Properties

Label 108.4.h.b.35.4
Level 108
Weight 4
Character 108.35
Analytic conductor 6.372
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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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 35.4
Character \(\chi\) \(=\) 108.35
Dual form 108.4.h.b.71.4

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

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

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 −0.982150 0.188097i \(-0.939768\pi\)
−0.328178 + 0.944616i \(0.606435\pi\)
\(6\) 0 0
\(7\) 3.08966 + 1.78382i 0.166826 + 0.0963170i 0.581088 0.813841i \(-0.302627\pi\)
−0.414262 + 0.910157i \(0.635960\pi\)
\(8\) 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 −0.285620 0.958343i \(-0.592199\pi\)
0.972759 0.231817i \(-0.0744672\pi\)
\(12\) 0 0
\(13\) −18.9966 32.9032i −0.405286 0.701977i 0.589068 0.808083i \(-0.299495\pi\)
−0.994355 + 0.106107i \(0.966162\pi\)
\(14\) −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 \(-0.794399\pi\)
0.798549 0.601930i \(-0.205601\pi\)
\(18\) 0 0
\(19\) 62.9237i 0.759773i −0.925033 0.379887i \(-0.875963\pi\)
0.925033 0.379887i \(-0.124037\pi\)
\(20\) 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 0.984607 0.174784i \(-0.0559227\pi\)
−0.643671 + 0.765302i \(0.722589\pi\)
\(24\) 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 0.122053 0.992524i \(-0.461052\pi\)
−0.798524 + 0.601963i \(0.794386\pi\)
\(30\) 0 0
\(31\) 17.2800 9.97659i 0.100115 0.0578016i −0.449106 0.893478i \(-0.648258\pi\)
0.549222 + 0.835677i \(0.314924\pi\)
\(32\) −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 −0.946233 0.323486i \(-0.895145\pi\)
−0.192969 + 0.981205i \(0.561812\pi\)
\(42\) 0 0
\(43\) −113.206 65.3596i −0.401483 0.231796i 0.285641 0.958337i \(-0.407794\pi\)
−0.687124 + 0.726540i \(0.741127\pi\)
\(44\) −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 −0.999593 0.0285243i \(-0.990919\pi\)
0.524499 + 0.851411i \(0.324253\pi\)
\(48\) 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 \(-0.786599\pi\)
0.783561 0.621315i \(-0.213401\pi\)
\(54\) 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 −0.998770 0.0495801i \(-0.984212\pi\)
0.456447 0.889750i \(1.65088\pi\)
\(60\) 0 0
\(61\) −49.9168 + 86.4585i −0.104774 + 0.181473i −0.913646 0.406511i \(-0.866745\pi\)
0.808872 + 0.587985i \(0.200079\pi\)
\(62\) −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 0.0767351 0.997052i \(-0.475550\pi\)
0.901839 + 0.432071i \(0.142217\pi\)
\(68\) −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 −0.254691 0.967022i \(-0.581974\pi\)
−0.964812 + 0.262942i \(0.915307\pi\)
\(80\) 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 −0.650150 0.759806i \(-0.725294\pi\)
0.983086 + 0.183143i \(0.0586272\pi\)
\(84\) 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 \(0.207761\pi\)
−0.794448 + 0.607333i \(0.792239\pi\)
\(90\) 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 0.472369 + 0.881401i \(0.343399\pi\)
−0.999500 + 0.0316171i \(0.989934\pi\)
\(98\) 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 0.668721 0.743513i \(-0.266842\pi\)
−0.309540 + 0.950886i \(0.600175\pi\)
\(102\) 0 0
\(103\) 1496.60 864.065i 1.43170 0.826591i 0.434447 0.900697i \(-0.356944\pi\)
0.997250 + 0.0741066i \(0.0236105\pi\)
\(104\) −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 −0.0804674 0.996757i \(-0.525641\pi\)
0.822983 + 0.568065i \(0.192308\pi\)
\(114\) 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 \(0.0895287\pi\)
−0.960706 + 0.277569i \(0.910471\pi\)
\(128\) −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 0.826619 0.562763i \(-0.190262\pi\)
−0.900676 + 0.434491i \(0.856928\pi\)
\(132\) 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 0.133842 0.991003i \(-0.457268\pi\)
−0.791312 + 0.611412i \(0.790602\pi\)
\(138\) 0 0
