Properties

Label 108.5.f.a.91.16
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 91.16
Character \(\chi\) \(=\) 108.91
Dual form 108.5.f.a.19.16

$q$-expansion

\(f(q)\) \(=\) \(q+(2.23562 - 3.31693i) q^{2} +(-6.00404 - 14.8308i) q^{4} +(23.3466 - 40.4374i) q^{5} +(-52.4363 + 30.2741i) q^{7} +(-62.6153 - 13.2409i) q^{8} +O(q^{10})\) \(q+(2.23562 - 3.31693i) q^{2} +(-6.00404 - 14.8308i) q^{4} +(23.3466 - 40.4374i) q^{5} +(-52.4363 + 30.2741i) q^{7} +(-62.6153 - 13.2409i) q^{8} +(-81.9341 - 167.841i) q^{10} +(63.7631 - 36.8136i) q^{11} +(15.5924 - 27.0068i) q^{13} +(-16.8104 + 241.609i) q^{14} +(-183.903 + 178.089i) q^{16} -53.8013 q^{17} +54.9619i q^{19} +(-739.891 - 103.459i) q^{20} +(20.4416 - 293.799i) q^{22} +(-243.863 - 140.795i) q^{23} +(-777.624 - 1346.88i) q^{25} +(-54.7210 - 112.096i) q^{26} +(763.818 + 595.904i) q^{28} +(-223.597 - 387.282i) q^{29} +(240.584 + 138.901i) q^{31} +(179.572 + 1008.13i) q^{32} +(-120.279 + 178.455i) q^{34} +2827.19i q^{35} +1016.51 q^{37} +(182.305 + 122.874i) q^{38} +(-1997.28 + 2222.87i) q^{40} +(946.158 - 1638.79i) q^{41} +(666.266 - 384.669i) q^{43} +(-928.811 - 724.625i) q^{44} +(-1012.19 + 494.115i) q^{46} +(2374.81 - 1371.10i) q^{47} +(632.546 - 1095.60i) q^{49} +(-6205.98 - 431.792i) q^{50} +(-494.148 - 69.0969i) q^{52} +4647.69 q^{53} -3437.89i q^{55} +(3684.18 - 1201.32i) q^{56} +(-1784.46 - 124.157i) q^{58} +(-262.792 - 151.723i) q^{59} +(-478.174 - 828.222i) q^{61} +(998.577 - 487.469i) q^{62} +(3745.36 + 1658.17i) q^{64} +(-728.057 - 1261.03i) q^{65} +(6010.96 + 3470.43i) q^{67} +(323.026 + 797.915i) q^{68} +(9377.58 + 6320.51i) q^{70} -5971.60i q^{71} -4339.17 q^{73} +(2272.53 - 3371.70i) q^{74} +(815.127 - 329.993i) q^{76} +(-2229.00 + 3860.75i) q^{77} +(-3294.15 + 1901.88i) q^{79} +(2907.96 + 11594.3i) q^{80} +(-3320.52 - 6802.05i) q^{82} +(-2730.64 + 1576.53i) q^{83} +(-1256.08 + 2175.59i) q^{85} +(213.596 - 3069.93i) q^{86} +(-4479.99 + 1460.82i) q^{88} +7132.44 q^{89} +1888.18i q^{91} +(-623.925 + 4462.02i) q^{92} +(761.331 - 10942.3i) q^{94} +(2222.52 + 1283.17i) q^{95} +(980.405 + 1698.11i) q^{97} +(-2219.91 - 4547.46i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.23562 3.31693i 0.558904 0.829232i
\(3\) 0 0
\(4\) −6.00404 14.8308i −0.375253 0.926923i
\(5\) 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 −0.928217 0.372040i \(-0.878659\pi\)
−0.141913 + 0.989879i \(0.545325\pi\)
\(8\) −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 −0.212813 0.977093i \(-0.568263\pi\)
0.739781 + 0.672848i \(0.234929\pi\)
\(12\) 0 0
\(13\) 15.5924 27.0068i 0.0922626 0.159803i −0.816200 0.577769i \(-0.803923\pi\)
0.908463 + 0.417966i \(0.137257\pi\)
\(14\) −16.8104 + 241.609i −0.0857671 + 1.23270i
\(15\) 0 0
\(16\) −183.903 + 178.089i −0.718371 + 0.695660i
\(17\) −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 \(0.0242546\pi\)
−0.997098 + 0.0761245i \(0.975745\pi\)
\(20\) −739.891 103.459i −1.84973 0.258648i
\(21\) 0 0
\(22\) 20.4416 293.799i 0.0422346 0.607023i
\(23\) −243.863 140.795i −0.460990 0.266152i 0.251471 0.967865i \(-0.419086\pi\)
−0.712460 + 0.701712i \(0.752419\pi\)
