Properties

Label 280.2.bo.a.17.4
Level $280$
Weight $2$
Character 280.17
Analytic conductor $2.236$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.bo (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 17.4
Character \(\chi\) \(=\) 280.17
Dual form 280.2.bo.a.33.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.35944 + 0.364260i) q^{3} +(-2.13431 - 0.666887i) q^{5} +(2.59782 - 0.501338i) q^{7} +(-0.882692 + 0.509622i) q^{9} +O(q^{10})\) \(q+(-1.35944 + 0.364260i) q^{3} +(-2.13431 - 0.666887i) q^{5} +(2.59782 - 0.501338i) q^{7} +(-0.882692 + 0.509622i) q^{9} +(1.86869 - 3.23667i) q^{11} +(-4.55026 - 4.55026i) q^{13} +(3.14438 + 0.129149i) q^{15} +(-1.58528 - 5.91633i) q^{17} +(-0.616087 - 1.06709i) q^{19} +(-3.34895 + 1.62782i) q^{21} +(-2.69174 - 0.721250i) q^{23} +(4.11052 + 2.84668i) q^{25} +(3.99986 - 3.99986i) q^{27} -2.82808i q^{29} +(5.94396 + 3.43175i) q^{31} +(-1.36138 + 5.08074i) q^{33} +(-5.87887 - 0.662443i) q^{35} +(-2.01646 + 7.52551i) q^{37} +(7.84327 + 4.52831i) q^{39} +5.56966i q^{41} +(-1.95176 + 1.95176i) q^{43} +(2.22379 - 0.499034i) q^{45} +(-11.1512 - 2.98797i) q^{47} +(6.49732 - 2.60477i) q^{49} +(4.31017 + 7.46543i) q^{51} +(-2.53082 - 9.44513i) q^{53} +(-6.14686 + 5.66184i) q^{55} +(1.22623 + 1.22623i) q^{57} +(-0.916152 + 1.58682i) q^{59} +(-3.43491 + 1.98315i) q^{61} +(-2.03758 + 1.76643i) q^{63} +(6.67713 + 12.7462i) q^{65} +(7.93605 - 2.12646i) q^{67} +3.92198 q^{69} +0.570063 q^{71} +(-2.03783 + 0.546036i) q^{73} +(-6.62493 - 2.37259i) q^{75} +(3.23186 - 9.34513i) q^{77} +(9.47466 - 5.47020i) q^{79} +(-2.45170 + 4.24647i) q^{81} +(8.80820 + 8.80820i) q^{83} +(-0.562062 + 13.6845i) q^{85} +(1.03016 + 3.84459i) q^{87} +(-3.00362 - 5.20243i) q^{89} +(-14.1020 - 9.53952i) q^{91} +(-9.33049 - 2.50010i) q^{93} +(0.603286 + 2.68836i) q^{95} +(3.70694 - 3.70694i) q^{97} +3.80931i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 4q^{7} + O(q^{10}) \) \( 48q - 4q^{7} + 4q^{11} + 8q^{15} - 4q^{21} - 4q^{23} - 8q^{25} - 36q^{33} + 24q^{35} + 8q^{37} - 16q^{43} + 48q^{45} + 24q^{51} + 16q^{53} - 96q^{57} - 36q^{61} - 68q^{63} + 12q^{65} - 16q^{67} - 64q^{71} - 48q^{73} - 48q^{75} + 4q^{77} - 40q^{85} - 12q^{87} - 80q^{91} + 24q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) −1.35944 + 0.364260i −0.784872 + 0.210306i −0.628931 0.777461i \(-0.716507\pi\)
−0.155940 + 0.987767i \(0.549841\pi\)
\(4\) 0 0
\(5\) −2.13431 0.666887i −0.954491 0.298241i
\(6\) 0 0
\(7\) 2.59782 0.501338i 0.981883 0.189488i
\(8\) 0 0
\(9\) −0.882692 + 0.509622i −0.294231 + 0.169874i
\(10\) 0 0
\(11\) 1.86869 3.23667i 0.563432 0.975893i −0.433762 0.901028i \(-0.642814\pi\)
0.997194 0.0748654i \(-0.0238527\pi\)
\(12\) 0 0
\(13\) −4.55026 4.55026i −1.26201 1.26201i −0.950115 0.311899i \(-0.899035\pi\)
−0.311899 0.950115i \(-0.600965\pi\)
\(14\) 0 0
\(15\) 3.14438 + 0.129149i 0.811874 + 0.0333461i
\(16\) 0 0
\(17\) −1.58528 5.91633i −0.384486 1.43492i −0.838975 0.544169i \(-0.816845\pi\)
0.454489 0.890752i \(-0.349822\pi\)
\(18\) 0 0
\(19\) −0.616087 1.06709i −0.141340 0.244808i 0.786661 0.617385i \(-0.211808\pi\)
−0.928001 + 0.372577i \(0.878474\pi\)
\(20\) 0 0
\(21\) −3.34895 + 1.62782i −0.730802 + 0.355219i
\(22\) 0 0
\(23\) −2.69174 0.721250i −0.561267 0.150391i −0.0329787 0.999456i \(-0.510499\pi\)
−0.528288 + 0.849065i \(0.677166\pi\)
\(24\) 0 0
\(25\) 4.11052 + 2.84668i 0.822105 + 0.569337i
\(26\) 0 0
\(27\) 3.99986 3.99986i 0.769774 0.769774i
\(28\) 0 0
\(29\) 2.82808i 0.525161i −0.964910 0.262580i \(-0.915427\pi\)
0.964910 0.262580i \(-0.0845735\pi\)
\(30\) 0 0
\(31\) 5.94396 + 3.43175i 1.06757 + 0.616360i 0.927516 0.373784i \(-0.121940\pi\)
0.140051 + 0.990144i \(0.455273\pi\)
\(32\) 0 0
\(33\) −1.36138 + 5.08074i −0.236986 + 0.884444i
\(34\) 0 0
\(35\) −5.87887 0.662443i −0.993711 0.111973i
\(36\) 0 0
\(37\) −2.01646 + 7.52551i −0.331503 + 1.23719i 0.576108 + 0.817374i \(0.304571\pi\)
−0.907611 + 0.419813i \(0.862096\pi\)
\(38\) 0 0
\(39\) 7.84327 + 4.52831i 1.25593 + 0.725110i
\(40\) 0 0
\(41\) 5.56966i 0.869835i 0.900470 + 0.434917i \(0.143222\pi\)
−0.900470 + 0.434917i \(0.856778\pi\)
\(42\) 0 0
\(43\) −1.95176 + 1.95176i −0.297641 + 0.297641i −0.840089 0.542448i \(-0.817497\pi\)
0.542448 + 0.840089i \(0.317497\pi\)
\(44\) 0 0
\(45\) 2.22379 0.499034i 0.331504 0.0743916i
\(46\) 0 0
\(47\) −11.1512 2.98797i −1.62658 0.435840i −0.673652 0.739048i \(-0.735275\pi\)
