Properties

Label 108.5.f.a.19.18
Level 108
Weight 5
Character 108.19
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 19.18
Character \(\chi\) \(=\) 108.19
Dual form 108.5.f.a.91.18

$q$-expansion

\(f(q)\) \(=\) \(q+(3.05951 - 2.57671i) q^{2} +(2.72116 - 15.7669i) q^{4} +(-14.3046 - 24.7763i) q^{5} +(22.2124 + 12.8243i) q^{7} +(-32.3013 - 55.2506i) q^{8} +O(q^{10})\) \(q+(3.05951 - 2.57671i) q^{2} +(2.72116 - 15.7669i) q^{4} +(-14.3046 - 24.7763i) q^{5} +(22.2124 + 12.8243i) q^{7} +(-32.3013 - 55.2506i) q^{8} +(-107.606 - 38.9445i) q^{10} +(-93.9677 - 54.2523i) q^{11} +(44.2246 + 76.5993i) q^{13} +(101.004 - 17.9987i) q^{14} +(-241.191 - 85.8084i) q^{16} -504.169 q^{17} -191.405i q^{19} +(-429.571 + 158.119i) q^{20} +(-427.287 + 76.1421i) q^{22} +(831.897 - 480.296i) q^{23} +(-96.7443 + 167.566i) q^{25} +(332.680 + 120.402i) q^{26} +(262.643 - 315.324i) q^{28} +(396.671 - 687.053i) q^{29} +(-285.428 + 164.792i) q^{31} +(-959.027 + 358.946i) q^{32} +(-1542.51 + 1299.10i) q^{34} -733.789i q^{35} +209.943 q^{37} +(-493.194 - 585.604i) q^{38} +(-906.848 + 1590.65i) q^{40} +(528.200 + 914.869i) q^{41} +(2887.45 + 1667.07i) q^{43} +(-1111.09 + 1333.95i) q^{44} +(1307.61 - 3613.02i) q^{46} +(977.185 + 564.178i) q^{47} +(-871.573 - 1509.61i) q^{49} +(135.779 + 761.951i) q^{50} +(1328.08 - 488.847i) q^{52} -1138.62 q^{53} +3104.23i q^{55} +(-8.93796 - 1641.49i) q^{56} +(-556.720 - 3124.15i) q^{58} +(4037.49 - 2331.05i) q^{59} +(2799.84 - 4849.46i) q^{61} +(-448.648 + 1239.65i) q^{62} +(-2009.25 + 3569.33i) q^{64} +(1265.23 - 2191.45i) q^{65} +(6127.74 - 3537.85i) q^{67} +(-1371.92 + 7949.19i) q^{68} +(-1890.76 - 2245.03i) q^{70} +4433.42i q^{71} -1953.21 q^{73} +(642.322 - 540.962i) q^{74} +(-3017.86 - 520.842i) q^{76} +(-1391.50 - 2410.15i) q^{77} +(-1523.90 - 879.826i) q^{79} +(1324.12 + 7203.27i) q^{80} +(3973.38 + 1438.03i) q^{82} +(-2621.64 - 1513.61i) q^{83} +(7211.95 + 12491.5i) q^{85} +(13129.7 - 2339.71i) q^{86} +(37.8113 + 6944.19i) q^{88} +559.336 q^{89} +2268.61i q^{91} +(-5309.06 - 14423.4i) q^{92} +(4443.42 - 791.814i) q^{94} +(-4742.31 + 2737.97i) q^{95} +(1100.89 - 1906.79i) q^{97} +(-6556.40 - 2372.87i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.05951 2.57671i 0.764877 0.644177i
\(3\) 0 0
\(4\) 2.72116 15.7669i 0.170072 0.985432i
\(5\) −14.3046 24.7763i −0.572185 0.991053i −0.996341 0.0854642i \(-0.972763\pi\)
0.424156 0.905589i \(-0.360571\pi\)
\(6\) 0 0
\(7\) 22.2124 + 12.8243i 0.453314 + 0.261721i 0.709229 0.704978i \(-0.249043\pi\)
−0.255915 + 0.966699i \(0.582377\pi\)
\(8\) −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 \(-0.481327\pi\)
−0.835221 + 0.549914i \(0.814661\pi\)
\(12\) 0 0
\(13\) 44.2246 + 76.5993i 0.261684 + 0.453250i 0.966690 0.255952i \(-0.0823888\pi\)
−0.705005 + 0.709202i \(0.749055\pi\)
\(14\) 101.004 17.9987i 0.515324 0.0918302i
\(15\) 0 0
\(16\) −241.191 85.8084i −0.942151 0.335189i
\(17\) −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 \(-0.0854062\pi\)
\(20\) −429.571 + 158.119i −1.07393 + 0.395298i
\(21\) 0 0
\(22\) −427.287 + 76.1421i −0.882825 + 0.157318i
\(23\) 831.897 480.296i 1.57258 0.907932i 0.576733 0.816933i \(-0.304327\pi\)
0.995851 0.0909988i \(-0.0290059\pi\)
\(24\) 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 −0.527809 0.849363i \(-0.676986\pi\)
0.999475 + 0.0324147i \(0.0103197\pi\)
\(30\) 0 0
\(31\) −285.428 + 164.792i −0.297011 + 0.171480i −0.641099 0.767458i \(-0.721521\pi\)
0.344088 + 0.938937i \(0.388188\pi\)
\(32\) −959.027 + 358.946i −0.936550 + 0.350534i
\(33\) 0 0
\(34\) −1542.51 + 1299.10i −1.33435 + 1.12379i
\(35\) 733.789i 0.599011i
