Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.a (trivial) |
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: | yes |
Analytic conductor: | \(64.1677830643\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 30 x^{18} + 128 x^{17} + 348 x^{16} - 1644 x^{15} - 1934 x^{14} + 10948 x^{13} + 4748 x^{12} - 40524 x^{11} - 220 x^{10} + 82500 x^{9} - 21992 x^{8} - 84720 x^{7} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(0.538932\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 0.538932 | 0.311152 | 0.155576 | − | 0.987824i | \(-0.450277\pi\) | ||||
0.155576 | + | 0.987824i | \(0.450277\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.810745 | 0.362576 | 0.181288 | − | 0.983430i | \(-0.441973\pi\) | ||||
0.181288 | + | 0.983430i | \(0.441973\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.70955 | −0.903184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.92893 | 1.48613 | 0.743064 | − | 0.669220i | \(-0.233372\pi\) | ||||
0.743064 | + | 0.669220i | \(0.233372\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0654121 | 0.0181421 | 0.00907103 | − | 0.999959i | \(-0.497113\pi\) | ||||
0.00907103 | + | 0.999959i | \(0.497113\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.436937 | 0.112817 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.24015 | −0.300782 | −0.150391 | − | 0.988627i | \(-0.548053\pi\) | ||||
−0.150391 | + | 0.988627i | \(0.548053\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.82383 | 0.877247 | 0.438623 | − | 0.898671i | \(-0.355466\pi\) | ||||
0.438623 | + | 0.898671i | \(0.355466\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.71957 | −0.358556 | −0.179278 | − | 0.983798i | \(-0.557376\pi\) | ||||
−0.179278 | + | 0.983798i | \(0.557376\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.34269 | −0.868538 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.07706 | −0.592180 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.89893 | 0.724014 | 0.362007 | − | 0.932175i | \(-0.382092\pi\) | ||||
0.362007 | + | 0.932175i | \(0.382092\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.19907 | 0.574570 | 0.287285 | − | 0.957845i | \(-0.407247\pi\) | ||||
0.287285 | + | 0.957845i | \(0.407247\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.65636 | 0.462413 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.0930044 | −0.0152898 | −0.00764492 | − | 0.999971i | \(-0.502433\pi\) | ||||
−0.00764492 | + | 0.999971i | \(0.502433\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0352527 | 0.00564495 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.5630 | 1.61084 | 0.805421 | − | 0.592703i | \(-0.201939\pi\) | ||||
0.805421 | + | 0.592703i | \(0.201939\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.19676 | −0.327473 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.959640 | −0.139978 | −0.0699889 | − | 0.997548i | \(-0.522296\pi\) | ||||
−0.0699889 | + | 0.997548i | \(0.522296\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.668359 | −0.0935890 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.72668 | −0.374539 | −0.187269 | − | 0.982309i | \(-0.559964\pi\) | ||||
−0.187269 | + | 0.982309i | \(0.559964\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.99611 | 0.538835 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.06078 | 0.272958 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.1898 | 1.45679 | 0.728393 | − | 0.685160i | \(-0.240268\pi\) | ||||
0.728393 | + | 0.685160i | \(0.240268\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8004 | −1.38285 | −0.691423 | − | 0.722450i | \(-0.743016\pi\) | ||||
−0.691423 | + | 0.722450i | \(0.743016\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0530326 | 0.00657788 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3531 | 1.26483 | 0.632414 | − | 0.774630i | \(-0.282064\pi\) | ||||
0.632414 | + | 0.774630i | \(0.282064\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.926733 | −0.111566 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.60052 | −0.664659 | −0.332330 | − | 0.943163i | \(-0.607835\pi\) | ||||
−0.332330 | + | 0.943163i | \(0.607835\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.76947 | 0.324141 | 0.162071 | − | 0.986779i | \(-0.448183\pi\) | ||||
0.162071 | + | 0.986779i | \(0.448183\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.34041 | −0.270248 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.2539 | −1.82870 | −0.914352 | − | 0.404921i | \(-0.867299\pi\) | ||||
−0.914352 | + | 0.404921i | \(0.867299\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.47033 | 0.718926 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.99122 | 1.09668 | 0.548340 | − | 0.836256i | \(-0.315260\pi\) | ||||
0.548340 | + | 0.836256i | \(0.315260\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.00545 | −0.109056 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.10126 | 0.225279 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.8641 | 1.25760 | 0.628799 | − | 0.777568i | \(-0.283547\pi\) | ||||
0.628799 | + | 0.777568i | \(0.283547\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.72408 | 0.178779 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.10015 | 0.318069 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.31445 | 0.641136 | 0.320568 | − | 0.947226i | \(-0.396126\pi\) | ||||
0.320568 | + | 0.947226i | \(0.396126\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.3552 | −1.34225 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.5369 | −1.24747 | −0.623735 | − | 0.781636i | \(-0.714386\pi\) | ||||
−0.623735 | + | 0.781636i | \(0.714386\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.0340 | 1.77695 | 0.888473 | − | 0.458929i | \(-0.151767\pi\) | ||||
0.888473 | + | 0.458929i | \(0.151767\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.09750 | 0.879488 | 0.439744 | − | 0.898123i | \(-0.355069\pi\) | ||||
