Properties

Label 320.2.j.b.143.4
Level $320$
Weight $2$
Character 320.143
Analytic conductor $2.555$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.j (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.55521286468\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
Defining polynomial: \(x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + 74 x^{8} + 24 x^{7} - 80 x^{6} - 224 x^{5} - 160 x^{4} - 256 x^{3} + 256 x^{2} + 512\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 143.4
Root \(-0.635486 + 1.26339i\) of defining polynomial
Character \(\chi\) \(=\) 320.143
Dual form 320.2.j.b.47.6

$q$-expansion

\(f(q)\) \(=\) \(q-0.692712i q^{3} +(2.22257 - 0.245325i) q^{5} +(0.343872 - 0.343872i) q^{7} +2.52015 q^{9} +O(q^{10})\) \(q-0.692712i q^{3} +(2.22257 - 0.245325i) q^{5} +(0.343872 - 0.343872i) q^{7} +2.52015 q^{9} +(-0.843672 + 0.843672i) q^{11} -3.68390 q^{13} +(-0.169939 - 1.53960i) q^{15} +(0.412137 - 0.412137i) q^{17} +(5.37721 - 5.37721i) q^{19} +(-0.238204 - 0.238204i) q^{21} +(3.08788 + 3.08788i) q^{23} +(4.87963 - 1.09050i) q^{25} -3.82387i q^{27} +(-4.22969 - 4.22969i) q^{29} +8.75966i q^{31} +(0.584422 + 0.584422i) q^{33} +(0.679919 - 0.848640i) q^{35} -5.41752 q^{37} +2.55188i q^{39} -2.54777i q^{41} -4.30732 q^{43} +(5.60121 - 0.618255i) q^{45} +(-4.56972 - 4.56972i) q^{47} +6.76350i q^{49} +(-0.285492 - 0.285492i) q^{51} +6.07536i q^{53} +(-1.66815 + 2.08209i) q^{55} +(-3.72486 - 3.72486i) q^{57} +(7.33694 + 7.33694i) q^{59} +(-4.81576 + 4.81576i) q^{61} +(0.866609 - 0.866609i) q^{63} +(-8.18773 + 0.903753i) q^{65} -14.3626 q^{67} +(2.13901 - 2.13901i) q^{69} +2.97605 q^{71} +(-6.87152 + 6.87152i) q^{73} +(-0.755404 - 3.38018i) q^{75} +0.580231i q^{77} -10.1654 q^{79} +4.91161 q^{81} +7.15276i q^{83} +(0.814896 - 1.01711i) q^{85} +(-2.92996 + 2.92996i) q^{87} +1.10953 q^{89} +(-1.26679 + 1.26679i) q^{91} +6.06792 q^{93} +(10.6321 - 13.2704i) q^{95} +(7.15920 - 7.15920i) q^{97} +(-2.12618 + 2.12618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 4q^{5} - 2q^{7} - 10q^{9} + O(q^{10}) \) \( 18q - 4q^{5} - 2q^{7} - 10q^{9} + 2q^{11} - 20q^{15} - 6q^{17} - 2q^{19} - 16q^{21} + 2q^{23} + 6q^{25} - 14q^{29} - 8q^{33} + 6q^{35} + 8q^{37} + 44q^{43} - 4q^{45} + 38q^{47} - 8q^{51} + 6q^{55} + 24q^{57} + 10q^{59} + 14q^{61} - 6q^{63} - 12q^{67} + 32q^{69} - 24q^{71} + 14q^{73} - 64q^{75} - 16q^{79} + 2q^{81} - 10q^{85} - 24q^{87} - 12q^{89} + 16q^{93} + 34q^{95} + 18q^{97} + 22q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) 0.692712i 0.399937i −0.979802 0.199969i \(-0.935916\pi\)
0.979802 0.199969i \(-0.0640841\pi\)
\(4\) 0 0
\(5\) 2.22257 0.245325i 0.993963 0.109713i
\(6\) 0 0
\(7\) 0.343872 0.343872i 0.129971 0.129971i −0.639129 0.769100i \(-0.720705\pi\)
0.769100 + 0.639129i \(0.220705\pi\)
\(8\) 0 0
\(9\) 2.52015 0.840050
\(10\) 0 0
\(11\) −0.843672 + 0.843672i −0.254377 + 0.254377i −0.822762 0.568386i \(-0.807568\pi\)
0.568386 + 0.822762i \(0.307568\pi\)
\(12\) 0 0
\(13\) −3.68390 −1.02173 −0.510865 0.859661i \(-0.670675\pi\)
−0.510865 + 0.859661i \(0.670675\pi\)
\(14\) 0 0
\(15\) −0.169939 1.53960i −0.0438782 0.397523i
\(16\) 0 0
\(17\) 0.412137 0.412137i 0.0999579 0.0999579i −0.655359 0.755317i \(-0.727483\pi\)
0.755317 + 0.655359i \(0.227483\pi\)
\(18\) 0 0
\(19\) 5.37721 5.37721i 1.23362 1.23362i 0.271052 0.962565i \(-0.412629\pi\)
0.962565 0.271052i \(-0.0873714\pi\)
\(20\) 0 0
\(21\) −0.238204 0.238204i −0.0519804 0.0519804i
\(22\) 0 0
\(23\) 3.08788 + 3.08788i 0.643868 + 0.643868i 0.951504 0.307636i \(-0.0995380\pi\)
−0.307636 + 0.951504i \(0.599538\pi\)
\(24\) 0 0
\(25\) 4.87963 1.09050i 0.975926 0.218101i
\(26\) 0 0
\(27\) 3.82387i 0.735905i
\(28\) 0 0
\(29\) −4.22969 4.22969i −0.785434 0.785434i 0.195308 0.980742i \(-0.437429\pi\)
−0.980742 + 0.195308i \(0.937429\pi\)
\(30\) 0 0
\(31\) 8.75966i 1.57328i 0.617411 + 0.786641i \(0.288182\pi\)
−0.617411 + 0.786641i \(0.711818\pi\)
\(32\) 0 0
\(33\) 0.584422 + 0.584422i 0.101735 + 0.101735i
\(34\) 0 0
\(35\) 0.679919 0.848640i 0.114927 0.143446i
\(36\) 0 0
\(37\) −5.41752 −0.890634 −0.445317 0.895373i \(-0.646909\pi\)
−0.445317 + 0.895373i \(0.646909\pi\)
