Properties

Label 525.2.j.b.218.8
Level 525
Weight 2
Character 525.218
Analytic conductor 4.192
Analytic rank 0
Dimension 24
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 218.8
Character \(\chi\) \(=\) 525.218
Dual form 525.2.j.b.407.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.347054 + 0.347054i) q^{2} +(-1.72305 - 0.176396i) q^{3} -1.75911i q^{4} +(-0.536770 - 0.659208i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.30461 - 1.30461i) q^{8} +(2.93777 + 0.607876i) q^{9} +O(q^{10})\) \(q+(0.347054 + 0.347054i) q^{2} +(-1.72305 - 0.176396i) q^{3} -1.75911i q^{4} +(-0.536770 - 0.659208i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.30461 - 1.30461i) q^{8} +(2.93777 + 0.607876i) q^{9} +2.67137i q^{11} +(-0.310299 + 3.03102i) q^{12} +(-2.14945 - 2.14945i) q^{13} +0.490808 q^{14} -2.61267 q^{16} +(-3.26719 - 3.26719i) q^{17} +(0.808598 + 1.23053i) q^{18} -5.24329i q^{19} +(-1.34311 + 1.09365i) q^{21} +(-0.927108 + 0.927108i) q^{22} +(2.54815 - 2.54815i) q^{23} +(-2.47803 + 2.01778i) q^{24} -1.49195i q^{26} +(-4.95468 - 1.56561i) q^{27} +(-1.24388 - 1.24388i) q^{28} -2.86924 q^{29} -5.28599 q^{31} +(-3.51596 - 3.51596i) q^{32} +(0.471218 - 4.60289i) q^{33} -2.26778i q^{34} +(1.06932 - 5.16785i) q^{36} +(2.14286 - 2.14286i) q^{37} +(1.81970 - 1.81970i) q^{38} +(3.32444 + 4.08274i) q^{39} -11.5768i q^{41} +(-0.845684 - 0.0865765i) q^{42} +(-0.759108 - 0.759108i) q^{43} +4.69922 q^{44} +1.76869 q^{46} +(7.66034 + 7.66034i) q^{47} +(4.50176 + 0.460865i) q^{48} -1.00000i q^{49} +(5.05320 + 6.20584i) q^{51} +(-3.78111 + 3.78111i) q^{52} +(-4.43577 + 4.43577i) q^{53} +(-1.17619 - 2.26289i) q^{54} -1.84500i q^{56} +(-0.924894 + 9.03442i) q^{57} +(-0.995779 - 0.995779i) q^{58} +0.159437 q^{59} +4.72534 q^{61} +(-1.83452 - 1.83452i) q^{62} +(2.50715 - 1.64748i) q^{63} +2.78490i q^{64} +(1.76099 - 1.43391i) q^{66} +(5.41156 - 5.41156i) q^{67} +(-5.74734 + 5.74734i) q^{68} +(-4.84006 + 3.94109i) q^{69} +13.5880i q^{71} +(4.62569 - 3.03961i) q^{72} +(-4.16486 - 4.16486i) q^{73} +1.48737 q^{74} -9.22351 q^{76} +(1.88894 + 1.88894i) q^{77} +(-0.263173 + 2.57069i) q^{78} -3.89710i q^{79} +(8.26097 + 3.57160i) q^{81} +(4.01778 - 4.01778i) q^{82} +(-4.03778 + 4.03778i) q^{83} +(1.92384 + 2.36267i) q^{84} -0.526902i q^{86} +(4.94383 + 0.506122i) q^{87} +(3.48510 + 3.48510i) q^{88} +3.95125 q^{89} -3.03977 q^{91} +(-4.48247 - 4.48247i) q^{92} +(9.10800 + 0.932426i) q^{93} +5.31710i q^{94} +(5.43796 + 6.67836i) q^{96} +(1.86878 - 1.86878i) q^{97} +(0.347054 - 0.347054i) q^{98} +(-1.62386 + 7.84786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{3} + O(q^{10}) \) \( 24q + 4q^{3} - 16q^{12} + 8q^{13} - 16q^{16} + 20q^{18} + 4q^{21} - 8q^{22} + 16q^{27} - 28q^{33} + 16q^{36} + 16q^{37} + 20q^{42} + 40q^{43} - 64q^{46} - 16q^{48} - 20q^{51} - 4q^{57} - 40q^{58} + 32q^{61} + 8q^{63} - 16q^{66} - 24q^{67} + 8q^{72} - 32q^{73} + 32q^{76} - 60q^{78} + 52q^{81} + 80q^{82} - 4q^{87} - 96q^{88} - 24q^{91} + 76q^{93} - 96q^{96} - 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.347054 + 0.347054i 0.245404 + 0.245404i 0.819081 0.573677i \(-0.194484\pi\)
−0.573677 + 0.819081i \(0.694484\pi\)
\(3\) −1.72305 0.176396i −0.994801 0.101842i
\(4\) 1.75911i 0.879554i
\(5\) 0 0
\(6\) −0.536770 0.659208i −0.219135 0.269120i
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) 1.30461 1.30461i 0.461250 0.461250i
\(9\) 2.93777 + 0.607876i 0.979256 + 0.202625i
\(10\) 0 0
\(11\) 2.67137i 0.805448i 0.915322 + 0.402724i \(0.131936\pi\)
−0.915322 + 0.402724i \(0.868064\pi\)
\(12\) −0.310299 + 3.03102i −0.0895757 + 0.874981i
\(13\) −2.14945 2.14945i −0.596149 0.596149i 0.343137 0.939285i \(-0.388511\pi\)
−0.939285 + 0.343137i \(0.888511\pi\)
\(14\) 0.490808 0.131174
\(15\) 0 0
\(16\) −2.61267 −0.653169
\(17\) −3.26719 3.26719i −0.792410 0.792410i 0.189475 0.981886i \(-0.439321\pi\)
−0.981886 + 0.189475i \(0.939321\pi\)
\(18\) 0.808598 + 1.23053i 0.190588 + 0.290038i
\(19\) 5.24329i 1.20289i −0.798913 0.601446i \(-0.794591\pi\)
0.798913 0.601446i \(-0.205409\pi\)
\(20\) 0 0
\(21\) −1.34311 + 1.09365i −0.293090 + 0.238653i
\(22\) −0.927108 + 0.927108i −0.197660 + 0.197660i
\(23\) 2.54815 2.54815i 0.531326 0.531326i −0.389641 0.920967i \(-0.627401\pi\)
0.920967 + 0.389641i \(0.127401\pi\)
\(24\) −2.47803 + 2.01778i −0.505826 + 0.411877i
\(25\) 0 0
\(26\) 1.49195i 0.292595i
\(27\) −4.95468 1.56561i −0.953529 0.301301i
\(28\) −1.24388 1.24388i −0.235071 0.235071i
\(29\) −2.86924 −0.532804 −0.266402 0.963862i \(-0.585835\pi\)
−0.266402 + 0.963862i \(0.585835\pi\)
\(30\) 0 0
\(31\) −5.28599 −0.949391 −0.474696 0.880150i \(-0.657442\pi\)
−0.474696 + 0.880150i \(0.657442\pi\)
\(32\) −3.51596 3.51596i −0.621540 0.621540i
\(33\) 0.471218 4.60289i 0.0820286 0.801260i
\(34\) 2.26778i 0.388921i
\(35\) 0 0
\(36\) 1.06932 5.16785i 0.178220 0.861309i
\(37\) 2.14286 2.14286i 0.352284 0.352284i −0.508675 0.860959i \(-0.669864\pi\)
0.860959 + 0.508675i \(0.169864\pi\)
\(38\) 1.81970 1.81970i 0.295195 0.295195i
\(39\) 3.32444 + 4.08274i 0.532336 + 0.653762i
