Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7800,2,Mod(1,7800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7800.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: | \(62.2833135766\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 6x - 2 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.12489\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7800.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.12489 | 0.803131 | 0.401566 | − | 0.915830i | \(-0.368466\pi\) | ||||
0.401566 | + | 0.915830i | \(0.368466\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.15516 | 0.951317 | 0.475658 | − | 0.879630i | \(-0.342210\pi\) | ||||
0.475658 | + | 0.879630i | \(0.342210\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.515138 | −0.124939 | −0.0624697 | − | 0.998047i | \(-0.519898\pi\) | ||||
−0.0624697 | + | 0.998047i | \(0.519898\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.73463 | 1.54503 | 0.772515 | − | 0.634996i | \(-0.218998\pi\) | ||||
0.772515 | + | 0.634996i | \(0.218998\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.12489 | 0.463688 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.24977 | 0.886138 | 0.443069 | − | 0.896487i | \(-0.353890\pi\) | ||||
0.443069 | + | 0.896487i | \(0.353890\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0302761 | 0.00562213 | 0.00281106 | − | 0.999996i | \(-0.499105\pi\) | ||||
0.00281106 | + | 0.999996i | \(0.499105\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.15516 | 1.28510 | 0.642552 | − | 0.766242i | \(-0.277875\pi\) | ||||
0.642552 | + | 0.766242i | \(0.277875\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.15516 | 0.549243 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.76491 | −0.947745 | −0.473873 | − | 0.880593i | \(-0.657144\pi\) | ||||
−0.473873 | + | 0.880593i | \(0.657144\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.76491 | −0.587980 | −0.293990 | − | 0.955808i | \(-0.594983\pi\) | ||||
−0.293990 | + | 0.955808i | \(0.594983\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.28005 | 0.500202 | 0.250101 | − | 0.968220i | \(-0.419536\pi\) | ||||
0.250101 | + | 0.968220i | \(0.419536\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.60975 | 0.672401 | 0.336200 | − | 0.941790i | \(-0.390858\pi\) | ||||
0.336200 | + | 0.941790i | \(0.390858\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.48486 | −0.354980 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.515138 | −0.0721338 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.280047 | −0.0384674 | −0.0192337 | − | 0.999815i | \(-0.506123\pi\) | ||||
−0.0192337 | + | 0.999815i | \(0.506123\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.73463 | 0.892024 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.3444 | 1.47691 | 0.738456 | − | 0.674301i | \(-0.235555\pi\) | ||||
0.738456 | + | 0.674301i | \(0.235555\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.01468 | −0.642064 | −0.321032 | − | 0.947068i | \(-0.604030\pi\) | ||||
−0.321032 | + | 0.947068i | \(0.604030\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.12489 | 0.267710 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.1093 | −1.84589 | −0.922947 | − | 0.384928i | \(-0.874226\pi\) | ||||
−0.922947 | + | 0.384928i | \(0.874226\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.24977 | 0.511612 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.23509 | 0.265257 | 0.132628 | − | 0.991166i | \(-0.457658\pi\) | ||||
0.132628 | + | 0.991166i | \(0.457658\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.96972 | 0.347580 | 0.173790 | − | 0.984783i | \(-0.444399\pi\) | ||||
0.173790 | + | 0.984783i | \(0.444399\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.70436 | 0.764032 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.98440 | −1.01082 | −0.505412 | − | 0.862878i | \(-0.668660\pi\) | ||||
−0.505412 | + | 0.862878i | \(0.668660\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.40493 | −0.593268 | −0.296634 | − | 0.954991i | \(-0.595864\pi\) | ||||
−0.296634 | + | 0.954991i | \(0.595864\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.0302761 | 0.00324594 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.5298 | −1.64616 | −0.823079 | − | 0.567927i | \(-0.807745\pi\) | ||||
−0.823079 | + | 0.567927i | \(0.807745\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.12489 | −0.222749 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.15516 | 0.741956 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.909172 | −0.0923124 | −0.0461562 | − | 0.998934i | \(-0.514697\pi\) | ||||
−0.0461562 | + | 0.998934i | \(0.514697\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.15516 | 0.317106 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.0450 | 1.59653 | 0.798266 | − | 0.602305i | \(-0.205751\pi\) | ||||
0.798266 | + | 0.602305i | \(0.205751\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.5601 | 1.04052 | 0.520258 | − | 0.854009i | \(-0.325836\pi\) | ||||
0.520258 | + | 0.854009i | \(0.325836\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.0450 | 1.06776 | 0.533878 | − | 0.845561i | \(-0.320734\pi\) | ||||
0.533878 | + | 0.845561i | \(0.320734\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.734633 | 0.0703651 | 0.0351825 | − | 0.999381i | \(-0.488799\pi\) | ||||
0.0351825 | + | 0.999381i | \(0.488799\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.76491 | −0.547181 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.93945 | 0.746880 | 0.373440 | − | 0.927654i | \(-0.378178\pi\) | ||||
