Properties

Label 450.2.p.e.443.1
Level 450
Weight 2
Character 450.443
Analytic conductor 3.593
Analytic rank 0
Dimension 8
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.p (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 443.1
Root \(0.258819 + 0.965926i\) of \(x^{8} - x^{4} + 1\)
Character \(\chi\) \(=\) 450.443
Dual form 450.2.p.e.257.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.965926 + 0.258819i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.866025 - 1.50000i) q^{6} +(-0.328169 - 1.22474i) q^{7} +(-0.707107 + 0.707107i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-0.965926 + 0.258819i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.866025 - 1.50000i) q^{6} +(-0.328169 - 1.22474i) q^{7} +(-0.707107 + 0.707107i) q^{8} -3.00000i q^{9} +(3.00000 + 1.73205i) q^{11} +(-0.448288 + 1.67303i) q^{12} +(0.328169 - 1.22474i) q^{13} +(0.633975 + 1.09808i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.776457 + 2.89778i) q^{18} -7.19615i q^{19} +(1.90192 + 1.09808i) q^{21} +(-3.34607 - 0.896575i) q^{22} +(7.91688 + 2.12132i) q^{23} -1.73205i q^{24} +1.26795i q^{26} +(3.67423 + 3.67423i) q^{27} +(-0.896575 - 0.896575i) q^{28} +(-3.63397 + 6.29423i) q^{29} +(5.09808 + 8.83013i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-5.79555 + 1.55291i) q^{33} +(-1.50000 - 2.59808i) q^{36} +(1.55291 - 1.55291i) q^{37} +(1.86250 + 6.95095i) q^{38} +(1.09808 + 1.90192i) q^{39} +(-1.50000 + 0.866025i) q^{41} +(-2.12132 - 0.568406i) q^{42} +(6.24384 - 1.67303i) q^{43} +3.46410 q^{44} -8.19615 q^{46} +(5.79555 - 1.55291i) q^{47} +(0.448288 + 1.67303i) q^{48} +(4.66987 - 2.69615i) q^{49} +(-0.328169 - 1.22474i) q^{52} +(1.55291 - 1.55291i) q^{53} +(-4.50000 - 2.59808i) q^{54} +(1.09808 + 0.633975i) q^{56} +(8.81345 + 8.81345i) q^{57} +(1.88108 - 7.02030i) q^{58} +(6.23205 + 10.7942i) q^{59} +(2.00000 - 3.46410i) q^{61} +(-7.20977 - 7.20977i) q^{62} +(-3.67423 + 0.984508i) q^{63} -1.00000i q^{64} +(5.19615 - 3.00000i) q^{66} +(-12.0394 - 3.22595i) q^{67} +(-12.2942 + 7.09808i) q^{69} -10.7321i q^{71} +(2.12132 + 2.12132i) q^{72} +(-3.67423 - 3.67423i) q^{73} +(-1.09808 + 1.90192i) q^{74} +(-3.59808 - 6.23205i) q^{76} +(1.13681 - 4.24264i) q^{77} +(-1.55291 - 1.55291i) q^{78} +(8.66025 + 5.00000i) q^{79} -9.00000 q^{81} +(1.22474 - 1.22474i) q^{82} +(-1.76097 - 6.57201i) q^{83} +2.19615 q^{84} +(-5.59808 + 3.23205i) q^{86} +(-3.25813 - 12.1595i) q^{87} +(-3.34607 + 0.896575i) q^{88} -8.66025 q^{89} -1.60770 q^{91} +(7.91688 - 2.12132i) q^{92} +(-17.0585 - 4.57081i) q^{93} +(-5.19615 + 3.00000i) q^{94} +(-0.866025 - 1.50000i) q^{96} +(3.79435 + 14.1607i) q^{97} +(-3.81294 + 3.81294i) q^{98} +(5.19615 - 9.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 24q^{11} + 12q^{14} + 4q^{16} + 36q^{21} - 36q^{29} + 20q^{31} - 12q^{36} - 12q^{39} - 12q^{41} - 24q^{46} + 72q^{49} - 36q^{54} - 12q^{56} + 36q^{59} + 16q^{61} - 36q^{69} + 12q^{74} - 8q^{76} - 72q^{81} - 24q^{84} - 24q^{86} - 96q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 + 0.258819i −0.683013 + 0.183013i
\(3\) −1.22474 + 1.22474i −0.707107 + 0.707107i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) 0 0
\(6\) 0.866025 1.50000i 0.353553 0.612372i
\(7\) −0.328169 1.22474i −0.124036 0.462910i 0.875767 0.482734i \(-0.160356\pi\)
−0.999803 + 0.0198238i \(0.993689\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 3.00000i 1.00000i
\(10\) 0 0
\(11\) 3.00000 + 1.73205i 0.904534 + 0.522233i 0.878668 0.477432i \(-0.158432\pi\)
0.0258656 + 0.999665i \(0.491766\pi\)
\(12\) −0.448288 + 1.67303i −0.129410 + 0.482963i
\(13\) 0.328169 1.22474i 0.0910178 0.339683i −0.905368 0.424628i \(-0.860405\pi\)
0.996386 + 0.0849451i \(0.0270715\pi\)
\(14\) 0.633975 + 1.09808i 0.169437 + 0.293473i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) 0.776457 + 2.89778i 0.183013 + 0.683013i
\(19\) 7.19615i 1.65091i −0.564467 0.825455i \(-0.690918\pi\)
0.564467 0.825455i \(-0.309082\pi\)
\(20\) 0 0
\(21\) 1.90192 + 1.09808i 0.415034 + 0.239620i
\(22\) −3.34607 0.896575i −0.713384 0.191151i
\(23\) 7.91688 + 2.12132i 1.65078 + 0.442326i 0.959832 0.280576i \(-0.0905255\pi\)
0.690951 + 0.722902i \(0.257192\pi\)
\(24\) 1.73205i 0.353553i
\(25\) 0 0
\(26\) 1.26795i 0.248665i
\(27\) 3.67423 + 3.67423i 0.707107 + 0.707107i
\(28\) −0.896575 0.896575i −0.169437 0.169437i
\(29\) −3.63397 + 6.29423i −0.674812 + 1.16881i 0.301712 + 0.953399i \(0.402442\pi\)
−0.976524 + 0.215410i \(0.930891\pi\)
\(30\) 0 0
\(31\) 5.09808 + 8.83013i 0.915642 + 1.58594i 0.805959 + 0.591971i \(0.201650\pi\)
0.109682 + 0.993967i \(0.465017\pi\)
\(32\) −0.258819 + 0.965926i −0.0457532 + 0.170753i
\(33\) −5.79555 + 1.55291i −1.00888 + 0.270328i
\(34\) 0 0
\(35\) 0 0
\(36\) −1.50000 2.59808i −0.250000 0.433013i
\(37\) 1.55291 1.55291i 0.255298 0.255298i −0.567841 0.823138i \(-0.692221\pi\)
0.823138 + 0.567841i \(0.192221\pi\)
\(38\) 1.86250 + 6.95095i 0.302138 + 1.12759i
\(39\) 1.09808 + 1.90192i 0.175833 + 0.304552i
\(40\) 0 0
\(41\) −1.50000 + 0.866025i −0.234261 + 0.135250i −0.612536 0.790443i \(-0.709851\pi\)
0.378275 + 0.925693i \(0.376517\pi\)
\(42\) −2.12132 0.568406i −0.327327 0.0877070i
