Properties

Label 210.3.k.a.83.8
Level 210
Weight 3
Character 210.83
Analytic conductor 5.722
Analytic rank 0
Dimension 32
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 83.8
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.a.167.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-0.00829838 - 2.99999i) q^{3} +2.00000i q^{4} +(-3.67015 - 3.39558i) q^{5} +(-2.99169 + 3.00829i) q^{6} +(1.45834 - 6.84640i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-8.99986 + 0.0497901i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-0.00829838 - 2.99999i) q^{3} +2.00000i q^{4} +(-3.67015 - 3.39558i) q^{5} +(-2.99169 + 3.00829i) q^{6} +(1.45834 - 6.84640i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-8.99986 + 0.0497901i) q^{9} +(0.274569 + 7.06574i) q^{10} +6.08610i q^{11} +(5.99998 - 0.0165968i) q^{12} +(-4.00045 + 4.00045i) q^{13} +(-8.30474 + 5.38806i) q^{14} +(-10.1563 + 11.0386i) q^{15} -4.00000 q^{16} +(14.8174 - 14.8174i) q^{17} +(9.04965 + 8.95007i) q^{18} -20.4190 q^{19} +(6.79117 - 7.34030i) q^{20} +(-20.5512 - 4.31819i) q^{21} +(6.08610 - 6.08610i) q^{22} +(-20.6285 + 20.6285i) q^{23} +(-6.01657 - 5.98338i) q^{24} +(1.94003 + 24.9246i) q^{25} +8.00089 q^{26} +(0.224054 + 26.9991i) q^{27} +(13.6928 + 2.91668i) q^{28} +19.5317 q^{29} +(21.1948 - 0.882337i) q^{30} -4.36235i q^{31} +(4.00000 + 4.00000i) q^{32} +(18.2582 - 0.0505048i) q^{33} -29.6348 q^{34} +(-28.5999 + 20.1754i) q^{35} +(-0.0995802 - 17.9997i) q^{36} +(-1.64351 + 1.64351i) q^{37} +(20.4190 + 20.4190i) q^{38} +(12.0345 + 11.9681i) q^{39} +(-14.1315 + 0.549137i) q^{40} -42.2693 q^{41} +(16.2330 + 24.8694i) q^{42} +(-45.0034 - 45.0034i) q^{43} -12.1722 q^{44} +(33.1999 + 30.3770i) q^{45} +41.2570 q^{46} +(36.6983 - 36.6983i) q^{47} +(0.0331935 + 12.0000i) q^{48} +(-44.7465 - 19.9688i) q^{49} +(22.9846 - 26.8646i) q^{50} +(-44.5749 - 44.3290i) q^{51} +(-8.00089 - 8.00089i) q^{52} +(0.652830 - 0.652830i) q^{53} +(26.7750 - 27.2231i) q^{54} +(20.6659 - 22.3369i) q^{55} +(-10.7761 - 16.6095i) q^{56} +(0.169444 + 61.2567i) q^{57} +(-19.5317 - 19.5317i) q^{58} +4.02656i q^{59} +(-22.0772 - 20.3125i) q^{60} -65.2074i q^{61} +(-4.36235 + 4.36235i) q^{62} +(-12.7840 + 61.6893i) q^{63} -8.00000i q^{64} +(28.2661 - 1.09840i) q^{65} +(-18.3087 - 18.2077i) q^{66} +(59.7184 - 59.7184i) q^{67} +(29.6348 + 29.6348i) q^{68} +(62.0565 + 61.7141i) q^{69} +(48.7753 + 8.42444i) q^{70} -122.856i q^{71} +(-17.9001 + 18.0993i) q^{72} +(13.1414 - 13.1414i) q^{73} +3.28701 q^{74} +(74.7575 - 6.02690i) q^{75} -40.8379i q^{76} +(41.6679 + 8.87561i) q^{77} +(-0.0663945 - 24.0026i) q^{78} -126.052i q^{79} +(14.6806 + 13.5823i) q^{80} +(80.9950 - 0.896208i) q^{81} +(42.2693 + 42.2693i) q^{82} +(12.2050 + 12.2050i) q^{83} +(8.63638 - 41.1025i) q^{84} +(-104.696 + 4.06839i) q^{85} +90.0068i q^{86} +(-0.162082 - 58.5950i) q^{87} +(12.1722 + 12.1722i) q^{88} +97.2971i q^{89} +(-2.82288 - 63.5770i) q^{90} +(21.5547 + 33.2227i) q^{91} +(-41.2570 - 41.2570i) q^{92} +(-13.0870 + 0.0362004i) q^{93} -73.3967 q^{94} +(74.9407 + 69.3343i) q^{95} +(11.9668 - 12.0331i) q^{96} +(-60.6217 - 60.6217i) q^{97} +(24.7777 + 64.7153i) q^{98} +(-0.303028 - 54.7741i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + O(q^{10}) \) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + 8q^{14} - 20q^{15} - 128q^{16} + 36q^{18} + 12q^{21} - 40q^{22} + 24q^{23} + 16q^{25} - 8q^{28} - 112q^{29} + 68q^{30} + 128q^{32} - 48q^{35} - 40q^{36} + 32q^{37} + 64q^{39} - 44q^{42} - 32q^{43} + 80q^{44} - 48q^{46} - 8q^{50} + 84q^{51} - 136q^{53} + 244q^{57} + 112q^{58} - 96q^{60} + 72q^{63} - 200q^{65} + 32q^{67} + 8q^{72} - 64q^{74} + 88q^{77} - 124q^{78} + 76q^{81} + 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} + 48q^{92} - 452q^{93} + 544q^{95} + 128q^{98} + 160q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) −0.00829838 2.99999i −0.00276613 0.999996i
\(4\) 2.00000i 0.500000i
\(5\) −3.67015 3.39558i −0.734030 0.679117i
\(6\) −2.99169 + 3.00829i −0.498615 + 0.501381i
\(7\) 1.45834 6.84640i 0.208334 0.978058i
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) −8.99986 + 0.0497901i −0.999985 + 0.00553223i
\(10\) 0.274569 + 7.06574i 0.0274569 + 0.706574i
\(11\) 6.08610i 0.553282i 0.960973 + 0.276641i \(0.0892213\pi\)
−0.960973 + 0.276641i \(0.910779\pi\)
\(12\) 5.99998 0.0165968i 0.499998 0.00138306i
\(13\) −4.00045 + 4.00045i −0.307727 + 0.307727i −0.844027 0.536300i \(-0.819821\pi\)
0.536300 + 0.844027i \(0.319821\pi\)
\(14\) −8.30474 + 5.38806i −0.593196 + 0.384862i
\(15\) −10.1563 + 11.0386i −0.677084 + 0.735906i
\(16\) −4.00000 −0.250000
\(17\) 14.8174 14.8174i 0.871610 0.871610i −0.121037 0.992648i \(-0.538622\pi\)
0.992648 + 0.121037i \(0.0386221\pi\)
\(18\) 9.04965 + 8.95007i 0.502758 + 0.497226i
\(19\) −20.4190 −1.07468 −0.537341 0.843365i \(-0.680571\pi\)
−0.537341 + 0.843365i \(0.680571\pi\)
\(20\) 6.79117 7.34030i 0.339558 0.367015i
\(21\) −20.5512 4.31819i −0.978630 0.205628i
\(22\) 6.08610 6.08610i 0.276641 0.276641i
\(23\) −20.6285 + 20.6285i −0.896892 + 0.896892i −0.995160 0.0982681i \(-0.968670\pi\)
0.0982681 + 0.995160i \(0.468670\pi\)
\(24\) −6.01657 5.98338i −0.250691 0.249308i
\(25\) 1.94003 + 24.9246i 0.0776012 + 0.996984i
\(26\) 8.00089 0.307727
\(27\) 0.224054 + 26.9991i 0.00829830 + 0.999966i
\(28\) 13.6928 + 2.91668i 0.489029 + 0.104167i
\(29\) 19.5317 0.673508 0.336754 0.941593i \(-0.390671\pi\)
0.336754 + 0.941593i \(0.390671\pi\)
\(30\) 21.1948 0.882337i 0.706495 0.0294112i
\(31\) 4.36235i 0.140721i −0.997522 0.0703605i \(-0.977585\pi\)
0.997522 0.0703605i \(-0.0224150\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 18.2582 0.0505048i 0.553280 0.00153045i
\(34\) −29.6348 −0.871610
\(35\) −28.5999 + 20.1754i −0.817139 + 0.576441i
\(36\) −0.0995802 17.9997i −0.00276612 0.499992i
