Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9360,2,Mod(1,9360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9360, 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("9360.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9360 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9360.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: | \(74.7399762919\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 585) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9360.1 |
$q$-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 | ||||||||
\(7\) | 4.56155 | 1.72410 | 0.862052 | − | 0.506819i | \(-0.169179\pi\) | ||||
0.862052 | + | 0.506819i | \(0.169179\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.56155 | −0.772337 | −0.386169 | − | 0.922428i | \(-0.626202\pi\) | ||||
−0.386169 | + | 0.922428i | \(0.626202\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.56155 | −0.621268 | −0.310634 | − | 0.950530i | \(-0.600541\pi\) | ||||
−0.310634 | + | 0.950530i | \(0.600541\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.12311 | −0.716490 | −0.358245 | − | 0.933628i | \(-0.616625\pi\) | ||||
−0.358245 | + | 0.933628i | \(0.616625\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.56155 | −1.36818 | −0.684089 | − | 0.729398i | \(-0.739800\pi\) | ||||
−0.684089 | + | 0.729398i | \(0.739800\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.12311 | 0.208555 | 0.104278 | − | 0.994548i | \(-0.466747\pi\) | ||||
0.104278 | + | 0.994548i | \(0.466747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.56155 | 0.771043 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.68466 | 0.276956 | 0.138478 | − | 0.990366i | \(-0.455779\pi\) | ||||
0.138478 | + | 0.990366i | \(0.455779\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.561553 | −0.0876998 | −0.0438499 | − | 0.999038i | \(-0.513962\pi\) | ||||
−0.0438499 | + | 0.999038i | \(0.513962\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.12311 | 0.781266 | 0.390633 | − | 0.920546i | \(-0.372256\pi\) | ||||
0.390633 | + | 0.920546i | \(0.372256\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.87689 | −0.419638 | −0.209819 | − | 0.977740i | \(-0.567288\pi\) | ||||
−0.209819 | + | 0.977740i | \(0.567288\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.8078 | 1.97254 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.68466 | 1.05557 | 0.527785 | − | 0.849378i | \(-0.323023\pi\) | ||||
0.527785 | + | 0.849378i | \(0.323023\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.56155 | −0.345400 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.0000 | −1.56227 | −0.781133 | − | 0.624364i | \(-0.785358\pi\) | ||||
−0.781133 | + | 0.624364i | \(0.785358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.68466 | 0.727846 | 0.363923 | − | 0.931429i | \(-0.381437\pi\) | ||||
0.363923 | + | 0.931429i | \(0.381437\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.3693 | −1.63332 | −0.816661 | − | 0.577118i | \(-0.804177\pi\) | ||||
−0.816661 | + | 0.577118i | \(0.804177\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.5616 | −1.72814 | −0.864069 | − | 0.503373i | \(-0.832092\pi\) | ||||
−0.864069 | + | 0.503373i | \(0.832092\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.6847 | −1.33159 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.68466 | 0.864592 | 0.432296 | − | 0.901732i | \(-0.357704\pi\) | ||||
0.432296 | + | 0.901732i | \(0.357704\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.4924 | −1.81028 | −0.905139 | − | 0.425115i | \(-0.860234\pi\) | ||||
−0.905139 | + | 0.425115i | \(0.860234\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.56155 | −0.277839 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.68466 | −0.178573 | −0.0892867 | − | 0.996006i | \(-0.528459\pi\) | ||||
−0.0892867 | + | 0.996006i | \(0.528459\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.56155 | −0.478181 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.12311 | −0.320424 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.9309 | −1.21140 | −0.605698 | − | 0.795695i | \(-0.707106\pi\) | ||||
−0.605698 | + | 0.795695i | \(0.707106\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.24621 | −0.621521 | −0.310761 | − | 0.950488i | \(-0.600584\pi\) | ||||
−0.310761 | + | 0.950488i | \(0.600584\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.87689 | 0.677601 | 0.338800 | − | 0.940858i | \(-0.389979\pi\) | ||||
0.338800 | + | 0.940858i | \(0.389979\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.9309 | 1.73344 | 0.866721 | − | 0.498793i | \(-0.166223\pi\) | ||||
0.866721 | + | 0.498793i | \(0.166223\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.1231 | −1.23452 | −0.617259 | − | 0.786760i | \(-0.711757\pi\) | ||||