\(36\) 0 0
\(37\) 209.943 0.153355 0.0766775 0.997056i \(-0.475569\pi\)
0.0766775 + 0.997056i \(0.475569\pi\)
\(38\) −493.194 585.604i −0.341547 0.405543i
\(39\) 0 0
\(40\) −906.848 + 1590.65i −0.566780 + 0.994154i
\(41\) 528.200 + 914.869i 0.314218 + 0.544241i 0.979271 0.202555i \(-0.0649245\pi\)
−0.665053 + 0.746796i \(0.731591\pi\)
\(42\) 0 0
\(43\) 2887.45 + 1667.07i 1.56163 + 0.901608i 0.997093 + 0.0762001i \(0.0242788\pi\)
0.564537 + 0.825407i \(0.309055\pi\)
\(44\) −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 \(-0.251126\pi\)
−0.262235 + 0.965004i \(0.584460\pi\)
\(48\) 0 0
\(49\) −871.573 1509.61i −0.363004 0.628742i
\(50\) 135.779 + 761.951i 0.0543116 + 0.304780i
\(51\) 0 0
\(52\) 1328.08 488.847i 0.491152 0.180787i
\(53\) −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
\(56\) −8.93796 1641.49i −0.00285011 0.523434i
\(57\) 0 0
\(58\) −556.720 3124.15i −0.165493 0.928700i
\(59\) 4037.49 2331.05i 1.15987 0.669648i 0.208593 0.978002i \(-0.433111\pi\)
0.951272 + 0.308354i \(0.0997781\pi\)
\(60\) 0 0
\(61\) 2799.84 4849.46i 0.752442 1.30327i −0.194193 0.980963i \(-0.562209\pi\)
0.946636 0.322305i \(-0.104458\pi\)
\(62\) −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 \(-0.377724\pi\)
0.990292 + 0.139004i \(0.0443902\pi\)
\(68\) −1371.92 + 7949.19i −0.296696 + 1.71911i
\(69\) 0 0
\(70\) −1890.76 2245.03i −0.385869 0.458170i
\(71\) 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 \(0.558666\pi\)
\(74\) 642.322 540.962i 0.117298 0.0987878i
\(75\) 0 0
\(76\) −3017.86 520.842i −0.522483 0.0901735i
\(77\) −1391.50 2410.15i −0.234694 0.406501i
\(78\) 0 0
\(79\) −1523.90 879.826i −0.244176 0.140975i 0.372918 0.927864i \(-0.378357\pi\)
−0.617095 + 0.786889i \(0.711690\pi\)
\(80\) 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 \(-0.403846\pi\)
−0.678060 + 0.735007i \(0.737179\pi\)
\(84\) 0 0
\(85\) 7211.95 + 12491.5i 0.998193 + 1.72892i
\(86\) 13129.7 2339.71i 1.77525 0.316348i
\(87\) 0 0
\(88\) 37.8113 + 6944.19i 0.00488266 + 0.896719i
\(89\) 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
\(92\) −5309.06 14423.4i −0.627252 1.70409i
\(93\) 0 0
\(94\) 4443.42 791.814i 0.502877 0.0896122i
\(95\) −4742.31 + 2737.97i −0.525463 + 0.303376i
\(96\) 0 0
\(97\) 1100.89 1906.79i 0.117004 0.202656i −0.801575 0.597894i \(-0.796004\pi\)
0.918579 + 0.395238i \(0.129338\pi\)
\(98\) −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 −0.883400 0.468620i \(-0.844751\pi\)
0.847537 + 0.530737i \(0.178085\pi\)
\(102\) 0 0
\(103\) −8533.78 + 4926.98i −0.804391 + 0.464415i −0.845004 0.534760i \(-0.820402\pi\)
0.0406134 + 0.999175i \(0.487069\pi\)
\(104\) 2803.64 4917.69i 0.259212 0.454668i
\(105\) 0 0
\(106\) −3483.60 + 2933.88i −0.310039 + 0.261114i
\(107\) 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 \(0.760062\pi\)
\(110\) 7998.70 + 9497.42i 0.661050 + 0.784911i
\(111\) 0 0
\(112\) −4256.99 4999.12i −0.339364 0.398527i
\(113\) 8573.94 + 14850.5i 0.671465 + 1.16301i 0.977489 + 0.210988i \(0.0676680\pi\)
−0.306024 + 0.952024i \(0.598999\pi\)
\(114\) 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
\(122\) −3929.52 22051.3i −0.264010 1.48155i
\(123\) 0 0
\(124\) 1821.56 + 4948.74i 0.118468 + 0.321848i
\(125\) −12345.2 −0.790094
\(126\) 0 0
\(127\) 9591.51i 0.594675i −0.954772 0.297337i \(-0.903901\pi\)
0.954772 0.297337i \(-0.0960986\pi\)
\(128\) 3049.81 + 16097.6i 0.186146 + 0.982522i
\(129\) 0 0
\(130\) −1775.73 9964.88i −0.105073 0.589638i
\(131\) −3933.27 + 2270.88i −0.229198 + 0.132328i −0.610202 0.792246i \(-0.708912\pi\)
0.381004 + 0.924573i \(0.375578\pi\)
