Properties

Label 43.10.a.a.1.11
Level 43
Weight 10
Character 43.1
Self dual yes
Analytic conductor 22.147
Analytic rank 1
Dimension 15
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 43.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(22.1465409550\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: multiple of \( 2^{10}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(-22.4329\) of \(x^{15} - 2 x^{14} - 5425 x^{13} + 14888 x^{12} + 11288030 x^{11} - 37600244 x^{10} - 11474166224 x^{9} + 47465836576 x^{8} + 5986976782464 x^{7} - 32493903147264 x^{6} - 1516975415483904 x^{5} + 10892588268404224 x^{4} + 139803541742443008 x^{3} - 1349125586394823680 x^{2} + 2103623681144094720 x + 529838441422848000\)
Character \(\chi\) \(=\) 43.1

$q$-expansion

\(f(q)\) \(=\) \(q+20.4329 q^{2} +231.971 q^{3} -94.4979 q^{4} -2583.58 q^{5} +4739.83 q^{6} -1769.99 q^{7} -12392.5 q^{8} +34127.5 q^{9} +O(q^{10})\) \(q+20.4329 q^{2} +231.971 q^{3} -94.4979 q^{4} -2583.58 q^{5} +4739.83 q^{6} -1769.99 q^{7} -12392.5 q^{8} +34127.5 q^{9} -52790.0 q^{10} -74570.0 q^{11} -21920.8 q^{12} +7100.10 q^{13} -36165.9 q^{14} -599316. q^{15} -204831. q^{16} -268650. q^{17} +697323. q^{18} +572153. q^{19} +244143. q^{20} -410586. q^{21} -1.52368e6 q^{22} +1.28932e6 q^{23} -2.87470e6 q^{24} +4.72177e6 q^{25} +145075. q^{26} +3.35071e6 q^{27} +167260. q^{28} -6.39915e6 q^{29} -1.22457e7 q^{30} -2.00450e6 q^{31} +2.15967e6 q^{32} -1.72981e7 q^{33} -5.48930e6 q^{34} +4.57291e6 q^{35} -3.22498e6 q^{36} +1.49299e7 q^{37} +1.16907e7 q^{38} +1.64702e6 q^{39} +3.20170e7 q^{40} -1.77326e7 q^{41} -8.38945e6 q^{42} -3.41880e6 q^{43} +7.04671e6 q^{44} -8.81712e7 q^{45} +2.63445e7 q^{46} +1.13138e7 q^{47} -4.75149e7 q^{48} -3.72207e7 q^{49} +9.64794e7 q^{50} -6.23191e7 q^{51} -670945. q^{52} -1.02987e8 q^{53} +6.84645e7 q^{54} +1.92658e8 q^{55} +2.19346e7 q^{56} +1.32723e8 q^{57} -1.30753e8 q^{58} -8.07005e7 q^{59} +5.66341e7 q^{60} +6.21644e7 q^{61} -4.09577e7 q^{62} -6.04053e7 q^{63} +1.49002e8 q^{64} -1.83437e7 q^{65} -3.53449e8 q^{66} +1.55110e8 q^{67} +2.53869e7 q^{68} +2.99084e8 q^{69} +9.34377e7 q^{70} -1.87869e8 q^{71} -4.22925e8 q^{72} +4.82049e7 q^{73} +3.05060e8 q^{74} +1.09531e9 q^{75} -5.40673e7 q^{76} +1.31988e8 q^{77} +3.36533e7 q^{78} -4.54354e8 q^{79} +5.29198e8 q^{80} +1.05534e8 q^{81} -3.62328e8 q^{82} +1.00047e8 q^{83} +3.87995e7 q^{84} +6.94081e8 q^{85} -6.98559e7 q^{86} -1.48442e9 q^{87} +9.24108e8 q^{88} +1.13769e9 q^{89} -1.80159e9 q^{90} -1.25671e7 q^{91} -1.21838e8 q^{92} -4.64985e8 q^{93} +2.31174e8 q^{94} -1.47821e9 q^{95} +5.00980e8 q^{96} -2.37271e8 q^{97} -7.60527e8 q^{98} -2.54489e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 32q^{2} - 317q^{3} + 3242q^{4} - 4717q^{5} + 687q^{6} - 9680q^{7} - 20394q^{8} + 69516q^{9} + O(q^{10}) \) \( 15q - 32q^{2} - 317q^{3} + 3242q^{4} - 4717q^{5} + 687q^{6} - 9680q^{7} - 20394q^{8} + 69516q^{9} - 36237q^{10} - 104484q^{11} - 266395q^{12} - 116174q^{13} + 416064q^{14} + 415388q^{15} + 996762q^{16} - 884265q^{17} - 588735q^{18} - 689535q^{19} - 3077879q^{20} - 2070198q^{21} - 7276218q^{22} - 2504077q^{23} - 11534895q^{24} + 1315350q^{25} - 13343414q^{26} - 12546986q^{27} - 28059568q^{28} - 18406221q^{29} - 39503820q^{30} - 12033699q^{31} - 18952630q^{32} - 14197716q^{33} - 30383125q^{34} - 27855546q^{35} - 18372959q^{36} - 8722847q^{37} - 63941843q^{38} - 30955510q^{39} - 39665611q^{40} - 18689389q^{41} - 73185310q^{42} - 51282015q^{43} - 68723220q^{44} - 216992888q^{45} - 2067521q^{46} - 104960741q^{47} - 145362479q^{48} + 92663095q^{49} - 42446347q^{50} + 37433407q^{51} + 149226080q^{52} - 215907800q^{53} + 419158122q^{54} + 384379852q^{55} + 430441344q^{56} + 258744488q^{57} + 295963139q^{58} + 185924544q^{59} + 973236172q^{60} + 247538102q^{61} + 139798853q^{62} + 405429926q^{63} + 848556290q^{64} + 94294394q^{65} + 667230492q^{66} + 467904656q^{67} - 88234341q^{68} + 163914994q^{69} + 647526126q^{70} - 8252944q^{71} + 889796745q^{72} - 715627902q^{73} + 725122989q^{74} - 18301762q^{75} + 346300359q^{76} - 1236779964q^{77} + 2058642146q^{78} + 560681783q^{79} - 1157214179q^{80} - 752010645q^{81} + 941346367q^{82} - 1442854698q^{83} + 1895248718q^{84} + 699302088q^{85} + 109401632q^{86} - 2094576907q^{87} - 1464507256q^{88} - 396710008q^{89} + 1411356270q^{90} - 3278076852q^{91} + 155864647q^{92} - 1424759183q^{93} + 4666638949q^{94} - 3854114395q^{95} - 952489551q^{96} - 3063837815q^{97} - 6161086984q^{98} - 6576160348q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 20.4329 0.903014 0.451507 0.892268i \(-0.350887\pi\)
0.451507 + 0.892268i \(0.350887\pi\)
\(3\) 231.971 1.65344 0.826719 0.562615i \(-0.190205\pi\)
0.826719 + 0.562615i \(0.190205\pi\)
\(4\) −94.4979 −0.184566
\(5\) −2583.58 −1.84866 −0.924331 0.381592i \(-0.875376\pi\)
−0.924331 + 0.381592i \(0.875376\pi\)
\(6\) 4739.83 1.49308
\(7\) −1769.99 −0.278631 −0.139315 0.990248i \(-0.544490\pi\)
−0.139315 + 0.990248i \(0.544490\pi\)
\(8\) −12392.5 −1.06968
\(9\) 34127.5 1.73386
\(10\) −52790.0 −1.66937
\(11\) −74570.0 −1.53567 −0.767833 0.640650i \(-0.778665\pi\)
−0.767833 + 0.640650i \(0.778665\pi\)
\(12\) −21920.8 −0.305169
\(13\) 7100.10 0.0689476 0.0344738 0.999406i \(-0.489024\pi\)
0.0344738 + 0.999406i \(0.489024\pi\)
\(14\) −36165.9 −0.251608
\(15\) −599316. −3.05665
\(16\) −204831. −0.781369
\(17\) −268650. −0.780131 −0.390065 0.920787i \(-0.627548\pi\)
−0.390065 + 0.920787i \(0.627548\pi\)
\(18\) 697323. 1.56570
\(19\) 572153. 1.00721 0.503606 0.863933i \(-0.332006\pi\)
0.503606 + 0.863933i \(0.332006\pi\)
\(20\) 244143. 0.341201
\(21\) −410586. −0.460699
\(22\) −1.52368e6 −1.38673
\(23\) 1.28932e6 0.960694 0.480347 0.877079i \(-0.340511\pi\)
0.480347 + 0.877079i \(0.340511\pi\)
