Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [810,3,Mod(809,810)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(810, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("810.809");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 810 = 2 \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 810.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(22.0709014132\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 809.1 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 810.809 |
Dual form | 810.3.b.a.809.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).
\(n\) | \(487\) | \(731\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | −4.87832 | − | 1.09638i | −0.975663 | − | 0.219275i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.10102i | 0.300146i | 0.988675 | + | 0.150073i | \(0.0479508\pi\) | ||||
−0.988675 | + | 0.150073i | \(0.952049\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.89898 | + | 1.55051i | 0.689898 | + | 0.155051i | ||||
\(11\) | − | 13.3636i | − | 1.21487i | −0.794368 | − | 0.607436i | \(-0.792198\pi\) | ||
0.794368 | − | 0.607436i | \(-0.207802\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 23.1464i | 1.78049i | 0.455478 | + | 0.890247i | \(0.349469\pi\) | ||||
−0.455478 | + | 0.890247i | \(0.650531\pi\) | |||||||
\(14\) | − | 2.97129i | − | 0.212235i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 27.5057 | 1.61798 | 0.808992 | − | 0.587819i | \(-0.200013\pi\) | ||||
0.808992 | + | 0.587819i | \(0.200013\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −15.5505 | −0.818448 | −0.409224 | − | 0.912434i | \(-0.634201\pi\) | ||||
−0.409224 | + | 0.912434i | \(0.634201\pi\) | |||||||
\(20\) | −9.75663 | − | 2.19275i | −0.487832 | − | 0.109638i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 18.8990i | 0.859045i | ||||||||
\(23\) | −14.9528 | −0.650121 | −0.325060 | − | 0.945693i | \(-0.605385\pi\) | ||||
−0.325060 | + | 0.945693i | \(0.605385\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 22.5959 | + | 10.6969i | 0.903837 | + | 0.427878i | ||||
\(26\) | − | 32.7340i | − | 1.25900i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.20204i | 0.150073i | ||||||||
\(29\) | 3.28913i | 0.113418i | 0.998391 | + | 0.0567091i | \(0.0180608\pi\) | ||||
−0.998391 | + | 0.0567091i | \(0.981939\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.84337 | −0.317528 | −0.158764 | − | 0.987317i | \(-0.550751\pi\) | ||||
−0.158764 | + | 0.987317i | \(0.550751\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −38.8990 | −1.14409 | ||||||||
\(35\) | 2.30351 | − | 10.2494i | 0.0658145 | − | 0.292841i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 33.3485i | − | 0.901310i | −0.892698 | − | 0.450655i | \(-0.851190\pi\) | ||
0.892698 | − | 0.450655i | \(-0.148810\pi\) | |||||||
\(38\) | 21.9917 | 0.578730 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 13.7980 | + | 3.10102i | 0.344949 | + | 0.0775255i | ||||
\(41\) | − | 10.8530i | − | 0.264707i | −0.991203 | − | 0.132354i | \(-0.957747\pi\) | ||
0.991203 | − | 0.132354i | \(-0.0422535\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 43.1918i | − | 1.00446i | −0.864734 | − | 0.502231i | \(-0.832513\pi\) | ||
0.864734 | − | 0.502231i | \(-0.167487\pi\) | |||||||
\(44\) | − | 26.7272i | − | 0.607436i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 21.1464 | 0.459705 | ||||||||
\(47\) | −36.0873 | −0.767816 | −0.383908 | − | 0.923371i | \(-0.625422\pi\) | ||||
−0.383908 | + | 0.923371i | \(0.625422\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 44.5857 | 0.909913 | ||||||||
\(50\) | −31.9555 | − | 15.1278i | −0.639109 | − | 0.302555i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 46.2929i | 0.890247i | ||||||||
\(53\) | −53.1687 | −1.00318 | −0.501591 | − | 0.865105i | \(-0.667252\pi\) | ||||
−0.501591 | + | 0.865105i | \(0.667252\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.6515 | + | 65.1918i | −0.266391 | + | 1.18531i | ||||
\(56\) | − | 5.94258i | − | 0.106118i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 4.65153i | − | 0.0801988i | ||||||
\(59\) | − | 101.252i | − | 1.71613i | −0.513538 | − | 0.858067i | \(-0.671665\pi\) | ||
0.513538 | − | 0.858067i | \(-0.328335\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.101021 | 0.00165607 | 0.000828037 | − | 1.00000i | \(-0.499736\pi\) | ||||
0.000828037 | 1.00000i | \(0.499736\pi\) | ||||||||
\(62\) | 13.9206 | 0.224526 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 25.3772 | − | 112.916i | 0.390418 | − | 1.73716i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 55.9898i | − | 0.835669i | −0.908523 | − | 0.417834i | \(-0.862789\pi\) | ||
0.908523 | − | 0.417834i | \(-0.137211\pi\) | |||||||
\(68\) | 55.0115 | 0.808992 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.25765 | + | 14.4949i | −0.0465379 | + | 0.207070i | ||||
\(71\) | 79.2457i | 1.11614i | 0.829795 | + | 0.558069i | \(0.188457\pi\) | ||||
−0.829795 | + | 0.558069i | \(0.811543\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 20.8990i | − | 0.286287i | −0.989702 | − | 0.143144i | \(-0.954279\pi\) | ||
0.989702 | − | 0.143144i | \(-0.0457211\pi\) | |||||||
\(74\) | 47.1619i | 0.637322i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −31.1010 | −0.409224 | ||||||||
\(77\) | 28.0772 | 0.364639 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.48469 | −0.0187936 | −0.00939679 | − | 0.999956i | \(-0.502991\pi\) | ||||
−0.00939679 | + | 0.999956i | \(0.502991\pi\) | |||||||
\(80\) | −19.5133 | − | 4.38551i | −0.243916 | − | 0.0548188i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 15.3485i | 0.187176i | ||||||||
\(83\) | −9.93160 | −0.119658 | −0.0598289 | − | 0.998209i | \(-0.519056\pi\) | ||||
−0.0598289 | + | 0.998209i | \(0.519056\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −134.182 | − | 30.1566i | −1.57861 | − | 0.354784i | ||||
\(86\) | 61.0825i | 0.710261i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 37.7980i | 0.429522i | ||||||||
\(89\) | − | 152.974i | − | 1.71881i | −0.511294 | − | 0.859406i | \(-0.670834\pi\) | ||
0.511294 | − | 0.859406i | \(-0.329166\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −48.6311 | −0.534408 | ||||||||
\(92\) | −29.9056 | −0.325060 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 51.0352 | 0.542928 | ||||||||
\(95\) | 75.8603 | + | 17.0492i | 0.798529 | + | 0.179465i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 38.7878i | − | 0.399874i | −0.979809 | − | 0.199937i | \(-0.935926\pi\) | ||
0.979809 | − | 0.199937i | \(-0.0640737\pi\) | |||||||
\(98\) | −63.0537 | −0.643405 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 45.1918 | + | 21.3939i | 0.451918 | + | 0.213939i | ||||
\(101\) | − | 81.9602i | − | 0.811487i | −0.913987 | − | 0.405743i | \(-0.867013\pi\) | ||
0.913987 | − | 0.405743i | \(-0.132987\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 115.778i | − | 1.12405i | −0.827119 | − | 0.562027i | \(-0.810022\pi\) | ||
0.827119 | − | 0.562027i | \(-0.189978\pi\) | |||||||
\(104\) | − | 65.4680i | − | 0.629500i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 75.1918 | 0.709357 | ||||||||
\(107\) | −119.512 | −1.11693 | −0.558465 | − | 0.829528i | \(-0.688609\pi\) | ||||
−0.558465 | + | 0.829528i | \(0.688609\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 62.9092 | 0.577148 | 0.288574 | − | 0.957458i | \(-0.406819\pi\) | ||||
0.288574 | + | 0.957458i | \(0.406819\pi\) | |||||||
\(110\) | 20.7204 | − | 92.1952i | 0.188367 | − | 0.838138i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.40408i | 0.0750364i | ||||||||
