Properties

Label 43.11.b.b.42.21
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 42.21
Character \(\chi\) \(=\) 43.42
Dual form 43.11.b.b.42.14

$q$-expansion

\(f(q)\) \(=\) \(q+16.6799i q^{2} -405.855i q^{3} +745.782 q^{4} +2509.28i q^{5} +6769.61 q^{6} +11110.8i q^{7} +29519.7i q^{8} -105670. q^{9} +O(q^{10})\) \(q+16.6799i q^{2} -405.855i q^{3} +745.782 q^{4} +2509.28i q^{5} +6769.61 q^{6} +11110.8i q^{7} +29519.7i q^{8} -105670. q^{9} -41854.4 q^{10} +76827.0 q^{11} -302680. i q^{12} -613775. q^{13} -185326. q^{14} +1.01840e6 q^{15} +271297. q^{16} -2.69195e6 q^{17} -1.76255e6i q^{18} +2.92835e6i q^{19} +1.87138e6i q^{20} +4.50936e6 q^{21} +1.28146e6i q^{22} +2.15323e6 q^{23} +1.19807e7 q^{24} +3.46914e6 q^{25} -1.02377e7i q^{26} +1.89212e7i q^{27} +8.28622e6i q^{28} +3.40359e7i q^{29} +1.69868e7i q^{30} -3.94514e7 q^{31} +3.47534e7i q^{32} -3.11807e7i q^{33} -4.49014e7i q^{34} -2.78800e7 q^{35} -7.88065e7 q^{36} -1.06797e8i q^{37} -4.88444e7 q^{38} +2.49104e8i q^{39} -7.40732e7 q^{40} -6.32205e7 q^{41} +7.52156e7i q^{42} +(6.01836e7 + 1.34125e8i) q^{43} +5.72962e7 q^{44} -2.65154e8i q^{45} +3.59156e7i q^{46} -7.95596e7 q^{47} -1.10107e8i q^{48} +1.59026e8 q^{49} +5.78648e7i q^{50} +1.09254e9i q^{51} -4.57743e8 q^{52} +5.81476e8 q^{53} -3.15603e8 q^{54} +1.92780e8i q^{55} -3.27987e8 q^{56} +1.18849e9 q^{57} -5.67714e8 q^{58} +6.19231e8 q^{59} +7.59508e8 q^{60} +7.79189e8i q^{61} -6.58043e8i q^{62} -1.17407e9i q^{63} -3.01874e8 q^{64} -1.54013e9i q^{65} +5.20089e8 q^{66} -6.11549e8 q^{67} -2.00761e9 q^{68} -8.73901e8i q^{69} -4.65035e8i q^{70} +7.76085e8i q^{71} -3.11934e9i q^{72} -2.33701e8i q^{73} +1.78136e9 q^{74} -1.40797e9i q^{75} +2.18391e9i q^{76} +8.53607e8i q^{77} -4.15502e9 q^{78} -2.30142e9 q^{79} +6.80759e8i q^{80} +1.43959e9 q^{81} -1.05451e9i q^{82} +9.15067e8 q^{83} +3.36301e9 q^{84} -6.75486e9i q^{85} +(-2.23718e9 + 1.00385e9i) q^{86} +1.38136e10 q^{87} +2.26791e9i q^{88} -4.73920e9i q^{89} +4.42274e9 q^{90} -6.81951e9i q^{91} +1.60584e9 q^{92} +1.60115e10i q^{93} -1.32704e9i q^{94} -7.34805e9 q^{95} +1.41048e10 q^{96} -1.01973e10 q^{97} +2.65253e9i q^{98} -8.11828e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} + O(q^{10}) \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} - 254122q^{10} - 218200q^{11} - 191008q^{13} - 1380228q^{14} - 512732q^{15} + 2224308q^{16} - 1070678q^{17} + 17857352q^{21} + 8915254q^{23} - 39666730q^{24} - 82938284q^{25} - 55042410q^{31} - 179227232q^{35} + 394381042q^{36} + 709061882q^{38} + 433255366q^{40} + 80370626q^{41} + 1585062q^{43} + 324477888q^{44} - 544910502q^{47} - 2479345922q^{49} - 987059452q^{52} - 915886820q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 3394816764q^{59} - 5474941192q^{60} + 2925325476q^{64} + 455136192q^{66} + 3405920388q^{67} + 664008226q^{68} + 16264108918q^{74} - 17800086268q^{78} - 13853150858q^{79} + 20444701546q^{81} + 113867236q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 41423783058q^{92} + 4107406010q^{95} + 33148445474q^{96} + 15795117154q^{97} + 1345877600q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 16.6799i 0.521245i 0.965441 + 0.260623i \(0.0839279\pi\)
−0.965441 + 0.260623i \(0.916072\pi\)
\(3\) 405.855i 1.67019i −0.550108 0.835093i \(-0.685414\pi\)
0.550108 0.835093i \(-0.314586\pi\)
\(4\) 745.782 0.728303
\(5\) 2509.28i 0.802969i 0.915866 + 0.401485i \(0.131506\pi\)
−0.915866 + 0.401485i \(0.868494\pi\)
\(6\) 6769.61 0.870577
\(7\) 11110.8i 0.661080i 0.943792 + 0.330540i \(0.107231\pi\)
−0.943792 + 0.330540i \(0.892769\pi\)
\(8\) 29519.7i 0.900870i
\(9\) −105670. −1.78952
\(10\) −41854.4 −0.418544
\(11\) 76827.0 0.477035 0.238518 0.971138i \(-0.423339\pi\)
0.238518 + 0.971138i \(0.423339\pi\)
\(12\) 302680.i 1.21640i
\(13\) −613775. −1.65307 −0.826537 0.562882i \(-0.809693\pi\)
−0.826537 + 0.562882i \(0.809693\pi\)
\(14\) −185326. −0.344585
\(15\) 1.01840e6 1.34111
\(16\) 271297. 0.258729
\(17\) −2.69195e6 −1.89593 −0.947967 0.318370i \(-0.896865\pi\)
−0.947967 + 0.318370i \(0.896865\pi\)
\(18\) 1.76255e6i 0.932781i
\(19\) 2.92835e6i 1.18265i 0.806435 + 0.591323i \(0.201394\pi\)
−0.806435 + 0.591323i \(0.798606\pi\)
\(20\) 1.87138e6i 0.584805i
\(21\) 4.50936e6 1.10413
\(22\) 1.28146e6i 0.248652i
\(23\) 2.15323e6 0.334543 0.167272 0.985911i \(-0.446504\pi\)
0.167272 + 0.985911i \(0.446504\pi\)
\(24\) 1.19807e7 1.50462
\(25\) 3.46914e6 0.355240
\(26\) 1.02377e7i 0.861658i
\(27\) 1.89212e7i 1.31865i
\(28\) 8.28622e6i 0.481467i
\(29\) 3.40359e7i 1.65938i 0.558221 + 0.829692i \(0.311484\pi\)
−0.558221 + 0.829692i \(0.688516\pi\)
