Properties

Label 960.2.bl.a.529.9
Level $960$
Weight $2$
Character 960.529
Analytic conductor $7.666$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 960.bl (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.66563859404\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 240)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 529.9
Character \(\chi\) \(=\) 960.529
Dual form 960.2.bl.a.49.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{3} +(0.860885 + 2.06370i) q^{5} +0.707398 q^{7} -1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{3} +(0.860885 + 2.06370i) q^{5} +0.707398 q^{7} -1.00000i q^{9} +(-1.79993 + 1.79993i) q^{11} +(-3.86348 + 3.86348i) q^{13} +(-2.06800 - 0.850522i) q^{15} +0.244884i q^{17} +(-1.53863 - 1.53863i) q^{19} +(-0.500206 + 0.500206i) q^{21} +6.92280 q^{23} +(-3.51775 + 3.55323i) q^{25} +(0.707107 + 0.707107i) q^{27} +(-4.89882 - 4.89882i) q^{29} -7.60734 q^{31} -2.54548i q^{33} +(0.608988 + 1.45986i) q^{35} +(8.47863 + 8.47863i) q^{37} -5.46378i q^{39} +2.12118i q^{41} +(-0.684507 - 0.684507i) q^{43} +(2.06370 - 0.860885i) q^{45} -4.47342i q^{47} -6.49959 q^{49} +(-0.173159 - 0.173159i) q^{51} +(-1.47026 - 1.47026i) q^{53} +(-5.26405 - 2.16499i) q^{55} +2.17595 q^{57} +(-5.86121 + 5.86121i) q^{59} +(0.0537432 + 0.0537432i) q^{61} -0.707398i q^{63} +(-11.2991 - 4.64706i) q^{65} +(-7.85550 + 7.85550i) q^{67} +(-4.89516 + 4.89516i) q^{69} +2.08595i q^{71} -9.69951 q^{73} +(-0.0250827 - 4.99994i) q^{75} +(-1.27326 + 1.27326i) q^{77} +7.34690 q^{79} -1.00000 q^{81} +(-6.80291 + 6.80291i) q^{83} +(-0.505369 + 0.210817i) q^{85} +6.92797 q^{87} -3.07483i q^{89} +(-2.73301 + 2.73301i) q^{91} +(5.37920 - 5.37920i) q^{93} +(1.85069 - 4.49986i) q^{95} +1.39922i q^{97} +(1.79993 + 1.79993i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 8 q^{19} + 48 q^{31} - 24 q^{35} + 48 q^{49} - 8 q^{51} + 32 q^{59} + 16 q^{61} + 16 q^{65} - 16 q^{69} + 16 q^{75} + 96 q^{79} - 48 q^{81} + 32 q^{91} + 48 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).

\(n\) \(511\) \(577\) \(641\) \(901\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) 0 0
\(5\) 0.860885 + 2.06370i 0.385000 + 0.922917i
\(6\) 0 0
\(7\) 0.707398 0.267371 0.133686 0.991024i \(-0.457319\pi\)
0.133686 + 0.991024i \(0.457319\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) −1.79993 + 1.79993i −0.542699 + 0.542699i −0.924319 0.381621i \(-0.875366\pi\)
0.381621 + 0.924319i \(0.375366\pi\)
\(12\) 0 0
\(13\) −3.86348 + 3.86348i −1.07154 + 1.07154i −0.0742996 + 0.997236i \(0.523672\pi\)
−0.997236 + 0.0742996i \(0.976328\pi\)
\(14\) 0 0
\(15\) −2.06800 0.850522i −0.533955 0.219604i
\(16\) 0 0
\(17\) 0.244884i 0.0593932i 0.999559 + 0.0296966i \(0.00945410\pi\)
−0.999559 + 0.0296966i \(0.990546\pi\)
\(18\) 0 0
\(19\) −1.53863 1.53863i −0.352986 0.352986i 0.508233 0.861219i \(-0.330299\pi\)
−0.861219 + 0.508233i \(0.830299\pi\)
\(20\) 0 0
\(21\) −0.500206 + 0.500206i −0.109154 + 0.109154i
\(22\) 0 0
\(23\) 6.92280 1.44350 0.721752 0.692152i \(-0.243337\pi\)
0.721752 + 0.692152i \(0.243337\pi\)
\(24\) 0 0
\(25\) −3.51775 + 3.55323i −0.703551 + 0.710645i
\(26\) 0 0
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 0 0
\(29\) −4.89882 4.89882i −0.909688 0.909688i 0.0865591 0.996247i \(-0.472413\pi\)
−0.996247 + 0.0865591i \(0.972413\pi\)
\(30\) 0 0
\(31\) −7.60734 −1.36632 −0.683159 0.730270i \(-0.739394\pi\)
−0.683159 + 0.730270i \(0.739394\pi\)
\(32\) 0 0
\(33\) 2.54548i 0.443112i
\(34\) 0 0
\(35\) 0.608988 + 1.45986i 0.102938 + 0.246761i
\(36\) 0 0
\(37\) 8.47863 + 8.47863i 1.39388 + 1.39388i 0.816420 + 0.577459i \(0.195956\pi\)
0.577459 + 0.816420i \(0.304044\pi\)
\(38\) 0 0
\(39\) 5.46378i 0.874905i
\(40\) 0 0
\(41\) 2.12118i 0.331272i 0.986187 + 0.165636i \(0.0529677\pi\)
−0.986187 + 0.165636i \(0.947032\pi\)
\(42\) 0 0
\(43\) −0.684507 0.684507i −0.104386 0.104386i 0.652985 0.757371i \(-0.273517\pi\)
−0.757371 + 0.652985i \(0.773517\pi\)
\(44\) 0 0
\(45\) 2.06370 0.860885i 0.307639 0.128333i
\(46\) 0 0
\(47\) 4.47342i 0.652515i −0.945281 0.326258i \(-0.894212\pi\)
0.945281 0.326258i \(-0.105788\pi\)
