Properties

Label 624.2.cn.c.353.2
Level $624$
Weight $2$
Character 624.353
Analytic conductor $4.983$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.cn (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.98266508613\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: 8.0.56070144.2
Defining polynomial: \(x^{8} - 4 x^{7} + 16 x^{6} - 34 x^{5} + 63 x^{4} - 74 x^{3} + 70 x^{2} - 38 x + 13\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 353.2
Root \(0.500000 - 1.19293i\) of defining polynomial
Character \(\chi\) \(=\) 624.353
Dual form 624.2.cn.c.449.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.28311 - 1.16345i) q^{3} +(1.69293 + 1.69293i) q^{5} +(1.36603 - 0.366025i) q^{7} +(0.292748 - 2.98568i) q^{9} +O(q^{10})\) \(q+(1.28311 - 1.16345i) q^{3} +(1.69293 + 1.69293i) q^{5} +(1.36603 - 0.366025i) q^{7} +(0.292748 - 2.98568i) q^{9} +(1.69293 + 0.453620i) q^{11} +(-1.59808 + 3.23205i) q^{13} +(4.14187 + 0.202571i) q^{15} +(1.07328 - 1.85897i) q^{17} +(0.267949 + 1.00000i) q^{19} +(1.32691 - 2.05896i) q^{21} +0.732051i q^{25} +(-3.09808 - 4.17156i) q^{27} +(4.79122 - 2.76621i) q^{29} +(-4.46410 + 4.46410i) q^{31} +(2.69999 - 1.38761i) q^{33} +(2.93225 + 1.69293i) q^{35} +(-1.76795 + 6.59808i) q^{37} +(1.70983 + 6.00637i) q^{39} +(-0.166037 + 0.619657i) q^{41} +(-7.09808 - 4.09808i) q^{43} +(5.55017 - 4.55896i) q^{45} +(6.77174 - 6.77174i) q^{47} +(-4.33013 + 2.50000i) q^{49} +(-0.785693 - 3.63397i) q^{51} -4.62518i q^{53} +(2.09808 + 3.63397i) q^{55} +(1.50726 + 0.971364i) q^{57} +(-1.23931 - 4.62518i) q^{59} +(3.50000 - 6.06218i) q^{61} +(-0.692934 - 4.18567i) q^{63} +(-8.17709 + 2.76621i) q^{65} +(8.46410 + 2.26795i) q^{67} +(-4.62518 + 1.23931i) q^{71} +(-6.09808 - 6.09808i) q^{73} +(0.851708 + 0.939303i) q^{75} +2.47863 q^{77} -2.00000 q^{79} +(-8.82860 - 1.74811i) q^{81} +(1.23931 + 1.23931i) q^{83} +(4.96410 - 1.33013i) q^{85} +(2.92931 - 9.12372i) q^{87} +(-9.70398 - 2.60017i) q^{89} +(-1.00000 + 5.00000i) q^{91} +(-0.534160 + 10.9217i) q^{93} +(-1.23931 + 2.14655i) q^{95} +(3.36603 + 12.5622i) q^{97} +(1.84997 - 4.92177i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{3} + 4q^{7} + 4q^{9} + O(q^{10}) \) \( 8q + 2q^{3} + 4q^{7} + 4q^{9} + 8q^{13} + 14q^{15} + 16q^{19} + 4q^{21} - 4q^{27} - 8q^{31} + 16q^{33} - 28q^{37} + 14q^{39} - 36q^{43} - 20q^{45} - 4q^{55} + 16q^{57} + 28q^{61} + 8q^{63} + 40q^{67} - 28q^{73} - 12q^{75} - 16q^{79} + 4q^{81} + 12q^{85} + 34q^{87} - 8q^{91} + 4q^{93} + 20q^{97} - 40q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(1\)

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 0
\(3\) 1.28311 1.16345i 0.740805 0.671721i
\(4\) 0 0
\(5\) 1.69293 + 1.69293i 0.757103 + 0.757103i 0.975794 0.218691i \(-0.0701787\pi\)
−0.218691 + 0.975794i \(0.570179\pi\)
\(6\) 0 0
\(7\) 1.36603 0.366025i 0.516309 0.138345i 0.00875026 0.999962i \(-0.497215\pi\)
0.507559 + 0.861617i \(0.330548\pi\)
\(8\) 0 0
\(9\) 0.292748 2.98568i 0.0975828 0.995227i
\(10\) 0 0
\(11\) 1.69293 + 0.453620i 0.510439 + 0.136772i 0.504840 0.863213i \(-0.331551\pi\)
0.00559833 + 0.999984i \(0.498218\pi\)
\(12\) 0 0
\(13\) −1.59808 + 3.23205i −0.443227 + 0.896410i
\(14\) 0 0
\(15\) 4.14187 + 0.202571i 1.06943 + 0.0523036i
\(16\) 0 0
\(17\) 1.07328 1.85897i 0.260308 0.450867i −0.706016 0.708196i \(-0.749509\pi\)
0.966324 + 0.257330i \(0.0828426\pi\)
\(18\) 0 0
\(19\) 0.267949 + 1.00000i 0.0614718 + 0.229416i 0.989826 0.142280i \(-0.0454432\pi\)
−0.928355 + 0.371695i \(0.878777\pi\)
\(20\) 0 0
\(21\) 1.32691 2.05896i 0.289555 0.449302i
\(22\) 0 0
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 0 0
\(25\) 0.732051i 0.146410i
\(26\) 0 0
\(27\) −3.09808 4.17156i −0.596225 0.802817i
\(28\) 0 0
\(29\) 4.79122 2.76621i 0.889707 0.513673i 0.0158603 0.999874i \(-0.494951\pi\)
0.873847 + 0.486202i \(0.161618\pi\)
\(30\) 0 0
\(31\) −4.46410 + 4.46410i −0.801776 + 0.801776i −0.983373 0.181597i \(-0.941873\pi\)
0.181597 + 0.983373i \(0.441873\pi\)
\(32\) 0 0
\(33\) 2.69999 1.38761i 0.470008 0.241551i
\(34\) 0 0
\(35\) 2.93225 + 1.69293i 0.495640 + 0.286158i
\(36\) 0 0
\(37\) −1.76795 + 6.59808i −0.290649 + 1.08472i 0.653963 + 0.756527i \(0.273105\pi\)
−0.944612 + 0.328190i \(0.893561\pi\)
\(38\) 0 0
\(39\) 1.70983 + 6.00637i 0.273793 + 0.961789i
\(40\) 0 0
\(41\) −0.166037 + 0.619657i −0.0259306 + 0.0967741i −0.977678 0.210107i \(-0.932619\pi\)
