Properties

Label 108.5.f.a.91.22
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 91.22
Character \(\chi\) \(=\) 108.91
Dual form 108.5.f.a.19.22

$q$-expansion

\(f(q)\) \(=\) \(q+(3.96529 + 0.525827i) q^{2} +(15.4470 + 4.17011i) q^{4} +(-11.0746 + 19.1817i) q^{5} +(-82.7885 + 47.7980i) q^{7} +(59.0591 + 24.6582i) q^{8} +O(q^{10})\) \(q+(3.96529 + 0.525827i) q^{2} +(15.4470 + 4.17011i) q^{4} +(-11.0746 + 19.1817i) q^{5} +(-82.7885 + 47.7980i) q^{7} +(59.0591 + 24.6582i) q^{8} +(-54.0000 + 70.2376i) q^{10} +(-18.9394 + 10.9346i) q^{11} +(-63.1124 + 109.314i) q^{13} +(-353.414 + 146.000i) q^{14} +(221.220 + 128.832i) q^{16} +283.865 q^{17} -323.729i q^{19} +(-251.059 + 250.118i) q^{20} +(-80.8497 + 33.4002i) q^{22} +(198.433 + 114.565i) q^{23} +(67.2085 + 116.409i) q^{25} +(-307.739 + 400.274i) q^{26} +(-1478.16 + 393.098i) q^{28} +(604.822 + 1047.58i) q^{29} +(-718.565 - 414.863i) q^{31} +(809.459 + 627.178i) q^{32} +(1125.61 + 149.264i) q^{34} -2117.36i q^{35} -318.650 q^{37} +(170.226 - 1283.68i) q^{38} +(-1127.04 + 859.775i) q^{40} +(164.418 - 284.781i) q^{41} +(179.336 - 103.539i) q^{43} +(-338.155 + 89.9283i) q^{44} +(726.602 + 558.626i) q^{46} +(-1062.42 + 613.390i) q^{47} +(3368.79 - 5834.92i) q^{49} +(205.290 + 496.933i) q^{50} +(-1430.75 + 1425.39i) q^{52} +2834.27 q^{53} -484.385i q^{55} +(-6068.02 + 781.492i) q^{56} +(1847.44 + 4471.99i) q^{58} +(1278.13 + 737.929i) q^{59} +(936.180 + 1621.51i) q^{61} +(-2631.17 - 2022.89i) q^{62} +(2879.95 + 2912.58i) q^{64} +(-1397.88 - 2421.20i) q^{65} +(-214.663 - 123.936i) q^{67} +(4384.87 + 1183.75i) q^{68} +(1113.37 - 8395.96i) q^{70} -4308.28i q^{71} +3010.75 q^{73} +(-1263.54 - 167.555i) q^{74} +(1349.99 - 5000.65i) q^{76} +(1045.31 - 1810.52i) q^{77} +(-6228.39 + 3595.96i) q^{79} +(-4921.12 + 2816.63i) q^{80} +(801.712 - 1042.78i) q^{82} +(2877.35 - 1661.24i) q^{83} +(-3143.68 + 5445.01i) q^{85} +(765.561 - 316.264i) q^{86} +(-1388.17 + 178.780i) q^{88} +1549.85 q^{89} -12066.6i q^{91} +(2587.44 + 2597.18i) q^{92} +(-4535.35 + 1873.62i) q^{94} +(6209.67 + 3585.16i) q^{95} +(-2918.68 - 5055.31i) q^{97} +(16426.4 - 21365.7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.96529 + 0.525827i 0.991322 + 0.131457i
\(3\) 0 0
\(4\) 15.4470 + 4.17011i 0.965438 + 0.260632i
\(5\) −11.0746 + 19.1817i −0.442982 + 0.767268i −0.997909 0.0646314i \(-0.979413\pi\)
0.554927 + 0.831899i \(0.312746\pi\)
\(6\) 0 0
\(7\) −82.7885 + 47.7980i −1.68956 + 0.975469i −0.734711 + 0.678380i \(0.762682\pi\)
−0.954850 + 0.297089i \(0.903984\pi\)
\(8\) 59.0591 + 24.6582i 0.922798 + 0.385284i
\(9\) 0 0
\(10\) −54.0000 + 70.2376i −0.540000 + 0.702376i
\(11\) −18.9394 + 10.9346i −0.156524 + 0.0903689i −0.576216 0.817297i \(-0.695471\pi\)
0.419692 + 0.907666i \(0.362138\pi\)
\(12\) 0 0
\(13\) −63.1124 + 109.314i −0.373446 + 0.646827i −0.990093 0.140412i \(-0.955157\pi\)
0.616647 + 0.787240i \(0.288491\pi\)
\(14\) −353.414 + 146.000i −1.80313 + 0.744899i
\(15\) 0 0
\(16\) 221.220 + 128.832i 0.864142 + 0.503248i
\(17\) 283.865 0.982232 0.491116 0.871094i \(-0.336589\pi\)
0.491116 + 0.871094i \(0.336589\pi\)
\(18\) 0 0
\(19\) 323.729i 0.896756i −0.893844 0.448378i \(-0.852002\pi\)
0.893844 0.448378i \(-0.147998\pi\)
\(20\) −251.059 + 250.118i −0.627646 + 0.625294i
\(21\) 0 0
\(22\) −80.8497 + 33.4002i −0.167045 + 0.0690086i
\(23\) 198.433 + 114.565i 0.375109 + 0.216570i 0.675688 0.737187i \(-0.263847\pi\)
−0.300579 + 0.953757i \(0.597180\pi\)
\(24\) 0 0
\(25\) 67.2085 + 116.409i 0.107534 + 0.186254i
\(26\) −307.739 + 400.274i −0.455235 + 0.592122i
\(27\) 0 0
\(28\) −1478.16 + 393.098i −1.88541 + 0.501401i
\(29\) 604.822 + 1047.58i 0.719170 + 1.24564i 0.961329 + 0.275402i \(0.0888109\pi\)
−0.242160 + 0.970236i \(0.577856\pi\)
\(30\) 0 0
\(31\) −718.565 414.863i −0.747726 0.431700i 0.0771458 0.997020i \(-0.475419\pi\)
−0.824872 + 0.565320i \(0.808753\pi\)
\(32\) 809.459 + 627.178i 0.790487 + 0.612478i
\(33\) 0 0
\(34\) 1125.61 + 149.264i 0.973708 + 0.129121i
\(35\) 2117.36i 1.72846i
\(36\) 0 0
\(37\) −318.650 −0.232761 −0.116380 0.993205i \(-0.537129\pi\)
−0.116380 + 0.993205i \(0.537129\pi\)
\(38\) 170.226 1283.68i 0.117885 0.888974i
\(39\) 0 0
\(40\) −1127.04 + 859.775i −0.704399 + 0.537359i
\(41\) 164.418 284.781i 0.0978099 0.169412i −0.812968 0.582308i \(-0.802150\pi\)
0.910778 + 0.412897i \(0.135483\pi\)
\(42\) 0 0
\(43\) 179.336 103.539i 0.0969906 0.0559976i −0.450720 0.892665i \(-0.648833\pi\)
0.547711 + 0.836668i \(0.315499\pi\)
\(44\) −338.155 + 89.9283i −0.174667 + 0.0464506i
\(45\) 0 0
\(46\) 726.602 + 558.626i 0.343385 + 0.264001i
\(47\) −1062.42 + 613.390i −0.480952 + 0.277678i −0.720813 0.693129i \(-0.756231\pi\)
0.239861 + 0.970807i \(0.422898\pi\)
\(48\) 0 0
\(49\) 3368.79 5834.92i 1.40308 2.43020i