\(24\) 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 0.619923 0.784663i \(-0.287164\pi\)
−0.369576 + 0.929200i \(0.620497\pi\)
\(32\) 179.572 + 1008.13i 0.175364 + 0.984504i
\(33\) 0 0
\(34\) −120.279 + 178.455i −0.104048 + 0.154373i
\(35\) 2827.19i 2.30791i
\(36\) 0 0
\(37\) 1016.51 0.742522 0.371261 0.928528i \(-0.378925\pi\)
0.371261 + 0.928528i \(0.378925\pi\)
\(38\) 182.305 + 122.874i 0.126250 + 0.0850926i
\(39\) 0 0
\(40\) −1997.28 + 2222.87i −1.24830 + 1.38930i
\(41\) 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 −0.308891 0.951098i \(-0.599958\pi\)
0.669229 + 0.743056i \(0.266624\pi\)
\(44\) −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 0.145502 0.989358i \(-0.453520\pi\)
0.929560 + 0.368671i \(0.120187\pi\)
\(48\) 0 0
\(49\) 632.546 1095.60i 0.263451 0.456311i
\(50\) −6205.98 431.792i −2.48239 0.172717i
\(51\) 0 0
\(52\) −494.148 69.0969i −0.182747 0.0255536i
\(53\) 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
\(56\) 3684.18 1201.32i 1.17480 0.383074i
\(57\) 0 0
\(58\) −1784.46 124.157i −0.530459 0.0369076i
\(59\) −262.792 151.723i −0.0754934 0.0435861i 0.461778 0.886995i \(-0.347212\pi\)
−0.537272 + 0.843409i \(0.680545\pi\)
\(60\) 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 0.986665 0.162762i \(-0.0520403\pi\)
0.352376 + 0.935858i \(0.385374\pi\)
\(68\) 323.026 + 797.915i 0.0698585 + 0.172559i
\(69\) 0 0
\(70\) 9377.58 + 6320.51i 1.91379 + 1.28990i
\(71\) 5971.60i 1.18461i −0.805715 0.592303i \(-0.798219\pi\)
0.805715 0.592303i \(-0.201781\pi\)
\(72\) 0 0
\(73\) −4339.17 −0.814257 −0.407128 0.913371i \(-0.633470\pi\)
−0.407128 + 0.913371i \(0.633470\pi\)
\(74\) 2272.53 3371.70i 0.414999 0.615724i
\(75\) 0 0
\(76\) 815.127 329.993i 0.141123 0.0571318i
\(77\) −2229.00 + 3860.75i −0.375949 + 0.651163i
\(78\) 0 0
\(79\) −3294.15 + 1901.88i −0.527824 + 0.304740i −0.740130 0.672464i \(-0.765236\pi\)
0.212306 + 0.977203i \(0.431903\pi\)
\(80\) 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 −0.684919 0.728619i \(-0.740163\pi\)
0.288543 + 0.957467i \(0.406829\pi\)
\(84\) 0 0
\(85\) −1256.08 + 2175.59i −0.173851 + 0.301119i
\(86\) 213.596 3069.93i 0.0288799 0.415080i
\(87\) 0 0
\(88\) −4479.99 + 1460.82i −0.578512 + 0.188639i
\(89\) 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
\(92\) −623.925 + 4462.02i −0.0737152 + 0.527176i
\(93\) 0 0
\(94\) 761.331 10942.3i 0.0861624 1.23838i
\(95\) 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 0.341793 0.939775i \(-0.388966\pi\)
−0.642973 + 0.765889i \(0.722299\pi\)
\(104\) −1333.92 + 1484.58i −0.123328 + 0.137258i
\(105\) 0 0
\(106\) 10390.5 15416.1i 0.924747 1.37203i
\(107\) 13741.5i 1.20024i 0.799911 + 0.600118i \(0.204880\pi\)
−0.799911 + 0.600118i \(0.795120\pi\)
\(108\) 0 0
\(109\) 18709.9 1.57478 0.787388 0.616458i \(-0.211433\pi\)
0.787388 + 0.616458i \(0.211433\pi\)
\(110\) −11403.2 7685.80i −0.942416 0.635190i
\(111\) 0 0
\(112\) 4251.71 14905.8i 0.338944 1.18828i
\(113\) −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
\(122\) −3816.17 265.516i −0.256394 0.0178390i
\(123\) 0 0
\(124\) 615.534 4402.00i 0.0400321 0.286291i
\(125\) −43436.1 −2.77991
\(126\) 0 0
\(127\) 18883.8i 1.17080i −0.810745 0.585400i \(-0.800937\pi\)
