Properties

Label 108.4.h.b.35.8
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 35.8
Character \(\chi\) \(=\) 108.35
Dual form 108.4.h.b.71.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.38284 - 2.46734i) q^{2} +(-4.17551 - 6.82387i) q^{4} +(-14.6499 + 8.45813i) q^{5} +(-3.08966 - 1.78382i) q^{7} +(-22.6108 + 0.866066i) q^{8} +O(q^{10})\) \(q+(1.38284 - 2.46734i) q^{2} +(-4.17551 - 6.82387i) q^{4} +(-14.6499 + 8.45813i) q^{5} +(-3.08966 - 1.78382i) q^{7} +(-22.6108 + 0.866066i) q^{8} +(0.610574 + 47.8425i) q^{10} +(-25.0688 + 43.4205i) q^{11} +(-18.9966 - 32.9032i) q^{13} +(-8.67378 + 5.15650i) q^{14} +(-29.1303 + 56.9862i) q^{16} -84.3819i q^{17} +62.9237i q^{19} +(118.888 + 64.6521i) q^{20} +(72.4668 + 121.897i) q^{22} +(-37.6066 - 65.1366i) q^{23} +(80.5801 - 139.569i) q^{25} +(-107.453 + 1.37133i) q^{26} +(0.728372 + 28.5317i) q^{28} +(-105.644 - 60.9938i) q^{29} +(-17.2800 + 9.97659i) q^{31} +(100.322 + 150.677i) q^{32} +(-208.199 - 116.687i) q^{34} +60.3510 q^{35} +17.7622 q^{37} +(155.254 + 87.0135i) q^{38} +(323.922 - 203.933i) q^{40} +(-299.072 + 172.670i) q^{41} +(113.206 + 65.3596i) q^{43} +(400.970 - 10.2362i) q^{44} +(-212.718 + 2.71474i) q^{46} +(153.083 - 265.147i) q^{47} +(-165.136 - 286.024i) q^{49} +(-232.934 - 391.820i) q^{50} +(-145.206 + 267.018i) q^{52} -479.464i q^{53} -848.142i q^{55} +(71.4047 + 37.6577i) q^{56} +(-296.581 + 176.316i) q^{58} +(245.774 + 425.693i) q^{59} +(-49.9168 + 86.4585i) q^{61} +(0.720188 + 56.4315i) q^{62} +(510.500 - 39.1649i) q^{64} +(556.599 + 321.352i) q^{65} +(-536.669 + 309.846i) q^{67} +(-575.811 + 352.337i) q^{68} +(83.4558 - 148.906i) q^{70} -254.455 q^{71} +100.485 q^{73} +(24.5622 - 43.8253i) q^{74} +(429.383 - 262.738i) q^{76} +(154.908 - 89.4363i) q^{77} +(856.295 + 494.382i) q^{79} +(-55.2404 - 1081.23i) q^{80} +(12.4646 + 976.687i) q^{82} +(-251.755 + 436.053i) q^{83} +(713.714 + 1236.19i) q^{85} +(317.810 - 188.936i) q^{86} +(529.222 - 1003.48i) q^{88} +1019.86i q^{89} +135.546i q^{91} +(-287.457 + 528.601i) q^{92} +(-442.518 - 744.363i) q^{94} +(-532.217 - 921.828i) q^{95} +(-503.589 + 872.242i) q^{97} +(-934.074 + 11.9208i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{4} + 72q^{5} + O(q^{10}) \) \( 24q - 12q^{4} + 72q^{5} + 96q^{10} - 216q^{13} + 36q^{14} - 72q^{16} + 540q^{20} - 192q^{22} + 252q^{25} - 672q^{28} - 576q^{29} - 360q^{32} - 660q^{34} + 1248q^{37} + 144q^{38} + 636q^{40} - 1116q^{41} + 960q^{46} + 348q^{49} + 648q^{50} + 132q^{52} + 1692q^{56} + 516q^{58} - 264q^{61} + 960q^{64} + 2592q^{65} - 5688q^{68} + 564q^{70} - 4776q^{73} - 5652q^{74} - 600q^{76} - 648q^{77} - 4104q^{82} + 720q^{85} + 9540q^{86} + 1956q^{88} + 7416q^{92} - 1188q^{94} + 588q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.38284 2.46734i 0.488908 0.872335i
\(3\) 0 0
\(4\) −4.17551 6.82387i −0.521938 0.852983i
\(5\) −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 0.414262 0.910157i \(-0.364040\pi\)
−0.581088 + 0.813841i \(0.697373\pi\)
\(8\) −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 \(0.407801\pi\)
−0.972759 + 0.231817i \(0.925533\pi\)
\(12\) 0 0
\(13\) −18.9966 32.9032i −0.405286 0.701977i 0.589068 0.808083i \(-0.299495\pi\)
