Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6032,2,Mod(1,6032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6032, 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("6032.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6032 = 2^{4} \cdot 13 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6032.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: | \(48.1657624992\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 5x^{10} - 9x^{9} + 65x^{8} + 19x^{7} - 298x^{6} + 17x^{5} + 541x^{4} - 60x^{3} - 287x^{2} + 16x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 3016) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.224040\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6032.1 |
$q$-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 | ||||||||
\(3\) | 1.22404 | 0.706700 | 0.353350 | − | 0.935491i | \(-0.385042\pi\) | ||||
0.353350 | + | 0.935491i | \(0.385042\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.27866 | −1.46626 | −0.733131 | − | 0.680088i | \(-0.761942\pi\) | ||||
−0.733131 | + | 0.680088i | \(0.761942\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.601962 | −0.227520 | −0.113760 | − | 0.993508i | \(-0.536290\pi\) | ||||
−0.113760 | + | 0.993508i | \(0.536290\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.50173 | −0.500575 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.827372 | −0.249462 | −0.124731 | − | 0.992191i | \(-0.539807\pi\) | ||||
−0.124731 | + | 0.992191i | \(0.539807\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.01321 | −1.03621 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.70818 | 0.656831 | 0.328415 | − | 0.944533i | \(-0.393485\pi\) | ||||
0.328415 | + | 0.944533i | \(0.393485\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.59408 | 0.595123 | 0.297562 | − | 0.954703i | \(-0.403827\pi\) | ||||
0.297562 | + | 0.954703i | \(0.403827\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.736826 | −0.160789 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.76786 | −0.577139 | −0.288569 | − | 0.957459i | \(-0.593180\pi\) | ||||
−0.288569 | + | 0.957459i | \(0.593180\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.74961 | 1.14992 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.51029 | −1.06046 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.65930 | −1.37565 | −0.687826 | − | 0.725876i | \(-0.741435\pi\) | ||||
−0.687826 | + | 0.725876i | \(0.741435\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.01274 | −0.176295 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.97363 | 0.333604 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.225685 | −0.0371024 | −0.0185512 | − | 0.999828i | \(-0.505905\pi\) | ||||
−0.0185512 | + | 0.999828i | \(0.505905\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.22404 | 0.196003 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.73068 | 0.738808 | 0.369404 | − | 0.929269i | \(-0.379562\pi\) | ||||
0.369404 | + | 0.929269i | \(0.379562\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.77861 | −0.423734 | −0.211867 | − | 0.977298i | \(-0.567954\pi\) | ||||
−0.211867 | + | 0.977298i | \(0.567954\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.92365 | 0.733974 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.82952 | 0.850323 | 0.425161 | − | 0.905118i | \(-0.360217\pi\) | ||||
0.425161 | + | 0.905118i | \(0.360217\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.63764 | −0.948235 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.31492 | 0.464182 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.2897 | −1.68812 | −0.844060 | − | 0.536249i | \(-0.819841\pi\) | ||||
−0.844060 | + | 0.536249i | \(0.819841\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.71267 | 0.365776 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.17526 | 0.420574 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.83353 | 1.28022 | 0.640108 | − | 0.768285i | \(-0.278890\pi\) | ||||
0.640108 | + | 0.768285i | \(0.278890\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9144 | 1.39745 | 0.698724 | − | 0.715391i | \(-0.253752\pi\) | ||||
0.698724 | + | 0.715391i | \(0.253752\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.903982 | 0.113891 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.27866 | −0.406668 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.31721 | −0.283092 | −0.141546 | − | 0.989932i | \(-0.545207\pi\) | ||||
−0.141546 | + | 0.989932i | \(0.545207\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.38797 | −0.407864 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.35144 | −0.872455 | −0.436228 | − | 0.899836i | \(-0.643686\pi\) | ||||
−0.436228 | + | 0.899836i | \(0.643686\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.82727 | 0.330906 | 0.165453 | − | 0.986218i | \(-0.447091\pi\) | ||||
0.165453 | + | 0.986218i | \(0.447091\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.03776 | 0.812650 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.498046 | 0.0567577 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.87837 | 0.436350 | 0.218175 | − | 0.975910i | \(-0.429990\pi\) | ||||
0.218175 | + | 0.975910i | \(0.429990\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.23965 | −0.248850 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.8866 | 1.41449 | 0.707246 | − | 0.706967i | \(-0.249937\pi\) | ||||
0.707246 | + | 0.706967i | \(0.249937\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.87921 | −0.963085 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.22404 | −0.131231 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.09649 | 0.646227 | 0.323114 | − | 0.946360i | \(-0.395270\pi\) | ||||
0.323114 | + | 0.946360i | \(0.395270\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.601962 | −0.0631028 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.37529 | −0.972173 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.50511 | −0.872606 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.349662 | −0.0355028 | −0.0177514 | − | 0.999842i | \(-0.505651\pi\) | ||||
−0.0177514 | + | 0.999842i | \(0.505651\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.24248 | 0.124874 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.06282 | −0.802281 | −0.401140 | − | 0.916017i | \(-0.631386\pi\) | ||||
−0.401140 | + | 0.916017i | \(0.631386\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.0253 | 1.08636 | 0.543178 | − | 0.839618i | \(-0.317221\pi\) | ||||