\(38\) 0 0
\(39\) 2.55188i 0.408628i
\(40\) 0 0
\(41\) 2.54777i 0.397895i −0.980010 0.198948i \(-0.936248\pi\)
0.980010 0.198948i \(-0.0637524\pi\)
\(42\) 0 0
\(43\) −4.30732 −0.656861 −0.328430 0.944528i \(-0.606520\pi\)
−0.328430 + 0.944528i \(0.606520\pi\)
\(44\) 0 0
\(45\) 5.60121 0.618255i 0.834979 0.0921641i
\(46\) 0 0
\(47\) −4.56972 4.56972i −0.666562 0.666562i 0.290356 0.956919i \(-0.406226\pi\)
−0.956919 + 0.290356i \(0.906226\pi\)
\(48\) 0 0
\(49\) 6.76350i 0.966215i
\(50\) 0 0
\(51\) −0.285492 0.285492i −0.0399769 0.0399769i
\(52\) 0 0
\(53\) 6.07536i 0.834515i 0.908788 + 0.417257i \(0.137009\pi\)
−0.908788 + 0.417257i \(0.862991\pi\)
\(54\) 0 0
\(55\) −1.66815 + 2.08209i −0.224933 + 0.280749i
\(56\) 0 0
\(57\) −3.72486 3.72486i −0.493369 0.493369i
\(58\) 0 0
\(59\) 7.33694 + 7.33694i 0.955189 + 0.955189i 0.999038 0.0438495i \(-0.0139622\pi\)
−0.0438495 + 0.999038i \(0.513962\pi\)
\(60\) 0 0
\(61\) −4.81576 + 4.81576i −0.616595 + 0.616595i −0.944656 0.328062i \(-0.893605\pi\)
0.328062 + 0.944656i \(0.393605\pi\)
\(62\) 0 0
\(63\) 0.866609 0.866609i 0.109183 0.109183i
\(64\) 0 0
\(65\) −8.18773 + 0.903753i −1.01556 + 0.112097i
\(66\) 0 0
\(67\) −14.3626 −1.75467 −0.877334 0.479880i \(-0.840680\pi\)
−0.877334 + 0.479880i \(0.840680\pi\)
\(68\) 0 0
\(69\) 2.13901 2.13901i 0.257507 0.257507i
\(70\) 0 0
\(71\) 2.97605 0.353193 0.176596 0.984283i \(-0.443491\pi\)
0.176596 + 0.984283i \(0.443491\pi\)
\(72\) 0 0
\(73\) −6.87152 + 6.87152i −0.804250 + 0.804250i −0.983757 0.179507i \(-0.942550\pi\)
0.179507 + 0.983757i \(0.442550\pi\)
\(74\) 0 0
\(75\) −0.755404 3.38018i −0.0872266 0.390309i
\(76\) 0 0
\(77\) 0.580231i 0.0661234i
\(78\) 0 0
\(79\) −10.1654 −1.14369 −0.571847 0.820360i \(-0.693773\pi\)
−0.571847 + 0.820360i \(0.693773\pi\)
\(80\) 0 0
\(81\) 4.91161 0.545734
\(82\) 0 0
\(83\) 7.15276i 0.785118i 0.919727 + 0.392559i \(0.128410\pi\)
−0.919727 + 0.392559i \(0.871590\pi\)
\(84\) 0 0
\(85\) 0.814896 1.01711i 0.0883878 0.110321i
\(86\) 0 0
\(87\) −2.92996 + 2.92996i −0.314124 + 0.314124i
\(88\) 0 0
\(89\) 1.10953 0.117610 0.0588050 0.998269i \(-0.481271\pi\)
0.0588050 + 0.998269i \(0.481271\pi\)
\(90\) 0 0
\(91\) −1.26679 + 1.26679i −0.132796 + 0.132796i
\(92\) 0 0
\(93\) 6.06792 0.629214
\(94\) 0 0
\(95\) 10.6321 13.2704i 1.09083 1.36151i
\(96\) 0 0
\(97\) 7.15920 7.15920i 0.726906 0.726906i −0.243096 0.970002i \(-0.578163\pi\)
0.970002 + 0.243096i \(0.0781630\pi\)
\(98\) 0 0
\(99\) −2.12618 + 2.12618i −0.213689 + 0.213689i
\(100\) 0 0
\(101\) 0.953394 + 0.953394i 0.0948663 + 0.0948663i 0.752947 0.658081i \(-0.228632\pi\)
−0.658081 + 0.752947i \(0.728632\pi\)
\(102\) 0 0
\(103\) −9.59425 9.59425i −0.945350 0.945350i 0.0532322 0.998582i \(-0.483048\pi\)
−0.998582 + 0.0532322i \(0.983048\pi\)
\(104\) 0 0
\(105\) −0.587863 0.470988i −0.0573696 0.0459637i
\(106\) 0 0
\(107\) 5.28201i 0.510631i −0.966858 0.255316i \(-0.917821\pi\)
0.966858 0.255316i \(-0.0821794\pi\)
\(108\) 0 0
\(109\) 1.53980 + 1.53980i 0.147486 + 0.147486i 0.776994 0.629508i \(-0.216744\pi\)
−0.629508 + 0.776994i \(0.716744\pi\)
\(110\) 0 0
\(111\) 3.75278i 0.356198i
\(112\) 0 0
\(113\) −2.99656 2.99656i −0.281893 0.281893i 0.551971 0.833863i \(-0.313876\pi\)
−0.833863 + 0.551971i \(0.813876\pi\)
\(114\) 0 0
\(115\) 7.62056 + 6.10550i 0.710621 + 0.569340i
\(116\) 0 0
\(117\) −9.28399 −0.858305
\(118\) 0 0
\(119\) 0.283445i 0.0259833i
\(120\) 0 0
\(121\) 9.57643i 0.870585i
\(122\) 0 0
\(123\) −1.76487 −0.159133
\(124\) 0 0
\(125\) 10.5778 3.62081i 0.946107 0.323855i
\(126\) 0 0
\(127\) 10.5522 + 10.5522i 0.936360 + 0.936360i 0.998093 0.0617330i \(-0.0196627\pi\)
−0.0617330 + 0.998093i \(0.519663\pi\)
\(128\) 0 0
\(129\) 2.98373i 0.262703i
\(130\) 0 0
\(131\) 0.850513 + 0.850513i 0.0743096 + 0.0743096i 0.743285 0.668975i \(-0.233267\pi\)
−0.668975 + 0.743285i \(0.733267\pi\)
\(132\) 0 0
\(133\) 3.69814i 0.320670i
\(134\) 0 0
\(135\) −0.938091 8.49883i −0.0807380 0.731463i
\(136\) 0 0
\(137\) −5.50145 5.50145i −0.470021 0.470021i 0.431901 0.901921i \(-0.357843\pi\)
−0.901921 + 0.431901i \(0.857843\pi\)
\(138\) 0 0
\(139\) −3.03517 3.03517i −0.257440 0.257440i 0.566572 0.824012i \(-0.308269\pi\)