\(48\) 0 0
\(49\) −6.49959 −0.928513
\(50\) 0 0
\(51\) −0.173159 0.173159i −0.0242472 0.0242472i
\(52\) 0 0
\(53\) −1.47026 1.47026i −0.201956 0.201956i 0.598881 0.800838i \(-0.295612\pi\)
−0.800838 + 0.598881i \(0.795612\pi\)
\(54\) 0 0
\(55\) −5.26405 2.16499i −0.709804 0.291927i
\(56\) 0 0
\(57\) 2.17595 0.288212
\(58\) 0 0
\(59\) −5.86121 + 5.86121i −0.763065 + 0.763065i −0.976875 0.213810i \(-0.931413\pi\)
0.213810 + 0.976875i \(0.431413\pi\)
\(60\) 0 0
\(61\) 0.0537432 + 0.0537432i 0.00688112 + 0.00688112i 0.710539 0.703658i \(-0.248451\pi\)
−0.703658 + 0.710539i \(0.748451\pi\)
\(62\) 0 0
\(63\) 0.707398i 0.0891237i
\(64\) 0 0
\(65\) −11.2991 4.64706i −1.40148 0.576397i
\(66\) 0 0
\(67\) −7.85550 + 7.85550i −0.959702 + 0.959702i −0.999219 0.0395170i \(-0.987418\pi\)
0.0395170 + 0.999219i \(0.487418\pi\)
\(68\) 0 0
\(69\) −4.89516 + 4.89516i −0.589308 + 0.589308i
\(70\) 0 0
\(71\) 2.08595i 0.247557i 0.992310 + 0.123778i \(0.0395012\pi\)
−0.992310 + 0.123778i \(0.960499\pi\)
\(72\) 0 0
\(73\) −9.69951 −1.13524 −0.567621 0.823290i \(-0.692136\pi\)
−0.567621 + 0.823290i \(0.692136\pi\)
\(74\) 0 0
\(75\) −0.0250827 4.99994i −0.00289630 0.577343i
\(76\) 0 0
\(77\) −1.27326 + 1.27326i −0.145102 + 0.145102i
\(78\) 0 0
\(79\) 7.34690 0.826591 0.413295 0.910597i \(-0.364378\pi\)
0.413295 + 0.910597i \(0.364378\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) 0 0
\(83\) −6.80291 + 6.80291i −0.746716 + 0.746716i −0.973861 0.227145i \(-0.927061\pi\)
0.227145 + 0.973861i \(0.427061\pi\)
\(84\) 0 0
\(85\) −0.505369 + 0.210817i −0.0548149 + 0.0228663i
\(86\) 0 0
\(87\) 6.92797 0.742757
\(88\) 0 0
\(89\) 3.07483i 0.325931i −0.986632 0.162966i \(-0.947894\pi\)
0.986632 0.162966i \(-0.0521060\pi\)
\(90\) 0 0
\(91\) −2.73301 + 2.73301i −0.286498 + 0.286498i
\(92\) 0 0
\(93\) 5.37920 5.37920i 0.557797 0.557797i
\(94\) 0 0
\(95\) 1.85069 4.49986i 0.189877 0.461676i
\(96\) 0 0
\(97\) 1.39922i 0.142070i 0.997474 + 0.0710348i \(0.0226301\pi\)
−0.997474 + 0.0710348i \(0.977370\pi\)
\(98\) 0 0
\(99\) 1.79993 + 1.79993i 0.180900 + 0.180900i
\(100\) 0 0
\(101\) 11.7916 11.7916i 1.17331 1.17331i 0.191895 0.981415i \(-0.438537\pi\)
0.981415 0.191895i \(-0.0614633\pi\)
\(102\) 0 0
\(103\) 2.29240 0.225877 0.112938 0.993602i \(-0.463974\pi\)
0.112938 + 0.993602i \(0.463974\pi\)
\(104\) 0 0
\(105\) −1.46290 0.601657i −0.142764 0.0587157i
\(106\) 0 0
\(107\) 9.49009 + 9.49009i 0.917442 + 0.917442i 0.996843 0.0794010i \(-0.0253008\pi\)
−0.0794010 + 0.996843i \(0.525301\pi\)
\(108\) 0 0
\(109\) 11.9058 + 11.9058i 1.14037 + 1.14037i 0.988383 + 0.151984i \(0.0485662\pi\)
0.151984 + 0.988383i \(0.451434\pi\)
\(110\) 0 0
\(111\) −11.9906 −1.13810
\(112\) 0 0
\(113\) 7.92806i 0.745809i −0.927870 0.372904i \(-0.878362\pi\)
0.927870 0.372904i \(-0.121638\pi\)
\(114\) 0 0
\(115\) 5.95974 + 14.2866i 0.555748 + 1.33223i
\(116\) 0 0
\(117\) 3.86348 + 3.86348i 0.357179 + 0.357179i
\(118\) 0 0
\(119\) 0.173231i 0.0158800i
\(120\) 0 0
\(121\) 4.52052i 0.410956i
\(122\) 0 0
\(123\) −1.49990 1.49990i −0.135241 0.135241i
\(124\) 0 0
\(125\) −10.3612 4.20068i −0.926733 0.375721i
\(126\) 0 0
\(127\) 19.4466i 1.72561i 0.505536 + 0.862806i \(0.331295\pi\)
−0.505536 + 0.862806i \(0.668705\pi\)
\(128\) 0 0
\(129\) 0.968040 0.0852311
\(130\) 0 0
\(131\) 0.354049 + 0.354049i 0.0309334 + 0.0309334i 0.722404 0.691471i \(-0.243037\pi\)
−0.691471 + 0.722404i \(0.743037\pi\)
\(132\) 0 0
\(133\) −1.08842 1.08842i −0.0943783 0.0943783i
\(134\) 0 0
\(135\) −0.850522 + 2.06800i −0.0732013 + 0.177985i
\(136\) 0 0
\(137\) 7.30033 0.623709 0.311854 0.950130i \(-0.399050\pi\)
0.311854 + 0.950130i \(0.399050\pi\)
\(138\) 0 0
\(139\) 8.85519 8.85519i 0.751087 0.751087i −0.223595 0.974682i \(-0.571779\pi\)
0.974682 + 0.223595i \(0.0717793\pi\)
\(140\) 0 0
\(141\) 3.16319 + 3.16319i 0.266388 + 0.266388i
\(142\) 0 0
\(143\) 13.9080i 1.16304i
\(144\) 0 0
\(145\) 5.89239 14.3270i 0.489337 1.18980i
\(146\) 0 0
\(147\) 4.59590 4.59590i 0.379064 0.379064i
\(148\) 0 0
\(149\) 5.41385 5.41385i 0.443520 0.443520i −0.449673 0.893193i \(-0.648460\pi\)
