Properties

Label 43.10.a.a.1.5
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: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Defining polynomial: \(x^{15} - 2 x^{14} - 5425 x^{13} + 14888 x^{12} + 11288030 x^{11} - 37600244 x^{10} - 11474166224 x^{9} + 47465836576 x^{8} + 5986976782464 x^{7} - 32493903147264 x^{6} - 1516975415483904 x^{5} + 10892588268404224 x^{4} + 139803541742443008 x^{3} - 1349125586394823680 x^{2} + 2103623681144094720 x + 529838441422848000\)
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 1.5
Root \(16.4876\) of defining polynomial
Character \(\chi\) \(=\) 43.1

$q$-expansion

\(f(q)\) \(=\) \(q-18.4876 q^{2} -262.112 q^{3} -170.210 q^{4} -2363.43 q^{5} +4845.81 q^{6} +7025.62 q^{7} +12612.4 q^{8} +49019.5 q^{9} +O(q^{10})\) \(q-18.4876 q^{2} -262.112 q^{3} -170.210 q^{4} -2363.43 q^{5} +4845.81 q^{6} +7025.62 q^{7} +12612.4 q^{8} +49019.5 q^{9} +43694.1 q^{10} -59098.5 q^{11} +44614.0 q^{12} -84020.4 q^{13} -129887. q^{14} +619483. q^{15} -146025. q^{16} +199182. q^{17} -906252. q^{18} +293458. q^{19} +402279. q^{20} -1.84150e6 q^{21} +1.09259e6 q^{22} +366554. q^{23} -3.30586e6 q^{24} +3.63268e6 q^{25} +1.55333e6 q^{26} -7.68944e6 q^{27} -1.19583e6 q^{28} -1.87481e6 q^{29} -1.14527e7 q^{30} +3.91740e6 q^{31} -3.75790e6 q^{32} +1.54904e7 q^{33} -3.68239e6 q^{34} -1.66046e7 q^{35} -8.34360e6 q^{36} +2.22050e7 q^{37} -5.42532e6 q^{38} +2.20227e7 q^{39} -2.98085e7 q^{40} +3.33190e6 q^{41} +3.40448e7 q^{42} -3.41880e6 q^{43} +1.00591e7 q^{44} -1.15854e8 q^{45} -6.77669e6 q^{46} -4.54124e7 q^{47} +3.82749e7 q^{48} +9.00569e6 q^{49} -6.71594e7 q^{50} -5.22079e7 q^{51} +1.43011e7 q^{52} +4.88629e7 q^{53} +1.42159e8 q^{54} +1.39675e8 q^{55} +8.86099e7 q^{56} -7.69187e7 q^{57} +3.46607e7 q^{58} +1.66035e8 q^{59} -1.05442e8 q^{60} -1.65599e8 q^{61} -7.24233e7 q^{62} +3.44392e8 q^{63} +1.44239e8 q^{64} +1.98576e8 q^{65} -2.86380e8 q^{66} +1.13400e7 q^{67} -3.39027e7 q^{68} -9.60781e7 q^{69} +3.06978e8 q^{70} -2.09329e8 q^{71} +6.18254e8 q^{72} +7.39810e6 q^{73} -4.10516e8 q^{74} -9.52167e8 q^{75} -4.99494e7 q^{76} -4.15204e8 q^{77} -4.07146e8 q^{78} +5.09343e8 q^{79} +3.45120e8 q^{80} +1.05064e9 q^{81} -6.15988e7 q^{82} -4.59491e8 q^{83} +3.13441e8 q^{84} -4.70753e8 q^{85} +6.32053e7 q^{86} +4.91410e8 q^{87} -7.45374e8 q^{88} -2.28949e8 q^{89} +2.14186e9 q^{90} -5.90295e8 q^{91} -6.23911e7 q^{92} -1.02680e9 q^{93} +8.39565e8 q^{94} -6.93567e8 q^{95} +9.84989e8 q^{96} -9.54121e8 q^{97} -1.66493e8 q^{98} -2.89698e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 32q^{2} - 317q^{3} + 3242q^{4} - 4717q^{5} + 687q^{6} - 9680q^{7} - 20394q^{8} + 69516q^{9} + O(q^{10}) \) \( 15q - 32q^{2} - 317q^{3} + 3242q^{4} - 4717q^{5} + 687q^{6} - 9680q^{7} - 20394q^{8} + 69516q^{9} - 36237q^{10} - 104484q^{11} - 266395q^{12} - 116174q^{13} + 416064q^{14} + 415388q^{15} + 996762q^{16} - 884265q^{17} - 588735q^{18} - 689535q^{19} - 3077879q^{20} - 2070198q^{21} - 7276218q^{22} - 2504077q^{23} - 11534895q^{24} + 1315350q^{25} - 13343414q^{26} - 12546986q^{27} - 28059568q^{28} - 18406221q^{29} - 39503820q^{30} - 12033699q^{31} - 18952630q^{32} - 14197716q^{33} - 30383125q^{34} - 27855546q^{35} - 18372959q^{36} - 8722847q^{37} - 63941843q^{38} - 30955510q^{39} - 39665611q^{40} - 18689389q^{41} - 73185310q^{42} - 51282015q^{43} - 68723220q^{44} - 216992888q^{45} - 2067521q^{46} - 104960741q^{47} - 145362479q^{48} + 92663095q^{49} - 42446347q^{50} + 37433407q^{51} + 149226080q^{52} - 215907800q^{53} + 419158122q^{54} + 384379852q^{55} + 430441344q^{56} + 258744488q^{57} + 295963139q^{58} + 185924544q^{59} + 973236172q^{60} + 247538102q^{61} + 139798853q^{62} + 405429926q^{63} + 848556290q^{64} + 94294394q^{65} + 667230492q^{66} + 467904656q^{67} - 88234341q^{68} + 163914994q^{69} + 647526126q^{70} - 8252944q^{71} + 889796745q^{72} - 715627902q^{73} + 725122989q^{74} - 18301762q^{75} + 346300359q^{76} - 1236779964q^{77} + 2058642146q^{78} + 560681783q^{79} - 1157214179q^{80} - 752010645q^{81} + 941346367q^{82} - 1442854698q^{83} + 1895248718q^{84} + 699302088q^{85} + 109401632q^{86} - 2094576907q^{87} - 1464507256q^{88} - 396710008q^{89} + 1411356270q^{90} - 3278076852q^{91} + 155864647q^{92} - 1424759183q^{93} + 4666638949q^{94} - 3854114395q^{95} - 952489551q^{96} - 3063837815q^{97} - 6161086984q^{98} - 6576160348q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −18.4876 −0.817043 −0.408521 0.912749i \(-0.633955\pi\)
−0.408521 + 0.912749i \(0.633955\pi\)
\(3\) −262.112 −1.86827 −0.934137 0.356914i \(-0.883829\pi\)
−0.934137 + 0.356914i \(0.883829\pi\)
\(4\) −170.210 −0.332441
\(5\) −2363.43 −1.69113 −0.845567 0.533870i \(-0.820737\pi\)
−0.845567 + 0.533870i \(0.820737\pi\)
\(6\) 4845.81 1.52646
\(7\) 7025.62 1.10597 0.552985 0.833191i \(-0.313489\pi\)
0.552985 + 0.833191i \(0.313489\pi\)
\(8\) 12612.4 1.08866
\(9\) 49019.5 2.49045
\(10\) 43694.1 1.38173
\(11\) −59098.5 −1.21705 −0.608526 0.793534i \(-0.708239\pi\)
−0.608526 + 0.793534i \(0.708239\pi\)
\(12\) 44614.0 0.621091
\(13\) −84020.4 −0.815905 −0.407952 0.913003i \(-0.633757\pi\)
−0.407952 + 0.913003i \(0.633757\pi\)
\(14\) −129887. −0.903625
\(15\) 619483. 3.15950
\(16\) −146025. −0.557042
\(17\) 199182. 0.578402 0.289201 0.957268i \(-0.406610\pi\)
0.289201 + 0.957268i \(0.406610\pi\)
\(18\) −906252. −2.03480
\(19\) 293458. 0.516600 0.258300 0.966065i \(-0.416838\pi\)
0.258300 + 0.966065i \(0.416838\pi\)
\(20\) 402279. 0.562202
\(21\) −1.84150e6 −2.06626
\(22\) 1.09259e6 0.994384
\(23\) 366554. 0.273126 0.136563 0.990631i \(-0.456394\pi\)
0.136563 + 0.990631i \(0.456394\pi\)
\(24\) −3.30586e6 −2.03392
\(25\) 3.63268e6 1.85993
\(26\) 1.55333e6 0.666629
\(27\) −7.68944e6 −2.78457
