Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.10 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.c.1609.29 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.504884 | − | 2.17832i | −0.225791 | − | 0.974176i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.91807i | − | 1.48089i | −0.672116 | − | 0.740446i | \(-0.734614\pi\) | ||
0.672116 | − | 0.740446i | \(-0.265386\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46196 | 1.04382 | 0.521910 | − | 0.853001i | \(-0.325220\pi\) | ||||
0.521910 | + | 0.853001i | \(0.325220\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.46128i | 1.79204i | 0.444018 | + | 0.896018i | \(0.353552\pi\) | ||||
−0.444018 | + | 0.896018i | \(0.646448\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.17832 | + | 0.504884i | −0.562441 | + | 0.130360i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.603948i | − | 0.146479i | −0.997314 | − | 0.0732395i | \(-0.976666\pi\) | ||
0.997314 | − | 0.0732395i | \(-0.0233337\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.547912 | −0.125700 | −0.0628498 | − | 0.998023i | \(-0.520019\pi\) | ||||
−0.0628498 | + | 0.998023i | \(0.520019\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.91807 | −0.854993 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.27671i | 1.51730i | 0.651499 | + | 0.758649i | \(0.274140\pi\) | ||||
−0.651499 | + | 0.758649i | \(0.725860\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.49019 | + | 2.19960i | −0.898037 | + | 0.439920i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.89848 | −1.09532 | −0.547660 | − | 0.836701i | \(-0.684481\pi\) | ||||
−0.547660 | + | 0.836701i | \(0.684481\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.98609 | −0.895529 | −0.447765 | − | 0.894152i | \(-0.647780\pi\) | ||||
−0.447765 | + | 0.894152i | \(0.647780\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.46196i | − | 0.602650i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.53483 | + | 1.97817i | −1.44265 | + | 0.334372i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.50660i | 0.412082i | 0.978543 | + | 0.206041i | \(0.0660581\pi\) | ||||
−0.978543 | + | 0.206041i | \(0.933942\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.46128 | 1.03463 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.9146 | −1.70458 | −0.852288 | − | 0.523073i | \(-0.824785\pi\) | ||||
−0.852288 | + | 0.523073i | \(0.824785\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.38640i | − | 0.516420i | −0.966089 | − | 0.258210i | \(-0.916867\pi\) | ||
0.966089 | − | 0.258210i | \(-0.0831327\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.504884 | + | 2.17832i | 0.0752636 | + | 0.324725i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 5.74394i | − | 0.837839i | −0.908023 | − | 0.418920i | \(-0.862409\pi\) | ||
0.908023 | − | 0.418920i | \(-0.137591\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.35128 | −1.19304 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.603948 | −0.0845697 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.06027i | 0.283000i | 0.989938 | + | 0.141500i | \(0.0451925\pi\) | ||||
−0.989938 | + | 0.141500i | \(0.954808\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.74789 | − | 7.54127i | −0.235685 | − | 1.01686i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.547912i | 0.0725727i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.6318 | −1.51433 | −0.757164 | − | 0.653225i | \(-0.773416\pi\) | ||||
−0.757164 | + | 0.653225i | \(0.773416\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.87755 | −1.13665 | −0.568327 | − | 0.822803i | \(-0.692409\pi\) | ||||
−0.568327 | + | 0.822803i | \(0.692409\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.91807i | 0.493631i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.0747 | − | 3.26219i | 1.74576 | − | 0.404625i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.00000i | − | 0.122169i | ||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.27671 | 0.876013 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.83462 | 0.455086 | 0.227543 | − | 0.973768i | \(-0.426931\pi\) | ||||
0.227543 | + | 0.973768i | \(0.426931\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.6619i | 1.83309i | 0.399936 | + | 0.916543i | \(0.369032\pi\) | ||||
−0.399936 | + | 0.916543i | \(0.630968\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.19960 | + | 4.49019i | 0.253988 | + | 0.518482i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 13.5642i | − | 1.54578i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.63769 | −0.971817 | −0.485908 | − | 0.874010i | \(-0.661511\pi\) | ||||
−0.485908 | + | 0.874010i | \(0.661511\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.96810i | − | 0.435556i | −0.975998 | − | 0.217778i | \(-0.930119\pi\) | ||
0.975998 | − | 0.217778i | \(-0.0698808\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.31559 | + | 0.304924i | −0.142696 | + | 0.0330736i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.89848i | 0.632383i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.55112 | −0.906417 | −0.453209 | − | 0.891404i | \(-0.649721\pi\) | ||||
−0.453209 | + | 0.891404i | \(0.649721\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25.3157 | 2.65381 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.98609i | 0.517034i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.276632 | + | 1.19353i | 0.0283818 | + | 0.122454i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.10602i | − | 0.619973i | −0.950741 | − | 0.309986i | \(-0.899676\pi\) | ||
0.950741 | − | 0.309986i | \(-0.100324\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.46196 | −0.347940 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.80936 | 0.578053 | 0.289027 | − | 0.957321i | \(-0.406668\pi\) | ||||
0.289027 | + | 0.957321i | \(0.406668\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.89577i | 0.876526i | 0.898847 | + | 0.438263i | \(0.144406\pi\) | ||||
−0.898847 | + | 0.438263i | \(0.855594\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.97817 | + | 8.53483i | 0.193050 | + | 0.832914i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.2578i | 1.47503i | 0.675333 | + | 0.737513i | \(0.264000\pi\) | ||||
−0.675333 | + | 0.737513i | \(0.736000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.6445 | −1.21112 | −0.605560 | − | 0.795800i | \(-0.707051\pi\) | ||||
−0.605560 | + | 0.795800i | \(0.707051\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.50660 | 0.237916 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 10.2895i | − | 0.967956i | −0.875080 | − | 0.483978i | \(-0.839191\pi\) | ||
