Properties

Label 43.9.b.b.42.16
Level 43
Weight 9
Character 43.42
Analytic conductor 17.517
Analytic rank 0
Dimension 28
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.5172802326\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.16
Character \(\chi\) \(=\) 43.42
Dual form 43.9.b.b.42.13

$q$-expansion

\(f(q)\) \(=\) \(q+6.19852i q^{2} -89.9215i q^{3} +217.578 q^{4} -140.759i q^{5} +557.380 q^{6} +4216.48i q^{7} +2935.49i q^{8} -1524.87 q^{9} +O(q^{10})\) \(q+6.19852i q^{2} -89.9215i q^{3} +217.578 q^{4} -140.759i q^{5} +557.380 q^{6} +4216.48i q^{7} +2935.49i q^{8} -1524.87 q^{9} +872.500 q^{10} -4220.20 q^{11} -19565.0i q^{12} +35375.6 q^{13} -26135.9 q^{14} -12657.3 q^{15} +37504.4 q^{16} +23089.9 q^{17} -9451.93i q^{18} -1755.68i q^{19} -30626.2i q^{20} +379152. q^{21} -26159.0i q^{22} -105858. q^{23} +263963. q^{24} +370812. q^{25} +219277. i q^{26} -452856. i q^{27} +917414. i q^{28} +807061. i q^{29} -78456.5i q^{30} +374092. q^{31} +983956. i q^{32} +379487. i q^{33} +143123. i q^{34} +593508. q^{35} -331778. q^{36} -2.09493e6i q^{37} +10882.6 q^{38} -3.18103e6i q^{39} +413197. q^{40} +3.35460e6 q^{41} +2.35018e6i q^{42} +(3.26825e6 - 1.00337e6i) q^{43} -918225. q^{44} +214639. i q^{45} -656161. i q^{46} -3.56896e6 q^{47} -3.37245e6i q^{48} -1.20139e7 q^{49} +2.29849e6i q^{50} -2.07628e6i q^{51} +7.69697e6 q^{52} -5.72503e6 q^{53} +2.80704e6 q^{54} +594033. i q^{55} -1.23774e7 q^{56} -157873. q^{57} -5.00258e6 q^{58} -1.72958e7 q^{59} -2.75395e6 q^{60} +1.48218e7i q^{61} +2.31882e6i q^{62} -6.42957e6i q^{63} +3.50204e6 q^{64} -4.97945e6i q^{65} -2.35226e6 q^{66} +1.67765e7 q^{67} +5.02386e6 q^{68} +9.51888e6i q^{69} +3.67887e6i q^{70} -1.93772e7i q^{71} -4.47623e6i q^{72} +1.18749e7i q^{73} +1.29855e7 q^{74} -3.33439e7i q^{75} -381998. i q^{76} -1.77944e7i q^{77} +1.97177e7 q^{78} -2.09356e7 q^{79} -5.27909e6i q^{80} -5.07262e7 q^{81} +2.07936e7i q^{82} +1.44138e6 q^{83} +8.24952e7 q^{84} -3.25012e6i q^{85} +(6.21938e6 + 2.02583e7i) q^{86} +7.25721e7 q^{87} -1.23883e7i q^{88} +5.12452e7i q^{89} -1.33045e6 q^{90} +1.49161e8i q^{91} -2.30323e7 q^{92} -3.36389e7i q^{93} -2.21223e7i q^{94} -247128. q^{95} +8.84788e7 q^{96} -7.77098e7 q^{97} -7.44682e7i q^{98} +6.43525e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + O(q^{10}) \) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + 24982q^{10} + 4538q^{11} + 22086q^{13} + 24732q^{14} + 15388q^{15} + 525812q^{16} - 135136q^{17} - 261352q^{21} - 184432q^{23} + 1770326q^{24} - 2640434q^{25} - 110272q^{31} + 10947816q^{35} + 11602066q^{36} - 7189158q^{38} - 21389338q^{40} + 1301336q^{41} + 2473420q^{43} - 8818480q^{44} + 1983566q^{47} - 15560936q^{49} + 12927876q^{52} + 23942594q^{53} - 13757972q^{54} + 34967256q^{56} + 35225148q^{57} + 22565734q^{58} - 5554336q^{59} - 44902072q^{60} - 170444572q^{64} - 48457584q^{66} - 130953802q^{67} + 150021122q^{68} + 205870278q^{74} + 267860612q^{78} + 7380250q^{79} - 57601004q^{81} - 42603970q^{83} + 251931292q^{84} - 45482652q^{86} - 106687410q^{87} - 255044692q^{90} - 409532014q^{92} + 123322986q^{95} - 692987086q^{96} - 318744840q^{97} - 609707206q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.19852i 0.387408i 0.981060 + 0.193704i \(0.0620501\pi\)
−0.981060 + 0.193704i \(0.937950\pi\)
\(3\) 89.9215i 1.11014i −0.831803 0.555071i \(-0.812691\pi\)
0.831803 0.555071i \(-0.187309\pi\)
\(4\) 217.578 0.849915
\(5\) 140.759i 0.225215i −0.993640 0.112607i \(-0.964080\pi\)
0.993640 0.112607i \(-0.0359202\pi\)
\(6\) 557.380 0.430077
\(7\) 4216.48i 1.75613i 0.478539 + 0.878067i \(0.341167\pi\)
−0.478539 + 0.878067i \(0.658833\pi\)
\(8\) 2935.49i 0.716671i
\(9\) −1524.87 −0.232414
\(10\) 872.500 0.0872500
\(11\) −4220.20 −0.288246 −0.144123 0.989560i \(-0.546036\pi\)
−0.144123 + 0.989560i \(0.546036\pi\)
\(12\) 19565.0i 0.943526i
\(13\) 35375.6 1.23860 0.619300 0.785155i \(-0.287417\pi\)
0.619300 + 0.785155i \(0.287417\pi\)
\(14\) −26135.9 −0.680340
\(15\) −12657.3 −0.250020
\(16\) 37504.4 0.572271
\(17\) 23089.9 0.276456 0.138228 0.990400i \(-0.455859\pi\)
0.138228 + 0.990400i \(0.455859\pi\)
\(18\) 9451.93i 0.0900390i
\(19\) 1755.68i 0.0134720i −0.999977 0.00673598i \(-0.997856\pi\)
0.999977 0.00673598i \(-0.00214415\pi\)
\(20\) 30626.2i 0.191414i
\(21\) 379152. 1.94956
\(22\) 26159.0i 0.111669i
\(23\) −105858. −0.378278 −0.189139 0.981950i \(-0.560570\pi\)
−0.189139 + 0.981950i \(0.560570\pi\)
\(24\) 263963. 0.795607
\(25\) 370812. 0.949278
\(26\) 219277.i 0.479843i
\(27\) 452856.i 0.852129i
\(28\) 917414.i 1.49256i
