Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,4,Mod(1,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, 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("475.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.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: | \(28.0259072527\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 19) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 475.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.00000 | 1.06066 | 0.530330 | − | 0.847791i | \(-0.322068\pi\) | ||||
0.530330 | + | 0.847791i | \(0.322068\pi\) | |||||||
\(3\) | 5.00000 | 0.962250 | 0.481125 | − | 0.876652i | \(-0.340228\pi\) | ||||
0.481125 | + | 0.876652i | \(0.340228\pi\) | |||||||
\(4\) | 1.00000 | 0.125000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 15.0000 | 1.02062 | ||||||||
\(7\) | −11.0000 | −0.593944 | −0.296972 | − | 0.954886i | \(-0.595977\pi\) | ||||
−0.296972 | + | 0.954886i | \(0.595977\pi\) | |||||||
\(8\) | −21.0000 | −0.928078 | ||||||||
\(9\) | −2.00000 | −0.0740741 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −54.0000 | −1.48015 | −0.740073 | − | 0.672526i | \(-0.765209\pi\) | ||||
−0.740073 | + | 0.672526i | \(0.765209\pi\) | |||||||
\(12\) | 5.00000 | 0.120281 | ||||||||
\(13\) | −11.0000 | −0.234681 | −0.117340 | − | 0.993092i | \(-0.537437\pi\) | ||||
−0.117340 | + | 0.993092i | \(0.537437\pi\) | |||||||
\(14\) | −33.0000 | −0.629973 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −71.0000 | −1.10938 | ||||||||
\(17\) | 93.0000 | 1.32681 | 0.663406 | − | 0.748259i | \(-0.269110\pi\) | ||||
0.663406 | + | 0.748259i | \(0.269110\pi\) | |||||||
\(18\) | −6.00000 | −0.0785674 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −55.0000 | −0.571523 | ||||||||
\(22\) | −162.000 | −1.56993 | ||||||||
\(23\) | −183.000 | −1.65905 | −0.829525 | − | 0.558470i | \(-0.811389\pi\) | ||||
−0.829525 | + | 0.558470i | \(0.811389\pi\) | |||||||
\(24\) | −105.000 | −0.893043 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −33.0000 | −0.248917 | ||||||||
\(27\) | −145.000 | −1.03353 | ||||||||
\(28\) | −11.0000 | −0.0742430 | ||||||||
\(29\) | −249.000 | −1.59442 | −0.797209 | − | 0.603703i | \(-0.793691\pi\) | ||||
−0.797209 | + | 0.603703i | \(0.793691\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 56.0000 | 0.324448 | 0.162224 | − | 0.986754i | \(-0.448133\pi\) | ||||
0.162224 | + | 0.986754i | \(0.448133\pi\) | |||||||
\(32\) | −45.0000 | −0.248592 | ||||||||
\(33\) | −270.000 | −1.42427 | ||||||||
\(34\) | 279.000 | 1.40730 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | −0.00925926 | ||||||||
\(37\) | 250.000 | 1.11080 | 0.555402 | − | 0.831582i | \(-0.312564\pi\) | ||||
0.555402 | + | 0.831582i | \(0.312564\pi\) | |||||||
\(38\) | 57.0000 | 0.243332 | ||||||||
\(39\) | −55.0000 | −0.225822 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 240.000 | 0.914188 | 0.457094 | − | 0.889418i | \(-0.348890\pi\) | ||||
0.457094 | + | 0.889418i | \(0.348890\pi\) | |||||||
\(42\) | −165.000 | −0.606192 | ||||||||
\(43\) | 196.000 | 0.695110 | 0.347555 | − | 0.937660i | \(-0.387012\pi\) | ||||
0.347555 | + | 0.937660i | \(0.387012\pi\) | |||||||
\(44\) | −54.0000 | −0.185018 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −549.000 | −1.75969 | ||||||||
\(47\) | 168.000 | 0.521390 | 0.260695 | − | 0.965421i | \(-0.416048\pi\) | ||||
0.260695 | + | 0.965421i | \(0.416048\pi\) | |||||||
\(48\) | −355.000 | −1.06750 | ||||||||
\(49\) | −222.000 | −0.647230 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 465.000 | 1.27673 | ||||||||
\(52\) | −11.0000 | −0.0293351 | ||||||||
\(53\) | −435.000 | −1.12739 | −0.563697 | − | 0.825982i | \(-0.690621\pi\) | ||||
−0.563697 | + | 0.825982i | \(0.690621\pi\) | |||||||
\(54\) | −435.000 | −1.09622 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 231.000 | 0.551226 | ||||||||
\(57\) | 95.0000 | 0.220755 | ||||||||
\(58\) | −747.000 | −1.69114 | ||||||||
\(59\) | 195.000 | 0.430285 | 0.215143 | − | 0.976583i | \(-0.430978\pi\) | ||||
0.215143 | + | 0.976583i | \(0.430978\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −358.000 | −0.751430 | −0.375715 | − | 0.926735i | \(-0.622603\pi\) | ||||
−0.375715 | + | 0.926735i | \(0.622603\pi\) | |||||||
\(62\) | 168.000 | 0.344129 | ||||||||
\(63\) | 22.0000 | 0.0439959 | ||||||||
\(64\) | 433.000 | 0.845703 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −810.000 | −1.51067 | ||||||||
\(67\) | 961.000 | 1.75231 | 0.876155 | − | 0.482029i | \(-0.160100\pi\) | ||||
0.876155 | + | 0.482029i | \(0.160100\pi\) | |||||||
\(68\) | 93.0000 | 0.165852 | ||||||||
\(69\) | −915.000 | −1.59642 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −246.000 | −0.411195 | −0.205597 | − | 0.978637i | \(-0.565914\pi\) | ||||
−0.205597 | + | 0.978637i | \(0.565914\pi\) | |||||||
\(72\) | 42.0000 | 0.0687465 | ||||||||
\(73\) | −353.000 | −0.565966 | −0.282983 | − | 0.959125i | \(-0.591324\pi\) | ||||
−0.282983 | + | 0.959125i | \(0.591324\pi\) | |||||||
\(74\) | 750.000 | 1.17819 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 19.0000 | 0.0286770 | ||||||||
\(77\) | 594.000 | 0.879124 | ||||||||
\(78\) | −165.000 | −0.239520 | ||||||||
\(79\) | −34.0000 | −0.0484215 | −0.0242108 | − | 0.999707i | \(-0.507707\pi\) | ||||
−0.0242108 | + | 0.999707i | \(0.507707\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −671.000 | −0.920439 | ||||||||
\(82\) | 720.000 | 0.969643 | ||||||||
\(83\) | −234.000 | −0.309456 | −0.154728 | − | 0.987957i | \(-0.549450\pi\) | ||||
−0.154728 | + | 0.987957i | \(0.549450\pi\) | |||||||
\(84\) | −55.0000 | −0.0714404 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 588.000 | 0.737275 | ||||||||
\(87\) | −1245.00 | −1.53423 | ||||||||
\(88\) | 1134.00 | 1.37369 | ||||||||
\(89\) | −168.000 | −0.200089 | −0.100045 | − | 0.994983i | \(-0.531899\pi\) | ||||
−0.100045 | + | 0.994983i | \(0.531899\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 121.000 | 0.139387 | ||||||||
\(92\) | −183.000 | −0.207381 | ||||||||
\(93\) | 280.000 | 0.312201 | ||||||||
\(94\) | 504.000 | 0.553017 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −225.000 | −0.239208 | ||||||||
\(97\) | −758.000 | −0.793435 | −0.396718 | − | 0.917941i | \(-0.629851\pi\) | ||||
−0.396718 | + | 0.917941i | \(0.629851\pi\) | |||||||
\(98\) | −666.000 | −0.686491 | ||||||||
\(99\) | 108.000 | 0.109640 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −726.000 | −0.715245 | −0.357622 | − | 0.933866i | \(-0.616412\pi\) | ||||
−0.357622 | + | 0.933866i | \(0.616412\pi\) | |||||||
\(102\) | 1395.00 | 1.35417 | ||||||||
\(103\) | −2.00000 | −0.00191326 | −0.000956630 | − | 1.00000i | \(-0.500305\pi\) | ||||
−0.000956630 | 1.00000i | \(0.500305\pi\) | ||||||||
\(104\) | 231.000 | 0.217802 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1305.00 | −1.19578 | ||||||||
\(107\) | −1413.00 | −1.27663 | −0.638317 | − | 0.769773i | \(-0.720369\pi\) | ||||
−0.638317 | + | 0.769773i | \(0.720369\pi\) | |||||||
\(108\) | −145.000 | −0.129191 | ||||||||