0.875080 | − | 0.483978i | \(-0.160809\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.8510 | − | 3.67389i | 1.47812 | − | 0.342592i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 6.46128i | − | 0.597345i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.36631 | −0.216920 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.985162 | 0.0895602 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.9146i | 0.984137i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.05846 | + | 8.67053i | 0.631328 | + | 0.775516i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.92997i | − | 0.614935i | −0.951559 | − | 0.307468i | \(-0.900518\pi\) | ||
0.951559 | − | 0.307468i | \(-0.0994816\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.38640 | −0.298156 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.2951 | 0.986861 | 0.493430 | − | 0.869785i | \(-0.335743\pi\) | ||||
0.493430 | + | 0.869785i | \(0.335743\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.14676i | 0.186148i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.17832 | − | 0.504884i | 0.187480 | − | 0.0434535i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.64778i | 0.653394i | 0.945129 | + | 0.326697i | \(0.105936\pi\) | ||||
−0.945129 | + | 0.326697i | \(0.894064\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.12792 | 0.265306 | 0.132653 | − | 0.991163i | \(-0.457650\pi\) | ||||
0.132653 | + | 0.991163i | \(0.457650\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.74394 | −0.483727 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.3687i | 1.87056i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.97804 | + | 12.8488i | 0.247313 | + | 1.06703i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.35128i | 0.688802i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.5824 | 1.11271 | 0.556357 | − | 0.830943i | \(-0.312199\pi\) | ||||
0.556357 | + | 0.830943i | \(0.312199\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.4695 | −1.17751 | −0.588756 | − | 0.808311i | \(-0.700382\pi\) | ||||
−0.588756 | + | 0.808311i | \(0.700382\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.603948i | 0.0488263i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.51740 | + | 10.8613i | 0.202202 | + | 0.872403i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 12.0664i | − | 0.963007i | −0.876444 | − | 0.481504i | \(-0.840091\pi\) | ||
0.876444 | − | 0.481504i | \(-0.159909\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.06027 | 0.163390 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 28.5107 | 2.24695 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.01144i | 0.235874i | 0.993021 | + | 0.117937i | \(0.0376281\pi\) | ||||
−0.993021 | + | 0.117937i | \(0.962372\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.54127 | + | 1.74789i | −0.587087 | + | 0.136073i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.13904i | 0.475053i | 0.971381 | + | 0.237527i | \(0.0763367\pi\) | ||||
−0.971381 | + | 0.237527i | \(0.923663\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −28.7481 | −2.21139 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.547912 | 0.0418999 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.831968i | 0.0632533i | 0.999500 | + | 0.0316267i | \(0.0100688\pi\) | ||||
−0.999500 | + | 0.0316267i | \(0.989931\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.61819 | + | 17.5929i | 0.651474 | + | 1.32990i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.6318i | 0.874298i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.4026 | 1.00175 | 0.500877 | − | 0.865518i | \(-0.333011\pi\) | ||||
0.500877 | + | 0.865518i | \(0.333011\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.84980 | −0.211824 | −0.105912 | − | 0.994375i | \(-0.533776\pi\) | ||||
−0.105912 | + | 0.994375i | \(0.533776\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.87755i | 0.656248i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.46018 | − | 1.26554i | 0.401441 | − | 0.0930444i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.09084i | − | 0.152898i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.91807 | 0.284998 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.8329 | 1.21798 | 0.608992 | − | 0.793176i | \(-0.291574\pi\) | ||||
0.608992 | + | 0.793176i | \(0.291574\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 25.5455i | − | 1.83881i | −0.393315 | − | 0.919404i | \(-0.628672\pi\) | ||
0.393315 | − | 0.919404i | \(-0.371328\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.26219 | − | 14.0747i | −0.233610 | − | 1.00791i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.3050i | 0.876695i | 0.898805 | + | 0.438348i | \(0.144436\pi\) | ||||
−0.898805 | + | 0.438348i | \(0.855564\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.79978 | 0.623800 | 0.311900 | − | 0.950115i | \(-0.399035\pi\) | ||||
0.311900 | + | 0.950115i | \(0.399035\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 23.1107i | 1.62205i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.51061 | + | 23.7755i | 0.384877 | + | 1.66056i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 7.27671i | − | 0.505766i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.89685 | −0.131208 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.6312 | −0.800726 | −0.400363 | − | 0.916357i | \(-0.631116\pi\) | ||||
−0.400363 | + | 0.916357i | \(0.631116\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 3.83462i | − | 0.262744i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.37666 | + | 1.70974i | −0.503084 | + | 0.116603i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.5359i | 1.32618i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.6619 | 1.05833 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.90228 | 0.262495 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 18.7044i | − | 1.25254i | −0.779607 | − | 0.626269i | \(-0.784581\pi\) | ||
0.779607 | − | 0.626269i | \(-0.215419\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.49019 | − | 2.19960i | 0.299346 | − | 0.146640i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 10.1922i | − | 0.676483i | −0.941059 | − | 0.338241i | \(-0.890168\pi\) | ||
0.941059 | − | 0.338241i | \(-0.109832\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.810691 | 0.0535719 | 0.0267860 | − | 0.999641i | \(-0.491473\pi\) | ||||
0.0267860 | + | 0.999641i | \(0.491473\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.5642 | −0.892459 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 25.4579i | − | 1.66780i | −0.551913 | − | 0.833902i | \(-0.686102\pi\) | ||
0.551913 | − | 0.833902i | \(-0.313898\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.5122 | + | 2.90002i | −0.816203 | + | 0.189176i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.63769i | 0.561079i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.47427 | −0.548155 | −0.274077 | − | 0.961708i | \(-0.588372\pi\) | ||||
−0.274077 | + | 0.961708i | \(0.588372\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.25751 | −0.467497 | −0.233749 | − | 0.972297i | \(-0.575099\pi\) | ||||
