Properties

Label 108.4.h.b.71.4
Level 108
Weight 4
Character 108.71
Analytic conductor 6.372
Analytic rank 0
Dimension 24
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.h (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 71.4
Character \(\chi\) \(=\) 108.71
Dual form 108.4.h.b.35.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.44536 - 2.43124i) q^{2} +(-3.82189 + 7.02803i) q^{4} +(-14.6499 - 8.45813i) q^{5} +(3.08966 - 1.78382i) q^{7} +(22.6108 - 0.866066i) q^{8} +O(q^{10})\) \(q+(-1.44536 - 2.43124i) q^{2} +(-3.82189 + 7.02803i) q^{4} +(-14.6499 - 8.45813i) q^{5} +(3.08966 - 1.78382i) q^{7} +(22.6108 - 0.866066i) q^{8} +(0.610574 + 47.8425i) q^{10} +(25.0688 + 43.4205i) q^{11} +(-18.9966 + 32.9032i) q^{13} +(-8.80255 - 4.93346i) q^{14} +(-34.7863 - 53.7207i) q^{16} +84.3819i q^{17} +62.9237i q^{19} +(115.434 - 70.6340i) q^{20} +(69.3323 - 123.706i) q^{22} +(37.6066 - 65.1366i) q^{23} +(80.5801 + 139.569i) q^{25} +(107.453 - 1.37133i) q^{26} +(0.728372 + 28.5317i) q^{28} +(-105.644 + 60.9938i) q^{29} +(17.2800 + 9.97659i) q^{31} +(-80.3294 + 162.220i) q^{32} +(205.153 - 121.962i) q^{34} -60.3510 q^{35} +17.7622 q^{37} +(152.983 - 90.9472i) q^{38} +(-338.572 - 178.558i) q^{40} +(-299.072 - 172.670i) q^{41} +(-113.206 + 65.3596i) q^{43} +(-400.970 + 10.2362i) q^{44} +(-212.718 + 2.71474i) q^{46} +(-153.083 - 265.147i) q^{47} +(-165.136 + 286.024i) q^{49} +(222.859 - 397.636i) q^{50} +(-158.641 - 259.261i) q^{52} +479.464i q^{53} -848.142i q^{55} +(68.3149 - 43.0094i) q^{56} +(300.984 + 168.689i) q^{58} +(-245.774 + 425.693i) q^{59} +(-49.9168 - 86.4585i) q^{61} +(-0.720188 - 56.4315i) q^{62} +(510.500 - 39.1649i) q^{64} +(556.599 - 321.352i) q^{65} +(536.669 + 309.846i) q^{67} +(-593.039 - 322.498i) q^{68} +(87.2287 + 146.728i) q^{70} +254.455 q^{71} +100.485 q^{73} +(-25.6727 - 43.1841i) q^{74} +(-442.230 - 240.488i) q^{76} +(154.908 + 89.4363i) q^{77} +(-856.295 + 494.382i) q^{79} +(55.2404 + 1081.23i) q^{80} +(12.4646 + 976.687i) q^{82} +(251.755 + 436.053i) q^{83} +(713.714 - 1236.19i) q^{85} +(322.528 + 180.764i) q^{86} +(604.432 + 960.062i) q^{88} -1019.86i q^{89} +135.546i q^{91} +(314.053 + 513.245i) q^{92} +(-423.378 + 755.413i) q^{94} +(532.217 - 921.828i) q^{95} +(-503.589 - 872.242i) q^{97} +(934.074 - 11.9208i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{4} + 72q^{5} + O(q^{10}) \) \( 24q - 12q^{4} + 72q^{5} + 96q^{10} - 216q^{13} + 36q^{14} - 72q^{16} + 540q^{20} - 192q^{22} + 252q^{25} - 672q^{28} - 576q^{29} - 360q^{32} - 660q^{34} + 1248q^{37} + 144q^{38} + 636q^{40} - 1116q^{41} + 960q^{46} + 348q^{49} + 648q^{50} + 132q^{52} + 1692q^{56} + 516q^{58} - 264q^{61} + 960q^{64} + 2592q^{65} - 5688q^{68} + 564q^{70} - 4776q^{73} - 5652q^{74} - 600q^{76} - 648q^{77} - 4104q^{82} + 720q^{85} + 9540q^{86} + 1956q^{88} + 7416q^{92} - 1188q^{94} + 588q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.44536 2.43124i −0.511011 0.859574i
\(3\) 0 0
\(4\) −3.82189 + 7.02803i −0.477736 + 0.878503i
\(5\) −14.6499 8.45813i −1.31033 0.756519i −0.328178 0.944616i \(-0.606435\pi\)
−0.982150 + 0.188097i \(0.939768\pi\)
\(6\) 0 0
\(7\) 3.08966 1.78382i 0.166826 0.0963170i −0.414262 0.910157i \(-0.635960\pi\)
0.581088 + 0.813841i \(0.302627\pi\)
\(8\) 22.6108 0.866066i 0.999267 0.0382750i
\(9\) 0 0
\(10\) 0.610574 + 47.8425i 0.0193080 + 1.51291i
\(11\) 25.0688 + 43.4205i 0.687139 + 1.19016i 0.972759 + 0.231817i \(0.0744672\pi\)
−0.285620 + 0.958343i \(0.592199\pi\)
\(12\) 0 0
\(13\) −18.9966 + 32.9032i −0.405286 + 0.701977i −0.994355 0.106107i \(-0.966162\pi\)
0.589068 + 0.808083i \(0.299495\pi\)
\(14\) −8.80255 4.93346i −0.168041 0.0941802i
\(15\) 0 0
\(16\) −34.7863 53.7207i −0.543537 0.839386i
\(17\) 84.3819i 1.20386i 0.798549 + 0.601930i \(0.205601\pi\)
−0.798549 + 0.601930i \(0.794399\pi\)
\(18\) 0 0
\(19\) 62.9237i 0.759773i 0.925033 + 0.379887i \(0.124037\pi\)
−0.925033 + 0.379887i \(0.875963\pi\)
\(20\) 115.434 70.6340i 1.29060 0.789712i
\(21\) 0 0
\(22\) 69.3323 123.706i 0.671896 1.19883i
\(23\) 37.6066 65.1366i 0.340936 0.590518i −0.643671 0.765302i \(-0.722589\pi\)
0.984607 + 0.174784i \(0.0559227\pi\)
\(24\) 0 0
\(25\) 80.5801 + 139.569i 0.644641 + 1.11655i
\(26\) 107.453 1.37133i 0.810507 0.0103438i
\(27\) 0 0
\(28\) 0.728372 + 28.5317i 0.00491605 + 0.192571i
\(29\) −105.644 + 60.9938i −0.676471 + 0.390561i −0.798524 0.601963i \(-0.794386\pi\)
0.122053 + 0.992524i \(0.461052\pi\)
\(30\) 0 0
\(31\) 17.2800 + 9.97659i 0.100115 + 0.0578016i 0.549222 0.835677i \(-0.314924\pi\)
−0.449106 + 0.893478i \(0.648258\pi\)
\(32\) −80.3294 + 162.220i −0.443761 + 0.896145i
\(33\) 0 0
\(34\) 205.153 121.962i 1.03481 0.615186i
\(35\) −60.3510 −0.291462
\(36\) 0 0
\(37\) 17.7622 0.0789211 0.0394606 0.999221i \(-0.487436\pi\)
0.0394606 + 0.999221i \(0.487436\pi\)
\(38\) 152.983 90.9472i 0.653082 0.388252i
\(39\) 0 0
