Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 14 x^{10} + 44 x^{9} + 65 x^{8} - 219 x^{7} - 123 x^{6} + 444 x^{5} + 105 x^{4} + \cdots - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 241) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-2.02418\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.02418 | 1.43131 | 0.715655 | − | 0.698454i | \(-0.246129\pi\) | ||||
0.715655 | + | 0.698454i | \(0.246129\pi\) | |||||||
\(3\) | −2.93498 | −1.69451 | −0.847256 | − | 0.531185i | \(-0.821747\pi\) | ||||
−0.847256 | + | 0.531185i | \(0.821747\pi\) | |||||||
\(4\) | 2.09729 | 1.04865 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.94092 | −2.42537 | ||||||||
\(7\) | −0.381245 | −0.144097 | −0.0720485 | − | 0.997401i | \(-0.522954\pi\) | ||||
−0.0720485 | + | 0.997401i | \(0.522954\pi\) | |||||||
\(8\) | 0.196936 | 0.0696273 | ||||||||
\(9\) | 5.61411 | 1.87137 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.280814 | 0.0846688 | 0.0423344 | − | 0.999103i | \(-0.486521\pi\) | ||||
0.0423344 | + | 0.999103i | \(0.486521\pi\) | |||||||
\(12\) | −6.15551 | −1.77694 | ||||||||
\(13\) | 4.00528 | 1.11087 | 0.555433 | − | 0.831561i | \(-0.312553\pi\) | ||||
0.555433 | + | 0.831561i | \(0.312553\pi\) | |||||||
\(14\) | −0.771706 | −0.206247 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.79595 | −0.948988 | ||||||||
\(17\) | −2.60326 | −0.631383 | −0.315691 | − | 0.948862i | \(-0.602236\pi\) | ||||
−0.315691 | + | 0.948862i | \(0.602236\pi\) | |||||||
\(18\) | 11.3640 | 2.67851 | ||||||||
\(19\) | −3.86940 | −0.887700 | −0.443850 | − | 0.896101i | \(-0.646388\pi\) | ||||
−0.443850 | + | 0.896101i | \(0.646388\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.11895 | 0.244174 | ||||||||
\(22\) | 0.568418 | 0.121187 | ||||||||
\(23\) | −0.698450 | −0.145637 | −0.0728185 | − | 0.997345i | \(-0.523199\pi\) | ||||
−0.0728185 | + | 0.997345i | \(0.523199\pi\) | |||||||
\(24\) | −0.578002 | −0.117984 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.10740 | 1.58999 | ||||||||
\(27\) | −7.67238 | −1.47655 | ||||||||
\(28\) | −0.799581 | −0.151107 | ||||||||
\(29\) | 1.62690 | 0.302107 | 0.151054 | − | 0.988526i | \(-0.451733\pi\) | ||||
0.151054 | + | 0.988526i | \(0.451733\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.73691 | 1.74880 | 0.874401 | − | 0.485205i | \(-0.161255\pi\) | ||||
0.874401 | + | 0.485205i | \(0.161255\pi\) | |||||||
\(32\) | −8.07755 | −1.42792 | ||||||||
\(33\) | −0.824185 | −0.143472 | ||||||||
\(34\) | −5.26945 | −0.903704 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 11.7744 | 1.96241 | ||||||||
\(37\) | −4.41735 | −0.726208 | −0.363104 | − | 0.931749i | \(-0.618283\pi\) | ||||
−0.363104 | + | 0.931749i | \(0.618283\pi\) | |||||||
\(38\) | −7.83234 | −1.27057 | ||||||||
\(39\) | −11.7554 | −1.88238 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.0157665 | −0.00246231 | −0.00123116 | − | 0.999999i | \(-0.500392\pi\) | ||||
−0.00123116 | + | 0.999999i | \(0.500392\pi\) | |||||||
\(42\) | 2.26494 | 0.349488 | ||||||||
\(43\) | 12.2173 | 1.86312 | 0.931562 | − | 0.363583i | \(-0.118447\pi\) | ||||
0.931562 | + | 0.363583i | \(0.118447\pi\) | |||||||
\(44\) | 0.588950 | 0.0887875 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.41379 | −0.208452 | ||||||||
\(47\) | −7.71890 | −1.12592 | −0.562958 | − | 0.826485i | \(-0.690337\pi\) | ||||
−0.562958 | + | 0.826485i | \(0.690337\pi\) | |||||||
\(48\) | 11.1410 | 1.60807 | ||||||||
\(49\) | −6.85465 | −0.979236 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.64051 | 1.06989 | ||||||||
\(52\) | 8.40025 | 1.16491 | ||||||||
\(53\) | 4.91852 | 0.675611 | 0.337806 | − | 0.941216i | \(-0.390315\pi\) | ||||
0.337806 | + | 0.941216i | \(0.390315\pi\) | |||||||
\(54\) | −15.5302 | −2.11340 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.0750807 | −0.0100331 | ||||||||
\(57\) | 11.3566 | 1.50422 | ||||||||
\(58\) | 3.29313 | 0.432409 | ||||||||
\(59\) | −14.1596 | −1.84342 | −0.921709 | − | 0.387882i | \(-0.873207\pi\) | ||||
−0.921709 | + | 0.387882i | \(0.873207\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.97043 | −0.892472 | −0.446236 | − | 0.894915i | \(-0.647236\pi\) | ||||
−0.446236 | + | 0.894915i | \(0.647236\pi\) | |||||||
\(62\) | 19.7092 | 2.50308 | ||||||||
\(63\) | −2.14035 | −0.269659 | ||||||||
\(64\) | −8.75848 | −1.09481 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.66830 | −0.205353 | ||||||||
\(67\) | 2.97942 | 0.363994 | 0.181997 | − | 0.983299i | \(-0.441744\pi\) | ||||
0.181997 | + | 0.983299i | \(0.441744\pi\) | |||||||
\(68\) | −5.45979 | −0.662097 | ||||||||
\(69\) | 2.04994 | 0.246784 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.28180 | 0.864191 | 0.432095 | − | 0.901828i | \(-0.357774\pi\) | ||||
0.432095 | + | 0.901828i | \(0.357774\pi\) | |||||||
\(72\) | 1.10562 | 0.130298 | ||||||||
\(73\) | 0.165424 | 0.0193614 | 0.00968072 | − | 0.999953i | \(-0.496918\pi\) | ||||
0.00968072 | + | 0.999953i | \(0.496918\pi\) | |||||||
\(74\) | −8.94150 | −1.03943 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.11525 | −0.930883 | ||||||||
\(77\) | −0.107059 | −0.0122005 | ||||||||
\(78\) | −23.7951 | −2.69426 | ||||||||
\(79\) | 11.1633 | 1.25597 | 0.627986 | − | 0.778225i | \(-0.283880\pi\) | ||||
0.627986 | + | 0.778225i | \(0.283880\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.67594 | 0.630660 | ||||||||
\(82\) | −0.0319141 | −0.00352433 | ||||||||
\(83\) | 14.6259 | 1.60540 | 0.802701 | − | 0.596382i | \(-0.203396\pi\) | ||||
0.802701 | + | 0.596382i | \(0.203396\pi\) | |||||||
\(84\) | 2.34676 | 0.256052 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 24.7300 | 2.66671 | ||||||||
\(87\) | −4.77491 | −0.511924 | ||||||||
\(88\) | 0.0553024 | 0.00589525 | ||||||||
\(89\) | 14.3374 | 1.51976 | 0.759878 | − | 0.650066i | \(-0.225259\pi\) | ||||
0.759878 | + | 0.650066i | \(0.225259\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.52699 | −0.160072 | ||||||||
\(92\) | −1.46485 | −0.152722 | ||||||||
\(93\) | −28.5777 | −2.96337 | ||||||||
\(94\) | −15.6244 | −1.61154 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 23.7074 | 2.41963 | ||||||||
\(97\) | −8.75687 | −0.889126 | −0.444563 | − | 0.895748i | \(-0.646641\pi\) | ||||
−0.444563 | + | 0.895748i | \(0.646641\pi\) | |||||||
\(98\) | −13.8750 | −1.40159 | ||||||||
\(99\) | 1.57652 | 0.158447 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.97227 | −0.594263 | −0.297132 | − | 0.954837i | \(-0.596030\pi\) | ||||
−0.297132 | + | 0.954837i | \(0.596030\pi\) | |||||||
\(102\) | 15.4658 | 1.53134 | ||||||||
\(103\) | 17.0246 | 1.67749 | 0.838743 | − | 0.544527i | \(-0.183291\pi\) | ||||
0.838743 | + | 0.544527i | \(0.183291\pi\) | |||||||
\(104\) | 0.788783 | 0.0773466 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.95596 | 0.967008 | ||||||||
\(107\) | 6.06814 | 0.586629 | 0.293315 | − | 0.956016i | \(-0.405242\pi\) | ||||
