Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,4,Mod(1,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.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: | \(39.8262892539\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.60555 | −1.27475 | −0.637377 | − | 0.770552i | \(-0.719981\pi\) | ||||
−0.637377 | + | 0.770552i | \(0.719981\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.00000 | 0.625000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.00000 | −0.485954 | −0.242977 | − | 0.970032i | \(-0.578124\pi\) | ||||
−0.242977 | + | 0.970032i | \(0.578124\pi\) | |||||||
\(8\) | 10.8167 | 0.478033 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14.4222 | −0.395314 | −0.197657 | − | 0.980271i | \(-0.563333\pi\) | ||||
−0.197657 | + | 0.980271i | \(0.563333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 34.0000 | 0.725377 | 0.362689 | − | 0.931910i | \(-0.381859\pi\) | ||||
0.362689 | + | 0.931910i | \(0.381859\pi\) | |||||||
\(14\) | 32.4500 | 0.619473 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −79.0000 | −1.23438 | ||||||||
\(17\) | 7.21110 | 0.102879 | 0.0514397 | − | 0.998676i | \(-0.483619\pi\) | ||||
0.0514397 | + | 0.998676i | \(0.483619\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −101.000 | −1.21953 | −0.609763 | − | 0.792584i | \(-0.708735\pi\) | ||||
−0.609763 | + | 0.792584i | \(0.708735\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 52.0000 | 0.503929 | ||||||||
\(23\) | 108.167 | 0.980621 | 0.490310 | − | 0.871548i | \(-0.336883\pi\) | ||||
0.490310 | + | 0.871548i | \(0.336883\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −122.589 | −0.924678 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −45.0000 | −0.303721 | ||||||||
\(29\) | 165.855 | 1.06202 | 0.531010 | − | 0.847366i | \(-0.321813\pi\) | ||||
0.531010 | + | 0.847366i | \(0.321813\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | −0.0173812 | −0.00869058 | − | 0.999962i | \(-0.502766\pi\) | ||||
−0.00869058 | + | 0.999962i | \(0.502766\pi\) | |||||||
\(32\) | 198.305 | 1.09549 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −26.0000 | −0.131146 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −67.0000 | −0.297695 | −0.148848 | − | 0.988860i | \(-0.547556\pi\) | ||||
−0.148848 | + | 0.988860i | \(0.547556\pi\) | |||||||
\(38\) | 364.161 | 1.55460 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −201.911 | −0.769102 | −0.384551 | − | 0.923104i | \(-0.625644\pi\) | ||||
−0.384551 | + | 0.923104i | \(0.625644\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −137.000 | −0.485868 | −0.242934 | − | 0.970043i | \(-0.578110\pi\) | ||||
−0.242934 | + | 0.970043i | \(0.578110\pi\) | |||||||
\(44\) | −72.1110 | −0.247072 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −390.000 | −1.25005 | ||||||||
\(47\) | 115.378 | 0.358076 | 0.179038 | − | 0.983842i | \(-0.442702\pi\) | ||||
0.179038 | + | 0.983842i | \(0.442702\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −262.000 | −0.763848 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 170.000 | 0.453361 | ||||||||
\(53\) | 677.844 | 1.75677 | 0.878387 | − | 0.477951i | \(-0.158620\pi\) | ||||
0.878387 | + | 0.477951i | \(0.158620\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −97.3499 | −0.232302 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −598.000 | −1.35381 | ||||||||
\(59\) | 872.543 | 1.92535 | 0.962674 | − | 0.270665i | \(-0.0872437\pi\) | ||||
0.962674 | + | 0.270665i | \(0.0872437\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −563.000 | −1.18172 | −0.590859 | − | 0.806775i | \(-0.701211\pi\) | ||||
−0.590859 | + | 0.806775i | \(0.701211\pi\) | |||||||
\(62\) | 10.8167 | 0.0221567 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −83.0000 | −0.162109 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1044.00 | 1.90366 | 0.951828 | − | 0.306634i | \(-0.0992026\pi\) | ||||
0.951828 | + | 0.306634i | \(0.0992026\pi\) | |||||||
\(68\) | 36.0555 | 0.0642996 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −786.010 | −1.31383 | −0.656917 | − | 0.753963i | \(-0.728140\pi\) | ||||
−0.656917 | + | 0.753963i | \(0.728140\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −503.000 | −0.806462 | −0.403231 | − | 0.915098i | \(-0.632113\pi\) | ||||
−0.403231 | + | 0.915098i | \(0.632113\pi\) | |||||||
\(74\) | 241.572 | 0.379489 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −505.000 | −0.762204 | ||||||||
\(77\) | 129.800 | 0.192105 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 615.000 | 0.875860 | 0.437930 | − | 0.899009i | \(-0.355712\pi\) | ||||
0.437930 | + | 0.899009i | \(0.355712\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 728.000 | 0.980416 | ||||||||
\(83\) | −237.966 | −0.314701 | −0.157351 | − | 0.987543i | \(-0.550295\pi\) | ||||
−0.157351 | + | 0.987543i | \(0.550295\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 493.961 | 0.619362 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −156.000 | −0.188973 | ||||||||
\(89\) | −973.499 | −1.15945 | −0.579723 | − | 0.814814i | \(-0.696839\pi\) | ||||
−0.579723 | + | 0.814814i | \(0.696839\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −306.000 | −0.352500 | ||||||||
\(92\) | 540.833 | 0.612888 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −416.000 | −0.456459 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −19.0000 | −0.0198882 | −0.00994411 | − | 0.999951i | \(-0.503165\pi\) | ||||
−0.00994411 | + | 0.999951i | \(0.503165\pi\) | |||||||
\(98\) | 944.654 | 0.973719 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −259.600 | −0.255754 | −0.127877 | − | 0.991790i | \(-0.540816\pi\) | ||||
−0.127877 | + | 0.991790i | \(0.540816\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 149.000 | 0.142538 | 0.0712690 | − | 0.997457i | \(-0.477295\pi\) | ||||
0.0712690 | + | 0.997457i | \(0.477295\pi\) | |||||||
\(104\) | 367.766 | 0.346754 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2444.00 | −2.23946 | ||||||||
\(107\) | −2055.16 | −1.85682 | −0.928412 | − | 0.371552i | \(-0.878826\pi\) | ||||