\(30\) 1.69868e7i 0.699047i
\(31\) −3.94514e7 −1.37801 −0.689007 0.724755i \(-0.741953\pi\)
−0.689007 + 0.724755i \(0.741953\pi\)
\(32\) 3.47534e7i 1.03573i
\(33\) 3.11807e7i 0.796738i
\(34\) 4.49014e7i 0.988247i
\(35\) −2.78800e7 −0.530827
\(36\) −7.88065e7 −1.30332
\(37\) 1.06797e8i 1.54010i −0.637981 0.770052i \(-0.720230\pi\)
0.637981 0.770052i \(-0.279770\pi\)
\(38\) −4.88444e7 −0.616449
\(39\) 2.49104e8i 2.76094i
\(40\) −7.40732e7 −0.723371
\(41\) −6.32205e7 −0.545680 −0.272840 0.962059i \(-0.587963\pi\)
−0.272840 + 0.962059i \(0.587963\pi\)
\(42\) 7.52156e7i 0.575521i
\(43\) 6.01836e7 + 1.34125e8i 0.409389 + 0.912360i
\(44\) 5.72962e7 0.347426
\(45\) 2.65154e8i 1.43693i
\(46\) 3.59156e7i 0.174379i
\(47\) −7.95596e7 −0.346899 −0.173450 0.984843i \(-0.555491\pi\)
−0.173450 + 0.984843i \(0.555491\pi\)
\(48\) 1.10107e8i 0.432125i
\(49\) 1.59026e8 0.562973
\(50\) 5.78648e7i 0.185167i
\(51\) 1.09254e9i 3.16656i
\(52\) −4.57743e8 −1.20394
\(53\) 5.81476e8 1.39044 0.695220 0.718797i \(-0.255307\pi\)
0.695220 + 0.718797i \(0.255307\pi\)
\(54\) −3.15603e8 −0.687341
\(55\) 1.92780e8i 0.383045i
\(56\) −3.27987e8 −0.595547
\(57\) 1.18849e9 1.97524
\(58\) −5.67714e8 −0.864947
\(59\) 6.19231e8 0.866149 0.433075 0.901358i \(-0.357429\pi\)
0.433075 + 0.901358i \(0.357429\pi\)
\(60\) 7.59508e8 0.976734
\(61\) 7.79189e8i 0.922558i 0.887255 + 0.461279i \(0.152609\pi\)
−0.887255 + 0.461279i \(0.847391\pi\)
\(62\) 6.58043e8i 0.718283i
\(63\) 1.17407e9i 1.18302i
\(64\) −3.01874e8 −0.281142
\(65\) 1.54013e9i 1.32737i
\(66\) 5.20089e8 0.415296
\(67\) −6.11549e8 −0.452958 −0.226479 0.974016i \(-0.572721\pi\)
−0.226479 + 0.974016i \(0.572721\pi\)
\(68\) −2.00761e9 −1.38081
\(69\) 8.73901e8i 0.558749i
\(70\) 4.65035e8i 0.276691i
\(71\) 7.76085e8i 0.430148i 0.976598 + 0.215074i \(0.0689992\pi\)
−0.976598 + 0.215074i \(0.931001\pi\)
\(72\) 3.11934e9i 1.61213i
\(73\) 2.33701e8i 0.112732i −0.998410 0.0563660i \(-0.982049\pi\)
0.998410 0.0563660i \(-0.0179514\pi\)
\(74\) 1.78136e9 0.802773
\(75\) 1.40797e9i 0.593317i
\(76\) 2.18391e9i 0.861325i
\(77\) 8.53607e8i 0.315358i
\(78\) −4.15502e9 −1.43913
\(79\) −2.30142e9 −0.747931 −0.373965 0.927443i \(-0.622002\pi\)
−0.373965 + 0.927443i \(0.622002\pi\)
\(80\) 6.80759e8i 0.207751i
\(81\) 1.43959e9 0.412871
\(82\) 1.05451e9i 0.284433i
\(83\) 9.15067e8 0.232307 0.116154 0.993231i \(-0.462944\pi\)
0.116154 + 0.993231i \(0.462944\pi\)
\(84\) 3.36301e9 0.804139
\(85\) 6.75486e9i 1.52238i
\(86\) −2.23718e9 + 1.00385e9i −0.475564 + 0.213392i
\(87\) 1.38136e10 2.77148
\(88\) 2.26791e9i 0.429747i
\(89\) 4.73920e9i 0.848702i −0.905498 0.424351i \(-0.860502\pi\)
0.905498 0.424351i \(-0.139498\pi\)
\(90\) 4.42274e9 0.748995
\(91\) 6.81951e9i 1.09281i
\(92\) 1.60584e9 0.243649
\(93\) 1.60115e10i 2.30154i
\(94\) 1.32704e9i 0.180820i
\(95\) −7.34805e9 −0.949629
\(96\) 1.41048e10 1.72986
\(97\) −1.01973e10 −1.18748 −0.593741 0.804656i \(-0.702350\pi\)
−0.593741 + 0.804656i \(0.702350\pi\)
\(98\) 2.65253e9i 0.293447i
\(99\) −8.11828e9 −0.853666
\(100\) 2.58723e9 0.258723
\(101\) 1.77471e8 0.0168858 0.00844289 0.999964i \(-0.497313\pi\)
0.00844289 + 0.999964i \(0.497313\pi\)
\(102\) −1.82235e10 −1.65056
\(103\) −1.35777e9 −0.117122 −0.0585610 0.998284i \(-0.518651\pi\)
−0.0585610 + 0.998284i \(0.518651\pi\)
\(104\) 1.81185e10i 1.48921i
\(105\) 1.13153e10i 0.886580i
\(106\) 9.69893e9i 0.724760i
\(107\) 1.66408e10 1.18646 0.593232 0.805031i \(-0.297852\pi\)
0.593232 + 0.805031i \(0.297852\pi\)
\(108\) 1.41111e10i 0.960378i
\(109\) −1.12385e10 −0.730423 −0.365211 0.930925i \(-0.619003\pi\)
−0.365211 + 0.930925i \(0.619003\pi\)
\(110\) −3.21555e9 −0.199660
\(111\) −4.33441e10 −2.57226
\(112\) 3.01431e9i 0.171040i
\(113\) 3.46564e10i 1.88101i −0.339782 0.940504i \(-0.610353\pi\)
0.339782 0.940504i \(-0.389647\pi\)
\(114\) 1.98238e10i 1.02959i
\(115\) 5.40306e9i 0.268628i
\(116\) 2.53834e10i 1.20854i
\(117\) 6.48574e10 2.95822
\(118\) 1.03287e10i 0.451476i
\(119\) 2.99097e10i 1.25336i
\(120\) 3.00630e10i 1.20816i
\(121\) −2.00350e10 −0.772437
\(122\) −1.29968e10 −0.480879
\(123\) 2.56584e10i 0.911388i
\(124\) −2.94221e10 −1.00361
\(125\) 3.32097e10i 1.08822i
\(126\) 1.95833e10 0.616643
\(127\) −2.00849e9 −0.0607928 −0.0303964 0.999538i \(-0.509677\pi\)
−0.0303964 + 0.999538i \(0.509677\pi\)
\(128\) 3.05523e10i 0.889188i
\(129\) 5.44352e10 2.44258e10i 1.52381 0.683756i
\(130\) 2.56892e10 0.691885
\(131\) 1.87042e10i 0.484822i −0.970174 0.242411i \(-0.922062\pi\)
0.970174 0.242411i \(-0.0779383\pi\)
\(132\) 2.32540e10i 0.580267i
