Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 8x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.57794\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.64575 | −1.18322 | −0.591608 | − | 0.806226i | \(-0.701507\pi\) | ||||
−0.591608 | + | 0.806226i | \(0.701507\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.74166 | 1.18322 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.74166 | 0.483049 | 0.241524 | − | 0.970395i | \(-0.422353\pi\) | ||||
0.241524 | + | 0.970395i | \(0.422353\pi\) | |||||||
\(14\) | −1.41421 | −0.377964 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | −0.182676 | −0.0443054 | −0.0221527 | − | 0.999755i | \(-0.507052\pi\) | ||||
−0.0221527 | + | 0.999755i | \(0.507052\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.74166 | −0.399564 | −0.199782 | − | 0.979840i | \(-0.564023\pi\) | ||||
−0.199782 | + | 0.979840i | \(0.564023\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.70572 | 1.39824 | 0.699119 | − | 0.715005i | \(-0.253576\pi\) | ||||
0.699119 | + | 0.715005i | \(0.253576\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | 0.400000 | ||||||||
\(26\) | −2.46308 | −0.483049 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.70572 | 1.24522 | 0.622610 | − | 0.782532i | \(-0.286072\pi\) | ||||
0.622610 | + | 0.782532i | \(0.286072\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.48331 | −1.70325 | −0.851627 | − | 0.524149i | \(-0.824384\pi\) | ||||
−0.851627 | + | 0.524149i | \(0.824384\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.258343 | 0.0443054 | ||||||||
\(35\) | −2.64575 | −0.447214 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.4833 | −1.88785 | −0.943923 | − | 0.330167i | \(-0.892895\pi\) | ||||
−0.943923 | + | 0.330167i | \(0.892895\pi\) | |||||||
\(38\) | 2.46308 | 0.399564 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.48331 | −1.18322 | ||||||||
\(41\) | 5.65685 | 0.883452 | 0.441726 | − | 0.897150i | \(-0.354366\pi\) | ||||
0.441726 | + | 0.897150i | \(0.354366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | −0.152499 | −0.0762493 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762493 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.48331 | −1.39824 | ||||||||
\(47\) | −0.182676 | −0.0266460 | −0.0133230 | − | 0.999911i | \(-0.504241\pi\) | ||||
−0.0133230 | + | 0.999911i | \(0.504241\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.82843 | −0.400000 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.75458 | −1.06517 | −0.532587 | − | 0.846376i | \(-0.678780\pi\) | ||||
−0.532587 | + | 0.846376i | \(0.678780\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.82843 | 0.377964 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.48331 | −1.24522 | ||||||||
\(59\) | 3.01110 | 0.392012 | 0.196006 | − | 0.980603i | \(-0.437203\pi\) | ||||
0.196006 | + | 0.980603i | \(0.437203\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.74166 | −0.735144 | −0.367572 | − | 0.929995i | \(-0.619811\pi\) | ||||
−0.367572 | + | 0.929995i | \(0.619811\pi\) | |||||||
\(62\) | 13.4114 | 1.70325 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | −4.60799 | −0.571551 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.48331 | 1.03640 | 0.518201 | − | 0.855259i | \(-0.326602\pi\) | ||||
0.518201 | + | 0.855259i | \(0.326602\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.74166 | 0.447214 | ||||||||
\(71\) | −1.41421 | −0.167836 | −0.0839181 | − | 0.996473i | \(-0.526743\pi\) | ||||
−0.0839181 | + | 0.996473i | \(0.526743\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.25834 | −0.966566 | −0.483283 | − | 0.875464i | \(-0.660556\pi\) | ||||
−0.483283 | + | 0.875464i | \(0.660556\pi\) | |||||||
\(74\) | 16.2399 | 1.88785 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.48331 | 0.166886 | 0.0834430 | − | 0.996513i | \(-0.473408\pi\) | ||||
0.0834430 | + | 0.996513i | \(0.473408\pi\) | |||||||
\(80\) | 10.5830 | 1.18322 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.00000 | −0.883452 | ||||||||
\(83\) | −5.83953 | −0.640972 | −0.320486 | − | 0.947253i | \(-0.603846\pi\) | ||||
−0.320486 | + | 0.947253i | \(0.603846\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.483315 | 0.0524228 | ||||||||
\(86\) | 1.41421 | 0.152499 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.1310 | 1.17989 | 0.589944 | − | 0.807444i | \(-0.299150\pi\) | ||||
0.589944 | + | 0.807444i | \(0.299150\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.74166 | 0.182575 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.258343 | 0.0266460 | ||||||||
\(95\) | 4.60799 | 0.472770 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.2250 | 1.54586 | 0.772931 | − | 0.634490i | \(-0.218790\pi\) | ||||
0.772931 | + | 0.634490i | \(0.218790\pi\) | |||||||
\(98\) | −1.41421 | −0.142857 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.9595 | 1.38902 | 0.694509 | − | 0.719484i | \(-0.255622\pi\) | ||||
0.694509 | + | 0.719484i | \(0.255622\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.22497 | 0.908964 | 0.454482 | − | 0.890756i | \(-0.349824\pi\) | ||||
0.454482 | + | 0.890756i | \(0.349824\pi\) | |||||||
\(104\) | 4.92615 | 0.483049 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.9666 | 1.06517 | ||||||||
\(107\) | −1.04886 | −0.101397 | −0.0506987 | − | 0.998714i | \(-0.516145\pi\) | ||||
−0.0506987 | + | 0.998714i | \(0.516145\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.51669 | 0.145272 | 0.0726360 | − | 0.997359i | \(-0.476859\pi\) | ||||
0.0726360 | + | 0.997359i | \(0.476859\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.00000 | −0.377964 | ||||||||
\(113\) | −5.29150 | −0.497783 | −0.248891 | − | 0.968531i | \(-0.580066\pi\) | ||||
