Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4788,2,Mod(1,4788)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4788, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4788.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4788 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4788.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: | \(38.2323724878\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 532) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4788.1 |
$q$-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 | ||||||||
\(5\) | 4.23607 | 1.89443 | 0.947214 | − | 0.320603i | \(-0.103886\pi\) | ||||
0.947214 | + | 0.320603i | \(0.103886\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.61803 | 0.789367 | 0.394683 | − | 0.918817i | \(-0.370854\pi\) | ||||
0.394683 | + | 0.918817i | \(0.370854\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.47214 | 0.962997 | 0.481499 | − | 0.876447i | \(-0.340093\pi\) | ||||
0.481499 | + | 0.876447i | \(0.340093\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.85410 | 1.41983 | 0.709914 | − | 0.704288i | \(-0.248734\pi\) | ||||
0.709914 | + | 0.704288i | \(0.248734\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.23607 | 1.71734 | 0.858669 | − | 0.512530i | \(-0.171292\pi\) | ||||
0.858669 | + | 0.512530i | \(0.171292\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.9443 | 2.58885 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.61803 | 0.857547 | 0.428774 | − | 0.903412i | \(-0.358946\pi\) | ||||
0.428774 | + | 0.903412i | \(0.358946\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.85410 | −0.692217 | −0.346109 | − | 0.938194i | \(-0.612497\pi\) | ||||
−0.346109 | + | 0.938194i | \(0.612497\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.23607 | −0.716026 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.23607 | −1.35400 | −0.677001 | − | 0.735982i | \(-0.736721\pi\) | ||||
−0.677001 | + | 0.735982i | \(0.736721\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.5623 | −1.80573 | −0.902864 | − | 0.429925i | \(-0.858540\pi\) | ||||
−0.902864 | + | 0.429925i | \(0.858540\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.47214 | 0.681994 | 0.340997 | − | 0.940064i | \(-0.389235\pi\) | ||||
0.340997 | + | 0.940064i | \(0.389235\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.47214 | −1.08992 | −0.544962 | − | 0.838461i | \(-0.683456\pi\) | ||||
−0.544962 | + | 0.838461i | \(0.683456\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.09017 | −0.836549 | −0.418275 | − | 0.908321i | \(-0.637365\pi\) | ||||
−0.418275 | + | 0.908321i | \(0.637365\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.0902 | 1.49540 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.0000 | −1.43208 | −0.716039 | − | 0.698060i | \(-0.754047\pi\) | ||||
−0.716039 | + | 0.698060i | \(0.754047\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.23607 | −0.542373 | −0.271186 | − | 0.962527i | \(-0.587416\pi\) | ||||
−0.271186 | + | 0.962527i | \(0.587416\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.7082 | 1.82433 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.56231 | −0.923883 | −0.461941 | − | 0.886910i | \(-0.652847\pi\) | ||||
−0.461941 | + | 0.886910i | \(0.652847\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.76393 | 0.446697 | 0.223348 | − | 0.974739i | \(-0.428301\pi\) | ||||
0.223348 | + | 0.974739i | \(0.428301\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.61803 | 0.423459 | 0.211729 | − | 0.977328i | \(-0.432090\pi\) | ||||
0.211729 | + | 0.977328i | \(0.432090\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.61803 | −0.298353 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.47214 | −0.503155 | −0.251577 | − | 0.967837i | \(-0.580949\pi\) | ||||
−0.251577 | + | 0.967837i | \(0.580949\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.5623 | −1.15936 | −0.579682 | − | 0.814843i | \(-0.696823\pi\) | ||||
−0.579682 | + | 0.814843i | \(0.696823\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 24.7984 | 2.68976 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.7082 | 1.66507 | 0.832533 | − | 0.553975i | \(-0.186890\pi\) | ||||
0.832533 | + | 0.553975i | \(0.186890\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.47214 | −0.363979 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.23607 | 0.434611 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.47214 | −0.352542 | −0.176271 | − | 0.984342i | \(-0.556404\pi\) | ||||
−0.176271 | + | 0.984342i | \(0.556404\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.4164 | 1.43449 | 0.717243 | − | 0.696823i | \(-0.245404\pi\) | ||||
0.717243 | + | 0.696823i | \(0.245404\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.52786 | 0.643210 | 0.321605 | − | 0.946874i | \(-0.395778\pi\) | ||||
0.321605 | + | 0.946874i | \(0.395778\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.1803 | −1.46754 | −0.733769 | − | 0.679399i | \(-0.762241\pi\) | ||||