\(24\) −2.87470e6 −1.76865
\(25\) 4.72177e6 2.41755
\(26\) 145075. 0.0622606
\(27\) 3.35071e6 1.21339
\(28\) 167260. 0.0514259
\(29\) −6.39915e6 −1.68009 −0.840043 0.542520i \(-0.817470\pi\)
−0.840043 + 0.542520i \(0.817470\pi\)
\(30\) −1.22457e7 −2.76019
\(31\) −2.00450e6 −0.389833 −0.194916 0.980820i \(-0.562444\pi\)
−0.194916 + 0.980820i \(0.562444\pi\)
\(32\) 2.15967e6 0.364093
\(33\) −1.72981e7 −2.53913
\(34\) −5.48930e6 −0.704469
\(35\) 4.57291e6 0.515094
\(36\) −3.22498e6 −0.320012
\(37\) 1.49299e7 1.30963 0.654815 0.755789i \(-0.272746\pi\)
0.654815 + 0.755789i \(0.272746\pi\)
\(38\) 1.16907e7 0.909527
\(39\) 1.64702e6 0.114001
\(40\) 3.20170e7 1.97748
\(41\) −1.77326e7 −0.980042 −0.490021 0.871711i \(-0.663011\pi\)
−0.490021 + 0.871711i \(0.663011\pi\)
\(42\) −8.38945e6 −0.416017
\(43\) −3.41880e6 −0.152499
\(44\) 7.04671e6 0.283432
\(45\) −8.81712e7 −3.20531
\(46\) 2.63445e7 0.867520
\(47\) 1.13138e7 0.338196 0.169098 0.985599i \(-0.445914\pi\)
0.169098 + 0.985599i \(0.445914\pi\)
\(48\) −4.75149e7 −1.29195
\(49\) −3.72207e7 −0.922365
\(50\) 9.64794e7 2.18308
\(51\) −6.23191e7 −1.28990
\(52\) −670945. −0.0127254
\(53\) −1.02987e8 −1.79283 −0.896417 0.443211i \(-0.853839\pi\)
−0.896417 + 0.443211i \(0.853839\pi\)
\(54\) 6.84645e7 1.09570
\(55\) 1.92658e8 2.83893
\(56\) 2.19346e7 0.298046
\(57\) 1.32723e8 1.66536
\(58\) −1.30753e8 −1.51714
\(59\) −8.07005e7 −0.867046 −0.433523 0.901143i \(-0.642730\pi\)
−0.433523 + 0.901143i \(0.642730\pi\)
\(60\) 5.66341e7 0.564154
\(61\) 6.21644e7 0.574854 0.287427 0.957803i \(-0.407200\pi\)
0.287427 + 0.957803i \(0.407200\pi\)
\(62\) −4.09577e7 −0.352024
\(63\) −6.04053e7 −0.483106
\(64\) 1.49002e8 1.11015
\(65\) −1.83437e7 −0.127461
\(66\) −3.53449e8 −2.29287
\(67\) 1.55110e8 0.940381 0.470191 0.882565i \(-0.344185\pi\)
0.470191 + 0.882565i \(0.344185\pi\)
\(68\) 2.53869e7 0.143986
\(69\) 2.99084e8 1.58845
\(70\) 9.34377e7 0.465137
\(71\) −1.87869e8 −0.877390 −0.438695 0.898636i \(-0.644559\pi\)
−0.438695 + 0.898636i \(0.644559\pi\)
\(72\) −4.22925e8 −1.85467
\(73\) 4.82049e7 0.198673 0.0993363 0.995054i \(-0.468328\pi\)
0.0993363 + 0.995054i \(0.468328\pi\)
\(74\) 3.05060e8 1.18261
\(75\) 1.09531e9 3.99727
\(76\) −5.40673e7 −0.185898
\(77\) 1.31988e8 0.427884
\(78\) 3.36533e7 0.102944
\(79\) −4.54354e8 −1.31242 −0.656210 0.754579i \(-0.727841\pi\)
−0.656210 + 0.754579i \(0.727841\pi\)
\(80\) 5.29198e8 1.44449
\(81\) 1.05534e8 0.272403
\(82\) −3.62328e8 −0.884991
\(83\) 1.00047e8 0.231394 0.115697 0.993285i \(-0.463090\pi\)
0.115697 + 0.993285i \(0.463090\pi\)
\(84\) 3.87995e7 0.0850295
\(85\) 6.94081e8 1.44220
\(86\) −6.98559e7 −0.137708
\(87\) −1.48442e9 −2.77792
\(88\) 9.24108e8 1.64267
\(89\) 1.13769e9 1.92207 0.961034 0.276431i \(-0.0891518\pi\)
0.961034 + 0.276431i \(0.0891518\pi\)
\(90\) −1.80159e9 −2.89444
\(91\) −1.25671e7 −0.0192109
\(92\) −1.21838e8 −0.177312
\(93\) −4.64985e8 −0.644564
\(94\) 2.31174e8 0.305396
\(95\) −1.47821e9 −1.86200
\(96\) 5.00980e8 0.602005
\(97\) −2.37271e8 −0.272127 −0.136064 0.990700i \(-0.543445\pi\)
−0.136064 + 0.990700i \(0.543445\pi\)
\(98\) −7.60527e8 −0.832908
\(99\) −2.54489e9 −2.66263
\(100\) −4.46198e8 −0.446198
\(101\) −7.88795e8 −0.754254 −0.377127 0.926162i \(-0.623088\pi\)
−0.377127 + 0.926162i \(0.623088\pi\)
\(102\) −1.27336e9 −1.16480
\(103\) −1.40500e9 −1.23001 −0.615004 0.788524i \(-0.710845\pi\)
−0.615004 + 0.788524i \(0.710845\pi\)
\(104\) −8.79879e7 −0.0737518
\(105\) 1.06078e9 0.851676
\(106\) −2.10432e9 −1.61895
\(107\) 1.23319e9 0.909499 0.454749 0.890619i \(-0.349729\pi\)
0.454749 + 0.890619i \(0.349729\pi\)
\(108\) −3.16635e8 −0.223950
\(109\) 5.28937e8 0.358909 0.179455 0.983766i \(-0.442567\pi\)
0.179455 + 0.983766i \(0.442567\pi\)
\(110\) 3.93655e9 2.56359
\(111\) 3.46330e9 2.16539
\(112\) 3.62549e8 0.217714
\(113\) 6.54283e8 0.377496 0.188748 0.982026i \(-0.439557\pi\)
0.188748 + 0.982026i \(0.439557\pi\)
\(114\) 2.71191e9 1.50385
\(115\) −3.33106e9 −1.77600
\(116\) 6.04706e8 0.310087
\(117\) 2.42309e8 0.119545
\(118\) −1.64894e9 −0.782954
\(119\) 4.75508e8 0.217369
\(120\) 7.42702e9 3.26963
\(121\) 3.20273e9 1.35827
\(122\) 1.27020e9 0.519101
\(123\) −4.11344e9 −1.62044
\(124\) 1.89421e8 0.0719500
\(125\) −7.15304e9 −2.62057
\(126\) −1.23425e9 −0.436251
\(127\) −3.42183e9 −1.16719 −0.583595 0.812045i \(-0.698354\pi\)
−0.583595 + 0.812045i \(0.698354\pi\)
\(128\) 1.93878e9 0.638388
\(129\) −7.93062e8 −0.252147
\(130\) −3.74814e8 −0.115099
\(131\) 2.65085e9 0.786439 0.393220 0.919445i \(-0.371361\pi\)
0.393220 + 0.919445i \(0.371361\pi\)
\(132\) 1.63463e9 0.468638
\(133\) −1.01270e9 −0.280641
\(134\) 3.16935e9 0.849177
\(135\) −8.65682e9 −2.24314
\(136\) 3.32925e9 0.834490
\(137\) −9.18404e7 −0.0222736 −0.0111368 0.999938i \(-0.503545\pi\)
−0.0111368 + 0.999938i \(0.503545\pi\)
\(138\) 6.11115e9 1.43439
\(139\) 7.61102e7 0.0172932 0.00864662 0.999963i \(-0.497248\pi\)
0.00864662 + 0.999963i \(0.497248\pi\)
\(140\) −4.32131e8 −0.0950690
\(141\) 2.62448e9 0.559187
\(142\) −3.83870e9 −0.792295
\(143\) −5.29454e8 −0.105881
\(144\) −6.99038e9 −1.35478
\(145\) 1.65327e10 3.10591
\(146\) 9.84964e8 0.179404
\(147\) −8.63413e9 −1.52507
\(148\) −1.41084e9 −0.241714
\(149\) 4.91840e9 0.817495 0.408748 0.912647i \(-0.365966\pi\)
0.408748 + 0.912647i \(0.365966\pi\)
\(150\) 2.23804e10 3.60959
\(151\) −6.55107e9 −1.02545 −0.512727 0.858552i \(-0.671365\pi\)
−0.512727 + 0.858552i \(0.671365\pi\)
\(152\) −7.09041e9 −1.07739
\(153\) −9.16837e9 −1.35264
\(154\) 2.69689e9 0.386385
\(155\) 5.17879e9 0.720668
\(156\) −1.55640e8 −0.0210407
\(157\) −2.66784e9 −0.350438 −0.175219 0.984530i \(-0.556063\pi\)
−0.175219 + 0.984530i \(0.556063\pi\)
\(158\) −9.28376e9 −1.18513