0.893193 + 0.449673i \(0.148460\pi\)
\(150\) 0 0
\(151\) 0.341548i 0.0277948i 0.999903 + 0.0138974i \(0.00442382\pi\)
−0.999903 + 0.0138974i \(0.995576\pi\)
\(152\) 0 0
\(153\) 0.244884 0.0197977
\(154\) 0 0
\(155\) −6.54904 15.6993i −0.526032 1.26100i
\(156\) 0 0
\(157\) 2.86465 2.86465i 0.228624 0.228624i −0.583494 0.812118i \(-0.698315\pi\)
0.812118 + 0.583494i \(0.198315\pi\)
\(158\) 0 0
\(159\) 2.07927 0.164897
\(160\) 0 0
\(161\) 4.89717 0.385951
\(162\) 0 0
\(163\) −5.94216 + 5.94216i −0.465426 + 0.465426i −0.900429 0.435003i \(-0.856747\pi\)
0.435003 + 0.900429i \(0.356747\pi\)
\(164\) 0 0
\(165\) 5.25312 2.19137i 0.408955 0.170598i
\(166\) 0 0
\(167\) 14.4595 1.11891 0.559454 0.828861i \(-0.311011\pi\)
0.559454 + 0.828861i \(0.311011\pi\)
\(168\) 0 0
\(169\) 16.8529i 1.29638i
\(170\) 0 0
\(171\) −1.53863 + 1.53863i −0.117662 + 0.117662i
\(172\) 0 0
\(173\) 6.65096 6.65096i 0.505663 0.505663i −0.407529 0.913192i \(-0.633610\pi\)
0.913192 + 0.407529i \(0.133610\pi\)
\(174\) 0 0
\(175\) −2.48845 + 2.51354i −0.188109 + 0.190006i
\(176\) 0 0
\(177\) 8.28901i 0.623040i
\(178\) 0 0
\(179\) −17.2660 17.2660i −1.29052 1.29052i −0.934466 0.356052i \(-0.884123\pi\)
−0.356052 0.934466i \(-0.615877\pi\)
\(180\) 0 0
\(181\) 5.12242 5.12242i 0.380746 0.380746i −0.490625 0.871371i \(-0.663231\pi\)
0.871371 + 0.490625i \(0.163231\pi\)
\(182\) 0 0
\(183\) −0.0760044 −0.00561841
\(184\) 0 0
\(185\) −10.1983 + 24.7965i −0.749791 + 1.82308i
\(186\) 0 0
\(187\) −0.440774 0.440774i −0.0322326 0.0322326i
\(188\) 0 0
\(189\) 0.500206 + 0.500206i 0.0363846 + 0.0363846i
\(190\) 0 0
\(191\) 17.8040 1.28825 0.644124 0.764921i \(-0.277222\pi\)
0.644124 + 0.764921i \(0.277222\pi\)
\(192\) 0 0
\(193\) 17.2222i 1.23968i 0.784727 + 0.619842i \(0.212803\pi\)
−0.784727 + 0.619842i \(0.787197\pi\)
\(194\) 0 0
\(195\) 11.2756 4.70369i 0.807465 0.336838i
\(196\) 0 0
\(197\) 10.0764 + 10.0764i 0.717915 + 0.717915i 0.968178 0.250263i \(-0.0805171\pi\)
−0.250263 + 0.968178i \(0.580517\pi\)
\(198\) 0 0
\(199\) 5.74179i 0.407025i 0.979072 + 0.203513i \(0.0652358\pi\)
−0.979072 + 0.203513i \(0.934764\pi\)
\(200\) 0 0
\(201\) 11.1094i 0.783593i
\(202\) 0 0
\(203\) −3.46541 3.46541i −0.243224 0.243224i
\(204\) 0 0
\(205\) −4.37748 + 1.82609i −0.305737 + 0.127540i
\(206\) 0 0
\(207\) 6.92280i 0.481168i
\(208\) 0 0
\(209\) 5.53885 0.383130
\(210\) 0 0
\(211\) 9.73318 + 9.73318i 0.670060 + 0.670060i 0.957730 0.287670i \(-0.0928806\pi\)
−0.287670 + 0.957730i \(0.592881\pi\)
\(212\) 0 0
\(213\) −1.47499 1.47499i −0.101065 0.101065i
\(214\) 0 0
\(215\) 0.823339 2.00190i 0.0561512 0.136529i
\(216\) 0 0
\(217\) −5.38141 −0.365314
\(218\) 0 0
\(219\) 6.85859 6.85859i 0.463460 0.463460i
\(220\) 0 0
\(221\) −0.946104 0.946104i −0.0636419 0.0636419i
\(222\) 0 0
\(223\) 22.1037i 1.48017i −0.672511 0.740087i \(-0.734784\pi\)
0.672511 0.740087i \(-0.265216\pi\)
\(224\) 0 0
\(225\) 3.55323 + 3.51775i 0.236882 + 0.234517i
\(226\) 0 0
\(227\) 5.35387 5.35387i 0.355349 0.355349i −0.506746 0.862095i \(-0.669152\pi\)
0.862095 + 0.506746i \(0.169152\pi\)
\(228\) 0 0
\(229\) −18.3018 + 18.3018i −1.20942 + 1.20942i −0.238204 + 0.971215i \(0.576559\pi\)
−0.971215 + 0.238204i \(0.923441\pi\)
\(230\) 0 0
\(231\) 1.80067i 0.118475i
\(232\) 0 0
\(233\) 12.0546 0.789721 0.394861 0.918741i \(-0.370793\pi\)
0.394861 + 0.918741i \(0.370793\pi\)
\(234\) 0 0
\(235\) 9.23182 3.85110i 0.602217 0.251218i
\(236\) 0 0
\(237\) −5.19504 + 5.19504i −0.337454 + 0.337454i
\(238\) 0 0
\(239\) 27.9193 1.80595 0.902974 0.429695i \(-0.141379\pi\)
0.902974 + 0.429695i \(0.141379\pi\)
\(240\) 0 0
\(241\) 13.7118 0.883253 0.441626 0.897199i \(-0.354402\pi\)
0.441626 + 0.897199i \(0.354402\pi\)
\(242\) 0 0
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) 0 0
\(245\) −5.59540 13.4132i −0.357477 0.856940i
\(246\) 0 0
\(247\) 11.8889 0.756474
\(248\) 0 0
\(249\) 9.62077i 0.609691i
\(250\) 0 0
\(251\) 9.07173 9.07173i 0.572602 0.572602i −0.360252 0.932855i \(-0.617309\pi\)
0.932855 + 0.360252i \(0.117309\pi\)
\(252\) 0 0
\(253\) −12.4605 + 12.4605i −0.783388 + 0.783388i
\(254\) 0 0
