Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,4,Mod(1,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2240.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.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: | \(132.164278413\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2240.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | −0.288675 | − | 0.957427i | \(-0.593215\pi\) | ||||
−0.288675 | + | 0.957427i | \(0.593215\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −18.0000 | −0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −17.0000 | −0.465972 | −0.232986 | − | 0.972480i | \(-0.574850\pi\) | ||||
−0.232986 | + | 0.972480i | \(0.574850\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 81.0000 | 1.72810 | 0.864052 | − | 0.503402i | \(-0.167919\pi\) | ||||
0.864052 | + | 0.503402i | \(0.167919\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −91.0000 | −1.29828 | −0.649139 | − | 0.760669i | \(-0.724871\pi\) | ||||
−0.649139 | + | 0.760669i | \(0.724871\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 102.000 | 1.23160 | 0.615800 | − | 0.787902i | \(-0.288833\pi\) | ||||
0.615800 | + | 0.787902i | \(0.288833\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 90.0000 | 0.815926 | 0.407963 | − | 0.912998i | \(-0.366239\pi\) | ||||
0.407963 | + | 0.912998i | \(0.366239\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 135.000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 129.000 | 0.826024 | 0.413012 | − | 0.910726i | \(-0.364477\pi\) | ||||
0.413012 | + | 0.910726i | \(0.364477\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −116.000 | −0.672071 | −0.336036 | − | 0.941849i | \(-0.609086\pi\) | ||||
−0.336036 | + | 0.941849i | \(0.609086\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 51.0000 | 0.269029 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −35.0000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −314.000 | −1.39517 | −0.697585 | − | 0.716502i | \(-0.745742\pi\) | ||||
−0.697585 | + | 0.716502i | \(0.745742\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −243.000 | −0.997722 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −124.000 | −0.472330 | −0.236165 | − | 0.971713i | \(-0.575891\pi\) | ||||
−0.236165 | + | 0.971713i | \(0.575891\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −434.000 | −1.53917 | −0.769586 | − | 0.638543i | \(-0.779537\pi\) | ||||
−0.769586 | + | 0.638543i | \(0.779537\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 90.0000 | 0.298142 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −497.000 | −1.54244 | −0.771222 | − | 0.636566i | \(-0.780354\pi\) | ||||
−0.771222 | + | 0.636566i | \(0.780354\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 273.000 | 0.749562 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 584.000 | 1.51356 | 0.756779 | − | 0.653671i | \(-0.226772\pi\) | ||||
0.756779 | + | 0.653671i | \(0.226772\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 85.0000 | 0.208389 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −306.000 | −0.711065 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −332.000 | −0.732588 | −0.366294 | − | 0.930499i | \(-0.619374\pi\) | ||||
−0.366294 | + | 0.930499i | \(0.619374\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −220.000 | −0.461772 | −0.230886 | − | 0.972981i | \(-0.574163\pi\) | ||||
−0.230886 | + | 0.972981i | \(0.574163\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −126.000 | −0.251976 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −405.000 | −0.772832 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 384.000 | 0.700195 | 0.350098 | − | 0.936713i | \(-0.386148\pi\) | ||||
0.350098 | + | 0.936713i | \(0.386148\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −270.000 | −0.471075 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 664.000 | 1.10989 | 0.554946 | − | 0.831887i | \(-0.312739\pi\) | ||||
0.554946 | + | 0.831887i | \(0.312739\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 230.000 | 0.368760 | 0.184380 | − | 0.982855i | \(-0.440972\pi\) | ||||
0.184380 | + | 0.982855i | \(0.440972\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −119.000 | −0.176121 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −361.000 | −0.514122 | −0.257061 | − | 0.966395i | \(-0.582754\pi\) | ||||
−0.257061 | + | 0.966395i | \(0.582754\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1172.00 | 1.54992 | 0.774962 | − | 0.632008i | \(-0.217769\pi\) | ||||
0.774962 | + | 0.632008i | \(0.217769\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 455.000 | 0.580608 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −387.000 | −0.476905 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 40.0000 | 0.0476404 | 0.0238202 | − | 0.999716i | \(-0.492417\pi\) | ||||
0.0238202 | + | 0.999716i | \(0.492417\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 567.000 | 0.653162 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 348.000 | 0.388021 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −510.000 | −0.550788 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −175.000 | −0.183181 | −0.0915905 | − | 0.995797i | \(-0.529195\pi\) | ||||
−0.0915905 | + | 0.995797i | \(0.529195\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 306.000 | 0.310648 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −270.000 | −0.266000 | −0.133000 | − | 0.991116i | \(-0.542461\pi\) | ||||
−0.133000 | + | 0.991116i | \(0.542461\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −565.000 | −0.540496 | −0.270248 | − | 0.962791i | \(-0.587106\pi\) | ||||
−0.270248 | + | 0.962791i | \(0.587106\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 105.000 | 0.0975900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1206.00 | −1.08961 | −0.544806 | − | 0.838562i | \(-0.683397\pi\) | ||||
−0.544806 | + | 0.838562i | \(0.683397\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1419.00 | 1.24693 | 0.623466 | − | 0.781851i | \(-0.285724\pi\) | ||||
0.623466 | + | 0.781851i | \(0.285724\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 942.000 | 0.805502 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −778.000 | −0.647682 | −0.323841 | − | 0.946111i | \(-0.604974\pi\) | ||||
−0.323841 | + | 0.946111i | \(0.604974\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −450.000 | −0.364893 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1458.00 | −1.15207 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −637.000 | −0.490703 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1042.00 | −0.782870 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 372.000 | 0.272700 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −316.000 | −0.220791 | −0.110396 | − | 0.993888i | \(-0.535212\pi\) | ||||
