05526
\(690\) −1.16143e11 −0.0195061
\(691\) −6.08618e12 −1.01553 −0.507766 0.861495i \(-0.669529\pi\)
−0.507766 + 0.861495i \(0.669529\pi\)
\(692\) −1.10117e13 −1.82549
\(693\) 1.16495e13 1.91870
\(694\) −1.15686e12 −0.189305
\(695\) −4.78124e12 −0.777335
\(696\) 6.32331e10 0.0102142
\(697\) 0 0
\(698\) −6.93495e11 −0.110584
\(699\) 1.00402e11 0.0159073
\(700\) 2.47548e13 3.89689
\(701\) −1.78933e12 −0.279872 −0.139936 0.990161i \(-0.544690\pi\)
−0.139936 + 0.990161i \(0.544690\pi\)
\(702\) −2.27524e11 −0.0353598
\(703\) −2.65314e12 −0.409695
\(704\) −6.57933e12 −1.00950
\(705\) 5.64909e11 0.0861246
\(706\) −2.34260e10 −0.00354876
\(707\) −1.19202e13 −1.79430
\(708\) 7.38190e11 0.110413
\(709\) 7.74406e12 1.15096 0.575481 0.817815i \(-0.304815\pi\)
0.575481 + 0.817815i \(0.304815\pi\)
\(710\) −9.76393e11 −0.144199
\(711\) 6.74782e12 0.990262
\(712\) 3.38347e12 0.493403
\(713\) 4.88964e12 0.708556
\(714\) 0 0
\(715\) 1.42416e13 2.03789
\(716\) 3.66655e12 0.521373
\(717\) 7.70432e11 0.108867
\(718\) −8.20249e11 −0.115182
\(719\) −7.67138e12 −1.07052 −0.535258 0.844688i \(-0.679786\pi\)
−0.535258 + 0.844688i \(0.679786\pi\)
\(720\) 1.21667e13 1.68724
\(721\) 1.29479e13 1.78439
\(722\) 8.10167e11 0.110958
\(723\) −3.09137e11 −0.0420755
\(724\) 1.38456e13 1.87279
\(725\) 4.90008e12 0.658691
\(726\) −3.83090e10 −0.00511783
\(727\) −8.22639e12 −1.09221 −0.546103 0.837718i \(-0.683889\pi\)
−0.546103 + 0.837718i \(0.683889\pi\)
\(728\) 3.48048e12 0.459249
\(729\) −6.83224e12 −0.895961
\(730\) 7.72780e10 0.0100717
\(731\) 0 0
\(732\) −4.98378e11 −0.0641592
\(733\) 9.55042e11 0.122195 0.0610977 0.998132i \(-0.480540\pi\)
0.0610977 + 0.998132i \(0.480540\pi\)
\(734\) 7.02929e11 0.0893880
\(735\) −3.75980e12 −0.475195
\(736\) 1.88482e12 0.236766
\(737\) −1.01545e13 −1.26781
\(738\) 1.62983e11 0.0202250
\(739\) −3.28401e12 −0.405046 −0.202523 0.979278i \(-0.564914\pi\)
−0.202523 + 0.979278i \(0.564914\pi\)
\(740\) 1.39203e13 1.70650
\(741\) 4.61396e11 0.0562201
\(742\) 2.06232e12 0.249769
\(743\) 2.11148e12 0.254178 0.127089 0.991891i \(-0.459437\pi\)
0.127089 + 0.991891i \(0.459437\pi\)
\(744\) −3.55249e11 −0.0425064
\(745\) −2.22011e13 −2.64041
\(746\) −1.90136e12 −0.224771
\(747\) 3.15426e12 0.370642
\(748\) 0 0
\(749\) 1.63712e13 1.90070
\(750\) 3.70007e11 0.0427007
\(751\) −3.55572e12 −0.407895 −0.203947 0.978982i \(-0.565377\pi\)
−0.203947 + 0.978982i \(0.565377\pi\)
\(752\) −2.96018e12 −0.337549