−0.928412 | + | 0.371552i | \(0.878826\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1177.00 | −1.03428 | −0.517138 | − | 0.855902i | \(-0.673003\pi\) | ||||
−0.517138 | + | 0.855902i | \(0.673003\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 711.000 | 0.599850 | ||||||||
\(113\) | −2004.69 | −1.66889 | −0.834447 | − | 0.551088i | \(-0.814213\pi\) | ||||
−0.834447 | + | 0.551088i | \(0.814213\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 829.277 | 0.663762 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3146.00 | −2.45435 | ||||||||
\(119\) | −64.8999 | −0.0499947 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1123.00 | −0.843727 | ||||||||
\(122\) | 2029.93 | 1.50640 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −15.0000 | −0.0108632 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −296.000 | −0.206817 | −0.103408 | − | 0.994639i | \(-0.532975\pi\) | ||||
−0.103408 | + | 0.994639i | \(0.532975\pi\) | |||||||
\(128\) | −1287.18 | −0.888843 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1665.76 | 1.11098 | 0.555491 | − | 0.831523i | \(-0.312530\pi\) | ||||
0.555491 | + | 0.831523i | \(0.312530\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 909.000 | 0.592634 | ||||||||
\(134\) | −3764.20 | −2.42669 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 78.0000 | 0.0491797 | ||||||||
\(137\) | −1211.47 | −0.755492 | −0.377746 | − | 0.925909i | \(-0.623301\pi\) | ||||
−0.377746 | + | 0.925909i | \(0.623301\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1873.00 | −1.14292 | −0.571460 | − | 0.820630i | \(-0.693623\pi\) | ||||
−0.571460 | + | 0.820630i | \(0.693623\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2834.00 | 1.67482 | ||||||||
\(143\) | −490.355 | −0.286752 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1813.59 | 1.02804 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −335.000 | −0.186060 | ||||||||
\(149\) | 2329.19 | 1.28063 | 0.640317 | − | 0.768111i | \(-0.278803\pi\) | ||||
0.640317 | + | 0.768111i | \(0.278803\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1031.00 | −0.555640 | −0.277820 | − | 0.960633i | \(-0.589612\pi\) | ||||
−0.277820 | + | 0.960633i | \(0.589612\pi\) | |||||||
\(152\) | −1092.48 | −0.582974 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −468.000 | −0.244886 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2443.00 | −1.24186 | −0.620932 | − | 0.783864i | \(-0.713246\pi\) | ||||
−0.620932 | + | 0.783864i | \(0.713246\pi\) | |||||||
\(158\) | −2217.41 | −1.11651 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −973.499 | −0.476537 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 188.000 | 0.0903392 | 0.0451696 | − | 0.998979i | \(-0.485617\pi\) | ||||
0.0451696 | + | 0.998979i | \(0.485617\pi\) | |||||||
\(164\) | −1009.55 | −0.480689 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 858.000 | 0.401167 | ||||||||
\(167\) | −1492.70 | −0.691667 | −0.345834 | − | 0.938296i | \(-0.612404\pi\) | ||||
−0.345834 | + | 0.938296i | \(0.612404\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1041.00 | −0.473828 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −685.000 | −0.303667 | ||||||||
\(173\) | −3136.83 | −1.37855 | −0.689274 | − | 0.724501i | \(-0.742070\pi\) | ||||
−0.689274 | + | 0.724501i | \(0.742070\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1139.35 | 0.487966 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3510.00 | 1.47801 | ||||||||
\(179\) | −2913.29 | −1.21648 | −0.608238 | − | 0.793755i | \(-0.708123\pi\) | ||||
−0.608238 | + | 0.793755i | \(0.708123\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −286.000 | −0.117449 | −0.0587243 | − | 0.998274i | \(-0.518703\pi\) | ||||
−0.0587243 | + | 0.998274i | \(0.518703\pi\) | |||||||
\(182\) | 1103.30 | 0.449351 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1170.00 | 0.468769 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −104.000 | −0.0406697 | ||||||||
\(188\) | 576.888 | 0.223797 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −850.910 | −0.322354 | −0.161177 | − | 0.986925i | \(-0.551529\pi\) | ||||
−0.161177 | + | 0.986925i | \(0.551529\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3001.00 | −1.11926 | −0.559629 | − | 0.828743i | \(-0.689056\pi\) | ||||
−0.559629 | + | 0.828743i | \(0.689056\pi\) | |||||||
\(194\) | 68.5055 | 0.0253526 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1310.00 | −0.477405 | ||||||||
\(197\) | −3807.46 | −1.37701 | −0.688504 | − | 0.725233i | \(-0.741732\pi\) | ||||
−0.688504 | + | 0.725233i | \(0.741732\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1544.00 | −0.550006 | −0.275003 | − | 0.961443i | \(-0.588679\pi\) | ||||
−0.275003 | + | 0.961443i | \(0.588679\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 936.000 | 0.326023 | ||||||||
\(203\) | −1492.70 | −0.516093 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −537.227 | −0.181701 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2686.00 | −0.895387 | ||||||||
\(209\) | 1456.64 | 0.482096 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1612.00 | −0.525946 | −0.262973 | − | 0.964803i | \(-0.584703\pi\) | ||||
−0.262973 | + | 0.964803i | \(0.584703\pi\) | |||||||
\(212\) | 3389.22 | 1.09798 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7410.00 | 2.36700 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.0000 | 0.00844645 | ||||||||
\(218\) | 4243.73 | 1.31845 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 245.177 | 0.0746263 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6113.00 | 1.83568 | 0.917840 | − | 0.396950i | \(-0.129931\pi\) | ||||
0.917840 | + | 0.396950i | \(0.129931\pi\) | |||||||
\(224\) | −1784.75 | −0.532359 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7228.00 | 2.12743 | ||||||||
\(227\) | 187.489 | 0.0548196 | 0.0274098 | − | 0.999624i | \(-0.491274\pi\) | ||||
0.0274098 | + | 0.999624i | \(0.491274\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2199.00 | 0.634559 | 0.317279 | − | 0.948332i | \(-0.397231\pi\) | ||||
0.317279 | + | 0.948332i | \(0.397231\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1794.00 | 0.507680 | ||||||||
