Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 825) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61803 | −1.14412 | −0.572061 | − | 0.820211i | \(-0.693856\pi\) | ||||
−0.572061 | + | 0.820211i | \(0.693856\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.61803 | −0.660560 | ||||||||
\(7\) | −3.00000 | −1.13389 | −0.566947 | − | 0.823754i | \(-0.691875\pi\) | ||||
−0.566947 | + | 0.823754i | \(0.691875\pi\) | |||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.618034 | 0.178411 | ||||||||
\(13\) | 1.85410 | 0.514235 | 0.257118 | − | 0.966380i | \(-0.417227\pi\) | ||||
0.257118 | + | 0.966380i | \(0.417227\pi\) | |||||||
\(14\) | 4.85410 | 1.29731 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | −7.47214 | −1.81226 | −0.906130 | − | 0.423000i | \(-0.860977\pi\) | ||||
−0.906130 | + | 0.423000i | \(0.860977\pi\) | |||||||
\(18\) | −1.61803 | −0.381374 | ||||||||
\(19\) | 2.76393 | 0.634089 | 0.317045 | − | 0.948411i | \(-0.397309\pi\) | ||||
0.317045 | + | 0.948411i | \(0.397309\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | −0.654654 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.61803 | 1.58847 | 0.794235 | − | 0.607611i | \(-0.207872\pi\) | ||||
0.794235 | + | 0.607611i | \(0.207872\pi\) | |||||||
\(24\) | 2.23607 | 0.456435 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.00000 | −0.588348 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.85410 | −0.350392 | ||||||||
\(29\) | −3.61803 | −0.671852 | −0.335926 | − | 0.941888i | \(-0.609049\pi\) | ||||
−0.335926 | + | 0.941888i | \(0.609049\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.85410 | −1.59024 | −0.795122 | − | 0.606450i | \(-0.792593\pi\) | ||||
−0.795122 | + | 0.606450i | \(0.792593\pi\) | |||||||
\(32\) | 3.38197 | 0.597853 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.0902 | 2.07345 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.618034 | 0.103006 | ||||||||
\(37\) | 8.85410 | 1.45561 | 0.727803 | − | 0.685787i | \(-0.240542\pi\) | ||||
0.727803 | + | 0.685787i | \(0.240542\pi\) | |||||||
\(38\) | −4.47214 | −0.725476 | ||||||||
\(39\) | 1.85410 | 0.296894 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.236068 | 0.0368676 | 0.0184338 | − | 0.999830i | \(-0.494132\pi\) | ||||
0.0184338 | + | 0.999830i | \(0.494132\pi\) | |||||||
\(42\) | 4.85410 | 0.749004 | ||||||||
\(43\) | −1.76393 | −0.268997 | −0.134499 | − | 0.990914i | \(-0.542942\pi\) | ||||
−0.134499 | + | 0.990914i | \(0.542942\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.3262 | −1.81740 | ||||||||
\(47\) | 9.38197 | 1.36850 | 0.684250 | − | 0.729247i | \(-0.260130\pi\) | ||||
0.684250 | + | 0.729247i | \(0.260130\pi\) | |||||||
\(48\) | −4.85410 | −0.700629 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.47214 | −1.04631 | ||||||||
\(52\) | 1.14590 | 0.158907 | ||||||||
\(53\) | −0.472136 | −0.0648529 | −0.0324264 | − | 0.999474i | \(-0.510323\pi\) | ||||
−0.0324264 | + | 0.999474i | \(0.510323\pi\) | |||||||
\(54\) | −1.61803 | −0.220187 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.70820 | −0.896421 | ||||||||
\(57\) | 2.76393 | 0.366092 | ||||||||
\(58\) | 5.85410 | 0.768681 | ||||||||
\(59\) | −4.14590 | −0.539750 | −0.269875 | − | 0.962895i | \(-0.586982\pi\) | ||||
−0.269875 | + | 0.962895i | \(0.586982\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.76393 | 0.737996 | 0.368998 | − | 0.929430i | \(-0.379701\pi\) | ||||
0.368998 | + | 0.929430i | \(0.379701\pi\) | |||||||
\(62\) | 14.3262 | 1.81943 | ||||||||
\(63\) | −3.00000 | −0.377964 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.70820 | −1.06388 | −0.531938 | − | 0.846783i | \(-0.678536\pi\) | ||||
−0.531938 | + | 0.846783i | \(0.678536\pi\) | |||||||
\(68\) | −4.61803 | −0.560019 | ||||||||
\(69\) | 7.61803 | 0.917104 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.47214 | 0.174710 | 0.0873552 | − | 0.996177i | \(-0.472158\pi\) | ||||
0.0873552 | + | 0.996177i | \(0.472158\pi\) | |||||||
\(72\) | 2.23607 | 0.263523 | ||||||||
\(73\) | 6.85410 | 0.802212 | 0.401106 | − | 0.916032i | \(-0.368626\pi\) | ||||
0.401106 | + | 0.916032i | \(0.368626\pi\) | |||||||
\(74\) | −14.3262 | −1.66539 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.70820 | 0.195944 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.00000 | −0.339683 | ||||||||
\(79\) | 7.56231 | 0.850826 | 0.425413 | − | 0.904999i | \(-0.360129\pi\) | ||||
0.425413 | + | 0.904999i | \(0.360129\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.381966 | −0.0421811 | ||||||||
\(83\) | −10.3820 | −1.13957 | −0.569784 | − | 0.821794i | \(-0.692973\pi\) | ||||
−0.569784 | + | 0.821794i | \(0.692973\pi\) | |||||||
\(84\) | −1.85410 | −0.202299 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.85410 | 0.307766 | ||||||||
\(87\) | −3.61803 | −0.387894 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.56231 | 0.271604 | 0.135802 | − | 0.990736i | \(-0.456639\pi\) | ||||
0.135802 | + | 0.990736i | \(0.456639\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.56231 | −0.583088 | ||||||||
\(92\) | 4.70820 | 0.490864 | ||||||||
\(93\) | −8.85410 | −0.918128 | ||||||||
\(94\) | −15.1803 | −1.56573 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.38197 | 0.345170 | ||||||||
\(97\) | −10.4164 | −1.05763 | −0.528813 | − | 0.848738i | \(-0.677363\pi\) | ||||
−0.528813 | + | 0.848738i | \(0.677363\pi\) | |||||||
\(98\) | −3.23607 | −0.326892 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.09017 | 0.108476 | 0.0542380 | − | 0.998528i | \(-0.482727\pi\) | ||||
0.0542380 | + | 0.998528i | \(0.482727\pi\) | |||||||
\(102\) | 12.0902 | 1.19711 | ||||||||
\(103\) | 15.1803 | 1.49576 | 0.747882 | − | 0.663832i | \(-0.231071\pi\) | ||||
0.747882 | + | 0.663832i | \(0.231071\pi\) | |||||||
\(104\) | 4.14590 | 0.406539 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.763932 | 0.0741996 | ||||||||
\(107\) | −16.4164 | −1.58703 | −0.793517 | − | 0.608548i | \(-0.791752\pi\) | ||||
−0.793517 | + | 0.608548i | \(0.791752\pi\) | |||||||
\(108\) | 0.618034 | 0.0594703 | ||||||||
\(109\) | −15.0000 | −1.43674 | −0.718370 | − | 0.695662i | \(-0.755111\pi\) | ||||
−0.718370 | + | 0.695662i | \(0.755111\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.85410 | 0.840394 | ||||||||
\(112\) | 14.5623 | 1.37601 | ||||||||
\(113\) | 8.47214 | 0.796992 | 0.398496 | − | 0.917170i | \(-0.369532\pi\) | ||||
0.398496 | + | 0.917170i | \(0.369532\pi\) | |||||||
\(114\) | −4.47214 | −0.418854 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.23607 | −0.207614 | ||||||||
\(117\) | 1.85410 | 0.171412 | ||||||||
\(118\) | 6.70820 | 0.617540 | ||||||||
