Properties

Label 108.5.f.a.19.16
Level 108
Weight 5
Character 108.19
Analytic conductor 11.164
Analytic rank 0
Dimension 44
CM no
Inner twists 4

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 19.16
Character \(\chi\) \(=\) 108.19
Dual form 108.5.f.a.91.16

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 0.776650 + 0.629932i \(0.216917\pi\)
0.157212 + 0.987565i \(0.449749\pi\)
\(6\) 0 0
\(7\) −52.4363 30.2741i −1.07013 0.617839i −0.141913 0.989879i \(-0.545325\pi\)
−0.928217 + 0.372040i \(0.878659\pi\)
\(8\) −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 \(-0.234929\pi\)
−0.212813 + 0.977093i \(0.568263\pi\)
\(12\) 0 0
\(13\) 15.5924 + 27.0068i 0.0922626 + 0.159803i 0.908463 0.417966i \(-0.137257\pi\)
−0.816200 + 0.577769i \(0.803923\pi\)
\(14\) −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 \(-0.975745\pi\)
0.997098 0.0761245i \(-0.0242546\pi\)
\(20\) −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 −0.712460 0.701712i \(-0.752419\pi\)
0.251471 + 0.967865i \(0.419086\pi\)
\(24\) 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 −0.967791 0.251753i \(-0.918993\pi\)
0.701921 + 0.712255i \(0.252326\pi\)
\(30\) 0 0
\(31\) 240.584 138.901i 0.250347 0.144538i −0.369576 0.929200i \(-0.620497\pi\)
0.619923 + 0.784663i \(0.287164\pi\)
\(32\) 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 0.997246 + 0.0741680i \(0.0236301\pi\)
−0.434392 + 0.900724i \(0.643037\pi\)
\(42\) 0 0
\(43\) 666.266 + 384.669i 0.360339 + 0.208042i 0.669229 0.743056i \(-0.266624\pi\)
−0.308891 + 0.951098i \(0.599958\pi\)
\(44\) −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 \(-0.120187\pi\)
0.145502 + 0.989358i \(0.453520\pi\)
\(48\) 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 −0.537272 0.843409i \(-0.680545\pi\)
0.461778 + 0.886995i \(0.347212\pi\)
\(60\) 0 0
\(61\) −478.174 + 828.222i −0.128507 + 0.222580i −0.923098 0.384564i \(-0.874352\pi\)
0.794591 + 0.607145i \(0.207685\pi\)
\(62\) 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 \(-0.385374\pi\)
0.986665 + 0.162762i \(0.0520403\pi\)
\(68\) 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 \(0.201781\pi\)
−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 \(0.633470\pi\)
\(74\) 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 0.212306 0.977203i \(-0.431903\pi\)
−0.740130 + 0.672464i \(0.765236\pi\)
\(80\) 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 \(-0.406829\pi\)
−0.684919 + 0.728619i \(0.740163\pi\)
\(84\) 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 −0.809212 0.587517i \(-0.800106\pi\)
0.913411 + 0.407040i \(0.133439\pi\)
\(98\) −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 −0.990685 0.136177i \(-0.956519\pi\)
0.613275 + 0.789870i \(0.289852\pi\)
\(102\) 0 0
\(103\) −3195.22 + 1844.76i −0.301180 + 0.173886i −0.642973 0.765889i \(-0.722299\pi\)
0.341793 + 0.939775i \(0.388966\pi\)
\(104\) −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 \(-0.795120\pi\)
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 \(0.211433\pi\)
\(110\) −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 0.601050 0.799212i \(-0.294749\pi\)
−0.992662 + 0.120919i \(0.961416\pi\)
\(114\) 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 \(0.199063\pi\)
−0.810745 + 0.585400i \(0.800937\pi\)
\(128\) 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 −0.999996 0.00272458i \(-0.999133\pi\)
−0.497639 + 0.867384i \(0.665799\pi\)
\(132\) 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 −0.554014 0.832507i \(-0.686905\pi\)
0.997980 + 0.0635366i \(0.0202380\pi\)
\(138\) 0 0
\(139\) −3545.95 + 2047.25i −0.183528 + 0.105960i −0.588949 0.808170i \(-0.700458\pi\)
0.405421 + 0.914130i \(0.367125\pi\)
\(140\) 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 0.792335 0.610086i \(-0.208865\pi\)
