Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1960,2,Mod(361,1960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1960.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1960.q (of order \(3\), degree \(2\), not 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: | \(15.6506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.21913473024.16 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 11x^{6} - 2x^{5} + 51x^{4} + 162x^{2} + 112x + 196 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 961.4 | ||
Root | \(-0.939980 - 1.62809i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1960.961 |
Dual form | 1960.2.q.x.361.4 |
$q$-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 \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).
\(n\) | \(981\) | \(1081\) | \(1177\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.939980 | + | 1.62809i | 0.542698 | + | 0.939980i | 0.998748 | + | 0.0500262i | \(0.0159305\pi\) |
−0.456050 | + | 0.889954i | \(0.650736\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.267126 | + | 0.462676i | −0.0890421 | + | 0.154225i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.64709 | + | 2.85284i | 0.496615 | + | 0.860163i | 0.999992 | − | 0.00390371i | \(-0.00124259\pi\) |
−0.503377 | + | 0.864067i | \(0.667909\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.19292 | 1.16291 | 0.581453 | − | 0.813580i | \(-0.302484\pi\) | ||||
0.581453 | + | 0.813580i | \(0.302484\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.87996 | −0.485404 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.718686 | + | 1.24480i | 0.174307 | + | 0.301908i | 0.939921 | − | 0.341392i | \(-0.110898\pi\) |
−0.765614 | + | 0.643300i | \(0.777565\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.622226 | + | 1.07773i | −0.142748 | + | 0.247248i | −0.928531 | − | 0.371256i | \(-0.878927\pi\) |
0.785782 | + | 0.618503i | \(0.212261\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.136414 | − | 0.236276i | 0.0284443 | − | 0.0492670i | −0.851453 | − | 0.524431i | \(-0.824278\pi\) |
0.879897 | + | 0.475164i | \(0.157611\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.63551 | 0.892104 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.36268 | −0.438739 | −0.219369 | − | 0.975642i | \(-0.570400\pi\) | ||||
−0.219369 | + | 0.975642i | \(0.570400\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.86359 | + | 3.22783i | 0.334710 | + | 0.579735i | 0.983429 | − | 0.181293i | \(-0.0580283\pi\) |
−0.648719 | + | 0.761028i | \(0.724695\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.09646 | + | 5.36323i | −0.539024 | + | 0.933618i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.0848805 | + | 0.147017i | −0.0139543 | + | 0.0241695i | −0.872918 | − | 0.487867i | \(-0.837775\pi\) |
0.858964 | + | 0.512036i | \(0.171109\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.94126 | + | 6.82647i | 0.631107 | + | 1.09311i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.6630 | 1.82146 | 0.910730 | − | 0.413001i | \(-0.135520\pi\) | ||||
0.910730 | + | 0.413001i | \(0.135520\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.1458 | −1.54721 | −0.773607 | − | 0.633666i | \(-0.781549\pi\) | ||||
−0.773607 | + | 0.633666i | \(0.781549\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.267126 | − | 0.462676i | −0.0398208 | − | 0.0689717i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.56221 | + | 2.70582i | −0.227871 | + | 0.394685i | −0.957177 | − | 0.289503i | \(-0.906510\pi\) |
0.729306 | + | 0.684188i | \(0.239843\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.35110 | + | 2.34018i | −0.189192 | + | 0.327690i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.62351 | − | 8.00815i | −0.635088 | − | 1.10000i | −0.986497 | − | 0.163782i | \(-0.947631\pi\) |
0.351409 | − | 0.936222i | \(-0.385703\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.29417 | −0.444186 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.33952 | −0.309877 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.53553 | − | 7.85578i | −0.590476 | − | 1.02273i | −0.994168 | − | 0.107840i | \(-0.965607\pi\) |
0.403692 | − | 0.914895i | \(-0.367727\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.63551 | + | 6.29689i | −0.465479 | + | 0.806234i | −0.999223 | − | 0.0394127i | \(-0.987451\pi\) |
0.533744 | + | 0.845646i | \(0.320785\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.09646 | + | 3.63117i | −0.260034 | + | 0.450392i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.57197 | + | 11.3830i | 0.802894 | + | 1.39065i | 0.917703 | + | 0.397266i | \(0.130041\pi\) |
−0.114809 | + | 0.993388i | \(0.536626\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.512907 | 0.0617467 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.87474 | 0.815882 | 0.407941 | − | 0.913008i | \(-0.366247\pi\) | ||||
0.407941 | + | 0.913008i | \(0.366247\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.62479 | + | 13.2065i | 0.892414 | + | 1.54571i | 0.836973 | + | 0.547244i | \(0.184323\pi\) |
0.0554412 | + | 0.998462i | \(0.482343\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.939980 | − | 1.62809i | 0.108540 | − | 0.187996i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.47551 | + | 12.9480i | −0.841061 | + | 1.45676i | 0.0479374 | + | 0.998850i | \(0.484735\pi\) |
−0.888998 | + | 0.457910i | \(0.848598\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.15867 | + | 8.93507i | 0.573185 | + | 0.992786i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.167199 | 0.0183524 | 0.00917622 | − | 0.999958i | \(-0.497079\pi\) | ||||
0.00917622 | + | 0.999958i | \(0.497079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.43737 | −0.155905 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.22087 | − | 3.84666i | −0.238103 | − | 0.412406i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.54935 | + | 2.68355i | −0.164230 | + | 0.284455i | −0.936382 | − | 0.350983i | \(-0.885847\pi\) |
0.772151 | + | 0.635439i | \(0.219181\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.50347 | + | 6.06819i | −0.363293 | + | 0.629241i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.622226 | − | 1.07773i | −0.0638391 | − | 0.110573i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.60894 | 0.671037 | 0.335518 | − | 0.942034i | \(-0.391089\pi\) | ||||
0.335518 | + | 0.942034i | \(0.391089\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.75992 | −0.176879 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.41859 | − | 16.3135i | −0.937185 | − | 1.62325i | −0.770691 | − | 0.637209i | \(-0.780089\pi\) |
−0.166493 | − | 0.986043i | \(-0.553244\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.733780 | − | 1.27094i | 0.0723014 | − | 0.125230i | −0.827608 | − | 0.561306i | \(-0.810299\pi\) |
0.899910 | + | 0.436077i | \(0.143632\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.78127 | + | 11.7455i | −0.655570 | + | 1.13548i | 0.326181 | + | 0.945307i | \(0.394238\pi\) |
