Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,2,Mod(1,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2205.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.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: | \(17.6070136457\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2205.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.732051 | −0.517638 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.46410 | −0.732051 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.53590 | 0.896575 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.732051 | 0.231495 | ||||||||
\(11\) | 2.73205 | 0.823744 | 0.411872 | − | 0.911242i | \(-0.364875\pi\) | ||||
0.411872 | + | 0.911242i | \(0.364875\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.73205 | 1.58978 | 0.794892 | − | 0.606750i | \(-0.207527\pi\) | ||||
0.794892 | + | 0.606750i | \(0.207527\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.07180 | 0.267949 | ||||||||
\(17\) | −6.73205 | −1.63276 | −0.816381 | − | 0.577514i | \(-0.804023\pi\) | ||||
−0.816381 | + | 0.577514i | \(0.804023\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.46410 | −0.565304 | −0.282652 | − | 0.959223i | \(-0.591214\pi\) | ||||
−0.282652 | + | 0.959223i | \(0.591214\pi\) | |||||||
\(20\) | 1.46410 | 0.327383 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | 1.26795 | 0.264386 | 0.132193 | − | 0.991224i | \(-0.457798\pi\) | ||||
0.132193 | + | 0.991224i | \(0.457798\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.19615 | −0.822933 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.19615 | −1.15060 | −0.575298 | − | 0.817944i | \(-0.695114\pi\) | ||||
−0.575298 | + | 0.817944i | \(0.695114\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.46410 | 1.16099 | 0.580493 | − | 0.814265i | \(-0.302860\pi\) | ||||
0.580493 | + | 0.814265i | \(0.302860\pi\) | |||||||
\(32\) | −5.85641 | −1.03528 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.92820 | 0.845180 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.19615 | 1.18304 | 0.591520 | − | 0.806290i | \(-0.298528\pi\) | ||||
0.591520 | + | 0.806290i | \(0.298528\pi\) | |||||||
\(38\) | 1.80385 | 0.292623 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.53590 | −0.400961 | ||||||||
\(41\) | −2.73205 | −0.426675 | −0.213337 | − | 0.976979i | \(-0.568433\pi\) | ||||
−0.213337 | + | 0.976979i | \(0.568433\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.19615 | −1.09740 | −0.548701 | − | 0.836018i | \(-0.684878\pi\) | ||||
−0.548701 | + | 0.836018i | \(0.684878\pi\) | |||||||
\(44\) | −4.00000 | −0.603023 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.928203 | −0.136856 | ||||||||
\(47\) | −2.00000 | −0.291730 | −0.145865 | − | 0.989305i | \(-0.546597\pi\) | ||||
−0.145865 | + | 0.989305i | \(0.546597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.732051 | −0.103528 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.39230 | −1.16380 | ||||||||
\(53\) | 8.39230 | 1.15277 | 0.576386 | − | 0.817178i | \(-0.304463\pi\) | ||||
0.576386 | + | 0.817178i | \(0.304463\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.73205 | −0.368390 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.53590 | 0.595593 | ||||||||
\(59\) | −10.1962 | −1.32743 | −0.663713 | − | 0.747987i | \(-0.731020\pi\) | ||||
−0.663713 | + | 0.747987i | \(0.731020\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | 0.512148 | 0.256074 | − | 0.966657i | \(-0.417571\pi\) | ||||
0.256074 | + | 0.966657i | \(0.417571\pi\) | |||||||
\(62\) | −4.73205 | −0.600971 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.14359 | 0.267949 | ||||||||
\(65\) | −5.73205 | −0.710973 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.66025 | 0.325002 | 0.162501 | − | 0.986708i | \(-0.448044\pi\) | ||||
0.162501 | + | 0.986708i | \(0.448044\pi\) | |||||||
\(68\) | 9.85641 | 1.19526 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.19615 | 0.497992 | 0.248996 | − | 0.968505i | \(-0.419899\pi\) | ||||
0.248996 | + | 0.968505i | \(0.419899\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.66025 | −0.545441 | −0.272721 | − | 0.962093i | \(-0.587924\pi\) | ||||
−0.272721 | + | 0.962093i | \(0.587924\pi\) | |||||||
\(74\) | −5.26795 | −0.612387 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.60770 | 0.413831 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.3923 | 1.50675 | 0.753376 | − | 0.657590i | \(-0.228424\pi\) | ||||
0.753376 | + | 0.657590i | \(0.228424\pi\) | |||||||
\(80\) | −1.07180 | −0.119831 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.00000 | 0.220863 | ||||||||
\(83\) | 9.12436 | 1.00153 | 0.500764 | − | 0.865584i | \(-0.333052\pi\) | ||||
0.500764 | + | 0.865584i | \(0.333052\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.73205 | 0.730193 | ||||||||
\(86\) | 5.26795 | 0.568058 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.92820 | 0.738549 | ||||||||
\(89\) | 9.12436 | 0.967180 | 0.483590 | − | 0.875295i | \(-0.339333\pi\) | ||||
0.483590 | + | 0.875295i | \(0.339333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.85641 | −0.193544 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.46410 | 0.151011 | ||||||||
\(95\) | 2.46410 | 0.252811 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.07180 | 0.108824 | 0.0544122 | − | 0.998519i | \(-0.482671\pi\) | ||||
0.0544122 | + | 0.998519i | \(0.482671\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.46410 | −0.146410 | ||||||||
\(101\) | 10.7321 | 1.06788 | 0.533939 | − | 0.845523i | \(-0.320711\pi\) | ||||
0.533939 | + | 0.845523i | \(0.320711\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.19615 | 0.117860 | 0.0589302 | − | 0.998262i | \(-0.481231\pi\) | ||||
0.0589302 | + | 0.998262i | \(0.481231\pi\) | |||||||
\(104\) | 14.5359 | 1.42536 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.14359 | −0.596719 | ||||||||
\(107\) | 8.19615 | 0.792352 | 0.396176 | − | 0.918175i | \(-0.370337\pi\) | ||||
0.396176 | + | 0.918175i | \(0.370337\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0000 | 1.05361 | 0.526804 | − | 0.849987i | \(-0.323390\pi\) | ||||
0.526804 | + | 0.849987i | \(0.323390\pi\) | |||||||
\(110\) | 2.00000 | 0.190693 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.92820 | 0.463606 | 0.231803 | − | 0.972763i | \(-0.425537\pi\) | ||||
