Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,2,Mod(31,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 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("2352.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.bl (of order \(6\), 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: | \(18.7808145554\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.339738624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.3 | ||
Root | \(1.60021 - 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.31 |
Dual form | 2352.2.bl.r.607.3 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.45849 | − | 0.842061i | 0.652258 | − | 0.376581i | −0.137063 | − | 0.990562i | \(-0.543766\pi\) |
0.789321 | + | 0.613981i | \(0.210433\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.05870 | + | 1.76594i | 0.922233 | + | 0.532451i | 0.884347 | − | 0.466831i | \(-0.154604\pi\) |
0.0378860 | + | 0.999282i | \(0.487938\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.93015i | 0.812678i | 0.913722 | + | 0.406339i | \(0.133195\pi\) | ||||
−0.913722 | + | 0.406339i | \(0.866805\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.68412i | − | 0.434839i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.74192 | + | 1.00570i | 0.422478 | + | 0.243918i | 0.696137 | − | 0.717909i | \(-0.254901\pi\) |
−0.273659 | + | 0.961827i | \(0.588234\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.848820 | + | 1.47020i | 0.194733 | + | 0.337287i | 0.946813 | − | 0.321785i | \(-0.104283\pi\) |
−0.752080 | + | 0.659072i | \(0.770949\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.38435 | − | 0.799257i | 0.288658 | − | 0.166657i | −0.348679 | − | 0.937242i | \(-0.613370\pi\) |
0.637336 | + | 0.770586i | \(0.280036\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.08187 | + | 1.87385i | −0.216373 | + | 0.374769i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.94028 | 1.47447 | 0.737237 | − | 0.675635i | \(-0.236130\pi\) | ||||
0.737237 | + | 0.675635i | \(0.236130\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.47683 | + | 4.29000i | −0.444853 | + | 0.770507i | −0.998042 | − | 0.0625483i | \(-0.980077\pi\) |
0.553189 | + | 0.833056i | \(0.313411\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.05870 | − | 1.76594i | 0.532451 | − | 0.307411i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.23317 | + | 9.06412i | 0.860328 | + | 1.49013i | 0.871612 | + | 0.490196i | \(0.163075\pi\) |
−0.0112836 | + | 0.999936i | \(0.503592\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.53759 | + | 1.46508i | 0.406339 | + | 0.234600i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.86237i | 0.447027i | 0.974701 | + | 0.223514i | \(0.0717527\pi\) | ||||
−0.974701 | + | 0.223514i | \(0.928247\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.7518i | − | 1.79214i | −0.443917 | − | 0.896068i | \(-0.646411\pi\) | ||
0.443917 | − | 0.896068i | \(-0.353589\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.45849 | − | 0.842061i | −0.217419 | − | 0.125527i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.35159 | − | 5.80513i | −0.488880 | − | 0.846765i | 0.511038 | − | 0.859558i | \(-0.329261\pi\) |
−0.999918 | + | 0.0127930i | \(0.995928\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.74192 | − | 1.00570i | 0.243918 | − | 0.140826i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.46054 | + | 2.52974i | −0.200621 | + | 0.347486i | −0.948729 | − | 0.316091i | \(-0.897629\pi\) |
0.748108 | + | 0.663578i | \(0.230963\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.94812 | 0.802045 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.69764 | 0.224858 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.87766 | + | 6.71630i | −0.504828 | + | 0.874388i | 0.495156 | + | 0.868804i | \(0.335111\pi\) |
−0.999984 | + | 0.00558422i | \(0.998222\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9055 | − | 6.29627i | 1.39630 | − | 0.806155i | 0.402299 | − | 0.915508i | \(-0.368211\pi\) |
0.994003 | + | 0.109353i | \(0.0348779\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.46737 | + | 4.27361i | 0.306039 | + | 0.530076i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.47393 | + | 0.850976i | 0.180070 | + | 0.103963i | 0.587325 | − | 0.809351i | \(-0.300181\pi\) |
−0.407256 | + | 0.913314i | \(0.633514\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 1.59851i | − | 0.192438i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.13052i | 0.727558i | 0.931485 | + | 0.363779i | \(0.118514\pi\) | ||||
−0.931485 | + | 0.363779i | \(0.881486\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.10588 | − | 1.21583i | −0.246475 | − | 0.142302i | 0.371674 | − | 0.928363i | \(-0.378784\pi\) |
−0.618149 | + | 0.786061i | \(0.712117\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.08187 | + | 1.87385i | 0.124923 | + | 0.216373i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.749517 | + | 0.432734i | −0.0843272 | + | 0.0486863i | −0.541571 | − | 0.840655i | \(-0.682170\pi\) |
0.457243 | + | 0.889342i | \(0.348837\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.5319 | −1.59508 | −0.797540 | − | 0.603266i | \(-0.793866\pi\) | ||||
−0.797540 | + | 0.603266i | \(0.793866\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.38744 | 0.367419 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.97014 | − | 6.87648i | 0.425644 | − | 0.737237i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.8033 | − | 7.96936i | 1.46315 | − | 0.844751i | 0.463995 | − | 0.885838i | \(-0.346415\pi\) |
0.999156 | + | 0.0410870i | \(0.0130821\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.47683 | + | 4.29000i | 0.256836 | + | 0.444853i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.47600 | + | 1.42952i | 0.254032 | + | 0.146665i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.82270i | − | 0.997344i | −0.866791 | − | 0.498672i | \(-0.833821\pi\) | ||
0.866791 | − | 0.498672i | \(-0.166179\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.53188i | − | 0.354967i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.16458 | − | 4.71382i | −0.812406 | − | 0.469043i | 0.0353847 | − | 0.999374i | \(-0.488734\pi\) |
−0.847791 | + | 0.530331i | \(0.822068\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.83133 | − | 13.5643i | −0.771644 | − | 1.33653i | −0.936662 | − | 0.350236i | \(-0.886102\pi\) |
0.165018 | − | 0.986291i | \(-0.447232\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.4365 | − | 9.48961i | 1.58898 | − | 0.917395i | 0.595499 | − | 0.803356i | \(-0.296954\pi\) |
0.993476 | − | 0.114039i | \(-0.0363790\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.27950 | + | 9.14437i | −0.505685 | + | 0.875872i | 0.494294 | + | 0.869295i | \(0.335427\pi\) |
−0.999978 | + | 0.00657678i | \(0.997907\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.4663 | 0.993422 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.4530 | 1.45369 | 0.726846 | − | 0.686800i | \(-0.240985\pi\) | ||||