−0.233749 | + | 0.972297i | \(0.575099\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.21642 | + | 18.1918i | 0.269378 | + | 1.16223i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.54021i | − | 0.225258i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.96810 | −0.251468 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.98355 | −0.567037 | −0.283518 | − | 0.958967i | \(-0.591502\pi\) | ||||
−0.283518 | + | 0.958967i | \(0.591502\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.1917i | 1.58379i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.304924 | + | 1.31559i | 0.0190951 | + | 0.0823857i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 8.42681i | − | 0.525650i | −0.964843 | − | 0.262825i | \(-0.915346\pi\) | ||
0.964843 | − | 0.262825i | \(-0.0846542\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.82103 | 0.610249 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.89848 | 0.365107 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 10.4437i | − | 0.643987i | −0.946742 | − | 0.321994i | \(-0.895647\pi\) | ||
0.946742 | − | 0.321994i | \(-0.104353\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.48793 | − | 1.04020i | 0.275691 | − | 0.0638987i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.55112i | 0.523320i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.6313 | −0.892083 | −0.446042 | − | 0.895012i | \(-0.647167\pi\) | ||||
−0.446042 | + | 0.895012i | \(0.647167\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.6460 | −1.55788 | −0.778940 | − | 0.627098i | \(-0.784243\pi\) | ||||
−0.778940 | + | 0.627098i | \(0.784243\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 25.3157i | − | 1.53218i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.5448 | + | 7.61492i | −0.937389 | + | 0.459197i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.7897i | 0.708373i | 0.935175 | + | 0.354186i | \(0.115242\pi\) | ||||
−0.935175 | + | 0.354186i | \(0.884758\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.98609 | 0.298510 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 33.1194 | 1.97573 | 0.987867 | − | 0.155299i | \(-0.0496342\pi\) | ||||
0.987867 | + | 0.155299i | \(0.0496342\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 17.9719i | − | 1.06832i | −0.845384 | − | 0.534159i | \(-0.820628\pi\) | ||
0.845384 | − | 0.534159i | \(-0.179372\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.19353 | − | 0.276632i | 0.0706986 | − | 0.0163863i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 42.7642i | 2.52429i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.6352 | 0.978544 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.10602 | −0.357941 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 5.64494i | − | 0.329781i | −0.986312 | − | 0.164890i | \(-0.947273\pi\) | ||
0.986312 | − | 0.164890i | \(-0.0527271\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.87269 | + | 25.3378i | 0.341921 | + | 1.47522i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.46196i | 0.200883i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −47.0168 | −2.71905 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.2681 | −0.764763 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 5.80936i | − | 0.333739i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.48213 | + | 19.3382i | 0.256646 | + | 1.10730i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.43241i | − | 0.538336i | −0.963093 | − | 0.269168i | \(-0.913251\pi\) | ||
0.963093 | − | 0.269168i | \(-0.0867487\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.89577 | 0.506062 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.9238 | 0.846251 | 0.423125 | − | 0.906071i | \(-0.360933\pi\) | ||||
0.423125 | + | 0.906071i | \(0.360933\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 11.8081i | − | 0.667436i | −0.942673 | − | 0.333718i | \(-0.891697\pi\) | ||
0.942673 | − | 0.333718i | \(-0.108303\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.53483 | − | 1.97817i | 0.480883 | − | 0.111457i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 8.68438i | − | 0.487764i | −0.969805 | − | 0.243882i | \(-0.921579\pi\) | ||
0.969805 | − | 0.243882i | \(-0.0784209\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.4203 | −1.14332 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.2578 | 0.851607 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.330911i | 0.0184124i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.2122 | − | 29.0123i | −0.788352 | − | 1.60931i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.6445i | 0.699240i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.5052 | −1.24075 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.2191 | −0.946446 | −0.473223 | − | 0.880943i | \(-0.656909\pi\) | ||||
−0.473223 | + | 0.880943i | \(0.656909\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.50660i | − | 0.137361i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.17832 | + | 0.504884i | −0.119015 | + | 0.0275847i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.800375i | 0.0435992i | 0.999762 | + | 0.0217996i | \(0.00693958\pi\) | ||||
−0.999762 | + | 0.0217996i | \(0.993060\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.2895 | −0.558850 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.2617 | −0.934771 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.29442i | 0.285872i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.67389 | − | 15.8510i | −0.197796 | − | 0.853390i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 7.50758i | − | 0.403028i | −0.979486 | − | 0.201514i | \(-0.935414\pi\) | ||
0.979486 | − | 0.201514i | \(-0.0645862\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.4840 | 0.561194 | 0.280597 | − | 0.959826i | \(-0.409468\pi\) | ||||
0.280597 | + | 0.959826i | \(0.409468\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.46128 | −0.344877 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 35.7951i | − | 1.90518i | −0.304255 | − | 0.952591i | \(-0.598408\pi\) | ||
0.304255 | − | 0.952591i | \(-0.401592\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.93604 | − | 8.35305i | −0.102754 | − | 0.443334i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.36631i | 0.125239i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.9078 | −1.57847 | −0.789236 | − | 0.614090i | \(-0.789523\pi\) | ||||
−0.789236 | + | 0.614090i | \(0.789523\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6998 | −0.984200 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 0.985162i | − | 0.0517076i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 34.1167 | − | 7.90743i | 1.78575 | − | 0.413894i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.6154i | 1.23271i | 0.787468 | + | 0.616356i | \(0.211392\pi\) | ||||
