Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(121,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.i (of order \(3\), degree \(2\), 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: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 9x^{6} + 2x^{5} + 65x^{4} - 20x^{3} + 25x^{2} + 6x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.4 | ||
Root | \(-1.26041 - 2.18309i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 380.121 |
Dual form | 380.2.i.c.201.4 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.26041 | + | 2.18309i | 0.727698 | + | 1.26041i | 0.957854 | + | 0.287256i | \(0.0927431\pi\) |
−0.230156 | + | 0.973154i | \(0.573924\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.72743 | 1.03087 | 0.515435 | − | 0.856928i | \(-0.327630\pi\) | ||||
0.515435 | + | 0.856928i | \(0.327630\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.67727 | + | 2.90511i | −0.559089 | + | 0.968370i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.31421 | 0.999273 | 0.499636 | − | 0.866235i | \(-0.333467\pi\) | ||||
0.499636 | + | 0.866235i | \(0.333467\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.62412 | + | 2.81306i | −0.450451 | + | 0.780204i | −0.998414 | − | 0.0562987i | \(-0.982070\pi\) |
0.547963 | + | 0.836502i | \(0.315403\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.26041 | − | 2.18309i | 0.325436 | − | 0.563672i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.17727 | + | 2.03909i | 0.285529 | + | 0.494551i | 0.972737 | − | 0.231910i | \(-0.0744974\pi\) |
−0.687208 | + | 0.726460i | \(0.741164\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.11494 | − | 3.04912i | −0.714617 | − | 0.699516i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.43768 | + | 5.95423i | 0.750163 | + | 1.29932i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.07396 | + | 1.86016i | −0.223937 | + | 0.387870i | −0.956000 | − | 0.293367i | \(-0.905224\pi\) |
0.732063 | + | 0.681237i | \(0.238558\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.893714 | −0.171995 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.96702 | − | 3.40697i | 0.365266 | − | 0.632659i | −0.623553 | − | 0.781781i | \(-0.714311\pi\) |
0.988819 | + | 0.149122i | \(0.0476447\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.1896 | −1.83010 | −0.915050 | − | 0.403340i | \(-0.867849\pi\) | ||||
−0.915050 | + | 0.403340i | \(0.867849\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.17727 | + | 7.23524i | 0.727169 | + | 1.25949i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.36371 | − | 2.36202i | −0.230510 | − | 0.399254i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.68579 | −0.605940 | −0.302970 | − | 0.953000i | \(-0.597978\pi\) | ||||
−0.302970 | + | 0.953000i | \(0.597978\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.18825 | −1.31117 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.363714 | + | 0.629971i | 0.0568025 | + | 0.0983849i | 0.893028 | − | 0.450000i | \(-0.148576\pi\) |
−0.836226 | + | 0.548385i | \(0.815243\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.18645 | + | 2.05499i | 0.180931 | + | 0.313383i | 0.942198 | − | 0.335057i | \(-0.108755\pi\) |
−0.761267 | + | 0.648439i | \(0.775422\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.35453 | 0.500064 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.51164 | − | 9.54644i | 0.803955 | − | 1.39249i | −0.113039 | − | 0.993591i | \(-0.536058\pi\) |
0.916994 | − | 0.398901i | \(-0.130608\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.438860 | 0.0626942 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.96768 | + | 5.14017i | −0.415558 | + | 0.719767i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.49148 | − | 7.77947i | 0.616952 | − | 1.06859i | −0.373087 | − | 0.927797i | \(-0.621701\pi\) |
0.990039 | − | 0.140796i | \(-0.0449661\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.65711 | − | 2.87019i | −0.223444 | − | 0.387017i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.73041 | − | 10.6434i | 0.361652 | − | 1.40975i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.48784 | + | 9.50521i | 0.714456 | + | 1.23747i | 0.963169 | + | 0.268896i | \(0.0866589\pi\) |
−0.248714 | + | 0.968577i | \(0.580008\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.22743 | − | 7.32212i | 0.541267 | − | 0.937501i | −0.457565 | − | 0.889176i | \(-0.651278\pi\) |
0.998832 | − | 0.0483251i | \(-0.0153884\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.57462 | + | 7.92348i | −0.576348 | + | 0.998264i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.24825 | 0.402895 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.87535 | − | 8.44436i | 0.595619 | − | 1.03164i | −0.397840 | − | 0.917455i | \(-0.630240\pi\) |
0.993459 | − | 0.114188i | \(-0.0364266\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.41453 | −0.651833 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.45850 | − | 5.99029i | −0.410448 | − | 0.710917i | 0.584491 | − | 0.811400i | \(-0.301294\pi\) |
−0.994939 | + | 0.100484i | \(0.967961\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.24025 | + | 2.14818i | 0.145160 | + | 0.251425i | 0.929433 | − | 0.368992i | \(-0.120297\pi\) |
−0.784272 | + | 0.620417i | \(0.786964\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.52082 | −0.291079 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.03927 | 1.03012 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.99948 | − | 10.3914i | −0.674994 | − | 1.16912i | −0.976471 | − | 0.215650i | \(-0.930813\pi\) |
0.301477 | − | 0.953474i | \(-0.402520\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.90535 | + | 6.76427i | 0.433928 | + | 0.751586i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.68711 | 0.514477 | 0.257238 | − | 0.966348i | \(-0.417187\pi\) | ||||
0.257238 | + | 0.966348i | \(0.417187\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.17727 | − | 2.03909i | 0.127692 | − | 0.221170i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.91699 | 1.06321 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.27205 | + | 7.39941i | −0.452836 | + | 0.784336i | −0.998561 | − | 0.0536291i | \(-0.982921\pi\) |
0.545725 | + | 0.837965i | \(0.316254\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.42968 | + | 7.67243i | −0.464357 | + | 0.804289i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.8430 | − | 22.2448i | −1.33176 | − | 2.30668i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.08314 | + | 4.22218i | −0.111128 | + | 0.433186i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.61494 | − | 6.26127i | −0.367042 | − | 0.635735i | 0.622060 | − | 0.782970i | \(-0.286296\pi\) |
−0.989102 | + | 0.147235i | \(0.952963\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.55882 | + | 9.62816i | −0.558682 | + | 0.967666i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.88818 | − | 5.00247i | 0.287384 | − | 0.497764i | −0.685800 | − | 0.727790i | \(-0.740548\pi\) |
0.973185 | + | 0.230026i | \(0.0738810\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.0576 | −1.48367 | −0.741836 | − | 0.670581i | \(-0.766045\pi\) | ||||
−0.741836 | + | 0.670581i | \(0.766045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.43768 | − | 5.95423i | 0.335483 | − | 0.581073i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.1896 | −1.46843 | −0.734215 | − | 0.678917i | \(-0.762450\pi\) | ||||
−0.734215 | + | 0.678917i | \(0.762450\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.31057 | + | 10.9302i | 0.604443 | + | 1.04693i | 0.992139 | + | 0.125139i | \(0.0399376\pi\) |
−0.387696 | + | 0.921787i | \(0.626729\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.64560 | − | 8.04642i | −0.440941 | − | 0.763732i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.10761 | −0.574555 | −0.287278 | − | 0.957847i | \(-0.592750\pi\) | ||||
