Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(78.2533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.239575536.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 12x^{4} + 8x^{3} + 35x^{2} - 15x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.319986\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.319986 | −0.184744 | −0.0923721 | − | 0.995725i | \(-0.529445\pi\) | ||||
−0.0923721 | + | 0.995725i | \(0.529445\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.89761 | −0.965870 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.16603 | 1.25610 | 0.628052 | − | 0.778171i | \(-0.283853\pi\) | ||||
0.628052 | + | 0.778171i | \(0.283853\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.89761 | −0.803652 | −0.401826 | − | 0.915716i | \(-0.631624\pi\) | ||||
−0.401826 | + | 0.915716i | \(0.631624\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.30274 | 1.04357 | 0.521784 | − | 0.853078i | \(-0.325267\pi\) | ||||
0.521784 | + | 0.853078i | \(0.325267\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.95888 | 0.449399 | 0.224700 | − | 0.974428i | \(-0.427860\pi\) | ||||
0.224700 | + | 0.974428i | \(0.427860\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.57762 | 0.537471 | 0.268736 | − | 0.963214i | \(-0.413394\pi\) | ||||
0.268736 | + | 0.963214i | \(0.413394\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.88715 | 0.363183 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.96541 | −1.10775 | −0.553874 | − | 0.832600i | \(-0.686851\pi\) | ||||
−0.553874 | + | 0.832600i | \(0.686851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.43018 | 1.69371 | 0.846856 | − | 0.531823i | \(-0.178493\pi\) | ||||
0.846856 | + | 0.531823i | \(0.178493\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.33307 | −0.232058 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.32942 | 1.04055 | 0.520275 | − | 0.853999i | \(-0.325829\pi\) | ||||
0.520275 | + | 0.853999i | \(0.325829\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.927195 | 0.148470 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.19271 | −1.12331 | −0.561656 | − | 0.827371i | \(-0.689836\pi\) | ||||
−0.561656 | + | 0.827371i | \(0.689836\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.73966 | 0.722792 | 0.361396 | − | 0.932412i | \(-0.382300\pi\) | ||||
0.361396 | + | 0.932412i | \(0.382300\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.43546 | 0.646979 | 0.323489 | − | 0.946232i | \(-0.395144\pi\) | ||||
0.323489 | + | 0.946232i | \(0.395144\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.37682 | −0.192793 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.35975 | −1.01094 | −0.505470 | − | 0.862844i | \(-0.668681\pi\) | ||||
−0.505470 | + | 0.862844i | \(0.668681\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.626816 | −0.0830239 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.22069 | −0.419297 | −0.209649 | − | 0.977777i | \(-0.567232\pi\) | ||||
−0.209649 | + | 0.977777i | \(0.567232\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.9000 | −1.52363 | −0.761817 | − | 0.647792i | \(-0.775693\pi\) | ||||
−0.761817 | + | 0.647792i | \(0.775693\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.6824 | −1.42723 | −0.713614 | − | 0.700539i | \(-0.752943\pi\) | ||||
−0.713614 | + | 0.700539i | \(0.752943\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.824804 | −0.0992947 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.58808 | 0.900539 | 0.450270 | − | 0.892893i | \(-0.351328\pi\) | ||||
0.450270 | + | 0.892893i | \(0.351328\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.90676 | 1.15950 | 0.579749 | − | 0.814795i | \(-0.303150\pi\) | ||||
0.579749 | + | 0.814795i | \(0.303150\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.8327 | −1.44379 | −0.721895 | − | 0.692003i | \(-0.756729\pi\) | ||||
−0.721895 | + | 0.692003i | \(0.756729\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.08896 | 0.898774 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.75180 | 0.631342 | 0.315671 | − | 0.948869i | \(-0.397770\pi\) | ||||
0.315671 | + | 0.948869i | \(0.397770\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.90885 | 0.204650 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.01815 | −0.319923 | −0.159961 | − | 0.987123i | \(-0.551137\pi\) | ||||
−0.159961 | + | 0.987123i | \(0.551137\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.01753 | −0.312903 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.414281 | −0.0420639 | −0.0210320 | − | 0.999779i | \(-0.506695\pi\) | ||||
−0.0210320 | + | 0.999779i | \(0.506695\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.0715 | −1.21323 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.9987 | 1.59193 | 0.795965 | − | 0.605342i | \(-0.206964\pi\) | ||||
0.795965 | + | 0.605342i | \(0.206964\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.59341 | 0.255536 | 0.127768 | − | 0.991804i | \(-0.459219\pi\) | ||||
0.127768 | + | 0.991804i | \(0.459219\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.7357 | −1.90793 | −0.953963 | − | 0.299925i | \(-0.903039\pi\) | ||||
−0.953963 | + | 0.299925i | \(0.903039\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.38469 | −0.898891 | −0.449445 | − | 0.893308i | \(-0.648378\pi\) | ||||