−0.787468 | + | 0.616356i | \(0.788608\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.9146 | 0.568192 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.07228 | 0.419092 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.2685i | 0.635238i | 0.948218 | + | 0.317619i | \(0.102883\pi\) | ||||
−0.948218 | + | 0.317619i | \(0.897117\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.67053 | − | 7.05846i | 0.447744 | − | 0.364497i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 38.1117i | − | 1.96285i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.4821 | −0.589797 | −0.294899 | − | 0.955529i | \(-0.595286\pi\) | ||||
−0.294899 | + | 0.955529i | \(0.595286\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.92997 | −0.355033 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 6.02874i | − | 0.308054i | −0.988067 | − | 0.154027i | \(-0.950776\pi\) | ||
0.988067 | − | 0.154027i | \(-0.0492243\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −29.5472 | + | 6.84834i | −1.50587 | + | 0.349024i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.38640i | 0.172140i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.23972 | 0.417770 | 0.208885 | − | 0.977940i | \(-0.433017\pi\) | ||||
0.208885 | + | 0.977940i | \(0.433017\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.39475 | 0.222252 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 11.2951i | − | 0.569764i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.36103 | + | 18.8157i | 0.219427 | + | 0.946720i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 34.4987i | − | 1.73144i | −0.500530 | − | 0.865719i | \(-0.666861\pi\) | ||
0.500530 | − | 0.865719i | \(-0.333139\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.14676 | 0.107472 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.541548 | −0.0270436 | −0.0135218 | − | 0.999909i | \(-0.504304\pi\) | ||||
−0.0135218 | + | 0.999909i | \(0.504304\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 32.2165i | − | 1.60482i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.504884 | − | 2.17832i | −0.0250879 | − | 0.108242i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.67775i | 0.430140i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.24012 | −0.259107 | −0.129554 | − | 0.991572i | \(-0.541354\pi\) | ||||
−0.129554 | + | 0.991572i | \(0.541354\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.64778 | 0.377237 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 45.5741i | 2.24256i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.64381 | + | 2.00343i | −0.424308 | + | 0.0983445i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 3.12792i | − | 0.153175i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.5486 | 1.15042 | 0.575212 | − | 0.818004i | \(-0.304919\pi\) | ||||
0.575212 | + | 0.818004i | \(0.304919\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.6193 | 0.712503 | 0.356252 | − | 0.934390i | \(-0.384055\pi\) | ||||
0.356252 | + | 0.934390i | \(0.384055\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.74394i | 0.279280i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.32844 | + | 2.71184i | 0.0644390 | + | 0.131544i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 34.7829i | 1.68326i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 22.3687 | 1.07997 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.4405 | 0.647406 | 0.323703 | − | 0.946159i | \(-0.395072\pi\) | ||||
0.323703 | + | 0.946159i | \(0.395072\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.12100i | 0.0538718i | 0.999637 | + | 0.0269359i | \(0.00857500\pi\) | ||||
−0.999637 | + | 0.0269359i | \(0.991425\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.8488 | − | 2.97804i | 0.616052 | − | 0.142786i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 3.98700i | − | 0.190724i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.7882 | −0.801258 | −0.400629 | − | 0.916240i | \(-0.631208\pi\) | ||||
−0.400629 | + | 0.916240i | \(0.631208\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.35128 | 0.397680 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.6154i | 0.694399i | 0.937791 | + | 0.347200i | \(0.112867\pi\) | ||||
−0.937791 | + | 0.347200i | \(0.887133\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.31732 | + | 18.6271i | 0.204661 | + | 0.883010i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 13.5824i | − | 0.642426i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.7499 | 0.932055 | 0.466027 | − | 0.884770i | \(-0.345685\pi\) | ||||
0.466027 | + | 0.884770i | \(0.345685\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37.7859 | −1.77927 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.4695i | 0.679837i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.7815 | − | 55.1459i | −0.599206 | − | 2.58528i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.6243i | 1.52610i | 0.646338 | + | 0.763051i | \(0.276299\pi\) | ||||
−0.646338 | + | 0.763051i | \(0.723701\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.603948 | 0.0281899 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.0149658 | −0.000697028 | −0.000348514 | − | 1.00000i | \(-0.500111\pi\) | ||||
−0.000348514 | 1.00000i | \(0.500111\pi\) | ||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 41.8885i | 1.94672i | 0.229276 | + | 0.973361i | \(0.426364\pi\) | ||||
−0.229276 | + | 0.973361i | \(0.573636\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.8613 | − | 2.51740i | 0.503682 | − | 0.116742i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 1.82257i | − | 0.0843383i | −0.999110 | − | 0.0421692i | \(-0.986573\pi\) | ||
0.999110 | − | 0.0421692i | \(-0.0134268\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.91807 | −0.180920 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.0664 | −0.555993 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 11.7236i | − | 0.539050i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.46023 | − | 1.20519i | 0.112883 | − | 0.0552978i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 2.06027i | − | 0.0943332i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.0426 | 1.50975 | 0.754877 | − | 0.655866i | \(-0.227696\pi\) | ||||
0.754877 | + | 0.655866i | \(0.227696\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.1958 | −0.738466 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 28.5107i | − | 1.29728i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.3009 | + | 3.08283i | −0.603962 | + | 0.139984i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.4966i | 0.838161i | 0.907949 | + | 0.419081i | \(0.137648\pi\) | ||||
−0.907949 | + | 0.419081i | \(0.862352\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.01144 | 0.136182 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.9057 | 1.03372 | 0.516861 | − | 0.856069i | \(-0.327100\pi\) | ||||