−0.733769 | + | 0.679399i | \(0.762241\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.527864 | 0.0505602 | 0.0252801 | − | 0.999680i | \(-0.491952\pi\) | ||||
0.0252801 | + | 0.999680i | \(0.491952\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.5623 | 1.55805 | 0.779025 | − | 0.626992i | \(-0.215714\pi\) | ||||
0.779025 | + | 0.626992i | \(0.215714\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 34.8885 | 3.25337 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.85410 | −0.536645 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.14590 | −0.376900 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 33.6525 | 3.00997 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.7082 | −1.39388 | −0.696939 | − | 0.717131i | \(-0.745455\pi\) | ||||
−0.696939 | + | 0.717131i | \(0.745455\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.90983 | −0.428974 | −0.214487 | − | 0.976727i | \(-0.568808\pi\) | ||||
−0.214487 | + | 0.976727i | \(0.568808\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.41641 | −0.462755 | −0.231377 | − | 0.972864i | \(-0.574323\pi\) | ||||
−0.231377 | + | 0.972864i | \(0.574323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.52786 | 0.214411 | 0.107205 | − | 0.994237i | \(-0.465810\pi\) | ||||
0.107205 | + | 0.994237i | \(0.465810\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.09017 | 0.760158 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.5623 | 1.62456 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.4164 | −0.853345 | −0.426673 | − | 0.904406i | \(-0.640314\pi\) | ||||
−0.426673 | + | 0.904406i | \(0.640314\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.09017 | 0.0887168 | 0.0443584 | − | 0.999016i | \(-0.485876\pi\) | ||||
0.0443584 | + | 0.999016i | \(0.485876\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.3262 | −1.31135 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.5623 | −0.922772 | −0.461386 | − | 0.887199i | \(-0.652648\pi\) | ||||
−0.461386 | + | 0.887199i | \(0.652648\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.23607 | −0.649093 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.14590 | −0.246406 | −0.123203 | − | 0.992382i | \(-0.539317\pi\) | ||||
−0.123203 | + | 0.992382i | \(0.539317\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.23607 | 0.482561 | 0.241281 | − | 0.970455i | \(-0.422433\pi\) | ||||
0.241281 | + | 0.970455i | \(0.422433\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.944272 | −0.0726363 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.70820 | −0.586044 | −0.293022 | − | 0.956106i | \(-0.594661\pi\) | ||||
−0.293022 | + | 0.956106i | \(0.594661\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.9443 | −0.978495 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.79837 | 0.508134 | 0.254067 | − | 0.967187i | \(-0.418232\pi\) | ||||
0.254067 | + | 0.967187i | \(0.418232\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.7984 | 0.802637 | 0.401318 | − | 0.915939i | \(-0.368552\pi\) | ||||
0.401318 | + | 0.915939i | \(0.368552\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −34.8885 | −2.56506 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.3262 | 1.12077 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.0902 | 1.16424 | 0.582122 | − | 0.813102i | \(-0.302223\pi\) | ||||
0.582122 | + | 0.813102i | \(0.302223\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.27051 | −0.667306 | −0.333653 | − | 0.942696i | \(-0.608281\pi\) | ||||
−0.333653 | + | 0.942696i | \(0.608281\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.90983 | 0.706046 | 0.353023 | − | 0.935615i | \(-0.385154\pi\) | ||||
0.353023 | + | 0.935615i | \(0.385154\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.00000 | −0.496217 | −0.248108 | − | 0.968732i | \(-0.579809\pi\) | ||||
−0.248108 | + | 0.968732i | \(0.579809\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.61803 | −0.324122 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −48.9787 | −3.42082 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.61803 | 0.181093 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.381966 | −0.0262956 | −0.0131478 | − | 0.999914i | \(-0.504185\pi\) | ||||
−0.0131478 | + | 0.999914i | \(0.504185\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.9443 | 1.29199 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.85410 | 0.261633 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.3262 | 1.36729 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.7639 | −1.45742 | −0.728710 | − | 0.684822i | \(-0.759880\pi\) | ||||
−0.728710 | + | 0.684822i | \(0.759880\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.14590 | −0.540662 | −0.270331 | − | 0.962767i | \(-0.587133\pi\) | ||||
−0.270331 | + | 0.962767i | \(0.587133\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.4721 | 1.61716 | 0.808582 | − | 0.588383i | \(-0.200235\pi\) | ||||