\(29\) 807061.i 1.14108i 0.821272 + 0.570538i \(0.193265\pi\)
−0.821272 + 0.570538i \(0.806735\pi\)
\(30\) 78456.5i 0.0968598i
\(31\) 374092. 0.405072 0.202536 0.979275i \(-0.435082\pi\)
0.202536 + 0.979275i \(0.435082\pi\)
\(32\) 983956.i 0.938374i
\(33\) 379487.i 0.319993i
\(34\) 143123.i 0.107101i
\(35\) 593508. 0.395507
\(36\) −331778. −0.197532
\(37\) 2.09493e6i 1.11780i −0.829236 0.558899i \(-0.811224\pi\)
0.829236 0.558899i \(-0.188776\pi\)
\(38\) 10882.6 0.00521914
\(39\) 3.18103e6i 1.37502i
\(40\) 413197. 0.161405
\(41\) 3.35460e6 1.18715 0.593574 0.804779i \(-0.297716\pi\)
0.593574 + 0.804779i \(0.297716\pi\)
\(42\) 2.35018e6i 0.755273i
\(43\) 3.26825e6 1.00337e6i 0.955964 0.293485i
\(44\) −918225. −0.244984
\(45\) 214639.i 0.0523431i
\(46\) 656161.i 0.146548i
\(47\) −3.56896e6 −0.731391 −0.365696 0.930734i \(-0.619169\pi\)
−0.365696 + 0.930734i \(0.619169\pi\)
\(48\) 3.37245e6i 0.635302i
\(49\) −1.20139e7 −2.08400
\(50\) 2.29849e6i 0.367758i
\(51\) 2.07628e6i 0.306905i
\(52\) 7.69697e6 1.05270
\(53\) −5.72503e6 −0.725562 −0.362781 0.931874i \(-0.618173\pi\)
−0.362781 + 0.931874i \(0.618173\pi\)
\(54\) 2.80704e6 0.330121
\(55\) 594033.i 0.0649172i
\(56\) −1.23774e7 −1.25857
\(57\) −157873. −0.0149558
\(58\) −5.00258e6 −0.442061
\(59\) −1.72958e7 −1.42735 −0.713677 0.700475i \(-0.752972\pi\)
−0.713677 + 0.700475i \(0.752972\pi\)
\(60\) −2.75395e6 −0.212496
\(61\) 1.48218e7i 1.07049i 0.844698 + 0.535243i \(0.179780\pi\)
−0.844698 + 0.535243i \(0.820220\pi\)
\(62\) 2.31882e6i 0.156928i
\(63\) 6.42957e6i 0.408150i
\(64\) 3.50204e6 0.208738
\(65\) 4.97945e6i 0.278951i
\(66\) −2.35226e6 −0.123968
\(67\) 1.67765e7 0.832537 0.416268 0.909242i \(-0.363338\pi\)
0.416268 + 0.909242i \(0.363338\pi\)
\(68\) 5.02386e6 0.234964
\(69\) 9.51888e6i 0.419942i
\(70\) 3.67887e6i 0.153223i
\(71\) 1.93772e7i 0.762532i −0.924465 0.381266i \(-0.875488\pi\)
0.924465 0.381266i \(-0.124512\pi\)
\(72\) 4.47623e6i 0.166564i
\(73\) 1.18749e7i 0.418155i 0.977899 + 0.209077i \(0.0670460\pi\)
−0.977899 + 0.209077i \(0.932954\pi\)
\(74\) 1.29855e7 0.433044
\(75\) 3.33439e7i 1.05383i
\(76\) 381998.i 0.0114500i
\(77\) 1.77944e7i 0.506198i
\(78\) 1.97177e7 0.532694
\(79\) −2.09356e7 −0.537497 −0.268749 0.963210i \(-0.586610\pi\)
−0.268749 + 0.963210i \(0.586610\pi\)
\(80\) 5.27909e6i 0.128884i
\(81\) −5.07262e7 −1.17840
\(82\) 2.07936e7i 0.459911i
\(83\) 1.44138e6 0.0303715 0.0151857 0.999885i \(-0.495166\pi\)
0.0151857 + 0.999885i \(0.495166\pi\)
\(84\) 8.24952e7 1.65696
\(85\) 3.25012e6i 0.0622620i
\(86\) 6.21938e6 + 2.02583e7i 0.113698 + 0.370348i
\(87\) 7.25721e7 1.26675
\(88\) 1.23883e7i 0.206577i
\(89\) 5.12452e7i 0.816757i 0.912813 + 0.408378i \(0.133906\pi\)
−0.912813 + 0.408378i \(0.866094\pi\)
\(90\) −1.33045e6 −0.0202781
\(91\) 1.49161e8i 2.17515i
\(92\) −2.30323e7 −0.321504
\(93\) 3.36389e7i 0.449687i
\(94\) 2.21223e7i 0.283347i
\(95\) −247128. −0.00303409
\(96\) 8.84788e7 1.04173
\(97\) −7.77098e7 −0.877787 −0.438893 0.898539i \(-0.644629\pi\)
−0.438893 + 0.898539i \(0.644629\pi\)
\(98\) 7.44682e7i 0.807359i
\(99\) 6.43525e6 0.0669923
\(100\) 8.06806e7 0.806806
\(101\) 1.66887e8 1.60375 0.801874 0.597493i \(-0.203836\pi\)
0.801874 + 0.597493i \(0.203836\pi\)
\(102\) 1.28698e7 0.118898
\(103\) −2.98518e6 −0.0265229 −0.0132615 0.999912i \(-0.504221\pi\)
−0.0132615 + 0.999912i \(0.504221\pi\)
\(104\) 1.03845e8i 0.887669i
\(105\) 5.33691e7i 0.439069i
\(106\) 3.54867e7i 0.281088i
\(107\) −2.42500e8 −1.85002 −0.925009 0.379944i \(-0.875943\pi\)
−0.925009 + 0.379944i \(0.875943\pi\)
\(108\) 9.85317e7i 0.724237i
\(109\) 9.64776e7 0.683471 0.341736 0.939796i \(-0.388985\pi\)
0.341736 + 0.939796i \(0.388985\pi\)
\(110\) −3.68213e6 −0.0251494
\(111\) −1.88379e8 −1.24091
\(112\) 1.58136e8i 1.00498i
\(113\) 1.85054e8i 1.13497i −0.823384 0.567484i \(-0.807917\pi\)
0.823384 0.567484i \(-0.192083\pi\)
\(114\) 978582.i 0.00579399i
\(115\) 1.49005e7i 0.0851938i
\(116\) 1.75599e8i 0.969817i
\(117\) −5.39432e7 −0.287868
\(118\) 1.07208e8i 0.552968i
\(119\) 9.73580e7i 0.485494i
\(120\) 3.71553e7i 0.179182i
\(121\) −1.96549e8 −0.916914
\(122\) −9.18732e7 −0.414715
\(123\) 3.01650e8i 1.31790i
\(124\) 8.13943e7 0.344276
\(125\) 1.07179e8i 0.439006i
\(126\) 3.98538e7 0.158120
\(127\) −2.87170e8 −1.10389 −0.551943 0.833882i \(-0.686113\pi\)
−0.551943 + 0.833882i \(0.686113\pi\)
\(128\) 2.73600e8i 1.01924i
\(129\) −9.02241e7 2.93886e8i −0.325809 1.06126i
\(130\) 3.08652e7 0.108068
\(131\) 2.85434e8i 0.969214i 0.874732 + 0.484607i \(0.161037\pi\)
−0.874732 + 0.484607i \(0.838963\pi\)