−0.924518 + 0.381139i \(0.875532\pi\)
\(150\) 0 0
\(151\) −28725.6 16584.7i −1.25984 0.727369i −0.286797 0.957991i \(-0.592591\pi\)
−0.973043 + 0.230622i \(0.925924\pi\)
\(152\) 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 0.548492 0.836156i \(-0.315202\pi\)
−0.998378 + 0.0569302i \(0.981869\pi\)
\(158\) −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 \(0.200519\pi\)
−0.808057 + 0.589104i \(0.799481\pi\)
\(164\) −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 −0.0378548 0.999283i \(-0.512052\pi\)
0.846477 + 0.532425i \(0.178719\pi\)
\(168\) 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 −0.705044 0.709164i \(-0.749073\pi\)
0.966676 + 0.256004i \(0.0824060\pi\)
\(174\) 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 \(0.194935\pi\)
−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 \(0.164543\pi\)
\(182\) 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 −0.0414986 0.999139i \(-0.513213\pi\)
−0.886029 + 0.463630i \(0.846547\pi\)
\(192\) 0 0
\(193\) −2025.97 3509.08i −0.0543898 0.0942059i 0.837549 0.546363i \(-0.183988\pi\)
−0.891938 + 0.452157i \(0.850655\pi\)
\(194\) 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 \(-0.748562\pi\)
0.703905 0.710294i \(-0.251438\pi\)
\(200\) 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 −0.996472 0.0839298i \(-0.973253\pi\)
−0.425551 + 0.904935i \(0.639920\pi\)
\(212\) −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 0.984032 0.177989i \(-0.0569591\pi\)
0.337873 + 0.941192i \(0.390292\pi\)
\(224\) −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 \(-0.464371\pi\)
−0.804756 + 0.593606i \(0.797704\pi\)
\(228\) 0 0
\(229\) −13792.1 23888.7i −0.263003 0.455534i 0.704036 0.710165i \(-0.251379\pi\)
−0.967038 + 0.254630i \(0.918046\pi\)
\(230\) −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 0.752091 0.659060i \(-0.229045\pi\)
0.946808 0.321800i \(-0.104288\pi\)
\(240\) 0 0
\(241\) −20548.3 + 35590.7i −0.353787 + 0.612776i −0.986910 0.161275i \(-0.948439\pi\)
0.633123 + 0.774051i \(0.281773\pi\)
\(242\) 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 \(-0.867776\pi\)
0.914958 0.403550i \(-0.132224\pi\)
\(252\) 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 0.910431 0.413662i \(-0.135750\pi\)
−0.813457 + 0.581625i \(0.802417\pi\)
\(258\) 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 \(-0.259760\pi\)
−0.288309 + 0.957537i \(0.593093\pi\)
\(264\) 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 \(-0.742335\pi\)
0.689877 0.723927i \(-0.257665\pi\)
\(272\) 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 −0.654121 0.756390i \(-0.726961\pi\)
0.982113 + 0.188290i \(0.0602945\pi\)
\(278\) −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 −0.884682 0.466195i \(-0.845624\pi\)
0.846078 + 0.533059i \(0.178958\pi\)
\(282\) 0 0
\(283\) 44494.8 25689.1i 0.555567 0.320757i −0.195797 0.980644i \(-0.562729\pi\)
0.751364 + 0.659888i \(0.229396\pi\)
\(284\) −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 0.999318 + 0.0369270i \(0.0117569\pi\)
−0.467679 + 0.883898i \(0.654910\pi\)
\(294\) 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 \(-0.805428\pi\)
0.818923 0.573904i \(-0.194572\pi\)
\(308\) 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 −0.875938 0.482424i \(-0.839757\pi\)
−0.0201778 + 0.999796i \(0.506423\pi\)
\(312\) 0 0
\(313\) 75895.3 131455.i 0.774687 1.34180i −0.160283 0.987071i \(-0.551241\pi\)
0.934970 0.354726i \(-0.115426\pi\)
\(314\) 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 −0.438271 0.898843i \(-0.644409\pi\)
0.997556 0.0698672i \(-0.0222575\pi\)
\(318\) 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 0.879927 0.475109i \(-0.157592\pi\)
0.0285065 + 0.999594i \(0.490925\pi\)
\(332\) 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 −0.998741 0.0501573i \(-0.984028\pi\)
