Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("8280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.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: | \(66.1161328736\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 18x^{5} + 46x^{4} + 60x^{3} - 76x^{2} - 51x - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.22540\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8280.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.82985 | −1.06958 | −0.534791 | − | 0.844984i | \(-0.679610\pi\) | ||||
−0.534791 | + | 0.844984i | \(0.679610\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.94410 | −1.49070 | −0.745350 | − | 0.666673i | \(-0.767718\pi\) | ||||
−0.745350 | + | 0.666673i | \(0.767718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.65799 | 1.29189 | 0.645947 | − | 0.763382i | \(-0.276463\pi\) | ||||
0.645947 | + | 0.763382i | \(0.276463\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.16509 | −0.525111 | −0.262556 | − | 0.964917i | \(-0.584565\pi\) | ||||
−0.262556 | + | 0.964917i | \(0.584565\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.347949 | −0.0798249 | −0.0399125 | − | 0.999203i | \(-0.512708\pi\) | ||||
−0.0399125 | + | 0.999203i | \(0.512708\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.32315 | 0.245702 | 0.122851 | − | 0.992425i | \(-0.460796\pi\) | ||||
0.122851 | + | 0.992425i | \(0.460796\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.0343 | 1.80222 | 0.901109 | − | 0.433593i | \(-0.142755\pi\) | ||||
0.901109 | + | 0.433593i | \(0.142755\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.82985 | −0.478332 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.95454 | −0.978920 | −0.489460 | − | 0.872026i | \(-0.662806\pi\) | ||||
−0.489460 | + | 0.872026i | \(0.662806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.98690 | −0.778822 | −0.389411 | − | 0.921064i | \(-0.627322\pi\) | ||||
−0.389411 | + | 0.921064i | \(0.627322\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.57815 | 0.240665 | 0.120333 | − | 0.992734i | \(-0.461604\pi\) | ||||
0.120333 | + | 0.992734i | \(0.461604\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.0205 | 1.89924 | 0.949619 | − | 0.313406i | \(-0.101470\pi\) | ||||
0.949619 | + | 0.313406i | \(0.101470\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00804 | 0.144006 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.12429 | 0.703876 | 0.351938 | − | 0.936023i | \(-0.385523\pi\) | ||||
0.351938 | + | 0.936023i | \(0.385523\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.94410 | −0.666662 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.4243 | −1.61750 | −0.808752 | − | 0.588149i | \(-0.799857\pi\) | ||||
−0.808752 | + | 0.588149i | \(0.799857\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.4630 | 1.33965 | 0.669827 | − | 0.742517i | \(-0.266368\pi\) | ||||
0.669827 | + | 0.742517i | \(0.266368\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.65799 | 0.577753 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.2600 | −1.49780 | −0.748898 | − | 0.662686i | \(-0.769417\pi\) | ||||
−0.748898 | + | 0.662686i | \(0.769417\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.84614 | 0.575131 | 0.287566 | − | 0.957761i | \(-0.407154\pi\) | ||||
0.287566 | + | 0.957761i | \(0.407154\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.3742 | 1.44829 | 0.724147 | − | 0.689646i | \(-0.242234\pi\) | ||||
0.724147 | + | 0.689646i | \(0.242234\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.9910 | 1.59443 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.81099 | −0.991313 | −0.495657 | − | 0.868519i | \(-0.665073\pi\) | ||||
−0.495657 | + | 0.868519i | \(0.665073\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.0533 | −1.54255 | −0.771274 | − | 0.636503i | \(-0.780380\pi\) | ||||
−0.771274 | + | 0.636503i | \(0.780380\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.16509 | −0.234837 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.2819 | −1.40788 | −0.703940 | − | 0.710259i | \(-0.748578\pi\) | ||||
−0.703940 | + | 0.710259i | \(0.748578\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.1814 | −1.38179 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.347949 | −0.0356988 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.56802 | −0.971485 | −0.485743 | − | 0.874102i | \(-0.661451\pi\) | ||||
−0.485743 | + | 0.874102i | \(0.661451\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.1041 | 1.00540 | 0.502699 | − | 0.864462i | \(-0.332340\pi\) | ||||
0.502699 | + | 0.864462i | \(0.332340\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.5213 | −1.13523 | −0.567613 | − | 0.823296i | \(-0.692133\pi\) | ||||
−0.567613 | + | 0.823296i | \(0.692133\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.1192 | −1.65497 | −0.827486 | − | 0.561486i | \(-0.810230\pi\) | ||||