\(132\) 8.25681e7i 0.271967i
\(133\) 7.40278e6 0.0236586
\(134\) 1.03990e8i 0.322531i
\(135\) −6.37437e7 −0.191912
\(136\) 6.77801e7i 0.198128i
\(137\) 4.75232e8i 1.34904i −0.738258 0.674518i \(-0.764351\pi\)
0.738258 0.674518i \(-0.235649\pi\)
\(138\) −5.90030e7 −0.162689
\(139\) −7.78267e7 −0.208482 −0.104241 0.994552i \(-0.533241\pi\)
−0.104241 + 0.994552i \(0.533241\pi\)
\(140\) 1.29134e8 0.336148
\(141\) 3.20926e8i 0.811948i
\(142\) 1.20110e8 0.295411
\(143\) −1.49292e8 −0.357021
\(144\) −5.71892e7 −0.133004
\(145\) 1.13601e8 0.256987
\(146\) −7.36066e7 −0.161996
\(147\) 1.08030e9i 2.31354i
\(148\) 4.55812e8i 0.950033i
\(149\) 9.54649e8i 1.93686i −0.249283 0.968431i \(-0.580195\pi\)
0.249283 0.968431i \(-0.419805\pi\)
\(150\) 2.06683e8 0.408263
\(151\) 1.36729e8i 0.262998i −0.991316 0.131499i \(-0.958021\pi\)
0.991316 0.131499i \(-0.0419791\pi\)
\(152\) 5.15378e6 0.00965498
\(153\) −3.52090e7 −0.0642523
\(154\) 1.10299e8 0.196105
\(155\) 5.26569e7i 0.0912281i
\(156\) 6.92123e8i 1.16865i
\(157\) 3.80057e8i 0.625533i 0.949830 + 0.312767i \(0.101256\pi\)
−0.949830 + 0.312767i \(0.898744\pi\)
\(158\) 1.29770e8i 0.208231i
\(159\) 5.14803e8i 0.805476i
\(160\) 1.38501e8 0.211336
\(161\) 4.46346e8i 0.664306i
\(162\) 3.14427e8i 0.456520i
\(163\) 3.81033e7i 0.0539774i 0.999636 + 0.0269887i \(0.00859182\pi\)
−0.999636 + 0.0269887i \(0.991408\pi\)
\(164\) 7.29888e8 1.00898
\(165\) 5.34163e7 0.0720673
\(166\) 8.93442e6i 0.0117661i
\(167\) 8.61000e8 1.10697 0.553487 0.832858i \(-0.313297\pi\)
0.553487 + 0.832858i \(0.313297\pi\)
\(168\) 1.11299e9i 1.39719i
\(169\) 4.35706e8 0.534129
\(170\) 2.01459e7 0.0241208
\(171\) 2.67718e6i 0.00313107i
\(172\) 7.11100e8 2.18311e8i 0.812488 0.249437i
\(173\) −1.34658e9 −1.50331 −0.751656 0.659556i \(-0.770744\pi\)
−0.751656 + 0.659556i \(0.770744\pi\)
\(174\) 4.49840e8i 0.490751i
\(175\) 1.56352e9i 1.66706i
\(176\) −1.58276e8 −0.164955
\(177\) 1.55526e9i 1.58457i
\(178\) −3.17644e8 −0.316418
\(179\) 5.56248e7i 0.0541821i −0.999633 0.0270911i \(-0.991376\pi\)
0.999633 0.0270911i \(-0.00862441\pi\)
\(180\) 4.67009e7i 0.0444872i
\(181\) 1.59189e9 1.48319 0.741597 0.670845i \(-0.234069\pi\)
0.741597 + 0.670845i \(0.234069\pi\)
\(182\) −9.24575e8 −0.842668
\(183\) 1.33280e9 1.18839
\(184\) 3.10744e8i 0.271101i
\(185\) −2.94881e8 −0.251745
\(186\) 2.08512e8 0.174212
\(187\) −9.74440e7 −0.0796872
\(188\) −7.76527e8 −0.621621
\(189\) 1.90946e9 1.49645
\(190\) 1.53183e6i 0.00117543i
\(191\) 2.47384e9i 1.85883i −0.369043 0.929413i \(-0.620314\pi\)
0.369043 0.929413i \(-0.379686\pi\)
\(192\) 3.14909e8i 0.231729i
\(193\) 1.23062e9 0.886940 0.443470 0.896289i \(-0.353747\pi\)
0.443470 + 0.896289i \(0.353747\pi\)
\(194\) 4.81686e8i 0.340061i
\(195\) −4.47759e8 −0.309675
\(196\) −2.61396e9 −1.77123
\(197\) −8.59728e8 −0.570816 −0.285408 0.958406i \(-0.592129\pi\)
−0.285408 + 0.958406i \(0.592129\pi\)
\(198\) 3.98891e7i 0.0259533i
\(199\) 2.49433e9i 1.59053i −0.606263 0.795264i \(-0.707332\pi\)
0.606263 0.795264i \(-0.292668\pi\)
\(200\) 1.08851e9i 0.680321i
\(201\) 1.50857e9i 0.924233i
\(202\) 1.03445e9i 0.621305i
\(203\) −3.40295e9 −2.00388
\(204\) 4.51753e8i 0.260844i
\(205\) 4.72191e8i 0.267364i
\(206\) 1.85037e7i 0.0102752i
\(207\) 1.61419e8 0.0879171
\(208\) 1.32674e9 0.708815
\(209\) 7.40933e6i 0.00388324i
\(210\) 3.30810e8 0.170099
\(211\) 2.64996e9i 1.33693i 0.743742 + 0.668467i \(0.233049\pi\)
−0.743742 + 0.668467i \(0.766951\pi\)
\(212\) −1.24564e9 −0.616666
\(213\) −1.74243e9 −0.846519
\(214\) 1.50314e9i 0.716712i
\(215\) −1.41233e8 4.60037e8i −0.0660971 0.215297i
\(216\) 1.32935e9 0.610697
\(217\) 1.57735e9i 0.711359i
\(218\) 5.98019e8i 0.264782i
\(219\) 1.06780e9 0.464211
\(220\) 1.29249e8i 0.0551741i
\(221\) 8.16820e8 0.342418
\(222\) 1.16767e9i 0.480740i
\(223\) 3.97186e9i 1.60611i −0.595908 0.803053i \(-0.703208\pi\)
0.595908 0.803053i \(-0.296792\pi\)
\(224\) −4.14883e9 −1.64791
\(225\) −5.65439e8 −0.220626
\(226\) 1.14706e9 0.439696
\(227\) 2.41318e9i 0.908839i 0.890788 + 0.454420i \(0.150153\pi\)
−0.890788 + 0.454420i \(0.849847\pi\)
\(228\) −3.43498e7 −0.0127112
\(229\) 3.15226e9 1.14625 0.573127 0.819467i \(-0.305730\pi\)
0.573127 + 0.819467i \(0.305730\pi\)
\(230\) −9.23608e7 −0.0330047
\(231\) −1.60010e9 −0.561951
\(232\) −2.36912e9 −0.817776
\(233\) 3.08875e9i 1.04800i 0.851720 + 0.523998i \(0.175560\pi\)
−0.851720 + 0.523998i \(0.824440\pi\)
\(234\) 3.34368e8i 0.111522i
\(235\) 5.02364e8i 0.164720i
\(236\) −3.76318e9 −1.21313
\(237\) 1.88256e9i 0.596698i
\(238\) −6.03476e8 −0.188084