\(109\) | 389.000 | 0.341830 | 0.170915 | − | 0.985286i | \(-0.445328\pi\) | ||||
0.170915 | + | 0.985286i | \(0.445328\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1250.00 | 1.06887 | ||||||||
\(112\) | 781.000 | 0.658907 | ||||||||
\(113\) | −342.000 | −0.284714 | −0.142357 | − | 0.989815i | \(-0.545468\pi\) | ||||
−0.142357 | + | 0.989815i | \(0.545468\pi\) | |||||||
\(114\) | 285.000 | 0.234146 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −249.000 | −0.199302 | ||||||||
\(117\) | 22.0000 | 0.0173838 | ||||||||
\(118\) | 585.000 | 0.456387 | ||||||||
\(119\) | −1023.00 | −0.788053 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1585.00 | 1.19083 | ||||||||
\(122\) | −1074.00 | −0.797011 | ||||||||
\(123\) | 1200.00 | 0.879678 | ||||||||
\(124\) | 56.0000 | 0.0405560 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 66.0000 | 0.0466647 | ||||||||
\(127\) | 1150.00 | 0.803512 | 0.401756 | − | 0.915747i | \(-0.368400\pi\) | ||||
0.401756 | + | 0.915747i | \(0.368400\pi\) | |||||||
\(128\) | 1659.00 | 1.14560 | ||||||||
\(129\) | 980.000 | 0.668870 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1452.00 | −0.968411 | −0.484205 | − | 0.874954i | \(-0.660891\pi\) | ||||
−0.484205 | + | 0.874954i | \(0.660891\pi\) | |||||||
\(132\) | −270.000 | −0.178034 | ||||||||
\(133\) | −209.000 | −0.136260 | ||||||||
\(134\) | 2883.00 | 1.85861 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1953.00 | −1.23139 | ||||||||
\(137\) | 1689.00 | 1.05329 | 0.526646 | − | 0.850085i | \(-0.323449\pi\) | ||||
0.526646 | + | 0.850085i | \(0.323449\pi\) | |||||||
\(138\) | −2745.00 | −1.69326 | ||||||||
\(139\) | 2144.00 | 1.30829 | 0.654143 | − | 0.756371i | \(-0.273030\pi\) | ||||
0.654143 | + | 0.756371i | \(0.273030\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 840.000 | 0.501708 | ||||||||
\(142\) | −738.000 | −0.436138 | ||||||||
\(143\) | 594.000 | 0.347362 | ||||||||
\(144\) | 142.000 | 0.0821759 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1059.00 | −0.600298 | ||||||||
\(147\) | −1110.00 | −0.622798 | ||||||||
\(148\) | 250.000 | 0.138850 | ||||||||
\(149\) | −3000.00 | −1.64946 | −0.824730 | − | 0.565527i | \(-0.808673\pi\) | ||||
−0.824730 | + | 0.565527i | \(0.808673\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1006.00 | −0.542166 | −0.271083 | − | 0.962556i | \(-0.587382\pi\) | ||||
−0.271083 | + | 0.962556i | \(0.587382\pi\) | |||||||
\(152\) | −399.000 | −0.212916 | ||||||||
\(153\) | −186.000 | −0.0982824 | ||||||||
\(154\) | 1782.00 | 0.932452 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −55.0000 | −0.0282277 | ||||||||
\(157\) | −2846.00 | −1.44672 | −0.723362 | − | 0.690469i | \(-0.757404\pi\) | ||||
−0.723362 | + | 0.690469i | \(0.757404\pi\) | |||||||
\(158\) | −102.000 | −0.0513588 | ||||||||
\(159\) | −2175.00 | −1.08483 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2013.00 | 0.985383 | ||||||||
\(162\) | −2013.00 | −0.976273 | ||||||||
\(163\) | 1600.00 | 0.768845 | 0.384422 | − | 0.923157i | \(-0.374401\pi\) | ||||
0.384422 | + | 0.923157i | \(0.374401\pi\) | |||||||
\(164\) | 240.000 | 0.114273 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −702.000 | −0.328228 | ||||||||
\(167\) | 2004.00 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 1155.00 | 0.530418 | ||||||||
\(169\) | −2076.00 | −0.944925 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −38.0000 | −0.0169938 | ||||||||
\(172\) | 196.000 | 0.0868887 | ||||||||
\(173\) | 462.000 | 0.203036 | 0.101518 | − | 0.994834i | \(-0.467630\pi\) | ||||
0.101518 | + | 0.994834i | \(0.467630\pi\) | |||||||
\(174\) | −3735.00 | −1.62730 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3834.00 | 1.64204 | ||||||||
\(177\) | 975.000 | 0.414042 | ||||||||
\(178\) | −504.000 | −0.212227 | ||||||||
\(179\) | 720.000 | 0.300644 | 0.150322 | − | 0.988637i | \(-0.451969\pi\) | ||||
0.150322 | + | 0.988637i | \(0.451969\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2338.00 | −0.960122 | −0.480061 | − | 0.877235i | \(-0.659386\pi\) | ||||
−0.480061 | + | 0.877235i | \(0.659386\pi\) | |||||||
\(182\) | 363.000 | 0.147843 | ||||||||
\(183\) | −1790.00 | −0.723063 | ||||||||
\(184\) | 3843.00 | 1.53973 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 840.000 | 0.331139 | ||||||||
\(187\) | −5022.00 | −1.96388 | ||||||||
\(188\) | 168.000 | 0.0651737 | ||||||||
\(189\) | 1595.00 | 0.613858 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2871.00 | 1.08763 | 0.543817 | − | 0.839204i | \(-0.316978\pi\) | ||||
0.543817 | + | 0.839204i | \(0.316978\pi\) | |||||||
\(192\) | 2165.00 | 0.813778 | ||||||||
\(193\) | −1658.00 | −0.618370 | −0.309185 | − | 0.951002i | \(-0.600056\pi\) | ||||
−0.309185 | + | 0.951002i | \(0.600056\pi\) | |||||||
\(194\) | −2274.00 | −0.841565 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −222.000 | −0.0809038 | ||||||||
\(197\) | 4176.00 | 1.51029 | 0.755146 | − | 0.655556i | \(-0.227566\pi\) | ||||
0.755146 | + | 0.655556i | \(0.227566\pi\) | |||||||
\(198\) | 324.000 | 0.116291 | ||||||||
\(199\) | −241.000 | −0.0858494 | −0.0429247 | − | 0.999078i | \(-0.513668\pi\) | ||||
−0.0429247 | + | 0.999078i | \(0.513668\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4805.00 | 1.68616 | ||||||||
\(202\) | −2178.00 | −0.758631 | ||||||||
\(203\) | 2739.00 | 0.946996 | ||||||||
\(204\) | 465.000 | 0.159591 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.00000 | −0.00202932 | ||||||||
\(207\) | 366.000 | 0.122893 | ||||||||
\(208\) | 781.000 | 0.260349 | ||||||||
\(209\) | −1026.00 | −0.339569 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −745.000 | −0.243071 | −0.121535 | − | 0.992587i | \(-0.538782\pi\) | ||||
−0.121535 | + | 0.992587i | \(0.538782\pi\) | |||||||
\(212\) | −435.000 | −0.140924 | ||||||||
\(213\) | −1230.00 | −0.395672 | ||||||||
\(214\) | −4239.00 | −1.35408 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3045.00 | 0.959194 | ||||||||
\(217\) | −616.000 | −0.192704 | ||||||||
\(218\) | 1167.00 | 0.362565 | ||||||||
\(219\) | −1765.00 | −0.544601 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1023.00 | −0.311377 | ||||||||
\(222\) | 3750.00 | 1.13371 | ||||||||
\(223\) | 1978.00 | 0.593976 | 0.296988 | − | 0.954881i | \(-0.404018\pi\) | ||||
0.296988 | + | 0.954881i | \(0.404018\pi\) | |||||||
\(224\) | 495.000 | 0.147650 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1026.00 | −0.301985 | ||||||||
\(227\) | −5355.00 | −1.56574 | −0.782872 | − | 0.622183i | \(-0.786246\pi\) | ||||
−0.782872 | + | 0.622183i | \(0.786246\pi\) | |||||||
\(228\) | 95.0000 | 0.0275944 | ||||||||
\(229\) | −6370.00 | −1.83817 | −0.919086 | − | 0.394057i | \(-0.871071\pi\) | ||||
−0.919086 | + | 0.394057i | \(0.871071\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2970.00 | 0.845938 | ||||||||
\(232\) | 5229.00 | 1.47974 | ||||||||
\(233\) | 2838.00 | 0.797955 | 0.398978 | − | 0.916961i | \(-0.369365\pi\) | ||||
0.398978 | + | 0.916961i | \(0.369365\pi\) | |||||||