0.726846 | + | 0.686800i | \(0.240985\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.34605 | − | 2.33142i | 0.125520 | − | 0.217406i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.53759 | − | 1.46508i | 0.234600 | − | 0.135446i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.737095 | + | 1.27669i | 0.0670086 | + | 0.116062i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.47889 | + | 1.43119i | 0.223514 | + | 0.129046i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0646i | 1.07909i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.16478i | − | 0.192094i | −0.995377 | − | 0.0960468i | \(-0.969380\pi\) | ||
0.995377 | − | 0.0960468i | \(-0.0306198\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.1774 | − | 5.87591i | −0.896068 | − | 0.517345i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.66096 | − | 13.2692i | −0.669341 | − | 1.15933i | −0.978089 | − | 0.208189i | \(-0.933243\pi\) |
0.308748 | − | 0.951144i | \(-0.400090\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.45849 | + | 0.842061i | −0.125527 | + | 0.0724731i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.43068 | + | 11.1383i | −0.549410 | + | 0.951607i | 0.448905 | + | 0.893580i | \(0.351814\pi\) |
−0.998315 | + | 0.0580272i | \(0.981519\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.743971 | 0.0631028 | 0.0315514 | − | 0.999502i | \(-0.489955\pi\) | ||||
0.0315514 | + | 0.999502i | \(0.489955\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.70319 | −0.564510 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.17447 | + | 8.96245i | −0.432711 | + | 0.749478i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.5808 | − | 6.68620i | 0.961737 | − | 0.555259i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.65131 | + | 6.32425i | 0.299127 | + | 0.518103i | 0.975936 | − | 0.218055i | \(-0.0699713\pi\) |
−0.676810 | + | 0.736158i | \(0.736638\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.44161 | + | 3.14172i | 0.442832 | + | 0.255669i | 0.704798 | − | 0.709408i | \(-0.251038\pi\) |
−0.261966 | + | 0.965077i | \(0.584371\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.01140i | − | 0.162612i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.34259i | 0.670093i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.71761 | − | 4.45576i | −0.615932 | − | 0.355608i | 0.159352 | − | 0.987222i | \(-0.449060\pi\) |
−0.775283 | + | 0.631613i | \(0.782393\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.46054 | + | 2.52974i | 0.115829 | + | 0.200621i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.209698 | + | 0.121069i | −0.0164248 | + | 0.00948287i | −0.508190 | − | 0.861245i | \(-0.669685\pi\) |
0.491765 | + | 0.870728i | \(0.336352\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.97406 | − | 5.15123i | 0.231530 | − | 0.401022i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.82817 | 0.450997 | 0.225499 | − | 0.974243i | \(-0.427599\pi\) | ||||
0.225499 | + | 0.974243i | \(0.427599\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.41421 | 0.339555 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.848820 | − | 1.47020i | 0.0649109 | − | 0.112429i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.5436 | + | 8.39673i | −1.10573 | + | 0.638392i | −0.937719 | − | 0.347394i | \(-0.887067\pi\) |
−0.168008 | + | 0.985786i | \(0.553733\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.87766 | + | 6.71630i | 0.291463 | + | 0.504828i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.3943 | − | 10.6199i | −1.37485 | − | 0.793771i | −0.383317 | − | 0.923617i | \(-0.625218\pi\) |
−0.991534 | + | 0.129846i | \(0.958552\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.74444i | − | 0.203993i | −0.994785 | − | 0.101996i | \(-0.967477\pi\) | ||
0.994785 | − | 0.101996i | \(-0.0325230\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 12.5925i | − | 0.930868i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.2651 | + | 8.81331i | 1.12231 | + | 0.647967i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.55201 | + | 6.15225i | 0.259748 | + | 0.449897i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.39364 | − | 0.804618i | 0.100840 | − | 0.0582201i | −0.448732 | − | 0.893666i | \(-0.648124\pi\) |
0.549572 | + | 0.835446i | \(0.314791\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00555 | + | 3.47371i | −0.144362 | + | 0.250043i | −0.929135 | − | 0.369741i | \(-0.879446\pi\) |
0.784773 | + | 0.619784i | \(0.212780\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.93473 | 0.353384 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.7413 | 0.836534 | 0.418267 | − | 0.908324i | \(-0.362638\pi\) | ||||
0.418267 | + | 0.908324i | \(0.362638\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.68015 | − | 15.0345i | 0.615319 | − | 1.06576i | −0.375009 | − | 0.927021i | \(-0.622360\pi\) |
0.990328 | − | 0.138743i | \(-0.0443063\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.47393 | − | 0.850976i | 0.103963 | − | 0.0600232i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.41029 | + | 4.17475i | 0.168342 | + | 0.291577i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.38435 | − | 0.799257i | −0.0962192 | − | 0.0555522i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.99586i | 0.414743i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 24.1172i | − | 1.66030i | −0.557543 | − | 0.830148i | \(-0.688256\pi\) | ||
0.557543 | − | 0.830148i | \(-0.311744\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.30918 | + | 3.06526i | 0.363779 | + | 0.210028i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.89576 | − | 17.1400i | −0.674885 | − | 1.16893i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.10588 | + | 1.21583i | −0.142302 | + | 0.0821582i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.94685 | + | 5.10409i | −0.198226 | + | 0.343338i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.1154 | 1.34702 | 0.673512 | − | 0.739176i | \(-0.264785\pi\) | ||||
0.673512 | + | 0.739176i | \(0.264785\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.16373 | 0.144249 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.79465 | + | 15.2328i | −0.583721 | + | 1.01103i | 0.411312 | + | 0.911494i | \(0.365071\pi\) |
−0.995034 | + | 0.0995403i | \(0.968263\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.45722 | − | 1.99602i | 0.228459 | − | 0.131901i | −0.381402 | − | 0.924409i | \(-0.624559\pi\) |
0.609861 | + | 0.792508i | \(0.291225\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.63484 | − | 2.83162i | −0.107102 | − | 0.185506i | 0.807493 | − | 0.589877i | \(-0.200824\pi\) |
−0.914595 | + | 0.404371i | \(0.867490\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.77655 | − | 5.64449i | −0.637752 | − | 0.368206i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.865467i | 0.0562181i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.9127i | 1.87021i | 0.354371 | + | 0.935105i | \(0.384695\pi\) | ||||
