Properties

Label 210.3.k.b.167.1
Level 210
Weight 3
Character 210.167
Analytic conductor 5.722
Analytic rank 0
Dimension 32
CM no
Inner twists 4

Related objects

Downloads

Learn more about

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 167.1
Character \(\chi\) \(=\) 210.167
Dual form 210.3.k.b.83.1

$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

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

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 \(0.0892213\pi\)
−0.960973 + 0.276641i \(0.910779\pi\)
\(12\) 0.0165968 + 5.99998i 0.00138306 + 0.499998i
\(13\) 4.00045 + 4.00045i 0.307727 + 0.307727i 0.844027 0.536300i \(-0.180179\pi\)
−0.536300 + 0.844027i \(0.680179\pi\)
\(14\) 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 \(-0.0386221\pi\)
−0.121037 + 0.992648i \(0.538622\pi\)
\(18\) 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 0.995160 0.0982681i \(-0.0313303\pi\)
−0.0982681 + 0.995160i \(0.531330\pi\)
\(24\) 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 \(-0.977585\pi\)
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
\(35\) −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 0.684548 0.728967i \(-0.259999\pi\)
−0.728967 + 0.684548i \(0.759999\pi\)
\(38\) 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 −0.0477300 + 0.998860i \(0.515199\pi\)
−0.998860 + 0.0477300i \(0.984801\pi\)
\(44\) 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 \(-0.0638191\pi\)
−0.199153 + 0.979968i \(0.563819\pi\)
\(48\) 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 0.700921 0.713239i \(-0.252772\pi\)
−0.713239 + 0.700921i \(0.752772\pi\)
\(54\) −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
\(63\) 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 0.994647 0.103327i \(-0.0329489\pi\)
−0.103327 + 0.994647i \(0.532949\pi\)
\(68\) 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 \(-0.667200\pi\)
0.501451 0.865186i \(-0.332800\pi\)
\(72\) −18.0993 17.9001i −0.251379 0.248613i
\(73\) −13.1414 13.1414i −0.180019 0.180019i 0.611345 0.791364i \(-0.290629\pi\)
−0.791364 + 0.611345i \(0.790629\pi\)
\(74\) −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 \(0.294001\pi\)
−0.602926 + 0.797797i \(0.705999\pi\)
\(80\) 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 \(-0.716843\pi\)
0.776798 + 0.629750i \(0.216843\pi\)
\(84\) −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 \(-0.815917\pi\)
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 \(-0.604298\pi\)
0.946797 + 0.321831i \(0.104298\pi\)
\(98\) 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 0.994055 + 0.108878i \(0.0347258\pi\)
0.108878 + 0.994055i \(0.465274\pi\)
\(104\) 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 −0.226097 0.974105i \(-0.572597\pi\)
0.974105 + 0.226097i \(0.0725966\pi\)
\(108\) 0.448108 + 53.9981i 0.00414915 + 0.499983i
\(109\) 193.662i 1.77672i −0.459150 0.888359i \(-0.651846\pi\)
0.459150 0.888359i \(-0.348154\pi\)
\(110\) −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 −0.986025 0.166596i \(-0.946722\pi\)
−0.166596 0.986025i \(-0.553278\pi\)
\(114\) −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 0.464353 0.885650i \(-0.346287\pi\)
−0.885650 + 0.464353i \(0.846287\pi\)
\(128\) 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 −0.765869 0.642997i \(-0.777691\pi\)
0.642997 + 0.765869i \(0.277691\pi\)
\(138\) −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 −0.946305 0.323275i \(-0.895216\pi\)
0.323275 + 0.946305i \(0.395216\pi\)
\(158\) 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 −0.704312 0.709890i \(-0.748745\pi\)
0.709890 + 0.704312i \(0.248745\pi\)
\(164\) 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 \(-0.0396381\pi\)
−0.124205 + 0.992257i \(0.539638\pi\)
\(168\) 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 −0.553831 0.832629i \(-0.686834\pi\)
0.832629 + 0.553831i \(0.186834\pi\)
\(174\) 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 \(0.269518\pi\)
−0.662448 + 0.749108i \(0.730482\pi\)
\(182\) 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 \(-0.843567\pi\)
0.881650 0.471904i \(-0.156433\pi\)
\(192\) −0.0663871 23.9999i −0.000345766 0.125000i
\(193\) −194.407 + 194.407i −1.00729 + 1.00729i −0.00731625 + 0.999973i \(0.502329\pi\)
−0.999973 + 0.00731625i \(0.997671\pi\)
