Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(2431,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4560.2431");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(36.4117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.9821011968.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 20x^{4} + 118x^{2} + 192 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2431.3 | ||
Root | \(-1.63858i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.2431 |
Dual form | 4560.2.d.e.2431.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4560\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(1711\) | \(1921\) | \(2737\) | \(3041\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.63858i | − | 0.619323i | −0.950847 | − | 0.309662i | \(-0.899784\pi\) | ||
0.950847 | − | 0.309662i | \(-0.100216\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.02200i | − | 0.308144i | −0.988060 | − | 0.154072i | \(-0.950761\pi\) | ||
0.988060 | − | 0.154072i | \(-0.0492388\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.63858i | − | 0.454459i | −0.973841 | − | 0.227230i | \(-0.927033\pi\) | ||
0.973841 | − | 0.227230i | \(-0.0729668\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.31507 | 0.804023 | 0.402011 | − | 0.915635i | \(-0.368311\pi\) | ||||
0.402011 | + | 0.915635i | \(0.368311\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.31507 | + | 0.616577i | 0.989945 | + | 0.141452i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.63858i | 0.357566i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.09257i | 1.68742i | 0.536802 | + | 0.843708i | \(0.319632\pi\) | ||||
−0.536802 | + | 0.843708i | \(0.680368\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.02200i | − | 0.189780i | −0.995488 | − | 0.0948902i | \(-0.969750\pi\) | ||
0.995488 | − | 0.0948902i | \(-0.0302500\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.30476 | −1.13237 | −0.566184 | − | 0.824279i | \(-0.691581\pi\) | ||||
−0.566184 | + | 0.824279i | \(0.691581\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.02200i | 0.177907i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.63858i | 0.276970i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.11457i | 1.49843i | 0.662330 | + | 0.749213i | \(0.269568\pi\) | ||||
−0.662330 | + | 0.749213i | \(0.730432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.63858i | 0.262382i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.25515i | − | 0.352196i | −0.984373 | − | 0.176098i | \(-0.943652\pi\) | ||
0.984373 | − | 0.176098i | \(-0.0563475\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.11457i | 1.38996i | 0.719030 | + | 0.694979i | \(0.244586\pi\) | ||||
−0.719030 | + | 0.694979i | \(0.755414\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.85941i | − | 1.00055i | −0.865867 | − | 0.500274i | \(-0.833233\pi\) | ||
0.865867 | − | 0.500274i | \(-0.166767\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.31507 | 0.616439 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.31507 | −0.464203 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8.09257i | − | 1.11160i | −0.831316 | − | 0.555800i | \(-0.812412\pi\) | ||
0.831316 | − | 0.555800i | \(-0.187588\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.02200i | 0.137806i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.31507 | − | 0.616577i | −0.571545 | − | 0.0816676i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.63014 | −0.863171 | −0.431585 | − | 0.902072i | \(-0.642046\pi\) | ||||
−0.431585 | + | 0.902072i | \(0.642046\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.30476 | −0.551168 | −0.275584 | − | 0.961277i | \(-0.588871\pi\) | ||||
−0.275584 | + | 0.961277i | \(0.588871\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.63858i | − | 0.206441i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.63858i | 0.203240i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.989692 | 0.120910 | 0.0604550 | − | 0.998171i | \(-0.480745\pi\) | ||||
0.0604550 | + | 0.998171i | \(0.480745\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 8.09257i | − | 0.974231i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.63014 | −0.786853 | −0.393426 | − | 0.919356i | \(-0.628710\pi\) | ||||
−0.393426 | + | 0.919356i | \(0.628710\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.2500 | 1.90192 | 0.950958 | − | 0.309321i | \(-0.100102\pi\) | ||||
0.950958 | + | 0.309321i | \(0.100102\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.67462 | −0.190841 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.61983 | −0.182245 | −0.0911227 | − | 0.995840i | \(-0.529046\pi\) | ||||
−0.0911227 | + | 0.995840i | \(0.529046\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 10.1366i | − | 1.11263i | −0.830971 | − | 0.556316i | \(-0.812214\pi\) | ||
0.830971 | − | 0.556316i | \(-0.187786\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.31507 | −0.359570 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.02200i | 0.109570i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.22084i | 0.553408i | 0.960955 | + | 0.276704i | \(0.0892421\pi\) | ||||
−0.960955 | + | 0.276704i | \(0.910758\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.68493 | −0.281457 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.30476 | 0.653773 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.31507 | − | 0.616577i | −0.442717 | − | 0.0632595i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 19.0569i | − | 1.93493i | −0.253002 | − | 0.967466i | \(-0.581418\pi\) | ||
0.253002 | − | 0.967466i | \(-0.418582\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.02200i | − | 0.102715i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.6095 | 1.05569 | 0.527844 | − | 0.849342i | \(-0.323001\pi\) | ||||
0.527844 | + | 0.849342i | \(0.323001\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.6301 | 1.04742 | 0.523709 | − | 0.851897i | \(-0.324548\pi\) | ||||
0.523709 | + | 0.851897i | \(0.324548\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 1.63858i | − | 0.159909i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.64045 | −0.738630 | −0.369315 | − | 0.929304i | \(-0.620408\pi\) | ||||
−0.369315 | + | 0.929304i | \(0.620408\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.4623i | 1.86415i | 0.362267 | + | 0.932074i | \(0.382003\pi\) | ||||
−0.362267 | + | 0.932074i | \(0.617997\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 9.11457i | − | 0.865116i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.90341i | 0.837562i | 0.908087 | + | 0.418781i | \(0.137543\pi\) | ||||