0.543178 | + | 0.839618i | \(0.317221\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.41580 | 0.235758 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.10422 | −0.686791 | −0.343396 | − | 0.939191i | \(-0.611577\pi\) | ||||
−0.343396 | + | 0.939191i | \(0.611577\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.85946 | 0.465452 | 0.232726 | − | 0.972542i | \(-0.425235\pi\) | ||||
0.232726 | + | 0.972542i | \(0.425235\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.276248 | −0.0262203 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.87435 | 0.552613 | 0.276306 | − | 0.961070i | \(-0.410890\pi\) | ||||
0.276306 | + | 0.961070i | \(0.410890\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.07487 | 0.846236 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.50173 | −0.138835 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.63022 | −0.149442 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3155 | −0.937769 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.79054 | 0.522116 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.45773 | −0.219826 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.3798 | 1.71968 | 0.859840 | − | 0.510564i | \(-0.170563\pi\) | ||||
0.859840 | + | 0.510564i | \(0.170563\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.40113 | −0.299453 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.2164 | 1.59157 | 0.795787 | − | 0.605576i | \(-0.207057\pi\) | ||||
0.795787 | + | 0.605576i | \(0.207057\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.56154 | −0.135403 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18.0664 | 1.55491 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.20370 | −0.102839 | −0.0514194 | − | 0.998677i | \(-0.516375\pi\) | ||||
−0.0514194 | + | 0.998677i | \(0.516375\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.8228 | 0.917974 | 0.458987 | − | 0.888443i | \(-0.348212\pi\) | ||||
0.458987 | + | 0.888443i | \(0.348212\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.13557 | 0.600923 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.827372 | −0.0691883 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.27866 | 0.272278 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.12474 | −0.670117 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.9856 | −0.899972 | −0.449986 | − | 0.893036i | \(-0.648571\pi\) | ||||
−0.449986 | + | 0.893036i | \(0.648571\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.21821 | −0.343273 | −0.171637 | − | 0.985160i | \(-0.554905\pi\) | ||||
−0.171637 | + | 0.985160i | \(0.554905\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.06694 | −0.328793 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.1122 | 2.01706 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.93213 | 0.553244 | 0.276622 | − | 0.960979i | \(-0.410785\pi\) | ||||
0.276622 | + | 0.960979i | \(0.410785\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.0431 | −1.19299 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.66615 | 0.131311 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.5223 | 1.52911 | 0.764554 | − | 0.644560i | \(-0.222959\pi\) | ||||
0.764554 | + | 0.644560i | \(0.222959\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.32042 | 0.258494 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.0763064 | −0.00590477 | −0.00295238 | − | 0.999996i | \(-0.500940\pi\) | ||||
−0.00295238 | + | 0.999996i | \(0.500940\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.89560 | −0.297904 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.843567 | 0.0641352 | 0.0320676 | − | 0.999486i | \(-0.489791\pi\) | ||||
0.0320676 | + | 0.999486i | \(0.489791\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.46105 | −0.261631 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.0366 | 0.904729 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.2736 | 1.06686 | 0.533430 | − | 0.845844i | \(-0.320903\pi\) | ||||
0.533430 | + | 0.845844i | \(0.320903\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3154 | 0.766740 | 0.383370 | − | 0.923595i | \(-0.374763\pi\) | ||||
0.383370 | + | 0.923595i | \(0.374763\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.3597 | 0.987576 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.739945 | 0.0544018 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.24067 | −0.163854 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.31699 | 0.241275 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.42264 | 0.175296 | 0.0876481 | − | 0.996151i | \(-0.472065\pi\) | ||||
0.0876481 | + | 0.996151i | \(0.472065\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.5027 | 1.33186 | 0.665928 | − | 0.746016i | \(-0.268036\pi\) | ||||
0.665928 | + | 0.746016i | \(0.268036\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.01321 | −0.287392 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.70796 | −0.549169 | −0.274585 | − | 0.961563i | \(-0.588540\pi\) | ||||
−0.274585 | + | 0.961563i | \(0.588540\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.31700 | 0.589576 | 0.294788 | − | 0.955563i | \(-0.404751\pi\) | ||||
0.294788 | + | 0.955563i | \(0.404751\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.83635 | −0.200061 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.601962 | 0.0422495 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.5103 | −1.08329 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.15656 | 0.288901 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.14627 | −0.148461 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.75591 | −0.189725 | −0.0948623 | − | 0.995490i | \(-0.530241\pi\) | ||||
−0.0948623 | + | 0.995490i | \(0.530241\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.99846 | −0.616564 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.11012 | 0.621305 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.61061 | 0.312989 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.46069 | 0.233852 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.70818 | 0.182172 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.8675 | 0.794709 | 0.397354 | − | 0.917665i | \(-0.369928\pi\) | ||||
0.397354 | + | 0.917665i | \(0.369928\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.63434 | −0.575623 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.5666 | 1.63054 | 0.815270 | − | 0.579081i | \(-0.196589\pi\) | ||||
0.815270 | + | 0.579081i | \(0.196589\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.8212 | 0.847246 | 0.423623 | − | 0.905839i | \(-0.360758\pi\) | ||||