\(43\) 6.24384 1.67303i 0.952177 0.255135i 0.250891 0.968015i \(-0.419276\pi\)
0.701286 + 0.712880i \(0.252610\pi\)
\(44\) 3.46410 0.522233
\(45\) 0 0
\(46\) −8.19615 −1.20846
\(47\) 5.79555 1.55291i 0.845369 0.226516i 0.189961 0.981792i \(-0.439164\pi\)
0.655407 + 0.755276i \(0.272497\pi\)
\(48\) 0.448288 + 1.67303i 0.0647048 + 0.241481i
\(49\) 4.66987 2.69615i 0.667125 0.385165i
\(50\) 0 0
\(51\) 0 0
\(52\) −0.328169 1.22474i −0.0455089 0.169842i
\(53\) 1.55291 1.55291i 0.213309 0.213309i −0.592362 0.805672i \(-0.701805\pi\)
0.805672 + 0.592362i \(0.201805\pi\)
\(54\) −4.50000 2.59808i −0.612372 0.353553i
\(55\) 0 0
\(56\) 1.09808 + 0.633975i 0.146737 + 0.0847184i
\(57\) 8.81345 + 8.81345i 1.16737 + 1.16737i
\(58\) 1.88108 7.02030i 0.246998 0.921811i
\(59\) 6.23205 + 10.7942i 0.811344 + 1.40529i 0.911924 + 0.410360i \(0.134597\pi\)
−0.100580 + 0.994929i \(0.532070\pi\)
\(60\) 0 0
\(61\) 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i \(-0.750904\pi\)
0.965187 + 0.261562i \(0.0842377\pi\)
\(62\) −7.20977 7.20977i −0.915642 0.915642i
\(63\) −3.67423 + 0.984508i −0.462910 + 0.124036i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 5.19615 3.00000i 0.639602 0.369274i
\(67\) −12.0394 3.22595i −1.47085 0.394112i −0.567625 0.823287i \(-0.692138\pi\)
−0.903221 + 0.429175i \(0.858804\pi\)
\(68\) 0 0
\(69\) −12.2942 + 7.09808i −1.48005 + 0.854508i
\(70\) 0 0
\(71\) 10.7321i 1.27366i −0.771004 0.636830i \(-0.780245\pi\)
0.771004 0.636830i \(-0.219755\pi\)
\(72\) 2.12132 + 2.12132i 0.250000 + 0.250000i
\(73\) −3.67423 3.67423i −0.430037 0.430037i 0.458604 0.888641i \(-0.348350\pi\)
−0.888641 + 0.458604i \(0.848350\pi\)
\(74\) −1.09808 + 1.90192i −0.127649 + 0.221094i
\(75\) 0 0
\(76\) −3.59808 6.23205i −0.412728 0.714865i
\(77\) 1.13681 4.24264i 0.129552 0.483494i
\(78\) −1.55291 1.55291i −0.175833 0.175833i
\(79\) 8.66025 + 5.00000i 0.974355 + 0.562544i 0.900561 0.434730i \(-0.143156\pi\)
0.0737937 + 0.997274i \(0.476489\pi\)
\(80\) 0 0
\(81\) −9.00000 −1.00000
\(82\) 1.22474 1.22474i 0.135250 0.135250i
\(83\) −1.76097 6.57201i −0.193291 0.721372i −0.992703 0.120588i \(-0.961522\pi\)
0.799412 0.600784i \(-0.205145\pi\)
\(84\) 2.19615 0.239620
\(85\) 0 0
\(86\) −5.59808 + 3.23205i −0.603656 + 0.348521i
\(87\) −3.25813 12.1595i −0.349308 1.30364i
\(88\) −3.34607 + 0.896575i −0.356692 + 0.0955753i
\(89\) −8.66025 −0.917985 −0.458993 0.888440i \(-0.651790\pi\)
−0.458993 + 0.888440i \(0.651790\pi\)
\(90\) 0 0
\(91\) −1.60770 −0.168532
\(92\) 7.91688 2.12132i 0.825391 0.221163i
\(93\) −17.0585 4.57081i −1.76888 0.473971i
\(94\) −5.19615 + 3.00000i −0.535942 + 0.309426i
\(95\) 0 0
\(96\) −0.866025 1.50000i −0.0883883 0.153093i
\(97\) 3.79435 + 14.1607i 0.385258 + 1.43780i 0.837760 + 0.546039i \(0.183865\pi\)
−0.452501 + 0.891764i \(0.649468\pi\)
\(98\) −3.81294 + 3.81294i −0.385165 + 0.385165i
\(99\) 5.19615 9.00000i 0.522233 0.904534i
\(100\) 0 0
\(101\) −9.29423 5.36603i −0.924810 0.533939i −0.0396438 0.999214i \(-0.512622\pi\)
−0.885167 + 0.465274i \(0.845956\pi\)
\(102\) 0 0
\(103\) 2.68973 10.0382i 0.265027 0.989093i −0.697207 0.716869i \(-0.745574\pi\)
0.962234 0.272223i \(-0.0877590\pi\)
\(104\) 0.633975 + 1.09808i 0.0621663 + 0.107675i
\(105\) 0 0
\(106\) −1.09808 + 1.90192i −0.106655 + 0.184731i
\(107\) −0.568406 0.568406i −0.0549499 0.0549499i 0.679098 0.734048i \(-0.262371\pi\)
−0.734048 + 0.679098i \(0.762371\pi\)
\(108\) 5.01910 + 1.34486i 0.482963 + 0.129410i
\(109\) 12.1962i 1.16818i −0.811689 0.584090i \(-0.801452\pi\)
0.811689 0.584090i \(-0.198548\pi\)
\(110\) 0 0
\(111\) 3.80385i 0.361045i
\(112\) −1.22474 0.328169i −0.115728 0.0310091i
\(113\) 7.14042 + 1.91327i 0.671714 + 0.179985i 0.578527 0.815663i \(-0.303628\pi\)
0.0931872 + 0.995649i \(0.470294\pi\)
\(114\) −10.7942 6.23205i −1.01097 0.583685i
\(115\) 0 0
\(116\) 7.26795i 0.674812i
\(117\) −3.67423 0.984508i −0.339683 0.0910178i
\(118\) −8.81345 8.81345i −0.811344 0.811344i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.500000 + 0.866025i 0.0454545 + 0.0787296i
\(122\) −1.03528 + 3.86370i −0.0937295 + 0.349803i
\(123\) 0.776457 2.89778i 0.0700108 0.261284i
\(124\) 8.83013 + 5.09808i 0.792969 + 0.457821i
\(125\) 0 0
\(126\) 3.29423 1.90192i 0.293473 0.169437i
\(127\) 1.55291 1.55291i 0.137799 0.137799i −0.634843 0.772641i \(-0.718935\pi\)
0.772641 + 0.634843i \(0.218935\pi\)
\(128\) 0.258819 + 0.965926i 0.0228766 + 0.0853766i
\(129\) −5.59808 + 9.69615i −0.492883 + 0.853699i
\(130\) 0 0
\(131\) −6.00000 + 3.46410i −0.524222 + 0.302660i −0.738661 0.674078i \(-0.764541\pi\)
0.214438 + 0.976738i \(0.431208\pi\)
\(132\) −4.24264 + 4.24264i −0.369274 + 0.369274i
\(133\) −8.81345 + 2.36156i −0.764223 + 0.204773i
\(134\) 12.4641 1.07673
\(135\) 0 0
\(136\) 0 0
\(137\) 7.14042 1.91327i 0.610047 0.163462i 0.0594480 0.998231i \(-0.481066\pi\)
0.550599 + 0.834770i \(0.314399\pi\)
\(138\) 10.0382 10.0382i 0.854508 0.854508i
\(139\) −6.92820 + 4.00000i −0.587643 + 0.339276i −0.764165 0.645021i \(-0.776849\pi\)
0.176522 + 0.984297i \(0.443515\pi\)
\(140\) 0 0
\(141\) −5.19615 + 9.00000i −0.437595 + 0.757937i
\(142\) 2.77766 + 10.3664i 0.233096 + 0.869926i