−0.908087 | + | 0.418781i | \(0.862457\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 8.09257i | − | 0.754636i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 1.63858i | − | 0.151486i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 5.43199i | − | 0.497950i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.95552 | 0.905047 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.25515i | 0.203340i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.2500 | 1.26448 | 0.632240 | − | 0.774772i | \(-0.282136\pi\) | ||||
0.632240 | + | 0.774772i | \(0.282136\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 9.11457i | − | 0.802493i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.2414i | 1.24428i | 0.782906 | + | 0.622141i | \(0.213737\pi\) | ||||
−0.782906 | + | 0.622141i | \(0.786263\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.01031 | − | 7.07057i | 0.0876048 | − | 0.613096i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.2500 | 1.55920 | 0.779600 | − | 0.626277i | \(-0.215422\pi\) | ||||
0.779600 | + | 0.626277i | \(0.215422\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.51031i | − | 0.382559i | −0.981536 | − | 0.191280i | \(-0.938736\pi\) | ||
0.981536 | − | 0.191280i | \(-0.0612637\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.85941i | 0.577667i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.67462 | −0.140039 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.02200i | 0.0848723i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.31507 | −0.355901 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.630141 | −0.0516231 | −0.0258116 | − | 0.999667i | \(-0.508217\pi\) | ||||
−0.0258116 | + | 0.999667i | \(0.508217\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.2945 | 0.919130 | 0.459565 | − | 0.888144i | \(-0.348005\pi\) | ||||
0.459565 | + | 0.888144i | \(0.348005\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.31507 | 0.268008 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.30476 | 0.506411 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.01031 | 0.399866 | 0.199933 | − | 0.979810i | \(-0.435928\pi\) | ||||
0.199933 | + | 0.979810i | \(0.435928\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.09257i | 0.641782i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.2603 | 1.04506 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 22.3340i | − | 1.74934i | −0.484723 | − | 0.874668i | \(-0.661080\pi\) | ||
0.484723 | − | 0.874668i | \(-0.338920\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 1.02200i | − | 0.0795625i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.31507 | −0.720822 | −0.360411 | − | 0.932794i | \(-0.617364\pi\) | ||||
−0.360411 | + | 0.932794i | \(0.617364\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.3151 | 0.793467 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.31507 | + | 0.616577i | 0.329982 | + | 0.0471508i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.67025i | 0.583159i | 0.956547 | + | 0.291579i | \(0.0941807\pi\) | ||||
−0.956547 | + | 0.291579i | \(0.905819\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.63858i | − | 0.123865i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.63014 | 0.498352 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 8.59830i | − | 0.639106i | −0.947568 | − | 0.319553i | \(-0.896467\pi\) | ||
0.947568 | − | 0.319553i | \(-0.103533\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.30476 | 0.318217 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 9.11457i | − | 0.670116i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.38800i | − | 0.247755i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.63858i | 0.119189i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.4843i | 1.48219i | 0.671400 | + | 0.741095i | \(0.265693\pi\) | ||||
−0.671400 | + | 0.741095i | \(0.734307\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 12.7032i | − | 0.914395i | −0.889365 | − | 0.457198i | \(-0.848853\pi\) | ||
0.889365 | − | 0.457198i | \(-0.151147\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 1.63858i | − | 0.117341i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.3151 | 1.09115 | 0.545577 | − | 0.838061i | \(-0.316311\pi\) | ||||
0.545577 | + | 0.838061i | \(0.316311\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.2291i | 1.29223i | 0.763241 | + | 0.646114i | \(0.223607\pi\) | ||||
−0.763241 | + | 0.646114i | \(0.776393\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.989692 | −0.0698075 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.67462 | −0.117535 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.25515i | 0.157507i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.09257i | 0.562472i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.630141 | − | 4.40999i | 0.0435878 | − | 0.305046i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.98969 | −0.618876 | −0.309438 | − | 0.950920i | \(-0.600141\pi\) | ||||
−0.309438 | + | 0.950920i | \(0.600141\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.63014 | 0.454290 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 9.11457i | − | 0.621608i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.3308i | 0.701302i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.2500 | −1.09807 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 5.43199i | − | 0.365395i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.8904 | 1.59982 | 0.799911 | − | 0.600119i | \(-0.204880\pi\) | ||||
0.799911 | + | 0.600119i | \(0.204880\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −27.1849 | −1.80432 | −0.902162 | − | 0.431398i | \(-0.858021\pi\) | ||||
−0.902162 | + | 0.431398i | \(0.858021\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.6849 | −0.838244 | −0.419122 | − | 0.907930i | \(-0.637662\pi\) | ||||
−0.419122 | + | 0.907930i | \(0.637662\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.67462 | 0.110182 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.2809 | 1.39416 | 0.697079 | − | 0.716994i | \(-0.254483\pi\) | ||||
0.697079 | + | 0.716994i | \(0.254483\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.85941i | 0.447459i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.61983 | 0.105219 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.64315i | 0.365025i | 0.983204 | + | 0.182512i | \(0.0584230\pi\) | ||||