−0.617259 | + | 0.786760i | \(0.711757\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.56155 | −0.611868 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.6847 | −1.07113 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.43845 | −0.403495 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.2462 | −1.61909 | −0.809545 | − | 0.587058i | \(-0.800286\pi\) | ||||
−0.809545 | + | 0.587058i | \(0.800286\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.2462 | −1.23530 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.12311 | −0.608568 | −0.304284 | − | 0.952581i | \(-0.598417\pi\) | ||||
−0.304284 | + | 0.952581i | \(0.598417\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.6847 | −1.33036 | −0.665178 | − | 0.746685i | \(-0.731644\pi\) | ||||
−0.665178 | + | 0.746685i | \(0.731644\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.56155 | 0.214208 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.12311 | 0.0932688 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.80776 | 0.230021 | 0.115010 | − | 0.993364i | \(-0.463310\pi\) | ||||
0.115010 | + | 0.993364i | \(0.463310\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.3693 | 1.08798 | 0.543990 | − | 0.839092i | \(-0.316913\pi\) | ||||
0.543990 | + | 0.839092i | \(0.316913\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.3693 | −1.70546 | −0.852729 | − | 0.522354i | \(-0.825054\pi\) | ||||
−0.852729 | + | 0.522354i | \(0.825054\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −29.9309 | −2.35888 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.0540 | 1.64907 | 0.824537 | − | 0.565808i | \(-0.191436\pi\) | ||||
0.824537 | + | 0.565808i | \(0.191436\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.1231 | −1.01550 | −0.507748 | − | 0.861506i | \(-0.669522\pi\) | ||||
−0.507748 | + | 0.861506i | \(0.669522\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.1231 | 1.60596 | 0.802980 | − | 0.596006i | \(-0.203247\pi\) | ||||
0.802980 | + | 0.596006i | \(0.203247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.56155 | 0.344821 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.1231 | 0.980867 | 0.490433 | − | 0.871479i | \(-0.336838\pi\) | ||||
0.490433 | + | 0.871479i | \(0.336838\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.6847 | 1.90913 | 0.954563 | − | 0.298010i | \(-0.0963228\pi\) | ||||
0.954563 | + | 0.298010i | \(0.0963228\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.68466 | 0.123859 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.56155 | 0.479828 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.6155 | 1.56404 | 0.782022 | − | 0.623250i | \(-0.214188\pi\) | ||||
0.782022 | + | 0.623250i | \(0.214188\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.4384 | 1.11128 | 0.555642 | − | 0.831422i | \(-0.312473\pi\) | ||||
0.555642 | + | 0.831422i | \(0.312473\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.3693 | 1.52250 | 0.761250 | − | 0.648458i | \(-0.224586\pi\) | ||||
0.761250 | + | 0.648458i | \(0.224586\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.12311 | 0.359572 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.561553 | −0.0392205 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.2462 | 0.705378 | 0.352689 | − | 0.935741i | \(-0.385267\pi\) | ||||
0.352689 | + | 0.935741i | \(0.385267\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.12311 | 0.349393 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −27.3693 | −1.85795 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.56155 | 0.172309 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.36932 | −0.627416 | −0.313708 | − | 0.949520i | \(-0.601571\pi\) | ||||
−0.313708 | + | 0.949520i | \(0.601571\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.2462 | −1.47653 | −0.738266 | − | 0.674509i | \(-0.764355\pi\) | ||||
−0.738266 | + | 0.674509i | \(0.764355\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.87689 | 0.586602 | 0.293301 | − | 0.956020i | \(-0.405246\pi\) | ||||
0.293301 | + | 0.956020i | \(0.405246\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.19224 | −0.471179 | −0.235590 | − | 0.971853i | \(-0.575702\pi\) | ||||
−0.235590 | + | 0.971853i | \(0.575702\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.87689 | −0.187668 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.93087 | 0.383636 | 0.191818 | − | 0.981431i | \(-0.438562\pi\) | ||||
0.191818 | + | 0.981431i | \(0.438562\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.7386 | −1.59356 | −0.796778 | − | 0.604272i | \(-0.793464\pi\) | ||||
−0.796778 | + | 0.604272i | \(0.793464\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.8078 | 0.882146 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.12311 | 0.198718 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.75379 | −0.615654 | −0.307827 | − | 0.951442i | \(-0.599602\pi\) | ||||