\(143\) 3.10583 3.10583i 0.259722 0.259722i
\(144\) −2.59808 1.50000i −0.216506 0.125000i
\(145\) 0 0
\(146\) 4.50000 + 2.59808i 0.372423 + 0.215018i
\(147\) −2.41730 + 9.02150i −0.199376 + 0.744081i
\(148\) 0.568406 2.12132i 0.0467227 0.174371i
\(149\) −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i \(-0.902763\pi\)
0.216394 0.976306i \(-0.430570\pi\)
\(150\) 0 0
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) 5.08845 + 5.08845i 0.412728 + 0.412728i
\(153\) 0 0
\(154\) 4.39230i 0.353942i
\(155\) 0 0
\(156\) 1.90192 + 1.09808i 0.152276 + 0.0879165i
\(157\) −7.58871 2.03339i −0.605645 0.162282i −0.0570512 0.998371i \(-0.518170\pi\)
−0.548593 + 0.836089i \(0.684837\pi\)
\(158\) −9.65926 2.58819i −0.768449 0.205905i
\(159\) 3.80385i 0.301665i
\(160\) 0 0
\(161\) 10.3923i 0.819028i
\(162\) 8.69333 2.32937i 0.683013 0.183013i
\(163\) 14.3688 + 14.3688i 1.12545 + 1.12545i 0.990908 + 0.134541i \(0.0429559\pi\)
0.134541 + 0.990908i \(0.457044\pi\)
\(164\) −0.866025 + 1.50000i −0.0676252 + 0.117130i
\(165\) 0 0
\(166\) 3.40192 + 5.89230i 0.264040 + 0.457332i
\(167\) −1.13681 + 4.24264i −0.0879692 + 0.328305i −0.995860 0.0909015i \(-0.971025\pi\)
0.907891 + 0.419207i \(0.137692\pi\)
\(168\) −2.12132 + 0.568406i −0.163663 + 0.0438535i
\(169\) 9.86603 + 5.69615i 0.758925 + 0.438166i
\(170\) 0 0
\(171\) −21.5885 −1.65091
\(172\) 4.57081 4.57081i 0.348521 0.348521i
\(173\) −1.13681 4.24264i −0.0864302 0.322562i 0.909151 0.416467i \(-0.136732\pi\)
−0.995581 + 0.0939047i \(0.970065\pi\)
\(174\) 6.29423 + 10.9019i 0.477164 + 0.826473i
\(175\) 0 0
\(176\) 3.00000 1.73205i 0.226134 0.130558i
\(177\) −20.8528 5.58750i −1.56740 0.419983i
\(178\) 8.36516 2.24144i 0.626995 0.168003i
\(179\) 4.85641 0.362985 0.181492 0.983392i \(-0.441907\pi\)
0.181492 + 0.983392i \(0.441907\pi\)
\(180\) 0 0
\(181\) 8.39230 0.623795 0.311898 0.950116i \(-0.399035\pi\)
0.311898 + 0.950116i \(0.399035\pi\)
\(182\) 1.55291 0.416102i 0.115110 0.0308435i
\(183\) 1.79315 + 6.69213i 0.132554 + 0.494697i
\(184\) −7.09808 + 4.09808i −0.523277 + 0.302114i
\(185\) 0 0
\(186\) 17.6603 1.29491
\(187\) 0 0
\(188\) 4.24264 4.24264i 0.309426 0.309426i
\(189\) 3.29423 5.70577i 0.239620 0.415034i
\(190\) 0 0
\(191\) 3.00000 + 1.73205i 0.217072 + 0.125327i 0.604594 0.796534i \(-0.293335\pi\)
−0.387522 + 0.921861i \(0.626669\pi\)
\(192\) 1.22474 + 1.22474i 0.0883883 + 0.0883883i
\(193\) −6.45189 + 24.0788i −0.464417 + 1.73323i 0.194396 + 0.980923i \(0.437725\pi\)
−0.658813 + 0.752306i \(0.728941\pi\)
\(194\) −7.33013 12.6962i −0.526272 0.911531i
\(195\) 0 0
\(196\) 2.69615 4.66987i 0.192582 0.333562i
\(197\) 2.68973 + 2.68973i 0.191635 + 0.191635i 0.796402 0.604767i \(-0.206734\pi\)
−0.604767 + 0.796402i \(0.706734\pi\)
\(198\) −2.68973 + 10.0382i −0.191151 + 0.713384i
\(199\) 0.392305i 0.0278098i 0.999903 + 0.0139049i \(0.00442620\pi\)
−0.999903 + 0.0139049i \(0.995574\pi\)
\(200\) 0 0
\(201\) 18.6962 10.7942i 1.31872 0.761366i
\(202\) 10.3664 + 2.77766i 0.729375 + 0.195435i
\(203\) 8.90138 + 2.38512i 0.624755 + 0.167403i
\(204\) 0 0
\(205\) 0 0
\(206\) 10.3923i 0.724066i
\(207\) 6.36396 23.7506i 0.442326 1.65078i
\(208\) −0.896575 0.896575i −0.0621663 0.0621663i
\(209\) 12.4641 21.5885i 0.862160 1.49330i
\(210\) 0 0
\(211\) 4.59808 + 7.96410i 0.316545 + 0.548271i 0.979765 0.200153i \(-0.0641440\pi\)
−0.663220 + 0.748424i \(0.730811\pi\)
\(212\) 0.568406 2.12132i 0.0390383 0.145693i
\(213\) 13.1440 + 13.1440i 0.900614 + 0.900614i
\(214\) 0.696152 + 0.401924i 0.0475880 + 0.0274749i
\(215\) 0 0
\(216\) −5.19615 −0.353553
\(217\) 9.14162 9.14162i 0.620574 0.620574i
\(218\) 3.15660 + 11.7806i 0.213792 + 0.797881i
\(219\) 9.00000 0.608164
\(220\) 0 0
\(221\) 0 0
\(222\) −0.984508 3.67423i −0.0660759 0.246598i
\(223\) −9.14162 + 2.44949i −0.612168 + 0.164030i −0.551565 0.834132i \(-0.685969\pi\)
−0.0606032 + 0.998162i \(0.519302\pi\)
\(224\) 1.26795 0.0847184
\(225\) 0 0
\(226\) −7.39230 −0.491729
\(227\) −22.4058 + 6.00361i −1.48712 + 0.398473i −0.908764 0.417310i \(-0.862973\pi\)
−0.578358 + 0.815783i \(0.696306\pi\)
\(228\) 12.0394 + 3.22595i 0.797329 + 0.213644i
\(229\) −14.0263 + 8.09808i −0.926883 + 0.535136i −0.885824 0.464021i \(-0.846406\pi\)
−0.0410583 + 0.999157i \(0.513073\pi\)
\(230\) 0 0
\(231\) 3.80385 + 6.58846i 0.250275 + 0.433489i
\(232\) −1.88108 7.02030i −0.123499 0.460905i
\(233\) −17.9551 + 17.9551i −1.17628 + 1.17628i −0.195590 + 0.980686i \(0.562662\pi\)
−0.980686 + 0.195590i \(0.937338\pi\)
\(234\) 3.80385 0.248665
\(235\) 0 0
\(236\) 10.7942 + 6.23205i 0.702644 + 0.405672i
\(237\) −16.7303 + 4.48288i −1.08675 + 0.291194i
\(238\) 0 0
\(239\) 7.09808 + 12.2942i 0.459136 + 0.795248i 0.998916 0.0465591i \(-0.0148256\pi\)
−0.539779 + 0.841807i \(0.681492\pi\)
\(240\) 0 0
\(241\) 5.69615 9.86603i 0.366921 0.635527i −0.622161 0.782889i \(-0.713745\pi\)
0.989083 + 0.147363i \(0.0470785\pi\)
\(242\) −0.707107 0.707107i −0.0454545 0.0454545i
\(243\) 11.0227 11.0227i 0.707107 0.707107i
\(244\) 4.00000i 0.256074i
\(245\) 0 0
\(246\) 3.00000i 0.191273i
\(247\) −8.81345 2.36156i −0.560786 0.150262i
\(248\) −9.84873 2.63896i −0.625395 0.167574i
