Properties

Label 289.10.a.i.1.20
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $2$

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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: \(52\)
Twist minimal: no (minimal twist has level 17)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-8.91738 q^{2} +33.9373 q^{3} -432.480 q^{4} -34.8748 q^{5} -302.632 q^{6} -8539.90 q^{7} +8422.29 q^{8} -18531.3 q^{9} +O(q^{10})\) \(q-8.91738 q^{2} +33.9373 q^{3} -432.480 q^{4} -34.8748 q^{5} -302.632 q^{6} -8539.90 q^{7} +8422.29 q^{8} -18531.3 q^{9} +310.992 q^{10} -828.804 q^{11} -14677.2 q^{12} +147504. q^{13} +76153.5 q^{14} -1183.55 q^{15} +146325. q^{16} +165250. q^{18} +385867. q^{19} +15082.7 q^{20} -289821. q^{21} +7390.76 q^{22} -1.98059e6 q^{23} +285830. q^{24} -1.95191e6 q^{25} -1.31535e6 q^{26} -1.29689e6 q^{27} +3.69334e6 q^{28} -2.63751e6 q^{29} +10554.2 q^{30} -6.41699e6 q^{31} -5.61705e6 q^{32} -28127.3 q^{33} +297827. q^{35} +8.01441e6 q^{36} -1.89325e7 q^{37} -3.44092e6 q^{38} +5.00588e6 q^{39} -293725. q^{40} +9.32654e6 q^{41} +2.58444e6 q^{42} -1.72009e7 q^{43} +358441. q^{44} +646274. q^{45} +1.76616e7 q^{46} +1.46297e7 q^{47} +4.96588e6 q^{48} +3.25763e7 q^{49} +1.74059e7 q^{50} -6.37925e7 q^{52} -9.96374e7 q^{53} +1.15648e7 q^{54} +28904.3 q^{55} -7.19255e7 q^{56} +1.30953e7 q^{57} +2.35197e7 q^{58} +7.35572e7 q^{59} +511864. q^{60} +643588. q^{61} +5.72227e7 q^{62} +1.58255e8 q^{63} -2.48292e7 q^{64} -5.14417e6 q^{65} +250822. q^{66} -2.31463e8 q^{67} -6.72157e7 q^{69} -2.65584e6 q^{70} -4.38074e7 q^{71} -1.56076e8 q^{72} +2.09768e8 q^{73} +1.68829e8 q^{74} -6.62425e7 q^{75} -1.66880e8 q^{76} +7.07790e6 q^{77} -4.46393e7 q^{78} +7.18393e7 q^{79} -5.10306e6 q^{80} +3.20738e8 q^{81} -8.31683e7 q^{82} -3.97394e8 q^{83} +1.25342e8 q^{84} +1.53387e8 q^{86} -8.95099e7 q^{87} -6.98042e6 q^{88} +2.63648e8 q^{89} -5.76307e6 q^{90} -1.25967e9 q^{91} +8.56565e8 q^{92} -2.17775e8 q^{93} -1.30459e8 q^{94} -1.34570e7 q^{95} -1.90627e8 q^{96} -3.00392e8 q^{97} -2.90495e8 q^{98} +1.53588e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 64q^{2} + 13312q^{4} + 49152q^{8} + 341172q^{9} + O(q^{10}) \) \( 52q + 64q^{2} + 13312q^{4} + 49152q^{8} + 341172q^{9} + 156200q^{13} + 1207872q^{15} + 3407880q^{16} + 2193336q^{18} + 1185568q^{19} + 5198336q^{21} + 13827692q^{25} + 3618944q^{26} - 9167544q^{30} + 61884888q^{32} + 1635208q^{33} + 46992776q^{35} + 156027320q^{36} + 84813952q^{38} - 4635776q^{42} + 125448912q^{43} + 164193176q^{47} + 270850284q^{49} - 226223888q^{50} + 103553016q^{52} + 426167208q^{53} + 677761520q^{55} + 375214512q^{59} + 336918024q^{60} + 190014416q^{64} + 1377178928q^{66} + 311910088q^{67} + 533688136q^{69} + 1477690280q^{70} + 2757942680q^{72} + 4047975520q^{76} + 3440336432q^{77} + 3266558756q^{81} + 2072890608q^{83} + 2630025952q^{84} + 1538547296q^{86} - 1010436256q^{87} + 1873849184q^{89} - 1998451624q^{93} - 6880776704q^{94} - 4667454128q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.91738 −0.394096 −0.197048 0.980394i \(-0.563136\pi\)
−0.197048 + 0.980394i \(0.563136\pi\)
\(3\) 33.9373 0.241897 0.120949 0.992659i \(-0.461406\pi\)
0.120949 + 0.992659i \(0.461406\pi\)
\(4\) −432.480 −0.844688
\(5\) −34.8748 −0.0249544 −0.0124772 0.999922i \(-0.503972\pi\)
−0.0124772 + 0.999922i \(0.503972\pi\)
\(6\) −302.632 −0.0953309
\(7\) −8539.90 −1.34435 −0.672174 0.740393i \(-0.734639\pi\)
−0.672174 + 0.740393i \(0.734639\pi\)
\(8\) 8422.29 0.726985
\(9\) −18531.3 −0.941486
\(10\) 310.992 0.00983442
\(11\) −828.804 −0.0170681 −0.00853404 0.999964i \(-0.502717\pi\)
−0.00853404 + 0.999964i \(0.502717\pi\)
\(12\) −14677.2 −0.204328
\(13\) 147504. 1.43238 0.716190 0.697905i \(-0.245884\pi\)
0.716190 + 0.697905i \(0.245884\pi\)
\(14\) 76153.5 0.529802
\(15\) −1183.55 −0.00603640
\(16\) 146325. 0.558186
\(17\) 0 0
\(18\) 165250. 0.371036
\(19\) 385867. 0.679277 0.339638 0.940556i \(-0.389695\pi\)
0.339638 + 0.940556i \(0.389695\pi\)
\(20\) 15082.7 0.0210787
\(21\) −289821. −0.325194
\(22\) 7390.76 0.00672646
\(23\) −1.98059e6 −1.47577 −0.737885 0.674927i \(-0.764175\pi\)
−0.737885 + 0.674927i \(0.764175\pi\)
\(24\) 285830. 0.175856
\(25\) −1.95191e6 −0.999377
\(26\) −1.31535e6 −0.564496
\(27\) −1.29689e6 −0.469640
\(28\) 3.69334e6 1.13555
\(29\) −2.63751e6 −0.692473 −0.346237 0.938147i \(-0.612541\pi\)
−0.346237 + 0.938147i \(0.612541\pi\)
\(30\) 10554.2 0.00237892
\(31\) −6.41699e6 −1.24797 −0.623984 0.781437i \(-0.714487\pi\)
−0.623984 + 0.781437i \(0.714487\pi\)
\(32\) −5.61705e6 −0.946964
\(33\) −28127.3 −0.00412873
\(34\) 0 0
\(35\) 297827. 0.0335473
\(36\) 8.01441e6 0.795262
\(37\) −1.89325e7 −1.66074 −0.830369 0.557214i \(-0.811870\pi\)
−0.830369 + 0.557214i \(0.811870\pi\)
\(38\) −3.44092e6 −0.267700
\(39\) 5.00588e6 0.346489
\(40\) −293725. −0.0181414
\(41\) 9.32654e6 0.515458 0.257729 0.966217i \(-0.417026\pi\)
0.257729 + 0.966217i \(0.417026\pi\)
\(42\) 2.58444e6 0.128158
\(43\) −1.72009e7 −0.767260 −0.383630 0.923487i \(-0.625326\pi\)
−0.383630 + 0.923487i \(0.625326\pi\)
\(44\) 358441. 0.0144172
\(45\) 646274. 0.0234942
\(46\) 1.76616e7 0.581595
\(47\) 1.46297e7 0.437317 0.218658 0.975801i \(-0.429832\pi\)
0.218658 + 0.975801i \(0.429832\pi\)
\(48\) 4.96588e6 0.135024
\(49\) 3.25763e7 0.807271
\(50\) 1.74059e7 0.393851
\(51\) 0 0
\(52\) −6.37925e7 −1.20991
\(53\) −9.96374e7 −1.73453 −0.867264 0.497849i \(-0.834123\pi\)
−0.867264 + 0.497849i \(0.834123\pi\)
\(54\) 1.15648e7 0.185083
\(55\) 28904.3 0.000425923 0