\(234\) | 66.0000 | 0.0184383 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 195.000 | 0.0537857 | ||||||||
\(237\) | −170.000 | −0.0465936 | ||||||||
\(238\) | −3069.00 | −0.835856 | ||||||||
\(239\) | −369.000 | −0.0998687 | −0.0499344 | − | 0.998753i | \(-0.515901\pi\) | ||||
−0.0499344 | + | 0.998753i | \(0.515901\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6608.00 | 1.76622 | 0.883109 | − | 0.469167i | \(-0.155446\pi\) | ||||
0.883109 | + | 0.469167i | \(0.155446\pi\) | |||||||
\(242\) | 4755.00 | 1.26307 | ||||||||
\(243\) | 560.000 | 0.147835 | ||||||||
\(244\) | −358.000 | −0.0939287 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3600.00 | 0.933039 | ||||||||
\(247\) | −209.000 | −0.0538395 | ||||||||
\(248\) | −1176.00 | −0.301113 | ||||||||
\(249\) | −1170.00 | −0.297774 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4674.00 | 1.17538 | 0.587690 | − | 0.809086i | \(-0.300038\pi\) | ||||
0.587690 | + | 0.809086i | \(0.300038\pi\) | |||||||
\(252\) | 22.0000 | 0.00549948 | ||||||||
\(253\) | 9882.00 | 2.45564 | ||||||||
\(254\) | 3450.00 | 0.852253 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1513.00 | 0.369385 | ||||||||
\(257\) | −4512.00 | −1.09514 | −0.547570 | − | 0.836760i | \(-0.684447\pi\) | ||||
−0.547570 | + | 0.836760i | \(0.684447\pi\) | |||||||
\(258\) | 2940.00 | 0.709443 | ||||||||
\(259\) | −2750.00 | −0.659756 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 498.000 | 0.118105 | ||||||||
\(262\) | −4356.00 | −1.02715 | ||||||||
\(263\) | −3768.00 | −0.883440 | −0.441720 | − | 0.897153i | \(-0.645632\pi\) | ||||
−0.441720 | + | 0.897153i | \(0.645632\pi\) | |||||||
\(264\) | 5670.00 | 1.32183 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −627.000 | −0.144526 | ||||||||
\(267\) | −840.000 | −0.192536 | ||||||||
\(268\) | 961.000 | 0.219039 | ||||||||
\(269\) | 4758.00 | 1.07844 | 0.539220 | − | 0.842165i | \(-0.318719\pi\) | ||||
0.539220 | + | 0.842165i | \(0.318719\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2041.00 | −0.457498 | −0.228749 | − | 0.973485i | \(-0.573463\pi\) | ||||
−0.228749 | + | 0.973485i | \(0.573463\pi\) | |||||||
\(272\) | −6603.00 | −1.47193 | ||||||||
\(273\) | 605.000 | 0.134126 | ||||||||
\(274\) | 5067.00 | 1.11718 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −915.000 | −0.199553 | ||||||||
\(277\) | −1964.00 | −0.426012 | −0.213006 | − | 0.977051i | \(-0.568325\pi\) | ||||
−0.213006 | + | 0.977051i | \(0.568325\pi\) | |||||||
\(278\) | 6432.00 | 1.38765 | ||||||||
\(279\) | −112.000 | −0.0240332 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5496.00 | −1.16678 | −0.583388 | − | 0.812194i | \(-0.698273\pi\) | ||||
−0.583388 | + | 0.812194i | \(0.698273\pi\) | |||||||
\(282\) | 2520.00 | 0.532141 | ||||||||
\(283\) | −3098.00 | −0.650731 | −0.325366 | − | 0.945588i | \(-0.605487\pi\) | ||||
−0.325366 | + | 0.945588i | \(0.605487\pi\) | |||||||
\(284\) | −246.000 | −0.0513993 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1782.00 | 0.368433 | ||||||||
\(287\) | −2640.00 | −0.542977 | ||||||||
\(288\) | 90.0000 | 0.0184142 | ||||||||
\(289\) | 3736.00 | 0.760432 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3790.00 | −0.763484 | ||||||||
\(292\) | −353.000 | −0.0707458 | ||||||||
\(293\) | −117.000 | −0.0233284 | −0.0116642 | − | 0.999932i | \(-0.503713\pi\) | ||||
−0.0116642 | + | 0.999932i | \(0.503713\pi\) | |||||||
\(294\) | −3330.00 | −0.660577 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5250.00 | −1.03091 | ||||||||
\(297\) | 7830.00 | 1.52977 | ||||||||
\(298\) | −9000.00 | −1.74952 | ||||||||
\(299\) | 2013.00 | 0.389347 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2156.00 | −0.412856 | ||||||||
\(302\) | −3018.00 | −0.575054 | ||||||||
\(303\) | −3630.00 | −0.688244 | ||||||||
\(304\) | −1349.00 | −0.254508 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −558.000 | −0.104244 | ||||||||
\(307\) | 1420.00 | 0.263986 | 0.131993 | − | 0.991251i | \(-0.457862\pi\) | ||||
0.131993 | + | 0.991251i | \(0.457862\pi\) | |||||||
\(308\) | 594.000 | 0.109891 | ||||||||
\(309\) | −10.0000 | −0.00184104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6561.00 | −1.19627 | −0.598135 | − | 0.801395i | \(-0.704091\pi\) | ||||
−0.598135 | + | 0.801395i | \(0.704091\pi\) | |||||||
\(312\) | 1155.00 | 0.209580 | ||||||||
\(313\) | 1483.00 | 0.267809 | 0.133904 | − | 0.990994i | \(-0.457249\pi\) | ||||
0.133904 | + | 0.990994i | \(0.457249\pi\) | |||||||
\(314\) | −8538.00 | −1.53448 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −34.0000 | −0.00605269 | ||||||||
\(317\) | 1239.00 | 0.219524 | 0.109762 | − | 0.993958i | \(-0.464991\pi\) | ||||
0.109762 | + | 0.993958i | \(0.464991\pi\) | |||||||
\(318\) | −6525.00 | −1.15064 | ||||||||
\(319\) | 13446.0 | 2.35997 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7065.00 | −1.22844 | ||||||||
\(322\) | 6039.00 | 1.04516 | ||||||||
\(323\) | 1767.00 | 0.304392 | ||||||||
\(324\) | −671.000 | −0.115055 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4800.00 | 0.815483 | ||||||||
\(327\) | 1945.00 | 0.328926 | ||||||||
\(328\) | −5040.00 | −0.848437 | ||||||||
\(329\) | −1848.00 | −0.309676 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8899.00 | −1.47774 | −0.738872 | − | 0.673846i | \(-0.764641\pi\) | ||||
−0.738872 | + | 0.673846i | \(0.764641\pi\) | |||||||
\(332\) | −234.000 | −0.0386820 | ||||||||
\(333\) | −500.000 | −0.0822818 | ||||||||
\(334\) | 6012.00 | 0.984916 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3905.00 | 0.634033 | ||||||||
\(337\) | −5816.00 | −0.940112 | −0.470056 | − | 0.882637i | \(-0.655766\pi\) | ||||
−0.470056 | + | 0.882637i | \(0.655766\pi\) | |||||||
\(338\) | −6228.00 | −1.00224 | ||||||||
\(339\) | −1710.00 | −0.273966 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3024.00 | −0.480231 | ||||||||
\(342\) | −114.000 | −0.0180246 | ||||||||
\(343\) | 6215.00 | 0.978363 | ||||||||
\(344\) | −4116.00 | −0.645116 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1386.00 | 0.215352 | ||||||||
\(347\) | 1578.00 | 0.244125 | 0.122063 | − | 0.992522i | \(-0.461049\pi\) | ||||
0.122063 | + | 0.992522i | \(0.461049\pi\) | |||||||
\(348\) | −1245.00 | −0.191779 | ||||||||
\(349\) | 1658.00 | 0.254300 | 0.127150 | − | 0.991883i | \(-0.459417\pi\) | ||||
0.127150 | + | 0.991883i | \(0.459417\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1595.00 | 0.242549 | ||||||||
\(352\) | 2430.00 | 0.367953 | ||||||||
\(353\) | 11367.0 | 1.71389 | 0.856947 | − | 0.515405i | \(-0.172359\pi\) | ||||
0.856947 | + | 0.515405i | \(0.172359\pi\) | |||||||
\(354\) | 2925.00 | 0.439158 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −168.000 | −0.0250112 | ||||||||
\(357\) | −5115.00 | −0.758304 | ||||||||
\(358\) | 2160.00 | 0.318881 | ||||||||
\(359\) | 2553.00 | 0.375326 | 0.187663 | − | 0.982233i | \(-0.439909\pi\) | ||||
0.187663 | + | 0.982233i | \(0.439909\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | −7014.00 | −1.01836 | ||||||||
\(363\) | 7925.00 | 1.14588 | ||||||||