−0.354371 | + | 0.935105i | \(0.615305\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.29374 | − | 3.05634i | −0.341000 | − | 0.196876i | 0.319714 | − | 0.947514i | \(-0.396413\pi\) |
−0.660714 | + | 0.750638i | \(0.729746\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.30791 | + | 2.48717i | −0.274105 | + | 0.158255i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.26593 | + | 12.5850i | −0.460460 | + | 0.797540i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.7471 | −1.75138 | −0.875691 | − | 0.482872i | \(-0.839594\pi\) | ||||
−0.875691 | + | 0.482872i | \(0.839594\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.64576 | 0.354946 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.69372 | − | 2.93361i | 0.106065 | − | 0.183710i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.47889 | + | 1.43119i | −0.154629 | + | 0.0892749i | −0.575318 | − | 0.817930i | \(-0.695122\pi\) |
0.420689 | + | 0.907205i | \(0.361788\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.97014 | − | 6.87648i | −0.245746 | − | 0.425644i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.8466 | + | 9.72639i | 1.03881 | + | 0.599755i | 0.919495 | − | 0.393102i | \(-0.128598\pi\) |
0.119311 | + | 0.992857i | \(0.461931\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.91947i | 0.302201i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 15.9387i | − | 0.975434i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.4480 | + | 8.34156i | 0.880910 | + | 0.508594i | 0.870959 | − | 0.491357i | \(-0.163499\pi\) |
0.00995197 | + | 0.999950i | \(0.496832\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.95283 | + | 17.2388i | 0.604591 | + | 1.04718i | 0.992116 | + | 0.125324i | \(0.0399969\pi\) |
−0.387525 | + | 0.921859i | \(0.626670\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.61820 | + | 3.82102i | −0.399092 | + | 0.230416i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.16373 | − | 12.4079i | 0.430427 | − | 0.745521i | −0.566483 | − | 0.824073i | \(-0.691696\pi\) |
0.996910 | + | 0.0785522i | \(0.0250297\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.95367 | 0.296568 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.5450 | 0.986992 | 0.493496 | − | 0.869748i | \(-0.335719\pi\) | ||||
0.493496 | + | 0.869748i | \(0.335719\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.9295 | − | 25.8587i | 0.887469 | − | 1.53714i | 0.0446112 | − | 0.999004i | \(-0.485795\pi\) |
0.842858 | − | 0.538137i | \(-0.180872\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.47600 | − | 1.42952i | 0.146665 | − | 0.0846773i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.47714 | − | 11.2187i | −0.381009 | − | 0.659926i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.50671 | − | 4.91135i | −0.498672 | − | 0.287908i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6.40183i | − | 0.373999i | −0.982360 | − | 0.187000i | \(-0.940124\pi\) | ||
0.982360 | − | 0.187000i | \(-0.0598763\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.0609i | 0.760436i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.05870 | − | 1.76594i | −0.177484 | − | 0.102470i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.34194 | + | 4.05637i | 0.135438 | + | 0.234586i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.16458 | + | 4.71382i | −0.469043 | + | 0.270802i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.6037 | − | 18.3661i | 0.607166 | − | 1.05164i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.6511 | −0.664961 | −0.332480 | − | 0.943110i | \(-0.607886\pi\) | ||||
−0.332480 | + | 0.943110i | \(0.607886\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.6627 | −0.891017 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.5386 | + | 19.9855i | −0.654295 | + | 1.13327i | 0.327775 | + | 0.944756i | \(0.393701\pi\) |
−0.982070 | + | 0.188516i | \(0.939632\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.4738 | + | 12.9752i | −1.27029 | + | 0.733404i | −0.975043 | − | 0.222017i | \(-0.928736\pi\) |
−0.295249 | + | 0.955420i | \(0.595403\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.2715 | − | 17.7907i | −0.576904 | − | 0.999227i | −0.995832 | − | 0.0912073i | \(-0.970927\pi\) |
0.418928 | − | 0.908019i | \(-0.362406\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.2869 | + | 14.0221i | 1.35981 | + | 0.785085i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 18.9792i | − | 1.05932i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.41462i | 0.189995i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.49065 | − | 3.17003i | −0.304566 | − | 0.175842i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.27950 | + | 9.14437i | 0.291957 | + | 0.505685i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.3851 | − | 16.3882i | 1.56019 | − | 0.900775i | 0.562951 | − | 0.826490i | \(-0.309666\pi\) |
0.997237 | − | 0.0742851i | \(-0.0236675\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.23317 | − | 9.06412i | 0.286776 | − | 0.496711i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.86630 | 0.156602 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.2791 | −1.81283 | −0.906414 | − | 0.422391i | \(-0.861191\pi\) | ||||
−0.906414 | + | 0.422391i | \(0.861191\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.72648 | − | 13.3827i | 0.419645 | − | 0.726846i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.1518 | + | 8.74789i | −0.820515 | + | 0.473725i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.34605 | − | 2.33142i | −0.0724687 | − | 0.125520i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.36516 | − | 4.82963i | −0.449065 | − | 0.259268i | 0.258370 | − | 0.966046i | \(-0.416815\pi\) |
−0.707435 | + | 0.706778i | \(0.750148\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.9525i | 0.639802i | 0.947451 | + | 0.319901i | \(0.103650\pi\) | ||||
−0.947451 | + | 0.319901i | \(0.896350\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2.93015i | − | 0.156400i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.1916 | + | 6.46148i | 0.595669 | + | 0.343910i | 0.767336 | − | 0.641245i | \(-0.221582\pi\) |
−0.171667 | + | 0.985155i | \(0.554915\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.16227 | + | 8.94132i | 0.273985 | + | 0.474556i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.58077 | + | 5.53146i | −0.505654 | + | 0.291939i | −0.731045 | − | 0.682329i | \(-0.760967\pi\) |
0.225392 | + | 0.974268i | \(0.427634\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.05901 | − | 13.9586i | 0.424158 | − | 0.734664i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.47419 | 0.0773749 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.09522 | −0.214353 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.94438 | + | 10.2960i | −0.310294 | + | 0.537445i | −0.978426 | − | 0.206598i | \(-0.933761\pi\) |
