Properties

Label 624.2.cn.c.449.1
Level $624$
Weight $2$
Character 624.449
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 449.1
Root \(0.500000 - 2.19293i\) of defining polynomial
Character \(\chi\) \(=\) 624.449
Dual form 624.2.cn.c.353.1

$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(1\)

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 −0.975794 0.218691i \(-0.929821\pi\)
0.218691 + 0.975794i \(0.429821\pi\)
\(6\) 0 0
\(7\) 1.36603 + 0.366025i 0.516309 + 0.138345i 0.507559 0.861617i \(-0.330548\pi\)
0.00875026 + 0.999962i \(0.497215\pi\)
\(8\) 0 0
\(9\) 2.43930 + 1.74637i 0.813101 + 0.582123i
\(10\) 0 0
\(11\) −1.69293 + 0.453620i −0.510439 + 0.136772i −0.504840 0.863213i \(-0.668449\pi\)
−0.00559833 + 0.999984i \(0.501782\pi\)
\(12\) 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 0.706016 0.708196i \(-0.250491\pi\)
−0.966324 + 0.257330i \(0.917157\pi\)
\(18\) 0 0
\(19\) 0.267949 1.00000i 0.0614718 0.229416i −0.928355 0.371695i \(-0.878777\pi\)
0.989826 + 0.142280i \(0.0454432\pi\)
\(20\) 0 0
\(21\) −2.05896 1.32691i −0.449302 0.289555i
\(22\) 0 0
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 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 \(-0.505049\pi\)
−0.873847 + 0.486202i \(0.838382\pi\)
\(30\) 0 0
\(31\) −4.46410 4.46410i −0.801776 0.801776i 0.181597 0.983373i \(-0.441873\pi\)
−0.983373 + 0.181597i \(0.941873\pi\)
\(32\) 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 −0.944612 0.328190i \(-0.893561\pi\)
0.653963 0.756527i \(-0.273105\pi\)
\(38\) 0 0
\(39\) 0.924141 + 6.17624i 0.147981 + 0.988990i
\(40\) 0 0
\(41\) 0.166037 + 0.619657i 0.0259306 + 0.0967741i 0.977678 0.210107i \(-0.0673812\pi\)
−0.951748 + 0.306881i \(0.900715\pi\)
\(42\) 0 0
\(43\) −7.09808 + 4.09808i −1.08245 + 0.624951i −0.931555 0.363600i \(-0.881548\pi\)
−0.150891 + 0.988550i \(0.548214\pi\)
\(44\) 0 0
\(45\) −7.08606 + 1.17309i −1.05633 + 0.174874i
\(46\) 0 0
\(47\) −6.77174 6.77174i −0.987759 0.987759i 0.0121668 0.999926i \(-0.496127\pi\)
−0.999926 + 0.0121668i \(0.996127\pi\)
\(48\) 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
\(57\) −0.971364 + 1.50726i −0.128660 + 0.199642i
\(58\) 0 0
\(59\) 1.23931 4.62518i 0.161345 0.602147i −0.837133 0.546999i \(-0.815770\pi\)
0.998478 0.0551484i \(-0.0175632\pi\)
\(60\) 0 0
\(61\) 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i \(-0.0187572\pi\)
−0.550135 + 0.835076i \(0.685424\pi\)
\(62\) 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 0.298407 0.954439i \(-0.403545\pi\)
0.735647 + 0.677365i \(0.236878\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 4.62518 + 1.23931i 0.548908 + 0.147079i 0.522606 0.852575i \(-0.324960\pi\)
0.0263025 + 0.999654i \(0.491627\pi\)
\(72\) 0 0
\(73\) −6.09808 + 6.09808i −0.713726 + 0.713726i −0.967313 0.253587i \(-0.918390\pi\)
0.253587 + 0.967313i \(0.418390\pi\)
\(74\) 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 −0.771844 0.635812i \(-0.780665\pi\)
0.635812 + 0.771844i \(0.280665\pi\)