−0.952924 + 0.303209i \(0.901942\pi\)
\(48\) 0 0
\(49\) 6.49732 2.60477i 0.928189 0.372110i
\(50\) 0 0
\(51\) 4.31017 + 7.46543i 0.603544 + 1.04537i
\(52\) 0 0
\(53\) −2.53082 9.44513i −0.347634 1.29739i −0.889504 0.456927i \(-0.848950\pi\)
0.541870 0.840462i \(-0.317716\pi\)
\(54\) 0 0
\(55\) −6.14686 + 5.66184i −0.828842 + 0.763442i
\(56\) 0 0
\(57\) 1.22623 + 1.22623i 0.162418 + 0.162418i
\(58\) 0 0
\(59\) −0.916152 + 1.58682i −0.119273 + 0.206587i −0.919480 0.393137i \(-0.871390\pi\)
0.800207 + 0.599724i \(0.204723\pi\)
\(60\) 0 0
\(61\) −3.43491 + 1.98315i −0.439795 + 0.253916i −0.703511 0.710685i \(-0.748385\pi\)
0.263716 + 0.964600i \(0.415052\pi\)
\(62\) 0 0
\(63\) −2.03758 + 1.76643i −0.256711 + 0.222550i
\(64\) 0 0
\(65\) 6.67713 + 12.7462i 0.828196 + 1.58097i
\(66\) 0 0
\(67\) 7.93605 2.12646i 0.969542 0.259788i 0.260908 0.965364i \(-0.415978\pi\)
0.708635 + 0.705576i \(0.249311\pi\)
\(68\) 0 0
\(69\) 3.92198 0.472151
\(70\) 0 0
\(71\) 0.570063 0.0676540 0.0338270 0.999428i \(-0.489230\pi\)
0.0338270 + 0.999428i \(0.489230\pi\)
\(72\) 0 0
\(73\) −2.03783 + 0.546036i −0.238510 + 0.0639087i −0.376094 0.926581i \(-0.622733\pi\)
0.137584 + 0.990490i \(0.456066\pi\)
\(74\) 0 0
\(75\) −6.62493 2.37259i −0.764981 0.273963i
\(76\) 0 0
\(77\) 3.23186 9.34513i 0.368304 1.06498i
\(78\) 0 0
\(79\) 9.47466 5.47020i 1.06598 0.615445i 0.138901 0.990306i \(-0.455643\pi\)
0.927081 + 0.374861i \(0.122310\pi\)
\(80\) 0 0
\(81\) −2.45170 + 4.24647i −0.272411 + 0.471831i
\(82\) 0 0
\(83\) 8.80820 + 8.80820i 0.966826 + 0.966826i 0.999467 0.0326414i \(-0.0103919\pi\)
−0.0326414 + 0.999467i \(0.510392\pi\)
\(84\) 0 0
\(85\) −0.562062 + 13.6845i −0.0609642 + 1.48429i
\(86\) 0 0
\(87\) 1.03016 + 3.84459i 0.110444 + 0.412184i
\(88\) 0 0
\(89\) −3.00362 5.20243i −0.318383 0.551456i 0.661767 0.749709i \(-0.269807\pi\)
−0.980151 + 0.198253i \(0.936473\pi\)
\(90\) 0 0
\(91\) −14.1020 9.53952i −1.47829 1.00001i
\(92\) 0 0
\(93\) −9.33049 2.50010i −0.967527 0.259248i
\(94\) 0 0
\(95\) 0.603286 + 2.68836i 0.0618959 + 0.275820i
\(96\) 0 0
\(97\) 3.70694 3.70694i 0.376383 0.376383i −0.493413 0.869795i \(-0.664251\pi\)
0.869795 + 0.493413i \(0.164251\pi\)
\(98\) 0 0
\(99\) 3.80931i 0.382850i
\(100\) 0 0
\(101\) 3.46339 + 1.99959i 0.344620 + 0.198967i 0.662313 0.749227i \(-0.269575\pi\)
−0.317693 + 0.948194i \(0.602908\pi\)
\(102\) 0 0
\(103\) 0.711944 2.65701i 0.0701500 0.261803i −0.921940 0.387333i \(-0.873396\pi\)
0.992090 + 0.125530i \(0.0400631\pi\)
\(104\) 0 0
\(105\) 8.23326 1.24089i 0.803484 0.121099i
\(106\) 0 0
\(107\) −2.19864 + 8.20544i −0.212551 + 0.793250i 0.774464 + 0.632618i \(0.218020\pi\)
−0.987014 + 0.160632i \(0.948647\pi\)
\(108\) 0 0
\(109\) −9.96993 5.75614i −0.954946 0.551339i −0.0603324 0.998178i \(-0.519216\pi\)
−0.894614 + 0.446840i \(0.852549\pi\)
\(110\) 0 0
\(111\) 10.9650i 1.04075i
\(112\) 0 0
\(113\) 7.36636 7.36636i 0.692969 0.692969i −0.269915 0.962884i \(-0.586996\pi\)
0.962884 + 0.269915i \(0.0869957\pi\)
\(114\) 0 0
\(115\) 5.26401 + 3.33446i 0.490871 + 0.310940i
\(116\) 0 0
\(117\) 6.33539 + 1.69756i 0.585707 + 0.156940i
\(118\) 0 0
\(119\) −7.08435 14.5748i −0.649421 1.33607i
\(120\) 0 0
\(121\) −1.48403 2.57041i −0.134912 0.233674i
\(122\) 0 0
\(123\) −2.02880 7.57160i −0.182931 0.682708i
\(124\) 0 0
\(125\) −6.87470 8.81695i −0.614892 0.788612i
\(126\) 0 0
\(127\) −8.56353 8.56353i −0.759890 0.759890i 0.216412 0.976302i \(-0.430565\pi\)
−0.976302 + 0.216412i \(0.930565\pi\)
\(128\) 0 0
\(129\) 1.94235 3.36425i 0.171014 0.296206i
\(130\) 0 0
\(131\) 1.01451 0.585728i 0.0886381 0.0511753i −0.455026 0.890478i \(-0.650370\pi\)
0.543664 + 0.839303i \(0.317037\pi\)
\(132\) 0 0
\(133\) −2.13546 2.46325i −0.185168 0.213591i
\(134\) 0 0
\(135\) −11.2044 + 5.86947i −0.964320 + 0.505164i
\(136\) 0 0
\(137\) 9.91154 2.65579i 0.846800 0.226899i 0.190770 0.981635i \(-0.438901\pi\)
0.656029 + 0.754735i \(0.272235\pi\)
\(138\) 0 0
\(139\) 8.10664 0.687596 0.343798 0.939044i \(-0.388286\pi\)
0.343798 + 0.939044i \(0.388286\pi\)
\(140\) 0 0
\(141\) 16.2478 1.36831
\(142\) 0 0
\(143\) −23.2307 + 6.22465i −1.94265 + 0.520532i
\(144\) 0 0
\(145\) −1.88601 + 6.03598i −0.156624 + 0.501261i
\(146\) 0 0
\(147\) −7.88388 + 5.90774i −0.650252 + 0.487262i
\(148\) 0 0
\(149\) −5.60127 + 3.23390i −0.458874 + 0.264931i −0.711571 0.702614i \(-0.752016\pi\)
