Properties

Label 640.2.j.d.607.6
Level $640$
Weight $2$
Character 640.607
Analytic conductor $5.110$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 640 = 2^{7} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 640.j (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.11042572936\)
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 607.6
Root \(-0.635486 - 1.26339i\) of defining polynomial
Character \(\chi\) \(=\) 640.607
Dual form 640.2.j.d.543.4

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(261\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.692712i 0.399937i 0.979802 + 0.199969i \(0.0640841\pi\)
−0.979802 + 0.199969i \(0.935916\pi\)
\(4\) 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 \(-0.279295\pi\)
−0.769100 + 0.639129i \(0.779295\pi\)
\(8\) 0 0
\(9\) 2.52015 0.840050
\(10\) 0 0
\(11\) −0.843672 0.843672i −0.254377 0.254377i 0.568386 0.822762i \(-0.307568\pi\)
−0.822762 + 0.568386i \(0.807568\pi\)
\(12\) 0 0
\(13\) 3.68390 1.02173 0.510865 0.859661i \(-0.329325\pi\)
0.510865 + 0.859661i \(0.329325\pi\)
\(14\) 0 0
\(15\) 0.169939 1.53960i 0.0438782 0.397523i
\(16\) 0 0
\(17\) 0.412137 + 0.412137i 0.0999579 + 0.0999579i 0.755317 0.655359i \(-0.227483\pi\)
−0.655359 + 0.755317i \(0.727483\pi\)
\(18\) 0 0
\(19\) 5.37721 + 5.37721i 1.23362 + 1.23362i 0.962565 + 0.271052i \(0.0873714\pi\)
0.271052 + 0.962565i \(0.412629\pi\)
\(20\) 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 \(-0.900462\pi\)
0.307636 + 0.951504i \(0.400462\pi\)
\(24\) 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 \(-0.562571\pi\)
0.980742 + 0.195308i \(0.0625707\pi\)
\(30\) 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 \(-0.353091\pi\)
0.445317 + 0.895373i \(0.353091\pi\)
\(38\) 0 0
\(39\) 2.55188i 0.408628i
\(40\) 0 0
\(41\) 2.54777i 0.397895i 0.980010 + 0.198948i \(0.0637524\pi\)
−0.980010 + 0.198948i \(0.936248\pi\)
\(42\) 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 \(-0.593774\pi\)
0.956919 + 0.290356i \(0.0937738\pi\)
\(48\) 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 −0.0438495 0.999038i \(-0.513962\pi\)
0.999038 + 0.0438495i \(0.0139622\pi\)
\(60\) 0 0
\(61\) 4.81576 + 4.81576i 0.616595 + 0.616595i 0.944656 0.328062i \(-0.106395\pi\)
−0.328062 + 0.944656i \(0.606395\pi\)
\(62\) 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 \(-0.556509\pi\)
−0.176596 + 0.984283i \(0.556509\pi\)
\(72\) 0 0
\(73\) −6.87152 6.87152i −0.804250 0.804250i 0.179507 0.983757i \(-0.442550\pi\)
−0.983757 + 0.179507i \(0.942550\pi\)
\(74\) 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 \(-0.306227\pi\)
0.571847 + 0.820360i \(0.306227\pi\)
\(80\) 0 0
\(81\) 4.91161 0.545734
\(82\) 0 0
\(83\) 7.15276i 0.785118i −0.919727 0.392559i \(-0.871590\pi\)
0.919727 0.392559i \(-0.128410\pi\)
\(84\) 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 0.970002 0.243096i \(-0.0781630\pi\)
−0.243096 + 0.970002i \(0.578163\pi\)
\(98\) 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 \(-0.771368\pi\)
0.658081 + 0.752947i \(0.271368\pi\)
\(102\) 0 0
\(103\) 9.59425 9.59425i 0.945350 0.945350i −0.0532322 0.998582i \(-0.516952\pi\)
0.998582 + 0.0532322i \(0.0169524\pi\)
\(104\) 0 0
\(105\) −0.587863 + 0.470988i −0.0573696 + 0.0459637i
\(106\) 0 0
\(107\) 5.28201i 0.510631i 0.966858 + 0.255316i \(0.0821794\pi\)
−0.966858 + 0.255316i \(0.917821\pi\)
\(108\) 0 0
\(109\) −1.53980 + 1.53980i −0.147486 + 0.147486i −0.776994 0.629508i \(-0.783256\pi\)
0.629508 + 0.776994i \(0.283256\pi\)
