Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4018,2,Mod(1,4018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4018 = 2 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4018.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: | \(32.0838915322\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.404.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.86620\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4018.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.517304 | −0.298666 | −0.149333 | − | 0.988787i | \(-0.547713\pi\) | ||||
−0.149333 | + | 0.988787i | \(0.547713\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.86620 | −0.834589 | −0.417295 | − | 0.908771i | \(-0.637022\pi\) | ||||
−0.417295 | + | 0.908771i | \(0.637022\pi\) | |||||||
\(6\) | 0.517304 | 0.211188 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.73240 | −0.910799 | ||||||||
\(10\) | 1.86620 | 0.590144 | ||||||||
\(11\) | −1.34889 | −0.406707 | −0.203353 | − | 0.979105i | \(-0.565184\pi\) | ||||
−0.203353 | + | 0.979105i | \(0.565184\pi\) | |||||||
\(12\) | −0.517304 | −0.149333 | ||||||||
\(13\) | −5.21509 | −1.44641 | −0.723203 | − | 0.690635i | \(-0.757331\pi\) | ||||
−0.723203 | + | 0.690635i | \(0.757331\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.965392 | 0.249263 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.51730 | 1.09561 | 0.547804 | − | 0.836607i | \(-0.315464\pi\) | ||||
0.547804 | + | 0.836607i | \(0.315464\pi\) | |||||||
\(18\) | 2.73240 | 0.644032 | ||||||||
\(19\) | −3.21509 | −0.737593 | −0.368796 | − | 0.929510i | \(-0.620230\pi\) | ||||
−0.368796 | + | 0.929510i | \(0.620230\pi\) | |||||||
\(20\) | −1.86620 | −0.417295 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.34889 | 0.287585 | ||||||||
\(23\) | −6.18048 | −1.28872 | −0.644360 | − | 0.764722i | \(-0.722876\pi\) | ||||
−0.644360 | + | 0.764722i | \(0.722876\pi\) | |||||||
\(24\) | 0.517304 | 0.105594 | ||||||||
\(25\) | −1.51730 | −0.303461 | ||||||||
\(26\) | 5.21509 | 1.02276 | ||||||||
\(27\) | 2.96539 | 0.570690 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.11590 | −1.50708 | −0.753542 | − | 0.657399i | \(-0.771656\pi\) | ||||
−0.753542 | + | 0.657399i | \(0.771656\pi\) | |||||||
\(30\) | −0.965392 | −0.176256 | ||||||||
\(31\) | −0.697788 | −0.125327 | −0.0626633 | − | 0.998035i | \(-0.519959\pi\) | ||||
−0.0626633 | + | 0.998035i | \(0.519959\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.697788 | 0.121469 | ||||||||
\(34\) | −4.51730 | −0.774711 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.73240 | −0.455399 | ||||||||
\(37\) | 7.03461 | 1.15648 | 0.578241 | − | 0.815866i | \(-0.303739\pi\) | ||||
0.578241 | + | 0.815866i | \(0.303739\pi\) | |||||||
\(38\) | 3.21509 | 0.521557 | ||||||||
\(39\) | 2.69779 | 0.431992 | ||||||||
\(40\) | 1.86620 | 0.295072 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.03461 | −0.767771 | −0.383885 | − | 0.923381i | \(-0.625414\pi\) | ||||
−0.383885 | + | 0.923381i | \(0.625414\pi\) | |||||||
\(44\) | −1.34889 | −0.203353 | ||||||||
\(45\) | 5.09919 | 0.760143 | ||||||||
\(46\) | 6.18048 | 0.911263 | ||||||||
\(47\) | 2.78491 | 0.406221 | 0.203110 | − | 0.979156i | \(-0.434895\pi\) | ||||
0.203110 | + | 0.979156i | \(0.434895\pi\) | |||||||
\(48\) | −0.517304 | −0.0746664 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.51730 | 0.214579 | ||||||||
\(51\) | −2.33682 | −0.327220 | ||||||||
\(52\) | −5.21509 | −0.723203 | ||||||||
\(53\) | −6.38350 | −0.876841 | −0.438421 | − | 0.898770i | \(-0.644462\pi\) | ||||
−0.438421 | + | 0.898770i | \(0.644462\pi\) | |||||||
\(54\) | −2.96539 | −0.403539 | ||||||||
\(55\) | 2.51730 | 0.339433 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.66318 | 0.220294 | ||||||||
\(58\) | 8.11590 | 1.06567 | ||||||||
\(59\) | 11.5986 | 1.51001 | 0.755004 | − | 0.655720i | \(-0.227635\pi\) | ||||
0.755004 | + | 0.655720i | \(0.227635\pi\) | |||||||
\(60\) | 0.965392 | 0.124632 | ||||||||
\(61\) | −13.5294 | −1.73226 | −0.866130 | − | 0.499819i | \(-0.833400\pi\) | ||||
−0.866130 | + | 0.499819i | \(0.833400\pi\) | |||||||
\(62\) | 0.697788 | 0.0886192 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.73240 | 1.20716 | ||||||||
\(66\) | −0.697788 | −0.0858918 | ||||||||
\(67\) | −9.77908 | −1.19470 | −0.597352 | − | 0.801979i | \(-0.703781\pi\) | ||||
−0.597352 | + | 0.801979i | \(0.703781\pi\) | |||||||
\(68\) | 4.51730 | 0.547804 | ||||||||
\(69\) | 3.19719 | 0.384896 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.66318 | 0.197383 | 0.0986916 | − | 0.995118i | \(-0.468534\pi\) | ||||
0.0986916 | + | 0.995118i | \(0.468534\pi\) | |||||||
\(72\) | 2.73240 | 0.322016 | ||||||||
\(73\) | 2.96539 | 0.347073 | 0.173536 | − | 0.984827i | \(-0.444481\pi\) | ||||
0.173536 | + | 0.984827i | \(0.444481\pi\) | |||||||
\(74\) | −7.03461 | −0.817757 | ||||||||
\(75\) | 0.784908 | 0.0906333 | ||||||||
\(76\) | −3.21509 | −0.368796 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.69779 | −0.305464 | ||||||||
\(79\) | −7.46479 | −0.839855 | −0.419927 | − | 0.907558i | \(-0.637944\pi\) | ||||
−0.419927 | + | 0.907558i | \(0.637944\pi\) | |||||||
\(80\) | −1.86620 | −0.208647 | ||||||||
\(81\) | 6.66318 | 0.740353 | ||||||||
\(82\) | 1.00000 | 0.110432 | ||||||||
\(83\) | −14.5640 | −1.59861 | −0.799303 | − | 0.600929i | \(-0.794798\pi\) | ||||
−0.799303 | + | 0.600929i | \(0.794798\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.43018 | −0.914382 | ||||||||
\(86\) | 5.03461 | 0.542896 | ||||||||
\(87\) | 4.19839 | 0.450114 | ||||||||
\(88\) | 1.34889 | 0.143793 | ||||||||
\(89\) | 15.1280 | 1.60356 | 0.801781 | − | 0.597618i | \(-0.203886\pi\) | ||||
0.801781 | + | 0.597618i | \(0.203886\pi\) | |||||||
\(90\) | −5.09919 | −0.537502 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.18048 | −0.644360 | ||||||||
\(93\) | 0.360969 | 0.0374307 | ||||||||
\(94\) | −2.78491 | −0.287241 | ||||||||
\(95\) | 6.00000 | 0.615587 | ||||||||
\(96\) | 0.517304 | 0.0527971 | ||||||||
\(97\) | −3.93078 | −0.399111 | −0.199555 | − | 0.979887i | \(-0.563950\pi\) | ||||
−0.199555 | + | 0.979887i | \(0.563950\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.68571 | 0.370428 | ||||||||
\(100\) | −1.51730 | −0.151730 | ||||||||
\(101\) | 14.2497 | 1.41790 | 0.708949 | − | 0.705260i | \(-0.249170\pi\) | ||||
0.708949 | + | 0.705260i | \(0.249170\pi\) | |||||||
\(102\) | 2.33682 | 0.231380 | ||||||||
\(103\) | 10.1626 | 1.00135 | 0.500674 | − | 0.865636i | \(-0.333085\pi\) | ||||
0.500674 | + | 0.865636i | \(0.333085\pi\) | |||||||
\(104\) | 5.21509 | 0.511382 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.38350 | 0.620021 | ||||||||
\(107\) | 1.30221 | 0.125890 | 0.0629448 | − | 0.998017i | \(-0.479951\pi\) | ||||
0.0629448 | + | 0.998017i | \(0.479951\pi\) | |||||||
\(108\) | 2.96539 | 0.285345 | ||||||||
\(109\) | 9.70986 | 0.930036 | 0.465018 | − | 0.885301i | \(-0.346048\pi\) | ||||
0.465018 | + | 0.885301i | \(0.346048\pi\) | |||||||