0.810745 0.585400i \(-0.199063\pi\)
\(128\) 13873.2 8716.06i 0.846753 0.531986i
\(129\) 0 0
\(130\) −5810.41 404.269i −0.343811 0.0239212i
\(131\) −25700.9 14838.4i −1.49763 0.864660i −0.497639 0.867384i \(-0.665799\pi\)
−0.999996 + 0.00272458i \(0.999133\pi\)
\(132\) 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 0.405421 0.914130i \(-0.367125\pi\)
−0.588949 + 0.808170i \(0.700458\pi\)
\(140\) 41929.3 16974.5i 2.13925 0.866048i
\(141\) 0 0
\(142\) −19807.4 13350.2i −0.982314 0.662081i
\(143\) 2296.05i 0.112282i
\(144\) 0 0
\(145\) −20880.9 −0.993147
\(146\) −9700.73 + 14392.7i −0.455091 + 0.675208i
\(147\) 0 0
\(148\) −6103.19 15075.7i −0.278633 0.688261i
\(149\) −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 −0.973043 0.230622i \(-0.925924\pi\)
−0.286797 + 0.957991i \(0.592591\pi\)
\(152\) 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 \(0.315202\pi\)
\(158\) −1056.06 + 15178.3i −0.0423033 + 0.608009i
\(159\) 0 0
\(160\) 44958.6 + 16275.0i 1.75620 + 0.635741i
\(161\) 17049.7 0.657758
\(162\) 0 0
\(163\) 31303.8i 1.17821i −0.808057 0.589104i \(-0.799481\pi\)
0.808057 0.589104i \(-0.200519\pi\)
\(164\) −29985.3 4192.86i −1.11486 0.155891i
\(165\) 0 0
\(166\) −875.403 + 12581.8i −0.0317682 + 0.456592i
\(167\) 22551.7 + 13020.2i 0.808622 + 0.466858i 0.846477 0.532425i \(-0.178719\pi\)
−0.0378548 + 0.999283i \(0.512052\pi\)
\(168\) 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
\(176\) −5170.12 + 18125.6i −0.166907 + 0.585151i
\(177\) 0 0
\(178\) 15945.4 23657.8i 0.503264 0.746680i
\(179\) 36836.7i 1.14967i −0.818268 0.574837i \(-0.805065\pi\)
0.818268 0.574837i \(-0.194935\pi\)
\(180\) 0 0
\(181\) 56961.0 1.73868 0.869342 0.494211i \(-0.164543\pi\)
0.869342 + 0.494211i \(0.164543\pi\)
\(182\) 6262.97 + 4221.25i 0.189076 + 0.127438i
\(183\) 0 0
\(184\) 13405.3 + 12044.9i 0.395952 + 0.355768i
\(185\) 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 −0.886029 0.463630i \(-0.846547\pi\)
−0.0414986 + 0.999139i \(0.513213\pi\)
\(192\) 0 0
\(193\) −2025.97 + 3509.08i −0.0543898 + 0.0942059i −0.891938 0.452157i \(-0.850655\pi\)
0.837549 + 0.546363i \(0.183988\pi\)
\(194\) 7824.33 + 544.391i 0.207895 + 0.0144646i
\(195\) 0 0
\(196\) −20046.5 2803.10i −0.521826 0.0729670i
\(197\) 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 \(0.251438\pi\)
−0.703905 + 0.710294i \(0.748562\pi\)
\(200\) 30857.2 + 94632.0i 0.771430 + 2.36580i
\(201\) 0 0
\(202\) −30725.4 2137.77i −0.752999 0.0523912i
\(203\) 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 −0.425551 0.904935i \(-0.639920\pi\)
−0.996472 + 0.0839298i \(0.973253\pi\)
\(212\) −27905.0 68928.9i −0.620883 1.53366i
\(213\) 0 0
\(214\) 45579.6 + 30720.7i 0.995275 + 0.670817i
\(215\) 35922.8i 0.777129i
\(216\) 0 0
\(217\) −16820.4 −0.357205
\(218\) 41828.2 62059.5i 0.880149 1.30586i
\(219\) 0 0
\(220\) −50986.5 + 20641.2i −1.05344 + 0.426472i
\(221\) −838.891 + 1453.00i −0.0171760 + 0.0297496i
\(222\) 0 0
\(223\) 65737.1 37953.3i 1.32191 0.763203i 0.337873 0.941192i \(-0.390292\pi\)
0.984032 + 0.177989i \(0.0569591\pi\)
\(224\) −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 −0.804756 0.593606i \(-0.797704\pi\)
