Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(95,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.95");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.r (of order \(6\), degree \(2\), 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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 28 x^{9} - 100 x^{8} + 140 x^{7} + 392 x^{6} + 1400 x^{5} + 8040 x^{4} + 11256 x^{3} + 9800 x^{2} + 13720 x + 9604 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 95.2 | ||
Root | \(3.45178 + 0.924901i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.95 |
Dual form | 224.3.r.c.191.2 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.51065 | − | 2.02688i | −1.17022 | − | 0.675626i | −0.216487 | − | 0.976286i | \(-0.569460\pi\) |
−0.953731 | + | 0.300660i | \(0.902793\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.21646 | + | 2.10698i | 0.243293 | + | 0.421395i | 0.961650 | − | 0.274279i | \(-0.0884391\pi\) |
−0.718358 | + | 0.695674i | \(0.755106\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.97300 | − | 6.33729i | 0.424714 | − | 0.905327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.71646 | + | 6.43710i | 0.412940 | + | 0.715234i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.39055 | − | 3.68959i | −0.580959 | − | 0.335417i | 0.180555 | − | 0.983565i | \(-0.442211\pi\) |
−0.761514 | + | 0.648148i | \(0.775544\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.56707 | −0.659006 | −0.329503 | − | 0.944155i | \(-0.606881\pi\) | ||||
−0.329503 | + | 0.944155i | \(0.606881\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 9.86249i | − | 0.657499i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.45812 | + | 12.9178i | −0.438713 | + | 0.759873i | −0.997591 | − | 0.0693771i | \(-0.977899\pi\) |
0.558878 | + | 0.829250i | \(0.311232\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −22.9151 | + | 13.2300i | −1.20606 | + | 0.696317i | −0.961895 | − | 0.273418i | \(-0.911846\pi\) |
−0.244161 | + | 0.969735i | \(0.578512\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −23.2821 | + | 16.2221i | −1.10867 | + | 0.772482i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −12.9208 | + | 7.45980i | −0.561772 | + | 0.324339i | −0.753856 | − | 0.657039i | \(-0.771809\pi\) |
0.192084 | + | 0.981378i | \(0.438475\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.54044 | − | 16.5245i | 0.381617 | − | 0.660981i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 6.35253i | 0.235279i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −52.0780 | −1.79579 | −0.897896 | − | 0.440207i | \(-0.854905\pi\) | ||||
−0.897896 | + | 0.440207i | \(0.854905\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −18.4688 | − | 10.6629i | −0.595767 | − | 0.343966i | 0.171608 | − | 0.985165i | \(-0.445104\pi\) |
−0.767374 | + | 0.641199i | \(0.778437\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.9567 | + | 25.9057i | 0.453233 | + | 0.785022i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 16.9691 | − | 1.44504i | 0.484830 | − | 0.0412868i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.9063 | + | 18.8902i | 0.294765 | + | 0.510547i | 0.974930 | − | 0.222511i | \(-0.0714255\pi\) |
−0.680166 | + | 0.733059i | \(0.738092\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 30.0760 | + | 17.3644i | 0.771180 | + | 0.445241i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 58.5138 | 1.42717 | 0.713583 | − | 0.700571i | \(-0.247071\pi\) | ||||
0.713583 | + | 0.700571i | \(0.247071\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 58.6983i | − | 1.36508i | −0.730849 | − | 0.682539i | \(-0.760876\pi\) | ||
0.730849 | − | 0.682539i | \(-0.239124\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.04188 | + | 15.6610i | −0.200931 | + | 0.348022i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −57.4110 | + | 33.1463i | −1.22151 | + | 0.705240i | −0.965240 | − | 0.261365i | \(-0.915827\pi\) |
−0.256271 | + | 0.966605i | \(0.582494\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −31.3225 | − | 37.6816i | −0.639235 | − | 0.769011i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 52.3658 | − | 30.2334i | 1.02678 | − | 0.592812i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 36.0642 | − | 62.4650i | 0.680456 | − | 1.17858i | −0.294385 | − | 0.955687i | \(-0.595115\pi\) |
0.974842 | − | 0.222898i | \(-0.0715517\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 17.9530i | − | 0.326418i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 107.263 | 1.88180 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 15.3096 | + | 8.83897i | 0.259484 | + | 0.149813i | 0.624099 | − | 0.781345i | \(-0.285466\pi\) |
−0.364615 | + | 0.931158i | \(0.618799\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −44.1746 | − | 76.5126i | −0.724173 | − | 1.25431i | −0.959313 | − | 0.282344i | \(-0.908888\pi\) |
0.235140 | − | 0.971962i | \(-0.424445\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 51.8428 | − | 4.41480i | 0.822902 | − | 0.0700761i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.4215 | − | 18.0506i | −0.160331 | − | 0.277702i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 80.0413 | + | 46.2119i | 1.19465 | + | 0.689730i | 0.959357 | − | 0.282196i | \(-0.0910627\pi\) |
0.235290 | + | 0.971925i | \(0.424396\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 60.4804 | 0.876528 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.8459i | − | 0.166844i | −0.996514 | − | 0.0834222i | \(-0.973415\pi\) | ||
0.996514 | − | 0.0834222i | \(-0.0265850\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −33.2555 | + | 57.6001i | −0.455554 | + | 0.789043i | −0.998720 | − | 0.0505826i | \(-0.983892\pi\) |
0.543166 | + | 0.839626i | \(0.317226\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −66.9863 | + | 38.6746i | −0.893151 | + | 0.515661i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −42.3811 | + | 29.5296i | −0.550404 | + | 0.383502i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.9202 | + | 9.19151i | −0.201521 | + | 0.116348i | −0.597365 | − | 0.801970i | \(-0.703786\pi\) |
0.395844 | + | 0.918318i | \(0.370452\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 46.3240 | − | 80.2355i | 0.571901 | − | 0.990561i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 101.779i | 1.22626i | 0.789984 | + | 0.613128i | \(0.210089\pi\) | ||||
−0.789984 | + | 0.613128i | \(0.789911\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −36.2901 | −0.426942 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 182.828 | + | 105.556i | 2.10147 | + | 1.21328i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −23.2850 | − | 40.3308i | −0.261629 | − | 0.453155i | 0.705046 | − | 0.709162i | \(-0.250926\pi\) |
−0.966675 | + | 0.256007i | \(0.917593\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25.4699 | + | 54.2920i | −0.279889 | + | 0.596616i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 43.2250 | + | 74.8678i | 0.464785 | + | 0.805031i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −55.7507 | − | 32.1877i | −0.586849 | − | 0.338818i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −135.924 | −1.40128 | −0.700639 | − | 0.713516i | \(-0.747102\pi\) | ||||
−0.700639 | + | 0.713516i | \(0.747102\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 54.8488i | − | 0.554029i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 44.7274 | − | 77.4701i | 0.442845 | − | 0.767030i | −0.555054 | − | 0.831814i | \(-0.687302\pi\) |
0.997899 | + | 0.0647838i | \(0.0206358\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.54400 | + | 2.62348i | −0.0441165 | + | 0.0254707i | −0.521896 | − | 0.853009i | \(-0.674775\pi\) |
0.477780 | + | 0.878480i | \(0.341442\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −62.5014 | − | 29.3212i | −0.595252 | − | 0.279249i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.0278 | − | 7.52159i | 0.121755 | − | 0.0702952i | −0.437886 | − | 0.899031i | \(-0.644273\pi\) |
