Properties

Label 43.11.b.b.42.10
Level 43
Weight 11
Character 43.42
Analytic conductor 27.320
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(27.3203618650\)
Analytic rank: \(0\)
Dimension: \(34\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.10
Character \(\chi\) \(=\) 43.42
Dual form 43.11.b.b.42.25

$q$-expansion

\(f(q)\) \(=\) \(q-30.3109i q^{2} -212.897i q^{3} +105.247 q^{4} -1632.05i q^{5} -6453.11 q^{6} +7423.10i q^{7} -34228.5i q^{8} +13723.9 q^{9} +O(q^{10})\) \(q-30.3109i q^{2} -212.897i q^{3} +105.247 q^{4} -1632.05i q^{5} -6453.11 q^{6} +7423.10i q^{7} -34228.5i q^{8} +13723.9 q^{9} -49468.9 q^{10} -129685. q^{11} -22406.7i q^{12} -477616. q^{13} +225001. q^{14} -347458. q^{15} -929727. q^{16} -239065. q^{17} -415984. i q^{18} -2.40703e6i q^{19} -171768. i q^{20} +1.58035e6 q^{21} +3.93086e6i q^{22} -1.07661e7 q^{23} -7.28715e6 q^{24} +7.10204e6 q^{25} +1.44770e7i q^{26} -1.54931e7i q^{27} +781256. i q^{28} +3.05676e7i q^{29} +1.05318e7i q^{30} +1.70986e7 q^{31} -6.86913e6i q^{32} +2.76094e7i q^{33} +7.24629e6i q^{34} +1.21149e7 q^{35} +1.44439e6 q^{36} +2.92417e7i q^{37} -7.29593e7 q^{38} +1.01683e8i q^{39} -5.58626e7 q^{40} -6.33921e7 q^{41} -4.79020e7i q^{42} +(5.97263e7 + 1.34329e8i) q^{43} -1.36489e7 q^{44} -2.23981e7i q^{45} +3.26331e8i q^{46} +1.73838e7 q^{47} +1.97936e8i q^{48} +2.27373e8 q^{49} -2.15270e8i q^{50} +5.08962e7i q^{51} -5.02674e7 q^{52} -9.26195e7 q^{53} -4.69611e8 q^{54} +2.11651e8i q^{55} +2.54082e8 q^{56} -5.12449e8 q^{57} +9.26533e8 q^{58} -8.79381e8 q^{59} -3.65688e7 q^{60} -1.35810e9i q^{61} -5.18273e8i q^{62} +1.01874e8i q^{63} -1.16025e9 q^{64} +7.79492e8i q^{65} +8.36868e8 q^{66} +1.86000e8 q^{67} -2.51608e7 q^{68} +2.29207e9i q^{69} -3.67213e8i q^{70} -3.17203e9i q^{71} -4.69749e8i q^{72} -2.67560e9i q^{73} +8.86342e8 q^{74} -1.51200e9i q^{75} -2.53332e8i q^{76} -9.62661e8i q^{77} +3.08210e9 q^{78} +5.12315e9 q^{79} +1.51736e9i q^{80} -2.48806e9 q^{81} +1.92148e9i q^{82} -9.86767e8 q^{83} +1.66327e8 q^{84} +3.90166e8i q^{85} +(4.07164e9 - 1.81036e9i) q^{86} +6.50775e9 q^{87} +4.43891e9i q^{88} +5.62804e8i q^{89} -6.78906e8 q^{90} -3.54539e9i q^{91} -1.13310e9 q^{92} -3.64023e9i q^{93} -5.26918e8i q^{94} -3.92839e9 q^{95} -1.46242e9 q^{96} -1.18206e10 q^{97} -6.89189e9i q^{98} -1.77978e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} + O(q^{10}) \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} - 254122q^{10} - 218200q^{11} - 191008q^{13} - 1380228q^{14} - 512732q^{15} + 2224308q^{16} - 1070678q^{17} + 17857352q^{21} + 8915254q^{23} - 39666730q^{24} - 82938284q^{25} - 55042410q^{31} - 179227232q^{35} + 394381042q^{36} + 709061882q^{38} + 433255366q^{40} + 80370626q^{41} + 1585062q^{43} + 324477888q^{44} - 544910502q^{47} - 2479345922q^{49} - 987059452q^{52} - 915886820q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 3394816764q^{59} - 5474941192q^{60} + 2925325476q^{64} + 455136192q^{66} + 3405920388q^{67} + 664008226q^{68} + 16264108918q^{74} - 17800086268q^{78} - 13853150858q^{79} + 20444701546q^{81} + 113867236q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 41423783058q^{92} + 4107406010q^{95} + 33148445474q^{96} + 15795117154q^{97} + 1345877600q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 30.3109i 0.947217i −0.880735 0.473609i \(-0.842951\pi\)
0.880735 0.473609i \(-0.157049\pi\)
\(3\) 212.897i 0.876119i −0.898946 0.438060i \(-0.855666\pi\)
0.898946 0.438060i \(-0.144334\pi\)
\(4\) 105.247 0.102780
\(5\) 1632.05i 0.522256i −0.965304 0.261128i \(-0.915906\pi\)
0.965304 0.261128i \(-0.0840944\pi\)
\(6\) −6453.11 −0.829875
\(7\) 7423.10i 0.441667i 0.975312 + 0.220833i \(0.0708777\pi\)
−0.975312 + 0.220833i \(0.929122\pi\)
\(8\) 34228.5i 1.04457i
\(9\) 13723.9 0.232415
\(10\) −49468.9 −0.494689
\(11\) −129685. −0.805239 −0.402619 0.915367i \(-0.631900\pi\)
−0.402619 + 0.915367i \(0.631900\pi\)
\(12\) 22406.7i 0.0900475i
\(13\) −477616. −1.28636 −0.643179 0.765716i \(-0.722385\pi\)
−0.643179 + 0.765716i \(0.722385\pi\)
\(14\) 225001. 0.418354
\(15\) −347458. −0.457558
\(16\) −929727. −0.886656
\(17\) −239065. −0.168373 −0.0841863 0.996450i \(-0.526829\pi\)
−0.0841863 + 0.996450i \(0.526829\pi\)
\(18\) 415984.i 0.220148i
\(19\) 2.40703e6i 0.972105i −0.873929 0.486053i \(-0.838436\pi\)
0.873929 0.486053i \(-0.161564\pi\)
\(20\) 171768.i 0.0536774i
\(21\) 1.58035e6 0.386953
\(22\) 3.93086e6i 0.762736i
\(23\) −1.07661e7 −1.67271 −0.836353 0.548192i \(-0.815316\pi\)
−0.836353 + 0.548192i \(0.815316\pi\)
\(24\) −7.28715e6 −0.915169
\(25\) 7.10204e6 0.727249
\(26\) 1.44770e7i 1.21846i