\(110\) | −2.51730 | −0.240016 | ||||||||
\(111\) | −3.63903 | −0.345402 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.48270 | −0.892057 | −0.446028 | − | 0.895019i | \(-0.647162\pi\) | ||||
−0.446028 | + | 0.895019i | \(0.647162\pi\) | |||||||
\(114\) | −1.66318 | −0.155771 | ||||||||
\(115\) | 11.5340 | 1.07555 | ||||||||
\(116\) | −8.11590 | −0.753542 | ||||||||
\(117\) | 14.2497 | 1.31739 | ||||||||
\(118\) | −11.5986 | −1.06774 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.965392 | −0.0881278 | ||||||||
\(121\) | −9.18048 | −0.834589 | ||||||||
\(122\) | 13.5294 | 1.22489 | ||||||||
\(123\) | 0.517304 | 0.0466437 | ||||||||
\(124\) | −0.697788 | −0.0626633 | ||||||||
\(125\) | 12.1626 | 1.08785 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.1805 | 1.61326 | 0.806629 | − | 0.591059i | \(-0.201290\pi\) | ||||
0.806629 | + | 0.591059i | \(0.201290\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.60442 | 0.229307 | ||||||||
\(130\) | −9.73240 | −0.853588 | ||||||||
\(131\) | −7.93541 | −0.693320 | −0.346660 | − | 0.937991i | \(-0.612684\pi\) | ||||
−0.346660 | + | 0.937991i | \(0.612684\pi\) | |||||||
\(132\) | 0.697788 | 0.0607347 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 9.77908 | 0.844784 | ||||||||
\(135\) | −5.53401 | −0.476292 | ||||||||
\(136\) | −4.51730 | −0.387356 | ||||||||
\(137\) | −9.19719 | −0.785769 | −0.392884 | − | 0.919588i | \(-0.628523\pi\) | ||||
−0.392884 | + | 0.919588i | \(0.628523\pi\) | |||||||
\(138\) | −3.19719 | −0.272163 | ||||||||
\(139\) | 0.831590 | 0.0705346 | 0.0352673 | − | 0.999378i | \(-0.488772\pi\) | ||||
0.0352673 | + | 0.999378i | \(0.488772\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.44064 | −0.121324 | ||||||||
\(142\) | −1.66318 | −0.139571 | ||||||||
\(143\) | 7.03461 | 0.588263 | ||||||||
\(144\) | −2.73240 | −0.227700 | ||||||||
\(145\) | 15.1459 | 1.25780 | ||||||||
\(146\) | −2.96539 | −0.245418 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.03461 | 0.578241 | ||||||||
\(149\) | 1.77908 | 0.145748 | 0.0728739 | − | 0.997341i | \(-0.476783\pi\) | ||||
0.0728739 | + | 0.997341i | \(0.476783\pi\) | |||||||
\(150\) | −0.784908 | −0.0640874 | ||||||||
\(151\) | −3.93078 | −0.319883 | −0.159941 | − | 0.987127i | \(-0.551131\pi\) | ||||
−0.159941 | + | 0.987127i | \(0.551131\pi\) | |||||||
\(152\) | 3.21509 | 0.260778 | ||||||||
\(153\) | −12.3431 | −0.997878 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.30221 | 0.104596 | ||||||||
\(156\) | 2.69779 | 0.215996 | ||||||||
\(157\) | −4.58652 | −0.366044 | −0.183022 | − | 0.983109i | \(-0.558588\pi\) | ||||
−0.183022 | + | 0.983109i | \(0.558588\pi\) | |||||||
\(158\) | 7.46479 | 0.593867 | ||||||||
\(159\) | 3.30221 | 0.261882 | ||||||||
\(160\) | 1.86620 | 0.147536 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −6.66318 | −0.523509 | ||||||||
\(163\) | −24.2318 | −1.89798 | −0.948990 | − | 0.315305i | \(-0.897893\pi\) | ||||
−0.948990 | + | 0.315305i | \(0.897893\pi\) | |||||||
\(164\) | −1.00000 | −0.0780869 | ||||||||
\(165\) | −1.30221 | −0.101377 | ||||||||
\(166\) | 14.5640 | 1.13038 | ||||||||
\(167\) | 3.23300 | 0.250177 | 0.125088 | − | 0.992146i | \(-0.460079\pi\) | ||||
0.125088 | + | 0.992146i | \(0.460079\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.1972 | 1.09209 | ||||||||
\(170\) | 8.43018 | 0.646566 | ||||||||
\(171\) | 8.78491 | 0.671799 | ||||||||
\(172\) | −5.03461 | −0.383885 | ||||||||
\(173\) | 3.23763 | 0.246152 | 0.123076 | − | 0.992397i | \(-0.460724\pi\) | ||||
0.123076 | + | 0.992397i | \(0.460724\pi\) | |||||||
\(174\) | −4.19839 | −0.318279 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.34889 | −0.101677 | ||||||||
\(177\) | −6.00000 | −0.450988 | ||||||||
\(178\) | −15.1280 | −1.13389 | ||||||||
\(179\) | 4.38350 | 0.327638 | 0.163819 | − | 0.986490i | \(-0.447619\pi\) | ||||
0.163819 | + | 0.986490i | \(0.447619\pi\) | |||||||
\(180\) | 5.09919 | 0.380071 | ||||||||
\(181\) | −4.18048 | −0.310733 | −0.155366 | − | 0.987857i | \(-0.549656\pi\) | ||||
−0.155366 | + | 0.987857i | \(0.549656\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.99880 | 0.517366 | ||||||||
\(184\) | 6.18048 | 0.455631 | ||||||||
\(185\) | −13.1280 | −0.965188 | ||||||||
\(186\) | −0.360969 | −0.0264675 | ||||||||
\(187\) | −6.09337 | −0.445591 | ||||||||
\(188\) | 2.78491 | 0.203110 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.00000 | −0.435286 | ||||||||
\(191\) | 20.5928 | 1.49004 | 0.745020 | − | 0.667042i | \(-0.232440\pi\) | ||||
0.745020 | + | 0.667042i | \(0.232440\pi\) | |||||||
\(192\) | −0.517304 | −0.0373332 | ||||||||
\(193\) | −4.76700 | −0.343137 | −0.171568 | − | 0.985172i | \(-0.554883\pi\) | ||||
−0.171568 | + | 0.985172i | \(0.554883\pi\) | |||||||
\(194\) | 3.93078 | 0.282214 | ||||||||
\(195\) | −5.03461 | −0.360536 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.0576 | 1.85652 | 0.928262 | − | 0.371927i | \(-0.121303\pi\) | ||||
0.928262 | + | 0.371927i | \(0.121303\pi\) | |||||||
\(198\) | −3.68571 | −0.261932 | ||||||||
\(199\) | 9.71449 | 0.688642 | 0.344321 | − | 0.938852i | \(-0.388109\pi\) | ||||
0.344321 | + | 0.938852i | \(0.388109\pi\) | |||||||
\(200\) | 1.51730 | 0.107290 | ||||||||
\(201\) | 5.05876 | 0.356817 | ||||||||
\(202\) | −14.2497 | −1.00261 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.33682 | −0.163610 | ||||||||
\(205\) | 1.86620 | 0.130341 | ||||||||
\(206\) | −10.1626 | −0.708061 | ||||||||
\(207\) | 16.8875 | 1.17376 | ||||||||
\(208\) | −5.21509 | −0.361602 | ||||||||
\(209\) | 4.33682 | 0.299984 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.4769 | −1.54737 | −0.773686 | − | 0.633570i | \(-0.781589\pi\) | ||||
−0.773686 | + | 0.633570i | \(0.781589\pi\) | |||||||
\(212\) | −6.38350 | −0.438421 | ||||||||
\(213\) | −0.860370 | −0.0589516 | ||||||||
\(214\) | −1.30221 | −0.0890173 | ||||||||
\(215\) | 9.39558 | 0.640773 | ||||||||
\(216\) | −2.96539 | −0.201769 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.70986 | −0.657635 | ||||||||
\(219\) | −1.53401 | −0.103659 | ||||||||
\(220\) | 2.51730 | 0.169717 | ||||||||
\(221\) | −23.5582 | −1.58469 | ||||||||
\(222\) | 3.63903 | 0.244236 | ||||||||
\(223\) | −17.5340 | −1.17416 | −0.587082 | − | 0.809527i | \(-0.699723\pi\) | ||||
−0.587082 | + | 0.809527i | \(0.699723\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.14588 | 0.276392 | ||||||||
\(226\) | 9.48270 | 0.630780 | ||||||||
\(227\) | 18.9475 | 1.25759 | 0.628795 | − | 0.777572i | \(-0.283549\pi\) | ||||
0.628795 | + | 0.777572i | \(0.283549\pi\) | |||||||
\(228\) | 1.66318 | 0.110147 | ||||||||
\(229\) | −9.75030 | −0.644318 | −0.322159 | − | 0.946686i | \(-0.604409\pi\) | ||||
−0.322159 | + | 0.946686i | \(0.604409\pi\) | |||||||
\(230\) | −11.5340 | −0.760530 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.11590 | 0.532835 | ||||||||
\(233\) | 16.5686 | 1.08545 | 0.542723 | − | 0.839912i | \(-0.317393\pi\) | ||||
