Properties

Label 108.5.f.a.91.1
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 91.1
Character \(\chi\) \(=\) 108.91
Dual form 108.5.f.a.19.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.99035 + 0.277636i) q^{2} +(15.8458 - 2.21573i) q^{4} +(23.3466 - 40.4374i) q^{5} +(52.4363 - 30.2741i) q^{7} +(-62.6153 + 13.2409i) q^{8} +O(q^{10})\) \(q+(-3.99035 + 0.277636i) q^{2} +(15.8458 - 2.21573i) q^{4} +(23.3466 - 40.4374i) q^{5} +(52.4363 - 30.2741i) q^{7} +(-62.6153 + 13.2409i) q^{8} +(-81.9341 + 167.841i) q^{10} +(-63.7631 + 36.8136i) q^{11} +(15.5924 - 27.0068i) q^{13} +(-200.834 + 135.363i) q^{14} +(246.181 - 70.2201i) q^{16} -53.8013 q^{17} -54.9619i q^{19} +(280.347 - 692.494i) q^{20} +(244.217 - 164.602i) q^{22} +(243.863 + 140.795i) q^{23} +(-777.624 - 1346.88i) q^{25} +(-54.7210 + 112.096i) q^{26} +(763.818 - 595.904i) q^{28} +(-223.597 - 387.282i) q^{29} +(-240.584 - 138.901i) q^{31} +(-962.854 + 348.552i) q^{32} +(214.686 - 14.9372i) q^{34} -2827.19i q^{35} +1016.51 q^{37} +(15.2594 + 219.317i) q^{38} +(-926.424 + 2841.13i) q^{40} +(946.158 - 1638.79i) q^{41} +(-666.266 + 384.669i) q^{43} +(-928.811 + 724.625i) q^{44} +(-1012.19 - 494.115i) q^{46} +(-2374.81 + 1371.10i) q^{47} +(632.546 - 1095.60i) q^{49} +(3476.94 + 5158.64i) q^{50} +(187.235 - 462.494i) q^{52} +4647.69 q^{53} +3437.89i q^{55} +(-2882.46 + 2589.93i) q^{56} +(999.756 + 1483.31i) q^{58} +(262.792 + 151.723i) q^{59} +(-478.174 - 828.222i) q^{61} +(998.577 + 487.469i) q^{62} +(3745.36 - 1658.17i) q^{64} +(-728.057 - 1261.03i) q^{65} +(-6010.96 - 3470.43i) q^{67} +(-852.527 + 119.209i) q^{68} +(784.928 + 11281.5i) q^{70} +5971.60i q^{71} -4339.17 q^{73} +(-4056.25 + 282.220i) q^{74} +(-121.781 - 870.917i) q^{76} +(-2229.00 + 3860.75i) q^{77} +(3294.15 - 1901.88i) q^{79} +(2907.96 - 11594.3i) q^{80} +(-3320.52 + 6802.05i) q^{82} +(2730.64 - 1576.53i) q^{83} +(-1256.08 + 2175.59i) q^{85} +(2551.84 - 1719.94i) q^{86} +(3505.10 - 3149.38i) q^{88} +7132.44 q^{89} -1888.18i q^{91} +(4176.18 + 1690.67i) q^{92} +(9095.67 - 6130.50i) q^{94} +(-2222.52 - 1283.17i) q^{95} +(980.405 + 1698.11i) q^{97} +(-2219.91 + 4547.46i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.99035 + 0.277636i −0.997588 + 0.0694089i
\(3\) 0 0
\(4\) 15.8458 2.21573i 0.990365 0.138483i
\(5\) 23.3466 40.4374i 0.933862 1.61750i 0.157212 0.987565i \(-0.449749\pi\)
0.776650 0.629932i \(-0.216917\pi\)
\(6\) 0 0
\(7\) 52.4363 30.2741i 1.07013 0.617839i 0.141913 0.989879i \(-0.454675\pi\)
0.928217 + 0.372040i \(0.121341\pi\)
\(8\) −62.6153 + 13.2409i −0.978364 + 0.206889i
\(9\) 0 0
\(10\) −81.9341 + 167.841i −0.819341 + 1.67841i
\(11\) −63.7631 + 36.8136i −0.526968 + 0.304245i −0.739781 0.672848i \(-0.765071\pi\)
0.212813 + 0.977093i \(0.431737\pi\)
\(12\) 0 0
\(13\) 15.5924 27.0068i 0.0922626 0.159803i −0.816200 0.577769i \(-0.803923\pi\)
0.908463 + 0.417966i \(0.137257\pi\)
\(14\) −200.834 + 135.363i −1.02466 + 0.690626i
\(15\) 0 0
\(16\) 246.181 70.2201i 0.961645 0.274297i
\(17\) −53.8013 −0.186164 −0.0930819 0.995658i \(-0.529672\pi\)
−0.0930819 + 0.995658i \(0.529672\pi\)
\(18\) 0 0
\(19\) 54.9619i 0.152249i −0.997098 0.0761245i \(-0.975745\pi\)
0.997098 0.0761245i \(-0.0242546\pi\)
\(20\) 280.347 692.494i 0.700869 1.73124i
\(21\) 0 0
\(22\) 244.217 164.602i 0.504580 0.340088i
\(23\) 243.863 + 140.795i 0.460990 + 0.266152i 0.712460 0.701712i \(-0.247581\pi\)
−0.251471 + 0.967865i \(0.580914\pi\)
\(24\) 0 0
\(25\) −777.624 1346.88i −1.24420 2.15501i
\(26\) −54.7210 + 112.096i −0.0809483 + 0.165822i
\(27\) 0 0
\(28\) 763.818 595.904i 0.974258 0.760081i
\(29\) −223.597 387.282i −0.265871 0.460502i 0.701921 0.712255i \(-0.252326\pi\)
−0.967791 + 0.251753i \(0.918993\pi\)
\(30\) 0 0
\(31\) −240.584 138.901i −0.250347 0.144538i 0.369576 0.929200i \(-0.379503\pi\)
−0.619923 + 0.784663i \(0.712836\pi\)
\(32\) −962.854 + 348.552i −0.940287 + 0.340383i
\(33\) 0 0
\(34\) 214.686 14.9372i 0.185715 0.0129214i
\(35\) 2827.19i 2.30791i
\(36\) 0 0
\(37\) 1016.51 0.742522 0.371261 0.928528i \(-0.378925\pi\)
0.371261 + 0.928528i \(0.378925\pi\)
\(38\) 15.2594 + 219.317i 0.0105674 + 0.151882i
\(39\) 0 0
\(40\) −926.424 + 2841.13i −0.579015 + 1.77571i
\(41\) 946.158 1638.79i 0.562854 0.974892i −0.434392 0.900724i \(-0.643037\pi\)
0.997246 0.0741680i \(-0.0236301\pi\)
\(42\) 0 0
\(43\) −666.266 + 384.669i −0.360339 + 0.208042i −0.669229 0.743056i \(-0.733376\pi\)
0.308891 + 0.951098i \(0.400042\pi\)
\(44\) −928.811 + 724.625i −0.479758 + 0.374290i
\(45\) 0 0
\(46\) −1012.19 494.115i −0.478351 0.233514i
\(47\) −2374.81 + 1371.10i −1.07506 + 0.620687i −0.929560 0.368671i \(-0.879813\pi\)
−0.145502 + 0.989358i \(0.546480\pi\)
\(48\) 0 0
\(49\) 632.546 1095.60i 0.263451 0.456311i
\(50\) 3476.94 + 5158.64i 1.39077 + 2.06346i