0.111700 + 0.993742i \(0.464371\pi\)
\(228\) 0 0
\(229\) −13792.1 + 23888.7i −0.263003 + 0.455534i −0.967038 0.254630i \(-0.918046\pi\)
0.704036 + 0.710165i \(0.251379\pi\)
\(230\) −3650.43 + 52466.3i −0.0690063 + 0.991801i
\(231\) 0 0
\(232\) 8872.66 + 27210.4i 0.164846 + 0.505544i
\(233\) −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
\(236\) −672.355 + 4808.36i −0.0120719 + 0.0863323i
\(237\) 0 0
\(238\) 904.420 12998.9i 0.0159667 0.229484i
\(239\) 97042.8 + 56027.7i 1.69890 + 0.980859i 0.946808 + 0.321800i \(0.104288\pi\)
0.752091 + 0.659060i \(0.229045\pi\)
\(240\) 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
\(248\) −13225.0 11882.9i −0.215027 0.193205i
\(249\) 0 0
\(250\) −97106.5 + 144075.i −1.55370 + 2.30519i
\(251\) 50848.1i 0.807099i 0.914958 + 0.403550i \(0.132224\pi\)
−0.914958 + 0.403550i \(0.867776\pi\)
\(252\) 0 0
\(253\) −20732.7 −0.323902
\(254\) −62636.4 42217.0i −0.970865 0.654365i
\(255\) 0 0
\(256\) 2104.60 65502.2i 0.0321137 0.999484i
\(257\) 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 −0.288309 0.957537i \(-0.593093\pi\)
0.685097 + 0.728452i \(0.259760\pi\)
\(264\) 0 0
\(265\) 108508. 187941.i 1.54514 2.67627i
\(266\) −13279.3 923.929i −0.187677 0.0130580i
\(267\) 0 0
\(268\) 15379.1 109984.i 0.214121 1.53129i
\(269\) 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 \(0.257665\pi\)
−0.689877 + 0.723927i \(0.742335\pi\)
\(272\) 9894.23 9581.43i 0.133735 0.129507i
\(273\) 0 0
\(274\) 66501.5 + 4626.96i 0.885789 + 0.0616303i
\(275\) −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 0.751364 0.659888i \(-0.229396\pi\)
−0.195797 + 0.980644i \(0.562729\pi\)
\(284\) −88563.4 + 35853.7i −1.09804 + 0.444527i
\(285\) 0 0
\(286\) −7615.83 5133.08i −0.0931076 0.0627547i
\(287\) 114576.i 1.39101i
\(288\) 0 0
\(289\) −80626.4 −0.965343
\(290\) −46681.7 + 69260.5i −0.555074 + 0.823550i
\(291\) 0 0
\(292\) 26052.6 + 64353.3i 0.305552 + 0.754753i
\(293\) 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
\(302\) −9209.03 + 132358.i −0.100972 + 1.45123i
\(303\) 0 0
\(304\) −9788.11 10107.7i −0.105914 0.109371i
\(305\) −44654.9 −0.480031
\(306\) 0 0
\(307\) 108180.i 1.14781i 0.818923 + 0.573904i \(0.194572\pi\)
−0.818923 + 0.573904i \(0.805428\pi\)
\(308\) 70640.8 + 9877.73i 0.744654 + 0.104125i
\(309\) 0 0
\(310\) 3601.33 51760.6i 0.0374749 0.538612i
\(311\) −86673.2 50040.8i −0.896116 0.517373i −0.0201778 0.999796i \(-0.506423\pi\)
−0.875938 + 0.482424i \(0.839757\pi\)
\(312\) 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
\(320\) 154493. 112740.i 1.50872 1.10098i
\(321\) 0 0
\(322\) 38116.7 56552.8i 0.367624 0.545434i
\(323\) 2957.02i 0.0283433i
\(324\) 0 0
\(325\) −48500.0 −0.459172
\(326\) −103832. 69983.3i −0.977008 0.658505i
\(327\) 0 0
\(328\) −80943.1 + 90085.6i −0.752371 + 0.837351i
\(329\) −83017.6 + 143791.i −0.766970 + 1.32843i
\(330\) 0 0
\(331\) 99528.9 57463.0i 0.908433 0.524484i 0.0285065 0.999594i \(-0.490925\pi\)
0.879927 + 0.475109i \(0.157592\pi\)
\(332\) 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 \(0.984028\pi\)
\(338\) 110088. + 7659.55i 0.963621 + 0.0670456i
\(339\) 0 0
\(340\) 39807.2 + 5566.25i 0.344353 + 0.0481509i