0.542723 | + | 0.839912i | \(0.317393\pi\) | |||||||
\(234\) | −14.2497 | −0.931532 | ||||||||
\(235\) | −5.19719 | −0.339027 | ||||||||
\(236\) | 11.5986 | 0.755004 | ||||||||
\(237\) | 3.86157 | 0.250836 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.06922 | 0.263216 | 0.131608 | − | 0.991302i | \(-0.457986\pi\) | ||||
0.131608 | + | 0.991302i | \(0.457986\pi\) | |||||||
\(240\) | 0.965392 | 0.0623158 | ||||||||
\(241\) | 3.89498 | 0.250898 | 0.125449 | − | 0.992100i | \(-0.459963\pi\) | ||||
0.125449 | + | 0.992100i | \(0.459963\pi\) | |||||||
\(242\) | 9.18048 | 0.590144 | ||||||||
\(243\) | −12.3431 | −0.791808 | ||||||||
\(244\) | −13.5294 | −0.866130 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.517304 | −0.0329821 | ||||||||
\(247\) | 16.7670 | 1.06686 | ||||||||
\(248\) | 0.697788 | 0.0443096 | ||||||||
\(249\) | 7.53401 | 0.477448 | ||||||||
\(250\) | −12.1626 | −0.769229 | ||||||||
\(251\) | −27.4244 | −1.73101 | −0.865505 | − | 0.500900i | \(-0.833002\pi\) | ||||
−0.865505 | + | 0.500900i | \(0.833002\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.33682 | 0.524131 | ||||||||
\(254\) | −18.1805 | −1.14075 | ||||||||
\(255\) | 4.36097 | 0.273094 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −28.5236 | −1.77925 | −0.889625 | − | 0.456692i | \(-0.849034\pi\) | ||||
−0.889625 | + | 0.456692i | \(0.849034\pi\) | |||||||
\(258\) | −2.60442 | −0.162144 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 9.73240 | 0.603578 | ||||||||
\(261\) | 22.1759 | 1.37265 | ||||||||
\(262\) | 7.93541 | 0.490252 | ||||||||
\(263\) | −10.4302 | −0.643153 | −0.321576 | − | 0.946884i | \(-0.604213\pi\) | ||||
−0.321576 | + | 0.946884i | \(0.604213\pi\) | |||||||
\(264\) | −0.697788 | −0.0429459 | ||||||||
\(265\) | 11.9129 | 0.731802 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.82576 | −0.478929 | ||||||||
\(268\) | −9.77908 | −0.597352 | ||||||||
\(269\) | −0.133802 | −0.00815804 | −0.00407902 | − | 0.999992i | \(-0.501298\pi\) | ||||
−0.00407902 | + | 0.999992i | \(0.501298\pi\) | |||||||
\(270\) | 5.53401 | 0.336789 | ||||||||
\(271\) | 28.9296 | 1.75735 | 0.878674 | − | 0.477423i | \(-0.158429\pi\) | ||||
0.878674 | + | 0.477423i | \(0.158429\pi\) | |||||||
\(272\) | 4.51730 | 0.273902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.19719 | 0.555623 | ||||||||
\(275\) | 2.04668 | 0.123420 | ||||||||
\(276\) | 3.19719 | 0.192448 | ||||||||
\(277\) | 19.1280 | 1.14929 | 0.574644 | − | 0.818403i | \(-0.305140\pi\) | ||||
0.574644 | + | 0.818403i | \(0.305140\pi\) | |||||||
\(278\) | −0.831590 | −0.0498755 | ||||||||
\(279\) | 1.90663 | 0.114147 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.49940 | −0.387722 | −0.193861 | − | 0.981029i | \(-0.562101\pi\) | ||||
−0.193861 | + | 0.981029i | \(0.562101\pi\) | |||||||
\(282\) | 1.44064 | 0.0857891 | ||||||||
\(283\) | 30.9942 | 1.84241 | 0.921206 | − | 0.389075i | \(-0.127205\pi\) | ||||
0.921206 | + | 0.389075i | \(0.127205\pi\) | |||||||
\(284\) | 1.66318 | 0.0986916 | ||||||||
\(285\) | −3.10382 | −0.183855 | ||||||||
\(286\) | −7.03461 | −0.415965 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.73240 | 0.161008 | ||||||||
\(289\) | 3.40604 | 0.200355 | ||||||||
\(290\) | −15.1459 | −0.889396 | ||||||||
\(291\) | 2.03341 | 0.119201 | ||||||||
\(292\) | 2.96539 | 0.173536 | ||||||||
\(293\) | 9.48270 | 0.553985 | 0.276993 | − | 0.960872i | \(-0.410662\pi\) | ||||
0.276993 | + | 0.960872i | \(0.410662\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.6453 | −1.26024 | ||||||||
\(296\) | −7.03461 | −0.408878 | ||||||||
\(297\) | −4.00000 | −0.232104 | ||||||||
\(298\) | −1.77908 | −0.103059 | ||||||||
\(299\) | 32.2318 | 1.86401 | ||||||||
\(300\) | 0.784908 | 0.0453167 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.93078 | 0.226191 | ||||||||
\(303\) | −7.37143 | −0.423477 | ||||||||
\(304\) | −3.21509 | −0.184398 | ||||||||
\(305\) | 25.2485 | 1.44573 | ||||||||
\(306\) | 12.3431 | 0.705606 | ||||||||
\(307\) | 31.1326 | 1.77683 | 0.888416 | − | 0.459040i | \(-0.151806\pi\) | ||||
0.888416 | + | 0.459040i | \(0.151806\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.25714 | −0.299069 | ||||||||
\(310\) | −1.30221 | −0.0739606 | ||||||||
\(311\) | 7.68108 | 0.435554 | 0.217777 | − | 0.975999i | \(-0.430119\pi\) | ||||
0.217777 | + | 0.975999i | \(0.430119\pi\) | |||||||
\(312\) | −2.69779 | −0.152732 | ||||||||
\(313\) | 24.3431 | 1.37595 | 0.687976 | − | 0.725734i | \(-0.258500\pi\) | ||||
0.687976 | + | 0.725734i | \(0.258500\pi\) | |||||||
\(314\) | 4.58652 | 0.258832 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.46479 | −0.419927 | ||||||||
\(317\) | 8.88290 | 0.498914 | 0.249457 | − | 0.968386i | \(-0.419748\pi\) | ||||
0.249457 | + | 0.968386i | \(0.419748\pi\) | |||||||
\(318\) | −3.30221 | −0.185179 | ||||||||
\(319\) | 10.9475 | 0.612942 | ||||||||
\(320\) | −1.86620 | −0.104324 | ||||||||
\(321\) | −0.673639 | −0.0375989 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.5236 | −0.808112 | ||||||||
\(324\) | 6.66318 | 0.370177 | ||||||||
\(325\) | 7.91288 | 0.438928 | ||||||||
\(326\) | 24.2318 | 1.34208 | ||||||||
\(327\) | −5.02295 | −0.277770 | ||||||||
\(328\) | 1.00000 | 0.0552158 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.30221 | 0.0716844 | ||||||||
\(331\) | −35.5356 | −1.95321 | −0.976607 | − | 0.215031i | \(-0.931015\pi\) | ||||
−0.976607 | + | 0.215031i | \(0.931015\pi\) | |||||||
\(332\) | −14.5640 | −0.799303 | ||||||||
\(333\) | −19.2213 | −1.05332 | ||||||||
\(334\) | −3.23300 | −0.176902 | ||||||||
\(335\) | 18.2497 | 0.997088 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.3252 | 0.780341 | 0.390171 | − | 0.920743i | \(-0.372416\pi\) | ||||
0.390171 | + | 0.920743i | \(0.372416\pi\) | |||||||
\(338\) | −14.1972 | −0.772225 | ||||||||
\(339\) | 4.90544 | 0.266427 | ||||||||
\(340\) | −8.43018 | −0.457191 | ||||||||
\(341\) | 0.941243 | 0.0509712 | ||||||||
\(342\) | −8.78491 | −0.475033 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.03461 | 0.271448 | ||||||||
\(345\) | −5.96659 | −0.321230 | ||||||||
\(346\) | −3.23763 | −0.174056 | ||||||||
\(347\) | 17.4423 | 0.936350 | 0.468175 | − | 0.883636i | \(-0.344912\pi\) | ||||
0.468175 | + | 0.883636i | \(0.344912\pi\) | |||||||
\(348\) | 4.19839 | 0.225057 | ||||||||
\(349\) | 12.7266 | 0.681238 | 0.340619 | − | 0.940201i | \(-0.389363\pi\) | ||||
0.340619 | + | 0.940201i | \(0.389363\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.4648 | −0.825450 | ||||||||
\(352\) | 1.34889 | 0.0718963 | ||||||||
\(353\) | 14.4060 | 0.766756 | 0.383378 | − | 0.923592i | \(-0.374761\pi\) | ||||
0.383378 | + | 0.923592i | \(0.374761\pi\) | |||||||
\(354\) | 6.00000 | 0.318896 | ||||||||
\(355\) | −3.10382 | −0.164734 | ||||||||
\(356\) | 15.1280 | 0.801781 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.38350 | −0.231675 | ||||||||
\(359\) | 5.30221 | 0.279840 | 0.139920 | − | 0.990163i | \(-0.455315\pi\) | ||||