\(113\) | −80.0243 | −0.708179 | −0.354090 | − | 0.935211i | \(-0.615209\pi\) | ||||
−0.354090 | + | 0.935211i | \(0.615209\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 72.9444 | + | 16.3939i | 0.634299 | + | 0.142555i | ||||
\(116\) | 6.57826i | 0.0567091i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 143.192i | 1.21349i | ||||||||
\(119\) | 57.7901i | 0.485631i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −57.5857 | −0.475915 | ||||||||
\(122\) | −0.142865 | −0.00117102 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −19.6867 | −0.158764 | ||||||||
\(125\) | −98.5021 | − | 76.9567i | −0.788017 | − | 0.615653i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 122.687i | − | 0.966037i | −0.875610 | − | 0.483019i | \(-0.839540\pi\) | ||
0.875610 | − | 0.483019i | \(-0.160460\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −35.8888 | + | 159.687i | −0.276067 | + | 1.22836i | ||||
\(131\) | − | 22.3417i | − | 0.170547i | −0.996358 | − | 0.0852736i | \(-0.972824\pi\) | ||
0.996358 | − | 0.0852736i | \(-0.0271764\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 32.6719i | − | 0.245654i | ||||||
\(134\) | 79.1815i | 0.590907i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −77.7980 | −0.572044 | ||||||||
\(137\) | 0.857187 | 0.00625684 | 0.00312842 | − | 0.999995i | \(-0.499004\pi\) | ||||
0.00312842 | + | 0.999995i | \(0.499004\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 235.283 | 1.69268 | 0.846340 | − | 0.532642i | \(-0.178801\pi\) | ||||
0.846340 | + | 0.532642i | \(0.178801\pi\) | |||||||
\(140\) | 4.60702 | − | 20.4989i | 0.0329073 | − | 0.146421i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 112.070i | − | 0.789228i | ||||||
\(143\) | 309.320 | 2.16307 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.60612 | − | 16.0454i | 0.0248698 | − | 0.110658i | ||||
\(146\) | 29.5556i | 0.202436i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 66.6969i | − | 0.450655i | ||||||
\(149\) | − | 131.204i | − | 0.880564i | −0.897860 | − | 0.440282i | \(-0.854878\pi\) | ||
0.897860 | − | 0.440282i | \(-0.145122\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −88.4495 | −0.585758 | −0.292879 | − | 0.956149i | \(-0.594613\pi\) | ||||
−0.292879 | + | 0.956149i | \(0.594613\pi\) | |||||||
\(152\) | 43.9835 | 0.289365 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −39.7071 | −0.257839 | ||||||||
\(155\) | 48.0190 | + | 10.7920i | 0.309800 | + | 0.0696260i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 162.697i | − | 1.03629i | −0.855294 | − | 0.518143i | \(-0.826623\pi\) | ||
0.855294 | − | 0.518143i | \(-0.173377\pi\) | |||||||
\(158\) | 2.09967 | 0.0132891 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 27.5959 | + | 6.20204i | 0.172474 | + | 0.0387628i | ||||
\(161\) | − | 31.4161i | − | 0.195131i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 275.192i | − | 1.68829i | −0.536112 | − | 0.844147i | \(-0.680108\pi\) | ||
0.536112 | − | 0.844147i | \(-0.319892\pi\) | |||||||
\(164\) | − | 21.7060i | − | 0.132354i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.0454 | 0.0846109 | ||||||||
\(167\) | −136.989 | −0.820295 | −0.410148 | − | 0.912019i | \(-0.634523\pi\) | ||||
−0.410148 | + | 0.912019i | \(0.634523\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −366.757 | −2.17016 | ||||||||
\(170\) | 189.761 | + | 42.6479i | 1.11624 | + | 0.250870i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 86.3837i | − | 0.502231i | ||||||
\(173\) | −92.7666 | −0.536223 | −0.268112 | − | 0.963388i | \(-0.586400\pi\) | ||||
−0.268112 | + | 0.963388i | \(0.586400\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −22.4745 | + | 47.4745i | −0.128426 | + | 0.271283i | ||||
\(176\) | − | 53.4544i | − | 0.303718i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 216.338i | 1.21538i | ||||||||
\(179\) | − | 103.273i | − | 0.576944i | −0.957488 | − | 0.288472i | \(-0.906853\pi\) | ||
0.957488 | − | 0.288472i | \(-0.0931472\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 215.050 | 1.18812 | 0.594061 | − | 0.804420i | \(-0.297524\pi\) | ||||
0.594061 | + | 0.804420i | \(0.297524\pi\) | |||||||
\(182\) | 68.7748 | 0.377883 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 42.2929 | 0.229852 | ||||||||
\(185\) | −36.5625 | + | 162.684i | −0.197635 | + | 0.879375i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 367.576i | − | 1.96564i | ||||||
\(188\) | −72.1747 | −0.383908 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −107.283 | − | 24.1112i | −0.564646 | − | 0.126901i | ||||
\(191\) | 272.693i | 1.42771i | 0.700293 | + | 0.713856i | \(0.253053\pi\) | ||||
−0.700293 | + | 0.713856i | \(0.746947\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 321.621i | 1.66643i | 0.552949 | + | 0.833215i | \(0.313502\pi\) | ||||
−0.552949 | + | 0.833215i | \(0.686498\pi\) | |||||||
\(194\) | 54.8542i | 0.282753i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 89.1714 | 0.454956 | ||||||||
\(197\) | −37.6267 | −0.190999 | −0.0954993 | − | 0.995429i | \(-0.530445\pi\) | ||||
−0.0954993 | + | 0.995429i | \(0.530445\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −318.520 | −1.60060 | −0.800301 | − | 0.599598i | \(-0.795327\pi\) | ||||
−0.800301 | + | 0.599598i | \(0.795327\pi\) | |||||||
\(200\) | −63.9109 | − | 30.2555i | −0.319555 | − | 0.151278i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 115.909i | 0.573808i | ||||||||
\(203\) | −6.91053 | −0.0340420 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.8990 | + | 52.9444i | −0.0580438 | + | 0.258265i | ||||
\(206\) | 163.734i | 0.794826i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 92.5857i | 0.445124i | ||||||||
\(209\) | 207.811i | 0.994310i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.75255 | 0.0272633 | 0.0136316 | − | 0.999907i | \(-0.495661\pi\) | ||||
0.0136316 | + | 0.999907i | \(0.495661\pi\) | |||||||
\(212\) | −106.337 | −0.501591 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 169.015 | 0.789789 | ||||||||
\(215\) | −47.3545 | + | 210.703i | −0.220254 | + | 0.980016i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 20.6811i | − | 0.0953047i | ||||||
\(218\) | −88.9670 | −0.408106 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −29.3031 | + | 130.384i | −0.133196 | + | 0.592653i | ||||
\(221\) | 636.659i | 2.88081i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 23.8990i | − | 0.107170i | −0.998563 | − | 0.0535852i | \(-0.982935\pi\) | ||
0.998563 | − | 0.0535852i | \(-0.0170649\pi\) | |||||||
\(224\) | − | 11.8852i | − | 0.0530588i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 113.171 | 0.500759 | ||||||||
\(227\) | 212.931 | 0.938024 | 0.469012 | − | 0.883192i | \(-0.344610\pi\) | ||||
0.469012 | + | 0.883192i | \(0.344610\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −337.474 | −1.47369 | −0.736844 | − | 0.676063i | \(-0.763685\pi\) | ||||
−0.736844 | + | 0.676063i | \(0.763685\pi\) | |||||||
\(230\) | −103.159 | − | 23.1844i | −0.448517 | − | 0.100802i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 9.30306i | − | 0.0400994i | ||||||
\(233\) | 198.996 | 0.854062 | 0.427031 | − | 0.904237i | \(-0.359560\pi\) | ||||
0.427031 | + | 0.904237i | \(0.359560\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 176.045 | + | 39.5653i | 0.749129 | + | 0.168363i | ||||
\(236\) | − | 202.504i | − | 0.858067i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 81.7276i | − | 0.343393i | ||||||
\(239\) | 76.1107i | 0.318455i | 0.987242 | + | 0.159227i | \(0.0509003\pi\) | ||||