0.808582 | + | 0.588383i | \(0.200235\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 27.0902 | 1.77474 | 0.887368 | − | 0.461062i | \(-0.152531\pi\) | ||||
0.887368 | + | 0.461062i | \(0.152531\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −31.6525 | −2.06478 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.6525 | −1.01247 | −0.506237 | − | 0.862394i | \(-0.668964\pi\) | ||||
−0.506237 | + | 0.862394i | \(0.668964\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.2361 | −0.723779 | −0.361889 | − | 0.932221i | \(-0.617868\pi\) | ||||
−0.361889 | + | 0.932221i | \(0.617868\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.23607 | 0.270632 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.47214 | 0.220927 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.85410 | 0.495747 | 0.247873 | − | 0.968792i | \(-0.420268\pi\) | ||||
0.247873 | + | 0.968792i | \(0.420268\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.5623 | 1.35561 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.90983 | 0.618158 | 0.309079 | − | 0.951036i | \(-0.399979\pi\) | ||||
0.309079 | + | 0.951036i | \(0.399979\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.23607 | 0.511764 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.43769 | 0.335303 | 0.167651 | − | 0.985846i | \(-0.446382\pi\) | ||||
0.167651 | + | 0.985846i | \(0.446382\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.7984 | −1.58478 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.32624 | 0.446689 | 0.223344 | − | 0.974740i | \(-0.428303\pi\) | ||||
0.223344 | + | 0.974740i | \(0.428303\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.2705 | 1.29209 | 0.646046 | − | 0.763299i | \(-0.276422\pi\) | ||||
0.646046 | + | 0.763299i | \(0.276422\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 33.8885 | 2.04356 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.18034 | −0.491509 | −0.245754 | − | 0.969332i | \(-0.579036\pi\) | ||||
−0.245754 | + | 0.969332i | \(0.579036\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.4164 | 0.979321 | 0.489660 | − | 0.871913i | \(-0.337121\pi\) | ||||
0.489660 | + | 0.871913i | \(0.337121\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.09017 | −0.480911 | −0.240455 | − | 0.970660i | \(-0.577297\pi\) | ||||
−0.240455 | + | 0.970660i | \(0.577297\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.5623 | 0.682501 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.2705 | 1.01591 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.236068 | −0.0137912 | −0.00689562 | − | 0.999976i | \(-0.502195\pi\) | ||||
−0.00689562 | + | 0.999976i | \(0.502195\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −46.5967 | −2.71297 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 28.5967 | 1.65379 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.47214 | −0.257770 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −17.9443 | −1.02749 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.8541 | 1.13313 | 0.566567 | − | 0.824016i | \(-0.308271\pi\) | ||||
0.566567 | + | 0.824016i | \(0.308271\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.7426 | −0.779274 | −0.389637 | − | 0.920969i | \(-0.627400\pi\) | ||||
−0.389637 | + | 0.920969i | \(0.627400\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.23607 | −0.409007 | −0.204503 | − | 0.978866i | \(-0.565558\pi\) | ||||
−0.204503 | + | 0.978866i | \(0.565558\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.5279 | 0.647469 | 0.323735 | − | 0.946148i | \(-0.395061\pi\) | ||||
0.323735 | + | 0.946148i | \(0.395061\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0902 | 0.676920 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.85410 | 0.325731 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 44.9443 | 2.49306 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.47214 | 0.411952 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.0344 | −0.606508 | −0.303254 | − | 0.952910i | \(-0.598073\pi\) | ||||
−0.303254 | + | 0.952910i | \(0.598073\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −32.0344 | −1.75023 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.38197 | −0.0752805 | −0.0376402 | − | 0.999291i | \(-0.511984\pi\) | ||||
−0.0376402 | + | 0.999291i | \(0.511984\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.0902 | −0.546413 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.9787 | −1.07251 | −0.536257 | − | 0.844055i | \(-0.680162\pi\) | ||||
−0.536257 | + | 0.844055i | \(0.680162\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.43769 | −0.0769580 | −0.0384790 | − | 0.999259i | \(-0.512251\pi\) | ||||
−0.0384790 | + | 0.999259i | \(0.512251\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.9787 | −0.584338 | −0.292169 | − | 0.956367i | \(-0.594377\pi\) | ||||
−0.292169 | + | 0.956367i | \(0.594377\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.9443 | 0.846234 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.2705 | −1.43928 | −0.719641 | − | 0.694346i | \(-0.755694\pi\) | ||||
