Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,4,Mod(1,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("315.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.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: | \(18.5856016518\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 315.1 |
$q$-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 | \(0.322068\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.125000 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −21.0000 | −0.928078 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 15.0000 | 0.474342 | ||||||||
\(11\) | 60.0000 | 1.64461 | 0.822304 | − | 0.569049i | \(-0.192689\pi\) | ||||
0.822304 | + | 0.569049i | \(0.192689\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 38.0000 | 0.810716 | 0.405358 | − | 0.914158i | \(-0.367147\pi\) | ||||
0.405358 | + | 0.914158i | \(0.367147\pi\) | |||||||
\(14\) | 21.0000 | 0.400892 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −71.0000 | −1.10938 | ||||||||
\(17\) | −84.0000 | −1.19841 | −0.599206 | − | 0.800595i | \(-0.704517\pi\) | ||||
−0.599206 | + | 0.800595i | \(0.704517\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 110.000 | 1.32820 | 0.664098 | − | 0.747645i | \(-0.268816\pi\) | ||||
0.664098 | + | 0.747645i | \(0.268816\pi\) | |||||||
\(20\) | 5.00000 | 0.0559017 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 180.000 | 1.74437 | ||||||||
\(23\) | 120.000 | 1.08790 | 0.543951 | − | 0.839117i | \(-0.316928\pi\) | ||||
0.543951 | + | 0.839117i | \(0.316928\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 114.000 | 0.859894 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.00000 | 0.0472456 | ||||||||
\(29\) | 162.000 | 1.03733 | 0.518666 | − | 0.854977i | \(-0.326429\pi\) | ||||
0.518666 | + | 0.854977i | \(0.326429\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 236.000 | 1.36732 | 0.683659 | − | 0.729802i | \(-0.260388\pi\) | ||||
0.683659 | + | 0.729802i | \(0.260388\pi\) | |||||||
\(32\) | −45.0000 | −0.248592 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −252.000 | −1.27111 | ||||||||
\(35\) | 35.0000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −376.000 | −1.67065 | −0.835325 | − | 0.549757i | \(-0.814720\pi\) | ||||
−0.835325 | + | 0.549757i | \(0.814720\pi\) | |||||||
\(38\) | 330.000 | 1.40876 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −105.000 | −0.415049 | ||||||||
\(41\) | −126.000 | −0.479949 | −0.239974 | − | 0.970779i | \(-0.577139\pi\) | ||||
−0.239974 | + | 0.970779i | \(0.577139\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −34.0000 | −0.120580 | −0.0602901 | − | 0.998181i | \(-0.519203\pi\) | ||||
−0.0602901 | + | 0.998181i | \(0.519203\pi\) | |||||||
\(44\) | 60.0000 | 0.205576 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 360.000 | 1.15389 | ||||||||
\(47\) | −6.00000 | −0.0186211 | −0.00931053 | − | 0.999957i | \(-0.502964\pi\) | ||||
−0.00931053 | + | 0.999957i | \(0.502964\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 75.0000 | 0.212132 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 38.0000 | 0.101339 | ||||||||
\(53\) | 582.000 | 1.50837 | 0.754187 | − | 0.656659i | \(-0.228031\pi\) | ||||
0.754187 | + | 0.656659i | \(0.228031\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 300.000 | 0.735491 | ||||||||
\(56\) | −147.000 | −0.350780 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 486.000 | 1.10026 | ||||||||
\(59\) | 492.000 | 1.08564 | 0.542822 | − | 0.839848i | \(-0.317356\pi\) | ||||
0.542822 | + | 0.839848i | \(0.317356\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −880.000 | −1.84709 | −0.923545 | − | 0.383491i | \(-0.874722\pi\) | ||||
−0.923545 | + | 0.383491i | \(0.874722\pi\) | |||||||
\(62\) | 708.000 | 1.45026 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 433.000 | 0.845703 | ||||||||
\(65\) | 190.000 | 0.362563 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −826.000 | −1.50615 | −0.753074 | − | 0.657935i | \(-0.771430\pi\) | ||||
−0.753074 | + | 0.657935i | \(0.771430\pi\) | |||||||
\(68\) | −84.0000 | −0.149801 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 105.000 | 0.179284 | ||||||||
\(71\) | −666.000 | −1.11323 | −0.556617 | − | 0.830769i | \(-0.687901\pi\) | ||||
−0.556617 | + | 0.830769i | \(0.687901\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −826.000 | −1.32433 | −0.662164 | − | 0.749359i | \(-0.730362\pi\) | ||||
−0.662164 | + | 0.749359i | \(0.730362\pi\) | |||||||
\(74\) | −1128.00 | −1.77199 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 110.000 | 0.166025 | ||||||||
\(77\) | 420.000 | 0.621603 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −592.000 | −0.843104 | −0.421552 | − | 0.906804i | \(-0.638514\pi\) | ||||
−0.421552 | + | 0.906804i | \(0.638514\pi\) | |||||||
\(80\) | −355.000 | −0.496128 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −378.000 | −0.509062 | ||||||||
\(83\) | 792.000 | 1.04739 | 0.523695 | − | 0.851906i | \(-0.324553\pi\) | ||||
0.523695 | + | 0.851906i | \(0.324553\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −420.000 | −0.535946 | ||||||||
\(86\) | −102.000 | −0.127895 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1260.00 | −1.52632 | ||||||||
\(89\) | 1002.00 | 1.19339 | 0.596695 | − | 0.802468i | \(-0.296480\pi\) | ||||
0.596695 | + | 0.802468i | \(0.296480\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 266.000 | 0.306422 | ||||||||
\(92\) | 120.000 | 0.135988 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −18.0000 | −0.0197506 | ||||||||
\(95\) | 550.000 | 0.593987 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1442.00 | 1.50941 | 0.754706 | − | 0.656063i | \(-0.227780\pi\) | ||||
0.754706 | + | 0.656063i | \(0.227780\pi\) | |||||||
\(98\) | 147.000 | 0.151523 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 25.0000 | 0.0250000 | ||||||||
\(101\) | −1182.00 | −1.16449 | −0.582245 | − | 0.813014i | \(-0.697825\pi\) | ||||
−0.582245 | + | 0.813014i | \(0.697825\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 56.0000 | 0.0535713 | 0.0267857 | − | 0.999641i | \(-0.491473\pi\) | ||||
0.0267857 | + | 0.999641i | \(0.491473\pi\) | |||||||
\(104\) | −798.000 | −0.752407 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1746.00 | 1.59987 | ||||||||
\(107\) | −1572.00 | −1.42029 | −0.710145 | − | 0.704056i | \(-0.751371\pi\) | ||||
−0.710145 | + | 0.704056i | \(0.751371\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1402.00 | −1.23199 | −0.615997 | − | 0.787749i | \(-0.711246\pi\) | ||||
−0.615997 | + | 0.787749i | \(0.711246\pi\) | |||||||
\(110\) | 900.000 | 0.780106 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −497.000 | −0.419304 | ||||||||