−0.981751 | + | 0.190173i | \(0.939095\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.40701 | − | 12.8293i | −0.709463 | − | 1.22883i | −0.965057 | − | 0.262041i | \(-0.915604\pi\) |
0.255594 | − | 0.966784i | \(-0.417729\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.319144 | −0.0302918 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.1903 | −1.24084 | −0.620418 | − | 0.784271i | \(-0.713037\pi\) | ||||
−0.620418 | + | 0.784271i | \(0.713037\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.136414 | + | 0.236276i | 0.0127207 | + | 0.0220329i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.12004 | + | 1.93996i | −0.103548 | + | 0.179350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.0742075 | − | 0.128531i | 0.00674614 | − | 0.0116847i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.9630 | + | 18.9885i | 0.988503 | + | 1.71214i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.86118 | 0.608831 | 0.304416 | − | 0.952539i | \(-0.401539\pi\) | ||||
0.304416 | + | 0.952539i | \(0.401539\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.53682 | − | 16.5182i | −0.839670 | − | 1.45435i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.172854 | − | 0.299392i | 0.0151023 | − | 0.0261580i | −0.858375 | − | 0.513022i | \(-0.828526\pi\) |
0.873478 | + | 0.486864i | \(0.161859\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.31775 | + | 4.01447i | −0.199481 | + | 0.345510i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.65685 | − | 9.79796i | −0.483298 | − | 0.837096i | 0.516518 | − | 0.856276i | \(-0.327228\pi\) |
−0.999816 | + | 0.0191800i | \(0.993894\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.68885 | 0.228066 | 0.114033 | − | 0.993477i | \(-0.463623\pi\) | ||||
0.114033 | + | 0.993477i | \(0.463623\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.87377 | −0.494661 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.90610 | + | 11.9617i | 0.577517 | + | 1.00029i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.18134 | − | 2.04614i | 0.0981049 | − | 0.169923i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.56700 | + | 11.3744i | −0.537990 | + | 0.931826i | 0.461022 | + | 0.887389i | \(0.347483\pi\) |
−0.999012 | + | 0.0444372i | \(0.985851\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.50570 | − | 2.60795i | −0.122532 | − | 0.212232i | 0.798233 | − | 0.602348i | \(-0.205768\pi\) |
−0.920766 | + | 0.390116i | \(0.872435\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.767920 | −0.0620826 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.72717 | −0.299374 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.73155 | − | 16.8555i | −0.776662 | − | 1.34522i | −0.933856 | − | 0.357650i | \(-0.883578\pi\) |
0.157194 | − | 0.987568i | \(-0.449755\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.69201 | − | 15.0550i | 0.689321 | − | 1.19394i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.74611 | + | 11.6846i | −0.528396 | + | 0.915209i | 0.471056 | + | 0.882103i | \(0.343873\pi\) |
−0.999452 | + | 0.0331054i | \(0.989460\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.09646 | − | 5.36323i | −0.241059 | − | 0.417527i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.3011 | 0.951889 | 0.475944 | − | 0.879475i | \(-0.342106\pi\) | ||||
0.475944 | + | 0.879475i | \(0.342106\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.58057 | 0.352351 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.332426 | − | 0.575779i | −0.0254213 | − | 0.0440309i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.24487 | + | 2.15619i | −0.0946461 | + | 0.163932i | −0.909461 | − | 0.415790i | \(-0.863505\pi\) |
0.814815 | + | 0.579721i | \(0.196839\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.52663 | − | 14.7685i | 0.640900 | − | 1.11007i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.56700 | − | 13.1064i | −0.565584 | − | 0.979621i | −0.996995 | − | 0.0774652i | \(-0.975317\pi\) |
0.431411 | − | 0.902156i | \(-0.358016\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0637 | 0.822357 | 0.411179 | − | 0.911555i | \(-0.365117\pi\) | ||||
0.411179 | + | 0.911555i | \(0.365117\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.6692 | −1.01046 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0848805 | − | 0.147017i | −0.00624054 | − | 0.0108089i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.36748 | + | 4.10059i | −0.173127 | + | 0.299865i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.2258 | − | 19.4437i | 0.812274 | − | 1.40690i | −0.0989957 | − | 0.995088i | \(-0.531563\pi\) |
0.911269 | − | 0.411811i | \(-0.135104\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.55741 | − | 2.69751i | −0.112105 | − | 0.194171i | 0.804514 | − | 0.593934i | \(-0.202426\pi\) |
−0.916619 | + | 0.399763i | \(0.869093\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.88252 | −0.564479 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.38765 | 0.0988659 | 0.0494330 | − | 0.998777i | \(-0.484259\pi\) | ||||
0.0494330 | + | 0.998777i | \(0.484259\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.206732 | + | 0.358070i | 0.0146548 | + | 0.0253829i | 0.873260 | − | 0.487255i | \(-0.162002\pi\) |
−0.858605 | + | 0.512638i | \(0.828668\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.3551 | + | 21.3996i | −0.871458 | + | 1.50941i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.83152 | + | 10.1005i | −0.407291 | + | 0.705449i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.0728797 | + | 0.126231i | 0.00506549 | + | 0.00877368i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.09944 | −0.283564 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.6203 | 1.69493 | 0.847464 | − | 0.530853i | \(-0.178128\pi\) | ||||
0.847464 | + | 0.530853i | \(0.178128\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.46212 | + | 11.1927i | 0.442777 | + | 0.766913i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.07288 | − | 8.78649i | 0.345968 | − | 0.599233i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.3343 | + | 24.8277i | −0.968622 | + | 1.67770i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.01339 | + | 5.21935i | 0.202703 | + | 0.351091i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.9065 | −1.19911 | −0.599555 | − | 0.800334i | \(-0.704656\pi\) | ||||
−0.599555 | + | 0.800334i | \(0.704656\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.534253 | 0.0356168 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.27428 | + | 10.8674i | 0.416439 | + | 0.721293i | 0.995578 | − | 0.0939352i | \(-0.0299447\pi\) |
−0.579139 | + | 0.815229i | \(0.696611\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.91768 | − | 13.7138i | 0.523215 | − | 0.906235i | −0.476420 | − | 0.879218i | \(-0.658066\pi\) |
0.999635 | − | 0.0270173i | \(-0.00860092\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.6896 | − | 20.2470i | 0.765811 | − | 1.32642i | −0.174005 | − | 0.984745i | \(-0.555671\pi\) |