\(341\) 20453.8 0.175900
\(342\) 0 0
\(343\) 68777.2i 0.584597i
\(344\) −46811.9 + 15264.2i −0.395584 + 0.128990i
\(345\) 0 0
\(346\) 62492.0 + 4347.99i 0.522002 + 0.0363192i
\(347\) −82843.4 47829.7i −0.688017 0.397227i 0.114852 0.993383i \(-0.463361\pi\)
−0.802869 + 0.596156i \(0.796694\pi\)
\(348\) 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
\(356\) −42823.5 105780.i −0.337895 0.834645i
\(357\) 0 0
\(358\) −122185. 82352.8i −0.953348 0.642558i
\(359\) 223134.i 1.73132i −0.500632 0.865660i \(-0.666899\pi\)
0.500632 0.865660i \(-0.333101\pi\)
\(360\) 0 0
\(361\) 127300. 0.976820
\(362\) 127343. 188936.i 0.971758 1.44177i
\(363\) 0 0
\(364\) 28003.2 11336.7i 0.211351 0.0855628i
\(365\) −101305. + 175465.i −0.760404 + 1.31706i
\(366\) 0 0
\(367\) 92257.6 53265.0i 0.684968 0.395466i −0.116756 0.993161i \(-0.537250\pi\)
0.801724 + 0.597694i \(0.203916\pi\)
\(368\) 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 \(0.995021\pi\)
\(374\) −1099.78 + 15806.8i −0.00786256 + 0.113006i
\(375\) 0 0
\(376\) −166854. + 54407.1i −1.18022 + 0.384840i
\(377\) −13945.7 −0.0981197
\(378\) 0 0
\(379\) 95242.7i 0.663061i 0.943445 + 0.331530i \(0.107565\pi\)
−0.943445 + 0.331530i \(0.892435\pi\)
\(380\) 5686.32 40665.8i 0.0393789 0.281619i
\(381\) 0 0
\(382\) −10847.7 + 155910.i −0.0743381 + 1.06843i
\(383\) 46899.6 + 27077.5i 0.319721 + 0.184591i 0.651268 0.758848i \(-0.274237\pi\)
−0.331547 + 0.943439i \(0.607571\pi\)
\(384\) 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
\(392\) −54113.9 + 60226.0i −0.352157 + 0.391933i
\(393\) 0 0
\(394\) 100311. 148829.i 0.646185 0.958730i
\(395\) 177609.i 1.13834i
\(396\) 0 0
\(397\) 54407.2 0.345204 0.172602 0.984992i \(-0.444783\pi\)
0.172602 + 0.984992i \(0.444783\pi\)
\(398\) 186599. + 125768.i 1.17800 + 0.793972i
\(399\) 0 0
\(400\) 382872. + 109210.i 2.39295 + 0.682560i
\(401\) 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 \(0.205614\pi\)
\(410\) −352580. 24531.4i −2.09744 0.145933i
\(411\) 0 0
\(412\) −8174.97 + 58463.5i −0.0481606 + 0.344422i
\(413\) 18373.2 0.107717
\(414\) 0 0
\(415\) 147226.i 0.854850i
\(416\) 30026.4 + 10869.5i 0.173507 + 0.0628091i
\(417\) 0 0
\(418\) 16147.7 + 1123.51i 0.0924186 + 0.00643018i
\(419\) 28866.9 + 16666.3i 0.164427 + 0.0949318i 0.579955 0.814648i \(-0.303070\pi\)
−0.415529 + 0.909580i \(0.636403\pi\)
\(420\) 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
\(428\) 203797. 82504.6i 1.11253 0.450392i
\(429\) 0 0
\(430\) −119153. 80309.6i −0.644421 0.434341i
\(431\) 88445.3i 0.476124i 0.971250 + 0.238062i \(0.0765122\pi\)
−0.971250 + 0.238062i \(0.923488\pi\)
\(432\) 0 0
\(433\) 119092. 0.635195 0.317598 0.948226i \(-0.397124\pi\)
0.317598 + 0.948226i \(0.397124\pi\)
\(434\) −37604.0 + 55792.2i −0.199643 + 0.296206i
\(435\) 0 0
\(436\) −112335. 277482.i −0.590939 1.45970i
\(437\) 7738.34 13403.2i 0.0405214 0.0701852i
\(438\) 0 0
\(439\) −103483. + 59746.2i −0.536960 + 0.310014i −0.743846 0.668351i \(-0.767000\pi\)
0.206886 + 0.978365i \(0.433667\pi\)
\(440\) −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 −0.876853 0.480759i \(-0.840361\pi\)
−0.0220772 + 0.999756i \(0.507028\pi\)
\(444\) 0 0
