Properties

Label 624.2.cn.c.353.1
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 353.1
Root \(0.500000 + 2.19293i\) of defining polynomial
Character \(\chi\) \(=\) 624.353
Dual form 624.2.cn.c.449.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.64914 + 0.529480i) q^{3} +(-1.69293 - 1.69293i) q^{5} +(1.36603 - 0.366025i) q^{7} +(2.43930 - 1.74637i) q^{9} +O(q^{10})\) \(q+(-1.64914 + 0.529480i) q^{3} +(-1.69293 - 1.69293i) q^{5} +(1.36603 - 0.366025i) q^{7} +(2.43930 - 1.74637i) q^{9} +(-1.69293 - 0.453620i) q^{11} +(-1.59808 + 3.23205i) q^{13} +(3.68825 + 1.89551i) q^{15} +(-1.07328 + 1.85897i) q^{17} +(0.267949 + 1.00000i) q^{19} +(-2.05896 + 1.32691i) q^{21} +0.732051i q^{25} +(-3.09808 + 4.17156i) q^{27} +(-4.79122 + 2.76621i) q^{29} +(-4.46410 + 4.46410i) q^{31} +(3.03206 - 0.148292i) q^{33} +(-2.93225 - 1.69293i) q^{35} +(-1.76795 + 6.59808i) q^{37} +(0.924141 - 6.17624i) q^{39} +(0.166037 - 0.619657i) q^{41} +(-7.09808 - 4.09808i) q^{43} +(-7.08606 - 1.17309i) q^{45} +(-6.77174 + 6.77174i) q^{47} +(-4.33013 + 2.50000i) q^{49} +(0.785693 - 3.63397i) q^{51} +4.62518i q^{53} +(2.09808 + 3.63397i) q^{55} +(-0.971364 - 1.50726i) q^{57} +(1.23931 + 4.62518i) q^{59} +(3.50000 - 6.06218i) q^{61} +(2.69293 - 3.27843i) q^{63} +(8.17709 - 2.76621i) q^{65} +(8.46410 + 2.26795i) q^{67} +(4.62518 - 1.23931i) q^{71} +(-6.09808 - 6.09808i) q^{73} +(-0.387606 - 1.20725i) q^{75} -2.47863 q^{77} -2.00000 q^{79} +(2.90039 - 8.51984i) q^{81} +(-1.23931 - 1.23931i) q^{83} +(4.96410 - 1.33013i) q^{85} +(6.43672 - 7.09871i) q^{87} +(9.70398 + 2.60017i) q^{89} +(-1.00000 + 5.00000i) q^{91} +(4.99826 - 9.72556i) q^{93} +(1.23931 - 2.14655i) q^{95} +(3.36603 + 12.5622i) q^{97} +(-4.92177 + 1.84997i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{3} + 4q^{7} + 4q^{9} + O(q^{10}) \) \( 8q + 2q^{3} + 4q^{7} + 4q^{9} + 8q^{13} + 14q^{15} + 16q^{19} + 4q^{21} - 4q^{27} - 8q^{31} + 16q^{33} - 28q^{37} + 14q^{39} - 36q^{43} - 20q^{45} - 4q^{55} + 16q^{57} + 28q^{61} + 8q^{63} + 40q^{67} - 28q^{73} - 12q^{75} - 16q^{79} + 4q^{81} + 12q^{85} + 34q^{87} - 8q^{91} + 4q^{93} + 20q^{97} - 40q^{99} + O(q^{100}) \)

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
\(3\) −1.64914 + 0.529480i −0.952129 + 0.305695i
\(4\) 0 0
\(5\) −1.69293 1.69293i −0.757103 0.757103i 0.218691 0.975794i \(-0.429821\pi\)
−0.975794 + 0.218691i \(0.929821\pi\)
\(6\) 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
\(9\) 2.43930 1.74637i 0.813101 0.582123i
\(10\) 0 0
\(11\) −1.69293 0.453620i −0.510439 0.136772i −0.00559833 0.999984i \(-0.501782\pi\)
−0.504840 + 0.863213i \(0.668449\pi\)
\(12\) 0 0
\(13\) −1.59808 + 3.23205i −0.443227 + 0.896410i
\(14\) 0 0
\(15\) 3.68825 + 1.89551i 0.952303 + 0.489417i
\(16\) 0 0
\(17\) −1.07328 + 1.85897i −0.260308 + 0.450867i −0.966324 0.257330i \(-0.917157\pi\)
0.706016 + 0.708196i \(0.250491\pi\)
\(18\) 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