\(28\) −1.19583e6 −0.367670
\(29\) −1.87481e6 −0.492228 −0.246114 0.969241i \(-0.579154\pi\)
−0.246114 + 0.969241i \(0.579154\pi\)
\(30\) −1.14527e7 −2.58145
\(31\) 3.91740e6 0.761852 0.380926 0.924605i \(-0.375605\pi\)
0.380926 + 0.924605i \(0.375605\pi\)
\(32\) −3.75790e6 −0.633534
\(33\) 1.54904e7 2.27379
\(34\) −3.68239e6 −0.472579
\(35\) −1.66046e7 −1.87034
\(36\) −8.34360e6 −0.827928
\(37\) 2.22050e7 1.94779 0.973895 0.226997i \(-0.0728907\pi\)
0.973895 + 0.226997i \(0.0728907\pi\)
\(38\) −5.42532e6 −0.422084
\(39\) 2.20227e7 1.52433
\(40\) −2.98085e7 −1.84107
\(41\) 3.33190e6 0.184147 0.0920736 0.995752i \(-0.470650\pi\)
0.0920736 + 0.995752i \(0.470650\pi\)
\(42\) 3.40448e7 1.68822
\(43\) −3.41880e6 −0.152499
\(44\) 1.00591e7 0.404598
\(45\) −1.15854e8 −4.21168
\(46\) −6.77669e6 −0.223156
\(47\) −4.54124e7 −1.35748 −0.678741 0.734378i \(-0.737474\pi\)
−0.678741 + 0.734378i \(0.737474\pi\)
\(48\) 3.82749e7 1.04071
\(49\) 9.00569e6 0.223169
\(50\) −6.71594e7 −1.51964
\(51\) −5.22079e7 −1.08061
\(52\) 1.43011e7 0.271240
\(53\) 4.88629e7 0.850624 0.425312 0.905047i \(-0.360164\pi\)
0.425312 + 0.905047i \(0.360164\pi\)
\(54\) 1.42159e8 2.27511
\(55\) 1.39675e8 2.05820
\(56\) 8.86099e7 1.20403
\(57\) −7.69187e7 −0.965150
\(58\) 3.46607e7 0.402172
\(59\) 1.66035e8 1.78387 0.891937 0.452159i \(-0.149346\pi\)
0.891937 + 0.452159i \(0.149346\pi\)
\(60\) −1.05442e8 −1.05035
\(61\) −1.65599e8 −1.53135 −0.765673 0.643230i \(-0.777594\pi\)
−0.765673 + 0.643230i \(0.777594\pi\)
\(62\) −7.24233e7 −0.622466
\(63\) 3.44392e8 2.75436
\(64\) 1.44239e8 1.07467
\(65\) 1.98576e8 1.37980
\(66\) −2.86380e8 −1.85778
\(67\) 1.13400e7 0.0687507 0.0343753 0.999409i \(-0.489056\pi\)
0.0343753 + 0.999409i \(0.489056\pi\)
\(68\) −3.39027e7 −0.192285
\(69\) −9.60781e7 −0.510274
\(70\) 3.06978e8 1.52815
\(71\) −2.09329e8 −0.977611 −0.488806 0.872393i \(-0.662567\pi\)
−0.488806 + 0.872393i \(0.662567\pi\)
\(72\) 6.18254e8 2.71126
\(73\) 7.39810e6 0.0304907 0.0152453 0.999884i \(-0.495147\pi\)
0.0152453 + 0.999884i \(0.495147\pi\)
\(74\) −4.10516e8 −1.59143
\(75\) −9.52167e8 −3.47486
\(76\) −4.99494e7 −0.171739
\(77\) −4.15204e8 −1.34602
\(78\) −4.07146e8 −1.24545
\(79\) 5.09343e8 1.47126 0.735629 0.677385i \(-0.236887\pi\)
0.735629 + 0.677385i \(0.236887\pi\)
\(80\) 3.45120e8 0.942032
\(81\) 1.05064e9 2.71189
\(82\) −6.15988e7 −0.150456
\(83\) −4.59491e8 −1.06274 −0.531369 0.847141i \(-0.678322\pi\)
−0.531369 + 0.847141i \(0.678322\pi\)
\(84\) 3.13441e8 0.686908
\(85\) −4.70753e8 −0.978155
\(86\) 6.32053e7 0.124598
\(87\) 4.91410e8 0.919618
\(88\) −7.45374e8 −1.32496
\(89\) −2.28949e8 −0.386798 −0.193399 0.981120i \(-0.561951\pi\)
−0.193399 + 0.981120i \(0.561951\pi\)
\(90\) 2.14186e9 3.44112
\(91\) −5.90295e8 −0.902366
\(92\) −6.23911e7 −0.0907983
\(93\) −1.02680e9 −1.42335
\(94\) 8.39565e8 1.10912
\(95\) −6.93567e8 −0.873639
\(96\) 9.84989e8 1.18362
\(97\) −9.54121e8 −1.09429 −0.547143 0.837039i \(-0.684285\pi\)
−0.547143 + 0.837039i \(0.684285\pi\)
\(98\) −1.66493e8 −0.182339
\(99\) −2.89698e9 −3.03101
\(100\) −6.18318e8 −0.618318
\(101\) 1.29443e9 1.23775 0.618876 0.785489i \(-0.287588\pi\)
0.618876 + 0.785489i \(0.287588\pi\)
\(102\) 9.65198e8 0.882908
\(103\) 5.67850e8 0.497126 0.248563 0.968616i \(-0.420042\pi\)
0.248563 + 0.968616i \(0.420042\pi\)
\(104\) −1.05970e9 −0.888244
\(105\) 4.35225e9 3.49431
\(106\) −9.03356e8 −0.694996
\(107\) 4.53655e8 0.334579 0.167290 0.985908i \(-0.446499\pi\)
0.167290 + 0.985908i \(0.446499\pi\)
\(108\) 1.30882e9 0.925705
\(109\) 9.29530e8 0.630731 0.315365 0.948970i \(-0.397873\pi\)
0.315365 + 0.948970i \(0.397873\pi\)
\(110\) −2.58226e9 −1.68164
\(111\) −5.82018e9 −3.63901
\(112\) −1.02592e9 −0.616071
\(113\) −3.79267e7 −0.0218822 −0.0109411 0.999940i \(-0.503483\pi\)
−0.0109411 + 0.999940i \(0.503483\pi\)
\(114\) 1.42204e9 0.788569
\(115\) −8.66325e8 −0.461892
\(116\) 3.19111e8 0.163637
\(117\) −4.11864e9 −2.03197
\(118\) −3.06957e9 −1.45750
\(119\) 1.39938e9 0.639696
\(120\) 7.81316e9 3.43963
\(121\) 1.13469e9 0.481218
\(122\) 3.06152e9 1.25118
\(123\) −8.73331e8 −0.344038
\(124\) −6.66781e8 −0.253271
\(125\) −3.96951e9 −1.45426
\(126\) −6.36698e9 −2.25043
\(127\) −3.97458e9 −1.35573 −0.677867 0.735185i \(-0.737095\pi\)
−0.677867 + 0.735185i \(0.737095\pi\)
\(128\) −7.42589e8 −0.244514
\(129\) 8.96108e8 0.284909
\(130\) −3.67119e9 −1.12736
\(131\) −1.80701e9 −0.536093 −0.268047 0.963406i \(-0.586378\pi\)
−0.268047 + 0.963406i \(0.586378\pi\)
\(132\) −2.63662e9 −0.755901
\(133\) 2.06172e9 0.571344
\(134\) −2.09649e8 −0.0561722
\(135\) 1.81735e10 4.70908
\(136\) 2.51216e9 0.629684
\(137\) −2.82788e9 −0.685834 −0.342917 0.939366i \(-0.611415\pi\)
−0.342917 + 0.939366i \(0.611415\pi\)
\(138\) 1.77625e9 0.416916
\(139\) 6.82579e9 1.55091 0.775454 0.631404i \(-0.217521\pi\)
0.775454 + 0.631404i \(0.217521\pi\)
\(140\) 2.82626e9 0.621779
\(141\) 1.19031e10 2.53615
\(142\) 3.86998e9 0.798750
\(143\) 4.96548e9 0.992999
\(144\) −7.15808e9 −1.38728
\(145\) 4.43099e9 0.832424
\(146\) −1.36773e8 −0.0249122
\(147\) −2.36050e9 −0.416942
\(148\) −3.77950e9 −0.647526
\(149\) −9.22449e9 −1.53322 −0.766610 0.642113i \(-0.778058\pi\)
−0.766610 + 0.642113i \(0.778058\pi\)
\(150\) 1.76033e10 2.83911
\(151\) 7.71760e9 1.20805 0.604027 0.796964i \(-0.293562\pi\)
0.604027 + 0.796964i \(0.293562\pi\)
\(152\) 3.70121e9 0.562402
\(153\) 9.76381e9 1.44048
\(154\) 7.67610e9 1.09976
\(155\) −9.25851e9 −1.28839
\(156\) −3.74848e9 −0.506751
\(157\) −1.03691e10 −1.36205 −0.681027 0.732259i \(-0.738466\pi\)
−0.681027 + 0.732259i \(0.738466\pi\)
\(158\) −9.41652e9 −1.20208
\(159\) −1.28075e10 −1.58920
\(160\) 8.88153e9 1.07139
\(161\) 2.57527e9 0.302069
\(162\) −1.94238e10 −2.21573