\(56\) −7.19255e7 −0.977320
\(57\) 1.30953e7 0.164315
\(58\) 2.35197e7 0.272901
\(59\) 7.35572e7 0.790298 0.395149 0.918617i \(-0.370693\pi\)
0.395149 + 0.918617i \(0.370693\pi\)
\(60\) 511864. 0.00509887
\(61\) 643588. 0.00595146 0.00297573 0.999996i \(-0.499053\pi\)
0.00297573 + 0.999996i \(0.499053\pi\)
\(62\) 5.72227e7 0.491820
\(63\) 1.58255e8 1.26568
\(64\) −2.48292e7 −0.184992
\(65\) −5.14417e6 −0.0357441
\(66\) 250822. 0.00162711
\(67\) −2.31463e8 −1.40328 −0.701642 0.712530i \(-0.747549\pi\)
−0.701642 + 0.712530i \(0.747549\pi\)
\(68\) 0 0
\(69\) −6.72157e7 −0.356985
\(70\) −2.65584e6 −0.0132209
\(71\) −4.38074e7 −0.204590 −0.102295 0.994754i \(-0.532619\pi\)
−0.102295 + 0.994754i \(0.532619\pi\)
\(72\) −1.56076e8 −0.684445
\(73\) 2.09768e8 0.864542 0.432271 0.901744i \(-0.357712\pi\)
0.432271 + 0.901744i \(0.357712\pi\)
\(74\) 1.68829e8 0.654490
\(75\) −6.62425e7 −0.241747
\(76\) −1.66880e8 −0.573777
\(77\) 7.07790e6 0.0229454
\(78\) −4.46393e7 −0.136550
\(79\) 7.18393e7 0.207511 0.103755 0.994603i \(-0.466914\pi\)
0.103755 + 0.994603i \(0.466914\pi\)
\(80\) −5.10306e6 −0.0139292
\(81\) 3.20738e8 0.827881
\(82\) −8.31683e7 −0.203140
\(83\) −3.97394e8 −0.919115 −0.459557 0.888148i \(-0.651992\pi\)
−0.459557 + 0.888148i \(0.651992\pi\)
\(84\) 1.25342e8 0.274688
\(85\) 0 0
\(86\) 1.53387e8 0.302374
\(87\) −8.95099e7 −0.167508
\(88\) −6.98042e6 −0.0124082
\(89\) 2.63648e8 0.445420 0.222710 0.974885i \(-0.428510\pi\)
0.222710 + 0.974885i \(0.428510\pi\)
\(90\) −5.76307e6 −0.00925896
\(91\) −1.25967e9 −1.92562
\(92\) 8.56565e8 1.24657
\(93\) −2.17775e8 −0.301881
\(94\) −1.30459e8 −0.172345
\(95\) −1.34570e7 −0.0169509
\(96\) −1.90627e8 −0.229068
\(97\) −3.00392e8 −0.344521 −0.172261 0.985051i \(-0.555107\pi\)
−0.172261 + 0.985051i \(0.555107\pi\)
\(98\) −2.90495e8 −0.318143
\(99\) 1.53588e7 0.0160694
\(100\) 8.44162e8 0.844162
\(101\) 1.66753e9 1.59451 0.797254 0.603644i \(-0.206285\pi\)
0.797254 + 0.603644i \(0.206285\pi\)
\(102\) 0 0
\(103\) 2.00995e8 0.175962 0.0879808 0.996122i \(-0.471959\pi\)
0.0879808 + 0.996122i \(0.471959\pi\)
\(104\) 1.24232e9 1.04132
\(105\) 1.01074e7 0.00811502
\(106\) 8.88505e8 0.683571
\(107\) 6.92487e8 0.510722 0.255361 0.966846i \(-0.417806\pi\)
0.255361 + 0.966846i \(0.417806\pi\)
\(108\) 5.60879e8 0.396700
\(109\) −9.89530e7 −0.0671444 −0.0335722 0.999436i \(-0.510688\pi\)
−0.0335722 + 0.999436i \(0.510688\pi\)
\(110\) −257751. −0.000167855 0
\(111\) −6.42519e8 −0.401728
\(112\) −1.24960e9 −0.750397
\(113\) −2.44334e9 −1.40972 −0.704858 0.709349i \(-0.748989\pi\)
−0.704858 + 0.709349i \(0.748989\pi\)
\(114\) −1.16776e8 −0.0647560
\(115\) 6.90725e7 0.0368269
\(116\) 1.14067e9 0.584924
\(117\) −2.73343e9 −1.34857
\(118\) −6.55937e8 −0.311454
\(119\) 0 0
\(120\) −9.96824e6 −0.00438837
\(121\) −2.35726e9 −0.999709
\(122\) −5.73911e6 −0.00234545
\(123\) 3.16517e8 0.124688
\(124\) 2.77522e9 1.05414
\(125\) 1.36187e8 0.0498932
\(126\) −1.41122e9 −0.498801
\(127\) 8.77474e8 0.299307 0.149654 0.988738i \(-0.452184\pi\)
0.149654 + 0.988738i \(0.452184\pi\)
\(128\) 3.09734e9 1.01987
\(129\) −5.83751e8 −0.185598
\(130\) 4.58725e7 0.0140866
\(131\) 1.44575e9 0.428916 0.214458 0.976733i \(-0.431202\pi\)
0.214458 + 0.976733i \(0.431202\pi\)
\(132\) 1.21645e7 0.00348749
\(133\) −3.29527e9 −0.913184
\(134\) 2.06405e9 0.553029
\(135\) 4.52287e7 0.0117196
\(136\) 0 0
\(137\) −2.23159e9 −0.541218 −0.270609 0.962689i \(-0.587225\pi\)
−0.270609 + 0.962689i \(0.587225\pi\)
\(138\) 5.99388e8 0.140686
\(139\) 7.93386e9 1.80268 0.901339 0.433115i \(-0.142586\pi\)
0.901339 + 0.433115i \(0.142586\pi\)
\(140\) −1.28804e8 −0.0283370
\(141\) 4.96493e8 0.105786
\(142\) 3.90647e8 0.0806281
\(143\) −1.22252e8 −0.0244480
\(144\) −2.71159e9 −0.525524
\(145\) 9.19826e7 0.0172802
\(146\) −1.87058e9 −0.340713
\(147\) 1.10555e9 0.195277
\(148\) 8.18795e9 1.40281
\(149\) 2.71032e9 0.450488 0.225244 0.974302i \(-0.427682\pi\)
0.225244 + 0.974302i \(0.427682\pi\)
\(150\) 5.90709e8 0.0952715
\(151\) −2.22864e9 −0.348853 −0.174427 0.984670i \(-0.555807\pi\)
−0.174427 + 0.984670i \(0.555807\pi\)
\(152\) 3.24989e9 0.493824
\(153\) 0 0
\(154\) −6.31163e7 −0.00904271
\(155\) 2.23791e8 0.0311423
\(156\) −2.16495e9 −0.292675
\(157\) 2.51657e9 0.330568 0.165284 0.986246i \(-0.447146\pi\)
0.165284 + 0.986246i \(0.447146\pi\)
\(158\) −6.40618e8 −0.0817791
\(159\) −3.38142e9 −0.419578
\(160\) 1.95893e8 0.0236309
\(161\) 1.69140e10 1.98395
\(162\) −2.86014e9 −0.326265
\(163\) −8.11516e9 −0.900436 −0.450218 0.892919i \(-0.648654\pi\)
−0.450218 + 0.892919i \(0.648654\pi\)
\(164\) −4.03355e9 −0.435401
\(165\) 980935. 0.000103030 0
\(166\) 3.54371e9 0.362220
\(167\) −1.50831e10 −1.50060 −0.750301 0.661096i \(-0.770092\pi\)
−0.750301 + 0.661096i \(0.770092\pi\)
\(168\) −2.44096e9 −0.236411
\(169\) 1.11529e10 1.05171
\(170\) 0 0
\(171\) −7.15061e9 −0.639529
\(172\) 7.43904e9 0.648096
\(173\) −2.04298e10 −1.73403 −0.867016 0.498281i \(-0.833965\pi\)
−0.867016 + 0.498281i \(0.833965\pi\)
\(174\) 7.98194e8 0.0660141
\(175\) 1.66691e10 1.34351
\(176\) −1.21275e8 −0.00952717
\(177\) 2.49633e9 0.191171
\(178\) −2.35105e9 −0.175538
\(179\) −7.07164e9 −0.514851 −0.257426 0.966298i \(-0.582874\pi\)
−0.257426 + 0.966298i \(0.582874\pi\)
\(180\) −2.79501e8 −0.0198452
\(181\) 7.59530e9 0.526007 0.263003 0.964795i \(-0.415287\pi\)
0.263003 + 0.964795i \(0.415287\pi\)
\(182\) 1.12329e10 0.758879
\(183\) 2.18416e7 0.00143964
\(184\) −1.66811e10 −1.07286
\(185\) 6.60268e8 0.0414426