\(119\) | 22.4164 | 2.05491 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −9.32624 | −0.844358 | ||||||||
\(123\) | 0.236068 | 0.0212855 | ||||||||
\(124\) | −5.47214 | −0.491412 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.85410 | 0.432438 | ||||||||
\(127\) | −6.61803 | −0.587256 | −0.293628 | − | 0.955920i | \(-0.594863\pi\) | ||||
−0.293628 | + | 0.955920i | \(0.594863\pi\) | |||||||
\(128\) | −13.6180 | −1.20368 | ||||||||
\(129\) | −1.76393 | −0.155306 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.32624 | −0.640096 | −0.320048 | − | 0.947401i | \(-0.603699\pi\) | ||||
−0.320048 | + | 0.947401i | \(0.603699\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.29180 | −0.718990 | ||||||||
\(134\) | 14.0902 | 1.21721 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −16.7082 | −1.43272 | ||||||||
\(137\) | 12.7984 | 1.09344 | 0.546719 | − | 0.837316i | \(-0.315876\pi\) | ||||
0.546719 | + | 0.837316i | \(0.315876\pi\) | |||||||
\(138\) | −12.3262 | −1.04928 | ||||||||
\(139\) | −5.85410 | −0.496538 | −0.248269 | − | 0.968691i | \(-0.579862\pi\) | ||||
−0.248269 | + | 0.968691i | \(0.579862\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.38197 | 0.790104 | ||||||||
\(142\) | −2.38197 | −0.199890 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.85410 | −0.404508 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.0902 | −0.917829 | ||||||||
\(147\) | 2.00000 | 0.164957 | ||||||||
\(148\) | 5.47214 | 0.449807 | ||||||||
\(149\) | −16.1803 | −1.32555 | −0.662773 | − | 0.748821i | \(-0.730620\pi\) | ||||
−0.662773 | + | 0.748821i | \(0.730620\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.18034 | 0.747085 | 0.373543 | − | 0.927613i | \(-0.378143\pi\) | ||||
0.373543 | + | 0.927613i | \(0.378143\pi\) | |||||||
\(152\) | 6.18034 | 0.501292 | ||||||||
\(153\) | −7.47214 | −0.604086 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.14590 | 0.0917453 | ||||||||
\(157\) | 17.7984 | 1.42046 | 0.710232 | − | 0.703967i | \(-0.248590\pi\) | ||||
0.710232 | + | 0.703967i | \(0.248590\pi\) | |||||||
\(158\) | −12.2361 | −0.973449 | ||||||||
\(159\) | −0.472136 | −0.0374428 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.8541 | −1.80116 | ||||||||
\(162\) | −1.61803 | −0.127125 | ||||||||
\(163\) | 17.0902 | 1.33861 | 0.669303 | − | 0.742990i | \(-0.266593\pi\) | ||||
0.669303 | + | 0.742990i | \(0.266593\pi\) | |||||||
\(164\) | 0.145898 | 0.0113927 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.7984 | 1.30381 | ||||||||
\(167\) | 20.9443 | 1.62072 | 0.810358 | − | 0.585935i | \(-0.199273\pi\) | ||||
0.810358 | + | 0.585935i | \(0.199273\pi\) | |||||||
\(168\) | −6.70820 | −0.517549 | ||||||||
\(169\) | −9.56231 | −0.735562 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.76393 | 0.211363 | ||||||||
\(172\) | −1.09017 | −0.0831247 | ||||||||
\(173\) | 5.47214 | 0.416039 | 0.208019 | − | 0.978125i | \(-0.433298\pi\) | ||||
0.208019 | + | 0.978125i | \(0.433298\pi\) | |||||||
\(174\) | 5.85410 | 0.443798 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.14590 | −0.311625 | ||||||||
\(178\) | −4.14590 | −0.310748 | ||||||||
\(179\) | −20.1246 | −1.50418 | −0.752092 | − | 0.659058i | \(-0.770955\pi\) | ||||
−0.752092 | + | 0.659058i | \(0.770955\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.7984 | −0.951296 | −0.475648 | − | 0.879636i | \(-0.657786\pi\) | ||||
−0.475648 | + | 0.879636i | \(0.657786\pi\) | |||||||
\(182\) | 9.00000 | 0.667124 | ||||||||
\(183\) | 5.76393 | 0.426082 | ||||||||
\(184\) | 17.0344 | 1.25580 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 14.3262 | 1.05045 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.79837 | 0.422890 | ||||||||
\(189\) | −3.00000 | −0.218218 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.7426 | 1.13910 | 0.569549 | − | 0.821957i | \(-0.307118\pi\) | ||||
0.569549 | + | 0.821957i | \(0.307118\pi\) | |||||||
\(192\) | 4.23607 | 0.305712 | ||||||||
\(193\) | −18.4721 | −1.32965 | −0.664827 | − | 0.746998i | \(-0.731495\pi\) | ||||
−0.664827 | + | 0.746998i | \(0.731495\pi\) | |||||||
\(194\) | 16.8541 | 1.21005 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.23607 | 0.0882906 | ||||||||
\(197\) | −9.70820 | −0.691681 | −0.345840 | − | 0.938293i | \(-0.612406\pi\) | ||||
−0.345840 | + | 0.938293i | \(0.612406\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.29180 | −0.587790 | −0.293895 | − | 0.955838i | \(-0.594952\pi\) | ||||
−0.293895 | + | 0.955838i | \(0.594952\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.70820 | −0.614229 | ||||||||
\(202\) | −1.76393 | −0.124110 | ||||||||
\(203\) | 10.8541 | 0.761809 | ||||||||
\(204\) | −4.61803 | −0.323327 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −24.5623 | −1.71134 | ||||||||
\(207\) | 7.61803 | 0.529490 | ||||||||
\(208\) | −9.00000 | −0.624038 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.1803 | −0.907372 | −0.453686 | − | 0.891162i | \(-0.649891\pi\) | ||||
−0.453686 | + | 0.891162i | \(0.649891\pi\) | |||||||
\(212\) | −0.291796 | −0.0200406 | ||||||||
\(213\) | 1.47214 | 0.100869 | ||||||||
\(214\) | 26.5623 | 1.81576 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.23607 | 0.152145 | ||||||||
\(217\) | 26.5623 | 1.80317 | ||||||||
\(218\) | 24.2705 | 1.64381 | ||||||||
\(219\) | 6.85410 | 0.463157 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.8541 | −0.931928 | ||||||||
\(222\) | −14.3262 | −0.961514 | ||||||||
\(223\) | −12.7082 | −0.851004 | −0.425502 | − | 0.904957i | \(-0.639903\pi\) | ||||
−0.425502 | + | 0.904957i | \(0.639903\pi\) | |||||||
\(224\) | −10.1459 | −0.677901 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.7082 | −0.911856 | ||||||||
\(227\) | 14.5623 | 0.966534 | 0.483267 | − | 0.875473i | \(-0.339450\pi\) | ||||
0.483267 | + | 0.875473i | \(0.339450\pi\) | |||||||
\(228\) | 1.70820 | 0.113129 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.09017 | −0.531146 | ||||||||
\(233\) | 6.32624 | 0.414446 | 0.207223 | − | 0.978294i | \(-0.433557\pi\) | ||||
0.207223 | + | 0.978294i | \(0.433557\pi\) | |||||||
\(234\) | −3.00000 | −0.196116 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.56231 | −0.166792 | ||||||||
\(237\) | 7.56231 | 0.491225 | ||||||||
\(238\) | −36.2705 | −2.35107 | ||||||||
\(239\) | 20.6525 | 1.33590 | 0.667949 | − | 0.744207i | \(-0.267173\pi\) | ||||
0.667949 | + | 0.744207i | \(0.267173\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.85410 | −0.505927 | −0.252964 | − | 0.967476i | \(-0.581405\pi\) | ||||
−0.252964 | + | 0.967476i | \(0.581405\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.56231 | 0.228053 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.381966 | −0.0243533 | ||||||||