\(40\) 0 0
\(41\) 11.5768i 1.80800i −0.427537 0.903998i \(-0.640619\pi\)
0.427537 0.903998i \(-0.359381\pi\)
\(42\) −0.845684 0.0865765i −0.130492 0.0133590i
\(43\) −0.759108 0.759108i −0.115763 0.115763i 0.646852 0.762615i \(-0.276085\pi\)
−0.762615 + 0.646852i \(0.776085\pi\)
\(44\) 4.69922 0.708434
\(45\) 0 0
\(46\) 1.76869 0.260779
\(47\) 7.66034 + 7.66034i 1.11738 + 1.11738i 0.992125 + 0.125250i \(0.0399734\pi\)
0.125250 + 0.992125i \(0.460027\pi\)
\(48\) 4.50176 + 0.460865i 0.649773 + 0.0665201i
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 5.05320 + 6.20584i 0.707589 + 0.868991i
\(52\) −3.78111 + 3.78111i −0.524345 + 0.524345i
\(53\) −4.43577 + 4.43577i −0.609300 + 0.609300i −0.942763 0.333463i \(-0.891783\pi\)
0.333463 + 0.942763i \(0.391783\pi\)
\(54\) −1.17619 2.26289i −0.160059 0.307940i
\(55\) 0 0
\(56\) 1.84500i 0.246548i
\(57\) −0.924894 + 9.03442i −0.122505 + 1.19664i
\(58\) −0.995779 0.995779i −0.130752 0.130752i
\(59\) 0.159437 0.0207569 0.0103785 0.999946i \(-0.496696\pi\)
0.0103785 + 0.999946i \(0.496696\pi\)
\(60\) 0 0
\(61\) 4.72534 0.605018 0.302509 0.953147i \(-0.402176\pi\)
0.302509 + 0.953147i \(0.402176\pi\)
\(62\) −1.83452 1.83452i −0.232984 0.232984i
\(63\) 2.50715 1.64748i 0.315871 0.207563i
\(64\) 2.78490i 0.348112i
\(65\) 0 0
\(66\) 1.76099 1.43391i 0.216762 0.176502i
\(67\) 5.41156 5.41156i 0.661127 0.661127i −0.294519 0.955646i \(-0.595159\pi\)
0.955646 + 0.294519i \(0.0951594\pi\)
\(68\) −5.74734 + 5.74734i −0.696967 + 0.696967i
\(69\) −4.84006 + 3.94109i −0.582675 + 0.474452i
\(70\) 0 0
\(71\) 13.5880i 1.61260i 0.591508 + 0.806299i \(0.298533\pi\)
−0.591508 + 0.806299i \(0.701467\pi\)
\(72\) 4.62569 3.03961i 0.545143 0.358221i
\(73\) −4.16486 4.16486i −0.487460 0.487460i 0.420044 0.907504i \(-0.362015\pi\)
−0.907504 + 0.420044i \(0.862015\pi\)
\(74\) 1.48737 0.172904
\(75\) 0 0
\(76\) −9.22351 −1.05801
\(77\) 1.88894 + 1.88894i 0.215265 + 0.215265i
\(78\) −0.263173 + 2.57069i −0.0297985 + 0.291073i
\(79\) 3.89710i 0.438458i −0.975673 0.219229i \(-0.929646\pi\)
0.975673 0.219229i \(-0.0703542\pi\)
\(80\) 0 0
\(81\) 8.26097 + 3.57160i 0.917886 + 0.396844i
\(82\) 4.01778 4.01778i 0.443689 0.443689i
\(83\) −4.03778 + 4.03778i −0.443204 + 0.443204i −0.893087 0.449883i \(-0.851466\pi\)
0.449883 + 0.893087i \(0.351466\pi\)
\(84\) 1.92384 + 2.36267i 0.209908 + 0.257789i
\(85\) 0 0
\(86\) 0.526902i 0.0568173i
\(87\) 4.94383 + 0.506122i 0.530034 + 0.0542619i
\(88\) 3.48510 + 3.48510i 0.371513 + 0.371513i
\(89\) 3.95125 0.418832 0.209416 0.977827i \(-0.432844\pi\)
0.209416 + 0.977827i \(0.432844\pi\)
\(90\) 0 0
\(91\) −3.03977 −0.318655
\(92\) −4.48247 4.48247i −0.467330 0.467330i
\(93\) 9.10800 + 0.932426i 0.944455 + 0.0966881i
\(94\) 5.31710i 0.548417i
\(95\) 0 0
\(96\) 5.43796 + 6.67836i 0.555009 + 0.681607i
\(97\) 1.86878 1.86878i 0.189746 0.189746i −0.605840 0.795586i \(-0.707163\pi\)
0.795586 + 0.605840i \(0.207163\pi\)
\(98\) 0.347054 0.347054i 0.0350577 0.0350577i
\(99\) −1.62386 + 7.84786i −0.163204 + 0.788740i
\(100\) 0 0
\(101\) 3.76115i 0.374249i −0.982336 0.187124i \(-0.940083\pi\)
0.982336 0.187124i \(-0.0599167\pi\)
\(102\) −0.400027 + 3.90749i −0.0396086 + 0.386899i
\(103\) 8.85701 + 8.85701i 0.872707 + 0.872707i 0.992767 0.120060i \(-0.0383086\pi\)
−0.120060 + 0.992767i \(0.538309\pi\)
\(104\) −5.60838 −0.549947
\(105\) 0 0
\(106\) −3.07890 −0.299049
\(107\) 0.710397 + 0.710397i 0.0686766 + 0.0686766i 0.740611 0.671934i \(-0.234536\pi\)
−0.671934 + 0.740611i \(0.734536\pi\)
\(108\) −2.75407 + 8.71582i −0.265011 + 0.838680i
\(109\) 19.0144i 1.82125i −0.413237 0.910623i \(-0.635602\pi\)
0.413237 0.910623i \(-0.364398\pi\)
\(110\) 0 0
\(111\) −4.07024 + 3.31425i −0.386330 + 0.314575i
\(112\) −1.84744 + 1.84744i −0.174567 + 0.174567i
\(113\) 5.69132 5.69132i 0.535394 0.535394i −0.386779 0.922173i \(-0.626412\pi\)
0.922173 + 0.386779i \(0.126412\pi\)
\(114\) −3.45642 + 2.81444i −0.323723 + 0.263597i
\(115\) 0 0
\(116\) 5.04730i 0.468630i
\(117\) −5.00798 7.62117i −0.462988 0.704577i
\(118\) 0.0553332 + 0.0553332i 0.00509383 + 0.00509383i
\(119\) −4.62051 −0.423561
\(120\) 0 0
\(121\) 3.86380 0.351254
\(122\) 1.63995 + 1.63995i 0.148474 + 0.148474i
\(123\) −2.04210 + 19.9474i −0.184130 + 1.79859i
\(124\) 9.29862i 0.835041i
\(125\) 0 0
\(126\) 1.44188 + 0.298350i 0.128453 + 0.0265792i
\(127\) 12.1366 12.1366i 1.07695 1.07695i 0.0801668 0.996781i \(-0.474455\pi\)
0.996781 0.0801668i \(-0.0255453\pi\)
\(128\) −7.99843 + 7.99843i −0.706968 + 0.706968i
\(129\) 1.17407 + 1.44188i 0.103371 + 0.126950i
\(130\) 0 0
\(131\) 9.94280i 0.868706i 0.900743 + 0.434353i \(0.143023\pi\)
−0.900743 + 0.434353i \(0.856977\pi\)
\(132\) −8.09697 0.828923i −0.704751 0.0721485i
\(133\) −3.70756 3.70756i −0.321487 0.321487i
\(134\) 3.75620 0.324486
\(135\) 0 0
\(136\) −8.52483 −0.730998
\(137\) 13.6645 + 13.6645i 1.16744 + 1.16744i 0.982808 + 0.184630i \(0.0591086\pi\)
0.184630 + 0.982808i \(0.440891\pi\)
\(138\) −3.04753 0.311989i −0.259423 0.0265583i