−0.287278 | + | 0.957847i | \(0.592750\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.14793 | 0.200295 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.44818 | − | 9.43652i | −0.503684 | − | 0.872406i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.21091 | + | 5.56146i | 0.294344 | + | 0.509818i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0159950 | −0.00145409 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.916857 | + | 1.58804i | −0.0826702 | + | 0.143189i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.56114 | − | 7.90013i | 0.404736 | − | 0.701023i | −0.589555 | − | 0.807728i | \(-0.700697\pi\) |
0.994291 | + | 0.106705i | \(0.0340302\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.99082 | + | 5.18025i | −0.263327 | + | 0.456096i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.1328 | − | 19.2825i | −0.972676 | − | 1.68472i | −0.687402 | − | 0.726277i | \(-0.741249\pi\) |
−0.285274 | − | 0.958446i | \(-0.592085\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.49578 | − | 8.31625i | −0.736678 | − | 0.721110i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.446857 | + | 0.773979i | 0.0384593 | + | 0.0666135i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.81355 | − | 6.60527i | 0.325814 | − | 0.564326i | −0.655863 | − | 0.754880i | \(-0.727695\pi\) |
0.981677 | + | 0.190554i | \(0.0610284\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.45916 | + | 14.6517i | −0.717496 | + | 1.24274i | 0.244493 | + | 0.969651i | \(0.421379\pi\) |
−0.961989 | + | 0.273089i | \(0.911955\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 27.7877 | 2.34015 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.38269 | + | 9.32309i | −0.450123 | + | 0.779636i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.93403 | −0.326704 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.553143 | + | 0.958072i | 0.0456225 | + | 0.0790204i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.19809 | + | 10.7354i | 0.507767 | + | 0.879478i | 0.999960 | + | 0.00899193i | \(0.00286226\pi\) |
−0.492193 | + | 0.870486i | \(0.663804\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.4549 | −1.17632 | −0.588160 | − | 0.808745i | \(-0.700147\pi\) | ||||
−0.588160 | + | 0.808745i | \(0.700147\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.89836 | −0.638544 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.09478 | + | 8.82442i | 0.409223 | + | 0.708795i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.10642 | + | 15.7728i | 0.726772 | + | 1.25881i | 0.958241 | + | 0.285963i | \(0.0923135\pi\) |
−0.231469 | + | 0.972842i | \(0.574353\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 22.6444 | 1.79582 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.92916 | + | 5.07345i | −0.230850 | + | 0.399844i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.2642 | 1.50889 | 0.754446 | − | 0.656362i | \(-0.227906\pi\) | ||||
0.754446 | + | 0.656362i | \(0.227906\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.17727 | − | 7.23524i | 0.325200 | − | 0.563263i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.84289 | + | 4.92404i | −0.219990 | + | 0.381033i | −0.954805 | − | 0.297234i | \(-0.903936\pi\) |
0.734815 | + | 0.678268i | \(0.237269\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.22445 | + | 2.12080i | 0.0941881 | + | 0.163139i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.0826 | − | 3.93507i | 1.07692 | − | 0.300922i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.57760 | + | 7.92864i | 0.348029 | + | 0.602804i | 0.985899 | − | 0.167340i | \(-0.0535178\pi\) |
−0.637870 | + | 0.770144i | \(0.720184\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.36371 | + | 2.36202i | −0.103087 | + | 0.178552i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.8338 | + | 23.9609i | −1.03982 | + | 1.80101i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.1810 | 0.910448 | 0.455224 | − | 0.890377i | \(-0.349559\pi\) | ||||
0.455224 | + | 0.890377i | \(0.349559\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.70608 | + | 13.3473i | −0.572789 | + | 0.992099i | 0.423489 | + | 0.905901i | \(0.360805\pi\) |
−0.996278 | + | 0.0861980i | \(0.972528\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.3132 | 1.57551 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.84289 | + | 3.19199i | 0.135492 | + | 0.234679i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.90171 | + | 6.75796i | 0.285321 | + | 0.494191i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.43754 | −0.177305 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.2482 | −1.17568 | −0.587841 | − | 0.808977i | \(-0.700022\pi\) | ||||
−0.587841 | + | 0.808977i | \(0.700022\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.425514 | − | 0.737011i | −0.0306292 | − | 0.0530512i | 0.850305 | − | 0.526291i | \(-0.176418\pi\) |
−0.880934 | + | 0.473240i | \(0.843084\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.09412 | + | 7.09123i | 0.293186 | + | 0.507813i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.9843 | 1.42382 | 0.711910 | − | 0.702270i | \(-0.247830\pi\) | ||||
0.711910 | + | 0.702270i | \(0.247830\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.22861 | − | 5.59212i | 0.228870 | − | 0.396415i | −0.728603 | − | 0.684936i | \(-0.759830\pi\) |
0.957474 | + | 0.288521i | \(0.0931636\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 24.5798 | 1.73372 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.36490 | − | 9.29227i | 0.376542 | − | 0.652190i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.363714 | − | 0.629971i | 0.0254029 | − | 0.0439990i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.60264 | − | 6.23996i | −0.250401 | − | 0.433707i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.3236 | − | 10.1054i | −0.714097 | − | 0.699007i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.27205 | − | 9.13146i | −0.362943 | − | 0.628635i | 0.625501 | − | 0.780223i | \(-0.284895\pi\) |
−0.988444 | + | 0.151588i | \(0.951561\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.71825 | − | 15.1004i | 0.597364 | − | 1.03467i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.18645 | − | 2.05499i | 0.0809150 | − | 0.140149i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −27.7913 | −1.88660 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.12645 | + | 5.41516i | −0.211266 | + | 0.365923i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.64811 | −0.514467 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.86319 | − | 8.42329i | −0.325663 | − | 0.564065i | 0.655983 | − | 0.754776i | \(-0.272254\pi\) |
−0.981646 | + | 0.190710i | \(0.938921\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.67727 | − | 2.90511i | −0.111818 | − | 0.193674i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.5798 | 1.49867 | 0.749336 | − | 0.662190i | \(-0.230373\pi\) | ||||
0.749336 | + | 0.662190i | \(0.230373\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.2239 | −1.07211 | −0.536053 | − | 0.844184i | \(-0.680085\pi\) | ||||
−0.536053 | + | 0.844184i | \(0.680085\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.3932 | + | 19.7336i | 0.749617 | + | 1.29837i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.33139 | + | 16.1624i | 0.611320 | + | 1.05884i | 0.991018 | + | 0.133727i | \(0.0426944\pi\) |
−0.379699 | + | 0.925110i | \(0.623972\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.0233 | −0.719079 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.1236 | − | 26.1948i | 0.982383 | − | 1.70154i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.602780 | 0.0389906 | 0.0194953 | − | 0.999810i | \(-0.493794\pi\) | ||||