\(255\) 0.208279 0.506420i 0.0130430 0.0317132i
\(256\) 0 0
\(257\) 9.23416i 0.576011i 0.957629 + 0.288006i \(0.0929922\pi\)
−0.957629 + 0.288006i \(0.907008\pi\)
\(258\) 0 0
\(259\) 5.99776 + 5.99776i 0.372683 + 0.372683i
\(260\) 0 0
\(261\) −4.89882 + 4.89882i −0.303229 + 0.303229i
\(262\) 0 0
\(263\) −18.5516 −1.14394 −0.571971 0.820274i \(-0.693821\pi\)
−0.571971 + 0.820274i \(0.693821\pi\)
\(264\) 0 0
\(265\) 1.76846 4.29992i 0.108636 0.264142i
\(266\) 0 0
\(267\) 2.17423 + 2.17423i 0.133061 + 0.133061i
\(268\) 0 0
\(269\) 14.3977 + 14.3977i 0.877844 + 0.877844i 0.993311 0.115467i \(-0.0368366\pi\)
−0.115467 + 0.993311i \(0.536837\pi\)
\(270\) 0 0
\(271\) −19.2974 −1.17224 −0.586118 0.810226i \(-0.699344\pi\)
−0.586118 + 0.810226i \(0.699344\pi\)
\(272\) 0 0
\(273\) 3.86507i 0.233924i
\(274\) 0 0
\(275\) −0.0638476 12.7272i −0.00385016 0.767482i
\(276\) 0 0
\(277\) −3.52269 3.52269i −0.211658 0.211658i 0.593314 0.804971i \(-0.297819\pi\)
−0.804971 + 0.593314i \(0.797819\pi\)
\(278\) 0 0
\(279\) 7.60734i 0.455439i
\(280\) 0 0
\(281\) 29.2076i 1.74238i 0.490945 + 0.871191i \(0.336652\pi\)
−0.490945 + 0.871191i \(0.663348\pi\)
\(282\) 0 0
\(283\) −9.84279 9.84279i −0.585093 0.585093i 0.351205 0.936298i \(-0.385772\pi\)
−0.936298 + 0.351205i \(0.885772\pi\)
\(284\) 0 0
\(285\) 1.87325 + 4.49052i 0.110961 + 0.265996i
\(286\) 0 0
\(287\) 1.50052i 0.0885726i
\(288\) 0 0
\(289\) 16.9400 0.996472
\(290\) 0 0
\(291\) −0.989400 0.989400i −0.0579997 0.0579997i
\(292\) 0 0
\(293\) −11.8238 11.8238i −0.690755 0.690755i 0.271643 0.962398i \(-0.412433\pi\)
−0.962398 + 0.271643i \(0.912433\pi\)
\(294\) 0 0
\(295\) −17.1416 7.04998i −0.998025 0.410466i
\(296\) 0 0
\(297\) −2.54548 −0.147704
\(298\) 0 0
\(299\) −26.7461 + 26.7461i −1.54677 + 1.54677i
\(300\) 0 0
\(301\) −0.484219 0.484219i −0.0279099 0.0279099i
\(302\) 0 0
\(303\) 16.6759i 0.958004i
\(304\) 0 0
\(305\) −0.0646434 + 0.157177i −0.00370147 + 0.00899992i
\(306\) 0 0
\(307\) 16.6232 16.6232i 0.948733 0.948733i −0.0500151 0.998748i \(-0.515927\pi\)
0.998748 + 0.0500151i \(0.0159269\pi\)
\(308\) 0 0
\(309\) −1.62097 + 1.62097i −0.0922139 + 0.0922139i
\(310\) 0 0
\(311\) 13.8069i 0.782920i −0.920195 0.391460i \(-0.871970\pi\)
0.920195 0.391460i \(-0.128030\pi\)
\(312\) 0 0
\(313\) 7.40380 0.418488 0.209244 0.977864i \(-0.432900\pi\)
0.209244 + 0.977864i \(0.432900\pi\)
\(314\) 0 0
\(315\) 1.45986 0.608988i 0.0822538 0.0343126i
\(316\) 0 0
\(317\) −1.80712 + 1.80712i −0.101498 + 0.101498i −0.756032 0.654534i \(-0.772865\pi\)
0.654534 + 0.756032i \(0.272865\pi\)
\(318\) 0 0
\(319\) 17.6350 0.987372
\(320\) 0 0
\(321\) −13.4210 −0.749088
\(322\) 0 0
\(323\) 0.376786 0.376786i 0.0209650 0.0209650i
\(324\) 0 0
\(325\) −0.137046 27.3186i −0.00760197 1.51536i
\(326\) 0 0
\(327\) −16.8373 −0.931106
\(328\) 0 0
\(329\) 3.16449i 0.174464i
\(330\) 0 0
\(331\) 5.82711 5.82711i 0.320287 0.320287i −0.528590 0.848877i \(-0.677279\pi\)
0.848877 + 0.528590i \(0.177279\pi\)
\(332\) 0 0
\(333\) 8.47863 8.47863i 0.464626 0.464626i
\(334\) 0 0
\(335\) −22.9741 9.44875i −1.25521 0.516240i
\(336\) 0 0
\(337\) 25.5357i 1.39102i 0.718516 + 0.695510i \(0.244822\pi\)
−0.718516 + 0.695510i \(0.755178\pi\)
\(338\) 0 0
\(339\) 5.60598 + 5.60598i 0.304475 + 0.304475i
\(340\) 0 0
\(341\) 13.6927 13.6927i 0.741499 0.741499i
\(342\) 0 0
\(343\) −9.54958 −0.515629
\(344\) 0 0
\(345\) −14.3163 5.88799i −0.770766 0.316999i
\(346\) 0 0
\(347\) 17.6028 + 17.6028i 0.944970 + 0.944970i 0.998563 0.0535933i \(-0.0170675\pi\)
−0.0535933 + 0.998563i \(0.517067\pi\)
\(348\) 0 0
\(349\) −5.07562 5.07562i −0.271692 0.271692i 0.558089 0.829781i \(-0.311535\pi\)
−0.829781 + 0.558089i \(0.811535\pi\)
\(350\) 0 0
\(351\) −5.46378 −0.291635
\(352\) 0 0
\(353\) 0.171535i 0.00912990i 0.999990 + 0.00456495i \(0.00145307\pi\)
−0.999990 + 0.00456495i \(0.998547\pi\)
\(354\) 0 0
\(355\) −4.30479 + 1.79576i −0.228474 + 0.0953093i
\(356\) 0 0
\(357\) −0.122492 0.122492i −0.00648299 0.00648299i
\(358\) 0 0
\(359\) 17.1694i 0.906169i 0.891468 + 0.453084i \(0.149676\pi\)
−0.891468 + 0.453084i \(0.850324\pi\)
\(360\) 0 0