0.951748 + 0.306881i \(0.0992854\pi\)
\(42\) 0 0
\(43\) −7.09808 4.09808i −1.08245 0.624951i −0.150891 0.988550i \(-0.548214\pi\)
−0.931555 + 0.363600i \(0.881548\pi\)
\(44\) 0 0
\(45\) 5.55017 4.55896i 0.827370 0.679610i
\(46\) 0 0
\(47\) 6.77174 6.77174i 0.987759 0.987759i −0.0121668 0.999926i \(-0.503873\pi\)
0.999926 + 0.0121668i \(0.00387290\pi\)
\(48\) 0 0
\(49\) −4.33013 + 2.50000i −0.618590 + 0.357143i
\(50\) 0 0
\(51\) −0.785693 3.63397i −0.110019 0.508858i
\(52\) 0 0
\(53\) 4.62518i 0.635318i −0.948205 0.317659i \(-0.897103\pi\)
0.948205 0.317659i \(-0.102897\pi\)
\(54\) 0 0
\(55\) 2.09808 + 3.63397i 0.282905 + 0.490005i
\(56\) 0 0
\(57\) 1.50726 + 0.971364i 0.199642 + 0.128660i
\(58\) 0 0
\(59\) −1.23931 4.62518i −0.161345 0.602147i −0.998478 0.0551484i \(-0.982437\pi\)
0.837133 0.546999i \(-0.184230\pi\)
\(60\) 0 0
\(61\) 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i \(-0.685424\pi\)
0.998264 + 0.0588933i \(0.0187572\pi\)
\(62\) 0 0
\(63\) −0.692934 4.18567i −0.0873015 0.527345i
\(64\) 0 0
\(65\) −8.17709 + 2.76621i −1.01424 + 0.343106i
\(66\) 0 0
\(67\) 8.46410 + 2.26795i 1.03405 + 0.277074i 0.735647 0.677365i \(-0.236878\pi\)
0.298407 + 0.954439i \(0.403545\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −4.62518 + 1.23931i −0.548908 + 0.147079i −0.522606 0.852575i \(-0.675040\pi\)
−0.0263025 + 0.999654i \(0.508373\pi\)
\(72\) 0 0
\(73\) −6.09808 6.09808i −0.713726 0.713726i 0.253587 0.967313i \(-0.418390\pi\)
−0.967313 + 0.253587i \(0.918390\pi\)
\(74\) 0 0
\(75\) 0.851708 + 0.939303i 0.0983467 + 0.108461i
\(76\) 0 0
\(77\) 2.47863 0.282466
\(78\) 0 0
\(79\) −2.00000 −0.225018 −0.112509 0.993651i \(-0.535889\pi\)
−0.112509 + 0.993651i \(0.535889\pi\)
\(80\) 0 0
\(81\) −8.82860 1.74811i −0.980955 0.194234i
\(82\) 0 0
\(83\) 1.23931 + 1.23931i 0.136032 + 0.136032i 0.771844 0.635812i \(-0.219335\pi\)
−0.635812 + 0.771844i \(0.719335\pi\)
\(84\) 0 0
\(85\) 4.96410 1.33013i 0.538432 0.144273i
\(86\) 0 0
\(87\) 2.92931 9.12372i 0.314054 0.978165i
\(88\) 0 0
\(89\) −9.70398 2.60017i −1.02862 0.275618i −0.295230 0.955426i \(-0.595396\pi\)
−0.733390 + 0.679808i \(0.762063\pi\)
\(90\) 0 0
\(91\) −1.00000 + 5.00000i −0.104828 + 0.524142i
\(92\) 0 0
\(93\) −0.534160 + 10.9217i −0.0553898 + 1.13253i
\(94\) 0 0
\(95\) −1.23931 + 2.14655i −0.127151 + 0.220232i
\(96\) 0 0
\(97\) 3.36603 + 12.5622i 0.341768 + 1.27550i 0.896343 + 0.443362i \(0.146214\pi\)
−0.554575 + 0.832134i \(0.687119\pi\)
\(98\) 0 0
\(99\) 1.84997 4.92177i 0.185929 0.494656i
\(100\) 0 0
\(101\) 9.87002 + 17.0954i 0.982104 + 1.70105i 0.654160 + 0.756356i \(0.273022\pi\)
0.327944 + 0.944697i \(0.393644\pi\)
\(102\) 0 0
\(103\) 6.92820i 0.682656i 0.939944 + 0.341328i \(0.110877\pi\)
−0.939944 + 0.341328i \(0.889123\pi\)
\(104\) 0 0
\(105\) 5.73205 1.23931i 0.559391 0.120945i
\(106\) 0 0
\(107\) −14.4507 + 8.34312i −1.39700 + 0.806560i −0.994078 0.108673i \(-0.965340\pi\)
−0.402925 + 0.915233i \(0.632007\pi\)
\(108\) 0 0
\(109\) −2.80385 + 2.80385i −0.268560 + 0.268560i −0.828520 0.559960i \(-0.810817\pi\)
0.559960 + 0.828520i \(0.310817\pi\)
\(110\) 0 0
\(111\) 5.40808 + 10.5230i 0.513313 + 0.998798i
\(112\) 0 0
\(113\) −11.2309 6.48415i −1.05651 0.609978i −0.132047 0.991243i \(-0.542155\pi\)
−0.924465 + 0.381266i \(0.875488\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 9.18204 + 5.71753i 0.848880 + 0.528585i
\(118\) 0 0
\(119\) 0.785693 2.93225i 0.0720244 0.268799i
\(120\) 0 0
\(121\) −6.86603 3.96410i −0.624184 0.360373i
\(122\) 0 0
\(123\) 0.507899 + 0.988265i 0.0457957 + 0.0891088i
\(124\) 0 0
\(125\) 7.22536 7.22536i 0.646255 0.646255i
\(126\) 0 0
\(127\) −13.0981 + 7.56218i −1.16227 + 0.671035i −0.951846 0.306576i \(-0.900817\pi\)
−0.210420 + 0.977611i \(0.567483\pi\)
\(128\) 0 0
\(129\) −13.8755 + 3.00000i −1.22167 + 0.264135i
\(130\) 0 0
\(131\) 0.907241i 0.0792660i 0.999214 + 0.0396330i \(0.0126189\pi\)
−0.999214 + 0.0396330i \(0.987381\pi\)
\(132\) 0 0
\(133\) 0.732051 + 1.26795i 0.0634769 + 0.109945i
\(134\) 0 0
\(135\) 1.81734 12.3070i 0.156412 1.05922i
\(136\) 0 0
\(137\) 1.52690 + 5.69846i 0.130452 + 0.486852i 0.999975 0.00703925i \(-0.00224068\pi\)
−0.869524 + 0.493891i \(0.835574\pi\)
\(138\) 0 0
\(139\) −1.19615 + 2.07180i −0.101456 + 0.175728i −0.912285 0.409556i \(-0.865684\pi\)
0.810829 + 0.585284i \(0.199017\pi\)
\(140\) 0 0
\(141\) 0.810284 16.5675i 0.0682383 1.39523i
\(142\) 0 0
