Properties

Label 483.3.f.a.22.4
Level $483$
Weight $3$
Character 483.22
Analytic conductor $13.161$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 483.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.1607967686\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 22.4
Character \(\chi\) \(=\) 483.22
Dual form 483.3.f.a.22.3

$q$-expansion

\(f(q)\) \(=\) \(q-3.83573 q^{2} +1.73205 q^{3} +10.7128 q^{4} +8.86189i q^{5} -6.64368 q^{6} -2.64575i q^{7} -25.7486 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-3.83573 q^{2} +1.73205 q^{3} +10.7128 q^{4} +8.86189i q^{5} -6.64368 q^{6} -2.64575i q^{7} -25.7486 q^{8} +3.00000 q^{9} -33.9918i q^{10} +2.29410i q^{11} +18.5552 q^{12} +15.0567 q^{13} +10.1484i q^{14} +15.3492i q^{15} +55.9134 q^{16} +7.09765i q^{17} -11.5072 q^{18} +22.0994i q^{19} +94.9359i q^{20} -4.58258i q^{21} -8.79953i q^{22} +(22.1641 - 6.14418i) q^{23} -44.5979 q^{24} -53.5331 q^{25} -57.7536 q^{26} +5.19615 q^{27} -28.3435i q^{28} +39.3447 q^{29} -58.8756i q^{30} +6.20172 q^{31} -111.474 q^{32} +3.97349i q^{33} -27.2247i q^{34} +23.4464 q^{35} +32.1385 q^{36} -33.2177i q^{37} -84.7673i q^{38} +26.0790 q^{39} -228.181i q^{40} -6.76874 q^{41} +17.5775i q^{42} +68.6344i q^{43} +24.5762i q^{44} +26.5857i q^{45} +(-85.0157 + 23.5674i) q^{46} -56.9055 q^{47} +96.8448 q^{48} -7.00000 q^{49} +205.339 q^{50} +12.2935i q^{51} +161.300 q^{52} -6.03878i q^{53} -19.9310 q^{54} -20.3300 q^{55} +68.1244i q^{56} +38.2772i q^{57} -150.916 q^{58} -103.615 q^{59} +164.434i q^{60} +30.0632i q^{61} -23.7881 q^{62} -7.93725i q^{63} +203.932 q^{64} +133.431i q^{65} -15.2412i q^{66} -129.206i q^{67} +76.0359i q^{68} +(38.3894 - 10.6420i) q^{69} -89.9339 q^{70} +25.8589 q^{71} -77.2458 q^{72} +0.973133 q^{73} +127.414i q^{74} -92.7221 q^{75} +236.747i q^{76} +6.06961 q^{77} -100.032 q^{78} +78.4213i q^{79} +495.498i q^{80} +9.00000 q^{81} +25.9630 q^{82} +71.3251i q^{83} -49.0923i q^{84} -62.8986 q^{85} -263.263i q^{86} +68.1470 q^{87} -59.0697i q^{88} +150.485i q^{89} -101.975i q^{90} -39.8364i q^{91} +(237.441 - 65.8216i) q^{92} +10.7417 q^{93} +218.274 q^{94} -195.842 q^{95} -193.079 q^{96} +164.879i q^{97} +26.8501 q^{98} +6.88229i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + O(q^{10}) \) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + 16q^{13} + 324q^{16} + 12q^{18} - 4q^{23} - 24q^{24} - 176q^{25} + 136q^{26} - 128q^{29} - 8q^{31} - 252q^{32} - 56q^{35} + 348q^{36} + 96q^{39} - 24q^{41} - 148q^{46} - 408q^{47} - 96q^{48} - 336q^{49} + 236q^{50} - 32q^{52} - 72q^{54} - 24q^{55} - 56q^{58} + 136q^{59} + 184q^{62} + 716q^{64} - 48q^{69} - 112q^{70} + 48q^{71} - 12q^{72} - 224q^{73} - 48q^{75} + 224q^{77} - 96q^{78} + 432q^{81} + 640q^{82} - 424q^{85} + 312q^{87} + 1060q^{92} + 192q^{93} + 216q^{94} + 624q^{95} + 48q^{96} - 28q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.83573 −1.91787 −0.958933 0.283634i \(-0.908460\pi\)
−0.958933 + 0.283634i \(0.908460\pi\)
\(3\) 1.73205 0.577350
\(4\) 10.7128 2.67821
\(5\) 8.86189i 1.77238i 0.463324 + 0.886189i \(0.346657\pi\)
−0.463324 + 0.886189i \(0.653343\pi\)
\(6\) −6.64368 −1.10728
\(7\) 2.64575i 0.377964i
\(8\) −25.7486 −3.21857
\(9\) 3.00000 0.333333
\(10\) 33.9918i 3.39918i
\(11\) 2.29410i 0.208554i 0.994548 + 0.104277i \(0.0332529\pi\)
−0.994548 + 0.104277i \(0.966747\pi\)
\(12\) 18.5552 1.54626
\(13\) 15.0567 1.15821 0.579105 0.815253i \(-0.303402\pi\)
0.579105 + 0.815253i \(0.303402\pi\)
\(14\) 10.1484i 0.724885i
\(15\) 15.3492i 1.02328i
\(16\) 55.9134 3.49459
\(17\) 7.09765i 0.417509i 0.977968 + 0.208754i \(0.0669409\pi\)
−0.977968 + 0.208754i \(0.933059\pi\)
\(18\) −11.5072 −0.639288
\(19\) 22.0994i 1.16313i 0.813502 + 0.581563i \(0.197558\pi\)
−0.813502 + 0.581563i \(0.802442\pi\)
\(20\) 94.9359i 4.74680i
\(21\) 4.58258i 0.218218i
\(22\) 8.79953i 0.399979i
\(23\) 22.1641 6.14418i 0.963658 0.267138i
\(24\) −44.5979 −1.85825
\(25\) −53.5331 −2.14132
\(26\) −57.7536 −2.22129
\(27\) 5.19615 0.192450
\(28\) 28.3435i 1.01227i
\(29\) 39.3447 1.35671 0.678356 0.734733i \(-0.262693\pi\)
0.678356 + 0.734733i \(0.262693\pi\)
\(30\) 58.8756i 1.96252i
\(31\) 6.20172 0.200055 0.100028 0.994985i \(-0.468107\pi\)
0.100028 + 0.994985i \(0.468107\pi\)
\(32\) −111.474 −3.48357
\(33\) 3.97349i 0.120409i
\(34\) 27.2247i 0.800725i
