Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7616,2,Mod(1,7616)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7616, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7616.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7616 = 2^{6} \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7616.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: | \(60.8140661794\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.4022000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 7x^{4} + 10x^{3} + 14x^{2} - 8x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 3808) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.775247\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7616.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.53790 | 1.46526 | 0.732628 | − | 0.680630i | \(-0.238294\pi\) | ||||
0.732628 | + | 0.680630i | \(0.238294\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.138905 | 0.0621201 | 0.0310600 | − | 0.999518i | \(-0.490112\pi\) | ||||
0.0310600 | + | 0.999518i | \(0.490112\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.44092 | 1.14697 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.938171 | −0.282869 | −0.141435 | − | 0.989948i | \(-0.545171\pi\) | ||||
−0.141435 | + | 0.989948i | \(0.545171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.02933 | 0.840184 | 0.420092 | − | 0.907482i | \(-0.361998\pi\) | ||||
0.420092 | + | 0.907482i | \(0.361998\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.352526 | 0.0910218 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.38098 | −0.546234 | −0.273117 | − | 0.961981i | \(-0.588055\pi\) | ||||
−0.273117 | + | 0.961981i | \(0.588055\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.53790 | 0.553814 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.51799 | 1.15058 | 0.575290 | − | 0.817949i | \(-0.304889\pi\) | ||||
0.575290 | + | 0.817949i | \(0.304889\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.98071 | −0.996141 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.11900 | 0.215352 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.99682 | 0.927887 | 0.463943 | − | 0.885865i | \(-0.346434\pi\) | ||||
0.463943 | + | 0.885865i | \(0.346434\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.85122 | 1.76933 | 0.884666 | − | 0.466225i | \(-0.154386\pi\) | ||||
0.884666 | + | 0.466225i | \(0.154386\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.38098 | −0.414475 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.138905 | 0.0234792 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.85312 | 1.12665 | 0.563323 | − | 0.826237i | \(-0.309523\pi\) | ||||
0.563323 | + | 0.826237i | \(0.309523\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.68812 | 1.23108 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.61308 | −0.720442 | −0.360221 | − | 0.932867i | \(-0.617299\pi\) | ||||
−0.360221 | + | 0.932867i | \(0.617299\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.86156 | 0.283886 | 0.141943 | − | 0.989875i | \(-0.454665\pi\) | ||||
0.141943 | + | 0.989875i | \(0.454665\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.477960 | 0.0712500 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.273295 | −0.0398641 | −0.0199321 | − | 0.999801i | \(-0.506345\pi\) | ||||
−0.0199321 | + | 0.999801i | \(0.506345\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.53790 | 0.355377 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.18574 | −0.849676 | −0.424838 | − | 0.905269i | \(-0.639669\pi\) | ||||
−0.424838 | + | 0.905269i | \(0.639669\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.130316 | −0.0175719 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.04268 | −0.800373 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.88562 | 0.375676 | 0.187838 | − | 0.982200i | \(-0.439852\pi\) | ||||
0.187838 | + | 0.982200i | \(0.439852\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.38822 | −0.689891 | −0.344946 | − | 0.938623i | \(-0.612103\pi\) | ||||
−0.344946 | + | 0.938623i | \(0.612103\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.44092 | 0.433515 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.420788 | 0.0521923 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.80476 | 0.709164 | 0.354582 | − | 0.935025i | \(-0.384623\pi\) | ||||
0.354582 | + | 0.935025i | \(0.384623\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.0041 | 1.68589 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.1978 | −1.32894 | −0.664468 | − | 0.747317i | \(-0.731342\pi\) | ||||
−0.664468 | + | 0.747317i | \(0.731342\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.3579 | 1.21230 | 0.606150 | − | 0.795350i | \(-0.292713\pi\) | ||||
0.606150 | + | 0.795350i | \(0.292713\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.6405 | −1.45960 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.938171 | −0.106914 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.96214 | −0.670793 | −0.335397 | − | 0.942077i | \(-0.608870\pi\) | ||||
−0.335397 | + | 0.942077i | \(0.608870\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.48284 | −0.831427 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.92830 | −0.980008 | −0.490004 | − | 0.871720i | \(-0.663005\pi\) | ||||
−0.490004 | + | 0.871720i | \(0.663005\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.138905 | 0.0150663 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.6814 | 1.35959 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.88635 | 0.305952 | 0.152976 | − | 0.988230i | \(-0.451114\pi\) | ||||
0.152976 | + | 0.988230i | \(0.451114\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.02933 | 0.317560 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 25.0014 | 2.59252 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.330729 | −0.0339321 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.9327 | 1.21158 | 0.605791 | − | 0.795624i | \(-0.292857\pi\) | ||||
0.605791 | + | 0.795624i | \(0.292857\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.22817 | −0.324443 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.53513 | 0.252255 | 0.126128 | − | 0.992014i | \(-0.459745\pi\) | ||||
0.126128 | + | 0.992014i | \(0.459745\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.82731 | −0.180050 | −0.0900251 | − | 0.995939i | \(-0.528695\pi\) | ||||
−0.0900251 | + | 0.995939i | \(0.528695\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.352526 | 0.0344030 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.80598 | 0.947980 | 0.473990 | − | 0.880530i | \(-0.342813\pi\) | ||||