0.252697 + 0.967546i \(0.418683\pi\)
\(150\) 0 0
\(151\) 3.00407 5.20320i 0.244468 0.423430i −0.717514 0.696544i \(-0.754720\pi\)
0.961982 + 0.273114i \(0.0880535\pi\)
\(152\) 0 0
\(153\) 4.41441 + 4.41441i 0.356884 + 0.356884i
\(154\) 0 0
\(155\) −10.3976 11.2884i −0.835159 0.906702i
\(156\) 0 0
\(157\) 1.77930 + 6.64043i 0.142003 + 0.529964i 0.999871 + 0.0160922i \(0.00512252\pi\)
−0.857867 + 0.513871i \(0.828211\pi\)
\(158\) 0 0
\(159\) 6.88097 + 11.9182i 0.545697 + 0.945174i
\(160\) 0 0
\(161\) −7.35425 0.524203i −0.579596 0.0413130i
\(162\) 0 0
\(163\) 12.6434 + 3.38778i 0.990305 + 0.265351i 0.717379 0.696683i \(-0.245342\pi\)
0.272926 + 0.962035i \(0.412008\pi\)
\(164\) 0 0
\(165\) 6.29389 9.93597i 0.489978 0.773514i
\(166\) 0 0
\(167\) 6.33743 6.33743i 0.490405 0.490405i −0.418029 0.908434i \(-0.637279\pi\)
0.908434 + 0.418029i \(0.137279\pi\)
\(168\) 0 0
\(169\) 28.4097i 2.18536i
\(170\) 0 0
\(171\) 1.08763 + 0.627943i 0.0831731 + 0.0480200i
\(172\) 0 0
\(173\) 0.523701 1.95448i 0.0398162 0.148596i −0.943156 0.332350i \(-0.892158\pi\)
0.982972 + 0.183754i \(0.0588250\pi\)
\(174\) 0 0
\(175\) 12.1055 + 5.33440i 0.915093 + 0.403243i
\(176\) 0 0
\(177\) 0.667435 2.49090i 0.0501675 0.187228i
\(178\) 0 0
\(179\) −3.54703 2.04788i −0.265118 0.153066i 0.361549 0.932353i \(-0.382248\pi\)
−0.626667 + 0.779287i \(0.715581\pi\)
\(180\) 0 0
\(181\) 10.6327i 0.790323i −0.918612 0.395162i \(-0.870689\pi\)
0.918612 0.395162i \(-0.129311\pi\)
\(182\) 0 0
\(183\) 3.94716 3.94716i 0.291783 0.291783i
\(184\) 0 0
\(185\) 9.32240 14.7170i 0.685397 1.08202i
\(186\) 0 0
\(187\) −22.1116 5.92479i −1.61696 0.433264i
\(188\) 0 0
\(189\) 8.38563 12.3962i 0.609965 0.901690i
\(190\) 0 0
\(191\) −6.36951 11.0323i −0.460882 0.798271i 0.538123 0.842866i \(-0.319133\pi\)
−0.999005 + 0.0445955i \(0.985800\pi\)
\(192\) 0 0
\(193\) −2.98349 11.1345i −0.214756 0.801482i −0.986252 0.165247i \(-0.947158\pi\)
0.771496 0.636234i \(-0.219509\pi\)
\(194\) 0 0
\(195\) −13.7201 14.8954i −0.982514 1.06668i
\(196\) 0 0
\(197\) −4.36293 4.36293i −0.310846 0.310846i 0.534391 0.845237i \(-0.320541\pi\)
−0.845237 + 0.534391i \(0.820541\pi\)
\(198\) 0 0
\(199\) −8.80171 + 15.2450i −0.623937 + 1.08069i 0.364809 + 0.931082i \(0.381134\pi\)
−0.988745 + 0.149608i \(0.952199\pi\)
\(200\) 0 0
\(201\) −10.0140 + 5.78157i −0.706331 + 0.407801i
\(202\) 0 0
\(203\) −1.41782 7.34683i −0.0995117 0.515646i
\(204\) 0 0
\(205\) 3.71433 11.8874i 0.259420 0.830249i
\(206\) 0 0
\(207\) 2.74354 0.735130i 0.190689 0.0510951i
\(208\) 0 0
\(209\) −4.60511 −0.318542
\(210\) 0 0
\(211\) 22.0556 1.51837 0.759185 0.650875i \(-0.225598\pi\)
0.759185 + 0.650875i \(0.225598\pi\)
\(212\) 0 0
\(213\) −0.774964 + 0.207651i −0.0530997 + 0.0142280i
\(214\) 0 0
\(215\) 5.46727 2.86405i 0.372864 0.195327i
\(216\) 0 0
\(217\) 17.1618 + 5.93512i 1.16502 + 0.402902i
\(218\) 0 0
\(219\) 2.57141 1.48460i 0.173760 0.100320i
\(220\) 0 0
\(221\) −19.7074 + 34.1343i −1.32566 + 2.29612i
\(222\) 0 0
\(223\) 8.37713 + 8.37713i 0.560974 + 0.560974i 0.929584 0.368610i \(-0.120166\pi\)
−0.368610 + 0.929584i \(0.620166\pi\)
\(224\) 0 0
\(225\) −5.07906 0.417929i −0.338604 0.0278620i
\(226\) 0 0
\(227\) 3.05323 + 11.3948i 0.202650 + 0.756300i 0.990153 + 0.139989i \(0.0447069\pi\)
−0.787503 + 0.616311i \(0.788626\pi\)
\(228\) 0 0
\(229\) −3.21704 5.57208i −0.212588 0.368214i 0.739936 0.672678i \(-0.234856\pi\)
−0.952524 + 0.304464i \(0.901523\pi\)
\(230\) 0 0
\(231\) −0.989449 + 13.8814i −0.0651010 + 0.913326i
\(232\) 0 0
\(233\) 14.6729 + 3.93160i 0.961256 + 0.257568i 0.705132 0.709076i \(-0.250888\pi\)
0.256124 + 0.966644i \(0.417554\pi\)
\(234\) 0 0
\(235\) 21.8075 + 13.8139i 1.42257 + 0.901117i
\(236\) 0 0
\(237\) −10.8876 + 10.8876i −0.707228 + 0.707228i
\(238\) 0 0
\(239\) 17.0337i 1.10182i −0.834566 0.550908i \(-0.814282\pi\)
0.834566 0.550908i \(-0.185718\pi\)
\(240\) 0 0
\(241\) −0.561340 0.324090i −0.0361591 0.0208765i 0.481811 0.876275i \(-0.339979\pi\)
−0.517971 + 0.855398i \(0.673312\pi\)
\(242\) 0 0
\(243\) −2.60604 + 9.72586i −0.167177 + 0.623914i
\(244\) 0 0
\(245\) −15.6044 + 1.22640i −0.996926 + 0.0783518i
\(246\) 0 0
\(247\) −2.05220 + 7.65890i −0.130578 + 0.487324i
\(248\) 0 0
\(249\) −15.1827 8.76572i −0.962163 0.555505i
\(250\) 0 0
\(251\) 2.99161i 0.188828i −0.995533 0.0944142i \(-0.969902\pi\)
0.995533 0.0944142i \(-0.0300978\pi\)
\(252\) 0 0