0.439744 | + | 0.898123i | \(0.355069\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.88562 | 0.946870 | 0.473435 | − | 0.880829i | \(-0.343014\pi\) | ||||
0.473435 | + | 0.880829i | \(0.343014\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0501230 | −0.00475747 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.45002 | −0.794911 | −0.397455 | − | 0.917622i | \(-0.630107\pi\) | ||||
−0.397455 | + | 0.917622i | \(0.630107\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.39414 | −0.130004 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.177238 | −0.0163856 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.2944 | 1.20858 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.538932 | −0.0485938 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.57454 | −0.677488 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.19115 | 0.549376 | 0.274688 | − | 0.961533i | \(-0.411425\pi\) | ||||
0.274688 | + | 0.961533i | \(0.411425\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.69274 | 0.501218 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.990027 | 0.0864990 | 0.0432495 | − | 0.999064i | \(-0.486229\pi\) | ||||
0.0432495 | + | 0.999064i | \(0.486229\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.49471 | −0.214711 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.78181 | 0.323102 | 0.161551 | − | 0.986864i | \(-0.448350\pi\) | ||||
0.161551 | + | 0.986864i | \(0.448350\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.3431 | −1.55584 | −0.777920 | − | 0.628364i | \(-0.783725\pi\) | ||||
−0.777920 | + | 0.628364i | \(0.783725\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.517181 | −0.0435545 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.322412 | 0.0269614 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.16104 | 0.262510 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.01195 | −0.410595 | −0.205297 | − | 0.978700i | \(-0.565816\pi\) | ||||
−0.205297 | + | 0.978700i | \(0.565816\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.4822 | 1.74819 | 0.874097 | − | 0.485751i | \(-0.161454\pi\) | ||||
0.874097 | + | 0.485751i | \(0.161454\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.36026 | 0.271661 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.59363 | 0.208325 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.8416 | −0.865255 | −0.432627 | − | 0.901573i | \(-0.642413\pi\) | ||||
−0.432627 | + | 0.901573i | \(0.642413\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.46950 | −0.116539 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.1435 | −1.49943 | −0.749717 | − | 0.661759i | \(-0.769810\pi\) | ||||
−0.749717 | + | 0.661759i | \(0.769810\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.15363 | 0.167660 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.3883 | 1.65508 | 0.827538 | − | 0.561409i | \(-0.189741\pi\) | ||||
0.827538 | + | 0.561409i | \(0.189741\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9957 | −0.999671 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.3609 | −0.792316 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.49170 | 0.645612 | 0.322806 | − | 0.946465i | \(-0.395374\pi\) | ||||
0.322806 | + | 0.946465i | \(0.395374\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.03053 | 0.453282 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.17881 | 0.312339 | 0.156169 | − | 0.987730i | \(-0.450085\pi\) | ||||
0.156169 | + | 0.987730i | \(0.450085\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.46457 | 0.554837 | 0.277418 | − | 0.960749i | \(-0.410521\pi\) | ||||
0.277418 | + | 0.960749i | \(0.410521\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.82066 | −0.430276 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0754029 | −0.00554373 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.11264 | −0.447000 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.0481 | 0.799413 | 0.399706 | − | 0.916643i | \(-0.369112\pi\) | ||||
0.399706 | + | 0.916643i | \(0.369112\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.37310 | 0.170819 | 0.0854097 | − | 0.996346i | \(-0.472780\pi\) | ||||
0.0854097 | + | 0.996346i | \(0.472780\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0285809 | 0.00204672 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.9369 | −1.70543 | −0.852717 | − | 0.522374i | \(-0.825047\pi\) | ||||
−0.852717 | + | 0.522374i | \(0.825047\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.28061 | 0.374333 | 0.187166 | − | 0.982328i | \(-0.440070\pi\) | ||||
0.187166 | + | 0.982328i | \(0.440070\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.57960 | 0.393555 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.810745 | −0.0566249 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.65928 | 0.323842 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.8474 | 1.30370 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.31065 | −0.227915 | −0.113957 | − | 0.993486i | \(-0.536353\pi\) | ||||
−0.113957 | + | 0.993486i | \(0.536353\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.01830 | −0.206810 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.56390 | 0.584053 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.49255 | 0.100857 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.0811212 | −0.00545680 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.6139 | −1.44738 | −0.723688 | − | 0.690127i | \(-0.757555\pi\) | ||||
−0.723688 | + | 0.690127i | \(0.757555\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.7668 | 0.784450 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.01651 | 0.532074 | 0.266037 | − | 0.963963i | \(-0.414286\pi\) | ||||
0.266037 | + | 0.963963i | \(0.414286\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.03296 | 0.0682598 | 0.0341299 | − | 0.999417i | \(-0.489134\pi\) | ||||