0.559641 | + | 0.828735i | \(0.310939\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.67603 | − | 6.36707i | 0.0337250 | − | 0.0584135i | −0.848670 | − | 0.528922i | \(-0.822596\pi\) |
0.882395 | + | 0.470509i | \(0.155930\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 88.4228i | − | 0.796602i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 170.683 | 1.51047 | 0.755236 | − | 0.655454i | \(-0.227522\pi\) | ||||
0.755236 | + | 0.655454i | \(0.227522\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −31.4353 | − | 18.1492i | −0.273350 | − | 0.157819i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −31.8392 | − | 55.1471i | −0.272130 | − | 0.471343i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 59.6911 | + | 85.6690i | 0.501606 | + | 0.719908i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −33.2739 | − | 57.6321i | −0.274991 | − | 0.476298i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −205.422 | − | 118.600i | −1.67010 | − | 0.964230i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 107.246 | 0.857964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 194.746i | − | 1.53343i | −0.641987 | − | 0.766716i | \(-0.721890\pi\) | ||
0.641987 | − | 0.766716i | \(-0.278110\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −118.974 | + | 206.070i | −0.922282 | + | 1.59744i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 25.9409 | − | 14.9770i | 0.198022 | − | 0.114328i | −0.397711 | − | 0.917511i | \(-0.630195\pi\) |
0.595732 | + | 0.803183i | \(0.296862\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.7160 | + | 184.552i | 0.118165 | + | 1.38761i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.3846 | + | 7.72762i | −0.0991454 | + | 0.0572416i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −88.9157 | + | 154.007i | −0.649020 | + | 1.12414i | 0.334337 | + | 0.942454i | \(0.391488\pi\) |
−0.983357 | + | 0.181682i | \(0.941846\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 120.142i | − | 0.864334i | −0.901793 | − | 0.432167i | \(-0.857749\pi\) | ||
0.901793 | − | 0.432167i | \(-0.142251\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 268.734 | 1.90591 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 54.7483 | + | 31.6090i | 0.382855 | + | 0.221042i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −63.3509 | − | 109.727i | −0.436903 | − | 0.756738i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 33.5867 | + | 195.774i | 0.228481 | + | 1.33179i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 41.2640 | + | 71.4713i | 0.276939 | + | 0.479673i | 0.970623 | − | 0.240607i | \(-0.0773466\pi\) |
−0.693683 | + | 0.720280i | \(0.744013\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −246.068 | − | 142.067i | −1.62959 | − | 0.940843i | −0.984215 | − | 0.176975i | \(-0.943369\pi\) |
−0.645373 | − | 0.763868i | \(-0.723298\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −110.871 | −0.724649 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 51.8843i | − | 0.334738i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −28.1271 | + | 48.7175i | −0.179153 | + | 0.310303i | −0.941591 | − | 0.336759i | \(-0.890669\pi\) |
0.762437 | + | 0.647062i | \(0.224003\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −253.218 | + | 146.195i | −1.59256 | + | 0.919468i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.86152 | + | 104.061i | 0.0550405 | + | 0.646339i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 166.695 | − | 96.2414i | 1.02267 | − | 0.590438i | 0.107793 | − | 0.994173i | \(-0.465622\pi\) |
0.914876 | + | 0.403735i | \(0.132288\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −36.3885 | + | 63.0267i | −0.220536 | + | 0.381980i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 132.185i | − | 0.791530i | −0.918352 | − | 0.395765i | \(-0.870480\pi\) | ||
0.918352 | − | 0.395765i | \(-0.129520\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −95.6052 | −0.565712 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −170.326 | − | 98.3378i | −0.996059 | − | 0.575075i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −102.145 | − | 176.920i | −0.590434 | − | 1.02266i | −0.994174 | − | 0.107788i | \(-0.965623\pi\) |
0.403740 | − | 0.914874i | \(-0.367710\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −76.3570 | − | 109.588i | −0.436326 | − | 0.626217i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −35.8310 | − | 62.0612i | −0.202435 | − | 0.350628i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 106.903 | + | 61.7205i | 0.597224 | + | 0.344808i | 0.767949 | − | 0.640511i | \(-0.221278\pi\) |
−0.170725 | + | 0.985319i | \(0.554611\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −131.612 | −0.727136 | −0.363568 | − | 0.931568i | \(-0.618442\pi\) | ||||
−0.363568 | + | 0.931568i | \(0.618442\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 358.146i | 1.95708i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −26.5342 | + | 45.9586i | −0.143428 | + | 0.248425i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 95.3230 | − | 55.0347i | 0.509749 | − | 0.294303i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 40.2579 | + | 18.8861i | 0.213005 | + | 0.0999264i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −149.814 | + | 86.4954i | −0.784369 | + | 0.452856i | −0.837976 | − | 0.545706i | \(-0.816261\pi\) |
0.0536074 | + | 0.998562i | \(0.482928\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −99.7579 | + | 172.786i | −0.516880 | + | 0.895263i | 0.482928 | + | 0.875660i | \(0.339573\pi\) |
−0.999808 | + | 0.0196024i | \(0.993760\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 84.4926i | 0.433296i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.40658 | −0.0477492 | −0.0238746 | − | 0.999715i | \(-0.507600\pi\) | ||||
−0.0238746 | + | 0.999715i | \(0.507600\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 266.746 | + | 154.006i | 1.34043 | + | 0.773899i | 0.986871 | − | 0.161513i | \(-0.0516372\pi\) |
0.353561 | + | 0.935411i | \(0.384971\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −187.332 | − | 324.468i | −0.931998 | − | 1.61427i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −154.828 | + | 330.033i | −0.762699 | + | 1.62578i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 71.1799 | + | 123.287i | 0.347219 | + | 0.601401i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −96.0390 | − | 55.4482i | −0.463957 | − | 0.267866i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 195.253 | 0.934226 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 274.103i | − | 1.29906i | −0.760334 | − | 0.649532i | \(-0.774965\pi\) | ||
0.760334 | − | 0.649532i | \(-0.225035\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −24.0103 | + | 41.5870i | −0.112724 | + | 0.195244i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 123.676 | − | 71.4044i | 0.575237 | − | 0.332113i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −122.482 | + | 85.3410i | −0.564433 | + | 0.393276i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 233.497 | − | 134.809i | 1.06620 | − | 0.615568i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 63.8943 | − | 110.668i | 0.289114 | − | 0.500761i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 93.9923i | − | 0.421490i | −0.977541 | − | 0.210745i | \(-0.932411\pi\) | ||
0.977541 | − | 0.210745i | \(-0.0675890\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 141.827 | 0.630341 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 136.226 | + | 78.6500i | 0.600113 | + | 0.346476i | 0.769086 | − | 0.639145i | \(-0.220712\pi\) |
−0.168973 | + | 0.985621i | \(0.554045\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −41.1365 | − | 71.2506i | −0.179636 | − | 0.311138i | 0.762120 | − | 0.647436i | \(-0.224159\pi\) |
−0.941756 | + | 0.336298i | \(0.890825\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 208.638 | − | 17.7671i | 0.903196 | − | 0.0769137i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 166.177 | + | 287.828i | 0.713207 | + | 1.23531i | 0.963647 | + | 0.267179i | \(0.0860915\pi\) |