\(139\) −1909.09 + 1102.21i −1.16494 + 0.672578i −0.952483 0.304592i \(-0.901480\pi\)
−0.212457 + 0.977170i \(0.568146\pi\)
\(140\) 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 −0.400065 0.916487i \(-0.631013\pi\)
0.593668 + 0.804710i \(0.297679\pi\)
\(150\) 0 0
\(151\) 2990.17 + 1726.37i 1.61150 + 0.930399i 0.989023 + 0.147759i \(0.0472060\pi\)
0.622475 + 0.782640i \(0.286127\pi\)
\(152\) 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 0.955963 0.293488i \(-0.0948160\pi\)
−0.732149 + 0.681144i \(0.761483\pi\)
\(158\) 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 \(0.133391\pi\)
−0.913472 + 0.406901i \(0.866609\pi\)
\(164\) 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 0.611075 0.791573i \(-0.290737\pi\)
−0.991060 + 0.133420i \(0.957404\pi\)
\(168\) 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 0.0236985 0.999719i \(-0.492456\pi\)
−0.853933 + 0.520383i \(0.825789\pi\)
\(174\) 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 0.205239 + 0.978712i \(0.434203\pi\)
−0.950209 + 0.311614i \(0.899130\pi\)
\(192\) 0 0
\(193\) −1356.60 2349.69i −0.505958 0.876346i −0.999976 0.00689392i \(-0.997806\pi\)
0.494018 0.869452i \(-0.335528\pi\)
\(194\) −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 \(-0.882339\pi\)
0.932456 0.361282i \(-0.117661\pi\)
\(198\) 0 0
\(199\) 2409.09i 0.858170i −0.903264 0.429085i \(-0.858836\pi\)
0.903264 0.429085i \(-0.141164\pi\)
\(200\) 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 −0.220420 0.975405i \(-0.570743\pi\)
0.734515 + 0.678592i \(0.237410\pi\)
\(212\) −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 0.805674 0.592359i \(-0.201803\pi\)
−0.110160 + 0.993914i \(0.535136\pi\)
\(224\) 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 −0.00715576 0.999974i \(-0.502278\pi\)
0.869581 0.493790i \(-0.164389\pi\)
\(228\) 0 0
\(229\) −1516.38 2626.44i −0.437576 0.757904i 0.559926 0.828543i \(-0.310830\pi\)
−0.997502 + 0.0706386i \(0.977496\pi\)
\(230\) 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 \(-0.941764\pi\)
0.983311 0.181934i \(-0.0582356\pi\)
\(234\) 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 0.933008 + 0.359856i \(0.117174\pi\)
−0.154859 + 0.987937i \(0.549492\pi\)
\(240\) 0 0
\(241\) −3008.82 + 5211.43i −0.804212 + 1.39294i 0.112611 + 0.993639i \(0.464079\pi\)
−0.916822 + 0.399296i \(0.869255\pi\)
\(242\) 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 −0.162219 0.986755i \(-0.551865\pi\)
0.773445 + 0.633863i \(0.218532\pi\)
\(258\) 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 −0.883740 0.467979i \(-0.844982\pi\)
0.847152 + 0.531351i \(0.178316\pi\)
\(264\) 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 \(0.0663600\pi\)
−0.978347 + 0.206969i \(0.933640\pi\)
\(270\) 0 0
\(271\) 4987.26i 1.11791i 0.829197 + 0.558956i \(0.188798\pi\)
−0.829197 + 0.558956i \(0.811202\pi\)
\(272\) 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 −0.999018 0.0443112i \(-0.985891\pi\)
0.537884 + 0.843019i \(0.319224\pi\)
\(278\) 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 0.744911 0.667164i \(-0.232492\pi\)
−0.205326 + 0.978694i \(0.565825\pi\)
\(282\) 0 0
\(283\) −3467.24 + 2001.81i −0.728289 + 0.420478i −0.817796 0.575508i \(-0.804804\pi\)
0.0895066 + 0.995986i \(0.471471\pi\)
\(284\) −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 −0.714322 0.699817i \(-0.753265\pi\)
0.248899 + 0.968530i \(0.419931\pi\)
\(294\) 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 \(-0.860178\pi\)
0.905065 0.425274i \(-0.139822\pi\)
\(308\) −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 0.947289 + 0.320381i \(0.103811\pi\)
−0.196186 + 0.980567i \(0.562856\pi\)
\(312\) 0 0
\(313\) 2659.91 4607.09i 0.480341 0.831975i −0.519405 0.854528i \(-0.673846\pi\)
0.999746 + 0.0225534i \(0.00717958\pi\)
\(314\) −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 0.988791 0.149307i \(-0.0477042\pi\)
0.365092 + 0.930971i \(0.381038\pi\)
