Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3380,2,Mod(1,3380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3380, 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("3380.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3380.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: | \(26.9894358832\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 260) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.51414\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3380.1 |
$q$-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 | ||||||||
\(3\) | 3.32088 | 1.91731 | 0.958657 | − | 0.284565i | \(-0.0918491\pi\) | ||||
0.958657 | + | 0.284565i | \(0.0918491\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.02827 | 1.90051 | 0.950254 | − | 0.311475i | \(-0.100823\pi\) | ||||
0.950254 | + | 0.311475i | \(0.100823\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.02827 | 2.67609 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.70739 | −0.514797 | −0.257399 | − | 0.966305i | \(-0.582865\pi\) | ||||
−0.257399 | + | 0.966305i | \(0.582865\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.32088 | −0.857449 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.64177 | −1.12579 | −0.562897 | − | 0.826527i | \(-0.690313\pi\) | ||||
−0.562897 | + | 0.826527i | \(0.690313\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.34916 | 0.997765 | 0.498883 | − | 0.866670i | \(-0.333744\pi\) | ||||
0.498883 | + | 0.866670i | \(0.333744\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 16.6983 | 3.64387 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.679116 | −0.141605 | −0.0708027 | − | 0.997490i | \(-0.522556\pi\) | ||||
−0.0708027 | + | 0.997490i | \(0.522556\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.6983 | 3.21359 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.02827 | −0.190946 | −0.0954728 | − | 0.995432i | \(-0.530436\pi\) | ||||
−0.0954728 | + | 0.995432i | \(0.530436\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.29261 | 0.411765 | 0.205883 | − | 0.978577i | \(-0.433994\pi\) | ||||
0.205883 | + | 0.978577i | \(0.433994\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.67004 | −0.987028 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.02827 | −0.849933 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.61350 | 0.265257 | 0.132628 | − | 0.991166i | \(-0.457658\pi\) | ||||
0.132628 | + | 0.991166i | \(0.457658\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.64177 | −0.724923 | −0.362461 | − | 0.931999i | \(-0.618063\pi\) | ||||
−0.362461 | + | 0.931999i | \(0.618063\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.32088 | −0.506430 | −0.253215 | − | 0.967410i | \(-0.581488\pi\) | ||||
−0.253215 | + | 0.967410i | \(0.581488\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.02827 | −1.19678 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.02827 | −0.149989 | −0.0749946 | − | 0.997184i | \(-0.523894\pi\) | ||||
−0.0749946 | + | 0.997184i | \(0.523894\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.2835 | 2.61193 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.4148 | −2.15850 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.41478 | −1.29322 | −0.646610 | − | 0.762821i | \(-0.723814\pi\) | ||||
−0.646610 | + | 0.762821i | \(0.723814\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.70739 | 0.230224 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.4431 | 1.91303 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.93438 | 1.16316 | 0.581579 | − | 0.813490i | \(-0.302435\pi\) | ||||
0.581579 | + | 0.813490i | \(0.302435\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.02827 | 1.15595 | 0.577976 | − | 0.816054i | \(-0.303843\pi\) | ||||
0.577976 | + | 0.816054i | \(0.303843\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 40.3684 | 5.08594 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.61350 | −0.685798 | −0.342899 | − | 0.939372i | \(-0.611409\pi\) | ||||
−0.342899 | + | 0.939372i | \(0.611409\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.25526 | −0.271502 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.70739 | −0.202630 | −0.101315 | − | 0.994854i | \(-0.532305\pi\) | ||||
−0.101315 | + | 0.994854i | \(0.532305\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.4431 | −1.45635 | −0.728175 | − | 0.685392i | \(-0.759631\pi\) | ||||
−0.728175 | + | 0.685392i | \(0.759631\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.32088 | 0.383463 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.58522 | −0.978377 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.64177 | −0.297222 | −0.148611 | − | 0.988896i | \(-0.547480\pi\) | ||||
−0.148611 | + | 0.988896i | \(0.547480\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 31.3684 | 3.48537 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.25526 | 0.906133 | 0.453066 | − | 0.891477i | \(-0.350330\pi\) | ||||
0.453066 | + | 0.891477i | \(0.350330\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.64177 | 0.503471 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.41478 | −0.366103 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.22699 | −0.130061 | −0.0650304 | − | 0.997883i | \(-0.520714\pi\) | ||||
−0.0650304 | + | 0.997883i | \(0.520714\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.61350 | 0.789483 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.34916 | −0.446214 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.0565477 | 0.00574155 | 0.00287078 | − | 0.999996i | \(-0.499086\pi\) | ||||
0.00287078 | + | 0.999996i | \(0.499086\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.7074 | −1.37764 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.37743 | 0.923986 | 0.461993 | − | 0.886884i | \(-0.347135\pi\) | ||||
0.461993 | + | 0.886884i | \(0.347135\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −16.6983 | −1.62959 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.3774 | −1.29325 | −0.646623 | − | 0.762810i | \(-0.723819\pi\) | ||||
−0.646623 | + | 0.762810i | \(0.723819\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.2835 | −1.08077 | −0.540383 | − | 0.841419i | \(-0.681721\pi\) | ||||