−0.449445 | + | 0.893308i | \(0.648378\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.02533 | −0.192236 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.61401 | −0.245906 | −0.122953 | − | 0.992413i | \(-0.539236\pi\) | ||||
−0.122953 | + | 0.992413i | \(0.539236\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.39614 | 0.776223 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.35577 | 0.577797 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.30157 | 0.207525 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.3587 | 1.80655 | 0.903273 | − | 0.429067i | \(-0.141157\pi\) | ||||
0.903273 | + | 0.429067i | \(0.141157\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.51663 | −0.133532 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.65075 | −0.318968 | −0.159484 | − | 0.987201i | \(-0.550983\pi\) | ||||
−0.159484 | + | 0.987201i | \(0.550983\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.6716 | 0.911740 | 0.455870 | − | 0.890046i | \(-0.349328\pi\) | ||||
0.455870 | + | 0.890046i | \(0.349328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0047 | 1.01823 | 0.509113 | − | 0.860699i | \(-0.329973\pi\) | ||||
0.509113 | + | 0.860699i | \(0.329973\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.41929 | −0.119526 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.0715 | −1.00947 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.4250 | 1.09982 | 0.549910 | − | 0.835224i | \(-0.314662\pi\) | ||||
0.549910 | + | 0.835224i | \(0.314662\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.57453 | −0.535028 | −0.267514 | − | 0.963554i | \(-0.586202\pi\) | ||||
−0.267514 | + | 0.963554i | \(0.586202\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.4676 | −1.00795 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.95052 | 0.235478 | 0.117739 | − | 0.993045i | \(-0.462435\pi\) | ||||
0.117739 | + | 0.993045i | \(0.462435\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.35502 | 0.186765 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.34161 | 0.418387 | 0.209194 | − | 0.977874i | \(-0.432916\pi\) | ||||
0.209194 | + | 0.977874i | \(0.432916\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.56009 | 0.120724 | 0.0603618 | − | 0.998177i | \(-0.480775\pi\) | ||||
0.0603618 | + | 0.998177i | \(0.480775\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.60386 | −0.354143 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.67608 | −0.434061 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.7156 | 1.19484 | 0.597418 | − | 0.801930i | \(-0.296193\pi\) | ||||
0.597418 | + | 0.801930i | \(0.296193\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.03058 | 0.0774628 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.0717 | 0.827535 | 0.413767 | − | 0.910383i | \(-0.364213\pi\) | ||||
0.413767 | + | 0.910383i | \(0.364213\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.8950 | 1.10713 | 0.553567 | − | 0.832805i | \(-0.313266\pi\) | ||||
0.553567 | + | 0.832805i | \(0.313266\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.80783 | 0.281483 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.9253 | 1.31083 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.01354 | −0.0733375 | −0.0366688 | − | 0.999327i | \(-0.511675\pi\) | ||||
−0.0366688 | + | 0.999327i | \(0.511675\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.54257 | 0.542926 | 0.271463 | − | 0.962449i | \(-0.412493\pi\) | ||||
0.271463 | + | 0.962449i | \(0.412493\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.26180 | 0.659876 | 0.329938 | − | 0.944003i | \(-0.392972\pi\) | ||||
0.329938 | + | 0.944003i | \(0.392972\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0992 | −1.14124 | −0.570622 | − | 0.821213i | \(-0.693298\pi\) | ||||
−0.570622 | + | 0.821213i | \(0.693298\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.73820 | 0.263672 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.46894 | −0.519127 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.16076 | 0.564492 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.20349 | 0.220537 | 0.110269 | − | 0.993902i | \(-0.464829\pi\) | ||||
0.110269 | + | 0.993902i | \(0.464829\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.42808 | −0.166369 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.17003 | −0.214211 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.4676 | −0.838665 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.7564 | 1.25602 | 0.628010 | − | 0.778206i | \(-0.283870\pi\) | ||||
0.628010 | + | 0.778206i | \(0.283870\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.75938 | 0.448636 | 0.224318 | − | 0.974516i | \(-0.427985\pi\) | ||||
0.224318 | + | 0.974516i | \(0.427985\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.163154 | 0.0107815 | 0.00539076 | − | 0.999985i | \(-0.498284\pi\) | ||||
0.00539076 | + | 0.999985i | \(0.498284\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −27.3516 | −1.79186 | −0.895931 | − | 0.444193i | \(-0.853490\pi\) | ||||
−0.895931 | + | 0.444193i | \(0.853490\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.10628 | 0.266732 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.3226 | 1.24988 | 0.624938 | − | 0.780674i | \(-0.285124\pi\) | ||||