−0.983204 | + | 0.182512i | \(0.941577\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.8068i | 1.14704i | 0.819192 | + | 0.573519i | \(0.194422\pi\) | ||||
−0.819192 | + | 0.573519i | \(0.805578\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.31507 | −0.275680 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.01031 | − | 7.07057i | 0.0642844 | − | 0.449890i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.1366i | 0.642379i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 15.0523i | − | 0.950092i | −0.879961 | − | 0.475046i | \(-0.842431\pi\) | ||
0.879961 | − | 0.475046i | \(-0.157569\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.27059 | 0.519968 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.31507 | 0.207598 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.7674i | 1.23306i | 0.787333 | + | 0.616528i | \(0.211461\pi\) | ||||
−0.787333 | + | 0.616528i | \(0.788539\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.9349 | 0.928010 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 1.02200i | − | 0.0632601i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.7674i | 1.21891i | 0.792821 | + | 0.609455i | \(0.208612\pi\) | ||||
−0.792821 | + | 0.609455i | \(0.791388\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.09257i | 0.497122i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 5.22084i | − | 0.319510i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 26.7271i | − | 1.62958i | −0.579755 | − | 0.814791i | \(-0.696852\pi\) | ||
0.579755 | − | 0.814791i | \(-0.303148\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5.74346i | − | 0.348890i | −0.984667 | − | 0.174445i | \(-0.944187\pi\) | ||
0.984667 | − | 0.174445i | \(-0.0558132\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.68493 | 0.162499 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1.02200i | − | 0.0616288i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.6095 | 1.11814 | 0.559069 | − | 0.829121i | \(-0.311159\pi\) | ||||
0.559069 | + | 0.829121i | \(0.311159\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.30476 | −0.377456 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 13.4306i | − | 0.801203i | −0.916252 | − | 0.400601i | \(-0.868801\pi\) | ||
0.916252 | − | 0.400601i | \(-0.131199\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.68257i | 0.218906i | 0.993992 | + | 0.109453i | \(0.0349099\pi\) | ||||
−0.993992 | + | 0.109453i | \(0.965090\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.31507 | + | 0.616577i | 0.255603 | + | 0.0365229i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.69524 | −0.218123 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.01031 | −0.353548 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.0569i | 1.11713i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6.04857i | − | 0.353361i | −0.984268 | − | 0.176681i | \(-0.943464\pi\) | ||
0.984268 | − | 0.176681i | \(-0.0565360\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.63014 | 0.386022 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.02200i | 0.0593024i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.2603 | 0.766862 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.9349 | 0.860833 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.6095 | −0.609501 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.30476 | 0.246490 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.6301 | 1.29157 | 0.645785 | − | 0.763519i | \(-0.276530\pi\) | ||||
0.645785 | + | 0.763519i | \(0.276530\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.6301 | −0.604728 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 30.0043i | − | 1.70139i | −0.525663 | − | 0.850693i | \(-0.676183\pi\) | ||
0.525663 | − | 0.850693i | \(-0.323817\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.8801 | 1.29326 | 0.646630 | − | 0.762804i | \(-0.276178\pi\) | ||||
0.646630 | + | 0.762804i | \(0.276178\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.63858i | 0.0923233i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 19.9680i | − | 1.12152i | −0.827980 | − | 0.560758i | \(-0.810510\pi\) | ||
0.827980 | − | 0.560758i | \(-0.189490\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.04448 | −0.0584797 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.64045 | 0.426448 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.3048 | + | 2.04400i | 0.795938 | + | 0.113731i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.63858i | − | 0.0908918i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 19.4623i | − | 1.07627i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.2397 | −0.619663 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.9452 | 1.09629 | 0.548144 | − | 0.836384i | \(-0.315335\pi\) | ||||
0.548144 | + | 0.836384i | \(0.315335\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.11457i | 0.499475i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.989692 | −0.0540726 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 33.6974i | − | 1.83561i | −0.397028 | − | 0.917807i | \(-0.629958\pi\) | ||
0.397028 | − | 0.917807i | \(-0.370042\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 8.90341i | − | 0.483567i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.44346i | 0.348933i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.5406i | − | 1.00110i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.09257i | 0.435689i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.3903i | 1.09461i | 0.836933 | + | 0.547305i | \(0.184346\pi\) | ||||
−0.836933 | + | 0.547305i | \(0.815654\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.2706 | −0.656830 | −0.328415 | − | 0.944534i | \(-0.606514\pi\) | ||||
−0.328415 | + | 0.944534i | \(0.606514\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.63858i | 0.0874607i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.2603 | 1.02512 | 0.512561 | − | 0.858651i | \(-0.328697\pi\) | ||||
0.512561 | + | 0.858651i | \(0.328697\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.63014 | 0.351891 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.43199i | 0.287492i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 9.84199i | − | 0.519440i | −0.965684 | − | 0.259720i | \(-0.916370\pi\) | ||
0.965684 | − | 0.259720i | \(-0.0836303\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.2397 | + | 5.32115i | 0.959982 | + | 0.280060i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.95552 | −0.522529 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.2500 | −0.850562 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 7.27119i | − | 0.379553i | −0.981827 | − | 0.189777i | \(-0.939224\pi\) | ||