\(194\) 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 −0.878041 0.478586i \(-0.841149\pi\)
0.478586 + 0.878041i \(0.341149\pi\)
\(198\) 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 −0.970475 0.241204i \(-0.922458\pi\)
−0.241204 0.970475i \(-0.577542\pi\)
\(224\) −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 \(-0.293535\pi\)
−0.796914 + 0.604093i \(0.793535\pi\)
\(228\) 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 −0.999595 0.0284664i \(-0.990938\pi\)
−0.0284664 0.999595i \(-0.509062\pi\)
\(234\) 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 \(-0.811538\pi\)
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
\(245\) −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 0.941675 0.336524i \(-0.109251\pi\)
−0.336524 + 0.941675i \(0.609251\pi\)
\(258\) −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 0.126821 0.991926i \(-0.459523\pi\)
−0.991926 + 0.126821i \(0.959523\pi\)
\(264\) −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
\(273\) −64.9394 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 0.815270 0.579080i \(-0.196588\pi\)
−0.579080 + 0.815270i \(0.696588\pi\)
\(278\) −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 \(0.278391\pi\)
−0.641311 + 0.767281i \(0.721609\pi\)
\(282\) −220.189 + 0.609073i −0.780812 + 0.00215984i
\(283\) −168.146 168.146i −0.594155 0.594155i 0.344596 0.938751i \(-0.388016\pi\)
−0.938751 + 0.344596i \(0.888016\pi\)
\(284\) −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 −0.0978068 0.995205i \(-0.531183\pi\)
0.995205 + 0.0978068i \(0.0311827\pi\)
\(294\) −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 0.218358 0.975869i \(-0.429930\pi\)
0.975869 0.218358i \(-0.0700701\pi\)
\(308\) 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 0.135615 0.990762i \(-0.456699\pi\)
−0.990762 + 0.135615i \(0.956699\pi\)
\(314\) 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 −0.279804 0.960057i \(-0.590270\pi\)
0.960057 + 0.279804i \(0.0902696\pi\)
\(318\) 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 0.647156 0.762357i \(-0.275958\pi\)
−0.762357 + 0.647156i \(0.775958\pi\)
\(338\) −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 −0.480788 0.876837i \(-0.659649\pi\)
0.876837 + 0.480788i \(0.159649\pi\)
\(348\) −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 −0.935794 0.352546i \(-0.885316\pi\)
0.352546 + 0.935794i \(0.385316\pi\)
\(354\) 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 −0.0707450 0.997494i \(-0.522538\pi\)
0.997494 + 0.0707450i \(0.0225377\pi\)
\(368\) −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 −0.412511 0.910952i \(-0.635348\pi\)
0.910952 + 0.412511i \(0.135348\pi\)
\(374\) 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 \(0.0520641\pi\)
−0.986653 + 0.162836i \(0.947936\pi\)
\(380\) 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 \(-0.724045\pi\)
0.762351 + 0.647164i \(0.224045\pi\)
\(384\) −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 −0.718024 0.696019i \(-0.754953\pi\)
0.696019 + 0.718024i \(0.254953\pi\)
\(398\) −203.776 + 203.776i −0.511999 + 0.511999i
\(399\) −419.635 88.1730i −1.05172 0.220985i
\(400\) −7.76012 + 99.6984i −0.0194003 + 0.249246i
\(401\) 27.9968i 0.0698174i 0.999391 + 0.0349087i \(0.0111140\pi\)
−0.999391 + 0.0349087i \(0.988886\pi\)
\(402\) −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 \(-0.867174\pi\)
0.914193 0.405279i \(-0.132826\pi\)
\(420\) −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 \(-0.759857\pi\)
0.728661 0.684875i \(-0.240143\pi\)
\(432\) 107.996 0.896216i 0.249991 0.00207457i
\(433\) 340.107 + 340.107i 0.785466 + 0.785466i 0.980747 0.195281i \(-0.0625619\pi\)
−0.195281 + 0.980747i \(0.562562\pi\)
\(434\) −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 0.821192 0.570651i \(-0.193309\pi\)
−0.570651 + 0.821192i \(0.693309\pi\)
\(444\) 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 0.762139 0.647413i \(-0.224149\pi\)
−0.647413 + 0.762139i \(0.724149\pi\)
\(458\) 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 −0.249164 0.968461i \(-0.580156\pi\)
0.968461 + 0.249164i \(0.0801558\pi\)
\(464\) 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 \(-0.254598\pi\)
−0.717247 + 0.696819i \(0.754598\pi\)
\(468\) 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