\(753\) 5.77636e11 0.0654752
\(754\) 3.41261e11 0.0384517
\(755\) −1.12144e13 −1.25607
\(756\) −3.99587e12 −0.444901
\(757\) −8.12210e12 −0.898953 −0.449476 0.893292i \(-0.648389\pi\)
−0.449476 + 0.893292i \(0.648389\pi\)
\(758\) −6.47963e11 −0.0712917
\(759\) −8.18244e11 −0.0894942
\(760\) 1.92774e12 0.209598
\(761\) 1.55670e13 1.68258 0.841289 0.540586i \(-0.181797\pi\)
0.841289 + 0.540586i \(0.181797\pi\)
\(762\) 1.57263e11 0.0168977
\(763\) 2.28273e13 2.43834
\(764\) −4.22140e12 −0.448267
\(765\) 0 0
\(766\) −9.31785e11 −0.0977881
\(767\) 8.04278e12 0.839125
\(768\) 1.04926e12 0.108833
\(769\) −1.59487e13 −1.64458 −0.822292 0.569066i \(-0.807305\pi\)
−0.822292 + 0.569066i \(0.807305\pi\)
\(770\) −4.70511e12 −0.482350
\(771\) 1.11289e12 0.113425
\(772\) −1.16831e13 −1.18381
\(773\) −4.36572e12 −0.439793 −0.219896 0.975523i \(-0.570572\pi\)
−0.219896 + 0.975523i \(0.570572\pi\)
\(774\) 2.11506e12 0.211830
\(775\) −2.75290e13 −2.74115
\(776\) −3.74801e11 −0.0371042
\(777\) −2.22219e12 −0.218719
\(778\) 9.44924e11 0.0924674
\(779\) −6.66946e11 −0.0648892
\(780\) −2.42082e12 −0.234173
\(781\) −6.87885e12 −0.661586
\(782\) 0 0
\(783\) −7.90961e11 −0.0752016
\(784\) 1.97017e13 1.86244
\(785\) −4.65376e12 −0.437411
\(786\) −2.97872e11 −0.0278373
\(787\) 1.29316e13 1.20162 0.600808 0.799393i \(-0.294846\pi\)
0.600808 + 0.799393i \(0.294846\pi\)
\(788\) −1.11864e13 −1.03353
\(789\) −5.93060e11 −0.0544819
\(790\) −2.72538e12 −0.248946
\(791\) 8.08685e12 0.734489
\(792\) −3.31887e12 −0.299728
\(793\) −5.42996e12 −0.487604
\(794\) 8.63499e11 0.0771027
\(795\) −2.89585e12 −0.257113
\(796\) 9.87748e12 0.872042
\(797\) 7.30256e12 0.641081 0.320540 0.947235i \(-0.396135\pi\)
0.320540 + 0.947235i \(0.396135\pi\)
\(798\) −1.52435e11 −0.0133067
\(799\) 0 0
\(800\) −1.06116e13 −0.915962
\(801\) −2.09734e13 −1.80021
\(802\) −9.63640e11 −0.0822489
\(803\) 5.44437e11 0.0462091
\(804\) 1.72608e12 0.145683
\(805\) −2.22236e13 −1.86523
\(806\) −1.91723e12 −0.160017
\(807\) −7.38849e11 −0.0613232
\(808\) 3.39600e12 0.280296
\(809\) 2.08963e13 1.71514 0.857571 0.514365i \(-0.171973\pi\)
0.857571 + 0.514365i \(0.171973\pi\)
\(810\) 2.86692e12 0.234009
\(811\) 8.60451e12 0.698445 0.349222 0.937040i \(-0.386446\pi\)
0.349222 + 0.937040i \(0.386446\pi\)
\(812\) 5.99338e12 0.483804
\(813\) 1.41226e12 0.113372
\(814\) −1.84487e12 −0.147284
\(815\) 7.76405e12 0.616423
\(816\) 0 0
\(817\) −8.65509e12 −0.679630
\(818\) −1.83025e12 −0.142929