0.981827 | − | 0.189777i | \(-0.0607763\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 2.25515i | − | 0.117399i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.2603 | −0.688440 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.3574i | 0.795176i | 0.917564 | + | 0.397588i | \(0.130153\pi\) | ||||
−0.917564 | + | 0.397588i | \(0.869847\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.67462 | −0.0862474 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.9452 | 1.02452 | 0.512258 | − | 0.858831i | \(-0.328809\pi\) | ||||
0.512258 | + | 0.858831i | \(0.328809\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.2500 | −0.730048 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.0000 | 1.22634 | 0.613171 | − | 0.789950i | \(-0.289894\pi\) | ||||
0.613171 | + | 0.789950i | \(0.289894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.67462 | 0.0853466 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.11457i | 0.463319i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.8904 | −1.31270 | −0.656348 | − | 0.754458i | \(-0.727900\pi\) | ||||
−0.656348 | + | 0.754458i | \(0.727900\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.8274i | 1.35672i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 14.2414i | − | 0.718386i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.61983 | 0.0815026 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.01031 | + | 7.07057i | −0.0505787 | + | 0.353971i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 27.0386i | − | 1.35024i | −0.737707 | − | 0.675121i | \(-0.764091\pi\) | ||
0.737707 | − | 0.675121i | \(-0.235909\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.3308i | 0.514615i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.31507 | 0.461731 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 23.5503i | − | 1.16449i | −0.813015 | − | 0.582243i | \(-0.802175\pi\) | ||
0.813015 | − | 0.582243i | \(-0.197825\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.2500 | −0.900205 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.8640i | 0.534582i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.1366i | 0.497584i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.51031i | 0.220871i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.6968i | 0.620281i | 0.950691 | + | 0.310140i | \(0.100376\pi\) | ||||
−0.950691 | + | 0.310140i | \(0.899624\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 20.2731i | − | 0.988052i | −0.869447 | − | 0.494026i | \(-0.835525\pi\) | ||
0.869447 | − | 0.494026i | \(-0.164475\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 6.85941i | − | 0.333516i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.31507 | 0.160805 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.05368i | 0.341351i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.67462 | 0.0808515 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.63014 | −0.319363 | −0.159681 | − | 0.987169i | \(-0.551047\pi\) | ||||
−0.159681 | + | 0.987169i | \(0.551047\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.68257i | 0.176973i | 0.996077 | + | 0.0884866i | \(0.0282030\pi\) | ||||
−0.996077 | + | 0.0884866i | \(0.971797\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 1.02200i | − | 0.0490011i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.98969 | + | 34.9200i | −0.238689 | + | 1.67045i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.00000 | −0.381819 | −0.190910 | − | 0.981608i | \(-0.561144\pi\) | ||||
−0.190910 | + | 0.981608i | \(0.561144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.31507 | 0.205480 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 5.23773i | − | 0.248852i | −0.992229 | − | 0.124426i | \(-0.960291\pi\) | ||
0.992229 | − | 0.124426i | \(-0.0397089\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 5.22084i | − | 0.247491i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.630141 | 0.0298046 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 41.6020i | 1.96332i | 0.190637 | + | 0.981661i | \(0.438945\pi\) | ||||
−0.190637 | + | 0.981661i | \(0.561055\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.30476 | −0.108527 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.2945 | −0.530660 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.68493 | 0.125871 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.98969 | 0.139852 | 0.0699259 | − | 0.997552i | \(-0.477724\pi\) | ||||
0.0699259 | + | 0.997552i | \(0.477724\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.31507 | −0.154734 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.2190 | 1.26772 | 0.633859 | − | 0.773449i | \(-0.281470\pi\) | ||||
0.633859 | + | 0.773449i | \(0.281470\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.92541i | 0.461273i | 0.973040 | + | 0.230636i | \(0.0740808\pi\) | ||||
−0.973040 | + | 0.230636i | \(0.925919\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.30476 | −0.292376 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.7440i | 1.23757i | 0.785562 | + | 0.618783i | \(0.212374\pi\) | ||||
−0.785562 | + | 0.618783i | \(0.787626\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.62168i | − | 0.0748824i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.01031 | −0.230863 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.31507 | 0.428307 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.31507 | + | 0.616577i | 0.197989 | + | 0.0282905i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 8.09257i | − | 0.370533i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 0.100311i | − | 0.00458330i | −0.999997 | − | 0.00229165i | \(-0.999271\pi\) | ||
0.999997 | − | 0.00229165i | \(-0.000729456\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.9349 | 0.680973 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.2603 | −0.603364 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.0569i | 0.865328i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.64045 | 0.436850 | 0.218425 | − | 0.975854i | \(-0.429908\pi\) | ||||
0.218425 | + | 0.975854i | \(0.429908\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.3340i | 1.00998i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3.06599i | − | 0.138366i | −0.997604 | − | 0.0691832i | \(-0.977961\pi\) | ||