−0.540383 | + | 0.841419i | \(0.681721\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.35823 | 0.508581 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.6983 | −1.75899 | −0.879495 | − | 0.475908i | \(-0.842119\pi\) | ||||
−0.879495 | + | 0.475908i | \(0.842119\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.679116 | 0.0633278 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −23.3401 | −2.13958 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.08482 | −0.734984 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.4148 | −1.38990 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.7357 | 0.952636 | 0.476318 | − | 0.879273i | \(-0.341971\pi\) | ||||
0.476318 | + | 0.879273i | \(0.341971\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.0283 | −0.970985 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.22699 | 0.631425 | 0.315713 | − | 0.948855i | \(-0.397756\pi\) | ||||
0.315713 | + | 0.948855i | \(0.397756\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.8688 | 1.89626 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −16.6983 | −1.43716 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.3401 | −1.48146 | −0.740732 | − | 0.671801i | \(-0.765521\pi\) | ||||
−0.740732 | + | 0.671801i | \(0.765521\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.35823 | 0.793755 | 0.396877 | − | 0.917872i | \(-0.370094\pi\) | ||||
0.396877 | + | 0.917872i | \(0.370094\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.41478 | −0.287576 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.02827 | 0.0853935 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 60.7175 | 5.00790 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.3401 | −1.42056 | −0.710278 | − | 0.703922i | \(-0.751431\pi\) | ||||
−0.710278 | + | 0.703922i | \(0.751431\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.57615 | −0.291023 | −0.145511 | − | 0.989357i | \(-0.546483\pi\) | ||||
−0.145511 | + | 0.989357i | \(0.546483\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −37.2654 | −3.01273 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.29261 | −0.184147 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.28354 | −0.581290 | −0.290645 | − | 0.956831i | \(-0.593870\pi\) | ||||
−0.290645 | + | 0.956831i | \(0.593870\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −31.2654 | −2.47951 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.41478 | −0.269122 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.840485 | −0.0658319 | −0.0329159 | − | 0.999458i | \(-0.510479\pi\) | ||||
−0.0329159 | + | 0.999458i | \(0.510479\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.67004 | 0.441412 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.0283 | 1.00816 | 0.504079 | − | 0.863658i | \(-0.331832\pi\) | ||||
0.504079 | + | 0.863658i | \(0.331832\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 34.9162 | 2.67011 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 25.9253 | 1.97106 | 0.985532 | − | 0.169488i | \(-0.0542113\pi\) | ||||
0.985532 | + | 0.169488i | \(0.0542113\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.02827 | 0.380102 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 29.6700 | 2.23014 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.77301 | −0.356751 | −0.178376 | − | 0.983962i | \(-0.557084\pi\) | ||||
−0.178376 | + | 0.983962i | \(0.557084\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.3118 | −1.06379 | −0.531894 | − | 0.846811i | \(-0.678520\pi\) | ||||
−0.531894 | + | 0.846811i | \(0.678520\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 29.9819 | 2.21632 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.61350 | −0.118627 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.92531 | 0.579556 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 83.9637 | 6.10746 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0000 | 0.868290 | 0.434145 | − | 0.900843i | \(-0.357051\pi\) | ||||
0.434145 | + | 0.900843i | \(0.357051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.05655 | −0.291997 | −0.145998 | − | 0.989285i | \(-0.546639\pi\) | ||||
−0.145998 | + | 0.989285i | \(0.546639\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.2835 | 1.08891 | 0.544453 | − | 0.838791i | \(-0.316737\pi\) | ||||
0.544453 | + | 0.838791i | \(0.316737\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.77301 | −0.621902 | −0.310951 | − | 0.950426i | \(-0.600648\pi\) | ||||
−0.310951 | + | 0.950426i | \(0.600648\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.6418 | −1.31489 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.17044 | −0.362894 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.64177 | 0.324195 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.45213 | −0.378949 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.42571 | −0.513647 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.773010 | 0.0532162 | 0.0266081 | − | 0.999646i | \(-0.491529\pi\) | ||||
0.0266081 | + | 0.999646i | \(0.491529\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.67004 | −0.388505 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.32088 | 0.226482 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.5279 | 0.782563 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −41.3219 | −2.79228 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.3118 | 0.958390 | 0.479195 | − | 0.877709i | \(-0.340929\pi\) | ||||
0.479195 | + | 0.877709i | \(0.340929\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.02827 | 0.535218 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.7266 | 0.911066 | 0.455533 | − | 0.890219i | \(-0.349449\pi\) | ||||
0.455533 | + | 0.890219i | \(0.349449\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.9253 | −1.44887 | −0.724433 | − | 0.689346i | \(-0.757898\pi\) | ||||
−0.724433 | + | 0.689346i | \(0.757898\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −28.5105 | −1.87586 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.02827 | 0.0670772 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.77301 | −0.569868 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.7639 | 1.01968 | 0.509842 | − | 0.860268i | \(-0.329704\pi\) | ||||