0.0341299 | + | 0.999417i | \(0.489134\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.7626 | 1.36020 | 0.680100 | − | 0.733119i | \(-0.261936\pi\) | ||||
0.680100 | + | 0.733119i | \(0.261936\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.778024 | −0.0507527 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.75973 | −0.569005 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.91757 | −0.512145 | −0.256073 | − | 0.966658i | \(-0.582429\pi\) | ||||
−0.256073 | + | 0.966658i | \(0.582429\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.2523 | 1.30457 | 0.652283 | − | 0.757975i | \(-0.273811\pi\) | ||||
0.652283 | + | 0.757975i | \(0.273811\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.7182 | 0.815876 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.250125 | 0.0159151 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.38459 | 0.341234 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.28654 | −0.0812058 | −0.0406029 | − | 0.999175i | \(-0.512928\pi\) | ||||
−0.0406029 | + | 0.999175i | \(0.512928\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.47567 | −0.532861 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.541869 | −0.0339331 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.86057 | 0.427951 | 0.213975 | − | 0.976839i | \(-0.431359\pi\) | ||||
0.213975 | + | 0.976839i | \(0.431359\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.5644 | −0.653918 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.28050 | 0.263947 | 0.131974 | − | 0.991253i | \(-0.457869\pi\) | ||||
0.131974 | + | 0.991253i | \(0.457869\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.21065 | −0.135799 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.39397 | 0.391304 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.24205 | 0.502527 | 0.251263 | − | 0.967919i | \(-0.419154\pi\) | ||||
0.251263 | + | 0.967919i | \(0.419154\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.4651 | 1.60764 | 0.803820 | − | 0.594873i | \(-0.202797\pi\) | ||||
0.803820 | + | 0.594873i | \(0.202797\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.4048 | −1.29076 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.1377 | 0.909537 | 0.454769 | − | 0.890610i | \(-0.349722\pi\) | ||||
0.454769 | + | 0.890610i | \(0.349722\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.66805 | −0.518942 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.51773 | −0.269505 | −0.134753 | − | 0.990879i | \(-0.543024\pi\) | ||||
−0.134753 | + | 0.990879i | \(0.543024\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.9377 | 1.83906 | 0.919529 | − | 0.393022i | \(-0.128571\pi\) | ||||
0.919529 | + | 0.393022i | \(0.128571\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.67077 | 0.0989679 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.4620 | −0.909530 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.40306 | 0.199491 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.5755 | 0.734667 | 0.367334 | − | 0.930089i | \(-0.380271\pi\) | ||||
0.367334 | + | 0.930089i | \(0.380271\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.07206 | 0.528196 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.1666 | −0.880056 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.112481 | −0.00650495 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.75655 | −0.388154 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.75635 | −0.501387 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.0695 | 0.745919 | 0.372959 | − | 0.927848i | \(-0.378343\pi\) | ||||
0.372959 | + | 0.927848i | \(0.378343\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.71911 | 0.552901 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.9072 | 1.01542 | 0.507712 | − | 0.861527i | \(-0.330492\pi\) | ||||
0.507712 | + | 0.861527i | \(0.330492\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.1024 | −0.684070 | −0.342035 | − | 0.939687i | \(-0.611116\pi\) | ||||
−0.342035 | + | 0.939687i | \(0.611116\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.9366 | −0.895089 | −0.447544 | − | 0.894262i | \(-0.647701\pi\) | ||||
−0.447544 | + | 0.894262i | \(0.647701\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.2176 | 1.07598 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.90293 | 0.273655 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.74214 | −0.263860 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.284065 | −0.0157571 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.32767 | 0.294621 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.4334 | 0.573473 | 0.286737 | − | 0.958009i | \(-0.407430\pi\) | ||||
0.286737 | + | 0.958009i | \(0.407430\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.252000 | 0.0138095 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.39370 | 0.458597 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.66374 | −0.417470 | −0.208735 | − | 0.977972i | \(-0.566935\pi\) | ||||
−0.208735 | + | 0.977972i | \(0.566935\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.55398 | −0.247338 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.7680 | 0.853885 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.751345 | −0.0404510 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.4021 | −1.25629 | −0.628146 | − | 0.778095i | \(-0.716186\pi\) | ||||
−0.628146 | + | 0.778095i | \(0.716186\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.4181 | 0.771781 | 0.385891 | − | 0.922545i | \(-0.373894\pi\) | ||||
0.385891 | + | 0.922545i | \(0.373894\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.201277 | −0.0107434 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.4990 | 1.83619 | 0.918097 | − | 0.396355i | \(-0.129725\pi\) | ||||