\(249\) 10.2058 + 5.89230i 0.646764 + 0.373410i
\(250\) 0 0
\(251\) 9.00000i 0.568075i −0.958813 0.284037i \(-0.908326\pi\)
0.958813 0.284037i \(-0.0916740\pi\)
\(252\) −2.68973 + 2.68973i −0.169437 + 0.169437i
\(253\) 20.0764 + 20.0764i 1.26219 + 1.26219i
\(254\) −1.09808 + 1.90192i −0.0688994 + 0.119337i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 1.19256 4.45069i 0.0743898 0.277627i −0.918704 0.394946i \(-0.870763\pi\)
0.993094 + 0.117319i \(0.0374301\pi\)
\(258\) 2.89778 10.8147i 0.180408 0.673291i
\(259\) −2.41154 1.39230i −0.149846 0.0865136i
\(260\) 0 0
\(261\) 18.8827 + 10.9019i 1.16881 + 0.674812i
\(262\) 4.89898 4.89898i 0.302660 0.302660i
\(263\) −4.81105 17.9551i −0.296662 1.10716i −0.939889 0.341481i \(-0.889071\pi\)
0.643227 0.765676i \(-0.277595\pi\)
\(264\) 3.00000 5.19615i 0.184637 0.319801i
\(265\) 0 0
\(266\) 7.90192 4.56218i 0.484498 0.279725i
\(267\) 10.6066 10.6066i 0.649113 0.649113i
\(268\) −12.0394 + 3.22595i −0.735423 + 0.197056i
\(269\) −28.0526 −1.71039 −0.855197 0.518303i \(-0.826564\pi\)
−0.855197 + 0.518303i \(0.826564\pi\)
\(270\) 0 0
\(271\) −4.58846 −0.278729 −0.139364 0.990241i \(-0.544506\pi\)
−0.139364 + 0.990241i \(0.544506\pi\)
\(272\) 0 0
\(273\) 1.96902 1.96902i 0.119170 0.119170i
\(274\) −6.40192 + 3.69615i −0.386754 + 0.223293i
\(275\) 0 0
\(276\) −7.09808 + 12.2942i −0.427254 + 0.740026i
\(277\) 6.60420 + 24.6472i 0.396808 + 1.48091i 0.818679 + 0.574251i \(0.194707\pi\)
−0.421871 + 0.906656i \(0.638627\pi\)
\(278\) 5.65685 5.65685i 0.339276 0.339276i
\(279\) 26.4904 15.2942i 1.58594 0.915642i
\(280\) 0 0
\(281\) 9.00000 + 5.19615i 0.536895 + 0.309976i 0.743820 0.668380i \(-0.233012\pi\)
−0.206925 + 0.978357i \(0.566345\pi\)
\(282\) 2.68973 10.0382i 0.160171 0.597766i
\(283\) −2.56961 + 9.58991i −0.152747 + 0.570061i 0.846540 + 0.532325i \(0.178681\pi\)
−0.999288 + 0.0377364i \(0.987985\pi\)
\(284\) −5.36603 9.29423i −0.318415 0.551511i
\(285\) 0 0
\(286\) −2.19615 + 3.80385i −0.129861 + 0.224926i
\(287\) 1.55291 + 1.55291i 0.0916656 + 0.0916656i
\(288\) 2.89778 + 0.776457i 0.170753 + 0.0457532i
\(289\) 17.0000i 1.00000i
\(290\) 0 0
\(291\) −21.9904 12.6962i −1.28910 0.744262i
\(292\) −5.01910 1.34486i −0.293720 0.0787022i
\(293\) −13.7124 3.67423i −0.801089 0.214651i −0.165027 0.986289i \(-0.552771\pi\)
−0.636062 + 0.771638i \(0.719438\pi\)
\(294\) 9.33975i 0.544705i
\(295\) 0 0
\(296\) 2.19615i 0.127649i
\(297\) 4.65874 + 17.3867i 0.270328 + 1.00888i
\(298\) 12.7279 + 12.7279i 0.737309 + 0.737309i
\(299\) 5.19615 9.00000i 0.300501 0.520483i
\(300\) 0 0
\(301\) −4.09808 7.09808i −0.236209 0.409126i
\(302\) −2.07055 + 7.72741i −0.119147 + 0.444662i
\(303\) 17.9551 4.81105i 1.03149 0.276387i
\(304\) −6.23205 3.59808i −0.357433 0.206364i
\(305\) 0 0
\(306\) 0 0
\(307\) 2.44949 2.44949i 0.139800 0.139800i −0.633743 0.773543i \(-0.718483\pi\)
0.773543 + 0.633743i \(0.218483\pi\)
\(308\) −1.13681 4.24264i −0.0647759 0.241747i
\(309\) 9.00000 + 15.5885i 0.511992 + 0.886796i
\(310\) 0 0
\(311\) 21.5885 12.4641i 1.22417 0.706774i 0.258365 0.966047i \(-0.416816\pi\)
0.965804 + 0.259273i \(0.0834829\pi\)
\(312\) −2.12132 0.568406i −0.120096 0.0321797i
\(313\) −3.22595 + 0.864390i −0.182341 + 0.0488582i −0.348834 0.937184i \(-0.613422\pi\)
0.166493 + 0.986043i \(0.446756\pi\)
\(314\) 7.85641 0.443363
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) −23.7506 + 6.36396i −1.33397 + 0.357436i −0.854193 0.519956i \(-0.825948\pi\)
−0.479775 + 0.877392i \(0.659282\pi\)
\(318\) −0.984508 3.67423i −0.0552085 0.206041i
\(319\) −21.8038 + 12.5885i −1.22078 + 0.704818i
\(320\) 0 0
\(321\) 1.39230 0.0777109
\(322\) 2.68973 + 10.0382i 0.149893 + 0.559407i
\(323\) 0 0
\(324\) −7.79423 + 4.50000i −0.433013 + 0.250000i
\(325\) 0 0
\(326\) −17.5981 10.1603i −0.974667 0.562724i
\(327\) 14.9372 + 14.9372i 0.826028 + 0.826028i
\(328\) 0.448288 1.67303i 0.0247525 0.0923778i
\(329\) −3.80385 6.58846i −0.209713 0.363233i
\(330\) 0 0
\(331\) −8.79423 + 15.2321i −0.483375 + 0.837229i −0.999818 0.0190922i \(-0.993922\pi\)
0.516443 + 0.856321i \(0.327256\pi\)
\(332\) −4.81105 4.81105i −0.264040 0.264040i
\(333\) −4.65874 4.65874i −0.255298 0.255298i
\(334\) 4.39230i 0.240336i
\(335\) 0 0
\(336\) 1.90192 1.09808i 0.103758 0.0599050i
\(337\) 26.5283 + 7.10823i 1.44509 + 0.387210i 0.894312 0.447443i \(-0.147665\pi\)
0.550775 + 0.834653i \(0.314332\pi\)
\(338\) −11.0041 2.94855i −0.598545 0.160380i
\(339\) −11.0885 + 6.40192i −0.602242 + 0.347705i
\(340\) 0 0
\(341\) 35.3205i 1.91271i
\(342\) 20.8528 5.58750i 1.12759 0.302138i
\(343\) −11.1106 11.1106i −0.599918 0.599918i
\(344\) −3.23205 + 5.59808i −0.174261 + 0.301828i
\(345\) 0 0
\(346\) 2.19615 + 3.80385i 0.118066 + 0.204496i
\(347\) −8.48528 + 31.6675i −0.455514 + 1.70000i 0.231059 + 0.972940i \(0.425781\pi\)
−0.686573 + 0.727061i \(0.740886\pi\)
\(348\) −8.90138 8.90138i −0.477164 0.477164i
\(349\) 1.73205 + 1.00000i 0.0927146 + 0.0535288i 0.545640 0.838019i \(-0.316286\pi\)
−0.452926 + 0.891548i \(0.649620\pi\)
\(350\) 0 0
\(351\) 5.70577 3.29423i 0.304552 0.175833i
\(352\) −2.44949 + 2.44949i −0.130558 + 0.130558i