0.293315 | + | 0.956016i | \(0.405242\pi\) | |||||||
\(108\) | −16.0912 | −1.54838 | ||||||||
\(109\) | −10.0495 | −0.962568 | −0.481284 | − | 0.876565i | \(-0.659829\pi\) | ||||
−0.481284 | + | 0.876565i | \(0.659829\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.9648 | 1.23057 | ||||||||
\(112\) | 1.44719 | 0.136746 | ||||||||
\(113\) | −3.24797 | −0.305543 | −0.152772 | − | 0.988262i | \(-0.548820\pi\) | ||||
−0.152772 | + | 0.988262i | \(0.548820\pi\) | |||||||
\(114\) | 22.9878 | 2.15300 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.41208 | 0.316803 | ||||||||
\(117\) | 22.4861 | 2.07884 | ||||||||
\(118\) | −28.6615 | −2.63850 | ||||||||
\(119\) | 0.992478 | 0.0909803 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9211 | −0.992831 | ||||||||
\(122\) | −14.1094 | −1.27740 | ||||||||
\(123\) | 0.0462743 | 0.00417241 | ||||||||
\(124\) | 20.4211 | 1.83387 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.33245 | −0.385965 | ||||||||
\(127\) | −0.309449 | −0.0274591 | −0.0137296 | − | 0.999906i | \(-0.504370\pi\) | ||||
−0.0137296 | + | 0.999906i | \(0.504370\pi\) | |||||||
\(128\) | −1.57362 | −0.139090 | ||||||||
\(129\) | −35.8576 | −3.15709 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.9939 | 1.57214 | 0.786068 | − | 0.618141i | \(-0.212114\pi\) | ||||
0.786068 | + | 0.618141i | \(0.212114\pi\) | |||||||
\(132\) | −1.72856 | −0.150452 | ||||||||
\(133\) | 1.47519 | 0.127915 | ||||||||
\(134\) | 6.03088 | 0.520989 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.512674 | −0.0439615 | ||||||||
\(137\) | 8.91168 | 0.761377 | 0.380688 | − | 0.924703i | \(-0.375687\pi\) | ||||
0.380688 | + | 0.924703i | \(0.375687\pi\) | |||||||
\(138\) | 4.14944 | 0.353224 | ||||||||
\(139\) | 7.82985 | 0.664119 | 0.332059 | − | 0.943258i | \(-0.392257\pi\) | ||||
0.332059 | + | 0.943258i | \(0.392257\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22.6548 | 1.90788 | ||||||||
\(142\) | 14.7396 | 1.23692 | ||||||||
\(143\) | 1.12474 | 0.0940557 | ||||||||
\(144\) | −21.3109 | −1.77591 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.334848 | 0.0277122 | ||||||||
\(147\) | 20.1183 | 1.65933 | ||||||||
\(148\) | −9.26447 | −0.761535 | ||||||||
\(149\) | 20.5561 | 1.68402 | 0.842010 | − | 0.539462i | \(-0.181372\pi\) | ||||
0.842010 | + | 0.539462i | \(0.181372\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.5866 | 0.861524 | 0.430762 | − | 0.902466i | \(-0.358245\pi\) | ||||
0.430762 | + | 0.902466i | \(0.358245\pi\) | |||||||
\(152\) | −0.762022 | −0.0618082 | ||||||||
\(153\) | −14.6150 | −1.18155 | ||||||||
\(154\) | −0.216706 | −0.0174627 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −24.6546 | −1.97395 | ||||||||
\(157\) | −7.79923 | −0.622447 | −0.311223 | − | 0.950337i | \(-0.600739\pi\) | ||||
−0.311223 | + | 0.950337i | \(0.600739\pi\) | |||||||
\(158\) | 22.5965 | 1.79768 | ||||||||
\(159\) | −14.4358 | −1.14483 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.266280 | 0.0209858 | ||||||||
\(162\) | 11.4891 | 0.902669 | ||||||||
\(163\) | −17.1362 | −1.34221 | −0.671104 | − | 0.741363i | \(-0.734180\pi\) | ||||
−0.671104 | + | 0.741363i | \(0.734180\pi\) | |||||||
\(164\) | −0.0330669 | −0.00258209 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 29.6054 | 2.29783 | ||||||||
\(167\) | 1.88493 | 0.145860 | 0.0729302 | − | 0.997337i | \(-0.476765\pi\) | ||||
0.0729302 | + | 0.997337i | \(0.476765\pi\) | |||||||
\(168\) | 0.220360 | 0.0170012 | ||||||||
\(169\) | 3.04231 | 0.234024 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −21.7232 | −1.66122 | ||||||||
\(172\) | 25.6233 | 1.95376 | ||||||||
\(173\) | 9.95946 | 0.757203 | 0.378602 | − | 0.925560i | \(-0.376405\pi\) | ||||
0.378602 | + | 0.925560i | \(0.376405\pi\) | |||||||
\(174\) | −9.66526 | −0.732722 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.06596 | −0.0803496 | ||||||||
\(177\) | 41.5581 | 3.12369 | ||||||||
\(178\) | 29.0213 | 2.17524 | ||||||||
\(179\) | 25.8971 | 1.93564 | 0.967820 | − | 0.251643i | \(-0.0809708\pi\) | ||||
0.967820 | + | 0.251643i | \(0.0809708\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.61696 | −0.640494 | −0.320247 | − | 0.947334i | \(-0.603766\pi\) | ||||
−0.320247 | + | 0.947334i | \(0.603766\pi\) | |||||||
\(182\) | −3.09090 | −0.229113 | ||||||||
\(183\) | 20.4581 | 1.51230 | ||||||||
\(184\) | −0.137550 | −0.0101403 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −57.8462 | −4.24149 | ||||||||
\(187\) | −0.731033 | −0.0534584 | ||||||||
\(188\) | −16.1888 | −1.18069 | ||||||||
\(189\) | 2.92505 | 0.212766 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.40808 | −0.536030 | −0.268015 | − | 0.963415i | \(-0.586368\pi\) | ||||
−0.268015 | + | 0.963415i | \(0.586368\pi\) | |||||||
\(192\) | 25.7060 | 1.85517 | ||||||||
\(193\) | 13.0485 | 0.939252 | 0.469626 | − | 0.882865i | \(-0.344389\pi\) | ||||
0.469626 | + | 0.882865i | \(0.344389\pi\) | |||||||
\(194\) | −17.7255 | −1.27261 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.3762 | −1.02687 | ||||||||
\(197\) | 2.32016 | 0.165305 | 0.0826524 | − | 0.996578i | \(-0.473661\pi\) | ||||
0.0826524 | + | 0.996578i | \(0.473661\pi\) | |||||||
\(198\) | 3.19116 | 0.226786 | ||||||||
\(199\) | 21.5958 | 1.53089 | 0.765444 | − | 0.643502i | \(-0.222519\pi\) | ||||
0.765444 | + | 0.643502i | \(0.222519\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.74455 | −0.616793 | ||||||||
\(202\) | −12.0889 | −0.850574 | ||||||||
\(203\) | −0.620245 | −0.0435327 | ||||||||
\(204\) | 16.0244 | 1.12193 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 34.4609 | 2.40100 | ||||||||
\(207\) | −3.92118 | −0.272541 | ||||||||
\(208\) | −15.2039 | −1.05420 | ||||||||
\(209\) | −1.08658 | −0.0751605 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.1477 | 1.38702 | 0.693512 | − | 0.720445i | \(-0.256062\pi\) | ||||
0.693512 | + | 0.720445i | \(0.256062\pi\) | |||||||
\(212\) | 10.3156 | 0.708477 | ||||||||
\(213\) | −21.3719 | −1.46438 | ||||||||
\(214\) | 12.2830 | 0.839648 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.51096 | −0.102808 | ||||||||
\(217\) | −3.71215 | −0.251997 | ||||||||
\(218\) | −20.3420 | −1.37773 | ||||||||
\(219\) | −0.485517 | −0.0328082 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.4268 | −0.701382 | ||||||||
\(222\) | 26.2431 | 1.76132 | ||||||||
\(223\) | 7.96809 | 0.533583 | 0.266792 | − | 0.963754i | \(-0.414036\pi\) | ||||
0.266792 | + | 0.963754i | \(0.414036\pi\) | |||||||
\(224\) | 3.07952 | 0.205759 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.57447 | −0.437327 | ||||||||
\(227\) | 19.2441 | 1.27728 | 0.638639 | − | 0.769506i | \(-0.279498\pi\) | ||||
0.638639 | + | 0.769506i | \(0.279498\pi\) | |||||||
\(228\) | 23.8181 | 1.57739 | ||||||||
\(229\) | 12.7475 | 0.842380 | 0.421190 | − | 0.906972i | \(-0.361612\pi\) | ||||
0.421190 | + | 0.906972i | \(0.361612\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.314216 | 0.0206739 | ||||||||