\(253\) −7.36449 + 7.36449i −0.463002 + 0.463002i
\(254\) 0 0
\(255\) −4.22062 18.8079i −0.264305 1.17780i
\(256\) 0 0
\(257\) 4.56640 + 1.22356i 0.284844 + 0.0763237i 0.398412 0.917206i \(-0.369561\pi\)
−0.113568 + 0.993530i \(0.536228\pi\)
\(258\) 0 0
\(259\) −1.46556 + 20.5608i −0.0910652 + 1.27759i
\(260\) 0 0
\(261\) 1.44125 + 2.49632i 0.0892112 + 0.154518i
\(262\) 0 0
\(263\) 6.44367 + 24.0481i 0.397334 + 1.48287i 0.817769 + 0.575547i \(0.195211\pi\)
−0.420435 + 0.907323i \(0.638123\pi\)
\(264\) 0 0
\(265\) −0.897304 + 21.8466i −0.0551210 + 1.34202i
\(266\) 0 0
\(267\) 5.97828 + 5.97828i 0.365865 + 0.365865i
\(268\) 0 0
\(269\) −0.153942 + 0.266636i −0.00938603 + 0.0162571i −0.870680 0.491849i \(-0.836321\pi\)
0.861294 + 0.508107i \(0.169654\pi\)
\(270\) 0 0
\(271\) 24.2593 14.0061i 1.47365 0.850812i 0.474089 0.880477i \(-0.342777\pi\)
0.999560 + 0.0296653i \(0.00944415\pi\)
\(272\) 0 0
\(273\) 22.6456 + 7.83160i 1.37057 + 0.473990i
\(274\) 0 0
\(275\) 16.8951 7.98483i 1.01881 0.481504i
\(276\) 0 0
\(277\) −27.3318 + 7.32354i −1.64221 + 0.440029i −0.957417 0.288708i \(-0.906774\pi\)
−0.684793 + 0.728737i \(0.740108\pi\)
\(278\) 0 0
\(279\) −6.99558 −0.418814
\(280\) 0 0
\(281\) −2.60283 −0.155272 −0.0776358 0.996982i \(-0.524737\pi\)
−0.0776358 + 0.996982i \(0.524737\pi\)
\(282\) 0 0
\(283\) 17.4371 4.67227i 1.03653 0.277738i 0.299856 0.953985i \(-0.403061\pi\)
0.736675 + 0.676247i \(0.236395\pi\)
\(284\) 0 0
\(285\) −1.79939 3.43491i −0.106587 0.203467i
\(286\) 0 0
\(287\) 2.79228 + 14.4690i 0.164823 + 0.854076i
\(288\) 0 0
\(289\) −17.7675 + 10.2581i −1.04515 + 0.603415i
\(290\) 0 0
\(291\) −3.68906 + 6.38965i −0.216257 + 0.374568i
\(292\) 0 0
\(293\) 17.2326 + 17.2326i 1.00674 + 1.00674i 0.999977 + 0.00676223i \(0.00215250\pi\)
0.00676223 + 0.999977i \(0.497848\pi\)
\(294\) 0 0
\(295\) 3.01358 2.77579i 0.175457 0.161613i
\(296\) 0 0
\(297\) −5.47172 20.4207i −0.317502 1.18493i
\(298\) 0 0
\(299\) 8.96625 + 15.5300i 0.518532 + 0.898123i
\(300\) 0 0
\(301\) −4.09183 + 6.04882i −0.235849 + 0.348648i
\(302\) 0 0
\(303\) −5.43663 1.45674i −0.312327 0.0836876i
\(304\) 0 0
\(305\) 8.65368 1.94194i 0.495508 0.111195i
\(306\) 0 0
\(307\) −11.3375 + 11.3375i −0.647063 + 0.647063i −0.952282 0.305219i \(-0.901270\pi\)
0.305219 + 0.952282i \(0.401270\pi\)
\(308\) 0 0
\(309\) 3.87137i 0.220235i
\(310\) 0 0
\(311\) 17.9899 + 10.3865i 1.02011 + 0.588962i 0.914136 0.405407i \(-0.132870\pi\)
0.105975 + 0.994369i \(0.466204\pi\)
\(312\) 0 0
\(313\) −1.96776 + 7.34380i −0.111225 + 0.415096i −0.998977 0.0452258i \(-0.985599\pi\)
0.887752 + 0.460322i \(0.152266\pi\)
\(314\) 0 0
\(315\) 5.52683 2.41127i 0.311402 0.135860i
\(316\) 0 0
\(317\) −0.442998 + 1.65329i −0.0248812 + 0.0928581i −0.977250 0.212091i \(-0.931973\pi\)
0.952369 + 0.304949i \(0.0986394\pi\)
\(318\) 0 0
\(319\) −9.15356 5.28481i −0.512501 0.295892i
\(320\) 0 0
\(321\) 11.9557i 0.667300i
\(322\) 0 0
\(323\) −5.33661 + 5.33661i −0.296937 + 0.296937i
\(324\) 0 0
\(325\) −5.75080 31.6571i −0.318997 1.75602i
\(326\) 0 0
\(327\) 15.6502 + 4.19347i 0.865460 + 0.231899i
\(328\) 0 0
\(329\) −30.4669 2.17165i −1.67969 0.119727i
\(330\) 0 0
\(331\) −13.0087 22.5317i −0.715023 1.23846i −0.962951 0.269678i \(-0.913083\pi\)
0.247928 0.968779i \(-0.420250\pi\)
\(332\) 0 0
\(333\) −2.05526 7.67034i −0.112628 0.420332i
\(334\) 0 0
\(335\) −18.3561 0.753938i −1.00290 0.0411921i
\(336\) 0 0
\(337\) −22.0521 22.0521i −1.20125 1.20125i −0.973785 0.227468i \(-0.926955\pi\)
−0.227468 0.973785i \(-0.573045\pi\)
\(338\) 0 0
\(339\) −7.33083 + 12.6974i −0.398156 + 0.689627i
\(340\) 0 0
\(341\) 22.2149 12.8258i 1.20300 0.694554i
\(342\) 0 0
\(343\) 15.5730 10.0241i 0.840862 0.541249i
\(344\) 0 0
\(345\) −8.37070 2.61552i −0.450663 0.140815i
\(346\) 0 0
\(347\) 21.3424 5.71867i 1.14572 0.306994i 0.364470 0.931215i \(-0.381250\pi\)
0.781248 + 0.624221i \(0.214583\pi\)
\(348\) 0 0
\(349\) 21.6246 1.15754 0.578770 0.815491i \(-0.303533\pi\)
0.578770 + 0.815491i \(0.303533\pi\)
\(350\) 0 0
\(351\) −36.4008 −1.94293
\(352\) 0 0
\(353\) −3.65400 + 0.979086i −0.194483 + 0.0521115i −0.354746 0.934963i \(-0.615433\pi\)
0.160263 + 0.987074i \(0.448766\pi\)
\(354\) 0 0
\(355\) −1.21669 0.380167i −0.0645751 0.0201772i
\(356\) 0 0
\(357\) 14.9397 + 17.2330i 0.790695 + 0.912066i
\(358\) 0 0
\(359\) 3.68781 2.12916i 0.194635 0.112373i −0.399516 0.916726i \(-0.630822\pi\)