0.509842 | + | 0.860268i | \(0.329704\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.92531 | −0.639345 | −0.319673 | − | 0.947528i | \(-0.603573\pi\) | ||||
−0.319673 | + | 0.947528i | \(0.603573\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 54.0757 | 3.46896 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.2835 | −1.16809 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 27.4148 | 1.73734 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.6983 | 1.55894 | 0.779472 | − | 0.626437i | \(-0.215487\pi\) | ||||
0.779472 | + | 0.626437i | \(0.215487\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.15951 | 0.0728981 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 15.4148 | 0.965311 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.0565 | −1.25109 | −0.625547 | − | 0.780187i | \(-0.715124\pi\) | ||||
−0.625547 | + | 0.780187i | \(0.715124\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.11310 | 0.504123 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.25526 | −0.510988 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.0757 | 1.60790 | 0.803950 | − | 0.594697i | \(-0.202728\pi\) | ||||
0.803950 | + | 0.594697i | \(0.202728\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.41478 | 0.578345 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.07469 | −0.249367 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.8296 | −0.782232 | −0.391116 | − | 0.920341i | \(-0.627911\pi\) | ||||
−0.391116 | + | 0.920341i | \(0.627911\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.7074 | 1.07565 | 0.537824 | − | 0.843057i | \(-0.319247\pi\) | ||||
0.537824 | + | 0.843057i | \(0.319247\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.70739 | −0.102959 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.4713 | −0.929582 | −0.464791 | − | 0.885420i | \(-0.653871\pi\) | ||||
−0.464791 | + | 0.885420i | \(0.653871\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 18.4057 | 1.10192 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.35823 | −0.438955 | −0.219478 | − | 0.975618i | \(-0.570435\pi\) | ||||
−0.219478 | + | 0.975618i | \(0.570435\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.604422 | −0.0359292 | −0.0179646 | − | 0.999839i | \(-0.505719\pi\) | ||||
−0.0179646 | + | 0.999839i | \(0.505719\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14.4431 | −0.855533 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −23.3401 | −1.37772 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.54602 | 0.267413 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.187788 | 0.0110084 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.0101 | −1.34427 | −0.672133 | − | 0.740430i | \(-0.734622\pi\) | ||||
−0.672133 | + | 0.740430i | \(0.734622\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.93438 | −0.520180 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −28.5105 | −1.65435 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.6983 | −0.962475 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.9253 | 1.14468 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.02827 | −0.516957 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.3684 | −1.16248 | −0.581242 | − | 0.813731i | \(-0.697433\pi\) | ||||
−0.581242 | + | 0.813731i | \(0.697433\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 31.1414 | 1.77157 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.9253 | −1.12986 | −0.564930 | − | 0.825139i | \(-0.691097\pi\) | ||||
−0.564930 | + | 0.825139i | \(0.691097\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.4713 | 1.77886 | 0.889432 | − | 0.457067i | \(-0.151100\pi\) | ||||
0.889432 | + | 0.457067i | \(0.151100\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −40.3684 | −2.27450 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.72659 | −0.0969750 | −0.0484875 | − | 0.998824i | \(-0.515440\pi\) | ||||
−0.0484875 | + | 0.998824i | \(0.515440\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.75566 | 0.0982983 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −44.4249 | −2.47956 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.1878 | −1.12328 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −37.4713 | −2.07217 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.17044 | −0.285056 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.4057 | −0.571949 | −0.285975 | − | 0.958237i | \(-0.592317\pi\) | ||||
−0.285975 | + | 0.958237i | \(0.592317\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.9536 | 0.709852 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.61350 | 0.306698 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.6983 | −0.582774 | −0.291387 | − | 0.956605i | \(-0.594117\pi\) | ||||
−0.291387 | + | 0.956605i | \(0.594117\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −62.0950 | −3.37253 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.91438 | −0.211976 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 56.7367 | 3.06349 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.25526 | 0.121419 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −32.6044 | −1.75030 | −0.875149 | − | 0.483854i | \(-0.839236\pi\) | ||||
−0.875149 | + | 0.483854i | \(0.839236\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.4148 | 0.718077 | 0.359038 | − | 0.933323i | \(-0.383105\pi\) | ||||
0.359038 | + | 0.933323i | \(0.383105\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 35.0101 | 1.86340 | 0.931701 | − | 0.363227i | \(-0.118325\pi\) | ||||
0.931701 | + | 0.363227i | \(0.118325\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.70739 | 0.0906188 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −77.5097 | −4.10225 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.9344 | −1.10487 | −0.552437 | − | 0.833555i | \(-0.686302\pi\) | ||||
−0.552437 | + | 0.833555i | \(0.686302\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.0848216 | −0.00446429 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −26.8488 | −1.40919 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.4431 | 0.651299 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.4340 | 0.596849 | 0.298424 | − | 0.954433i | \(-0.403539\pi\) | ||||