\(21\) −2.05896 + 1.32691i −0.449302 + 0.289555i
\(22\) 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 −0.873847 0.486202i \(-0.838382\pi\)
−0.0158603 + 0.999874i \(0.505049\pi\)
\(30\) 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
\(33\) 3.03206 0.148292i 0.527814 0.0258144i
\(34\) 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
\(39\) 0.924141 6.17624i 0.147981 0.988990i
\(40\) 0 0
\(41\) 0.166037 0.619657i 0.0259306 0.0967741i −0.951748 0.306881i \(-0.900715\pi\)
0.977678 + 0.210107i \(0.0673812\pi\)
\(42\) 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
\(45\) −7.08606 1.17309i −1.05633 0.174874i
\(46\) 0 0
\(47\) −6.77174 + 6.77174i −0.987759 + 0.987759i −0.999926 0.0121668i \(-0.996127\pi\)
0.0121668 + 0.999926i \(0.496127\pi\)
\(48\) 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 \(0.102897\pi\)
−0.948205 + 0.317659i \(0.897103\pi\)
\(54\) 0 0
\(55\) 2.09808 + 3.63397i 0.282905 + 0.490005i
\(56\) 0 0
\(57\) −0.971364 1.50726i −0.128660 0.199642i
\(58\) 0 0
\(59\) 1.23931 + 4.62518i 0.161345 + 0.602147i 0.998478 + 0.0551484i \(0.0175632\pi\)
−0.837133 + 0.546999i \(0.815770\pi\)
\(60\) 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
\(63\) 2.69293 3.27843i 0.339278 0.413043i
\(64\) 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 0.0263025 0.999654i \(-0.491627\pi\)
0.522606 + 0.852575i \(0.324960\pi\)
\(72\) 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
\(75\) −0.387606 1.20725i −0.0447569 0.139401i
\(76\) 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
\(81\) 2.90039 8.51984i 0.322266 0.946649i
\(82\) 0 0
\(83\) −1.23931 1.23931i −0.136032 0.136032i 0.635812 0.771844i \(-0.280665\pi\)
−0.771844 + 0.635812i \(0.780665\pi\)
\(84\) 0 0
\(85\) 4.96410 1.33013i 0.538432 0.144273i
\(86\) 0 0
\(87\) 6.43672 7.09871i 0.690089 0.761062i
\(88\) 0 0
\(89\) 9.70398 + 2.60017i 1.02862 + 0.275618i 0.733390 0.679808i \(-0.237937\pi\)
0.295230 + 0.955426i \(0.404604\pi\)
\(90\) 0 0
\(91\) −1.00000 + 5.00000i −0.104828 + 0.524142i
\(92\) 0 0
\(93\) 4.99826 9.72556i 0.518296 1.00849i
\(94\) 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
\(99\) −4.92177 + 1.84997i −0.494656 + 0.185929i
\(100\) 0 0
\(101\) −9.87002 17.0954i −0.982104 1.70105i −0.654160 0.756356i \(-0.726978\pi\)
−0.327944 0.944697i \(-0.606356\pi\)
\(102\) 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 0.402925 0.915233i \(-0.367993\pi\)
0.994078 + 0.108673i \(0.0346600\pi\)
\(108\) 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
\(111\) −0.577958 11.8172i −0.0548573 1.12164i
\(112\) 0 0
\(113\) 11.2309 + 6.48415i 1.05651 + 0.609978i 0.924465 0.381266i \(-0.124512\pi\)
0.132047 + 0.991243i \(0.457845\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.74616 + 10.6748i 0.161433 + 0.986884i
\(118\) 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
\(123\) 0.0542788 + 1.10981i 0.00489415 + 0.100068i