\(163\) 1.24179e10 1.37786 0.688929 0.724829i \(-0.258081\pi\)
0.688929 + 0.724829i \(0.258081\pi\)
\(164\) −5.67123e8 −0.0612181
\(165\) −3.66105e10 −3.84528
\(166\) 8.49488e9 0.868302
\(167\) 8.49813e8 0.0845472 0.0422736 0.999106i \(-0.486540\pi\)
0.0422736 + 0.999106i \(0.486540\pi\)
\(168\) −2.32257e10 −2.24945
\(169\) −3.54508e9 −0.334300
\(170\) 8.70308e9 0.799195
\(171\) 1.43852e10 1.28657
\(172\) 5.81914e8 0.0506968
\(173\) −2.05242e10 −1.74204 −0.871022 0.491244i \(-0.836542\pi\)
−0.871022 + 0.491244i \(0.836542\pi\)
\(174\) −9.08498e9 −0.751367
\(175\) 2.55218e10 2.05703
\(176\) 8.62987e9 0.677949
\(177\) −4.35196e10 −3.33277
\(178\) 4.23271e9 0.316030
\(179\) 2.24623e8 0.0163537 0.00817684 0.999967i \(-0.497397\pi\)
0.00817684 + 0.999967i \(0.497397\pi\)
\(180\) 1.97195e10 1.40014
\(181\) 1.28374e10 0.889043 0.444522 0.895768i \(-0.353374\pi\)
0.444522 + 0.895768i \(0.353374\pi\)
\(182\) 1.09131e10 0.737272
\(183\) 4.34054e10 2.86097
\(184\) 4.62313e9 0.297342
\(185\) −5.24799e10 −3.29397
\(186\) 1.89830e10 1.16294
\(187\) −1.17714e10 −0.703946
\(188\) 7.72964e9 0.451283
\(189\) −5.40231e10 −3.07965
\(190\) 1.28224e10 0.713801
\(191\) 1.84958e9 0.100560 0.0502798 0.998735i \(-0.483989\pi\)
0.0502798 + 0.998735i \(0.483989\pi\)
\(192\) −3.78068e10 −2.00777
\(193\) 7.73188e9 0.401123 0.200561 0.979681i \(-0.435723\pi\)
0.200561 + 0.979681i \(0.435723\pi\)
\(194\) 1.76394e10 0.894078
\(195\) −5.20492e10 −2.57785
\(196\) −1.53286e9 −0.0741907
\(197\) 2.41118e10 1.14060 0.570298 0.821438i \(-0.306828\pi\)
0.570298 + 0.821438i \(0.306828\pi\)
\(198\) 5.35581e10 2.47646
\(199\) 2.46274e10 1.11322 0.556609 0.830775i \(-0.312102\pi\)
0.556609 + 0.830775i \(0.312102\pi\)
\(200\) 4.58168e10 2.02484
\(201\) −2.97235e9 −0.128445
\(202\) −2.39309e10 −1.01130
\(203\) −1.31717e10 −0.544390
\(204\) 8.88630e9 0.359241
\(205\) −7.87472e9 −0.311417
\(206\) −1.04982e10 −0.406173
\(207\) 1.79683e10 0.680206
\(208\) 1.22691e10 0.454493
\(209\) −1.73429e10 −0.628729
\(210\) −8.04625e10 −2.85500
\(211\) −1.54470e10 −0.536504 −0.268252 0.963349i \(-0.586446\pi\)
−0.268252 + 0.963349i \(0.586446\pi\)
\(212\) −8.31695e9 −0.282782
\(213\) 5.48675e10 1.82645
\(214\) −8.38698e9 −0.273365
\(215\) 8.08010e9 0.257895
\(216\) −9.69823e10 −3.03145
\(217\) 2.75222e10 0.842586
\(218\) −1.71847e10 −0.515334
\(219\) −1.93913e9 −0.0569650
\(220\) −2.37741e10 −0.684230
\(221\) −1.67353e10 −0.471921
\(222\) 1.07601e11 2.97323
\(223\) −6.69002e10 −1.81157 −0.905786 0.423736i \(-0.860718\pi\)
−0.905786 + 0.423736i \(0.860718\pi\)
\(224\) −2.64016e10 −0.700670
\(225\) 1.78072e11 4.63207
\(226\) 7.01172e8 0.0178787
\(227\) −2.18215e10 −0.545466 −0.272733 0.962090i \(-0.587928\pi\)
−0.272733 + 0.962090i \(0.587928\pi\)
\(228\) 1.30923e10 0.320856
\(229\) −4.48901e9 −0.107868 −0.0539338 0.998545i \(-0.517176\pi\)
−0.0539338 + 0.998545i \(0.517176\pi\)
\(230\) 1.60162e10 0.377386
\(231\) 1.08830e11 2.51474
\(232\) −2.36459e10 −0.535870
\(233\) 2.75398e9 0.0612151 0.0306076 0.999531i \(-0.490256\pi\)
0.0306076 + 0.999531i \(0.490256\pi\)
\(234\) 7.61436e10 1.66021
\(235\) 1.07329e11 2.29568
\(236\) −2.82607e10 −0.593033
\(237\) −1.33505e11 −2.74871
\(238\) −2.58711e10 −0.522659
\(239\) 2.52877e10 0.501324 0.250662 0.968075i \(-0.419352\pi\)
0.250662 + 0.968075i \(0.419352\pi\)
\(240\) −9.04601e10 −1.75997
\(241\) 1.07229e10 0.204755 0.102377 0.994746i \(-0.467355\pi\)
0.102377 + 0.994746i \(0.467355\pi\)
\(242\) −2.09776e10 −0.393176
\(243\) −1.24034e11 −2.28198
\(244\) 2.81866e10 0.509082
\(245\) −2.12843e10 −0.377409
\(246\) 1.61458e10 0.281093
\(247\) −2.46564e10 −0.421496
\(248\) 4.94079e10 0.829399
\(249\) 1.20438e11 1.98549
\(250\) 7.33866e10 1.18819
\(251\) 4.66245e10 0.741451 0.370725 0.928743i \(-0.379109\pi\)
0.370725 + 0.928743i \(0.379109\pi\)
\(252\) −5.86190e10 −0.915663
\(253\) −2.16628e10 −0.332409
\(254\) 7.34803e10 1.10769
\(255\) 1.23390e11 1.82746
\(256\) −6.01218e10 −0.874888
\(257\) −2.77809e10 −0.397234 −0.198617 0.980077i \(-0.563645\pi\)
−0.198617 + 0.980077i \(0.563645\pi\)
\(258\) −1.65668e10 −0.232783
\(259\) 1.56004e11 2.15420
\(260\) −3.37996e10 −0.458703
\(261\) −9.19024e10 −1.22587
\(262\) 3.34073e10 0.438011
\(263\) −7.66179e10 −0.987482 −0.493741 0.869609i \(-0.664371\pi\)
−0.493741 + 0.869609i \(0.664371\pi\)
\(264\) 1.95371e11 2.47539
\(265\) −1.15484e11 −1.43852
\(266\) −3.81162e10 −0.466812
\(267\) 6.00102e10 0.722645
\(268\) −1.93018e9 −0.0228556
\(269\) −5.82715e10 −0.678533 −0.339266 0.940690i \(-0.610179\pi\)
−0.339266 + 0.940690i \(0.610179\pi\)
\(270\) −3.35983e11 −3.84752
\(271\) 5.01640e10 0.564977 0.282488 0.959271i \(-0.408840\pi\)
0.282488 + 0.959271i \(0.408840\pi\)
\(272\) −2.90856e10 −0.322194
\(273\) 1.54723e11 1.68587
\(274\) 5.22807e10 0.560356
\(275\) −2.14686e11 −2.26364
\(276\) 1.63534e10 0.169636
\(277\) −6.47834e10 −0.661157 −0.330579 0.943778i \(-0.607244\pi\)
−0.330579 + 0.943778i \(0.607244\pi\)
\(278\) −1.26192e11 −1.26716
\(279\) 1.92029e11 1.89735
\(280\) −2.09423e11 −2.03617
\(281\) 5.01006e10 0.479363 0.239682 0.970852i \(-0.422957\pi\)
0.239682 + 0.970852i \(0.422957\pi\)
\(282\) −2.20060e11 −2.07214
\(283\) 2.09526e11 1.94177 0.970887 0.239540i \(-0.0769966\pi\)
0.970887 + 0.239540i \(0.0769966\pi\)
\(284\) 3.56298e10 0.324998
\(285\) 1.81792e11 1.63220
\(286\) −9.17996e10 −0.811323
\(287\) 2.34087e10 0.203661
\(288\) −1.84210e11 −1.57779
\(289\) −7.89144e10 −0.665451
\(290\) −8.19182e10 −0.680126
\(291\) 2.50086e11 2.04443
\(292\) −1.25923e9 −0.0101364
\(293\) −2.20081e11 −1.74453 −0.872264 0.489035i \(-0.837349\pi\)
−0.872264 + 0.489035i \(0.837349\pi\)
\(294\) 4.36398e10 0.340659
\(295\) −3.92411e11 −3.01677