0.373440 | + | 0.927654i | \(0.378178\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.09461 | −0.100343 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.04496 | −0.0949960 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.76491 | −0.339470 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.51514 | −0.311918 | −0.155959 | − | 0.987764i | \(-0.549847\pi\) | ||||
−0.155959 | + | 0.987764i | \(0.549847\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.28005 | 0.288792 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.76491 | 0.678423 | 0.339212 | − | 0.940710i | \(-0.389840\pi\) | ||||
0.339212 | + | 0.940710i | \(0.389840\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.3103 | 1.24086 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.2039 | −1.55526 | −0.777632 | − | 0.628720i | \(-0.783579\pi\) | ||||
−0.777632 | + | 0.628720i | \(0.783579\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.7493 | −1.08138 | −0.540691 | − | 0.841221i | \(-0.681837\pi\) | ||||
−0.540691 | + | 0.841221i | \(0.681837\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.60975 | 0.388211 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.15516 | −0.263848 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.48486 | −0.204948 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.52982 | −0.780713 | −0.390357 | − | 0.920664i | \(-0.627648\pi\) | ||||
−0.390357 | + | 0.920664i | \(0.627648\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.6244 | 1.51563 | 0.757817 | − | 0.652467i | \(-0.226266\pi\) | ||||
0.757817 | + | 0.652467i | \(0.226266\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.515138 | −0.0416464 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.6741 | 0.931693 | 0.465847 | − | 0.884866i | \(-0.345750\pi\) | ||||
0.465847 | + | 0.884866i | \(0.345750\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.280047 | −0.0222092 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.03028 | 0.711685 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.03028 | −0.0806975 | −0.0403487 | − | 0.999186i | \(-0.512847\pi\) | ||||
−0.0403487 | + | 0.999186i | \(0.512847\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.7346 | −0.830671 | −0.415335 | − | 0.909668i | \(-0.636336\pi\) | ||||
−0.415335 | + | 0.909668i | \(0.636336\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.73463 | 0.515010 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.74931 | −0.285055 | −0.142527 | − | 0.989791i | \(-0.545523\pi\) | ||||
−0.142527 | + | 0.989791i | \(0.545523\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.3444 | 0.852696 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.4390 | 0.780247 | 0.390123 | − | 0.920763i | \(-0.372432\pi\) | ||||
0.390123 | + | 0.920763i | \(0.372432\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.17454 | 0.384620 | 0.192310 | − | 0.981334i | \(-0.438402\pi\) | ||||
0.192310 | + | 0.981334i | \(0.438402\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.01468 | −0.370696 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.62534 | −0.118857 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.12489 | 0.154563 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.15894 | 0.518003 | 0.259001 | − | 0.965877i | \(-0.416607\pi\) | ||||
0.259001 | + | 0.965877i | \(0.416607\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.5601 | −1.04806 | −0.524029 | − | 0.851700i | \(-0.675572\pi\) | ||||
−0.524029 | + | 0.851700i | \(0.675572\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.5601 | 1.03736 | 0.518682 | − | 0.854967i | \(-0.326423\pi\) | ||||
0.518682 | + | 0.854967i | \(0.326423\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.1055 | 1.21258 | 0.606289 | − | 0.795245i | \(-0.292658\pi\) | ||||
0.606289 | + | 0.795245i | \(0.292658\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.1093 | −1.06573 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.0643332 | 0.00451531 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.24977 | 0.295379 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.2489 | 1.46981 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.1892 | 0.976826 | 0.488413 | − | 0.872613i | \(-0.337576\pi\) | ||||
0.488413 | + | 0.872613i | \(0.337576\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.23509 | 0.153146 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.2039 | 1.03211 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.96972 | 0.200675 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.515138 | 0.0346519 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.06055 | 0.271915 | 0.135957 | − | 0.990715i | \(-0.456589\pi\) | ||||
0.135957 | + | 0.990715i | \(0.456589\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.6850 | −0.974676 | −0.487338 | − | 0.873213i | \(-0.662032\pi\) | ||||
−0.487338 | + | 0.873213i | \(0.662032\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.3250 | −1.60744 | −0.803721 | − | 0.595007i | \(-0.797149\pi\) | ||||
−0.803721 | + | 0.595007i | \(0.797149\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.70436 | 0.441114 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.6509 | 0.894302 | 0.447151 | − | 0.894459i | \(-0.352439\pi\) | ||||
0.447151 | + | 0.894459i | \(0.352439\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.98440 | −0.583600 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.0341 | 0.972472 | 0.486236 | − | 0.873827i | \(-0.338369\pi\) | ||||
