Properties

Label 108.5.f.a.91.13
Level 108
Weight 5
Character 108.91
Analytic conductor 11.164
Analytic rank 0
Dimension 44
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 91.13
Character \(\chi\) \(=\) 108.91
Dual form 108.5.f.a.19.13

$q$-expansion

\(f(q)\) \(=\) \(q+(0.701741 + 3.93796i) q^{2} +(-15.0151 + 5.52686i) q^{4} +(-14.3046 + 24.7763i) q^{5} +(-22.2124 + 12.8243i) q^{7} +(-32.3013 - 55.2506i) q^{8} +O(q^{10})\) \(q+(0.701741 + 3.93796i) q^{2} +(-15.0151 + 5.52686i) q^{4} +(-14.3046 + 24.7763i) q^{5} +(-22.2124 + 12.8243i) q^{7} +(-32.3013 - 55.2506i) q^{8} +(-107.606 - 38.9445i) q^{10} +(93.9677 - 54.2523i) q^{11} +(44.2246 - 76.5993i) q^{13} +(-66.0891 - 78.4722i) q^{14} +(194.908 - 165.973i) q^{16} -504.169 q^{17} -191.405i q^{19} +(77.8502 - 451.079i) q^{20} +(279.585 + 331.970i) q^{22} +(-831.897 - 480.296i) q^{23} +(-96.7443 - 167.566i) q^{25} +(332.680 + 120.402i) q^{26} +(262.643 - 315.324i) q^{28} +(396.671 + 687.053i) q^{29} +(285.428 + 164.792i) q^{31} +(790.370 + 651.069i) q^{32} +(-353.796 - 1985.40i) q^{34} -733.789i q^{35} +209.943 q^{37} +(753.745 - 134.317i) q^{38} +(1830.96 - 9.96965i) q^{40} +(528.200 - 914.869i) q^{41} +(-2887.45 + 1667.07i) q^{43} +(-1111.09 + 1333.95i) q^{44} +(1307.61 - 3613.02i) q^{46} +(-977.185 + 564.178i) q^{47} +(-871.573 + 1509.61i) q^{49} +(591.979 - 498.563i) q^{50} +(-240.684 + 1394.57i) q^{52} -1138.62 q^{53} +3104.23i q^{55} +(1426.04 + 813.005i) q^{56} +(-2427.23 + 2044.21i) q^{58} +(-4037.49 - 2331.05i) q^{59} +(2799.84 + 4849.46i) q^{61} +(-448.648 + 1239.65i) q^{62} +(-2009.25 + 3569.33i) q^{64} +(1265.23 + 2191.45i) q^{65} +(-6127.74 - 3537.85i) q^{67} +(7570.16 - 2786.47i) q^{68} +(2889.63 - 514.930i) q^{70} +4433.42i q^{71} -1953.21 q^{73} +(147.326 + 826.748i) q^{74} +(1057.87 + 2873.97i) q^{76} +(-1391.50 + 2410.15i) q^{77} +(1523.90 - 879.826i) q^{79} +(1324.12 + 7203.27i) q^{80} +(3973.38 + 1438.03i) q^{82} +(2621.64 - 1513.61i) q^{83} +(7211.95 - 12491.5i) q^{85} +(-8591.12 - 10200.8i) q^{86} +(-6032.75 - 3439.35i) q^{88} +559.336 q^{89} +2268.61i q^{91} +(15145.6 + 2613.92i) q^{92} +(-2907.44 - 3452.21i) q^{94} +(4742.31 + 2737.97i) q^{95} +(1100.89 + 1906.79i) q^{97} +(-6556.40 - 2372.87i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.701741 + 3.93796i 0.175435 + 0.984491i
\(3\) 0 0
\(4\) −15.0151 + 5.52686i −0.938445 + 0.345429i
\(5\) −14.3046 + 24.7763i −0.572185 + 0.991053i 0.424156 + 0.905589i \(0.360571\pi\)
−0.996341 + 0.0854642i \(0.972763\pi\)
\(6\) 0 0
\(7\) −22.2124 + 12.8243i −0.453314 + 0.261721i −0.709229 0.704978i \(-0.750957\pi\)
0.255915 + 0.966699i \(0.417623\pi\)
\(8\) −32.3013 55.2506i −0.504708 0.863290i
\(9\) 0 0
\(10\) −107.606 38.9445i −1.07606 0.389445i
\(11\) 93.9677 54.2523i 0.776593 0.448366i −0.0586287 0.998280i \(-0.518673\pi\)
0.835221 + 0.549914i \(0.185339\pi\)
\(12\) 0 0
\(13\) 44.2246 76.5993i 0.261684 0.453250i −0.705005 0.709202i \(-0.749055\pi\)
0.966690 + 0.255952i \(0.0823888\pi\)
\(14\) −66.0891 78.4722i −0.337189 0.400369i
\(15\) 0 0
\(16\) 194.908 165.973i 0.761358 0.648332i
\(17\) −504.169 −1.74453 −0.872265 0.489034i \(-0.837349\pi\)
−0.872265 + 0.489034i \(0.837349\pi\)
\(18\) 0 0
\(19\) 191.405i 0.530207i −0.964220 0.265104i \(-0.914594\pi\)
0.964220 0.265104i \(-0.0854062\pi\)
\(20\) 77.8502 451.079i 0.194625 1.12770i
\(21\) 0 0
\(22\) 279.585 + 331.970i 0.577654 + 0.685889i
\(23\) −831.897 480.296i −1.57258 0.907932i −0.995851 0.0909988i \(-0.970994\pi\)
−0.576733 0.816933i \(1.30433\pi\)
\(24\) 0 0
\(25\) −96.7443 167.566i −0.154791 0.268106i
\(26\) 332.680 + 120.402i 0.492129 + 0.178110i
\(27\) 0 0
\(28\) 262.643 315.324i 0.335004 0.402199i
\(29\) 396.671 + 687.053i 0.471665 + 0.816948i 0.999475 0.0324147i \(-0.0103197\pi\)
−0.527809 + 0.849363i \(0.676986\pi\)
\(30\) 0 0
\(31\) 285.428 + 164.792i 0.297011 + 0.171480i 0.641099 0.767458i \(-0.278479\pi\)
−0.344088 + 0.938937i \(0.611812\pi\)
\(32\) 790.370 + 651.069i 0.771846 + 0.635809i
\(33\) 0 0
\(34\) −353.796 1985.40i −0.306052 1.71747i
\(35\) 733.789i 0.599011i
\(36\) 0 0
\(37\) 209.943 0.153355 0.0766775 0.997056i \(-0.475569\pi\)
0.0766775 + 0.997056i \(0.475569\pi\)
\(38\) 753.745 134.317i 0.521984 0.0930171i
\(39\) 0 0
\(40\) 1830.96 9.96965i 1.14435 0.00623103i
\(41\) 528.200 914.869i 0.314218 0.544241i −0.665053 0.746796i \(-0.731591\pi\)
0.979271 + 0.202555i \(0.0649245\pi\)
\(42\) 0 0
\(43\) −2887.45 + 1667.07i −1.56163 + 0.901608i −0.564537 + 0.825407i \(0.690945\pi\)
−0.997093 + 0.0762001i \(0.975721\pi\)
\(44\) −1111.09 + 1333.95i −0.573911 + 0.689024i
\(45\) 0 0
\(46\) 1307.61 3613.02i 0.617964 1.70748i
\(47\) −977.185 + 564.178i −0.442365 + 0.255400i −0.704600 0.709604i \(-0.748874\pi\)
0.262235 + 0.965004i \(0.415540\pi\)
\(48\) 0 0