\(296\) 2.80058e11 2.12048
\(297\) 4.54435e11 3.38897
\(298\) 1.70538e11 1.25271
\(299\) −3.07980e10 −0.222845
\(300\) 1.62068e11 1.15519
\(301\) −2.40192e10 −0.168659
\(302\) −1.42680e11 −0.987031
\(303\) −3.39286e11 −2.31246
\(304\) −4.28522e10 −0.287768
\(305\) 3.91382e11 2.58971
\(306\) −1.80509e11 −1.17694
\(307\) 4.15422e10 0.266911 0.133455 0.991055i \(-0.457393\pi\)
0.133455 + 0.991055i \(0.457393\pi\)
\(308\) 7.06717e10 0.447474
\(309\) −1.48840e11 −0.928767
\(310\) 1.71167e11 1.05267
\(311\) 7.16229e10 0.434140 0.217070 0.976156i \(-0.430350\pi\)
0.217070 + 0.976156i \(0.430350\pi\)
\(312\) 2.77759e11 1.65948
\(313\) −1.61891e11 −0.953398 −0.476699 0.879067i \(-0.658167\pi\)
−0.476699 + 0.879067i \(0.658167\pi\)
\(314\) 1.91700e11 1.11286
\(315\) −8.13947e11 −4.65799
\(316\) −8.66953e10 −0.489107
\(317\) −7.64203e9 −0.0425052 −0.0212526 0.999774i \(-0.506765\pi\)
−0.0212526 + 0.999774i \(0.506765\pi\)
\(318\) 2.36780e11 1.29844
\(319\) 1.10799e11 0.599068
\(320\) −3.40900e11 −1.81740
\(321\) −1.18908e11 −0.625085
\(322\) −4.76105e10 −0.246803
\(323\) 5.84515e10 0.298803
\(324\) −1.78829e11 −0.901543
\(325\) −3.05219e11 −1.51753
\(326\) −2.29577e11 −1.12577
\(327\) −2.43641e11 −1.17838
\(328\) 4.20233e10 0.200474
\(329\) −3.19050e11 −1.50133
\(330\) 6.76839e11 3.14176
\(331\) 1.41081e11 0.646014 0.323007 0.946396i \(-0.395306\pi\)
0.323007 + 0.946396i \(0.395306\pi\)
\(332\) 7.82100e10 0.353298
\(333\) 1.08848e12 4.85087
\(334\) −1.57110e10 −0.0690787
\(335\) −2.68013e10 −0.116267
\(336\) 2.68905e11 1.15099
\(337\) 1.00695e11 0.425279 0.212640 0.977131i \(-0.431794\pi\)
0.212640 + 0.977131i \(0.431794\pi\)
\(338\) 6.55399e10 0.273137
\(339\) 9.94103e9 0.0408820
\(340\) 8.01268e10 0.325179
\(341\) −2.31513e11 −0.927215
\(342\) −2.65947e11 −1.05118
\(343\) −2.20238e11 −0.859151
\(344\) −4.31193e10 −0.166019
\(345\) 2.27074e11 0.862941
\(346\) 3.79443e11 1.42332
\(347\) −2.91880e11 −1.08074 −0.540370 0.841428i \(-0.681716\pi\)
−0.540370 + 0.841428i \(0.681716\pi\)
\(348\) −8.36428e10 −0.305719
\(349\) −7.88123e10 −0.284367 −0.142184 0.989840i \(-0.545412\pi\)
−0.142184 + 0.989840i \(0.545412\pi\)
\(350\) −4.71836e11 −1.68068
\(351\) 6.46070e11 2.27194
\(352\) 2.22086e11 0.771045
\(353\) −4.57862e11 −1.56945 −0.784726 0.619842i \(-0.787197\pi\)
−0.784726 + 0.619842i \(0.787197\pi\)
\(354\) 8.04571e11 2.72301
\(355\) 4.94734e11 1.65327
\(356\) 3.89694e10 0.128588
\(357\) −3.66793e11 −1.19513
\(358\) −4.15273e9 −0.0133617
\(359\) −6.39676e10 −0.203252 −0.101626 0.994823i \(-0.532405\pi\)
−0.101626 + 0.994823i \(0.532405\pi\)
\(360\) −1.46120e12 −4.58510
\(361\) −2.36570e11 −0.733125
\(362\) −2.37332e11 −0.726387
\(363\) −2.97415e11 −0.899047
\(364\) 1.00474e11 0.299984
\(365\) −1.74849e10 −0.0515638
\(366\) −8.02461e11 −2.33754
\(367\) 5.56082e10 0.160008 0.0800039 0.996795i \(-0.474507\pi\)
0.0800039 + 0.996795i \(0.474507\pi\)
\(368\) −5.35261e10 −0.152143
\(369\) 1.63328e11 0.458609
\(370\) 9.70226e11 2.69132
\(371\) 3.43292e11 0.940765
\(372\) 1.74771e11 0.473180
\(373\) −2.47592e11 −0.662289 −0.331145 0.943580i \(-0.607435\pi\)
−0.331145 + 0.943580i \(0.607435\pi\)
\(374\) 2.17624e11 0.575154
\(375\) 1.04045e12 2.71696
\(376\) −5.72759e11 −1.47784
\(377\) 1.57522e11 0.401612
\(378\) 9.98755e11 2.51620
\(379\) 2.02764e11 0.504794 0.252397 0.967624i \(-0.418781\pi\)
0.252397 + 0.967624i \(0.418781\pi\)
\(380\) 1.18052e11 0.290434
\(381\) 1.04178e12 2.53288
\(382\) −3.41943e10 −0.0821615
\(383\) −7.84097e10 −0.186198 −0.0930990 0.995657i \(-0.529677\pi\)
−0.0930990 + 0.995657i \(0.529677\pi\)
\(384\) 1.94641e11 0.456819
\(385\) 9.81305e11 2.27631
\(386\) −1.42944e11 −0.327734
\(387\) −1.67588e11 −0.379790
\(388\) 1.62401e11 0.363786
\(389\) 2.70312e11 0.598539 0.299270 0.954169i \(-0.403257\pi\)
0.299270 + 0.954169i \(0.403257\pi\)
\(390\) 9.62262e11 2.10622
\(391\) 7.30110e10 0.157977
\(392\) 1.13583e11 0.242956
\(393\) 4.73639e11 1.00157
\(394\) −4.45769e11 −0.931915
\(395\) −1.20380e12 −2.48809
\(396\) 4.93095e11 1.00763
\(397\) −6.70016e11 −1.35372 −0.676859 0.736113i \(-0.736659\pi\)
−0.676859 + 0.736113i \(0.736659\pi\)
\(398\) −4.55301e11 −0.909546
\(399\) −5.40401e11 −1.06743
\(400\) −5.30463e11 −1.03606
\(401\) 3.58493e11 0.692359 0.346179 0.938168i \(-0.387479\pi\)
0.346179 + 0.938168i \(0.387479\pi\)
\(402\) 5.49515e10 0.104945
\(403\) −3.29142e11 −0.621599
\(404\) −2.20325e11 −0.411480
\(405\) −2.48312e12 −4.58616
\(406\) 2.43513e11 0.444790
\(407\) −1.31228e12 −2.37056
\(408\) −6.58467e11 −1.17642
\(409\) −2.93226e11 −0.518140 −0.259070 0.965859i \(-0.583416\pi\)
−0.259070 + 0.965859i \(0.583416\pi\)
\(410\) 1.45584e11 0.254441
\(411\) 7.41221e11 1.28133
\(412\) −9.66537e10 −0.165265
\(413\) 1.16649e12 1.97291
\(414\) −3.32190e11 −0.555757
\(415\) 1.08598e12 1.79723
\(416\) 3.15740e11 0.516904
\(417\) −1.78912e12 −2.89752
\(418\) 3.20628e11 0.513699
\(419\) −2.52617e11 −0.400404 −0.200202 0.979755i \(-0.564160\pi\)
−0.200202 + 0.979755i \(0.564160\pi\)
\(420\) −7.40796e11 −1.16165
\(421\) 1.22137e11 0.189486 0.0947429 0.995502i \(-0.469797\pi\)
0.0947429 + 0.995502i \(0.469797\pi\)
\(422\) 2.85578e11 0.438347
\(423\) −2.22609e12 −3.38074
\(424\) 6.16278e11 0.926042
\(425\) 7.23564e11 1.07579
\(426\) −1.01437e12 −1.49228
\(427\) −1.16343e12 −1.69362
\(428\) −7.72166e10 −0.111228
\(429\) −1.30151e12 −1.85519
\(430\) −1.49381e11 −0.210712
\(431\) 1.01246e12 1.41329 0.706643 0.707571i \(-0.250209\pi\)
0.706643 + 0.707571i \(0.250209\pi\)
\(432\) 1.12285e12 1.55112
\(433\) −9.36722e11 −1.28061 −0.640303 0.768123i \(-0.721191\pi\)
−0.640303 + 0.768123i \(0.721191\pi\)
\(434\) −5.08818e11 −0.688429
\(435\) −1.16141e12 −1.55520