0.486236 | + | 0.873827i | \(0.338369\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.5601 | 0.937898 | 0.468949 | − | 0.883225i | \(-0.344633\pi\) | ||||
0.468949 | + | 0.883225i | \(0.344633\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.73463 | −0.428514 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.40493 | −0.342524 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.20482 | −0.581003 | −0.290501 | − | 0.956875i | \(-0.593822\pi\) | ||||
−0.290501 | + | 0.956875i | \(0.593822\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.4087 | 0.842999 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.7952 | −0.860520 | −0.430260 | − | 0.902705i | \(-0.641578\pi\) | ||||
−0.430260 | + | 0.902705i | \(0.641578\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.2498 | −0.761164 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0302761 | 0.00187404 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.03028 | 0.186855 | 0.0934274 | − | 0.995626i | \(-0.470218\pi\) | ||||
0.0934274 | + | 0.995626i | \(0.470218\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.5298 | −0.950409 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.469266 | −0.0286116 | −0.0143058 | − | 0.999898i | \(-0.504554\pi\) | ||||
−0.0143058 | + | 0.999898i | \(0.504554\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.87420 | −0.174595 | −0.0872975 | − | 0.996182i | \(-0.527823\pi\) | ||||
−0.0872975 | + | 0.996182i | \(0.527823\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.12489 | −0.128604 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.87890 | −0.112892 | −0.0564459 | − | 0.998406i | \(-0.517977\pi\) | ||||
−0.0564459 | + | 0.998406i | \(0.517977\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.15516 | 0.428368 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.2342 | 1.38603 | 0.693017 | − | 0.720921i | \(-0.256281\pi\) | ||||
0.693017 | + | 0.720921i | \(0.256281\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.8099 | −1.59368 | −0.796841 | − | 0.604190i | \(-0.793497\pi\) | ||||
−0.796841 | + | 0.604190i | \(0.793497\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.00000 | −0.472225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7346 | −0.984390 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.909172 | −0.0532966 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.4702 | 0.611675 | 0.305837 | − | 0.952084i | \(-0.401064\pi\) | ||||
0.305837 | + | 0.952084i | \(0.401064\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.15516 | 0.183081 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.24977 | −0.245771 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.96972 | 0.401728 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.0450 | 0.921759 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.3856 | −1.50590 | −0.752952 | − | 0.658076i | \(-0.771371\pi\) | ||||
−0.752952 | + | 0.658076i | \(0.771371\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.5601 | 0.600743 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.2791 | −1.37674 | −0.688372 | − | 0.725358i | \(-0.741674\pi\) | ||||
−0.688372 | + | 0.725358i | \(0.741674\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.2800 | −0.807156 | −0.403578 | − | 0.914945i | \(-0.632234\pi\) | ||||
−0.403578 | + | 0.914945i | \(0.632234\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.5298 | −1.20924 | −0.604618 | − | 0.796516i | \(-0.706674\pi\) | ||||
−0.604618 | + | 0.796516i | \(0.706674\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0955260 | 0.00534843 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.0450 | 0.616469 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.46927 | −0.193035 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.734633 | 0.0406253 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.79518 | 0.540026 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.5904 | 1.73636 | 0.868182 | − | 0.496246i | \(-0.165289\pi\) | ||||
0.868182 | + | 0.496246i | \(0.165289\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.76491 | −0.315915 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.42431 | −0.404428 | −0.202214 | − | 0.979341i | \(-0.564814\pi\) | ||||
−0.202214 | + | 0.979341i | \(0.564814\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.93945 | 0.431212 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.5757 | 1.22254 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1542 | −1.08823 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.9541 | 0.749097 | 0.374548 | − | 0.927207i | \(-0.377798\pi\) | ||||
0.374548 | + | 0.927207i | \(0.377798\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.06055 | −0.217356 | −0.108678 | − | 0.994077i | \(-0.534662\pi\) | ||||
−0.108678 | + | 0.994077i | \(0.534662\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.3856 | 1.29791 | 0.648956 | − | 0.760826i | \(-0.275206\pi\) | ||||
0.648956 | + | 0.760826i | \(0.275206\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.09461 | −0.0579329 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.76869 | −0.198904 | −0.0994519 | − | 0.995042i | \(-0.531709\pi\) | ||||
−0.0994519 | + | 0.995042i | \(0.531709\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.3553 | 1.38712 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.04496 | −0.0548460 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.2654 | −1.00564 | −0.502822 | − | 0.864390i | \(-0.667705\pi\) | ||||