−0.250440 | + | 0.968132i | \(0.580575\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −139.677 | − | 80.6424i | −0.594369 | − | 0.343159i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 74.5202 | 0.314431 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 36.6386i | 0.153300i | 0.997058 | + | 0.0766499i | \(0.0244224\pi\) | ||||
−0.997058 | + | 0.0766499i | \(0.975578\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 230.374 | − | 399.020i | 0.955910 | − | 1.65568i | 0.223637 | − | 0.974673i | \(-0.428207\pi\) |
0.732273 | − | 0.681011i | \(-0.238460\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −275.742 | + | 159.200i | −1.13474 | + | 0.655142i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 41.2914 | − | 111.834i | 0.168536 | − | 0.456465i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 196.315 | − | 113.343i | 0.794798 | − | 0.458877i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 206.294 | − | 357.312i | 0.828490 | − | 1.43499i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 23.1867i | − | 0.0923775i | −0.998933 | − | 0.0461887i | \(-0.985292\pi\) | ||
0.998933 | − | 0.0461887i | \(-0.0147076\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 110.094 | 0.435155 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 127.402 | + | 73.5556i | 0.499616 | + | 0.288453i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 101.126 | + | 175.155i | 0.393486 | + | 0.681538i | 0.992907 | − | 0.118896i | \(-0.0379356\pi\) |
−0.599420 | + | 0.800434i | \(0.704602\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 152.137 | − | 12.9556i | 0.587403 | − | 0.0500216i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −193.546 | − | 335.231i | −0.741555 | − | 1.28441i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.1209 | + | 15.6583i | 0.103121 | + | 0.0595372i | 0.550674 | − | 0.834721i | \(-0.314371\pi\) |
−0.447552 | + | 0.894258i | \(0.647704\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 175.483 | 0.662200 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 188.783i | 0.707053i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −44.6656 | + | 77.3631i | −0.166043 | + | 0.287595i | −0.937025 | − | 0.349262i | \(-0.886432\pi\) |
0.770982 | + | 0.636857i | \(0.219766\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 46.3103 | − | 26.7372i | 0.170887 | − | 0.0986614i | −0.412117 | − | 0.911131i | \(-0.635211\pi\) |
0.583004 | + | 0.812469i | \(0.301877\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 199.459 | − | 138.976i | 0.730621 | − | 0.509070i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −121.937 | + | 70.4005i | −0.443408 | + | 0.256002i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.3184 | + | 35.1924i | −0.0733515 | + | 0.127048i | −0.900368 | − | 0.435129i | \(-0.856703\pi\) |
0.827017 | + | 0.562177i | \(0.190036\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 158.514i | − | 0.568150i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.49585 | 0.0195582 | 0.00977910 | − | 0.999952i | \(-0.496887\pi\) | ||||
0.00977910 | + | 0.999952i | \(0.496887\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −255.061 | − | 147.260i | −0.901276 | − | 0.520352i | −0.0236618 | − | 0.999720i | \(-0.507533\pi\) |
−0.877614 | + | 0.479368i | \(0.840866\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 130.481 | + | 226.000i | 0.457828 | + | 0.792981i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 173.962 | − | 370.819i | 0.606138 | − | 1.29205i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 33.2529 | + | 57.5957i | 0.115062 | + | 0.199293i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 477.182 | + | 275.501i | 1.63980 | + | 0.946739i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −163.827 | −0.559135 | −0.279568 | − | 0.960126i | \(-0.590191\pi\) | ||||
−0.279568 | + | 0.960126i | \(0.590191\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 43.0091i | 0.145794i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 23.4382 | − | 40.5962i | 0.0789165 | − | 0.136687i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 110.693 | − | 63.9087i | 0.370211 | − | 0.213741i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −371.988 | − | 174.510i | −1.23584 | − | 0.579768i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −314.045 | + | 181.314i | −1.03645 | + | 0.598395i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 107.473 | − | 186.150i | 0.352372 | − | 0.610326i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 559.026i | 1.82093i | 0.413586 | + | 0.910465i | \(0.364276\pi\) | ||||
−0.413586 | + | 0.910465i | \(0.635724\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21.2699 | 0.0688346 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 280.938 | + | 162.199i | 0.903336 | + | 0.521541i | 0.878281 | − | 0.478145i | \(-0.158691\pi\) |
0.0250551 | + | 0.999686i | \(0.492024\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 50.9596 | + | 88.2646i | 0.162810 | + | 0.281995i | 0.935875 | − | 0.352331i | \(-0.114611\pi\) |
−0.773065 | + | 0.634326i | \(0.781278\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 72.3668 | + | 103.861i | 0.229736 | + | 0.329718i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −274.099 | − | 474.754i | −0.864667 | − | 1.49765i | −0.867377 | − | 0.497651i | \(-0.834196\pi\) |
0.00271028 | − | 0.999996i | \(-0.499137\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 332.807 | + | 192.146i | 1.04328 | + | 0.602339i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −60.9813 | −0.189973 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 394.684i | − | 1.22193i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −81.7336 | + | 141.567i | −0.251488 | + | 0.435590i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −25.8105 | + | 14.9017i | −0.0789313 | + | 0.0455710i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 39.3745 | + | 462.374i | 0.119679 | + | 1.40539i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 140.905 | − | 81.3518i | 0.425696 | − | 0.245776i | −0.271815 | − | 0.962349i | \(-0.587624\pi\) |
0.697511 | + | 0.716574i | \(0.254291\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −81.0656 | + | 140.410i | −0.243440 | + | 0.421651i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 224.860i | 0.671225i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −598.848 | −1.77700 | −0.888499 | − | 0.458879i | \(-0.848251\pi\) | ||||
−0.888499 | + | 0.458879i | \(0.848251\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −599.210 | − | 345.954i | −1.76758 | − | 1.02051i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 78.6837 | + | 136.284i | 0.230744 | + | 0.399660i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −331.921 | + | 86.4727i | −0.967699 | + | 0.252107i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 73.5722 | + | 127.431i | 0.213253 | + | 0.369365i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 94.3313 | + | 54.4622i | 0.271848 | + | 0.156952i | 0.629727 | − | 0.776816i | \(-0.283167\pi\) |
−0.357879 | + | 0.933768i | \(0.616500\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −277.893 | −0.796255 | −0.398128 | − | 0.917330i | \(-0.630340\pi\) | ||||
−0.398128 | + | 0.917330i | \(0.630340\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 54.4226i | − | 0.155050i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 52.0900 | − | 90.2225i | 0.147564 | − | 0.255588i | −0.782763 | − | 0.622320i | \(-0.786190\pi\) |
0.930327 | + | 0.366732i | \(0.119524\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.9591 | − | 14.4102i | 0.0703074 | − | 0.0405920i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −35.9143 | − | 421.741i | −0.100600 | − | 1.18135i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −581.956 | + | 335.992i | −1.62105 | + | 0.935911i | −0.634405 | + | 0.773001i | \(0.718755\pi\) |