\(247\) | 5.12461 | 0.326071 | ||||||||
\(248\) | −19.7984 | −1.25720 | ||||||||
\(249\) | −10.3820 | −0.657930 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.5623 | −1.29788 | −0.648941 | − | 0.760839i | \(-0.724788\pi\) | ||||
−0.648941 | + | 0.760839i | \(0.724788\pi\) | |||||||
\(252\) | −1.85410 | −0.116797 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 10.7082 | 0.671892 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | 10.0344 | 0.625931 | 0.312966 | − | 0.949764i | \(-0.398678\pi\) | ||||
0.312966 | + | 0.949764i | \(0.398678\pi\) | |||||||
\(258\) | 2.85410 | 0.177689 | ||||||||
\(259\) | −26.5623 | −1.65050 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.61803 | −0.223951 | ||||||||
\(262\) | 11.8541 | 0.732349 | ||||||||
\(263\) | 11.1246 | 0.685973 | 0.342986 | − | 0.939340i | \(-0.388561\pi\) | ||||
0.342986 | + | 0.939340i | \(0.388561\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 13.4164 | 0.822613 | ||||||||
\(267\) | 2.56231 | 0.156811 | ||||||||
\(268\) | −5.38197 | −0.328756 | ||||||||
\(269\) | −0.527864 | −0.0321844 | −0.0160922 | − | 0.999871i | \(-0.505123\pi\) | ||||
−0.0160922 | + | 0.999871i | \(0.505123\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.2705 | 1.35284 | 0.676419 | − | 0.736517i | \(-0.263531\pi\) | ||||
0.676419 | + | 0.736517i | \(0.263531\pi\) | |||||||
\(272\) | 36.2705 | 2.19922 | ||||||||
\(273\) | −5.56231 | −0.336646 | ||||||||
\(274\) | −20.7082 | −1.25103 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.70820 | 0.283401 | ||||||||
\(277\) | −23.9787 | −1.44074 | −0.720371 | − | 0.693589i | \(-0.756028\pi\) | ||||
−0.720371 | + | 0.693589i | \(0.756028\pi\) | |||||||
\(278\) | 9.47214 | 0.568101 | ||||||||
\(279\) | −8.85410 | −0.530081 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.32624 | 0.198427 | 0.0992134 | − | 0.995066i | \(-0.468367\pi\) | ||||
0.0992134 | + | 0.995066i | \(0.468367\pi\) | |||||||
\(282\) | −15.1803 | −0.903976 | ||||||||
\(283\) | −27.0902 | −1.61034 | −0.805172 | − | 0.593042i | \(-0.797927\pi\) | ||||
−0.805172 | + | 0.593042i | \(0.797927\pi\) | |||||||
\(284\) | 0.909830 | 0.0539885 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.708204 | −0.0418040 | ||||||||
\(288\) | 3.38197 | 0.199284 | ||||||||
\(289\) | 38.8328 | 2.28428 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.4164 | −0.610621 | ||||||||
\(292\) | 4.23607 | 0.247897 | ||||||||
\(293\) | 19.4164 | 1.13432 | 0.567159 | − | 0.823608i | \(-0.308042\pi\) | ||||
0.567159 | + | 0.823608i | \(0.308042\pi\) | |||||||
\(294\) | −3.23607 | −0.188731 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 19.7984 | 1.15076 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 26.1803 | 1.51659 | ||||||||
\(299\) | 14.1246 | 0.816847 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.29180 | 0.305014 | ||||||||
\(302\) | −14.8541 | −0.854758 | ||||||||
\(303\) | 1.09017 | 0.0626286 | ||||||||
\(304\) | −13.4164 | −0.769484 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 12.0902 | 0.691149 | ||||||||
\(307\) | −15.8885 | −0.906807 | −0.453404 | − | 0.891305i | \(-0.649790\pi\) | ||||
−0.453404 | + | 0.891305i | \(0.649790\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.1803 | 0.863579 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.5279 | −1.05062 | −0.525309 | − | 0.850911i | \(-0.676050\pi\) | ||||
−0.525309 | + | 0.850911i | \(0.676050\pi\) | |||||||
\(312\) | 4.14590 | 0.234715 | ||||||||
\(313\) | 30.7082 | 1.73573 | 0.867865 | − | 0.496800i | \(-0.165492\pi\) | ||||
0.867865 | + | 0.496800i | \(0.165492\pi\) | |||||||
\(314\) | −28.7984 | −1.62519 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.67376 | 0.262920 | ||||||||
\(317\) | 9.18034 | 0.515619 | 0.257810 | − | 0.966196i | \(-0.416999\pi\) | ||||
0.257810 | + | 0.966196i | \(0.416999\pi\) | |||||||
\(318\) | 0.763932 | 0.0428392 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.4164 | −0.916275 | ||||||||
\(322\) | 36.9787 | 2.06074 | ||||||||
\(323\) | −20.6525 | −1.14913 | ||||||||
\(324\) | 0.618034 | 0.0343352 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −27.6525 | −1.53153 | ||||||||
\(327\) | −15.0000 | −0.829502 | ||||||||
\(328\) | 0.527864 | 0.0291464 | ||||||||
\(329\) | −28.1459 | −1.55173 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.4164 | −0.902327 | −0.451164 | − | 0.892441i | \(-0.648991\pi\) | ||||
−0.451164 | + | 0.892441i | \(0.648991\pi\) | |||||||
\(332\) | −6.41641 | −0.352146 | ||||||||
\(333\) | 8.85410 | 0.485202 | ||||||||
\(334\) | −33.8885 | −1.85430 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 14.5623 | 0.794439 | ||||||||
\(337\) | 23.7082 | 1.29147 | 0.645734 | − | 0.763562i | \(-0.276551\pi\) | ||||
0.645734 | + | 0.763562i | \(0.276551\pi\) | |||||||
\(338\) | 15.4721 | 0.841573 | ||||||||
\(339\) | 8.47214 | 0.460143 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −4.47214 | −0.241825 | ||||||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | −3.94427 | −0.212661 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.85410 | −0.475999 | ||||||||
\(347\) | 12.3262 | 0.661707 | 0.330854 | − | 0.943682i | \(-0.392663\pi\) | ||||
0.330854 | + | 0.943682i | \(0.392663\pi\) | |||||||
\(348\) | −2.23607 | −0.119866 | ||||||||
\(349\) | −28.9443 | −1.54935 | −0.774676 | − | 0.632359i | \(-0.782087\pi\) | ||||
−0.774676 | + | 0.632359i | \(0.782087\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.85410 | 0.0989646 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.88854 | −0.473089 | −0.236545 | − | 0.971621i | \(-0.576015\pi\) | ||||
−0.236545 | + | 0.971621i | \(0.576015\pi\) | |||||||
\(354\) | 6.70820 | 0.356537 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.58359 | 0.0839302 | ||||||||
\(357\) | 22.4164 | 1.18640 | ||||||||
\(358\) | 32.5623 | 1.72097 | ||||||||
\(359\) | −18.2148 | −0.961339 | −0.480670 | − | 0.876902i | \(-0.659606\pi\) | ||||
−0.480670 | + | 0.876902i | \(0.659606\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.3607 | −0.597931 | ||||||||
\(362\) | 20.7082 | 1.08840 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.43769 | −0.180184 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.32624 | −0.487490 | ||||||||
\(367\) | −18.8328 | −0.983065 | −0.491532 | − | 0.870859i | \(-0.663563\pi\) | ||||
−0.491532 | + | 0.870859i | \(0.663563\pi\) | |||||||
\(368\) | −36.9787 | −1.92765 | ||||||||
\(369\) | 0.236068 | 0.0122892 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.41641 | 0.0735362 | ||||||||
\(372\) | −5.47214 | −0.283717 | ||||||||
\(373\) | −17.4164 | −0.901787 | −0.450894 | − | 0.892578i | \(-0.648895\pi\) | ||||
