Properties

Label 210.3.k.b.83.16
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 83.16
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.b.167.16

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(2.99999 + 0.00829838i) q^{3} +2.00000i q^{4} +(3.67015 + 3.39558i) q^{5} +(2.99169 + 3.00829i) q^{6} +(1.45834 - 6.84640i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(8.99986 + 0.0497901i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(2.99999 + 0.00829838i) 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} +(-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} +(4.43182 - 20.5270i) 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} +(13.6928 + 2.91668i) 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} +(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} +(24.9588 - 16.0952i) 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} +(13.4657 - 61.5441i) 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} +(-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} +(-41.6679 - 8.87561i) 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} +(41.0541 + 8.86364i) 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} +(-24.7777 - 64.7153i) q^{98} +(0.303028 - 54.7741i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} + O(q^{10}) \) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} - 8q^{14} - 4q^{15} - 128q^{16} - 4q^{18} + 12q^{21} - 40q^{22} - 24q^{23} + 16q^{25} - 8q^{28} + 112q^{29} + 28q^{30} - 128q^{32} + 48q^{35} - 40q^{36} + 32q^{37} - 64q^{39} - 20q^{42} - 32q^{43} - 80q^{44} - 48q^{46} + 8q^{50} + 84q^{51} + 136q^{53} + 340q^{57} + 112q^{58} + 64q^{60} + 168q^{63} + 200q^{65} + 32q^{67} - 72q^{72} + 64q^{74} - 88q^{77} - 4q^{78} + 76q^{81} - 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} - 48q^{92} - 388q^{93} - 544q^{95} - 128q^{98} - 160q^{99} + O(q^{100}) \)

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
\(7\) 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 \(-0.910779\pi\)
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 −0.844027 0.536300i \(-0.819821\pi\)
0.536300 + 0.844027i \(0.319821\pi\)
\(14\) 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 −0.992648 0.121037i \(-0.961378\pi\)
0.121037 + 0.992648i \(0.461378\pi\)
\(18\) 8.95007 + 9.04965i 0.497226 + 0.502758i
\(19\) −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
\(21\) 4.43182 20.5270i 0.211039 0.977478i
\(22\) 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
\(28\) 13.6928 + 2.91668i 0.489029 + 0.104167i
\(29\) −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 \(-0.977585\pi\)
0.997522 0.0703605i \(-0.0224150\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 0.0505048 18.2582i 0.00153045 0.553280i
\(34\) −29.6348 −0.871610
\(35\) 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 \(-0.327614\pi\)
0.515480 + 0.856902i \(0.327614\pi\)
\(42\) 24.9588 16.0952i 0.594258 0.383219i
\(43\) −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 −0.979968 0.199153i \(-0.936181\pi\)
0.199153 + 0.979968i \(0.436181\pi\)
\(48\) −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 \(-0.989136\pi\)
0.999418 0.0341234i \(-0.0108639\pi\)
\(60\) −20.4343 + 21.9645i −0.340572 + 0.366075i
\(61\) 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
\(63\) 13.4657 61.5441i 0.213742 0.976890i
\(64\) 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 \(0.332800\pi\)
−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 −0.611345 0.791364i \(-0.709371\pi\)
0.791364 + 0.611345i \(0.209371\pi\)
\(74\) −3.28701 −0.0444191
\(75\) 5.61323 + 74.7896i 0.0748431 + 0.997195i
\(76\) 40.8379i 0.537341i
\(77\) −41.6679 8.87561i −0.541142 0.115268i
\(78\) −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 0.629750 0.776798i \(-0.283157\pi\)
−0.776798 + 0.629750i \(0.783157\pi\)
\(84\) 41.0541 + 8.86364i 0.488739 + 0.105519i
\(85\) −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 \(-0.815917\pi\)
0.837385 0.546613i \(-0.184083\pi\)
\(90\) 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 0.321831 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 \(-0.341802\pi\)
0.476786 + 0.879019i \(0.341802\pi\)
\(102\) −88.9039 0.245921i −0.871607 0.00241099i
\(103\) −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