−0.994355 + 0.106107i \(0.966162\pi\)
\(14\) −8.67378 + 5.15650i −0.165583 + 0.0984380i
\(15\) 0 0
\(16\) −29.1303 + 56.9862i −0.455161 + 0.890409i
\(17\) 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 \(0.124037\pi\)
−0.925033 + 0.379887i \(0.875963\pi\)
\(20\) 118.888 + 64.6521i 1.32921 + 0.722832i
\(21\) 0 0
\(22\) 72.4668 + 121.897i 0.702271 + 1.18129i
\(23\) −37.6066 65.1366i −0.340936 0.590518i 0.643671 0.765302i \(-0.277411\pi\)
−0.984607 + 0.174784i \(0.944077\pi\)
\(24\) 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 −0.549222 0.835677i \(-0.685076\pi\)
0.449106 + 0.893478i \(0.351742\pi\)
\(32\) 100.322 + 150.677i 0.554204 + 0.832381i
\(33\) 0 0
\(34\) −208.199 116.687i −1.05017 0.588577i
\(35\) 60.3510 0.291462
\(36\) 0 0
\(37\) 17.7622 0.0789211 0.0394606 0.999221i \(-0.487436\pi\)
0.0394606 + 0.999221i \(0.487436\pi\)
\(38\) 155.254 + 87.0135i 0.662777 + 0.371459i
\(39\) 0 0
\(40\) 323.922 203.933i 1.28041 0.806117i
\(41\) −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 0.687124 0.726540i \(-0.258873\pi\)
−0.285641 + 0.958337i \(0.592206\pi\)
\(44\) 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 \(-0.675747\pi\)
0.999593 + 0.0285243i \(0.00908080\pi\)
\(48\) 0 0
\(49\) −165.136 286.024i −0.481446 0.833889i
\(50\) −232.934 391.820i −0.658837 1.10823i
\(51\) 0 0
\(52\) −145.206 + 267.018i −0.387240 + 0.712091i
\(53\) 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
\(56\) 71.4047 + 37.6577i 0.170390 + 0.0898611i
\(57\) 0 0
\(58\) −296.581 + 176.316i −0.671432 + 0.399161i
\(59\) 245.774 + 425.693i 0.542323 + 0.939330i 0.998770 + 0.0495801i \(0.0157883\pi\)
−0.456447 + 0.889750i \(0.650878\pi\)
\(60\) 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 −0.901839 0.432071i \(-0.857783\pi\)
−0.0767351 + 0.997052i \(0.524450\pi\)
\(68\) −575.811 + 352.337i −1.02687 + 0.628341i
\(69\) 0 0
\(70\) 83.4558 148.906i 0.142498 0.254253i
\(71\) −254.455 −0.425327 −0.212663 0.977125i \(-0.568214\pi\)
−0.212663 + 0.977125i \(0.568214\pi\)
\(72\) 0 0
\(73\) 100.485 0.161108 0.0805541 0.996750i \(-0.474331\pi\)
0.0805541 + 0.996750i \(0.474331\pi\)
\(74\) 24.5622 43.8253i 0.0385852 0.0688457i
\(75\) 0 0
\(76\) 429.383 262.738i 0.648074 0.396555i
\(77\) 154.908 89.4363i 0.229265 0.132366i
\(78\) 0 0
\(79\) 856.295 + 494.382i 1.21950 + 0.704080i 0.964812 0.262942i \(-0.0846928\pi\)
0.254691 + 0.967022i \(0.418026\pi\)
\(80\) −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 \(-0.941373\pi\)
0.650150 + 0.759806i \(0.274706\pi\)
\(84\) 0 0
\(85\) 713.714 + 1236.19i 0.910743 + 1.57745i
\(86\) 317.810 188.936i 0.398492 0.236901i
\(87\) 0 0
\(88\) 529.222 1003.48i 0.641082 1.21559i
\(89\) 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
\(92\) −287.457 + 528.601i −0.325755 + 0.599027i
\(93\) 0 0
\(94\) −442.518 744.363i −0.485556 0.816757i
\(95\) −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 −0.997250 0.0741066i \(-0.976389\pi\)
−0.434447 + 0.900697i \(0.643056\pi\)
\(104\) 458.026 + 727.516i 0.431858 + 0.685950i
\(105\) 0 0
\(106\) −1183.00 663.022i −1.08399 0.607532i
\(107\) −63.1607 −0.0570652 −0.0285326 0.999593i \(-0.509083\pi\)
−0.0285326 + 0.999593i \(0.509083\pi\)
\(108\) 0 0