\(239\) 1.33859e9 0.410258 0.205129 0.978735i \(-0.434239\pi\)
0.205129 + 0.978735i \(0.434239\pi\)
\(240\) −4.74703e8 −0.143079
\(241\) 1.86107e9i 0.551690i −0.961202 0.275845i \(-0.911042\pi\)
0.961202 0.275845i \(-0.0889577\pi\)
\(242\) 1.21831e9i 0.355220i
\(243\) 1.59018e9i 0.456059i
\(244\) 3.22490e9i 0.909823i
\(245\) 1.69106e9i 0.469349i
\(246\) 1.86979e9 0.510566
\(247\) 6.21083e7i 0.0166864i
\(248\) 1.09814e9i 0.290303i
\(249\) 1.29611e8i 0.0337166i
\(250\) 6.64354e8 0.170075
\(251\) −2.82095e9 −0.710724 −0.355362 0.934729i \(-0.615642\pi\)
−0.355362 + 0.934729i \(0.615642\pi\)
\(252\) 1.39893e9i 0.346893i
\(253\) 4.46741e8 0.109037
\(254\) 1.78003e9i 0.427654i
\(255\) −2.92255e8 −0.0691197
\(256\) −7.99395e8 −0.186124
\(257\) 3.36017e8i 0.0770244i −0.999258 0.0385122i \(-0.987738\pi\)
0.999258 0.0385122i \(-0.0122619\pi\)
\(258\) 1.82166e9 5.59256e8i 0.411138 0.126221i
\(259\) 8.83323e9 1.96300
\(260\) 1.08342e9i 0.237085i
\(261\) 1.23066e9i 0.265202i
\(262\) −1.76927e9 −0.375481
\(263\) 8.88343e9i 1.85677i −0.371622 0.928384i \(-0.621198\pi\)
0.371622 0.928384i \(-0.378802\pi\)
\(264\) −1.11398e9 −0.229330
\(265\) 8.05851e8i 0.163407i
\(266\) 4.58863e7i 0.00916551i
\(267\) 4.60804e9 0.906716
\(268\) 3.65021e9 0.707586
\(269\) −7.83974e7 −0.0149724 −0.00748622 0.999972i \(-0.502383\pi\)
−0.00748622 + 0.999972i \(0.502383\pi\)
\(270\) 3.95117e8i 0.0743482i
\(271\) 4.00424e9 0.742408 0.371204 0.928551i \(-0.378945\pi\)
0.371204 + 0.928551i \(0.378945\pi\)
\(272\) 8.65972e8 0.158208
\(273\) 1.34127e10 2.41472
\(274\) 2.94574e9 0.522627
\(275\) −1.56490e9 −0.273625
\(276\) 2.07110e9i 0.356915i
\(277\) 1.39104e9i 0.236277i 0.992997 + 0.118138i \(0.0376926\pi\)
−0.992997 + 0.118138i \(0.962307\pi\)
\(278\) 4.82411e8i 0.0807677i
\(279\) −5.70441e8 −0.0941443
\(280\) 1.74223e9i 0.283449i
\(281\) 2.05907e9 0.330252 0.165126 0.986272i \(-0.447197\pi\)
0.165126 + 0.986272i \(0.447197\pi\)
\(282\) −1.98927e9 −0.314555
\(283\) −8.81758e9 −1.37469 −0.687343 0.726333i \(-0.741223\pi\)
−0.687343 + 0.726333i \(0.741223\pi\)
\(284\) 4.21606e9i 0.648088i
\(285\) 2.22221e7i 0.00336827i
\(286\) 9.25393e8i 0.138313i
\(287\) 1.41446e10i 2.08479i
\(288\) 1.50040e9i 0.218091i
\(289\) −6.44261e9 −0.923572
\(290\) 7.04160e8i 0.0995588i
\(291\) 6.98778e9i 0.974467i
\(292\) 2.58371e9i 0.355396i
\(293\) −1.94964e9 −0.264536 −0.132268 0.991214i \(-0.542226\pi\)
−0.132268 + 0.991214i \(0.542226\pi\)
\(294\) −6.69629e9 −0.896283
\(295\) 2.43454e9i 0.321461i
\(296\) 6.14965e9 0.801094
\(297\) 1.91115e9i 0.245622i
\(298\) 5.91741e9 0.750355
\(299\) −3.74478e9 −0.468535
\(300\) 7.25492e9i 0.895669i
\(301\) 4.23067e9 + 1.37805e10i 0.515398 + 1.67880i
\(302\) 8.47518e8 0.101888
\(303\) 1.50067e10i 1.78039i
\(304\) 6.58457e7i 0.00770962i
\(305\) 2.08630e9 0.241090
\(306\) 2.18244e8i 0.0248918i
\(307\) −1.10645e10 −1.24560 −0.622801 0.782380i \(-0.714005\pi\)
−0.622801 + 0.782380i \(0.714005\pi\)
\(308\) 3.87167e9i 0.430225i
\(309\) 2.68432e8i 0.0294442i
\(310\) 3.26395e8 0.0353425
\(311\) −8.38501e9 −0.896318 −0.448159 0.893954i \(-0.647920\pi\)
−0.448159 + 0.893954i \(0.647920\pi\)
\(312\) 9.33787e9 0.985438
\(313\) 1.38945e10i 1.44766i −0.689981 0.723828i \(-0.742381\pi\)
0.689981 0.723828i \(-0.257619\pi\)
\(314\) −2.35579e9 −0.242336
\(315\) −9.05022e8 −0.0919214
\(316\) −4.55512e9 −0.456827
\(317\) −1.61767e10 −1.60196 −0.800980 0.598691i \(-0.795688\pi\)
−0.800980 + 0.598691i \(0.795688\pi\)
\(318\) −3.19102e9 −0.312048
\(319\) 3.40596e9i 0.328910i
\(320\) 4.92945e8i 0.0470109i
\(321\) 2.18059e10i 2.05378i
\(322\) 2.76669e9 0.257357
\(323\) 4.05385e7i 0.00372441i
\(324\) −1.10369e10 −1.00154
\(325\) 1.31177e10 1.17578
\(326\) −2.36184e8 −0.0209113
\(327\) 8.67540e9i 0.758750i
\(328\) 9.84738e9i 0.850796i
\(329\) 1.50484e10i 1.28442i
\(330\) 3.31102e8i 0.0279194i
\(331\) 8.96226e8i 0.0746630i 0.999303 + 0.0373315i \(0.0118858\pi\)
−0.999303 + 0.0373315i \(0.988114\pi\)
\(332\) 3.13613e8 0.0258132
\(333\) 3.19450e9i 0.259792i
\(334\) 5.33693e9i 0.428850i
\(335\) 2.36145e9i 0.187500i
\(336\) 1.42198e10 1.11567
\(337\) −1.07917e10 −0.836701 −0.418351 0.908286i \(-0.637392\pi\)
−0.418351 + 0.908286i \(0.637392\pi\)
\(338\) 2.70073e9i 0.206926i
\(339\) −1.66403e10 −1.25998
\(340\) 7.07155e8i 0.0529174i
\(341\) −1.57874e9 −0.116760
\(342\) −1.65946e7 −0.00121300
\(343\) 2.63490e10i 1.90365i
\(344\) 2.94537e9 + 9.59390e9i 0.210332 + 0.685112i
\(345\) 1.33987e9 0.0945772
\(346\) 8.34683e9i 0.582394i
\(347\) 1.26533e9i 0.0872743i −0.999047 0.0436371i \(-0.986105\pi\)