−0.987242 | + | 0.159227i | \(0.949100\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 326.757 | 1.35584 | 0.677919 | − | 0.735136i | \(-0.262882\pi\) | ||||
0.677919 | + | 0.735136i | \(0.262882\pi\) | |||||||
\(242\) | 81.4385 | 0.336523 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.202041 | 0.000828037 | ||||||||
\(245\) | −217.503 | − | 48.8827i | −0.887768 | − | 0.199521i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 359.939i | − | 1.45724i | ||||||
\(248\) | 27.8412 | 0.112263 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 139.303 | + | 108.833i | 0.557212 | + | 0.435333i | ||||
\(251\) | 289.663i | 1.15404i | 0.816731 | + | 0.577019i | \(0.195784\pi\) | ||||
−0.816731 | + | 0.577019i | \(0.804216\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 199.823i | 0.789814i | ||||||||
\(254\) | 173.505i | 0.683092i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 460.533 | 1.79196 | 0.895978 | − | 0.444098i | \(-0.146476\pi\) | ||||
0.895978 | + | 0.444098i | \(0.146476\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 70.0658 | 0.270524 | ||||||||
\(260\) | 50.7544 | − | 225.831i | 0.195209 | − | 0.868581i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 31.5959i | 0.120595i | ||||||||
\(263\) | 211.053 | 0.802484 | 0.401242 | − | 0.915972i | \(-0.368579\pi\) | ||||
0.401242 | + | 0.915972i | \(0.368579\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 259.373 | + | 58.2929i | 0.978768 | + | 0.219973i | ||||
\(266\) | 46.2051i | 0.173703i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 111.980i | − | 0.417834i | ||||||
\(269\) | 187.201i | 0.695915i | 0.937510 | + | 0.347957i | \(0.113125\pi\) | ||||
−0.937510 | + | 0.347957i | \(0.886875\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −199.914 | −0.737689 | −0.368845 | − | 0.929491i | \(-0.620247\pi\) | ||||
−0.368845 | + | 0.929491i | \(0.620247\pi\) | |||||||
\(272\) | 110.023 | 0.404496 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.21225 | −0.00442426 | ||||||||
\(275\) | 142.950 | − | 301.963i | 0.519817 | − | 1.09805i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 107.187i | 0.386958i | 0.981104 | + | 0.193479i | \(0.0619771\pi\) | ||||
−0.981104 | + | 0.193479i | \(0.938023\pi\) | |||||||
\(278\) | −332.740 | −1.19691 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.51531 | + | 28.9898i | −0.0232690 | + | 0.103535i | ||||
\(281\) | 330.786i | 1.17718i | 0.808433 | + | 0.588588i | \(0.200316\pi\) | ||||
−0.808433 | + | 0.588588i | \(0.799684\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 316.576i | 1.11864i | 0.828951 | + | 0.559321i | \(0.188938\pi\) | ||||
−0.828951 | + | 0.559321i | \(0.811062\pi\) | |||||||
\(284\) | 158.491i | 0.558069i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −437.444 | −1.52952 | ||||||||
\(287\) | 22.8024 | 0.0794508 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 467.565 | 1.61787 | ||||||||
\(290\) | −5.09983 | + | 22.6916i | −0.0175856 | + | 0.0782470i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 41.7980i | − | 0.143144i | ||||||
\(293\) | −85.0022 | −0.290110 | −0.145055 | − | 0.989424i | \(-0.546336\pi\) | ||||
−0.145055 | + | 0.989424i | \(0.546336\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −111.010 | + | 493.939i | −0.376306 | + | 1.67437i | ||||
\(296\) | 94.3237i | 0.318661i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 185.551i | 0.622653i | ||||||||
\(299\) | − | 346.104i | − | 1.15754i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 90.7469 | 0.301485 | ||||||||
\(302\) | 125.086 | 0.414194 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −62.2020 | −0.204612 | ||||||||
\(305\) | −0.492810 | − | 0.110756i | −0.00161577 | − | 0.000363136i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 34.5959i | − | 0.112690i | −0.998411 | − | 0.0563451i | \(-0.982055\pi\) | ||
0.998411 | − | 0.0563451i | \(-0.0179447\pi\) | |||||||
\(308\) | 56.1544 | 0.182319 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −67.9092 | − | 15.2622i | −0.219062 | − | 0.0492330i | ||||
\(311\) | − | 42.3478i | − | 0.136166i | −0.997680 | − | 0.0680832i | \(-0.978312\pi\) | ||
0.997680 | − | 0.0680832i | \(-0.0216883\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 366.924i | 1.17228i | 0.810209 | + | 0.586141i | \(0.199353\pi\) | ||||
−0.810209 | + | 0.586141i | \(0.800647\pi\) | |||||||
\(314\) | 230.088i | 0.732765i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.96938 | −0.00939679 | ||||||||
\(317\) | 87.1307 | 0.274860 | 0.137430 | − | 0.990511i | \(-0.456116\pi\) | ||||
0.137430 | + | 0.990511i | \(0.456116\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 43.9546 | 0.137789 | ||||||||
\(320\) | −39.0265 | − | 8.77101i | −0.121958 | − | 0.0274094i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 44.4291i | 0.137979i | ||||||||
\(323\) | −427.728 | −1.32424 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −247.596 | + | 523.015i | −0.761834 | + | 1.60928i | ||||
\(326\) | 389.180i | 1.19380i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 30.6969i | 0.0935882i | ||||||||
\(329\) | − | 75.8202i | − | 0.230457i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −127.333 | −0.384691 | −0.192345 | − | 0.981327i | \(-0.561609\pi\) | ||||
−0.192345 | + | 0.981327i | \(0.561609\pi\) | |||||||
\(332\) | −19.8632 | −0.0598289 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 193.732 | 0.580036 | ||||||||
\(335\) | −61.3859 | + | 273.136i | −0.183241 | + | 0.815331i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 428.595i | − | 1.27179i | −0.771774 | − | 0.635897i | \(-0.780630\pi\) | ||
0.771774 | − | 0.635897i | \(-0.219370\pi\) | |||||||
\(338\) | 518.673 | 1.53454 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −268.363 | − | 60.3133i | −0.789304 | − | 0.177392i | ||||
\(341\) | 131.543i | 0.385756i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 196.626i | 0.573252i | ||||||||
\(344\) | 122.165i | 0.355131i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 131.192 | 0.379167 | ||||||||
\(347\) | −350.503 | −1.01010 | −0.505048 | − | 0.863091i | \(-0.668525\pi\) | ||||
−0.505048 | + | 0.863091i | \(0.668525\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 603.170 | 1.72828 | 0.864141 | − | 0.503250i | \(-0.167862\pi\) | ||||
0.864141 | + | 0.503250i | \(0.167862\pi\) | |||||||
\(350\) | 31.7837 | − | 67.1391i | 0.0908106 | − | 0.191826i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 75.5959i | 0.214761i | ||||||||
\(353\) | 7.81426 | 0.0221367 | 0.0110684 | − | 0.999939i | \(-0.496477\pi\) | ||||
0.0110684 | + | 0.999939i | \(0.496477\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 86.8832 | − | 386.586i | 0.244741 | − | 1.08897i | ||||
\(356\) | − | 305.949i | − | 0.859406i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 146.050i | 0.407961i | ||||||||
\(359\) | 159.113i | 0.443211i | 0.975136 | + | 0.221605i | \(0.0711297\pi\) | ||||
−0.975136 | + | 0.221605i | \(0.928870\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −119.182 | −0.330143 | ||||||||
\(362\) | −304.127 | −0.840129 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −97.2622 | −0.267204 | ||||||||
\(365\) | −22.9131 | + | 101.952i | −0.0627757 | + | 0.279320i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 563.292i | − | 1.53486i | −0.641136 | − | 0.767428i | \(-0.721536\pi\) | ||
0.641136 | − | 0.767428i | \(-0.278464\pi\) | |||||||
\(368\) | −59.8111 | −0.162530 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 51.7071 | − | 230.070i | 0.139749 | − | 0.621812i | ||||