\(232\) | 0.320394 | 0.0210349 | ||||||||
\(233\) | 10.2413 | 0.670931 | 0.335465 | − | 0.942053i | \(-0.391106\pi\) | ||||
0.335465 | + | 0.942053i | \(0.391106\pi\) | |||||||
\(234\) | 45.5159 | 2.97547 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −29.6967 | −1.93309 | ||||||||
\(237\) | −32.7641 | −2.12826 | ||||||||
\(238\) | 2.00895 | 0.130221 | ||||||||
\(239\) | 22.4264 | 1.45064 | 0.725321 | − | 0.688411i | \(-0.241691\pi\) | ||||
0.725321 | + | 0.688411i | \(0.241691\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | −22.1063 | −1.42105 | ||||||||
\(243\) | 6.35836 | 0.407889 | ||||||||
\(244\) | −14.6190 | −0.935887 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.0936674 | 0.00597202 | ||||||||
\(247\) | −15.4980 | −0.986116 | ||||||||
\(248\) | 1.91755 | 0.121764 | ||||||||
\(249\) | −42.9267 | −2.72037 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.0729 | 0.888274 | 0.444137 | − | 0.895959i | \(-0.353510\pi\) | ||||
0.444137 | + | 0.895959i | \(0.353510\pi\) | |||||||
\(252\) | −4.48894 | −0.282777 | ||||||||
\(253\) | −0.196135 | −0.0123309 | ||||||||
\(254\) | −0.626379 | −0.0393025 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.3317 | 0.895730 | ||||||||
\(257\) | −1.46464 | −0.0913619 | −0.0456809 | − | 0.998956i | \(-0.514546\pi\) | ||||
−0.0456809 | + | 0.998956i | \(0.514546\pi\) | |||||||
\(258\) | −72.5821 | −4.51877 | ||||||||
\(259\) | 1.68409 | 0.104644 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.13358 | 0.565355 | ||||||||
\(262\) | 36.4229 | 2.25021 | ||||||||
\(263\) | −8.09273 | −0.499019 | −0.249509 | − | 0.968372i | \(-0.580269\pi\) | ||||
−0.249509 | + | 0.968372i | \(0.580269\pi\) | |||||||
\(264\) | −0.162311 | −0.00998958 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.98604 | 0.183086 | ||||||||
\(267\) | −42.0799 | −2.57525 | ||||||||
\(268\) | 6.24872 | 0.381701 | ||||||||
\(269\) | −25.2517 | −1.53962 | −0.769812 | − | 0.638271i | \(-0.779650\pi\) | ||||
−0.769812 | + | 0.638271i | \(0.779650\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.04109 | 0.366970 | 0.183485 | − | 0.983023i | \(-0.441262\pi\) | ||||
0.183485 | + | 0.983023i | \(0.441262\pi\) | |||||||
\(272\) | 9.88184 | 0.599175 | ||||||||
\(273\) | 4.48170 | 0.271245 | ||||||||
\(274\) | 18.0388 | 1.08977 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.29932 | 0.258789 | ||||||||
\(277\) | 17.9271 | 1.07714 | 0.538568 | − | 0.842582i | \(-0.318966\pi\) | ||||
0.538568 | + | 0.842582i | \(0.318966\pi\) | |||||||
\(278\) | 15.8490 | 0.950559 | ||||||||
\(279\) | 54.6641 | 3.27266 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.13276 | 0.246540 | 0.123270 | − | 0.992373i | \(-0.460662\pi\) | ||||
0.123270 | + | 0.992373i | \(0.460662\pi\) | |||||||
\(282\) | 45.8574 | 2.73077 | ||||||||
\(283\) | −13.7771 | −0.818962 | −0.409481 | − | 0.912319i | \(-0.634290\pi\) | ||||
−0.409481 | + | 0.912319i | \(0.634290\pi\) | |||||||
\(284\) | 15.2721 | 0.906230 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.27668 | 0.134623 | ||||||||
\(287\) | 0.00601088 | 0.000354811 0 | ||||||||
\(288\) | −45.3483 | −2.67217 | ||||||||
\(289\) | −10.2230 | −0.601356 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 25.7013 | 1.50663 | ||||||||
\(292\) | 0.346943 | 0.0203033 | ||||||||
\(293\) | −21.6053 | −1.26220 | −0.631098 | − | 0.775703i | \(-0.717395\pi\) | ||||
−0.631098 | + | 0.775703i | \(0.717395\pi\) | |||||||
\(294\) | 40.7229 | 2.37501 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.869934 | −0.0505639 | ||||||||
\(297\) | −2.15451 | −0.125018 | ||||||||
\(298\) | 41.6091 | 2.41035 | ||||||||
\(299\) | −2.79749 | −0.161783 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.65779 | −0.268470 | ||||||||
\(302\) | 21.4291 | 1.23311 | ||||||||
\(303\) | 17.5285 | 1.00699 | ||||||||
\(304\) | 14.6880 | 0.842417 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −29.5833 | −1.69117 | ||||||||
\(307\) | −20.3178 | −1.15960 | −0.579800 | − | 0.814759i | \(-0.696869\pi\) | ||||
−0.579800 | + | 0.814759i | \(0.696869\pi\) | |||||||
\(308\) | −0.224534 | −0.0127940 | ||||||||
\(309\) | −49.9670 | −2.84252 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.4778 | 1.16119 | 0.580595 | − | 0.814193i | \(-0.302820\pi\) | ||||
0.580595 | + | 0.814193i | \(0.302820\pi\) | |||||||
\(312\) | −2.31506 | −0.131065 | ||||||||
\(313\) | −1.98489 | −0.112192 | −0.0560962 | − | 0.998425i | \(-0.517865\pi\) | ||||
−0.0560962 | + | 0.998425i | \(0.517865\pi\) | |||||||
\(314\) | −15.7870 | −0.890913 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 23.4127 | 1.31707 | ||||||||
\(317\) | 28.5808 | 1.60526 | 0.802630 | − | 0.596477i | \(-0.203433\pi\) | ||||
0.802630 | + | 0.596477i | \(0.203433\pi\) | |||||||
\(318\) | −29.2206 | −1.63861 | ||||||||
\(319\) | 0.456856 | 0.0255790 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.8099 | −0.994051 | ||||||||
\(322\) | 0.538999 | 0.0300372 | ||||||||
\(323\) | 10.0730 | 0.560479 | ||||||||
\(324\) | 11.9041 | 0.661339 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −34.6867 | −1.92112 | ||||||||
\(327\) | 29.4951 | 1.63108 | ||||||||
\(328\) | −0.00310498 | −0.000171444 0 | ||||||||
\(329\) | 2.94279 | 0.162241 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.4089 | −1.28667 | −0.643334 | − | 0.765585i | \(-0.722449\pi\) | ||||
−0.643334 | + | 0.765585i | \(0.722449\pi\) | |||||||
\(332\) | 30.6748 | 1.68350 | ||||||||
\(333\) | −24.7995 | −1.35900 | ||||||||
\(334\) | 3.81544 | 0.208771 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.24746 | −0.231718 | ||||||||
\(337\) | −2.23389 | −0.121688 | −0.0608440 | − | 0.998147i | \(-0.519379\pi\) | ||||
−0.0608440 | + | 0.998147i | \(0.519379\pi\) | |||||||
\(338\) | 6.15817 | 0.334960 | ||||||||
\(339\) | 9.53273 | 0.517747 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.73427 | 0.148069 | ||||||||
\(342\) | −43.9717 | −2.37772 | ||||||||
\(343\) | 5.28201 | 0.285202 | ||||||||
\(344\) | 2.40603 | 0.129724 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.1597 | 1.08379 | ||||||||
\(347\) | −17.2084 | −0.923793 | −0.461897 | − | 0.886934i | \(-0.652831\pi\) | ||||
−0.461897 | + | 0.886934i | \(0.652831\pi\) | |||||||
\(348\) | −10.0144 | −0.536827 | ||||||||
\(349\) | 21.1996 | 1.13479 | 0.567394 | − | 0.823447i | \(-0.307952\pi\) | ||||
0.567394 | + | 0.823447i | \(0.307952\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −30.7301 | −1.64025 | ||||||||
\(352\) | −2.26829 | −0.120900 | ||||||||
\(353\) | 9.42434 | 0.501607 | 0.250803 | − | 0.968038i | \(-0.419305\pi\) | ||||
0.250803 | + | 0.968038i | \(0.419305\pi\) | |||||||
\(354\) | 84.1209 | 4.47097 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 30.0696 | 1.59369 | ||||||||
\(357\) | −2.91290 | −0.154167 | ||||||||
\(358\) | 52.4203 | 2.77050 | ||||||||
\(359\) | 8.50212 | 0.448725 | 0.224362 | − | 0.974506i | \(-0.427970\pi\) | ||||
