Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.34309996544.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 8x^{6} + 28x^{5} + 31x^{4} - 36x^{3} - 22x^{2} + 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 2432) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.836706\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-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 | ||||||||
\(3\) | 0.222191 | 0.128282 | 0.0641411 | − | 0.997941i | \(-0.479569\pi\) | ||||
0.0641411 | + | 0.997941i | \(0.479569\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.55081 | −0.693543 | −0.346772 | − | 0.937950i | \(-0.612722\pi\) | ||||
−0.346772 | + | 0.937950i | \(0.612722\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.06334 | 1.15783 | 0.578917 | − | 0.815387i | \(-0.303476\pi\) | ||||
0.578917 | + | 0.815387i | \(0.303476\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.95063 | −0.983544 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.950631 | 0.286626 | 0.143313 | − | 0.989677i | \(-0.454224\pi\) | ||||
0.143313 | + | 0.989677i | \(0.454224\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.36113 | −0.932209 | −0.466105 | − | 0.884730i | \(-0.654343\pi\) | ||||
−0.466105 | + | 0.884730i | \(0.654343\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.344577 | −0.0889693 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.82843 | 0.443459 | 0.221729 | − | 0.975108i | \(-0.428830\pi\) | ||||
0.221729 | + | 0.975108i | \(0.428830\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.680647 | 0.148529 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.36113 | 0.700844 | 0.350422 | − | 0.936592i | \(-0.386038\pi\) | ||||
0.350422 | + | 0.936592i | \(0.386038\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.59499 | −0.518998 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.32218 | −0.254453 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.95873 | −0.920812 | −0.460406 | − | 0.887708i | \(-0.652296\pi\) | ||||
−0.460406 | + | 0.887708i | \(0.652296\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.44620 | 0.618955 | 0.309478 | − | 0.950907i | \(-0.399846\pi\) | ||||
0.309478 | + | 0.950907i | \(0.399846\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.211222 | 0.0367690 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.75066 | −0.803007 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.95889 | 0.486439 | 0.243219 | − | 0.969971i | \(-0.421797\pi\) | ||||
0.243219 | + | 0.969971i | \(0.421797\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.746814 | −0.119586 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.55687 | −0.711663 | −0.355832 | − | 0.934550i | \(-0.615802\pi\) | ||||
−0.355832 | + | 0.934550i | \(0.615802\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.69373 | −0.258291 | −0.129145 | − | 0.991626i | \(-0.541223\pi\) | ||||
−0.129145 | + | 0.991626i | \(0.541223\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.57587 | 0.682130 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.39941 | 0.495855 | 0.247927 | − | 0.968779i | \(-0.420251\pi\) | ||||
0.247927 | + | 0.968779i | \(0.420251\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.38404 | 0.340578 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.406261 | 0.0568879 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.47142 | −0.614197 | −0.307098 | − | 0.951678i | \(-0.599358\pi\) | ||||
−0.307098 | + | 0.951678i | \(0.599358\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.47425 | −0.198788 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.222191 | 0.0294300 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.395014 | 0.0514264 | 0.0257132 | − | 0.999669i | \(-0.491814\pi\) | ||||
0.0257132 | + | 0.999669i | \(0.491814\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.34158 | −0.683920 | −0.341960 | − | 0.939715i | \(-0.611091\pi\) | ||||
−0.341960 | + | 0.939715i | \(0.611091\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.03878 | −1.13878 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.21247 | 0.646528 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.85064 | −0.836939 | −0.418470 | − | 0.908231i | \(-0.637433\pi\) | ||||
−0.418470 | + | 0.908231i | \(0.637433\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.746814 | 0.0899058 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.15207 | −0.611438 | −0.305719 | − | 0.952122i | \(-0.598897\pi\) | ||||
−0.305719 | + | 0.952122i | \(0.598897\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.19998 | −0.140446 | −0.0702232 | − | 0.997531i | \(-0.522371\pi\) | ||||
−0.0702232 | + | 0.997531i | \(0.522371\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.576584 | −0.0665782 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.91210 | 0.331865 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.7249 | 1.65669 | 0.828343 | − | 0.560222i | \(-0.189284\pi\) | ||||
0.828343 | + | 0.560222i | \(0.189284\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.55812 | 0.950902 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.35564 | −0.368330 | −0.184165 | − | 0.982895i | \(-0.558958\pi\) | ||||
−0.184165 | + | 0.982895i | \(0.558958\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.83554 | −0.307558 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.10179 | −0.118124 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.64561 | −1.02243 | −0.511216 | − | 0.859452i | \(-0.670805\pi\) | ||||
−0.511216 | + | 0.859452i | \(0.670805\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.2963 | −1.07934 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.765715 | 0.0794010 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.55081 | −0.159110 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.55562 | 0.361018 | 0.180509 | − | 0.983573i | \(-0.442225\pi\) | ||||
0.180509 | + | 0.983573i | \(0.442225\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.80496 | −0.281909 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.5381 | −1.34709 | −0.673545 | − | 0.739146i | \(-0.735229\pi\) | ||||
−0.673545 | + | 0.739146i | \(0.735229\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.64570 | −0.654820 | −0.327410 | − | 0.944882i | \(-0.606176\pi\) | ||||
−0.327410 | + | 0.944882i | \(0.606176\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.05555 | −0.103012 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.8519 | −1.53246 | −0.766230 | − | 0.642566i | \(-0.777870\pi\) | ||||