\(110\) 0 0
\(111\) 3.75278i 0.356198i
\(112\) 0 0
\(113\) −2.99656 + 2.99656i −0.281893 + 0.281893i −0.833863 0.551971i \(-0.813876\pi\)
0.551971 + 0.833863i \(0.313876\pi\)
\(114\) 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 \(-0.980337\pi\)
0.0617330 + 0.998093i \(0.480337\pi\)
\(128\) 0 0
\(129\) 2.98373i 0.262703i
\(130\) 0 0
\(131\) 0.850513 0.850513i 0.0743096 0.0743096i −0.668975 0.743285i \(-0.733267\pi\)
0.743285 + 0.668975i \(0.233267\pi\)
\(132\) 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 −0.901921 0.431901i \(-0.857843\pi\)
0.431901 + 0.901921i \(0.357843\pi\)
\(138\) 0 0
\(139\) −3.03517 + 3.03517i −0.257440 + 0.257440i −0.824012 0.566572i \(-0.808269\pi\)
0.566572 + 0.824012i \(0.308269\pi\)
\(140\) 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 \(-0.473690\pi\)
−0.996586 + 0.0825625i \(0.973690\pi\)
\(150\) 0 0
\(151\) 3.18265 0.259000 0.129500 0.991579i \(-0.458663\pi\)
0.129500 + 0.991579i \(0.458663\pi\)
\(152\) 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 \(-0.784110\pi\)
0.778680 0.627422i \(-0.215890\pi\)
\(164\) 0 0
\(165\) −1.44229 + 1.15554i −0.112282 + 0.0899591i
\(166\) 0 0
\(167\) −16.6023 16.6023i −1.28473 1.28473i −0.937946 0.346780i \(-0.887275\pi\)
−0.346780 0.937946i \(-0.612725\pi\)
\(168\) 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 \(-0.693078\pi\)
−0.570054 + 0.821607i \(0.693078\pi\)
\(174\) 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 0.972759 0.231819i \(-0.0744678\pi\)
−0.231819 + 0.972759i \(0.574468\pi\)
\(180\) 0 0
\(181\) −1.04015 + 1.04015i −0.0773139 + 0.0773139i −0.744706 0.667392i \(-0.767410\pi\)
0.667392 + 0.744706i \(0.267410\pi\)
\(182\) 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 −0.992512 0.122144i \(-0.961023\pi\)
0.122144 + 0.992512i \(0.461023\pi\)
\(194\) 0 0
\(195\) 0.626040 5.67174i 0.0448317 0.406162i
\(196\) 0 0
\(197\) −13.0186 −0.927540 −0.463770 0.885956i \(-0.653504\pi\)
−0.463770 + 0.885956i \(0.653504\pi\)
\(198\) 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 −0.981546 0.191225i \(-0.938754\pi\)
0.191225 + 0.981546i \(0.438754\pi\)
\(212\) 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 \(-0.217104\pi\)
−0.630388 + 0.776280i \(0.717104\pi\)
\(224\) 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 \(-0.209395\pi\)
−0.611404 + 0.791318i \(0.709395\pi\)
\(230\) 0 0
\(231\) −0.401933 −0.0264452
\(232\) 0 0
\(233\) 12.3897 + 12.3897i 0.811679 + 0.811679i 0.984886 0.173206i \(-0.0554127\pi\)
−0.173206 + 0.984886i \(0.555413\pi\)
\(234\) 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 \(-0.196402\pi\)
0.815609 + 0.578604i \(0.196402\pi\)
\(240\) 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 0.430081 0.902790i \(-0.358485\pi\)
−0.902790 + 0.430081i \(0.858485\pi\)
\(252\) 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 0.318942 0.947774i \(-0.396672\pi\)
−0.947774 + 0.318942i \(0.896672\pi\)
\(258\) 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 \(-0.803491\pi\)
0.578877 + 0.815415i \(0.303491\pi\)
\(264\) 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 \(-0.553523\pi\)
0.985896 + 0.167357i \(0.0535233\pi\)
\(270\) 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 \(-0.434630\pi\)
0.203927 + 0.978986i \(0.434630\pi\)
\(278\) 0 0
\(279\) 22.0757i 1.32164i
\(280\) 0 0
\(281\) 21.5509i 1.28562i 0.766026 + 0.642810i \(0.222232\pi\)
−0.766026 + 0.642810i \(0.777768\pi\)
\(282\) 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 \(-0.561854\pi\)