0.594151 + 0.804354i \(0.297488\pi\)
\(360\) 0 0
\(361\) 8.74087 15.1396i 0.460046 0.796823i
\(362\) 0 0
\(363\) 2.95374 + 2.95374i 0.155031 + 0.155031i
\(364\) 0 0
\(365\) 4.71351 + 0.193598i 0.246716 + 0.0101334i
\(366\) 0 0
\(367\) −6.08811 22.7211i −0.317797 1.18603i −0.921357 0.388716i \(-0.872919\pi\)
0.603561 0.797317i \(-0.293748\pi\)
\(368\) 0 0
\(369\) −2.83842 4.91629i −0.147762 0.255932i
\(370\) 0 0
\(371\) −11.3098 23.2679i −0.587176 1.20801i
\(372\) 0 0
\(373\) 7.55500 + 2.02436i 0.391183 + 0.104817i 0.449049 0.893507i \(-0.351763\pi\)
−0.0578658 + 0.998324i \(0.518430\pi\)
\(374\) 0 0
\(375\) 12.5574 + 9.48191i 0.648460 + 0.489644i
\(376\) 0 0
\(377\) −12.8685 + 12.8685i −0.662760 + 0.662760i
\(378\) 0 0
\(379\) 24.6449i 1.26592i −0.774184 0.632961i \(-0.781839\pi\)
0.774184 0.632961i \(-0.218161\pi\)
\(380\) 0 0
\(381\) 14.7609 + 8.52223i 0.756225 + 0.436607i
\(382\) 0 0
\(383\) 6.07201 22.6611i 0.310265 1.15793i −0.618052 0.786137i \(-0.712078\pi\)
0.928317 0.371789i \(-0.121255\pi\)
\(384\) 0 0
\(385\) −13.1299 + 17.7901i −0.669163 + 0.906667i
\(386\) 0 0
\(387\) 0.728143 2.71747i 0.0370136 0.138137i
\(388\) 0 0
\(389\) 20.5933 + 11.8895i 1.04412 + 0.602823i 0.920998 0.389568i \(-0.127376\pi\)
0.123123 + 0.992391i \(0.460709\pi\)
\(390\) 0 0
\(391\) 17.0686i 0.863198i
\(392\) 0 0
\(393\) −1.16581 + 1.16581i −0.0588071 + 0.0588071i
\(394\) 0 0
\(395\) −23.8698 + 5.35654i −1.20102 + 0.269517i
\(396\) 0 0
\(397\) 22.3418 + 5.98647i 1.12130 + 0.300452i 0.771410 0.636338i \(-0.219552\pi\)
0.349892 + 0.936790i \(0.386218\pi\)
\(398\) 0 0
\(399\) 3.80028 + 2.57077i 0.190252 + 0.128699i
\(400\) 0 0
\(401\) −18.8264 32.6083i −0.940147 1.62838i −0.765187 0.643808i \(-0.777354\pi\)
−0.174960 0.984576i \(-0.555980\pi\)
\(402\) 0 0
\(403\) −11.4312 42.6619i −0.569430 2.12514i
\(404\) 0 0
\(405\) 8.06461 7.42827i 0.400733 0.369114i
\(406\) 0 0
\(407\) 20.5895 + 20.5895i 1.02058 + 1.02058i
\(408\) 0 0
\(409\) −3.10540 + 5.37871i −0.153552 + 0.265960i −0.932531 0.361090i \(-0.882405\pi\)
0.778979 + 0.627050i \(0.215738\pi\)
\(410\) 0 0
\(411\) −12.5067 + 7.22076i −0.616911 + 0.356174i
\(412\) 0 0
\(413\) −1.58446 + 4.58158i −0.0779663 + 0.225445i
\(414\) 0 0
\(415\) −12.9253 24.6735i −0.634479 1.21117i
\(416\) 0 0
\(417\) −11.0205 + 2.95292i −0.539674 + 0.144605i
\(418\) 0 0
\(419\) −12.9069 −0.630541 −0.315270 0.949002i \(-0.602095\pi\)
−0.315270 + 0.949002i \(0.602095\pi\)
\(420\) 0 0
\(421\) −25.0983 −1.22322 −0.611608 0.791161i \(-0.709477\pi\)
−0.611608 + 0.791161i \(0.709477\pi\)
\(422\) 0 0
\(423\) 11.3658 3.04547i 0.552626 0.148076i
\(424\) 0 0
\(425\) 10.3256 28.8320i 0.500866 1.39856i
\(426\) 0 0
\(427\) −7.92904 + 6.87390i −0.383713 + 0.332651i
\(428\) 0 0
\(429\) 29.3133 16.9241i 1.41526 0.817101i
\(430\) 0 0
\(431\) −14.1918 + 24.5809i −0.683593 + 1.18402i 0.290283 + 0.956941i \(0.406250\pi\)
−0.973877 + 0.227078i \(0.927083\pi\)
\(432\) 0 0
\(433\) −20.7667 20.7667i −0.997984 0.997984i 0.00201350 0.999998i \(-0.499359\pi\)
−0.999998 + 0.00201350i \(0.999359\pi\)
\(434\) 0 0
\(435\) 0.365243 8.89254i 0.0175121 0.426365i
\(436\) 0 0
\(437\) 0.888706 + 3.31669i 0.0425125 + 0.158659i
\(438\) 0 0
\(439\) −2.84512 4.92790i −0.135790 0.235196i 0.790109 0.612967i \(-0.210024\pi\)
−0.925899 + 0.377771i \(0.876691\pi\)
\(440\) 0 0
\(441\) −4.40768 + 5.61039i −0.209890 + 0.267161i
\(442\) 0 0
\(443\) 12.6459 + 3.38845i 0.600824 + 0.160990i 0.546395 0.837527i \(-0.316000\pi\)
0.0544285 + 0.998518i \(0.482666\pi\)
\(444\) 0 0
\(445\) 2.94122 + 13.1067i 0.139427 + 0.621315i
\(446\) 0 0
\(447\) 6.43660 6.43660i 0.304441 0.304441i
\(448\) 0 0
\(449\) 11.4035i 0.538163i 0.963117 + 0.269081i \(0.0867200\pi\)
−0.963117 + 0.269081i \(0.913280\pi\)
\(450\) 0 0
\(451\) 18.0272 + 10.4080i 0.848866 + 0.490093i
\(452\) 0 0
\(453\) −2.18853 + 8.16769i −0.102826 + 0.383751i
\(454\) 0 0
\(455\) 23.7361 + 29.7647i 1.11277 + 1.39539i
\(456\) 0 0
\(457\) −0.658264 + 2.45668i −0.0307923 + 0.114918i −0.979611 0.200901i \(-0.935613\pi\)
0.948819 + 0.315820i \(0.102280\pi\)
\(458\) 0 0
\(459\) −30.0054 17.3236i −1.40053 0.808597i
\(460\) 0 0
\(461\) 28.3975i 1.32260i −0.750121 0.661301i \(-0.770005\pi\)
0.750121 0.661301i \(-0.229995\pi\)
\(462\) 0 0
\(463\) −8.29144 + 8.29144i −0.385336 + 0.385336i −0.873020 0.487684i \(-0.837842\pi\)
0.487684 + 0.873020i \(0.337842\pi\)
\(464\) 0 0