0.231803 | + | 0.972763i | \(0.425537\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.26795 | −0.118237 | ||||||||
\(116\) | 9.07180 | 0.842295 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.46410 | 0.687126 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.53590 | −0.321445 | ||||||||
\(122\) | −2.92820 | −0.265107 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.46410 | −0.849901 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.1962 | 1.34844 | 0.674220 | − | 0.738530i | \(-0.264480\pi\) | ||||
0.674220 | + | 0.738530i | \(0.264480\pi\) | |||||||
\(128\) | 10.1436 | 0.896575 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.19615 | 0.368027 | ||||||||
\(131\) | −8.53590 | −0.745785 | −0.372892 | − | 0.927875i | \(-0.621634\pi\) | ||||
−0.372892 | + | 0.927875i | \(0.621634\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.94744 | −0.168233 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −17.0718 | −1.46389 | ||||||||
\(137\) | 8.19615 | 0.700245 | 0.350122 | − | 0.936704i | \(-0.386140\pi\) | ||||
0.350122 | + | 0.936704i | \(0.386140\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.92820 | −0.672461 | −0.336231 | − | 0.941780i | \(-0.609152\pi\) | ||||
−0.336231 | + | 0.941780i | \(0.609152\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.07180 | −0.257779 | ||||||||
\(143\) | 15.6603 | 1.30958 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.19615 | 0.514562 | ||||||||
\(146\) | 3.41154 | 0.282341 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.5359 | −0.866046 | ||||||||
\(149\) | 21.8564 | 1.79055 | 0.895273 | − | 0.445517i | \(-0.146980\pi\) | ||||
0.895273 | + | 0.445517i | \(0.146980\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.92820 | 0.401051 | 0.200526 | − | 0.979688i | \(-0.435735\pi\) | ||||
0.200526 | + | 0.979688i | \(0.435735\pi\) | |||||||
\(152\) | −6.24871 | −0.506837 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.46410 | −0.519209 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.3923 | −1.14863 | −0.574315 | − | 0.818634i | \(-0.694732\pi\) | ||||
−0.574315 | + | 0.818634i | \(0.694732\pi\) | |||||||
\(158\) | −9.80385 | −0.779952 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.85641 | 0.462990 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.85641 | −0.458709 | −0.229355 | − | 0.973343i | \(-0.573662\pi\) | ||||
−0.229355 | + | 0.973343i | \(0.573662\pi\) | |||||||
\(164\) | 4.00000 | 0.312348 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.67949 | −0.518429 | ||||||||
\(167\) | 0.339746 | 0.0262903 | 0.0131452 | − | 0.999914i | \(-0.495816\pi\) | ||||
0.0131452 | + | 0.999914i | \(0.495816\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.8564 | 1.52742 | ||||||||
\(170\) | −4.92820 | −0.377976 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.5359 | 0.803355 | ||||||||
\(173\) | −21.4641 | −1.63189 | −0.815943 | − | 0.578133i | \(-0.803782\pi\) | ||||
−0.815943 | + | 0.578133i | \(0.803782\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.92820 | 0.220722 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.67949 | −0.500649 | ||||||||
\(179\) | 10.0000 | 0.747435 | 0.373718 | − | 0.927543i | \(-0.378083\pi\) | ||||
0.373718 | + | 0.927543i | \(0.378083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3205 | 0.767117 | 0.383559 | − | 0.923517i | \(-0.374698\pi\) | ||||
0.383559 | + | 0.923517i | \(0.374698\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.21539 | 0.237042 | ||||||||
\(185\) | −7.19615 | −0.529072 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.3923 | −1.34498 | ||||||||
\(188\) | 2.92820 | 0.213561 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.80385 | −0.130865 | ||||||||
\(191\) | −4.92820 | −0.356592 | −0.178296 | − | 0.983977i | \(-0.557059\pi\) | ||||
−0.178296 | + | 0.983977i | \(0.557059\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.19615 | −0.661954 | −0.330977 | − | 0.943639i | \(-0.607378\pi\) | ||||
−0.330977 | + | 0.943639i | \(0.607378\pi\) | |||||||
\(194\) | −0.784610 | −0.0563317 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.6603 | 1.25824 | 0.629121 | − | 0.777308i | \(-0.283415\pi\) | ||||
0.629121 | + | 0.777308i | \(0.283415\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.0000 | 1.55954 | 0.779769 | − | 0.626067i | \(-0.215336\pi\) | ||||
0.779769 | + | 0.626067i | \(0.215336\pi\) | |||||||
\(200\) | 2.53590 | 0.179315 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.85641 | −0.552775 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.73205 | 0.190815 | ||||||||
\(206\) | −0.875644 | −0.0610090 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.14359 | 0.425982 | ||||||||
\(209\) | −6.73205 | −0.465666 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.9282 | 1.44076 | 0.720378 | − | 0.693581i | \(-0.243968\pi\) | ||||
0.720378 | + | 0.693581i | \(0.243968\pi\) | |||||||
\(212\) | −12.2872 | −0.843887 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.00000 | −0.410152 | ||||||||
\(215\) | 7.19615 | 0.490774 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −8.05256 | −0.545388 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.00000 | 0.269680 | ||||||||
\(221\) | −38.5885 | −2.59574 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.392305 | 0.0262707 | 0.0131353 | − | 0.999914i | \(-0.495819\pi\) | ||||
0.0131353 | + | 0.999914i | \(0.495819\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.60770 | −0.239980 | ||||||||
\(227\) | −15.6603 | −1.03941 | −0.519704 | − | 0.854347i | \(-0.673958\pi\) | ||||
−0.519704 | + | 0.854347i | \(0.673958\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.00000 | −0.198246 | −0.0991228 | − | 0.995075i | \(-0.531604\pi\) | ||||
−0.0991228 | + | 0.995075i | \(0.531604\pi\) | |||||||
\(230\) | 0.928203 | 0.0612039 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15.7128 | −1.03160 | ||||||||
\(233\) | 17.3205 | 1.13470 | 0.567352 | − | 0.823475i | \(-0.307968\pi\) | ||||
0.567352 | + | 0.823475i | \(0.307968\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.00000 | 0.130466 | ||||||||
\(236\) | 14.9282 | 0.971743 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.9282 | −1.35373 | −0.676866 | − | 0.736106i | \(-0.736663\pi\) | ||||
−0.676866 | + | 0.736106i | \(0.736663\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.53590 | 0.421014 | 0.210507 | − | 0.977592i | \(-0.432488\pi\) | ||||