\(233\) | 1492.70 | 0.419699 | 0.209850 | − | 0.977734i | \(-0.432703\pi\) | ||||
0.209850 | + | 0.977734i | \(0.432703\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4362.72 | 1.20334 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 234.000 | 0.0637310 | ||||||||
\(239\) | 5350.64 | 1.44813 | 0.724067 | − | 0.689730i | \(-0.242271\pi\) | ||||
0.724067 | + | 0.689730i | \(0.242271\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1930.00 | 0.515860 | 0.257930 | − | 0.966164i | \(-0.416960\pi\) | ||||
0.257930 | + | 0.966164i | \(0.416960\pi\) | |||||||
\(242\) | 4049.03 | 1.07554 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2815.00 | −0.738573 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3434.00 | −0.884616 | ||||||||
\(248\) | −32.4500 | −0.00830877 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3526.23 | −0.886747 | −0.443374 | − | 0.896337i | \(-0.646219\pi\) | ||||
−0.443374 | + | 0.896337i | \(0.646219\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1560.00 | −0.387654 | ||||||||
\(254\) | 1067.24 | 0.263641 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5305.00 | 1.29517 | ||||||||
\(257\) | −995.132 | −0.241536 | −0.120768 | − | 0.992681i | \(-0.538536\pi\) | ||||
−0.120768 | + | 0.992681i | \(0.538536\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 603.000 | 0.144666 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6006.00 | −1.41623 | ||||||||
\(263\) | 2026.32 | 0.475088 | 0.237544 | − | 0.971377i | \(-0.423658\pi\) | ||||
0.237544 | + | 0.971377i | \(0.423658\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3277.45 | −0.755463 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5220.00 | 1.18978 | ||||||||
\(269\) | 2040.74 | 0.462551 | 0.231276 | − | 0.972888i | \(-0.425710\pi\) | ||||
0.231276 | + | 0.972888i | \(0.425710\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6691.00 | 1.49981 | 0.749906 | − | 0.661544i | \(-0.230098\pi\) | ||||
0.749906 | + | 0.661544i | \(0.230098\pi\) | |||||||
\(272\) | −569.677 | −0.126992 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4368.00 | 0.963068 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2139.00 | 0.463971 | 0.231986 | − | 0.972719i | \(-0.425478\pi\) | ||||
0.231986 | + | 0.972719i | \(0.425478\pi\) | |||||||
\(278\) | 6753.20 | 1.45694 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7614.92 | −1.61661 | −0.808307 | − | 0.588762i | \(-0.799616\pi\) | ||||
−0.808307 | + | 0.588762i | \(0.799616\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3297.00 | 0.692531 | 0.346266 | − | 0.938137i | \(-0.387450\pi\) | ||||
0.346266 | + | 0.938137i | \(0.387450\pi\) | |||||||
\(284\) | −3930.05 | −0.821147 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1768.00 | 0.365539 | ||||||||
\(287\) | 1817.20 | 0.373748 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4861.00 | −0.989416 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2515.00 | −0.504039 | ||||||||
\(293\) | 7247.16 | 1.44499 | 0.722497 | − | 0.691374i | \(-0.242994\pi\) | ||||
0.722497 | + | 0.691374i | \(0.242994\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −724.716 | −0.142308 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8398.00 | −1.63249 | ||||||||
\(299\) | 3677.66 | 0.711320 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1233.00 | 0.236109 | ||||||||
\(302\) | 3717.32 | 0.708304 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7979.00 | 1.50535 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6335.00 | −1.17771 | −0.588856 | − | 0.808238i | \(-0.700421\pi\) | ||||
−0.588856 | + | 0.808238i | \(0.700421\pi\) | |||||||
\(308\) | 648.999 | 0.120065 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −173.066 | −0.0315553 | −0.0157777 | − | 0.999876i | \(-0.505022\pi\) | ||||
−0.0157777 | + | 0.999876i | \(0.505022\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9542.00 | 1.72315 | 0.861575 | − | 0.507631i | \(-0.169479\pi\) | ||||
0.861575 | + | 0.507631i | \(0.169479\pi\) | |||||||
\(314\) | 8808.36 | 1.58307 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3075.00 | 0.547412 | ||||||||
\(317\) | 1723.45 | 0.305359 | 0.152679 | − | 0.988276i | \(-0.451210\pi\) | ||||
0.152679 | + | 0.988276i | \(0.451210\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2392.00 | −0.419832 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3510.00 | 0.607468 | ||||||||
\(323\) | −728.321 | −0.125464 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −677.844 | −0.115160 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2184.00 | −0.367656 | ||||||||
\(329\) | −1038.40 | −0.174008 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6273.00 | −1.04168 | −0.520839 | − | 0.853655i | \(-0.674381\pi\) | ||||
−0.520839 | + | 0.853655i | \(0.674381\pi\) | |||||||
\(332\) | −1189.83 | −0.196688 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5382.00 | 0.881706 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6854.00 | −1.10790 | −0.553948 | − | 0.832551i | \(-0.686879\pi\) | ||||
−0.553948 | + | 0.832551i | \(0.686879\pi\) | |||||||
\(338\) | 3753.38 | 0.604014 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 43.2666 | 0.00687102 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5445.00 | 0.857150 | ||||||||
\(344\) | −1481.88 | −0.232261 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11310.0 | 1.75731 | ||||||||
\(347\) | −5530.92 | −0.855663 | −0.427832 | − | 0.903858i | \(-0.640722\pi\) | ||||
−0.427832 | + | 0.903858i | \(0.640722\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5495.00 | −0.842810 | −0.421405 | − | 0.906873i | \(-0.638463\pi\) | ||||
−0.421405 | + | 0.906873i | \(0.638463\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2860.00 | −0.433064 | ||||||||
\(353\) | 432.666 | 0.0652365 | 0.0326183 | − | 0.999468i | \(-0.489615\pi\) | ||||
0.0326183 | + | 0.999468i | \(0.489615\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4867.49 | −0.724654 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10504.0 | 1.55071 | ||||||||
\(359\) | 6857.76 | 1.00819 | 0.504093 | − | 0.863649i | \(-0.331827\pi\) | ||||