\(40\) −338.572 178.558i −1.33832 0.705811i
\(41\) −299.072 172.670i −1.13920 0.657718i −0.192969 0.981205i \(-0.561812\pi\)
−0.946233 + 0.323486i \(0.895145\pi\)
\(42\) 0 0
\(43\) −113.206 + 65.3596i −0.401483 + 0.231796i −0.687124 0.726540i \(-0.741127\pi\)
0.285641 + 0.958337i \(0.407794\pi\)
\(44\) −400.970 + 10.2362i −1.37383 + 0.0350718i
\(45\) 0 0
\(46\) −212.718 + 2.71474i −0.681816 + 0.00870145i
\(47\) −153.083 265.147i −0.475094 0.822887i 0.524499 0.851411i \(-0.324253\pi\)
−0.999593 + 0.0285243i \(0.990919\pi\)
\(48\) 0 0
\(49\) −165.136 + 286.024i −0.481446 + 0.833889i
\(50\) 222.859 397.636i 0.630340 1.12469i
\(51\) 0 0
\(52\) −158.641 259.261i −0.423069 0.691405i
\(53\) 479.464i 1.24263i 0.783561 + 0.621315i \(0.213401\pi\)
−0.783561 + 0.621315i \(0.786599\pi\)
\(54\) 0 0
\(55\) 848.142i 2.07933i
\(56\) 68.3149 43.0094i 0.163017 0.102632i
\(57\) 0 0
\(58\) 300.984 + 168.689i 0.681400 + 0.381896i
\(59\) −245.774 + 425.693i −0.542323 + 0.939330i 0.456447 + 0.889750i \(0.349122\pi\)
−0.998770 + 0.0495801i \(0.984212\pi\)
\(60\) 0 0
\(61\) −49.9168 86.4585i −0.104774 0.181473i 0.808872 0.587985i \(-0.200079\pi\)
−0.913646 + 0.406511i \(0.866745\pi\)
\(62\) −0.720188 56.4315i −0.00147523 0.115594i
\(63\) 0 0
\(64\) 510.500 39.1649i 0.997070 0.0764940i
\(65\) 556.599 321.352i 1.06212 0.613213i
\(66\) 0 0
\(67\) 536.669 + 309.846i 0.978575 + 0.564980i 0.901839 0.432071i \(-0.142217\pi\)
0.0767351 + 0.997052i \(0.475550\pi\)
\(68\) −593.039 322.498i −1.05760 0.575127i
\(69\) 0 0
\(70\) 87.2287 + 146.728i 0.148940 + 0.250534i
\(71\) 254.455 0.425327 0.212663 0.977125i \(-0.431786\pi\)
0.212663 + 0.977125i \(0.431786\pi\)
\(72\) 0 0
\(73\) 100.485 0.161108 0.0805541 0.996750i \(-0.474331\pi\)
0.0805541 + 0.996750i \(0.474331\pi\)
\(74\) −25.6727 43.1841i −0.0403295 0.0678386i
\(75\) 0 0
\(76\) −442.230 240.488i −0.667464 0.362971i
\(77\) 154.908 + 89.4363i 0.229265 + 0.132366i
\(78\) 0 0
\(79\) −856.295 + 494.382i −1.21950 + 0.704080i −0.964812 0.262942i \(-0.915307\pi\)
−0.254691 + 0.967022i \(0.581974\pi\)
\(80\) 55.2404 + 1081.23i 0.0772008 + 1.51107i
\(81\) 0 0
\(82\) 12.4646 + 976.687i 0.0167864 + 1.31533i
\(83\) 251.755 + 436.053i 0.332936 + 0.576663i 0.983086 0.183143i \(-0.0586272\pi\)
−0.650150 + 0.759806i \(0.725294\pi\)
\(84\) 0 0
\(85\) 713.714 1236.19i 0.910743 1.57745i
\(86\) 322.528 + 180.764i 0.404408 + 0.226654i
\(87\) 0 0
\(88\) 604.432 + 960.062i 0.732189 + 1.16299i
\(89\) 1019.86i 1.21467i −0.794448 0.607333i \(-0.792239\pi\)
0.794448 0.607333i \(-0.207761\pi\)
\(90\) 0 0
\(91\) 135.546i 0.156144i
\(92\) 314.053 + 513.245i 0.355895 + 0.581625i
\(93\) 0 0
\(94\) −423.378 + 755.413i −0.464554 + 0.828882i
\(95\) 532.217 921.828i 0.574783 0.995553i
\(96\) 0 0
\(97\) −503.589 872.242i −0.527131 0.913018i −0.999500 0.0316171i \(-0.989934\pi\)
0.472369 0.881401i \(-0.343399\pi\)
\(98\) 934.074 11.9208i 0.962814 0.0122876i
\(99\) 0 0
\(100\) −1288.86 + 32.9027i −1.28886 + 0.0329027i
\(101\) 364.582 210.492i 0.359181 0.207373i −0.309540 0.950886i \(-0.600175\pi\)
0.668721 + 0.743513i \(0.266842\pi\)
\(102\) 0 0
\(103\) 1496.60 + 864.065i 1.43170 + 0.826591i 0.997250 0.0741066i \(-0.0236105\pi\)
0.434447 + 0.900697i \(0.356944\pi\)
\(104\) −401.034 + 760.420i −0.378121 + 0.716975i
\(105\) 0 0
\(106\) 1165.69 692.996i 1.06813 0.634998i
\(107\) 63.1607 0.0570652 0.0285326 0.999593i \(-0.490917\pi\)
0.0285326 + 0.999593i \(0.490917\pi\)
\(108\) 0 0
\(109\) −835.373 −0.734076 −0.367038 0.930206i \(-0.619628\pi\)
−0.367038 + 0.930206i \(0.619628\pi\)
\(110\) −2062.04 + 1225.87i −1.78734 + 1.06256i
\(111\) 0 0
\(112\) −203.306 103.926i −0.171523 0.0876794i
\(113\) 891.915 + 514.947i 0.742516 + 0.428692i 0.822983 0.568065i \(-0.192308\pi\)
−0.0804674 + 0.996757i \(0.525641\pi\)
\(114\) 0 0
\(115\) −1101.87 + 636.164i −0.893476 + 0.515849i
\(116\) −24.9051 975.583i −0.0199343 0.780867i
\(117\) 0 0
\(118\) 1390.19 17.7419i 1.08456 0.0138413i
\(119\) 150.522 + 260.711i 0.115952 + 0.200835i
\(120\) 0 0
\(121\) −591.391 + 1024.32i −0.444321 + 0.769587i
\(122\) −138.054 + 246.323i −0.102449 + 0.182796i
\(123\) 0 0
\(124\) −136.158 + 83.3146i −0.0986075 + 0.0603377i
\(125\) 611.695i 0.437693i
\(126\) 0 0
\(127\) 794.523i 0.555138i −0.960706 0.277569i \(-0.910471\pi\)
0.960706 0.277569i \(-0.0895287\pi\)
\(128\) −833.074 1184.54i −0.575266 0.817967i
\(129\) 0 0
\(130\) −1585.77 888.758i −1.06986 0.599610i
\(131\) −111.039 + 192.325i −0.0740575 + 0.128271i −0.900676 0.434491i \(-0.856928\pi\)
0.826619 + 0.562763i \(0.190262\pi\)
\(132\) 0 0
\(133\) 112.244 + 194.413i 0.0731791 + 0.126750i
\(134\) −22.3671 1752.61i −0.0144196 1.12987i
\(135\) 0 0
\(136\) 73.0803 + 1907.95i 0.0460778 + 1.20298i
\(137\) −1054.28 + 608.690i −0.657470 + 0.379591i −0.791312 0.611412i \(-0.790602\pi\)
0.133842 + 0.991003i \(0.457268\pi\)
\(138\) 0 0