\(50\) 205.290 + 496.933i 0.0821161 + 0.198773i
\(51\) 0 0
\(52\) −1430.75 + 1425.39i −0.529123 + 0.527140i
\(53\) 2834.27 1.00900 0.504499 0.863412i \(-0.331677\pi\)
0.504499 + 0.863412i \(0.331677\pi\)
\(54\) 0 0
\(55\) 484.385i 0.160127i
\(56\) −6068.02 + 781.492i −1.93496 + 0.249200i
\(57\) 0 0
\(58\) 1847.44 + 4471.99i 0.549181 + 1.32937i
\(59\) 1278.13 + 737.929i 0.367173 + 0.211988i 0.672223 0.740349i \(-0.265340\pi\)
−0.305049 + 0.952337i \(0.598673\pi\)
\(60\) 0 0
\(61\) 936.180 + 1621.51i 0.251594 + 0.435773i 0.963965 0.266030i \(-0.0857120\pi\)
−0.712371 + 0.701803i \(0.752379\pi\)
\(62\) −2631.17 2022.89i −0.684487 0.526247i
\(63\) 0 0
\(64\) 2879.95 + 2912.58i 0.703113 + 0.711078i
\(65\) −1397.88 2421.20i −0.330860 0.573066i
\(66\) 0 0
\(67\) −214.663 123.936i −0.0478197 0.0276087i 0.475900 0.879500i \(-0.342123\pi\)
−0.523719 + 0.851891i \(0.675456\pi\)
\(68\) 4384.87 + 1183.75i 0.948284 + 0.256001i
\(69\) 0 0
\(70\) 1113.37 8395.96i 0.227218 1.71346i
\(71\) 4308.28i 0.854648i −0.904099 0.427324i \(-0.859456\pi\)
0.904099 0.427324i \(-0.140544\pi\)
\(72\) 0 0
\(73\) 3010.75 0.564974 0.282487 0.959271i \(-0.408841\pi\)
0.282487 + 0.959271i \(0.408841\pi\)
\(74\) −1263.54 167.555i −0.230741 0.0305980i
\(75\) 0 0
\(76\) 1349.99 5000.65i 0.233723 0.865763i
\(77\) 1045.31 1810.52i 0.176304 0.305368i
\(78\) 0 0
\(79\) −6228.39 + 3595.96i −0.997980 + 0.576184i −0.907650 0.419728i \(-0.862126\pi\)
−0.0903300 + 0.995912i \(0.528792\pi\)
\(80\) −4921.12 + 2816.63i −0.768926 + 0.440098i
\(81\) 0 0
\(82\) 801.712 1042.78i 0.119231 0.155084i
\(83\) 2877.35 1661.24i 0.417673 0.241144i −0.276408 0.961040i \(-0.589144\pi\)
0.694081 + 0.719897i \(0.255811\pi\)
\(84\) 0 0
\(85\) −3143.68 + 5445.01i −0.435111 + 0.753635i
\(86\) 765.561 316.264i 0.103510 0.0427615i
\(87\) 0 0
\(88\) −1388.17 + 178.780i −0.179257 + 0.0230863i
\(89\) 1549.85 0.195664 0.0978318 0.995203i \(-0.468809\pi\)
0.0978318 + 0.995203i \(0.468809\pi\)
\(90\) 0 0
\(91\) 12066.6i 1.45714i
\(92\) 2587.44 + 2597.18i 0.305700 + 0.306850i
\(93\) 0 0
\(94\) −4535.35 + 1873.62i −0.513281 + 0.212044i
\(95\) 6209.67 + 3585.16i 0.688052 + 0.397247i
\(96\) 0 0
\(97\) −2918.68 5055.31i −0.310201 0.537285i 0.668204 0.743978i \(-0.267063\pi\)
−0.978406 + 0.206693i \(0.933730\pi\)
\(98\) 16426.4 21365.7i 1.71037 2.22467i
\(99\) 0 0
\(100\) 552.734 + 2078.43i 0.0552734 + 0.207843i
\(101\) −2749.50 4762.27i −0.269532 0.466844i 0.699209 0.714918i \(-0.253536\pi\)
−0.968741 + 0.248074i \(0.920202\pi\)
\(102\) 0 0
\(103\) 15530.7 + 8966.63i 1.46391 + 0.845191i 0.999189 0.0402641i \(-0.0128199\pi\)
0.464725 + 0.885455i \(0.346153\pi\)
\(104\) −6422.83 + 4899.74i −0.593827 + 0.453008i
\(105\) 0 0
\(106\) 11238.7 + 1490.34i 1.00024 + 0.132640i
\(107\) 8715.17i 0.761217i 0.924736 + 0.380608i \(0.124285\pi\)
−0.924736 + 0.380608i \(0.875715\pi\)
\(108\) 0 0
\(109\) −12162.1 −1.02366 −0.511830 0.859087i \(-0.671032\pi\)
−0.511830 + 0.859087i \(0.671032\pi\)
\(110\) 254.703 1920.73i 0.0210498 0.158738i
\(111\) 0 0
\(112\) −24472.4 91.8909i −1.95092 0.00732549i
\(113\) −10236.7 + 17730.5i −0.801684 + 1.38856i 0.116823 + 0.993153i \(0.462729\pi\)
−0.918507 + 0.395404i \(0.870604\pi\)
\(114\) 0 0
\(115\) −4395.11 + 2537.52i −0.332334 + 0.191873i
\(116\) 4974.15 + 18704.2i 0.369661 + 1.39003i
\(117\) 0 0
\(118\) 4680.13 + 3598.18i 0.336120 + 0.258415i
\(119\) −23500.8 + 13568.2i −1.65954 + 0.958136i
\(120\) 0 0
\(121\) −7081.37 + 12265.3i −0.483667 + 0.837736i
\(122\) 2859.59 + 6922.03i 0.192125 + 0.465065i
\(123\) 0 0
\(124\) −9369.65 9404.89i −0.609368 0.611661i
\(125\) −16820.4 −1.07651
\(126\) 0 0
\(127\) 8130.42i 0.504087i 0.967716 + 0.252044i \(0.0811026\pi\)
−0.967716 + 0.252044i \(0.918897\pi\)
\(128\) 9888.32 + 13063.6i 0.603535 + 0.797336i
\(129\) 0 0
\(130\) −4269.87 10335.8i −0.252655 0.611586i
\(131\) −14095.1 8137.79i −0.821343 0.474203i 0.0295362 0.999564i \(-0.490597\pi\)
−0.850879 + 0.525361i \(0.823930\pi\)
\(132\) 0 0
\(133\) 15473.6 + 26801.0i 0.874758 + 1.51512i
\(134\) −786.030 604.315i −0.0437754 0.0336554i
\(135\) 0 0
\(136\) 16764.8 + 6999.59i 0.906402 + 0.378438i
\(137\) 12331.4 + 21358.7i 0.657011 + 1.13798i 0.981386 + 0.192047i \(0.0615126\pi\)
−0.324375 + 0.945929i \(0.605154\pi\)
\(138\) 0 0
\(139\) 17078.1 + 9860.04i 0.883913 + 0.510328i 0.871947 0.489601i \(-0.162857\pi\)
0.0119667 + 0.999928i \(0.496191\pi\)
\(140\) 8829.65 32707.0i 0.450492 1.66872i
\(141\) 0 0
\(142\) 2265.41 17083.6i 0.112349 0.847231i
\(143\) 2760.44i 0.134992i
\(144\) 0 0
\(145\) −26792.5 −1.27432
\(146\) 11938.5 + 1583.13i 0.560072 + 0.0742697i
\(147\) 0 0
\(148\) −4922.18 1328.80i −0.224716 0.0606649i
\(149\) 14942.7 25881.6i 0.673066 1.16578i −0.303965 0.952683i \(-0.598310\pi\)
0.977030 0.213101i \(-0.0683562\pi\)