−0.824012 + 0.566572i \(0.808269\pi\)
\(140\) 0 0
\(141\) −3.16550 + 3.16550i −0.266583 + 0.266583i
\(142\) 0 0
\(143\) 3.10801 3.10801i 0.259905 0.259905i
\(144\) 0 0
\(145\) −10.4384 8.36313i −0.866864 0.694520i
\(146\) 0 0
\(147\) 4.68516 0.386425
\(148\) 0 0
\(149\) 11.1571 11.1571i 0.914023 0.914023i −0.0825625 0.996586i \(-0.526310\pi\)
0.996586 + 0.0825625i \(0.0263104\pi\)
\(150\) 0 0
\(151\) −3.18265 −0.259000 −0.129500 0.991579i \(-0.541337\pi\)
−0.129500 + 0.991579i \(0.541337\pi\)
\(152\) 0 0
\(153\) 1.03865 1.03865i 0.0839696 0.0839696i
\(154\) 0 0
\(155\) 2.14896 + 19.4690i 0.172609 + 1.56378i
\(156\) 0 0
\(157\) 7.05454i 0.563014i 0.959559 + 0.281507i \(0.0908342\pi\)
−0.959559 + 0.281507i \(0.909166\pi\)
\(158\) 0 0
\(159\) 4.20847 0.333754
\(160\) 0 0
\(161\) 2.12367 0.167369
\(162\) 0 0
\(163\) 16.0208i 1.25484i 0.778680 + 0.627422i \(0.215890\pi\)
−0.778680 + 0.627422i \(0.784110\pi\)
\(164\) 0 0
\(165\) 1.44229 + 1.15554i 0.112282 + 0.0899591i
\(166\) 0 0
\(167\) 16.6023 16.6023i 1.28473 1.28473i 0.346780 0.937946i \(-0.387275\pi\)
0.937946 0.346780i \(-0.112725\pi\)
\(168\) 0 0
\(169\) 0.571141 0.0439339
\(170\) 0 0
\(171\) 13.5514 13.5514i 1.03630 1.03630i
\(172\) 0 0
\(173\) 14.9958 1.14011 0.570054 0.821607i \(-0.306922\pi\)
0.570054 + 0.821607i \(0.306922\pi\)
\(174\) 0 0
\(175\) 1.30298 2.05296i 0.0984957 0.155189i
\(176\) 0 0
\(177\) 5.08239 5.08239i 0.382016 0.382016i
\(178\) 0 0
\(179\) 9.91310 9.91310i 0.740940 0.740940i −0.231819 0.972759i \(-0.574468\pi\)
0.972759 + 0.231819i \(0.0744678\pi\)
\(180\) 0 0
\(181\) 1.04015 + 1.04015i 0.0773139 + 0.0773139i 0.744706 0.667392i \(-0.232590\pi\)
−0.667392 + 0.744706i \(0.732590\pi\)
\(182\) 0 0
\(183\) 3.33593 + 3.33593i 0.246599 + 0.246599i
\(184\) 0 0
\(185\) −12.0408 + 1.32905i −0.885258 + 0.0977138i
\(186\) 0 0
\(187\) 0.695417i 0.0508539i
\(188\) 0 0
\(189\) −1.31492 1.31492i −0.0956466 0.0956466i
\(190\) 0 0
\(191\) 3.08419i 0.223164i −0.993755 0.111582i \(-0.964408\pi\)
0.993755 0.111582i \(-0.0355918\pi\)
\(192\) 0 0
\(193\) −12.0915 12.0915i −0.870368 0.870368i 0.122144 0.992512i \(-0.461023\pi\)
−0.992512 + 0.122144i \(0.961023\pi\)
\(194\) 0 0
\(195\) 0.626040 + 5.67174i 0.0448317 + 0.406162i
\(196\) 0 0
\(197\) 13.0186 0.927540 0.463770 0.885956i \(-0.346496\pi\)
0.463770 + 0.885956i \(0.346496\pi\)
\(198\) 0 0
\(199\) 10.6279i 0.753395i −0.926336 0.376697i \(-0.877060\pi\)
0.926336 0.376697i \(-0.122940\pi\)
\(200\) 0 0
\(201\) 9.94913i 0.701758i
\(202\) 0 0
\(203\) −2.90894 −0.204168
\(204\) 0 0
\(205\) −0.625032 5.66260i −0.0436541 0.395493i
\(206\) 0 0
\(207\) 7.78192 + 7.78192i 0.540881 + 0.540881i
\(208\) 0 0
\(209\) 9.07320i 0.627607i
\(210\) 0 0
\(211\) −11.4801 11.4801i −0.790321 0.790321i 0.191225 0.981546i \(-0.438754\pi\)
−0.981546 + 0.191225i \(0.938754\pi\)
\(212\) 0 0
\(213\) 2.06155i 0.141255i
\(214\) 0 0
\(215\) −9.57332 + 1.05669i −0.652895 + 0.0720659i
\(216\) 0 0
\(217\) 3.01220 + 3.01220i 0.204482 + 0.204482i
\(218\) 0 0
\(219\) 4.75998 + 4.75998i 0.321650 + 0.321650i
\(220\) 0 0
\(221\) −1.51827 + 1.51827i −0.102130 + 0.102130i
\(222\) 0 0
\(223\) −2.17863 + 2.17863i −0.145892 + 0.145892i −0.776280 0.630388i \(-0.782896\pi\)
0.630388 + 0.776280i \(0.282896\pi\)
\(224\) 0 0
\(225\) 12.2974 2.74823i 0.819827 0.183215i
\(226\) 0 0
\(227\) −9.32318 −0.618801 −0.309401 0.950932i \(-0.600128\pi\)
−0.309401 + 0.950932i \(0.600128\pi\)
\(228\) 0 0
\(229\) −2.72259 + 2.72259i −0.179914 + 0.179914i −0.791318 0.611404i \(-0.790605\pi\)
0.611404 + 0.791318i \(0.290605\pi\)
\(230\) 0 0
\(231\) 0.401933 0.0264452
\(232\) 0 0
\(233\) 12.3897 12.3897i 0.811679 0.811679i −0.173206 0.984886i \(-0.555413\pi\)
0.984886 + 0.173206i \(0.0554127\pi\)
\(234\) 0 0
\(235\) −11.2776 9.03546i −0.735669 0.589408i
\(236\) 0 0
\(237\) 7.04168i 0.457406i
\(238\) 0 0
\(239\) −25.2180 −1.63122 −0.815609 0.578604i \(-0.803598\pi\)
−0.815609 + 0.578604i \(0.803598\pi\)
\(240\) 0 0
\(241\) 12.0218 0.774391 0.387195 0.921998i \(-0.373444\pi\)
0.387195 + 0.921998i \(0.373444\pi\)
\(242\) 0 0
\(243\) 14.8740i 0.954164i
\(244\) 0 0