−0.766230 | + | 0.642566i | \(0.777870\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.4213 | 1.28553 | 0.642764 | − | 0.766064i | \(-0.277788\pi\) | ||||
0.642764 | + | 0.766064i | \(0.277788\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.657440 | 0.0624015 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.65810 | 0.626342 | 0.313171 | − | 0.949697i | \(-0.398609\pi\) | ||||
0.313171 | + | 0.949697i | \(0.398609\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.21247 | −0.486065 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.91745 | 0.916869 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.60109 | 0.513451 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0963 | −0.917846 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.01250 | −0.0912937 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.7784 | 1.05349 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.54782 | −0.581025 | −0.290512 | − | 0.956871i | \(-0.593826\pi\) | ||||
−0.290512 | + | 0.956871i | \(0.593826\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.376331 | −0.0331341 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.2838 | −1.24798 | −0.623990 | − | 0.781432i | \(-0.714489\pi\) | ||||
−0.623990 | + | 0.781432i | \(0.714489\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.06334 | 0.265625 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.05045 | 0.176474 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.9138 | −1.01786 | −0.508931 | − | 0.860808i | \(-0.669959\pi\) | ||||
−0.508931 | + | 0.860808i | \(0.669959\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.1950 | −0.949551 | −0.474775 | − | 0.880107i | \(-0.657471\pi\) | ||||
−0.474775 | + | 0.880107i | \(0.657471\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.755320 | 0.0636094 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.19519 | −0.267195 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.69004 | 0.638623 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.529714 | 0.0436901 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.67749 | 0.628964 | 0.314482 | − | 0.949263i | \(-0.398169\pi\) | ||||
0.314482 | + | 0.949263i | \(0.398169\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.10162 | −0.252406 | −0.126203 | − | 0.992004i | \(-0.540279\pi\) | ||||
−0.126203 | + | 0.992004i | \(0.540279\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.39501 | −0.436161 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.34440 | −0.429272 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.8994 | −1.18910 | −0.594550 | − | 0.804059i | \(-0.702670\pi\) | ||||
−0.594550 | + | 0.804059i | \(0.702670\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.993511 | −0.0787905 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.2963 | 0.811460 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.5481 | −1.45280 | −0.726400 | − | 0.687272i | \(-0.758808\pi\) | ||||
−0.726400 | + | 0.687272i | \(0.758808\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.327565 | −0.0255009 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.4532 | 0.886274 | 0.443137 | − | 0.896454i | \(-0.353865\pi\) | ||||
0.443137 | + | 0.896454i | \(0.353865\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.70281 | −0.130986 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.95063 | −0.225640 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.20956 | 0.548133 | 0.274066 | − | 0.961711i | \(-0.411631\pi\) | ||||
0.274066 | + | 0.961711i | \(0.411631\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.94933 | −0.600913 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0877686 | 0.00659710 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.90251 | 0.366431 | 0.183215 | − | 0.983073i | \(-0.441349\pi\) | ||||
0.183215 | + | 0.983073i | \(0.441349\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.1775 | 1.42545 | 0.712725 | − | 0.701444i | \(-0.247461\pi\) | ||||
0.712725 | + | 0.701444i | \(0.247461\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.18685 | −0.0877347 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.58868 | −0.337366 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.73816 | 0.127107 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.05028 | −0.294615 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.8812 | −1.65563 | −0.827814 | − | 0.561003i | \(-0.810416\pi\) | ||||
−0.827814 | + | 0.561003i | \(0.810416\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.11248 | −0.152060 | −0.0760300 | − | 0.997106i | \(-0.524224\pi\) | ||||
−0.0760300 | + | 0.997106i | \(0.524224\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.15817 | 0.0829380 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.05012 | −0.431053 | −0.215526 | − | 0.976498i | \(-0.569147\pi\) | ||||
−0.215526 | + | 0.976498i | \(0.569147\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.03090 | −0.285743 | −0.142872 | − | 0.989741i | \(-0.545634\pi\) | ||||
−0.142872 | + | 0.989741i | \(0.545634\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.52215 | −0.107364 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.1903 | −1.06615 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.06683 | 0.493569 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.91745 | −0.689310 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.950631 | 0.0657565 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.66532 | −0.114646 | −0.0573228 | − | 0.998356i | \(-0.518256\pi\) | ||||
−0.0573228 | + | 0.998356i | \(0.518256\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.14475 | −0.0784366 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.62665 | 0.179136 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.5569 | 0.716647 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.266624 | −0.0180168 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.14558 | −0.413396 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.9352 | 1.93764 | 0.968821 | − | 0.247761i | \(-0.0796948\pi\) | ||||
0.968821 | + | 0.247761i | \(0.0796948\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.65685 | 0.510457 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.0519 | −1.33089 | −0.665445 | − | 0.746447i | \(-0.731758\pi\) | ||||
−0.665445 | + | 0.746447i | \(0.731758\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.9953 | 0.990919 | 0.495459 | − | 0.868631i | \(-0.335000\pi\) | ||||
0.495459 | + | 0.868631i | \(0.335000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.647045 | 0.0425724 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.2738 | 0.738570 | 0.369285 | − | 0.929316i | \(-0.379603\pi\) | ||||