0.668132 | + | 0.744043i | \(0.267094\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.47889 | − | 1.43119i | 0.129046 | − | 0.0745045i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.76290 | + | 8.24959i | 0.246614 | + | 0.427148i | 0.962584 | − | 0.270983i | \(-0.0873487\pi\) |
−0.715970 | + | 0.698131i | \(0.754015\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.4483 | + | 6.03230i | 0.539545 | + | 0.311507i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.2662i | 1.19827i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.52128i | 0.232243i | 0.993235 | + | 0.116121i | \(0.0370461\pi\) | ||||
−0.993235 | + | 0.116121i | \(0.962954\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.87476 | − | 1.08239i | −0.0960468 | − | 0.0554526i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.17157 | − | 2.02922i | −0.0598646 | − | 0.103688i | 0.834540 | − | 0.550947i | \(-0.185734\pi\) |
−0.894404 | + | 0.447259i | \(0.852400\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.1774 | + | 5.87591i | −0.517345 | + | 0.298689i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.04905 | + | 15.6734i | −0.458805 | + | 0.794674i | −0.998898 | − | 0.0469316i | \(-0.985056\pi\) |
0.540093 | + | 0.841605i | \(0.318389\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.21524 | 0.162602 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.3219 | −0.772888 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.728777 | + | 1.26228i | −0.0366687 | + | 0.0635121i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.43793 | − | 1.40754i | 0.122356 | − | 0.0706425i | −0.437573 | − | 0.899183i | \(-0.644162\pi\) |
0.559929 | + | 0.828541i | \(0.310828\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.04121 | − | 5.26753i | −0.151871 | − | 0.263048i | 0.780044 | − | 0.625724i | \(-0.215196\pi\) |
−0.931915 | + | 0.362676i | \(0.881863\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.5704 | − | 7.25750i | −0.626174 | − | 0.361522i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.68412i | 0.0836847i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 36.9659i | 1.83233i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.28566 | − | 4.20638i | −0.360253 | − | 0.207992i | 0.308939 | − | 0.951082i | \(-0.400026\pi\) |
−0.669192 | + | 0.743090i | \(0.733359\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.43068 | + | 11.1383i | 0.317202 | + | 0.549410i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.1946 | + | 12.2367i | −1.04040 | + | 0.600677i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.371985 | − | 0.644298i | 0.0182162 | − | 0.0315514i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.6496 | −0.911094 | −0.455547 | − | 0.890212i | \(-0.650556\pi\) | ||||
−0.455547 | + | 0.890212i | \(0.650556\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.6274 | −1.10279 | −0.551396 | − | 0.834243i | \(-0.685905\pi\) | ||||
−0.551396 | + | 0.834243i | \(0.685905\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.35159 | + | 5.80513i | −0.162960 | + | 0.282255i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.76904 | + | 2.17606i | −0.182825 | + | 0.105554i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.17447 | + | 8.96245i | 0.249826 | + | 0.432711i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.7759 | − | 7.95352i | −0.663561 | − | 0.383107i | 0.130071 | − | 0.991505i | \(-0.458479\pi\) |
−0.793633 | + | 0.608397i | \(0.791813\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 14.4650i | − | 0.695146i | −0.937653 | − | 0.347573i | \(-0.887006\pi\) | ||
0.937653 | − | 0.347573i | \(-0.112994\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 13.3724i | − | 0.641158i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.35013 | + | 1.35685i | 0.112422 | + | 0.0649070i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.8981 | + | 18.8760i | 0.520136 | + | 0.900901i | 0.999726 | + | 0.0234089i | \(0.00745195\pi\) |
−0.479590 | + | 0.877493i | \(0.659215\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.2743 | − | 5.93187i | 0.488147 | − | 0.281832i | −0.235658 | − | 0.971836i | \(-0.575725\pi\) |
0.723805 | + | 0.690004i | \(0.242391\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.4214 | − | 23.2465i | 0.636235 | − | 1.10199i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.30262 | 0.345402 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.6472 | −1.82388 | −0.911938 | − | 0.410329i | \(-0.865414\pi\) | ||||
−0.911938 | + | 0.410329i | \(0.865414\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.05478 | + | 8.75513i | −0.238020 | + | 0.412263i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.44161 | − | 3.14172i | 0.255669 | − | 0.147611i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.47189 | − | 16.4058i | −0.443076 | − | 0.767431i | 0.554840 | − | 0.831957i | \(-0.312780\pi\) |
−0.997916 | + | 0.0645264i | \(0.979446\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.74192 | − | 1.00570i | −0.0813058 | − | 0.0469419i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 24.5269i | − | 1.14233i | −0.820834 | − | 0.571167i | \(-0.806491\pi\) | ||
0.820834 | − | 0.571167i | \(-0.193509\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7.59791i | − | 0.353105i | −0.984291 | − | 0.176552i | \(-0.943505\pi\) | ||
0.984291 | − | 0.176552i | \(-0.0564945\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.22489 | + | 4.17129i | 0.335046 | + | 0.193439i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.50941 | + | 9.54258i | 0.254945 | + | 0.441578i | 0.964881 | − | 0.262689i | \(-0.0846092\pi\) |
−0.709935 | + | 0.704267i | \(0.751276\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.71761 | + | 4.45576i | −0.355608 | + | 0.205311i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.7530 | − | 35.9453i | 0.954225 | − | 1.65277i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.67323 | −0.168540 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.92109 | 0.133747 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.1014 | + | 31.3525i | −0.827073 | + | 1.43253i | 0.0732525 | + | 0.997313i | \(0.476662\pi\) |
−0.900325 | + | 0.435218i | \(0.856671\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.5593 | + | 15.3340i | −1.21100 | + | 0.699170i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.27131 | − | 14.3263i | −0.375581 | − | 0.650525i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.0792 | + | 8.70596i | 0.683302 | + | 0.394505i | 0.801098 | − | 0.598533i | \(-0.204249\pi\) |
−0.117796 | + | 0.993038i | \(0.537583\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.242138i | 0.0109499i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.5154i | 0.970977i | 0.874243 | + | 0.485489i | \(0.161358\pi\) | ||||
−0.874243 | + | 0.485489i | \(0.838642\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.8313 | + | 7.98552i | 0.622932 | + | 0.359650i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.97406 | − | 5.15123i | −0.133674 | − | 0.231530i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.5566 | + | 18.2192i | −1.41267 | + | 0.815604i | −0.995639 | − | 0.0932893i | \(-0.970262\pi\) |
