Properties

Label 525.2.j.b.218.5
Level 525
Weight 2
Character 525.218
Analytic conductor 4.192
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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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 218.5
Character \(\chi\) \(=\) 525.218
Dual form 525.2.j.b.407.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.347054 - 0.347054i) q^{2} +(-0.176396 - 1.72305i) q^{3} -1.75911i q^{4} +(-0.536770 + 0.659208i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.30461 + 1.30461i) q^{8} +(-2.93777 + 0.607876i) q^{9} +O(q^{10})\) \(q+(-0.347054 - 0.347054i) q^{2} +(-0.176396 - 1.72305i) 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} +(-3.03102 + 0.310299i) q^{12} +(-2.14945 - 2.14945i) q^{13} -0.490808 q^{14} -2.61267 q^{16} +(3.26719 + 3.26719i) q^{17} +(1.23053 + 0.808598i) 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} +(1.56561 + 4.95468i) q^{27} +(-1.24388 - 1.24388i) q^{28} +2.86924 q^{29} -5.28599 q^{31} +(3.51596 + 3.51596i) q^{32} +(-4.60289 + 0.471218i) 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} +(0.0865765 + 0.845684i) q^{42} +(-0.759108 - 0.759108i) q^{43} -4.69922 q^{44} +1.76869 q^{46} +(-7.66034 - 7.66034i) q^{47} +(0.460865 + 4.50176i) 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} +(-9.03442 + 0.924894i) q^{57} +(-0.995779 - 0.995779i) q^{58} -0.159437 q^{59} +4.72534 q^{61} +(1.83452 + 1.83452i) q^{62} +(-1.64748 + 2.50715i) 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} +(3.03961 - 4.62569i) q^{72} +(-4.16486 - 4.16486i) q^{73} -1.48737 q^{74} -9.22351 q^{76} +(-1.88894 - 1.88894i) q^{77} +(2.57069 - 0.263173i) 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} +(-0.506122 - 4.94383i) q^{87} +(3.48510 + 3.48510i) q^{88} -3.95125 q^{89} -3.03977 q^{91} +(4.48247 + 4.48247i) q^{92} +(0.932426 + 9.10800i) 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 0.573677 0.819081i \(-0.305516\pi\)
−0.819081 + 0.573677i \(0.805516\pi\)
\(3\) −0.176396 1.72305i −0.101842 0.994801i
\(4\) 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 \(-0.868064\pi\)
0.915322 0.402724i \(-0.131936\pi\)
\(12\) −3.03102 + 0.310299i −0.874981 + 0.0895757i
\(13\) −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 0.981886 0.189475i \(-0.0606787\pi\)
−0.189475 + 0.981886i \(0.560679\pi\)
\(18\) 1.23053 + 0.808598i 0.290038 + 0.190588i
\(19\) 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 −0.920967 0.389641i \(-0.872599\pi\)
0.389641 + 0.920967i \(0.372599\pi\)
\(24\) 2.47803 + 2.01778i 0.505826 + 0.411877i
\(25\) 0 0
\(26\) 1.49195i 0.292595i
\(27\) 1.56561 + 4.95468i 0.301301 + 0.953529i
\(28\) −1.24388 1.24388i −0.235071 0.235071i
\(29\) 2.86924 0.532804 0.266402 0.963862i \(-0.414165\pi\)
0.266402 + 0.963862i \(0.414165\pi\)
\(30\) 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
\(33\) −4.60289 + 0.471218i −0.801260 + 0.0820286i
\(34\) 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 \(0.359381\pi\)
−0.427537 + 0.903998i \(0.640619\pi\)
\(42\) 0.0865765 + 0.845684i 0.0133590 + 0.130492i
\(43\) −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 \(-0.960027\pi\)
−0.125250 0.992125i \(-0.539973\pi\)
\(48\) 0.460865 + 4.50176i 0.0665201 + 0.649773i
\(49\) 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 −0.333463 0.942763i \(-0.608217\pi\)
0.942763 + 0.333463i \(0.108217\pi\)
\(54\) 1.17619 2.26289i 0.160059 0.307940i
\(55\) 0 0
\(56\) 1.84500i 0.246548i
\(57\) −9.03442 + 0.924894i −1.19664 + 0.122505i