0.516861 | + | 0.856069i | \(0.327100\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.56238i | 0.160441i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.74789 | + | 7.54127i | 0.0785617 | + | 0.338955i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 15.0243i | − | 0.673933i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.99474 | 0.313127 | 0.156564 | − | 0.987668i | \(-0.449958\pi\) | ||||
0.156564 | + | 0.987668i | \(0.449958\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.13904 | 0.274272 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.7114i | 0.878887i | 0.898270 | + | 0.439443i | \(0.144824\pi\) | ||||
−0.898270 | + | 0.439443i | \(0.855176\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.93305 | − | 12.6547i | −0.130519 | − | 0.563125i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28.7481i | 1.27675i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.6555 | −0.472298 | −0.236149 | − | 0.971717i | \(-0.575885\pi\) | ||||
−0.236149 | + | 0.971717i | \(0.575885\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 61.3644 | 2.71460 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 0.547912i | − | 0.0241909i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.3779 | − | 4.49133i | 0.853890 | − | 0.197911i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 19.8853i | − | 0.874554i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.831968 | 0.0365193 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.2288 | 1.32435 | 0.662173 | − | 0.749351i | \(-0.269634\pi\) | ||||
0.662173 | + | 0.749351i | \(0.269634\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 22.0987i | − | 0.966307i | −0.875536 | − | 0.483154i | \(-0.839491\pi\) | ||
0.875536 | − | 0.483154i | \(-0.160509\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.5929 | − | 8.61819i | 0.767816 | − | 0.376129i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.01134i | 0.131176i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −29.9505 | −1.30219 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.6318 | 0.504776 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 70.5223i | − | 3.05466i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.2364 | − | 7.70341i | 1.43693 | − | 0.333047i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 13.4026i | − | 0.578363i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −28.9118 | −1.24532 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.7919 | 1.40983 | 0.704917 | − | 0.709290i | \(-0.250984\pi\) | ||||
0.704917 | + | 0.709290i | \(0.250984\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.84980i | 0.122297i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.38398 | + | 27.5437i | 0.273460 | + | 1.17984i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.72673i | 0.159344i | 0.996821 | + | 0.0796718i | \(0.0253872\pi\) | ||||
−0.996821 | + | 0.0796718i | \(0.974613\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.87755 | 0.378885 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.23185 | 0.137681 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 33.8431i | 1.43916i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.26554 | − | 5.46018i | −0.0537192 | − | 0.231772i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.1249i | 1.53066i | 0.643637 | + | 0.765331i | \(0.277425\pi\) | ||||
−0.643637 | + | 0.765331i | \(0.722575\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.8804 | 0.925444 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.09084 | −0.0882755 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.1739i | 0.723795i | 0.932218 | + | 0.361897i | \(0.117871\pi\) | ||||
−0.932218 | + | 0.361897i | \(0.882129\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.4139 | + | 5.19501i | −0.942959 | + | 0.218556i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 3.91807i | − | 0.164544i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.6756 | −0.950611 | −0.475306 | − | 0.879821i | \(-0.657662\pi\) | ||||
−0.475306 | + | 0.879821i | \(0.657662\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.6790 | −1.70236 | −0.851181 | − | 0.524871i | \(-0.824113\pi\) | ||||
−0.851181 | + | 0.524871i | \(0.824113\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 16.8329i | − | 0.703203i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.0058 | − | 32.6738i | −0.667490 | − | 1.36259i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 3.02853i | − | 0.126079i | −0.998011 | − | 0.0630397i | \(-0.979921\pi\) | ||
0.998011 | − | 0.0630397i | \(-0.0200795\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −25.5455 | −1.06164 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.5473 | −0.645011 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.13256i | 0.295401i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14.0747 | + | 3.26219i | −0.581919 | + | 0.134875i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.9045i | 0.450077i | 0.974350 | + | 0.225038i | \(0.0722508\pi\) | ||||
−0.974350 | + | 0.225038i | \(0.927749\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.73194 | 0.112568 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.3050 | 0.506160 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.8092i | 1.34731i | 0.739045 | + | 0.673656i | \(0.235277\pi\) | ||||
−0.739045 | + | 0.673656i | \(0.764723\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.19471 | + | 5.15459i | 0.0489784 | + | 0.211318i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 8.79978i | − | 0.360151i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.48832 | −0.265105 | −0.132553 | − | 0.991176i | \(-0.542317\pi\) | ||||
−0.132553 | + | 0.991176i | \(0.542317\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.7975 | −1.41942 | −0.709709 | − | 0.704495i | \(-0.751174\pi\) | ||||
−0.709709 | + | 0.704495i | \(0.751174\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000i | 0.0407231i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.497392 | − | 2.14600i | −0.0202219 | − | 0.0872474i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.6684i | 1.61009i | 0.593214 | + | 0.805045i | \(0.297859\pi\) | ||||
−0.593214 | + | 0.805045i | \(0.702141\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 23.1107 | 0.936491 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.1132 | 1.50144 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 39.2040i | − | 1.58343i | −0.610888 | − | 0.791717i | \(-0.709187\pi\) | ||
0.610888 | − | 0.791717i | \(-0.290813\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 23.7755 | − | 5.51061i | 0.958723 | − | 0.222209i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.92069i | − | 0.318875i | −0.987208 | − | 0.159438i | \(-0.949032\pi\) | ||