\(27\) 1.54931e7i 1.07974i
\(28\) 781256.i 0.0453945i
\(29\) 3.05676e7i 1.49029i 0.666901 + 0.745146i \(0.267620\pi\)
−0.666901 + 0.745146i \(0.732380\pi\)
\(30\) 1.05318e7i 0.433407i
\(31\) 1.70986e7 0.597243 0.298621 0.954372i \(-0.403473\pi\)
0.298621 + 0.954372i \(0.403473\pi\)
\(32\) 6.86913e6i 0.204716i
\(33\) 2.76094e7i 0.705485i
\(34\) 7.24629e6i 0.159485i
\(35\) 1.21149e7 0.230663
\(36\) 1.44439e6 0.0238876
\(37\) 2.92417e7i 0.421690i 0.977519 + 0.210845i \(0.0676216\pi\)
−0.977519 + 0.210845i \(0.932378\pi\)
\(38\) −7.29593e7 −0.920795
\(39\) 1.01683e8i 1.12700i
\(40\) −5.58626e7 −0.545533
\(41\) −6.33921e7 −0.547162 −0.273581 0.961849i \(-0.588208\pi\)
−0.273581 + 0.961849i \(0.588208\pi\)
\(42\) 4.79020e7i 0.366528i
\(43\) 5.97263e7 + 1.34329e8i 0.406278 + 0.913749i
\(44\) −1.36489e7 −0.0827624
\(45\) 2.23981e7i 0.121380i
\(46\) 3.26331e8i 1.58442i
\(47\) 1.73838e7 0.0757974 0.0378987 0.999282i \(-0.487934\pi\)
0.0378987 + 0.999282i \(0.487934\pi\)
\(48\) 1.97936e8i 0.776817i
\(49\) 2.27373e8 0.804930
\(50\) 2.15270e8i 0.688863i
\(51\) 5.08962e7i 0.147514i
\(52\) −5.02674e7 −0.132212
\(53\) −9.26195e7 −0.221474 −0.110737 0.993850i \(-0.535321\pi\)
−0.110737 + 0.993850i \(0.535321\pi\)
\(54\) −4.69611e8 −1.02275
\(55\) 2.11651e8i 0.420540i
\(56\) 2.54082e8 0.461353
\(57\) −5.12449e8 −0.851680
\(58\) 9.26533e8 1.41163
\(59\) −8.79381e8 −1.23003 −0.615017 0.788514i \(-0.710851\pi\)
−0.615017 + 0.788514i \(0.710851\pi\)
\(60\) −3.65688e7 −0.0470278
\(61\) 1.35810e9i 1.60799i −0.594634 0.803996i \(-0.702703\pi\)
0.594634 0.803996i \(-0.297297\pi\)
\(62\) 5.18273e8i 0.565719i
\(63\) 1.01874e8i 0.102650i
\(64\) −1.16025e9 −1.08057
\(65\) 7.79492e8i 0.671807i
\(66\) 8.36868e8 0.668247
\(67\) 1.86000e8 0.137765 0.0688824 0.997625i \(-0.478057\pi\)
0.0688824 + 0.997625i \(0.478057\pi\)
\(68\) −2.51608e7 −0.0173053
\(69\) 2.29207e9i 1.46549i
\(70\) 3.67213e8i 0.218488i
\(71\) 3.17203e9i 1.75811i −0.476721 0.879055i \(-0.658175\pi\)
0.476721 0.879055i \(-0.341825\pi\)
\(72\) 4.69749e8i 0.242775i
\(73\) 2.67560e9i 1.29064i −0.763911 0.645321i \(-0.776723\pi\)
0.763911 0.645321i \(-0.223277\pi\)
\(74\) 8.86342e8 0.399432
\(75\) 1.51200e9i 0.637157i
\(76\) 2.53332e8i 0.0999129i
\(77\) 9.62661e8i 0.355647i
\(78\) 3.08210e9 1.06752
\(79\) 5.12315e9 1.66495 0.832477 0.554060i \(-0.186922\pi\)
0.832477 + 0.554060i \(0.186922\pi\)
\(80\) 1.51736e9i 0.463061i
\(81\) −2.48806e9 −0.713568
\(82\) 1.92148e9i 0.518281i
\(83\) −9.86767e8 −0.250509 −0.125255 0.992125i \(-0.539975\pi\)
−0.125255 + 0.992125i \(0.539975\pi\)
\(84\) 1.66327e8 0.0397710
\(85\) 3.90166e8i 0.0879336i
\(86\) 4.07164e9 1.81036e9i 0.865519 0.384834i
\(87\) 6.50775e9 1.30567
\(88\) 4.43891e9i 0.841130i
\(89\) 5.62804e8i 0.100788i 0.998729 + 0.0503938i \(0.0160476\pi\)
−0.998729 + 0.0503938i \(0.983952\pi\)
\(90\) −6.78906e8 −0.114973
\(91\) 3.54539e9i 0.568142i
\(92\) −1.13310e9 −0.171921
\(93\) 3.64023e9i 0.523256i
\(94\) 5.26918e8i 0.0717966i
\(95\) −3.92839e9 −0.507687
\(96\) −1.46242e9 −0.179356
\(97\) −1.18206e10 −1.37651 −0.688256 0.725468i \(-0.741624\pi\)
−0.688256 + 0.725468i \(0.741624\pi\)
\(98\) 6.89189e9i 0.762444i
\(99\) −1.77978e9 −0.187150
\(100\) 7.47466e8 0.0747466
\(101\) 4.69755e9 0.446956 0.223478 0.974709i \(-0.428259\pi\)
0.223478 + 0.974709i \(0.428259\pi\)
\(102\) 1.54271e9 0.139728
\(103\) −1.46350e10 −1.26243 −0.631213 0.775609i \(-0.717443\pi\)
−0.631213 + 0.775609i \(0.717443\pi\)
\(104\) 1.63481e10i 1.34369i
\(105\) 2.57922e9i 0.202088i
\(106\) 2.80738e9i 0.209784i
\(107\) −2.01715e10 −1.43820 −0.719101 0.694906i \(-0.755446\pi\)
−0.719101 + 0.694906i \(0.755446\pi\)
\(108\) 1.63060e9i 0.110976i
\(109\) −7.33490e8 −0.0476718 −0.0238359 0.999716i \(-0.507588\pi\)
−0.0238359 + 0.999716i \(0.507588\pi\)
\(110\) 6.41535e9 0.398343
\(111\) 6.22546e9 0.369451
\(112\) 6.90145e9i 0.391607i
\(113\) 1.80819e9i 0.0981412i −0.998795 0.0490706i \(-0.984374\pi\)
0.998795 0.0490706i \(-0.0156259\pi\)
\(114\) 1.55328e10i 0.806726i
\(115\) 1.75708e10i 0.873580i
\(116\) 3.21714e9i 0.153172i
\(117\) −6.55474e9 −0.298969
\(118\) 2.66549e10i 1.16511i
\(119\) 1.77460e9i 0.0743646i
\(120\) 1.18930e10i 0.477952i
\(121\) −9.11935e9 −0.351590
\(122\) −4.11654e10 −1.52312
\(123\) 1.34960e10i 0.479379i
\(124\) 1.79957e9 0.0613846
\(125\) 2.75289e10i 0.902065i
\(126\) 3.08789e9 0.0972320
\(127\) 6.50848e10 1.96998 0.984989 0.172619i \(-0.0552231\pi\)
0.984989 + 0.172619i \(0.0552231\pi\)
\(128\) 2.81343e10i 0.818815i
\(129\) 2.85982e10 1.27156e10i 0.800553 0.355948i
\(130\) 2.36271e10 0.636347
\(131\) 7.67234e9i 0.198871i −0.995044 0.0994355i \(-0.968296\pi\)