\(364\) | 121.000 | 0.0174234 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5370.00 | −0.766925 | ||||||||
\(367\) | 196.000 | 0.0278777 | 0.0139389 | − | 0.999903i | \(-0.495563\pi\) | ||||
0.0139389 | + | 0.999903i | \(0.495563\pi\) | |||||||
\(368\) | 12993.0 | 1.84051 | ||||||||
\(369\) | −480.000 | −0.0677176 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4785.00 | 0.669609 | ||||||||
\(372\) | 280.000 | 0.0390251 | ||||||||
\(373\) | −9353.00 | −1.29834 | −0.649169 | − | 0.760644i | \(-0.724883\pi\) | ||||
−0.649169 | + | 0.760644i | \(0.724883\pi\) | |||||||
\(374\) | −15066.0 | −2.08301 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3528.00 | −0.483890 | ||||||||
\(377\) | 2739.00 | 0.374180 | ||||||||
\(378\) | 4785.00 | 0.651095 | ||||||||
\(379\) | 3827.00 | 0.518680 | 0.259340 | − | 0.965786i | \(-0.416495\pi\) | ||||
0.259340 | + | 0.965786i | \(0.416495\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5750.00 | 0.773180 | ||||||||
\(382\) | 8613.00 | 1.15361 | ||||||||
\(383\) | −5694.00 | −0.759660 | −0.379830 | − | 0.925056i | \(-0.624018\pi\) | ||||
−0.379830 | + | 0.925056i | \(0.624018\pi\) | |||||||
\(384\) | 8295.00 | 1.10235 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4974.00 | −0.655881 | ||||||||
\(387\) | −392.000 | −0.0514896 | ||||||||
\(388\) | −758.000 | −0.0991794 | ||||||||
\(389\) | 1290.00 | 0.168138 | 0.0840689 | − | 0.996460i | \(-0.473208\pi\) | ||||
0.0840689 | + | 0.996460i | \(0.473208\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17019.0 | −2.20125 | ||||||||
\(392\) | 4662.00 | 0.600680 | ||||||||
\(393\) | −7260.00 | −0.931854 | ||||||||
\(394\) | 12528.0 | 1.60191 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 108.000 | 0.0137051 | ||||||||
\(397\) | −6536.00 | −0.826278 | −0.413139 | − | 0.910668i | \(-0.635568\pi\) | ||||
−0.413139 | + | 0.910668i | \(0.635568\pi\) | |||||||
\(398\) | −723.000 | −0.0910571 | ||||||||
\(399\) | −1045.00 | −0.131116 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2328.00 | 0.289912 | 0.144956 | − | 0.989438i | \(-0.453696\pi\) | ||||
0.144956 | + | 0.989438i | \(0.453696\pi\) | |||||||
\(402\) | 14415.0 | 1.78844 | ||||||||
\(403\) | −616.000 | −0.0761418 | ||||||||
\(404\) | −726.000 | −0.0894056 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8217.00 | 1.00444 | ||||||||
\(407\) | −13500.0 | −1.64415 | ||||||||
\(408\) | −9765.00 | −1.18490 | ||||||||
\(409\) | −6676.00 | −0.807107 | −0.403554 | − | 0.914956i | \(-0.632225\pi\) | ||||
−0.403554 | + | 0.914956i | \(0.632225\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8445.00 | 1.01353 | ||||||||
\(412\) | −2.00000 | −0.000239158 0 | ||||||||
\(413\) | −2145.00 | −0.255565 | ||||||||
\(414\) | 1098.00 | 0.130347 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 495.000 | 0.0583398 | ||||||||
\(417\) | 10720.0 | 1.25890 | ||||||||
\(418\) | −3078.00 | −0.360167 | ||||||||
\(419\) | −8136.00 | −0.948615 | −0.474307 | − | 0.880359i | \(-0.657301\pi\) | ||||
−0.474307 | + | 0.880359i | \(0.657301\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8665.00 | −1.00310 | −0.501551 | − | 0.865128i | \(-0.667237\pi\) | ||||
−0.501551 | + | 0.865128i | \(0.667237\pi\) | |||||||
\(422\) | −2235.00 | −0.257815 | ||||||||
\(423\) | −336.000 | −0.0386215 | ||||||||
\(424\) | 9135.00 | 1.04631 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3690.00 | −0.419674 | ||||||||
\(427\) | 3938.00 | 0.446307 | ||||||||
\(428\) | −1413.00 | −0.159579 | ||||||||
\(429\) | 2970.00 | 0.334249 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 750.000 | 0.0838196 | 0.0419098 | − | 0.999121i | \(-0.486656\pi\) | ||||
0.0419098 | + | 0.999121i | \(0.486656\pi\) | |||||||
\(432\) | 10295.0 | 1.14657 | ||||||||
\(433\) | 4858.00 | 0.539170 | 0.269585 | − | 0.962977i | \(-0.413113\pi\) | ||||
0.269585 | + | 0.962977i | \(0.413113\pi\) | |||||||
\(434\) | −1848.00 | −0.204394 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 389.000 | 0.0427287 | ||||||||
\(437\) | −3477.00 | −0.380612 | ||||||||
\(438\) | −5295.00 | −0.577637 | ||||||||
\(439\) | 6500.00 | 0.706670 | 0.353335 | − | 0.935497i | \(-0.385048\pi\) | ||||
0.353335 | + | 0.935497i | \(0.385048\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 444.000 | 0.0479430 | ||||||||
\(442\) | −3069.00 | −0.330266 | ||||||||
\(443\) | −3486.00 | −0.373871 | −0.186936 | − | 0.982372i | \(-0.559856\pi\) | ||||
−0.186936 | + | 0.982372i | \(0.559856\pi\) | |||||||
\(444\) | 1250.00 | 0.133609 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5934.00 | 0.630007 | ||||||||
\(447\) | −15000.0 | −1.58719 | ||||||||
\(448\) | −4763.00 | −0.502300 | ||||||||
\(449\) | −15030.0 | −1.57975 | −0.789877 | − | 0.613265i | \(-0.789856\pi\) | ||||
−0.789877 | + | 0.613265i | \(0.789856\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12960.0 | −1.35313 | ||||||||
\(452\) | −342.000 | −0.0355892 | ||||||||
\(453\) | −5030.00 | −0.521700 | ||||||||
\(454\) | −16065.0 | −1.66072 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1995.00 | −0.204878 | ||||||||
\(457\) | 2959.00 | 0.302880 | 0.151440 | − | 0.988466i | \(-0.451609\pi\) | ||||
0.151440 | + | 0.988466i | \(0.451609\pi\) | |||||||
\(458\) | −19110.0 | −1.94968 | ||||||||
\(459\) | −13485.0 | −1.37130 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −156.000 | −0.0157606 | −0.00788031 | − | 0.999969i | \(-0.502508\pi\) | ||||
−0.00788031 | + | 0.999969i | \(0.502508\pi\) | |||||||
\(462\) | 8910.00 | 0.897253 | ||||||||
\(463\) | −4484.00 | −0.450085 | −0.225042 | − | 0.974349i | \(-0.572252\pi\) | ||||
−0.225042 | + | 0.974349i | \(0.572252\pi\) | |||||||
\(464\) | 17679.0 | 1.76881 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8514.00 | 0.846359 | ||||||||
\(467\) | −8766.00 | −0.868613 | −0.434306 | − | 0.900765i | \(-0.643006\pi\) | ||||
−0.434306 | + | 0.900765i | \(0.643006\pi\) | |||||||
\(468\) | 22.0000 | 0.00217297 | ||||||||
\(469\) | −10571.0 | −1.04077 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14230.0 | −1.39211 | ||||||||
\(472\) | −4095.00 | −0.399338 | ||||||||
\(473\) | −10584.0 | −1.02886 | ||||||||
\(474\) | −510.000 | −0.0494200 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1023.00 | −0.0985066 | ||||||||
\(477\) | 870.000 | 0.0835106 | ||||||||
\(478\) | −1107.00 | −0.105927 | ||||||||
\(479\) | −18996.0 | −1.81200 | −0.906001 | − | 0.423275i | \(-0.860881\pi\) | ||||
−0.906001 | + | 0.423275i | \(0.860881\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2750.00 | −0.260684 | ||||||||
\(482\) | 19824.0 | 1.87336 | ||||||||
\(483\) | 10065.0 | 0.948185 | ||||||||
\(484\) | 1585.00 | 0.148854 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1680.00 | 0.156803 | ||||||||
\(487\) | 7450.00 | 0.693207 | 0.346603 | − | 0.938012i | \(-0.387335\pi\) | ||||
0.346603 | + | 0.938012i | \(0.387335\pi\) | |||||||
\(488\) | 7518.00 | 0.697385 | ||||||||
\(489\) | 8000.00 | 0.739821 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6180.00 | 0.568023 | 0.284012 | − | 0.958821i | \(-0.408335\pi\) | ||||