\(84\) 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 0.295230 0.955426i \(-0.404604\pi\)
0.733390 + 0.679808i \(0.237937\pi\)
\(90\) 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 −0.554575 0.832134i \(-0.687119\pi\)
0.896343 0.443362i \(-0.146214\pi\)
\(98\) 0 0
\(99\) −4.92177 1.84997i −0.494656 0.185929i
\(100\) 0 0
\(101\) −9.87002 + 17.0954i −0.982104 + 1.70105i −0.327944 + 0.944697i \(0.606356\pi\)
−0.654160 + 0.756356i \(0.726978\pi\)
\(102\) 0 0
\(103\) 6.92820i 0.682656i −0.939944 0.341328i \(-0.889123\pi\)
0.939944 0.341328i \(-0.110877\pi\)
\(104\) 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 \(-0.0346600\pi\)
0.402925 + 0.915233i \(0.367993\pi\)
\(108\) 0 0
\(109\) −2.80385 2.80385i −0.268560 0.268560i 0.559960 0.828520i \(-0.310817\pi\)
−0.828520 + 0.559960i \(0.810817\pi\)
\(110\) 0 0
\(111\) −0.577958 + 11.8172i −0.0548573 + 1.12164i
\(112\) 0 0
\(113\) 11.2309 6.48415i 1.05651 0.609978i 0.132047 0.991243i \(-0.457845\pi\)
0.924465 + 0.381266i \(0.124512\pi\)
\(114\) 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 −0.210420 0.977611i \(-0.567483\pi\)
−0.951846 + 0.306576i \(0.900817\pi\)
\(128\) 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
\(135\) 12.3070 + 1.81734i 1.05922 + 0.156412i
\(136\) 0 0
\(137\) −1.52690 + 5.69846i −0.130452 + 0.486852i −0.999975 0.00703925i \(-0.997759\pi\)
0.869524 + 0.493891i \(0.164426\pi\)
\(138\) 0 0
\(139\) −1.19615 2.07180i −0.101456 0.175728i 0.810829 0.585284i \(-0.199017\pi\)
−0.912285 + 0.409556i \(0.865684\pi\)
\(140\) 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 0.467173 0.884166i \(-0.345272\pi\)
−0.0374992 + 0.999297i \(0.511939\pi\)
\(150\) 0 0
\(151\) −7.46410 + 7.46410i −0.607420 + 0.607420i −0.942271 0.334851i \(-0.891314\pi\)
0.334851 + 0.942271i \(0.391314\pi\)
\(152\) 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 0.790661 0.612254i \(-0.209737\pi\)
0.378606 + 0.925558i \(0.376404\pi\)
\(164\) 0 0
\(165\) −5.38413 + 4.88203i −0.419154 + 0.380066i
\(166\) 0 0
\(167\) 11.3969 3.05379i 0.881920 0.236310i 0.210685 0.977554i \(-0.432431\pi\)
0.671235 + 0.741244i \(0.265764\pi\)
\(168\) 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 0.689372 0.724408i \(-0.257887\pi\)
−0.972041 + 0.234809i \(0.924553\pi\)
\(174\) 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 0.267805 + 0.963473i \(0.413702\pi\)
−0.968295 + 0.249810i \(0.919632\pi\)
\(180\) 0 0
\(181\) 3.00000i 0.222988i −0.993765 0.111494i \(-0.964436\pi\)
0.993765 0.111494i \(-0.0355636\pi\)
\(182\) 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 −0.964096 0.265553i \(-0.914446\pi\)
−0.252073 + 0.967708i \(0.581112\pi\)
\(192\) 0 0
\(193\) 1.86603 + 6.96410i 0.134319 + 0.501287i 1.00000 0.000689767i \(0.000219560\pi\)
−0.865680 + 0.500597i \(0.833114\pi\)
\(194\) 0 0
\(195\) −12.0205 8.89146i −0.860804 0.636731i
\(196\) 0 0
\(197\) 0.453620 + 1.69293i 0.0323191 + 0.120617i 0.980201 0.198006i \(-0.0634465\pi\)
−0.947882 + 0.318622i \(0.896780\pi\)
\(198\) 0 0
\(199\) −0.803848 + 0.464102i −0.0569832 + 0.0328993i −0.528221 0.849107i \(-0.677141\pi\)