−0.307827 | + | 0.951442i | \(0.599602\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.8078 | 1.05670 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.1231 | −1.31762 | −0.658812 | − | 0.752308i | \(-0.728941\pi\) | ||||
−0.658812 | + | 0.752308i | \(0.728941\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.68466 | 0.477501 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.2462 | −0.878459 | −0.439230 | − | 0.898375i | \(-0.644749\pi\) | ||||
−0.439230 | + | 0.898375i | \(0.644749\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.68466 | 0.472065 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.12311 | −0.556246 | −0.278123 | − | 0.960546i | \(-0.589712\pi\) | ||||
−0.278123 | + | 0.960546i | \(0.589712\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.36932 | −0.326163 | −0.163081 | − | 0.986613i | \(-0.552143\pi\) | ||||
−0.163081 | + | 0.986613i | \(0.552143\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.56155 | −0.154467 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.24621 | 0.255130 | 0.127565 | − | 0.991830i | \(-0.459284\pi\) | ||||
0.127565 | + | 0.991830i | \(0.459284\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.2462 | −0.730548 | −0.365274 | − | 0.930900i | \(-0.619025\pi\) | ||||
−0.365274 | + | 0.930900i | \(0.619025\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000 | 0.237775 | 0.118888 | − | 0.992908i | \(-0.462067\pi\) | ||||
0.118888 | + | 0.992908i | \(0.462067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.56155 | −0.151204 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.4384 | −0.614026 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.75379 | −0.219299 | −0.109649 | − | 0.993970i | \(-0.534973\pi\) | ||||
−0.109649 | + | 0.993970i | \(0.534973\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.0000 | −0.698667 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.56155 | 0.379464 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.3693 | 1.34699 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.68466 | 0.325503 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.43845 | −0.196243 | −0.0981213 | − | 0.995174i | \(-0.531283\pi\) | ||||
−0.0981213 | + | 0.995174i | \(0.531283\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.3693 | −1.55197 | −0.775986 | − | 0.630750i | \(-0.782747\pi\) | ||||
−0.775986 | + | 0.630750i | \(0.782747\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.8769 | 1.18003 | 0.590016 | − | 0.807392i | \(-0.299121\pi\) | ||||
0.590016 | + | 0.807392i | \(0.299121\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 34.4924 | 1.93729 | 0.968644 | − | 0.248454i | \(-0.0799224\pi\) | ||||
0.968644 | + | 0.248454i | \(0.0799224\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.87689 | −0.161075 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000 | 0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.1231 | −0.723500 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.8769 | −1.14750 | −0.573749 | − | 0.819031i | \(-0.694511\pi\) | ||||
−0.573749 | + | 0.819031i | \(0.694511\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.3693 | −0.730444 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.49242 | 0.135771 | 0.0678855 | − | 0.997693i | \(-0.478375\pi\) | ||||
0.0678855 | + | 0.997693i | \(0.478375\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.3693 | 0.832295 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 31.0540 | 1.67676 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.0540 | −0.593408 | −0.296704 | − | 0.954969i | \(-0.595888\pi\) | ||||
−0.296704 | + | 0.954969i | \(0.595888\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.36932 | 0.0732979 | 0.0366489 | − | 0.999328i | \(-0.488332\pi\) | ||||
0.0366489 | + | 0.999328i | \(0.488332\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.4924 | 0.558455 | 0.279228 | − | 0.960225i | \(-0.409922\pi\) | ||||
0.279228 | + | 0.960225i | \(0.409922\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.5616 | −0.772847 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.24621 | −0.118550 | −0.0592752 | − | 0.998242i | \(-0.518879\pi\) | ||||
−0.0592752 | + | 0.998242i | \(0.518879\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.24621 | −0.486643 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.2462 | 0.952444 | 0.476222 | − | 0.879325i | \(-0.342006\pi\) | ||||
0.476222 | + | 0.879325i | \(0.342006\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 35.0540 | 1.81991 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.24621 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.12311 | −0.0578429 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.49242 | −0.128027 | −0.0640136 | − | 0.997949i | \(-0.520390\pi\) | ||||