\(109\) −835.373 −0.734076 −0.367038 0.930206i \(-0.619628\pi\)
−0.367038 + 0.930206i \(0.619628\pi\)
\(110\) −2092.65 1172.84i −1.81388 1.01660i
\(111\) 0 0
\(112\) 191.656 124.105i 0.161694 0.104704i
\(113\) 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
\(122\) 144.295 + 242.720i 0.107081 + 0.180122i
\(123\) 0 0
\(124\) 140.231 + 76.2588i 0.101558 + 0.0552278i
\(125\) 611.695i 0.437693i
\(126\) 0 0
\(127\) 794.523i 0.555138i −0.960706 0.277569i \(-0.910471\pi\)
0.960706 0.277569i \(-0.0895287\pi\)
\(128\) 609.307 1313.73i 0.420747 0.907178i
\(129\) 0 0
\(130\) 1562.57 928.938i 1.05420 0.626717i
\(131\) 111.039 + 192.325i 0.0740575 + 0.128271i 0.900676 0.434491i \(-0.143072\pi\)
−0.826619 + 0.562763i \(0.809738\pi\)
\(132\) 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 0.212457 0.977170i \(-0.431854\pi\)
0.952483 + 0.304592i \(0.0985202\pi\)
\(140\) −251.996 411.827i −0.152125 0.248612i
\(141\) 0 0
\(142\) −351.870 + 627.826i −0.207946 + 0.371028i
\(143\) 1904.89 1.11395
\(144\) 0 0
\(145\) 2063.57 1.18187
\(146\) 138.955 247.931i 0.0787671 0.140540i
\(147\) 0 0
\(148\) −74.1660 121.207i −0.0411920 0.0673184i
\(149\) 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 \(-0.952794\pi\)
−0.622475 0.782640i \(1.28613\pi\)
\(152\) −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 \(0.761483\pi\)
\(158\) 2403.93 1429.12i 1.21042 0.719585i
\(159\) 0 0
\(160\) −2744.15 1358.87i −1.35590 0.671427i
\(161\) 268.333i 0.131352i
\(162\) 0 0
\(163\) 1693.56i 0.813802i −0.913472 0.406901i \(-0.866609\pi\)
0.913472 0.406901i \(-0.133391\pi\)
\(164\) 2427.05 + 1319.85i 1.15562 + 0.628432i
\(165\) 0 0
\(166\) 727.752 + 1224.16i 0.340268 + 0.572367i
\(167\) 820.051 + 1420.37i 0.379985 + 0.658153i 0.991060 0.133420i \(-0.0425959\pi\)
−0.611075 + 0.791573i \(0.709263\pi\)
\(168\) 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
\(176\) −1744.10 2693.43i −0.746971 1.15355i
\(177\) 0 0
\(178\) 2516.35 + 1410.31i 1.05960 + 0.593859i
\(179\) −2350.24 −0.981370 −0.490685 0.871337i \(-0.663253\pi\)
−0.490685 + 0.871337i \(0.663253\pi\)
\(180\) 0 0
\(181\) −2280.14 −0.936362 −0.468181 0.883633i \(-0.655090\pi\)
−0.468181 + 0.883633i \(0.655090\pi\)
\(182\) 334.438 + 187.439i 0.136210 + 0.0763399i
\(183\) 0 0
\(184\) 906.730 + 1440.22i 0.363288 + 0.577036i
\(185\) −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 \(-0.565797\pi\)
0.950209 0.311614i \(-0.100870\pi\)
\(192\) 0 0
\(193\) −1356.60 2349.69i −0.505958 0.876346i −0.999976 0.00689392i \(-0.997806\pi\)
0.494018 0.869452i \(-0.335528\pi\)
\(194\) 1455.73 + 2448.70i 0.538739 + 0.906217i
\(195\) 0 0
\(196\) −1262.26 + 2321.16i −0.460008 + 0.845904i
\(197\) 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 \(0.141164\pi\)
−0.903264 + 0.429085i \(0.858836\pi\)
\(200\) −1701.11 + 3225.55i −0.601432 + 1.14041i
\(201\) 0 0
\(202\) 1023.51 608.471i 0.356505 0.211940i
\(203\) 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 \(-0.762590\pi\)
0.220420 + 0.975405i \(0.429257\pi\)
\(212\) −3271.80 + 2002.00i −1.05994 + 0.648577i
\(213\) 0 0
\(214\) −87.3411 + 155.839i −0.0278996 + 0.0497800i
\(215\) −2211.28 −0.701433
\(216\) 0 0
\(217\) 71.1856 0.0222691
\(218\) −1155.19 + 2061.15i −0.358895 + 0.640360i