\(105\) 85.9667 60.2887i 0.818730 0.574178i
\(106\) −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
\(112\) −5.83336 + 27.3856i −0.0520836 + 0.244514i
\(113\) −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
\(126\) 75.0098 48.0783i 0.595316 0.381574i
\(127\) −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 \(-0.164468\pi\)
0.869459 + 0.494005i \(0.164468\pi\)
\(132\) 36.5165 + 0.101010i 0.276640 + 0.000765224i
\(133\) −29.7778 + 139.797i −0.223893 + 1.05110i
\(134\) 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 \(-0.465535\pi\)
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
\(147\) −134.073 60.2774i −0.912063 0.410050i
\(148\) −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 0.946305 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
\(162\) 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 −0.992257 0.124205i \(-0.960362\pi\)
0.124205 + 0.992257i \(0.460362\pi\)
\(168\) 32.1904 + 49.9177i 0.191610 + 0.297129i
\(169\) 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 0.553831 0.832629i \(-0.313166\pi\)
−0.832629 + 0.553831i \(0.813166\pi\)
\(174\) −58.4329 58.7571i −0.335821 0.337684i
\(175\) 173.473 + 23.0663i 0.991275 + 0.131808i
\(176\) 24.3444i 0.138321i
\(177\) 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 \(0.269518\pi\)
−0.662448 + 0.749108i \(0.730482\pi\)
\(182\) −11.6680 + 54.7773i −0.0641100 + 0.300974i
\(183\) 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
\(189\) 40.9078 184.520i 0.216443 0.976295i
\(190\) −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 \(-0.328905\pi\)
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
\(207\) 186.681 184.627i 0.901840 0.891916i
\(208\) 16.0018 16.0018i 0.0769317 0.0769317i
\(209\) 124.272i 0.594603i
\(210\) 146.255 + 25.6780i 0.696454 + 0.122276i
\(211\) −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
\(217\) −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
\(222\) −9.86100 0.0272769i −0.0444189 0.000122869i
\(223\) 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
\(225\) 16.2190 + 224.415i 0.0720844 + 0.997399i
\(226\) −260.492 −1.15262
\(227\) 43.7703 43.7703i 0.192821 0.192821i −0.604093 0.796914i \(-0.706465\pi\)
0.796914 + 0.604093i \(0.206465\pi\)
\(228\) 0.338889 122.513i 0.00148635 0.537339i
\(229\) −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
\(231\) −124.930 26.9725i −0.540821 0.116764i
\(232\) 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
\(238\) −43.2176 + 202.892i −0.181586 + 0.852485i
\(239\) −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 \(-0.811538\pi\)
0.829786 0.558081i \(-0.188462\pi\)
\(242\) 83.9594 + 83.9594i 0.346939 + 0.346939i
\(243\) 242.977 + 3.36074i 0.999904 + 0.0138302i
\(244\) 130.415 0.534487
\(245\) −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 \(-0.511272\pi\)
−0.0354032 + 0.999373i \(0.511272\pi\)
\(252\) 123.088 + 26.9315i 0.488445 + 0.106871i
\(253\) −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 −0.941675 0.336524i \(-0.890749\pi\)
0.336524 + 0.941675i \(0.390749\pi\)
\(258\) 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 \(-0.946657\pi\)
0.985991 0.166799i \(-0.0533431\pi\)
\(270\) 5.82999 + 190.830i 0.0215926 + 0.706777i
\(271\) 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
\(273\) 64.3880 + 99.8465i 0.235854 + 0.365738i
\(274\) 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 \(-0.721609\pi\)
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 −0.344596 0.938751i \(-0.611984\pi\)
0.938751 + 0.344596i \(0.111984\pi\)
\(284\) −245.713 −0.865186
\(285\) −224.246 208.624i −0.786828 0.732014i
\(286\) 48.6943i 0.170260i
\(287\) 61.6431 289.393i 0.214784 1.00834i
\(288\) −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 0.0978068 0.995205i \(-0.468817\pi\)
−0.995205 + 0.0978068i \(0.968817\pi\)
\(294\) −73.7958 194.351i −0.251006 0.661057i
\(295\) 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 \(-0.929930\pi\)
−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 \(-0.558546\pi\)
−0.182893 + 0.983133i \(0.558546\pi\)
\(312\) 0.132789 48.0052i 0.000425606 0.153863i
\(313\) 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
\(315\) 258.399 180.152i 0.820315 0.571911i