0.999047 0.0436371i \(-0.0138945\pi\)
\(348\) 1.57901e10 1.07663
\(349\) 2.38133e10i 1.60516i −0.596545 0.802580i \(-0.703460\pi\)
0.596545 0.802580i \(-0.296540\pi\)
\(350\) −9.69151e9 −0.645832
\(351\) 1.60201e10i 1.05545i
\(352\) 4.15250e9i 0.270482i
\(353\) −3.78085e9 −0.243495 −0.121748 0.992561i \(-0.538850\pi\)
−0.121748 + 0.992561i \(0.538850\pi\)
\(354\) −9.64032e9 −0.613873
\(355\) −2.72752e9 −0.171734
\(356\) 1.11498e10i 0.694174i
\(357\) 8.75457e9 0.538967
\(358\) 3.44792e8 0.0209906
\(359\) −1.74348e10 −1.04964 −0.524819 0.851214i \(-0.675867\pi\)
−0.524819 + 0.851214i \(0.675867\pi\)
\(360\) −6.30071e8 −0.0375128
\(361\) 1.69805e10 0.999819
\(362\) 9.86735e9i 0.574601i
\(363\) 1.76740e10i 1.01790i
\(364\) 3.24541e10i 1.84869i
\(365\) 1.67150e9 0.0941746
\(366\) 8.26137e9i 0.460392i
\(367\) 3.93525e9 0.216924 0.108462 0.994101i \(-0.465407\pi\)
0.108462 + 0.994101i \(0.465407\pi\)
\(368\) −3.97012e9 −0.216478
\(369\) −5.11532e9 −0.275910
\(370\) 1.82783e9i 0.0975278i
\(371\) 2.41395e10i 1.27418i
\(372\) 7.31910e9i 0.382196i
\(373\) 2.77364e10i 1.43290i 0.697640 + 0.716449i \(0.254234\pi\)
−0.697640 + 0.716449i \(0.745766\pi\)
\(374\) 6.04009e8i 0.0308715i
\(375\) −9.63772e9 −0.487359
\(376\) 1.04766e10i 0.524167i
\(377\) 2.85503e10i 1.41334i
\(378\) 1.18358e10i 0.579737i
\(379\) 1.96568e10 0.952699 0.476349 0.879256i \(-0.341960\pi\)
0.476349 + 0.879256i \(0.341960\pi\)
\(380\) −5.37698e7 −0.00257872
\(381\) 2.58228e10i 1.22547i
\(382\) 1.53342e10 0.720123
\(383\) 1.18324e10i 0.549894i −0.961459 0.274947i \(-0.911340\pi\)
0.961459 0.274947i \(-0.0886604\pi\)
\(384\) 2.46025e10 1.13150
\(385\) −2.50472e9 −0.114003
\(386\) 7.62802e9i 0.343607i
\(387\) −4.98365e9 + 1.53000e9i −0.222179 + 0.0682099i
\(388\) −1.69080e10 −0.746044
\(389\) 2.37789e10i 1.03847i −0.854631 0.519235i \(-0.826217\pi\)
0.854631 0.519235i \(-0.173783\pi\)
\(390\) 2.77545e9i 0.119971i
\(391\) −2.44424e9 −0.104577
\(392\) 3.52665e10i 1.49355i
\(393\) 2.56666e10 1.07596
\(394\) 5.32904e9i 0.221138i
\(395\) 2.94687e9i 0.121052i
\(396\) 1.40017e9 0.0569378
\(397\) −5.51944e9 −0.222194 −0.111097 0.993810i \(-0.535436\pi\)
−0.111097 + 0.993810i \(0.535436\pi\)
\(398\) 1.54612e10 0.616183
\(399\) 6.65669e8i 0.0262644i
\(400\) 1.39071e10 0.543245
\(401\) 3.15069e10 1.21851 0.609254 0.792975i \(-0.291469\pi\)
0.609254 + 0.792975i \(0.291469\pi\)
\(402\) 9.35092e9 0.358055
\(403\) 1.32337e10 0.501721
\(404\) 3.63109e10 1.36305
\(405\) 7.14018e9i 0.265393i
\(406\) 2.10933e10i 0.776318i
\(407\) 8.84104e9i 0.322200i
\(408\) 6.09488e9 0.219950
\(409\) 2.58140e10i 0.922490i 0.887273 + 0.461245i \(0.152597\pi\)
−0.887273 + 0.461245i \(0.847403\pi\)
\(410\) 2.92689e9 0.103579
\(411\) −4.27336e10 −1.49762
\(412\) −6.49510e8 −0.0225423
\(413\) 7.29272e10i 2.50662i
\(414\) 1.00056e9i 0.0340598i
\(415\) 2.02887e8i 0.00684011i
\(416\) 3.48081e10i 1.16227i
\(417\) 6.99829e9i 0.231445i
\(418\) −4.59269e7 −0.00150440
\(419\) 3.60078e10i 1.16826i 0.811659 + 0.584131i \(0.198565\pi\)
−0.811659 + 0.584131i \(0.801435\pi\)
\(420\) 1.16120e10i 0.373171i
\(421\) 2.96419e10i 0.943578i 0.881712 + 0.471789i \(0.156392\pi\)
−0.881712 + 0.471789i \(0.843608\pi\)
\(422\) −1.64259e10 −0.517939
\(423\) 5.44219e9 0.169986
\(424\) 1.68058e10i 0.519989i
\(425\) 8.56200e9 0.262434
\(426\) 1.08005e10i 0.327948i
\(427\) −6.24957e10 −1.87992
\(428\) −5.27627e10 −1.57236
\(429\) 1.34246e10i 0.396344i
\(430\) 2.85155e9 8.75436e8i 0.0834078 0.0256065i
\(431\) 4.11603e10 1.19281 0.596403 0.802685i \(-0.296596\pi\)
0.596403 + 0.802685i \(0.296596\pi\)
\(432\) 1.69841e10i 0.487649i
\(433\) 4.48811e10i 1.27677i 0.769719 + 0.638383i \(0.220396\pi\)
−0.769719 + 0.638383i \(0.779604\pi\)
\(434\) −9.77724e9 −0.275586
\(435\) 1.02152e10i 0.285292i
\(436\) 2.09914e10 0.580893
\(437\) 1.85852e8i 0.00509615i
\(438\) 6.61881e9i 0.179839i
\(439\) −4.80869e10 −1.29470 −0.647349 0.762194i \(-0.724122\pi\)
−0.647349 + 0.762194i \(0.724122\pi\)
\(440\) −1.74378e9 −0.0465243
\(441\) 1.83196e10 0.484351
\(442\) 5.06308e9i 0.132656i
\(443\) 3.84372e10 0.998015 0.499007 0.866598i \(-0.333698\pi\)
0.499007 + 0.866598i \(0.333698\pi\)
\(444\) −4.09873e10 −1.05467
\(445\) 7.21323e9 0.183946
\(446\) 2.46196e10 0.622218
\(447\) −8.58434e10 −2.15019
\(448\) 1.47663e10i 0.366572i
\(449\) 5.91790e10i 1.45607i −0.685540 0.728035i \(-0.740434\pi\)
0.685540 0.728035i \(-0.259566\pi\)
\(450\) 3.50489e9i 0.0854720i
\(451\) −1.41571e10 −0.342190
\(452\) 4.02637e10i 0.964627i
\(453\) −1.22949e10 −0.291965
\(454\) −1.49582e10 −0.352091