0.473990 | + | 0.880530i | \(0.342813\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.2351 | 0.980342 | 0.490171 | − | 0.871626i | \(-0.336934\pi\) | ||||
0.490171 | + | 0.871626i | \(0.336934\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.3925 | 1.65082 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.1561 | 1.42576 | 0.712881 | − | 0.701285i | \(-0.247390\pi\) | ||||
0.712881 | + | 0.701285i | \(0.247390\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.766475 | 0.0714742 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.4237 | 0.963668 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.00000 | 0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.1198 | −0.919985 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.7075 | −1.05563 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.38637 | −0.124000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.4576 | 1.37164 | 0.685819 | − | 0.727772i | \(-0.259444\pi\) | ||||
0.685819 | + | 0.727772i | \(0.259444\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.72445 | 0.415965 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.6280 | 1.19068 | 0.595342 | − | 0.803473i | \(-0.297017\pi\) | ||||
0.595342 | + | 0.803473i | \(0.297017\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.38098 | −0.206457 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.155435 | 0.0133777 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.07795 | −0.348403 | −0.174201 | − | 0.984710i | \(-0.555734\pi\) | ||||
−0.174201 | + | 0.984710i | \(0.555734\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.0637 | −1.02323 | −0.511613 | − | 0.859216i | \(-0.670952\pi\) | ||||
−0.511613 | + | 0.859216i | \(0.670952\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.693594 | −0.0584111 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.84203 | −0.237662 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.694082 | 0.0576404 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.53790 | 0.209322 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.3610 | −1.09458 | −0.547288 | − | 0.836944i | \(-0.684340\pi\) | ||||
−0.547288 | + | 0.836944i | \(0.684340\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.65958 | 0.297813 | 0.148906 | − | 0.988851i | \(-0.452425\pi\) | ||||
0.148906 | + | 0.988851i | \(0.452425\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.44092 | 0.278182 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.36838 | 0.109911 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.47275 | −0.756007 | −0.378004 | − | 0.925804i | \(-0.623389\pi\) | ||||
−0.378004 | + | 0.925804i | \(0.623389\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.6988 | −1.24499 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.51799 | 0.434879 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.34703 | −0.262159 | −0.131080 | − | 0.991372i | \(-0.541844\pi\) | ||||
−0.131080 | + | 0.991372i | \(0.541844\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.330729 | −0.0257472 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.8902 | 0.997470 | 0.498735 | − | 0.866754i | \(-0.333798\pi\) | ||||
0.498735 | + | 0.866754i | \(0.333798\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.82318 | −0.294091 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.19275 | −0.626516 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.8208 | 0.898716 | 0.449358 | − | 0.893352i | \(-0.351653\pi\) | ||||
0.449358 | + | 0.893352i | \(0.351653\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.98071 | −0.376506 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.32340 | 0.550460 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.9257 | −1.63880 | −0.819401 | − | 0.573221i | \(-0.805694\pi\) | ||||
−0.819401 | + | 0.573221i | \(0.805694\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.65319 | 0.717516 | 0.358758 | − | 0.933431i | \(-0.383200\pi\) | ||||
0.358758 | + | 0.933431i | \(0.383200\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.6747 | −1.01087 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.951930 | 0.0699873 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.938171 | −0.0686058 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.11900 | 0.0813953 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.1319 | 1.89084 | 0.945419 | − | 0.325857i | \(-0.105653\pi\) | ||||
0.945419 | + | 0.325857i | \(0.105653\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.23660 | 0.520902 | 0.260451 | − | 0.965487i | \(-0.416129\pi\) | ||||
0.260451 | + | 0.965487i | \(0.416129\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.06792 | 0.0764750 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.65989 | 0.332003 | 0.166002 | − | 0.986125i | \(-0.446914\pi\) | ||||
0.166002 | + | 0.986125i | \(0.446914\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.39673 | 0.240788 | 0.120394 | − | 0.992726i | \(-0.461584\pi\) | ||||
0.120394 | + | 0.992726i | \(0.461584\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.7319 | 1.03911 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.99682 | 0.350708 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.640778 | −0.0447539 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.9870 | 1.31968 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.23377 | 0.154513 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.15000 | 0.148012 | 0.0740060 | − | 0.997258i | \(-0.476422\pi\) | ||||
0.0740060 | + | 0.997258i | \(0.476422\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −28.4189 | −1.94723 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.258580 | 0.0176350 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.85122 | 0.668745 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 26.2873 | 1.77633 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.02933 | 0.203775 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.1006 | 1.21211 | 0.606053 | − | 0.795424i | \(-0.292752\pi\) | ||||
0.606053 | + | 0.795424i | \(0.292752\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −17.1382 | −1.14255 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.5802 | −1.03410 | −0.517049 | − | 0.855956i | \(-0.672969\pi\) | ||||
−0.517049 | + | 0.855956i | \(0.672969\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.0701 | −1.45844 | −0.729218 | − | 0.684282i | \(-0.760116\pi\) | ||||