\(51\) 0 0
\(52\) 187.235 462.494i 0.0692435 0.171041i
\(53\) 4647.69 1.65457 0.827286 0.561780i \(-0.189883\pi\)
0.827286 + 0.561780i \(0.189883\pi\)
\(54\) 0 0
\(55\) 3437.89i 1.13649i
\(56\) −2882.46 + 2589.93i −0.919152 + 0.825870i
\(57\) 0 0
\(58\) 999.756 + 1483.31i 0.297193 + 0.440937i
\(59\) 262.792 + 151.723i 0.0754934 + 0.0435861i 0.537272 0.843409i \(-0.319455\pi\)
−0.461778 + 0.886995i \(0.652788\pi\)
\(60\) 0 0
\(61\) −478.174 828.222i −0.128507 0.222580i 0.794591 0.607145i \(-0.207685\pi\)
−0.923098 + 0.384564i \(0.874352\pi\)
\(62\) 998.577 + 487.469i 0.259776 + 0.126813i
\(63\) 0 0
\(64\) 3745.36 1658.17i 0.914394 0.404826i
\(65\) −728.057 1261.03i −0.172321 0.298469i
\(66\) 0 0
\(67\) −6010.96 3470.43i −1.33904 0.773096i −0.352376 0.935858i \(-0.614626\pi\)
−0.986665 + 0.162762i \(0.947960\pi\)
\(68\) −852.527 + 119.209i −0.184370 + 0.0257805i
\(69\) 0 0
\(70\) 784.928 + 11281.5i 0.160189 + 2.30234i
\(71\) 5971.60i 1.18461i 0.805715 + 0.592303i \(0.201781\pi\)
−0.805715 + 0.592303i \(0.798219\pi\)
\(72\) 0 0
\(73\) −4339.17 −0.814257 −0.407128 0.913371i \(-0.633470\pi\)
−0.407128 + 0.913371i \(0.633470\pi\)
\(74\) −4056.25 + 282.220i −0.740732 + 0.0515377i
\(75\) 0 0
\(76\) −121.781 870.917i −0.0210839 0.150782i
\(77\) −2229.00 + 3860.75i −0.375949 + 0.651163i
\(78\) 0 0
\(79\) 3294.15 1901.88i 0.527824 0.304740i −0.212306 0.977203i \(-0.568097\pi\)
0.740130 + 0.672464i \(0.234764\pi\)
\(80\) 2907.96 11594.3i 0.454369 1.81161i
\(81\) 0 0
\(82\) −3320.52 + 6802.05i −0.493831 + 1.01161i
\(83\) 2730.64 1576.53i 0.396376 0.228848i −0.288543 0.957467i \(-0.593171\pi\)
0.684919 + 0.728619i \(0.259837\pi\)
\(84\) 0 0
\(85\) −1256.08 + 2175.59i −0.173851 + 0.301119i
\(86\) 2551.84 1719.94i 0.345030 0.232551i
\(87\) 0 0
\(88\) 3505.10 3149.38i 0.452622 0.406686i
\(89\) 7132.44 0.900447 0.450224 0.892916i \(-0.351344\pi\)
0.450224 + 0.892916i \(0.351344\pi\)
\(90\) 0 0
\(91\) 1888.18i 0.228014i
\(92\) 4176.18 + 1690.67i 0.493405 + 0.199749i
\(93\) 0 0
\(94\) 9095.67 6130.50i 1.02939 0.693809i
\(95\) −2222.52 1283.17i −0.246262 0.142180i
\(96\) 0 0
\(97\) 980.405 + 1698.11i 0.104199 + 0.180477i 0.913411 0.407040i \(-0.133439\pi\)
−0.809212 + 0.587517i \(0.800106\pi\)
\(98\) −2219.91 + 4547.46i −0.231144 + 0.473496i
\(99\) 0 0
\(100\) −15306.4 19619.5i −1.53064 1.96195i
\(101\) −3849.96 6668.32i −0.377410 0.653693i 0.613275 0.789870i \(-0.289852\pi\)
−0.990685 + 0.136177i \(0.956519\pi\)
\(102\) 0 0
\(103\) 3195.22 + 1844.76i 0.301180 + 0.173886i 0.642973 0.765889i \(-0.277701\pi\)
−0.341793 + 0.939775i \(0.611034\pi\)
\(104\) −618.727 + 1897.50i −0.0572048 + 0.175434i
\(105\) 0 0
\(106\) −18545.9 + 1290.37i −1.65058 + 0.114842i
\(107\) 13741.5i 1.20024i −0.799911 0.600118i \(-0.795120\pi\)
0.799911 0.600118i \(-0.204880\pi\)
\(108\) 0 0
\(109\) 18709.9 1.57478 0.787388 0.616458i \(-0.211433\pi\)
0.787388 + 0.616458i \(0.211433\pi\)
\(110\) −954.480 13718.4i −0.0788826 1.13375i
\(111\) 0 0
\(112\) 10783.0 11135.0i 0.859613 0.887676i
\(113\) −5000.50 + 8661.12i −0.391613 + 0.678293i −0.992662 0.120919i \(-0.961416\pi\)
0.601050 + 0.799212i \(0.294749\pi\)
\(114\) 0 0
\(115\) 11386.7 6574.14i 0.861002 0.497099i
\(116\) −4401.20 5641.38i −0.327081 0.419246i
\(117\) 0 0
\(118\) −1090.76 532.469i −0.0783366 0.0382411i
\(119\) −2821.15 + 1628.79i −0.199219 + 0.115019i
\(120\) 0 0
\(121\) −4610.01 + 7984.77i −0.314870 + 0.545371i
\(122\) 2138.03 + 3172.14i 0.143646 + 0.213124i
\(123\) 0 0
\(124\) −4120.01 1667.93i −0.267951 0.108477i
\(125\) −43436.1 −2.77991
\(126\) 0 0
\(127\) 18883.8i 1.17080i 0.810745 + 0.585400i \(0.199063\pi\)
−0.810745 + 0.585400i \(0.800937\pi\)
\(128\) −14484.9 + 7656.52i −0.884090 + 0.467317i
\(129\) 0 0
\(130\) 3255.31 + 4829.82i 0.192622 + 0.285788i
\(131\) 25700.9 + 14838.4i 1.49763 + 0.864660i 0.999996 0.00272458i \(-0.000867262\pi\)
0.497639 + 0.867384i \(0.334201\pi\)
\(132\) 0 0
\(133\) −1663.92 2882.00i −0.0940654 0.162926i
\(134\) 24949.4 + 12179.4i 1.38947 + 0.678290i
\(135\) 0 0
\(136\) 3368.79 712.379i 0.182136 0.0385153i
\(137\) 8332.79 + 14432.8i 0.443965 + 0.768971i 0.997980 0.0635366i \(-0.0202380\pi\)
−0.554014 + 0.832507i \(0.686905\pi\)
\(138\) 0 0
\(139\) 3545.95 + 2047.25i 0.183528 + 0.105960i 0.588949 0.808170i \(-0.299542\pi\)
−0.405421 + 0.914130i \(0.632875\pi\)
\(140\) −6264.28 44799.1i −0.319606 2.28567i
\(141\) 0 0
\(142\) −1657.93 23828.8i −0.0822222 1.18175i
\(143\) 2296.05i 0.112282i
\(144\) 0 0
\(145\) −20880.9 −0.993147
\(146\) 17314.8 1204.71i 0.812293 0.0565167i
\(147\) 0 0
\(148\) 16107.5 2252.32i 0.735368 0.102827i
\(149\) −2934.59 + 5082.86i −0.132183 + 0.228947i −0.924518 0.381139i \(-0.875532\pi\)
0.792335 + 0.610086i \(0.208865\pi\)
\(150\) 0 0
