Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.6152203125.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 8x^{6} + 20x^{5} + 26x^{4} - 35x^{3} - 27x^{2} + 16x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 625) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.499011\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500989 | 0.354253 | 0.177126 | − | 0.984188i | \(-0.443320\pi\) | ||||
0.177126 | + | 0.984188i | \(0.443320\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.74901 | −0.874505 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0237879 | −0.00899097 | −0.00449549 | − | 0.999990i | \(-0.501431\pi\) | ||||
−0.00449549 | + | 0.999990i | \(0.501431\pi\) | |||||||
\(8\) | −1.87821 | −0.664049 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.58329 | −1.08040 | −0.540201 | − | 0.841536i | \(-0.681652\pi\) | ||||
−0.540201 | + | 0.841536i | \(0.681652\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.77587 | −1.04724 | −0.523619 | − | 0.851952i | \(-0.675418\pi\) | ||||
−0.523619 | + | 0.851952i | \(0.675418\pi\) | |||||||
\(14\) | −0.0119175 | −0.00318508 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.55705 | 0.639264 | ||||||||
\(17\) | −3.62303 | −0.878713 | −0.439357 | − | 0.898313i | \(-0.644794\pi\) | ||||
−0.439357 | + | 0.898313i | \(0.644794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.43084 | −0.557672 | −0.278836 | − | 0.960339i | \(-0.589949\pi\) | ||||
−0.278836 | + | 0.960339i | \(0.589949\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.79519 | −0.382736 | ||||||||
\(23\) | 1.71538 | 0.357682 | 0.178841 | − | 0.983878i | \(-0.442765\pi\) | ||||
0.178841 | + | 0.983878i | \(0.442765\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.89167 | −0.370987 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.0416052 | 0.00786265 | ||||||||
\(29\) | −3.85734 | −0.716290 | −0.358145 | − | 0.933666i | \(-0.616591\pi\) | ||||
−0.358145 | + | 0.933666i | \(0.616591\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.00979 | −1.07939 | −0.539695 | − | 0.841861i | \(-0.681460\pi\) | ||||
−0.539695 | + | 0.841861i | \(0.681460\pi\) | |||||||
\(32\) | 5.03748 | 0.890510 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.81510 | −0.311287 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.369309 | 0.0607139 | 0.0303570 | − | 0.999539i | \(-0.490336\pi\) | ||||
0.0303570 | + | 0.999539i | \(0.490336\pi\) | |||||||
\(38\) | −1.21782 | −0.197557 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.80900 | 1.21956 | 0.609780 | − | 0.792570i | \(-0.291258\pi\) | ||||
0.609780 | + | 0.792570i | \(0.291258\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.174574 | −0.0266224 | −0.0133112 | − | 0.999911i | \(-0.504237\pi\) | ||||
−0.0133112 | + | 0.999911i | \(0.504237\pi\) | |||||||
\(44\) | 6.26720 | 0.944817 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.859388 | 0.126710 | ||||||||
\(47\) | 7.81082 | 1.13932 | 0.569662 | − | 0.821879i | \(-0.307074\pi\) | ||||
0.569662 | + | 0.821879i | \(0.307074\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99943 | −0.999919 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.60403 | 0.915815 | ||||||||
\(53\) | −8.97184 | −1.23238 | −0.616189 | − | 0.787599i | \(-0.711324\pi\) | ||||
−0.616189 | + | 0.787599i | \(0.711324\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.0446787 | 0.00597045 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.93249 | −0.253748 | ||||||||
\(59\) | 4.45536 | 0.580038 | 0.290019 | − | 0.957021i | \(-0.406338\pi\) | ||||
0.290019 | + | 0.957021i | \(0.406338\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.21403 | 1.17974 | 0.589868 | − | 0.807500i | \(-0.299180\pi\) | ||||
0.589868 | + | 0.807500i | \(0.299180\pi\) | |||||||
\(62\) | −3.01084 | −0.382377 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.59038 | −0.323798 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.47385 | 0.546568 | 0.273284 | − | 0.961933i | \(-0.411890\pi\) | ||||
0.273284 | + | 0.961933i | \(0.411890\pi\) | |||||||
\(68\) | 6.33671 | 0.768439 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.69458 | 1.15054 | 0.575268 | − | 0.817965i | \(-0.304898\pi\) | ||||
0.575268 | + | 0.817965i | \(0.304898\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.95387 | 0.462765 | 0.231383 | − | 0.972863i | \(-0.425675\pi\) | ||||
0.231383 | + | 0.972863i | \(0.425675\pi\) | |||||||
\(74\) | 0.185020 | 0.0215081 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.25156 | 0.487687 | ||||||||
\(77\) | 0.0852388 | 0.00971386 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.68349 | −1.08948 | −0.544739 | − | 0.838606i | \(-0.683371\pi\) | ||||
−0.544739 | + | 0.838606i | \(0.683371\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.91223 | 0.432033 | ||||||||
\(83\) | −8.95717 | −0.983177 | −0.491589 | − | 0.870828i | \(-0.663584\pi\) | ||||
−0.491589 | + | 0.870828i | \(0.663584\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.0874600 | −0.00943105 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.73018 | 0.717440 | ||||||||
\(89\) | 17.0151 | 1.80359 | 0.901797 | − | 0.432161i | \(-0.142249\pi\) | ||||
0.901797 | + | 0.432161i | \(0.142249\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0898200 | 0.00941569 | ||||||||
\(92\) | −3.00022 | −0.312795 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.91314 | 0.403609 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.76438 | −0.280680 | −0.140340 | − | 0.990103i | \(-0.544820\pi\) | ||||
−0.140340 | + | 0.990103i | \(0.544820\pi\) | |||||||
\(98\) | −3.50664 | −0.354224 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.3526 | −1.03012 | −0.515062 | − | 0.857153i | \(-0.672231\pi\) | ||||
−0.515062 | + | 0.857153i | \(0.672231\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.2913 | −1.80230 | −0.901150 | − | 0.433508i | \(-0.857276\pi\) | ||||
−0.901150 | + | 0.433508i | \(0.857276\pi\) | |||||||
\(104\) | 7.09189 | 0.695417 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.49480 | −0.436573 | ||||||||
\(107\) | 15.8786 | 1.53504 | 0.767522 | − | 0.641023i | \(-0.221490\pi\) | ||||
0.767522 | + | 0.641023i | \(0.221490\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.96109 | 0.570969 | 0.285484 | − | 0.958383i | \(-0.407845\pi\) | ||||
