Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8820,2,Mod(1,8820)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8820, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8820.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8820 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8820.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: | \(70.4280545828\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.404.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 1260) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.86620\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8820.1 |
$q$-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 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.38350 | −0.718653 | −0.359326 | − | 0.933212i | \(-0.616994\pi\) | ||||
−0.359326 | + | 0.933212i | \(0.616994\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.38350 | 0.383715 | 0.191857 | − | 0.981423i | \(-0.438549\pi\) | ||||
0.191857 | + | 0.981423i | \(0.438549\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.831590 | 0.201690 | 0.100845 | − | 0.994902i | \(-0.467845\pi\) | ||||
0.100845 | + | 0.994902i | \(0.467845\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.21509 | −0.967009 | −0.483504 | − | 0.875342i | \(-0.660636\pi\) | ||||
−0.483504 | + | 0.875342i | \(0.660636\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.59859 | 1.16739 | 0.583694 | − | 0.811974i | \(-0.301607\pi\) | ||||
0.583694 | + | 0.811974i | \(0.301607\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.0467 | −1.86562 | −0.932811 | − | 0.360366i | \(-0.882652\pi\) | ||||
−0.932811 | + | 0.360366i | \(0.882652\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | −0.0898027 | − | 0.995960i | \(-0.528624\pi\) | ||||
−0.0898027 | + | 0.995960i | \(0.528624\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.59859 | 0.756004 | 0.378002 | − | 0.925805i | \(-0.376611\pi\) | ||||
0.378002 | + | 0.925805i | \(0.376611\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.81369 | −1.37647 | −0.688233 | − | 0.725489i | \(-0.741613\pi\) | ||||
−0.688233 | + | 0.725489i | \(0.741613\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.83159 | −0.279315 | −0.139657 | − | 0.990200i | \(-0.544600\pi\) | ||||
−0.139657 | + | 0.990200i | \(0.544600\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.4302 | 1.81313 | 0.906564 | − | 0.422067i | \(-0.138695\pi\) | ||||
0.906564 | + | 0.422067i | \(0.138695\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.66318 | 0.228455 | 0.114228 | − | 0.993455i | \(-0.463561\pi\) | ||||
0.114228 | + | 0.993455i | \(0.463561\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.38350 | −0.321391 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.38350 | −1.09144 | −0.545720 | − | 0.837968i | \(-0.683744\pi\) | ||||
−0.545720 | + | 0.837968i | \(0.683744\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.21509 | 0.667724 | 0.333862 | − | 0.942622i | \(-0.391648\pi\) | ||||
0.333862 | + | 0.942622i | \(0.391648\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.38350 | 0.171602 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.38350 | 0.169022 | 0.0845109 | − | 0.996423i | \(-0.473067\pi\) | ||||
0.0845109 | + | 0.996423i | \(0.473067\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.61650 | −0.429199 | −0.214600 | − | 0.976702i | \(-0.568845\pi\) | ||||
−0.214600 | + | 0.976702i | \(0.568845\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.5986 | −1.47455 | −0.737277 | − | 0.675591i | \(-0.763889\pi\) | ||||
−0.737277 | + | 0.675591i | \(0.763889\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.8783 | −1.33641 | −0.668205 | − | 0.743977i | \(-0.732937\pi\) | ||||
−0.668205 | + | 0.743977i | \(0.732937\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.93541 | 0.431968 | 0.215984 | − | 0.976397i | \(-0.430704\pi\) | ||||
0.215984 | + | 0.976397i | \(0.430704\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.831590 | 0.0901986 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.720322 | 0.0763540 | 0.0381770 | − | 0.999271i | \(-0.487845\pi\) | ||||
0.0381770 | + | 0.999271i | \(0.487845\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.21509 | −0.432459 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.44809 | −0.248566 | −0.124283 | − | 0.992247i | \(-0.539663\pi\) | ||||
−0.124283 | + | 0.992247i | \(0.539663\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.1505 | −1.30852 | −0.654262 | − | 0.756268i | \(-0.727021\pi\) | ||||