0.918097 | + | 0.396355i | \(0.129725\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.54060 | −0.240990 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.75593 | −0.198231 | −0.0991153 | − | 0.995076i | \(-0.531601\pi\) | ||||
−0.0991153 | + | 0.995076i | \(0.531601\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.37832 | −0.230438 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.16476 | 0.376052 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.24533 | 0.117526 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.7801 | 1.03251 | 0.516255 | − | 0.856435i | \(-0.327326\pi\) | ||||
0.516255 | + | 0.856435i | \(0.327326\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.70955 | 0.141054 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.5124 | −1.32098 | −0.660490 | − | 0.750835i | \(-0.729651\pi\) | ||||
−0.660490 | + | 0.750835i | \(0.729651\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.08216 | −0.210802 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.255038 | 0.0131351 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.1317 | 0.674529 | 0.337264 | − | 0.941410i | \(-0.390498\pi\) | ||||
0.337264 | + | 0.941410i | \(0.390498\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.33661 | 0.170940 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.2494 | −1.08579 | −0.542897 | − | 0.839799i | \(-0.682673\pi\) | ||||
−0.542897 | + | 0.839799i | \(0.682673\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −28.6210 | −1.45489 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 37.7262 | 1.91280 | 0.956398 | − | 0.292068i | \(-0.0943432\pi\) | ||||
0.956398 | + | 0.292068i | \(0.0943432\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.13254 | 0.107847 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.533557 | 0.0269144 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.1777 | −0.663045 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.20513 | 0.461992 | 0.230996 | − | 0.972955i | \(-0.425802\pi\) | ||||
0.230996 | + | 0.972955i | \(0.425802\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.2942 | 0.813694 | 0.406847 | − | 0.913496i | \(-0.366628\pi\) | ||||
0.406847 | + | 0.913496i | \(0.366628\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.209258 | 0.0104239 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.24579 | 0.260666 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.458413 | −0.0227227 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.569169 | −0.0281436 | −0.0140718 | − | 0.999901i | \(-0.504479\pi\) | ||||
−0.0140718 | + | 0.999901i | \(0.504479\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.03814 | 0.100534 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.10034 | 0.397630 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.88567 | −0.484103 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.91313 | −0.191169 | −0.0955845 | − | 0.995421i | \(-0.530472\pi\) | ||||
−0.0955845 | + | 0.995421i | \(0.530472\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.6649 | 0.665985 | 0.332992 | − | 0.942930i | \(-0.391942\pi\) | ||||
0.332992 | + | 0.942930i | \(0.391942\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.60020 | 0.126426 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.38561 | 0.261240 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.173758 | 0.00838912 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.84032 | 0.329487 | 0.164743 | − | 0.986336i | \(-0.447320\pi\) | ||||
0.164743 | + | 0.986336i | \(0.447320\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.46375 | −0.0703434 | −0.0351717 | − | 0.999381i | \(-0.511198\pi\) | ||||
−0.0351717 | + | 0.999381i | \(0.511198\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.70359 | 0.0816807 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.57536 | −0.314542 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.39866 | −0.0667542 | −0.0333771 | − | 0.999443i | \(-0.510626\pi\) | ||||
−0.0333771 | + | 0.999443i | \(0.510626\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.1620 | −0.862902 | −0.431451 | − | 0.902136i | \(-0.641998\pi\) | ||||
−0.431451 | + | 0.902136i | \(0.641998\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.61880 | 0.455975 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.70110 | −0.127758 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.4896 | −1.81644 | −0.908219 | − | 0.418495i | \(-0.862558\pi\) | ||||
−0.908219 | + | 0.418495i | \(0.862558\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.92893 | −0.232094 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.5774 | 0.543955 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.6702 | −0.920135 | −0.460067 | − | 0.887884i | \(-0.652175\pi\) | ||||
−0.460067 | + | 0.887884i | \(0.652175\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.81603 | 0.178117 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.3526 | 0.994488 | 0.497244 | − | 0.867611i | \(-0.334345\pi\) | ||||
0.497244 | + | 0.867611i | \(0.334345\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.5941 | −0.538823 | −0.269412 | − | 0.963025i | \(-0.586829\pi\) | ||||
−0.269412 | + | 0.963025i | \(0.586829\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.39779 | 0.0648210 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15.4316 | −0.714087 | −0.357044 | − | 0.934088i | \(-0.616215\pi\) | ||||
−0.357044 | + | 0.934088i | \(0.616215\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.84289 | −0.269226 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 52.0643 | 2.39392 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.6057 | −0.761923 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.38809 | 0.338278 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.3619 | 0.930361 | 0.465180 | − | 0.885216i | \(-0.345989\pi\) | ||||