\(819\) −2.15748e13 −1.67560
\(820\) 3.49929e12 0.270282
\(821\) 1.33422e13 1.02491 0.512453 0.858716i \(-0.328737\pi\)
0.512453 + 0.858716i \(0.328737\pi\)
\(822\) −3.54097e11 −0.0270520
\(823\) 9.21038e12 0.699807 0.349903 0.936786i \(-0.386214\pi\)
0.349903 + 0.936786i \(0.386214\pi\)
\(824\) −3.68878e12 −0.278747
\(825\) 4.60677e12 0.346221
\(826\) −2.65716e12 −0.198613
\(827\) −1.73042e13 −1.28640 −0.643202 0.765696i \(-0.722395\pi\)
−0.643202 + 0.765696i \(0.722395\pi\)
\(828\) −7.76496e12 −0.574120
\(829\) −1.69425e13 −1.24590 −0.622949 0.782263i \(-0.714065\pi\)
−0.622949 + 0.782263i \(0.714065\pi\)
\(830\) −1.27398e12 −0.0931773
\(831\) −1.30855e12 −0.0951889
\(832\) 1.21849e13 0.881593
\(833\) 0 0
\(834\) −1.07711e11 −0.00770928
\(835\) −1.40739e13 −1.00190
\(836\) 6.72735e12 0.476339
\(837\) 4.44368e12 0.312952
\(838\) 1.11321e12 0.0779790
\(839\) 2.51719e13 1.75383 0.876915 0.480645i \(-0.159598\pi\)
0.876915 + 0.480645i \(0.159598\pi\)
\(840\) 1.61462e12 0.111896
\(841\) −1.33208e13 −0.918223
\(842\) −3.12604e12 −0.214334
\(843\) 7.94698e11 0.0541973
\(844\) 1.07178e13 0.727053
\(845\) 5.60606e11 0.0378270
\(846\) −7.10480e11 −0.0476854
\(847\) −7.33034e12 −0.489383
\(848\) 1.51745e13 1.00771
\(849\) −3.71934e11 −0.0245687
\(850\) 0 0
\(851\) −8.71385e12 −0.569544
\(852\) 1.16928e12 0.0760224
\(853\) 1.68384e13 1.08901 0.544503 0.838759i \(-0.316718\pi\)
0.544503 + 0.838759i \(0.316718\pi\)
\(854\) 1.79394e12 0.115411
\(855\) −1.19497e13 −0.764732
\(856\) −4.66408e12 −0.296916
\(857\) −1.45946e13 −0.924225 −0.462113 0.886821i \(-0.652908\pi\)
−0.462113 + 0.886821i \(0.652908\pi\)
\(858\) 3.20834e11 0.0202110
\(859\) −2.05283e13 −1.28642 −0.643211 0.765689i \(-0.722398\pi\)
−0.643211 + 0.765689i \(0.722398\pi\)
\(860\) 4.54110e13 2.83086
\(861\) −5.58614e11 −0.0346416
\(862\) 2.58988e12 0.159771
\(863\) 2.15891e13 1.32491 0.662453 0.749104i \(-0.269515\pi\)
0.662453 + 0.749104i \(0.269515\pi\)
\(864\) 1.71291e12 0.104574
\(865\) −5.56576e13 −3.38027
\(866\) −3.64582e12 −0.220275
\(867\) 0 0
\(868\) −3.36713e13 −2.01336
\(869\) −1.92008e13 −1.14217
\(870\) 1.58313e11 0.00936872
\(871\) 1.88061e13 1.10718
\(872\) −6.50338e12 −0.380903
\(873\) 2.32332e12 0.135377
\(874\) −5.97743e11 −0.0346508
\(875\) 7.08000e13 4.08317
\(876\) −9.25446e10 −0.00530985
\(877\) −1.82834e13 −1.04366 −0.521830 0.853049i \(-0.674750\pi\)
−0.521830 + 0.853049i \(0.674750\pi\)
\(878\) −8.61383e11 −0.0489182