\(58\) −0.995779 0.995779i −0.130752 0.130752i
\(59\) −0.159437 −0.0207569 −0.0103785 0.999946i \(-0.503304\pi\)
−0.0103785 + 0.999946i \(0.503304\pi\)
\(60\) 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
\(63\) −1.64748 + 2.50715i −0.207563 + 0.315871i
\(64\) 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 \(-0.701467\pi\)
0.591508 0.806299i \(-0.298533\pi\)
\(72\) 3.03961 4.62569i 0.358221 0.545143i
\(73\) −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
\(78\) 2.57069 0.263173i 0.291073 0.0297985i
\(79\) 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 −0.449883 0.893087i \(-0.648534\pi\)
0.893087 + 0.449883i \(0.148534\pi\)
\(84\) −1.92384 + 2.36267i −0.209908 + 0.257789i
\(85\) 0 0
\(86\) 0.526902i 0.0568173i
\(87\) −0.506122 4.94383i −0.0542619 0.530034i
\(88\) 3.48510 + 3.48510i 0.371513 + 0.371513i
\(89\) −3.95125 −0.418832 −0.209416 0.977827i \(-0.567156\pi\)
−0.209416 + 0.977827i \(0.567156\pi\)
\(90\) 0 0
\(91\) −3.03977 −0.318655
\(92\) 4.48247 + 4.48247i 0.467330 + 0.467330i
\(93\) 0.932426 + 9.10800i 0.0966881 + 0.944455i
\(94\) 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 \(0.0599167\pi\)
−0.982336 + 0.187124i \(0.940083\pi\)
\(102\) −3.90749 + 0.400027i −0.386899 + 0.0396086i
\(103\) 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 0.671934 0.740611i \(-0.265464\pi\)
−0.740611 + 0.671934i \(0.765464\pi\)
\(108\) 8.71582 2.75407i 0.838680 0.265011i
\(109\) 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 −0.922173 0.386779i \(-0.873588\pi\)
0.386779 + 0.922173i \(0.373588\pi\)
\(114\) 3.45642 + 2.81444i 0.323723 + 0.263597i
\(115\) 0 0
\(116\) 5.04730i 0.468630i
\(117\) 7.62117 + 5.00798i 0.704577 + 0.462988i
\(118\) 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
\(123\) 19.9474 2.04210i 1.79859 0.184130i
\(124\) 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 \(-0.856977\pi\)
0.900743 0.434353i \(-0.143023\pi\)
\(132\) 0.828923 + 8.09697i 0.0721485 + 0.704751i
\(133\) −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 \(-0.940891\pi\)
−0.184630 0.982808i \(-0.559109\pi\)
\(138\) −0.311989 3.04753i −0.0265583 0.259423i
\(139\) 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
\(147\) −1.72305 + 0.176396i −0.142114 + 0.0145489i
\(148\) −3.76952 3.76952i −0.309853 0.309853i
\(149\) 9.31256 0.762915 0.381458 0.924386i \(-0.375422\pi\)
0.381458 + 0.924386i \(0.375422\pi\)
\(150\) 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
\(153\) −11.5843 7.61221i −0.936535 0.615410i
\(154\) 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
\(162\) −4.10654 1.62746i −0.322640 0.127866i
\(163\) 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 0.643325 0.765593i \(-0.277554\pi\)
−0.765593 + 0.643325i \(0.777554\pi\)
\(168\) 3.17902 0.325450i 0.245267 0.0251090i
\(169\) 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 −0.639536 0.768761i \(-0.720873\pi\)
0.768761 + 0.639536i \(0.220873\pi\)
\(174\) −1.54012 + 1.89142i −0.116756 + 0.143388i
\(175\) 0 0
\(176\) 6.97941i 0.526093i
\(177\) 0.0281240 + 0.274717i 0.00211393 + 0.0206490i
\(178\) 1.37130 + 1.37130i 0.102783 + 0.102783i
\(179\) −8.44380 −0.631119 −0.315560 0.948906i \(-0.602192\pi\)
−0.315560 + 0.948906i \(0.602192\pi\)
\(180\) 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
\(183\) −0.833531 8.14198i −0.0616164 0.601872i
\(184\) 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 \(-0.993556\pi\)
0.999795 0.0202429i \(-0.00644395\pi\)
\(192\) 4.79850 0.491244i 0.346302 0.0354525i