0.139920 | + | 0.990163i | \(0.455315\pi\) | |||||||
\(360\) | −5.09919 | −0.268751 | ||||||||
\(361\) | −8.66318 | −0.455957 | ||||||||
\(362\) | 4.18048 | 0.219721 | ||||||||
\(363\) | 4.74910 | 0.249263 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.53401 | −0.289663 | ||||||||
\(366\) | −6.99880 | −0.365833 | ||||||||
\(367\) | −13.6032 | −0.710083 | −0.355041 | − | 0.934851i | \(-0.615533\pi\) | ||||
−0.355041 | + | 0.934851i | \(0.615533\pi\) | |||||||
\(368\) | −6.18048 | −0.322180 | ||||||||
\(369\) | 2.73240 | 0.142243 | ||||||||
\(370\) | 13.1280 | 0.682491 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.360969 | 0.0187154 | ||||||||
\(373\) | −20.3010 | −1.05115 | −0.525573 | − | 0.850748i | \(-0.676149\pi\) | ||||
−0.525573 | + | 0.850748i | \(0.676149\pi\) | |||||||
\(374\) | 6.09337 | 0.315080 | ||||||||
\(375\) | −6.29175 | −0.324905 | ||||||||
\(376\) | −2.78491 | −0.143621 | ||||||||
\(377\) | 42.3252 | 2.17986 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.29175 | −0.323186 | −0.161593 | − | 0.986858i | \(-0.551663\pi\) | ||||
−0.161593 | + | 0.986858i | \(0.551663\pi\) | |||||||
\(380\) | 6.00000 | 0.307794 | ||||||||
\(381\) | −9.40484 | −0.481824 | ||||||||
\(382\) | −20.5928 | −1.05362 | ||||||||
\(383\) | 18.3010 | 0.935138 | 0.467569 | − | 0.883957i | \(-0.345130\pi\) | ||||
0.467569 | + | 0.883957i | \(0.345130\pi\) | |||||||
\(384\) | 0.517304 | 0.0263986 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.76700 | 0.242634 | ||||||||
\(387\) | 13.7565 | 0.699285 | ||||||||
\(388\) | −3.93078 | −0.199555 | ||||||||
\(389\) | 1.32636 | 0.0672492 | 0.0336246 | − | 0.999435i | \(-0.489295\pi\) | ||||
0.0336246 | + | 0.999435i | \(0.489295\pi\) | |||||||
\(390\) | 5.03461 | 0.254937 | ||||||||
\(391\) | −27.9191 | −1.41193 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.10502 | 0.207071 | ||||||||
\(394\) | −26.0576 | −1.31276 | ||||||||
\(395\) | 13.9308 | 0.700934 | ||||||||
\(396\) | 3.68571 | 0.185214 | ||||||||
\(397\) | −8.31892 | −0.417514 | −0.208757 | − | 0.977967i | \(-0.566942\pi\) | ||||
−0.208757 | + | 0.977967i | \(0.566942\pi\) | |||||||
\(398\) | −9.71449 | −0.486944 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.51730 | −0.0758652 | ||||||||
\(401\) | 13.0859 | 0.653480 | 0.326740 | − | 0.945114i | \(-0.394050\pi\) | ||||
0.326740 | + | 0.945114i | \(0.394050\pi\) | |||||||
\(402\) | −5.05876 | −0.252308 | ||||||||
\(403\) | 3.63903 | 0.181273 | ||||||||
\(404\) | 14.2497 | 0.708949 | ||||||||
\(405\) | −12.4348 | −0.617891 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.48894 | −0.470349 | ||||||||
\(408\) | 2.33682 | 0.115690 | ||||||||
\(409\) | −15.9308 | −0.787727 | −0.393863 | − | 0.919169i | \(-0.628862\pi\) | ||||
−0.393863 | + | 0.919169i | \(0.628862\pi\) | |||||||
\(410\) | −1.86620 | −0.0921650 | ||||||||
\(411\) | 4.75774 | 0.234682 | ||||||||
\(412\) | 10.1626 | 0.500674 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −16.8875 | −0.829977 | ||||||||
\(415\) | 27.1793 | 1.33418 | ||||||||
\(416\) | 5.21509 | 0.255691 | ||||||||
\(417\) | −0.430185 | −0.0210662 | ||||||||
\(418\) | −4.33682 | −0.212121 | ||||||||
\(419\) | 8.92496 | 0.436013 | 0.218006 | − | 0.975947i | \(-0.430045\pi\) | ||||
0.218006 | + | 0.975947i | \(0.430045\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.08129 | 0.345121 | 0.172560 | − | 0.984999i | \(-0.444796\pi\) | ||||
0.172560 | + | 0.984999i | \(0.444796\pi\) | |||||||
\(422\) | 22.4769 | 1.09416 | ||||||||
\(423\) | −7.60947 | −0.369985 | ||||||||
\(424\) | 6.38350 | 0.310010 | ||||||||
\(425\) | −6.85412 | −0.332474 | ||||||||
\(426\) | 0.860370 | 0.0416851 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.30221 | 0.0629448 | ||||||||
\(429\) | −3.63903 | −0.175694 | ||||||||
\(430\) | −9.39558 | −0.453095 | ||||||||
\(431\) | 14.1805 | 0.683050 | 0.341525 | − | 0.939873i | \(-0.389057\pi\) | ||||
0.341525 | + | 0.939873i | \(0.389057\pi\) | |||||||
\(432\) | 2.96539 | 0.142672 | ||||||||
\(433\) | 15.0346 | 0.722517 | 0.361259 | − | 0.932466i | \(-0.382347\pi\) | ||||
0.361259 | + | 0.932466i | \(0.382347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.83502 | −0.375661 | ||||||||
\(436\) | 9.70986 | 0.465018 | ||||||||
\(437\) | 19.8708 | 0.950551 | ||||||||
\(438\) | 1.53401 | 0.0732978 | ||||||||
\(439\) | −22.7491 | −1.08576 | −0.542878 | − | 0.839812i | \(-0.682665\pi\) | ||||
−0.542878 | + | 0.839812i | \(0.682665\pi\) | |||||||
\(440\) | −2.51730 | −0.120008 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 23.5582 | 1.12055 | ||||||||
\(443\) | −13.3956 | −0.636443 | −0.318222 | − | 0.948016i | \(-0.603086\pi\) | ||||
−0.318222 | + | 0.948016i | \(0.603086\pi\) | |||||||
\(444\) | −3.63903 | −0.172701 | ||||||||
\(445\) | −28.2318 | −1.33832 | ||||||||
\(446\) | 17.5340 | 0.830259 | ||||||||
\(447\) | −0.920325 | −0.0435299 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.6632 | −1.11673 | −0.558367 | − | 0.829594i | \(-0.688572\pi\) | ||||
−0.558367 | + | 0.829594i | \(0.688572\pi\) | |||||||
\(450\) | −4.14588 | −0.195438 | ||||||||
\(451\) | 1.34889 | 0.0635169 | ||||||||
\(452\) | −9.48270 | −0.446028 | ||||||||
\(453\) | 2.03341 | 0.0955380 | ||||||||
\(454\) | −18.9475 | −0.889250 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.66318 | −0.0778856 | ||||||||
\(457\) | −12.5928 | −0.589065 | −0.294532 | − | 0.955641i | \(-0.595164\pi\) | ||||
−0.294532 | + | 0.955641i | \(0.595164\pi\) | |||||||
\(458\) | 9.75030 | 0.455602 | ||||||||
\(459\) | 13.3956 | 0.625252 | ||||||||
\(460\) | 11.5340 | 0.537776 | ||||||||
\(461\) | 35.1326 | 1.63629 | 0.818144 | − | 0.575013i | \(-0.195003\pi\) | ||||
0.818144 | + | 0.575013i | \(0.195003\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.6861 | 1.51905 | 0.759527 | − | 0.650476i | \(-0.225431\pi\) | ||||
0.759527 | + | 0.650476i | \(0.225431\pi\) | |||||||
\(464\) | −8.11590 | −0.376771 | ||||||||
\(465\) | −0.673639 | −0.0312393 | ||||||||
\(466\) | −16.5686 | −0.767526 | ||||||||
\(467\) | 15.4244 | 0.713754 | 0.356877 | − | 0.934151i | \(-0.383842\pi\) | ||||
0.356877 | + | 0.934151i | \(0.383842\pi\) | |||||||
\(468\) | 14.2497 | 0.658693 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.19719 | 0.239728 | ||||||||
\(471\) | 2.37263 | 0.109325 | ||||||||
\(472\) | −11.5986 | −0.533869 | ||||||||
\(473\) | 6.79115 | 0.312258 | ||||||||
\(474\) | −3.86157 | −0.177368 | ||||||||
\(475\) | 4.87827 | 0.223831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.4423 | 0.798626 | ||||||||
\(478\) | −4.06922 | −0.186122 | ||||||||
\(479\) | −30.0397 | −1.37255 | −0.686273 | − | 0.727344i | \(-0.740755\pi\) | ||||
−0.686273 | + | 0.727344i | \(0.740755\pi\) | |||||||
\(480\) | −0.965392 | −0.0440639 | ||||||||
\(481\) | −36.6861 | −1.67274 | ||||||||
\(482\) | −3.89498 | −0.177411 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.18048 | −0.417295 | ||||||||
\(485\) | 7.33562 | 0.333093 | ||||||||
\(486\) | 12.3431 | 0.559893 | ||||||||