\(113\) | −846.000 | −0.704292 | −0.352146 | − | 0.935945i | \(-0.614548\pi\) | ||||
−0.352146 | + | 0.935945i | \(0.614548\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 600.000 | 0.486524 | ||||||||
\(116\) | 162.000 | 0.129667 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1476.00 | 1.15150 | ||||||||
\(119\) | −588.000 | −0.452957 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2269.00 | 1.70473 | ||||||||
\(122\) | −2640.00 | −1.95913 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 236.000 | 0.170915 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1096.00 | −0.765782 | −0.382891 | − | 0.923794i | \(-0.625071\pi\) | ||||
−0.382891 | + | 0.923794i | \(0.625071\pi\) | |||||||
\(128\) | 1659.00 | 1.14560 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 570.000 | 0.384556 | ||||||||
\(131\) | −492.000 | −0.328139 | −0.164070 | − | 0.986449i | \(-0.552462\pi\) | ||||
−0.164070 | + | 0.986449i | \(0.552462\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 770.000 | 0.502011 | ||||||||
\(134\) | −2478.00 | −1.59751 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1764.00 | 1.11222 | ||||||||
\(137\) | −282.000 | −0.175860 | −0.0879302 | − | 0.996127i | \(-0.528025\pi\) | ||||
−0.0879302 | + | 0.996127i | \(0.528025\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000 | 0.00122042 | 0.000610208 | − | 1.00000i | \(-0.499806\pi\) | ||||
0.000610208 | 1.00000i | \(0.499806\pi\) | ||||||||
\(140\) | 35.0000 | 0.0211289 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1998.00 | −1.18076 | ||||||||
\(143\) | 2280.00 | 1.33331 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 810.000 | 0.463909 | ||||||||
\(146\) | −2478.00 | −1.40466 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −376.000 | −0.208831 | ||||||||
\(149\) | 606.000 | 0.333191 | 0.166595 | − | 0.986025i | \(-0.446723\pi\) | ||||
0.166595 | + | 0.986025i | \(0.446723\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2176.00 | −1.17272 | −0.586359 | − | 0.810051i | \(-0.699439\pi\) | ||||
−0.586359 | + | 0.810051i | \(0.699439\pi\) | |||||||
\(152\) | −2310.00 | −1.23267 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1260.00 | 0.659310 | ||||||||
\(155\) | 1180.00 | 0.611483 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 146.000 | 0.0742170 | 0.0371085 | − | 0.999311i | \(-0.488185\pi\) | ||||
0.0371085 | + | 0.999311i | \(0.488185\pi\) | |||||||
\(158\) | −1776.00 | −0.894247 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −225.000 | −0.111174 | ||||||||
\(161\) | 840.000 | 0.411188 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −826.000 | −0.396916 | −0.198458 | − | 0.980109i | \(-0.563593\pi\) | ||||
−0.198458 | + | 0.980109i | \(0.563593\pi\) | |||||||
\(164\) | −126.000 | −0.0599936 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2376.00 | 1.11092 | ||||||||
\(167\) | 1206.00 | 0.558821 | 0.279410 | − | 0.960172i | \(-0.409861\pi\) | ||||
0.279410 | + | 0.960172i | \(0.409861\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −753.000 | −0.342740 | ||||||||
\(170\) | −1260.00 | −0.568456 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −34.0000 | −0.0150725 | ||||||||
\(173\) | 1398.00 | 0.614381 | 0.307191 | − | 0.951648i | \(-0.400611\pi\) | ||||
0.307191 | + | 0.951648i | \(0.400611\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 175.000 | 0.0755929 | ||||||||
\(176\) | −4260.00 | −1.82449 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3006.00 | 1.26578 | ||||||||
\(179\) | −2424.00 | −1.01217 | −0.506085 | − | 0.862484i | \(-0.668908\pi\) | ||||
−0.506085 | + | 0.862484i | \(0.668908\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3728.00 | 1.53094 | 0.765470 | − | 0.643472i | \(-0.222507\pi\) | ||||
0.765470 | + | 0.643472i | \(0.222507\pi\) | |||||||
\(182\) | 798.000 | 0.325009 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2520.00 | −1.00966 | ||||||||
\(185\) | −1880.00 | −0.747137 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5040.00 | −1.97092 | ||||||||
\(188\) | −6.00000 | −0.00232763 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1650.00 | 0.630019 | ||||||||
\(191\) | 2550.00 | 0.966029 | 0.483014 | − | 0.875612i | \(-0.339542\pi\) | ||||
0.483014 | + | 0.875612i | \(0.339542\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1978.00 | −0.737718 | −0.368859 | − | 0.929485i | \(-0.620251\pi\) | ||||
−0.368859 | + | 0.929485i | \(0.620251\pi\) | |||||||
\(194\) | 4326.00 | 1.60097 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 49.0000 | 0.0178571 | ||||||||
\(197\) | −1170.00 | −0.423142 | −0.211571 | − | 0.977363i | \(-0.567858\pi\) | ||||
−0.211571 | + | 0.977363i | \(0.567858\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3584.00 | 1.27670 | 0.638349 | − | 0.769747i | \(-0.279618\pi\) | ||||
0.638349 | + | 0.769747i | \(0.279618\pi\) | |||||||
\(200\) | −525.000 | −0.185616 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3546.00 | −1.23513 | ||||||||
\(203\) | 1134.00 | 0.392075 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −630.000 | −0.214640 | ||||||||
\(206\) | 168.000 | 0.0568209 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2698.00 | −0.899388 | ||||||||
\(209\) | 6600.00 | 2.18436 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1640.00 | 0.535082 | 0.267541 | − | 0.963547i | \(-0.413789\pi\) | ||||
0.267541 | + | 0.963547i | \(0.413789\pi\) | |||||||
\(212\) | 582.000 | 0.188547 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4716.00 | −1.50644 | ||||||||
\(215\) | −170.000 | −0.0539251 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1652.00 | 0.516798 | ||||||||
\(218\) | −4206.00 | −1.30673 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 300.000 | 0.0919363 | ||||||||
\(221\) | −3192.00 | −0.971571 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1888.00 | −0.566950 | −0.283475 | − | 0.958980i | \(-0.591487\pi\) | ||||
−0.283475 | + | 0.958980i | \(0.591487\pi\) | |||||||
\(224\) | −315.000 | −0.0939590 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2538.00 | −0.747014 | ||||||||
\(227\) | −2244.00 | −0.656121 | −0.328061 | − | 0.944657i | \(-0.606395\pi\) | ||||
−0.328061 | + | 0.944657i | \(0.606395\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4084.00 | −1.17851 | −0.589254 | − | 0.807948i | \(-0.700578\pi\) | ||||
−0.589254 | + | 0.807948i | \(0.700578\pi\) | |||||||
\(230\) | 1800.00 | 0.516037 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3402.00 | −0.962725 | ||||||||
\(233\) | 4026.00 | 1.13198 | 0.565991 | − | 0.824411i | \(-0.308494\pi\) | ||||
0.565991 | + | 0.824411i | \(0.308494\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −30.0000 | −0.00832759 | ||||||||
\(236\) | 492.000 | 0.135705 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1764.00 | −0.480433 | ||||||||