−0.827486 | + | 0.561486i | \(0.810230\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.6603 | 1.02107 | 0.510537 | − | 0.859856i | \(-0.329447\pi\) | ||||
0.510537 | + | 0.859856i | \(0.329447\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.61589 | 0.246082 | 0.123041 | − | 0.992402i | \(-0.460735\pi\) | ||||
0.123041 | + | 0.992402i | \(0.460735\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.12687 | 0.561650 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.4441 | 1.22219 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.23348 | 0.375660 | 0.187830 | − | 0.982202i | \(-0.439855\pi\) | ||||
0.187830 | + | 0.982202i | \(0.439855\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.87807 | 0.863051 | 0.431525 | − | 0.902101i | \(-0.357976\pi\) | ||||
0.431525 | + | 0.902101i | \(0.357976\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.984642 | 0.0853793 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.2618 | 0.962159 | 0.481080 | − | 0.876677i | \(-0.340245\pi\) | ||||
0.481080 | + | 0.876677i | \(0.340245\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.5163 | −1.90981 | −0.954905 | − | 0.296913i | \(-0.904043\pi\) | ||||
−0.954905 | + | 0.296913i | \(0.904043\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.0296 | −1.92583 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.32315 | 0.109881 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.0435 | −1.64203 | −0.821015 | − | 0.570907i | \(-0.806592\pi\) | ||||
−0.821015 | + | 0.570907i | \(0.806592\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.7448 | −1.44405 | −0.722025 | − | 0.691867i | \(-0.756788\pi\) | ||||
−0.722025 | + | 0.691867i | \(0.756788\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.0343 | 0.805976 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.47753 | 0.277537 | 0.138769 | − | 0.990325i | \(-0.455686\pi\) | ||||
0.138769 | + | 0.990325i | \(0.455686\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.82985 | −0.223023 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.93108 | 0.621210 | 0.310605 | − | 0.950539i | \(-0.399468\pi\) | ||||
0.310605 | + | 0.950539i | \(0.399468\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.59285 | −0.587552 | −0.293776 | − | 0.955874i | \(-0.594912\pi\) | ||||
−0.293776 | + | 0.955874i | \(0.594912\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.69689 | 0.668992 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.24531 | −0.550850 | −0.275425 | − | 0.961323i | \(-0.588819\pi\) | ||||
−0.275425 | + | 0.961323i | \(0.588819\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.82985 | −0.213916 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.54920 | −0.115793 | −0.0578964 | − | 0.998323i | \(-0.518439\pi\) | ||||
−0.0578964 | + | 0.998323i | \(0.518439\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.41079 | −0.104863 | −0.0524316 | − | 0.998625i | \(-0.516697\pi\) | ||||
−0.0524316 | + | 0.998625i | \(0.516697\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.95454 | −0.437786 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.7044 | 0.782784 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.5973 | −0.766795 | −0.383398 | − | 0.923583i | \(-0.625246\pi\) | ||||
−0.383398 | + | 0.923583i | \(0.625246\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.7209 | −1.49152 | −0.745760 | − | 0.666215i | \(-0.767914\pi\) | ||||
−0.745760 | + | 0.666215i | \(0.767914\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.8915 | −1.48846 | −0.744228 | − | 0.667926i | \(-0.767182\pi\) | ||||
−0.744228 | + | 0.667926i | \(0.767182\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.0562 | −1.77618 | −0.888092 | − | 0.459665i | \(-0.847969\pi\) | ||||
−0.888092 | + | 0.459665i | \(0.847969\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.74430 | −0.262799 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.98690 | −0.348300 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.72029 | 0.118995 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.6415 | 0.801436 | 0.400718 | − | 0.916201i | \(-0.368761\pi\) | ||||
0.400718 | + | 0.916201i | \(0.368761\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.57815 | 0.107629 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −28.3956 | −1.92762 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.0850 | −0.678388 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.4037 | 1.29937 | 0.649685 | − | 0.760204i | \(-0.274901\pi\) | ||||
0.649685 | + | 0.760204i | \(0.274901\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.44027 | −0.427456 | −0.213728 | − | 0.976893i | \(-0.568561\pi\) | ||||
−0.213728 | + | 0.976893i | \(0.568561\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.42608 | −0.0942380 | −0.0471190 | − | 0.998889i | \(-0.515004\pi\) | ||||