\(49\) −871.573 + 1509.61i −0.363004 + 0.628742i
\(50\) 591.979 498.563i 0.236792 0.199425i
\(51\) 0 0
\(52\) −240.684 + 1394.57i −0.0890104 + 0.515744i
\(53\) −1138.62 −0.405346 −0.202673 0.979247i \(-0.564963\pi\)
−0.202673 + 0.979247i \(0.564963\pi\)
\(54\) 0 0
\(55\) 3104.23i 1.02619i
\(56\) 1426.04 + 813.005i 0.454732 + 0.259249i
\(57\) 0 0
\(58\) −2427.23 + 2044.21i −0.721531 + 0.607672i
\(59\) −4037.49 2331.05i −1.15987 0.669648i −0.208593 0.978002i \(-0.566889\pi\)
−0.951272 + 0.308354i \(0.900222\pi\)
\(60\) 0 0
\(61\) 2799.84 + 4849.46i 0.752442 + 1.30327i 0.946636 + 0.322305i \(0.104458\pi\)
−0.194193 + 0.980963i \(0.562209\pi\)
\(62\) −448.648 + 1239.65i −0.116714 + 0.322488i
\(63\) 0 0
\(64\) −2009.25 + 3569.33i −0.490540 + 0.871419i
\(65\) 1265.23 + 2191.45i 0.299463 + 0.518686i
\(66\) 0 0
\(67\) −6127.74 3537.85i −1.36506 0.788116i −0.374764 0.927120i \(-0.622276\pi\)
−0.990292 + 0.139004i \(0.955610\pi\)
\(68\) 7570.16 2786.47i 1.63715 0.602611i
\(69\) 0 0
\(70\) 2889.63 514.930i 0.589721 0.105088i
\(71\) 4433.42i 0.879472i 0.898127 + 0.439736i \(0.144928\pi\)
−0.898127 + 0.439736i \(0.855072\pi\)
\(72\) 0 0
\(73\) −1953.21 −0.366524 −0.183262 0.983064i \(-0.558666\pi\)
−0.183262 + 0.983064i \(0.558666\pi\)
\(74\) 147.326 + 826.748i 0.0269039 + 0.150977i
\(75\) 0 0
\(76\) 1057.87 + 2873.97i 0.183149 + 0.497570i
\(77\) −1391.50 + 2410.15i −0.234694 + 0.406501i
\(78\) 0 0
\(79\) 1523.90 879.826i 0.244176 0.140975i −0.372918 0.927864i \(-0.621643\pi\)
0.617095 + 0.786889i \(0.288310\pi\)
\(80\) 1324.12 + 7203.27i 0.206894 + 1.12551i
\(81\) 0 0
\(82\) 3973.38 + 1438.03i 0.590925 + 0.213865i
\(83\) 2621.64 1513.61i 0.380555 0.219714i −0.297505 0.954720i \(-0.596154\pi\)
0.678060 + 0.735007i \(0.262821\pi\)
\(84\) 0 0
\(85\) 7211.95 12491.5i 0.998193 1.72892i
\(86\) −8591.12 10200.8i −1.16159 1.37924i
\(87\) 0 0
\(88\) −6032.75 3439.35i −0.779023 0.444131i
\(89\) 559.336 0.0706144 0.0353072 0.999377i \(-0.488759\pi\)
0.0353072 + 0.999377i \(0.488759\pi\)
\(90\) 0 0
\(91\) 2268.61i 0.273953i
\(92\) 15145.6 + 2613.92i 1.78941 + 0.308828i
\(93\) 0 0
\(94\) −2907.44 3452.21i −0.329045 0.390698i
\(95\) 4742.31 + 2737.97i 0.525463 + 0.303376i
\(96\) 0 0
\(97\) 1100.89 + 1906.79i 0.117004 + 0.202656i 0.918579 0.395238i \(-0.129338\pi\)
−0.801575 + 0.597894i \(0.796004\pi\)
\(98\) −6556.40 2372.87i −0.682674 0.247071i
\(99\) 0 0
\(100\) 2378.74 + 1981.33i 0.237874 + 0.198133i
\(101\) −365.841 633.655i −0.0358632 0.0621170i 0.847537 0.530737i \(-0.178085\pi\)
−0.883400 + 0.468620i \(0.844751\pi\)
\(102\) 0 0
\(103\) 8533.78 + 4926.98i 0.804391 + 0.464415i 0.845004 0.534760i \(-0.179598\pi\)
−0.0406134 + 0.999175i \(0.512931\pi\)
\(104\) −5660.67 + 30.8225i −0.523361 + 0.00284971i
\(105\) 0 0
\(106\) −799.013 4483.83i −0.0711119 0.399059i
\(107\) 804.642i 0.0702806i 0.999382 + 0.0351403i \(0.0111878\pi\)
−0.999382 + 0.0351403i \(0.988812\pi\)
\(108\) 0 0
\(109\) −17324.9 −1.45820 −0.729102 0.684405i \(-0.760062\pi\)
−0.729102 + 0.684405i \(0.760062\pi\)
\(110\) −12224.4 + 2178.37i −1.01028 + 0.180030i
\(111\) 0 0
\(112\) −2200.87 + 6186.22i −0.175452 + 0.493161i
\(113\) 8573.94 14850.5i 0.671465 1.16301i −0.306024 0.952024i \(-0.598999\pi\)
0.977489 0.210988i \(-0.0676680\pi\)
\(114\) 0 0
\(115\) 23799.9 13740.9i 1.79962 1.03901i
\(116\) −9753.31 8123.85i −0.724829 0.603734i
\(117\) 0 0
\(118\) 6346.30 17535.3i 0.455782 1.25936i
\(119\) 11198.8 6465.63i 0.790820 0.456580i
\(120\) 0 0
\(121\) −1433.88 + 2483.55i −0.0979359 + 0.169630i
\(122\) −17132.2 + 14428.7i −1.15105 + 0.969412i
\(123\) 0 0
\(124\) −5196.51 896.848i −0.337963 0.0583278i
\(125\) −12345.2 −0.790094
\(126\) 0 0
\(127\) 9591.51i 0.594675i −0.954772 0.297337i \(-0.903901\pi\)
0.954772 0.297337i \(-0.0960986\pi\)
\(128\) −15465.9 5407.61i −0.943962 0.330054i
\(129\) 0 0
\(130\) −7741.98 + 6520.27i −0.458105 + 0.385815i
\(131\) 3933.27 + 2270.88i 0.229198 + 0.132328i 0.610202 0.792246i \(-0.291088\pi\)
−0.381004 + 0.924573i \(0.624422\pi\)
\(132\) 0 0
\(133\) 2454.64 + 4251.56i 0.138766 + 0.240350i
\(134\) 9631.84 26613.5i 0.536414 1.48215i
\(135\) 0 0
\(136\) 16285.3 + 27855.6i 0.880478 + 1.50604i
\(137\) −2450.82 4244.95i −0.130578 0.226168i 0.793321 0.608803i \(-0.208350\pi\)
−0.923900 + 0.382635i \(0.875017\pi\)
\(138\) 0 0
\(139\) −7491.80 4325.39i −0.387754 0.223870i 0.293432 0.955980i \(-0.405202\pi\)
−0.681187 + 0.732110i \(0.738536\pi\)
\(140\) 4055.55 + 11017.9i 0.206916 + 0.562139i
\(141\) 0 0
\(142\) −17458.6 + 3111.11i −0.865832 + 0.154290i
\(143\) 9597.15i 0.469321i
\(144\) 0 0
\(145\) −22696.9 −1.07952
\(146\) −1370.65 7691.66i −0.0643013 0.360840i
\(147\) 0 0
\(148\) −3152.32 + 1160.33i −0.143915 + 0.0529733i
\(149\) −6346.46 + 10992.4i −0.285863 + 0.495130i −0.972818 0.231570i \(-0.925614\pi\)