−0.729218 | + | 0.684282i | \(0.760116\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.38098 | −0.156657 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.15371 | −0.206607 | −0.103303 | − | 0.994650i | \(-0.532941\pi\) | ||||
−0.103303 | + | 0.994650i | \(0.532941\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.0379619 | −0.00247636 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.1313 | −0.982883 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.33493 | 0.0863492 | 0.0431746 | − | 0.999068i | \(-0.486253\pi\) | ||||
0.0431746 | + | 0.999068i | \(0.486253\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.7400 | 0.949487 | 0.474743 | − | 0.880124i | \(-0.342541\pi\) | ||||
0.474743 | + | 0.880124i | \(0.342541\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.3477 | −1.43360 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.138905 | 0.00887430 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.21277 | −0.458937 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −22.6591 | −1.43596 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.0232 | −1.57945 | −0.789725 | − | 0.613462i | \(-0.789777\pi\) | ||||
−0.789725 | + | 0.613462i | \(0.789777\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.17682 | −0.325464 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.352526 | 0.0220760 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.9222 | 1.24271 | 0.621356 | − | 0.783528i | \(-0.286582\pi\) | ||||
0.621356 | + | 0.783528i | \(0.286582\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.85312 | 0.425832 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.1937 | 1.06426 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.2979 | 1.37495 | 0.687473 | − | 0.726210i | \(-0.258720\pi\) | ||||
0.687473 | + | 0.726210i | \(0.258720\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.859228 | −0.0527820 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.32525 | 0.448298 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.9673 | 0.668686 | 0.334343 | − | 0.942451i | \(-0.391486\pi\) | ||||
0.334343 | + | 0.942451i | \(0.391486\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.55873 | −0.459160 | −0.229580 | − | 0.973290i | \(-0.573735\pi\) | ||||
−0.229580 | + | 0.973290i | \(0.573735\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.68812 | 0.465306 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.67275 | 0.281778 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.7682 | −1.54826 | −0.774130 | − | 0.633027i | \(-0.781812\pi\) | ||||
−0.774130 | + | 0.633027i | \(0.781812\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 33.8972 | 2.02937 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.20981 | −0.191481 | −0.0957405 | − | 0.995406i | \(-0.530522\pi\) | ||||
−0.0957405 | + | 0.995406i | \(0.530522\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.57421 | 0.331353 | 0.165676 | − | 0.986180i | \(-0.447019\pi\) | ||||
0.165676 | + | 0.986180i | \(0.447019\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.839357 | −0.0497192 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.61308 | −0.272301 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 30.2839 | 1.77528 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.0232 | −1.34503 | −0.672514 | − | 0.740084i | \(-0.734786\pi\) | ||||
−0.672514 | + | 0.740084i | \(0.734786\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.400826 | 0.0233370 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.04981 | −0.0609164 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.7158 | 0.966700 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.86156 | 0.107299 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.43390 | 0.369618 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.748449 | −0.0428561 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.7365 | −0.669839 | −0.334920 | − | 0.942247i | \(-0.608709\pi\) | ||||
−0.334920 | + | 0.942247i | \(0.608709\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.63752 | −0.263819 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.8083 | 0.726293 | 0.363146 | − | 0.931732i | \(-0.381703\pi\) | ||||
0.363146 | + | 0.931732i | \(0.381703\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.3719 | −1.77325 | −0.886624 | − | 0.462492i | \(-0.846955\pi\) | ||||
−0.886624 | + | 0.462492i | \(0.846955\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.477960 | 0.0269300 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.2659 | −1.64374 | −0.821869 | − | 0.569677i | \(-0.807068\pi\) | ||||
−0.821869 | + | 0.569677i | \(0.807068\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.68787 | −0.262471 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.8866 | 1.38903 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.38098 | −0.132481 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.0882 | −0.836942 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.9755 | 1.43645 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.273295 | −0.0150672 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.0653 | 0.608202 | 0.304101 | − | 0.952640i | \(-0.401644\pi\) | ||||
0.304101 | + | 0.952640i | \(0.401644\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 23.5810 | 1.29223 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.806308 | 0.0440533 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.8288 | 1.62488 | 0.812440 | − | 0.583045i | \(-0.198139\pi\) | ||||
0.812440 | + | 0.583045i | \(0.198139\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 38.4645 | 2.08911 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.24213 | −0.500489 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.94523 | 0.104728 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.22486 | −0.387851 | −0.193925 | − | 0.981016i | \(-0.562122\pi\) | ||||
−0.193925 | + | 0.981016i | \(0.562122\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.8155 | −1.00717 | −0.503584 | − | 0.863946i | \(-0.667986\pi\) | ||||
−0.503584 | + | 0.863946i | \(0.667986\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.38982 | 0.180935 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.99112 | −0.212426 | −0.106213 | − | 0.994343i | \(-0.533873\pi\) | ||||
−0.106213 | + | 0.994343i | \(0.533873\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.55543 | −0.0825536 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.53790 | 0.134320 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.36828 | 0.494439 | 0.247219 | − | 0.968960i | \(-0.420483\pi\) | ||||