0.504093 | + | 0.863649i | \(0.331827\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3342.00 | 0.487243 | ||||||||
\(362\) | 1031.19 | 0.149718 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1530.00 | −0.220313 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9180.00 | −1.30570 | −0.652850 | − | 0.757487i | \(-0.726427\pi\) | ||||
−0.652850 | + | 0.757487i | \(0.726427\pi\) | |||||||
\(368\) | −8545.16 | −1.21045 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6100.59 | −0.853712 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7393.00 | 1.02626 | 0.513130 | − | 0.858311i | \(-0.328486\pi\) | ||||
0.513130 | + | 0.858311i | \(0.328486\pi\) | |||||||
\(374\) | 374.977 | 0.0518439 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1248.00 | 0.171172 | ||||||||
\(377\) | 5639.08 | 0.770365 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8480.00 | −1.14931 | −0.574655 | − | 0.818396i | \(-0.694864\pi\) | ||||
−0.574655 | + | 0.818396i | \(0.694864\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3068.00 | 0.410923 | ||||||||
\(383\) | 7160.62 | 0.955329 | 0.477664 | − | 0.878542i | \(-0.341484\pi\) | ||||
0.477664 | + | 0.878542i | \(0.341484\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10820.3 | 1.42678 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −95.0000 | −0.0124301 | ||||||||
\(389\) | −6446.73 | −0.840262 | −0.420131 | − | 0.907463i | \(-0.638016\pi\) | ||||
−0.420131 | + | 0.907463i | \(0.638016\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 780.000 | 0.100886 | ||||||||
\(392\) | −2833.96 | −0.365145 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13728.0 | 1.75535 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4957.00 | 0.626662 | 0.313331 | − | 0.949644i | \(-0.398555\pi\) | ||||
0.313331 | + | 0.949644i | \(0.398555\pi\) | |||||||
\(398\) | 5566.97 | 0.701123 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8307.19 | 1.03452 | 0.517258 | − | 0.855829i | \(-0.326953\pi\) | ||||
0.517258 | + | 0.855829i | \(0.326953\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −102.000 | −0.0126079 | ||||||||
\(404\) | −1298.00 | −0.159846 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5382.00 | 0.657892 | ||||||||
\(407\) | 966.288 | 0.117683 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10630.0 | −1.28513 | −0.642567 | − | 0.766230i | \(-0.722130\pi\) | ||||
−0.642567 | + | 0.766230i | \(0.722130\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 745.000 | 0.0890862 | ||||||||
\(413\) | −7852.89 | −0.935631 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6742.38 | 0.794645 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5252.00 | −0.614554 | ||||||||
\(419\) | −15366.9 | −1.79170 | −0.895848 | − | 0.444362i | \(-0.853431\pi\) | ||||
−0.895848 | + | 0.444362i | \(0.853431\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10277.0 | −1.18972 | −0.594858 | − | 0.803831i | \(-0.702792\pi\) | ||||
−0.594858 | + | 0.803831i | \(0.702792\pi\) | |||||||
\(422\) | 5812.15 | 0.670453 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7332.00 | 0.839796 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5067.00 | 0.574261 | ||||||||
\(428\) | −10275.8 | −1.16052 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7636.56 | 0.853457 | 0.426729 | − | 0.904380i | \(-0.359666\pi\) | ||||
0.426729 | + | 0.904380i | \(0.359666\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12173.0 | −1.35103 | −0.675516 | − | 0.737345i | \(-0.736079\pi\) | ||||
−0.675516 | + | 0.737345i | \(0.736079\pi\) | |||||||
\(434\) | −97.3499 | −0.0107672 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5885.00 | −0.646423 | ||||||||
\(437\) | −10924.8 | −1.19589 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8989.00 | 0.977270 | 0.488635 | − | 0.872488i | \(-0.337495\pi\) | ||||
0.488635 | + | 0.872488i | \(0.337495\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −884.000 | −0.0951303 | ||||||||
\(443\) | −11141.2 | −1.19488 | −0.597440 | − | 0.801913i | \(-0.703816\pi\) | ||||
−0.597440 | + | 0.801913i | \(0.703816\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −22040.7 | −2.34004 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 747.000 | 0.0787778 | ||||||||
\(449\) | 7968.27 | 0.837519 | 0.418759 | − | 0.908097i | \(-0.362465\pi\) | ||||
0.418759 | + | 0.908097i | \(0.362465\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2912.00 | 0.304037 | ||||||||
\(452\) | −10023.4 | −1.04306 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −676.000 | −0.0698816 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3566.00 | −0.365012 | −0.182506 | − | 0.983205i | \(-0.558421\pi\) | ||||
−0.182506 | + | 0.983205i | \(0.558421\pi\) | |||||||
\(458\) | −7928.61 | −0.808907 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9280.69 | 0.937624 | 0.468812 | − | 0.883298i | \(-0.344682\pi\) | ||||
0.468812 | + | 0.883298i | \(0.344682\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.0000 | −0.00150564 | −0.000752818 | − | 1.00000i | \(-0.500240\pi\) | ||||
−0.000752818 | 1.00000i | \(0.500240\pi\) | ||||||||
\(464\) | −13102.6 | −1.31093 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5382.00 | −0.535014 | ||||||||
\(467\) | 6396.25 | 0.633797 | 0.316898 | − | 0.948460i | \(-0.397359\pi\) | ||||
0.316898 | + | 0.948460i | \(0.397359\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9396.00 | −0.925089 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9438.00 | 0.920380 | ||||||||
\(473\) | 1975.84 | 0.192070 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −324.500 | −0.0312467 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −19292.0 | −1.84602 | ||||||||
\(479\) | −12525.7 | −1.19481 | −0.597404 | − | 0.801940i | \(-0.703801\pi\) | ||||
−0.597404 | + | 0.801940i | \(0.703801\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2278.00 | −0.215941 | ||||||||
\(482\) | −6958.71 | −0.657595 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5615.00 | −0.527329 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6088.00 | −0.566476 | −0.283238 | − | 0.959050i | \(-0.591409\pi\) | ||||
