Properties

Label 43.11.b.b.42.7
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 42.7
Character \(\chi\) \(=\) 43.42
Dual form 43.11.b.b.42.28

$q$-expansion

\(f(q)\) \(=\) \(q-43.4520i q^{2} -375.725i q^{3} -864.079 q^{4} -561.891i q^{5} -16326.0 q^{6} -26275.3i q^{7} -6948.90i q^{8} -82120.5 q^{9} +O(q^{10})\) \(q-43.4520i q^{2} -375.725i q^{3} -864.079 q^{4} -561.891i q^{5} -16326.0 q^{6} -26275.3i q^{7} -6948.90i q^{8} -82120.5 q^{9} -24415.3 q^{10} +176463. q^{11} +324656. i q^{12} -466723. q^{13} -1.14171e6 q^{14} -211117. q^{15} -1.18676e6 q^{16} +237914. q^{17} +3.56830e6i q^{18} +519568. i q^{19} +485518. i q^{20} -9.87229e6 q^{21} -7.66767e6i q^{22} +1.16024e7 q^{23} -2.61088e6 q^{24} +9.44990e6 q^{25} +2.02801e7i q^{26} +8.66853e6i q^{27} +2.27039e7i q^{28} -2.76466e7i q^{29} +9.17344e6i q^{30} +6.10392e6 q^{31} +4.44515e7i q^{32} -6.63016e7i q^{33} -1.03379e7i q^{34} -1.47638e7 q^{35} +7.09586e7 q^{36} -1.86749e7i q^{37} +2.25763e7 q^{38} +1.75360e8i q^{39} -3.90452e6 q^{40} +1.74564e8 q^{41} +4.28971e8i q^{42} +(-4.17760e7 + 1.40948e8i) q^{43} -1.52478e8 q^{44} +4.61427e7i q^{45} -5.04148e8i q^{46} +3.46204e8 q^{47} +4.45896e8i q^{48} -4.07916e8 q^{49} -4.10617e8i q^{50} -8.93904e7i q^{51} +4.03285e8 q^{52} +2.36698e8 q^{53} +3.76665e8 q^{54} -9.91528e7i q^{55} -1.82584e8 q^{56} +1.95215e8 q^{57} -1.20130e9 q^{58} -8.09457e8 q^{59} +1.82421e8 q^{60} +4.73248e8i q^{61} -2.65227e8i q^{62} +2.15774e9i q^{63} +7.16264e8 q^{64} +2.62247e8i q^{65} -2.88094e9 q^{66} +2.10865e8 q^{67} -2.05577e8 q^{68} -4.35932e9i q^{69} +6.41519e8i q^{70} +1.02027e9i q^{71} +5.70647e8i q^{72} -7.03992e8i q^{73} -8.11462e8 q^{74} -3.55057e9i q^{75} -4.48948e8i q^{76} -4.63661e9i q^{77} +7.61973e9 q^{78} -1.85363e9 q^{79} +6.66830e8i q^{80} -1.59214e9 q^{81} -7.58515e9i q^{82} +9.78789e8 q^{83} +8.53044e9 q^{84} -1.33682e8i q^{85} +(6.12446e9 + 1.81525e9i) q^{86} -1.03875e10 q^{87} -1.22622e9i q^{88} +4.53014e9i q^{89} +2.00499e9 q^{90} +1.22633e10i q^{91} -1.00254e10 q^{92} -2.29340e9i q^{93} -1.50433e10i q^{94} +2.91941e8 q^{95} +1.67015e10 q^{96} +1.30294e10 q^{97} +1.77248e10i q^{98} -1.44912e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} + O(q^{10}) \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} - 254122q^{10} - 218200q^{11} - 191008q^{13} - 1380228q^{14} - 512732q^{15} + 2224308q^{16} - 1070678q^{17} + 17857352q^{21} + 8915254q^{23} - 39666730q^{24} - 82938284q^{25} - 55042410q^{31} - 179227232q^{35} + 394381042q^{36} + 709061882q^{38} + 433255366q^{40} + 80370626q^{41} + 1585062q^{43} + 324477888q^{44} - 544910502q^{47} - 2479345922q^{49} - 987059452q^{52} - 915886820q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 3394816764q^{59} - 5474941192q^{60} + 2925325476q^{64} + 455136192q^{66} + 3405920388q^{67} + 664008226q^{68} + 16264108918q^{74} - 17800086268q^{78} - 13853150858q^{79} + 20444701546q^{81} + 113867236q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 41423783058q^{92} + 4107406010q^{95} + 33148445474q^{96} + 15795117154q^{97} + 1345877600q^{99} + O(q^{100}) \)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 43.4520i 1.35788i −0.734196 0.678938i \(-0.762441\pi\)
0.734196 0.678938i \(-0.237559\pi\)
\(3\) 375.725i 1.54619i −0.634288 0.773097i \(-0.718706\pi\)
0.634288 0.773097i \(-0.281294\pi\)
\(4\) −864.079 −0.843827
\(5\) 561.891i 0.179805i −0.995951 0.0899025i \(-0.971344\pi\)
0.995951 0.0899025i \(-0.0286555\pi\)
\(6\) −16326.0 −2.09954
\(7\) 26275.3i 1.56335i −0.623683 0.781677i \(-0.714365\pi\)
0.623683 0.781677i \(-0.285635\pi\)
\(8\) 6948.90i 0.212064i
\(9\) −82120.5 −1.39072
\(10\) −24415.3 −0.244153
\(11\) 176463. 1.09570 0.547848 0.836578i \(-0.315447\pi\)
0.547848 + 0.836578i \(0.315447\pi\)
\(12\) 324656.i 1.30472i
\(13\) −466723. −1.25702 −0.628510 0.777801i \(-0.716335\pi\)
−0.628510 + 0.777801i \(0.716335\pi\)
\(14\) −1.14171e6 −2.12284
\(15\) −211117. −0.278014
\(16\) −1.18676e6 −1.13178
\(17\) 237914. 0.167562 0.0837810 0.996484i \(-0.473300\pi\)
0.0837810 + 0.996484i \(0.473300\pi\)
\(18\) 3.56830e6i 1.88842i
\(19\) 519568.i 0.209833i 0.994481 + 0.104917i \(0.0334576\pi\)
−0.994481 + 0.104917i \(0.966542\pi\)
\(20\) 485518.i 0.151724i
\(21\) −9.87229e6 −2.41725
\(22\) 7.66767e6i 1.48782i
\(23\) 1.16024e7 1.80264 0.901320 0.433155i \(-0.142600\pi\)
0.901320 + 0.433155i \(0.142600\pi\)
\(24\) −2.61088e6 −0.327892
\(25\) 9.44990e6 0.967670
\(26\) 2.02801e7i 1.70688i
\(27\) 8.66853e6i 0.604125i
\(28\) 2.27039e7i 1.31920i
\(29\) 2.76466e7i 1.34788i −0.738786 0.673940i \(-0.764601\pi\)