\(239\) | −4590.00 | −1.24227 | −0.621135 | − | 0.783704i | \(-0.713328\pi\) | ||||
−0.621135 | + | 0.783704i | \(0.713328\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1946.00 | 0.520136 | 0.260068 | − | 0.965590i | \(-0.416255\pi\) | ||||
0.260068 | + | 0.965590i | \(0.416255\pi\) | |||||||
\(242\) | 6807.00 | 1.80814 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −880.000 | −0.230886 | ||||||||
\(245\) | 245.000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4180.00 | 1.07679 | ||||||||
\(248\) | −4956.00 | −1.26898 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 375.000 | 0.0948683 | ||||||||
\(251\) | 3636.00 | 0.914352 | 0.457176 | − | 0.889376i | \(-0.348861\pi\) | ||||
0.457176 | + | 0.889376i | \(0.348861\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7200.00 | 1.78917 | ||||||||
\(254\) | −3288.00 | −0.812234 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1513.00 | 0.369385 | ||||||||
\(257\) | 4152.00 | 1.00776 | 0.503881 | − | 0.863773i | \(-0.331905\pi\) | ||||
0.503881 | + | 0.863773i | \(0.331905\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2632.00 | −0.631446 | ||||||||
\(260\) | 190.000 | 0.0453204 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1476.00 | −0.348044 | ||||||||
\(263\) | 5388.00 | 1.26326 | 0.631632 | − | 0.775269i | \(-0.282385\pi\) | ||||
0.631632 | + | 0.775269i | \(0.282385\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2910.00 | 0.674566 | ||||||||
\(266\) | 2310.00 | 0.532463 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −826.000 | −0.188269 | ||||||||
\(269\) | 1194.00 | 0.270630 | 0.135315 | − | 0.990803i | \(-0.456795\pi\) | ||||
0.135315 | + | 0.990803i | \(0.456795\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6788.00 | 1.52156 | 0.760778 | − | 0.649012i | \(-0.224818\pi\) | ||||
0.760778 | + | 0.649012i | \(0.224818\pi\) | |||||||
\(272\) | 5964.00 | 1.32949 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −846.000 | −0.186528 | ||||||||
\(275\) | 1500.00 | 0.328921 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8908.00 | −1.93224 | −0.966119 | − | 0.258098i | \(-0.916904\pi\) | ||||
−0.966119 | + | 0.258098i | \(0.916904\pi\) | |||||||
\(278\) | 6.00000 | 0.00129445 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −735.000 | −0.156874 | ||||||||
\(281\) | 6408.00 | 1.36039 | 0.680194 | − | 0.733032i | \(-0.261895\pi\) | ||||
0.680194 | + | 0.733032i | \(0.261895\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3652.00 | −0.767098 | −0.383549 | − | 0.923520i | \(-0.625298\pi\) | ||||
−0.383549 | + | 0.923520i | \(0.625298\pi\) | |||||||
\(284\) | −666.000 | −0.139154 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6840.00 | 1.41419 | ||||||||
\(287\) | −882.000 | −0.181404 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2143.00 | 0.436190 | ||||||||
\(290\) | 2430.00 | 0.492050 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −826.000 | −0.165541 | ||||||||
\(293\) | −2214.00 | −0.441445 | −0.220722 | − | 0.975337i | \(-0.570841\pi\) | ||||
−0.220722 | + | 0.975337i | \(0.570841\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2460.00 | 0.485514 | ||||||||
\(296\) | 7896.00 | 1.55049 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1818.00 | 0.353402 | ||||||||
\(299\) | 4560.00 | 0.881979 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −238.000 | −0.0455751 | ||||||||
\(302\) | −6528.00 | −1.24385 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7810.00 | −1.47347 | ||||||||
\(305\) | −4400.00 | −0.826043 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5452.00 | −1.01356 | −0.506779 | − | 0.862076i | \(-0.669164\pi\) | ||||
−0.506779 | + | 0.862076i | \(0.669164\pi\) | |||||||
\(308\) | 420.000 | 0.0777004 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3540.00 | 0.648576 | ||||||||
\(311\) | −300.000 | −0.0546992 | −0.0273496 | − | 0.999626i | \(-0.508707\pi\) | ||||
−0.0273496 | + | 0.999626i | \(0.508707\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3994.00 | −0.721260 | −0.360630 | − | 0.932709i | \(-0.617438\pi\) | ||||
−0.360630 | + | 0.932709i | \(0.617438\pi\) | |||||||
\(314\) | 438.000 | 0.0787190 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −592.000 | −0.105388 | ||||||||
\(317\) | 2586.00 | 0.458184 | 0.229092 | − | 0.973405i | \(-0.426424\pi\) | ||||
0.229092 | + | 0.973405i | \(0.426424\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9720.00 | 1.70600 | ||||||||
\(320\) | 2165.00 | 0.378210 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2520.00 | 0.436131 | ||||||||
\(323\) | −9240.00 | −1.59173 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 950.000 | 0.162143 | ||||||||
\(326\) | −2478.00 | −0.420993 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2646.00 | 0.445430 | ||||||||
\(329\) | −42.0000 | −0.00703810 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6248.00 | 1.03753 | 0.518763 | − | 0.854918i | \(-0.326393\pi\) | ||||
0.518763 | + | 0.854918i | \(0.326393\pi\) | |||||||
\(332\) | 792.000 | 0.130924 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3618.00 | 0.592719 | ||||||||
\(335\) | −4130.00 | −0.673570 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3062.00 | 0.494949 | 0.247474 | − | 0.968894i | \(-0.420399\pi\) | ||||
0.247474 | + | 0.968894i | \(0.420399\pi\) | |||||||
\(338\) | −2259.00 | −0.363531 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −420.000 | −0.0669932 | ||||||||
\(341\) | 14160.0 | 2.24870 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 714.000 | 0.111908 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4194.00 | 0.651650 | ||||||||
\(347\) | −5196.00 | −0.803850 | −0.401925 | − | 0.915673i | \(-0.631659\pi\) | ||||
−0.401925 | + | 0.915673i | \(0.631659\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8660.00 | 1.32825 | 0.664125 | − | 0.747622i | \(-0.268804\pi\) | ||||
0.664125 | + | 0.747622i | \(0.268804\pi\) | |||||||
\(350\) | 525.000 | 0.0801784 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2700.00 | −0.408837 | ||||||||
\(353\) | −1128.00 | −0.170078 | −0.0850388 | − | 0.996378i | \(-0.527101\pi\) | ||||
−0.0850388 | + | 0.996378i | \(0.527101\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3330.00 | −0.497854 | ||||||||
\(356\) | 1002.00 | 0.149174 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7272.00 | −1.07357 | ||||||||
\(359\) | 6618.00 | 0.972938 | 0.486469 | − | 0.873698i | \(-0.338285\pi\) | ||||
0.486469 | + | 0.873698i | \(0.338285\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5241.00 | 0.764106 | ||||||||
\(362\) | 11184.0 | 1.62381 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 266.000 | 0.0383027 | ||||||||