−0.450894 | + | 0.892578i | \(0.648895\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.9787 | 1.08189 | ||||||||
\(377\) | −6.70820 | −0.345490 | ||||||||
\(378\) | 4.85410 | 0.249668 | ||||||||
\(379\) | −23.2148 | −1.19246 | −0.596232 | − | 0.802812i | \(-0.703336\pi\) | ||||
−0.596232 | + | 0.802812i | \(0.703336\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.61803 | −0.339052 | ||||||||
\(382\) | −25.4721 | −1.30327 | ||||||||
\(383\) | −21.5279 | −1.10002 | −0.550011 | − | 0.835157i | \(-0.685377\pi\) | ||||
−0.550011 | + | 0.835157i | \(0.685377\pi\) | |||||||
\(384\) | −13.6180 | −0.694942 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 29.8885 | 1.52129 | ||||||||
\(387\) | −1.76393 | −0.0896657 | ||||||||
\(388\) | −6.43769 | −0.326824 | ||||||||
\(389\) | −18.0902 | −0.917208 | −0.458604 | − | 0.888641i | \(-0.651650\pi\) | ||||
−0.458604 | + | 0.888641i | \(0.651650\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −56.9230 | −2.87872 | ||||||||
\(392\) | 4.47214 | 0.225877 | ||||||||
\(393\) | −7.32624 | −0.369560 | ||||||||
\(394\) | 15.7082 | 0.791368 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.5623 | −0.981804 | −0.490902 | − | 0.871215i | \(-0.663333\pi\) | ||||
−0.490902 | + | 0.871215i | \(0.663333\pi\) | |||||||
\(398\) | 13.4164 | 0.672504 | ||||||||
\(399\) | −8.29180 | −0.415109 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.819660 | 0.0409319 | 0.0204659 | − | 0.999791i | \(-0.493485\pi\) | ||||
0.0204659 | + | 0.999791i | \(0.493485\pi\) | |||||||
\(402\) | 14.0902 | 0.702754 | ||||||||
\(403\) | −16.4164 | −0.817760 | ||||||||
\(404\) | 0.673762 | 0.0335209 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.5623 | −0.871603 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −16.7082 | −0.827179 | ||||||||
\(409\) | 10.1246 | 0.500630 | 0.250315 | − | 0.968164i | \(-0.419466\pi\) | ||||
0.250315 | + | 0.968164i | \(0.419466\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.7984 | 0.631297 | ||||||||
\(412\) | 9.38197 | 0.462216 | ||||||||
\(413\) | 12.4377 | 0.612019 | ||||||||
\(414\) | −12.3262 | −0.605802 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.27051 | 0.307437 | ||||||||
\(417\) | −5.85410 | −0.286677 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.9443 | 0.925488 | 0.462744 | − | 0.886492i | \(-0.346865\pi\) | ||||
0.462744 | + | 0.886492i | \(0.346865\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.27051 | −0.354343 | −0.177171 | − | 0.984180i | \(-0.556695\pi\) | ||||
−0.177171 | + | 0.984180i | \(0.556695\pi\) | |||||||
\(422\) | 21.3262 | 1.03815 | ||||||||
\(423\) | 9.38197 | 0.456167 | ||||||||
\(424\) | −1.05573 | −0.0512707 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.38197 | −0.115407 | ||||||||
\(427\) | −17.2918 | −0.836809 | ||||||||
\(428\) | −10.1459 | −0.490420 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.1459 | −0.777721 | −0.388860 | − | 0.921297i | \(-0.627131\pi\) | ||||
−0.388860 | + | 0.921297i | \(0.627131\pi\) | |||||||
\(432\) | −4.85410 | −0.233543 | ||||||||
\(433\) | −27.1803 | −1.30620 | −0.653102 | − | 0.757270i | \(-0.726533\pi\) | ||||
−0.653102 | + | 0.757270i | \(0.726533\pi\) | |||||||
\(434\) | −42.9787 | −2.06304 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.27051 | −0.443977 | ||||||||
\(437\) | 21.0557 | 1.00723 | ||||||||
\(438\) | −11.0902 | −0.529909 | ||||||||
\(439\) | −7.43769 | −0.354982 | −0.177491 | − | 0.984122i | \(-0.556798\pi\) | ||||
−0.177491 | + | 0.984122i | \(0.556798\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.00000 | 0.0952381 | ||||||||
\(442\) | 22.4164 | 1.06624 | ||||||||
\(443\) | −27.5066 | −1.30688 | −0.653438 | − | 0.756980i | \(-0.726674\pi\) | ||||
−0.653438 | + | 0.756980i | \(0.726674\pi\) | |||||||
\(444\) | 5.47214 | 0.259696 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 20.5623 | 0.973653 | ||||||||
\(447\) | −16.1803 | −0.765304 | ||||||||
\(448\) | −12.7082 | −0.600406 | ||||||||
\(449\) | 14.4721 | 0.682982 | 0.341491 | − | 0.939885i | \(-0.389068\pi\) | ||||
0.341491 | + | 0.939885i | \(0.389068\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 5.23607 | 0.246284 | ||||||||
\(453\) | 9.18034 | 0.431330 | ||||||||
\(454\) | −23.5623 | −1.10583 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.18034 | 0.289421 | ||||||||
\(457\) | −23.5279 | −1.10059 | −0.550294 | − | 0.834971i | \(-0.685484\pi\) | ||||
−0.550294 | + | 0.834971i | \(0.685484\pi\) | |||||||
\(458\) | 16.1803 | 0.756058 | ||||||||
\(459\) | −7.47214 | −0.348769 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.18034 | 0.427571 | 0.213786 | − | 0.976881i | \(-0.431421\pi\) | ||||
0.213786 | + | 0.976881i | \(0.431421\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.29180 | −0.431826 | −0.215913 | − | 0.976413i | \(-0.569273\pi\) | ||||
−0.215913 | + | 0.976413i | \(0.569273\pi\) | |||||||
\(464\) | 17.5623 | 0.815310 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.2361 | −0.474177 | ||||||||
\(467\) | −4.96556 | −0.229779 | −0.114889 | − | 0.993378i | \(-0.536651\pi\) | ||||
−0.114889 | + | 0.993378i | \(0.536651\pi\) | |||||||
\(468\) | 1.14590 | 0.0529692 | ||||||||
\(469\) | 26.1246 | 1.20632 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.7984 | 0.820106 | ||||||||
\(472\) | −9.27051 | −0.426710 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −12.2361 | −0.562021 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 13.8541 | 0.635002 | ||||||||
\(477\) | −0.472136 | −0.0216176 | ||||||||
\(478\) | −33.4164 | −1.52843 | ||||||||
\(479\) | −7.36068 | −0.336318 | −0.168159 | − | 0.985760i | \(-0.553782\pi\) | ||||
−0.168159 | + | 0.985760i | \(0.553782\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.4164 | 0.748524 | ||||||||
\(482\) | 12.7082 | 0.578843 | ||||||||
\(483\) | −22.8541 | −1.03990 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.61803 | −0.0733955 | ||||||||
\(487\) | −1.27051 | −0.0575723 | −0.0287861 | − | 0.999586i | \(-0.509164\pi\) | ||||
−0.0287861 | + | 0.999586i | \(0.509164\pi\) | |||||||
\(488\) | 12.8885 | 0.583437 | ||||||||
\(489\) | 17.0902 | 0.772844 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.8541 | 0.625227 | 0.312613 | − | 0.949880i | \(-0.398796\pi\) | ||||
0.312613 | + | 0.949880i | \(0.398796\pi\) | |||||||
\(492\) | 0.145898 | 0.00657759 | ||||||||
\(493\) | 27.0344 | 1.21757 | ||||||||
\(494\) | −8.29180 | −0.373066 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 42.9787 | 1.92980 | ||||||||
\(497\) | −4.41641 | −0.198103 | ||||||||
\(498\) | 16.7984 | 0.752753 | ||||||||
\(499\) | 11.8328 | 0.529710 | 0.264855 | − | 0.964288i | \(-0.414676\pi\) | ||||