\(37\) −1.64351 + 1.64351i −0.0444191 + 0.0444191i −0.728967 0.684548i \(-0.759999\pi\)
0.684548 + 0.728967i \(0.259999\pi\)
\(38\) 20.4190 + 20.4190i 0.537341 + 0.537341i
\(39\) 12.0345 + 11.9681i 0.308577 + 0.306874i
\(40\) −14.1315 + 0.549137i −0.353287 + 0.0137284i
\(41\) −42.2693 −1.03096 −0.515480 0.856902i \(-0.672386\pi\)
−0.515480 + 0.856902i \(0.672386\pi\)
\(42\) 16.2330 + 24.8694i 0.386501 + 0.592129i
\(43\) −45.0034 45.0034i −1.04659 1.04659i −0.998860 0.0477300i \(-0.984801\pi\)
−0.0477300 0.998860i \(-0.515199\pi\)
\(44\) −12.1722 −0.276641
\(45\) 33.1999 + 30.3770i 0.737776 + 0.675045i
\(46\) 41.2570 0.896892
\(47\) 36.6983 36.6983i 0.780815 0.780815i −0.199153 0.979968i \(-0.563819\pi\)
0.979968 + 0.199153i \(0.0638191\pi\)
\(48\) 0.0331935 + 12.0000i 0.000691532 + 0.249999i
\(49\) −44.7465 19.9688i −0.913194 0.407526i
\(50\) 22.9846 26.8646i 0.459692 0.537293i
\(51\) −44.5749 44.3290i −0.874018 0.869196i
\(52\) −8.00089 8.00089i −0.153863 0.153863i
\(53\) 0.652830 0.652830i 0.0123176 0.0123176i −0.700921 0.713239i \(-0.747228\pi\)
0.713239 + 0.700921i \(0.247228\pi\)
\(54\) 26.7750 27.2231i 0.495834 0.504132i
\(55\) 20.6659 22.3369i 0.375743 0.406126i
\(56\) −10.7761 16.6095i −0.192431 0.296598i
\(57\) 0.169444 + 61.2567i 0.00297271 + 1.07468i
\(58\) −19.5317 19.5317i −0.336754 0.336754i
\(59\) 4.02656i 0.0682467i 0.999418 + 0.0341234i \(0.0108639\pi\)
−0.999418 + 0.0341234i \(0.989136\pi\)
\(60\) −22.0772 20.3125i −0.367953 0.338542i
\(61\) 65.2074i 1.06897i −0.845177 0.534487i \(-0.820505\pi\)
0.845177 0.534487i \(-0.179495\pi\)
\(62\) −4.36235 + 4.36235i −0.0703605 + 0.0703605i
\(63\) −12.7840 + 61.6893i −0.202920 + 0.979195i
\(64\) 8.00000i 0.125000i
\(65\) 28.2661 1.09840i 0.434863 0.0168984i
\(66\) −18.3087 18.2077i −0.277405 0.275875i
\(67\) 59.7184 59.7184i 0.891320 0.891320i −0.103327 0.994647i \(-0.532949\pi\)
0.994647 + 0.103327i \(0.0329489\pi\)
\(68\) 29.6348 + 29.6348i 0.435805 + 0.435805i
\(69\) 62.0565 + 61.7141i 0.899369 + 0.894408i
\(70\) 48.7753 + 8.42444i 0.696790 + 0.120349i
\(71\) 122.856i 1.73037i −0.501451 0.865186i \(-0.667200\pi\)
0.501451 0.865186i \(-0.332800\pi\)
\(72\) −17.9001 + 18.0993i −0.248613 + 0.251379i
\(73\) 13.1414 13.1414i 0.180019 0.180019i −0.611345 0.791364i \(-0.709371\pi\)
0.791364 + 0.611345i \(0.209371\pi\)
\(74\) 3.28701 0.0444191
\(75\) 74.7575 6.02690i 0.996766 0.0803587i
\(76\) 40.8379i 0.537341i
\(77\) 41.6679 + 8.87561i 0.541142 + 0.115268i
\(78\) −0.0663945 24.0026i −0.000851211 0.307725i
\(79\) 126.052i 1.59559i −0.602926 0.797797i \(-0.705999\pi\)
0.602926 0.797797i \(-0.294001\pi\)
\(80\) 14.6806 + 13.5823i 0.183508 + 0.169779i
\(81\) 80.9950 0.896208i 0.999939 0.0110643i
\(82\) 42.2693 + 42.2693i 0.515480 + 0.515480i
\(83\) 12.2050 + 12.2050i 0.147048 + 0.147048i 0.776798 0.629750i \(-0.216843\pi\)
−0.629750 + 0.776798i \(0.716843\pi\)
\(84\) 8.63638 41.1025i 0.102814 0.489315i
\(85\) −104.696 + 4.06839i −1.23171 + 0.0478634i
\(86\) 90.0068i 1.04659i
\(87\) −0.162082 58.5950i −0.00186301 0.673506i
\(88\) 12.1722 + 12.1722i 0.138321 + 0.138321i
\(89\) 97.2971i 1.09323i 0.837385 + 0.546613i \(0.184083\pi\)
−0.837385 + 0.546613i \(0.815917\pi\)
\(90\) −2.82288 63.5770i −0.0313654 0.706411i
\(91\) 21.5547 + 33.2227i 0.236864 + 0.365084i
\(92\) −41.2570 41.2570i −0.448446 0.448446i
\(93\) −13.0870 + 0.0362004i −0.140720 + 0.000389252i
\(94\) −73.3967 −0.780815
\(95\) 74.9407 + 69.3343i 0.788850 + 0.729835i
\(96\) 11.9668 12.0331i 0.124654 0.125345i
\(97\) −60.6217 60.6217i −0.624966 0.624966i 0.321831 0.946797i \(-0.395702\pi\)
−0.946797 + 0.321831i \(0.895702\pi\)
\(98\) 24.7777 + 64.7153i 0.252834 + 0.660360i
\(99\) −0.303028 54.7741i −0.00306089 0.553274i
\(100\) −49.8492 + 3.88006i −0.498492 + 0.0388006i
\(101\) −96.3108 −0.953572 −0.476786 0.879019i \(-0.658198\pi\)
−0.476786 + 0.879019i \(0.658198\pi\)
\(102\) 0.245921 + 88.9039i 0.00241099 + 0.871607i
\(103\) −113.602 + 113.602i −1.10293 + 1.10293i −0.108878 + 0.994055i \(0.534726\pi\)
−0.994055 + 0.108878i \(0.965274\pi\)
\(104\) 16.0018i 0.153863i
\(105\) 60.7634 + 85.6318i 0.578699 + 0.815541i
\(106\) −1.30566 −0.0123176
\(107\) −80.0368 80.0368i −0.748008 0.748008i 0.226097 0.974105i \(-0.427403\pi\)
−0.974105 + 0.226097i \(0.927403\pi\)
\(108\) −53.9981 + 0.448108i −0.499983 + 0.00414915i
\(109\) 193.662i 1.77672i 0.459150 + 0.888359i \(0.348154\pi\)
−0.459150 + 0.888359i \(0.651846\pi\)
\(110\) −43.0028 + 1.67105i −0.390934 + 0.0151914i
\(111\) 4.94414 + 4.91686i 0.0445418 + 0.0442960i
\(112\) −5.83336 + 27.3856i −0.0520836 + 0.244514i
\(113\) 130.246 130.246i 1.15262 1.15262i 0.166596 0.986025i \(-0.446722\pi\)
0.986025 0.166596i \(-0.0532776\pi\)
\(114\) 61.0872 61.4261i 0.535853 0.538826i
\(115\) 145.756 5.66394i 1.26744 0.0492517i
\(116\) 39.0635i 0.336754i
\(117\) 35.8043 36.2026i 0.306020 0.309424i
\(118\) 4.02656 4.02656i 0.0341234 0.0341234i
\(119\) −79.8370 123.055i −0.670899 1.03407i
\(120\) 1.76467 + 42.3897i 0.0147056 + 0.353247i
\(121\) 83.9594 0.693879
\(122\) −65.2074 + 65.2074i −0.534487 + 0.534487i
\(123\) 0.350767 + 126.807i 0.00285176 + 1.03096i
\(124\) 8.72470 0.0703605
\(125\) 77.5134 98.0646i 0.620107 0.784517i
\(126\) 74.4733 48.9053i 0.591058 0.388137i
\(127\) −53.5048 + 53.5048i −0.421297 + 0.421297i −0.885650 0.464353i \(-0.846287\pi\)
0.464353 + 0.885650i \(0.346287\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) −134.636 + 135.383i −1.04369 + 1.04948i
\(130\) −29.3645 27.1677i −0.225881 0.208982i
\(131\) −227.798 −1.73892 −0.869459 0.494005i \(-0.835532\pi\)
−0.869459 + 0.494005i \(0.835532\pi\)
\(132\) 0.101010 + 36.5165i 0.000765224 + 0.276640i
\(133\) −29.7778 + 139.797i −0.223893 + 1.05110i
\(134\) −119.437 −0.891320
\(135\) 90.8553 99.8515i 0.673002 0.739641i
\(136\) 59.2695i 0.435805i