0.284012 | + | 0.958821i | \(0.408335\pi\) | |||||||
\(492\) | 1200.00 | 0.109960 | ||||||||
\(493\) | −23157.0 | −2.11549 | ||||||||
\(494\) | −627.000 | −0.0571054 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3976.00 | −0.359935 | ||||||||
\(497\) | 2706.00 | 0.244227 | ||||||||
\(498\) | −3510.00 | −0.315837 | ||||||||
\(499\) | 2576.00 | 0.231097 | 0.115549 | − | 0.993302i | \(-0.463137\pi\) | ||||
0.115549 | + | 0.993302i | \(0.463137\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10020.0 | 0.893534 | ||||||||
\(502\) | 14022.0 | 1.24668 | ||||||||
\(503\) | 10545.0 | 0.934748 | 0.467374 | − | 0.884060i | \(-0.345200\pi\) | ||||
0.467374 | + | 0.884060i | \(0.345200\pi\) | |||||||
\(504\) | −462.000 | −0.0408316 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 29646.0 | 2.60460 | ||||||||
\(507\) | −10380.0 | −0.909254 | ||||||||
\(508\) | 1150.00 | 0.100439 | ||||||||
\(509\) | −14694.0 | −1.27957 | −0.639784 | − | 0.768555i | \(-0.720976\pi\) | ||||
−0.639784 | + | 0.768555i | \(0.720976\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3883.00 | 0.336152 | ||||||||
\(512\) | −8733.00 | −0.753804 | ||||||||
\(513\) | −2755.00 | −0.237108 | ||||||||
\(514\) | −13536.0 | −1.16157 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 980.000 | 0.0836087 | ||||||||
\(517\) | −9072.00 | −0.771733 | ||||||||
\(518\) | −8250.00 | −0.699776 | ||||||||
\(519\) | 2310.00 | 0.195371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10332.0 | 0.868816 | 0.434408 | − | 0.900716i | \(-0.356958\pi\) | ||||
0.434408 | + | 0.900716i | \(0.356958\pi\) | |||||||
\(522\) | 1494.00 | 0.125269 | ||||||||
\(523\) | −10937.0 | −0.914420 | −0.457210 | − | 0.889359i | \(-0.651151\pi\) | ||||
−0.457210 | + | 0.889359i | \(0.651151\pi\) | |||||||
\(524\) | −1452.00 | −0.121051 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11304.0 | −0.937030 | ||||||||
\(527\) | 5208.00 | 0.430482 | ||||||||
\(528\) | 19170.0 | 1.58005 | ||||||||
\(529\) | 21322.0 | 1.75245 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −390.000 | −0.0318730 | ||||||||
\(532\) | −209.000 | −0.0170325 | ||||||||
\(533\) | −2640.00 | −0.214542 | ||||||||
\(534\) | −2520.00 | −0.204215 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −20181.0 | −1.62628 | ||||||||
\(537\) | 3600.00 | 0.289295 | ||||||||
\(538\) | 14274.0 | 1.14386 | ||||||||
\(539\) | 11988.0 | 0.957996 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18578.0 | 1.47640 | 0.738198 | − | 0.674584i | \(-0.235677\pi\) | ||||
0.738198 | + | 0.674584i | \(0.235677\pi\) | |||||||
\(542\) | −6123.00 | −0.485250 | ||||||||
\(543\) | −11690.0 | −0.923878 | ||||||||
\(544\) | −4185.00 | −0.329835 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1815.00 | 0.142262 | ||||||||
\(547\) | −21404.0 | −1.67307 | −0.836535 | − | 0.547914i | \(-0.815422\pi\) | ||||
−0.836535 | + | 0.547914i | \(0.815422\pi\) | |||||||
\(548\) | 1689.00 | 0.131662 | ||||||||
\(549\) | 716.000 | 0.0556614 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4731.00 | −0.365785 | ||||||||
\(552\) | 19215.0 | 1.48160 | ||||||||
\(553\) | 374.000 | 0.0287597 | ||||||||
\(554\) | −5892.00 | −0.451854 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2144.00 | 0.163536 | ||||||||
\(557\) | 3948.00 | 0.300327 | 0.150163 | − | 0.988661i | \(-0.452020\pi\) | ||||
0.150163 | + | 0.988661i | \(0.452020\pi\) | |||||||
\(558\) | −336.000 | −0.0254911 | ||||||||
\(559\) | −2156.00 | −0.163129 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25110.0 | −1.88974 | ||||||||
\(562\) | −16488.0 | −1.23755 | ||||||||
\(563\) | −5724.00 | −0.428486 | −0.214243 | − | 0.976780i | \(-0.568729\pi\) | ||||
−0.214243 | + | 0.976780i | \(0.568729\pi\) | |||||||
\(564\) | 840.000 | 0.0627134 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9294.00 | −0.690205 | ||||||||
\(567\) | 7381.00 | 0.546689 | ||||||||
\(568\) | 5166.00 | 0.381621 | ||||||||
\(569\) | −20592.0 | −1.51716 | −0.758578 | − | 0.651582i | \(-0.774105\pi\) | ||||
−0.758578 | + | 0.651582i | \(0.774105\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20684.0 | 1.51593 | 0.757967 | − | 0.652293i | \(-0.226193\pi\) | ||||
0.757967 | + | 0.652293i | \(0.226193\pi\) | |||||||
\(572\) | 594.000 | 0.0434203 | ||||||||
\(573\) | 14355.0 | 1.04658 | ||||||||
\(574\) | −7920.00 | −0.575914 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −866.000 | −0.0626447 | ||||||||
\(577\) | 19573.0 | 1.41219 | 0.706096 | − | 0.708116i | \(-0.250455\pi\) | ||||
0.706096 | + | 0.708116i | \(0.250455\pi\) | |||||||
\(578\) | 11208.0 | 0.806559 | ||||||||
\(579\) | −8290.00 | −0.595027 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2574.00 | 0.183800 | ||||||||
\(582\) | −11370.0 | −0.809797 | ||||||||
\(583\) | 23490.0 | 1.66871 | ||||||||
\(584\) | 7413.00 | 0.525260 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −351.000 | −0.0247435 | ||||||||
\(587\) | −13524.0 | −0.950929 | −0.475464 | − | 0.879735i | \(-0.657720\pi\) | ||||
−0.475464 | + | 0.879735i | \(0.657720\pi\) | |||||||
\(588\) | −1110.00 | −0.0778497 | ||||||||
\(589\) | 1064.00 | 0.0744335 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20880.0 | 1.45328 | ||||||||
\(592\) | −17750.0 | −1.23230 | ||||||||
\(593\) | −8994.00 | −0.622832 | −0.311416 | − | 0.950274i | \(-0.600803\pi\) | ||||
−0.311416 | + | 0.950274i | \(0.600803\pi\) | |||||||
\(594\) | 23490.0 | 1.62257 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3000.00 | −0.206183 | ||||||||
\(597\) | −1205.00 | −0.0826087 | ||||||||
\(598\) | 6039.00 | 0.412965 | ||||||||
\(599\) | 10128.0 | 0.690850 | 0.345425 | − | 0.938446i | \(-0.387735\pi\) | ||||
0.345425 | + | 0.938446i | \(0.387735\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22696.0 | −1.54041 | −0.770207 | − | 0.637794i | \(-0.779847\pi\) | ||||
−0.770207 | + | 0.637794i | \(0.779847\pi\) | |||||||
\(602\) | −6468.00 | −0.437900 | ||||||||
\(603\) | −1922.00 | −0.129801 | ||||||||
\(604\) | −1006.00 | −0.0677708 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −10890.0 | −0.729993 | ||||||||
\(607\) | 5182.00 | 0.346509 | 0.173254 | − | 0.984877i | \(-0.444572\pi\) | ||||
0.173254 | + | 0.984877i | \(0.444572\pi\) | |||||||
\(608\) | −855.000 | −0.0570310 | ||||||||
\(609\) | 13695.0 | 0.911247 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1848.00 | −0.122360 | ||||||||
\(612\) | −186.000 | −0.0122853 | ||||||||
\(613\) | −10082.0 | −0.664287 | −0.332144 | − | 0.943229i | \(-0.607772\pi\) | ||||
−0.332144 | + | 0.943229i | \(0.607772\pi\) | |||||||
\(614\) | 4260.00 | 0.279999 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12474.0 | −0.815896 | ||||||||
\(617\) | 12174.0 | 0.794338 | 0.397169 | − | 0.917745i | \(-0.369993\pi\) | ||||
0.397169 | + | 0.917745i | \(0.369993\pi\) | |||||||
\(618\) | −30.0000 | −0.00195271 | ||||||||
\(619\) | 7490.00 | 0.486347 | 0.243173 | − | 0.969983i | \(-0.421812\pi\) | ||||