0.210507 | + | 0.977592i | \(0.432488\pi\) | |||||||
\(242\) | 2.58846 | 0.166392 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.85641 | −0.374918 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.1244 | −0.898711 | ||||||||
\(248\) | 16.3923 | 1.04091 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.732051 | 0.0462990 | ||||||||
\(251\) | −6.58846 | −0.415860 | −0.207930 | − | 0.978144i | \(-0.566673\pi\) | ||||
−0.207930 | + | 0.978144i | \(0.566673\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.46410 | 0.217786 | ||||||||
\(254\) | −11.1244 | −0.698004 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.7128 | −0.732051 | ||||||||
\(257\) | −11.6603 | −0.727347 | −0.363673 | − | 0.931527i | \(-0.618478\pi\) | ||||
−0.363673 | + | 0.931527i | \(0.618478\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 8.39230 | 0.520469 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.24871 | 0.386047 | ||||||||
\(263\) | 12.3923 | 0.764142 | 0.382071 | − | 0.924133i | \(-0.375211\pi\) | ||||
0.382071 | + | 0.924133i | \(0.375211\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.39230 | −0.515535 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.89488 | −0.237918 | ||||||||
\(269\) | 19.4641 | 1.18675 | 0.593374 | − | 0.804927i | \(-0.297796\pi\) | ||||
0.593374 | + | 0.804927i | \(0.297796\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.9282 | 1.02832 | 0.514158 | − | 0.857696i | \(-0.328105\pi\) | ||||
0.514158 | + | 0.857696i | \(0.328105\pi\) | |||||||
\(272\) | −7.21539 | −0.437497 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | 2.73205 | 0.164749 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.66025 | 0.159839 | 0.0799196 | − | 0.996801i | \(-0.474534\pi\) | ||||
0.0799196 | + | 0.996801i | \(0.474534\pi\) | |||||||
\(278\) | 5.80385 | 0.348092 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.8564 | 0.826604 | 0.413302 | − | 0.910594i | \(-0.364375\pi\) | ||||
0.413302 | + | 0.910594i | \(0.364375\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.124356 | 0.00739218 | 0.00369609 | − | 0.999993i | \(-0.498823\pi\) | ||||
0.00369609 | + | 0.999993i | \(0.498823\pi\) | |||||||
\(284\) | −6.14359 | −0.364555 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.4641 | −0.677887 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.3205 | 1.66591 | ||||||||
\(290\) | −4.53590 | −0.266357 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.82309 | 0.399291 | ||||||||
\(293\) | −5.07180 | −0.296298 | −0.148149 | − | 0.988965i | \(-0.547331\pi\) | ||||
−0.148149 | + | 0.988965i | \(0.547331\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.1962 | 0.593643 | ||||||||
\(296\) | 18.2487 | 1.06068 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.0000 | −0.926855 | ||||||||
\(299\) | 7.26795 | 0.420316 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.60770 | −0.207600 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.64102 | −0.151473 | ||||||||
\(305\) | −4.00000 | −0.229039 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.87564 | −0.449487 | −0.224743 | − | 0.974418i | \(-0.572154\pi\) | ||||
−0.224743 | + | 0.974418i | \(0.572154\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.73205 | 0.268762 | ||||||||
\(311\) | 15.1244 | 0.857624 | 0.428812 | − | 0.903394i | \(-0.358932\pi\) | ||||
0.428812 | + | 0.903394i | \(0.358932\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.66025 | 0.263413 | 0.131707 | − | 0.991289i | \(-0.457954\pi\) | ||||
0.131707 | + | 0.991289i | \(0.457954\pi\) | |||||||
\(314\) | 10.5359 | 0.594575 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.6077 | −1.10302 | ||||||||
\(317\) | −30.4449 | −1.70995 | −0.854977 | − | 0.518666i | \(-0.826429\pi\) | ||||
−0.854977 | + | 0.518666i | \(0.826429\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.9282 | −0.947797 | ||||||||
\(320\) | −2.14359 | −0.119831 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.5885 | 0.923006 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.73205 | 0.317957 | ||||||||
\(326\) | 4.28719 | 0.237445 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.92820 | −0.382546 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.9282 | 1.20528 | 0.602642 | − | 0.798012i | \(-0.294115\pi\) | ||||
0.602642 | + | 0.798012i | \(0.294115\pi\) | |||||||
\(332\) | −13.3590 | −0.733169 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.248711 | −0.0136089 | ||||||||
\(335\) | −2.66025 | −0.145345 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.9808 | −1.85105 | −0.925525 | − | 0.378686i | \(-0.876376\pi\) | ||||
−0.925525 | + | 0.378686i | \(0.876376\pi\) | |||||||
\(338\) | −14.5359 | −0.790649 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.85641 | −0.534539 | ||||||||
\(341\) | 17.6603 | 0.956356 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −18.2487 | −0.983905 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.7128 | 0.844726 | ||||||||
\(347\) | 34.9282 | 1.87504 | 0.937522 | − | 0.347926i | \(-0.113114\pi\) | ||||
0.937522 | + | 0.347926i | \(0.113114\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.0000 | 1.17763 | 0.588817 | − | 0.808267i | \(-0.299594\pi\) | ||||
0.588817 | + | 0.808267i | \(0.299594\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −16.0000 | −0.852803 | ||||||||
\(353\) | −21.1244 | −1.12434 | −0.562168 | − | 0.827023i | \(-0.690033\pi\) | ||||
−0.562168 | + | 0.827023i | \(0.690033\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.19615 | −0.222709 | ||||||||
\(356\) | −13.3590 | −0.708025 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.32051 | −0.386901 | ||||||||
\(359\) | 4.73205 | 0.249748 | 0.124874 | − | 0.992173i | \(-0.460147\pi\) | ||||
0.124874 | + | 0.992173i | \(0.460147\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.9282 | −0.680432 | ||||||||
\(362\) | −7.55514 | −0.397089 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.66025 | 0.243929 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.803848 | 0.0419605 | 0.0209803 | − | 0.999780i | \(-0.493321\pi\) | ||||
0.0209803 | + | 0.999780i | \(0.493321\pi\) | |||||||
\(368\) | 1.35898 | 0.0708419 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.26795 | 0.273868 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.5167 | −0.958756 | −0.479378 | − | 0.877608i | \(-0.659138\pi\) | ||||