\(132\) 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 −0.923900 0.382635i \(-0.875017\pi\)
0.793321 + 0.608803i \(0.208350\pi\)
\(138\) 0 0
\(139\) 7491.80 4325.39i 0.387754 0.223870i −0.293432 0.955980i \(-0.594798\pi\)
0.681187 + 0.732110i \(0.261464\pi\)
\(140\) −11569.6 1996.75i −0.590285 0.101875i
\(141\) 0 0
\(142\) 11423.6 + 13564.1i 0.566535 + 0.672687i
\(143\) 9597.15i 0.469321i
\(144\) 0 0
\(145\) −22696.9 −1.07952
\(146\) −5975.85 + 5032.84i −0.280346 + 0.236106i
\(147\) 0 0
\(148\) 571.288 3310.15i 0.0260814 0.151121i
\(149\) −6346.46 10992.4i −0.285863 0.495130i 0.686955 0.726700i \(-0.258947\pi\)
−0.972818 + 0.231570i \(0.925614\pi\)
\(150\) 0 0
\(151\) −11055.3 6382.78i −0.484860 0.279934i 0.237579 0.971368i \(-0.423646\pi\)
−0.722440 + 0.691434i \(0.756979\pi\)
\(152\) −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 0.903534 + 0.428516i \(0.140963\pi\)
−0.0806612 + 0.996742i \(0.525703\pi\)
\(158\) −6929.45 + 1234.82i −0.277578 + 0.0494641i
\(159\) 0 0
\(160\) 22611.9 + 18626.6i 0.883277 + 0.727601i
\(161\) 24637.9 0.950499
\(162\) 0 0
\(163\) 6872.98i 0.258684i 0.991600 + 0.129342i \(0.0412865\pi\)
−0.991600 + 0.129342i \(0.958713\pi\)
\(164\) 15862.0 5838.58i 0.589752 0.217080i
\(165\) 0 0
\(166\) −11921.1 + 2124.32i −0.432612 + 0.0770910i
\(167\) −30405.5 + 17554.6i −1.09023 + 0.629447i −0.933639 0.358216i \(-0.883385\pi\)
−0.156595 + 0.987663i \(0.550052\pi\)
\(168\) 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 −0.840028 0.542543i \(-0.817462\pi\)
0.889870 + 0.456214i \(0.150795\pi\)
\(174\) 0 0
\(175\) −4297.84 + 2481.36i −0.140338 + 0.0810240i
\(176\) 18008.8 + 21148.4i 0.581380 + 0.682734i
\(177\) 0 0
\(178\) 1711.29 1441.25i 0.0540113 0.0454881i
\(179\) 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 \(0.361593\pi\)
\(182\) 5845.53 + 6940.81i 0.176474 + 0.209540i
\(183\) 0 0
\(184\) −53408.0 30448.6i −1.57750 0.899356i
\(185\) −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 \(-0.250277\pi\)
−0.259659 + 0.965700i \(0.583610\pi\)
\(192\) 0 0
\(193\) −4727.11 8187.59i −0.126906 0.219807i 0.795571 0.605861i \(-0.207171\pi\)
−0.922476 + 0.386054i \(0.873838\pi\)
\(194\) −1545.08 8670.52i −0.0410532 0.230378i
\(195\) 0 0
\(196\) −26173.5 + 9634.13i −0.681319 + 0.250784i
\(197\) 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 \(0.896670\pi\)
\(200\) 12383.1 67.4262i 0.309577 0.00168566i
\(201\) 0 0
\(202\) 513.451 + 2881.34i 0.0125834 + 0.0706141i
\(203\) 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 \(-0.588809\pi\)
0.694839 + 0.719165i \(0.255476\pi\)
\(212\) −3098.35 + 17952.4i −0.0689380 + 0.399440i
\(213\) 0 0
\(214\) 2073.33 + 2461.81i 0.0452731 + 0.0537559i
\(215\) 95387.3i 2.06354i
\(216\) 0 0
\(217\) −8453.38 −0.179519
\(218\) −53005.7 + 44641.3i −1.11535 + 0.939342i
\(219\) 0 0
\(220\) 48944.2 + 8447.10i 1.01124 + 0.174527i
\(221\) −22296.7 38619.0i −0.456516 0.790709i
\(222\) 0 0
\(223\) 16709.5 + 9647.22i 0.336011 + 0.193996i 0.658507 0.752575i \(-0.271188\pi\)
−0.322496 + 0.946571i \(0.604522\pi\)
\(224\) −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 \(-0.116772\pi\)
0.156107 + 0.987740i \(0.450105\pi\)
\(228\) 0 0
\(229\) −19575.4 33905.7i −0.373285 0.646549i 0.616784 0.787133i \(-0.288435\pi\)
−0.990069 + 0.140584i \(0.955102\pi\)
\(230\) −108222. + 19285.1i −2.04579 + 0.364558i
\(231\) 0 0
\(232\) −50773.1 + 276.461i −0.943317 + 0.00513639i
\(233\) 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
\(236\) −25766.7 70001.9i −0.462632 1.25686i
\(237\) 0 0
\(238\) −50922.8 + 9074.40i −0.898998 + 0.160201i
\(239\) 65999.7 38104.9i 1.15544 0.667091i 0.205230 0.978714i \(-0.434206\pi\)