\(124\) 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 \(-0.987381\pi\)
0.999214 0.0396330i \(-0.0126189\pi\)
\(132\) 0 0
\(133\) 0.732051 + 1.26795i 0.0634769 + 0.109945i
\(134\) 0 0
\(135\) 12.3070 1.81734i 1.05922 0.156412i
\(136\) 0 0
\(137\) −1.52690 5.69846i −0.130452 0.486852i 0.869524 0.493891i \(-0.164426\pi\)
−0.999975 + 0.00703925i \(0.997759\pi\)
\(138\) 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
\(141\) 7.58202 14.7530i 0.638521 1.24243i
\(142\) 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
\(147\) 5.81727 6.41556i 0.479800 0.529146i
\(148\) 0 0
\(149\) 5.24484 1.40535i 0.429674 0.115131i −0.0374992 0.999297i \(-0.511939\pi\)
0.467173 + 0.884166i \(0.345272\pi\)
\(150\) 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
\(153\) 0.628400 + 6.40893i 0.0508031 + 0.518131i
\(154\) 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
\(159\) −2.44894 7.62756i −0.194214 0.604905i
\(160\) 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
\(165\) −5.38413 4.88203i −0.419154 0.380066i
\(166\) 0 0
\(167\) 11.3969 + 3.05379i 0.881920 + 0.236310i 0.671235 0.741244i \(-0.265764\pi\)
0.210685 + 0.977554i \(0.432431\pi\)
\(168\) 0 0
\(169\) −7.89230 10.3301i −0.607100 0.794625i
\(170\) 0 0
\(171\) 2.39998 + 1.97136i 0.183531 + 0.150754i
\(172\) 0 0
\(173\) −3.71794 + 6.43966i −0.282670 + 0.489598i −0.972041 0.234809i \(-0.924553\pi\)
0.689372 + 0.724408i \(0.257887\pi\)
\(174\) 0 0
\(175\) 0.267949 + 1.00000i 0.0202551 + 0.0755929i
\(176\) 0 0
\(177\) −4.49274 6.97136i −0.337695 0.524000i
\(178\) 0 0
\(179\) −9.37191 16.2326i −0.700489 1.21328i −0.968295 0.249810i \(-0.919632\pi\)
0.267805 0.963473i \(-0.413702\pi\)
\(180\) 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
\(189\) −2.70515 + 6.83243i −0.196771 + 0.496986i
\(190\) 0 0
\(191\) −16.8078 9.70398i −1.21617 0.702156i −0.252073 0.967708i \(-0.581112\pi\)
−0.964096 + 0.265553i \(0.914446\pi\)
\(192\) 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
\(195\) −12.0205 + 8.89146i −0.860804 + 0.636731i
\(196\) 0 0
\(197\) 0.453620 1.69293i 0.0323191 0.120617i −0.947882 0.318622i \(-0.896780\pi\)
0.980201 + 0.198006i \(0.0634465\pi\)
\(198\) 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
\(201\) −15.1593 + 0.741412i −1.06925 + 0.0522952i
\(202\) 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
\(213\) −6.97136 + 4.49274i −0.477670 + 0.307837i
\(214\) 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
\(219\) 13.2854 + 6.82775i 0.897742 + 0.461377i
\(220\) 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
\(225\) 1.27843 + 1.78569i 0.0852287 + 0.119046i
\(226\) 0 0
\(227\) −15.1149 + 4.05001i −1.00321 + 0.268809i −0.722789 0.691069i \(-0.757140\pi\)
−0.280419 + 0.959878i \(0.590474\pi\)
\(228\) 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
\(231\) 4.08759 1.31238i 0.268944 0.0863485i
\(232\) 0 0