0.247219 | + | 0.968960i | \(0.420483\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.3309 | −0.701628 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −25.6831 | −1.34801 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.43876 | 0.0753082 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.9267 | 0.831368 | 0.415684 | − | 0.909509i | \(-0.363542\pi\) | ||||
0.415684 | + | 0.909509i | \(0.363542\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.8732 | −0.826327 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.18574 | −0.321148 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.4079 | 0.901347 | 0.450674 | − | 0.892689i | \(-0.351184\pi\) | ||||
0.450674 | + | 0.892689i | \(0.351184\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.51846 | −0.181692 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.1370 | 0.779596 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.9504 | 1.28161 | 0.640807 | − | 0.767702i | \(-0.278600\pi\) | ||||
0.640807 | + | 0.767702i | \(0.278600\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 39.2297 | 2.00980 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.5500 | −1.20335 | −0.601675 | − | 0.798741i | \(-0.705500\pi\) | ||||
−0.601675 | + | 0.798741i | \(0.705500\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.130316 | −0.00664154 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.40548 | 0.325609 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.3562 | −0.879995 | −0.439997 | − | 0.897999i | \(-0.645021\pi\) | ||||
−0.439997 | + | 0.897999i | \(0.645021\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.51799 | 0.279057 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 34.5864 | 1.74465 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.828169 | −0.0416697 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.6590 | 1.38817 | 0.694084 | − | 0.719894i | \(-0.255810\pi\) | ||||
0.694084 | + | 0.719894i | \(0.255810\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.04268 | −0.302512 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.40006 | 0.119853 | 0.0599266 | − | 0.998203i | \(-0.480913\pi\) | ||||
0.0599266 | + | 0.998203i | \(0.480913\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.8426 | 1.48656 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.03940 | −0.0516483 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.42939 | −0.318693 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.2419 | −1.00090 | −0.500450 | − | 0.865765i | \(-0.666832\pi\) | ||||
−0.500450 | + | 0.865765i | \(0.666832\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.3494 | −0.510499 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.88562 | 0.141992 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.24018 | −0.0608782 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −30.6163 | −1.49929 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.9192 | 1.55935 | 0.779677 | − | 0.626181i | \(-0.215383\pi\) | ||||
0.779677 | + | 0.626181i | \(0.215383\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.5192 | −0.951309 | −0.475655 | − | 0.879632i | \(-0.657789\pi\) | ||||
−0.475655 | + | 0.879632i | \(0.657789\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.940384 | −0.0457230 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.98071 | −0.241600 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.38822 | −0.260754 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.21277 | −0.348236 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.7756 | 0.856222 | 0.428111 | − | 0.903726i | \(-0.359179\pi\) | ||||
0.428111 | + | 0.903726i | \(0.359179\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.1099 | −0.774194 | −0.387097 | − | 0.922039i | \(-0.626522\pi\) | ||||
−0.387097 | + | 0.922039i | \(0.626522\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.76151 | 0.0844579 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.1382 | −0.628487 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.6115 | −0.506461 | −0.253230 | − | 0.967406i | \(-0.581493\pi\) | ||||
−0.253230 | + | 0.967406i | \(0.581493\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.44092 | 0.163853 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.75390 | 0.273376 | 0.136688 | − | 0.990614i | \(-0.456354\pi\) | ||||
0.136688 | + | 0.990614i | \(0.456354\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.400927 | 0.0190058 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −33.9089 | −1.60383 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.4469 | −1.15372 | −0.576860 | − | 0.816843i | \(-0.695722\pi\) | ||||
−0.576860 | + | 0.816843i | \(0.695722\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.32786 | 0.203791 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.28764 | 0.436371 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.420788 | 0.0197268 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.71086 | −0.313921 | −0.156960 | − | 0.987605i | \(-0.550170\pi\) | ||||
−0.156960 | + | 0.987605i | \(0.550170\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.11900 | 0.0522305 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.0532 | −1.67917 | −0.839583 | − | 0.543231i | \(-0.817201\pi\) | ||||
−0.839583 | + | 0.543231i | \(0.817201\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.0397 | −1.21017 | −0.605083 | − | 0.796162i | \(-0.706860\pi\) | ||||
−0.605083 | + | 0.796162i | \(0.706860\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.47281 | 0.161048 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.7790 | −0.683889 | −0.341945 | − | 0.939720i | \(-0.611086\pi\) | ||||
−0.341945 | + | 0.939720i | \(0.611086\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.80476 | 0.268039 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.0408 | −1.10774 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.74646 | −0.0803025 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.8590 | 0.544126 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.2846 | −0.974555 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.0317 | −0.458360 | −0.229180 | − | 0.973384i | \(-0.573604\pi\) | ||||
−0.229180 | + | 0.973384i | \(0.573604\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.7603 | 0.946589 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.0041 | 0.637208 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.65751 | 0.0752636 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.9436 | 0.949047 | 0.474524 | − | 0.880243i | \(-0.342620\pi\) | ||||