−0.719641 | + | 0.694346i | \(0.755694\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.3262 | 0.802212 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.7082 | −1.18536 | −0.592679 | − | 0.805439i | \(-0.701930\pi\) | ||||
−0.592679 | + | 0.805439i | \(0.701930\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.09017 | 0.316186 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.7984 | 1.23223 | 0.616117 | − | 0.787655i | \(-0.288705\pi\) | ||||
0.616117 | + | 0.787655i | \(0.288705\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.0344 | 0.825816 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.0000 | −0.667765 | −0.333883 | − | 0.942615i | \(-0.608359\pi\) | ||||
−0.333883 | + | 0.942615i | \(0.608359\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.4164 | −0.736644 | −0.368322 | − | 0.929698i | \(-0.620068\pi\) | ||||
−0.368322 | + | 0.929698i | \(0.620068\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.0902 | −0.565207 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.43769 | −0.123596 | −0.0617980 | − | 0.998089i | \(-0.519683\pi\) | ||||
−0.0617980 | + | 0.998089i | \(0.519683\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 48.2148 | 2.43833 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.9443 | −0.953190 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.70820 | −0.186109 | −0.0930547 | − | 0.995661i | \(-0.529663\pi\) | ||||
−0.0930547 | + | 0.995661i | \(0.529663\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.72949 | −0.136304 | −0.0681521 | − | 0.997675i | \(-0.521710\pi\) | ||||
−0.0681521 | + | 0.997675i | \(0.521710\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.3820 | −0.666603 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.5623 | −1.06880 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.8541 | 0.734488 | 0.367244 | − | 0.930125i | \(-0.380301\pi\) | ||||
0.367244 | + | 0.930125i | \(0.380301\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.0000 | 0.541275 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −44.7426 | −2.19633 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.5279 | −1.00285 | −0.501426 | − | 0.865201i | \(-0.667191\pi\) | ||||
−0.501426 | + | 0.865201i | \(0.667191\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.1246 | −0.493443 | −0.246722 | − | 0.969086i | \(-0.579353\pi\) | ||||
−0.246722 | + | 0.969086i | \(0.579353\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 75.7771 | 3.67573 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.23607 | 0.204998 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.0000 | 0.481683 | 0.240842 | − | 0.970564i | \(-0.422577\pi\) | ||||
0.240842 | + | 0.970564i | \(0.422577\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −36.5967 | −1.75873 | −0.879364 | − | 0.476151i | \(-0.842032\pi\) | ||||
−0.879364 | + | 0.476151i | \(0.842032\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.23607 | 0.393985 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0000 | 0.763638 | 0.381819 | − | 0.924237i | \(-0.375298\pi\) | ||||
0.381819 | + | 0.924237i | \(0.375298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.5623 | −0.501830 | −0.250915 | − | 0.968009i | \(-0.580732\pi\) | ||||
−0.250915 | + | 0.968009i | \(0.580732\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 66.5410 | 3.15435 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.27051 | 0.295924 | 0.147962 | − | 0.988993i | \(-0.452729\pi\) | ||||
0.147962 | + | 0.988993i | \(0.452729\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.2705 | −1.42538 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.7082 | −0.689531 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.7984 | −1.30035 | −0.650177 | − | 0.759783i | \(-0.725305\pi\) | ||||
−0.650177 | + | 0.759783i | \(0.725305\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.2148 | −1.45382 | −0.726909 | − | 0.686734i | \(-0.759044\pi\) | ||||
−0.726909 | + | 0.686734i | \(0.759044\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.05573 | −0.188486 | −0.0942428 | − | 0.995549i | \(-0.530043\pi\) | ||||
−0.0942428 | + | 0.995549i | \(0.530043\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 40.4508 | 1.87184 | 0.935921 | − | 0.352210i | \(-0.114570\pi\) | ||||
0.935921 | + | 0.352210i | \(0.114570\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.56231 | 0.349195 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.7082 | 0.538344 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.9443 | 0.593924 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.3262 | 0.563200 | 0.281600 | − | 0.959532i | \(-0.409135\pi\) | ||||
0.281600 | + | 0.959532i | \(0.409135\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.5967 | −1.30390 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.7082 | −0.667865 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.1803 | 1.50354 | 0.751772 | − | 0.659423i | \(-0.229199\pi\) | ||||