\(151\) 28725.6 16584.7i 1.25984 0.727369i 0.286797 0.957991i \(-0.407409\pi\)
0.973043 + 0.230622i \(0.0740760\pi\)
\(152\) 727.745 + 3441.46i 0.0314987 + 0.148955i
\(153\) 0 0
\(154\) 7822.63 16024.6i 0.329846 0.675687i
\(155\) −11233.6 + 6485.72i −0.467579 + 0.269957i
\(156\) 0 0
\(157\) −11089.2 + 19207.1i −0.449886 + 0.779226i −0.998378 0.0569302i \(-0.981869\pi\)
0.548492 + 0.836156i \(0.315202\pi\)
\(158\) −12616.8 + 8503.74i −0.505400 + 0.340640i
\(159\) 0 0
\(160\) −8384.79 + 47072.8i −0.327531 + 1.83878i
\(161\) 17049.7 0.657758
\(162\) 0 0
\(163\) 31303.8i 1.17821i 0.808057 + 0.589104i \(0.200519\pi\)
−0.808057 + 0.589104i \(0.799481\pi\)
\(164\) 11361.5 28064.5i 0.422425 1.04344i
\(165\) 0 0
\(166\) −10458.5 + 7049.04i −0.379536 + 0.255808i
\(167\) −22551.7 13020.2i −0.808622 0.466858i 0.0378548 0.999283i \(-0.487948\pi\)
−0.846477 + 0.532425i \(0.821281\pi\)
\(168\) 0 0
\(169\) 13794.3 + 23892.4i 0.482975 + 0.836538i
\(170\) 4408.17 9030.10i 0.152532 0.312460i
\(171\) 0 0
\(172\) −9705.23 + 7571.67i −0.328057 + 0.255938i
\(173\) 7830.38 + 13562.6i 0.261632 + 0.453160i 0.966676 0.256004i \(-0.0824060\pi\)
−0.705044 + 0.709164i \(0.749073\pi\)
\(174\) 0 0
\(175\) −81551.5 47083.8i −2.66290 1.53743i
\(176\) −13112.2 + 13540.3i −0.423302 + 0.437122i
\(177\) 0 0
\(178\) −28461.0 + 1980.22i −0.898276 + 0.0624991i
\(179\) 36836.7i 1.14967i 0.818268 + 0.574837i \(0.194935\pi\)
−0.818268 + 0.574837i \(0.805065\pi\)
\(180\) 0 0
\(181\) 56961.0 1.73868 0.869342 0.494211i \(-0.164543\pi\)
0.869342 + 0.494211i \(0.164543\pi\)
\(182\) 524.227 + 7534.52i 0.0158262 + 0.227464i
\(183\) 0 0
\(184\) −17133.8 5586.93i −0.506080 0.165020i
\(185\) 23732.1 41105.2i 0.693414 1.20103i
\(186\) 0 0
\(187\) 3430.54 1980.62i 0.0981024 0.0566394i
\(188\) −34592.9 + 26988.1i −0.978749 + 0.763584i
\(189\) 0 0
\(190\) 9224.88 + 4503.26i 0.255537 + 0.124744i
\(191\) 33837.1 19535.9i 0.927527 0.535508i 0.0414986 0.999139i \(-0.486787\pi\)
0.886029 + 0.463630i \(0.153453\pi\)
\(192\) 0 0
\(193\) −2025.97 + 3509.08i −0.0543898 + 0.0942059i −0.891938 0.452157i \(-0.850655\pi\)
0.837549 + 0.546363i \(0.183988\pi\)
\(194\) −4383.62 6503.87i −0.116474 0.172810i
\(195\) 0 0
\(196\) 7595.67 18762.3i 0.197721 0.488398i
\(197\) 44869.6 1.15617 0.578083 0.815978i \(-0.303801\pi\)
0.578083 + 0.815978i \(0.303801\pi\)
\(198\) 0 0
\(199\) 56256.7i 1.42059i −0.703905 0.710294i \(-0.748562\pi\)
0.703905 0.710294i \(-0.251438\pi\)
\(200\) 66525.1 + 74039.1i 1.66313 + 1.85098i
\(201\) 0 0
\(202\) 17214.1 + 25540.1i 0.421872 + 0.625921i
\(203\) −23449.3 13538.4i −0.569032 0.328531i
\(204\) 0 0
\(205\) −44179.1 76520.4i −1.05126 1.82083i
\(206\) −13262.2 6474.13i −0.312523 0.152562i
\(207\) 0 0
\(208\) 1942.13 7743.46i 0.0448902 0.178982i
\(209\) 2023.35 + 3504.54i 0.0463210 + 0.0802303i
\(210\) 0 0
\(211\) 63309.8 + 36552.0i 1.42202 + 0.821005i 0.996472 0.0839298i \(-0.0267471\pi\)
0.425551 + 0.904935i \(0.360080\pi\)
\(212\) 73646.6 10298.0i 1.63863 0.229130i
\(213\) 0 0
\(214\) 3815.13 + 54833.4i 0.0833071 + 1.19734i
\(215\) 35922.8i 0.777129i
\(216\) 0 0
\(217\) −16820.4 −0.357205
\(218\) −74659.2 + 5194.54i −1.57098 + 0.109303i
\(219\) 0 0
\(220\) 7617.42 + 54476.2i 0.157385 + 1.12554i
\(221\) −838.891 + 1453.00i −0.0171760 + 0.0297496i
\(222\) 0 0
\(223\) −65737.1 + 37953.3i −1.32191 + 0.763203i −0.984032 0.177989i \(-0.943041\pi\)
−0.337873 + 0.941192i \(0.609708\pi\)
\(224\) −39936.4 + 47426.3i −0.795927 + 0.945200i
\(225\) 0 0
\(226\) 17549.1 35949.3i 0.343589 0.703839i
\(227\) 35712.5 20618.6i 0.693057 0.400136i −0.111700 0.993742i \(-0.535629\pi\)
0.804756 + 0.593606i \(0.202296\pi\)
\(228\) 0 0
\(229\) −13792.1 + 23888.7i −0.263003 + 0.455534i −0.967038 0.254630i \(-0.918046\pi\)
0.704036 + 0.710165i \(0.251379\pi\)
\(230\) −43611.9 + 29394.5i −0.824422 + 0.555662i
\(231\) 0 0
\(232\) 19128.6 + 21289.2i 0.355391 + 0.395533i
\(233\) −49430.2 −0.910502 −0.455251 0.890363i \(-0.650450\pi\)
−0.455251 + 0.890363i \(0.650450\pi\)
\(234\) 0 0
\(235\) 128042.i 2.31855i
\(236\) 4500.34 + 1821.91i 0.0808019 + 0.0327116i
\(237\) 0 0
\(238\) 10805.2 7282.69i 0.190756 0.128570i
\(239\) −97042.8 56027.7i −1.69890 0.980859i −0.946808 0.321800i \(-0.895712\pi\)
−0.752091 0.659060i \(1.22905\pi\)
\(240\) 0 0
\(241\) −20548.3 35590.7i −0.353787 0.612776i 0.633123 0.774051i \(-0.281773\pi\)
−0.986910 + 0.161275i \(0.948439\pi\)
\(242\) 16178.7 33142.0i 0.276257 0.565910i
\(243\) 0 0
\(244\) −9412.18 12064.4i −0.158092 0.202640i
\(245\) −29535.6 51157.1i −0.492054 0.852263i
\(246\) 0 0
\(247\) −1484.34 856.986i −0.0243299 0.0140469i
\(248\) 16903.4 + 5511.79i 0.274834 + 0.0896167i
\(249\) 0 0
\(250\) 173326. 12059.4i 2.77321 0.192951i
\(251\) 50848.1i 0.807099i −0.914958 0.403550i \(-0.867776\pi\)