−0.193101 + 0.981179i \(0.561854\pi\)
\(312\) 0 0
\(313\) −1.20933 1.20933i −0.0683555 0.0683555i 0.672103 0.740458i \(-0.265391\pi\)
−0.740458 + 0.672103i \(0.765391\pi\)
\(314\) 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 0.746730 0.665128i \(-0.231623\pi\)
−0.665128 + 0.746730i \(0.731623\pi\)
\(332\) 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 0.855763 0.517368i \(-0.173088\pi\)
−0.517368 + 0.855763i \(0.673088\pi\)
\(338\) 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 \(-0.912168\pi\)
0.962171 0.272445i \(-0.0878321\pi\)
\(348\) 0 0
\(349\) 3.99595 3.99595i 0.213898 0.213898i −0.592023 0.805921i \(-0.701671\pi\)
0.805921 + 0.592023i \(0.201671\pi\)
\(350\) 0 0
\(351\) 14.0868i 0.751897i
\(352\) 0 0
\(353\) 22.6637 22.6637i 1.20627 1.20627i 0.234043 0.972226i \(-0.424804\pi\)
0.972226 0.234043i \(-0.0751957\pi\)
\(354\) 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 \(-0.826751\pi\)
0.517801 + 0.855501i \(0.326751\pi\)
\(368\) 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 −0.493967 0.869480i \(-0.664454\pi\)
0.869480 + 0.493967i \(0.164454\pi\)
\(380\) 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 \(-0.311509\pi\)
−0.829736 + 0.558156i \(0.811509\pi\)
\(384\) 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 \(-0.235291\pi\)
−0.673688 + 0.739016i \(0.735291\pi\)
\(390\) 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 0.849129 0.528185i \(-0.177127\pi\)
−0.528185 + 0.849129i \(0.677127\pi\)
\(420\) 0 0
\(421\) −13.8805 + 13.8805i −0.676493 + 0.676493i −0.959205 0.282712i \(-0.908766\pi\)
0.282712 + 0.959205i \(0.408766\pi\)
\(422\) 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 −0.710590 0.703606i \(-0.751572\pi\)
0.703606 + 0.710590i \(0.251572\pi\)
\(434\) 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 \(0.354041\pi\)
−0.442642 + 0.896698i \(0.645959\pi\)
\(450\) 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 −0.142454 0.989801i \(-0.545499\pi\)
0.989801 + 0.142454i \(0.0454993\pi\)
\(458\) 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 \(-0.384069\pi\)
−0.934406 + 0.356209i \(0.884069\pi\)
\(462\) 0 0
\(463\) −8.56578 8.56578i −0.398085 0.398085i 0.479472 0.877557i \(-0.340828\pi\)
−0.877557 + 0.479472i \(0.840828\pi\)
\(464\) 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 \(-0.679966\pi\)
−0.535738 + 0.844384i \(0.679966\pi\)
\(480\) 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 \(-0.304445\pi\)
−0.817146 + 0.576430i \(0.804445\pi\)
\(488\) 0 0
\(489\) 11.0978 0.501859
\(490\) 0 0
\(491\) 3.71980 + 3.71980i 0.167872 + 0.167872i 0.786044 0.618171i \(-0.212126\pi\)
−0.618171 + 0.786044i \(0.712126\pi\)
\(492\) 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 0.333603 0.942714i \(-0.391736\pi\)
−0.942714 + 0.333603i \(0.891736\pi\)
\(500\) 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 \(-0.844852\pi\)
0.468342 + 0.883547i \(0.344852\pi\)
\(504\) 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 \(-0.830140\pi\)
0.508662 + 0.860966i \(0.330140\pi\)
\(510\) 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 \(-0.777285\pi\)
0.765048 0.643974i \(-0.222715\pi\)
\(522\) 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 \(-0.332916\pi\)
−0.865369 + 0.501136i \(0.832916\pi\)
\(542\) 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 \(-0.858964\pi\)
0.903436 0.428723i \(-0.141036\pi\)
\(564\) 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 0.564298 0.825571i \(-0.309147\pi\)