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.91409 | − | 5.04734i | 0.130192 | − | 0.225499i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.5840 | −1.76496 | −0.882482 | − | 0.470347i | \(-0.844129\pi\) | ||||
−0.882482 | + | 0.470347i | \(0.844129\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.8773 | −0.706531 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.20711 | − | 3.82282i | 0.0980211 | − | 0.169777i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.4632 | + | 17.5879i | −1.35026 | + | 0.779572i | −0.988285 | − | 0.152617i | \(-0.951230\pi\) |
−0.361972 | + | 0.932189i | \(0.617896\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.848820 | − | 1.47020i | −0.0374763 | − | 0.0649109i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22.8439 | − | 13.1889i | −1.00662 | − | 0.581173i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 23.6749i | − | 1.04122i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.7935i | 0.737151i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.9510 | + | 9.78669i | 0.742638 | + | 0.428762i | 0.823028 | − | 0.568001i | \(-0.192283\pi\) |
−0.0803894 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.33120 | + | 7.50186i | 0.189390 | + | 0.328033i | 0.945047 | − | 0.326934i | \(-0.106016\pi\) |
−0.755657 | + | 0.654968i | \(0.772682\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.62889 | + | 4.98189i | −0.375880 | + | 0.217015i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.2224 | + | 17.7057i | −0.444451 | + | 0.769812i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.75532 | 0.336552 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.38718 | −0.363289 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.9817 | − | 27.6811i | 0.690948 | − | 1.19676i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.3943 | + | 10.6199i | −0.793771 | + | 0.458284i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.5453 | − | 21.7290i | −0.539363 | − | 0.934204i | −0.998938 | − | 0.0460651i | \(-0.985332\pi\) |
0.459576 | − | 0.888139i | \(-0.348001\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.37676 | − | 1.37222i | −0.101996 | − | 0.0588876i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.7827i | 0.761726i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 0.523032i | − | 0.0223632i | −0.999937 | − | 0.0111816i | \(-0.996441\pi\) | ||
0.999937 | − | 0.0111816i | \(-0.00355929\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.9055 | − | 6.29627i | −0.465434 | − | 0.268718i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.73987 | + | 11.6738i | 0.287128 | + | 0.497320i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.2651 | − | 8.81331i | 0.647967 | − | 0.374104i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.0670 | + | 19.1685i | −0.468922 | + | 0.812197i | −0.999369 | − | 0.0355210i | \(-0.988691\pi\) |
0.530447 | + | 0.847718i | \(0.322024\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.4346 | 1.45643 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.10401 | 0.299932 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.30382 | − | 9.18648i | 0.223529 | − | 0.387164i | −0.732348 | − | 0.680931i | \(-0.761575\pi\) |
0.955877 | + | 0.293767i | \(0.0949088\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.5380 | − | 13.0123i | 0.948182 | − | 0.547433i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.19939 | − | 9.00561i | −0.217970 | − | 0.377535i | 0.736217 | − | 0.676745i | \(-0.236610\pi\) |
−0.954187 | + | 0.299210i | \(0.903277\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.4912 | − | 10.6759i | −0.773832 | − | 0.446772i | 0.0604077 | − | 0.998174i | \(-0.480760\pi\) |
−0.834240 | + | 0.551402i | \(0.814093\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1.60924i | − | 0.0672268i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.45875i | 0.144240i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.798556 | + | 0.461047i | 0.0332443 | + | 0.0191936i | 0.516530 | − | 0.856269i | \(-0.327223\pi\) |
−0.483286 | + | 0.875463i | \(0.660557\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.00555 | + | 3.47371i | 0.0833476 | + | 0.144362i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.93473 | + | 5.15847i | −0.370039 | + | 0.213642i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.46737 | − | 4.27361i | 0.102013 | − | 0.176692i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.11149 | −0.376071 | −0.188036 | − | 0.982162i | \(-0.560212\pi\) | ||||
−0.188036 | + | 0.982162i | \(0.560212\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.40955 | −0.346509 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.87066 | − | 10.1683i | 0.241486 | − | 0.418267i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.5720 | + | 6.10377i | −0.434142 | + | 0.250652i | −0.701110 | − | 0.713054i | \(-0.747312\pi\) |
0.266968 | + | 0.963705i | \(0.413978\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.68015 | − | 15.0345i | −0.355255 | − | 0.615319i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.4985 | + | 17.6083i | 1.24614 | + | 0.719457i | 0.970337 | − | 0.241758i | \(-0.0777241\pi\) |
0.275800 | + | 0.961215i | \(0.411057\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 30.6430i | − | 1.24995i | −0.780644 | − | 0.624976i | \(-0.785109\pi\) | ||
0.780644 | − | 0.624976i | \(-0.214891\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.70195i | − | 0.0693088i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.15010 | + | 1.24136i | 0.0874138 | + | 0.0504684i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.98251 | − | 8.62996i | −0.202234 | − | 0.350279i | 0.747014 | − | 0.664808i | \(-0.231487\pi\) |
−0.949248 | + | 0.314529i | \(0.898153\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.0099 | − | 9.82067i | 0.688147 | − | 0.397302i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.56293 | − | 13.0994i | 0.305464 | − | 0.529079i | −0.671901 | − | 0.740641i | \(-0.734522\pi\) |
0.977365 | + | 0.211562i | \(0.0678551\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.82058 | 0.194385 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.7055 | 0.471245 | 0.235622 | − | 0.971845i | \(-0.424287\pi\) | ||||
0.235622 | + | 0.971845i | \(0.424287\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.63382 | − | 6.29396i | 0.146055 | − | 0.252975i | −0.783711 | − | 0.621126i | \(-0.786676\pi\) |
0.929766 | + | 0.368150i | \(0.120009\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.38435 | + | 0.799257i | −0.0555522 | + | 0.0320731i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.74981 | + | 8.22691i | 0.189992 | + | 0.329077i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.19257 | + | 2.99793i | 0.207371 | + | 0.119726i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.0520i | 0.839397i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.40366i | 0.0558789i | 0.999610 | + | 0.0279395i | \(0.00889456\pi\) | ||||