−0.0471190 | + | 0.998889i | \(0.515004\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.9705 | −0.718702 | −0.359351 | − | 0.933202i | \(-0.617002\pi\) | ||||
−0.359351 | + | 0.933202i | \(0.617002\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.0205 | 0.849365 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.7873 | −0.956514 | −0.478257 | − | 0.878220i | \(-0.658731\pi\) | ||||
−0.478257 | + | 0.878220i | \(0.658731\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0504 | 0.647401 | 0.323700 | − | 0.946160i | \(-0.395073\pi\) | ||||
0.323700 | + | 0.946160i | \(0.395073\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00804 | 0.0644013 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.62074 | −0.103125 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.54142 | 0.223532 | 0.111766 | − | 0.993735i | \(-0.464349\pi\) | ||||
0.111766 | + | 0.993735i | \(0.464349\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.94410 | −0.310833 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.8020 | −1.23522 | −0.617608 | − | 0.786486i | \(-0.711898\pi\) | ||||
−0.617608 | + | 0.786486i | \(0.711898\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.8504 | 1.04703 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.13769 | 0.378466 | 0.189233 | − | 0.981932i | \(-0.439400\pi\) | ||||
0.189233 | + | 0.981932i | \(0.439400\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.12429 | 0.314783 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.27775 | −0.138877 | −0.0694385 | − | 0.997586i | \(-0.522121\pi\) | ||||
−0.0694385 | + | 0.997586i | \(0.522121\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.8457 | 1.87374 | 0.936872 | − | 0.349674i | \(-0.113707\pi\) | ||||
0.936872 | + | 0.349674i | \(0.113707\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.94410 | −0.298140 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.69943 | 0.522698 | 0.261349 | − | 0.965244i | \(-0.415833\pi\) | ||||
0.261349 | + | 0.965244i | \(0.415833\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.86657 | 0.349970 | 0.174985 | − | 0.984571i | \(-0.444012\pi\) | ||||
0.174985 | + | 0.984571i | \(0.444012\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.30578 | −0.315396 | −0.157698 | − | 0.987487i | \(-0.550407\pi\) | ||||
−0.157698 | + | 0.987487i | \(0.550407\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.1122 | 0.833015 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.3124 | −0.724258 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.61142 | −0.0941401 | −0.0470701 | − | 0.998892i | \(-0.514988\pi\) | ||||
−0.0470701 | + | 0.998892i | \(0.514988\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.4243 | −0.723370 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.65799 | 0.269379 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.46592 | −0.257411 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.4630 | 0.599112 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.0852 | −1.08925 | −0.544626 | − | 0.838679i | \(-0.683328\pi\) | ||||
−0.544626 | + | 0.838679i | \(0.683328\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −33.9003 | −1.92231 | −0.961155 | − | 0.276011i | \(-0.910988\pi\) | ||||
−0.961155 | + | 0.276011i | \(0.910988\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.8734 | 1.34940 | 0.674702 | − | 0.738090i | \(-0.264272\pi\) | ||||
0.674702 | + | 0.738090i | \(0.264272\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.3541 | 0.750041 | 0.375021 | − | 0.927016i | \(-0.377636\pi\) | ||||
0.375021 | + | 0.927016i | \(0.377636\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.54176 | −0.366268 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.753340 | 0.0419170 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.65799 | 0.258379 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −36.8461 | −2.03139 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.5923 | 1.29675 | 0.648376 | − | 0.761320i | \(-0.275449\pi\) | ||||
0.648376 | + | 0.761320i | \(0.275449\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.2600 | −0.669834 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.1866 | 1.42647 | 0.713237 | − | 0.700923i | \(-0.247228\pi\) | ||||
0.713237 | + | 0.700923i | \(0.247228\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −49.6106 | −2.68657 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9563 | 0.915556 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −33.4133 | −1.79372 | −0.896859 | − | 0.442316i | \(-0.854157\pi\) | ||||
−0.896859 | + | 0.442316i | \(0.854157\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.7105 | 0.733904 | 0.366952 | − | 0.930240i | \(-0.380401\pi\) | ||||
0.366952 | + | 0.930240i | \(0.380401\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.6135 | −1.73584 | −0.867920 | − | 0.496704i | \(-0.834544\pi\) | ||||