0.471238 + 0.882006i \(0.343807\pi\)
\(200\) 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 −0.995920 0.0902411i \(-0.971236\pi\)
0.576111 + 0.817371i \(0.304570\pi\)
\(212\) 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 −0.910726 0.413011i \(-0.864477\pi\)
−0.582206 + 0.813041i \(0.697810\pi\)
\(224\) 0 0
\(225\) 1.27843 1.78569i 0.0852287 0.119046i
\(226\) 0 0
\(227\) −15.1149 4.05001i −1.00321 0.268809i −0.280419 0.959878i \(-0.590474\pi\)
−0.722789 + 0.691069i \(0.757140\pi\)
\(228\) 0 0
\(229\) 10.1244 10.1244i 0.669036 0.669036i −0.288457 0.957493i \(-0.593142\pi\)
0.957493 + 0.288457i \(0.0931421\pi\)
\(230\) 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 −0.898494 0.438986i \(-0.855338\pi\)
0.438986 + 0.898494i \(0.355338\pi\)
\(240\) 0 0
\(241\) 7.23205 + 1.93782i 0.465857 + 0.124826i 0.484110 0.875007i \(-0.339144\pi\)
−0.0182524 + 0.999833i \(0.505810\pi\)
\(242\) 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 −0.971597 0.236640i \(-0.923954\pi\)
0.280863 0.959748i \(-0.409379\pi\)
\(252\) 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 0.482135 + 0.876097i \(0.339861\pi\)
−0.999790 + 0.0205071i \(0.993472\pi\)
\(258\) 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 \(-0.212994\pi\)
−0.145029 + 0.989427i \(0.546327\pi\)
\(264\) 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 −0.762821 0.646610i \(-0.776186\pi\)
0.178570 + 0.983927i \(0.442853\pi\)
\(270\) 0 0
\(271\) −0.535898 2.00000i −0.0325535 0.121491i 0.947737 0.319052i \(-0.103365\pi\)
−0.980291 + 0.197561i \(0.936698\pi\)
\(272\) 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 −0.403724 0.914881i \(-0.632285\pi\)
0.590448 + 0.807076i \(0.298951\pi\)
\(278\) 0 0
\(279\) −3.09333 18.6853i −0.185193 1.11866i
\(280\) 0 0
\(281\) −15.9006 15.9006i −0.948547 0.948547i 0.0501922 0.998740i \(-0.484017\pi\)
−0.998740 + 0.0501922i \(0.984017\pi\)
\(282\) 0 0
\(283\) 21.2942 + 12.2942i 1.26581 + 0.730816i 0.974192 0.225719i \(-0.0724731\pi\)
0.291618 + 0.956535i \(0.405806\pi\)
\(284\) 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 −0.573212 0.819407i \(-0.694303\pi\)
0.906120 0.423021i \(-0.139030\pi\)
\(294\) 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 −0.258693 0.965960i \(-0.583292\pi\)
0.965960 + 0.258693i \(0.0832919\pi\)
\(308\) 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 −0.948891 0.315603i \(-0.897793\pi\)
0.315603 + 0.948891i \(0.397793\pi\)
\(318\) 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 0.676287 + 0.736638i \(0.263588\pi\)
−0.954001 + 0.299804i \(0.903079\pi\)
\(332\) 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 \(0.101736\pi\)
−0.949357 + 0.314200i \(0.898264\pi\)
\(338\) 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 \(-0.421550\pi\)
0.961841 + 0.273608i \(0.0882171\pi\)
\(348\) 0 0
\(349\) 1.50962 + 5.63397i 0.0808080 + 0.301580i 0.994487 0.104856i \(-0.0334382\pi\)
−0.913679 + 0.406436i \(0.866772\pi\)
\(350\) 0 0
\(351\) −8.53174 + 16.6796i −0.455390 + 0.890292i