\(35\) 23.4464 0.669896
\(36\) 32.1385 0.892736
\(37\) 33.2177i 0.897776i −0.893588 0.448888i \(-0.851820\pi\)
0.893588 0.448888i \(-0.148180\pi\)
\(38\) 84.7673i 2.23072i
\(39\) 26.0790 0.668693
\(40\) 228.181i 5.70453i
\(41\) −6.76874 −0.165091 −0.0825456 0.996587i \(-0.526305\pi\)
−0.0825456 + 0.996587i \(0.526305\pi\)
\(42\) 17.5775i 0.418513i
\(43\) 68.6344i 1.59615i 0.602559 + 0.798074i \(0.294148\pi\)
−0.602559 + 0.798074i \(0.705852\pi\)
\(44\) 24.5762i 0.558551i
\(45\) 26.5857i 0.590793i
\(46\) −85.0157 + 23.5674i −1.84817 + 0.512336i
\(47\) −56.9055 −1.21076 −0.605378 0.795938i \(-0.706978\pi\)
−0.605378 + 0.795938i \(0.706978\pi\)
\(48\) 96.8448 2.01760
\(49\) −7.00000 −0.142857
\(50\) 205.339 4.10677
\(51\) 12.2935i 0.241049i
\(52\) 161.300 3.10193
\(53\) 6.03878i 0.113939i −0.998376 0.0569696i \(-0.981856\pi\)
0.998376 0.0569696i \(-0.0181438\pi\)
\(54\) −19.9310 −0.369093
\(55\) −20.3300 −0.369637
\(56\) 68.1244i 1.21651i
\(57\) 38.2772i 0.671531i
\(58\) −150.916 −2.60199
\(59\) −103.615 −1.75618 −0.878092 0.478492i \(-0.841183\pi\)
−0.878092 + 0.478492i \(0.841183\pi\)
\(60\) 164.434i 2.74056i
\(61\) 30.0632i 0.492839i 0.969163 + 0.246420i \(0.0792541\pi\)
−0.969163 + 0.246420i \(0.920746\pi\)
\(62\) −23.7881 −0.383679
\(63\) 7.93725i 0.125988i
\(64\) 203.932 3.18643
\(65\) 133.431i 2.05279i
\(66\) 15.2412i 0.230928i
\(67\) 129.206i 1.92844i −0.265100 0.964221i \(-0.585405\pi\)
0.265100 0.964221i \(-0.414595\pi\)
\(68\) 76.0359i 1.11817i
\(69\) 38.3894 10.6420i 0.556368 0.154232i
\(70\) −89.9339 −1.28477
\(71\) 25.8589 0.364210 0.182105 0.983279i \(-0.441709\pi\)
0.182105 + 0.983279i \(0.441709\pi\)
\(72\) −77.2458 −1.07286
\(73\) 0.973133 0.0133306 0.00666529 0.999978i \(-0.497878\pi\)
0.00666529 + 0.999978i \(0.497878\pi\)
\(74\) 127.414i 1.72181i
\(75\) −92.7221 −1.23629
\(76\) 236.747i 3.11509i
\(77\) 6.06961 0.0788260
\(78\) −100.032 −1.28246
\(79\) 78.4213i 0.992675i 0.868130 + 0.496338i \(0.165322\pi\)
−0.868130 + 0.496338i \(0.834678\pi\)
\(80\) 495.498i 6.19373i
\(81\) 9.00000 0.111111
\(82\) 25.9630 0.316623
\(83\) 71.3251i 0.859339i 0.902986 + 0.429669i \(0.141370\pi\)
−0.902986 + 0.429669i \(0.858630\pi\)
\(84\) 49.0923i 0.584433i
\(85\) −62.8986 −0.739983
\(86\) 263.263i 3.06120i
\(87\) 68.1470 0.783298
\(88\) 59.0697i 0.671247i
\(89\) 150.485i 1.69084i 0.534101 + 0.845421i \(0.320650\pi\)
−0.534101 + 0.845421i \(0.679350\pi\)
\(90\) 101.975i 1.13306i
\(91\) 39.8364i 0.437762i
\(92\) 237.441 65.8216i 2.58088 0.715452i
\(93\) 10.7417 0.115502
\(94\) 218.274 2.32206
\(95\) −195.842 −2.06150
\(96\) −193.079 −2.01124
\(97\) 164.879i 1.69978i 0.526961 + 0.849889i \(0.323331\pi\)
−0.526961 + 0.849889i \(0.676669\pi\)
\(98\) 26.8501 0.273981
\(99\) 6.88229i 0.0695180i
\(100\) −573.491 −5.73491
\(101\) −4.46324 −0.0441905 −0.0220953 0.999756i \(-0.507034\pi\)
−0.0220953 + 0.999756i \(0.507034\pi\)
\(102\) 47.1545i 0.462299i
\(103\) 17.4220i 0.169146i 0.996417 + 0.0845730i \(0.0269526\pi\)
−0.996417 + 0.0845730i \(0.973047\pi\)
\(104\) −387.690 −3.72779
\(105\) 40.6103 0.386765
\(106\) 23.1631i 0.218520i
\(107\) 174.982i 1.63535i −0.575681 0.817674i \(-0.695263\pi\)
0.575681 0.817674i \(-0.304737\pi\)
\(108\) 55.6655 0.515421
\(109\) 126.918i 1.16439i 0.813051 + 0.582193i \(0.197805\pi\)
−0.813051 + 0.582193i \(0.802195\pi\)
\(110\) 77.9805 0.708913
\(111\) 57.5347i 0.518331i
\(112\) 147.933i 1.32083i
\(113\) 28.0406i 0.248147i 0.992273 + 0.124073i \(0.0395958\pi\)
−0.992273 + 0.124073i \(0.960404\pi\)
\(114\) 146.821i 1.28791i
\(115\) 54.4491 + 196.416i 0.473470 + 1.70797i
\(116\) 421.493 3.63356
\(117\) 45.1702 0.386070
\(118\) 397.439 3.36812
\(119\) 18.7786 0.157803
\(120\) 395.222i 3.29351i
\(121\) 115.737 0.956505
\(122\) 115.314i 0.945199i
\(123\) −11.7238 −0.0953154
\(124\) 66.4379 0.535790
\(125\) 252.857i 2.02286i
\(126\) 30.4452i 0.241628i
\(127\) 136.369 1.07377 0.536886 0.843655i \(-0.319600\pi\)
0.536886 + 0.843655i \(0.319600\pi\)
\(128\) −336.330 −2.62758
\(129\) 118.878i 0.921536i
\(130\) 511.806i 3.93697i
\(131\) −109.648 −0.837005 −0.418502 0.908216i \(-0.637445\pi\)
−0.418502 + 0.908216i \(0.637445\pi\)
\(132\) 42.5673i 0.322480i
\(133\) 58.4695 0.439620
\(134\) 495.598i 3.69849i
\(135\) 46.0477i 0.341094i
\(136\) 182.754i 1.34378i