0.298424 | + | 0.954433i | \(0.403539\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −37.2654 | −1.93996 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −47.3401 | −2.45777 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.1131 | −0.730748 | −0.365374 | − | 0.930861i | \(-0.619059\pi\) | ||||
−0.365374 | + | 0.930861i | \(0.619059\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.32088 | −0.171490 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.89518 | 0.0973487 | 0.0486744 | − | 0.998815i | \(-0.484500\pi\) | ||||
0.0486744 | + | 0.998815i | \(0.484500\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 35.6519 | 1.82650 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.3118 | 1.14008 | 0.570040 | − | 0.821617i | \(-0.306928\pi\) | ||||
0.570040 | + | 0.821617i | \(0.306928\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.58522 | 0.437543 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −26.6610 | −1.35525 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −28.6802 | −1.45414 | −0.727071 | − | 0.686562i | \(-0.759119\pi\) | ||||
−0.727071 | + | 0.686562i | \(0.759119\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.15230 | 0.159419 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.0000 | 1.21064 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.64177 | 0.132922 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.5569 | −0.780781 | −0.390390 | − | 0.920649i | \(-0.627660\pi\) | ||||
−0.390390 | + | 0.920649i | \(0.627660\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 72.6236 | 3.63573 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.1696 | 1.20697 | 0.603487 | − | 0.797373i | \(-0.293777\pi\) | ||||
0.603487 | + | 0.797373i | \(0.293777\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −31.3684 | −1.55871 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.75486 | −0.136554 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.9253 | 1.47971 | 0.739856 | − | 0.672766i | \(-0.234894\pi\) | ||||
0.739856 | + | 0.672766i | \(0.234894\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −57.5844 | −2.84043 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 44.9245 | 2.21059 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.25526 | −0.405235 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 31.0776 | 1.52188 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.58522 | −0.419416 | −0.209708 | − | 0.977764i | \(-0.567251\pi\) | ||||
−0.209708 | + | 0.977764i | \(0.567251\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.7375 | 1.05942 | 0.529711 | − | 0.848178i | \(-0.322300\pi\) | ||||
0.529711 | + | 0.848178i | \(0.322300\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.25526 | −0.401385 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.64177 | −0.225159 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 45.3966 | 2.19690 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.7074 | −0.660262 | −0.330131 | − | 0.943935i | \(-0.607093\pi\) | ||||
−0.330131 | + | 0.943935i | \(0.607093\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −40.5671 | −1.94953 | −0.974765 | − | 0.223235i | \(-0.928338\pi\) | ||||
−0.974765 | + | 0.223235i | \(0.928338\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.41478 | 0.163726 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.95358 | −0.141289 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.5671 | 1.26798 | 0.633989 | − | 0.773342i | \(-0.281417\pi\) | ||||
0.633989 | + | 0.773342i | \(0.281417\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 146.785 | 6.98977 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.7922 | −0.797822 | −0.398911 | − | 0.916990i | \(-0.630612\pi\) | ||||
−0.398911 | + | 0.916990i | \(0.630612\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.22699 | 0.0581649 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −57.5844 | −2.72365 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.2443 | 0.766618 | 0.383309 | − | 0.923620i | \(-0.374785\pi\) | ||||
0.383309 | + | 0.923620i | \(0.374785\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.92531 | 0.373188 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.8760 | −0.557982 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.77301 | −0.316828 | −0.158414 | − | 0.987373i | \(-0.550638\pi\) | ||||
−0.158414 | + | 0.987373i | \(0.550638\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −77.5097 | −3.61784 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.8114 | 1.06243 | 0.531217 | − | 0.847236i | \(-0.321735\pi\) | ||||
0.531217 | + | 0.847236i | \(0.321735\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.3300 | 0.758917 | 0.379459 | − | 0.925209i | \(-0.376110\pi\) | ||||
0.379459 | + | 0.925209i | \(0.376110\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.61350 | −0.353067 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.6610 | 0.493331 | 0.246665 | − | 0.969101i | \(-0.420665\pi\) | ||||
0.246665 | + | 0.969101i | \(0.420665\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.2262 | −1.30336 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.1878 | −1.11451 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.67004 | 0.260709 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.34916 | 0.199553 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −75.5844 | −3.46077 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.48040 | −0.296097 | −0.148048 | − | 0.988980i | \(-0.547299\pi\) | ||||
−0.148048 | + | 0.988980i | \(0.547299\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.3401 | −0.515992 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.0565477 | −0.00256770 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.7831 | −1.07772 | −0.538858 | − | 0.842396i | \(-0.681144\pi\) | ||||
−0.538858 | + | 0.842396i | \(0.681144\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.79116 | −0.126220 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.13124 | −0.276699 | −0.138350 | − | 0.990383i | \(-0.544180\pi\) | ||||