\(143\) −4.17156 + 4.74673i −0.348843 + 0.396941i
\(144\) 0 0
\(145\) 12.7942 + 3.42820i 1.06250 + 0.284697i
\(146\) 0 0
\(147\) −2.64740 + 8.24568i −0.218354 + 0.680092i
\(148\) 0 0
\(149\) −5.24484 + 1.40535i −0.429674 + 0.115131i −0.467173 0.884166i \(-0.654728\pi\)
0.0374992 + 0.999297i \(0.488061\pi\)
\(150\) 0 0
\(151\) −7.46410 7.46410i −0.607420 0.607420i 0.334851 0.942271i \(-0.391314\pi\)
−0.942271 + 0.334851i \(0.891314\pi\)
\(152\) 0 0
\(153\) −5.23610 3.74867i −0.423313 0.303062i
\(154\) 0 0
\(155\) −15.1149 −1.21405
\(156\) 0 0
\(157\) −15.1962 −1.21278 −0.606392 0.795165i \(-0.707384\pi\)
−0.606392 + 0.795165i \(0.707384\pi\)
\(158\) 0 0
\(159\) −5.38119 5.93462i −0.426756 0.470646i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 14.9282 4.00000i 1.16927 0.313304i 0.378606 0.925558i \(-0.376404\pi\)
0.790661 + 0.612254i \(0.209737\pi\)
\(164\) 0 0
\(165\) 6.92003 + 2.22178i 0.538723 + 0.172965i
\(166\) 0 0
\(167\) −11.3969 3.05379i −0.881920 0.236310i −0.210685 0.977554i \(-0.567569\pi\)
−0.671235 + 0.741244i \(0.734236\pi\)
\(168\) 0 0
\(169\) −7.89230 10.3301i −0.607100 0.794625i
\(170\) 0 0
\(171\) 3.06412 0.507263i 0.234319 0.0387914i
\(172\) 0 0
\(173\) 3.71794 6.43966i 0.282670 0.489598i −0.689372 0.724408i \(-0.742113\pi\)
0.972041 + 0.234809i \(0.0754466\pi\)
\(174\) 0 0
\(175\) 0.267949 + 1.00000i 0.0202551 + 0.0755929i
\(176\) 0 0
\(177\) −6.97136 4.49274i −0.524000 0.337695i
\(178\) 0 0
\(179\) 9.37191 + 16.2326i 0.700489 + 1.21328i 0.968295 + 0.249810i \(0.0803683\pi\)
−0.267805 + 0.963473i \(0.586298\pi\)
\(180\) 0 0
\(181\) 3.00000i 0.222988i 0.993765 + 0.111494i \(0.0355636\pi\)
−0.993765 + 0.111494i \(0.964436\pi\)
\(182\) 0 0
\(183\) −2.56218 11.8505i −0.189402 0.876017i
\(184\) 0 0
\(185\) −14.1631 + 8.17709i −1.04129 + 0.601191i
\(186\) 0 0
\(187\) 2.66025 2.66025i 0.194537 0.194537i
\(188\) 0 0
\(189\) −5.75895 4.56448i −0.418902 0.332017i
\(190\) 0 0
\(191\) 16.8078 + 9.70398i 1.21617 + 0.702156i 0.964096 0.265553i \(-0.0855544\pi\)
0.252073 + 0.967708i \(0.418888\pi\)
\(192\) 0 0
\(193\) 1.86603 6.96410i 0.134319 0.501287i −0.865680 0.500597i \(-0.833114\pi\)
1.00000 0.000689767i \(-0.000219560\pi\)
\(194\) 0 0
\(195\) −7.27375 + 13.0630i −0.520884 + 0.935462i
\(196\) 0 0
\(197\) −0.453620 + 1.69293i −0.0323191 + 0.120617i −0.980201 0.198006i \(-0.936554\pi\)
0.947882 + 0.318622i \(0.103220\pi\)
\(198\) 0 0
\(199\) −0.803848 0.464102i −0.0569832 0.0328993i 0.471238 0.882006i \(-0.343807\pi\)
−0.528221 + 0.849107i \(0.677141\pi\)
\(200\) 0 0
\(201\) 13.4990 6.93756i 0.952149 0.489338i
\(202\) 0 0
\(203\) 5.53242 5.53242i 0.388300 0.388300i
\(204\) 0 0
\(205\) −1.33013 + 0.767949i −0.0929001 + 0.0536359i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.81448i 0.125510i
\(210\) 0 0
\(211\) −6.09808 10.5622i −0.419809 0.727130i 0.576111 0.817371i \(-0.304570\pi\)
−0.995920 + 0.0902411i \(0.971236\pi\)
\(212\) 0 0
\(213\) −4.49274 + 6.97136i −0.307837 + 0.477670i
\(214\) 0 0
\(215\) −5.07880 18.9543i −0.346371 1.29268i
\(216\) 0 0
\(217\) −4.46410 + 7.73205i −0.303043 + 0.524886i
\(218\) 0 0
\(219\) −14.9193 0.729677i −1.00816 0.0493070i
\(220\) 0 0
\(221\) 4.29311 + 6.43966i 0.288786 + 0.433179i
\(222\) 0 0
\(223\) −22.2942 5.97372i −1.49293 0.400030i −0.582206 0.813041i \(-0.697810\pi\)
−0.910726 + 0.413011i \(0.864477\pi\)
\(224\) 0 0
\(225\) 2.18567 + 0.214307i 0.145711 + 0.0142871i
\(226\) 0 0
\(227\) 15.1149 4.05001i 1.00321 0.268809i 0.280419 0.959878i \(-0.409526\pi\)
0.722789 + 0.691069i \(0.242860\pi\)
\(228\) 0 0
\(229\) 10.1244 + 10.1244i 0.669036 + 0.669036i 0.957493 0.288457i \(-0.0931421\pi\)
−0.288457 + 0.957493i \(0.593142\pi\)
\(230\) 0 0
\(231\) 3.18035 2.88377i 0.209252 0.189738i
\(232\) 0 0
\(233\) −7.43588 −0.487141 −0.243570 0.969883i \(-0.578319\pi\)
−0.243570 + 0.969883i \(0.578319\pi\)
\(234\) 0 0
\(235\) 22.9282 1.49567
\(236\) 0 0
\(237\) −2.56622 + 2.32691i −0.166694 + 0.151149i
\(238\) 0 0
\(239\) 7.10381 + 7.10381i 0.459507 + 0.459507i 0.898494 0.438986i \(-0.144662\pi\)
−0.438986 + 0.898494i \(0.644662\pi\)
\(240\) 0 0
\(241\) 7.23205 1.93782i 0.465857 0.124826i −0.0182524 0.999833i \(-0.505810\pi\)
0.484110 + 0.875007i \(0.339144\pi\)
\(242\) 0 0
\(243\) −13.3619 + 8.02865i −0.857167 + 0.515038i
\(244\) 0 0
\(245\) −11.5630 3.09828i −0.738730 0.197942i
\(246\) 0 0
\(247\) −3.66025 0.732051i −0.232896 0.0465793i