\(445\) 166518. 288418.i 0.840894 1.45647i
\(446\) 21074.4 302894.i 0.105946 1.52272i
\(447\) 0 0
\(448\) −246592. + 26439.2i −1.22864 + 0.131732i
\(449\) −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
\(452\) 158474. + 22159.5i 0.775679 + 0.108463i
\(453\) 0 0
\(454\) −11448.9 + 164551.i −0.0555461 + 0.798343i
\(455\) 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 0.374275 0.927318i \(-0.377892\pi\)
−0.615943 + 0.787791i \(0.711225\pi\)
\(464\) 110091. + 31402.1i 0.511347 + 0.145855i
\(465\) 0 0
\(466\) −110507. + 163957.i −0.508883 + 0.755018i
\(467\) 208473.i 0.955909i −0.878385 0.477955i \(-0.841378\pi\)
0.878385 0.477955i \(-0.158622\pi\)
\(468\) 0 0
\(469\) −420257. −1.91060
\(470\) −424705. 286252.i −1.92261 1.29584i
\(471\) 0 0
\(472\) 14445.9 + 12979.8i 0.0648425 + 0.0582619i
\(473\) 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 −0.166390 0.986060i \(-0.553211\pi\)
0.770758 + 0.637128i \(0.219878\pi\)
\(480\) 0 0
\(481\) 15849.9 27452.8i 0.0685070 0.118658i
\(482\) −163990. 11409.9i −0.705867 0.0491119i
\(483\) 0 0
\(484\) 146099. + 20429.1i 0.623672 + 0.0872083i
\(485\) 91556.4 0.389229
\(486\) 0 0
\(487\) 371960.i 1.56834i 0.620549 + 0.784168i \(0.286910\pi\)
−0.620549 + 0.784168i \(0.713090\pi\)
\(488\) 18974.6 + 58190.8i 0.0796771 + 0.244351i
\(489\) 0 0
\(490\) −235715. 16400.2i −0.981735 0.0683059i
\(491\) 57863.4 + 33407.4i 0.240016 + 0.138574i 0.615184 0.788383i \(-0.289082\pi\)
−0.375168 + 0.926957i \(0.622415\pi\)
\(492\) 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 −0.206591 0.978427i \(-0.566237\pi\)
−0.950638 + 0.310301i \(0.899570\pi\)
\(500\) 260792. + 644191.i 1.04317 + 2.57676i
\(501\) 0 0
\(502\) 168659. + 113677.i 0.669273 + 0.451091i
\(503\) 12673.0i 0.0500892i −0.999686 0.0250446i \(-0.992027\pi\)
0.999686 0.0250446i \(-0.00797278\pi\)
\(504\) 0 0
\(505\) −359533. −1.40980
\(506\) −46350.3 + 68768.8i −0.181030 + 0.268590i
\(507\) 0 0
\(508\) −280062. + 113379.i −1.08524 + 0.439346i
\(509\) −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
\(518\) −17087.9 + 245599.i −0.0636840 + 0.915306i
\(519\) 0 0
\(520\) 28890.3 + 88600.0i 0.106843 + 0.327663i
\(521\) −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 \(-0.810743\pi\)
0.828391 0.560151i \(-0.189257\pi\)
\(524\) −65755.8 + 470255.i −0.239481 + 1.71266i
\(525\) 0 0
\(526\) 8798.63 126459.i 0.0318012 0.457067i
\(527\) −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
\(536\) −330426. 296893.i −1.15013 1.03340i
\(537\) 0 0
\(538\) 122719. 182076.i 0.423983 0.629054i
\(539\) 93145.3i 0.320615i
\(540\) 0 0
\(541\) 387269. 1.32318 0.661590 0.749866i \(-0.269882\pi\)
0.661590 + 0.749866i \(0.269882\pi\)
\(542\) 352695. + 237717.i 1.20061 + 0.809211i
\(543\) 0 0
\(544\) −9661.23 54238.9i −0.0326464 0.183279i
\(545\) 436812. 756581.i 1.47062 2.54720i
\(546\) 0 0
\(547\) −220183. + 127123.i −0.735883 + 0.424862i −0.820570 0.571545i \(-0.806344\pi\)
0.0846877 + 0.996408i \(0.473011\pi\)
\(548\) 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
\(554\) 200847. + 13974.3i 0.654404 + 0.0455312i
\(555\) 0 0
\(556\) −9072.31 + 64880.9i −0.0293473 + 0.209878i