0.369285 | + | 0.929316i | \(0.379603\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.27184 | −0.343897 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.27176 | 0.212523 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.9049 | 1.28754 | 0.643770 | − | 0.765219i | \(-0.277369\pi\) | ||||
0.643770 | + | 0.765219i | \(0.277369\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.8163 | −1.01882 | −0.509408 | − | 0.860525i | \(-0.670135\pi\) | ||||
−0.509408 | + | 0.860525i | \(0.670135\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.86808 | 0.376437 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.69720 | −0.236205 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.36113 | −0.213863 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.745595 | −0.0472501 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.5087 | 0.663306 | 0.331653 | − | 0.943401i | \(-0.392394\pi\) | ||||
0.331653 | + | 0.943401i | \(0.392394\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.19519 | 0.200880 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.630033 | −0.0394542 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.70129 | −0.106123 | −0.0530617 | − | 0.998591i | \(-0.516898\pi\) | ||||
−0.0530617 | + | 0.998591i | \(0.516898\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.06409 | 0.563215 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.6314 | 0.905659 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.8359 | 0.853157 | 0.426578 | − | 0.904451i | \(-0.359719\pi\) | ||||
0.426578 | + | 0.904451i | \(0.359719\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.93432 | 0.425972 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.14317 | −0.131160 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.9655 | −0.912466 | −0.456233 | − | 0.889860i | \(-0.650802\pi\) | ||||
−0.456233 | + | 0.889860i | \(0.650802\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.12684 | −0.250688 | −0.125344 | − | 0.992113i | \(-0.540003\pi\) | ||||
−0.125344 | + | 0.992113i | \(0.540003\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.28774 | −0.138461 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.46688 | −0.148758 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.7721 | −1.54849 | −0.774247 | − | 0.632884i | \(-0.781871\pi\) | ||||
−0.774247 | + | 0.632884i | \(0.781871\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.1685 | −0.608769 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.2694 | −0.612621 | −0.306311 | − | 0.951932i | \(-0.599095\pi\) | ||||
−0.306311 | + | 0.951932i | \(0.599095\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.99506 | 0.415813 | 0.207907 | − | 0.978149i | \(-0.433335\pi\) | ||||
0.207907 | + | 0.978149i | \(0.433335\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.344577 | −0.0204110 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.9592 | −0.823987 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.6569 | −0.803344 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.790027 | 0.0463122 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −31.8434 | −1.86031 | −0.930157 | − | 0.367162i | \(-0.880330\pi\) | ||||
−0.930157 | + | 0.367162i | \(0.880330\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.612591 | −0.0356664 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.25690 | −0.0729330 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.2972 | −0.653333 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.18846 | −0.299058 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.00805 | −0.172808 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.28378 | 0.474328 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.45813 | −0.368585 | −0.184292 | − | 0.982871i | \(-0.558999\pi\) | ||||
−0.184292 | + | 0.982871i | \(0.558999\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.47662 | −0.0840018 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.1973 | −1.59892 | −0.799462 | − | 0.600716i | \(-0.794882\pi\) | ||||
−0.799462 | + | 0.600716i | \(0.794882\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.1212 | 0.967746 | 0.483873 | − | 0.875138i | \(-0.339230\pi\) | ||||
0.483873 | + | 0.875138i | \(0.339230\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.0174 | 0.789793 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.5841 | −1.66161 | −0.830804 | − | 0.556564i | \(-0.812119\pi\) | ||||
−0.830804 | + | 0.556564i | \(0.812119\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.71392 | −0.263929 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.52215 | −0.196587 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.82843 | 0.101736 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.72209 | 0.483815 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.98210 | 0.164910 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.4135 | 0.574117 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.5519 | −1.12964 | −0.564818 | − | 0.825215i | \(-0.691054\pi\) | ||||
−0.564818 | + | 0.825215i | \(0.691054\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.73060 | −0.478434 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.6240 | 0.580454 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.1832 | −1.04497 | −0.522487 | − | 0.852647i | \(-0.674996\pi\) | ||||
−0.522487 | + | 0.852647i | \(0.674996\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.47937 | 0.0803485 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.27606 | 0.177409 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.1402 | −0.763501 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.15817 | −0.0623536 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.5507 | −0.566390 | −0.283195 | − | 0.959062i | \(-0.591394\pi\) | ||||
−0.283195 | + | 0.959062i | \(0.591394\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.4693 | 1.57745 | 0.788727 | − | 0.614744i | \(-0.210741\pi\) | ||||
0.788727 | + | 0.614744i | \(0.210741\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.44401 | 0.237204 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.98903 | −0.212315 | −0.106157 | − | 0.994349i | \(-0.533855\pi\) | ||||
−0.106157 | + | 0.994349i | \(0.533855\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.98988 | 0.424059 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.24451 | 0.0658667 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.9377 | −0.788380 | −0.394190 | − | 0.919029i | \(-0.628975\pi\) | ||||