\(193\) −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 0.969254 0.246064i \(-0.0791372\pi\)
−0.246064 + 0.969254i \(0.579137\pi\)
\(198\) 2.16006 3.28719i 0.153509 0.233611i
\(199\) 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
\(207\) 5.93692 9.03483i 0.412644 0.627964i
\(208\) 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
\(213\) −23.4127 + 2.39687i −1.60421 + 0.164231i
\(214\) 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
\(222\) 0.262367 + 2.56281i 0.0176089 + 0.172005i
\(223\) 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 0.699019 0.715103i \(-0.253620\pi\)
−0.715103 + 0.699019i \(0.753620\pi\)
\(228\) 1.62699 + 15.8925i 0.107750 + 1.05251i
\(229\) 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 −0.745092 0.666962i \(-0.767594\pi\)
0.666962 + 0.745092i \(0.267594\pi\)
\(234\) −0.906918 4.38299i −0.0592871 0.286525i
\(235\) 0 0
\(236\) 0.280467i 0.0182568i
\(237\) −6.71488 + 0.687432i −0.436178 + 0.0446535i
\(238\) −1.60356 1.60356i −0.103944 0.103944i
\(239\) 5.15325 0.333336 0.166668 0.986013i \(-0.446699\pi\)
0.166668 + 0.986013i \(0.446699\pi\)
\(240\) 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
\(243\) −7.61123 13.6040i −0.488261 0.872698i
\(244\) 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 \(-0.956639\pi\)
0.990736 0.135802i \(-0.0433613\pi\)
\(252\) 4.41035 + 2.89810i 0.277826 + 0.182563i
\(253\) 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 0.865134 0.501540i \(-0.167233\pi\)
−0.501540 + 0.865134i \(0.667233\pi\)
\(258\) 0.907876 0.0929433i 0.0565219 0.00578640i
\(259\) 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 −0.705177 0.709031i \(-0.749133\pi\)
0.709031 + 0.705177i \(0.249133\pi\)
\(264\) 5.39022 6.61974i 0.331745 0.407417i
\(265\) 0 0
\(266\) 2.57345i 0.157788i
\(267\) 0.696985 + 6.80819i 0.0426548 + 0.416654i
\(268\) −9.51951 9.51951i −0.581497 0.581497i
\(269\) −29.6699 −1.80901 −0.904504 0.426465i \(-0.859759\pi\)
−0.904504 + 0.426465i \(0.859759\pi\)
\(270\) 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
\(273\) 0.536204 + 5.23767i 0.0324525 + 0.316998i
\(274\) 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 \(0.227957\pi\)
−0.754341 + 0.656483i \(0.772043\pi\)
\(282\) 9.16160 0.937914i 0.545565 0.0558520i
\(283\) −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
\(288\) −12.4664 8.19181i −0.734587 0.482707i
\(289\) 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 −0.803497 0.595309i \(-0.797030\pi\)
0.595309 + 0.803497i \(0.297030\pi\)
\(294\) 0.659208 + 0.536770i 0.0384458 + 0.0313051i
\(295\) 0 0
\(296\) 5.59120i 0.324982i
\(297\) 13.2358 4.18231i 0.768018 0.242683i
\(298\) −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
\(303\) 6.48063 0.663452i 0.372303 0.0381143i
\(304\) 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 \(0.196699\pi\)
−0.815068 + 0.579365i \(0.803301\pi\)
\(312\) −0.989296 9.66350i −0.0560078 0.547088i
\(313\) 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 \(0.115167\pi\)
0.353965 + 0.935259i \(0.384833\pi\)
\(318\) 0.543105 + 5.30509i 0.0304558 + 0.297494i
\(319\) 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
\(327\) −32.7626 + 3.35406i −1.81178 + 0.185480i
\(328\) −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
\(333\) −4.99263 + 7.59782i −0.273595 + 0.416358i
\(334\) 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
\(342\) 4.23971 6.45202i 0.229257 0.348885i
\(343\) −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 0.829832 0.558014i \(-0.188436\pi\)