0.0194953 | + | 0.999810i | \(0.493794\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.9408 | + | 18.9500i | −0.704759 | + | 1.22068i | 0.262020 | + | 0.965062i | \(0.415611\pi\) |
−0.966779 | + | 0.255615i | \(0.917722\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.1853 | + | 19.3734i | −0.717535 | + | 1.24281i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.219430 | − | 0.380064i | −0.0140189 | − | 0.0242814i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.6364 | − | 3.81039i | 0.867665 | − | 0.242449i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.90768 | + | 10.2324i | 0.374384 | + | 0.648452i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.13629 | + | 7.16426i | −0.261080 | + | 0.452204i | −0.966529 | − | 0.256557i | \(-0.917412\pi\) |
0.705449 | + | 0.708761i | \(0.250745\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.55934 | + | 6.16496i | −0.223774 | + | 0.387588i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.93535 | 0.371686 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.09544 | + | 12.2897i | −0.442602 | + | 0.766608i | −0.997882 | − | 0.0650550i | \(-0.979278\pi\) |
0.555280 | + | 0.831663i | \(0.312611\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.0527 | −0.624645 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.59842 | + | 11.4288i | 0.408432 | + | 0.707425i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.27153 | + | 16.0588i | 0.571707 | + | 0.990225i | 0.996391 | + | 0.0848836i | \(0.0270518\pi\) |
−0.424684 | + | 0.905342i | \(0.639615\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.98296 | −0.551819 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.5381 | −1.31811 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.33371 | − | 5.77416i | −0.203260 | − | 0.352057i | 0.746317 | − | 0.665591i | \(-0.231820\pi\) |
−0.949577 | + | 0.313534i | \(0.898487\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.0331 | − | 19.1099i | −0.670214 | − | 1.16085i | −0.977843 | − | 0.209339i | \(-0.932869\pi\) |
0.307629 | − | 0.951506i | \(-0.400464\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −22.3328 | −1.35165 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.65711 | + | 2.87019i | −0.0999273 | + | 0.173079i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.4624 | −1.46980 | −0.734902 | − | 0.678173i | \(-0.762772\pi\) | ||||
−0.734902 | + | 0.678173i | \(0.762772\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.0906 | − | 29.6018i | 1.02319 | − | 1.77221i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.33139 | + | 16.1624i | −0.556664 | + | 0.964170i | 0.441108 | + | 0.897454i | \(0.354586\pi\) |
−0.997772 | + | 0.0667164i | \(0.978748\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.24811 | − | 3.89384i | −0.133636 | − | 0.231465i | 0.791439 | − | 0.611248i | \(-0.209332\pi\) |
−0.925076 | + | 0.379783i | \(0.875999\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.5826 | + | 2.95707i | −0.626860 | + | 0.175162i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.992002 | + | 1.71820i | 0.0585561 | + | 0.101422i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.72809 | − | 9.92134i | 0.336946 | − | 0.583608i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.11262 | − | 15.7835i | 0.534191 | − | 0.925246i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.27021 | 0.0742063 | 0.0371031 | − | 0.999311i | \(-0.488187\pi\) | ||||
0.0371031 | + | 0.999311i | \(0.488187\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.48784 | − | 9.50521i | 0.319514 | − | 0.553415i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.96196 | −0.171870 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.48850 | − | 6.04225i | −0.201745 | − | 0.349433i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.23595 | + | 5.60483i | 0.186517 | + | 0.323057i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.5611 | 0.836516 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.45485 | −0.484124 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.32638 | + | 7.49350i | 0.246919 | + | 0.427677i | 0.962669 | − | 0.270680i | \(-0.0872484\pi\) |
−0.715750 | + | 0.698356i | \(0.753915\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.9788 | − | 32.8722i | −1.07967 | − | 1.87004i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.8497 | 1.35239 | 0.676196 | − | 0.736721i | \(-0.263627\pi\) | ||||
0.676196 | + | 0.736721i | \(0.263627\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.388175 | − | 0.672340i | 0.0219410 | − | 0.0380029i | −0.854846 | − | 0.518881i | \(-0.826349\pi\) |
0.876787 | + | 0.480878i | \(0.159682\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.14925 | 0.515502 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.92116 | − | 11.9878i | 0.388731 | − | 0.673302i | −0.603548 | − | 0.797327i | \(-0.706247\pi\) |
0.992279 | + | 0.124025i | \(0.0395802\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.51911 | − | 11.2914i | 0.365000 | − | 0.632199i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −19.1451 | − | 33.1603i | −1.06857 | − | 1.85082i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.55030 | − | 9.94126i | 0.141902 | − | 0.553147i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.62412 | − | 2.81306i | −0.0900902 | − | 0.156041i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.9078 | + | 27.5531i | −0.879704 | + | 1.52369i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.0326 | − | 26.0372i | 0.828774 | − | 1.43548i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.6993 | 1.57746 | 0.788728 | − | 0.614742i | \(-0.210740\pi\) | ||||
0.788728 | + | 0.614742i | \(0.210740\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.18205 | − | 10.7076i | 0.338774 | − | 0.586774i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.75071 | −0.532738 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.6628 | + | 30.5928i | 0.962153 | + | 1.66650i | 0.717077 | + | 0.696994i | \(0.245480\pi\) |
0.245076 | + | 0.969504i | \(0.421187\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.69809 | − | 13.3335i | −0.418103 | − | 0.724175i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −33.7704 | −1.82877 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.8950 | −0.966241 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.70727 | + | 4.68912i | 0.145754 | + | 0.252454i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.0031 | − | 22.5221i | −0.698044 | − | 1.20905i | −0.969144 | − | 0.246496i | \(-0.920721\pi\) |
0.271100 | − | 0.962551i | \(-0.412613\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.44757 | 0.131015 | 0.0655077 | − | 0.997852i | \(-0.479133\pi\) | ||||
0.0655077 | + | 0.997852i | \(0.479133\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.45150 | − | 2.51408i | 0.0774755 | − | 0.134191i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.85103 | −0.258194 | −0.129097 | − | 0.991632i | \(-0.541208\pi\) | ||||
−0.129097 | + | 0.991632i | \(0.541208\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.45850 | + | 5.99029i | −0.183558 | + | 0.317932i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.09412 | + | 14.0194i | −0.428386 | + | 0.741987i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.67376 | + | 6.36314i | 0.193894 | + | 0.335834i | 0.946537 | − | 0.322594i | \(-0.104555\pi\) |
−0.752644 | + | 0.658428i | \(0.771222\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.405741 | + | 18.9957i | 0.0213548 | + | 0.999772i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.0201603 | − | 0.0349186i | −0.00105814 | − | 0.00183275i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.24025 | − | 2.14818i | 0.0649176 | − | 0.112441i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.51784 | + | 11.2892i | −0.340228 | + | 0.589293i | −0.984475 | − | 0.175525i | \(-0.943838\pi\) |