\(316\) 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
\(322\) 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
\(327\) −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
\(336\) −17.7273 + 82.1081i −0.0527597 + 0.244369i
\(337\) −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
\(343\) −201.970 + 277.231i −0.588833 + 0.808254i
\(344\) 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 \(-0.239928\pi\)
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 0.935794 0.352546i \(-0.114684\pi\)
−0.352546 + 0.935794i \(0.614684\pi\)
\(354\) 12.1130 12.0462i 0.0342176 0.0340288i
\(355\) −417.169 + 450.902i −1.17512 + 1.27015i
\(356\) 194.594 0.546613
\(357\) 238.489 + 369.825i 0.668036 + 1.03592i
\(358\) 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 0.0707450 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
\(372\) 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
\(378\) 225.428 143.612i 0.596369 0.379926i
\(379\) 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 0.647164 0.762351i \(-0.275955\pi\)
−0.762351 + 0.647164i \(0.775955\pi\)
\(384\) 24.0663 23.9335i 0.0626726 0.0623269i
\(385\) −122.790 174.062i −0.318934 0.452108i
\(386\) 388.814i 1.00729i
\(387\) −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
\(392\) 129.431 49.5554i 0.330180 0.126417i
\(393\) 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 0.718024 0.696019i \(-0.245047\pi\)
−0.696019 + 0.718024i \(0.745047\pi\)
\(398\) 203.776 + 203.776i 0.511999 + 0.511999i
\(399\) −90.4932 + 419.141i −0.226800 + 1.05048i
\(400\) −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 \(-0.407450\pi\)
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
\(417\) 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 \(-0.867174\pi\)
0.914193 0.405279i \(-0.132826\pi\)
\(420\) 120.577 + 171.933i 0.287089 + 0.409365i
\(421\) 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
\(427\) −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 \(0.240143\pi\)
−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 −0.980747 0.195281i \(-0.937438\pi\)
0.195281 + 0.980747i \(0.437438\pi\)
\(434\) −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 \(-0.814337\pi\)
−0.834661 + 0.550764i \(0.814337\pi\)
\(440\) 3.34211 + 86.0056i 0.00759570 + 0.195467i
\(441\) −401.718 181.944i −0.910925 0.412572i
\(442\) 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
\(448\) −54.7712 11.6667i −0.122257 0.0260418i
\(449\) −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
\(455\) −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 \(-0.703347\pi\)
−0.596259 + 0.802792i \(0.703347\pi\)
\(462\) −97.9571 151.902i −0.212028 0.328792i
\(463\) 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 −0.696819 0.717247i \(-0.745402\pi\)
0.717247 + 0.696819i \(0.245402\pi\)
\(468\) −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 \(-0.989950\pi\)
0.999502 0.0315670i \(-0.0100497\pi\)
\(480\) −3.06027 84.7976i −0.00637557 0.176662i
\(481\) 13.1495i 0.0273379i
\(482\) 268.995 268.995i 0.558081 0.558081i
\(483\) −332.020 514.864i −0.687413 1.06597i
\(484\) 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 \(-0.710323\pi\)
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
\(497\) 841.124 + 179.166i 1.69240 + 0.360496i
\(498\) 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 \(-0.879813\pi\)
−0.368671 0.929560i \(-0.620187\pi\)
\(504\) 96.1567 + 150.020i 0.190787 + 0.297658i
\(505\) 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 \(-0.908668\pi\)
0.959118 0.283007i \(-0.0913320\pi\)
\(510\) −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
\(518\) −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 \(-0.558420\pi\)
−0.182502 + 0.983206i \(0.558420\pi\)
\(522\) −174.811 176.756i −0.334886 0.338612i
\(523\) 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
\(525\) 520.226 + 70.6383i 0.990907 + 0.134549i
\(526\) −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
\(532\) −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
\(537\) 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
\(546\) −35.4585 + 164.235i −0.0649423 + 0.300796i
\(547\) 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
\(553\) −863.002 183.827i −1.56058 0.332417i