\(233\) 7.43588 0.487141 0.243570 0.969883i \(-0.421681\pi\)
0.243570 + 0.969883i \(0.421681\pi\)
\(234\) 0 0
\(235\) 22.9282 1.49567
\(236\) 0 0
\(237\) 3.29827 1.05896i 0.214246 0.0687868i
\(238\) 0 0
\(239\) −7.10381 7.10381i −0.459507 0.459507i 0.438986 0.898494i \(-0.355338\pi\)
−0.898494 + 0.438986i \(0.855338\pi\)
\(240\) 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
\(243\) −0.272062 + 15.5861i −0.0174528 + 0.999848i
\(244\) 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
\(249\) 2.69999 + 1.38761i 0.171105 + 0.0879360i
\(250\) 0 0
\(251\) −10.9433 + 18.9543i −0.690735 + 1.19639i 0.280863 + 0.959748i \(0.409379\pi\)
−0.971597 + 0.236640i \(0.923954\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −7.48221 + 4.82195i −0.468554 + 0.301962i
\(256\) 0 0
\(257\) −8.29863 14.3737i −0.517655 0.896604i −0.999790 0.0205071i \(-0.993472\pi\)
0.482135 0.876097i \(-0.339861\pi\)
\(258\) 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 −0.145029 0.989427i \(-0.546327\pi\)
0.784355 + 0.620312i \(0.212994\pi\)
\(264\) 0 0
\(265\) 7.83013 7.83013i 0.481001 0.481001i
\(266\) 0 0
\(267\) −17.3799 + 0.850019i −1.06363 + 0.0520203i
\(268\) 0 0
\(269\) −9.58244 5.53242i −0.584251 0.337318i 0.178570 0.983927i \(-0.442853\pi\)
−0.762821 + 0.646610i \(0.776186\pi\)
\(270\) 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
\(273\) −0.998262 8.77516i −0.0604176 0.531097i
\(274\) 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
\(279\) −3.09333 + 18.6853i −0.185193 + 1.11866i
\(280\) 0 0
\(281\) −15.9006 + 15.9006i −0.948547 + 0.948547i −0.998740 0.0501922i \(-0.984017\pi\)
0.0501922 + 0.998740i \(0.484017\pi\)
\(282\) 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
\(291\) −12.2025 18.9345i −0.715320 1.10996i
\(292\) 0 0
\(293\) 5.69846 + 21.2669i 0.332908 + 1.24243i 0.906120 + 0.423021i \(0.139030\pi\)
−0.573212 + 0.819407i \(0.694303\pi\)
\(294\) 0 0
\(295\) 5.73205 9.92820i 0.333733 0.578042i
\(296\) 0 0
\(297\) 7.13714 5.65683i 0.414139 0.328242i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −11.1962 3.00000i −0.645335 0.172917i
\(302\) 0 0
\(303\) 25.3287 + 22.9666i 1.45509 + 1.31940i
\(304\) 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
\(309\) −3.66834 11.4256i −0.208685 0.649977i
\(310\) 0 0
\(311\) 4.29311 0.243440 0.121720 0.992564i \(-0.461159\pi\)
0.121720 + 0.992564i \(0.461159\pi\)
\(312\) 0 0
\(313\) 2.00000 0.113047 0.0565233 0.998401i \(-0.481998\pi\)
0.0565233 + 0.998401i \(0.481998\pi\)
\(314\) 0 0
\(315\) −10.1091 + 0.991207i −0.569585 + 0.0558482i
\(316\) 0 0
\(317\) −11.2754 11.2754i −0.633288 0.633288i 0.315603 0.948891i \(-0.397793\pi\)
−0.948891 + 0.315603i \(0.897793\pi\)
\(318\) 0 0
\(319\) 9.36603 2.50962i 0.524397 0.140512i
\(320\) 0 0
\(321\) −19.4137 + 21.4103i −1.08357 + 1.19501i
\(322\) 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
\(327\) 3.13935 6.10851i 0.173606 0.337801i