−0.138350 | + | 0.990383i | \(0.544180\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.77301 | 0.214966 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.7074 | 0.616101 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.58522 | −0.385100 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.0475 | −0.942214 | −0.471107 | − | 0.882076i | \(-0.656146\pi\) | ||||
−0.471107 | + | 0.882076i | \(0.656146\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 43.2654 | 1.93296 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.5652 | 1.49660 | 0.748300 | − | 0.663361i | \(-0.230871\pi\) | ||||
0.748300 | + | 0.663361i | \(0.230871\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.00000 | −0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.5852 | 0.646479 | 0.323239 | − | 0.946317i | \(-0.395228\pi\) | ||||
0.323239 | + | 0.946317i | \(0.395228\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −62.5671 | −2.76780 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 72.6236 | 3.20641 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.37743 | −0.413219 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.75566 | 0.0772140 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 86.0950 | 3.77915 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.48225 | −0.152560 | −0.0762802 | − | 0.997086i | \(-0.524304\pi\) | ||||
−0.0762802 | + | 0.997086i | \(0.524304\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.5087 | −0.503239 | −0.251620 | − | 0.967826i | \(-0.580963\pi\) | ||||
−0.251620 | + | 0.967826i | \(0.580963\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.6983 | 0.728774 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.6418 | −0.463563 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5388 | −0.979948 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 71.7276 | 3.11271 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.3774 | 0.578357 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.8506 | −0.684004 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −31.2171 | −1.34462 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.8122 | 0.593833 | 0.296917 | − | 0.954903i | \(-0.404042\pi\) | ||||
0.296917 | + | 0.954903i | \(0.404042\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −47.5279 | −2.03962 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.2835 | 0.483334 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.37743 | −0.229922 | −0.114961 | − | 0.993370i | \(-0.536674\pi\) | ||||
−0.114961 | + | 0.993370i | \(0.536674\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 72.4815 | 3.09343 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.47213 | −0.190519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.2835 | −0.564873 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.35823 | −0.227444 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.0674757 | 0.00285904 | 0.00142952 | − | 0.999999i | \(-0.499545\pi\) | ||||
0.00142952 | + | 0.999999i | \(0.499545\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 26.3190 | 1.11119 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.20779 | −0.303772 | −0.151886 | − | 0.988398i | \(-0.548535\pi\) | ||||
−0.151886 | + | 0.988398i | \(0.548535\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.6983 | 0.786644 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 157.729 | 6.62398 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.85783 | −0.329417 | −0.164709 | − | 0.986342i | \(-0.552668\pi\) | ||||
−0.164709 | + | 0.986342i | \(0.552668\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.9253 | −1.00124 | −0.500621 | − | 0.865666i | \(-0.666895\pi\) | ||||
−0.500621 | + | 0.865666i | \(0.666895\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 39.8506 | 1.66478 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.679116 | −0.0283211 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.0101 | −1.29097 | −0.645484 | − | 0.763774i | \(-0.723344\pi\) | ||||
−0.645484 | + | 0.763774i | \(0.723344\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.4713 | −0.559849 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 41.5097 | 1.72211 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.0747 | 0.665746 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −47.4076 | −1.95672 | −0.978360 | − | 0.206911i | \(-0.933659\pi\) | ||||
−0.978360 | + | 0.206911i | \(0.933659\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.97093 | 0.410845 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 50.7549 | 2.08778 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.8861 | 0.611299 | 0.305650 | − | 0.952144i | \(-0.401126\pi\) | ||||
0.305650 | + | 0.952144i | \(0.401126\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.3401 | 0.956850 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −29.1342 | −1.19238 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.8680 | 1.75154 | 0.875769 | − | 0.482731i | \(-0.160355\pi\) | ||||
0.875769 | + | 0.482731i | \(0.160355\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −45.0667 | −1.83526 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.08482 | 0.328695 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.7357 | −0.760457 | −0.380229 | − | 0.924893i | \(-0.624155\pi\) | ||||
−0.380229 | + | 0.924893i | \(0.624155\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.1704 | −0.695781 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.6802 | −1.48150 | −0.740749 | − | 0.671782i | \(-0.765529\pi\) | ||||
−0.740749 | + | 0.671782i | \(0.765529\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.4148 | 0.621584 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.05655 | 0.324344 | 0.162172 | − | 0.986762i | \(-0.448150\pi\) | ||||
0.162172 | + | 0.986762i | \(0.448150\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.1606 | 1.33284 | 0.666418 | − | 0.745578i | \(-0.267827\pi\) | ||||
0.666418 | + | 0.745578i | \(0.267827\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.3401 | −0.455062 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.16964 | −0.247182 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −24.6599 | −0.984822 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.48947 | −0.298625 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.8205 | 1.34637 | 0.673186 | − | 0.739473i | \(-0.264925\pi\) | ||||