0.914958 0.403550i \(-0.132224\pi\)
\(252\) 0 0
\(253\) −20732.7 −0.323902
\(254\) −5242.83 75353.2i −0.0812640 1.16798i
\(255\) 0 0
\(256\) 55674.3 34573.7i 0.849522 0.527553i
\(257\) 6405.02 11093.8i 0.0969738 0.167964i −0.813457 0.581625i \(-0.802417\pi\)
0.910431 + 0.413662i \(0.135750\pi\)
\(258\) 0 0
\(259\) 53302.2 30774.1i 0.794595 0.458760i
\(260\) −14330.8 18368.9i −0.211994 0.271730i
\(261\) 0 0
\(262\) −106675. 52075.1i −1.55404 0.758625i
\(263\) −27445.5 + 15845.6i −0.396789 + 0.229086i −0.685097 0.728452i \(-0.740240\pi\)
0.288309 + 0.957537i \(0.406907\pi\)
\(264\) 0 0
\(265\) 108508. 187941.i 1.54514 2.67627i
\(266\) 7439.79 + 11038.2i 0.105147 + 0.156004i
\(267\) 0 0
\(268\) −102938. 41673.2i −1.43320 0.580213i
\(269\) 54892.9 0.758598 0.379299 0.925274i \(-0.376165\pi\)
0.379299 + 0.925274i \(0.376165\pi\)
\(270\) 0 0
\(271\) 106332.i 1.44785i −0.689877 0.723927i \(-0.742335\pi\)
0.689877 0.723927i \(-0.257665\pi\)
\(272\) −13244.9 + 3777.94i −0.179024 + 0.0510643i
\(273\) 0 0
\(274\) −37257.8 55278.5i −0.496268 0.736301i
\(275\) 99167.4 + 57254.3i 1.31130 + 0.757082i
\(276\) 0 0
\(277\) 25166.6 + 43589.8i 0.327993 + 0.568100i 0.982113 0.188290i \(-0.0602945\pi\)
−0.654121 + 0.756390i \(0.726961\pi\)
\(278\) −14718.0 7184.78i −0.190440 0.0929660i
\(279\) 0 0
\(280\) 37434.5 + 177025.i 0.477481 + 2.25797i
\(281\) −3048.20 5279.64i −0.0386039 0.0668640i 0.846078 0.533059i \(-0.178958\pi\)
−0.884682 + 0.466195i \(0.845624\pi\)
\(282\) 0 0
\(283\) −44494.8 25689.1i −0.555567 0.320757i 0.195797 0.980644i \(-0.437271\pi\)
−0.751364 + 0.659888i \(0.770604\pi\)
\(284\) 13231.4 + 94625.0i 0.164048 + 1.17319i
\(285\) 0 0
\(286\) −637.465 9162.05i −0.00779335 0.112011i
\(287\) 114576.i 1.39101i
\(288\) 0 0
\(289\) −80626.4 −0.965343
\(290\) 83322.2 5797.29i 0.990752 0.0689332i
\(291\) 0 0
\(292\) −68757.8 + 9614.43i −0.806411 + 0.112761i
\(293\) 45640.7 79051.9i 0.531639 0.920825i −0.467679 0.883898i \(-0.654910\pi\)
0.999318 0.0369270i \(-0.0117569\pi\)
\(294\) 0 0
\(295\) 12270.6 7084.43i 0.141001 0.0814068i
\(296\) −63649.3 + 13459.6i −0.726457 + 0.153620i
\(297\) 0 0
\(298\) 10298.9 21097.1i 0.115973 0.237570i
\(299\) 7604.82 4390.65i 0.0850642 0.0491118i
\(300\) 0 0
\(301\) −23291.0 + 40341.3i −0.257073 + 0.445263i
\(302\) −110021. + 74154.3i −1.20632 + 0.813059i
\(303\) 0 0
\(304\) −3859.43 13530.6i −0.0417615 0.146409i
\(305\) −44654.9 −0.480031
\(306\) 0 0
\(307\) 108180.i 1.14781i −0.818923 0.573904i \(-0.805428\pi\)
0.818923 0.573904i \(-0.194572\pi\)
\(308\) −26766.0 + 66115.6i −0.282152 + 0.696952i
\(309\) 0 0
\(310\) 43025.4 28999.2i 0.447714 0.301760i
\(311\) 86673.2 + 50040.8i 0.896116 + 0.517373i 0.875938 0.482424i \(-0.160243\pi\)
0.0201778 + 0.999796i \(0.493577\pi\)
\(312\) 0 0
\(313\) 75895.3 + 131455.i 0.774687 + 1.34180i 0.934970 + 0.354726i \(0.115426\pi\)
−0.160283 + 0.987071i \(0.551241\pi\)
\(314\) 38917.4 79722.0i 0.394716 0.808572i
\(315\) 0 0
\(316\) 47984.5 37435.8i 0.480537 0.374898i
\(317\) 56202.0 + 97344.7i 0.559285 + 0.968710i 0.997556 + 0.0698672i \(0.0222575\pi\)
−0.438271 + 0.898843i \(0.644409\pi\)
\(318\) 0 0
\(319\) 28514.5 + 16462.9i 0.280211 + 0.161780i
\(320\) 20389.2 190165.i 0.199113 1.85708i
\(321\) 0 0
\(322\) −68034.5 + 4733.62i −0.656172 + 0.0456543i
\(323\) 2957.02i 0.0283433i
\(324\) 0 0
\(325\) −48500.0 −0.459172
\(326\) −8691.05 124913.i −0.0817781 1.17537i
\(327\) 0 0
\(328\) −37544.9 + 115142.i −0.348982 + 1.07025i
\(329\) −83017.6 + 143791.i −0.766970 + 1.32843i
\(330\) 0 0
\(331\) −99528.9 + 57463.0i −0.908433 + 0.524484i −0.879927 0.475109i \(-0.842408\pi\)
−0.0285065 + 0.999594i \(0.509075\pi\)
\(332\) 39776.0 31031.8i 0.360865 0.281534i
\(333\) 0 0
\(334\) 93604.0 + 45694.1i 0.839076 + 0.409607i
\(335\) −280670. + 162045.i −2.50096 + 1.44393i
\(336\) 0 0
\(337\) −61646.2 + 106774.i −0.542808 + 0.940171i 0.455933 + 0.890014i \(0.349306\pi\)
−0.998741 + 0.0501573i \(0.984028\pi\)
\(338\) −61677.3 91509.1i −0.539874 0.800997i
\(339\) 0 0
\(340\) −15083.1 + 37257.1i −0.130476 + 0.322294i
\(341\) 20453.8 0.175900
\(342\) 0 0
\(343\) 68777.2i 0.584597i
\(344\) 36625.1 32908.2i 0.309501 0.278091i
\(345\) 0 0
\(346\) −35011.5 51945.7i −0.292454 0.433907i
\(347\) 82843.4 + 47829.7i 0.688017 + 0.397227i 0.802869 0.596156i \(-0.203306\pi\)
−0.114852 + 0.993383i \(0.536639\pi\)
\(348\) 0 0
\(349\) −21543.6 37314.5i −0.176875 0.306357i 0.763934 0.645295i \(-0.223266\pi\)
−0.940809 + 0.338938i \(0.889932\pi\)
\(350\) 338491. + 165239.i 2.76319 + 1.34889i
\(351\) 0 0
\(352\) 48563.1 57670.9i 0.391941 0.465448i
\(353\) −56436.9 97751.7i −0.452912 0.784467i 0.545653 0.838011i \(-0.316282\pi\)
−0.998565 + 0.0535440i \(0.982948\pi\)
\(354\) 0 0
\(355\) 241476. + 139416.i 1.91610 + 1.10626i