0.243173 | + | 0.969983i | \(0.421812\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26535.0 | 1.71467 | ||||||||
\(622\) | −19683.0 | −1.26884 | ||||||||
\(623\) | 1848.00 | 0.118842 | ||||||||
\(624\) | 3905.00 | 0.250521 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4449.00 | 0.284054 | ||||||||
\(627\) | −5130.00 | −0.326750 | ||||||||
\(628\) | −2846.00 | −0.180840 | ||||||||
\(629\) | 23250.0 | 1.47383 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11072.0 | 0.698525 | 0.349263 | − | 0.937025i | \(-0.386432\pi\) | ||||
0.349263 | + | 0.937025i | \(0.386432\pi\) | |||||||
\(632\) | 714.000 | 0.0449389 | ||||||||
\(633\) | −3725.00 | −0.233895 | ||||||||
\(634\) | 3717.00 | 0.232841 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2175.00 | −0.135604 | ||||||||
\(637\) | 2442.00 | 0.151893 | ||||||||
\(638\) | 40338.0 | 2.50313 | ||||||||
\(639\) | 492.000 | 0.0304589 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18894.0 | −1.16422 | −0.582112 | − | 0.813108i | \(-0.697774\pi\) | ||||
−0.582112 | + | 0.813108i | \(0.697774\pi\) | |||||||
\(642\) | −21195.0 | −1.30296 | ||||||||
\(643\) | 19834.0 | 1.21645 | 0.608224 | − | 0.793765i | \(-0.291882\pi\) | ||||
0.608224 | + | 0.793765i | \(0.291882\pi\) | |||||||
\(644\) | 2013.00 | 0.123173 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5301.00 | 0.322856 | ||||||||
\(647\) | −3375.00 | −0.205077 | −0.102539 | − | 0.994729i | \(-0.532697\pi\) | ||||
−0.102539 | + | 0.994729i | \(0.532697\pi\) | |||||||
\(648\) | 14091.0 | 0.854239 | ||||||||
\(649\) | −10530.0 | −0.636885 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3080.00 | −0.185430 | ||||||||
\(652\) | 1600.00 | 0.0961056 | ||||||||
\(653\) | 24948.0 | 1.49509 | 0.747543 | − | 0.664214i | \(-0.231234\pi\) | ||||
0.747543 | + | 0.664214i | \(0.231234\pi\) | |||||||
\(654\) | 5835.00 | 0.348879 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −17040.0 | −1.01418 | ||||||||
\(657\) | 706.000 | 0.0419234 | ||||||||
\(658\) | −5544.00 | −0.328461 | ||||||||
\(659\) | −9879.00 | −0.583962 | −0.291981 | − | 0.956424i | \(-0.594314\pi\) | ||||
−0.291981 | + | 0.956424i | \(0.594314\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14155.0 | −0.832928 | −0.416464 | − | 0.909152i | \(-0.636731\pi\) | ||||
−0.416464 | + | 0.909152i | \(0.636731\pi\) | |||||||
\(662\) | −26697.0 | −1.56738 | ||||||||
\(663\) | −5115.00 | −0.299623 | ||||||||
\(664\) | 4914.00 | 0.287199 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1500.00 | −0.0872730 | ||||||||
\(667\) | 45567.0 | 2.64522 | ||||||||
\(668\) | 2004.00 | 0.116073 | ||||||||
\(669\) | 9890.00 | 0.571554 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19332.0 | 1.11223 | ||||||||
\(672\) | 2475.00 | 0.142076 | ||||||||
\(673\) | −8948.00 | −0.512511 | −0.256256 | − | 0.966609i | \(-0.582489\pi\) | ||||
−0.256256 | + | 0.966609i | \(0.582489\pi\) | |||||||
\(674\) | −17448.0 | −0.997139 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2076.00 | −0.118116 | ||||||||
\(677\) | 11511.0 | 0.653477 | 0.326738 | − | 0.945115i | \(-0.394050\pi\) | ||||
0.326738 | + | 0.945115i | \(0.394050\pi\) | |||||||
\(678\) | −5130.00 | −0.290585 | ||||||||
\(679\) | 8338.00 | 0.471256 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26775.0 | −1.50664 | ||||||||
\(682\) | −9072.00 | −0.509362 | ||||||||
\(683\) | 10476.0 | 0.586900 | 0.293450 | − | 0.955974i | \(-0.405197\pi\) | ||||
0.293450 | + | 0.955974i | \(0.405197\pi\) | |||||||
\(684\) | −38.0000 | −0.00212422 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18645.0 | 1.03771 | ||||||||
\(687\) | −31850.0 | −1.76878 | ||||||||
\(688\) | −13916.0 | −0.771137 | ||||||||
\(689\) | 4785.00 | 0.264578 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30098.0 | 1.65699 | 0.828496 | − | 0.559995i | \(-0.189197\pi\) | ||||
0.828496 | + | 0.559995i | \(0.189197\pi\) | |||||||
\(692\) | 462.000 | 0.0253795 | ||||||||
\(693\) | −1188.00 | −0.0651203 | ||||||||
\(694\) | 4734.00 | 0.258934 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 26145.0 | 1.42388 | ||||||||
\(697\) | 22320.0 | 1.21296 | ||||||||
\(698\) | 4974.00 | 0.269726 | ||||||||
\(699\) | 14190.0 | 0.767833 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14700.0 | −0.792028 | −0.396014 | − | 0.918245i | \(-0.629607\pi\) | ||||
−0.396014 | + | 0.918245i | \(0.629607\pi\) | |||||||
\(702\) | 4785.00 | 0.257262 | ||||||||
\(703\) | 4750.00 | 0.254836 | ||||||||
\(704\) | −23382.0 | −1.25176 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 34101.0 | 1.81786 | ||||||||
\(707\) | 7986.00 | 0.424815 | ||||||||
\(708\) | 975.000 | 0.0517553 | ||||||||
\(709\) | 31178.0 | 1.65150 | 0.825751 | − | 0.564035i | \(-0.190752\pi\) | ||||
0.825751 | + | 0.564035i | \(0.190752\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 68.0000 | 0.00358678 | ||||||||
\(712\) | 3528.00 | 0.185699 | ||||||||
\(713\) | −10248.0 | −0.538276 | ||||||||
\(714\) | −15345.0 | −0.804303 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 720.000 | 0.0375805 | ||||||||
\(717\) | −1845.00 | −0.0960987 | ||||||||
\(718\) | 7659.00 | 0.398094 | ||||||||
\(719\) | −33285.0 | −1.72645 | −0.863227 | − | 0.504815i | \(-0.831561\pi\) | ||||
−0.863227 | + | 0.504815i | \(0.831561\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.0000 | 0.00113637 | ||||||||
\(722\) | 1083.00 | 0.0558242 | ||||||||
\(723\) | 33040.0 | 1.69954 | ||||||||
\(724\) | −2338.00 | −0.120015 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 23775.0 | 1.21539 | ||||||||
\(727\) | 34729.0 | 1.77170 | 0.885851 | − | 0.463970i | \(-0.153575\pi\) | ||||
0.885851 | + | 0.463970i | \(0.153575\pi\) | |||||||
\(728\) | −2541.00 | −0.129362 | ||||||||
\(729\) | 20917.0 | 1.06269 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18228.0 | 0.922280 | ||||||||
\(732\) | −1790.00 | −0.0903829 | ||||||||
\(733\) | −4196.00 | −0.211436 | −0.105718 | − | 0.994396i | \(-0.533714\pi\) | ||||
−0.105718 | + | 0.994396i | \(0.533714\pi\) | |||||||
\(734\) | 588.000 | 0.0295688 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8235.00 | 0.412427 | ||||||||
\(737\) | −51894.0 | −2.59368 | ||||||||
\(738\) | −1440.00 | −0.0718254 | ||||||||
\(739\) | −10744.0 | −0.534810 | −0.267405 | − | 0.963584i | \(-0.586166\pi\) | ||||
−0.267405 | + | 0.963584i | \(0.586166\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1045.00 | −0.0518071 | ||||||||
\(742\) | 14355.0 | 0.710227 | ||||||||
\(743\) | 2208.00 | 0.109022 | 0.0545112 | − | 0.998513i | \(-0.482640\pi\) | ||||
0.0545112 | + | 0.998513i | \(0.482640\pi\) | |||||||
\(744\) | −5880.00 | −0.289746 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −28059.0 | −1.37710 | ||||||||
\(747\) | 468.000 | 0.0229227 | ||||||||
\(748\) | −5022.00 | −0.245485 | ||||||||
\(749\) | 15543.0 | 0.758249 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13160.0 | 0.639434 | 0.319717 | − | 0.947513i | \(-0.396412\pi\) | ||||
0.319717 | + | 0.947513i | \(0.396412\pi\) | |||||||
\(752\) | −11928.0 | −0.578417 | ||||||||
\(753\) | 23370.0 | 1.13101 | ||||||||