\(150\) 0 0
\(151\) −5164.11 + 2981.50i −0.226486 + 0.130762i −0.608950 0.793209i \(-0.708409\pi\)
0.382464 + 0.923970i \(0.375076\pi\)
\(152\) 7982.56 19119.1i 0.345506 0.827525i
\(153\) 0 0
\(154\) 5096.97 6629.60i 0.214917 0.279541i
\(155\) 15915.6 9188.85i 0.662458 0.382471i
\(156\) 0 0
\(157\) 17493.5 30299.6i 0.709704 1.22924i −0.255262 0.966872i \(-0.582162\pi\)
0.964967 0.262372i \(-0.0845048\pi\)
\(158\) −26588.2 + 10984.0i −1.06506 + 0.439993i
\(159\) 0 0
\(160\) −20994.7 + 8581.08i −0.820107 + 0.335198i
\(161\) −21903.9 −0.845027
\(162\) 0 0
\(163\) 14509.8i 0.546118i −0.961997 0.273059i \(-0.911965\pi\)
0.961997 0.273059i \(-0.0880354\pi\)
\(164\) 3727.34 3713.37i 0.138584 0.138064i
\(165\) 0 0
\(166\) 12283.0 5074.30i 0.445749 0.184145i
\(167\) 38640.1 + 22308.9i 1.38550 + 0.799917i 0.992804 0.119753i \(-0.0382102\pi\)
0.392693 + 0.919670i \(0.371543\pi\)
\(168\) 0 0
\(169\) 6314.16 + 10936.5i 0.221076 + 0.382916i
\(170\) −15328.7 + 19938.0i −0.530406 + 0.689896i
\(171\) 0 0
\(172\) 3201.97 851.526i 0.108233 0.0287833i
\(173\) −26443.3 45801.1i −0.883534 1.53033i −0.847385 0.530979i \(-0.821824\pi\)
−0.0361488 0.999346i \(-0.511509\pi\)
\(174\) 0 0
\(175\) −11128.2 6424.86i −0.363369 0.209791i
\(176\) −5598.50 21.0217i −0.180737 0.000678644i
\(177\) 0 0
\(178\) 6145.61 + 814.954i 0.193966 + 0.0257213i
\(179\) 32840.8i 1.02496i 0.858698 + 0.512482i \(0.171274\pi\)
−0.858698 + 0.512482i \(0.828726\pi\)
\(180\) 0 0
\(181\) −22758.6 −0.694685 −0.347343 0.937738i \(-0.612916\pi\)
−0.347343 + 0.937738i \(0.612916\pi\)
\(182\) 6344.93 47847.4i 0.191551 1.44449i
\(183\) 0 0
\(184\) 8894.30 + 11659.1i 0.262710 + 0.344373i
\(185\) 3528.90 6112.24i 0.103109 0.178590i
\(186\) 0 0
\(187\) −5376.22 + 3103.96i −0.153742 + 0.0887632i
\(188\) −18969.2 + 5044.62i −0.536701 + 0.142729i
\(189\) 0 0
\(190\) 22738.0 + 17481.4i 0.629860 + 0.484249i
\(191\) 49799.3 28751.7i 1.36508 0.788127i 0.374782 0.927113i \(-0.377718\pi\)
0.990294 + 0.138986i \(0.0443843\pi\)
\(192\) 0 0
\(193\) 22470.8 38920.5i 0.603259 1.04488i −0.389065 0.921210i \(-0.627202\pi\)
0.992324 0.123665i \(-0.0394648\pi\)
\(194\) −8915.21 21580.5i −0.236880 0.573400i
\(195\) 0 0
\(196\) 76370.0 76083.8i 1.98797 1.98052i
\(197\) 44514.7 1.14702 0.573510 0.819198i \(-0.305581\pi\)
0.573510 + 0.819198i \(0.305581\pi\)
\(198\) 0 0
\(199\) 19066.9i 0.481474i −0.970590 0.240737i \(-0.922611\pi\)
0.970590 0.240737i \(-0.0773892\pi\)
\(200\) 1098.85 + 8532.22i 0.0274713 + 0.213305i
\(201\) 0 0
\(202\) −8398.42 20329.5i −0.205824 0.498224i
\(203\) −100145. 57818.5i −2.43016 1.40305i
\(204\) 0 0
\(205\) 3641.72 + 6307.65i 0.0866561 + 0.150093i
\(206\) 56868.6 + 43721.7i 1.34010 + 1.03030i
\(207\) 0 0
\(208\) −28044.8 + 16051.6i −0.648225 + 0.371014i
\(209\) 3539.86 + 6131.22i 0.0810389 + 0.140364i
\(210\) 0 0
\(211\) 825.251 + 476.459i 0.0185362 + 0.0107019i 0.509239 0.860625i \(-0.329927\pi\)
−0.490703 + 0.871327i \(0.663260\pi\)
\(212\) 43781.1 + 11819.2i 0.974125 + 0.262977i
\(213\) 0 0
\(214\) −4582.67 + 34558.1i −0.100067 + 0.754611i
\(215\) 4586.61i 0.0992237i
\(216\) 0 0
\(217\) 79318.5 1.68444
\(218\) −48226.2 6395.17i −1.01478 0.134567i
\(219\) 0 0
\(220\) 2019.94 7482.30i 0.0417343 0.154593i
\(221\) −17915.4 + 31030.4i −0.366810 + 0.635334i
\(222\) 0 0
\(223\) −37535.4 + 21671.1i −0.754800 + 0.435784i −0.827426 0.561575i \(-0.810195\pi\)
0.0726258 + 0.997359i \(0.476862\pi\)
\(224\) −96991.7 13232.6i −1.93303 0.263724i
\(225\) 0 0
\(226\) −49914.6 + 64923.7i −0.977262 + 1.27112i
\(227\) 5202.66 3003.76i 0.100966 0.0582925i −0.448667 0.893699i \(-0.648101\pi\)
0.549633 + 0.835406i \(0.314768\pi\)
\(228\) 0 0
\(229\) 2038.17 3530.22i 0.0388660 0.0673180i −0.845938 0.533281i \(-0.820959\pi\)
0.884804 + 0.465963i \(0.154292\pi\)
\(230\) −18762.2 + 7750.92i −0.354673 + 0.146520i
\(231\) 0 0
\(232\) 9888.77 + 76783.0i 0.183724 + 1.42656i
\(233\) 37427.6 0.689414 0.344707 0.938710i \(-0.387978\pi\)
0.344707 + 0.938710i \(0.387978\pi\)
\(234\) 0 0
\(235\) 27172.1i 0.492025i
\(236\) 16666.1 + 16728.7i 0.299232 + 0.300358i
\(237\) 0 0
\(238\) −100322. + 41444.4i −1.77109 + 0.731664i
\(239\) 22212.3 + 12824.3i 0.388865 + 0.224511i 0.681668 0.731662i \(-0.261255\pi\)
−0.292804 + 0.956173i \(0.594588\pi\)
\(240\) 0 0
\(241\) −38300.8 66339.0i −0.659438 1.14218i −0.980761 0.195211i \(-0.937461\pi\)
0.321323 0.946970i \(-0.395872\pi\)
\(242\) −34529.1 + 44911.8i −0.589596 + 0.766884i
\(243\) 0 0
\(244\) 7699.30 + 28951.5i 0.129322 + 0.486285i
\(245\) 74615.7 + 129238.i 1.24308 + 2.15307i
\(246\) 0 0
\(247\) 35388.1 + 20431.3i 0.580046 + 0.334890i
\(248\) −32208.0 42219.9i −0.523673 0.686458i
\(249\) 0 0
\(250\) −66697.8 8844.63i −1.06716 0.141514i
\(251\) 66642.6i 1.05780i −0.848683 0.528902i \(-0.822604\pi\)