\(557\) 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
\(560\) −503491. 519928.i −1.60552 1.65793i
\(561\) 0 0
\(562\) −24326.8 1692.58i −0.0770216 0.00535891i
\(563\) 188653. + 108919.i 0.595177 + 0.343626i 0.767142 0.641477i \(-0.221678\pi\)
−0.171965 + 0.985103i \(0.555012\pi\)
\(564\) 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 0.109387 0.993999i \(-0.465111\pi\)
−0.806135 + 0.591732i \(0.798445\pi\)
\(572\) −34052.2 + 13785.6i −0.104076 + 0.0421340i
\(573\) 0 0
\(574\) 380042. + 256149.i 1.15347 + 0.777443i
\(575\) 437941.i 1.32458i
\(576\) 0 0
\(577\) 450994. 1.35462 0.677312 0.735696i \(-0.263145\pi\)
0.677312 + 0.735696i \(0.263145\pi\)
\(578\) −180250. + 267432.i −0.539534 + 0.800494i
\(579\) 0 0
\(580\) 125370. + 309680.i 0.372681 + 0.920570i
\(581\) 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 0.0181523 0.999835i \(-0.494222\pi\)
0.874959 + 0.484197i \(0.160888\pi\)
\(588\) 0 0
\(589\) −7634.26 + 13222.9i −0.0220058 + 0.0381151i
\(590\) −3933.78 + 56538.8i −0.0113007 + 0.162421i
\(591\) 0 0
\(592\) −186940. + 181030.i −0.533406 + 0.516543i
\(593\) −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
\(596\) 93002.0 + 13004.5i 0.261818 + 0.0366101i
\(597\) 0 0
\(598\) −2438.00 + 35040.5i −0.00681759 + 0.0979868i
\(599\) 357687. + 206511.i 0.996896 + 0.575558i 0.907328 0.420422i \(-0.138118\pi\)
0.0895677 + 0.995981i \(0.471451\pi\)
\(600\) 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 0.816893 0.576789i \(-0.195695\pi\)
−0.0910678 + 0.995845i \(0.529028\pi\)
\(608\) −55408.8 + 9869.63i −0.149890 + 0.0266989i
\(609\) 0 0
\(610\) −99831.1 + 148117.i −0.268291 + 0.398057i
\(611\) 85514.7i 0.229065i
\(612\) 0 0
\(613\) −464349. −1.23573 −0.617865 0.786284i \(-0.712002\pi\)
−0.617865 + 0.786284i \(0.712002\pi\)
\(614\) 358825. + 241848.i 0.951800 + 0.641515i
\(615\) 0 0
\(616\) 190689. 212228.i 0.502534 0.559295i
\(617\) −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 −0.145159 0.989408i \(-0.546369\pi\)
0.784273 + 0.620415i \(0.213036\pi\)
\(620\) −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
\(626\) 605698. + 42142.5i 1.54564 + 0.107540i
\(627\) 0 0
\(628\) 351437. + 49141.5i 0.891103 + 0.124603i
\(629\) −54689.8 −0.138231
\(630\) 0 0
\(631\) 403620.i 1.01371i −0.862031 0.506855i \(-0.830808\pi\)
0.862031 0.506855i \(-0.169192\pi\)
\(632\) 231447. 75469.2i 0.579452 0.188945i
\(633\) 0 0
\(634\) 448531. + 31207.3i 1.11587 + 0.0776387i
\(635\) −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 0.856733 0.515761i \(-0.172491\pi\)
−0.0182957 + 0.999833i \(0.505824\pi\)
\(644\) −102367. 252861.i −0.246825 0.609691i
\(645\) 0 0
\(646\) −9808.24 6610.77i −0.0235031 0.0158412i
\(647\) 98990.1i 0.236474i −0.992985 0.118237i \(-0.962276\pi\)
0.992985 0.118237i \(-0.0377242\pi\)
\(648\) 0 0
\(649\) −22341.9 −0.0530434
\(650\) −108427. + 160871.i −0.256633 + 0.380760i
\(651\) 0 0
\(652\) −464259. + 187949.i −1.09211 + 0.442125i
\(653\) −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 −0.347591 0.937646i \(-0.613000\pi\)
0.638230 + 0.769846i \(0.279667\pi\)
\(660\) 0 0
\(661\) 126176. 218543.i 0.288784 0.500189i −0.684736 0.728792i \(-0.740082\pi\)
0.973520 + 0.228603i \(0.0734157\pi\)