0.224362 | + | 0.974506i | \(0.427970\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.02777 | −0.211988 | ||||||||
\(362\) | −17.4423 | −0.916744 | ||||||||
\(363\) | 32.0533 | 1.68236 | ||||||||
\(364\) | −3.20255 | −0.167859 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 41.4108 | 2.16458 | ||||||||
\(367\) | −5.48335 | −0.286229 | −0.143114 | − | 0.989706i | \(-0.545712\pi\) | ||||
−0.143114 | + | 0.989706i | \(0.545712\pi\) | |||||||
\(368\) | 2.65128 | 0.138208 | ||||||||
\(369\) | −0.0885148 | −0.00460790 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.87516 | −0.0973535 | ||||||||
\(372\) | −59.9357 | −3.10752 | ||||||||
\(373\) | 23.6497 | 1.22454 | 0.612268 | − | 0.790650i | \(-0.290257\pi\) | ||||
0.612268 | + | 0.790650i | \(0.290257\pi\) | |||||||
\(374\) | −1.47974 | −0.0765155 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.52013 | −0.0783945 | ||||||||
\(377\) | 6.51618 | 0.335601 | ||||||||
\(378\) | 5.92082 | 0.304534 | ||||||||
\(379\) | 4.37392 | 0.224673 | 0.112336 | − | 0.993670i | \(-0.464167\pi\) | ||||
0.112336 | + | 0.993670i | \(0.464167\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.908227 | 0.0465299 | ||||||||
\(382\) | −14.9953 | −0.767224 | ||||||||
\(383\) | −22.2150 | −1.13514 | −0.567568 | − | 0.823327i | \(-0.692115\pi\) | ||||
−0.567568 | + | 0.823327i | \(0.692115\pi\) | |||||||
\(384\) | 4.61855 | 0.235689 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.4125 | 1.34436 | ||||||||
\(387\) | 68.5894 | 3.48660 | ||||||||
\(388\) | −18.3657 | −0.932378 | ||||||||
\(389\) | −9.47112 | −0.480205 | −0.240102 | − | 0.970748i | \(-0.577181\pi\) | ||||
−0.240102 | + | 0.970748i | \(0.577181\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.81825 | 0.0919527 | ||||||||
\(392\) | −1.34993 | −0.0681815 | ||||||||
\(393\) | −52.8118 | −2.66400 | ||||||||
\(394\) | 4.69642 | 0.236602 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.30643 | 0.166154 | ||||||||
\(397\) | −33.8693 | −1.69985 | −0.849925 | − | 0.526904i | \(-0.823353\pi\) | ||||
−0.849925 | + | 0.526904i | \(0.823353\pi\) | |||||||
\(398\) | 43.7138 | 2.19118 | ||||||||
\(399\) | −4.32964 | −0.216753 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.1950 | 1.30812 | 0.654059 | − | 0.756444i | \(-0.273065\pi\) | ||||
0.654059 | + | 0.756444i | \(0.273065\pi\) | |||||||
\(402\) | −17.7005 | −0.882822 | ||||||||
\(403\) | 38.9991 | 1.94268 | ||||||||
\(404\) | −12.5256 | −0.623172 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.25549 | −0.0623087 | ||||||||
\(407\) | −1.24046 | −0.0614871 | ||||||||
\(408\) | 1.50469 | 0.0744932 | ||||||||
\(409\) | −23.3301 | −1.15360 | −0.576800 | − | 0.816885i | \(-0.695699\pi\) | ||||
−0.576800 | + | 0.816885i | \(0.695699\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −26.1556 | −1.29016 | ||||||||
\(412\) | 35.7056 | 1.75909 | ||||||||
\(413\) | 5.39826 | 0.265631 | ||||||||
\(414\) | −7.93716 | −0.390090 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −32.3529 | −1.58623 | ||||||||
\(417\) | −22.9805 | −1.12536 | ||||||||
\(418\) | −2.19944 | −0.107578 | ||||||||
\(419\) | −17.9680 | −0.877794 | −0.438897 | − | 0.898537i | \(-0.644631\pi\) | ||||
−0.438897 | + | 0.898537i | \(0.644631\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.6124 | 1.00459 | 0.502294 | − | 0.864697i | \(-0.332489\pi\) | ||||
0.502294 | + | 0.864697i | \(0.332489\pi\) | |||||||
\(422\) | 40.7825 | 1.98526 | ||||||||
\(423\) | −43.3348 | −2.10701 | ||||||||
\(424\) | 0.968633 | 0.0470410 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −43.2606 | −2.09598 | ||||||||
\(427\) | 2.65744 | 0.128602 | ||||||||
\(428\) | 12.7267 | 0.615166 | ||||||||
\(429\) | −3.30110 | −0.159378 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.74707 | −0.228659 | −0.114329 | − | 0.993443i | \(-0.536472\pi\) | ||||
−0.114329 | + | 0.993443i | \(0.536472\pi\) | |||||||
\(432\) | 29.1240 | 1.40123 | ||||||||
\(433\) | 40.8642 | 1.96381 | 0.981904 | − | 0.189378i | \(-0.0606471\pi\) | ||||
0.981904 | + | 0.189378i | \(0.0606471\pi\) | |||||||
\(434\) | −7.51404 | −0.360685 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −21.0767 | −1.00939 | ||||||||
\(437\) | 2.70258 | 0.129282 | ||||||||
\(438\) | −0.982772 | −0.0469587 | ||||||||
\(439\) | −23.5388 | −1.12344 | −0.561722 | − | 0.827326i | \(-0.689861\pi\) | ||||
−0.561722 | + | 0.827326i | \(0.689861\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −38.4828 | −1.83251 | ||||||||
\(442\) | −21.1057 | −1.00389 | ||||||||
\(443\) | −27.9145 | −1.32626 | −0.663129 | − | 0.748505i | \(-0.730772\pi\) | ||||
−0.663129 | + | 0.748505i | \(0.730772\pi\) | |||||||
\(444\) | 27.1910 | 1.29043 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 16.1288 | 0.763722 | ||||||||
\(447\) | −60.3317 | −2.85359 | ||||||||
\(448\) | 3.33912 | 0.157759 | ||||||||
\(449\) | 23.7869 | 1.12258 | 0.561288 | − | 0.827621i | \(-0.310306\pi\) | ||||
0.561288 | + | 0.827621i | \(0.310306\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.00442746 | −0.000208481 0 | ||||||||
\(452\) | −6.81194 | −0.320407 | ||||||||
\(453\) | −31.0714 | −1.45986 | ||||||||
\(454\) | 38.9536 | 1.82818 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.23652 | 0.104735 | ||||||||
\(457\) | −33.9948 | −1.59021 | −0.795106 | − | 0.606471i | \(-0.792585\pi\) | ||||
−0.795106 | + | 0.606471i | \(0.792585\pi\) | |||||||
\(458\) | 25.8032 | 1.20571 | ||||||||
\(459\) | 19.9732 | 0.932268 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.0014 | 0.838410 | 0.419205 | − | 0.907892i | \(-0.362309\pi\) | ||||
0.419205 | + | 0.907892i | \(0.362309\pi\) | |||||||
\(462\) | 0.636029 | 0.0295908 | ||||||||
\(463\) | −11.9773 | −0.556634 | −0.278317 | − | 0.960489i | \(-0.589777\pi\) | ||||
−0.278317 | + | 0.960489i | \(0.589777\pi\) | |||||||
\(464\) | −6.17562 | −0.286696 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.7302 | 0.960310 | ||||||||
\(467\) | −22.0474 | −1.02023 | −0.510117 | − | 0.860105i | \(-0.670398\pi\) | ||||
−0.510117 | + | 0.860105i | \(0.670398\pi\) | |||||||
\(468\) | 47.1600 | 2.17997 | ||||||||
\(469\) | −1.13589 | −0.0524505 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.8906 | 1.05474 | ||||||||
\(472\) | −2.78852 | −0.128352 | ||||||||
\(473\) | 3.43080 | 0.157748 | ||||||||
\(474\) | −66.3204 | −3.04620 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.08152 | 0.0954061 | ||||||||
\(477\) | 27.6132 | 1.26432 | ||||||||
\(478\) | 45.3950 | 2.07632 | ||||||||
\(479\) | 14.1990 | 0.648769 | 0.324385 | − | 0.945925i | \(-0.394843\pi\) | ||||
0.324385 | + | 0.945925i | \(0.394843\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.6927 | −0.806720 | ||||||||
\(482\) | 2.02418 | 0.0921987 | ||||||||
\(483\) | −0.781528 | −0.0355608 | ||||||||
\(484\) | −22.9048 | −1.04113 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 12.8704 | 0.583815 | ||||||||