\(436\) −1.58215e11 −0.209681
\(437\) 1.07568e11 0.141097
\(438\) 3.58498e10 0.0465428
\(439\) −5.85451e10 −0.0752316 −0.0376158 0.999292i \(-0.511976\pi\)
−0.0376158 + 0.999292i \(0.511976\pi\)
\(440\) 1.76164e12 2.24068
\(441\) 4.41455e11 0.555792
\(442\) 3.09396e11 0.385580
\(443\) 1.20731e12 1.48936 0.744681 0.667421i \(-0.232602\pi\)
0.744681 + 0.667421i \(0.232602\pi\)
\(444\) 9.90652e11 1.20976
\(445\) 5.41105e11 0.654127
\(446\) 1.23682e12 1.48013
\(447\) 2.41785e12 2.86447
\(448\) 1.01337e12 1.18855
\(449\) −1.34315e11 −0.155961 −0.0779807 0.996955i \(-0.524847\pi\)
−0.0779807 + 0.996955i \(0.524847\pi\)
\(450\) −3.29212e12 −3.78460
\(451\) −1.96911e11 −0.224117
\(452\) 6.45550e9 0.00727456
\(453\) −2.02287e12 −2.25698
\(454\) 4.03426e11 0.445669
\(455\) 1.39512e12 1.52602
\(456\) −9.70129e11 −1.05072
\(457\) 6.04169e11 0.647941 0.323970 0.946067i \(-0.394982\pi\)
0.323970 + 0.946067i \(0.394982\pi\)
\(458\) 8.29909e10 0.0881325
\(459\) −1.53160e12 −1.61060
\(460\) 1.47457e11 0.153552
\(461\) −7.96508e11 −0.821364 −0.410682 0.911779i \(-0.634709\pi\)
−0.410682 + 0.911779i \(0.634709\pi\)
\(462\) −2.01200e12 −2.05465
\(463\) 1.60119e12 1.61930 0.809652 0.586910i \(-0.199656\pi\)
0.809652 + 0.586910i \(0.199656\pi\)
\(464\) 2.73770e11 0.274192
\(465\) 2.42676e12 2.40707
\(466\) −5.09144e10 −0.0500154
\(467\) 1.97526e11 0.192176 0.0960879 0.995373i \(-0.469367\pi\)
0.0960879 + 0.995373i \(0.469367\pi\)
\(468\) 7.01033e11 0.675510
\(469\) 7.96706e10 0.0760362
\(470\) −1.98425e12 −1.87567
\(471\) 2.71787e12 2.54469
\(472\) 2.09409e12 1.94204
\(473\) 2.02046e11 0.185599
\(474\) 2.46818e12 2.24582
\(475\) 1.06604e12 0.960841
\(476\) −2.38188e11 −0.212661
\(477\) 2.39524e12 2.11844
\(478\) −4.67508e11 −0.409604
\(479\) −1.31380e12 −1.14030 −0.570149 0.821541i \(-0.693115\pi\)
−0.570149 + 0.821541i \(0.693115\pi\)
\(480\) −2.32795e12 −2.00165
\(481\) −1.86567e12 −1.58921
\(482\) −1.98240e11 −0.167293
\(483\) −6.75008e11 −0.564348
\(484\) −1.93135e11 −0.159977
\(485\) 2.25500e12 1.85058
\(486\) 2.29309e12 1.86448
\(487\) −1.13531e12 −0.914604 −0.457302 0.889312i \(-0.651184\pi\)
−0.457302 + 0.889312i \(0.651184\pi\)
\(488\) −2.08860e12 −1.66712
\(489\) −3.25488e12 −2.57422
\(490\) 3.93495e11 0.308360
\(491\) −2.16799e11 −0.168341 −0.0841707 0.996451i \(-0.526824\pi\)
−0.0841707 + 0.996451i \(0.526824\pi\)
\(492\) 1.48650e11 0.114372
\(493\) −3.73429e11 −0.284706
\(494\) 4.55837e11 0.344380
\(495\) 6.84681e12 5.12584
\(496\) −5.72040e11 −0.424384
\(497\) −1.47066e12 −1.08121
\(498\) −2.22661e12 −1.62223
\(499\) −1.61040e12 −1.16274 −0.581368 0.813641i \(-0.697482\pi\)
−0.581368 + 0.813641i \(0.697482\pi\)
\(500\) 6.75650e11 0.483456
\(501\) −2.22746e11 −0.157957
\(502\) −8.61973e11 −0.605797
\(503\) −1.85720e12 −1.29361 −0.646803 0.762657i \(-0.723894\pi\)
−0.646803 + 0.762657i \(0.723894\pi\)
\(504\) 4.34361e12 2.99857
\(505\) −3.05930e12 −2.09320
\(506\) 4.00493e11 0.271592
\(507\) 9.29207e11 0.624563
\(508\) 6.76513e11 0.450702
\(509\) 1.23771e11 0.0817312 0.0408656 0.999165i \(-0.486988\pi\)
0.0408656 + 0.999165i \(0.486988\pi\)
\(510\) −2.28118e12 −1.49312
\(511\) 5.19762e10 0.0337218
\(512\) 1.49171e12 0.959335
\(513\) −2.25653e12 −1.43851
\(514\) 5.13601e11 0.324557
\(515\) −1.34207e12 −0.840705
\(516\) −1.52526e11 −0.0947155
\(517\) 2.68380e12 1.65213
\(518\) −2.88413e12 −1.76007
\(519\) 5.37964e12 3.25462
\(520\) 2.50452e12 1.50214
\(521\) −3.54135e11 −0.210571 −0.105286 0.994442i \(-0.533576\pi\)
−0.105286 + 0.994442i \(0.533576\pi\)
\(522\) 1.69905e12 1.00159
\(523\) −9.79180e11 −0.572275 −0.286138 0.958188i \(-0.592371\pi\)
−0.286138 + 0.958188i \(0.592371\pi\)
\(524\) 3.07571e11 0.178219
\(525\) −6.68956e12 −3.84309
\(526\) 1.41648e12 0.806815
\(527\) 7.80277e11 0.440657
\(528\) −2.26199e12 −1.26660
\(529\) −1.66679e12 −0.925402
\(530\) 2.13502e12 1.17533
\(531\) 8.13893e12 4.44265
\(532\) −3.50925e11 −0.189938
\(533\) −2.79948e11 −0.150247
\(534\) −1.10944e12 −0.590431
\(535\) −1.07218e12 −0.565818
\(536\) 1.43025e11 0.0748462
\(537\) −5.88763e10 −0.0305532
\(538\) 1.07730e12 0.554390
\(539\) −5.32223e11 −0.271609
\(540\) −3.09330e12 −1.56549
\(541\) −1.88732e12 −0.947234 −0.473617 0.880731i \(-0.657052\pi\)
−0.473617 + 0.880731i \(0.657052\pi\)
\(542\) −9.27411e11 −0.461610
\(543\) −3.36483e12 −1.66098
\(544\) −7.48506e11 −0.366438
\(545\) −2.19688e12 −1.06665
\(546\) −2.86045e12 −1.37743
\(547\) −9.25517e11 −0.442020 −0.221010 0.975272i \(-0.570935\pi\)
−0.221010 + 0.975272i \(0.570935\pi\)
\(548\) 4.81334e11 0.227999
\(549\) −8.11758e12 −3.81374
\(550\) 3.96902e12 1.84949
\(551\) −5.50178e11 −0.254285
\(552\) −1.21178e12 −0.555516
\(553\) 3.57845e12 1.62717
\(554\) 1.19769e12 0.540194
\(555\) 1.37556e13 6.15405
\(556\) −1.16182e12 −0.515586
\(557\) 4.04068e12 1.77871 0.889356 0.457215i \(-0.151153\pi\)
0.889356 + 0.457215i \(0.151153\pi\)
\(558\) −3.55015e12 −1.55022
\(559\) 2.87249e11 0.124424
\(560\) 2.42468e12 1.04186
\(561\) 3.08541e12 1.31516
\(562\) −9.26239e11 −0.391660
\(563\) −1.31953e12 −0.553517 −0.276758 0.960940i \(-0.589260\pi\)
−0.276758 + 0.960940i \(0.589260\pi\)
\(564\) −2.02603e12 −0.843120
\(565\) 8.96371e10 0.0370058
\(566\) −3.87362e12 −1.58651
\(567\) 7.38140e12 2.99927
\(568\) −2.64014e12 −1.06429
\(569\) −1.40113e12 −0.560366 −0.280183 0.959947i \(-0.590395\pi\)
−0.280183 + 0.959947i \(0.590395\pi\)
\(570\) −3.36089e12 −1.33358
\(571\) −7.55062e11 −0.297249 −0.148624 0.988894i \(-0.547485\pi\)
−0.148624 + 0.988894i \(0.547485\pi\)
\(572\) −8.45173e11 −0.330114
\(573\) −4.84797e11 −0.187873
\(574\) −4.32770e11 −0.166400
\(575\) 1.33157e12 0.507995
\(576\) 7.07054e12 2.67640
\(577\) 2.44025e12 0.916521 0.458261 0.888818i \(-0.348473\pi\)