0.751772 | + | 0.659423i | \(0.229199\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.4164 | 1.05677 | 0.528384 | − | 0.849006i | \(-0.322798\pi\) | ||||
0.528384 | + | 0.849006i | \(0.322798\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.0344 | 1.21757 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.76393 | −0.168835 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.6180 | 1.59448 | 0.797241 | − | 0.603661i | \(-0.206292\pi\) | ||||
0.797241 | + | 0.603661i | \(0.206292\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.9443 | 0.577157 | 0.288578 | − | 0.957456i | \(-0.406817\pi\) | ||||
0.288578 | + | 0.957456i | \(0.406817\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 61.0689 | 2.71753 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.8328 | −1.45529 | −0.727644 | − | 0.685954i | \(-0.759385\pi\) | ||||
−0.727644 | + | 0.685954i | \(0.759385\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.61803 | −0.160052 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 27.6525 | 1.21851 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.5623 | −0.860349 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.1803 | −1.71652 | −0.858261 | − | 0.513214i | \(-0.828455\pi\) | ||||
−0.858261 | + | 0.513214i | \(0.828455\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.5967 | 1.51281 | 0.756405 | − | 0.654103i | \(-0.226954\pi\) | ||||
0.756405 | + | 0.654103i | \(0.226954\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.5623 | −0.982829 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.8328 | 1.94925 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −40.1459 | −1.73891 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −64.3050 | −2.78015 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.61803 | 0.112767 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.3607 | −1.13333 | −0.566667 | − | 0.823947i | \(-0.691767\pi\) | ||||
−0.566667 | + | 0.823947i | \(0.691767\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.23607 | 0.0957826 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.3951 | 1.51339 | 0.756693 | − | 0.653770i | \(-0.226814\pi\) | ||||
0.756693 | + | 0.653770i | \(0.226814\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.61803 | 0.196735 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.47214 | 0.190175 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.3262 | 0.776508 | 0.388254 | − | 0.921552i | \(-0.373078\pi\) | ||||
0.388254 | + | 0.921552i | \(0.373078\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.5279 | 0.656759 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.8328 | 1.59446 | 0.797232 | − | 0.603674i | \(-0.206297\pi\) | ||||
0.797232 | + | 0.603674i | \(0.206297\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 70.1591 | 2.95161 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 38.0132 | 1.59359 | 0.796797 | − | 0.604247i | \(-0.206526\pi\) | ||||
0.796797 | + | 0.604247i | \(0.206526\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.527864 | 0.0220904 | 0.0110452 | − | 0.999939i | \(-0.496484\pi\) | ||||
0.0110452 | + | 0.999939i | \(0.496484\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 106.610 | 4.44594 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.6869 | −0.986099 | −0.493050 | − | 0.870001i | \(-0.664118\pi\) | ||||
−0.493050 | + | 0.870001i | \(0.664118\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.5623 | 0.438198 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.9443 | −0.660344 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.5836 | −0.436832 | −0.218416 | − | 0.975856i | \(-0.570089\pi\) | ||||
−0.218416 | + | 0.975856i | \(0.570089\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.85410 | −0.158806 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.5279 | 1.08937 | 0.544684 | − | 0.838641i | \(-0.316649\pi\) | ||||
0.544684 | + | 0.838641i | \(0.316649\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.7984 | −1.01663 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.5623 | −0.513282 | −0.256641 | − | 0.966507i | \(-0.582616\pi\) | ||||
−0.256641 | + | 0.966507i | \(0.582616\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.14590 | −0.128324 | −0.0641619 | − | 0.997940i | \(-0.520437\pi\) | ||||
−0.0641619 | + | 0.997940i | \(0.520437\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.5623 | −0.714009 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.00000 | 0.121766 | 0.0608831 | − | 0.998145i | \(-0.480608\pi\) | ||||
0.0608831 | + | 0.998145i | \(0.480608\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.9443 | −1.04959 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.0902 | −0.569097 | −0.284548 | − | 0.958662i | \(-0.591844\pi\) | ||||
−0.284548 | + | 0.958662i | \(0.591844\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.4377 | −0.661757 | −0.330878 | − | 0.943673i | \(-0.607345\pi\) | ||||