\(245\) 1.65926 + 15.0324i 0.106006 + 0.960382i
\(246\) 0 0
\(247\) −19.8091 + 19.8091i −1.26042 + 1.26042i
\(248\) 0 0
\(249\) 4.95480 0.313998
\(250\) 0 0
\(251\) −7.48911 + 7.48911i −0.472709 + 0.472709i −0.902790 0.430081i \(-0.858485\pi\)
0.430081 + 0.902790i \(0.358485\pi\)
\(252\) 0 0
\(253\) −5.21032 −0.327570
\(254\) 0 0
\(255\) −0.704565 0.564488i −0.0441215 0.0353496i
\(256\) 0 0
\(257\) −10.0809 + 10.0809i −0.628832 + 0.628832i −0.947774 0.318942i \(-0.896672\pi\)
0.318942 + 0.947774i \(0.396672\pi\)
\(258\) 0 0
\(259\) −1.86293 + 1.86293i −0.115757 + 0.115757i
\(260\) 0 0
\(261\) −10.6595 10.6595i −0.659804 0.659804i
\(262\) 0 0
\(263\) 3.83599 + 3.83599i 0.236537 + 0.236537i 0.815415 0.578877i \(-0.196509\pi\)
−0.578877 + 0.815415i \(0.696509\pi\)
\(264\) 0 0
\(265\) 1.49044 + 13.5029i 0.0915568 + 0.829477i
\(266\) 0 0
\(267\) 0.768585i 0.0470367i
\(268\) 0 0
\(269\) −13.4250 13.4250i −0.818539 0.818539i 0.167357 0.985896i \(-0.446477\pi\)
−0.985896 + 0.167357i \(0.946477\pi\)
\(270\) 0 0
\(271\) 12.3519i 0.750326i −0.926959 0.375163i \(-0.877587\pi\)
0.926959 0.375163i \(-0.122413\pi\)
\(272\) 0 0
\(273\) 0.877522 + 0.877522i 0.0531100 + 0.0531100i
\(274\) 0 0
\(275\) −3.19678 + 5.03684i −0.192773 + 0.303733i
\(276\) 0 0
\(277\) −6.78804 −0.407854 −0.203927 0.978986i \(-0.565370\pi\)
−0.203927 + 0.978986i \(0.565370\pi\)
\(278\) 0 0
\(279\) 22.0757i 1.32164i
\(280\) 0 0
\(281\) 21.5509i 1.28562i −0.766026 0.642810i \(-0.777768\pi\)
0.766026 0.642810i \(-0.222232\pi\)
\(282\) 0 0
\(283\) 9.86809 0.586597 0.293299 0.956021i \(-0.405247\pi\)
0.293299 + 0.956021i \(0.405247\pi\)
\(284\) 0 0
\(285\) −9.19255 7.36495i −0.544520 0.436262i
\(286\) 0 0
\(287\) −0.876108 0.876108i −0.0517150 0.0517150i
\(288\) 0 0
\(289\) 16.6603i 0.980017i
\(290\) 0 0
\(291\) −4.95926 4.95926i −0.290717 0.290717i
\(292\) 0 0
\(293\) 14.1972i 0.829410i 0.909956 + 0.414705i \(0.136115\pi\)
−0.909956 + 0.414705i \(0.863885\pi\)
\(294\) 0 0
\(295\) 18.1068 + 14.5069i 1.05422 + 0.844626i
\(296\) 0 0
\(297\) 3.22610 + 3.22610i 0.187197 + 0.187197i
\(298\) 0 0
\(299\) −11.3755 11.3755i −0.657859 0.657859i
\(300\) 0 0
\(301\) −1.48117 + 1.48117i −0.0853731 + 0.0853731i
\(302\) 0 0
\(303\) 0.660428 0.660428i 0.0379406 0.0379406i
\(304\) 0 0
\(305\) −9.52194 + 11.8848i −0.545224 + 0.680521i
\(306\) 0 0
\(307\) 20.4161 1.16521 0.582604 0.812756i \(-0.302034\pi\)
0.582604 + 0.812756i \(0.302034\pi\)
\(308\) 0 0
\(309\) −6.64605 + 6.64605i −0.378081 + 0.378081i
\(310\) 0 0
\(311\) 6.81074 0.386202 0.193101 0.981179i \(-0.438146\pi\)
0.193101 + 0.981179i \(0.438146\pi\)
\(312\) 0 0
\(313\) −1.20933 + 1.20933i −0.0683555 + 0.0683555i −0.740458 0.672103i \(-0.765391\pi\)
0.672103 + 0.740458i \(0.265391\pi\)
\(314\) 0 0
\(315\) 1.71350 2.13870i 0.0965447 0.120502i
\(316\) 0 0
\(317\) 3.44178i 0.193310i 0.995318 + 0.0966548i \(0.0308143\pi\)
−0.995318 + 0.0966548i \(0.969186\pi\)
\(318\) 0 0
\(319\) 7.13694 0.399592
\(320\) 0 0
\(321\) −3.65891 −0.204221
\(322\) 0 0
\(323\) 4.43229i 0.246619i
\(324\) 0 0
\(325\) −17.9761 + 4.01731i −0.997134 + 0.222840i
\(326\) 0 0
\(327\) 1.06664 1.06664i 0.0589852 0.0589852i
\(328\) 0 0
\(329\) −3.14280 −0.173268
\(330\) 0 0
\(331\) 1.48462 1.48462i 0.0816019 0.0816019i −0.665128 0.746730i \(-0.731623\pi\)
0.746730 + 0.665128i \(0.231623\pi\)
\(332\) 0 0
\(333\) −13.6530 −0.748177
\(334\) 0 0
\(335\) −31.9218 + 3.52350i −1.74408 + 0.192509i
\(336\) 0 0
\(337\) 6.21211 6.21211i 0.338395 0.338395i −0.517368 0.855763i \(-0.673088\pi\)
0.855763 + 0.517368i \(0.173088\pi\)
\(338\) 0 0
\(339\) −2.07575 + 2.07575i −0.112739 + 0.112739i
\(340\) 0 0
\(341\) −7.39028 7.39028i −0.400206 0.400206i
\(342\) 0 0
\(343\) 4.73288 + 4.73288i 0.255552 + 0.255552i
\(344\) 0 0
\(345\) 4.22935 5.27886i 0.227701 0.284204i
\(346\) 0 0
\(347\) 10.1502i 0.544889i 0.962171 + 0.272445i \(0.0878321\pi\)
−0.962171 + 0.272445i \(0.912168\pi\)
\(348\) 0 0
\(349\) −3.99595 3.99595i −0.213898 0.213898i 0.592023 0.805921i \(-0.298329\pi\)
−0.805921 + 0.592023i \(0.798329\pi\)
\(350\) 0 0
\(351\) 14.0868i 0.751897i
\(352\) 0 0