\(754\) | 8217.00 | 0.396877 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1595.00 | 0.0767323 | ||||||||
\(757\) | −758.000 | −0.0363936 | −0.0181968 | − | 0.999834i | \(-0.505793\pi\) | ||||
−0.0181968 | + | 0.999834i | \(0.505793\pi\) | |||||||
\(758\) | 11481.0 | 0.550143 | ||||||||
\(759\) | 49410.0 | 2.36294 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4851.00 | 0.231076 | 0.115538 | − | 0.993303i | \(-0.463141\pi\) | ||||
0.115538 | + | 0.993303i | \(0.463141\pi\) | |||||||
\(762\) | 17250.0 | 0.820081 | ||||||||
\(763\) | −4279.00 | −0.203028 | ||||||||
\(764\) | 2871.00 | 0.135954 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17082.0 | −0.805741 | ||||||||
\(767\) | −2145.00 | −0.100980 | ||||||||
\(768\) | 7565.00 | 0.355441 | ||||||||
\(769\) | −33091.0 | −1.55175 | −0.775873 | − | 0.630890i | \(-0.782690\pi\) | ||||
−0.775873 | + | 0.630890i | \(0.782690\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22560.0 | −1.05380 | ||||||||
\(772\) | −1658.00 | −0.0772963 | ||||||||
\(773\) | −42357.0 | −1.97086 | −0.985430 | − | 0.170079i | \(-0.945598\pi\) | ||||
−0.985430 | + | 0.170079i | \(0.945598\pi\) | |||||||
\(774\) | −1176.00 | −0.0546130 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 15918.0 | 0.736370 | ||||||||
\(777\) | −13750.0 | −0.634850 | ||||||||
\(778\) | 3870.00 | 0.178337 | ||||||||
\(779\) | 4560.00 | 0.209729 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13284.0 | 0.608629 | ||||||||
\(782\) | −51057.0 | −2.33478 | ||||||||
\(783\) | 36105.0 | 1.64788 | ||||||||
\(784\) | 15762.0 | 0.718021 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −21780.0 | −0.988380 | ||||||||
\(787\) | 39877.0 | 1.80618 | 0.903089 | − | 0.429454i | \(-0.141294\pi\) | ||||
0.903089 | + | 0.429454i | \(0.141294\pi\) | |||||||
\(788\) | 4176.00 | 0.188787 | ||||||||
\(789\) | −18840.0 | −0.850091 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3762.00 | 0.169104 | ||||||||
\(792\) | −2268.00 | −0.101755 | ||||||||
\(793\) | 3938.00 | 0.176346 | ||||||||
\(794\) | −19608.0 | −0.876400 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −241.000 | −0.0107312 | ||||||||
\(797\) | 30033.0 | 1.33478 | 0.667392 | − | 0.744706i | \(-0.267410\pi\) | ||||
0.667392 | + | 0.744706i | \(0.267410\pi\) | |||||||
\(798\) | −3135.00 | −0.139070 | ||||||||
\(799\) | 15624.0 | 0.691786 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 336.000 | 0.0148214 | ||||||||
\(802\) | 6984.00 | 0.307498 | ||||||||
\(803\) | 19062.0 | 0.837713 | ||||||||
\(804\) | 4805.00 | 0.210770 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1848.00 | −0.0807606 | ||||||||
\(807\) | 23790.0 | 1.03773 | ||||||||
\(808\) | 15246.0 | 0.663802 | ||||||||
\(809\) | 585.000 | 0.0254234 | 0.0127117 | − | 0.999919i | \(-0.495954\pi\) | ||||
0.0127117 | + | 0.999919i | \(0.495954\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28361.0 | 1.22798 | 0.613989 | − | 0.789315i | \(-0.289564\pi\) | ||||
0.613989 | + | 0.789315i | \(0.289564\pi\) | |||||||
\(812\) | 2739.00 | 0.118374 | ||||||||
\(813\) | −10205.0 | −0.440228 | ||||||||
\(814\) | −40500.0 | −1.74389 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −33015.0 | −1.41637 | ||||||||
\(817\) | 3724.00 | 0.159469 | ||||||||
\(818\) | −20028.0 | −0.856067 | ||||||||
\(819\) | −242.000 | −0.0103250 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25068.0 | 1.06563 | 0.532813 | − | 0.846233i | \(-0.321135\pi\) | ||||
0.532813 | + | 0.846233i | \(0.321135\pi\) | |||||||
\(822\) | 25335.0 | 1.07501 | ||||||||
\(823\) | −10901.0 | −0.461707 | −0.230854 | − | 0.972989i | \(-0.574152\pi\) | ||||
−0.230854 | + | 0.972989i | \(0.574152\pi\) | |||||||
\(824\) | 42.0000 | 0.00177565 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6435.00 | −0.271068 | ||||||||
\(827\) | −12027.0 | −0.505707 | −0.252854 | − | 0.967505i | \(-0.581369\pi\) | ||||
−0.252854 | + | 0.967505i | \(0.581369\pi\) | |||||||
\(828\) | 366.000 | 0.0153616 | ||||||||
\(829\) | −19339.0 | −0.810219 | −0.405109 | − | 0.914268i | \(-0.632767\pi\) | ||||
−0.405109 | + | 0.914268i | \(0.632767\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9820.00 | −0.409930 | ||||||||
\(832\) | −4763.00 | −0.198470 | ||||||||
\(833\) | −20646.0 | −0.858753 | ||||||||
\(834\) | 32160.0 | 1.33526 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1026.00 | −0.0424461 | ||||||||
\(837\) | −8120.00 | −0.335326 | ||||||||
\(838\) | −24408.0 | −1.00616 | ||||||||
\(839\) | −13188.0 | −0.542670 | −0.271335 | − | 0.962485i | \(-0.587465\pi\) | ||||
−0.271335 | + | 0.962485i | \(0.587465\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37612.0 | 1.54217 | ||||||||
\(842\) | −25995.0 | −1.06395 | ||||||||
\(843\) | −27480.0 | −1.12273 | ||||||||
\(844\) | −745.000 | −0.0303838 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1008.00 | −0.0409642 | ||||||||
\(847\) | −17435.0 | −0.707289 | ||||||||
\(848\) | 30885.0 | 1.25070 | ||||||||
\(849\) | −15490.0 | −0.626167 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −45750.0 | −1.84288 | ||||||||
\(852\) | −1230.00 | −0.0494590 | ||||||||
\(853\) | 4678.00 | 0.187775 | 0.0938873 | − | 0.995583i | \(-0.470071\pi\) | ||||
0.0938873 | + | 0.995583i | \(0.470071\pi\) | |||||||
\(854\) | 11814.0 | 0.473380 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29673.0 | 1.18482 | ||||||||
\(857\) | −15252.0 | −0.607933 | −0.303966 | − | 0.952683i | \(-0.598311\pi\) | ||||
−0.303966 | + | 0.952683i | \(0.598311\pi\) | |||||||
\(858\) | 8910.00 | 0.354525 | ||||||||
\(859\) | −610.000 | −0.0242293 | −0.0121146 | − | 0.999927i | \(-0.503856\pi\) | ||||
−0.0121146 | + | 0.999927i | \(0.503856\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13200.0 | −0.522479 | ||||||||
\(862\) | 2250.00 | 0.0889041 | ||||||||
\(863\) | −774.000 | −0.0305299 | −0.0152649 | − | 0.999883i | \(-0.504859\pi\) | ||||
−0.0152649 | + | 0.999883i | \(0.504859\pi\) | |||||||
\(864\) | 6525.00 | 0.256927 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14574.0 | 0.571876 | ||||||||
\(867\) | 18680.0 | 0.731726 | ||||||||
\(868\) | −616.000 | −0.0240880 | ||||||||
\(869\) | 1836.00 | 0.0716709 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10571.0 | −0.411234 | ||||||||
\(872\) | −8169.00 | −0.317245 | ||||||||
\(873\) | 1516.00 | 0.0587730 | ||||||||
\(874\) | −10431.0 | −0.403700 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1765.00 | −0.0680751 | ||||||||
\(877\) | 31039.0 | 1.19511 | 0.597556 | − | 0.801827i | \(-0.296139\pi\) | ||||
0.597556 | + | 0.801827i | \(0.296139\pi\) | |||||||
\(878\) | 19500.0 | 0.749537 | ||||||||
\(879\) | −585.000 | −0.0224477 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33678.0 | 1.28790 | 0.643950 | − | 0.765067i | \(-0.277294\pi\) | ||||
0.643950 | + | 0.765067i | \(0.277294\pi\) | |||||||
\(882\) | 1332.00 | 0.0508512 | ||||||||
\(883\) | 42982.0 | 1.63812 | 0.819060 | − | 0.573708i | \(-0.194496\pi\) | ||||
0.819060 | + | 0.573708i | \(0.194496\pi\) | |||||||