−0.394190 | + | 0.919029i | \(0.628975\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.24331 | −0.117743 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.86093 | 0.0974057 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.1009 | −0.997059 | −0.498529 | − | 0.866873i | \(-0.666126\pi\) | ||||
−0.498529 | + | 0.866873i | \(0.666126\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.4456 | 0.699952 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.6975 | −0.711137 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.461357 | 0.0238882 | 0.0119441 | − | 0.999929i | \(-0.496198\pi\) | ||||
0.0119441 | + | 0.999929i | \(0.496198\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.61706 | 0.135144 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.6669 | 0.858390 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.9622 | 1.53906 | 0.769528 | − | 0.638613i | \(-0.220492\pi\) | ||||
0.769528 | + | 0.638613i | \(0.220492\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.45487 | −0.0745352 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.9077 | 0.863944 | 0.431972 | − | 0.901887i | \(-0.357818\pi\) | ||||
0.431972 | + | 0.901887i | \(0.357818\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.51612 | −0.230163 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.99756 | 0.254040 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.92418 | 0.401772 | 0.200886 | − | 0.979615i | \(-0.435618\pi\) | ||||
0.200886 | + | 0.979615i | \(0.435618\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.14558 | 0.310795 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.17373 | −0.160094 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −22.8356 | −1.14898 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.6718 | −0.686170 | −0.343085 | − | 0.939304i | \(-0.611472\pi\) | ||||
−0.343085 | + | 0.939304i | \(0.611472\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.680647 | 0.0340750 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0107 | 0.599785 | 0.299893 | − | 0.953973i | \(-0.403049\pi\) | ||||
0.299893 | + | 0.953973i | \(0.403049\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.5831 | −0.576996 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.2720 | −0.659492 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.81281 | 0.139426 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.47063 | 0.468292 | 0.234146 | − | 0.972201i | \(-0.424771\pi\) | ||||
0.234146 | + | 0.972201i | \(0.424771\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.64713 | −0.130574 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.21006 | 0.0595432 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.20396 | 0.255453 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.48744 | −0.121811 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.0843 | −1.37201 | −0.686004 | − | 0.727598i | \(-0.740637\pi\) | ||||
−0.686004 | + | 0.727598i | \(0.740637\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.83238 | −0.479201 | −0.239601 | − | 0.970872i | \(-0.577016\pi\) | ||||
−0.239601 | + | 0.970872i | \(0.577016\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.0304 | −0.487695 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.74475 | −0.230154 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.3631 | −0.791865 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.709944 | −0.0342764 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.94284 | 0.430761 | 0.215381 | − | 0.976530i | \(-0.430901\pi\) | ||||
0.215381 | + | 0.976530i | \(0.430901\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.5274 | −1.41900 | −0.709499 | − | 0.704707i | \(-0.751079\pi\) | ||||
−0.709499 | + | 0.704707i | \(0.751079\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.70866 | 0.0819240 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.36113 | 0.160785 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.5113 | 0.978953 | 0.489477 | − | 0.872016i | \(-0.337188\pi\) | ||||
0.489477 | + | 0.872016i | \(0.337188\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.03444 | −0.334973 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.3188 | 0.632794 | 0.316397 | − | 0.948627i | \(-0.397527\pi\) | ||||
0.316397 | + | 0.948627i | \(0.397527\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.9585 | 0.709101 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.70587 | 0.0806850 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.5138 | 0.496177 | 0.248089 | − | 0.968737i | \(-0.420198\pi\) | ||||
0.248089 | + | 0.968737i | \(0.420198\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.33190 | −0.203981 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.689153 | −0.0323792 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.9676 | 0.748571 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.5831 | 1.24351 | 0.621753 | − | 0.783214i | \(-0.286421\pi\) | ||||
0.621753 | + | 0.783214i | \(0.286421\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.41751 | −0.112840 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.2417 | −0.896175 | −0.448087 | − | 0.893990i | \(-0.647895\pi\) | ||||
−0.448087 | + | 0.893990i | \(0.647895\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.24701 | −0.104427 | −0.0522137 | − | 0.998636i | \(-0.516628\pi\) | ||||
−0.0522137 | + | 0.998636i | \(0.516628\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.18748 | −0.0550680 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.5682 | −1.27570 | −0.637852 | − | 0.770159i | \(-0.720177\pi\) | ||||
−0.637852 | + | 0.770159i | \(0.720177\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.9858 | −0.969036 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.31051 | −0.152540 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.61011 | −0.0740329 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.59499 | −0.119066 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.1935 | 0.604089 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.5447 | −0.481802 | −0.240901 | − | 0.970550i | \(-0.577443\pi\) | ||||
−0.240901 | + | 0.970550i | \(0.577443\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.94521 | −0.453463 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.28774 | 0.104096 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.51409 | −0.250382 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.7294 | 1.80031 | 0.900154 | − | 0.435571i | \(-0.143454\pi\) | ||||