−0.330878 | + | 0.943673i | \(0.607345\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.3820 | −1.46231 | −0.731157 | − | 0.682209i | \(-0.761019\pi\) | ||||
−0.731157 | + | 0.682209i | \(0.761019\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.7082 | −0.629336 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 77.8328 | 3.11331 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −48.2148 | −1.92245 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.8885 | 0.513085 | 0.256542 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256542 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −66.5410 | −2.64060 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.47214 | 0.137571 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.6738 | 0.935057 | 0.467529 | − | 0.883978i | \(-0.345144\pi\) | ||||
0.467529 | + | 0.883978i | \(0.345144\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.1803 | 0.914143 | 0.457072 | − | 0.889430i | \(-0.348898\pi\) | ||||
0.457072 | + | 0.889430i | \(0.348898\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.41641 | −0.173627 | −0.0868135 | − | 0.996225i | \(-0.527668\pi\) | ||||
−0.0868135 | + | 0.996225i | \(0.527668\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.7984 | −1.13044 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.1246 | −0.709271 | −0.354635 | − | 0.935005i | \(-0.615395\pi\) | ||||
−0.354635 | + | 0.935005i | \(0.615395\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.7984 | −0.812660 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.6180 | −0.725256 | −0.362628 | − | 0.931934i | \(-0.618120\pi\) | ||||
−0.362628 | + | 0.931934i | \(0.618120\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.0557 | −0.974555 | −0.487277 | − | 0.873247i | \(-0.662010\pi\) | ||||
−0.487277 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.23607 | −0.164268 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 38.0344 | 1.47270 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.0902 | −0.428131 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.5623 | −0.484241 | −0.242121 | − | 0.970246i | \(-0.577843\pi\) | ||||
−0.242121 | + | 0.970246i | \(0.577843\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.3820 | 1.16767 | 0.583837 | − | 0.811871i | \(-0.301551\pi\) | ||||
0.583837 | + | 0.811871i | \(0.301551\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.47214 | 0.133248 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.2361 | 0.391672 | 0.195836 | − | 0.980637i | \(-0.437258\pi\) | ||||
0.195836 | + | 0.980637i | \(0.437258\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.9443 | −0.876656 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21.1459 | −0.805595 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.2918 | −0.543686 | −0.271843 | − | 0.962342i | \(-0.587633\pi\) | ||||
−0.271843 | + | 0.962342i | \(0.587633\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.7082 | 0.406185 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −67.6869 | −2.56382 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.3607 | −0.769012 | −0.384506 | − | 0.923122i | \(-0.625628\pi\) | ||||
−0.384506 | + | 0.923122i | \(0.625628\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.23607 | −0.310629 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.4164 | −0.542185 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.2918 | 1.32541 | 0.662706 | − | 0.748880i | \(-0.269408\pi\) | ||||
0.662706 | + | 0.748880i | \(0.269408\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31.7426 | −1.18877 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 38.5066 | 1.44006 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.9443 | 0.631915 | 0.315957 | − | 0.948773i | \(-0.397674\pi\) | ||||
0.315957 | + | 0.948773i | \(0.397674\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.52786 | −0.243110 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 59.7771 | 2.22007 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.0689 | 1.37481 | 0.687404 | − | 0.726275i | \(-0.258750\pi\) | ||||
0.687404 | + | 0.726275i | \(0.258750\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.1803 | 0.968315 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.0000 | −1.18195 | −0.590973 | − | 0.806691i | \(-0.701256\pi\) | ||||
−0.590973 | + | 0.806691i | \(0.701256\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −19.7984 | −0.729282 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.29180 | 0.121091 | 0.0605453 | − | 0.998165i | \(-0.480716\pi\) | ||||
0.0605453 | + | 0.998165i | \(0.480716\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −41.5410 | −1.52399 | −0.761996 | − | 0.647582i | \(-0.775780\pi\) | ||||
−0.761996 | + | 0.647582i | \(0.775780\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −44.1246 | −1.61660 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.1803 | 0.554678 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0902 | 0.368196 | 0.184098 | − | 0.982908i | \(-0.441064\pi\) | ||||