0.686955 + 0.726700i \(0.258947\pi\)
\(150\) 0 0
\(151\) 11055.3 6382.78i 0.484860 0.279934i −0.237579 0.971368i \(-0.576354\pi\)
0.722440 + 0.691434i \(0.243021\pi\)
\(152\) −10575.2 + 6182.63i −0.457723 + 0.267600i
\(153\) 0 0
\(154\) −10467.5 3788.37i −0.441370 0.159739i
\(155\) −8165.87 + 4714.57i −0.339891 + 0.196236i
\(156\) 0 0
\(157\) 20283.0 35131.2i 0.822873 1.42526i −0.0806612 0.996742i \(-0.525703\pi\)
0.903534 0.428516i \(-0.140963\pi\)
\(158\) 4534.11 + 5383.67i 0.181626 + 0.215657i
\(159\) 0 0
\(160\) −27437.0 + 10269.2i −1.07176 + 0.401140i
\(161\) 24637.9 0.950499
\(162\) 0 0
\(163\) 6872.98i 0.258684i 0.991600 + 0.129342i \(0.0412865\pi\)
−0.991600 + 0.129342i \(0.958713\pi\)
\(164\) −2874.63 + 16656.2i −0.106879 + 0.619280i
\(165\) 0 0
\(166\) 7800.24 + 9261.78i 0.283069 + 0.336108i
\(167\) 30405.5 + 17554.6i 1.09023 + 0.629447i 0.933639 0.358216i \(-0.116615\pi\)
0.156595 + 0.987663i \(0.449948\pi\)
\(168\) 0 0
\(169\) 10368.9 + 17959.4i 0.363043 + 0.628809i
\(170\) 54251.8 + 19634.6i 1.87723 + 0.679398i
\(171\) 0 0
\(172\) 34141.8 40989.9i 1.15406 1.38554i
\(173\) 1491.72 + 2583.74i 0.0498420 + 0.0863290i 0.889870 0.456214i \(-0.150795\pi\)
−0.840028 + 0.542543i \(0.817462\pi\)
\(174\) 0 0
\(175\) 4297.84 + 2481.36i 0.140338 + 0.0810240i
\(176\) 9310.60 26170.3i 0.300575 0.844857i
\(177\) 0 0
\(178\) 392.509 + 2202.65i 0.0123883 + 0.0695192i
\(179\) 45199.3i 1.41067i 0.708874 + 0.705335i \(0.249203\pi\)
−0.708874 + 0.705335i \(0.750797\pi\)
\(180\) 0 0
\(181\) 27600.9 0.842492 0.421246 0.906946i \(-0.361593\pi\)
0.421246 + 0.906946i \(0.361593\pi\)
\(182\) −8933.68 + 1591.97i −0.269704 + 0.0480610i
\(183\) 0 0
\(184\) 334.744 + 61477.0i 0.00988728 + 1.81584i
\(185\) −3003.16 + 5201.62i −0.0877474 + 0.151983i
\(186\) 0 0
\(187\) −47375.6 + 27352.3i −1.35479 + 0.782188i
\(188\) 11554.4 13872.0i 0.326913 0.392484i
\(189\) 0 0
\(190\) −7454.16 + 20596.4i −0.206487 + 0.570537i
\(191\) −16300.9 + 9411.33i −0.446833 + 0.257979i −0.706492 0.707721i \(-0.749723\pi\)
0.259659 + 0.965700i \(0.416390\pi\)
\(192\) 0 0
\(193\) −4727.11 + 8187.59i −0.126906 + 0.219807i −0.922476 0.386054i \(-0.873838\pi\)
0.795571 + 0.605861i \(0.207171\pi\)
\(194\) −6736.35 + 5673.33i −0.178987 + 0.150742i
\(195\) 0 0
\(196\) 4743.37 27484.0i 0.123474 0.715432i
\(197\) 21650.0 0.557860 0.278930 0.960311i \(-0.410020\pi\)
0.278930 + 0.960311i \(0.410020\pi\)
\(198\) 0 0
\(199\) 25261.4i 0.637898i 0.947772 + 0.318949i \(0.103330\pi\)
−0.947772 + 0.318949i \(0.896670\pi\)
\(200\) −6133.15 + 10757.8i −0.153329 + 0.268944i
\(201\) 0 0
\(202\) 2238.58 1885.33i 0.0548619 0.0462045i
\(203\) −17622.0 10174.1i −0.427625 0.246889i
\(204\) 0 0
\(205\) 15111.4 + 26173.7i 0.359581 + 0.622813i
\(206\) −13413.8 + 37063.2i −0.316094 + 0.873390i
\(207\) 0 0
\(208\) −4093.70 22269.9i −0.0946214 0.514744i
\(209\) −10384.1 17985.9i −0.237727 0.411755i
\(210\) 0 0
\(211\) −18674.0 10781.5i −0.419443 0.242166i 0.275396 0.961331i \(-0.411191\pi\)
−0.694839 + 0.719165i \(0.744524\pi\)
\(212\) 17096.4 6292.97i 0.380394 0.140018i
\(213\) 0 0
\(214\) −3168.65 + 564.650i −0.0691906 + 0.0123297i
\(215\) 95387.3i 2.06354i
\(216\) 0 0
\(217\) −8453.38 −0.179519
\(218\) −12157.6 68224.9i −0.255821 1.43559i
\(219\) 0 0
\(220\) −17156.7 46610.4i −0.354477 0.963025i
\(221\) −22296.7 + 38619.0i −0.456516 + 0.790709i
\(222\) 0 0
\(223\) −16709.5 + 9647.22i −0.336011 + 0.193996i −0.658507 0.752575i \(-0.728812\pi\)
0.322496 + 0.946571i \(0.395478\pi\)
\(224\) −25905.5 4325.83i −0.516293 0.0862130i
\(225\) 0 0
\(226\) 64497.4 + 23342.7i 1.26277 + 0.457018i
\(227\) −56144.4 + 32415.0i −1.08957 + 0.629063i −0.933462 0.358677i \(-0.883228\pi\)
−0.156107 + 0.987740i \(0.549895\pi\)
\(228\) 0 0
\(229\) −19575.4 + 33905.7i −0.373285 + 0.646549i −0.990069 0.140584i \(-0.955102\pi\)
0.616784 + 0.787133i \(0.288435\pi\)
\(230\) 70812.6 + 84080.7i 1.33861 + 1.58943i
\(231\) 0 0
\(232\) 25147.1 44109.0i 0.467210 0.819504i
\(233\) 2307.53 0.0425045 0.0212522 0.999774i \(-0.493235\pi\)
0.0212522 + 0.999774i \(0.493235\pi\)
\(234\) 0 0
\(235\) 32281.4i 0.584543i
\(236\) 73506.8 + 12686.3i 1.31979 + 0.227777i
\(237\) 0 0
\(238\) 33320.1 + 39563.3i 0.588237 + 0.698455i
\(239\) −65999.7 38104.9i −1.15544 0.667091i −0.205230 0.978714i \(-0.565794\pi\)
−0.950206 + 0.311623i \(0.899128\pi\)
\(240\) 0 0
\(241\) −8157.12 14128.5i −0.140444 0.243256i 0.787220 0.616672i \(-0.211520\pi\)
−0.927664 + 0.373416i \(0.878186\pi\)
\(242\) −10786.3 3903.75i −0.184180 0.0666579i
\(243\) 0 0
\(244\) −68842.2 57340.9i −1.15631 0.963130i
\(245\) −24935.0 43188.8i −0.415411 0.719513i
\(246\) 0 0
\(247\) −14661.5 8464.81i −0.240317 0.138747i
\(248\) −114.852 21093.0i −0.00186739 0.342954i
\(249\) 0 0