0.644247 | + | 0.764818i | \(0.277171\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.44018 | −0.127031 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.2502 | − | 21.2179i | 0.635998 | − | 1.10158i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.5514 | −1.47833 | −0.739167 | − | 0.673522i | \(-0.764781\pi\) | ||||
−0.739167 | + | 0.673522i | \(0.764781\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.26041 | + | 2.18309i | 0.0650873 | + | 0.112734i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.38936 | + | 11.0667i | 0.329069 | + | 0.569964i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.2128 | 0.678698 | 0.339349 | − | 0.940661i | \(-0.389793\pi\) | ||||
0.339349 | + | 0.940661i | \(0.389793\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.9956 | 1.17810 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.8309 | + | 32.6160i | 0.962212 | + | 1.66660i | 0.716925 | + | 0.697150i | \(0.245549\pi\) |
0.245287 | + | 0.969450i | \(0.421118\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.51964 | − | 7.82824i | −0.230342 | − | 0.398964i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.95995 | −0.404627 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.8223 | − | 22.2090i | 0.650119 | − | 1.12604i | −0.332975 | − | 0.942936i | \(-0.608052\pi\) |
0.983094 | − | 0.183103i | \(-0.0586142\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.05736 | −0.255762 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 28.0637 | − | 48.6078i | 1.41563 | − | 2.45194i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.99948 | + | 10.3914i | −0.301866 | + | 0.522848i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.6366 | + | 28.8154i | 0.834965 | + | 1.44620i | 0.894059 | + | 0.447949i | \(0.147845\pi\) |
−0.0590940 | + | 0.998252i | \(0.518821\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.44699 | − | 29.0290i | 0.372816 | − | 1.45327i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.70674 | − | 8.15232i | −0.235044 | − | 0.407107i | 0.724242 | − | 0.689546i | \(-0.242190\pi\) |
−0.959285 | + | 0.282439i | \(0.908857\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.5491 | − | 28.6639i | 0.824370 | − | 1.42785i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.90535 | − | 6.76427i | 0.194059 | − | 0.336119i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.2155 | −0.605499 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.25545 | − | 2.17450i | 0.0620779 | − | 0.107522i | −0.833316 | − | 0.552797i | \(-0.813561\pi\) |
0.895394 | + | 0.445275i | \(0.146894\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.2266 | 0.948376 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.9677 | + | 25.9248i | 0.736511 | + | 1.27567i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.34355 | − | 4.05915i | −0.115041 | − | 0.199256i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −42.6480 | −2.08848 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −39.5638 | −1.93282 | −0.966409 | − | 0.257011i | \(-0.917262\pi\) | ||||
−0.966409 | + | 0.257011i | \(0.917262\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.07892 | + | 12.2611i | 0.345006 | + | 0.597567i | 0.985355 | − | 0.170517i | \(-0.0545437\pi\) |
−0.640349 | + | 0.768084i | \(0.721210\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.4890 | + | 32.0238i | 0.898965 | + | 1.55705i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.35453 | −0.114212 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.5300 | − | 19.9705i | 0.557976 | − | 0.966442i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −27.1376 | −1.31022 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.26287 | − | 5.65145i | 0.157167 | − | 0.272221i | −0.776679 | − | 0.629897i | \(-0.783097\pi\) |
0.933846 | + | 0.357676i | \(0.116431\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.30073 | − | 7.44908i | 0.206680 | − | 0.357980i | −0.743987 | − | 0.668194i | \(-0.767067\pi\) |
0.950667 | + | 0.310214i | \(0.100401\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.95850 | − | 8.58837i | −0.237742 | − | 0.411781i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.01718 | − | 2.51965i | 0.431350 | − | 0.120531i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.77939 | + | 10.0102i | 0.275835 | + | 0.477760i | 0.970345 | − | 0.241722i | \(-0.0777123\pi\) |
−0.694510 | + | 0.719483i | \(0.744379\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.736084 | + | 1.27494i | −0.0350516 | + | 0.0607112i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.69629 | − | 9.86626i | 0.270639 | − | 0.468760i | −0.698387 | − | 0.715721i | \(-0.746098\pi\) |
0.969026 | + | 0.246960i | \(0.0794318\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.54410 | 0.405029 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.6243 | + | 27.0620i | −0.739002 | + | 1.27999i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.2252 | 0.812909 | 0.406455 | − | 0.913671i | \(-0.366765\pi\) | ||||
0.406455 | + | 0.913671i | \(0.366765\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.20542 | + | 2.08786i | 0.0567612 | + | 0.0983133i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.2190 | − | 31.5563i | −0.856005 | − | 1.48264i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.85936 | 0.415333 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.1885 | −1.22505 | −0.612524 | − | 0.790452i | \(-0.709846\pi\) | ||||
−0.612524 | + | 0.790452i | \(0.709846\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.05214 | − | 1.82236i | −0.0491097 | − | 0.0850605i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.2166 | − | 35.0162i | −0.941580 | − | 1.63086i | −0.762458 | − | 0.647038i | \(-0.776008\pi\) |
−0.179122 | − | 0.983827i | \(-0.557326\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.48542 | 0.440825 | 0.220412 | − | 0.975407i | \(-0.429260\pi\) | ||||
0.220412 | + | 0.975407i | \(0.429260\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.8430 | + | 22.2448i | −0.595581 | + | 1.03158i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −39.2462 | −1.81610 | −0.908048 | − | 0.418867i | \(-0.862427\pi\) | ||||
−0.908048 | + | 0.418867i | \(0.862427\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.2972 | − | 23.0314i | 0.614006 | − | 1.06349i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.9557 | + | 39.7604i | −1.05774 | + | 1.83206i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.93214 | + | 6.81066i | 0.180800 | + | 0.313155i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.19809 | − | 1.17306i | 0.192621 | − | 0.0538237i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.0668 | + | 26.0965i | 0.689862 | + | 1.19488i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.72677 | + | 4.72290i | −0.124589 | + | 0.215795i | −0.921572 | − | 0.388207i | \(-0.873095\pi\) |
0.796983 | + | 0.604002i | \(0.206428\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.98617 | − | 10.3684i | 0.272946 | − | 0.472756i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.7677 | −0.671956 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.61494 | + | 6.26127i | −0.164146 | + | 0.284309i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.0662 | 1.13586 | 0.567930 | − | 0.823077i | \(-0.307744\pi\) | ||||
0.567930 | + | 0.823077i | \(0.307744\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.2808 | + | 42.0557i | 1.09802 | + | 1.90182i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.8412 | − | 25.7057i | −0.669773 | − | 1.16008i | −0.977967 | − | 0.208758i | \(-0.933058\pi\) |