0.624938 | + | 0.780674i | \(0.285124\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.3519 | −1.56865 | −0.784323 | − | 0.620353i | \(-0.786989\pi\) | ||||
−0.784323 | + | 0.620353i | \(0.786989\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.24982 | −0.529226 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.67608 | −0.361160 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.84050 | −0.116637 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.53106 | −0.538476 | −0.269238 | − | 0.963074i | \(-0.586772\pi\) | ||||
−0.269238 | + | 0.963074i | \(0.586772\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.7384 | 0.675120 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.9333 | 1.36816 | 0.684080 | − | 0.729407i | \(-0.260204\pi\) | ||||
0.684080 | + | 0.729407i | \(0.260204\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.2854 | 1.06994 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.8432 | 0.668622 | 0.334311 | − | 0.942463i | \(-0.391496\pi\) | ||||
0.334311 | + | 0.942463i | \(0.391496\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.965765 | 0.0591039 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.1669 | 1.16862 | 0.584312 | − | 0.811529i | \(-0.301364\pi\) | ||||
0.584312 | + | 0.811529i | \(0.301364\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.9137 | 0.723703 | 0.361851 | − | 0.932236i | \(-0.382145\pi\) | ||||
0.361851 | + | 0.932236i | \(0.382145\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.39149 | −0.564280 | −0.282140 | − | 0.959373i | \(-0.591044\pi\) | ||||
−0.282140 | + | 0.959373i | \(0.591044\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −27.3250 | −1.63590 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.15248 | 0.0687513 | 0.0343756 | − | 0.999409i | \(-0.489056\pi\) | ||||
0.0343756 | + | 0.999409i | \(0.489056\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.0762 | 1.25285 | 0.626424 | − | 0.779483i | \(-0.284518\pi\) | ||||
0.626424 | + | 0.779483i | \(0.284518\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.51355 | 0.0890321 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.132564 | 0.00777106 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.92590 | 0.579877 | 0.289939 | − | 0.957045i | \(-0.406365\pi\) | ||||
0.289939 | + | 0.957045i | \(0.406365\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.86193 | 0.456196 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.46894 | −0.431940 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.11937 | −0.294100 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.94680 | −0.168183 | −0.0840915 | − | 0.996458i | \(-0.526799\pi\) | ||||
−0.0840915 | + | 0.996458i | \(0.526799\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.829856 | −0.0472088 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.0825 | −1.19548 | −0.597740 | − | 0.801690i | \(-0.703934\pi\) | ||||
−0.597740 | + | 0.801690i | \(0.703934\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.7810 | 0.722423 | 0.361211 | − | 0.932484i | \(-0.382363\pi\) | ||||
0.361211 | + | 0.932484i | \(0.382363\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.10773 | −0.399210 | −0.199605 | − | 0.979876i | \(-0.563966\pi\) | ||||
−0.199605 | + | 0.979876i | \(0.563966\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.8520 | −1.39145 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.31517 | 0.352478 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.42857 | 0.468978 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.00297 | 0.166065 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.41204 | −0.297473 | −0.148736 | − | 0.988877i | \(-0.547521\pi\) | ||||
−0.148736 | + | 0.988877i | \(0.547521\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −18.3402 | −1.00504 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.9764 | 0.924765 | 0.462382 | − | 0.886681i | \(-0.346995\pi\) | ||||
0.462382 | + | 0.886681i | \(0.346995\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.836448 | 0.0454296 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 39.2864 | 2.12748 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.8683 | −0.851855 | −0.425928 | − | 0.904757i | \(-0.640052\pi\) | ||||
−0.425928 | + | 0.904757i | \(0.640052\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.1130 | 1.02309 | 0.511547 | − | 0.859255i | \(-0.329073\pi\) | ||||
0.511547 | + | 0.859255i | \(0.329073\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.46823 | −0.291873 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.1090 | 1.38964 | 0.694820 | − | 0.719184i | \(-0.255484\pi\) | ||||
0.694820 | + | 0.719184i | \(0.255484\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.0133 | 1.21460 | 0.607298 | − | 0.794474i | \(-0.292253\pi\) | ||||
0.607298 | + | 0.794474i | \(0.292253\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.1628 | −0.798041 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.03376 | −0.106745 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.6624 | 1.70496 | 0.852482 | − | 0.522756i | \(-0.175096\pi\) | ||||