\(248\) 0 0
\(249\) 3.03206 + 0.148292i 0.192149 + 0.00939765i
\(250\) 0 0
\(251\) 10.9433 18.9543i 0.690735 1.19639i −0.280863 0.959748i \(-0.590621\pi\)
0.971597 0.236640i \(-0.0760461\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 4.82195 7.48221i 0.301962 0.468554i
\(256\) 0 0
\(257\) 8.29863 + 14.3737i 0.517655 + 0.896604i 0.999790 + 0.0205071i \(0.00652807\pi\)
−0.482135 + 0.876097i \(0.660139\pi\)
\(258\) 0 0
\(259\) 9.66025i 0.600259i
\(260\) 0 0
\(261\) −6.85641 15.1149i −0.424401 0.935586i
\(262\) 0 0
\(263\) −10.3681 + 5.98604i −0.639326 + 0.369115i −0.784355 0.620312i \(-0.787006\pi\)
0.145029 + 0.989427i \(0.453673\pi\)
\(264\) 0 0
\(265\) 7.83013 7.83013i 0.481001 0.481001i
\(266\) 0 0
\(267\) −15.4765 + 7.95383i −0.947145 + 0.486766i
\(268\) 0 0
\(269\) 9.58244 + 5.53242i 0.584251 + 0.337318i 0.762821 0.646610i \(-0.223814\pi\)
−0.178570 + 0.983927i \(0.557147\pi\)
\(270\) 0 0
\(271\) −0.535898 + 2.00000i −0.0325535 + 0.121491i −0.980291 0.197561i \(-0.936698\pi\)
0.947737 + 0.319052i \(0.103365\pi\)
\(272\) 0 0
\(273\) 4.53416 + 7.57901i 0.274420 + 0.458703i
\(274\) 0 0
\(275\) −0.332073 + 1.23931i −0.0200248 + 0.0747334i
\(276\) 0 0
\(277\) 3.10770 + 1.79423i 0.186723 + 0.107805i 0.590448 0.807076i \(-0.298951\pi\)
−0.403724 + 0.914881i \(0.632285\pi\)
\(278\) 0 0
\(279\) 12.0215 + 14.6352i 0.719710 + 0.876189i
\(280\) 0 0
\(281\) 15.9006 15.9006i 0.948547 0.948547i −0.0501922 0.998740i \(-0.515983\pi\)
0.998740 + 0.0501922i \(0.0159834\pi\)
\(282\) 0 0
\(283\) 21.2942 12.2942i 1.26581 0.730816i 0.291618 0.956535i \(-0.405806\pi\)
0.974192 + 0.225719i \(0.0724731\pi\)
\(284\) 0 0
\(285\) 0.907241 + 4.19615i 0.0537403 + 0.248559i
\(286\) 0 0
\(287\) 0.907241i 0.0535527i
\(288\) 0 0
\(289\) 6.19615 + 10.7321i 0.364480 + 0.631297i
\(290\) 0 0
\(291\) 18.9345 + 12.2025i 1.10996 + 0.715320i
\(292\) 0 0
\(293\) −5.69846 21.2669i −0.332908 1.24243i −0.906120 0.423021i \(-0.860970\pi\)
0.573212 0.819407i \(-0.305697\pi\)
\(294\) 0 0
\(295\) 5.73205 9.92820i 0.333733 0.578042i
\(296\) 0 0
\(297\) −3.35253 8.46753i −0.194534 0.491336i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −11.1962 3.00000i −0.645335 0.172917i
\(302\) 0 0
\(303\) 32.5540 + 10.4520i 1.87018 + 0.600449i
\(304\) 0 0
\(305\) 16.1881 4.33760i 0.926930 0.248370i
\(306\) 0 0
\(307\) 12.3923 + 12.3923i 0.707266 + 0.707266i 0.965960 0.258693i \(-0.0832919\pi\)
−0.258693 + 0.965960i \(0.583292\pi\)
\(308\) 0 0
\(309\) 8.06065 + 8.88965i 0.458554 + 0.505715i
\(310\) 0 0
\(311\) −4.29311 −0.243440 −0.121720 0.992564i \(-0.538841\pi\)
−0.121720 + 0.992564i \(0.538841\pi\)
\(312\) 0 0
\(313\) 2.00000 0.113047 0.0565233 0.998401i \(-0.481998\pi\)
0.0565233 + 0.998401i \(0.481998\pi\)
\(314\) 0 0
\(315\) 5.91297 8.25916i 0.333158 0.465351i
\(316\) 0 0
\(317\) 11.2754 + 11.2754i 0.633288 + 0.633288i 0.948891 0.315603i \(-0.102207\pi\)
−0.315603 + 0.948891i \(0.602207\pi\)
\(318\) 0 0
\(319\) 9.36603 2.50962i 0.524397 0.140512i
\(320\) 0 0
\(321\) −8.83503 + 27.5179i −0.493123 + 1.53590i
\(322\) 0 0
\(323\) 2.14655 + 0.575167i 0.119437 + 0.0320032i
\(324\) 0 0
\(325\) −2.36603 1.16987i −0.131243 0.0648929i
\(326\) 0 0
\(327\) −0.335500 + 6.85980i −0.0185532 + 0.379348i
\(328\) 0 0
\(329\) 6.77174 11.7290i 0.373338 0.646640i
\(330\) 0 0
\(331\) −5.05256 18.8564i −0.277714 1.03644i −0.954001 0.299804i \(-0.903079\pi\)
0.676287 0.736638i \(-0.263588\pi\)
\(332\) 0 0
\(333\) 19.1822 + 7.21011i 1.05118 + 0.395112i
\(334\) 0 0
\(335\) 10.4897 + 18.1687i 0.573112 + 0.992660i
\(336\) 0 0
\(337\) 11.5359i 0.628400i −0.949357 0.314200i \(-0.898264\pi\)
0.949357 0.314200i \(-0.101736\pi\)
\(338\) 0 0
\(339\) −21.9545 + 4.74673i −1.19240 + 0.257807i
\(340\) 0 0
\(341\) −9.58244 + 5.53242i −0.518918 + 0.299597i
\(342\) 0 0
\(343\) −12.0000 + 12.0000i −0.647939 + 0.647939i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −22.4618 12.9683i −1.20581 0.696175i −0.243969 0.969783i \(-0.578450\pi\)
−0.961841 + 0.273608i \(0.911783\pi\)
\(348\) 0 0
\(349\) 1.50962 5.63397i 0.0808080 0.301580i −0.913679 0.406436i \(-0.866772\pi\)
0.994487 + 0.104856i \(0.0334382\pi\)
\(350\) 0 0
\(351\) 18.4337 3.34667i 0.983916 0.178632i
\(352\) 0 0
\(353\) 7.05932 26.3457i 0.375730 1.40224i −0.476546 0.879149i \(-0.658111\pi\)
0.852276 0.523093i \(-0.175222\pi\)
\(354\) 0 0
\(355\) −9.92820 5.73205i −0.526934 0.304226i