\(250\) −8663.15 48615.0i −0.138610 0.777840i
\(251\) 33833.6i 0.537033i −0.963275 0.268517i \(-0.913467\pi\)
0.963275 0.268517i \(-0.0865334\pi\)
\(252\) 0 0
\(253\) −104229. −1.62834
\(254\) 37771.0 6730.76i 0.585452 0.104327i
\(255\) 0 0
\(256\) 10441.9 64698.8i 0.159331 0.987225i
\(257\) −28773.1 + 49836.4i −0.435632 + 0.754537i −0.997347 0.0727940i \(-0.976808\pi\)
0.561715 + 0.827331i \(0.310142\pi\)
\(258\) 0 0
\(259\) −4663.34 + 2692.38i −0.0695180 + 0.0401362i
\(260\) −31109.5 25912.1i −0.460199 0.383315i
\(261\) 0 0
\(262\) −6182.49 + 17082.6i −0.0900659 + 0.248859i
\(263\) 68019.2 39270.9i 0.983378 0.567753i 0.0800895 0.996788i \(-0.474479\pi\)
0.903288 + 0.429034i \(0.141146\pi\)
\(264\) 0 0
\(265\) 16287.5 28210.7i 0.231933 0.401719i
\(266\) −15020.0 + 12649.8i −0.212278 + 0.178780i
\(267\) 0 0
\(268\) 111562. + 19254.1i 1.55327 + 0.268073i
\(269\) 5376.96 0.0743074 0.0371537 0.999310i \(-0.488171\pi\)
0.0371537 + 0.999310i \(0.488171\pi\)
\(270\) 0 0
\(271\) 108113.i 1.47211i 0.676924 + 0.736053i \(0.263312\pi\)
−0.676924 + 0.736053i \(0.736688\pi\)
\(272\) −98266.4 + 83678.5i −1.32821 + 1.13103i
\(273\) 0 0
\(274\) 14996.6 12630.1i 0.199752 0.168231i
\(275\) −18181.7 10497.2i −0.240419 0.138806i
\(276\) 0 0
\(277\) 21971.1 + 38055.1i 0.286347 + 0.495968i 0.972935 0.231079i \(-0.0742255\pi\)
−0.686588 + 0.727047i \(0.740892\pi\)
\(278\) 11775.9 32537.8i 0.152372 0.421015i
\(279\) 0 0
\(280\) −40542.2 + 23702.3i −0.517120 + 0.302326i
\(281\) 25435.7 + 44055.9i 0.322130 + 0.557945i 0.980927 0.194375i \(-0.0622680\pi\)
−0.658798 + 0.752320i \(0.728935\pi\)
\(282\) 0 0
\(283\) −22858.8 13197.5i −0.285418 0.164786i 0.350456 0.936579i \(-0.386027\pi\)
−0.635873 + 0.771793i \(0.719360\pi\)
\(284\) −24502.9 66568.3i −0.303795 0.825336i
\(285\) 0 0
\(286\) 37793.2 6734.71i 0.462042 0.0823355i
\(287\) 27095.2i 0.328950i
\(288\) 0 0
\(289\) 170665. 2.04338
\(290\) −15927.3 89379.5i −0.189386 1.06278i
\(291\) 0 0
\(292\) 29327.6 10795.1i 0.343963 0.126608i
\(293\) 65395.3 113268.i 0.761748 1.31939i −0.180201 0.983630i \(-0.557675\pi\)
0.941949 0.335757i \(-0.108992\pi\)
\(294\) 0 0
\(295\) 115510. 66689.5i 1.32731 0.766325i
\(296\) −6781.44 11599.5i −0.0773995 0.132390i
\(297\) 0 0
\(298\) −47741.2 17278.3i −0.537602 0.194567i
\(299\) −73580.7 + 42481.8i −0.823041 + 0.475183i
\(300\) 0 0
\(301\) 42758.2 74059.3i 0.471939 0.817423i
\(302\) 32893.1 + 39056.3i 0.360654 + 0.428230i
\(303\) 0 0
\(304\) −31768.0 37306.2i −0.343750 0.403677i
\(305\) −160202. −1.72214
\(306\) 0 0
\(307\) 54227.3i 0.575362i −0.957726 0.287681i \(-0.907116\pi\)
0.957726 0.287681i \(-0.0928843\pi\)
\(308\) 7572.97 43879.3i 0.0798297 0.462549i
\(309\) 0 0
\(310\) −24296.1 28848.5i −0.252821 0.300193i
\(311\) 117745. + 67980.1i 1.21737 + 0.702847i 0.964354 0.264616i \(-0.0852451\pi\)
0.253013 + 0.967463i \(0.418578\pi\)
\(312\) 0 0
\(313\) −82194.2 142364.i −0.838981 1.45316i −0.890747 0.454499i \(-0.849818\pi\)
0.0517658 0.998659i \(-0.483515\pi\)
\(314\) 152579. + 55220.7i 1.54751 + 0.560070i
\(315\) 0 0
\(316\) −18018.9 + 21633.1i −0.180449 + 0.216643i
\(317\) 60309.5 + 104459.i 0.600160 + 1.03951i 0.992796 + 0.119814i \(0.0382297\pi\)
−0.392637 + 0.919694i \(0.628437\pi\)
\(318\) 0 0
\(319\) 74548.4 + 43040.6i 0.732584 + 0.422957i
\(320\) −59693.4 100840.i −0.582943 0.984763i
\(321\) 0 0
\(322\) 17289.4 + 97023.1i 0.166751 + 0.935758i
\(323\) 96500.4i 0.924962i
\(324\) 0 0
\(325\) −17113.9 −0.162025
\(326\) −27065.5 + 4823.05i −0.254672 + 0.0453823i
\(327\) 0 0
\(328\) −67608.6 + 368.131i −0.628426 + 0.00342180i
\(329\) 14470.4 25063.5i 0.133687 0.231553i
\(330\) 0 0
\(331\) −100184. + 57841.2i −0.914412 + 0.527936i −0.881848 0.471534i \(-0.843701\pi\)
−0.0325639 + 0.999470i \(0.510367\pi\)
\(332\) −30998.8 + 37216.5i −0.281235 + 0.337644i
\(333\) 0 0
\(334\) −47792.7 + 132055.i −0.428419 + 1.18375i
\(335\) 175310. 101215.i 1.56213 0.901895i
\(336\) 0 0
\(337\) −93868.0 + 162584.i −0.826528 + 1.43159i 0.0742175 + 0.997242i \(0.476354\pi\)
−0.900746 + 0.434347i \(0.856979\pi\)
\(338\) −63447.2 + 53435.1i −0.555366 + 0.467728i
\(339\) 0 0
\(340\) −39249.7 + 227420.i −0.339530 + 1.96730i
\(341\) 35761.3 0.307542
\(342\) 0 0
\(343\) 106292.i 0.903465i
\(344\) 185375. + 105685.i 1.56652 + 0.893091i
\(345\) 0 0
\(346\) −9127.87 + 7687.47i −0.0762460 + 0.0642142i
\(347\) −117124. 67621.8i −0.972721 0.561601i −0.0726566 0.997357i \(-0.523148\pi\)
−0.900065 + 0.435756i \(0.856481\pi\)
\(348\) 0 0
\(349\) −1651.44 2860.38i −0.0135585 0.0234841i 0.859167 0.511696i \(-0.170983\pi\)
−0.872725 + 0.488212i \(0.837649\pi\)
\(350\) −6755.54 + 18666.0i −0.0551472 + 0.152376i
\(351\) 0 0
\(352\) 109591. + 18300.1i 0.884485 + 0.147695i
\(353\) 21366.4 + 37007.7i 0.171467 + 0.296990i 0.938933 0.344100i \(-0.111816\pi\)