0.848683 0.528902i \(-0.177396\pi\)
\(252\) 0 0
\(253\) −5010.92 −0.0782846
\(254\) −4275.20 + 32239.5i −0.0662657 + 0.499713i
\(255\) 0 0
\(256\) 32340.9 + 57000.3i 0.493482 + 0.869756i
\(257\) 29713.2 51464.8i 0.449866 0.779191i −0.548511 0.836143i \(-0.684805\pi\)
0.998377 + 0.0569526i \(0.0181384\pi\)
\(258\) 0 0
\(259\) 26380.5 15230.8i 0.393264 0.227051i
\(260\) −11496.4 43229.7i −0.170065 0.639492i
\(261\) 0 0
\(262\) −51611.9 39680.3i −0.751878 0.578059i
\(263\) −21772.1 + 12570.2i −0.314767 + 0.181731i −0.649058 0.760739i \(-0.724837\pi\)
0.334290 + 0.942470i \(0.391503\pi\)
\(264\) 0 0
\(265\) −31388.3 + 54366.2i −0.446968 + 0.774171i
\(266\) 47264.5 + 114410.i 0.667993 + 1.61697i
\(267\) 0 0
\(268\) −2799.07 2809.60i −0.0389712 0.0391179i
\(269\) −2553.46 −0.0352877 −0.0176439 0.999844i \(-0.505617\pi\)
−0.0176439 + 0.999844i \(0.505617\pi\)
\(270\) 0 0
\(271\) 4623.11i 0.0629499i 0.999505 + 0.0314750i \(0.0100204\pi\)
−0.999505 + 0.0314750i \(0.989980\pi\)
\(272\) 62796.7 + 36570.8i 0.848788 + 0.494307i
\(273\) 0 0
\(274\) 37666.7 + 91177.4i 0.501714 + 1.21447i
\(275\) −2545.77 1469.80i −0.0336631 0.0194354i
\(276\) 0 0
\(277\) 4927.19 + 8534.14i 0.0642154 + 0.111224i 0.896346 0.443356i \(-0.146212\pi\)
−0.832130 + 0.554580i \(0.812879\pi\)
\(278\) 62534.9 + 48078.0i 0.809157 + 0.622095i
\(279\) 0 0
\(280\) 52210.3 125050.i 0.665948 1.59502i
\(281\) −24208.6 41930.5i −0.306589 0.531028i 0.671025 0.741435i \(-0.265854\pi\)
−0.977614 + 0.210407i \(0.932521\pi\)
\(282\) 0 0
\(283\) −114515. 66115.1i −1.42984 0.825520i −0.432735 0.901521i \(-0.642451\pi\)
−0.997108 + 0.0760012i \(0.975785\pi\)
\(284\) 17966.0 66550.0i 0.222749 0.825110i
\(285\) 0 0
\(286\) 1451.52 10946.0i 0.0177456 0.133820i
\(287\) 31435.5i 0.381642i
\(288\) 0 0
\(289\) −2941.65 −0.0352205
\(290\) −106240. 14088.2i −1.26326 0.167518i
\(291\) 0 0
\(292\) 46507.1 + 12555.2i 0.545448 + 0.147250i
\(293\) −44759.6 + 77525.8i −0.521375 + 0.903049i 0.478315 + 0.878188i \(0.341248\pi\)
−0.999691 + 0.0248607i \(0.992086\pi\)
\(294\) 0 0
\(295\) −28309.5 + 16344.5i −0.325303 + 0.187814i
\(296\) −18819.1 7857.31i −0.214791 0.0896789i
\(297\) 0 0
\(298\) 72861.5 94770.6i 0.820475 1.06719i
\(299\) −25047.1 + 14461.0i −0.280166 + 0.161754i
\(300\) 0 0
\(301\) −9897.95 + 17143.8i −0.109248 + 0.189223i
\(302\) −22044.9 + 9107.08i −0.241710 + 0.0998540i
\(303\) 0 0
\(304\) 41706.5 71615.4i 0.451291 0.774925i
\(305\) −41471.1 −0.445806
\(306\) 0 0
\(307\) 62726.9i 0.665545i −0.943007 0.332772i \(-0.892016\pi\)
0.943007 0.332772i \(-0.107984\pi\)
\(308\) 23697.0 23608.2i 0.249799 0.248863i
\(309\) 0 0
\(310\) 67941.5 28067.6i 0.706988 0.292067i
\(311\) 106333. + 61391.4i 1.09938 + 0.634726i 0.936058 0.351847i \(-0.114446\pi\)
0.163321 + 0.986573i \(0.447779\pi\)
\(312\) 0 0
\(313\) 24294.6 + 42079.4i 0.247982 + 0.429518i 0.962966 0.269623i \(-0.0868992\pi\)
−0.714984 + 0.699141i \(0.753566\pi\)
\(314\) 85299.2 110948.i 0.865138 1.12528i
\(315\) 0 0
\(316\) −111206. + 29573.8i −1.11366 + 0.296164i
\(317\) −55066.7 95378.4i −0.547988 0.949143i −0.998412 0.0563282i \(-0.982061\pi\)
0.450425 0.892815i \(-0.351273\pi\)
\(318\) 0 0
\(319\) −22909.9 13227.0i −0.225134 0.129981i
\(320\) −87762.3 + 22986.8i −0.857054 + 0.224481i
\(321\) 0 0
\(322\) −86855.5 11517.7i −0.837694 0.111085i
\(323\) 91895.4i 0.880823i
\(324\) 0 0
\(325\) −16966.7 −0.160632
\(326\) 7629.65 57535.6i 0.0717909 0.541379i
\(327\) 0 0
\(328\) 16732.6 12764.7i 0.155530 0.118648i
\(329\) 58637.6 101563.i 0.541732 0.938308i
\(330\) 0 0
\(331\) 159800. 92260.3i 1.45854 0.842091i 0.459605 0.888124i \(-0.347991\pi\)
0.998940 + 0.0460325i \(0.0146578\pi\)
\(332\) 51374.0 13662.3i 0.466087 0.123950i
\(333\) 0 0
\(334\) 141489. + 108779.i 1.26832 + 0.975108i
\(335\) 4754.59 2745.06i 0.0423665 0.0244603i
\(336\) 0 0
\(337\) −32813.1 + 56833.9i −0.288926 + 0.500435i −0.973554 0.228458i \(-0.926632\pi\)
0.684628 + 0.728893i \(0.259965\pi\)
\(338\) 19286.8 + 46686.3i 0.168821 + 0.408655i
\(339\) 0 0
\(340\) −71266.7 + 70999.7i −0.616494 + 0.614184i
\(341\) 18145.5 0.156049
\(342\) 0 0
\(343\) 414560.i 3.52370i
\(344\) 13144.5 1692.86i 0.111078 0.0143055i
\(345\) 0 0
\(346\) −80771.7 195519.i −0.674695 1.63319i
\(347\) 90819.3 + 52434.6i 0.754257 + 0.435470i 0.827230 0.561864i \(-0.189915\pi\)
−0.0729731 + 0.997334i \(0.523249\pi\)
\(348\) 0 0
\(349\) −43672.0 75642.1i −0.358552 0.621030i 0.629167 0.777270i \(-0.283396\pi\)
−0.987719 + 0.156240i \(0.950063\pi\)
\(350\) −40748.1 31327.9i −0.332637 0.255738i
\(351\) 0 0
\(352\) −22188.6 3027.20i −0.179079 0.0244318i
\(353\) −24354.3 42182.9i −0.195446 0.338522i 0.751601 0.659618i \(-0.229282\pi\)
−0.947047 + 0.321096i \(0.895949\pi\)
\(354\) 0 0