\(356\) 0 0
\(357\) −2.40340 4.67652i −0.127202 0.247508i
\(358\) 0 0
\(359\) 12.0611 12.0611i 0.636559 0.636559i −0.313146 0.949705i \(-0.601383\pi\)
0.949705 + 0.313146i \(0.101383\pi\)
\(360\) 0 0
\(361\) 15.5263 8.96410i 0.817173 0.471795i
\(362\) 0 0
\(363\) −13.4219 + 2.90192i −0.704468 + 0.152311i
\(364\) 0 0
\(365\) 20.6473i 1.08073i
\(366\) 0 0
\(367\) 4.80385 + 8.32051i 0.250759 + 0.434327i 0.963735 0.266861i \(-0.0859866\pi\)
−0.712976 + 0.701188i \(0.752653\pi\)
\(368\) 0 0
\(369\) 1.80149 + 0.677136i 0.0937819 + 0.0352503i
\(370\) 0 0
\(371\) −1.69293 6.31812i −0.0878928 0.328020i
\(372\) 0 0
\(373\) 9.79423 16.9641i 0.507126 0.878368i −0.492840 0.870120i \(-0.664041\pi\)
0.999966 0.00824796i \(-0.00262544\pi\)
\(374\) 0 0
\(375\) 0.864563 17.6773i 0.0446459 0.912852i
\(376\) 0 0
\(377\) 1.28380 + 19.9061i 0.0661192 + 1.02522i
\(378\) 0 0
\(379\) 4.83013 + 1.29423i 0.248107 + 0.0664801i 0.380729 0.924687i \(-0.375673\pi\)
−0.132622 + 0.991167i \(0.542340\pi\)
\(380\) 0 0
\(381\) −8.00804 + 24.9421i −0.410264 + 1.27782i
\(382\) 0 0
\(383\) 13.5435 3.62896i 0.692039 0.185431i 0.104377 0.994538i \(-0.466715\pi\)
0.587662 + 0.809106i \(0.300048\pi\)
\(384\) 0 0
\(385\) 4.19615 + 4.19615i 0.213856 + 0.213856i
\(386\) 0 0
\(387\) −14.3135 + 19.9929i −0.727596 + 1.01630i
\(388\) 0 0
\(389\) −5.28933 −0.268180 −0.134090 0.990969i \(-0.542811\pi\)
−0.134090 + 0.990969i \(0.542811\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 1.05553 + 1.16409i 0.0532446 + 0.0587206i
\(394\) 0 0
\(395\) −3.38587 3.38587i −0.170362 0.170362i
\(396\) 0 0
\(397\) 8.56218 2.29423i 0.429723 0.115144i −0.0374729 0.999298i \(-0.511931\pi\)
0.467196 + 0.884154i \(0.345264\pi\)
\(398\) 0 0
\(399\) 2.41450 + 0.775212i 0.120876 + 0.0388091i
\(400\) 0 0
\(401\) 27.1314 + 7.26985i 1.35488 + 0.363039i 0.861933 0.507021i \(-0.169253\pi\)
0.492946 + 0.870060i \(0.335920\pi\)
\(402\) 0 0
\(403\) −7.29423 21.5622i −0.363351 1.07409i
\(404\) 0 0
\(405\) −11.9868 17.9057i −0.595629 0.889739i
\(406\) 0 0
\(407\) −5.98604 + 10.3681i −0.296717 + 0.513929i
\(408\) 0 0
\(409\) 3.00962 + 11.2321i 0.148816 + 0.555389i 0.999556 + 0.0298020i \(0.00948767\pi\)
−0.850740 + 0.525587i \(0.823846\pi\)
\(410\) 0 0
\(411\) 8.58908 + 5.53528i 0.423668 + 0.273035i
\(412\) 0 0
\(413\) −3.38587 5.86450i −0.166608 0.288573i
\(414\) 0 0
\(415\) 4.19615i 0.205981i
\(416\) 0 0
\(417\) 0.875644 + 4.05001i 0.0428805 + 0.198330i
\(418\) 0 0
\(419\) 7.22536 4.17156i 0.352982 0.203794i −0.313016 0.949748i \(-0.601339\pi\)
0.665998 + 0.745954i \(0.268006\pi\)
\(420\) 0 0
\(421\) 0.830127 0.830127i 0.0404579 0.0404579i −0.686588 0.727046i \(-0.740893\pi\)
0.727046 + 0.686588i \(0.240893\pi\)
\(422\) 0 0
\(423\) −18.2358 22.2007i −0.886657 1.07943i
\(424\) 0 0
\(425\) 1.36086 + 0.785693i 0.0660114 + 0.0381117i
\(426\) 0 0
\(427\) 2.56218 9.56218i 0.123992 0.462746i
\(428\) 0 0
\(429\) 0.170025 + 10.9440i 0.00820890 + 0.528381i
\(430\) 0 0
\(431\) −0.542599 + 2.02501i −0.0261361 + 0.0975412i −0.977762 0.209718i \(-0.932745\pi\)
0.951626 + 0.307260i \(0.0994120\pi\)
\(432\) 0 0
\(433\) −6.10770 3.52628i −0.293517 0.169462i 0.346010 0.938231i \(-0.387536\pi\)
−0.639527 + 0.768769i \(0.720870\pi\)
\(434\) 0 0
\(435\) 20.4050 10.4867i 0.978344 0.502800i
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 4.09808 2.36603i 0.195591 0.112924i −0.399007 0.916948i \(-0.630645\pi\)
0.594597 + 0.804024i \(0.297312\pi\)
\(440\) 0 0
\(441\) 6.19657 + 13.6603i 0.295075 + 0.650488i
\(442\) 0 0
\(443\) 29.5656i 1.40470i −0.711830 0.702351i \(-0.752134\pi\)
0.711830 0.702351i \(-0.247866\pi\)
\(444\) 0 0
\(445\) −12.0263 20.8301i −0.570100 0.987443i
\(446\) 0 0
\(447\) −5.09465 + 7.90535i −0.240969 + 0.373910i
\(448\) 0 0
\(449\) −2.26810 8.46467i −0.107038 0.399472i 0.891530 0.452961i \(-0.149632\pi\)
−0.998568 + 0.0534890i \(0.982966\pi\)
\(450\) 0 0
\(451\) −0.562178 + 0.973721i −0.0264719 + 0.0458507i
\(452\) 0 0
\(453\) −18.2614 0.893131i −0.857996 0.0419629i
\(454\) 0 0
\(455\) −10.1576 + 6.77174i −0.476196 + 0.317464i
\(456\) 0 0
\(457\) −26.9904 7.23205i −1.26256 0.338301i −0.435382 0.900246i \(-0.643387\pi\)
−0.827175 + 0.561945i \(0.810053\pi\)
\(458\) 0 0
\(459\) −11.0799 + 1.28199i −0.517166 + 0.0598382i
\(460\) 0 0
\(461\) −23.4135 + 6.27363i −1.09048 + 0.292192i −0.758880 0.651230i \(-0.774253\pi\)
−0.331595 + 0.943422i \(0.607587\pi\)