\(133\) −3.25362e10 −0.781824
\(134\) 1.02006e10i 0.236102i
\(135\) −4.74786e10 −1.05884
\(136\) 7.94657e10i 1.70799i
\(137\) 2.95801e10i 0.612910i 0.951885 + 0.306455i \(0.0991428\pi\)
−0.951885 + 0.306455i \(0.900857\pi\)
\(138\) 1.45765e10 0.291246
\(139\) 7.84492e10 1.51187 0.755935 0.654647i \(-0.227183\pi\)
0.755935 + 0.654647i \(0.227183\pi\)
\(140\) −2.07924e10 −0.386603
\(141\) 3.22897e10i 0.579386i
\(142\) −1.29450e10 −0.224213
\(143\) −4.71545e10 −0.788575
\(144\) −2.86678e10 −0.463001
\(145\) −8.54055e10 −1.33244
\(146\) 3.89811e9 0.0587610
\(147\) 6.45416e10i 0.940271i
\(148\) 7.96473e10i 1.12166i
\(149\) 2.73820e10i 0.372849i −0.982469 0.186425i \(-0.940310\pi\)
0.982469 0.186425i \(-0.0596900\pi\)
\(150\) 2.34847e10 0.309264
\(151\) 5.86731e10i 0.747402i 0.927549 + 0.373701i \(0.121911\pi\)
−0.927549 + 0.373701i \(0.878089\pi\)
\(152\) −8.64440e10 −1.06541
\(153\) 2.84458e11 3.39282
\(154\) −1.42380e10 −0.164379
\(155\) 9.89945e10i 1.10650i
\(156\) 1.85777e11i 2.01080i
\(157\) 4.25794e10i 0.446377i 0.974775 + 0.223188i \(0.0716465\pi\)
−0.974775 + 0.223188i \(0.928353\pi\)
\(158\) 3.83874e10i 0.389855i
\(159\) 2.35995e11i 2.32229i
\(160\) −8.72059e10 −0.831661
\(161\) 2.39241e10i 0.221160i
\(162\) 2.40122e10i 0.215207i
\(163\) 1.20452e11i 1.04683i −0.852077 0.523416i \(-0.824658\pi\)
0.852077 0.523416i \(-0.175342\pi\)
\(164\) −4.71487e10 −0.397421
\(165\) 7.82410e10 0.639756
\(166\) 1.52632e10i 0.121089i
\(167\) −1.41144e11 −1.08662 −0.543312 0.839531i \(-0.682830\pi\)
−0.543312 + 0.839531i \(0.682830\pi\)
\(168\) 1.33115e11i 0.994675i
\(169\) 2.38861e11 1.73266
\(170\) 1.12670e11 0.793532
\(171\) 3.09437e11i 2.11637i
\(172\) 4.48839e10 + 1.00028e11i 0.298159 + 0.664475i
\(173\) 1.24656e11 0.804419 0.402210 0.915548i \(-0.368242\pi\)
0.402210 + 0.915548i \(0.368242\pi\)
\(174\) 2.30410e11i 1.44462i
\(175\) 3.85448e10i 0.234842i
\(176\) 2.08429e10 0.123423
\(177\) 2.51318e11i 1.44663i
\(178\) 7.90492e10 0.442382
\(179\) 2.61895e11i 1.42515i 0.701595 + 0.712576i \(0.252472\pi\)
−0.701595 + 0.712576i \(0.747528\pi\)
\(180\) 1.97748e11i 1.04652i
\(181\) −3.23826e11 −1.66694 −0.833468 0.552568i \(-0.813648\pi\)
−0.833468 + 0.552568i \(0.813648\pi\)
\(182\) 1.13749e11 0.569625
\(183\) 3.16238e11 1.54084
\(184\) 6.35628e10i 0.301380i
\(185\) 2.67983e11 1.23666
\(186\) −2.67070e11 −1.19967
\(187\) −2.06815e11 −0.904427
\(188\) −5.93342e10 −0.252648
\(189\) −2.10229e11 −0.871734
\(190\) 1.22564e11i 0.494990i
\(191\) 1.60403e11i 0.631024i 0.948922 + 0.315512i \(0.102176\pi\)
−0.948922 + 0.315512i \(0.897824\pi\)
\(192\) 1.22517e11i 0.469559i
\(193\) −1.46793e11 −0.548176 −0.274088 0.961705i \(-0.588376\pi\)
−0.274088 + 0.961705i \(0.588376\pi\)
\(194\) 1.70090e11i 0.618969i
\(195\) −6.25071e11 −2.21695
\(196\) 1.18599e11 0.410015
\(197\) 1.50878e11 0.508505 0.254253 0.967138i \(-0.418171\pi\)
0.254253 + 0.967138i \(0.418171\pi\)
\(198\) 1.35412e11i 0.444969i
\(199\) 2.23559e11i 0.716352i 0.933654 + 0.358176i \(0.116601\pi\)
−0.933654 + 0.358176i \(0.883399\pi\)
\(200\) 1.02408e11i 0.320025i
\(201\) 2.48201e11i 0.756524i
\(202\) 2.96019e9i 0.00880164i
\(203\) −3.78165e11 −1.09699
\(204\) 8.14800e11i 2.30622i
\(205\) 1.58638e11i 0.438165i
\(206\) 2.26473e10i 0.0610493i
\(207\) −2.27531e11 −0.598673
\(208\) −1.66515e11 −0.427698
\(209\) 2.24976e11i 0.564164i
\(210\) −1.88737e11 −0.462126
\(211\) 2.74080e11i 0.655337i −0.944793 0.327668i \(-0.893737\pi\)
0.944793 0.327668i \(-0.106263\pi\)
\(212\) 4.33654e11 1.01266
\(213\) 3.14978e11 0.718427
\(214\) 2.77566e11i 0.618439i
\(215\) −3.36556e11 + 1.51018e11i −0.732597 + 0.328727i
\(216\) −5.58549e11 −1.18793
\(217\) 4.38335e11i 0.910977i
\(218\) 1.87456e11i 0.380730i
\(219\) −9.48490e10 −0.188283
\(220\) 1.43772e11i 0.278973i
\(221\) 1.65225e12 3.13412
\(222\) 7.22974e11i 1.34078i
\(223\) 2.54207e11i 0.460960i 0.973077 + 0.230480i \(0.0740296\pi\)
−0.973077 + 0.230480i \(0.925970\pi\)
\(224\) −3.86137e11 −0.684701
\(225\) −3.66583e11 −0.635711
\(226\) 5.78063e11 0.980467
\(227\) 9.29507e10i 0.154214i −0.997023 0.0771070i \(-0.975432\pi\)
0.997023 0.0771070i \(-0.0245683\pi\)
\(228\) 8.86352e11 1.43857
\(229\) −1.73944e11 −0.276206 −0.138103 0.990418i \(-0.544100\pi\)
−0.138103 + 0.990418i \(0.544100\pi\)
\(230\) −9.01223e10 −0.140021
\(231\) 3.46441e11 0.526707
\(232\) −1.00473e12 −1.49489
\(233\) 2.89273e11i 0.421238i −0.977568 0.210619i \(-0.932452\pi\)
0.977568 0.210619i \(-0.0675479\pi\)
\(234\) 1.08181e12i 1.54196i
\(235\) 1.99637e11i 0.278549i
\(236\) 4.61812e11 0.630819
\(237\) 9.34045e11i 1.24918i