−0.502822 | + | 0.864390i | \(0.667705\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.76491 | −0.195993 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.595068 | −0.0308944 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.3553 | 0.743288 | 0.371644 | − | 0.928375i | \(-0.378794\pi\) | ||||
0.371644 | + | 0.928375i | \(0.378794\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.0302761 | −0.00155930 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.1845 | 1.70457 | 0.852287 | − | 0.523074i | \(-0.175215\pi\) | ||||
0.852287 | + | 0.523074i | \(0.175215\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.51514 | −0.180086 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.8851 | 1.57815 | 0.789077 | − | 0.614294i | \(-0.210559\pi\) | ||||
0.789077 | + | 0.614294i | \(0.210559\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.28005 | 0.166734 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.295643 | 0.0149897 | 0.00749486 | − | 0.999972i | \(-0.497614\pi\) | ||||
0.00749486 | + | 0.999972i | \(0.497614\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.18922 | −0.110714 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.76491 | 0.391688 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.3250 | −0.819328 | −0.409664 | − | 0.912236i | \(-0.634354\pi\) | ||||
−0.409664 | + | 0.912236i | \(0.634354\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.3103 | 0.716412 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.4390 | 1.42018 | 0.710088 | − | 0.704113i | \(-0.248655\pi\) | ||||
0.710088 | + | 0.704113i | \(0.248655\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.15516 | −0.356424 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.1892 | −0.901606 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.3784 | −0.809862 | −0.404931 | − | 0.914347i | \(-0.632704\pi\) | ||||
−0.404931 | + | 0.914347i | \(0.632704\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.2039 | −0.897932 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.1055 | 1.18615 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.7493 | −0.624337 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.4158 | 1.53476 | 0.767382 | − | 0.641190i | \(-0.221559\pi\) | ||||
0.767382 | + | 0.641190i | \(0.221559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.5298 | 1.14677 | 0.573387 | − | 0.819285i | \(-0.305629\pi\) | ||||
0.573387 | + | 0.819285i | \(0.305629\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.60975 | 0.224134 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.6556 | −0.515662 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.15516 | −0.152333 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.3553 | −0.932311 | −0.466155 | − | 0.884703i | \(-0.654361\pi\) | ||||
−0.466155 | + | 0.884703i | \(0.654361\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.7044 | −0.946931 | −0.473465 | − | 0.880812i | \(-0.656997\pi\) | ||||
−0.473465 | + | 0.880812i | \(0.656997\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 28.6206 | 1.36911 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.98440 | 0.428802 | 0.214401 | − | 0.976746i | \(-0.431220\pi\) | ||||
0.214401 | + | 0.976746i | \(0.431220\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.48486 | −0.118327 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.92385 | 0.138916 | 0.0694582 | − | 0.997585i | \(-0.477873\pi\) | ||||
0.0694582 | + | 0.997585i | \(0.477873\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.52982 | −0.450745 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.3553 | −0.819046 | −0.409523 | − | 0.912300i | \(-0.634305\pi\) | ||||
−0.409523 | + | 0.912300i | \(0.634305\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.8789 | −0.559355 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.6244 | 0.875052 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.05964 | −0.330236 | −0.165118 | − | 0.986274i | \(-0.552800\pi\) | ||||
−0.165118 | + | 0.986274i | \(0.552800\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.515138 | −0.0240446 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.52982 | −0.0712507 | −0.0356254 | − | 0.999365i | \(-0.511342\pi\) | ||||
−0.0356254 | + | 0.999365i | \(0.511342\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.3132 | 1.26935 | 0.634676 | − | 0.772779i | \(-0.281134\pi\) | ||||
0.634676 | + | 0.772779i | \(0.281134\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.29564 | −0.291328 | −0.145664 | − | 0.989334i | \(-0.546532\pi\) | ||||
−0.145664 | + | 0.989334i | \(0.546532\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.1055 | −1.48249 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.6741 | 0.537913 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.3491 | 0.475851 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.280047 | −0.0128225 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.9806 | 1.23278 | 0.616388 | − | 0.787443i | \(-0.288595\pi\) | ||||
0.616388 | + | 0.787443i | \(0.288595\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.76491 | 0.262857 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.03028 | 0.410892 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.8751 | −0.538113 | −0.269056 | − | 0.963124i | \(-0.586712\pi\) | ||||