−0.867920 | + | 0.496704i | \(0.834544\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.84614 | 0.257207 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.30182 | −0.227042 | −0.113521 | − | 0.993536i | \(-0.536213\pi\) | ||||
−0.113521 | + | 0.993536i | \(0.536213\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8789 | −0.993628 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.3742 | 0.647697 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.5453 | −1.33345 | −0.666727 | − | 0.745302i | \(-0.732305\pi\) | ||||
−0.666727 | + | 0.745302i | \(0.732305\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.5010 | −0.752853 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.08868 | −0.0563697 | −0.0281848 | − | 0.999603i | \(-0.508973\pi\) | ||||
−0.0281848 | + | 0.999603i | \(0.508973\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.16321 | 0.317421 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.5620 | −1.10756 | −0.553782 | − | 0.832662i | \(-0.686816\pi\) | ||||
−0.553782 | + | 0.832662i | \(0.686816\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.31231 | −0.322544 | −0.161272 | − | 0.986910i | \(-0.551560\pi\) | ||||
−0.161272 | + | 0.986910i | \(0.551560\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.9910 | 0.713049 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.52936 | 0.381754 | 0.190877 | − | 0.981614i | \(-0.438867\pi\) | ||||
0.190877 | + | 0.981614i | \(0.438867\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.16509 | −0.109493 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.81099 | −0.443329 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.5533 | 1.23229 | 0.616147 | − | 0.787631i | \(-0.288693\pi\) | ||||
0.616147 | + | 0.787631i | \(0.288693\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.4811 | −1.52215 | −0.761077 | − | 0.648662i | \(-0.775329\pi\) | ||||
−0.761077 | + | 0.648662i | \(0.775329\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 46.7398 | 2.32827 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.4398 | 1.45928 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.8239 | 1.87027 | 0.935136 | − | 0.354290i | \(-0.115277\pi\) | ||||
0.935136 | + | 0.354290i | \(0.115277\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 35.1589 | 1.73005 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.0533 | −0.689848 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.9254 | −1.07112 | −0.535562 | − | 0.844496i | \(-0.679900\pi\) | ||||
−0.535562 | + | 0.844496i | \(0.679900\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.1125 | 1.76002 | 0.880008 | − | 0.474960i | \(-0.157537\pi\) | ||||
0.880008 | + | 0.474960i | \(0.157537\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.16509 | −0.105022 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −29.6088 | −1.43287 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.4074 | 1.60918 | 0.804590 | − | 0.593831i | \(-0.202385\pi\) | ||||
0.804590 | + | 0.593831i | \(0.202385\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.9892 | −1.20090 | −0.600451 | − | 0.799661i | \(-0.705012\pi\) | ||||
−0.600451 | + | 0.799661i | \(0.705012\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.347949 | −0.0166446 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.5951 | 0.982950 | 0.491475 | − | 0.870892i | \(-0.336458\pi\) | ||||
0.491475 | + | 0.870892i | \(0.336458\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.4349 | −0.638312 | −0.319156 | − | 0.947702i | \(-0.603399\pi\) | ||||
−0.319156 | + | 0.947702i | \(0.603399\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.2819 | −0.629623 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.0435 | 0.473980 | 0.236990 | − | 0.971512i | \(-0.423839\pi\) | ||||
0.236990 | + | 0.971512i | \(0.423839\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.6557 | 1.16099 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.1814 | −0.617954 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.60889 | 0.262373 | 0.131186 | − | 0.991358i | \(-0.458121\pi\) | ||||
0.131186 | + | 0.991358i | \(0.458121\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.8370 | −1.76224 | −0.881121 | − | 0.472890i | \(-0.843211\pi\) | ||||
−0.881121 | + | 0.472890i | \(0.843211\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.0326 | −1.81400 | −0.907000 | − | 0.421131i | \(-0.861633\pi\) | ||||
−0.907000 | + | 0.421131i | \(0.861633\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.70089 | −0.217531 | −0.108766 | − | 0.994067i | \(-0.534690\pi\) | ||||
−0.108766 | + | 0.994067i | \(0.534690\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 34.6939 | 1.60201 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.80251 | −0.358760 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.347949 | −0.0159650 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.8361 | 0.723570 | 0.361785 | − | 0.932262i | \(-0.382167\pi\) | ||||