0.738786 0.673940i \(-0.235399\pi\)
\(30\) 9.17344e6i 0.377508i
\(31\) 6.10392e6 0.213206 0.106603 0.994302i \(-0.466003\pi\)
0.106603 + 0.994302i \(0.466003\pi\)
\(32\) 4.44515e7i 1.32476i
\(33\) 6.63016e7i 1.69416i
\(34\) 1.03379e7i 0.227528i
\(35\) −1.47638e7 −0.281099
\(36\) 7.09586e7 1.17352
\(37\) 1.86749e7i 0.269308i −0.990893 0.134654i \(-0.957008\pi\)
0.990893 0.134654i \(-0.0429923\pi\)
\(38\) 2.25763e7 0.284928
\(39\) 1.75360e8i 1.94360i
\(40\) −3.90452e6 −0.0381301
\(41\) 1.74564e8 1.50673 0.753364 0.657603i \(-0.228430\pi\)
0.753364 + 0.657603i \(0.228430\pi\)
\(42\) 4.28971e8i 3.28232i
\(43\) −4.17760e7 + 1.40948e8i −0.284174 + 0.958773i
\(44\) −1.52478e8 −0.924578
\(45\) 4.61427e7i 0.250058i
\(46\) 5.04148e8i 2.44776i
\(47\) 3.46204e8 1.50953 0.754767 0.655993i \(-0.227750\pi\)
0.754767 + 0.655993i \(0.227750\pi\)
\(48\) 4.45896e8i 1.74996i
\(49\) −4.07916e8 −1.44408
\(50\) 4.10617e8i 1.31398i
\(51\) 8.93904e7i 0.259084i
\(52\) 4.03285e8 1.06071
\(53\) 2.36698e8 0.565998 0.282999 0.959120i \(-0.408671\pi\)
0.282999 + 0.959120i \(0.408671\pi\)
\(54\) 3.76665e8 0.820327
\(55\) 9.91528e7i 0.197012i
\(56\) −1.82584e8 −0.331531
\(57\) 1.95215e8 0.324443
\(58\) −1.20130e9 −1.83025
\(59\) −8.09457e8 −1.13223 −0.566114 0.824327i \(-0.691554\pi\)
−0.566114 + 0.824327i \(0.691554\pi\)
\(60\) 1.82421e8 0.234595
\(61\) 4.73248e8i 0.560324i 0.959953 + 0.280162i \(0.0903882\pi\)
−0.959953 + 0.280162i \(0.909612\pi\)
\(62\) 2.65227e8i 0.289508i
\(63\) 2.15774e9i 2.17418i
\(64\) 7.16264e8 0.667073
\(65\) 2.62247e8i 0.226019i
\(66\) −2.88094e9 −2.30046
\(67\) 2.10865e8 0.156182 0.0780909 0.996946i \(-0.475118\pi\)
0.0780909 + 0.996946i \(0.475118\pi\)
\(68\) −2.05577e8 −0.141393
\(69\) 4.35932e9i 2.78723i
\(70\) 6.41519e8i 0.381697i
\(71\) 1.02027e9i 0.565488i 0.959195 + 0.282744i \(0.0912447\pi\)
−0.959195 + 0.282744i \(0.908755\pi\)
\(72\) 5.70647e8i 0.294921i
\(73\) 7.03992e8i 0.339589i −0.985480 0.169794i \(-0.945690\pi\)
0.985480 0.169794i \(-0.0543103\pi\)
\(74\) −8.11462e8 −0.365687
\(75\) 3.55057e9i 1.49621i
\(76\) 4.48948e8i 0.177063i
\(77\) 4.63661e9i 1.71296i
\(78\) 7.61973e9 2.63916
\(79\) −1.85363e9 −0.602402 −0.301201 0.953561i \(-0.597388\pi\)
−0.301201 + 0.953561i \(0.597388\pi\)
\(80\) 6.66830e8i 0.203500i
\(81\) −1.59214e9 −0.456623
\(82\) 7.58515e9i 2.04595i
\(83\) 9.78789e8 0.248484 0.124242 0.992252i \(-0.460350\pi\)
0.124242 + 0.992252i \(0.460350\pi\)
\(84\) 8.53044e9 2.03974
\(85\) 1.33682e8i 0.0301285i
\(86\) 6.12446e9 + 1.81525e9i 1.30189 + 0.385873i
\(87\) −1.03875e10 −2.08409
\(88\) 1.22622e9i 0.232357i
\(89\) 4.53014e9i 0.811263i 0.914037 + 0.405631i \(0.132948\pi\)
−0.914037 + 0.405631i \(0.867052\pi\)
\(90\) 2.00499e9 0.339548
\(91\) 1.22633e10i 1.96517i
\(92\) −1.00254e10 −1.52112
\(93\) 2.29340e9i 0.329658i
\(94\) 1.50433e10i 2.04976i
\(95\) 2.91941e8 0.0377291
\(96\) 1.67015e10 2.04833
\(97\) 1.30294e10 1.51728 0.758640 0.651510i \(-0.225864\pi\)
0.758640 + 0.651510i \(0.225864\pi\)
\(98\) 1.77248e10i 1.96088i
\(99\) −1.44912e10 −1.52380
\(100\) −8.16546e9 −0.816546
\(101\) −1.99566e10 −1.89881 −0.949403 0.314059i \(-0.898311\pi\)
−0.949403 + 0.314059i \(0.898311\pi\)
\(102\) −3.88419e9 −0.351803
\(103\) 4.65480e9 0.401527 0.200764 0.979640i \(-0.435658\pi\)
0.200764 + 0.979640i \(0.435658\pi\)
\(104\) 3.24321e9i 0.266568i
\(105\) 5.54715e9i 0.434634i
\(106\) 1.02850e10i 0.768556i
\(107\) −1.84503e10 −1.31548 −0.657739 0.753246i \(-0.728487\pi\)
−0.657739 + 0.753246i \(0.728487\pi\)
\(108\) 7.49029e9i 0.509777i
\(109\) −1.22798e10 −0.798100 −0.399050 0.916929i \(-0.630660\pi\)
−0.399050 + 0.916929i \(0.630660\pi\)
\(110\) −4.30839e9 −0.267517
\(111\) −7.01663e9 −0.416403
\(112\) 3.11825e10i 1.76938i
\(113\) 3.19317e10i 1.73312i 0.499069 + 0.866562i \(0.333676\pi\)
−0.499069 + 0.866562i \(0.666324\pi\)
\(114\) 8.48248e9i 0.440554i
\(115\) 6.51928e9i 0.324124i
\(116\) 2.38888e10i 1.13738i
\(117\) 3.83275e10 1.74816
\(118\) 3.51725e10i 1.53742i
\(119\) 6.25126e9i 0.261959i
\(120\) 1.46703e9i 0.0589566i
\(121\) 5.20173e9 0.200549
\(122\) 2.05636e10 0.760851
\(123\) 6.55881e10i 2.32970i
\(124\) −5.27426e9 −0.179909
\(125\) 1.07970e10i 0.353797i
\(126\) 9.37581e10 2.95227
\(127\) −1.15922e10 −0.350870 −0.175435 0.984491i \(-0.556133\pi\)
−0.175435 + 0.984491i \(0.556133\pi\)
\(128\) 1.43952e10i 0.418955i
\(129\) 5.29576e10 + 1.56963e10i 1.48245 + 0.439388i
\(130\) 1.13952e10 0.306905
\(131\) 5.90260e10i 1.52998i −0.644039 0.764992i \(-0.722743\pi\)
0.644039 0.764992i \(-0.277257\pi\)