−0.110396 | + | 0.993888i | \(0.535212\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1302.00 | 0.888641 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1750.00 | −1.16716 | −0.583581 | − | 0.812055i | \(-0.698349\pi\) | ||||
−0.583581 | + | 0.812055i | \(0.698349\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 714.000 | 0.465501 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −675.000 | −0.430331 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 48.0000 | 0.0299337 | 0.0149668 | − | 0.999888i | \(-0.495236\pi\) | ||||
0.0149668 | + | 0.999888i | \(0.495236\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −38.0000 | −0.0231879 | −0.0115939 | − | 0.999933i | \(-0.503691\pi\) | ||||
−0.0115939 | + | 0.999933i | \(0.503691\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1491.00 | 0.890531 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1377.00 | −0.805248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −645.000 | −0.369409 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3582.00 | 1.96946 | 0.984728 | − | 0.174101i | \(-0.0557020\pi\) | ||||
0.984728 | + | 0.174101i | \(0.0557020\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1927.00 | 1.03852 | 0.519262 | − | 0.854615i | \(-0.326207\pi\) | ||||
0.519262 | + | 0.854615i | \(0.326207\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1638.00 | 0.865519 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 580.000 | 0.300559 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2510.00 | 1.27592 | 0.637961 | − | 0.770069i | \(-0.279778\pi\) | ||||
0.637961 | + | 0.770069i | \(0.279778\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1752.00 | −0.873853 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 630.000 | 0.308391 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1870.00 | −0.898587 | −0.449294 | − | 0.893384i | \(-0.648324\pi\) | ||||
−0.449294 | + | 0.893384i | \(0.648324\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −255.000 | −0.120313 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2019.00 | 0.935538 | 0.467769 | − | 0.883851i | \(-0.345058\pi\) | ||||
0.467769 | + | 0.883851i | \(0.345058\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4364.00 | 1.98635 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1836.00 | −0.821067 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1253.00 | −0.550658 | −0.275329 | − | 0.961350i | \(-0.588787\pi\) | ||||
−0.275329 | + | 0.961350i | \(0.588787\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 175.000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 996.000 | 0.422960 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 492.000 | 0.205440 | 0.102720 | − | 0.994710i | \(-0.467245\pi\) | ||||
0.102720 | + | 0.994710i | \(0.467245\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4448.00 | 1.82661 | 0.913307 | − | 0.407271i | \(-0.133520\pi\) | ||||
0.913307 | + | 0.407271i | \(0.133520\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 660.000 | 0.266604 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1570.00 | 0.623939 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1547.00 | 0.604962 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 945.000 | 0.363696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3999.00 | −1.51496 | −0.757480 | − | 0.652858i | \(-0.773570\pi\) | ||||
−0.757480 | + | 0.652858i | \(0.773570\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4880.00 | 1.82005 | 0.910026 | − | 0.414551i | \(-0.136061\pi\) | ||||
0.910026 | + | 0.414551i | \(0.136061\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1215.00 | 0.446195 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4712.00 | −1.70414 | −0.852071 | − | 0.523426i | \(-0.824654\pi\) | ||||
−0.852071 | + | 0.523426i | \(0.824654\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2756.00 | −0.981747 | −0.490874 | − | 0.871231i | \(-0.663322\pi\) | ||||
−0.490874 | + | 0.871231i | \(0.663322\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1152.00 | −0.404258 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 903.000 | 0.312208 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 620.000 | 0.211233 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1620.00 | −0.543951 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1734.00 | −0.573891 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 697.000 | 0.227410 | 0.113705 | − | 0.993515i | \(-0.463728\pi\) | ||||
0.113705 | + | 0.993515i | \(0.463728\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1992.00 | −0.640796 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2170.00 | 0.688338 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −812.000 | −0.254019 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −690.000 | −0.212904 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7371.00 | −2.24356 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 707.000 | 0.212306 | 0.106153 | − | 0.994350i | \(-0.466147\pi\) | ||||
0.106153 | + | 0.994350i | \(0.466147\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −450.000 | −0.133333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −559.000 | −0.163446 | −0.0817228 | − | 0.996655i | \(-0.526042\pi\) | ||||
−0.0817228 | + | 0.996655i | \(0.526042\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3836.00 | 1.10694 | 0.553472 | − | 0.832868i | \(-0.313303\pi\) | ||||
0.553472 | + | 0.832868i | \(0.313303\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 357.000 | 0.101683 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1368.00 | −0.384638 | −0.192319 | − | 0.981332i | \(-0.561601\pi\) | ||||
−0.192319 | + | 0.981332i | \(0.561601\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2485.00 | 0.689802 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1083.00 | 0.296829 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3803.00 | 1.02927 | 0.514635 | − | 0.857409i | \(-0.327927\pi\) | ||||
0.514635 | + | 0.857409i | \(0.327927\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5650.00 | 1.51016 | 0.755080 | − | 0.655633i | \(-0.227598\pi\) | ||||