\(465\) 18.2468 + 11.5584i 0.846177 + 0.536006i
\(466\) 0 0
\(467\) 1.67367 + 0.448458i 0.0774481 + 0.0207522i 0.297335 0.954773i \(-0.403902\pi\)
−0.219887 + 0.975525i \(0.570569\pi\)
\(468\) 0 0
\(469\) 19.5503 9.50279i 0.902751 0.438798i
\(470\) 0 0
\(471\) −4.83768 8.37912i −0.222909 0.386089i
\(472\) 0 0
\(473\) 2.66997 + 9.96446i 0.122765 + 0.458166i
\(474\) 0 0
\(475\) 0.505238 6.14012i 0.0231819 0.281728i
\(476\) 0 0
\(477\) 7.04738 + 7.04738i 0.322677 + 0.322677i
\(478\) 0 0
\(479\) −10.7131 + 18.5557i −0.489496 + 0.847831i −0.999927 0.0120872i \(-0.996152\pi\)
0.510431 + 0.859919i \(0.329486\pi\)
\(480\) 0 0
\(481\) 43.4184 25.0676i 1.97971 1.14299i
\(482\) 0 0
\(483\) 10.1886 1.96624i 0.463597 0.0894669i
\(484\) 0 0
\(485\) −10.3839 + 5.43963i −0.471507 + 0.247001i
\(486\) 0 0
\(487\) −37.5562 + 10.0631i −1.70183 + 0.456005i −0.973400 0.229112i \(-0.926418\pi\)
−0.728433 + 0.685117i \(0.759751\pi\)
\(488\) 0 0
\(489\) −18.4219 −0.833067
\(490\) 0 0
\(491\) −5.54467 −0.250228 −0.125114 0.992142i \(-0.539930\pi\)
−0.125114 + 0.992142i \(0.539930\pi\)
\(492\) 0 0
\(493\) −16.7318 + 4.48329i −0.753565 + 0.201917i
\(494\) 0 0
\(495\) 2.54038 8.13023i 0.114182 0.365427i
\(496\) 0 0
\(497\) 1.48092 0.285794i 0.0664283 0.0128196i
\(498\) 0 0
\(499\) 4.28573 2.47437i 0.191856 0.110768i −0.400995 0.916080i \(-0.631336\pi\)
0.592851 + 0.805312i \(0.298002\pi\)
\(500\) 0 0
\(501\) −6.30686 + 10.9238i −0.281770 + 0.488040i
\(502\) 0 0
\(503\) 14.3450 + 14.3450i 0.639614 + 0.639614i 0.950460 0.310846i \(-0.100612\pi\)
−0.310846 + 0.950460i \(0.600612\pi\)
\(504\) 0 0
\(505\) −6.05844 6.57743i −0.269597 0.292692i
\(506\) 0 0
\(507\) −10.3485 38.6212i −0.459594 1.71523i
\(508\) 0 0
\(509\) 17.6679 + 30.6017i 0.783116 + 1.35640i 0.930118 + 0.367260i \(0.119704\pi\)
−0.147002 + 0.989136i \(0.546962\pi\)
\(510\) 0 0
\(511\) −5.02017 + 2.44015i −0.222079 + 0.107946i
\(512\) 0 0
\(513\) −6.73249 1.80396i −0.297247 0.0796470i
\(514\) 0 0
\(515\) −3.29143 + 5.19609i −0.145038 + 0.228967i
\(516\) 0 0
\(517\) −30.5093 + 30.5093i −1.34180 + 1.34180i
\(518\) 0 0
\(519\) 2.84775i 0.125002i
\(520\) 0 0
\(521\) −19.0681 11.0090i −0.835388 0.482312i 0.0203058 0.999794i \(-0.493536\pi\)
−0.855694 + 0.517482i \(0.826869\pi\)
\(522\) 0 0
\(523\) −6.80926 + 25.4125i −0.297748 + 1.11121i 0.641262 + 0.767322i \(0.278411\pi\)
−0.939010 + 0.343889i \(0.888256\pi\)
\(524\) 0 0
\(525\) −18.3998 2.84222i −0.803035 0.124045i
\(526\) 0 0
\(527\) 10.8805 40.6067i 0.473964 1.76886i
\(528\) 0 0
\(529\) −13.1933 7.61716i −0.573622 0.331181i
\(530\) 0 0
\(531\) 1.86757i 0.0810454i
\(532\) 0 0
\(533\) 25.3434 25.3434i 1.09774 1.09774i
\(534\) 0 0
\(535\) 10.1647 16.0467i 0.439457 0.693758i
\(536\) 0 0
\(537\) 5.56793 + 1.49192i 0.240274 + 0.0643812i
\(538\) 0 0
\(539\) 3.71071 25.8972i 0.159831 1.11547i
\(540\) 0 0
\(541\) 3.33567 + 5.77755i 0.143412 + 0.248396i 0.928779 0.370633i \(-0.120859\pi\)
−0.785368 + 0.619030i \(0.787526\pi\)
\(542\) 0 0
\(543\) 3.87307 + 14.4545i 0.166209 + 0.620302i
\(544\) 0 0
\(545\) 17.4402 + 18.9342i 0.747056 + 0.811052i
\(546\) 0 0
\(547\) 8.18996 + 8.18996i 0.350177 + 0.350177i 0.860175 0.509998i \(-0.170354\pi\)
−0.509998 + 0.860175i \(0.670354\pi\)
\(548\) 0 0
\(549\) 2.02131 3.50101i 0.0862674 0.149420i
\(550\) 0 0
\(551\) −3.01782 + 1.74234i −0.128564 + 0.0742262i
\(552\) 0 0
\(553\) 21.8710 18.9606i 0.930050 0.806286i
\(554\) 0 0
\(555\) −7.31240 + 23.4026i −0.310394 + 0.993386i
\(556\) 0 0
\(557\) 36.4271 9.76062i 1.54347 0.413571i 0.616083 0.787681i \(-0.288719\pi\)
0.927384 + 0.374111i \(0.122052\pi\)
\(558\) 0 0
\(559\) 17.7621 0.751255
\(560\) 0 0
\(561\) 32.2175 1.36023
\(562\) 0 0
\(563\) −37.2256 + 9.97457i −1.56887 + 0.420378i −0.935459 0.353436i \(-0.885013\pi\)
−0.633413 + 0.773814i \(0.718347\pi\)
\(564\) 0 0
\(565\) −20.6346 + 10.8095i −0.868104 + 0.454760i
\(566\) 0 0
\(567\) −4.24016 + 12.2607i −0.178070 + 0.514901i
\(568\) 0 0
\(569\) 10.4114 6.01105i 0.436470 0.251996i −0.265629 0.964075i \(-0.585580\pi\)
0.702099 + 0.712079i \(0.252246\pi\)
\(570\) 0 0
\(571\) −15.7498 + 27.2794i −0.659107 + 1.14161i 0.321740 + 0.946828i \(0.395732\pi\)
−0.980847 + 0.194779i \(0.937601\pi\)
\(572\) 0 0
\(573\) 12.6776 + 12.6776i 0.529614 + 0.529614i
\(574\) 0 0
\(575\) −9.01130 10.6273i −0.375797 0.443187i
\(576\) 0 0
\(577\) 3.14609 + 11.7414i 0.130973 + 0.488800i 0.999982 0.00599739i \(-0.00190904\pi\)