−0.999610 | + | 0.0279395i | \(0.991105\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.8861 | − | 12.0586i | −0.830148 | − | 0.479286i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.82288 | − | 3.15732i | −0.0723388 | − | 0.125295i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.30918 | − | 3.06526i | 0.210028 | − | 0.121260i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.6136 | − | 28.7756i | 0.656198 | − | 1.13657i | −0.325394 | − | 0.945579i | \(-0.605497\pi\) |
0.981592 | − | 0.190990i | \(-0.0611697\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −46.2604 | −1.82433 | −0.912166 | − | 0.409820i | \(-0.865591\pi\) | ||||
−0.912166 | + | 0.409820i | \(0.865591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −19.7915 | −0.779290 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.3166 | − | 29.9932i | 0.680786 | − | 1.17916i | −0.293955 | − | 0.955819i | \(-0.594972\pi\) |
0.974741 | − | 0.223337i | \(-0.0716950\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.7212 | + | 13.6954i | −0.931138 | + | 0.537593i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.11432 | − | 7.12620i | −0.161006 | − | 0.278870i | 0.774224 | − | 0.632912i | \(-0.218140\pi\) |
−0.935230 | + | 0.354042i | \(0.884807\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.3469 | − | 12.9020i | −0.873166 | − | 0.504123i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.43166i | 0.0948681i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 10.9381i | − | 0.426087i | −0.977043 | − | 0.213044i | \(-0.931662\pi\) | ||
0.977043 | − | 0.213044i | \(-0.0683376\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.8198 | + | 12.5977i | 0.848692 | + | 0.489993i | 0.860209 | − | 0.509941i | \(-0.170333\pi\) |
−0.0115171 | + | 0.999934i | \(0.503666\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.94685 | + | 5.10409i | 0.114446 | + | 0.198226i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.9922 | − | 6.34632i | 0.425618 | − | 0.245731i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.0577 | − | 17.4204i | 0.388852 | − | 0.673512i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 44.4754 | 1.71695 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.5831 | 0.446497 | 0.223248 | − | 0.974762i | \(-0.428334\pi\) | ||||
0.223248 | + | 0.974762i | \(0.428334\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.08187 | − | 1.87385i | 0.0416410 | − | 0.0721243i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.1066 | + | 17.3820i | −1.15709 | + | 0.668046i | −0.950605 | − | 0.310404i | \(-0.899536\pi\) |
−0.206485 | + | 0.978450i | \(0.566202\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.79465 | + | 15.2328i | 0.337012 | + | 0.583721i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.1924 | − | 5.88459i | −0.390002 | − | 0.225167i | 0.292159 | − | 0.956370i | \(-0.405626\pi\) |
−0.682161 | + | 0.731202i | \(0.738960\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.6601i | 0.827591i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 3.99205i | − | 0.152306i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.41251 | − | 4.27962i | −0.282394 | − | 0.163040i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.65157 | + | 9.78880i | 0.214996 | + | 0.372383i | 0.953271 | − | 0.302116i | \(-0.0976929\pi\) |
−0.738276 | + | 0.674499i | \(0.764360\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.08508 | − | 0.626469i | 0.0411593 | − | 0.0237633i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.87868 | + | 4.98602i | −0.109038 | + | 0.188859i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.26967 | −0.123670 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.9265 | 0.941462 | 0.470731 | − | 0.882277i | \(-0.343990\pi\) | ||||
0.470731 | + | 0.882277i | \(0.343990\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.88404 | + | 15.3876i | −0.335068 | + | 0.580355i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.77655 | + | 5.64449i | −0.368206 | + | 0.212584i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.1190 | − | 38.3113i | −0.830697 | − | 1.43881i | −0.897486 | − | 0.441043i | \(-0.854609\pi\) |
0.0667887 | − | 0.997767i | \(-0.478725\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.749517 | + | 0.432734i | 0.0281091 | + | 0.0162288i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.91851i | 0.296551i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.4289i | 0.651804i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.0392 | + | 14.4564i | 0.935105 | + | 0.539883i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.70319 | − | 4.68205i | −0.100812 | − | 0.174611i | 0.811208 | − | 0.584758i | \(-0.198811\pi\) |
−0.912019 | + | 0.410147i | \(0.865477\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.29374 | + | 3.05634i | −0.196876 | + | 0.113667i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.59031 | + | 14.8789i | −0.319036 | + | 0.552587i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.5459 | 1.35541 | 0.677706 | − | 0.735333i | \(-0.262974\pi\) | ||||
0.677706 | + | 0.735333i | \(0.262974\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.8188 | − | 20.4707i | 0.437133 | − | 0.757137i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.6637 | + | 13.6622i | −0.874038 | + | 0.504626i | −0.868688 | − | 0.495359i | \(-0.835036\pi\) |
−0.00535017 | + | 0.999986i | \(0.501703\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.00555 | + | 5.20576i | 0.110711 | + | 0.191757i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.4043 | − | 8.89369i | −0.566657 | − | 0.327160i | 0.189156 | − | 0.981947i | \(-0.439425\pi\) |
−0.755813 | + | 0.654787i | \(0.772758\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.97434i | 0.182737i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.1701i | 1.10683i | 0.832904 | + | 0.553417i | \(0.186676\pi\) | ||||
−0.832904 | + | 0.553417i | \(0.813324\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.6508 | + | 6.14925i | 0.390216 | + | 0.225291i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.26593 | + | 12.5850i | 0.265847 | + | 0.460460i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.2330 | + | 21.4965i | −1.35865 | + | 0.784418i | −0.989442 | − | 0.144928i | \(-0.953705\pi\) |
−0.369210 | + | 0.929346i | \(0.620372\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.8736 | + | 24.0297i | −0.505581 | + | 0.875691i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.5821 | 0.385121 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.2021 | −0.479839 | −0.239919 | − | 0.970793i | \(-0.577121\pi\) | ||||
−0.239919 | + | 0.970793i | \(0.577121\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.82288 | − | 4.88937i | 0.102464 | − | 0.177473i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.7032 | − | 9.06624i | 0.569240 | − | 0.328651i | −0.187605 | − | 0.982244i | \(-0.560073\pi\) |