−0.558014 + 0.829832i \(0.688436\pi\)
\(348\) −8.69672 + 0.890323i −0.466193 + 0.0477263i
\(349\) 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 −0.906352 0.422523i \(-0.861144\pi\)
0.422523 + 0.906352i \(0.361144\pi\)
\(354\) 0.0855810 0.105102i 0.00454858 0.00558611i
\(355\) 0 0
\(356\) 6.95068i 0.368385i
\(357\) −0.815038 7.96134i −0.0431364 0.421359i
\(358\) 2.93045 + 2.93045i 0.154879 + 0.154879i
\(359\) 25.2640 1.33338 0.666692 0.745333i \(-0.267710\pi\)
0.666692 + 0.745333i \(0.267710\pi\)
\(360\) 0 0
\(361\) −8.49208 −0.446951
\(362\) −1.91394 1.91394i −0.100594 0.100594i
\(363\) −0.681558 6.65750i −0.0357725 0.349428i
\(364\) 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
\(372\) 16.0219 1.64024i 0.830699 0.0850424i
\(373\) −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
\(378\) −0.768413 2.43180i −0.0395229 0.125078i
\(379\) 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 −0.995919 0.0902463i \(-0.971235\pi\)
0.0902463 + 0.995919i \(0.471235\pi\)
\(384\) −15.1925 12.3708i −0.775291 0.631293i
\(385\) 0 0
\(386\) 4.89484i 0.249141i
\(387\) 2.69153 + 1.76864i 0.136818 + 0.0899050i
\(388\) −3.28738 3.28738i −0.166892 0.166892i
\(389\) 18.3513 0.930446 0.465223 0.885193i \(-0.345974\pi\)
0.465223 + 0.885193i \(0.345974\pi\)
\(390\) 0 0
\(391\) −16.6506 −0.842056
\(392\) 1.30461 + 1.30461i 0.0658928 + 0.0658928i
\(393\) −17.1319 + 1.75387i −0.864189 + 0.0884710i
\(394\) 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 \(-0.670754\pi\)
0.511079 0.859534i \(-0.329246\pi\)
\(402\) 0.662578 + 6.47210i 0.0330464 + 0.322799i
\(403\) 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
\(408\) 1.50375 + 14.6887i 0.0744465 + 0.727198i
\(409\) 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
\(417\) 28.9356 2.96227i 1.41698 0.145063i
\(418\) 4.86109 + 4.86109i 0.237764 + 0.237764i
\(419\) 6.20644 0.303204 0.151602 0.988442i \(-0.451557\pi\)
0.151602 + 0.988442i \(0.451557\pi\)
\(420\) 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
\(423\) 27.1608 + 17.8478i 1.32061 + 0.867788i
\(424\) 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 \(0.0650963\pi\)
−0.979161 + 0.203084i \(0.934904\pi\)
\(432\) −4.09043 12.9450i −0.196801 0.622815i
\(433\) 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
\(438\) 4.98108 0.509935i 0.238005 0.0243657i
\(439\) 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 \(-0.453341\pi\)
0.989276 0.146059i \(-0.0466590\pi\)
\(444\) −5.83013 + 7.15998i −0.276686 + 0.339798i
\(445\) 0 0
\(446\) 2.31700i 0.109713i
\(447\) −1.64270 16.0460i −0.0776970 0.758948i
\(448\) 1.96922 + 1.96922i 0.0930368 + 0.0930368i
\(449\) 23.6736 1.11723 0.558613 0.829428i \(-0.311334\pi\)
0.558613 + 0.829428i \(0.311334\pi\)
\(450\) 0 0
\(451\) 30.9259 1.45625
\(452\) 10.0116 + 10.0116i 0.470908 + 0.470908i
\(453\) −3.59615 35.1274i −0.168962 1.65043i
\(454\) 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 \(-0.817307\pi\)
0.839764 0.542951i \(-0.182693\pi\)
\(462\) 2.25913 0.231278i 0.105104 0.0107600i
\(463\) 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 0.497170 0.867653i \(-0.334373\pi\)
−0.867653 + 0.497170i \(0.834373\pi\)
\(468\) 8.80957 13.4065i 0.407223 0.619714i
\(469\) 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
\(477\) −10.3349 + 15.7277i −0.473201 + 0.720121i
\(478\) −1.78845 1.78845i −0.0818019 0.0818019i
\(479\) 20.1199 0.919304 0.459652 0.888099i \(-0.347974\pi\)
0.459652 + 0.888099i \(0.347974\pi\)
\(480\) 0 0
\(481\) −9.21192 −0.420027