0.755080 | + | 0.655633i | \(0.227598\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3888.00 | −1.02640 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −245.000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8262.00 | 2.12833 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3516.00 | −0.894849 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1650.00 | −0.414929 | −0.207464 | − | 0.978243i | \(-0.566521\pi\) | ||||
−0.207464 | + | 0.978243i | \(0.566521\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1530.00 | −0.380199 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1365.00 | −0.335214 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5810.00 | 1.41019 | 0.705093 | − | 0.709115i | \(-0.250905\pi\) | ||||
0.705093 | + | 0.709115i | \(0.250905\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2198.00 | −0.527325 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2322.00 | −0.550683 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2758.00 | 0.646637 | 0.323319 | − | 0.946290i | \(-0.395201\pi\) | ||||
0.323319 | + | 0.946290i | \(0.395201\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2920.00 | −0.676884 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −120.000 | −0.0275052 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −186.000 | −0.0421584 | −0.0210792 | − | 0.999778i | \(-0.506710\pi\) | ||||
−0.0210792 | + | 0.999778i | \(0.506710\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6828.00 | 1.53052 | 0.765261 | − | 0.643720i | \(-0.222610\pi\) | ||||
0.765261 | + | 0.643720i | \(0.222610\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1701.00 | −0.377103 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −425.000 | −0.0931944 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8214.00 | 1.78170 | 0.890851 | − | 0.454296i | \(-0.150109\pi\) | ||||
0.890851 | + | 0.454296i | \(0.150109\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2088.00 | 0.448048 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6707.00 | 1.42387 | 0.711933 | − | 0.702248i | \(-0.247820\pi\) | ||||
0.711933 | + | 0.702248i | \(0.247820\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5497.00 | −1.15464 | −0.577319 | − | 0.816518i | \(-0.695901\pi\) | ||||
−0.577319 | + | 0.816518i | \(0.695901\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1530.00 | 0.317998 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −868.000 | −0.178524 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3368.00 | 0.685528 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 525.000 | 0.105760 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −313.000 | −0.0624084 | −0.0312042 | − | 0.999513i | \(-0.509934\pi\) | ||||
−0.0312042 | + | 0.999513i | \(0.509934\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1660.00 | 0.327624 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2295.00 | −0.448382 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7290.00 | 1.41001 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3038.00 | −0.581752 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 810.000 | 0.153575 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1100.00 | 0.206511 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5479.00 | 1.01858 | 0.509288 | − | 0.860596i | \(-0.329909\pi\) | ||||
0.509288 | + | 0.860596i | \(0.329909\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1695.00 | 0.312056 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4422.00 | −0.806266 | −0.403133 | − | 0.915141i | \(-0.632079\pi\) | ||||
−0.403133 | + | 0.915141i | \(0.632079\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 275.000 | 0.0496611 | 0.0248305 | − | 0.999692i | \(-0.492095\pi\) | ||||
0.0248305 | + | 0.999692i | \(0.492095\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 630.000 | 0.112687 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4106.00 | 0.727495 | 0.363748 | − | 0.931498i | \(-0.381497\pi\) | ||||
0.363748 | + | 0.931498i | \(0.381497\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2193.00 | −0.384904 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3618.00 | 0.629087 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9282.00 | −1.59896 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2025.00 | 0.345621 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4257.00 | −0.719916 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3479.00 | −0.582989 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8260.00 | 1.37163 | 0.685817 | − | 0.727774i | \(-0.259445\pi\) | ||||
0.685817 | + | 0.727774i | \(0.259445\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5652.00 | 0.930113 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1920.00 | −0.313137 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9946.00 | 1.60769 | 0.803847 | − | 0.594836i | \(-0.202783\pi\) | ||||
0.803847 | + | 0.594836i | \(0.202783\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2334.00 | 0.373939 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1972.00 | 0.313167 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1350.00 | 0.210671 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8798.00 | −1.36110 | −0.680550 | − | 0.732702i | \(-0.738259\pi\) | ||||
−0.680550 | + | 0.732702i | \(0.738259\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1838.00 | 0.281908 | 0.140954 | − | 0.990016i | \(-0.454983\pi\) | ||||
0.140954 | + | 0.990016i | \(0.454983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10935.0 | 1.66287 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2265.00 | 0.341512 | 0.170756 | − | 0.985313i | \(-0.445379\pi\) | ||||
0.170756 | + | 0.985313i | \(0.445379\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3320.00 | −0.496359 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1911.00 | 0.283308 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4136.00 | −0.608049 | −0.304025 | − | 0.952664i | \(-0.598331\pi\) | ||||
−0.304025 | + | 0.952664i | \(0.598331\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3545.00 | 0.516839 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3126.00 | 0.451990 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1150.00 | −0.164914 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10031.0 | 1.42674 | 0.713370 | − | 0.700787i | \(-0.247168\pi\) | ||||
0.713370 | + | 0.700787i | \(0.247168\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2232.00 | 0.314887 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4088.00 | 0.572071 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2792.00 | −0.387572 | −0.193786 | − | 0.981044i | \(-0.562077\pi\) | ||||
