Properties

Label 210.3.k.b.83.1
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 83.1
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.b.167.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-2.99999 - 0.00829838i) q^{3} +2.00000i q^{4} +(-3.67015 - 3.39558i) q^{5} +(-2.99169 - 3.00829i) q^{6} +(6.84640 - 1.45834i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(8.99986 + 0.0497901i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(-2.99999 - 0.00829838i) q^{3} +2.00000i q^{4} +(-3.67015 - 3.39558i) q^{5} +(-2.99169 - 3.00829i) q^{6} +(6.84640 - 1.45834i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(8.99986 + 0.0497901i) q^{9} +(-0.274569 - 7.06574i) q^{10} -6.08610i q^{11} +(0.0165968 - 5.99998i) q^{12} +(4.00045 - 4.00045i) q^{13} +(8.30474 + 5.38806i) q^{14} +(10.9822 + 10.2172i) q^{15} -4.00000 q^{16} +(14.8174 - 14.8174i) q^{17} +(8.95007 + 9.04965i) 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} +(-26.9991 - 0.224054i) q^{27} +(2.91668 + 13.6928i) q^{28} -19.5317 q^{29} +(0.765069 + 21.1994i) q^{30} +4.36235i q^{31} +(-4.00000 - 4.00000i) q^{32} +(-0.0505048 + 18.2582i) q^{33} +29.6348 q^{34} +(-30.0793 - 17.8952i) 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} +(-24.8694 - 16.2330i) q^{42} +(-45.0034 - 45.0034i) q^{43} +12.1722 q^{44} +(-32.8618 - 30.7425i) q^{45} +41.2570 q^{46} +(36.6983 - 36.6983i) q^{47} +(12.0000 + 0.0331935i) 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} +(-61.2567 - 0.169444i) q^{57} +(-19.5317 - 19.5317i) q^{58} +4.02656i q^{59} +(-20.4343 + 21.9645i) q^{60} +65.2074i q^{61} +(-4.36235 + 4.36235i) q^{62} +(61.6893 - 12.7840i) 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} +(-12.1841 - 47.9745i) q^{70} +122.856i q^{71} +(-18.0993 + 17.9001i) q^{72} +(-13.1414 + 13.1414i) q^{73} -3.28701 q^{74} +(-5.61323 - 74.7896i) q^{75} +40.8379i q^{76} +(-8.87561 - 41.6679i) q^{77} +(-24.0026 - 0.0663945i) 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} +(58.5950 + 0.162082i) q^{87} +(12.1722 + 12.1722i) q^{88} +97.2971i q^{89} +(-2.11928 - 63.6043i) q^{90} +(21.5547 - 33.2227i) q^{91} +(41.2570 + 41.2570i) q^{92} +(0.0362004 - 13.0870i) q^{93} +73.3967 q^{94} +(-74.9407 - 69.3343i) q^{95} +(11.9668 + 12.0331i) q^{96} +(60.6217 + 60.6217i) q^{97} +(64.7153 + 24.7777i) q^{98} +(0.303028 - 54.7741i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} + O(q^{10}) \) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} - 8q^{14} - 4q^{15} - 128q^{16} - 4q^{18} + 12q^{21} - 40q^{22} - 24q^{23} + 16q^{25} - 8q^{28} + 112q^{29} + 28q^{30} - 128q^{32} + 48q^{35} - 40q^{36} + 32q^{37} - 64q^{39} - 20q^{42} - 32q^{43} - 80q^{44} - 48q^{46} + 8q^{50} + 84q^{51} + 136q^{53} + 340q^{57} + 112q^{58} + 64q^{60} + 168q^{63} + 200q^{65} + 32q^{67} - 72q^{72} + 64q^{74} - 88q^{77} - 4q^{78} + 76q^{81} - 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} - 48q^{92} - 388q^{93} - 544q^{95} - 128q^{98} - 160q^{99} + O(q^{100}) \)

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
\(3\) −2.99999 0.00829838i −0.999996 0.00276613i
\(4\) 2.00000i 0.500000i
\(5\) −3.67015 3.39558i −0.734030 0.679117i
\(6\) −2.99169 3.00829i −0.498615 0.501381i
\(7\) 6.84640 1.45834i 0.978058 0.208334i
\(8\) −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 \(-0.910779\pi\)
0.960973 0.276641i \(-0.0892213\pi\)
\(12\) 0.0165968 5.99998i 0.00138306 0.499998i
\(13\) 4.00045 4.00045i 0.307727 0.307727i −0.536300 0.844027i \(-0.680179\pi\)
0.844027 + 0.536300i \(0.180179\pi\)
\(14\) 8.30474 + 5.38806i 0.593196 + 0.384862i
\(15\) 10.9822 + 10.2172i 0.732149 + 0.681144i
\(16\) −4.00000 −0.250000
\(17\) 14.8174 14.8174i 0.871610 0.871610i −0.121037 0.992648i \(-0.538622\pi\)
0.992648 + 0.121037i \(0.0386221\pi\)
\(18\) 8.95007 + 9.04965i 0.497226 + 0.502758i
\(19\) 20.4190 1.07468 0.537341 0.843365i \(-0.319429\pi\)
0.537341 + 0.843365i \(0.319429\pi\)
\(20\) 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 −0.0982681 0.995160i \(-0.531330\pi\)
0.995160 + 0.0982681i \(0.0313303\pi\)
