Properties

Label 43.10.a.a.1.12
Level 43
Weight 10
Character 43.1
Self dual yes
Analytic conductor 22.147
Analytic rank 1
Dimension 15
CM no
Inner twists 1

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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 1.12
Root \(-25.8680\) 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

\(f(q)\) \(=\) \(q+23.8680 q^{2} +64.8300 q^{3} +57.6838 q^{4} -578.837 q^{5} +1547.37 q^{6} -413.035 q^{7} -10843.6 q^{8} -15480.1 q^{9} +O(q^{10})\) \(q+23.8680 q^{2} +64.8300 q^{3} +57.6838 q^{4} -578.837 q^{5} +1547.37 q^{6} -413.035 q^{7} -10843.6 q^{8} -15480.1 q^{9} -13815.7 q^{10} +40989.1 q^{11} +3739.64 q^{12} -154895. q^{13} -9858.34 q^{14} -37526.0 q^{15} -288351. q^{16} -37046.5 q^{17} -369479. q^{18} -572136. q^{19} -33389.5 q^{20} -26777.1 q^{21} +978329. q^{22} +1.53076e6 q^{23} -702993. q^{24} -1.61807e6 q^{25} -3.69704e6 q^{26} -2.27962e6 q^{27} -23825.4 q^{28} +5.10452e6 q^{29} -895673. q^{30} -6.63330e6 q^{31} -1.33042e6 q^{32} +2.65732e6 q^{33} -884227. q^{34} +239080. q^{35} -892949. q^{36} +1.17863e7 q^{37} -1.36558e7 q^{38} -1.00418e7 q^{39} +6.27670e6 q^{40} -1.86693e7 q^{41} -639117. q^{42} -3.41880e6 q^{43} +2.36440e6 q^{44} +8.96043e6 q^{45} +3.65362e7 q^{46} -4.17423e7 q^{47} -1.86938e7 q^{48} -4.01830e7 q^{49} -3.86202e7 q^{50} -2.40172e6 q^{51} -8.93492e6 q^{52} +1.09354e8 q^{53} -5.44101e7 q^{54} -2.37260e7 q^{55} +4.47880e6 q^{56} -3.70916e7 q^{57} +1.21835e8 q^{58} +1.08726e8 q^{59} -2.16464e6 q^{60} +8.96497e7 q^{61} -1.58324e8 q^{62} +6.39381e6 q^{63} +1.15881e8 q^{64} +8.96588e7 q^{65} +6.34251e7 q^{66} -2.02489e8 q^{67} -2.13698e6 q^{68} +9.92390e7 q^{69} +5.70637e6 q^{70} +1.86518e8 q^{71} +1.67860e8 q^{72} +2.88219e8 q^{73} +2.81315e8 q^{74} -1.04900e8 q^{75} -3.30030e7 q^{76} -1.69299e7 q^{77} -2.39679e8 q^{78} +1.54282e8 q^{79} +1.66908e8 q^{80} +1.56906e8 q^{81} -4.45599e8 q^{82} +1.44177e8 q^{83} -1.54460e6 q^{84} +2.14439e7 q^{85} -8.16001e7 q^{86} +3.30926e8 q^{87} -4.44471e8 q^{88} -5.50623e8 q^{89} +2.13868e8 q^{90} +6.39770e7 q^{91} +8.82999e7 q^{92} -4.30037e8 q^{93} -9.96306e8 q^{94} +3.31174e8 q^{95} -8.62514e7 q^{96} -1.15464e9 q^{97} -9.59090e8 q^{98} -6.34514e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 32q^{2} - 317q^{3} + 3242q^{4} - 4717q^{5} + 687q^{6} - 9680q^{7} - 20394q^{8} + 69516q^{9} + O(q^{10}) \) \( 15q - 32q^{2} - 317q^{3} + 3242q^{4} - 4717q^{5} + 687q^{6} - 9680q^{7} - 20394q^{8} + 69516q^{9} - 36237q^{10} - 104484q^{11} - 266395q^{12} - 116174q^{13} + 416064q^{14} + 415388q^{15} + 996762q^{16} - 884265q^{17} - 588735q^{18} - 689535q^{19} - 3077879q^{20} - 2070198q^{21} - 7276218q^{22} - 2504077q^{23} - 11534895q^{24} + 1315350q^{25} - 13343414q^{26} - 12546986q^{27} - 28059568q^{28} - 18406221q^{29} - 39503820q^{30} - 12033699q^{31} - 18952630q^{32} - 14197716q^{33} - 30383125q^{34} - 27855546q^{35} - 18372959q^{36} - 8722847q^{37} - 63941843q^{38} - 30955510q^{39} - 39665611q^{40} - 18689389q^{41} - 73185310q^{42} - 51282015q^{43} - 68723220q^{44} - 216992888q^{45} - 2067521q^{46} - 104960741q^{47} - 145362479q^{48} + 92663095q^{49} - 42446347q^{50} + 37433407q^{51} + 149226080q^{52} - 215907800q^{53} + 419158122q^{54} + 384379852q^{55} + 430441344q^{56} + 258744488q^{57} + 295963139q^{58} + 185924544q^{59} + 973236172q^{60} + 247538102q^{61} + 139798853q^{62} + 405429926q^{63} + 848556290q^{64} + 94294394q^{65} + 667230492q^{66} + 467904656q^{67} - 88234341q^{68} + 163914994q^{69} + 647526126q^{70} - 8252944q^{71} + 889796745q^{72} - 715627902q^{73} + 725122989q^{74} - 18301762q^{75} + 346300359q^{76} - 1236779964q^{77} + 2058642146q^{78} + 560681783q^{79} - 1157214179q^{80} - 752010645q^{81} + 941346367q^{82} - 1442854698q^{83} + 1895248718q^{84} + 699302088q^{85} + 109401632q^{86} - 2094576907q^{87} - 1464507256q^{88} - 396710008q^{89} + 1411356270q^{90} - 3278076852q^{91} + 155864647q^{92} - 1424759183q^{93} + 4666638949q^{94} - 3854114395q^{95} - 952489551q^{96} - 3063837815q^{97} - 6161086984q^{98} - 6576160348q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 23.8680 1.05483 0.527414 0.849608i \(-0.323162\pi\)
0.527414 + 0.849608i \(0.323162\pi\)
\(3\) 64.8300 0.462094 0.231047 0.972943i \(-0.425785\pi\)
0.231047 + 0.972943i \(0.425785\pi\)
\(4\) 57.6838 0.112664
\(5\) −578.837 −0.414182 −0.207091 0.978322i \(-0.566400\pi\)
−0.207091 + 0.978322i \(0.566400\pi\)
\(6\) 1547.37 0.487430
\(7\) −413.035 −0.0650198 −0.0325099 0.999471i \(-0.510350\pi\)
−0.0325099 + 0.999471i \(0.510350\pi\)
\(8\) −10843.6 −0.935988
\(9\) −15480.1 −0.786469
\(10\) −13815.7 −0.436891
\(11\) 40989.1 0.844114 0.422057 0.906569i \(-0.361308\pi\)
0.422057 + 0.906569i \(0.361308\pi\)
\(12\) 3739.64 0.0520612
\(13\) −154895. −1.50415 −0.752076 0.659076i \(-0.770947\pi\)
−0.752076 + 0.659076i \(0.770947\pi\)
\(14\) −9858.34 −0.0685848
\(15\) −37526.0 −0.191391
\(16\) −288351. −1.09997
\(17\) −37046.5 −0.107579 −0.0537894 0.998552i \(-0.517130\pi\)
−0.0537894 + 0.998552i \(0.517130\pi\)
\(18\) −369479. −0.829590
\(19\) −572136. −1.00718 −0.503591 0.863942i \(-0.667988\pi\)
−0.503591 + 0.863942i \(0.667988\pi\)
\(20\) −33389.5 −0.0466632
\(21\) −26777.1 −0.0300453
\(22\) 978329. 0.890395
\(23\) 1.53076e6 1.14059 0.570297 0.821439i \(-0.306828\pi\)
0.570297 + 0.821439i \(0.306828\pi\)
\(24\) −702993. −0.432515
\(25\) −1.61807e6 −0.828453
\(26\) −3.69704e6 −1.58662
\(27\) −2.27962e6 −0.825517
\(28\) −23825.4 −0.00732537
\(29\) 5.10452e6 1.34018 0.670091 0.742279i \(-0.266255\pi\)
0.670091 + 0.742279i \(0.266255\pi\)
\(30\) −895673. −0.201885
\(31\) −6.63330e6 −1.29004 −0.645018 0.764167i \(-0.723150\pi\)
−0.645018 + 0.764167i \(0.723150\pi\)
\(32\) −1.33042e6 −0.224293