\(219\) 0 0
\(220\) −5787.61 + 3541.42i −1.77364 + 1.08528i
\(221\) −2776.43 + 1602.97i −0.845082 + 0.487908i
\(222\) 0 0
\(223\) −2316.13 1337.22i −0.695514 0.401555i 0.110160 0.993914i \(-0.464864\pi\)
−0.805674 + 0.592359i \(0.798197\pi\)
\(224\) −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 \(0.497722\pi\)
−0.869581 + 0.493790i \(0.835611\pi\)
\(228\) 0 0
\(229\) −1516.38 2626.44i −0.437576 0.757904i 0.559926 0.828543i \(-0.310830\pi\)
−0.997502 + 0.0706386i \(0.977496\pi\)
\(230\) 3093.34 1838.97i 0.886821 0.527208i
\(231\) 0 0
\(232\) 2441.53 + 1287.63i 0.690924 + 0.364383i
\(233\) 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
\(236\) 1878.64 3454.61i 0.518174 0.952865i
\(237\) 0 0
\(238\) 435.115 + 731.910i 0.118506 + 0.199339i
\(239\) −2875.14 4979.89i −0.778149 1.34779i −0.933008 0.359856i \(-0.882826\pi\)
0.154859 0.987937i \(1.54949\pi\)
\(240\) 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
\(248\) 382.074 240.545i 0.0978295 0.0615911i
\(249\) 0 0
\(250\) 1509.26 + 845.876i 0.381815 + 0.213992i
\(251\) 3207.28 0.806541 0.403270 0.915081i \(-0.367873\pi\)
0.403270 + 0.915081i \(0.367873\pi\)
\(252\) 0 0
\(253\) 3771.02 0.937082
\(254\) −1960.36 1098.70i −0.484266 0.271411i
\(255\) 0 0
\(256\) −2398.85 3320.05i −0.585657 0.810559i
\(257\) 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 −0.847152 0.531351i \(-0.821684\pi\)
0.883740 + 0.467979i \(0.155018\pi\)
\(264\) 0 0
\(265\) 4055.37 + 7024.11i 0.940073 + 1.62825i
\(266\) −324.466 545.787i −0.0747906 0.125806i
\(267\) 0 0
\(268\) 4355.21 + 2368.39i 0.992674 + 0.539823i
\(269\) 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 \(-0.811202\pi\)
0.829197 0.558956i \(-0.188798\pi\)
\(272\) 4808.60 + 2458.07i 1.07193 + 0.547950i
\(273\) 0 0
\(274\) −2959.75 + 1759.55i −0.652573 + 0.387950i
\(275\) 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 −0.0895066 0.995986i \(-0.528529\pi\)
0.817796 + 0.575508i \(0.195196\pi\)
\(284\) 1062.48 + 1736.36i 0.221994 + 0.362797i
\(285\) 0 0
\(286\) 2634.16 4700.02i 0.544620 0.971741i
\(287\) 1232.04 0.253398
\(288\) 0 0
\(289\) −2207.31 −0.449280
\(290\) 2853.59 5091.53i 0.577823 1.03098i
\(291\) 0 0
\(292\) −419.576 685.697i −0.0840886 0.137423i
\(293\) −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
\(302\) −8394.46 + 4990.45i −1.59949 + 0.950888i
\(303\) 0 0
\(304\) −3585.78 1832.99i −0.676509 0.345819i
\(305\) 1688.81i 0.317053i
\(306\) 0 0
\(307\) 4575.16i 0.850547i 0.905065 + 0.425274i \(0.139822\pi\)
−0.905065 + 0.425274i \(0.860178\pi\)
\(308\) −1257.12 683.631i −0.232569 0.126472i
\(309\) 0 0
\(310\) −487.856 820.626i −0.0893818 0.150350i
\(311\) −4119.46 7135.11i −0.751103 1.30095i −0.947289 0.320381i \(-0.896189\pi\)
0.196186 0.980567i \(1.56286\pi\)
\(312\) 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
\(320\) −7147.52 + 4891.64i −1.24862 + 0.854534i
\(321\) 0 0
\(322\) 662.068 + 371.062i 0.114583 + 0.0642189i
\(323\) 5309.63 0.914661
\(324\) 0 0
\(325\) −6123.01 −1.04506
\(326\) −4178.58 2341.92i −0.709908 0.397874i
\(327\) 0 0
\(328\) 6612.74 4163.22i 1.11319 0.700840i
\(329\) −945.947 + 546.143i −0.158516 + 0.0915192i
\(330\) 0 0