\(24\) 6.01657 5.98338i 0.250691 0.249308i
\(25\) 1.94003 + 24.9246i 0.0776012 + 0.996984i
\(26\) 8.00089 0.307727
\(27\) −26.9991 0.224054i −0.999966 0.00829830i
\(28\) 2.91668 + 13.6928i 0.104167 + 0.489029i
\(29\) −19.5317 −0.673508 −0.336754 0.941593i \(-0.609329\pi\)
−0.336754 + 0.941593i \(0.609329\pi\)
\(30\) 0.765069 + 21.1994i 0.0255023 + 0.706647i
\(31\) 4.36235i 0.140721i 0.997522 + 0.0703605i \(0.0224150\pi\)
−0.997522 + 0.0703605i \(0.977585\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −0.0505048 + 18.2582i −0.00153045 + 0.553280i
\(34\) 29.6348 0.871610
\(35\) −30.0793 17.8952i −0.859407 0.511292i
\(36\) −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 \(0.672386\pi\)
\(42\) −24.8694 16.2330i −0.592129 0.386501i
\(43\) −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
\(45\) −32.8618 30.7425i −0.730262 0.683167i
\(46\) 41.2570 0.896892
\(47\) 36.6983 36.6983i 0.780815 0.780815i −0.199153 0.979968i \(-0.563819\pi\)
0.979968 + 0.199153i \(0.0638191\pi\)
\(48\) 12.0000 + 0.0331935i 0.249999 + 0.000691532i
\(49\) 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 −0.713239 0.700921i \(-0.752772\pi\)
0.700921 + 0.713239i \(0.252772\pi\)
\(54\) −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
\(57\) −61.2567 0.169444i −1.07468 0.00297271i
\(58\) −19.5317 19.5317i −0.336754 0.336754i
\(59\) 4.02656i 0.0682467i 0.999418 + 0.0341234i \(0.0108639\pi\)
−0.999418 + 0.0341234i \(0.989136\pi\)
\(60\) −20.4343 + 21.9645i −0.340572 + 0.366075i
\(61\) 65.2074i 1.06897i 0.845177 + 0.534487i \(0.179495\pi\)
−0.845177 + 0.534487i \(0.820505\pi\)
\(62\) −4.36235 + 4.36235i −0.0703605 + 0.0703605i
\(63\) 61.6893 12.7840i 0.979195 0.202920i
\(64\) 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
\(70\) −12.1841 47.9745i −0.174058 0.685349i
\(71\) 122.856i 1.73037i 0.501451 + 0.865186i \(0.332800\pi\)
−0.501451 + 0.865186i \(0.667200\pi\)
\(72\) −18.0993 + 17.9001i −0.251379 + 0.248613i
\(73\) −13.1414 + 13.1414i −0.180019 + 0.180019i −0.791364 0.611345i \(-0.790629\pi\)
0.611345 + 0.791364i \(0.290629\pi\)
\(74\) −3.28701 −0.0444191
\(75\) −5.61323 74.7896i −0.0748431 0.997195i
\(76\) 40.8379i 0.537341i
\(77\) −8.87561 41.6679i −0.115268 0.541142i
\(78\) −24.0026 0.0663945i −0.307725 0.000851211i
\(79\) 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
\(87\) 58.5950 + 0.162082i 0.673506 + 0.00186301i
\(88\) 12.1722 + 12.1722i 0.138321 + 0.138321i
\(89\) 97.2971i 1.09323i 0.837385 + 0.546613i \(0.184083\pi\)
−0.837385 + 0.546613i \(0.815917\pi\)
\(90\) −2.11928 63.6043i −0.0235475 0.706715i
\(91\) 21.5547 33.2227i 0.236864 0.365084i
\(92\) 41.2570 + 41.2570i 0.448446 + 0.448446i
\(93\) 0.0362004 13.0870i 0.000389252 0.140720i
\(94\) 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 0.946797 0.321831i \(-0.104298\pi\)
−0.321831 + 0.946797i \(0.604298\pi\)
\(98\) 64.7153 + 24.7777i 0.660360 + 0.252834i
\(99\) 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 \(0.658198\pi\)
\(102\) −88.9039 0.245921i −0.871607 0.00241099i
\(103\) 113.602 113.602i 1.10293 1.10293i 0.108878 0.994055i \(-0.465274\pi\)
0.994055 0.108878i \(-0.0347258\pi\)
\(104\) 16.0018i 0.153863i
\(105\) 90.0889 + 53.9350i 0.857990 + 0.513667i
\(106\) −1.30566 −0.0123176
\(107\) 80.0368 + 80.0368i 0.748008 + 0.748008i 0.974105 0.226097i \(-0.0725966\pi\)
−0.226097 + 0.974105i \(0.572597\pi\)
\(108\) 0.448108 53.9981i 0.00414915 0.499983i
\(109\) 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
\(112\) −27.3856 + 5.83336i −0.244514 + 0.0520836i
\(113\) −130.246 + 130.246i −1.15262 + 1.15262i −0.166596 + 0.986025i \(0.553278\pi\)
−0.986025 + 0.166596i \(0.946722\pi\)
\(114\) −61.0872 61.4261i −0.535853 0.538826i
\(115\) −145.756 + 5.66394i −1.26744 + 0.0492517i
\(116\) 39.0635i 0.336754i
\(117\) 36.2026 35.8043i 0.309424 0.306020i
\(118\) −4.02656 + 4.02656i −0.0341234 + 0.0341234i
\(119\) 79.8370 123.055i 0.670899 1.03407i
\(120\) −42.3988 + 1.53014i −0.353323 + 0.0127511i
\(121\) 83.9594 0.693879
\(122\) −65.2074 + 65.2074i −0.534487 + 0.534487i