\(355\) 82640.1 + 47712.3i 0.655744 + 0.378594i
\(356\) 23940.6 + 6463.06i 0.188901 + 0.0509962i
\(357\) 0 0
\(358\) −17268.6 + 130223.i −0.134738 + 1.01607i
\(359\) 109409.i 0.848911i 0.905449 + 0.424456i \(0.139535\pi\)
−0.905449 + 0.424456i \(0.860465\pi\)
\(360\) 0 0
\(361\) 25520.5 0.195828
\(362\) −90244.4 11967.1i −0.688657 0.0913211i
\(363\) 0 0
\(364\) 50318.9 186392.i 0.379777 1.40678i
\(365\) −33342.7 + 57751.3i −0.250274 + 0.433487i
\(366\) 0 0
\(367\) −1112.82 + 642.487i −0.00826215 + 0.00477015i −0.504125 0.863630i \(-0.668185\pi\)
0.495863 + 0.868401i \(0.334852\pi\)
\(368\) 29137.8 + 50908.6i 0.215160 + 0.375920i
\(369\) 0 0
\(370\) 17207.1 22381.2i 0.125691 0.163486i
\(371\) −234645. + 135473.i −1.70476 + 0.984246i
\(372\) 0 0
\(373\) 36777.2 63699.9i 0.264339 0.457848i −0.703052 0.711139i \(-0.748180\pi\)
0.967390 + 0.253291i \(0.0815130\pi\)
\(374\) −22950.4 + 9481.14i −0.164077 + 0.0677825i
\(375\) 0 0
\(376\) −77870.8 + 10028.9i −0.550807 + 0.0709376i
\(377\) −152687. −1.07428
\(378\) 0 0
\(379\) 139070.i 0.968176i −0.875019 0.484088i \(-0.839152\pi\)
0.875019 0.484088i \(-0.160848\pi\)
\(380\) 80970.4 + 81275.0i 0.560737 + 0.562846i
\(381\) 0 0
\(382\) 212587. 87822.8i 1.45683 0.601839i
\(383\) −90000.3 51961.7i −0.613545 0.354230i 0.160807 0.986986i \(-0.448590\pi\)
−0.774352 + 0.632756i \(0.781924\pi\)
\(384\) 0 0
\(385\) 23152.6 + 40101.5i 0.156199 + 0.270545i
\(386\) 109569. 142515.i 0.735380 0.956505i
\(387\) 0 0
\(388\) −24003.7 90260.7i −0.159447 0.599563i
\(389\) −50040.9 86673.4i −0.330694 0.572778i 0.651954 0.758258i \(-0.273949\pi\)
−0.982648 + 0.185480i \(0.940616\pi\)
\(390\) 0 0
\(391\) 56328.2 + 32521.1i 0.368444 + 0.212721i
\(392\) 342836. 261537.i 2.23108 1.70200i
\(393\) 0 0
\(394\) 176514. + 23407.1i 1.13707 + 0.150784i
\(395\) 159295.i 1.02096i
\(396\) 0 0
\(397\) 164388. 1.04301 0.521507 0.853247i \(-0.325370\pi\)
0.521507 + 0.853247i \(0.325370\pi\)
\(398\) 10025.9 75605.6i 0.0632931 0.477296i
\(399\) 0 0
\(400\) −129.207 + 34410.5i −0.000807546 + 0.215066i
\(401\) −78226.6 + 135492.i −0.486481 + 0.842609i −0.999879 0.0155412i \(-0.995053\pi\)
0.513399 + 0.858150i \(0.328386\pi\)
\(402\) 0 0
\(403\) 90700.6 52366.0i 0.558470 0.322433i
\(404\) −22612.3 85028.6i −0.138542 0.520958i
\(405\) 0 0
\(406\) −366699. 281926.i −2.22463 1.71034i
\(407\) 6035.02 3484.32i 0.0364325 0.0210343i
\(408\) 0 0
\(409\) −135351. + 234435.i −0.809125 + 1.40145i 0.104346 + 0.994541i \(0.466725\pi\)
−0.913471 + 0.406904i \(0.866608\pi\)
\(410\) 11123.7 + 26926.6i 0.0661734 + 0.160182i
\(411\) 0 0
\(412\) 202510. + 203272.i 1.19303 + 1.19752i
\(413\) −141086. −0.827149
\(414\) 0 0
\(415\) 73589.9i 0.427290i
\(416\) −119646. + 48902.4i −0.691372 + 0.282581i
\(417\) 0 0
\(418\) 10812.6 + 26173.4i 0.0618839 + 0.149799i
\(419\) −49366.2 28501.6i −0.281191 0.162346i 0.352771 0.935710i \(-0.385239\pi\)
−0.633963 + 0.773364i \(0.718573\pi\)
\(420\) 0 0
\(421\) −116812. 202325.i −0.659059 1.14152i −0.980860 0.194716i \(-0.937621\pi\)
0.321801 0.946807i \(-0.395712\pi\)
\(422\) 3021.82 + 2323.24i 0.0169685 + 0.0130457i
\(423\) 0 0
\(424\) 167390. + 69888.0i 0.931101 + 0.388750i
\(425\) 19078.1 + 33044.3i 0.105623 + 0.182944i
\(426\) 0 0
\(427\) −155010. 89495.0i −0.850166 0.490843i
\(428\) −36343.2 + 134623.i −0.198397 + 0.734908i
\(429\) 0 0
\(430\) −2411.77 + 18187.2i −0.0130436 + 0.0983626i
\(431\) 333180.i 1.79360i 0.442439 + 0.896798i \(0.354113\pi\)
−0.442439 + 0.896798i \(0.645887\pi\)
\(432\) 0 0
\(433\) −215343. −1.14856 −0.574282 0.818657i \(-0.694719\pi\)
−0.574282 + 0.818657i \(0.694719\pi\)
\(434\) 314521. + 41707.8i 1.66982 + 0.221431i
\(435\) 0 0
\(436\) −187868. 50717.3i −0.988280 0.266799i
\(437\) 37088.1 64238.5i 0.194210 0.336382i
\(438\) 0 0
\(439\) 27053.2 15619.2i 0.140375 0.0810455i −0.428168 0.903699i \(-0.640841\pi\)
0.568543 + 0.822654i \(0.307507\pi\)
\(440\) 11944.0 28607.3i 0.0616944 0.147765i
\(441\) 0 0
\(442\) −87356.3 + 113624.i −0.447146 + 0.581601i
\(443\) 184829. 106711.i 0.941809 0.543754i 0.0512822 0.998684i \(-0.483669\pi\)
0.890527 + 0.454930i \(0.150336\pi\)
\(444\) 0 0
\(445\) −17163.9 + 29728.8i −0.0866755 + 0.150126i
\(446\) −160234. + 66195.0i −0.805536 + 0.332779i
\(447\) 0 0
\(448\) −377642. 103472.i −1.88159 0.515546i
\(449\) 393053. 1.94966 0.974828 0.222956i \(-0.0715707\pi\)
0.974828 + 0.222956i \(0.0715707\pi\)
\(450\) 0 0
\(451\) 7191.43i 0.0353559i
\(452\) −232065. + 231195.i −1.13588 + 1.13162i
\(453\) 0 0
\(454\) 22209.5 9175.06i 0.107752 0.0445141i
\(455\) 231457. + 133632.i 1.11802 + 0.645487i
\(456\) 0 0
\(457\) 36178.7 + 62663.4i 0.173229 + 0.300042i 0.939547 0.342420i \(-0.111247\pi\)
−0.766318 + 0.642462i \(0.777913\pi\)
\(458\) 9938.23 12926.6i 0.0473782 0.0616246i
\(459\) 0 0