0.997604 | − | 0.0691832i | \(-0.0220393\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.38800i | − | 0.152588i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.02200i | 0.0459354i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.8640i | 0.487316i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 16.9960i | − | 0.760844i | −0.924813 | − | 0.380422i | \(-0.875779\pi\) | ||
0.924813 | − | 0.380422i | \(-0.124221\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.31507 | 0.416167 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 19.7674i | − | 0.881385i | −0.897658 | − | 0.440692i | \(-0.854733\pi\) | ||
0.897658 | − | 0.440692i | \(-0.145267\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.6095 | −0.472118 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.3151 | −0.458108 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.1837i | 1.07193i | 0.844242 | + | 0.535963i | \(0.180051\pi\) | ||||
−0.844242 | + | 0.535963i | \(0.819949\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 26.6268i | − | 1.17790i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.31507 | − | 0.616577i | −0.190515 | − | 0.0272225i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.6301 | −0.468420 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.01031 | −0.308313 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 7.67025i | − | 0.336687i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 3.79977i | − | 0.166471i | −0.996530 | − | 0.0832355i | \(-0.973475\pi\) | ||
0.996530 | − | 0.0832355i | \(-0.0265254\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.1404 | 1.49286 | 0.746428 | − | 0.665467i | \(-0.231767\pi\) | ||||
0.746428 | + | 0.665467i | \(0.231767\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.63858i | 0.0715133i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.9007 | −0.910450 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −42.4896 | −1.84738 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.63014 | −0.287724 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.69524 | −0.160059 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.64045 | 0.330325 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 4.40999i | − | 0.189952i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.2190 | −1.25623 | −0.628113 | − | 0.778123i | \(-0.716172\pi\) | ||||
−0.628113 | + | 0.778123i | \(0.716172\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.59830i | 0.368988i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 19.4623i | − | 0.833673i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.6095 | −0.539144 | −0.269572 | − | 0.962980i | \(-0.586882\pi\) | ||||
−0.269572 | + | 0.962980i | \(0.586882\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.30476 | −0.183723 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.630141 | − | 4.40999i | 0.0268449 | − | 0.187872i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.65422i | 0.112869i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.11457i | 0.386892i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −41.4896 | −1.75797 | −0.878986 | − | 0.476847i | \(-0.841780\pi\) | ||||
−0.878986 | + | 0.476847i | \(0.841780\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.9349 | 0.631679 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.38800i | 0.143041i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.9246 | −0.586852 | −0.293426 | − | 0.955982i | \(-0.594795\pi\) | ||||
−0.293426 | + | 0.955982i | \(0.594795\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 8.90341i | − | 0.374569i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1.63858i | − | 0.0688137i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 27.6488i | − | 1.15910i | −0.814937 | − | 0.579549i | \(-0.803229\pi\) | ||
0.814937 | − | 0.579549i | \(-0.196771\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 16.3858i | − | 0.685722i | −0.939386 | − | 0.342861i | \(-0.888604\pi\) | ||
0.939386 | − | 0.342861i | \(-0.111396\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 20.4843i | − | 0.855743i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.09257i | 0.337483i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.64045 | −0.151554 | −0.0757769 | − | 0.997125i | \(-0.524144\pi\) | ||||
−0.0757769 | + | 0.997125i | \(0.524144\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.7032i | 0.527926i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.6095 | −0.689079 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.27059 | −0.342533 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.63858i | 0.0677468i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 40.2411i | − | 1.66093i | −0.557071 | − | 0.830465i | \(-0.688075\pi\) | ||
0.557071 | − | 0.830465i | \(-0.311925\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.2055 | − | 3.88737i | −1.12098 | − | 0.160176i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.3151 | −0.629978 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.27059 | 0.339632 | 0.169816 | − | 0.985476i | \(-0.445683\pi\) | ||||
0.169816 | + | 0.985476i | \(0.445683\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.43199i | 0.222690i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 18.2291i | − | 0.746069i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.39048 | −0.301967 | −0.150983 | − | 0.988536i | \(-0.548244\pi\) | ||||
−0.150983 | + | 0.988536i | \(0.548244\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.89884i | 0.199828i | 0.994996 | + | 0.0999138i | \(0.0318567\pi\) | ||||
−0.994996 | + | 0.0999138i | \(0.968143\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.989692 | 0.0403034 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.95552 | −0.404749 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.5103 | 1.11661 | 0.558303 | − | 0.829637i | \(-0.311453\pi\) | ||||
0.558303 | + | 0.829637i | \(0.311453\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.67462 | 0.0678591 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.2397 | −0.454708 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.5992 | 0.791605 | 0.395802 | − | 0.918336i | \(-0.370467\pi\) | ||||
0.395802 | + | 0.918336i | \(0.370467\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 2.25515i | − | 0.0909365i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.94521 | −0.400379 | −0.200190 | − | 0.979757i | \(-0.564156\pi\) | ||||
−0.200190 | + | 0.979757i | \(0.564156\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 32.5709i | − | 1.30913i | −0.756004 | − | 0.654567i | \(-0.772851\pi\) | ||