0.474524 | + | 0.880243i | \(0.342620\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.49440 | −0.384130 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.90982 | −0.402095 | −0.201047 | − | 0.979582i | \(-0.564435\pi\) | ||||
−0.201047 | + | 0.979582i | \(0.564435\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.99682 | 0.225046 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.448408 | −0.0201544 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.1978 | −0.502290 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.3335 | 1.13408 | 0.567041 | − | 0.823690i | \(-0.308088\pi\) | ||||
0.567041 | + | 0.823690i | \(0.308088\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 32.7139 | 1.46155 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.23099 | 0.277826 | 0.138913 | − | 0.990305i | \(-0.455639\pi\) | ||||
0.138913 | + | 0.990305i | \(0.455639\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.352142 | 0.0156701 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.70283 | −0.430918 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.7013 | 0.695949 | 0.347974 | − | 0.937504i | \(-0.386870\pi\) | ||||
0.347974 | + | 0.937504i | \(0.386870\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.3579 | 0.458207 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.66432 | −0.117633 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.253822 | −0.0111847 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.256397 | 0.0112763 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.9999 | 1.31685 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.95507 | −0.304707 | −0.152354 | − | 0.988326i | \(-0.548685\pi\) | ||||
−0.152354 | + | 0.988326i | \(0.548685\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.8463 | 1.17391 | 0.586954 | − | 0.809620i | \(-0.300327\pi\) | ||||
0.586954 | + | 0.809620i | \(0.300327\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.6405 | −0.551677 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.85122 | 0.429126 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.44824 | 0.323837 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.92917 | 0.430889 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.9745 | −0.605304 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.36210 | 0.0588886 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −55.6451 | −2.40126 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.938171 | −0.0404099 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.3480 | −1.00381 | −0.501904 | − | 0.864923i | \(-0.667367\pi\) | ||||
−0.501904 | + | 0.864923i | \(0.667367\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.4988 | 1.05134 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.42170 | 0.0608989 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.980079 | −0.0419052 | −0.0209526 | − | 0.999780i | \(-0.506670\pi\) | ||||
−0.0209526 | + | 0.999780i | \(0.506670\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.5404 | −0.791286 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.8973 | −0.506844 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.96214 | −0.253536 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.41590 | 0.102549 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.24073 | −0.0949428 | −0.0474714 | − | 0.998873i | \(-0.515116\pi\) | ||||
−0.0474714 | + | 0.998873i | \(0.515116\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.63928 | 0.238516 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.38098 | −0.100525 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.5876 | −0.446213 | −0.223107 | − | 0.974794i | \(-0.571620\pi\) | ||||
−0.223107 | + | 0.974794i | \(0.571620\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.10525 | 0.0885685 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.48284 | −0.314250 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.0567 | −1.26004 | −0.630021 | − | 0.776578i | \(-0.716954\pi\) | ||||
−0.630021 | + | 0.776578i | \(0.716954\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.8476 | 0.746900 | 0.373450 | − | 0.927650i | \(-0.378175\pi\) | ||||
0.373450 | + | 0.927650i | \(0.378175\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 66.3201 | 2.77056 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −27.4835 | −1.14614 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.188036 | −0.00782805 | −0.00391402 | − | 0.999992i | \(-0.501246\pi\) | ||||
−0.00391402 | + | 0.999992i | \(0.501246\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.3657 | 0.763254 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.92830 | −0.370408 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.80328 | 0.240347 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.44790 | 0.0598631 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.4145 | −1.50299 | −0.751493 | − | 0.659742i | \(-0.770666\pi\) | ||||
−0.751493 | + | 0.659742i | \(0.770666\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.4556 | −0.966470 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.8263 | 0.486469 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.58451 | 0.147198 | 0.0735990 | − | 0.997288i | \(-0.476551\pi\) | ||||
0.0735990 | + | 0.997288i | \(0.476551\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.138905 | 0.00569454 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.62055 | 0.352816 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.3830 | 1.32313 | 0.661566 | − | 0.749887i | \(-0.269892\pi\) | ||||
0.661566 | + | 0.749887i | \(0.269892\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.9279 | −0.445757 | −0.222879 | − | 0.974846i | \(-0.571545\pi\) | ||||
−0.222879 | + | 0.974846i | \(0.571545\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.9737 | 0.813391 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.40569 | −0.0571495 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.2301 | −0.455818 | −0.227909 | − | 0.973682i | \(-0.573189\pi\) | ||||
−0.227909 | + | 0.973682i | \(0.573189\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.6814 | 0.513877 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.827899 | −0.0334932 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.0099 | 0.565854 | 0.282927 | − | 0.959141i | \(-0.408695\pi\) | ||||