0.361785 | + | 0.932262i | \(0.382167\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.7362 | −1.26466 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.56802 | −0.434461 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.6167 | −0.752973 | −0.376487 | − | 0.926422i | \(-0.622868\pi\) | ||||
−0.376487 | + | 0.926422i | \(0.622868\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.9471 | 1.21611 | 0.608054 | − | 0.793896i | \(-0.291951\pi\) | ||||
0.608054 | + | 0.793896i | \(0.291951\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.86473 | −0.129021 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.7139 | −0.615150 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.5034 | 0.694029 | 0.347015 | − | 0.937860i | \(-0.387195\pi\) | ||||
0.347015 | + | 0.937860i | \(0.387195\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.4518 | 1.40236 | 0.701182 | − | 0.712982i | \(-0.252656\pi\) | ||||
0.701182 | + | 0.712982i | \(0.252656\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.1041 | 0.449628 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.46634 | 0.0649943 | 0.0324971 | − | 0.999472i | \(-0.489654\pi\) | ||||
0.0324971 | + | 0.999472i | \(0.489654\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.0172 | −1.54907 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.5213 | −0.507688 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −64.3747 | −2.83120 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.58182 | −0.244544 | −0.122272 | − | 0.992497i | \(-0.539018\pi\) | ||||
−0.122272 | + | 0.992497i | \(0.539018\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.2870 | −0.493548 | −0.246774 | − | 0.969073i | \(-0.579371\pi\) | ||||
−0.246774 | + | 0.969073i | \(0.579371\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.7252 | −0.946365 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.2289 | −1.00616 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.1192 | −0.740126 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.98385 | −0.214670 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.9045 | 0.769773 | 0.384887 | − | 0.922964i | \(-0.374241\pi\) | ||||
0.384887 | + | 0.922964i | \(0.374241\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.6603 | 0.456638 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.1535 | −0.690673 | −0.345336 | − | 0.938479i | \(-0.612235\pi\) | ||||
−0.345336 | + | 0.938479i | \(0.612235\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.460387 | −0.0196132 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.9338 | 1.06029 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.90248 | 0.334839 | 0.167419 | − | 0.985886i | \(-0.446457\pi\) | ||||
0.167419 | + | 0.985886i | \(0.446457\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.35100 | 0.310914 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.36386 | 0.310350 | 0.155175 | − | 0.987887i | \(-0.450406\pi\) | ||||
0.155175 | + | 0.987887i | \(0.450406\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.61589 | 0.110051 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.18004 | −0.0494698 | −0.0247349 | − | 0.999694i | \(-0.507874\pi\) | ||||
−0.0247349 | + | 0.999694i | \(0.507874\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.59220 | 0.401421 | 0.200711 | − | 0.979651i | \(-0.435675\pi\) | ||||
0.200711 | + | 0.979651i | \(0.435675\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.2966 | −0.886589 | −0.443294 | − | 0.896376i | \(-0.646190\pi\) | ||||
−0.443294 | + | 0.896376i | \(0.646190\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 39.7686 | 1.64988 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.3350 | −1.04927 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.2149 | 1.12328 | 0.561640 | − | 0.827382i | \(-0.310171\pi\) | ||||
0.561640 | + | 0.827382i | \(0.310171\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.49143 | −0.143862 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.6044 | −1.01038 | −0.505191 | − | 0.863008i | \(-0.668578\pi\) | ||||
−0.505191 | + | 0.863008i | \(0.668578\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.12687 | 0.251177 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.9286 | 0.855120 | 0.427560 | − | 0.903987i | \(-0.359373\pi\) | ||||
0.427560 | + | 0.903987i | \(0.359373\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.1317 | 1.14752 | 0.573758 | − | 0.819025i | \(-0.305485\pi\) | ||||
0.573758 | + | 0.819025i | \(0.305485\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.4441 | 0.546580 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.02339 | 0.163304 | 0.0816522 | − | 0.996661i | \(-0.473980\pi\) | ||||
0.0816522 | + | 0.996661i | \(0.473980\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 60.6495 | 2.45362 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.9604 | −1.25048 | −0.625240 | − | 0.780432i | \(-0.714999\pi\) | ||||