\(328\) 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
\(333\) 7.21011 + 19.1822i 0.395112 + 1.05118i
\(334\) 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 0.961841 0.273608i \(-0.0882171\pi\)
0.243969 + 0.969783i \(0.421550\pi\)
\(348\) 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
\(351\) −8.53174 16.6796i −0.455390 0.890292i
\(352\) 0 0
\(353\) −7.05932 + 26.3457i −0.375730 + 1.40224i 0.476546 + 0.879149i \(0.341889\pi\)
−0.852276 + 0.523093i \(0.824778\pi\)
\(354\) 0 0
\(355\) −9.92820 5.73205i −0.526934 0.304226i
\(356\) 0 0
\(357\) −0.256850 5.25169i −0.0135939 0.277949i
\(358\) 0 0
\(359\) −12.0611 + 12.0611i −0.636559 + 0.636559i −0.949705 0.313146i \(-0.898617\pi\)
0.313146 + 0.949705i \(0.398617\pi\)
\(360\) 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
\(369\) −0.677136 1.80149i −0.0352503 0.0937819i
\(370\) 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
\(375\) 8.08992 15.7413i 0.417762 0.812876i
\(376\) 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
\(381\) 17.5965 19.4062i 0.901496 0.994211i
\(382\) 0 0
\(383\) −13.5435 + 3.62896i −0.692039 + 0.185431i −0.587662 0.809106i \(-0.699952\pi\)
−0.104377 + 0.994538i \(0.533285\pi\)
\(384\) 0 0
\(385\) 4.19615 + 4.19615i 0.213856 + 0.213856i
\(386\) 0 0
\(387\) −24.4711 + 2.39941i −1.24394 + 0.121969i
\(388\) 0 0
\(389\) 5.28933 0.268180 0.134090 0.990969i \(-0.457189\pi\)
0.134090 + 0.990969i \(0.457189\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0.480365 + 1.49616i 0.0242312 + 0.0754715i
\(394\) 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
\(399\) −1.87861 1.70342i −0.0940479 0.0852774i
\(400\) 0 0
\(401\) −27.1314 7.26985i −1.35488 0.363039i −0.492946 0.870060i \(-0.664080\pi\)
−0.861933 + 0.507021i \(0.830747\pi\)
\(402\) 0 0
\(403\) −7.29423 21.5622i −0.363351 1.07409i
\(404\) 0 0
\(405\) −19.3337 + 9.51336i −0.960700 + 0.472722i
\(406\) 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
\(411\) 5.53528 + 8.58908i 0.273035 + 0.423668i
\(412\) 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 −0.665998 0.745954i \(-0.731994\pi\)
0.313016 + 0.949748i \(0.398661\pi\)
\(420\) 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
\(423\) −4.69237 + 28.3443i −0.228151 + 1.37815i
\(424\) 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
\(429\) −4.36618 + 10.0368i −0.210801 + 0.484579i
\(430\) 0 0
\(431\) 0.542599 2.02501i 0.0261361 0.0975412i −0.951626 0.307260i \(-0.900588\pi\)
0.977762 + 0.209718i \(0.0672547\pi\)
\(432\) 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
\(435\) −22.9146 + 1.12071i −1.09867 + 0.0537339i
\(436\) 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 \(0.247866\pi\)
−0.711830 + 0.702351i \(0.752134\pi\)
\(444\) 0 0
\(445\) −12.0263 20.8301i −0.570100 0.987443i
\(446\) 0 0
\(447\) −7.90535 + 5.09465i −0.373910 + 0.240969i
\(448\) 0 0
\(449\) 2.26810 + 8.46467i 0.107038 + 0.399472i 0.998568 0.0534890i \(-0.0170342\pi\)