\(186\) 1.94198e9 0.118970
\(187\) 0 0
\(188\) −6.32707e9 −0.369396
\(189\) 1.10753e10 0.631360
\(190\) 1.20001e8 0.00668029
\(191\) 3.32722e10 1.80897 0.904484 0.426508i \(-0.140256\pi\)
0.904484 + 0.426508i \(0.140256\pi\)
\(192\) −8.42634e8 −0.0447490
\(193\) 1.62233e10 0.841652 0.420826 0.907141i \(-0.361740\pi\)
0.420826 + 0.907141i \(0.361740\pi\)
\(194\) 2.67871e9 0.135775
\(195\) −1.74579e8 −0.00864642
\(196\) −1.40886e10 −0.681893
\(197\) −3.49292e10 −1.65231 −0.826154 0.563445i \(-0.809476\pi\)
−0.826154 + 0.563445i \(0.809476\pi\)
\(198\) −1.36960e8 −0.00633287
\(199\) 2.91611e10 1.31815 0.659076 0.752076i \(-0.270947\pi\)
0.659076 + 0.752076i \(0.270947\pi\)
\(200\) −1.64395e10 −0.726532
\(201\) −7.85524e9 −0.339451
\(202\) −1.48700e10 −0.628390
\(203\) 2.25241e10 0.930925
\(204\) 0 0
\(205\) −3.25261e8 −0.0128629
\(206\) −1.79235e9 −0.0693458
\(207\) 3.67028e10 1.38942
\(208\) 2.15835e10 0.799535
\(209\) −3.19808e8 −0.0115940
\(210\) −9.01319e7 −0.00319810
\(211\) −3.70370e10 −1.28637 −0.643183 0.765713i \(-0.722386\pi\)
−0.643183 + 0.765713i \(0.722386\pi\)
\(212\) 4.30912e10 1.46513
\(213\) −1.48670e9 −0.0494898
\(214\) −6.17516e9 −0.201273
\(215\) 5.99877e8 0.0191465
\(216\) −1.09228e10 −0.341421
\(217\) 5.48005e10 1.67770
\(218\) 8.82401e8 0.0264613
\(219\) 7.11895e9 0.209131
\(220\) −1.25006e7 −0.000359772 0
\(221\) 0 0
\(222\) 5.72958e9 0.158320
\(223\) 4.79718e10 1.29902 0.649508 0.760355i \(-0.274975\pi\)
0.649508 + 0.760355i \(0.274975\pi\)
\(224\) 4.79690e10 1.27305
\(225\) 3.61713e10 0.940899
\(226\) 2.17882e10 0.555563
\(227\) 1.11013e10 0.277497 0.138748 0.990328i \(-0.455692\pi\)
0.138748 + 0.990328i \(0.455692\pi\)
\(228\) −5.66345e9 −0.138795
\(229\) 3.41722e10 0.821134 0.410567 0.911831i \(-0.365331\pi\)
0.410567 + 0.911831i \(0.365331\pi\)
\(230\) −6.15946e8 −0.0145133
\(231\) 2.40205e8 0.00555044
\(232\) −2.22139e10 −0.503417
\(233\) 8.01980e10 1.78263 0.891317 0.453381i \(-0.149782\pi\)
0.891317 + 0.453381i \(0.149782\pi\)
\(234\) 2.43751e10 0.531465
\(235\) −5.10208e8 −0.0109130
\(236\) −3.18120e10 −0.667556
\(237\) 2.43803e9 0.0501963
\(238\) 0 0
\(239\) 4.68969e10 0.929723 0.464861 0.885384i \(-0.346104\pi\)
0.464861 + 0.885384i \(0.346104\pi\)
\(240\) −1.73184e8 −0.00336943
\(241\) −2.38227e9 −0.0454899 −0.0227449 0.999741i \(-0.507241\pi\)
−0.0227449 + 0.999741i \(0.507241\pi\)
\(242\) 2.10206e10 0.393981
\(243\) 3.64116e10 0.669903
\(244\) −2.78339e8 −0.00502713
\(245\) −1.13609e9 −0.0201449
\(246\) −2.82251e9 −0.0491391
\(247\) 5.69169e10 0.972983
\(248\) −5.40457e10 −0.907254
\(249\) −1.34865e10 −0.222332
\(250\) −1.21443e9 −0.0196627
\(251\) −9.82275e10 −1.56207 −0.781037 0.624485i \(-0.785309\pi\)
−0.781037 + 0.624485i \(0.785309\pi\)
\(252\) −6.84422e10 −1.06911
\(253\) 1.64152e9 0.0251885
\(254\) −7.82477e9 −0.117956
\(255\) 0 0
\(256\) −1.49076e10 −0.216934
\(257\) 9.68357e10 1.38464 0.692319 0.721591i \(-0.256589\pi\)
0.692319 + 0.721591i \(0.256589\pi\)
\(258\) 5.20553e9 0.0731436
\(259\) 1.61682e11 2.23261
\(260\) 2.22475e9 0.0301926
\(261\) 4.88764e10 0.651954
\(262\) −1.28923e10 −0.169034
\(263\) 6.80816e10 0.877463 0.438731 0.898618i \(-0.355428\pi\)
0.438731 + 0.898618i \(0.355428\pi\)
\(264\) −2.36897e8 −0.00300152
\(265\) 3.47483e9 0.0432840
\(266\) 2.93852e10 0.359882
\(267\) 8.94749e9 0.107746
\(268\) 1.00103e11 1.18534
\(269\) −9.55603e10 −1.11274 −0.556368 0.830936i \(-0.687805\pi\)
−0.556368 + 0.830936i \(0.687805\pi\)
\(270\) −4.03321e8 −0.00461864
\(271\) 1.38416e11 1.55893 0.779463 0.626449i \(-0.215492\pi\)
0.779463 + 0.626449i \(0.215492\pi\)
\(272\) 0 0
\(273\) −4.27497e10 −0.465802
\(274\) 1.98999e10 0.213292
\(275\) 1.61775e9 0.0170575
\(276\) 2.90695e10 0.301541
\(277\) 8.21346e10 0.838238 0.419119 0.907931i \(-0.362339\pi\)
0.419119 + 0.907931i \(0.362339\pi\)
\(278\) −7.07492e10 −0.710428
\(279\) 1.18915e11 1.17494
\(280\) 2.50839e9 0.0243884
\(281\) −1.69825e11 −1.62489 −0.812444 0.583039i \(-0.801864\pi\)
−0.812444 + 0.583039i \(0.801864\pi\)
\(282\) −4.42742e9 −0.0416898
\(283\) −8.41175e10 −0.779556 −0.389778 0.920909i \(-0.627448\pi\)
−0.389778 + 0.920909i \(0.627448\pi\)
\(284\) 1.89458e10 0.172815
\(285\) −4.56695e8 −0.00410038
\(286\) 1.09017e9 0.00963486
\(287\) −7.96478e10 −0.692955
\(288\) 1.04091e11 0.891553
\(289\) 0 0
\(290\) −8.20243e8 −0.00681007
\(291\) −1.01945e10 −0.0833389
\(292\) −9.07205e10 −0.730269
\(293\) −1.20546e11 −0.955536 −0.477768 0.878486i \(-0.658554\pi\)
−0.477768 + 0.878486i \(0.658554\pi\)
\(294\) −9.85862e9 −0.0769579
\(295\) −2.56529e9 −0.0197214
\(296\) −1.59455e11 −1.20733
\(297\) 1.07487e9 0.00801586
\(298\) −2.41690e10 −0.177535
\(299\) −2.92144e11 −2.11386
\(300\) 2.86486e10 0.204201
\(301\) 1.46894e11 1.03146
\(302\) 1.98736e10 0.137482
\(303\) 5.65913e10 0.385708
\(304\) 5.64621e10 0.379163
\(305\) −2.24450e7 −0.000148515 0
\(306\) 0 0
\(307\) −8.75885e10 −0.562762 −0.281381 0.959596i \(-0.590792\pi\)
−0.281381 + 0.959596i \(0.590792\pi\)
\(308\) −3.06105e9 −0.0193817
\(309\) 6.82123e9 0.0425647
\(310\) −1.99563e9 −0.0122730
\(311\) 1.24191e10 0.0752780 0.0376390 0.999291i \(-0.488016\pi\)
0.0376390 + 0.999291i \(0.488016\pi\)
\(312\) 4.21610e10 0.251892
\(313\) 2.38814e9 0.0140640 0.00703201 0.999975i \(-0.497762\pi\)
0.00703201 + 0.999975i \(0.497762\pi\)
\(314\) −2.24412e10 −0.130275
\(315\) −5.51911e9 −0.0315843
\(316\) −3.10691e10 −0.175282
\(317\) 6.54695e10 0.364144 0.182072 0.983285i \(-0.441720\pi\)
0.182072 + 0.983285i \(0.441720\pi\)