0.950206 + 0.311623i \(0.100872\pi\)
\(240\) 0 0
\(241\) −8157.12 + 14128.5i −0.140444 + 0.243256i −0.927664 0.373416i \(-0.878186\pi\)
0.787220 + 0.616672i \(0.211520\pi\)
\(242\) −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
\(248\) 18324.5 + 10447.1i 0.297941 + 0.169860i
\(249\) 0 0
\(250\) −37770.3 + 31810.0i −0.604324 + 0.508960i
\(251\) 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
\(254\) −24714.5 29345.3i −0.383076 0.454853i
\(255\) 0 0
\(256\) 50809.8 + 41392.4i 0.775297 + 0.631597i
\(257\) −28773.1 49836.4i −0.435632 0.754537i 0.561715 0.827331i \(-0.310142\pi\)
−0.997347 + 0.0727940i \(0.976808\pi\)
\(258\) 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 \(-0.525521\pi\)
−0.903288 + 0.429034i \(0.858854\pi\)
\(264\) 0 0
\(265\) 16287.5 + 28210.7i 0.231933 + 0.401719i
\(266\) −3445.04 19332.6i −0.0486890 0.273229i
\(267\) 0 0
\(268\) −39106.4 106242.i −0.544476 1.47921i
\(269\) 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 \(0.736688\pi\)
\(272\) 121601. + 43261.9i 1.64361 + 0.584747i
\(273\) 0 0
\(274\) 3439.68 + 19302.5i 0.0458160 + 0.257106i
\(275\) 18181.7 10497.2i 0.240419 0.138806i
\(276\) 0 0
\(277\) 21971.1 38055.1i 0.286347 0.495968i −0.686588 0.727047i \(-0.740892\pi\)
0.972935 + 0.231079i \(0.0742255\pi\)
\(278\) 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 −0.658798 0.752320i \(-0.728935\pi\)
0.980927 + 0.194375i \(0.0622680\pi\)
\(282\) 0 0
\(283\) 22858.8 13197.5i 0.285418 0.164786i −0.350456 0.936579i \(-0.613973\pi\)
0.635873 + 0.771793i \(0.280640\pi\)
\(284\) 69901.3 + 12064.0i 0.866659 + 0.149574i
\(285\) 0 0
\(286\) −24729.0 29362.5i −0.302326 0.358973i
\(287\) 27095.2i 0.328950i
\(288\) 0 0
\(289\) 170665. 2.04338
\(290\) −69441.2 + 58483.2i −0.825699 + 0.695401i
\(291\) 0 0
\(292\) −5314.98 + 30796.0i −0.0623356 + 0.361184i
\(293\) 65395.3 + 113268.i 0.761748 + 1.31939i 0.941949 + 0.335757i \(0.108992\pi\)
−0.180201 + 0.983630i \(0.557675\pi\)
\(294\) 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
\(302\) −50270.3 + 8958.12i −0.551186 + 0.0982207i
\(303\) 0 0
\(304\) −16424.1 + 46165.0i −0.177720 + 0.499535i
\(305\) −160202. −1.72214
\(306\) 0 0
\(307\) 54227.3i 0.575362i −0.957726 0.287681i \(-0.907116\pi\)
0.957726 0.287681i \(-0.0928843\pi\)
\(308\) −41787.0 + 15381.2i −0.440494 + 0.162140i
\(309\) 0 0
\(310\) 37131.6 6616.81i 0.386385 0.0688534i
\(311\) −117745. + 67980.1i −1.21737 + 0.702847i −0.964354 0.264616i \(-0.914755\pi\)
−0.253013 + 0.967463i \(0.581422\pi\)
\(312\) 0 0
\(313\) −82194.2 + 142364.i −0.838981 + 1.45316i 0.0517658 + 0.998659i \(0.483515\pi\)
−0.890747 + 0.454499i \(0.849818\pi\)
\(314\) 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 −0.392637 0.919694i \(-0.628437\pi\)
0.992796 0.119814i \(-0.0382297\pi\)
\(318\) 0 0
\(319\) −74548.4 + 43040.6i −0.732584 + 0.422957i
\(320\) 117176. 1276.10i 1.14430 0.0124619i
\(321\) 0 0
\(322\) 75379.8 63484.6i 0.727015 0.612290i
\(323\) 96500.4i 0.924962i
\(324\) 0 0
\(325\) −17113.9 −0.162025
\(326\) 17709.6 + 21027.9i 0.166638 + 0.197861i
\(327\) 0 0
\(328\) 33485.5 58734.8i 0.311250 0.545944i
\(329\) 14470.4 + 25063.5i 0.133687 + 0.231553i
\(330\) 0 0
\(331\) 100184. + 57841.2i 0.914412 + 0.527936i 0.881848 0.471534i \(-0.156299\pi\)
0.0325639 + 0.999470i \(0.489633\pi\)
\(332\) −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 −0.900746 0.434347i \(-0.856979\pi\)
0.0742175 0.997242i \(-0.476354\pi\)
\(338\) −14552.5 81664.4i −0.127381 0.714825i
\(339\) 0 0
\(340\) 216576. 79718.9i 1.87350 0.689610i
\(341\) 35761.3 0.307542
\(342\) 0 0