\(482\) 5.17713 + 5.17713i 0.235812 + 0.235812i
\(483\) 6.20921 0.635665i 0.282529 0.0289238i
\(484\) 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 \(0.0164947\pi\)
−0.998658 + 0.0517963i \(0.983505\pi\)
\(492\) −3.59228 35.0896i −0.161952 1.58196i
\(493\) 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
\(498\) 0.494377 + 4.82910i 0.0221536 + 0.216397i
\(499\) 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 −0.596434 0.802662i \(-0.703416\pi\)
0.802662 + 0.596434i \(0.203416\pi\)
\(504\) −1.12153 5.42018i −0.0499570 0.241434i
\(505\) 0 0
\(506\) 4.72482i 0.210044i
\(507\) −6.47826 + 0.663208i −0.287709 + 0.0294541i
\(508\) −21.3496 21.3496i −0.947234 0.947234i
\(509\) −13.6161 −0.603525 −0.301762 0.953383i \(-0.597575\pi\)
−0.301762 + 0.953383i \(0.597575\pi\)
\(510\) 0 0
\(511\) −5.89000 −0.260558
\(512\) −16.0031 16.0031i −0.707245 0.707245i
\(513\) 25.9788 8.20894i 1.14699 0.362433i
\(514\) 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 \(0.131954\pi\)
−0.915299 + 0.402775i \(0.868046\pi\)
\(522\) 3.53068 + 2.32006i 0.154534 + 0.101546i
\(523\) 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
\(528\) 12.0258 1.23114i 0.523358 0.0535785i
\(529\) 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
\(537\) 1.48945 + 14.5491i 0.0642746 + 0.627838i
\(538\) 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
\(543\) −0.972793 9.50229i −0.0417465 0.407783i
\(544\) 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
\(552\) −11.4560 + 1.17280i −0.487600 + 0.0499178i
\(553\) −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 0.451566 0.892238i \(-0.350866\pi\)
−0.892238 + 0.451566i \(0.850866\pi\)
\(558\) −6.50456 4.27424i −0.275360 0.180943i
\(559\) 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 −0.459755 0.888046i \(-0.652063\pi\)
0.888046 + 0.459755i \(0.152063\pi\)
\(564\) 25.5957 + 20.8417i 1.07777 + 0.877592i
\(565\) 0 0
\(566\) 6.66273i 0.280055i
\(567\) 3.31589 8.36689i 0.139254 0.351376i
\(568\) 17.7271 + 17.7271i 0.743811 + 0.743811i
\(569\) −39.8275 −1.66965 −0.834827 0.550512i \(-0.814433\pi\)
−0.834827 + 0.550512i \(0.814433\pi\)
\(570\) 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
\(573\) −0.964086 + 0.0986978i −0.0402753 + 0.00412316i
\(574\) 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
\(582\) 0.228809 + 2.23502i 0.00948443 + 0.0926445i
\(583\) −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 \(0.0431144\pi\)
0.135034 + 0.990841i \(0.456886\pi\)
\(588\) 0.310299 + 3.03102i 0.0127965 + 0.124997i
\(589\) 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 −0.731515 0.681826i \(-0.761186\pi\)
0.681826 + 0.731515i \(0.261186\pi\)
\(594\) −6.04501 3.14204i −0.248030 0.128919i
\(595\) 0 0
\(596\) 16.3818i 0.671025i
\(597\) −20.1162 + 2.05939i −0.823301 + 0.0842850i
\(598\) −3.80170 3.80170i −0.155463 0.155463i
\(599\) 15.6005 0.637421 0.318710 0.947852i \(-0.396750\pi\)
0.318710 + 0.947852i \(0.396750\pi\)
\(600\) 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
\(603\) −12.6083 + 19.1875i −0.513452 + 0.781374i
\(604\) 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
\(612\) −13.3907 + 20.3780i −0.541287 + 0.823733i
\(613\) −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 0.639431 0.768848i \(-0.279170\pi\)
−0.768848 + 0.639431i \(0.779170\pi\)
\(618\) −10.5928 + 1.08443i −0.426104 + 0.0436222i
\(619\) 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
\(627\) 2.47073 + 24.1343i 0.0986716 + 0.963830i