\(487\) | 40.8500 | 1.85109 | 0.925544 | − | 0.378639i | \(-0.123608\pi\) | ||||
0.925544 | + | 0.378639i | \(0.123608\pi\) | |||||||
\(488\) | −1.37273 | −0.0621404 | ||||||||
\(489\) | 50.2944 | 2.27439 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.70287 | 0.347626 | 0.173813 | − | 0.984779i | \(-0.444391\pi\) | ||||
0.173813 | + | 0.984779i | \(0.444391\pi\) | |||||||
\(492\) | 0.0970507 | 0.00437539 | ||||||||
\(493\) | −4.23523 | −0.190745 | ||||||||
\(494\) | −31.3708 | −1.41144 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −36.9608 | −1.65959 | ||||||||
\(497\) | −2.77615 | −0.124527 | ||||||||
\(498\) | −86.8913 | −3.89369 | ||||||||
\(499\) | −1.84960 | −0.0827996 | −0.0413998 | − | 0.999143i | \(-0.513182\pi\) | ||||
−0.0413998 | + | 0.999143i | \(0.513182\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.53224 | −0.247162 | ||||||||
\(502\) | 28.4860 | 1.27139 | ||||||||
\(503\) | −16.8921 | −0.753181 | −0.376590 | − | 0.926380i | \(-0.622904\pi\) | ||||
−0.376590 | + | 0.926380i | \(0.622904\pi\) | |||||||
\(504\) | −0.421511 | −0.0187756 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.397012 | −0.0176493 | ||||||||
\(507\) | −8.92911 | −0.396556 | ||||||||
\(508\) | −0.649005 | −0.0287949 | ||||||||
\(509\) | 2.10162 | 0.0931524 | 0.0465762 | − | 0.998915i | \(-0.485169\pi\) | ||||
0.0465762 | + | 0.998915i | \(0.485169\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0630671 | −0.00278992 | ||||||||
\(512\) | 32.1571 | 1.42116 | ||||||||
\(513\) | 29.6875 | 1.31073 | ||||||||
\(514\) | −2.96470 | −0.130767 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −75.2039 | −3.31067 | ||||||||
\(517\) | −2.16758 | −0.0953300 | ||||||||
\(518\) | 3.40890 | 0.149778 | ||||||||
\(519\) | −29.2308 | −1.28309 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.90175 | −0.0833170 | −0.0416585 | − | 0.999132i | \(-0.513264\pi\) | ||||
−0.0416585 | + | 0.999132i | \(0.513264\pi\) | |||||||
\(522\) | 18.4880 | 0.809197 | ||||||||
\(523\) | −2.87743 | −0.125821 | −0.0629105 | − | 0.998019i | \(-0.520038\pi\) | ||||
−0.0629105 | + | 0.998019i | \(0.520038\pi\) | |||||||
\(524\) | 37.7385 | 1.64861 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.3811 | −0.714250 | ||||||||
\(527\) | −25.3477 | −1.10416 | ||||||||
\(528\) | 3.12857 | 0.136153 | ||||||||
\(529\) | −22.5122 | −0.978790 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −79.4934 | −3.44972 | ||||||||
\(532\) | 3.09390 | 0.134137 | ||||||||
\(533\) | −0.0631492 | −0.00273530 | ||||||||
\(534\) | −85.1771 | −3.68597 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.586755 | 0.0253439 | ||||||||
\(537\) | −76.0075 | −3.27997 | ||||||||
\(538\) | −51.1139 | −2.20368 | ||||||||
\(539\) | −1.92489 | −0.0829107 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.56338 | 0.153202 | 0.0766009 | − | 0.997062i | \(-0.475593\pi\) | ||||
0.0766009 | + | 0.997062i | \(0.475593\pi\) | |||||||
\(542\) | 12.2282 | 0.525247 | ||||||||
\(543\) | 25.2906 | 1.08532 | ||||||||
\(544\) | 21.0279 | 0.901565 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 9.07175 | 0.388235 | ||||||||
\(547\) | −8.83030 | −0.377557 | −0.188778 | − | 0.982020i | \(-0.560453\pi\) | ||||
−0.188778 | + | 0.982020i | \(0.560453\pi\) | |||||||
\(548\) | 18.6904 | 0.798414 | ||||||||
\(549\) | −39.1328 | −1.67015 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.29511 | −0.268181 | ||||||||
\(552\) | 0.403706 | 0.0171829 | ||||||||
\(553\) | −4.25595 | −0.180982 | ||||||||
\(554\) | 36.2876 | 1.54171 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.4215 | 0.696425 | ||||||||
\(557\) | 8.23306 | 0.348846 | 0.174423 | − | 0.984671i | \(-0.444194\pi\) | ||||
0.174423 | + | 0.984671i | \(0.444194\pi\) | |||||||
\(558\) | 110.650 | 4.68418 | ||||||||
\(559\) | 48.9338 | 2.06968 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.14557 | 0.0905859 | ||||||||
\(562\) | 8.36544 | 0.352875 | ||||||||
\(563\) | 40.7923 | 1.71919 | 0.859596 | − | 0.510974i | \(-0.170715\pi\) | ||||
0.859596 | + | 0.510974i | \(0.170715\pi\) | |||||||
\(564\) | 47.5138 | 2.00069 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −27.8872 | −1.17219 | ||||||||
\(567\) | −2.16392 | −0.0908761 | ||||||||
\(568\) | 1.43405 | 0.0601712 | ||||||||
\(569\) | 17.6055 | 0.738063 | 0.369031 | − | 0.929417i | \(-0.379689\pi\) | ||||
0.369031 | + | 0.929417i | \(0.379689\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.2781 | 0.681216 | 0.340608 | − | 0.940205i | \(-0.389367\pi\) | ||||
0.340608 | + | 0.940205i | \(0.389367\pi\) | |||||||
\(572\) | 2.35891 | 0.0986311 | ||||||||
\(573\) | 21.7426 | 0.908309 | ||||||||
\(574\) | 0.0121671 | 0.000507845 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −49.1711 | −2.04880 | ||||||||
\(577\) | −25.7002 | −1.06991 | −0.534956 | − | 0.844880i | \(-0.679672\pi\) | ||||
−0.534956 | + | 0.844880i | \(0.679672\pi\) | |||||||
\(578\) | −20.6933 | −0.860726 | ||||||||
\(579\) | −38.2971 | −1.59157 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.57604 | −0.231333 | ||||||||
\(582\) | 52.0239 | 2.15646 | ||||||||
\(583\) | 1.38119 | 0.0572032 | ||||||||
\(584\) | 0.0325779 | 0.00134808 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −43.7329 | −1.80659 | ||||||||
\(587\) | −35.7831 | −1.47693 | −0.738464 | − | 0.674293i | \(-0.764448\pi\) | ||||
−0.738464 | + | 0.674293i | \(0.764448\pi\) | |||||||
\(588\) | 42.1939 | 1.74005 | ||||||||
\(589\) | −37.6760 | −1.55241 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.80964 | −0.280111 | ||||||||
\(592\) | 16.7680 | 0.689162 | ||||||||
\(593\) | 5.87794 | 0.241378 | 0.120689 | − | 0.992690i | \(-0.461490\pi\) | ||||
0.120689 | + | 0.992690i | \(0.461490\pi\) | |||||||
\(594\) | −4.36112 | −0.178939 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 43.1121 | 1.76594 | ||||||||
\(597\) | −63.3834 | −2.59411 | ||||||||
\(598\) | −5.66262 | −0.231562 | ||||||||
\(599\) | 21.9834 | 0.898218 | 0.449109 | − | 0.893477i | \(-0.351741\pi\) | ||||
0.449109 | + | 0.893477i | \(0.351741\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.9020 | 0.893400 | 0.446700 | − | 0.894684i | \(-0.352599\pi\) | ||||
0.446700 | + | 0.894684i | \(0.352599\pi\) | |||||||
\(602\) | −9.42818 | −0.384264 | ||||||||
\(603\) | 16.7268 | 0.681169 | ||||||||
\(604\) | 22.2031 | 0.903433 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 35.4808 | 1.44131 | ||||||||
\(607\) | −23.4846 | −0.953209 | −0.476604 | − | 0.879118i | \(-0.658133\pi\) | ||||
−0.476604 | + | 0.879118i | \(0.658133\pi\) | |||||||
\(608\) | 31.2552 | 1.26757 | ||||||||
\(609\) | 1.82041 | 0.0737667 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −30.9164 | −1.25074 | ||||||||
\(612\) | −30.6519 | −1.23903 | ||||||||
\(613\) | −8.60887 | −0.347709 | −0.173854 | − | 0.984771i | \(-0.555622\pi\) | ||||
−0.173854 | + | 0.984771i | \(0.555622\pi\) | |||||||
\(614\) | −41.1269 | −1.65975 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.0210837 | −0.000849488 0 | ||||||||