−0.625240 | + | 0.780432i | \(0.714999\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.4413 | 1.42681 | 0.713407 | − | 0.700750i | \(-0.247151\pi\) | ||||
0.713407 | + | 0.700750i | \(0.247151\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.61916 | 0.306240 | 0.153120 | − | 0.988208i | \(-0.451068\pi\) | ||||
0.153120 | + | 0.988208i | \(0.451068\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 37.5858 | 1.50584 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.8921 | 0.514042 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.6842 | −0.863235 | −0.431618 | − | 0.902057i | \(-0.642057\pi\) | ||||
−0.431618 | + | 0.902057i | \(0.642057\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.23348 | 0.168000 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.69544 | 0.186040 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.4616 | 1.55864 | 0.779320 | − | 0.626626i | \(-0.215565\pi\) | ||||
0.779320 | + | 0.626626i | \(0.215565\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.18996 | 0.125800 | 0.0628999 | − | 0.998020i | \(-0.479965\pi\) | ||||
0.0628999 | + | 0.998020i | \(0.479965\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.2970 | −0.719330 | −0.359665 | − | 0.933081i | \(-0.617109\pi\) | ||||
−0.359665 | + | 0.933081i | \(0.617109\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 61.4269 | 2.41122 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −33.0406 | −1.29298 | −0.646490 | − | 0.762923i | \(-0.723764\pi\) | ||||
−0.646490 | + | 0.762923i | \(0.723764\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.87807 | 0.385968 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.7651 | −1.08157 | −0.540787 | − | 0.841160i | \(-0.681873\pi\) | ||||
−0.540787 | + | 0.841160i | \(0.681873\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.2032 | −1.17477 | −0.587384 | − | 0.809308i | \(-0.699842\pi\) | ||||
−0.587384 | + | 0.809308i | \(0.699842\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.984642 | 0.0381828 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.32315 | 0.0512324 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −51.7303 | −1.99702 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.3010 | −0.898187 | −0.449093 | − | 0.893485i | \(-0.648253\pi\) | ||||
−0.449093 | + | 0.893485i | \(0.648253\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −43.2511 | −1.66228 | −0.831138 | − | 0.556066i | \(-0.812310\pi\) | ||||
−0.831138 | + | 0.556066i | \(0.812310\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.0760 | 1.03908 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24.0271 | 0.919372 | 0.459686 | − | 0.888082i | \(-0.347962\pi\) | ||||
0.459686 | + | 0.888082i | \(0.347962\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.2618 | 0.430291 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 23.8689 | 0.909333 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.0742 | −0.687574 | −0.343787 | − | 0.939048i | \(-0.611710\pi\) | ||||
−0.343787 | + | 0.939048i | \(0.611710\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.5163 | −0.854093 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.7971 | 0.408968 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.35858 | −0.164621 | −0.0823107 | − | 0.996607i | \(-0.526230\pi\) | ||||
−0.0823107 | + | 0.996607i | \(0.526230\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.07187 | 0.0781422 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.5931 | −1.07536 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.28641 | 0.236091 | 0.118045 | − | 0.993008i | \(-0.462337\pi\) | ||||
0.118045 | + | 0.993008i | \(0.462337\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.0343 | 0.375788 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.0296 | −0.861257 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.9514 | 1.67640 | 0.838202 | − | 0.545360i | \(-0.183607\pi\) | ||||
0.838202 | + | 0.545360i | \(0.183607\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.6035 | 1.21422 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.32315 | 0.0491404 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.6212 | −0.838972 | −0.419486 | − | 0.907762i | \(-0.637790\pi\) | ||||
−0.419486 | + | 0.907762i | \(0.637790\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.41683 | −0.126376 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.9519 | 1.69727 | 0.848636 | − | 0.528977i | \(-0.177424\pi\) | ||||
0.848636 | + | 0.528977i | \(0.177424\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 60.6145 | 2.23276 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.1925 | 0.448509 | 0.224255 | − | 0.974531i | \(-0.428005\pi\) | ||||
0.224255 | + | 0.974531i | \(0.428005\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.03362 | 0.0746063 | 0.0373032 | − | 0.999304i | \(-0.488123\pi\) | ||||