0.900154 | + | 0.435571i | \(0.143454\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.12123 | −0.186369 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.0150 | −1.39969 | −0.699844 | − | 0.714296i | \(-0.746747\pi\) | ||||
−0.699844 | + | 0.714296i | \(0.746747\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.06667 | −0.408342 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.34996 | 0.195516 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.7825 | −0.707943 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.90620 | 0.219632 | 0.109816 | − | 0.993952i | \(-0.464974\pi\) | ||||
0.109816 | + | 0.993952i | \(0.464974\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.54480 | 0.113693 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.6847 | 0.654759 | 0.327380 | − | 0.944893i | \(-0.393834\pi\) | ||||
0.327380 | + | 0.944893i | \(0.393834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.9950 | 0.934265 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.378351 | −0.0168031 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.3988 | 0.904159 | 0.452080 | − | 0.891978i | \(-0.350682\pi\) | ||||
0.452080 | + | 0.891978i | \(0.350682\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.67593 | −0.162614 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.32218 | −0.0583756 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.3062 | 0.454146 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.23158 | 0.142125 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.60190 | 0.0703157 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.4356 | 0.982923 | 0.491462 | − | 0.870899i | \(-0.336463\pi\) | ||||
0.491462 | + | 0.870899i | \(0.336463\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.71531 | 0.424821 | 0.212410 | − | 0.977181i | \(-0.431869\pi\) | ||||
0.212410 | + | 0.977181i | \(0.431869\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.76627 | −0.0770865 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.30112 | 0.274481 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.7028 | −0.508818 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.16554 | −0.0505801 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.3162 | 0.663419 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.5833 | 1.06283 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.08930 | 0.0470066 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.26635 | 0.0976185 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.7230 | 0.632991 | 0.316496 | − | 0.948594i | \(-0.397494\pi\) | ||||
0.316496 | + | 0.948594i | \(0.397494\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.26107 | 0.182860 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.8139 | −0.891569 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.9906 | 0.469922 | 0.234961 | − | 0.972005i | \(-0.424504\pi\) | ||||
0.234961 | + | 0.972005i | \(0.424504\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.7610 | 0.672665 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.95873 | −0.211249 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 45.1075 | 1.91817 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.01956 | −0.0432781 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.9252 | 1.09849 | 0.549243 | − | 0.835663i | \(-0.314916\pi\) | ||||
0.549243 | + | 0.835663i | \(0.314916\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.69283 | 0.240781 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.386204 | 0.0163055 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.0775 | 0.888310 | 0.444155 | − | 0.895950i | \(-0.353504\pi\) | ||||
0.444155 | + | 0.895950i | \(0.353504\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.3255 | −0.434395 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.2164 | 1.10099 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.2369 | −0.471076 | −0.235538 | − | 0.971865i | \(-0.575685\pi\) | ||||
−0.235538 | + | 0.971865i | \(0.575685\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.5037 | 1.77872 | 0.889362 | − | 0.457204i | \(-0.151149\pi\) | ||||
0.889362 | + | 0.457204i | \(0.151149\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.08401 | −0.212388 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.72209 | −0.363736 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.6503 | −1.10947 | −0.554733 | − | 0.832029i | \(-0.687179\pi\) | ||||
−0.554733 | + | 0.832029i | \(0.687179\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.469376 | −0.0195066 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.2795 | −0.426464 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.25067 | −0.176045 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.3801 | −0.635888 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.2195 | −1.37111 | −0.685557 | − | 0.728019i | \(-0.740441\pi\) | ||||
−0.685557 | + | 0.728019i | \(0.740441\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.44620 | 0.141998 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.34428 | −0.0552964 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.4149 | −1.04367 | −0.521833 | − | 0.853047i | \(-0.674752\pi\) | ||||
−0.521833 | + | 0.853047i | \(0.674752\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.68623 | −0.356101 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.895632 | −0.0366558 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −46.6431 | −1.90578 | −0.952892 | − | 0.303310i | \(-0.901908\pi\) | ||||
−0.952892 | + | 0.303310i | \(0.901908\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 47.4644 | 1.93611 | 0.968056 | − | 0.250734i | \(-0.0806718\pi\) | ||||
0.968056 | + | 0.250734i | \(0.0806718\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.2137 | 0.823166 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.6574 | 0.636566 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.4897 | 0.994006 | 0.497003 | − | 0.867749i | \(-0.334434\pi\) | ||||
0.497003 | + | 0.867749i | \(0.334434\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.37514 | −0.136768 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.4259 | −0.462241 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.9950 | 0.767201 | 0.383600 | − | 0.923499i | \(-0.374684\pi\) | ||||
0.383600 | + | 0.923499i | \(0.374684\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.57019 | 0.0633162 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.219907 | −0.00885311 | −0.00442656 | − | 0.999990i | \(-0.501409\pi\) | ||||
−0.00442656 | + | 0.999990i | \(0.501409\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.9136 | 0.639623 | 0.319811 | − | 0.947481i | \(-0.396380\pi\) | ||||