0.423623 | + | 0.905839i | \(0.360758\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.609629 | 0.0401106 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.73990 | −0.113985 | −0.0569924 | − | 0.998375i | \(-0.518151\pi\) | ||||
−0.0569924 | + | 0.998375i | \(0.518151\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.1130 | −1.24680 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.74728 | 0.308369 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.66422 | 0.107650 | 0.0538248 | − | 0.998550i | \(-0.482859\pi\) | ||||
0.0538248 | + | 0.998550i | \(0.482859\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.9604 | 1.15693 | 0.578466 | − | 0.815707i | \(-0.303652\pi\) | ||||
0.578466 | + | 0.815707i | \(0.303652\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.7895 | 0.884594 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21.7626 | 1.39036 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.59408 | 0.165058 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.7738 | 0.999622 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.3300 | −0.778260 | −0.389130 | − | 0.921183i | \(-0.627224\pi\) | ||||
−0.389130 | + | 0.921183i | \(0.627224\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.29005 | 0.143974 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.8685 | −0.680612 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.6115 | −1.72236 | −0.861178 | − | 0.508303i | \(-0.830273\pi\) | ||||
−0.861178 | + | 0.508303i | \(0.830273\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.135854 | 0.00844155 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.50173 | 0.0929544 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.7647 | −0.910433 | −0.455217 | − | 0.890381i | \(-0.650438\pi\) | ||||
−0.455217 | + | 0.890381i | \(0.650438\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 40.2937 | 2.47522 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.46236 | 0.456689 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.4044 | −1.18311 | −0.591554 | − | 0.806265i | \(-0.701486\pi\) | ||||
−0.591554 | + | 0.806265i | \(0.701486\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.7055 | 0.954041 | 0.477021 | − | 0.878892i | \(-0.341717\pi\) | ||||
0.477021 | + | 0.878892i | \(0.341717\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.736826 | −0.0445947 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.75707 | −0.286862 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.1155 | 1.32879 | 0.664395 | − | 0.747382i | \(-0.268689\pi\) | ||||
0.664395 | + | 0.747382i | \(0.268689\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.5022 | 0.688617 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.6693 | −1.65061 | −0.825307 | − | 0.564684i | \(-0.808998\pi\) | ||||
−0.825307 | + | 0.564684i | \(0.808998\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.45624 | −0.324340 | −0.162170 | − | 0.986763i | \(-0.551849\pi\) | ||||
−0.162170 | + | 0.986763i | \(0.551849\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.4106 | −0.616671 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.84769 | −0.168094 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.66575 | −0.568574 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.428001 | −0.0250898 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.54294 | 0.265402 | 0.132701 | − | 0.991156i | \(-0.457635\pi\) | ||||
0.132701 | + | 0.991156i | \(0.457635\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −32.2408 | −1.87713 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.55906 | 0.264544 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.76786 | −0.160069 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.67262 | 0.0964081 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.86922 | −0.566972 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −35.7847 | −2.04902 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.63926 | 0.321850 | 0.160925 | − | 0.986967i | \(-0.448552\pi\) | ||||
0.160925 | + | 0.986967i | \(0.448552\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.4954 | 0.767728 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.42432 | −0.307585 | −0.153792 | − | 0.988103i | \(-0.549149\pi\) | ||||
−0.153792 | + | 0.988103i | \(0.549149\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.4594 | 1.15643 | 0.578217 | − | 0.815883i | \(-0.303749\pi\) | ||||
0.578217 | + | 0.815883i | \(0.303749\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.96385 | −0.166994 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.27849 | −0.464966 | −0.232483 | − | 0.972600i | \(-0.574685\pi\) | ||||
−0.232483 | + | 0.972600i | \(0.574685\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.827372 | 0.0463239 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.69586 | −0.485355 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.02525 | 0.390895 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.74961 | 0.318931 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.94818 | 0.328935 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.50915 | −0.193466 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.1014 | 1.32473 | 0.662366 | − | 0.749181i | \(-0.269553\pi\) | ||||
0.662366 | + | 0.749181i | \(0.269553\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.338917 | 0.0185725 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.59733 | 0.415087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.3743 | −1.16433 | −0.582165 | − | 0.813071i | \(-0.697794\pi\) | ||||
−0.582165 | + | 0.813071i | \(0.697794\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.19044 | 0.390531 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.33709 | 0.343173 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.20934 | 0.443263 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.1080 | 0.598035 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.4461 | 0.614460 | 0.307230 | − | 0.951635i | \(-0.400598\pi\) | ||||
0.307230 | + | 0.951635i | \(0.400598\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.9218 | 1.01286 | 0.506431 | − | 0.862280i | \(-0.330964\pi\) | ||||
0.506431 | + | 0.862280i | \(0.330964\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.51029 | −0.294118 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.2270 | 0.757229 | 0.378615 | − | 0.925554i | \(-0.376401\pi\) | ||||