0.939817 | − | 0.341680i | \(-0.110996\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.56221 | − | 2.70582i | −0.101907 | − | 0.176508i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −28.1073 | −1.82577 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.9135 | 1.35278 | 0.676390 | − | 0.736544i | \(-0.263544\pi\) | ||||
0.676390 | + | 0.736544i | \(0.263544\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.67873 | + | 2.90765i | 0.108137 | + | 0.187298i | 0.915015 | − | 0.403419i | \(-0.132178\pi\) |
−0.806879 | + | 0.590717i | \(0.798845\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.74483 | + | 4.75418i | −0.176081 | + | 0.304981i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.60894 | + | 4.51882i | −0.166003 | + | 0.287526i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.157163 | + | 0.272215i | 0.00995983 | + | 0.0172509i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.5717 | 1.04600 | 0.522999 | − | 0.852333i | \(-0.324813\pi\) | ||||
0.522999 | + | 0.852333i | \(0.324813\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.898744 | 0.0565036 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.35110 | − | 2.34018i | −0.0846092 | − | 0.146547i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.57069 | + | 11.3808i | −0.409869 | + | 0.709913i | −0.994875 | − | 0.101116i | \(-0.967759\pi\) |
0.585006 | + | 0.811029i | \(0.301092\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.631134 | − | 1.09316i | 0.0390662 | − | 0.0676647i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.87740 | + | 3.25175i | 0.115765 | + | 0.200511i | 0.918085 | − | 0.396383i | \(-0.129735\pi\) |
−0.802320 | + | 0.596894i | \(0.796401\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.24701 | 0.568040 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.82542 | −0.356510 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.24761 | − | 14.2853i | −0.502866 | − | 0.870989i | −0.999995 | − | 0.00331226i | \(-0.998946\pi\) |
0.497129 | − | 0.867677i | \(-0.334388\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.2710 | − | 19.5220i | 0.684665 | − | 1.18588i | −0.288876 | − | 0.957366i | \(-0.593282\pi\) |
0.973542 | − | 0.228509i | \(-0.0733850\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.64709 | − | 2.85284i | 0.0993231 | − | 0.172033i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.49909 | + | 12.9888i | 0.450577 | + | 0.780422i | 0.998422 | − | 0.0561578i | \(-0.0178850\pi\) |
−0.547845 | + | 0.836580i | \(0.684552\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.99125 | −0.119213 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.0283 | −1.67203 | −0.836014 | − | 0.548709i | \(-0.815120\pi\) | ||||
−0.836014 | + | 0.548709i | \(0.815120\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.0857 | + | 22.6652i | 0.777866 | + | 1.34730i | 0.933169 | + | 0.359437i | \(0.117031\pi\) |
−0.155303 | + | 0.987867i | \(0.549635\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.16976 | − | 2.02609i | 0.0692907 | − | 0.120015i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.46698 | − | 12.9332i | 0.439234 | − | 0.760776i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.21228 | + | 10.7600i | 0.364170 | + | 0.630761i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.6061 | 0.911716 | 0.455858 | − | 0.890052i | \(-0.349332\pi\) | ||||
0.455858 | + | 0.890052i | \(0.349332\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.07107 | 0.528138 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.63509 | + | 13.2244i | 0.443033 | + | 0.767355i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.571974 | − | 0.990688i | 0.0330781 | − | 0.0572929i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.7066 | − | 30.6687i | 1.01722 | − | 1.76187i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.63551 | − | 6.29689i | −0.208169 | − | 0.360559i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.3055 | 1.21597 | 0.607984 | − | 0.793949i | \(-0.291978\pi\) | ||||
0.607984 | + | 0.793949i | \(0.291978\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.75895 | 0.156951 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.43993 | + | 12.8863i | 0.421880 | + | 0.730717i | 0.996123 | − | 0.0879671i | \(-0.0280370\pi\) |
−0.574243 | + | 0.818685i | \(0.694704\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.08137 | + | 1.87298i | −0.0611224 | + | 0.105867i | −0.894967 | − | 0.446132i | \(-0.852801\pi\) |
0.833845 | + | 0.551999i | \(0.186135\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.7297 | − | 18.5844i | 0.602642 | − | 1.04381i | −0.389777 | − | 0.920909i | \(-0.627448\pi\) |
0.992419 | − | 0.122897i | \(-0.0392186\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.89154 | − | 6.74034i | −0.217884 | − | 0.377387i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −25.4970 | −1.42311 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.78874 | −0.0995282 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.09646 | − | 3.63117i | −0.116291 | − | 0.201421i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.9249 | − | 24.1186i | 0.770048 | − | 1.33376i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.83461 | − | 10.1058i | 0.320699 | − | 0.555468i | −0.659933 | − | 0.751324i | \(-0.729415\pi\) |
0.980633 | + | 0.195857i | \(0.0627488\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.0453476 | − | 0.0785444i | −0.00248504 | − | 0.00430421i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.1439 | −0.718131 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.1403 | 0.933693 | 0.466846 | − | 0.884338i | \(-0.345390\pi\) | ||||
0.466846 | + | 0.884338i | \(0.345390\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.3986 | − | 21.4750i | −0.673399 | − | 1.16636i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.13898 | + | 10.6330i | −0.332444 | + | 0.575810i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.256453 | + | 0.444190i | −0.0138070 | + | 0.0239144i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.60035 | − | 4.50394i | −0.139594 | − | 0.241784i | 0.787749 | − | 0.615996i | \(-0.211246\pi\) |
−0.927343 | + | 0.374212i | \(0.877913\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.8645 | −1.81272 | −0.906362 | − | 0.422501i | \(-0.861152\pi\) | ||||
−0.906362 | + | 0.422501i | \(0.861152\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.4363 | 1.03743 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.6226 | + | 20.1309i | 0.618606 | + | 1.07146i | 0.989740 | + | 0.142878i | \(0.0456357\pi\) |
−0.371134 | + | 0.928579i | \(0.621031\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.43737 | + | 5.95370i | −0.182437 | + | 0.315990i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.1421 | − | 17.5667i | 0.535281 | − | 0.927135i | −0.463868 | − | 0.885904i | \(-0.653539\pi\) |