\(139\) 16.7933i 1.42439i 0.701982 + 0.712195i \(0.252299\pi\)
−0.701982 + 0.712195i \(0.747701\pi\)
\(140\) 0 0
\(141\) −11.8479 14.5504i −0.997770 1.22536i
\(142\) −4.71576 + 4.71576i −0.395738 + 0.395738i
\(143\) 5.74196 5.74196i 0.480167 0.480167i
\(144\) −7.67544 1.58818i −0.639620 0.132349i
\(145\) 0 0
\(146\) 2.89086i 0.239249i
\(147\) −0.176396 + 1.72305i −0.0145489 + 0.142114i
\(148\) −3.76952 3.76952i −0.309853 0.309853i
\(149\) −9.31256 −0.762915 −0.381458 0.924386i \(-0.624578\pi\)
−0.381458 + 0.924386i \(0.624578\pi\)
\(150\) 0 0
\(151\) 20.3868 1.65905 0.829527 0.558466i \(-0.188610\pi\)
0.829527 + 0.558466i \(0.188610\pi\)
\(152\) −6.84046 6.84046i −0.554834 0.554834i
\(153\) −7.61221 11.5843i −0.615410 0.936535i
\(154\) 1.31113i 0.105654i
\(155\) 0 0
\(156\) 7.18199 5.84804i 0.575019 0.468218i
\(157\) −6.32887 + 6.32887i −0.505098 + 0.505098i −0.913018 0.407919i \(-0.866254\pi\)
0.407919 + 0.913018i \(0.366254\pi\)
\(158\) 1.35250 1.35250i 0.107599 0.107599i
\(159\) 8.42549 6.86058i 0.668185 0.544080i
\(160\) 0 0
\(161\) 3.60363i 0.284006i
\(162\) 1.62746 + 4.10654i 0.127866 + 0.322640i
\(163\) 6.45638 + 6.45638i 0.505703 + 0.505703i 0.913205 0.407502i \(-0.133600\pi\)
−0.407502 + 0.913205i \(0.633600\pi\)
\(164\) −20.3649 −1.59023
\(165\) 0 0
\(166\) −2.80266 −0.217528
\(167\) 1.58004 + 1.58004i 0.122268 + 0.122268i 0.765593 0.643325i \(-0.222446\pi\)
−0.643325 + 0.765593i \(0.722446\pi\)
\(168\) −0.325450 + 3.17902i −0.0251090 + 0.245267i
\(169\) 3.75977i 0.289213i
\(170\) 0 0
\(171\) 3.18727 15.4036i 0.243737 1.17794i
\(172\) −1.33535 + 1.33535i −0.101820 + 0.101820i
\(173\) −1.69970 + 1.69970i −0.129226 + 0.129226i −0.768761 0.639536i \(-0.779127\pi\)
0.639536 + 0.768761i \(0.279127\pi\)
\(174\) 1.54012 + 1.89142i 0.116756 + 0.143388i
\(175\) 0 0
\(176\) 6.97941i 0.526093i
\(177\) −0.274717 0.0281240i −0.0206490 0.00211393i
\(178\) 1.37130 + 1.37130i 0.102783 + 0.102783i
\(179\) 8.44380 0.631119 0.315560 0.948906i \(-0.397808\pi\)
0.315560 + 0.948906i \(0.397808\pi\)
\(180\) 0 0
\(181\) 5.51483 0.409914 0.204957 0.978771i \(-0.434295\pi\)
0.204957 + 0.978771i \(0.434295\pi\)
\(182\) −1.05496 1.05496i −0.0781992 0.0781992i
\(183\) −8.14198 0.833531i −0.601872 0.0616164i
\(184\) 6.64869i 0.490148i
\(185\) 0 0
\(186\) 2.83736 + 3.48456i 0.208045 + 0.255501i
\(187\) 8.72787 8.72787i 0.638245 0.638245i
\(188\) 13.4754 13.4754i 0.982792 0.982792i
\(189\) −4.61054 + 2.39644i −0.335368 + 0.174315i
\(190\) 0 0
\(191\) 0.559524i 0.0404858i 0.999795 + 0.0202429i \(0.00644395\pi\)
−0.999795 + 0.0202429i \(0.993556\pi\)
\(192\) 0.491244 4.79850i 0.0354525 0.346302i
\(193\) −7.05199 7.05199i −0.507613 0.507613i 0.406180 0.913793i \(-0.366861\pi\)
−0.913793 + 0.406180i \(0.866861\pi\)
\(194\) 1.29713 0.0931287
\(195\) 0 0
\(196\) −1.75911 −0.125651
\(197\) −10.1505 10.1505i −0.723190 0.723190i 0.246064 0.969254i \(-0.420863\pi\)
−0.969254 + 0.246064i \(0.920863\pi\)
\(198\) −3.28719 + 2.16006i −0.233611 + 0.153509i
\(199\) 11.6748i 0.827604i −0.910367 0.413802i \(-0.864201\pi\)
0.910367 0.413802i \(-0.135799\pi\)
\(200\) 0 0
\(201\) −10.2789 + 8.36978i −0.725020 + 0.590359i
\(202\) 1.30532 1.30532i 0.0918421 0.0918421i
\(203\) −2.02886 + 2.02886i −0.142398 + 0.142398i
\(204\) 10.9167 8.88912i 0.764324 0.622363i
\(205\) 0 0
\(206\) 6.14771i 0.428332i
\(207\) 9.03483 5.93692i 0.627964 0.412644i
\(208\) 5.61580 + 5.61580i 0.389386 + 0.389386i
\(209\) 14.0067 0.968867
\(210\) 0 0
\(211\) −0.777102 −0.0534979 −0.0267490 0.999642i \(-0.508515\pi\)
−0.0267490 + 0.999642i \(0.508515\pi\)
\(212\) 7.80300 + 7.80300i 0.535912 + 0.535912i
\(213\) 2.39687 23.4127i 0.164231 1.60421i
\(214\) 0.493091i 0.0337070i
\(215\) 0 0
\(216\) −8.50645 + 4.42142i −0.578790 + 0.300840i
\(217\) −3.73776 + 3.73776i −0.253736 + 0.253736i
\(218\) 6.59901 6.59901i 0.446941 0.446941i
\(219\) 6.44157 + 7.91090i 0.435281 + 0.534569i
\(220\) 0 0
\(221\) 14.0453i 0.944789i
\(222\) −2.56281 0.262367i −0.172005 0.0176089i
\(223\) 3.33811 + 3.33811i 0.223536 + 0.223536i 0.809986 0.586450i \(-0.199475\pi\)
−0.586450 + 0.809986i \(0.699475\pi\)
\(224\) −4.97232 −0.332227
\(225\) 0 0
\(226\) 3.95038 0.262776
\(227\) 0.242326 + 0.242326i 0.0160838 + 0.0160838i 0.715103 0.699019i \(-0.246380\pi\)
−0.699019 + 0.715103i \(0.746380\pi\)
\(228\) 15.8925 + 1.62699i 1.05251 + 0.107750i
\(229\) 13.4793i 0.890735i 0.895348 + 0.445368i \(0.146927\pi\)
−0.895348 + 0.445368i \(0.853073\pi\)
\(230\) 0 0
\(231\) −2.92153 3.58793i −0.192223 0.236069i
\(232\) −3.74324 + 3.74324i −0.245756 + 0.245756i
\(233\) 1.19260 1.19260i 0.0781301 0.0781301i −0.666962 0.745092i \(-0.732406\pi\)
0.745092 + 0.666962i \(0.232406\pi\)
\(234\) 0.906918 4.38299i 0.0592871 0.286525i
\(235\) 0 0
\(236\) 0.280467i 0.0182568i
\(237\) −0.687432 + 6.71488i −0.0446535 + 0.436178i
\(238\) −1.60356 1.60356i −0.103944 0.103944i
\(239\) −5.15325 −0.333336 −0.166668 0.986013i \(-0.553301\pi\)
−0.166668 + 0.986013i \(0.553301\pi\)
\(240\) 0 0
\(241\) −14.9174 −0.960914 −0.480457 0.877018i \(-0.659529\pi\)