\(331\) −2056.23 1187.17i −0.341452 0.197138i 0.319462 0.947599i \(-0.396498\pi\)
−0.660914 + 0.750462i \(0.729831\pi\)
\(332\) 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 \(0.816764\pi\)
\(338\) −1089.09 1831.96i −0.175262 0.294810i
\(339\) 0 0
\(340\) 5455.47 10032.0i 0.870189 1.60018i
\(341\) 1000.41i 0.158871i
\(342\) 0 0
\(343\) 2401.99i 0.378120i
\(344\) −2616.29 1379.79i −0.410061 0.216260i
\(345\) 0 0
\(346\) −5303.56 + 3152.93i −0.824050 + 0.489892i
\(347\) 768.265 + 1330.67i 0.118855 + 0.205863i 0.919314 0.393525i \(-0.128744\pi\)
−0.800459 + 0.599387i \(0.795411\pi\)
\(348\) 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
\(356\) 6959.41 4258.44i 1.03609 0.633980i
\(357\) 0 0
\(358\) −3250.01 + 5798.84i −0.479799 + 0.856084i
\(359\) −4489.49 −0.660017 −0.330009 0.943978i \(-0.607052\pi\)
−0.330009 + 0.943978i \(0.607052\pi\)
\(360\) 0 0
\(361\) 2899.60 0.422744
\(362\) −3153.07 + 5625.87i −0.457794 + 0.816821i
\(363\) 0 0
\(364\) 924.948 565.973i 0.133188 0.0814974i
\(365\) −1472.10 + 849.917i −0.211105 + 0.121881i
\(366\) 0 0
\(367\) −750.997 433.589i −0.106817 0.0616707i 0.445640 0.895212i \(-0.352976\pi\)
−0.552457 + 0.833542i \(0.686310\pi\)
\(368\) 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 \(0.735956\pi\)
\(374\) 10285.9 6114.89i 1.42211 0.845436i
\(375\) 0 0
\(376\) −3231.69 + 6127.78i −0.443250 + 0.840468i
\(377\) 4634.71i 0.633156i
\(378\) 0 0
\(379\) 14096.9i 1.91058i 0.295677 + 0.955288i \(0.404455\pi\)
−0.295677 + 0.955288i \(0.595545\pi\)
\(380\) −4068.15 + 7480.88i −0.549189 + 1.00990i
\(381\) 0 0
\(382\) −5684.52 9561.97i −0.761375 1.28071i
\(383\) 4134.45 + 7161.08i 0.551594 + 0.955390i 0.998160 + 0.0606386i \(0.0193137\pi\)
−0.446565 + 0.894751i \(0.647353\pi\)
\(384\) 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
\(392\) 3981.58 + 6324.22i 0.513010 + 0.814851i
\(393\) 0 0
\(394\) −4929.52 2762.79i −0.630319 0.353267i
\(395\) −16726.2 −2.13060
\(396\) 0 0
\(397\) 10494.4 1.32670 0.663349 0.748310i \(-0.269134\pi\)
0.663349 + 0.748310i \(0.269134\pi\)
\(398\) 5944.04 + 3331.39i 0.748612 + 0.419566i
\(399\) 0 0
\(400\) 5606.17 + 8657.63i 0.700771 + 1.08220i
\(401\) 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 \(0.912554\pi\)
\(410\) −8443.56 14203.0i −1.01707 1.71081i
\(411\) 0 0
\(412\) 12145.3 + 6604.72i 1.45233 + 0.789784i
\(413\) 1753.66i 0.208940i
\(414\) 0 0
\(415\) 8517.52i 1.00749i
\(416\) 3051.98 6163.26i 0.359701 0.726391i
\(417\) 0 0
\(418\) −7670.20 + 4559.88i −0.897516 + 0.533567i
\(419\) −346.536 600.219i −0.0404043 0.0699823i 0.845116 0.534583i \(-0.179531\pi\)
−0.885520 + 0.464601i \(0.846198\pi\)
\(420\) 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
\(428\) 263.728 + 431.000i 0.0297845 + 0.0486756i
\(429\) 0 0
\(430\) −3057.85 + 5455.98i −0.342936 + 0.611885i
\(431\) 10013.8 1.11914 0.559569 0.828784i \(-0.310967\pi\)
0.559569 + 0.828784i \(0.310967\pi\)
\(432\) 0 0
\(433\) −9726.02 −1.07945 −0.539726 0.841841i \(-0.681472\pi\)
−0.539726 + 0.841841i \(0.681472\pi\)
\(434\) 98.4383 175.639i 0.0108875 0.0194261i
\(435\) 0 0
\(436\) 3488.11 + 5700.47i 0.383142 + 0.626154i
\(437\) 4098.64 2366.35i 0.448660 0.259034i
\(438\) 0 0
\(439\) 5675.95 + 3277.01i 0.617080 + 0.356271i 0.775731 0.631063i \(-0.217381\pi\)