\(318\) 3.01534e10 0.165354
\(319\) 2.18598e9 0.0118192
\(320\) 8.65912e8 0.00461635
\(321\) 2.35011e10 0.123542
\(322\) −1.50829e11 −0.781866
\(323\) 0 0
\(324\) −1.38713e11 −0.699301
\(325\) −2.87914e11 −1.43149
\(326\) 7.23659e10 0.354858
\(327\) −3.35819e9 −0.0162421
\(328\) 7.85508e10 0.374730
\(329\) −1.24936e11 −0.587906
\(330\) −8.74737e6 −4.06036e−5 0
\(331\) 2.74512e10 0.125700 0.0628501 0.998023i \(-0.479981\pi\)
0.0628501 + 0.998023i \(0.479981\pi\)
\(332\) 1.71865e11 0.776365
\(333\) 3.50844e11 1.56356
\(334\) 1.34501e11 0.591382
\(335\) 8.07223e9 0.0350181
\(336\) −4.24081e10 −0.181519
\(337\) −3.74823e11 −1.58304 −0.791519 0.611145i \(-0.790709\pi\)
−0.791519 + 0.611145i \(0.790709\pi\)
\(338\) −9.94546e10 −0.414476
\(339\) −8.29204e10 −0.341007
\(340\) 0 0
\(341\) 5.31843e9 0.0213004
\(342\) 6.37647e10 0.252036
\(343\) 6.64173e10 0.259094
\(344\) −1.44871e11 −0.557786
\(345\) 2.34413e9 0.00890833
\(346\) 1.82180e11 0.683375
\(347\) −9.76618e10 −0.361611 −0.180806 0.983519i \(-0.557871\pi\)
−0.180806 + 0.983519i \(0.557871\pi\)
\(348\) 3.87113e10 0.141492
\(349\) 2.22229e11 0.801839 0.400920 0.916113i \(-0.368691\pi\)
0.400920 + 0.916113i \(0.368691\pi\)
\(350\) −1.48645e11 −0.529472
\(351\) −1.91296e11 −0.672704
\(352\) 4.65543e9 0.0161629
\(353\) −1.85396e9 −0.00635500 −0.00317750 0.999995i \(-0.501011\pi\)
−0.00317750 + 0.999995i \(0.501011\pi\)
\(354\) −2.22607e10 −0.0753398
\(355\) 1.52777e9 0.00510541
\(356\) −1.14023e11 −0.376241
\(357\) 0 0
\(358\) 6.30605e10 0.202901
\(359\) −2.26386e11 −0.719323 −0.359662 0.933083i \(-0.617108\pi\)
−0.359662 + 0.933083i \(0.617108\pi\)
\(360\) 5.44310e9 0.0170799
\(361\) −1.73794e11 −0.538583
\(362\) −6.77301e10 −0.207297
\(363\) −7.99990e10 −0.241827
\(364\) 5.44782e11 1.62655
\(365\) −7.31561e9 −0.0215741
\(366\) −1.94770e8 −0.000567358 0
\(367\) 3.46886e11 0.998135 0.499067 0.866563i \(-0.333676\pi\)
0.499067 + 0.866563i \(0.333676\pi\)
\(368\) −2.89810e11 −0.823754
\(369\) −1.72833e11 −0.485296
\(370\) −5.88786e9 −0.0163324
\(371\) 8.50894e11 2.33181
\(372\) 9.41835e10 0.254995
\(373\) 2.60856e11 0.697768 0.348884 0.937166i \(-0.386561\pi\)
0.348884 + 0.937166i \(0.386561\pi\)
\(374\) 0 0
\(375\) 4.62182e9 0.0120690
\(376\) 1.23216e11 0.317922
\(377\) −3.89043e11 −0.991885
\(378\) −9.87626e10 −0.248817
\(379\) −8.02252e10 −0.199726 −0.0998629 0.995001i \(-0.531840\pi\)
−0.0998629 + 0.995001i \(0.531840\pi\)
\(380\) 5.81990e9 0.0143182
\(381\) 2.97791e10 0.0724017
\(382\) −2.96700e11 −0.712907
\(383\) −5.97457e10 −0.141877 −0.0709386 0.997481i \(-0.522599\pi\)
−0.0709386 + 0.997481i \(0.522599\pi\)
\(384\) 1.05115e11 0.246704
\(385\) −2.46840e8 −0.000572589 0
\(386\) −1.44670e11 −0.331692
\(387\) 3.18754e11 0.722364
\(388\) 1.29914e11 0.291013
\(389\) 3.76555e11 0.833786 0.416893 0.908956i \(-0.363119\pi\)
0.416893 + 0.908956i \(0.363119\pi\)
\(390\) 1.55679e9 0.00340752
\(391\) 0 0
\(392\) 2.74367e11 0.586874
\(393\) 4.90647e10 0.103754
\(394\) 3.11477e11 0.651168
\(395\) −2.50538e9 −0.00517829
\(396\) −6.64237e9 −0.0135736
\(397\) −6.14963e11 −1.24249 −0.621244 0.783618i \(-0.713372\pi\)
−0.621244 + 0.783618i \(0.713372\pi\)
\(398\) −2.60041e11 −0.519479
\(399\) −1.11832e11 −0.220897
\(400\) −2.85613e11 −0.557839
\(401\) −5.71865e9 −0.0110444 −0.00552222 0.999985i \(-0.501758\pi\)
−0.00552222 + 0.999985i \(0.501758\pi\)
\(402\) 7.00481e10 0.133776
\(403\) −9.46531e11 −1.78757
\(404\) −7.21173e11 −1.34686
\(405\) −1.11857e10 −0.0206592
\(406\) −2.00856e11 −0.366874
\(407\) 1.56914e10 0.0283456
\(408\) 0 0
\(409\) 6.18179e11 1.09234 0.546172 0.837673i \(-0.316085\pi\)
0.546172 + 0.837673i \(0.316085\pi\)
\(410\) 2.90048e9 0.00506923
\(411\) −7.57341e10 −0.130919
\(412\) −8.69264e10 −0.148633
\(413\) −6.28171e11 −1.06244
\(414\) −3.27292e11 −0.547563
\(415\) 1.38590e10 0.0229359
\(416\) −8.28537e11 −1.35641
\(417\) 2.69254e11 0.436063
\(418\) 2.85185e9 0.00456913
\(419\) 5.15438e11 0.816983 0.408492 0.912762i \(-0.366055\pi\)
0.408492 + 0.912762i \(0.366055\pi\)
\(420\) −4.37127e9 −0.00685466
\(421\) −1.89025e11 −0.293258 −0.146629 0.989192i \(-0.546842\pi\)
−0.146629 + 0.989192i \(0.546842\pi\)
\(422\) 3.30273e11 0.506952
\(423\) −2.71107e11 −0.411727
\(424\) −8.39175e11 −1.26097
\(425\) 0 0
\(426\) 1.32575e10 0.0195037
\(427\) −5.49618e9 −0.00800083
\(428\) −2.99487e11 −0.431401
\(429\) −4.14889e9 −0.00591391
\(430\) −5.34933e9 −0.00754555
\(431\) 1.00192e12 1.39858 0.699289 0.714840i \(-0.253500\pi\)
0.699289 + 0.714840i \(0.253500\pi\)
\(432\) −1.89767e11 −0.262147
\(433\) −6.95832e11 −0.951281 −0.475640 0.879640i \(-0.657784\pi\)
−0.475640 + 0.879640i \(0.657784\pi\)
\(434\) −4.88676e11 −0.661177
\(435\) 3.12164e9 0.00418004
\(436\) 4.27952e10 0.0567161
\(437\) −7.64244e11 −1.00246
\(438\) −6.34824e10 −0.0824176
\(439\) 8.70444e11 1.11854 0.559269 0.828987i \(-0.311082\pi\)
0.559269 + 0.828987i \(0.311082\pi\)
\(440\) 2.43441e8 0.000309639 0
\(441\) −6.03680e11 −0.760034
\(442\) 0 0
\(443\) −7.60593e11 −0.938286 −0.469143 0.883122i \(-0.655437\pi\)
−0.469143 + 0.883122i \(0.655437\pi\)
\(444\) 2.77877e11 0.339335
\(445\) −9.19466e9 −0.0111152
\(446\) −4.27783e11 −0.511937
\(447\) 9.19810e10 0.108972
\(448\) 2.12039e11 0.248693
\(449\) 5.88029e11 0.682795 0.341397 0.939919i \(-0.389100\pi\)
0.341397 + 0.939919i \(0.389100\pi\)
\(450\) −3.22553e11 −0.370805
\(451\) −7.72987e9 −0.00879788
\(452\) 1.05670e12 1.19077
\(453\) −7.56338e10 −0.0843867
\(454\) −9.89946e10 −0.109360