−0.654262 | + | 0.756268i | \(0.727021\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.26178 | 0.616991 | 0.308496 | − | 0.951226i | \(-0.400175\pi\) | ||||
0.308496 | + | 0.951226i | \(0.400175\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.5986 | −1.12128 | −0.560639 | − | 0.828060i | \(-0.689445\pi\) | ||||
−0.560639 | + | 0.828060i | \(0.689445\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.9821 | 1.24346 | 0.621730 | − | 0.783232i | \(-0.286430\pi\) | ||||
0.621730 | + | 0.783232i | \(0.286430\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.7670 | −1.57731 | −0.788654 | − | 0.614838i | \(-0.789221\pi\) | ||||
−0.788654 | + | 0.614838i | \(0.789221\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.59859 | 0.522072 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.31892 | −0.483538 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.8137 | 1.22577 | 0.612883 | − | 0.790173i | \(-0.290010\pi\) | ||||
0.612883 | + | 0.790173i | \(0.290010\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.23300 | 0.107727 | 0.0538637 | − | 0.998548i | \(-0.482846\pi\) | ||||
0.0538637 | + | 0.998548i | \(0.482846\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.401405 | −0.0342944 | −0.0171472 | − | 0.999853i | \(-0.505458\pi\) | ||||
−0.0171472 | + | 0.999853i | \(0.505458\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.888732 | −0.0753812 | −0.0376906 | − | 0.999289i | \(-0.512000\pi\) | ||||
−0.0376906 | + | 0.999289i | \(0.512000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.29758 | −0.275758 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.0467 | −0.834332 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.7491 | −1.36302 | −0.681511 | − | 0.731808i | \(-0.738677\pi\) | ||||
−0.681511 | + | 0.731808i | \(0.738677\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.66318 | 0.292354 | 0.146177 | − | 0.989258i | \(-0.453303\pi\) | ||||
0.146177 | + | 0.989258i | \(0.453303\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.0934 | 1.26053 | 0.630265 | − | 0.776380i | \(-0.282946\pi\) | ||||
0.630265 | + | 0.776380i | \(0.282946\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.5986 | 0.897526 | 0.448763 | − | 0.893651i | \(-0.351865\pi\) | ||||
0.448763 | + | 0.893651i | \(0.351865\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0859 | −0.852763 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.4302 | 0.945049 | 0.472525 | − | 0.881317i | \(-0.343343\pi\) | ||||
0.472525 | + | 0.881317i | \(0.343343\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.10382 | 0.231991 | 0.115995 | − | 0.993250i | \(-0.462994\pi\) | ||||
0.115995 | + | 0.993250i | \(0.462994\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.98210 | −0.221658 | −0.110829 | − | 0.993840i | \(-0.535351\pi\) | ||||
−0.110829 | + | 0.993840i | \(0.535351\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.59859 | 0.338095 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.98210 | −0.144945 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.1038 | −1.09287 | −0.546437 | − | 0.837500i | \(-0.684016\pi\) | ||||
−0.546437 | + | 0.837500i | \(0.684016\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.7958 | −1.28097 | −0.640484 | − | 0.767971i | \(-0.721266\pi\) | ||||
−0.640484 | + | 0.767971i | \(0.721266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.1684 | −1.22320 | −0.611599 | − | 0.791168i | \(-0.709474\pi\) | ||||
−0.611599 | + | 0.791168i | \(0.709474\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.7491 | 1.47086 | 0.735432 | − | 0.677598i | \(-0.236979\pi\) | ||||
0.735432 | + | 0.677598i | \(0.236979\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.81369 | −0.615575 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.0467 | 0.694944 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.12173 | 0.214909 | 0.107454 | − | 0.994210i | \(-0.465730\pi\) | ||||
0.107454 | + | 0.994210i | \(0.465730\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.83159 | −0.124913 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.15051 | 0.0773915 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.32636 | −0.490609 | −0.245305 | − | 0.969446i | \(-0.578888\pi\) | ||||
−0.245305 | + | 0.969446i | \(0.578888\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.2618 | −1.67668 | −0.838341 | − | 0.545145i | \(-0.816474\pi\) | ||||
−0.838341 | + | 0.545145i | \(0.816474\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.3264 | −0.682385 | −0.341193 | − | 0.939993i | \(-0.610831\pi\) | ||||