0.999150 | − | 0.0412304i | \(-0.0131278\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.72567 | + | 15.1133i | 0.459246 | + | 0.795437i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.279014 | 0.0146445 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.2496 | −0.798199 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.63690 | + | 11.4954i | 0.346443 | + | 0.600057i | 0.985615 | − | 0.169007i | \(-0.0540560\pi\) |
−0.639172 | + | 0.769064i | \(0.720723\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.11551 | + | 5.39621i | −0.162187 | + | 0.280916i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.8541 | − | 30.9243i | 0.924453 | − | 1.60120i | 0.132014 | − | 0.991248i | \(-0.457856\pi\) |
0.792439 | − | 0.609951i | \(-0.208811\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.939980 | + | 1.62809i | 0.0485404 | + | 0.0840744i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.90652 | −0.510212 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.6878 | −0.651728 | −0.325864 | − | 0.945417i | \(-0.605655\pi\) | ||||
−0.325864 | + | 0.945417i | \(0.605655\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.44937 | + | 11.1706i | 0.330411 | + | 0.572289i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.2853 | + | 31.6711i | −0.934337 | + | 1.61832i | −0.158525 | + | 0.987355i | \(0.550674\pi\) |
−0.775812 | + | 0.630964i | \(0.782660\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.71020 | − | 4.69420i | 0.137767 | − | 0.238620i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.0543 | − | 26.0748i | −0.763282 | − | 1.32204i | −0.941150 | − | 0.337989i | \(-0.890253\pi\) |
0.177868 | − | 0.984054i | \(-0.443080\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.392156 | 0.0198322 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.649918 | 0.0327840 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.47551 | − | 12.9480i | −0.376134 | − | 0.651483i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.73378 | − | 6.46710i | 0.187393 | − | 0.324574i | −0.756987 | − | 0.653430i | \(-0.773330\pi\) |
0.944380 | + | 0.328855i | \(0.106663\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.86657 | − | 10.1612i | 0.292963 | − | 0.507426i | −0.681546 | − | 0.731775i | \(-0.738692\pi\) |
0.974509 | + | 0.224349i | \(0.0720255\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.81386 | + | 13.5340i | 0.389236 | + | 0.674177i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.3173 | −0.512672 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.559222 | −0.0277196 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.43006 | − | 14.6013i | −0.416840 | − | 0.721987i | 0.578780 | − | 0.815484i | \(-0.303529\pi\) |
−0.995620 | + | 0.0934964i | \(0.970196\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.6347 | − | 18.4198i | 0.524569 | − | 0.908581i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0835993 | + | 0.144798i | −0.00410373 | + | 0.00710787i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.52747 | + | 4.37771i | 0.123771 | + | 0.214377i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.3884 | −0.507507 | −0.253753 | − | 0.967269i | \(-0.581665\pi\) | ||||
−0.253753 | + | 0.967269i | \(0.581665\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7758 | 0.671393 | 0.335696 | − | 0.941970i | \(-0.391028\pi\) | ||||
0.335696 | + | 0.941970i | \(0.391028\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.834613 | − | 1.44559i | −0.0405803 | − | 0.0702871i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.718686 | − | 1.24480i | 0.0348614 | − | 0.0603817i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.9832 | + | 22.4876i | −0.626835 | + | 1.08571i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.2284 | − | 26.3764i | −0.733527 | − | 1.27051i | −0.955367 | − | 0.295422i | \(-0.904540\pi\) |
0.221840 | − | 0.975083i | \(-0.428794\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.9182 | 1.24555 | 0.622774 | − | 0.782402i | \(-0.286006\pi\) | ||||
0.622774 | + | 0.782402i | \(0.286006\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.44175 | 0.212965 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.169761 | + | 0.294035i | 0.00812077 | + | 0.0140656i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.4707 | − | 23.3320i | 0.642922 | − | 1.11357i | −0.341855 | − | 0.939753i | \(-0.611055\pi\) |
0.984777 | − | 0.173821i | \(-0.0556115\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.19292 | − | 14.1906i | 0.389257 | − | 0.674213i | −0.603093 | − | 0.797671i | \(-0.706065\pi\) |
0.992350 | + | 0.123458i | \(0.0393984\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.54935 | − | 2.68355i | −0.0734461 | − | 0.127212i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.6914 | −1.16786 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.2152 | 0.670858 | 0.335429 | − | 0.942065i | \(-0.391119\pi\) | ||||
0.335429 | + | 0.942065i | \(0.391119\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.2100 | + | 33.2728i | 0.904566 | + | 1.56675i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.83066 | − | 4.90285i | 0.132996 | − | 0.230356i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.25464 | − | 12.5654i | 0.339358 | − | 0.587785i | −0.644954 | − | 0.764221i | \(-0.723124\pi\) |
0.984312 | + | 0.176436i | \(0.0564569\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.33147 | + | 5.77028i | 0.155500 | + | 0.269334i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.8933 | −0.833374 | −0.416687 | − | 0.909050i | \(-0.636809\pi\) | ||||
−0.416687 | + | 0.909050i | \(0.636809\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.2657 | 0.709457 | 0.354729 | − | 0.934969i | \(-0.384573\pi\) | ||||
0.354729 | + | 0.934969i | \(0.384573\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.50347 | − | 6.06819i | −0.162469 | − | 0.281405i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.7746 | + | 20.3942i | −0.544863 | + | 0.943731i | 0.453752 | + | 0.891128i | \(0.350085\pi\) |
−0.998616 | + | 0.0526029i | \(0.983248\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.2949 | − | 31.6877i | 0.842986 | − | 1.46009i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.7110 | − | 28.9442i | −0.768370 | − | 1.33086i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.24445 | 0.0570994 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.94024 | 0.226198 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.32933 | − | 4.03452i | −0.106430 | − | 0.184342i | 0.807892 | − | 0.589331i | \(-0.200609\pi\) |
−0.914322 | + | 0.404989i | \(0.867275\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.355897 | + | 0.616432i | −0.0162275 | + | 0.0281069i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.30447 | + | 5.72351i | −0.150048 | + | 0.259891i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.76052 | − | 9.97751i | −0.261034 | − | 0.452124i | 0.705483 | − | 0.708727i | \(-0.250730\pi\) |