\(238\) 4.98889e11 0.653310
\(239\) 9.33811e11 1.19748 0.598742 0.800942i \(-0.295668\pi\)
0.598742 + 0.800942i \(0.295668\pi\)
\(240\) 2.76290e11 0.346983
\(241\) 1.41097e12i 1.73553i 0.496974 + 0.867765i \(0.334444\pi\)
−0.496974 + 0.867765i \(0.665556\pi\)
\(242\) 3.34181e11i 0.402629i
\(243\) 5.33013e11i 0.629080i
\(244\) 5.81105e11i 0.671902i
\(245\) 3.99041e11i 0.452050i
\(246\) −4.27978e11 −0.475057
\(247\) 1.79735e12i 1.95500i
\(248\) 1.16459e12i 1.24141i
\(249\) 3.71385e11i 0.387996i
\(250\) −5.53933e11 −0.567228
\(251\) 5.56452e11 0.558546 0.279273 0.960212i \(-0.409906\pi\)
0.279273 + 0.960212i \(0.409906\pi\)
\(252\) 8.75601e11i 0.861596i
\(253\) 1.65427e11 0.159589
\(254\) 3.35014e10i 0.0316879i
\(255\) −2.74150e12 −2.54265
\(256\) −8.18726e11 −0.744627
\(257\) 1.29683e12i 1.15669i −0.815792 0.578345i \(-0.803699\pi\)
0.815792 0.578345i \(-0.196301\pi\)
\(258\) 4.07420e11 + 9.07971e11i 0.356405 + 0.794280i
\(259\) 1.18660e12 1.01813
\(260\) 1.14860e12i 0.966727i
\(261\) 3.59656e12i 2.96951i
\(262\) 3.11983e11 0.252711
\(263\) 1.45763e12i 1.15843i −0.815175 0.579215i \(-0.803359\pi\)
0.815175 0.579215i \(-0.196641\pi\)
\(264\) 9.20444e11 0.717758
\(265\) 1.45908e12i 1.11648i
\(266\) 5.42699e11i 0.407522i
\(267\) −1.92343e12 −1.41749
\(268\) −4.56083e11 −0.329890
\(269\) −6.65425e11 −0.472430 −0.236215 0.971701i \(-0.575907\pi\)
−0.236215 + 0.971701i \(0.575907\pi\)
\(270\) 7.91936e11i 0.551914i
\(271\) 4.95618e11 0.339079 0.169539 0.985523i \(-0.445772\pi\)
0.169539 + 0.985523i \(0.445772\pi\)
\(272\) −7.30318e11 −0.490532
\(273\) −2.76774e12 −1.82520
\(274\) −4.93391e11 −0.319476
\(275\) 2.66524e11 0.169462
\(276\) 6.51740e11i 0.406939i
\(277\) 2.78269e12i 1.70634i 0.521632 + 0.853170i \(0.325323\pi\)
−0.521632 + 0.853170i \(0.674677\pi\)
\(278\) 1.30852e12i 0.788055i
\(279\) 4.16881e12 2.46599
\(280\) 8.23010e11i 0.478206i
\(281\) −5.43758e11 −0.310366 −0.155183 0.987886i \(-0.549597\pi\)
−0.155183 + 0.987886i \(0.549597\pi\)
\(282\) −5.38587e11 −0.302003
\(283\) 1.78970e12 0.985933 0.492966 0.870048i \(-0.335913\pi\)
0.492966 + 0.870048i \(0.335913\pi\)
\(284\) 5.78791e11i 0.313278i
\(285\) 2.98224e12i 1.58606i
\(286\) 7.86530e11i 0.411041i
\(287\) 7.02428e11i 0.360738i
\(288\) 3.67237e12i 1.85347i
\(289\) 5.23062e12 2.59456
\(290\) 1.42455e12i 0.694526i
\(291\) 4.13863e12i 1.98332i
\(292\) 1.74290e11i 0.0821030i
\(293\) 1.63092e12 0.755257 0.377628 0.925957i \(-0.376740\pi\)
0.377628 + 0.925957i \(0.376740\pi\)
\(294\) 1.07654e12 0.490112
\(295\) 1.55382e12i 0.695491i
\(296\) 3.15262e12 1.38743
\(297\) 1.45366e12i 0.629043i
\(298\) 4.56727e11 0.194346
\(299\) −1.32160e12 −0.553025
\(300\) 1.05004e12i 0.432115i
\(301\) −1.49023e12 + 6.68686e11i −0.603143 + 0.270639i
\(302\) −9.78658e11 −0.389580
\(303\) 7.20276e10i 0.0282024i
\(304\) 7.94451e11i 0.305984i
\(305\) −1.95520e12 −0.740786
\(306\) 4.74471e12i 1.76849i
\(307\) −4.22741e12 −1.55018 −0.775091 0.631850i \(-0.782296\pi\)
−0.775091 + 0.631850i \(0.782296\pi\)
\(308\) 6.36605e11i 0.229677i
\(309\) 5.51056e11i 0.195616i
\(310\) 1.65121e12 0.576760
\(311\) −2.41955e12 −0.831635 −0.415817 0.909448i \(-0.636504\pi\)
−0.415817 + 0.909448i \(0.636504\pi\)
\(312\) −7.35348e12 −2.48725
\(313\) 3.43794e12i 1.14440i 0.820116 + 0.572198i \(0.193909\pi\)
−0.820116 + 0.572198i \(0.806091\pi\)
\(314\) −7.10219e11 −0.232672
\(315\) 2.94607e12 0.949927
\(316\) −1.71636e12 −0.544720
\(317\) 3.70850e11 0.115852 0.0579258 0.998321i \(-0.481551\pi\)
0.0579258 + 0.998321i \(0.481551\pi\)
\(318\) 3.93636e12 1.21049
\(319\) 2.61488e12i 0.791585i
\(320\) 7.57485e11i 0.225748i
\(321\) 6.75375e12i 1.98162i
\(322\) −3.99050e11 −0.115278
\(323\) 7.88298e12i 2.24222i
\(324\) 1.07362e12 0.300695
\(325\) −2.12927e12 −0.587239
\(326\) 2.00913e12 0.545656
\(327\) 4.56119e12i 1.21994i
\(328\) 1.86625e12i 0.491587i
\(329\) 8.83968e11i 0.229328i
\(330\) 1.30505e12i 0.333470i
\(331\) 1.08567e11i 0.0273247i 0.999907 + 0.0136624i \(0.00434900\pi\)
−0.999907 + 0.0136624i \(0.995651\pi\)
\(332\) 6.82441e11 0.169190
\(333\) 1.12852e13i 2.75605i
\(334\) 2.35426e12i 0.566398i
\(335\) 1.53455e12i 0.363711i
\(336\) 1.22338e12 0.285669
\(337\) −4.77947e12 −1.09959 −0.549795 0.835300i \(-0.685294\pi\)
−0.549795 + 0.835300i \(0.685294\pi\)
\(338\) 3.98417e12i 0.903140i
\(339\) −1.40655e13 −3.14164
\(340\) 5.03766e12i 1.10875i
\(341\) −3.03093e12 −0.657361
\(342\) 5.16137e12 1.10315
\(343\) 4.90542e12i 1.03325i
\(344\) −3.95932e12 + 1.77660e12i −0.821918 + 0.368806i
\(345\) 2.19286e12 0.448659
\(346\) 2.07924e12i 0.419300i