0.308194 | − | 0.951324i | \(-0.400275\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.26281 | 0.417176 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.1176 | 0.499701 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.43280 | − | 16.3381i | −0.423119 | − | 0.732863i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.85519 | + | 11.8735i | 0.306881 | + | 0.531533i | 0.977678 | − | 0.210108i | \(-0.0673814\pi\) |
−0.670798 | + | 0.741640i | \(0.734048\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.3328 | −0.640344 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.3253 | + | 31.7404i | −0.817086 | + | 1.41523i | 0.0907343 | + | 0.995875i | \(0.471079\pi\) |
−0.907820 | + | 0.419359i | \(0.862255\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.77635 | −0.257044 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.08661 | + | 5.34616i | −0.137081 | + | 0.237431i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.32519 | − | 10.9556i | 0.280359 | − | 0.485596i | −0.691114 | − | 0.722746i | \(-0.742880\pi\) |
0.971473 | + | 0.237149i | \(0.0762131\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.38269 | + | 5.85899i | 0.149641 | + | 0.259187i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.78387 | + | 2.72504i | 0.122911 | + | 0.120314i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.52882 | + | 13.0403i | 0.331759 | + | 0.574624i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.2667 | − | 31.6389i | 0.803371 | − | 1.39148i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.5393 | + | 19.9867i | −0.506520 | + | 0.877318i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.3339 | 0.715601 | 0.357800 | − | 0.933798i | \(-0.383527\pi\) | ||||
0.357800 | + | 0.933798i | \(0.383527\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.56734 | − | 7.91086i | 0.199716 | − | 0.345918i | −0.748720 | − | 0.662886i | \(-0.769331\pi\) |
0.948436 | + | 0.316968i | \(0.102665\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.87535 | −0.300065 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.9958 | − | 20.7774i | −0.522547 | − | 0.905078i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.19321 | + | 15.9231i | 0.399705 | + | 0.692309i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −36.8183 | −1.59778 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.36286 | −0.102347 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.59478 | + | 13.1545i | 0.328351 | + | 0.568721i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.3530 | + | 26.5922i | 0.662531 | + | 1.14754i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.45447 | 0.0626486 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.45954 | − | 2.52800i | 0.0627507 | − | 0.108687i | −0.832943 | − | 0.553358i | \(-0.813346\pi\) |
0.895694 | + | 0.444671i | \(0.146679\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −38.8513 | −1.66727 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.31057 | − | 10.9302i | 0.270315 | − | 0.468200i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.73973 | − | 3.01329i | 0.0743853 | − | 0.128839i | −0.826433 | − | 0.563034i | \(-0.809634\pi\) |
0.900819 | + | 0.434195i | \(0.142967\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.1810 | + | 24.5623i | 0.605232 | + | 1.04829i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.5154 | + | 4.61486i | −0.703580 | + | 0.196600i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.3631 | − | 28.3418i | −0.695831 | − | 1.20522i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.64560 | + | 8.04642i | −0.197195 | + | 0.341552i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.96280 | + | 13.7920i | −0.337395 | + | 0.584385i | −0.983942 | − | 0.178489i | \(-0.942879\pi\) |
0.646547 | + | 0.762874i | \(0.276212\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.70775 | −0.326003 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.83551 | + | 17.0356i | −0.415256 | + | 0.719244i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.6274 | 0.827195 | 0.413598 | − | 0.910460i | \(-0.364272\pi\) | ||||
0.413598 | + | 0.910460i | \(0.364272\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.05380 | + | 5.28934i | 0.128474 | + | 0.222524i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.6516 | + | 18.4491i | 0.447324 | + | 0.774788i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.7544 | −0.492770 | −0.246385 | − | 0.969172i | \(-0.579243\pi\) | ||||
−0.246385 | + | 0.969172i | \(0.579243\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.4868 | 1.35953 | 0.679766 | − | 0.733429i | \(-0.262081\pi\) | ||||
0.679766 | + | 0.733429i | \(0.262081\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.4795 | − | 35.4715i | −0.855541 | − | 1.48184i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.07396 | − | 1.86016i | −0.0447873 | − | 0.0775740i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.7287 | 1.07110 | 0.535551 | − | 0.844503i | \(-0.320104\pi\) | ||||
0.535551 | + | 0.844503i | \(0.320104\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.07264 | − | 1.85787i | 0.0445775 | − | 0.0772106i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.7837 | 0.530359 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.8857 | − | 25.7828i | 0.616503 | − | 1.06782i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.44818 | + | 9.43652i | −0.225254 | + | 0.390152i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.8279 | + | 36.0750i | 0.859659 | + | 1.48897i | 0.872255 | + | 0.489052i | \(0.162657\pi\) |
−0.0125958 | + | 0.999921i | \(0.504009\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.7399 | + | 31.0692i | 1.30782 | + | 1.28018i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.1884 | + | 43.6276i | 1.03611 | + | 1.79460i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.83267 | + | 15.2986i | −0.362714 | + | 0.628239i | −0.988407 | − | 0.151831i | \(-0.951483\pi\) |
0.625692 | + | 0.780070i | \(0.284817\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.21091 | − | 5.56146i | 0.131634 | − | 0.227998i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.2775 | 0.666193 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.1925 | − | 22.8502i | 0.539033 | − | 0.933632i | −0.459924 | − | 0.887959i | \(-0.652123\pi\) |
0.998956 | − | 0.0456738i | \(-0.0145435\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.46838 | 0.386223 | 0.193112 | − | 0.981177i | \(-0.438142\pi\) | ||||
0.193112 | + | 0.981177i | \(0.438142\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.3545 | + | 28.3269i | 0.666008 | + | 1.15356i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.00799750 | + | 0.0138521i | 0.000325145 | + | 0.000563167i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.26529 | −0.335478 | −0.167739 | − | 0.985831i | \(-0.553647\pi\) | ||||
−0.167739 | + | 0.985831i | \(0.553647\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27.0479 | 1.09604 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.9032 | + | 31.0092i | 0.724285 | + | 1.25450i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.40417 | − | 5.89620i | −0.137493 | − | 0.238145i | 0.789054 | − | 0.614324i | \(-0.210571\pi\) |
−0.926547 | + | 0.376179i | \(0.877238\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.83371 | 0.0739425 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.00668 | + | 5.20772i | −0.121044 | + | 0.209655i | −0.920180 | − | 0.391496i | \(-0.871958\pi\) |
0.799135 | + | 0.601151i | \(0.205291\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.2299 | 0.531754 | 0.265877 | − | 0.964007i | \(-0.414338\pi\) | ||||
0.265877 | + | 0.964007i | \(0.414338\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.959816 | − | 1.66245i | 0.0385161 | − | 0.0667118i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.6517 | + | 20.1813i | −0.466816 | + | 0.808548i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.04916 | − | 35.2743i | 0.361389 | − | 1.40872i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.33915 | − | 7.51564i | −0.173013 | − | 0.299668i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.8932 | − | 20.5996i | 0.473460 | − | 0.820058i | −0.526078 | − | 0.850436i | \(-0.676338\pi\) |