−0.193786 | + | 0.981044i | \(0.562077\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 375.000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10449.0 | 1.42746 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9948.00 | 1.34827 | 0.674135 | − | 0.738608i | \(-0.264517\pi\) | ||||
0.674135 | + | 0.738608i | \(0.264517\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 948.000 | 0.127474 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2700.00 | −0.360218 | −0.180109 | − | 0.983647i | \(-0.557645\pi\) | ||||
−0.180109 | + | 0.983647i | \(0.557645\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 595.000 | 0.0787637 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7812.00 | 1.02611 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 631.000 | 0.0822441 | 0.0411221 | − | 0.999154i | \(-0.486907\pi\) | ||||
0.0411221 | + | 0.999154i | \(0.486907\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8190.00 | −1.05930 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5250.00 | 0.673861 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1805.00 | 0.229923 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13139.0 | 1.66103 | 0.830513 | − | 0.556999i | \(-0.188047\pi\) | ||||
0.830513 | + | 0.556999i | \(0.188047\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2142.00 | −0.268757 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −887.000 | −0.110461 | −0.0552303 | − | 0.998474i | \(-0.517589\pi\) | ||||
−0.0552303 | + | 0.998474i | \(0.517589\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9396.00 | −1.16141 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −405.000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5338.00 | 0.650110 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5190.00 | −0.627455 | −0.313727 | − | 0.949513i | \(-0.601578\pi\) | ||||
−0.313727 | + | 0.949513i | \(0.601578\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −144.000 | −0.0172822 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2324.00 | −0.276892 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5860.00 | −0.693147 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 114.000 | 0.0133875 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5712.00 | −0.665989 | −0.332995 | − | 0.942929i | \(-0.608059\pi\) | ||||
−0.332995 | + | 0.942929i | \(0.608059\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11155.0 | 1.29136 | 0.645679 | − | 0.763609i | \(-0.276575\pi\) | ||||
0.645679 | + | 0.763609i | \(0.276575\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8946.00 | 1.02830 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2275.00 | −0.259656 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1540.00 | −0.174534 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4131.00 | 0.464910 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8499.00 | −0.949843 | −0.474922 | − | 0.880028i | \(-0.657524\pi\) | ||||
−0.474922 | + | 0.880028i | \(0.657524\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5102.00 | 0.566251 | 0.283125 | − | 0.959083i | \(-0.408629\pi\) | ||||
0.283125 | + | 0.959083i | \(0.408629\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1935.00 | 0.213279 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9180.00 | 1.00489 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15694.0 | −1.70623 | −0.853114 | − | 0.521725i | \(-0.825289\pi\) | ||||
−0.853114 | + | 0.521725i | \(0.825289\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −882.000 | −0.0952381 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9142.00 | 0.980473 | 0.490236 | − | 0.871589i | \(-0.336910\pi\) | ||||
0.490236 | + | 0.871589i | \(0.336910\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −200.000 | −0.0213054 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10746.0 | −1.13707 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17145.0 | −1.80205 | −0.901027 | − | 0.433762i | \(-0.857186\pi\) | ||||
−0.901027 | + | 0.433762i | \(0.857186\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2108.00 | 0.220093 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5781.00 | −0.599592 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2835.00 | −0.292103 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10184.0 | −1.04242 | −0.521212 | − | 0.853427i | \(-0.674520\pi\) | ||||
−0.521212 | + | 0.853427i | \(0.674520\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12285.0 | −1.24927 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9152.00 | 0.924623 | 0.462311 | − | 0.886718i | \(-0.347020\pi\) | ||||
0.462311 | + | 0.886718i | \(0.347020\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1084.00 | 0.108807 | 0.0544036 | − | 0.998519i | \(-0.482674\pi\) | ||||
0.0544036 | + | 0.998519i | \(0.482674\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1740.00 | −0.173528 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19283.0 | 1.91073 | 0.955365 | − | 0.295428i | \(-0.0954624\pi\) | ||||
0.955365 | + | 0.295428i | \(0.0954624\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2688.00 | 0.264649 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7530.00 | −0.736654 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7378.00 | 0.717211 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2550.00 | 0.246320 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10512.0 | −1.00904 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5118.00 | 0.488199 | 0.244100 | − | 0.969750i | \(-0.421508\pi\) | ||||
0.244100 | + | 0.969750i | \(0.421508\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25434.0 | −2.41100 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1890.00 | −0.178050 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 875.000 | 0.0819210 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2918.00 | −0.271514 | −0.135757 | − | 0.990742i | \(-0.543347\pi\) | ||||
−0.135757 | + | 0.990742i | \(0.543347\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5610.00 | 0.518800 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18627.0 | −1.71207 | −0.856033 | − | 0.516921i | \(-0.827078\pi\) | ||||
−0.856033 | + | 0.516921i | \(0.827078\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11739.0 | −1.07241 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1530.00 | −0.138926 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4648.00 | 0.419500 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12843.0 | 1.15217 | 0.576084 | − | 0.817391i | \(-0.304580\pi\) | ||||