0.285484 | + | 0.958383i | \(0.407845\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.0608269 | −0.00574760 | ||||||||
\(113\) | 2.42830 | 0.228435 | 0.114218 | − | 0.993456i | \(-0.463564\pi\) | ||||
0.114218 | + | 0.993456i | \(0.463564\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.74652 | 0.626399 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.23209 | 0.205480 | ||||||||
\(119\) | 0.0861842 | 0.00790049 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.83995 | 0.167268 | ||||||||
\(122\) | 4.61613 | 0.417925 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.5112 | 0.943932 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.1073 | 1.51803 | 0.759013 | − | 0.651075i | \(-0.225682\pi\) | ||||
0.759013 | + | 0.651075i | \(0.225682\pi\) | |||||||
\(128\) | −11.3727 | −1.00522 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.78955 | −0.418464 | −0.209232 | − | 0.977866i | \(-0.567096\pi\) | ||||
−0.209232 | + | 0.977866i | \(0.567096\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0578245 | 0.00501402 | ||||||||
\(134\) | 2.24135 | 0.193623 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.80482 | 0.583509 | ||||||||
\(137\) | 12.8104 | 1.09446 | 0.547231 | − | 0.836982i | \(-0.315682\pi\) | ||||
0.547231 | + | 0.836982i | \(0.315682\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.94020 | −0.673479 | −0.336739 | − | 0.941598i | \(-0.609324\pi\) | ||||
−0.336739 | + | 0.941598i | \(0.609324\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.85688 | 0.407581 | ||||||||
\(143\) | 13.5300 | 1.13144 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.98085 | 0.163936 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.645924 | −0.0530946 | ||||||||
\(149\) | 5.62724 | 0.461002 | 0.230501 | − | 0.973072i | \(-0.425964\pi\) | ||||
0.230501 | + | 0.973072i | \(0.425964\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.36960 | −0.599730 | −0.299865 | − | 0.953982i | \(-0.596942\pi\) | ||||
−0.299865 | + | 0.953982i | \(0.596942\pi\) | |||||||
\(152\) | 4.56563 | 0.370322 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.0427037 | 0.00344116 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.63091 | −0.688822 | −0.344411 | − | 0.938819i | \(-0.611921\pi\) | ||||
−0.344411 | + | 0.938819i | \(0.611921\pi\) | |||||||
\(158\) | −4.85133 | −0.385951 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.0408053 | −0.00321591 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.74964 | −0.372020 | −0.186010 | − | 0.982548i | \(-0.559556\pi\) | ||||
−0.186010 | + | 0.982548i | \(0.559556\pi\) | |||||||
\(164\) | −13.6580 | −1.06651 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.48745 | −0.348293 | ||||||||
\(167\) | 18.5967 | 1.43906 | 0.719528 | − | 0.694463i | \(-0.244358\pi\) | ||||
0.719528 | + | 0.694463i | \(0.244358\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.25720 | 0.0967079 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.305332 | 0.0232814 | ||||||||
\(173\) | 15.7957 | 1.20092 | 0.600462 | − | 0.799653i | \(-0.294983\pi\) | ||||
0.600462 | + | 0.799653i | \(0.294983\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9.16266 | −0.690661 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.52437 | 0.638928 | ||||||||
\(179\) | −9.36946 | −0.700306 | −0.350153 | − | 0.936692i | \(-0.613870\pi\) | ||||
−0.350153 | + | 0.936692i | \(0.613870\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.84630 | −0.434552 | −0.217276 | − | 0.976110i | \(-0.569717\pi\) | ||||
−0.217276 | + | 0.976110i | \(0.569717\pi\) | |||||||
\(182\) | 0.0449988 | 0.00333554 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.22186 | −0.237518 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.9824 | 0.949364 | ||||||||
\(188\) | −13.6612 | −0.996345 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.8947 | 1.58425 | 0.792123 | − | 0.610362i | \(-0.208976\pi\) | ||||
0.792123 | + | 0.610362i | \(0.208976\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.2541 | 1.81783 | 0.908916 | − | 0.416980i | \(-0.136911\pi\) | ||||
0.908916 | + | 0.416980i | \(0.136911\pi\) | |||||||
\(194\) | −1.38492 | −0.0994317 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.2421 | 0.874434 | ||||||||
\(197\) | 14.4538 | 1.02979 | 0.514897 | − | 0.857252i | \(-0.327830\pi\) | ||||
0.514897 | + | 0.857252i | \(0.327830\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.77734 | −0.267768 | −0.133884 | − | 0.990997i | \(-0.542745\pi\) | ||||
−0.133884 | + | 0.990997i | \(0.542745\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.18655 | −0.364924 | ||||||||
\(203\) | 0.0917579 | 0.00644014 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.16377 | −0.638470 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −9.65511 | −0.669461 | ||||||||
\(209\) | 8.71039 | 0.602510 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.9006 | −1.30117 | −0.650586 | − | 0.759432i | \(-0.725477\pi\) | ||||
−0.650586 | + | 0.759432i | \(0.725477\pi\) | |||||||
\(212\) | 15.6918 | 1.07772 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.95502 | 0.543794 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.142960 | 0.00970477 | ||||||||
\(218\) | 2.98644 | 0.202267 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.6801 | 0.920222 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.3556 | 0.760426 | 0.380213 | − | 0.924899i | \(-0.375851\pi\) | ||||
0.380213 | + | 0.924899i | \(0.375851\pi\) | |||||||
\(224\) | −0.119831 | −0.00800655 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.21655 | 0.0809239 | ||||||||
\(227\) | 11.1977 | 0.743216 | 0.371608 | − | 0.928390i | \(-0.378806\pi\) | ||||
0.371608 | + | 0.928390i | \(0.378806\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.64969 | 0.637669 | 0.318835 | − | 0.947810i | \(-0.396709\pi\) | ||||
0.318835 | + | 0.947810i | \(0.396709\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.24491 | 0.475651 | ||||||||
\(233\) | −15.5261 | −1.01715 | −0.508573 | − | 0.861019i | \(-0.669827\pi\) | ||||
−0.508573 | + | 0.861019i | \(0.669827\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.79246 | −0.507246 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.0431773 | 0.00279877 | ||||||||
\(239\) | −14.3342 | −0.927203 | −0.463601 | − | 0.886044i | \(-0.653443\pi\) | ||||