−0.480457 + 0.877018i \(0.659529\pi\)
\(242\) 1.34094 + 1.34094i 0.0861992 + 0.0861992i
\(243\) −13.6040 7.61123i −0.872698 0.488261i
\(244\) 8.31238i 0.532146i
\(245\) 0 0
\(246\) −7.63153 + 6.21409i −0.486569 + 0.396196i
\(247\) −11.2702 + 11.2702i −0.717103 + 0.717103i
\(248\) −6.89616 + 6.89616i −0.437907 + 0.437907i
\(249\) 7.66953 6.24504i 0.486037 0.395763i
\(250\) 0 0
\(251\) 4.30303i 0.271605i 0.990736 + 0.135802i \(0.0433613\pi\)
−0.990736 + 0.135802i \(0.956639\pi\)
\(252\) −2.89810 4.41035i −0.182563 0.277826i
\(253\) 6.80704 + 6.80704i 0.427955 + 0.427955i
\(254\) 8.42409 0.528575
\(255\) 0 0
\(256\) 0.0180230 0.00112644
\(257\) −5.82885 5.82885i −0.363594 0.363594i 0.501540 0.865134i \(-0.332767\pi\)
−0.865134 + 0.501540i \(0.832767\pi\)
\(258\) −0.0929433 + 0.907876i −0.00578640 + 0.0565219i
\(259\) 3.03046i 0.188304i
\(260\) 0 0
\(261\) −8.42916 1.74414i −0.521752 0.107960i
\(262\) −3.45068 + 3.45068i −0.213184 + 0.213184i
\(263\) −0.0624909 + 0.0624909i −0.00385335 + 0.00385335i −0.709031 0.705177i \(-0.750867\pi\)
0.705177 + 0.709031i \(0.250867\pi\)
\(264\) −5.39022 6.61974i −0.331745 0.407417i
\(265\) 0 0
\(266\) 2.57345i 0.157788i
\(267\) −6.80819 0.696985i −0.416654 0.0426548i
\(268\) −9.51951 9.51951i −0.581497 0.581497i
\(269\) 29.6699 1.80901 0.904504 0.426465i \(-0.140241\pi\)
0.904504 + 0.426465i \(0.140241\pi\)
\(270\) 0 0
\(271\) 22.6377 1.37514 0.687571 0.726117i \(-0.258677\pi\)
0.687571 + 0.726117i \(0.258677\pi\)
\(272\) 8.53611 + 8.53611i 0.517578 + 0.517578i
\(273\) 5.23767 + 0.536204i 0.316998 + 0.0324525i
\(274\) 9.48463i 0.572988i
\(275\) 0 0
\(276\) 6.93281 + 8.51419i 0.417306 + 0.512494i
\(277\) −4.21136 + 4.21136i −0.253036 + 0.253036i −0.822214 0.569178i \(-0.807262\pi\)
0.569178 + 0.822214i \(0.307262\pi\)
\(278\) −5.82817 + 5.82817i −0.349551 + 0.349551i
\(279\) −15.5290 3.21323i −0.929698 0.192371i
\(280\) 0 0
\(281\) 22.0093i 1.31297i −0.754341 0.656483i \(-0.772043\pi\)
0.754341 0.656483i \(-0.227957\pi\)
\(282\) 0.937914 9.16160i 0.0558520 0.545565i
\(283\) −9.59899 9.59899i −0.570601 0.570601i 0.361695 0.932296i \(-0.382198\pi\)
−0.932296 + 0.361695i \(0.882198\pi\)
\(284\) 23.9027 1.41837
\(285\) 0 0
\(286\) 3.98553 0.235670
\(287\) −8.18605 8.18605i −0.483207 0.483207i
\(288\) −8.19181 12.4664i −0.482707 0.734587i
\(289\) 4.34908i 0.255828i
\(290\) 0 0
\(291\) −3.54963 + 2.89034i −0.208083 + 0.169435i
\(292\) −7.32643 + 7.32643i −0.428747 + 0.428747i
\(293\) 3.56359 3.56359i 0.208187 0.208187i −0.595309 0.803497i \(-0.702970\pi\)
0.803497 + 0.595309i \(0.202970\pi\)
\(294\) −0.659208 + 0.536770i −0.0384458 + 0.0313051i
\(295\) 0 0
\(296\) 5.59120i 0.324982i
\(297\) 4.18231 13.2358i 0.242683 0.768018i
\(298\) −3.23196 3.23196i −0.187222 0.187222i
\(299\) −10.9542 −0.633499
\(300\) 0 0
\(301\) −1.07354 −0.0618778
\(302\) 7.07531 + 7.07531i 0.407139 + 0.407139i
\(303\) −0.663452 + 6.48063i −0.0381143 + 0.372303i
\(304\) 13.6990i 0.785692i
\(305\) 0 0
\(306\) 1.37853 6.66222i 0.0788053 0.380854i
\(307\) −10.4746 + 10.4746i −0.597814 + 0.597814i −0.939730 0.341916i \(-0.888924\pi\)
0.341916 + 0.939730i \(0.388924\pi\)
\(308\) 3.32285 3.32285i 0.189337 0.189337i
\(309\) −13.6987 16.8234i −0.779291 0.957048i
\(310\) 0 0
\(311\) 20.4344i 1.15873i −0.815068 0.579365i \(-0.803301\pi\)
0.815068 0.579365i \(-0.196699\pi\)
\(312\) 9.66350 + 0.989296i 0.547088 + 0.0560078i
\(313\) 16.4829 + 16.4829i 0.931670 + 0.931670i 0.997810 0.0661408i \(-0.0210686\pi\)
−0.0661408 + 0.997810i \(0.521069\pi\)
\(314\) −4.39291 −0.247906
\(315\) 0 0
\(316\) −6.85542 −0.385647
\(317\) −22.9540 22.9540i −1.28922 1.28922i −0.935259 0.353965i \(-0.884833\pi\)
−0.353965 0.935259i \(-0.615167\pi\)
\(318\) 5.30509 + 0.543105i 0.297494 + 0.0304558i
\(319\) 7.66479i 0.429146i
\(320\) 0 0
\(321\) −1.09873 1.34936i −0.0613254 0.0753137i
\(322\) 1.25065 1.25065i 0.0696961 0.0696961i
\(323\) −17.1308 + 17.1308i −0.953185 + 0.953185i
\(324\) 6.28283 14.5319i 0.349046 0.807330i
\(325\) 0 0
\(326\) 4.48142i 0.248203i
\(327\) −3.35406 + 32.7626i −0.185480 + 1.81178i
\(328\) −15.1033 15.1033i −0.833938 0.833938i
\(329\) 10.8334 0.597262
\(330\) 0 0
\(331\) −2.21461 −0.121726 −0.0608631 0.998146i \(-0.519385\pi\)
−0.0608631 + 0.998146i \(0.519385\pi\)
\(332\) 7.10290 + 7.10290i 0.389822 + 0.389822i
\(333\) 7.59782 4.99263i 0.416358 0.273595i
\(334\) 1.09672i 0.0600099i
\(335\) 0 0
\(336\) 3.50910 2.85734i 0.191437 0.155881i
\(337\) −10.8541 + 10.8541i −0.591263 + 0.591263i −0.937972 0.346710i \(-0.887299\pi\)
0.346710 + 0.937972i \(0.387299\pi\)
\(338\) 1.30484 1.30484i 0.0709741 0.0709741i
\(339\) −10.8103 + 8.80247i −0.587136 + 0.478085i
\(340\) 0 0
\(341\) 14.1208i 0.764685i
\(342\) 6.45202 4.23971i 0.348885 0.229257i
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) −1.98068 −0.106791
\(345\) 0 0
\(346\) −1.17977 −0.0634251
\(347\) −5.06341 5.06341i −0.271818 0.271818i 0.558014 0.829832i \(-0.311564\pi\)
−0.829832 + 0.558014i \(0.811564\pi\)
\(348\) 0.890323 8.69672i 0.0477263 0.466193i