0.458261 + 0.888818i \(0.348473\pi\)
\(578\) 1.45894e12 0.543702
\(579\) −2.02662e12 −0.749407
\(580\) −7.54198e11 −0.276732
\(581\) −3.22821e12 −1.17536
\(582\) −4.62349e12 −1.67038
\(583\) −2.88772e12 −1.03525
\(584\) 9.33078e10 0.0331940
\(585\) 9.73411e12 3.43633
\(586\) 4.06876e12 1.42535
\(587\) −5.63814e12 −1.96004 −0.980019 0.198906i \(-0.936261\pi\)
−0.980019 + 0.198906i \(0.936261\pi\)
\(588\) 4.01780e11 0.138609
\(589\) 1.14959e12 0.393573
\(590\) 7.25473e12 2.46483
\(591\) −6.31998e12 −2.13095
\(592\) −3.24248e12 −1.08500
\(593\) 2.07785e12 0.690031 0.345016 0.938597i \(-0.387874\pi\)
0.345016 + 0.938597i \(0.387874\pi\)
\(594\) −8.40139e12 −2.76893
\(595\) −3.30733e12 −1.08181
\(596\) 1.57010e12 0.509705
\(597\) −6.45513e12 −2.07980
\(598\) 5.69380e11 0.182074
\(599\) 2.05195e12 0.651248 0.325624 0.945499i \(-0.394426\pi\)
0.325624 + 0.945499i \(0.394426\pi\)
\(600\) −1.20091e13 −3.78295
\(601\) −3.93140e12 −1.22917 −0.614586 0.788850i \(-0.710677\pi\)
−0.614586 + 0.788850i \(0.710677\pi\)
\(602\) 4.44056e11 0.137801
\(603\) 5.55882e11 0.171220
\(604\) −1.31361e12 −0.401607
\(605\) −2.68175e12 −0.813803
\(606\) 6.27257e12 1.88938
\(607\) 2.33530e12 0.698221 0.349110 0.937082i \(-0.386484\pi\)
0.349110 + 0.937082i \(0.386484\pi\)
\(608\) −1.10278e12 −0.327284
\(609\) 3.45246e12 1.01707
\(610\) −7.23569e12 −2.11590
\(611\) 3.81557e12 1.10758
\(612\) −1.66190e12 −0.478875
\(613\) 1.39331e12 0.398544 0.199272 0.979944i \(-0.436142\pi\)
0.199272 + 0.979944i \(0.436142\pi\)
\(614\) −7.68013e11 −0.218078
\(615\) 2.06406e12 0.581813
\(616\) −5.23671e12 −1.46536
\(617\) 6.75919e11 0.187764 0.0938818 0.995583i \(-0.470072\pi\)
0.0938818 + 0.995583i \(0.470072\pi\)
\(618\) 2.75169e12 0.758842
\(619\) −3.04638e12 −0.834019 −0.417010 0.908902i \(-0.636922\pi\)
−0.417010 + 0.908902i \(0.636922\pi\)
\(620\) 1.57589e12 0.428315
\(621\) −2.81860e12 −0.760538
\(622\) −1.32413e12 −0.354711
\(623\) −1.60851e12 −0.427787
\(624\) −3.21587e12 −0.849118
\(625\) 2.28658e12 0.599414
\(626\) 2.99298e12 0.778967
\(627\) 4.54578e12 1.17464
\(628\) 1.76493e12 0.452802
\(629\) 4.42283e12 1.12661
\(630\) 1.50479e13 3.80578
\(631\) −5.72611e12 −1.43790 −0.718948 0.695064i \(-0.755376\pi\)
−0.718948 + 0.695064i \(0.755376\pi\)
\(632\) 6.42404e12 1.60170
\(633\) 4.04884e12 1.00234
\(634\) 1.41283e11 0.0347286
\(635\) 9.39364e12 2.29273
\(636\) 2.17997e12 0.528315
\(637\) −7.56661e11 −0.182085
\(638\) −2.04840e12 −0.489464
\(639\) −1.02612e13 −2.43469
\(640\) 1.75506e12 0.413506
\(641\) 7.81185e10 0.0182765 0.00913825 0.999958i \(-0.497091\pi\)
0.00913825 + 0.999958i \(0.497091\pi\)
\(642\) 2.19832e12 0.510722
\(643\) −1.63383e12 −0.376927 −0.188464 0.982080i \(-0.560351\pi\)
−0.188464 + 0.982080i \(0.560351\pi\)
\(644\) −4.38336e11 −0.100420
\(645\) −2.11789e12 −0.481819
\(646\) −1.08063e12 −0.244134
\(647\) 4.02702e12 0.903471 0.451735 0.892152i \(-0.350805\pi\)
0.451735 + 0.892152i \(0.350805\pi\)
\(648\) 1.32511e13 2.95233
\(649\) −9.81239e12 −2.17107
\(650\) 5.64276e12 1.23988
\(651\) −7.21389e12 −1.57418
\(652\) −2.11365e12 −0.458057
\(653\) 5.84257e12 1.25746 0.628730 0.777623i \(-0.283575\pi\)
0.628730 + 0.777623i \(0.283575\pi\)
\(654\) 4.50432e12 0.962785
\(655\) 4.27075e12 0.906605
\(656\) −4.86542e11 −0.102578
\(657\) 3.62651e11 0.0759355
\(658\) 5.89846e12 1.22665
\(659\) 4.19256e11 0.0865955 0.0432977 0.999062i \(-0.486214\pi\)
0.0432977 + 0.999062i \(0.486214\pi\)
\(660\) 6.23147e12 1.27833
\(661\) −4.51791e12 −0.920515 −0.460258 0.887785i \(-0.652243\pi\)
−0.460258 + 0.887785i \(0.652243\pi\)
\(662\) −2.60824e12 −0.527821
\(663\) 4.38653e12 0.881678
\(664\) −5.79529e12 −1.15696
\(665\) −4.87274e12 −0.966219
\(666\) −2.01233e13 −3.96337
\(667\) −6.87220e11 −0.134440
\(668\) −1.44647e11 −0.0281070
\(669\) 1.75353e13 3.38451
\(670\) 4.95492e11 0.0949948
\(671\) 9.78665e12 1.86373
\(672\) 6.92016e12 1.30904
\(673\) −3.13452e12 −0.588983 −0.294492 0.955654i \(-0.595150\pi\)
−0.294492 + 0.955654i \(0.595150\pi\)
\(674\) −1.86161e12 −0.347471
\(675\) −2.79333e13 −5.17911
\(676\) 6.03407e11 0.111135
\(677\) 9.08025e12 1.66130 0.830651 0.556793i \(-0.187968\pi\)
0.830651 + 0.556793i \(0.187968\pi\)
\(678\) −1.83785e11 −0.0334024
\(679\) −6.70329e12 −1.21025
\(680\) −5.93732e12 −1.06488
\(681\) 5.71966e12 1.01908
\(682\) 4.28011e12 0.757574
\(683\) 9.92561e12 1.74528 0.872638 0.488367i \(-0.162407\pi\)
0.872638 + 0.488367i \(0.162407\pi\)
\(684\) −2.44850e12 −0.427707
\(685\) 6.68351e12 1.15984
\(686\) 4.07167e12 0.701963
\(687\) 1.17662e12 0.201526
\(688\) 4.99231e11 0.0849481
\(689\) −4.10548e12 −0.694028
\(690\) −4.19804e12 −0.705060
\(691\) 2.83695e12 0.473370 0.236685 0.971586i \(-0.423939\pi\)
0.236685 + 0.971586i \(0.423939\pi\)
\(692\) 3.49342e12 0.579127
\(693\) −2.03531e13 −3.35220
\(694\) 5.39614e12 0.883011
\(695\) −1.61323e13 −2.62279
\(696\) 6.19786e12 1.00115
\(697\) 6.63655e11 0.106511
\(698\) 1.45705e12 0.232340
\(699\) −7.21850e11 −0.114367
\(700\) −4.34406e12 −0.683841
\(701\) −9.36363e11 −0.146458 −0.0732290 0.997315i \(-0.523330\pi\)
−0.0732290 + 0.997315i \(0.523330\pi\)
\(702\) −1.19443e13 −1.85627
\(703\) 6.51622e12 1.00623
\(704\) −8.52433e12 −1.30793
\(705\) −2.81322e13 −4.28896
\(706\) 8.46475e12 1.28231
\(707\) 9.09420e12 1.36892
\(708\) 7.40746e12 1.10795
\(709\) 5.31394e12 0.789785 0.394892 0.918727i \(-0.370782\pi\)
0.394892 + 0.918727i \(0.370782\pi\)
\(710\) −9.14643e12 −1.35079
\(711\) 2.49678e13 3.66409
\(712\) −2.88760e12 −0.421092
\(713\) 1.43594e12 0.208082
\(714\) 6.78111e12 0.976470
\(715\) −1.17356e13 −1.67929
\(716\) −3.82330e10 −0.00543663
\(717\) −6.62820e12 −0.936612
\(718\) 1.18261e12 0.166066