\(462\) 0 0
\(463\) 15.0526 + 15.0526i 0.699552 + 0.699552i 0.964314 0.264762i \(-0.0852934\pi\)
−0.264762 + 0.964314i \(0.585293\pi\)
\(464\) 0 0
\(465\) −19.3940 + 17.5854i −0.899377 + 0.815506i
\(466\) 0 0
\(467\) 30.4728 1.41011 0.705057 0.709151i \(-0.250921\pi\)
0.705057 + 0.709151i \(0.250921\pi\)
\(468\) 0 0
\(469\) 12.3923 0.572223
\(470\) 0 0
\(471\) −19.4984 + 17.6800i −0.898437 + 0.814653i
\(472\) 0 0
\(473\) −10.1576 10.1576i −0.467047 0.467047i
\(474\) 0 0
\(475\) −0.732051 + 0.196152i −0.0335888 + 0.00900009i
\(476\) 0 0
\(477\) −13.8093 1.35401i −0.632285 0.0619960i
\(478\) 0 0
\(479\) −8.46467 2.26810i −0.386761 0.103632i 0.0601988 0.998186i \(-0.480827\pi\)
−0.446959 + 0.894554i \(0.647493\pi\)
\(480\) 0 0
\(481\) −18.5000 16.2583i −0.843527 0.741316i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −15.5685 + 26.9654i −0.706928 + 1.22444i
\(486\) 0 0
\(487\) 6.56218 + 24.4904i 0.297361 + 1.10977i 0.939324 + 0.343030i \(0.111453\pi\)
−0.641964 + 0.766735i \(0.721880\pi\)
\(488\) 0 0
\(489\) 14.5007 22.5007i 0.655746 1.01752i
\(490\) 0 0
\(491\) 12.5147 + 21.6761i 0.564780 + 0.978227i 0.997070 + 0.0764928i \(0.0243722\pi\)
−0.432290 + 0.901734i \(0.642294\pi\)
\(492\) 0 0
\(493\) 11.8756i 0.534852i
\(494\) 0 0
\(495\) 11.4641 5.20035i 0.515273 0.233738i
\(496\) 0 0
\(497\) −5.86450 + 3.38587i −0.263059 + 0.151877i
\(498\) 0 0
\(499\) −4.46410 + 4.46410i −0.199841 + 0.199841i −0.799932 0.600091i \(-0.795131\pi\)
0.600091 + 0.799932i \(0.295131\pi\)
\(500\) 0 0
\(501\) −18.1765 + 9.34143i −0.812064 + 0.417345i
\(502\) 0 0
\(503\) −24.8188 14.3292i −1.10662 0.638906i −0.168666 0.985673i \(-0.553946\pi\)
−0.937951 + 0.346767i \(0.887279\pi\)
\(504\) 0 0
\(505\) −12.2321 + 45.6506i −0.544319 + 2.03143i
\(506\) 0 0
\(507\) −22.1453 4.07236i −0.983509 0.180860i
\(508\) 0 0
\(509\) −3.88398 + 14.4952i −0.172154 + 0.642489i 0.824865 + 0.565330i \(0.191251\pi\)
−0.997019 + 0.0771582i \(0.975415\pi\)
\(510\) 0 0
\(511\) −10.5622 6.09808i −0.467243 0.269763i
\(512\) 0 0
\(513\) 3.34143 4.21584i 0.147528 0.186134i
\(514\) 0 0
\(515\) −11.7290 + 11.7290i −0.516841 + 0.516841i
\(516\) 0 0
\(517\) 14.5359 8.39230i 0.639288 0.369093i
\(518\) 0 0
\(519\) −2.72172 12.5885i −0.119470 0.552572i
\(520\) 0 0
\(521\) 33.2835i 1.45818i 0.684419 + 0.729089i \(0.260056\pi\)
−0.684419 + 0.729089i \(0.739944\pi\)
\(522\) 0 0
\(523\) 6.49038 + 11.2417i 0.283805 + 0.491564i 0.972319 0.233659i \(-0.0750700\pi\)
−0.688514 + 0.725223i \(0.741737\pi\)
\(524\) 0 0
\(525\) 1.50726 + 0.971364i 0.0657823 + 0.0423938i
\(526\) 0 0
\(527\) 3.50742 + 13.0899i 0.152785 + 0.570203i
\(528\) 0 0
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) 0 0
\(531\) −14.1721 + 2.34618i −0.615018 + 0.101816i
\(532\) 0 0
\(533\) −1.73742 1.52690i −0.0752562 0.0661373i
\(534\) 0 0
\(535\) −38.5885 10.3397i −1.66832 0.447026i
\(536\) 0 0
\(537\) 30.9111 + 9.92447i 1.33391 + 0.428273i
\(538\) 0 0
\(539\) −8.46467 + 2.26810i −0.364599 + 0.0976940i
\(540\) 0 0
\(541\) 23.6865 + 23.6865i 1.01836 + 1.01836i 0.999828 + 0.0185354i \(0.00590034\pi\)
0.0185354 + 0.999828i \(0.494100\pi\)
\(542\) 0 0
\(543\) 3.49036 + 3.84933i 0.149786 + 0.165191i
\(544\) 0 0
\(545\) −9.49346 −0.406655
\(546\) 0 0
\(547\) −2.00000 −0.0855138 −0.0427569 0.999086i \(-0.513614\pi\)
−0.0427569 + 0.999086i \(0.513614\pi\)
\(548\) 0 0
\(549\) −17.0751 12.2246i −0.728748 0.521732i
\(550\) 0 0
\(551\) 4.05001 + 4.05001i 0.172536 + 0.172536i
\(552\) 0 0
\(553\) −2.73205 + 0.732051i −0.116179 + 0.0311300i
\(554\) 0 0
\(555\) −8.65920 + 26.9703i −0.367563 + 1.14482i
\(556\) 0 0
\(557\) −39.3140 10.5342i −1.66579 0.446347i −0.701819 0.712355i \(-0.747628\pi\)
−0.963971 + 0.266009i \(0.914295\pi\)
\(558\) 0 0
\(559\) 24.5885 16.3923i 1.03998 0.693321i
\(560\) 0 0
\(561\) 0.318318 6.50849i 0.0134394 0.274788i
\(562\) 0 0
\(563\) −2.14655 + 3.71794i −0.0904665 + 0.156693i −0.907708 0.419603i \(-0.862169\pi\)
0.817241 + 0.576296i \(0.195502\pi\)
\(564\) 0 0
\(565\) −8.03590 29.9904i −0.338073 1.26170i
\(566\) 0 0
\(567\) −12.6999 + 0.843533i −0.533347 + 0.0354250i
\(568\) 0 0
\(569\) 8.01105 + 13.8755i 0.335841 + 0.581693i 0.983646 0.180113i \(-0.0576463\pi\)
−0.647805 + 0.761806i \(0.724313\pi\)
\(570\) 0 0
\(571\) 40.0526i 1.67615i −0.545557 0.838074i \(-0.683682\pi\)
0.545557 0.838074i \(-0.316318\pi\)
\(572\) 0 0