−0.463601 | + | 0.886044i | \(0.653443\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.3114 | 1.63045 | 0.815224 | − | 0.579145i | \(-0.196614\pi\) | ||||
0.815224 | + | 0.579145i | \(0.196614\pi\) | |||||||
\(242\) | 0.921794 | 0.0592552 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −16.1154 | −1.03168 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.17853 | 0.584016 | ||||||||
\(248\) | 11.2877 | 0.716768 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.23698 | −0.267436 | −0.133718 | − | 0.991019i | \(-0.542692\pi\) | ||||
−0.133718 | + | 0.991019i | \(0.542692\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.14671 | −0.386440 | ||||||||
\(254\) | 8.57057 | 0.537766 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.516849 | −0.0323031 | ||||||||
\(257\) | −20.4007 | −1.27256 | −0.636281 | − | 0.771458i | \(-0.719528\pi\) | ||||
−0.636281 | + | 0.771458i | \(0.719528\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.00878507 | −0.000545877 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.39951 | −0.148242 | ||||||||
\(263\) | 28.6678 | 1.76773 | 0.883865 | − | 0.467741i | \(-0.154932\pi\) | ||||
0.883865 | + | 0.467741i | \(0.154932\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.0289694 | 0.00177623 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.82481 | −0.477977 | ||||||||
\(269\) | −7.94652 | −0.484508 | −0.242254 | − | 0.970213i | \(-0.577887\pi\) | ||||
−0.242254 | + | 0.970213i | \(0.577887\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.55487 | 0.580417 | 0.290208 | − | 0.956963i | \(-0.406275\pi\) | ||||
0.290208 | + | 0.956963i | \(0.406275\pi\) | |||||||
\(272\) | −9.26428 | −0.561729 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.41785 | 0.387717 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.1904 | −1.03287 | −0.516436 | − | 0.856326i | \(-0.672742\pi\) | ||||
−0.516436 | + | 0.856326i | \(0.672742\pi\) | |||||||
\(278\) | −3.97795 | −0.238582 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.2182 | −1.62370 | −0.811851 | − | 0.583864i | \(-0.801540\pi\) | ||||
−0.811851 | + | 0.583864i | \(0.801540\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.47901 | 0.206806 | 0.103403 | − | 0.994640i | \(-0.467027\pi\) | ||||
0.103403 | + | 0.994640i | \(0.467027\pi\) | |||||||
\(284\) | −16.9559 | −1.00615 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.77840 | 0.400815 | ||||||||
\(287\) | −0.185760 | −0.0109650 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.87366 | −0.227863 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.91535 | −0.404690 | ||||||||
\(293\) | 23.4941 | 1.37254 | 0.686271 | − | 0.727346i | \(-0.259246\pi\) | ||||
0.686271 | + | 0.727346i | \(0.259246\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.693640 | −0.0403170 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.81919 | 0.163311 | ||||||||
\(299\) | −6.47706 | −0.374578 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.00415276 | 0.000239361 0 | ||||||||
\(302\) | −3.69209 | −0.212456 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.21578 | −0.356500 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.11253 | −0.0634952 | −0.0317476 | − | 0.999496i | \(-0.510107\pi\) | ||||
−0.0317476 | + | 0.999496i | \(0.510107\pi\) | |||||||
\(308\) | −0.149083 | −0.00849482 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.7529 | 0.836561 | 0.418280 | − | 0.908318i | \(-0.362633\pi\) | ||||
0.418280 | + | 0.908318i | \(0.362633\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.94834 | −0.279697 | −0.139848 | − | 0.990173i | \(-0.544661\pi\) | ||||
−0.139848 | + | 0.990173i | \(0.544661\pi\) | |||||||
\(314\) | −4.32400 | −0.244017 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.9365 | 0.952754 | ||||||||
\(317\) | 22.6855 | 1.27414 | 0.637072 | − | 0.770804i | \(-0.280145\pi\) | ||||
0.637072 | + | 0.770804i | \(0.280145\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.8220 | 0.773881 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.0204430 | −0.00113925 | ||||||||
\(323\) | 8.80699 | 0.490034 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.37952 | −0.131789 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −14.6670 | −0.809848 | ||||||||
\(329\) | −0.185803 | −0.0102436 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.73258 | 0.0952312 | 0.0476156 | − | 0.998866i | \(-0.484838\pi\) | ||||
0.0476156 | + | 0.998866i | \(0.484838\pi\) | |||||||
\(332\) | 15.6662 | 0.859793 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.31676 | 0.509790 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.9811 | −0.761596 | −0.380798 | − | 0.924658i | \(-0.624351\pi\) | ||||
−0.380798 | + | 0.924658i | \(0.624351\pi\) | |||||||
\(338\) | 0.629845 | 0.0342590 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.5348 | 1.16617 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.333017 | 0.0179812 | ||||||||
\(344\) | 0.327888 | 0.0176785 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.91347 | 0.425431 | ||||||||
\(347\) | 5.08173 | 0.272802 | 0.136401 | − | 0.990654i | \(-0.456447\pi\) | ||||
0.136401 | + | 0.990654i | \(0.456447\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.88643 | −0.475680 | −0.237840 | − | 0.971304i | \(-0.576439\pi\) | ||||
−0.237840 | + | 0.971304i | \(0.576439\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −18.0508 | −0.962108 | ||||||||
\(353\) | 9.41440 | 0.501078 | 0.250539 | − | 0.968107i | \(-0.419392\pi\) | ||||
0.250539 | + | 0.968107i | \(0.419392\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −29.7595 | −1.57725 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.69400 | −0.248086 | ||||||||
\(359\) | −9.11498 | −0.481070 | −0.240535 | − | 0.970640i | \(-0.577323\pi\) | ||||
−0.240535 | + | 0.970640i | \(0.577323\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0910 | −0.689002 | ||||||||
\(362\) | −2.92893 | −0.153941 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.157096 | −0.00823407 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.8784 | 0.933246 | 0.466623 | − | 0.884456i | \(-0.345471\pi\) | ||||
0.466623 | + | 0.884456i | \(0.345471\pi\) | |||||||
\(368\) | 4.38633 | 0.228653 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.213421 | 0.0110803 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.07395 | 0.159163 | 0.0795814 | − | 0.996828i | \(-0.474642\pi\) | ||||