\(455\) 4.39307e10 0.0480526
\(456\) 1.10292e11 0.119455
\(457\) 7.74899e11 0.831041 0.415520 0.909584i \(-0.363599\pi\)
0.415520 + 0.909584i \(0.363599\pi\)
\(458\) −3.04727e11 −0.323606
\(459\) 0 0
\(460\) −2.98725e10 −0.0311072
\(461\) −1.26161e12 −1.30099 −0.650493 0.759512i \(-0.725438\pi\)
−0.650493 + 0.759512i \(0.725438\pi\)
\(462\) −2.14200e9 −0.00218741
\(463\) −1.80501e12 −1.82543 −0.912715 0.408596i \(-0.866018\pi\)
−0.912715 + 0.408596i \(0.866018\pi\)
\(464\) −3.85934e11 −0.386529
\(465\) 7.59486e9 0.00753323
\(466\) −7.15156e11 −0.702529
\(467\) 1.38727e12 1.34969 0.674846 0.737959i \(-0.264210\pi\)
0.674846 + 0.737959i \(0.264210\pi\)
\(468\) 1.18216e12 1.13912
\(469\) 1.97667e12 1.88650
\(470\) 4.54972e9 0.00430075
\(471\) 8.54055e10 0.0799635
\(472\) 6.19520e11 0.574535
\(473\) 1.42562e10 0.0130957
\(474\) −2.17408e10 −0.0197822
\(475\) −7.53178e11 −0.678854
\(476\) 0 0
\(477\) 1.84641e12 1.63303
\(478\) −4.18197e11 −0.366400
\(479\) 2.10470e11 0.182675 0.0913376 0.995820i \(-0.470886\pi\)
0.0913376 + 0.995820i \(0.470886\pi\)
\(480\) 6.64809e9 0.00571625
\(481\) −2.79262e12 −2.37881
\(482\) 2.12436e10 0.0179274
\(483\) 5.74015e11 0.479912
\(484\) 1.01947e12 0.844442
\(485\) 1.04761e10 0.00859731
\(486\) −3.24696e11 −0.264006
\(487\) 1.10325e12 0.888778 0.444389 0.895834i \(-0.353421\pi\)
0.444389 + 0.895834i \(0.353421\pi\)
\(488\) 5.42048e9 0.00432662
\(489\) −2.75406e11 −0.217813
\(490\) 1.01310e10 0.00793904
\(491\) 1.63476e12 1.26937 0.634684 0.772771i \(-0.281130\pi\)
0.634684 + 0.772771i \(0.281130\pi\)
\(492\) −1.36888e11 −0.105322
\(493\) 0 0
\(494\) −5.07550e11 −0.383449
\(495\) −5.35634e8 −0.000401000 0
\(496\) −9.38968e11 −0.696599
\(497\) 3.74111e11 0.275040
\(498\) 1.20264e11 0.0876200
\(499\) −4.41359e11 −0.318669 −0.159334 0.987225i \(-0.550935\pi\)
−0.159334 + 0.987225i \(0.550935\pi\)
\(500\) −5.88983e10 −0.0421442
\(501\) −5.11878e11 −0.362992
\(502\) 8.75932e11 0.615607
\(503\) 2.37298e11 0.165287 0.0826434 0.996579i \(-0.473664\pi\)
0.0826434 + 0.996579i \(0.473664\pi\)
\(504\) 1.33287e12 0.920133
\(505\) −5.81546e10 −0.0397899
\(506\) −1.46380e10 −0.00992671
\(507\) 3.78499e11 0.254407
\(508\) −3.79490e11 −0.252821
\(509\) 9.67033e10 0.0638574 0.0319287 0.999490i \(-0.489835\pi\)
0.0319287 + 0.999490i \(0.489835\pi\)
\(510\) 0 0
\(511\) −1.79140e12 −1.16225
\(512\) −1.45290e12 −0.934375
\(513\) −5.00427e11 −0.319016
\(514\) −8.63520e11 −0.545681
\(515\) −7.00966e9 −0.00439101
\(516\) 2.52461e11 0.156773
\(517\) −1.21252e10 −0.00746415
\(518\) −1.44178e12 −0.879863
\(519\) −6.93332e11 −0.419458
\(520\) −4.33256e10 −0.0259854
\(521\) −2.00394e12 −1.19156 −0.595779 0.803149i \(-0.703156\pi\)
−0.595779 + 0.803149i \(0.703156\pi\)
\(522\) −4.35849e11 −0.256932
\(523\) −2.38851e12 −1.39595 −0.697975 0.716122i \(-0.745916\pi\)
−0.697975 + 0.716122i \(0.745916\pi\)
\(524\) −6.25258e11 −0.362300
\(525\) 5.65704e11 0.324992
\(526\) −6.07109e11 −0.345805
\(527\) 0 0
\(528\) −4.11574e9 −0.00230460
\(529\) 2.12157e12 1.17790
\(530\) −3.09864e10 −0.0170581
\(531\) −1.36311e12 −0.744055
\(532\) 1.42514e12 0.771356
\(533\) 1.37570e12 0.738332
\(534\) −7.97882e10 −0.0424622
\(535\) −2.41503e10 −0.0127447
\(536\) −1.94945e12 −1.02017
\(537\) −2.39992e11 −0.124541
\(538\) 8.52147e11 0.438525
\(539\) −2.69994e10 −0.0137786
\(540\) −1.95605e10 −0.00989939
\(541\) −4.38039e10 −0.0219849 −0.0109925 0.999940i \(-0.503499\pi\)
−0.0109925 + 0.999940i \(0.503499\pi\)
\(542\) −1.23431e12 −0.614366
\(543\) 2.57764e11 0.127240
\(544\) 0 0
\(545\) 3.45096e9 0.00167554
\(546\) 3.81215e11 0.183571
\(547\) −1.45378e12 −0.694316 −0.347158 0.937807i \(-0.612853\pi\)
−0.347158 + 0.937807i \(0.612853\pi\)
\(548\) 9.65119e11 0.457160
\(549\) −1.19265e10 −0.00560321
\(550\) −1.44261e10 −0.00672228
\(551\) −1.01773e12 −0.470381
\(552\) −5.66110e11 −0.259522
\(553\) −6.13501e11 −0.278966
\(554\) −7.32426e11 −0.330346
\(555\) 2.24077e10 0.0100249
\(556\) −3.43124e12 −1.52270
\(557\) 2.18164e12 0.960363 0.480181 0.877169i \(-0.340571\pi\)
0.480181 + 0.877169i \(0.340571\pi\)
\(558\) −1.06041e12 −0.463041
\(559\) −2.53720e12 −1.09901
\(560\) 4.35796e10 0.0187257
\(561\) 0 0
\(562\) 1.51440e12 0.640362
\(563\) 5.13044e10 0.0215212 0.0107606 0.999942i \(-0.496575\pi\)
0.0107606 + 0.999942i \(0.496575\pi\)
\(564\) −2.14724e11 −0.0893560
\(565\) 8.52110e10 0.0351785
\(566\) 7.50107e11 0.307220
\(567\) −2.73907e12 −1.11296
\(568\) −3.68958e11 −0.148734
\(569\) −3.00090e12 −1.20018 −0.600090 0.799933i \(-0.704869\pi\)
−0.600090 + 0.799933i \(0.704869\pi\)
\(570\) 4.07252e9 0.00161595
\(571\) −1.84446e12 −0.726116 −0.363058 0.931767i \(-0.618267\pi\)
−0.363058 + 0.931767i \(0.618267\pi\)
\(572\) 5.28715e10 0.0206509
\(573\) 1.12917e12 0.437585
\(574\) 7.10249e11 0.273091
\(575\) 3.86592e12 1.47485
\(576\) 4.60116e11 0.174167
\(577\) 3.01920e12 1.13397 0.566984 0.823729i \(-0.308110\pi\)
0.566984 + 0.823729i \(0.308110\pi\)
\(578\) 0 0
\(579\) 5.50576e11 0.203593
\(580\) −3.97806e10 −0.0145964
\(581\) 3.39370e12 1.23561
\(582\) 9.09082e10 0.0328435
\(583\) 8.25799e10 0.0296051
\(584\) 1.76673e12 0.628509
\(585\) 9.53279e10 0.0336526
\(586\) 1.07495e12 0.376573
\(587\) 1.79991e12 0.625719 0.312860 0.949799i \(-0.398713\pi\)
0.312860 + 0.949799i \(0.398713\pi\)
\(588\) −4.78129e11 −0.164948
\(589\) −2.47611e12 −0.847716
\(590\) 2.28757e10 0.00777212
\(591\) −1.18540e12 −0.399689
\(592\) −2.77031e12 −0.927001
\(593\) 2.90587e12 0.965006 0.482503 0.875894i \(-0.339728\pi\)