\(353\) −3.88229 14.4889i −0.206633 0.771166i −0.988946 0.148279i \(-0.952627\pi\)
0.782312 0.622886i \(-0.214040\pi\)
\(354\) 21.5885 1.14741
\(355\) 0 0
\(356\) −7.50000 + 4.33013i −0.397499 + 0.229496i
\(357\) 0 0
\(358\) −4.69093 + 1.25693i −0.247923 + 0.0664308i
\(359\) 0.679492 0.0358622 0.0179311 0.999839i \(-0.494292\pi\)
0.0179311 + 0.999839i \(0.494292\pi\)
\(360\) 0 0
\(361\) −32.7846 −1.72551
\(362\) −8.10634 + 2.17209i −0.426060 + 0.114162i
\(363\) −1.67303 0.448288i −0.0878114 0.0235290i
\(364\) −1.39230 + 0.803848i −0.0729766 + 0.0421331i
\(365\) 0 0
\(366\) −3.46410 6.00000i −0.181071 0.313625i
\(367\) −8.24504 30.7709i −0.430388 1.60623i −0.751868 0.659313i \(-0.770847\pi\)
0.321481 0.946916i \(-0.395819\pi\)
\(368\) 5.79555 5.79555i 0.302114 0.302114i
\(369\) 2.59808 + 4.50000i 0.135250 + 0.234261i
\(370\) 0 0
\(371\) −2.41154 1.39230i −0.125201 0.0722849i
\(372\) −17.0585 + 4.57081i −0.884442 + 0.236985i
\(373\) 2.92996 10.9348i 0.151708 0.566181i −0.847657 0.530545i \(-0.821987\pi\)
0.999365 0.0356365i \(-0.0113458\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) 6.51626 + 6.51626i 0.335605 + 0.335605i
\(378\) −1.70522 + 6.36396i −0.0877070 + 0.327327i
\(379\) 20.3923i 1.04748i 0.851877 + 0.523741i \(0.175464\pi\)
−0.851877 + 0.523741i \(0.824536\pi\)
\(380\) 0 0
\(381\) 3.80385i 0.194877i
\(382\) −3.34607 0.896575i −0.171200 0.0458728i
\(383\) −35.3417 9.46979i −1.80588 0.483884i −0.811007 0.585036i \(-0.801080\pi\)
−0.994871 + 0.101152i \(0.967747\pi\)
\(384\) −1.50000 0.866025i −0.0765466 0.0441942i
\(385\) 0 0
\(386\) 24.9282i 1.26881i
\(387\) −5.01910 18.7315i −0.255135 0.952177i
\(388\) 10.3664 + 10.3664i 0.526272 + 0.526272i
\(389\) 5.19615 9.00000i 0.263455 0.456318i −0.703702 0.710495i \(-0.748471\pi\)
0.967158 + 0.254177i \(0.0818045\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.39563 + 5.20857i −0.0704900 + 0.263072i
\(393\) 3.10583 11.5911i 0.156668 0.584694i
\(394\) −3.29423 1.90192i −0.165961 0.0958175i
\(395\) 0 0
\(396\) 10.3923i 0.522233i
\(397\) 6.03579 6.03579i 0.302928 0.302928i −0.539231 0.842158i \(-0.681285\pi\)
0.842158 + 0.539231i \(0.181285\pi\)
\(398\) −0.101536 0.378937i −0.00508954 0.0189944i
\(399\) 7.90192 13.6865i 0.395591 0.685184i
\(400\) 0 0
\(401\) 9.00000 5.19615i 0.449439 0.259483i −0.258154 0.966104i \(-0.583114\pi\)
0.707593 + 0.706620i \(0.249781\pi\)
\(402\) −15.2653 + 15.2653i −0.761366 + 0.761366i
\(403\) 12.4877 3.34607i 0.622056 0.166679i
\(404\) −10.7321 −0.533939
\(405\) 0 0
\(406\) −9.21539 −0.457352
\(407\) 7.34847 1.96902i 0.364250 0.0976005i
\(408\) 0 0
\(409\) −0.526279 + 0.303848i −0.0260228 + 0.0150243i −0.512955 0.858416i \(-0.671449\pi\)
0.486932 + 0.873440i \(0.338116\pi\)
\(410\) 0 0
\(411\) −6.40192 + 11.0885i −0.315784 + 0.546953i
\(412\) −2.68973 10.0382i −0.132513 0.494546i
\(413\) 11.1750 11.1750i 0.549886 0.549886i
\(414\) 24.5885i 1.20846i
\(415\) 0 0
\(416\) 1.09808 + 0.633975i 0.0538376 + 0.0310832i
\(417\) 3.58630 13.3843i 0.175622 0.655430i
\(418\) −6.45189 + 24.0788i −0.315572 + 1.17773i
\(419\) 4.50000 + 7.79423i 0.219839 + 0.380773i 0.954759 0.297382i \(-0.0961133\pi\)
−0.734919 + 0.678155i \(0.762780\pi\)
\(420\) 0 0
\(421\) 4.29423 7.43782i 0.209288 0.362497i −0.742203 0.670176i \(-0.766219\pi\)
0.951490 + 0.307678i \(0.0995521\pi\)
\(422\) −6.50266 6.50266i −0.316545 0.316545i
\(423\) −4.65874 17.3867i −0.226516 0.845369i
\(424\) 2.19615i 0.106655i
\(425\) 0 0
\(426\) −16.0981 9.29423i −0.779954 0.450307i
\(427\) −4.89898 1.31268i −0.237078 0.0635249i
\(428\) −0.776457 0.208051i −0.0375315 0.0100565i
\(429\) 7.60770i 0.367303i
\(430\) 0 0
\(431\) 3.12436i 0.150495i −0.997165 0.0752475i \(-0.976025\pi\)
0.997165 0.0752475i \(-0.0239747\pi\)
\(432\) 5.01910 1.34486i 0.241481 0.0647048i
\(433\) −21.8695 21.8695i −1.05098 1.05098i −0.998629 0.0523546i \(-0.983327\pi\)
−0.0523546 0.998629i \(-0.516673\pi\)
\(434\) −6.46410 + 11.1962i −0.310287 + 0.537433i
\(435\) 0 0
\(436\) −6.09808 10.5622i −0.292045 0.505837i
\(437\) 15.2653 56.9710i 0.730240 2.72529i
\(438\) −8.69333 + 2.32937i −0.415383 + 0.111302i
\(439\) −28.2224 16.2942i −1.34698 0.777681i −0.359162 0.933275i \(-0.616937\pi\)
−0.987821 + 0.155594i \(0.950271\pi\)
\(440\) 0 0
\(441\) −8.08846 14.0096i −0.385165 0.667125i
\(442\) 0 0
\(443\) 2.68973 + 10.0382i 0.127793 + 0.476929i 0.999924 0.0123433i \(-0.00392908\pi\)
−0.872131 + 0.489272i \(0.837262\pi\)
\(444\) 1.90192 + 3.29423i 0.0902613 + 0.156337i
\(445\) 0 0
\(446\) 8.19615 4.73205i 0.388099 0.224069i
\(447\) 30.1146 + 8.06918i 1.42437 + 0.381659i
\(448\) −1.22474 + 0.328169i −0.0578638 + 0.0155045i
\(449\) −5.87564 −0.277289 −0.138644 0.990342i \(-0.544275\pi\)
−0.138644 + 0.990342i \(0.544275\pi\)
\(450\) 0 0
\(451\) −6.00000 −0.282529
\(452\) 7.14042 1.91327i 0.335857 0.0899926i
\(453\) 3.58630 + 13.3843i 0.168499 + 0.628847i
\(454\) 20.0885 11.5981i 0.942798 0.544325i
\(455\) 0 0
\(456\) −12.4641 −0.583685
\(457\) −0.928761 3.46618i −0.0434456 0.162141i 0.940795 0.338976i \(-0.110081\pi\)
−0.984240 + 0.176835i \(0.943414\pi\)
\(458\) 11.4524 11.4524i 0.535136 0.535136i
\(459\) 0 0
\(460\) 0 0