0.995044 0.0994355i \(-0.0317037\pi\)
\(132\) 2.90580e9i 0.0725097i
\(133\) 1.78676e10 0.429347
\(134\) 5.63783e9i 0.130493i
\(135\) −2.52855e10 −0.563902
\(136\) 8.18285e9i 0.175877i
\(137\) 3.77817e10i 0.782850i 0.920210 + 0.391425i \(0.128018\pi\)
−0.920210 + 0.391425i \(0.871982\pi\)
\(138\) 6.94748e10 1.38814
\(139\) 1.48235e10 0.285679 0.142839 0.989746i \(-0.454377\pi\)
0.142839 + 0.989746i \(0.454377\pi\)
\(140\) 1.27505e9 0.0237075
\(141\) 3.70095e9i 0.0664076i
\(142\) −9.61473e10 −1.66531
\(143\) 6.19393e10 1.03582
\(144\) −1.27595e10 −0.206073
\(145\) 4.98878e10 0.778314
\(146\) −8.10998e10 −1.22252
\(147\) 4.84070e10i 0.705215i
\(148\) 3.07759e9i 0.0433413i
\(149\) 3.79213e10i 0.516359i −0.966097 0.258179i \(-0.916877\pi\)
0.966097 0.258179i \(-0.0831226\pi\)
\(150\) −4.58302e10 −0.603526
\(151\) 1.08043e11i 1.37629i −0.725571 0.688147i \(-0.758424\pi\)
0.725571 0.688147i \(-0.241576\pi\)
\(152\) −8.23891e10 −1.01543
\(153\) −3.28090e9 −0.0391324
\(154\) −2.91792e10 −0.336875
\(155\) 2.79057e10i 0.311913i
\(156\) 1.07018e10i 0.115833i
\(157\) 6.90568e10i 0.723950i −0.932188 0.361975i \(-0.882103\pi\)
0.932188 0.361975i \(-0.117897\pi\)
\(158\) 1.55288e11i 1.57707i
\(159\) 1.97184e10i 0.194038i
\(160\) −1.12107e10 −0.106914
\(161\) 7.99178e10i 0.738779i
\(162\) 7.54154e10i 0.675904i
\(163\) 4.29270e10i 0.373071i 0.982448 + 0.186536i \(0.0597260\pi\)
−0.982448 + 0.186536i \(0.940274\pi\)
\(164\) −6.67181e9 −0.0562373
\(165\) 4.50599e10 0.368443
\(166\) 2.99098e10i 0.237287i
\(167\) 2.11428e10 0.162772 0.0813861 0.996683i \(-0.474065\pi\)
0.0813861 + 0.996683i \(0.474065\pi\)
\(168\) 5.40932e10i 0.404200i
\(169\) 9.02581e10 0.654716
\(170\) 1.18263e10 0.0832922
\(171\) 3.30338e10i 0.225932i
\(172\) 6.28600e9 + 1.41377e10i 0.0417572 + 0.0939151i
\(173\) 8.80695e10 0.568323 0.284161 0.958776i \(-0.408285\pi\)
0.284161 + 0.958776i \(0.408285\pi\)
\(174\) 1.97256e11i 1.23676i
\(175\) 5.27192e10i 0.321202i
\(176\) 1.20571e11 0.713970
\(177\) 1.87217e11i 1.07766i
\(178\) 1.70591e10 0.0954677
\(179\) 1.34447e11i 0.731623i −0.930689 0.365811i \(-0.880792\pi\)
0.930689 0.365811i \(-0.119208\pi\)
\(180\) 2.35732e9i 0.0124754i
\(181\) 2.75284e11 1.41706 0.708529 0.705682i \(-0.249359\pi\)
0.708529 + 0.705682i \(0.249359\pi\)
\(182\) −1.07464e11 −0.538153
\(183\) −2.89136e11 −1.40879
\(184\) 3.68508e11i 1.74726i
\(185\) 4.77238e10 0.220230
\(186\) −1.10339e11 −0.495637
\(187\) 3.10030e10 0.135580
\(188\) 1.82958e9 0.00779045
\(189\) 1.15007e11 0.476887
\(190\) 1.19073e11i 0.480890i
\(191\) 8.67688e10i 0.341347i −0.985328 0.170674i \(-0.945406\pi\)
0.985328 0.170674i \(-0.0545944\pi\)
\(192\) 2.47014e11i 0.946705i
\(193\) −2.71466e10 −0.101374 −0.0506872 0.998715i \(-0.516141\pi\)
−0.0506872 + 0.998715i \(0.516141\pi\)
\(194\) 3.58293e11i 1.30386i
\(195\) 1.65951e11 0.588583
\(196\) 2.39302e10 0.0827307
\(197\) −2.23494e11 −0.753244 −0.376622 0.926367i \(-0.622914\pi\)
−0.376622 + 0.926367i \(0.622914\pi\)
\(198\) 5.39467e10i 0.177272i
\(199\) 3.59302e11i 1.15132i −0.817691 0.575658i \(-0.804746\pi\)
0.817691 0.575658i \(-0.195254\pi\)
\(200\) 2.43092e11i 0.759664i
\(201\) 3.95988e10i 0.120698i
\(202\) 1.42387e11i 0.423364i
\(203\) −2.26906e11 −0.658213
\(204\) 5.35666e9i 0.0151615i
\(205\) 1.03459e11i 0.285759i
\(206\) 4.43600e11i 1.19579i
\(207\) −1.47753e11 −0.388762
\(208\) 4.44052e11 1.14056
\(209\) 3.12154e11i 0.782777i
\(210\) −7.81785e10 −0.191421
\(211\) 2.78564e11i 0.666060i −0.942916 0.333030i \(-0.891929\pi\)
0.942916 0.333030i \(-0.108071\pi\)
\(212\) −9.74789e9 −0.0227631
\(213\) −6.75316e11 −1.54031
\(214\) 6.11418e11i 1.36229i
\(215\) 2.19231e11 9.74763e10i 0.477211 0.212181i
\(216\) −5.30307e11 −1.12787
\(217\) 1.26924e11i 0.263782i
\(218\) 2.22328e10i 0.0451555i
\(219\) −5.69626e11 −1.13076
\(220\) 2.22756e10i 0.0432231i
\(221\) 1.14181e11 0.216587
\(222\) 1.88700e11i 0.349950i
\(223\) 1.02679e12i 1.86191i 0.365136 + 0.930954i \(0.381023\pi\)
−0.365136 + 0.930954i \(0.618977\pi\)
\(224\) 5.09902e10 0.0904163
\(225\) 9.74677e10 0.169024
\(226\) −5.48079e10 −0.0929610
\(227\) 1.07728e12i 1.78731i −0.448756 0.893654i \(-0.648133\pi\)
0.448756 0.893654i \(-0.351867\pi\)
\(228\) −5.39336e10 −0.0875356
\(229\) 1.64721e11 0.261561 0.130780 0.991411i \(-0.458252\pi\)
0.130780 + 0.991411i \(0.458252\pi\)
\(230\) 5.32588e11 0.827470
\(231\) −2.04948e11 −0.311589
\(232\) 1.04628e12 1.55672
\(233\) 8.24421e10i 0.120052i 0.998197 + 0.0600260i \(0.0191184\pi\)
−0.998197 + 0.0600260i \(0.980882\pi\)
\(234\) 1.98681e11i 0.283189i
\(235\) 2.83711e10i 0.0395856i