\(617\) | 33.1258 | 1.33360 | 0.666798 | − | 0.745238i | \(-0.267664\pi\) | ||||
0.666798 | + | 0.745238i | \(0.267664\pi\) | |||||||
\(618\) | −101.142 | −4.06853 | ||||||||
\(619\) | −15.7965 | −0.634915 | −0.317457 | − | 0.948273i | \(-0.602829\pi\) | ||||
−0.317457 | + | 0.948273i | \(0.602829\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.35878 | 0.215040 | ||||||||
\(622\) | 41.4507 | 1.66202 | ||||||||
\(623\) | −5.46604 | −0.218992 | ||||||||
\(624\) | 44.6231 | 1.78635 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.01776 | −0.160582 | ||||||||
\(627\) | 3.18910 | 0.127360 | ||||||||
\(628\) | −16.3573 | −0.652726 | ||||||||
\(629\) | 11.4995 | 0.458515 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.7674 | −1.66273 | −0.831367 | − | 0.555724i | \(-0.812441\pi\) | ||||
−0.831367 | + | 0.555724i | \(0.812441\pi\) | |||||||
\(632\) | 2.19846 | 0.0874499 | ||||||||
\(633\) | −59.1331 | −2.35033 | ||||||||
\(634\) | 57.8527 | 2.29762 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −30.2760 | −1.20052 | ||||||||
\(637\) | −27.4548 | −1.08780 | ||||||||
\(638\) | 0.924758 | 0.0366115 | ||||||||
\(639\) | 40.8809 | 1.61722 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.5409 | 0.495337 | 0.247669 | − | 0.968845i | \(-0.420336\pi\) | ||||
0.247669 | + | 0.968845i | \(0.420336\pi\) | |||||||
\(642\) | −36.0503 | −1.42279 | ||||||||
\(643\) | 15.0272 | 0.592616 | 0.296308 | − | 0.955092i | \(-0.404244\pi\) | ||||
0.296308 | + | 0.955092i | \(0.404244\pi\) | |||||||
\(644\) | 0.558468 | 0.0220067 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.3896 | 0.802218 | ||||||||
\(647\) | −0.131198 | −0.00515792 | −0.00257896 | − | 0.999997i | \(-0.500821\pi\) | ||||
−0.00257896 | + | 0.999997i | \(0.500821\pi\) | |||||||
\(648\) | 1.11779 | 0.0439111 | ||||||||
\(649\) | −3.97621 | −0.156080 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.8951 | 0.427012 | ||||||||
\(652\) | −35.9396 | −1.40750 | ||||||||
\(653\) | −29.9259 | −1.17109 | −0.585546 | − | 0.810639i | \(-0.699120\pi\) | ||||
−0.585546 | + | 0.810639i | \(0.699120\pi\) | |||||||
\(654\) | 59.7033 | 2.33458 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.0598488 | 0.00233670 | ||||||||
\(657\) | 0.928710 | 0.0362324 | ||||||||
\(658\) | 5.95672 | 0.232217 | ||||||||
\(659\) | −38.8457 | −1.51321 | −0.756606 | − | 0.653871i | \(-0.773144\pi\) | ||||
−0.756606 | + | 0.653871i | \(0.773144\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.0165 | −1.59536 | −0.797678 | − | 0.603084i | \(-0.793938\pi\) | ||||
−0.797678 | + | 0.603084i | \(0.793938\pi\) | |||||||
\(662\) | −47.3837 | −1.84162 | ||||||||
\(663\) | 30.6024 | 1.18850 | ||||||||
\(664\) | 2.88036 | 0.111780 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −50.1986 | −1.94516 | ||||||||
\(667\) | −1.13631 | −0.0439980 | ||||||||
\(668\) | 3.95325 | 0.152956 | ||||||||
\(669\) | −23.3862 | −0.904163 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.95740 | −0.0755645 | ||||||||
\(672\) | −9.03834 | −0.348661 | ||||||||
\(673\) | −8.97729 | −0.346049 | −0.173024 | − | 0.984918i | \(-0.555354\pi\) | ||||
−0.173024 | + | 0.984918i | \(0.555354\pi\) | |||||||
\(674\) | −4.52180 | −0.174173 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.38060 | 0.245408 | ||||||||
\(677\) | −4.52843 | −0.174042 | −0.0870209 | − | 0.996206i | \(-0.527735\pi\) | ||||
−0.0870209 | + | 0.996206i | \(0.527735\pi\) | |||||||
\(678\) | 19.2959 | 0.741056 | ||||||||
\(679\) | 3.33851 | 0.128120 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −56.4812 | −2.16436 | ||||||||
\(682\) | 5.53464 | 0.211932 | ||||||||
\(683\) | −3.48350 | −0.133292 | −0.0666462 | − | 0.997777i | \(-0.521230\pi\) | ||||
−0.0666462 | + | 0.997777i | \(0.521230\pi\) | |||||||
\(684\) | −45.5600 | −1.74203 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10.6917 | 0.408212 | ||||||||
\(687\) | −37.4138 | −1.42742 | ||||||||
\(688\) | −46.3763 | −1.76808 | ||||||||
\(689\) | 19.7001 | 0.750514 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.5762 | −1.69576 | −0.847879 | − | 0.530190i | \(-0.822121\pi\) | ||||
−0.847879 | + | 0.530190i | \(0.822121\pi\) | |||||||
\(692\) | 20.8879 | 0.794038 | ||||||||
\(693\) | −0.601042 | −0.0228317 | ||||||||
\(694\) | −34.8328 | −1.32223 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.940350 | −0.0356439 | ||||||||
\(697\) | 0.0410442 | 0.00155466 | ||||||||
\(698\) | 42.9117 | 1.62423 | ||||||||
\(699\) | −30.0581 | −1.13690 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.90961 | 0.336511 | 0.168256 | − | 0.985743i | \(-0.446187\pi\) | ||||
0.168256 | + | 0.985743i | \(0.446187\pi\) | |||||||
\(702\) | −62.2031 | −2.34770 | ||||||||
\(703\) | 17.0925 | 0.644655 | ||||||||
\(704\) | −2.45951 | −0.0926962 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.0765 | 0.717955 | ||||||||
\(707\) | 2.27690 | 0.0856315 | ||||||||
\(708\) | 87.1594 | 3.27565 | ||||||||
\(709\) | −13.4817 | −0.506315 | −0.253158 | − | 0.967425i | \(-0.581469\pi\) | ||||
−0.253158 | + | 0.967425i | \(0.581469\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 62.6721 | 2.35039 | ||||||||
\(712\) | 2.82354 | 0.105816 | ||||||||
\(713\) | −6.80075 | −0.254690 | ||||||||
\(714\) | −5.89623 | −0.220661 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 54.3138 | 2.02980 | ||||||||
\(717\) | −65.8210 | −2.45813 | ||||||||
\(718\) | 17.2098 | 0.642264 | ||||||||
\(719\) | 25.1548 | 0.938118 | 0.469059 | − | 0.883167i | \(-0.344593\pi\) | ||||
0.469059 | + | 0.883167i | \(0.344593\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.49055 | −0.241721 | ||||||||
\(722\) | −8.15293 | −0.303421 | ||||||||
\(723\) | −2.93498 | −0.109153 | ||||||||
\(724\) | −18.0723 | −0.671651 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 64.8816 | 2.40798 | ||||||||
\(727\) | 1.31218 | 0.0486659 | 0.0243330 | − | 0.999704i | \(-0.492254\pi\) | ||||
0.0243330 | + | 0.999704i | \(0.492254\pi\) | |||||||
\(728\) | −0.300719 | −0.0111454 | ||||||||
\(729\) | −35.6895 | −1.32183 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.8048 | −1.17634 | ||||||||
\(732\) | 42.9066 | 1.58587 | ||||||||
\(733\) | −22.8551 | −0.844173 | −0.422087 | − | 0.906556i | \(-0.638702\pi\) | ||||
−0.422087 | + | 0.906556i | \(0.638702\pi\) | |||||||
\(734\) | −11.0993 | −0.409682 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.64177 | 0.207958 | ||||||||
\(737\) | 0.836665 | 0.0308190 | ||||||||
\(738\) | −0.179170 | −0.00659533 | ||||||||
\(739\) | 10.2085 | 0.375525 | 0.187762 | − | 0.982214i | \(-0.439877\pi\) | ||||
0.187762 | + | 0.982214i | \(0.439877\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 45.4864 | 1.67099 | ||||||||
\(742\) | −3.79566 | −0.139343 | ||||||||
\(743\) | −26.3806 | −0.967810 | −0.483905 | − | 0.875120i | \(-0.660782\pi\) | ||||
−0.483905 | + | 0.875120i | \(0.660782\pi\) | |||||||