\(365\) | −4130.00 | −0.592258 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1568.00 | 0.223022 | 0.111511 | − | 0.993763i | \(-0.464431\pi\) | ||||
0.111511 | + | 0.993763i | \(0.464431\pi\) | |||||||
\(368\) | −8520.00 | −1.20689 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5640.00 | −0.792458 | ||||||||
\(371\) | 4074.00 | 0.570112 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5200.00 | −0.721839 | −0.360919 | − | 0.932597i | \(-0.617537\pi\) | ||||
−0.360919 | + | 0.932597i | \(0.617537\pi\) | |||||||
\(374\) | −15120.0 | −2.09047 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 126.000 | 0.0172818 | ||||||||
\(377\) | 6156.00 | 0.840982 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1096.00 | −0.148543 | −0.0742714 | − | 0.997238i | \(-0.523663\pi\) | ||||
−0.0742714 | + | 0.997238i | \(0.523663\pi\) | |||||||
\(380\) | 550.000 | 0.0742484 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7650.00 | 1.02463 | ||||||||
\(383\) | −12318.0 | −1.64340 | −0.821698 | − | 0.569924i | \(-0.806973\pi\) | ||||
−0.821698 | + | 0.569924i | \(0.806973\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2100.00 | 0.277989 | ||||||||
\(386\) | −5934.00 | −0.782468 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1442.00 | 0.188676 | ||||||||
\(389\) | 6558.00 | 0.854766 | 0.427383 | − | 0.904071i | \(-0.359436\pi\) | ||||
0.427383 | + | 0.904071i | \(0.359436\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10080.0 | −1.30375 | ||||||||
\(392\) | −1029.00 | −0.132583 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3510.00 | −0.448810 | ||||||||
\(395\) | −2960.00 | −0.377048 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1258.00 | −0.159036 | −0.0795179 | − | 0.996833i | \(-0.525338\pi\) | ||||
−0.0795179 | + | 0.996833i | \(0.525338\pi\) | |||||||
\(398\) | 10752.0 | 1.35414 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1775.00 | −0.221875 | ||||||||
\(401\) | −2976.00 | −0.370609 | −0.185305 | − | 0.982681i | \(-0.559327\pi\) | ||||
−0.185305 | + | 0.982681i | \(0.559327\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8968.00 | 1.10851 | ||||||||
\(404\) | −1182.00 | −0.145561 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3402.00 | 0.415858 | ||||||||
\(407\) | −22560.0 | −2.74756 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9070.00 | −1.09653 | −0.548267 | − | 0.836303i | \(-0.684712\pi\) | ||||
−0.548267 | + | 0.836303i | \(0.684712\pi\) | |||||||
\(410\) | −1890.00 | −0.227660 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 56.0000 | 0.00669641 | ||||||||
\(413\) | 3444.00 | 0.410335 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3960.00 | 0.468407 | ||||||||
\(416\) | −1710.00 | −0.201538 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 19800.0 | 2.31687 | ||||||||
\(419\) | 6156.00 | 0.717757 | 0.358879 | − | 0.933384i | \(-0.383159\pi\) | ||||
0.358879 | + | 0.933384i | \(0.383159\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6874.00 | −0.795768 | −0.397884 | − | 0.917436i | \(-0.630255\pi\) | ||||
−0.397884 | + | 0.917436i | \(0.630255\pi\) | |||||||
\(422\) | 4920.00 | 0.567540 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12222.0 | −1.39989 | ||||||||
\(425\) | −2100.00 | −0.239682 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6160.00 | −0.698134 | ||||||||
\(428\) | −1572.00 | −0.177536 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −510.000 | −0.0571962 | ||||||||
\(431\) | −10218.0 | −1.14196 | −0.570979 | − | 0.820965i | \(-0.693436\pi\) | ||||
−0.570979 | + | 0.820965i | \(0.693436\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5830.00 | −0.647048 | −0.323524 | − | 0.946220i | \(-0.604868\pi\) | ||||
−0.323524 | + | 0.946220i | \(0.604868\pi\) | |||||||
\(434\) | 4956.00 | 0.548147 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1402.00 | −0.153999 | ||||||||
\(437\) | 13200.0 | 1.44495 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8588.00 | 0.933674 | 0.466837 | − | 0.884343i | \(-0.345393\pi\) | ||||
0.466837 | + | 0.884343i | \(0.345393\pi\) | |||||||
\(440\) | −6300.00 | −0.682593 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9576.00 | −1.03051 | ||||||||
\(443\) | −12660.0 | −1.35778 | −0.678888 | − | 0.734242i | \(-0.737538\pi\) | ||||
−0.678888 | + | 0.734242i | \(0.737538\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5010.00 | 0.533701 | ||||||||
\(446\) | −5664.00 | −0.601341 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3031.00 | 0.319646 | ||||||||
\(449\) | 3636.00 | 0.382168 | 0.191084 | − | 0.981574i | \(-0.438800\pi\) | ||||
0.191084 | + | 0.981574i | \(0.438800\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7560.00 | −0.789327 | ||||||||
\(452\) | −846.000 | −0.0880365 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6732.00 | −0.695922 | ||||||||
\(455\) | 1330.00 | 0.137036 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3022.00 | −0.309329 | −0.154664 | − | 0.987967i | \(-0.549430\pi\) | ||||
−0.154664 | + | 0.987967i | \(0.549430\pi\) | |||||||
\(458\) | −12252.0 | −1.25000 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 600.000 | 0.0608155 | ||||||||
\(461\) | −14742.0 | −1.48938 | −0.744689 | − | 0.667411i | \(-0.767402\pi\) | ||||
−0.744689 | + | 0.667411i | \(0.767402\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9268.00 | −0.930282 | −0.465141 | − | 0.885237i | \(-0.653996\pi\) | ||||
−0.465141 | + | 0.885237i | \(0.653996\pi\) | |||||||
\(464\) | −11502.0 | −1.15079 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12078.0 | 1.20065 | ||||||||
\(467\) | −13920.0 | −1.37932 | −0.689658 | − | 0.724135i | \(-0.742239\pi\) | ||||
−0.689658 | + | 0.724135i | \(0.742239\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5782.00 | −0.569271 | ||||||||
\(470\) | −90.0000 | −0.00883275 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10332.0 | −1.00756 | ||||||||
\(473\) | −2040.00 | −0.198307 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2750.00 | 0.265639 | ||||||||
\(476\) | −588.000 | −0.0566196 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13770.0 | −1.31763 | ||||||||
\(479\) | −8220.00 | −0.784095 | −0.392047 | − | 0.919945i | \(-0.628233\pi\) | ||||
−0.392047 | + | 0.919945i | \(0.628233\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14288.0 | −1.35442 | ||||||||
\(482\) | 5838.00 | 0.551688 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2269.00 | 0.213092 | ||||||||
\(485\) | 7210.00 | 0.675029 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15752.0 | 1.46569 | 0.732845 | − | 0.680395i | \(-0.238192\pi\) | ||||
0.732845 | + | 0.680395i | \(0.238192\pi\) | |||||||
\(488\) | 18480.0 | 1.71424 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 735.000 | 0.0677631 | ||||||||