0.319811 | + | 0.947481i | \(0.396380\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.44401 | −0.178332 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29.5478 | −1.18381 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.29109 | −0.211644 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.211222 | 0.00843539 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.41012 | 0.215716 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.6207 | 1.09956 | 0.549781 | − | 0.835309i | \(-0.314711\pi\) | ||||
0.549781 | + | 0.835309i | \(0.314711\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.370021 | −0.0147070 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.1544 | 0.402966 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.01308 | −0.317490 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.2019 | 0.601376 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.17066 | −0.164731 | −0.0823656 | − | 0.996602i | \(-0.526248\pi\) | ||||
−0.0823656 | + | 0.996602i | \(0.526248\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.8643 | 0.822806 | 0.411403 | − | 0.911453i | \(-0.365039\pi\) | ||||
0.411403 | + | 0.911453i | \(0.365039\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.583619 | 0.0229800 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.7924 | −1.24989 | −0.624943 | − | 0.780670i | \(-0.714878\pi\) | ||||
−0.624943 | + | 0.780670i | \(0.714878\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.375512 | 0.0147401 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.34564 | 0.0919331 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.2099 | −1.06481 | −0.532403 | − | 0.846491i | \(-0.678711\pi\) | ||||
−0.532403 | + | 0.846491i | \(0.678711\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.1514 | 0.865528 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.54068 | 0.138135 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.8090 | 1.27806 | 0.639030 | − | 0.769182i | \(-0.279336\pi\) | ||||
0.639030 | + | 0.769182i | \(0.279336\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.5824 | 0.489398 | 0.244699 | − | 0.969599i | \(-0.421311\pi\) | ||||
0.244699 | + | 0.969599i | \(0.421311\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.36549 | −0.0530314 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.75066 | −0.184223 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.6669 | −0.645345 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.42915 | 0.248565 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.07787 | −0.196029 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.58049 | −0.0994704 | −0.0497352 | − | 0.998762i | \(-0.515838\pi\) | ||||
−0.0497352 | + | 0.998762i | \(0.515838\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.43104 | 0.132061 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.86443 | 0.225388 | 0.112694 | − | 0.993630i | \(-0.464052\pi\) | ||||
0.112694 | + | 0.993630i | \(0.464052\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.8921 | 0.417999 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.45535 | −0.170729 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.3162 | 0.509531 | 0.254765 | − | 0.967003i | \(-0.418002\pi\) | ||||
0.254765 | + | 0.967003i | \(0.418002\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.4760 | 0.705931 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.33183 | 0.127117 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.0290 | 0.572560 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.9751 | 1.33051 | 0.665257 | − | 0.746614i | \(-0.268322\pi\) | ||||
0.665257 | + | 0.746614i | \(0.268322\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.59255 | −0.326404 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.3614 | 0.658555 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.33190 | −0.315593 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.50494 | 0.0947454 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.91851 | 0.185769 | 0.0928847 | − | 0.995677i | \(-0.470391\pi\) | ||||
0.0928847 | + | 0.995677i | \(0.470391\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.95889 | 0.111597 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.17136 | −0.0441159 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −41.4717 | −1.55971 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.4930 | 1.03252 | 0.516261 | − | 0.856431i | \(-0.327324\pi\) | ||||
0.516261 | + | 0.856431i | \(0.327324\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −43.4479 | −1.62942 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.5831 | 0.433791 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.95514 | 0.185312 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.42270 | 0.165169 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.8746 | −0.405553 | −0.202777 | − | 0.979225i | \(-0.564996\pi\) | ||||
−0.202777 | + | 0.979225i | \(0.564996\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.3580 | −0.758172 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.51424 | −0.130696 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.8678 | 0.477899 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.13818 | 0.0422127 | 0.0211063 | − | 0.999777i | \(-0.493281\pi\) | ||||
0.0211063 | + | 0.999777i | \(0.493281\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.3705 | −0.902612 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.09686 | −0.114541 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.9950 | −1.03402 | −0.517010 | − | 0.855980i | \(-0.672955\pi\) | ||||
−0.517010 | + | 0.855980i | \(0.672955\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.821486 | −0.0303010 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.51243 | −0.239889 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.2375 | 1.62730 | 0.813652 | − | 0.581352i | \(-0.197476\pi\) | ||||
0.813652 | + | 0.581352i | \(0.197476\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.746814 | −0.0274349 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −49.4810 | −1.81528 | −0.907640 | − | 0.419749i | \(-0.862118\pi\) | ||||
−0.907640 | + | 0.419749i | \(0.862118\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.9063 | −0.436214 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.90126 | 0.362268 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −48.5597 | −1.77433 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.9833 | −0.948145 | −0.474073 | − | 0.880486i | \(-0.657217\pi\) | ||||