\(461\) −24.2942 14.0263i −1.13150 0.653269i −0.187185 0.982325i \(-0.559936\pi\)
−0.944310 + 0.329056i \(0.893270\pi\)
\(462\) −5.37945 5.37945i −0.250275 0.250275i
\(463\) 2.12132 7.91688i 0.0985861 0.367928i −0.898953 0.438046i \(-0.855671\pi\)
0.997539 + 0.0701175i \(0.0223374\pi\)
\(464\) 3.63397 + 6.29423i 0.168703 + 0.292202i
\(465\) 0 0
\(466\) 12.6962 21.9904i 0.588138 1.01868i
\(467\) 15.2653 + 15.2653i 0.706396 + 0.706396i 0.965775 0.259380i \(-0.0835181\pi\)
−0.259380 + 0.965775i \(0.583518\pi\)
\(468\) −3.67423 + 0.984508i −0.169842 + 0.0455089i
\(469\) 15.8038i 0.729754i
\(470\) 0 0
\(471\) 11.7846 6.80385i 0.543006 0.313505i
\(472\) −12.0394 3.22595i −0.554158 0.148486i
\(473\) 21.6293 + 5.79555i 0.994517 + 0.266480i
\(474\) 15.0000 8.66025i 0.688973 0.397779i
\(475\) 0 0
\(476\) 0 0
\(477\) −4.65874 4.65874i −0.213309 0.213309i
\(478\) −10.0382 10.0382i −0.459136 0.459136i
\(479\) −10.5622 + 18.2942i −0.482598 + 0.835885i −0.999800 0.0199786i \(-0.993640\pi\)
0.517202 + 0.855863i \(0.326974\pi\)
\(480\) 0 0
\(481\) −1.39230 2.41154i −0.0634836 0.109957i
\(482\) −2.94855 + 11.0041i −0.134303 + 0.501224i
\(483\) 12.7279 + 12.7279i 0.579141 + 0.579141i
\(484\) 0.866025 + 0.500000i 0.0393648 + 0.0227273i
\(485\) 0 0
\(486\) −7.79423 + 13.5000i −0.353553 + 0.612372i
\(487\) 15.5935 15.5935i 0.706610 0.706610i −0.259211 0.965821i \(-0.583463\pi\)
0.965821 + 0.259211i \(0.0834625\pi\)
\(488\) 1.03528 + 3.86370i 0.0468648 + 0.174902i
\(489\) −35.1962 −1.59163
\(490\) 0 0
\(491\) −31.7942 + 18.3564i −1.43485 + 0.828413i −0.997486 0.0708697i \(-0.977423\pi\)
−0.437368 + 0.899283i \(0.644089\pi\)
\(492\) −0.776457 2.89778i −0.0350054 0.130642i
\(493\) 0 0
\(494\) 9.12436 0.410524
\(495\) 0 0
\(496\) 10.1962 0.457821
\(497\) −13.1440 + 3.52193i −0.589590 + 0.157980i
\(498\) −11.3831 3.05008i −0.510087 0.136677i
\(499\) −16.9641 + 9.79423i −0.759417 + 0.438450i −0.829087 0.559120i \(-0.811139\pi\)
0.0696691 + 0.997570i \(0.477806\pi\)
\(500\) 0 0
\(501\) −3.80385 6.58846i −0.169943 0.294351i
\(502\) 2.32937 + 8.69333i 0.103965 + 0.388002i
\(503\) −25.8719 + 25.8719i −1.15357 + 1.15357i −0.167742 + 0.985831i \(0.553648\pi\)
−0.985831 + 0.167742i \(0.946352\pi\)
\(504\) 1.90192 3.29423i 0.0847184 0.146737i
\(505\) 0 0
\(506\) −24.5885 14.1962i −1.09309 0.631096i
\(507\) −19.0597 + 5.10703i −0.846471 + 0.226811i
\(508\) 0.568406 2.12132i 0.0252189 0.0941184i
\(509\) 10.3923 + 18.0000i 0.460631 + 0.797836i 0.998992 0.0448779i \(-0.0142899\pi\)
−0.538362 + 0.842714i \(0.680957\pi\)
\(510\) 0 0
\(511\) −3.29423 + 5.70577i −0.145728 + 0.252408i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 26.4404 26.4404i 1.16737 1.16737i
\(514\) 4.60770i 0.203237i
\(515\) 0 0
\(516\) 11.1962i 0.492883i
\(517\) 20.0764 + 5.37945i 0.882959 + 0.236588i
\(518\) 2.68973 + 0.720710i 0.118180 + 0.0316662i
\(519\) 6.58846 + 3.80385i 0.289201 + 0.166970i
\(520\) 0 0
\(521\) 38.7846i 1.69918i 0.527440 + 0.849592i \(0.323152\pi\)
−0.527440 + 0.849592i \(0.676848\pi\)
\(522\) −21.0609 5.64325i −0.921811 0.246998i
\(523\) −14.1929 14.1929i −0.620612 0.620612i 0.325076 0.945688i \(-0.394610\pi\)
−0.945688 + 0.325076i \(0.894610\pi\)
\(524\) −3.46410 + 6.00000i −0.151330 + 0.262111i
\(525\) 0 0
\(526\) 9.29423 + 16.0981i 0.405248 + 0.701909i
\(527\) 0 0
\(528\) −1.55291 + 5.79555i −0.0675819 + 0.252219i
\(529\) 38.2583 + 22.0885i 1.66341 + 0.960368i
\(530\) 0 0
\(531\) 32.3827 18.6962i 1.40529 0.811344i
\(532\) −6.45189 + 6.45189i −0.279725 + 0.279725i
\(533\) 0.568406 + 2.12132i 0.0246204 + 0.0918846i
\(534\) −7.50000 + 12.9904i −0.324557 + 0.562149i
\(535\) 0 0
\(536\) 10.7942 6.23205i 0.466240 0.269184i
\(537\) −5.94786 + 5.94786i −0.256669 + 0.256669i
\(538\) 27.0967 7.26054i 1.16822 0.313024i
\(539\) 18.6795 0.804583
\(540\) 0 0
\(541\) 12.3923 0.532787 0.266393 0.963864i \(-0.414168\pi\)
0.266393 + 0.963864i \(0.414168\pi\)
\(542\) 4.43211 1.18758i 0.190375 0.0510109i
\(543\) −10.2784 + 10.2784i −0.441090 + 0.441090i
\(544\) 0 0
\(545\) 0 0
\(546\) −1.39230 + 2.41154i −0.0595851 + 0.103205i
\(547\) 5.73981 + 21.4213i 0.245416 + 0.915907i 0.973174 + 0.230072i \(0.0738961\pi\)
−0.727757 + 0.685835i \(0.759437\pi\)
\(548\) 5.22715 5.22715i 0.223293 0.223293i
\(549\) −10.3923 6.00000i −0.443533 0.256074i
\(550\) 0 0
\(551\) 45.2942 + 26.1506i 1.92960 + 1.11405i
\(552\) 3.67423 13.7124i 0.156386 0.583640i
\(553\) 3.28169 12.2474i 0.139552 0.520814i
\(554\) −12.7583 22.0981i −0.542050 0.938857i
\(555\) 0 0
\(556\) −4.00000 + 6.92820i −0.169638 + 0.293821i
\(557\) 11.5911 + 11.5911i 0.491131 + 0.491131i 0.908662 0.417531i \(-0.137105\pi\)
−0.417531 + 0.908662i \(0.637105\pi\)
\(558\) −21.6293 + 21.6293i −0.915642 + 0.915642i
\(559\) 8.19615i 0.346660i
\(560\) 0 0
\(561\) 0 0
\(562\) −10.0382 2.68973i −0.423436 0.113459i
\(563\) 32.4440 + 8.69333i 1.36735 + 0.366380i 0.866510 0.499160i \(-0.166358\pi\)
0.500840 + 0.865540i \(0.333025\pi\)
\(564\) 10.3923i 0.437595i
\(565\) 0 0
\(566\) 9.92820i 0.417314i
\(567\) 2.95352 + 11.0227i 0.124036 + 0.462910i
\(568\) 7.58871 + 7.58871i 0.318415 + 0.318415i
\(569\) 5.53590 9.58846i 0.232077 0.401969i −0.726342 0.687333i \(-0.758781\pi\)