0.0373032 | + | 0.999304i | \(0.488123\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.0435 | −0.734338 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 48.4447 | 1.77013 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.935597 | −0.0341404 | −0.0170702 | − | 0.999854i | \(-0.505434\pi\) | ||||
−0.0170702 | + | 0.999854i | \(0.505434\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.7448 | −0.645798 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.4242 | −1.03310 | −0.516548 | − | 0.856258i | \(-0.672783\pi\) | ||||
−0.516548 | + | 0.856258i | \(0.672783\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.5123 | −1.64982 | −0.824909 | − | 0.565265i | \(-0.808774\pi\) | ||||
−0.824909 | + | 0.565265i | \(0.808774\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.1671 | −1.09212 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −57.8723 | −2.08965 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.93028 | 0.177790 | 0.0888952 | − | 0.996041i | \(-0.471666\pi\) | ||||
0.0888952 | + | 0.996041i | \(0.471666\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.2800 | 0.477648 | 0.238824 | − | 0.971063i | \(-0.423238\pi\) | ||||
0.238824 | + | 0.971063i | \(0.423238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.0343 | 0.360443 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.73518 | 0.0621694 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.9598 | −0.857349 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.47753 | 0.124118 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.94763 | −0.354595 | −0.177297 | − | 0.984157i | \(-0.556735\pi\) | ||||
−0.177297 | + | 0.984157i | \(0.556735\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.40256 | −0.263205 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.7368 | 1.73069 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.1642 | −1.06847 | −0.534236 | − | 0.845335i | \(-0.679401\pi\) | ||||
−0.534236 | + | 0.845335i | \(0.679401\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.1906 | −0.997312 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −61.1794 | −2.15897 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.82985 | −0.0997390 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.2734 | −0.747935 | −0.373967 | − | 0.927442i | \(-0.622003\pi\) | ||||
−0.373967 | + | 0.927442i | \(0.622003\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.697841 | −0.0245045 | −0.0122523 | − | 0.999925i | \(-0.503900\pi\) | ||||
−0.0122523 | + | 0.999925i | \(0.503900\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.93108 | 0.277814 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.549114 | −0.0192111 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.8586 | 1.07697 | 0.538486 | − | 0.842635i | \(-0.318997\pi\) | ||||
0.538486 | + | 0.842635i | \(0.318997\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.6298 | 0.684253 | 0.342127 | − | 0.939654i | \(-0.388853\pi\) | ||||
0.342127 | + | 0.939654i | \(0.388853\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.73006 | −0.338347 | −0.169174 | − | 0.985586i | \(-0.554110\pi\) | ||||
−0.169174 | + | 0.985586i | \(0.554110\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.6529 | −0.682573 | −0.341287 | − | 0.939959i | \(-0.610863\pi\) | ||||
−0.341287 | + | 0.939959i | \(0.610863\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.18250 | −0.0756191 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.59285 | −0.262761 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.1900 | −1.11132 | −0.555661 | − | 0.831409i | \(-0.687535\pi\) | ||||
−0.555661 | + | 0.831409i | \(0.687535\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.2493 | −0.939630 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.69689 | 0.299182 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −38.0447 | −1.30723 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.95454 | −0.204119 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −55.8766 | −1.91318 | −0.956590 | − | 0.291438i | \(-0.905866\pi\) | ||||
−0.956590 | + | 0.291438i | \(0.905866\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.15146 | −0.210130 | −0.105065 | − | 0.994465i | \(-0.533505\pi\) | ||||
−0.105065 | + | 0.994465i | \(0.533505\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.7220 | −1.04822 | −0.524111 | − | 0.851650i | \(-0.675602\pi\) | ||||
−0.524111 | + | 0.851650i | \(0.675602\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.2001 | 1.02802 | 0.514012 | − | 0.857783i | \(-0.328159\pi\) | ||||
0.514012 | + | 0.857783i | \(0.328159\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.24531 | −0.246348 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 43.5624 | 1.47775 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −57.1069 | −1.93499 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.82985 | −0.0956663 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.8280 | −0.669546 | −0.334773 | − | 0.942299i | \(-0.608660\pi\) | ||||