\(455\) 2.09957e10 0.489875
\(456\) 4.63435e8i 0.0107184i
\(457\) 8.35413e10i 1.91530i −0.287937 0.957649i \(-0.592969\pi\)
0.287937 0.957649i \(-0.407031\pi\)
\(458\) 1.95394e10i 0.444067i
\(459\) 1.04564e10i 0.235576i
\(460\) 3.24201e9i 0.0724075i
\(461\) 6.16922e10 1.36592 0.682962 0.730454i \(-0.260691\pi\)
0.682962 + 0.730454i \(0.260691\pi\)
\(462\) 9.91824e9i 0.217704i
\(463\) 3.62772e10i 0.789423i 0.918805 + 0.394711i \(0.129155\pi\)
−0.918805 + 0.394711i \(0.870845\pi\)
\(464\) 3.02683e10i 0.653004i
\(465\) −4.73499e9 −0.101276
\(466\) −1.91457e10 −0.406001
\(467\) 1.81888e10i 0.382417i 0.981549 + 0.191208i \(0.0612407\pi\)
−0.981549 + 0.191208i \(0.938759\pi\)
\(468\) −1.17369e10 −0.244663
\(469\) 7.07379e10i 1.46205i
\(470\) −3.11391e9 −0.0638139
\(471\) 3.41753e10 0.694431
\(472\) 5.07715e10i 1.02294i
\(473\) −1.37927e10 + 4.23441e9i −0.275552 + 0.0845956i
\(474\) −1.16691e10 −0.231165
\(475\) 6.51027e8i 0.0127886i
\(476\) 2.11830e10i 0.412628i
\(477\) 8.72992e9 0.168631
\(478\) 8.29730e9i 0.158937i
\(479\) −5.57712e10 −1.05942 −0.529709 0.848179i \(-0.677699\pi\)
−0.529709 + 0.848179i \(0.677699\pi\)
\(480\) 1.24542e10i 0.234613i
\(481\) 7.41096e10i 1.38450i
\(482\) 1.15359e10 0.213729
\(483\) −4.01361e10 −0.737474
\(484\) −4.27647e10 −0.779300
\(485\) 1.09384e10i 0.197691i
\(486\) −9.85677e9 −0.176681
\(487\) 1.61482e10 0.287084 0.143542 0.989644i \(-0.454151\pi\)
0.143542 + 0.989644i \(0.454151\pi\)
\(488\) −4.35092e10 −0.767187
\(489\) 3.42631e9 0.0599226
\(490\) −1.04821e10 −0.181829
\(491\) 8.23887e10i 1.41756i 0.705430 + 0.708780i \(0.250754\pi\)
−0.705430 + 0.708780i \(0.749246\pi\)
\(492\) 6.56326e10i 1.12011i
\(493\) 1.86349e10i 0.315457i
\(494\) 3.84980e8 0.00646443
\(495\) 9.05822e8i 0.0150877i
\(496\) 1.40301e10 0.231811
\(497\) 8.17036e10 1.33911
\(498\) 8.03396e8 0.0130621
\(499\) 5.34881e10i 0.862690i −0.902187 0.431345i \(-0.858039\pi\)
0.902187 0.431345i \(-0.141961\pi\)
\(500\) 2.33199e10i 0.373118i
\(501\) 7.74224e10i 1.22890i
\(502\) 1.74857e10i 0.275340i
\(503\) 6.30412e10i 0.984810i 0.870366 + 0.492405i \(0.163882\pi\)
−0.870366 + 0.492405i \(0.836118\pi\)
\(504\) 1.88739e10 0.292509
\(505\) 2.34909e10i 0.361188i
\(506\) 2.76913e9i 0.0422417i
\(507\) 3.91793e10i 0.592959i
\(508\) −6.24820e10 −0.938210
\(509\) 5.80654e10 0.865060 0.432530 0.901620i \(-0.357621\pi\)
0.432530 + 0.901620i \(0.357621\pi\)
\(510\) 1.81155e9i 0.0267775i
\(511\) −5.00700e10 −0.734335
\(512\) 6.50866e10i 0.947135i
\(513\) −7.95071e8 −0.0114799
\(514\) 2.08281e9 0.0298399
\(515\) 4.20192e8i 0.00597336i
\(516\) −1.96308e10 6.39432e10i −0.276910 0.901977i
\(517\) 1.50617e10 0.210820
\(518\) 5.47530e10i 0.760482i
\(519\) 1.21087e11i 1.66889i
\(520\) 1.46171e10 0.199916
\(521\) 7.31840e10i 0.993265i 0.867961 + 0.496632i \(0.165430\pi\)
−0.867961 + 0.496632i \(0.834570\pi\)
\(522\) 7.62828e9 0.102741
\(523\) 2.88133e10i 0.385112i 0.981286 + 0.192556i \(0.0616776\pi\)
−0.981286 + 0.192556i \(0.938322\pi\)
\(524\) 6.21041e10i 0.823750i
\(525\) 1.40594e11 1.85067
\(526\) 5.50642e10 0.719327
\(527\) 8.63774e9 0.111984
\(528\) 1.42324e10i 0.183123i
\(529\) −6.71051e10 −0.856906
\(530\) −4.99509e9 −0.0633053
\(531\) 2.63738e10 0.331737
\(532\) 1.61068e9 0.0201078
\(533\) 1.18671e11 1.47040
\(534\) 2.85630e10i 0.351269i
\(535\) 3.41341e10i 0.416652i
\(536\) 4.92473e10i 0.596655i
\(537\) −5.00186e9 −0.0601498
\(538\) 4.85948e8i 0.00580044i
\(539\) 5.07009e10 0.600705
\(540\) −1.38693e10 −0.163109
\(541\) 8.36247e10 0.976215 0.488107 0.872784i \(-0.337687\pi\)
0.488107 + 0.872784i \(0.337687\pi\)
\(542\) 2.48204e10i 0.287615i
\(543\) 1.43145e11i 1.64656i
\(544\) 2.27194e10i 0.259419i
\(545\) 1.35801e10i 0.153928i
\(546\) 8.31391e10i 0.935481i
\(547\) −1.08156e11 −1.20809 −0.604046 0.796950i \(-0.706446\pi\)
−0.604046 + 0.796950i \(0.706446\pi\)
\(548\) 1.03400e11i 1.14657i
\(549\) 2.26013e10i 0.248796i
\(550\) 9.70008e9i 0.106005i
\(551\) 1.41694e9 0.0153725
\(552\) −2.79425e10 −0.300960
\(553\) 8.82743e10i 0.943916i
\(554\) −8.62240e9 −0.0915354
\(555\) 2.65162e10i 0.279472i
\(556\) −1.69334e10 −0.177192
\(557\) 1.66283e11 1.72754 0.863770 0.503887i \(-0.168097\pi\)
0.863770 + 0.503887i \(0.168097\pi\)
\(558\) 3.53589e9i 0.0364722i
\(559\) 1.15616e11 3.54947e10i 1.18406 0.363510i
\(560\) 2.22591e10 0.226337
\(561\) 8.76231e9i 0.0884641i
\(562\) 1.27632e10i 0.127942i
\(563\) −1.22197e10 −0.121626 −0.0608132 0.998149i \(-0.519369\pi\)
−0.0608132 + 0.998149i \(0.519369\pi\)
\(564\) 6.98265e10i 0.690087i
\(565\) −2.60480e10 −0.255612