\(353\) 22.6637 + 22.6637i 1.20627 + 1.20627i 0.972226 + 0.234043i \(0.0751957\pi\)
0.234043 + 0.972226i \(0.424804\pi\)
\(354\) 0 0
\(355\) 6.61449 0.730100i 0.351061 0.0387497i
\(356\) 0 0
\(357\) −0.196346 −0.0103917
\(358\) 0 0
\(359\) 4.31874i 0.227934i 0.993485 + 0.113967i \(0.0363559\pi\)
−0.993485 + 0.113967i \(0.963644\pi\)
\(360\) 0 0
\(361\) 38.8288i 2.04362i
\(362\) 0 0
\(363\) 6.63371 0.348180
\(364\) 0 0
\(365\) −13.5867 + 16.9582i −0.711159 + 0.887632i
\(366\) 0 0
\(367\) 6.46940 + 6.46940i 0.337700 + 0.337700i 0.855501 0.517801i \(-0.173249\pi\)
−0.517801 + 0.855501i \(0.673249\pi\)
\(368\) 0 0
\(369\) 6.42077i 0.334252i
\(370\) 0 0
\(371\) 2.08915 + 2.08915i 0.108463 + 0.108463i
\(372\) 0 0
\(373\) 16.7831i 0.868995i −0.900673 0.434497i \(-0.856926\pi\)
0.900673 0.434497i \(-0.143074\pi\)
\(374\) 0 0
\(375\) −2.50818 7.32736i −0.129522 0.378383i
\(376\) 0 0
\(377\) 15.5818 + 15.5818i 0.802502 + 0.802502i
\(378\) 0 0
\(379\) 7.31046 + 7.31046i 0.375513 + 0.375513i 0.869480 0.493967i \(-0.164454\pi\)
−0.493967 + 0.869480i \(0.664454\pi\)
\(380\) 0 0
\(381\) 7.30966 7.30966i 0.374485 0.374485i
\(382\) 0 0
\(383\) 5.31492 5.31492i 0.271580 0.271580i −0.558156 0.829736i \(-0.688491\pi\)
0.829736 + 0.558156i \(0.188491\pi\)
\(384\) 0 0
\(385\) 0.142345 + 1.28960i 0.00725457 + 0.0657242i
\(386\) 0 0
\(387\) −10.8551 −0.551796
\(388\) 0 0
\(389\) −1.28845 + 1.28845i −0.0653271 + 0.0653271i −0.739016 0.673688i \(-0.764709\pi\)
0.673688 + 0.739016i \(0.264709\pi\)
\(390\) 0 0
\(391\) 2.54526 0.128719
\(392\) 0 0
\(393\) 0.589160 0.589160i 0.0297192 0.0297192i
\(394\) 0 0
\(395\) −22.5933 + 2.49382i −1.13679 + 0.125478i
\(396\) 0 0
\(397\) 9.53832i 0.478715i −0.970932 0.239357i \(-0.923063\pi\)
0.970932 0.239357i \(-0.0769367\pi\)
\(398\) 0 0
\(399\) −2.56175 −0.128248
\(400\) 0 0
\(401\) −24.6103 −1.22898 −0.614491 0.788924i \(-0.710638\pi\)
−0.614491 + 0.788924i \(0.710638\pi\)
\(402\) 0 0
\(403\) 32.2697i 1.60747i
\(404\) 0 0
\(405\) 10.9164 1.20494i 0.542440 0.0598739i
\(406\) 0 0
\(407\) 4.57061 4.57061i 0.226557 0.226557i
\(408\) 0 0
\(409\) −16.9457 −0.837911 −0.418955 0.908007i \(-0.637604\pi\)
−0.418955 + 0.908007i \(0.637604\pi\)
\(410\) 0 0
\(411\) −3.81092 + 3.81092i −0.187979 + 0.187979i
\(412\) 0 0
\(413\) 5.04594 0.248294
\(414\) 0 0
\(415\) 1.75475 + 15.8975i 0.0861373 + 0.780378i
\(416\) 0 0
\(417\) −2.10250 + 2.10250i −0.102960 + 0.102960i
\(418\) 0 0
\(419\) 6.56956 6.56956i 0.320944 0.320944i −0.528185 0.849129i \(-0.677127\pi\)
0.849129 + 0.528185i \(0.177127\pi\)
\(420\) 0 0
\(421\) 13.8805 + 13.8805i 0.676493 + 0.676493i 0.959205 0.282712i \(-0.0912341\pi\)
−0.282712 + 0.959205i \(0.591234\pi\)
\(422\) 0 0
\(423\) −11.5164 11.5164i −0.559946 0.559946i
\(424\) 0 0
\(425\) 1.56164 2.46051i 0.0757507 0.119352i
\(426\) 0 0
\(427\) 3.31201i 0.160279i
\(428\) 0 0
\(429\) −2.15295 2.15295i −0.103946 0.103946i
\(430\) 0 0
\(431\) 12.3740i 0.596035i −0.954560 0.298017i \(-0.903675\pi\)
0.954560 0.298017i \(-0.0963254\pi\)
\(432\) 0 0
\(433\) −0.145326 0.145326i −0.00698392 0.00698392i 0.703606 0.710590i \(-0.251572\pi\)
−0.710590 + 0.703606i \(0.751572\pi\)
\(434\) 0 0
\(435\) −5.79324 + 7.23082i −0.277765 + 0.346691i
\(436\) 0 0
\(437\) 33.2084 1.58857
\(438\) 0 0
\(439\) 3.65842i 0.174607i −0.996182 0.0873035i \(-0.972175\pi\)
0.996182 0.0873035i \(-0.0278250\pi\)
\(440\) 0 0
\(441\) 17.0450i 0.811669i
\(442\) 0 0
\(443\) −3.94027 −0.187208 −0.0936039 0.995610i \(-0.529839\pi\)
−0.0936039 + 0.995610i \(0.529839\pi\)
\(444\) 0 0
\(445\) 2.46601 0.272195i 0.116900 0.0129033i
\(446\) 0 0
\(447\) −7.72864 7.72864i −0.365552 0.365552i
\(448\) 0 0
\(449\) 38.0014i 1.79340i −0.442642 0.896698i \(-0.645959\pi\)
0.442642 0.896698i \(-0.354041\pi\)
\(450\) 0 0
\(451\) 2.14949 + 2.14949i 0.101215 + 0.101215i
\(452\) 0 0
\(453\) 2.20466i 0.103584i
\(454\) 0 0
\(455\) −2.50476 + 3.12631i −0.117425 + 0.146564i
\(456\) 0 0
\(457\) 18.1142 + 18.1142i 0.847348 + 0.847348i 0.989801 0.142454i \(-0.0454993\pi\)
−0.142454 + 0.989801i \(0.545499\pi\)
\(458\) 0 0
\(459\) −1.57596 1.57596i −0.0735595 0.0735595i
\(460\) 0 0
\(461\) 12.4144 12.4144i 0.578197 0.578197i −0.356209 0.934406i \(-0.615931\pi\)