0.465180 | + | 0.885216i | \(0.345989\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.00608362 | −0.000277389 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.11942 | 0.232461 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.90723 | −0.448939 | −0.224470 | − | 0.974481i | \(-0.572065\pi\) | ||||
−0.224470 | + | 0.974481i | \(0.572065\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.3170 | −0.466552 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.11988 | −0.411574 | −0.205787 | − | 0.978597i | \(-0.565975\pi\) | ||||
−0.205787 | + | 0.978597i | \(0.565975\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.83528 | −0.217770 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.8277 | −0.486667 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.1763 | −0.589852 | −0.294926 | − | 0.955520i | \(-0.595295\pi\) | ||||
−0.294926 | + | 0.955520i | \(0.595295\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.5268 | 0.514981 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.6192 | −1.49901 | −0.749504 | − | 0.662000i | \(-0.769708\pi\) | ||||
−0.749504 | + | 0.662000i | \(0.769708\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.1643 | −0.452303 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.00381 | −0.311050 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.7381 | 1.31812 | 0.659059 | − | 0.752091i | \(-0.270955\pi\) | ||||
0.659059 | + | 0.752091i | \(0.270955\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11.7662 | −0.519488 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.6210 | 0.644279 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.73000 | −0.208025 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.57645 | 0.200884 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.710103 | −0.0311102 | −0.0155551 | − | 0.999879i | \(-0.504952\pi\) | ||||
−0.0155551 | + | 0.999879i | \(0.504952\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.85319 | 0.168488 | 0.0842441 | − | 0.996445i | \(-0.473152\pi\) | ||||
0.0842441 | + | 0.996445i | \(0.473152\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.96734 | −0.172820 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.0431 | −0.871438 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −30.3193 | −1.31575 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.0654121 | −0.00283331 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.37575 | 0.318882 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.25209 | 0.0971849 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.9199 | −0.684448 | −0.342224 | − | 0.939618i | \(-0.611180\pi\) | ||||
−0.342224 | + | 0.939618i | \(0.611180\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.02289 | 0.172639 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.01472 | 0.343313 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.91366 | 0.210093 | 0.105047 | − | 0.994467i | \(-0.466501\pi\) | ||||
0.105047 | + | 0.994467i | \(0.466501\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 29.2642 | 1.24896 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.9089 | 0.635139 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.0406370 | −0.00172495 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.2303 | −1.11141 | −0.555706 | − | 0.831379i | \(-0.687552\pi\) | ||||
−0.555706 | + | 0.831379i | \(0.687552\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.690948 | 0.0292240 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.29430 | −0.139085 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.73653 | 0.199621 | 0.0998105 | − | 0.995006i | \(-0.468176\pi\) | ||||
0.0998105 | + | 0.995006i | \(0.468176\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.85081 | −0.288216 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.8284 | 0.705482 | 0.352741 | − | 0.935721i | \(-0.385250\pi\) | ||||
0.352741 | + | 0.935721i | \(0.385250\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.4408 | −0.855420 | −0.427710 | − | 0.903916i | \(-0.640680\pi\) | ||||
−0.427710 | + | 0.903916i | \(0.640680\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.95417 | 0.248739 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.46758 | 0.311420 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.1297 | −0.629859 | −0.314930 | − | 0.949115i | \(-0.601981\pi\) | ||||
−0.314930 | + | 0.949115i | \(0.601981\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.27894 | 0.0531509 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.4396 | −0.556613 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.143695 | −0.00594104 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −44.9665 | −1.85597 | −0.927984 | − | 0.372620i | \(-0.878459\pi\) | ||||
−0.927984 | + | 0.372620i | \(0.878459\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.2327 | 0.504040 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.9004 | −0.530650 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.8232 | 0.896171 | 0.448085 | − | 0.893991i | \(-0.352106\pi\) | ||||
0.448085 | + | 0.893991i | \(0.352106\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.84589 | 0.116474 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.1256 | 0.904028 | 0.452014 | − | 0.892011i | \(-0.350706\pi\) | ||||
0.452014 | + | 0.892011i | \(0.350706\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.2542 | 1.68279 | 0.841396 | − | 0.540418i | \(-0.181734\pi\) | ||||
0.841396 | + | 0.540418i | \(0.181734\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −28.0522 | −1.14237 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.7784 | 0.438202 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.98200 | −0.121036 | −0.0605178 | − | 0.998167i | \(-0.519275\pi\) | ||||
−0.0605178 | + | 0.998167i | \(0.519275\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.0627721 | −0.00253949 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.1475 | −0.894527 | −0.447264 | − | 0.894402i | \(-0.647601\pi\) | ||||