\(159\) −2.38899e10 −2.96434
\(160\) −5.57968e9 −0.673084
\(161\) −2.28208e9 −0.267679
\(162\) 2.15637e9 0.245983
\(163\) −9.83535e8 −0.109130 −0.0545652 0.998510i \(-0.517377\pi\)
−0.0545652 + 0.998510i \(0.517377\pi\)
\(164\) 1.67569e9 0.180883
\(165\) 4.46910e10 4.69399
\(166\) 2.04425e9 0.208952
\(167\) 9.80315e9 0.975307 0.487654 0.873037i \(-0.337853\pi\)
0.487654 + 0.873037i \(0.337853\pi\)
\(168\) 5.08818e9 0.492800
\(169\) −1.05541e10 −0.995246
\(170\) 1.41821e10 1.30232
\(171\) 1.95262e10 1.74636
\(172\) 3.23070e8 0.0281461
\(173\) −3.11130e9 −0.264079 −0.132040 0.991244i \(-0.542153\pi\)
−0.132040 + 0.991244i \(0.542153\pi\)
\(174\) −3.03309e10 −2.50850
\(175\) −8.35749e9 −0.673604
\(176\) 1.52743e10 1.19992
\(177\) −1.87202e10 −1.43361
\(178\) 2.32463e10 1.73565
\(179\) −1.52460e10 −1.10999 −0.554993 0.831855i \(-0.687279\pi\)
−0.554993 + 0.831855i \(0.687279\pi\)
\(180\) 8.33200e9 0.591593
\(181\) −2.42388e10 −1.67864 −0.839319 0.543640i \(-0.817046\pi\)
−0.839319 + 0.543640i \(0.817046\pi\)
\(182\) −2.56782e8 −0.0173477
\(183\) 1.44203e10 0.950485
\(184\) −1.59779e10 −1.02763
\(185\) −3.85726e10 −2.42106
\(186\) −9.50098e9 −0.582050
\(187\) 2.00333e10 1.19802
\(188\) −1.06913e9 −0.0624197
\(189\) −5.93071e9 −0.338087
\(190\) −3.02040e10 −1.68141
\(191\) 8.62554e9 0.468960 0.234480 0.972121i \(-0.424661\pi\)
0.234480 + 0.972121i \(0.424661\pi\)
\(192\) 3.45641e10 1.83556
\(193\) 3.46237e10 1.79624 0.898122 0.439747i \(-0.144932\pi\)
0.898122 + 0.439747i \(0.144932\pi\)
\(194\) −4.84813e9 −0.245735
\(195\) −4.25520e9 −0.210748
\(196\) 3.51728e9 0.170237
\(197\) −2.05360e10 −0.971444 −0.485722 0.874113i \(-0.661443\pi\)
−0.485722 + 0.874113i \(0.661443\pi\)
\(198\) −5.19993e10 −2.40439
\(199\) −1.56130e10 −0.705745 −0.352873 0.935671i \(-0.614795\pi\)
−0.352873 + 0.935671i \(0.614795\pi\)
\(200\) −5.85146e10 −2.58600
\(201\) 3.59811e10 1.55486
\(202\) −1.61173e10 −0.681102
\(203\) 1.13264e10 0.468124
\(204\) 5.88903e9 0.238072
\(205\) 4.58136e10 1.81177
\(206\) −2.87081e10 −1.11071
\(207\) 4.40012e10 1.66571
\(208\) −1.45432e9 −0.0538735
\(209\) −4.26655e10 −1.54674
\(210\) 2.16748e10 0.769075
\(211\) −3.30552e10 −1.14807 −0.574036 0.818830i \(-0.694623\pi\)
−0.574036 + 0.818830i \(0.694623\pi\)
\(212\) 9.73204e9 0.330897
\(213\) −4.35801e10 −1.45071
\(214\) 2.51976e10 0.821290
\(215\) 8.83276e9 0.281918
\(216\) −4.15236e10 −1.29794
\(217\) 3.54794e9 0.108619
\(218\) 1.08077e10 0.324100
\(219\) 1.11821e10 0.328493
\(220\) −1.82058e10 −0.523970
\(221\) −1.90744e9 −0.0537882
\(222\) 7.07652e10 1.95538
\(223\) 2.45049e10 0.663560 0.331780 0.943357i \(-0.392351\pi\)
0.331780 + 0.943357i \(0.392351\pi\)
\(224\) −3.82259e9 −0.101447
\(225\) 1.61142e11 4.19168
\(226\) 1.33689e10 0.340884
\(227\) −2.42024e10 −0.604981 −0.302490 0.953152i \(-0.597818\pi\)
−0.302490 + 0.953152i \(0.597818\pi\)
\(228\) −1.25420e10 −0.307370
\(229\) −3.44206e10 −0.827102 −0.413551 0.910481i \(-0.635712\pi\)
−0.413551 + 0.910481i \(0.635712\pi\)
\(230\) −6.80631e10 −1.60375
\(231\) 3.06174e10 0.707480
\(232\) 7.93014e10 1.79715
\(233\) 4.12963e10 0.917929 0.458964 0.888455i \(-0.348221\pi\)
0.458964 + 0.888455i \(0.348221\pi\)
\(234\) 4.95106e9 0.107951
\(235\) −2.92302e10 −0.625211
\(236\) 7.62603e9 0.160027
\(237\) −1.05397e11 −2.17000
\(238\) 9.71600e9 0.196287
\(239\) −2.39540e10 −0.474883 −0.237442 0.971402i \(-0.576309\pi\)
−0.237442 + 0.971402i \(0.576309\pi\)
\(240\) 1.22759e11 2.38837
\(241\) 3.26986e10 0.624385 0.312192 0.950019i \(-0.398937\pi\)
0.312192 + 0.950019i \(0.398937\pi\)
\(242\) 6.54410e10 1.22654
\(243\) −4.14710e10 −0.762986
\(244\) −5.87441e9 −0.106099
\(245\) 9.61629e10 1.70514
\(246\) −8.40495e10 −1.46328
\(247\) 4.06234e9 0.0694449
\(248\) 2.48407e10 0.416996
\(249\) 2.32080e10 0.382596
\(250\) −1.46157e11 −2.36641
\(251\) −4.46019e10 −0.709286 −0.354643 0.935002i \(-0.615398\pi\)
−0.354643 + 0.935002i \(0.615398\pi\)
\(252\) 5.70818e9 0.0891651
\(253\) −9.61445e10 −1.47531
\(254\) −6.99178e10 −1.05399
\(255\) 1.61007e11 2.38458
\(256\) −3.66740e10 −0.533677
\(257\) 4.55935e10 0.651935 0.325967 0.945381i \(-0.394310\pi\)
0.325967 + 0.945381i \(0.394310\pi\)
\(258\) −1.62045e10 −0.227692
\(259\) −2.64257e10 −0.364904
\(260\) 1.73344e9 0.0235250
\(261\) −2.18387e11 −2.91303
\(262\) 5.41646e10 0.710165
\(263\) −8.02154e10 −1.03385 −0.516924 0.856031i \(-0.672923\pi\)
−0.516924 + 0.856031i \(0.672923\pi\)
\(264\) 2.14366e11 2.71605
\(265\) 2.66075e11 3.31434
\(266\) −2.06925e10 −0.253422
\(267\) 2.63911e11 3.17802
\(268\) −1.46576e10 −0.173563
\(269\) 1.79789e10 0.209352 0.104676 0.994506i \(-0.466619\pi\)
0.104676 + 0.994506i \(0.466619\pi\)
\(270\) −1.76884e11 −2.02559
\(271\) −5.80992e10 −0.654347 −0.327173 0.944964i \(-0.606096\pi\)
−0.327173 + 0.944964i \(0.606096\pi\)
\(272\) 5.50280e10 0.609570
\(273\) −2.91520e9 −0.0317641
\(274\) −1.87656e9 −0.0201134
\(275\) −3.52103e11 −3.71255
\(276\) −2.82629e10 −0.293174
\(277\) 7.56051e10 0.771600 0.385800 0.922582i \(-0.373925\pi\)
0.385800 + 0.922582i \(0.373925\pi\)
\(278\) 1.55515e9 0.0156160
\(279\) −6.84085e10 −0.675914
\(280\) −5.66698e10 −0.550986
\(281\) 7.81929e10 0.748151 0.374075 0.927398i \(-0.377960\pi\)
0.374075 + 0.927398i \(0.377960\pi\)
\(282\) 5.36256e10 0.504953
\(283\) 1.17607e11 1.08992 0.544961 0.838462i \(-0.316545\pi\)
0.544961 + 0.838462i \(0.316545\pi\)
\(284\) 1.77532e10 0.161937
\(285\) −3.42901e11 −3.07869
\(286\) −1.08183e10 −0.0956116
\(287\) 3.13865e10 0.273070
\(288\) 7.37041e10 0.631285
\(289\) −4.64148e10 −0.391396
\(290\) 3.37811e11 2.80468
\(291\) −5.50400e10 −0.449946
\(292\) −4.55526e9 −0.0366683
\(293\) 1.39474e11 1.10557 0.552787 0.833323i \(-0.313564\pi\)
0.552787 + 0.833323i \(0.313564\pi\)