−0.767466 + 0.641090i \(0.778483\pi\)
\(354\) 0 0
\(355\) −109844. 63418.4i −0.871603 0.503220i
\(356\) −8398.50 + 3091.38i −0.0662677 + 0.0243922i
\(357\) 0 0
\(358\) −177993. + 31718.2i −1.38879 + 0.247481i
\(359\) 175816.i 1.36418i 0.731270 + 0.682088i \(0.238928\pi\)
−0.731270 + 0.682088i \(0.761072\pi\)
\(360\) 0 0
\(361\) 93685.2 0.718880
\(362\) 19368.7 + 108691.i 0.147803 + 0.829426i
\(363\) 0 0
\(364\) −12538.3 34063.4i −0.0946313 0.257090i
\(365\) 27939.9 48393.3i 0.209719 0.363245i
\(366\) 0 0
\(367\) −6867.31 + 3964.84i −0.0509864 + 0.0294370i −0.525277 0.850932i \(-0.676038\pi\)
0.474290 + 0.880369i \(0.342705\pi\)
\(368\) −241859. + 44459.1i −1.78594 + 0.328296i
\(369\) 0 0
\(370\) −22591.2 8176.13i −0.165020 0.0597234i
\(371\) 25291.4 14602.0i 0.183749 0.106087i
\(372\) 0 0
\(373\) −123336. + 213624.i −0.886486 + 1.53544i −0.0424851 + 0.999097i \(0.513527\pi\)
−0.844001 + 0.536342i \(0.819806\pi\)
\(374\) −140958. 167369.i −1.00773 1.19655i
\(375\) 0 0
\(376\) 62735.5 + 35766.3i 0.443749 + 0.252987i
\(377\) 70170.4 0.493709
\(378\) 0 0
\(379\) 147423.i 1.02633i −0.858291 0.513163i \(-0.828474\pi\)
0.858291 0.513163i \(-0.171526\pi\)
\(380\) −86338.7 14900.9i −0.597914 0.103192i
\(381\) 0 0
\(382\) −48500.5 57588.0i −0.332368 0.394644i
\(383\) 105968. + 61180.9i 0.722402 + 0.417079i 0.815636 0.578565i \(-0.196387\pi\)
−0.0932341 + 0.995644i \(0.529720\pi\)
\(384\) 0 0
\(385\) −39809.7 68952.5i −0.268576 0.465188i
\(386\) −35559.6 12869.6i −0.238662 0.0863755i
\(387\) 0 0
\(388\) −27068.6 22546.3i −0.179805 0.149765i
\(389\) −91728.1 158878.i −0.606182 1.04994i −0.991863 0.127306i \(-0.959367\pi\)
0.385682 0.922632i \(-0.373966\pi\)
\(390\) 0 0
\(391\) 419417. + 242150.i 2.74342 + 1.58391i
\(392\) 111560. 607.446i 0.725998 0.00395308i
\(393\) 0 0
\(394\) 15192.7 + 85256.9i 0.0978684 + 0.549208i
\(395\) 50342.3i 0.322656i
\(396\) 0 0
\(397\) 81466.1 0.516887 0.258444 0.966026i \(-0.416790\pi\)
0.258444 + 0.966026i \(0.416790\pi\)
\(398\) −99478.5 + 17727.0i −0.628005 + 0.111910i
\(399\) 0 0
\(400\) −46667.6 16602.9i −0.291673 0.103768i
\(401\) 100584. 174217.i 0.625518 1.08343i −0.362922 0.931820i \(-0.618221\pi\)
0.988440 0.151610i \(-0.0484459\pi\)
\(402\) 0 0
\(403\) 25245.9 14575.7i 0.155446 0.0897469i
\(404\) 8995.27 + 7492.45i 0.0551127 + 0.0459051i
\(405\) 0 0
\(406\) 27699.0 76534.4i 0.168040 0.464306i
\(407\) 19727.9 11389.9i 0.119094 0.0687592i
\(408\) 0 0
\(409\) 70320.1 121798.i 0.420371 0.728104i −0.575605 0.817728i \(-0.695233\pi\)
0.995976 + 0.0896241i \(0.0285666\pi\)
\(410\) −92466.8 + 77875.3i −0.550070 + 0.463268i
\(411\) 0 0
\(412\) −155367. 26814.2i −0.915299 0.157968i
\(413\) 119576. 0.701044
\(414\) 0 0
\(415\) 86606.3i 0.502867i
\(416\) 84825.3 31748.5i 0.490161 0.183458i
\(417\) 0 0
\(418\) 63540.7 53513.8i 0.363663 0.306276i
\(419\) 133102. + 76846.6i 0.758154 + 0.437720i 0.828633 0.559793i \(-0.189119\pi\)
−0.0704785 + 0.997513i \(0.522453\pi\)
\(420\) 0 0
\(421\) −77206.0 133725.i −0.435599 0.754479i 0.561746 0.827310i \(-0.310130\pi\)
−0.997344 + 0.0728309i \(0.976797\pi\)
\(422\) 29352.6 81103.5i 0.164825 0.455422i
\(423\) 0 0
\(424\) 36778.8 + 62909.2i 0.204581 + 0.349931i
\(425\) 48775.5 + 84481.6i 0.270037 + 0.467718i
\(426\) 0 0
\(427\) −124382. 71812.1i −0.682186 0.393860i
\(428\) −4447.15 12081.8i −0.0242769 0.0659544i
\(429\) 0 0
\(430\) 375632. 66937.2i 2.03154 0.362019i
\(431\) 191579.i 1.03132i −0.856793 0.515660i \(-0.827547\pi\)
0.856793 0.515660i \(-0.172453\pi\)
\(432\) 0 0
\(433\) −53963.8 −0.287824 −0.143912 0.989591i \(-0.545968\pi\)
−0.143912 + 0.989591i \(0.545968\pi\)
\(434\) −5932.08 33289.1i −0.0314940 0.176735i
\(435\) 0 0
\(436\) 260136. 95752.5i 1.36844 0.503706i
\(437\) −91930.9 + 159229.i −0.481392 + 0.833795i
\(438\) 0 0
\(439\) 14586.4 8421.44i 0.0756864 0.0436976i −0.461679 0.887047i \(-0.652753\pi\)
0.537366 + 0.843349i \(0.319420\pi\)
\(440\) 171511. 100271.i 0.885902 0.517928i
\(441\) 0 0
\(442\) −167727. 60703.0i −0.858534 0.310718i
\(443\) −140111. + 80892.9i −0.713943 + 0.412195i −0.812519 0.582934i \(-0.801905\pi\)
0.0985761 + 0.995130i \(0.468571\pi\)
\(444\) 0 0
\(445\) −8001.09 + 13858.3i −0.0404045 + 0.0699826i
\(446\) −49716.1 59031.5i −0.249935 0.296766i
\(447\) 0 0
\(448\) −1144.04 105051.i −0.00570015 0.523411i
\(449\) −127200. −0.630949 −0.315475 0.948934i \(-0.602164\pi\)
−0.315475 + 0.948934i \(0.602164\pi\)
\(450\) 0 0
\(451\) 114624.i 0.563538i
\(452\) −46662.0 + 270369.i −0.228395 + 1.32337i
\(453\) 0 0
\(454\) −167048. 198348.i −0.810456 0.962311i
\(455\) −56207.7 32451.5i −0.271502 0.156752i
\(456\) 0 0
\(457\) 9423.93 + 16322.7i 0.0451232 + 0.0781556i 0.887705 0.460413i \(-0.152299\pi\)
−0.842582 + 0.538569i \(0.818965\pi\)