−0.479378 | + | 0.877608i | \(0.659138\pi\) | |||||||
\(374\) | 13.4641 | 0.696212 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.07180 | −0.261558 | ||||||||
\(377\) | −35.5167 | −1.82920 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.3205 | −1.45473 | −0.727363 | − | 0.686253i | \(-0.759255\pi\) | ||||
−0.727363 | + | 0.686253i | \(0.759255\pi\) | |||||||
\(380\) | −3.60770 | −0.185071 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.60770 | 0.184586 | ||||||||
\(383\) | −11.3205 | −0.578451 | −0.289225 | − | 0.957261i | \(-0.593398\pi\) | ||||
−0.289225 | + | 0.957261i | \(0.593398\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.73205 | 0.342652 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.56922 | −0.0796650 | ||||||||
\(389\) | −36.5885 | −1.85511 | −0.927554 | − | 0.373689i | \(-0.878093\pi\) | ||||
−0.927554 | + | 0.373689i | \(0.878093\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.53590 | −0.431679 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.9282 | −0.651313 | ||||||||
\(395\) | −13.3923 | −0.673840 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.8038 | −1.04412 | −0.522058 | − | 0.852910i | \(-0.674835\pi\) | ||||
−0.522058 | + | 0.852910i | \(0.674835\pi\) | |||||||
\(398\) | −16.1051 | −0.807277 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.07180 | 0.0535898 | ||||||||
\(401\) | −4.39230 | −0.219341 | −0.109671 | − | 0.993968i | \(-0.534980\pi\) | ||||
−0.109671 | + | 0.993968i | \(0.534980\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 37.0526 | 1.84572 | ||||||||
\(404\) | −15.7128 | −0.781742 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.6603 | 0.974523 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.8564 | 1.52575 | 0.762876 | − | 0.646545i | \(-0.223787\pi\) | ||||
0.762876 | + | 0.646545i | \(0.223787\pi\) | |||||||
\(410\) | −2.00000 | −0.0987730 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.75129 | −0.0862798 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.12436 | −0.447897 | ||||||||
\(416\) | −33.5692 | −1.64587 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.92820 | 0.241046 | ||||||||
\(419\) | 28.5359 | 1.39407 | 0.697035 | − | 0.717037i | \(-0.254502\pi\) | ||||
0.697035 | + | 0.717037i | \(0.254502\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.9282 | 0.678819 | 0.339410 | − | 0.940639i | \(-0.389773\pi\) | ||||
0.339410 | + | 0.940639i | \(0.389773\pi\) | |||||||
\(422\) | −15.3205 | −0.745791 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 21.2820 | 1.03355 | ||||||||
\(425\) | −6.73205 | −0.326552 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.26795 | −0.254043 | ||||||||
\(431\) | 17.3205 | 0.834300 | 0.417150 | − | 0.908838i | \(-0.363029\pi\) | ||||
0.417150 | + | 0.908838i | \(0.363029\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.80385 | 0.230858 | 0.115429 | − | 0.993316i | \(-0.463176\pi\) | ||||
0.115429 | + | 0.993316i | \(0.463176\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.1051 | −0.771295 | ||||||||
\(437\) | −3.12436 | −0.149458 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.46410 | 0.356242 | 0.178121 | − | 0.984009i | \(-0.442998\pi\) | ||||
0.178121 | + | 0.984009i | \(0.442998\pi\) | |||||||
\(440\) | −6.92820 | −0.330289 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 28.2487 | 1.34365 | ||||||||
\(443\) | −2.53590 | −0.120484 | −0.0602421 | − | 0.998184i | \(-0.519187\pi\) | ||||
−0.0602421 | + | 0.998184i | \(0.519187\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.12436 | −0.432536 | ||||||||
\(446\) | −0.287187 | −0.0135987 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.14359 | 0.384320 | 0.192160 | − | 0.981364i | \(-0.438451\pi\) | ||||
0.192160 | + | 0.981364i | \(0.438451\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.46410 | −0.351471 | ||||||||
\(452\) | −7.21539 | −0.339383 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.4641 | 0.538037 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.660254 | 0.0308854 | 0.0154427 | − | 0.999881i | \(-0.495084\pi\) | ||||
0.0154427 | + | 0.999881i | \(0.495084\pi\) | |||||||
\(458\) | 2.19615 | 0.102619 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.85641 | 0.0865554 | ||||||||
\(461\) | 34.9808 | 1.62922 | 0.814608 | − | 0.580012i | \(-0.196952\pi\) | ||||
0.814608 | + | 0.580012i | \(0.196952\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.2679 | 1.03488 | 0.517440 | − | 0.855720i | \(-0.326885\pi\) | ||||
0.517440 | + | 0.855720i | \(0.326885\pi\) | |||||||
\(464\) | −6.64102 | −0.308301 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.6795 | −0.587366 | ||||||||
\(467\) | 27.8564 | 1.28904 | 0.644520 | − | 0.764587i | \(-0.277057\pi\) | ||||
0.644520 | + | 0.764587i | \(0.277057\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.46410 | −0.0675340 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −25.8564 | −1.19014 | ||||||||
\(473\) | −19.6603 | −0.903979 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.46410 | −0.113061 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.3205 | 0.700744 | ||||||||
\(479\) | 32.7846 | 1.49797 | 0.748984 | − | 0.662589i | \(-0.230542\pi\) | ||||
0.748984 | + | 0.662589i | \(0.230542\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 41.2487 | 1.88078 | ||||||||
\(482\) | −4.78461 | −0.217933 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.17691 | 0.235314 | ||||||||
\(485\) | −1.07180 | −0.0486678 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.5885 | −1.43141 | −0.715705 | − | 0.698403i | \(-0.753894\pi\) | ||||
−0.715705 | + | 0.698403i | \(0.753894\pi\) | |||||||
\(488\) | 10.1436 | 0.459179 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.2487 | −0.462518 | −0.231259 | − | 0.972892i | \(-0.574284\pi\) | ||||
−0.231259 | + | 0.972892i | \(0.574284\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 41.7128 | 1.87865 | ||||||||
\(494\) | 10.3397 | 0.465207 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.92820 | 0.311086 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.4641 | −0.916099 | −0.458050 | − | 0.888927i | \(-0.651452\pi\) | ||||
−0.458050 | + | 0.888927i | \(0.651452\pi\) | |||||||
\(500\) | 1.46410 | 0.0654766 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.82309 | 0.215265 | ||||||||