−0.447264 | + | 0.894402i | \(0.647601\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.436937 | −0.0176190 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.94230 | −0.198970 | −0.0994848 | − | 0.995039i | \(-0.531719\pi\) | ||||
−0.0994848 | + | 0.995039i | \(0.531719\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.4913 | −1.42651 | −0.713257 | − | 0.700902i | \(-0.752781\pi\) | ||||
−0.713257 | + | 0.700902i | \(0.752781\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.29123 | 0.212330 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.5724 | 0.622897 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.1575 | 0.405650 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.115340 | 0.00459890 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.6549 | −1.61844 | −0.809222 | − | 0.587503i | \(-0.800111\pi\) | ||||
−0.809222 | + | 0.587503i | \(0.800111\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.78422 | −0.0709163 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.01945 | 0.199191 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.1749 | 0.600310 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.3461 | 1.63307 | 0.816536 | − | 0.577295i | \(-0.195892\pi\) | ||||
0.816536 | + | 0.577295i | \(0.195892\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.9995 | 0.985883 | 0.492942 | − | 0.870062i | \(-0.335922\pi\) | ||||
0.492942 | + | 0.870062i | \(0.335922\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.61536 | 0.181730 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.1819 | −0.990003 | −0.495002 | − | 0.868892i | \(-0.664832\pi\) | ||||
−0.495002 | + | 0.868892i | \(0.664832\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 55.1537 | 2.16497 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.3606 | 1.50117 | 0.750583 | − | 0.660776i | \(-0.229773\pi\) | ||||
0.750583 | + | 0.660776i | \(0.229773\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.802660 | 0.0313625 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.50401 | −0.292759 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.7750 | 1.51046 | 0.755230 | − | 0.655459i | \(-0.227525\pi\) | ||||
0.755230 | + | 0.655459i | \(0.227525\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.8665 | 1.47284 | 0.736419 | − | 0.676526i | \(-0.236515\pi\) | ||||
0.736419 | + | 0.676526i | \(0.236515\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.0437188 | −0.00169790 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.70451 | −0.259600 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.6484 | −0.450355 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −53.2343 | −2.05509 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.05883 | −0.195004 | −0.0975018 | − | 0.995235i | \(-0.531085\pi\) | ||||
−0.0975018 | + | 0.995235i | \(0.531085\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.3627 | 0.514331 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −44.1411 | −1.69648 | −0.848241 | − | 0.529611i | \(-0.822338\pi\) | ||||
−0.848241 | + | 0.529611i | \(0.822338\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.32035 | 0.165556 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.5732 | 0.404572 | 0.202286 | − | 0.979326i | \(-0.435163\pi\) | ||||
0.202286 | + | 0.979326i | \(0.435163\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.06609 | 0.117149 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.556694 | 0.0212392 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.178358 | −0.00679491 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.1100 | −1.06936 | −0.534678 | − | 0.845056i | \(-0.679567\pi\) | ||||
−0.534678 | + | 0.845056i | \(0.679567\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.8716 | −0.564111 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.24015 | 0.0469742 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.1896 | 0.423230 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.99389 | −0.150847 | −0.0754236 | − | 0.997152i | \(-0.524031\pi\) | ||||
−0.0754236 | + | 0.997152i | \(0.524031\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.355633 | −0.0134130 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.419302 | −0.0157918 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.43794 | 0.0540028 | 0.0270014 | − | 0.999635i | \(-0.491404\pi\) | ||||
0.0270014 | + | 0.999635i | \(0.491404\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 44.0407 | 1.65166 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.50104 | −0.206016 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.261394 | 0.00977558 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.26703 | −0.159355 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.38732 | 0.163619 | 0.0818097 | − | 0.996648i | \(-0.473930\pi\) | ||||
0.0818097 | + | 0.996648i | \(0.473930\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.9146 | 0.405919 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.9319 | −0.628834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.95216 | −0.220753 | −0.110377 | − | 0.993890i | \(-0.535206\pi\) | ||||
−0.110377 | + | 0.993890i | \(0.535206\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.5567 | −0.465064 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.0998 | −0.484512 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.7441 | 1.17249 | 0.586247 | − | 0.810132i | \(-0.300605\pi\) | ||||
0.586247 | + | 0.810132i | \(0.300605\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 51.0296 | 1.87970 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.49001 | 0.0548109 | 0.0274055 | − | 0.999624i | \(-0.491275\pi\) | ||||