−0.341193 | + | 0.939993i | \(0.610831\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.0934 | −1.70943 | −0.854717 | − | 0.519095i | \(-0.826269\pi\) | ||||
−0.854717 | + | 0.519095i | \(0.826269\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.4302 | 0.810856 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.86037 | 0.443760 | 0.221880 | − | 0.975074i | \(-0.428781\pi\) | ||||
0.221880 | + | 0.975074i | \(0.428781\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.87827 | −0.185406 | −0.0927029 | − | 0.995694i | \(-0.529551\pi\) | ||||
−0.0927029 | + | 0.995694i | \(0.529551\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.83159 | −0.371055 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.1400 | 1.52371 | 0.761853 | − | 0.647750i | \(-0.224290\pi\) | ||||
0.761853 | + | 0.647750i | \(0.224290\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.3443 | −0.838947 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.4590 | −1.52571 | −0.762854 | − | 0.646571i | \(-0.776203\pi\) | ||||
−0.762854 | + | 0.646571i | \(0.776203\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.8604 | −1.16298 | −0.581490 | − | 0.813553i | \(-0.697530\pi\) | ||||
−0.581490 | + | 0.813553i | \(0.697530\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.66318 | 0.102168 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.19719 | 0.316878 | 0.158439 | − | 0.987369i | \(-0.449354\pi\) | ||||
0.158439 | + | 0.987369i | \(0.449354\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.9821 | 1.69979 | 0.849896 | − | 0.526951i | \(-0.176665\pi\) | ||||
0.849896 | + | 0.526951i | \(0.176665\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.38350 | −0.143731 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.16841 | −0.370624 | −0.185312 | − | 0.982680i | \(-0.559330\pi\) | ||||
−0.185312 | + | 0.982680i | \(0.559330\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.5698 | −0.690197 | −0.345099 | − | 0.938566i | \(-0.612155\pi\) | ||||
−0.345099 | + | 0.938566i | \(0.612155\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.7958 | −1.77118 | −0.885588 | − | 0.464472i | \(-0.846244\pi\) | ||||
−0.885588 | + | 0.464472i | \(0.846244\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3085 | −0.959321 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.6632 | 1.14874 | 0.574368 | − | 0.818597i | \(-0.305248\pi\) | ||||
0.574368 | + | 0.818597i | \(0.305248\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.38350 | −0.488106 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.74567 | 0.447944 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.21509 | 0.298615 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.8137 | 1.13083 | 0.565413 | − | 0.824808i | \(-0.308717\pi\) | ||||
0.565413 | + | 0.824808i | \(0.308717\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.0467 | −1.25015 | −0.625076 | − | 0.780564i | \(-0.714932\pi\) | ||||
−0.625076 | + | 0.780564i | \(0.714932\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.5052 | −0.593791 | −0.296895 | − | 0.954910i | \(-0.595951\pi\) | ||||
−0.296895 | + | 0.954910i | \(0.595951\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.73822 | −0.266125 | −0.133063 | − | 0.991108i | \(-0.542481\pi\) | ||||
−0.133063 | + | 0.991108i | \(0.542481\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.9463 | 1.34073 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.50523 | −0.195036 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.38350 | 0.0767429 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.8604 | 0.981695 | 0.490847 | − | 0.871246i | \(-0.336687\pi\) | ||||
0.490847 | + | 0.871246i | \(0.336687\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.38350 | 0.0755888 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.4769 | −0.625185 | −0.312592 | − | 0.949887i | \(-0.601197\pi\) | ||||
−0.312592 | + | 0.949887i | \(0.601197\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.38350 | 0.129074 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.56982 | 0.299003 | 0.149502 | − | 0.988761i | \(-0.452233\pi\) | ||||
0.149502 | + | 0.988761i | \(0.452233\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.66318 | 0.196086 | 0.0980428 | − | 0.995182i | \(-0.468742\pi\) | ||||
0.0980428 | + | 0.995182i | \(0.468742\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.401405 | −0.0213646 | −0.0106823 | − | 0.999943i | \(-0.503400\pi\) | ||||
−0.0106823 | + | 0.999943i | \(0.503400\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.61650 | −0.191944 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.8137 | −1.41517 | −0.707586 | − | 0.706627i | \(-0.750216\pi\) | ||||