\(294\) −1.76420e11 −1.37716
\(295\) 2.08496e11 1.60287
\(296\) −1.85019e11 −1.40089
\(297\) −2.49862e11 −1.86336
\(298\) 1.00497e11 0.738209
\(299\) 9.15429e9 0.0662375
\(300\) −1.03505e11 −0.737761
\(301\) 6.05124e9 0.0424908
\(302\) −1.33857e11 −0.925999
\(303\) −1.82977e11 −1.24711
\(304\) −1.17195e11 −0.787005
\(305\) −1.60607e11 −1.06271
\(306\) −1.87336e11 −1.22145
\(307\) 3.89983e10 0.250567 0.125283 0.992121i \(-0.460016\pi\)
0.125283 + 0.992121i \(0.460016\pi\)
\(308\) −1.24726e10 −0.0789730
\(309\) −3.25918e11 −2.03374
\(310\) 1.05817e11 0.650773
\(311\) 2.46919e11 1.49669 0.748347 0.663308i \(-0.230848\pi\)
0.748347 + 0.663308i \(0.230848\pi\)
\(312\) −2.04106e10 −0.121944
\(313\) 1.43556e11 0.845416 0.422708 0.906266i \(-0.361080\pi\)
0.422708 + 0.906266i \(0.361080\pi\)
\(314\) −5.45115e10 −0.316450
\(315\) 1.56062e11 0.893100
\(316\) 4.29355e10 0.242228
\(317\) −2.92123e11 −1.62480 −0.812399 0.583102i \(-0.801839\pi\)
−0.812399 + 0.583102i \(0.801839\pi\)
\(318\) −4.88140e11 −2.67684
\(319\) 4.77184e11 2.58005
\(320\) −3.84958e11 −2.05229
\(321\) 2.86064e11 1.50380
\(322\) −4.66294e10 −0.241718
\(323\) −1.53709e11 −0.785758
\(324\) −9.97279e9 −0.0502764
\(325\) 3.35251e10 0.166684
\(326\) −2.00964e10 −0.0985462
\(327\) 1.22698e11 0.593434
\(328\) 2.19751e11 1.04833
\(329\) −2.00253e10 −0.0942320
\(330\) 9.13165e11 4.23874
\(331\) −3.59742e10 −0.164727 −0.0823636 0.996602i \(-0.526247\pi\)
−0.0823636 + 0.996602i \(0.526247\pi\)
\(332\) −9.45423e9 −0.0427076
\(333\) 5.09520e11 2.27071
\(334\) 2.00306e11 0.880716
\(335\) −4.00740e11 −1.73845
\(336\) 8.41008e10 0.359976
\(337\) 4.12227e11 1.74101 0.870506 0.492157i \(-0.163791\pi\)
0.870506 + 0.492157i \(0.163791\pi\)
\(338\) −2.15650e11 −0.898721
\(339\) 1.51775e11 0.624167
\(340\) −6.55892e10 −0.266181
\(341\) 1.49475e11 0.598653
\(342\) 3.98976e11 1.57699
\(343\) 1.37306e11 0.535630
\(344\) 4.23675e10 0.163125
\(345\) −7.72709e11 −2.93650
\(346\) −6.35728e10 −0.238467
\(347\) −7.23809e10 −0.268004 −0.134002 0.990981i \(-0.542783\pi\)
−0.134002 + 0.990981i \(0.542783\pi\)
\(348\) 1.40274e11 0.512710
\(349\) 2.59445e11 0.936119 0.468060 0.883697i \(-0.344953\pi\)
0.468060 + 0.883697i \(0.344953\pi\)
\(350\) −1.70767e11 −0.608273
\(351\) 2.37903e10 0.0836601
\(352\) −1.61046e11 −0.559125
\(353\) 8.53217e10 0.292465 0.146232 0.989250i \(-0.453285\pi\)
0.146232 + 0.989250i \(0.453285\pi\)
\(354\) −3.82507e11 −1.29457
\(355\) 4.85375e11 1.62200
\(356\) −1.07509e11 −0.354749
\(357\) 1.10304e11 0.359405
\(358\) −3.11520e11 −1.00233
\(359\) −2.92377e11 −0.929005 −0.464503 0.885572i \(-0.653767\pi\)
−0.464503 + 0.885572i \(0.653767\pi\)
\(360\) 1.09266e12 3.42866
\(361\) 4.67171e9 0.0144775
\(362\) −4.95267e11 −1.51583
\(363\) 7.42941e11 2.24582
\(364\) 1.18756e9 0.00354569
\(365\) −1.24541e11 −0.367278
\(366\) 2.94649e11 0.858301
\(367\) 5.23535e11 1.50643 0.753214 0.657775i \(-0.228502\pi\)
0.753214 + 0.657775i \(0.228502\pi\)
\(368\) −2.64093e11 −0.750656
\(369\) −6.05169e11 −1.69925
\(370\) −7.88149e11 −2.18625
\(371\) 1.82285e11 0.499539
\(372\) 4.39402e10 0.118965
\(373\) 2.22087e11 0.594063 0.297032 0.954868i \(-0.404003\pi\)
0.297032 + 0.954868i \(0.404003\pi\)
\(374\) 4.09337e11 1.08183
\(375\) −1.65930e12 −4.33295
\(376\) −1.40206e11 −0.361762
\(377\) −4.54346e10 −0.115838
\(378\) −1.21181e11 −0.305297
\(379\) 5.93299e10 0.147706 0.0738528 0.997269i \(-0.476470\pi\)
0.0738528 + 0.997269i \(0.476470\pi\)
\(380\) 1.39687e11 0.343662
\(381\) −7.93765e11 −1.92988
\(382\) 1.76244e11 0.423478
\(383\) 3.66860e11 0.871175 0.435587 0.900146i \(-0.356541\pi\)
0.435587 + 0.900146i \(0.356541\pi\)
\(384\) 4.49741e11 1.05553
\(385\) −3.41002e11 −0.791013
\(386\) 7.07461e11 1.62203
\(387\) −1.16675e11 −0.264411
\(388\) 2.24216e10 0.0502255
\(389\) −8.75015e11 −1.93750 −0.968751 0.248035i \(-0.920215\pi\)
−0.968751 + 0.248035i \(0.920215\pi\)
\(390\) −8.69460e10 −0.190309
\(391\) −3.46376e11 −0.749467
\(392\) 4.61258e11 0.986635
\(393\) 6.14921e11 1.30033
\(394\) −4.19609e11 −0.877227
\(395\) 1.17386e12 2.42622
\(396\) 2.40487e11 0.491431
\(397\) −5.04810e11 −1.01993 −0.509965 0.860195i \(-0.670342\pi\)
−0.509965 + 0.860195i \(0.670342\pi\)
\(398\) −3.19019e11 −0.637298
\(399\) −2.34918e11 −0.464022
\(400\) −9.67167e11 −1.88900
\(401\) 7.68568e11 1.48434 0.742169 0.670213i \(-0.233797\pi\)
0.742169 + 0.670213i \(0.233797\pi\)
\(402\) 7.35197e11 1.40406
\(403\) −1.42321e10 −0.0268780
\(404\) 7.45395e10 0.139210
\(405\) −2.72657e11 −0.503581
\(406\) 2.31431e11 0.422722
\(407\) −1.11332e12 −2.01116
\(408\) 7.72289e11 1.37978
\(409\) −6.22133e11 −1.09933 −0.549665 0.835385i \(-0.685245\pi\)
−0.549665 + 0.835385i \(0.685245\pi\)
\(410\) 9.36103e11 1.63605
\(411\) −2.13043e10 −0.0368281
\(412\) 1.32769e11 0.227018
\(413\) 1.42839e11 0.241586
\(414\) 8.99071e11 1.50416
\(415\) −2.58479e11 −0.427769
\(416\) 1.53338e10 0.0251033
\(417\) 1.76554e10 0.0285933
\(418\) −8.71778e11 −1.39673
\(419\) −1.15967e12 −1.83812 −0.919058 0.394122i \(-0.871049\pi\)
−0.919058 + 0.394122i \(0.871049\pi\)
\(420\) −1.00242e11 −0.157191
\(421\) 8.01209e10 0.124302 0.0621508 0.998067i \(-0.480204\pi\)
0.0621508 + 0.998067i \(0.480204\pi\)
\(422\) −6.75413e11 −1.03672
\(423\) 3.86113e11 0.586384
\(424\) 1.27626e12 1.91776
\(425\) −1.26851e12 −1.88600
\(426\) −8.90467e11 −1.31001
\(427\) −1.10030e11 −0.160172
\(428\) −1.16534e11 −0.167863
\(429\) −1.22818e11 −0.175067
\(430\) 1.80479e11 0.254576
\(431\) 3.08981e11 0.431304 0.215652 0.976470i \(-0.430812\pi\)
0.215652 + 0.976470i \(0.430812\pi\)
\(432\) −6.86329e11 −0.948103
\(433\) 7.06997e11 0.966544 0.483272 0.875470i \(-0.339448\pi\)
0.483272 + 0.875470i \(0.339448\pi\)
\(434\) 7.24946e10 0.0980848