\(356\) 113020. 15803.6i 0.891771 0.124697i
\(357\) 0 0
\(358\) −10227.2 146992.i −0.0797977 1.14690i
\(359\) 223134.i 1.73132i 0.500632 + 0.865660i \(0.333101\pi\)
−0.500632 + 0.865660i \(0.666899\pi\)
\(360\) 0 0
\(361\) 127300. 0.976820
\(362\) −227295. + 15814.4i −1.73449 + 0.120680i
\(363\) 0 0
\(364\) −4183.70 29919.8i −0.0315760 0.225817i
\(365\) −101305. + 175465.i −0.760404 + 1.31706i
\(366\) 0 0
\(367\) −92257.6 + 53265.0i −0.684968 + 0.395466i −0.801724 0.597694i \(-0.796084\pi\)
0.116756 + 0.993161i \(0.462750\pi\)
\(368\) 69921.2 + 17536.9i 0.516313 + 0.129496i
\(369\) 0 0
\(370\) −83287.1 + 170613.i −0.608379 + 1.24626i
\(371\) 243708. 140705.i 1.77061 1.02226i
\(372\) 0 0
\(373\) −71440.5 + 123739.i −0.513484 + 0.889380i 0.486394 + 0.873740i \(0.338312\pi\)
−0.999878 + 0.0156403i \(0.995021\pi\)
\(374\) −13139.2 + 8855.83i −0.0939345 + 0.0633120i
\(375\) 0 0
\(376\) 130545. 117296.i 0.923389 0.829677i
\(377\) −13945.7 −0.0981197
\(378\) 0 0
\(379\) 95242.7i 0.663061i −0.943445 0.331530i \(-0.892435\pi\)
0.943445 0.331530i \(-0.107565\pi\)
\(380\) −38060.8 15408.4i −0.263579 0.106707i
\(381\) 0 0
\(382\) −129598. + 87349.4i −0.888121 + 0.598595i
\(383\) −46899.6 27077.5i −0.319721 0.184591i 0.331547 0.943439i \(-0.392429\pi\)
−0.651268 + 0.758848i \(0.725763\pi\)
\(384\) 0 0
\(385\) 104079. + 180270.i 0.702169 + 1.21619i
\(386\) 7110.07 14564.9i 0.0477199 0.0977538i
\(387\) 0 0
\(388\) 19297.9 + 24735.7i 0.128188 + 0.164309i
\(389\) 6513.23 + 11281.2i 0.0430425 + 0.0745518i 0.886744 0.462261i \(-0.152962\pi\)
−0.843702 + 0.536813i \(0.819628\pi\)
\(390\) 0 0
\(391\) −13120.2 7574.94i −0.0858196 0.0495480i
\(392\) −25100.3 + 76977.0i −0.163346 + 0.500943i
\(393\) 0 0
\(394\) −179046. + 12457.4i −1.15338 + 0.0802481i
\(395\) 177609.i 1.13834i
\(396\) 0 0
\(397\) 54407.2 0.345204 0.172602 0.984992i \(-0.444783\pi\)
0.172602 + 0.984992i \(0.444783\pi\)
\(398\) 15618.9 + 224484.i 0.0986014 + 1.41716i
\(399\) 0 0
\(400\) −286015. 276972.i −1.78759 1.73108i
\(401\) 25211.2 43667.1i 0.156785 0.271560i −0.776922 0.629596i \(-0.783220\pi\)
0.933708 + 0.358036i \(0.116554\pi\)
\(402\) 0 0
\(403\) −7502.54 + 4331.59i −0.0461953 + 0.0266709i
\(404\) −75781.0 97134.7i −0.464299 0.595130i
\(405\) 0 0
\(406\) 97329.6 + 47512.8i 0.590463 + 0.288243i
\(407\) −64816.0 + 37421.6i −0.391285 + 0.225909i
\(408\) 0 0
\(409\) −20416.9 + 35363.2i −0.122052 + 0.211400i −0.920577 0.390562i \(-0.872281\pi\)
0.798525 + 0.601962i \(0.205614\pi\)
\(410\) 197535. + 293078.i 1.17510 + 1.74347i
\(411\) 0 0
\(412\) 54718.4 + 22152.0i 0.322358 + 0.130503i
\(413\) 18373.2 0.107717
\(414\) 0 0
\(415\) 147226.i 0.854850i
\(416\) −5599.92 + 31438.3i −0.0323590 + 0.181666i
\(417\) 0 0
\(418\) −9046.86 13422.6i −0.0517780 0.0768217i
\(419\) −28866.9 16666.3i −0.164427 0.0949318i 0.415529 0.909580i \(-0.363597\pi\)
−0.579955 + 0.814648i \(0.696930\pi\)
\(420\) 0 0
\(421\) −4180.31 7240.51i −0.0235855 0.0408512i 0.853992 0.520287i \(-0.174175\pi\)
−0.877577 + 0.479435i \(0.840842\pi\)
\(422\) −262777. 128278.i −1.47558 0.720324i
\(423\) 0 0
\(424\) −291017. + 61539.7i −1.61877 + 0.342313i
\(425\) 41837.2 + 72464.1i 0.231625 + 0.401186i
\(426\) 0 0
\(427\) −50147.4 28952.6i −0.275038 0.158793i
\(428\) −30447.4 217746.i −0.166212 1.18867i
\(429\) 0 0
\(430\) −9973.45 143345.i −0.0539397 0.775255i
\(431\) 88445.3i 0.476124i −0.971250 0.238062i \(-0.923488\pi\)
0.971250 0.238062i \(-0.0765122\pi\)
\(432\) 0 0
\(433\) 119092. 0.635195 0.317598 0.948226i \(-0.397124\pi\)
0.317598 + 0.948226i \(0.397124\pi\)
\(434\) 67119.5 4669.95i 0.356344 0.0247932i
\(435\) 0 0
\(436\) 296474. 41456.1i 1.55960 0.218080i
\(437\) 7738.34 13403.2i 0.0405214 0.0701852i
\(438\) 0 0
\(439\) 103483. 59746.2i 0.536960 0.310014i −0.206886 0.978365i \(-0.566333\pi\)
0.743846 + 0.668351i \(0.233000\pi\)
\(440\) −45520.7 215264.i −0.235128 1.11190i
\(441\) 0 0
\(442\) 2944.07 6030.90i 0.0150696 0.0308700i
\(443\) 176414. 101853.i 0.898930 0.518998i 0.0220772 0.999756i \(-0.492972\pi\)
0.876853 + 0.480759i \(0.159639\pi\)
\(444\) 0 0
\(445\) 166518. 288418.i 0.840894 1.45647i
\(446\) 251777. 169698.i 1.26574 0.853114i
\(447\) 0 0
\(448\) 146193. 200336.i 0.728402 0.998165i
\(449\) −77156.2 −0.382717 −0.191359 0.981520i \(-0.561289\pi\)
−0.191359 + 0.981520i \(0.561289\pi\)
\(450\) 0 0
\(451\) 139326.i 0.684982i
\(452\) −60046.4 + 148322.i −0.293907 + 0.725989i
\(453\) 0 0
\(454\) −136781. + 92190.7i −0.663612 + 0.447276i
\(455\) −76353.2 44082.6i −0.368812 0.212934i
\(456\) 0 0
\(457\) −140420. 243215.i −0.672353 1.16455i −0.977235 0.212159i \(-0.931951\pi\)
0.304882 0.952390i \(-0.401383\pi\)
\(458\) 48403.1 99153.4i 0.230750 0.472690i
\(459\) 0 0
\(460\) 165866. 129403.i 0.783866 0.611544i