0.455933 0.890014i \(-0.349306\pi\)
\(338\) 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 −0.802869 0.596156i \(-0.796694\pi\)
0.114852 + 0.993383i \(0.463361\pi\)
\(348\) 0 0
\(349\) −21543.6 + 37314.5i −0.176875 + 0.306357i −0.940809 0.338938i \(-0.889932\pi\)
0.763934 + 0.645295i \(0.223266\pi\)
\(350\) 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 −0.998565 0.0535440i \(-0.982948\pi\)
0.545653 + 0.838011i \(0.316282\pi\)
\(354\) 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 \(0.333101\pi\)
−0.500632 + 0.865660i \(0.666899\pi\)
\(360\) 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 0.801724 0.597694i \(-0.203916\pi\)
−0.116756 + 0.993161i \(0.537250\pi\)
\(368\) 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 −0.999878 0.0156403i \(-0.995021\pi\)
0.486394 0.873740i \(-0.338312\pi\)
\(374\) −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 \(-0.892435\pi\)
0.943445 0.331530i \(-0.107565\pi\)
\(380\) 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 −0.331547 0.943439i \(-0.607571\pi\)
0.651268 + 0.758848i \(0.274237\pi\)
\(384\) 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 −0.843702 0.536813i \(-0.819628\pi\)
0.886744 + 0.462261i \(0.152962\pi\)
\(390\) 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 0.933708 0.358036i \(-0.116554\pi\)
−0.776922 + 0.629596i \(0.783220\pi\)
\(402\) 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 0.798525 0.601962i \(-0.205614\pi\)
−0.920577 + 0.390562i \(0.872281\pi\)
\(410\) −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 −0.415529 0.909580i \(-0.636403\pi\)
0.579955 + 0.814648i \(0.303070\pi\)
\(420\) 0 0
\(421\) −4180.31 + 7240.51i −0.0235855 + 0.0408512i −0.877577 0.479435i \(-0.840842\pi\)
0.853992 + 0.520287i \(0.174175\pi\)
\(422\) −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 \(-0.923488\pi\)
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 \(0.397124\pi\)
\(434\) −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 0.206886 0.978365i \(-0.433667\pi\)
−0.743846 + 0.668351i \(0.767000\pi\)
\(440\) −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 \(-0.507028\pi\)
−0.876853 + 0.480759i \(0.840361\pi\)
\(444\) 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 0.304882 + 0.952390i \(0.401383\pi\)
−0.977235 + 0.212159i \(0.931951\pi\)
\(458\) 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 −0.188942 + 0.981988i \(0.560506\pi\)
−0.755956 + 0.654623i \(0.772827\pi\)
\(462\) 0 0
\(463\) −51806.1 + 29910.3i −0.241668 + 0.139527i −0.615943 0.787791i \(-0.711225\pi\)
0.374275 + 0.927318i \(0.377892\pi\)
\(464\) 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 \(0.158622\pi\)
−0.878385 + 0.477955i \(0.841378\pi\)
\(468\) 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 0.770758 0.637128i \(-0.219878\pi\)
−0.166390 + 0.986060i \(0.553211\pi\)
\(480\) 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 \(-0.713090\pi\)
0.620549 0.784168i \(-0.286910\pi\)
\(488\) 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 −0.375168 0.926957i \(-0.622415\pi\)
0.615184 + 0.788383i \(0.289082\pi\)
\(492\) 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 \(-0.899570\pi\)
−0.206591 + 0.978427i \(0.566237\pi\)
\(500\) 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 \(0.00797278\pi\)
−0.999686 + 0.0250446i \(0.992027\pi\)
\(504\) 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 0.826039 0.563613i \(-0.190589\pi\)
−0.901123 + 0.433564i \(0.857256\pi\)
\(510\) 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 \(0.189257\pi\)
−0.828391 + 0.560151i \(0.810743\pi\)
\(524\) −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 0.0846877 0.996408i \(-0.473011\pi\)
−0.820570 + 0.571545i \(0.806344\pi\)
\(548\) 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 −0.171965 0.985103i \(-0.555012\pi\)