\(487\) | 6.83622 | 0.309779 | 0.154889 | − | 0.987932i | \(-0.450498\pi\) | ||||
0.154889 | + | 0.987932i | \(0.450498\pi\) | |||||||
\(488\) | 13.5294 | 0.612446 | ||||||||
\(489\) | 12.5352 | 0.566862 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.4302 | 0.470708 | 0.235354 | − | 0.971910i | \(-0.424375\pi\) | ||||
0.235354 | + | 0.971910i | \(0.424375\pi\) | |||||||
\(492\) | 0.517304 | 0.0233219 | ||||||||
\(493\) | −36.6620 | −1.65117 | ||||||||
\(494\) | −16.7670 | −0.754383 | ||||||||
\(495\) | −6.87827 | −0.309155 | ||||||||
\(496\) | −0.697788 | −0.0313316 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.53401 | −0.337607 | ||||||||
\(499\) | −12.7895 | −0.572538 | −0.286269 | − | 0.958149i | \(-0.592415\pi\) | ||||
−0.286269 | + | 0.958149i | \(0.592415\pi\) | |||||||
\(500\) | 12.1626 | 0.543927 | ||||||||
\(501\) | −1.67244 | −0.0747192 | ||||||||
\(502\) | 27.4244 | 1.22401 | ||||||||
\(503\) | 33.3956 | 1.48904 | 0.744518 | − | 0.667603i | \(-0.232680\pi\) | ||||
0.744518 | + | 0.667603i | \(0.232680\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.5928 | −1.18336 | ||||||||
\(506\) | −8.33682 | −0.370617 | ||||||||
\(507\) | −7.34426 | −0.326170 | ||||||||
\(508\) | 18.1805 | 0.806629 | ||||||||
\(509\) | −20.6799 | −0.916620 | −0.458310 | − | 0.888792i | \(-0.651545\pi\) | ||||
−0.458310 | + | 0.888792i | \(0.651545\pi\) | |||||||
\(510\) | −4.36097 | −0.193107 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −9.53401 | −0.420937 | ||||||||
\(514\) | 28.5236 | 1.25812 | ||||||||
\(515\) | −18.9654 | −0.835715 | ||||||||
\(516\) | 2.60442 | 0.114653 | ||||||||
\(517\) | −3.75655 | −0.165213 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.67484 | −0.0735172 | ||||||||
\(520\) | −9.73240 | −0.426794 | ||||||||
\(521\) | 9.23924 | 0.404779 | 0.202389 | − | 0.979305i | \(-0.435129\pi\) | ||||
0.202389 | + | 0.979305i | \(0.435129\pi\) | |||||||
\(522\) | −22.1759 | −0.970611 | ||||||||
\(523\) | −3.46016 | −0.151302 | −0.0756512 | − | 0.997134i | \(-0.524104\pi\) | ||||
−0.0756512 | + | 0.997134i | \(0.524104\pi\) | |||||||
\(524\) | −7.93541 | −0.346660 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.4302 | 0.454778 | ||||||||
\(527\) | −3.15212 | −0.137309 | ||||||||
\(528\) | 0.697788 | 0.0303673 | ||||||||
\(529\) | 15.1984 | 0.660799 | ||||||||
\(530\) | −11.9129 | −0.517462 | ||||||||
\(531\) | −31.6920 | −1.37531 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.21509 | 0.225891 | ||||||||
\(534\) | 7.82576 | 0.338654 | ||||||||
\(535\) | −2.43018 | −0.105066 | ||||||||
\(536\) | 9.77908 | 0.422392 | ||||||||
\(537\) | −2.26760 | −0.0978543 | ||||||||
\(538\) | 0.133802 | 0.00576860 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.53401 | −0.238146 | ||||||||
\(541\) | −23.7207 | −1.01983 | −0.509917 | − | 0.860224i | \(-0.670324\pi\) | ||||
−0.509917 | + | 0.860224i | \(0.670324\pi\) | |||||||
\(542\) | −28.9296 | −1.24263 | ||||||||
\(543\) | 2.16258 | 0.0928053 | ||||||||
\(544\) | −4.51730 | −0.193678 | ||||||||
\(545\) | −18.1205 | −0.776198 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.6165 | −1.26631 | −0.633155 | − | 0.774025i | \(-0.718240\pi\) | ||||
−0.633155 | + | 0.774025i | \(0.718240\pi\) | |||||||
\(548\) | −9.19719 | −0.392884 | ||||||||
\(549\) | 36.9676 | 1.57774 | ||||||||
\(550\) | −2.04668 | −0.0872708 | ||||||||
\(551\) | 26.0934 | 1.11161 | ||||||||
\(552\) | −3.19719 | −0.136081 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −19.1280 | −0.812670 | ||||||||
\(555\) | 6.79115 | 0.288268 | ||||||||
\(556\) | 0.831590 | 0.0352673 | ||||||||
\(557\) | 11.6406 | 0.493230 | 0.246615 | − | 0.969114i | \(-0.420682\pi\) | ||||
0.246615 | + | 0.969114i | \(0.420682\pi\) | |||||||
\(558\) | −1.90663 | −0.0807143 | ||||||||
\(559\) | 26.2559 | 1.11051 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.15212 | 0.133083 | ||||||||
\(562\) | 6.49940 | 0.274161 | ||||||||
\(563\) | 37.9129 | 1.59784 | 0.798919 | − | 0.601439i | \(-0.205406\pi\) | ||||
0.798919 | + | 0.601439i | \(0.205406\pi\) | |||||||
\(564\) | −1.44064 | −0.0606621 | ||||||||
\(565\) | 17.6966 | 0.744501 | ||||||||
\(566\) | −30.9942 | −1.30278 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.66318 | −0.0697855 | ||||||||
\(569\) | 13.4827 | 0.565224 | 0.282612 | − | 0.959234i | \(-0.408799\pi\) | ||||
0.282612 | + | 0.959234i | \(0.408799\pi\) | |||||||
\(570\) | 3.10382 | 0.130005 | ||||||||
\(571\) | −7.52313 | −0.314833 | −0.157417 | − | 0.987532i | \(-0.550317\pi\) | ||||
−0.157417 | + | 0.987532i | \(0.550317\pi\) | |||||||
\(572\) | 7.03461 | 0.294132 | ||||||||
\(573\) | −10.6527 | −0.445024 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.37767 | 0.391076 | ||||||||
\(576\) | −2.73240 | −0.113850 | ||||||||
\(577\) | −44.1688 | −1.83877 | −0.919386 | − | 0.393356i | \(-0.871314\pi\) | ||||
−0.919386 | + | 0.393356i | \(0.871314\pi\) | |||||||
\(578\) | −3.40604 | −0.141672 | ||||||||
\(579\) | 2.46599 | 0.102483 | ||||||||
\(580\) | 15.1459 | 0.628898 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.03341 | −0.0842876 | ||||||||
\(583\) | 8.61067 | 0.356617 | ||||||||
\(584\) | −2.96539 | −0.122709 | ||||||||
\(585\) | −26.5928 | −1.09948 | ||||||||
\(586\) | −9.48270 | −0.391727 | ||||||||
\(587\) | 31.4018 | 1.29609 | 0.648046 | − | 0.761601i | \(-0.275586\pi\) | ||||
0.648046 | + | 0.761601i | \(0.275586\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.24345 | 0.0924399 | ||||||||
\(590\) | 21.6453 | 0.891122 | ||||||||
\(591\) | −13.4797 | −0.554480 | ||||||||
\(592\) | 7.03461 | 0.289121 | ||||||||
\(593\) | −20.4302 | −0.838967 | −0.419484 | − | 0.907763i | \(-0.637789\pi\) | ||||
−0.419484 | + | 0.907763i | \(0.637789\pi\) | |||||||
\(594\) | 4.00000 | 0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.77908 | 0.0728739 | ||||||||
\(597\) | −5.02535 | −0.205674 | ||||||||
\(598\) | −32.2318 | −1.31806 | ||||||||
\(599\) | 6.30101 | 0.257452 | 0.128726 | − | 0.991680i | \(-0.458911\pi\) | ||||
0.128726 | + | 0.991680i | \(0.458911\pi\) | |||||||
\(600\) | −0.784908 | −0.0320437 | ||||||||
\(601\) | −43.0501 | −1.75605 | −0.878025 | − | 0.478614i | \(-0.841139\pi\) | ||||
−0.878025 | + | 0.478614i | \(0.841139\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 26.7203 | 1.08814 | ||||||||
\(604\) | −3.93078 | −0.159941 | ||||||||
\(605\) | 17.1326 | 0.696539 | ||||||||
\(606\) | 7.37143 | 0.299444 | ||||||||
\(607\) | −10.0000 | −0.405887 | −0.202944 | − | 0.979190i | \(-0.565051\pi\) | ||||
−0.202944 | + | 0.979190i | \(0.565051\pi\) | |||||||
\(608\) | 3.21509 | 0.130389 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −25.2485 | −1.02228 | ||||||||
\(611\) | −14.5236 | −0.587560 | ||||||||
\(612\) | −12.3431 | −0.498939 | ||||||||
\(613\) | −33.0680 | −1.33560 | −0.667802 | − | 0.744339i | \(-0.732765\pi\) | ||||
−0.667802 | + | 0.744339i | \(0.732765\pi\) | |||||||
\(614\) | −31.1326 | −1.25641 | ||||||||