\(503\) | 6.39230 | 0.285019 | 0.142509 | − | 0.989793i | \(-0.454483\pi\) | ||||
0.142509 | + | 0.989793i | \(0.454483\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.7321 | −0.477570 | ||||||||
\(506\) | −2.53590 | −0.112734 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −22.2487 | −0.987127 | ||||||||
\(509\) | −11.4641 | −0.508137 | −0.254069 | − | 0.967186i | \(-0.581769\pi\) | ||||
−0.254069 | + | 0.967186i | \(0.581769\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11.7128 | −0.517638 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.53590 | 0.376502 | ||||||||
\(515\) | −1.19615 | −0.0527088 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.46410 | −0.240311 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −14.5359 | −0.637441 | ||||||||
\(521\) | −1.46410 | −0.0641435 | −0.0320717 | − | 0.999486i | \(-0.510210\pi\) | ||||
−0.0320717 | + | 0.999486i | \(0.510210\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.2679 | −1.06116 | −0.530582 | − | 0.847634i | \(-0.678026\pi\) | ||||
−0.530582 | + | 0.847634i | \(0.678026\pi\) | |||||||
\(524\) | 12.4974 | 0.545952 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.07180 | −0.395549 | ||||||||
\(527\) | −43.5167 | −1.89562 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.3923 | −0.930100 | ||||||||
\(530\) | 6.14359 | 0.266861 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.6603 | −0.678321 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.19615 | −0.354351 | ||||||||
\(536\) | 6.74613 | 0.291389 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14.2487 | −0.614306 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.7846 | −1.53850 | −0.769250 | − | 0.638948i | \(-0.779370\pi\) | ||||
−0.769250 | + | 0.638948i | \(0.779370\pi\) | |||||||
\(542\) | −12.3923 | −0.532295 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 39.4256 | 1.69036 | ||||||||
\(545\) | −11.0000 | −0.471188 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.2487 | 0.951286 | 0.475643 | − | 0.879638i | \(-0.342215\pi\) | ||||
0.475643 | + | 0.879638i | \(0.342215\pi\) | |||||||
\(548\) | −12.0000 | −0.512615 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.00000 | −0.0852803 | ||||||||
\(551\) | 15.2679 | 0.650437 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.94744 | −0.0827388 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.6077 | 0.492276 | ||||||||
\(557\) | 26.7846 | 1.13490 | 0.567450 | − | 0.823408i | \(-0.307930\pi\) | ||||
0.567450 | + | 0.823408i | \(0.307930\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.2487 | −1.74463 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.1436 | −0.427882 | ||||||||
\(563\) | 18.0000 | 0.758610 | 0.379305 | − | 0.925272i | \(-0.376163\pi\) | ||||
0.379305 | + | 0.925272i | \(0.376163\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.92820 | −0.207331 | ||||||||
\(566\) | −0.0910347 | −0.00382647 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.6410 | 0.446487 | ||||||||
\(569\) | 26.4449 | 1.10863 | 0.554313 | − | 0.832308i | \(-0.312981\pi\) | ||||
0.554313 | + | 0.832308i | \(0.312981\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.3923 | 1.64852 | 0.824258 | − | 0.566214i | \(-0.191592\pi\) | ||||
0.824258 | + | 0.566214i | \(0.191592\pi\) | |||||||
\(572\) | −22.9282 | −0.958676 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.26795 | 0.0528771 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.3397 | 0.472080 | 0.236040 | − | 0.971743i | \(-0.424150\pi\) | ||||
0.236040 | + | 0.971743i | \(0.424150\pi\) | |||||||
\(578\) | −20.7321 | −0.862340 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.07180 | −0.376686 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.9282 | 0.949589 | ||||||||
\(584\) | −11.8179 | −0.489029 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.71281 | 0.153375 | ||||||||
\(587\) | −37.2679 | −1.53821 | −0.769106 | − | 0.639121i | \(-0.779298\pi\) | ||||
−0.769106 | + | 0.639121i | \(0.779298\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.9282 | −0.656310 | ||||||||
\(590\) | −7.46410 | −0.307292 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.71281 | 0.316995 | ||||||||
\(593\) | 37.9090 | 1.55673 | 0.778367 | − | 0.627809i | \(-0.216048\pi\) | ||||
0.778367 | + | 0.627809i | \(0.216048\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −32.0000 | −1.31077 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.32051 | −0.217572 | ||||||||
\(599\) | −10.2487 | −0.418751 | −0.209375 | − | 0.977835i | \(-0.567143\pi\) | ||||
−0.209375 | + | 0.977835i | \(0.567143\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.9282 | −0.568143 | −0.284072 | − | 0.958803i | \(-0.591685\pi\) | ||||
−0.284072 | + | 0.958803i | \(0.591685\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.21539 | −0.293590 | ||||||||
\(605\) | 3.53590 | 0.143755 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.19615 | −0.292083 | −0.146041 | − | 0.989278i | \(-0.546653\pi\) | ||||
−0.146041 | + | 0.989278i | \(0.546653\pi\) | |||||||
\(608\) | 14.4308 | 0.585245 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.92820 | 0.118559 | ||||||||
\(611\) | −11.4641 | −0.463788 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.0718 | −0.527965 | −0.263982 | − | 0.964527i | \(-0.585036\pi\) | ||||
−0.263982 | + | 0.964527i | \(0.585036\pi\) | |||||||
\(614\) | 5.76537 | 0.232671 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.2487 | −0.493115 | −0.246557 | − | 0.969128i | \(-0.579299\pi\) | ||||
−0.246557 | + | 0.969128i | \(0.579299\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −43.9282 | −1.76562 | −0.882812 | − | 0.469727i | \(-0.844352\pi\) | ||||
−0.882812 | + | 0.469727i | \(0.844352\pi\) | |||||||
\(620\) | 9.46410 | 0.380087 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.0718 | −0.443939 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −3.41154 | −0.136353 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21.0718 | 0.840856 | ||||||||
\(629\) | −48.4449 | −1.93162 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.21539 | 0.287240 | 0.143620 | − | 0.989633i | \(-0.454126\pi\) | ||||
0.143620 | + | 0.989633i | \(0.454126\pi\) | |||||||
\(632\) | 33.9615 | 1.35092 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 22.2872 | 0.885137 | ||||||||