−0.869009 + 0.494797i \(0.835242\pi\)
\(578\) 0 0
\(579\) 8.11174 + 14.0499i 0.337112 + 0.583896i
\(580\) 0 0
\(581\) 27.2980 + 18.4662i 1.13251 + 0.766108i
\(582\) 0 0
\(583\) −35.3001 9.45864i −1.46198 0.391737i
\(584\) 0 0
\(585\) −12.3896 7.84811i −0.512246 0.324479i
\(586\) 0 0
\(587\) 19.1797 19.1797i 0.791631 0.791631i −0.190128 0.981759i \(-0.560890\pi\)
0.981759 + 0.190128i \(0.0608905\pi\)
\(588\) 0 0
\(589\) 8.45702i 0.348465i
\(590\) 0 0
\(591\) 7.52038 + 4.34189i 0.309347 + 0.178602i
\(592\) 0 0
\(593\) −7.89583 + 29.4676i −0.324243 + 1.21009i 0.590828 + 0.806797i \(0.298801\pi\)
−0.915071 + 0.403293i \(0.867866\pi\)
\(594\) 0 0
\(595\) 5.40041 + 35.8315i 0.221395 + 1.46895i
\(596\) 0 0
\(597\) 6.41223 23.9307i 0.262435 0.979420i
\(598\) 0 0
\(599\) −13.8406 7.99090i −0.565513 0.326499i 0.189842 0.981815i \(-0.439202\pi\)
−0.755355 + 0.655315i \(0.772536\pi\)
\(600\) 0 0
\(601\) 35.9834i 1.46779i −0.679260 0.733897i \(-0.737699\pi\)
0.679260 0.733897i \(-0.262301\pi\)
\(602\) 0 0
\(603\) −5.92139 + 5.92139i −0.241138 + 0.241138i
\(604\) 0 0
\(605\) 1.45319 + 6.47572i 0.0590807 + 0.263275i
\(606\) 0 0
\(607\) −1.70600 0.457120i −0.0692442 0.0185539i 0.224031 0.974582i \(-0.428078\pi\)
−0.293275 + 0.956028i \(0.594745\pi\)
\(608\) 0 0
\(609\) 4.60360 + 9.47110i 0.186547 + 0.383788i
\(610\) 0 0
\(611\) 37.1450 + 64.3371i 1.50273 + 2.60280i
\(612\) 0 0
\(613\) −0.979533 3.65567i −0.0395629 0.147651i 0.943319 0.331887i \(-0.107685\pi\)
−0.982882 + 0.184237i \(0.941019\pi\)
\(614\) 0 0
\(615\) −0.719316 + 17.5131i −0.0290056 + 0.706196i
\(616\) 0 0
\(617\) −2.94869 2.94869i −0.118710 0.118710i 0.645256 0.763966i \(-0.276751\pi\)
−0.763966 + 0.645256i \(0.776751\pi\)
\(618\) 0 0
\(619\) 15.6267 27.0662i 0.628088 1.08788i −0.359847 0.933011i \(-0.617171\pi\)
0.987935 0.154869i \(-0.0494956\pi\)
\(620\) 0 0
\(621\) −13.6515 + 7.88169i −0.547816 + 0.316282i
\(622\) 0 0
\(623\) −10.4110 12.0091i −0.417110 0.481136i
\(624\) 0 0
\(625\) 8.79279 + 23.4027i 0.351712 + 0.936108i
\(626\) 0 0
\(627\) 6.26036 1.67746i 0.250015 0.0669912i
\(628\) 0 0
\(629\) 47.7201 1.90272
\(630\) 0 0
\(631\) −19.8658 −0.790844 −0.395422 0.918500i \(-0.629402\pi\)
−0.395422 + 0.918500i \(0.629402\pi\)
\(632\) 0 0
\(633\) −29.9832 + 8.03397i −1.19173 + 0.319322i
\(634\) 0 0
\(635\) 12.5663 + 23.9881i 0.498677 + 0.951938i
\(636\) 0 0
\(637\) −41.4169 17.7121i −1.64100 0.701779i
\(638\) 0 0
\(639\) −0.503189 + 0.290517i −0.0199059 + 0.0114927i
\(640\) 0 0
\(641\) −20.8732 + 36.1535i −0.824443 + 1.42798i 0.0779013 + 0.996961i \(0.475178\pi\)
−0.902344 + 0.431016i \(0.858155\pi\)
\(642\) 0 0
\(643\) −4.58193 4.58193i −0.180694 0.180694i 0.610964 0.791658i \(-0.290782\pi\)
−0.791658 + 0.610964i \(0.790782\pi\)
\(644\) 0 0
\(645\) −6.38915 + 5.88501i −0.251572 + 0.231722i
\(646\) 0 0
\(647\) 2.26436 + 8.45072i 0.0890213 + 0.332232i 0.996045 0.0888468i \(-0.0283182\pi\)
−0.907024 + 0.421079i \(0.861652\pi\)
\(648\) 0 0
\(649\) 3.42401 + 5.93056i 0.134404 + 0.232795i
\(650\) 0 0
\(651\) −25.4923 1.81707i −0.999123 0.0712165i
\(652\) 0 0
\(653\) 3.34030 + 0.895030i 0.130716 + 0.0350252i 0.323584 0.946199i \(-0.395112\pi\)
−0.192868 + 0.981225i \(0.561779\pi\)
\(654\) 0 0
\(655\) −2.55589 + 0.573558i −0.0998668 + 0.0224108i
\(656\) 0 0
\(657\) 1.52051 1.52051i 0.0593206 0.0593206i
\(658\) 0 0
\(659\) 1.86861i 0.0727907i 0.999337 + 0.0363953i \(0.0115876\pi\)
−0.999337 + 0.0363953i \(0.988412\pi\)
\(660\) 0 0
\(661\) 40.7798 + 23.5442i 1.58615 + 0.915764i 0.993933 + 0.109984i \(0.0350801\pi\)
0.592216 + 0.805779i \(0.298253\pi\)
\(662\) 0 0
\(663\) 14.3573 53.5820i 0.557590 2.08095i
\(664\) 0 0
\(665\) 2.91501 + 6.68143i 0.113039 + 0.259095i
\(666\) 0 0
\(667\) −2.03975 + 7.61246i −0.0789795 + 0.294755i
\(668\) 0 0
\(669\) −14.4396 8.33672i −0.558268 0.322316i
\(670\) 0 0
\(671\) 14.8236i 0.572257i
\(672\) 0 0
\(673\) −3.20914 + 3.20914i −0.123703 + 0.123703i −0.766248 0.642545i \(-0.777879\pi\)
0.642545 + 0.766248i \(0.277879\pi\)
\(674\) 0 0
\(675\) 27.8279 5.05518i 1.07109 0.194574i
\(676\) 0 0
\(677\) −15.0789 4.04037i −0.579528 0.155284i −0.0428651 0.999081i \(-0.513649\pi\)
−0.536663 + 0.843797i \(0.680315\pi\)
\(678\) 0 0
\(679\) 7.77153 11.4884i 0.298244 0.440884i
\(680\) 0 0
\(681\) −8.30135 14.3784i −0.318109 0.550980i
\(682\) 0 0