0.576084 | + | 0.817391i | \(0.304580\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6057.00 | −0.540133 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18837.0 | 1.66978 | 0.834891 | − | 0.550415i | \(-0.185531\pi\) | ||||
0.834891 | + | 0.550415i | \(0.185531\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1350.00 | 0.118959 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13092.0 | −1.14682 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7742.00 | 0.674181 | 0.337090 | − | 0.941472i | \(-0.390557\pi\) | ||||
0.337090 | + | 0.941472i | \(0.390557\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1610.00 | 0.139378 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13770.0 | 1.18511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2825.00 | 0.241717 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8449.00 | 0.718736 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3759.00 | 0.317923 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 614.000 | 0.0516311 | 0.0258156 | − | 0.999667i | \(-0.491782\pi\) | ||||
0.0258156 | + | 0.999667i | \(0.491782\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17836.0 | 1.49123 | 0.745616 | − | 0.666376i | \(-0.232156\pi\) | ||||
0.745616 | + | 0.666376i | \(0.232156\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −525.000 | −0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10556.0 | 0.872536 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4067.00 | −0.334265 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5976.00 | 0.488392 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10044.0 | −0.816236 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6030.00 | 0.487289 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1476.00 | −0.118611 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −833.000 | −0.0665674 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23463.0 | −1.86461 | −0.932304 | − | 0.361675i | \(-0.882205\pi\) | ||||
−0.932304 | + | 0.361675i | \(0.882205\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13344.0 | −1.05460 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7095.00 | −0.557645 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1860.00 | −0.145389 | −0.0726946 | − | 0.997354i | \(-0.523160\pi\) | ||||
−0.0726946 | + | 0.997354i | \(0.523160\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3960.00 | 0.307848 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13158.0 | 1.01733 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2527.00 | −0.194320 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4710.00 | −0.360231 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10288.0 | −0.782615 | −0.391307 | − | 0.920260i | \(-0.627977\pi\) | ||||
−0.391307 | + | 0.920260i | \(0.627977\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −35154.0 | −2.65985 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4641.00 | −0.349275 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2356.00 | −0.176365 | −0.0881826 | − | 0.996104i | \(-0.528106\pi\) | ||||
−0.0881826 | + | 0.996104i | \(0.528106\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3890.00 | 0.289652 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15318.0 | −1.12858 | −0.564292 | − | 0.825575i | \(-0.690851\pi\) | ||||
−0.564292 | + | 0.825575i | \(0.690851\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13164.0 | −0.964792 | −0.482396 | − | 0.875953i | \(-0.660233\pi\) | ||||
−0.482396 | + | 0.875953i | \(0.660233\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11997.0 | 0.874663 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2250.00 | 0.163185 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8959.00 | 0.646392 | 0.323196 | − | 0.946332i | \(-0.395243\pi\) | ||||
0.323196 | + | 0.946332i | \(0.395243\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14640.0 | −1.05081 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8204.00 | 0.585816 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9928.00 | −0.705276 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7290.00 | 0.515221 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16952.0 | 1.19197 | 0.595983 | − | 0.802997i | \(-0.296763\pi\) | ||||
0.595983 | + | 0.802997i | \(0.296763\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11832.0 | −0.827723 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14136.0 | 0.983887 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10071.0 | 0.697414 | 0.348707 | − | 0.937232i | \(-0.386621\pi\) | ||||
0.348707 | + | 0.937232i | \(0.386621\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3185.00 | 0.219449 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8268.00 | 0.566812 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2829.00 | 0.192971 | 0.0964856 | − | 0.995334i | \(-0.469240\pi\) | ||||
0.0964856 | + | 0.995334i | \(0.469240\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7662.00 | −0.520032 | −0.260016 | − | 0.965604i | \(-0.583728\pi\) | ||||
−0.260016 | + | 0.965604i | \(0.583728\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6912.00 | −0.466797 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5210.00 | 0.350110 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −907.000 | −0.0606491 | −0.0303245 | − | 0.999540i | \(-0.509654\pi\) | ||||
−0.0303245 | + | 0.999540i | \(0.509654\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2709.00 | −0.180253 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −40257.0 | −2.66551 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29646.0 | 1.95333 | 0.976664 | − | 0.214771i | \(-0.0689004\pi\) | ||||
0.976664 | + | 0.214771i | \(0.0689004\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1860.00 | −0.121955 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11006.0 | 0.718128 | 0.359064 | − | 0.933313i | \(-0.383096\pi\) | ||||
0.359064 | + | 0.933313i | \(0.383096\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21098.0 | 1.36995 | 0.684976 | − | 0.728566i | \(-0.259813\pi\) | ||||
0.684976 | + | 0.728566i | \(0.259813\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12150.0 | 0.785125 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 280.000 | 0.0180064 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5202.00 | 0.331336 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28574.0 | 1.81132 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21707.0 | −1.36948 | −0.684740 | − | 0.728787i | \(-0.740084\pi\) | ||||