\(139\) −1909.09 1102.21i −1.16494 0.672578i −0.212457 0.977170i \(-0.568146\pi\)
−0.952483 + 0.304592i \(0.901480\pi\)
\(140\) 230.655 424.148i 0.139242 0.256051i
\(141\) 0 0
\(142\) −367.778 618.641i −0.217347 0.365600i
\(143\) −1904.89 −1.11395
\(144\) 0 0
\(145\) 2063.57 1.18187
\(146\) −145.237 244.304i −0.0823280 0.138485i
\(147\) 0 0
\(148\) −67.8850 + 124.833i −0.0377035 + 0.0693325i
\(149\) 352.120 + 203.297i 0.193603 + 0.111777i 0.593668 0.804710i \(-0.297679\pi\)
−0.400065 + 0.916487i \(0.631013\pi\)
\(150\) 0 0
\(151\) 2990.17 1726.37i 1.61150 0.930399i 0.622475 0.782640i \(-0.286127\pi\)
0.989023 0.147759i \(-0.0472060\pi\)
\(152\) 54.4961 + 1422.76i 0.0290804 + 0.759217i
\(153\) 0 0
\(154\) −6.45621 505.887i −0.00337829 0.264711i
\(155\) −168.767 292.312i −0.0874559 0.151478i
\(156\) 0 0
\(157\) 440.287 762.599i 0.223813 0.387656i −0.732149 0.681144i \(-0.761483\pi\)
0.955963 + 0.293488i \(0.0948160\pi\)
\(158\) 2439.62 + 1367.30i 1.22839 + 0.688461i
\(159\) 0 0
\(160\) 2548.89 1697.07i 1.25942 0.838531i
\(161\) 268.333i 0.131352i
\(162\) 0 0
\(163\) 1693.56i 0.813802i −0.913472 0.406901i \(-0.866609\pi\)
0.913472 0.406901i \(-0.133391\pi\)
\(164\) 2356.55 1441.97i 1.12205 0.686577i
\(165\) 0 0
\(166\) 696.274 1242.33i 0.325550 0.580864i
\(167\) −820.051 + 1420.37i −0.379985 + 0.658153i −0.991060 0.133420i \(-0.957404\pi\)
0.611075 + 0.791573i \(0.290737\pi\)
\(168\) 0 0
\(169\) 376.755 + 652.558i 0.171486 + 0.297022i
\(170\) −4037.05 + 51.5214i −1.82134 + 0.0232442i
\(171\) 0 0
\(172\) −26.6878 1045.41i −0.0118310 0.463442i
\(173\) −1889.17 + 1090.71i −0.830234 + 0.479336i −0.853933 0.520383i \(-0.825789\pi\)
0.0236985 + 0.999719i \(0.492456\pi\)
\(174\) 0 0
\(175\) 497.930 + 287.480i 0.215085 + 0.124180i
\(176\) 1460.52 2857.15i 0.625518 1.22367i
\(177\) 0 0
\(178\) −2479.53 + 1474.07i −1.04410 + 0.620707i
\(179\) 2350.24 0.981370 0.490685 0.871337i \(-0.336747\pi\)
0.490685 + 0.871337i \(0.336747\pi\)
\(180\) 0 0
\(181\) −2280.14 −0.936362 −0.468181 0.883633i \(-0.655090\pi\)
−0.468181 + 0.883633i \(0.655090\pi\)
\(182\) 329.545 195.912i 0.134217 0.0797912i
\(183\) 0 0
\(184\) 793.905 1505.36i 0.318084 0.603135i
\(185\) −260.214 150.235i −0.103413 0.0597053i
\(186\) 0 0
\(187\) −3663.90 + 2115.36i −1.43279 + 0.827220i
\(188\) 2448.53 62.5071i 0.949878 0.0242489i
\(189\) 0 0
\(190\) −3010.43 + 38.4196i −1.14947 + 0.0146697i
\(191\) −1966.48 3406.04i −0.744970 1.29033i −0.950209 0.311614i \(-0.899130\pi\)
0.205239 0.978712i \(1.56580\pi\)
\(192\) 0 0
\(193\) −1356.60 + 2349.69i −0.505958 + 0.876346i 0.494018 + 0.869452i \(0.335528\pi\)
−0.999976 + 0.00689392i \(0.997806\pi\)
\(194\) −1392.77 + 2485.05i −0.515437 + 0.919671i
\(195\) 0 0
\(196\) −1379.05 2253.73i −0.502570 0.821331i
\(197\) 1997.91i 0.722565i 0.932456 + 0.361282i \(0.117661\pi\)
−0.932456 + 0.361282i \(0.882339\pi\)
\(198\) 0 0
\(199\) 2409.09i 0.858170i 0.903264 + 0.429085i \(0.141164\pi\)
−0.903264 + 0.429085i \(0.858836\pi\)
\(200\) 1942.86 + 3085.98i 0.686904 + 1.09106i
\(201\) 0 0
\(202\) −1038.71 582.153i −0.361798 0.202773i
\(203\) −217.603 + 376.900i −0.0752353 + 0.130311i
\(204\) 0 0
\(205\) 2920.92 + 5059.19i 0.995152 + 1.72365i
\(206\) −62.3750 4887.49i −0.0210965 1.65305i
\(207\) 0 0
\(208\) 2428.40 124.068i 0.809517 0.0413584i
\(209\) −2732.18 + 1577.42i −0.904252 + 0.522070i
\(210\) 0 0
\(211\) 1575.68 + 909.717i 0.514095 + 0.296813i 0.734515 0.678592i \(-0.237410\pi\)
−0.220420 + 0.975405i \(0.570743\pi\)
\(212\) −3369.69 1832.46i −1.09166 0.593650i
\(213\) 0 0
\(214\) −91.2897 153.559i −0.0291609 0.0490518i
\(215\) 2211.28 0.701433
\(216\) 0 0
\(217\) 71.1856 0.0222691
\(218\) 1207.41 + 2031.00i 0.375120 + 0.630992i
\(219\) 0 0
\(220\) 5960.76 + 3241.50i 1.82670 + 0.993373i
\(221\) −2776.43 1602.97i −0.845082 0.487908i
\(222\) 0 0
\(223\) 2316.13 1337.22i 0.695514 0.401555i −0.110160 0.993914i \(-0.535136\pi\)
0.805674 + 0.592359i \(0.201803\pi\)
\(224\) 41.1795 + 644.496i 0.0122831 + 0.192242i
\(225\) 0 0
\(226\) −37.1729 2912.74i −0.0109412 0.857314i
\(227\) 2949.58 + 5108.82i 0.862425 + 1.49376i 0.869581 + 0.493790i \(0.164389\pi\)
−0.00715576 + 0.999974i \(0.502278\pi\)
\(228\) 0 0
\(229\) −1516.38 + 2626.44i −0.437576 + 0.757904i −0.997502 0.0706386i \(-0.977496\pi\)
0.559926 + 0.828543i \(0.310830\pi\)
\(230\) 3139.26 + 1759.43i 0.899986 + 0.504405i
\(231\) 0 0
\(232\) −2335.88 + 1470.62i −0.661027 + 0.416167i
\(233\) 1294.13i 0.363867i 0.983311 + 0.181934i \(0.0582356\pi\)
−0.983311 + 0.181934i \(0.941764\pi\)
\(234\) 0 0
\(235\) 5179.18i 1.43767i
\(236\) −2052.46 3354.26i −0.566118 0.925184i
\(237\) 0 0
\(238\) 416.295 742.776i 0.113380 0.202298i
\(239\) 2875.14 4979.89i 0.778149 1.34779i −0.154859 0.987937i \(-0.549492\pi\)
0.933008 0.359856i \(-0.117174\pi\)
\(240\) 0 0
\(241\) −3008.82 5211.43i −0.804212 1.39294i −0.916822 0.399296i \(-0.869255\pi\)