\(573\) 32.8564 7.10381i 1.37260 0.296766i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 3.49038 3.49038i 0.145306 0.145306i −0.630711 0.776018i \(-0.717237\pi\)
0.776018 + 0.630711i \(0.217237\pi\)
\(578\) 0 0
\(579\) −5.70810 11.1068i −0.237220 0.461581i
\(580\) 0 0
\(581\) 2.14655 + 1.23931i 0.0890541 + 0.0514154i
\(582\) 0 0
\(583\) 2.09808 7.83013i 0.0868934 0.324291i
\(584\) 0 0
\(585\) 5.86520 + 25.2240i 0.242496 + 1.04288i
\(586\) 0 0
\(587\) −5.20035 + 19.4080i −0.214641 + 0.801053i 0.771651 + 0.636046i \(0.219431\pi\)
−0.986292 + 0.165006i \(0.947235\pi\)
\(588\) 0 0
\(589\) −5.66025 3.26795i −0.233227 0.134654i
\(590\) 0 0
\(591\) 1.38761 + 2.69999i 0.0570785 + 0.111063i
\(592\) 0 0
\(593\) 10.6112 10.6112i 0.435751 0.435751i −0.454828 0.890579i \(-0.650299\pi\)
0.890579 + 0.454828i \(0.150299\pi\)
\(594\) 0 0
\(595\) 6.29423 3.63397i 0.258038 0.148978i
\(596\) 0 0
\(597\) −1.57139 + 0.339746i −0.0643126 + 0.0139049i
\(598\) 0 0
\(599\) 21.2224i 0.867126i 0.901123 + 0.433563i \(0.142744\pi\)
−0.901123 + 0.433563i \(0.857256\pi\)
\(600\) 0 0
\(601\) 3.79423 + 6.57180i 0.154770 + 0.268069i 0.932975 0.359941i \(-0.117203\pi\)
−0.778205 + 0.628010i \(0.783870\pi\)
\(602\) 0 0
\(603\) 9.24923 24.6072i 0.376658 1.00208i
\(604\) 0 0
\(605\) −4.91277 18.3347i −0.199732 0.745411i
\(606\) 0 0
\(607\) 5.09808 8.83013i 0.206925 0.358404i −0.743820 0.668380i \(-0.766988\pi\)
0.950744 + 0.309977i \(0.100321\pi\)
\(608\) 0 0
\(609\) 0.661992 13.5354i 0.0268253 0.548483i
\(610\) 0 0
\(611\) 11.0648 + 32.7083i 0.447636 + 1.32324i
\(612\) 0 0
\(613\) 16.3564 + 4.38269i 0.660629 + 0.177015i 0.573530 0.819185i \(-0.305574\pi\)
0.0870991 + 0.996200i \(0.472240\pi\)
\(614\) 0 0
\(615\) −0.813227 + 2.53291i −0.0327925 + 0.102137i
\(616\) 0 0
\(617\) 36.3818 9.74847i 1.46468 0.392459i 0.563574 0.826066i \(-0.309426\pi\)
0.901102 + 0.433607i \(0.142759\pi\)
\(618\) 0 0
\(619\) 14.3397 + 14.3397i 0.576363 + 0.576363i 0.933899 0.357536i \(-0.116383\pi\)
−0.357536 + 0.933899i \(0.616383\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −14.2076 −0.569216
\(624\) 0 0
\(625\) 28.1244 1.12497
\(626\) 0 0
\(627\) 2.11107 + 2.32818i 0.0843078 + 0.0929786i
\(628\) 0 0
\(629\) 10.3681 + 10.3681i 0.413404 + 0.413404i
\(630\) 0 0
\(631\) −2.26795 + 0.607695i −0.0902856 + 0.0241920i −0.303679 0.952774i \(-0.598215\pi\)
0.213393 + 0.976966i \(0.431548\pi\)
\(632\) 0 0
\(633\) −20.1131 6.45761i −0.799425 0.256667i
\(634\) 0 0
\(635\) −34.9764 9.37191i −1.38800 0.371913i
\(636\) 0 0
\(637\) −1.16025 17.9904i −0.0459709 0.712805i
\(638\) 0 0
\(639\) 2.34618 + 14.1721i 0.0928136 + 0.560641i
\(640\) 0 0
\(641\) −9.65949 + 16.7307i −0.381527 + 0.660824i −0.991281 0.131767i \(-0.957935\pi\)
0.609754 + 0.792591i \(0.291268\pi\)
\(642\) 0 0
\(643\) −7.00000 26.1244i −0.276053 1.03024i −0.955132 0.296179i \(-0.904287\pi\)
0.679079 0.734065i \(-0.262379\pi\)
\(644\) 0 0
\(645\) −28.5692 18.4116i −1.12491 0.724955i
\(646\) 0 0
\(647\) −7.22536 12.5147i −0.284058 0.492003i 0.688322 0.725405i \(-0.258348\pi\)
−0.972380 + 0.233402i \(0.925014\pi\)
\(648\) 0 0
\(649\) 8.39230i 0.329427i
\(650\) 0 0
\(651\) 3.26795 + 15.1149i 0.128081 + 0.592398i
\(652\) 0 0
\(653\) −33.6156 + 19.4080i −1.31548 + 0.759492i −0.982998 0.183617i \(-0.941219\pi\)
−0.332482 + 0.943110i \(0.607886\pi\)
\(654\) 0 0
\(655\) −1.53590 + 1.53590i −0.0600125 + 0.0600125i
\(656\) 0 0
\(657\) −19.9921 + 16.4217i −0.779967 + 0.640672i
\(658\) 0 0
\(659\) −27.1759 15.6900i −1.05862 0.611197i −0.133572 0.991039i \(-0.542645\pi\)
−0.925051 + 0.379842i \(0.875978\pi\)
\(660\) 0 0
\(661\) −4.42820 + 16.5263i −0.172237 + 0.642798i 0.824769 + 0.565470i \(0.191305\pi\)
−0.997006 + 0.0773274i \(0.975361\pi\)
\(662\) 0 0
\(663\) 13.0008 + 3.26797i 0.504909 + 0.126917i
\(664\) 0 0
\(665\) −0.907241 + 3.38587i −0.0351813 + 0.131298i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −35.5561 + 18.2734i −1.37468 + 0.706489i
\(670\) 0 0
\(671\) 8.67520 8.67520i 0.334902 0.334902i
\(672\) 0 0
\(673\) −11.0096 + 6.35641i −0.424390 + 0.245021i −0.696954 0.717116i \(-0.745462\pi\)
0.272564 + 0.962138i \(0.412128\pi\)
\(674\) 0 0
\(675\) 3.05379 2.26795i 0.117541 0.0872934i
\(676\) 0 0
\(677\) 38.8159i 1.49182i −0.666048 0.745909i \(-0.732015\pi\)
0.666048 0.745909i \(-0.267985\pi\)
\(678\) 0 0
\(679\) 9.19615 + 15.9282i 0.352916 + 0.611268i
\(680\) 0 0
\(681\) 14.6820 22.7821i 0.562617 0.873011i