0.934406 + 0.356209i \(0.115931\pi\)
\(462\) 0 0
\(463\) 8.56578 8.56578i 0.398085 0.398085i −0.479472 0.877557i \(-0.659172\pi\)
0.877557 + 0.479472i \(0.159172\pi\)
\(464\) 0 0
\(465\) 13.4864 1.48861i 0.625416 0.0690327i
\(466\) 0 0
\(467\) 34.3465 1.58937 0.794684 0.607023i \(-0.207636\pi\)
0.794684 + 0.607023i \(0.207636\pi\)
\(468\) 0 0
\(469\) −4.93889 + 4.93889i −0.228057 + 0.228057i
\(470\) 0 0
\(471\) 4.88677 0.225170
\(472\) 0 0
\(473\) 3.63397 3.63397i 0.167090 0.167090i
\(474\) 0 0
\(475\) 20.3749 32.1027i 0.934866 1.47297i
\(476\) 0 0
\(477\) 15.3108i 0.701034i
\(478\) 0 0
\(479\) 23.4504 1.07148 0.535738 0.844384i \(-0.320034\pi\)
0.535738 + 0.844384i \(0.320034\pi\)
\(480\) 0 0
\(481\) 19.9576 0.909988
\(482\) 0 0
\(483\) 1.47109i 0.0669370i
\(484\) 0 0
\(485\) 14.1555 17.6681i 0.642767 0.802269i
\(486\) 0 0
\(487\) 5.31215 5.31215i 0.240716 0.240716i −0.576430 0.817146i \(-0.695555\pi\)
0.817146 + 0.576430i \(0.195555\pi\)
\(488\) 0 0
\(489\) 11.0978 0.501859
\(490\) 0 0
\(491\) 3.71980 3.71980i 0.167872 0.167872i −0.618171 0.786044i \(-0.712126\pi\)
0.786044 + 0.618171i \(0.212126\pi\)
\(492\) 0 0
\(493\) −3.48642 −0.157021
\(494\) 0 0
\(495\) −4.20398 + 5.24719i −0.188955 + 0.235844i
\(496\) 0 0
\(497\) 1.02338 1.02338i 0.0459050 0.0459050i
\(498\) 0 0
\(499\) −13.6065 + 13.6065i −0.609111 + 0.609111i −0.942714 0.333603i \(-0.891736\pi\)
0.333603 + 0.942714i \(0.391736\pi\)
\(500\) 0 0
\(501\) −11.5006 11.5006i −0.513810 0.513810i
\(502\) 0 0
\(503\) 9.31208 + 9.31208i 0.415205 + 0.415205i 0.883547 0.468342i \(-0.155148\pi\)
−0.468342 + 0.883547i \(0.655148\pi\)
\(504\) 0 0
\(505\) 2.35288 + 1.88509i 0.104702 + 0.0838856i
\(506\) 0 0
\(507\) 0.395636i 0.0175708i
\(508\) 0 0
\(509\) 7.94836 + 7.94836i 0.352305 + 0.352305i 0.860966 0.508662i \(-0.169860\pi\)
−0.508662 + 0.860966i \(0.669860\pi\)
\(510\) 0 0
\(511\) 4.72585i 0.209059i
\(512\) 0 0
\(513\) −20.5618 20.5618i −0.907824 0.907824i
\(514\) 0 0
\(515\) −23.6776 18.9702i −1.04336 0.835926i
\(516\) 0 0
\(517\) 7.71069 0.339116
\(518\) 0 0
\(519\) 10.3878i 0.455972i
\(520\) 0 0
\(521\) 29.3979i 1.28795i 0.765048 + 0.643974i \(0.222715\pi\)
−0.765048 + 0.643974i \(0.777285\pi\)
\(522\) 0 0
\(523\) 19.5121 0.853205 0.426602 0.904439i \(-0.359710\pi\)
0.426602 + 0.904439i \(0.359710\pi\)
\(524\) 0 0
\(525\) −1.42211 0.902587i −0.0620660 0.0393921i
\(526\) 0 0
\(527\) 3.61018 + 3.61018i 0.157262 + 0.157262i
\(528\) 0 0
\(529\) 3.92999i 0.170869i
\(530\) 0 0
\(531\) 18.4902 + 18.4902i 0.802406 + 0.802406i
\(532\) 0 0
\(533\) 9.38575i 0.406542i
\(534\) 0 0
\(535\) −1.29581 11.7396i −0.0560227 0.507549i
\(536\) 0 0
\(537\) −6.86692 6.86692i −0.296329 0.296329i
\(538\) 0 0
\(539\) −5.70618 5.70618i −0.245783 0.245783i
\(540\) 0 0
\(541\) 8.47183 8.47183i 0.364232 0.364232i −0.501136 0.865369i \(-0.667084\pi\)
0.865369 + 0.501136i \(0.167084\pi\)
\(542\) 0 0
\(543\) 0.720526 0.720526i 0.0309207 0.0309207i
\(544\) 0 0
\(545\) 3.80006 + 3.04456i 0.162777 + 0.130415i
\(546\) 0 0
\(547\) −9.97988 −0.426709 −0.213355 0.976975i \(-0.568439\pi\)
−0.213355 + 0.976975i \(0.568439\pi\)
\(548\) 0 0
\(549\) −12.1364 + 12.1364i −0.517971 + 0.517971i
\(550\) 0 0
\(551\) −45.4879 −1.93785
\(552\) 0 0
\(553\) −3.49559 + 3.49559i −0.148648 + 0.148648i
\(554\) 0 0
\(555\) 0.920650 + 8.34081i 0.0390794 + 0.354048i
\(556\) 0 0
\(557\) 13.4866i 0.571445i −0.958312 0.285722i \(-0.907766\pi\)
0.958312 0.285722i \(-0.0922335\pi\)
\(558\) 0 0
\(559\) 15.8678 0.671135
\(560\) 0 0
\(561\) 0.481724 0.0203384
\(562\) 0 0
\(563\) 20.3451i 0.857445i 0.903436 + 0.428723i \(0.141036\pi\)
−0.903436 + 0.428723i \(0.858964\pi\)
\(564\) 0 0
\(565\) −7.39519 5.92493i −0.311118 0.249264i
\(566\) 0 0
\(567\) 1.68896 1.68896i 0.0709298 0.0709298i
\(568\) 0 0
\(569\) −17.1460 −0.718797 −0.359399 0.933184i \(-0.617018\pi\)
−0.359399 + 0.933184i \(0.617018\pi\)
\(570\) 0 0
\(571\) −6.24329 + 6.24329i −0.261274 + 0.261274i −0.825571 0.564298i \(-0.809147\pi\)
0.564298 + 0.825571i \(0.309147\pi\)
\(572\) 0 0
\(573\) −2.13645 −0.0892516
\(574\) 0 0
\(575\) 18.4351 + 11.7004i 0.768795 + 0.487939i