0.112611 0.993639i \(-0.464079\pi\)
\(242\) 3345.14 42.6912i 0.888570 0.0113401i
\(243\) 0 0
\(244\) 798.409 20.3822i 0.209479 0.00534769i
\(245\) 4838.46 2793.49i 1.26171 0.728446i
\(246\) 0 0
\(247\) −2070.39 1195.34i −0.533343 0.307926i
\(248\) 399.355 + 210.613i 0.102254 + 0.0539273i
\(249\) 0 0
\(250\) −1487.18 + 884.117i −0.376230 + 0.223666i
\(251\) −3207.28 −0.806541 −0.403270 0.915081i \(-0.632127\pi\)
−0.403270 + 0.915081i \(0.632127\pi\)
\(252\) 0 0
\(253\) 3771.02 0.937082
\(254\) −1931.68 + 1148.37i −0.477182 + 0.283681i
\(255\) 0 0
\(256\) −1675.82 + 3737.49i −0.409136 + 0.912473i
\(257\) 2518.27 + 1453.92i 0.611226 + 0.352892i 0.773445 0.633863i \(-0.218532\pi\)
−0.162219 + 0.986755i \(0.551865\pi\)
\(258\) 0 0
\(259\) 54.8790 31.6844i 0.0131661 0.00760144i
\(260\) 131.215 + 5139.96i 0.0312986 + 1.22603i
\(261\) 0 0
\(262\) 628.081 8.01567i 0.148103 0.00189011i
\(263\) −156.053 270.292i −0.0365880 0.0633723i 0.847152 0.531351i \(-0.178316\pi\)
−0.883740 + 0.467979i \(0.844982\pi\)
\(264\) 0 0
\(265\) 4055.37 7024.11i 0.940073 1.62825i
\(266\) 310.432 553.889i 0.0715556 0.127673i
\(267\) 0 0
\(268\) −4228.69 + 2587.53i −0.963838 + 0.589770i
\(269\) 1826.27i 0.413939i −0.978347 0.206969i \(-0.933640\pi\)
0.978347 0.206969i \(-0.0663600\pi\)
\(270\) 0 0
\(271\) 4987.26i 1.11791i −0.829197 0.558956i \(-0.811202\pi\)
0.829197 0.558956i \(-0.188798\pi\)
\(272\) 4533.05 2935.34i 1.01050 0.654342i
\(273\) 0 0
\(274\) 3003.69 + 1683.44i 0.662261 + 0.371170i
\(275\) −4040.09 + 6997.65i −0.885916 + 1.53445i
\(276\) 0 0
\(277\) −2125.92 3682.20i −0.461134 0.798708i 0.537884 0.843019i \(-0.319224\pi\)
−0.999018 + 0.0443112i \(0.985891\pi\)
\(278\) 79.5662 + 6234.54i 0.0171657 + 1.34505i
\(279\) 0 0
\(280\) −1364.59 + 52.2679i −0.291249 + 0.0111557i
\(281\) 2541.67 1467.43i 0.539585 0.311529i −0.205326 0.978694i \(-0.565825\pi\)
0.744911 + 0.667164i \(0.232492\pi\)
\(282\) 0 0
\(283\) −3467.24 2001.81i −0.728289 0.420478i 0.0895066 0.995986i \(-0.471471\pi\)
−0.817796 + 0.575508i \(0.804804\pi\)
\(284\) −972.497 + 1788.31i −0.203194 + 0.373651i
\(285\) 0 0
\(286\) 2753.25 + 4631.26i 0.569242 + 0.957525i
\(287\) −1232.04 −0.253398
\(288\) 0 0
\(289\) −2207.31 −0.449280
\(290\) −2982.60 5017.05i −0.603946 1.01590i
\(291\) 0 0
\(292\) −384.043 + 706.213i −0.0769672 + 0.141534i
\(293\) −2334.26 1347.69i −0.465423 0.268712i 0.248899 0.968530i \(-0.419931\pi\)
−0.714322 + 0.699817i \(0.753265\pi\)
\(294\) 0 0
\(295\) 7201.14 4157.58i 1.42124 0.820554i
\(296\) 401.617 15.3832i 0.0788633 0.00302071i
\(297\) 0 0
\(298\) −14.6755 1149.93i −0.00285279 0.223535i
\(299\) 1428.80 + 2474.75i 0.276353 + 0.478658i
\(300\) 0 0
\(301\) −233.179 + 403.878i −0.0446518 + 0.0773393i
\(302\) −8519.09 4774.60i −1.62324 0.909759i
\(303\) 0 0
\(304\) 3380.31 2188.89i 0.637743 0.412965i
\(305\) 1688.81i 0.317053i
\(306\) 0 0
\(307\) 4575.16i 0.850547i 0.905065 + 0.425274i \(0.139822\pi\)
−0.905065 + 0.425274i \(0.860178\pi\)
\(308\) −1220.60 + 746.883i −0.225813 + 0.138174i
\(309\) 0 0
\(310\) −466.755 + 832.809i −0.0855158 + 0.152582i
\(311\) 4119.46 7135.11i 0.751103 1.30095i −0.196186 0.980567i \(-0.562856\pi\)
0.947289 0.320381i \(-0.103811\pi\)
\(312\) 0 0
\(313\) 2659.91 + 4607.09i 0.480341 + 0.831975i 0.999746 0.0225534i \(-0.00717958\pi\)
−0.519405 + 0.854528i \(0.673846\pi\)
\(314\) −2490.44 + 31.7833i −0.447591 + 0.00571222i
\(315\) 0 0
\(316\) −201.867 7907.54i −0.0359365 1.40770i
\(317\) 7641.35 4411.73i 1.35388 0.781665i 0.365092 0.930971i \(-0.381038\pi\)
0.988791 + 0.149307i \(0.0477042\pi\)
\(318\) 0 0
\(319\) −5296.76 3058.08i −0.929660 0.536739i
\(320\) −7810.04 3744.11i −1.36436 0.654070i
\(321\) 0 0
\(322\) −652.383 + 387.837i −0.112907 + 0.0671221i
\(323\) −5309.63 −0.914661
\(324\) 0 0
\(325\) −6123.01 −1.04506
\(326\) −4117.45 + 2447.80i −0.699523 + 0.415862i
\(327\) 0 0
\(328\) −6911.82 3645.19i −1.16354 0.613633i
\(329\) −945.947 546.143i −0.158516 0.0915192i
\(330\) 0 0
\(331\) 2056.23 1187.17i 0.341452 0.197138i −0.319462 0.947599i \(-0.603502\pi\)
0.660914 + 0.750462i \(0.270169\pi\)
\(332\) −4026.77 + 102.797i −0.665656 + 0.0169932i
\(333\) 0 0
\(334\) 4638.53 59.1977i 0.759908 0.00969806i
\(335\) −5241.43 9078.43i −0.854836 1.48062i
\(336\) 0 0
\(337\) 321.888 557.527i 0.0520308 0.0901199i −0.838837 0.544383i \(-0.816764\pi\)
0.890868 + 0.454263i \(0.150097\pi\)
\(338\) 1041.98 1859.16i 0.167682 0.299187i
\(339\) 0 0
\(340\) 5960.23 + 9740.57i 0.950703 + 1.55370i
\(341\) 1000.41i 0.158871i
\(342\) 0 0
\(343\) 2401.99i 0.378120i
\(344\) −2503.08 + 1575.88i −0.392317 + 0.246993i
\(345\) 0 0
\(346\) 5382.30 + 3016.56i 0.836284 + 0.468702i
\(347\) −768.265 + 1330.67i −0.118855 + 0.205863i −0.919314 0.393525i \(-0.871256\pi\)
0.800459 + 0.599387i \(0.204589\pi\)
\(348\) 0 0
\(349\) −3432.65 5945.53i −0.526492 0.911910i −0.999524 0.0308650i \(-0.990174\pi\)