\(361\) 14.2652i 0.750802i
\(362\) 0 0
\(363\) −3.19649 3.19649i −0.167772 0.167772i
\(364\) 0 0
\(365\) −8.35016 20.0169i −0.437068 1.04773i
\(366\) 0 0
\(367\) 23.3124i 1.21690i 0.793593 + 0.608450i \(0.208208\pi\)
−0.793593 + 0.608450i \(0.791792\pi\)
\(368\) 0 0
\(369\) 2.12118 0.110424
\(370\) 0 0
\(371\) −1.04006 1.04006i −0.0539973 0.0539973i
\(372\) 0 0
\(373\) −1.11817 1.11817i −0.0578964 0.0578964i 0.677566 0.735462i \(-0.263035\pi\)
−0.735462 + 0.677566i \(0.763035\pi\)
\(374\) 0 0
\(375\) 10.2968 4.35614i 0.531724 0.224950i
\(376\) 0 0
\(377\) 37.8529 1.94953
\(378\) 0 0
\(379\) −22.3707 + 22.3707i −1.14910 + 1.14910i −0.162375 + 0.986729i \(0.551915\pi\)
−0.986729 + 0.162375i \(0.948085\pi\)
\(380\) 0 0
\(381\) −13.7509 13.7509i −0.704478 0.704478i
\(382\) 0 0
\(383\) 32.1168i 1.64109i 0.571579 + 0.820547i \(0.306331\pi\)
−0.571579 + 0.820547i \(0.693669\pi\)
\(384\) 0 0
\(385\) −3.72378 1.53151i −0.189781 0.0780528i
\(386\) 0 0
\(387\) −0.684507 + 0.684507i −0.0347955 + 0.0347955i
\(388\) 0 0
\(389\) −22.7409 + 22.7409i −1.15301 + 1.15301i −0.167062 + 0.985946i \(0.553428\pi\)
−0.985946 + 0.167062i \(0.946572\pi\)
\(390\) 0 0
\(391\) 1.69529i 0.0857342i
\(392\) 0 0
\(393\) −0.500701 −0.0252570
\(394\) 0 0
\(395\) 6.32484 + 15.1618i 0.318237 + 0.762874i
\(396\) 0 0
\(397\) 21.6530 21.6530i 1.08673 1.08673i 0.0908707 0.995863i \(-0.471035\pi\)
0.995863 0.0908707i \(-0.0289650\pi\)
\(398\) 0 0
\(399\) 1.53926 0.0770596
\(400\) 0 0
\(401\) 17.1600 0.856931 0.428466 0.903558i \(-0.359054\pi\)
0.428466 + 0.903558i \(0.359054\pi\)
\(402\) 0 0
\(403\) 29.3908 29.3908i 1.46406 1.46406i
\(404\) 0 0
\(405\) −0.860885 2.06370i −0.0427777 0.102546i
\(406\) 0 0
\(407\) −30.5218 −1.51291
\(408\) 0 0
\(409\) 17.9588i 0.888006i −0.896025 0.444003i \(-0.853558\pi\)
0.896025 0.444003i \(-0.146442\pi\)
\(410\) 0 0
\(411\) −5.16211 + 5.16211i −0.254628 + 0.254628i
\(412\) 0 0
\(413\) −4.14621 + 4.14621i −0.204022 + 0.204022i
\(414\) 0 0
\(415\) −19.8957 8.18267i −0.976642 0.401671i
\(416\) 0 0
\(417\) 12.5231i 0.613260i
\(418\) 0 0
\(419\) −23.4031 23.4031i −1.14332 1.14332i −0.987840 0.155476i \(-0.950309\pi\)
−0.155476 0.987840i \(-0.549691\pi\)
\(420\) 0 0
\(421\) −27.0016 + 27.0016i −1.31598 + 1.31598i −0.399043 + 0.916932i \(0.630658\pi\)
−0.916932 + 0.399043i \(0.869342\pi\)
\(422\) 0 0
\(423\) −4.47342 −0.217505
\(424\) 0 0
\(425\) −0.870129 0.861442i −0.0422075 0.0417861i
\(426\) 0 0
\(427\) 0.0380178 + 0.0380178i 0.00183981 + 0.00183981i
\(428\) 0 0
\(429\) 9.83441 + 9.83441i 0.474810 + 0.474810i
\(430\) 0 0
\(431\) 28.4043 1.36819 0.684093 0.729395i \(-0.260198\pi\)
0.684093 + 0.729395i \(0.260198\pi\)
\(432\) 0 0
\(433\) 4.04564i 0.194421i −0.995264 0.0972106i \(-0.969008\pi\)
0.995264 0.0972106i \(-0.0309920\pi\)
\(434\) 0 0
\(435\) 5.96419 + 14.2973i 0.285961 + 0.685503i
\(436\) 0 0
\(437\) −10.6516 10.6516i −0.509537 0.509537i
\(438\) 0 0
\(439\) 10.4690i 0.499660i −0.968290 0.249830i \(-0.919625\pi\)
0.968290 0.249830i \(-0.0803748\pi\)
\(440\) 0 0
\(441\) 6.49959i 0.309504i
\(442\) 0 0
\(443\) −1.81582 1.81582i −0.0862722 0.0862722i 0.662654 0.748926i \(-0.269430\pi\)
−0.748926 + 0.662654i \(0.769430\pi\)
\(444\) 0 0
\(445\) 6.34554 2.64707i 0.300807 0.125483i
\(446\) 0 0
\(447\) 7.65634i 0.362132i
\(448\) 0 0
\(449\) −22.2064 −1.04799 −0.523993 0.851723i \(-0.675558\pi\)
−0.523993 + 0.851723i \(0.675558\pi\)
\(450\) 0 0
\(451\) −3.81797 3.81797i −0.179781 0.179781i
\(452\) 0 0
\(453\) −0.241511 0.241511i −0.0113472 0.0113472i
\(454\) 0 0
\(455\) −7.99294 3.28732i −0.374715 0.154112i
\(456\) 0 0
\(457\) −12.2280 −0.572000 −0.286000 0.958230i \(-0.592326\pi\)
−0.286000 + 0.958230i \(0.592326\pi\)
\(458\) 0 0
\(459\) −0.173159 + 0.173159i −0.00808238 + 0.00808238i
\(460\) 0 0
\(461\) 0.723447 + 0.723447i 0.0336943 + 0.0336943i 0.723753 0.690059i \(-0.242415\pi\)
−0.690059 + 0.723753i \(0.742415\pi\)
\(462\) 0 0
\(463\) 5.42343i 0.252048i 0.992027 + 0.126024i \(0.0402217\pi\)
−0.992027 + 0.126024i \(0.959778\pi\)
\(464\) 0 0
\(465\) 15.7320 + 6.47021i 0.729552 + 0.300049i
\(466\) 0 0