0.673186 | + | 0.739473i | \(0.264925\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.56708 | 0.102032 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.7357 | −0.426032 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.7074 | −0.542256 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.8296 | 0.506737 | 0.253369 | − | 0.967370i | \(-0.418461\pi\) | ||||
0.253369 | + | 0.967370i | \(0.418461\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.7084 | −1.72369 | −0.861846 | − | 0.507169i | \(-0.830692\pi\) | ||||
−0.861846 | + | 0.507169i | \(0.830692\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.0283 | 0.434238 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.4158 | 0.999200 | 0.499600 | − | 0.866256i | \(-0.333480\pi\) | ||||
0.499600 | + | 0.866256i | \(0.333480\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.2545 | −0.598790 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 38.2827 | 1.50042 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.94345 | −0.154319 | −0.0771596 | − | 0.997019i | \(-0.524585\pi\) | ||||
−0.0771596 | + | 0.997019i | \(0.524585\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.22699 | −0.282382 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −99.8962 | −3.89732 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.0950 | −1.48397 | −0.741984 | − | 0.670417i | \(-0.766115\pi\) | ||||
−0.741984 | + | 0.670417i | \(0.766115\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.1131 | −0.704518 | −0.352259 | − | 0.935903i | \(-0.614586\pi\) | ||||
−0.352259 | + | 0.935903i | \(0.614586\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −21.8688 | −0.848034 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.698317 | 0.0270389 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 47.5279 | 1.83753 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.4148 | −0.595081 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.2088 | 1.66558 | 0.832789 | − | 0.553590i | \(-0.186743\pi\) | ||||
0.832789 | + | 0.553590i | \(0.186743\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.6983 | 0.642719 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.6983 | −1.17983 | −0.589916 | − | 0.807465i | \(-0.700839\pi\) | ||||
−0.589916 | + | 0.807465i | \(0.700839\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.284337 | 0.0109119 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 45.5844 | 1.74680 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.9536 | 1.26093 | 0.630467 | − | 0.776216i | \(-0.282863\pi\) | ||||
0.630467 | + | 0.776216i | \(0.282863\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.3401 | 0.662531 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −72.8114 | −2.77793 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.1222 | −1.41219 | −0.706097 | − | 0.708115i | \(-0.749546\pi\) | ||||
−0.706097 | + | 0.708115i | \(0.749546\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −68.9245 | −2.61823 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.35823 | −0.354978 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.5460 | 0.816114 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.9253 | −0.753644 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.39663 | −0.279367 | −0.139683 | − | 0.990196i | \(-0.544609\pi\) | ||||
−0.139683 | + | 0.990196i | \(0.544609\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.01735 | 0.264664 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.41478 | 0.128608 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 30.1696 | 1.13465 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.7549 | −1.07991 | −0.539956 | − | 0.841693i | \(-0.681559\pi\) | ||||
−0.539956 | + | 0.841693i | \(0.681559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21.2088 | −0.795394 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.55695 | −0.0583081 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 52.3502 | 1.95505 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.4532 | −1.47136 | −0.735678 | − | 0.677332i | \(-0.763136\pi\) | ||||
−0.735678 | + | 0.677332i | \(0.763136\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 47.1523 | 1.75604 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −32.9608 | −1.22583 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.02827 | −0.0381891 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.866904 | −0.0321517 | −0.0160758 | − | 0.999871i | \(-0.505117\pi\) | ||||
−0.0160758 | + | 0.999871i | \(0.505117\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 85.4742 | 3.16571 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.4148 | 0.570136 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.0000 | 0.369358 | 0.184679 | − | 0.982799i | \(-0.440875\pi\) | ||||
0.184679 | + | 0.982799i | \(0.440875\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −60.7175 | −2.23960 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.58442 | 0.353047 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.5015 | 1.15880 | 0.579400 | − | 0.815043i | \(-0.303287\pi\) | ||||
0.579400 | + | 0.815043i | \(0.303287\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.8578 | 1.16875 | 0.584375 | − | 0.811484i | \(-0.301340\pi\) | ||||
0.584375 | + | 0.811484i | \(0.301340\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.3401 | 0.635292 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 66.2755 | 2.42489 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −67.2654 | −2.45782 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.0950 | 1.68203 | 0.841014 | − | 0.541013i | \(-0.181959\pi\) | ||||
0.841014 | + | 0.541013i | \(0.181959\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 82.0203 | 2.98898 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.57615 | 0.130149 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.01735 | 0.182359 | 0.0911793 | − | 0.995834i | \(-0.470936\pi\) | ||||