0.0795814 | + | 0.996828i | \(0.474642\pi\) | |||||||
\(374\) | 6.50402 | 0.336315 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14.6704 | −0.756567 | ||||||||
\(377\) | 14.5648 | 0.750126 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.5866 | 1.31430 | 0.657149 | − | 0.753761i | \(-0.271762\pi\) | ||||
0.657149 | + | 0.753761i | \(0.271762\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.9690 | 0.561224 | ||||||||
\(383\) | −2.22529 | −0.113707 | −0.0568535 | − | 0.998383i | \(-0.518107\pi\) | ||||
−0.0568535 | + | 0.998383i | \(0.518107\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.6520 | 0.643972 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.83492 | 0.245456 | ||||||||
\(389\) | −4.64413 | −0.235467 | −0.117733 | − | 0.993045i | \(-0.537563\pi\) | ||||
−0.117733 | + | 0.993045i | \(0.537563\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.21488 | −0.314300 | ||||||||
\(392\) | 13.1464 | 0.663995 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.24122 | 0.364807 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.9452 | 1.90442 | 0.952208 | − | 0.305452i | \(-0.0988074\pi\) | ||||
0.952208 | + | 0.305452i | \(0.0988074\pi\) | |||||||
\(398\) | −1.89241 | −0.0948577 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.7187 | 0.834890 | 0.417445 | − | 0.908702i | \(-0.362926\pi\) | ||||
0.417445 | + | 0.908702i | \(0.362926\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.6922 | 1.13038 | ||||||||
\(404\) | 18.1068 | 0.900848 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.0459697 | 0.00228144 | ||||||||
\(407\) | −1.32334 | −0.0655955 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.473132 | 0.0233949 | 0.0116974 | − | 0.999932i | \(-0.496277\pi\) | ||||
0.0116974 | + | 0.999932i | \(0.496277\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 31.9917 | 1.57612 | ||||||||
\(413\) | −0.105983 | −0.00521511 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −19.0209 | −0.932576 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.36381 | 0.213441 | ||||||||
\(419\) | −24.2348 | −1.18395 | −0.591975 | − | 0.805957i | \(-0.701651\pi\) | ||||
−0.591975 | + | 0.805957i | \(0.701651\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.3482 | −1.52782 | −0.763908 | − | 0.645325i | \(-0.776722\pi\) | ||||
−0.763908 | + | 0.645325i | \(0.776722\pi\) | |||||||
\(422\) | −9.46901 | −0.460944 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 16.8510 | 0.818359 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.219182 | −0.0106070 | ||||||||
\(428\) | −27.7719 | −1.34240 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.00066 | 0.0963686 | 0.0481843 | − | 0.998838i | \(-0.484657\pi\) | ||||
0.0481843 | + | 0.998838i | \(0.484657\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.07253 | −0.339884 | −0.169942 | − | 0.985454i | \(-0.554358\pi\) | ||||
−0.169942 | + | 0.985454i | \(0.554358\pi\) | |||||||
\(434\) | 0.0716215 | 0.00343794 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.4260 | −0.499315 | ||||||||
\(437\) | −4.16981 | −0.199469 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.9620 | 0.618644 | 0.309322 | − | 0.950957i | \(-0.399898\pi\) | ||||
0.309322 | + | 0.950957i | \(0.399898\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.85358 | 0.325991 | ||||||||
\(443\) | 21.8687 | 1.03901 | 0.519506 | − | 0.854467i | \(-0.326116\pi\) | ||||
0.519506 | + | 0.854467i | \(0.326116\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.68902 | 0.269383 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.0616197 | 0.00291126 | ||||||||
\(449\) | −0.399626 | −0.0188595 | −0.00942976 | − | 0.999956i | \(-0.503002\pi\) | ||||
−0.00942976 | + | 0.999956i | \(0.503002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.9819 | −1.31762 | ||||||||
\(452\) | −4.24712 | −0.199768 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.60992 | 0.263287 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.2247 | 1.64774 | 0.823872 | − | 0.566777i | \(-0.191810\pi\) | ||||
0.823872 | + | 0.566777i | \(0.191810\pi\) | |||||||
\(458\) | 4.83439 | 0.225896 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.9615 | 0.743402 | 0.371701 | − | 0.928353i | \(-0.378775\pi\) | ||||
0.371701 | + | 0.928353i | \(0.378775\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.4831 | 1.41667 | 0.708336 | − | 0.705875i | \(-0.249446\pi\) | ||||
0.708336 | + | 0.705875i | \(0.249446\pi\) | |||||||
\(464\) | −9.86342 | −0.457898 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.77839 | −0.360327 | ||||||||
\(467\) | 6.64657 | 0.307567 | 0.153783 | − | 0.988105i | \(-0.450854\pi\) | ||||
0.153783 | + | 0.988105i | \(0.450854\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.106424 | −0.00491418 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.36811 | −0.385174 | ||||||||
\(473\) | 0.625551 | 0.0287628 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.150737 | −0.00690902 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.18129 | −0.328464 | ||||||||
\(479\) | −22.2408 | −1.01621 | −0.508104 | − | 0.861296i | \(-0.669653\pi\) | ||||
−0.508104 | + | 0.861296i | \(0.669653\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.39446 | −0.0635820 | ||||||||
\(482\) | 12.6807 | 0.577591 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.21809 | −0.146277 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.1851 | −0.461531 | −0.230765 | − | 0.973009i | \(-0.574123\pi\) | ||||
−0.230765 | + | 0.973009i | \(0.574123\pi\) | |||||||
\(488\) | −17.3059 | −0.783402 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.64004 | −0.299661 | −0.149830 | − | 0.988712i | \(-0.547873\pi\) | ||||
−0.149830 | + | 0.988712i | \(0.547873\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.9752 | 0.629413 | ||||||||
\(494\) | 4.59834 | 0.206889 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.3674 | −0.690015 | ||||||||
\(497\) | −0.230614 | −0.0103444 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.08397 | 0.0485253 | 0.0242626 | − | 0.999706i | \(-0.492276\pi\) | ||||
0.0242626 | + | 0.999706i | \(0.492276\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.12268 | −0.0947399 | ||||||||