0.264855 | + | 0.964288i | \(0.414676\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.9443 | 0.935721 | ||||||||
\(502\) | 33.2705 | 1.48494 | ||||||||
\(503\) | 3.43769 | 0.153279 | 0.0766396 | − | 0.997059i | \(-0.475581\pi\) | ||||
0.0766396 | + | 0.997059i | \(0.475581\pi\) | |||||||
\(504\) | −6.70820 | −0.298807 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.56231 | −0.424677 | ||||||||
\(508\) | −4.09017 | −0.181472 | ||||||||
\(509\) | −14.7984 | −0.655926 | −0.327963 | − | 0.944691i | \(-0.606362\pi\) | ||||
−0.327963 | + | 0.944691i | \(0.606362\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.5623 | −0.909623 | ||||||||
\(512\) | 5.29180 | 0.233867 | ||||||||
\(513\) | 2.76393 | 0.122031 | ||||||||
\(514\) | −16.2361 | −0.716142 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.09017 | −0.0479921 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 42.9787 | 1.88838 | ||||||||
\(519\) | 5.47214 | 0.240200 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −43.2492 | −1.89478 | −0.947391 | − | 0.320077i | \(-0.896291\pi\) | ||||
−0.947391 | + | 0.320077i | \(0.896291\pi\) | |||||||
\(522\) | 5.85410 | 0.256227 | ||||||||
\(523\) | −38.7984 | −1.69653 | −0.848267 | − | 0.529568i | \(-0.822354\pi\) | ||||
−0.848267 | + | 0.529568i | \(0.822354\pi\) | |||||||
\(524\) | −4.52786 | −0.197801 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.0000 | −0.784837 | ||||||||
\(527\) | 66.1591 | 2.88193 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.0344 | 1.52324 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.14590 | −0.179917 | ||||||||
\(532\) | −5.12461 | −0.222180 | ||||||||
\(533\) | 0.437694 | 0.0189586 | ||||||||
\(534\) | −4.14590 | −0.179411 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −19.4721 | −0.841068 | ||||||||
\(537\) | −20.1246 | −0.868441 | ||||||||
\(538\) | 0.854102 | 0.0368230 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.8328 | 1.06765 | 0.533823 | − | 0.845596i | \(-0.320755\pi\) | ||||
0.533823 | + | 0.845596i | \(0.320755\pi\) | |||||||
\(542\) | −36.0344 | −1.54781 | ||||||||
\(543\) | −12.7984 | −0.549231 | ||||||||
\(544\) | −25.2705 | −1.08346 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 9.00000 | 0.385164 | ||||||||
\(547\) | −21.2918 | −0.910371 | −0.455186 | − | 0.890397i | \(-0.650427\pi\) | ||||
−0.455186 | + | 0.890397i | \(0.650427\pi\) | |||||||
\(548\) | 7.90983 | 0.337891 | ||||||||
\(549\) | 5.76393 | 0.245999 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.0000 | −0.426014 | ||||||||
\(552\) | 17.0344 | 0.725034 | ||||||||
\(553\) | −22.6869 | −0.964746 | ||||||||
\(554\) | 38.7984 | 1.64838 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.61803 | −0.153439 | ||||||||
\(557\) | 30.5410 | 1.29406 | 0.647032 | − | 0.762463i | \(-0.276010\pi\) | ||||
0.647032 | + | 0.762463i | \(0.276010\pi\) | |||||||
\(558\) | 14.3262 | 0.606478 | ||||||||
\(559\) | −3.27051 | −0.138328 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.38197 | −0.227025 | ||||||||
\(563\) | 17.8328 | 0.751564 | 0.375782 | − | 0.926708i | \(-0.377374\pi\) | ||||
0.375782 | + | 0.926708i | \(0.377374\pi\) | |||||||
\(564\) | 5.79837 | 0.244156 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 43.8328 | 1.84243 | ||||||||
\(567\) | −3.00000 | −0.125988 | ||||||||
\(568\) | 3.29180 | 0.138121 | ||||||||
\(569\) | −15.5279 | −0.650962 | −0.325481 | − | 0.945549i | \(-0.605526\pi\) | ||||
−0.325481 | + | 0.945549i | \(0.605526\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.5836 | −0.568456 | −0.284228 | − | 0.958757i | \(-0.591737\pi\) | ||||
−0.284228 | + | 0.958757i | \(0.591737\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.7426 | 0.657658 | ||||||||
\(574\) | 1.14590 | 0.0478289 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.23607 | 0.176503 | ||||||||
\(577\) | −20.2148 | −0.841552 | −0.420776 | − | 0.907164i | \(-0.638242\pi\) | ||||
−0.420776 | + | 0.907164i | \(0.638242\pi\) | |||||||
\(578\) | −62.8328 | −2.61350 | ||||||||
\(579\) | −18.4721 | −0.767676 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.1459 | 1.29215 | ||||||||
\(582\) | 16.8541 | 0.698625 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 15.3262 | 0.634204 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −31.4164 | −1.29780 | ||||||||
\(587\) | 34.3050 | 1.41592 | 0.707958 | − | 0.706254i | \(-0.249616\pi\) | ||||
0.707958 | + | 0.706254i | \(0.249616\pi\) | |||||||
\(588\) | 1.23607 | 0.0509746 | ||||||||
\(589\) | −24.4721 | −1.00836 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.70820 | −0.399342 | ||||||||
\(592\) | −42.9787 | −1.76641 | ||||||||
\(593\) | −25.5066 | −1.04743 | −0.523715 | − | 0.851894i | \(-0.675454\pi\) | ||||
−0.523715 | + | 0.851894i | \(0.675454\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.0000 | −0.409616 | ||||||||
\(597\) | −8.29180 | −0.339361 | ||||||||
\(598\) | −22.8541 | −0.934574 | ||||||||
\(599\) | 34.4721 | 1.40849 | 0.704247 | − | 0.709955i | \(-0.251285\pi\) | ||||
0.704247 | + | 0.709955i | \(0.251285\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.3820 | 1.19852 | 0.599258 | − | 0.800556i | \(-0.295462\pi\) | ||||
0.599258 | + | 0.800556i | \(0.295462\pi\) | |||||||
\(602\) | −8.56231 | −0.348974 | ||||||||
\(603\) | −8.70820 | −0.354625 | ||||||||
\(604\) | 5.67376 | 0.230862 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.76393 | −0.0716548 | ||||||||
\(607\) | −28.8541 | −1.17115 | −0.585576 | − | 0.810618i | \(-0.699132\pi\) | ||||
−0.585576 | + | 0.810618i | \(0.699132\pi\) | |||||||
\(608\) | 9.34752 | 0.379092 | ||||||||
\(609\) | 10.8541 | 0.439830 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.3951 | 0.703731 | ||||||||
\(612\) | −4.61803 | −0.186673 | ||||||||
\(613\) | −24.9787 | −1.00888 | −0.504440 | − | 0.863447i | \(-0.668301\pi\) | ||||
−0.504440 | + | 0.863447i | \(0.668301\pi\) | |||||||
\(614\) | 25.7082 | 1.03750 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.05573 | 0.364570 | 0.182285 | − | 0.983246i | \(-0.441651\pi\) | ||||
0.182285 | + | 0.983246i | \(0.441651\pi\) | |||||||
\(618\) | −24.5623 | −0.988041 | ||||||||
\(619\) | 2.63932 | 0.106083 | 0.0530416 | − | 0.998592i | \(-0.483108\pi\) | ||||
0.0530416 | + | 0.998592i | \(0.483108\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.61803 | 0.305701 | ||||||||
\(622\) | 29.9787 | 1.20204 | ||||||||
\(623\) | −7.68692 | −0.307970 | ||||||||
\(624\) | −9.00000 | −0.360288 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −49.6869 | −1.98589 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.0000 | 0.438948 | ||||||||
\(629\) | −66.1591 | −2.63793 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −49.1803 | −1.95784 | −0.978919 | − | 0.204248i | \(-0.934525\pi\) | ||||