\(467\) −13.3242 + 13.3242i −0.616571 + 0.616571i −0.944650 0.328079i \(-0.893599\pi\)
0.328079 + 0.944650i \(0.393599\pi\)
\(468\) 0 0
\(469\) −5.55696 + 5.55696i −0.256597 + 0.256597i
\(470\) 0 0
\(471\) 4.05122i 0.186671i
\(472\) 0 0
\(473\) 2.46413 0.113301
\(474\) 0 0
\(475\) 10.8796 0.0545788i 0.499191 0.00250425i
\(476\) 0 0
\(477\) −1.47026 + 1.47026i −0.0673188 + 0.0673188i
\(478\) 0 0
\(479\) 1.25963 0.0575541 0.0287771 0.999586i \(-0.490839\pi\)
0.0287771 + 0.999586i \(0.490839\pi\)
\(480\) 0 0
\(481\) −65.5140 −2.98718
\(482\) 0 0
\(483\) −3.46282 + 3.46282i −0.157564 + 0.157564i
\(484\) 0 0
\(485\) −2.88758 + 1.20457i −0.131118 + 0.0546967i
\(486\) 0 0
\(487\) 15.8116 0.716491 0.358246 0.933627i \(-0.383375\pi\)
0.358246 + 0.933627i \(0.383375\pi\)
\(488\) 0 0
\(489\) 8.40349i 0.380019i
\(490\) 0 0
\(491\) 15.6008 15.6008i 0.704054 0.704054i −0.261224 0.965278i \(-0.584126\pi\)
0.965278 + 0.261224i \(0.0841263\pi\)
\(492\) 0 0
\(493\) 1.19964 1.19964i 0.0540292 0.0540292i
\(494\) 0 0
\(495\) −2.16499 + 5.26405i −0.0973090 + 0.236601i
\(496\) 0 0
\(497\) 1.47560i 0.0661896i
\(498\) 0 0
\(499\) −25.6650 25.6650i −1.14892 1.14892i −0.986765 0.162159i \(-0.948154\pi\)
−0.162159 0.986765i \(-0.551846\pi\)
\(500\) 0 0
\(501\) −10.2244 + 10.2244i −0.456792 + 0.456792i
\(502\) 0 0
\(503\) 4.72004 0.210456 0.105228 0.994448i \(-0.466443\pi\)
0.105228 + 0.994448i \(0.466443\pi\)
\(504\) 0 0
\(505\) 34.4857 + 14.1832i 1.53459 + 0.631144i
\(506\) 0 0
\(507\) 11.9168 + 11.9168i 0.529244 + 0.529244i
\(508\) 0 0
\(509\) −11.8862 11.8862i −0.526848 0.526848i 0.392783 0.919631i \(-0.371512\pi\)
−0.919631 + 0.392783i \(0.871512\pi\)
\(510\) 0 0
\(511\) −6.86141 −0.303531
\(512\) 0 0
\(513\) 2.17595i 0.0960706i
\(514\) 0 0
\(515\) 1.97349 + 4.73084i 0.0869625 + 0.208466i
\(516\) 0 0
\(517\) 8.05183 + 8.05183i 0.354119 + 0.354119i
\(518\) 0 0
\(519\) 9.40587i 0.412872i
\(520\) 0 0
\(521\) 5.01467i 0.219696i −0.993948 0.109848i \(-0.964964\pi\)
0.993948 0.109848i \(-0.0350365\pi\)
\(522\) 0 0
\(523\) 18.9502 + 18.9502i 0.828635 + 0.828635i 0.987328 0.158693i \(-0.0507279\pi\)
−0.158693 + 0.987328i \(0.550728\pi\)
\(524\) 0 0
\(525\) −0.0177435 3.53694i −0.000774388 0.154365i
\(526\) 0 0
\(527\) 1.86292i 0.0811499i
\(528\) 0 0
\(529\) 24.9252 1.08370
\(530\) 0 0
\(531\) 5.86121 + 5.86121i 0.254355 + 0.254355i
\(532\) 0 0
\(533\) −8.19512 8.19512i −0.354970 0.354970i
\(534\) 0 0
\(535\) −11.4149 + 27.7546i −0.493508 + 1.19994i
\(536\) 0 0
\(537\) 24.4178 1.05370
\(538\) 0 0
\(539\) 11.6988 11.6988i 0.503903 0.503903i
\(540\) 0 0
\(541\) −22.8366 22.8366i −0.981822 0.981822i 0.0180153 0.999838i \(-0.494265\pi\)
−0.999838 + 0.0180153i \(0.994265\pi\)
\(542\) 0 0
\(543\) 7.24419i 0.310878i
\(544\) 0 0
\(545\) −14.3205 + 34.8195i −0.613423 + 1.49150i
\(546\) 0 0
\(547\) −0.00963023 + 0.00963023i −0.000411759 + 0.000411759i −0.707313 0.706901i \(-0.750093\pi\)
0.706901 + 0.707313i \(0.250093\pi\)
\(548\) 0 0
\(549\) 0.0537432 0.0537432i 0.00229371 0.00229371i
\(550\) 0 0
\(551\) 15.0749i 0.642214i
\(552\) 0 0
\(553\) 5.19718 0.221006
\(554\) 0 0
\(555\) −10.3225 24.7450i −0.438167 1.05037i
\(556\) 0 0
\(557\) −25.6660 + 25.6660i −1.08750 + 1.08750i −0.0917192 + 0.995785i \(0.529236\pi\)
−0.995785 + 0.0917192i \(0.970764\pi\)
\(558\) 0 0
\(559\) 5.28916 0.223707
\(560\) 0 0
\(561\) 0.623348 0.0263178
\(562\) 0 0
\(563\) −6.16719 + 6.16719i −0.259916 + 0.259916i −0.825020 0.565104i \(-0.808836\pi\)
0.565104 + 0.825020i \(0.308836\pi\)
\(564\) 0 0
\(565\) 16.3612 6.82515i 0.688319 0.287136i
\(566\) 0 0
\(567\) −0.707398 −0.0297079
\(568\) 0 0
\(569\) 4.05892i 0.170159i −0.996374 0.0850794i \(-0.972886\pi\)
0.996374 0.0850794i \(-0.0271144\pi\)
\(570\) 0 0
\(571\) 12.9113 12.9113i 0.540323 0.540323i −0.383301 0.923624i \(-0.625213\pi\)
0.923624 + 0.383301i \(0.125213\pi\)
\(572\) 0 0
\(573\) −12.5893 + 12.5893i −0.525925 + 0.525925i
\(574\) 0 0
\(575\) −24.3527 + 24.5983i −1.01558 + 1.02582i
\(576\) 0 0
\(577\) 10.4193i 0.433761i −0.976198 0.216880i \(-0.930412\pi\)
0.976198 0.216880i \(-0.0695882\pi\)
\(578\) 0 0