\(635\) | −15.1962 | −0.603041 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12.3923 | 0.490616 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.1436 | −0.400961 | ||||||||
\(641\) | −14.1962 | −0.560714 | −0.280357 | − | 0.959896i | \(-0.590453\pi\) | ||||
−0.280357 | + | 0.959896i | \(0.590453\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.5167 | −1.59782 | −0.798911 | − | 0.601450i | \(-0.794590\pi\) | ||||
−0.798911 | + | 0.601450i | \(0.794590\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.1436 | −0.477783 | ||||||||
\(647\) | −37.9090 | −1.49036 | −0.745178 | − | 0.666866i | \(-0.767635\pi\) | ||||
−0.745178 | + | 0.666866i | \(0.767635\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.8564 | −1.09346 | ||||||||
\(650\) | −4.19615 | −0.164587 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.57437 | 0.335798 | ||||||||
\(653\) | 13.4115 | 0.524834 | 0.262417 | − | 0.964955i | \(-0.415480\pi\) | ||||
0.262417 | + | 0.964955i | \(0.415480\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.53590 | 0.333525 | ||||||||
\(656\) | −2.92820 | −0.114327 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.9282 | 0.425702 | 0.212851 | − | 0.977085i | \(-0.431725\pi\) | ||||
0.212851 | + | 0.977085i | \(0.431725\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.53590 | 0.137531 | 0.0687653 | − | 0.997633i | \(-0.478094\pi\) | ||||
0.0687653 | + | 0.997633i | \(0.478094\pi\) | |||||||
\(662\) | −16.0526 | −0.623900 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 23.1384 | 0.897946 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.85641 | −0.304201 | ||||||||
\(668\) | −0.497423 | −0.0192459 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.94744 | 0.0752362 | ||||||||
\(671\) | 10.9282 | 0.421879 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.6603 | −1.72153 | −0.860763 | − | 0.509006i | \(-0.830013\pi\) | ||||
−0.860763 | + | 0.509006i | \(0.830013\pi\) | |||||||
\(674\) | 24.8756 | 0.958174 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −29.0718 | −1.11815 | ||||||||
\(677\) | 8.87564 | 0.341119 | 0.170559 | − | 0.985347i | \(-0.445443\pi\) | ||||
0.170559 | + | 0.985347i | \(0.445443\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 17.0718 | 0.654674 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.9282 | −0.495046 | ||||||||
\(683\) | −10.0526 | −0.384650 | −0.192325 | − | 0.981331i | \(-0.561603\pi\) | ||||
−0.192325 | + | 0.981331i | \(0.561603\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.19615 | −0.313159 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.71281 | −0.294048 | ||||||||
\(689\) | 48.1051 | 1.83266 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.8564 | −0.717332 | −0.358666 | − | 0.933466i | \(-0.616768\pi\) | ||||
−0.358666 | + | 0.933466i | \(0.616768\pi\) | |||||||
\(692\) | 31.4256 | 1.19462 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25.5692 | −0.970594 | ||||||||
\(695\) | 7.92820 | 0.300734 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.3923 | 0.696658 | ||||||||
\(698\) | −16.1051 | −0.609588 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.5885 | −0.853154 | −0.426577 | − | 0.904451i | \(-0.640281\pi\) | ||||
−0.426577 | + | 0.904451i | \(0.640281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.7321 | −0.668777 | ||||||||
\(704\) | 5.85641 | 0.220722 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.4641 | 0.581999 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.9282 | −0.560640 | −0.280320 | − | 0.959907i | \(-0.590441\pi\) | ||||
−0.280320 | + | 0.959907i | \(0.590441\pi\) | |||||||
\(710\) | 3.07180 | 0.115282 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 23.1384 | 0.867150 | ||||||||
\(713\) | 8.19615 | 0.306948 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.6603 | −0.585660 | ||||||||
\(716\) | −14.6410 | −0.547160 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.46410 | −0.129279 | ||||||||
\(719\) | 27.4641 | 1.02424 | 0.512119 | − | 0.858914i | \(-0.328861\pi\) | ||||
0.512119 | + | 0.858914i | \(0.328861\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.46410 | 0.352217 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −15.1103 | −0.561569 | ||||||||
\(725\) | −6.19615 | −0.230119 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.6603 | −1.13713 | −0.568563 | − | 0.822640i | \(-0.692500\pi\) | ||||
−0.568563 | + | 0.822640i | \(0.692500\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.41154 | −0.126267 | ||||||||
\(731\) | 48.4449 | 1.79180 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.6603 | −0.689232 | −0.344616 | − | 0.938744i | \(-0.611991\pi\) | ||||
−0.344616 | + | 0.938744i | \(0.611991\pi\) | |||||||
\(734\) | −0.588457 | −0.0217204 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.42563 | −0.273712 | ||||||||
\(737\) | 7.26795 | 0.267718 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.7846 | −0.507075 | −0.253538 | − | 0.967326i | \(-0.581594\pi\) | ||||
−0.253538 | + | 0.967326i | \(0.581594\pi\) | |||||||
\(740\) | 10.5359 | 0.387307 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −49.9090 | −1.83098 | −0.915491 | − | 0.402338i | \(-0.868198\pi\) | ||||
−0.915491 | + | 0.402338i | \(0.868198\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.8564 | −0.800757 | ||||||||
\(746\) | 13.5551 | 0.496289 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 26.9282 | 0.984593 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.9282 | 1.16508 | 0.582538 | − | 0.812803i | \(-0.302060\pi\) | ||||
0.582538 | + | 0.812803i | \(0.302060\pi\) | |||||||
\(752\) | −2.14359 | −0.0781688 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 26.0000 | 0.946864 | ||||||||
\(755\) | −4.92820 | −0.179356 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.143594 | −0.00521900 | −0.00260950 | − | 0.999997i | \(-0.500831\pi\) | ||||
−0.00260950 | + | 0.999997i | \(0.500831\pi\) | |||||||
\(758\) | 20.7321 | 0.753022 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.24871 | 0.226665 | ||||||||
\(761\) | −43.2679 | −1.56846 | −0.784231 | − | 0.620469i | \(-0.786942\pi\) | ||||
−0.784231 | + | 0.620469i | \(0.786942\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 7.21539 | 0.261044 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.28719 | 0.299428 | ||||||||
\(767\) | −58.4449 | −2.11032 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.6795 | 0.637539 | 0.318769 | − | 0.947832i | \(-0.396730\pi\) | ||||