\(349\) 7.42733i 0.397576i 0.980043 + 0.198788i \(0.0637005\pi\)
−0.980043 + 0.198788i \(0.936300\pi\)
\(350\) 0 0
\(351\) 7.28463 + 14.0150i 0.388825 + 0.748066i
\(352\) 9.39243 9.39243i 0.500618 0.500618i
\(353\) 9.09032 9.09032i 0.483829 0.483829i −0.422523 0.906352i \(-0.638856\pi\)
0.906352 + 0.422523i \(0.138856\pi\)
\(354\) −0.0855810 0.105102i −0.00454858 0.00558611i
\(355\) 0 0
\(356\) 6.95068i 0.368385i
\(357\) 7.96134 + 0.815038i 0.421359 + 0.0431364i
\(358\) 2.93045 + 2.93045i 0.154879 + 0.154879i
\(359\) −25.2640 −1.33338 −0.666692 0.745333i \(-0.732290\pi\)
−0.666692 + 0.745333i \(0.732290\pi\)
\(360\) 0 0
\(361\) −8.49208 −0.446951
\(362\) 1.91394 + 1.91394i 0.100594 + 0.100594i
\(363\) −6.65750 0.681558i −0.349428 0.0357725i
\(364\) 5.34729i 0.280274i
\(365\) 0 0
\(366\) −2.53642 3.11498i −0.132581 0.162823i
\(367\) −1.61189 + 1.61189i −0.0841399 + 0.0841399i −0.747924 0.663784i \(-0.768949\pi\)
0.663784 + 0.747924i \(0.268949\pi\)
\(368\) −6.65749 + 6.65749i −0.347045 + 0.347045i
\(369\) 7.03727 34.0100i 0.366346 1.77049i
\(370\) 0 0
\(371\) 6.27313i 0.325685i
\(372\) 1.64024 16.0219i 0.0850424 0.830699i
\(373\) −13.0455 13.0455i −0.675469 0.675469i 0.283502 0.958972i \(-0.408504\pi\)
−0.958972 + 0.283502i \(0.908504\pi\)
\(374\) 6.05808 0.313256
\(375\) 0 0
\(376\) 19.9875 1.03078
\(377\) 6.16727 + 6.16727i 0.317630 + 0.317630i
\(378\) −2.43180 0.768413i −0.125078 0.0395229i
\(379\) 19.0635i 0.979228i 0.871939 + 0.489614i \(0.162862\pi\)
−0.871939 + 0.489614i \(0.837138\pi\)
\(380\) 0 0
\(381\) −23.0527 + 18.7710i −1.18103 + 0.961670i
\(382\) −0.194185 + 0.194185i −0.00993537 + 0.00993537i
\(383\) 17.7244 17.7244i 0.905673 0.905673i −0.0902463 0.995919i \(-0.528765\pi\)
0.995919 + 0.0902463i \(0.0287654\pi\)
\(384\) 15.1925 12.3708i 0.775291 0.631293i
\(385\) 0 0
\(386\) 4.89484i 0.249141i
\(387\) −1.76864 2.69153i −0.0899050 0.136818i
\(388\) −3.28738 3.28738i −0.166892 0.166892i
\(389\) −18.3513 −0.930446 −0.465223 0.885193i \(-0.654026\pi\)
−0.465223 + 0.885193i \(0.654026\pi\)
\(390\) 0 0
\(391\) −16.6506 −0.842056
\(392\) −1.30461 1.30461i −0.0658928 0.0658928i
\(393\) 1.75387 17.1319i 0.0884710 0.864189i
\(394\) 7.04550i 0.354947i
\(395\) 0 0
\(396\) 13.8052 + 2.85655i 0.693739 + 0.143547i
\(397\) 10.9124 10.9124i 0.547679 0.547679i −0.378090 0.925769i \(-0.623419\pi\)
0.925769 + 0.378090i \(0.123419\pi\)
\(398\) 4.05178 4.05178i 0.203097 0.203097i
\(399\) 5.73430 + 7.04230i 0.287074 + 0.352556i
\(400\) 0 0
\(401\) 34.4243i 1.71907i 0.511079 + 0.859534i \(0.329246\pi\)
−0.511079 + 0.859534i \(0.670754\pi\)
\(402\) −6.47210 0.662578i −0.322799 0.0330464i
\(403\) 11.3619 + 11.3619i 0.565979 + 0.565979i
\(404\) −6.61627 −0.329172
\(405\) 0 0
\(406\) −1.40824 −0.0698900
\(407\) 5.72437 + 5.72437i 0.283746 + 0.283746i
\(408\) 14.6887 + 1.50375i 0.727198 + 0.0744465i
\(409\) 7.59254i 0.375427i 0.982224 + 0.187714i \(0.0601077\pi\)
−0.982224 + 0.187714i \(0.939892\pi\)
\(410\) 0 0
\(411\) −21.1342 25.9549i −1.04247 1.28026i
\(412\) 15.5804 15.5804i 0.767593 0.767593i
\(413\) 0.112739 0.112739i 0.00554752 0.00554752i
\(414\) 5.19600 + 1.07514i 0.255369 + 0.0528404i
\(415\) 0 0
\(416\) 15.1147i 0.741061i
\(417\) 2.96227 28.9356i 0.145063 1.41698i
\(418\) 4.86109 + 4.86109i 0.237764 + 0.237764i
\(419\) −6.20644 −0.303204 −0.151602 0.988442i \(-0.548443\pi\)
−0.151602 + 0.988442i \(0.548443\pi\)
\(420\) 0 0
\(421\) 25.1339 1.22495 0.612474 0.790490i \(-0.290174\pi\)
0.612474 + 0.790490i \(0.290174\pi\)
\(422\) −0.269696 0.269696i −0.0131286 0.0131286i
\(423\) 17.8478 + 27.1608i 0.867788 + 1.32061i
\(424\) 11.5739i 0.562079i
\(425\) 0 0
\(426\) 8.95731 7.29363i 0.433983 0.353377i
\(427\) 3.34132 3.34132i 0.161698 0.161698i
\(428\) 1.24966 1.24966i 0.0604048 0.0604048i
\(429\) −10.9065 + 8.88079i −0.526571 + 0.428769i
\(430\) 0 0
\(431\) 8.43225i 0.406167i −0.979161 0.203084i \(-0.934904\pi\)
0.979161 0.203084i \(-0.0650963\pi\)
\(432\) 12.9450 + 4.09043i 0.622815 + 0.196801i
\(433\) 18.8277 + 18.8277i 0.904802 + 0.904802i 0.995847 0.0910444i \(-0.0290205\pi\)
−0.0910444 + 0.995847i \(0.529021\pi\)
\(434\) −2.59440 −0.124535
\(435\) 0 0
\(436\) −33.4483 −1.60188
\(437\) −13.3607 13.3607i −0.639128 0.639128i
\(438\) −0.509935 + 4.98108i −0.0243657 + 0.238005i
\(439\) 4.88270i 0.233039i 0.993188 + 0.116519i \(0.0371737\pi\)
−0.993188 + 0.116519i \(0.962826\pi\)
\(440\) 0 0
\(441\) 0.607876 2.93777i 0.0289465 0.139894i
\(442\) −4.87447 + 4.87447i −0.231855 + 0.231855i
\(443\) −23.8960 + 23.8960i −1.13534 + 1.13534i −0.146059 + 0.989276i \(0.546659\pi\)
−0.989276 + 0.146059i \(0.953341\pi\)
\(444\) 5.83013 + 7.15998i 0.276686 + 0.339798i
\(445\) 0 0
\(446\) 2.31700i 0.109713i
\(447\) 16.0460 + 1.64270i 0.758948 + 0.0776970i
\(448\) 1.96922 + 1.96922i 0.0930368 + 0.0930368i
\(449\) −23.6736 −1.11723 −0.558613 0.829428i \(-0.688666\pi\)
−0.558613 + 0.829428i \(0.688666\pi\)
\(450\) 0 0
\(451\) 30.9259 1.45625
\(452\) −10.0116 10.0116i −0.470908 0.470908i
\(453\) −35.1274 3.59615i −1.65043 0.168962i
\(454\) 0.168200i 0.00789404i