\(461\) −200811. 347814.i −0.944898 1.63661i −0.755956 0.654623i \(-0.772827\pi\)
−0.188942 0.981988i \(-0.560506\pi\)
\(462\) 0 0
\(463\) 51806.1 + 29910.3i 0.241668 + 0.139527i 0.615943 0.787791i \(-0.288775\pi\)
−0.374275 + 0.927318i \(0.622108\pi\)
\(464\) −82240.4 79640.5i −0.381988 0.369912i
\(465\) 0 0
\(466\) 197244. 13723.6i 0.908306 0.0631969i
\(467\) 208473.i 0.955909i 0.878385 + 0.477955i \(0.158622\pi\)
−0.878385 + 0.477955i \(0.841378\pi\)
\(468\) 0 0
\(469\) −420257. −1.91060
\(470\) −35548.9 510931.i −0.160928 2.31295i
\(471\) 0 0
\(472\) −18463.8 6020.59i −0.0828775 0.0270243i
\(473\) 28322.1 49055.4i 0.126591 0.219263i
\(474\) 0 0
\(475\) −74027.3 + 42739.7i −0.328099 + 0.189428i
\(476\) −41094.5 + 32060.4i −0.181372 + 0.141500i
\(477\) 0 0
\(478\) 402790. + 196628.i 1.76288 + 0.860575i
\(479\) −138667. + 80059.3i −0.604368 + 0.348932i −0.770758 0.637128i \(-0.780122\pi\)
0.166390 + 0.986060i \(0.446789\pi\)
\(480\) 0 0
\(481\) 15849.9 27452.8i 0.0685070 0.118658i
\(482\) 91876.1 + 136314.i 0.395466 + 0.586743i
\(483\) 0 0
\(484\) −55357.4 + 136740.i −0.236312 + 0.583720i
\(485\) 91556.4 0.389229
\(486\) 0 0
\(487\) 371960.i 1.56834i −0.620549 0.784168i \(-0.713090\pi\)
0.620549 0.784168i \(-0.286910\pi\)
\(488\) 40907.4 + 45527.9i 0.171776 + 0.191178i
\(489\) 0 0
\(490\) 132060. + 195935.i 0.550022 + 0.816055i
\(491\) −57863.4 33407.4i −0.240016 0.138574i 0.375168 0.926957i \(-0.377585\pi\)
−0.615184 + 0.788383i \(0.710918\pi\)
\(492\) 0 0
\(493\) 12029.8 + 20836.3i 0.0494955 + 0.0857288i
\(494\) 6160.99 + 3007.57i 0.0252462 + 0.0123243i
\(495\) 0 0
\(496\) −68980.8 17301.0i −0.280391 0.0703246i
\(497\) 180785. + 313129.i 0.731896 + 1.26768i
\(498\) 0 0
\(499\) 288151. + 166364.i 1.15723 + 0.668127i 0.950638 0.310301i \(-0.100430\pi\)
0.206591 + 0.978427i \(0.433763\pi\)
\(500\) −688282. + 96242.7i −2.75313 + 0.384971i
\(501\) 0 0
\(502\) 14117.2 + 202902.i 0.0560199 + 0.805153i
\(503\) 12673.0i 0.0500892i 0.999686 + 0.0250446i \(0.00797278\pi\)
−0.999686 + 0.0250446i \(0.992027\pi\)
\(504\) 0 0
\(505\) −359533. −1.40980
\(506\) 82730.6 5756.12i 0.323121 0.0224817i
\(507\) 0 0
\(508\) 41841.5 + 299230.i 0.162136 + 1.15952i
\(509\) −19452.7 + 33693.0i −0.0750834 + 0.130048i −0.901123 0.433564i \(-0.857256\pi\)
0.826039 + 0.563613i \(0.190589\pi\)
\(510\) 0 0
\(511\) −227530. + 131365.i −0.871360 + 0.503080i
\(512\) −212561. + 153419.i −0.810856 + 0.585245i
\(513\) 0 0
\(514\) −22478.3 + 46046.5i −0.0850817 + 0.174289i
\(515\) 149195. 86137.5i 0.562521 0.324772i
\(516\) 0 0
\(517\) 100950. 174851.i 0.377682 0.654164i
\(518\) −204151. + 137598.i −0.760837 + 0.512805i
\(519\) 0 0
\(520\) 62284.7 + 69319.7i 0.230343 + 0.256360i
\(521\) −28001.3 −0.103158 −0.0515790 0.998669i \(-0.516425\pi\)
−0.0515790 + 0.998669i \(0.516425\pi\)
\(522\) 0 0
\(523\) 306435.i 1.12030i 0.828391 + 0.560151i \(0.189257\pi\)
−0.828391 + 0.560151i \(0.810743\pi\)
\(524\) 440130. + 178181.i 1.60295 + 0.648932i
\(525\) 0 0
\(526\) 105118. 70849.6i 0.379931 0.256074i
\(527\) 12943.7 + 7473.06i 0.0466056 + 0.0269077i
\(528\) 0 0
\(529\) −100274. 173680.i −0.358326 0.620638i
\(530\) −380805. + 780076.i −1.35566 + 2.77706i
\(531\) 0 0
\(532\) −32752.0 41980.9i −0.115722 0.148330i
\(533\) −29505.7 51105.4i −0.103861 0.179892i
\(534\) 0 0
\(535\) −555671. 320817.i −1.94138 1.12086i
\(536\) 422330. + 137711.i 1.47002 + 0.479336i
\(537\) 0 0
\(538\) −219042. + 15240.2i −0.756768 + 0.0526534i
\(539\) 93145.3i 0.320615i
\(540\) 0 0
\(541\) 387269. 1.32318 0.661590 0.749866i \(-0.269882\pi\)
0.661590 + 0.749866i \(0.269882\pi\)
\(542\) 29521.5 + 424302.i 0.100494 + 1.44436i
\(543\) 0 0
\(544\) 51802.8 18752.6i 0.175047 0.0633669i
\(545\) 436812. 756581.i 1.47062 2.54720i
\(546\) 0 0
\(547\) 220183. 127123.i 0.735883 0.424862i −0.0846877 0.996408i \(-0.526989\pi\)
0.820570 + 0.571545i \(0.193656\pi\)
\(548\) 164019. + 210237.i 0.546177 + 0.700080i
\(549\) 0 0
\(550\) −411609. 200933.i −1.36069 0.664240i
\(551\) −21285.8 + 12289.3i −0.0701109 + 0.0404786i
\(552\) 0 0
\(553\) 115156. 199455.i 0.376560 0.652221i
\(554\) −112526. 166951.i −0.366633 0.543965i
\(555\) 0 0
\(556\) 60724.6 + 24583.6i 0.196433 + 0.0795235i
\(557\) 154243. 0.497159 0.248580 0.968611i \(-0.420036\pi\)
0.248580 + 0.968611i \(0.420036\pi\)
\(558\) 0 0
\(559\) 23991.6i 0.0767779i
\(560\) −198525. 696000.i −0.633053 2.21939i
\(561\) 0 0
\(562\) 13629.2 + 20221.4i 0.0431518 + 0.0640232i
\(563\) −188653. 108919.i −0.595177 0.343626i 0.171965 0.985103i \(-0.444988\pi\)
−0.767142 + 0.641477i \(0.778322\pi\)
\(564\) 0 0
\(565\) 233489. + 404415.i 0.731425 + 1.26686i
\(566\) 184682. + 90155.2i 0.576490 + 0.281422i
\(567\) 0 0
\(568\) −79069.4 373914.i −0.245082 1.15898i