0.184098 | + | 0.982908i | \(0.441064\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.61803 | 0.168067 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.52786 | 0.273605 | 0.136802 | − | 0.990598i | \(-0.456317\pi\) | ||||
0.136802 | + | 0.990598i | \(0.456317\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46.5967 | −1.68913 | −0.844565 | − | 0.535452i | \(-0.820141\pi\) | ||||
−0.844565 | + | 0.535452i | \(0.820141\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.527864 | −0.0191100 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −38.1935 | −1.37909 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.9443 | 0.899513 | 0.449757 | − | 0.893151i | \(-0.351511\pi\) | ||||
0.449757 | + | 0.893151i | \(0.351511\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.7082 | 1.06853 | 0.534265 | − | 0.845317i | \(-0.320588\pi\) | ||||
0.534265 | + | 0.845317i | \(0.320588\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −49.8885 | −1.79205 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.5623 | −0.414263 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.85410 | 0.352607 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −48.9787 | −1.74813 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.4164 | 1.11987 | 0.559937 | − | 0.828535i | \(-0.310825\pi\) | ||||
0.559937 | + | 0.828535i | \(0.310825\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.5623 | −0.588888 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.7082 | −0.522304 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.9787 | 0.813948 | 0.406974 | − | 0.913440i | \(-0.366584\pi\) | ||||
0.406974 | + | 0.913440i | \(0.366584\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43.7426 | −1.54750 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.47214 | 0.334264 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −34.8885 | −1.22966 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.0689 | −0.389161 | −0.194581 | − | 0.980887i | \(-0.562335\pi\) | ||||
−0.194581 | + | 0.980887i | \(0.562335\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.8328 | −1.71475 | −0.857376 | − | 0.514691i | \(-0.827907\pi\) | ||||
−0.857376 | + | 0.514691i | \(0.827907\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.3262 | −0.466798 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.47214 | 0.156460 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.3607 | −1.54820 | −0.774099 | − | 0.633064i | \(-0.781797\pi\) | ||||
−0.774099 | + | 0.633064i | \(0.781797\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.76393 | −0.305491 | −0.152746 | − | 0.988266i | \(-0.548812\pi\) | ||||
−0.152746 | + | 0.988266i | \(0.548812\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.29180 | −0.253561 | −0.126780 | − | 0.991931i | \(-0.540464\pi\) | ||||
−0.126780 | + | 0.991931i | \(0.540464\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.11146 | −0.212260 | −0.106130 | − | 0.994352i | \(-0.533846\pi\) | ||||
−0.106130 | + | 0.994352i | \(0.533846\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.85410 | 0.202833 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.4164 | 0.914177 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.4721 | −1.19011 | −0.595055 | − | 0.803685i | \(-0.702870\pi\) | ||||
−0.595055 | + | 0.803685i | \(0.702870\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.67376 | −0.264612 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.00000 | −0.137604 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.14590 | 0.142455 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −67.8328 | −2.32528 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.6180 | −1.08258 | −0.541290 | − | 0.840836i | \(-0.682064\pi\) | ||||
−0.541290 | + | 0.840836i | \(0.682064\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 49.9230 | 1.70534 | 0.852668 | − | 0.522453i | \(-0.174983\pi\) | ||||
0.852668 | + | 0.522453i | \(0.174983\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.4508 | −0.663654 | −0.331827 | − | 0.943340i | \(-0.607665\pi\) | ||||
−0.331827 | + | 0.943340i | \(0.607665\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.1591 | 0.958545 | 0.479273 | − | 0.877666i | \(-0.340901\pi\) | ||||
0.479273 | + | 0.877666i | \(0.340901\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.6525 | −1.11022 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.7082 | −0.397174 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.2574 | −0.889697 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −33.6525 | −1.13766 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.5410 | 1.84172 | 0.920860 | − | 0.389894i | \(-0.127488\pi\) | ||||
0.920860 | + | 0.389894i | \(0.127488\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.21478 | 0.175690 | 0.0878452 | − | 0.996134i | \(-0.472002\pi\) | ||||