\(435\) 3.83511e12 5.13543
\(436\) −4.99834e10 −0.0662425
\(437\) 7.37688e11 0.967623
\(438\) 2.28483e11 0.296634
\(439\) −1.15067e12 −1.47864 −0.739318 0.673356i \(-0.764852\pi\)
−0.739318 + 0.673356i \(0.764852\pi\)
\(440\) −2.38751e12 −3.03674
\(441\) −1.27025e12 −1.59925
\(442\) −3.89746e10 −0.0485714
\(443\) 1.45765e12 1.79819 0.899095 0.437754i \(-0.144226\pi\)
0.899095 + 0.437754i \(0.144226\pi\)
\(444\) −3.27275e11 −0.399659
\(445\) −2.93931e12 −3.55325
\(446\) 5.00705e11 0.599204
\(447\) 1.14092e12 1.35168
\(448\) −2.63731e11 −0.309322
\(449\) 1.51686e12 1.76132 0.880658 0.473753i \(-0.157101\pi\)
0.880658 + 0.473753i \(0.157101\pi\)
\(450\) 3.29260e12 3.78515
\(451\) 1.32232e12 1.50502
\(452\) −6.18284e10 −0.0696731
\(453\) −1.51966e12 −1.69552
\(454\) −4.94524e11 −0.546306
\(455\) 3.24681e10 0.0355145
\(456\) −1.64477e12 −1.78141
\(457\) −1.58795e12 −1.70300 −0.851501 0.524354i \(-0.824307\pi\)
−0.851501 + 0.524354i \(0.824307\pi\)
\(458\) −7.03312e11 −0.746884
\(459\) −9.00169e11 −0.946601
\(460\) 3.14778e11 0.327789
\(461\) −5.06836e11 −0.522653 −0.261326 0.965251i \(-0.584160\pi\)
−0.261326 + 0.965251i \(0.584160\pi\)
\(462\) 6.25601e11 0.638864
\(463\) −1.40219e12 −1.41806 −0.709028 0.705180i \(-0.750866\pi\)
−0.709028 + 0.705180i \(0.750866\pi\)
\(464\) 1.31075e12 1.31277
\(465\) 1.20133e12 1.19158
\(466\) 8.43801e11 0.828902
\(467\) −9.39462e11 −0.914015 −0.457008 0.889463i \(-0.651079\pi\)
−0.457008 + 0.889463i \(0.651079\pi\)
\(468\) −2.28977e10 −0.0220640
\(469\) −2.74543e11 −0.262019
\(470\) −5.97257e11 −0.564574
\(471\) −6.18860e11 −0.579427
\(472\) 1.00008e12 0.927461
\(473\) 2.54940e11 0.234187
\(474\) −2.15356e12 −1.95954
\(475\) 2.70158e12 2.43499
\(476\) −4.49346e10 −0.0401189
\(477\) −3.51468e12 −3.10852
\(478\) −4.89448e11 −0.428826
\(479\) −9.05240e11 −0.785695 −0.392847 0.919604i \(-0.628510\pi\)
−0.392847 + 0.919604i \(0.628510\pi\)
\(480\) −1.29432e12 −1.11290
\(481\) 1.06004e11 0.0902959
\(482\) 6.68126e11 0.563828
\(483\) −5.29376e11 −0.442591
\(484\) −3.02652e11 −0.250691
\(485\) 6.13010e11 0.503071
\(486\) −8.47372e11 −0.688986
\(487\) −6.82703e11 −0.549986 −0.274993 0.961446i \(-0.588675\pi\)
−0.274993 + 0.961446i \(0.588675\pi\)
\(488\) −7.70372e11 −0.614909
\(489\) −2.28151e11 −0.180440
\(490\) 1.96488e12 1.53976
\(491\) 2.15045e11 0.166979 0.0834897 0.996509i \(-0.473393\pi\)
0.0834897 + 0.996509i \(0.473393\pi\)
\(492\) 3.88712e11 0.299078
\(493\) 1.71913e12 1.31069
\(494\) 8.30053e10 0.0627097
\(495\) 6.57493e12 4.92229
\(496\) 4.10584e11 0.304603
\(497\) 3.32526e11 0.244468
\(498\) 4.74205e11 0.345489
\(499\) −5.06026e10 −0.0365359 −0.0182680 0.999833i \(-0.505815\pi\)
−0.0182680 + 0.999833i \(0.505815\pi\)
\(500\) 6.75947e11 0.483668
\(501\) 2.27404e12 1.61261
\(502\) −9.11345e11 −0.640495
\(503\) 2.64497e12 1.84232 0.921161 0.389183i \(-0.127242\pi\)
0.921161 + 0.389183i \(0.127242\pi\)
\(504\) 7.48572e11 0.516769
\(505\) 2.03792e12 1.39436
\(506\) −1.96451e12 −1.33222
\(507\) −2.44824e12 −1.64558
\(508\) 3.23356e11 0.215424
\(509\) 1.81937e12 1.20141 0.600703 0.799472i \(-0.294887\pi\)
0.600703 + 0.799472i \(0.294887\pi\)
\(510\) 3.28983e12 2.15331
\(511\) −8.53221e10 −0.0553563
\(512\) −1.74201e12 −1.12031
\(513\) 1.91712e12 1.22214
\(514\) 9.31607e11 0.588706
\(515\) 3.62992e12 2.27387
\(516\) 7.49428e10 0.0465378
\(517\) −8.43671e11 −0.519357
\(518\) −5.39954e11 −0.329513
\(519\) −7.21731e11 −0.436639
\(520\) 2.27324e11 0.136342
\(521\) −6.58651e11 −0.391639 −0.195819 0.980640i \(-0.562737\pi\)
−0.195819 + 0.980640i \(0.562737\pi\)
\(522\) −4.46227e12 −2.63050
\(523\) −2.09316e12 −1.22333 −0.611666 0.791116i \(-0.709500\pi\)
−0.611666 + 0.791116i \(0.709500\pi\)
\(524\) −2.50500e11 −0.145150
\(525\) −1.93869e12 −1.11376
\(526\) −1.63903e12 −0.933579
\(527\) 5.38510e11 0.304120
\(528\) 3.54318e12 1.98400
\(529\) −1.38810e11 −0.0770672
\(530\) 5.43667e12 2.99290
\(531\) −2.75411e12 −1.50333
\(532\) 9.56985e10 0.0517968
\(533\) −1.25903e11 −0.0675716
\(534\) 5.39245e12 2.86979
\(535\) −3.18604e12 −1.68135
\(536\) −1.92220e12 −1.00591
\(537\) −3.53663e12 −1.83529
\(538\) 3.67360e11 0.189048
\(539\) 2.77555e12 1.41644
\(540\) 8.18052e11 0.414008
\(541\) 2.75220e12 1.38131 0.690656 0.723184i \(-0.257322\pi\)
0.690656 + 0.723184i \(0.257322\pi\)
\(542\) −1.18713e12 −0.590884
\(543\) −5.62269e12 −2.77552
\(544\) −5.80196e11 −0.284040
\(545\) −1.36655e12 −0.663502
\(546\) −5.95659e10 −0.0286834
\(547\) −1.67438e12 −0.799669 −0.399835 0.916587i \(-0.630932\pi\)
−0.399835 + 0.916587i \(0.630932\pi\)
\(548\) 8.67873e9 0.00411096
\(549\) 2.12152e12 0.996714
\(550\) −7.19447e12 −3.35248
\(551\) −3.66129e12 −1.69220
\(552\) −3.70640e12 −1.69913
\(553\) 8.04202e11 0.365681
\(554\) 1.54483e12 0.696765
\(555\) −8.94772e12 −4.00308
\(556\) −7.19226e9 −0.00319175
\(557\) 2.66058e12 1.17119 0.585596 0.810603i \(-0.300860\pi\)
0.585596 + 0.810603i \(0.300860\pi\)
\(558\) −1.39778e12 −0.610360
\(559\) −2.42738e10 −0.0105144
\(560\) −9.36675e11 −0.402479
\(561\) 4.64713e12 1.98085
\(562\) 1.59771e12 0.675590
\(563\) −1.80763e12 −0.758268 −0.379134 0.925342i \(-0.623778\pi\)
−0.379134 + 0.925342i \(0.623778\pi\)
\(564\) −2.48008e11 −0.103207
\(565\) −1.69040e12 −0.697863
\(566\) 2.40305e12 0.984214
\(567\) −1.86795e11 −0.0758999
\(568\) 2.32817e12 0.938526
\(569\) −3.50663e12 −1.40244 −0.701220 0.712944i \(-0.747361\pi\)
−0.701220 + 0.712944i \(0.747361\pi\)
\(570\) −7.00644e12 −2.78010
\(571\) 2.95802e12 1.16450 0.582248 0.813011i \(-0.302173\pi\)
0.582248 + 0.813011i \(0.302173\pi\)
\(572\) 5.00323e10 0.0195420
\(573\) 2.00087e12 0.775397
\(574\) 6.41316e11 0.246586
\(575\) 6.08787e12 2.32252
\(576\) 5.08506e12 1.92484