\(884\) | −1023.00 | −0.0389222 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10458.0 | −0.396550 | ||||||||
\(887\) | −4494.00 | −0.170117 | −0.0850585 | − | 0.996376i | \(-0.527108\pi\) | ||||
−0.0850585 | + | 0.996376i | \(0.527108\pi\) | |||||||
\(888\) | −26250.0 | −0.991996 | ||||||||
\(889\) | −12650.0 | −0.477241 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 36234.0 | 1.36238 | ||||||||
\(892\) | 1978.00 | 0.0742470 | ||||||||
\(893\) | 3192.00 | 0.119615 | ||||||||
\(894\) | −45000.0 | −1.68347 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −18249.0 | −0.680420 | ||||||||
\(897\) | 10065.0 | 0.374649 | ||||||||
\(898\) | −45090.0 | −1.67558 | ||||||||
\(899\) | −13944.0 | −0.517306 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −40455.0 | −1.49584 | ||||||||
\(902\) | −38880.0 | −1.43521 | ||||||||
\(903\) | −10780.0 | −0.397271 | ||||||||
\(904\) | 7182.00 | 0.264236 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −15090.0 | −0.553346 | ||||||||
\(907\) | 23839.0 | 0.872724 | 0.436362 | − | 0.899771i | \(-0.356267\pi\) | ||||
0.436362 | + | 0.899771i | \(0.356267\pi\) | |||||||
\(908\) | −5355.00 | −0.195718 | ||||||||
\(909\) | 1452.00 | 0.0529811 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10332.0 | −0.375757 | −0.187878 | − | 0.982192i | \(-0.560161\pi\) | ||||
−0.187878 | + | 0.982192i | \(0.560161\pi\) | |||||||
\(912\) | −6745.00 | −0.244901 | ||||||||
\(913\) | 12636.0 | 0.458040 | ||||||||
\(914\) | 8877.00 | 0.321253 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6370.00 | −0.229772 | ||||||||
\(917\) | 15972.0 | 0.575182 | ||||||||
\(918\) | −40455.0 | −1.45448 | ||||||||
\(919\) | −14371.0 | −0.515838 | −0.257919 | − | 0.966166i | \(-0.583037\pi\) | ||||
−0.257919 | + | 0.966166i | \(0.583037\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7100.00 | 0.254021 | ||||||||
\(922\) | −468.000 | −0.0167167 | ||||||||
\(923\) | 2706.00 | 0.0964995 | ||||||||
\(924\) | 2970.00 | 0.105742 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −13452.0 | −0.477387 | ||||||||
\(927\) | 4.00000 | 0.000141723 0 | ||||||||
\(928\) | 11205.0 | 0.396360 | ||||||||
\(929\) | 26889.0 | 0.949623 | 0.474811 | − | 0.880088i | \(-0.342516\pi\) | ||||
0.474811 | + | 0.880088i | \(0.342516\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4218.00 | −0.148485 | ||||||||
\(932\) | 2838.00 | 0.0997444 | ||||||||
\(933\) | −32805.0 | −1.15111 | ||||||||
\(934\) | −26298.0 | −0.921303 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −462.000 | −0.0161335 | ||||||||
\(937\) | −785.000 | −0.0273691 | −0.0136845 | − | 0.999906i | \(-0.504356\pi\) | ||||
−0.0136845 | + | 0.999906i | \(0.504356\pi\) | |||||||
\(938\) | −31713.0 | −1.10391 | ||||||||
\(939\) | 7415.00 | 0.257699 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18141.0 | −0.628459 | −0.314229 | − | 0.949347i | \(-0.601746\pi\) | ||||
−0.314229 | + | 0.949347i | \(0.601746\pi\) | |||||||
\(942\) | −42690.0 | −1.47656 | ||||||||
\(943\) | −43920.0 | −1.51668 | ||||||||
\(944\) | −13845.0 | −0.477348 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −31752.0 | −1.09128 | ||||||||
\(947\) | −23100.0 | −0.792660 | −0.396330 | − | 0.918108i | \(-0.629716\pi\) | ||||
−0.396330 | + | 0.918108i | \(0.629716\pi\) | |||||||
\(948\) | −170.000 | −0.00582420 | ||||||||
\(949\) | 3883.00 | 0.132821 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6195.00 | 0.211237 | ||||||||
\(952\) | 21483.0 | 0.731374 | ||||||||
\(953\) | −45690.0 | −1.55304 | −0.776519 | − | 0.630094i | \(-0.783016\pi\) | ||||
−0.776519 | + | 0.630094i | \(0.783016\pi\) | |||||||
\(954\) | 2610.00 | 0.0885764 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −369.000 | −0.0124836 | ||||||||
\(957\) | 67230.0 | 2.27089 | ||||||||
\(958\) | −56988.0 | −1.92192 | ||||||||
\(959\) | −18579.0 | −0.625597 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26655.0 | −0.894733 | ||||||||
\(962\) | −8250.00 | −0.276498 | ||||||||
\(963\) | 2826.00 | 0.0945655 | ||||||||
\(964\) | 6608.00 | 0.220777 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 30195.0 | 1.00570 | ||||||||
\(967\) | −21584.0 | −0.717781 | −0.358891 | − | 0.933380i | \(-0.616845\pi\) | ||||
−0.358891 | + | 0.933380i | \(0.616845\pi\) | |||||||
\(968\) | −33285.0 | −1.10519 | ||||||||
\(969\) | 8835.00 | 0.292901 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50556.0 | −1.67087 | −0.835437 | − | 0.549586i | \(-0.814786\pi\) | ||||
−0.835437 | + | 0.549586i | \(0.814786\pi\) | |||||||
\(972\) | 560.000 | 0.0184794 | ||||||||
\(973\) | −23584.0 | −0.777049 | ||||||||
\(974\) | 22350.0 | 0.735257 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 25418.0 | 0.833617 | ||||||||
\(977\) | −8568.00 | −0.280568 | −0.140284 | − | 0.990111i | \(-0.544802\pi\) | ||||
−0.140284 | + | 0.990111i | \(0.544802\pi\) | |||||||
\(978\) | 24000.0 | 0.784699 | ||||||||
\(979\) | 9072.00 | 0.296162 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −778.000 | −0.0253207 | ||||||||
\(982\) | 18540.0 | 0.602480 | ||||||||
\(983\) | −29706.0 | −0.963860 | −0.481930 | − | 0.876210i | \(-0.660064\pi\) | ||||
−0.481930 | + | 0.876210i | \(0.660064\pi\) | |||||||
\(984\) | −25200.0 | −0.816409 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −69471.0 | −2.24382 | ||||||||
\(987\) | −9240.00 | −0.297986 | ||||||||
\(988\) | −209.000 | −0.00672993 | ||||||||
\(989\) | −35868.0 | −1.15322 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30512.0 | 0.978048 | 0.489024 | − | 0.872270i | \(-0.337353\pi\) | ||||
0.489024 | + | 0.872270i | \(0.337353\pi\) | |||||||
\(992\) | −2520.00 | −0.0806553 | ||||||||
\(993\) | −44495.0 | −1.42196 | ||||||||
\(994\) | 8118.00 | 0.259042 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1170.00 | −0.0372218 | ||||||||
\(997\) | −47756.0 | −1.51700 | −0.758499 | − | 0.651674i | \(-0.774067\pi\) | ||||
−0.758499 | + | 0.651674i | \(0.774067\pi\) | |||||||
\(998\) | 7728.00 | 0.245116 | ||||||||
\(999\) | −36250.0 | −1.14805 |
(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 | 475.4.a.e.1.1 | 1 | ||
5.2 | odd | 4 | 475.4.b.c.324.2 | 2 | |||
5.3 | odd | 4 | 475.4.b.c.324.1 | 2 | |||
5.4 | even | 2 | 19.4.a.a.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 171.4.a.d.1.1 | 1 | |||
20.19 | odd | 2 | 304.4.a.b.1.1 | 1 | |||
35.34 | odd | 2 | 931.4.a.a.1.1 | 1 | |||
40.19 | odd | 2 | 1216.4.a.a.1.1 | 1 | |||
40.29 | even | 2 | 1216.4.a.f.1.1 | 1 | |||
55.54 | odd | 2 | 2299.4.a.b.1.1 | 1 | |||
95.94 | odd | 2 | 361.4.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
19.4.a.a.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
171.4.a.d.1.1 | 1 | 15.14 | odd | 2 | |||
304.4.a.b.1.1 | 1 | 20.19 | odd | 2 | |||
361.4.a.b.1.1 | 1 | 95.94 | odd | 2 | |||
475.4.a.e.1.1 | 1 | 1.1 | even | 1 | trivial | ||
475.4.b.c.324.1 | 2 | 5.3 | odd | 4 | |||
475.4.b.c.324.2 | 2 | 5.2 | odd | 4 | |||
931.4.a.a.1.1 | 1 | 35.34 | odd | 2 | |||
1216.4.a.a.1.1 | 1 | 40.19 | odd | 2 | |||
1216.4.a.f.1.1 | 1 | 40.29 | even | 2 | |||
2299.4.a.b.1.1 | 1 | 55.54 | odd | 2 |