\(137\) 265.750i 1.93978i −0.243537 0.969892i \(-0.578308\pi\)
0.243537 0.969892i \(-0.421692\pi\)
\(138\) −147.251 + 40.8200i −1.06704 + 0.295797i
\(139\) −202.123 −1.45412 −0.727061 0.686573i \(-0.759114\pi\)
−0.727061 + 0.686573i \(0.759114\pi\)
\(140\) 251.177 1.79412
\(141\) −98.5632 −0.699030
\(142\) −99.1878 −0.698505
\(143\) 34.5416i 0.241549i
\(144\) 167.740 1.16486
\(145\) 348.668i 2.40461i
\(146\) −3.73267 −0.0255663
\(147\) −12.1244 −0.0824786
\(148\) 355.856i 2.40443i
\(149\) 99.4774i 0.667634i 0.942638 + 0.333817i \(0.108337\pi\)
−0.942638 + 0.333817i \(0.891663\pi\)
\(150\) 355.657 2.37105
\(151\) −40.4629 −0.267966 −0.133983 0.990984i \(-0.542777\pi\)
−0.133983 + 0.990984i \(0.542777\pi\)
\(152\) 569.028i 3.74361i
\(153\) 21.2929i 0.139170i
\(154\) −23.2814 −0.151178
\(155\) 54.9589i 0.354574i
\(156\) 279.380 1.79090
\(157\) 154.947i 0.986925i −0.869767 0.493462i \(-0.835731\pi\)
0.869767 0.493462i \(-0.164269\pi\)
\(158\) 300.803i 1.90382i
\(159\) 10.4595i 0.0657829i
\(160\) 987.872i 6.17420i
\(161\) −16.2560 58.6408i −0.100969 0.364229i
\(162\) −34.5216 −0.213096
\(163\) −157.550 −0.966562 −0.483281 0.875465i \(-0.660555\pi\)
−0.483281 + 0.875465i \(0.660555\pi\)
\(164\) −72.5123 −0.442148
\(165\) −35.2126 −0.213410
\(166\) 273.584i 1.64810i
\(167\) −57.3615 −0.343482 −0.171741 0.985142i \(-0.554939\pi\)
−0.171741 + 0.985142i \(0.554939\pi\)
\(168\) 117.995i 0.702351i
\(169\) 57.7051 0.341450
\(170\) 241.262 1.41919
\(171\) 66.2981i 0.387708i
\(172\) 735.268i 4.27481i
\(173\) 268.463 1.55181 0.775903 0.630852i \(-0.217294\pi\)
0.775903 + 0.630852i \(0.217294\pi\)
\(174\) −261.393 −1.50226
\(175\) 141.635i 0.809344i
\(176\) 128.271i 0.728810i
\(177\) −179.466 −1.01393
\(178\) 577.219i 3.24281i
\(179\) −90.7832 −0.507169 −0.253584 0.967313i \(-0.581610\pi\)
−0.253584 + 0.967313i \(0.581610\pi\)
\(180\) 284.808i 1.58227i
\(181\) 0.138624i 0.000765878i 1.00000 0.000382939i \(0.000121893\pi\)
−1.00000 0.000382939i \(0.999878\pi\)
\(182\) 152.802i 0.839569i
\(183\) 52.0710i 0.284541i
\(184\) −570.695 + 158.204i −3.10161 + 0.859805i
\(185\) 294.372 1.59120
\(186\) −41.2022 −0.221517
\(187\) −16.2827 −0.0870731
\(188\) −609.619 −3.24265
\(189\) 13.7477i 0.0727393i
\(190\) 751.198 3.95367
\(191\) 147.161i 0.770475i −0.922818 0.385237i \(-0.874120\pi\)
0.922818 0.385237i \(-0.125880\pi\)
\(192\) 353.220 1.83969
\(193\) 103.961 0.538659 0.269329 0.963048i \(-0.413198\pi\)
0.269329 + 0.963048i \(0.413198\pi\)
\(194\) 632.430i 3.25995i
\(195\) 231.109i 1.18518i
\(196\) −74.9898 −0.382601
\(197\) −104.624 −0.531089 −0.265544 0.964099i \(-0.585552\pi\)
−0.265544 + 0.964099i \(0.585552\pi\)
\(198\) 26.3986i 0.133326i
\(199\) 67.7199i 0.340301i 0.985418 + 0.170151i \(0.0544254\pi\)
−0.985418 + 0.170151i \(0.945575\pi\)
\(200\) 1378.40 6.89201
\(201\) 223.791i 1.11339i
\(202\) 17.1198 0.0847514
\(203\) 104.096i 0.512789i
\(204\) 131.698i 0.645578i
\(205\) 59.9838i 0.292604i
\(206\) 66.8262i 0.324399i
\(207\) 66.4924 18.4326i 0.321219 0.0890462i
\(208\) 841.872 4.04746
\(209\) −50.6981 −0.242575
\(210\) −155.770 −0.741762
\(211\) 205.955 0.976089 0.488045 0.872819i \(-0.337710\pi\)
0.488045 + 0.872819i \(0.337710\pi\)
\(212\) 64.6924i 0.305153i
\(213\) 44.7889 0.210277
\(214\) 671.185i 3.13638i
\(215\) −608.230 −2.82898
\(216\) −133.794 −0.619415
\(217\) 16.4082i 0.0756138i
\(218\) 486.823i 2.23313i
\(219\) 1.68552 0.00769642
\(220\) −217.792 −0.989964
\(221\) 106.867i 0.483562i
\(222\) 220.688i 0.994089i
\(223\) −222.235 −0.996569 −0.498285 0.867013i \(-0.666037\pi\)
−0.498285 + 0.867013i \(0.666037\pi\)
\(224\) 294.933i 1.31667i
\(225\) −160.599 −0.713775
\(226\) 107.556i 0.475912i
\(227\) 122.880i 0.541323i 0.962675 + 0.270662i \(0.0872424\pi\)
−0.962675 + 0.270662i \(0.912758\pi\)
\(228\) 410.058i 1.79850i
\(229\) 46.7869i 0.204309i 0.994769 + 0.102155i \(0.0325737\pi\)
−0.994769 + 0.102155i \(0.967426\pi\)
\(230\) −208.852 753.399i −0.908052 3.27565i
\(231\) 10.5129 0.0455102
\(232\) −1013.07 −4.36668
\(233\) 370.382 1.58962 0.794812 0.606856i \(-0.207569\pi\)
0.794812 + 0.606856i \(0.207569\pi\)
\(234\) −173.261 −0.740430
\(235\) 504.290i 2.14592i
\(236\) −1110.01 −4.70342
\(237\) 135.830i 0.573121i
\(238\) −72.0297 −0.302646
\(239\) 244.361 1.02243 0.511216 0.859452i \(-0.329195\pi\)
0.511216 + 0.859452i \(0.329195\pi\)