−0.269056 | + | 0.963124i | \(0.586712\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.03028 | −0.0465907 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.8695 | −1.88954 | −0.944772 | − | 0.327728i | \(-0.893717\pi\) | ||||
−0.944772 | + | 0.327728i | \(0.893717\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.0155964 | −0.000702425 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.74931 | 0.213036 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.5786 | 1.36888 | 0.684442 | − | 0.729067i | \(-0.260046\pi\) | ||||
0.684442 | + | 0.729067i | \(0.260046\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.7346 | −0.479588 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.9991 | 1.47136 | 0.735678 | − | 0.677331i | \(-0.236864\pi\) | ||||
0.735678 | + | 0.677331i | \(0.236864\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 41.6197 | 1.84476 | 0.922381 | − | 0.386281i | \(-0.126241\pi\) | ||||
0.922381 | + | 0.386281i | \(0.126241\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.31032 | 0.279152 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.73463 | 0.297341 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.5445 | 0.639666 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.74931 | −0.164577 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.47018 | 0.283464 | 0.141732 | − | 0.989905i | \(-0.454733\pi\) | ||||
0.141732 | + | 0.989905i | \(0.454733\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.8401 | −1.65463 | −0.827317 | − | 0.561735i | \(-0.810134\pi\) | ||||
−0.827317 | + | 0.561735i | \(0.810134\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.68590 | −0.160560 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.93945 | −0.214759 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.3444 | 0.492304 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.76491 | 0.163076 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.4390 | 0.450476 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.84014 | −0.337699 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.37844 | 0.274230 | 0.137115 | − | 0.990555i | \(-0.456217\pi\) | ||||
0.137115 | + | 0.990555i | \(0.456217\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.17454 | 0.222061 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.0899 | 0.431413 | 0.215707 | − | 0.976458i | \(-0.430794\pi\) | ||||
0.215707 | + | 0.976458i | \(0.430794\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.01468 | −0.214021 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.203898 | 0.00868636 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.0908 | −0.811825 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.96972 | 0.210574 | 0.105287 | − | 0.994442i | \(-0.466424\pi\) | ||||
0.105287 | + | 0.994442i | \(0.466424\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.28005 | −0.138731 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.62534 | −0.0686221 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.8027 | −0.623861 | −0.311931 | − | 0.950105i | \(-0.600976\pi\) | ||||
−0.311931 | + | 0.950105i | \(0.600976\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.12489 | 0.0892368 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.85574 | −0.161641 | −0.0808205 | − | 0.996729i | \(-0.525754\pi\) | ||||
−0.0808205 | + | 0.996729i | \(0.525754\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.6282 | 1.03066 | 0.515329 | − | 0.856992i | \(-0.327670\pi\) | ||||
0.515329 | + | 0.856992i | \(0.327670\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.15894 | 0.299069 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.02936 | 0.251006 | 0.125503 | − | 0.992093i | \(-0.459946\pi\) | ||||
0.125503 | + | 0.992093i | \(0.459946\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.5601 | −0.605097 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.4849 | −0.476472 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.883593 | −0.0365947 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.0861 | 0.581397 | 0.290698 | − | 0.956815i | \(-0.406112\pi\) | ||||
0.290698 | + | 0.956815i | \(0.406112\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 48.1874 | 1.98553 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.5601 | 0.598922 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.2333 | −1.15940 | −0.579700 | − | 0.814830i | \(-0.696830\pi\) | ||||
−0.579700 | + | 0.814830i | \(0.696830\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.1055 | 0.700082 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.0596 | −0.942191 | −0.471096 | − | 0.882082i | \(-0.656141\pi\) | ||||
−0.471096 | + | 0.882082i | \(0.656141\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.1901 | 0.578828 | 0.289414 | − | 0.957204i | \(-0.406540\pi\) | ||||
0.289414 | + | 0.957204i | \(0.406540\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.1093 | −0.615298 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.9229 | −1.78278 | −0.891388 | − | 0.453240i | \(-0.850268\pi\) | ||||
−0.891388 | + | 0.453240i | \(0.850268\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.0643332 | 0.00260691 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.60975 | −0.186490 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.62156 | 0.0654943 | 0.0327472 | − | 0.999464i | \(-0.489574\pi\) | ||||
0.0327472 | + | 0.999464i | \(0.489574\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.3250 | −0.496186 | −0.248093 | − | 0.968736i | \(-0.579804\pi\) | ||||