−0.986641 | + | 0.162911i | \(0.947912\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 169.567 | − | 293.699i | 0.469714 | − | 0.813569i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 269.769i | 0.743164i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −161.816 | −0.443332 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −86.1727 | − | 49.7518i | −0.234803 | − | 0.135564i | 0.377983 | − | 0.925813i | \(-0.376618\pi\) |
−0.612786 | + | 0.790249i | \(0.709951\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 217.464 | + | 376.659i | 0.589334 | + | 1.02076i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −288.640 | − | 414.258i | −0.778006 | − | 1.11660i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 308.281 | + | 533.959i | 0.826491 | + | 1.43152i | 0.900775 | + | 0.434287i | \(0.143000\pi\) |
−0.0742836 | + | 0.997237i | \(0.523667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −376.502 | − | 217.373i | −1.00401 | − | 0.579663i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 446.156 | 1.18344 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 212.094i | − | 0.559616i | −0.960056 | − | 0.279808i | \(-0.909729\pi\) | ||
0.960056 | − | 0.279808i | \(-0.0902707\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −394.726 | + | 683.685i | −1.03603 | + | 1.79445i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −388.045 | + | 224.038i | −1.01317 | + | 0.584955i | −0.912119 | − | 0.409926i | \(-0.865555\pi\) |
−0.101053 | + | 0.994881i | \(0.532221\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −113.773 | − | 53.3742i | −0.295515 | − | 0.138634i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 377.847 | − | 218.150i | 0.976349 | − | 0.563696i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.0297 | − | 26.0322i | 0.0386368 | − | 0.0669208i | −0.846060 | − | 0.533087i | \(-0.821032\pi\) |
0.884697 | + | 0.466166i | \(0.154365\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 222.544i | − | 0.569167i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −121.426 | −0.308972 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −38.7326 | − | 22.3623i | −0.0980571 | − | 0.0566133i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 150.913 | + | 261.389i | 0.380133 | + | 0.658410i | 0.991081 | − | 0.133261i | \(-0.0425448\pi\) |
−0.610948 | + | 0.791671i | \(0.709211\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 318.892 | − | 679.754i | 0.799227 | − | 1.70364i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.1956 | − | 47.1042i | −0.0678195 | − | 0.117467i | 0.830122 | − | 0.557582i | \(-0.188271\pi\) |
−0.897941 | + | 0.440115i | \(0.854938\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 158.223 | + | 91.3503i | 0.392614 | + | 0.226676i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 225.406 | 0.556557 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 160.959i | − | 0.395476i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 77.7710 | − | 134.703i | 0.190149 | − | 0.329348i | −0.755150 | − | 0.655552i | \(-0.772436\pi\) |
0.945300 | + | 0.326204i | \(0.105769\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 624.305 | − | 360.443i | 1.51899 | − | 0.876989i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 101.530 | − | 70.7428i | 0.245837 | − | 0.171290i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −214.446 | + | 123.811i | −0.516738 | + | 0.298339i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −243.514 | + | 421.779i | −0.583967 | + | 1.01146i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 384.000i | − | 0.916468i | −0.888832 | − | 0.458234i | \(-0.848482\pi\) | ||
0.888832 | − | 0.458234i | \(-0.151518\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −295.132 | −0.701026 | −0.350513 | − | 0.936558i | \(-0.613993\pi\) | ||||
−0.350513 | + | 0.936558i | \(0.613993\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −426.732 | − | 246.374i | −1.00882 | − | 0.582444i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 142.307 | + | 246.484i | 0.334841 | + | 0.579962i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −616.214 | + | 52.4751i | −1.44312 | + | 0.122892i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −128.135 | − | 221.936i | −0.298683 | − | 0.517334i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 417.311 | + | 240.935i | 0.968239 | + | 0.559013i | 0.898699 | − | 0.438566i | \(-0.144514\pi\) |
0.0695400 | + | 0.997579i | \(0.477847\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.18001 | 0.0212009 | 0.0106005 | − | 0.999944i | \(-0.496626\pi\) | ||||
0.0106005 | + | 0.999944i | \(0.496626\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 513.618i | 1.18073i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 197.387 | − | 341.884i | 0.451686 | − | 0.782343i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 169.939 | − | 98.1143i | 0.387105 | − | 0.223495i | −0.293800 | − | 0.955867i | \(-0.594920\pi\) |
0.680905 | + | 0.732372i | \(0.261587\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 126.151 | − | 341.668i | 0.286057 | − | 0.774758i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −55.9819 | + | 32.3212i | −0.126370 | + | 0.0729598i | −0.561852 | − | 0.827237i | \(-0.689911\pi\) |
0.435482 | + | 0.900197i | \(0.356578\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 56.6506 | − | 98.1218i | 0.127305 | − | 0.220498i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 334.548i | − | 0.748429i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −834.833 | −1.85932 | −0.929658 | − | 0.368424i | \(-0.879898\pi\) | ||||
−0.929658 | + | 0.368424i | \(0.879898\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −373.935 | − | 215.892i | −0.829125 | − | 0.478696i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 575.906 | + | 997.498i | 1.27132 | + | 2.20198i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −145.375 | + | 12.3798i | −0.319506 | + | 0.0272083i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.0154 | − | 43.3280i | −0.0547383 | − | 0.0948095i | 0.837358 | − | 0.546655i | \(-0.184099\pi\) |
−0.892096 | + | 0.451846i | \(0.850766\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −82.0610 | − | 47.3780i | −0.178782 | − | 0.103220i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −439.355 | −0.953048 | −0.476524 | − | 0.879161i | \(-0.658104\pi\) | ||||
−0.476524 | + | 0.879161i | \(0.658104\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 244.469i | 0.528010i | 0.964521 | + | 0.264005i | \(0.0850435\pi\) | ||||
−0.964521 | + | 0.264005i | \(0.914956\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −105.163 | + | 182.148i | −0.226157 | + | 0.391716i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −385.416 | + | 222.520i | −0.825301 | + | 0.476488i | −0.852241 | − | 0.523149i | \(-0.824757\pi\) |
0.0269400 | + | 0.999637i | \(0.491424\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 530.821 | − | 369.857i | 1.13181 | − | 0.788608i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 197.489 | − | 114.020i | 0.419297 | − | 0.242081i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −216.573 | + | 375.115i | −0.457870 | + | 0.793054i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 504.881i | 1.06291i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 536.125 | 1.12395 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 230.123 | + | 132.862i | 0.480424 | + | 0.277373i | 0.720593 | − | 0.693358i | \(-0.243869\pi\) |
−0.240169 | + | 0.970731i | \(0.577203\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −93.4350 | − | 161.834i | −0.194251 | − | 0.336453i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 179.808 | − | 383.282i | 0.372274 | − | 0.793545i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −165.346 | − | 286.388i | −0.340920 | − | 0.590492i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.3034 | + | 12.2995i | 0.0437441 | + | 0.0252557i | 0.521713 | − | 0.853121i | \(-0.325293\pi\) |
−0.477968 | + | 0.878377i | \(0.658627\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −780.278 | −1.59566 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 532.126i | 1.08376i | 0.840456 | + | 0.541880i | \(0.182287\pi\) | ||||