0.0878452 | + | 0.996134i | \(0.472002\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.0689 | −1.51669 | −0.758344 | − | 0.651854i | \(-0.773991\pi\) | ||||
−0.758344 | + | 0.651854i | \(0.773991\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.1246 | 0.541411 | 0.270706 | − | 0.962662i | \(-0.412743\pi\) | ||||
0.270706 | + | 0.962662i | \(0.412743\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.7082 | 0.526836 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.47214 | −0.250045 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.7984 | 0.962623 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.7984 | −0.593609 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −35.6525 | −1.18776 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 45.7426 | 1.52054 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46.1935 | 1.53383 | 0.766915 | − | 0.641749i | \(-0.221791\pi\) | ||||
0.766915 | + | 0.641749i | \(0.221791\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.58359 | 0.218124 | 0.109062 | − | 0.994035i | \(-0.465215\pi\) | ||||
0.109062 | + | 0.994035i | \(0.465215\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.6525 | −0.915163 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.90983 | 0.162137 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.63932 | 0.0870631 | 0.0435316 | − | 0.999052i | \(-0.486139\pi\) | ||||
0.0435316 | + | 0.999052i | \(0.486139\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.0689 | 0.430168 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −106.610 | −3.50531 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.4508 | −0.539735 | −0.269867 | − | 0.962897i | \(-0.586980\pi\) | ||||
−0.269867 | + | 0.962897i | \(0.586980\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000 | 0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 64.9230 | 2.12321 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.2148 | −1.24842 | −0.624211 | − | 0.781256i | \(-0.714580\pi\) | ||||
−0.624211 | + | 0.781256i | \(0.714580\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.4721 | 0.797769 | 0.398884 | − | 0.917001i | \(-0.369397\pi\) | ||||
0.398884 | + | 0.917001i | \(0.369397\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −95.2279 | −3.10105 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.4508 | 0.859537 | 0.429769 | − | 0.902939i | \(-0.358595\pi\) | ||||
0.429769 | + | 0.902939i | \(0.358595\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.5623 | 0.407790 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.4508 | 1.01879 | 0.509396 | − | 0.860532i | \(-0.329869\pi\) | ||||
0.509396 | + | 0.860532i | \(0.329869\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 68.1591 | 2.20558 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.41641 | 0.174905 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.1459 | −0.520835 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −39.2705 | −1.26416 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.6869 | −0.793878 | −0.396939 | − | 0.917845i | \(-0.629928\pi\) | ||||
−0.396939 | + | 0.917845i | \(0.629928\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50.8885 | −1.63309 | −0.816546 | − | 0.577281i | \(-0.804114\pi\) | ||||
−0.816546 | + | 0.577281i | \(0.804114\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.52786 | −0.0810396 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.7639 | 1.30415 | 0.652077 | − | 0.758153i | \(-0.273898\pi\) | ||||
0.652077 | + | 0.758153i | \(0.273898\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 41.1246 | 1.31435 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.5836 | −1.07115 | −0.535575 | − | 0.844488i | \(-0.679905\pi\) | ||||
−0.535575 | + | 0.844488i | \(0.679905\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.9787 | 1.33755 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 36.8328 | 1.17122 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.763932 | −0.0242671 | −0.0121336 | − | 0.999926i | \(-0.503862\pi\) | ||||
−0.0121336 | + | 0.999926i | \(0.503862\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.6525 | −0.940047 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.6312 | 0.716737 | 0.358368 | − | 0.933580i | \(-0.383333\pi\) | ||||
0.358368 | + | 0.933580i | \(0.383333\pi\) | |||||||
\(998\) | 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 | 4788.2.a.n.1.2 | 2 | ||
3.2 | odd | 2 | 532.2.a.d.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 2128.2.a.e.1.1 | 2 | |||
21.20 | even | 2 | 3724.2.a.d.1.1 | 2 | |||
24.5 | odd | 2 | 8512.2.a.s.1.1 | 2 | |||
24.11 | even | 2 | 8512.2.a.z.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
532.2.a.d.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
2128.2.a.e.1.1 | 2 | 12.11 | even | 2 | |||
3724.2.a.d.1.1 | 2 | 21.20 | even | 2 | |||
4788.2.a.n.1.2 | 2 | 1.1 | even | 1 | trivial | ||
8512.2.a.s.1.1 | 2 | 24.5 | odd | 2 | |||
8512.2.a.z.1.2 | 2 | 24.11 | even | 2 |