−0.248093 | + | 0.968736i | \(0.579804\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.15138 | −0.207051 | −0.103526 | − | 0.994627i | \(-0.533012\pi\) | ||||
−0.103526 | + | 0.994627i | \(0.533012\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.24977 | 0.170537 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −32.9991 | −1.32208 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21.2489 | 0.848597 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.96972 | 0.118411 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.97064 | 0.0784500 | 0.0392250 | − | 0.999230i | \(-0.487511\pi\) | ||||
0.0392250 | + | 0.999230i | \(0.487511\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.1892 | 0.563971 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.48486 | 0.0984538 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.23509 | 0.0884188 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.33348 | 0.171162 | 0.0855811 | − | 0.996331i | \(-0.472725\pi\) | ||||
0.0855811 | + | 0.996331i | \(0.472725\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.85574 | −0.270364 | −0.135182 | − | 0.990821i | \(-0.543162\pi\) | ||||
−0.135182 | + | 0.990821i | \(0.543162\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.93945 | −0.233504 | −0.116752 | − | 0.993161i | \(-0.537248\pi\) | ||||
−0.116752 | + | 0.993161i | \(0.537248\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.7934 | 1.40501 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.2039 | 0.595888 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.61353 | 0.376206 | 0.188103 | − | 0.982149i | \(-0.439766\pi\) | ||||
0.188103 | + | 0.982149i | \(0.439766\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.96972 | 0.115860 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.455503 | 0.0177439 | 0.00887193 | − | 0.999961i | \(-0.497176\pi\) | ||||
0.00887193 | + | 0.999961i | \(0.497176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.2635 | −1.13822 | −0.569110 | − | 0.822262i | \(-0.692712\pi\) | ||||
−0.569110 | + | 0.822262i | \(0.692712\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.515138 | 0.0200063 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.128666 | 0.00498199 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.06055 | 0.156990 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.8221 | −0.610806 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.7796 | −0.955183 | −0.477591 | − | 0.878582i | \(-0.658490\pi\) | ||||
−0.477591 | + | 0.878582i | \(0.658490\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.93945 | 0.305138 | 0.152569 | − | 0.988293i | \(-0.451245\pi\) | ||||
0.152569 | + | 0.988293i | \(0.451245\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.93189 | −0.0741390 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.6850 | −0.562730 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.53360 | 0.288265 | 0.144133 | − | 0.989558i | \(-0.453961\pi\) | ||||
0.144133 | + | 0.989558i | \(0.453961\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.3250 | −0.928057 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.280047 | 0.0106689 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −51.4490 | −1.95721 | −0.978606 | − | 0.205745i | \(-0.934038\pi\) | ||||
−0.978606 | + | 0.205745i | \(0.934038\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.70436 | 0.254677 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.93945 | 0.0734618 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.6509 | 0.516325 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.35620 | −0.202301 | −0.101150 | − | 0.994871i | \(-0.532252\pi\) | ||||
−0.101150 | + | 0.994871i | \(0.532252\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −38.8245 | −1.46430 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 34.0937 | 1.28223 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.969724 | 0.0364187 | 0.0182094 | − | 0.999834i | \(-0.494203\pi\) | ||||
0.0182094 | + | 0.999834i | \(0.494203\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.98440 | −0.336941 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.4078 | 1.13878 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.0341 | 0.561457 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.5592 | 0.878609 | 0.439305 | − | 0.898338i | \(-0.355225\pi\) | ||||
0.439305 | + | 0.898338i | \(0.355225\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.4390 | 0.835672 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.5601 | 0.541496 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.3179 | −0.827725 | −0.413862 | − | 0.910340i | \(-0.635820\pi\) | ||||
−0.413862 | + | 0.910340i | \(0.635820\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.68968 | −0.0624950 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.7034 | 1.72503 | 0.862515 | − | 0.506031i | \(-0.168888\pi\) | ||||
0.862515 | + | 0.506031i | \(0.168888\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −47.6722 | −1.75603 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.2985 | −1.07776 | −0.538882 | − | 0.842382i | \(-0.681153\pi\) | ||||
−0.538882 | + | 0.842382i | \(0.681153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.73463 | −0.247403 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 51.0175 | 1.87165 | 0.935826 | − | 0.352462i | \(-0.114655\pi\) | ||||