−0.840456 | + | 0.541880i | \(0.817713\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 388.404 | − | 672.735i | 0.787837 | − | 1.36457i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 115.565 | − | 66.7216i | 0.233465 | − | 0.134791i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −75.0712 | − | 35.2180i | −0.151049 | − | 0.0708612i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −628.228 | + | 362.708i | −1.25897 | + | 0.726869i | −0.972875 | − | 0.231330i | \(-0.925692\pi\) |
−0.286100 | + | 0.958200i | \(0.592359\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −267.924 | + | 464.058i | −0.534778 | + | 0.926263i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 46.8524i | − | 0.0931459i | −0.998915 | − | 0.0465729i | \(-0.985170\pi\) | ||
0.998915 | − | 0.0465729i | \(-0.0148300\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 217.637 | 0.430964 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 335.637 | + | 193.780i | 0.662006 | + | 0.382209i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −431.957 | − | 748.172i | −0.848639 | − | 1.46989i | −0.882423 | − | 0.470457i | \(-0.844089\pi\) |
0.0337834 | − | 0.999429i | \(-0.489244\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 266.160 | + | 381.995i | 0.520862 | + | 0.747544i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −84.0441 | − | 145.569i | −0.163829 | − | 0.283760i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.0552 | − | 6.38273i | −0.0214664 | − | 0.0123937i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 489.184 | 0.946197 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 828.142i | 1.59565i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 169.288 | − | 293.215i | 0.324928 | − | 0.562792i | −0.656570 | − | 0.754265i | \(-0.727993\pi\) |
0.981498 | + | 0.191473i | \(0.0613266\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 323.498 | − | 186.772i | 0.618544 | − | 0.357116i | −0.157758 | − | 0.987478i | \(-0.550427\pi\) |
0.776302 | + | 0.630361i | \(0.217093\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 45.9416 | + | 539.492i | 0.0875079 | + | 1.02760i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 275.485 | − | 159.051i | 0.522741 | − | 0.301805i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −153.203 | + | 265.355i | −0.289608 | + | 0.501616i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 131.399i | 0.247456i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −501.292 | −0.940510 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.6956 | + | 18.2995i | 0.0592441 | + | 0.0342046i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −250.200 | − | 433.359i | −0.465922 | − | 0.807000i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 61.1389 | + | 356.373i | 0.113430 | + | 0.661174i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 294.267 | + | 509.685i | 0.543931 | + | 0.942116i | 0.998673 | + | 0.0514928i | \(0.0163979\pi\) |
−0.454743 | + | 0.890623i | \(0.650269\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 462.043 | + | 266.761i | 0.850908 | + | 0.491272i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.8870 | 0.0328202 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 206.784i | − | 0.378032i | −0.981974 | − | 0.189016i | \(-0.939470\pi\) | ||
0.981974 | − | 0.189016i | \(-0.0605298\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 328.346 | − | 568.713i | 0.598081 | − | 1.03591i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1193.37 | − | 688.993i | 2.16583 | − | 1.25044i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.9186 | + | 128.217i | 0.0197443 | + | 0.231857i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 186.305 | − | 107.563i | 0.335684 | − | 0.193807i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 238.327 | − | 412.794i | 0.427876 | − | 0.741103i | −0.568808 | − | 0.822470i | \(-0.692595\pi\) |
0.996684 | + | 0.0813674i | \(0.0259287\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 502.873i | 0.899594i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −446.195 | −0.795356 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −405.901 | − | 234.347i | −0.720961 | − | 0.416247i | 0.0941451 | − | 0.995558i | \(-0.469988\pi\) |
−0.815106 | + | 0.579311i | \(0.803322\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 207.630 | + | 359.625i | 0.367486 | + | 0.636505i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −370.754 | − | 532.109i | −0.653888 | − | 0.938463i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −179.141 | − | 310.282i | −0.314835 | − | 0.545311i | 0.664567 | − | 0.747228i | \(-0.268616\pi\) |
−0.979402 | + | 0.201918i | \(0.935283\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 321.513 | + | 185.626i | 0.563070 | + | 0.325089i | 0.754377 | − | 0.656442i | \(-0.227939\pi\) |
−0.191307 | + | 0.981530i | \(0.561273\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 701.262 | 1.22384 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 284.679i | 0.495094i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 535.691 | − | 927.844i | 0.928408 | − | 1.60805i | 0.142421 | − | 0.989806i | \(-0.454511\pi\) |
0.785987 | − | 0.618243i | \(-0.212155\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 700.431 | − | 404.394i | 1.20972 | − | 0.698435i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 645.004 | + | 302.590i | 1.11016 | + | 0.520808i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −460.940 | + | 266.124i | −0.790635 | + | 0.456473i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 77.4625 | − | 134.169i | 0.132414 | − | 0.229349i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 283.490i | − | 0.482948i | −0.970407 | − | 0.241474i | \(-0.922369\pi\) | ||
0.970407 | − | 0.241474i | \(-0.0776308\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 564.284 | 0.958037 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 33.0233 | + | 19.0660i | 0.0558769 | + | 0.0322606i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 310.680 | + | 538.113i | 0.523912 | + | 0.907442i | 0.999613 | + | 0.0278350i | \(0.00886130\pi\) |
−0.475700 | + | 0.879607i | \(0.657805\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −107.891 | + | 229.981i | −0.181329 | + | 0.386523i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −624.302 | − | 1081.32i | −1.04573 | − | 1.81126i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −910.469 | − | 525.659i | −1.51998 | − | 0.877562i | −0.999723 | − | 0.0235529i | \(-0.992502\pi\) |
−0.520259 | − | 0.854009i | \(-0.674164\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −427.201 | −0.710817 | −0.355409 | − | 0.934711i | \(-0.615658\pi\) | ||||
−0.355409 | + | 0.934711i | \(0.615658\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 686.979i | 1.13927i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 80.9530 | − | 140.215i | 0.133807 | − | 0.231760i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 621.252 | − | 358.680i | 1.02348 | − | 0.590906i | 0.108369 | − | 0.994111i | \(-0.465437\pi\) |
0.915110 | + | 0.403205i | \(0.132104\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1212.48 | − | 844.816i | 1.99094 | − | 1.38722i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 491.844 | − | 283.966i | 0.804983 | − | 0.464757i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.87305 | − | 8.44037i | 0.00794951 | − | 0.0137690i | −0.862023 | − | 0.506869i | \(-0.830803\pi\) |
0.869973 | + | 0.493100i | \(0.164136\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 577.091i | − | 0.938360i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 505.878 | 0.819900 | 0.409950 | − | 0.912108i | \(-0.365546\pi\) | ||||
0.409950 | + | 0.912108i | \(0.365546\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 272.815 | + | 157.510i | 0.440735 | + | 0.254458i | 0.703909 | − | 0.710290i | \(-0.251436\pi\) |