\(33\) 2.65732e6 0.390060
\(34\) −884227. −0.113477
\(35\) 239080. 0.0269300
\(36\) −892949. −0.0886065
\(37\) 1.17863e7 1.03387 0.516937 0.856023i \(-0.327072\pi\)
0.516937 + 0.856023i \(0.327072\pi\)
\(38\) −1.36558e7 −1.06241
\(39\) −1.00418e7 −0.695060
\(40\) 6.27670e6 0.387669
\(41\) −1.86693e7 −1.03181 −0.515905 0.856646i \(-0.672544\pi\)
−0.515905 + 0.856646i \(0.672544\pi\)
\(42\) −639117. −0.0316926
\(43\) −3.41880e6 −0.152499
\(44\) 2.36440e6 0.0951009
\(45\) 8.96043e6 0.325741
\(46\) 3.65362e7 1.20313
\(47\) −4.17423e7 −1.24777 −0.623886 0.781515i \(-0.714447\pi\)
−0.623886 + 0.781515i \(0.714447\pi\)
\(48\) −1.86938e7 −0.508290
\(49\) −4.01830e7 −0.995772
\(50\) −3.86202e7 −0.873876
\(51\) −2.40172e6 −0.0497116
\(52\) −8.93492e6 −0.169463
\(53\) 1.09354e8 1.90368 0.951842 0.306590i \(-0.0991880\pi\)
0.951842 + 0.306590i \(0.0991880\pi\)
\(54\) −5.44101e7 −0.870779
\(55\) −2.37260e7 −0.349617
\(56\) 4.47880e6 0.0608578
\(57\) −3.70916e7 −0.465413
\(58\) 1.21835e8 1.41366
\(59\) 1.08726e8 1.16815 0.584075 0.811699i \(-0.301457\pi\)
0.584075 + 0.811699i \(0.301457\pi\)
\(60\) −2.16464e6 −0.0215628
\(61\) 8.96497e7 0.829019 0.414510 0.910045i \(-0.363953\pi\)
0.414510 + 0.910045i \(0.363953\pi\)
\(62\) −1.58324e8 −1.36077
\(63\) 6.39381e6 0.0511361
\(64\) 1.15881e8 0.863380
\(65\) 8.96588e7 0.622993
\(66\) 6.34251e7 0.411447
\(67\) −2.02489e8 −1.22762 −0.613810 0.789454i \(-0.710364\pi\)
−0.613810 + 0.789454i \(0.710364\pi\)
\(68\) −2.13698e6 −0.0121202
\(69\) 9.92390e7 0.527062
\(70\) 5.70637e6 0.0284066
\(71\) 1.86518e8 0.871081 0.435541 0.900169i \(-0.356557\pi\)
0.435541 + 0.900169i \(0.356557\pi\)
\(72\) 1.67860e8 0.736125
\(73\) 2.88219e8 1.18787 0.593937 0.804512i \(-0.297573\pi\)
0.593937 + 0.804512i \(0.297573\pi\)
\(74\) 2.81315e8 1.09056
\(75\) −1.04900e8 −0.382823
\(76\) −3.30030e7 −0.113473
\(77\) −1.69299e7 −0.0548841
\(78\) −2.39679e8 −0.733169
\(79\) 1.54282e8 0.445650 0.222825 0.974858i \(-0.428472\pi\)
0.222825 + 0.974858i \(0.428472\pi\)
\(80\) 1.66908e8 0.455588
\(81\) 1.56906e8 0.405002
\(82\) −4.45599e8 −1.08838
\(83\) 1.44177e8 0.333461 0.166730 0.986003i \(-0.446679\pi\)
0.166730 + 0.986003i \(0.446679\pi\)
\(84\) −1.54460e6 −0.00338501
\(85\) 2.14439e7 0.0445572
\(86\) −8.16001e7 −0.160860
\(87\) 3.30926e8 0.619291
\(88\) −4.44471e8 −0.790080
\(89\) −5.50623e8 −0.930248 −0.465124 0.885245i \(-0.653990\pi\)
−0.465124 + 0.885245i \(0.653990\pi\)
\(90\) 2.13868e8 0.343601
\(91\) 6.39770e7 0.0977997
\(92\) 8.82999e7 0.128503
\(93\) −4.30037e8 −0.596118
\(94\) −9.96306e8 −1.31619
\(95\) 3.31174e8 0.417157
\(96\) −8.62514e7 −0.103644
\(97\) −1.15464e9 −1.32427 −0.662133 0.749387i \(-0.730348\pi\)
−0.662133 + 0.749387i \(0.730348\pi\)
\(98\) −9.59090e8 −1.05037
\(99\) −6.34514e8 −0.663869
\(100\) −9.33366e7 −0.0933366
\(101\) −1.66204e9 −1.58926 −0.794630 0.607094i \(-0.792335\pi\)
−0.794630 + 0.607094i \(0.792335\pi\)
\(102\) −5.73245e7 −0.0524372
\(103\) −2.01491e8 −0.176396 −0.0881979 0.996103i \(-0.528111\pi\)
−0.0881979 + 0.996103i \(0.528111\pi\)
\(104\) 1.67962e9 1.40787
\(105\) 1.54996e7 0.0124442
\(106\) 2.61008e9 2.00806
\(107\) −2.22025e9 −1.63748 −0.818738 0.574168i \(-0.805326\pi\)
−0.818738 + 0.574168i \(0.805326\pi\)
\(108\) −1.31497e8 −0.0930057
\(109\) −1.44526e9 −0.980679 −0.490340 0.871531i \(-0.663127\pi\)
−0.490340 + 0.871531i \(0.663127\pi\)
\(110\) −5.66293e8 −0.368786
\(111\) 7.64103e8 0.477748
\(112\) 1.19099e8 0.0715199
\(113\) 1.98255e9 1.14385 0.571927 0.820304i \(-0.306196\pi\)
0.571927 + 0.820304i \(0.306196\pi\)
\(114\) −8.85304e8 −0.490931
\(115\) −8.86059e8 −0.472413
\(116\) 2.94448e8 0.150990
\(117\) 2.39778e9 1.18297
\(118\) 2.59507e9 1.23220
\(119\) 1.53015e7 0.00699476
\(120\) 4.06919e8 0.179140
\(121\) −6.77844e8 −0.287472
\(122\) 2.13976e9 0.874473
\(123\) −1.21033e9 −0.476793
\(124\) −3.82634e8 −0.145340
\(125\) 2.06714e9 0.757312
\(126\) 1.52608e8 0.0539398
\(127\) −5.25769e9 −1.79340 −0.896702 0.442635i \(-0.854044\pi\)
−0.896702 + 0.442635i \(0.854044\pi\)
\(128\) 3.44703e9 1.13501
\(129\) −2.21641e8 −0.0704687
\(130\) 2.13998e9 0.657150
\(131\) 4.26420e8 0.126508 0.0632538 0.997997i \(-0.479852\pi\)
0.0632538 + 0.997997i \(0.479852\pi\)
\(132\) 1.53284e8 0.0439456
\(133\) 2.36312e8 0.0654868
\(134\) −4.83301e9 −1.29493
\(135\) 1.31953e9 0.341914
\(136\) 4.01719e8 0.100693
\(137\) 2.39976e9 0.582003 0.291002 0.956723i \(-0.406011\pi\)
0.291002 + 0.956723i \(0.406011\pi\)
\(138\) 2.36864e9 0.555960
\(139\) 4.62160e8 0.105009 0.0525044 0.998621i \(-0.483280\pi\)
0.0525044 + 0.998621i \(0.483280\pi\)
\(140\) 1.37910e7 0.00303404
\(141\) −2.70615e9 −0.576589
\(142\) 4.45183e9 0.918842
\(143\) −6.34899e9 −1.26968
\(144\) 4.46369e9 0.865093
\(145\) −2.95468e9 −0.555079
\(146\) 6.87923e9 1.25300
\(147\) −2.60507e9 −0.460141
\(148\) 6.79876e8 0.116480
\(149\) 1.41734e8 0.0235578 0.0117789 0.999931i \(-0.496251\pi\)
0.0117789 + 0.999931i \(0.496251\pi\)
\(150\) −2.50375e9 −0.403813
\(151\) −7.41576e9 −1.16081 −0.580403 0.814330i \(-0.697105\pi\)
−0.580403 + 0.814330i \(0.697105\pi\)
\(152\) 6.20404e9 0.942711
\(153\) 5.73482e8 0.0846074
\(154\) −4.04084e8 −0.0578933
\(155\) 3.83960e9 0.534310
\(156\) −5.79251e8 −0.0783080
\(157\) −1.10190e10 −1.44742 −0.723709 0.690106i \(-0.757564\pi\)
−0.723709 + 0.690106i \(0.757564\pi\)
\(158\) 3.68242e9 0.470085
\(159\) 7.08945e9 0.879681
\(160\) 7.70098e8 0.0928980
\(161\) −6.32256e8 −0.0741612
\(162\) 3.74505e9 0.427208
\(163\) −1.12939e10 −1.25314 −0.626571 0.779364i \(-0.715542\pi\)
−0.626571 + 0.779364i \(0.715542\pi\)
\(164\) −1.07691e9 −0.116247
\(165\) −1.53816e9 −0.161556
\(166\) 3.44123e9 0.351744
\(167\) 2.07229e9 0.206171 0.103085 0.994673i \(-0.467128\pi\)