−0.283238 | + | 0.959050i | \(0.591409\pi\) | |||||||
\(488\) | −6089.78 | −0.564900 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15071.2 | 1.38524 | 0.692621 | − | 0.721302i | \(-0.256456\pi\) | ||||
0.692621 | + | 0.721302i | \(0.256456\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1196.00 | 0.109260 | ||||||||
\(494\) | 12381.5 | 1.12767 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 237.000 | 0.0214549 | ||||||||
\(497\) | 7074.09 | 0.638464 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2389.00 | 0.214321 | 0.107161 | − | 0.994242i | \(-0.465824\pi\) | ||||
0.107161 | + | 0.994242i | \(0.465824\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12714.0 | 1.13039 | ||||||||
\(503\) | −17054.3 | −1.51175 | −0.755877 | − | 0.654714i | \(-0.772789\pi\) | ||||
−0.755877 | + | 0.654714i | \(0.772789\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5624.66 | 0.494163 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1480.00 | −0.129261 | ||||||||
\(509\) | −8624.48 | −0.751028 | −0.375514 | − | 0.926817i | \(-0.622534\pi\) | ||||
−0.375514 | + | 0.926817i | \(0.622534\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4527.00 | 0.391904 | ||||||||
\(512\) | −8830.00 | −0.762176 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3588.00 | 0.307899 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1664.00 | −0.141552 | ||||||||
\(518\) | −2174.15 | −0.184414 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7888.95 | 0.663380 | 0.331690 | − | 0.943388i | \(-0.392381\pi\) | ||||
0.331690 | + | 0.943388i | \(0.392381\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6163.00 | 0.515276 | 0.257638 | − | 0.966242i | \(-0.417056\pi\) | ||||
0.257638 | + | 0.966242i | \(0.417056\pi\) | |||||||
\(524\) | 8328.82 | 0.694363 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7306.00 | −0.605621 | ||||||||
\(527\) | −21.6333 | −0.00178816 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −467.000 | −0.0383825 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4545.00 | 0.370396 | ||||||||
\(533\) | −6864.97 | −0.557889 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11292.6 | 0.910010 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7358.00 | −0.589639 | ||||||||
\(539\) | 3778.62 | 0.301960 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15765.0 | −1.25285 | −0.626424 | − | 0.779483i | \(-0.715482\pi\) | ||||
−0.626424 | + | 0.779483i | \(0.715482\pi\) | |||||||
\(542\) | −24124.7 | −1.91189 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1430.00 | 0.112704 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7591.00 | 0.593360 | 0.296680 | − | 0.954977i | \(-0.404121\pi\) | ||||
0.296680 | + | 0.954977i | \(0.404121\pi\) | |||||||
\(548\) | −6057.33 | −0.472183 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16751.4 | −1.29516 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5535.00 | −0.425628 | ||||||||
\(554\) | −7712.27 | −0.591450 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9365.00 | −0.714325 | ||||||||
\(557\) | 18366.7 | 1.39717 | 0.698583 | − | 0.715529i | \(-0.253814\pi\) | ||||
0.698583 | + | 0.715529i | \(0.253814\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4658.00 | −0.352437 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27456.0 | 2.06079 | ||||||||
\(563\) | 14018.4 | 1.04939 | 0.524693 | − | 0.851291i | \(-0.324180\pi\) | ||||
0.524693 | + | 0.851291i | \(0.324180\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11887.5 | −0.882807 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8502.00 | −0.628056 | ||||||||
\(569\) | −15035.1 | −1.10774 | −0.553872 | − | 0.832602i | \(-0.686850\pi\) | ||||
−0.553872 | + | 0.832602i | \(0.686850\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2725.00 | −0.199716 | −0.0998579 | − | 0.995002i | \(-0.531839\pi\) | ||||
−0.0998579 | + | 0.995002i | \(0.531839\pi\) | |||||||
\(572\) | −2451.77 | −0.179220 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6552.00 | −0.476438 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12815.0 | 0.924602 | 0.462301 | − | 0.886723i | \(-0.347024\pi\) | ||||
0.462301 | + | 0.886723i | \(0.347024\pi\) | |||||||
\(578\) | 17526.6 | 1.26126 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2141.70 | 0.152930 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9776.00 | −0.694478 | ||||||||
\(584\) | −5440.78 | −0.385515 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26130.0 | −1.84201 | ||||||||
\(587\) | 10189.3 | 0.716451 | 0.358226 | − | 0.933635i | \(-0.383382\pi\) | ||||
0.358226 | + | 0.933635i | \(0.383382\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 303.000 | 0.0211968 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5293.00 | 0.367468 | ||||||||
\(593\) | 3454.12 | 0.239197 | 0.119598 | − | 0.992822i | \(-0.461839\pi\) | ||||
0.119598 | + | 0.992822i | \(0.461839\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11645.9 | 0.800396 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −13260.0 | −0.906759 | ||||||||
\(599\) | 6374.61 | 0.434824 | 0.217412 | − | 0.976080i | \(-0.430238\pi\) | ||||
0.217412 | + | 0.976080i | \(0.430238\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25645.0 | −1.74057 | −0.870284 | − | 0.492550i | \(-0.836065\pi\) | ||||
−0.870284 | + | 0.492550i | \(0.836065\pi\) | |||||||
\(602\) | −4445.64 | −0.300982 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5155.00 | −0.347275 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27923.0 | −1.86715 | −0.933575 | − | 0.358383i | \(-0.883328\pi\) | ||||
−0.933575 | + | 0.358383i | \(0.883328\pi\) | |||||||
\(608\) | −20028.8 | −1.33598 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3922.84 | 0.259740 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27817.0 | 1.83282 | 0.916410 | − | 0.400242i | \(-0.131074\pi\) | ||||
0.916410 | + | 0.400242i | \(0.131074\pi\) | |||||||
\(614\) | 22841.2 | 1.50129 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1404.00 | 0.0918324 | ||||||||
\(617\) | −3677.66 | −0.239963 | −0.119981 | − | 0.992776i | \(-0.538284\pi\) | ||||