\(236\) −9.25519e10 −0.126423
\(237\) 1.09070e12i 1.45870i
\(238\) −5.37899e10 −0.0704395
\(239\) −1.36817e12 −1.75448 −0.877241 0.480049i \(-0.840619\pi\)
−0.877241 + 0.480049i \(0.840619\pi\)
\(240\) 3.23041e11 0.405697
\(241\) 1.06468e11i 0.130959i −0.997854 0.0654796i \(-0.979142\pi\)
0.997854 0.0654796i \(-0.0208577\pi\)
\(242\) 2.76416e11i 0.333033i
\(243\) 3.85154e11i 0.454572i
\(244\) 1.42936e11i 0.165269i
\(245\) 3.71084e11i 0.420379i
\(246\) 4.09076e11 0.454076
\(247\) 1.14963e12i 1.25048i
\(248\) 5.85258e11i 0.623863i
\(249\) 2.10080e11i 0.219476i
\(250\) −8.34426e11 −0.854452
\(251\) 8.97688e11 0.901066 0.450533 0.892760i \(-0.351234\pi\)
0.450533 + 0.892760i \(0.351234\pi\)
\(252\) 1.07219e10i 0.0105504i
\(253\) 1.39620e12 1.34693
\(254\) 1.97278e12i 1.86600i
\(255\) 8.30651e10 0.0770403
\(256\) −3.35319e11 −0.304971
\(257\) 7.32413e11i 0.653266i 0.945151 + 0.326633i \(0.105914\pi\)
−0.945151 + 0.326633i \(0.894086\pi\)
\(258\) −3.85420e11 8.66839e11i −0.337160 0.758298i
\(259\) −2.17064e11 −0.186247
\(260\) 8.20389e10i 0.0690483i
\(261\) 4.19507e11i 0.346367i
\(262\) −2.32556e11 −0.188374
\(263\) 6.19909e11i 0.492662i −0.969186 0.246331i \(-0.920775\pi\)
0.969186 0.246331i \(-0.0792250\pi\)
\(264\) 9.45030e11 0.736930
\(265\) 1.51159e11i 0.115666i
\(266\) 5.41584e11i 0.406685i
\(267\) 1.19819e11 0.0883019
\(268\) 1.95758e10 0.0141595
\(269\) 2.54278e12 1.80529 0.902647 0.430383i \(-0.141621\pi\)
0.902647 + 0.430383i \(0.141621\pi\)
\(270\) 7.66428e11i 0.534137i
\(271\) −3.45095e11 −0.236098 −0.118049 0.993008i \(-0.537664\pi\)
−0.118049 + 0.993008i \(0.537664\pi\)
\(272\) 2.22265e11 0.149289
\(273\) −7.54802e11 −0.497760
\(274\) 1.14520e12 0.741529
\(275\) −9.21025e11 −0.585609
\(276\) 2.41233e11i 0.150623i
\(277\) 8.63431e11i 0.529455i −0.964323 0.264727i \(-0.914718\pi\)
0.964323 0.264727i \(-0.0852820\pi\)
\(278\) 4.49315e11i 0.270600i
\(279\) 2.34659e11 0.138808
\(280\) 4.14674e11i 0.240944i
\(281\) 1.86458e12 1.06426 0.532131 0.846662i \(-0.321391\pi\)
0.532131 + 0.846662i \(0.321391\pi\)
\(282\) −1.12179e11 −0.0629024
\(283\) −1.56730e12 −0.863414 −0.431707 0.902014i \(-0.642089\pi\)
−0.431707 + 0.902014i \(0.642089\pi\)
\(284\) 3.33846e11i 0.180698i
\(285\) 8.36342e11i 0.444795i
\(286\) 1.87744e12i 0.981151i
\(287\) 4.70566e11i 0.241664i
\(288\) 9.42712e10i 0.0475791i
\(289\) −1.95884e12 −0.971651
\(290\) 1.51215e12i 0.737232i
\(291\) 2.51657e12i 1.20599i
\(292\) 2.81597e11i 0.132652i
\(293\) 2.56310e11 0.118694 0.0593469 0.998237i \(-0.481098\pi\)
0.0593469 + 0.998237i \(0.481098\pi\)
\(294\) −1.46726e12 −0.667991
\(295\) 1.43519e12i 0.642392i
\(296\) 1.00090e12 0.440486
\(297\) 2.00922e12i 0.869451i
\(298\) −1.14943e12 −0.489104
\(299\) 5.14206e12 2.15170
\(300\) 1.59133e11i 0.0654869i
\(301\) −9.97136e11 + 4.43354e11i −0.403573 + 0.179440i
\(302\) −3.27488e12 −1.30365
\(303\) 1.00009e12i 0.391586i
\(304\) 2.23788e12i 0.861923i
\(305\) −2.21649e12 −0.839783
\(306\) 9.94473e10i 0.0370669i
\(307\) −3.71438e12 −1.36205 −0.681027 0.732258i \(-0.738466\pi\)
−0.681027 + 0.732258i \(0.738466\pi\)
\(308\) 1.01317e11i 0.0365534i
\(309\) 3.11574e12i 1.10604i
\(310\) −8.45847e11 −0.295450
\(311\) 3.09364e12 1.06333 0.531665 0.846955i \(-0.321567\pi\)
0.531665 + 0.846955i \(0.321567\pi\)
\(312\) 3.48046e12 1.17724
\(313\) 2.23969e11i 0.0745530i −0.999305 0.0372765i \(-0.988132\pi\)
0.999305 0.0372765i \(-0.0118682\pi\)
\(314\) −2.09318e12 −0.685738
\(315\) 1.66263e11 0.0536096
\(316\) 5.39195e11 0.171124
\(317\) −4.04325e12 −1.26309 −0.631545 0.775339i \(-0.717579\pi\)
−0.631545 + 0.775339i \(0.717579\pi\)
\(318\) 5.97683e11 0.183796
\(319\) 3.96415e12i 1.20004i
\(320\) 1.89358e12i 0.564332i
\(321\) 4.29446e12i 1.26004i
\(322\) −2.42239e12 −0.699784
\(323\) 5.75437e11i 0.163676i
\(324\) −2.61860e11 −0.0733404
\(325\) −3.39205e12 −0.935502
\(326\) 1.30116e12 0.353380
\(327\) 1.56158e11i 0.0417662i
\(328\) 2.16982e12i 0.571550i
\(329\) 1.29041e11i 0.0334772i
\(330\) 1.36581e12i 0.348996i
\(331\) 5.99907e11i 0.150988i 0.997146 + 0.0754942i \(0.0240534\pi\)
−0.997146 + 0.0754942i \(0.975947\pi\)
\(332\) −1.03854e11 −0.0257473
\(333\) 4.01309e11i 0.0980073i
\(334\) 6.40859e11i 0.154181i
\(335\) 3.03561e11i 0.0719484i
\(336\) −1.46930e12 −0.343094
\(337\) 3.55603e12 0.818118 0.409059 0.912508i \(-0.365857\pi\)
0.409059 + 0.912508i \(0.365857\pi\)
\(338\) 2.73581e12i 0.620158i
\(339\) −3.84958e11 −0.0859833
\(340\) 4.10636e10i 0.00903780i
\(341\) −2.21742e12 −0.480923
\(342\) −1.00129e12 −0.214007
\(343\) 3.78465e12i 0.797178i
\(344\) 4.59788e12 2.04434e12i 0.954477 0.424387i