0.756004 | − | 0.654567i | \(-0.227149\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 8.09257i | − | 0.324744i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.55474 | 0.342738 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.630141 | + | 4.40999i | −0.0251654 | + | 0.176118i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30.2154i | 1.20477i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 27.0491i | − | 1.07681i | −0.842687 | − | 0.538404i | \(-0.819027\pi\) | ||
0.842687 | − | 0.538404i | \(-0.180973\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.98969 | 0.357308 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.2500 | −0.565493 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 7.07057i | − | 0.280146i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.63014 | −0.262284 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.0729i | 0.950822i | 0.879764 | + | 0.475411i | \(0.157701\pi\) | ||||
−0.879764 | + | 0.475411i | \(0.842299\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.56026i | − | 0.100967i | −0.998725 | − | 0.0504835i | \(-0.983924\pi\) | ||
0.998725 | − | 0.0504835i | \(-0.0160762\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.11457i | 0.358886i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.1572i | 0.753146i | 0.926387 | + | 0.376573i | \(0.122898\pi\) | ||||
−0.926387 | + | 0.376573i | \(0.877102\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.77599i | 0.265981i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 10.3308i | − | 0.404897i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.8150 | 1.55808 | 0.779041 | − | 0.626973i | \(-0.215706\pi\) | ||||
0.779041 | + | 0.626973i | \(0.215706\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 14.2414i | − | 0.556459i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.2500 | 0.633972 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.760335 | −0.0296184 | −0.0148092 | − | 0.999890i | \(-0.504714\pi\) | ||||
−0.0148092 | + | 0.999890i | \(0.504714\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.6474i | 1.38652i | 0.720686 | + | 0.693262i | \(0.243827\pi\) | ||||
−0.720686 | + | 0.693262i | \(0.756173\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.43199i | 0.210961i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.01031 | + | 7.07057i | −0.0391781 | + | 0.274185i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.27059 | 0.320239 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23.8904 | −0.923657 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.39946i | 0.169839i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.8255i | 0.532934i | 0.963844 | + | 0.266467i | \(0.0858563\pi\) | ||||
−0.963844 | + | 0.266467i | \(0.914144\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 44.5508i | − | 1.71223i | −0.516788 | − | 0.856114i | \(-0.672872\pi\) | ||
0.516788 | − | 0.856114i | \(-0.327128\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −31.2261 | −1.19835 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.1849 | 1.04173 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.8389 | 1.02696 | 0.513481 | − | 0.858101i | \(-0.328356\pi\) | ||||
0.513481 | + | 0.858101i | \(0.328356\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.2500 | −0.697296 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.6849 | 0.483960 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.2603 | −0.505176 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 48.1331i | 1.83107i | 0.402239 | + | 0.915535i | \(0.368232\pi\) | ||||
−0.402239 | + | 0.915535i | \(0.631768\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.67462 | −0.0636136 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.51031i | 0.171086i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 7.47599i | − | 0.283173i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.2809 | −0.804917 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.8904 | −0.977868 | −0.488934 | − | 0.872321i | \(-0.662614\pi\) | ||||
−0.488934 | + | 0.872321i | \(0.662614\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.61983 | + | 39.3300i | −0.211956 | + | 1.48336i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 6.85941i | − | 0.258340i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 17.3845i | − | 0.653812i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.2158 | −0.984555 | −0.492278 | − | 0.870438i | \(-0.663835\pi\) | ||||
−0.492278 | + | 0.870438i | \(0.663835\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.61983 | −0.0607485 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 51.0217i | − | 1.91078i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.67462 | 0.0626273 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 5.64315i | − | 0.210747i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 5.84377i | − | 0.217936i | −0.994045 | − | 0.108968i | \(-0.965245\pi\) | ||
0.994045 | − | 0.108968i | \(-0.0347546\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 17.4183i | − | 0.648691i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 17.8068i | − | 0.662243i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1.02200i | − | 0.0379561i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.8237i | 0.661045i | 0.943798 | + | 0.330522i | \(0.107225\pi\) | ||||
−0.943798 | + | 0.330522i | \(0.892775\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.2154i | 1.11756i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.75003 | 0.138510 | 0.0692552 | − | 0.997599i | \(-0.477938\pi\) | ||||
0.0692552 | + | 0.997599i | \(0.477938\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.31507 | 0.159164 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.01146i | − | 0.0372577i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.7588i | 1.20505i | 0.798099 | + | 0.602526i | \(0.205839\pi\) | ||||
−0.798099 | + | 0.602526i | \(0.794161\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.01031 | + | 7.07057i | −0.0371146 | + | 0.259744i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −47.2397 | −1.73306 | −0.866528 | − | 0.499129i | \(-0.833653\pi\) | ||||
−0.866528 | + | 0.499129i | \(0.833653\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.630141 | 0.0230866 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 10.1366i | − | 0.370877i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.5195i | 0.457451i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.96583 | −0.0717341 | −0.0358670 | − | 0.999357i | \(-0.511419\pi\) | ||||