0.999538 | + | 0.0303788i | \(0.00967135\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.2899 | − | 23.0188i | 0.528226 | − | 0.914914i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.12228 | −0.362007 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.712762 | + | 1.23454i | −0.0282407 | + | 0.0489143i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23.2033 | 0.917908 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.14239 | − | 10.6389i | −0.242610 | − | 0.420212i | 0.718847 | − | 0.695168i | \(-0.244670\pi\) |
−0.961457 | + | 0.274956i | \(0.911337\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.5776 | − | 25.2492i | −0.574885 | − | 0.995729i | −0.996054 | − | 0.0887474i | \(-0.971714\pi\) |
0.421170 | − | 0.906982i | \(-0.361620\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.98164 | 0.235527 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.7499 | −1.44479 | −0.722394 | − | 0.691481i | \(-0.756958\pi\) | ||||
−0.722394 | + | 0.691481i | \(0.756958\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.1879 | + | 31.5023i | 0.713936 | + | 1.23657i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −35.0284 | − | 60.6710i | −1.37287 | − | 2.37788i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.7707 | 0.969351 | 0.484675 | − | 0.874694i | \(-0.338938\pi\) | ||||
0.484675 | + | 0.874694i | \(0.338938\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.1328 | + | 19.2825i | −0.434994 | + | 0.753431i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.32092 | −0.324630 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.1156 | + | 19.2528i | −0.433002 | + | 0.749982i | −0.997130 | − | 0.0757053i | \(-0.975879\pi\) |
0.564128 | + | 0.825687i | \(0.309213\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.4684 | + | 35.4524i | −0.796130 | + | 1.37894i | 0.125990 | + | 0.992032i | \(0.459789\pi\) |
−0.922119 | + | 0.386905i | \(0.873544\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.63975 | − | 16.6965i | −0.374377 | − | 0.648440i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.95419 | + | 11.5157i | −0.114559 | + | 0.446559i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.22501 | + | 7.31793i | 0.163593 | + | 0.283351i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.2592 | − | 21.2336i | 0.473969 | − | 0.820939i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.0106 | − | 24.2671i | 0.540873 | − | 0.936819i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.5992 | −1.29515 | −0.647577 | − | 0.762000i | \(-0.724217\pi\) | ||||
−0.647577 | + | 0.762000i | \(0.724217\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.446857 | − | 0.773979i | 0.0171995 | − | 0.0297905i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.5883 | 1.13717 | 0.568585 | − | 0.822624i | \(-0.307491\pi\) | ||||
0.568585 | + | 0.822624i | \(0.307491\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.85949 | − | 17.0771i | −0.378373 | − | 0.655361i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.4598 | + | 49.2938i | 1.09058 | + | 1.88894i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.0567 | 1.57099 | 0.785495 | − | 0.618868i | \(-0.212408\pi\) | ||||
0.785495 | + | 0.618868i | \(0.212408\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.62711 | −0.291417 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.4488 | − | 35.4183i | −0.780170 | − | 1.35129i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.5894 | + | 25.2696i | 0.555813 | + | 0.962697i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.22497 | 0.0466000 | 0.0233000 | − | 0.999729i | \(-0.492583\pi\) | ||||
0.0233000 | + | 0.999729i | \(0.492583\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −15.1613 | + | 26.2601i | −0.575929 | + | 0.997538i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.9183 | 0.641748 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.856376 | + | 1.48329i | −0.0324375 | + | 0.0561835i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.5228 | + | 40.7426i | −0.889712 | + | 1.54103i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.0101 | − | 38.1226i | −0.831309 | − | 1.43987i | −0.897001 | − | 0.442029i | \(-0.854259\pi\) |
0.0656918 | − | 0.997840i | \(-0.479075\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.4810 | + | 11.2384i | 0.433015 | + | 0.423865i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.8939 | − | 24.0649i | −0.523273 | − | 0.906335i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.87729 | − | 13.6439i | 0.296256 | − | 0.513130i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.16255 | + | 14.1379i | −0.306551 | + | 0.530962i | −0.977605 | − | 0.210446i | \(-0.932508\pi\) |
0.671055 | + | 0.741408i | \(0.265842\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 40.2509 | 1.50953 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.9432 | − | 18.9542i | 0.409827 | − | 0.709841i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.7654 | 0.402602 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.759750 | + | 1.31593i | 0.0283734 | + | 0.0491442i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.08574 | − | 8.80876i | −0.189666 | − | 0.328511i | 0.755473 | − | 0.655180i | \(-0.227407\pi\) |
−0.945139 | + | 0.326669i | \(0.894074\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −41.0686 | −1.52947 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −55.1595 | −2.05141 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.96702 | + | 3.40697i | 0.0730532 | + | 0.126532i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.02148 | − | 6.96541i | −0.149148 | − | 0.258333i | 0.781765 | − | 0.623574i | \(-0.214320\pi\) |
−0.930913 | + | 0.365241i | \(0.880987\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −32.9600 | −1.22074 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.79353 | + | 4.83853i | −0.103322 | + | 0.178960i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.2325 | 1.52296 | 0.761479 | − | 0.648190i | \(-0.224474\pi\) | ||||
0.761479 | + | 0.648190i | \(0.224474\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.553143 | − | 0.958072i | 0.0204030 | − | 0.0353390i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.1580 | − | 27.9864i | 0.595186 | − | 1.03089i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.5253 | − | 28.6227i | −0.607893 | − | 1.05290i | −0.991587 | − | 0.129442i | \(-0.958681\pi\) |
0.383694 | − | 0.923460i | \(-0.374652\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.5059 | + | 24.9669i | 0.936983 | + | 0.917184i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.3933 | − | 30.1261i | −0.638099 | − | 1.10522i | −0.985849 | − | 0.167633i | \(-0.946388\pi\) |
0.347750 | − | 0.937587i | \(-0.386946\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.19809 | − | 10.7354i | 0.227080 | − | 0.393315i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.86153 | + | 13.6166i | −0.287638 | + | 0.498204i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −41.4284 | −1.51376 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.7350 | − | 37.6462i | 0.793123 | − | 1.37373i | −0.130902 | − | 0.991395i | \(-0.541787\pi\) |
0.924024 | − | 0.382334i | \(-0.124879\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.8537 | −0.759950 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.22743 | + | 12.5183i | 0.263033 | + | 0.455587i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.08494 | + | 5.34328i | 0.112124 | + | 0.194205i | 0.916626 | − | 0.399745i | \(-0.130901\pi\) |