\(719\) 6.83793e12 0.954212 0.477106 0.878846i \(-0.341686\pi\)
0.477106 + 0.878846i \(0.341686\pi\)
\(720\) 1.69176e13 2.34608
\(721\) 3.98950e12 0.549806
\(722\) 4.37361e12 0.598994
\(723\) −2.81059e12 −0.382538
\(724\) −2.18505e12 −0.295555
\(725\) −6.81059e12 −0.915511
\(726\) 5.49847e12 0.734560
\(727\) 6.36741e12 0.845392 0.422696 0.906272i \(-0.361084\pi\)
0.422696 + 0.906272i \(0.361084\pi\)
\(728\) −7.44504e12 −0.982371
\(729\) 1.18310e13 1.55148
\(730\) 3.23253e11 0.0421299
\(731\) −6.80964e11 −0.0882055
\(732\) −7.38803e12 −0.951106
\(733\) 5.47275e12 0.700226 0.350113 0.936708i \(-0.386143\pi\)
0.350113 + 0.936708i \(0.386143\pi\)
\(734\) −1.02806e12 −0.130733
\(735\) 5.57887e12 0.705104
\(736\) −1.37747e12 −0.173035
\(737\) −6.70178e11 −0.0836732
\(738\) −3.01954e12 −0.374703
\(739\) −1.09212e13 −1.34701 −0.673503 0.739185i \(-0.735211\pi\)
−0.673503 + 0.739185i \(0.735211\pi\)
\(740\) 8.93260e12 1.09505
\(741\) 6.46274e12 0.787471
\(742\) −6.34663e12 −0.768645
\(743\) 1.41066e11 0.0169813 0.00849066 0.999964i \(-0.497297\pi\)
0.00849066 + 0.999964i \(0.497297\pi\)
\(744\) −1.29504e13 −1.54955
\(745\) 2.18014e13 2.59288
\(746\) 4.57738e12 0.541118
\(747\) −2.25240e13 −2.64669
\(748\) 2.00360e12 0.234021
\(749\) 3.18721e12 0.370034
\(750\) −1.92355e13 −2.21987
\(751\) 1.07431e13 1.23240 0.616200 0.787590i \(-0.288671\pi\)
0.616200 + 0.787590i \(0.288671\pi\)
\(752\) 6.63135e12 0.756174
\(753\) −1.22208e13 −1.38523
\(754\) −2.91221e12 −0.328134
\(755\) −1.82400e13 −2.04298
\(756\) 9.19526e12 1.02380
\(757\) −3.92377e12 −0.434282 −0.217141 0.976140i \(-0.569673\pi\)
−0.217141 + 0.976140i \(0.569673\pi\)
\(758\) −3.74861e12 −0.412438
\(759\) 5.67807e12 0.621031
\(760\) −8.74754e12 −0.951097
\(761\) 2.65761e12 0.287250 0.143625 0.989632i \(-0.454124\pi\)
0.143625 + 0.989632i \(0.454124\pi\)
\(762\) −1.92600e13 −2.06947
\(763\) 6.53052e12 0.697569
\(764\) −3.14817e11 −0.0334302
\(765\) −2.30761e13 −2.43605
\(766\) 1.44960e12 0.152132
\(767\) −1.39503e13 −1.45547
\(768\) 1.57586e13 1.63453
\(769\) 3.14923e12 0.324740 0.162370 0.986730i \(-0.448086\pi\)
0.162370 + 0.986730i \(0.448086\pi\)
\(770\) −1.81419e13 −1.85984
\(771\) 7.28169e12 0.742143
\(772\) −1.31604e12 −0.133350
\(773\) 3.67725e11 0.0370438 0.0185219 0.999828i \(-0.494104\pi\)
0.0185219 + 0.999828i \(0.494104\pi\)
\(774\) 3.09829e12 0.310305
\(775\) 1.42307e13 1.41699
\(776\) −1.20338e13 −1.19131
\(777\) −4.08904e13 −4.02463
\(778\) −4.99742e12 −0.489032
\(779\) 9.77773e11 0.0951304
\(780\) 8.85928e12 0.856984
\(781\) 1.23710e13 1.18980
\(782\) −1.34980e12 −0.129074
\(783\) 1.44163e13 1.37064
\(784\) −1.31506e12 −0.124315
\(785\) 2.45067e13 2.30341
\(786\) −8.75643e12 −0.818325
\(787\) −1.46553e13 −1.36179 −0.680895 0.732381i \(-0.738409\pi\)
−0.680895 + 0.732381i \(0.738409\pi\)
\(788\) −4.10407e12 −0.379181
\(789\) 2.00824e13 1.84489
\(790\) 2.22553e13 2.03288
\(791\) −2.66458e11 −0.0242011
\(792\) −3.65379e13 −3.29974
\(793\) 1.39137e13 1.24943
\(794\) 1.23870e13 1.10604
\(795\) 3.02697e13 2.68755
\(796\) −4.19183e12 −0.370079
\(797\) −2.07106e13 −1.81815 −0.909075 0.416633i \(-0.863210\pi\)
−0.909075 + 0.416633i \(0.863210\pi\)
\(798\) 9.99070e12 0.872134
\(799\) −9.04533e12 −0.785171
\(800\) −1.36512e13 −1.17833
\(801\) −1.12230e13 −0.963300
\(802\) −6.62767e12 −0.565687
\(803\) −4.37217e11 −0.0371088
\(804\) 5.05923e11 0.0427004
\(805\) −6.08647e12 −0.510839
\(806\) 6.08503e12 0.507873
\(807\) 1.52736e13 1.26768
\(808\) 1.63259e13 1.34749
\(809\) 1.94599e12 0.159725 0.0798623 0.996806i \(-0.474552\pi\)
0.0798623 + 0.996806i \(0.474552\pi\)
\(810\) 4.59068e13 3.74709
\(811\) 1.32679e11 0.0107698 0.00538491 0.999986i \(-0.498286\pi\)
0.00538491 + 0.999986i \(0.498286\pi\)
\(812\) 2.24196e12 0.180978
\(813\) −1.31486e13 −1.05553
\(814\) 2.42609e13 1.93685
\(815\) −2.93489e13 −2.33014
\(816\) 7.62367e12 0.601947
\(817\) −1.00327e12 −0.0787807
\(818\) 5.42103e12 0.423343
\(819\) −2.89360e13 −2.24730
\(820\) 1.34036e12 0.103528
\(821\) 1.39889e13 1.07458 0.537290 0.843398i \(-0.319448\pi\)
0.537290 + 0.843398i \(0.319448\pi\)
\(822\) −1.37034e13 −1.04690
\(823\) −2.70521e12 −0.205543 −0.102771 0.994705i \(-0.532771\pi\)
−0.102771 + 0.994705i \(0.532771\pi\)
\(824\) 7.16195e12 0.541201
\(825\) 5.62717e13 4.22909
\(826\) −2.15657e13 −1.61195
\(827\) −7.17939e11 −0.0533719 −0.0266859 0.999644i \(-0.508495\pi\)
−0.0266859 + 0.999644i \(0.508495\pi\)
\(828\) −3.05838e12 −0.226128
\(829\) −1.65304e12 −0.121559 −0.0607796 0.998151i \(-0.519359\pi\)
−0.0607796 + 0.998151i \(0.519359\pi\)
\(830\) −2.00771e13 −1.46841
\(831\) 1.69805e13 1.23522
\(832\) −1.21190e13 −0.876825
\(833\) 1.79377e12 0.129082
\(834\) 3.30764e13 2.36740
\(835\) −2.00848e12 −0.142981
\(836\) 2.95193e12 0.209016
\(837\) −3.01227e13 −2.12143
\(838\) 4.67027e12 0.327148
\(839\) 1.51228e13 1.05366 0.526832 0.849969i \(-0.323380\pi\)
0.526832 + 0.849969i \(0.323380\pi\)
\(840\) 5.48923e13 3.80412
\(841\) −1.09922e13 −0.757711
\(842\) −2.25801e12 −0.154818
\(843\) −1.31320e13 −0.895582
\(844\) 2.62923e12 0.178356
\(845\) 8.37855e12 0.565345
\(846\) 4.11550e13 2.76221
\(847\) 7.97187e12 0.532212
\(848\) −7.13521e12 −0.473833
\(849\) −5.49191e13 −3.62776
\(850\) −1.33769e13 −0.878965
\(851\) 8.13932e12 0.531992
\(852\) −9.33899e12 −0.607186
\(853\) −1.14817e13 −0.742568 −0.371284 0.928519i \(-0.621082\pi\)
−0.371284 + 0.928519i \(0.621082\pi\)
\(854\) 2.15091e13 1.38376
\(855\) −3.39983e13 −2.17575
\(856\) 5.72168e12 0.364243
\(857\) 1.99397e13 1.26271 0.631356 0.775493i \(-0.282499\pi\)
0.631356 + 0.775493i \(0.282499\pi\)
\(858\) 2.40617e13 1.51577
\(859\) 1.38539e13 0.868164 0.434082 0.900873i \(-0.357073\pi\)
0.434082 + 0.900873i \(0.357073\pi\)