−0.978919 | + | 0.204248i | \(0.934525\pi\) | |||||||
\(632\) | 16.9098 | 0.672637 | ||||||||
\(633\) | −13.1803 | −0.523871 | ||||||||
\(634\) | −14.8541 | −0.589932 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.291796 | −0.0115705 | ||||||||
\(637\) | 3.70820 | 0.146924 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.47214 | 0.0582368 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.1591 | 1.54669 | 0.773345 | − | 0.633986i | \(-0.218582\pi\) | ||||
0.773345 | + | 0.633986i | \(0.218582\pi\) | |||||||
\(642\) | 26.5623 | 1.04833 | ||||||||
\(643\) | 20.3820 | 0.803786 | 0.401893 | − | 0.915687i | \(-0.368352\pi\) | ||||
0.401893 | + | 0.915687i | \(0.368352\pi\) | |||||||
\(644\) | −14.1246 | −0.556588 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 33.4164 | 1.31475 | ||||||||
\(647\) | 13.2016 | 0.519009 | 0.259505 | − | 0.965742i | \(-0.416441\pi\) | ||||
0.259505 | + | 0.965742i | \(0.416441\pi\) | |||||||
\(648\) | 2.23607 | 0.0878410 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26.5623 | 1.04106 | ||||||||
\(652\) | 10.5623 | 0.413652 | ||||||||
\(653\) | −4.94427 | −0.193484 | −0.0967422 | − | 0.995309i | \(-0.530842\pi\) | ||||
−0.0967422 | + | 0.995309i | \(0.530842\pi\) | |||||||
\(654\) | 24.2705 | 0.949052 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.14590 | −0.0447398 | ||||||||
\(657\) | 6.85410 | 0.267404 | ||||||||
\(658\) | 45.5410 | 1.77537 | ||||||||
\(659\) | 44.0689 | 1.71668 | 0.858340 | − | 0.513081i | \(-0.171496\pi\) | ||||
0.858340 | + | 0.513081i | \(0.171496\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.00000 | −0.116686 | −0.0583432 | − | 0.998297i | \(-0.518582\pi\) | ||||
−0.0583432 | + | 0.998297i | \(0.518582\pi\) | |||||||
\(662\) | 26.5623 | 1.03237 | ||||||||
\(663\) | −13.8541 | −0.538049 | ||||||||
\(664\) | −23.2148 | −0.900908 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.3262 | −0.555130 | ||||||||
\(667\) | −27.5623 | −1.06722 | ||||||||
\(668\) | 12.9443 | 0.500829 | ||||||||
\(669\) | −12.7082 | −0.491328 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −10.1459 | −0.391387 | ||||||||
\(673\) | 22.5066 | 0.867565 | 0.433782 | − | 0.901018i | \(-0.357179\pi\) | ||||
0.433782 | + | 0.901018i | \(0.357179\pi\) | |||||||
\(674\) | −38.3607 | −1.47760 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.90983 | −0.227301 | ||||||||
\(677\) | 7.52786 | 0.289319 | 0.144660 | − | 0.989481i | \(-0.453791\pi\) | ||||
0.144660 | + | 0.989481i | \(0.453791\pi\) | |||||||
\(678\) | −13.7082 | −0.526460 | ||||||||
\(679\) | 31.2492 | 1.19924 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.5623 | 0.558029 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.7082 | −0.486266 | −0.243133 | − | 0.969993i | \(-0.578175\pi\) | ||||
−0.243133 | + | 0.969993i | \(0.578175\pi\) | |||||||
\(684\) | 1.70820 | 0.0653148 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24.2705 | −0.926652 | ||||||||
\(687\) | −10.0000 | −0.381524 | ||||||||
\(688\) | 8.56231 | 0.326435 | ||||||||
\(689\) | −0.875388 | −0.0333496 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.7082 | −0.939944 | −0.469972 | − | 0.882681i | \(-0.655736\pi\) | ||||
−0.469972 | + | 0.882681i | \(0.655736\pi\) | |||||||
\(692\) | 3.38197 | 0.128563 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.9443 | −0.757074 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.09017 | −0.306657 | ||||||||
\(697\) | −1.76393 | −0.0668137 | ||||||||
\(698\) | 46.8328 | 1.77265 | ||||||||
\(699\) | 6.32624 | 0.239280 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.2361 | −0.537689 | −0.268844 | − | 0.963184i | \(-0.586642\pi\) | ||||
−0.268844 | + | 0.963184i | \(0.586642\pi\) | |||||||
\(702\) | −3.00000 | −0.113228 | ||||||||
\(703\) | 24.4721 | 0.922984 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.3820 | 0.541272 | ||||||||
\(707\) | −3.27051 | −0.123000 | ||||||||
\(708\) | −2.56231 | −0.0962974 | ||||||||
\(709\) | −9.47214 | −0.355734 | −0.177867 | − | 0.984055i | \(-0.556920\pi\) | ||||
−0.177867 | + | 0.984055i | \(0.556920\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.56231 | 0.283609 | ||||||||
\(712\) | 5.72949 | 0.214722 | ||||||||
\(713\) | −67.4508 | −2.52605 | ||||||||
\(714\) | −36.2705 | −1.35739 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.4377 | −0.464818 | ||||||||
\(717\) | 20.6525 | 0.771281 | ||||||||
\(718\) | 29.4721 | 1.09989 | ||||||||
\(719\) | −26.0557 | −0.971715 | −0.485857 | − | 0.874038i | \(-0.661493\pi\) | ||||
−0.485857 | + | 0.874038i | \(0.661493\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −45.5410 | −1.69604 | ||||||||
\(722\) | 18.3820 | 0.684106 | ||||||||
\(723\) | −7.85410 | −0.292097 | ||||||||
\(724\) | −7.90983 | −0.293967 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.236068 | 0.00875528 | 0.00437764 | − | 0.999990i | \(-0.498607\pi\) | ||||
0.00437764 | + | 0.999990i | \(0.498607\pi\) | |||||||
\(728\) | −12.4377 | −0.460972 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.1803 | 0.487492 | ||||||||
\(732\) | 3.56231 | 0.131667 | ||||||||
\(733\) | −6.43769 | −0.237782 | −0.118891 | − | 0.992907i | \(-0.537934\pi\) | ||||
−0.118891 | + | 0.992907i | \(0.537934\pi\) | |||||||
\(734\) | 30.4721 | 1.12475 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 25.7639 | 0.949671 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.381966 | −0.0140604 | ||||||||
\(739\) | −44.2705 | −1.62852 | −0.814259 | − | 0.580502i | \(-0.802856\pi\) | ||||
−0.814259 | + | 0.580502i | \(0.802856\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.12461 | 0.188257 | ||||||||
\(742\) | −2.29180 | −0.0841345 | ||||||||
\(743\) | 37.1803 | 1.36401 | 0.682007 | − | 0.731345i | \(-0.261107\pi\) | ||||
0.682007 | + | 0.731345i | \(0.261107\pi\) | |||||||
\(744\) | −19.7984 | −0.725844 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 28.1803 | 1.03176 | ||||||||
\(747\) | −10.3820 | −0.379856 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 49.2492 | 1.79953 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.4721 | −0.637567 | −0.318784 | − | 0.947828i | \(-0.603274\pi\) | ||||
−0.318784 | + | 0.947828i | \(0.603274\pi\) | |||||||
\(752\) | −45.5410 | −1.66071 | ||||||||
\(753\) | −20.5623 | −0.749332 | ||||||||
\(754\) | 10.8541 | 0.395283 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.85410 | −0.0674330 | ||||||||
\(757\) | −39.0344 | −1.41873 | −0.709365 | − | 0.704841i | \(-0.751018\pi\) | ||||
−0.709365 | + | 0.704841i | \(0.751018\pi\) | |||||||