0.103085 + 0.994673i \(0.467128\pi\)
\(168\) 2.90361e8 0.0281220
\(169\) 1.33879e10 1.26247
\(170\) 5.11823e8 0.0470002
\(171\) 8.85671e9 0.792118
\(172\) −1.97209e8 −0.0171810
\(173\) −1.50835e10 −1.28025 −0.640125 0.768271i \(-0.721117\pi\)
−0.640125 + 0.768271i \(0.721117\pi\)
\(174\) 7.89856e9 0.653245
\(175\) 6.68321e8 0.0538659
\(176\) −1.18192e10 −0.928500
\(177\) 7.04870e9 0.539796
\(178\) −1.31423e10 −0.981253
\(179\) 1.57672e10 1.14793 0.573967 0.818878i \(-0.305404\pi\)
0.573967 + 0.818878i \(0.305404\pi\)
\(180\) 5.16872e8 0.0366992
\(181\) 6.68229e8 0.0462777 0.0231388 0.999732i \(-0.492634\pi\)
0.0231388 + 0.999732i \(0.492634\pi\)
\(182\) 1.52701e9 0.103162
\(183\) 5.81199e9 0.383085
\(184\) −1.65990e10 −1.06758
\(185\) −6.82232e9 −0.428212
\(186\) −1.02641e10 −0.628803
\(187\) −1.51850e9 −0.0908088
\(188\) −2.40785e9 −0.140579
\(189\) 9.41564e8 0.0536750
\(190\) 7.90447e9 0.440029
\(191\) −3.50164e10 −1.90380 −0.951901 0.306407i \(-0.900873\pi\)
−0.951901 + 0.306407i \(0.900873\pi\)
\(192\) 7.51256e9 0.398963
\(193\) 2.42400e10 1.25755 0.628775 0.777587i \(-0.283557\pi\)
0.628775 + 0.777587i \(0.283557\pi\)
\(194\) −2.75591e10 −1.39687
\(195\) 5.81258e9 0.287881
\(196\) −2.31791e9 −0.112187
\(197\) 1.04603e10 0.494819 0.247409 0.968911i \(-0.420421\pi\)
0.247409 + 0.968911i \(0.420421\pi\)
\(198\) −1.51446e10 −0.700268
\(199\) −1.66270e10 −0.751580 −0.375790 0.926705i \(-0.622629\pi\)
−0.375790 + 0.926705i \(0.622629\pi\)
\(200\) 1.75458e10 0.775422
\(201\) −1.31273e10 −0.567276
\(202\) −3.96696e10 −1.67640
\(203\) −2.10835e9 −0.0871384
\(204\) −1.38541e8 −0.00560069
\(205\) 1.08065e10 0.427357
\(206\) −4.80920e9 −0.186067
\(207\) −2.36962e10 −0.897042
\(208\) 4.46640e10 1.65452
\(209\) −2.34513e10 −0.850177
\(210\) 3.69944e8 0.0131265
\(211\) 2.94765e10 1.02378 0.511888 0.859052i \(-0.328946\pi\)
0.511888 + 0.859052i \(0.328946\pi\)
\(212\) 6.30797e9 0.214476
\(213\) 1.20920e10 0.402522
\(214\) −5.29930e10 −1.72726
\(215\) 1.97893e9 0.0631622
\(216\) 2.47194e10 0.772674
\(217\) 2.73978e9 0.0838779
\(218\) −3.44956e10 −1.03445
\(219\) 1.86853e10 0.548909
\(220\) −1.36860e9 −0.0393891
\(221\) 5.73831e9 0.161815
\(222\) 1.82376e10 0.503942
\(223\) −3.58102e9 −0.0969694 −0.0484847 0.998824i \(-0.515439\pi\)
−0.0484847 + 0.998824i \(0.515439\pi\)
\(224\) 5.49512e8 0.0145835
\(225\) 2.50479e10 0.651553
\(226\) 4.73196e10 1.20657
\(227\) 2.60470e10 0.651090 0.325545 0.945527i \(-0.394452\pi\)
0.325545 + 0.945527i \(0.394452\pi\)
\(228\) −2.13958e9 −0.0524352
\(229\) 7.05669e9 0.169567 0.0847836 0.996399i \(-0.472980\pi\)
0.0847836 + 0.996399i \(0.472980\pi\)
\(230\) −2.11485e10 −0.498315
\(231\) −1.09757e9 −0.0253616
\(232\) −5.53516e10 −1.25439
\(233\) −6.66600e10 −1.48171 −0.740856 0.671664i \(-0.765580\pi\)
−0.740856 + 0.671664i \(0.765580\pi\)
\(234\) 5.72304e10 1.24783
\(235\) 2.41620e10 0.516805
\(236\) 6.27172e9 0.131608
\(237\) 1.00021e10 0.205932
\(238\) 3.65217e8 0.00737827
\(239\) 4.25444e10 0.843435 0.421717 0.906727i \(-0.361427\pi\)
0.421717 + 0.906727i \(0.361427\pi\)
\(240\) 1.08206e10 0.210525
\(241\) 1.80531e10 0.344727 0.172364 0.985033i \(-0.444860\pi\)
0.172364 + 0.985033i \(0.444860\pi\)
\(242\) −1.61788e10 −0.303234
\(243\) 5.50420e10 1.01267
\(244\) 5.17133e9 0.0934003
\(245\) 2.32594e10 0.412431
\(246\) −2.88882e10 −0.502935
\(247\) 8.86209e10 1.51496
\(248\) 7.19291e10 1.20746
\(249\) 9.34701e9 0.154090
\(250\) 4.93386e10 0.798835
\(251\) −3.95656e10 −0.629196 −0.314598 0.949225i \(-0.601870\pi\)
−0.314598 + 0.949225i \(0.601870\pi\)
\(252\) 3.68819e8 0.00576118
\(253\) 6.27443e10 0.962791
\(254\) −1.25491e11 −1.89173
\(255\) 1.39021e9 0.0205896
\(256\) 2.29428e10 0.333862
\(257\) 7.15316e10 1.02282 0.511410 0.859337i \(-0.329124\pi\)
0.511410 + 0.859337i \(0.329124\pi\)
\(258\) −5.29014e9 −0.0743324
\(259\) −4.86814e9 −0.0672224
\(260\) 5.17186e9 0.0701886
\(261\) −7.90183e10 −1.05401
\(262\) 1.01778e10 0.133444
\(263\) −6.08596e10 −0.784384 −0.392192 0.919883i \(-0.628283\pi\)
−0.392192 + 0.919883i \(0.628283\pi\)
\(264\) −2.88150e10 −0.365091
\(265\) −6.32983e10 −0.788471
\(266\) 5.64032e9 0.0690774
\(267\) −3.56969e10 −0.429862
\(268\) −1.16803e10 −0.138308
\(269\) −5.96377e10 −0.694441 −0.347221 0.937783i \(-0.612875\pi\)
−0.347221 + 0.937783i \(0.612875\pi\)
\(270\) 3.14946e10 0.360661
\(271\) 7.16434e9 0.0806890 0.0403445 0.999186i \(-0.487154\pi\)
0.0403445 + 0.999186i \(0.487154\pi\)
\(272\) 1.06824e10 0.118334
\(273\) 4.14763e9 0.0451927
\(274\) 5.72776e10 0.613914
\(275\) −6.63233e10 −0.699309
\(276\) 5.72448e9 0.0593807
\(277\) 5.21051e10 0.531767 0.265883 0.964005i \(-0.414336\pi\)
0.265883 + 0.964005i \(0.414336\pi\)
\(278\) 1.10308e10 0.110766
\(279\) 1.02684e11 1.01457
\(280\) −2.59250e9 −0.0252062
\(281\) −1.92655e10 −0.184333 −0.0921663 0.995744i \(-0.529379\pi\)
−0.0921663 + 0.995744i \(0.529379\pi\)
\(282\) −6.45905e10 −0.608202
\(283\) 2.24601e10 0.208148 0.104074 0.994570i \(-0.466812\pi\)
0.104074 + 0.994570i \(0.466812\pi\)
\(284\) 1.07591e10 0.0981392
\(285\) 2.14700e10 0.192766
\(286\) −1.51538e11 −1.33929
\(287\) 7.71106e9 0.0670881
\(288\) 2.05950e10 0.176399
\(289\) −1.17215e11 −0.988427
\(290\) −7.05226e10 −0.585514
\(291\) −7.48555e10 −0.611935
\(292\) 1.66256e10 0.133830
\(293\) 4.53637e10 0.359587 0.179794 0.983704i \(-0.442457\pi\)
0.179794 + 0.983704i \(0.442457\pi\)
\(294\) −6.21778e10 −0.485370
\(295\) −6.29346e10 −0.483827
\(296\) −1.27806e11 −0.967694
\(297\) −9.34396e10 −0.696830
\(298\) 3.38291e9 0.0248495
\(299\) −2.37106e11 −1.71563
\(300\) −6.05101e9 −0.0431303
\(301\) 1.41208e9 0.00991543
\(302\) −1.77000e11 −1.22445
\(303\) −1.07750e11 −0.734388