\(137\) 16.8334 + 16.8334i 0.122872 + 0.122872i 0.765869 0.642997i \(-0.222309\pi\)
−0.642997 + 0.765869i \(0.722309\pi\)
\(138\) −0.342367 123.771i −0.00248092 0.896888i
\(139\) 30.0414 0.216125 0.108063 0.994144i \(-0.465535\pi\)
0.108063 + 0.994144i \(0.465535\pi\)
\(140\) −40.3509 57.1997i −0.288220 0.408569i
\(141\) −110.399 109.790i −0.782972 0.778653i
\(142\) −122.856 + 122.856i −0.865186 + 0.865186i
\(143\) −24.3471 24.3471i −0.170260 0.170260i
\(144\) 35.9994 0.199160i 0.249996 0.00138306i
\(145\) −71.6845 66.3217i −0.494376 0.457391i
\(146\) −26.2828 −0.180019
\(147\) −59.5348 + 134.405i −0.404998 + 0.914317i
\(148\) −3.28701 3.28701i −0.0222095 0.0222095i
\(149\) 7.65497 0.0513756 0.0256878 0.999670i \(-0.491822\pi\)
0.0256878 + 0.999670i \(0.491822\pi\)
\(150\) −80.7844 68.7306i −0.538562 0.458204i
\(151\) 236.474 1.56605 0.783027 0.621987i \(-0.213674\pi\)
0.783027 + 0.621987i \(0.213674\pi\)
\(152\) −40.8379 + 40.8379i −0.268671 + 0.268671i
\(153\) −132.617 + 134.092i −0.866775 + 0.876419i
\(154\) −32.7923 50.5435i −0.212937 0.328205i
\(155\) −14.8127 + 16.0105i −0.0955659 + 0.103293i
\(156\) −23.9362 + 24.0690i −0.153437 + 0.154288i
\(157\) 97.8157 + 97.8157i 0.623030 + 0.623030i 0.946305 0.323275i \(-0.104784\pi\)
−0.323275 + 0.946305i \(0.604784\pi\)
\(158\) −126.052 + 126.052i −0.797797 + 0.797797i
\(159\) −1.96390 1.95307i −0.0123516 0.0122834i
\(160\) −1.09827 28.2629i −0.00686422 0.176643i
\(161\) 111.148 + 171.315i 0.690359 + 1.06407i
\(162\) −81.8913 80.0988i −0.505502 0.494437i
\(163\) 0.909159 + 0.909159i 0.00557766 + 0.00557766i 0.709890 0.704312i \(-0.248745\pi\)
−0.704312 + 0.709890i \(0.748745\pi\)
\(164\) 84.5387i 0.515480i
\(165\) −67.1820 61.8120i −0.407164 0.374618i
\(166\) 24.4100i 0.147048i
\(167\) 144.965 144.965i 0.868051 0.868051i −0.124205 0.992257i \(-0.539638\pi\)
0.992257 + 0.124205i \(0.0396381\pi\)
\(168\) −49.7388 + 32.4661i −0.296065 + 0.193251i
\(169\) 136.993i 0.810609i
\(170\) 108.764 + 100.627i 0.639789 + 0.591925i
\(171\) 183.768 1.01666i 1.07467 0.00594540i
\(172\) 90.0068 90.0068i 0.523295 0.523295i
\(173\) 48.2322 + 48.2322i 0.278799 + 0.278799i 0.832629 0.553831i \(-0.186834\pi\)
−0.553831 + 0.832629i \(0.686834\pi\)
\(174\) −58.4329 + 58.7571i −0.335821 + 0.337684i
\(175\) 173.473 + 23.0663i 0.991275 + 0.131808i
\(176\) 24.3444i 0.138321i
\(177\) 12.0796 0.0334139i 0.0682465 0.000188779i
\(178\) 97.2971 97.2971i 0.546613 0.546613i
\(179\) −277.037 −1.54769 −0.773847 0.633372i \(-0.781670\pi\)
−0.773847 + 0.633372i \(0.781670\pi\)
\(180\) −60.7541 + 66.3999i −0.337523 + 0.368888i
\(181\) 271.177i 1.49822i 0.662448 + 0.749108i \(0.269518\pi\)
−0.662448 + 0.749108i \(0.730482\pi\)
\(182\) 11.6680 54.7773i 0.0641100 0.300974i
\(183\) −195.621 + 0.541116i −1.06897 + 0.00295692i
\(184\) 82.5141i 0.448446i
\(185\) 11.6126 0.451255i 0.0627707 0.00243922i
\(186\) 13.1232 + 13.0508i 0.0705548 + 0.0701656i
\(187\) 90.1801 + 90.1801i 0.482246 + 0.482246i
\(188\) 73.3967 + 73.3967i 0.390408 + 0.390408i
\(189\) 185.173 + 37.8399i 0.979753 + 0.200211i
\(190\) −5.60641 144.275i −0.0295074 0.759342i
\(191\) 180.267i 0.943807i −0.881650 0.471904i \(-0.843567\pi\)
0.881650 0.471904i \(-0.156433\pi\)
\(192\) −23.9999 + 0.0663871i −0.125000 + 0.000345766i
\(193\) −194.407 194.407i −1.00729 1.00729i −0.999973 0.00731625i \(-0.997671\pi\)
−0.00731625 0.999973i \(-0.502329\pi\)
\(194\) 121.243i 0.624966i
\(195\) −3.52974 84.7888i −0.0181012 0.434815i
\(196\) 39.9375 89.4930i 0.203763 0.456597i
\(197\) 78.6926 + 78.6926i 0.399455 + 0.399455i 0.878041 0.478586i \(-0.158851\pi\)
−0.478586 + 0.878041i \(0.658851\pi\)
\(198\) −54.4711 + 55.0771i −0.275106 + 0.278167i
\(199\) 203.776 1.02400 0.511999 0.858986i \(-0.328905\pi\)
0.511999 + 0.858986i \(0.328905\pi\)
\(200\) 53.7293 + 45.9692i 0.268646 + 0.229846i
\(201\) −179.650 178.659i −0.893782 0.888851i
\(202\) 96.3108 + 96.3108i 0.476786 + 0.476786i
\(203\) 28.4839 133.722i 0.140315 0.658730i
\(204\) 88.6580 89.1499i 0.434598 0.437009i
\(205\) 155.135 + 143.529i 0.756755 + 0.700142i
\(206\) 227.204 1.10293
\(207\) 184.627 186.681i 0.891916 0.901840i
\(208\) 16.0018 16.0018i 0.0769317 0.0769317i
\(209\) 124.272i 0.594603i
\(210\) 24.8685 146.395i 0.118421 0.697120i
\(211\) −267.545 −1.26798 −0.633992 0.773340i \(-0.718585\pi\)
−0.633992 + 0.773340i \(0.718585\pi\)
\(212\) 1.30566 + 1.30566i 0.00615878 + 0.00615878i
\(213\) −368.568 + 1.01951i −1.73037 + 0.00478643i
\(214\) 160.074i 0.748008i
\(215\) 12.3565 + 317.982i 0.0574722 + 1.47899i
\(216\) 54.4462 + 53.5500i 0.252066 + 0.247917i
\(217\) −29.8664 6.36179i −0.137633 0.0293170i
\(218\) 193.662 193.662i 0.888359 0.888359i
\(219\) −39.5331 39.3150i −0.180516 0.179520i
\(220\) 44.6738 + 41.3317i 0.203063 + 0.187872i
\(221\) 118.552i 0.536436i
\(222\) −0.0272769 9.86100i −0.000122869 0.0444189i
\(223\) 270.204 270.204i 1.21168 1.21168i 0.241204 0.970475i \(-0.422458\pi\)
0.970475 0.241204i \(-0.0775422\pi\)
\(224\) 33.2190 21.5523i 0.148299 0.0962154i
\(225\) −18.7010 224.221i −0.0831155 0.996540i
\(226\) −260.492 −1.15262
\(227\) −43.7703 + 43.7703i −0.192821 + 0.192821i −0.796914 0.604093i \(-0.793535\pi\)
0.604093 + 0.796914i \(0.293535\pi\)
\(228\) −122.513 + 0.338889i −0.537339 + 0.00148635i
\(229\) −74.6694 −0.326067 −0.163034 0.986621i \(-0.552128\pi\)
−0.163034 + 0.986621i \(0.552128\pi\)
\(230\) −151.420 140.092i −0.658346 0.609094i
\(231\) 26.2809 125.077i 0.113770 0.541459i
\(232\) 39.0635 39.0635i 0.168377 0.168377i
\(233\) 239.538 239.538i 1.02806 1.02806i 0.0284664 0.999595i \(-0.490938\pi\)
0.999595 0.0284664i \(-0.00906237\pi\)
\(234\) −72.0069 + 0.398365i −0.307722 + 0.00170242i
\(235\) −259.301 + 10.0762i −1.10341 + 0.0428775i
\(236\) −8.05312 −0.0341234
\(237\) −378.154 + 1.04603i −1.59559 + 0.00441362i
\(238\) −43.2176 + 202.892i −0.181586 + 0.852485i