−0.0358670 | + | 0.999357i | \(0.511419\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.0523i | 0.548536i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.2945 | −0.411047 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.6095 | −0.967140 | −0.483570 | − | 0.875306i | \(-0.660660\pi\) | ||||
−0.483570 | + | 0.875306i | \(0.660660\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.27059 | −0.300203 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.3904 | 1.39165 | 0.695825 | − | 0.718211i | \(-0.255039\pi\) | ||||
0.695825 | + | 0.718211i | \(0.255039\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.8904 | 1.15451 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.31507 | −0.119857 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.8640i | 0.392276i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.2809 | −0.406800 | −0.203400 | − | 0.979096i | \(-0.565199\pi\) | ||||
−0.203400 | + | 0.979096i | \(0.565199\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 19.7674i | − | 0.711905i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 11.5703i | − | 0.416156i | −0.978112 | − | 0.208078i | \(-0.933279\pi\) | ||
0.978112 | − | 0.208078i | \(-0.0667208\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.30476 | −0.226474 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.9349 | −0.535787 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.39048 | − | 9.73114i | 0.0498190 | − | 0.348654i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.77599i | 0.242464i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.02200i | 0.0365232i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.01031 | −0.178826 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.6198 | 0.699372 | 0.349686 | − | 0.936867i | \(-0.386288\pi\) | ||||
0.349686 | + | 0.936867i | \(0.386288\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 19.7674i | − | 0.703738i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.5889 | 0.518722 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.05368i | 0.250483i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 8.09257i | − | 0.287014i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.8966i | 1.48405i | 0.670370 | + | 0.742027i | \(0.266135\pi\) | ||||
−0.670370 | + | 0.742027i | \(0.733865\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 22.7394i | − | 0.804463i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.22084i | 0.184469i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 16.6074i | − | 0.586064i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.2603 | −0.467364 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.7271i | 0.940839i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.9110 | −0.559402 | −0.279701 | − | 0.960087i | \(-0.590235\pi\) | ||||
−0.279701 | + | 0.960087i | \(0.590235\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.5206 | 1.07172 | 0.535861 | − | 0.844306i | \(-0.319987\pi\) | ||||
0.535861 | + | 0.844306i | \(0.319987\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.74346i | 0.201432i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22.3340i | 0.782326i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.61983 | + | 39.3300i | −0.196613 | + | 1.37598i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.68493 | −0.0938190 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.2397 | −1.02047 | −0.510236 | − | 0.860035i | \(-0.670442\pi\) | ||||
−0.510236 | + | 0.860035i | \(0.670442\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 30.1985i | − | 1.05265i | −0.850282 | − | 0.526327i | \(-0.823569\pi\) | ||
0.850282 | − | 0.526327i | \(-0.176431\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.02200i | 0.0355814i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −50.4245 | −1.75343 | −0.876717 | − | 0.481007i | \(-0.840271\pi\) | ||||
−0.876717 | + | 0.481007i | \(0.840271\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 3.66568i | − | 0.127314i | −0.997972 | − | 0.0636572i | \(-0.979724\pi\) | ||
0.997972 | − | 0.0636572i | \(-0.0202764\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.6095 | −0.645557 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.3048 | 0.495631 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.31507 | 0.322361 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.30476 | 0.217924 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 52.6095 | 1.81628 | 0.908141 | − | 0.418664i | \(-0.137501\pi\) | ||||
0.908141 | + | 0.418664i | \(0.137501\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.9555 | 0.963983 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.4306i | 0.462575i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.3151 | −0.354849 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 16.3129i | − | 0.560517i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 3.68257i | − | 0.126386i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −73.7602 | −2.52847 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.6508 | 0.775547 | 0.387774 | − | 0.921755i | \(-0.373244\pi\) | ||||
0.387774 | + | 0.921755i | \(0.373244\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.31507 | − | 0.616577i | −0.147572 | − | 0.0210865i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.01604i | 0.171345i | 0.996323 | + | 0.0856723i | \(0.0273038\pi\) | ||||
−0.996323 | + | 0.0856723i | \(0.972696\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.9360i | 1.36260i | 0.732004 | + | 0.681300i | \(0.238585\pi\) | ||||
−0.732004 | + | 0.681300i | \(0.761415\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.69524 | 0.125933 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.11989 | 0.174283 | 0.0871415 | − | 0.996196i | \(-0.472227\pi\) | ||||
0.0871415 | + | 0.996196i | \(0.472227\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 7.67025i | − | 0.260796i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.01031 | 0.204121 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.65547i | 0.0561578i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.62168i | − | 0.0549487i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 19.0569i | − | 0.644977i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.63858i | 0.0553940i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.5728i | 1.53888i | 0.638716 | + | 0.769442i | \(0.279466\pi\) | ||||