−0.804502 | + | 0.593949i | \(0.797568\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17.9449 | −0.651359 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.81318 | −0.355728 | −0.177864 | − | 0.984055i | \(-0.556919\pi\) | ||||
−0.177864 | + | 0.984055i | \(0.556919\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.2116 | + | 29.8114i | 0.623103 | + | 1.07925i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.94918 | + | 6.84018i | 0.142783 | + | 0.247307i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35.6517 | −1.28731 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.7452 | − | 35.9317i | 0.748090 | − | 1.29573i | −0.200647 | − | 0.979664i | \(-0.564305\pi\) |
0.948737 | − | 0.316066i | \(-0.102362\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −35.7727 | −1.28832 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.8584 | + | 36.1279i | −0.750226 | + | 1.29943i | 0.197487 | + | 0.980306i | \(0.436722\pi\) |
−0.947713 | + | 0.319124i | \(0.896611\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.09478 | − | 8.82442i | 0.183010 | − | 0.316983i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.6705 | − | 21.9460i | −0.454553 | − | 0.787309i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.787908 | − | 3.07133i | 0.0282297 | − | 0.110042i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.4622 | − | 19.8531i | −0.410149 | − | 0.710400i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.75795 | + | 3.04486i | −0.0628240 | + | 0.108814i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.10642 | − | 15.7728i | 0.325022 | − | 0.562955i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.0342 | −0.464621 | −0.232310 | − | 0.972642i | \(-0.574629\pi\) | ||||
−0.232310 | + | 0.972642i | \(0.574629\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −23.3718 | + | 40.4812i | −0.832060 | + | 1.44117i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.6580 | −0.592292 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.7317 | + | 23.7841i | 0.487628 | + | 0.844596i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.3222 | − | 19.6106i | −0.401557 | − | 0.695518i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.1911 | 1.17569 | 0.587844 | − | 0.808974i | \(-0.299977\pi\) | ||||
0.587844 | + | 0.808974i | \(0.299977\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.9547 | 0.918210 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.3307 | − | 24.8216i | −0.506351 | − | 0.877026i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.11045 | + | 7.11951i | 0.145055 | + | 0.251242i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.85831 | 0.206478 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.40369 | − | 14.5556i | 0.295824 | − | 0.512382i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.5271 | −1.03812 | −0.519058 | − | 0.854739i | \(-0.673717\pi\) | ||||
−0.519058 | + | 0.854739i | \(0.673717\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.4097 | + | 24.9583i | −0.505993 | + | 0.876406i | 0.493983 | + | 0.869472i | \(0.335541\pi\) |
−0.999976 | + | 0.00693438i | \(0.997793\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.8125 | − | 48.1727i | 0.975427 | − | 1.68949i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.63212 | − | 16.6833i | −0.337398 | − | 0.584391i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.57018 | − | 10.0188i | 0.0899194 | − | 0.350513i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.8595 | − | 25.7374i | −0.519233 | − | 0.899338i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.40280 | − | 16.2861i | 0.328160 | − | 0.568390i | −0.653987 | − | 0.756506i | \(-0.726905\pi\) |
0.982147 | + | 0.188116i | \(0.0602382\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.78479 | + | 6.55545i | −0.131929 | + | 0.228509i | −0.924420 | − | 0.381375i | \(-0.875451\pi\) |
0.792491 | + | 0.609884i | \(0.208784\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.35453 | −0.290868 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.4683 | + | 30.2560i | −0.607434 | + | 1.05211i | 0.384228 | + | 0.923238i | \(0.374468\pi\) |
−0.991662 | + | 0.128868i | \(0.958866\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.8376 | −1.59201 | −0.796003 | − | 0.605293i | \(-0.793056\pi\) | ||||
−0.796003 | + | 0.605293i | \(0.793056\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.8327 | − | 53.4037i | −1.06957 | − | 1.85256i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.516655 | + | 0.894872i | 0.0179010 | + | 0.0310055i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.68579 | 0.196765 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.10656 | 0.314769 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.00502 | − | 12.1330i | −0.241840 | − | 0.418879i | 0.719398 | − | 0.694598i | \(-0.244418\pi\) |
−0.961238 | + | 0.275719i | \(0.911084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.76169 | + | 11.7116i | 0.233162 | + | 0.403848i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −47.0455 | −1.62033 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.22445 | − | 2.12080i | 0.0421222 | − | 0.0729578i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.0436252 | −0.00149898 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.66708 | − | 9.81568i | 0.194494 | − | 0.336873i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.95840 | − | 6.85615i | 0.135692 | − | 0.235026i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.7757 | + | 32.5205i | 0.642869 | + | 1.11348i | 0.984789 | + | 0.173753i | \(0.0555895\pi\) |
−0.341920 | + | 0.939729i | \(0.611077\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.4492 | − | 10.2284i | −0.357354 | − | 0.349803i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.03378 | − | 3.52261i | −0.0694726 | − | 0.120330i | 0.829197 | − | 0.558957i | \(-0.188798\pi\) |
−0.898669 | + | 0.438627i | \(0.855465\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.31785 | + | 10.9428i | −0.215562 | + | 0.373365i | −0.953446 | − | 0.301563i | \(-0.902492\pi\) |
0.737884 | + | 0.674928i | \(0.235825\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.50066 | + | 4.33127i | −0.0852223 | + | 0.147609i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.5147 | −0.494085 | −0.247042 | − | 0.969005i | \(-0.579459\pi\) | ||||
−0.247042 | + | 0.969005i | \(0.579459\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.57760 | − | 7.92864i | 0.155643 | − | 0.269582i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.8790 | 0.980781 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.8835 | − | 34.4393i | −0.674503 | − | 1.16827i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.8364 | + | 27.4294i | 0.536594 | + | 0.929409i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24.2529 | 0.820836 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.72743 | 0.0922039 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.967541 | − | 1.67583i | −0.0326715 | − | 0.0565887i | 0.849227 | − | 0.528027i | \(-0.177068\pi\) |
−0.881899 | + | 0.471439i | \(0.843735\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.60098 | + | 2.77298i | 0.0539998 | + | 0.0935303i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.9037 | 0.535811 | 0.267905 | − | 0.963445i | \(-0.413669\pi\) | ||||
0.267905 | + | 0.963445i | \(0.413669\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.5216 | − | 30.3483i | 0.589648 | − | 1.02130i | −0.404631 | − | 0.914480i | \(-0.632600\pi\) |
0.994278 | − | 0.106820i | \(-0.0340668\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 27.6677 | 0.930040 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.08806 | − | 14.0089i | 0.271571 | − | 0.470374i | −0.697694 | − | 0.716396i | \(-0.745790\pi\) |