\(576\) 0 0
\(577\) −10.0373 + 10.0373i −0.417859 + 0.417859i −0.884465 0.466606i \(-0.845477\pi\)
0.466606 + 0.884465i \(0.345477\pi\)
\(578\) 0 0
\(579\) −8.37596 + 8.37596i −0.348093 + 0.348093i
\(580\) 0 0
\(581\) 2.45963 + 2.45963i 0.102043 + 0.102043i
\(582\) 0 0
\(583\) −5.12561 5.12561i −0.212281 0.212281i
\(584\) 0 0
\(585\) −20.6343 + 2.27759i −0.853124 + 0.0941669i
\(586\) 0 0
\(587\) 30.6857i 1.26654i 0.773933 + 0.633268i \(0.218287\pi\)
−0.773933 + 0.633268i \(0.781713\pi\)
\(588\) 0 0
\(589\) 47.1025 + 47.1025i 1.94083 + 1.94083i
\(590\) 0 0
\(591\) 9.01817i 0.370958i
\(592\) 0 0
\(593\) −2.10671 2.10671i −0.0865123 0.0865123i 0.662526 0.749039i \(-0.269484\pi\)
−0.749039 + 0.662526i \(0.769484\pi\)
\(594\) 0 0
\(595\) −0.0695360 0.629976i −0.00285070 0.0258265i
\(596\) 0 0
\(597\) −7.36210 −0.301311
\(598\) 0 0
\(599\) 32.1322i 1.31289i −0.754375 0.656444i \(-0.772060\pi\)
0.754375 0.656444i \(-0.227940\pi\)
\(600\) 0 0
\(601\) 14.9811i 0.611091i −0.952177 0.305546i \(-0.901161\pi\)
0.952177 0.305546i \(-0.0988388\pi\)
\(602\) 0 0
\(603\) −36.1959 −1.47401
\(604\) 0 0
\(605\) 2.34934 + 21.2843i 0.0955141 + 0.865330i
\(606\) 0 0
\(607\) −27.3357 27.3357i −1.10952 1.10952i −0.993213 0.116310i \(-0.962893\pi\)
−0.116310 0.993213i \(-0.537107\pi\)
\(608\) 0 0
\(609\) 2.01506i 0.0816544i
\(610\) 0 0
\(611\) 16.8344 + 16.8344i 0.681047 + 0.681047i
\(612\) 0 0
\(613\) 48.3829i 1.95417i −0.212859 0.977083i \(-0.568277\pi\)
0.212859 0.977083i \(-0.431723\pi\)
\(614\) 0 0
\(615\) −3.92255 + 0.432967i −0.158173 + 0.0174589i
\(616\) 0 0
\(617\) −31.1565 31.1565i −1.25432 1.25432i −0.953766 0.300549i \(-0.902830\pi\)
−0.300549 0.953766i \(-0.597170\pi\)
\(618\) 0 0
\(619\) −0.198272 0.198272i −0.00796922 0.00796922i 0.703111 0.711080i \(-0.251794\pi\)
−0.711080 + 0.703111i \(0.751794\pi\)
\(620\) 0 0
\(621\) 11.8077 11.8077i 0.473825 0.473825i
\(622\) 0 0
\(623\) 0.381537 0.381537i 0.0152859 0.0152859i
\(624\) 0 0
\(625\) 22.6216 10.6425i 0.904864 0.425700i
\(626\) 0 0
\(627\) 6.28512 0.251003
\(628\) 0 0
\(629\) −2.23276 + 2.23276i −0.0890259 + 0.0890259i
\(630\) 0 0
\(631\) 32.3314 1.28709 0.643547 0.765407i \(-0.277462\pi\)
0.643547 + 0.765407i \(0.277462\pi\)
\(632\) 0 0
\(633\) −7.95239 + 7.95239i −0.316079 + 0.316079i
\(634\) 0 0
\(635\) 26.0418 + 20.8644i 1.03344 + 0.827977i
\(636\) 0 0
\(637\) 24.9161i 0.987212i
\(638\) 0 0
\(639\) 7.50010 0.296700
\(640\) 0 0
\(641\) −46.5662 −1.83926 −0.919628 0.392790i \(-0.871510\pi\)
−0.919628 + 0.392790i \(0.871510\pi\)
\(642\) 0 0
\(643\) 40.2247i 1.58631i 0.609021 + 0.793154i \(0.291563\pi\)
−0.609021 + 0.793154i \(0.708437\pi\)
\(644\) 0 0
\(645\) 0.731984 + 6.63156i 0.0288218 + 0.261117i
\(646\) 0 0
\(647\) 10.7938 10.7938i 0.424349 0.424349i −0.462349 0.886698i \(-0.652993\pi\)
0.886698 + 0.462349i \(0.152993\pi\)
\(648\) 0 0
\(649\) −12.3799 −0.485956
\(650\) 0 0
\(651\) 2.08659 2.08659i 0.0817799 0.0817799i
\(652\) 0 0
\(653\) −3.92443 −0.153575 −0.0767875 0.997047i \(-0.524466\pi\)
−0.0767875 + 0.997047i \(0.524466\pi\)
\(654\) 0 0
\(655\) 2.09898 + 1.68167i 0.0820138 + 0.0657084i
\(656\) 0 0
\(657\) −17.3173 + 17.3173i −0.675610 + 0.675610i
\(658\) 0 0
\(659\) −34.6142 + 34.6142i −1.34838 + 1.34838i −0.460952 + 0.887425i \(0.652492\pi\)
−0.887425 + 0.460952i \(0.847508\pi\)
\(660\) 0 0
\(661\) 21.7641 + 21.7641i 0.846525 + 0.846525i 0.989698 0.143173i \(-0.0457304\pi\)
−0.143173 + 0.989698i \(0.545730\pi\)
\(662\) 0 0
\(663\) 1.05173 + 1.05173i 0.0408456 + 0.0408456i
\(664\) 0 0
\(665\) −0.907246 8.21938i −0.0351815 0.318734i
\(666\) 0 0
\(667\) 26.1216i 1.01143i
\(668\) 0 0
\(669\) 1.50917 + 1.50917i 0.0583477 + 0.0583477i
\(670\) 0 0
\(671\) 8.12584i 0.313695i
\(672\) 0 0
\(673\) 29.4450 + 29.4450i 1.13502 + 1.13502i 0.989330 + 0.145691i \(0.0465405\pi\)
0.145691 + 0.989330i \(0.453459\pi\)
\(674\) 0 0
\(675\) −4.16995 18.6591i −0.160501 0.718189i
\(676\) 0 0
\(677\) −34.7351 −1.33498 −0.667490 0.744619i \(-0.732631\pi\)
−0.667490 + 0.744619i \(0.732631\pi\)
\(678\) 0 0
\(679\) 4.92370i 0.188954i
\(680\) 0 0
\(681\) 6.45828i 0.247482i
\(682\) 0 0
\(683\) 22.2693 0.852110 0.426055 0.904697i \(-0.359903\pi\)