\(503\) | −1.98603 | −0.0885525 | −0.0442762 | − | 0.999019i | \(-0.514098\pi\) | ||||
−0.0442762 | + | 0.999019i | \(0.514098\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.07944 | −0.136898 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −29.9208 | −1.32752 | ||||||||
\(509\) | −2.30915 | −0.102351 | −0.0511757 | − | 0.998690i | \(-0.516297\pi\) | ||||
−0.0511757 | + | 0.998690i | \(0.516297\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0940541 | −0.00416071 | ||||||||
\(512\) | 22.4865 | 0.993773 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.2205 | −0.450809 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.9884 | −1.23093 | ||||||||
\(518\) | −0.00440122 | −0.000193379 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.0447 | 0.483879 | 0.241940 | − | 0.970291i | \(-0.422216\pi\) | ||||
0.241940 | + | 0.970291i | \(0.422216\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.0025 | −1.13701 | −0.568505 | − | 0.822680i | \(-0.692478\pi\) | ||||
−0.568505 | + | 0.822680i | \(0.692478\pi\) | |||||||
\(524\) | 8.37696 | 0.365949 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.3623 | 0.626224 | ||||||||
\(527\) | 21.7736 | 0.948475 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.0575 | −0.872064 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.101136 | −0.00438478 | ||||||||
\(533\) | −29.4858 | −1.27717 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.40286 | −0.362948 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.98112 | −0.171638 | ||||||||
\(539\) | 25.0810 | 1.08031 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.0182391 | −0.000784162 0 | −0.000392081 | − | 1.00000i | \(-0.500125\pi\) | ||||
−0.000392081 | 1.00000i | \(0.500125\pi\) | ||||||||
\(542\) | 4.78689 | 0.205614 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −18.2510 | −0.782503 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.96048 | 0.425879 | 0.212940 | − | 0.977065i | \(-0.431696\pi\) | ||||
0.212940 | + | 0.977065i | \(0.431696\pi\) | |||||||
\(548\) | −22.4054 | −0.957113 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.37656 | 0.399455 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.230350 | 0.00979547 | ||||||||
\(554\) | −8.61222 | −0.365898 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.8875 | 0.588960 | ||||||||
\(557\) | −34.9291 | −1.47999 | −0.739996 | − | 0.672611i | \(-0.765173\pi\) | ||||
−0.739996 | + | 0.672611i | \(0.765173\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.659171 | 0.0278800 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.6360 | −0.575201 | ||||||||
\(563\) | 15.7939 | 0.665634 | 0.332817 | − | 0.942991i | \(-0.392001\pi\) | ||||
0.332817 | + | 0.942991i | \(0.392001\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.74295 | 0.0732616 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −18.2085 | −0.764012 | ||||||||
\(569\) | 14.5605 | 0.610408 | 0.305204 | − | 0.952287i | \(-0.401275\pi\) | ||||
0.305204 | + | 0.952287i | \(0.401275\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.6138 | 1.15560 | 0.577802 | − | 0.816177i | \(-0.303911\pi\) | ||||
0.577802 | + | 0.816177i | \(0.303911\pi\) | |||||||
\(572\) | −23.6642 | −0.989448 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.0930636 | −0.00388440 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.1520 | 1.13035 | 0.565176 | − | 0.824970i | \(-0.308808\pi\) | ||||
0.565176 | + | 0.824970i | \(0.308808\pi\) | |||||||
\(578\) | −1.94066 | −0.0807210 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.213072 | 0.00883972 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.1487 | 1.33146 | ||||||||
\(584\) | −7.42621 | −0.307299 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.7703 | 0.486227 | ||||||||
\(587\) | −10.7037 | −0.441787 | −0.220894 | − | 0.975298i | \(-0.570897\pi\) | ||||
−0.220894 | + | 0.975298i | \(0.570897\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.6088 | 0.601946 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.944342 | 0.0388122 | ||||||||
\(593\) | −3.84629 | −0.157948 | −0.0789740 | − | 0.996877i | \(-0.525164\pi\) | ||||
−0.0789740 | + | 0.996877i | \(0.525164\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.84210 | −0.403148 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.24494 | −0.132695 | ||||||||
\(599\) | −46.1423 | −1.88532 | −0.942662 | − | 0.333750i | \(-0.891686\pi\) | ||||
−0.942662 | + | 0.333750i | \(0.891686\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.3119 | −0.543005 | −0.271503 | − | 0.962438i | \(-0.587521\pi\) | ||||
−0.271503 | + | 0.962438i | \(0.587521\pi\) | |||||||
\(602\) | 0.00208049 | 8.47943e−5 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.8895 | 0.524466 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.0838 | −1.38342 | −0.691709 | − | 0.722176i | \(-0.743142\pi\) | ||||
−0.691709 | + | 0.722176i | \(0.743142\pi\) | |||||||
\(608\) | −12.2453 | −0.496613 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.4926 | −1.19314 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.4809 | −1.02916 | −0.514582 | − | 0.857441i | \(-0.672053\pi\) | ||||
−0.514582 | + | 0.857441i | \(0.672053\pi\) | |||||||
\(614\) | −0.557363 | −0.0224933 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.160097 | −0.00645048 | ||||||||
\(617\) | −26.9453 | −1.08478 | −0.542389 | − | 0.840127i | \(-0.682480\pi\) | ||||
−0.542389 | + | 0.840127i | \(0.682480\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.3289 | 1.58076 | 0.790381 | − | 0.612615i | \(-0.209882\pi\) | ||||
0.790381 | + | 0.612615i | \(0.209882\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.39105 | 0.296354 | ||||||||
\(623\) | −0.404752 | −0.0162161 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.47906 | −0.0990833 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.0956 | 0.602378 | ||||||||
\(629\) | −1.33802 | −0.0533502 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.2443 | 0.447630 | 0.223815 | − | 0.974632i | \(-0.428149\pi\) | ||||
0.223815 | + | 0.974632i | \(0.428149\pi\) | |||||||
\(632\) | 18.1877 | 0.723467 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.3652 | 0.451369 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.4290 | 1.04715 | ||||||||