−0.248891 | + | 0.968531i | \(0.580066\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.7417 | −1.65442 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.25834 | −0.392012 | ||||||||
\(119\) | −0.182676 | −0.0167459 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 8.11993 | 0.735144 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.93725 | 0.709930 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.51669 | −0.134584 | −0.0672920 | − | 0.997733i | \(-0.521436\pi\) | ||||
−0.0672920 | + | 0.997733i | \(0.521436\pi\) | |||||||
\(128\) | −11.3137 | −1.00000 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.51669 | 0.571551 | ||||||||
\(131\) | −13.9595 | −1.21964 | −0.609822 | − | 0.792539i | \(-0.708759\pi\) | ||||
−0.609822 | + | 0.792539i | \(0.708759\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.74166 | −0.151021 | ||||||||
\(134\) | −11.9972 | −1.03640 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.516685 | −0.0443054 | ||||||||
\(137\) | −22.9456 | −1.96037 | −0.980186 | − | 0.198077i | \(-0.936530\pi\) | ||||
−0.980186 | + | 0.198077i | \(0.936530\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.74166 | −0.317363 | −0.158682 | − | 0.987330i | \(-0.550724\pi\) | ||||
−0.158682 | + | 0.987330i | \(0.550724\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.00000 | 0.167836 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.7417 | −1.47336 | ||||||||
\(146\) | 11.6791 | 0.966566 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.14492 | −0.175718 | −0.0878592 | − | 0.996133i | \(-0.528003\pi\) | ||||
−0.0878592 | + | 0.996133i | \(0.528003\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.4833 | −1.82967 | −0.914833 | − | 0.403832i | \(-0.867678\pi\) | ||||
−0.914833 | + | 0.403832i | \(0.867678\pi\) | |||||||
\(152\) | −4.92615 | −0.399564 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.0905 | 2.01532 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.9666 | 1.35408 | 0.677042 | − | 0.735944i | \(-0.263261\pi\) | ||||
0.677042 | + | 0.735944i | \(0.263261\pi\) | |||||||
\(158\) | −2.09772 | −0.166886 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.70572 | 0.528484 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.4499 | 1.60176 | 0.800882 | − | 0.598823i | \(-0.204365\pi\) | ||||
0.800882 | + | 0.598823i | \(0.204365\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.25834 | 0.640972 | ||||||||
\(167\) | 13.9595 | 1.08022 | 0.540108 | − | 0.841596i | \(-0.318383\pi\) | ||||
0.540108 | + | 0.841596i | \(0.318383\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.96663 | −0.766664 | ||||||||
\(170\) | −0.683510 | −0.0524228 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.7657 | 0.818500 | 0.409250 | − | 0.912422i | \(-0.365790\pi\) | ||||
0.409250 | + | 0.912422i | \(0.365790\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | 0.151186 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.7417 | −1.17989 | ||||||||
\(179\) | 14.1421 | 1.05703 | 0.528516 | − | 0.848923i | \(-0.322748\pi\) | ||||
0.528516 | + | 0.848923i | \(0.322748\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | −2.46308 | −0.182575 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 18.9666 | 1.39824 | ||||||||
\(185\) | 30.3820 | 2.23373 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.51669 | −0.472770 | ||||||||
\(191\) | −1.41421 | −0.102329 | −0.0511645 | − | 0.998690i | \(-0.516293\pi\) | ||||
−0.0511645 | + | 0.998690i | \(0.516293\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.51669 | −0.109173 | −0.0545867 | − | 0.998509i | \(-0.517384\pi\) | ||||
−0.0545867 | + | 0.998509i | \(0.517384\pi\) | |||||||
\(194\) | −21.5314 | −1.54586 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.6791 | −0.832099 | −0.416049 | − | 0.909342i | \(-0.636586\pi\) | ||||
−0.416049 | + | 0.909342i | \(0.636586\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.74166 | 0.690568 | 0.345284 | − | 0.938498i | \(-0.387783\pi\) | ||||
0.345284 | + | 0.938498i | \(0.387783\pi\) | |||||||
\(200\) | 5.65685 | 0.400000 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −19.7417 | −1.38902 | ||||||||
\(203\) | 6.70572 | 0.470649 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.9666 | −1.04531 | ||||||||
\(206\) | −13.0461 | −0.908964 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.96663 | −0.483049 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.4833 | −1.68550 | −0.842750 | − | 0.538304i | \(-0.819065\pi\) | ||||
−0.842750 | + | 0.538304i | \(0.819065\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.48331 | 0.101397 | ||||||||
\(215\) | 2.64575 | 0.180439 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.48331 | −0.643769 | ||||||||
\(218\) | −2.14492 | −0.145272 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.318159 | −0.0214017 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.51669 | 0.168530 | 0.0842649 | − | 0.996443i | \(-0.473146\pi\) | ||||
0.0842649 | + | 0.996443i | \(0.473146\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.48331 | 0.497783 | ||||||||
\(227\) | −11.8617 | −0.787291 | −0.393646 | − | 0.919262i | \(-0.628786\pi\) | ||||
−0.393646 | + | 0.919262i | \(0.628786\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.48331 | −0.0980202 | −0.0490101 | − | 0.998798i | \(-0.515607\pi\) | ||||
−0.0490101 | + | 0.998798i | \(0.515607\pi\) | |||||||
\(230\) | 25.0905 | 1.65442 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.9666 | 1.24522 | ||||||||
\(233\) | 14.8256 | 0.971260 | 0.485630 | − | 0.874164i | \(-0.338590\pi\) | ||||
0.485630 | + | 0.874164i | \(0.338590\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.483315 | 0.0315280 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.258343 | 0.0167459 | ||||||||
\(239\) | −2.46308 | −0.159323 | −0.0796616 | − | 0.996822i | \(-0.525384\pi\) | ||||