−0.684740 | + | 0.728787i | \(0.740084\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2091.00 | −0.131295 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1580.00 | 0.0987408 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3969.00 | 0.246872 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11952.0 | −0.739928 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11090.0 | 0.683352 | 0.341676 | − | 0.939818i | \(-0.389005\pi\) | ||||
0.341676 | + | 0.939818i | \(0.389005\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −995.000 | −0.0610248 | −0.0305124 | − | 0.999534i | \(-0.509714\pi\) | ||||
−0.0305124 | + | 0.999534i | \(0.509714\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6510.00 | −0.397412 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20792.0 | 1.26340 | 0.631699 | − | 0.775214i | \(-0.282358\pi\) | ||||
0.631699 | + | 0.775214i | \(0.282358\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5644.00 | 0.341366 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2436.00 | 0.146658 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10498.0 | 0.629125 | 0.314562 | − | 0.949237i | \(-0.398142\pi\) | ||||
0.314562 | + | 0.949237i | \(0.398142\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8750.00 | 0.521971 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4140.00 | −0.245840 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6749.00 | −0.398943 | −0.199472 | − | 0.979904i | \(-0.563923\pi\) | ||||
−0.199472 | + | 0.979904i | \(0.563923\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12400.0 | −0.729658 | −0.364829 | − | 0.931074i | \(-0.618873\pi\) | ||||
−0.364829 | + | 0.931074i | \(0.618873\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 22113.0 | 1.29532 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3570.00 | −0.208178 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11610.0 | 0.673975 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2121.00 | −0.122575 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3740.00 | 0.215173 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16024.0 | 0.917801 | 0.458900 | − | 0.888488i | \(-0.348244\pi\) | ||||
0.458900 | + | 0.888488i | \(0.348244\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3375.00 | 0.192450 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18735.0 | −1.06358 | −0.531791 | − | 0.846876i | \(-0.678481\pi\) | ||||
−0.531791 | + | 0.846876i | \(0.678481\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1225.00 | −0.0692359 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1677.00 | 0.0943653 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12844.0 | −0.719564 | −0.359782 | − | 0.933036i | \(-0.617149\pi\) | ||||
−0.359782 | + | 0.933036i | \(0.617149\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −240.000 | −0.0133868 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11508.0 | −0.639094 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 47304.0 | 2.61559 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25996.0 | 1.43116 | 0.715582 | − | 0.698529i | \(-0.246162\pi\) | ||||
0.715582 | + | 0.698529i | \(0.246162\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2142.00 | 0.117414 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 190.000 | 0.0103699 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11284.0 | 0.613217 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4104.00 | 0.222071 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25435.0 | −1.37042 | −0.685212 | − | 0.728344i | \(-0.740290\pi\) | ||||
−0.685212 | + | 0.728344i | \(0.740290\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32028.0 | −1.71829 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7455.00 | −0.398258 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1890.00 | −0.100539 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3823.00 | −0.202505 | −0.101252 | − | 0.994861i | \(-0.532285\pi\) | ||||
−0.101252 | + | 0.994861i | \(0.532285\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6498.00 | 0.342748 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10440.0 | −0.548361 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6885.00 | 0.360118 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11409.0 | −0.594250 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21090.0 | −1.09391 | −0.546957 | − | 0.837161i | \(-0.684214\pi\) | ||||
−0.546957 | + | 0.837161i | \(0.684214\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3955.00 | −0.204288 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16950.0 | −0.871891 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3225.00 | 0.165205 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7992.00 | 0.407712 | 0.203856 | − | 0.979001i | \(-0.434653\pi\) | ||||
0.203856 | + | 0.979001i | \(0.434653\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9477.00 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39494.0 | 1.99827 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36965.0 | 1.86266 | 0.931332 | − | 0.364170i | \(-0.118647\pi\) | ||||
0.931332 | + | 0.364170i | \(0.118647\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 735.000 | 0.0368856 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6528.00 | −0.326271 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3305.00 | −0.164515 | −0.0822574 | − | 0.996611i | \(-0.526213\pi\) | ||||
−0.0822574 | + | 0.996611i | \(0.526213\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24786.0 | −1.22879 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2208.00 | 0.109022 | 0.0545112 | − | 0.998513i | \(-0.482640\pi\) | ||||
0.0545112 | + | 0.998513i | \(0.482640\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17910.0 | −0.880767 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −21096.0 | −1.03328 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8442.00 | −0.411834 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11551.0 | 0.561254 | 0.280627 | − | 0.959817i | \(-0.409458\pi\) | ||||
0.280627 | + | 0.959817i | \(0.409458\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4950.00 | 0.239559 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9635.00 | −0.464442 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9688.00 | −0.465147 | −0.232574 | − | 0.972579i | \(-0.574715\pi\) | ||||
−0.232574 | + | 0.972579i | \(0.574715\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4590.00 | 0.219508 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7014.00 | −0.334109 | −0.167055 | − | 0.985948i | \(-0.553426\pi\) | ||||