\(615\) | −0.965392 | −0.0389284 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.5519 | 1.27023 | 0.635116 | − | 0.772417i | \(-0.280952\pi\) | ||||
0.635116 | + | 0.772417i | \(0.280952\pi\) | |||||||
\(618\) | 5.25714 | 0.211473 | ||||||||
\(619\) | 2.92496 | 0.117564 | 0.0587819 | − | 0.998271i | \(-0.481278\pi\) | ||||
0.0587819 | + | 0.998271i | \(0.481278\pi\) | |||||||
\(620\) | 1.30221 | 0.0522981 | ||||||||
\(621\) | −18.3276 | −0.735460 | ||||||||
\(622\) | −7.68108 | −0.307983 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.69779 | 0.107998 | ||||||||
\(625\) | −15.1113 | −0.604451 | ||||||||
\(626\) | −24.3431 | −0.972945 | ||||||||
\(627\) | −2.24345 | −0.0895949 | ||||||||
\(628\) | −4.58652 | −0.183022 | ||||||||
\(629\) | 31.7775 | 1.26705 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.87827 | −0.353438 | −0.176719 | − | 0.984261i | \(-0.556548\pi\) | ||||
−0.176719 | + | 0.984261i | \(0.556548\pi\) | |||||||
\(632\) | 7.46479 | 0.296934 | ||||||||
\(633\) | 11.6274 | 0.462147 | ||||||||
\(634\) | −8.88290 | −0.352785 | ||||||||
\(635\) | −33.9284 | −1.34641 | ||||||||
\(636\) | 3.30221 | 0.130941 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10.9475 | −0.433415 | ||||||||
\(639\) | −4.54447 | −0.179776 | ||||||||
\(640\) | 1.86620 | 0.0737680 | ||||||||
\(641\) | 8.49014 | 0.335340 | 0.167670 | − | 0.985843i | \(-0.446376\pi\) | ||||
0.167670 | + | 0.985843i | \(0.446376\pi\) | |||||||
\(642\) | 0.673639 | 0.0265864 | ||||||||
\(643\) | 45.3777 | 1.78952 | 0.894760 | − | 0.446547i | \(-0.147346\pi\) | ||||
0.894760 | + | 0.446547i | \(0.147346\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.86037 | −0.191377 | ||||||||
\(646\) | 14.5236 | 0.571421 | ||||||||
\(647\) | 11.5940 | 0.455806 | 0.227903 | − | 0.973684i | \(-0.426813\pi\) | ||||
0.227903 | + | 0.973684i | \(0.426813\pi\) | |||||||
\(648\) | −6.66318 | −0.261754 | ||||||||
\(649\) | −15.6453 | −0.614131 | ||||||||
\(650\) | −7.91288 | −0.310369 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −24.2318 | −0.948990 | ||||||||
\(653\) | −5.82415 | −0.227916 | −0.113958 | − | 0.993486i | \(-0.536353\pi\) | ||||
−0.113958 | + | 0.993486i | \(0.536353\pi\) | |||||||
\(654\) | 5.02295 | 0.196413 | ||||||||
\(655\) | 14.8091 | 0.578638 | ||||||||
\(656\) | −1.00000 | −0.0390434 | ||||||||
\(657\) | −8.10263 | −0.316114 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.1863 | 0.513666 | 0.256833 | − | 0.966456i | \(-0.417321\pi\) | ||||
0.256833 | + | 0.966456i | \(0.417321\pi\) | |||||||
\(660\) | −1.30221 | −0.0506885 | ||||||||
\(661\) | −23.5052 | −0.914247 | −0.457124 | − | 0.889403i | \(-0.651120\pi\) | ||||
−0.457124 | + | 0.889403i | \(0.651120\pi\) | |||||||
\(662\) | 35.5356 | 1.38113 | ||||||||
\(663\) | 12.1867 | 0.473293 | ||||||||
\(664\) | 14.5640 | 0.565192 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 19.2213 | 0.744812 | ||||||||
\(667\) | 50.1602 | 1.94221 | ||||||||
\(668\) | 3.23300 | 0.125088 | ||||||||
\(669\) | 9.07041 | 0.350682 | ||||||||
\(670\) | −18.2497 | −0.705047 | ||||||||
\(671\) | 18.2497 | 0.704522 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.4531 | 1.21243 | 0.606215 | − | 0.795301i | \(-0.292687\pi\) | ||||
0.606215 | + | 0.795301i | \(0.292687\pi\) | |||||||
\(674\) | −14.3252 | −0.551785 | ||||||||
\(675\) | −4.49940 | −0.173182 | ||||||||
\(676\) | 14.1972 | 0.546046 | ||||||||
\(677\) | −45.7495 | −1.75830 | −0.879148 | − | 0.476548i | \(-0.841888\pi\) | ||||
−0.879148 | + | 0.476548i | \(0.841888\pi\) | |||||||
\(678\) | −4.90544 | −0.188392 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8.43018 | 0.323283 | ||||||||
\(681\) | −9.80161 | −0.375599 | ||||||||
\(682\) | −0.941243 | −0.0360420 | ||||||||
\(683\) | 15.2105 | 0.582012 | 0.291006 | − | 0.956721i | \(-0.406010\pi\) | ||||
0.291006 | + | 0.956721i | \(0.406010\pi\) | |||||||
\(684\) | 8.78491 | 0.335899 | ||||||||
\(685\) | 17.1638 | 0.655794 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.04387 | 0.192436 | ||||||||
\(688\) | −5.03461 | −0.191943 | ||||||||
\(689\) | 33.2906 | 1.26827 | ||||||||
\(690\) | 5.96659 | 0.227144 | ||||||||
\(691\) | 7.17929 | 0.273113 | 0.136556 | − | 0.990632i | \(-0.456396\pi\) | ||||
0.136556 | + | 0.990632i | \(0.456396\pi\) | |||||||
\(692\) | 3.23763 | 0.123076 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.4423 | −0.662099 | ||||||||
\(695\) | −1.55191 | −0.0588674 | ||||||||
\(696\) | −4.19839 | −0.159139 | ||||||||
\(697\) | −4.51730 | −0.171105 | ||||||||
\(698\) | −12.7266 | −0.481708 | ||||||||
\(699\) | −8.57101 | −0.324185 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.5928 | −1.00439 | −0.502197 | − | 0.864753i | \(-0.667475\pi\) | ||||
−0.502197 | + | 0.864753i | \(0.667475\pi\) | |||||||
\(702\) | 15.4648 | 0.583681 | ||||||||
\(703\) | −22.6169 | −0.853013 | ||||||||
\(704\) | −1.34889 | −0.0508384 | ||||||||
\(705\) | 2.68853 | 0.101256 | ||||||||
\(706\) | −14.4060 | −0.542178 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.00000 | −0.225494 | ||||||||
\(709\) | −6.20926 | −0.233194 | −0.116597 | − | 0.993179i | \(-0.537199\pi\) | ||||
−0.116597 | + | 0.993179i | \(0.537199\pi\) | |||||||
\(710\) | 3.10382 | 0.116484 | ||||||||
\(711\) | 20.3968 | 0.764939 | ||||||||
\(712\) | −15.1280 | −0.566945 | ||||||||
\(713\) | 4.31267 | 0.161511 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.1280 | −0.490958 | ||||||||
\(716\) | 4.38350 | 0.163819 | ||||||||
\(717\) | −2.10502 | −0.0786135 | ||||||||
\(718\) | −5.30221 | −0.197877 | ||||||||
\(719\) | −17.3022 | −0.645264 | −0.322632 | − | 0.946525i | \(-0.604568\pi\) | ||||
−0.322632 | + | 0.946525i | \(0.604568\pi\) | |||||||
\(720\) | 5.09919 | 0.190036 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 8.66318 | 0.322410 | ||||||||
\(723\) | −2.01489 | −0.0749345 | ||||||||
\(724\) | −4.18048 | −0.155366 | ||||||||
\(725\) | 12.3143 | 0.457341 | ||||||||
\(726\) | −4.74910 | −0.176256 | ||||||||
\(727\) | 2.55936 | 0.0949213 | 0.0474606 | − | 0.998873i | \(-0.484887\pi\) | ||||
0.0474606 | + | 0.998873i | \(0.484887\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.6044 | −0.503868 | ||||||||
\(730\) | 5.53401 | 0.204823 | ||||||||
\(731\) | −22.7429 | −0.841175 | ||||||||
\(732\) | 6.99880 | 0.258683 | ||||||||
\(733\) | −23.6678 | −0.874191 | −0.437095 | − | 0.899415i | \(-0.643993\pi\) | ||||
−0.437095 | + | 0.899415i | \(0.643993\pi\) | |||||||
\(734\) | 13.6032 | 0.502104 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.18048 | 0.227816 | ||||||||
\(737\) | 13.1909 | 0.485895 | ||||||||
\(738\) | −2.73240 | −0.100581 | ||||||||
\(739\) | −13.8950 | −0.511135 | −0.255568 | − | 0.966791i | \(-0.582262\pi\) | ||||
−0.255568 | + | 0.966791i | \(0.582262\pi\) | |||||||
\(740\) | −13.1280 | −0.482594 | ||||||||
\(741\) | −8.67364 | −0.318634 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.8592 | 1.53566 | 0.767832 | − | 0.640651i | \(-0.221336\pi\) | ||||