0.482503 + 0.875894i \(0.339728\pi\)
\(594\) −9.58498e9 −0.00315902
\(595\) 0 0
\(596\) −1.17216e12 −0.380522
\(597\) 9.89650e11 0.318858
\(598\) 2.60516e12 0.833065
\(599\) 4.72811e12 1.50061 0.750303 0.661094i \(-0.229908\pi\)
0.750303 + 0.661094i \(0.229908\pi\)
\(600\) −5.57913e11 −0.175746
\(601\) −2.89176e12 −0.904121 −0.452061 0.891987i \(-0.649311\pi\)
−0.452061 + 0.891987i \(0.649311\pi\)
\(602\) −1.30991e12 −0.406496
\(603\) 4.28931e12 1.32117
\(604\) 9.63841e11 0.294672
\(605\) 8.22089e10 0.0249471
\(606\) −5.04646e11 −0.152006
\(607\) 6.45254e12 1.92922 0.964610 0.263680i \(-0.0849363\pi\)
0.964610 + 0.263680i \(0.0849363\pi\)
\(608\) −2.16744e12 −0.643250
\(609\) 7.64406e11 0.225188
\(610\) 2.00150e8 5.85291e−5 0
\(611\) 2.15794e12 0.626404
\(612\) 0 0
\(613\) 2.51234e12 0.718631 0.359316 0.933216i \(-0.383010\pi\)
0.359316 + 0.933216i \(0.383010\pi\)
\(614\) 7.81060e11 0.221782
\(615\) −1.10385e10 −0.00311151
\(616\) 5.96121e10 0.0166810
\(617\) 4.19165e12 1.16440 0.582199 0.813046i \(-0.302193\pi\)
0.582199 + 0.813046i \(0.302193\pi\)
\(618\) −6.08274e10 −0.0167746
\(619\) 5.81865e12 1.59299 0.796497 0.604642i \(-0.206684\pi\)
0.796497 + 0.604642i \(0.206684\pi\)
\(620\) −9.67853e10 −0.0263055
\(621\) 2.56860e12 0.693081
\(622\) −1.10746e11 −0.0296668
\(623\) −2.25153e12 −0.598799
\(624\) 7.32487e11 0.193406
\(625\) 3.80757e12 0.998132
\(626\) −2.12959e10 −0.00554258
\(627\) −1.08534e10 −0.00280455
\(628\) −1.08837e12 −0.279227
\(629\) 0 0
\(630\) 4.92160e10 0.0124473
\(631\) −3.40483e12 −0.854995 −0.427498 0.904017i \(-0.640605\pi\)
−0.427498 + 0.904017i \(0.640605\pi\)
\(632\) 6.05051e11 0.150857
\(633\) −1.25693e12 −0.311169
\(634\) −5.83817e11 −0.143508
\(635\) −3.06017e10 −0.00746902
\(636\) 1.46240e12 0.354412
\(637\) 4.80513e12 1.15632
\(638\) −1.94932e10 −0.00465790
\(639\) 8.11806e11 0.192619
\(640\) −1.08019e11 −0.0254502
\(641\) −1.37939e12 −0.322721 −0.161360 0.986896i \(-0.551588\pi\)
−0.161360 + 0.986896i \(0.551588\pi\)
\(642\) −2.09568e11 −0.0486875
\(643\) −6.11870e12 −1.41159 −0.705797 0.708414i \(-0.749411\pi\)
−0.705797 + 0.708414i \(0.749411\pi\)
\(644\) −7.31498e12 −1.67582
\(645\) 2.03582e10 0.00463149
\(646\) 0 0
\(647\) −3.49553e12 −0.784231 −0.392116 0.919916i \(-0.628257\pi\)
−0.392116 + 0.919916i \(0.628257\pi\)
\(648\) 2.70135e12 0.601857
\(649\) −6.09645e10 −0.0134889
\(650\) 2.56744e12 0.564144
\(651\) 1.85978e12 0.405832
\(652\) 3.50965e12 0.760588
\(653\) −5.24011e12 −1.12780 −0.563899 0.825844i \(-0.690699\pi\)
−0.563899 + 0.825844i \(0.690699\pi\)
\(654\) 2.99463e10 0.00640093
\(655\) −5.04201e10 −0.0107033
\(656\) 1.36471e12 0.287722
\(657\) −3.88727e12 −0.813954
\(658\) 1.11411e12 0.231691
\(659\) 6.99007e12 1.44377 0.721883 0.692015i \(-0.243277\pi\)
0.721883 + 0.692015i \(0.243277\pi\)
\(660\) −4.24235e8 −8.70280e−5 0
\(661\) 5.79186e11 0.118008 0.0590040 0.998258i \(-0.481208\pi\)
0.0590040 + 0.998258i \(0.481208\pi\)
\(662\) −2.44793e11 −0.0495380
\(663\) 0 0
\(664\) −3.34697e12 −0.668182
\(665\) 1.14922e11 0.0227879
\(666\) −3.12861e12 −0.616193
\(667\) 5.22382e12 1.02193
\(668\) 6.52313e12 1.26754
\(669\) 1.62803e12 0.314229
\(670\) −7.19831e10 −0.0138005
\(671\) −5.33408e8 −0.000101580 0
\(672\) 1.62794e12 0.307947
\(673\) −8.24877e12 −1.54996 −0.774982 0.631984i \(-0.782241\pi\)
−0.774982 + 0.631984i \(0.782241\pi\)
\(674\) 3.34244e12 0.623869
\(675\) 2.53141e12 0.469348
\(676\) −4.82341e12 −0.888370
\(677\) −3.10253e12 −0.567633 −0.283816 0.958879i \(-0.591601\pi\)
−0.283816 + 0.958879i \(0.591601\pi\)
\(678\) 7.39432e11 0.134389
\(679\) 2.56532e12 0.463157
\(680\) 0 0
\(681\) 3.76748e11 0.0671257
\(682\) −4.74264e10 −0.00839442
\(683\) 6.90971e12 1.21497 0.607486 0.794330i \(-0.292178\pi\)
0.607486 + 0.794330i \(0.292178\pi\)
\(684\) 3.09250e12 0.540203
\(685\) 7.78262e10 0.0135057
\(686\) −5.92269e11 −0.102108
\(687\) 1.15971e12 0.198630
\(688\) −2.51692e12 −0.428274
\(689\) −1.46969e13 −2.48450
\(690\) −2.09035e10 −0.00351074
\(691\) 6.42061e12 1.07133 0.535667 0.844429i \(-0.320060\pi\)
0.535667 + 0.844429i \(0.320060\pi\)
\(692\) 8.83549e12 1.46472
\(693\) −1.31162e11 −0.0216028
\(694\) 8.70887e11 0.142510
\(695\) −2.76692e11 −0.0449846
\(696\) −7.53878e11 −0.121775
\(697\) 0 0
\(698\) −1.98170e12 −0.316002
\(699\) 2.72170e12 0.431215
\(700\) −7.20906e12 −1.13485
\(701\) −1.11002e12 −0.173620 −0.0868102 0.996225i \(-0.527667\pi\)
−0.0868102 + 0.996225i \(0.527667\pi\)
\(702\) 1.70586e12 0.265110
\(703\) −7.30545e12 −1.12810
\(704\) 2.05785e10 0.00315745
\(705\) −1.73151e10 −0.00263982
\(706\) 1.65325e10 0.00250448
\(707\) −1.42405e13 −2.14357
\(708\) −1.07961e12 −0.161480
\(709\) 7.66189e12 1.13875 0.569374 0.822079i \(-0.307186\pi\)
0.569374 + 0.822079i \(0.307186\pi\)
\(710\) −1.36237e10 −0.00201202
\(711\) −1.33127e12 −0.195368
\(712\) 2.22052e12 0.323813
\(713\) 1.27094e13 1.84171
\(714\) 0 0
\(715\) 4.26350e9 0.000610084 0
\(716\) 3.05835e12 0.434889
\(717\) 1.59155e12 0.224898
\(718\) 2.01877e12 0.283483
\(719\) −8.97215e12 −1.25204 −0.626018 0.779809i \(-0.715316\pi\)
−0.626018 + 0.779809i \(0.715316\pi\)
\(720\) 9.45661e10 0.0131141
\(721\) −1.71648e12 −0.236554
\(722\) 1.54979e12 0.212253
\(723\) −8.08479e10 −0.0110039
\(724\) −3.28482e12 −0.444312
\(725\) 5.14818e12 0.692042
\(726\) 7.13381e11 0.0953031
\(727\) 8.45878e12 1.12306 0.561530 0.827456i \(-0.310213\pi\)
0.561530 + 0.827456i \(0.310213\pi\)
\(728\) −1.06093e13 −1.39989
\(729\) −5.07737e12 −0.665833