0.473032 0.881045i \(-0.343160\pi\)
\(350\) −20.7525 1626.10i −0.00316934 0.248339i
\(351\) 0 0
\(352\) −9057.41 + 578.715i −1.37148 + 0.0876296i
\(353\) −107.968 + 62.3355i −0.0162792 + 0.00939881i −0.508118 0.861288i \(-0.669658\pi\)
0.491838 + 0.870687i \(0.336325\pi\)
\(354\) 0 0
\(355\) −3727.74 2152.21i −0.557318 0.321768i
\(356\) 7167.62 + 3897.80i 1.06709 + 0.580289i
\(357\) 0 0
\(358\) −3396.94 5714.01i −0.501491 0.843560i
\(359\) 4489.49 0.660017 0.330009 0.943978i \(-0.392948\pi\)
0.330009 + 0.943978i \(0.392948\pi\)
\(360\) 0 0
\(361\) 2899.60 0.422744
\(362\) 3295.61 + 5543.57i 0.478491 + 0.804872i
\(363\) 0 0
\(364\) −952.621 518.042i −0.137173 0.0745955i
\(365\) −1472.10 849.917i −0.211105 0.121881i
\(366\) 0 0
\(367\) 750.997 433.589i 0.106817 0.0616707i −0.445640 0.895212i \(-0.647024\pi\)
0.552457 + 0.833542i \(0.313690\pi\)
\(368\) −4807.38 + 245.610i −0.680984 + 0.0347916i
\(369\) 0 0
\(370\) 10.8451 + 849.787i 0.00152381 + 0.119401i
\(371\) 855.275 + 1481.38i 0.119686 + 0.207303i
\(372\) 0 0
\(373\) 2169.58 3757.82i 0.301170 0.521642i −0.675231 0.737606i \(-0.735956\pi\)
0.976401 + 0.215964i \(0.0692895\pi\)
\(374\) 10438.6 + 5850.40i 1.44323 + 0.808869i
\(375\) 0 0
\(376\) −3690.96 5862.62i −0.506242 0.804099i
\(377\) 4634.71i 0.633156i
\(378\) 0 0
\(379\) 14096.9i 1.91058i 0.295677 + 0.955288i \(0.404455\pi\)
−0.295677 + 0.955288i \(0.595545\pi\)
\(380\) 4444.55 + 7263.56i 0.600002 + 0.980560i
\(381\) 0 0
\(382\) −5438.65 + 9703.92i −0.728443 + 1.29973i
\(383\) −4134.45 + 7161.08i −0.551594 + 0.955390i 0.446565 + 0.894751i \(0.352647\pi\)
−0.998160 + 0.0606386i \(0.980686\pi\)
\(384\) 0 0
\(385\) −1512.93 2620.47i −0.200275 0.346887i
\(386\) 7673.45 97.9297i 1.01183 0.0129132i
\(387\) 0 0
\(388\) 8054.80 205.627i 1.05392 0.0269050i
\(389\) −4972.96 + 2871.14i −0.648173 + 0.374223i −0.787756 0.615987i \(-0.788757\pi\)
0.139583 + 0.990210i \(0.455424\pi\)
\(390\) 0 0
\(391\) 5496.35 + 3173.32i 0.710902 + 0.410439i
\(392\) −3486.15 + 6610.26i −0.449176 + 0.851705i
\(393\) 0 0
\(394\) 4857.41 2887.69i 0.621098 0.369238i
\(395\) 16726.2 2.13060
\(396\) 0 0
\(397\) 10494.4 1.32670 0.663349 0.748310i \(-0.269134\pi\)
0.663349 + 0.748310i \(0.269134\pi\)
\(398\) 5857.08 3481.99i 0.737661 0.438534i
\(399\) 0 0
\(400\) 4694.64 9183.90i 0.586830 1.14799i
\(401\) 7070.19 + 4081.97i 0.880469 + 0.508339i 0.870813 0.491614i \(-0.163593\pi\)
0.00965631 + 0.999953i \(0.496926\pi\)
\(402\) 0 0
\(403\) −656.523 + 379.044i −0.0811507 + 0.0468524i
\(404\) 85.9485 + 3366.77i 0.0105844 + 0.414611i
\(405\) 0 0
\(406\) 1230.85 15.7083i 0.150458 0.00192017i
\(407\) 445.277 + 771.242i 0.0542298 + 0.0939288i
\(408\) 0 0
\(409\) −2037.43 + 3528.93i −0.246319 + 0.426637i −0.962502 0.271276i \(-0.912554\pi\)
0.716183 + 0.697913i \(0.245888\pi\)
\(410\) 8078.34 14413.8i 0.973076 1.73621i
\(411\) 0 0
\(412\) −11792.5 + 7215.82i −1.41014 + 0.862859i
\(413\) 1753.66i 0.208940i
\(414\) 0 0
\(415\) 8517.52i 1.00749i
\(416\) −3811.55 5724.72i −0.449222 0.674705i
\(417\) 0 0
\(418\) 7784.07 + 4362.65i 0.910841 + 0.510489i
\(419\) 346.536 600.219i 0.0404043 0.0699823i −0.845116 0.534583i \(-0.820469\pi\)
0.885520 + 0.464601i \(0.153802\pi\)
\(420\) 0 0
\(421\) 5362.68 + 9288.44i 0.620810 + 1.07527i 0.989335 + 0.145657i \(0.0465296\pi\)
−0.368525 + 0.929618i \(0.620137\pi\)
\(422\) −65.6705 5145.72i −0.00757533 0.593577i
\(423\) 0 0
\(424\) 415.247 + 10841.1i 0.0475618 + 1.24172i
\(425\) −11777.1 + 6799.50i −1.34417 + 0.776057i
\(426\) 0 0
\(427\) −308.452 178.085i −0.0349579 0.0201830i
\(428\) −241.393 + 443.895i −0.0272621 + 0.0501319i
\(429\) 0 0
\(430\) −3196.09 5376.16i −0.358440 0.602934i
\(431\) −10013.8 −1.11914 −0.559569 0.828784i \(-0.689033\pi\)
−0.559569 + 0.828784i \(0.689033\pi\)
\(432\) 0 0
\(433\) −9726.02 −1.07945 −0.539726 0.841841i \(-0.681472\pi\)
−0.539726 + 0.841841i \(0.681472\pi\)
\(434\) −102.889 173.069i −0.0113797 0.0191419i
\(435\) 0 0
\(436\) 3192.70 5871.03i 0.350694 0.644888i
\(437\) 4098.64 + 2366.35i 0.448660 + 0.259034i
\(438\) 0 0
\(439\) −5675.95 + 3277.01i −0.617080 + 0.356271i −0.775731 0.631063i \(-0.782619\pi\)
0.158651 + 0.987335i \(0.449285\pi\)
\(440\) −734.546 19177.2i −0.0795866 2.07781i
\(441\) 0 0
\(442\) 115.715 + 9067.05i 0.0124525 + 0.975737i
\(443\) 2939.61 + 5091.55i 0.315271 + 0.546065i 0.979495 0.201468i \(-0.0645713\pi\)
−0.664224 + 0.747533i \(0.731238\pi\)
\(444\) 0 0
\(445\) −8626.14 + 14940.9i −0.918917 + 1.59161i
\(446\) −6598.74 3698.32i −0.700582 0.392647i
\(447\) 0 0
\(448\) 1507.41 1031.64i 0.158969 0.108796i
\(449\) 6761.00i 0.710627i −0.934747 0.355313i \(-0.884374\pi\)
0.934747 0.355313i \(-0.115626\pi\)
\(450\) 0 0
\(451\) 17314.5i 1.80778i
\(452\) −7027.86 + 4300.33i −0.731334 + 0.447501i
\(453\) 0 0
\(454\) 8157.60 14555.2i 0.843293 1.50465i
\(455\) 1146.47 1985.74i 0.118126 0.204600i