\(240\) 858.228i 3.57595i
\(241\) 144.596i 0.599984i 0.953942 + 0.299992i \(0.0969840\pi\)
−0.953942 + 0.299992i \(0.903016\pi\)
\(242\) −443.936 −1.83445
\(243\) 15.5885 0.0641500
\(244\) 322.062i 1.31993i
\(245\) 62.0332i 0.253197i
\(246\) 44.9693 0.182802
\(247\) 332.744i 1.34714i
\(248\) −159.685 −0.643893
\(249\) 123.539i 0.496140i
\(250\) 969.892i 3.87957i
\(251\) 164.873i 0.656866i 0.944527 + 0.328433i \(0.106521\pi\)
−0.944527 + 0.328433i \(0.893479\pi\)
\(252\) 85.0304i 0.337422i
\(253\) 14.0953 + 50.8466i 0.0557128 + 0.200975i
\(254\) −523.075 −2.05935
\(255\) −108.943 −0.427229
\(256\) 474.344 1.85291
\(257\) 70.0744 0.272663 0.136332 0.990663i \(-0.456469\pi\)
0.136332 + 0.990663i \(0.456469\pi\)
\(258\) 455.985i 1.76738i
\(259\) −87.8858 −0.339327
\(260\) 1429.42i 5.49779i
\(261\) 118.034 0.452238
\(262\) 420.579 1.60526
\(263\) 37.4693i 0.142469i 0.997460 + 0.0712344i \(0.0226938\pi\)
−0.997460 + 0.0712344i \(0.977306\pi\)
\(264\) 102.312i 0.387545i
\(265\) 53.5150 0.201943
\(266\) −224.273 −0.843132
\(267\) 260.647i 0.976208i
\(268\) 1384.16i 5.16477i
\(269\) −231.229 −0.859586 −0.429793 0.902927i \(-0.641414\pi\)
−0.429793 + 0.902927i \(0.641414\pi\)
\(270\) 176.627i 0.654173i
\(271\) 48.6653 0.179577 0.0897884 0.995961i \(-0.471381\pi\)
0.0897884 + 0.995961i \(0.471381\pi\)
\(272\) 396.853i 1.45902i
\(273\) 68.9986i 0.252742i
\(274\) 1019.35i 3.72024i
\(275\) 122.810i 0.446582i
\(276\) 411.259 114.006i 1.49007 0.413066i
\(277\) −12.4790 −0.0450504 −0.0225252 0.999746i \(-0.507171\pi\)
−0.0225252 + 0.999746i \(0.507171\pi\)
\(278\) 775.289 2.78881
\(279\) 18.6051 0.0666851
\(280\) −603.711 −2.15611
\(281\) 265.717i 0.945613i −0.881166 0.472807i \(-0.843241\pi\)
0.881166 0.472807i \(-0.156759\pi\)
\(282\) 378.062 1.34064
\(283\) 463.763i 1.63874i −0.573266 0.819370i \(-0.694324\pi\)
0.573266 0.819370i \(-0.305676\pi\)
\(284\) 277.022 0.975429
\(285\) −339.209 −1.19021
\(286\) 132.492i 0.463259i
\(287\) 17.9084i 0.0623986i
\(288\) −334.423 −1.16119
\(289\) 238.623 0.825687
\(290\) 1337.40i 4.61171i
\(291\) 285.578i 0.981368i
\(292\) 10.4250 0.0357021
\(293\) 299.454i 1.02203i −0.859572 0.511014i \(-0.829270\pi\)
0.859572 0.511014i \(-0.170730\pi\)
\(294\) 46.5058 0.158183
\(295\) 918.223i 3.11262i
\(296\) 855.309i 2.88956i
\(297\) 11.9205i 0.0401363i
\(298\) 381.569i 1.28043i
\(299\) 333.719 92.5113i 1.11612 0.309402i
\(300\) −993.315 −3.31105
\(301\) 181.589 0.603287
\(302\) 155.205 0.513923
\(303\) −7.73056 −0.0255134
\(304\) 1235.65i 4.06464i
\(305\) −266.417 −0.873497
\(306\) 81.6740i 0.266908i
\(307\) 562.045 1.83077 0.915383 0.402583i \(-0.131888\pi\)
0.915383 + 0.402583i \(0.131888\pi\)
\(308\) 65.0226 0.211112
\(309\) 30.1759i 0.0976565i
\(310\) 210.808i 0.680025i
\(311\) 153.549 0.493726 0.246863 0.969050i \(-0.420600\pi\)
0.246863 + 0.969050i \(0.420600\pi\)
\(312\) −671.498 −2.15224
\(313\) 360.712i 1.15243i −0.817297 0.576217i \(-0.804528\pi\)
0.817297 0.576217i \(-0.195472\pi\)
\(314\) 594.336i 1.89279i
\(315\) 70.3391 0.223299
\(316\) 840.114i 2.65859i
\(317\) 168.048 0.530119 0.265059 0.964232i \(-0.414608\pi\)
0.265059 + 0.964232i \(0.414608\pi\)
\(318\) 40.1197i 0.126163i
\(319\) 90.2604i 0.282948i
\(320\) 1807.22i 5.64756i
\(321\) 303.078i 0.944169i
\(322\) 62.3536 + 224.930i 0.193645 + 0.698541i
\(323\) −156.854 −0.485615
\(324\) 96.4155 0.297579
\(325\) −806.033 −2.48010
\(326\) 604.318 1.85374
\(327\) 219.828i 0.672258i
\(328\) 174.285 0.531358
\(329\) 150.558i 0.457622i
\(330\) 135.066 0.409291
\(331\) 546.021 1.64961 0.824805 0.565417i \(-0.191285\pi\)
0.824805 + 0.565417i \(0.191285\pi\)
\(332\) 764.094i 2.30149i
\(333\) 99.6531i 0.299259i
\(334\) 220.023 0.658752
\(335\) 1145.01 3.41793
\(336\) 256.227i 0.762581i
\(337\) 283.226i 0.840434i −0.907424 0.420217i \(-0.861954\pi\)
0.907424 0.420217i \(-0.138046\pi\)
\(338\) −221.341 −0.654855
\(339\) 48.5677i 0.143268i
\(340\) −673.821 −1.98183
\(341\) 14.2273i 0.0417224i
\(342\) 254.302i 0.743572i
\(343\) 18.5203i 0.0539949i
\(344\) 1767.24i 5.13732i
\(345\) 94.3086 + 340.203i 0.273358 + 0.986095i
\(346\) −1029.75 −2.97616
\(347\) 123.133 0.354850 0.177425 0.984134i \(-0.443223\pi\)
0.177425 + 0.984134i \(0.443223\pi\)
\(348\) 730.047 2.09784
\(349\) −330.667 −0.947470 −0.473735 0.880667i \(-0.657095\pi\)