−0.891530 + 0.452961i \(0.850368\pi\)
\(450\) 0 0
\(451\) −0.562178 + 0.973721i −0.0264719 + 0.0458507i
\(452\) 0 0
\(453\) 16.2614 + 8.35723i 0.764028 + 0.392657i
\(454\) 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
\(459\) −4.42972 10.2365i −0.206761 0.477798i
\(460\) 0 0
\(461\) 23.4135 6.27363i 1.09048 0.292192i 0.331595 0.943422i \(-0.392413\pi\)
0.758880 + 0.651230i \(0.225747\pi\)
\(462\) 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
\(465\) −24.9265 + 8.00301i −1.15594 + 0.371131i
\(466\) 0 0
\(467\) −30.4728 −1.41011 −0.705057 0.709151i \(-0.749079\pi\)
−0.705057 + 0.709151i \(0.749079\pi\)
\(468\) 0 0
\(469\) 12.3923 0.572223
\(470\) 0 0
\(471\) 25.0605 8.04605i 1.15473 0.370743i
\(472\) 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
\(477\) 8.07727 + 11.2822i 0.369833 + 0.516577i
\(478\) 0 0
\(479\) 8.46467 + 2.26810i 0.386761 + 0.103632i 0.446959 0.894554i \(-0.352507\pi\)
−0.0601988 + 0.998186i \(0.519173\pi\)
\(480\) 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
\(489\) −22.5007 + 14.5007i −1.01752 + 0.655746i
\(490\) 0 0
\(491\) −12.5147 21.6761i −0.564780 0.978227i −0.997070 0.0764928i \(-0.975628\pi\)
0.432290 0.901734i \(-0.357706\pi\)
\(492\) 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
\(501\) −20.4120 + 0.998312i −0.911941 + 0.0446013i
\(502\) 0 0
\(503\) 24.8188 + 14.3292i 1.10662 + 0.638906i 0.937951 0.346767i \(-0.112721\pi\)
0.168666 + 0.985673i \(0.446054\pi\)
\(504\) 0 0
\(505\) −12.2321 + 45.6506i −0.544319 + 2.03143i
\(506\) 0 0
\(507\) 18.4851 + 12.8570i 0.820951 + 0.570998i
\(508\) 0 0
\(509\) 3.88398 14.4952i 0.172154 0.642489i −0.824865 0.565330i \(-0.808749\pi\)
0.997019 0.0771582i \(-0.0245846\pi\)
\(510\) 0 0
\(511\) −10.5622 6.09808i −0.467243 0.269763i
\(512\) 0 0
\(513\) −5.00169 1.98031i −0.220830 0.0874328i
\(514\) 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 \(-0.739944\pi\)
0.684419 0.729089i \(-0.260056\pi\)
\(522\) 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
\(525\) −0.971364 1.50726i −0.0423938 0.0657823i
\(526\) 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
\(531\) 11.1003 + 9.11792i 0.481713 + 0.395684i
\(532\) 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
\(537\) 24.0504 + 21.8076i 1.03785 + 0.941066i
\(538\) 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
\(543\) −1.58844 4.94741i −0.0681664 0.212314i
\(544\) 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
\(549\) −2.04924 20.8998i −0.0874593 0.891981i
\(550\) 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
\(555\) −19.0273 + 20.9842i −0.807665 + 0.890731i
\(556\) 0 0
\(557\) 39.3140 + 10.5342i 1.66579 + 0.446347i 0.963971 0.266009i \(-0.0857049\pi\)
0.701819 + 0.712355i \(0.252372\pi\)
\(558\) 0 0
\(559\) 24.5885 16.3923i 1.03998 0.693321i
\(560\) 0 0
\(561\) −2.97857 + 5.79567i −0.125755 + 0.244693i
\(562\) 0 0