\(371\) | − | 111.708i | − | 0.301101i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 469.312i | 1.25821i | 0.777320 | + | 0.629105i | \(0.216578\pi\) | ||||
−0.777320 | + | 0.629105i | \(0.783422\pi\) | |||||||
\(374\) | 519.830i | 1.38992i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 102.070 | 0.271464 | ||||||||
\(377\) | −76.1316 | −0.201941 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −339.101 | −0.894726 | −0.447363 | − | 0.894353i | \(-0.647637\pi\) | ||||
−0.447363 | + | 0.894353i | \(0.647637\pi\) | |||||||
\(380\) | 151.721 | + | 34.0984i | 0.399265 | + | 0.0897327i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 385.646i | − | 1.00954i | ||||||
\(383\) | −5.62150 | −0.0146776 | −0.00733878 | − | 0.999973i | \(-0.502336\pi\) | ||||
−0.00733878 | + | 0.999973i | \(0.502336\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −136.969 | − | 30.7832i | −0.355765 | − | 0.0799563i | ||||
\(386\) | − | 454.841i | − | 1.17834i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 77.5755i | − | 0.199937i | ||||||
\(389\) | − | 635.621i | − | 1.63399i | −0.576647 | − | 0.816993i | \(-0.695639\pi\) | ||
0.576647 | − | 0.816993i | \(-0.304361\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −411.287 | −1.05189 | ||||||||
\(392\) | −126.107 | −0.321703 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 53.2122 | 0.135056 | ||||||||
\(395\) | 7.24280 | + | 1.62778i | 0.0183362 | + | 0.00412097i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 626.656i | − | 1.57848i | −0.614086 | − | 0.789239i | \(-0.710475\pi\) | ||
0.614086 | − | 0.789239i | \(-0.289525\pi\) | |||||||
\(398\) | 450.455 | 1.13180 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 90.3837 | + | 42.7878i | 0.225959 | + | 0.106969i | ||||
\(401\) | − | 459.826i | − | 1.14670i | −0.819311 | − | 0.573350i | \(-0.805644\pi\) | ||
0.819311 | − | 0.573350i | \(-0.194356\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 227.839i | − | 0.565357i | ||||||
\(404\) | − | 163.920i | − | 0.405743i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.77296 | 0.0240713 | ||||||||
\(407\) | −445.655 | −1.09498 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −59.9592 | −0.146599 | −0.0732997 | − | 0.997310i | \(-0.523353\pi\) | ||||
−0.0732997 | + | 0.997310i | \(0.523353\pi\) | |||||||
\(410\) | 16.8277 | − | 74.8747i | 0.0410432 | − | 0.182621i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 231.555i | − | 0.562027i | ||||||
\(413\) | 212.732 | 0.515090 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 48.4495 | + | 10.8888i | 0.116746 | + | 0.0262380i | ||||
\(416\) | − | 130.936i | − | 0.314750i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 293.889i | − | 0.703083i | ||||||
\(419\) | 221.438i | 0.528491i | 0.964455 | + | 0.264245i | \(0.0851229\pi\) | ||||
−0.964455 | + | 0.264245i | \(0.914877\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −133.171 | −0.316322 | −0.158161 | − | 0.987413i | \(-0.550556\pi\) | ||||
−0.158161 | + | 0.987413i | \(0.550556\pi\) | |||||||
\(422\) | −8.13534 | −0.0192780 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 150.384 | 0.354678 | ||||||||
\(425\) | 621.517 | + | 294.227i | 1.46239 | + | 0.692299i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.212246i | 0.000497064i | ||||||||
\(428\) | −239.023 | −0.558465 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 66.9694 | − | 297.980i | 0.155743 | − | 0.692976i | ||||
\(431\) | − | 458.090i | − | 1.06285i | −0.847104 | − | 0.531427i | \(-0.821656\pi\) | ||
0.847104 | − | 0.531427i | \(-0.178344\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 240.318i | 0.555007i | 0.960725 | + | 0.277503i | \(0.0895069\pi\) | ||||
−0.960725 | + | 0.277503i | \(0.910493\pi\) | |||||||
\(434\) | 29.2475i | 0.0673906i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 125.818 | 0.288574 | ||||||||
\(437\) | 232.523 | 0.532090 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 440.908 | 1.00435 | 0.502173 | − | 0.864767i | \(-0.332534\pi\) | ||||
0.502173 | + | 0.864767i | \(0.332534\pi\) | |||||||
\(440\) | 41.4408 | − | 184.390i | 0.0941836 | − | 0.419069i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 900.372i | − | 2.03704i | ||||||
\(443\) | −607.808 | −1.37203 | −0.686014 | − | 0.727588i | \(-0.740641\pi\) | ||||
−0.686014 | + | 0.727588i | \(0.740641\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −167.717 | + | 746.257i | −0.376893 | + | 1.67698i | ||||
\(446\) | 33.7983i | 0.0757809i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16.8082i | 0.0375182i | ||||||||
\(449\) | − | 56.1962i | − | 0.125159i | −0.998040 | − | 0.0625793i | \(-0.980067\pi\) | ||
0.998040 | − | 0.0625793i | \(-0.0199326\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −145.035 | −0.321586 | ||||||||
\(452\) | −160.049 | −0.354090 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −301.131 | −0.663283 | ||||||||
\(455\) | 237.238 | + | 53.3180i | 0.521402 | + | 0.117182i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 213.975i | 0.468217i | 0.972211 | + | 0.234108i | \(0.0752170\pi\) | ||||
−0.972211 | + | 0.234108i | \(0.924783\pi\) | |||||||
\(458\) | 477.261 | 1.04205 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 145.889 | + | 32.7878i | 0.317150 | + | 0.0712777i | ||||
\(461\) | − | 217.749i | − | 0.472340i | −0.971712 | − | 0.236170i | \(-0.924108\pi\) | ||
0.971712 | − | 0.236170i | \(-0.0758923\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 141.637i | − | 0.305911i | −0.988233 | − | 0.152955i | \(-0.951121\pi\) | ||
0.988233 | − | 0.152955i | \(-0.0488791\pi\) | |||||||
\(464\) | 13.1565i | 0.0283546i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −281.423 | −0.603913 | ||||||||
\(467\) | 254.279 | 0.544495 | 0.272248 | − | 0.962227i | \(-0.412233\pi\) | ||||
0.272248 | + | 0.962227i | \(0.412233\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 117.636 | 0.250822 | ||||||||
\(470\) | −248.966 | − | 55.9538i | −0.529714 | − | 0.119051i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 286.384i | 0.606745i | ||||||||
\(473\) | −577.198 | −1.22029 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −351.378 | − | 166.343i | −0.739743 | − | 0.350195i | ||||
\(476\) | 115.580i | 0.242816i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 107.637i | − | 0.225181i | ||||||
\(479\) | − | 853.370i | − | 1.78157i | −0.454430 | − | 0.890783i | \(-0.650157\pi\) | ||
0.454430 | − | 0.890783i | \(-0.349843\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 771.898 | 1.60478 | ||||||||
\(482\) | −462.104 | −0.958723 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −115.171 | −0.237957 | ||||||||
\(485\) | −42.5260 | + | 189.219i | −0.0876824 | + | 0.390142i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 504.261i | − | 1.03544i | −0.855549 | − | 0.517722i | \(-0.826780\pi\) | ||
0.855549 | − | 0.517722i | \(-0.173220\pi\) | |||||||
\(488\) | −0.285729 | −0.000585511 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 307.596 | + | 69.1306i | 0.627747 | + | 0.141083i | ||||
\(491\) | − | 439.748i | − | 0.895618i | −0.894129 | − | 0.447809i | \(-0.852205\pi\) | ||
0.894129 | − | 0.447809i | \(-0.147795\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 90.4699i | 0.183509i | ||||||||
\(494\) | 509.030i | 1.03043i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −39.3735 | −0.0793820 | ||||||||
\(497\) | −166.497 | −0.335004 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −807.614 | −1.61847 | −0.809233 | − | 0.587488i | \(-0.800117\pi\) | ||||