\(132\) 5.72898e10i 1.42958i
\(133\) 1.36518e10 0.328044
\(134\) 9.16252e9i 0.212076i
\(135\) 4.87077e9 0.108625
\(136\) 1.65324e9i 0.0355338i
\(137\) 1.69458e10i 0.351123i 0.984468 + 0.175562i \(0.0561742\pi\)
−0.984468 + 0.175562i \(0.943826\pi\)
\(138\) −1.89421e11 −3.78471
\(139\) 9.47193e10 1.82543 0.912714 0.408600i \(-0.133983\pi\)
0.912714 + 0.408600i \(0.133983\pi\)
\(140\) 1.27571e10 0.237199
\(141\) 1.30078e11i 2.33403i
\(142\) 4.43328e10 0.767862
\(143\) −8.23592e10 −1.37731
\(144\) 9.74573e10 1.57399
\(145\) −1.55344e10 −0.242356
\(146\) −3.05899e10 −0.461119
\(147\) 1.53264e11i 2.23282i
\(148\) 1.61366e10i 0.227249i
\(149\) 1.91153e10i 0.260285i −0.991495 0.130142i \(-0.958457\pi\)
0.991495 0.130142i \(-0.0415435\pi\)
\(150\) −1.54279e11 −2.03166
\(151\) 5.07838e10i 0.646905i 0.946244 + 0.323452i \(0.104844\pi\)
−0.946244 + 0.323452i \(0.895156\pi\)
\(152\) 3.61043e9 0.0444980
\(153\) −1.95376e10 −0.233031
\(154\) −2.01470e11 −2.32599
\(155\) 3.42973e9i 0.0383356i
\(156\) 1.51524e11i 1.64006i
\(157\) 6.24319e10i 0.654498i −0.944938 0.327249i \(-0.893878\pi\)
0.944938 0.327249i \(-0.106122\pi\)
\(158\) 8.05438e10i 0.817987i
\(159\) 8.89334e10i 0.875144i
\(160\) 2.49769e10 0.238198
\(161\) 3.04857e11i 2.81816i
\(162\) 6.91819e10i 0.620037i
\(163\) 5.90994e10i 0.513624i −0.966461 0.256812i \(-0.917328\pi\)
0.966461 0.256812i \(-0.0826721\pi\)
\(164\) −1.50837e11 −1.27142
\(165\) −3.72542e10 −0.304618
\(166\) 4.25304e10i 0.337410i
\(167\) 7.76679e10 0.597942 0.298971 0.954262i \(-0.403357\pi\)
0.298971 + 0.954262i \(0.403357\pi\)
\(168\) 6.86016e10i 0.512611i
\(169\) 7.99717e10 0.580100
\(170\) −5.80874e9 −0.0409108
\(171\) 4.26672e10i 0.291819i
\(172\) 3.60977e10 1.21790e11i 0.239794 0.809038i
\(173\) −3.37221e10 −0.217613 −0.108806 0.994063i \(-0.534703\pi\)
−0.108806 + 0.994063i \(0.534703\pi\)
\(174\) 4.51359e11i 2.82993i
\(175\) 2.48299e11i 1.51281i
\(176\) −2.09419e11 −1.24009
\(177\) 3.04133e11i 1.75064i
\(178\) 1.96844e11 1.10159
\(179\) 1.44240e11i 0.784909i 0.919771 + 0.392455i \(0.128374\pi\)
−0.919771 + 0.392455i \(0.871626\pi\)
\(180\) 3.98709e10i 0.211006i
\(181\) 2.04299e11 1.05166 0.525829 0.850590i \(-0.323755\pi\)
0.525829 + 0.850590i \(0.323755\pi\)
\(182\) 5.32864e11 2.66845
\(183\) 1.77811e11 0.866370
\(184\) 8.06240e10i 0.382274i
\(185\) −1.04932e10 −0.0484229
\(186\) −9.96527e10 −0.447635
\(187\) 4.19830e10 0.183597
\(188\) −2.99148e11 −1.27379
\(189\) 2.27768e11 0.944461
\(190\) 1.26854e10i 0.0512314i
\(191\) 5.85874e9i 0.0230482i 0.999934 + 0.0115241i \(0.00366832\pi\)
−0.999934 + 0.0115241i \(0.996332\pi\)
\(192\) 2.69118e11i 1.03142i
\(193\) 1.76086e11 0.657565 0.328783 0.944406i \(-0.393362\pi\)
0.328783 + 0.944406i \(0.393362\pi\)
\(194\) 5.66154e11i 2.06028i
\(195\) 9.85329e10 0.349469
\(196\) 3.52471e11 1.21855
\(197\) −5.11182e11 −1.72284 −0.861419 0.507895i \(-0.830424\pi\)
−0.861419 + 0.507895i \(0.830424\pi\)
\(198\) 6.29673e11i 2.06914i
\(199\) 1.88481e11i 0.603951i −0.953316 0.301975i \(-0.902354\pi\)
0.953316 0.301975i \(-0.0976460\pi\)
\(200\) 6.56665e10i 0.205208i
\(201\) 7.92273e10i 0.241488i
\(202\) 8.67157e11i 2.57834i
\(203\) −7.26422e11 −2.10721
\(204\) 7.72403e10i 0.218622i
\(205\) 9.80858e10i 0.270917i
\(206\) 2.02261e11i 0.545224i
\(207\) −9.52795e11 −2.50696
\(208\) 5.53888e11 1.42267
\(209\) 9.16845e10i 0.229914i
\(210\) 2.41035e11 0.590178
\(211\) 4.33240e11i 1.03590i 0.855412 + 0.517949i \(0.173304\pi\)
−0.855412 + 0.517949i \(0.826696\pi\)
\(212\) −2.04526e11 −0.477605
\(213\) 3.83341e11 0.874354
\(214\) 8.01702e11i 1.78626i
\(215\) 7.91972e10 + 2.34735e10i 0.172392 + 0.0510959i
\(216\) 6.02368e10 0.128113
\(217\) 1.60382e11i 0.333317i
\(218\) 5.33581e11i 1.08372i
\(219\) −2.64507e11 −0.525070
\(220\) 8.56759e10i 0.166244i
\(221\) −1.11040e11 −0.210629
\(222\) 3.04887e11i 0.565423i
\(223\) 5.26107e11i 0.954003i −0.878903 0.477001i \(-0.841724\pi\)
0.878903 0.477001i \(-0.158276\pi\)
\(224\) 1.16798e12 2.07106
\(225\) −7.76031e11 −1.34576
\(226\) 1.38750e12 2.35337
\(227\) 7.92335e11i 1.31456i 0.753647 + 0.657279i \(0.228293\pi\)
−0.753647 + 0.657279i \(0.771707\pi\)
\(228\) −1.68681e11 −0.273774
\(229\) 5.71371e11 0.907278 0.453639 0.891185i \(-0.350125\pi\)
0.453639 + 0.891185i \(0.350125\pi\)
\(230\) −2.83276e11 −0.440120
\(231\) −1.74209e12 −2.64857
\(232\) −1.92113e11 −0.285836
\(233\) 5.38816e11i 0.784623i −0.919833 0.392311i \(-0.871676\pi\)
0.919833 0.392311i \(-0.128324\pi\)
\(234\) 1.66541e12i 2.37378i
\(235\) 1.94529e11i 0.271422i
\(236\) 6.99434e11 0.955404