0.0274055 | + | 0.999624i | \(0.491275\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.134800 | 0.00495201 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.63999 | −0.0968519 | −0.0484259 | − | 0.998827i | \(-0.515420\pi\) | ||||
−0.0484259 | + | 0.998827i | \(0.515420\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.06341 | −0.148872 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −27.0717 | −0.990503 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.58728 | −0.0579206 | −0.0289603 | − | 0.999581i | \(-0.509220\pi\) | ||||
−0.0289603 | + | 0.999581i | \(0.509220\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.693358 | −0.0252674 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.4166 | 0.633854 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.41445 | −0.0514090 | −0.0257045 | − | 0.999670i | \(-0.508183\pi\) | ||||
−0.0257045 | + | 0.999670i | \(0.508183\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.56781 | −0.165801 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.5791 | 1.25349 | 0.626746 | − | 0.779224i | \(-0.284387\pi\) | ||||
0.626746 | + | 0.779224i | \(0.284387\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.72432 | 0.0984980 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.731947 | 0.0264291 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.3841 | 1.63659 | 0.818297 | − | 0.574796i | \(-0.194919\pi\) | ||||
0.818297 | + | 0.574796i | \(0.194919\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.69738 | 0.133158 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.04090 | −0.325179 | −0.162589 | − | 0.986694i | \(-0.551985\pi\) | ||||
−0.162589 | + | 0.986694i | \(0.551985\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.8926 | −0.499036 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.82383 | −0.137003 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.6046 | −0.987770 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.9973 | −0.428747 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.78979 | −0.313721 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.1214 | 0.503372 | 0.251686 | − | 0.967809i | \(-0.419015\pi\) | ||||
0.251686 | + | 0.967809i | \(0.419015\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.30690 | 0.0821278 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.706475 | −0.0250877 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.19139 | −0.0422542 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −52.9069 | −1.87406 | −0.937029 | − | 0.349252i | \(-0.886436\pi\) | ||||
−0.937029 | + | 0.349252i | \(0.886436\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.19010 | 0.0421028 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.1465 | −1.13584 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.6505 | 0.481716 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.44190 | 0.156362 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.4156 | −1.35062 | −0.675311 | − | 0.737533i | \(-0.735991\pi\) | ||||
−0.675311 | + | 0.737533i | \(0.735991\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.9375 | 0.384068 | 0.192034 | − | 0.981388i | \(-0.438492\pi\) | ||||
0.192034 | + | 0.981388i | \(0.438492\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.2629 | 0.500221 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.5205 | −0.543659 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40.3911 | 1.41311 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −52.1638 | −1.82053 | −0.910265 | − | 0.414027i | \(-0.864122\pi\) | ||||
−0.910265 | + | 0.414027i | \(0.864122\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.4953 | 0.818995 | 0.409498 | − | 0.912311i | \(-0.365704\pi\) | ||||
0.409498 | + | 0.912311i | \(0.365704\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.5357 | −0.401623 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.66381 | 0.0926298 | 0.0463149 | − | 0.998927i | \(-0.485252\pi\) | ||||
0.0463149 | + | 0.998927i | \(0.485252\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.4035 | 1.36854 | 0.684270 | − | 0.729229i | \(-0.260121\pi\) | ||||
0.684270 | + | 0.729229i | \(0.260121\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.15820 | 0.283005 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.3405 | 0.600092 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.84373 | −0.340249 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.2979 | 0.804334 | 0.402167 | − | 0.915566i | \(-0.368257\pi\) | ||||
0.402167 | + | 0.915566i | \(0.368257\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.7983 | −0.475804 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.43475 | −0.0838572 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.5362 | −0.362457 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.6733 | 0.572227 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.159928 | 0.00548226 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.1155 | −1.16809 | −0.584047 | − | 0.811720i | \(-0.698532\pi\) | ||||
−0.584047 | + | 0.811720i | \(0.698532\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.40003 | −0.287275 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.7004 | −0.604633 | −0.302317 | − | 0.953208i | \(-0.597760\pi\) | ||||
−0.302317 | + | 0.953208i | \(0.597760\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.5431 | 0.700922 | 0.350461 | − | 0.936577i | \(-0.386025\pi\) | ||||
0.350461 | + | 0.936577i | \(0.386025\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.0834 | 0.479404 | 0.239702 | − | 0.970847i | \(-0.422950\pi\) | ||||
0.239702 | + | 0.970847i | \(0.422950\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.88460 | 0.234084 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.33297 | −0.283003 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −80.1142 | −2.71769 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.677216 | 0.0229466 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −17.1093 | −0.579064 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.75794 | −0.228199 | −0.114100 | − | 0.993469i | \(-0.536398\pi\) | ||||