0.282927 | + | 0.959141i | \(0.408695\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.62623 | −0.0655759 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.36529 | 0.0952231 | 0.0476115 | − | 0.998866i | \(-0.484839\pi\) | ||||
0.0476115 | + | 0.998866i | \(0.484839\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.4323 | −1.22318 | −0.611588 | − | 0.791177i | \(-0.709469\pi\) | ||||
−0.611588 | + | 0.791177i | \(0.709469\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.17464 | 0.247780 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.88635 | 0.115639 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.7110 | 0.988438 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.66907 | 0.226401 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.85312 | 0.273252 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.85815 | 0.113781 | 0.0568906 | − | 0.998380i | \(-0.481881\pi\) | ||||
0.0568906 | + | 0.998380i | \(0.481881\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.45647 | 0.216875 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.14713 | 0.0852063 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.02933 | 0.120026 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −38.5307 | −1.52425 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.3550 | −1.51493 | −0.757465 | − | 0.652875i | \(-0.773562\pi\) | ||||
−0.757465 | + | 0.652875i | \(0.773562\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.82210 | 0.0718564 | 0.0359282 | − | 0.999354i | \(-0.488561\pi\) | ||||
0.0359282 | + | 0.999354i | \(0.488561\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.656249 | 0.0258398 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.1683 | 1.18604 | 0.593019 | − | 0.805188i | \(-0.297936\pi\) | ||||
0.593019 | + | 0.805188i | \(0.297936\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.70720 | −0.106267 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25.0014 | 0.979881 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.9106 | 0.622632 | 0.311316 | − | 0.950306i | \(-0.399230\pi\) | ||||
0.311316 | + | 0.950306i | \(0.399230\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.89299 | 0.0739653 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 35.6407 | 1.39048 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −47.3825 | −1.84576 | −0.922880 | − | 0.385088i | \(-0.874171\pi\) | ||||
−0.922880 | + | 0.385088i | \(0.874171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.9297 | −0.619594 | −0.309797 | − | 0.950803i | \(-0.600261\pi\) | ||||
−0.309797 | + | 0.950803i | \(0.600261\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.68812 | 0.298582 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.330729 | −0.0128251 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.5724 | 1.06761 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 45.9375 | 1.77604 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.05507 | 0.195149 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −50.8478 | −1.96004 | −0.980020 | − | 0.198898i | \(-0.936264\pi\) | ||||
−0.980020 | + | 0.198898i | \(0.936264\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.57341 | −0.214521 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.74262 | −0.374439 | −0.187220 | − | 0.982318i | \(-0.559948\pi\) | ||||
−0.187220 | + | 0.982318i | \(0.559948\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.9327 | 0.457935 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −39.5410 | −1.51522 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −37.5069 | −1.43516 | −0.717581 | − | 0.696475i | \(-0.754751\pi\) | ||||
−0.717581 | + | 0.696475i | \(0.754751\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.566446 | −0.0216428 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −56.0117 | −2.13698 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.7386 | −0.713885 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.46101 | −0.321872 | −0.160936 | − | 0.986965i | \(-0.551451\pi\) | ||||
−0.160936 | + | 0.986965i | \(0.551451\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.22817 | −0.122628 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.67570 | −0.0635629 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.61308 | −0.174733 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.00380 | −0.302732 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.07563 | −0.267243 | −0.133621 | − | 0.991032i | \(-0.542661\pi\) | ||||
−0.133621 | + | 0.991032i | \(0.542661\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.3171 | −0.615412 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.0963434 | −0.00362850 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.53513 | 0.0953434 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.7504 | −0.666632 | −0.333316 | − | 0.942815i | \(-0.608168\pi\) | ||||
−0.333316 | + | 0.942815i | \(0.608168\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.5152 | −0.769381 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 54.3590 | 2.03576 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.394771 | −0.0147636 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.38790 | 0.126524 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.2756 | −1.01721 | −0.508604 | − | 0.861000i | \(-0.669838\pi\) | ||||
−0.508604 | + | 0.861000i | \(0.669838\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.82731 | −0.0680526 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 37.4086 | 1.39124 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24.8877 | −0.924306 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.7713 | 0.770365 | 0.385182 | − | 0.922840i | \(-0.374139\pi\) | ||||
0.385182 | + | 0.922840i | \(0.374139\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −34.2676 | −1.26917 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.86156 | 0.0688524 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.9928 | 1.73572 | 0.867859 | − | 0.496810i | \(-0.165495\pi\) | ||||
0.867859 | + | 0.496810i | \(0.165495\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.352526 | 0.0130031 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.44585 | −0.200601 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.8966 | 1.06298 | 0.531490 | − | 0.847065i | \(-0.321632\pi\) | ||||
0.531490 | + | 0.847065i | \(0.321632\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.3053 | −0.672460 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.3956 | 0.418064 | 0.209032 | − | 0.977909i | \(-0.432969\pi\) | ||||