0.426055 + 0.904697i \(0.359903\pi\)
\(684\) 0 0
\(685\) −13.5770 10.8777i −0.518750 0.415616i
\(686\) 0 0
\(687\) 1.88597 + 1.88597i 0.0719543 + 0.0719543i
\(688\) 0 0
\(689\) 22.3810i 0.852650i
\(690\) 0 0
\(691\) −15.7043 15.7043i −0.597420 0.597420i 0.342205 0.939625i \(-0.388826\pi\)
−0.939625 + 0.342205i \(0.888826\pi\)
\(692\) 0 0
\(693\) 1.46227i 0.0555470i
\(694\) 0 0
\(695\) −7.49048 6.00128i −0.284130 0.227641i
\(696\) 0 0
\(697\) −1.05003 1.05003i −0.0397728 0.0397728i
\(698\) 0 0
\(699\) −8.58253 8.58253i −0.324621 0.324621i
\(700\) 0 0
\(701\) −21.5588 + 21.5588i −0.814266 + 0.814266i −0.985270 0.171004i \(-0.945299\pi\)
0.171004 + 0.985270i \(0.445299\pi\)
\(702\) 0 0
\(703\) −29.1311 + 29.1311i −1.09870 + 1.09870i
\(704\) 0 0
\(705\) −6.25897 + 7.81212i −0.235726 + 0.294221i
\(706\) 0 0
\(707\) 0.655691 0.0246598
\(708\) 0 0
\(709\) −2.96687 + 2.96687i −0.111423 + 0.111423i −0.760620 0.649197i \(-0.775105\pi\)
0.649197 + 0.760620i \(0.275105\pi\)
\(710\) 0 0
\(711\) −25.6183 −0.960760
\(712\) 0 0
\(713\) −27.0488 + 27.0488i −1.01299 + 1.01299i
\(714\) 0 0
\(715\) 6.14529 7.67023i 0.229821 0.286850i
\(716\) 0 0
\(717\) 17.4688i 0.652385i
\(718\) 0 0
\(719\) 25.8357 0.963509 0.481755 0.876306i \(-0.340000\pi\)
0.481755 + 0.876306i \(0.340000\pi\)
\(720\) 0 0
\(721\) −6.59839 −0.245737
\(722\) 0 0
\(723\) 8.32763i 0.309708i
\(724\) 0 0
\(725\) −25.2518 16.0268i −0.937829 0.595222i
\(726\) 0 0
\(727\) −28.9620 + 28.9620i −1.07414 + 1.07414i −0.0771198 + 0.997022i \(0.524572\pi\)
−0.997022 + 0.0771198i \(0.975428\pi\)
\(728\) 0 0
\(729\) 4.43146 0.164128
\(730\) 0 0
\(731\) −1.77521 + 1.77521i −0.0656584 + 0.0656584i
\(732\) 0 0
\(733\) 21.1673 0.781832 0.390916 0.920426i \(-0.372158\pi\)
0.390916 + 0.920426i \(0.372158\pi\)
\(734\) 0 0
\(735\) 10.4131 1.14939i 0.384093 0.0423957i
\(736\) 0 0
\(737\) 12.1173 12.1173i 0.446347 0.446347i
\(738\) 0 0
\(739\) −2.23302 + 2.23302i −0.0821431 + 0.0821431i −0.746985 0.664841i \(-0.768499\pi\)
0.664841 + 0.746985i \(0.268499\pi\)
\(740\) 0 0
\(741\) 13.7220 + 13.7220i 0.504091 + 0.504091i
\(742\) 0 0
\(743\) 18.4514 + 18.4514i 0.676915 + 0.676915i 0.959301 0.282386i \(-0.0911258\pi\)
−0.282386 + 0.959301i \(0.591126\pi\)
\(744\) 0 0
\(745\) 22.0603 27.5345i 0.808226 1.00879i
\(746\) 0 0
\(747\) 18.0260i 0.659538i
\(748\) 0 0
\(749\) −1.81634 1.81634i −0.0663675 0.0663675i
\(750\) 0 0
\(751\) 42.4243i 1.54808i −0.633134 0.774042i \(-0.718232\pi\)
0.633134 0.774042i \(-0.281768\pi\)
\(752\) 0 0
\(753\) 5.18780 + 5.18780i 0.189054 + 0.189054i
\(754\) 0 0
\(755\) −7.07365 + 0.780782i −0.257437 + 0.0284156i
\(756\) 0 0
\(757\) −19.7595 −0.718170 −0.359085 0.933305i \(-0.616911\pi\)
−0.359085 + 0.933305i \(0.616911\pi\)
\(758\) 0 0
\(759\) 3.60925i 0.131007i
\(760\) 0 0
\(761\) 48.0351i 1.74127i 0.491928 + 0.870636i \(0.336292\pi\)
−0.491928 + 0.870636i \(0.663708\pi\)
\(762\) 0 0
\(763\) 1.05899 0.0383379
\(764\) 0 0
\(765\) 2.05366 2.56327i 0.0742502 0.0926753i
\(766\) 0 0
\(767\) −27.0286 27.0286i −0.975946 0.975946i
\(768\) 0 0
\(769\) 24.0184i 0.866127i −0.901363 0.433064i \(-0.857433\pi\)
0.901363 0.433064i \(-0.142567\pi\)
\(770\) 0 0
\(771\) 6.98319 + 6.98319i 0.251493 + 0.251493i
\(772\) 0 0
\(773\) 22.4630i 0.807937i 0.914773 + 0.403969i \(0.132370\pi\)
−0.914773 + 0.403969i \(0.867630\pi\)
\(774\) 0 0
\(775\) 9.55244 + 42.7439i 0.343134 + 1.53541i
\(776\) 0 0
\(777\) 1.29048 + 1.29048i 0.0462956 + 0.0462956i
\(778\) 0 0
\(779\) −13.6999 13.6999i −0.490850 0.490850i
\(780\) 0 0
\(781\) −2.51081 + 2.51081i −0.0898440 + 0.0898440i
\(782\) 0 0
\(783\) −16.1738 + 16.1738i −0.578005 + 0.578005i
\(784\) 0 0
\(785\) 1.73065 + 15.6792i 0.0617697 + 0.559615i
\(786\) 0 0
\(787\) −26.1054 −0.930556 −0.465278 0.885165i \(-0.654046\pi\)
−0.465278 + 0.885165i \(0.654046\pi\)
\(788\) 0 0
\(789\) 2.65724 2.65724i 0.0946001 0.0946001i
\(790\) 0 0
\(791\) −2.06087 −0.0732759
\(792\) 0 0
\(793\) 17.7408 17.7408i 0.629994 0.629994i
\(794\) 0 0
\(795\) 9.35363 1.03244i 0.331739 0.0366170i
\(796\) 0 0
\(797\) 43.4888i 1.54045i −0.637770 0.770227i \(-0.720143\pi\)
0.637770 0.770227i