0.969264 | + | 0.246022i | \(0.0791237\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.4402 | − | 21.5470i | 0.417230 | − | 0.722664i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.9432 | + | 22.4182i | 0.433613 | + | 0.751039i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −46.2767 | + | 12.9310i | −1.54859 | + | 0.432718i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.09048 | − | 10.5490i | −0.203582 | − | 0.352615i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.79387 | − | 15.2314i | 0.293619 | − | 0.508563i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.0431 | + | 34.7156i | −0.668473 | + | 1.15783i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.1507 | 0.704631 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.15724 | + | 14.1288i | −0.271456 | + | 0.470176i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.4122 | 0.512318 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.4975 | − | 19.9143i | −0.381770 | − | 0.661244i | 0.609546 | − | 0.792751i | \(-0.291352\pi\) |
−0.991315 | + | 0.131507i | \(0.958019\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.68848 | + | 16.7809i | 0.321347 | + | 0.556589i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.0833 | −0.764783 | −0.382392 | − | 0.924000i | \(-0.624899\pi\) | ||||
−0.382392 | + | 0.924000i | \(0.624899\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.5341 | 0.514103 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.6566 | − | 18.4577i | −0.352296 | − | 0.610194i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.3638 | − | 52.5917i | −1.00270 | − | 1.73673i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.5454 | 0.413835 | 0.206918 | − | 0.978358i | \(-0.433657\pi\) | ||||
0.206918 | + | 0.978358i | \(0.433657\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.9060 | + | 18.8898i | −0.359365 | + | 0.622439i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.4681 | 0.739547 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.84289 | − | 3.19199i | 0.0605940 | − | 0.104952i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 25.2557 | − | 43.7441i | 0.829505 | − | 1.43674i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.6494 | + | 46.1581i | 0.874338 | + | 1.51440i | 0.857466 | + | 0.514540i | \(0.172037\pi\) |
0.0168714 | + | 0.999858i | \(0.494629\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.36702 | − | 1.33814i | −0.0448024 | − | 0.0438556i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 30.0604 | + | 52.0662i | 0.984134 | + | 1.70457i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.90171 | − | 6.75796i | 0.127600 | − | 0.221009i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.5602 | − | 30.4152i | 0.573668 | − | 0.993622i | −0.422517 | − | 0.906355i | \(-0.638853\pi\) |
0.996185 | − | 0.0872667i | \(-0.0278132\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.95704 | 0.0638656 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.57898 | + | 11.3951i | −0.214469 | + | 0.371470i | −0.953108 | − | 0.302630i | \(-0.902135\pi\) |
0.738639 | + | 0.674101i | \(0.235469\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.56246 | −0.0508807 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.21877 | + | 2.11097i | 0.0396466 | + | 0.0686699i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.22510 | + | 9.05015i | 0.169793 | + | 0.294090i | 0.938347 | − | 0.345695i | \(-0.112357\pi\) |
−0.768554 | + | 0.639785i | \(0.779023\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.05728 | −0.261550 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 34.8940 | 1.13152 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.17117 | − | 3.76057i | −0.0703310 | − | 0.121817i | 0.828715 | − | 0.559670i | \(-0.189072\pi\) |
−0.899046 | + | 0.437853i | \(0.855739\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.12412 | + | 14.0714i | 0.262890 | + | 0.455340i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 32.8670 | 1.06244 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.4012 | − | 18.0154i | 0.335872 | − | 0.581747i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 72.8272 | 2.34927 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 25.4770 | − | 44.1274i | 0.820983 | − | 1.42198i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.425514 | + | 0.737011i | −0.0136978 | + | 0.0237252i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.84100 | + | 13.5810i | 0.252149 | + | 0.436736i | 0.964117 | − | 0.265476i | \(-0.0855292\pi\) |
−0.711968 | + | 0.702212i | \(0.752196\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 24.9171 | − | 6.96253i | 0.800454 | − | 0.223669i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.33867 | − | 2.31865i | −0.0429601 | − | 0.0744091i | 0.843746 | − | 0.536743i | \(-0.180346\pi\) |
−0.886706 | + | 0.462334i | \(0.847012\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.0717 | + | 39.9614i | −0.739646 | + | 1.28110i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.09412 | − | 7.09123i | 0.131117 | − | 0.227101i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.87156 | 0.0918693 | 0.0459347 | − | 0.998944i | \(-0.485373\pi\) | ||||
0.0459347 | + | 0.998944i | \(0.485373\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.1585 | + | 24.5232i | −0.452507 | + | 0.783765i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −42.3380 | −1.35175 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.9545 | + | 29.3660i | 0.540764 | + | 0.936630i | 0.998860 | + | 0.0477276i | \(0.0151979\pi\) |
−0.458097 | + | 0.888902i | \(0.651469\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.99214 | − | 17.3069i | −0.318376 | − | 0.551443i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 75.7889 | 2.41239 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.09680 | −0.162069 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0649 | + | 34.7535i | 0.637383 | + | 1.10398i | 0.986005 | + | 0.166716i | \(0.0533165\pi\) |
−0.348622 | + | 0.937264i | \(0.613350\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 36.1729 | + | 62.6533i | 1.14791 | + | 1.98824i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.45722 | −0.204708 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.75369 | + | 3.03748i | −0.0555399 | + | 0.0961979i | −0.892459 | − | 0.451129i | \(-0.851021\pi\) |
0.836919 | + | 0.547327i | \(0.184355\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.29404 | 0.104219 |
(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 | 380.2.i.c.121.4 | ✓ | 8 | |
3.2 | odd | 2 | 3420.2.t.w.1261.3 | 8 | |||
4.3 | odd | 2 | 1520.2.q.m.881.1 | 8 | |||
5.2 | odd | 4 | 1900.2.s.d.349.7 | 16 | |||
5.3 | odd | 4 | 1900.2.s.d.349.2 | 16 | |||
5.4 | even | 2 | 1900.2.i.d.501.1 | 8 | |||
19.7 | even | 3 | 7220.2.a.r.1.1 | 4 | |||
19.11 | even | 3 | inner | 380.2.i.c.201.4 | yes | 8 | |
19.12 | odd | 6 | 7220.2.a.p.1.4 | 4 | |||
57.11 | odd | 6 | 3420.2.t.w.3241.3 | 8 | |||
76.11 | odd | 6 | 1520.2.q.m.961.1 | 8 | |||
95.49 | even | 6 | 1900.2.i.d.201.1 | 8 | |||
95.68 | odd | 12 | 1900.2.s.d.49.7 | 16 | |||
95.87 | odd | 12 | 1900.2.s.d.49.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.i.c.121.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
380.2.i.c.201.4 | yes | 8 | 19.11 | even | 3 | inner | |
1520.2.q.m.881.1 | 8 | 4.3 | odd | 2 | |||
1520.2.q.m.961.1 | 8 | 76.11 | odd | 6 | |||
1900.2.i.d.201.1 | 8 | 95.49 | even | 6 | |||
1900.2.i.d.501.1 | 8 | 5.4 | even | 2 | |||
1900.2.s.d.49.2 | 16 | 95.87 | odd | 12 | |||
1900.2.s.d.49.7 | 16 | 95.68 | odd | 12 | |||
1900.2.s.d.349.2 | 16 | 5.3 | odd | 4 | |||
1900.2.s.d.349.7 | 16 | 5.2 | odd | 4 | |||
3420.2.t.w.1261.3 | 8 | 3.2 | odd | 2 | |||
3420.2.t.w.3241.3 | 8 | 57.11 | odd | 6 | |||
7220.2.a.p.1.4 | 4 | 19.12 | odd | 6 | |||
7220.2.a.r.1.1 | 4 | 19.7 | even | 3 |