−0.707586 | + | 0.706627i | \(0.750216\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.23300 | −0.0648945 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.5986 | −0.659441 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.523132 | 0.0273073 | 0.0136536 | − | 0.999907i | \(-0.495654\pi\) | ||||
0.0136536 | + | 0.999907i | \(0.495654\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.2439 | 1.66952 | 0.834762 | − | 0.550611i | \(-0.185605\pi\) | ||||
0.834762 | + | 0.550611i | \(0.185605\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.8996 | −0.715866 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.5236 | 1.00286 | 0.501429 | − | 0.865199i | \(-0.332808\pi\) | ||||
0.501429 | + | 0.865199i | \(0.332808\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.802810 | 0.0410217 | 0.0205108 | − | 0.999790i | \(-0.493471\pi\) | ||||
0.0205108 | + | 0.999790i | \(0.493471\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −29.9175 | −1.51688 | −0.758439 | − | 0.651744i | \(-0.774038\pi\) | ||||
−0.758439 | + | 0.651744i | \(0.774038\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.65574 | 0.235451 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.8783 | −0.597661 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.4590 | 1.47850 | 0.739252 | − | 0.673429i | \(-0.235179\pi\) | ||||
0.739252 | + | 0.673429i | \(0.235179\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.5236 | −1.32452 | −0.662261 | − | 0.749273i | \(-0.730403\pi\) | ||||
−0.662261 | + | 0.749273i | \(0.730403\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.38350 | −0.0689172 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.9608 | −0.543305 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.5236 | 1.55874 | 0.779370 | − | 0.626564i | \(-0.215539\pi\) | ||||
0.779370 | + | 0.626564i | \(0.215539\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.93541 | 0.193182 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.802810 | 0.0392199 | 0.0196099 | − | 0.999808i | \(-0.493758\pi\) | ||||
0.0196099 | + | 0.999808i | \(0.493758\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.8425 | 1.84433 | 0.922164 | − | 0.386798i | \(-0.126419\pi\) | ||||
0.922164 | + | 0.386798i | \(0.126419\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.831590 | 0.0403380 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.1972 | 0.828359 | 0.414180 | − | 0.910195i | \(-0.364068\pi\) | ||||
0.414180 | + | 0.910195i | \(0.364068\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.1505 | 0.583916 | 0.291958 | − | 0.956431i | \(-0.405693\pi\) | ||||
0.291958 | + | 0.956431i | \(0.405693\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −23.5986 | −1.12887 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.2727 | −1.49256 | −0.746281 | − | 0.665631i | \(-0.768163\pi\) | ||||
−0.746281 | + | 0.665631i | \(0.768163\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.86037 | 0.325946 | 0.162973 | − | 0.986631i | \(-0.447892\pi\) | ||||
0.162973 | + | 0.986631i | \(0.447892\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.720322 | 0.0341465 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.1038 | −1.27911 | −0.639554 | − | 0.768746i | \(-0.720881\pi\) | ||||
−0.639554 | + | 0.768746i | \(0.720881\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.0074 | 0.989202 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.8137 | 0.926845 | 0.463423 | − | 0.886137i | \(-0.346621\pi\) | ||||
0.463423 | + | 0.886137i | \(0.346621\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.82415 | 0.178108 | 0.0890541 | − | 0.996027i | \(-0.471616\pi\) | ||||
0.0890541 | + | 0.996027i | \(0.471616\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.95332 | −0.416096 | −0.208048 | − | 0.978119i | \(-0.566711\pi\) | ||||
−0.208048 | + | 0.978119i | \(0.566711\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.3368 | 0.478331 | 0.239165 | − | 0.970979i | \(-0.423126\pi\) | ||||
0.239165 | + | 0.970979i | \(0.423126\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.36560 | 0.200730 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.21509 | −0.193402 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −40.3944 | −1.84567 | −0.922833 | − | 0.385200i | \(-0.874132\pi\) | ||||
−0.922833 | + | 0.385200i | \(0.874132\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.36217 | 0.290090 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.44809 | −0.111162 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.1400 | −0.595432 | −0.297716 | − | 0.954654i | \(-0.596225\pi\) | ||||