−0.119981 | + | 0.992776i | \(0.538284\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16729.0 | −1.08626 | −0.543130 | − | 0.839648i | \(-0.682761\pi\) | ||||
−0.543130 | + | 0.839648i | \(0.682761\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 624.000 | 0.0402253 | ||||||||
\(623\) | 8761.49 | 0.563438 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −34404.2 | −2.19659 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12215.0 | −0.776165 | ||||||||
\(629\) | −483.144 | −0.0306267 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1748.00 | −0.110280 | −0.0551401 | − | 0.998479i | \(-0.517561\pi\) | ||||
−0.0551401 | + | 0.998479i | \(0.517561\pi\) | |||||||
\(632\) | 6652.24 | 0.418690 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6214.00 | −0.389258 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8908.00 | −0.554078 | ||||||||
\(638\) | 8624.48 | 0.535182 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1492.70 | 0.0919782 | 0.0459891 | − | 0.998942i | \(-0.485356\pi\) | ||||
0.0459891 | + | 0.998942i | \(0.485356\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2076.00 | −0.127324 | −0.0636621 | − | 0.997972i | \(-0.520278\pi\) | ||||
−0.0636621 | + | 0.997972i | \(0.520278\pi\) | |||||||
\(644\) | −4867.49 | −0.297836 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2626.00 | 0.159936 | ||||||||
\(647\) | 11710.8 | 0.711592 | 0.355796 | − | 0.934564i | \(-0.384210\pi\) | ||||
0.355796 | + | 0.934564i | \(0.384210\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12584.0 | −0.761117 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 940.000 | 0.0564620 | ||||||||
\(653\) | 20825.7 | 1.24804 | 0.624021 | − | 0.781408i | \(-0.285498\pi\) | ||||
0.624021 | + | 0.781408i | \(0.285498\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 15951.0 | 0.949360 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3744.00 | 0.221818 | ||||||||
\(659\) | −4276.18 | −0.252772 | −0.126386 | − | 0.991981i | \(-0.540338\pi\) | ||||
−0.126386 | + | 0.991981i | \(0.540338\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23987.0 | −1.41148 | −0.705738 | − | 0.708473i | \(-0.749385\pi\) | ||||
−0.705738 | + | 0.708473i | \(0.749385\pi\) | |||||||
\(662\) | 22617.6 | 1.32788 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2574.00 | −0.150438 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17940.0 | 1.04144 | ||||||||
\(668\) | −7463.49 | −0.432292 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8119.70 | 0.467150 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10965.0 | −0.628038 | −0.314019 | − | 0.949417i | \(-0.601676\pi\) | ||||
−0.314019 | + | 0.949417i | \(0.601676\pi\) | |||||||
\(674\) | 24712.4 | 1.41230 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5205.00 | −0.296142 | ||||||||
\(677\) | 15273.1 | 0.867051 | 0.433525 | − | 0.901141i | \(-0.357269\pi\) | ||||
0.433525 | + | 0.901141i | \(0.357269\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 171.000 | 0.00966477 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −156.000 | −0.00875887 | ||||||||
\(683\) | 33985.9 | 1.90400 | 0.952002 | − | 0.306090i | \(-0.0990210\pi\) | ||||
0.952002 | + | 0.306090i | \(0.0990210\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −19632.2 | −1.09266 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10823.0 | 0.599743 | ||||||||
\(689\) | 23046.7 | 1.27432 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23500.0 | 1.29375 | 0.646876 | − | 0.762596i | \(-0.276075\pi\) | ||||
0.646876 | + | 0.762596i | \(0.276075\pi\) | |||||||
\(692\) | −15684.1 | −0.861592 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19942.0 | 1.09076 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1456.00 | −0.0791247 | ||||||||
\(698\) | 19812.5 | 1.07438 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28173.8 | −1.51799 | −0.758994 | − | 0.651098i | \(-0.774309\pi\) | ||||
−0.758994 | + | 0.651098i | \(0.774309\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6767.00 | 0.363047 | ||||||||
\(704\) | 1197.04 | 0.0640842 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1560.00 | −0.0831606 | ||||||||
\(707\) | 2336.40 | 0.124285 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14213.0 | −0.752864 | −0.376432 | − | 0.926444i | \(-0.622849\pi\) | ||||
−0.376432 | + | 0.926444i | \(0.622849\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10530.0 | −0.554253 | ||||||||
\(713\) | −324.500 | −0.0170443 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −14566.4 | −0.760297 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −24726.0 | −1.28519 | ||||||||
\(719\) | −28058.4 | −1.45536 | −0.727679 | − | 0.685918i | \(-0.759401\pi\) | ||||
−0.727679 | + | 0.685918i | \(0.759401\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1341.00 | −0.0692669 | ||||||||
\(722\) | −12049.8 | −0.621115 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1430.00 | −0.0734054 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13541.0 | 0.690795 | 0.345397 | − | 0.938456i | \(-0.387744\pi\) | ||||
0.345397 | + | 0.938456i | \(0.387744\pi\) | |||||||
\(728\) | −3309.90 | −0.168507 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −987.921 | −0.0499857 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23482.0 | −1.18326 | −0.591629 | − | 0.806211i | \(-0.701515\pi\) | ||||
−0.591629 | + | 0.806211i | \(0.701515\pi\) | |||||||
\(734\) | 33099.0 | 1.66445 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21450.0 | 1.07426 | ||||||||
\(737\) | −15056.8 | −0.752542 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11420.0 | −0.568459 | −0.284230 | − | 0.958756i | \(-0.591738\pi\) | ||||
−0.284230 | + | 0.958756i | \(0.591738\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 21996.0 | 1.08827 | ||||||||
\(743\) | −4038.22 | −0.199391 | −0.0996957 | − | 0.995018i | \(-0.531787\pi\) | ||||
−0.0996957 | + | 0.995018i | \(0.531787\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −26655.8 | −1.30823 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −520.000 | −0.0254186 | ||||||||
\(749\) | 18496.5 | 0.902332 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15737.0 | −0.764649 | −0.382324 | − | 0.924028i | \(-0.624876\pi\) | ||||