\(566\) 5.46560e10i 0.532564i
\(567\) 2.13886e11i 2.06942i
\(568\) 5.68816e10 0.546485
\(569\) 8.95928e10 0.854720 0.427360 0.904081i \(-0.359444\pi\)
0.427360 + 0.904081i \(0.359444\pi\)
\(570\) −1.37744e8 −0.00130489
\(571\) 5.66255e8i 0.00532681i −0.999996 0.00266341i \(-0.999152\pi\)
0.999996 0.00266341i \(-0.000847790\pi\)
\(572\) −3.24828e10 −0.303437
\(573\) −2.22451e11 −2.06356
\(574\) −8.76755e10 −0.807664
\(575\) −3.92533e10 −0.359091
\(576\) −5.34015e9 −0.0485136
\(577\) 1.04421e11i 0.942071i 0.882114 + 0.471036i \(0.156120\pi\)
−0.882114 + 0.471036i \(0.843880\pi\)
\(578\) 3.99347e10i 0.357799i
\(579\) 1.10659e11i 0.984629i
\(580\) 2.47172e10 0.218417
\(581\) 6.07754e9i 0.0533363i
\(582\) −4.33139e10 −0.377516
\(583\) 2.41608e10 0.209140
\(584\) −3.48585e10 −0.299679
\(585\) 7.59301e9i 0.0648321i
\(586\) 1.20849e10i 0.102483i
\(587\) 4.44016e10i 0.373978i 0.982362 + 0.186989i \(0.0598729\pi\)
−0.982362 + 0.186989i \(0.940127\pi\)
\(588\) 2.35051e11i 1.96631i
\(589\) 6.56786e8i 0.00545711i
\(590\) −1.50906e10 −0.124537
\(591\) 7.73079e10i 0.633686i
\(592\) 7.85691e10i 0.639683i
\(593\) 1.07081e11i 0.865953i −0.901405 0.432976i \(-0.857463\pi\)
0.901405 0.432976i \(-0.142537\pi\)
\(594\) −1.18463e10 −0.0951560
\(595\) 1.37040e10 0.109340
\(596\) 2.07711e11i 1.64617i
\(597\) −2.24294e11 −1.76571
\(598\) 2.32121e10i 0.181514i
\(599\) 1.07496e11 0.834999 0.417499 0.908677i \(-0.362907\pi\)
0.417499 + 0.908677i \(0.362907\pi\)
\(600\) 9.78807e10 0.755252
\(601\) 2.12585e11i 1.62943i 0.579863 + 0.814714i \(0.303106\pi\)
−0.579863 + 0.814714i \(0.696894\pi\)
\(602\) −8.54187e10 + 2.62239e10i −0.650380 + 0.199669i
\(603\) −2.55820e10 −0.193493
\(604\) 2.97493e10i 0.223526i
\(605\) 2.76661e10i 0.206503i
\(606\) 9.30194e10 0.689736
\(607\) 2.78462e10i 0.205121i −0.994727 0.102561i \(-0.967296\pi\)
0.994727 0.102561i \(-0.0327036\pi\)
\(608\) 1.72751e9 0.0126417
\(609\) 3.05998e11i 2.22459i
\(610\) 1.29320e10i 0.0933999i
\(611\) −1.26254e11 −0.905901
\(612\) −7.66072e9 −0.0546090
\(613\) −1.26904e11 −0.898739 −0.449370 0.893346i \(-0.648351\pi\)
−0.449370 + 0.893346i \(0.648351\pi\)
\(614\) 6.85837e10i 0.482556i
\(615\) −4.24601e10 −0.296811
\(616\) 5.22352e10 0.362777
\(617\) −1.25509e11 −0.866030 −0.433015 0.901387i \(-0.642550\pi\)
−0.433015 + 0.901387i \(0.642550\pi\)
\(618\) −1.66388e9 −0.0114069
\(619\) 2.99312e10 0.203874 0.101937 0.994791i \(-0.467496\pi\)
0.101937 + 0.994791i \(0.467496\pi\)
\(620\) 1.14570e10i 0.0775362i
\(621\) 4.79383e10i 0.322342i
\(622\) 5.19747e10i 0.347240i
\(623\) −2.16074e11 −1.43433
\(624\) 1.19302e11i 0.786885i
\(625\) 1.29762e11 0.850407
\(626\) 8.61253e10 0.560833
\(627\) 6.66258e8 0.00431094
\(628\) 8.26922e10i 0.531650i
\(629\) 4.83718e10i 0.309022i
\(630\) 5.60980e9i 0.0356111i
\(631\) 3.36616e10i 0.212333i −0.994348 0.106167i \(-0.966142\pi\)
0.994348 0.106167i \(-0.0338577\pi\)
\(632\) 6.14560e10i 0.385209i
\(633\) 2.38289e11 1.48419
\(634\) 1.00271e11i 0.620612i
\(635\) 4.04219e10i 0.248612i
\(636\) 1.12010e11i 0.684586i
\(637\) −4.24998e11 −2.58125
\(638\) 2.11119e10 0.127422
\(639\) 2.95477e10i 0.177223i
\(640\) 3.85118e10 0.229548
\(641\) 1.32805e11i 0.786653i 0.919399 + 0.393327i \(0.128676\pi\)
−0.919399 + 0.393327i \(0.871324\pi\)
\(642\) −1.35165e11 −0.795651
\(643\) −2.41777e11 −1.41440 −0.707199 0.707014i \(-0.750042\pi\)
−0.707199 + 0.707014i \(0.750042\pi\)
\(644\) 9.71153e10i 0.564604i
\(645\) −4.13672e10 + 1.26999e10i −0.239010 + 0.0733771i
\(646\) 2.51279e8 0.00144286
\(647\) 4.66897e10i 0.266443i −0.991086 0.133221i \(-0.957468\pi\)
0.991086 0.133221i \(-0.0425321\pi\)
\(648\) 1.48906e11i 0.844524i
\(649\) 7.29917e10 0.411429
\(650\) 8.13104e10i 0.455505i
\(651\) 1.41838e11 0.789710
\(652\) 8.29045e9i 0.0458762i
\(653\) 1.07246e11i 0.589834i −0.955523 0.294917i \(-0.904708\pi\)
0.955523 0.294917i \(-0.0952919\pi\)
\(654\) 5.37747e10 0.293946
\(655\) 4.01774e10 0.218281
\(656\) 1.25812e11 0.679371
\(657\) 1.81076e10i 0.0971850i
\(658\) 9.32780e10 0.497594
\(659\) −3.07254e11 −1.62913 −0.814565 0.580072i \(-0.803025\pi\)
−0.814565 + 0.580072i \(0.803025\pi\)
\(660\) 1.16222e10 0.0612511
\(661\) 3.43900e11 1.80147 0.900733 0.434372i \(-0.143030\pi\)
0.900733 + 0.434372i \(0.143030\pi\)
\(662\) −5.55528e9 −0.0289250
\(663\) 7.34496e10i 0.380133i
\(664\) 4.23115e9i 0.0217664i
\(665\) 1.04201e9i 0.00532826i
\(666\) −1.98012e10 −0.100645
\(667\) 8.54336e10i 0.431643i
\(668\) 1.87335e11 0.940834
\(669\) −3.57155e11 −1.78300
\(670\) 1.46375e10 0.0726388
\(671\) 6.25510e10i 0.308563i