0.767832 | + | 0.640651i | \(0.221336\pi\) | |||||||
\(744\) | −0.360969 | −0.0132338 | ||||||||
\(745\) | −3.32011 | −0.121640 | ||||||||
\(746\) | 20.3010 | 0.743273 | ||||||||
\(747\) | 39.7946 | 1.45601 | ||||||||
\(748\) | −6.09337 | −0.222796 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 6.29175 | 0.229742 | ||||||||
\(751\) | 37.1163 | 1.35439 | 0.677197 | − | 0.735802i | \(-0.263195\pi\) | ||||
0.677197 | + | 0.735802i | \(0.263195\pi\) | |||||||
\(752\) | 2.78491 | 0.101555 | ||||||||
\(753\) | 14.1867 | 0.516993 | ||||||||
\(754\) | −42.3252 | −1.54139 | ||||||||
\(755\) | 7.33562 | 0.266971 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.7779 | 0.827876 | 0.413938 | − | 0.910305i | \(-0.364153\pi\) | ||||
0.413938 | + | 0.910305i | \(0.364153\pi\) | |||||||
\(758\) | 6.29175 | 0.228527 | ||||||||
\(759\) | −4.31267 | −0.156540 | ||||||||
\(760\) | −6.00000 | −0.217643 | ||||||||
\(761\) | −31.7324 | −1.15030 | −0.575149 | − | 0.818049i | \(-0.695056\pi\) | ||||
−0.575149 | + | 0.818049i | \(0.695056\pi\) | |||||||
\(762\) | 9.40484 | 0.340701 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 20.5928 | 0.745020 | ||||||||
\(765\) | 23.0346 | 0.832818 | ||||||||
\(766\) | −18.3010 | −0.661243 | ||||||||
\(767\) | −60.4877 | −2.18409 | ||||||||
\(768\) | −0.517304 | −0.0186666 | ||||||||
\(769\) | 15.9191 | 0.574058 | 0.287029 | − | 0.957922i | \(-0.407332\pi\) | ||||
0.287029 | + | 0.957922i | \(0.407332\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.7553 | 0.531401 | ||||||||
\(772\) | −4.76700 | −0.171568 | ||||||||
\(773\) | 3.18168 | 0.114437 | 0.0572186 | − | 0.998362i | \(-0.481777\pi\) | ||||
0.0572186 | + | 0.998362i | \(0.481777\pi\) | |||||||
\(774\) | −13.7565 | −0.494469 | ||||||||
\(775\) | 1.05876 | 0.0380317 | ||||||||
\(776\) | 3.93078 | 0.141107 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.32636 | −0.0475523 | ||||||||
\(779\) | 3.21509 | 0.115193 | ||||||||
\(780\) | −5.03461 | −0.180268 | ||||||||
\(781\) | −2.24345 | −0.0802771 | ||||||||
\(782\) | 27.9191 | 0.998386 | ||||||||
\(783\) | −24.0668 | −0.860078 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.55936 | 0.305497 | ||||||||
\(786\) | −4.10502 | −0.146421 | ||||||||
\(787\) | −32.4014 | −1.15499 | −0.577493 | − | 0.816396i | \(-0.695969\pi\) | ||||
−0.577493 | + | 0.816396i | \(0.695969\pi\) | |||||||
\(788\) | 26.0576 | 0.928262 | ||||||||
\(789\) | 5.39558 | 0.192088 | ||||||||
\(790\) | −13.9308 | −0.495635 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.68571 | −0.130966 | ||||||||
\(793\) | 70.5570 | 2.50555 | ||||||||
\(794\) | 8.31892 | 0.295227 | ||||||||
\(795\) | −6.16258 | −0.218564 | ||||||||
\(796\) | 9.71449 | 0.344321 | ||||||||
\(797\) | −36.5974 | −1.29635 | −0.648173 | − | 0.761493i | \(-0.724467\pi\) | ||||
−0.648173 | + | 0.761493i | \(0.724467\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.5803 | 0.445058 | ||||||||
\(800\) | 1.51730 | 0.0536448 | ||||||||
\(801\) | −41.3356 | −1.46052 | ||||||||
\(802\) | −13.0859 | −0.462080 | ||||||||
\(803\) | −4.00000 | −0.141157 | ||||||||
\(804\) | 5.05876 | 0.178409 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.63903 | −0.128179 | ||||||||
\(807\) | 0.0692162 | 0.00243652 | ||||||||
\(808\) | −14.2497 | −0.501303 | ||||||||
\(809\) | −45.7658 | −1.60904 | −0.804520 | − | 0.593926i | \(-0.797577\pi\) | ||||
−0.804520 | + | 0.593926i | \(0.797577\pi\) | |||||||
\(810\) | 12.4348 | 0.436915 | ||||||||
\(811\) | −23.7612 | −0.834368 | −0.417184 | − | 0.908822i | \(-0.636983\pi\) | ||||
−0.417184 | + | 0.908822i | \(0.636983\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.9654 | −0.524859 | ||||||||
\(814\) | 9.48894 | 0.332587 | ||||||||
\(815\) | 45.2213 | 1.58403 | ||||||||
\(816\) | −2.33682 | −0.0818051 | ||||||||
\(817\) | 16.1867 | 0.566302 | ||||||||
\(818\) | 15.9308 | 0.557007 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.86620 | 0.0651705 | ||||||||
\(821\) | −35.5698 | −1.24140 | −0.620698 | − | 0.784050i | \(-0.713151\pi\) | ||||
−0.620698 | + | 0.784050i | \(0.713151\pi\) | |||||||
\(822\) | −4.75774 | −0.165945 | ||||||||
\(823\) | 20.0576 | 0.699163 | 0.349581 | − | 0.936906i | \(-0.386324\pi\) | ||||
0.349581 | + | 0.936906i | \(0.386324\pi\) | |||||||
\(824\) | −10.1626 | −0.354030 | ||||||||
\(825\) | −1.05876 | −0.0368612 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.1839 | −1.64075 | −0.820373 | − | 0.571829i | \(-0.806234\pi\) | ||||
−0.820373 | + | 0.571829i | \(0.806234\pi\) | |||||||
\(828\) | 16.8875 | 0.586882 | ||||||||
\(829\) | −55.7612 | −1.93667 | −0.968333 | − | 0.249663i | \(-0.919680\pi\) | ||||
−0.968333 | + | 0.249663i | \(0.919680\pi\) | |||||||
\(830\) | −27.1793 | −0.943407 | ||||||||
\(831\) | −9.89498 | −0.343253 | ||||||||
\(832\) | −5.21509 | −0.180801 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.430185 | 0.0148961 | ||||||||
\(835\) | −6.03341 | −0.208795 | ||||||||
\(836\) | 4.33682 | 0.149992 | ||||||||
\(837\) | −2.06922 | −0.0715226 | ||||||||
\(838\) | −8.92496 | −0.308307 | ||||||||
\(839\) | −29.0050 | −1.00137 | −0.500683 | − | 0.865631i | \(-0.666918\pi\) | ||||
−0.500683 | + | 0.865631i | \(0.666918\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.8678 | 1.27130 | ||||||||
\(842\) | −7.08129 | −0.244037 | ||||||||
\(843\) | 3.36217 | 0.115799 | ||||||||
\(844\) | −22.4769 | −0.773686 | ||||||||
\(845\) | −26.4948 | −0.911448 | ||||||||
\(846\) | 7.60947 | 0.261619 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.38350 | −0.219210 | ||||||||
\(849\) | −16.0334 | −0.550265 | ||||||||
\(850\) | 6.85412 | 0.235095 | ||||||||
\(851\) | −43.4773 | −1.49038 | ||||||||
\(852\) | −0.860370 | −0.0294758 | ||||||||
\(853\) | 47.1660 | 1.61493 | 0.807467 | − | 0.589913i | \(-0.200838\pi\) | ||||
0.807467 | + | 0.589913i | \(0.200838\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.3944 | −0.560676 | ||||||||
\(856\) | −1.30221 | −0.0445087 | ||||||||
\(857\) | −11.7565 | −0.401596 | −0.200798 | − | 0.979633i | \(-0.564353\pi\) | ||||
−0.200798 | + | 0.979633i | \(0.564353\pi\) | |||||||
\(858\) | 3.63903 | 0.124234 | ||||||||
\(859\) | −15.3551 | −0.523911 | −0.261955 | − | 0.965080i | \(-0.584367\pi\) | ||||
−0.261955 | + | 0.965080i | \(0.584367\pi\) | |||||||
\(860\) | 9.39558 | 0.320387 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.1805 | −0.482989 | ||||||||
\(863\) | −6.55936 | −0.223283 | −0.111642 | − | 0.993749i | \(-0.535611\pi\) | ||||
−0.111642 | + | 0.993749i | \(0.535611\pi\) | |||||||
\(864\) | −2.96539 | −0.100885 | ||||||||
\(865\) | −6.04205 | −0.205436 | ||||||||
\(866\) | −15.0346 | −0.510897 | ||||||||
\(867\) | −1.76196 | −0.0598392 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.0692 | 0.341575 | ||||||||
\(870\) | 7.83502 | 0.265632 | ||||||||
\(871\) | 50.9988 | 1.72803 | ||||||||
\(872\) | −9.70986 | −0.328817 | ||||||||
\(873\) | 10.7405 | 0.363509 | ||||||||