\(345\) 3.74077e12 0.765360
\(346\) 2.66947e12i 0.538325i
\(347\) 5.19453e12i 1.03252i −0.856432 0.516261i \(-0.827324\pi\)
0.856432 0.516261i \(-0.172676\pi\)
\(348\) 6.84919e11 0.134197
\(349\) 7.54441e12i 1.45713i 0.684977 + 0.728565i \(0.259812\pi\)
−0.684977 + 0.728565i \(0.740188\pi\)
\(350\) 1.59797e12 0.304248
\(351\) 7.39976e12i 1.38894i
\(352\) 8.90819e11i 0.164845i
\(353\) 2.57237e12 0.469310 0.234655 0.972079i \(-0.424604\pi\)
0.234655 + 0.972079i \(0.424604\pi\)
\(354\) 5.67474e12 1.02077
\(355\) −5.17691e12 −0.918182
\(356\) 5.92332e10i 0.0103589i
\(357\) −3.77808e11 −0.0651523
\(358\) −4.07523e12 −0.693005
\(359\) 8.39475e12 1.40778 0.703891 0.710308i \(-0.251444\pi\)
0.703891 + 0.710308i \(0.251444\pi\)
\(360\) −7.66653e11 −0.126790
\(361\) 3.37276e11 0.0550110
\(362\) 8.34411e12i 1.34226i
\(363\) 1.94148e12i 0.308035i
\(364\) 3.73140e11i 0.0583936i
\(365\) −4.36670e12 −0.674045
\(366\) 8.76400e12i 1.33443i
\(367\) 4.84782e12 0.728142 0.364071 0.931371i \(-0.381386\pi\)
0.364071 + 0.931371i \(0.381386\pi\)
\(368\) 1.00095e13 1.48311
\(369\) −8.69987e11 −0.127169
\(370\) 1.44655e12i 0.208606i
\(371\) 6.87523e11i 0.0978178i
\(372\) 3.83122e11i 0.0537802i
\(373\) 2.39635e12i 0.331899i −0.986134 0.165949i \(-0.946931\pi\)
0.986134 0.165949i \(-0.0530688\pi\)
\(374\) 9.39731e11i 0.128424i
\(375\) −5.86081e12 −0.790317
\(376\) 5.95021e11i 0.0791759i
\(377\) 1.45996e13i 1.91705i
\(378\) 3.48597e12i 0.451715i
\(379\) 1.05843e12 0.135352 0.0676759 0.997707i \(-0.478442\pi\)
0.0676759 + 0.997707i \(0.478442\pi\)
\(380\) −4.13450e11 −0.0521801
\(381\) 1.38564e13i 1.72593i
\(382\) −2.63004e12 −0.323330
\(383\) 6.61173e12i 0.802271i −0.916019 0.401135i \(-0.868616\pi\)
0.916019 0.401135i \(-0.131384\pi\)
\(384\) 5.98970e12 0.717380
\(385\) −1.57111e12 −0.185739
\(386\) 8.22838e11i 0.0960236i
\(387\) 8.19678e11 + 1.84352e12i 0.0944253 + 0.212369i
\(388\) −1.24408e12 −0.141478
\(389\) 1.12412e13i 1.26202i 0.775774 + 0.631010i \(0.217359\pi\)
−0.775774 + 0.631010i \(0.782641\pi\)
\(390\) 5.03014e12i 0.557516i
\(391\) 2.57380e12 0.281638
\(392\) 7.78264e12i 0.840808i
\(393\) −1.63342e12 −0.174235
\(394\) 6.77433e12i 0.713485i
\(395\) 8.36124e12i 0.869531i
\(396\) −1.87315e11 −0.0192352
\(397\) −6.78427e12 −0.687940 −0.343970 0.938981i \(-0.611772\pi\)
−0.343970 + 0.938981i \(0.611772\pi\)
\(398\) −1.08908e13 −1.09055
\(399\) 3.80396e12i 0.376159i
\(400\) −6.60296e12 −0.644820
\(401\) −6.72300e12 −0.648398 −0.324199 0.945989i \(-0.605095\pi\)
−0.324199 + 0.945989i \(0.605095\pi\)
\(402\) −1.20028e12 −0.114328
\(403\) −8.16653e12 −0.768268
\(404\) 4.94401e11 0.0459381
\(405\) 4.06063e12i 0.372665i
\(406\) 6.87775e12i 0.623471i
\(407\) 3.79219e12i 0.339561i
\(408\) 1.74210e12 0.154090
\(409\) 1.25823e13i 1.09937i −0.835374 0.549683i \(-0.814749\pi\)
0.835374 0.549683i \(-0.185251\pi\)
\(410\) 3.13594e12 0.270675
\(411\) 8.04361e12 0.685870
\(412\) −1.54028e12 −0.129752
\(413\) 6.52773e12i 0.543265i
\(414\) 4.47853e12i 0.368242i
\(415\) 1.61045e12i 0.130830i
\(416\) 3.28080e12i 0.263338i
\(417\) 3.15588e12i 0.250288i
\(418\) 9.46170e12 0.741460
\(419\) 8.22754e12i 0.637089i 0.947908 + 0.318545i \(0.103194\pi\)
−0.947908 + 0.318545i \(0.896806\pi\)
\(420\) 2.71454e11i 0.0207706i
\(421\) 1.51716e12i 0.114715i −0.998354 0.0573577i \(-0.981732\pi\)
0.998354 0.0573577i \(-0.0182676\pi\)
\(422\) −8.44355e12 −0.630903
\(423\) 2.38573e11 0.0176165
\(424\) 3.17023e12i 0.231346i
\(425\) −1.69785e12 −0.122449
\(426\) 2.04695e13i 1.45901i
\(427\) 1.00813e13 0.710197
\(428\) −2.12299e12 −0.147818
\(429\) 1.31867e13i 0.907506i
\(430\) −2.95460e12 6.64511e12i −0.200982 0.452022i
\(431\) 2.29491e13 1.54304 0.771522 0.636202i \(-0.219496\pi\)
0.771522 + 0.636202i \(0.219496\pi\)
\(432\) 1.44044e13i 0.957361i
\(433\) 1.61671e13i 1.06216i 0.847321 + 0.531082i \(0.178214\pi\)
−0.847321 + 0.531082i \(0.821786\pi\)
\(434\) 3.84719e12 0.249859
\(435\) 1.06210e13i 0.681895i
\(436\) −7.71973e10 −0.00489970
\(437\) 2.59143e13i 1.62605i
\(438\) 1.72659e13i 1.07107i
\(439\) 8.69720e12 0.533404 0.266702 0.963779i \(-0.414066\pi\)
0.266702 + 0.963779i \(0.414066\pi\)
\(440\) 7.24452e12 0.439285
\(441\) 3.12044e12 0.187078
\(442\) 3.46094e12i 0.205155i
\(443\) 3.97589e11 0.0233032 0.0116516 0.999932i \(-0.496291\pi\)
0.0116516 + 0.999932i \(0.496291\pi\)
\(444\) 6.55209e11 0.0379721
\(445\) 9.18523e11 0.0526369
\(446\) 3.11230e13 1.76363
\(447\) −8.07333e12 −0.452392
\(448\) 8.61265e12i 0.477251i
\(449\) 9.74296e12i 0.533899i 0.963711 + 0.266949i \(0.0860157\pi\)
−0.963711 + 0.266949i \(0.913984\pi\)