0.0911793 | + | 0.995834i | \(0.470936\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.85061 | 0.139768 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.8296 | −0.900071 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −56.7367 | −2.05401 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 37.2654 | 1.34733 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.9427 | −1.33219 | −0.666093 | − | 0.745869i | \(-0.732035\pi\) | ||||
−0.666093 | + | 0.745869i | \(0.732035\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −66.6055 | −2.39874 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.4431 | 0.591415 | 0.295708 | − | 0.955278i | \(-0.404445\pi\) | ||||
0.295708 | + | 0.955278i | \(0.404445\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.29261 | 0.0823530 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 26.9427 | 0.966562 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.1878 | −0.723303 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.91518 | 0.104313 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.1704 | −0.613622 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.28354 | 0.259961 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.2553 | −1.43495 | −0.717473 | − | 0.696587i | \(-0.754701\pi\) | ||||
−0.717473 | + | 0.696587i | \(0.754701\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 86.5946 | 3.08285 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −94.0203 | −3.34298 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 31.2654 | 1.10887 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.2835 | 0.966432 | 0.483216 | − | 0.875501i | \(-0.339468\pi\) | ||||
0.483216 | + | 0.875501i | \(0.339468\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.77301 | 0.168857 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.85061 | −0.348054 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.2451 | 0.749725 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.41478 | 0.120355 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −42.6055 | −1.49978 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.4815 | −1.00135 | −0.500677 | − | 0.865634i | \(-0.666916\pi\) | ||||
−0.500677 | + | 0.865634i | \(0.666916\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.6892 | −1.11276 | −0.556380 | − | 0.830928i | \(-0.687810\pi\) | ||||
−0.556380 | + | 0.830928i | \(0.687810\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 58.8042 | 2.06235 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.840485 | 0.0294409 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.4431 | −0.505298 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.65991 | 0.232433 | 0.116216 | − | 0.993224i | \(-0.462923\pi\) | ||||
0.116216 | + | 0.993224i | \(0.462923\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.79301 | −0.271647 | −0.135824 | − | 0.990733i | \(-0.543368\pi\) | ||||
−0.135824 | + | 0.990733i | \(0.543368\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.67004 | −0.197406 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.4249 | −0.918884 | −0.459442 | − | 0.888208i | \(-0.651951\pi\) | ||||
−0.459442 | + | 0.888208i | \(0.651951\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.7447 | 0.407912 | 0.203956 | − | 0.978980i | \(-0.434620\pi\) | ||||
0.203956 | + | 0.978980i | \(0.434620\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −51.3785 | −1.78230 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −84.8680 | −2.94050 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.0283 | −0.450862 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 38.2827 | 1.32325 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.5753 | 1.53891 | 0.769456 | − | 0.638700i | \(-0.220527\pi\) | ||||
0.769456 | + | 0.638700i | \(0.220527\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9427 | −0.963540 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.4358 | −0.841615 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −40.6527 | −1.39684 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.00722 | −0.0688875 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.09575 | −0.0375618 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.6135 | −1.01395 | −0.506973 | − | 0.861962i | \(-0.669236\pi\) | ||||
−0.506973 | + | 0.861962i | \(0.669236\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −34.9162 | −1.19411 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.5105 | 0.768945 | 0.384472 | − | 0.923136i | \(-0.374383\pi\) | ||||
0.384472 | + | 0.923136i | \(0.374383\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.585221 | −0.0199675 | −0.00998375 | − | 0.999950i | \(-0.503178\pi\) | ||||
−0.00998375 | + | 0.999950i | \(0.503178\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −77.5097 | −2.64152 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −45.6519 | −1.55401 | −0.777004 | − | 0.629495i | \(-0.783262\pi\) | ||||
−0.777004 | + | 0.629495i | \(0.783262\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.9253 | −0.881487 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.0968 | 0.512714 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.51053 | 0.153009 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.453981 | 0.0153649 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.02827 | −0.169987 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.0000 | 0.337676 | 0.168838 | − | 0.985644i | \(-0.445999\pi\) | ||||
0.168838 | + | 0.985644i | \(0.445999\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −76.4140 | −2.57738 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.5380 | 1.43314 | 0.716571 | − | 0.697514i | \(-0.245711\pi\) | ||||
0.716571 | + | 0.697514i | \(0.245711\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.22513 | 0.209492 | 0.104746 | − | 0.994499i | \(-0.466597\pi\) | ||||
0.104746 | + | 0.994499i | \(0.466597\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −29.6700 | −0.997348 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.0011 | 0.738723 | 0.369362 | − | 0.929286i | \(-0.379576\pi\) | ||||