\(237\) 6.96454e11i 0.931431i
\(238\) −2.71630e11 −0.355708
\(239\) 4.82176e10 0.0618324 0.0309162 0.999522i \(-0.490157\pi\)
0.0309162 + 0.999522i \(0.490157\pi\)
\(240\) 2.50545e11 0.314651
\(241\) 1.10028e12i 1.35338i −0.736269 0.676689i \(-0.763414\pi\)
0.736269 0.676689i \(-0.236586\pi\)
\(242\) 2.26026e11i 0.272321i
\(243\) 1.11008e12i 1.31015i
\(244\) 4.08923e11i 0.472817i
\(245\) 2.29204e11i 0.259652i
\(246\) −2.84993e12 −3.16344
\(247\) 2.42494e11i 0.263765i
\(248\) 4.24155e10i 0.0452133i
\(249\) 3.67756e11i 0.384205i
\(250\) −4.69153e11 −0.480412
\(251\) 3.93709e11 0.395191 0.197596 0.980284i \(-0.436687\pi\)
0.197596 + 0.980284i \(0.436687\pi\)
\(252\) 1.86446e12i 1.83463i
\(253\) 2.04739e12 1.97514
\(254\) 5.03704e11i 0.476438i
\(255\) −5.02276e10 −0.0465845
\(256\) 1.35895e12 1.23596
\(257\) 1.34133e12i 1.19638i −0.801354 0.598191i \(-0.795887\pi\)
0.801354 0.598191i \(-0.204113\pi\)
\(258\) 6.82036e11 2.30112e12i 0.596635 2.01298i
\(259\) −4.90688e11 −0.421024
\(260\) 2.26602e11i 0.190721i
\(261\) 2.27035e12i 1.87452i
\(262\) −2.56480e12 −2.07753
\(263\) 2.02530e12i 1.60957i 0.593567 + 0.804785i \(0.297719\pi\)
−0.593567 + 0.804785i \(0.702281\pi\)
\(264\) −4.60723e11 −0.359269
\(265\) 1.32998e11i 0.101769i
\(266\) 5.93199e11i 0.445443i
\(267\) 1.70209e12 1.25437
\(268\) −1.82204e11 −0.131790
\(269\) 6.43203e11 0.456653 0.228327 0.973585i \(-0.426675\pi\)
0.228327 + 0.973585i \(0.426675\pi\)
\(270\) 2.11645e11i 0.147499i
\(271\) −2.70274e12 −1.84909 −0.924544 0.381075i \(-0.875554\pi\)
−0.924544 + 0.381075i \(0.875554\pi\)
\(272\) −2.82347e11 −0.189644
\(273\) 4.60762e12 3.03853
\(274\) 7.36330e11 0.476782
\(275\) 1.66756e12 1.06027
\(276\) 3.76679e12i 2.35194i
\(277\) 8.73863e11i 0.535851i 0.963440 + 0.267926i \(0.0863382\pi\)
−0.963440 + 0.267926i \(0.913662\pi\)
\(278\) 4.11575e12i 2.47870i
\(279\) −5.01256e11 −0.296510
\(280\) 1.02592e11i 0.0596109i
\(281\) 2.33248e12 1.33133 0.665665 0.746251i \(-0.268148\pi\)
0.665665 + 0.746251i \(0.268148\pi\)
\(282\) −5.65214e12 −3.16933
\(283\) −7.70322e11 −0.424366 −0.212183 0.977230i \(-0.568057\pi\)
−0.212183 + 0.977230i \(0.568057\pi\)
\(284\) 8.81593e11i 0.477174i
\(285\) 1.09689e11i 0.0583365i
\(286\) 3.57868e12i 1.87022i
\(287\) 4.58672e12i 2.35555i
\(288\) 3.65038e12i 1.84236i
\(289\) −1.95939e12 −0.971923
\(290\) 6.74999e11i 0.329089i
\(291\) 4.89547e12i 2.34601i
\(292\) 6.08304e11i 0.286554i
\(293\) −3.93334e12 −1.82148 −0.910738 0.412985i \(-0.864486\pi\)
−0.910738 + 0.412985i \(0.864486\pi\)
\(294\) 6.65964e12 3.03190
\(295\) 4.54826e11i 0.203580i
\(296\) −1.29770e11 −0.0571104
\(297\) 1.52967e12i 0.661937i
\(298\) −8.30597e11 −0.353435
\(299\) −5.41511e12 −2.26595
\(300\) 3.06797e12i 1.26254i
\(301\) 3.70344e12 + 1.09768e12i 1.49890 + 0.444265i
\(302\) 2.20666e12 0.878416
\(303\) 7.49822e12i 2.93592i
\(304\) 6.16603e11i 0.237486i
\(305\) 2.65913e11 0.100749
\(306\) 8.48949e11i 0.316428i
\(307\) 3.55464e12 1.30348 0.651740 0.758443i \(-0.274039\pi\)
0.651740 + 0.758443i \(0.274039\pi\)
\(308\) 4.00640e12i 1.44544i
\(309\) 1.74893e12i 0.620839i
\(310\) −1.49029e11 −0.0520549
\(311\) 8.84075e11 0.303870 0.151935 0.988391i \(-0.451450\pi\)
0.151935 + 0.988391i \(0.451450\pi\)
\(312\) 1.21856e12 0.412166
\(313\) 2.78961e12i 0.928587i 0.885681 + 0.464293i \(0.153692\pi\)
−0.885681 + 0.464293i \(0.846308\pi\)
\(314\) −2.71279e12 −0.888727
\(315\) 1.21241e12 0.390929
\(316\) 1.60168e12 0.508323
\(317\) 2.58249e12 0.806758 0.403379 0.915033i \(-0.367836\pi\)
0.403379 + 0.915033i \(0.367836\pi\)
\(318\) −3.86434e12 −1.18834
\(319\) 4.87859e12i 1.47687i
\(320\) 4.02462e11i 0.119943i
\(321\) 6.93223e12i 2.03399i
\(322\) −1.32466e13 −3.82672
\(323\) 1.23613e11i 0.0351601i
\(324\) 1.37574e12 0.385311
\(325\) −4.41049e12 −1.21638
\(326\) −2.56799e12 −0.697438
\(327\) 4.61382e12i 1.23402i
\(328\) 1.21303e12i 0.319522i
\(329\) 9.09662e12i 2.35994i
\(330\) 1.61877e12i 0.413634i
\(331\) 6.69456e12i 1.68493i 0.538751 + 0.842465i \(0.318896\pi\)
−0.538751 + 0.842465i \(0.681104\pi\)
\(332\) −8.45750e11 −0.209678
\(333\) 1.53359e12i 0.374531i
\(334\) 3.37483e12i 0.811931i
\(335\) 1.18483e11i 0.0280823i
\(336\) 1.17160e13 2.73580
\(337\) −4.74772e12 −1.09228 −0.546142 0.837693i \(-0.683904\pi\)
−0.546142 + 0.837693i \(0.683904\pi\)
\(338\) 3.47493e12i 0.787703i
\(339\) 1.19975e13 2.67975
\(340\) 1.15512e11i 0.0254232i
\(341\) 1.07711e12 0.233609
\(342\) −1.85398e12 −0.396254
\(343\) 3.29599e12i 0.694248i
\(344\) 9.79432e11 + 2.90297e11i 0.203321 + 0.0602630i
\(345\) −2.44946e12 −0.501158