\(491\) | 6552.00 | 0.602215 | 0.301108 | − | 0.953590i | \(-0.402644\pi\) | ||||
0.301108 | + | 0.953590i | \(0.402644\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13608.0 | −1.24315 | ||||||||
\(494\) | 12540.0 | 1.14211 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16756.0 | −1.51687 | ||||||||
\(497\) | −4662.00 | −0.420763 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4160.00 | 0.373201 | 0.186600 | − | 0.982436i | \(-0.440253\pi\) | ||||
0.186600 | + | 0.982436i | \(0.440253\pi\) | |||||||
\(500\) | 125.000 | 0.0111803 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10908.0 | 0.969816 | ||||||||
\(503\) | 5166.00 | 0.457934 | 0.228967 | − | 0.973434i | \(-0.426465\pi\) | ||||
0.228967 | + | 0.973434i | \(0.426465\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5910.00 | −0.520775 | ||||||||
\(506\) | 21600.0 | 1.89770 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1096.00 | −0.0957227 | ||||||||
\(509\) | −12066.0 | −1.05072 | −0.525360 | − | 0.850880i | \(-0.676069\pi\) | ||||
−0.525360 | + | 0.850880i | \(0.676069\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5782.00 | −0.500549 | ||||||||
\(512\) | −8733.00 | −0.753804 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12456.0 | 1.06889 | ||||||||
\(515\) | 280.000 | 0.0239578 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −360.000 | −0.0306243 | ||||||||
\(518\) | −7896.00 | −0.669750 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3990.00 | −0.336487 | ||||||||
\(521\) | −17886.0 | −1.50403 | −0.752015 | − | 0.659146i | \(-0.770918\pi\) | ||||
−0.752015 | + | 0.659146i | \(0.770918\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5168.00 | 0.432086 | 0.216043 | − | 0.976384i | \(-0.430685\pi\) | ||||
0.216043 | + | 0.976384i | \(0.430685\pi\) | |||||||
\(524\) | −492.000 | −0.0410174 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16164.0 | 1.33989 | ||||||||
\(527\) | −19824.0 | −1.63861 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2233.00 | 0.183529 | ||||||||
\(530\) | 8730.00 | 0.715485 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 770.000 | 0.0627514 | ||||||||
\(533\) | −4788.00 | −0.389102 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7860.00 | −0.635173 | ||||||||
\(536\) | 17346.0 | 1.39782 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3582.00 | 0.287046 | ||||||||
\(539\) | 2940.00 | 0.234944 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7850.00 | 0.623841 | 0.311920 | − | 0.950108i | \(-0.399028\pi\) | ||||
0.311920 | + | 0.950108i | \(0.399028\pi\) | |||||||
\(542\) | 20364.0 | 1.61385 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3780.00 | 0.297916 | ||||||||
\(545\) | −7010.00 | −0.550964 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2990.00 | 0.233717 | 0.116858 | − | 0.993149i | \(-0.462718\pi\) | ||||
0.116858 | + | 0.993149i | \(0.462718\pi\) | |||||||
\(548\) | −282.000 | −0.0219826 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4500.00 | 0.348874 | ||||||||
\(551\) | 17820.0 | 1.37778 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4144.00 | −0.318663 | ||||||||
\(554\) | −26724.0 | −2.04945 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | 0.000152552 0 | ||||||||
\(557\) | −12486.0 | −0.949818 | −0.474909 | − | 0.880035i | \(-0.657519\pi\) | ||||
−0.474909 | + | 0.880035i | \(0.657519\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1292.00 | −0.0977563 | ||||||||
\(560\) | −2485.00 | −0.187519 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 19224.0 | 1.44291 | ||||||||
\(563\) | −732.000 | −0.0547960 | −0.0273980 | − | 0.999625i | \(-0.508722\pi\) | ||||
−0.0273980 | + | 0.999625i | \(0.508722\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4230.00 | −0.314969 | ||||||||
\(566\) | −10956.0 | −0.813631 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13986.0 | 1.03317 | ||||||||
\(569\) | −456.000 | −0.0335967 | −0.0167983 | − | 0.999859i | \(-0.505347\pi\) | ||||
−0.0167983 | + | 0.999859i | \(0.505347\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14092.0 | −1.03281 | −0.516403 | − | 0.856346i | \(-0.672729\pi\) | ||||
−0.516403 | + | 0.856346i | \(0.672729\pi\) | |||||||
\(572\) | 2280.00 | 0.166664 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2646.00 | −0.192408 | ||||||||
\(575\) | 3000.00 | 0.217580 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10190.0 | 0.735208 | 0.367604 | − | 0.929982i | \(-0.380178\pi\) | ||||
0.367604 | + | 0.929982i | \(0.380178\pi\) | |||||||
\(578\) | 6429.00 | 0.462649 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 810.000 | 0.0579887 | ||||||||
\(581\) | 5544.00 | 0.395876 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 34920.0 | 2.48068 | ||||||||
\(584\) | 17346.0 | 1.22908 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6642.00 | −0.468223 | ||||||||
\(587\) | 23220.0 | 1.63270 | 0.816348 | − | 0.577561i | \(-0.195995\pi\) | ||||
0.816348 | + | 0.577561i | \(0.195995\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25960.0 | 1.81607 | ||||||||
\(590\) | 7380.00 | 0.514966 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 26696.0 | 1.85338 | ||||||||
\(593\) | 14916.0 | 1.03293 | 0.516464 | − | 0.856309i | \(-0.327248\pi\) | ||||
0.516464 | + | 0.856309i | \(0.327248\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2940.00 | −0.202568 | ||||||||
\(596\) | 606.000 | 0.0416489 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13680.0 | 0.935480 | ||||||||
\(599\) | −16914.0 | −1.15374 | −0.576868 | − | 0.816838i | \(-0.695725\pi\) | ||||
−0.576868 | + | 0.816838i | \(0.695725\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5762.00 | 0.391076 | 0.195538 | − | 0.980696i | \(-0.437355\pi\) | ||||
0.195538 | + | 0.980696i | \(0.437355\pi\) | |||||||
\(602\) | −714.000 | −0.0483396 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2176.00 | −0.146590 | ||||||||
\(605\) | 11345.0 | 0.762380 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28528.0 | −1.90760 | −0.953802 | − | 0.300435i | \(-0.902868\pi\) | ||||
−0.953802 | + | 0.300435i | \(0.902868\pi\) | |||||||
\(608\) | −4950.00 | −0.330179 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13200.0 | −0.876151 | ||||||||
\(611\) | −228.000 | −0.0150964 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12976.0 | −0.854969 | −0.427484 | − | 0.904023i | \(-0.640600\pi\) | ||||
−0.427484 | + | 0.904023i | \(0.640600\pi\) | |||||||
\(614\) | −16356.0 | −1.07504 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8820.00 | −0.576896 | ||||||||
\(617\) | 8874.00 | 0.579017 | 0.289509 | − | 0.957175i | \(-0.406508\pi\) | ||||