\(879\) 1.93625e12 0.109399
\(880\) −3.46201e13 −1.94606
\(881\) −1.70514e12 −0.0953604 −0.0476802 0.998863i \(-0.515183\pi\)
−0.0476802 + 0.998863i \(0.515183\pi\)
\(882\) 4.72866e12 0.263105
\(883\) −2.21871e13 −1.22822 −0.614112 0.789219i \(-0.710486\pi\)
−0.614112 + 0.789219i \(0.710486\pi\)
\(884\) 0 0
\(885\) 3.73110e12 0.204452
\(886\) 3.18682e12 0.173742
\(887\) −2.47842e13 −1.34437 −0.672186 0.740382i \(-0.734644\pi\)
−0.672186 + 0.740382i \(0.734644\pi\)
\(888\) 6.33090e11 0.0341670
\(889\) 3.00919e13 1.61581
\(890\) 8.47099e12 0.452563
\(891\) 2.01979e13 1.07364
\(892\) −8.06474e12 −0.426529
\(893\) 2.90738e12 0.152992
\(894\) −5.00145e11 −0.0261865
\(895\) 1.85321e13 0.965433
\(896\) −1.72491e13 −0.894088
\(897\) 1.51539e12 0.0781553
\(898\) −2.92548e12 −0.150125
\(899\) −6.66504e12 −0.340317
\(900\) 4.37172e13 2.22107
\(901\) 0 0
\(902\) −4.63764e11 −0.0233275
\(903\) −7.24925e12 −0.362826
\(904\) −2.30390e12 −0.114738
\(905\) 6.99812e13 3.46787
\(906\) −2.52637e11 −0.0124572
\(907\) 2.81679e13 1.38204 0.691021 0.722835i \(-0.257161\pi\)
0.691021 + 0.722835i \(0.257161\pi\)
\(908\) 3.32513e13 1.62339
\(909\) −2.10512e13 −1.02268
\(910\) 8.71388e12 0.421236
\(911\) −2.22649e12 −0.107100 −0.0535498 0.998565i \(-0.517054\pi\)
−0.0535498 + 0.998565i \(0.517054\pi\)
\(912\) −1.12161e12 −0.0536867
\(913\) −8.97539e12 −0.427499
\(914\) −1.61095e12 −0.0763527
\(915\) −2.51899e12 −0.118804
\(916\) 2.22853e13 1.04590
\(917\) −5.69970e13 −2.66189
\(918\) 0 0
\(919\) 2.93520e13 1.35743 0.678715 0.734402i \(-0.262537\pi\)
0.678715 + 0.734402i \(0.262537\pi\)
\(920\) 6.33139e12 0.291376
\(921\) 3.43240e12 0.157192
\(922\) 4.83820e12 0.220493
\(923\) 1.27396e13 0.577763
\(924\) 5.63463e12 0.254297
\(925\) 4.90596e13 2.20336
\(926\) −2.49416e12 −0.111475
\(927\) 2.28660e13 1.01703
\(928\) −2.56918e12 −0.113718
\(929\) 7.11576e12 0.313437 0.156719 0.987643i \(-0.449908\pi\)
0.156719 + 0.987643i \(0.449908\pi\)
\(930\) −8.89416e11 −0.0389881
\(931\) −1.93503e13 −0.844139
\(932\) −2.71115e12 −0.117702
\(933\) −2.28657e12 −0.0987911
\(934\) 4.41585e12 0.189869
\(935\) 0 0
\(936\) 6.14656e12 0.261752
\(937\) 1.06889e13 0.453007 0.226503 0.974010i \(-0.427271\pi\)
0.226503 + 0.974010i \(0.427271\pi\)
\(938\) −6.21312e12 −0.262058
\(939\) 8.87750e11 0.0372645
\(940\) −1.52542e13 −0.637257
\(941\) −1.96244e13 −0.815910 −0.407955 0.913002i \(-0.633758\pi\)
−0.407955 + 0.913002i \(0.633758\pi\)