0.852482 | + | 0.522756i | \(0.175096\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 20.8417 | 1.08497 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.1480 | 1.25034 | 0.625169 | − | 0.780489i | \(-0.285030\pi\) | ||||
0.625169 | + | 0.780489i | \(0.285030\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.2854 | 0.890244 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.6614 | 1.57497 | 0.787484 | − | 0.616335i | \(-0.211383\pi\) | ||||
0.787484 | + | 0.616335i | \(0.211383\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.51452 | −0.333749 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.9748 | 1.63384 | 0.816919 | − | 0.576753i | \(-0.195680\pi\) | ||||
0.816919 | + | 0.576753i | \(0.195680\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.7337 | −0.698123 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.4488 | 0.681883 | 0.340942 | − | 0.940084i | \(-0.389254\pi\) | ||||
0.340942 | + | 0.940084i | \(0.389254\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.0908 | 0.560887 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.16819 | 0.0589275 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.9998 | 0.602251 | 0.301125 | − | 0.953585i | \(-0.402638\pi\) | ||||
0.301125 | + | 0.953585i | \(0.402638\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.8936 | −1.64263 | −0.821315 | − | 0.570476i | \(-0.806759\pi\) | ||||
−0.821315 | + | 0.570476i | \(0.806759\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −27.3250 | −1.36115 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.3685 | 1.30704 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.4024 | 1.00883 | 0.504416 | − | 0.863461i | \(-0.331708\pi\) | ||||
0.504416 | + | 0.863461i | \(0.331708\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.41478 | −0.168439 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.84135 | −0.188111 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.0820 | −1.37190 | −0.685949 | − | 0.727650i | \(-0.740613\pi\) | ||||
−0.685949 | + | 0.727650i | \(0.740613\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.4438 | −0.703949 | −0.351974 | − | 0.936010i | \(-0.614490\pi\) | ||||
−0.351974 | + | 0.936010i | \(0.614490\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.8522 | −0.624897 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.86272 | 0.186494 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.3456 | −0.642835 | −0.321417 | − | 0.946938i | \(-0.604159\pi\) | ||||
−0.321417 | + | 0.946938i | \(0.604159\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.96912 | −0.142687 | −0.0713434 | − | 0.997452i | \(-0.522729\pi\) | ||||
−0.0713434 | + | 0.997452i | \(0.522729\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.04927 | 0.241539 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.5380 | −1.36205 | −0.681023 | − | 0.732262i | \(-0.738464\pi\) | ||||
−0.681023 | + | 0.732262i | \(0.738464\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.95266 | 0.330331 | 0.165165 | − | 0.986266i | \(-0.447184\pi\) | ||||
0.165165 | + | 0.986266i | \(0.447184\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.29582 | −0.203185 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.33832 | 0.251931 | 0.125965 | − | 0.992035i | \(-0.459797\pi\) | ||||
0.125965 | + | 0.992035i | \(0.459797\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.9650 | −1.41100 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.10376 | 0.0988433 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.78096 | −0.223644 | −0.111822 | − | 0.993728i | \(-0.535669\pi\) | ||||
−0.111822 | + | 0.993728i | \(0.535669\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.11993 | 0.379006 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.39398 | −0.0649242 | −0.0324621 | − | 0.999473i | \(-0.510335\pi\) | ||||
−0.0324621 | + | 0.999473i | \(0.510335\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.4620 | −1.27627 | −0.638135 | − | 0.769925i | \(-0.720294\pi\) | ||||
−0.638135 | + | 0.769925i | \(0.720294\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 39.2446 | 1.81602 | 0.908012 | − | 0.418945i | \(-0.137600\pi\) | ||||
0.908012 | + | 0.418945i | \(0.137600\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.944128 | −0.0435031 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.7456 | 0.907902 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.3257 | 0.976436 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.28135 | −0.424076 | −0.212038 | − | 0.977261i | \(-0.568010\pi\) | ||||
−0.212038 | + | 0.977261i | \(0.568010\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.3402 | −0.836240 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.9601 | 0.541965 | 0.270983 | − | 0.962584i | \(-0.412651\pi\) | ||||
0.270983 | + | 0.962584i | \(0.412651\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.70924 | −0.0772946 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.6956 | −1.74631 | −0.873153 | − | 0.487446i | \(-0.837928\pi\) | ||||
−0.873153 | + | 0.487446i | \(0.837928\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.6676 | −1.15601 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.2882 | −1.26635 | −0.633177 | − | 0.774007i | \(-0.718249\pi\) | ||||