\(455\) 0 0
\(456\) 10.5798 + 12.9930i 0.495444 + 0.608455i
\(457\) −10.2580 + 10.2580i −0.479849 + 0.479849i −0.905083 0.425234i \(-0.860192\pi\)
0.425234 + 0.905083i \(0.360192\pi\)
\(458\) −4.67803 + 4.67803i −0.218590 + 0.218590i
\(459\) 11.0728 + 21.3030i 0.516832 + 0.994341i
\(460\) 0 0
\(461\) 23.3153i 1.08590i 0.839764 + 0.542951i \(0.182693\pi\)
−0.839764 + 0.542951i \(0.817307\pi\)
\(462\) 0.231278 2.25913i 0.0107600 0.105104i
\(463\) 17.0563 + 17.0563i 0.792672 + 0.792672i 0.981928 0.189256i \(-0.0606077\pi\)
−0.189256 + 0.981928i \(0.560608\pi\)
\(464\) 7.49639 0.348011
\(465\) 0 0
\(466\) 0.827796 0.0383469
\(467\) 8.00621 + 8.00621i 0.370483 + 0.370483i 0.867653 0.497170i \(-0.165627\pi\)
−0.497170 + 0.867653i \(0.665627\pi\)
\(468\) −13.4065 + 8.80957i −0.619714 + 0.407223i
\(469\) 7.65310i 0.353387i
\(470\) 0 0
\(471\) 12.0213 9.78854i 0.553913 0.451032i
\(472\) 0.208003 0.208003i 0.00957413 0.00957413i
\(473\) 2.02786 2.02786i 0.0932409 0.0932409i
\(474\) −2.56900 + 2.09185i −0.117998 + 0.0960817i
\(475\) 0 0
\(476\) 8.12797i 0.372545i
\(477\) −15.7277 + 10.3349i −0.720121 + 0.473201i
\(478\) −1.78845 1.78845i −0.0818019 0.0818019i
\(479\) −20.1199 −0.919304 −0.459652 0.888099i \(-0.652026\pi\)
−0.459652 + 0.888099i \(0.652026\pi\)
\(480\) 0 0
\(481\) −9.21192 −0.420027
\(482\) −5.17713 5.17713i −0.235812 0.235812i
\(483\) −0.635665 + 6.20921i −0.0289238 + 0.282529i
\(484\) 6.79683i 0.308947i
\(485\) 0 0
\(486\) −2.07982 7.36283i −0.0943425 0.333985i
\(487\) −7.77959 + 7.77959i −0.352527 + 0.352527i −0.861049 0.508522i \(-0.830192\pi\)
0.508522 + 0.861049i \(0.330192\pi\)
\(488\) 6.16474 6.16474i 0.279064 0.279064i
\(489\) −9.98576 12.2635i −0.451572 0.554576i
\(490\) 0 0
\(491\) 2.29546i 0.103593i −0.998658 0.0517963i \(-0.983505\pi\)
0.998658 0.0517963i \(-0.0164947\pi\)
\(492\) 35.0896 + 3.59228i 1.58196 + 0.161952i
\(493\) 9.37435 + 9.37435i 0.422199 + 0.422199i
\(494\) −7.82270 −0.351960
\(495\) 0 0
\(496\) 13.8106 0.620113
\(497\) 9.60816 + 9.60816i 0.430985 + 0.430985i
\(498\) 4.82910 + 0.494377i 0.216397 + 0.0221536i
\(499\) 12.3264i 0.551806i 0.961185 + 0.275903i \(0.0889769\pi\)
−0.961185 + 0.275903i \(0.911023\pi\)
\(500\) 0 0
\(501\) −2.44378 3.00120i −0.109180 0.134084i
\(502\) −1.49338 + 1.49338i −0.0666529 + 0.0666529i
\(503\) −4.62523 + 4.62523i −0.206229 + 0.206229i −0.802662 0.596434i \(-0.796584\pi\)
0.596434 + 0.802662i \(0.296584\pi\)
\(504\) 1.12153 5.42018i 0.0499570 0.241434i
\(505\) 0 0
\(506\) 4.72482i 0.210044i
\(507\) −0.663208 + 6.47826i −0.0294541 + 0.287709i
\(508\) −21.3496 21.3496i −0.947234 0.947234i
\(509\) 13.6161 0.603525 0.301762 0.953383i \(-0.402425\pi\)
0.301762 + 0.953383i \(0.402425\pi\)
\(510\) 0 0
\(511\) −5.89000 −0.260558
\(512\) 16.0031 + 16.0031i 0.707245 + 0.707245i
\(513\) −8.20894 + 25.9788i −0.362433 + 1.14699i
\(514\) 4.04585i 0.178455i
\(515\) 0 0
\(516\) 2.53642 2.06532i 0.111660 0.0909207i
\(517\) −20.4636 + 20.4636i −0.899987 + 0.899987i
\(518\) 1.05173 1.05173i 0.0462105 0.0462105i
\(519\) 3.22848 2.62884i 0.141715 0.115393i
\(520\) 0 0
\(521\) 18.3870i 0.805550i −0.915299 0.402775i \(-0.868046\pi\)
0.915299 0.402775i \(-0.131954\pi\)
\(522\) −2.32006 3.53068i −0.101546 0.154534i
\(523\) 8.91043 + 8.91043i 0.389626 + 0.389626i 0.874554 0.484928i \(-0.161154\pi\)
−0.484928 + 0.874554i \(0.661154\pi\)
\(524\) 17.4905 0.764074
\(525\) 0 0
\(526\) −0.0433754 −0.00189126
\(527\) 17.2703 + 17.2703i 0.752308 + 0.752308i
\(528\) −1.23114 + 12.0258i −0.0535785 + 0.523358i
\(529\) 10.0139i 0.435385i
\(530\) 0 0
\(531\) 0.468389 + 0.0969179i 0.0203264 + 0.00420588i
\(532\) −6.52201 + 6.52201i −0.282765 + 0.282765i
\(533\) −24.8837 + 24.8837i −1.07783 + 1.07783i
\(534\) −2.12091 2.60470i −0.0917810 0.112716i
\(535\) 0 0
\(536\) 14.1200i 0.609889i
\(537\) −14.5491 1.48945i −0.627838 0.0642746i
\(538\) 10.2971 + 10.2971i 0.443938 + 0.443938i
\(539\) 2.67137 0.115064
\(540\) 0 0
\(541\) 27.8258 1.19632 0.598162 0.801375i \(-0.295898\pi\)
0.598162 + 0.801375i \(0.295898\pi\)
\(542\) 7.85649 + 7.85649i 0.337465 + 0.337465i
\(543\) −9.50229 0.972793i −0.407783 0.0417465i
\(544\) 22.9746i 0.985030i
\(545\) 0 0
\(546\) 1.63166 + 2.00384i 0.0698286 + 0.0857566i
\(547\) 13.2773 13.2773i 0.567695 0.567695i −0.363787 0.931482i \(-0.618517\pi\)
0.931482 + 0.363787i \(0.118517\pi\)
\(548\) 24.0373 24.0373i 1.02682 1.02682i
\(549\) 13.8820 + 2.87242i 0.592468 + 0.122592i
\(550\) 0 0
\(551\) 15.0442i 0.640906i
\(552\) −1.17280 + 11.4560i −0.0499178 + 0.487600i
\(553\) −2.75566 2.75566i −0.117183 0.117183i
\(554\) −2.92314 −0.124192
\(555\) 0 0
\(556\) 29.5412 1.25283
\(557\) 10.4002 + 10.4002i 0.440672 + 0.440672i 0.892238 0.451566i \(-0.149134\pi\)
−0.451566 + 0.892238i \(0.649134\pi\)
\(558\) −4.27424 6.50456i −0.180943 0.275360i
\(559\) 3.26332i 0.138024i
\(560\) 0 0
\(561\) −16.5781 + 13.4990i −0.699927 + 0.569926i
\(562\) 7.63842 7.63842i 0.322207 0.322207i
\(563\) −10.1623 + 10.1623i −0.428291 + 0.428291i −0.888046 0.459755i \(-0.847937\pi\)