\(346\) 1.46529e12i 0.295491i
\(347\) 2.39973e12i 0.476996i −0.971143 0.238498i \(-0.923345\pi\)
0.971143 0.238498i \(-0.0766550\pi\)
\(348\) 8.97563e12 1.75861
\(349\) 2.58521e12i 0.499309i 0.968335 + 0.249655i \(0.0803171\pi\)
−0.968335 + 0.249655i \(0.919683\pi\)
\(350\) −1.07891e13 −2.05421
\(351\) 4.04580e12i 0.759397i
\(352\) 7.84404e12i 1.45153i
\(353\) 4.03701e12 0.736522 0.368261 0.929722i \(-0.379953\pi\)
0.368261 + 0.929722i \(0.379953\pi\)
\(354\) 1.32152e13 2.37716
\(355\) 5.73280e11 0.101678
\(356\) 3.91440e12i 0.684565i
\(357\) −2.34876e12 −0.405039
\(358\) 6.26751e12 1.06581
\(359\) 8.09958e12 1.35828 0.679141 0.734007i \(-0.262352\pi\)
0.679141 + 0.734007i \(0.262352\pi\)
\(360\) 3.20641e11 0.0530282
\(361\) 5.86112e12 0.955970
\(362\) 8.87723e12i 1.42802i
\(363\) 1.95442e12i 0.310088i
\(364\) 1.05964e13i 1.65826i
\(365\) −3.95566e11 −0.0610597
\(366\) 7.72625e12i 1.17642i
\(367\) 2.38660e11 0.0358467 0.0179233 0.999839i \(-0.494295\pi\)
0.0179233 + 0.999839i \(0.494295\pi\)
\(368\) −1.37693e13 −2.04020
\(369\) −1.43353e13 −2.09543
\(370\) 4.55953e11i 0.0657523i
\(371\) 6.21931e12i 0.884856i
\(372\) 1.98167e12i 0.278175i
\(373\) 1.04130e13i 1.44222i 0.692819 + 0.721112i \(0.256369\pi\)
−0.692819 + 0.721112i \(0.743631\pi\)
\(374\) 1.82425e12i 0.249302i
\(375\) −4.05672e12 −0.547039
\(376\) 2.40574e12i 0.320117i
\(377\) 1.29033e13i 1.69431i
\(378\) 9.89699e12i 1.28246i
\(379\) −4.27776e12 −0.547041 −0.273521 0.961866i \(-0.588188\pi\)
−0.273521 + 0.961866i \(0.588188\pi\)
\(380\) −2.52260e11 −0.0318368
\(381\) 4.35547e12i 0.542514i
\(382\) 2.54574e11 0.0312966
\(383\) 2.12063e12i 0.257318i 0.991689 + 0.128659i \(0.0410673\pi\)
−0.991689 + 0.128659i \(0.958933\pi\)
\(384\) 5.40863e12 0.647786
\(385\) −2.60527e12 −0.307999
\(386\) 7.65130e12i 0.892892i
\(387\) 3.43066e12 1.15747e13i 0.395206 1.33338i
\(388\) −1.12584e13 −1.28032
\(389\) 1.74998e13i 1.96465i −0.187190 0.982324i \(-0.559938\pi\)
0.187190 0.982324i \(-0.440062\pi\)
\(390\) 4.28145e12i 0.474535i
\(391\) 2.76038e12 0.302054
\(392\) 2.83457e12i 0.306236i
\(393\) −2.21776e13 −2.36565
\(394\) 2.22119e13i 2.33940i
\(395\) 1.04153e12i 0.108315i
\(396\) 1.25216e13 1.28583
\(397\) −1.30082e13 −1.31906 −0.659532 0.751677i \(-0.729245\pi\)
−0.659532 + 0.751677i \(0.729245\pi\)
\(398\) −8.18987e12 −0.820090
\(399\) 5.12933e12i 0.507220i
\(400\) −1.12148e13 −1.09519
\(401\) −1.61167e12 −0.155437 −0.0777184 0.996975i \(-0.524764\pi\)
−0.0777184 + 0.996975i \(0.524764\pi\)
\(402\) −3.44259e12 −0.327910
\(403\) −2.84884e12 −0.268005
\(404\) 1.72441e13 1.60226
\(405\) 8.94611e11i 0.0821031i
\(406\) 3.15645e13i 2.86134i
\(407\) 3.29542e12i 0.295080i
\(408\) −6.21165e11 −0.0549422
\(409\) 1.49548e12i 0.130667i −0.997864 0.0653333i \(-0.979189\pi\)
0.997864 0.0653333i \(-0.0208110\pi\)
\(410\) −4.26203e12 −0.367872
\(411\) 6.36697e12 0.542905
\(412\) −4.02211e12 −0.338819
\(413\) 2.12687e13i 1.77007i
\(414\) 4.14009e13i 3.40414i
\(415\) 5.49972e11i 0.0446787i
\(416\) 2.07465e13i 1.66525i
\(417\) 3.55884e13i 2.82247i
\(418\) 3.98388e12 0.312194
\(419\) 1.62703e13i 1.25987i −0.776650 0.629933i \(-0.783082\pi\)
0.776650 0.629933i \(-0.216918\pi\)
\(420\) 4.79317e12i 0.366756i
\(421\) 6.86747e12i 0.519262i −0.965708 0.259631i \(-0.916399\pi\)
0.965708 0.259631i \(-0.0836009\pi\)
\(422\) 1.88252e13 1.40662
\(423\) −2.84304e13 −2.09934
\(424\) 1.64479e12i 0.120028i
\(425\) 2.24827e12 0.162145
\(426\) 1.66569e13i 1.18726i
\(427\) 1.24347e13 0.875985
\(428\) 1.59425e13 1.11004
\(429\) 3.09444e13i 2.12959i
\(430\) 1.01997e12 3.44128e12i 0.0693819 0.234087i
\(431\) 7.11864e12 0.478642 0.239321 0.970941i \(-0.423075\pi\)
0.239321 + 0.970941i \(0.423075\pi\)
\(432\) 1.02875e13i 0.683738i
\(433\) 2.59233e13i 1.70314i −0.524240 0.851570i \(-0.675651\pi\)
0.524240 0.851570i \(-0.324349\pi\)
\(434\) −6.96893e12 −0.452603
\(435\) 5.83665e12i 0.374729i
\(436\) 1.06107e13 0.673459
\(437\) 6.02824e12i 0.378254i
\(438\) 1.14934e13i 0.712980i
\(439\) 5.68385e12 0.348594 0.174297 0.984693i \(-0.444235\pi\)
0.174297 + 0.984693i \(0.444235\pi\)
\(440\) −6.89003e11 −0.0417790
\(441\) 3.34982e13 2.00830
\(442\) 4.82491e12i 0.286008i
\(443\) 2.10962e13 1.23648 0.618238 0.785991i \(-0.287847\pi\)
0.618238 + 0.785991i \(0.287847\pi\)
\(444\) 6.06292e12 0.351372
\(445\) 2.54544e12 0.145869
\(446\) −2.28604e13 −1.29542
\(447\) −7.18209e12 −0.402451
\(448\) 1.88200e13i 1.04287i
\(449\) 2.64710e13i 1.45057i 0.688448 + 0.725285i \(0.258292\pi\)
−0.688448 + 0.725285i \(0.741708\pi\)
\(450\) 3.37201e13i 1.82737i