−0.473735 + 0.880667i \(0.657095\pi\)
\(350\) 543.275i 1.55221i
\(351\) 78.2371 0.222898
\(352\) 255.733i 0.726513i
\(353\) −2.49981 −0.00708161 −0.00354080 0.999994i \(-0.501127\pi\)
−0.00354080 + 0.999994i \(0.501127\pi\)
\(354\) 688.384 1.94459
\(355\) 229.159i 0.645518i
\(356\) 1612.12i 4.52842i
\(357\) 32.5255 0.0911078
\(358\) 348.220 0.972681
\(359\) 142.325i 0.396449i −0.980157 0.198224i \(-0.936483\pi\)
0.980157 0.198224i \(-0.0635175\pi\)
\(360\) 684.544i 1.90151i
\(361\) −127.383 −0.352860
\(362\) 0.531724i 0.00146885i
\(363\) 200.463 0.552239
\(364\) 426.760i 1.17242i
\(365\) 8.62379i 0.0236268i
\(366\) 199.730i 0.545711i
\(367\) 35.9679i 0.0980053i 0.998799 + 0.0490027i \(0.0156043\pi\)
−0.998799 + 0.0490027i \(0.984396\pi\)
\(368\) 1239.27 343.542i 3.36759 0.933538i
\(369\) −20.3062 −0.0550304
\(370\) −1129.13 −3.05170
\(371\) −15.9771 −0.0430650
\(372\) 115.074 0.309338
\(373\) 422.662i 1.13314i 0.824013 + 0.566571i \(0.191730\pi\)
−0.824013 + 0.566571i \(0.808270\pi\)
\(374\) 62.4559 0.166995
\(375\) 437.962i 1.16790i
\(376\) 1465.24 3.89691
\(377\) 592.402 1.57136
\(378\) 52.7326i 0.139504i
\(379\) 533.484i 1.40761i −0.710394 0.703805i \(-0.751483\pi\)
0.710394 0.703805i \(-0.248517\pi\)
\(380\) −2098.02 −5.52112
\(381\) 236.198 0.619943
\(382\) 564.469i 1.47767i
\(383\) 447.089i 1.16734i −0.811993 0.583668i \(-0.801617\pi\)
0.811993 0.583668i \(-0.198383\pi\)
\(384\) −582.540 −1.51703
\(385\) 53.7882i 0.139710i
\(386\) −398.767 −1.03308
\(387\) 205.903i 0.532049i
\(388\) 1766.32i 4.55236i
\(389\) 384.353i 0.988055i 0.869446 + 0.494027i \(0.164476\pi\)
−0.869446 + 0.494027i \(0.835524\pi\)
\(390\) 886.473i 2.27301i
\(391\) 43.6092 + 157.313i 0.111533 + 0.402335i
\(392\) 180.240 0.459796
\(393\) −189.915 −0.483245
\(394\) 401.311 1.01856
\(395\) −694.961 −1.75940
\(396\) 73.7287i 0.186184i
\(397\) −427.857 −1.07772 −0.538862 0.842394i \(-0.681146\pi\)
−0.538862 + 0.842394i \(0.681146\pi\)
\(398\) 259.755i 0.652652i
\(399\) 101.272 0.253815
\(400\) −2993.22 −7.48304
\(401\) 52.0462i 0.129791i −0.997892 0.0648955i \(-0.979329\pi\)
0.997892 0.0648955i \(-0.0206714\pi\)
\(402\) 858.401i 2.13533i
\(403\) 93.3775 0.231706
\(404\) −47.8139 −0.118351
\(405\) 79.7570i 0.196931i
\(406\) 399.285i 0.983461i
\(407\) 76.2046 0.187235
\(408\) 316.540i 0.775833i
\(409\) 409.460 1.00112 0.500562 0.865701i \(-0.333127\pi\)
0.500562 + 0.865701i \(0.333127\pi\)
\(410\) 230.082i 0.561175i
\(411\) 460.293i 1.11993i
\(412\) 186.639i 0.453008i
\(413\) 274.139i 0.663775i
\(414\) −255.047 + 70.7023i −0.616055 + 0.170779i
\(415\) −632.076 −1.52307
\(416\) −1678.44 −4.03470
\(417\) −350.087 −0.839537
\(418\) 194.464 0.465225
\(419\) 718.694i 1.71526i −0.514266 0.857631i \(-0.671936\pi\)
0.514266 0.857631i \(-0.328064\pi\)
\(420\) 435.051 1.03584
\(421\) 320.503i 0.761290i −0.924721 0.380645i \(-0.875702\pi\)
0.924721 0.380645i \(-0.124298\pi\)
\(422\) −789.987 −1.87201
\(423\) −170.716 −0.403585
\(424\) 155.490i 0.366722i
\(425\) 379.959i 0.894021i
\(426\) −171.798 −0.403282
\(427\) 79.5397 0.186276
\(428\) 1874.56i 4.37980i
\(429\) 59.8277i 0.139459i
\(430\) 2333.01 5.42560
\(431\) 420.620i 0.975918i −0.872867 0.487959i \(-0.837742\pi\)
0.872867 0.487959i \(-0.162258\pi\)
\(432\) 290.534 0.672533
\(433\) 317.443i 0.733125i 0.930393 + 0.366562i \(0.119465\pi\)
−0.930393 + 0.366562i \(0.880535\pi\)
\(434\) 62.9374i 0.145017i
\(435\) 603.911i 1.38830i
\(436\) 1359.65i 3.11847i
\(437\) 135.783 + 489.814i 0.310716 + 1.12086i
\(438\) −6.46518 −0.0147607
\(439\) 151.755 0.345684 0.172842 0.984950i \(-0.444705\pi\)
0.172842 + 0.984950i \(0.444705\pi\)
\(440\) 523.470 1.18970
\(441\) −21.0000 −0.0476190
\(442\) 409.914i 0.927408i
\(443\) −170.396 −0.384641 −0.192320 0.981332i \(-0.561601\pi\)
−0.192320 + 0.981332i \(0.561601\pi\)
\(444\) 616.360i 1.38820i
\(445\) −1333.58 −2.99681
\(446\) 852.433 1.91129
\(447\) 172.300i 0.385458i
\(448\) 539.552i 1.20436i
\(449\) 632.355 1.40836 0.704181 0.710020i \(-0.251314\pi\)
0.704181 + 0.710020i \(0.251314\pi\)
\(450\) 616.016 1.36892
\(451\) 15.5281i 0.0344304i
\(452\) 300.394i 0.664588i
\(453\) −70.0838 −0.154710
\(454\) 471.336i 1.03818i
\(455\) 353.025 0.775880
\(456\) 985.586i 2.16137i
\(457\) 228.388i 0.499756i 0.968277 + 0.249878i \(0.0803905\pi\)