−0.114100 | + | 0.993469i | \(0.536398\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.77733 | 0.228594 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.5704 | 1.02994 | 0.514972 | − | 0.857207i | \(-0.327802\pi\) | ||||
0.514972 | + | 0.857207i | \(0.327802\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.0224 | 1.85165 | 0.925825 | − | 0.377952i | \(-0.123372\pi\) | ||||
0.925825 | + | 0.377952i | \(0.123372\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.88922 | 0.164349 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.5153 | −0.957450 | −0.478725 | − | 0.877965i | \(-0.658901\pi\) | ||||
−0.478725 | + | 0.877965i | \(0.658901\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 31.8918 | 1.06842 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.66950 | −0.122795 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.38795 | 0.113247 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.0606196 | −0.00202403 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.4730 | 0.415997 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.38151 | 0.112654 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.05186 | 0.201171 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.7081 | −1.01965 | −0.509823 | − | 0.860279i | \(-0.670289\pi\) | ||||
−0.509823 | + | 0.860279i | \(0.670289\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 33.9695 | 1.12670 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.7191 | −0.818981 | −0.409491 | − | 0.912314i | \(-0.634294\pi\) | ||||
−0.409491 | + | 0.912314i | \(0.634294\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 49.2461 | 1.62981 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.71907 | −0.156008 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.6530 | −1.20907 | −0.604535 | − | 0.796579i | \(-0.706641\pi\) | ||||
−0.604535 | + | 0.796579i | \(0.706641\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.04360 | 0.232094 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.366342 | −0.0120583 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.403890 | 0.0132798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −48.8642 | −1.60491 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.8880 | 1.04621 | 0.523105 | − | 0.852268i | \(-0.324774\pi\) | ||||
0.523105 | + | 0.852268i | \(0.324774\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.65075 | 0.315951 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.95579 | −0.162072 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.5949 | 1.62019 | 0.810097 | − | 0.586295i | \(-0.199414\pi\) | ||||
0.810097 | + | 0.586295i | \(0.199414\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.52238 | −0.212850 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.24569 | −0.0406084 | −0.0203042 | − | 0.999794i | \(-0.506463\pi\) | ||||
−0.0203042 | + | 0.999794i | \(0.506463\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.71957 | 0.0559971 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.8351 | −0.482076 | −0.241038 | − | 0.970516i | \(-0.577488\pi\) | ||||
−0.241038 | + | 0.970516i | \(0.577488\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.181157 | 0.00588059 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.58874 | −0.278509 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.5263 | 1.02124 | 0.510618 | − | 0.859808i | \(-0.329417\pi\) | ||||
0.510618 | + | 0.859808i | \(0.329417\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.95720 | 0.289848 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.3570 | 0.334793 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.7660 | −0.669869 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −24.6501 | −0.794340 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.92398 | 0.0619351 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.43038 | 0.238945 | 0.119472 | − | 0.992838i | \(-0.461880\pi\) | ||||
0.119472 | + | 0.992838i | \(0.461880\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.55569 | −0.0821006 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.3316 | −0.652472 | −0.326236 | − | 0.945288i | \(-0.605780\pi\) | ||||
−0.326236 | + | 0.945288i | \(0.605780\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.153092 | −0.00490285 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.88193 | −0.316151 | −0.158076 | − | 0.987427i | \(-0.550529\pi\) | ||||
−0.158076 | + | 0.987427i | \(0.550529\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58.4776 | 1.86895 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.7856 | −0.855198 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.4507 | 0.971225 | 0.485612 | − | 0.874174i | \(-0.338597\pi\) | ||||
0.485612 | + | 0.874174i | \(0.338597\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.4067 | −0.618350 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.1639 | −0.577577 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.0806 | 1.17791 | 0.588953 | − | 0.808167i | \(-0.299540\pi\) | ||||
0.588953 | + | 0.808167i | \(0.299540\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.62291 | 0.178438 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.28123 | 0.135724 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.49925 | −0.0474818 | −0.0237409 | − | 0.999718i | \(-0.507558\pi\) | ||||
−0.0237409 | + | 0.999718i | \(0.507558\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.286180 | 0.00905434 |
(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 | 8036.2.a.t.1.12 | yes | 20 | |
7.6 | odd | 2 | 8036.2.a.s.1.9 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.s.1.9 | ✓ | 20 | 7.6 | odd | 2 | ||
8036.2.a.t.1.12 | yes | 20 | 1.1 | even | 1 | trivial |