−0.297716 | + | 0.954654i | \(0.596225\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.1972 | −0.776098 | −0.388049 | − | 0.921639i | \(-0.626851\pi\) | ||||
−0.388049 | + | 0.921639i | \(0.626851\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.35472 | −0.376278 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.66318 | −0.119220 | −0.0596102 | − | 0.998222i | \(-0.518986\pi\) | ||||
−0.0596102 | + | 0.998222i | \(0.518986\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.0000 | −0.535054 | −0.267527 | − | 0.963550i | \(-0.586206\pi\) | ||||
−0.267527 | + | 0.963550i | \(0.586206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.1505 | −0.585190 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.0576 | 1.06633 | 0.533166 | − | 0.846010i | \(-0.321002\pi\) | ||||
0.533166 | + | 0.846010i | \(0.321002\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.26178 | 0.275927 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −29.6274 | −1.30301 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.6274 | 0.772269 | 0.386135 | − | 0.922442i | \(-0.373810\pi\) | ||||
0.386135 | + | 0.922442i | \(0.373810\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.1863 | −0.707778 | −0.353889 | − | 0.935287i | \(-0.615141\pi\) | ||||
−0.353889 | + | 0.935287i | \(0.615141\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.831590 | −0.0362246 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.34426 | 0.362794 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.1938 | −0.528170 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.5986 | −0.501451 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.5594 | −0.754936 | −0.377468 | − | 0.926023i | \(-0.623205\pi\) | ||||
−0.377468 | + | 0.926023i | \(0.623205\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.9821 | 0.556092 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.96419 | −0.340524 | −0.170262 | − | 0.985399i | \(-0.554461\pi\) | ||||
−0.170262 | + | 0.985399i | \(0.554461\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42.3477 | 1.80407 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.5340 | −1.16665 | −0.583327 | − | 0.812238i | \(-0.698249\pi\) | ||||
−0.583327 | + | 0.812238i | \(0.698249\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.53401 | −0.107177 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.9747 | −0.968266 | −0.484133 | − | 0.874994i | \(-0.660865\pi\) | ||||
−0.484133 | + | 0.874994i | \(0.660865\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.7670 | −0.705393 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.24387 | 0.135990 | 0.0679951 | − | 0.997686i | \(-0.478340\pi\) | ||||
0.0679951 | + | 0.997686i | \(0.478340\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.2151 | −1.18076 | −0.590382 | − | 0.807124i | \(-0.701023\pi\) | ||||
−0.590382 | + | 0.807124i | \(0.701023\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.59859 | 0.233478 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.4769 | −0.727572 | −0.363786 | − | 0.931483i | \(-0.618516\pi\) | ||||
−0.363786 | + | 0.931483i | \(0.618516\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.96419 | −0.164180 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.1580 | −0.419264 | −0.209632 | − | 0.977780i | \(-0.567227\pi\) | ||||
−0.209632 | + | 0.977780i | \(0.567227\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.21509 | 0.173680 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.39095 | −0.221380 | −0.110690 | − | 0.993855i | \(-0.535306\pi\) | ||||
−0.110690 | + | 0.993855i | \(0.535306\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.9895 | 0.939327 | 0.469664 | − | 0.882845i | \(-0.344375\pi\) | ||||
0.469664 | + | 0.882845i | \(0.344375\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.2727 | 1.56117 | 0.780587 | − | 0.625047i | \(-0.214920\pi\) | ||||
0.780587 | + | 0.625047i | \(0.214920\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.31892 | −0.216245 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.7203 | 0.475713 | 0.237857 | − | 0.971300i | \(-0.423555\pi\) | ||||
0.237857 | + | 0.971300i | \(0.423555\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.1972 | 0.695724 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.9821 | 1.13019 | 0.565093 | − | 0.825027i | \(-0.308840\pi\) | ||||
0.565093 | + | 0.825027i | \(0.308840\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.0680 | −1.25075 | −0.625376 | − | 0.780324i | \(-0.715054\pi\) | ||||