−0.263175 | + | 0.964748i | \(0.584770\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −47.3886 | − | 82.0795i | −0.0763102 | − | 0.132173i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −324.814 | + | 27.6603i | −0.521371 | + | 0.0443985i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −108.051 | − | 187.149i | −0.172881 | − | 0.299439i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −685.466 | − | 395.754i | −1.09325 | − | 0.631187i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −325.362 | −0.517268 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 381.905i | 0.605238i | 0.953112 | + | 0.302619i | \(0.0978609\pi\) | ||||
−0.953112 | + | 0.302619i | \(0.902139\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −555.573 | + | 962.280i | −0.877682 | + | 1.52019i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 410.325 | − | 236.901i | 0.646181 | − | 0.373073i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 268.342 | + | 322.821i | 0.421260 | + | 0.506783i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 76.2536 | − | 44.0250i | 0.119333 | − | 0.0688968i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −68.4839 | + | 118.618i | −0.106839 | + | 0.185051i | −0.914488 | − | 0.404613i | \(-0.867406\pi\) |
0.807649 | + | 0.589664i | \(0.200740\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 260.130i | 0.404556i | 0.979328 | + | 0.202278i | \(0.0648345\pi\) | ||||
−0.979328 | + | 0.202278i | \(0.935166\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −578.911 | −0.897537 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −378.735 | − | 218.663i | −0.585371 | − | 0.337964i | 0.177894 | − | 0.984050i | \(-0.443071\pi\) |
−0.763265 | + | 0.646086i | \(0.776405\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −65.2243 | − | 112.972i | −0.100500 | − | 0.174071i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 602.967 | − | 51.3470i | 0.926217 | − | 0.0788741i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 590.447 | + | 1022.68i | 0.904206 | + | 1.56613i | 0.821979 | + | 0.569518i | \(0.192870\pi\) |
0.0822270 | + | 0.996614i | \(0.473797\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 63.1122 | + | 36.4379i | 0.0963545 | + | 0.0556303i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −494.371 | −0.752467 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 129.818i | 0.196992i | 0.995137 | + | 0.0984960i | \(0.0314032\pi\) | ||||
−0.995137 | + | 0.0984960i | \(0.968597\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 316.779 | − | 548.677i | 0.479241 | − | 0.830070i | −0.520475 | − | 0.853877i | \(-0.674245\pi\) |
0.999717 | + | 0.0238063i | \(0.00757850\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −448.621 | + | 259.012i | −0.676654 | + | 0.390666i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −369.729 | + | 257.614i | −0.555984 | + | 0.387390i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 672.887 | − | 388.491i | 1.00883 | − | 0.582446i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −190.511 | + | 329.975i | −0.284770 | + | 0.493235i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 651.944i | 0.971600i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1074.74 | 1.59694 | 0.798471 | − | 0.602033i | \(-0.205642\pi\) | ||||
0.798471 | + | 0.602033i | \(0.205642\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 104.973 | + | 60.6059i | 0.155515 | + | 0.0897866i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −277.711 | − | 481.010i | −0.410208 | − | 0.710502i | 0.584704 | − | 0.811247i | \(-0.301211\pi\) |
−0.994912 | + | 0.100745i | \(0.967877\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −404.102 | + | 861.390i | −0.595143 | + | 1.26861i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −318.828 | − | 552.226i | −0.468176 | − | 0.810904i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −128.117 | − | 73.9682i | −0.187579 | − | 0.108299i | 0.403270 | − | 0.915081i | \(-0.367874\pi\) |
−0.590849 | + | 0.806782i | \(0.701207\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −432.651 | −0.631607 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 333.515i | 0.485466i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −308.965 | + | 535.142i | −0.448425 | + | 0.776694i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −506.502 | + | 292.429i | −0.732999 | + | 0.423197i | −0.819518 | − | 0.573053i | \(-0.805759\pi\) |
0.0865192 | + | 0.996250i | \(0.472426\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −347.593 | − | 163.066i | −0.501577 | − | 0.235304i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 253.137 | − | 146.149i | 0.364226 | − | 0.210286i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −436.403 | + | 755.872i | −0.626116 | + | 1.08446i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1347.28i | − | 1.92745i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1138.04 | −1.62345 | −0.811727 | − | 0.584037i | \(-0.801472\pi\) | ||||
−0.811727 | + | 0.584037i | \(0.801472\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −499.837 | − | 288.581i | −0.711005 | − | 0.410499i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 326.905 | + | 566.215i | 0.463694 | + | 0.803142i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −357.976 | − | 513.769i | −0.506331 | − | 0.726689i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 421.341 | + | 729.785i | 0.594276 | + | 1.02932i | 0.993649 | + | 0.112527i | \(0.0358945\pi\) |
−0.399373 | + | 0.916789i | \(0.630772\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −118.333 | − | 68.3198i | −0.166432 | − | 0.0960897i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 318.174 | 0.446247 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 153.804i | 0.215111i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 74.2620 | − | 128.626i | 0.103573 | − | 0.179394i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −48.8258 | + | 28.1896i | −0.0679079 | + | 0.0392066i | −0.533570 | − | 0.845756i | \(-0.679150\pi\) |
0.465662 | + | 0.884963i | \(0.345816\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.11644 | + | 36.5963i | 0.00432238 | + | 0.0507576i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1617.53 | + | 933.880i | −2.23725 | + | 1.29167i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −496.847 | + | 860.564i | −0.685306 | + | 1.18698i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 929.204i | 1.27813i | 0.769151 | + | 0.639067i | \(0.220680\pi\) | ||||
−0.769151 | + | 0.639067i | \(0.779320\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 456.881 | 0.626723 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 758.256 | + | 437.779i | 1.03729 | + | 0.598877i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −273.917 | − | 474.437i | −0.373692 | − | 0.647254i | 0.616438 | − | 0.787403i | \(-0.288575\pi\) |
−0.990130 | + | 0.140149i | \(0.955242\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −371.634 | + | 308.918i | −0.505624 | + | 0.420297i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −341.005 | − | 590.639i | −0.462694 | − | 0.801409i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 473.319 | + | 273.271i | 0.640485 | + | 0.369784i | 0.784801 | − | 0.619747i | \(-0.212765\pi\) |
−0.144316 | + | 0.989532i | \(0.546098\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −918.926 | −1.24012 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 904.617i | − | 1.21752i | −0.793354 | − | 0.608760i | \(-0.791667\pi\) | ||
0.793354 | − | 0.608760i | \(-0.208333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −100.392 | + | 173.884i | −0.134755 | + | 0.233402i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −655.163 | + | 378.259i | −0.877059 | + | 0.506370i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.93491 | − | 104.922i | −0.0119291 | − | 0.140083i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 792.217 | − | 457.386i | 1.05488 | − | 0.609037i | 0.130870 | − | 0.991400i | \(-0.458223\pi\) |