−0.0796616 | + | 0.996822i | \(0.525384\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.2250 | −1.23839 | −0.619195 | − | 0.785238i | \(-0.712541\pi\) | ||||
−0.619195 | + | 0.785238i | \(0.712541\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.64575 | −0.169031 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.03337 | −0.193009 | ||||||||
\(248\) | −26.8229 | −1.70325 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.2250 | −0.709930 | ||||||||
\(251\) | 19.0683 | 1.20358 | 0.601790 | − | 0.798655i | \(-0.294455\pi\) | ||||
0.601790 | + | 0.798655i | \(0.294455\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 2.14492 | 0.134584 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.4225 | 1.02441 | 0.512205 | − | 0.858863i | \(-0.328829\pi\) | ||||
0.512205 | + | 0.858863i | \(0.328829\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.4833 | −0.713538 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 19.7417 | 1.21964 | ||||||||
\(263\) | −11.6319 | −0.717252 | −0.358626 | − | 0.933481i | \(-0.616755\pi\) | ||||
−0.358626 | + | 0.933481i | \(0.616755\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.5167 | 1.26033 | ||||||||
\(266\) | 2.46308 | 0.151021 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.38923 | 0.450529 | 0.225265 | − | 0.974298i | \(-0.427675\pi\) | ||||
0.225265 | + | 0.974298i | \(0.427675\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.9666 | 1.27363 | 0.636816 | − | 0.771016i | \(-0.280251\pi\) | ||||
0.636816 | + | 0.771016i | \(0.280251\pi\) | |||||||
\(272\) | 0.730703 | 0.0443054 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 32.4499 | 1.96037 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.96663 | 0.598837 | 0.299418 | − | 0.954122i | \(-0.403207\pi\) | ||||
0.299418 | + | 0.954122i | \(0.403207\pi\) | |||||||
\(278\) | 5.29150 | 0.317363 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.48331 | −0.447214 | ||||||||
\(281\) | −4.92615 | −0.293870 | −0.146935 | − | 0.989146i | \(-0.546941\pi\) | ||||
−0.146935 | + | 0.989146i | \(0.546941\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.9666 | −1.24634 | −0.623168 | − | 0.782088i | \(-0.714155\pi\) | ||||
−0.623168 | + | 0.782088i | \(0.714155\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.65685 | 0.333914 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9666 | −0.998037 | ||||||||
\(290\) | 25.0905 | 1.47336 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.8101 | 1.33258 | 0.666290 | − | 0.745693i | \(-0.267881\pi\) | ||||
0.666290 | + | 0.745693i | \(0.267881\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.96663 | −0.463835 | ||||||||
\(296\) | −32.4797 | −1.88785 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.03337 | 0.175718 | ||||||||
\(299\) | 11.6791 | 0.675417 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00000 | −0.0576390 | ||||||||
\(302\) | 31.7962 | 1.82967 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.96663 | 0.399564 | ||||||||
\(305\) | 15.1910 | 0.869834 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.7083 | 1.75261 | 0.876307 | − | 0.481753i | \(-0.160000\pi\) | ||||
0.876307 | + | 0.481753i | \(0.160000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −35.4833 | −2.01532 | ||||||||
\(311\) | −32.2970 | −1.83140 | −0.915699 | − | 0.401866i | \(-0.868362\pi\) | ||||
−0.915699 | + | 0.401866i | \(0.868362\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.4833 | −1.10126 | −0.550631 | − | 0.834749i | \(-0.685613\pi\) | ||||
−0.550631 | + | 0.834749i | \(0.685613\pi\) | |||||||
\(314\) | −23.9944 | −1.35408 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.04886 | −0.0589100 | −0.0294550 | − | 0.999566i | \(-0.509377\pi\) | ||||
−0.0294550 | + | 0.999566i | \(0.509377\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −21.1660 | −1.18322 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.48331 | −0.528484 | ||||||||
\(323\) | 0.318159 | 0.0177028 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.48331 | 0.193220 | ||||||||
\(326\) | −28.9206 | −1.60176 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 16.0000 | 0.883452 | ||||||||
\(329\) | −0.182676 | −0.0100712 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.51669 | 0.303224 | 0.151612 | − | 0.988440i | \(-0.451554\pi\) | ||||
0.151612 | + | 0.988440i | \(0.451554\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.7417 | −1.08022 | ||||||||
\(335\) | −22.4447 | −1.22629 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.96663 | −0.379496 | −0.189748 | − | 0.981833i | \(-0.560767\pi\) | ||||
−0.189748 | + | 0.981833i | \(0.560767\pi\) | |||||||
\(338\) | 14.0949 | 0.766664 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −2.82843 | −0.152499 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.2250 | −0.818500 | ||||||||
\(347\) | 30.3348 | 1.62846 | 0.814229 | − | 0.580544i | \(-0.197160\pi\) | ||||
0.814229 | + | 0.580544i | \(0.197160\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.5167 | −0.991175 | −0.495588 | − | 0.868558i | \(-0.665047\pi\) | ||||
−0.495588 | + | 0.868558i | \(0.665047\pi\) | |||||||
\(350\) | −2.82843 | −0.151186 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −33.5758 | −1.78706 | −0.893529 | − | 0.449005i | \(-0.851778\pi\) | ||||
−0.893529 | + | 0.449005i | \(0.851778\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.74166 | 0.198587 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.0000 | −1.05703 | ||||||||
\(359\) | −28.2371 | −1.49030 | −0.745148 | − | 0.666899i | \(-0.767621\pi\) | ||||
−0.745148 | + | 0.666899i | \(0.767621\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.9666 | −0.840349 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.8495 | 1.14366 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.22497 | −0.272741 | −0.136371 | − | 0.990658i | \(-0.543544\pi\) | ||||