−0.0640136 | + | 0.997949i | \(0.520390\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −36.4924 | −1.86468 | −0.932338 | − | 0.361588i | \(-0.882235\pi\) | ||||
−0.932338 | + | 0.361588i | \(0.882235\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.6847 | −0.595505 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.8617 | −1.00703 | −0.503515 | − | 0.863986i | \(-0.667960\pi\) | ||||
−0.503515 | + | 0.863986i | \(0.667960\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.8078 | 0.850005 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.68466 | 0.386657 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.56155 | −0.429692 | −0.214846 | − | 0.976648i | \(-0.568925\pi\) | ||||
−0.214846 | + | 0.976648i | \(0.568925\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.2462 | 1.01105 | 0.505524 | − | 0.862813i | \(-0.331299\pi\) | ||||
0.505524 | + | 0.862813i | \(0.331299\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.00000 | 0.298881 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.31534 | −0.213904 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.1231 | −0.747789 | −0.373895 | − | 0.927471i | \(-0.621978\pi\) | ||||
−0.373895 | + | 0.927471i | \(0.621978\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −54.7386 | −2.69351 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.4924 | −0.809581 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.6155 | 1.64223 | 0.821113 | − | 0.570766i | \(-0.193354\pi\) | ||||
0.821113 | + | 0.570766i | \(0.193354\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.6307 | 0.713056 | 0.356528 | − | 0.934285i | \(-0.383960\pi\) | ||||
0.356528 | + | 0.934285i | \(0.383960\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.56155 | −0.124254 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.9309 | 1.25488 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.4924 | 1.75778 | 0.878889 | − | 0.477026i | \(-0.158285\pi\) | ||||
0.878889 | + | 0.477026i | \(0.158285\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.6155 | 1.51935 | 0.759673 | − | 0.650306i | \(-0.225359\pi\) | ||||
0.759673 | + | 0.650306i | \(0.225359\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.4924 | 0.980286 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.0540 | 0.718487 | 0.359244 | − | 0.933244i | \(-0.383035\pi\) | ||||
0.359244 | + | 0.933244i | \(0.383035\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.8078 | −0.608515 | −0.304258 | − | 0.952590i | \(-0.598408\pi\) | ||||
−0.304258 | + | 0.952590i | \(0.598408\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.68466 | −0.0798605 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.1771 | 0.480286 | 0.240143 | − | 0.970738i | \(-0.422806\pi\) | ||||
0.240143 | + | 0.970738i | \(0.422806\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.43845 | 0.0677338 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.56155 | −0.213849 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.6847 | −1.20148 | −0.600739 | − | 0.799445i | \(-0.705127\pi\) | ||||
−0.600739 | + | 0.799445i | \(0.705127\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.0540 | −1.35318 | −0.676589 | − | 0.736361i | \(-0.736543\pi\) | ||||
−0.676589 | + | 0.736361i | \(0.736543\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.0691303 | 0.00321276 | 0.00160638 | − | 0.999999i | \(-0.499489\pi\) | ||||
0.00160638 | + | 0.999999i | \(0.499489\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.9309 | 1.01484 | 0.507420 | − | 0.861699i | \(-0.330599\pi\) | ||||
0.507420 | + | 0.861699i | \(0.330599\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −60.9848 | −2.81602 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.1231 | −0.603401 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.12311 | −0.143298 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.0540 | 0.505069 | 0.252535 | − | 0.967588i | \(-0.418736\pi\) | ||||
0.252535 | + | 0.967588i | \(0.418736\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.68466 | −0.0768138 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.9309 | −0.541753 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.05398 | −0.229017 | −0.114509 | − | 0.993422i | \(-0.536529\pi\) | ||||
−0.114509 | + | 0.993422i | \(0.536529\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.6155 | −0.614460 | −0.307230 | − | 0.951635i | \(-0.599402\pi\) | ||||
−0.307230 | + | 0.951635i | \(0.599402\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.87689 | −0.129569 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −66.4233 | −2.97949 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.9848 | 1.38707 | 0.693536 | − | 0.720422i | \(-0.256052\pi\) | ||||