−0.966517 | + | 0.256603i | \(0.917397\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −25.3648 | −1.14704 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.2771 | −0.644317 | −0.322158 | − | 0.946686i | \(-0.604408\pi\) | ||||
−0.322158 | + | 0.946686i | \(0.604408\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.69802 | − | 2.94106i | −0.0764752 | − | 0.132459i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.879961 | − | 1.52414i | 0.0395513 | − | 0.0685049i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.4895 | + | 32.0247i | −0.827703 | + | 1.43362i | 0.0721332 | + | 0.997395i | \(0.477019\pi\) |
−0.899836 | + | 0.436228i | \(0.856314\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.5628 | + | 20.0274i | 0.516588 | + | 0.894757i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.08985 | −0.360709 | −0.180354 | − | 0.983602i | \(-0.557724\pi\) | ||||
−0.180354 | + | 0.983602i | \(0.557724\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.8372 | 0.838243 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.30564 | + | 7.45760i | 0.191220 | + | 0.331203i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.0403 | − | 24.3185i | 0.622325 | − | 1.07790i | −0.366727 | − | 0.930329i | \(-0.619522\pi\) |
0.989052 | − | 0.147569i | \(-0.0471449\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.88434 | + | 4.99581i | −0.127347 | + | 0.220571i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.733780 | + | 1.27094i | 0.0323342 | + | 0.0560045i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.2924 | −0.452658 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.68063 | −0.205457 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.29048 | + | 10.8954i | 0.275591 | + | 0.477338i | 0.970284 | − | 0.241969i | \(-0.0777931\pi\) |
−0.694693 | + | 0.719306i | \(0.744460\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.742265 | − | 1.28564i | 0.0324570 | − | 0.0562172i | −0.849341 | − | 0.527845i | \(-0.823000\pi\) |
0.881798 | + | 0.471628i | \(0.156333\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.67866 | + | 4.63958i | −0.116684 | + | 0.202103i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4628 | + | 19.8541i | 0.498382 | + | 0.863223i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.84624 | 0.210309 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 48.9022 | 2.11819 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.78127 | − | 11.7455i | −0.293180 | − | 0.507802i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.2257 | − | 24.6396i | 0.613883 | − | 1.06328i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.45673 | + | 16.3795i | −0.406577 | + | 0.704211i | −0.994504 | − | 0.104703i | \(-0.966611\pi\) |
0.587927 | + | 0.808914i | \(0.299944\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.3997 | + | 18.0127i | 0.446292 | + | 0.773000i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.8140 | 0.634563 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.4403 | −0.745693 | −0.372846 | − | 0.927893i | \(-0.621618\pi\) | ||||
−0.372846 | + | 0.927893i | \(0.621618\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.94228 | − | 3.36413i | −0.0828945 | − | 0.143577i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.47012 | − | 2.54633i | 0.0626293 | − | 0.108477i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.159572 | − | 0.276387i | 0.00677346 | − | 0.0117320i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.60532 | − | 16.6369i | −0.406990 | − | 0.704928i | 0.587560 | − | 0.809180i | \(-0.300088\pi\) |
−0.994551 | + | 0.104252i | \(0.966755\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −42.5403 | −1.79926 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.90152 | −0.375823 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.8976 | − | 29.2675i | −0.712150 | − | 1.23348i | −0.964049 | − | 0.265726i | \(-0.914388\pi\) |
0.251899 | − | 0.967754i | \(-0.418945\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.59513 | − | 11.4231i | 0.277459 | − | 0.480574i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.31818 | + | 4.01520i | −0.0971830 | + | 0.168326i | −0.910518 | − | 0.413470i | \(-0.864317\pi\) |
0.813335 | + | 0.581796i | \(0.197650\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.9341 | − | 37.9909i | −0.917912 | − | 1.58987i | −0.802581 | − | 0.596543i | \(-0.796541\pi\) |
−0.115330 | − | 0.993327i | \(-0.536793\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 42.2083 | 1.76328 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.272828 | −0.0113777 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.63878 | − | 8.03460i | −0.193115 | − | 0.334485i | 0.753166 | − | 0.657830i | \(-0.228526\pi\) |
−0.946281 | + | 0.323346i | \(0.895192\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.92787 | − | 5.07122i | 0.121678 | − | 0.210753i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.2306 | − | 26.3802i | 0.630789 | − | 1.09256i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.12004 | − | 1.93996i | −0.0463079 | − | 0.0802077i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.9971 | 1.19684 | 0.598420 | − | 0.801183i | \(-0.295796\pi\) | ||||
0.598420 | + | 0.801183i | \(0.295796\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.63829 | −0.191117 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.30436 | + | 2.25922i | 0.0536543 | + | 0.0929320i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.7614 | − | 22.1034i | 0.524047 | − | 0.907676i | −0.475561 | − | 0.879683i | \(-0.657755\pi\) |
0.999608 | − | 0.0279933i | \(-0.00891171\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.388647 | + | 0.673157i | −0.0159063 | + | 0.0275505i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.5182 | − | 26.8783i | −0.634057 | − | 1.09822i | −0.986714 | − | 0.162466i | \(-0.948055\pi\) |
0.352657 | − | 0.935752i | \(-0.385278\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.56479 | 0.145411 | 0.0727054 | − | 0.997353i | \(-0.476837\pi\) | ||||
0.0727054 | + | 0.997353i | \(0.476837\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.02219 | −0.285966 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.0742075 | + | 0.128531i | 0.00301697 | + | 0.00522554i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.36310 | − | 5.82506i | 0.136504 | − | 0.236432i | −0.789667 | − | 0.613536i | \(-0.789747\pi\) |
0.926171 | + | 0.377104i | \(0.123080\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.55021 | + | 11.3453i | −0.264993 | + | 0.458981i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.87112 | + | 17.0973i | 0.398691 | + | 0.690553i | 0.993565 | − | 0.113266i | \(-0.0361314\pi\) |
−0.594874 | + | 0.803819i | \(0.702798\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.9261 | −0.884144 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.3958 | −0.660069 | −0.330035 | − | 0.943969i | \(-0.607060\pi\) | ||||
−0.330035 | + | 0.943969i | \(0.607060\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.7755 | − | 30.7881i | −0.714458 | − | 1.23748i | −0.963168 | − | 0.268900i | \(-0.913340\pi\) |