\(451\) 3.08040e13 1.65092
\(452\) 2.75915e13i 1.46246i
\(453\) 1.90808e13 1.00024
\(454\) 3.44286e13 1.78501
\(455\) 6.89062e12 0.353347
\(456\) 1.35653e12i 0.0688026i
\(457\) 1.62983e13i 0.817638i 0.912616 + 0.408819i \(0.134059\pi\)
−0.912616 + 0.408819i \(0.865941\pi\)
\(458\) 2.48272e13i 1.23197i
\(459\) 2.06237e12i 0.101228i
\(460\) 5.63317e12i 0.273504i
\(461\) −1.08374e13 −0.520499 −0.260249 0.965541i \(-0.583805\pi\)
−0.260249 + 0.965541i \(0.583805\pi\)
\(462\) 7.56975e13i 3.59643i
\(463\) 2.34477e13i 1.10204i −0.834493 0.551018i \(-0.814239\pi\)
0.834493 0.551018i \(-0.185761\pi\)
\(464\) 3.28099e13i 1.52551i
\(465\) −1.28864e12 −0.0592742
\(466\) −2.34126e13 −1.06542
\(467\) 5.80691e12i 0.261433i −0.991420 0.130717i \(-0.958272\pi\)
0.991420 0.130717i \(-0.0417278\pi\)
\(468\) −3.31180e13 −1.47514
\(469\) 5.54054e12i 0.244168i
\(470\) −8.45267e12 −0.368557
\(471\) −2.34572e13 −1.01198
\(472\) 5.62484e12i 0.240104i
\(473\) −7.37191e12 + 2.48720e13i −0.311368 + 1.05052i
\(474\) 3.02623e13 1.26477
\(475\) 4.90987e12i 0.203050i
\(476\) 5.40158e12i 0.221048i
\(477\) −1.94377e13 −0.787144
\(478\) 2.09515e12i 0.0839608i
\(479\) −1.59691e13 −0.633289 −0.316645 0.948544i \(-0.602556\pi\)
−0.316645 + 0.948544i \(0.602556\pi\)
\(480\) 9.38444e12i 0.368300i
\(481\) 8.71599e12i 0.338526i
\(482\) −4.78095e13 −1.83772
\(483\) −1.14542e14 −4.35743
\(484\) −4.49470e12 −0.169229
\(485\) 7.32110e12i 0.272815i
\(486\) 4.82351e13 1.77902
\(487\) 3.83538e13 1.40012 0.700058 0.714086i \(-0.253158\pi\)
0.700058 + 0.714086i \(0.253158\pi\)
\(488\) 3.28855e12 0.118824
\(489\) −2.22051e13 −0.794162
\(490\) 9.95938e12 0.352575
\(491\) 2.92677e13i 1.02561i −0.858506 0.512803i \(-0.828607\pi\)
0.858506 0.512803i \(-0.171393\pi\)
\(492\) 5.66732e13i 1.96586i
\(493\) 6.57751e12i 0.225854i
\(494\) −1.05369e13 −0.358160
\(495\) 8.14248e12i 0.273987i
\(496\) −7.24389e12 −0.241303
\(497\) 2.68079e13 0.884058
\(498\) −1.59797e13 −0.521702
\(499\) 4.70754e13i 1.52157i −0.649005 0.760784i \(-0.724815\pi\)
0.649005 0.760784i \(-0.275185\pi\)
\(500\) 9.32948e12i 0.298543i
\(501\) 2.91818e13i 0.924535i
\(502\) 1.71075e13i 0.536621i
\(503\) 3.71078e13i 1.15246i −0.817288 0.576229i \(-0.804524\pi\)
0.817288 0.576229i \(-0.195476\pi\)
\(504\) 1.49939e13 0.461065
\(505\) 1.12135e13i 0.341415i
\(506\) 8.89634e13i 2.68200i
\(507\) 3.00474e13i 0.896947i
\(508\) 1.00166e13 0.296074
\(509\) 1.67021e13 0.488859 0.244429 0.969667i \(-0.421399\pi\)
0.244429 + 0.969667i \(0.421399\pi\)
\(510\) 2.18249e12i 0.0632560i
\(511\) −1.84976e13 −0.530897
\(512\) 4.43087e13i 1.25933i
\(513\) −4.50389e12 −0.126766
\(514\) −5.82835e13 −1.62454
\(515\) 2.61549e12i 0.0721966i
\(516\) −4.57595e13 1.35628e13i −1.25093 0.370768i
\(517\) 6.10922e13 1.65399
\(518\) 2.13214e13i 0.571698i
\(519\) 1.26703e13i 0.336472i
\(520\) 1.82233e12 0.0479303
\(521\) 4.21766e13i 1.09871i 0.835589 + 0.549355i \(0.185126\pi\)
−0.835589 + 0.549355i \(0.814874\pi\)
\(522\) 9.86513e13 2.54537
\(523\) 3.37686e13i 0.862989i 0.902116 + 0.431494i \(0.142014\pi\)
−0.902116 + 0.431494i \(0.857986\pi\)
\(524\) 5.10031e13i 1.29104i
\(525\) −9.32922e13 −2.33910
\(526\) 8.80032e13 2.18560
\(527\) 1.45221e12 0.0357253
\(528\) 7.86841e13i 1.91742i
\(529\) 9.31893e13 2.24951
\(530\) −5.77905e12 −0.138190
\(531\) 6.64730e13 1.57461
\(532\) −1.17962e13 −0.276812
\(533\) −8.14729e13 −1.89399
\(534\) 7.39592e13i 1.70328i
\(535\) 1.03670e13i 0.236530i
\(536\) 1.46528e12i 0.0331205i
\(537\) 5.41945e13 1.21362
\(538\) 2.79485e13i 0.620078i
\(539\) −7.19820e13 −1.58227
\(540\) −4.20873e12 −0.0916604
\(541\) 5.98775e13 1.29204 0.646022 0.763319i \(-0.276431\pi\)
0.646022 + 0.763319i \(0.276431\pi\)
\(542\) 1.17439e14i 2.51083i
\(543\) 7.67605e13i 1.62607i
\(544\) 1.05756e13i 0.221979i
\(545\) 6.89988e12i 0.143502i
\(546\) 2.00211e14i 4.12595i
\(547\) −1.75237e13 −0.357840 −0.178920 0.983864i \(-0.557260\pi\)
−0.178920 + 0.983864i \(0.557260\pi\)
\(548\) 1.46425e13i 0.296287i
\(549\) 3.88633e13i 0.779252i
\(550\) 7.24587e13i 1.43972i
\(551\) 1.43643e13 0.282830
\(552\) −3.02925e13 −0.591070
\(553\) 4.87045e13i 0.941768i
\(554\) 3.79711e13 0.727620
\(555\) 3.94258e12i 0.0748713i
\(556\) −8.18449e13 −1.54034
\(557\) 5.45729e13 1.01789 0.508946 0.860799i \(-0.330035\pi\)
0.508946 + 0.860799i \(0.330035\pi\)
\(558\) 2.17806e13i 0.402623i
\(559\) 1.94978e13 6.57835e13i 0.357212 1.20520i
\(560\) 1.75211e13 0.318143
\(561\) 1.57741e13i 0.283877i
\(562\) 1.01351e14i 1.80778i
\(563\) −2.58971e13 −0.457835 −0.228917 0.973446i \(-0.573519\pi\)