\(352\) 0 0
\(353\) −7.05932 26.3457i −0.375730 1.40224i −0.852276 0.523093i \(-0.824778\pi\)
0.476546 0.879149i \(-0.341889\pi\)
\(354\) 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 0.313146 0.949705i \(-0.398617\pi\)
−0.949705 + 0.313146i \(0.898617\pi\)
\(360\) 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 −0.712976 0.701188i \(-0.752653\pi\)
0.963735 + 0.266861i \(0.0859866\pi\)
\(368\) 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 0.999966 + 0.00824796i \(0.00262544\pi\)
−0.492840 + 0.870120i \(0.664041\pi\)
\(374\) 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 −0.132622 0.991167i \(-0.542340\pi\)
0.380729 + 0.924687i \(0.375673\pi\)
\(380\) 0 0
\(381\) 17.5965 + 19.4062i 0.901496 + 0.994211i
\(382\) 0 0
\(383\) −13.5435 3.62896i −0.692039 0.185431i −0.104377 0.994538i \(-0.533285\pi\)
−0.587662 + 0.809106i \(0.699952\pi\)
\(384\) 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 0.467196 0.884154i \(-0.345264\pi\)
−0.0374729 + 0.999298i \(0.511931\pi\)
\(398\) 0 0
\(399\) −1.87861 + 1.70342i −0.0940479 + 0.0852774i
\(400\) 0 0
\(401\) −27.1314 + 7.26985i −1.35488 + 0.363039i −0.861933 0.507021i \(-0.830747\pi\)
−0.492946 + 0.870060i \(0.664080\pi\)
\(402\) 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 −0.850740 0.525587i \(-0.823846\pi\)
0.999556 0.0298020i \(-0.00948767\pi\)
\(410\) 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 0.313016 0.949748i \(-0.398661\pi\)
−0.665998 + 0.745954i \(0.731994\pi\)
\(420\) 0 0
\(421\) 0.830127 + 0.830127i 0.0404579 + 0.0404579i 0.727046 0.686588i \(-0.240893\pi\)
−0.686588 + 0.727046i \(0.740893\pi\)
\(422\) 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 0.977762 0.209718i \(-0.0672547\pi\)
−0.951626 + 0.307260i \(0.900588\pi\)
\(432\) 0 0
\(433\) −6.10770 + 3.52628i −0.293517 + 0.169462i −0.639527 0.768769i \(-0.720870\pi\)
0.346010 + 0.938231i \(0.387536\pi\)
\(434\) 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 0.594597 0.804024i \(-0.297312\pi\)
−0.399007 + 0.916948i \(0.630645\pi\)
\(440\) 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
\(447\) −7.90535 5.09465i −0.373910 0.240969i
\(448\) 0 0
\(449\) 2.26810 8.46467i 0.107038 0.399472i −0.891530 0.452961i \(-0.850368\pi\)
0.998568 + 0.0534890i \(0.0170342\pi\)
\(450\) 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 −0.827175 0.561945i \(-0.810053\pi\)
−0.435382 + 0.900246i \(0.643387\pi\)
\(458\) 0 0
\(459\) −4.42972 + 10.2365i −0.206761 + 0.477798i
\(460\) 0 0
\(461\) 23.4135 + 6.27363i 1.09048 + 0.292192i 0.758880 0.651230i \(-0.225747\pi\)
0.331595 + 0.943422i \(0.392413\pi\)
\(462\) 0 0
\(463\) 15.0526 15.0526i 0.699552 0.699552i −0.264762 0.964314i \(-0.585293\pi\)
0.964314 + 0.264762i \(0.0852934\pi\)
\(464\) 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 −0.0601988 0.998186i \(-0.519173\pi\)
0.446959 + 0.894554i \(0.352507\pi\)
\(480\) 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 −0.641964 0.766735i \(-0.721880\pi\)
0.939324 0.343030i \(-0.111453\pi\)