−0.633177 | + | 0.774007i | \(0.718249\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.499208 | −0.0223030 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.88492 | −0.396159 | −0.198079 | − | 0.980186i | \(-0.563470\pi\) | ||||
−0.198079 | + | 0.980186i | \(0.563470\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.47317 | 0.0654259 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.16317 | 0.0958807 | 0.0479404 | − | 0.998850i | \(-0.484734\pi\) | ||||
0.0479404 | + | 0.998850i | \(0.484734\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.69672 | 0.163214 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.4783 | 0.812673 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.02878 | −0.220739 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.7025 | 1.30129 | 0.650646 | − | 0.759381i | \(-0.274498\pi\) | ||||
0.650646 | + | 0.759381i | \(0.274498\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.9601 | −0.522980 | −0.261490 | − | 0.965206i | \(-0.584214\pi\) | ||||
−0.261490 | + | 0.965206i | \(0.584214\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 40.5756 | 1.76750 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.3559 | −0.711124 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.33229 | 0.404987 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.8417 | 0.902752 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.54278 | −0.152882 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.9682 | 0.471558 | 0.235779 | − | 0.971807i | \(-0.424236\pi\) | ||||
0.235779 | + | 0.971807i | \(0.424236\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.76618 | −0.204537 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.4206 | −1.30069 | −0.650346 | − | 0.759638i | \(-0.725376\pi\) | ||||
−0.650346 | + | 0.759638i | \(0.725376\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 34.4814 | 1.47163 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.6855 | −0.497821 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.1740 | −1.61748 | −0.808742 | − | 0.588164i | \(-0.799851\pi\) | ||||
−0.808742 | + | 0.588164i | \(0.799851\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.7337 | −0.580873 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.73586 | −0.242168 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.8585 | 0.794792 | 0.397396 | − | 0.917647i | \(-0.369914\pi\) | ||||
0.397396 | + | 0.917647i | \(0.369914\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 43.5494 | 1.82569 | 0.912844 | − | 0.408309i | \(-0.133881\pi\) | ||||
0.912844 | + | 0.408309i | \(0.133881\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.4287 | 0.603824 | 0.301912 | − | 0.953336i | \(-0.402375\pi\) | ||||
0.301912 | + | 0.953336i | \(0.402375\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.324320 | 0.0135487 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.5072 | 1.43655 | 0.718276 | − | 0.695758i | \(-0.244931\pi\) | ||||
0.718276 | + | 0.695758i | \(0.244931\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.41352 | −0.100302 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.6609 | −1.26985 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.37071 | 0.386771 | 0.193385 | − | 0.981123i | \(-0.438053\pi\) | ||||
0.193385 | + | 0.981123i | \(0.438053\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.4726 | 0.761152 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.96365 | −0.121908 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −40.9347 | −1.68099 | −0.840494 | − | 0.541821i | \(-0.817735\pi\) | ||||
−0.840494 | + | 0.541821i | \(0.817735\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.15153 | 0.210838 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.6448 | 1.45641 | 0.728203 | − | 0.685362i | \(-0.240356\pi\) | ||||
0.728203 | + | 0.685362i | \(0.240356\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.3323 | 0.625417 | 0.312708 | − | 0.949849i | \(-0.398764\pi\) | ||||
0.312708 | + | 0.949849i | \(0.398764\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 33.8509 | 1.37852 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.4053 | 0.909403 | 0.454701 | − | 0.890644i | \(-0.349746\pi\) | ||||
0.454701 | + | 0.890644i | \(0.349746\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.8522 | −0.519946 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.1930 | −1.13871 | −0.569353 | − | 0.822093i | \(-0.692806\pi\) | ||||
−0.569353 | + | 0.822093i | \(0.692806\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.0381 | 1.24955 | 0.624773 | − | 0.780807i | \(-0.285192\pi\) | ||||
0.624773 | + | 0.780807i | \(0.285192\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.0462 | −1.20766 | −0.603829 | − | 0.797114i | \(-0.706359\pi\) | ||||
−0.603829 | + | 0.797114i | \(0.706359\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.86437 | 0.195200 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.61133 | −0.104287 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.2338 | 1.08588 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.4263 | 1.05201 | 0.526007 | − | 0.850480i | \(-0.323688\pi\) | ||||
0.526007 | + | 0.850480i | \(0.323688\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.02507 | −0.0407430 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −21.9873 | −0.869803 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.00977 | 0.276869 | 0.138435 | − | 0.990372i | \(-0.455793\pi\) | ||||