0.987208 | − | 0.159438i | \(-0.0509681\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.6071 | −0.788075 | −0.394038 | − | 0.919094i | \(-0.628922\pi\) | ||||
−0.394038 | + | 0.919094i | \(0.628922\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.27671 | −0.292004 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 33.5039i | 1.34231i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.3235 | − | 19.7532i | 0.612941 | − | 0.790129i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.89685i | 0.0757529i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.51386 | 0.0603614 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.0601 | 1.35591 | 0.677956 | − | 0.735103i | \(-0.262866\pi\) | ||||
0.677956 | + | 0.735103i | \(0.262866\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.6312i | 0.462300i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.0957 | + | 3.49883i | −0.599055 | + | 0.138847i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 53.9599i | − | 2.13797i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.83462 | −0.151695 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.5681 | −0.496410 | −0.248205 | − | 0.968708i | \(-0.579841\pi\) | ||||
−0.248205 | + | 0.968708i | \(0.579841\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 32.1584i | − | 1.26821i | −0.773249 | − | 0.634103i | \(-0.781370\pi\) | ||
0.773249 | − | 0.634103i | \(-0.218630\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.70974 | + | 7.37666i | 0.0673208 | + | 0.290456i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.2256i | 1.58143i | 0.612183 | + | 0.790716i | \(0.290291\pi\) | ||||
−0.612183 | + | 0.790716i | \(0.709709\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −40.2687 | −1.58069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.5359 | 0.765671 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.59191i | 0.218828i | 0.993996 | + | 0.109414i | \(0.0348975\pi\) | ||||
−0.993996 | + | 0.109414i | \(0.965103\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.70273 | − | 24.6045i | −0.222824 | − | 0.961376i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 15.6619i | − | 0.611029i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.77383 | −0.341780 | −0.170890 | − | 0.985290i | \(-0.554664\pi\) | ||||
−0.170890 | + | 0.985290i | \(0.554664\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.1677 | −0.395476 | −0.197738 | − | 0.980255i | \(-0.563360\pi\) | ||||
−0.197738 | + | 0.980255i | \(0.563360\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 3.90228i | − | 0.151552i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.67633 | − | 1.08386i | 0.181340 | − | 0.0420304i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 42.9215i | − | 1.66193i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.7044 | −0.723153 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.7337 | −1.18646 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 40.4943i | − | 1.56094i | −0.625193 | − | 0.780470i | \(-0.714980\pi\) | ||
0.625193 | − | 0.780470i | \(-0.285020\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.19960 | − | 4.49019i | −0.0846626 | − | 0.172827i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 24.3471i | − | 0.935736i | −0.883798 | − | 0.467868i | \(-0.845022\pi\) | ||
0.883798 | − | 0.467868i | \(-0.154978\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.9238 | −0.918112 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.1922 | −0.390568 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 33.2757i | − | 1.27326i | −0.771170 | − | 0.636629i | \(-0.780328\pi\) | ||
0.771170 | − | 0.636629i | \(-0.219672\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.6593 | − | 3.86124i | 0.636521 | − | 0.147530i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 0.810691i | − | 0.0309298i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.3120 | −0.507145 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.3331 | −1.68651 | −0.843254 | − | 0.537515i | \(-0.819363\pi\) | ||||
−0.843254 | + | 0.537515i | \(0.819363\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.5642i | 0.515261i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.57923 | − | 6.81361i | −0.0599037 | − | 0.258455i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.59186i | 0.249684i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.4579 | −0.962907 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.22873 | −0.197486 | −0.0987432 | − | 0.995113i | \(-0.531482\pi\) | ||||
−0.0987432 | + | 0.995113i | \(0.531482\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.37340i | − | 0.0517986i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.90002 | + | 12.5122i | 0.109221 | + | 0.471235i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 22.7615i | − | 0.856034i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.0683 | −0.565904 | −0.282952 | − | 0.959134i | \(-0.591314\pi\) | ||||
−0.282952 | + | 0.959134i | \(0.591314\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.63769 | 0.323939 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 36.2823i | − | 1.35878i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 48.7262 | − | 11.2936i | 1.82226 | − | 0.422356i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.47427i | 0.316477i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.7462 | −1.22123 | −0.610613 | − | 0.791929i | \(-0.709077\pi\) | ||||
−0.610613 | + | 0.791929i | \(0.709077\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.8542 | 1.29804 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.25751i | 0.269910i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 26.4853 | − | 12.9743i | 0.983638 | − | 0.481853i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.0445i | 1.00302i | 0.865151 | + | 0.501512i | \(0.167223\pi\) | ||||
−0.865151 | + | 0.501512i | \(0.832777\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.04521 | −0.0756447 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 48.5035i | − | 1.79152i | −0.444540 | − | 0.895759i | \(-0.646633\pi\) | ||
0.444540 | − | 0.895759i | \(-0.353367\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18.1918 | − | 4.21642i | 0.671014 | − | 0.155525i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 3.46196i | − | 0.127523i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.1169 | 0.813585 | 0.406793 | − | 0.913521i | \(-0.366647\pi\) | ||||
0.406793 | + | 0.913521i | \(0.366647\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.54021 | −0.130053 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.8252i | 1.31430i | 0.753760 | + | 0.657149i | \(0.228238\pi\) | ||||