\(450\) 2.95434e12i 0.160102i
\(451\) 8.22098e12 0.440596
\(452\) 1.90306e11i 0.0100869i
\(453\) −2.30020e13 −1.20580
\(454\) −3.26534e13 −1.69297
\(455\) −5.78624e12 −0.296715
\(456\) 1.75404e13i 0.889641i
\(457\) 3.12316e13i 1.56680i 0.621517 + 0.783400i \(0.286517\pi\)
−0.621517 + 0.783400i \(0.713483\pi\)
\(458\) 4.99286e12i 0.247755i
\(459\) 3.70387e12i 0.181799i
\(460\) 1.84927e12i 0.0897865i
\(461\) −2.87113e12 −0.137895 −0.0689474 0.997620i \(-0.521964\pi\)
−0.0689474 + 0.997620i \(0.521964\pi\)
\(462\) 6.21215e12i 0.295143i
\(463\) 5.12515e11i 0.0240881i −0.999927 0.0120440i \(-0.996166\pi\)
0.999927 0.0120440i \(-0.00383383\pi\)
\(464\) 2.84195e13i 1.32138i
\(465\) −5.94103e12 −0.273273
\(466\) 2.49890e12 0.113715
\(467\) 1.78913e13i 0.805487i −0.915313 0.402743i \(-0.868057\pi\)
0.915313 0.402743i \(-0.131943\pi\)
\(468\) −6.89865e11 −0.0307280
\(469\) 1.38069e12i 0.0608462i
\(470\) −8.59956e11 −0.0374962
\(471\) −1.47020e13 −0.634266
\(472\) 3.00999e13i 1.28486i
\(473\) −7.74558e12 1.74204e13i −0.327151 0.735786i
\(474\) −3.30603e13 −1.38170
\(475\) 1.70948e13i 0.706963i
\(476\) 1.86771e11i 0.00764319i
\(477\) −1.27110e12 −0.0514740
\(478\) 4.14704e13i 1.66188i
\(479\) 1.85935e13 0.737365 0.368683 0.929555i \(-0.379809\pi\)
0.368683 + 0.929555i \(0.379809\pi\)
\(480\) 2.38673e12i 0.0936694i
\(481\) 1.39663e13i 0.542444i
\(482\) −3.22716e12 −0.124047
\(483\) −1.70143e13 −0.647258
\(484\) −9.59781e11 −0.0361364
\(485\) 1.92918e13i 0.718891i
\(486\) −1.16744e13 −0.430579
\(487\) 3.72914e13 1.36133 0.680666 0.732594i \(-0.261691\pi\)
0.680666 + 0.732594i \(0.261691\pi\)
\(488\) −4.64859e13 −1.67966
\(489\) 9.13902e12 0.326855
\(490\) −1.12479e13 −0.398190
\(491\) 4.75070e13i 1.66475i −0.554210 0.832377i \(-0.686980\pi\)
0.554210 0.832377i \(-0.313020\pi\)
\(492\) 1.42041e12i 0.0492706i
\(493\) 7.30765e12i 0.250925i
\(494\) 3.48465e13 1.18447
\(495\) 2.90468e12i 0.0977400i
\(496\) −1.58970e13 −0.529549
\(497\) 2.35463e13 0.776499
\(498\) 6.36771e12 0.207891
\(499\) 2.21002e13i 0.714322i 0.934043 + 0.357161i \(0.116255\pi\)
−0.934043 + 0.357161i \(0.883745\pi\)
\(500\) 2.89732e12i 0.0927142i
\(501\) 4.50124e12i 0.142608i
\(502\) 2.72098e13i 0.853505i
\(503\) 5.70484e13i 1.77176i −0.463918 0.885878i \(-0.653557\pi\)
0.463918 0.885878i \(-0.346443\pi\)
\(504\) 3.48699e12 0.107226
\(505\) 7.66663e12i 0.233425i
\(506\) 4.23201e13i 1.27583i
\(507\) 1.92157e13i 0.573609i
\(508\) 6.84996e12 0.202474
\(509\) −3.84448e13 −1.12525 −0.562625 0.826713i \(-0.690208\pi\)
−0.562625 + 0.826713i \(0.690208\pi\)
\(510\) 2.51778e12i 0.0729739i
\(511\) 1.98612e13 0.570034
\(512\) 3.89733e13i 1.10769i
\(513\) −3.72924e13 −1.04962
\(514\) 2.22001e13 0.618785
\(515\) 2.38850e13i 0.659309i
\(516\) 3.00987e12 1.33827e12i 0.0822808 0.0365843i
\(517\) −2.25440e12 −0.0610350
\(518\) 6.57941e12i 0.176416i
\(519\) 1.87497e13i 0.497918i
\(520\) 2.66809e13 0.701751
\(521\) 4.87724e13i 1.27053i 0.772294 + 0.635266i \(0.219109\pi\)
−0.772294 + 0.635266i \(0.780891\pi\)
\(522\) 1.27156e13 0.328085
\(523\) 4.72530e12i 0.120759i 0.998175 + 0.0603797i \(0.0192311\pi\)
−0.998175 + 0.0603797i \(0.980769\pi\)
\(524\) 8.07488e11i 0.0204399i
\(525\) 1.12237e13 0.281411
\(526\) −1.87900e13 −0.466658
\(527\) −4.08767e12 −0.100559
\(528\) 2.56692e13i 0.625523i
\(529\) 7.44825e13 1.79794
\(530\) 4.58179e12 0.109561
\(531\) −1.20685e13 −0.285879
\(532\) 1.88051e12 0.0441282
\(533\) 3.02771e13 0.703846
\(534\) 3.63183e12i 0.0836411i
\(535\) 3.29209e13i 0.751109i
\(536\) 6.36650e12i 0.143905i
\(537\) −2.86234e13 −0.640989
\(538\) 7.70741e13i 1.71000i
\(539\) −2.94867e13 −0.648161
\(540\) −2.66122e12 −0.0579578
\(541\) 9.01800e13 1.94592 0.972958 0.230982i \(-0.0741940\pi\)
0.972958 + 0.230982i \(0.0741940\pi\)
\(542\) 1.04602e13i 0.223636i
\(543\) 5.86071e13i 1.24151i
\(544\) 1.64217e12i 0.0344686i
\(545\) 1.19709e12i 0.0248969i
\(546\) 2.28788e13i 0.471487i
\(547\) 4.49477e13 0.917848 0.458924 0.888476i \(-0.348235\pi\)
0.458924 + 0.888476i \(0.348235\pi\)
\(548\) 3.97640e12i 0.0804613i
\(549\) 1.86385e13i 0.373722i
\(550\) 2.79171e13i 0.554699i
\(551\) 7.35771e13 1.44872
\(552\) 7.84542e13 1.53081
\(553\) 3.80297e13i 0.735355i
\(554\) −2.61714e13 −0.501509
\(555\) 1.01603e13i 0.192948i
\(556\) 1.56013e12 0.0293620
\(557\) −2.31786e12 −0.0432325 −0.0216163 0.999766i \(-0.506881\pi\)
−0.0216163 + 0.999766i \(0.506881\pi\)
\(558\) 7.11273e12i 0.131482i
\(559\) −2.85262e13 6.41576e13i −0.522619 1.17541i
\(560\) −1.12635e13 −0.204519
\(561\) 6.60045e12i 0.118784i
\(562\) 5.65170e13i 1.00809i
\(563\) −6.76439e13 −1.19588 −0.597939 0.801542i \(-0.704013\pi\)