\(239\) 34.0240 0.142360 0.0711799 0.997463i \(-0.477324\pi\)
0.0711799 + 0.997463i \(0.477324\pi\)
\(240\) 40.6250 44.1544i 0.169271 0.183977i
\(241\) 268.995i 1.11616i −0.829786 0.558081i \(-0.811538\pi\)
0.829786 0.558081i \(-0.188462\pi\)
\(242\) −83.9594 83.9594i −0.346939 0.346939i
\(243\) −3.36074 242.977i −0.0138302 0.999904i
\(244\) 130.415 0.534487
\(245\) 96.4208 + 225.229i 0.393554 + 0.919301i
\(246\) 126.457 127.158i 0.514052 0.516904i
\(247\) 81.6850 81.6850i 0.330709 0.330709i
\(248\) −8.72470 8.72470i −0.0351802 0.0351802i
\(249\) 36.5136 36.7162i 0.146641 0.147455i
\(250\) −175.578 + 20.5513i −0.702312 + 0.0822050i
\(251\) 17.7724 0.0708064 0.0354032 0.999373i \(-0.488728\pi\)
0.0354032 + 0.999373i \(0.488728\pi\)
\(252\) −123.379 25.5680i −0.489598 0.101460i
\(253\) −125.547 125.547i −0.496234 0.496234i
\(254\) 107.010 0.421297
\(255\) 13.0739 + 314.052i 0.0512703 + 1.23158i
\(256\) 16.0000 0.0625000
\(257\) 155.524 155.524i 0.605151 0.605151i −0.336524 0.941675i \(-0.609251\pi\)
0.941675 + 0.336524i \(0.109251\pi\)
\(258\) 270.019 0.746911i 1.04659 0.00289500i
\(259\) 8.85531 + 13.6489i 0.0341904 + 0.0526984i
\(260\) 2.19679 + 56.5322i 0.00844921 + 0.217431i
\(261\) −175.783 + 0.972488i −0.673498 + 0.00372601i
\(262\) 227.798 + 227.798i 0.869459 + 0.869459i
\(263\) 227.523 227.523i 0.865105 0.865105i −0.126821 0.991926i \(-0.540477\pi\)
0.991926 + 0.126821i \(0.0404772\pi\)
\(264\) 36.4155 36.6175i 0.137937 0.138703i
\(265\) −4.61273 + 0.179247i −0.0174065 + 0.000676403i
\(266\) 169.574 110.019i 0.637497 0.413604i
\(267\) 291.890 0.807409i 1.09322 0.00302400i
\(268\) 119.437 + 119.437i 0.445660 + 0.445660i
\(269\) 89.7378i 0.333598i 0.985991 + 0.166799i \(0.0533431\pi\)
−0.985991 + 0.166799i \(0.946657\pi\)
\(270\) −190.707 + 8.99621i −0.706321 + 0.0333193i
\(271\) 318.345i 1.17470i 0.809332 + 0.587352i \(0.199830\pi\)
−0.809332 + 0.587352i \(0.800170\pi\)
\(272\) −59.2695 + 59.2695i −0.217903 + 0.217903i
\(273\) 99.4888 64.9394i 0.364428 0.237873i
\(274\) 33.6668i 0.122872i
\(275\) −151.694 + 11.8072i −0.551614 + 0.0429353i
\(276\) −123.428 + 124.113i −0.447204 + 0.449685i
\(277\) 65.4246 65.4246i 0.236190 0.236190i −0.579080 0.815270i \(-0.696588\pi\)
0.815270 + 0.579080i \(0.196588\pi\)
\(278\) −30.0414 30.0414i −0.108063 0.108063i
\(279\) 0.217202 + 39.2605i 0.000778501 + 0.140719i
\(280\) −16.8489 + 97.5506i −0.0601746 + 0.348395i
\(281\) 431.212i 1.53456i 0.641311 + 0.767281i \(0.278391\pi\)
−0.641311 + 0.767281i \(0.721609\pi\)
\(282\) 0.609073 + 220.189i 0.00215984 + 0.780812i
\(283\) 168.146 168.146i 0.594155 0.594155i −0.344596 0.938751i \(-0.611984\pi\)
0.938751 + 0.344596i \(0.111984\pi\)
\(284\) 245.713 0.865186
\(285\) 207.380 225.397i 0.727650 0.790866i
\(286\) 48.6943i 0.170260i
\(287\) −61.6431 + 289.393i −0.214784 + 1.00834i
\(288\) −36.1986 35.8003i −0.125690 0.124307i
\(289\) 150.109i 0.519410i
\(290\) 5.36281 + 138.006i 0.0184924 + 0.475883i
\(291\) −181.361 + 182.367i −0.623235 + 0.626692i
\(292\) 26.2828 + 26.2828i 0.0900095 + 0.0900095i
\(293\) 262.938 + 262.938i 0.897399 + 0.897399i 0.995205 0.0978068i \(-0.0311827\pi\)
−0.0978068 + 0.995205i \(0.531183\pi\)
\(294\) 193.939 74.8699i 0.659658 0.254659i
\(295\) 13.6725 14.7781i 0.0463475 0.0500952i
\(296\) 6.57402i 0.0222095i
\(297\) −164.319 + 1.36362i −0.553263 + 0.00459130i
\(298\) −7.65497 7.65497i −0.0256878 0.0256878i
\(299\) 165.047i 0.551995i
\(300\) 12.0538 + 149.515i 0.0401793 + 0.498383i
\(301\) −373.742 + 242.481i −1.24167 + 0.805585i
\(302\) −236.474 236.474i −0.783027 0.783027i
\(303\) 0.799223 + 288.931i 0.00263770 + 0.953568i
\(304\) 81.6759 0.268671
\(305\) −221.417 + 239.321i −0.725958 + 0.784659i
\(306\) 266.709 1.47552i 0.871597 0.00482195i
\(307\) −366.628 366.628i −1.19423 1.19423i −0.975869 0.218358i \(-0.929930\pi\)
−0.218358 0.975869i \(-0.570070\pi\)
\(308\) −17.7512 + 83.3358i −0.0576338 + 0.270571i
\(309\) 341.748 + 339.862i 1.10598 + 1.09988i
\(310\) 30.8232 1.19776i 0.0994297 0.00386376i
\(311\) 113.759 0.365785 0.182893 0.983133i \(-0.441454\pi\)
0.182893 + 0.983133i \(0.441454\pi\)
\(312\) 48.0052 0.132789i 0.153863 0.000425606i
\(313\) 267.661 267.661i 0.855146 0.855146i −0.135615 0.990762i \(-0.543301\pi\)
0.990762 + 0.135615i \(0.0433012\pi\)
\(314\) 195.631i 0.623030i
\(315\) 256.390 183.000i 0.813937 0.580953i
\(316\) 252.104 0.797797
\(317\) −215.640 215.640i −0.680253 0.680253i 0.279804 0.960057i \(-0.409730\pi\)
−0.960057 + 0.279804i \(0.909730\pi\)
\(318\) 0.0108349 + 3.91697i 3.40719e−5 + 0.0123175i
\(319\) 118.872i 0.372640i
\(320\) −27.1647 + 29.3612i −0.0848896 + 0.0917538i
\(321\) −239.445 + 240.774i −0.745936 + 0.750074i
\(322\) 60.1668 282.462i 0.186853 0.877212i
\(323\) −302.556 + 302.556i −0.936705 + 0.936705i
\(324\) 1.79242 + 161.990i 0.00553215 + 0.499969i
\(325\) −107.471 91.9486i −0.330679 0.282919i
\(326\) 1.81832i 0.00557766i
\(327\) 580.984 1.60708i 1.77671 0.00491463i
\(328\) −84.5387 + 84.5387i −0.257740 + 0.257740i
\(329\) −197.733 304.770i −0.601012 0.926353i
\(330\) 5.36999 + 128.994i 0.0162727 + 0.390891i
\(331\) 70.4637 0.212881 0.106441 0.994319i \(-0.466055\pi\)
0.106441 + 0.994319i \(0.466055\pi\)
\(332\) −24.4100 + 24.4100i −0.0735242 + 0.0735242i
\(333\) 14.7095 14.8732i 0.0441727 0.0446641i
\(334\) −289.929 −0.868051
\(335\) −421.955 + 16.3968i −1.25957 + 0.0489457i
\(336\) 82.2049 + 17.2728i 0.244658 + 0.0514070i
\(337\) −38.8228 + 38.8228i −0.115201 + 0.115201i −0.762357 0.647156i \(-0.775958\pi\)
0.647156 + 0.762357i \(0.275958\pi\)
\(338\) 136.993 136.993i 0.405304 0.405304i
\(339\) −391.818 389.656i −1.15581 1.14943i
\(340\) −8.13678 209.391i −0.0239317 0.615857i
\(341\) 26.5497 0.0778584
\(342\) −184.785 182.751i −0.540306 0.534360i
\(343\) −201.970 + 277.231i −0.588833 + 0.808254i