−0.809233 | + | 0.587488i | \(0.800117\pi\) | |||||||
\(500\) | −197.004 | − | 153.913i | −0.394009 | − | 0.307827i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 409.646i | − | 0.816028i | ||||||
\(503\) | 526.962 | 1.04764 | 0.523819 | − | 0.851829i | \(-0.324507\pi\) | ||||
0.523819 | + | 0.851829i | \(0.324507\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −89.8592 | + | 399.828i | −0.177939 | + | 0.791738i | ||||
\(506\) | − | 282.592i | − | 0.558483i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 245.373i | − | 0.483019i | ||||||
\(509\) | − | 120.439i | − | 0.236620i | −0.992977 | − | 0.118310i | \(-0.962252\pi\) | ||
0.992977 | − | 0.118310i | \(-0.0377476\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 43.9092 | 0.0859280 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −651.292 | −1.26710 | ||||||||
\(515\) | −126.936 | + | 564.799i | −0.246477 | + | 1.09670i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 482.257i | 0.932798i | ||||||||
\(518\) | −99.0880 | −0.191290 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −71.7775 | + | 319.373i | −0.138034 | + | 0.614180i | ||||
\(521\) | 34.7871i | 0.0667699i | 0.999443 | + | 0.0333850i | \(0.0106287\pi\) | ||||
−0.999443 | + | 0.0333850i | \(0.989371\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 210.535i | − | 0.402552i | −0.979535 | − | 0.201276i | \(-0.935491\pi\) | ||
0.979535 | − | 0.201276i | \(-0.0645088\pi\) | |||||||
\(524\) | − | 44.6834i | − | 0.0852736i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −298.474 | −0.567442 | ||||||||
\(527\) | −270.749 | −0.513755 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −305.414 | −0.577343 | ||||||||
\(530\) | −366.809 | − | 82.4385i | −0.692093 | − | 0.155544i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 65.3439i | − | 0.122827i | ||||||
\(533\) | 251.208 | 0.471310 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 583.015 | + | 131.030i | 1.08975 | + | 0.244915i | ||||
\(536\) | 158.363i | 0.295453i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 264.742i | − | 0.492086i | ||||||
\(539\) | − | 595.825i | − | 1.10543i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −123.070 | −0.227487 | −0.113743 | − | 0.993510i | \(-0.536284\pi\) | ||||
−0.113743 | + | 0.993510i | \(0.536284\pi\) | |||||||
\(542\) | 282.721 | 0.521625 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −155.596 | −0.286022 | ||||||||
\(545\) | −306.891 | − | 68.9721i | −0.563102 | − | 0.126554i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 219.627i | − | 0.401511i | −0.979641 | − | 0.200756i | \(-0.935660\pi\) | ||
0.979641 | − | 0.200756i | \(-0.0643397\pi\) | |||||||
\(548\) | 1.71437 | 0.00312842 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −202.161 | + | 427.040i | −0.367566 | + | 0.776436i | ||||
\(551\) | − | 51.1476i | − | 0.0928269i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 3.11937i | − | 0.00564081i | ||||||
\(554\) | − | 151.586i | − | 0.273620i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 470.565 | 0.846340 | ||||||||
\(557\) | 351.396 | 0.630873 | 0.315436 | − | 0.948947i | \(-0.397849\pi\) | ||||
0.315436 | + | 0.948947i | \(0.397849\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 999.737 | 1.78844 | ||||||||
\(560\) | 9.21404 | − | 40.9978i | 0.0164536 | − | 0.0732103i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 467.803i | − | 0.832389i | ||||||
\(563\) | 338.321 | 0.600926 | 0.300463 | − | 0.953793i | \(-0.402859\pi\) | ||||
0.300463 | + | 0.953793i | \(0.402859\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 390.384 | + | 87.7367i | 0.690945 | + | 0.155286i | ||||
\(566\) | − | 447.705i | − | 0.790999i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 224.141i | − | 0.394614i | ||||||
\(569\) | 75.6741i | 0.132995i | 0.997787 | + | 0.0664975i | \(0.0211824\pi\) | ||||
−0.997787 | + | 0.0664975i | \(0.978818\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 503.596 | 0.881954 | 0.440977 | − | 0.897518i | \(-0.354632\pi\) | ||||
0.440977 | + | 0.897518i | \(0.354632\pi\) | |||||||
\(572\) | 618.639 | 1.08154 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −32.2474 | −0.0561802 | ||||||||
\(575\) | −337.872 | − | 159.949i | −0.587603 | − | 0.278172i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 665.090i | 1.15267i | 0.817214 | + | 0.576334i | \(0.195517\pi\) | ||||
−0.817214 | + | 0.576334i | \(0.804483\pi\) | |||||||
\(578\) | −661.237 | −1.14401 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.21225 | − | 32.0908i | 0.0124349 | − | 0.0553290i | ||||
\(581\) | − | 20.8665i | − | 0.0359148i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 710.524i | 1.21874i | ||||||||
\(584\) | 59.1112i | 0.101218i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 120.211 | 0.205139 | ||||||||
\(587\) | 460.672 | 0.784791 | 0.392396 | − | 0.919797i | \(-0.371646\pi\) | ||||
0.392396 | + | 0.919797i | \(0.371646\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 153.069 | 0.259880 | ||||||||
\(590\) | 156.992 | − | 698.535i | 0.266088 | − | 1.18396i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 133.394i | − | 0.225327i | ||||||
\(593\) | −585.162 | −0.986782 | −0.493391 | − | 0.869808i | \(-0.664243\pi\) | ||||
−0.493391 | + | 0.869808i | \(0.664243\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 63.3597 | − | 281.918i | 0.106487 | − | 0.473812i | ||||
\(596\) | − | 262.408i | − | 0.440282i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 489.464i | 0.818502i | ||||||||
\(599\) | − | 2.79956i | − | 0.00467373i | −0.999997 | − | 0.00233686i | \(-0.999256\pi\) | ||
0.999997 | − | 0.00233686i | \(-0.000743847\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −498.869 | −0.830066 | −0.415033 | − | 0.909806i | \(-0.636230\pi\) | ||||
−0.415033 | + | 0.909806i | \(0.636230\pi\) | |||||||
\(602\) | −128.336 | −0.213182 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −176.899 | −0.292879 | ||||||||
\(605\) | 280.921 | + | 63.1356i | 0.464333 | + | 0.104356i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.3847i | 0.0500572i | 0.999687 | + | 0.0250286i | \(0.00796768\pi\) | ||||
−0.999687 | + | 0.0250286i | \(0.992032\pi\) | |||||||
\(608\) | 87.9670 | 0.144683 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.696938 | + | 0.156633i | 0.00114252 | + | 0.000256776i | ||||
\(611\) | − | 835.293i | − | 1.36709i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 448.449i | 0.731565i | 0.930700 | + | 0.365783i | \(0.119199\pi\) | ||||
−0.930700 | + | 0.365783i | \(0.880801\pi\) | |||||||
\(614\) | 48.9260i | 0.0796841i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −79.4143 | −0.128919 | ||||||||
\(617\) | 170.733 | 0.276715 | 0.138357 | − | 0.990382i | \(-0.455818\pi\) | ||||
0.138357 | + | 0.990382i | \(0.455818\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 238.247 | 0.384891 | 0.192445 | − | 0.981308i | \(-0.438358\pi\) | ||||
0.192445 | + | 0.981308i | \(0.438358\pi\) | |||||||
\(620\) | 96.0381 | + | 21.5841i | 0.154900 | + | 0.0348130i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 59.8888i | 0.0962842i | ||||||||
\(623\) | 321.402 | 0.515894 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 396.151 | + | 483.414i | 0.633842 | + | 0.773463i | ||||
\(626\) | − | 518.909i | − | 0.828928i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 325.394i | − | 0.518143i | ||||||
\(629\) | − | 917.274i | − | 1.45831i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1148.15 | 1.81957 | 0.909786 | − | 0.415078i | \(-0.136246\pi\) | ||||