−0.158651 + 0.987335i \(0.550715\pi\)
\(440\) 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 \(-0.935429\pi\)
0.664224 + 0.747533i \(0.268762\pi\)
\(444\) 0 0
\(445\) −8626.14 14940.9i −0.918917 1.59161i
\(446\) −6502.21 + 3865.52i −0.690333 + 0.410398i
\(447\) 0 0
\(448\) −1647.13 789.631i −0.173705 0.0832736i
\(449\) 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
\(452\) −7238.13 3936.14i −0.753214 0.409603i
\(453\) 0 0
\(454\) 8526.39 + 14342.3i 0.881417 + 1.48264i
\(455\) −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 \(0.679986\pi\)
−0.999125 + 0.0418305i \(0.986681\pi\)
\(464\) 6553.25 4243.50i 0.655662 0.424568i
\(465\) 0 0
\(466\) −3193.05 1789.57i −0.317414 0.177898i
\(467\) 6165.12 0.610895 0.305447 0.952209i \(-0.401194\pi\)
0.305447 + 0.952209i \(0.401194\pi\)
\(468\) 0 0
\(469\) 2210.83 0.217669
\(470\) 12778.8 + 7161.97i 1.25413 + 0.702888i
\(471\) 0 0
\(472\) −5925.83 9412.42i −0.577878 0.917885i
\(473\) −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 \(0.476042\pi\)
−0.901171 + 0.433464i \(0.857291\pi\)
\(480\) 0 0
\(481\) −337.422 584.431i −0.0319857 0.0554008i
\(482\) 8697.63 + 14630.3i 0.821921 + 1.38256i
\(483\) 0 0
\(484\) −4520.46 + 8312.63i −0.424536 + 0.780675i
\(485\) 17037.7i 1.59514i
\(486\) 0 0
\(487\) 7352.14i 0.684101i 0.939682 + 0.342050i \(0.111121\pi\)
−0.939682 + 0.342050i \(0.888879\pi\)
\(488\) 1053.78 1998.13i 0.0977510 0.185351i
\(489\) 0 0
\(490\) 13583.3 8075.16i 1.25231 0.744487i
\(491\) −4221.27 7311.46i −0.387991 0.672019i 0.604189 0.796841i \(-0.293497\pi\)
−0.992179 + 0.124822i \(0.960164\pi\)
\(492\) 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 \(-0.556625\pi\)
0.763880 + 0.645358i \(0.223292\pi\)
\(500\) 4174.12 2554.14i 0.373345 0.228449i
\(501\) 0 0
\(502\) 4435.16 7913.44i 0.394324 0.703574i
\(503\) 604.632 0.0535968 0.0267984 0.999641i \(-0.491469\pi\)
0.0267984 + 0.999641i \(0.491469\pi\)
\(504\) 0 0
\(505\) −7121.47 −0.627527
\(506\) 5214.71 9304.37i 0.458147 0.817450i
\(507\) 0 0
\(508\) −5421.72 + 3317.54i −0.473523 + 0.289748i
\(509\) −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
\(518\) −154.065 + 91.5906i −0.0130680 + 0.00776884i
\(519\) 0 0
\(520\) −12863.5 6784.00i −1.08481 0.572111i
\(521\) 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 \(-0.767827\pi\)
0.745579 0.666418i \(-0.232173\pi\)
\(524\) 848.759 1560.77i 0.0707599 0.130120i
\(525\) 0 0
\(526\) −451.105 758.807i −0.0373938 0.0629003i
\(527\) 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
\(536\) 11866.2 7470.66i 0.956233 0.602021i
\(537\) 0 0
\(538\) 4506.02 + 2525.44i 0.361093 + 0.202378i
\(539\) 16559.1 1.32328
\(540\) 0 0
\(541\) 7256.04 0.576638 0.288319 0.957534i \(-0.406904\pi\)
0.288319 + 0.957534i \(0.406904\pi\)
\(542\) −12305.2 6896.58i −0.975195 0.546556i
\(543\) 0 0
\(544\) 12714.4 8465.33i 1.00207 0.667184i
\(545\) 12238.1 7065.70i 0.961880 0.555342i
\(546\) 0 0
\(547\) −374.999 216.506i −0.0293122 0.0169234i 0.485272 0.874363i \(-0.338720\pi\)
−0.514585 + 0.857440i \(0.672054\pi\)
\(548\) 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
\(554\) 6145.43 + 10337.3i 0.471289 + 0.792758i
\(555\) 0 0