\(123\) 126.807 + 0.350767i 1.03096 + 0.00285176i
\(124\) −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 \(0.835532\pi\)
\(132\) −36.5165 0.101010i −0.276640 0.000765224i
\(133\) 139.797 29.7778i 1.05110 0.223893i
\(134\) 119.437 0.891320
\(135\) 98.3299 + 92.4999i 0.728370 + 0.685184i
\(136\) 59.2695i 0.435805i
\(137\) −16.8334 16.8334i −0.122872 0.122872i 0.642997 0.765869i \(-0.277691\pi\)
−0.765869 + 0.642997i \(0.777691\pi\)
\(138\) −123.771 0.342367i −0.896888 0.00248092i
\(139\) −30.0414 −0.216125 −0.108063 0.994144i \(-0.534465\pi\)
−0.108063 + 0.994144i \(0.534465\pi\)
\(140\) 35.7904 60.1585i 0.255646 0.429704i
\(141\) −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
\(147\) −134.405 + 59.5348i −0.914317 + 0.404998i
\(148\) −3.28701 3.28701i −0.0222095 0.0222095i
\(149\) −7.65497 −0.0513756 −0.0256878 0.999670i \(-0.508178\pi\)
−0.0256878 + 0.999670i \(0.508178\pi\)
\(150\) 69.1764 80.4029i 0.461176 0.536019i
\(151\) 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
\(153\) 134.092 132.617i 0.876419 0.866775i
\(154\) 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 0.323275 0.946305i \(-0.395216\pi\)
−0.946305 + 0.323275i \(0.895216\pi\)
\(158\) 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
\(162\) 80.0988 + 81.8913i 0.494437 + 0.505502i
\(163\) 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
\(165\) 62.1827 66.8390i 0.376865 0.405085i
\(166\) 24.4100i 0.147048i
\(167\) 144.965 144.965i 0.868051 0.868051i −0.124205 0.992257i \(-0.539638\pi\)
0.992257 + 0.124205i \(0.0396381\pi\)
\(168\) 32.4661 49.7388i 0.193251 0.296065i
\(169\) 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
\(175\) 49.6308 + 167.815i 0.283605 + 0.958941i
\(176\) 24.3444i 0.138321i
\(177\) 0.0334139 12.0796i 0.000188779 0.0682465i
\(178\) −97.2971 + 97.2971i −0.546613 + 0.546613i
\(179\) 277.037 1.54769 0.773847 0.633372i \(-0.218330\pi\)
0.773847 + 0.633372i \(0.218330\pi\)
\(180\) 61.4850 65.7236i 0.341584 0.365131i
\(181\) 271.177i 1.49822i −0.662448 0.749108i \(-0.730482\pi\)
0.662448 0.749108i \(-0.269518\pi\)
\(182\) 54.7773 11.6680i 0.300974 0.0641100i
\(183\) 0.541116 195.621i 0.00295692 1.06897i
\(184\) 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 \(0.156433\pi\)
−0.881650 + 0.471904i \(0.843567\pi\)
\(192\) −0.0663871 + 23.9999i −0.000345766 + 0.125000i
\(193\) −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
\(195\) 84.8071 3.06062i 0.434908 0.0156955i
\(196\) 39.9375 + 89.4930i 0.203763 + 0.456597i
\(197\) −78.6926 78.6926i −0.399455 0.399455i 0.478586 0.878041i \(-0.341149\pi\)
−0.878041 + 0.478586i \(0.841149\pi\)
\(198\) 55.0771 54.4711i 0.278167 0.275106i
\(199\) −203.776 −1.02400 −0.511999 0.858986i \(-0.671095\pi\)
−0.511999 + 0.858986i \(0.671095\pi\)
\(200\) −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
\(203\) −133.722 + 28.4839i −0.658730 + 0.140315i
\(204\) −88.6580 89.1499i −0.434598 0.437009i
\(205\) 155.135 + 143.529i 0.756755 + 0.700142i
\(206\) 227.204 1.10293
\(207\) 186.681 184.627i 0.901840 0.891916i
\(208\) −16.0018 + 16.0018i −0.0769317 + 0.0769317i
\(209\) 124.272i 0.594603i
\(210\) 36.1539 + 144.024i 0.172161 + 0.685828i
\(211\) −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
\(213\) 1.01951 368.568i 0.00478643 1.73037i
\(214\) 160.074i 0.748008i
\(215\) 12.3565 + 317.982i 0.0574722 + 1.47899i
\(216\) 54.4462 53.5500i 0.252066 0.247917i
\(217\) 6.36179 + 29.8664i 0.0293170 + 0.137633i
\(218\) −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
\(222\) 9.86100 + 0.0272769i 0.0444189 + 0.000122869i
\(223\) −270.204 + 270.204i −1.21168 + 1.21168i −0.241204 + 0.970475i \(0.577542\pi\)
−0.970475 + 0.241204i \(0.922458\pi\)
\(224\) −33.2190 21.5523i −0.148299 0.0962154i
\(225\) 16.2190 + 224.415i 0.0720844 + 0.997399i
\(226\) −260.492 −1.15262
\(227\) −43.7703 + 43.7703i −0.192821 + 0.192821i −0.796914 0.604093i \(-0.793535\pi\)
0.604093 + 0.796914i \(0.293535\pi\)
\(228\) 0.338889 122.513i 0.00148635 0.537339i
\(229\) 74.6694 0.326067 0.163034 0.986621i \(-0.447872\pi\)