\(638\) | 6.92465 | 0.274150 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.4773 | −0.690311 | −0.345155 | − | 0.938546i | \(-0.612174\pi\) | ||||
−0.345155 | + | 0.938546i | \(0.612174\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.72320 | 0.344009 | 0.172005 | − | 0.985096i | \(-0.444976\pi\) | ||||
0.172005 | + | 0.985096i | \(0.444976\pi\) | |||||||
\(644\) | 0.0713689 | 0.00281233 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.41221 | 0.173596 | ||||||||
\(647\) | 25.0654 | 0.985421 | 0.492710 | − | 0.870193i | \(-0.336006\pi\) | ||||
0.492710 | + | 0.870193i | \(0.336006\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.9648 | −0.626674 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.30716 | 0.325334 | ||||||||
\(653\) | 29.9777 | 1.17312 | 0.586559 | − | 0.809906i | \(-0.300482\pi\) | ||||
0.586559 | + | 0.809906i | \(0.300482\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 19.9680 | 0.779621 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.0930852 | −0.00362884 | ||||||||
\(659\) | 4.36601 | 0.170076 | 0.0850379 | − | 0.996378i | \(-0.472899\pi\) | ||||
0.0850379 | + | 0.996378i | \(0.472899\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.4529 | −0.756628 | −0.378314 | − | 0.925677i | \(-0.623496\pi\) | ||||
−0.378314 | + | 0.925677i | \(0.623496\pi\) | |||||||
\(662\) | 0.868004 | 0.0337359 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16.8235 | 0.652878 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.61681 | −0.256204 | ||||||||
\(668\) | −32.5258 | −1.25846 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.0165 | −1.27459 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.2275 | 1.39647 | 0.698234 | − | 0.715870i | \(-0.253970\pi\) | ||||
0.698234 | + | 0.715870i | \(0.253970\pi\) | |||||||
\(674\) | −7.00436 | −0.269798 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.19886 | −0.0845715 | ||||||||
\(677\) | 2.04046 | 0.0784214 | 0.0392107 | − | 0.999231i | \(-0.487516\pi\) | ||||
0.0392107 | + | 0.999231i | \(0.487516\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.0657586 | 0.00252359 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.7887 | 0.413121 | ||||||||
\(683\) | 15.9105 | 0.608799 | 0.304400 | − | 0.952544i | \(-0.401544\pi\) | ||||
0.304400 | + | 0.952544i | \(0.401544\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.166838 | 0.00636990 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.446396 | −0.0170187 | ||||||||
\(689\) | 33.8765 | 1.29059 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.90166 | −0.148426 | −0.0742130 | − | 0.997242i | \(-0.523644\pi\) | ||||
−0.0742130 | + | 0.997242i | \(0.523644\pi\) | |||||||
\(692\) | −27.6268 | −1.05021 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.54589 | 0.0966408 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.2922 | −1.07164 | ||||||||
\(698\) | −4.45201 | −0.168511 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.3587 | −1.14663 | −0.573316 | − | 0.819335i | \(-0.694343\pi\) | ||||
−0.573316 | + | 0.819335i | \(0.694343\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.897729 | −0.0338585 | ||||||||
\(704\) | 9.28208 | 0.349832 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.71651 | 0.177508 | ||||||||
\(707\) | 0.246267 | 0.00926181 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −48.5677 | −1.82400 | −0.911999 | − | 0.410193i | \(-0.865461\pi\) | ||||
−0.911999 | + | 0.410193i | \(0.865461\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −31.9579 | −1.19767 | ||||||||
\(713\) | −10.3091 | −0.386078 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.3873 | 0.612421 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.56651 | −0.170421 | ||||||||
\(719\) | −4.76238 | −0.177607 | −0.0888033 | − | 0.996049i | \(-0.528304\pi\) | ||||
−0.0888033 | + | 0.996049i | \(0.528304\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.435112 | 0.0162044 | ||||||||
\(722\) | −6.55847 | −0.244081 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.2252 | 0.380018 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.38691 | 0.125614 | 0.0628068 | − | 0.998026i | \(-0.479995\pi\) | ||||
0.0628068 | + | 0.998026i | \(0.479995\pi\) | |||||||
\(728\) | −0.168701 | −0.00625248 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.632488 | 0.0233934 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.4009 | −0.568847 | −0.284423 | − | 0.958699i | \(-0.591802\pi\) | ||||
−0.284423 | + | 0.958699i | \(0.591802\pi\) | |||||||
\(734\) | 8.95690 | 0.330605 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.64121 | 0.318519 | ||||||||
\(737\) | −16.0311 | −0.590513 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.98465 | 0.367291 | 0.183646 | − | 0.982993i | \(-0.441210\pi\) | ||||
0.183646 | + | 0.982993i | \(0.441210\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.106922 | 0.00392522 | ||||||||
\(743\) | −41.4419 | −1.52036 | −0.760178 | − | 0.649715i | \(-0.774888\pi\) | ||||
−0.760178 | + | 0.649715i | \(0.774888\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.54001 | 0.0563839 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −22.7063 | −0.830223 | ||||||||
\(749\) | −0.377719 | −0.0138015 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.1036 | 0.770082 | 0.385041 | − | 0.922900i | \(-0.374187\pi\) | ||||
0.385041 | + | 0.922900i | \(0.374187\pi\) | |||||||
\(752\) | 19.9727 | 0.728329 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.29682 | 0.265734 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.7168 | −1.47988 | −0.739938 | − | 0.672675i | \(-0.765145\pi\) | ||||
−0.739938 | + | 0.672675i | \(0.765145\pi\) | |||||||
\(758\) | 12.8186 | 0.465594 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.07664 | 0.184028 | 0.0920140 | − | 0.995758i | \(-0.470670\pi\) | ||||
0.0920140 | + | 0.995758i | \(0.470670\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.141802 | −0.00513357 | ||||||||
\(764\) | −38.2941 | −1.38543 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.11485 | −0.0402810 | ||||||||
\(767\) | −16.8229 | −0.607438 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −46.7687 | −1.68652 | −0.843261 | − | 0.537505i | \(-0.819367\pi\) | ||||
−0.843261 | + | 0.537505i | \(0.819367\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −44.1697 | −1.58970 | ||||||||