−0.597939 + 0.801542i \(0.704013\pi\)
\(564\) 3.89512e11i 0.00682536i
\(565\) −2.95105e12 −0.0512548
\(566\) 4.75063e13i 0.817841i
\(567\) 1.84691e13i 0.315159i
\(568\) −1.08574e14 −1.83647
\(569\) −3.69123e13 −0.618885 −0.309442 0.950918i \(-0.600142\pi\)
−0.309442 + 0.950918i \(0.600142\pi\)
\(570\) 2.53503e13 0.421317
\(571\) 7.73272e13i 1.27395i 0.770885 + 0.636974i \(0.219814\pi\)
−0.770885 + 0.636974i \(0.780186\pi\)
\(572\) 6.51891e12 0.106462
\(573\) −1.84728e13 −0.299061
\(574\) −1.42633e13 −0.228908
\(575\) −7.64613e13 −1.21647
\(576\) −1.59231e13 −0.251140
\(577\) 7.14931e13i 1.11785i 0.829217 + 0.558927i \(0.188787\pi\)
−0.829217 + 0.558927i \(0.811213\pi\)
\(578\) 5.93743e13i 0.920364i
\(579\) 5.77942e12i 0.0888161i
\(580\) 5.25053e12 0.0799950
\(581\) 7.32487e12i 0.110642i
\(582\) 7.62795e13 1.14233
\(583\) 1.20113e13 0.178340
\(584\) −9.15817e13 −1.34817
\(585\) 1.06977e13i 0.156138i
\(586\) 7.76901e12i 0.112429i
\(587\) 5.18469e13i 0.743930i −0.928247 0.371965i \(-0.878684\pi\)
0.928247 0.371965i \(-0.121316\pi\)
\(588\) 5.09467e12i 0.0724819i
\(589\) 4.11567e13i 0.580583i
\(590\) 4.35020e13 0.608484
\(591\) 4.75813e13i 0.659931i
\(592\) 2.71868e13i 0.373894i
\(593\) 4.78819e13i 0.652977i 0.945201 + 0.326488i \(0.105865\pi\)
−0.945201 + 0.326488i \(0.894135\pi\)
\(594\) 6.09013e13 0.823558
\(595\) −2.89624e12 −0.0388373
\(596\) 3.99109e12i 0.0530713i
\(597\) −7.64943e13 −1.00869
\(598\) 1.55861e14i 2.03812i
\(599\) −3.77465e13 −0.489489 −0.244744 0.969588i \(-0.578704\pi\)
−0.244744 + 0.969588i \(0.578704\pi\)
\(600\) −5.17536e13 −0.665556
\(601\) 9.77475e13i 1.24662i 0.781976 + 0.623309i \(0.214212\pi\)
−0.781976 + 0.623309i \(0.785788\pi\)
\(602\) 1.34385e13 + 3.02241e13i 0.169968 + 0.382271i
\(603\) 2.55264e12 0.0320187
\(604\) 1.13711e13i 0.141455i
\(605\) 1.48832e13i 0.183620i
\(606\) −3.03138e13 −0.370917
\(607\) 8.67443e13i 1.05268i 0.850273 + 0.526341i \(0.176437\pi\)
−0.850273 + 0.526341i \(0.823563\pi\)
\(608\) −1.65342e13 −0.199005
\(609\) 4.83077e13i 0.576673i
\(610\) 6.71840e13i 0.795457i
\(611\) −8.30275e12 −0.0975026
\(612\) −3.45304e11 −0.00402202
\(613\) −9.99251e13 −1.15444 −0.577221 0.816588i \(-0.695863\pi\)
−0.577221 + 0.816588i \(0.695863\pi\)
\(614\) 1.12586e14i 1.29016i
\(615\) 2.20261e13 0.250358
\(616\) −3.29505e13 −0.371499
\(617\) 1.05976e14 1.18517 0.592587 0.805506i \(-0.298107\pi\)
0.592587 + 0.805506i \(0.298107\pi\)
\(618\) 9.44411e13 1.04766
\(619\) −3.85612e13 −0.424324 −0.212162 0.977235i \(-0.568050\pi\)
−0.212162 + 0.977235i \(0.568050\pi\)
\(620\) 2.93698e12i 0.0320584i
\(621\) 1.66801e14i 1.80609i
\(622\) 9.37712e13i 1.00720i
\(623\) −4.17775e12 −0.0445146
\(624\) 9.45373e13i 0.999264i
\(625\) 2.44275e13 0.256140
\(626\) −6.78870e12 −0.0706179
\(627\) 6.64567e13 0.685806
\(628\) 7.26800e12i 0.0744075i
\(629\) 6.99066e12i 0.0710011i
\(630\) 5.03959e12i 0.0507800i
\(631\) 5.20514e13i 0.520338i −0.965563 0.260169i \(-0.916222\pi\)
0.965563 0.260169i \(-0.0837783\pi\)
\(632\) 1.75358e14i 1.73916i
\(633\) −5.93055e13 −0.583548
\(634\) 1.22555e14i 1.19642i
\(635\) 1.06222e14i 1.02883i
\(636\) 2.07530e12i 0.0199432i
\(637\) −1.08597e14 −1.03543
\(638\) −1.20157e14 −1.13670
\(639\) 4.35326e13i 0.408612i
\(640\) 4.59165e13 0.427631
\(641\) 1.95638e14i 1.80785i 0.427689 + 0.903926i \(0.359328\pi\)
−0.427689 + 0.903926i \(0.640672\pi\)
\(642\) 1.30169e14 1.19353
\(643\) 9.21963e13 0.838800 0.419400 0.907802i \(-0.362240\pi\)
0.419400 + 0.907802i \(0.362240\pi\)
\(644\) 8.41108e12i 0.0759316i
\(645\) −2.07524e13 4.66737e13i −0.185896 0.418093i
\(646\) 1.74420e13 0.155037
\(647\) 6.37692e13i 0.562458i −0.959641 0.281229i \(-0.909258\pi\)
0.959641 0.281229i \(-0.0907420\pi\)
\(648\) 8.51625e13i 0.745373i
\(649\) 1.14042e14 0.990470
\(650\) 1.02816e14i 0.886124i
\(651\) 2.70218e13 0.231105
\(652\) 4.51792e12i 0.0383443i
\(653\) 2.02229e14i 1.70325i 0.524155 + 0.851623i \(0.324381\pi\)
−0.524155 + 0.851623i \(0.675619\pi\)
\(654\) 4.73329e12 0.0395616
\(655\) −1.25216e13 −0.103861
\(656\) 5.89374e13 0.485145
\(657\) 3.67196e13i 0.299965i
\(658\) 3.91137e12 0.0317102
\(659\) −8.46543e13 −0.681118 −0.340559 0.940223i \(-0.610616\pi\)
−0.340559 + 0.940223i \(0.610616\pi\)
\(660\) 4.74241e12 0.0378686
\(661\) −1.47490e14 −1.16884 −0.584419 0.811452i \(-0.698678\pi\)
−0.584419 + 0.811452i \(0.698678\pi\)
\(662\) 1.81837e13 0.143019
\(663\) 2.43088e13i 0.189756i
\(664\) 3.37756e13i 0.261675i
\(665\) 2.91608e13i 0.224229i
\(666\) 1.21641e13 0.0928341
\(667\) 3.29094e14i 2.49282i
\(668\) 2.22521e12 0.0167297