\(563\) 2.14655 3.71794i 0.0904665 0.156693i −0.817241 0.576296i \(-0.804498\pi\)
0.907708 + 0.419603i \(0.137831\pi\)
\(564\) 0 0
\(565\) −8.03590 29.9904i −0.338073 1.26170i
\(566\) 0 0
\(567\) 0.843533 12.6999i 0.0354250 0.533347i
\(568\) 0 0
\(569\) −8.01105 13.8755i −0.335841 0.581693i 0.647805 0.761806i \(-0.275687\pi\)
−0.983646 + 0.180113i \(0.942354\pi\)
\(570\) 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
\(579\) 0.610020 + 12.4728i 0.0253516 + 0.518351i
\(580\) 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
\(585\) 15.1156 21.0278i 0.624952 0.869394i
\(586\) 0 0
\(587\) 5.20035 19.4080i 0.214641 0.801053i −0.771651 0.636046i \(-0.780569\pi\)
0.986292 0.165006i \(-0.0527645\pi\)
\(588\) 0 0
\(589\) −5.66025 3.26795i −0.233227 0.134654i
\(590\) 0 0
\(591\) 0.148292 + 3.03206i 0.00609993 + 0.124722i
\(592\) 0 0
\(593\) −10.6112 + 10.6112i −0.435751 + 0.435751i −0.890579 0.454828i \(-0.849701\pi\)
0.454828 + 0.890579i \(0.349701\pi\)
\(594\) 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 \(-0.857256\pi\)
0.901123 0.433563i \(-0.142744\pi\)
\(600\) 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
\(603\) 24.6072 9.24923i 1.00208 0.376658i
\(604\) 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
\(609\) 6.19441 12.0530i 0.251010 0.488413i
\(610\) 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
\(615\) 1.78695 1.97073i 0.0720567 0.0794674i
\(616\) 0 0
\(617\) −36.3818 + 9.74847i −1.46468 + 0.392459i −0.901102 0.433607i \(-0.857241\pi\)
−0.563574 + 0.826066i \(0.690574\pi\)
\(618\) 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
\(627\) 0.960731 + 2.99233i 0.0383679 + 0.119502i
\(628\) 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
\(633\) 15.6490 + 14.1897i 0.621993 + 0.563989i
\(634\) 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
\(639\) 9.11792 11.1003i 0.360699 0.439122i
\(640\) 0 0
\(641\) 9.65949 16.7307i 0.381527 0.660824i −0.609754 0.792591i \(-0.708732\pi\)
0.991281 + 0.131767i \(0.0420650\pi\)
\(642\) 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
\(645\) −18.4116 28.5692i −0.724955 1.12491i
\(646\) 0 0
\(647\) 7.22536 + 12.5147i 0.284058 + 0.492003i 0.972380 0.233402i \(-0.0749858\pi\)
−0.688322 + 0.725405i \(0.741652\pi\)
\(648\) 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 0.332482 0.943110i \(-0.392114\pi\)
0.982998 + 0.183617i \(0.0587807\pi\)
\(654\) 0 0
\(655\) −1.53590 + 1.53590i −0.0600125 + 0.0600125i
\(656\) 0 0
\(657\) −25.5245 4.22556i −0.995807 0.164855i
\(658\) 0 0
\(659\) 27.1759 + 15.6900i 1.05862 + 0.611197i 0.925051 0.379842i \(-0.124022\pi\)
0.133572 + 0.991039i \(0.457355\pi\)
\(660\) 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
\(663\) 10.4896 + 8.34677i 0.407382 + 0.324162i
\(664\) 0 0
\(665\) 0.907241 3.38587i 0.0351813 0.131298i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 39.9292 1.95286i 1.54375 0.0755019i