\(773\) | 19.0938 | 0.686756 | 0.343378 | − | 0.939197i | \(-0.388429\pi\) | ||||
0.343378 | + | 0.939197i | \(0.388429\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.19209 | 0.186385 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.32666 | −0.0834147 | ||||||||
\(779\) | −18.9824 | −0.680115 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.7385 | −1.24304 | ||||||||
\(782\) | −3.11359 | −0.111342 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −17.8979 | −0.639212 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.02513 | 0.143481 | 0.0717403 | − | 0.997423i | \(-0.477145\pi\) | ||||
0.0717403 | + | 0.997423i | \(0.477145\pi\) | |||||||
\(788\) | −25.2799 | −0.900559 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.0577642 | −0.00205386 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −34.7910 | −1.23546 | ||||||||
\(794\) | 19.0101 | 0.674645 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.60660 | 0.234165 | ||||||||
\(797\) | −15.9847 | −0.566205 | −0.283103 | − | 0.959090i | \(-0.591364\pi\) | ||||
−0.283103 | + | 0.959090i | \(0.591364\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.2988 | −1.00114 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.37587 | 0.295762 | ||||||||
\(803\) | −14.1678 | −0.499972 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.3685 | 0.400440 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 19.4444 | 0.684052 | ||||||||
\(809\) | 29.2015 | 1.02667 | 0.513335 | − | 0.858188i | \(-0.328410\pi\) | ||||
0.513335 | + | 0.858188i | \(0.328410\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.11719 | 0.249918 | 0.124959 | − | 0.992162i | \(-0.460120\pi\) | ||||
0.124959 | + | 0.992162i | \(0.460120\pi\) | |||||||
\(812\) | −0.160485 | −0.00563194 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.662978 | −0.0232374 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.424362 | 0.0148466 | ||||||||
\(818\) | 0.237034 | 0.00828770 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.6032 | 1.13786 | 0.568929 | − | 0.822387i | \(-0.307358\pi\) | ||||
0.568929 | + | 0.822387i | \(0.307358\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.1361 | −0.945905 | −0.472953 | − | 0.881088i | \(-0.656812\pi\) | ||||
−0.472953 | + | 0.881088i | \(0.656812\pi\) | |||||||
\(824\) | 34.3551 | 1.19681 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.0530966 | −0.00184747 | ||||||||
\(827\) | −54.8232 | −1.90639 | −0.953195 | − | 0.302357i | \(-0.902226\pi\) | ||||
−0.953195 | + | 0.302357i | \(0.902226\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.471969 | 0.0163922 | 0.00819608 | − | 0.999966i | \(-0.497391\pi\) | ||||
0.00819608 | + | 0.999966i | \(0.497391\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.78095 | 0.339093 | ||||||||
\(833\) | 25.3591 | 0.878642 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −15.2346 | −0.526898 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.1414 | −0.419418 | ||||||||
\(839\) | 38.4737 | 1.32826 | 0.664129 | − | 0.747618i | \(-0.268802\pi\) | ||||
0.664129 | + | 0.747618i | \(0.268802\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.1209 | −0.486929 | ||||||||
\(842\) | −15.7051 | −0.541233 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 33.0574 | 1.13788 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.0437684 | −0.00150390 | ||||||||
\(848\) | −22.9415 | −0.787814 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.633505 | 0.0217163 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.8541 | 1.22762 | 0.613811 | − | 0.789453i | \(-0.289636\pi\) | ||||
0.613811 | + | 0.789453i | \(0.289636\pi\) | |||||||
\(854\) | −0.109808 | −0.00375755 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −29.8234 | −1.01934 | ||||||||
\(857\) | 0.386299 | 0.0131957 | 0.00659786 | − | 0.999978i | \(-0.497900\pi\) | ||||
0.00659786 | + | 0.999978i | \(0.497900\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.2889 | 0.760487 | 0.380244 | − | 0.924886i | \(-0.375840\pi\) | ||||
0.380244 | + | 0.924886i | \(0.375840\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.00231 | 0.0341389 | ||||||||
\(863\) | 9.29808 | 0.316510 | 0.158255 | − | 0.987398i | \(-0.449413\pi\) | ||||
0.158255 | + | 0.987398i | \(0.449413\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.54326 | −0.120405 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.250039 | −0.00848686 | ||||||||
\(869\) | 34.6987 | 1.17707 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.8927 | −0.572387 | ||||||||
\(872\) | −11.1962 | −0.379151 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.08903 | −0.0706626 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.1786 | −0.985292 | −0.492646 | − | 0.870230i | \(-0.663970\pi\) | ||||
−0.492646 | + | 0.870230i | \(0.663970\pi\) | |||||||
\(878\) | 6.49384 | 0.219156 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.0737 | 1.35012 | 0.675059 | − | 0.737764i | \(-0.264118\pi\) | ||||
0.675059 | + | 0.737764i | \(0.264118\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.8339 | −1.03764 | −0.518822 | − | 0.854882i | \(-0.673629\pi\) | ||||
−0.518822 | + | 0.854882i | \(0.673629\pi\) | |||||||
\(884\) | −23.9266 | −0.804739 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.9560 | 0.368073 | ||||||||
\(887\) | −38.5528 | −1.29448 | −0.647239 | − | 0.762287i | \(-0.724076\pi\) | ||||
−0.647239 | + | 0.762287i | \(0.724076\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.406946 | −0.0136485 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.8610 | −0.664996 | ||||||||
\(893\) | −18.9868 | −0.635370 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.270533 | 0.00903787 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.200208 | −0.00668104 | ||||||||
\(899\) | 23.1818 | 0.773156 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.5052 | 1.08291 | ||||||||
\(902\) | −14.0186 | −0.466769 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.56087 | −0.151692 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.77670 | 0.158608 | 0.0793038 | − | 0.996850i | \(-0.474730\pi\) | ||||
0.0793038 | + | 0.996850i | \(0.474730\pi\) | |||||||
\(908\) | −19.5849 | −0.649946 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.5332 | 0.382111 | 0.191056 | − | 0.981579i | \(-0.438809\pi\) | ||||