0.693536 | + | 0.720422i | \(0.256052\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.2462 | −1.34861 | −0.674306 | − | 0.738452i | \(-0.735557\pi\) | ||||
−0.674306 | + | 0.738452i | \(0.735557\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.24621 | −0.277953 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.4384 | −0.861594 | −0.430797 | − | 0.902449i | \(-0.641768\pi\) | ||||
−0.430797 | + | 0.902449i | \(0.641768\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.3693 | −1.21075 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.87689 | 0.303032 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.36932 | 0.324102 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.8617 | 1.39589 | 0.697944 | − | 0.716152i | \(-0.254098\pi\) | ||||
0.697944 | + | 0.716152i | \(0.254098\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.7386 | −0.819383 | −0.409692 | − | 0.912224i | \(-0.634364\pi\) | ||||
−0.409692 | + | 0.912224i | \(0.634364\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.3693 | 0.669498 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.0540 | 0.871912 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.561553 | 0.0243236 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.9309 | 0.775219 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −35.3693 | −1.52346 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.1231 | 1.16611 | 0.583057 | − | 0.812431i | \(-0.301857\pi\) | ||||
0.583057 | + | 0.812431i | \(0.301857\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.3693 | −0.828172 | −0.414086 | − | 0.910238i | \(-0.635899\pi\) | ||||
−0.414086 | + | 0.910238i | \(0.635899\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.50758 | −0.149428 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35.0540 | 1.49065 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.4924 | −1.12252 | −0.561260 | − | 0.827640i | \(-0.689683\pi\) | ||||
−0.561260 | + | 0.827640i | \(0.689683\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.12311 | −0.216684 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.6847 | 1.33535 | 0.667675 | − | 0.744453i | \(-0.267290\pi\) | ||||
0.667675 | + | 0.744453i | \(0.267290\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.1231 | −0.552093 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.1231 | −1.72397 | −0.861985 | − | 0.506934i | \(-0.830779\pi\) | ||||
−0.861985 | + | 0.506934i | \(0.830779\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.0540 | −0.629989 | −0.314995 | − | 0.949093i | \(-0.602003\pi\) | ||||
−0.314995 | + | 0.949093i | \(0.602003\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.56155 | −0.273636 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.5616 | 1.18903 | 0.594517 | − | 0.804083i | \(-0.297343\pi\) | ||||
0.594517 | + | 0.804083i | \(0.297343\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −75.2311 | −3.12111 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.6847 | −0.815255 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.492423 | −0.0203245 | −0.0101622 | − | 0.999948i | \(-0.503235\pi\) | ||||
−0.0101622 | + | 0.999948i | \(0.503235\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.7386 | 0.772112 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.75379 | 0.318410 | 0.159205 | − | 0.987246i | \(-0.449107\pi\) | ||||
0.159205 | + | 0.987246i | \(0.449107\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.6847 | −0.479024 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.3693 | −0.627973 | −0.313987 | − | 0.949427i | \(-0.601665\pi\) | ||||
−0.313987 | + | 0.949427i | \(0.601665\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.5464 | 1.69471 | 0.847356 | − | 0.531025i | \(-0.178193\pi\) | ||||
0.847356 | + | 0.531025i | \(0.178193\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.43845 | −0.180449 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.0000 | 0.974130 | 0.487065 | − | 0.873366i | \(-0.338067\pi\) | ||||
0.487065 | + | 0.873366i | \(0.338067\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.87689 | 0.116387 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.5464 | 1.51648 | 0.758242 | − | 0.651973i | \(-0.226058\pi\) | ||||
0.758242 | + | 0.651973i | \(0.226058\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −48.7386 | −1.96214 | −0.981072 | − | 0.193645i | \(-0.937969\pi\) | ||||
−0.981072 | + | 0.193645i | \(0.937969\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.3693 | 1.34123 | 0.670613 | − | 0.741807i | \(-0.266031\pi\) | ||||
0.670613 | + | 0.741807i | \(0.266031\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.68466 | −0.307879 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.31534 | −0.172064 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.7386 | −0.666354 | −0.333177 | − | 0.942864i | \(-0.608121\pi\) | ||||