0.909786 | + | 0.415078i | \(0.136246\pi\) | |||||||
\(632\) | 4.19934 | 0.00664453 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −123.221 | −0.194356 | ||||||||
\(635\) | −134.511 | + | 598.505i | −0.211828 | + | 0.942527i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1032.00i | 1.62009i | ||||||||
\(638\) | −62.1612 | −0.0974313 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 55.1918 | + | 12.4041i | 0.0862372 | + | 0.0193814i | ||||
\(641\) | 388.533i | 0.606136i | 0.952969 | + | 0.303068i | \(0.0980109\pi\) | ||||
−0.952969 | + | 0.303068i | \(0.901989\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 928.980i | − | 1.44476i | −0.691497 | − | 0.722379i | \(-0.743049\pi\) | ||
0.691497 | − | 0.722379i | \(-0.256951\pi\) | |||||||
\(644\) | − | 62.8322i | − | 0.0975655i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 604.899 | 0.936376 | ||||||||
\(647\) | −485.464 | −0.750330 | −0.375165 | − | 0.926958i | \(-0.622414\pi\) | ||||
−0.375165 | + | 0.926958i | \(0.622414\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1353.09 | −2.08488 | ||||||||
\(650\) | 350.154 | − | 739.655i | 0.538698 | − | 1.13793i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 550.384i | − | 0.844147i | ||||||
\(653\) | −33.9620 | −0.0520093 | −0.0260046 | − | 0.999662i | \(-0.508278\pi\) | ||||
−0.0260046 | + | 0.999662i | \(0.508278\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.4949 | + | 108.990i | −0.0373968 | + | 0.166397i | ||||
\(656\) | − | 43.4120i | − | 0.0661769i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 107.226i | 0.162957i | ||||||||
\(659\) | 67.9818i | 0.103159i | 0.998669 | + | 0.0515795i | \(0.0164256\pi\) | ||||
−0.998669 | + | 0.0515795i | \(0.983574\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −883.959 | −1.33731 | −0.668653 | − | 0.743575i | \(-0.733129\pi\) | ||||
−0.668653 | + | 0.743575i | \(0.733129\pi\) | |||||||
\(662\) | 180.076 | 0.272017 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 28.0908 | 0.0423054 | ||||||||
\(665\) | −35.8207 | + | 159.384i | −0.0538658 | + | 0.239675i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 49.1816i | − | 0.0737356i | ||||||
\(668\) | −273.979 | −0.410148 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 86.8128 | − | 386.272i | 0.129571 | − | 0.576526i | ||||
\(671\) | − | 1.35000i | − | 0.00201192i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 217.448i | 0.323103i | 0.986864 | + | 0.161552i | \(0.0516498\pi\) | ||||
−0.986864 | + | 0.161552i | \(0.948350\pi\) | |||||||
\(674\) | 606.125i | 0.899295i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −733.514 | −1.08508 | ||||||||
\(677\) | −926.345 | −1.36831 | −0.684155 | − | 0.729337i | \(-0.739829\pi\) | ||||
−0.684155 | + | 0.729337i | \(0.739829\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 81.4939 | 0.120020 | ||||||||
\(680\) | 379.523 | + | 85.2958i | 0.558122 | + | 0.125435i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 186.030i | − | 0.272771i | ||||||
\(683\) | −586.563 | −0.858804 | −0.429402 | − | 0.903113i | \(-0.641276\pi\) | ||||
−0.429402 | + | 0.903113i | \(0.641276\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.18163 | − | 0.939800i | −0.00610457 | − | 0.00137197i | ||||
\(686\) | − | 278.070i | − | 0.405351i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 172.767i | − | 0.251115i | ||||||
\(689\) | − | 1230.66i | − | 1.78616i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −830.161 | −1.20139 | −0.600696 | − | 0.799478i | \(-0.705110\pi\) | ||||
−0.600696 | + | 0.799478i | \(0.705110\pi\) | |||||||
\(692\) | −185.533 | −0.268112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 495.687 | 0.714246 | ||||||||
\(695\) | −1147.78 | − | 257.958i | −1.65149 | − | 0.371163i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 298.520i | − | 0.428293i | ||||||
\(698\) | −853.012 | −1.22208 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −44.9490 | + | 94.9490i | −0.0642128 | + | 0.135641i | ||||
\(701\) | 915.199i | 1.30556i | 0.757547 | + | 0.652781i | \(0.226398\pi\) | ||||
−0.757547 | + | 0.652781i | \(0.773602\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 518.586i | 0.737675i | ||||||||
\(704\) | − | 106.909i | − | 0.151859i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.0510 | −0.0156530 | ||||||||
\(707\) | 172.200 | 0.243564 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.8480 | −0.0265839 | −0.0132919 | − | 0.999912i | \(-0.504231\pi\) | ||||
−0.0132919 | + | 0.999912i | \(0.504231\pi\) | |||||||
\(710\) | −122.871 | + | 546.715i | −0.173058 | + | 0.770021i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 432.677i | 0.607692i | ||||||||
\(713\) | 147.186 | 0.206432 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1508.96 | − | 339.131i | −2.11043 | − | 0.474309i | ||||
\(716\) | − | 206.546i | − | 0.288472i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 225.019i | − | 0.313397i | ||||||
\(719\) | 65.5964i | 0.0912328i | 0.998959 | + | 0.0456164i | \(0.0145252\pi\) | ||||
−0.998959 | + | 0.0456164i | \(0.985475\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 243.251 | 0.337380 | ||||||||
\(722\) | 168.548 | 0.233446 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 430.100 | 0.594061 | ||||||||
\(725\) | −35.1836 | + | 74.3209i | −0.0485291 | + | 0.102512i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1249.52i | − | 1.71873i | −0.511364 | − | 0.859364i | \(-0.670860\pi\) | ||
0.511364 | − | 0.859364i | \(-0.329140\pi\) | |||||||
\(728\) | 137.550 | 0.188942 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 32.4041 | − | 144.182i | 0.0443892 | − | 0.197509i | ||||
\(731\) | − | 1188.02i | − | 1.62520i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 195.991i | − | 0.267382i | −0.991023 | − | 0.133691i | \(-0.957317\pi\) | ||
0.991023 | − | 0.133691i | \(-0.0426829\pi\) | |||||||
\(734\) | 796.615i | 1.08531i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 84.5857 | 0.114926 | ||||||||
\(737\) | −748.225 | −1.01523 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 376.536 | 0.509521 | 0.254760 | − | 0.967004i | \(-0.418003\pi\) | ||||
0.254760 | + | 0.967004i | \(0.418003\pi\) | |||||||
\(740\) | −73.1249 | + | 325.369i | −0.0988175 | + | 0.439687i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 157.980i | 0.212910i | ||||||||
\(743\) | 1293.12 | 1.74041 | 0.870204 | − | 0.492692i | \(-0.163987\pi\) | ||||
0.870204 | + | 0.492692i | \(0.163987\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −143.849 | + | 640.055i | −0.193086 | + | 0.859134i | ||||
\(746\) | − | 663.708i | − | 0.889689i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 735.151i | − | 0.982822i | ||||||
\(749\) | − | 251.096i | − | 0.335242i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.50866 | 0.0113298 | 0.00566489 | − | 0.999984i | \(-0.498197\pi\) | ||||
0.00566489 | + | 0.999984i | \(0.498197\pi\) | |||||||
\(752\) | −144.349 | −0.191954 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 107.666 | 0.142794 | ||||||||
\(755\) | 431.484 | + | 96.9739i | 0.571503 | + | 0.128442i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 759.469i | 1.00326i | 0.865082 | + | 0.501631i | \(0.167266\pi\) | ||||
−0.865082 | + | 0.501631i | \(0.832734\pi\) | |||||||
\(758\) | 479.561 | 0.632667 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −214.565 | − | 48.2225i | −0.282323 | − | 0.0634506i | ||||
\(761\) | − | 452.801i | − | 0.595007i | −0.954721 | − | 0.297504i | \(-0.903846\pi\) | ||