\(347\) 1.41224e12i 0.280713i −0.990101 0.140357i \(-0.955175\pi\)
0.990101 0.140357i \(-0.0448249\pi\)
\(348\) 1.03020e13 2.01848
\(349\) 1.72628e12i 0.333414i −0.986006 0.166707i \(-0.946687\pi\)
0.986006 0.166707i \(-0.0533134\pi\)
\(350\) −6.42922e11 −0.122410
\(351\) 1.16134e13i 2.17983i
\(352\) 2.67000e12i 0.494080i
\(353\) 6.27311e12 1.14448 0.572241 0.820085i \(-0.306074\pi\)
0.572241 + 0.820085i \(0.306074\pi\)
\(354\) 4.19195e12 0.754050
\(355\) −1.94741e12 −0.345396
\(356\) 3.53441e12i 0.618112i
\(357\) −1.21390e13 −2.09335
\(358\) −4.36836e12 −0.742854
\(359\) 6.17964e12 1.03631 0.518156 0.855286i \(-0.326619\pi\)
0.518156 + 0.855286i \(0.326619\pi\)
\(360\) 7.82728e12 1.29449
\(361\) −2.44416e12 −0.398653
\(362\) 5.40137e12i 0.868883i
\(363\) 8.13133e12i 1.29011i
\(364\) 5.08587e12i 0.795900i
\(365\) 5.86422e11 0.0905203
\(366\) 5.27480e12i 0.803158i
\(367\) 2.58037e12 0.387571 0.193785 0.981044i \(-0.437923\pi\)
0.193785 + 0.981044i \(0.437923\pi\)
\(368\) 5.84165e11 0.0865559
\(369\) 6.68048e12 0.976508
\(370\) 4.46992e12i 0.644602i
\(371\) 6.46064e12i 0.919192i
\(372\) 1.19411e13i 1.67622i
\(373\) 3.98350e12i 0.551722i −0.961198 0.275861i \(-0.911037\pi\)
0.961198 0.275861i \(-0.0889630\pi\)
\(374\) 3.44964e12i 0.471428i
\(375\) 1.34783e13 1.81752
\(376\) 2.34858e12i 0.312511i
\(377\) 2.08904e13i 2.74309i
\(378\) 3.50659e12i 0.454387i
\(379\) 5.15467e12 0.659181 0.329591 0.944124i \(-0.393089\pi\)
0.329591 + 0.944124i \(0.393089\pi\)
\(380\) −5.48004e12 −0.691618
\(381\) 8.15158e11i 0.101535i
\(382\) −2.67550e12 −0.328918
\(383\) 5.06981e11i 0.0615174i 0.999527 + 0.0307587i \(0.00979234\pi\)
−0.999527 + 0.0307587i \(0.990208\pi\)
\(384\) 1.23998e13 1.48511
\(385\) −2.14194e12 −0.253223
\(386\) 2.44849e12i 0.285734i
\(387\) −6.35958e12 1.41729e13i −0.732611 1.63269i
\(388\) −7.60497e12 −0.864847
\(389\) 5.06187e12i 0.568280i 0.958783 + 0.284140i \(0.0917081\pi\)
−0.958783 + 0.284140i \(0.908292\pi\)
\(390\) 1.04261e13i 1.15558i
\(391\) −5.79641e12 −0.634271
\(392\) 4.69440e12i 0.507166i
\(393\) −7.59120e12 −0.809744
\(394\) 2.51663e12i 0.265056i
\(395\) 5.77492e12i 0.600565i
\(396\) −6.05447e12 −0.621728
\(397\) 6.66168e12 0.675509 0.337755 0.941234i \(-0.390333\pi\)
0.337755 + 0.941234i \(0.390333\pi\)
\(398\) −3.72893e12 −0.373395
\(399\) 1.32050e13i 1.30579i
\(400\) 9.41167e11 0.0919108
\(401\) 8.84283e12 0.852844 0.426422 0.904524i \(-0.359774\pi\)
0.426422 + 0.904524i \(0.359774\pi\)
\(402\) −4.13995e12 −0.394335
\(403\) 2.42143e13 2.27796
\(404\) 1.32355e11 0.0122980
\(405\) 3.61234e12i 0.331522i
\(406\) 6.30774e12i 0.571799i
\(407\) 8.20489e12i 0.734684i
\(408\) −3.22516e13 −2.85266
\(409\) 1.85041e12i 0.161678i −0.996727 0.0808391i \(-0.974240\pi\)
0.996727 0.0808391i \(-0.0257600\pi\)
\(410\) 2.64606e12 0.228391
\(411\) 1.20052e13 1.02367
\(412\) −1.01260e12 −0.0853004
\(413\) 6.88013e12i 0.572594i
\(414\) 3.79519e12i 0.312055i
\(415\) 2.29616e12i 0.186536i
\(416\) 2.13308e13i 1.71214i
\(417\) 3.18390e13i 2.52511i
\(418\) −3.75257e12 −0.294068
\(419\) 4.49945e12i 0.348409i −0.984709 0.174204i \(-0.944265\pi\)
0.984709 0.174204i \(-0.0557354\pi\)
\(420\) 8.43872e12i 0.645699i
\(421\) 1.73413e13i 1.31121i 0.755105 + 0.655604i \(0.227586\pi\)
−0.755105 + 0.655604i \(0.772414\pi\)
\(422\) 4.57161e12 0.341591
\(423\) 8.40703e12 0.620784
\(424\) 1.71650e13i 1.25261i
\(425\) −9.33877e12 −0.673512
\(426\) 5.25379e12i 0.374477i
\(427\) −8.65739e12 −0.609884
\(428\) 1.24104e13 0.864106
\(429\) 1.91379e13i 1.31707i
\(430\) −2.51895e12 5.61371e12i −0.171347 0.381863i
\(431\) −1.53852e13 −1.03447 −0.517234 0.855844i \(-0.673038\pi\)
−0.517234 + 0.855844i \(0.673038\pi\)
\(432\) 5.13326e12i 0.341173i
\(433\) 8.11708e12i 0.533286i 0.963795 + 0.266643i \(0.0859144\pi\)
−0.963795 + 0.266643i \(0.914086\pi\)
\(434\) 7.31136e12 0.474843
\(435\) 3.46623e13i 2.22542i
\(436\) −8.38144e12 −0.531969
\(437\) 6.30542e12i 0.395646i
\(438\) 1.58207e12i 0.0981419i
\(439\) 1.67646e13 1.02819 0.514093 0.857734i \(-0.328129\pi\)
0.514093 + 0.857734i \(0.328129\pi\)
\(440\) −5.69082e12 −0.345074
\(441\) −1.68042e13 −1.00745
\(442\) 2.75594e13i 1.63365i
\(443\) 2.29764e13 1.34668 0.673338 0.739335i \(-0.264860\pi\)
0.673338 + 0.739335i \(0.264860\pi\)
\(444\) −3.23253e13 −1.87339
\(445\) 1.18920e13 0.681481
\(446\) −4.24013e12 −0.240273
\(447\) −1.11131e13 −0.622728
\(448\) 3.35405e12i 0.185857i
\(449\) 1.16891e13i 0.640546i 0.947325 + 0.320273i \(0.103775\pi\)
−0.947325 + 0.320273i \(0.896225\pi\)
\(450\) 6.11455e12i 0.331361i
\(451\) −4.85704e12 −0.260309