−0.753760 | + | 0.657149i | \(0.771762\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.85754 | − | 29.5869i | −0.251241 | − | 1.08398i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.96810i | 0.145185i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 59.7811 | 2.18435 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.8290 | −1.63583 | −0.817916 | − | 0.575337i | \(-0.804871\pi\) | ||||
−0.817916 | + | 0.575337i | \(0.804871\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.98355i | 0.327379i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.30542 | + | 31.5193i | 0.265871 | + | 1.14710i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 9.34434i | − | 0.339626i | −0.985476 | − | 0.169813i | \(-0.945684\pi\) | ||
0.985476 | − | 0.169813i | \(-0.0543163\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25.1917 | 0.914399 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.3896 | −0.557872 | −0.278936 | − | 0.960310i | \(-0.589982\pi\) | ||||
−0.278936 | + | 0.960310i | \(0.589982\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 49.5419i | 1.79354i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.31559 | − | 0.304924i | 0.0475654 | − | 0.0110245i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 75.1561i | − | 2.71373i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.737169 | 0.0265830 | 0.0132915 | − | 0.999912i | \(-0.495769\pi\) | ||||
0.0132915 | + | 0.999912i | \(0.495769\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.42681 | −0.303484 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 23.9712i | − | 0.862183i | −0.902308 | − | 0.431092i | \(-0.858129\pi\) | ||
0.902308 | − | 0.431092i | \(-0.141871\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.3885 | − | 10.9674i | 0.804218 | − | 0.393961i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 9.82103i | − | 0.352328i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.98025 | 0.214265 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.2753 | 0.475028 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 5.89848i | − | 0.210794i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26.2846 | + | 6.09215i | −0.938139 | + | 0.217438i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.7716i | 1.63158i | 0.578348 | + | 0.815790i | \(0.303698\pi\) | ||||
−0.578348 | + | 0.815790i | \(0.696302\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.4437 | −0.371806 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −40.3150 | −1.43344 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 57.3603i | − | 2.03692i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.04020 | − | 4.48793i | −0.0368919 | − | 0.159170i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.1114i | 0.606118i | 0.952972 | + | 0.303059i | \(0.0980079\pi\) | ||||
−0.952972 | + | 0.303059i | \(0.901992\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.46904 | −0.122726 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.55112 | 0.302139 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 54.2208i | 1.91341i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.3946 | − | 62.1054i | −0.507342 | − | 2.18893i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.6313i | 0.515044i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.4356 | −0.859108 | −0.429554 | − | 0.903041i | \(-0.641329\pi\) | ||||
−0.429554 | + | 0.903041i | \(0.641329\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.8846 | 0.979159 | 0.489580 | − | 0.871959i | \(-0.337150\pi\) | ||||
0.489580 | + | 0.871959i | \(0.337150\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.6460i | 0.899443i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.55988 | − | 1.52043i | 0.229783 | − | 0.0532582i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.85545i | 0.0649139i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −25.3157 | −0.884603 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 50.5171 | 1.76306 | 0.881529 | − | 0.472130i | \(-0.156515\pi\) | ||||
0.881529 | + | 0.472130i | \(0.156515\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.27173i | 0.0791877i | 0.999216 | + | 0.0395938i | \(0.0126064\pi\) | ||||
−0.999216 | + | 0.0395938i | \(0.987394\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.61492 | + | 15.5448i | 0.265118 | + | 0.541202i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.1035i | 0.977255i | 0.872493 | + | 0.488628i | \(0.162502\pi\) | ||||
−0.872493 | + | 0.488628i | \(0.837498\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.32146 | 0.289016 | 0.144508 | − | 0.989504i | \(-0.453840\pi\) | ||||
0.144508 | + | 0.989504i | \(0.453840\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.7897 | 0.408979 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.04374i | 0.174755i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.3728 | − | 3.09950i | 0.462785 | − | 0.107263i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 4.98609i | − | 0.172345i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.9638 | 0.620180 | 0.310090 | − | 0.950707i | \(-0.399641\pi\) | ||||
0.310090 | + | 0.950707i | \(0.399641\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.79204 | 0.199726 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 33.1194i | − | 1.14069i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.5144 | + | 62.6226i | 0.499312 | + | 2.15428i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 3.85994i | − | 0.132629i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.9719 | −0.616793 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.2398 | −0.625252 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.3553i | 0.799670i | 0.916587 | + | 0.399835i | \(0.130933\pi\) | ||||
−0.916587 | + | 0.399835i | \(0.869067\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.276632 | − | 1.19353i | −0.00946061 | − | 0.0408179i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 30.8571i | − | 1.05406i | −0.849847 | − | 0.527030i | \(-0.823306\pi\) | ||
0.849847 | − | 0.527030i | \(-0.176694\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.73172 | 0.263803 | 0.131901 | − | 0.991263i | \(-0.457892\pi\) | ||||
0.131901 | + | 0.991263i | \(0.457892\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 42.7642 | 1.45740 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 25.8219i | − | 0.878988i | −0.898246 | − | 0.439494i | \(-0.855158\pi\) | ||
0.898246 | − | 0.439494i | \(-0.144842\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.81229 | − | 0.420047i | 0.0616199 | − | 0.0142820i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 16.6352i | − | 0.564963i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.9033 | −1.01440 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.46128 | 0.218932 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.10602i | 0.206658i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 33.9718 | − | 27.6555i | 1.14846 | − | 0.934928i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 34.9129i | − | 1.17893i | −0.807796 | − | 0.589463i | \(-0.799340\pi\) | ||