−0.333177 | + | 0.942864i | \(0.608121\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.2462 | −0.724079 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.8078 | −0.547084 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.9848 | 1.30282 | 0.651412 | − | 0.758725i | \(-0.274177\pi\) | ||||
0.651412 | + | 0.758725i | \(0.274177\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.68466 | −0.0664364 | −0.0332182 | − | 0.999448i | \(-0.510576\pi\) | ||||
−0.0332182 | + | 0.999448i | \(0.510576\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.1922 | −0.440012 | −0.220006 | − | 0.975498i | \(-0.570608\pi\) | ||||
−0.220006 | + | 0.975498i | \(0.570608\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.7386 | 1.20660 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.63068 | −0.337745 | −0.168872 | − | 0.985638i | \(-0.554013\pi\) | ||||
−0.168872 | + | 0.985638i | \(0.554013\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.12311 | −0.355386 | −0.177693 | − | 0.984086i | \(-0.556863\pi\) | ||||
−0.177693 | + | 0.984086i | \(0.556863\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.4924 | −1.03044 | −0.515218 | − | 0.857059i | \(-0.672289\pi\) | ||||
−0.515218 | + | 0.857059i | \(0.672289\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.2462 | −0.552444 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.36932 | −0.285341 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.5616 | −0.562143 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.7386 | −1.26198 | −0.630991 | − | 0.775790i | \(-0.717351\pi\) | ||||
−0.630991 | + | 0.775790i | \(0.717351\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.5616 | −0.713378 | −0.356689 | − | 0.934223i | \(-0.616094\pi\) | ||||
−0.356689 | + | 0.934223i | \(0.616094\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −54.4233 | −2.08857 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.492423 | 0.0188420 | 0.00942101 | − | 0.999956i | \(-0.497001\pi\) | ||||
0.00942101 | + | 0.999956i | \(0.497001\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.12311 | −0.272160 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.68466 | −0.292762 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.6155 | −0.746210 | −0.373105 | − | 0.927789i | \(-0.621707\pi\) | ||||
−0.373105 | + | 0.927789i | \(0.621707\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.6847 | −0.594953 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.43845 | 0.0544851 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.9848 | 0.641509 | 0.320754 | − | 0.947162i | \(-0.396064\pi\) | ||||
0.320754 | + | 0.947162i | \(0.396064\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.26137 | −0.198436 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.4924 | −1.07157 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.876894 | 0.0329325 | 0.0164662 | − | 0.999864i | \(-0.494758\pi\) | ||||
0.0164662 | + | 0.999864i | \(0.494758\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 39.3693 | 1.47439 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.56155 | 0.0957966 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36.0000 | −1.34257 | −0.671287 | − | 0.741198i | \(-0.734258\pi\) | ||||
−0.671287 | + | 0.741198i | \(0.734258\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31.3693 | 1.16825 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.12311 | 0.0417111 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.1231 | −0.783413 | −0.391706 | − | 0.920090i | \(-0.628115\pi\) | ||||
−0.391706 | + | 0.920090i | \(0.628115\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.1231 | −0.485376 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.5616 | −0.759458 | −0.379729 | − | 0.925098i | \(-0.623983\pi\) | ||||
−0.379729 | + | 0.925098i | \(0.623983\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 34.2462 | 1.26148 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.738634 | 0.0271711 | 0.0135855 | − | 0.999908i | \(-0.495675\pi\) | ||||
0.0135855 | + | 0.999908i | \(0.495675\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.7386 | 1.12769 | 0.563846 | − | 0.825880i | \(-0.309321\pi\) | ||||
0.563846 | + | 0.825880i | \(0.309321\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.80776 | 0.102869 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 81.7926 | 2.98864 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.0540 | 0.841252 | 0.420626 | − | 0.907234i | \(-0.361811\pi\) | ||||
0.420626 | + | 0.907234i | \(0.361811\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.3693 | 0.486559 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.4924 | 0.672119 | 0.336059 | − | 0.941841i | \(-0.390906\pi\) | ||||
0.336059 | + | 0.941841i | \(0.390906\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.2311 | −1.34962 | −0.674812 | − | 0.737989i | \(-0.735775\pi\) | ||||