0.954721 | − | 0.297504i | \(-0.0961540\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 132.173i | 0.173229i | ||||||||
\(764\) | 545.386i | 0.713856i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.95001 | 0.0103786 | ||||||||
\(767\) | 2343.62 | 3.05557 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1196.72 | 1.55620 | 0.778099 | − | 0.628142i | \(-0.216184\pi\) | ||||
0.778099 | + | 0.628142i | \(0.216184\pi\) | |||||||
\(770\) | 193.704 | + | 43.5340i | 0.251564 | + | 0.0565376i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 643.242i | 0.833215i | ||||||||
\(773\) | −287.556 | −0.372000 | −0.186000 | − | 0.982550i | \(-0.559552\pi\) | ||||
−0.186000 | + | 0.982550i | \(0.559552\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −222.420 | − | 105.294i | −0.286993 | − | 0.135863i | ||||
\(776\) | 109.708i | 0.141377i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 898.904i | 1.15540i | ||||||||
\(779\) | 168.770i | 0.216649i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1059.01 | 1.35596 | ||||||||
\(782\) | 581.648 | 0.743795 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 178.343 | 0.227478 | ||||||||
\(785\) | −178.377 | + | 793.687i | −0.227232 | + | 1.01107i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 341.757i | 0.434253i | 0.976143 | + | 0.217127i | \(0.0696684\pi\) | ||||
−0.976143 | + | 0.217127i | \(0.930332\pi\) | |||||||
\(788\) | −75.2535 | −0.0954993 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −10.2429 | − | 2.30203i | −0.0129656 | − | 0.00291396i | ||||
\(791\) | − | 168.133i | − | 0.212557i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.33826i | 0.00294863i | ||||||||
\(794\) | 886.226i | 1.11615i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −637.040 | −0.800301 | ||||||||
\(797\) | −423.701 | −0.531619 | −0.265810 | − | 0.964026i | \(-0.585639\pi\) | ||||
−0.265810 | + | 0.964026i | \(0.585639\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −992.609 | −1.24231 | ||||||||
\(800\) | −127.822 | − | 60.5110i | −0.159777 | − | 0.0756388i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 650.293i | 0.810839i | ||||||||
\(803\) | −279.286 | −0.347803 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −34.4439 | + | 153.258i | −0.0427874 | + | 0.190382i | ||||
\(806\) | 322.213i | 0.399768i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 231.818i | 0.286904i | ||||||||
\(809\) | 46.4331i | 0.0573957i | 0.999588 | + | 0.0286978i | \(0.00913606\pi\) | ||||
−0.999588 | + | 0.0286978i | \(0.990864\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −511.160 | −0.630284 | −0.315142 | − | 0.949045i | \(-0.602052\pi\) | ||||
−0.315142 | + | 0.949045i | \(0.602052\pi\) | |||||||
\(812\) | −13.8211 | −0.0170210 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 630.252 | 0.774265 | ||||||||
\(815\) | −301.714 | + | 1342.47i | −0.370201 | + | 1.64721i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 671.655i | 0.822099i | ||||||||
\(818\) | 84.7951 | 0.103661 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −23.7980 | + | 105.889i | −0.0290219 | + | 0.129133i | ||||
\(821\) | − | 154.461i | − | 0.188137i | −0.995566 | − | 0.0940686i | \(-0.970013\pi\) | ||
0.995566 | − | 0.0940686i | \(-0.0299873\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1038.95i | 1.26239i | 0.775624 | + | 0.631196i | \(0.217435\pi\) | ||||
−0.775624 | + | 0.631196i | \(0.782565\pi\) | |||||||
\(824\) | 327.468i | 0.397413i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −300.849 | −0.364224 | ||||||||
\(827\) | 792.713 | 0.958540 | 0.479270 | − | 0.877668i | \(-0.340901\pi\) | ||||
0.479270 | + | 0.877668i | \(0.340901\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1143.31 | 1.37914 | 0.689572 | − | 0.724217i | \(-0.257798\pi\) | ||||
0.689572 | + | 0.724217i | \(0.257798\pi\) | |||||||
\(830\) | −68.5179 | − | 15.3991i | −0.0825517 | − | 0.0185531i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 185.171i | 0.222562i | ||||||||
\(833\) | 1226.36 | 1.47222 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 668.277 | + | 150.192i | 0.800332 | + | 0.179870i | ||||
\(836\) | 415.621i | 0.497155i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 313.160i | − | 0.373700i | ||||||
\(839\) | 1121.25i | 1.33641i | 0.743976 | + | 0.668206i | \(0.232938\pi\) | ||||
−0.743976 | + | 0.668206i | \(0.767062\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 830.182 | 0.987136 | ||||||||
\(842\) | 188.333 | 0.223673 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.5051 | 0.0136316 | ||||||||
\(845\) | 1789.16 | + | 402.104i | 2.11735 | + | 0.475863i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 120.989i | − | 0.142844i | ||||||
\(848\) | −212.675 | −0.250796 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −878.958 | − | 416.100i | −1.03407 | − | 0.489529i | ||||
\(851\) | 498.652i | 0.585961i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1571.03i | − | 1.84177i | −0.389830 | − | 0.920887i | \(-0.627466\pi\) | ||
0.389830 | − | 0.920887i | \(-0.372534\pi\) | |||||||
\(854\) | − | 0.300161i | − | 0.000351477i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 338.030 | 0.394894 | ||||||||
\(857\) | −1566.41 | −1.82778 | −0.913892 | − | 0.405957i | \(-0.866938\pi\) | ||||
−0.913892 | + | 0.405957i | \(0.866938\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −54.9240 | −0.0639394 | −0.0319697 | − | 0.999489i | \(-0.510178\pi\) | ||||
−0.0319697 | + | 0.999489i | \(0.510178\pi\) | |||||||
\(860\) | −94.7090 | + | 421.407i | −0.110127 | + | 0.490008i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 647.837i | 0.751551i | ||||||||
\(863\) | −397.076 | −0.460111 | −0.230056 | − | 0.973177i | \(-0.573891\pi\) | ||||
−0.230056 | + | 0.973177i | \(0.573891\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 452.545 | + | 101.707i | 0.523173 | + | 0.117581i | ||||
\(866\) | − | 339.861i | − | 0.392449i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 41.3622i | − | 0.0476523i | ||||||
\(869\) | 19.8408i | 0.0228318i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1295.96 | 1.48790 | ||||||||
\(872\) | −177.934 | −0.204053 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −328.838 | −0.376245 | ||||||||
\(875\) | 161.688 | − | 206.955i | 0.184786 | − | 0.236520i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 94.0250i | − | 0.107212i | −0.998562 | − | 0.0536060i | \(-0.982928\pi\) | ||
0.998562 | − | 0.0536060i | \(-0.0170715\pi\) | |||||||
\(878\) | −623.538 | −0.710180 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −58.6061 | + | 260.767i | −0.0665979 | + | 0.296327i | ||||
\(881\) | − | 283.024i | − | 0.321253i | −0.987015 | − | 0.160627i | \(-0.948648\pi\) | ||
0.987015 | − | 0.160627i | \(-0.0513515\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1194.90i | − | 1.35323i | −0.736339 | − | 0.676613i | \(-0.763447\pi\) | ||
0.736339 | − | 0.676613i | \(-0.236553\pi\) | |||||||
\(884\) | 1273.32i | 1.44041i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 859.571 | 0.970170 | ||||||||
\(887\) | −714.584 | −0.805619 | −0.402810 | − | 0.915284i | \(-0.631966\pi\) | ||||
−0.402810 | + | 0.915284i | \(0.631966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 257.767 | 0.289952 | ||||||||
\(890\) | 237.188 | − | 1055.37i | 0.266504 | − | 1.18580i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 47.7980i | − | 0.0535852i | ||||||
\(893\) | 561.177 | 0.628417 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −113.226 | + | 503.798i | −0.126510 | + | 0.562903i | ||||