\(579\) −12.1780 12.1780i −0.506099 0.506099i
\(580\) 0 0
\(581\) −4.81236 + 4.81236i −0.199650 + 0.199650i
\(582\) 0 0
\(583\) 5.29274 0.219203
\(584\) 0 0
\(585\) −4.64706 + 11.2991i −0.192132 + 0.467160i
\(586\) 0 0
\(587\) −27.7728 27.7728i −1.14631 1.14631i −0.987273 0.159033i \(-0.949162\pi\)
−0.159033 0.987273i \(-0.550838\pi\)
\(588\) 0 0
\(589\) 11.7049 + 11.7049i 0.482291 + 0.482291i
\(590\) 0 0
\(591\) −14.2502 −0.586175
\(592\) 0 0
\(593\) 25.4466i 1.04496i 0.852650 + 0.522482i \(0.174994\pi\)
−0.852650 + 0.522482i \(0.825006\pi\)
\(594\) 0 0
\(595\) −0.357497 + 0.149132i −0.0146559 + 0.00611380i
\(596\) 0 0
\(597\) −4.06006 4.06006i −0.166167 0.166167i
\(598\) 0 0
\(599\) 1.32051i 0.0539544i −0.999636 0.0269772i \(-0.991412\pi\)
0.999636 0.0269772i \(-0.00858816\pi\)
\(600\) 0 0
\(601\) 23.8236i 0.971787i 0.874018 + 0.485893i \(0.161506\pi\)
−0.874018 + 0.485893i \(0.838494\pi\)
\(602\) 0 0
\(603\) 7.85550 + 7.85550i 0.319901 + 0.319901i
\(604\) 0 0
\(605\) −9.32902 + 3.89165i −0.379279 + 0.158218i
\(606\) 0 0
\(607\) 1.20300i 0.0488283i 0.999702 + 0.0244141i \(0.00777203\pi\)
−0.999702 + 0.0244141i \(0.992228\pi\)
\(608\) 0 0
\(609\) 4.90083 0.198592
\(610\) 0 0
\(611\) 17.2830 + 17.2830i 0.699193 + 0.699193i
\(612\) 0 0
\(613\) 4.84340 + 4.84340i 0.195623 + 0.195623i 0.798121 0.602498i \(-0.205828\pi\)
−0.602498 + 0.798121i \(0.705828\pi\)
\(614\) 0 0
\(615\) 1.80411 4.38659i 0.0727486 0.176884i
\(616\) 0 0
\(617\) −26.9719 −1.08585 −0.542924 0.839782i \(-0.682683\pi\)
−0.542924 + 0.839782i \(0.682683\pi\)
\(618\) 0 0
\(619\) −19.9202 + 19.9202i −0.800660 + 0.800660i −0.983199 0.182539i \(-0.941568\pi\)
0.182539 + 0.983199i \(0.441568\pi\)
\(620\) 0 0
\(621\) 4.89516 + 4.89516i 0.196436 + 0.196436i
\(622\) 0 0
\(623\) 2.17513i 0.0871446i
\(624\) 0 0
\(625\) −0.250824 24.9987i −0.0100330 0.999950i
\(626\) 0 0
\(627\) −3.91656 + 3.91656i −0.156412 + 0.156412i
\(628\) 0 0
\(629\) −2.07628 + 2.07628i −0.0827868 + 0.0827868i
\(630\) 0 0
\(631\) 12.7975i 0.509462i 0.967012 + 0.254731i \(0.0819870\pi\)
−0.967012 + 0.254731i \(0.918013\pi\)
\(632\) 0 0
\(633\) −13.7648 −0.547101
\(634\) 0 0
\(635\) −40.1321 + 16.7413i −1.59260 + 0.664360i
\(636\) 0 0
\(637\) 25.1110 25.1110i 0.994934 0.994934i
\(638\) 0 0
\(639\) 2.08595 0.0825190
\(640\) 0 0
\(641\) 10.9406 0.432129 0.216064 0.976379i \(-0.430678\pi\)
0.216064 + 0.976379i \(0.430678\pi\)
\(642\) 0 0
\(643\) 18.2613 18.2613i 0.720157 0.720157i −0.248480 0.968637i \(-0.579931\pi\)
0.968637 + 0.248480i \(0.0799311\pi\)
\(644\) 0 0
\(645\) 0.833371 + 1.99775i 0.0328140 + 0.0786612i
\(646\) 0 0
\(647\) 10.5055 0.413014 0.206507 0.978445i \(-0.433790\pi\)
0.206507 + 0.978445i \(0.433790\pi\)
\(648\) 0 0
\(649\) 21.0995i 0.828228i
\(650\) 0 0
\(651\) 3.80523 3.80523i 0.149139 0.149139i
\(652\) 0 0
\(653\) 11.1836 11.1836i 0.437648 0.437648i −0.453572 0.891220i \(-0.649850\pi\)
0.891220 + 0.453572i \(0.149850\pi\)
\(654\) 0 0
\(655\) −0.425857 + 1.03545i −0.0166396 + 0.0404583i
\(656\) 0 0
\(657\) 9.69951i 0.378414i
\(658\) 0 0
\(659\) −2.60687 2.60687i −0.101549 0.101549i 0.654507 0.756056i \(-0.272876\pi\)
−0.756056 + 0.654507i \(0.772876\pi\)
\(660\) 0 0
\(661\) 15.9084 15.9084i 0.618766 0.618766i −0.326449 0.945215i \(-0.605852\pi\)
0.945215 + 0.326449i \(0.105852\pi\)
\(662\) 0 0
\(663\) 1.33799 0.0519634
\(664\) 0 0
\(665\) 1.30918 3.18319i 0.0507677 0.123439i
\(666\) 0 0
\(667\) −33.9135 33.9135i −1.31314 1.31314i
\(668\) 0 0
\(669\) 15.6297 + 15.6297i 0.604278 + 0.604278i
\(670\) 0 0
\(671\) −0.193468 −0.00746874
\(672\) 0 0
\(673\) 27.1091i 1.04498i −0.852645 0.522490i \(-0.825003\pi\)
0.852645 0.522490i \(-0.174997\pi\)
\(674\) 0 0
\(675\) −4.99994 + 0.0250827i −0.192448 + 0.000965434i
\(676\) 0 0
\(677\) −11.0637 11.0637i −0.425211 0.425211i 0.461782 0.886993i \(-0.347210\pi\)
−0.886993 + 0.461782i \(0.847210\pi\)
\(678\) 0 0
\(679\) 0.989807i 0.0379853i
\(680\) 0 0
\(681\) 7.57152i 0.290141i
\(682\) 0 0
\(683\) 17.4289 + 17.4289i 0.666898 + 0.666898i 0.956997 0.290098i \(-0.0936881\pi\)
−0.290098 + 0.956997i \(0.593688\pi\)
\(684\) 0 0