0.756846 | + | 0.653593i | \(0.226739\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.69372 | − | 2.93361i | −0.0612365 | − | 0.106065i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.6798 | − | 11.3621i | −0.710596 | − | 0.410263i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.0980i | 1.62628i | 0.582070 | + | 0.813139i | \(0.302243\pi\) | ||||
−0.582070 | + | 0.813139i | \(0.697757\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.86237i | 0.103086i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.2176 | − | 18.0235i | −1.12282 | − | 0.648259i | −0.180699 | − | 0.983538i | \(-0.557836\pi\) |
−0.942119 | + | 0.335279i | \(0.891169\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.35920 | − | 9.28241i | −0.192508 | − | 0.333434i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.20826 | + | 2.42964i | −0.150776 | + | 0.0870508i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.8261 | + | 18.7514i | −0.387389 | + | 0.670978i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.94028 | −0.283762 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.0081 | −0.535662 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.1922 | + | 22.8496i | −0.470251 | + | 0.814499i | −0.999421 | − | 0.0340166i | \(-0.989170\pi\) |
0.529170 | + | 0.848516i | \(0.322503\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.8466 | − | 9.72639i | 0.599755 | − | 0.346269i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.4490 | + | 31.9547i | 0.655145 | + | 1.13474i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.26039 | + | 2.45974i | 0.151100 | + | 0.0872379i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 52.8839i | − | 1.87324i | −0.350344 | − | 0.936621i | \(-0.613935\pi\) | ||
0.350344 | − | 0.936621i | \(-0.386065\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 13.4828i | − | 0.476986i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.8033 | − | 7.96936i | −0.487717 | − | 0.281584i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.29417 | − | 7.43772i | −0.151538 | − | 0.262471i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.4480 | − | 8.34156i | 0.508594 | − | 0.293637i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.08508 | + | 14.0038i | −0.284256 | + | 0.492346i | −0.972429 | − | 0.233201i | \(-0.925080\pi\) |
0.688172 | + | 0.725547i | \(0.258413\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.18532 | 0.146967 | 0.0734833 | − | 0.997296i | \(-0.476588\pi\) | ||||
0.0734833 | + | 0.997296i | \(0.476588\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.9057 | 0.698122 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.203895 | + | 0.353157i | −0.00714214 | + | 0.0123706i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.2775 | − | 9.97518i | 0.604464 | − | 0.348987i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.44860 | + | 4.24110i | 0.0854567 | + | 0.148015i | 0.905586 | − | 0.424163i | \(-0.139432\pi\) |
−0.820129 | + | 0.572179i | \(0.806098\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.62077 | − | 3.24515i | −0.195928 | − | 0.113119i | 0.398827 | − | 0.917026i | \(-0.369417\pi\) |
−0.594755 | + | 0.803907i | \(0.702751\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.64204i | 0.266062i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 18.8437i | − | 0.655258i | −0.944806 | − | 0.327629i | \(-0.893750\pi\) | ||
0.944806 | − | 0.327629i | \(-0.106250\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.6919 | + | 7.90504i | 0.475540 | + | 0.274553i | 0.718556 | − | 0.695469i | \(-0.244803\pi\) |
−0.243016 | + | 0.970022i | \(0.578137\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.16373 | − | 12.4079i | −0.248507 | − | 0.430427i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.50035 | − | 4.90768i | 0.294167 | − | 0.169837i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.47683 | − | 4.29000i | 0.0856119 | − | 0.148284i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.1313 | 0.867629 | 0.433814 | − | 0.901002i | \(-0.357167\pi\) | ||||
0.433814 | + | 0.901002i | \(0.357167\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.0481 | 1.17407 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.27250 | − | 14.3284i | 0.284920 | − | 0.493496i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.43810 | − | 3.71704i | 0.221477 | − | 0.127870i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.9295 | − | 25.8587i | −0.512380 | − | 0.887469i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.4891 | + | 8.36530i | 0.496681 | + | 0.286759i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 31.5399i | − | 1.07991i | −0.841695 | − | 0.539953i | \(-0.818442\pi\) | ||
0.841695 | − | 0.539953i | \(-0.181558\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 2.85903i | − | 0.0977769i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.5514 | + | 14.1748i | 0.838660 | + | 0.484201i | 0.856809 | − | 0.515635i | \(-0.172444\pi\) |
−0.0181483 | + | 0.999835i | \(0.505777\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.3399 | − | 30.0336i | −0.591630 | − | 1.02473i | −0.994013 | − | 0.109262i | \(-0.965151\pi\) |
0.402383 | − | 0.915471i | \(-0.368182\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.0002 | + | 9.23770i | −0.544652 | + | 0.314455i | −0.746962 | − | 0.664867i | \(-0.768488\pi\) |
0.202310 | + | 0.979321i | \(0.435155\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.1411 | + | 24.4932i | −0.480813 | + | 0.832792i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.9543 | −0.439951 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.05673 | −0.103692 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.49349 | + | 4.31885i | −0.0844886 | + | 0.146339i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.50671 | + | 4.91135i | −0.287908 | + | 0.166224i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.4892 | + | 37.2204i | 0.725639 | + | 1.25684i | 0.958711 | + | 0.284384i | \(0.0917890\pi\) |
−0.233072 | + | 0.972460i | \(0.574878\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.54415 | − | 3.20092i | −0.187000 | − | 0.107964i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 4.50973i | − | 0.151937i | −0.997110 | − | 0.0759684i | \(-0.975795\pi\) | ||
0.997110 | − | 0.0759684i | \(-0.0242048\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 42.8824i | − | 1.44311i | −0.692359 | − | 0.721553i | \(-0.743429\pi\) | ||
0.692359 | − | 0.721553i | \(-0.256571\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.3111 | + | 6.53046i | 0.380218 | + | 0.219519i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.37863 | − | 4.11990i | −0.0798665 | − | 0.138333i | 0.823326 | − | 0.567569i | \(-0.192116\pi\) |