−0.167055 | + | 0.985948i | \(0.553426\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9933.00 | 0.471296 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8190.00 | −0.387072 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26892.0 | −1.26599 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6278.00 | −0.294396 | −0.147198 | − | 0.989107i | \(-0.547025\pi\) | ||||
−0.147198 | + | 0.989107i | \(0.547025\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17430.0 | −0.814171 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21351.0 | −0.993457 | −0.496728 | − | 0.867906i | \(-0.665465\pi\) | ||||
−0.496728 | + | 0.867906i | \(0.665465\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2900.00 | −0.134414 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6594.00 | 0.304451 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12648.0 | −0.581722 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11288.0 | −0.517178 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17415.0 | 0.794842 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12550.0 | −0.570610 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25967.0 | −1.17614 | −0.588071 | − | 0.808809i | \(-0.700112\pi\) | ||||
−0.588071 | + | 0.808809i | \(0.700112\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8274.00 | −0.373336 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5446.00 | −0.244801 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17820.0 | −0.797991 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8760.00 | 0.390799 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8595.00 | 0.381996 | 0.190998 | − | 0.981590i | \(-0.438828\pi\) | ||||
0.190998 | + | 0.981590i | \(0.438828\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45227.0 | 2.00252 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −720.000 | −0.0317602 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3910.00 | −0.171832 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3150.00 | −0.137917 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 558.000 | 0.0243402 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13671.0 | −0.594125 | −0.297062 | − | 0.954858i | \(-0.596007\pi\) | ||||
−0.297062 | + | 0.954858i | \(0.596007\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11986.0 | −0.518971 | −0.259485 | − | 0.965747i | \(-0.583553\pi\) | ||||
−0.259485 | + | 0.965747i | \(0.583553\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20484.0 | −0.883647 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9350.00 | 0.401860 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −44268.0 | −1.89564 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10206.0 | −0.435441 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12951.0 | 0.550540 | 0.275270 | − | 0.961367i | \(-0.411233\pi\) | ||||
0.275270 | + | 0.961367i | \(0.411233\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12788.0 | 0.541630 | 0.270815 | − | 0.962631i | \(-0.412707\pi\) | ||||
0.270815 | + | 0.962631i | \(0.412707\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1275.00 | 0.0538058 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24662.0 | 1.03698 | 0.518490 | − | 0.855084i | \(-0.326495\pi\) | ||||
0.518490 | + | 0.855084i | \(0.326495\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4124.00 | −0.172777 | −0.0863887 | − | 0.996262i | \(-0.527533\pi\) | ||||
−0.0863887 | + | 0.996262i | \(0.527533\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24642.0 | −1.02867 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4459.00 | −0.185468 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10095.0 | −0.418385 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15660.0 | −0.646701 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33154.0 | 1.36425 | 0.682123 | − | 0.731237i | \(-0.261057\pi\) | ||||
0.682123 | + | 0.731237i | \(0.261057\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7748.00 | −0.317684 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20121.0 | −0.822069 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21820.0 | −0.888320 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7294.00 | −0.295897 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16491.0 | 0.666631 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28260.0 | −1.13836 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12050.0 | −0.483686 | −0.241843 | − | 0.970315i | \(-0.577752\pi\) | ||||
−0.241843 | + | 0.970315i | \(0.577752\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9180.00 | 0.367192 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15270.0 | 0.608650 | 0.304325 | − | 0.952568i | \(-0.401569\pi\) | ||||
0.304325 | + | 0.952568i | \(0.401569\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12564.0 | −0.499043 | −0.249522 | − | 0.968369i | \(-0.580273\pi\) | ||||
−0.249522 | + | 0.968369i | \(0.580273\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2604.00 | 0.103071 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12976.0 | −0.511829 | −0.255914 | − | 0.966699i | \(-0.582377\pi\) | ||||
−0.255914 | + | 0.966699i | \(0.582377\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6265.00 | 0.246262 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10104.0 | −0.395790 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6137.00 | 0.239567 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31104.0 | 1.21001 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3150.00 | 0.122121 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −875.000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15634.0 | 0.601964 | 0.300982 | − | 0.953630i | \(-0.402686\pi\) | ||||
0.300982 | + | 0.953630i | \(0.402686\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 939.000 | 0.0360315 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8896.00 | −0.340197 | −0.170099 | − | 0.985427i | \(-0.554409\pi\) | ||||
−0.170099 | + | 0.985427i | \(0.554409\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33456.0 | −1.27507 | −0.637533 | − | 0.770423i | \(-0.720045\pi\) | ||||
−0.637533 | + | 0.770423i | \(0.720045\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4980.00 | −0.189154 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8288.00 | −0.313736 | −0.156868 | − | 0.987620i | \(-0.550140\pi\) | ||||