0.318769 | + | 0.947832i | \(0.396730\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.4641 | 0.484584 | ||||||||
\(773\) | 1.51666 | 0.0545505 | 0.0272752 | − | 0.999628i | \(-0.491317\pi\) | ||||
0.0272752 | + | 0.999628i | \(0.491317\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.46410 | 0.232197 | ||||||||
\(776\) | 2.71797 | 0.0975694 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26.7846 | 0.960275 | ||||||||
\(779\) | 6.73205 | 0.241201 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.4641 | 0.410218 | ||||||||
\(782\) | 6.24871 | 0.223453 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.3923 | 0.513683 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.53590 | 0.232980 | 0.116490 | − | 0.993192i | \(-0.462836\pi\) | ||||
0.116490 | + | 0.993192i | \(0.462836\pi\) | |||||||
\(788\) | −25.8564 | −0.921096 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 9.80385 | 0.348805 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.9282 | 0.814204 | ||||||||
\(794\) | 15.2295 | 0.540474 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −32.2102 | −1.14166 | ||||||||
\(797\) | 42.0526 | 1.48958 | 0.744789 | − | 0.667300i | \(-0.232550\pi\) | ||||
0.744789 | + | 0.667300i | \(0.232550\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.4641 | 0.476326 | ||||||||
\(800\) | −5.85641 | −0.207055 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.21539 | 0.113539 | ||||||||
\(803\) | −12.7321 | −0.449304 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −27.1244 | −0.955415 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 27.2154 | 0.957434 | ||||||||
\(809\) | 29.7128 | 1.04465 | 0.522323 | − | 0.852747i | \(-0.325065\pi\) | ||||
0.522323 | + | 0.852747i | \(0.325065\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.46410 | 0.121641 | 0.0608205 | − | 0.998149i | \(-0.480628\pi\) | ||||
0.0608205 | + | 0.998149i | \(0.480628\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −14.3923 | −0.504450 | ||||||||
\(815\) | 5.85641 | 0.205141 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.7321 | 0.620366 | ||||||||
\(818\) | −22.5885 | −0.789787 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.00000 | −0.139686 | ||||||||
\(821\) | −19.5167 | −0.681136 | −0.340568 | − | 0.940220i | \(-0.610619\pi\) | ||||
−0.340568 | + | 0.940220i | \(0.610619\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.1769 | −0.807896 | −0.403948 | − | 0.914782i | \(-0.632362\pi\) | ||||
−0.403948 | + | 0.914782i | \(0.632362\pi\) | |||||||
\(824\) | 3.03332 | 0.105671 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.2487 | 1.81687 | 0.908433 | − | 0.418031i | \(-0.137280\pi\) | ||||
0.908433 | + | 0.418031i | \(0.137280\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.3923 | −0.881911 | −0.440956 | − | 0.897529i | \(-0.645360\pi\) | ||||
−0.440956 | + | 0.897529i | \(0.645360\pi\) | |||||||
\(830\) | 6.67949 | 0.231849 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 12.2872 | 0.425982 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.339746 | −0.0117574 | ||||||||
\(836\) | 9.85641 | 0.340891 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20.8897 | −0.721624 | ||||||||
\(839\) | 40.4449 | 1.39631 | 0.698156 | − | 0.715946i | \(-0.254004\pi\) | ||||
0.698156 | + | 0.715946i | \(0.254004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.39230 | 0.323873 | ||||||||
\(842\) | −10.1962 | −0.351383 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −30.6410 | −1.05471 | ||||||||
\(845\) | −19.8564 | −0.683081 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.99485 | 0.308884 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.92820 | 0.169036 | ||||||||
\(851\) | 9.12436 | 0.312779 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.9808 | 0.684128 | 0.342064 | − | 0.939677i | \(-0.388874\pi\) | ||||
0.342064 | + | 0.939677i | \(0.388874\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.7846 | 0.710403 | ||||||||
\(857\) | −4.87564 | −0.166549 | −0.0832744 | − | 0.996527i | \(-0.526538\pi\) | ||||
−0.0832744 | + | 0.996527i | \(0.526538\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.535898 | 0.0182846 | 0.00914231 | − | 0.999958i | \(-0.497090\pi\) | ||||
0.00914231 | + | 0.999958i | \(0.497090\pi\) | |||||||
\(860\) | −10.5359 | −0.359271 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.6795 | −0.431865 | ||||||||
\(863\) | 6.39230 | 0.217597 | 0.108798 | − | 0.994064i | \(-0.465300\pi\) | ||||
0.108798 | + | 0.994064i | \(0.465300\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.4641 | 0.729801 | ||||||||
\(866\) | −3.51666 | −0.119501 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36.5885 | 1.24118 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.2487 | 0.516683 | ||||||||
\(872\) | 27.8949 | 0.944640 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.28719 | 0.0773653 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.8564 | −1.07571 | −0.537857 | − | 0.843036i | \(-0.680766\pi\) | ||||
−0.537857 | + | 0.843036i | \(0.680766\pi\) | |||||||
\(878\) | −5.46410 | −0.184404 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.92820 | −0.0987097 | ||||||||
\(881\) | 17.8564 | 0.601598 | 0.300799 | − | 0.953688i | \(-0.402747\pi\) | ||||
0.300799 | + | 0.953688i | \(0.402747\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.4115 | 0.754208 | 0.377104 | − | 0.926171i | \(-0.376920\pi\) | ||||
0.377104 | + | 0.926171i | \(0.376920\pi\) | |||||||
\(884\) | 56.4974 | 1.90021 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.85641 | 0.0623672 | ||||||||
\(887\) | 28.7321 | 0.964728 | 0.482364 | − | 0.875971i | \(-0.339778\pi\) | ||||
0.482364 | + | 0.875971i | \(0.339778\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.67949 | 0.223897 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.574374 | −0.0192315 | ||||||||
\(893\) | 4.92820 | 0.164916 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.0000 | −0.334263 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.96152 | −0.198939 | ||||||||
\(899\) | −40.0526 | −1.33583 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −56.4974 | −1.88220 | ||||||||
\(902\) | 5.46410 | 0.181935 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.4974 | 0.415658 | ||||||||
