Properties

Label 108.4.h.b.71.8
Level 108
Weight 4
Character 108.71
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 71.8
Character \(\chi\) \(=\) 108.71
Dual form 108.4.h.b.35.8

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.38284 + 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 −0.328178 0.944616i \(-0.606435\pi\)
−0.982150 + 0.188097i \(0.939768\pi\)
\(6\) 0 0
\(7\) −3.08966 + 1.78382i −0.166826 + 0.0963170i −0.581088 0.813841i \(-0.697373\pi\)
0.414262 + 0.910157i \(0.364040\pi\)
\(8\) −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 \(-0.925533\pi\)
0.285620 0.958343i \(1.59220\pi\)
\(12\) 0 0
\(13\) −18.9966 + 32.9032i −0.405286 + 0.701977i −0.994355 0.106107i \(-0.966162\pi\)
0.589068 + 0.808083i \(0.299495\pi\)
\(14\) −8.67378 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 \(0.205601\pi\)
−0.798549 + 0.601930i \(0.794399\pi\)
\(18\) 0 0
\(19\) 62.9237i 0.759773i −0.925033 0.379887i \(-0.875963\pi\)
0.925033 0.379887i \(-0.124037\pi\)
\(20\) 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 −0.984607 0.174784i \(-0.944077\pi\)
0.643671 + 0.765302i \(0.277411\pi\)
\(24\) 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 0.449106 0.893478i \(-0.351742\pi\)
−0.549222 + 0.835677i \(0.685076\pi\)
\(32\) 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 −0.192969 0.981205i \(-0.561812\pi\)
−0.946233 + 0.323486i \(0.895145\pi\)
\(42\) 0 0
\(43\) 113.206 65.3596i 0.401483 0.231796i −0.285641 0.958337i \(-0.592206\pi\)
0.687124 + 0.726540i \(0.258873\pi\)
\(44\) 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 \(-0.00908080\pi\)
−0.524499 + 0.851411i \(0.675747\pi\)
\(48\) 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 \(0.213401\pi\)
−0.783561 + 0.621315i \(0.786599\pi\)
\(54\) 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 −0.456447 0.889750i \(-0.650878\pi\)
0.998770 0.0495801i \(-0.0157883\pi\)
\(60\) 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 −0.0767351 0.997052i \(-0.524450\pi\)
−0.901839 + 0.432071i \(0.857783\pi\)
\(68\) −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 0.254691 0.967022i \(-0.418026\pi\)
0.964812 + 0.262942i \(0.0846928\pi\)
\(80\) −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 \(-0.274706\pi\)
−0.983086 + 0.183143i \(0.941373\pi\)
\(84\) 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 \(-0.792239\pi\)
0.794448 0.607333i \(-0.207761\pi\)
\(90\) 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 −0.999500 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 −0.434447 0.900697i \(-0.643056\pi\)
−0.997250 + 0.0741066i \(0.976389\pi\)
\(104\) 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 0.822983 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
\(122\) 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 \(0.0895287\pi\)
−0.960706 + 0.277569i \(0.910471\pi\)
\(128\) 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 −0.826619 0.562763i \(-0.809738\pi\)
0.900676 + 0.434491i \(0.143072\pi\)
\(132\) 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 0.952483 0.304592i \(-0.0985202\pi\)
0.212457 + 0.977170i \(0.431854\pi\)
\(140\) −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 0.593668 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 \(0.713873\pi\)
−0.989023 + 0.147759i \(0.952794\pi\)
\(152\) −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 \(0.0948160\pi\)
\(158\) 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 \(0.133391\pi\)
−0.913472 + 0.406901i \(0.866609\pi\)
\(164\) 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 −0.611075 0.791573i \(-0.709263\pi\)
0.991060 + 0.133420i \(0.0425959\pi\)
\(168\) 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
\(176\) −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 0.950209 + 0.311614i \(0.100870\pi\)
−0.205239 + 0.978712i \(0.565797\pi\)
\(192\) 0 0
\(193\) −1356.60 + 2349.69i −0.505958 + 0.876346i 0.494018 + 0.869452i \(0.335528\pi\)
−0.999976 + 0.00689392i \(0.997806\pi\)
\(194\) 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 \(0.117661\pi\)
−0.932456 + 0.361282i \(0.882339\pi\)