\(672\) 3.73069e11i 1.82941i
\(673\) 1.66827e11i 0.813215i −0.913603 0.406607i \(-0.866712\pi\)
0.913603 0.406607i \(-0.133288\pi\)
\(674\) 6.68926e10i 0.324145i
\(675\) 1.67924e11i 0.808908i
\(676\) 9.48001e10 0.453965
\(677\) 2.52379e11i 1.20143i 0.799464 + 0.600714i \(0.205117\pi\)
−0.799464 + 0.600714i \(0.794883\pi\)
\(678\) 1.03145e11i 0.488124i
\(679\) 3.27661e11i 1.54151i
\(680\) 9.54067e9 0.0446214
\(681\) 2.16997e11 1.00894
\(682\) 9.78589e9i 0.0452338i
\(683\) 3.34778e11 1.53842 0.769208 0.638999i \(-0.220651\pi\)
0.769208 + 0.638999i \(0.220651\pi\)
\(684\) 5.82497e8i 0.00266115i
\(685\) −6.68933e10 −0.303823
\(686\) 1.63325e11 0.737490
\(687\) 2.83456e11i 1.27250i
\(688\) 1.22574e11 3.76306e10i 0.547071 0.167953i
\(689\) −2.02527e11 −0.898681
\(690\) 8.30522e9i 0.0366399i
\(691\) 1.61389e10i 0.0707883i −0.999373 0.0353942i \(-0.988731\pi\)
0.999373 0.0353942i \(-0.0112687\pi\)
\(692\) −2.92987e11 −1.27769
\(693\) 2.71341e10i 0.117647i
\(694\) 7.84318e9 0.0338107
\(695\) 1.09548e10i 0.0469533i
\(696\) 2.13034e11i 0.907847i
\(697\) 7.74573e10 0.328195
\(698\) 1.47607e11 0.621851
\(699\) 2.77745e11 1.16342
\(700\) 3.40188e11i 1.41686i
\(701\) 2.44331e11 1.01183 0.505914 0.862584i \(-0.331155\pi\)
0.505914 + 0.862584i \(0.331155\pi\)
\(702\) 9.93009e10 0.408888
\(703\) −3.67803e9 −0.0150589
\(704\) −1.47793e10 −0.0601678
\(705\) 4.51733e10 0.182863
\(706\) 2.34357e10i 0.0943320i
\(707\) 7.03674e11i 2.81640i
\(708\) 3.38391e11i 1.34675i
\(709\) 3.90020e10 0.154348 0.0771742 0.997018i \(-0.475410\pi\)
0.0771742 + 0.997018i \(0.475410\pi\)
\(710\) 1.69066e10i 0.0665309i
\(711\) 3.19240e10 0.124922
\(712\) −1.50429e11 −0.585346
\(713\) −3.96005e10 −0.153230
\(714\) 5.42654e10i 0.208800i
\(715\) 2.10143e10i 0.0804064i
\(716\) 1.21027e10i 0.0460502i
\(717\) 1.20368e11i 0.455444i
\(718\) 1.08070e11i 0.406638i
\(719\) 8.75513e10 0.327602 0.163801 0.986493i \(-0.447624\pi\)
0.163801 + 0.986493i \(0.447624\pi\)
\(720\) 8.04991e9i 0.0299544i
\(721\) 1.25869e10i 0.0465778i
\(722\) 1.05254e11i 0.387337i
\(723\) −1.67350e11 −0.612454
\(724\) 3.46360e11 1.26059
\(725\) 2.99268e11i 1.08320i
\(726\) −1.09552e11 −0.394344
\(727\) 3.34970e10i 0.119914i 0.998201 + 0.0599568i \(0.0190963\pi\)
−0.998201 + 0.0599568i \(0.980904\pi\)
\(728\) −4.37859e11 −1.55886
\(729\) −1.89823e11 −0.672108
\(730\) 1.03608e10i 0.0364840i
\(731\) 7.54635e10 2.31676e10i 0.264282 0.0811356i
\(732\) 2.89988e11 1.01003
\(733\) 6.98062e8i 0.00241812i −0.999999 0.00120906i \(-0.999615\pi\)
0.999999 0.00120906i \(-0.000384856\pi\)
\(734\) 2.43927e10i 0.0840381i
\(735\) 1.52063e11 0.521043
\(736\) 1.04159e11i 0.354966i
\(737\) −7.08004e10 −0.239975
\(738\) 3.17074e10i 0.106890i
\(739\) 3.81398e11i 1.27879i 0.768877 + 0.639397i \(0.220816\pi\)
−0.768877 + 0.639397i \(0.779184\pi\)
\(740\) −6.41598e10 −0.213962
\(741\) −5.58487e9 −0.0185242
\(742\) 1.49629e11 0.493628
\(743\) 2.30989e11i 0.757942i −0.925409 0.378971i \(-0.876278\pi\)
0.925409 0.378971i \(-0.123722\pi\)
\(744\) 9.87465e10 0.322278
\(745\) −1.34376e11 −0.436210
\(746\) −1.71925e11 −0.555116
\(747\) −2.19791e9 −0.00705875
\(748\) −2.12017e10 −0.0677274
\(749\) 1.02249e12i 3.24888i
\(750\) 5.97396e10i 0.188807i
\(751\) 6.12180e10i 0.192451i −0.995360 0.0962254i \(-0.969323\pi\)
0.995360 0.0962254i \(-0.0306769\pi\)
\(752\) −1.33851e11 −0.418554
\(753\) 2.53664e11i 0.789004i
\(754\) −1.76970e11 −0.547537
\(755\) −1.92459e10 −0.0592311
\(756\) 4.15457e11 1.27186
\(757\) 2.31493e10i 0.0704944i −0.999379 0.0352472i \(-0.988778\pi\)
0.999379 0.0352472i \(-0.0112219\pi\)
\(758\) 1.21843e11i 0.369083i
\(759\) 4.01716e10i 0.121046i
\(760\) 7.25442e8i 0.00217444i
\(761\) 4.87918e11i 1.45482i −0.686205 0.727408i \(-0.740725\pi\)
0.686205 0.727408i \(-0.259275\pi\)
\(762\) −1.60063e11 −0.474757
\(763\) 4.06795e11i 1.20027i
\(764\) 5.38254e11i 1.57984i
\(765\) 4.95600e9i 0.0144706i
\(766\) 7.33437e10 0.213033
\(767\) −6.11849e11 −1.76792
\(768\) 7.18828e10i 0.206624i
\(769\) −4.35322e11 −1.24482 −0.622408 0.782693i \(-0.713846\pi\)
−0.622408 + 0.782693i \(0.713846\pi\)
\(770\) 1.55256e10i 0.0441657i
\(771\) −3.02151e10 −0.0855080
\(772\) 2.67756e11 0.753824
\(773\) 4.66145e11i 1.30558i 0.757540 + 0.652789i \(0.226401\pi\)
−0.757540 + 0.652789i \(0.773599\pi\)
\(774\) −9.48374e9 3.08913e10i −0.0264250 0.0860740i
\(775\) 1.38718e11 0.384526
\(776\) 2.28116e11i 0.629085i
\(777\) 7.94297e11i 2.17921i
\(778\) 1.47394e11 0.402312
\(779\) 5.88960e9i 0.0159932i
\(780\) −9.74228e10 −0.263198
\(781\) 8.17758e10i 0.219797i