\(669\) 2.18601e14 1.63125
\(670\) −9.20121e12 −0.0681508
\(671\) 1.76125e14i 1.29482i
\(672\) 1.08557e13i 0.0792154i
\(673\) 1.06345e14i 0.770264i −0.922861 0.385132i \(-0.874156\pi\)
0.922861 0.385132i \(-0.125844\pi\)
\(674\) 1.07787e14i 0.774936i
\(675\) 1.10033e14i 0.785242i
\(676\) 9.49936e12 0.0672916
\(677\) 1.02179e14i 0.718488i 0.933244 + 0.359244i \(0.116965\pi\)
−0.933244 + 0.359244i \(0.883035\pi\)
\(678\) 1.16684e13i 0.0814449i
\(679\) 8.77453e13i 0.607960i
\(680\) 1.33548e13 0.0918529
\(681\) −2.29350e14 −1.56590
\(682\) 6.72120e13i 0.455538i
\(683\) −3.50693e13 −0.235952 −0.117976 0.993016i \(-0.537641\pi\)
−0.117976 + 0.993016i \(0.537641\pi\)
\(684\) 3.47670e12i 0.0232213i
\(685\) 6.16616e13 0.408848
\(686\) 1.14716e14 0.755101
\(687\) 3.50687e13i 0.229158i
\(688\) −5.55292e13 1.24889e14i −0.360229 0.810182i
\(689\) 4.42365e13 0.284895
\(690\) 1.13386e14i 0.724962i
\(691\) 6.02940e13i 0.382722i −0.981520 0.191361i \(-0.938710\pi\)
0.981520 0.191361i \(-0.0612901\pi\)
\(692\) 9.26902e12 0.0584122
\(693\) 1.32115e13i 0.0826579i
\(694\) −1.57451e14 −0.978022
\(695\) 2.41927e13i 0.149197i
\(696\) 2.22751e14i 1.36387i
\(697\) 1.51548e13 0.0921272
\(698\) 2.28678e14 1.38022
\(699\) 1.75517e13 0.105180
\(700\) 5.54851e12i 0.0330131i
\(701\) −2.04936e14 −1.21068 −0.605338 0.795968i \(-0.706962\pi\)
−0.605338 + 0.795968i \(0.706962\pi\)
\(702\) 2.24294e14 1.31562
\(703\) 7.03855e13 0.409927
\(704\) 1.50466e14 0.870114
\(705\) −6.04013e12 −0.0346817
\(706\) 7.79709e13i 0.444538i
\(707\) 3.48704e13i 0.197406i
\(708\) 1.97040e13i 0.110761i
\(709\) 4.40105e13 0.245655 0.122827 0.992428i \(-0.460804\pi\)
0.122827 + 0.992428i \(0.460804\pi\)
\(710\) 1.56917e14i 0.869718i
\(711\) 7.03096e13 0.386961
\(712\) 1.92640e13 0.105280
\(713\) −1.84085e14 −0.999011
\(714\) 1.14517e13i 0.0617134i
\(715\) 1.01088e14i 0.540965i
\(716\) 1.41501e13i 0.0751961i
\(717\) 2.91278e14i 1.53714i
\(718\) 2.54453e14i 1.33347i
\(719\) 9.39253e13 0.488808 0.244404 0.969674i \(-0.421408\pi\)
0.244404 + 0.969674i \(0.421408\pi\)
\(720\) 2.08241e13i 0.107623i
\(721\) 1.08637e14i 0.557572i
\(722\) 1.02232e13i 0.0521073i
\(723\) −2.26668e13 −0.114736
\(724\) 2.89727e13 0.145645
\(725\) 2.17092e14i 1.08381i
\(726\) 5.88482e13 0.291776
\(727\) 2.05262e14i 1.01074i 0.862904 + 0.505368i \(0.168643\pi\)
−0.862904 + 0.505368i \(0.831357\pi\)
\(728\) −1.21353e14 −0.593465
\(729\) −2.28915e14 −1.11183
\(730\) 1.32359e14i 0.638467i
\(731\) −1.42785e13 3.21133e13i −0.0684061 0.153850i
\(732\) −3.04306e13 −0.144796
\(733\) 3.06949e14i 1.45059i −0.688436 0.725297i \(-0.741703\pi\)
0.688436 0.725297i \(-0.258297\pi\)
\(734\) 1.46942e14i 0.689709i
\(735\) −7.90026e13 −0.368302
\(736\) 7.39537e13i 0.342429i
\(737\) −2.41213e13 −0.110934
\(738\) 2.63701e13i 0.120457i
\(739\) 1.84860e14i 0.838728i −0.907818 0.419364i \(-0.862253\pi\)
0.907818 0.419364i \(-0.137747\pi\)
\(740\) 5.02277e12 0.0226352
\(741\) 2.44754e14 1.09557
\(742\) −2.08395e13 −0.0926547
\(743\) 2.60027e14i 1.14835i 0.818732 + 0.574175i \(0.194677\pi\)
−0.818732 + 0.574175i \(0.805323\pi\)
\(744\) −1.24600e14 −0.546578
\(745\) −6.18894e13 −0.269671
\(746\) −7.26355e13 −0.314380
\(747\) −1.35423e13 −0.0582222
\(748\) 3.26297e12 0.0139349
\(749\) 1.49735e14i 0.635206i
\(750\) 1.77647e14i 0.748601i
\(751\) 3.93218e14i 1.64601i 0.568031 + 0.823007i \(0.307705\pi\)
−0.568031 + 0.823007i \(0.692295\pi\)
\(752\) −1.61621e13 −0.0672063
\(753\) 1.91115e14i 0.789441i
\(754\) −4.42527e14 −1.81586
\(755\) −1.76331e14 −0.718777
\(756\) 1.21041e13 0.0490144
\(757\) 1.83250e14i 0.737163i −0.929595 0.368582i \(-0.879843\pi\)
0.929595 0.368582i \(-0.120157\pi\)
\(758\) 3.20819e13i 0.128208i
\(759\) 2.97246e14i 1.18007i
\(760\) 1.34463e14i 0.530316i
\(761\) 7.87814e13i 0.308674i −0.988018 0.154337i \(-0.950676\pi\)
0.988018 0.154337i \(-0.0493242\pi\)
\(762\) −4.19999e14 −1.63483
\(763\) 5.44477e12i 0.0210551i
\(764\) 9.13212e12i 0.0350837i
\(765\) 5.35459e12i 0.0204371i
\(766\) −2.00408e14 −0.759925
\(767\) 4.20006e14 1.58226
\(768\) 7.13884e13i 0.267191i
\(769\) 3.29751e14 1.22618 0.613091 0.790012i \(-0.289926\pi\)
0.613091 + 0.790012i \(0.289926\pi\)
\(770\) 4.76218e13i 0.175935i
\(771\) 1.55928e14 0.572339
\(772\) −2.85709e12 −0.0104193
\(773\) 5.25997e13i 0.190584i 0.995449 + 0.0952919i \(0.0303785\pi\)
−0.995449 + 0.0952919i \(0.969622\pi\)
\(774\) 5.58787e13 2.48452e13i 0.201160 0.0894412i
\(775\) 1.21435e14 0.434344
\(776\) 4.04601e14i 1.43787i
\(777\) 4.62122e13i 0.163174i
\(778\) 3.40733e14 1.19541
\(779\) 1.52587e14i 0.531899i
\(780\) 1.74658e13 0.0604945
\(781\) 4.11363e14i