−0.825571 + 0.564298i \(0.809147\pi\)
\(572\) 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 0.466606 0.884465i \(-0.345477\pi\)
−0.884465 + 0.466606i \(0.845477\pi\)
\(578\) 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 \(-0.781713\pi\)
0.773933 0.633268i \(-0.218287\pi\)
\(588\) 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 −0.749039 0.662526i \(-0.769484\pi\)
0.662526 + 0.749039i \(0.269484\pi\)
\(594\) 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 \(0.0988388\pi\)
−0.952177 + 0.305546i \(0.901161\pi\)
\(602\) 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 0.116310 0.993213i \(-0.462893\pi\)
0.993213 0.116310i \(-0.0371067\pi\)
\(608\) 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 −0.300549 + 0.953766i \(0.597170\pi\)
−0.953766 + 0.300549i \(0.902830\pi\)
\(618\) 0 0
\(619\) −0.198272 + 0.198272i −0.00796922 + 0.00796922i −0.711080 0.703111i \(-0.751794\pi\)
0.703111 + 0.711080i \(0.251794\pi\)
\(620\) 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 \(-0.722538\pi\)
−0.643547 + 0.765407i \(0.722538\pi\)
\(632\) 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 \(-0.708437\pi\)
0.609021 0.793154i \(-0.291563\pi\)
\(644\) 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 \(-0.347007\pi\)
−0.886698 + 0.462349i \(0.847007\pi\)
\(648\) 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 \(-0.475534\pi\)
0.0767875 + 0.997047i \(0.475534\pi\)
\(654\) 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 −0.887425 0.460952i \(-0.847508\pi\)
−0.460952 0.887425i \(-0.652492\pi\)
\(660\) 0 0
\(661\) −21.7641 + 21.7641i −0.846525 + 0.846525i −0.989698 0.143173i \(-0.954270\pi\)
0.143173 + 0.989698i \(0.454270\pi\)
\(662\) 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 0.145691 0.989330i \(-0.453459\pi\)
0.989330 0.145691i \(-0.0465405\pi\)
\(674\) 0 0
\(675\) −4.16995 + 18.6591i −0.160501 + 0.718189i
\(676\) 0 0
\(677\) 34.7351 1.33498 0.667490 0.744619i \(-0.267369\pi\)
0.667490 + 0.744619i \(0.267369\pi\)
\(678\) 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 −0.939625 0.342205i \(-0.888826\pi\)
0.342205 + 0.939625i \(0.388826\pi\)
\(692\) 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 \(-0.0547011\pi\)
−0.171004 + 0.985270i \(0.554701\pi\)
\(702\) 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 \(-0.224895\pi\)
−0.649197 + 0.760620i \(0.724895\pi\)
\(710\) 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 \(-0.660000\pi\)
−0.481755 + 0.876306i \(0.660000\pi\)
\(720\) 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 0.997022 + 0.0771198i \(0.0245724\pi\)
0.0771198 + 0.997022i \(0.475428\pi\)
\(728\) 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 \(-0.627842\pi\)
−0.390916 + 0.920426i \(0.627842\pi\)
\(734\) 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 0.664841 0.746985i \(-0.268499\pi\)
−0.746985 + 0.664841i \(0.768499\pi\)
\(740\) 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 \(-0.908874\pi\)
0.282386 + 0.959301i \(0.408874\pi\)
\(744\) 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 \(-0.383089\pi\)
0.359085 + 0.933305i \(0.383089\pi\)
\(758\) 0 0
\(759\) 3.60925i 0.131007i
\(760\) 0 0
\(761\) 48.0351i 1.74127i −0.491928 0.870636i \(-0.663708\pi\)
0.491928 0.870636i \(-0.336292\pi\)
\(762\) 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 \(0.142567\pi\)
−0.901363 + 0.433064i \(0.857433\pi\)
\(770\) 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 \(-0.720143\pi\)