\(343\) 106292.i 0.903465i
\(344\) −1161.87 213382.i −0.00981841 1.80319i
\(345\) 0 0
\(346\) −2093.61 11748.7i −0.0174881 0.0981381i
\(347\) 117124. 67621.8i 0.972721 0.561601i 0.0726566 0.997357i \(-0.476852\pi\)
0.900065 + 0.435756i \(0.143519\pi\)
\(348\) 0 0
\(349\) −1651.44 + 2860.38i −0.0135585 + 0.0234841i −0.872725 0.488212i \(-0.837649\pi\)
0.859167 + 0.511696i \(0.170983\pi\)
\(350\) −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 −0.767466 0.641090i \(-0.778483\pi\)
0.938933 + 0.344100i \(0.111816\pi\)
\(354\) 0 0
\(355\) 109844. 63418.4i 0.871603 0.503220i
\(356\) 1522.04 8819.00i 0.0120095 0.0695856i
\(357\) 0 0
\(358\) 116465. + 138287.i 0.908721 + 1.07899i
\(359\) 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
\(362\) 84445.1 71119.4i 0.644402 0.542714i
\(363\) 0 0
\(364\) 35768.9 + 6173.23i 0.269962 + 0.0465918i
\(365\) 27939.9 + 48393.3i 0.209719 + 0.363245i
\(366\) 0 0
\(367\) 6867.31 + 3964.84i 0.0509864 + 0.0294370i 0.525277 0.850932i \(-0.323962\pi\)
−0.474290 + 0.880369i \(0.657295\pi\)
\(368\) −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 −0.844001 0.536342i \(-0.819806\pi\)
−0.0424851 0.999097i \(-0.513527\pi\)
\(374\) 215425. 38388.5i 1.54011 0.274447i
\(375\) 0 0
\(376\) −393.206 72213.7i −0.00278128 0.510792i
\(377\) 70170.4 0.493709
\(378\) 0 0
\(379\) 147423.i 1.02633i −0.858291 0.513163i \(-0.828474\pi\)
0.858291 0.513163i \(-0.171526\pi\)
\(380\) 30264.8 + 82222.0i 0.209590 + 0.569404i
\(381\) 0 0
\(382\) 74123.0 13208.6i 0.507956 0.0905172i
\(383\) −105968. + 61180.9i −0.722402 + 0.417079i −0.815636 0.578565i \(-0.803613\pi\)
0.0932341 + 0.995644i \(0.470280\pi\)
\(384\) 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 0.385682 + 0.922632i \(0.373966\pi\)
−0.991863 + 0.127306i \(0.959367\pi\)
\(390\) 0 0
\(391\) −419417. + 242150.i −2.74342 + 1.58391i
\(392\) −55253.8 + 96917.3i −0.359575 + 0.630709i
\(393\) 0 0
\(394\) 66238.3 55785.7i 0.426694 0.359361i
\(395\) 50342.3i 0.322656i
\(396\) 0 0
\(397\) 81466.1 0.516887 0.258444 0.966026i \(-0.416790\pi\)
0.258444 + 0.966026i \(0.416790\pi\)
\(398\) 65091.2 + 77287.4i 0.410919 + 0.487913i
\(399\) 0 0
\(400\) 37712.4 32113.9i 0.235702 0.200712i
\(401\) 100584. + 174217.i 0.625518 + 1.08343i 0.988440 + 0.151610i \(0.0484459\pi\)
−0.362922 + 0.931820i \(0.618221\pi\)
\(402\) 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 0.995976 0.0896241i \(-0.0285666\pi\)
−0.575605 + 0.817728i \(0.695233\pi\)
\(410\) −21208.6 119016.i −0.126166 0.708009i
\(411\) 0 0
\(412\) 54461.5 + 147958.i 0.320845 + 0.871656i
\(413\) 119576. 0.701044
\(414\) 0 0
\(415\) 86606.3i 0.502867i
\(416\) −69907.7 57586.6i −0.403960 0.332763i
\(417\) 0 0
\(418\) 14574.0 + 81784.8i 0.0834114 + 0.468080i
\(419\) −133102. + 76846.6i −0.758154 + 0.437720i −0.828633 0.559793i \(-0.810881\pi\)
0.0704785 + 0.997513i \(0.477547\pi\)
\(420\) 0 0
\(421\) −77206.0 + 133725.i −0.435599 + 0.754479i −0.997344 0.0728309i \(-0.976797\pi\)
0.561746 + 0.827310i \(0.310130\pi\)
\(422\) 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
\(428\) 12686.7 + 2189.56i 0.0692567 + 0.0119528i
\(429\) 0 0
\(430\) −245785. 291838.i −1.32929 1.57836i
\(431\) 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 \(0.545968\pi\)
\(434\) −25863.2 + 21781.9i −0.137310 + 0.115642i
\(435\) 0 0
\(436\) −47143.8 + 273160.i −0.248000 + 1.43696i
\(437\) −91930.9 159229.i −0.481392 0.833795i
\(438\) 0 0
\(439\) −14586.4 8421.44i −0.0756864 0.0436976i 0.461679 0.887047i \(-0.347247\pi\)
−0.537366 + 0.843349i \(0.680580\pi\)
\(440\) 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 \(-0.198095\pi\)