\(344\) −180.014 −0.523295
\(345\) −18.2013 437.218i −0.0527574 1.26730i
\(346\) 96.4644i 0.278799i
\(347\) −137.429 137.429i −0.396050 0.396050i 0.480788 0.876837i \(-0.340351\pi\)
−0.876837 + 0.480788i \(0.840351\pi\)
\(348\) 117.190 0.324164i 0.336753 0.000931505i
\(349\) 508.928 1.45825 0.729123 0.684383i \(-0.239928\pi\)
0.729123 + 0.684383i \(0.239928\pi\)
\(350\) −150.407 196.540i −0.429734 0.561541i
\(351\) −108.905 107.112i −0.310270 0.305162i
\(352\) −24.3444 + 24.3444i −0.0691603 + 0.0691603i
\(353\) −205.887 205.887i −0.583248 0.583248i 0.352546 0.935794i \(-0.385316\pi\)
−0.935794 + 0.352546i \(0.885316\pi\)
\(354\) −12.1130 12.0462i −0.0342176 0.0340288i
\(355\) −417.169 + 450.902i −1.17512 + 1.27015i
\(356\) −194.594 −0.546613
\(357\) −368.500 + 240.531i −1.03221 + 0.673757i
\(358\) 277.037 + 277.037i 0.773847 + 0.773847i
\(359\) −51.9892 −0.144817 −0.0724084 0.997375i \(-0.523068\pi\)
−0.0724084 + 0.997375i \(0.523068\pi\)
\(360\) 127.154 5.64577i 0.353205 0.0156827i
\(361\) 55.9344 0.154943
\(362\) 271.177 271.177i 0.749108 0.749108i
\(363\) −0.696727 251.877i −0.00191936 0.693876i
\(364\) −66.4454 + 43.1093i −0.182542 + 0.118432i
\(365\) −92.8536 + 3.60821i −0.254393 + 0.00988552i
\(366\) 196.163 + 195.080i 0.535963 + 0.533006i
\(367\) −340.117 340.117i −0.926749 0.926749i 0.0707450 0.997494i \(-0.477462\pi\)
−0.997494 + 0.0707450i \(0.977462\pi\)
\(368\) 82.5141 82.5141i 0.224223 0.224223i
\(369\) 380.418 2.10459i 1.03094 0.00570351i
\(370\) −12.0638 11.1613i −0.0326050 0.0301657i
\(371\) −3.51749 5.42159i −0.00948111 0.0146134i
\(372\) −0.0724009 26.1740i −0.000194626 0.0703602i
\(373\) 185.919 + 185.919i 0.498441 + 0.498441i 0.910952 0.412511i \(-0.135348\pi\)
−0.412511 + 0.910952i \(0.635348\pi\)
\(374\) 180.360i 0.482246i
\(375\) −294.836 231.726i −0.786229 0.617935i
\(376\) 146.793i 0.390408i
\(377\) −78.1357 + 78.1357i −0.207257 + 0.207257i
\(378\) −147.333 223.013i −0.389771 0.589982i
\(379\) 123.430i 0.325672i −0.986653 0.162836i \(-0.947936\pi\)
0.986653 0.162836i \(-0.0520641\pi\)
\(380\) −138.669 + 149.881i −0.364917 + 0.394425i
\(381\) 160.958 + 160.070i 0.422461 + 0.420130i
\(382\) −180.267 + 180.267i −0.471904 + 0.471904i
\(383\) 44.1167 + 44.1167i 0.115187 + 0.115187i 0.762351 0.647164i \(-0.224045\pi\)
−0.647164 + 0.762351i \(0.724045\pi\)
\(384\) 24.0663 + 23.9335i 0.0626726 + 0.0623269i
\(385\) −122.790 174.062i −0.318934 0.452108i
\(386\) 388.814i 1.00729i
\(387\) 407.265 + 402.784i 1.05236 + 1.04078i
\(388\) 121.243 121.243i 0.312483 0.312483i
\(389\) −116.363 −0.299133 −0.149566 0.988752i \(-0.547788\pi\)
−0.149566 + 0.988752i \(0.547788\pi\)
\(390\) −81.2591 + 88.3186i −0.208357 + 0.226458i
\(391\) 611.321i 1.56348i
\(392\) −129.431 + 49.5554i −0.330180 + 0.126417i
\(393\) 1.89036 + 683.392i 0.00481007 + 1.73891i
\(394\) 157.385i 0.399455i
\(395\) −428.020 + 462.630i −1.08359 + 1.17121i
\(396\) 109.548 0.606055i 0.276637 0.00153044i
\(397\) 8.73597 + 8.73597i 0.0220050 + 0.0220050i 0.718024 0.696019i \(-0.245047\pi\)
−0.696019 + 0.718024i \(0.745047\pi\)
\(398\) −203.776 203.776i −0.511999 0.511999i
\(399\) 419.635 + 88.1730i 1.05172 + 0.220985i
\(400\) −7.76012 99.6984i −0.0194003 0.249246i
\(401\) 27.9968i 0.0698174i 0.999391 + 0.0349087i \(0.0111140\pi\)
−0.999391 + 0.0349087i \(0.988886\pi\)
\(402\) 0.991133 + 358.309i 0.00246551 + 0.891317i
\(403\) 17.4513 + 17.4513i 0.0433036 + 0.0433036i
\(404\) 192.622i 0.476786i
\(405\) −300.307 271.736i −0.741499 0.670954i
\(406\) −162.206 + 105.238i −0.399523 + 0.259208i
\(407\) −10.0025 10.0025i −0.0245763 0.0245763i
\(408\) −177.808 + 0.491841i −0.435804 + 0.00120549i
\(409\) 234.500 0.573349 0.286675 0.958028i \(-0.407450\pi\)
0.286675 + 0.958028i \(0.407450\pi\)
\(410\) −11.6058 298.664i −0.0283069 0.728448i
\(411\) 50.3604 50.6397i 0.122531 0.123211i
\(412\) −227.204 227.204i −0.551467 0.551467i
\(413\) 27.5674 + 5.87209i 0.0667492 + 0.0142181i
\(414\) −371.308 + 2.05419i −0.896878 + 0.00496182i
\(415\) −3.35112 86.2375i −0.00807498 0.207801i
\(416\) −32.0036 −0.0769317
\(417\) −0.249295 90.1239i −0.000597830 0.216125i
\(418\) −124.272 + 124.272i −0.297301 + 0.297301i
\(419\) 339.624i 0.810559i 0.914193 + 0.405279i \(0.132826\pi\)
−0.914193 + 0.405279i \(0.867174\pi\)
\(420\) −171.264 + 121.527i −0.407771 + 0.289349i
\(421\) 699.038 1.66042 0.830211 0.557449i \(-0.188220\pi\)
0.830211 + 0.557449i \(0.188220\pi\)
\(422\) 267.545 + 267.545i 0.633992 + 0.633992i
\(423\) −328.453 + 332.107i −0.776484 + 0.785123i
\(424\) 2.61132i 0.00615878i
\(425\) 398.064 + 340.571i 0.936620 + 0.801344i
\(426\) 369.587 + 367.548i 0.867576 + 0.862789i
\(427\) −446.436 95.0946i −1.04552 0.222704i
\(428\) 160.074 160.074i 0.374004 0.374004i
\(429\) −72.8391 + 73.2431i −0.169788 + 0.170730i
\(430\) 305.625 330.338i 0.710757 0.768229i
\(431\) 590.362i 1.36975i −0.728661 0.684875i \(-0.759857\pi\)
0.728661 0.684875i \(-0.240143\pi\)
\(432\) −0.896216 107.996i −0.00207457 0.249991i
\(433\) −340.107 + 340.107i −0.785466 + 0.785466i −0.980747 0.195281i \(-0.937438\pi\)
0.195281 + 0.980747i \(0.437438\pi\)
\(434\) 23.5046 + 36.2282i 0.0541581 + 0.0834751i
\(435\) −198.369 + 215.603i −0.456022 + 0.495639i
\(436\) −387.324 −0.888359
\(437\) 421.213 421.213i 0.963874 0.963874i
\(438\) 0.218105 + 78.8480i 0.000497956 + 0.180018i
\(439\) −732.833 −1.66932 −0.834661 0.550764i \(-0.814337\pi\)
−0.834661 + 0.550764i \(0.814337\pi\)
\(440\) −3.34211 86.0056i −0.00759570 0.195467i
\(441\) 403.706 + 177.488i 0.915434 + 0.402468i
\(442\) 118.552 118.552i 0.268218 0.268218i
\(443\) −110.990 + 110.990i −0.250541 + 0.250541i −0.821192 0.570651i \(-0.806691\pi\)
0.570651 + 0.821192i \(0.306691\pi\)
\(444\) −9.83372 + 9.88827i −0.0221480 + 0.0222709i
\(445\) 330.380 357.095i 0.742428 0.802461i
\(446\) −540.408 −1.21168