\(458\) −147256. 53294.4i −0.702009 0.254068i
\(459\) 0 0
\(460\) −281415. + 337860.i −1.32994 + 1.59669i
\(461\) −29335.9 50811.3i −0.138038 0.239088i 0.788716 0.614758i \(-0.210746\pi\)
−0.926754 + 0.375669i \(0.877413\pi\)
\(462\) 0 0
\(463\) −41167.7 23768.2i −0.192041 0.110875i 0.400897 0.916123i \(-0.368699\pi\)
−0.592938 + 0.805248i \(0.702032\pi\)
\(464\) 191346. + 68075.3i 0.888760 + 0.316194i
\(465\) 0 0
\(466\) 1619.29 + 9086.96i 0.00745679 + 0.0418453i
\(467\) 150686.i 0.690936i −0.938431 0.345468i \(-0.887720\pi\)
0.938431 0.345468i \(-0.112280\pi\)
\(468\) 0 0
\(469\) 181482. 0.825066
\(470\) 127123. 22653.2i 0.575478 0.102550i
\(471\) 0 0
\(472\) 1624.63 + 298370.i 0.00729240 + 1.33928i
\(473\) −180885. + 313302.i −0.808500 + 1.40036i
\(474\) 0 0
\(475\) −32072.9 + 18517.3i −0.142152 + 0.0820712i
\(476\) −132417. + 158976.i −0.584425 + 0.701647i
\(477\) 0 0
\(478\) 103741. 286644.i 0.454041 1.25455i
\(479\) 47830.3 27614.8i 0.208464 0.120357i −0.392133 0.919908i \(-0.628263\pi\)
0.600598 + 0.799551i \(0.294929\pi\)
\(480\) 0 0
\(481\) 9284.65 16081.5i 0.0401306 0.0695082i
\(482\) 49913.5 42037.0i 0.214844 0.180941i
\(483\) 0 0
\(484\) 7803.61 45215.7i 0.0333123 0.193018i
\(485\) −62991.1 −0.267791
\(486\) 0 0
\(487\) 2975.59i 0.0125463i 0.999980 + 0.00627313i \(0.00199681\pi\)
−0.999980 + 0.00627313i \(0.998003\pi\)
\(488\) 177497. 311337.i 0.745335 1.30735i
\(489\) 0 0
\(490\) 152578. 128501.i 0.635476 0.535196i
\(491\) −234443. 135356.i −0.972467 0.561454i −0.0724794 0.997370i \(-0.523091\pi\)
−0.899987 + 0.435916i \(0.856424\pi\)
\(492\) 0 0
\(493\) −199989. 346391.i −0.822834 1.42519i
\(494\) 23045.5 63676.5i 0.0944350 0.260931i
\(495\) 0 0
\(496\) 82983.0 15254.1i 0.337307 0.0620047i
\(497\) −56855.6 98476.8i −0.230176 0.398677i
\(498\) 0 0
\(499\) −226339. 130677.i −0.908988 0.524805i −0.0288827 0.999583i \(-0.509195\pi\)
−0.880105 + 0.474778i \(0.842528\pi\)
\(500\) 185365. 68230.3i 0.741459 0.272921i
\(501\) 0 0
\(502\) 133236. 23742.5i 0.528704 0.0942146i
\(503\) 283008.i 1.11857i −0.828976 0.559284i \(-0.811076\pi\)
0.828976 0.559284i \(-0.188924\pi\)
\(504\) 0 0
\(505\) 20932.9 0.0820816
\(506\) −73141.5 410448.i −0.285669 1.60309i
\(507\) 0 0
\(508\) 53010.9 + 144018.i 0.205418 + 0.558069i
\(509\) −106839. + 185051.i −0.412378 + 0.714259i −0.995149 0.0983769i \(-0.968635\pi\)
0.582772 + 0.812636i \(0.301968\pi\)
\(510\) 0 0
\(511\) 43385.4 25048.6i 0.166151 0.0959271i
\(512\) 262109. 4281.91i 0.999867 0.0163342i
\(513\) 0 0
\(514\) −216445. 78335.0i −0.819260 0.296503i
\(515\) −244145. + 140957.i −0.920520 + 0.531463i
\(516\) 0 0
\(517\) −61215.9 + 106029.i −0.229025 + 0.396683i
\(518\) −13874.9 16474.7i −0.0517097 0.0613985i
\(519\) 0 0
\(520\) 80210.0 140691.i 0.296635 0.520309i
\(521\) −168525. −0.620854 −0.310427 0.950597i \(-0.600472\pi\)
−0.310427 + 0.950597i \(0.600472\pi\)
\(522\) 0 0
\(523\) 231592.i 0.846681i 0.905971 + 0.423340i \(0.139143\pi\)
−0.905971 + 0.423340i \(0.860857\pi\)
\(524\) −71609.4 12358.8i −0.260800 0.0450105i
\(525\) 0 0
\(526\) 202379. + 240299.i 0.731467 + 0.868522i
\(527\) −143904. 83082.9i −0.518145 0.299151i
\(528\) 0 0
\(529\) 321448. + 556764.i 1.14868 + 1.98957i
\(530\) 122522. + 44342.8i 0.436178 + 0.157860i
\(531\) 0 0
\(532\) −60354.5 50271.2i −0.213249 0.177622i
\(533\) −46718.9 80919.5i −0.164452 0.284839i
\(534\) 0 0
\(535\) −19936.1 11510.1i −0.0696518 0.0402135i
\(536\) 2465.72 + 452838.i 0.00858250 + 1.57621i
\(537\) 0 0
\(538\) 3773.23 + 21174.3i 0.0130361 + 0.0731550i
\(539\) 189139.i 0.651035i
\(540\) 0 0
\(541\) −3552.06 −0.0121363 −0.00606815 0.999982i \(-0.501932\pi\)
−0.00606815 + 0.999982i \(0.501932\pi\)
\(542\) −425745. + 75867.3i −1.44927 + 0.258259i
\(543\) 0 0
\(544\) −398480. 328249.i −1.34651 1.10919i
\(545\) 247826. 429248.i 0.834362 1.44516i
\(546\) 0 0
\(547\) −444293. + 256513.i −1.48489 + 0.857302i −0.999852 0.0171904i \(-0.994528\pi\)
−0.485039 + 0.874493i \(0.661195\pi\)
\(548\) 60260.6 + 50193.0i 0.200665 + 0.167141i
\(549\) 0 0
\(550\) 28578.7 78965.1i 0.0944752 0.261042i
\(551\) 131505. 75924.6i 0.433152 0.250080i
\(552\) 0 0
\(553\) −22566.4 + 39086.1i −0.0737924 + 0.127812i
\(554\) −134442. + 113226.i −0.438041 + 0.368917i
\(555\) 0 0
\(556\) 136396. + 23540.1i 0.441217 + 0.0761482i
\(557\) 269383. 0.868281 0.434141 0.900845i \(-0.357052\pi\)
0.434141 + 0.900845i \(0.357052\pi\)
\(558\) 0 0
\(559\) 294903.i 0.943746i
\(560\) −121789. 143021.i −0.388358 0.456062i
\(561\) 0 0
\(562\) −155641. + 131081.i −0.492779 + 0.415017i
\(563\) 48439.2 + 27966.4i 0.152820 + 0.0882307i 0.574460 0.818533i \(-0.305212\pi\)
−0.421640 + 0.906763i \(0.638545\pi\)
\(564\) 0 0
\(565\) 245294. + 424861.i 0.768404 + 1.33092i
\(566\) 35930.5 99278.4i 0.112158 0.309900i