\(460\) −78473.1 + 20869.0i −0.370856 + 0.0986246i
\(461\) 29095.9 + 50395.5i 0.136908 + 0.237132i 0.926325 0.376726i \(-0.122950\pi\)
−0.789417 + 0.613858i \(0.789617\pi\)
\(462\) 0 0
\(463\) −64721.6 37367.0i −0.301917 0.174312i 0.341387 0.939923i \(-0.389103\pi\)
−0.643304 + 0.765611i \(0.722437\pi\)
\(464\) −1162.76 + 309666.i −0.00540075 + 1.43833i
\(465\) 0 0
\(466\) 148411. + 19680.5i 0.683431 + 0.0906282i
\(467\) 264366.i 1.21219i −0.795392 0.606096i \(-0.792735\pi\)
0.795392 0.606096i \(-0.207265\pi\)
\(468\) 0 0
\(469\) 23695.5 0.107726
\(470\) 14287.8 107745.i 0.0646801 0.487756i
\(471\) 0 0
\(472\) 57289.3 + 75097.8i 0.257152 + 0.337088i
\(473\) −2264.33 + 3921.94i −0.0101209 + 0.0175299i
\(474\) 0 0
\(475\) 37684.8 21757.3i 0.167024 0.0964314i
\(476\) −419597. + 111587.i −1.85191 + 0.492492i
\(477\) 0 0
\(478\) 81334.9 + 62531.9i 0.355976 + 0.273682i
\(479\) 242211. 139840.i 1.05566 0.609483i 0.131429 0.991326i \(-0.458044\pi\)
0.924228 + 0.381842i \(0.124710\pi\)
\(480\) 0 0
\(481\) 20110.7 34832.8i 0.0869236 0.150556i
\(482\) −116991. 283193.i −0.503568 1.21896i
\(483\) 0 0
\(484\) −160534. + 159932.i −0.685291 + 0.682723i
\(485\) 129293. 0.549655
\(486\) 0 0
\(487\) 62506.3i 0.263552i −0.991280 0.131776i \(-0.957932\pi\)
0.991280 0.131776i \(-0.0420679\pi\)
\(488\) 15306.5 + 118849.i 0.0642739 + 0.499065i
\(489\) 0 0
\(490\) 227916. + 551702.i 0.949254 + 2.29780i
\(491\) −291742. 168437.i −1.21014 0.698674i −0.247350 0.968926i \(-0.579560\pi\)
−0.962790 + 0.270252i \(0.912893\pi\)
\(492\) 0 0
\(493\) 171688. + 297372.i 0.706391 + 1.22351i
\(494\) 129580. + 99624.0i 0.530989 + 0.408235i
\(495\) 0 0
\(496\) −105514. 184350.i −0.428889 0.749342i
\(497\) 205927. + 356676.i 0.833682 + 1.44398i
\(498\) 0 0
\(499\) −276635. 159715.i −1.11098 0.641424i −0.171896 0.985115i \(-0.554989\pi\)
−0.939083 + 0.343691i \(0.888323\pi\)
\(500\) −259825. 70143.0i −1.03930 0.280572i
\(501\) 0 0
\(502\) 35042.5 264257.i 0.139055 1.04862i
\(503\) 28287.7i 0.111805i −0.998436 0.0559025i \(-0.982196\pi\)
0.998436 0.0559025i \(-0.0178036\pi\)
\(504\) 0 0
\(505\) 121798. 0.477592
\(506\) −19869.7 2634.88i −0.0776053 0.0102910i
\(507\) 0 0
\(508\) −33904.8 + 125591.i −0.131381 + 0.486665i
\(509\) 47278.6 81888.9i 0.182486 0.316074i −0.760241 0.649641i \(-0.774919\pi\)
0.942726 + 0.333567i \(0.108252\pi\)
\(510\) 0 0
\(511\) −249255. + 143908.i −0.954559 + 0.551115i
\(512\) 98268.5 + 243028.i 0.374865 + 0.927080i
\(513\) 0 0
\(514\) 144883. 188449.i 0.548392 0.713291i
\(515\) −343990. + 198603.i −1.29698 + 0.748809i
\(516\) 0 0
\(517\) 13414.4 23234.4i 0.0501869 0.0869263i
\(518\) 112615. 46522.9i 0.419698 0.173383i
\(519\) 0 0
\(520\) −22855.2 177463.i −0.0845238 0.656299i
\(521\) −369932. −1.36285 −0.681423 0.731890i \(-0.738638\pi\)
−0.681423 + 0.731890i \(0.738638\pi\)
\(522\) 0 0
\(523\) 65267.4i 0.238612i 0.992858 + 0.119306i \(0.0380670\pi\)
−0.992858 + 0.119306i \(0.961933\pi\)
\(524\) −183791. 184483.i −0.669364 0.671882i
\(525\) 0 0
\(526\) −92942.5 + 38395.9i −0.335925 + 0.138776i
\(527\) −203975. 117765.i −0.734440 0.424029i
\(528\) 0 0
\(529\) −113670. 196882.i −0.406195 0.703551i
\(530\) −153051. + 199073.i −0.544859 + 0.708696i
\(531\) 0 0
\(532\) 127257. + 478523.i 0.449634 + 1.69075i
\(533\) 20753.7 + 35946.4i 0.0730534 + 0.126532i
\(534\) 0 0
\(535\) −167172. 96516.6i −0.584057 0.337205i
\(536\) −9621.76 12612.7i −0.0334907 0.0439014i
\(537\) 0 0
\(538\) −10125.2 1342.68i −0.0349815 0.00463882i
\(539\) 147346.i 0.507179i
\(540\) 0 0
\(541\) 176002. 0.601343 0.300671 0.953728i \(-0.402789\pi\)
0.300671 + 0.953728i \(0.402789\pi\)
\(542\) −2430.96 + 18331.9i −0.00827520 + 0.0624036i
\(543\) 0 0
\(544\) 229777. + 178034.i 0.776442 + 0.601596i
\(545\) 134690. 233290.i 0.453463 0.785421i
\(546\) 0 0
\(547\) 236509. 136549.i 0.790448 0.456365i −0.0496725 0.998766i \(-0.515818\pi\)
0.840120 + 0.542400i \(0.182484\pi\)
\(548\) 101416. + 381351.i 0.337710 + 1.26988i
\(549\) 0 0
\(550\) −9321.85 7166.82i −0.0308160 0.0236920i
\(551\) 339133. 195798.i 1.11703 0.644920i
\(552\) 0 0
\(553\) 343760. 595409.i 1.12410 1.94700i
\(554\) 15050.2 + 36431.2i 0.0490370 + 0.118701i
\(555\) 0 0
\(556\) 222688. + 223526.i 0.720356 + 0.723066i
\(557\) 454335. 1.46442 0.732211 0.681078i \(-0.238489\pi\)
0.732211 + 0.681078i \(0.238489\pi\)
\(558\) 0 0
\(559\) 26138.5i 0.0836482i
\(560\) 272783. 468404.i 0.869845 1.49364i
\(561\) 0 0
\(562\) −73945.8 178996.i −0.234121 0.566723i
\(563\) −27753.2 16023.3i −0.0875582 0.0505518i 0.455582 0.890194i \(-0.349431\pi\)
−0.543140 + 0.839642i \(0.682765\pi\)
\(564\) 0 0
\(565\) −226734. 392714.i −0.710263 1.23021i
\(566\) −419318. 322380.i −1.30891 1.00632i
\(567\) 0 0
\(568\) 106234. 254443.i 0.329282 0.788667i