0.767142 + 0.641477i \(0.221678\pi\)
\(564\) 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 −0.639172 0.769064i \(-0.720723\pi\)
0.985615 + 0.169007i \(0.0540561\pi\)
\(570\) 0 0
\(571\) −227168. + 131156.i −0.696748 + 0.402268i −0.806135 0.591732i \(-0.798445\pi\)
0.109387 + 0.993999i \(0.465111\pi\)
\(572\) −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 0.874959 0.484197i \(-0.160888\pi\)
0.0181523 + 0.999835i \(0.494222\pi\)
\(588\) 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 0.0895677 0.995981i \(-0.471451\pi\)
0.907328 + 0.420422i \(0.138118\pi\)
\(600\) 0 0
\(601\) −129317. + 223984.i −0.358020 + 0.620110i −0.987630 0.156802i \(-0.949882\pi\)
0.629610 + 0.776912i \(0.283215\pi\)
\(602\) 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 \(-0.529028\pi\)
0.816893 + 0.576789i \(0.195695\pi\)
\(608\) −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 −0.978906 0.204312i \(-0.934504\pi\)
0.312513 0.949913i \(-0.398829\pi\)
\(618\) 0 0
\(619\) 244884. + 141384.i 0.639115 + 0.368993i 0.784273 0.620415i \(-0.213036\pi\)
−0.145159 + 0.989408i \(0.546369\pi\)
\(620\) −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 \(0.169192\pi\)
−0.862031 + 0.506855i \(0.830808\pi\)
\(632\) 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 −0.997733 0.0672990i \(-0.978562\pi\)
0.557149 + 0.830413i \(0.311895\pi\)
\(642\) 0 0
\(643\) 346651. 200139.i 0.838437 0.484072i −0.0182957 0.999833i \(-0.505824\pi\)
0.856733 + 0.515761i \(0.172491\pi\)
\(644\) −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 \(0.0377242\pi\)
−0.992985 + 0.118237i \(0.962276\pi\)
\(648\) 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 −0.987299 0.158872i \(-0.949214\pi\)
0.356062 0.934462i \(-0.384119\pi\)
\(654\) 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 \(-0.279667\pi\)
−0.347591 + 0.937646i \(0.613000\pi\)
\(660\) 0 0
\(661\) 126176. + 218543.i 0.288784 + 0.500189i 0.973520 0.228603i \(-0.0734157\pi\)
−0.684736 + 0.728792i \(0.740082\pi\)
\(662\) 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 0.237213 + 0.971458i \(0.423766\pi\)
−0.959913 + 0.280297i \(0.909567\pi\)
\(674\) 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 −0.958667 0.284529i \(-0.908163\pi\)
0.725743 + 0.687966i \(0.241496\pi\)
\(678\) 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 \(0.397517\pi\)
−0.316425 + 0.948618i \(0.602483\pi\)
\(684\) 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 0.0425567 0.999094i \(-0.486450\pi\)
−0.843963 + 0.536402i \(0.819783\pi\)
\(692\) 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 −0.412886 0.910783i \(-0.635479\pi\)
0.995204 0.0978214i \(-0.0311874\pi\)
\(710\) −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 \(0.0959581\pi\)
−0.954904 + 0.296916i \(0.904042\pi\)
\(720\) 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 0.884981 0.465627i \(-0.154171\pi\)
0.0392459 + 0.999230i \(0.487504\pi\)
\(728\) 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 −0.998816 0.0486418i \(-0.984511\pi\)
0.457283 0.889321i \(-0.348823\pi\)
\(734\) 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 \(0.0567715\pi\)
−0.984137 + 0.177409i \(0.943228\pi\)
\(740\) −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 −0.429128 0.903244i \(-0.641179\pi\)
0.567668 + 0.823258i \(0.307846\pi\)
\(744\) 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 \(-0.827994\pi\)
0.0167738 + 0.999859i \(0.494660\pi\)
\(752\) −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 0.766471 0.642279i \(-0.222011\pi\)
−0.939465 + 0.342644i \(0.888678\pi\)
\(762\) 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 0.628039 0.778181i \(-0.283858\pi\)
−0.987945 + 0.154807i \(0.950524\pi\)
\(770\) 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 + 0.198130<