\(730\) 6.52361e10 0.00850227
\(731\) 0 0
\(732\) −9.44607e9 −0.00121605
\(733\) −2.56649e12 −0.328377 −0.164188 0.986429i \(-0.552501\pi\)
−0.164188 + 0.986429i \(0.552501\pi\)
\(734\) −3.09331e12 −0.393361
\(735\) −3.85558e10 −0.00487301
\(736\) 1.11250e13 1.39750
\(737\) 1.91838e11 0.0239514
\(738\) 1.54121e12 0.191253
\(739\) 9.87426e12 1.21788 0.608940 0.793216i \(-0.291595\pi\)
0.608940 + 0.793216i \(0.291595\pi\)
\(740\) −2.85553e11 −0.0350061
\(741\) 1.93161e12 0.235362
\(742\) −7.58774e12 −0.918957
\(743\) −8.12358e12 −0.977907 −0.488954 0.872310i \(-0.662621\pi\)
−0.488954 + 0.872310i \(0.662621\pi\)
\(744\) −1.83417e12 −0.219462
\(745\) −9.45219e10 −0.0112416
\(746\) −2.32615e12 −0.274988
\(747\) 7.36421e12 0.865333
\(748\) 0 0
\(749\) −5.91377e12 −0.686588
\(750\) −4.12145e10 −0.00475636
\(751\) 8.29551e11 0.0951619 0.0475810 0.998867i \(-0.484849\pi\)
0.0475810 + 0.998867i \(0.484849\pi\)
\(752\) 2.14070e12 0.244104
\(753\) −3.33357e12 −0.377862
\(754\) 3.46924e12 0.390898
\(755\) 7.77231e10 0.00870541
\(756\) −4.78985e12 −0.533303
\(757\) −3.65926e12 −0.405007 −0.202503 0.979282i \(-0.564908\pi\)
−0.202503 + 0.979282i \(0.564908\pi\)
\(758\) 7.15398e11 0.0787112
\(759\) 5.57086e10 0.00609305
\(760\) −1.13339e11 −0.0123231
\(761\) −2.33882e12 −0.252793 −0.126396 0.991980i \(-0.540341\pi\)
−0.126396 + 0.991980i \(0.540341\pi\)
\(762\) −2.65551e11 −0.0285332
\(763\) 8.45049e11 0.0902654
\(764\) −1.43896e13 −1.52801
\(765\) 0 0
\(766\) 5.32775e11 0.0559132
\(767\) 1.08500e13 1.13201
\(768\) −5.05924e11 −0.0524759
\(769\) 7.17500e12 0.739866 0.369933 0.929058i \(-0.379381\pi\)
0.369933 + 0.929058i \(0.379381\pi\)
\(770\) 2.20117e9 0.000225655 0
\(771\) 3.28634e12 0.334941
\(772\) −7.01628e12 −0.710933
\(773\) 1.41219e13 1.42261 0.711303 0.702886i \(-0.248106\pi\)
0.711303 + 0.702886i \(0.248106\pi\)
\(774\) −2.84245e12 −0.284681
\(775\) 1.25254e13 1.24719
\(776\) −2.52999e12 −0.250462
\(777\) 5.48705e12 0.540062
\(778\) −3.35788e12 −0.328592
\(779\) 3.59881e12 0.350139
\(780\) 7.55020e10 0.00730353
\(781\) 3.63077e10 0.00349196
\(782\) 0 0
\(783\) 3.42055e12 0.325214
\(784\) 4.76674e12 0.450608
\(785\) −8.77648e10 −0.00824910
\(786\) −4.37529e11 −0.0408889
\(787\) 5.29148e12 0.491689 0.245845 0.969309i \(-0.420935\pi\)
0.245845 + 0.969309i \(0.420935\pi\)
\(788\) 1.51062e13 1.39568
\(789\) 2.31050e12 0.212256
\(790\) 2.23414e10 0.00204075
\(791\) 2.08659e13 1.89515
\(792\) 1.29356e11 0.0116822
\(793\) 9.49317e10 0.00852475
\(794\) 5.48386e12 0.489659
\(795\) 1.17926e11 0.0104703
\(796\) −1.26116e13 −1.11343
\(797\) 1.06101e13 0.931444 0.465722 0.884931i \(-0.345795\pi\)
0.465722 + 0.884931i \(0.345795\pi\)
\(798\) 9.97252e11 0.0870547
\(799\) 0 0
\(800\) 1.09640e13 0.946374
\(801\) −4.88573e12 −0.419356
\(802\) 5.09954e10 0.00435257
\(803\) −1.73856e11 −0.0147561
\(804\) 3.39724e12 0.286730
\(805\) −5.89872e11 −0.0495081
\(806\) 8.44058e12 0.704473
\(807\) −3.24306e12 −0.269168
\(808\) 1.40444e13 1.15918
\(809\) 8.09411e11 0.0664356 0.0332178 0.999448i \(-0.489424\pi\)
0.0332178 + 0.999448i \(0.489424\pi\)
\(810\) 9.97468e10 0.00814172
\(811\) −3.97455e11 −0.0322622 −0.0161311 0.999870i \(-0.505135\pi\)
−0.0161311 + 0.999870i \(0.505135\pi\)
\(812\) −9.74122e12 −0.786341
\(813\) 4.69747e12 0.377100
\(814\) −1.39926e11 −0.0111709
\(815\) 2.83014e11 0.0224698
\(816\) 0 0
\(817\) −6.63726e12 −0.521182
\(818\) −5.51253e12 −0.430488
\(819\) 2.33433e13 1.81294
\(820\) 1.40669e11 0.0108652
\(821\) −1.51125e13 −1.16089 −0.580447 0.814298i \(-0.697122\pi\)
−0.580447 + 0.814298i \(0.697122\pi\)
\(822\) 6.75349e11 0.0515947
\(823\) −2.13194e13 −1.61986 −0.809928 0.586530i \(-0.800494\pi\)
−0.809928 + 0.586530i \(0.800494\pi\)
\(824\) 1.69284e12 0.127921
\(825\) 5.49020e10 0.00412615
\(826\) 5.60164e12 0.418702
\(827\) −9.73433e12 −0.723655 −0.361827 0.932245i \(-0.617847\pi\)
−0.361827 + 0.932245i \(0.617847\pi\)
\(828\) −1.58732e13 −1.17362
\(829\) 1.44405e13 1.06191 0.530954 0.847400i \(-0.321834\pi\)
0.530954 + 0.847400i \(0.321834\pi\)
\(830\) −1.23586e11 −0.00903896
\(831\) 2.78743e12 0.202768
\(832\) −3.66240e12 −0.264979
\(833\) 0 0
\(834\) −2.40104e12 −0.171851
\(835\) 5.26019e11 0.0374466
\(836\) 1.38311e11 0.00979327
\(837\) 8.32212e12 0.586097
\(838\) −4.59635e12 −0.321970
\(839\) −2.39510e13 −1.66877 −0.834383 0.551185i \(-0.814176\pi\)
−0.834383 + 0.551185i \(0.814176\pi\)
\(840\) 8.51278e10 0.00589949
\(841\) −7.55069e12 −0.520481
\(842\) 1.68561e12 0.115572
\(843\) −5.76340e12 −0.393057
\(844\) 1.60178e13 1.08658
\(845\) −3.88955e11 −0.0262448
\(846\) 2.41757e12 0.162260
\(847\) 2.01308e13 1.34396
\(848\) −1.45795e13 −0.968190
\(849\) −2.85472e12 −0.188573
\(850\) 0 0
\(851\) 3.74975e13 2.45087
\(852\) 6.42970e11 0.0418035
\(853\) 8.01694e12 0.518487 0.259244 0.965812i \(-0.416527\pi\)
0.259244 + 0.965812i \(0.416527\pi\)
\(854\) 4.90115e10 0.00315310
\(855\) 2.49376e11 0.0159590
\(856\) 5.83232e12 0.371287
\(857\) −4.38404e12 −0.277626 −0.138813 0.990319i \(-0.544329\pi\)
−0.138813 + 0.990319i \(0.544329\pi\)
\(858\) 3.69972e10 0.00233065
\(859\) −3.16658e13 −1.98436 −0.992181 0.124805i \(-0.960169\pi\)
−0.992181 + 0.124805i \(0.960169\pi\)
\(860\) −2.59435e11 −0.0161728
\(861\) −2.70303e12 −0.167624
\(862\) −8.93452e12 −0.551174
\(863\) −1.32337e13 −0.812141 −0.406071 0.913842i \(-0.633101\pi\)
−0.406071 + 0.913842i \(0.633101\pi\)
\(864\) 7.28468e12 0.444732
\(865\) 7.12485e11 0.0432716
\(866\) 6.20500e12 0.374896
\(867\) 0 0
\(868\) −2.37001e13 −1.41714