0.378615 | + | 0.925554i | \(0.376401\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.1029 | 1.27925 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.99546 | −0.105611 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.7948 | −0.991952 | −0.495976 | − | 0.868336i | \(-0.665190\pi\) | ||||
−0.495976 | + | 0.868336i | \(0.665190\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.2707 | −0.645828 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.6265 | −0.662721 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.26964 | −0.485195 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.7747 | −0.980032 | −0.490016 | − | 0.871713i | \(-0.663009\pi\) | ||||
−0.490016 | + | 0.871713i | \(0.663009\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.10418 | −0.369829 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.39793 | 0.384081 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.5892 | −1.73918 | −0.869591 | − | 0.493773i | \(-0.835617\pi\) | ||||
−0.869591 | + | 0.493773i | \(0.835617\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.00836 | −0.155351 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.00000 | −0.0515026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.40087 | 0.431524 | 0.215762 | − | 0.976446i | \(-0.430777\pi\) | ||||
0.215762 | + | 0.976446i | \(0.430777\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 23.7217 | 1.21530 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.27010 | −0.218192 | −0.109096 | − | 0.994031i | \(-0.534796\pi\) | ||||
−0.109096 | + | 0.994031i | \(0.534796\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.63292 | −0.0832216 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.17271 | 0.212111 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.2951 | 0.775491 | 0.387746 | − | 0.921766i | \(-0.373254\pi\) | ||||
0.387746 | + | 0.921766i | \(0.373254\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.49587 | −0.379082 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22.2976 | 1.12477 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.7158 | −0.639803 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.9177 | −0.547944 | −0.273972 | − | 0.961738i | \(-0.588338\pi\) | ||||
−0.273972 | + | 0.961738i | \(0.588338\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.91139 | −0.0956890 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.1764 | 1.00756 | 0.503779 | − | 0.863832i | \(-0.331942\pi\) | ||||
0.503779 | + | 0.863832i | \(0.331942\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.65930 | −0.381537 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.34304 | 0.364879 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.186725 | 0.00925564 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.4756 | 1.11135 | 0.555673 | − | 0.831401i | \(-0.312461\pi\) | ||||
0.555673 | + | 0.831401i | \(0.312461\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.47337 | −0.0726762 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.91941 | −0.291275 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −42.2509 | −2.07402 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.2475 | 0.648733 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.43850 | 0.265688 | 0.132844 | − | 0.991137i | \(-0.457589\pi\) | ||||
0.132844 | + | 0.991137i | \(0.457589\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.4707 | 1.29010 | 0.645051 | − | 0.764140i | \(-0.276836\pi\) | ||||
0.645051 | + | 0.764140i | \(0.276836\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.75434 | −0.425650 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.5710 | 0.755304 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.57006 | −0.317948 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.01274 | −0.0488954 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.0342 | −0.483328 | −0.241664 | − | 0.970360i | \(-0.577693\pi\) | ||||
−0.241664 | + | 0.970360i | \(0.577693\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.9045 | 1.00461 | 0.502304 | − | 0.864691i | \(-0.332486\pi\) | ||||
0.502304 | + | 0.864691i | \(0.332486\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.01321 | 0.192419 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.18006 | −0.343469 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.1346 | −0.913244 | −0.456622 | − | 0.889661i | \(-0.650941\pi\) | ||||
−0.456622 | + | 0.889661i | \(0.650941\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.96791 | 0.474663 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.99943 | 0.0949959 | 0.0474979 | − | 0.998871i | \(-0.484875\pi\) | ||||
0.0474979 | + | 0.998871i | \(0.484875\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.9883 | −0.947538 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.4468 | −0.636010 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.7572 | −1.16836 | −0.584182 | − | 0.811623i | \(-0.698585\pi\) | ||||
−0.584182 | + | 0.811623i | \(0.698585\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.91403 | −0.184305 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.16326 | −0.242591 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.97363 | 0.0925252 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.22345 | 0.384677 | 0.192338 | − | 0.981329i | \(-0.438393\pi\) | ||||
0.192338 | + | 0.981329i | \(0.438393\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.9229 | −0.696540 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.64673 | 0.123271 | 0.0616353 | − | 0.998099i | \(-0.480368\pi\) | ||||
0.0616353 | + | 0.998099i | \(0.480368\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.12629 | −0.238239 | −0.119119 | − | 0.992880i | \(-0.538007\pi\) | ||||
−0.119119 | + | 0.992880i | \(0.538007\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 30.7384 | 1.42546 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.3745 | 0.757722 | 0.378861 | − | 0.925454i | \(-0.376316\pi\) | ||||
0.378861 | + | 0.925454i | \(0.376316\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.39487 | 0.0644091 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.48521 | 0.390978 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.29894 | 0.105706 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.9150 | 0.684346 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.4557 | 0.845030 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.3991 | 1.06913 | 0.534566 | − | 0.845127i | \(-0.320475\pi\) | ||||