\(452\) 2.58461e13i 1.36994i
\(453\) 2.38128e13 1.24830
\(454\) 1.55041e12 0.0803833
\(455\) 1.71121e13 0.877497
\(456\) 3.50838e13i 1.77944i
\(457\) 1.33810e13i 0.671286i −0.941989 0.335643i \(-0.891046\pi\)
0.941989 0.335643i \(-0.108954\pi\)
\(458\) 2.90136e12i 0.143971i
\(459\) 5.09350e13i 2.50007i
\(460\) 4.02951e12i 0.195642i
\(461\) −1.17208e13 −0.562927 −0.281464 0.959572i \(-0.590820\pi\)
−0.281464 + 0.959572i \(0.590820\pi\)
\(462\) 5.77859e12i 0.274544i
\(463\) 2.52630e13i 1.18735i −0.804704 0.593676i \(-0.797676\pi\)
0.804704 0.593676i \(-0.202324\pi\)
\(464\) 9.23382e12i 0.429330i
\(465\) −4.01774e13 −1.84807
\(466\) 4.82502e12 0.219568
\(467\) 4.89076e10i 0.00220187i 0.999999 + 0.00110093i \(0.000350438\pi\)
−0.999999 + 0.00110093i \(0.999650\pi\)
\(468\) 4.83695e13 2.15448
\(469\) 6.79478e12i 0.299441i
\(470\) 3.32992e12 0.145193
\(471\) 1.72811e13 0.745533
\(472\) 1.82795e13i 0.780288i
\(473\) 4.62373e12 + 1.03044e13i 0.195293 + 0.435228i
\(474\) −1.55797e13 −0.651131
\(475\) 1.01589e13i 0.420124i
\(476\) 2.23061e13i 0.912828i
\(477\) −6.14443e13 −2.48822
\(478\) 1.55758e13i 0.624183i
\(479\) 3.88075e13 1.53900 0.769499 0.638648i \(-0.220506\pi\)
0.769499 + 0.638648i \(0.220506\pi\)
\(480\) 3.53930e13i 1.38903i
\(481\) 6.55493e13i 2.54591i
\(482\) −2.35348e13 −0.904637
\(483\) 9.70972e12 0.369378
\(484\) −1.49418e13 −0.562569
\(485\) 2.55879e13i 0.953511i
\(486\) −8.89057e12 −0.327905
\(487\) 5.88432e11 0.0214808 0.0107404 0.999942i \(-0.496581\pi\)
0.0107404 + 0.999942i \(0.496581\pi\)
\(488\) −2.30014e13 −0.831105
\(489\) −4.88862e13 −1.74840
\(490\) −6.65594e12 −0.235629
\(491\) 5.31550e13i 1.86267i −0.364158 0.931337i \(-0.618643\pi\)
0.364158 0.931337i \(-0.381357\pi\)
\(492\) 1.91356e13i 0.663767i
\(493\) 9.16230e13i 3.14608i
\(494\) 2.99795e13 1.01904
\(495\) 2.03710e13i 0.685468i
\(496\) −1.07030e13 −0.356532
\(497\) −8.62290e12 −0.284362
\(498\) 6.19465e12 0.202241
\(499\) 3.18268e13i 1.02870i 0.857579 + 0.514352i \(0.171967\pi\)
−0.857579 + 0.514352i \(0.828033\pi\)
\(500\) 2.47672e13i 0.792551i
\(501\) 5.72839e13i 1.81486i
\(502\) 9.28154e12i 0.291140i
\(503\) 4.15805e13i 1.29137i 0.763605 + 0.645684i \(0.223428\pi\)
−0.763605 + 0.645684i \(0.776572\pi\)
\(504\) 3.46582e13 1.06575
\(505\) 4.45325e11i 0.0135588i
\(506\) 2.75929e12i 0.0831850i
\(507\) 9.69432e13i 2.89386i
\(508\) −1.49790e12 −0.0442756
\(509\) 6.77543e13 1.98312 0.991558 0.129662i \(-0.0413892\pi\)
0.991558 + 0.129662i \(0.0413892\pi\)
\(510\) 4.57278e13i 1.32535i
\(511\) 2.59660e12 0.0745248
\(512\) 1.76293e13i 0.501054i
\(513\) −5.54079e13 −1.55950
\(514\) 2.16309e13 0.602920
\(515\) 3.40701e12i 0.0940454i
\(516\) 4.05968e13 1.82164e13i 1.10980 0.497982i
\(517\) −6.11233e12 −0.165483
\(518\) 1.97923e13i 0.530697i
\(519\) 5.05923e13i 1.34353i
\(520\) 4.54643e13 1.19579
\(521\) 2.87429e13i 0.748758i 0.927276 + 0.374379i \(0.122144\pi\)
−0.927276 + 0.374379i \(0.877856\pi\)
\(522\) 5.99901e13 1.54784
\(523\) 3.41560e12i 0.0872888i 0.999047 + 0.0436444i \(0.0138969\pi\)
−0.999047 + 0.0436444i \(0.986103\pi\)
\(524\) 1.39493e13i 0.353098i
\(525\) 1.56436e13 0.392230
\(526\) 2.43131e13 0.603826
\(527\) 1.06201e14 2.61262
\(528\) 8.45921e12i 0.206139i
\(529\) −3.67901e13 −0.888081
\(530\) −2.43373e13 −0.581960
\(531\) −6.54339e13 −1.54999
\(532\) −2.42649e13 −0.569405
\(533\) 3.88031e13 0.902051
\(534\) 3.20825e13i 0.738860i
\(535\) 4.17564e13i 0.952694i
\(536\) 1.80528e13i 0.408056i
\(537\) 1.06291e14 2.38027
\(538\) 1.10992e13i 0.246252i
\(539\) 1.22175e13 0.268558
\(540\) −3.54087e13 −0.771154
\(541\) −8.41281e13 −1.81533 −0.907664 0.419698i \(-0.862136\pi\)
−0.907664 + 0.419698i \(0.862136\pi\)
\(542\) 8.26683e12i 0.176743i
\(543\) 1.31427e14i 2.78409i
\(544\) 9.35545e13i 1.96368i
\(545\) 2.82004e13i 0.586507i
\(546\) 4.61654e13i 0.951379i
\(547\) −6.17362e13 −1.26067 −0.630337 0.776321i \(-0.717083\pi\)
−0.630337 + 0.776321i \(0.717083\pi\)
\(548\) 2.20603e13i 0.446384i
\(549\) 8.23366e13i 1.65094i
\(550\) 4.44558e12i 0.0883314i
\(551\) −9.96690e13 −1.96247
\(552\) 2.57973e13 0.503361
\(553\) 2.55706e13i 0.494442i
\(554\) −4.64148e13 −0.889422
\(555\) 1.08763e14i 2.06545i
\(556\) 5.85060e13 1.10110
\(557\) −1.78793e12 −0.0333483 −0.0166742 0.999861i \(-0.505308\pi\)
−0.0166742 + 0.999861i \(0.505308\pi\)
\(558\) 6.95351e13i 1.28539i
\(559\) −3.69392e13 8.23224e13i −0.676751 1.50820i
\(560\) −7.56376e12 −0.137340
\(561\) 8.39369e13i 1.51056i
\(562\) 9.06980e12i 0.161777i
\(563\) −9.07777e13 −1.60486 −0.802430 0.596747i \(-0.796460\pi\)