\(685\) 6.28474 + 15.0657i 0.240128 + 0.575631i
\(686\) 0 0
\(687\) 25.8827i 0.987487i
\(688\) 0 0
\(689\) 11.3607 0.432807
\(690\) 0 0
\(691\) −26.0352 26.0352i −0.990426 0.990426i 0.00952887 0.999955i \(-0.496967\pi\)
−0.999955 + 0.00952887i \(0.996967\pi\)
\(692\) 0 0
\(693\) 1.27326 + 1.27326i 0.0483673 + 0.0483673i
\(694\) 0 0
\(695\) 25.8978 + 10.6512i 0.982359 + 0.404023i
\(696\) 0 0
\(697\) −0.519443 −0.0196753
\(698\) 0 0
\(699\) −8.52387 + 8.52387i −0.322402 + 0.322402i
\(700\) 0 0
\(701\) 2.08057 + 2.08057i 0.0785822 + 0.0785822i 0.745305 0.666723i \(-0.232304\pi\)
−0.666723 + 0.745305i \(0.732304\pi\)
\(702\) 0 0
\(703\) 26.0910i 0.984039i
\(704\) 0 0
\(705\) −3.80474 + 9.25102i −0.143295 + 0.348414i
\(706\) 0 0
\(707\) 8.34137 8.34137i 0.313709 0.313709i
\(708\) 0 0
\(709\) −3.27484 + 3.27484i −0.122989 + 0.122989i −0.765922 0.642933i \(-0.777717\pi\)
0.642933 + 0.765922i \(0.277717\pi\)
\(710\) 0 0
\(711\) 7.34690i 0.275530i
\(712\) 0 0
\(713\) −52.6641 −1.97229
\(714\) 0 0
\(715\) 28.7019 11.9732i 1.07339 0.447771i
\(716\) 0 0
\(717\) −19.7419 + 19.7419i −0.737275 + 0.737275i
\(718\) 0 0
\(719\) 2.03220 0.0757882 0.0378941 0.999282i \(-0.487935\pi\)
0.0378941 + 0.999282i \(0.487935\pi\)
\(720\) 0 0
\(721\) 1.62164 0.0603930
\(722\) 0 0
\(723\) −9.69568 + 9.69568i −0.360586 + 0.360586i
\(724\) 0 0
\(725\) 34.6394 0.173772i 1.28648 0.00645375i
\(726\) 0 0
\(727\) −6.37077 −0.236279 −0.118139 0.992997i \(-0.537693\pi\)
−0.118139 + 0.992997i \(0.537693\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 0.167625 0.167625i 0.00619984 0.00619984i
\(732\) 0 0
\(733\) −6.95026 + 6.95026i −0.256714 + 0.256714i −0.823716 0.567002i \(-0.808103\pi\)
0.567002 + 0.823716i \(0.308103\pi\)
\(734\) 0 0
\(735\) 13.4411 + 5.52804i 0.495784 + 0.203905i
\(736\) 0 0
\(737\) 28.2787i 1.04166i
\(738\) 0 0
\(739\) −0.0483355 0.0483355i −0.00177805 0.00177805i 0.706217 0.707995i \(-0.250400\pi\)
−0.707995 + 0.706217i \(0.750400\pi\)
\(740\) 0 0
\(741\) −8.40674 + 8.40674i −0.308829 + 0.308829i
\(742\) 0 0
\(743\) 0.148848 0.00546069 0.00273035 0.999996i \(-0.499131\pi\)
0.00273035 + 0.999996i \(0.499131\pi\)
\(744\) 0 0
\(745\) 15.8333 + 6.51188i 0.580087 + 0.238577i
\(746\) 0 0
\(747\) 6.80291 + 6.80291i 0.248905 + 0.248905i
\(748\) 0 0
\(749\) 6.71327 + 6.71327i 0.245297 + 0.245297i
\(750\) 0 0
\(751\) −1.69304 −0.0617798 −0.0308899 0.999523i \(-0.509834\pi\)
−0.0308899 + 0.999523i \(0.509834\pi\)
\(752\) 0 0
\(753\) 12.8294i 0.467528i
\(754\) 0 0
\(755\) −0.704855 + 0.294034i −0.0256523 + 0.0107010i
\(756\) 0 0
\(757\) −26.6876 26.6876i −0.969977 0.969977i 0.0295851 0.999562i \(-0.490581\pi\)
−0.999562 + 0.0295851i \(0.990581\pi\)
\(758\) 0 0
\(759\) 17.6219i 0.639633i
\(760\) 0 0
\(761\) 17.1363i 0.621189i −0.950542 0.310595i \(-0.899472\pi\)
0.950542 0.310595i \(-0.100528\pi\)
\(762\) 0 0
\(763\) 8.42212 + 8.42212i 0.304901 + 0.304901i
\(764\) 0 0
\(765\) 0.210817 + 0.505369i 0.00762211 + 0.0182716i
\(766\) 0 0
\(767\) 45.2893i 1.63530i
\(768\) 0 0
\(769\) −25.6406 −0.924622 −0.462311 0.886718i \(-0.652980\pi\)
−0.462311 + 0.886718i \(0.652980\pi\)
\(770\) 0 0
\(771\) −6.52954 6.52954i −0.235156 0.235156i
\(772\) 0 0
\(773\) 27.4452 + 27.4452i 0.987137 + 0.987137i 0.999918 0.0127818i \(-0.00406868\pi\)
−0.0127818 + 0.999918i \(0.504069\pi\)
\(774\) 0 0
\(775\) 26.7607 27.0306i 0.961274 0.970967i
\(776\) 0 0
\(777\) −8.48212 −0.304294
\(778\) 0 0
\(779\) 3.26371 3.26371i 0.116934 0.116934i
\(780\) 0 0
\(781\) −3.75456 3.75456i −0.134349 0.134349i
\(782\) 0 0
\(783\) 6.92797i 0.247586i
\(784\) 0 0
\(785\) 8.37792 + 3.44565i 0.299021 + 0.122981i
\(786\) 0 0
\(787\) 9.65912 9.65912i 0.344310 0.344310i −0.513675 0.857985i \(-0.671716\pi\)
0.857985 + 0.513675i \(0.171716\pi\)
\(788\) 0 0
\(789\) 13.1180 13.1180i 0.467012 0.467012i
\(790\) 0 0
\(791\) 5.60829i 0.199408i
\(792\) 0 0
\(793\) −0.415271 −0.0147467
\(794\) 0 0
\(795\) 1.79001 + 4.29099i 0.0634851 + 0.152186i
\(796\) 0 0
\(797\) −11.9978 + 11.9978i −0.424984 + 0.424984i −0.886916 0.461931i \(-0.847157\pi\)
0.461931 + 0.886916i \(0.347157\pi\)
\(798\) 0 0
\(799\) 1.09547