\(318\) 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 0.660914 0.750462i \(-0.270169\pi\)
−0.319462 + 0.947599i \(0.603502\pi\)
\(332\) −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 0.890868 0.454263i \(-0.150097\pi\)
−0.838837 + 0.544383i \(0.816764\pi\)
\(338\) 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 0.800459 0.599387i \(-0.204589\pi\)
−0.919314 + 0.393525i \(0.871256\pi\)
\(348\) 0 0
\(349\) −3432.65 + 5945.53i −0.526492 + 0.911910i 0.473032 + 0.881045i \(0.343160\pi\)
−0.999524 + 0.0308650i \(0.990174\pi\)
\(350\) −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 0.491838 0.870687i \(-0.336325\pi\)
−0.508118 + 0.861288i \(0.669658\pi\)
\(354\) 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 0.552457 0.833542i \(-0.313690\pi\)
−0.445640 + 0.895212i \(0.647024\pi\)
\(368\) −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 0.976401 0.215964i \(-0.0692895\pi\)
−0.675231 + 0.737606i \(0.735956\pi\)
\(374\) 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 \(-0.595545\pi\)
0.295677 0.955288i \(-0.404455\pi\)
\(380\) 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 −0.998160 0.0606386i \(-0.980686\pi\)
0.446565 0.894751i \(1.64735\pi\)
\(384\) 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 0.139583 0.990210i \(-0.455424\pi\)
−0.787756 + 0.615987i \(0.788757\pi\)
\(390\) 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 0.00965631 0.999953i \(-0.496926\pi\)
0.870813 + 0.491614i \(0.163593\pi\)
\(402\) 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 0.716183 0.697913i \(-0.245888\pi\)
−0.962502 + 0.271276i \(0.912554\pi\)
\(410\) 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 0.885520 0.464601i \(-0.153802\pi\)
−0.845116 + 0.534583i \(0.820469\pi\)
\(420\) 0 0
\(421\) 5362.68 9288.44i 0.620810 1.07527i −0.368525 0.929618i \(-0.620137\pi\)
0.989335 0.145657i \(-0.0465296\pi\)
\(422\) −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 0.158651 0.987335i \(-0.449285\pi\)
−0.775731 + 0.631063i \(0.782619\pi\)
\(440\) −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 −0.664224 0.747533i \(-0.731238\pi\)
0.979495 + 0.201468i \(0.0645713\pi\)
\(444\) 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 \(0.115626\pi\)
−0.934747 + 0.355313i \(0.884374\pi\)
\(450\) 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 −0.151954 0.988388i \(-0.548557\pi\)
0.931946 0.362598i \(-0.118110\pi\)
\(458\) 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 −0.241226 0.970469i \(-0.577550\pi\)
−0.961064 + 0.276327i \(0.910883\pi\)
\(462\) 0 0
\(463\) 15291.7 8828.66i 1.53491 0.886183i 0.535789 0.844352i \(-0.320014\pi\)
0.999125 0.0418305i \(-0.0133190\pi\)
\(464\) 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 −0.0751944 0.997169i \(-0.523958\pi\)
0.901171 0.433464i \(-0.142709\pi\)
\(480\) 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 \(-0.888879\pi\)
0.939682 0.342050i \(-0.111121\pi\)
\(488\) −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 0.992179 0.124822i \(-0.0398360\pi\)
−0.604189 + 0.796841i \(0.706503\pi\)
\(492\) 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 −0.763880 0.645358i \(-0.776708\pi\)
0.176956 + 0.984219i \(0.443375\pi\)
\(500\) 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 −0.833474 0.552558i \(-0.813652\pi\)
0.0617925 + 0.998089i \(0.480318\pi\)
\(510\) 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 \(0.282942\pi\)
−0.630276 + 0.776371i \(0.717058\pi\)
\(522\) 0 0
\(523\) 15941.5i 1.33284i 0.745579 + 0.666418i \(0.232173\pi\)
−0.745579 + 0.666418i \(0.767827\pi\)
\(524\) −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 0.514585 0.857440i \(-0.327946\pi\)
−0.485272 + 0.874363i \(0.661280\pi\)
\(548\) −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 \(-0.886390\pi\)
0.936978 0.349388i \(-0.113610\pi\)