−0.802430 + 0.596747i \(0.796460\pi\)
\(564\) 2.40811e13i 0.421969i
\(565\) 8.69625e13 1.51039
\(566\) 2.98519e13i 0.513913i
\(567\) 1.59950e13i 0.272940i
\(568\) −2.29098e13 −0.387507
\(569\) −3.84255e13 −0.644255 −0.322128 0.946696i \(-0.604398\pi\)
−0.322128 + 0.946696i \(0.604398\pi\)
\(570\) −4.97434e13 −0.826725
\(571\) 3.72579e13i 0.613816i −0.951739 0.306908i \(-0.900706\pi\)
0.951739 0.306908i \(-0.0992943\pi\)
\(572\) −3.51670e13 −0.574322
\(573\) 6.51005e13 1.05393
\(574\) 1.17164e13 0.188033
\(575\) 7.46987e12 0.118843
\(576\) 3.18988e13 0.503110
\(577\) 1.11966e13i 0.175068i 0.996162 + 0.0875338i \(0.0278986\pi\)
−0.996162 + 0.0875338i \(0.972101\pi\)
\(578\) 8.72460e13i 1.35240i
\(579\) 5.95768e13i 0.915556i
\(580\) −6.36940e13 −0.970417
\(581\) 1.01671e13i 0.153574i
\(582\) −6.90318e13 −1.03379
\(583\) 4.46730e13 0.663289
\(584\) 6.89880e12 0.101557
\(585\) 1.62745e14i 2.37536i
\(586\) 2.72035e13i 0.393674i
\(587\) 1.88182e13i 0.270014i 0.990845 + 0.135007i \(0.0431057\pi\)
−0.990845 + 0.135007i \(0.956894\pi\)
\(588\) 4.81340e13i 0.684802i
\(589\) 1.15527e14i 1.62970i
\(590\) −2.59176e13 −0.362522
\(591\) 6.12347e13i 0.849299i
\(592\) 2.89737e13i 0.398469i
\(593\) 4.85616e13i 0.662246i 0.943588 + 0.331123i \(0.107428\pi\)
−0.943588 + 0.331123i \(0.892572\pi\)
\(594\) −2.42468e13 −0.327886
\(595\) 7.50517e13 1.00641
\(596\) 2.04210e13i 0.271547i
\(597\) 9.07326e13 1.19644
\(598\) 2.20441e13i 0.288262i
\(599\) 4.38950e12 0.0569222 0.0284611 0.999595i \(-0.490939\pi\)
0.0284611 + 0.999595i \(0.490939\pi\)
\(600\) 4.15629e13 0.534502
\(601\) 1.15896e14i 1.47808i 0.673664 + 0.739038i \(0.264720\pi\)
−0.673664 + 0.739038i \(0.735280\pi\)
\(602\) −1.11536e13 2.48568e13i −0.141069 0.314385i
\(603\) 6.46222e13 0.810578
\(604\) 4.37574e13i 0.544335i
\(605\) 5.02735e13i 0.620243i
\(606\) 1.20141e12 0.0147004
\(607\) 1.57153e14i 1.90712i 0.301200 + 0.953561i \(0.402613\pi\)
−0.301200 + 0.953561i \(0.597387\pi\)
\(608\) −1.01770e14 −1.22490
\(609\) 1.53480e14i 1.83217i
\(610\) 3.26125e13i 0.386131i
\(611\) 4.88317e13 0.573450
\(612\) 2.12143e14 2.47100
\(613\) 3.49249e13 0.403490 0.201745 0.979438i \(-0.435339\pi\)
0.201745 + 0.979438i \(0.435339\pi\)
\(614\) 7.05126e13i 0.808025i
\(615\) −6.43840e13 −0.731817
\(616\) −2.51982e13 −0.284097
\(617\) 7.37831e13 0.825147 0.412573 0.910924i \(-0.364630\pi\)
0.412573 + 0.910924i \(0.364630\pi\)
\(618\) −9.19154e12 −0.101964
\(619\) −1.02207e14 −1.12467 −0.562337 0.826908i \(-0.690098\pi\)
−0.562337 + 0.826908i \(0.690098\pi\)
\(620\) 7.38283e13i 0.805869i
\(621\) 4.07418e13i 0.441146i
\(622\) 4.03578e13i 0.433486i
\(623\) 5.26562e13 0.561059
\(624\) 6.75811e13i 0.714335i
\(625\) −4.94541e13 −0.518564
\(626\) −5.73443e13 −0.596511
\(627\) 9.13079e13 0.942259
\(628\) 3.17550e13i 0.325098i
\(629\) 2.87493e14i 2.91994i
\(630\) 4.91400e13i 0.495145i
\(631\) 1.28225e14i 1.28182i −0.767618 0.640908i \(-0.778558\pi\)
0.767618 0.640908i \(-0.221442\pi\)
\(632\) 6.79374e13i 0.673788i
\(633\) −1.11237e14 −1.09454
\(634\) 6.18572e12i 0.0603871i
\(635\) 5.03987e12i 0.0488147i
\(636\) 1.76001e14i 1.69133i
\(637\) −9.76063e13 −0.930637
\(638\) −4.36157e13 −0.412610
\(639\) 8.20086e13i 0.769760i
\(640\) −7.66641e13 −0.713990
\(641\) 8.53595e13i 0.788791i 0.918941 + 0.394395i \(0.129046\pi\)
−0.918941 + 0.394395i \(0.870954\pi\)
\(642\) 1.12652e14 1.03291
\(643\) −1.93404e14 −1.75959 −0.879795 0.475354i \(-0.842320\pi\)
−0.879795 + 0.475354i \(0.842320\pi\)
\(644\) 1.78422e13i 0.161071i
\(645\) 6.12913e13 + 1.36593e14i 0.549035 + 1.22357i
\(646\) 1.31487e14 1.16875
\(647\) 7.73921e12i 0.0682614i 0.999417 + 0.0341307i \(0.0108663\pi\)
−0.999417 + 0.0341307i \(0.989134\pi\)
\(648\) 4.24963e13i 0.371943i
\(649\) 4.75737e13 0.413184
\(650\) 3.55160e13i 0.306096i
\(651\) −1.77901e14 −1.52150
\(652\) 8.98311e13i 0.762411i
\(653\) 1.09094e14i 0.918832i 0.888221 + 0.459416i \(0.151941\pi\)
−0.888221 + 0.459416i \(0.848059\pi\)
\(654\) −7.60800e13 −0.635889
\(655\) 4.69341e13 0.389298
\(656\) −1.71515e13 −0.141183
\(657\) 2.46951e13i 0.201736i
\(658\) 1.47445e13 0.119536
\(659\) −1.90131e14 −1.52977 −0.764885 0.644167i \(-0.777204\pi\)
−0.764885 + 0.644167i \(0.777204\pi\)
\(660\) 5.83507e13 0.465936
\(661\) 1.49707e14 1.18641 0.593205 0.805052i \(-0.297863\pi\)
0.593205 + 0.805052i \(0.297863\pi\)
\(662\) −1.81087e12 −0.0142429
\(663\) 6.70576e14i 5.23456i
\(664\) 2.70125e13i 0.209279i
\(665\) 8.16424e13i 0.627780i
\(666\) −1.88235e14 −1.43658
\(667\) 7.32872e13i 0.555136i
\(668\) −1.05263e14 −0.791392
\(669\) 1.03171e14 0.769889