0.958419 + 0.285364i \(0.0921146\pi\)
\(570\) 0 0
\(571\) −4.40192 7.62436i −0.184215 0.319069i 0.759097 0.650978i \(-0.225641\pi\)
−0.943312 + 0.331908i \(0.892308\pi\)
\(572\) 1.13681 4.24264i 0.0475325 0.177394i
\(573\) −5.79555 + 1.55291i −0.242113 + 0.0648739i
\(574\) −1.90192 1.09808i −0.0793848 0.0458328i
\(575\) 0 0
\(576\) −3.00000 −0.125000
\(577\) −15.9217 + 15.9217i −0.662828 + 0.662828i −0.956046 0.293217i \(-0.905274\pi\)
0.293217 + 0.956046i \(0.405274\pi\)
\(578\) 4.39992 + 16.4207i 0.183013 + 0.683013i
\(579\) −21.5885 37.3923i −0.897186 1.55397i
\(580\) 0 0
\(581\) −7.47114 + 4.31347i −0.309955 + 0.178953i
\(582\) 24.5271 + 6.57201i 1.01668 + 0.272419i
\(583\) 7.34847 1.96902i 0.304342 0.0815483i
\(584\) 5.19615 0.215018
\(585\) 0 0
\(586\) 14.1962 0.586438
\(587\) 15.8338 4.24264i 0.653529 0.175113i 0.0832050 0.996532i \(-0.473484\pi\)
0.570324 + 0.821420i \(0.306818\pi\)
\(588\) 2.41730 + 9.02150i 0.0996879 + 0.372040i
\(589\) 63.5429 36.6865i 2.61824 1.51164i
\(590\) 0 0
\(591\) −6.58846 −0.271013
\(592\) −0.568406 2.12132i −0.0233613 0.0871857i
\(593\) 14.8492 14.8492i 0.609785 0.609785i −0.333105 0.942890i \(-0.608096\pi\)
0.942890 + 0.333105i \(0.108096\pi\)
\(594\) −9.00000 15.5885i −0.369274 0.639602i
\(595\) 0 0
\(596\) −15.5885 9.00000i −0.638528 0.368654i
\(597\) −0.480473 0.480473i −0.0196645 0.0196645i
\(598\) −2.68973 + 10.0382i −0.109991 + 0.410492i
\(599\) 5.36603 + 9.29423i 0.219250 + 0.379752i 0.954579 0.297958i \(-0.0963057\pi\)
−0.735329 + 0.677710i \(0.762972\pi\)
\(600\) 0 0
\(601\) −6.39230 + 11.0718i −0.260748 + 0.451628i −0.966441 0.256890i \(-0.917302\pi\)
0.705693 + 0.708518i \(0.250636\pi\)
\(602\) 5.79555 + 5.79555i 0.236209 + 0.236209i
\(603\) −9.67784 + 36.1182i −0.394112 + 1.47085i
\(604\) 8.00000i 0.325515i
\(605\) 0 0
\(606\) −16.0981 + 9.29423i −0.653940 + 0.377552i
\(607\) −16.8183 4.50644i −0.682632 0.182911i −0.0991937 0.995068i \(-0.531626\pi\)
−0.583438 + 0.812157i \(0.698293\pi\)
\(608\) 6.95095 + 1.86250i 0.281898 + 0.0755344i
\(609\) −13.8231 + 7.98076i −0.560140 + 0.323397i
\(610\) 0 0
\(611\) 7.60770i 0.307774i
\(612\) 0 0
\(613\) −2.68973 2.68973i −0.108637 0.108637i 0.650699 0.759336i \(-0.274476\pi\)
−0.759336 + 0.650699i \(0.774476\pi\)
\(614\) −1.73205 + 3.00000i −0.0698999 + 0.121070i
\(615\) 0 0
\(616\) 2.19615 + 3.80385i 0.0884855 + 0.153261i
\(617\) 7.70882 28.7697i 0.310346 1.15823i −0.617900 0.786257i \(-0.712016\pi\)
0.928245 0.371969i \(-0.121317\pi\)
\(618\) −12.7279 12.7279i −0.511992 0.511992i
\(619\) −14.2128 8.20577i −0.571261 0.329818i 0.186392 0.982476i \(-0.440321\pi\)
−0.757653 + 0.652658i \(0.773654\pi\)
\(620\) 0 0
\(621\) 21.2942 + 36.8827i 0.854508 + 1.48005i
\(622\) −17.6269 + 17.6269i −0.706774 + 0.706774i
\(623\) 2.84203 + 10.6066i 0.113864 + 0.424945i
\(624\) 2.19615 0.0879165
\(625\) 0 0
\(626\) 2.89230 1.66987i 0.115600 0.0667415i
\(627\) 11.1750 + 41.7057i 0.446287 + 1.66557i
\(628\) −7.58871 + 2.03339i −0.302822 + 0.0811410i
\(629\) 0 0
\(630\) 0 0
\(631\) 40.7846 1.62361 0.811805 0.583929i \(-0.198485\pi\)
0.811805 + 0.583929i \(0.198485\pi\)
\(632\) −9.65926 + 2.58819i −0.384225 + 0.102953i
\(633\) −15.3855 4.12252i −0.611517 0.163856i
\(634\) 21.2942 12.2942i 0.845702 0.488266i
\(635\) 0 0
\(636\) 1.90192 + 3.29423i 0.0754162 + 0.130625i
\(637\) −1.76959 6.60420i −0.0701137 0.261668i
\(638\) 17.8028 17.8028i 0.704818 0.704818i
\(639\) −32.1962 −1.27366
\(640\) 0 0
\(641\) −0.911543 0.526279i −0.0360038 0.0207868i 0.481890 0.876232i \(-0.339950\pi\)
−0.517894 + 0.855445i \(0.673284\pi\)
\(642\) −1.34486 + 0.360355i −0.0530775 + 0.0142221i
\(643\) 4.29839 16.0418i 0.169512 0.632627i −0.827910 0.560861i \(-0.810470\pi\)
0.997422 0.0717654i \(-0.0228633\pi\)
\(644\) −5.19615 9.00000i −0.204757 0.354650i
\(645\) 0 0
\(646\) 0 0
\(647\) −2.68973 2.68973i −0.105744 0.105744i 0.652255 0.757999i \(-0.273823\pi\)
−0.757999 + 0.652255i \(0.773823\pi\)
\(648\) 6.36396 6.36396i 0.250000 0.250000i
\(649\) 43.1769i 1.69484i
\(650\) 0 0
\(651\) 22.3923i 0.877624i
\(652\) 19.6281 + 5.25933i 0.768696 + 0.205971i
\(653\) −2.12132 0.568406i −0.0830137 0.0222434i 0.217073 0.976155i \(-0.430349\pi\)
−0.300087 + 0.953912i \(0.597016\pi\)
\(654\) −18.2942 10.5622i −0.715361 0.413014i
\(655\) 0 0
\(656\) 1.73205i 0.0676252i
\(657\) −11.0227 + 11.0227i −0.430037 + 0.430037i
\(658\) 5.37945 + 5.37945i 0.209713 + 0.209713i
\(659\) 11.0885 19.2058i 0.431945 0.748151i −0.565096 0.825025i \(-0.691161\pi\)
0.997041 + 0.0768747i \(0.0244941\pi\)
\(660\) 0 0
\(661\) −11.5885 20.0718i −0.450739 0.780702i 0.547693 0.836679i \(-0.315506\pi\)
−0.998432 + 0.0559768i \(0.982173\pi\)
\(662\) 4.55223 16.9891i 0.176927 0.660302i
\(663\) 0 0
\(664\) 5.89230 + 3.40192i 0.228666 + 0.132020i
\(665\) 0 0
\(666\) 5.70577 + 3.29423i 0.221094 + 0.127649i
\(667\) −42.1218 + 42.1218i −1.63096 + 1.63096i
\(668\) 1.13681 + 4.24264i 0.0439846 + 0.164153i
\(669\) 8.19615 14.1962i 0.316882 0.548855i
\(670\) 0 0
\(671\) 12.0000 6.92820i 0.463255 0.267460i
\(672\) −1.55291 + 1.55291i −0.0599050 + 0.0599050i
\(673\) −1.55291 + 0.416102i −0.0598604 + 0.0160396i −0.288625 0.957442i \(-0.593198\pi\)