\(744\) | −5.62796 | −0.206331 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 47.8712 | 1.75269 | ||||||||
\(747\) | 82.1115 | 3.00430 | ||||||||
\(748\) | −1.53319 | −0.0560589 | ||||||||
\(749\) | −2.31345 | −0.0845315 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.8074 | −1.16067 | −0.580335 | − | 0.814378i | \(-0.697078\pi\) | ||||
−0.580335 | + | 0.814378i | \(0.697078\pi\) | |||||||
\(752\) | 29.3006 | 1.06848 | ||||||||
\(753\) | −41.3037 | −1.50519 | ||||||||
\(754\) | 13.1899 | 0.480348 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 6.13469 | 0.223116 | ||||||||
\(757\) | 33.6767 | 1.22400 | 0.612000 | − | 0.790858i | \(-0.290365\pi\) | ||||
0.612000 | + | 0.790858i | \(0.290365\pi\) | |||||||
\(758\) | 8.85358 | 0.321576 | ||||||||
\(759\) | 0.575653 | 0.0208949 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.9020 | −0.540197 | −0.270098 | − | 0.962833i | \(-0.587056\pi\) | ||||
−0.270098 | + | 0.962833i | \(0.587056\pi\) | |||||||
\(762\) | 1.83841 | 0.0665986 | ||||||||
\(763\) | 3.83132 | 0.138703 | ||||||||
\(764\) | −15.5369 | −0.562105 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −44.9672 | −1.62473 | ||||||||
\(767\) | −56.7131 | −2.04779 | ||||||||
\(768\) | −42.0632 | −1.51782 | ||||||||
\(769\) | −23.5992 | −0.851010 | −0.425505 | − | 0.904956i | \(-0.639904\pi\) | ||||
−0.425505 | + | 0.904956i | \(0.639904\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.29870 | 0.154814 | ||||||||
\(772\) | 27.3665 | 0.984943 | ||||||||
\(773\) | −30.4365 | −1.09472 | −0.547362 | − | 0.836896i | \(-0.684368\pi\) | ||||
−0.547362 | + | 0.836896i | \(0.684368\pi\) | |||||||
\(774\) | 138.837 | 4.99040 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.72454 | −0.0619074 | ||||||||
\(777\) | −4.94277 | −0.177321 | ||||||||
\(778\) | −19.1712 | −0.687321 | ||||||||
\(779\) | 0.0610068 | 0.00218579 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.04483 | 0.0731699 | ||||||||
\(782\) | 3.68045 | 0.131613 | ||||||||
\(783\) | −12.4822 | −0.446076 | ||||||||
\(784\) | 26.0199 | 0.929283 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −106.900 | −3.81301 | ||||||||
\(787\) | −0.281399 | −0.0100308 | −0.00501539 | − | 0.999987i | \(-0.501596\pi\) | ||||
−0.00501539 | + | 0.999987i | \(0.501596\pi\) | |||||||
\(788\) | 4.86606 | 0.173346 | ||||||||
\(789\) | 23.7520 | 0.845593 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.23827 | 0.0440279 | ||||||||
\(792\) | 0.310474 | 0.0110322 | ||||||||
\(793\) | −27.9185 | −0.991417 | ||||||||
\(794\) | −68.5574 | −2.43301 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 45.2928 | 1.60536 | ||||||||
\(797\) | −26.6128 | −0.942673 | −0.471336 | − | 0.881954i | \(-0.656228\pi\) | ||||
−0.471336 | + | 0.881954i | \(0.656228\pi\) | |||||||
\(798\) | −8.76396 | −0.310241 | ||||||||
\(799\) | 20.0943 | 0.710885 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 80.4915 | 2.84403 | ||||||||
\(802\) | 53.0234 | 1.87232 | ||||||||
\(803\) | 0.0464535 | 0.00163931 | ||||||||
\(804\) | −18.3399 | −0.646798 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 78.9411 | 2.78058 | ||||||||
\(807\) | 74.1133 | 2.60891 | ||||||||
\(808\) | −1.17615 | −0.0413769 | ||||||||
\(809\) | 13.2472 | 0.465748 | 0.232874 | − | 0.972507i | \(-0.425187\pi\) | ||||
0.232874 | + | 0.972507i | \(0.425187\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.8348 | 1.25833 | 0.629165 | − | 0.777272i | \(-0.283397\pi\) | ||||
0.629165 | + | 0.777272i | \(0.283397\pi\) | |||||||
\(812\) | −1.30084 | −0.0456504 | ||||||||
\(813\) | −17.7305 | −0.621835 | ||||||||
\(814\) | −2.51090 | −0.0880071 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −29.0030 | −1.01531 | ||||||||
\(817\) | −47.2737 | −1.65390 | ||||||||
\(818\) | −47.2243 | −1.65116 | ||||||||
\(819\) | −8.57271 | −0.299555 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.76973 | −0.0617640 | −0.0308820 | − | 0.999523i | \(-0.509832\pi\) | ||||
−0.0308820 | + | 0.999523i | \(0.509832\pi\) | |||||||
\(822\) | −52.9436 | −1.84662 | ||||||||
\(823\) | 29.0119 | 1.01129 | 0.505645 | − | 0.862742i | \(-0.331255\pi\) | ||||
0.505645 | + | 0.862742i | \(0.331255\pi\) | |||||||
\(824\) | 3.35276 | 0.116799 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.9270 | 0.380200 | ||||||||
\(827\) | 15.9224 | 0.553675 | 0.276838 | − | 0.960917i | \(-0.410714\pi\) | ||||
0.276838 | + | 0.960917i | \(0.410714\pi\) | |||||||
\(828\) | −8.22386 | −0.285799 | ||||||||
\(829\) | −31.0294 | −1.07770 | −0.538849 | − | 0.842403i | \(-0.681141\pi\) | ||||
−0.538849 | + | 0.842403i | \(0.681141\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −52.6157 | −1.82522 | ||||||||
\(832\) | −35.0802 | −1.21619 | ||||||||
\(833\) | 17.8444 | 0.618273 | ||||||||
\(834\) | −46.5165 | −1.61073 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.27888 | −0.0788167 | ||||||||
\(837\) | −74.7053 | −2.58219 | ||||||||
\(838\) | −36.3704 | −1.25639 | ||||||||
\(839\) | −54.4602 | −1.88017 | −0.940087 | − | 0.340935i | \(-0.889256\pi\) | ||||
−0.940087 | + | 0.340935i | \(0.889256\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.3532 | −0.908731 | ||||||||
\(842\) | 41.7232 | 1.43788 | ||||||||
\(843\) | −12.1296 | −0.417765 | ||||||||
\(844\) | 42.2556 | 1.45450 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −87.7172 | −3.01578 | ||||||||
\(847\) | 4.16363 | 0.143064 | ||||||||
\(848\) | −18.6705 | −0.641147 | ||||||||
\(849\) | 40.4355 | 1.38774 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.08530 | 0.105763 | ||||||||
\(852\) | −44.8232 | −1.53562 | ||||||||
\(853\) | 5.82777 | 0.199539 | 0.0997694 | − | 0.995011i | \(-0.468189\pi\) | ||||
0.0997694 | + | 0.995011i | \(0.468189\pi\) | |||||||
\(854\) | 5.37912 | 0.184070 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.19503 | 0.0408454 | ||||||||
\(857\) | 48.9503 | 1.67211 | 0.836056 | − | 0.548644i | \(-0.184856\pi\) | ||||
0.836056 | + | 0.548644i | \(0.184856\pi\) | |||||||
\(858\) | −6.68200 | −0.228120 | ||||||||
\(859\) | −23.1193 | −0.788819 | −0.394409 | − | 0.918935i | \(-0.629051\pi\) | ||||
−0.394409 | + | 0.918935i | \(0.629051\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.0176418 | −0.000601232 0 | ||||||||
\(862\) | −9.60892 | −0.327281 | ||||||||
\(863\) | 24.5041 | 0.834129 | 0.417065 | − | 0.908877i | \(-0.363059\pi\) | ||||
0.417065 | + | 0.908877i | \(0.363059\pi\) | |||||||
\(864\) | 61.9740 | 2.10840 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 82.7164 | 2.81082 | ||||||||
\(867\) | 30.0045 | 1.01900 | ||||||||
\(868\) | −7.78545 | −0.264255 | ||||||||
\(869\) | 3.13482 | 0.106342 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.9334 | 0.404349 | ||||||||
\(872\) | −1.97911 | −0.0670210 | ||||||||
\(873\) | −49.1621 | −1.66388 | ||||||||
\(874\) | 5.47050 | 0.185043 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.01827 | −0.0344042 | ||||||||