0.138435 | + | 0.990372i | \(0.455793\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.0207 | −1.26277 | −0.631386 | − | 0.775469i | \(-0.717514\pi\) | ||||
−0.631386 | + | 0.775469i | \(0.717514\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.5411 | 1.08275 | 0.541377 | − | 0.840780i | \(-0.317903\pi\) | ||||
0.541377 | + | 0.840780i | \(0.317903\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.4175 | −0.526681 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.7793 | −0.460960 | −0.230480 | − | 0.973077i | \(-0.574030\pi\) | ||||
−0.230480 | + | 0.973077i | \(0.574030\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −28.7059 | −1.11992 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.11635 | −0.277214 | −0.138607 | − | 0.990347i | \(-0.544262\pi\) | ||||
−0.138607 | + | 0.990347i | \(0.544262\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.9047 | 1.16316 | 0.581579 | − | 0.813490i | \(-0.302435\pi\) | ||||
0.581579 | + | 0.813490i | \(0.302435\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.98948 | 0.154938 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.3766 | −0.595383 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.00178 | −0.232042 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −49.5756 | −1.91384 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.8573 | 0.418520 | 0.209260 | − | 0.977860i | \(-0.432895\pi\) | ||||
0.209260 | + | 0.977860i | \(0.432895\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.3099 | 0.819005 | 0.409503 | − | 0.912309i | \(-0.365702\pi\) | ||||
0.409503 | + | 0.912309i | \(0.365702\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.16291 | −0.0828829 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.7566 | 0.679438 | 0.339719 | − | 0.940527i | \(-0.389668\pi\) | ||||
0.339719 | + | 0.940527i | \(0.389668\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.0522070 | −0.00199182 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.3257 | 0.812444 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.5734 | −0.744609 | −0.372304 | − | 0.928111i | \(-0.621432\pi\) | ||||
−0.372304 | + | 0.928111i | \(0.621432\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.9483 | −1.17225 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.75213 | 0.331036 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.10176 | −0.154921 | −0.0774607 | − | 0.996995i | \(-0.524681\pi\) | ||||
−0.0774607 | + | 0.996995i | \(0.524681\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.3986 | 0.467622 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.7479 | 0.516312 | 0.258156 | − | 0.966103i | \(-0.416885\pi\) | ||||
0.258156 | + | 0.966103i | \(0.416885\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 37.1841 | 1.39451 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.3075 | 0.910321 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.18298 | −0.230907 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.1859 | 0.566340 | 0.283170 | − | 0.959070i | \(-0.408614\pi\) | ||||
0.283170 | + | 0.959070i | \(0.408614\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.79228 | 0.289798 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.68973 | −0.0997565 | −0.0498783 | − | 0.998755i | \(-0.515883\pi\) | ||||
−0.0498783 | + | 0.998755i | \(0.515883\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.6271 | −0.801002 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.3935 | 0.754282 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.8630 | 1.21382 | 0.606911 | − | 0.794770i | \(-0.292408\pi\) | ||||
0.606911 | + | 0.794770i | \(0.292408\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −48.6691 | −1.79275 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.1963 | 1.00043 | 0.500216 | − | 0.865901i | \(-0.333254\pi\) | ||||
0.500216 | + | 0.865901i | \(0.333254\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.81627 | 0.0667223 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.8026 | −0.873233 | −0.436617 | − | 0.899648i | \(-0.643823\pi\) | ||||
−0.436617 | + | 0.899648i | \(0.643823\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.6665 | −0.609794 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.4543 | −0.928840 | −0.464420 | − | 0.885615i | \(-0.653737\pi\) | ||||
−0.464420 | + | 0.885615i | \(0.653737\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.72982 | 0.0994803 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.9982 | 0.799537 | 0.399769 | − | 0.916616i | \(-0.369091\pi\) | ||||
0.399769 | + | 0.916616i | \(0.369091\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.43615 | −0.124725 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.77983 | 0.173269 | 0.0866343 | − | 0.996240i | \(-0.472389\pi\) | ||||
0.0866343 | + | 0.996240i | \(0.472389\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.33229 | 0.336969 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.775623 | 0.0279697 | 0.0139848 | − | 0.999902i | \(-0.495548\pi\) | ||||
0.0139848 | + | 0.999902i | \(0.495548\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.01835 | −0.252760 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.25550 | −0.0811246 | −0.0405623 | − | 0.999177i | \(-0.512915\pi\) | ||||