0.534566 | + | 0.845127i | \(0.320475\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.225685 | −0.0102904 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.03943 | 0.0927973 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.14642 | 0.0520564 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.7683 | −0.487958 | −0.243979 | − | 0.969780i | \(-0.578453\pi\) | ||||
−0.243979 | + | 0.969780i | \(0.578453\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.8961 | 1.08062 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.9891 | 1.17287 | 0.586436 | − | 0.809995i | \(-0.300530\pi\) | ||||
0.586436 | + | 0.809995i | \(0.300530\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.70818 | −0.121970 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.07369 | −0.183099 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.42529 | 0.198501 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.2986 | 0.819160 | 0.409580 | − | 0.912274i | \(-0.365675\pi\) | ||||
0.409580 | + | 0.912274i | \(0.365675\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.0934021 | −0.00417290 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −26.0611 | −1.16201 | −0.581003 | − | 0.813901i | \(-0.697340\pi\) | ||||
−0.581003 | + | 0.813901i | \(0.697340\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.4352 | 1.17635 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.22404 | 0.0543615 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −44.4586 | −1.97059 | −0.985296 | − | 0.170858i | \(-0.945346\pi\) | ||||
−0.985296 | + | 0.170858i | \(0.945346\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.70191 | −0.0752879 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.2942 | −0.631102 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −36.1482 | −1.59288 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.82318 | −0.212123 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.03256 | 0.0453244 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.4671 | −1.33479 | −0.667394 | − | 0.744705i | \(-0.732590\pi\) | ||||
−0.667394 | + | 0.744705i | \(0.732590\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.1943 | −0.926761 | −0.463381 | − | 0.886159i | \(-0.653364\pi\) | ||||
−0.463381 | + | 0.886159i | \(0.653364\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.23646 | −0.184894 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.7428 | −0.903570 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.3390 | −0.666911 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.7673 | −0.640844 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.73068 | 0.204909 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.2923 | 1.00702 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.4715 | 0.753950 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.49180 | 0.236548 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.1472 | 0.823203 | 0.411601 | − | 0.911364i | \(-0.364970\pi\) | ||||
0.411601 | + | 0.911364i | \(0.364970\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.6265 | 0.541855 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.9325 | −0.682474 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.6301 | −0.882078 | −0.441039 | − | 0.897488i | \(-0.645390\pi\) | ||||
−0.441039 | + | 0.897488i | \(0.645390\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.3905 | −0.699527 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.59408 | −0.110512 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.33463 | −0.0992785 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.905722 | 0.0384458 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.91634 | −0.250683 | −0.125342 | − | 0.992114i | \(-0.540003\pi\) | ||||
−0.125342 | + | 0.992114i | \(0.540003\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.77861 | −0.117523 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.74267 | −0.115796 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.1661 | −0.428451 | −0.214225 | − | 0.976784i | \(-0.568723\pi\) | ||||
−0.214225 | + | 0.976784i | \(0.568723\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.2600 | −0.810274 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.34818 | 0.0566183 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −37.8937 | −1.58859 | −0.794294 | − | 0.607534i | \(-0.792159\pi\) | ||||
−0.794294 | + | 0.607534i | \(0.792159\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.6930 | 1.20076 | 0.600382 | − | 0.799713i | \(-0.295015\pi\) | ||||
0.600382 | + | 0.799713i | \(0.295015\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.96541 | 0.123882 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.9141 | −0.663665 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 42.2707 | 1.75975 | 0.879875 | − | 0.475204i | \(-0.157626\pi\) | ||||
0.879875 | + | 0.475204i | \(0.157626\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.6481 | 0.941223 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.75727 | −0.321826 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.1681 | 0.421122 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.92365 | 0.203568 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.2525 | 0.464440 | 0.232220 | − | 0.972663i | \(-0.425401\pi\) | ||||
0.232220 | + | 0.972663i | \(0.425401\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.8689 | −0.818682 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.43485 | −0.388098 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.6952 | −0.973047 | −0.486523 | − | 0.873668i | \(-0.661735\pi\) | ||||
−0.486523 | + | 0.873668i | \(0.661735\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.34495 | 0.219121 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.1803 | 0.416654 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.45553 | −0.182048 | −0.0910240 | − | 0.995849i | \(-0.529014\pi\) | ||||
−0.0910240 | + | 0.995849i | \(0.529014\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.2125 | −0.946857 | −0.473428 | − | 0.880832i | \(-0.656984\pi\) | ||||
−0.473428 | + | 0.880832i | \(0.656984\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.47981 | 0.141709 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33.8209 | 1.37501 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.3209 | −1.55540 | −0.777698 | − | 0.628638i | \(-0.783613\pi\) | ||||
−0.777698 | + | 0.628638i | \(0.783613\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.736826 | 0.0298577 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.82952 | 0.235837 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.1580 | −0.450666 | −0.225333 | − | 0.974282i | \(-0.572347\pi\) | ||||