−0.903192 | + | 0.429236i | \(0.858783\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.05870 | + | 1.76594i | −0.102470 | + | 0.0591612i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.68980 | − | 9.85502i | 0.190402 | − | 0.329786i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −35.7705 | −1.19568 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.68389 | 0.156390 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.6668 | + | 34.0638i | −0.655923 | + | 1.13609i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.08830 | + | 2.93773i | −0.169516 | + | 0.0978701i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.31099 | − | 4.00275i | −0.0768199 | − | 0.133056i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.6921 | + | 7.90513i | 0.454639 | + | 0.262486i | 0.709787 | − | 0.704416i | \(-0.248791\pi\) |
−0.255149 | + | 0.966902i | \(0.582124\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.42764i | 0.312695i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 15.5236i | − | 0.514320i | −0.966369 | − | 0.257160i | \(-0.917213\pi\) | ||
0.966369 | − | 0.257160i | \(-0.0827868\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −44.4486 | − | 25.6624i | −1.47103 | − | 0.849302i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.6037 | − | 18.3661i | −0.350548 | − | 0.607166i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.6854 | − | 29.2632i | 1.67196 | − | 0.965304i | 0.705413 | − | 0.708796i | \(-0.250761\pi\) |
0.966542 | − | 0.256508i | \(-0.0825719\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.82553 | + | 10.0901i | −0.191958 | + | 0.332480i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.9633 | −0.591271 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.6464 | −0.744607 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.83133 | + | 13.5643i | −0.257215 | + | 0.445509i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46.0423 | − | 26.5825i | 1.51060 | − | 0.872144i | 0.510674 | − | 0.859774i | \(-0.329396\pi\) |
0.999923 | − | 0.0123696i | \(-0.00393746\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.5386 | + | 19.9855i | 0.377757 | + | 0.654295i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.3612 | + | 5.98201i | 0.338846 | + | 0.195633i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 17.0577i | − | 0.557250i | −0.960400 | − | 0.278625i | \(-0.910121\pi\) | ||
0.960400 | − | 0.278625i | \(-0.0898787\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.9505i | 0.846861i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.2306 | − | 8.21605i | −0.463905 | − | 0.267836i | 0.249780 | − | 0.968303i | \(-0.419642\pi\) |
−0.713685 | + | 0.700467i | \(0.752975\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.28777 | + | 3.96253i | 0.0745000 | + | 0.129038i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.3879 | + | 12.9256i | −0.727508 | + | 0.420027i | −0.817510 | − | 0.575915i | \(-0.804646\pi\) |
0.0900020 | + | 0.995942i | \(0.471313\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.56257 | − | 6.17055i | 0.115646 | − | 0.200304i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.5430 | −0.666151 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.79848 | −0.123045 | −0.0615224 | − | 0.998106i | \(-0.519596\pi\) | ||||
−0.0615224 | + | 0.998106i | \(0.519596\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.35508 | − | 2.34706i | 0.0438492 | − | 0.0759491i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24.2869 | − | 14.0221i | 0.785085 | − | 0.453269i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.23058 | + | 5.59553i | 0.104212 | + | 0.180501i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.4365 | − | 9.48961i | −0.529658 | − | 0.305798i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.75517i | 0.217457i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.7285i | 0.666582i | 0.942824 | + | 0.333291i | \(0.108159\pi\) | ||||
−0.942824 | + | 0.333291i | \(0.891841\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.95715 | + | 1.70731i | 0.0949974 | + | 0.0548468i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.7594 | + | 34.2243i | 0.634110 | + | 1.09831i | 0.986703 | + | 0.162534i | \(0.0519667\pi\) |
−0.352593 | + | 0.935777i | \(0.614700\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.49065 | + | 3.17003i | −0.175842 | + | 0.101522i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.5617 | − | 18.2935i | 0.337900 | − | 0.585259i | −0.646138 | − | 0.763221i | \(-0.723617\pi\) |
0.984037 | + | 0.177961i | \(0.0569502\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 56.2937 | 1.79915 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.5590 | 0.337123 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.9788 | − | 39.8004i | 0.732909 | − | 1.26944i | −0.222726 | − | 0.974881i | \(-0.571495\pi\) |
0.955635 | − | 0.294554i | \(-0.0951712\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.1246 | − | 9.88690i | 0.545636 | − | 0.315023i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.39273 | − | 16.2687i | −0.298671 | − | 0.517314i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.40626 | − | 1.96661i | −0.108204 | − | 0.0624714i | 0.444922 | − | 0.895570i | \(-0.353232\pi\) |
−0.553125 | + | 0.833098i | \(0.686565\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 32.7763i | − | 1.04013i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 29.2369i | − | 0.926871i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.27071 | − | 5.35244i | −0.293606 | − | 0.169514i | 0.345961 | − | 0.938249i | \(-0.387553\pi\) |
−0.639567 | + | 0.768735i | \(0.720886\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.23317 | − | 9.06412i | −0.165570 | − | 0.286776i |
(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 | 2352.2.bl.r.31.3 | 8 | ||
4.3 | odd | 2 | 2352.2.bl.q.31.3 | 8 | |||
7.2 | even | 3 | 2352.2.bl.t.607.2 | 8 | |||
7.3 | odd | 6 | 2352.2.b.l.1567.3 | yes | 8 | ||
7.4 | even | 3 | 2352.2.b.k.1567.6 | yes | 8 | ||
7.5 | odd | 6 | 2352.2.bl.q.607.3 | 8 | |||
7.6 | odd | 2 | 2352.2.bl.o.31.2 | 8 | |||
21.11 | odd | 6 | 7056.2.b.x.1567.3 | 8 | |||
21.17 | even | 6 | 7056.2.b.w.1567.6 | 8 | |||
28.3 | even | 6 | 2352.2.b.k.1567.3 | ✓ | 8 | ||
28.11 | odd | 6 | 2352.2.b.l.1567.6 | yes | 8 | ||
28.19 | even | 6 | inner | 2352.2.bl.r.607.3 | 8 | ||
28.23 | odd | 6 | 2352.2.bl.o.607.2 | 8 | |||
28.27 | even | 2 | 2352.2.bl.t.31.2 | 8 | |||
84.11 | even | 6 | 7056.2.b.w.1567.3 | 8 | |||
84.59 | odd | 6 | 7056.2.b.x.1567.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2352.2.b.k.1567.3 | ✓ | 8 | 28.3 | even | 6 | ||
2352.2.b.k.1567.6 | yes | 8 | 7.4 | even | 3 | ||
2352.2.b.l.1567.3 | yes | 8 | 7.3 | odd | 6 | ||
2352.2.b.l.1567.6 | yes | 8 | 28.11 | odd | 6 | ||
2352.2.bl.o.31.2 | 8 | 7.6 | odd | 2 | |||
2352.2.bl.o.607.2 | 8 | 28.23 | odd | 6 | |||
2352.2.bl.q.31.3 | 8 | 4.3 | odd | 2 | |||
2352.2.bl.q.607.3 | 8 | 7.5 | odd | 6 | |||
2352.2.bl.r.31.3 | 8 | 1.1 | even | 1 | trivial | ||
2352.2.bl.r.607.3 | 8 | 28.19 | even | 6 | inner | ||
2352.2.bl.t.31.2 | 8 | 28.27 | even | 2 | |||
2352.2.bl.t.607.2 | 8 | 7.2 | even | 3 | |||
7056.2.b.w.1567.3 | 8 | 84.11 | even | 6 | |||
7056.2.b.w.1567.6 | 8 | 21.17 | even | 6 | |||
7056.2.b.x.1567.3 | 8 | 21.11 | odd | 6 | |||
7056.2.b.x.1567.6 | 8 | 84.59 | odd | 6 |