\(304\) 1.64976e11 1.10787
\(305\) −5.18926e10 −0.343365
\(306\) 1.36879e10 0.0892464
\(307\) 2.52635e11 1.62320 0.811598 0.584216i \(-0.198598\pi\)
0.811598 + 0.584216i \(0.198598\pi\)
\(308\) −9.76582e8 −0.00618344
\(309\) −1.30627e10 −0.0815115
\(310\) 9.16437e10 0.563605
\(311\) 1.44034e11 0.873057 0.436529 0.899690i \(-0.356208\pi\)
0.436529 + 0.899690i \(0.356208\pi\)
\(312\) 1.08890e11 0.650568
\(313\) 1.80382e10 0.106229 0.0531147 0.998588i \(-0.483085\pi\)
0.0531147 + 0.998588i \(0.483085\pi\)
\(314\) −2.63002e11 −1.52678
\(315\) −3.70097e9 −0.0211796
\(316\) 8.89959e9 0.0502086
\(317\) 7.77758e9 0.0432591 0.0216296 0.999766i \(-0.493115\pi\)
0.0216296 + 0.999766i \(0.493115\pi\)
\(318\) 1.69211e11 0.927913
\(319\) 2.09230e11 1.13127
\(320\) −6.70762e10 −0.357597
\(321\) −1.43939e11 −0.756668
\(322\) −1.50907e10 −0.0782274
\(323\) 2.11956e10 0.108352
\(324\) 9.05095e9 0.0456290
\(325\) 2.50631e11 1.24612
\(326\) −2.69564e11 −1.32185
\(327\) −9.36963e10 −0.453166
\(328\) 2.02443e11 0.965761
\(329\) 1.72410e10 0.0811300
\(330\) −3.67128e10 −0.170414
\(331\) 2.82639e11 1.29421 0.647106 0.762400i \(-0.275979\pi\)
0.647106 + 0.762400i \(0.275979\pi\)
\(332\) 8.31668e9 0.0375689
\(333\) −1.82452e11 −0.813111
\(334\) 4.94616e10 0.217475
\(335\) 1.17208e11 0.508458
\(336\) 7.72119e9 0.0330489
\(337\) 1.43617e11 0.606557 0.303279 0.952902i \(-0.401919\pi\)
0.303279 + 0.952902i \(0.401919\pi\)
\(338\) 3.19543e11 1.33169
\(339\) 1.28529e11 0.528568
\(340\) 1.23696e9 0.00501998
\(341\) −2.71893e11 −1.08894
\(342\) 2.11392e11 0.835549
\(343\) 3.32644e10 0.129765
\(344\) 3.70723e10 0.142737
\(345\) −5.74432e10 −0.218299
\(346\) −3.60014e11 −1.35044
\(347\) −1.75323e10 −0.0649168 −0.0324584 0.999473i \(-0.510334\pi\)
−0.0324584 + 0.999473i \(0.510334\pi\)
\(348\) 1.90891e10 0.0697715
\(349\) 6.51688e10 0.235139 0.117570 0.993065i \(-0.462490\pi\)
0.117570 + 0.993065i \(0.462490\pi\)
\(350\) 1.59515e10 0.0568193
\(351\) 3.53102e11 1.24170
\(352\) −5.45328e10 −0.189328
\(353\) 2.83965e11 0.973372 0.486686 0.873577i \(-0.338206\pi\)
0.486686 + 0.873577i \(0.338206\pi\)
\(354\) 1.68239e11 0.569392
\(355\) −1.07964e11 −0.360786
\(356\) −3.17620e10 −0.104805
\(357\) 9.91997e8 0.00323224
\(358\) 3.76333e11 1.21087
\(359\) −7.02188e10 −0.223115 −0.111557 0.993758i \(-0.535584\pi\)
−0.111557 + 0.993758i \(0.535584\pi\)
\(360\) −9.71637e10 −0.304890
\(361\) 4.65223e9 0.0144171
\(362\) 1.59493e10 0.0488150
\(363\) −4.39447e10 −0.132839
\(364\) 3.69043e9 0.0110185
\(365\) −1.66832e11 −0.491996
\(366\) 1.38721e11 0.404089
\(367\) −3.53552e11 −1.01732 −0.508658 0.860969i \(-0.669858\pi\)
−0.508658 + 0.860969i \(0.669858\pi\)
\(368\) −4.41395e11 −1.25462
\(369\) 2.89001e11 0.811486
\(370\) −1.62835e11 −0.451691
\(371\) −4.51672e10 −0.123777
\(372\) −2.48061e10 −0.0671608
\(373\) 6.13570e11 1.64125 0.820624 0.571468i \(-0.193626\pi\)
0.820624 + 0.571468i \(0.193626\pi\)
\(374\) −3.62437e10 −0.0957877
\(375\) 1.34013e11 0.349950
\(376\) 4.52638e11 1.16790
\(377\) −7.90664e11 −2.01584
\(378\) 2.24733e10 0.0566179
\(379\) −2.66556e11 −0.663609 −0.331804 0.943348i \(-0.607657\pi\)
−0.331804 + 0.943348i \(0.607657\pi\)
\(380\) 1.91033e10 0.0469984
\(381\) −3.40856e11 −0.828721
\(382\) −8.35774e11 −2.00818
\(383\) −2.18172e11 −0.518090 −0.259045 0.965865i \(-0.583408\pi\)
−0.259045 + 0.965865i \(0.583408\pi\)
\(384\) 2.23471e11 0.524482
\(385\) 9.79966e9 0.0227320
\(386\) 5.78562e11 1.32650
\(387\) 5.29233e10 0.119935
\(388\) −6.66042e10 −0.149197
\(389\) 8.62682e10 0.191019 0.0955097 0.995428i \(-0.469552\pi\)
0.0955097 + 0.995428i \(0.469552\pi\)
\(390\) 1.38735e11 0.303665
\(391\) −5.67092e10 −0.122704
\(392\) 4.35730e11 0.932031
\(393\) 2.76448e10 0.0584584
\(394\) 2.49667e11 0.521949
\(395\) −8.93043e10 −0.184580
\(396\) −3.66011e10 −0.0747939
\(397\) −9.38797e11 −1.89677 −0.948384 0.317124i \(-0.897283\pi\)
−0.948384 + 0.317124i \(0.897283\pi\)
\(398\) −3.96854e11 −0.792789
\(399\) 1.53201e10 0.0302611
\(400\) 4.66572e11 0.911274
\(401\) −4.13612e11 −0.798810 −0.399405 0.916775i \(-0.630783\pi\)
−0.399405 + 0.916775i \(0.630783\pi\)
\(402\) −3.13324e11 −0.598379
\(403\) 1.02746e12 1.94041
\(404\) −9.58727e10 −0.179052
\(405\) −9.08231e10 −0.167745
\(406\) −5.03221e10 −0.0919161
\(407\) 4.83107e11 0.872708
\(408\) 2.60434e10 0.0465294
\(409\) 9.59930e10 0.169623 0.0848115 0.996397i \(-0.472971\pi\)
0.0848115 + 0.996397i \(0.472971\pi\)
\(410\) 2.57929e11 0.450788
\(411\) 1.55577e11 0.268940
\(412\) −1.16228e10 −0.0198734
\(413\) −4.49076e10 −0.0759530
\(414\) −5.65583e11 −0.946225
\(415\) −8.34550e10 −0.138113
\(416\) 2.06076e11 0.337370
\(417\) 2.99618e10 0.0485239
\(418\) −5.59738e11 −0.896791
\(419\) −6.82383e10 −0.108160 −0.0540798 0.998537i \(-0.517223\pi\)
−0.0540798 + 0.998537i \(0.517223\pi\)
\(420\) 8.94073e8 0.00140201
\(421\) −3.11922e11 −0.483923 −0.241961 0.970286i \(-0.577791\pi\)
−0.241961 + 0.970286i \(0.577791\pi\)
\(422\) 7.03546e11 1.07991
\(423\) 6.46173e11 0.981335
\(424\) −1.18580e12 −1.78182
\(425\) 5.99439e10 0.0891241
\(426\) 2.88612e11 0.424591
\(427\) −3.70285e10 −0.0539027
\(428\) −1.28072e11 −0.184484
\(429\) −4.11605e11 −0.586710
\(430\) 4.72332e10 0.0666253
\(431\) −1.57117e11 −0.219318 −0.109659 0.993969i \(-0.534976\pi\)
−0.109659 + 0.993969i \(0.534976\pi\)
\(432\) 6.57331e11 0.908044
\(433\) −1.09449e12 −1.49629 −0.748143 0.663537i \(-0.769054\pi\)
−0.748143 + 0.663537i \(0.769054\pi\)
\(434\) 6.53933e10 0.0884768
\(435\) −1.91552e11 −0.256499
\(436\) −8.33681e10 −0.110487
\(437\) −8.75802e11 −1.14879
\(438\) 4.45981e11 0.579005
\(439\) −7.01115e11 −0.900947 −0.450473 0.892790i \(-0.648745\pi\)
−0.450473 + 0.892790i \(0.648745\pi\)