−0.228917 + 0.973446i \(0.573519\pi\)
\(564\) 1.12397e14i 1.96952i
\(565\) 1.79421e13 0.311625
\(566\) 3.34721e13i 0.576236i
\(567\) 4.18341e13i 0.713863i
\(568\) 7.08975e12 0.119919
\(569\) −4.99939e13 −0.838216 −0.419108 0.907936i \(-0.637657\pi\)
−0.419108 + 0.907936i \(0.637657\pi\)
\(570\) −4.76623e12 −0.0792138
\(571\) 1.15462e14i 1.90220i 0.308877 + 0.951102i \(0.400047\pi\)
−0.308877 + 0.951102i \(0.599953\pi\)
\(572\) 7.11649e13 1.16221
\(573\) 2.20128e12 0.0356370
\(574\) −1.99302e14 −3.19855
\(575\) 1.09642e14 1.74436
\(576\) −5.88199e13 −0.927710
\(577\) 8.08399e13i 1.26400i −0.774969 0.632000i \(-0.782234\pi\)
0.774969 0.632000i \(-0.217766\pi\)
\(578\) 8.51395e13i 1.31975i
\(579\) 6.61600e13i 1.01672i
\(580\) 1.34229e13 0.204506
\(581\) 2.57180e13i 0.388469i
\(582\) −2.12718e14 −3.18559
\(583\) 4.17684e13 0.620162
\(584\) −4.89197e12 −0.0720144
\(585\) 2.15359e13i 0.314328i
\(586\) 1.70912e14i 2.47334i
\(587\) 7.86996e12i 0.112923i −0.998405 0.0564614i \(-0.982018\pi\)
0.998405 0.0564614i \(-0.0179818\pi\)
\(588\) 1.32432e14i 1.88412i
\(589\) 3.17140e12i 0.0447378i
\(590\) 1.97631e13 0.276437
\(591\) 1.92064e14i 2.66384i
\(592\) 2.21626e13i 0.304798i
\(593\) 8.56253e13i 1.16769i 0.811864 + 0.583847i \(0.198453\pi\)
−0.811864 + 0.583847i \(0.801547\pi\)
\(594\) 6.64674e13 0.898828
\(595\) −3.51253e12 −0.0471015
\(596\) 1.65171e13i 0.219635i
\(597\) −7.08170e13 −0.933825
\(598\) 2.35297e14i 3.07688i
\(599\) −1.48717e13 −0.192852 −0.0964262 0.995340i \(-0.530741\pi\)
−0.0964262 + 0.995340i \(0.530741\pi\)
\(600\) −2.46725e13 −0.317291
\(601\) 8.31585e13i 1.06056i 0.847823 + 0.530279i \(0.177913\pi\)
−0.847823 + 0.530279i \(0.822087\pi\)
\(602\) 4.76962e13 1.60922e14i 0.603256 2.03532i
\(603\) −1.73163e13 −0.217205
\(604\) 4.38812e13i 0.545876i
\(605\) 2.92280e12i 0.0360597i
\(606\) 3.25813e14 3.98662
\(607\) 1.20141e14i 1.45797i −0.684529 0.728985i \(-0.739992\pi\)
0.684529 0.728985i \(-0.260008\pi\)
\(608\) −2.30956e13 −0.277978
\(609\) 2.72935e14i 3.25816i
\(610\) 1.15545e13i 0.136805i
\(611\) −1.61581e14 −1.89751
\(612\) 1.68820e13 0.196638
\(613\) 1.06650e14 1.23213 0.616066 0.787694i \(-0.288725\pi\)
0.616066 + 0.787694i \(0.288725\pi\)
\(614\) 1.54457e14i 1.76996i
\(615\) −3.68533e13 −0.418891
\(616\) −3.22194e13 −0.363257
\(617\) −1.07278e14 −1.19973 −0.599865 0.800101i \(-0.704779\pi\)
−0.599865 + 0.800101i \(0.704779\pi\)
\(618\) −7.59944e13 −0.843023
\(619\) −9.90190e13 −1.08960 −0.544798 0.838568i \(-0.683394\pi\)
−0.544798 + 0.838568i \(0.683394\pi\)
\(620\) 2.96356e12i 0.0323486i
\(621\) 1.00576e14i 1.08902i
\(622\) 3.84149e13i 0.412617i
\(623\) 1.19031e14 1.26829
\(624\) 2.08110e14i 2.19973i
\(625\) 8.62175e13 0.904056
\(626\) 1.21214e14 1.26091
\(627\) 3.44482e13 0.355491
\(628\) 5.39461e13i 0.552283i
\(629\) 4.44302e12i 0.0451258i
\(630\) 5.26818e13i 0.530833i
\(631\) 2.23891e13i 0.223815i −0.993719 0.111908i \(-0.964304\pi\)
0.993719 0.111908i \(-0.0356961\pi\)
\(632\) 1.28807e13i 0.127748i
\(633\) 1.62779e14 1.60170
\(634\) 1.12215e14i 1.09548i
\(635\) 6.51354e12i 0.0630882i
\(636\) 7.68455e13i 0.738470i
\(637\) 1.90384e14 1.81523
\(638\) −2.11985e14 −2.00540
\(639\) 8.37850e13i 0.786434i
\(640\) 8.08852e12 0.0753302
\(641\) 6.25113e13i 0.577654i 0.957381 + 0.288827i \(0.0932653\pi\)
−0.957381 + 0.288827i \(0.906735\pi\)
\(642\) 3.01220e14 2.76190
\(643\) −2.02908e14 −1.84606 −0.923028 0.384732i \(-0.874294\pi\)
−0.923028 + 0.384732i \(0.874294\pi\)
\(644\) 2.63420e14i 2.37804i
\(645\) 8.81960e12 2.97564e13i 0.0790042 0.266552i
\(646\) 5.37122e12 0.0477431
\(647\) 1.49018e13i 0.131437i −0.997838 0.0657184i \(-0.979066\pi\)
0.997838 0.0657184i \(-0.0209339\pi\)
\(648\) 1.10637e13i 0.0968331i
\(649\) −1.42839e14 −1.24058
\(650\) 1.91645e14i 1.65169i
\(651\) −6.02596e13 −0.515373
\(652\) 5.10666e13i 0.433410i
\(653\) 1.18155e14i 0.995141i −0.867423 0.497571i \(-0.834226\pi\)
0.867423 0.497571i \(-0.165774\pi\)
\(654\) 2.00480e14 1.67564
\(655\) −3.31662e13 −0.275099
\(656\) −2.07166e14 −1.70529
\(657\) 5.78121e13i 0.472272i
\(658\) −3.95266e14 −3.20450
\(659\) −1.21811e13 −0.0980078 −0.0490039 0.998799i \(-0.515605\pi\)
−0.0490039 + 0.998799i \(0.515605\pi\)
\(660\) 3.21906e13 0.257045
\(661\) 3.48800e13 0.276420 0.138210 0.990403i \(-0.455865\pi\)
0.138210 + 0.990403i \(0.455865\pi\)
\(662\) 2.90892e14 2.28793
\(663\) 4.17205e13i 0.325673i
\(664\) 6.80151e12i 0.0526944i
\(665\) 7.67082e12i 0.0589839i
\(666\) 6.66376e13 0.508567
\(667\) 3.20767e14i 2.42974i
\(668\) −6.71112e13 −0.504560
\(669\) −1.97672e14 −1.47507