\(758\) | 37.5623 | 1.36432 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.111456 | 0.00404028 | 0.00202014 | − | 0.999998i | \(-0.499357\pi\) | ||||
0.00202014 | + | 0.999998i | \(0.499357\pi\) | |||||||
\(762\) | 10.7082 | 0.387917 | ||||||||
\(763\) | 45.0000 | 1.62911 | ||||||||
\(764\) | 9.72949 | 0.352001 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34.8328 | 1.25856 | ||||||||
\(767\) | −7.68692 | −0.277559 | ||||||||
\(768\) | 13.5623 | 0.489388 | ||||||||
\(769\) | 24.1459 | 0.870723 | 0.435362 | − | 0.900256i | \(-0.356620\pi\) | ||||
0.435362 | + | 0.900256i | \(0.356620\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.0344 | 0.361382 | ||||||||
\(772\) | −11.4164 | −0.410886 | ||||||||
\(773\) | −21.6525 | −0.778785 | −0.389393 | − | 0.921072i | \(-0.627315\pi\) | ||||
−0.389393 | + | 0.921072i | \(0.627315\pi\) | |||||||
\(774\) | 2.85410 | 0.102589 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −23.2918 | −0.836127 | ||||||||
\(777\) | −26.5623 | −0.952917 | ||||||||
\(778\) | 29.2705 | 1.04940 | ||||||||
\(779\) | 0.652476 | 0.0233774 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 92.1033 | 3.29361 | ||||||||
\(783\) | −3.61803 | −0.129298 | ||||||||
\(784\) | −9.70820 | −0.346722 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 11.8541 | 0.422822 | ||||||||
\(787\) | 25.6180 | 0.913184 | 0.456592 | − | 0.889676i | \(-0.349070\pi\) | ||||
0.456592 | + | 0.889676i | \(0.349070\pi\) | |||||||
\(788\) | −6.00000 | −0.213741 | ||||||||
\(789\) | 11.1246 | 0.396047 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.4164 | −0.903703 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.6869 | 0.379504 | ||||||||
\(794\) | 31.6525 | 1.12330 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.12461 | −0.181637 | ||||||||
\(797\) | −41.3951 | −1.46629 | −0.733145 | − | 0.680072i | \(-0.761948\pi\) | ||||
−0.733145 | + | 0.680072i | \(0.761948\pi\) | |||||||
\(798\) | 13.4164 | 0.474936 | ||||||||
\(799\) | −70.1033 | −2.48008 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.56231 | 0.0905346 | ||||||||
\(802\) | −1.32624 | −0.0468311 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −5.38197 | −0.189807 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26.5623 | 0.935617 | ||||||||
\(807\) | −0.527864 | −0.0185817 | ||||||||
\(808\) | 2.43769 | 0.0857578 | ||||||||
\(809\) | −2.23607 | −0.0786160 | −0.0393080 | − | 0.999227i | \(-0.512515\pi\) | ||||
−0.0393080 | + | 0.999227i | \(0.512515\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.7082 | 0.692049 | 0.346024 | − | 0.938226i | \(-0.387531\pi\) | ||||
0.346024 | + | 0.938226i | \(0.387531\pi\) | |||||||
\(812\) | 6.70820 | 0.235412 | ||||||||
\(813\) | 22.2705 | 0.781061 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 36.2705 | 1.26972 | ||||||||
\(817\) | −4.87539 | −0.170568 | ||||||||
\(818\) | −16.3820 | −0.572782 | ||||||||
\(819\) | −5.56231 | −0.194363 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −56.3951 | −1.96820 | −0.984102 | − | 0.177606i | \(-0.943165\pi\) | ||||
−0.984102 | + | 0.177606i | \(0.943165\pi\) | |||||||
\(822\) | −20.7082 | −0.722282 | ||||||||
\(823\) | 3.47214 | 0.121031 | 0.0605155 | − | 0.998167i | \(-0.480726\pi\) | ||||
0.0605155 | + | 0.998167i | \(0.480726\pi\) | |||||||
\(824\) | 33.9443 | 1.18250 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −20.1246 | −0.700225 | ||||||||
\(827\) | −46.8673 | −1.62973 | −0.814867 | − | 0.579648i | \(-0.803190\pi\) | ||||
−0.814867 | + | 0.579648i | \(0.803190\pi\) | |||||||
\(828\) | 4.70820 | 0.163621 | ||||||||
\(829\) | −25.3262 | −0.879617 | −0.439808 | − | 0.898092i | \(-0.644954\pi\) | ||||
−0.439808 | + | 0.898092i | \(0.644954\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.9787 | −0.831812 | ||||||||
\(832\) | 7.85410 | 0.272292 | ||||||||
\(833\) | −14.9443 | −0.517788 | ||||||||
\(834\) | 9.47214 | 0.327993 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.85410 | −0.306043 | ||||||||
\(838\) | −30.6525 | −1.05887 | ||||||||
\(839\) | 24.7984 | 0.856135 | 0.428067 | − | 0.903747i | \(-0.359195\pi\) | ||||
0.428067 | + | 0.903747i | \(0.359195\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9098 | −0.548615 | ||||||||
\(842\) | 11.7639 | 0.405412 | ||||||||
\(843\) | 3.32624 | 0.114562 | ||||||||
\(844\) | −8.14590 | −0.280393 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −15.1803 | −0.521911 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.29180 | 0.0787006 | ||||||||
\(849\) | −27.0902 | −0.929732 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 67.4508 | 2.31219 | ||||||||
\(852\) | 0.909830 | 0.0311703 | ||||||||
\(853\) | 53.6869 | 1.83821 | 0.919103 | − | 0.394018i | \(-0.128915\pi\) | ||||
0.919103 | + | 0.394018i | \(0.128915\pi\) | |||||||
\(854\) | 27.9787 | 0.957412 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −36.7082 | −1.25466 | ||||||||
\(857\) | 10.0902 | 0.344674 | 0.172337 | − | 0.985038i | \(-0.444868\pi\) | ||||
0.172337 | + | 0.985038i | \(0.444868\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.56231 | −0.0874247 | −0.0437124 | − | 0.999044i | \(-0.513919\pi\) | ||||
−0.0437124 | + | 0.999044i | \(0.513919\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.708204 | −0.0241355 | ||||||||
\(862\) | 26.1246 | 0.889808 | ||||||||
\(863\) | −34.6180 | −1.17841 | −0.589206 | − | 0.807983i | \(-0.700559\pi\) | ||||
−0.589206 | + | 0.807983i | \(0.700559\pi\) | |||||||
\(864\) | 3.38197 | 0.115057 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 43.9787 | 1.49446 | ||||||||
\(867\) | 38.8328 | 1.31883 | ||||||||
\(868\) | 16.4164 | 0.557209 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.1459 | −0.547083 | ||||||||
\(872\) | −33.5410 | −1.13584 | ||||||||
\(873\) | −10.4164 | −0.352542 | ||||||||
\(874\) | −34.0689 | −1.15240 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.23607 | 0.143123 | ||||||||
\(877\) | −29.5836 | −0.998967 | −0.499483 | − | 0.866323i | \(-0.666477\pi\) | ||||
−0.499483 | + | 0.866323i | \(0.666477\pi\) | |||||||
\(878\) | 12.0344 | 0.406143 | ||||||||
\(879\) | 19.4164 | 0.654899 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.1803 | −1.15156 | −0.575782 | − | 0.817603i | \(-0.695302\pi\) | ||||
−0.575782 | + | 0.817603i | \(0.695302\pi\) | |||||||
\(882\) | −3.23607 | −0.108964 | ||||||||
\(883\) | 16.6869 | 0.561559 | 0.280780 | − | 0.959772i | \(-0.409407\pi\) | ||||
0.280780 | + | 0.959772i | \(0.409407\pi\) | |||||||
\(884\) | −8.56231 | −0.287982 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 44.5066 | 1.49523 | ||||||||
\(887\) | 18.1803 | 0.610436 | 0.305218 | − | 0.952282i | \(-0.401271\pi\) | ||||
0.305218 | + | 0.952282i | \(0.401271\pi\) | |||||||