\(556\) −15492.7 8425.06i −1.18172 0.642630i
\(557\) 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
\(560\) −1758.04 + 3439.17i −0.132662 + 0.259521i
\(561\) 0 0
\(562\) 7135.38 4241.93i 0.535565 0.318390i
\(563\) −6499.11 11256.8i −0.486510 0.842659i 0.513370 0.858167i \(-0.328397\pi\)
−0.999880 + 0.0155079i \(0.995063\pi\)
\(564\) 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 \(0.708473\pi\)
−0.991388 + 0.130961i \(0.958194\pi\)
\(572\) −7953.90 12998.7i −0.581415 0.950183i
\(573\) 0 0
\(574\) 1703.72 3039.86i 0.123888 0.221048i
\(575\) −12121.4 −0.879125
\(576\) 0 0
\(577\) 18112.2 1.30680 0.653398 0.757014i \(-0.273343\pi\)
0.653398 + 0.757014i \(0.273343\pi\)
\(578\) −3052.36 + 5446.18i −0.219656 + 0.391923i
\(579\) 0 0
\(580\) −8616.47 14081.6i −0.616861 1.00811i
\(581\) 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 \(0.543602\pi\)
−0.789638 + 0.613573i \(0.789732\pi\)
\(588\) 0 0
\(589\) −627.764 1087.32i −0.0439161 0.0760649i
\(590\) −20216.2 + 12018.4i −1.41065 + 0.838624i
\(591\) 0 0
\(592\) −517.417 + 1012.20i −0.0359218 + 0.0702721i
\(593\) 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
\(596\) −2857.55 1553.96i −0.196392 0.106799i
\(597\) 0 0
\(598\) 4130.25 + 6947.52i 0.282439 + 0.475092i
\(599\) 11060.5 + 19157.3i 0.754454 + 1.30675i 0.945645 + 0.325200i \(0.105432\pi\)
−0.191191 + 0.981553i \(0.561235\pi\)
\(600\) 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 −0.0670351 0.997751i \(-0.521354\pi\)
0.830560 + 0.556929i \(0.188021\pi\)
\(608\) −9481.16 + 6312.61i −0.632421 + 0.421069i
\(609\) 0 0
\(610\) −4166.87 2335.36i −0.276577 0.155010i
\(611\) −11632.2 −0.770196
\(612\) 0 0
\(613\) −18052.3 −1.18944 −0.594719 0.803934i \(-0.702737\pi\)
−0.594719 + 0.803934i \(0.702737\pi\)
\(614\) 11288.5 + 6326.71i 0.741962 + 0.415839i
\(615\) 0 0
\(616\) −3425.15 + 2156.39i −0.224031 + 0.141045i
\(617\) 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 −0.102736 0.994709i \(-0.532760\pi\)
−0.912811 + 0.408382i \(0.866093\pi\)
\(620\) −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
\(626\) −7689.02 12933.8i −0.490919 0.825778i
\(627\) 0 0
\(628\) 3365.45 6188.70i 0.213848 0.393242i
\(629\) 1498.81i 0.0950100i
\(630\) 0 0
\(631\) 7301.94i 0.460674i 0.973111 + 0.230337i \(0.0739829\pi\)
−0.973111 + 0.230337i \(0.926017\pi\)
\(632\) −19789.7 10436.8i −1.24556 0.656888i
\(633\) 0 0
\(634\) 21452.0 12753.1i 1.34380 0.798878i
\(635\) 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 −0.529888 0.848068i \(-0.677766\pi\)
0.469504 + 0.882930i \(0.344433\pi\)
\(644\) 1831.07 1120.43i 0.112041 0.0685575i
\(645\) 0 0
\(646\) 7342.37 13100.6i 0.447185 0.797891i
\(647\) −995.889 −0.0605138 −0.0302569 0.999542i \(-0.509633\pi\)
−0.0302569 + 0.999542i \(0.509633\pi\)
\(648\) 0 0
\(649\) −24645.0 −1.49061
\(650\) −8467.14 + 15107.5i −0.510936 + 0.911640i
\(651\) 0 0
\(652\) −11556.6 + 7071.46i −0.694160 + 0.424754i
\(653\) −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 \(-0.562416\pi\)
0.946845 0.321690i \(-0.104251\pi\)
\(660\) 0 0
\(661\) 2109.30 + 3653.42i 0.124119 + 0.214980i 0.921388 0.388644i \(-0.127056\pi\)
−0.797269 + 0.603624i \(0.793723\pi\)
\(662\) −5772.58 + 3431.76i −0.338909 + 0.201479i