−0.225333 | + | 0.974282i | \(0.572347\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.9852 | −0.765558 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.05538 | −0.123005 | −0.0615026 | − | 0.998107i | \(-0.519589\pi\) | ||||
−0.0615026 | + | 0.998107i | \(0.519589\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.47159 | 0.0993416 | 0.0496708 | − | 0.998766i | \(-0.484183\pi\) | ||||
0.0496708 | + | 0.998766i | \(0.484183\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.2517 | 0.612030 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.66986 | −0.147030 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.6900 | −0.827601 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.62712 | −0.104917 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.611196 | −0.0243700 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.6543 | −0.862044 | −0.431022 | − | 0.902341i | \(-0.641847\pi\) | ||||
−0.431022 | + | 0.902341i | \(0.641847\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.37334 | −0.134078 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −63.5398 | −2.52150 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.63764 | −0.262993 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.0398 | 0.436729 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.1650 | 0.440989 | 0.220495 | − | 0.975388i | \(-0.429233\pi\) | ||||
0.220495 | + | 0.975388i | \(0.429233\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.1880 | −1.50599 | −0.752995 | − | 0.658027i | \(-0.771391\pi\) | ||||
−0.752995 | + | 0.658027i | \(0.771391\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.1512 | 0.439076 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.1272 | 1.57756 | 0.788782 | − | 0.614674i | \(-0.210712\pi\) | ||||
0.788782 | + | 0.614674i | \(0.210712\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.13598 | −0.319365 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.64357 | 0.221189 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −33.2910 | −1.30278 | −0.651389 | − | 0.758744i | \(-0.725813\pi\) | ||||
−0.651389 | + | 0.758744i | \(0.725813\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −59.7254 | −2.33366 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.24578 | −0.165643 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.5133 | 0.915948 | 0.457974 | − | 0.888965i | \(-0.348575\pi\) | ||||
0.457974 | + | 0.888965i | \(0.348575\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.2981 | 0.672818 | 0.336409 | − | 0.941716i | \(-0.390788\pi\) | ||||
0.336409 | + | 0.941716i | \(0.390788\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.31492 | 0.128741 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.11976 | 0.198536 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.76786 | 0.107172 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.5263 | 0.561621 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.03028 | −0.348610 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.2017 | −0.778719 | −0.389359 | − | 0.921086i | \(-0.627304\pi\) | ||||
−0.389359 | + | 0.921086i | \(0.627304\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −31.6821 | −1.21944 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.2741 | −0.471732 | −0.235866 | − | 0.971786i | \(-0.575793\pi\) | ||||
−0.235866 | + | 0.971786i | \(0.575793\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.210483 | 0.00807761 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30.0705 | 1.15230 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.4703 | 1.01286 | 0.506429 | − | 0.862282i | \(-0.330965\pi\) | ||||
0.506429 | + | 0.862282i | \(0.330965\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.94652 | 0.150789 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.6936 | 0.598749 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.2897 | −0.468200 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.6836 | 1.09118 | 0.545588 | − | 0.838054i | \(-0.316306\pi\) | ||||
0.545588 | + | 0.838054i | \(0.316306\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.747929 | −0.0284115 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −35.4841 | −1.34599 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.8115 | 0.485272 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.12971 | −0.0805531 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.08141 | −0.305231 | −0.152615 | − | 0.988286i | \(-0.548770\pi\) | ||||
−0.152615 | + | 0.988286i | \(0.548770\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.585446 | −0.0220805 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −23.3951 | −0.881111 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.85351 | 0.182535 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.8243 | −0.556737 | −0.278368 | − | 0.960474i | \(-0.589794\pi\) | ||||
−0.278368 | + | 0.960474i | \(0.589794\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.82424 | −0.218426 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.1999 | 0.793941 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.71267 | 0.101448 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.03708 | 0.0760760 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.0604 | −1.00918 | −0.504591 | − | 0.863359i | \(-0.668357\pi\) | ||||
−0.504591 | + | 0.863359i | \(0.668357\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.63682 | −0.247168 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.9843 | 0.817604 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.74961 | −0.213535 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.9983 | 0.704609 | 0.352304 | − | 0.935885i | \(-0.385398\pi\) | ||||
0.352304 | + | 0.935885i | \(0.385398\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.5978 | 0.873993 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.52498 | −0.278322 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.8868 | −0.549855 | −0.274928 | − | 0.961465i | \(-0.588654\pi\) | ||||
−0.274928 | + | 0.961465i | \(0.588654\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 26.6383 | 0.982567 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.91719 | 0.0706206 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.5322 | 0.718502 | 0.359251 | − | 0.933241i | \(-0.383032\pi\) | ||||