−0.334773 | + | 0.942299i | \(0.608660\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −55.1069 | −1.85660 | −0.928300 | − | 0.371833i | \(-0.878729\pi\) | ||||
−0.928300 | + | 0.371833i | \(0.878729\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.8178 | −0.902490 | −0.451245 | − | 0.892400i | \(-0.649020\pi\) | ||||
−0.451245 | + | 0.892400i | \(0.649020\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40.8503 | −1.37162 | −0.685810 | − | 0.727781i | \(-0.740552\pi\) | ||||
−0.685810 | + | 0.727781i | \(0.740552\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.9801 | −0.401799 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.53047 | −0.151607 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.54920 | −0.0517841 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.2769 | 0.442809 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.0945 | −0.369613 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.41079 | −0.0468962 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.16440 | −0.304299 | −0.152150 | − | 0.988357i | \(-0.548620\pi\) | ||||
−0.152150 | + | 0.988357i | \(0.548620\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.72553 | 0.255958 | 0.127979 | − | 0.991777i | \(-0.459151\pi\) | ||||
0.127979 | + | 0.991777i | \(0.459151\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 69.4808 | 2.29948 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −27.9534 | −0.923103 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.8924 | 0.788139 | 0.394069 | − | 0.919081i | \(-0.371067\pi\) | ||||
0.394069 | + | 0.919081i | \(0.371067\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.5733 | 0.743009 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.95454 | −0.195784 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.6787 | 0.645636 | 0.322818 | − | 0.946461i | \(-0.395370\pi\) | ||||
0.322818 | + | 0.946461i | \(0.395370\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.350746 | −0.0114952 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.7044 | 0.350072 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52.6536 | −1.72012 | −0.860058 | − | 0.510196i | \(-0.829573\pi\) | ||||
−0.860058 | + | 0.510196i | \(0.829573\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.34001 | 0.141480 | 0.0707401 | − | 0.997495i | \(-0.477464\pi\) | ||||
0.0707401 | + | 0.997495i | \(0.477464\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.98690 | −0.162396 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.0278 | −0.585825 | −0.292912 | − | 0.956139i | \(-0.594624\pi\) | ||||
−0.292912 | + | 0.956139i | \(0.594624\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 57.6391 | 1.87104 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43.3464 | −1.40413 | −0.702064 | − | 0.712113i | \(-0.747738\pi\) | ||||
−0.702064 | + | 0.712113i | \(0.747738\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.5973 | −0.342921 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −31.8691 | −1.02911 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 69.6876 | 2.24799 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.7209 | −0.667028 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.5215 | 1.04582 | 0.522911 | − | 0.852387i | \(-0.324846\pi\) | ||||
0.522911 | + | 0.852387i | \(0.324846\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34.0432 | −1.09250 | −0.546249 | − | 0.837623i | \(-0.683945\pi\) | ||||
−0.546249 | + | 0.837623i | \(0.683945\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 63.7178 | 2.04270 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.8626 | 1.01937 | 0.509687 | − | 0.860360i | \(-0.329761\pi\) | ||||
0.509687 | + | 0.860360i | \(0.329761\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 65.6671 | 2.09873 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.9450 | 0.572357 | 0.286178 | − | 0.958176i | \(-0.407615\pi\) | ||||
0.286178 | + | 0.958176i | \(0.407615\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.8915 | −0.665658 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.57815 | 0.0501822 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.1482 | −1.33888 | −0.669441 | − | 0.742865i | \(-0.733466\pi\) | ||||
−0.669441 | + | 0.742865i | \(0.733466\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.0562 | −0.794334 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.0852 | −1.58622 | −0.793108 | − | 0.609082i | \(-0.791538\pi\) | ||||
−0.793108 | + | 0.609082i | \(0.791538\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 8280.2.a.bw.1.3 | yes | 7 | |
3.2 | odd | 2 | 8280.2.a.bv.1.3 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8280.2.a.bv.1.3 | ✓ | 7 | 3.2 | odd | 2 | ||
8280.2.a.bw.1.3 | yes | 7 | 1.1 | even | 1 | trivial |