−0.382324 | + | 0.924028i | \(0.624876\pi\) | |||||||
\(752\) | −9114.83 | −0.442000 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −20332.0 | −0.982026 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23539.0 | 1.13017 | 0.565086 | − | 0.825032i | \(-0.308843\pi\) | ||||
0.565086 | + | 0.825032i | \(0.308843\pi\) | |||||||
\(758\) | 30575.1 | 1.46509 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31238.5 | 1.48803 | 0.744017 | − | 0.668160i | \(-0.232918\pi\) | ||||
0.744017 | + | 0.668160i | \(0.232918\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10593.0 | 0.502611 | ||||||||
\(764\) | −4254.55 | −0.201472 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25818.0 | −1.21781 | ||||||||
\(767\) | 29666.5 | 1.39660 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26126.0 | 1.22513 | 0.612567 | − | 0.790419i | \(-0.290137\pi\) | ||||
0.612567 | + | 0.790419i | \(0.290137\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15005.0 | −0.699536 | ||||||||
\(773\) | 9929.69 | 0.462026 | 0.231013 | − | 0.972951i | \(-0.425796\pi\) | ||||
0.231013 | + | 0.972951i | \(0.425796\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −205.516 | −0.00950723 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23244.0 | 1.07113 | ||||||||
\(779\) | 20393.0 | 0.937940 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11336.0 | 0.519378 | ||||||||
\(782\) | −2812.33 | −0.128604 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 20698.0 | 0.942875 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34985.0 | −1.58460 | −0.792300 | − | 0.610131i | \(-0.791117\pi\) | ||||
−0.792300 | + | 0.610131i | \(0.791117\pi\) | |||||||
\(788\) | −19037.3 | −0.860630 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18042.2 | 0.811006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19142.0 | −0.857191 | ||||||||
\(794\) | −17872.7 | −0.798840 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7720.00 | −0.343754 | ||||||||
\(797\) | 11696.4 | 0.519834 | 0.259917 | − | 0.965631i | \(-0.416305\pi\) | ||||
0.259917 | + | 0.965631i | \(0.416305\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 832.000 | 0.0368386 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −29952.0 | −1.31876 | ||||||||
\(803\) | 7254.37 | 0.318806 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 367.766 | 0.0160720 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2808.00 | −0.122259 | ||||||||
\(809\) | −33409.0 | −1.45191 | −0.725957 | − | 0.687740i | \(-0.758603\pi\) | ||||
−0.725957 | + | 0.687740i | \(0.758603\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44817.0 | 1.94049 | 0.970245 | − | 0.242124i | \(-0.0778442\pi\) | ||||
0.970245 | + | 0.242124i | \(0.0778442\pi\) | |||||||
\(812\) | −7463.49 | −0.322558 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3484.00 | −0.150017 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13837.0 | 0.592528 | ||||||||
\(818\) | 38327.0 | 1.63823 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42660.9 | −1.81349 | −0.906745 | − | 0.421680i | \(-0.861441\pi\) | ||||
−0.906745 | + | 0.421680i | \(0.861441\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16952.0 | 0.717995 | 0.358997 | − | 0.933339i | \(-0.383119\pi\) | ||||
0.358997 | + | 0.933339i | \(0.383119\pi\) | |||||||
\(824\) | 1611.68 | 0.0681378 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 28314.0 | 1.19270 | ||||||||
\(827\) | −11566.6 | −0.486349 | −0.243174 | − | 0.969983i | \(-0.578189\pi\) | ||||
−0.243174 | + | 0.969983i | \(0.578189\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39723.0 | 1.66422 | 0.832109 | − | 0.554612i | \(-0.187133\pi\) | ||||
0.832109 | + | 0.554612i | \(0.187133\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2822.00 | −0.117590 | ||||||||
\(833\) | −1889.31 | −0.0785842 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7283.21 | 0.301310 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 55406.0 | 2.28397 | ||||||||
\(839\) | 27943.0 | 1.14982 | 0.574911 | − | 0.818216i | \(-0.305037\pi\) | ||||
0.574911 | + | 0.818216i | \(0.305037\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3119.00 | 0.127886 | ||||||||
\(842\) | 37054.3 | 1.51660 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8060.00 | −0.328716 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10107.0 | 0.410013 | ||||||||
\(848\) | −53549.6 | −2.16852 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7247.16 | −0.291926 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26046.0 | −1.04548 | −0.522742 | − | 0.852491i | \(-0.675091\pi\) | ||||
−0.522742 | + | 0.852491i | \(0.675091\pi\) | |||||||
\(854\) | −18269.3 | −0.732042 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −22230.0 | −0.887624 | ||||||||
\(857\) | −1312.42 | −0.0523121 | −0.0261560 | − | 0.999658i | \(-0.508327\pi\) | ||||
−0.0261560 | + | 0.999658i | \(0.508327\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34207.0 | 1.35871 | 0.679353 | − | 0.733812i | \(-0.262261\pi\) | ||||
0.679353 | + | 0.733812i | \(0.262261\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27534.0 | −1.08795 | ||||||||
\(863\) | −9915.27 | −0.391100 | −0.195550 | − | 0.980694i | \(-0.562649\pi\) | ||||
−0.195550 | + | 0.980694i | \(0.562649\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 43890.4 | 1.72224 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 135.000 | 0.00527903 | ||||||||
\(869\) | −8869.66 | −0.346240 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35496.0 | 1.38087 | ||||||||
\(872\) | −12731.2 | −0.494418 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 39390.0 | 1.52447 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19965.0 | 0.768723 | 0.384362 | − | 0.923183i | \(-0.374422\pi\) | ||||
0.384362 | + | 0.923183i | \(0.374422\pi\) | |||||||
\(878\) | −32410.3 | −1.24578 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20025.2 | −0.765797 | −0.382899 | − | 0.923790i | \(-0.625074\pi\) | ||||
−0.382899 | + | 0.923790i | \(0.625074\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36041.0 | 1.37359 | 0.686793 | − | 0.726853i | \(-0.259018\pi\) | ||||