\(888\) | 19.7984 | 0.664390 | ||||||||
\(889\) | 19.8541 | 0.665885 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.85410 | −0.262975 | ||||||||
\(893\) | 25.9311 | 0.867752 | ||||||||
\(894\) | 26.1803 | 0.875602 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 40.8541 | 1.36484 | ||||||||
\(897\) | 14.1246 | 0.471607 | ||||||||
\(898\) | −23.4164 | −0.781416 | ||||||||
\(899\) | 32.0344 | 1.06841 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.52786 | 0.117530 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.29180 | 0.176100 | ||||||||
\(904\) | 18.9443 | 0.630077 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −14.8541 | −0.493494 | ||||||||
\(907\) | −53.8328 | −1.78749 | −0.893745 | − | 0.448576i | \(-0.851931\pi\) | ||||
−0.893745 | + | 0.448576i | \(0.851931\pi\) | |||||||
\(908\) | 9.00000 | 0.298675 | ||||||||
\(909\) | 1.09017 | 0.0361587 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.0344 | 1.79024 | 0.895120 | − | 0.445824i | \(-0.147089\pi\) | ||||
0.895120 | + | 0.445824i | \(0.147089\pi\) | |||||||
\(912\) | −13.4164 | −0.444262 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 38.0689 | 1.25921 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.18034 | −0.204204 | ||||||||
\(917\) | 21.9787 | 0.725801 | ||||||||
\(918\) | 12.0902 | 0.399035 | ||||||||
\(919\) | −15.8541 | −0.522979 | −0.261489 | − | 0.965206i | \(-0.584214\pi\) | ||||
−0.261489 | + | 0.965206i | \(0.584214\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.8885 | −0.523545 | ||||||||
\(922\) | −14.8541 | −0.489194 | ||||||||
\(923\) | 2.72949 | 0.0898423 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.0344 | 0.494062 | ||||||||
\(927\) | 15.1803 | 0.498588 | ||||||||
\(928\) | −12.2361 | −0.401669 | ||||||||
\(929\) | −54.4721 | −1.78717 | −0.893586 | − | 0.448891i | \(-0.851819\pi\) | ||||
−0.893586 | + | 0.448891i | \(0.851819\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.52786 | 0.181168 | ||||||||
\(932\) | 3.90983 | 0.128071 | ||||||||
\(933\) | −18.5279 | −0.606575 | ||||||||
\(934\) | 8.03444 | 0.262895 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.14590 | 0.135513 | ||||||||
\(937\) | −36.4164 | −1.18967 | −0.594836 | − | 0.803847i | \(-0.702783\pi\) | ||||
−0.594836 | + | 0.803847i | \(0.702783\pi\) | |||||||
\(938\) | −42.2705 | −1.38018 | ||||||||
\(939\) | 30.7082 | 1.00212 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.00000 | 0.0977972 | 0.0488986 | − | 0.998804i | \(-0.484429\pi\) | ||||
0.0488986 | + | 0.998804i | \(0.484429\pi\) | |||||||
\(942\) | −28.7984 | −0.938302 | ||||||||
\(943\) | 1.79837 | 0.0585631 | ||||||||
\(944\) | 20.1246 | 0.655000 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.4934 | 0.698442 | 0.349221 | − | 0.937040i | \(-0.386446\pi\) | ||||
0.349221 | + | 0.937040i | \(0.386446\pi\) | |||||||
\(948\) | 4.67376 | 0.151797 | ||||||||
\(949\) | 12.7082 | 0.412526 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.18034 | 0.297693 | ||||||||
\(952\) | 50.1246 | 1.62455 | ||||||||
\(953\) | 55.7214 | 1.80499 | 0.902496 | − | 0.430698i | \(-0.141733\pi\) | ||||
0.902496 | + | 0.430698i | \(0.141733\pi\) | |||||||
\(954\) | 0.763932 | 0.0247332 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.7639 | 0.412815 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.9098 | 0.384789 | ||||||||
\(959\) | −38.3951 | −1.23984 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 47.3951 | 1.52887 | ||||||||
\(962\) | −26.5623 | −0.856403 | ||||||||
\(963\) | −16.4164 | −0.529011 | ||||||||
\(964\) | −4.85410 | −0.156340 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 36.9787 | 1.18977 | ||||||||
\(967\) | 5.21478 | 0.167696 | 0.0838480 | − | 0.996479i | \(-0.473279\pi\) | ||||
0.0838480 | + | 0.996479i | \(0.473279\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.6525 | −0.663453 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 59.4853 | 1.90897 | 0.954487 | − | 0.298253i | \(-0.0964038\pi\) | ||||
0.954487 | + | 0.298253i | \(0.0964038\pi\) | |||||||
\(972\) | 0.618034 | 0.0198234 | ||||||||
\(973\) | 17.5623 | 0.563022 | ||||||||
\(974\) | 2.05573 | 0.0658698 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27.9787 | −0.895577 | ||||||||
\(977\) | −36.2705 | −1.16040 | −0.580198 | − | 0.814475i | \(-0.697025\pi\) | ||||
−0.580198 | + | 0.814475i | \(0.697025\pi\) | |||||||
\(978\) | −27.6525 | −0.884229 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.0000 | −0.478913 | ||||||||
\(982\) | −22.4164 | −0.715336 | ||||||||
\(983\) | −0.875388 | −0.0279205 | −0.0139603 | − | 0.999903i | \(-0.504444\pi\) | ||||
−0.0139603 | + | 0.999903i | \(0.504444\pi\) | |||||||
\(984\) | 0.527864 | 0.0168277 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −43.7426 | −1.39305 | ||||||||
\(987\) | −28.1459 | −0.895894 | ||||||||
\(988\) | 3.16718 | 0.100762 | ||||||||
\(989\) | −13.4377 | −0.427294 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.4508 | −1.53909 | −0.769546 | − | 0.638591i | \(-0.779517\pi\) | ||||
−0.769546 | + | 0.638591i | \(0.779517\pi\) | |||||||
\(992\) | −29.9443 | −0.950732 | ||||||||
\(993\) | −16.4164 | −0.520959 | ||||||||
\(994\) | 7.14590 | 0.226654 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.41641 | −0.203312 | ||||||||
\(997\) | −14.7082 | −0.465813 | −0.232907 | − | 0.972499i | \(-0.574824\pi\) | ||||
−0.232907 | + | 0.972499i | \(0.574824\pi\) | |||||||
\(998\) | −19.1459 | −0.606053 | ||||||||
\(999\) | 8.85410 | 0.280131 |
(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 | 9075.2.a.bb.1.1 | 2 | ||
5.4 | even | 2 | 9075.2.a.bu.1.2 | 2 | |||
11.2 | odd | 10 | 825.2.n.a.301.1 | ✓ | 4 | ||
11.6 | odd | 10 | 825.2.n.a.751.1 | yes | 4 | ||
11.10 | odd | 2 | 9075.2.a.bz.1.2 | 2 | |||
55.2 | even | 20 | 825.2.bx.a.499.2 | 8 | |||
55.13 | even | 20 | 825.2.bx.a.499.1 | 8 | |||
55.17 | even | 20 | 825.2.bx.a.124.1 | 8 | |||
55.24 | odd | 10 | 825.2.n.e.301.1 | yes | 4 | ||
55.28 | even | 20 | 825.2.bx.a.124.2 | 8 | |||
55.39 | odd | 10 | 825.2.n.e.751.1 | yes | 4 | ||
55.54 | odd | 2 | 9075.2.a.y.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.n.a.301.1 | ✓ | 4 | 11.2 | odd | 10 | ||
825.2.n.a.751.1 | yes | 4 | 11.6 | odd | 10 | ||
825.2.n.e.301.1 | yes | 4 | 55.24 | odd | 10 | ||
825.2.n.e.751.1 | yes | 4 | 55.39 | odd | 10 | ||
825.2.bx.a.124.1 | 8 | 55.17 | even | 20 | |||
825.2.bx.a.124.2 | 8 | 55.28 | even | 20 | |||
825.2.bx.a.499.1 | 8 | 55.13 | even | 20 | |||
825.2.bx.a.499.2 | 8 | 55.2 | even | 20 | |||
9075.2.a.y.1.1 | 2 | 55.54 | odd | 2 | |||
9075.2.a.bb.1.1 | 2 | 1.1 | even | 1 | trivial | ||
9075.2.a.bu.1.2 | 2 | 5.4 | even | 2 | |||
9075.2.a.bz.1.2 | 2 | 11.10 | odd | 2 |