\(683\) −6.07444 22.6701i −0.232432 0.867448i −0.979290 0.202464i \(-0.935105\pi\)
0.746858 0.664984i \(-0.231562\pi\)
\(684\) 0 0
\(685\) −22.9254 0.941613i −0.875933 0.0359772i
\(686\) 0 0
\(687\) 6.40306 + 6.40306i 0.244292 + 0.244292i
\(688\) 0 0
\(689\) −31.4619 + 54.4937i −1.19860 + 2.07604i
\(690\) 0 0
\(691\) 12.8955 7.44520i 0.490566 0.283229i −0.234243 0.972178i \(-0.575261\pi\)
0.724809 + 0.688949i \(0.241928\pi\)
\(692\) 0 0
\(693\) 1.90975 + 9.89590i 0.0725455 + 0.375914i
\(694\) 0 0
\(695\) −17.3020 5.40621i −0.656304 0.205069i
\(696\) 0 0
\(697\) 32.9520 8.82945i 1.24814 0.334439i
\(698\) 0 0
\(699\) −21.3791 −0.808630
\(700\) 0 0
\(701\) 23.9673 0.905232 0.452616 0.891705i \(-0.350491\pi\)
0.452616 + 0.891705i \(0.350491\pi\)
\(702\) 0 0
\(703\) 9.27274 2.48462i 0.349728 0.0937093i
\(704\) 0 0
\(705\) −34.6778 10.8355i −1.30604 0.408087i
\(706\) 0 0
\(707\) 9.99973 + 3.45824i 0.376079 + 0.130061i
\(708\) 0 0
\(709\) 0.893033 0.515593i 0.0335386 0.0193635i −0.483137 0.875545i \(-0.660503\pi\)
0.516676 + 0.856181i \(0.327169\pi\)
\(710\) 0 0
\(711\) −5.57547 + 9.65699i −0.209096 + 0.362166i
\(712\) 0 0
\(713\) −13.5245 13.5245i −0.506495 0.506495i
\(714\) 0 0
\(715\) 53.7326 + 2.20696i 2.00949 + 0.0825356i
\(716\) 0 0
\(717\) 6.20468 + 23.1562i 0.231718 + 0.864784i
\(718\) 0 0
\(719\) −12.0529 20.8762i −0.449497 0.778552i 0.548856 0.835917i \(-0.315063\pi\)
−0.998353 + 0.0573650i \(0.981730\pi\)
\(720\) 0 0
\(721\) 0.517440 7.25936i 0.0192705 0.270353i
\(722\) 0 0
\(723\) 0.881160 + 0.236106i 0.0327707 + 0.00878088i
\(724\) 0 0
\(725\) 8.05064 11.6249i 0.298993 0.431737i
\(726\) 0 0
\(727\) −0.650788 + 0.650788i −0.0241364 + 0.0241364i −0.719072 0.694936i \(-0.755433\pi\)
0.694936 + 0.719072i \(0.255433\pi\)
\(728\) 0 0
\(729\) 28.8812i 1.06967i
\(730\) 0 0
\(731\) 14.6414 + 8.45320i 0.541531 + 0.312653i
\(732\) 0 0
\(733\) −3.56180 + 13.2928i −0.131558 + 0.490981i −0.999988 0.00483005i \(-0.998463\pi\)
0.868430 + 0.495811i \(0.165129\pi\)
\(734\) 0 0
\(735\) 20.7664 7.35126i 0.765981 0.271155i
\(736\) 0 0
\(737\) 7.94739 29.6601i 0.292746 1.09254i
\(738\) 0 0
\(739\) 12.8236 + 7.40373i 0.471725 + 0.272351i 0.716962 0.697113i \(-0.245532\pi\)
−0.245236 + 0.969463i \(0.578866\pi\)
\(740\) 0 0
\(741\) 11.1593i 0.409948i
\(742\) 0 0
\(743\) −32.2779 + 32.2779i −1.18416 + 1.18416i −0.205505 + 0.978656i \(0.565884\pi\)
−0.978656 + 0.205505i \(0.934116\pi\)
\(744\) 0 0
\(745\) 14.1115 3.16671i 0.517005 0.116019i
\(746\) 0 0
\(747\) −12.2638 3.28607i −0.448708 0.120231i
\(748\) 0 0
\(749\) −1.59797 + 22.4185i −0.0583885 + 0.819154i
\(750\) 0 0
\(751\) −0.115708 0.200412i −0.00422223 0.00731312i 0.863907 0.503652i \(-0.168011\pi\)
−0.868129 + 0.496339i \(0.834677\pi\)
\(752\) 0 0
\(753\) 1.08972 + 4.06690i 0.0397117 + 0.148206i
\(754\) 0 0
\(755\) −9.88155 + 9.10184i −0.359626 + 0.331250i
\(756\) 0 0
\(757\) −33.8884 33.8884i −1.23169 1.23169i −0.963313 0.268382i \(-0.913511\pi\)
−0.268382 0.963313i \(-0.586489\pi\)
\(758\) 0 0
\(759\) 7.32897 12.6942i 0.266025 0.460769i
\(760\) 0 0
\(761\) −17.9623 + 10.3705i −0.651132 + 0.375931i −0.788890 0.614535i \(-0.789344\pi\)
0.137758 + 0.990466i \(0.456010\pi\)
\(762\) 0 0
\(763\) −28.7858 9.95511i −1.04212 0.360399i
\(764\) 0 0
\(765\) −6.47778 12.3656i −0.234205 0.447079i
\(766\) 0 0
\(767\) 11.3892 3.05172i 0.411239 0.110191i
\(768\) 0 0
\(769\) 52.0182 1.87583 0.937913 0.346872i \(-0.112756\pi\)
0.937913 + 0.346872i \(0.112756\pi\)
\(770\) 0 0
\(771\) −6.65342 −0.239617
\(772\) 0 0
\(773\) −47.9189 + 12.8398i −1.72352 + 0.461817i −0.978675 0.205415i \(-0.934146\pi\)
−0.744850 + 0.667232i \(0.767479\pi\)
\(774\) 0 0
\(775\) 14.6637 + 31.0269i 0.526735 + 1.11452i
\(776\) 0 0
\(777\) −5.49716 28.4850i −0.197210 1.02189i
\(778\) 0 0
\(779\) 5.94335 3.43139i 0.212943 0.122942i
\(780\) 0 0
\(781\) 1.06527 1.84511i 0.0381184 0.0660230i
\(782\) 0 0
\(783\) −11.3119 11.3119i −0.404255 0.404255i
\(784\) 0 0
\(785\) 0.630852 15.3593i 0.0225161 0.548197i
\(786\) 0 0
\(787\) −5.89457 21.9988i −0.210119 0.784174i −0.987828 0.155550i \(-0.950285\pi\)
0.777709 0.628624i \(-0.216382\pi\)
\(788\) 0 0
\(789\) −17.5195 30.3447i −0.623712 1.08030i
\(790\) 0 0
\(791\) 15.4434 22.8295i 0.549105 0.811724i
\(792\) 0 0
\(793\) 24.6535 + 6.60590i 0.875473 + 0.234582i
\(794\) 0 0
\(795\) −6.73801 30.0259i −0.238972 1.06491i
\(796\) 0 0
\(797\) −19.2056 + 19.2056i −0.680298