0.935826 | + | 0.352462i | \(0.114655\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.40493 | −0.197756 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.4693 | 0.857548 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.36376 | 0.159236 | 0.0796179 | − | 0.996825i | \(-0.474630\pi\) | ||||
0.0796179 | + | 0.996825i | \(0.474630\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.20482 | −0.335442 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.6344 | −1.54957 | −0.774787 | − | 0.632222i | \(-0.782143\pi\) | ||||
−0.774787 | + | 0.632222i | \(0.782143\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.4087 | 0.486705 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.73372 | −0.135347 | −0.0676736 | − | 0.997708i | \(-0.521558\pi\) | ||||
−0.0676736 | + | 0.997708i | \(0.521558\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.56101 | 0.0565124 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.3444 | −0.409622 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.3784 | −0.734865 | −0.367433 | − | 0.930050i | \(-0.619763\pi\) | ||||
−0.367433 | + | 0.930050i | \(0.619763\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.7952 | −0.496821 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.5289 | −0.522568 | −0.261284 | − | 0.965262i | \(-0.584146\pi\) | ||||
−0.261284 | + | 0.965262i | \(0.584146\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.2498 | −0.439458 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.3553 | −0.908447 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.05207 | 0.252343 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.0302761 | 0.00108198 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.00470 | −0.178398 | −0.0891991 | − | 0.996014i | \(-0.528431\pi\) | ||||
−0.0891991 | + | 0.996014i | \(0.528431\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.03028 | 0.107881 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.8704 | 0.599843 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.01468 | 0.178076 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 48.3846 | 1.71387 | 0.856936 | − | 0.515423i | \(-0.172365\pi\) | ||||
0.856936 | + | 0.515423i | \(0.172365\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.37466 | −0.0840093 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.5298 | −0.548719 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.36996 | 0.330659 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.469266 | −0.0165189 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.18074 | 0.322778 | 0.161389 | − | 0.986891i | \(-0.448403\pi\) | ||||
0.161389 | + | 0.986891i | \(0.448403\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.2224 | 1.06125 | 0.530625 | − | 0.847607i | \(-0.321957\pi\) | ||||
0.530625 | + | 0.847607i | \(0.321957\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.87420 | −0.100803 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.0899 | 0.772828 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.12489 | −0.0742495 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.6197 | 1.10354 | 0.551768 | − | 0.833998i | \(-0.313953\pi\) | ||||
0.551768 | + | 0.833998i | \(0.313953\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.4158 | −1.09509 | −0.547544 | − | 0.836777i | \(-0.684437\pi\) | ||||
−0.547544 | + | 0.836777i | \(0.684437\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.2838 | −0.392377 | −0.196189 | − | 0.980566i | \(-0.562856\pi\) | ||||
−0.196189 | + | 0.980566i | \(0.562856\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.83302 | −0.167858 | −0.0839289 | − | 0.996472i | \(-0.526747\pi\) | ||||
−0.0839289 | + | 0.996472i | \(0.526747\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.87890 | −0.0651782 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.28005 | 0.0443510 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.15516 | 0.247319 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.4693 | −0.534058 | −0.267029 | − | 0.963688i | \(-0.586042\pi\) | ||||
−0.267029 | + | 0.963688i | \(0.586042\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9991 | −0.999968 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23.2342 | 0.800227 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.22041 | −0.0762942 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.8099 | −0.920112 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.4995 | −0.839833 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41.2635 | −1.41284 | −0.706418 | − | 0.707795i | \(-0.749690\pi\) | ||||
−0.706418 | + | 0.707795i | \(0.749690\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.87890 | 0.337457 | 0.168728 | − | 0.985663i | \(-0.446034\pi\) | ||||
0.168728 | + | 0.985663i | \(0.446034\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.7200 | −0.706956 | −0.353478 | − | 0.935443i | \(-0.615001\pi\) | ||||
−0.353478 | + | 0.935443i | \(0.615001\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.00000 | −0.272639 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.91915 | −0.0653288 | −0.0326644 | − | 0.999466i | \(-0.510399\pi\) | ||||
−0.0326644 | + | 0.999466i | \(0.510399\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.7346 | −0.568338 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.3472 | −0.961614 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.1093 | 0.511959 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.909172 | −0.0307708 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.3250 | −0.618791 | −0.309396 | − | 0.950933i | \(-0.600127\pi\) | ||||