−0.136371 | + | 0.990658i | \(0.543544\pi\) | |||||||
\(368\) | −26.8229 | −1.39824 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −42.9666 | −2.23373 | ||||||||
\(371\) | −7.75458 | −0.402598 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.4499 | 1.31775 | 0.658874 | − | 0.752253i | \(-0.271033\pi\) | ||||
0.658874 | + | 0.752253i | \(0.271033\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.516685 | −0.0266460 | ||||||||
\(377\) | 11.6791 | 0.601502 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.5167 | −1.00250 | −0.501252 | − | 0.865301i | \(-0.667127\pi\) | ||||
−0.501252 | + | 0.865301i | \(0.667127\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.00000 | 0.102329 | ||||||||
\(383\) | 15.6918 | 0.801815 | 0.400908 | − | 0.916119i | \(-0.368695\pi\) | ||||
0.400908 | + | 0.916119i | \(0.368695\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.14492 | 0.109173 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.9928 | −1.16578 | −0.582890 | − | 0.812551i | \(-0.698078\pi\) | ||||
−0.582890 | + | 0.812551i | \(0.698078\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.22497 | −0.0619495 | ||||||||
\(392\) | 2.82843 | 0.142857 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16.5167 | 0.832099 | ||||||||
\(395\) | −3.92448 | −0.197462 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.4833 | −0.676708 | −0.338354 | − | 0.941019i | \(-0.609870\pi\) | ||||
−0.338354 | + | 0.941019i | \(0.609870\pi\) | |||||||
\(398\) | −13.7768 | −0.690568 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.00000 | −0.400000 | ||||||||
\(401\) | −2.46308 | −0.123000 | −0.0615001 | − | 0.998107i | \(-0.519588\pi\) | ||||
−0.0615001 | + | 0.998107i | \(0.519588\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.5167 | −0.822755 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.48331 | −0.470649 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.2250 | −0.653933 | −0.326966 | − | 0.945036i | \(-0.606026\pi\) | ||||
−0.326966 | + | 0.945036i | \(0.606026\pi\) | |||||||
\(410\) | 21.1660 | 1.04531 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.01110 | 0.148167 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.4499 | 0.758408 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.1549 | 0.886925 | 0.443463 | − | 0.896293i | \(-0.353750\pi\) | ||||
0.443463 | + | 0.896293i | \(0.353750\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.4833 | −1.09577 | −0.547885 | − | 0.836554i | \(-0.684567\pi\) | ||||
−0.547885 | + | 0.836554i | \(0.684567\pi\) | |||||||
\(422\) | 34.6246 | 1.68550 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −21.9333 | −1.06517 | ||||||||
\(425\) | −0.365352 | −0.0177222 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.74166 | −0.277858 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.74166 | −0.180439 | ||||||||
\(431\) | −15.8745 | −0.764648 | −0.382324 | − | 0.924028i | \(-0.624876\pi\) | ||||
−0.382324 | + | 0.924028i | \(0.624876\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.74166 | 0.275926 | 0.137963 | − | 0.990437i | \(-0.455944\pi\) | ||||
0.137963 | + | 0.990437i | \(0.455944\pi\) | |||||||
\(434\) | 13.4114 | 0.643769 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.6791 | −0.558685 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.51669 | −0.215570 | −0.107785 | − | 0.994174i | \(-0.534376\pi\) | ||||
−0.107785 | + | 0.994174i | \(0.534376\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.449944 | 0.0214017 | ||||||||
\(443\) | −37.8184 | −1.79681 | −0.898404 | − | 0.439171i | \(-0.855272\pi\) | ||||
−0.898404 | + | 0.439171i | \(0.855272\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −29.4499 | −1.39606 | ||||||||
\(446\) | −3.55913 | −0.168530 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.00000 | 0.377964 | ||||||||
\(449\) | −21.5314 | −1.01613 | −0.508064 | − | 0.861319i | \(-0.669639\pi\) | ||||
−0.508064 | + | 0.861319i | \(0.669639\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.7750 | 0.787291 | ||||||||
\(455\) | −4.60799 | −0.216026 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.0000 | −1.07589 | −0.537947 | − | 0.842978i | \(-0.680800\pi\) | ||||
−0.537947 | + | 0.842978i | \(0.680800\pi\) | |||||||
\(458\) | 2.09772 | 0.0980202 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.8340 | 1.38951 | 0.694753 | − | 0.719248i | \(-0.255514\pi\) | ||||
0.694753 | + | 0.719248i | \(0.255514\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.51669 | −0.116960 | −0.0584801 | − | 0.998289i | \(-0.518625\pi\) | ||||
−0.0584801 | + | 0.998289i | \(0.518625\pi\) | |||||||
\(464\) | −26.8229 | −1.24522 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.9666 | −0.971260 | ||||||||
\(467\) | −32.1144 | −1.48608 | −0.743038 | − | 0.669249i | \(-0.766616\pi\) | ||||
−0.743038 | + | 0.669249i | \(0.766616\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.48331 | 0.391723 | ||||||||
\(470\) | −0.683510 | −0.0315280 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.51669 | 0.392012 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.48331 | −0.159825 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.48331 | 0.159323 | ||||||||
\(479\) | −39.0500 | −1.78424 | −0.892119 | − | 0.451801i | \(-0.850782\pi\) | ||||
−0.892119 | + | 0.451801i | \(0.850782\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0000 | −0.911922 | ||||||||
\(482\) | 27.1882 | 1.23839 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −40.2815 | −1.82909 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.4833 | 0.928188 | 0.464094 | − | 0.885786i | \(-0.346380\pi\) | ||||
0.464094 | + | 0.885786i | \(0.346380\pi\) | |||||||
\(488\) | −16.2399 | −0.735144 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.74166 | 0.169031 | ||||||||