\(905\) | −10.3205 | −0.343065 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.41154 | 0.0800740 | 0.0400370 | − | 0.999198i | \(-0.487252\pi\) | ||||
0.0400370 | + | 0.999198i | \(0.487252\pi\) | |||||||
\(908\) | 22.9282 | 0.760899 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.2679 | 0.373324 | 0.186662 | − | 0.982424i | \(-0.440233\pi\) | ||||
0.186662 | + | 0.982424i | \(0.440233\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.9282 | 0.825003 | ||||||||
\(914\) | −0.483340 | −0.0159874 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.39230 | 0.145126 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.14359 | −0.103698 | −0.0518488 | − | 0.998655i | \(-0.516511\pi\) | ||||
−0.0518488 | + | 0.998655i | \(0.516511\pi\) | |||||||
\(920\) | −3.21539 | −0.106008 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −25.6077 | −0.843345 | ||||||||
\(923\) | 24.0526 | 0.791700 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.19615 | 0.236608 | ||||||||
\(926\) | −16.3013 | −0.535693 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 36.2872 | 1.19119 | ||||||||
\(929\) | −6.44486 | −0.211449 | −0.105725 | − | 0.994395i | \(-0.533716\pi\) | ||||
−0.105725 | + | 0.994395i | \(0.533716\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −25.3590 | −0.830661 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −20.3923 | −0.667257 | ||||||||
\(935\) | 18.3923 | 0.601493 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.2679 | 0.923474 | 0.461737 | − | 0.887017i | \(-0.347226\pi\) | ||||
0.461737 | + | 0.887017i | \(0.347226\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.92820 | −0.0955075 | ||||||||
\(941\) | −8.05256 | −0.262506 | −0.131253 | − | 0.991349i | \(-0.541900\pi\) | ||||
−0.131253 | + | 0.991349i | \(0.541900\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.46410 | −0.112807 | ||||||||
\(944\) | −10.9282 | −0.355683 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.3923 | 0.467934 | ||||||||
\(947\) | −11.6603 | −0.378907 | −0.189454 | − | 0.981890i | \(-0.560672\pi\) | ||||
−0.189454 | + | 0.981890i | \(0.560672\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.7128 | −0.867135 | ||||||||
\(950\) | 1.80385 | 0.0585245 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.1051 | −1.29913 | −0.649566 | − | 0.760305i | \(-0.725049\pi\) | ||||
−0.649566 | + | 0.760305i | \(0.725049\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.92820 | 0.159473 | ||||||||
\(956\) | 30.6410 | 0.991001 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.0000 | −0.775405 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.7846 | 0.347891 | ||||||||
\(962\) | −30.1962 | −0.973563 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.56922 | −0.308204 | ||||||||
\(965\) | 9.19615 | 0.296035 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.1244 | 0.454209 | 0.227104 | − | 0.973870i | \(-0.427074\pi\) | ||||
0.227104 | + | 0.973870i | \(0.427074\pi\) | |||||||
\(968\) | −8.96668 | −0.288200 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.784610 | 0.0251923 | ||||||||
\(971\) | 24.0000 | 0.770197 | 0.385098 | − | 0.922876i | \(-0.374168\pi\) | ||||
0.385098 | + | 0.922876i | \(0.374168\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 23.1244 | 0.740952 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.28719 | 0.137230 | ||||||||
\(977\) | −14.5885 | −0.466726 | −0.233363 | − | 0.972390i | \(-0.574973\pi\) | ||||
−0.233363 | + | 0.972390i | \(0.574973\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.9282 | 0.796709 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.50258 | 0.239417 | ||||||||
\(983\) | −20.1962 | −0.644157 | −0.322079 | − | 0.946713i | \(-0.604382\pi\) | ||||
−0.322079 | + | 0.946713i | \(0.604382\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.6603 | −0.562702 | ||||||||
\(986\) | −30.5359 | −0.972461 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20.6795 | 0.657902 | ||||||||
\(989\) | −9.12436 | −0.290138 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.1051 | 1.75047 | 0.875236 | − | 0.483696i | \(-0.160706\pi\) | ||||
0.875236 | + | 0.483696i | \(0.160706\pi\) | |||||||
\(992\) | −37.8564 | −1.20194 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.0000 | −0.697447 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.01924 | −0.127291 | −0.0636453 | − | 0.997973i | \(-0.520273\pi\) | ||||
−0.0636453 | + | 0.997973i | \(0.520273\pi\) | |||||||
\(998\) | 14.9808 | 0.474208 | ||||||||
\(999\) | 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 | 2205.2.a.z.1.1 | 2 | ||
3.2 | odd | 2 | 735.2.a.g.1.2 | 2 | |||
7.2 | even | 3 | 315.2.j.c.46.2 | 4 | |||
7.4 | even | 3 | 315.2.j.c.226.2 | 4 | |||
7.6 | odd | 2 | 2205.2.a.ba.1.1 | 2 | |||
15.14 | odd | 2 | 3675.2.a.bg.1.1 | 2 | |||
21.2 | odd | 6 | 105.2.i.d.46.1 | yes | 4 | ||
21.5 | even | 6 | 735.2.i.l.361.1 | 4 | |||
21.11 | odd | 6 | 105.2.i.d.16.1 | ✓ | 4 | ||
21.17 | even | 6 | 735.2.i.l.226.1 | 4 | |||
21.20 | even | 2 | 735.2.a.h.1.2 | 2 | |||
84.11 | even | 6 | 1680.2.bg.o.961.2 | 4 | |||
84.23 | even | 6 | 1680.2.bg.o.1201.2 | 4 | |||
105.2 | even | 12 | 525.2.r.f.424.1 | 4 | |||
105.23 | even | 12 | 525.2.r.a.424.2 | 4 | |||
105.32 | even | 12 | 525.2.r.a.499.2 | 4 | |||
105.44 | odd | 6 | 525.2.i.f.151.2 | 4 | |||
105.53 | even | 12 | 525.2.r.f.499.1 | 4 | |||
105.74 | odd | 6 | 525.2.i.f.226.2 | 4 | |||
105.104 | even | 2 | 3675.2.a.be.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.i.d.16.1 | ✓ | 4 | 21.11 | odd | 6 | ||
105.2.i.d.46.1 | yes | 4 | 21.2 | odd | 6 | ||
315.2.j.c.46.2 | 4 | 7.2 | even | 3 | |||
315.2.j.c.226.2 | 4 | 7.4 | even | 3 | |||
525.2.i.f.151.2 | 4 | 105.44 | odd | 6 | |||
525.2.i.f.226.2 | 4 | 105.74 | odd | 6 | |||
525.2.r.a.424.2 | 4 | 105.23 | even | 12 | |||
525.2.r.a.499.2 | 4 | 105.32 | even | 12 | |||
525.2.r.f.424.1 | 4 | 105.2 | even | 12 | |||
525.2.r.f.499.1 | 4 | 105.53 | even | 12 | |||
735.2.a.g.1.2 | 2 | 3.2 | odd | 2 | |||
735.2.a.h.1.2 | 2 | 21.20 | even | 2 | |||
735.2.i.l.226.1 | 4 | 21.17 | even | 6 | |||
735.2.i.l.361.1 | 4 | 21.5 | even | 6 | |||
1680.2.bg.o.961.2 | 4 | 84.11 | even | 6 | |||
1680.2.bg.o.1201.2 | 4 | 84.23 | even | 6 | |||
2205.2.a.z.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2205.2.a.ba.1.1 | 2 | 7.6 | odd | 2 | |||
3675.2.a.be.1.1 | 2 | 105.104 | even | 2 | |||
3675.2.a.bg.1.1 | 2 | 15.14 | odd | 2 |