0.359251 | + | 0.933241i | \(0.383032\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.17526 | 0.116646 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.94584 | −0.291505 | −0.145752 | − | 0.989321i | \(-0.546560\pi\) | ||||
−0.145752 | + | 0.989321i | \(0.546560\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 36.0179 | 1.31959 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.3522 | −0.708060 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.27647 | 0.156259 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.5062 | 1.51458 | 0.757291 | − | 0.653077i | \(-0.226522\pi\) | ||||
0.757291 | + | 0.653077i | \(0.226522\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.0924 | −0.549996 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.8301 | 0.503328 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.188655 | −0.00685679 | −0.00342839 | − | 0.999994i | \(-0.501091\pi\) | ||||
−0.00342839 | + | 0.999994i | \(0.501091\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.80311 | 0.101747 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.1966 | 1.45712 | 0.728562 | − | 0.684980i | \(-0.240189\pi\) | ||||
0.728562 | + | 0.684980i | \(0.240189\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.92521 | −0.105900 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.3341 | 0.482096 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.83353 | 0.355068 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.0868 | 1.08496 | 0.542480 | − | 0.840069i | \(-0.317486\pi\) | ||||
0.542480 | + | 0.840069i | \(0.317486\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33.7976 | −1.21719 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.3747 | 0.588957 | 0.294479 | − | 0.955658i | \(-0.404854\pi\) | ||||
0.294479 | + | 0.955658i | \(0.404854\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −44.0380 | −1.58189 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.166291 | 0.00596564 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.2718 | 0.439682 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.08237 | 0.217644 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.51029 | 0.196922 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.7281 | −0.811201 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −49.3784 | −1.76015 | −0.880075 | − | 0.474834i | \(-0.842508\pi\) | ||||
−0.880075 | + | 0.474834i | \(0.842508\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.0726 | −0.643403 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.53614 | −0.125731 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.9144 | 0.387582 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 49.3212 | 1.74924 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.4158 | 1.28991 | 0.644956 | − | 0.764220i | \(-0.276876\pi\) | ||||
0.644956 | + | 0.764220i | \(0.276876\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.7874 | 0.558518 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.15526 | −0.323485 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.33920 | −0.0825486 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.46273 | −0.192536 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.7518 | −0.836103 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.2602 | 1.02873 | 0.514367 | − | 0.857570i | \(-0.328027\pi\) | ||||
0.514367 | + | 0.857570i | \(0.328027\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.304733 | 0.0107006 | 0.00535032 | − | 0.999986i | \(-0.498297\pi\) | ||||
0.00535032 | + | 0.999986i | \(0.498297\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.2242 | 0.674221 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −64.0071 | −2.24207 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.20795 | −0.252174 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.903982 | 0.0315877 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.799463 | 0.0279015 | 0.0139507 | − | 0.999903i | \(-0.495559\pi\) | ||||
0.0139507 | + | 0.999903i | \(0.495559\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.0421 | 0.594049 | 0.297024 | − | 0.954870i | \(-0.404006\pi\) | ||||
0.297024 | + | 0.954870i | \(0.404006\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.82284 | −0.202725 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.03107 | −0.0358537 | −0.0179268 | − | 0.999839i | \(-0.505707\pi\) | ||||
−0.0179268 | + | 0.999839i | \(0.505707\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.74405 | 0.164768 | 0.0823838 | − | 0.996601i | \(-0.473747\pi\) | ||||
0.0823838 | + | 0.996601i | \(0.473747\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.0702 | 0.939055 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.9759 | −0.622829 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.250183 | 0.00865793 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 42.2050 | 1.45882 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.4304 | −0.463668 | −0.231834 | − | 0.972755i | \(-0.574473\pi\) | ||||
−0.231834 | + | 0.972755i | \(0.574473\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −33.8684 | −1.16649 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.27866 | −0.112789 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.20951 | 0.213361 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.67866 | −0.229211 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.624665 | 0.0214132 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.41618 | 0.116968 | 0.0584839 | − | 0.998288i | \(-0.481373\pi\) | ||||
0.0584839 | + | 0.998288i | \(0.481373\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.7723 | 0.436805 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 50.4323 | 1.72273 | 0.861367 | − | 0.507983i | \(-0.169609\pi\) | ||||
0.861367 | + | 0.507983i | \(0.169609\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.273275 | −0.00932403 | −0.00466202 | − | 0.999989i | \(-0.501484\pi\) | ||||
−0.00466202 | + | 0.999989i | \(0.501484\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.48569 | −0.118792 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.64202 | −0.192057 | −0.0960284 | − | 0.995379i | \(-0.530614\pi\) | ||||
−0.0960284 | + | 0.995379i | \(0.530614\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.76577 | −0.0940390 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.8313 | −0.401811 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.20885 | −0.108853 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.31721 | −0.0785155 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.525097 | 0.0177718 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.47946 | 0.0500148 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.5694 | −0.390669 | −0.195335 | − | 0.980737i | \(-0.562579\pi\) | ||||