−0.474073 | + | 0.880486i | \(0.657217\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.33495 | 0.0850904 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.81002 | 0.175055 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.1605 | 1.56869 | 0.784347 | − | 0.620322i | \(-0.212998\pi\) | ||||
0.784347 | + | 0.620322i | \(0.212998\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.709944 | 0.0257693 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.16498 | 0.150981 | 0.0754903 | − | 0.997147i | \(-0.475948\pi\) | ||||
0.0754903 | + | 0.997147i | \(0.475948\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 41.1140 | 1.48843 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.36664 | 0.302497 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.32769 | −0.0479402 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.24441 | 0.189118 | 0.0945591 | − | 0.995519i | \(-0.469856\pi\) | ||||
0.0945591 | + | 0.995519i | \(0.469856\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.378011 | −0.0136137 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.91186 | 0.140700 | 0.0703499 | − | 0.997522i | \(-0.477588\pi\) | ||||
0.0703499 | + | 0.997522i | \(0.477588\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.94284 | −0.321236 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.01396 | 0.0722505 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.55687 | −0.163267 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.89772 | −0.175254 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.55632 | 0.234304 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.1061 | 0.824692 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.8869 | 0.601952 | 0.300976 | − | 0.953632i | \(-0.402688\pi\) | ||||
0.300976 | + | 0.953632i | \(0.402688\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.07421 | 0.109445 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.3960 | 0.725199 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.9537 | 0.637556 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.54075 | 0.0546447 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.3722 | 0.898729 | 0.449365 | − | 0.893348i | \(-0.351650\pi\) | ||||
0.449365 | + | 0.893348i | \(0.351650\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.21557 | 0.219891 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28.4606 | 1.00561 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.14073 | −0.0402556 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.9676 | −0.562783 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.32522 | −0.117053 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31.5640 | −1.10973 | −0.554866 | − | 0.831940i | \(-0.687230\pi\) | ||||
−0.554866 | + | 0.831940i | \(0.687230\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.1203 | −1.54927 | −0.774636 | − | 0.632407i | \(-0.782067\pi\) | ||||
−0.774636 | + | 0.632407i | \(0.782067\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.916949 | −0.0321588 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.7646 | 1.00758 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.69373 | −0.0592560 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 30.3805 | 1.06158 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.81015 | 0.132975 | 0.0664876 | − | 0.997787i | \(-0.478821\pi\) | ||||
0.0664876 | + | 0.997787i | \(0.478821\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.3301 | −1.19667 | −0.598336 | − | 0.801245i | \(-0.704171\pi\) | ||||
−0.598336 | + | 0.801245i | \(0.704171\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.548119 | −0.0190830 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.7484 | 1.06923 | 0.534613 | − | 0.845097i | \(-0.320457\pi\) | ||||
0.534613 | + | 0.845097i | \(0.320457\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.1917 | −0.353971 | −0.176986 | − | 0.984213i | \(-0.556635\pi\) | ||||
−0.176986 | + | 0.984213i | \(0.556635\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.72633 | −0.198644 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.35905 | 0.151032 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.7617 | −0.614669 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.55649 | −0.157495 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.81123 | 0.269674 | 0.134837 | − | 0.990868i | \(-0.456949\pi\) | ||||
0.134837 | + | 0.990868i | \(0.456949\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.41104 | −0.152105 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.28177 | −0.0785884 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.64074 | 0.0908442 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30.9284 | −1.06271 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.55424 | 0.0533415 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.94521 | 0.340918 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46.9706 | −1.60824 | −0.804122 | − | 0.594465i | \(-0.797364\pi\) | ||||
−0.804122 | + | 0.594465i | \(0.797364\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.57587 | 0.156491 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.24191 | 0.0765821 | 0.0382911 | − | 0.999267i | \(-0.487809\pi\) | ||||
0.0382911 | + | 0.999267i | \(0.487809\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.9456 | 1.70412 | 0.852061 | − | 0.523442i | \(-0.175352\pi\) | ||||
0.852061 | + | 0.523442i | \(0.175352\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.10162 | −0.105703 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.4322 | 0.355115 | 0.177557 | − | 0.984110i | \(-0.443180\pi\) | ||||
0.177557 | + | 0.984110i | \(0.443180\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.1807 | −0.380154 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.03444 | −0.103055 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.9980 | 0.474849 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.0259 | 0.780203 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.4913 | −0.355077 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36.0812 | 1.21977 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.6385 | 0.798215 | 0.399107 | − | 0.916904i | \(-0.369320\pi\) | ||||
0.399107 | + | 0.916904i | \(0.369320\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.07534 | −0.238645 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.2713 | −0.986175 | −0.493087 | − | 0.869980i | \(-0.664132\pi\) | ||||