0.209032 | + | 0.977909i | \(0.432969\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.85591 | −0.0679952 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −30.7215 | −1.12404 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.80598 | 0.358303 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.1482 | −0.625746 | −0.312873 | − | 0.949795i | \(-0.601291\pi\) | ||||
−0.312873 | + | 0.949795i | \(0.601291\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −63.5062 | −2.31430 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.508333 | 0.0185001 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.2242 | −1.35293 | −0.676467 | − | 0.736473i | \(-0.736490\pi\) | ||||
−0.676467 | + | 0.736473i | \(0.736490\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.1382 | −0.476888 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.38531 | −0.340217 | −0.170109 | − | 0.985425i | \(-0.554412\pi\) | ||||
−0.170109 | + | 0.985425i | \(0.554412\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.2351 | 0.370534 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.477960 | 0.0172807 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.74148 | 0.315637 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.29898 | 0.263208 | 0.131604 | − | 0.991302i | \(-0.457987\pi\) | ||||
0.131604 | + | 0.991302i | \(0.457987\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 50.5604 | 1.82089 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.3839 | 0.445418 | 0.222709 | − | 0.974885i | \(-0.428510\pi\) | ||||
0.222709 | + | 0.974885i | \(0.428510\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −49.0660 | −1.76250 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.3925 | 0.623952 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.9837 | 0.393530 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.5055 | 0.375915 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.59145 | 0.199822 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.31581 | −0.0469632 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.5306 | 1.37347 | 0.686733 | − | 0.726910i | \(-0.259044\pi\) | ||||
0.686733 | + | 0.726910i | \(0.259044\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 56.5897 | 2.01465 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.1561 | 0.538888 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.3227 | −0.579636 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.18063 | −0.0773390 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.7736 | −0.735839 | −0.367920 | − | 0.929858i | \(-0.619930\pi\) | ||||
−0.367920 | + | 0.929858i | \(0.619930\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.273295 | −0.00966847 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.93168 | 0.350919 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.71748 | −0.342922 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.766475 | 0.0270147 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.8338 | 0.979796 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.39047 | 0.154361 | 0.0771803 | − | 0.997017i | \(-0.475408\pi\) | ||||
0.0771803 | + | 0.997017i | \(0.475408\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.0547 | −0.739330 | −0.369665 | − | 0.929165i | \(-0.620528\pi\) | ||||
−0.369665 | + | 0.929165i | \(0.620528\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.1833 | −0.672787 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.464918 | −0.0162854 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.43234 | −0.155068 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.4237 | 0.364232 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.9979 | −1.29124 | −0.645618 | − | 0.763661i | \(-0.723400\pi\) | ||||
−0.645618 | + | 0.763661i | \(0.723400\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.4809 | 1.41107 | 0.705537 | − | 0.708673i | \(-0.250706\pi\) | ||||
0.705537 | + | 0.708673i | \(0.250706\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.8590 | 0.412876 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.83822 | 0.272562 | 0.136281 | − | 0.990670i | \(-0.456485\pi\) | ||||
0.136281 | + | 0.990670i | \(0.456485\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.3043 | −0.496810 | −0.248405 | − | 0.968656i | \(-0.579906\pi\) | ||||
−0.248405 | + | 0.968656i | \(0.579906\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −65.3969 | −2.26859 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.00000 | 0.0346479 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.79050 | 0.0619629 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.0235 | 0.381029 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.6526 | −0.989198 | −0.494599 | − | 0.869121i | \(-0.664685\pi\) | ||||
−0.494599 | + | 0.869121i | \(0.664685\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.03175 | −0.139026 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.14615 | −0.280568 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.531058 | −0.0182689 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.1198 | −0.347722 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.1468 | 0.485516 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 37.8154 | 1.29630 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.5582 | 1.25173 | 0.625865 | − | 0.779931i | \(-0.284746\pi\) | ||||
0.625865 | + | 0.779931i | \(0.284746\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.13801 | −0.0389192 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.14903 | −0.312525 | −0.156262 | − | 0.987716i | \(-0.549945\pi\) | ||||
−0.156262 | + | 0.987716i | \(0.549945\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.9610 | −0.442223 | −0.221112 | − | 0.975248i | \(-0.570969\pi\) | ||||
−0.221112 | + | 0.975248i | \(0.570969\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.7075 | −0.398991 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.92253 | −0.269686 | −0.134843 | − | 0.990867i | \(-0.543053\pi\) | ||||
−0.134843 | + | 0.990867i | \(0.543053\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.64196 | 0.0558283 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.53790 | 0.0861915 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.59351 | 0.189747 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.5845 | 0.595828 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 41.0594 | 1.38965 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.38637 | −0.0468678 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.34688 | 0.0792484 | 0.0396242 | − | 0.999215i | \(-0.487384\pi\) | ||||