\(456\) 0 0
\(457\) 7620.16 + 13198.5i 0.779992 + 1.35099i 0.931946 + 0.362598i \(0.118110\pi\)
−0.151954 + 0.988388i \(0.548557\pi\)
\(458\) 8577.22 109.464i 0.875081 0.0111679i
\(459\) 0 0
\(460\) −259.760 10175.3i −0.0263291 1.03136i
\(461\) −11900.4 + 6870.68i −1.20229 + 0.694142i −0.961064 0.276327i \(-0.910883\pi\)
−0.241226 + 0.970469i \(0.577550\pi\)
\(462\) 0 0
\(463\) 15291.7 + 8828.66i 1.53491 + 0.886183i 0.999125 + 0.0418305i \(0.0133190\pi\)
0.535789 + 0.844352i \(0.320014\pi\)
\(464\) 6951.61 + 3553.53i 0.695518 + 0.355536i
\(465\) 0 0
\(466\) 3146.34 1870.48i 0.312771 0.185940i
\(467\) −6165.12 −0.610895 −0.305447 0.952209i \(-0.598806\pi\)
−0.305447 + 0.952209i \(0.598806\pi\)
\(468\) 0 0
\(469\) 2210.83 0.217669
\(470\) 12591.8 7485.76i 1.23578 0.734664i
\(471\) 0 0
\(472\) −5188.48 + 9838.13i −0.505972 + 0.959400i
\(473\) −5675.89 3276.98i −0.551750 0.318553i
\(474\) 0 0
\(475\) −8782.19 + 5070.40i −0.848325 + 0.489781i
\(476\) −2407.56 + 61.4614i −0.231829 + 0.00591824i
\(477\) 0 0
\(478\) −16262.9 + 207.550i −1.55617 + 0.0198601i
\(479\) 8659.06 + 14997.9i 0.825976 + 1.43063i 0.901171 + 0.433464i \(0.142709\pi\)
−0.0751944 + 0.997169i \(0.523958\pi\)
\(480\) 0 0
\(481\) −337.422 + 584.431i −0.0319857 + 0.0554008i
\(482\) −8321.43 + 14847.5i −0.786371 + 1.40308i
\(483\) 0 0
\(484\) −4938.72 8071.15i −0.463816 0.757997i
\(485\) 17037.7i 1.59514i
\(486\) 0 0
\(487\) 7352.14i 0.684101i 0.939682 + 0.342050i \(0.111121\pi\)
−0.939682 + 0.342050i \(0.888879\pi\)
\(488\) −1203.54 1911.67i −0.111643 0.177330i
\(489\) 0 0
\(490\) −13784.9 7725.89i −1.27090 0.712286i
\(491\) 4221.27 7311.46i 0.387991 0.672019i −0.604189 0.796841i \(-0.706503\pi\)
0.992179 + 0.124822i \(0.0398360\pi\)
\(492\) 0 0
\(493\) −5146.77 8914.47i −0.470181 0.814377i
\(494\) 86.2890 + 6761.31i 0.00785896 + 0.615801i
\(495\) 0 0
\(496\) −65.1574 1275.34i −0.00589850 0.115453i
\(497\) 786.178 453.900i 0.0709555 0.0409662i
\(498\) 0 0
\(499\) −6542.34 3777.22i −0.586924 0.338861i 0.176956 0.984219i \(-0.443375\pi\)
−0.763880 + 0.645358i \(0.776708\pi\)
\(500\) 4299.01 + 2337.83i 0.384515 + 0.209102i
\(501\) 0 0
\(502\) 4635.66 + 7797.68i 0.412151 + 0.693282i
\(503\) −604.632 −0.0535968 −0.0267984 0.999641i \(-0.508531\pi\)
−0.0267984 + 0.999641i \(0.508531\pi\)
\(504\) 0 0
\(505\) −7121.47 −0.627527
\(506\) −5450.46 9168.26i −0.478859 0.805492i
\(507\) 0 0
\(508\) 5583.93 + 3036.58i 0.487691 + 0.265209i
\(509\) −8861.66 5116.28i −0.771682 0.445531i 0.0617925 0.998089i \(-0.480318\pi\)
−0.833474 + 0.552558i \(0.813652\pi\)
\(510\) 0 0
\(511\) 310.465 179.247i 0.0268770 0.0155175i
\(512\) 11508.9 1327.68i 0.993412 0.114601i
\(513\) 0 0
\(514\) −104.955 8223.96i −0.00900659 0.705726i
\(515\) −14616.8 25317.0i −1.25066 2.16621i
\(516\) 0 0
\(517\) 7675.21 13293.8i 0.652911 1.13088i
\(518\) −156.352 87.6290i −0.0132620 0.00743281i
\(519\) 0 0
\(520\) 12306.9 7748.10i 1.03787 0.653416i
\(521\) 18465.3i 1.55274i −0.630276 0.776371i \(-0.717058\pi\)
0.630276 0.776371i \(-0.282942\pi\)
\(522\) 0 0
\(523\) 15941.5i 1.33284i −0.745579 0.666418i \(-0.767827\pi\)
0.745579 0.666418i \(-0.232173\pi\)
\(524\) −927.289 1515.43i −0.0773069 0.126340i
\(525\) 0 0
\(526\) −431.593 + 770.072i −0.0357764 + 0.0638341i
\(527\) −841.844 + 1458.12i −0.0695850 + 0.120525i
\(528\) 0 0
\(529\) 3254.98 + 5637.79i 0.267525 + 0.463368i
\(530\) −22938.8 + 292.748i −1.87999 + 0.0239928i
\(531\) 0 0
\(532\) −1795.32 + 45.8319i −0.146310 + 0.00373508i
\(533\) 11362.7 6560.29i 0.923406 0.533129i
\(534\) 0 0
\(535\) −925.299 534.221i −0.0747741 0.0431709i
\(536\) 12402.9 + 6541.08i 0.999482 + 0.527111i
\(537\) 0 0
\(538\) −4440.10 + 2639.61i −0.355811 + 0.211527i
\(539\) −16559.1 −1.32328
\(540\) 0 0
\(541\) 7256.04 0.576638 0.288319 0.957534i \(-0.406904\pi\)
0.288319 + 0.957534i \(0.406904\pi\)
\(542\) −12125.2 + 7208.37i −0.960929 + 0.571265i
\(543\) 0 0
\(544\) −13688.4 6778.35i −1.07883 0.534227i
\(545\) 12238.1 + 7065.70i 0.961880 + 0.555342i
\(546\) 0 0
\(547\) 374.999 216.506i 0.0293122 0.0169234i −0.485272 0.874363i \(-0.661280\pi\)
0.514585 + 0.857440i \(0.327946\pi\)
\(548\) −248.542 9735.87i −0.0193744 0.758934i
\(549\) 0 0
\(550\) 22852.4 291.646i 1.77169 0.0226106i
\(551\) −3837.96 6647.54i −0.296738 0.513965i
\(552\) 0 0
\(553\) −1763.77 + 3054.94i −0.135630 + 0.234918i
\(554\) −5879.62 + 10490.7i −0.450904 + 0.804527i
\(555\) 0 0
\(556\) 15042.7 9204.58i 1.14740 0.702089i
\(557\) 9185.88i 0.698776i 0.936978 + 0.349388i \(0.113610\pi\)
−0.936978 + 0.349388i \(0.886390\pi\)
\(558\) 0 0
\(559\) 4966.45i 0.375776i
\(560\) 2099.39 + 3242.10i 0.158420 + 0.244649i
\(561\) 0 0
\(562\) −7241.31 4058.45i −0.543516 0.304618i
\(563\) 6499.11 11256.8i 0.486510 0.842659i −0.513370 0.858167i \(-0.671603\pi\)
0.999880 + 0.0155079i \(0.00493650\pi\)
\(564\) 0 0