\(860\) −1.37531e12 −0.0857350
\(861\) −6.13569e12 −0.380495
\(862\) −1.87179e13 −1.15471
\(863\) −2.96018e13 −1.81664 −0.908321 0.418275i \(-0.862635\pi\)
−0.908321 + 0.418275i \(0.862635\pi\)
\(864\) 2.88961e13 1.76412
\(865\) 4.85076e13 2.94603
\(866\) 1.73177e13 1.04631
\(867\) 2.06844e13 1.24324
\(868\) −4.68455e12 −0.280110
\(869\) −3.01014e13 −1.79060
\(870\) 2.14717e13 1.27066
\(871\) −9.52792e11 −0.0560940
\(872\) 1.17236e13 0.686652
\(873\) −4.67706e13 −2.72526
\(874\) −1.98867e12 −0.115282
\(875\) −2.78883e13 −1.60837
\(876\) 3.30059e11 0.0189375
\(877\) −5.98845e12 −0.341835 −0.170918 0.985285i \(-0.554673\pi\)
−0.170918 + 0.985285i \(0.554673\pi\)
\(878\) 1.08236e12 0.0614674
\(879\) 5.76858e13 3.25926
\(880\) −2.03961e13 −1.14650
\(881\) 4.47788e10 0.00250427 0.00125213 0.999999i \(-0.499601\pi\)
0.00125213 + 0.999999i \(0.499601\pi\)
\(882\) −8.16142e12 −0.454106
\(883\) 1.82152e13 1.00835 0.504175 0.863601i \(-0.331797\pi\)
0.504175 + 0.863601i \(0.331797\pi\)
\(884\) 2.84852e12 0.156886
\(885\) 1.02856e14 5.63615
\(886\) −2.23201e13 −1.21687
\(887\) −1.08674e13 −0.589483 −0.294741 0.955577i \(-0.595234\pi\)
−0.294741 + 0.955577i \(0.595234\pi\)
\(888\) −7.34064e13 −3.96165
\(889\) −2.79239e13 −1.49940
\(890\) −1.00037e13 −0.534450
\(891\) −6.20913e13 −3.30051
\(892\) 1.13871e13 0.602241
\(893\) −1.33266e13 −0.701275
\(894\) −4.47001e13 −2.34040
\(895\) −5.30881e11 −0.0276562
\(896\) −5.21715e12 −0.270425
\(897\) 8.07252e12 0.416335
\(898\) 2.48316e12 0.127427
\(899\) −7.34440e12 −0.375005
\(900\) −3.03096e13 −1.53989
\(901\) 9.73261e12 0.492003
\(902\) 3.64040e12 0.183113
\(903\) 6.29571e12 0.315101
\(904\) −4.78347e11 −0.0238224
\(905\) −3.03403e13 −1.50349
\(906\) 3.73980e13 1.84405
\(907\) −2.21516e13 −1.08686 −0.543429 0.839455i \(-0.682874\pi\)
−0.543429 + 0.839455i \(0.682874\pi\)
\(908\) 3.71423e12 0.181335
\(909\) 6.34525e13 3.08256
\(910\) −2.57924e13 −1.24682
\(911\) 8.34279e12 0.401309 0.200654 0.979662i \(-0.435693\pi\)
0.200654 + 0.979662i \(0.435693\pi\)
\(912\) 1.12321e13 0.537629
\(913\) 2.71553e13 1.29341
\(914\) −1.11696e13 −0.529395
\(915\) −1.02586e14 −4.83829
\(916\) 7.64074e11 0.0358596
\(917\) −1.26954e13 −0.592903
\(918\) 2.83155e13 1.31593
\(919\) −1.73492e13 −0.802341 −0.401170 0.916003i \(-0.631396\pi\)
−0.401170 + 0.916003i \(0.631396\pi\)
\(920\) −1.09264e13 −0.502844
\(921\) −1.08887e13 −0.498663
\(922\) 1.47255e13 0.671090
\(923\) 1.75879e13 0.797638
\(924\) −1.85239e13 −0.836004
\(925\) 8.06635e13 3.62276
\(926\) −2.96021e13 −1.32304
\(927\) 2.78357e13 1.23807
\(928\) 7.04535e12 0.311844
\(929\) −1.11298e13 −0.490247 −0.245124 0.969492i \(-0.578829\pi\)
−0.245124 + 0.969492i \(0.578829\pi\)
\(930\) −4.48650e13 −1.96668
\(931\) 2.64279e12 0.115289
\(932\) −4.68754e11 −0.0203504
\(933\) −1.87732e13 −0.811093
\(934\) −3.65178e12 −0.157016
\(935\) 2.78208e13 1.19047
\(936\) −5.19459e13 −2.21213
\(937\) −2.31541e13 −0.981297 −0.490648 0.871358i \(-0.663240\pi\)
−0.490648 + 0.871358i \(0.663240\pi\)
\(938\) −1.47292e12 −0.0621248
\(939\) 4.24336e13 1.78121
\(940\) −1.82685e13 −0.763179
\(941\) 6.27432e12 0.260864 0.130432 0.991457i \(-0.458364\pi\)
0.130432 + 0.991457i \(0.458364\pi\)
\(942\) −5.02468e13 −2.07912
\(943\) 1.22132e12 0.0502954
\(944\) −2.42452e13 −0.993693
\(945\) 1.27680e14 5.20810
\(946\) −3.73534e12 −0.151642
\(947\) −1.95848e12 −0.0791305 −0.0395652 0.999217i \(-0.512597\pi\)
−0.0395652 + 0.999217i \(0.512597\pi\)
\(948\) 2.27238e13 0.913785
\(949\) −6.21591e11 −0.0248775
\(950\) −1.97084e13 −0.785048
\(951\) 2.00306e12 0.0794114
\(952\) 1.76495e13 0.696412
\(953\) −3.01343e13 −1.18343 −0.591716 0.806146i \(-0.701549\pi\)
−0.591716 + 0.806146i \(0.701549\pi\)
\(954\) −4.42821e13 −1.73085
\(955\) −4.37136e12 −0.170060
\(956\) −4.30422e12 −0.166661
\(957\) −2.90416e13 −1.11922
\(958\) 2.42889e13 0.931672
\(959\) −1.98676e13 −0.758512
\(960\) 8.93537e13 3.39541
\(961\) −1.10936e13 −0.419581
\(962\) 3.44917e13 1.29845
\(963\) 2.22379e13 0.833252
\(964\) −1.82514e12 −0.0680689
\(965\) −1.82738e13 −0.678352
\(966\) 1.24793e13 0.461096
\(967\) −4.59576e13 −1.69020 −0.845099 0.534609i \(-0.820459\pi\)
−0.845099 + 0.534609i \(0.820459\pi\)
\(968\) 1.43111e13 0.523883
\(969\) −1.53208e13 −0.558245
\(970\) −4.16895e13 −1.51201
\(971\) 5.92518e11 0.0213902 0.0106951 0.999943i \(-0.496596\pi\)
0.0106951 + 0.999943i \(0.496596\pi\)
\(972\) 2.11118e13 0.758625
\(973\) 4.79554e13 1.71526
\(974\) 2.09891e13 0.747270
\(975\) 8.00015e13 2.83516
\(976\) 2.41816e13 0.853024
\(977\) −3.04374e13 −1.06876 −0.534382 0.845243i \(-0.679456\pi\)
−0.534382 + 0.845243i \(0.679456\pi\)
\(978\) 6.01748e13 2.10325
\(979\) 1.35306e13 0.470753
\(980\) 3.62280e12 0.125466
\(981\) 4.55651e13 1.57080
\(982\) 4.00809e12 0.137542
\(983\) 2.48900e13 0.850225 0.425113 0.905140i \(-0.360235\pi\)
0.425113 + 0.905140i \(0.360235\pi\)
\(984\) −1.10148e13 −0.374540
\(985\) −5.69866e13 −1.92890
\(986\) 6.90379e12 0.232617
\(987\) 8.36267e13 2.80490
\(988\) 4.19677e12 0.140123
\(989\) −1.25318e12 −0.0416513
\(990\) −1.26581e14 −4.18803
\(991\) 7.06033e12 0.232538 0.116269 0.993218i \(-0.462907\pi\)
0.116269 + 0.993218i \(0.462907\pi\)
\(992\) −1.47212e13 −0.482660
\(993\) −3.69789e13 −1.20693
\(994\) 2.71890e13 0.883394
\(995\) −5.82052e13 −1.88260
\(996\) −2.04997e13 −0.660057
\(997\) −1.27122e13 −0.407468 −0.203734 0.979026i \(-0.565308\pi\)
−0.203734 + 0.979026i \(0.565308\pi\)
\(998\) 2.97724e13 0.950005
\(999\) −1.70744e14 −5.42376
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.1.5 15
3.2 odd 2 387.10.a.c.1.11 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.10.a.a.1.5 15 1.1 even 1 trivial
387.10.a.c.1.11 15 3.2 odd 2