\(670\) 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 \(0.267985\pi\)
−0.666048 + 0.745909i \(0.732015\pi\)
\(678\) 0 0
\(679\) 9.19615 + 15.9282i 0.352916 + 0.611268i
\(680\) 0 0
\(681\) 22.7821 14.6820i 0.873011 0.562617i
\(682\) 0 0
\(683\) −4.26054 15.9006i −0.163025 0.608418i −0.998284 0.0585607i \(-0.981349\pi\)
0.835259 0.549857i \(-0.185318\pi\)
\(684\) 0 0
\(685\) −7.06218 + 12.2321i −0.269832 + 0.467363i
\(686\) 0 0
\(687\) −22.0571 11.3358i −0.841530 0.432488i
\(688\) 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
\(693\) −6.04612 + 4.32860i −0.229673 + 0.164430i
\(694\) 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
\(699\) −12.2628 + 3.93715i −0.463821 + 0.148917i
\(700\) 0 0
\(701\) −20.3152 −0.767295 −0.383647 0.923480i \(-0.625332\pi\)
−0.383647 + 0.923480i \(0.625332\pi\)
\(702\) 0 0
\(703\) −7.07180 −0.266718
\(704\) 0 0
\(705\) −37.8117 + 12.1400i −1.42407 + 0.457220i
\(706\) 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
\(711\) −4.87861 + 3.49274i −0.182962 + 0.130988i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −15.0981 + 0.973721i −0.564636 + 0.0364151i
\(716\) 0 0
\(717\) 15.4765 + 7.95383i 0.577979 + 0.297041i
\(718\) 0 0
\(719\) −5.86450 + 10.1576i −0.218709 + 0.378815i −0.954413 0.298488i \(-0.903518\pi\)
0.735705 + 0.677302i \(0.236851\pi\)
\(720\) 0 0
\(721\) 2.53590 + 9.46410i 0.0944418 + 0.352462i
\(722\) 0 0
\(723\) −10.9006 + 7.02496i −0.405398 + 0.261261i
\(724\) 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
\(735\) −20.7094 + 1.01286i −0.763877 + 0.0373597i
\(736\) 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
\(741\) 6.42386 0.730778i 0.235987 0.0268458i
\(742\) 0 0
\(743\) −13.5435 + 50.5449i −0.496862 + 1.85431i 0.0224808 + 0.999747i \(0.492844\pi\)
−0.519343 + 0.854566i \(0.673823\pi\)
\(744\) 0 0
\(745\) −11.2583 6.50000i −0.412473 0.238142i
\(746\) 0 0
\(747\) −5.18736 0.858763i −0.189796 0.0314205i
\(748\) 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 0.983222 0.182415i \(-0.0583916\pi\)
−0.942703 + 0.333634i \(0.891725\pi\)
\(762\) 0 0
\(763\) −2.80385 + 4.85641i −0.101506 + 0.175814i
\(764\) 0 0
\(765\) 9.78605 11.9137i 0.353816 0.430742i
\(766\) 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
\(771\) 21.2961 + 19.3102i 0.766962 + 0.695438i
\(772\) 0 0
\(773\) −5.98604 + 1.60396i −0.215303 + 0.0576903i −0.364858 0.931063i \(-0.618883\pi\)
0.149555 + 0.988753i \(0.452216\pi\)
\(774\) 0 0
\(775\) −3.26795 3.26795i −0.117388 0.117388i
\(776\) 0 0
\(777\) −5.11491 15.9311i −0.183496 0.571524i
\(778\) 0 0
\(779\) 0.664146 0.0237955
\(780\) 0 0
\(781\) −8.39230 −0.300300
\(782\) 0 0
\(783\) 3.30414 28.5568i 0.118080 1.02054i
\(784\) 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
\(789\) −13.9290 + 15.3615i −0.495885 + 0.546884i
\(790\) 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
\(795\) −8.76706 + 17.0588i −0.310935 + 0.605015i