−0.309396 | + | 0.950933i | \(0.600127\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.4702 | 0.353150 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.7649 | 0.430061 | 0.215030 | − | 0.976607i | \(-0.431015\pi\) | ||||
0.215030 | + | 0.976607i | \(0.431015\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.8789 | −0.399757 | −0.199878 | − | 0.979821i | \(-0.564055\pi\) | ||||
−0.199878 | + | 0.979821i | \(0.564055\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40.7493 | −1.36823 | −0.684114 | − | 0.729375i | \(-0.739811\pi\) | ||||
−0.684114 | + | 0.729375i | \(0.739811\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.46927 | −0.250511 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.15516 | 0.105702 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 31.0450 | 1.03888 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.24977 | −0.141896 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.216630 | 0.00722503 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.144263 | 0.00480609 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.96972 | 0.231938 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.5289 | 1.08010 | 0.540052 | − | 0.841632i | \(-0.318404\pi\) | ||||
0.540052 | + | 0.841632i | \(0.318404\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.0450 | 0.532178 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.2810 | −0.738201 | −0.369101 | − | 0.929389i | \(-0.620334\pi\) | ||||
−0.369101 | + | 0.929389i | \(0.620334\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.0534 | −0.564386 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.4995 | 0.544863 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.9239 | 0.888136 | 0.444068 | − | 0.895993i | \(-0.353535\pi\) | ||||
0.444068 | + | 0.895993i | \(0.353535\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.3856 | −0.869434 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.23509 | −0.0735689 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.5601 | 0.346839 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.4755 | −1.19672 | −0.598361 | − | 0.801227i | \(-0.704181\pi\) | ||||
−0.598361 | + | 0.801227i | \(0.704181\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.7346 | −0.548455 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.2791 | −0.794863 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.26445 | 0.237319 | 0.118660 | − | 0.992935i | \(-0.462140\pi\) | ||||
0.118660 | + | 0.992935i | \(0.462140\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.2800 | −0.466012 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.08991 | −0.263724 | −0.131862 | − | 0.991268i | \(-0.542096\pi\) | ||||
−0.131862 | + | 0.991268i | \(0.542096\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.0000 | −0.521032 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −48.9036 | −1.58915 | −0.794576 | − | 0.607165i | \(-0.792307\pi\) | ||||
−0.794576 | + | 0.607165i | \(0.792307\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.96972 | −0.0964013 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.5298 | −0.698152 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.58325 | 0.213252 | 0.106626 | − | 0.994299i | \(-0.465995\pi\) | ||||
0.106626 | + | 0.994299i | \(0.465995\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.0955260 | 0.00308792 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −38.6812 | −1.24908 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.1963 | 0.651495 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.0450 | 0.355919 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.58659 | −0.308284 | −0.154142 | − | 0.988049i | \(-0.549261\pi\) | ||||
−0.154142 | + | 0.988049i | \(0.549261\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.46927 | −0.111449 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.1358 | −1.15965 | −0.579826 | − | 0.814740i | \(-0.696880\pi\) | ||||
−0.579826 | + | 0.814740i | \(0.696880\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27.0908 | −0.868492 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.0303 | 0.864775 | 0.432388 | − | 0.901688i | \(-0.357671\pi\) | ||||
0.432388 | + | 0.901688i | \(0.357671\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −48.9991 | −1.56602 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.734633 | 0.0234550 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −49.9338 | −1.59264 | −0.796321 | − | 0.604874i | \(-0.793223\pi\) | ||||
−0.796321 | + | 0.604874i | \(0.793223\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.79518 | 0.311784 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.9394 | 0.443249 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.4849 | 0.650723 | 0.325362 | − | 0.945590i | \(-0.394514\pi\) | ||||
0.325362 | + | 0.945590i | \(0.394514\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 31.5904 | 1.00249 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.9541 | 1.29703 | 0.648515 | − | 0.761202i | \(-0.275390\pi\) | ||||
0.648515 | + | 0.761202i | \(0.275390\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.76491 | −0.182394 |
(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 | 7800.2.a.bn.1.3 | yes | 3 | |
5.4 | even | 2 | 7800.2.a.bm.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7800.2.a.bm.1.1 | ✓ | 3 | 5.4 | even | 2 | ||
7800.2.a.bn.1.3 | yes | 3 | 1.1 | even | 1 | trivial |