0.163034 + 0.986621i \(0.447872\pi\)
\(230\) −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 \(0.509062\pi\)
−0.999595 + 0.0284664i \(0.990938\pi\)
\(234\) 72.0069 + 0.398365i 0.307722 + 0.00170242i
\(235\) −259.301 + 10.0762i −1.10341 + 0.0428775i
\(236\) −8.05312 −0.0341234
\(237\) −1.04603 + 378.154i −0.00441362 + 1.59559i
\(238\) 202.892 43.2176i 0.852485 0.181586i
\(239\) −34.0240 −0.142360 −0.0711799 0.997463i \(-0.522676\pi\)
−0.0711799 + 0.997463i \(0.522676\pi\)
\(240\) −43.9289 40.8687i −0.183037 0.170286i
\(241\) 268.995i 1.11616i 0.829786 + 0.558081i \(0.188462\pi\)
−0.829786 + 0.558081i \(0.811538\pi\)
\(242\) 83.9594 + 83.9594i 0.346939 + 0.346939i
\(243\) −242.977 3.36074i −0.999904 0.0138302i
\(244\) −130.415 −0.534487
\(245\) −232.032 78.6520i −0.947070 0.321029i
\(246\) 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 \(0.488728\pi\)
\(252\) 25.5680 + 123.379i 0.101460 + 0.489598i
\(253\) −125.547 125.547i −0.496234 0.496234i
\(254\) −107.010 −0.421297
\(255\) 314.120 11.3363i 1.23184 0.0444561i
\(256\) 16.0000 0.0625000
\(257\) 155.524 155.524i 0.605151 0.605151i −0.336524 0.941675i \(-0.609251\pi\)
0.941675 + 0.336524i \(0.109251\pi\)
\(258\) −0.746911 + 270.019i −0.00289500 + 1.04659i
\(259\) −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 −0.991926 0.126821i \(-0.959523\pi\)
0.126821 + 0.991926i \(0.459523\pi\)
\(264\) −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
\(267\) 0.807409 291.890i 0.00302400 1.09322i
\(268\) 119.437 + 119.437i 0.445660 + 0.445660i
\(269\) 89.7378i 0.333598i 0.985991 + 0.166799i \(0.0533431\pi\)
−0.985991 + 0.166799i \(0.946657\pi\)
\(270\) 5.82999 + 190.830i 0.0215926 + 0.706777i
\(271\) 318.345i 1.17470i −0.809332 0.587352i \(-0.800170\pi\)
0.809332 0.587352i \(-0.199830\pi\)
\(272\) −59.2695 + 59.2695i −0.217903 + 0.217903i
\(273\) −64.9394 + 99.4888i −0.237873 + 0.364428i
\(274\) 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
\(280\) 95.9489 24.3681i 0.342675 0.0870290i
\(281\) 431.212i 1.53456i −0.641311 0.767281i \(-0.721609\pi\)
0.641311 0.767281i \(-0.278391\pi\)
\(282\) −220.189 0.609073i −0.780812 0.00215984i
\(283\) −168.146 + 168.146i −0.594155 + 0.594155i −0.938751 0.344596i \(-0.888016\pi\)
0.344596 + 0.938751i \(0.388016\pi\)
\(284\) −245.713 −0.865186
\(285\) 224.246 + 208.624i 0.786828 + 0.732014i
\(286\) 48.6943i 0.170260i
\(287\) −289.393 + 61.6431i −1.00834 + 0.214784i
\(288\) −35.8003 36.1986i −0.124307 0.125690i
\(289\) 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
\(297\) −1.36362 + 164.319i −0.00459130 + 0.553263i
\(298\) −7.65497 7.65497i −0.0256878 0.0256878i
\(299\) 165.047i 0.551995i
\(300\) 149.579 11.2265i 0.498598 0.0374215i
\(301\) −373.742 242.481i −1.24167 0.805585i
\(302\) 236.474 + 236.474i 0.783027 + 0.783027i
\(303\) 288.931 + 0.799223i 0.953568 + 0.00263770i
\(304\) −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 \(0.0700701\pi\)
0.218358 + 0.975869i \(0.429930\pi\)
\(308\) 83.3358 17.7512i 0.270571 0.0576338i
\(309\) −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 \(0.441454\pi\)
\(312\) 0.132789 48.0052i 0.000425606 0.153863i
\(313\) −267.661 + 267.661i −0.855146 + 0.855146i −0.990762 0.135615i \(-0.956699\pi\)
0.135615 + 0.990762i \(0.456699\pi\)
\(314\) 195.631i 0.623030i
\(315\) −269.818 162.552i −0.856566 0.516038i
\(316\) 252.104 0.797797
\(317\) 215.640 + 215.640i 0.680253 + 0.680253i 0.960057 0.279804i \(-0.0902696\pi\)
−0.279804 + 0.960057i \(0.590270\pi\)
\(318\) 3.91697 + 0.0108349i 0.0123175 + 3.40719e-5i
\(319\) 118.872i 0.372640i
\(320\) −27.1647 + 29.3612i −0.0848896 + 0.0917538i
\(321\) −239.445 240.774i −0.745936 0.750074i
\(322\) 282.462 60.1668i 0.877212 0.186853i
\(323\) 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
\(327\) 1.60708 580.984i 0.00491463 1.77671i
\(328\) 84.5387 84.5387i 0.257740 0.257740i
\(329\) 197.733 304.770i 0.601012 0.926353i
\(330\) 129.022 4.65629i 0.390975 0.0141100i
\(331\) 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