\(447\) −0.0635238 22.9648i −0.000142111 0.0513754i
\(448\) −54.7712 11.6667i −0.122257 0.0260418i
\(449\) 196.292 0.437175 0.218588 0.975817i \(-0.429855\pi\)
0.218588 + 0.975817i \(0.429855\pi\)
\(450\) −205.520 + 242.922i −0.456712 + 0.539828i
\(451\) 257.255i 0.570411i
\(452\) 260.492 + 260.492i 0.576311 + 0.576311i
\(453\) −1.96235 709.420i −0.00433191 1.56605i
\(454\) 87.5405 0.192821
\(455\) 33.7015 195.123i 0.0740693 0.428842i
\(456\) 122.852 + 122.174i 0.269413 + 0.267926i
\(457\) 52.4299 52.4299i 0.114726 0.114726i −0.647413 0.762139i \(-0.724149\pi\)
0.762139 + 0.647413i \(0.224149\pi\)
\(458\) 74.6694 + 74.6694i 0.163034 + 0.163034i
\(459\) 403.375 + 396.736i 0.878813 + 0.864348i
\(460\) 11.3279 + 291.511i 0.0246258 + 0.633720i
\(461\) 549.751 1.19252 0.596259 0.802792i \(-0.296653\pi\)
0.596259 + 0.802792i \(0.296653\pi\)
\(462\) −151.358 + 98.7960i −0.327614 + 0.213844i
\(463\) 333.035 + 333.035i 0.719298 + 0.719298i 0.968461 0.249164i \(-0.0801558\pi\)
−0.249164 + 0.968461i \(0.580156\pi\)
\(464\) −78.1270 −0.168377
\(465\) 48.1542 + 44.3051i 0.103557 + 0.0952798i
\(466\) −479.077 −1.02806
\(467\) −9.53974 + 9.53974i −0.0204277 + 0.0204277i −0.717247 0.696819i \(-0.754598\pi\)
0.696819 + 0.717247i \(0.254598\pi\)
\(468\) 72.4053 + 71.6086i 0.154712 + 0.153010i
\(469\) −321.767 495.946i −0.686070 1.05746i
\(470\) 269.377 + 249.224i 0.573142 + 0.530265i
\(471\) 292.634 294.258i 0.621304 0.624751i
\(472\) 8.05312 + 8.05312i 0.0170617 + 0.0170617i
\(473\) 273.895 273.895i 0.579060 0.579060i
\(474\) 379.200 + 377.108i 0.800001 + 0.795587i
\(475\) −39.6134 508.935i −0.0833966 1.07144i
\(476\) 246.109 159.674i 0.517036 0.335449i
\(477\) −5.84288 + 5.90789i −0.0122492 + 0.0123855i
\(478\) −34.0240 34.0240i −0.0711799 0.0711799i
\(479\) 30.2411i 0.0631339i 0.999502 + 0.0315670i \(0.0100497\pi\)
−0.999502 + 0.0315670i \(0.989950\pi\)
\(480\) −84.7794 + 3.52935i −0.176624 + 0.00735281i
\(481\) 13.1495i 0.0273379i
\(482\) −268.995 + 268.995i −0.558081 + 0.558081i
\(483\) 513.019 334.864i 1.06215 0.693299i
\(484\) 167.919i 0.346939i
\(485\) 16.6448 + 428.337i 0.0343192 + 0.883169i
\(486\) −239.616 + 246.338i −0.493037 + 0.506867i
\(487\) −249.687 + 249.687i −0.512704 + 0.512704i −0.915354 0.402650i \(-0.868089\pi\)
0.402650 + 0.915354i \(0.368089\pi\)
\(488\) −130.415 130.415i −0.267243 0.267243i
\(489\) 2.71992 2.73501i 0.00556221 0.00559307i
\(490\) 128.808 321.650i 0.262874 0.656428i
\(491\) 775.321i 1.57907i 0.613708 + 0.789533i \(0.289677\pi\)
−0.613708 + 0.789533i \(0.710323\pi\)
\(492\) −253.615 + 0.701534i −0.515478 + 0.00142588i
\(493\) 289.409 289.409i 0.587037 0.587037i
\(494\) −163.370 −0.330709
\(495\) −184.878 + 202.058i −0.373491 + 0.408198i
\(496\) 17.4494i 0.0351802i
\(497\) −841.124 179.166i −1.69240 0.360496i
\(498\) −73.2299 + 0.202564i −0.147048 + 0.000406755i
\(499\) 596.688i 1.19577i −0.801583 0.597884i \(-0.796009\pi\)
0.801583 0.597884i \(-0.203991\pi\)
\(500\) 196.129 + 155.027i 0.392259 + 0.310054i
\(501\) −436.095 433.689i −0.870449 0.865647i
\(502\) −17.7724 17.7724i −0.0354032 0.0354032i
\(503\) 653.010 + 653.010i 1.29823 + 1.29823i 0.929560 + 0.368671i \(0.120187\pi\)
0.368671 + 0.929560i \(0.379813\pi\)
\(504\) 97.8106 + 148.947i 0.194069 + 0.295529i
\(505\) 353.475 + 327.031i 0.699951 + 0.647586i
\(506\) 251.095i 0.496234i
\(507\) 410.977 1.13682i 0.810606 0.00224225i
\(508\) −107.010 107.010i −0.210649 0.210649i
\(509\) 288.101i 0.566014i 0.959118 + 0.283007i \(0.0913320\pi\)
−0.959118 + 0.283007i \(0.908668\pi\)
\(510\) 300.978 327.126i 0.590153 0.641423i
\(511\) −70.8066 109.136i −0.138565 0.213573i
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −4.57495 551.293i −0.00891804 1.07465i
\(514\) −311.048 −0.605151
\(515\) 802.683 31.1916i 1.55861 0.0605662i
\(516\) −270.766 269.272i −0.524741 0.521846i
\(517\) 223.350 + 223.350i 0.432011 + 0.432011i
\(518\) 4.79358 22.5042i 0.00925402 0.0434444i
\(519\) 144.296 145.096i 0.278027 0.279569i
\(520\) 54.3354 58.7290i 0.104491 0.112940i
\(521\) 190.167 0.365004 0.182502 0.983206i \(-0.441580\pi\)
0.182502 + 0.983206i \(0.441580\pi\)
\(522\) 176.756 + 174.811i 0.338612 + 0.334886i
\(523\) 315.417 315.417i 0.603093 0.603093i −0.338039 0.941132i \(-0.609764\pi\)
0.941132 + 0.338039i \(0.109764\pi\)
\(524\) 455.597i 0.869459i
\(525\) 67.7592 520.609i 0.129065 0.991636i
\(526\) −455.045 −0.865105
\(527\) −64.6386 64.6386i −0.122654 0.122654i
\(528\) −73.0330 + 0.202019i −0.138320 + 0.000382612i
\(529\) 322.071i 0.608830i
\(530\) 4.79197 + 4.43348i 0.00904146 + 0.00836506i
\(531\) −0.200483 36.2385i −0.000377557 0.0682457i
\(532\) −279.593 59.5556i −0.525551 0.111947i
\(533\) 169.096 169.096i 0.317254 0.317254i
\(534\) −292.698 291.083i −0.548123 0.545099i
\(535\) 21.9756 + 565.519i 0.0410759 + 1.05705i
\(536\) 238.874i 0.445660i
\(537\) 2.29896 + 831.109i 0.00428112 + 1.54769i
\(538\) 89.7378 89.7378i 0.166799 0.166799i
\(539\) 121.532 272.332i 0.225477 0.505254i
\(540\) 199.703 + 181.711i 0.369820 + 0.336501i
\(541\) 219.489 0.405710 0.202855 0.979209i \(-0.434978\pi\)
0.202855 + 0.979209i \(0.434978\pi\)
\(542\) 318.345 318.345i 0.587352 0.587352i
\(543\) 813.528 2.25033i 1.49821 0.00414426i
\(544\) 118.539 0.217903
\(545\) 657.596 710.770i 1.20660 1.30416i
\(546\) −164.428 34.5494i −0.301151 0.0632772i
\(547\) 44.8504 44.8504i 0.0819934 0.0819934i −0.664921 0.746914i \(-0.731535\pi\)
0.746914 + 0.664921i \(0.231535\pi\)
\(548\) −33.6668 + 33.6668i −0.0614358 + 0.0614358i
\(549\) 3.24668 + 586.858i 0.00591381 + 1.06896i
\(550\) 163.501 + 139.887i 0.297274 + 0.254339i
\(551\) −398.818 −0.723808
\(552\) 247.541 0.684733i 0.448444 0.00124046i
\(553\) −863.002 183.827i −1.56058 0.332417i
\(554\) −130.849 −0.236190
\(555\) −1.45013 34.8339i −0.00261284 0.0627637i
\(556\) 60.0828i 0.108063i