0.289509 | + | 0.957175i | \(0.406508\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17170.0 | −1.11490 | −0.557448 | − | 0.830212i | \(-0.688219\pi\) | ||||
−0.557448 | + | 0.830212i | \(0.688219\pi\) | |||||||
\(620\) | 1180.00 | 0.0764354 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −900.000 | −0.0580172 | ||||||||
\(623\) | 7014.00 | 0.451059 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −11982.0 | −0.765011 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 146.000 | 0.00927712 | ||||||||
\(629\) | 31584.0 | 2.00212 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26728.0 | −1.68625 | −0.843126 | − | 0.537716i | \(-0.819287\pi\) | ||||
−0.843126 | + | 0.537716i | \(0.819287\pi\) | |||||||
\(632\) | 12432.0 | 0.782466 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7758.00 | 0.485977 | ||||||||
\(635\) | −5480.00 | −0.342468 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1862.00 | 0.115817 | ||||||||
\(638\) | 29160.0 | 1.80949 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8295.00 | 0.512326 | ||||||||
\(641\) | −24492.0 | −1.50917 | −0.754583 | − | 0.656204i | \(-0.772161\pi\) | ||||
−0.754583 | + | 0.656204i | \(0.772161\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1888.00 | −0.115794 | −0.0578969 | − | 0.998323i | \(-0.518439\pi\) | ||||
−0.0578969 | + | 0.998323i | \(0.518439\pi\) | |||||||
\(644\) | 840.000 | 0.0513985 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −27720.0 | −1.68828 | ||||||||
\(647\) | −13134.0 | −0.798069 | −0.399035 | − | 0.916936i | \(-0.630655\pi\) | ||||
−0.399035 | + | 0.916936i | \(0.630655\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29520.0 | 1.78546 | ||||||||
\(650\) | 2850.00 | 0.171979 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −826.000 | −0.0496145 | ||||||||
\(653\) | 12882.0 | 0.771993 | 0.385997 | − | 0.922500i | \(-0.373858\pi\) | ||||
0.385997 | + | 0.922500i | \(0.373858\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2460.00 | −0.146748 | ||||||||
\(656\) | 8946.00 | 0.532443 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −126.000 | −0.00746503 | ||||||||
\(659\) | 7380.00 | 0.436243 | 0.218121 | − | 0.975922i | \(-0.430007\pi\) | ||||
0.218121 | + | 0.975922i | \(0.430007\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 560.000 | 0.0329523 | 0.0164762 | − | 0.999864i | \(-0.494755\pi\) | ||||
0.0164762 | + | 0.999864i | \(0.494755\pi\) | |||||||
\(662\) | 18744.0 | 1.10046 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16632.0 | −0.972058 | ||||||||
\(665\) | 3850.00 | 0.224506 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19440.0 | 1.12852 | ||||||||
\(668\) | 1206.00 | 0.0698526 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12390.0 | −0.714429 | ||||||||
\(671\) | −52800.0 | −3.03774 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5722.00 | −0.327737 | −0.163868 | − | 0.986482i | \(-0.552397\pi\) | ||||
−0.163868 | + | 0.986482i | \(0.552397\pi\) | |||||||
\(674\) | 9186.00 | 0.524973 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −753.000 | −0.0428425 | ||||||||
\(677\) | −13650.0 | −0.774907 | −0.387454 | − | 0.921889i | \(-0.626645\pi\) | ||||
−0.387454 | + | 0.921889i | \(0.626645\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10094.0 | 0.570504 | ||||||||
\(680\) | 8820.00 | 0.497399 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 42480.0 | 2.38511 | ||||||||
\(683\) | 1140.00 | 0.0638666 | 0.0319333 | − | 0.999490i | \(-0.489834\pi\) | ||||
0.0319333 | + | 0.999490i | \(0.489834\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1410.00 | −0.0786472 | ||||||||
\(686\) | 1029.00 | 0.0572703 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2414.00 | 0.133769 | ||||||||
\(689\) | 22116.0 | 1.22286 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32510.0 | 1.78978 | 0.894891 | − | 0.446286i | \(-0.147254\pi\) | ||||
0.894891 | + | 0.446286i | \(0.147254\pi\) | |||||||
\(692\) | 1398.00 | 0.0767977 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15588.0 | −0.852612 | ||||||||
\(695\) | 10.0000 | 0.000545787 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10584.0 | 0.575176 | ||||||||
\(698\) | 25980.0 | 1.40882 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 175.000 | 0.00944911 | ||||||||
\(701\) | 21402.0 | 1.15313 | 0.576564 | − | 0.817052i | \(-0.304393\pi\) | ||||
0.576564 | + | 0.817052i | \(0.304393\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −41360.0 | −2.21895 | ||||||||
\(704\) | 25980.0 | 1.39085 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3384.00 | −0.180395 | ||||||||
\(707\) | −8274.00 | −0.440135 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12170.0 | 0.644646 | 0.322323 | − | 0.946630i | \(-0.395536\pi\) | ||||
0.322323 | + | 0.946630i | \(0.395536\pi\) | |||||||
\(710\) | −9990.00 | −0.528054 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −21042.0 | −1.10756 | ||||||||
\(713\) | 28320.0 | 1.48751 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11400.0 | 0.596274 | ||||||||
\(716\) | −2424.00 | −0.126521 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19854.0 | 1.03196 | ||||||||
\(719\) | −12012.0 | −0.623049 | −0.311524 | − | 0.950238i | \(-0.600840\pi\) | ||||
−0.311524 | + | 0.950238i | \(0.600840\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 392.000 | 0.0202480 | ||||||||
\(722\) | 15723.0 | 0.810456 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3728.00 | 0.191367 | ||||||||
\(725\) | 4050.00 | 0.207467 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8480.00 | 0.432608 | 0.216304 | − | 0.976326i | \(-0.430600\pi\) | ||||
0.216304 | + | 0.976326i | \(0.430600\pi\) | |||||||
\(728\) | −5586.00 | −0.284383 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12390.0 | −0.628184 | ||||||||
\(731\) | 2856.00 | 0.144505 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10906.0 | −0.549553 | −0.274776 | − | 0.961508i | \(-0.588604\pi\) | ||||
−0.274776 | + | 0.961508i | \(0.588604\pi\) | |||||||
\(734\) | 4704.00 | 0.236550 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5400.00 | −0.270444 | ||||||||
\(737\) | −49560.0 | −2.47702 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11104.0 | −0.552730 | −0.276365 | − | 0.961053i | \(-0.589130\pi\) | ||||
−0.276365 | + | 0.961053i | \(0.589130\pi\) | |||||||
\(740\) | −1880.00 | −0.0933921 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12222.0 | 0.604695 | ||||||||
\(743\) | 25416.0 | 1.25494 | 0.627471 | − | 0.778640i | \(-0.284090\pi\) | ||||
0.627471 | + | 0.778640i | \(0.284090\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3030.00 | 0.149008 | ||||||||
\(746\) | −15600.0 | −0.765625 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5040.00 | −0.246365 | ||||||||