\(628\) 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
\(633\) 0.137078 + 1.33898i 0.00544834 + 0.0532197i
\(634\) 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 \(0.362309\pi\)
−0.419204 + 0.907892i \(0.637691\pi\)
\(642\) 0.849619 0.0869793i 0.0335318 0.00343280i
\(643\) 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 0.453949 0.891028i \(-0.350015\pi\)
−0.891028 + 0.453949i \(0.850015\pi\)
\(648\) −6.11781 + 15.4369i −0.240330 + 0.606419i
\(649\) 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 \(0.572267\pi\)
−0.974339 + 0.225088i \(0.927733\pi\)
\(654\) 12.5344 + 10.2063i 0.490135 + 0.399100i
\(655\) 0 0
\(656\) 30.2465i 1.18093i
\(657\) 14.7671 + 9.70367i 0.576120 + 0.378576i
\(658\) 3.75976 + 3.75976i 0.146571 + 0.146571i
\(659\) −50.9397 −1.98433 −0.992165 0.124933i \(-0.960129\pi\)
−0.992165 + 0.124933i \(0.960129\pi\)
\(660\) 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
\(663\) −24.2007 + 2.47753i −0.939877 + 0.0962194i
\(664\) 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
\(672\) −0.877097 8.56753i −0.0338347 0.330500i
\(673\) −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 0.853895 0.520445i \(-0.174234\pi\)
−0.520445 + 0.853895i \(0.674234\pi\)
\(678\) −0.696831 6.80669i −0.0267616 0.261409i
\(679\) 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 −0.996911 0.0785378i \(-0.974975\pi\)
0.0785378 + 0.996911i \(0.474975\pi\)
\(684\) 27.0965 5.60675i 1.03606 0.214379i
\(685\) 0 0
\(686\) 0.490808i 0.0187391i
\(687\) 23.2254 2.37769i 0.886104 0.0907145i
\(688\) 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
\(693\) 6.69752 + 4.40103i 0.254418 + 0.167181i
\(694\) 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 \(-0.985366\pi\)
0.998943 0.0459577i \(-0.0146340\pi\)
\(702\) −7.39211 + 2.33580i −0.278997 + 0.0881592i
\(703\) −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
\(708\) 0.483257 0.0494732i 0.0181619 0.00185932i
\(709\) 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
\(717\) −0.909011 8.87927i −0.0339476 0.331603i
\(718\) −8.76797 8.76797i −0.327218 0.327218i
\(719\) −24.2165 −0.903125 −0.451562 0.892240i \(-0.649133\pi\)
−0.451562 + 0.892240i \(0.649133\pi\)
\(720\) 0 0
\(721\) 12.5257 0.466482
\(722\) 2.94721 + 2.94721i 0.109684 + 0.109684i
\(723\) 2.63137 + 25.7033i 0.0978616 + 0.955917i
\(724\) 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
\(732\) −14.3226 + 1.46627i −0.529379 + 0.0541949i
\(733\) −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
\(738\) −9.36099 + 14.2456i −0.344583 + 0.524388i
\(739\) 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 −0.785574 0.618768i \(-0.787632\pi\)
0.618768 + 0.785574i \(0.287632\pi\)
\(744\) −13.0989 10.6659i −0.480227 0.391032i
\(745\) 0 0
\(746\) 9.05496i 0.331526i
\(747\) −9.40761 + 14.3166i −0.344206 + 0.523815i
\(748\) −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
\(753\) −7.41432 + 0.759037i −0.270193 + 0.0276609i
\(754\) 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 \(0.162259\pi\)
−0.872865 + 0.487961i \(0.837741\pi\)
\(762\) 1.48598 + 14.5151i 0.0538312 + 0.525826i
\(763\) −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
\(768\) −0.00317918 0.0310544i −0.000114719 0.00112058i
\(769\) 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 −0.423979 0.905672i \(-0.639367\pi\)
0.905672 + 0.423979i \(0.139367\pi\)
\(774\) −0.320291 1.54792i −0.0115126 0.0556387i
\(775\) 0 0
\(776\) 4.87606i 0.175040i
\(777\) −5.22162 + 0.534561i −0.187325 + 0.0191773i
\(778\) −6.36887