\(554\) 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
\(560\) −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 0.741317 0.671155i \(-0.234202\pi\)
−0.671155 + 0.741317i \(0.734202\pi\)
\(564\) −219.580 220.798i −0.389326 0.391486i
\(565\) −920.285 + 35.7615i −1.62882 + 0.0632947i
\(566\) 336.292 0.594155
\(567\) 124.254 553.218i 0.219143 0.975693i
\(568\) −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 \(0.0200910\pi\)
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
\(582\) 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 −0.484966 0.874533i \(-0.661168\pi\)
0.874533 + 0.484966i \(0.161168\pi\)
\(588\) 120.555 268.146i 0.205025 0.456031i
\(589\) 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 0.999632 0.0271286i \(-0.00863635\pi\)
−0.0271286 + 0.999632i \(0.508636\pi\)
\(594\) 165.683 162.956i 0.278927 0.274336i
\(595\) −124.828 + 722.722i −0.209795 + 1.21466i
\(596\) 15.3099i 0.0256878i
\(597\) 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 \(-0.823798\pi\)
0.850662 0.525713i \(-0.176202\pi\)
\(602\) −616.223 131.260i −1.02363 0.218041i
\(603\) 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 0.976973 0.213363i \(-0.0684418\pi\)
−0.213363 + 0.976973i \(0.568442\pi\)
\(608\) 81.6759 + 81.6759i 0.134335 + 0.134335i
\(609\) −86.5611 + 400.929i −0.142137 + 0.658339i
\(610\) 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 \(-0.198106\pi\)
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
\(627\) −1.03126 + 372.814i −0.00164475 + 0.594600i
\(628\) −195.631 + 195.631i −0.311515 + 0.311515i
\(629\) 48.7049i 0.0774323i
\(630\) 438.551 + 78.2473i 0.696113 + 0.124202i
\(631\) 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
\(637\) 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 \(-0.968960\pi\)
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 −0.820996 0.570934i \(-0.806581\pi\)
0.570934 + 0.820996i \(0.306581\pi\)
\(644\) 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 −0.479389 0.877602i \(-0.659142\pi\)
0.877602 + 0.479389i \(0.159142\pi\)
\(648\) −163.783 + 160.198i −0.252751 + 0.247219i
\(649\) −24.5060 −0.0377597
\(650\) −15.5220 199.419i −0.0238800 0.306799i
\(651\) −89.5461 19.3331i −0.137552 0.0296976i
\(652\) −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
\(658\) −107.037 + 502.503i −0.162671 + 0.763683i
\(659\) 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 \(-0.745783\pi\)
0.697678 0.716412i \(-0.254217\pi\)
\(662\) 70.4637 + 70.4637i 0.106441 + 0.106441i
\(663\) 0.983792 355.655i 0.00148385 0.536433i
\(664\) 48.8201 0.0735242
\(665\) −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
\(672\) −99.8354 + 64.3808i −0.148565 + 0.0958048i
\(673\) −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 \(0.509587\pi\)
−0.999546 + 0.0301147i \(0.990413\pi\)
\(678\) −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 \(-0.795156\pi\)
0.799979 0.600028i \(-0.204844\pi\)
\(692\) 96.4644 96.4644i 0.139399 0.139399i
\(693\) −374.564 81.9539i −0.540496 0.118260i
\(694\) 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 \(0.157093\pi\)
−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
\(707\) 140.454 659.382i 0.198662 0.932648i
\(708\) 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
\(714\) −131.336 + 608.314i −0.183944 + 0.851980i
\(715\) 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 \(0.0504612\pi\)
−0.987461 + 0.157865i \(0.949539\pi\)
\(720\) −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 0.443895 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
\(732\) 391.243 + 1.08223i 0.534485 + 0.00147846i
\(733\) −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
\(735\) −287.392 676.484i −0.391010 0.920387i
\(736\) −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
\(742\) −1.90410 + 8.93908i −0.00256617 + 0.0120473i
\(743\) 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
\(756\) 369.040 + 81.8156i 0.488148 + 0.108222i
\(757\) −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 \(-0.422324\pi\)
0.241611 + 0.970373i \(0.422324\pi\)
\(762\) −321.027 0.888006i −0.421296 0.00116536i
\(763\) 1325.89 + 282.425i 1.73773 + 0.370151i
\(764\) −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 +