0.248710 | − | 0.968578i | \(-0.419994\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.632349 | − | 1.09526i | 0.0253753 | − | 0.0439513i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.85340 | − | 6.67428i | −0.153890 | − | 0.266545i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.244010 | −0.00972930 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.58569 | −0.381600 | −0.190800 | − | 0.981629i | \(-0.561108\pi\) | ||||
−0.190800 | + | 0.981629i | \(0.561108\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.1426 | + | 40.0841i | 0.919834 | + | 1.59320i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.43059 | + | 5.94195i | −0.136139 | + | 0.235799i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.83643 | + | 3.18078i | −0.0726479 | + | 0.125830i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.75727 | − | 16.9001i | −0.385389 | − | 0.667513i | 0.606434 | − | 0.795134i | \(-0.292599\pi\) |
−0.991823 | + | 0.127621i | \(0.959266\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.9895 | −0.748872 | −0.374436 | − | 0.927253i | \(-0.622164\pi\) | ||||
−0.374436 | + | 0.927253i | \(0.622164\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.0736 | 0.751023 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.6285 | − | 35.7296i | −0.810989 | − | 1.40467i | −0.912172 | − | 0.409807i | \(-0.865596\pi\) |
0.101183 | − | 0.994868i | \(-0.467737\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.9408 | − | 25.8783i | 0.586479 | − | 1.01581i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.87474 | − | 17.1036i | 0.386429 | − | 0.669314i | −0.605538 | − | 0.795817i | \(-0.707042\pi\) |
0.991966 | + | 0.126503i | \(0.0403753\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.172854 | + | 0.299392i | 0.00675397 | + | 0.0116982i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.14713 | −0.317850 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.1830 | 0.396672 | 0.198336 | − | 0.980134i | \(-0.436446\pi\) | ||||
0.198336 | + | 0.980134i | \(0.436446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.39543 | + | 2.41696i | 0.0542759 | + | 0.0940087i | 0.891887 | − | 0.452259i | \(-0.149382\pi\) |
−0.837611 | + | 0.546267i | \(0.816048\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.66506 | + | 9.81217i | −0.220013 | + | 0.381073i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.322303 | + | 0.558245i | −0.0124796 | + | 0.0216153i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.8318 | − | 29.1535i | −0.650754 | − | 1.12714i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.9520 | −0.924657 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.2879 | 0.704947 | 0.352473 | − | 0.935822i | \(-0.385341\pi\) | ||||
0.352473 | + | 0.935822i | \(0.385341\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.31775 | − | 4.01447i | −0.0892104 | − | 0.154517i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.0261 | + | 20.8299i | −0.462202 | + | 0.800558i | −0.999070 | − | 0.0431084i | \(-0.986274\pi\) |
0.536868 | + | 0.843666i | \(0.319607\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.7954 | + | 20.4302i | −0.452001 | + | 0.782889i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.1100 | + | 33.0995i | 0.731224 | + | 1.26652i | 0.956360 | + | 0.292190i | \(0.0943839\pi\) |
−0.225136 | + | 0.974327i | \(0.572283\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.3137 | 0.432275 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.7699 | 1.13579 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.3860 | − | 33.5775i | −0.738547 | − | 1.27920i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.2312 | + | 22.9171i | −0.503337 | + | 0.871806i | 0.496655 | + | 0.867948i | \(0.334561\pi\) |
−0.999993 | + | 0.00385805i | \(0.998772\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.34443 | + | 2.32862i | −0.0509970 | + | 0.0883294i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.38206 | + | 14.5182i | 0.317493 | + | 0.549914i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 43.9520 | 1.66242 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.5136 | −1.30356 | −0.651780 | − | 0.758408i | \(-0.725977\pi\) | ||||
−0.651780 | + | 0.758408i | \(0.725977\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.105630 | − | 0.182956i | −0.00398390 | − | 0.00690032i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.93689 | − | 5.08684i | 0.110610 | − | 0.191581i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.20450 | + | 5.55035i | −0.120347 | + | 0.208448i | −0.919905 | − | 0.392142i | \(-0.871734\pi\) |
0.799557 | + | 0.600590i | \(0.205068\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.99381 | − | 6.91749i | −0.149780 | − | 0.259426i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.01688 | 0.0380824 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.8122 | −0.516547 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.6582 | + | 34.0491i | 0.734151 | + | 1.27159i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.3035 | + | 33.4347i | −0.719900 | + | 1.24690i | 0.241139 | + | 0.970491i | \(0.422479\pi\) |
−0.961039 | + | 0.276413i | \(0.910854\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.15595 | + | 5.46626i | −0.117371 | + | 0.203293i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.18134 | + | 2.04614i | 0.0438739 | + | 0.0759918i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.5280 | −0.835516 | −0.417758 | − | 0.908558i | \(-0.637184\pi\) | ||||
−0.417758 | + | 0.908558i | \(0.637184\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.6317 | 0.764136 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.29161 | − | 12.6294i | −0.269690 | − | 0.467117i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.75075 | − | 6.49649i | 0.138537 | − | 0.239953i | −0.788406 | − | 0.615155i | \(-0.789093\pi\) |
0.926943 | + | 0.375202i | \(0.122427\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.6492 | + | 37.4976i | −0.797460 | + | 1.38124i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.5432 | − | 30.3857i | −0.645336 | − | 1.11776i | −0.984224 | − | 0.176928i | \(-0.943384\pi\) |
0.338888 | − | 0.940827i | \(-0.389949\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.80943 | −0.360358 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.42902 | −0.0891122 | −0.0445561 | − | 0.999007i | \(-0.514187\pi\) | ||||
−0.0445561 | + | 0.999007i | \(0.514187\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.56700 | − | 11.3744i | −0.240596 | − | 0.416725i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.0446632 | + | 0.0773589i | −0.00163414 | + | 0.00283041i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.4799 | + | 18.1517i | −0.382417 | + | 0.662365i | −0.991407 | − | 0.130813i | \(-0.958241\pi\) |