0.807796 | − | 0.589463i | \(-0.200660\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.64494 | −0.190399 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.64568 | −0.257590 | −0.128795 | − | 0.991671i | \(-0.541111\pi\) | ||||
−0.128795 | + | 0.991671i | \(0.541111\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 39.8365i | − | 1.34061i | −0.742088 | − | 0.670303i | \(-0.766164\pi\) | ||
0.742088 | − | 0.670303i | \(-0.233836\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 25.3378 | − | 5.87269i | 0.851720 | − | 0.197408i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 44.8255i | − | 1.50509i | −0.658540 | − | 0.752546i | \(-0.728825\pi\) | ||
0.658540 | − | 0.752546i | \(-0.271175\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.1521 | −0.910652 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.46196 | 0.115980 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.14717i | 0.105316i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.76673 | − | 29.1951i | −0.226187 | − | 0.975885i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 47.0168i | 1.56985i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 29.4104 | 0.980891 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.24430 | 0.0414535 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13.2681i | 0.441536i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.43882 | + | 6.20779i | 0.0478280 | + | 0.206354i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 44.9035i | − | 1.49100i | −0.666507 | − | 0.745499i | \(-0.732211\pi\) | ||
0.666507 | − | 0.745499i | \(-0.267789\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.80936 | −0.192684 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.4536 | 1.67160 | 0.835801 | − | 0.549033i | \(-0.185004\pi\) | ||||
0.835801 | + | 0.549033i | \(0.185004\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 13.7374i | − | 0.454642i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 19.3382 | − | 4.48213i | 0.639301 | − | 0.148175i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 44.2552i | − | 1.46143i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.06058 | 0.298881 | 0.149440 | − | 0.988771i | \(-0.452253\pi\) | ||||
0.149440 | + | 0.988771i | \(0.452253\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.43241 | −0.310809 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.7765i | 0.815530i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.51351 | − | 11.2551i | −0.181283 | − | 0.370065i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 8.89577i | − | 0.292175i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.64875 | 0.316565 | 0.158283 | − | 0.987394i | \(-0.449404\pi\) | ||||
0.158283 | + | 0.987394i | \(0.449404\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.57577 | 0.149965 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 14.9238i | − | 0.488583i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.55454 | + | 1.05563i | −0.148949 | + | 0.0345229i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 55.2866i | 1.80614i | 0.429498 | + | 0.903068i | \(0.358691\pi\) | ||||
−0.429498 | + | 0.903068i | \(0.641309\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.8081 | −0.385344 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.1042 | −0.329389 | −0.164694 | − | 0.986345i | \(-0.552664\pi\) | ||||
−0.164694 | + | 0.986345i | \(0.552664\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 79.4224i | − | 2.58635i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.97817 | − | 8.53483i | −0.0643499 | − | 0.277638i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37.8353i | 1.22948i | 0.788729 | + | 0.614742i | \(0.210740\pi\) | ||||
−0.788729 | + | 0.614742i | \(0.789260\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −101.196 | −3.28495 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.68438 | −0.281610 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 7.04738i | − | 0.228287i | −0.993464 | − | 0.114144i | \(-0.963588\pi\) | ||
0.993464 | − | 0.114144i | \(-0.0364124\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.49864 | − | 36.6674i | −0.275010 | − | 1.18653i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.4203i | 0.660094i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29.9646 | 0.967606 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.13886 | −0.198028 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 15.2578i | − | 0.491675i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −55.6464 | + | 12.8975i | −1.79132 | + | 0.415186i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.1142i | 1.06488i | 0.846468 | + | 0.532440i | \(0.178725\pi\) | ||||
−0.846468 | + | 0.532440i | \(0.821275\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.330911 | 0.0106304 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.1803 | −0.743892 | −0.371946 | − | 0.928254i | \(-0.621309\pi\) | ||||
−0.371946 | + | 0.928254i | \(0.621309\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 12.2554i | − | 0.392890i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −29.0123 | + | 14.2122i | −0.929138 | + | 0.455155i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 4.06291i | − | 0.129984i | −0.997886 | − | 0.0649920i | \(-0.979298\pi\) | ||
0.997886 | − | 0.0649920i | \(-0.0207022\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.6036 | −0.946137 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.6445 | 0.403707 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 56.3829i | 1.79834i | 0.437604 | + | 0.899168i | \(0.355827\pi\) | ||||
−0.437604 | + | 0.899168i | \(0.644173\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.8043 | − | 6.21260i | 0.854056 | − | 0.197950i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.5052i | 0.716347i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.6418 | 0.783564 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.0186 | −0.667677 | −0.333838 | − | 0.942630i | \(-0.608344\pi\) | ||||
−0.333838 | + | 0.942630i | \(0.608344\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.2191i | 0.546431i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.44287 | − | 19.1688i | −0.140848 | − | 0.607691i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 39.5688i | − | 1.25316i | −0.779358 | − | 0.626578i | \(-0.784455\pi\) | ||
0.779358 | − | 0.626578i | \(-0.215545\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.50660 | −0.0793053 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4020.2.g.c.1609.10 | ✓ | 38 | |
5.4 | even | 2 | inner | 4020.2.g.c.1609.29 | yes | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.c.1609.10 | ✓ | 38 | 1.1 | even | 1 | trivial | |
4020.2.g.c.1609.29 | yes | 38 | 5.4 | even | 2 | inner |