−0.0405623 | + | 0.999177i | \(0.512915\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.0897 | −0.504815 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31.6121 | 1.13117 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.2576 | −0.402315 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.0436 | −1.56999 | −0.784993 | − | 0.619504i | \(-0.787334\pi\) | ||||
−0.784993 | + | 0.619504i | \(0.787334\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.46969 | −0.123524 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34.4814 | 1.22447 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.05089 | 0.0372245 | 0.0186122 | − | 0.999827i | \(-0.494075\pi\) | ||||
0.0186122 | + | 0.999827i | \(0.494075\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.0846 | 0.675166 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.74540 | 0.309004 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 41.2718 | 1.45645 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.13314 | −0.215897 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.5501 | 0.511555 | 0.255777 | − | 0.966736i | \(-0.417669\pi\) | ||||
0.255777 | + | 0.966736i | \(0.417669\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.0148 | 0.457010 | 0.228505 | − | 0.973543i | \(-0.426616\pi\) | ||||
0.228505 | + | 0.973543i | \(0.426616\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.81221 | −0.133700 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.28445 | 0.324822 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.51532 | −0.122685 | −0.0613427 | − | 0.998117i | \(-0.519538\pi\) | ||||
−0.0613427 | + | 0.998117i | \(0.519538\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.2284 | −1.43713 | −0.718567 | − | 0.695458i | \(-0.755201\pi\) | ||||
−0.718567 | + | 0.695458i | \(0.755201\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.21314 | 0.216052 | 0.108026 | − | 0.994148i | \(-0.465547\pi\) | ||||
0.108026 | + | 0.994148i | \(0.465547\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.53879 | −0.261833 | −0.130917 | − | 0.991393i | \(-0.541792\pi\) | ||||
−0.130917 | + | 0.991393i | \(0.541792\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.00515 | 0.104247 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.7962 | 0.615127 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.2861 | 0.562259 | 0.281129 | − | 0.959670i | \(-0.409291\pi\) | ||||
0.281129 | + | 0.959670i | \(0.409291\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.58608 | 0.227106 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.368778 | −0.0127014 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.74408 | −0.231456 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.3149 | 0.559266 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.0261 | 1.02808 | 0.514038 | − | 0.857768i | \(-0.328149\pi\) | ||||
0.514038 | + | 0.857768i | \(0.328149\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.2140 | −0.758815 | −0.379407 | − | 0.925230i | \(-0.623872\pi\) | ||||
−0.379407 | + | 0.925230i | \(0.623872\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.4485 | 0.868291 | 0.434146 | − | 0.900843i | \(-0.357050\pi\) | ||||
0.434146 | + | 0.900843i | \(0.357050\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.55988 | −0.291382 | −0.145691 | − | 0.989330i | \(-0.546540\pi\) | ||||
−0.145691 | + | 0.989330i | \(0.546540\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.484314 | −0.0164482 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −53.4613 | −1.81355 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.8509 | 1.14700 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.20043 | 0.0406282 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42.6895 | −1.44152 | −0.720760 | − | 0.693184i | \(-0.756207\pi\) | ||||
−0.720760 | + | 0.693184i | \(0.756207\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.17615 | −0.107129 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.0315 | −0.674879 | −0.337439 | − | 0.941347i | \(-0.609561\pi\) | ||||
−0.337439 | + | 0.941347i | \(0.609561\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.5719 | 0.456730 | 0.228365 | − | 0.973576i | \(-0.426662\pi\) | ||||
0.228365 | + | 0.973576i | \(0.426662\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.1571 | −0.979000 | −0.489500 | − | 0.872003i | \(-0.662821\pi\) | ||||
−0.489500 | + | 0.872003i | \(0.662821\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33.6988 | 1.12895 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.68856 | 0.290752 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.38996 | 0.0797984 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −56.2549 | −1.87621 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.6671 | −1.05498 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.9742 | 1.59296 | 0.796479 | − | 0.604666i | \(-0.206693\pi\) | ||||
0.796479 | + | 0.604666i | \(0.206693\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −46.3580 | −1.53760 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.2832 | 1.40091 | 0.700453 | − | 0.713699i | \(-0.252981\pi\) | ||||