\(577\) −9.05526e11 −0.340103 −0.170051 0.985435i \(-0.554393\pi\)
−0.170051 + 0.985435i \(0.554393\pi\)
\(578\) −9.48387e11 −0.353436
\(579\) 8.03168e12 2.96998
\(580\) −1.56231e12 −0.573246
\(581\) −1.77082e11 −0.0644735
\(582\) −1.12463e12 −0.406307
\(583\) 7.67972e12 2.75320
\(584\) −5.97378e11 −0.212516
\(585\) −6.26024e11 −0.220999
\(586\) 2.84985e12 0.998348
\(587\) −6.85640e11 −0.238355 −0.119178 0.992873i \(-0.538026\pi\)
−0.119178 + 0.992873i \(0.538026\pi\)
\(588\) 8.15908e11 0.281477
\(589\) −1.14688e12 −0.392644
\(590\) 4.26018e12 1.44742
\(591\) −4.76376e12 −1.60622
\(592\) −3.05811e12 −1.02330
\(593\) −6.58143e11 −0.218562 −0.109281 0.994011i \(-0.534855\pi\)
−0.109281 + 0.994011i \(0.534855\pi\)
\(594\) −5.10540e12 −1.68264
\(595\) −1.22852e12 −0.401841
\(596\) −4.64778e11 −0.150882
\(597\) −3.62177e12 −1.16691
\(598\) 1.87048e11 0.0598134
\(599\) −1.58033e12 −0.501564 −0.250782 0.968044i \(-0.580688\pi\)
−0.250782 + 0.968044i \(0.580688\pi\)
\(600\) −1.35737e13 −4.27579
\(601\) −1.50248e12 −0.469756 −0.234878 0.972025i \(-0.575469\pi\)
−0.234878 + 0.972025i \(0.575469\pi\)
\(602\) 1.23644e11 0.0383698
\(603\) 5.29353e12 1.63049
\(604\) 6.19063e11 0.189264
\(605\) −8.27452e12 −2.51098
\(606\) −3.73875e12 −1.12616
\(607\) 5.26894e12 1.57534 0.787670 0.616097i \(-0.211287\pi\)
0.787670 + 0.616097i \(0.211287\pi\)
\(608\) 1.23566e12 0.366719
\(609\) 2.62740e12 0.774013
\(610\) −3.28166e12 −0.959642
\(611\) 8.03292e10 0.0233178
\(612\) 8.66392e11 0.249651
\(613\) 2.66173e12 0.761364 0.380682 0.924706i \(-0.375689\pi\)
0.380682 + 0.924706i \(0.375689\pi\)
\(614\) 7.96848e11 0.226265
\(615\) 1.06274e13 2.99564
\(616\) −1.63566e12 −0.457699
\(617\) 3.08426e12 0.856777 0.428388 0.903595i \(-0.359082\pi\)
0.428388 + 0.903595i \(0.359082\pi\)
\(618\) −6.65944e12 −1.83650
\(619\) 1.96063e12 0.536769 0.268384 0.963312i \(-0.413510\pi\)
0.268384 + 0.963312i \(0.413510\pi\)
\(620\) −4.89385e11 −0.133011
\(621\) 4.32013e12 1.16569
\(622\) 5.04526e12 1.35153
\(623\) −2.01370e12 −0.535547
\(624\) −3.37360e11 −0.0890765
\(625\) 9.25824e12 2.42699
\(626\) 2.93325e12 0.763423
\(627\) −9.89714e12 −2.55744
\(628\) 2.52105e11 0.0646790
\(629\) −4.01092e12 −1.02168
\(630\) 3.18880e12 0.806481
\(631\) 1.03708e12 0.260424 0.130212 0.991486i \(-0.458434\pi\)
0.130212 + 0.991486i \(0.458434\pi\)
\(632\) 5.63058e12 1.40387
\(633\) −7.66785e12 −1.89827
\(634\) −5.96892e12 −1.46722
\(635\) 8.84058e12 2.15774
\(636\) 2.25755e12 0.547117
\(637\) −2.64271e11 −0.0635948
\(638\) 9.75025e12 2.32982
\(639\) −6.41150e12 −1.52127
\(640\) −5.00901e12 −1.18016
\(641\) 5.27910e12 1.23509 0.617545 0.786535i \(-0.288127\pi\)
0.617545 + 0.786535i \(0.288127\pi\)
\(642\) 5.84510e12 1.35795
\(643\) 3.47722e11 0.0802201 0.0401100 0.999195i \(-0.487229\pi\)
0.0401100 + 0.999195i \(0.487229\pi\)
\(644\) 2.15652e11 0.0494045
\(645\) 2.04894e12 0.466134
\(646\) −3.14072e12 −0.709550
\(647\) 7.11791e11 0.159692 0.0798460 0.996807i \(-0.474557\pi\)
0.0798460 + 0.996807i \(0.474557\pi\)
\(648\) −1.30783e12 −0.291384
\(649\) 6.01783e12 1.33149
\(650\) 6.85013e11 0.150518
\(651\) 8.23019e11 0.179595
\(652\) 9.29420e10 0.0201418
\(653\) −1.71011e12 −0.368056 −0.184028 0.982921i \(-0.558914\pi\)
−0.184028 + 0.982921i \(0.558914\pi\)
\(654\) 2.50707e12 0.535879
\(655\) −6.84870e12 −1.45386
\(656\) 3.63219e12 0.765775
\(657\) 1.64511e12 0.344470
\(658\) −4.09175e11 −0.0850928
\(659\) −3.21878e12 −0.664825 −0.332412 0.943134i \(-0.607863\pi\)
−0.332412 + 0.943134i \(0.607863\pi\)
\(660\) −4.22321e12 −0.866352
\(661\) −1.29023e12 −0.262882 −0.131441 0.991324i \(-0.541960\pi\)
−0.131441 + 0.991324i \(0.541960\pi\)
\(662\) −7.35056e11 −0.148751
\(663\) −4.42472e11 −0.0889354
\(664\) −1.23983e12 −0.247518
\(665\) 2.61641e12 0.518809
\(666\) 1.04110e13 2.05048
\(667\) −8.25054e12 −1.61405
\(668\) −9.26377e11 −0.180009
\(669\) 5.68442e12 1.09716
\(670\) −8.18827e12 −1.56984
\(671\) −4.63560e12 −0.882784
\(672\) −8.86729e11 −0.167737
\(673\) −2.68951e12 −0.505365 −0.252682 0.967549i \(-0.581313\pi\)
−0.252682 + 0.967549i \(0.581313\pi\)
\(674\) 8.42298e12 1.57216
\(675\) 1.58213e13 2.93342
\(676\) 9.97340e11 0.183689
\(677\) 3.07951e12 0.563421 0.281710 0.959500i \(-0.409098\pi\)
0.281710 + 0.959500i \(0.409098\pi\)
\(678\) 3.10119e12 0.563631
\(679\) 4.19967e11 0.0758231
\(680\) −8.60139e12 −1.54269
\(681\) −5.61425e12 −1.00030
\(682\) 3.05421e12 0.540592
\(683\) −1.87777e12 −0.330178 −0.165089 0.986279i \(-0.552791\pi\)
−0.165089 + 0.986279i \(0.552791\pi\)
\(684\) −1.84518e12 −0.322320
\(685\) 2.37277e11 0.0411764
\(686\) 2.80555e12 0.483681
\(687\) −7.98458e12 −1.36756
\(688\) 7.00277e11 0.119158
\(689\) −7.31216e11 −0.123612
\(690\) −1.57887e13 −2.65170
\(691\) −1.40579e12 −0.234568 −0.117284 0.993098i \(-0.537419\pi\)
−0.117284 + 0.993098i \(0.537419\pi\)
\(692\) 2.94012e11 0.0487402
\(693\) 4.50442e12 0.741890
\(694\) −1.47895e12 −0.242011
\(695\) −1.96637e11 −0.0319693
\(696\) 1.83956e13 2.97148
\(697\) 4.76387e12 0.764561
\(698\) 5.30121e12 0.845328
\(699\) 9.57953e12 1.51774
\(700\) 7.89765e11 0.124325
\(701\) −1.02642e13 −1.60544 −0.802720 0.596356i \(-0.796615\pi\)
−0.802720 + 0.596356i \(0.796615\pi\)
\(702\) 4.86105e11 0.0755462
\(703\) 8.54219e12 1.31908
\(704\) −1.11111e13 −1.70482
\(705\) −6.78056e12 −1.03375
\(706\) 1.74337e12 0.264100
\(707\) 1.39616e12 0.210159
\(708\) 1.76902e12 0.264595
\(709\) −6.07076e12 −0.902267 −0.451133 0.892457i \(-0.648980\pi\)
−0.451133 + 0.892457i \(0.648980\pi\)
\(710\) 9.91761e12 1.46469
\(711\) −1.55060e13 −2.27555
\(712\) −1.40988e13 −2.05600
\(713\) −2.58444e12 −0.374510
\(714\) 2.25383e12 0.324548
\(715\) 1.36789e12 0.195737
\(716\) 1.44072e12 0.204866
\(717\) −5.55662e12 −0.785190
\(718\) −5.97410e12 −0.838905