\(896\) | − | 23.7703i | − | 0.0265294i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 79.4735i | 0.0885005i | ||||||||
\(899\) | − | 32.3761i | − | 0.0360135i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1462.44 | −1.62313 | ||||||||
\(902\) | 205.111 | 0.227396 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 226.343 | 0.250379 | ||||||||
\(905\) | −1049.08 | − | 235.776i | −1.15921 | − | 0.260526i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 645.000i | − | 0.711136i | −0.934650 | − | 0.355568i | \(-0.884288\pi\) | ||
0.934650 | − | 0.355568i | \(-0.115712\pi\) | |||||||
\(908\) | 425.863 | 0.469012 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −335.505 | − | 75.4031i | −0.368687 | − | 0.0828605i | ||||
\(911\) | 1002.58i | 1.10052i | 0.834992 | + | 0.550261i | \(0.185472\pi\) | ||||
−0.834992 | + | 0.550261i | \(0.814528\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 132.722i | 0.145369i | ||||||||
\(914\) | − | 302.606i | − | 0.331079i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −674.949 | −0.736844 | ||||||||
\(917\) | 46.9403 | 0.0511890 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1583.98 | −1.72359 | −0.861794 | − | 0.507258i | \(-0.830659\pi\) | ||||
−0.861794 | + | 0.507258i | \(0.830659\pi\) | |||||||
\(920\) | −206.318 | − | 46.3689i | −0.224259 | − | 0.0504010i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 307.943i | 0.333995i | ||||||||
\(923\) | −1834.26 | −1.98728 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 356.727 | − | 753.539i | 0.385650 | − | 0.814637i | ||||
\(926\) | 200.305i | 0.216312i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 18.6061i | − | 0.0200497i | ||||||
\(929\) | 636.903i | 0.685579i | 0.939412 | + | 0.342790i | \(0.111372\pi\) | ||||
−0.939412 | + | 0.342790i | \(0.888628\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −693.331 | −0.744716 | ||||||||
\(932\) | 397.993 | 0.427031 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −359.605 | −0.385016 | ||||||||
\(935\) | −403.001 | + | 1793.15i | −0.431017 | + | 1.91781i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 398.688i | − | 0.425494i | −0.977107 | − | 0.212747i | \(-0.931759\pi\) | ||
0.977107 | − | 0.212747i | \(-0.0682410\pi\) | |||||||
\(938\) | −166.362 | −0.177358 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 352.091 | + | 79.1306i | 0.374565 | + | 0.0841815i | ||||
\(941\) | 523.582i | 0.556410i | 0.960522 | + | 0.278205i | \(0.0897395\pi\) | ||||
−0.960522 | + | 0.278205i | \(0.910261\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 162.283i | 0.172092i | ||||||||
\(944\) | − | 405.008i | − | 0.429034i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 816.282 | 0.862877 | ||||||||
\(947\) | −317.944 | −0.335739 | −0.167869 | − | 0.985809i | \(-0.553689\pi\) | ||||
−0.167869 | + | 0.985809i | \(0.553689\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 483.737 | 0.509733 | ||||||||
\(950\) | 496.924 | + | 235.244i | 0.523077 | + | 0.247626i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 163.455i | − | 0.171697i | ||||||
\(953\) | 848.148 | 0.889977 | 0.444988 | − | 0.895536i | \(-0.353208\pi\) | ||||
0.444988 | + | 0.895536i | \(0.353208\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 298.974 | − | 1330.28i | 0.313062 | − | 1.39297i | ||||
\(956\) | 152.221i | 0.159227i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1206.85i | 1.25976i | ||||||||
\(959\) | 1.80097i | 0.00187797i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −864.108 | −0.899176 | ||||||||
\(962\) | −1091.63 | −1.13475 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 653.514 | 0.677919 | ||||||||
\(965\) | 352.618 | − | 1568.97i | 0.365407 | − | 1.62587i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 998.725i | 1.03281i | 0.856345 | + | 0.516404i | \(0.172730\pi\) | ||||
−0.856345 | + | 0.516404i | \(0.827270\pi\) | |||||||
\(968\) | 162.877 | 0.168261 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 60.1408 | − | 267.596i | 0.0620008 | − | 0.275872i | ||||
\(971\) | 1392.89i | 1.43449i | 0.696820 | + | 0.717246i | \(0.254598\pi\) | ||||
−0.696820 | + | 0.717246i | \(0.745402\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 494.334i | 0.508051i | ||||||||
\(974\) | 713.133i | 0.732169i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.404082 | 0.000414019 | ||||||||
\(977\) | −618.875 | −0.633444 | −0.316722 | − | 0.948518i | \(-0.602582\pi\) | ||||
−0.316722 | + | 0.948518i | \(0.602582\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2044.29 | −2.08814 | ||||||||
\(980\) | −435.006 | − | 97.7654i | −0.443884 | − | 0.0997607i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 621.898i | 0.633297i | ||||||||
\(983\) | 192.813 | 0.196148 | 0.0980739 | − | 0.995179i | \(-0.468732\pi\) | ||||
0.0980739 | + | 0.995179i | \(0.468732\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 183.555 | + | 41.2531i | 0.186350 | + | 0.0418813i | ||||
\(986\) | − | 127.944i | − | 0.129760i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 719.878i | − | 0.728621i | ||||||
\(989\) | 645.838i | 0.653021i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 410.243 | 0.413969 | 0.206984 | − | 0.978344i | \(-0.433635\pi\) | ||||
0.206984 | + | 0.978344i | \(0.433635\pi\) | |||||||
\(992\) | 55.6825 | 0.0561315 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 235.462 | 0.236884 | ||||||||
\(995\) | 1553.84 | + | 349.218i | 1.56165 | + | 0.350973i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 453.648i | 0.455013i | 0.973777 | + | 0.227507i | \(0.0730573\pi\) | ||||
−0.973777 | + | 0.227507i | \(0.926943\pi\) | |||||||
\(998\) | 1142.14 | 1.14443 | ||||||||
\(999\) | 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 | 810.3.b.a.809.1 | 8 | ||
3.2 | odd | 2 | inner | 810.3.b.a.809.8 | 8 | ||
5.4 | even | 2 | inner | 810.3.b.a.809.7 | 8 | ||
9.2 | odd | 6 | 270.3.j.a.179.1 | 8 | |||
9.4 | even | 3 | 270.3.j.a.89.3 | 8 | |||
9.5 | odd | 6 | 90.3.j.a.29.1 | ✓ | 8 | ||
9.7 | even | 3 | 90.3.j.a.59.4 | yes | 8 | ||
15.14 | odd | 2 | inner | 810.3.b.a.809.2 | 8 | ||
45.2 | even | 12 | 1350.3.i.c.1151.2 | 4 | |||
45.4 | even | 6 | 270.3.j.a.89.1 | 8 | |||
45.7 | odd | 12 | 450.3.i.c.401.1 | 4 | |||
45.13 | odd | 12 | 1350.3.i.a.251.1 | 4 | |||
45.14 | odd | 6 | 90.3.j.a.29.4 | yes | 8 | ||
45.22 | odd | 12 | 1350.3.i.c.251.2 | 4 | |||
45.23 | even | 12 | 450.3.i.a.101.2 | 4 | |||
45.29 | odd | 6 | 270.3.j.a.179.3 | 8 | |||
45.32 | even | 12 | 450.3.i.c.101.1 | 4 | |||
45.34 | even | 6 | 90.3.j.a.59.1 | yes | 8 | ||
45.38 | even | 12 | 1350.3.i.a.1151.1 | 4 | |||
45.43 | odd | 12 | 450.3.i.a.401.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.3.j.a.29.1 | ✓ | 8 | 9.5 | odd | 6 | ||
90.3.j.a.29.4 | yes | 8 | 45.14 | odd | 6 | ||
90.3.j.a.59.1 | yes | 8 | 45.34 | even | 6 | ||
90.3.j.a.59.4 | yes | 8 | 9.7 | even | 3 | ||
270.3.j.a.89.1 | 8 | 45.4 | even | 6 | |||
270.3.j.a.89.3 | 8 | 9.4 | even | 3 | |||
270.3.j.a.179.1 | 8 | 9.2 | odd | 6 | |||
270.3.j.a.179.3 | 8 | 45.29 | odd | 6 | |||
450.3.i.a.101.2 | 4 | 45.23 | even | 12 | |||
450.3.i.a.401.2 | 4 | 45.43 | odd | 12 | |||
450.3.i.c.101.1 | 4 | 45.32 | even | 12 | |||
450.3.i.c.401.1 | 4 | 45.7 | odd | 12 | |||
810.3.b.a.809.1 | 8 | 1.1 | even | 1 | trivial | ||
810.3.b.a.809.2 | 8 | 15.14 | odd | 2 | inner | ||
810.3.b.a.809.7 | 8 | 5.4 | even | 2 | inner | ||
810.3.b.a.809.8 | 8 | 3.2 | odd | 2 | inner | ||
1350.3.i.a.251.1 | 4 | 45.13 | odd | 12 | |||
1350.3.i.a.1151.1 | 4 | 45.38 | even | 12 | |||
1350.3.i.c.251.2 | 4 | 45.22 | odd | 12 | |||
1350.3.i.c.1151.2 | 4 | 45.2 | even | 12 |