−0.493087 | + | 0.869980i | \(0.664132\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.1875 | 1.41972 | 0.709862 | − | 0.704341i | \(-0.248757\pi\) | ||||
0.709862 | + | 0.704341i | \(0.248757\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.136112 | −0.00457537 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.32254 | −0.0444064 | −0.0222032 | − | 0.999753i | \(-0.507068\pi\) | ||||
−0.0222032 | + | 0.999753i | \(0.507068\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.0582 | −0.672730 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.13561 | 0.272553 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.39941 | 0.113757 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.60286 | −0.254136 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.51014 | −0.0838110 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.0887 | −0.569941 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.17567 | −0.272371 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.15283 | −0.0383638 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −29.7406 | −0.988611 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.58771 | 0.119128 | 0.0595639 | − | 0.998224i | \(-0.481029\pi\) | ||||
0.0595639 | + | 0.998224i | \(0.481029\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 39.9459 | 1.32492 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.6828 | −0.486464 | −0.243232 | − | 0.969968i | \(-0.578208\pi\) | ||||
−0.243232 | + | 0.969968i | \(0.578208\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.18998 | −0.105573 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.84058 | 0.0608478 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −43.7561 | −1.44495 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.2168 | −1.26066 | −0.630328 | − | 0.776329i | \(-0.717080\pi\) | ||||
−0.630328 | + | 0.776329i | \(0.717080\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.43494 | −0.0472829 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.3168 | 0.569988 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.67829 | −0.252461 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.6090 | 0.644044 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36.8919 | 1.21038 | 0.605192 | − | 0.796080i | \(-0.293096\pi\) | ||||
0.605192 | + | 0.796080i | \(0.293096\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.38404 | 0.0781339 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.26521 | −0.205114 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.69555 | −0.0881541 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.7347 | 1.10206 | 0.551032 | − | 0.834484i | \(-0.314234\pi\) | ||||
0.551032 | + | 0.834484i | \(0.314234\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.80418 | 0.124145 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.91029 | 0.127472 | 0.0637360 | − | 0.997967i | \(-0.479698\pi\) | ||||
0.0637360 | + | 0.997967i | \(0.479698\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.3162 | −0.498765 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.28122 | 0.204328 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.8518 | 1.52248 | 0.761240 | − | 0.648470i | \(-0.224591\pi\) | ||||
0.761240 | + | 0.648470i | \(0.224591\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.03327 | 0.130925 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.57333 | −0.213155 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.5470 | 0.859941 | 0.429971 | − | 0.902843i | \(-0.358524\pi\) | ||||
0.429971 | + | 0.902843i | \(0.358524\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 35.4844 | 1.14825 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.04739 | −0.0338574 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −36.4959 | −1.17851 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.1237 | −0.616895 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 46.7731 | 1.50724 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.27606 | 0.105460 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.80878 | 0.218956 | 0.109478 | − | 0.993989i | \(-0.465082\pi\) | ||||
0.109478 | + | 0.993989i | \(0.465082\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.406261 | 0.0130510 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.4549 | −1.55499 | −0.777496 | − | 0.628887i | \(-0.783511\pi\) | ||||
−0.777496 | + | 0.628887i | \(0.783511\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −34.2942 | −1.09942 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.93797 | 0.0620648 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46.0137 | 1.47211 | 0.736055 | − | 0.676922i | \(-0.236686\pi\) | ||||
0.736055 | + | 0.676922i | \(0.236686\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.16941 | −0.293056 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −39.6013 | −1.26437 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.8031 | 0.886782 | 0.443391 | − | 0.896328i | \(-0.353775\pi\) | ||||
0.443391 | + | 0.896328i | \(0.353775\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.38258 | 0.298954 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.31380 | 0.0736490 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.69283 | −0.181022 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.16951 | 0.164215 | 0.0821074 | − | 0.996623i | \(-0.473835\pi\) | ||||
0.0821074 | + | 0.996623i | \(0.473835\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.56646 | −0.144912 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.25116 | 0.198175 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.7227 | 0.592953 | 0.296476 | − | 0.955040i | \(-0.404188\pi\) | ||||
0.296476 | + | 0.955040i | \(0.404188\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.91218 | −0.123776 |
(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 | 4864.2.a.bm.1.5 | 8 | ||
4.3 | odd | 2 | 4864.2.a.br.1.3 | 8 | |||
8.3 | odd | 2 | inner | 4864.2.a.bm.1.6 | 8 | ||
8.5 | even | 2 | 4864.2.a.br.1.4 | 8 | |||
16.3 | odd | 4 | 2432.2.c.i.1217.8 | yes | 16 | ||
16.5 | even | 4 | 2432.2.c.i.1217.7 | ✓ | 16 | ||
16.11 | odd | 4 | 2432.2.c.i.1217.9 | yes | 16 | ||
16.13 | even | 4 | 2432.2.c.i.1217.10 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.i.1217.7 | ✓ | 16 | 16.5 | even | 4 | ||
2432.2.c.i.1217.8 | yes | 16 | 16.3 | odd | 4 | ||
2432.2.c.i.1217.9 | yes | 16 | 16.11 | odd | 4 | ||
2432.2.c.i.1217.10 | yes | 16 | 16.13 | even | 4 | ||
4864.2.a.bm.1.5 | 8 | 1.1 | even | 1 | trivial | ||
4864.2.a.bm.1.6 | 8 | 8.3 | odd | 2 | inner | ||
4864.2.a.br.1.3 | 8 | 4.3 | odd | 2 | |||
4864.2.a.br.1.4 | 8 | 8.5 | even | 2 |