\(491\) | 29.6985 | 1.34027 | 0.670137 | − | 0.742237i | \(-0.266235\pi\) | ||||
0.670137 | + | 0.742237i | \(0.266235\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.22497 | −0.0551700 | ||||||||
\(494\) | 4.28983 | 0.193009 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 37.9333 | 1.70325 | ||||||||
\(497\) | −1.41421 | −0.0634361 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.9666 | 0.535700 | 0.267850 | − | 0.963461i | \(-0.413687\pi\) | ||||
0.267850 | + | 0.963461i | \(0.413687\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −26.9666 | −1.20358 | ||||||||
\(503\) | −34.3948 | −1.53359 | −0.766793 | − | 0.641894i | \(-0.778149\pi\) | ||||
−0.766793 | + | 0.641894i | \(0.778149\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.9333 | −1.64351 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.7362 | −1.22939 | −0.614694 | − | 0.788766i | \(-0.710720\pi\) | ||||
−0.614694 | + | 0.788766i | \(0.710720\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.25834 | −0.365328 | ||||||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −23.2250 | −1.02441 | ||||||||
\(515\) | −24.4070 | −1.07550 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 16.2399 | 0.713538 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −13.0334 | −0.571551 | ||||||||
\(521\) | 29.8340 | 1.30705 | 0.653525 | − | 0.756905i | \(-0.273289\pi\) | ||||
0.653525 | + | 0.756905i | \(0.273289\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.2250 | −0.665742 | −0.332871 | − | 0.942972i | \(-0.608017\pi\) | ||||
−0.332871 | + | 0.942972i | \(0.608017\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.4499 | 0.717252 | ||||||||
\(527\) | 1.73237 | 0.0754633 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.9666 | 0.955071 | ||||||||
\(530\) | −29.0150 | −1.26033 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.85230 | 0.426751 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.77503 | 0.119975 | ||||||||
\(536\) | 23.9944 | 1.03640 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.4499 | −0.450529 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0000 | −0.644900 | −0.322450 | − | 0.946586i | \(-0.604506\pi\) | ||||
−0.322450 | + | 0.946586i | \(0.604506\pi\) | |||||||
\(542\) | −29.6513 | −1.27363 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.01277 | −0.171888 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.0000 | 0.427569 | 0.213785 | − | 0.976881i | \(-0.431421\pi\) | ||||
0.213785 | + | 0.976881i | \(0.431421\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.6791 | −0.497545 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.48331 | 0.0630770 | ||||||||
\(554\) | −14.0949 | −0.598837 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.2382 | 0.645663 | 0.322831 | − | 0.946456i | \(-0.395365\pi\) | ||||
0.322831 | + | 0.946456i | \(0.395365\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.74166 | −0.0736643 | ||||||||
\(560\) | 10.5830 | 0.447214 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.96663 | 0.293870 | ||||||||
\(563\) | −13.2288 | −0.557526 | −0.278763 | − | 0.960360i | \(-0.589924\pi\) | ||||
−0.278763 | + | 0.960360i | \(0.589924\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.0000 | 0.588984 | ||||||||
\(566\) | 29.6513 | 1.24634 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.00000 | −0.167836 | ||||||||
\(569\) | −18.3848 | −0.770730 | −0.385365 | − | 0.922764i | \(-0.625924\pi\) | ||||
−0.385365 | + | 0.922764i | \(0.625924\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.96663 | 0.124150 | 0.0620748 | − | 0.998072i | \(-0.480228\pi\) | ||||
0.0620748 | + | 0.998072i | \(0.480228\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.00000 | −0.333914 | ||||||||
\(575\) | 13.4114 | 0.559295 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.7083 | 0.778836 | 0.389418 | − | 0.921061i | \(-0.372676\pi\) | ||||
0.389418 | + | 0.921061i | \(0.372676\pi\) | |||||||
\(578\) | 23.9944 | 0.998037 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.83953 | −0.242265 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −23.3581 | −0.966566 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −32.2583 | −1.33258 | ||||||||
\(587\) | −35.4908 | −1.46486 | −0.732431 | − | 0.680841i | \(-0.761615\pi\) | ||||
−0.732431 | + | 0.680841i | \(0.761615\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.5167 | 0.680558 | ||||||||
\(590\) | 11.2665 | 0.463835 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 45.9333 | 1.88785 | ||||||||
\(593\) | −39.6863 | −1.62972 | −0.814860 | − | 0.579658i | \(-0.803186\pi\) | ||||
−0.814860 | + | 0.579658i | \(0.803186\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.483315 | 0.0198140 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −16.5167 | −0.675417 | ||||||||
\(599\) | −12.6807 | −0.518121 | −0.259060 | − | 0.965861i | \(-0.583413\pi\) | ||||
−0.259060 | + | 0.965861i | \(0.583413\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.7750 | −0.602686 | −0.301343 | − | 0.953516i | \(-0.597435\pi\) | ||||
−0.301343 | + | 0.953516i | \(0.597435\pi\) | |||||||
\(602\) | 1.41421 | 0.0576390 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.2583 | −1.14697 | −0.573485 | − | 0.819216i | \(-0.694409\pi\) | ||||
−0.573485 | + | 0.819216i | \(0.694409\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −21.4833 | −0.869834 | ||||||||
\(611\) | −0.318159 | −0.0128713 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.5167 | −0.465155 | −0.232577 | − | 0.972578i | \(-0.574716\pi\) | ||||
−0.232577 | + | 0.972578i | \(0.574716\pi\) | |||||||
\(614\) | −43.4281 | −1.75261 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.0683 | 0.767660 | 0.383830 | − | 0.923404i | \(-0.374605\pi\) | ||||