0.459755 + 0.888046i \(0.347937\pi\)
\(564\) −25.5957 + 20.8417i −1.07777 + 0.877592i
\(565\) 0 0
\(566\) 6.66273i 0.280055i
\(567\) 8.36689 3.31589i 0.351376 0.139254i
\(568\) 17.7271 + 17.7271i 0.743811 + 0.743811i
\(569\) 39.8275 1.66965 0.834827 0.550512i \(-0.185567\pi\)
0.834827 + 0.550512i \(0.185567\pi\)
\(570\) 0 0
\(571\) −43.8314 −1.83429 −0.917143 0.398558i \(-0.869511\pi\)
−0.917143 + 0.398558i \(0.869511\pi\)
\(572\) −10.1007 10.1007i −0.422332 0.422332i
\(573\) 0.0986978 0.964086i 0.00412316 0.0402753i
\(574\) 5.68199i 0.237162i
\(575\) 0 0
\(576\) −1.69287 + 8.18138i −0.0705363 + 0.340891i
\(577\) 27.8182 27.8182i 1.15809 1.15809i 0.173202 0.984886i \(-0.444589\pi\)
0.984886 0.173202i \(-0.0554114\pi\)
\(578\) −1.50936 + 1.50936i −0.0627812 + 0.0627812i
\(579\) 10.9070 + 13.3948i 0.453278 + 0.556670i
\(580\) 0 0
\(581\) 5.71029i 0.236903i
\(582\) −2.23502 0.228809i −0.0926445 0.00948443i
\(583\) −11.8496 11.8496i −0.490759 0.490759i
\(584\) −10.8670 −0.449681
\(585\) 0 0
\(586\) 2.47352 0.102180
\(587\) −27.2778 27.2778i −1.12588 1.12588i −0.990841 0.135034i \(-0.956886\pi\)
−0.135034 0.990841i \(-0.543114\pi\)
\(588\) 3.03102 + 0.310299i 0.124997 + 0.0127965i
\(589\) 27.7160i 1.14202i
\(590\) 0 0
\(591\) 15.6992 + 19.2802i 0.645779 + 0.793081i
\(592\) −5.59860 + 5.59860i −0.230101 + 0.230101i
\(593\) 1.21000 1.21000i 0.0496886 0.0496886i −0.681826 0.731515i \(-0.738814\pi\)
0.731515 + 0.681826i \(0.238814\pi\)
\(594\) 6.04501 3.14204i 0.248030 0.128919i
\(595\) 0 0
\(596\) 16.3818i 0.671025i
\(597\) −2.05939 + 20.1162i −0.0842850 + 0.823301i
\(598\) −3.80170 3.80170i −0.155463 0.155463i
\(599\) −15.6005 −0.637421 −0.318710 0.947852i \(-0.603250\pi\)
−0.318710 + 0.947852i \(0.603250\pi\)
\(600\) 0 0
\(601\) 14.2954 0.583122 0.291561 0.956552i \(-0.405825\pi\)
0.291561 + 0.956552i \(0.405825\pi\)
\(602\) −0.372576 0.372576i −0.0151851 0.0151851i
\(603\) 19.1875 12.6083i 0.781374 0.513452i
\(604\) 35.8626i 1.45923i
\(605\) 0 0
\(606\) −2.47938 + 2.01887i −0.100718 + 0.0820111i
\(607\) 26.8784 26.8784i 1.09096 1.09096i 0.0955365 0.995426i \(-0.469543\pi\)
0.995426 0.0955365i \(-0.0304567\pi\)
\(608\) −18.4352 + 18.4352i −0.747646 + 0.747646i
\(609\) 3.85369 3.13793i 0.156160 0.127155i
\(610\) 0 0
\(611\) 32.9310i 1.33224i
\(612\) −20.3780 + 13.3907i −0.823733 + 0.541287i
\(613\) −2.77744 2.77744i −0.112180 0.112180i 0.648789 0.760969i \(-0.275276\pi\)
−0.760969 + 0.648789i \(0.775276\pi\)
\(614\) −7.27046 −0.293412
\(615\) 0 0
\(616\) 4.92867 0.198582
\(617\) 3.21465 + 3.21465i 0.129417 + 0.129417i 0.768848 0.639431i \(-0.220830\pi\)
−0.639431 + 0.768848i \(0.720830\pi\)
\(618\) 1.08443 10.5928i 0.0436222 0.426104i
\(619\) 48.7011i 1.95746i −0.205146 0.978731i \(-0.565767\pi\)
0.205146 0.978731i \(-0.434233\pi\)
\(620\) 0 0
\(621\) −16.6147 + 8.63587i −0.666724 + 0.346545i
\(622\) 7.09184 7.09184i 0.284357 0.284357i
\(623\) 2.79396 2.79396i 0.111938 0.111938i
\(624\) −8.68567 10.6669i −0.347705 0.427017i
\(625\) 0 0
\(626\) 11.4409i 0.457271i
\(627\) −24.1343 2.47073i −0.963830 0.0986716i
\(628\) 11.1332 + 11.1332i 0.444261 + 0.444261i
\(629\) −14.0023 −0.558307
\(630\) 0 0
\(631\) 15.0588 0.599480 0.299740 0.954021i \(-0.403100\pi\)
0.299740 + 0.954021i \(0.403100\pi\)
\(632\) −5.08420 5.08420i −0.202239 0.202239i
\(633\) 1.33898 + 0.137078i 0.0532197 + 0.00544834i
\(634\) 15.9325i 0.632761i
\(635\) 0 0
\(636\) −12.0685 14.8213i −0.478547 0.587704i
\(637\) −2.14945 + 2.14945i −0.0851641 + 0.0851641i
\(638\) 2.66009 2.66009i 0.105314 0.105314i
\(639\) −8.25981 + 39.9184i −0.326753 + 1.57915i
\(640\) 0 0
\(641\) 45.9720i 1.81578i −0.419204 0.907892i \(-0.637691\pi\)
0.419204 0.907892i \(-0.362309\pi\)
\(642\) 0.0869793 0.849619i 0.00343280 0.0335318i
\(643\) 5.91991 + 5.91991i 0.233458 + 0.233458i 0.814135 0.580676i \(-0.197212\pi\)
−0.580676 + 0.814135i \(0.697212\pi\)
\(644\) −6.33917 −0.249798
\(645\) 0 0
\(646\) −11.8906 −0.467831
\(647\) 11.1176 + 11.1176i 0.437079 + 0.437079i 0.891028 0.453949i \(-0.149985\pi\)
−0.453949 + 0.891028i \(0.649985\pi\)
\(648\) 15.4369 6.11781i 0.606419 0.240330i
\(649\) 0.425915i 0.0167186i
\(650\) 0 0
\(651\) 7.09965 5.78100i 0.278257 0.226575i
\(652\) 11.3575 11.3575i 0.444793 0.444793i
\(653\) 30.6500 30.6500i 1.19943 1.19943i 0.225088 0.974339i \(-0.427733\pi\)
0.974339 0.225088i \(-0.0722669\pi\)
\(654\) −12.5344 + 10.2063i −0.490135 + 0.399100i
\(655\) 0 0
\(656\) 30.2465i 1.18093i
\(657\) −9.70367 14.7671i −0.378576 0.576120i
\(658\) 3.75976 + 3.75976i 0.146571 + 0.146571i
\(659\) 50.9397 1.98433 0.992165 0.124933i \(-0.0398714\pi\)
0.992165 + 0.124933i \(0.0398714\pi\)
\(660\) 0 0
\(661\) −20.5394 −0.798889 −0.399445 0.916757i \(-0.630797\pi\)
−0.399445 + 0.916757i \(0.630797\pi\)
\(662\) −0.768589 0.768589i −0.0298721 0.0298721i
\(663\) 2.47753 24.2007i 0.0962194 0.939877i
\(664\) 10.5355i 0.408856i
\(665\) 0 0
\(666\) 4.36956 + 0.904139i 0.169317 + 0.0350347i
\(667\) −7.31125 + 7.31125i −0.283093 + 0.283093i
\(668\) 2.77947 2.77947i 0.107541 0.107541i