−0.968277 + 0.249878i \(0.919609\pi\)
\(458\) 179.462i 0.391838i
\(459\) 36.8804i 0.0803496i
\(460\) 583.304 + 2104.17i 1.26805 + 4.57429i
\(461\) 577.925 1.25363 0.626817 0.779167i \(-0.284357\pi\)
0.626817 + 0.779167i \(0.284357\pi\)
\(462\) −40.3245 −0.0872825
\(463\) −175.547 −0.379151 −0.189576 0.981866i \(-0.560711\pi\)
−0.189576 + 0.981866i \(0.560711\pi\)
\(464\) 2199.89 4.74115
\(465\) 95.1916i 0.204713i
\(466\) −1420.69 −3.04868
\(467\) 789.029i 1.68957i −0.535107 0.844784i \(-0.679729\pi\)
0.535107 0.844784i \(-0.320271\pi\)
\(468\) 483.900 1.03398
\(469\) −341.846 −0.728883
\(470\) 1934.32i 4.11558i
\(471\) 268.376i 0.569801i
\(472\) 2667.94 5.65241
\(473\) −157.454 −0.332883
\(474\) 521.006i 1.09917i
\(475\) 1183.05i 2.49063i
\(476\) 201.172 0.422630
\(477\) 18.1163i 0.0379798i
\(478\) −937.303 −1.96089
\(479\) 441.484i 0.921680i 0.887483 + 0.460840i \(0.152452\pi\)
−0.887483 + 0.460840i \(0.847548\pi\)
\(480\) 1711.05i 3.56468i
\(481\) 500.150i 1.03981i
\(482\) 554.632i 1.15069i
\(483\) −28.1562 101.569i −0.0582944 0.210287i
\(484\) 1239.87 2.56172
\(485\) −1461.14 −3.01265
\(486\) −59.7931 −0.123031
\(487\) −516.547 −1.06067 −0.530335 0.847788i \(-0.677934\pi\)
−0.530335 + 0.847788i \(0.677934\pi\)
\(488\) 774.085i 1.58624i
\(489\) −272.884 −0.558045
\(490\) 237.943i 0.485597i
\(491\) −23.6429 −0.0481525 −0.0240763 0.999710i \(-0.507664\pi\)
−0.0240763 + 0.999710i \(0.507664\pi\)
\(492\) −125.595 −0.255274
\(493\) 279.254i 0.566439i
\(494\) 1276.32i 2.58364i
\(495\) −60.9901 −0.123212
\(496\) 346.759 0.699111
\(497\) 68.4162i 0.137658i
\(498\) 473.861i 0.951529i
\(499\) 88.3199 0.176994 0.0884969 0.996076i \(-0.471794\pi\)
0.0884969 + 0.996076i \(0.471794\pi\)
\(500\) 2708.82i 5.41763i
\(501\) −99.3530 −0.198309
\(502\) 632.410i 1.25978i
\(503\) 579.131i 1.15135i 0.817677 + 0.575677i \(0.195261\pi\)
−0.817677 + 0.575677i \(0.804739\pi\)
\(504\) 204.373i 0.405502i
\(505\) 39.5528i 0.0783223i
\(506\) −54.0659 195.034i −0.106850 0.385443i
\(507\) 99.9481 0.197136
\(508\) 1460.90 2.87578
\(509\) −345.867 −0.679502 −0.339751 0.940515i \(-0.610343\pi\)
−0.339751 + 0.940515i \(0.610343\pi\)
\(510\) 417.878 0.819368
\(511\) 2.57467i 0.00503849i
\(512\) −474.136 −0.926047
\(513\) 114.832i 0.223844i
\(514\) −268.787 −0.522931
\(515\) −154.392 −0.299791
\(516\) 1273.52i 2.46807i
\(517\) 130.547i 0.252508i
\(518\) 337.106 0.650784
\(519\) 464.991 0.895936
\(520\) 3435.66i 6.60704i
\(521\) 441.530i 0.847466i 0.905787 + 0.423733i \(0.139281\pi\)
−0.905787 + 0.423733i \(0.860719\pi\)
\(522\) −452.747 −0.867331
\(523\) 62.9887i 0.120437i −0.998185 0.0602187i \(-0.980820\pi\)
0.998185 0.0602187i \(-0.0191798\pi\)
\(524\) −1174.64 −2.24167
\(525\) 245.319i 0.467275i
\(526\) 143.722i 0.273236i
\(527\) 44.0176i 0.0835248i
\(528\) 222.171i 0.420779i
\(529\) 453.498 272.361i 0.857274 0.514860i
\(530\) −205.269 −0.387300
\(531\) −310.844 −0.585395
\(532\) 626.373 1.17739
\(533\) −101.915 −0.191210
\(534\) 999.773i 1.87223i
\(535\) 1550.67 2.89846
\(536\) 3326.86i 6.20684i
\(537\) −157.241 −0.292814
\(538\) 886.931 1.64857
\(539\) 16.0587i 0.0297934i
\(540\) 493.301i 0.913521i
\(541\) −618.050 −1.14242 −0.571211 0.820803i \(-0.693526\pi\)
−0.571211 + 0.820803i \(0.693526\pi\)
\(542\) −186.667 −0.344404
\(543\) 0.240104i 0.000442180i
\(544\) 791.205i 1.45442i
\(545\) −1124.73 −2.06373
\(546\) 264.660i 0.484725i
\(547\) −315.255 −0.576334 −0.288167 0.957580i \(-0.593046\pi\)
−0.288167 + 0.957580i \(0.593046\pi\)
\(548\) 2846.94i 5.19514i
\(549\) 90.1896i 0.164280i
\(550\) 471.066i 0.856484i
\(551\) 869.493i 1.57803i
\(552\) −988.474 + 274.018i −1.79071 + 0.496409i
\(553\) 207.483 0.375196
\(554\) 47.8659 0.0864006
\(555\) 509.867 0.918679
\(556\) −2165.31 −3.89444
\(557\) 210.920i 0.378671i 0.981912 + 0.189335i \(0.0606333\pi\)
−0.981912 + 0.189335i \(0.939367\pi\)
\(558\) −71.3643 −0.127893
\(559\) 1033.41i 1.84867i
\(560\) 1310.96 2.34101
\(561\) −28.2024 −0.0502717
\(562\) 1019.22i 1.81356i
\(563\) 548.549i 0.974332i −0.873309 0.487166i \(-0.838031\pi\)
0.873309 0.487166i \(-0.161969\pi\)
\(564\) −1055.89 −1.87215
\(565\) −248.493 −0.439810
\(566\) 1778.87i 3.14288i
\(567\) 23.8118i 0.0419961i
\(568\) −665.830 −1.17224
\(569\) 569.440i 1.00077i −0.865802 0.500386i \(-0.833191\pi\)
0.865802 0.500386i \(-0.166809\pi\)