\(565\) −8710.99 15087.9i −0.648627 1.12345i
\(566\) 144.506 + 11323.0i 0.0107315 + 0.840888i
\(567\) 0 0
\(568\) 5753.43 220.374i 0.425015 0.0162794i
\(569\) −5424.42 + 3131.79i −0.399655 + 0.230741i −0.686335 0.727286i \(-0.740782\pi\)
0.286680 + 0.958026i \(0.407448\pi\)
\(570\) 0 0
\(571\) 21837.8 + 12608.1i 1.60050 + 0.924047i 0.991388 + 0.130961i \(0.0418063\pi\)
0.609109 + 0.793086i \(0.291527\pi\)
\(572\) 7280.29 13387.6i 0.532175 0.978611i
\(573\) 0 0
\(574\) 1780.74 + 2995.39i 0.129489 + 0.217814i
\(575\) 12121.4 0.879125
\(576\) 0 0
\(577\) 18112.2 1.30680 0.653398 0.757014i \(-0.273343\pi\)
0.653398 + 0.757014i \(0.273343\pi\)
\(578\) 3190.35 + 5366.51i 0.229587 + 0.386189i
\(579\) 0 0
\(580\) −7886.75 + 14502.9i −0.564620 + 1.03827i
\(581\) 1555.67 + 898.169i 0.111085 + 0.0641348i
\(582\) 0 0
\(583\) −20818.6 + 12019.6i −1.47893 + 0.853861i
\(584\) 2272.05 87.0268i 0.160990 0.00616643i
\(585\) 0 0
\(586\) 97.2865 + 7623.04i 0.00685813 + 0.537380i
\(587\) 13172.1 + 22814.8i 0.926189 + 1.60421i 0.789638 + 0.613573i \(0.210268\pi\)
0.136551 + 0.990633i \(0.456398\pi\)
\(588\) 0 0
\(589\) −627.764 + 1087.32i −0.0439161 + 0.0760649i
\(590\) −20516.3 11498.5i −1.43160 0.802351i
\(591\) 0 0
\(592\) −617.881 954.195i −0.0428965 0.0662453i
\(593\) 11633.4i 0.805609i −0.915286 0.402804i \(-0.868035\pi\)
0.915286 0.402804i \(-0.131965\pi\)
\(594\) 0 0
\(595\) 5092.53i 0.350880i
\(596\) −2774.54 + 1697.73i −0.190687 + 0.116681i
\(597\) 0 0
\(598\) 3951.60 7050.66i 0.270223 0.482146i
\(599\) −11060.5 + 19157.3i −0.754454 + 1.30675i 0.191191 + 0.981553i \(0.438765\pi\)
−0.945645 + 0.325200i \(0.894568\pi\)
\(600\) 0 0
\(601\) 846.923 + 1466.91i 0.0574820 + 0.0995618i 0.893334 0.449392i \(-0.148359\pi\)
−0.835852 + 0.548954i \(0.815026\pi\)
\(602\) 1318.95 16.8327i 0.0892964 0.00113962i
\(603\) 0 0
\(604\) 704.917 + 27613.0i 0.0474879 + 1.86019i
\(605\) 17327.7 10004.1i 1.16441 0.672274i
\(606\) 0 0
\(607\) −11418.4 6592.43i −0.763525 0.440821i 0.0670351 0.997751i \(-0.478646\pi\)
−0.830560 + 0.556929i \(0.811979\pi\)
\(608\) −10207.5 5054.62i −0.680867 0.337158i
\(609\) 0 0
\(610\) 4105.92 2440.94i 0.272531 0.162018i
\(611\) 11632.2 0.770196
\(612\) 0 0
\(613\) −18052.3 −1.18944 −0.594719 0.803934i \(-0.702737\pi\)
−0.594719 + 0.803934i \(0.702737\pi\)
\(614\) 11123.3 6612.73i 0.731108 0.434639i
\(615\) 0 0
\(616\) 3580.06 + 1888.07i 0.234164 + 0.123494i
\(617\) 18897.2 + 10910.3i 1.23302 + 0.711884i 0.967658 0.252266i \(-0.0811756\pi\)
0.265361 + 0.964149i \(0.414509\pi\)
\(618\) 0 0
\(619\) 15640.0 9029.74i 1.01555 0.586326i 0.102736 0.994709i \(-0.467240\pi\)
0.912811 + 0.408382i \(0.133907\pi\)
\(620\) 2699.39 68.9112i 0.174855 0.00446378i
\(621\) 0 0
\(622\) −23301.3 + 297.374i −1.50208 + 0.0191698i
\(623\) −1819.25 3151.03i −0.116993 0.202638i
\(624\) 0 0
\(625\) 4898.71 8484.82i 0.313518 0.543028i
\(626\) 7356.45 13125.8i 0.469685 0.838037i
\(627\) 0 0
\(628\) 3676.84 + 6008.92i 0.233634 + 0.381818i
\(629\) 1498.81i 0.0950100i
\(630\) 0 0
\(631\) 7301.94i 0.460674i 0.973111 + 0.230337i \(0.0739829\pi\)
−0.973111 + 0.230337i \(0.926017\pi\)
\(632\) −18933.4 + 11920.0i −1.19166 + 0.750241i
\(633\) 0 0
\(634\) −21770.5 12201.4i −1.36375 0.764324i
\(635\) −6720.18 + 11639.7i −0.419972 + 0.727413i
\(636\) 0 0
\(637\) −6274.06 10867.0i −0.390247 0.675928i
\(638\) 220.756 + 17297.7i 0.0136988 + 1.07339i
\(639\) 0 0
\(640\) 2185.45 + 24399.7i 0.134980 + 1.50700i
\(641\) −735.990 + 424.924i −0.0453508 + 0.0261833i −0.522504 0.852637i \(-0.675002\pi\)
0.477153 + 0.878820i \(0.341669\pi\)
\(642\) 0 0
\(643\) 984.538 + 568.423i 0.0603832 + 0.0348622i 0.529888 0.848068i \(-0.322234\pi\)
−0.469504 + 0.882930i \(0.655567\pi\)
\(644\) 1885.85 + 1025.54i 0.115393 + 0.0627514i
\(645\) 0 0
\(646\) 7674.30 + 12909.0i 0.467402 + 0.786219i
\(647\) 995.889 0.0605138 0.0302569 0.999542i \(-0.490367\pi\)
0.0302569 + 0.999542i \(0.490367\pi\)
\(648\) 0 0
\(649\) −24645.0 −1.49061
\(650\) 8849.93 + 14886.5i 0.534035 + 0.898303i
\(651\) 0 0
\(652\) 11902.4 + 6472.59i 0.714928 + 0.388783i
\(653\) −24496.2 14142.9i −1.46801 0.847557i −0.468654 0.883382i \(-0.655261\pi\)
−0.999358 + 0.0358245i \(0.988594\pi\)
\(654\) 0 0
\(655\) 3253.43 1878.37i 0.194079 0.112052i
\(656\) 1127.71 + 22072.9i 0.0671185 + 1.31372i
\(657\) 0 0
\(658\) 39.4248 + 3089.20i 0.00233577 + 0.183023i
\(659\) −12722.0 22035.1i −0.752014 1.30253i −0.946845 0.321690i \(-0.895749\pi\)
0.194831 0.980837i \(1.56242\pi\)
\(660\) 0 0
\(661\) 2109.30 3653.42i 0.124119 0.214980i −0.797269 0.603624i \(-0.793723\pi\)
0.921388 + 0.388644i \(0.127056\pi\)
\(662\) −5858.28 3283.32i −0.343940 0.192764i
\(663\) 0 0
\(664\) 6070.04 + 9641.48i 0.354764 + 0.563497i
\(665\) 3797.51i 0.221445i
\(666\) 0 0
\(667\) 9175.09i 0.532625i
\(668\) −6848.26 11191.8i −0.396657 0.648241i
\(669\) 0 0
\(670\) −14496.1 + 25864.8i −0.835872 + 1.49141i