−0.156868 | + | 0.987620i | \(0.550140\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2212.00 | −0.0834512 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1377.00 | −0.0517747 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −50694.0 | −1.89968 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2460.00 | −0.0918757 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21870.0 | −0.814067 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14964.0 | −0.555147 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53144.0 | −1.96502 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9114.00 | 0.335875 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22240.0 | −0.816887 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15398.0 | 0.563707 | 0.281853 | − | 0.959457i | \(-0.409051\pi\) | ||||
0.281853 | + | 0.959457i | \(0.409051\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4860.00 | 0.177333 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22656.0 | −0.823959 | −0.411980 | − | 0.911193i | \(-0.635162\pi\) | ||||
−0.411980 | + | 0.911193i | \(0.635162\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19924.0 | −0.722221 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3300.00 | −0.119229 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12250.0 | −0.441146 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9149.00 | −0.328398 | −0.164199 | − | 0.986427i | \(-0.552504\pi\) | ||||
−0.164199 | + | 0.986427i | \(0.552504\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16437.0 | −0.588076 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 53784.0 | 1.91801 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7850.00 | −0.279034 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10170.0 | 0.360331 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27272.0 | −0.963149 | −0.481574 | − | 0.876405i | \(-0.659935\pi\) | ||||
−0.481574 | + | 0.876405i | \(0.659935\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4998.00 | 0.175943 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13266.0 | 0.465498 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7735.00 | −0.270547 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44177.0 | 1.54023 | 0.770117 | − | 0.637902i | \(-0.220198\pi\) | ||||
0.770117 | + | 0.637902i | \(0.220198\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −825.000 | −0.0286718 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2236.00 | 0.0774618 | 0.0387309 | − | 0.999250i | \(-0.487668\pi\) | ||||
0.0387309 | + | 0.999250i | \(0.487668\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11160.0 | −0.385387 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4725.00 | −0.162650 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17464.0 | −0.599265 | −0.299632 | − | 0.954055i | \(-0.596864\pi\) | ||||
−0.299632 | + | 0.954055i | \(0.596864\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18630.0 | 0.637255 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12318.0 | −0.420019 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18336.0 | −0.623254 | −0.311627 | − | 0.950204i | \(-0.600874\pi\) | ||||
−0.311627 | + | 0.950204i | \(0.600874\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19995.0 | 0.677511 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6579.00 | 0.222225 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 336.000 | 0.0113139 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16335.0 | −0.548320 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21708.0 | 0.726408 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −24400.0 | −0.813952 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46802.0 | 1.55641 | 0.778206 | − | 0.628009i | \(-0.216130\pi\) | ||||
0.778206 | + | 0.628009i | \(0.216130\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 27846.0 | 0.923160 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45024.0 | 1.48804 | 0.744021 | − | 0.668156i | \(-0.232916\pi\) | ||||
0.744021 | + | 0.668156i | \(0.232916\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −266.000 | −0.00876420 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6075.00 | −0.199544 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12786.0 | 0.418690 | 0.209345 | − | 0.977842i | \(-0.432867\pi\) | ||||
0.209345 | + | 0.977842i | \(0.432867\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −680.000 | −0.0221991 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25542.0 | −0.831288 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33539.0 | −1.08823 | −0.544114 | − | 0.839011i | \(-0.683134\pi\) | ||||
−0.544114 | + | 0.839011i | \(0.683134\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23560.0 | 0.762116 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10437.0 | 0.336589 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −39060.0 | −1.25585 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18200.0 | 0.583393 | 0.291696 | − | 0.956511i | \(-0.405780\pi\) | ||||
0.291696 | + | 0.956511i | \(0.405780\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24780.0 | −0.791913 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13780.0 | 0.439051 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32599.0 | 1.03553 | 0.517764 | − | 0.855524i | \(-0.326765\pi\) | ||||
0.517764 | + | 0.855524i | \(0.326765\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −42390.0 | −1.34250 |
(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 | 2240.4.a.p.1.1 | 1 | ||
4.3 | odd | 2 | 2240.4.a.w.1.1 | 1 | |||
8.3 | odd | 2 | 70.4.a.b.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 560.4.a.k.1.1 | 1 | |||
24.11 | even | 2 | 630.4.a.m.1.1 | 1 | |||
40.3 | even | 4 | 350.4.c.j.99.2 | 2 | |||
40.19 | odd | 2 | 350.4.a.t.1.1 | 1 | |||
40.27 | even | 4 | 350.4.c.j.99.1 | 2 | |||
56.3 | even | 6 | 490.4.e.l.471.1 | 2 | |||
56.11 | odd | 6 | 490.4.e.p.471.1 | 2 | |||
56.19 | even | 6 | 490.4.e.l.361.1 | 2 | |||
56.27 | even | 2 | 490.4.a.f.1.1 | 1 | |||
56.51 | odd | 6 | 490.4.e.p.361.1 | 2 | |||
280.139 | even | 2 | 2450.4.a.ba.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.4.a.b.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
350.4.a.t.1.1 | 1 | 40.19 | odd | 2 | |||
350.4.c.j.99.1 | 2 | 40.27 | even | 4 | |||
350.4.c.j.99.2 | 2 | 40.3 | even | 4 | |||
490.4.a.f.1.1 | 1 | 56.27 | even | 2 | |||
490.4.e.l.361.1 | 2 | 56.19 | even | 6 | |||
490.4.e.l.471.1 | 2 | 56.3 | even | 6 | |||
490.4.e.p.361.1 | 2 | 56.51 | odd | 6 | |||
490.4.e.p.471.1 | 2 | 56.11 | odd | 6 | |||
560.4.a.k.1.1 | 1 | 8.5 | even | 2 | |||
630.4.a.m.1.1 | 1 | 24.11 | even | 2 | |||
2240.4.a.p.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2240.4.a.w.1.1 | 1 | 4.3 | odd | 2 | |||
2450.4.a.ba.1.1 | 1 | 280.139 | even | 2 |