\(869\) −5.95407e10 −0.00354181
\(870\) −2.78368e10 −0.00164734
\(871\) −3.41417e13 −2.01004
\(872\) −8.33411e11 −0.0488129
\(873\) 5.56665e12 0.324362
\(874\) 6.81505e12 0.395064
\(875\) −1.16303e12 −0.0670738
\(876\) −3.07881e12 −0.176650
\(877\) −6.75147e12 −0.385390 −0.192695 0.981259i \(-0.561723\pi\)
−0.192695 + 0.981259i \(0.561723\pi\)
\(878\) −7.76208e12 −0.440811
\(879\) −4.09099e12 −0.231142
\(880\) 4.22943e9 0.000237744 0
\(881\) 2.18093e13 1.21969 0.609846 0.792520i \(-0.291231\pi\)
0.609846 + 0.792520i \(0.291231\pi\)
\(882\) 5.38324e12 0.299527
\(883\) 5.52011e12 0.305580 0.152790 0.988259i \(-0.451174\pi\)
0.152790 + 0.988259i \(0.451174\pi\)
\(884\) 0 0
\(885\) −8.70590e10 −0.00477055
\(886\) 6.78249e12 0.369775
\(887\) −2.50221e13 −1.35727 −0.678636 0.734475i \(-0.737429\pi\)
−0.678636 + 0.734475i \(0.737429\pi\)
\(888\) −5.41148e12 −0.292050
\(889\) −7.49354e12 −0.402373
\(890\) 8.19923e10 0.00438044
\(891\) −2.65829e11 −0.0141303
\(892\) −2.07469e13 −1.09726
\(893\) 5.64513e12 0.297059
\(894\) −8.20229e11 −0.0429454
\(895\) 2.46622e11 0.0128478
\(896\) −2.64510e13 −1.37106
\(897\) −9.91458e12 −0.511338
\(898\) −5.24368e12 −0.269087
\(899\) 1.69249e13 0.864185
\(900\) −1.56434e13 −0.794767
\(901\) 0 0
\(902\) 6.89302e10 0.00346721
\(903\) 4.98518e12 0.249509
\(904\) −2.05785e13 −1.02484
\(905\) −2.64884e11 −0.0131262
\(906\) 6.74455e11 0.0332565
\(907\) 1.30935e13 0.642427 0.321214 0.947007i \(-0.395909\pi\)
0.321214 + 0.947007i \(0.395909\pi\)
\(908\) −4.80110e12 −0.234398
\(909\) −3.09014e13 −1.50121
\(910\) −3.91746e11 −0.0189373
\(911\) 2.89525e13 1.39269 0.696343 0.717709i \(-0.254809\pi\)
0.696343 + 0.717709i \(0.254809\pi\)
\(912\) 1.91617e12 0.0917186
\(913\) 3.29362e11 0.0156875
\(914\) −6.91007e12 −0.327510
\(915\) −7.61721e8 −3.59254e−5 0
\(916\) −1.47788e13 −0.693602
\(917\) −1.23465e13 −0.576612
\(918\) 0 0
\(919\) 1.28385e13 0.593738 0.296869 0.954918i \(-0.404057\pi\)
0.296869 + 0.954918i \(0.404057\pi\)
\(920\) 5.81748e11 0.0267726
\(921\) −2.97252e12 −0.136131
\(922\) 1.12503e13 0.512714
\(923\) −6.46176e12 −0.293051
\(924\) −1.03884e11 −0.00468839
\(925\) 3.69546e13 1.65970
\(926\) 1.60960e13 0.719395
\(927\) −3.72469e12 −0.165665
\(928\) 1.48150e13 0.655747
\(929\) 3.18274e13 1.40194 0.700972 0.713189i \(-0.252750\pi\)
0.700972 + 0.713189i \(0.252750\pi\)
\(930\) −6.77262e10 −0.00296882
\(931\) 1.25701e13 0.548361
\(932\) −3.46841e13 −1.50577
\(933\) 4.21470e11 0.0182095
\(934\) −1.23708e13 −0.531908
\(935\) 0 0
\(936\) −2.30218e13 −0.980386
\(937\) −4.48583e13 −1.90114 −0.950570 0.310509i \(-0.899501\pi\)
−0.950570 + 0.310509i \(0.899501\pi\)
\(938\) −1.76268e13 −0.743463
\(939\) 8.10468e10 0.00340205
\(940\) 2.20655e11 0.00921804
\(941\) −4.15108e13 −1.72587 −0.862934 0.505317i \(-0.831376\pi\)
−0.862934 + 0.505317i \(0.831376\pi\)
\(942\) −7.61593e11 −0.0315133
\(943\) −1.84720e13 −0.760697
\(944\) 1.07633e13 0.441134
\(945\) −3.86248e11 −0.0157552
\(946\) −1.27128e11 −0.00516095
\(947\) −3.14548e12 −0.127090 −0.0635451 0.997979i \(-0.520241\pi\)
−0.0635451 + 0.997979i \(0.520241\pi\)
\(948\) −1.05440e12 −0.0424002
\(949\) 3.09416e13 1.23835
\(950\) 6.71637e12 0.267534
\(951\) 2.22186e12 0.0880854
\(952\) 0 0
\(953\) −7.48692e12 −0.294026 −0.147013 0.989135i \(-0.546966\pi\)
−0.147013 + 0.989135i \(0.546966\pi\)
\(954\) −1.64651e13 −0.643572
\(955\) −1.16036e12 −0.0451416
\(956\) −2.02820e13 −0.785326
\(957\) 7.41861e10 0.00285903
\(958\) −1.87684e12 −0.0719916
\(959\) 1.90576e13 0.727585
\(960\) 2.93867e10 0.00111668
\(961\) 1.47381e13 0.557427
\(962\) 2.49029e13 0.937479
\(963\) −1.28327e13 −0.480837
\(964\) 1.03029e12 0.0384248
\(965\) −5.65786e11 −0.0210029
\(966\) −5.11871e12 −0.189131
\(967\) 2.43528e13 0.895633 0.447817 0.894125i \(-0.352202\pi\)
0.447817 + 0.894125i \(0.352202\pi\)
\(968\) −1.98535e13 −0.726773
\(969\) 0 0
\(970\) −9.34195e10 −0.00338817
\(971\) −1.44805e12 −0.0522753 −0.0261376 0.999658i \(-0.508321\pi\)
−0.0261376 + 0.999658i \(0.508321\pi\)
\(972\) −1.57473e13 −0.565859
\(973\) −6.77544e13 −2.42343
\(974\) −9.83809e12 −0.350264
\(975\) −9.77102e12 −0.346273
\(976\) 9.41731e10 0.00332202
\(977\) 2.93210e13 1.02956 0.514782 0.857321i \(-0.327873\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(978\) 2.45590e12 0.0858393
\(979\) −2.18512e11 −0.00760246
\(980\) 4.91337e11 0.0170162
\(981\) 1.83372e12 0.0632155
\(982\) −1.45778e13 −0.500253
\(983\) 3.94450e13 1.34741 0.673706 0.738999i \(-0.264701\pi\)
0.673706 + 0.738999i \(0.264701\pi\)
\(984\) 2.66580e12 0.0906462
\(985\) 1.21815e12 0.0412323
\(986\) 0 0
\(987\) −4.24000e12 −0.142213
\(988\) −2.46155e13 −0.821867
\(989\) 3.40678e13 1.13230
\(990\) 4.77645e9 0.000158033 0
\(991\) −5.47857e13 −1.80441 −0.902207 0.431304i \(-0.858054\pi\)
−0.902207 + 0.431304i \(0.858054\pi\)
\(992\) 3.60446e13 1.18178
\(993\) 9.31620e11 0.0304066
\(994\) −3.33608e12 −0.108392
\(995\) −1.01699e12 −0.0328936
\(996\) 5.83263e12 0.187801
\(997\) 4.35512e12 0.139596 0.0697979 0.997561i \(-0.477765\pi\)
0.0697979 + 0.997561i \(0.477765\pi\)
\(998\) 3.93577e12 0.125586
\(999\) 2.45534e13 0.779950
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.i.1.20 52
17.10 odd 16 17.10.d.a.15.9 yes 52
17.12 odd 16 17.10.d.a.8.9 52
17.16 even 2 inner 289.10.a.i.1.19 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.d.a.8.9 52 17.12 odd 16
17.10.d.a.15.9 yes 52 17.10 odd 16
289.10.a.i.1.19 52 17.16 even 2 inner
289.10.a.i.1.20 52 1.1 even 1 trivial