−0.638716 | + | 0.769442i | \(0.720534\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.04857i | 0.204013i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.76033 | 0.227761 | 0.113881 | − | 0.993494i | \(-0.463672\pi\) | ||||
0.113881 | + | 0.993494i | \(0.463672\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 28.8883i | − | 0.972169i | −0.873912 | − | 0.486085i | \(-0.838425\pi\) | ||
0.873912 | − | 0.486085i | \(-0.161575\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.63014 | −0.222870 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −49.7602 | −1.67078 | −0.835392 | − | 0.549654i | \(-0.814760\pi\) | ||||
−0.835392 | + | 0.549654i | \(0.814760\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 23.3497i | − | 0.783122i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1.02200i | − | 0.0342382i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.22936 | − | 29.5988i | 0.141530 | − | 0.990488i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13.2603 | −0.442748 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.44346i | 0.214901i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 26.8274i | − | 0.893751i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.9349 | −0.497002 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.59830i | 0.285817i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.5309 | 0.582103 | 0.291052 | − | 0.956707i | \(-0.405995\pi\) | ||||
0.291052 | + | 0.956707i | \(0.405995\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.6095 | 0.351896 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.6714 | 0.353558 | 0.176779 | − | 0.984251i | \(-0.443432\pi\) | ||||
0.176779 | + | 0.984251i | \(0.443432\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.3596 | −0.342851 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.30476 | −0.142311 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23.3357 | 0.770612 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 32.9805i | − | 1.08793i | −0.839109 | − | 0.543963i | \(-0.816923\pi\) | ||
0.839109 | − | 0.543963i | \(-0.183077\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.6301 | −0.745688 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.8640i | 0.357592i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.11457i | 0.299685i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.6301 | 0.349140 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −57.7808 | −1.89573 | −0.947864 | − | 0.318675i | \(-0.896762\pi\) | ||||
−0.947864 | + | 0.318675i | \(0.896762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.6198 | + | 2.66057i | 0.610240 | + | 0.0871968i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 30.0043i | 0.982296i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.38800i | 0.110799i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.3492 | −0.436101 | −0.218050 | − | 0.975938i | \(-0.569970\pi\) | ||||
−0.218050 | + | 0.975938i | \(0.569970\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.8801 | −0.746664 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 51.0882i | − | 1.66543i | −0.553703 | − | 0.832714i | \(-0.686786\pi\) | ||
0.553703 | − | 0.832714i | \(-0.313214\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.2500 | 0.594301 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 1.63858i | − | 0.0533029i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.4509i | 1.57444i | 0.616670 | + | 0.787222i | \(0.288481\pi\) | ||||
−0.616670 | + | 0.787222i | \(0.711519\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 26.6268i | − | 0.864343i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.9680i | 0.647507i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.9319i | 0.872410i | 0.899847 | + | 0.436205i | \(0.143678\pi\) | ||||
−0.899847 | + | 0.436205i | \(0.856322\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 20.4843i | − | 0.662856i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.04448 | 0.0337633 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 29.9040i | − | 0.965649i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.75003 | 0.282259 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.64045 | −0.246210 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.7032i | 0.408930i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.9002i | 0.672106i | 0.941843 | + | 0.336053i | \(0.109092\pi\) | ||||
−0.941843 | + | 0.336053i | \(0.890908\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.3048 | − | 2.04400i | −0.459535 | − | 0.0656626i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.7602 | 0.826685 | 0.413343 | − | 0.910576i | \(-0.364361\pi\) | ||||
0.413343 | + | 0.910576i | \(0.364361\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.39048 | −0.236928 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.63858i | 0.0524764i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 24.2777i | − | 0.776712i | −0.921509 | − | 0.388356i | \(-0.873043\pi\) | ||
0.921509 | − | 0.388356i | \(-0.126957\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.33569 | 0.170529 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.4623i | 0.621383i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.6643 | −0.786669 | −0.393335 | − | 0.919395i | \(-0.628679\pi\) | ||||
−0.393335 | + | 0.919395i | \(0.628679\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.3151 | −0.487979 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.2397 | 0.357762 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −73.7602 | −2.34544 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.3699 | 0.615304 | 0.307652 | − | 0.951499i | \(-0.400457\pi\) | ||||
0.307652 | + | 0.951499i | \(0.400457\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.9452 | −0.632942 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 18.2291i | − | 0.577902i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.2294 | 0.450648 | 0.225324 | − | 0.974284i | \(-0.427656\pi\) | ||||
0.225324 | + | 0.974284i | \(0.427656\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 9.11457i | − | 0.288372i |
(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 | 4560.2.d.e.2431.3 | ✓ | 6 | |
4.3 | odd | 2 | 4560.2.d.g.2431.4 | yes | 6 | ||
19.18 | odd | 2 | 4560.2.d.g.2431.3 | yes | 6 | ||
76.75 | even | 2 | inner | 4560.2.d.e.2431.4 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4560.2.d.e.2431.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
4560.2.d.e.2431.4 | yes | 6 | 76.75 | even | 2 | inner | |
4560.2.d.g.2431.3 | yes | 6 | 19.18 | odd | 2 | ||
4560.2.d.g.2431.4 | yes | 6 | 4.3 | odd | 2 |