\(567\) 0 0
\(568\) 244949. 143205.i 0.759239 0.443877i
\(569\) 212266. + 367655.i 0.655625 + 1.13558i 0.981737 + 0.190245i \(0.0609282\pi\)
−0.326111 + 0.945331i \(0.605738\pi\)
\(570\) 0 0
\(571\) −25297.4 14605.5i −0.0775897 0.0447964i 0.460703 0.887554i \(-0.347597\pi\)
−0.538293 + 0.842758i \(0.680931\pi\)
\(572\) 53042.1 + 144102.i 0.162117 + 0.440432i
\(573\) 0 0
\(574\) −106700. + 19013.9i −0.323848 + 0.0577094i
\(575\) 185863.i 0.562158i
\(576\) 0 0
\(577\) −494524. −1.48537 −0.742687 0.669639i \(-0.766449\pi\)
−0.742687 + 0.669639i \(0.766449\pi\)
\(578\) 119763. + 672074.i 0.358482 + 2.01169i
\(579\) 0 0
\(580\) 340796. 125443.i 1.01307 0.372897i
\(581\) −38822.0 + 67241.7i −0.115007 + 0.199199i
\(582\) 0 0
\(583\) −106993. + 61772.5i −0.314788 + 0.181743i
\(584\) 63091.1 + 107916.i 0.184988 + 0.316417i
\(585\) 0 0
\(586\) 491936. + 178040.i 1.43256 + 0.518467i
\(587\) −208206. + 120208.i −0.604251 + 0.348865i −0.770712 0.637183i \(-0.780099\pi\)
0.166461 + 0.986048i \(0.446766\pi\)
\(588\) 0 0
\(589\) 31541.9 54632.2i 0.0909197 0.157477i
\(590\) 343678. + 408074.i 0.987298 + 1.17229i
\(591\) 0 0
\(592\) 40919.5 34844.9i 0.116758 0.0994250i
\(593\) 470902. 1.33912 0.669562 0.742756i \(-0.266482\pi\)
0.669562 + 0.742756i \(0.266482\pi\)
\(594\) 0 0
\(595\) 369954.i 1.04499i
\(596\) 34539.4 200128.i 0.0972349 0.563398i
\(597\) 0 0
\(598\) −218926. 259947.i −0.612203 0.726912i
\(599\) 8669.92 + 5005.58i 0.0241636 + 0.0139509i 0.512033 0.858966i \(-0.328892\pi\)
−0.487870 + 0.872917i \(0.662226\pi\)
\(600\) 0 0
\(601\) −196449. 340259.i −0.543876 0.942021i −0.998677 0.0514280i \(-0.983623\pi\)
0.454800 0.890593i \(-0.349711\pi\)
\(602\) 321648. + 116410.i 0.887540 + 0.321215i
\(603\) 0 0
\(604\) −130720. + 156939.i −0.358317 + 0.430188i
\(605\) −41022.2 71052.5i −0.112075 0.194119i
\(606\) 0 0
\(607\) −375426. 216752.i −1.01894 0.588283i −0.105141 0.994457i \(-0.533529\pi\)
−0.913796 + 0.406174i \(0.866863\pi\)
\(608\) 124618. 151281.i 0.337111 0.409238i
\(609\) 0 0
\(610\) −112421. 630872.i −0.302125 1.69544i
\(611\) 99802.2i 0.267336i
\(612\) 0 0
\(613\) 301951. 0.803555 0.401778 0.915737i \(-0.368393\pi\)
0.401778 + 0.915737i \(0.368393\pi\)
\(614\) 213545. 38053.5i 0.566439 0.100939i
\(615\) 0 0
\(616\) 178109. 969.810i 0.469380 0.00255579i
\(617\) 98373.3 170388.i 0.258409 0.447577i −0.707407 0.706806i \(-0.750135\pi\)
0.965816 + 0.259229i \(0.0834686\pi\)
\(618\) 0 0
\(619\) 536199. 309575.i 1.39941 0.807949i 0.405078 0.914282i \(-0.367244\pi\)
0.994331 + 0.106333i \(0.0339110\pi\)
\(620\) 96554.8 115921.i 0.251183 0.301565i
\(621\) 0 0
\(622\) −185077. + 511380.i −0.478378 + 1.32179i
\(623\) −12424.2 + 7173.12i −0.0320105 + 0.0184813i
\(624\) 0 0
\(625\) 237059. 410598.i 0.606870 1.05113i
\(626\) 502947. 423581.i 1.28343 1.08090i
\(627\) 0 0
\(628\) −110386. + 639600.i −0.279896 + 1.62177i
\(629\) −105847. −0.267532
\(630\) 0 0
\(631\) 308766.i 0.775479i −0.921769 0.387740i \(-0.873256\pi\)
0.921769 0.387740i \(-0.126744\pi\)
\(632\) −97835.0 55777.0i −0.244940 0.139644i
\(633\) 0 0
\(634\) −369034. + 310800.i −0.918096 + 0.773218i
\(635\) 237642. + 137203.i 0.589354 + 0.340264i
\(636\) 0 0
\(637\) 77090.0 + 133524.i 0.189985 + 0.329064i
\(638\) −117178. + 323772.i −0.287877 + 0.795424i
\(639\) 0 0
\(640\) 355214. 305834.i 0.867222 0.746665i
\(641\) −171200. 296528.i −0.416666 0.721687i 0.578935 0.815373i \(-0.303468\pi\)
−0.995602 + 0.0936860i \(0.970135\pi\)
\(642\) 0 0
\(643\) 478867. + 276474.i 1.15823 + 0.668702i 0.950878 0.309566i \(-0.100184\pi\)
0.207347 + 0.978267i \(0.433517\pi\)
\(644\) −369941. + 136170.i −0.891991 + 0.328330i
\(645\) 0 0
\(646\) −380015. + 67718.3i −0.910617 + 0.162271i
\(647\) 576814.i 1.37793i −0.724794 0.688965i \(-0.758065\pi\)
0.724794 0.688965i \(-0.241935\pi\)
\(648\) 0 0
\(649\) −505858. −1.20099
\(650\) −12009.5 67394.0i −0.0284250 0.159512i
\(651\) 0 0
\(652\) −37986.0 103199.i −0.0893569 0.242761i
\(653\) −286795. + 496744.i −0.672583 + 1.16495i 0.304586 + 0.952485i \(0.401482\pi\)
−0.977169 + 0.212463i \(0.931852\pi\)
\(654\) 0 0
\(655\) −112528. + 64968.0i −0.262288 + 0.151432i
\(656\) −48893.4 265982.i −0.113617 0.618080i
\(657\) 0 0
\(658\) 108854. + 39395.9i 0.251415 + 0.0909911i
\(659\) −299298. + 172800.i −0.689180 + 0.397899i −0.803305 0.595568i \(-0.796927\pi\)
0.114125 + 0.993466i \(0.463594\pi\)
\(660\) 0 0
\(661\) 187583. 324904.i 0.429330 0.743622i −0.567484 0.823385i \(-0.692083\pi\)
0.996814 + 0.0797628i \(0.0254163\pi\)
\(662\) −298080. 353931.i −0.680168 0.807612i
\(663\) 0 0
\(664\) −168310. 95955.8i −0.381746 0.217638i
\(665\) −140451. −0.317600
\(666\) 0 0
\(667\) 762077.i 1.71296i
\(668\) −553565. 95537.8i −1.24055 0.214103i
\(669\) 0 0