0.608991 | + | 0.793177i | \(0.291575\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.5771 | + | 26.9803i | 0.567661 | + | 0.983218i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.01140 | 0.109596 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.9748 | −1.30753 | −0.653763 | − | 0.756699i | \(-0.726811\pi\) | ||||
−0.653763 | + | 0.756699i | \(0.726811\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.844802 | + | 1.46324i | 0.0306644 | + | 0.0531123i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.22876 | − | 2.12828i | 0.0445426 | − | 0.0771500i | −0.842895 | − | 0.538079i | \(-0.819150\pi\) |
0.887437 | + | 0.460929i | \(0.152484\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.383960 | − | 0.665038i | 0.0138821 | − | 0.0240445i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.0171 | − | 32.9386i | −0.686669 | − | 1.18934i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.6994 | 0.782501 | 0.391250 | − | 0.920284i | \(-0.372043\pi\) | ||||
0.391250 | + | 0.920284i | \(0.372043\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.7053 | −0.889739 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.84900 | − | 13.5949i | −0.282309 | − | 0.488973i | 0.689644 | − | 0.724149i | \(-0.257767\pi\) |
−0.971953 | + | 0.235175i | \(0.924434\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.86359 | − | 3.22783i | 0.0669420 | − | 0.115947i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.25705 | + | 12.5696i | −0.260011 | + | 0.450352i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.3233 | + | 19.6125i | 0.405180 | + | 0.701792i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.9522 | −0.391400 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.4631 | 0.694668 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.2537 | + | 21.2240i | 0.436797 | + | 0.756554i | 0.997440 | − | 0.0715029i | \(-0.0227795\pi\) |
−0.560644 | + | 0.828057i | \(0.689446\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.52944 | + | 6.11316i | −0.125651 | + | 0.217634i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.2434 | + | 26.4023i | −0.541309 | + | 0.937574i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.69201 | + | 15.0550i | 0.308274 | + | 0.533946i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.73557 | 0.203164 | 0.101582 | − | 0.994827i | \(-0.467610\pi\) | ||||
0.101582 | + | 0.994827i | \(0.467610\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.49094 | −0.158878 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.827743 | − | 1.43369i | −0.0292468 | − | 0.0506570i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.1174 | + | 43.5046i | −0.886373 | + | 1.53524i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.5052 | − | 26.8558i | 0.545808 | − | 0.945368i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.74216 | − | 3.01750i | −0.0612510 | − | 0.106090i | 0.833774 | − | 0.552106i | \(-0.186176\pi\) |
−0.895025 | + | 0.446016i | \(0.852842\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.9953 | 0.912819 | 0.456409 | − | 0.889770i | \(-0.349135\pi\) | ||||
0.456409 | + | 0.889770i | \(0.349135\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 42.3781 | 1.48627 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.74611 | − | 11.6846i | −0.236306 | − | 0.409294i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.31296 | − | 10.9344i | 0.220862 | − | 0.382545i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.2494 | − | 43.7332i | 0.881210 | − | 1.52630i | 0.0312136 | − | 0.999513i | \(-0.490063\pi\) |
0.849997 | − | 0.526788i | \(-0.176604\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.4350 | + | 38.8585i | 0.782034 | + | 1.35452i | 0.930755 | + | 0.365643i | \(0.119151\pi\) |
−0.148722 | + | 0.988879i | \(0.547516\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.19292 | 0.215610 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.7323 | −0.547066 | −0.273533 | − | 0.961863i | \(-0.588192\pi\) | ||||
−0.273533 | + | 0.961863i | \(0.588192\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.8863 | + | 44.8364i | 0.899068 | + | 1.55723i | 0.828687 | + | 0.559712i | \(0.189088\pi\) |
0.0703811 | + | 0.997520i | \(0.477578\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.0980 | + | 24.4185i | −0.489054 | + | 0.847067i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.15056 | + | 10.6531i | −0.212849 | + | 0.368665i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.63867 | + | 14.9626i | 0.298596 | + | 0.517183i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.86118 | −0.0987788 | −0.0493894 | − | 0.998780i | \(-0.515728\pi\) | ||||
−0.0493894 | + | 0.998780i | \(0.515728\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4177 | −0.807508 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26.3460 | − | 45.6327i | −0.907406 | − | 1.57167i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.29028 | + | 3.96689i | −0.0787882 | + | 0.136465i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −24.6007 | + | 42.6096i | −0.844293 | + | 1.46236i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.0231578 | + | 0.0401105i | 0.000793840 | + | 0.00137497i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.8645 | 1.57037 | 0.785185 | − | 0.619261i | \(-0.212568\pi\) | ||||
0.785185 | + | 0.619261i | \(0.212568\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.664852 | 0.0227375 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.5751 | + | 20.0486i | 0.395397 | + | 0.684847i | 0.993152 | − | 0.116832i | \(-0.0372738\pi\) |
−0.597755 | + | 0.801679i | \(0.703940\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.23192 | − | 7.32990i | 0.144391 | − | 0.250093i | −0.784754 | − | 0.619807i | \(-0.787211\pi\) |
0.929146 | + | 0.369714i | \(0.120544\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.5462 | − | 30.3908i | 0.597278 | − | 1.03452i | −0.395943 | − | 0.918275i | \(-0.629582\pi\) |
0.993221 | − | 0.116241i | \(-0.0370845\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.24487 | − | 2.15619i | −0.0423270 | − | 0.0733125i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.0753 | 0.953486 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −49.2513 | −1.67074 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.5558 | + | 47.7280i | 0.933691 | + | 1.61720i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.76542 | + | 3.05780i | −0.0597505 | + | 0.103491i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.66861 | + | 16.7465i | −0.326486 | + | 0.565490i | −0.981812 | − | 0.189856i | \(-0.939198\pi\) |
0.655326 | + | 0.755346i | \(0.272531\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.6694 | + | 25.4081i | 0.494787 | + | 0.856996i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.0573 | −1.11373 | −0.556865 | − | 0.830603i | \(-0.687996\pi\) | ||||
−0.556865 | + | 0.830603i | \(0.687996\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.6238 | −0.963267 | −0.481634 | − | 0.876373i | \(-0.659956\pi\) | ||||