\(942\) −1.04839e11 −0.00433806
\(943\) −2.19049e12 −0.0902067
\(944\) −1.95513e13 −0.801312
\(945\) −2.01967e13 −0.823829
\(946\) −6.01836e12 −0.244325
\(947\) 1.29410e13 0.522870 0.261435 0.965221i \(-0.415804\pi\)
0.261435 + 0.965221i \(0.415804\pi\)
\(948\) 3.26379e12 0.131246
\(949\) −1.00830e12 −0.0403544
\(950\) 3.36533e12 0.134052
\(951\) −3.92183e12 −0.155481
\(952\) 0 0
\(953\) −1.09666e13 −0.430680 −0.215340 0.976539i \(-0.569086\pi\)
−0.215340 + 0.976539i \(0.569086\pi\)
\(954\) 3.64208e12 0.142358
\(955\) −2.13366e13 −0.830060
\(956\) −2.08040e13 −0.805537
\(957\) 1.11534e12 0.0429838
\(958\) 3.68636e11 0.0141401
\(959\) −6.77556e13 −2.58679
\(960\) 5.65267e12 0.214799
\(961\) 1.10051e13 0.416235
\(962\) 3.41670e12 0.128623
\(963\) 2.89117e13 1.08332
\(964\) 8.34763e12 0.311327
\(965\) −5.90511e13 −2.19207
\(966\) −5.00651e11 −0.0184986
\(967\) 3.26302e13 1.20005 0.600027 0.799980i \(-0.295157\pi\)
0.600027 + 0.799980i \(0.295157\pi\)
\(968\) 2.08838e12 0.0764486
\(969\) 0 0
\(970\) −9.38368e11 −0.0340330
\(971\) 1.49723e13 0.540507 0.270253 0.962789i \(-0.412893\pi\)
0.270253 + 0.962789i \(0.412893\pi\)
\(972\) −1.06164e13 −0.381488
\(973\) −2.06103e13 −0.737185
\(974\) 3.74178e12 0.133218
\(975\) −8.53174e12 −0.302355
\(976\) 1.31998e13 0.465631
\(977\) 1.12933e13 0.396548 0.198274 0.980147i \(-0.436466\pi\)
0.198274 + 0.980147i \(0.436466\pi\)
\(978\) 1.74908e11 0.00611342
\(979\) 5.96795e13 2.07636
\(980\) 1.01526e14 3.51608
\(981\) 4.03132e13 1.38975
\(982\) −3.38916e12 −0.116303
\(983\) 5.44159e13 1.85881 0.929404 0.369063i \(-0.120321\pi\)
0.929404 + 0.369063i \(0.120321\pi\)
\(984\) 1.59146e11 0.00541151
\(985\) −5.65403e13 −1.91379
\(986\) 0 0
\(987\) 2.43513e12 0.0816761
\(988\) −1.24591e13 −0.415987
\(989\) −2.84264e13 −0.944798
\(990\) −8.30927e12 −0.274919
\(991\) 3.13975e13 1.03410 0.517052 0.855954i \(-0.327029\pi\)
0.517052 + 0.855954i \(0.327029\pi\)
\(992\) 1.44339e13 0.473238
\(993\) −6.18105e11 −0.0201740
\(994\) −4.20890e12 −0.136751
\(995\) 4.99246e13 1.61477
\(996\) 1.52566e12 0.0491235
\(997\) −3.75262e11 −0.0120284 −0.00601419 0.999982i \(-0.501914\pi\)
−0.00601419 + 0.999982i \(0.501914\pi\)
\(998\) −5.65193e12 −0.180347
\(999\) −7.91910e12 −0.251554
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.1.18 36
17.16 even 2 289.10.a.h.1.18 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.18 36 1.1 even 1 trivial
289.10.a.h.1.18 yes 36 17.16 even 2