\(670\) 521604. + 619337.i 1.16196 + 1.37968i
\(671\) 526189. + 303795.i 1.16868 + 0.674739i
\(672\) 0 0
\(673\) 286866. + 496866.i 0.633358 + 1.09701i 0.986861 + 0.161574i \(0.0516571\pi\)
−0.353503 + 0.935433i \(0.615010\pi\)
\(674\) −706121. 255557.i −1.55439 0.562558i
\(675\) 0 0
\(676\) −254949. 212355.i −0.557904 0.464697i
\(677\) −13789.2 23883.6i −0.0300859 0.0521103i 0.850590 0.525829i \(-0.176245\pi\)
−0.880676 + 0.473719i \(0.842911\pi\)
\(678\) 0 0
\(679\) −48906.7 28236.3i −0.106079 0.0612447i
\(680\) −923116. + 5026.39i −1.99636 + 0.0108702i
\(681\) 0 0
\(682\) 25095.2 + 140827.i 0.0539538 + 0.302773i
\(683\) 1038.30i 0.00222578i 0.999999 + 0.00111289i \(0.000354244\pi\)
−0.999999 + 0.00111289i \(0.999646\pi\)
\(684\) 0 0
\(685\) 140232. 0.298859
\(686\) 418573. 74589.3i 0.889454 0.158500i
\(687\) 0 0
\(688\) −286098. + 804164.i −0.604418 + 1.69890i
\(689\) −50354.8 + 87217.2i −0.106073 + 0.183723i
\(690\) 0 0
\(691\) 289343. 167052.i 0.605978 0.349862i −0.165411 0.986225i \(-0.552895\pi\)
0.771390 + 0.636363i \(0.219562\pi\)
\(692\) −36678.4 30550.6i −0.0765945 0.0637981i
\(693\) 0 0
\(694\) 184101. 508685.i 0.382241 1.05616i
\(695\) 214335. 123746.i 0.443734 0.256190i
\(696\) 0 0
\(697\) −266302. + 461249.i −0.548162 + 0.949445i
\(698\) 10105.2 8510.57i 0.0207412 0.0174682i
\(699\) 0 0
\(700\) −78246.8 13504.3i −0.159687 0.0275599i
\(701\) −177927. −0.362082 −0.181041 0.983476i \(-0.557947\pi\)
−0.181041 + 0.983476i \(0.557947\pi\)
\(702\) 0 0
\(703\) 40184.1i 0.0813100i
\(704\) 4839.78 + 444408.i 0.00976517 + 0.896679i
\(705\) 0 0
\(706\) −130741. + 110110.i −0.262303 + 0.220911i
\(707\) 16252.4 + 9383.33i 0.0325146 + 0.0187723i
\(708\) 0 0
\(709\) −362484. 627841.i −0.721102 1.24899i −0.960558 0.278079i \(-0.910302\pi\)
0.239456 0.970907i \(-0.423031\pi\)
\(710\) 172657. 477064.i 0.342506 0.946368i
\(711\) 0 0
\(712\) −18067.3 30903.7i −0.0356396 0.0609607i
\(713\) −158298. 274180.i −0.311383 0.539332i
\(714\) 0 0
\(715\) 237782. + 137284.i 0.465122 + 0.268538i
\(716\) −249810. 678672.i −0.487286 1.32384i
\(717\) 0 0
\(718\) −692358. + 123378.i −1.34302 + 0.239325i
\(719\) 536436.i 1.03767i 0.854874 + 0.518836i \(0.173634\pi\)
−0.854874 + 0.518836i \(0.826366\pi\)
\(720\) 0 0
\(721\) −252741. −0.486189
\(722\) 65742.8 + 368929.i 0.126117 + 0.707731i
\(723\) 0 0
\(724\) −414431. + 152546.i −0.790632 + 0.291021i
\(725\) 76751.2 132937.i 0.146019 0.252912i
\(726\) 0 0
\(727\) 375814. 216977.i 0.711057 0.410529i −0.100395 0.994948i \(-0.532011\pi\)
0.811452 + 0.584418i \(0.198677\pi\)
\(728\) 125342. 73278.9i 0.236501 0.138266i
\(729\) 0 0
\(730\) 210178. + 76066.7i 0.394403 + 0.142741i
\(731\) 1.45577e6 840486.i 2.72431 1.57288i
\(732\) 0 0
\(733\) 390208. 675860.i 0.726254 1.25791i −0.232202 0.972667i \(-0.574593\pi\)
0.958456 0.285241i \(-0.0920735\pi\)
\(734\) −20432.5 24260.9i −0.0379253 0.0450314i
\(735\) 0 0
\(736\) −344801. 921234.i −0.636521 1.70065i
\(737\) −767746. −1.41346
\(738\) 0 0
\(739\) 215142.i 0.393947i 0.980409 + 0.196973i \(0.0631112\pi\)
−0.980409 + 0.196973i \(0.936889\pi\)
\(740\) 16344.1 94700.9i 0.0298468 0.172938i
\(741\) 0 0
\(742\) 75250.1 + 89349.7i 0.136678 + 0.162288i
\(743\) −250360. 144546.i −0.453511 0.261835i 0.255801 0.966730i \(-0.417661\pi\)
−0.709312 + 0.704895i \(0.750994\pi\)
\(744\) 0 0
\(745\) −181567. 314484.i −0.327133 0.566612i
\(746\) −927794. 335784.i −1.66715 0.603367i
\(747\) 0 0
\(748\) 560178. 672537.i 1.00120 1.20202i
\(749\) −10319.0 17873.0i −0.0183939 0.0318592i
\(750\) 0 0
\(751\) 593117. + 342436.i 1.05162 + 0.607156i 0.923104 0.384551i \(-0.125644\pi\)
0.128521 + 0.991707i \(0.458977\pi\)
\(752\) −96822.4 + 272149.i −0.171214 + 0.481250i
\(753\) 0 0
\(754\) 49241.5 + 276329.i 0.0866141 + 0.486052i
\(755\) 365213.i 0.640697i
\(756\) 0 0
\(757\) −646906. −1.12888 −0.564442 0.825472i \(-0.690909\pi\)
−0.564442 + 0.825472i \(0.690909\pi\)
\(758\) 580545. 103452.i 1.01041 0.180054i
\(759\) 0 0
\(760\) −1908.24 350455.i −0.00330374 0.606744i
\(761\) 383411. 664087.i 0.662057 1.14672i −0.318018 0.948085i \(-0.603017\pi\)
0.980074 0.198631i \(-0.0636495\pi\)
\(762\) 0 0
\(763\) 384828. 222181.i 0.661025 0.381643i
\(764\) 192745. 231405.i 0.330214 0.396448i
\(765\) 0 0
\(766\) −166566. + 460233.i −0.283876 + 0.784369i
\(767\) −357113. + 206179.i −0.607037 + 0.350473i
\(768\) 0 0
\(769\) 289867. 502065.i 0.490170 0.848999i −0.509766 0.860313i \(-0.670268\pi\)
0.999936 + 0.0113137i \(0.00360135\pi\)
\(770\) 243596. 205156.i 0.410855 0.346021i
\(771\) 0 0
\(772\) 25726.4 149064.i 0.0431662 0.250114i
\(773\) 885783. 1.48241 0.741205 0.671279i \(-0.234255\pi\)
0.741205 + 0.671279i \(0.234255\pi\)
\(774\) 0 0
\(775\) 63770.7i 0.106174i
\(776\) 69791.3 122417.i 0.115899 0.203291i
\(777\) 0 0