−0.0985761 + 0.995130i \(0.531429\pi\)
\(444\) 0 0
\(445\) −8001.09 13858.3i −0.0404045 0.0699826i
\(446\) 75980.8 13539.7i 0.381974 0.0680674i
\(447\) 0 0
\(448\) −90404.5 + 53516.1i −0.450437 + 0.266642i
\(449\) −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
\(452\) 257477. 94774.0i 1.26027 0.463887i
\(453\) 0 0
\(454\) 255298. 45493.9i 1.23861 0.220720i
\(455\) 56207.7 32451.5i 0.271502 0.156752i
\(456\) 0 0
\(457\) 9423.93 16322.7i 0.0451232 0.0781556i −0.842582 0.538569i \(-0.818965\pi\)
0.887705 + 0.460413i \(0.152299\pi\)
\(458\) −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 −0.926754 0.375669i \(-0.877413\pi\)
0.788716 + 0.614758i \(0.210746\pi\)
\(462\) 0 0
\(463\) 41167.7 23768.2i 0.192041 0.110875i −0.400897 0.916123i \(-0.631301\pi\)
0.592938 + 0.805248i \(0.297968\pi\)
\(464\) −154628. + 131673.i −0.718212 + 0.611591i
\(465\) 0 0
\(466\) 7059.89 5945.82i 0.0325107 0.0273804i
\(467\) 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
\(470\) −83179.7 98765.1i −0.376549 0.447103i
\(471\) 0 0
\(472\) −259208. 147778.i −1.16349 0.663323i
\(473\) −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 \(-0.371737\pi\)
−0.600598 + 0.799551i \(0.705071\pi\)
\(480\) 0 0
\(481\) 9284.65 + 16081.5i 0.0401306 + 0.0695082i
\(482\) 11448.4 + 64244.9i 0.0492776 + 0.276531i
\(483\) 0 0
\(484\) −43059.7 + 15849.7i −0.183815 + 0.0676598i
\(485\) −62991.1 −0.267791
\(486\) 0 0
\(487\) 2975.59i 0.0125463i 0.999980 + 0.00627313i \(0.00199681\pi\)
−0.999980 + 0.00627313i \(0.998003\pi\)
\(488\) −358374. + 1951.36i −1.50486 + 0.00819402i
\(489\) 0 0
\(490\) 34995.9 + 196387.i 0.145755 + 0.817937i
\(491\) 234443. 135356.i 0.972467 0.561454i 0.0724794 0.997370i \(-0.476909\pi\)
0.899987 + 0.435916i \(0.143576\pi\)
\(492\) 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 \(-0.490805\pi\)
0.880105 + 0.474778i \(0.157472\pi\)
\(500\) −33593.2 + 194646.i −0.134373 + 0.778583i
\(501\) 0 0
\(502\) −87179.4 103514.i −0.345944 0.410764i
\(503\) 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
\(506\) −318888. + 268567.i −1.24548 + 1.04894i
\(507\) 0 0
\(508\) −151228. 26100.0i −0.586011 0.101138i
\(509\) −106839. 185051.i −0.412378 0.714259i 0.582772 0.812636i \(-0.301968\pi\)
−0.995149 + 0.0983769i \(0.968635\pi\)
\(510\) 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
\(518\) 21205.0 3778.71i 0.0790275 0.0140826i
\(519\) 0 0
\(520\) −161947. + 881.808i −0.598918 + 0.00326113i
\(521\) −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 \(0.860857\pi\)
\(524\) 25101.6 + 68194.9i 0.0914196 + 0.248364i
\(525\) 0 0
\(526\) −309295. + 55116.1i −1.11790 + 0.199208i
\(527\) 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
\(536\) −393402. 224284.i −1.36933 0.780671i
\(537\) 0 0
\(538\) 16450.8 13854.8i 0.0568360 0.0478671i
\(539\) 189139.i 0.651035i
\(540\) 0 0
\(541\) −3552.06 −0.0121363 −0.00606815 0.999982i \(-0.501932\pi\)
−0.00606815 + 0.999982i \(0.501932\pi\)
\(542\) 278575. + 330772.i 0.948296 + 1.12598i
\(543\) 0 0
\(544\) 483512. 180970.i 1.63384 0.611516i
\(545\) 247826. + 429248.i 0.834362 + 1.44516i
\(546\) 0 0
\(547\) 444293. + 256513.i 1.48489 + 0.857302i 0.999852 0.0171904i \(-0.00547213\pi\)
0.485039 + 0.874493i \(0.338805\pi\)
\(548\) 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
\(554\) −30836.1 173043.i −0.100471 0.563813i
\(555\) 0 0
\(556\) −47811.7 129893.i −0.154662 0.420180i
\(557\) 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
\(560\) −62965.2 + 176983.i −0.200782 + 0.564359i
\(561\) 0 0
\(562\) −35698.5 200330.i −0.113026 0.634267i