\(877\) | 11.9231 | 0.402614 | 0.201307 | − | 0.979528i | \(-0.435481\pi\) | ||||
0.201307 | + | 0.979528i | \(0.435481\pi\) | |||||||
\(878\) | −47.6466 | −1.60800 | ||||||||
\(879\) | 63.4112 | 2.13881 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.2901 | −0.414063 | −0.207032 | − | 0.978334i | \(-0.566380\pi\) | ||||
−0.207032 | + | 0.978334i | \(0.566380\pi\) | |||||||
\(882\) | −77.8960 | −2.62289 | ||||||||
\(883\) | 48.1400 | 1.62004 | 0.810020 | − | 0.586403i | \(-0.199456\pi\) | ||||
0.810020 | + | 0.586403i | \(0.199456\pi\) | |||||||
\(884\) | −21.8680 | −0.735501 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −56.5039 | −1.89829 | ||||||||
\(887\) | −20.7341 | −0.696184 | −0.348092 | − | 0.937460i | \(-0.613170\pi\) | ||||
−0.348092 | + | 0.937460i | \(0.613170\pi\) | |||||||
\(888\) | 2.55324 | 0.0856811 | ||||||||
\(889\) | 0.117976 | 0.00395678 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.59389 | 0.0533972 | ||||||||
\(892\) | 16.7114 | 0.559540 | ||||||||
\(893\) | 29.8675 | 0.999477 | ||||||||
\(894\) | −122.122 | −4.08437 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.599935 | 0.0200424 | ||||||||
\(897\) | 8.21059 | 0.274144 | ||||||||
\(898\) | 48.1490 | 1.60675 | ||||||||
\(899\) | 15.8410 | 0.528325 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.8042 | −0.426569 | ||||||||
\(902\) | −0.00896195 | −0.000298400 0 | ||||||||
\(903\) | 13.6705 | 0.454926 | ||||||||
\(904\) | −0.639641 | −0.0212742 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −62.8940 | −2.08951 | ||||||||
\(907\) | 7.02598 | 0.233294 | 0.116647 | − | 0.993173i | \(-0.462785\pi\) | ||||
0.116647 | + | 0.993173i | \(0.462785\pi\) | |||||||
\(908\) | 40.3606 | 1.33941 | ||||||||
\(909\) | −33.5290 | −1.11209 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 58.0477 | 1.92320 | 0.961602 | − | 0.274446i | \(-0.0884946\pi\) | ||||
0.961602 | + | 0.274446i | \(0.0884946\pi\) | |||||||
\(912\) | −43.1091 | −1.42749 | ||||||||
\(913\) | 4.10716 | 0.135927 | ||||||||
\(914\) | −68.8116 | −2.27608 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26.7353 | 0.883359 | ||||||||
\(917\) | −6.86008 | −0.226540 | ||||||||
\(918\) | 40.4292 | 1.33436 | ||||||||
\(919\) | 17.9524 | 0.592194 | 0.296097 | − | 0.955158i | \(-0.404315\pi\) | ||||
0.296097 | + | 0.955158i | \(0.404315\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 59.6324 | 1.96496 | ||||||||
\(922\) | 36.4381 | 1.20002 | ||||||||
\(923\) | 29.1657 | 0.960000 | ||||||||
\(924\) | 0.659003 | 0.0216796 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −24.2442 | −0.796715 | ||||||||
\(927\) | 95.5782 | 3.13920 | ||||||||
\(928\) | −13.1413 | −0.431385 | ||||||||
\(929\) | −20.8907 | −0.685403 | −0.342701 | − | 0.939444i | \(-0.611342\pi\) | ||||
−0.342701 | + | 0.939444i | \(0.611342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.5234 | 0.869268 | ||||||||
\(932\) | 21.4790 | 0.703569 | ||||||||
\(933\) | −60.1019 | −1.96765 | ||||||||
\(934\) | −44.6279 | −1.46027 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.42832 | 0.144744 | ||||||||
\(937\) | 39.5712 | 1.29273 | 0.646367 | − | 0.763027i | \(-0.276288\pi\) | ||||
0.646367 | + | 0.763027i | \(0.276288\pi\) | |||||||
\(938\) | −2.29924 | −0.0750728 | ||||||||
\(939\) | 5.82561 | 0.190112 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.21402 | −0.0721750 | −0.0360875 | − | 0.999349i | \(-0.511490\pi\) | ||||
−0.0360875 | + | 0.999349i | \(0.511490\pi\) | |||||||
\(942\) | 46.3346 | 1.50966 | ||||||||
\(943\) | 0.0110121 | 0.000358603 0 | ||||||||
\(944\) | 53.7490 | 1.74938 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.94455 | 0.225787 | ||||||||
\(947\) | 27.2239 | 0.884659 | 0.442330 | − | 0.896853i | \(-0.354152\pi\) | ||||
0.442330 | + | 0.896853i | \(0.354152\pi\) | |||||||
\(948\) | −68.7159 | −2.23179 | ||||||||
\(949\) | 0.662571 | 0.0215080 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −83.8842 | −2.72013 | ||||||||
\(952\) | 0.195454 | 0.00633471 | ||||||||
\(953\) | 49.1033 | 1.59061 | 0.795305 | − | 0.606209i | \(-0.207311\pi\) | ||||
0.795305 | + | 0.606209i | \(0.207311\pi\) | |||||||
\(954\) | 55.8939 | 1.80963 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 47.0347 | 1.52121 | ||||||||
\(957\) | −1.34086 | −0.0433440 | ||||||||
\(958\) | 28.7413 | 0.928590 | ||||||||
\(959\) | −3.39753 | −0.109712 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 63.8075 | 2.05831 | ||||||||
\(962\) | −35.8132 | −1.15467 | ||||||||
\(963\) | 34.0672 | 1.09780 | ||||||||
\(964\) | 2.09729 | 0.0675492 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.58195 | −0.0508984 | ||||||||
\(967\) | 2.12457 | 0.0683214 | 0.0341607 | − | 0.999416i | \(-0.489124\pi\) | ||||
0.0341607 | + | 0.999416i | \(0.489124\pi\) | |||||||
\(968\) | −2.15076 | −0.0691281 | ||||||||
\(969\) | −29.5642 | −0.949738 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.0749 | 1.02933 | 0.514666 | − | 0.857391i | \(-0.327916\pi\) | ||||
0.514666 | + | 0.857391i | \(0.327916\pi\) | |||||||
\(972\) | 13.3353 | 0.427731 | ||||||||
\(973\) | −2.98509 | −0.0956975 | ||||||||
\(974\) | 82.6876 | 2.64948 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 26.4594 | 0.846945 | ||||||||
\(977\) | 1.85481 | 0.0593406 | 0.0296703 | − | 0.999560i | \(-0.490554\pi\) | ||||
0.0296703 | + | 0.999560i | \(0.490554\pi\) | |||||||
\(978\) | 101.805 | 3.25535 | ||||||||
\(979\) | 4.02614 | 0.128676 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −56.4190 | −1.80132 | ||||||||
\(982\) | 15.5920 | 0.497560 | ||||||||
\(983\) | 48.0786 | 1.53347 | 0.766734 | − | 0.641965i | \(-0.221881\pi\) | ||||
0.766734 | + | 0.641965i | \(0.221881\pi\) | |||||||
\(984\) | 0.00911306 | 0.000290514 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −8.57286 | −0.273015 | ||||||||
\(987\) | −8.63703 | −0.274920 | ||||||||
\(988\) | −32.5039 | −1.03409 | ||||||||
\(989\) | −8.53319 | −0.271340 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.7585 | 1.45357 | 0.726783 | − | 0.686867i | \(-0.241015\pi\) | ||||
0.726783 | + | 0.686867i | \(0.241015\pi\) | |||||||
\(992\) | −78.6504 | −2.49715 | ||||||||
\(993\) | 68.7046 | 2.18028 | ||||||||
\(994\) | −5.61941 | −0.178237 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −90.0299 | −2.85271 | ||||||||
\(997\) | 17.8475 | 0.565235 | 0.282618 | − | 0.959233i | \(-0.408797\pi\) | ||||
0.282618 | + | 0.959233i | \(0.408797\pi\) | |||||||
\(998\) | −3.74393 | −0.118512 | ||||||||
\(999\) | 33.8916 | 1.07228 |
(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 | 6025.2.a.h.1.11 | 12 | ||
5.4 | even | 2 | 241.2.a.b.1.2 | ✓ | 12 | ||
15.14 | odd | 2 | 2169.2.a.h.1.11 | 12 | |||
20.19 | odd | 2 | 3856.2.a.n.1.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
241.2.a.b.1.2 | ✓ | 12 | 5.4 | even | 2 | ||
2169.2.a.h.1.11 | 12 | 15.14 | odd | 2 | |||
3856.2.a.n.1.1 | 12 | 20.19 | odd | 2 | |||
6025.2.a.h.1.11 | 12 | 1.1 | even | 1 | trivial |