\(671\) 2502.71 4334.83i 0.143988 0.249395i
\(672\) 0 0
\(673\) −7212.87 12493.0i −0.413129 0.715560i 0.582101 0.813116i \(-0.302231\pi\)
−0.995230 + 0.0975565i \(0.968897\pi\)
\(674\) −1820.73 + 23.2364i −0.104053 + 0.00132794i
\(675\) 0 0
\(676\) −6026.11 + 153.837i −0.342860 + 0.00875270i
\(677\) 27870.5 16091.1i 1.58220 0.913486i 0.587666 0.809103i \(-0.300047\pi\)
0.994537 0.104382i \(-0.0332865\pi\)
\(678\) 0 0
\(679\) −3111.84 1796.62i −0.175878 0.101543i
\(680\) 15067.0 28569.4i 0.849698 1.61116i
\(681\) 0 0
\(682\) 2432.23 1445.94i 0.136561 0.0811847i
\(683\) 28383.3 1.59012 0.795062 0.606528i \(-0.207438\pi\)
0.795062 + 0.606528i \(0.207438\pi\)
\(684\) 0 0
\(685\) 20593.5 1.14867
\(686\) 5839.81 3471.73i 0.325022 0.193223i
\(687\) 0 0
\(688\) 7449.19 + 3807.89i 0.412787 + 0.211009i
\(689\) −15775.9 9108.21i −0.872298 0.503621i
\(690\) 0 0
\(691\) −4592.61 + 2651.54i −0.252838 + 0.145976i −0.621063 0.783761i \(-0.713299\pi\)
0.368225 + 0.929737i \(0.379966\pi\)
\(692\) −445.362 17445.7i −0.0244655 0.958360i
\(693\) 0 0
\(694\) 4345.61 55.4594i 0.237690 0.00303344i
\(695\) 18645.3 + 32294.6i 1.01764 + 1.76260i
\(696\) 0 0
\(697\) 14570.2 25236.3i 0.791801 1.37144i
\(698\) −9493.61 + 16939.0i −0.514812 + 0.918555i
\(699\) 0 0
\(700\) −3923.45 + 2400.75i −0.211846 + 0.129628i
\(701\) 10087.7i 0.543519i 0.962365 + 0.271760i \(0.0876056\pi\)
−0.962365 + 0.271760i \(0.912394\pi\)
\(702\) 0 0
\(703\) 1117.66i 0.0599622i
\(704\) 14498.2 + 21184.3i 0.776166 + 1.13411i
\(705\) 0 0
\(706\) 307.605 + 172.400i 0.0163978 + 0.00919031i
\(707\) 750.956 1300.69i 0.0399471 0.0691905i
\(708\) 0 0
\(709\) 12869.6 + 22290.9i 0.681706 + 1.18075i 0.974460 + 0.224561i \(0.0720949\pi\)
−0.292754 + 0.956188i \(0.594572\pi\)
\(710\) 155.363 + 12173.8i 0.00821223 + 0.643483i
\(711\) 0 0
\(712\) −883.268 23059.9i −0.0464914 1.21378i
\(713\) 1299.68 750.372i 0.0682658 0.0394133i
\(714\) 0 0
\(715\) 27906.5 + 16111.9i 1.45964 + 0.842726i
\(716\) −8982.36 + 16517.6i −0.468836 + 0.862137i
\(717\) 0 0
\(718\) −6488.92 10915.0i −0.337276 0.567334i
\(719\) −7178.86 −0.372359 −0.186180 0.982516i \(-0.559611\pi\)
−0.186180 + 0.982516i \(0.559611\pi\)
\(720\) 0 0
\(721\) 6165.33 0.318459
\(722\) −4190.96 7049.64i −0.216027 0.363380i
\(723\) 0 0
\(724\) 8714.44 16024.9i 0.447334 0.822597i
\(725\) −17025.7 9829.77i −0.872161 0.503543i
\(726\) 0 0
\(727\) −18250.7 + 10537.0i −0.931061 + 0.537548i −0.887147 0.461487i \(-0.847316\pi\)
−0.0439138 + 0.999035i \(0.513983\pi\)
\(728\) 117.392 + 3064.81i 0.00597641 + 0.156029i
\(729\) 0 0
\(730\) 61.3537 + 4807.47i 0.00311069 + 0.243743i
\(731\) −5515.17 9552.55i −0.279050 0.483330i
\(732\) 0 0
\(733\) −10114.0 + 17518.0i −0.509645 + 0.882730i 0.490293 + 0.871558i \(0.336890\pi\)
−0.999938 + 0.0111727i \(0.996444\pi\)
\(734\) −2139.62 1199.17i −0.107595 0.0603026i
\(735\) 0 0
\(736\) 7545.52 + 11332.9i 0.377896 + 0.567577i
\(737\) 31069.9i 1.55288i
\(738\) 0 0
\(739\) 8782.55i 0.437173i −0.975818 0.218587i \(-0.929855\pi\)
0.975818 0.218587i \(-0.0701447\pi\)
\(740\) 2050.36 1254.61i 0.101855 0.0623250i
\(741\) 0 0
\(742\) 2365.42 4220.50i 0.117031 0.208813i
\(743\) 11676.8 20224.8i 0.576553 0.998620i −0.419318 0.907840i \(-0.637731\pi\)
0.995871 0.0907800i \(-0.0289360\pi\)
\(744\) 0 0
\(745\) −3439.02 5956.56i −0.169122 0.292928i
\(746\) −12272.0 + 156.617i −0.602291 + 0.00768654i
\(747\) 0 0
\(748\) −863.747 33834.7i −0.0422216 1.65390i
\(749\) 195.145 112.667i 0.00951995 0.00549634i
\(750\) 0 0
\(751\) −14625.3 8443.94i −0.710634 0.410285i 0.100662 0.994921i \(-0.467904\pi\)
−0.811296 + 0.584636i \(0.801237\pi\)
\(752\) −8918.69 + 17447.2i −0.432488 + 0.846056i
\(753\) 0 0
\(754\) −11268.1 + 6698.81i −0.544244 + 0.323549i
\(755\) −58407.6 −2.81546
\(756\) 0 0
\(757\) 6838.01 0.328311 0.164156 0.986434i \(-0.447510\pi\)
0.164156 + 0.986434i \(0.447510\pi\)
\(758\) 34272.9 20375.0i 1.64228 0.976325i
\(759\) 0 0
\(760\) 11235.5 21304.2i 0.536257 1.01682i
\(761\) 20503.9 + 11837.9i 0.976696 + 0.563896i 0.901271 0.433256i \(-0.142635\pi\)
0.0754248 + 0.997151i \(0.475969\pi\)
\(762\) 0 0
\(763\) −2581.02 + 1490.15i −0.122463 + 0.0707039i
\(764\) 31453.4 802.957i 1.48945 0.0380235i
\(765\) 0 0
\(766\) 23386.1 298.457i 1.10310 0.0140779i
\(767\) −9337.76 16173.5i −0.439592 0.761396i
\(768\) 0 0
\(769\) −18418.7 + 31902.0i −0.863711 + 1.49599i 0.00461075 + 0.999989i \(0.498532\pi\)
−0.868322 + 0.496002i \(0.834801\pi\)
\(770\) −4184.28 + 7465.81i −0.195832 + 0.349414i
\(771\) 0 0
\(772\) −11329.0 18514.5i −0.528158 0.863148i
\(773\) 7505.51i 0.349230i 0.984637 + 0.174615i \(0.0558680\pi\)
−0.984637 + 0.174615i \(0.944132\pi\)
\(774\) 0 0
\(775\) 3215.66i 0.149045i
\(776\) −12142.0 19286.0i −0.561691 0.892173i
\(777\) 0 0
\(778\) 14168.2 + 7940.66i 0.652896 + 0.365921i
\(779\) 10865.0 18818.8i 0.499717 0.865535i
\(780\) 0 0