\(563\) −48439.2 + 27966.4i −0.152820 + 0.0882307i −0.574460 0.818533i \(-0.694788\pi\)
0.421640 + 0.906763i \(0.361455\pi\)
\(564\) 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 −0.326111 0.945331i \(-0.605738\pi\)
0.981737 0.190245i \(-0.0609282\pi\)
\(570\) 0 0
\(571\) 25297.4 14605.5i 0.0775897 0.0447964i −0.460703 0.887554i \(-0.652403\pi\)
0.538293 + 0.842758i \(0.319069\pi\)
\(572\) −151317. 26115.3i −0.462484 0.0798185i
\(573\) 0 0
\(574\) 69816.5 + 82898.1i 0.211902 + 0.251606i
\(575\) 185863.i 0.562158i
\(576\) 0 0
\(577\) −494524. −1.48537 −0.742687 0.669639i \(-0.766449\pi\)
−0.742687 + 0.669639i \(0.766449\pi\)
\(578\) 522152. 439755.i 1.56294 1.31630i
\(579\) 0 0
\(580\) −61761.7 + 357860.i −0.183596 + 1.06379i
\(581\) −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 \(-0.219901\pi\)
−0.166461 + 0.986048i \(0.553234\pi\)
\(588\) 0 0
\(589\) 31541.9 + 54632.2i 0.0909197 + 0.157477i
\(590\) −525241. + 93597.5i −1.50888 + 0.268881i
\(591\) 0 0
\(592\) −50636.3 18014.9i −0.144484 0.0514029i
\(593\) 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
\(596\) −190586. + 70152.0i −0.536534 + 0.197491i
\(597\) 0 0
\(598\) 334584. 59622.5i 0.935626 0.166728i
\(599\) −8669.92 + 5005.58i −0.0241636 + 0.0139509i −0.512033 0.858966i \(-0.671108\pi\)
0.487870 + 0.872917i \(0.337774\pi\)
\(600\) 0 0
\(601\) −196449. + 340259.i −0.543876 + 0.942021i 0.454800 + 0.890593i \(0.349711\pi\)
−0.998677 + 0.0514280i \(0.983623\pi\)
\(602\) 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 \(-0.466471\pi\)
0.913796 + 0.406174i \(0.133137\pi\)
\(608\) 68704.1 + 183562.i 0.185855 + 0.496566i
\(609\) 0 0
\(610\) −490140. + 412795.i −1.31723 + 1.10937i
\(611\) 99802.2i 0.267336i
\(612\) 0 0
\(613\) 301951. 0.803555 0.401778 0.915737i \(-0.368393\pi\)
0.401778 + 0.915737i \(0.368393\pi\)
\(614\) −139728. 165909.i −0.370635 0.440081i
\(615\) 0 0
\(616\) −88214.7 + 154732.i −0.232477 + 0.407773i
\(617\) 98373.3 + 170388.i 0.258409 + 0.447577i 0.965816 0.259229i \(-0.0834686\pi\)
−0.707407 + 0.706806i \(0.750135\pi\)
\(618\) 0 0
\(619\) −536199. 309575.i −1.39941 0.807949i −0.405078 0.914282i \(-0.632756\pi\)
−0.994331 + 0.106333i \(0.966089\pi\)
\(620\) 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
\(626\) 115358. + 647355.i 0.294374 + 1.65194i
\(627\) 0 0
\(628\) 609103. 224203.i 1.54444 0.568488i
\(629\) −105847. −0.267532
\(630\) 0 0
\(631\) 308766.i 0.775479i −0.921769 0.387740i \(-0.873256\pi\)
0.921769 0.387740i \(-0.126744\pi\)
\(632\) 613.198 + 112616.i 0.00153521 + 0.281946i
\(633\) 0 0
\(634\) −84643.3 474993.i −0.210578 1.18170i
\(635\) −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 −0.995602 0.0936860i \(-0.970135\pi\)
0.578935 + 0.815373i \(0.303468\pi\)
\(642\) 0 0
\(643\) −478867. + 276474.i −1.15823 + 0.668702i −0.950878 0.309566i \(-0.899816\pi\)
−0.207347 + 0.978267i \(0.566483\pi\)
\(644\) 67043.5 388463.i 0.161654 0.936652i
\(645\) 0 0
\(646\) 248653. + 295244.i 0.595839 + 0.707482i
\(647\) 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
\(650\) −52360.1 + 44097.6i −0.123929 + 0.104373i
\(651\) 0 0
\(652\) 108366. + 18702.4i 0.254915 + 0.0439950i
\(653\) −286795. 496744.i −0.672583 1.16495i −0.977169 0.212463i \(-0.931852\pi\)
0.304586 0.952485i \(-0.401482\pi\)
\(654\) 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 \(-0.203073\pi\)
−0.114125 + 0.993466i \(0.536406\pi\)
\(660\) 0 0
\(661\) 187583. + 324904.i 0.429330 + 0.743622i 0.996814 0.0797628i \(-0.0254163\pi\)
−0.567484 + 0.823385i \(0.692083\pi\)
\(662\) 455553. 81179.1i 1.03950 0.185237i
\(663\) 0 0
\(664\) 1054.91 + 193739.i 0.00239266 + 0.439421i