\(333\) −14.8732 + 14.7095i −0.0446641 + 0.0441727i
\(334\) 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
\(342\) 182.751 + 184.785i 0.534360 + 0.540306i
\(343\) 277.231 201.970i 0.808254 0.588833i
\(344\) 180.014 0.523295
\(345\) 437.312 15.7822i 1.26757 0.0457456i
\(346\) 96.4644i 0.278799i
\(347\) 137.429 + 137.429i 0.396050 + 0.396050i 0.876837 0.480788i \(-0.159649\pi\)
−0.480788 + 0.876837i \(0.659649\pi\)
\(348\) −0.324164 + 117.190i −0.000931505 + 0.336753i
\(349\) −508.928 −1.45825 −0.729123 0.684383i \(-0.760072\pi\)
−0.729123 + 0.684383i \(0.760072\pi\)
\(350\) −118.184 + 217.446i −0.337668 + 0.621273i
\(351\) −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
\(357\) −240.531 + 368.500i −0.673757 + 1.03221i
\(358\) 277.037 + 277.037i 0.773847 + 0.773847i
\(359\) 51.9892 0.144817 0.0724084 0.997375i \(-0.476932\pi\)
0.0724084 + 0.997375i \(0.476932\pi\)
\(360\) 127.209 4.23855i 0.353357 0.0117738i
\(361\) 55.9344 0.154943
\(362\) 271.177 271.177i 0.749108 0.749108i
\(363\) −251.877 0.696727i −0.693876 0.00191936i
\(364\) 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 0.997494 0.0707450i \(-0.0225377\pi\)
−0.0707450 + 0.997494i \(0.522538\pi\)
\(368\) −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
\(372\) 26.1740 + 0.0724009i 0.0703602 + 0.000194626i
\(373\) 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
\(375\) −233.353 + 293.550i −0.622275 + 0.782799i
\(376\) 146.793i 0.390408i
\(377\) −78.1357 + 78.1357i −0.207257 + 0.207257i
\(378\) −223.013 147.333i −0.589982 0.389771i
\(379\) 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
\(385\) −108.912 + 183.065i −0.282888 + 0.475495i
\(386\) 388.814i 1.00729i
\(387\) −402.784 407.265i −1.04078 1.05236i
\(388\) −121.243 + 121.243i −0.312483 + 0.312483i
\(389\) 116.363 0.299133 0.149566 0.988752i \(-0.452212\pi\)
0.149566 + 0.988752i \(0.452212\pi\)
\(390\) 87.8677 + 81.7465i 0.225302 + 0.209606i
\(391\) 611.321i 1.56348i
\(392\) −49.5554 + 129.431i −0.126417 + 0.330180i
\(393\) 683.392 + 1.89036i 1.73891 + 0.00481007i
\(394\) 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 0.696019 0.718024i \(-0.254953\pi\)
−0.718024 + 0.696019i \(0.754953\pi\)
\(398\) −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 \(-0.988886\pi\)
0.999391 0.0349087i \(-0.0111140\pi\)
\(402\) −358.309 0.991133i −0.891317 0.00246551i
\(403\) 17.4513 + 17.4513i 0.0433036 + 0.0433036i
\(404\) 192.622i 0.476786i
\(405\) −294.221 278.315i −0.726471 0.687197i
\(406\) −162.206 105.238i −0.399523 0.259208i
\(407\) 10.0025 + 10.0025i 0.0245763 + 0.0245763i
\(408\) 0.491841 177.808i 0.00120549 0.435804i
\(409\) −234.500 −0.573349 −0.286675 0.958028i \(-0.592550\pi\)
−0.286675 + 0.958028i \(0.592550\pi\)
\(410\) 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
\(413\) 5.87209 + 27.5674i 0.0142181 + 0.0667492i
\(414\) 371.308 + 2.05419i 0.896878 + 0.00496182i
\(415\) −3.35112 86.2375i −0.00807498 0.207801i
\(416\) −32.0036 −0.0769317
\(417\) 90.1239 + 0.249295i 0.216125 + 0.000597830i
\(418\) 124.272 124.272i 0.297301 0.297301i
\(419\) 339.624i 0.810559i 0.914193 + 0.405279i \(0.132826\pi\)
−0.914193 + 0.405279i \(0.867174\pi\)
\(420\) −107.870 + 180.178i −0.256833 + 0.428995i
\(421\) 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
\(423\) 332.107 328.453i 0.785123 0.776484i
\(424\) 2.61132i 0.00615878i
\(425\) 398.064 + 340.571i 0.936620 + 0.801344i
\(426\) 369.587 367.548i 0.867576 0.862789i
\(427\) 95.0946 + 446.436i 0.222704 + 1.04552i
\(428\) −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 \(0.240143\pi\)
−0.728661 + 0.684875i \(0.759857\pi\)
\(432\) 107.996 + 0.896216i 0.249991 + 0.00207457i
\(433\) 340.107 340.107i 0.785466 0.785466i −0.195281 0.980747i \(-0.562562\pi\)
0.980747 + 0.195281i \(0.0625619\pi\)
\(434\) −23.5046 + 36.2282i −0.0541581 + 0.0834751i
\(435\) −214.502 199.559i −0.493109 0.458757i
\(436\) −387.324 −0.888359
\(437\) 421.213 421.213i 0.963874 0.963874i
\(438\) 78.8480 + 0.218105i 0.180018 + 0.000497956i
\(439\) 732.833 1.66932 0.834661 0.550764i \(-0.185663\pi\)