−0.195335 | + | 0.980737i | \(0.562579\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.56075 | 0.187559 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.9099 | −1.51305 | −0.756526 | − | 0.653964i | \(-0.773105\pi\) | ||||
−0.756526 | + | 0.653964i | \(0.773105\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.2202 | −1.18525 | −0.592627 | − | 0.805477i | \(-0.701909\pi\) | ||||
−0.592627 | + | 0.805477i | \(0.701909\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −39.4640 | −1.32657 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.3479 | −1.28760 | −0.643798 | − | 0.765196i | \(-0.722642\pi\) | ||||
−0.643798 | + | 0.765196i | \(0.722642\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.6659 | −0.391262 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.85302 | 0.0620785 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.1223 | 0.506047 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −46.7984 | −1.56430 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.38797 | −0.113121 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.65930 | 0.255452 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.2827 | −1.10881 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.04735 | 0.0681316 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33.8208 | −1.12424 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.7790 | 1.58648 | 0.793238 | − | 0.608912i | \(-0.208394\pi\) | ||||
0.793238 | + | 0.608912i | \(0.208394\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.1081 | 0.401602 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.9606 | 1.42335 | 0.711674 | − | 0.702510i | \(-0.247937\pi\) | ||||
0.711674 | + | 0.702510i | \(0.247937\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.6620 | −0.352862 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −43.8019 | −1.44805 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.9656 | −0.362115 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.0897 | 0.530749 | 0.265374 | − | 0.964145i | \(-0.414504\pi\) | ||||
0.265374 | + | 0.964145i | \(0.414504\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.90269 | 0.227451 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.35144 | −0.241976 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.29760 | −0.0426649 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.5570 | −0.543803 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.21769 | −0.0399511 | −0.0199756 | − | 0.999800i | \(-0.506359\pi\) | ||||
−0.0199756 | + | 0.999800i | \(0.506359\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.2186 | −0.564316 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.63958 | −0.217370 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.34640 | 0.240253 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.85548 | −0.321965 | −0.160982 | − | 0.986957i | \(-0.551466\pi\) | ||||
−0.160982 | + | 0.986957i | \(0.551466\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.0431 | 0.817252 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.3188 | 1.02096 | 0.510481 | − | 0.859889i | \(-0.329467\pi\) | ||||
0.510481 | + | 0.859889i | \(0.329467\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.0939 | −0.426395 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.8753 | −0.353773 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.90100 | 0.289243 | 0.144622 | − | 0.989487i | \(-0.453803\pi\) | ||||
0.144622 | + | 0.989487i | \(0.453803\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.82727 | 0.0917769 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.1332 | −0.328592 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.6383 | −1.12205 | −0.561023 | − | 0.827800i | \(-0.689592\pi\) | ||||
−0.561023 | + | 0.827800i | \(0.689592\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.94302 | −0.257030 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.01274 | 0.0327371 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.724580 | 0.0233979 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.6649 | 0.892416 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.6686 | 0.343790 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −60.6642 | −1.95285 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 58.8955 | 1.89395 | 0.946976 | − | 0.321306i | \(-0.104122\pi\) | ||||
0.946976 | + | 0.321306i | \(0.104122\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.59918 | 0.276246 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.25044 | 0.232678 | 0.116339 | − | 0.993210i | \(-0.462884\pi\) | ||||
0.116339 | + | 0.993210i | \(0.462884\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.51489 | −0.208858 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.03776 | 0.225389 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.2906 | 0.585167 | 0.292584 | − | 0.956240i | \(-0.405485\pi\) | ||||
0.292584 | + | 0.956240i | \(0.405485\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.04407 | −0.161209 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.29758 | −0.232994 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.4487 | −0.684109 | −0.342054 | − | 0.939680i | \(-0.611123\pi\) | ||||
−0.342054 | + | 0.939680i | \(0.611123\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.2718 | 0.805226 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.29534 | −0.136722 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.69081 | 0.244553 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56.1990 | 1.78522 | 0.892609 | − | 0.450831i | \(-0.148872\pi\) | ||||
0.892609 | + | 0.450831i | \(0.148872\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29.5011 | 0.936188 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.2686 | −0.864473 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.2578 | 1.43333 | 0.716664 | − | 0.697418i | \(-0.245668\pi\) | ||||
0.716664 | + | 0.697418i | \(0.245668\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.24359 | 0.0393455 |
(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 | 6032.2.a.bc.1.7 | 11 | ||
4.3 | odd | 2 | 3016.2.a.i.1.5 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3016.2.a.i.1.5 | ✓ | 11 | 4.3 | odd | 2 | ||
6032.2.a.bc.1.7 | 11 | 1.1 | even | 1 | trivial |