0.924012 | + | 0.382363i | \(0.124890\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −46.9967 | + | 81.4006i | −0.0624126 | + | 0.108102i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 691.278i | − | 0.915601i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −780.766 | −1.03140 | −0.515698 | − | 0.856771i | \(-0.672467\pi\) | ||||
−0.515698 | + | 0.856771i | \(0.672467\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −386.503 | − | 223.148i | −0.509227 | − | 0.294002i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −77.5839 | − | 134.379i | −0.101950 | − | 0.176583i | 0.810538 | − | 0.585686i | \(-0.199175\pi\) |
−0.912488 | + | 0.409104i | \(0.865841\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.4211 | − | 42.2254i | −0.0385598 | − | 0.0553412i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −134.871 | − | 233.603i | −0.176302 | − | 0.305364i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −131.158 | − | 75.7242i | −0.171001 | − | 0.0987277i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 354.951 | 0.461575 | 0.230788 | − | 0.973004i | \(-0.425870\pi\) | ||||
0.230788 | + | 0.973004i | \(0.425870\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 819.880i | − | 1.06340i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −433.669 | + | 751.136i | −0.561020 | + | 0.971715i | 0.436388 | + | 0.899759i | \(0.356258\pi\) |
−0.997408 | + | 0.0719566i | \(0.977076\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −352.400 | + | 203.458i | −0.454710 | + | 0.262527i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −560.361 | − | 262.881i | −0.721186 | − | 0.338328i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1340.85 | + | 774.139i | −1.72124 | + | 0.993760i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −43.7066 | + | 75.7021i | −0.0559624 | + | 0.0969297i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 330.827i | − | 0.422512i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −136.862 | −0.174347 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −81.7643 | − | 47.2066i | −0.103894 | − | 0.0599830i | 0.447153 | − | 0.894458i | \(-0.352438\pi\) |
−0.551046 | + | 0.834475i | \(0.685771\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −63.4748 | − | 109.942i | −0.0804497 | − | 0.139343i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 507.441 | − | 1081.67i | 0.641519 | − | 1.36747i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 378.447 | + | 655.489i | 0.477234 | + | 0.826594i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −616.060 | − | 355.682i | −0.774918 | − | 0.447399i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1065.20 | 1.33651 | 0.668256 | − | 0.743931i | \(-0.267041\pi\) | ||||
0.668256 | + | 0.743931i | \(0.267041\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 988.835i | − | 1.23759i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 173.076 | − | 299.776i | 0.216074 | − | 0.374252i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 425.041 | − | 245.398i | 0.529317 | − | 0.305601i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −208.473 | + | 145.257i | −0.258973 | + | 0.180443i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 313.611 | − | 181.063i | 0.388613 | − | 0.224366i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 254.373 | − | 440.587i | 0.314429 | − | 0.544607i | −0.664887 | − | 0.746944i | \(-0.731520\pi\) |
0.979316 | + | 0.202337i | \(0.0648537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 652.893i | 0.805047i | 0.915410 | + | 0.402524i | \(0.131867\pi\) | ||||
−0.915410 | + | 0.402524i | \(0.868133\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −216.772 | −0.266633 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 405.557 | + | 234.148i | 0.497616 | + | 0.287298i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 776.580 | + | 1345.08i | 0.950527 | + | 1.64636i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −444.141 | + | 37.8219i | −0.542297 | + | 0.0461806i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 87.7543 | + | 151.995i | 0.106887 | + | 0.185134i | 0.914508 | − | 0.404569i | \(-0.132578\pi\) |
−0.807621 | + | 0.589702i | \(0.799245\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 753.427 | + | 434.991i | 0.915464 | + | 0.528544i | 0.882185 | − | 0.470902i | \(-0.156072\pi\) |
0.0332791 | + | 0.999446i | \(0.489405\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 570.773 | 0.691846 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 269.724i | 0.326148i | 0.986614 | + | 0.163074i | \(0.0521409\pi\) | ||||
−0.986614 | + | 0.163074i | \(0.947859\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −72.2989 | + | 125.225i | −0.0872122 | + | 0.151056i | −0.906332 | − | 0.422567i | \(-0.861129\pi\) |
0.819120 | + | 0.573623i | \(0.194462\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 142.661 | − | 82.3656i | 0.171674 | − | 0.0991163i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 720.372 | − | 123.586i | 0.864792 | − | 0.148362i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 278.512 | − | 160.799i | 0.333547 | − | 0.192573i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 67.7367 | − | 117.323i | 0.0809280 | − | 0.140171i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 920.554i | − | 1.09720i | −0.836084 | − | 0.548602i | \(-0.815160\pi\) | ||
0.836084 | − | 0.548602i | \(-0.184840\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1871.12 | 2.22487 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.2940 | − | 11.1394i | −0.0228874 | − | 0.0132140i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −116.300 | − | 201.438i | −0.137633 | − | 0.238388i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −464.155 | + | 39.5262i | −0.547999 | + | 0.0466661i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 596.954 | + | 1033.95i | 0.703126 | + | 1.21785i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −281.835 | − | 162.718i | −0.331181 | − | 0.191207i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −206.715 | −0.242338 | −0.121169 | − | 0.992632i | \(-0.538664\pi\) | ||||
−0.121169 | + | 0.992632i | \(0.538664\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 478.497i | − | 0.559646i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −560.474 | + | 970.769i | −0.653995 | + | 1.13275i | 0.328150 | + | 0.944626i | \(0.393575\pi\) |
−0.982145 | + | 0.188127i | \(0.939758\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.2497 | + | 13.4232i | −0.0270660 | + | 0.0156265i | −0.513472 | − | 0.858106i | \(-0.671641\pi\) |
0.486406 | + | 0.873733i | \(0.338308\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1362.32 | + | 949.219i | −1.58226 | + | 1.10246i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −338.354 | + | 195.349i | −0.392067 | + | 0.226360i | −0.683055 | − | 0.730367i | \(-0.739349\pi\) |
0.290988 | + | 0.956727i | \(0.406016\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 248.511 | − | 430.434i | 0.287296 | − | 0.497612i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 269.598i | − | 0.310955i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 135.651 | 0.156101 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −685.720 | − | 395.901i | −0.787279 | − | 0.454536i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −505.156 | − | 874.956i | −0.578644 | − | 1.00224i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 318.841 | − | 679.646i | 0.364390 | − | 0.776738i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −72.5325 | − | 125.630i | −0.0827053 | − | 0.143250i | 0.821706 | − | 0.569912i | \(-0.193023\pi\) |
−0.904411 | + | 0.426662i | \(0.859689\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 575.139 | + | 332.057i | 0.654311 | + | 0.377766i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −360.233 | −0.408891 | −0.204445 | − | 0.978878i | \(-0.565539\pi\) | ||||
−0.204445 | + | 0.978878i | \(0.565539\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 145.555i | 0.164841i | 0.996598 | + | 0.0824205i | \(0.0262650\pi\) | ||||