−0.481634 | + | 0.876373i | \(0.659956\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.52663 | + | 14.7685i | 0.286619 | + | 0.496439i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.56444 | + | 16.5661i | −0.321142 | + | 0.556235i | −0.980724 | − | 0.195398i | \(-0.937400\pi\) |
0.659582 | + | 0.751633i | \(0.270734\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.9935 | + | 29.4337i | −0.569305 | + | 0.986066i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.94409 | − | 3.36727i | −0.0650566 | − | 0.112681i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.1340 | 0.505874 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.15058 | 0.0718057 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.40306 | − | 7.62632i | −0.146850 | − | 0.254352i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.64570 | − | 11.5107i | 0.221400 | − | 0.383477i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.53184 | + | 9.58144i | −0.183885 | + | 0.318498i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.4891 | + | 44.1483i | 0.846350 | + | 1.46592i | 0.884443 | + | 0.466648i | \(0.154538\pi\) |
−0.0380931 | + | 0.999274i | \(0.512128\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.0638 | 0.333796 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.52585 | −0.183080 | −0.0915399 | − | 0.995801i | \(-0.529179\pi\) | ||||
−0.0915399 | + | 0.995801i | \(0.529179\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.275391 | + | 0.476991i | 0.00911410 | + | 0.0157861i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.83461 | − | 11.8379i | 0.225945 | − | 0.391349i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.3163 | − | 35.1889i | 0.670173 | − | 1.16077i | −0.307681 | − | 0.951489i | \(-0.599553\pi\) |
0.977855 | − | 0.209285i | \(-0.0671136\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.0267 | + | 34.6873i | 0.659903 | + | 1.14299i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28.8252 | 0.948794 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.169761 | 0.00558171 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.392024 | + | 0.679005i | 0.0128757 | + | 0.0223015i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.79395 | − | 13.4995i | 0.255711 | − | 0.442905i | −0.709377 | − | 0.704829i | \(-0.751024\pi\) |
0.965088 | + | 0.261924i | \(0.0843570\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.9868 | + | 24.2258i | −0.457907 | + | 0.793118i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.36748 | − | 4.10059i | −0.0774247 | − | 0.134104i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.4794 | −0.669034 | −0.334517 | − | 0.942390i | \(-0.608573\pi\) | ||||
−0.334517 | + | 0.942390i | \(0.608573\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.06585 | −0.132684 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.39362 | − | 14.5382i | −0.273624 | − | 0.473931i | 0.696163 | − | 0.717884i | \(-0.254889\pi\) |
−0.969787 | + | 0.243953i | \(0.921556\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.59100 | − | 2.75570i | 0.0518102 | − | 0.0897380i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.71964 | − | 2.97850i | 0.0558807 | − | 0.0967883i | −0.836732 | − | 0.547613i | \(-0.815537\pi\) |
0.892613 | + | 0.450825i | \(0.148870\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.9701 | + | 55.3739i | 1.03779 | + | 1.79751i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 40.3430 | 1.30821 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.8610 | −0.999686 | −0.499843 | − | 0.866116i | \(-0.666609\pi\) | ||||
−0.499843 | + | 0.866116i | \(0.666609\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.2258 | + | 19.4437i | 0.363260 | + | 0.629184i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.31594 | − | 12.6716i | 0.236491 | − | 0.409614i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.55410 | − | 14.8161i | 0.275939 | − | 0.477940i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.62291 | − | 6.27507i | −0.116747 | − | 0.202211i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.11482 | 0.100270 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.3195 | −1.10364 | −0.551820 | − | 0.833964i | \(-0.686066\pi\) | ||||
−0.551820 | + | 0.833964i | \(0.686066\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.68138 | − | 2.91224i | −0.0540137 | − | 0.0935545i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.8102 | + | 27.3840i | −0.507373 | + | 0.878795i | 0.492591 | + | 0.870261i | \(0.336050\pi\) |
−0.999964 | + | 0.00853421i | \(0.997283\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.94126 | − | 6.82647i | 0.126221 | − | 0.218622i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.47268 | + | 16.4072i | 0.303058 | + | 0.524912i | 0.976827 | − | 0.214030i | \(-0.0686591\pi\) |
−0.673769 | + | 0.738942i | \(0.735326\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.2076 | −0.326237 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.91443 | 0.252688 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.60937 | − | 13.1798i | −0.242701 | − | 0.420371i | 0.718782 | − | 0.695236i | \(-0.244700\pi\) |
−0.961483 | + | 0.274865i | \(0.911367\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.693825 | + | 1.20174i | −0.0221071 | + | 0.0382906i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.38403 | + | 2.39720i | −0.0440095 | + | 0.0762266i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.6534 | − | 27.1126i | −0.497248 | − | 0.861259i | 0.502747 | − | 0.864434i | \(-0.332323\pi\) |
−0.999995 | + | 0.00317464i | \(0.998989\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.9377 | 0.696172 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.413463 | −0.0131077 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.0527 | − | 34.7323i | −0.635076 | − | 1.09998i | −0.986499 | − | 0.163767i | \(-0.947636\pi\) |
0.351424 | − | 0.936217i | \(-0.385698\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.393464 | + | 0.681500i | −0.0124487 | + | 0.0215617i |
(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 | 1960.2.q.x.961.4 | 8 | ||
7.2 | even | 3 | 1960.2.a.y.1.1 | yes | 4 | ||
7.3 | odd | 6 | 1960.2.q.y.361.1 | 8 | |||
7.4 | even | 3 | inner | 1960.2.q.x.361.4 | 8 | ||
7.5 | odd | 6 | 1960.2.a.x.1.4 | ✓ | 4 | ||
7.6 | odd | 2 | 1960.2.q.y.961.1 | 8 | |||
28.19 | even | 6 | 3920.2.a.ce.1.1 | 4 | |||
28.23 | odd | 6 | 3920.2.a.cd.1.4 | 4 | |||
35.9 | even | 6 | 9800.2.a.cl.1.4 | 4 | |||
35.19 | odd | 6 | 9800.2.a.cs.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1960.2.a.x.1.4 | ✓ | 4 | 7.5 | odd | 6 | ||
1960.2.a.y.1.1 | yes | 4 | 7.2 | even | 3 | ||
1960.2.q.x.361.4 | 8 | 7.4 | even | 3 | inner | ||
1960.2.q.x.961.4 | 8 | 1.1 | even | 1 | trivial | ||
1960.2.q.y.361.1 | 8 | 7.3 | odd | 6 | |||
1960.2.q.y.961.1 | 8 | 7.6 | odd | 2 | |||
3920.2.a.cd.1.4 | 4 | 28.23 | odd | 6 | |||
3920.2.a.ce.1.1 | 4 | 28.19 | even | 6 | |||
9800.2.a.cl.1.4 | 4 | 35.9 | even | 6 | |||
9800.2.a.cs.1.1 | 4 | 35.19 | odd | 6 |