\(570\) 1301.11 2.28266
\(571\) 124.187i 0.217490i −0.994070 0.108745i \(-0.965317\pi\)
0.994070 0.108745i \(-0.0346832\pi\)
\(572\) 370.038i 0.646919i
\(573\) 254.890i 0.444834i
\(574\) 68.6918i 0.119672i
\(575\) −1186.52 + 328.917i −2.06350 + 0.572030i
\(576\) 611.795 1.06214
\(577\) 880.984 1.52684 0.763418 0.645905i \(-0.223520\pi\)
0.763418 + 0.645905i \(0.223520\pi\)
\(578\) −915.295 −1.58356
\(579\) 180.066 0.310995
\(580\) 3735.22i 6.44004i
\(581\) 188.709 0.324800
\(582\) 1095.40i 1.88213i
\(583\) 13.8535 0.0237625
\(584\) −25.0568 −0.0429055
\(585\) 400.293i 0.684262i
\(586\) 1148.63i 1.96011i
\(587\) 740.530 1.26155 0.630775 0.775965i \(-0.282737\pi\)
0.630775 + 0.775965i \(0.282737\pi\)
\(588\) −129.886 −0.220895
\(589\) 137.054i 0.232689i
\(590\) 3522.06i 5.96959i
\(591\) −181.215 −0.306624
\(592\) 1857.31i 3.13735i
\(593\) 602.557 1.01612 0.508059 0.861323i \(-0.330363\pi\)
0.508059 + 0.861323i \(0.330363\pi\)
\(594\) 45.7237i 0.0769759i
\(595\) 166.414i 0.279687i
\(596\) 1065.68i 1.78806i
\(597\) 117.294i 0.196473i
\(598\) −1280.06 + 354.848i −2.14056 + 0.593392i
\(599\) 643.607 1.07447 0.537235 0.843433i \(-0.319469\pi\)
0.537235 + 0.843433i \(0.319469\pi\)
\(600\) 2387.46 3.97911
\(601\) 177.729 0.295723 0.147861 0.989008i \(-0.452761\pi\)
0.147861 + 0.989008i \(0.452761\pi\)
\(602\) −696.528 −1.15702
\(603\) 387.617i 0.642814i
\(604\) −433.472 −0.717669
\(605\) 1025.65i 1.69529i
\(606\) 29.6523 0.0489313
\(607\) −388.983 −0.640829 −0.320414 0.947277i \(-0.603822\pi\)
−0.320414 + 0.947277i \(0.603822\pi\)
\(608\) 2463.51i 4.05183i
\(609\) 180.300i 0.296059i
\(610\) 1021.90 1.67525
\(611\) −856.810 −1.40231
\(612\) 228.108i 0.372725i
\(613\) 217.931i 0.355515i −0.984074 0.177758i \(-0.943116\pi\)
0.984074 0.177758i \(-0.0568843\pi\)
\(614\) −2155.85 −3.51116
\(615\) 103.895i 0.168935i
\(616\) −156.284 −0.253708
\(617\) 907.090i 1.47016i 0.677979 + 0.735081i \(0.262856\pi\)
−0.677979 + 0.735081i \(0.737144\pi\)
\(618\) 115.746i 0.187292i
\(619\) 974.089i 1.57365i −0.617177 0.786824i \(-0.711724\pi\)
0.617177 0.786824i \(-0.288276\pi\)
\(620\) 588.765i 0.949622i
\(621\) 115.168 31.9261i 0.185456 0.0514108i
\(622\) −588.971 −0.946899
\(623\) 398.146 0.639078
\(624\) 1458.17 2.33680
\(625\) 902.466 1.44394
\(626\) 1383.59i 2.21021i
\(627\) −87.8117 −0.140050
\(628\) 1659.92i 2.64319i
\(629\) 235.767 0.374829
\(630\) −269.802 −0.428257
\(631\) 217.964i 0.345426i 0.984972 + 0.172713i \(0.0552533\pi\)
−0.984972 + 0.172713i \(0.944747\pi\)
\(632\) 2019.24i 3.19500i
\(633\) 356.724 0.563545
\(634\) −644.585 −1.01670
\(635\) 1208.49i 1.90313i
\(636\) 112.051i 0.176180i
\(637\) −105.397 −0.165459
\(638\) 346.215i 0.542656i
\(639\) 77.5767 0.121403
\(640\) 2980.52i 4.65706i
\(641\) 776.091i 1.21075i 0.795940 + 0.605375i \(0.206977\pi\)
−0.795940 + 0.605375i \(0.793023\pi\)
\(642\) 1162.53i 1.81079i
\(643\) 405.054i 0.629945i 0.949101 + 0.314972i \(0.101995\pi\)
−0.949101 + 0.314972i \(0.898005\pi\)
\(644\) −174.148 628.209i −0.270415 0.975479i
\(645\) −1053.49 −1.63331
\(646\) 601.648 0.931344
\(647\) 65.6081 0.101404 0.0507018 0.998714i \(-0.483854\pi\)
0.0507018 + 0.998714i \(0.483854\pi\)
\(648\) −231.737 −0.357619
\(649\) 237.702i 0.366259i
\(650\) 3091.73 4.75650
\(651\) 28.4198i 0.0436557i
\(652\) −1687.80 −2.58865
\(653\) 1053.55 1.61340 0.806701 0.590960i \(-0.201251\pi\)
0.806701 + 0.590960i \(0.201251\pi\)
\(654\) 843.203i 1.28930i
\(655\) 971.685i 1.48349i
\(656\) −378.463 −0.576925
\(657\) 2.91940 0.00444353
\(658\) 577.499i 0.877658i
\(659\) 932.060i 1.41436i 0.707036 + 0.707178i \(0.250032\pi\)
−0.707036 + 0.707178i \(0.749968\pi\)
\(660\) −377.227 −0.571556
\(661\) 573.064i 0.866965i −0.901162 0.433483i \(-0.857285\pi\)
0.901162 0.433483i \(-0.142715\pi\)
\(662\) −2094.39 −3.16373
\(663\) 185.100i 0.279185i
\(664\) 1836.52i 2.76585i
\(665\) 518.150i 0.779173i
\(666\) 382.242i 0.573938i
\(667\) 872.041 241.741i 1.30741 0.362430i
\(668\) −614.504 −0.919915
\(669\) −384.922 −0.575370
\(670\) −4391.93 −6.55513
\(671\) −68.9678 −0.102784
\(672\) 510.839i 0.760177i
\(673\) −754.416 −1.12098 −0.560488 0.828163i \(-0.689386\pi\)
−0.560488 + 0.828163i \(0.689386\pi\)
\(674\) 1086.38i 1.61184i
\(675\) −278.166 −0.412098
\(676\) 618.184 0.914474
\(677\) 437.536i 0.646286i 0.946350 + 0.323143i \(0.104739\pi\)