\(558\) 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 0.999880 0.0155079i \(-0.00493650\pi\)
−0.513370 + 0.858167i \(0.671603\pi\)
\(564\) 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 0.286680 0.958026i \(-0.407448\pi\)
−0.686335 + 0.727286i \(0.740782\pi\)
\(570\) 0 0
\(571\) 21837.8 12608.1i 1.60050 0.924047i 0.609109 0.793086i \(-0.291527\pi\)
0.991388 0.130961i \(-0.0418063\pi\)
\(572\) 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 0.136551 0.990633i \(-0.456398\pi\)
0.789638 0.613573i \(-0.210268\pi\)
\(588\) 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 \(0.131965\pi\)
−0.915286 + 0.402804i \(0.868035\pi\)
\(594\) 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 −0.945645 0.325200i \(-0.894568\pi\)
0.191191 0.981553i \(1.56124\pi\)
\(600\) 0 0
\(601\) 846.923 1466.91i 0.0574820 0.0995618i −0.835852 0.548954i \(-0.815026\pi\)
0.893334 + 0.449392i \(0.148359\pi\)
\(602\) 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 −0.830560 0.556929i \(-0.811979\pi\)
0.0670351 + 0.997751i \(0.478646\pi\)
\(608\) −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 0.265361 0.964149i \(-0.414509\pi\)
0.967658 + 0.252266i \(0.0811756\pi\)
\(618\) 0 0
\(619\) 15640.0 + 9029.74i 1.01555 + 0.586326i 0.912811 0.408382i \(-0.133907\pi\)
0.102736 + 0.994709i \(0.467240\pi\)
\(620\) 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 \(-0.926017\pi\)
0.973111 0.230337i \(-0.0739829\pi\)
\(632\) −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 0.477153 0.878820i \(-0.341669\pi\)
−0.522504 + 0.852637i \(0.675002\pi\)
\(642\) 0 0
\(643\) 984.538 568.423i 0.0603832 0.0348622i −0.469504 0.882930i \(-0.655567\pi\)
0.529888 + 0.848068i \(0.322234\pi\)
\(644\) 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 −0.999358 0.0358245i \(-0.988594\pi\)
−0.468654 + 0.883382i \(0.655261\pi\)
\(654\) 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 0.194831 + 0.980837i \(0.437584\pi\)
−0.946845 + 0.321690i \(0.895749\pi\)
\(660\) 0 0
\(661\) 2109.30 + 3653.42i 0.124119 + 0.214980i 0.921388 0.388644i \(-0.127056\pi\)
−0.797269 + 0.603624i \(0.793723\pi\)
\(662\) −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 −0.995230 0.0975565i \(-0.968897\pi\)
0.582101 + 0.813116i \(0.302231\pi\)
\(674\) −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 0.994537 + 0.104382i \(0.0332865\pi\)
0.587666 + 0.809103i \(0.300047\pi\)
\(678\) 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 0.368225 0.929737i \(-0.379966\pi\)
−0.621063 + 0.783761i \(0.713299\pi\)
\(692\) −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 \(-0.912394\pi\)
0.962365 0.271760i \(-0.0876056\pi\)
\(702\) 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 −0.292754 0.956188i \(-0.594572\pi\)
0.974460 0.224561i \(-0.0720949\pi\)
\(710\) 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 −0.0439138 0.999035i \(-0.513983\pi\)
−0.887147 + 0.461487i \(0.847316\pi\)
\(728\) 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 −0.999938 0.0111727i \(-0.996444\pi\)
0.490293 0.871558i \(-0.336890\pi\)
\(734\) −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 \(0.0701447\pi\)
−0.975818 + 0.218587i \(0.929855\pi\)
\(740\) 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 0.995871 + 0.0907800i \(0.0289360\pi\)
−0.419318 + 0.907840i \(0.637731\pi\)
\(744\) 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 −0.811296 0.584636i \(-0.801237\pi\)
0.100662 + 0.994921i \(0.467904\pi\)
\(752\) −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 0.0754248 0.997151i \(-0.475969\pi\)
0.901271 + 0.433256i \(0.142635\pi\)
\(762\) 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 −0.868322 0.496002i \(-0.834801\pi\)
0.00461075 0.999989i \(-0.498532\pi\)
\(770\) −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 \(-0.944132\pi\)
0.984637 0.174615i \(-0.0558680\pi\)
\(774\) 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