\(569\) 112165. + 194275.i 0.346443 + 0.600057i 0.985615 0.169007i \(-0.0540561\pi\)
−0.639172 + 0.769064i \(0.720723\pi\)
\(570\) 0 0
\(571\) 227168. + 131156.i 0.696748 + 0.402268i 0.806135 0.591732i \(-0.201555\pi\)
−0.109387 + 0.993999i \(0.534889\pi\)
\(572\) 5087.42 + 36382.8i 0.0155491 + 0.111200i
\(573\) 0 0
\(574\) 31810.5 + 457201.i 0.0965488 + 1.38766i
\(575\) 437941.i 1.32458i
\(576\) 0 0
\(577\) 450994. 1.35462 0.677312 0.735696i \(-0.263145\pi\)
0.677312 + 0.735696i \(0.263145\pi\)
\(578\) 321728. 22384.8i 0.963015 0.0670034i
\(579\) 0 0
\(580\) −330876. + 46266.4i −0.983578 + 0.137534i
\(581\) 95456.3 165335.i 0.282782 0.489794i
\(582\) 0 0
\(583\) −296351. + 171099.i −0.871907 + 0.503396i
\(584\) 271699. 57454.6i 0.796640 0.168461i
\(585\) 0 0
\(586\) −160175. + 328117.i −0.466443 + 0.955505i
\(587\) −307738. + 177673.i −0.893111 + 0.515638i −0.874959 0.484197i \(-0.839112\pi\)
−0.0181523 + 0.999835i \(0.505778\pi\)
\(588\) 0 0
\(589\) −7634.26 + 13222.9i −0.0220058 + 0.0381151i
\(590\) −46997.1 + 31676.1i −0.135010 + 0.0909972i
\(591\) 0 0
\(592\) 250246. 71379.7i 0.714043 0.203672i
\(593\) −89819.5 −0.255424 −0.127712 0.991811i \(-0.540763\pi\)
−0.127712 + 0.991811i \(0.540763\pi\)
\(594\) 0 0
\(595\) 152106.i 0.429649i
\(596\) −35238.8 + 87044.4i −0.0992038 + 0.245046i
\(597\) 0 0
\(598\) −29126.9 + 19631.6i −0.0814502 + 0.0548976i
\(599\) −357687. 206511.i −0.996896 0.575558i −0.0895677 0.995981i \(-0.528549\pi\)
−0.907328 + 0.420422i \(0.861882\pi\)
\(600\) 0 0
\(601\) −129317. 223984.i −0.358020 0.620110i 0.629610 0.776912i \(-0.283215\pi\)
−0.987630 + 0.156802i \(0.949882\pi\)
\(602\) 81739.3 167442.i 0.225548 0.462032i
\(603\) 0 0
\(604\) 418434. 326447.i 1.14697 0.894828i
\(605\) 215256. + 372834.i 0.588090 + 1.01860i
\(606\) 0 0
\(607\) −267430. 154401.i −0.725825 0.419055i 0.0910678 0.995845i \(-0.470972\pi\)
−0.816893 + 0.576789i \(0.804305\pi\)
\(608\) 19157.1 + 52920.3i 0.0518229 + 0.143158i
\(609\) 0 0
\(610\) 178189. 12397.8i 0.478873 0.0333184i
\(611\) 85514.7i 0.229065i
\(612\) 0 0
\(613\) −464349. −1.23573 −0.617865 0.786284i \(-0.712002\pi\)
−0.617865 + 0.786284i \(0.712002\pi\)
\(614\) 30034.6 + 431675.i 0.0796681 + 1.14504i
\(615\) 0 0
\(616\) 88449.9 271256.i 0.233097 0.714855i
\(617\) −253688. + 439401.i −0.666392 + 1.15423i 0.312513 + 0.949913i \(0.398829\pi\)
−0.978906 + 0.204312i \(0.934504\pi\)
\(618\) 0 0
\(619\) −244884. + 141384.i −0.639115 + 0.368993i −0.784273 0.620415i \(-0.786964\pi\)
0.145159 + 0.989408i \(0.453631\pi\)
\(620\) −163635. + 127662.i −0.425690 + 0.332108i
\(621\) 0 0
\(622\) −359750. 175617.i −0.929865 0.453927i
\(623\) 373999. 215929.i 0.963595 0.556332i
\(624\) 0 0
\(625\) −528069. + 914643.i −1.35186 + 2.34149i
\(626\) −339346. 503479.i −0.865951 1.28479i
\(627\) 0 0
\(628\) −133161. + 328924.i −0.337642 + 0.834019i
\(629\) −54689.8 −0.138231
\(630\) 0 0
\(631\) 403620.i 1.01371i 0.862031 + 0.506855i \(0.169192\pi\)
−0.862031 + 0.506855i \(0.830808\pi\)
\(632\) −181082. + 162704.i −0.453357 + 0.407347i
\(633\) 0 0
\(634\) −251292. 372836.i −0.625173 0.927554i
\(635\) 763614. + 440873.i 1.89377 + 1.09337i
\(636\) 0 0
\(637\) −19725.8 34166.1i −0.0486134 0.0842008i
\(638\) −118354. 57776.0i −0.290764 0.141940i
\(639\) 0 0
\(640\) −28563.4 + 764487.i −0.0697350 + 1.86642i
\(641\) −181028. 313549.i −0.440584 0.763114i 0.557149 0.830413i \(-0.311895\pi\)
−0.997733 + 0.0672990i \(0.978562\pi\)
\(642\) 0 0
\(643\) −346651. 200139.i −0.838437 0.484072i 0.0182957 0.999833i \(-0.494176\pi\)
−0.856733 + 0.515761i \(0.827509\pi\)
\(644\) 270167. 37777.6i 0.651420 0.0910883i
\(645\) 0 0
\(646\) −820.975 11799.6i −0.00196727 0.0282749i
\(647\) 98990.1i 0.236474i 0.992985 + 0.118237i \(0.0377242\pi\)
−0.992985 + 0.118237i \(0.962276\pi\)
\(648\) 0 0
\(649\) −22341.9 −0.0530434
\(650\) 193532. 13465.3i 0.458064 0.0318706i
\(651\) 0 0
\(652\) 69360.7 + 496035.i 0.163162 + 1.16686i
\(653\) −269165. + 466208.i −0.631237 + 1.09333i 0.356062 + 0.934462i \(0.384119\pi\)
−0.987299 + 0.158872i \(0.949214\pi\)
\(654\) 0 0
\(655\) 1.20006e6 692852.i 2.79717 1.61495i
\(656\) 117850. 469879.i 0.273856 1.09189i
\(657\) 0 0
\(658\) 291348. 596824.i 0.672915 1.37846i
\(659\) −126219. + 72872.6i −0.290639 + 0.167801i −0.638230 0.769846i \(-0.720333\pi\)
0.347591 + 0.937646i \(0.387000\pi\)
\(660\) 0 0
\(661\) 126176. 218543.i 0.288784 0.500189i −0.684736 0.728792i \(-0.740082\pi\)
0.973520 + 0.228603i \(0.0734157\pi\)
\(662\) 381201. 256930.i 0.869838 0.586273i
\(663\) 0 0
\(664\) −150105. + 134871.i −0.340454 + 0.305903i
\(665\) −155388. −0.351377
\(666\) 0 0
\(667\) 125925.i 0.283049i
\(668\) −386199. 156348.i −0.865483 0.350380i
\(669\) 0 0
\(670\) 1.07498e6 724541.i 2.39471 1.61404i
\(671\) 60979.7 + 35206.7i 0.135438 + 0.0781951i