\(198\) 0 0
\(199\) 2409.09i 0.858170i −0.903264 0.429085i \(-0.858836\pi\)
0.903264 0.429085i \(-0.141164\pi\)
\(200\) −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 0.220420 0.975405i \(-0.429257\pi\)
−0.734515 + 0.678592i \(0.762590\pi\)
\(212\) −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 −0.805674 0.592359i \(-0.798197\pi\)
0.110160 + 0.993914i \(0.464864\pi\)
\(224\) −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 \(-0.835611\pi\)
0.00715576 0.999974i \(1.50228\pi\)
\(228\) 0 0
\(229\) −1516.38 + 2626.44i −0.437576 + 0.757904i −0.997502 0.0706386i \(-0.977496\pi\)
0.559926 + 0.828543i \(0.310830\pi\)
\(230\) 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 \(0.0582356\pi\)
−0.983311 + 0.181934i \(0.941764\pi\)
\(234\) 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 0.154859 + 0.987937i \(0.450508\pi\)
−0.933008 + 0.359856i \(0.882826\pi\)
\(240\) 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
\(248\) 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 0.773445 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 0.883740 0.467979i \(-0.155018\pi\)
−0.847152 + 0.531351i \(0.821684\pi\)
\(264\) 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 \(-0.933640\pi\)
0.978347 0.206969i \(-0.0663600\pi\)
\(270\) 0 0
\(271\) 4987.26i 1.11791i 0.829197 + 0.558956i \(0.188798\pi\)
−0.829197 + 0.558956i \(0.811202\pi\)
\(272\) 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 0.537884 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 0.817796 0.575508i \(-0.195196\pi\)
−0.0895066 + 0.995986i \(0.528529\pi\)
\(284\) 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 0.248899 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
\(302\) −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 \(-0.860178\pi\)
0.905065 0.425274i \(-0.139822\pi\)
\(308\) −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 0.196186 + 0.980567i \(0.437144\pi\)
−0.947289 + 0.320381i \(0.896189\pi\)
\(312\) 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
\(320\) −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 −0.660914 0.750462i \(-0.729831\pi\)
0.319462 + 0.947599i \(0.396498\pi\)
\(332\) 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 \(0.150097\pi\)
\(338\) −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 −0.800459 0.599387i \(-0.795411\pi\)
0.919314 + 0.393525i \(0.128744\pi\)
\(348\) 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
\(356\) 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 −0.552457 0.833542i \(-0.686310\pi\)
0.445640 + 0.895212i \(0.352976\pi\)
\(368\) 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 \(0.0692895\pi\)
\(374\) 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 \(-0.595545\pi\)
0.295677 0.955288i \(-0.404455\pi\)
\(380\) −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 −0.446565 0.894751i \(-0.647353\pi\)
0.998160 0.0606386i \(-0.0193137\pi\)
\(384\) 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
\(392\) 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 0.870813 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 \(0.245888\pi\)
\(410\) −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 −0.885520 0.464601i \(-0.846198\pi\)
0.845116 + 0.534583i \(0.179531\pi\)
\(420\) 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
\(428\) 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 −0.158651 0.987335i \(-0.550715\pi\)
0.775731 + 0.631063i \(0.217381\pi\)
\(440\) 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 \(-0.268762\pi\)
−0.979495 + 0.201468i \(0.935429\pi\)
\(444\) 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 \(-0.884374\pi\)
0.934747 0.355313i \(-0.115626\pi\)
\(450\) 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 0.931946 + 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 \(-0.986681\pi\)
−0.535789 0.844352i \(1.32001\pi\)
\(464\) 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 −0.901171 0.433464i \(-0.857291\pi\)
0.0751944 0.997169i \(1.52396\pi\)
\(480\) 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 \(-0.888879\pi\)