\(440\) 2.57276e11 0.327237
\(441\) 6.22036e11 0.783144
\(442\) 1.36962e11 0.170687
\(443\) 4.23032e11 0.521863 0.260932 0.965357i \(-0.415970\pi\)
0.260932 + 0.965357i \(0.415970\pi\)
\(444\) 4.40763e10 0.0538248
\(445\) 3.18721e11 0.385292
\(446\) −8.54720e10 −0.102286
\(447\) 9.18860e9 0.0108859
\(448\) −4.78629e10 −0.0561368
\(449\) −1.04536e11 −0.121383 −0.0606916 0.998157i \(-0.519331\pi\)
−0.0606916 + 0.998157i \(0.519331\pi\)
\(450\) 5.97844e11 0.687277
\(451\) −7.65235e11 −0.870965
\(452\) 1.14361e11 0.128871
\(453\) −4.80764e11 −0.536402
\(454\) 6.21690e11 0.686788
\(455\) −3.70322e10 −0.0405069
\(456\) 4.02208e11 0.435621
\(457\) 5.68647e11 0.609845 0.304923 0.952377i \(-0.401369\pi\)
0.304923 + 0.952377i \(0.401369\pi\)
\(458\) 1.68430e11 0.178864
\(459\) 8.44520e10 0.0888082
\(460\) −5.11112e10 −0.0532238
\(461\) −1.55226e12 −1.60070 −0.800349 0.599535i \(-0.795352\pi\)
−0.800349 + 0.599535i \(0.795352\pi\)
\(462\) −2.61968e10 −0.0267522
\(463\) 1.18555e12 1.19897 0.599483 0.800387i \(-0.295373\pi\)
0.599483 + 0.800387i \(0.295373\pi\)
\(464\) −1.47189e12 −1.47416
\(465\) 2.48921e11 0.246901
\(466\) −1.59104e12 −1.56295
\(467\) 7.96561e11 0.774985 0.387492 0.921873i \(-0.373341\pi\)
0.387492 + 0.921873i \(0.373341\pi\)
\(468\) 1.38313e11 0.133278
\(469\) 8.36349e10 0.0798196
\(470\) 5.76699e11 0.545141
\(471\) −7.14362e11 −0.668843
\(472\) −1.17898e12 −1.09338
\(473\) −1.40133e11 −0.128726
\(474\) 2.38731e11 0.217223
\(475\) 9.25758e11 0.834404
\(476\) 8.82648e8 0.000788055 0
\(477\) −1.69281e12 −1.49719
\(478\) 1.01545e12 0.889679
\(479\) −1.33615e12 −1.15970 −0.579848 0.814725i \(-0.696888\pi\)
−0.579848 + 0.814725i \(0.696888\pi\)
\(480\) 4.99255e10 0.0429276
\(481\) −1.82563e12 −1.55510
\(482\) 4.30893e11 0.363628
\(483\) −4.09892e10 −0.0342695
\(484\) −3.91006e10 −0.0323877
\(485\) 6.68350e11 0.548487
\(486\) 1.31375e12 1.06819
\(487\) 1.33606e12 1.07633 0.538165 0.842839i \(-0.319118\pi\)
0.538165 + 0.842839i \(0.319118\pi\)
\(488\) −9.72129e11 −0.775952
\(489\) −7.32185e11 −0.579070
\(490\) 5.55157e11 0.435044
\(491\) 1.45714e12 1.13145 0.565725 0.824594i \(-0.308596\pi\)
0.565725 + 0.824594i \(0.308596\pi\)
\(492\) −6.98163e10 −0.0537173
\(493\) −1.89105e11 −0.144175
\(494\) 2.11521e12 1.59802
\(495\) 3.67280e11 0.274963
\(496\) 1.91272e12 1.41900
\(497\) −7.70386e10 −0.0566376
\(498\) 2.23095e11 0.162539
\(499\) −9.98947e11 −0.721257 −0.360628 0.932710i \(-0.617438\pi\)
−0.360628 + 0.932710i \(0.617438\pi\)
\(500\) 1.19241e11 0.0853216
\(501\) 1.34347e11 0.0952704
\(502\) −9.44354e11 −0.663694
\(503\) 2.25381e12 1.56986 0.784930 0.619584i \(-0.212699\pi\)
0.784930 + 0.619584i \(0.212699\pi\)
\(504\) −6.93322e10 −0.0478627
\(505\) 9.62049e11 0.658243
\(506\) 1.49758e12 1.01558
\(507\) 8.67937e11 0.583381
\(508\) −3.03283e11 −0.202051
\(509\) 2.45200e12 1.61916 0.809581 0.587008i \(-0.199694\pi\)
0.809581 + 0.587008i \(0.199694\pi\)
\(510\) 3.31815e10 0.0217185
\(511\) −1.19045e11 −0.0772353
\(512\) −1.21728e12 −0.782844
\(513\) 1.30425e12 0.831446
\(514\) 1.70732e12 1.07890
\(515\) 1.16630e11 0.0730600
\(516\) −1.27851e10 −0.00793926
\(517\) −1.71098e12 −1.05326
\(518\) −1.16193e11 −0.0709081
\(519\) −9.77864e11 −0.591596
\(520\) −9.72228e11 −0.583113
\(521\) 2.99007e12 1.77791 0.888957 0.457990i \(-0.151430\pi\)
0.888957 + 0.457990i \(0.151430\pi\)
\(522\) −1.88601e12 −1.11180
\(523\) 1.07354e12 0.627425 0.313713 0.949518i \(-0.398427\pi\)
0.313713 + 0.949518i \(0.398427\pi\)
\(524\) 2.45975e10 0.0142528
\(525\) 4.33273e10 0.0248911
\(526\) −1.45260e12 −0.827390
\(527\) 2.45740e11 0.138781
\(528\) −7.66241e11 −0.429055
\(529\) 5.42065e11 0.300954
\(530\) −1.51081e12 −0.831702
\(531\) −1.68308e12 −0.918714
\(532\) 1.36314e10 0.00737799
\(533\) 2.89177e12 1.55200
\(534\) −8.52015e11 −0.453431
\(535\) 1.28516e12 0.678213
\(536\) 2.19571e12 1.14904
\(537\) 1.02219e12 0.530454
\(538\) −1.42344e12 −0.732517
\(539\) −1.64706e12 −0.840545
\(540\) 7.61155e10 0.0385213
\(541\) −2.99583e12 −1.50359 −0.751796 0.659395i \(-0.770812\pi\)
−0.751796 + 0.659395i \(0.770812\pi\)
\(542\) 1.70999e11 0.0851131
\(543\) 4.33213e10 0.0213846
\(544\) 4.92875e10 0.0241291
\(545\) 8.36570e11 0.406180
\(546\) 9.89958e10 0.0476705
\(547\) −2.38362e11 −0.113840 −0.0569199 0.998379i \(-0.518128\pi\)
−0.0569199 + 0.998379i \(0.518128\pi\)
\(548\) 1.38427e11 0.0655706
\(549\) −1.38778e12 −0.651998
\(550\) −1.58301e12 −0.737651
\(551\) −2.92048e12 −1.34981
\(552\) −1.07611e12 −0.493323
\(553\) −6.37240e10 −0.0289761
\(554\) 1.24365e12 0.560923
\(555\) −4.42291e11 −0.197874
\(556\) 2.66591e10 0.0118307
\(557\) −3.97940e12 −1.75174 −0.875870 0.482548i \(-0.839711\pi\)
−0.875870 + 0.482548i \(0.839711\pi\)
\(558\) 2.45086e12 1.07020
\(559\) 5.29554e11 0.229381
\(560\) −6.89389e10 −0.0296222
\(561\) −9.84444e10 −0.0419622
\(562\) −4.59830e11 −0.194439
\(563\) 9.04378e11 0.379369 0.189685 0.981845i \(-0.439253\pi\)
0.189685 + 0.981845i \(0.439253\pi\)
\(564\) −1.56101e11 −0.0649606
\(565\) −1.14757e12 −0.473764
\(566\) 5.36078e11 0.219560
\(567\) −6.48078e10 −0.0263332
\(568\) −2.02254e12 −0.815322
\(569\) −1.36290e12 −0.545079 −0.272539 0.962145i \(-0.587864\pi\)
−0.272539 + 0.962145i \(0.587864\pi\)
\(570\) 5.12447e11 0.203335
\(571\) 2.48489e12 0.978240 0.489120 0.872217i \(-0.337318\pi\)
0.489120 + 0.872217i \(0.337318\pi\)
\(572\) −3.66234e11 −0.143046
\(573\) −2.27011e12 −0.879735
\(574\) 1.84048e11 0.0707664
\(575\) −2.47688e12 −0.944929
\(576\) −1.79384e12 −0.679022
\(577\) −1.75235e12 −0.658156 −0.329078 0.944303i \(-0.606738\pi\)
−0.329078 + 0.944303i \(0.606738\pi\)
\(578\) −2.79770e12 −1.04262
\(579\) 1.57148e12 0.581107
\(580\) −1.70437e11 −0.0625373