\(483\) −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 0.402650 0.915354i \(-0.368089\pi\)
−0.915354 + 0.402650i \(0.868089\pi\)
\(488\) −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 \(0.289677\pi\)
−0.613708 + 0.789533i \(0.710323\pi\)
\(492\) −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 \(0.203991\pi\)
−0.801583 + 0.597884i \(0.796009\pi\)
\(500\) 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 0.368671 0.929560i \(-0.379813\pi\)
0.929560 0.368671i \(-0.120187\pi\)
\(504\) −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 \(-0.908668\pi\)
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
\(518\) −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 0.338039 0.941132i \(-0.390236\pi\)
−0.941132 + 0.338039i \(0.890236\pi\)
\(524\) 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 0.746914 0.664921i \(-0.231535\pi\)
−0.664921 + 0.746914i \(0.731535\pi\)
\(548\) 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 −0.479598 0.877488i \(-0.659218\pi\)
0.877488 + 0.479598i \(0.159218\pi\)
\(558\) −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 −0.741317 0.671155i \(-0.765798\pi\)
0.671155 + 0.741317i \(0.265798\pi\)
\(564\) −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 −0.0630759 + 0.998009i \(0.520091\pi\)
−0.998009 + 0.0630759i \(0.979909\pi\)
\(578\) 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 \(-0.338832\pi\)
−0.874533 + 0.484966i \(0.838832\pi\)
\(588\) −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 −0.999632 0.0271286i \(-0.991364\pi\)
0.0271286 + 0.999632i \(0.491364\pi\)
\(594\) −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 \(-0.823798\pi\)
0.850662 0.525713i \(-0.176202\pi\)
\(602\) −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 −0.976973 0.213363i \(-0.931558\pi\)
0.213363 + 0.976973i \(0.431558\pi\)
\(608\) −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 −0.983261 0.182204i \(-0.941677\pi\)
0.182204 + 0.983261i \(0.441677\pi\)
\(614\) 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 −0.949507 0.313747i \(-0.898416\pi\)
0.313747 + 0.949507i \(0.398416\pi\)
\(618\) −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 \(0.0310400\pi\)
−0.995249 + 0.0973607i \(0.968960\pi\)
\(642\) 1.32835 + 480.219i 0.00206909 + 0.748005i
\(643\) 160.790 + 160.790i 0.250062 + 0.250062i 0.820996 0.570934i \(-0.193419\pi\)
−0.570934 + 0.820996i \(0.693419\pi\)
\(644\) 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 \(-0.340858\pi\)
−0.877602 + 0.479389i \(0.840858\pi\)
\(648\) −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 0.979835 + 0.199809i \(0.0640321\pi\)
0.199809 + 0.979835i \(0.435968\pi\)
\(654\) 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 \(-0.745783\pi\)
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
\(665\) −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 −0.828068 0.560628i \(-0.810560\pi\)
0.560628 + 0.828068i \(0.310560\pi\)
\(674\) −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 0.999546 + 0.0301147i \(0.00958726\pi\)
0.0301147 + 0.999546i \(0.490413\pi\)
\(678\) 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 0.952705 0.303896i \(-0.0982875\pi\)
−0.303896 + 0.952705i \(0.598288\pi\)
\(684\) −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
\(693\) −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 \(-0.842907\pi\)
0.880670 0.473730i \(-0.157093\pi\)
\(702\) −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 \(-0.749639\pi\)
0.706304 0.707909i \(-0.250361\pi\)
\(710\) 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 \(0.0504612\pi\)
−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 \(-0.646404\pi\)
0.896079 + 0.443895i \(0.146404\pi\)
\(728\) 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 0.891287 0.453439i \(-0.149803\pi\)
−0.453439 + 0.891287i \(0.649803\pi\)
\(734\) 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 \(0.167620\pi\)
−0.864524 + 0.502591i \(0.832380\pi\)
\(740\) 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 0.888708 0.458474i \(-0.151604\pi\)
−0.458474 + 0.888708i \(0.651604\pi\)
\(744\) 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 0.443699 0.896176i \(-0.353666\pi\)
−0.896176 + 0.443699i \(0.853666\pi\)
\(758\) 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