\(663\) 0 0
\(664\) 5314.74 10077.6i 0.310621 0.588983i
\(665\) 3797.51i 0.221445i
\(666\) 0 0
\(667\) 9175.09i 0.532625i
\(668\) 6268.29 11526.7i 0.363065 0.667636i
\(669\) 0 0
\(670\) −15151.5 25486.4i −0.873661 1.46959i
\(671\) −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
\(680\) −17208.3 27333.1i −0.970452 1.54144i
\(681\) 0 0
\(682\) −2468.34 1383.40i −0.138589 0.0776732i
\(683\) −28383.3 −1.59012 −0.795062 0.606528i \(-0.792562\pi\)
−0.795062 + 0.606528i \(0.792562\pi\)
\(684\) 0 0
\(685\) 20593.5 1.14867
\(686\) 5926.51 + 3321.56i 0.329847 + 0.184866i
\(687\) 0 0
\(688\) −7022.32 + 4547.24i −0.389133 + 0.251980i
\(689\) −15775.9 + 9108.21i −0.872298 + 0.503621i
\(690\) 0 0
\(691\) 4592.61 + 2651.54i 0.252838 + 0.145976i 0.621063 0.783761i \(-0.286701\pi\)
−0.368225 + 0.929737i \(0.620034\pi\)
\(692\) 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
\(698\) 9922.81 + 16691.2i 0.538086 + 0.905117i
\(699\) 0 0
\(700\) 4040.83 + 2197.43i 0.218185 + 0.118650i
\(701\) 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
\(704\) −11097.1 + 23148.0i −0.594086 + 1.23924i
\(705\) 0 0
\(706\) −303.105 + 180.194i −0.0161580 + 0.00960579i
\(707\) −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
\(716\) 9813.44 + 16037.7i 0.512215 + 0.837092i
\(717\) 0 0
\(718\) −6208.25 + 11077.1i −0.322688 + 0.575757i
\(719\) 7178.86 0.372359 0.186180 0.982516i \(-0.440389\pi\)
0.186180 + 0.982516i \(0.440389\pi\)
\(720\) 0 0
\(721\) 6165.33 0.318459
\(722\) 4009.69 7154.30i 0.206683 0.368775i
\(723\) 0 0
\(724\) 9520.74 + 15559.4i 0.488723 + 0.798701i
\(725\) −17025.7 + 9829.77i −0.872161 + 0.503543i
\(726\) 0 0
\(727\) 18250.7 + 10537.0i 0.931061 + 0.537548i 0.887147 0.461487i \(-0.152684\pi\)
0.0439138 + 0.999035i \(0.486017\pi\)
\(728\) −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 \(-0.336890\pi\)
\(734\) −2108.32 + 1253.38i −0.106021 + 0.0630288i
\(735\) 0 0
\(736\) 6041.83 12201.1i 0.302588 0.611056i
\(737\) 31069.9i 1.55288i
\(738\) 0 0
\(739\) 8782.55i 0.437173i −0.975818 0.218587i \(-0.929855\pi\)
0.975818 0.218587i \(-0.0701447\pi\)
\(740\) 2111.71 + 1148.36i 0.104903 + 0.0570467i
\(741\) 0 0
\(742\) 2472.36 + 4158.76i 0.122322 + 0.205759i
\(743\) −11676.8 20224.8i −0.576553 0.998620i −0.995871 0.0907800i \(-0.971064\pi\)
0.419318 0.907840i \(1.63773\pi\)
\(744\) 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 \(-0.532096\pi\)
0.811296 + 0.584636i \(0.198763\pi\)
\(752\) 10650.4 + 16447.4i 0.516462 + 0.797574i
\(753\) 0 0
\(754\) 11435.4 + 6409.06i 0.552324 + 0.309555i
\(755\) 58407.6 2.81546
\(756\) 0 0
\(757\) 6838.01 0.328311 0.164156 0.986434i \(-0.447510\pi\)
0.164156 + 0.986434i \(0.447510\pi\)
\(758\) 34781.8 + 19493.7i 1.66666 + 0.934095i
\(759\) 0 0
\(760\) 12832.2 + 20382.4i 0.612466 + 0.972824i
\(761\) 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 \(-0.498532\pi\)
\(770\) 4373.44 + 7356.59i 0.204686 + 0.344303i
\(771\) 0 0
\(772\) −10369.5 + 19068.4i −0.483429 + 0.888972i
\(773\) 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
\(776\) 10631.2 20158.3i 0.491799 0.932525i
\(777\) 0 0
\(778\) −13960.9 + 8299.65i −0.643345 + 0.382464i
\(779\) −10865.0 18818.8i −0.499717 0.865535i
\(780\) 0 0