−0.625376 | + | 0.780324i | \(0.715054\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.30101 | 0.293453 | 0.146726 | − | 0.989177i | \(-0.453126\pi\) | ||||
0.146726 | + | 0.989177i | \(0.453126\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.82415 | 0.152479 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.4877 | −0.895223 | −0.447611 | − | 0.894228i | \(-0.647725\pi\) | ||||
−0.447611 | + | 0.894228i | \(0.647725\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.8137 | 0.548179 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −44.0109 | −1.73833 | −0.869163 | − | 0.494526i | \(-0.835341\pi\) | ||||
−0.869163 | + | 0.494526i | \(0.835341\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.1863 | −0.401709 | −0.200854 | − | 0.979621i | \(-0.564372\pi\) | ||||
−0.200854 | + | 0.979621i | \(0.564372\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.5523 | 1.27976 | 0.639882 | − | 0.768473i | \(-0.278983\pi\) | ||||
0.639882 | + | 0.768473i | \(0.278983\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.9821 | 0.784366 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.9250 | 0.818857 | 0.409428 | − | 0.912342i | \(-0.365728\pi\) | ||||
0.409428 | + | 0.912342i | \(0.365728\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.23300 | 0.0481771 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.7207 | −1.46939 | −0.734696 | − | 0.678397i | \(-0.762675\pi\) | ||||
−0.734696 | + | 0.678397i | \(0.762675\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.22555 | 0.358832 | 0.179416 | − | 0.983773i | \(-0.442579\pi\) | ||||
0.179416 | + | 0.983773i | \(0.442579\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −56.2473 | −2.17790 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.4302 | −0.479862 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.2797 | −1.16720 | −0.583598 | − | 0.812043i | \(-0.698356\pi\) | ||||
−0.583598 | + | 0.812043i | \(0.698356\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.7853 | 1.29848 | 0.649238 | − | 0.760586i | \(-0.275088\pi\) | ||||
0.649238 | + | 0.760586i | \(0.275088\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.1326 | 1.26778 | 0.633892 | − | 0.773422i | \(-0.281456\pi\) | ||||
0.633892 | + | 0.773422i | \(0.281456\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.401405 | −0.0153369 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.30101 | 0.0876616 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.9642 | 1.71052 | 0.855259 | − | 0.518200i | \(-0.173398\pi\) | ||||
0.855259 | + | 0.518200i | \(0.173398\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.888732 | −0.0337115 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.32938 | −0.277620 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.5702 | −1.60786 | −0.803928 | − | 0.594727i | \(-0.797260\pi\) | ||||
−0.803928 | + | 0.594727i | \(0.797260\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.3835 | −0.731063 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.2046 | 0.383243 | 0.191622 | − | 0.981469i | \(-0.438625\pi\) | ||||
0.191622 | + | 0.981469i | \(0.438625\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.59859 | −0.209669 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.29758 | −0.123323 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.09337 | −0.0780694 | −0.0390347 | − | 0.999238i | \(-0.512428\pi\) | ||||
−0.0390347 | + | 0.999238i | \(0.512428\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.0467 | −0.373124 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.8211 | 1.29144 | 0.645722 | − | 0.763572i | \(-0.276556\pi\) | ||||
0.645722 | + | 0.763572i | \(0.276556\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.52313 | −0.0563351 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −47.4769 | −1.75360 | −0.876799 | − | 0.480857i | \(-0.840326\pi\) | ||||
−0.876799 | + | 0.480857i | \(0.840326\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.29758 | −0.121468 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.2727 | −1.48145 | −0.740727 | − | 0.671806i | \(-0.765519\pi\) | ||||
−0.740727 | + | 0.671806i | \(0.765519\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.7853 | −1.01934 | −0.509672 | − | 0.860369i | \(-0.670233\pi\) | ||||
−0.509672 | + | 0.860369i | \(0.670233\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.00000 | −0.219823 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.80281 | −0.0657855 | −0.0328927 | − | 0.999459i | \(-0.510472\pi\) | ||||