0.383830 | + | 0.923404i | \(0.374605\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.4499 | −0.420019 | −0.210009 | − | 0.977699i | \(-0.567349\pi\) | ||||
−0.210009 | + | 0.977699i | \(0.567349\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 45.6749 | 1.83140 | ||||||||
\(623\) | 11.1310 | 0.445955 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 27.5536 | 1.10126 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.09772 | 0.0836417 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.4499 | 0.774290 | 0.387145 | − | 0.922019i | \(-0.373461\pi\) | ||||
0.387145 | + | 0.922019i | \(0.373461\pi\) | |||||||
\(632\) | 4.19545 | 0.166886 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.48331 | 0.0589100 | ||||||||
\(635\) | 4.01277 | 0.159242 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.74166 | 0.0690070 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 29.9333 | 1.18322 | ||||||||
\(641\) | 31.0655 | 1.22701 | 0.613507 | − | 0.789689i | \(-0.289758\pi\) | ||||
0.613507 | + | 0.789689i | \(0.289758\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.44994 | 0.175489 | 0.0877443 | − | 0.996143i | \(-0.472034\pi\) | ||||
0.0877443 | + | 0.996143i | \(0.472034\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.449944 | −0.0177028 | ||||||||
\(647\) | 42.6091 | 1.67514 | 0.837568 | − | 0.546333i | \(-0.183977\pi\) | ||||
0.837568 | + | 0.546333i | \(0.183977\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.92615 | −0.193220 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.0433 | −0.980020 | −0.490010 | − | 0.871717i | \(-0.663007\pi\) | ||||
−0.490010 | + | 0.871717i | \(0.663007\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 36.9333 | 1.44310 | ||||||||
\(656\) | −22.6274 | −0.883452 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.258343 | 0.0100712 | ||||||||
\(659\) | 32.5269 | 1.26707 | 0.633534 | − | 0.773715i | \(-0.281604\pi\) | ||||
0.633534 | + | 0.773715i | \(0.281604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.0000 | 1.55582 | 0.777910 | − | 0.628376i | \(-0.216280\pi\) | ||||
0.777910 | + | 0.628376i | \(0.216280\pi\) | |||||||
\(662\) | −7.80177 | −0.303224 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.5167 | −0.640972 | ||||||||
\(665\) | 4.60799 | 0.178690 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.9666 | 1.74111 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 31.7417 | 1.22629 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.4499 | −1.52068 | −0.760342 | − | 0.649523i | \(-0.774969\pi\) | ||||
−0.760342 | + | 0.649523i | \(0.774969\pi\) | |||||||
\(674\) | 9.85230 | 0.379496 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.2970 | 1.24128 | 0.620638 | − | 0.784097i | \(-0.286874\pi\) | ||||
0.620638 | + | 0.784097i | \(0.286874\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.2250 | 0.584281 | ||||||||
\(680\) | 1.36702 | 0.0524228 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.1421 | −0.541134 | −0.270567 | − | 0.962701i | \(-0.587211\pi\) | ||||
−0.270567 | + | 0.962701i | \(0.587211\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 60.7083 | 2.31954 | ||||||||
\(686\) | −1.41421 | −0.0539949 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.00000 | 0.152499 | ||||||||
\(689\) | −13.5058 | −0.514531 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.4499 | 1.31054 | 0.655269 | − | 0.755396i | \(-0.272555\pi\) | ||||
0.655269 | + | 0.755396i | \(0.272555\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −42.8999 | −1.62846 | ||||||||
\(695\) | 9.89949 | 0.375509 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.03337 | −0.0391417 | ||||||||
\(698\) | 26.1865 | 0.991175 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.1394 | −0.987270 | −0.493635 | − | 0.869669i | \(-0.664332\pi\) | ||||
−0.493635 | + | 0.869669i | \(0.664332\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.0000 | 0.754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 47.4833 | 1.78706 | ||||||||
\(707\) | 13.9595 | 0.525000 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.4166 | −1.29254 | −0.646271 | − | 0.763108i | \(-0.723672\pi\) | ||||
−0.646271 | + | 0.763108i | \(0.723672\pi\) | |||||||
\(710\) | −5.29150 | −0.198587 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 31.4833 | 1.17989 | ||||||||
\(713\) | −63.5924 | −2.38155 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 39.9333 | 1.49030 | ||||||||
\(719\) | −2.82843 | −0.105483 | −0.0527413 | − | 0.998608i | \(-0.516796\pi\) | ||||
−0.0527413 | + | 0.998608i | \(0.516796\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.22497 | 0.343556 | ||||||||
\(722\) | 22.5802 | 0.840349 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.4114 | 0.498088 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.1916 | −1.56480 | −0.782400 | − | 0.622776i | \(-0.786005\pi\) | ||||
−0.782400 | + | 0.622776i | \(0.786005\pi\) | |||||||
\(728\) | 4.92615 | 0.182575 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −30.8999 | −1.14366 | ||||||||
\(731\) | 0.182676 | 0.00675651 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.7083 | 1.42972 | 0.714862 | − | 0.699266i | \(-0.246490\pi\) | ||||
0.714862 | + | 0.699266i | \(0.246490\pi\) | |||||||
\(734\) | 7.38923 | 0.272741 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.9333 | −1.17468 | −0.587342 | − | 0.809339i | \(-0.699826\pi\) | ||||
−0.587342 | + | 0.809339i | \(0.699826\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.9666 | 0.402598 | ||||||||
\(743\) | 21.5786 | 0.791640 | 0.395820 | − | 0.918328i | \(-0.370460\pi\) | ||||
0.395820 | + | 0.918328i | \(0.370460\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.67492 | 0.207913 | ||||||||
\(746\) | −35.9917 | −1.31775 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.04886 | −0.0383246 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.03337 | −0.0741987 | −0.0370994 | − | 0.999312i | \(-0.511812\pi\) | ||||