0.834661 + 0.550764i \(0.185663\pi\)
\(440\) −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 −0.570651 0.821192i \(-0.693309\pi\)
0.821192 + 0.570651i \(0.193309\pi\)
\(444\) 9.83372 + 9.88827i 0.0221480 + 0.0222709i
\(445\) 330.380 357.095i 0.742428 0.802461i
\(446\) −540.408 −1.21168
\(447\) 22.9648 + 0.0635238i 0.0513754 + 0.000142111i
\(448\) −11.6667 54.7712i −0.0260418 0.122257i
\(449\) −196.292 −0.437175 −0.218588 0.975817i \(-0.570145\pi\)
−0.218588 + 0.975817i \(0.570145\pi\)
\(450\) −208.196 + 240.634i −0.462657 + 0.534741i
\(451\) 257.255i 0.570411i
\(452\) −260.492 260.492i −0.576311 0.576311i
\(453\) −709.420 1.96235i −1.56605 0.00433191i
\(454\) −87.5405 −0.192821
\(455\) −191.919 + 48.7417i −0.421801 + 0.107125i
\(456\) 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 \(0.296653\pi\)
\(462\) −98.7960 + 151.358i −0.213844 + 0.327614i
\(463\) 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
\(465\) −44.5708 + 47.9083i −0.0958513 + 0.103029i
\(466\) −479.077 −1.02806
\(467\) −9.53974 + 9.53974i −0.0204277 + 0.0204277i −0.717247 0.696819i \(-0.754598\pi\)
0.696819 + 0.717247i \(0.254598\pi\)
\(468\) 71.6086 + 72.4053i 0.153010 + 0.154712i
\(469\) 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
\(477\) −5.90789 + 5.84288i −0.0123855 + 0.0122492i
\(478\) −34.0240 34.0240i −0.0711799 0.0711799i
\(479\) 30.2411i 0.0631339i 0.999502 + 0.0315670i \(0.0100497\pi\)
−0.999502 + 0.0315670i \(0.989950\pi\)
\(480\) −3.06027 84.7976i −0.00637557 0.176662i
\(481\) 13.1495i 0.0273379i
\(482\) −268.995 + 268.995i −0.558081 + 0.558081i
\(483\) −334.864 + 513.019i −0.693299 + 1.06215i
\(484\) 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
\(490\) −153.380 310.684i −0.313020 0.634049i
\(491\) 775.321i 1.57907i −0.613708 0.789533i \(-0.710323\pi\)
0.613708 0.789533i \(-0.289677\pi\)
\(492\) −0.701534 + 253.615i −0.00142588 + 0.515478i
\(493\) −289.409 + 289.409i −0.587037 + 0.587037i
\(494\) 163.370 0.330709
\(495\) −187.102 + 200.000i −0.377984 + 0.404041i
\(496\) 17.4494i 0.0351802i
\(497\) 179.166 + 841.124i 0.360496 + 1.69240i
\(498\) 0.202564 73.2299i 0.000406755 0.147048i
\(499\) 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
\(507\) 1.13682 410.977i 0.00224225 0.810606i
\(508\) −107.010 107.010i −0.210649 0.210649i
\(509\) 288.101i 0.566014i 0.959118 + 0.283007i \(0.0913320\pi\)
−0.959118 + 0.283007i \(0.908668\pi\)
\(510\) 325.456 + 302.783i 0.638149 + 0.593693i
\(511\) −70.8066 + 109.136i −0.138565 + 0.213573i
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −551.293 4.57495i −1.07465 0.00891804i
\(514\) 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
\(518\) −22.5042 + 4.79358i −0.0434444 + 0.00925402i
\(519\) −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 \(0.441580\pi\)
\(522\) −174.811 176.756i −0.334886 0.338612i
\(523\) −315.417 + 315.417i −0.603093 + 0.603093i −0.941132 0.338039i \(-0.890236\pi\)
0.338039 + 0.941132i \(0.390236\pi\)
\(524\) 455.597i 0.869459i
\(525\) −147.499 503.854i −0.280951 0.959722i
\(526\) −455.045 −0.865105
\(527\) 64.6386 + 64.6386i 0.122654 + 0.122654i
\(528\) 0.202019 73.0330i 0.000382612 0.138320i
\(529\) 322.071i 0.608830i
\(530\) 4.79197 + 4.43348i 0.00904146 + 0.00836506i
\(531\) −0.200483 + 36.2385i −0.000377557 + 0.0682457i
\(532\) 59.5556 + 279.593i 0.111947 + 0.525551i
\(533\) −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
\(537\) −831.109 2.29896i −1.54769 0.00428112i
\(538\) −89.7378 + 89.7378i −0.166799 + 0.166799i
\(539\) −121.532 272.332i −0.225477 0.505254i
\(540\) −185.000 + 196.660i −0.342592 + 0.364185i
\(541\) 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
\(543\) −2.25033 + 813.528i −0.00414426 + 1.49821i
\(544\) −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
\(552\) 0.684733 247.541i 0.00124046 0.448444i
\(553\) −183.827 863.002i −0.332417 1.56058i
\(554\) 130.849 0.236190
\(555\) −34.8413 + 1.25739i −0.0627772 + 0.00226558i
\(556\) 60.0828i 0.108063i
\(557\) 221.625 + 221.625i 0.397890 + 0.397890i 0.877488 0.479598i \(-0.159218\pi\)