−0.0328927 | + | 0.999459i | \(0.510472\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.7491 | −0.609562 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.8708 | 0.794909 | 0.397454 | − | 0.917622i | \(-0.369894\pi\) | ||||
0.397454 | + | 0.917622i | \(0.369894\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.0467 | −0.799192 | −0.399596 | − | 0.916691i | \(-0.630850\pi\) | ||||
−0.399596 | + | 0.916691i | \(0.630850\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.5986 | −0.418801 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.2727 | −1.01954 | −0.509769 | − | 0.860311i | \(-0.670269\pi\) | ||||
−0.509769 | + | 0.860311i | \(0.670269\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39.9930 | −1.43845 | −0.719224 | − | 0.694779i | \(-0.755502\pi\) | ||||
−0.719224 | + | 0.694779i | \(0.755502\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 37.1505 | 1.33106 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.61993 | 0.308445 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.66318 | 0.130745 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.1614 | 1.25337 | 0.626684 | − | 0.779273i | \(-0.284412\pi\) | ||||
0.626684 | + | 0.779273i | \(0.284412\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.21509 | 0.256215 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 49.0968 | 1.73910 | 0.869549 | − | 0.493847i | \(-0.164410\pi\) | ||||
0.869549 | + | 0.493847i | \(0.164410\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.3368 | 0.365690 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.0288 | 1.05969 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.2906 | 0.467271 | 0.233636 | − | 0.972324i | \(-0.424938\pi\) | ||||
0.233636 | + | 0.972324i | \(0.424938\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.9358 | −1.57791 | −0.788955 | − | 0.614451i | \(-0.789378\pi\) | ||||
−0.788955 | + | 0.614451i | \(0.789378\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.0934 | 0.563726 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.72032 | 0.270100 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.4411 | 0.503997 | 0.251998 | − | 0.967728i | \(-0.418912\pi\) | ||||
0.251998 | + | 0.967728i | \(0.418912\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.1113 | 0.910182 | 0.455091 | − | 0.890445i | \(-0.349607\pi\) | ||||
0.455091 | + | 0.890445i | \(0.349607\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.5236 | 1.13095 | 0.565477 | − | 0.824764i | \(-0.308692\pi\) | ||||
0.565477 | + | 0.824764i | \(0.308692\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.0397 | −1.35590 | −0.677952 | − | 0.735106i | \(-0.737132\pi\) | ||||
−0.677952 | + | 0.735106i | \(0.737132\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.5986 | 0.401386 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.7099 | −1.23284 | −0.616421 | − | 0.787417i | \(-0.711418\pi\) | ||||
−0.616421 | + | 0.787417i | \(0.711418\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 71.9358 | 2.48055 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.0859 | −0.381367 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.7457 | 0.882550 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.0968 | −1.50985 | −0.754923 | − | 0.655814i | \(-0.772326\pi\) | ||||
−0.754923 | + | 0.655814i | \(0.772326\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.30804 | 0.147160 | 0.0735799 | − | 0.997289i | \(-0.476558\pi\) | ||||
0.0735799 | + | 0.997289i | \(0.476558\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.2727 | 0.794053 | 0.397026 | − | 0.917807i | \(-0.370042\pi\) | ||||
0.397026 | + | 0.917807i | \(0.370042\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −54.9179 | −1.86943 | −0.934714 | − | 0.355401i | \(-0.884344\pi\) | ||||
−0.934714 | + | 0.355401i | \(0.884344\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.4302 | 0.422639 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.3119 | 0.960415 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.91408 | 0.0648561 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.09337 | −0.205758 | −0.102879 | − | 0.994694i | \(-0.532805\pi\) | ||||
−0.102879 | + | 0.994694i | \(0.532805\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.3264 | 0.718503 | 0.359252 | − | 0.933241i | \(-0.383032\pi\) | ||||
0.359252 | + | 0.933241i | \(0.383032\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.3761 | −0.820320 | −0.410160 | − | 0.912014i | \(-0.634527\pi\) | ||||