−0.0370994 | + | 0.999312i | \(0.511812\pi\) | |||||||
\(752\) | 0.730703 | 0.0266460 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16.5167 | −0.601502 | ||||||||
\(755\) | 59.4853 | 2.16489 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.51669 | −0.345890 | −0.172945 | − | 0.984932i | \(-0.555328\pi\) | ||||
−0.172945 | + | 0.984932i | \(0.555328\pi\) | |||||||
\(758\) | 27.6008 | 1.00250 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.0334 | 0.472770 | ||||||||
\(761\) | 15.0555 | 0.545762 | 0.272881 | − | 0.962048i | \(-0.412023\pi\) | ||||
0.272881 | + | 0.962048i | \(0.412023\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.51669 | 0.0549077 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.1916 | −0.801815 | ||||||||
\(767\) | 5.24431 | 0.189361 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.4499 | −1.74715 | −0.873575 | − | 0.486690i | \(-0.838204\pi\) | ||||
−0.873575 | + | 0.486690i | \(0.838204\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.76401 | −0.351187 | −0.175594 | − | 0.984463i | \(-0.556184\pi\) | ||||
−0.175594 | + | 0.984463i | \(0.556184\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.9666 | −0.681301 | ||||||||
\(776\) | 43.0627 | 1.54586 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 32.5167 | 1.16578 | ||||||||
\(779\) | −9.85230 | −0.352995 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.73237 | 0.0619495 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.00000 | −0.142857 | ||||||||
\(785\) | −44.8895 | −1.60217 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −52.4499 | −1.86964 | −0.934819 | − | 0.355124i | \(-0.884439\pi\) | ||||
−0.934819 | + | 0.355124i | \(0.884439\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.55006 | 0.197462 | ||||||||
\(791\) | −5.29150 | −0.188144 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.0000 | −0.355110 | ||||||||
\(794\) | 19.0683 | 0.676708 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 53.8284 | 1.90670 | 0.953350 | − | 0.301867i | \(-0.0976099\pi\) | ||||
0.953350 | + | 0.301867i | \(0.0976099\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.0333705 | 0.00118056 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.48331 | 0.123000 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.7417 | −0.625311 | ||||||||
\(806\) | 23.3581 | 0.822755 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 39.4833 | 1.38902 | ||||||||
\(809\) | 42.7446 | 1.50282 | 0.751409 | − | 0.659836i | \(-0.229374\pi\) | ||||
0.751409 | + | 0.659836i | \(0.229374\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.2250 | −1.72852 | −0.864261 | − | 0.503043i | \(-0.832214\pi\) | ||||
−0.864261 | + | 0.503043i | \(0.832214\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −54.1055 | −1.89523 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.74166 | 0.0609329 | ||||||||
\(818\) | 18.7029 | 0.653933 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.9411 | −1.18455 | −0.592277 | − | 0.805735i | \(-0.701771\pi\) | ||||
−0.592277 | + | 0.805735i | \(0.701771\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.93326 | 0.137105 | 0.0685524 | − | 0.997648i | \(-0.478162\pi\) | ||||
0.0685524 | + | 0.997648i | \(0.478162\pi\) | |||||||
\(824\) | 26.0922 | 0.908964 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.25834 | −0.148167 | ||||||||
\(827\) | −52.5969 | −1.82897 | −0.914486 | − | 0.404617i | \(-0.867405\pi\) | ||||
−0.914486 | + | 0.404617i | \(0.867405\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.2250 | 0.945562 | 0.472781 | − | 0.881180i | \(-0.343250\pi\) | ||||
0.472781 | + | 0.881180i | \(0.343250\pi\) | |||||||
\(830\) | −21.8495 | −0.758408 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13.9333 | 0.483049 | ||||||||
\(833\) | −0.182676 | −0.00632934 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −36.9333 | −1.27813 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −25.6749 | −0.886925 | ||||||||
\(839\) | −6.20488 | −0.214216 | −0.107108 | − | 0.994247i | \(-0.534159\pi\) | ||||
−0.107108 | + | 0.994247i | \(0.534159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.9666 | 0.550573 | ||||||||
\(842\) | 31.7962 | 1.09577 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.3692 | 0.907129 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 31.0183 | 1.06517 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.516685 | 0.0177222 | ||||||||
\(851\) | −77.0038 | −2.63966 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.03337 | 0.309297 | 0.154648 | − | 0.987970i | \(-0.450576\pi\) | ||||
0.154648 | + | 0.987970i | \(0.450576\pi\) | |||||||
\(854\) | 8.11993 | 0.277858 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.96663 | −0.101397 | ||||||||
\(857\) | −24.1771 | −0.825874 | −0.412937 | − | 0.910759i | \(-0.635497\pi\) | ||||
−0.412937 | + | 0.910759i | \(0.635497\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.4499 | 0.493026 | 0.246513 | − | 0.969140i | \(-0.420715\pi\) | ||||
0.246513 | + | 0.969140i | \(0.420715\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 22.4499 | 0.764648 | ||||||||
\(863\) | −13.0461 | −0.444094 | −0.222047 | − | 0.975036i | \(-0.571274\pi\) | ||||
−0.222047 | + | 0.975036i | \(0.571274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.4833 | −0.968462 | ||||||||
\(866\) | −8.11993 | −0.275926 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.7750 | 0.500633 | ||||||||
\(872\) | 4.28983 | 0.145272 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 16.5167 | 0.558685 | ||||||||
\(875\) | 7.93725 | 0.268328 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.8999 | −1.38109 | −0.690546 | − | 0.723289i | \(-0.742629\pi\) | ||||
−0.690546 | + | 0.723289i | \(0.742629\pi\) | |||||||