−0.674812 | + | 0.737989i | \(0.735775\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.12311 | −0.330279 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.0000 | 0.433295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.0000 | −1.08183 | −0.540914 | − | 0.841078i | \(-0.681921\pi\) | ||||
−0.540914 | + | 0.841078i | \(0.681921\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.876894 | −0.0315397 | −0.0157698 | − | 0.999876i | \(-0.505020\pi\) | ||||
−0.0157698 | + | 0.999876i | \(0.505020\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.00000 | −0.215526 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.75379 | 0.0628360 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 37.3002 | 1.33471 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.3693 | −0.762704 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.3693 | 0.476565 | 0.238282 | − | 0.971196i | \(-0.423416\pi\) | ||||
0.238282 | + | 0.971196i | \(0.423416\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −59.8617 | −2.12844 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.68466 | −0.201868 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.68466 | −0.272205 | −0.136102 | − | 0.990695i | \(-0.543458\pi\) | ||||
−0.136102 | + | 0.990695i | \(0.543458\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.36932 | 0.260708 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.3693 | 0.542371 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −29.9309 | −1.05492 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40.4924 | 1.42364 | 0.711819 | − | 0.702363i | \(-0.247872\pi\) | ||||
0.711819 | + | 0.702363i | \(0.247872\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.2462 | 0.430023 | 0.215011 | − | 0.976612i | \(-0.431021\pi\) | ||||
0.215011 | + | 0.976612i | \(0.431021\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.0540 | 0.737489 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.0000 | −0.559769 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.5464 | −0.751974 | −0.375987 | − | 0.926625i | \(-0.622696\pi\) | ||||
−0.375987 | + | 0.926625i | \(0.622696\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.2462 | 1.61204 | 0.806021 | − | 0.591887i | \(-0.201617\pi\) | ||||
0.806021 | + | 0.591887i | \(0.201617\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.12311 | 0.0390542 | 0.0195271 | − | 0.999809i | \(-0.493784\pi\) | ||||
0.0195271 | + | 0.999809i | \(0.493784\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −48.7386 | −1.69276 | −0.846381 | − | 0.532577i | \(-0.821224\pi\) | ||||
−0.846381 | + | 0.532577i | \(0.821224\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −35.3693 | −1.22547 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.1231 | −0.454144 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.7926 | −1.44284 | −0.721421 | − | 0.692497i | \(-0.756510\pi\) | ||||
−0.721421 | + | 0.692497i | \(0.756510\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.7386 | −0.956505 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.2462 | −0.695668 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.0540 | −0.378925 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.4233 | −0.699280 | −0.349640 | − | 0.936884i | \(-0.613696\pi\) | ||||
−0.349640 | + | 0.936884i | \(0.613696\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.56155 | 0.224138 | 0.112069 | − | 0.993700i | \(-0.464252\pi\) | ||||
0.112069 | + | 0.993700i | \(0.464252\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.8078 | 0.573474 | 0.286737 | − | 0.958009i | \(-0.407429\pi\) | ||||
0.286737 | + | 0.958009i | \(0.407429\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.3693 | −0.523178 | −0.261589 | − | 0.965179i | \(-0.584246\pi\) | ||||
−0.261589 | + | 0.965179i | \(0.584246\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.1231 | 0.718207 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.6847 | −0.667756 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.3693 | 0.453002 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.56155 | 0.154209 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.9848 | −0.641073 | −0.320536 | − | 0.947236i | \(-0.603863\pi\) | ||||
−0.320536 | + | 0.947236i | \(0.603863\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.36932 | 0.113515 | 0.0567576 | − | 0.998388i | \(-0.481924\pi\) | ||||
0.0567576 | + | 0.998388i | \(0.481924\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.1080 | −0.609381 | −0.304691 | − | 0.952451i | \(-0.598553\pi\) | ||||
−0.304691 | + | 0.952451i | \(0.598553\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.43845 | −0.0482983 | −0.0241492 | − | 0.999708i | \(-0.507688\pi\) | ||||