\(749\) | −11004.0 | −0.536819 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30904.0 | −1.50160 | −0.750801 | − | 0.660529i | \(-0.770332\pi\) | ||||
−0.750801 | + | 0.660529i | \(0.770332\pi\) | |||||||
\(752\) | 426.000 | 0.0206577 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 18468.0 | 0.891996 | ||||||||
\(755\) | −10880.0 | −0.524455 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16216.0 | −0.778574 | −0.389287 | − | 0.921117i | \(-0.627279\pi\) | ||||
−0.389287 | + | 0.921117i | \(0.627279\pi\) | |||||||
\(758\) | −3288.00 | −0.157553 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11550.0 | −0.551266 | ||||||||
\(761\) | 7230.00 | 0.344399 | 0.172199 | − | 0.985062i | \(-0.444913\pi\) | ||||
0.172199 | + | 0.985062i | \(0.444913\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9814.00 | −0.465650 | ||||||||
\(764\) | 2550.00 | 0.120754 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −36954.0 | −1.74308 | ||||||||
\(767\) | 18696.0 | 0.880148 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4790.00 | 0.224619 | 0.112309 | − | 0.993673i | \(-0.464175\pi\) | ||||
0.112309 | + | 0.993673i | \(0.464175\pi\) | |||||||
\(770\) | 6300.00 | 0.294852 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1978.00 | −0.0922147 | ||||||||
\(773\) | 36114.0 | 1.68038 | 0.840188 | − | 0.542296i | \(-0.182445\pi\) | ||||
0.840188 | + | 0.542296i | \(0.182445\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5900.00 | 0.273464 | ||||||||
\(776\) | −30282.0 | −1.40085 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 19674.0 | 0.906616 | ||||||||
\(779\) | −13860.0 | −0.637466 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −39960.0 | −1.83083 | ||||||||
\(782\) | −30240.0 | −1.38284 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3479.00 | −0.158482 | ||||||||
\(785\) | 730.000 | 0.0331909 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13556.0 | 0.614002 | 0.307001 | − | 0.951709i | \(-0.400675\pi\) | ||||
0.307001 | + | 0.951709i | \(0.400675\pi\) | |||||||
\(788\) | −1170.00 | −0.0528928 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8880.00 | −0.399919 | ||||||||
\(791\) | −5922.00 | −0.266197 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33440.0 | −1.49746 | ||||||||
\(794\) | −3774.00 | −0.168683 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3584.00 | 0.159587 | ||||||||
\(797\) | 39006.0 | 1.73358 | 0.866790 | − | 0.498673i | \(-0.166179\pi\) | ||||
0.866790 | + | 0.498673i | \(0.166179\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 504.000 | 0.0223157 | ||||||||
\(800\) | −1125.00 | −0.0497184 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8928.00 | −0.393091 | ||||||||
\(803\) | −49560.0 | −2.17800 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4200.00 | 0.183889 | ||||||||
\(806\) | 26904.0 | 1.17575 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 24822.0 | 1.08074 | ||||||||
\(809\) | 21480.0 | 0.933494 | 0.466747 | − | 0.884391i | \(-0.345426\pi\) | ||||
0.466747 | + | 0.884391i | \(0.345426\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 146.000 | 0.00632152 | 0.00316076 | − | 0.999995i | \(-0.498994\pi\) | ||||
0.00316076 | + | 0.999995i | \(0.498994\pi\) | |||||||
\(812\) | 1134.00 | 0.0490094 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −67680.0 | −2.91423 | ||||||||
\(815\) | −4130.00 | −0.177506 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3740.00 | −0.160154 | ||||||||
\(818\) | −27210.0 | −1.16305 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −630.000 | −0.0268299 | ||||||||
\(821\) | 35562.0 | 1.51172 | 0.755860 | − | 0.654733i | \(-0.227219\pi\) | ||||
0.755860 | + | 0.654733i | \(0.227219\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33964.0 | −1.43853 | −0.719265 | − | 0.694736i | \(-0.755521\pi\) | ||||
−0.719265 | + | 0.694736i | \(0.755521\pi\) | |||||||
\(824\) | −1176.00 | −0.0497183 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10332.0 | 0.435225 | ||||||||
\(827\) | −23292.0 | −0.979374 | −0.489687 | − | 0.871898i | \(-0.662889\pi\) | ||||
−0.489687 | + | 0.871898i | \(0.662889\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33716.0 | 1.41255 | 0.706276 | − | 0.707937i | \(-0.250374\pi\) | ||||
0.706276 | + | 0.707937i | \(0.250374\pi\) | |||||||
\(830\) | 11880.0 | 0.496820 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 16454.0 | 0.685625 | ||||||||
\(833\) | −4116.00 | −0.171202 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6030.00 | 0.249912 | ||||||||
\(836\) | 6600.00 | 0.273045 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18468.0 | 0.761297 | ||||||||
\(839\) | −35280.0 | −1.45173 | −0.725865 | − | 0.687838i | \(-0.758560\pi\) | ||||
−0.725865 | + | 0.687838i | \(0.758560\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1855.00 | 0.0760589 | ||||||||
\(842\) | −20622.0 | −0.844039 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1640.00 | 0.0668852 | ||||||||
\(845\) | −3765.00 | −0.153278 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15883.0 | 0.644329 | ||||||||
\(848\) | −41322.0 | −1.67335 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6300.00 | −0.254221 | ||||||||
\(851\) | −45120.0 | −1.81750 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36902.0 | 1.48124 | 0.740622 | − | 0.671922i | \(-0.234531\pi\) | ||||
0.740622 | + | 0.671922i | \(0.234531\pi\) | |||||||
\(854\) | −18480.0 | −0.740483 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 33012.0 | 1.31814 | ||||||||
\(857\) | −30648.0 | −1.22161 | −0.610803 | − | 0.791783i | \(-0.709153\pi\) | ||||
−0.610803 | + | 0.791783i | \(0.709153\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20918.0 | 0.830865 | 0.415432 | − | 0.909624i | \(-0.363630\pi\) | ||||
0.415432 | + | 0.909624i | \(0.363630\pi\) | |||||||
\(860\) | −170.000 | −0.00674064 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −30654.0 | −1.21123 | ||||||||
\(863\) | 19812.0 | 0.781470 | 0.390735 | − | 0.920503i | \(-0.372221\pi\) | ||||
0.390735 | + | 0.920503i | \(0.372221\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6990.00 | 0.274760 | ||||||||
\(866\) | −17490.0 | −0.686298 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1652.00 | 0.0645997 | ||||||||
\(869\) | −35520.0 | −1.38657 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31388.0 | −1.22106 | ||||||||
\(872\) | 29442.0 | 1.14339 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 39600.0 | 1.53260 | ||||||||
\(875\) | 875.000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38900.0 | 1.49779 | 0.748894 | − | 0.662690i | \(-0.230585\pi\) | ||||
0.748894 | + | 0.662690i | \(0.230585\pi\) | |||||||
\(878\) | 25764.0 | 0.990311 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −21300.0 | −0.815935 | ||||||||