\(878\) | 6.38756 | 0.215570 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.2621 | 0.750028 | 0.375014 | − | 0.927019i | \(-0.377638\pi\) | ||||
0.375014 | + | 0.927019i | \(0.377638\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.4166 | −0.754378 | −0.377189 | − | 0.926136i | \(-0.623109\pi\) | ||||
−0.377189 | + | 0.926136i | \(0.623109\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 53.4833 | 1.79681 | ||||||||
\(887\) | −18.1549 | −0.609582 | −0.304791 | − | 0.952419i | \(-0.598587\pi\) | ||||
−0.304791 | + | 0.952419i | \(0.598587\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.51669 | −0.0508680 | ||||||||
\(890\) | 41.6485 | 1.39606 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.318159 | 0.0106468 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −37.4166 | −1.25070 | ||||||||
\(896\) | −11.3137 | −0.377964 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30.4499 | 1.01613 | ||||||||
\(899\) | −63.5924 | −2.12093 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.41657 | 0.0471929 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.9666 | −0.497783 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.4833 | 0.447706 | 0.223853 | − | 0.974623i | \(-0.428136\pi\) | ||||
0.223853 | + | 0.974623i | \(0.428136\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.51669 | 0.216026 | ||||||||
\(911\) | −17.7013 | −0.586469 | −0.293235 | − | 0.956041i | \(-0.594732\pi\) | ||||
−0.293235 | + | 0.956041i | \(0.594732\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 32.5269 | 1.07589 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.9595 | −0.460982 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −56.9666 | −1.87916 | −0.939578 | − | 0.342335i | \(-0.888782\pi\) | ||||
−0.939578 | + | 0.342335i | \(0.888782\pi\) | |||||||
\(920\) | −50.1810 | −1.65442 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −42.1916 | −1.38951 | ||||||||
\(923\) | −2.46308 | −0.0810731 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.9666 | −0.755138 | ||||||||
\(926\) | 3.55913 | 0.116960 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.548027 | −0.0179802 | −0.00899010 | − | 0.999960i | \(-0.502862\pi\) | ||||
−0.00899010 | + | 0.999960i | \(0.502862\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.74166 | −0.0570805 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 45.4166 | 1.48608 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.2583 | 0.923160 | 0.461580 | − | 0.887099i | \(-0.347283\pi\) | ||||
0.461580 | + | 0.887099i | \(0.347283\pi\) | |||||||
\(938\) | −11.9972 | −0.391723 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.2415 | 0.562058 | 0.281029 | − | 0.959699i | \(-0.409324\pi\) | ||||
0.281029 | + | 0.959699i | \(0.409324\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 37.9333 | 1.23528 | ||||||||
\(944\) | −12.0444 | −0.392012 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.7751 | −0.415135 | −0.207568 | − | 0.978221i | \(-0.566555\pi\) | ||||
−0.207568 | + | 0.978221i | \(0.566555\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.3832 | −0.466899 | ||||||||
\(950\) | 4.92615 | 0.159825 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.516685 | −0.0167459 | ||||||||
\(953\) | 39.9633 | 1.29454 | 0.647270 | − | 0.762261i | \(-0.275911\pi\) | ||||
0.647270 | + | 0.762261i | \(0.275911\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.74166 | 0.121077 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 55.2250 | 1.78424 | ||||||||
\(959\) | −22.9456 | −0.740951 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 58.9333 | 1.90107 | ||||||||
\(962\) | 28.2843 | 0.911922 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.01277 | 0.129176 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.9333 | −0.930431 | −0.465215 | − | 0.885197i | \(-0.654023\pi\) | ||||
−0.465215 | + | 0.885197i | \(0.654023\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 56.9666 | 1.82909 | ||||||||
\(971\) | 32.2970 | 1.03646 | 0.518231 | − | 0.855241i | \(-0.326591\pi\) | ||||
0.518231 | + | 0.855241i | \(0.326591\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.74166 | −0.119952 | ||||||||
\(974\) | −28.9678 | −0.928188 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.9666 | 0.735144 | ||||||||
\(977\) | −22.5802 | −0.722405 | −0.361203 | − | 0.932487i | \(-0.617634\pi\) | ||||
−0.361203 | + | 0.932487i | \(0.617634\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −42.0000 | −1.34027 | ||||||||
\(983\) | 2.82843 | 0.0902128 | 0.0451064 | − | 0.998982i | \(-0.485637\pi\) | ||||
0.0451064 | + | 0.998982i | \(0.485637\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30.8999 | 0.984552 | ||||||||
\(986\) | 1.73237 | 0.0551700 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.70572 | −0.213229 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.4499 | −1.41200 | −0.706000 | − | 0.708212i | \(-0.749502\pi\) | ||||
−0.706000 | + | 0.708212i | \(0.749502\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.00000 | 0.0634361 | ||||||||
\(995\) | −25.7740 | −0.817091 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.9666 | −0.600679 | −0.300340 | − | 0.953832i | \(-0.597100\pi\) | ||||
−0.300340 | + | 0.953832i | \(0.597100\pi\) | |||||||
\(998\) | −16.9234 | −0.535700 | ||||||||
\(999\) | 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 | 7623.2.a.ck.1.1 | yes | 4 | |
3.2 | odd | 2 | inner | 7623.2.a.ck.1.4 | yes | 4 | |
11.10 | odd | 2 | 7623.2.a.cj.1.3 | yes | 4 | ||
33.32 | even | 2 | 7623.2.a.cj.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7623.2.a.cj.1.2 | ✓ | 4 | 33.32 | even | 2 | ||
7623.2.a.cj.1.3 | yes | 4 | 11.10 | odd | 2 | ||
7623.2.a.ck.1.1 | yes | 4 | 1.1 | even | 1 | trivial | |
7623.2.a.ck.1.4 | yes | 4 | 3.2 | odd | 2 | inner |