−0.479598 + 0.877488i \(0.659218\pi\)
\(558\) −39.4777 + 39.0433i −0.0707486 + 0.0699701i
\(559\) −360.067 −0.644127
\(560\) 120.317 + 71.5808i 0.214852 + 0.127823i
\(561\) 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
\(567\) 555.832 111.983i 0.980303 0.197500i
\(568\) −245.713 245.713i −0.432593 0.432593i
\(569\) 63.0549 0.110817 0.0554085 0.998464i \(-0.482354\pi\)
0.0554085 + 0.998464i \(0.482354\pi\)
\(570\) 15.6219 + 432.870i 0.0274069 + 0.759421i
\(571\) −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
\(573\) 1.49593 540.800i 0.00261069 0.943804i
\(574\) −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 \(-0.979909\pi\)
−0.0630759 0.998009i \(-0.520091\pi\)
\(578\) 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
\(582\) 1.00612 363.729i 0.00172874 0.624964i
\(583\) 3.97319 + 3.97319i 0.00681508 + 0.00681508i
\(584\) 52.5656i 0.0900095i
\(585\) −254.446 + 8.47805i −0.434950 + 0.0144924i
\(586\) 525.876i 0.897399i
\(587\) −228.676 + 228.676i −0.389567 + 0.389567i −0.874533 0.484966i \(-0.838832\pi\)
0.484966 + 0.874533i \(0.338832\pi\)
\(588\) −119.070 268.809i −0.202499 0.457159i
\(589\) 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
\(595\) −710.856 + 180.536i −1.19472 + 0.303421i
\(596\) 15.3099i 0.0256878i
\(597\) 611.325 + 1.69101i 1.02399 + 0.00283251i
\(598\) 165.047 165.047i 0.275998 0.275998i
\(599\) −456.495 −0.762095 −0.381048 0.924555i \(-0.624437\pi\)
−0.381048 + 0.924555i \(0.624437\pi\)
\(600\) 160.806 + 138.353i 0.268010 + 0.230588i
\(601\) 631.907i 1.05143i 0.850662 + 0.525713i \(0.176202\pi\)
−0.850662 + 0.525713i \(0.823798\pi\)
\(602\) −131.260 616.223i −0.218041 1.02363i
\(603\) 540.431 534.484i 0.896237 0.886376i
\(604\) 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 0.213363 0.976973i \(-0.431558\pi\)
−0.976973 + 0.213363i \(0.931558\pi\)
\(608\) −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
\(612\) 265.233 + 268.184i 0.433388 + 0.438210i
\(613\) −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
\(615\) −464.212 431.873i −0.754816 0.702232i
\(616\) 101.087 + 65.5846i 0.164102 + 0.106469i
\(617\) −392.264 392.264i −0.635759 0.635759i 0.313747 0.949507i \(-0.398416\pi\)
−0.949507 + 0.313747i \(0.898416\pi\)
\(618\) −681.610 1.88543i −1.10293 0.00305085i
\(619\) −1005.88 −1.62500 −0.812500 0.582961i \(-0.801894\pi\)
−0.812500 + 0.582961i \(0.801894\pi\)
\(620\) 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
\(623\) 141.892 + 666.135i 0.227757 + 1.06924i
\(624\) 48.1380 47.8724i 0.0771442 0.0767186i
\(625\) −617.473 + 96.7090i −0.987956 + 0.154734i
\(626\) −535.321 −0.855146
\(627\) −1.03126 + 372.814i −0.00164475 + 0.594600i
\(628\) 195.631 195.631i 0.311515 0.311515i
\(629\) 48.7049i 0.0774323i
\(630\) −107.266 432.370i −0.170264 0.686302i
\(631\) 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
\(633\) 802.631 + 2.22019i 1.26798 + 0.00350741i
\(634\) 431.280i 0.680253i
\(635\) 378.050 14.6907i 0.595355 0.0231350i
\(636\) 3.90613 + 3.92780i 0.00614172 + 0.00617579i
\(637\) 99.1219 258.890i 0.155607 0.406421i
\(638\) −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 \(-0.968960\pi\)
0.995249 0.0973607i \(-0.0310400\pi\)
\(642\) 1.32835 480.219i 0.00206909 0.748005i
\(643\) 160.790 160.790i 0.250062 0.250062i −0.570934 0.820996i \(-0.693419\pi\)
0.820996 + 0.570934i \(0.193419\pi\)
\(644\) 342.629 + 222.295i 0.532033 + 0.345179i
\(645\) −34.4307 954.045i −0.0533809 1.47914i
\(646\) 605.111 0.936705
\(647\) −257.644 + 257.644i −0.398213 + 0.398213i −0.877602 0.479389i \(-0.840858\pi\)
0.479389 + 0.877602i \(0.340858\pi\)
\(648\) −163.783 + 160.198i −0.252751 + 0.247219i
\(649\) 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 \(-0.435968\pi\)
0.979835 0.199809i \(-0.0640321\pi\)
\(654\) 582.592 579.377i 0.890813 0.885898i
\(655\) 836.054 + 773.508i 1.27642 + 1.18093i
\(656\) 169.077 0.257740
\(657\) −118.925 + 117.616i −0.181012 + 0.179020i
\(658\) 502.503 107.037i 0.763683 0.162671i