0.0396242 | + | 0.999215i | \(0.487384\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −58.4304 | −1.97081 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.2775 | 1.12115 | 0.560573 | − | 0.828105i | \(-0.310581\pi\) | ||||
0.560573 | + | 0.828105i | \(0.310581\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.6831 | 0.527780 | 0.263890 | − | 0.964553i | \(-0.414994\pi\) | ||||
0.263890 | + | 0.964553i | \(0.414994\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.01725 | 0.0341946 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.95317 | −0.0655811 | −0.0327906 | − | 0.999462i | \(-0.510439\pi\) | ||||
−0.0327906 | + | 0.999462i | \(0.510439\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.4576 | 0.518431 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.02018 | 0.235185 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.650709 | 0.0217752 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.04558 | −0.101802 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 42.4230 | 1.41646 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 49.2248 | 1.64174 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.18574 | −0.206077 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.72445 | 0.157220 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.34087 | 0.0445722 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.5462 | 0.848247 | 0.424123 | − | 0.905604i | \(-0.360582\pi\) | ||||
0.424123 | + | 0.905604i | \(0.360582\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.72318 | 0.289329 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.9725 | −0.628586 | −0.314293 | − | 0.949326i | \(-0.601767\pi\) | ||||
−0.314293 | + | 0.949326i | \(0.601767\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.37627 | 0.277214 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.89949 | −0.0627951 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.6280 | 0.450036 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.0055 | 0.527973 | 0.263987 | − | 0.964526i | \(-0.414963\pi\) | ||||
0.263987 | + | 0.964526i | \(0.414963\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.7861 | −0.981485 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.9218 | −1.11655 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.1334 | −1.12230 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.28762 | −0.206513 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.2945 | −1.12516 | −0.562582 | − | 0.826741i | \(-0.690192\pi\) | ||||
−0.562582 | + | 0.826741i | \(0.690192\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.38098 | −0.0780335 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.5062 | 1.06420 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.130316 | −0.00426180 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.4116 | 1.51620 | 0.758101 | − | 0.652137i | \(-0.226127\pi\) | ||||
0.758101 | + | 0.652137i | \(0.226127\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −79.6187 | −2.59826 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33.8074 | −1.10209 | −0.551044 | − | 0.834476i | \(-0.685770\pi\) | ||||
−0.551044 | + | 0.834476i | \(0.685770\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.4549 | −0.828927 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.155435 | 0.00505629 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.4012 | −0.630454 | −0.315227 | − | 0.949016i | \(-0.602081\pi\) | ||||
−0.315227 | + | 0.949016i | \(0.602081\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.3775 | 1.01856 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −74.2738 | −2.40849 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.4748 | −1.05196 | −0.525981 | − | 0.850497i | \(-0.676302\pi\) | ||||
−0.525981 | + | 0.850497i | \(0.676302\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.62985 | 0.117459 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.8973 | −0.384586 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.07795 | −0.131684 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 66.0466 | 2.13054 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 33.7416 | 1.08731 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.00520 | 0.0323585 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53.5070 | −1.72067 | −0.860334 | − | 0.509730i | \(-0.829745\pi\) | ||||
−0.860334 | + | 0.509730i | \(0.829745\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.04268 | −0.194119 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.00403 | −0.288953 | −0.144476 | − | 0.989508i | \(-0.546150\pi\) | ||||
−0.144476 | + | 0.989508i | \(0.546150\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0637 | −0.386743 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −38.2922 | −1.22633 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.0369 | −1.21691 | −0.608454 | − | 0.793589i | \(-0.708210\pi\) | ||||
−0.608454 | + | 0.793589i | \(0.708210\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.70789 | −0.0865445 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 35.2180 | 1.12442 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.3788 | −0.362927 | −0.181464 | − | 0.983398i | \(-0.558083\pi\) | ||||
−0.181464 | + | 0.983398i | \(0.558083\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.647280 | 0.0206241 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.693594 | −0.0220773 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.2721 | 0.326633 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.7450 | 1.48490 | 0.742452 | − | 0.669900i | \(-0.233663\pi\) | ||||
0.742452 | + | 0.669900i | \(0.233663\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.0825 | 0.891171 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.471822 | 0.0149578 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.5528 | −1.37933 | −0.689665 | − | 0.724128i | \(-0.742242\pi\) | ||||
−0.689665 | + | 0.724128i | \(0.742242\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.66864 | 0.242625 |
(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 | 7616.2.a.bw.1.6 | 6 | ||
4.3 | odd | 2 | 7616.2.a.ca.1.1 | 6 | |||
8.3 | odd | 2 | 3808.2.a.j.1.6 | ✓ | 6 | ||
8.5 | even | 2 | 3808.2.a.n.1.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3808.2.a.j.1.6 | ✓ | 6 | 8.3 | odd | 2 | ||
3808.2.a.n.1.1 | yes | 6 | 8.5 | even | 2 | ||
7616.2.a.bw.1.6 | 6 | 1.1 | even | 1 | trivial | ||
7616.2.a.ca.1.1 | 6 | 4.3 | odd | 2 |