\(488\) 0 0
\(489\) −22.5007 14.5007i −1.01752 0.655746i
\(490\) 0 0
\(491\) −12.5147 + 21.6761i −0.564780 + 0.978227i 0.432290 + 0.901734i \(0.357706\pi\)
−0.997070 + 0.0764928i \(0.975628\pi\)
\(492\) 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 0.600091 0.799932i \(-0.295131\pi\)
−0.799932 + 0.600091i \(0.795131\pi\)
\(500\) 0 0
\(501\) −20.4120 0.998312i −0.911941 0.0446013i
\(502\) 0 0
\(503\) 24.8188 14.3292i 1.10662 0.638906i 0.168666 0.985673i \(-0.446054\pi\)
0.937951 + 0.346767i \(0.112721\pi\)
\(504\) 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 0.997019 + 0.0771582i \(0.0245846\pi\)
−0.824865 + 0.565330i \(0.808749\pi\)
\(510\) 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 \(0.260056\pi\)
−0.684419 + 0.729089i \(0.739944\pi\)
\(522\) 0 0
\(523\) 6.49038 11.2417i 0.283805 0.491564i −0.688514 0.725223i \(-0.741737\pi\)
0.972319 + 0.233659i \(0.0750700\pi\)
\(524\) 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 0.0185354 0.999828i \(-0.494100\pi\)
0.999828 0.0185354i \(-0.00590034\pi\)
\(542\) 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 0.701819 0.712355i \(-0.252372\pi\)
0.963971 + 0.266009i \(0.0857049\pi\)
\(558\) 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 0.907708 0.419603i \(-0.137831\pi\)
−0.817241 + 0.576296i \(0.804498\pi\)
\(564\) 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 −0.983646 0.180113i \(-0.942354\pi\)
0.647805 + 0.761806i \(0.275687\pi\)
\(570\) 0 0
\(571\) 40.0526i 1.67615i 0.545557 + 0.838074i \(0.316318\pi\)
−0.545557 + 0.838074i \(0.683682\pi\)
\(572\) 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 0.776018 0.630711i \(-0.217237\pi\)
−0.630711 + 0.776018i \(0.717237\pi\)
\(578\) 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 0.986292 + 0.165006i \(0.0527645\pi\)
−0.771651 + 0.636046i \(0.780569\pi\)
\(588\) 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 0.454828 0.890579i \(-0.349701\pi\)
−0.890579 + 0.454828i \(0.849701\pi\)
\(594\) 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 −0.778205 0.628010i \(-0.783870\pi\)
0.932975 + 0.359941i \(0.117203\pi\)
\(602\) 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 0.950744 0.309977i \(-0.100321\pi\)
−0.743820 + 0.668380i \(0.766988\pi\)
\(608\) 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 0.0870991 0.996200i \(-0.472240\pi\)
0.573530 + 0.819185i \(0.305574\pi\)
\(614\) 0 0
\(615\) 1.78695 + 1.97073i 0.0720567 + 0.0794674i
\(616\) 0 0
\(617\) −36.3818 9.74847i −1.46468 0.392459i −0.563574 0.826066i \(-0.690574\pi\)
−0.901102 + 0.433607i \(0.857241\pi\)
\(618\) 0 0
\(619\) 14.3397 14.3397i 0.576363 0.576363i −0.357536 0.933899i \(-0.616383\pi\)
0.933899 + 0.357536i \(0.116383\pi\)
\(620\) 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 0.213393 0.976966i \(-0.431548\pi\)
−0.303679 + 0.952774i \(0.598215\pi\)
\(632\) 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 0.991281 0.131767i \(-0.0420650\pi\)
−0.609754 + 0.792591i \(0.708732\pi\)
\(642\) 0 0