0.369362 | + | 0.929286i | \(0.379576\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 53.9819 | 1.81049 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −53.5580 | −1.79426 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.47213 | −0.149654 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.77301 | 0.159544 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.35743 | −0.0786247 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.7012 | 1.45590 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −55.4532 | −1.84537 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.3118 | 0.475741 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.2070 | 0.936598 | 0.468299 | − | 0.883570i | \(-0.344867\pi\) | ||||
0.468299 | + | 0.883570i | \(0.344867\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 48.1696 | 1.59769 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.5105 | 1.34217 | 0.671087 | − | 0.741379i | \(-0.265828\pi\) | ||||
0.671087 | + | 0.741379i | \(0.265828\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.0950 | −0.466475 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −29.9819 | −0.991170 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.3393 | 1.20003 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.0746930 | 0.00246389 | 0.00123195 | − | 0.999999i | \(-0.499608\pi\) | ||||
0.00123195 | + | 0.999999i | \(0.499608\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −67.6410 | −2.22885 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.61350 | 0.0530514 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 75.2846 | 2.47267 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53.6410 | −1.75990 | −0.879952 | − | 0.475063i | \(-0.842425\pi\) | ||||
−0.879952 | + | 0.475063i | \(0.842425\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 79.5180 | 2.60610 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −66.1696 | −2.16630 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.92531 | −0.259185 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0000 | 0.849383 | 0.424691 | − | 0.905338i | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 104.513 | 3.41064 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 49.9253 | 1.62752 | 0.813759 | − | 0.581202i | \(-0.197417\pi\) | ||||
0.813759 | + | 0.581202i | \(0.197417\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.15230 | 0.102653 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −83.9637 | −2.73134 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.80128 | 0.188516 | 0.0942582 | − | 0.995548i | \(-0.469952\pi\) | ||||
0.0942582 | + | 0.995548i | \(0.469952\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.73381 | −0.185931 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.2270 | −0.428464 | −0.214232 | − | 0.976783i | \(-0.568725\pi\) | ||||
−0.214232 | + | 0.976783i | \(0.568725\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.0000 | −0.388311 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.83036 | 0.188469 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −87.1907 | −2.81553 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.7439 | −0.830450 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −107.398 | −3.46084 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.05655 | 0.130585 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.61350 | 0.0518865 | 0.0259433 | − | 0.999663i | \(-0.491741\pi\) | ||||
0.0259433 | + | 0.999663i | \(0.491741\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −67.0413 | −2.15368 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.7730 | 0.538271 | 0.269136 | − | 0.963102i | \(-0.413262\pi\) | ||||
0.269136 | + | 0.963102i | \(0.413262\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 47.0557 | 1.50854 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47.6700 | 1.52510 | 0.762550 | − | 0.646929i | \(-0.223947\pi\) | ||||
0.762550 | + | 0.646929i | \(0.223947\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.09495 | 0.0669549 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −90.5873 | −2.89223 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.4996 | −0.972786 | −0.486393 | − | 0.873740i | \(-0.661688\pi\) | ||||
−0.486393 | + | 0.873740i | \(0.661688\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.2835 | −0.486974 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −17.1704 | −0.546541 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.25526 | 0.0717132 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.8506 | −0.630576 | −0.315288 | − | 0.948996i | \(-0.602101\pi\) | ||||
−0.315288 | + | 0.948996i | \(0.602101\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −34.5561 | −1.09661 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.77301 | 0.278123 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.6410 | −1.06542 | −0.532710 | − | 0.846298i | \(-0.678826\pi\) | ||||
−0.532710 | + | 0.846298i | \(0.678826\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 26.9427 | 0.852428 |
(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 | 3380.2.a.o.1.3 | 3 | ||
13.5 | odd | 4 | 3380.2.f.h.3041.6 | 6 | |||
13.8 | odd | 4 | 3380.2.f.h.3041.5 | 6 | |||
13.12 | even | 2 | 260.2.a.b.1.3 | ✓ | 3 | ||
39.38 | odd | 2 | 2340.2.a.n.1.1 | 3 | |||
52.51 | odd | 2 | 1040.2.a.o.1.1 | 3 | |||
65.12 | odd | 4 | 1300.2.c.f.1249.1 | 6 | |||
65.38 | odd | 4 | 1300.2.c.f.1249.6 | 6 | |||
65.64 | even | 2 | 1300.2.a.i.1.1 | 3 | |||
104.51 | odd | 2 | 4160.2.a.br.1.3 | 3 | |||
104.77 | even | 2 | 4160.2.a.bo.1.1 | 3 | |||
156.155 | even | 2 | 9360.2.a.da.1.3 | 3 | |||
260.259 | odd | 2 | 5200.2.a.ci.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.a.b.1.3 | ✓ | 3 | 13.12 | even | 2 | ||
1040.2.a.o.1.1 | 3 | 52.51 | odd | 2 | |||
1300.2.a.i.1.1 | 3 | 65.64 | even | 2 | |||
1300.2.c.f.1249.1 | 6 | 65.12 | odd | 4 | |||
1300.2.c.f.1249.6 | 6 | 65.38 | odd | 4 | |||
2340.2.a.n.1.1 | 3 | 39.38 | odd | 2 | |||
3380.2.a.o.1.3 | 3 | 1.1 | even | 1 | trivial | ||
3380.2.f.h.3041.5 | 6 | 13.8 | odd | 4 | |||
3380.2.f.h.3041.6 | 6 | 13.5 | odd | 4 | |||
4160.2.a.bo.1.1 | 3 | 104.77 | even | 2 | |||
4160.2.a.br.1.3 | 3 | 104.51 | odd | 2 | |||
5200.2.a.ci.1.3 | 3 | 260.259 | odd | 2 | |||
9360.2.a.da.1.3 | 3 | 156.155 | even | 2 |