0.191056 | + | 0.981579i | \(0.438809\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.0961 | 1.06223 | ||||||||
\(914\) | 17.6472 | 0.583718 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.8774 | −0.557645 | ||||||||
\(917\) | 0.113933 | 0.00376240 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.3268 | −1.36325 | −0.681623 | − | 0.731704i | \(-0.738726\pi\) | ||||
−0.681623 | + | 0.731704i | \(0.738726\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.99655 | 0.263352 | ||||||||
\(923\) | −36.6055 | −1.20488 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.2717 | 0.501860 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −19.4313 | −0.637863 | ||||||||
\(929\) | 13.4174 | 0.440212 | 0.220106 | − | 0.975476i | \(-0.429360\pi\) | ||||
0.220106 | + | 0.975476i | \(0.429360\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.0145 | 0.557627 | ||||||||
\(932\) | 27.1552 | 0.889499 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.32986 | 0.108956 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.9929 | −1.37185 | −0.685923 | − | 0.727674i | \(-0.740602\pi\) | ||||
−0.685923 | + | 0.727674i | \(0.740602\pi\) | |||||||
\(938\) | −0.0533170 | −0.00174086 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.0565 | −1.30580 | −0.652902 | − | 0.757443i | \(-0.726449\pi\) | ||||
−0.652902 | + | 0.757443i | \(0.726449\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.3954 | 0.436215 | ||||||||
\(944\) | 11.3926 | 0.370797 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.313394 | 0.0101893 | ||||||||
\(947\) | 43.9751 | 1.42900 | 0.714499 | − | 0.699637i | \(-0.246655\pi\) | ||||
0.714499 | + | 0.699637i | \(0.246655\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.9293 | −0.484625 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.161872 | −0.00524631 | ||||||||
\(953\) | 40.6171 | 1.31572 | 0.657859 | − | 0.753141i | \(-0.271462\pi\) | ||||
0.657859 | + | 0.753141i | \(0.271462\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 25.0707 | 0.810843 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11.1424 | −0.359994 | ||||||||
\(959\) | −0.304731 | −0.00984028 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.11756 | 0.165083 | ||||||||
\(962\) | −0.698610 | −0.0225241 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −44.2698 | −1.42584 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.0002 | 0.514531 | 0.257265 | − | 0.966341i | \(-0.417179\pi\) | ||||
0.257265 | + | 0.966341i | \(0.417179\pi\) | |||||||
\(968\) | −3.45581 | −0.111074 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −55.5201 | −1.78173 | −0.890863 | − | 0.454272i | \(-0.849899\pi\) | ||||
−0.890863 | + | 0.454272i | \(0.849899\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.188880 | 0.00605523 | ||||||||
\(974\) | −5.10263 | −0.163499 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 23.5608 | 0.754162 | ||||||||
\(977\) | 6.32539 | 0.202367 | 0.101184 | − | 0.994868i | \(-0.467737\pi\) | ||||
0.101184 | + | 0.994868i | \(0.467737\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −60.9699 | −1.94861 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.32659 | −0.106156 | ||||||||
\(983\) | 48.6422 | 1.55144 | 0.775722 | − | 0.631074i | \(-0.217386\pi\) | ||||
0.775722 | + | 0.631074i | \(0.217386\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.00145 | 0.222972 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16.0533 | −0.510725 | ||||||||
\(989\) | −0.299462 | −0.00952234 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.1763 | −1.40331 | −0.701653 | − | 0.712519i | \(-0.747554\pi\) | ||||
−0.701653 | + | 0.712519i | \(0.747554\pi\) | |||||||
\(992\) | −30.2742 | −0.961207 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.115535 | −0.00366455 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.2262 | −1.27398 | −0.636988 | − | 0.770873i | \(-0.719820\pi\) | ||||
−0.636988 | + | 0.770873i | \(0.719820\pi\) | |||||||
\(998\) | 0.543059 | 0.0171902 | ||||||||
\(999\) | 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 | 5625.2.a.be.1.4 | 8 | ||
3.2 | odd | 2 | 625.2.a.e.1.5 | ✓ | 8 | ||
5.4 | even | 2 | 5625.2.a.s.1.5 | 8 | |||
12.11 | even | 2 | 10000.2.a.bn.1.8 | 8 | |||
15.2 | even | 4 | 625.2.b.d.624.7 | 16 | |||
15.8 | even | 4 | 625.2.b.d.624.10 | 16 | |||
15.14 | odd | 2 | 625.2.a.g.1.4 | yes | 8 | ||
60.59 | even | 2 | 10000.2.a.be.1.1 | 8 | |||
75.2 | even | 20 | 625.2.e.k.124.4 | 32 | |||
75.8 | even | 20 | 625.2.e.j.374.4 | 32 | |||
75.11 | odd | 10 | 625.2.d.p.501.3 | 16 | |||
75.14 | odd | 10 | 625.2.d.n.501.2 | 16 | |||
75.17 | even | 20 | 625.2.e.j.374.5 | 32 | |||
75.23 | even | 20 | 625.2.e.k.124.5 | 32 | |||
75.29 | odd | 10 | 625.2.d.m.376.3 | 16 | |||
75.38 | even | 20 | 625.2.e.k.499.4 | 32 | |||
75.41 | odd | 10 | 625.2.d.p.126.3 | 16 | |||
75.44 | odd | 10 | 625.2.d.m.251.3 | 16 | |||
75.47 | even | 20 | 625.2.e.j.249.4 | 32 | |||
75.53 | even | 20 | 625.2.e.j.249.5 | 32 | |||
75.56 | odd | 10 | 625.2.d.q.251.2 | 16 | |||
75.59 | odd | 10 | 625.2.d.n.126.2 | 16 | |||
75.62 | even | 20 | 625.2.e.k.499.5 | 32 | |||
75.71 | odd | 10 | 625.2.d.q.376.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
625.2.a.e.1.5 | ✓ | 8 | 3.2 | odd | 2 | ||
625.2.a.g.1.4 | yes | 8 | 15.14 | odd | 2 | ||
625.2.b.d.624.7 | 16 | 15.2 | even | 4 | |||
625.2.b.d.624.10 | 16 | 15.8 | even | 4 | |||
625.2.d.m.251.3 | 16 | 75.44 | odd | 10 | |||
625.2.d.m.376.3 | 16 | 75.29 | odd | 10 | |||
625.2.d.n.126.2 | 16 | 75.59 | odd | 10 | |||
625.2.d.n.501.2 | 16 | 75.14 | odd | 10 | |||
625.2.d.p.126.3 | 16 | 75.41 | odd | 10 | |||
625.2.d.p.501.3 | 16 | 75.11 | odd | 10 | |||
625.2.d.q.251.2 | 16 | 75.56 | odd | 10 | |||
625.2.d.q.376.2 | 16 | 75.71 | odd | 10 | |||
625.2.e.j.249.4 | 32 | 75.47 | even | 20 | |||
625.2.e.j.249.5 | 32 | 75.53 | even | 20 | |||
625.2.e.j.374.4 | 32 | 75.8 | even | 20 | |||
625.2.e.j.374.5 | 32 | 75.17 | even | 20 | |||
625.2.e.k.124.4 | 32 | 75.2 | even | 20 | |||
625.2.e.k.124.5 | 32 | 75.23 | even | 20 | |||
625.2.e.k.499.4 | 32 | 75.38 | even | 20 | |||
625.2.e.k.499.5 | 32 | 75.62 | even | 20 | |||
5625.2.a.s.1.5 | 8 | 5.4 | even | 2 | |||
5625.2.a.be.1.4 | 8 | 1.1 | even | 1 | trivial | ||
10000.2.a.be.1.1 | 8 | 60.59 | even | 2 | |||
10000.2.a.bn.1.8 | 8 | 12.11 | even | 2 |