0.700453 | + | 0.713699i | \(0.252981\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.9621 | 0.793031 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.9642 | −1.25232 | −0.626162 | − | 0.779693i | \(-0.715375\pi\) | ||||
−0.626162 | + | 0.779693i | \(0.715375\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.942937 | 0.0310708 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21.9873 | −0.723720 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.51469 | −0.246815 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.52762 | −0.0829286 | −0.0414643 | − | 0.999140i | \(-0.513202\pi\) | ||||
−0.0414643 | + | 0.999140i | \(0.513202\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.74611 | 0.220858 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.05740 | 0.0345438 | 0.0172719 | − | 0.999851i | \(-0.494502\pi\) | ||||
0.0172719 | + | 0.999851i | \(0.494502\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.08973 | −0.133463 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.6758 | −0.348022 | −0.174011 | − | 0.984744i | \(-0.555673\pi\) | ||||
−0.174011 | + | 0.984744i | \(0.555673\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.5401 | −0.603748 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.2566 | 0.950712 | 0.475356 | − | 0.879793i | \(-0.342319\pi\) | ||||
0.475356 | + | 0.879793i | \(0.342319\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.7059 | −0.931834 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.27438 | 0.0737517 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.31630 | 0.204605 | 0.102302 | − | 0.994753i | \(-0.467379\pi\) | ||||
0.102302 | + | 0.994753i | \(0.467379\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.95231 | 0.257062 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 57.9284 | 1.86866 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 57.1864 | 1.84281 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.2185 | 1.74355 | 0.871775 | − | 0.489906i | \(-0.162969\pi\) | ||||
0.871775 | + | 0.489906i | \(0.162969\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.69703 | −0.0866410 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.4079 | −0.462372 | −0.231186 | − | 0.972910i | \(-0.574261\pi\) | ||||
−0.231186 | + | 0.972910i | \(0.574261\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.3238 | 0.778187 | 0.389093 | − | 0.921198i | \(-0.372788\pi\) | ||||
0.389093 | + | 0.921198i | \(0.372788\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.5737 | −0.401856 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27.1932 | 0.868211 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.2385 | −0.709297 | −0.354649 | − | 0.935000i | \(-0.615400\pi\) | ||||
−0.354649 | + | 0.935000i | \(0.615400\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.2171 | 0.388480 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.2655 | −0.389626 | −0.194813 | − | 0.980840i | \(-0.562410\pi\) | ||||
−0.194813 | + | 0.980840i | \(0.562410\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.73178 | 0.0549563 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.82783 | 0.152899 | 0.0764495 | − | 0.997073i | \(-0.475642\pi\) | ||||
0.0764495 | + | 0.997073i | \(0.475642\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.9446 | 0.377910 |
(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 | 9800.2.a.cx.1.3 | 6 | ||
5.2 | odd | 4 | 1960.2.g.f.1569.7 | 12 | |||
5.3 | odd | 4 | 1960.2.g.f.1569.6 | 12 | |||
5.4 | even | 2 | 9800.2.a.cv.1.4 | 6 | |||
7.2 | even | 3 | 1400.2.q.n.1201.4 | 12 | |||
7.4 | even | 3 | 1400.2.q.n.401.4 | 12 | |||
7.6 | odd | 2 | 9800.2.a.cw.1.4 | 6 | |||
35.2 | odd | 12 | 280.2.bg.a.249.6 | yes | 24 | ||
35.4 | even | 6 | 1400.2.q.o.401.3 | 12 | |||
35.9 | even | 6 | 1400.2.q.o.1201.3 | 12 | |||
35.13 | even | 4 | 1960.2.g.e.1569.7 | 12 | |||
35.18 | odd | 12 | 280.2.bg.a.9.6 | ✓ | 24 | ||
35.23 | odd | 12 | 280.2.bg.a.249.7 | yes | 24 | ||
35.27 | even | 4 | 1960.2.g.e.1569.6 | 12 | |||
35.32 | odd | 12 | 280.2.bg.a.9.7 | yes | 24 | ||
35.34 | odd | 2 | 9800.2.a.cy.1.3 | 6 | |||
140.23 | even | 12 | 560.2.bw.f.529.6 | 24 | |||
140.67 | even | 12 | 560.2.bw.f.289.6 | 24 | |||
140.107 | even | 12 | 560.2.bw.f.529.7 | 24 | |||
140.123 | even | 12 | 560.2.bw.f.289.7 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.bg.a.9.6 | ✓ | 24 | 35.18 | odd | 12 | ||
280.2.bg.a.9.7 | yes | 24 | 35.32 | odd | 12 | ||
280.2.bg.a.249.6 | yes | 24 | 35.2 | odd | 12 | ||
280.2.bg.a.249.7 | yes | 24 | 35.23 | odd | 12 | ||
560.2.bw.f.289.6 | 24 | 140.67 | even | 12 | |||
560.2.bw.f.289.7 | 24 | 140.123 | even | 12 | |||
560.2.bw.f.529.6 | 24 | 140.23 | even | 12 | |||
560.2.bw.f.529.7 | 24 | 140.107 | even | 12 | |||
1400.2.q.n.401.4 | 12 | 7.4 | even | 3 | |||
1400.2.q.n.1201.4 | 12 | 7.2 | even | 3 | |||
1400.2.q.o.401.3 | 12 | 35.4 | even | 6 | |||
1400.2.q.o.1201.3 | 12 | 35.9 | even | 6 | |||
1960.2.g.e.1569.6 | 12 | 35.27 | even | 4 | |||
1960.2.g.e.1569.7 | 12 | 35.13 | even | 4 | |||
1960.2.g.f.1569.6 | 12 | 5.3 | odd | 4 | |||
1960.2.g.f.1569.7 | 12 | 5.2 | odd | 4 | |||
9800.2.a.cv.1.4 | 6 | 5.4 | even | 2 | |||
9800.2.a.cw.1.4 | 6 | 7.6 | odd | 2 | |||
9800.2.a.cx.1.3 | 6 | 1.1 | even | 1 | trivial | ||
9800.2.a.cy.1.3 | 6 | 35.34 | odd | 2 |