\(719\) −4.59470e12 −0.641175 −0.320588 0.947219i \(-0.603880\pi\)
−0.320588 + 0.947219i \(0.603880\pi\)
\(720\) 1.80602e13 2.50453
\(721\) 2.48683e12 0.342718
\(722\) 9.54564e10 0.0130734
\(723\) 7.58512e12 1.03238
\(724\) 2.29051e12 0.309820
\(725\) −3.02153e13 −4.06169
\(726\) 1.51804e13 2.02800
\(727\) 3.53648e12 0.469533 0.234767 0.972052i \(-0.424567\pi\)
0.234767 + 0.972052i \(0.424567\pi\)
\(728\) 1.55738e11 0.0205495
\(729\) −1.16973e13 −1.53395
\(730\) −2.54474e12 −0.331657
\(731\) 9.18463e11 0.118969
\(732\) −1.36269e12 −0.175427
\(733\) −5.36402e12 −0.686314 −0.343157 0.939278i \(-0.611496\pi\)
−0.343157 + 0.939278i \(0.611496\pi\)
\(734\) 1.06973e13 1.36033
\(735\) 2.23070e13 2.81934
\(736\) 2.78450e12 0.349782
\(737\) −1.15666e13 −1.44411
\(738\) −1.23653e13 −1.53445
\(739\) 1.14197e12 0.140850 0.0704249 0.997517i \(-0.477564\pi\)
0.0704249 + 0.997517i \(0.477564\pi\)
\(740\) 3.64503e12 0.446847
\(741\) 9.42346e11 0.114823
\(742\) 3.72462e12 0.451091
\(743\) −6.88545e11 −0.0828863 −0.0414431 0.999141i \(-0.513196\pi\)
−0.0414431 + 0.999141i \(0.513196\pi\)
\(744\) 5.76233e12 0.689477
\(745\) −1.27071e13 −1.51127
\(746\) 4.53787e12 0.536447
\(747\) 3.41435e12 0.401204
\(748\) −1.89310e12 −0.221114
\(749\) −2.18273e12 −0.253414
\(750\) −3.39042e13 −3.91271
\(751\) 4.45256e12 0.510776 0.255388 0.966839i \(-0.417797\pi\)
0.255388 + 0.966839i \(0.417797\pi\)
\(752\) −2.31742e12 −0.264256
\(753\) −1.03463e13 −1.17276
\(754\) −9.28359e11 −0.104603
\(755\) 1.69252e13 1.89572
\(756\) 5.60440e11 0.0623995
\(757\) 8.14319e12 0.901287 0.450643 0.892704i \(-0.351195\pi\)
0.450643 + 0.892704i \(0.351195\pi\)
\(758\) 1.21228e12 0.133380
\(759\) −2.23027e13 −2.43933
\(760\) 1.83186e13 1.99174
\(761\) −7.09695e12 −0.767080 −0.383540 0.923524i \(-0.625295\pi\)
−0.383540 + 0.923524i \(0.625295\pi\)
\(762\) −1.62189e13 −1.74270
\(763\) −9.36212e11 −0.100003
\(764\) −8.15096e11 −0.0865543
\(765\) 2.36872e13 2.50056
\(766\) 7.49599e12 0.786683
\(767\) −5.72981e11 −0.0597807
\(768\) −8.50730e12 −0.882402
\(769\) −1.45984e13 −1.50535 −0.752673 0.658395i \(-0.771236\pi\)
−0.752673 + 0.658395i \(0.771236\pi\)
\(770\) −6.96765e12 −0.714295
\(771\) 1.05764e13 1.07793
\(772\) −3.27187e12 −0.331526
\(773\) 4.52458e11 0.0455796 0.0227898 0.999740i \(-0.492745\pi\)
0.0227898 + 0.999740i \(0.492745\pi\)
\(774\) −2.38401e12 −0.238766
\(775\) −9.46479e12 −0.942439
\(776\) 2.94038e12 0.291089
\(777\) −6.13000e12 −0.603346
\(778\) −1.78791e13 −1.74959
\(779\) −1.01458e13 −0.987111
\(780\) 4.02108e11 0.0388971
\(781\) 1.40094e13 1.34738
\(782\) −7.07746e12 −0.676779
\(783\) −2.14417e13 −2.03859
\(784\) 7.62397e12 0.720707
\(785\) 6.89257e12 0.647840
\(786\) 1.25646e13 1.17421
\(787\) 1.47638e13 1.37187 0.685935 0.727663i \(-0.259394\pi\)
0.685935 + 0.727663i \(0.259394\pi\)
\(788\) 1.94061e12 0.179296
\(789\) −1.86076e13 −1.70940
\(790\) 2.39854e13 2.19091
\(791\) −1.15807e12 −0.105182
\(792\) 3.15375e13 2.84816
\(793\) 4.41373e11 0.0396348
\(794\) −1.03147e13 −0.921011
\(795\) 6.17217e13 5.48006
\(796\) 1.47540e12 0.130257
\(797\) −1.34285e13 −1.17887 −0.589435 0.807816i \(-0.700649\pi\)
−0.589435 + 0.807816i \(0.700649\pi\)
\(798\) −4.80005e12 −0.419018
\(799\) −3.03946e12 −0.263837
\(800\) 1.01975e13 0.880212
\(801\) 3.88265e13 3.33259
\(802\) 1.57041e13 1.34038
\(803\) −3.59464e12 −0.305095
\(804\) −3.40014e12 −0.286975
\(805\) 5.89594e12 0.494848
\(806\) −2.90803e11 −0.0242712
\(807\) 4.17057e12 0.346150
\(808\) 9.77513e12 0.806810
\(809\) 6.69281e12 0.549338 0.274669 0.961539i \(-0.411432\pi\)
0.274669 + 0.961539i \(0.411432\pi\)
\(810\) −5.57116e12 −0.454740
\(811\) −3.84593e11 −0.0312182 −0.0156091 0.999878i \(-0.504969\pi\)
−0.0156091 + 0.999878i \(0.504969\pi\)
\(812\) −1.07032e12 −0.0863998
\(813\) −1.34773e13 −1.08192
\(814\) −2.27484e13 −1.81610
\(815\) 2.54104e12 0.201745
\(816\) 1.27649e13 1.00789
\(817\) −1.95608e12 −0.153599
\(818\) −1.27120e13 −0.992711
\(819\) −4.28883e11 −0.0333090
\(820\) −4.32929e12 −0.334391
\(821\) −2.49941e13 −1.91997 −0.959983 0.280057i \(-0.909647\pi\)
−0.959983 + 0.280057i \(0.909647\pi\)
\(822\) −4.35308e11 −0.0332563
\(823\) 6.40992e12 0.487027 0.243514 0.969897i \(-0.421700\pi\)
0.243514 + 0.969897i \(0.421700\pi\)
\(824\) 1.74114e13 1.31571
\(825\) −8.16776e13 −6.13847
\(826\) 2.91861e12 0.218155
\(827\) 1.16763e13 0.868019 0.434010 0.900908i \(-0.357098\pi\)
0.434010 + 0.900908i \(0.357098\pi\)
\(828\) −4.15803e12 −0.307433
\(829\) −1.45512e13 −1.07005 −0.535024 0.844837i \(-0.679698\pi\)
−0.535024 + 0.844837i \(0.679698\pi\)
\(830\) −5.28148e12 −0.386282
\(831\) 1.75382e13 1.27579
\(832\) 1.05793e12 0.0765422
\(833\) 9.99937e12 0.719565
\(834\) 3.60750e11 0.0258201
\(835\) −2.53272e13 −1.80301
\(836\) 4.03180e12 0.285477
\(837\) −6.71648e12 −0.473018
\(838\) −2.36955e13 −1.65984
\(839\) −1.63671e13 −1.14036 −0.570180 0.821519i \(-0.693127\pi\)
−0.570180 + 0.821519i \(0.693127\pi\)
\(840\) −1.31457e13 −0.911021
\(841\) 2.64420e13 1.82269
\(842\) 1.63710e12 0.112246
\(843\) 1.81385e13 1.23702
\(844\) 3.12365e12 0.211895
\(845\) 2.72674e13 1.83987
\(846\) 7.88939e12 0.529513
\(847\) −5.66880e12 −0.378456
\(848\) 2.10949e13 1.40087
\(849\) 2.72815e13 1.80212
\(850\) −2.59192e13 −1.70309
\(851\) 1.92494e13 1.25815
\(852\) 4.11823e12 0.267752
\(853\) 5.19459e12 0.335954 0.167977 0.985791i \(-0.446276\pi\)
0.167977 + 0.985791i \(0.446276\pi\)
\(854\) −2.24823e12 −0.144638
\(855\) −5.04475e13 −3.22843
\(856\) −1.52823e13 −0.972872
\(857\) −2.66688e12 −0.168885 −0.0844423 0.996428i \(-0.526911\pi\)
−0.0844423 + 0.996428i \(0.526911\pi\)
\(858\) −2.50952e12 −0.158088
\(859\) −1.08042e13 −0.677054 −0.338527 0.940957i \(-0.609929\pi\)
−0.338527 + 0.940957i \(0.609929\pi\)