0.686793 | + | 0.726853i | \(0.259018\pi\) | |||||||
\(884\) | 1225.89 | 0.0466415 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 40170.0 | 1.52318 | ||||||||
\(887\) | −3634.40 | −0.137577 | −0.0687886 | − | 0.997631i | \(-0.521913\pi\) | ||||
−0.0687886 | + | 0.997631i | \(0.521913\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2664.00 | 0.100504 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 30565.0 | 1.14730 | ||||||||
\(893\) | −11653.1 | −0.436683 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 11584.6 | 0.431937 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28730.0 | −1.06763 | ||||||||
\(899\) | −497.566 | −0.0184591 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4888.00 | 0.180736 | ||||||||
\(902\) | −10499.4 | −0.387573 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −21684.0 | −0.797787 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45339.0 | −1.65982 | −0.829910 | − | 0.557897i | \(-0.811608\pi\) | ||||
−0.829910 | + | 0.557897i | \(0.811608\pi\) | |||||||
\(908\) | 937.443 | 0.0342623 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30034.2 | 1.09229 | 0.546146 | − | 0.837690i | \(-0.316094\pi\) | ||||
0.546146 | + | 0.837690i | \(0.316094\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3432.00 | 0.124406 | ||||||||
\(914\) | 12857.4 | 0.465301 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10995.0 | 0.396599 | ||||||||
\(917\) | −14991.9 | −0.539886 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8693.00 | −0.312030 | −0.156015 | − | 0.987755i | \(-0.549865\pi\) | ||||
−0.156015 | + | 0.987755i | \(0.549865\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −33462.0 | −1.19524 | ||||||||
\(923\) | −26724.3 | −0.953026 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 54.0833 | 0.00191932 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 32890.0 | 1.16343 | ||||||||
\(929\) | −30164.0 | −1.06529 | −0.532643 | − | 0.846340i | \(-0.678801\pi\) | ||||
−0.532643 | + | 0.846340i | \(0.678801\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26462.0 | 0.931533 | ||||||||
\(932\) | 7463.49 | 0.262312 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −23062.0 | −0.807935 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22767.0 | 0.793773 | 0.396887 | − | 0.917868i | \(-0.370091\pi\) | ||||
0.396887 | + | 0.917868i | \(0.370091\pi\) | |||||||
\(938\) | 33877.8 | 1.17926 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47737.5 | 1.65377 | 0.826885 | − | 0.562371i | \(-0.190111\pi\) | ||||
0.826885 | + | 0.562371i | \(0.190111\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21840.0 | −0.754198 | ||||||||
\(944\) | −68930.9 | −2.37660 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7124.00 | −0.244843 | ||||||||
\(947\) | −27669.0 | −0.949442 | −0.474721 | − | 0.880136i | \(-0.657451\pi\) | ||||
−0.474721 | + | 0.880136i | \(0.657451\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17102.0 | −0.584989 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −702.000 | −0.0238991 | ||||||||
\(953\) | −2177.75 | −0.0740234 | −0.0370117 | − | 0.999315i | \(-0.511784\pi\) | ||||
−0.0370117 | + | 0.999315i | \(0.511784\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 26753.2 | 0.905084 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 45162.0 | 1.52309 | ||||||||
\(959\) | 10903.2 | 0.367135 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29782.0 | −0.999698 | ||||||||
\(962\) | 8213.45 | 0.275272 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9650.00 | 0.322412 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5389.00 | −0.179213 | −0.0896063 | − | 0.995977i | \(-0.528561\pi\) | ||||
−0.0896063 | + | 0.995977i | \(0.528561\pi\) | |||||||
\(968\) | −12147.1 | −0.403329 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36863.2 | −1.21833 | −0.609163 | − | 0.793045i | \(-0.708495\pi\) | ||||
−0.609163 | + | 0.793045i | \(0.708495\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16857.0 | 0.555407 | ||||||||
\(974\) | 21950.6 | 0.722118 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 44477.0 | 1.45868 | ||||||||
\(977\) | 6973.14 | 0.228342 | 0.114171 | − | 0.993461i | \(-0.463579\pi\) | ||||
0.114171 | + | 0.993461i | \(0.463579\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14040.0 | 0.458346 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −54340.0 | −1.76584 | ||||||||
\(983\) | −50232.5 | −1.62988 | −0.814939 | − | 0.579547i | \(-0.803229\pi\) | ||||
−0.814939 | + | 0.579547i | \(0.803229\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4312.24 | −0.139280 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17170.0 | −0.552885 | ||||||||
\(989\) | −14818.8 | −0.476452 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5303.00 | 0.169985 | 0.0849926 | − | 0.996382i | \(-0.472913\pi\) | ||||
0.0849926 | + | 0.996382i | \(0.472913\pi\) | |||||||
\(992\) | −594.916 | −0.0190409 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −25506.0 | −0.813885 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38274.0 | −1.21580 | −0.607899 | − | 0.794015i | \(-0.707987\pi\) | ||||
−0.607899 | + | 0.794015i | \(0.707987\pi\) | |||||||
\(998\) | −8613.66 | −0.273207 | ||||||||
\(999\) | 0 | 0 |
(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 | 675.4.a.l.1.1 | ✓ | 2 | |
3.2 | odd | 2 | inner | 675.4.a.l.1.2 | yes | 2 | |
5.2 | odd | 4 | 675.4.b.j.649.1 | 4 | |||
5.3 | odd | 4 | 675.4.b.j.649.4 | 4 | |||
5.4 | even | 2 | 675.4.a.m.1.2 | yes | 2 | ||
15.2 | even | 4 | 675.4.b.j.649.3 | 4 | |||
15.8 | even | 4 | 675.4.b.j.649.2 | 4 | |||
15.14 | odd | 2 | 675.4.a.m.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
675.4.a.l.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
675.4.a.l.1.2 | yes | 2 | 3.2 | odd | 2 | inner | |
675.4.a.m.1.1 | yes | 2 | 15.14 | odd | 2 | ||
675.4.a.m.1.2 | yes | 2 | 5.4 | even | 2 | ||
675.4.b.j.649.1 | 4 | 5.2 | odd | 4 | |||
675.4.b.j.649.2 | 4 | 15.8 | even | 4 | |||
675.4.b.j.649.3 | 4 | 15.2 | even | 4 | |||
675.4.b.j.649.4 | 4 | 5.3 | odd | 4 |