\(581\) −5.95502e10 −0.0216816
\(582\) −1.78666e12 −0.645487
\(583\) 4.48233e12 1.60693
\(584\) −3.12535e12 −1.11184
\(585\) −1.38792e12 −0.489964
\(586\) 1.08274e12 0.379303
\(587\) 2.44179e12 0.848862 0.424431 0.905460i \(-0.360474\pi\)
0.424431 + 0.905460i \(0.360474\pi\)
\(588\) −1.50270e11 −0.0518411
\(589\) 3.79515e12 1.29930
\(590\) −1.50213e12 −0.510355
\(591\) 6.78141e11 0.228653
\(592\) −3.39857e12 −1.13723
\(593\) 4.50598e12 1.49638 0.748192 0.663482i \(-0.230922\pi\)
0.748192 + 0.663482i \(0.230922\pi\)
\(594\) −2.23022e12 −0.735036
\(595\) −8.85707e9 −0.00289710
\(596\) 8.17574e9 0.00265411
\(597\) −1.07793e12 −0.347301
\(598\) −5.65926e12 −1.80969
\(599\) −7.19552e11 −0.228371 −0.114186 0.993459i \(-0.536426\pi\)
−0.114186 + 0.993459i \(0.536426\pi\)
\(600\) 1.13749e12 0.358318
\(601\) 2.18823e12 0.684160 0.342080 0.939671i \(-0.388869\pi\)
0.342080 + 0.939671i \(0.388869\pi\)
\(602\) 3.37037e10 0.0104591
\(603\) 3.13454e12 0.965485
\(604\) −4.27769e11 −0.130781
\(605\) 3.92361e11 0.119066
\(606\) −2.57178e12 −0.774653
\(607\) −4.88532e12 −1.46064 −0.730321 0.683104i \(-0.760630\pi\)
−0.730321 + 0.683104i \(0.760630\pi\)
\(608\) 7.61184e11 0.225904
\(609\) −1.36684e11 −0.0402662
\(610\) −1.23857e12 −0.362191
\(611\) 6.46566e12 1.87684
\(612\) 3.30806e10 0.00953218
\(613\) 6.65380e11 0.190326 0.0951629 0.995462i \(-0.469663\pi\)
0.0951629 + 0.995462i \(0.469663\pi\)
\(614\) 6.02991e12 1.71219
\(615\) 7.00582e11 0.197479
\(616\) 1.83582e11 0.0513709
\(617\) −5.62159e12 −1.56162 −0.780812 0.624767i \(-0.785194\pi\)
−0.780812 + 0.624767i \(0.785194\pi\)
\(618\) −3.11780e11 −0.0859807
\(619\) 4.24453e12 1.16204 0.581020 0.813889i \(-0.302654\pi\)
0.581020 + 0.813889i \(0.302654\pi\)
\(620\) 2.21482e11 0.0601973
\(621\) −3.48955e12 −0.941580
\(622\) 3.43781e12 0.920926
\(623\) 2.27426e11 0.0604846
\(624\) 2.89557e12 0.764545
\(625\) 1.96376e12 0.514788
\(626\) 4.30538e11 0.112054
\(627\) −1.52035e12 −0.392862
\(628\) −6.35618e11 −0.163071
\(629\) −4.36639e11 −0.111223
\(630\) −8.83350e10 −0.0223409
\(631\) 4.66852e12 1.17232 0.586161 0.810194i \(-0.300638\pi\)
0.586161 + 0.810194i \(0.300638\pi\)
\(632\) −1.67298e12 −0.417123
\(633\) 1.91096e12 0.473081
\(634\) 1.85636e11 0.0456310
\(635\) 3.04334e12 0.742795
\(636\) 4.08946e11 0.0991081
\(637\) 6.22414e12 1.49779
\(638\) 4.99390e12 1.19329
\(639\) −2.88732e12 −0.685078
\(640\) −1.99527e12 −0.470101
\(641\) −3.61791e12 −0.846440 −0.423220 0.906027i \(-0.639100\pi\)
−0.423220 + 0.906027i \(0.639100\pi\)
\(642\) −3.43554e12 −0.798155
\(643\) −8.06383e12 −1.86034 −0.930169 0.367132i \(-0.880340\pi\)
−0.930169 + 0.367132i \(0.880340\pi\)
\(644\) −3.64709e10 −0.00835527
\(645\) 1.28294e11 0.0291869
\(646\) 5.05899e11 0.114292
\(647\) 5.05529e12 1.13417 0.567083 0.823661i \(-0.308072\pi\)
0.567083 + 0.823661i \(0.308072\pi\)
\(648\) −1.70144e12 −0.379077
\(649\) 4.45657e12 0.986052
\(650\) 5.98207e12 1.31444
\(651\) 1.77620e11 0.0387595
\(652\) −6.51476e11 −0.141184
\(653\) −1.57457e11 −0.0338886 −0.0169443 0.999856i \(-0.505394\pi\)
−0.0169443 + 0.999856i \(0.505394\pi\)
\(654\) −2.23635e12 −0.478013
\(655\) −2.46827e11 −0.0523971
\(656\) 5.38329e12 1.13496
\(657\) −4.46165e12 −0.934226
\(658\) 4.11509e11 0.0855782
\(659\) 6.64168e11 0.137181 0.0685904 0.997645i \(-0.478150\pi\)
0.0685904 + 0.997645i \(0.478150\pi\)
\(660\) −8.87266e10 −0.0182015
\(661\) 6.99786e12 1.42580 0.712900 0.701265i \(-0.247381\pi\)
0.712900 + 0.701265i \(0.247381\pi\)
\(662\) 6.74603e12 1.36517
\(663\) 3.72015e11 0.0747737
\(664\) −1.56341e12 −0.312115
\(665\) −1.36786e11 −0.0271235
\(666\) −4.35477e12 −0.857692
\(667\) 7.81378e12 1.52860
\(668\) 1.19538e11 0.0232280
\(669\) −2.32158e11 −0.0448090
\(670\) 2.79752e12 0.536336
\(671\) 3.67466e12 0.699787
\(672\) 3.56248e10 0.00673894
\(673\) −9.28905e12 −1.74543 −0.872717 0.488226i \(-0.837644\pi\)
−0.872717 + 0.488226i \(0.837644\pi\)
\(674\) 3.42786e12 0.639814
\(675\) 3.68860e12 0.683902
\(676\) 7.72264e11 0.142235
\(677\) −7.12215e12 −1.30305 −0.651526 0.758626i \(-0.725871\pi\)
−0.651526 + 0.758626i \(0.725871\pi\)
\(678\) 3.06773e12 0.557549
\(679\) 4.76908e11 0.0861035
\(680\) −2.32530e11 −0.0417050
\(681\) 1.68863e12 0.300865
\(682\) −6.48955e12 −1.14864
\(683\) −8.49722e12 −1.49411 −0.747057 0.664760i \(-0.768534\pi\)
−0.747057 + 0.664760i \(0.768534\pi\)
\(684\) 5.10888e11 0.0892429
\(685\) −1.38907e12 −0.241055
\(686\) 7.93958e11 0.136880
\(687\) 4.57486e11 0.0783560
\(688\) 9.85814e11 0.167744
\(689\) −1.69384e13 −2.86343
\(690\) −1.37106e12 −0.230269
\(691\) −1.99151e12 −0.332300 −0.166150 0.986100i \(-0.553134\pi\)
−0.166150 + 0.986100i \(0.553134\pi\)
\(692\) −8.70073e11 −0.144238
\(693\) 2.62076e11 0.0431647
\(694\) −4.18462e11 −0.0684761
\(695\) −2.67515e11 −0.0434927
\(696\) −3.58844e12 −0.579648
\(697\) 6.91630e11 0.111001
\(698\) 1.55545e12 0.248032
\(699\) −4.32157e12 −0.684690
\(700\) 3.85513e10 0.00606873
\(701\) 5.43004e12 0.849321 0.424661 0.905353i \(-0.360393\pi\)
0.424661 + 0.905353i \(0.360393\pi\)
\(702\) 8.42785e12 1.30978
\(703\) −6.74334e12 −1.04130
\(704\) 4.74985e12 0.728791
\(705\) 1.56642e12 0.238813
\(706\) 6.77769e12 1.02674
\(707\) 6.86480e11 0.103333
\(708\) 4.06596e11 0.0608153
\(709\) 1.00333e13 1.49120 0.745599 0.666395i \(-0.232163\pi\)
0.745599 + 0.666395i \(0.232163\pi\)
\(710\) −2.57688e12 −0.380568
\(711\) −2.38830e12 −0.350490
\(712\) 5.97075e12 0.870701
\(713\) −1.01540e13 −1.47141
\(714\) 2.36770e10 0.00340946
\(715\) 3.67503e12 0.525877
\(716\) 9.09514e11 0.129330
\(717\) 2.75815e12 0.389746
\(718\) −1.67599e12 −0.235348
\(719\) −6.12483e12 −0.854701 −0.427351 0.904086i \(-0.640553\pi\)
−0.427351 + 0.904086i \(0.640553\pi\)