\(557\) −221.625 221.625i −0.397890 0.397890i 0.479598 0.877488i \(-0.340782\pi\)
−0.877488 + 0.479598i \(0.840782\pi\)
\(558\) 39.0433 39.4777i 0.0699701 0.0707486i
\(559\) 360.067 0.644127
\(560\) 114.399 80.7017i 0.204285 0.144110i
\(561\) 269.791 271.288i 0.480911 0.483579i
\(562\) 431.212 431.212i 0.767281 0.767281i
\(563\) −39.5010 39.5010i −0.0701616 0.0701616i 0.671155 0.741317i \(-0.265798\pi\)
−0.741317 + 0.671155i \(0.765798\pi\)
\(564\) 219.580 220.798i 0.389326 0.391486i
\(565\) −920.285 + 35.7615i −1.62882 + 0.0632947i
\(566\) −336.292 −0.594155
\(567\) 111.983 555.832i 0.197500 0.980303i
\(568\) −245.713 245.713i −0.432593 0.432593i
\(569\) −63.0549 −0.110817 −0.0554085 0.998464i \(-0.517646\pi\)
−0.0554085 + 0.998464i \(0.517646\pi\)
\(570\) −432.777 + 18.0164i −0.759258 + 0.0316077i
\(571\) −269.370 −0.471751 −0.235875 0.971783i \(-0.575796\pi\)
−0.235875 + 0.971783i \(0.575796\pi\)
\(572\) 48.6943 48.6943i 0.0851298 0.0851298i
\(573\) −540.800 + 1.49593i −0.943804 + 0.00261069i
\(574\) 351.036 227.750i 0.611561 0.396777i
\(575\) −554.178 474.138i −0.963787 0.824587i
\(576\) 0.398321 + 71.9989i 0.000691529 + 0.124998i
\(577\) 612.246 + 612.246i 1.06108 + 1.06108i 0.998009 + 0.0630759i \(0.0200910\pi\)
0.0630759 + 0.998009i \(0.479909\pi\)
\(578\) −150.109 + 150.109i −0.259705 + 0.259705i
\(579\) −581.605 + 584.832i −1.00450 + 1.01007i
\(580\) 132.643 143.369i 0.228695 0.247188i
\(581\) 101.360 65.7614i 0.174457 0.113187i
\(582\) 363.729 1.00612i 0.624964 0.00172874i
\(583\) 3.97319 + 3.97319i 0.00681508 + 0.00681508i
\(584\) 52.5656i 0.0900095i
\(585\) −254.336 + 11.2928i −0.434763 + 0.0193039i
\(586\) 525.876i 0.897399i
\(587\) −228.676 + 228.676i −0.389567 + 0.389567i −0.874533 0.484966i \(-0.838832\pi\)
0.484966 + 0.874533i \(0.338832\pi\)
\(588\) −268.809 119.070i −0.457159 0.202499i
\(589\) 89.0747i 0.151230i
\(590\) −28.4506 + 1.10557i −0.0482213 + 0.00187384i
\(591\) 235.424 236.730i 0.398348 0.400558i
\(592\) 6.57402 6.57402i 0.0111048 0.0111048i
\(593\) −576.695 576.695i −0.972503 0.972503i 0.0271286 0.999632i \(-0.491364\pi\)
−0.999632 + 0.0271286i \(0.991364\pi\)
\(594\) 165.683 + 162.956i 0.278927 + 0.274336i
\(595\) −124.828 + 722.722i −0.209795 + 1.21466i
\(596\) 15.3099i 0.0256878i
\(597\) −1.69101 611.325i −0.00283251 1.02399i
\(598\) −165.047 + 165.047i −0.275998 + 0.275998i
\(599\) 456.495 0.762095 0.381048 0.924555i \(-0.375563\pi\)
0.381048 + 0.924555i \(0.375563\pi\)
\(600\) 137.461 161.569i 0.229102 0.269281i
\(601\) 631.907i 1.05143i −0.850662 0.525713i \(-0.823798\pi\)
0.850662 0.525713i \(-0.176202\pi\)
\(602\) 616.223 + 131.260i 1.02363 + 0.218041i
\(603\) −534.484 + 540.431i −0.886376 + 0.896237i
\(604\) 472.948i 0.783027i
\(605\) −308.144 285.091i −0.509328 0.471225i
\(606\) 288.132 289.730i 0.475465 0.478103i
\(607\) 463.511 + 463.511i 0.763610 + 0.763610i 0.976973 0.213363i \(-0.0684418\pi\)
−0.213363 + 0.976973i \(0.568442\pi\)
\(608\) −81.6759 81.6759i −0.134335 0.134335i
\(609\) −401.401 84.3418i −0.659116 0.138492i
\(610\) 460.738 17.9039i 0.755309 0.0293507i
\(611\) 293.619i 0.480555i
\(612\) −268.184 265.233i −0.438210 0.433388i
\(613\) −491.048 491.048i −0.801057 0.801057i 0.182204 0.983261i \(-0.441677\pi\)
−0.983261 + 0.182204i \(0.941677\pi\)
\(614\) 733.255i 1.19423i
\(615\) 429.298 466.594i 0.698046 0.758689i
\(616\) 101.087 65.5846i 0.164102 0.106469i
\(617\) 392.264 + 392.264i 0.635759 + 0.635759i 0.949507 0.313747i \(-0.101584\pi\)
−0.313747 + 0.949507i \(0.601584\pi\)
\(618\) −1.88543 681.610i −0.00305085 1.10293i
\(619\) 1005.88 1.62500 0.812500 0.582961i \(-0.198106\pi\)
0.812500 + 0.582961i \(0.198106\pi\)
\(620\) −32.0210 29.6254i −0.0516467 0.0477830i
\(621\) −561.573 552.329i −0.904304 0.889418i
\(622\) −113.759 113.759i −0.182893 0.182893i
\(623\) 666.135 + 141.892i 1.06924 + 0.227757i
\(624\) −48.1380 47.8724i −0.0771442 0.0767186i
\(625\) −617.473 + 96.7090i −0.987956 + 0.154734i
\(626\) −535.321 −0.855146
\(627\) −372.814 + 1.03126i −0.594600 + 0.00164475i
\(628\) −195.631 + 195.631i −0.311515 + 0.311515i
\(629\) 48.7049i 0.0774323i
\(630\) −439.390 73.3903i −0.697445 0.116492i
\(631\) 499.042 0.790874 0.395437 0.918493i \(-0.370593\pi\)
0.395437 + 0.918493i \(0.370593\pi\)
\(632\) −252.104 252.104i −0.398898 0.398898i
\(633\) 2.22019 + 802.631i 0.00350741 + 1.26798i
\(634\) 431.280i 0.680253i
\(635\) 378.050 14.6907i 0.595355 0.0231350i
\(636\) 3.90613 3.92780i 0.00614172 0.00617579i
\(637\) 258.890 99.1219i 0.406421 0.155607i
\(638\) 118.872 118.872i 0.186320 0.186320i
\(639\) 6.11703 + 1105.69i 0.00957282 + 1.73035i
\(640\) 56.5259 2.19655i 0.0883217 0.00343211i
\(641\) 124.816i 0.194721i 0.995249 + 0.0973607i \(0.0310400\pi\)
−0.995249 + 0.0973607i \(0.968960\pi\)
\(642\) 480.219 1.32835i 0.748005 0.00206909i
\(643\) −160.790 + 160.790i −0.250062 + 0.250062i −0.820996 0.570934i \(-0.806581\pi\)
0.570934 + 0.820996i \(0.306581\pi\)
\(644\) −342.629 + 222.295i −0.532033 + 0.345179i
\(645\) 953.840 39.7081i 1.47882 0.0615630i
\(646\) 605.111 0.936705
\(647\) −257.644 + 257.644i −0.398213 + 0.398213i −0.877602 0.479389i \(-0.840858\pi\)
0.479389 + 0.877602i \(0.340858\pi\)
\(648\) 160.198 163.783i 0.247219 0.252751i
\(649\) −24.5060 −0.0377597
\(650\) 15.5220 + 199.419i 0.0238800 + 0.306799i
\(651\) −18.8374 + 89.6516i −0.0289362 + 0.137714i
\(652\) −1.81832 + 1.81832i −0.00278883 + 0.00278883i
\(653\) −770.307 + 770.307i −1.17964 + 1.17964i −0.199809 + 0.979835i \(0.564032\pi\)
−0.979835 + 0.199809i \(0.935968\pi\)
\(654\) −582.592 579.377i −0.890813 0.885898i
\(655\) 836.054 + 773.508i 1.27642 + 1.18093i
\(656\) 169.077 0.257740
\(657\) −117.616 + 118.925i −0.179020 + 0.181012i
\(658\) −107.037 + 502.503i −0.162671 + 0.763683i
\(659\) −112.781 −0.171139 −0.0855695 0.996332i \(-0.527271\pi\)