\(874\) | −19.8708 | −0.672141 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.53401 | −0.0518294 | ||||||||
\(877\) | −7.52475 | −0.254093 | −0.127046 | − | 0.991897i | \(-0.540550\pi\) | ||||
−0.127046 | + | 0.991897i | \(0.540550\pi\) | |||||||
\(878\) | 22.7491 | 0.767745 | ||||||||
\(879\) | −4.90544 | −0.165456 | ||||||||
\(880\) | 2.51730 | 0.0848583 | ||||||||
\(881\) | −1.59396 | −0.0537020 | −0.0268510 | − | 0.999639i | \(-0.508548\pi\) | ||||
−0.0268510 | + | 0.999639i | \(0.508548\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.98793 | −0.302468 | −0.151234 | − | 0.988498i | \(-0.548325\pi\) | ||||
−0.151234 | + | 0.988498i | \(0.548325\pi\) | |||||||
\(884\) | −23.5582 | −0.792347 | ||||||||
\(885\) | 11.1972 | 0.376389 | ||||||||
\(886\) | 13.3956 | 0.450033 | ||||||||
\(887\) | 37.0050 | 1.24251 | 0.621254 | − | 0.783609i | \(-0.286624\pi\) | ||||
0.621254 | + | 0.783609i | \(0.286624\pi\) | |||||||
\(888\) | 3.63903 | 0.122118 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 28.2318 | 0.946332 | ||||||||
\(891\) | −8.98793 | −0.301107 | ||||||||
\(892\) | −17.5340 | −0.587082 | ||||||||
\(893\) | −8.95374 | −0.299625 | ||||||||
\(894\) | 0.920325 | 0.0307803 | ||||||||
\(895\) | −8.18048 | −0.273443 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.6736 | −0.556717 | ||||||||
\(898\) | 23.6632 | 0.789651 | ||||||||
\(899\) | 5.66318 | 0.188878 | ||||||||
\(900\) | 4.14588 | 0.138196 | ||||||||
\(901\) | −28.8362 | −0.960674 | ||||||||
\(902\) | −1.34889 | −0.0449133 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.48270 | 0.315390 | ||||||||
\(905\) | 7.80161 | 0.259334 | ||||||||
\(906\) | −2.03341 | −0.0675555 | ||||||||
\(907\) | −2.79115 | −0.0926787 | −0.0463394 | − | 0.998926i | \(-0.514756\pi\) | ||||
−0.0463394 | + | 0.998926i | \(0.514756\pi\) | |||||||
\(908\) | 18.9475 | 0.628795 | ||||||||
\(909\) | −38.9358 | −1.29142 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.2485 | 1.36662 | 0.683312 | − | 0.730127i | \(-0.260539\pi\) | ||||
0.683312 | + | 0.730127i | \(0.260539\pi\) | |||||||
\(912\) | 1.66318 | 0.0550734 | ||||||||
\(913\) | 19.6453 | 0.650164 | ||||||||
\(914\) | 12.5928 | 0.416532 | ||||||||
\(915\) | −13.0612 | −0.431788 | ||||||||
\(916\) | −9.75030 | −0.322159 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −13.3956 | −0.442120 | ||||||||
\(919\) | −31.7324 | −1.04676 | −0.523378 | − | 0.852101i | \(-0.675328\pi\) | ||||
−0.523378 | + | 0.852101i | \(0.675328\pi\) | |||||||
\(920\) | −11.5340 | −0.380265 | ||||||||
\(921\) | −16.1050 | −0.530679 | ||||||||
\(922\) | −35.1326 | −1.15703 | ||||||||
\(923\) | −8.67364 | −0.285496 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.6736 | −0.350947 | ||||||||
\(926\) | −32.6861 | −1.07413 | ||||||||
\(927\) | −27.7682 | −0.912027 | ||||||||
\(928\) | 8.11590 | 0.266417 | ||||||||
\(929\) | −35.3022 | −1.15823 | −0.579114 | − | 0.815247i | \(-0.696601\pi\) | ||||
−0.579114 | + | 0.815247i | \(0.696601\pi\) | |||||||
\(930\) | 0.673639 | 0.0220895 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 16.5686 | 0.542723 | ||||||||
\(933\) | −3.97346 | −0.130085 | ||||||||
\(934\) | −15.4244 | −0.504700 | ||||||||
\(935\) | 11.3714 | 0.371885 | ||||||||
\(936\) | −14.2497 | −0.465766 | ||||||||
\(937\) | −21.4290 | −0.700054 | −0.350027 | − | 0.936740i | \(-0.613828\pi\) | ||||
−0.350027 | + | 0.936740i | \(0.613828\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.5928 | −0.410949 | ||||||||
\(940\) | −5.19719 | −0.169514 | ||||||||
\(941\) | −37.9930 | −1.23854 | −0.619268 | − | 0.785180i | \(-0.712570\pi\) | ||||
−0.619268 | + | 0.785180i | \(0.712570\pi\) | |||||||
\(942\) | −2.37263 | −0.0773043 | ||||||||
\(943\) | 6.18048 | 0.201264 | ||||||||
\(944\) | 11.5986 | 0.377502 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.79115 | −0.220799 | ||||||||
\(947\) | −57.5465 | −1.87001 | −0.935005 | − | 0.354634i | \(-0.884605\pi\) | ||||
−0.935005 | + | 0.354634i | \(0.884605\pi\) | |||||||
\(948\) | 3.86157 | 0.125418 | ||||||||
\(949\) | −15.4648 | −0.502008 | ||||||||
\(950\) | −4.87827 | −0.158272 | ||||||||
\(951\) | −4.59516 | −0.149008 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53.5044 | −1.73318 | −0.866590 | − | 0.499022i | \(-0.833693\pi\) | ||||
−0.866590 | + | 0.499022i | \(0.833693\pi\) | |||||||
\(954\) | −17.4423 | −0.564714 | ||||||||
\(955\) | −38.4302 | −1.24357 | ||||||||
\(956\) | 4.06922 | 0.131608 | ||||||||
\(957\) | −5.66318 | −0.183065 | ||||||||
\(958\) | 30.0397 | 0.970537 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.965392 | 0.0311579 | ||||||||
\(961\) | −30.5131 | −0.984293 | ||||||||
\(962\) | 36.6861 | 1.18281 | ||||||||
\(963\) | −3.55816 | −0.114660 | ||||||||
\(964\) | 3.89498 | 0.125449 | ||||||||
\(965\) | 8.89618 | 0.286378 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.9895 | 0.739294 | 0.369647 | − | 0.929172i | \(-0.379479\pi\) | ||||
0.369647 | + | 0.929172i | \(0.379479\pi\) | |||||||
\(968\) | 9.18048 | 0.295072 | ||||||||
\(969\) | 7.51309 | 0.241355 | ||||||||
\(970\) | −7.33562 | −0.235533 | ||||||||
\(971\) | −17.4585 | −0.560271 | −0.280136 | − | 0.959960i | \(-0.590379\pi\) | ||||
−0.280136 | + | 0.959960i | \(0.590379\pi\) | |||||||
\(972\) | −12.3431 | −0.395904 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6.83622 | −0.219047 | ||||||||
\(975\) | −4.09337 | −0.131093 | ||||||||
\(976\) | −13.5294 | −0.433065 | ||||||||
\(977\) | −5.45553 | −0.174538 | −0.0872690 | − | 0.996185i | \(-0.527814\pi\) | ||||
−0.0872690 | + | 0.996185i | \(0.527814\pi\) | |||||||
\(978\) | −12.5352 | −0.400832 | ||||||||
\(979\) | −20.4060 | −0.652180 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.5312 | −0.847076 | ||||||||
\(982\) | −10.4302 | −0.332841 | ||||||||
\(983\) | −5.95493 | −0.189933 | −0.0949664 | − | 0.995480i | \(-0.530274\pi\) | ||||
−0.0949664 | + | 0.995480i | \(0.530274\pi\) | |||||||
\(984\) | −0.517304 | −0.0164911 | ||||||||
\(985\) | −48.6286 | −1.54944 | ||||||||
\(986\) | 36.6620 | 1.16756 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.7670 | 0.533429 | ||||||||
\(989\) | 31.1163 | 0.989441 | ||||||||
\(990\) | 6.87827 | 0.218606 | ||||||||
\(991\) | 22.3010 | 0.708415 | 0.354208 | − | 0.935167i | \(-0.384751\pi\) | ||||
0.354208 | + | 0.935167i | \(0.384751\pi\) | |||||||
\(992\) | 0.697788 | 0.0221548 | ||||||||
\(993\) | 18.3827 | 0.583358 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.1292 | −0.574733 | ||||||||
\(996\) | 7.53401 | 0.238724 | ||||||||
\(997\) | −44.4123 | −1.40655 | −0.703276 | − | 0.710917i | \(-0.748280\pi\) | ||||
−0.703276 | + | 0.710917i | \(0.748280\pi\) | |||||||
\(998\) | 12.7895 | 0.404846 | ||||||||
\(999\) | 20.8604 | 0.659993 |
(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 | 4018.2.a.be.1.2 | yes | 3 | |
7.6 | odd | 2 | 4018.2.a.bd.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4018.2.a.bd.1.2 | ✓ | 3 | 7.6 | odd | 2 | ||
4018.2.a.be.1.2 | yes | 3 | 1.1 | even | 1 | trivial |