\(670\) −5.14833e12 −0.0381323
\(671\) 8.35106e13i 0.613945i
\(672\) 4.38838e14i 3.20227i
\(673\) 1.15973e14i 0.840001i 0.907524 + 0.420001i \(0.137970\pi\)
−0.907524 + 0.420001i \(0.862030\pi\)
\(674\) 2.06298e14i 1.48319i
\(675\) 8.19168e13i 0.584594i
\(676\) −6.91018e13 −0.489504
\(677\) 6.79252e13i 0.477626i 0.971066 + 0.238813i \(0.0767583\pi\)
−0.971066 + 0.238813i \(0.923242\pi\)
\(678\) 5.21318e14i 3.63877i
\(679\) 3.42351e14i 2.37205i
\(680\) −9.28941e11 −0.00638916
\(681\) 2.97700e14 2.03256
\(682\) 4.68028e13i 0.317212i
\(683\) 3.79254e13 0.255168 0.127584 0.991828i \(-0.459278\pi\)
0.127584 + 0.991828i \(0.459278\pi\)
\(684\) 3.68678e13i 0.246245i
\(685\) 9.52170e12 0.0631338
\(686\) 1.43217e14 0.942703
\(687\) 2.14678e14i 1.40283i
\(688\) 4.95781e13 1.67271e14i 0.321623 1.08512i
\(689\) −1.10472e14 −0.711471
\(690\) 1.06434e14i 0.680510i
\(691\) 1.15244e14i 0.731521i 0.930709 + 0.365760i \(0.119191\pi\)
−0.930709 + 0.365760i \(0.880809\pi\)
\(692\) 2.91386e13 0.183628
\(693\) 3.80761e14i 2.38224i
\(694\) −1.04273e14 −0.647701
\(695\) 5.32219e13i 0.328221i
\(696\) 7.21818e13i 0.441959i
\(697\) 4.15312e13 0.252471
\(698\) 1.12333e14 0.678000
\(699\) −2.02447e14 −1.21318
\(700\) 2.14550e14i 1.27655i
\(701\) 3.65272e13 0.215787 0.107894 0.994162i \(-0.465589\pi\)
0.107894 + 0.994162i \(0.465589\pi\)
\(702\) −1.75798e14 −1.03117
\(703\) 9.70288e12 0.0565098
\(704\) 1.26394e14 0.730909
\(705\) −7.30894e13 −0.419671
\(706\) 1.75416e14i 1.00011i
\(707\) 5.24367e14i 2.96851i
\(708\) 2.62795e14i 1.47724i
\(709\) −1.34678e14 −0.751737 −0.375868 0.926673i \(-0.622656\pi\)
−0.375868 + 0.926673i \(0.622656\pi\)
\(710\) 2.49102e13i 0.138065i
\(711\) 1.52221e14 0.837771
\(712\) 3.14795e13 0.172039
\(713\) 7.08201e13 0.384334
\(714\) 1.02058e14i 0.549993i
\(715\) 4.62769e13i 0.247648i
\(716\) 1.24634e14i 0.662328i
\(717\) 1.81166e13i 0.0956050i
\(718\) 3.51943e14i 1.84438i
\(719\) −1.03604e14 −0.539177 −0.269588 0.962976i \(-0.586888\pi\)
−0.269588 + 0.962976i \(0.586888\pi\)
\(720\) 5.47604e13i 0.283011i
\(721\) 1.22306e14i 0.627729i
\(722\) 2.54677e14i 1.29809i
\(723\) −4.13404e14 −2.09258
\(724\) −1.76531e14 −0.887417
\(725\) 2.61257e14i 1.30430i
\(726\) −8.49235e13 −0.421061
\(727\) 4.43628e13i 0.218447i −0.994017 0.109224i \(-0.965164\pi\)
0.994017 0.109224i \(-0.0348365\pi\)
\(728\) 8.52163e13 0.416741
\(729\) 3.23069e14 1.56913
\(730\) 1.71882e13i 0.0829116i
\(731\) −9.93909e12 + 3.35334e13i −0.0476168 + 0.160654i
\(732\) −1.53643e14 −0.731066
\(733\) 1.70067e14i 0.803713i 0.915703 + 0.401856i \(0.131635\pi\)
−0.915703 + 0.401856i \(0.868365\pi\)
\(734\) 1.03702e13i 0.0486753i
\(735\) 8.61178e13 0.401473
\(736\) 5.15744e14i 2.38806i
\(737\) 3.72099e13 0.171128
\(738\) 6.22896e14i 2.84534i
\(739\) 1.97546e14i 0.896283i −0.893963 0.448142i \(-0.852086\pi\)
0.893963 0.448142i \(-0.147914\pi\)
\(740\) 9.06699e12 0.0408606
\(741\) −9.11112e13 −0.407832
\(742\) −2.70242e14 −1.20152
\(743\) 1.19187e14i 0.526363i −0.964746 0.263182i \(-0.915228\pi\)
0.964746 0.263182i \(-0.0847719\pi\)
\(744\) −1.59366e13 −0.0699086
\(745\) −1.07407e13 −0.0468005
\(746\) 4.52467e14 1.95836
\(747\) −8.03786e13 −0.345571
\(748\) −3.62766e13 −0.154924
\(749\) 4.84786e14i 2.05656i
\(750\) 1.76273e14i 0.742811i
\(751\) 1.42115e14i 0.594893i 0.954738 + 0.297447i \(0.0961350\pi\)
−0.954738 + 0.297447i \(0.903865\pi\)
\(752\) −4.10861e14 −1.70847
\(753\) 1.47927e14i 0.611042i
\(754\) 5.60674e14 2.30067
\(755\) 2.85349e13 0.116317
\(756\) −1.96810e14 −0.796962
\(757\) 9.54159e13i 0.383832i −0.981411 0.191916i \(-0.938530\pi\)
0.981411 0.191916i \(-0.0614701\pi\)
\(758\) 1.85877e14i 0.742814i
\(759\) 7.69258e14i 3.05396i
\(760\) 2.02867e12i 0.00800097i
\(761\) 4.55346e14i 1.78410i −0.451939 0.892049i \(-0.649268\pi\)
0.451939 0.892049i \(-0.350732\pi\)
\(762\) 1.89254e14 0.736666
\(763\) 3.22654e14i 1.24771i
\(764\) 5.06241e12i 0.0194487i
\(765\) 1.09780e13i 0.0419002i
\(766\) 9.21455e13 0.349406
\(767\) 3.77792e14 1.42323
\(768\) 5.10593e14i 1.91104i
\(769\) −1.21914e13 −0.0453338 −0.0226669 0.999743i \(-0.507216\pi\)
−0.0226669 + 0.999743i \(0.507216\pi\)
\(770\) 1.13204e14i 0.418224i
\(771\) −5.03971e14 −1.84984
\(772\) −1.52152e14 −0.554871
\(773\) 3.40763e14i 1.23468i 0.786696 + 0.617340i \(0.211790\pi\)
−0.786696 + 0.617340i \(0.788210\pi\)
\(774\) −5.02944e14 1.49069e14i −1.81057 0.536640i
\(775\) 5.76814e13 0.206313
\(776\) 9.05400e13i 0.321760i
\(777\) 1.84364e14i 0.650985i
\(778\) −7.60401e14 −2.66775
\(779\) 9.06978e13i 0.316162i
\(780\) −8.51402e13