\(569\) −138564. 240000.i −0.427982 0.741287i 0.568712 0.822537i \(-0.307442\pi\)
−0.996694 + 0.0812502i \(0.974109\pi\)
\(570\) 0 0
\(571\) 556449. + 321266.i 1.70668 + 0.985355i 0.938600 + 0.345007i \(0.112123\pi\)
0.768085 + 0.640348i \(0.221210\pi\)
\(572\) 11511.4 42640.6i 0.0351831 0.130326i
\(573\) 0 0
\(574\) −16529.6 + 124651.i −0.0501694 + 0.378330i
\(575\) 30799.0i 0.0931540i
\(576\) 0 0
\(577\) 451002. 1.35465 0.677324 0.735685i \(-0.263140\pi\)
0.677324 + 0.735685i \(0.263140\pi\)
\(578\) −11664.5 1546.80i −0.0349148 0.00462997i
\(579\) 0 0
\(580\) −413864. 111728.i −1.23027 0.332128i
\(581\) −158808. + 275063.i −0.470456 + 0.814854i
\(582\) 0 0
\(583\) −53679.3 + 30991.8i −0.157932 + 0.0911820i
\(584\) 177812. + 74239.5i 0.521357 + 0.217675i
\(585\) 0 0
\(586\) −218250. + 283876.i −0.635563 + 0.826674i
\(587\) 327761. 189233.i 0.951221 0.549188i 0.0577610 0.998330i \(-0.481604\pi\)
0.893460 + 0.449143i \(0.148271\pi\)
\(588\) 0 0
\(589\) −134303. + 232620.i −0.387129 + 0.670528i
\(590\) −120850. + 49924.6i −0.347169 + 0.143420i
\(591\) 0 0
\(592\) −70491.8 41052.1i −0.201138 0.117136i
\(593\) −137966. −0.392339 −0.196170 0.980570i \(-0.562850\pi\)
−0.196170 + 0.980570i \(0.562850\pi\)
\(594\) 0 0
\(595\) 601046.i 1.69775i
\(596\) 338750. 337480.i 0.953644 0.950070i
\(597\) 0 0
\(598\) −106923. + 44171.4i −0.298998 + 0.123521i
\(599\) 180870. + 104426.i 0.504096 + 0.291040i 0.730404 0.683016i \(-0.239332\pi\)
−0.226307 + 0.974056i \(0.572665\pi\)
\(600\) 0 0
\(601\) −180004. 311775.i −0.498348 0.863163i 0.501651 0.865070i \(-0.332726\pi\)
−0.999998 + 0.00190701i \(0.999393\pi\)
\(602\) −48262.9 + 62775.3i −0.133174 + 0.173219i
\(603\) 0 0
\(604\) −92203.3 + 24520.4i −0.252739 + 0.0672130i
\(605\) −156846. 271665.i −0.428512 0.742204i
\(606\) 0 0
\(607\) 279709. + 161490.i 0.759152 + 0.438297i 0.828991 0.559262i \(-0.188915\pi\)
−0.0698392 + 0.997558i \(0.522249\pi\)
\(608\) 203036. 262045.i 0.549244 0.708875i
\(609\) 0 0
\(610\) −164445. 21806.6i −0.441937 0.0586042i
\(611\) 154850.i 0.414791i
\(612\) 0 0
\(613\) −392554. −1.04467 −0.522334 0.852741i \(-0.674939\pi\)
−0.522334 + 0.852741i \(0.674939\pi\)
\(614\) 32983.5 248730.i 0.0874904 0.659769i
\(615\) 0 0
\(616\) 106379. 81152.6i 0.280346 0.213866i
\(617\) 192102. 332730.i 0.504616 0.874020i −0.495370 0.868682i \(-0.664968\pi\)
0.999986 0.00533786i \(-0.00169910\pi\)
\(618\) 0 0
\(619\) −602573. + 347896.i −1.57264 + 0.907962i −0.576792 + 0.816891i \(0.695696\pi\)
−0.995844 + 0.0910712i \(0.970971\pi\)
\(620\) 284166. 75570.6i 0.739247 0.196594i
\(621\) 0 0
\(622\) 389360. + 299347.i 1.00640 + 0.773739i
\(623\) −128310. + 74079.7i −0.330586 + 0.190864i
\(624\) 0 0
\(625\) 144273. 249889.i 0.369339 0.639715i
\(626\) 74208.4 + 179632.i 0.189367 + 0.458389i
\(627\) 0 0
\(628\) 396575. 395089.i 1.00556 1.00179i
\(629\) −90453.5 −0.228625
\(630\) 0 0
\(631\) 230753.i 0.579546i −0.957095 0.289773i \(-0.906420\pi\)
0.957095 0.289773i \(-0.0935798\pi\)
\(632\) −456513. + 58793.7i −1.14293 + 0.147196i
\(633\) 0 0
\(634\) −168203. 407158.i −0.418461 1.01294i
\(635\) −155955. 90040.8i −0.386770 0.223302i
\(636\) 0 0
\(637\) 425225. + 736511.i 1.04795 + 1.81510i
\(638\) −83889.0 64495.5i −0.206093 0.158449i
\(639\) 0 0
\(640\) −360090. + 45001.6i −0.879126 + 0.109867i
\(641\) 259471. + 449416.i 0.631498 + 1.09379i 0.987246 + 0.159205i \(0.0508931\pi\)
−0.355747 + 0.934582i \(0.615774\pi\)
\(642\) 0 0
\(643\) −195039. 112606.i −0.471738 0.272358i 0.245229 0.969465i \(-0.421137\pi\)
−0.716967 + 0.697107i \(0.754470\pi\)
\(644\) −338351. 91341.9i −0.815821 0.220241i
\(645\) 0 0
\(646\) 48321.1 364392.i 0.115790 0.873179i
\(647\) 153505.i 0.366703i −0.983047 0.183352i \(-0.941305\pi\)
0.983047 0.183352i \(-0.0586947\pi\)
\(648\) 0 0
\(649\) −32276.0 −0.0766284
\(650\) −67278.0 8921.58i −0.159238 0.0211162i
\(651\) 0 0
\(652\) 60507.5 224133.i 0.142336 0.527243i
\(653\) 36120.4 62562.3i 0.0847082 0.146719i −0.820559 0.571562i \(-0.806338\pi\)
0.905267 + 0.424843i \(0.139671\pi\)
\(654\) 0 0
\(655\) 312193. 180245.i 0.727681 0.420127i
\(656\) 73061.5 41817.1i 0.169778 0.0971731i
\(657\) 0 0
\(658\) 285920. 371895.i 0.660378 0.858950i
\(659\) −203157. + 117293.i −0.467802 + 0.270086i −0.715319 0.698798i \(-0.753719\pi\)
0.247517 + 0.968883i \(0.420385\pi\)
\(660\) 0 0
\(661\) −298973. + 517837.i −0.684274 + 1.18520i 0.289391 + 0.957211i \(0.406547\pi\)
−0.973665 + 0.227986i \(0.926786\pi\)
\(662\) 682164. 281812.i 1.55659 0.643048i
\(663\) 0 0
\(664\) 210897. 27161.1i 0.478337 0.0616043i
\(665\) −685452. −1.55001
\(666\) 0 0
\(667\) 277166.i 0.623001i
\(668\) 503844. + 505739.i 1.12913 + 1.13338i
\(669\) 0 0
\(670\) 20296.7 8384.87i 0.0452144 0.0186787i
\(671\) −35461.3 20473.6i −0.0787607 0.0454725i