0.228765 + 0.973482i \(0.426531\pi\)
\(674\) −27.4641 −1.05788
\(675\) 0 0
\(676\) 11.3923 0.438166
\(677\) 6.36396 1.70522i 0.244587 0.0655369i −0.134443 0.990921i \(-0.542924\pi\)
0.379030 + 0.925384i \(0.376258\pi\)
\(678\) 9.05369 9.05369i 0.347705 0.347705i
\(679\) 16.0981 9.29423i 0.617787 0.356680i
\(680\) 0 0
\(681\) 20.0885 34.7942i 0.769791 1.33332i
\(682\) −9.14162 34.1170i −0.350051 1.30641i
\(683\) −27.9933 + 27.9933i −1.07113 + 1.07113i −0.0738643 + 0.997268i \(0.523533\pi\)
−0.997268 + 0.0738643i \(0.976467\pi\)
\(684\) −18.6962 + 10.7942i −0.714865 + 0.412728i
\(685\) 0 0
\(686\) 13.6077 + 7.85641i 0.519544 + 0.299959i
\(687\) 7.26054 27.0967i 0.277007 1.03380i
\(688\) 1.67303 6.24384i 0.0637838 0.238044i
\(689\) −1.39230 2.41154i −0.0530426 0.0918725i
\(690\) 0 0
\(691\) −6.20577 + 10.7487i −0.236079 + 0.408900i −0.959586 0.281417i \(-0.909196\pi\)
0.723507 + 0.690317i \(0.242529\pi\)
\(692\) −3.10583 3.10583i −0.118066 0.118066i
\(693\) −12.7279 3.41044i −0.483494 0.129552i
\(694\) 32.7846i 1.24449i
\(695\) 0 0
\(696\) 10.9019 + 6.29423i 0.413236 + 0.238582i
\(697\) 0 0
\(698\) −1.93185 0.517638i −0.0731217 0.0195929i
\(699\) 43.9808i 1.66351i
\(700\) 0 0
\(701\) 21.4641i 0.810688i −0.914164 0.405344i \(-0.867152\pi\)
0.914164 0.405344i \(-0.132848\pi\)
\(702\) −4.65874 + 4.65874i −0.175833 + 0.175833i
\(703\) −11.1750 11.1750i −0.421473 0.421473i
\(704\) 1.73205 3.00000i 0.0652791 0.113067i
\(705\) 0 0
\(706\) 7.50000 + 12.9904i 0.282266 + 0.488899i
\(707\) −3.52193 + 13.1440i −0.132456 + 0.494332i
\(708\) −20.8528 + 5.58750i −0.783698 + 0.209991i
\(709\) −22.3468 12.9019i −0.839251 0.484542i 0.0177584 0.999842i \(-0.494347\pi\)
−0.857010 + 0.515300i \(0.827680\pi\)
\(710\) 0 0
\(711\) 15.0000 25.9808i 0.562544 0.974355i
\(712\) 6.12372 6.12372i 0.229496 0.229496i
\(713\) 21.6293 + 80.7217i 0.810024 + 3.02305i
\(714\) 0 0
\(715\) 0 0
\(716\) 4.20577 2.42820i 0.157177 0.0907462i
\(717\) −23.7506 6.36396i −0.886983 0.237666i
\(718\) −0.656339 + 0.175865i −0.0244943 + 0.00656324i
\(719\) 39.1244 1.45909 0.729546 0.683932i \(-0.239731\pi\)
0.729546 + 0.683932i \(0.239731\pi\)
\(720\) 0 0
\(721\) −13.1769 −0.490734
\(722\) 31.6675 8.48528i 1.17854 0.315789i
\(723\) 5.10703 + 19.0597i 0.189933 + 0.708838i
\(724\) 7.26795 4.19615i 0.270111 0.155949i
\(725\) 0 0
\(726\) 1.73205 0.0642824
\(727\) −1.79315 6.69213i −0.0665043 0.248197i 0.924669 0.380773i \(-0.124342\pi\)
−0.991173 + 0.132575i \(0.957675\pi\)
\(728\) 1.13681 1.13681i 0.0421331 0.0421331i
\(729\) 27.0000i 1.00000i
\(730\) 0 0
\(731\) 0 0
\(732\) 4.89898 + 4.89898i 0.181071 + 0.181071i
\(733\) 8.90138 33.2204i 0.328780 1.22702i −0.581677 0.813420i \(-0.697603\pi\)
0.910457 0.413604i \(-0.135730\pi\)
\(734\) 15.9282 + 27.5885i 0.587921 + 1.01831i
\(735\) 0 0
\(736\) −4.09808 + 7.09808i −0.151057 + 0.261639i
\(737\) −30.5307 30.5307i −1.12461 1.12461i
\(738\) −3.67423 3.67423i −0.135250 0.135250i
\(739\) 11.5885i 0.426288i −0.977021 0.213144i \(-0.931630\pi\)
0.977021 0.213144i \(-0.0683704\pi\)
\(740\) 0 0
\(741\) 13.6865 7.90192i 0.502787 0.290284i
\(742\) 2.68973 + 0.720710i 0.0987430 + 0.0264581i
\(743\) 38.0315 + 10.1905i 1.39524 + 0.373853i 0.876633 0.481160i \(-0.159784\pi\)
0.518606 + 0.855013i \(0.326451\pi\)
\(744\) 15.2942 8.83013i 0.560714 0.323728i
\(745\) 0 0
\(746\) 11.3205i 0.414473i
\(747\) −19.7160 + 5.28290i −0.721372 + 0.193291i
\(748\) 0 0
\(749\) −0.509619 + 0.882686i −0.0186211 + 0.0322526i
\(750\) 0 0
\(751\) 10.2942 + 17.8301i 0.375642 + 0.650631i 0.990423 0.138067i \(-0.0440890\pi\)
−0.614781 + 0.788698i \(0.710756\pi\)
\(752\) 1.55291 5.79555i 0.0566290 0.211342i
\(753\) 11.0227 + 11.0227i 0.401690 + 0.401690i
\(754\) −7.98076 4.60770i −0.290642 0.167802i
\(755\) 0 0
\(756\) 6.58846i 0.239620i
\(757\) −10.5187 + 10.5187i −0.382308 + 0.382308i −0.871933 0.489625i \(-0.837134\pi\)
0.489625 + 0.871933i \(0.337134\pi\)
\(758\) −5.27792 19.6975i −0.191703 0.715444i
\(759\) −49.1769 −1.78501
\(760\) 0 0
\(761\) −9.91154 + 5.72243i −0.359293 + 0.207438i −0.668771 0.743469i \(-0.733179\pi\)
0.309478 + 0.950907i \(0.399846\pi\)
\(762\) −0.984508 3.67423i −0.0356650 0.133103i
\(763\) −14.9372 + 4.00240i −0.540762 + 0.144897i
\(764\) 3.46410 0.125327
\(765\) 0 0
\(766\) 36.5885 1.32199
\(767\) 15.2653 4.09034i 0.551200 0.147693i
\(768\) 1.67303 + 0.448288i 0.0603704 + 0.0161762i
\(769\) 28.9186 16.6962i 1.04283 0.602079i 0.122197 0.992506i \(-0.461006\pi\)
0.920634 + 0.390427i \(0.127673\pi\)
\(770\) 0 0
\(771\) 3.99038 + 6.91154i 0.143710 + 0.248913i
\(772\) 6.45189 + 24.0788i 0.232209 + 0.866615i
\(773\) −6.51626 + 6.51626i −0.234374 + 0.234374i −0.814516 0.580142i \(-0.802997\pi\)
0.580142 + 0.814516i \(0.302997\pi\)
\(774\) 9.69615 + 16.7942i 0.348521 + 0.603656i
\(775\) 0 0
\(776\) −12.6962 7.33013i −0.455765 0.263136i
\(777\) 4.65874 1.24831i 0.167131 0.0447827i
\(778\) −2.68973 + 10.0382i −0.0964314 + 0.359887i
\(779\) 6.23205 + 10.7942i 0.223286 + 0.386743i
\(780\) 0 0
\(781\) 18.5885 32.1962i 0.665147 1.15207i
\(782\) 0 0
\(783\) −36.4785 + 9.77440i −1.30364 + 0.349308i
\(784\) 5.39230i 0.192582i
\(785\) 0