−0.946350 + 0.323143i \(0.895261\pi\)
\(678\) 186.293i 0.274768i
\(679\) 436.228 0.642456
\(680\) 1619.55 2.38169
\(681\) 212.835i 0.312533i
\(682\) 54.5722i 0.0800179i
\(683\) −89.0019 −0.130310 −0.0651551 0.997875i \(-0.520754\pi\)
−0.0651551 + 0.997875i \(0.520754\pi\)
\(684\) 710.241i 1.03836i
\(685\) 2355.05 3.43803
\(686\) 71.0387i 0.103555i
\(687\) 81.0372i 0.117958i
\(688\) 3837.58i 5.57788i
\(689\) 90.9243i 0.131966i
\(690\) −361.742 1304.93i −0.524264 1.89120i
\(691\) 1196.81 1.73199 0.865995 0.500053i \(-0.166686\pi\)
0.865995 + 0.500053i \(0.166686\pi\)
\(692\) 2875.99 4.15606
\(693\) 18.2088 0.0262753
\(694\) −472.305 −0.680554
\(695\) 1791.19i 2.57725i
\(696\) −1754.69 −2.52110
\(697\) 48.0421i 0.0689269i
\(698\) 1268.35 1.81712
\(699\) 641.521 0.917770
\(700\) 1517.31i 2.16759i
\(701\) 906.332i 1.29291i −0.762951 0.646456i \(-0.776250\pi\)
0.762951 0.646456i \(-0.223750\pi\)
\(702\) −300.096 −0.427488
\(703\) 734.091 1.04423
\(704\) 467.839i 0.664543i
\(705\) 873.456i 1.23894i
\(706\) 9.58859 0.0135816
\(707\) 11.8086i 0.0167024i
\(708\) −1922.59 −2.71552
\(709\) 1293.05i 1.82377i 0.410447 + 0.911885i \(0.365373\pi\)
−0.410447 + 0.911885i \(0.634627\pi\)
\(710\) 878.991i 1.23802i
\(711\) 235.264i 0.330892i
\(712\) 3874.77i 5.44210i
\(713\) 137.456 38.1045i 0.192785 0.0534425i
\(714\) −124.759 −0.174733
\(715\) −306.104 −0.428117
\(716\) −972.545 −1.35830
\(717\) 423.246 0.590301
\(718\) 545.921i 0.760336i
\(719\) −149.666 −0.208159 −0.104079 0.994569i \(-0.533190\pi\)
−0.104079 + 0.994569i \(0.533190\pi\)
\(720\) 1486.49i 2.06458i
\(721\) 46.0944 0.0639312
\(722\) 488.605 0.676739
\(723\) 250.448i 0.346401i
\(724\) 1.48505i 0.00205118i
\(725\) −2106.24 −2.90516
\(726\) −768.920 −1.05912
\(727\) 1022.15i 1.40599i 0.711195 + 0.702995i \(0.248154\pi\)
−0.711195 + 0.702995i \(0.751846\pi\)
\(728\) 1025.73i 1.40897i
\(729\) 27.0000 0.0370370
\(730\) 33.0785i 0.0453131i
\(731\) −487.142 −0.666405
\(732\) 557.827i 0.762059i
\(733\) 913.532i 1.24629i −0.782105 0.623146i \(-0.785854\pi\)
0.782105 0.623146i \(-0.214146\pi\)
\(734\) 137.963i 0.187961i
\(735\) 107.445i 0.146183i
\(736\) −2470.73 + 684.918i −3.35697 + 0.930596i
\(737\) 296.410 0.402185
\(738\) 77.8891 0.105541
\(739\) 127.300 0.172260 0.0861300 0.996284i \(-0.472550\pi\)
0.0861300 + 0.996284i \(0.472550\pi\)
\(740\) 3153.55 4.26156
\(741\) 576.330i 0.777773i
\(742\) 61.2839 0.0825929
\(743\) 344.634i 0.463841i −0.972735 0.231920i \(-0.925499\pi\)
0.972735 0.231920i \(-0.0745009\pi\)
\(744\) −276.583 −0.371752
\(745\) −881.558 −1.18330
\(746\) 1621.22i 2.17321i
\(747\) 213.975i 0.286446i
\(748\) −174.433 −0.233200
\(749\) −462.960 −0.618104
\(750\) 1679.90i 2.23987i
\(751\) 588.204i 0.783228i −0.920130 0.391614i \(-0.871917\pi\)
0.920130 0.391614i \(-0.128083\pi\)
\(752\) −3181.78 −4.23109
\(753\) 285.569i 0.379242i
\(754\) −2272.29 −3.01365
\(755\) 358.578i 0.474938i
\(756\) 147.277i 0.194811i
\(757\) 6.00617i 0.00793417i 0.999992 + 0.00396709i \(0.00126277\pi\)
−0.999992 + 0.00396709i \(0.998737\pi\)
\(758\) 2046.30i 2.69960i
\(759\) 24.4139 + 88.0690i 0.0321658 + 0.116033i
\(760\) 5042.66 6.63508
\(761\) 659.193 0.866219 0.433109 0.901341i \(-0.357416\pi\)
0.433109 + 0.901341i \(0.357416\pi\)
\(762\) −905.993 −1.18897
\(763\) 335.794 0.440096
\(764\) 1576.51i 2.06349i
\(765\) −188.696 −0.246661
\(766\) 1714.91i 2.23879i
\(767\) −1560.10 −2.03403
\(768\) 821.588 1.06978
\(769\) 299.704i 0.389732i 0.980830 + 0.194866i \(0.0624272\pi\)
−0.980830 + 0.194866i \(0.937573\pi\)
\(770\) 206.317i 0.267944i
\(771\) 121.372 0.157422
\(772\) 1113.72 1.44264
\(773\) 374.493i 0.484468i −0.970218 0.242234i \(-0.922120\pi\)
0.970218 0.242234i \(-0.0778801\pi\)
\(774\) 789.789i 1.02040i
\(775\) −331.997 −0.428383
\(776\) 4245.39i 5.47087i
\(777\) −152.223 −0.195911
\(778\) 1474.28i 1.89496i
\(779\) 149.585i 0.192022i
\(780\) 2475.84i 3.17415i
\(781\) 59.3228i 0.0759575i
\(782\) −167.273 603.411i −0.213904 0.771625i
\(783\) 204.441 0.261099
\(784\) −391.394 −0.499227
\(785\) 1373.13 1.74920
\(786\) 728.464 0.926799
\(787\) 62.4755i 0.0793843i −0.999212 0.0396922i \(-0.987362\pi\)
0.999212 0.0396922i \(-0.0126377\pi\)
\(788\) −1120.82 −1.42237
\(789\) 64.8987i 0.0822544i
\(790\) 2665.68 3.37428
\(791\) 74.1884 0.0937906