\(672\) 0 0
\(673\) −327332. 566956.i −0.722701 1.25175i −0.959913 0.280297i \(-0.909567\pi\)
0.237213 0.971458i \(-0.423766\pi\)
\(674\) 216346. 443182.i 0.476243 0.975580i
\(675\) 0 0
\(676\) 271520. + 348030.i 0.594168 + 0.761594i
\(677\) −106756. 184907.i −0.232924 0.403437i 0.725743 0.687966i \(-0.241496\pi\)
−0.958667 + 0.284529i \(0.908163\pi\)
\(678\) 0 0
\(679\) 102818. + 59361.8i 0.223012 + 0.128756i
\(680\) 49842.9 152857.i 0.107792 0.330572i
\(681\) 0 0
\(682\) −81617.9 + 5678.71i −0.175476 + 0.0122090i
\(683\) 885039.i 1.89724i 0.316425 + 0.948618i \(0.397517\pi\)
−0.316425 + 0.948618i \(0.602483\pi\)
\(684\) 0 0
\(685\) 778168. 1.65841
\(686\) −19095.0 274445.i −0.0405762 0.583187i
\(687\) 0 0
\(688\) −137011. + 141484.i −0.289453 + 0.298902i
\(689\) 72468.6 125519.i 0.152655 0.264406i
\(690\) 0 0
\(691\) 382656. 220927.i 0.801406 0.462692i −0.0425567 0.999094i \(-0.513550\pi\)
0.843963 + 0.536402i \(0.180217\pi\)
\(692\) 154130. + 197561.i 0.321866 + 0.412562i
\(693\) 0 0
\(694\) −343854. 167857.i −0.713929 0.348514i
\(695\) 165571. 95592.6i 0.342780 0.197904i
\(696\) 0 0
\(697\) −50904.6 + 88169.3i −0.104783 + 0.181490i
\(698\) 96326.3 + 142917.i 0.197712 + 0.293341i
\(699\) 0 0
\(700\) −1.39658e6 565386.i −2.85015 1.15385i
\(701\) −340679. −0.693281 −0.346640 0.937998i \(-0.612678\pi\)
−0.346640 + 0.937998i \(0.612678\pi\)
\(702\) 0 0
\(703\) 55869.5i 0.113048i
\(704\) −177772. + 243610.i −0.358690 + 0.491530i
\(705\) 0 0
\(706\) 252343. + 374395.i 0.506269 + 0.751139i
\(707\) −403755. 233108.i −0.807755 0.466357i
\(708\) 0 0
\(709\) 292720. + 507006.i 0.582318 + 1.00860i 0.995204 + 0.0978214i \(0.0311874\pi\)
−0.412886 + 0.910783i \(0.635479\pi\)
\(710\) −1.00228e6 489278.i −1.98826 0.970597i
\(711\) 0 0
\(712\) −446600. + 94440.0i −0.880966 + 0.186293i
\(713\) −39113.0 67745.8i −0.0769383 0.133261i
\(714\) 0 0
\(715\) 92846.3 + 53604.8i 0.181615 + 0.104856i
\(716\) 81620.2 + 583709.i 0.159210 + 1.13860i
\(717\) 0 0
\(718\) −61950.0 890385.i −0.120169 1.72715i
\(719\) 306988.i 0.593832i 0.954904 + 0.296916i \(0.0959581\pi\)
−0.954904 + 0.296916i \(0.904042\pi\)
\(720\) 0 0
\(721\) 223394. 0.429735
\(722\) −507973. + 35343.1i −0.974464 + 0.0678000i
\(723\) 0 0
\(724\) 902595. 126210.i 1.72193 0.240778i
\(725\) −347749. + 602319.i −0.661592 + 1.14591i
\(726\) 0 0
\(727\) −488481. + 282025.i −0.924227 + 0.533603i −0.884981 0.465627i \(-0.845829\pi\)
−0.0392459 + 0.999230i \(0.512496\pi\)
\(728\) 25001.2 + 118229.i 0.0471736 + 0.223081i
\(729\) 0 0
\(730\) 355526. 728293.i 0.667154 1.36666i
\(731\) 35846.0 20695.7i 0.0670821 0.0387298i
\(732\) 0 0
\(733\) −290960. + 503957.i −0.541533 + 0.937963i 0.457283 + 0.889321i \(0.348823\pi\)
−0.998816 + 0.0486418i \(0.984511\pi\)
\(734\) 353352. 238160.i 0.655867 0.442055i
\(735\) 0 0
\(736\) −283879. 50565.6i −0.524056 0.0933469i
\(737\) 511037. 0.940843
\(738\) 0 0
\(739\) 193774.i 0.354818i 0.984137 + 0.177409i \(0.0567715\pi\)
−0.984137 + 0.177409i \(0.943228\pi\)
\(740\) 284977. 703930.i 0.520411 1.28548i
\(741\) 0 0
\(742\) −933417. + 629124.i −1.69538 + 1.14269i
\(743\) −76480.8 44156.2i −0.138540 0.0799861i 0.429128 0.903244i \(-0.358821\pi\)
−0.567668 + 0.823258i \(0.692154\pi\)
\(744\) 0 0
\(745\) 137025. + 237334.i 0.246881 + 0.427610i
\(746\) 250719. 513595.i 0.450514 0.922875i
\(747\) 0 0
\(748\) 49971.3 38985.8i 0.0893135 0.0696792i
\(749\) −416012. 720554.i −0.741553 1.28441i
\(750\) 0 0
\(751\) 474180. + 273768.i 0.840743 + 0.485403i 0.857517 0.514456i \(-0.172006\pi\)
−0.0167738 + 0.999859i \(0.505340\pi\)
\(752\) −488355. + 504298.i −0.863575 + 0.891767i
\(753\) 0 0
\(754\) 55648.1 3871.81i 0.0978831 0.00681038i
\(755\) 1.54879e6i 2.71705i
\(756\) 0 0
\(757\) −45164.0 −0.0788135 −0.0394068 0.999223i \(-0.512547\pi\)
−0.0394068 + 0.999223i \(0.512547\pi\)
\(758\) 26442.8 + 380052.i 0.0460223 + 0.661462i
\(759\) 0 0
\(760\) 156154. + 50918.0i 0.270350 + 0.0881545i
\(761\) −100185. + 173525.i −0.172995 + 0.299636i −0.939465 0.342644i \(-0.888678\pi\)
0.766471 + 0.642279i \(0.222011\pi\)
\(762\) 0 0
\(763\) 981079. 566426.i 1.68521 0.972959i
\(764\) 492891. 384536.i 0.844432 0.658795i
\(765\) 0 0
\(766\) 194663. + 95027.7i 0.331762 + 0.161954i
\(767\) 8195.11 4731.45i 0.0139304 0.00804273i
\(768\) 0 0
\(769\) −212834. + 368639.i −0.359905 + 0.623374i −0.987945 0.154807i \(-0.950524\pi\)
0.628039 + 0.778181i \(0.283858\pi\)
\(770\) −465362. 690446.i −0.784891 1.16452i
\(771\) 0 0
\(772\) −24328.0 + 60093.2i −0.0408198 + 0.100830i
\(773\) −199528. −0.333922 −0.166961 0.985964i \(-0.553395\pi\)
−0.166961 + 0.985964i \(0.553395\pi\)
\(774\) 0 0
\(775\) 432051.i 0.719335i
\(776\) −83872.9 93346.4i −0.139283 0.155015i
\(777\) 0 0
\(778\) −29122.2 <