\(720\) −2.58375e12 −0.358306
\(721\) 8.32229e10 0.0114692
\(722\) 1.11040e11 0.0152076
\(723\) 1.17038e12 0.159297
\(724\) 3.85460e10 0.00521381
\(725\) −8.25949e12 −1.11028
\(726\) −1.04887e12 −0.140123
\(727\) −9.66565e12 −1.28329 −0.641647 0.767000i \(-0.721749\pi\)
−0.641647 + 0.767000i \(0.721749\pi\)
\(728\) −6.93743e11 −0.0915393
\(729\) 4.79991e11 0.0629447
\(730\) −3.98195e12 −0.518971
\(731\) 1.26655e11 0.0164056
\(732\) 3.35258e11 0.0431598
\(733\) −6.58742e12 −0.842845 −0.421423 0.906864i \(-0.638469\pi\)
−0.421423 + 0.906864i \(0.638469\pi\)
\(734\) −8.43859e12 −1.07309
\(735\) 1.50791e12 0.190582
\(736\) −2.03656e12 −0.255827
\(737\) −8.29982e12 −1.03625
\(738\) 6.89790e12 0.855979
\(739\) −1.58773e13 −1.95829 −0.979147 0.203152i \(-0.934882\pi\)
−0.979147 + 0.203152i \(0.934882\pi\)
\(740\) −3.93537e11 −0.0482440
\(741\) 5.74530e12 0.700052
\(742\) −1.07805e12 −0.130564
\(743\) 9.03557e12 1.08769 0.543846 0.839185i \(-0.316968\pi\)
0.543846 + 0.839185i \(0.316968\pi\)
\(744\) 4.66316e12 0.557959
\(745\) −8.20407e10 −0.00975722
\(746\) 1.46447e13 1.73124
\(747\) −2.23187e12 −0.262257
\(748\) −8.75929e10 −0.0102308
\(749\) 9.17041e11 0.106468
\(750\) 3.19862e12 0.369137
\(751\) 1.57604e13 1.80795 0.903976 0.427583i \(-0.140635\pi\)
0.903976 + 0.427583i \(0.140635\pi\)
\(752\) 1.20364e13 1.37251
\(753\) −2.56504e12 −0.290748
\(754\) −1.88716e13 −2.12636
\(755\) 4.29252e12 0.480785
\(756\) 5.43130e10 0.00604722
\(757\) −1.06961e12 −0.118384 −0.0591919 0.998247i \(-0.518852\pi\)
−0.0591919 + 0.998247i \(0.518852\pi\)
\(758\) −6.36217e12 −0.699994
\(759\) 4.06771e12 0.444900
\(760\) −3.59113e12 −0.390454
\(761\) 3.35960e12 0.363125 0.181562 0.983379i \(-0.441885\pi\)
0.181562 + 0.983379i \(0.441885\pi\)
\(762\) −8.13557e12 −0.874159
\(763\) 5.96944e11 0.0637636
\(764\) −2.01988e12 −0.214489
\(765\) −3.31953e11 −0.0350429
\(766\) −5.20734e12 −0.546496
\(767\) −1.68411e13 −1.75708
\(768\) 1.48738e12 0.154276
\(769\) −8.70807e12 −0.897952 −0.448976 0.893544i \(-0.648211\pi\)
−0.448976 + 0.893544i \(0.648211\pi\)
\(770\) 2.33899e11 0.0239784
\(771\) 4.63739e12 0.472639
\(772\) 1.39826e12 0.141680
\(773\) −5.58286e12 −0.562405 −0.281202 0.959649i \(-0.590733\pi\)
−0.281202 + 0.959649i \(0.590733\pi\)
\(774\) 1.26318e12 0.126511
\(775\) 1.07332e13 1.06873
\(776\) 1.25205e13 1.23950
\(777\) −3.15601e11 −0.0310631
\(778\) 2.05905e12 0.201493
\(779\) 1.06814e13 1.03922
\(780\) 3.35292e11 0.0324337
\(781\) 7.64521e12 0.735292
\(782\) −1.35354e12 −0.129431
\(783\) −1.16364e13 −1.10634
\(784\) 1.15868e13 1.09532
\(785\) 6.37820e12 0.599494
\(786\) 6.59827e11 0.0616636
\(787\) 1.08054e13 1.00405 0.502025 0.864853i \(-0.332588\pi\)
0.502025 + 0.864853i \(0.332588\pi\)
\(788\) 6.03390e11 0.0557481
\(789\) −3.94553e12 −0.362459
\(790\) −2.13152e12 −0.194701
\(791\) −8.18862e11 −0.0743732
\(792\) 6.88044e12 0.621374
\(793\) −1.38863e13 −1.24697
\(794\) −2.24072e13 −2.00077
\(795\) −4.10363e12 −0.364348
\(796\) −9.59109e11 −0.0846758
\(797\) −1.72340e13 −1.51294 −0.756472 0.654026i \(-0.773079\pi\)
−0.756472 + 0.654026i \(0.773079\pi\)
\(798\) 3.65662e11 0.0319203
\(799\) 1.54640e12 0.134234
\(800\) 2.15272e12 0.185816
\(801\) 8.52367e12 0.731612
\(802\) −9.87211e12 −0.842608
\(803\) 1.18138e13 1.00270
\(804\) −7.57235e11 −0.0639114
\(805\) 3.65973e11 0.0307162
\(806\) 2.45235e13 2.04680
\(807\) −3.86631e12 −0.320897
\(808\) 1.80226e13 1.48753
\(809\) 8.74791e12 0.718019 0.359009 0.933334i \(-0.383115\pi\)
0.359009 + 0.933334i \(0.383115\pi\)
\(810\) −2.16777e12 −0.176942
\(811\) −1.63936e13 −1.33070 −0.665349 0.746532i \(-0.731717\pi\)
−0.665349 + 0.746532i \(0.731717\pi\)
\(812\) −1.21617e11 −0.00981733
\(813\) 4.64464e11 0.0372859
\(814\) 1.15308e13 0.920557
\(815\) 6.53734e12 0.519029
\(816\) 6.92539e11 0.0546813
\(817\) 1.95602e12 0.153594
\(818\) 2.29117e12 0.178923
\(819\) −9.90368e11 −0.0769164
\(820\) 6.23357e11 0.0481476
\(821\) −6.80456e12 −0.522704 −0.261352 0.965244i \(-0.584168\pi\)
−0.261352 + 0.965244i \(0.584168\pi\)
\(822\) 3.71331e12 0.283686
\(823\) −1.21597e13 −0.923900 −0.461950 0.886906i \(-0.652850\pi\)
−0.461950 + 0.886906i \(0.652850\pi\)
\(824\) 2.18490e12 0.165104
\(825\) −4.29974e12 −0.323147
\(826\) −1.07186e12 −0.0801174
\(827\) −6.47949e10 −0.00481688 −0.00240844 0.999997i \(-0.500767\pi\)
−0.00240844 + 0.999997i \(0.500767\pi\)
\(828\) −1.36689e12 −0.101064
\(829\) −1.16602e13 −0.857452 −0.428726 0.903434i \(-0.641037\pi\)
−0.428726 + 0.903434i \(0.641037\pi\)
\(830\) −1.99191e12 −0.145686
\(831\) 3.37797e12 0.245726
\(832\) −1.79494e13 −1.29865
\(833\) 1.48864e12 0.107124
\(834\) 7.15130e11 0.0511844
\(835\) −1.19952e12 −0.0853923
\(836\) −1.35276e12 −0.0957840
\(837\) 1.51214e13 1.06495
\(838\) −1.62872e12 −0.114090
\(839\) −3.85423e12 −0.268540 −0.134270 0.990945i \(-0.542869\pi\)
−0.134270 + 0.990945i \(0.542869\pi\)
\(840\) −1.68072e11 −0.0116476
\(841\) 1.15490e13 0.796089
\(842\) −7.44496e12 −0.510456
\(843\) −1.24898e12 −0.0851791
\(844\) 1.70032e12 0.115342
\(845\) −7.74941e12 −0.522893
\(846\) 1.54229e13 1.03514
\(847\) 2.79973e11 0.0186914
\(848\) −3.15324e13 −2.09400
\(849\) 1.45609e12 0.0961839
\(850\) 1.43074e12 0.0940106
\(851\) 1.80419e13 1.17923
\(852\) 6.97511e11 0.0453495
\(853\) 1.14995e13 0.743717 0.371858 0.928289i \(-0.378721\pi\)
0.371858 + 0.928289i \(0.378721\pi\)
\(854\) −8.83798e11 −0.0568581
\(855\) −5.12659e12 −0.328081
\(856\) 2.40756e13 1.53266
\(857\) 4.75467e12 0.301097 0.150549 0.988603i \(-0.451896\pi\)
0.150549 + 0.988603i \(0.451896\pi\)
\(858\) −9.82422e12 −0.618878
\(859\) 2.09739e13 1.31434 0.657172 0.753741i \(-0.271753\pi\)
0.657172 + 0.753741i \(0.271753\pi\)
\(860\) 1.14152e11 0.00711608