\(881\) | 16398.0 | 0.627086 | 0.313543 | − | 0.949574i | \(-0.398484\pi\) | ||||
0.313543 | + | 0.949574i | \(0.398484\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30422.0 | 1.15944 | 0.579718 | − | 0.814817i | \(-0.303163\pi\) | ||||
0.579718 | + | 0.814817i | \(0.303163\pi\) | |||||||
\(884\) | −3192.00 | −0.121446 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −37980.0 | −1.44014 | ||||||||
\(887\) | 6222.00 | 0.235529 | 0.117765 | − | 0.993042i | \(-0.462427\pi\) | ||||
0.117765 | + | 0.993042i | \(0.462427\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7672.00 | −0.289438 | ||||||||
\(890\) | 15030.0 | 0.566075 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1888.00 | −0.0708687 | ||||||||
\(893\) | −660.000 | −0.0247324 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12120.0 | −0.452656 | ||||||||
\(896\) | 11613.0 | 0.432995 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10908.0 | 0.405350 | ||||||||
\(899\) | 38232.0 | 1.41836 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48888.0 | −1.80765 | ||||||||
\(902\) | −22680.0 | −0.837208 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17766.0 | 0.653638 | ||||||||
\(905\) | 18640.0 | 0.684657 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21926.0 | 0.802691 | 0.401346 | − | 0.915927i | \(-0.368543\pi\) | ||||
0.401346 | + | 0.915927i | \(0.368543\pi\) | |||||||
\(908\) | −2244.00 | −0.0820151 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3990.00 | 0.145349 | ||||||||
\(911\) | 40662.0 | 1.47881 | 0.739403 | − | 0.673263i | \(-0.235108\pi\) | ||||
0.739403 | + | 0.673263i | \(0.235108\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 47520.0 | 1.72254 | ||||||||
\(914\) | −9066.00 | −0.328093 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4084.00 | −0.147313 | ||||||||
\(917\) | −3444.00 | −0.124025 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25688.0 | 0.922055 | 0.461028 | − | 0.887386i | \(-0.347481\pi\) | ||||
0.461028 | + | 0.887386i | \(0.347481\pi\) | |||||||
\(920\) | −12600.0 | −0.451532 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −44226.0 | −1.57972 | ||||||||
\(923\) | −25308.0 | −0.902517 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9400.00 | −0.334130 | ||||||||
\(926\) | −27804.0 | −0.986713 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7290.00 | −0.257873 | ||||||||
\(929\) | −16026.0 | −0.565981 | −0.282990 | − | 0.959123i | \(-0.591326\pi\) | ||||
−0.282990 | + | 0.959123i | \(0.591326\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5390.00 | 0.189742 | ||||||||
\(932\) | 4026.00 | 0.141498 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −41760.0 | −1.46299 | ||||||||
\(935\) | −25200.0 | −0.881420 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18362.0 | 0.640193 | 0.320096 | − | 0.947385i | \(-0.396285\pi\) | ||||
0.320096 | + | 0.947385i | \(0.396285\pi\) | |||||||
\(938\) | −17346.0 | −0.603803 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −30.0000 | −0.00104095 | ||||||||
\(941\) | 8034.00 | 0.278322 | 0.139161 | − | 0.990270i | \(-0.455559\pi\) | ||||
0.139161 | + | 0.990270i | \(0.455559\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15120.0 | −0.522137 | ||||||||
\(944\) | −34932.0 | −1.20439 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6120.00 | −0.210337 | ||||||||
\(947\) | −30732.0 | −1.05455 | −0.527273 | − | 0.849696i | \(-0.676786\pi\) | ||||
−0.527273 | + | 0.849696i | \(0.676786\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31388.0 | −1.07365 | ||||||||
\(950\) | 8250.00 | 0.281753 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12348.0 | 0.420379 | ||||||||
\(953\) | 28242.0 | 0.959967 | 0.479983 | − | 0.877278i | \(-0.340643\pi\) | ||||
0.479983 | + | 0.877278i | \(0.340643\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12750.0 | 0.432021 | ||||||||
\(956\) | −4590.00 | −0.155284 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24660.0 | −0.831658 | ||||||||
\(959\) | −1974.00 | −0.0664690 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25905.0 | 0.869558 | ||||||||
\(962\) | −42864.0 | −1.43658 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1946.00 | 0.0650171 | ||||||||
\(965\) | −9890.00 | −0.329917 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37496.0 | 1.24694 | 0.623470 | − | 0.781848i | \(-0.285723\pi\) | ||||
0.623470 | + | 0.781848i | \(0.285723\pi\) | |||||||
\(968\) | −47649.0 | −1.58212 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 21630.0 | 0.715977 | ||||||||
\(971\) | −27204.0 | −0.899092 | −0.449546 | − | 0.893257i | \(-0.648414\pi\) | ||||
−0.449546 | + | 0.893257i | \(0.648414\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.0000 | 0.000461274 0 | ||||||||
\(974\) | 47256.0 | 1.55460 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 62480.0 | 2.04911 | ||||||||
\(977\) | 42954.0 | 1.40657 | 0.703286 | − | 0.710907i | \(-0.251715\pi\) | ||||
0.703286 | + | 0.710907i | \(0.251715\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 60120.0 | 1.96266 | ||||||||
\(980\) | 245.000 | 0.00798596 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19656.0 | 0.638746 | ||||||||
\(983\) | −10182.0 | −0.330372 | −0.165186 | − | 0.986262i | \(-0.552822\pi\) | ||||
−0.165186 | + | 0.986262i | \(0.552822\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5850.00 | −0.189235 | ||||||||
\(986\) | −40824.0 | −1.31856 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4180.00 | 0.134599 | ||||||||
\(989\) | −4080.00 | −0.131179 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30008.0 | 0.961893 | 0.480946 | − | 0.876750i | \(-0.340293\pi\) | ||||
0.480946 | + | 0.876750i | \(0.340293\pi\) | |||||||
\(992\) | −10620.0 | −0.339905 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −13986.0 | −0.446287 | ||||||||
\(995\) | 17920.0 | 0.570957 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47554.0 | −1.51058 | −0.755291 | − | 0.655390i | \(-0.772504\pi\) | ||||
−0.755291 | + | 0.655390i | \(0.772504\pi\) | |||||||
\(998\) | 12480.0 | 0.395839 | ||||||||
\(999\) | 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 | 315.4.a.e.1.1 | yes | 1 | |
3.2 | odd | 2 | 315.4.a.b.1.1 | ✓ | 1 | ||
5.4 | even | 2 | 1575.4.a.c.1.1 | 1 | |||
7.6 | odd | 2 | 2205.4.a.p.1.1 | 1 | |||
15.14 | odd | 2 | 1575.4.a.i.1.1 | 1 | |||
21.20 | even | 2 | 2205.4.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.4.a.b.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
315.4.a.e.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
1575.4.a.c.1.1 | 1 | 5.4 | even | 2 | |||
1575.4.a.i.1.1 | 1 | 15.14 | odd | 2 | |||
2205.4.a.f.1.1 | 1 | 21.20 | even | 2 | |||
2205.4.a.p.1.1 | 1 | 7.6 | odd | 2 |