\(670\) 2.55960e13 0.189583
\(671\) 5.98628e13i 0.440093i
\(672\) 1.56716e14i 1.14358i
\(673\) 9.38323e13i 0.679637i −0.940491 0.339819i \(-0.889634\pi\)
0.940491 0.339819i \(-0.110366\pi\)
\(674\) 7.97209e13i 0.573156i
\(675\) 6.56404e13i 0.468438i
\(676\) 1.78139e14 1.26190
\(677\) 1.72758e14i 1.21477i 0.794408 + 0.607385i \(0.207781\pi\)
−0.794408 + 0.607385i \(0.792219\pi\)
\(678\) 2.34610e14i 1.63756i
\(679\) 1.13300e14i 0.785020i
\(680\) 1.99402e14 1.37146
\(681\) −3.77246e13 −0.257566
\(682\) 5.05555e13i 0.342647i
\(683\) 5.54255e12 0.0372912 0.0186456 0.999826i \(-0.494065\pi\)
0.0186456 + 0.999826i \(0.494065\pi\)
\(684\) 2.30773e14i 1.54136i
\(685\) −7.42247e13 −0.492148
\(686\) −8.18217e13 −0.538577
\(687\) 7.05962e13i 0.461315i
\(688\) 1.63276e13 + 3.63876e13i 0.105921 + 0.236054i
\(689\) −3.56895e14 −2.29850
\(690\) 3.65766e13i 0.233861i
\(691\) 1.88483e14i 1.19642i −0.801341 0.598208i \(-0.795879\pi\)
0.801341 0.598208i \(-0.204121\pi\)
\(692\) 9.29662e13 0.585861
\(693\) 9.02003e13i 0.564341i
\(694\) 2.35560e13 0.146320
\(695\) 1.96851e14i 1.21399i
\(696\) 4.07775e14i 2.49675i
\(697\) 1.70187e14 1.03457
\(698\) 2.87941e13 0.173791
\(699\) −1.17403e14 −0.703546
\(700\) 2.87461e13i 0.171036i
\(701\) 2.13063e14 1.25869 0.629345 0.777126i \(-0.283323\pi\)
0.629345 + 0.777126i \(0.283323\pi\)
\(702\) 1.93709e14 1.13623
\(703\) 3.12739e14 1.82140
\(704\) −2.31920e13 −0.134114
\(705\) −8.10239e13 −0.465230
\(706\) 1.04635e14i 0.596556i
\(707\) 1.97184e12i 0.0111628i
\(708\) 1.87429e14i 1.05359i
\(709\) −2.23426e14 −1.24710 −0.623551 0.781782i \(-0.714311\pi\)
−0.623551 + 0.781782i \(0.714311\pi\)
\(710\) 3.24826e13i 0.180036i
\(711\) 2.43191e14 1.33844
\(712\) 1.39900e14 0.764570
\(713\) −8.49480e13 −0.461005
\(714\) 2.02477e14i 1.09115i
\(715\) 1.18324e14i 0.633202i
\(716\) 1.95316e14i 1.03794i
\(717\) 3.78992e14i 2.00002i
\(718\) 1.03075e14i 0.540173i
\(719\) 1.59686e13 0.0831039 0.0415519 0.999136i \(-0.486770\pi\)
0.0415519 + 0.999136i \(0.486770\pi\)
\(720\) 7.19355e13i 0.371776i
\(721\) 1.50858e13i 0.0774270i
\(722\) 4.07683e13i 0.207796i
\(723\) 5.72649e14 2.89866
\(724\) −2.41504e14 −1.21403
\(725\) 1.18075e14i 0.589480i
\(726\) −1.35629e14 −0.672466
\(727\) 1.71498e14i 0.844478i −0.906485 0.422239i \(-0.861244\pi\)
0.906485 0.422239i \(-0.138756\pi\)
\(728\) 2.01310e14 0.984484
\(729\) 3.01332e14 1.46355
\(730\) 9.78143e12i 0.0471833i
\(731\) −1.62012e14 3.61057e14i −0.776174 1.72977i
\(732\) 2.35845e14 1.12220
\(733\) 2.82615e14i 1.33560i 0.744342 + 0.667799i \(0.232763\pi\)
−0.744342 + 0.667799i \(0.767237\pi\)
\(734\) 4.30401e13i 0.202019i
\(735\) 1.61953e14 0.755009
\(736\) 7.48321e13i 0.346497i
\(737\) −4.69835e13 −0.216077
\(738\) 1.11429e14i 0.509000i
\(739\) 2.45807e14i 1.11525i 0.830093 + 0.557625i \(0.188287\pi\)
−0.830093 + 0.557625i \(0.811713\pi\)
\(740\) 1.99857e14 0.900661
\(741\) −7.29463e14 −3.26522
\(742\) −1.07763e14 −0.479124
\(743\) 1.73003e14i 0.764030i 0.924156 + 0.382015i \(0.124770\pi\)
−0.924156 + 0.382015i \(0.875230\pi\)
\(744\) −4.72656e14 −2.07339
\(745\) 6.87090e13 0.299387
\(746\) 6.64442e13 0.287583
\(747\) −9.66948e13 −0.415719
\(748\) −1.54239e14 −0.658697
\(749\) 1.84892e14i 0.784348i
\(750\) 2.24817e14i 0.947376i
\(751\) 1.68192e14i 0.704054i 0.935990 + 0.352027i \(0.114507\pi\)
−0.935990 + 0.352027i \(0.885493\pi\)
\(752\) −2.15843e13 −0.0897528
\(753\) 2.25839e14i 0.932877i
\(754\) 3.48449e14 1.42982
\(755\) −1.47227e14 −0.600141
\(756\) −1.56785e14 −0.634887
\(757\) 1.98344e14i 0.797883i 0.916976 + 0.398942i \(0.130622\pi\)
−0.916976 + 0.398942i \(0.869378\pi\)
\(758\) 8.59791e13i 0.343595i
\(759\) 6.71392e13i 0.266543i
\(760\) 2.16912e14i 0.855492i
\(761\) 2.64042e14i 1.03455i −0.855820 0.517273i \(-0.826947\pi\)
0.855820 0.517273i \(-0.173053\pi\)
\(762\) −1.35967e13 −0.0529248
\(763\) 1.24868e14i 0.482868i
\(764\) 1.19626e14i 0.459577i
\(765\) 7.13784e14i 2.72433i
\(766\) −8.45637e12 −0.0320657
\(767\) −3.80069e14 −1.43181
\(768\) 3.32284e14i 1.24367i
\(769\) 4.16117e14 1.54733 0.773667 0.633592i \(-0.218420\pi\)
0.773667 + 0.633592i \(0.218420\pi\)
\(770\) 3.57272e13i 0.131991i
\(771\) −5.26325e14 −1.93189
\(772\) −1.09476e14 −0.399238
\(773\) 8.38066e13i 0.303655i 0.988407 + 0.151828i \(0.0485158\pi\)
−0.988407 + 0.151828i \(0.951484\pi\)
\(774\) 2.36402e14 1.06077e14i 0.851032 0.381870i
\(775\) −1.36862e14 −0.489526
\(776\) 3.01022e14i 1.06977i
\(777\) 4.81587e14i 1.70047i
\(778\) −8.44312e13 −0.296214
\(779\) 1.85132e14i 0.645347i
\(780\) −4.66167e14 −1.61461
\(781\) 5.96243e13i 0.205196i