\(861\) 4.99908e11 0.0310010
\(862\) −3.75007e12 −0.231343
\(863\) −7.42352e12 −0.455576 −0.227788 0.973711i \(-0.573149\pi\)
−0.227788 + 0.973711i \(0.573149\pi\)
\(864\) 3.03286e12 0.185157
\(865\) 8.73089e12 0.530256
\(866\) −2.61232e13 −1.57833
\(867\) −7.59908e12 −0.456746
\(868\) 1.58041e11 0.00944999
\(869\) 6.32389e12 0.376180
\(870\) −4.57198e12 −0.270562
\(871\) 3.13644e13 1.84653
\(872\) 1.56719e13 0.917904
\(873\) 1.78740e13 1.04149
\(874\) −2.09037e13 −1.21177
\(875\) −8.53802e11 −0.0492403
\(876\) 1.07784e12 0.0618421
\(877\) 8.71674e12 0.497572 0.248786 0.968558i \(-0.419968\pi\)
0.248786 + 0.968558i \(0.419968\pi\)
\(878\) −1.67343e13 −0.950345
\(879\) 2.94093e12 0.166163
\(880\) 6.84140e12 0.384568
\(881\) 7.91000e12 0.442369 0.221185 0.975232i \(-0.429008\pi\)
0.221185 + 0.975232i \(0.429008\pi\)
\(882\) 1.48468e13 0.826083
\(883\) −1.42391e12 −0.0788244 −0.0394122 0.999223i \(-0.512549\pi\)
−0.0394122 + 0.999223i \(0.512549\pi\)
\(884\) 3.31007e11 0.0182307
\(885\) −4.08005e12 −0.223574
\(886\) 1.00970e13 0.550476
\(887\) 2.10969e13 1.14436 0.572179 0.820129i \(-0.306098\pi\)
0.572179 + 0.820129i \(0.306098\pi\)
\(888\) −8.28566e12 −0.447166
\(889\) 2.17161e12 0.116607
\(890\) 7.60724e12 0.406417
\(891\) 6.43144e12 0.341868
\(892\) −2.06567e11 −0.0109249
\(893\) 2.38823e13 1.25674
\(894\) 2.19314e11 0.0114828
\(895\) −9.12666e12 −0.475454
\(896\) −1.42374e12 −0.0737982
\(897\) −1.53716e13 −0.792781
\(898\) −2.49508e12 −0.128038
\(899\) −3.38598e13 −1.72888
\(900\) 1.44486e12 0.0734063
\(901\) −4.05120e12 −0.204796
\(902\) −1.82647e13 −0.918718
\(903\) 9.15455e10 0.00458186
\(904\) −2.14980e13 −1.07063
\(905\) −3.86795e11 −0.0191674
\(906\) −1.14749e13 −0.565812
\(907\) −7.10519e12 −0.348613 −0.174306 0.984691i \(-0.555768\pi\)
−0.174306 + 0.984691i \(0.555768\pi\)
\(908\) 1.50249e12 0.0733541
\(909\) 2.57285e13 1.24990
\(910\) −8.83887e11 −0.0427278
\(911\) −2.23287e13 −1.07407 −0.537034 0.843561i \(-0.680455\pi\)
−0.537034 + 0.843561i \(0.680455\pi\)
\(912\) 1.06954e13 0.511941
\(913\) 5.90969e12 0.281479
\(914\) 1.35725e13 0.643283
\(915\) −3.36420e12 −0.158667
\(916\) 4.07057e11 0.0191040
\(917\) −1.76126e11 −0.00822550
\(918\) 2.01570e12 0.0936774
\(919\) −2.55522e13 −1.18170 −0.590852 0.806780i \(-0.701208\pi\)
−0.590852 + 0.806780i \(0.701208\pi\)
\(920\) 9.60810e12 0.442173
\(921\) 1.63783e13 0.750070
\(922\) −3.70493e13 −1.68846
\(923\) −2.88907e13 −1.31024
\(924\) −6.33118e10 −0.00285733
\(925\) −1.90710e13 −0.856517
\(926\) 2.82969e13 1.26470
\(927\) 3.11910e12 0.138730
\(928\) −6.79117e12 −0.300593
\(929\) 4.00707e13 1.76505 0.882523 0.470270i \(-0.155843\pi\)
0.882523 + 0.470270i \(0.155843\pi\)
\(930\) 5.94126e12 0.260439
\(931\) 2.29902e13 1.00292
\(932\) −3.84520e12 −0.166935
\(933\) 9.33771e12 0.403435
\(934\) 1.90124e13 0.817476
\(935\) 8.78964e11 0.0376114
\(936\) −2.60007e13 −1.10724
\(937\) 5.88813e12 0.249545 0.124773 0.992185i \(-0.460180\pi\)
0.124773 + 0.992185i \(0.460180\pi\)
\(938\) 1.99620e12 0.0841961
\(939\) 1.16942e12 0.0490880
\(940\) 1.39375e12 0.0582251
\(941\) −1.42277e13 −0.591537 −0.295768 0.955260i \(-0.595576\pi\)
−0.295768 + 0.955260i \(0.595576\pi\)
\(942\) −1.70504e13 −0.705515
\(943\) −2.85781e13 −1.17688
\(944\) −3.13512e13 −1.28493
\(945\) −5.45012e11 −0.0222312
\(946\) −3.34471e12 −0.135784
\(947\) −8.76631e12 −0.354195 −0.177097 0.984193i \(-0.556671\pi\)
−0.177097 + 0.984193i \(0.556671\pi\)
\(948\) 5.76961e11 0.0232011
\(949\) −4.46437e13 −1.78674
\(950\) 2.20960e13 0.880153
\(951\) 5.04221e11 0.0199898
\(952\) −1.65924e11 −0.00654701
\(953\) −4.63164e13 −1.81893 −0.909467 0.415775i \(-0.863510\pi\)
−0.909467 + 0.415775i \(0.863510\pi\)
\(954\) −4.04041e13 −1.57928
\(955\) 2.02688e13 0.788520
\(956\) 2.45412e12 0.0950244
\(957\) 1.35644e13 0.522752
\(958\) −3.18912e13 −1.22328
\(959\) −9.91185e11 −0.0378417
\(960\) −4.34855e12 −0.165243
\(961\) 1.75610e13 0.664193
\(962\) −4.35742e13 −1.64037
\(963\) 3.43696e13 1.28782
\(964\) 1.04137e12 0.0388382
\(965\) −1.40310e13 −0.520854
\(966\) −9.78332e11 −0.0361484
\(967\) −2.72329e12 −0.100155 −0.0500777 0.998745i \(-0.515947\pi\)
−0.0500777 + 0.998745i \(0.515947\pi\)
\(968\) 7.35030e12 0.269070
\(969\) 1.37411e12 0.0500686
\(970\) 1.59522e13 0.578560
\(971\) −4.44982e13 −1.60641 −0.803203 0.595705i \(-0.796873\pi\)
−0.803203 + 0.595705i \(0.796873\pi\)
\(972\) 3.17503e12 0.114091
\(973\) −1.90888e11 −0.00682765
\(974\) 3.18891e13 1.13534
\(975\) 1.62484e13 0.575825
\(976\) −2.58506e13 −0.911897
\(977\) −8.92268e12 −0.313307 −0.156653 0.987654i \(-0.550071\pi\)
−0.156653 + 0.987654i \(0.550071\pi\)
\(978\) −1.74758e13 −0.610820
\(979\) −2.25695e13 −0.785235
\(980\) 1.34169e12 0.0464660
\(981\) 2.23727e13 0.771274
\(982\) 3.47792e13 1.19349
\(983\) −2.04743e13 −0.699389 −0.349694 0.936864i \(-0.613715\pi\)
−0.349694 + 0.936864i \(0.613715\pi\)
\(984\) 1.31244e13 0.446273
\(985\) −6.05481e12 −0.204945
\(986\) −4.51356e12 −0.152080
\(987\) 1.11774e12 0.0374897
\(988\) 5.11199e12 0.170680
\(989\) −5.23335e12 −0.173939
\(990\) 8.76625e12 0.290038
\(991\) 4.30681e13 1.41848 0.709241 0.704966i \(-0.249038\pi\)
0.709241 + 0.704966i \(0.249038\pi\)
\(992\) 8.82509e12 0.289346
\(993\) 1.83235e13 0.598048
\(994\) −1.83876e12 −0.0597429
\(995\) 9.62433e12 0.311291
\(996\) 5.39171e11 0.0173604
\(997\) 1.53746e13 0.492806 0.246403 0.969167i \(-0.420751\pi\)
0.246403 + 0.969167i \(0.420751\pi\)
\(998\) −2.38429e13 −0.760802
\(999\) −2.68682e13 −0.853481
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.1.12 15
3.2 odd 2 387.10.a.c.1.4 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.10.a.a.1.12 15 1.1 even 1 trivial
387.10.a.c.1.4 15 3.2 odd 2