\(860\) −8.34677e11 −0.0520326
\(861\) 7.28075e12 0.451504
\(862\) 6.31336e12 0.389474
\(863\) −1.34009e13 −0.822407 −0.411204 0.911544i \(-0.634891\pi\)
−0.411204 + 0.911544i \(0.634891\pi\)
\(864\) 7.23641e12 0.441785
\(865\) 8.03830e12 0.488193
\(866\) 1.44460e13 0.872803
\(867\) −1.07669e13 −0.647149
\(868\) −3.35273e11 −0.0200475
\(869\) 3.38812e13 2.01544
\(870\) 7.83624e13 4.63736
\(871\) 1.10130e12 0.0648370
\(872\) −6.55485e12 −0.383918
\(873\) −8.09748e12 −0.471830
\(874\) 1.50731e13 0.873777
\(875\) 1.26608e13 0.730171
\(876\) −1.05669e12 −0.0606287
\(877\) 7.67119e12 0.437890 0.218945 0.975737i \(-0.429739\pi\)
0.218945 + 0.975737i \(0.429739\pi\)
\(878\) −2.35115e13 −1.33523
\(879\) 3.23538e13 1.82800
\(880\) −3.94623e13 −2.21825
\(881\) −2.06346e13 −1.15400 −0.576998 0.816746i \(-0.695776\pi\)
−0.576998 + 0.816746i \(0.695776\pi\)
\(882\) −2.59549e13 −1.44414
\(883\) −2.76514e13 −1.53071 −0.765357 0.643606i \(-0.777438\pi\)
−0.765357 + 0.643606i \(0.777438\pi\)
\(884\) 1.80250e11 0.00992748
\(885\) 4.83651e13 2.65025
\(886\) 2.97839e13 1.62379
\(887\) −8.21082e12 −0.445379 −0.222690 0.974889i \(-0.571484\pi\)
−0.222690 + 0.974889i \(0.571484\pi\)
\(888\) −4.29189e13 −2.31628
\(889\) 6.05660e12 0.325215
\(890\) −6.00586e13 −3.20863
\(891\) −7.86970e12 −0.418320
\(892\) −2.31566e12 −0.122471
\(893\) 6.47324e12 0.340636
\(894\) 2.33124e13 1.22058
\(895\) 3.93893e13 2.05199
\(896\) −3.43162e12 −0.177875
\(897\) 2.12353e12 0.109520
\(898\) 3.09938e13 1.59049
\(899\) 1.28271e13 0.654952
\(900\) −1.52276e13 −0.773643
\(901\) 2.76675e13 1.39865
\(902\) 2.70188e13 1.35905
\(903\) 1.40371e12 0.0702559
\(904\) −8.10820e12 −0.403800
\(905\) 6.26229e13 3.10323
\(906\) −3.10510e13 −1.53108
\(907\) 2.10695e13 1.03376 0.516881 0.856057i \(-0.327093\pi\)
0.516881 + 0.856057i \(0.327093\pi\)
\(908\) 2.28707e12 0.111659
\(909\) −2.69196e13 −1.30777
\(910\) 6.63417e11 0.0320701
\(911\) 2.33428e13 1.12285 0.561423 0.827529i \(-0.310254\pi\)
0.561423 + 0.827529i \(0.310254\pi\)
\(912\) −2.71858e13 −1.30126
\(913\) −7.46050e12 −0.355344
\(914\) −3.24464e13 −1.53783
\(915\) −3.72561e13 −1.75712
\(916\) 3.25268e12 0.152655
\(917\) −4.69198e12 −0.219126
\(918\) −1.83930e13 −0.854793
\(919\) −2.76026e13 −1.27653 −0.638264 0.769818i \(-0.720347\pi\)
−0.638264 + 0.769818i \(0.720347\pi\)
\(920\) 4.12802e13 1.89975
\(921\) 9.04648e12 0.414296
\(922\) −1.03561e13 −0.471962
\(923\) −1.33389e12 −0.0604939
\(924\) −2.89328e12 −0.130577
\(925\) 7.04956e13 3.16610
\(926\) −2.86508e13 −1.28052
\(927\) −4.79490e13 −2.13266
\(928\) −1.38200e13 −0.611707
\(929\) −1.82656e13 −0.804570 −0.402285 0.915514i \(-0.631784\pi\)
−0.402285 + 0.915514i \(0.631784\pi\)
\(930\) 2.45466e13 1.07601
\(931\) −2.12960e13 −0.929018
\(932\) −3.90241e12 −0.169419
\(933\) 5.72780e13 2.47469
\(934\) −1.91959e13 −0.825368
\(935\) −5.17576e13 −2.21473
\(936\) −3.00281e12 −0.127875
\(937\) 1.64822e12 0.0698534 0.0349267 0.999390i \(-0.488880\pi\)
0.0349267 + 0.999390i \(0.488880\pi\)
\(938\) −5.60971e12 −0.236607
\(939\) 3.33007e13 1.39784
\(940\) 2.76219e12 0.115393
\(941\) −1.96652e13 −0.817608 −0.408804 0.912622i \(-0.634054\pi\)
−0.408804 + 0.912622i \(0.634054\pi\)
\(942\) −1.26451e13 −0.523230
\(943\) −2.28630e13 −0.941521
\(944\) 1.65300e13 0.677483
\(945\) 1.53225e13 0.625008
\(946\) 5.20915e12 0.211474
\(947\) −2.10340e13 −0.849860 −0.424930 0.905226i \(-0.639701\pi\)
−0.424930 + 0.905226i \(0.639701\pi\)
\(948\) 9.95979e12 0.400510
\(949\) 3.42259e11 0.0136980
\(950\) 5.52010e13 2.19883
\(951\) −6.77641e13 −2.68650
\(952\) −5.89273e12 −0.232515
\(953\) 1.36899e13 0.537629 0.268814 0.963192i \(-0.413368\pi\)
0.268814 + 0.963192i \(0.413368\pi\)
\(954\) −7.18151e13 −2.80703
\(955\) −2.22848e13 −0.866949
\(956\) 2.26360e12 0.0876474
\(957\) 1.10693e14 4.26595
\(958\) −1.84966e13 −0.709493
\(959\) 1.62556e11 0.00620612
\(960\) −8.92991e13 −3.39334
\(961\) −2.24216e13 −0.848031
\(962\) 2.16596e12 0.0815384
\(963\) 4.20856e13 1.57694
\(964\) −3.08995e12 −0.115240
\(965\) −8.94531e13 −3.32065
\(966\) −1.08167e13 −0.399665
\(967\) 1.15243e12 0.0423835 0.0211917 0.999775i \(-0.493254\pi\)
0.0211917 + 0.999775i \(0.493254\pi\)
\(968\) −3.96898e13 −1.45291
\(969\) −3.56561e13 −1.29920
\(970\) 1.25255e13 0.454280
\(971\) −3.56388e13 −1.28658 −0.643290 0.765623i \(-0.722431\pi\)
−0.643290 + 0.765623i \(0.722431\pi\)
\(972\) 3.91892e12 0.140821
\(973\) −1.34714e11 −0.00481843
\(974\) −1.39496e13 −0.496645
\(975\) 7.77684e12 0.275602
\(976\) −1.27332e13 −0.449173
\(977\) −2.68281e13 −0.942029 −0.471014 0.882126i \(-0.656112\pi\)
−0.471014 + 0.882126i \(0.656112\pi\)
\(978\) −4.66179e12 −0.162940
\(979\) −8.48374e13 −2.95165
\(980\) −9.08719e12 −0.314711
\(981\) 1.80513e13 0.622297
\(982\) 4.39399e12 0.150785
\(983\) −3.23922e12 −0.110649 −0.0553247 0.998468i \(-0.517619\pi\)
−0.0553247 + 0.998468i \(0.517619\pi\)
\(984\) 5.09758e13 1.73335
\(985\) 5.30565e13 1.79587
\(986\) 3.51269e13 1.18357
\(987\) −4.64530e12 −0.155807
\(988\) −3.83883e11 −0.0128172
\(989\) −4.40792e12 −0.146504
\(990\) 1.34345e14 4.44490
\(991\) −1.57632e13 −0.519174 −0.259587 0.965720i \(-0.583586\pi\)
−0.259587 + 0.965720i \(0.583586\pi\)
\(992\) −4.32905e12 −0.141935
\(993\) −8.34497e12 −0.272366
\(994\) 6.79446e12 0.220758
\(995\) 4.03375e13 1.30468
\(996\) −2.19311e12 −0.0706143
\(997\) −6.52488e12 −0.209144 −0.104572 0.994517i \(-0.533347\pi\)
−0.104572 + 0.994517i \(0.533347\pi\)
\(998\) −1.03396e12 −0.0329924
\(999\) 5.00257e13 1.58909
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 43.10.a.a.1.11 15
3.2 odd 2 387.10.a.c.1.5 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.10.a.a.1.11 15 1.1 even 1 trivial
387.10.a.c.1.5 15 3.2 odd 2