−0.0241492 | + | 0.999708i | \(0.507688\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −83.2311 | −2.79148 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.98485 | 0.300666 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.1231 | 0.438657 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.73863 | −0.224746 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.6847 | −0.655791 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.6847 | 0.853787 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.3693 | 0.908783 | 0.454392 | − | 0.890802i | \(-0.349857\pi\) | ||||
0.454392 | + | 0.890802i | \(0.349857\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.2462 | 1.39815 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.0540 | −1.28827 | −0.644136 | − | 0.764911i | \(-0.722783\pi\) | ||||
−0.644136 | + | 0.764911i | \(0.722783\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.5616 | 0.479299 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.68466 | 0.0553912 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.6695 | −1.26871 | −0.634353 | − | 0.773044i | \(-0.718733\pi\) | ||||
−0.634353 | + | 0.773044i | \(0.718733\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −43.1231 | −1.41330 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.56155 | 0.214586 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.63068 | −0.0859407 | −0.0429703 | − | 0.999076i | \(-0.513682\pi\) | ||||
−0.0429703 | + | 0.999076i | \(0.513682\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.1922 | −0.690847 | −0.345424 | − | 0.938447i | \(-0.612265\pi\) | ||||
−0.345424 | + | 0.938447i | \(0.612265\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.68466 | 0.119989 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.6004 | 1.51431 | 0.757154 | − | 0.653236i | \(-0.226589\pi\) | ||||
0.757154 | + | 0.653236i | \(0.226589\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.00000 | 0.194768 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.4384 | 0.824032 | 0.412016 | − | 0.911177i | \(-0.364825\pi\) | ||||
0.412016 | + | 0.911177i | \(0.364825\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.6155 | 0.699462 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.4924 | −1.04924 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.4384 | 0.496981 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.3693 | −0.558560 | −0.279280 | − | 0.960210i | \(-0.590096\pi\) | ||||
−0.279280 | + | 0.960210i | \(0.590096\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.49242 | −0.272535 | −0.136267 | − | 0.990672i | \(-0.543511\pi\) | ||||
−0.136267 | + | 0.990672i | \(0.543511\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −71.5464 | −2.29367 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 55.4773 | 1.77488 | 0.887438 | − | 0.460928i | \(-0.152483\pi\) | ||||
0.887438 | + | 0.460928i | \(0.152483\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.31534 | 0.137919 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.73863 | 0.214929 | 0.107465 | − | 0.994209i | \(-0.465727\pi\) | ||||
0.107465 | + | 0.994209i | \(0.465727\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.3693 | 0.680883 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33.6155 | −1.06891 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.0540 | 0.859398 | 0.429699 | − | 0.902972i | \(-0.358620\pi\) | ||||
0.429699 | + | 0.902972i | \(0.358620\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.00000 | 0.253617 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.7538 | 0.372246 | 0.186123 | − | 0.982526i | \(-0.440408\pi\) | ||||
0.186123 | + | 0.982526i | \(0.440408\pi\) | |||||||
\(998\) | 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 | 9360.2.a.cw.1.2 | 2 | ||
3.2 | odd | 2 | 9360.2.a.cl.1.2 | 2 | |||
4.3 | odd | 2 | 585.2.a.l.1.1 | yes | 2 | ||
12.11 | even | 2 | 585.2.a.j.1.2 | ✓ | 2 | ||
20.3 | even | 4 | 2925.2.c.p.2224.3 | 4 | |||
20.7 | even | 4 | 2925.2.c.p.2224.2 | 4 | |||
20.19 | odd | 2 | 2925.2.a.x.1.2 | 2 | |||
52.51 | odd | 2 | 7605.2.a.bd.1.2 | 2 | |||
60.23 | odd | 4 | 2925.2.c.o.2224.2 | 4 | |||
60.47 | odd | 4 | 2925.2.c.o.2224.3 | 4 | |||
60.59 | even | 2 | 2925.2.a.bc.1.1 | 2 | |||
156.155 | even | 2 | 7605.2.a.bi.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.a.j.1.2 | ✓ | 2 | 12.11 | even | 2 | ||
585.2.a.l.1.1 | yes | 2 | 4.3 | odd | 2 | ||
2925.2.a.x.1.2 | 2 | 20.19 | odd | 2 | |||
2925.2.a.bc.1.1 | 2 | 60.59 | even | 2 | |||
2925.2.c.o.2224.2 | 4 | 60.23 | odd | 4 | |||
2925.2.c.o.2224.3 | 4 | 60.47 | odd | 4 | |||
2925.2.c.p.2224.2 | 4 | 20.7 | even | 4 | |||
2925.2.c.p.2224.3 | 4 | 20.3 | even | 4 | |||
7605.2.a.bd.1.2 | 2 | 52.51 | odd | 2 | |||
7605.2.a.bi.1.1 | 2 | 156.155 | even | 2 | |||
9360.2.a.cl.1.2 | 2 | 3.2 | odd | 2 | |||
9360.2.a.cw.1.2 | 2 | 1.1 | even | 1 | trivial |