−0.0855695 + 0.996332i \(0.527271\pi\)
\(660\) 123.624 134.364i 0.187309 0.203582i
\(661\) 947.097i 1.43282i −0.697678 0.716412i \(-0.745783\pi\)
0.697678 0.716412i \(-0.254217\pi\)
\(662\) −70.4637 70.4637i −0.106441 0.106441i
\(663\) 355.655 0.983792i 0.536433 0.00148385i
\(664\) 48.8201 0.0735242
\(665\) 583.980 411.961i 0.878165 0.619491i
\(666\) −29.5827 + 0.163661i −0.0444184 + 0.000245737i
\(667\) −402.911 + 402.911i −0.604064 + 0.604064i
\(668\) 289.929 + 289.929i 0.434026 + 0.434026i
\(669\) −812.852 808.367i −1.21503 1.20832i
\(670\) 438.352 + 405.558i 0.654256 + 0.605310i
\(671\) 396.859 0.591444
\(672\) −64.9322 99.4777i −0.0966253 0.148032i
\(673\) −179.988 179.988i −0.267441 0.267441i 0.560628 0.828068i \(-0.310560\pi\)
−0.828068 + 0.560628i \(0.810560\pi\)
\(674\) 77.6457 0.115201
\(675\) −672.507 + 57.9635i −0.996306 + 0.0858718i
\(676\) −273.986 −0.405304
\(677\) 697.081 697.081i 1.02966 1.02966i 0.0301147 0.999546i \(-0.490413\pi\)
0.999546 0.0301147i \(-0.00958726\pi\)
\(678\) 2.16167 + 781.474i 0.00318830 + 1.15262i
\(679\) −503.448 + 326.634i −0.741455 + 0.481051i
\(680\) −201.255 + 217.528i −0.295963 + 0.319894i
\(681\) 131.673 + 130.947i 0.193353 + 0.192286i
\(682\) −26.5497 26.5497i −0.0389292 0.0389292i
\(683\) −443.137 + 443.137i −0.648809 + 0.648809i −0.952705 0.303896i \(-0.901712\pi\)
0.303896 + 0.952705i \(0.401712\pi\)
\(684\) 2.03333 + 367.536i 0.00297270 + 0.537333i
\(685\) −4.62193 118.940i −0.00674734 0.173636i
\(686\) 479.201 75.2614i 0.698544 0.109710i
\(687\) 0.619635 + 224.007i 0.000901944 + 0.326066i
\(688\) 180.014 + 180.014i 0.261648 + 0.261648i
\(689\) 5.22323i 0.00758088i
\(690\) −419.017 + 455.419i −0.607271 + 0.660028i
\(691\) 829.239i 1.20006i −0.799979 0.600028i \(-0.795156\pi\)
0.799979 0.600028i \(-0.204844\pi\)
\(692\) −96.4644 + 96.4644i −0.139399 + 0.139399i
\(693\) −375.447 77.8046i −0.541771 0.112272i
\(694\) 274.858i 0.396050i
\(695\) −110.257 102.008i −0.158643 0.146774i
\(696\) −117.514 116.866i −0.168842 0.167911i
\(697\) −626.321 + 626.321i −0.898595 + 0.898595i
\(698\) −508.928 508.928i −0.729123 0.729123i
\(699\) −720.600 716.624i −1.03090 1.02521i
\(700\) −46.1327 + 346.946i −0.0659038 + 0.495638i
\(701\) 664.169i 0.947460i −0.880670 0.473730i \(-0.842907\pi\)
0.880670 0.473730i \(-0.157093\pi\)
\(702\) 1.79263 + 216.017i 0.00255361 + 0.307716i
\(703\) 33.5587 33.5587i 0.0477364 0.0477364i
\(704\) 48.6888 0.0691603
\(705\) 32.3803 + 777.815i 0.0459295 + 1.10328i
\(706\) 411.773i 0.583248i
\(707\) −140.454 + 659.382i −0.198662 + 0.932648i
\(708\) 0.0668278 + 24.1593i 9.43896e−5 + 0.0341232i
\(709\) 1003.81i 1.41582i 0.706304 + 0.707909i \(0.250361\pi\)
−0.706304 + 0.707909i \(0.749639\pi\)
\(710\) 868.071 33.7325i 1.22263 0.0475106i
\(711\) 6.27614 + 1134.45i 0.00882720 + 1.59557i
\(712\) 194.594 + 194.594i 0.273307 + 0.273307i
\(713\) 89.9888 + 89.9888i 0.126211 + 0.126211i
\(714\) 609.031 + 127.969i 0.852984 + 0.179228i
\(715\) 6.68496 + 172.030i 0.00934959 + 0.240602i
\(716\) 554.075i 0.773847i
\(717\) −0.282344 102.072i −0.000393786 0.142359i
\(718\) 51.9892 + 51.9892i 0.0724084 + 0.0724084i
\(719\) 227.010i 0.315731i −0.987461 0.157865i \(-0.949539\pi\)
0.987461 0.157865i \(-0.0504612\pi\)
\(720\) −132.800 121.508i −0.184444 0.168761i
\(721\) 612.095 + 943.437i 0.848953 + 1.30851i
\(722\) −55.9344 55.9344i −0.0774715 0.0774715i
\(723\) −806.982 + 2.23222i −1.11616 + 0.00308745i
\(724\) −542.354 −0.749108
\(725\) 37.8922 + 486.821i 0.0522651 + 0.671478i
\(726\) −251.180 + 252.574i −0.345978 + 0.347898i
\(727\) −328.738 328.738i −0.452184 0.452184i 0.443895 0.896079i \(-0.353596\pi\)
−0.896079 + 0.443895i \(0.853596\pi\)
\(728\) 109.555 + 23.3360i 0.150487 + 0.0320550i
\(729\) −728.900 + 12.0985i −0.999862 + 0.0165960i
\(730\) 96.4618 + 89.2454i 0.132139 + 0.122254i
\(731\) −1333.66 −1.82444
\(732\) −1.08223 391.243i −0.00147846 0.534485i
\(733\) −320.943 + 320.943i −0.437848 + 0.437848i −0.891287 0.453439i \(-0.850197\pi\)
0.453439 + 0.891287i \(0.350197\pi\)
\(734\) 680.234i 0.926749i
\(735\) 674.884 291.130i 0.918209 0.396096i
\(736\) −165.028 −0.224223
\(737\) 363.453 + 363.453i 0.493151 + 0.493151i
\(738\) −382.523 378.314i −0.518323 0.512620i
\(739\) 742.829i 1.00518i −0.864524 0.502591i \(-0.832380\pi\)
0.864524 0.502591i \(-0.167620\pi\)
\(740\) 0.902510 + 23.2252i 0.00121961 + 0.0313853i
\(741\) −245.732 244.376i −0.331622 0.329792i
\(742\) −1.90410 + 8.93908i −0.00256617 + 0.0120473i
\(743\) −319.664 + 319.664i −0.430234 + 0.430234i −0.888708 0.458474i \(-0.848396\pi\)
0.458474 + 0.888708i \(0.348396\pi\)
\(744\) −26.1016 + 26.2464i −0.0350828 + 0.0352774i
\(745\) −28.0949 25.9931i −0.0377113 0.0348900i
\(746\) 371.837i 0.498441i
\(747\) −110.451 109.236i −0.147860 0.146233i
\(748\) −180.360 + 180.360i −0.241123 + 0.241123i
\(749\) −664.686 + 431.244i −0.887431 + 0.575759i
\(750\) 63.1105 + 526.562i 0.0841474 + 0.702082i
\(751\) −467.775 −0.622870 −0.311435 0.950267i \(-0.600810\pi\)
−0.311435 + 0.950267i \(0.600810\pi\)
\(752\) −146.793 + 146.793i −0.195204 + 0.195204i
\(753\) −0.147482 53.3170i −0.000195860 0.0708062i
\(754\) 156.271 0.207257
\(755\) −867.896 802.968i −1.14953 1.06353i
\(756\) −75.6797 + 370.347i −0.100105 + 0.489876i
\(757\) −342.526 + 342.526i −0.452478 + 0.452478i −0.896176 0.443699i \(-0.853666\pi\)
0.443699 + 0.896176i \(0.353666\pi\)
\(758\) −123.430 + 123.430i −0.162836 + 0.162836i
\(759\) −375.598 + 377.682i −0.494860 + 0.497605i
\(760\) 288.550 11.2128i 0.379671 0.0147537i
\(761\) −367.731 −0.483221 −0.241611 0.970373i \(-0.577676\pi\)
−0.241611 + 0.970373i \(0.577676\pi\)
\(762\) −0.888006 321.027i −0.00116536 0.421296i
\(763\) 1325.89 + 282.425i 1.73773 + 0.370151i
\(764\) 360.534 0.471904
\(765\) 942.044 41.8277i 1.23143 0.0546768i
\(766\) 88.2335i 0.115187i