\(672\) 0 0
\(673\) 375852. + 650996.i 0.829826 + 1.43730i 0.898174 + 0.439640i \(0.144894\pi\)
−0.0683477 + 0.997662i \(0.521773\pi\)
\(674\) −159998. + 208109.i −0.352204 + 0.458111i
\(675\) 0 0
\(676\) 51928.7 + 195266.i 0.113636 + 0.427301i
\(677\) −42323.8 73307.0i −0.0923437 0.159944i 0.816153 0.577836i \(-0.196103\pi\)
−0.908497 + 0.417892i \(0.862769\pi\)
\(678\) 0 0
\(679\) 483267. + 279014.i 1.04821 + 0.605183i
\(680\) −319927. + 244060.i −0.691883 + 0.527812i
\(681\) 0 0
\(682\) 71952.2 + 9541.41i 0.154695 + 0.0205137i
\(683\) 635506.i 1.36232i 0.732136 + 0.681159i \(0.238524\pi\)
−0.732136 + 0.681159i \(0.761476\pi\)
\(684\) 0 0
\(685\) −546260. −1.16418
\(686\) −217987. + 1.64385e6i −0.463214 + 3.49312i
\(687\) 0 0
\(688\) 53011.8 + 199.053i 0.111994 + 0.000420525i
\(689\) −178878. + 309825.i −0.376806 + 0.652647i
\(690\) 0 0
\(691\) −384843. + 222189.i −0.805986 + 0.465336i −0.845560 0.533881i \(-0.820733\pi\)
0.0395741 + 0.999217i \(0.487400\pi\)
\(692\) −217474. 817762.i −0.454145 1.70771i
\(693\) 0 0
\(694\) 332553. + 255673.i 0.690466 + 0.530844i
\(695\) −378265. + 218391.i −0.783116 + 0.452132i
\(696\) 0 0
\(697\) 46672.6 80839.4i 0.0960720 0.166402i
\(698\) −133397. 322906.i −0.273802 0.662775i
\(699\) 0 0
\(700\) −145105. 145651.i −0.296132 0.297246i
\(701\) 374624. 0.762359 0.381179 0.924501i \(-0.375518\pi\)
0.381179 + 0.924501i \(0.375518\pi\)
\(702\) 0 0
\(703\) 103156.i 0.208730i
\(704\) −86392.4 23671.1i −0.174313 0.0477609i
\(705\) 0 0
\(706\) −74390.9 180073.i −0.149249 0.361277i
\(707\) 455254. + 262841.i 0.910783 + 0.525841i
\(708\) 0 0
\(709\) −92815.5 160761.i −0.184641 0.319808i 0.758814 0.651307i \(-0.225779\pi\)
−0.943456 + 0.331499i \(0.892446\pi\)
\(710\) 302603. + 232647.i 0.600284 + 0.461510i
\(711\) 0 0
\(712\) 91532.8 + 38216.5i 0.180558 + 0.0753860i
\(713\) −95057.9 164645.i −0.186986 0.323869i
\(714\) 0 0
\(715\) 52950.0 + 30570.7i 0.103575 + 0.0597989i
\(716\) −136950. + 507293.i −0.267138 + 0.989539i
\(717\) 0 0
\(718\) −57530.0 + 433836.i −0.111595 + 0.841544i
\(719\) 651163.i 1.25960i 0.776759 + 0.629799i \(0.216863\pi\)
−0.776759 + 0.629799i \(0.783137\pi\)
\(720\) 0 0
\(721\) −1.71435e6 −3.29783
\(722\) 101196. + 13419.4i 0.194129 + 0.0257429i
\(723\) 0 0
\(724\) −351552. 94905.9i −0.670676 0.181057i
\(725\) −81298.3 + 140813.i −0.154670 + 0.267896i
\(726\) 0 0
\(727\) −207917. + 120041.i −0.393389 + 0.227123i −0.683627 0.729831i \(-0.739599\pi\)
0.290239 + 0.956954i \(0.406265\pi\)
\(728\) 297539. 712640.i 0.561412 1.34465i
\(729\) 0 0
\(730\) −162581. + 211468.i −0.305086 + 0.396825i
\(731\) 50907.1 29391.2i 0.0952673 0.0550026i
\(732\) 0 0
\(733\) 27840.0 48220.4i 0.0518158 0.0897475i −0.838954 0.544202i \(-0.816832\pi\)
0.890770 + 0.454455i \(0.150166\pi\)
\(734\) −4750.49 + 1962.49i −0.00881752 + 0.00364264i
\(735\) 0 0
\(736\) 88770.5 + 217189.i 0.163875 + 0.400942i
\(737\) 5420.76 0.00997988
\(738\) 0 0
\(739\) 327859.i 0.600341i 0.953886 + 0.300170i \(0.0970435\pi\)
−0.953886 + 0.300170i \(0.902957\pi\)
\(740\) 79999.7 79699.9i 0.146091 0.145544i
\(741\) 0 0
\(742\) −1.00167e6 + 413805.i −1.81936 + 0.751602i
\(743\) −11150.8 6437.91i −0.0201989 0.0116618i 0.489867 0.871797i \(-0.337045\pi\)
−0.510065 + 0.860136i \(0.670379\pi\)
\(744\) 0 0
\(745\) 330968. + 573254.i 0.596312 + 1.03284i
\(746\) 179327. 233250.i 0.322232 0.419126i
\(747\) 0 0
\(748\) −95990.4 + 25527.5i −0.171563 + 0.0456252i
\(749\) −416567. 721516.i −0.742543 1.28612i
\(750\) 0 0
\(751\) −460430. 265829.i −0.816363 0.471328i 0.0327975 0.999462i \(-0.489558\pi\)
−0.849161 + 0.528134i \(0.822892\pi\)
\(752\) −314054. 1179.23i −0.555352 0.00208528i
\(753\) 0 0
\(754\) −605447. 80286.9i −1.06496 0.141222i
\(755\) 132075.i 0.231701i
\(756\) 0 0
\(757\) 614542. 1.07241 0.536204 0.844089i \(-0.319858\pi\)
0.536204 + 0.844089i \(0.319858\pi\)
\(758\) 73126.6 551451.i 0.127273 0.959774i
\(759\) 0 0
\(760\) 278334. + 364855.i 0.481880 + 0.631674i
\(761\) −410349. + 710745.i −0.708571 + 1.22728i 0.256816 + 0.966460i \(0.417327\pi\)
−0.965387 + 0.260821i \(0.916007\pi\)
\(762\) 0 0
\(763\) 1.00688e6 581324.i 1.72954 0.998548i
\(764\) 889149. 236458.i 1.52331 0.405105i
\(765\) 0 0
\(766\) −329554. 253368.i −0.561654 0.431811i
\(767\) −161332. + 93144.9i −0.274239 + 0.158332i
\(768\) 0 0
\(769\) 65721.6 113833.i 0.111136 0.192494i −0.805092 0.593149i \(-0.797884\pi\)
0.916229 + 0.400656i \(0.131218\pi\)
\(770\) 70720.3 + 171188.i 0.119279 + 0.288730i
\(771\) 0 0
\(772\) 509410. 507500.i 0.854737 0.851534i
\(773\) 629.598 0.00105367 0.000526834 1.00000i \(-0.499832\pi\)
0.000526834 1.00000i \(0.499832\pi\)
\(774\) 0 0
\(775\) 111529.i 0.185689i
\(776\) −47720.2 370531.i −0.0792463 0.615321i
\(777\) 0 0
\(778\) −152851. 369998.i </