\(643\) −7.00000 + 26.1244i −0.276053 + 1.03024i 0.679079 + 0.734065i \(0.262379\pi\)
−0.955132 + 0.296179i \(0.904287\pi\)
\(644\) 0 0
\(645\) −18.4116 + 28.5692i −0.724955 + 1.12491i
\(646\) 0 0
\(647\) 7.22536 12.5147i 0.284058 0.492003i −0.688322 0.725405i \(-0.741652\pi\)
0.972380 + 0.233402i \(0.0749858\pi\)
\(648\) 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 \(-0.0587807\pi\)
0.332482 + 0.943110i \(0.392114\pi\)
\(654\) 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 0.133572 0.991039i \(-0.457355\pi\)
0.925051 + 0.379842i \(0.124022\pi\)
\(660\) 0 0
\(661\) −4.42820 16.5263i −0.172237 0.642798i −0.997006 0.0773274i \(-0.975361\pi\)
0.824769 0.565470i \(-0.191305\pi\)
\(662\) 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 0.272564 0.962138i \(-0.412128\pi\)
−0.696954 + 0.717116i \(0.745462\pi\)
\(674\) 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
\(681\) 22.7821 + 14.6820i 0.873011 + 0.562617i
\(682\) 0 0
\(683\) −4.26054 + 15.9006i −0.163025 + 0.608418i 0.835259 + 0.549857i \(0.185318\pi\)
−0.998284 + 0.0585607i \(0.981349\pi\)
\(684\) 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 0.650284 0.759691i \(-0.274650\pi\)
0.943008 + 0.332770i \(0.107983\pi\)
\(692\) 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 0.0668121 0.997766i \(-0.478717\pi\)
−0.441022 + 0.897496i \(0.645384\pi\)
\(710\) 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 0.735705 0.677302i \(-0.236851\pi\)
−0.954413 + 0.298488i \(0.903518\pi\)
\(720\) 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 \(0.156894\pi\)
−0.880966 + 0.473180i \(0.843106\pi\)
\(728\) 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 −0.898086 0.439820i \(-0.855042\pi\)
−0.439820 0.898086i \(-0.644958\pi\)
\(734\) 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 −0.589825 0.807531i \(-0.700803\pi\)
0.107037 0.994255i \(-0.465864\pi\)
\(740\) 0 0
\(741\) 6.42386 + 0.730778i 0.235987 + 0.0268458i
\(742\) 0 0
\(743\) −13.5435 50.5449i −0.496862 1.85431i −0.519343 0.854566i \(-0.673823\pi\)
0.0224808 0.999747i \(-0.492844\pi\)
\(744\) 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 −0.402632 0.915362i \(-0.631904\pi\)
−0.994043 + 0.108992i \(0.965238\pi\)
\(752\) 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 −0.548005 0.836475i \(-0.684613\pi\)
0.998411 + 0.0563489i \(0.0179459\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.11777 4.17156i 0.0405190 0.151219i −0.942703 0.333634i \(-0.891725\pi\)
0.983222 + 0.182415i \(0.0583916\pi\)
\(762\) 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 −0.297730 0.954650i \(-0.596230\pi\)
0.219483 + 0.975616i \(0.429563\pi\)
\(770\) 0 0
\(771\) 21.2961 19.3102i 0.766962 0.695438i
\(772\) 0 0
\(773\) −5.98604 1.60396i −0.215303 0.0576903i 0.149555 0.988753i \(-0.452216\pi\)
−0.364858 + 0.931063i \(0.618883\pi\)
\(774\) 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 0.454434 0.890780i \(-0.349841\pi\)
−0.0518385 + 0.998655i \(0.516508\pi\)
\(788\) 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