−0.410160 | + | 0.912014i | \(0.634527\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.3298 | 1.48845 | 0.744224 | − | 0.667930i | \(-0.232819\pi\) | ||||
0.744224 | + | 0.667930i | \(0.232819\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −52.3944 | −1.75331 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.10382 | 0.103749 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.0467 | 0.335076 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.38308 | 0.0460772 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.98210 | −0.0991283 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.5986 | 0.351921 | 0.175960 | − | 0.984397i | \(-0.443697\pi\) | ||||
0.175960 | + | 0.984397i | \(0.443697\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.1400 | 0.799795 | 0.399898 | − | 0.916560i | \(-0.369046\pi\) | ||||
0.399898 | + | 0.916560i | \(0.369046\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.38007 | −0.310435 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.98954 | 0.329525 | 0.164762 | − | 0.986333i | \(-0.447314\pi\) | ||||
0.164762 | + | 0.986333i | \(0.447314\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.00343 | −0.164690 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.59859 | 0.151201 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.6741 | −1.49852 | −0.749259 | − | 0.662278i | \(-0.769590\pi\) | ||||
−0.749259 | + | 0.662278i | \(0.769590\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.98210 | −0.0648215 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.4948 | −0.506192 | −0.253096 | − | 0.967441i | \(-0.581449\pi\) | ||||
−0.253096 | + | 0.967441i | \(0.581449\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.8032 | −0.645567 | −0.322783 | − | 0.946473i | \(-0.604619\pi\) | ||||
−0.322783 | + | 0.946473i | \(0.604619\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −49.3443 | −1.60687 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.1580 | −0.330089 | −0.165045 | − | 0.986286i | \(-0.552777\pi\) | ||||
−0.165045 | + | 0.986286i | \(0.552777\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.4302 | −0.565808 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.09337 | 0.262170 | 0.131085 | − | 0.991371i | \(-0.458154\pi\) | ||||
0.131085 | + | 0.991371i | \(0.458154\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.1038 | −0.488748 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0000 | −0.967742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.7958 | −0.572867 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.2513 | 0.940659 | 0.470329 | − | 0.882491i | \(-0.344135\pi\) | ||||
0.470329 | + | 0.882491i | \(0.344135\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.3944 | −0.526121 | −0.263060 | − | 0.964779i | \(-0.584732\pi\) | ||||
−0.263060 | + | 0.964779i | \(0.584732\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.0968 | 0.994875 | 0.497437 | − | 0.867500i | \(-0.334274\pi\) | ||||
0.497437 | + | 0.867500i | \(0.334274\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.71689 | −0.0548720 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.36560 | −0.139241 | −0.0696205 | − | 0.997574i | \(-0.522179\pi\) | ||||
−0.0696205 | + | 0.997574i | \(0.522179\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.1684 | −0.547031 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.2543 | −0.326069 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.2980 | 0.867150 | 0.433575 | − | 0.901118i | \(-0.357252\pi\) | ||||
0.433575 | + | 0.901118i | \(0.357252\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.7491 | 0.657791 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.4843 | 0.965448 | 0.482724 | − | 0.875773i | \(-0.339647\pi\) | ||||
0.482724 | + | 0.875773i | \(0.339647\pi\) | |||||||
\(998\) | 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 | 8820.2.a.bq.1.1 | 3 | ||
3.2 | odd | 2 | 8820.2.a.bn.1.3 | 3 | |||
7.2 | even | 3 | 1260.2.s.g.361.1 | ✓ | 6 | ||
7.4 | even | 3 | 1260.2.s.g.541.1 | yes | 6 | ||
7.6 | odd | 2 | 8820.2.a.bo.1.1 | 3 | |||
21.2 | odd | 6 | 1260.2.s.h.361.1 | yes | 6 | ||
21.11 | odd | 6 | 1260.2.s.h.541.1 | yes | 6 | ||
21.20 | even | 2 | 8820.2.a.bp.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1260.2.s.g.361.1 | ✓ | 6 | 7.2 | even | 3 | ||
1260.2.s.g.541.1 | yes | 6 | 7.4 | even | 3 | ||
1260.2.s.h.361.1 | yes | 6 | 21.2 | odd | 6 | ||
1260.2.s.h.541.1 | yes | 6 | 21.11 | odd | 6 | ||
8820.2.a.bn.1.3 | 3 | 3.2 | odd | 2 | |||
8820.2.a.bo.1.1 | 3 | 7.6 | odd | 2 | |||
8820.2.a.bp.1.3 | 3 | 21.20 | even | 2 | |||
8820.2.a.bq.1.1 | 3 | 1.1 | even | 1 | trivial |