\(662\) 31907.6 458595.i 0.0728077 1.04644i
\(663\) 0 0
\(664\) 191854. 62559.0i 0.435146 0.141891i
\(665\) −155388. −0.351377
\(666\) 0 0
\(667\) 125925.i 0.283049i
\(668\) 57698.5 412632.i 0.129304 0.924720i
\(669\) 0 0
\(670\) 89979.0 1.29323e6i 0.200443 2.88090i
\(671\) −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
\(680\) 107456. 119594.i 0.232388 0.258637i
\(681\) 0 0
\(682\) 45726.9 67843.8i 0.0983111 0.145862i
\(683\) 885039.i 1.89724i −0.316425 0.948618i \(-0.602483\pi\)
0.316425 0.948618i \(-0.397517\pi\)
\(684\) 0 0
\(685\) 778168. 1.65841
\(686\) −228129. 153759.i −0.484767 0.326733i
\(687\) 0 0
\(688\) −54023.0 + 189397.i −0.114131 + 0.400124i
\(689\) 72468.6 125519.i 0.152655 0.264406i
\(690\) 0 0
\(691\) −382656. + 220927.i −0.801406 + 0.462692i −0.843963 0.536402i \(-0.819783\pi\)
0.0425567 + 0.999094i \(0.486450\pi\)
\(692\) 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
\(698\) −171933. 11962.5i −0.352897 0.0245534i
\(699\) 0 0
\(700\) 208650. 1.49216e6i 0.425816 3.04523i
\(701\) −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
\(704\) 299859. 32150.4i 0.605022 0.0648695i
\(705\) 0 0
\(706\) −450407. 31337.8i −0.903640 0.0628723i
\(707\) 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
\(716\) −546317. + 221169.i −1.06566 + 0.431419i
\(717\) 0 0
\(718\) −740121. 498843.i −1.43567 0.967642i
\(719\) 306988.i 0.593832i −0.954904 0.296916i \(-0.904042\pi\)
0.954904 0.296916i \(-0.0959581\pi\)
\(720\) 0 0
\(721\) 223394. 0.429735
\(722\) 284594. 422246.i 0.545949 0.810011i
\(723\) 0 0
\(724\) −341996. 844775.i −0.652446 1.61163i
\(725\) −347749. + 602319.i −0.661592 + 1.14591i
\(726\) 0 0
\(727\) 488481. 282025.i 0.924227 0.533603i 0.0392459 0.999230i \(-0.487504\pi\)
0.884981 + 0.465627i \(0.154171\pi\)
\(728\) 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 \(0.984511\pi\)
\(734\) 29576.5 425092.i 0.0548978 0.789025i
\(735\) 0 0
\(736\) 98148.4 271129.i 0.181187 0.500519i
\(737\) 511037. 0.940843
\(738\) 0 0
\(739\) 193774.i 0.354818i −0.984137 0.177409i \(-0.943228\pi\)
0.984137 0.177409i \(-0.0567715\pi\)
\(740\) −752109. 105168.i −1.37346 0.192052i
\(741\) 0 0
\(742\) −78129.4 + 1.12292e6i −0.141908 + 2.03959i
\(743\) 76480.8 + 44156.2i 0.138540 + 0.0799861i 0.567668 0.823258i \(-0.307846\pi\)
−0.429128 + 0.903244i \(0.641179\pi\)
\(744\) 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 0.0167738 0.999859i \(-0.494660\pi\)
−0.857517 + 0.514456i \(0.827994\pi\)
\(752\) −192557. + 675077.i −0.340506 + 1.19376i
\(753\) 0 0
\(754\) −31177.1 + 46256.8i −0.0548395 + 0.0813640i
\(755\) 1.54879e6i 2.71705i
\(756\) 0 0
\(757\) −45164.0 −0.0788135 −0.0394068 0.999223i \(-0.512547\pi\)
−0.0394068 + 0.999223i \(0.512547\pi\)
\(758\) 315913. + 212926.i 0.549831 + 0.370587i
\(759\) 0 0
\(760\) −122173. 109774.i −0.211519 0.190052i
\(761\) −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 \(0.283858\pi\)
\(770\) 830625. + 57792.1i 1.40095 + 0.0974736i
\(771\) 0 0
\(772\) 64206.2 + 8977.98i 0.107731 + 0.0150641i
\(773\) −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
\(776\) −38903.9 119309.i −0.0646055 0.198130i
\(777\) 0 0
\(778\)