\(659\) 112.781 0.171139 0.0855695 0.996332i \(-0.472729\pi\)
0.0855695 + 0.996332i \(0.472729\pi\)
\(660\) 133.678 + 124.365i 0.202542 + 0.188433i
\(661\) 947.097i 1.43282i 0.697678 + 0.716412i \(0.254217\pi\)
−0.697678 + 0.716412i \(0.745783\pi\)
\(662\) 70.4637 + 70.4637i 0.106441 + 0.106441i
\(663\) −0.983792 + 355.655i −0.00148385 + 0.536433i
\(664\) −48.8201 −0.0735242
\(665\) −614.188 365.402i −0.923590 0.549476i
\(666\) −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
\(672\) 99.4777 + 64.9322i 0.148032 + 0.0966253i
\(673\) −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
\(675\) −46.7945 673.376i −0.0693252 0.997594i
\(676\) −273.986 −0.405304
\(677\) 697.081 697.081i 1.02966 1.02966i 0.0301147 0.999546i \(-0.490413\pi\)
0.999546 0.0301147i \(-0.00958726\pi\)
\(678\) 781.474 + 2.16167i 1.15262 + 0.00318830i
\(679\) 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 −0.303896 0.952705i \(-0.598288\pi\)
0.952705 + 0.303896i \(0.0982875\pi\)
\(684\) −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
\(687\) −224.007 0.619635i −0.326066 0.000901944i
\(688\) 180.014 + 180.014i 0.261648 + 0.261648i
\(689\) 5.22323i 0.00758088i
\(690\) 453.094 + 421.530i 0.656659 + 0.610913i
\(691\) 829.239i 1.20006i 0.799979 + 0.600028i \(0.204844\pi\)
−0.799979 + 0.600028i \(0.795156\pi\)
\(692\) −96.4644 + 96.4644i −0.139399 + 0.139399i
\(693\) −77.8046 375.447i −0.112272 0.541771i
\(694\) 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
\(700\) −335.629 + 99.2616i −0.479471 + 0.141802i
\(701\) 664.169i 0.947460i 0.880670 + 0.473730i \(0.157093\pi\)
−0.880670 + 0.473730i \(0.842907\pi\)
\(702\) −216.017 1.79263i −0.307716 0.00255361i
\(703\) −33.5587 + 33.5587i −0.0477364 + 0.0477364i
\(704\) −48.6888 −0.0691603
\(705\) 777.983 28.0767i 1.10352 0.0398252i
\(706\) 411.773i 0.583248i
\(707\) −659.382 + 140.454i −0.932648 + 0.198662i
\(708\) 24.1593 + 0.0668278i 0.0341232 + 9.43896e-5i
\(709\) 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
\(717\) 102.072 + 0.282344i 0.142359 + 0.000393786i
\(718\) 51.9892 + 51.9892i 0.0724084 + 0.0724084i
\(719\) 227.010i 0.315731i −0.987461 0.157865i \(-0.949539\pi\)
0.987461 0.157865i \(-0.0504612\pi\)
\(720\) 131.447 + 122.970i 0.182566 + 0.170792i
\(721\) 612.095 943.437i 0.848953 1.30851i
\(722\) 55.9344 + 55.9344i 0.0774715 + 0.0774715i
\(723\) 2.23222 806.982i 0.00308745 1.11616i
\(724\) 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 0.896079 0.443895i \(-0.146404\pi\)
−0.443895 + 0.896079i \(0.646404\pi\)
\(728\) 23.3360 + 109.555i 0.0320550 + 0.150487i
\(729\) 728.900 + 12.0985i 0.999862 + 0.0165960i
\(730\) 96.4618 + 89.2454i 0.132139 + 0.122254i
\(731\) −1333.66 −1.82444
\(732\) 391.243 + 1.08223i 0.534485 + 0.00147846i
\(733\) 320.943 320.943i 0.437848 0.437848i −0.453439 0.891287i \(-0.649803\pi\)
0.891287 + 0.453439i \(0.149803\pi\)
\(734\) 680.234i 0.926749i
\(735\) 695.441 + 237.881i 0.946178 + 0.323647i
\(736\) −165.028 −0.224223
\(737\) −363.453 363.453i −0.493151 0.493151i
\(738\) −378.314 382.523i −0.512620 0.518323i
\(739\) 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
\(742\) −8.93908 + 1.90410i −0.0120473 + 0.00256617i
\(743\) 319.664 319.664i 0.430234 0.430234i −0.458474 0.888708i \(-0.651604\pi\)
0.888708 + 0.458474i \(0.151604\pi\)
\(744\) 26.1016 + 26.2464i 0.0350828 + 0.0352774i
\(745\) 28.0949 + 25.9931i 0.0377113 + 0.0348900i
\(746\) 371.837i 0.498441i
\(747\) 109.236 + 110.451i 0.146233 + 0.147860i
\(748\) 180.360 180.360i 0.241123 0.241123i
\(749\) 664.686 + 431.244i 0.887431 + 0.575759i
\(750\) −526.903 + 60.1965i −0.702537 + 0.0802620i
\(751\) −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
\(753\) −53.3170 0.147482i −0.0708062 0.000195860i
\(754\) −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 \(0.577676\pi\)
\(762\) 321.027 + 0.888006i 0.421296 + 0.00116536i
\(763\) 282.425 + 1325.89i 0.370151 + 1.73773i
\(764\) −360.534 −0.471904
\(765\) −942.449 + 31.4021i −1.23196 + 0.0410485i
\(766\) 88.2335i 0.115187i
\(767\) 16.1080 + 16.1080i 0.0210013 + 0.0210013i