\(669\) −5.16288 6.34054i −0.199609 0.245139i
\(670\) 0 0
\(671\) 12.6231i 0.487310i
\(672\) 8.56753 + 0.877097i 0.330500 + 0.0338347i
\(673\) −25.4635 25.4635i −0.981544 0.981544i 0.0182887 0.999833i \(-0.494178\pi\)
−0.999833 + 0.0182887i \(0.994178\pi\)
\(674\) −7.53394 −0.290196
\(675\) 0 0
\(676\) −6.61384 −0.254379
\(677\) −8.67613 8.67613i −0.333451 0.333451i 0.520445 0.853895i \(-0.325766\pi\)
−0.853895 + 0.520445i \(0.825766\pi\)
\(678\) −6.80669 0.696831i −0.261409 0.0267616i
\(679\) 2.64285i 0.101423i
\(680\) 0 0
\(681\) −0.374794 0.460284i −0.0143621 0.0176381i
\(682\) 4.90068 4.90068i 0.187657 0.187657i
\(683\) 24.0010 24.0010i 0.918373 0.918373i −0.0785378 0.996911i \(-0.525025\pi\)
0.996911 + 0.0785378i \(0.0250251\pi\)
\(684\) −27.0965 5.60675i −1.03606 0.214379i
\(685\) 0 0
\(686\) 0.490808i 0.0187391i
\(687\) 2.37769 23.2254i 0.0907145 0.886104i
\(688\) 1.98330 + 1.98330i 0.0756127 + 0.0756127i
\(689\) 19.0689 0.726467
\(690\) 0 0
\(691\) −32.5680 −1.23894 −0.619472 0.785019i \(-0.712653\pi\)
−0.619472 + 0.785019i \(0.712653\pi\)
\(692\) 2.98996 + 2.98996i 0.113661 + 0.113661i
\(693\) 4.40103 + 6.69752i 0.167181 + 0.254418i
\(694\) 3.51455i 0.133410i
\(695\) 0 0
\(696\) 7.11007 5.78948i 0.269506 0.219450i
\(697\) −37.8237 + 37.8237i −1.43267 + 1.43267i
\(698\) −2.57768 + 2.57768i −0.0975667 + 0.0975667i
\(699\) −2.26528 + 1.84454i −0.0856808 + 0.0697670i
\(700\) 0 0
\(701\) 2.43359i 0.0919155i 0.998943 + 0.0459577i \(0.0146340\pi\)
−0.998943 + 0.0459577i \(0.985366\pi\)
\(702\) −2.33580 + 7.39211i −0.0881592 + 0.278997i
\(703\) −11.2356 11.2356i −0.423760 0.423760i
\(704\) −7.43948 −0.280386
\(705\) 0 0
\(706\) 6.30965 0.237467
\(707\) −2.65954 2.65954i −0.100022 0.100022i
\(708\) −0.0494732 + 0.483257i −0.00185932 + 0.0181619i
\(709\) 12.3477i 0.463728i −0.972748 0.231864i \(-0.925518\pi\)
0.972748 0.231864i \(-0.0744825\pi\)
\(710\) 0 0
\(711\) 2.36895 11.4488i 0.0888427 0.429363i
\(712\) 5.15485 5.15485i 0.193186 0.193186i
\(713\) −13.4695 + 13.4695i −0.504436 + 0.504436i
\(714\) 2.48015 + 3.04587i 0.0928173 + 0.113989i
\(715\) 0 0
\(716\) 14.8536i 0.555103i
\(717\) 8.87927 + 0.909011i 0.331603 + 0.0339476i
\(718\) −8.76797 8.76797i −0.327218 0.327218i
\(719\) 24.2165 0.903125 0.451562 0.892240i \(-0.350867\pi\)
0.451562 + 0.892240i \(0.350867\pi\)
\(720\) 0 0
\(721\) 12.5257 0.466482
\(722\) −2.94721 2.94721i −0.109684 0.109684i
\(723\) 25.7033 + 2.63137i 0.955917 + 0.0978616i
\(724\) 9.70117i 0.360541i
\(725\) 0 0
\(726\) −2.07397 2.54704i −0.0769723 0.0945297i
\(727\) 25.8923 25.8923i 0.960293 0.960293i −0.0389483 0.999241i \(-0.512401\pi\)
0.999241 + 0.0389483i \(0.0124008\pi\)
\(728\) −3.96573 + 3.96573i −0.146980 + 0.146980i
\(729\) 22.0977 + 15.5142i 0.818435 + 0.574599i
\(730\) 0 0
\(731\) 4.96030i 0.183463i
\(732\) −1.46627 + 14.3226i −0.0541949 + 0.529379i
\(733\) −13.4535 13.4535i −0.496918 0.496918i 0.413559 0.910477i \(-0.364285\pi\)
−0.910477 + 0.413559i \(0.864285\pi\)
\(734\) −1.11882 −0.0412965
\(735\) 0 0
\(736\) −17.9184 −0.660481
\(737\) 14.4563 + 14.4563i 0.532503 + 0.532503i
\(738\) 14.2456 9.36099i 0.524388 0.344583i
\(739\) 1.96813i 0.0723987i −0.999345 0.0361994i \(-0.988475\pi\)
0.999345 0.0361994i \(-0.0115251\pi\)
\(740\) 0 0
\(741\) 21.4070 17.4310i 0.786406 0.640343i
\(742\) −2.17711 + 2.17711i −0.0799243 + 0.0799243i
\(743\) 4.54680 4.54680i 0.166806 0.166806i −0.618768 0.785574i \(-0.712368\pi\)
0.785574 + 0.618768i \(0.212368\pi\)
\(744\) 13.0989 10.6659i 0.480227 0.391032i
\(745\) 0 0
\(746\) 9.05496i 0.331526i
\(747\) −14.3166 + 9.40761i −0.523815 + 0.344206i
\(748\) −15.3533 15.3533i −0.561371 0.561371i
\(749\) 1.00465 0.0367092
\(750\) 0 0
\(751\) −0.491718 −0.0179430 −0.00897152 0.999960i \(-0.502856\pi\)
−0.00897152 + 0.999960i \(0.502856\pi\)
\(752\) −20.0140 20.0140i −0.729835 0.729835i
\(753\) 0.759037 7.41432i 0.0276609 0.270193i
\(754\) 4.28075i 0.155896i
\(755\) 0 0
\(756\) 4.21559 + 8.11044i 0.153320 + 0.294974i
\(757\) −3.50957 + 3.50957i −0.127558 + 0.127558i −0.768003 0.640446i \(-0.778750\pi\)
0.640446 + 0.768003i \(0.278750\pi\)
\(758\) −6.61607 + 6.61607i −0.240306 + 0.240306i
\(759\) −10.5281 12.9296i −0.382146 0.469314i
\(760\) 0 0
\(761\) 26.9220i 0.975922i −0.872865 0.487961i \(-0.837741\pi\)
0.872865 0.487961i \(-0.162259\pi\)
\(762\) −14.5151 1.48598i −0.525826 0.0538312i
\(763\) −13.4452 13.4452i −0.486749 0.486749i
\(764\) 0.984264 0.0356094
\(765\) 0 0
\(766\) 12.3026 0.444512
\(767\) −0.342701 0.342701i −0.0123742 0.0123742i
\(768\) −0.0310544 0.00317918i −0.00112058 0.000114719i
\(769\) 31.3935i 1.13208i −0.824378 0.566040i \(-0.808475\pi\)
0.824378 0.566040i \(-0.191525\pi\)
\(770\) 0 0
\(771\) 9.01519 + 11.0716i 0.324674 + 0.398733i
\(772\) −12.4052 + 12.4052i −0.446473 + 0.446473i
\(773\) −13.3925 + 13.3925i −0.481693 + 0.481693i −0.905672 0.423979i \(-0.860633\pi\)
0.423979 + 0.905672i \(0.360633\pi\)
\(774\) 0.320291 1.54792i 0.0115126 0.0556387i
\(775\) 0 0
\(776\) 4.87606i 0.175040i
\(777\) −0.534561 + 5.22162i −0.0191773 + 0.187325i