−0.996598 | + | 0.0824205i | \(0.973735\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 87.1743 | − | 150.990i | 0.0985020 | − | 0.170610i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1149.57 | + | 663.707i | −1.29603 | + | 0.748261i | −0.979715 | − | 0.200395i | \(-0.935777\pi\) |
−0.316310 | + | 0.948656i | \(0.602444\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1234.16 | − | 578.980i | −1.38826 | − | 0.651271i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −592.071 | + | 341.833i | −0.664502 | + | 0.383650i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 877.051 | − | 1519.10i | 0.982140 | − | 1.70112i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 300.323i | 0.335556i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −518.140 | −0.577637 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 961.816 | + | 555.305i | 1.06987 | + | 0.617692i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 537.942 | + | 931.743i | 0.597050 | + | 1.03412i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 952.212 | + | 1366.62i | 1.05450 | + | 1.51342i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −160.101 | − | 277.303i | −0.176907 | − | 0.306412i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 392.834 | + | 226.803i | 0.433114 | + | 0.250058i | 0.700672 | − | 0.713483i | \(-0.252884\pi\) |
−0.267558 | + | 0.963542i | \(0.586217\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 664.910 | 0.731475 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 891.300i | − | 0.978376i | −0.872178 | − | 0.489188i | \(-0.837293\pi\) | ||
0.872178 | − | 0.489188i | \(-0.162707\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 375.523 | − | 650.425i | 0.411307 | − | 0.712404i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −754.605 | + | 435.671i | −0.824704 | + | 0.476143i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.7912 | − | 208.921i | −0.0194015 | − | 0.227831i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1405.23 | − | 811.309i | 1.52909 | − | 0.882818i | 0.529685 | − | 0.848195i | \(-0.322310\pi\) |
0.999400 | − | 0.0346230i | \(-0.0110230\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1133.08 | − | 1962.55i | 1.23027 | − | 2.13089i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 101.485i | 0.109951i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 416.203 | 0.449949 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −33.7752 | − | 19.5001i | −0.0364350 | − | 0.0210357i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −255.412 | − | 442.387i | −0.274932 | − | 0.476197i | 0.695186 | − | 0.718830i | \(-0.255322\pi\) |
−0.970118 | + | 0.242634i | \(0.921989\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1216.29 | + | 449.078i | 1.30643 | + | 0.482361i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −657.516 | − | 1138.85i | −0.704734 | − | 1.22063i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 231.914 | + | 133.895i | 0.248036 | + | 0.143204i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 898.415 | 0.958820 | 0.479410 | − | 0.877591i | \(-0.340851\pi\) | ||||
0.479410 | + | 0.877591i | \(0.340851\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 413.155i | − | 0.439995i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −853.746 | + | 1478.73i | −0.907276 | + | 1.57145i | −0.0894429 | + | 0.995992i | \(0.528509\pi\) |
−0.817833 | + | 0.575456i | \(0.804825\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −756.043 | + | 436.501i | −0.801742 | + | 0.462886i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.17966 | + | 107.797i | 0.00971393 | + | 0.114070i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1211.13 | − | 699.247i | 1.27891 | − | 0.738381i | 0.302265 | − | 0.953224i | \(-0.402257\pi\) |
0.976649 | + | 0.214843i | \(0.0689238\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 284.902 | − | 493.465i | 0.300213 | − | 0.519984i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2222.26i | 2.33677i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −99.5631 | −0.104473 | −0.0522367 | − | 0.998635i | \(-0.516635\pi\) | ||||
−0.0522367 | + | 0.998635i | \(0.516635\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −364.488 | − | 210.437i | −0.381662 | − | 0.220353i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −778.913 | − | 1349.12i | −0.813912 | − | 1.40974i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 711.638 | + | 1021.35i | 0.742063 | + | 1.06501i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −253.103 | − | 438.387i | −0.263375 | − | 0.456178i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 96.8345 | + | 55.9074i | 0.100555 | + | 0.0580555i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −485.407 | −0.503012 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 272.789i | − | 0.282099i | −0.990003 | − | 0.141049i | \(-0.954952\pi\) | ||
0.990003 | − | 0.141049i | \(-0.0450476\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −799.977 | + | 1385.60i | −0.825569 | + | 1.42993i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1039.50 | + | 600.155i | −1.07055 | + | 0.618080i | −0.928330 | − | 0.371756i | \(-0.878756\pi\) |
−0.142215 | + | 0.989836i | \(0.545422\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −761.378 | − | 357.184i | −0.782506 | − | 0.367095i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 573.877 | − | 331.328i | 0.588592 | − | 0.339824i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −269.972 | + | 467.606i | −0.276328 | + | 0.478614i | −0.970469 | − | 0.241225i | \(-0.922451\pi\) |
0.694141 | + | 0.719839i | \(0.255784\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 343.648i | 0.351019i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 54.6473 | 0.0557057 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 487.338 | + | 281.365i | 0.495766 | + | 0.286231i | 0.726963 | − | 0.686676i | \(-0.240931\pi\) |
−0.231197 | + | 0.972907i | \(0.574264\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.4428 | − | 19.8194i | −0.0116170 | − | 0.0201213i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 798.945 | − | 1703.04i | 0.809468 | − | 1.72547i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 437.878 | + | 758.427i | 0.442748 | + | 0.766862i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −424.335 | − | 244.990i | −0.428189 | − | 0.247215i | 0.270386 | − | 0.962752i | \(-0.412849\pi\) |
−0.698575 | + | 0.715537i | \(0.746182\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −659.561 | −0.664210 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 749.370i | 0.753135i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 832.723 | − | 1442.32i | 0.835229 | − | 1.44666i | −0.0586148 | − | 0.998281i | \(-0.518668\pi\) |
0.893844 | − | 0.448378i | \(-0.147998\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −120.001 | + | 69.2826i | −0.120121 | + | 0.0693519i |
(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 | 224.3.r.c.95.2 | ✓ | 12 | |
4.3 | odd | 2 | inner | 224.3.r.c.95.5 | yes | 12 | |
7.2 | even | 3 | inner | 224.3.r.c.191.5 | yes | 12 | |
7.3 | odd | 6 | 1568.3.d.k.1471.2 | 6 | |||
7.4 | even | 3 | 1568.3.d.j.1471.5 | 6 | |||
8.3 | odd | 2 | 448.3.r.g.319.2 | 12 | |||
8.5 | even | 2 | 448.3.r.g.319.5 | 12 | |||
28.3 | even | 6 | 1568.3.d.k.1471.5 | 6 | |||
28.11 | odd | 6 | 1568.3.d.j.1471.2 | 6 | |||
28.23 | odd | 6 | inner | 224.3.r.c.191.2 | yes | 12 | |
56.37 | even | 6 | 448.3.r.g.191.2 | 12 | |||
56.51 | odd | 6 | 448.3.r.g.191.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.r.c.95.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
224.3.r.c.95.5 | yes | 12 | 4.3 | odd | 2 | inner | |
224.3.r.c.191.2 | yes | 12 | 28.23 | odd | 6 | inner | |
224.3.r.c.191.5 | yes | 12 | 7.2 | even | 3 | inner | |
448.3.r.g.191.2 | 12 | 56.37 | even | 6 | |||
448.3.r.g.191.5 | 12 | 56.51 | odd | 6 | |||
448.3.r.g.319.2 | 12 | 8.3 | odd | 2 | |||
448.3.r.g.319.5 | 12 | 8.5 | even | 2 | |||
1568.3.d.j.1471.2 | 6 | 28.11 | odd | 6 | |||
1568.3.d.j.1471.5 | 6 | 7.4 | even | 3 | |||
1568.3.d.k.1471.2 | 6 | 7.3 | odd | 6 | |||
1568.3.d.k.1471.5 | 6 | 28.3 | even | 6 |