0.939682 0.342050i \(-0.111121\pi\)
\(488\) 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 −0.992179 0.124822i \(-0.960164\pi\)
0.604189 + 0.796841i \(0.293497\pi\)
\(492\) 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 \(-0.223292\pi\)
−0.176956 + 0.984219i \(0.556625\pi\)
\(500\) 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 0.0617925 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
\(518\) −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 \(-0.717058\pi\)
0.630276 0.776371i \(-0.282942\pi\)
\(522\) 0 0
\(523\) 15941.5i 1.33284i 0.745579 + 0.666418i \(0.232173\pi\)
−0.745579 + 0.666418i \(0.767827\pi\)
\(524\) 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 −0.514585 0.857440i \(-0.672054\pi\)
0.485272 + 0.874363i \(0.338720\pi\)
\(548\) 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 \(0.113610\pi\)
−0.936978 + 0.349388i \(0.886390\pi\)
\(558\) 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 −0.999880 0.0155079i \(-0.995063\pi\)
0.513370 + 0.858167i \(0.328397\pi\)
\(564\) 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 \(-0.958194\pi\)
−0.609109 0.793086i \(1.29153\pi\)
\(572\) −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 −0.789638 0.613573i \(-0.789732\pi\)
−0.136551 0.990633i \(1.45640\pi\)
\(588\) 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 \(-0.868035\pi\)
0.915286 0.402804i \(-0.131965\pi\)
\(594\) 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 −0.191191 0.981553i \(-0.561235\pi\)
0.945645 0.325200i \(-0.105432\pi\)
\(600\) 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 0.830560 0.556929i \(-0.188021\pi\)
−0.0670351 + 0.997751i \(0.521354\pi\)
\(608\) −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 0.967658 0.252266i \(-0.0811756\pi\)
0.265361 + 0.964149i \(0.414509\pi\)
\(618\) 0 0
\(619\) −15640.0 + 9029.74i −1.01555 + 0.586326i −0.912811 0.408382i \(-0.866093\pi\)
−0.102736 + 0.994709i \(0.532760\pi\)
\(620\) −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 \(-0.926017\pi\)
0.973111 0.230337i \(-0.0739829\pi\)
\(632\) −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 −0.522504 0.852637i \(-0.675002\pi\)
0.477153 + 0.878820i \(0.341669\pi\)
\(642\) 0 0
\(643\) −984.538 568.423i −0.0603832 0.0348622i 0.469504 0.882930i \(-0.344433\pi\)
−0.529888 + 0.848068i \(0.677766\pi\)
\(644\) 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 −0.468654 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 \(0.104251\pi\)
−0.194831 + 0.980837i \(0.562416\pi\)
\(660\) 0 0
\(661\) 2109.30 3653.42i 0.124119 0.214980i −0.797269 0.603624i \(-0.793723\pi\)
0.921388 + 0.388644i \(0.127056\pi\)
\(662\) −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 0.582101 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
\(680\) −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 −0.368225 0.929737i \(-0.620034\pi\)
0.621063 + 0.783761i \(0.286701\pi\)
\(692\) 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 \(0.0876056\pi\)
−0.962365 + 0.271760i \(0.912394\pi\)
\(702\) 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 0.974460 + 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
\(716\) 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 0.0439138 0.999035i \(-0.486017\pi\)
0.887147 + 0.461487i \(0.152684\pi\)
\(728\) −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 \(0.996444\pi\)
\(734\) −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 \(0.0701447\pi\)
−0.975818 + 0.218587i \(0.929855\pi\)
\(740\) 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 0.419318 + 0.907840i \(0.362269\pi\)
−0.995871 + 0.0907800i \(0.971064\pi\)
\(744\) 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 \(-0.198763\pi\)
−0.100662 + 0.994921i \(0.532096\pi\)
\(752\) 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 0.901271 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 \(0.834801\pi\)
\(770\) 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 \(0.0558680\pi\)
−0.984637 + 0.174615i \(0.944132\pi\)
\(774\) 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