\(665\) −140451. −0.317600
\(666\) 0 0
\(667\) 762077.i 1.71296i
\(668\) 194044. + 527170.i 0.434858 + 1.18140i
\(669\) 0 0
\(670\) −797164. + 142054.i −1.77582 + 0.316449i
\(671\) −526189. + 303795.i −1.16868 + 0.674739i
\(672\) 0 0
\(673\) 286866. 496866.i 0.633358 1.09701i −0.353503 0.935433i \(-0.615010\pi\)
0.986861 0.161574i \(-0.0516571\pi\)
\(674\) −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 −0.880676 0.473719i \(-0.842911\pi\)
0.850590 + 0.525829i \(0.176245\pi\)
\(678\) 0 0
\(679\) 48906.7 28236.3i 0.106079 0.0612447i
\(680\) 457205. 801955.i 0.988765 1.73433i
\(681\) 0 0
\(682\) 109412. 92146.5i 0.235232 0.198112i
\(683\) 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
\(686\) −273883. 325200.i −0.581992 0.691040i
\(687\) 0 0
\(688\) −553378. 649850.i −1.16908 1.37289i
\(689\) −50354.8 87217.2i −0.106073 0.183723i
\(690\) 0 0
\(691\) −289343. 167052.i −0.605978 0.349862i 0.165411 0.986225i \(-0.447105\pi\)
−0.771390 + 0.636363i \(0.780438\pi\)
\(692\) −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
\(698\) 2317.77 + 13006.6i 0.00475729 + 0.0266965i
\(699\) 0 0
\(700\) 27428.3 + 74515.9i 0.0559761 + 0.152073i
\(701\) −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
\(704\) 382449. 226396.i 0.771664 0.456796i
\(705\) 0 0
\(706\) −29987.3 168280.i −0.0601629 0.337616i
\(707\) −16252.4 + 9383.33i −0.0325146 + 0.0187723i
\(708\) 0 0
\(709\) −362484. + 627841.i −0.721102 + 1.24899i 0.239456 + 0.970907i \(0.423031\pi\)
−0.960558 + 0.278079i \(0.910302\pi\)
\(710\) 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
\(716\) 712652. + 122994.i 1.39012 + 0.239916i
\(717\) 0 0
\(718\) 453027. + 537911.i 0.878770 + 1.04343i
\(719\) 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
\(722\) 286630. 241399.i 0.549855 0.463086i
\(723\) 0 0
\(724\) 75106.3 435181.i 0.143284 0.830218i
\(725\) 76751.2 + 132937.i 0.146019 + 0.252912i
\(726\) 0 0
\(727\) −375814. 216977.i −0.711057 0.410529i 0.100395 0.994948i \(-0.467989\pi\)
−0.811452 + 0.584418i \(0.801323\pi\)
\(728\) 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 0.958456 + 0.285241i \(0.0920735\pi\)
−0.232202 + 0.972667i \(0.574593\pi\)
\(734\) 31226.8 5564.59i 0.0579610 0.0103286i
\(735\) 0 0
\(736\) −625411. + 759223.i −1.15454 + 1.40157i
\(737\) −767746. −1.41346
\(738\) 0 0
\(739\) 215142.i 0.393947i 0.980409 + 0.196973i \(0.0631112\pi\)
−0.980409 + 0.196973i \(0.936889\pi\)
\(740\) −90185.5 + 33196.1i −0.164692 + 0.0606210i
\(741\) 0 0
\(742\) −115004. + 20493.6i −0.208884 + 0.0372230i
\(743\) 250360. 144546.i 0.453511 0.261835i −0.255801 0.966730i \(-0.582339\pi\)
0.709312 + 0.704895i \(0.249006\pi\)
\(744\) 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 \(-0.874356\pi\)
−0.128521 + 0.991707i \(0.541023\pi\)
\(752\) −187277. 219925.i −0.331168 0.388901i
\(753\) 0 0
\(754\) 214687. 180809.i 0.377627 0.318036i
\(755\) 365213.i 0.640697i
\(756\) 0 0
\(757\) −646906. −1.12888 −0.564442 0.825472i \(-0.690909\pi\)
−0.564442 + 0.825472i \(0.690909\pi\)
\(758\) −379865. 451040.i −0.661136 0.785013i
\(759\) 0 0
\(760\) 304457. + 173575.i 0.527108 + 0.300511i
\(761\) 383411. + 664087.i 0.662057 + 1.14672i 0.980074 + 0.198631i \(0.0636495\pi\)
−0.318018 + 0.948085i \(0.603017\pi\)
\(762\) 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 0.999936 0.0113137i \(-0.00360135\pi\)
−0.509766 + 0.860313i \(0.670268\pi\)
\(770\) 55872.2 + 313538.i 0.0942355 + 0.528822i
\(771\) 0 0
\(772\) −141956. + 52252.2i −0.238188 + 0.0876738i
\(773\) 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
\(776\) −140912. + 767.268i −0.234004 + 0.00127416i