\(682\) 0 0
\(683\) 4.26054 + 15.9006i 0.163025 + 0.608418i 0.998284 + 0.0585607i \(0.0186511\pi\)
−0.835259 + 0.549857i \(0.814682\pi\)
\(684\) 0 0
\(685\) −7.06218 + 12.2321i −0.269832 + 0.467363i
\(686\) 0 0
\(687\) 24.7699 + 1.21145i 0.945031 + 0.0462196i
\(688\) 0 0
\(689\) 14.9488 + 7.39139i 0.569505 + 0.281590i
\(690\) 0 0
\(691\) 41.8827 + 11.2224i 1.59329 + 0.426921i 0.943008 0.332770i \(-0.107983\pi\)
0.650284 + 0.759691i \(0.274650\pi\)
\(692\) 0 0
\(693\) 0.725614 7.40039i 0.0275638 0.281118i
\(694\) 0 0
\(695\) −5.53242 + 1.48241i −0.209857 + 0.0562309i
\(696\) 0 0
\(697\) 0.973721 + 0.973721i 0.0368823 + 0.0368823i
\(698\) 0 0
\(699\) −9.54106 + 8.65131i −0.360876 + 0.327223i
\(700\) 0 0
\(701\) 20.3152 0.767295 0.383647 0.923480i \(-0.374668\pi\)
0.383647 + 0.923480i \(0.374668\pi\)
\(702\) 0 0
\(703\) −7.07180 −0.266718
\(704\) 0 0
\(705\) 29.4194 26.6759i 1.10800 1.00467i
\(706\) 0 0
\(707\) 19.7400 + 19.7400i 0.742401 + 0.742401i
\(708\) 0 0
\(709\) −9.96410 + 2.66987i −0.374210 + 0.100269i −0.441022 0.897496i \(-0.645384\pi\)
0.0668121 + 0.997766i \(0.478717\pi\)
\(710\) 0 0
\(711\) −0.585497 + 5.97136i −0.0219578 + 0.223944i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −15.0981 + 0.973721i −0.564636 + 0.0364151i
\(716\) 0 0
\(717\) 17.3799 + 0.850019i 0.649065 + 0.0317446i
\(718\) 0 0
\(719\) 5.86450 10.1576i 0.218709 0.378815i −0.735705 0.677302i \(-0.763149\pi\)
0.954413 + 0.298488i \(0.0964822\pi\)
\(720\) 0 0
\(721\) 2.53590 + 9.46410i 0.0944418 + 0.352462i
\(722\) 0 0
\(723\) 7.02496 10.9006i 0.261261 0.405398i
\(724\) 0 0
\(725\) 2.02501 + 3.50742i 0.0752069 + 0.130262i
\(726\) 0 0
\(727\) 25.5167i 0.946361i −0.880966 0.473180i \(-0.843106\pi\)
0.880966 0.473180i \(-0.156894\pi\)
\(728\) 0 0
\(729\) −7.80385 + 25.8476i −0.289031 + 0.957320i
\(730\) 0 0
\(731\) −15.2364 + 8.79674i −0.563539 + 0.325359i
\(732\) 0 0
\(733\) −36.2224 + 36.2224i −1.33791 + 1.33791i −0.439820 + 0.898086i \(0.644958\pi\)
−0.898086 + 0.439820i \(0.855042\pi\)
\(734\) 0 0
\(735\) −18.4413 + 9.47753i −0.680216 + 0.349584i
\(736\) 0 0
\(737\) 13.3004 + 7.67898i 0.489926 + 0.282859i
\(738\) 0 0
\(739\) −13.1244 + 48.9808i −0.482787 + 1.80179i 0.107037 + 0.994255i \(0.465864\pi\)
−0.589825 + 0.807531i \(0.700803\pi\)
\(740\) 0 0
\(741\) −5.54822 + 3.31924i −0.203819 + 0.121935i
\(742\) 0 0
\(743\) 13.5435 50.5449i 0.496862 1.85431i −0.0224808 0.999747i \(-0.507156\pi\)
0.519343 0.854566i \(-0.326177\pi\)
\(744\) 0 0
\(745\) −11.2583 6.50000i −0.412473 0.238142i
\(746\) 0 0
\(747\) 4.06300 3.33739i 0.148658 0.122109i
\(748\) 0 0
\(749\) −16.6862 + 16.6862i −0.609702 + 0.609702i
\(750\) 0 0
\(751\) −38.2750 + 22.0981i −1.39667 + 0.806370i −0.994043 0.108992i \(-0.965238\pi\)
−0.402632 + 0.915362i \(0.631904\pi\)
\(752\) 0 0
\(753\) −8.01105 37.0526i −0.291939 1.35027i
\(754\) 0 0
\(755\) 25.2725i 0.919759i
\(756\) 0 0
\(757\) 12.3923 + 21.4641i 0.450406 + 0.780126i 0.998411 0.0563489i \(-0.0179459\pi\)
−0.548005 + 0.836475i \(0.684613\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.11777 4.17156i −0.0405190 0.151219i 0.942703 0.333634i \(-0.108275\pi\)
−0.983222 + 0.182415i \(0.941608\pi\)
\(762\) 0 0
\(763\) −2.80385 + 4.85641i −0.101506 + 0.175814i
\(764\) 0 0
\(765\) −2.51810 15.2106i −0.0910423 0.549941i
\(766\) 0 0
\(767\) 16.9293 + 3.38587i 0.611283 + 0.122257i
\(768\) 0 0
\(769\) −2.16987 0.581416i −0.0782476 0.0209664i 0.219483 0.975616i \(-0.429563\pi\)
−0.297730 + 0.954650i \(0.596230\pi\)
\(770\) 0 0
\(771\) 27.3712 + 8.78792i 0.985748 + 0.316489i
\(772\) 0 0
\(773\) 5.98604 1.60396i 0.215303 0.0576903i −0.149555 0.988753i \(-0.547784\pi\)
0.364858 + 0.931063i \(0.381117\pi\)
\(774\) 0 0
\(775\) −3.26795 3.26795i −0.117388 0.117388i
\(776\) 0 0
\(777\) 11.2393 + 12.3952i 0.403206 + 0.444675i
\(778\) 0 0
\(779\) −0.664146 −0.0237955
\(780\) 0 0
\(781\) −8.39230 −0.300300
\(782\) 0 0
\(783\) −26.3830 11.4169i −0.942851 0.408008i
\(784\) 0 0
\(785\) −25.7261 25.7261i −0.918203 0.918203i
\(786\) 0 0
\(787\) 11.2942 3.02628i 0.402596 0.107875i −0.0518385 0.998655i \(-0.516508\pi\)
0.454434 + 0.890780i \(0.349841\pi\)
\(788\) 0 0
\(789\) −6.33898 + 19.7436i −0.225674 + 0.702891i
\(790\) 0 0
\(791\) −17.7150 4.74673i −0.629874 0.168774i
\(792\) 0 0
\(793\) 14.0000 + 21.0000i 0.497155 + 0.745732i
\(794\) 0 0
\(795\) 0.936928 19.1569i 0.0332294 0.679426i