Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(353,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.353");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.m (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: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 653.9 | ||
Character | \(\chi\) | \(=\) | 684.653 |
Dual form | 684.3.m.a.353.9 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | −2.38029 | − | 1.82598i | −0.793431 | − | 0.608660i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 5.89395i | − | 1.17879i | −0.807845 | − | 0.589395i | \(-0.799366\pi\) | ||
0.807845 | − | 0.589395i | \(-0.200634\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.351537 | − | 0.608880i | −0.0502196 | − | 0.0869828i | 0.839823 | − | 0.542861i | \(-0.182659\pi\) |
−0.890042 | + | 0.455878i | \(0.849325\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.33159 | + | 8.69274i | 0.259066 | + | 0.965860i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.3415 | − | 8.85744i | 1.39468 | − | 0.805222i | 0.400856 | − | 0.916141i | \(-0.368713\pi\) |
0.993829 | + | 0.110920i | \(0.0353796\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.81809 | + | 13.5413i | 0.601391 | + | 1.04164i | 0.992611 | + | 0.121343i | \(0.0387201\pi\) |
−0.391219 | + | 0.920298i | \(0.627947\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.7622 | + | 14.0293i | −0.717483 | + | 0.935289i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 19.3842 | − | 11.1915i | 1.14025 | − | 0.658322i | 0.193755 | − | 0.981050i | \(-0.437933\pi\) |
0.946492 | + | 0.322728i | \(0.104600\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 18.0937 | + | 5.79811i | 0.952300 | + | 0.305164i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.275041 | + | 2.09121i | −0.0130972 | + | 0.0995815i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.81046 | − | 1.62262i | 0.122194 | − | 0.0705487i | −0.437657 | − | 0.899142i | \(-0.644192\pi\) |
0.559851 | + | 0.828593i | \(0.310858\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.73867 | −0.389547 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.3229 | − | 24.9487i | 0.382329 | − | 0.924026i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.47447i | − | 0.257740i | −0.991661 | − | 0.128870i | \(-0.958865\pi\) | ||
0.991661 | − | 0.128870i | \(-0.0411351\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.28250 | − | 7.41751i | 0.138145 | − | 0.239275i | −0.788649 | − | 0.614843i | \(-0.789219\pi\) |
0.926795 | + | 0.375569i | \(0.122553\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −52.6909 | − | 6.93003i | −1.59669 | − | 0.210001i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.58871 | + | 2.07194i | −0.102535 | + | 0.0591983i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −37.7752 | −1.02095 | −0.510476 | − | 0.859892i | \(-0.670531\pi\) | ||||
−0.510476 | + | 0.859892i | \(0.670531\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.11685 | − | 46.5080i | 0.156842 | − | 1.19251i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 52.3411i | 1.27661i | 0.769783 | + | 0.638306i | \(0.220364\pi\) | ||||
−0.769783 | + | 0.638306i | \(0.779636\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.07286 | + | 5.32236i | −0.0714620 | + | 0.123776i | −0.899542 | − | 0.436834i | \(-0.856100\pi\) |
0.828080 | + | 0.560610i | \(0.189433\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 51.2346 | − | 13.7423i | 1.13855 | − | 0.305384i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 71.9825i | − | 1.53154i | −0.643113 | − | 0.765771i | \(-0.722358\pi\) | ||
0.643113 | − | 0.765771i | \(-0.277642\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 24.2528 | − | 42.0072i | 0.494956 | − | 0.857289i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −66.5755 | − | 8.75617i | −1.30540 | − | 0.171690i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −20.4757 | − | 11.8217i | −0.386334 | − | 0.223050i | 0.294236 | − | 0.955733i | \(-0.404935\pi\) |
−0.680571 | + | 0.732682i | \(0.738268\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −52.2053 | − | 90.4223i | −0.949188 | − | 1.64404i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −32.4811 | − | 46.8399i | −0.569843 | − | 0.821753i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 54.8968i | 0.930454i | 0.885192 | + | 0.465227i | \(0.154027\pi\) | ||||
−0.885192 | + | 0.465227i | \(0.845973\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −69.6850 | −1.14238 | −0.571189 | − | 0.820819i | \(-0.693518\pi\) | ||||
−0.571189 | + | 0.820819i | \(0.693518\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.47319 | − | 4.47548i | 0.0710030 | − | 0.0710393i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 79.8119 | − | 46.0794i | 1.22788 | − | 0.708915i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 51.2608 | + | 88.7864i | 0.765087 | + | 1.32517i | 0.940201 | + | 0.340621i | \(0.110637\pi\) |
−0.175114 | + | 0.984548i | \(0.556029\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.65260 | − | 1.26953i | −0.139893 | − | 0.0183990i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.22572 | + | 4.17177i | −0.101771 | + | 0.0587573i | −0.550021 | − | 0.835151i | \(-0.685380\pi\) |
0.448251 | + | 0.893908i | \(0.352047\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −39.6816 | − | 68.7305i | −0.543583 | − | 0.941513i | −0.998695 | − | 0.0510789i | \(-0.983734\pi\) |
0.455112 | − | 0.890434i | \(-0.349599\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 23.1809 | + | 17.7826i | 0.309079 | + | 0.237102i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.7862 | − | 6.22743i | −0.140081 | − | 0.0808758i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 58.3917 | − | 101.137i | 0.739136 | − | 1.28022i | −0.213749 | − | 0.976889i | \(-0.568567\pi\) |
0.952885 | − | 0.303332i | \(-0.0980992\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −70.1273 | + | 40.5359i | −0.865770 | + | 0.500443i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 86.3290 | − | 49.8421i | 1.04011 | − | 0.600507i | 0.120244 | − | 0.992744i | \(-0.461632\pi\) |
0.919864 | + | 0.392238i | \(0.128299\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −65.9620 | − | 114.250i | −0.776023 | − | 1.34411i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13.6482 | + | 17.7914i | −0.156876 | + | 0.204499i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.82896 | + | 2.78800i | 0.0542580 | + | 0.0313259i | 0.526884 | − | 0.849937i | \(-0.323360\pi\) |
−0.472626 | + | 0.881263i | \(0.656694\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.49669 | − | 9.52055i | 0.0604032 | − | 0.104621i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −23.7378 | + | 9.83609i | −0.255246 | + | 0.105764i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 34.1738 | − | 106.643i | 0.359724 | − | 1.12256i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −52.8639 | + | 91.5630i | −0.544989 | + | 0.943948i | 0.453619 | + | 0.891196i | \(0.350133\pi\) |
−0.998608 | + | 0.0527524i | \(0.983201\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 112.766 | + | 112.708i | 1.13905 | + | 1.13846i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 116.203i | 1.15053i | 0.817969 | + | 0.575263i | \(0.195100\pi\) | ||||
−0.817969 | + | 0.575263i | \(0.804900\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 42.8692 | − | 74.2516i | 0.416205 | − | 0.720889i | −0.579349 | − | 0.815080i | \(-0.696693\pi\) |
0.995554 | + | 0.0941908i | \(0.0300264\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.3255 | + | 1.62108i | 0.117386 | + | 0.0154389i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 197.729i | − | 1.84794i | −0.382467 | − | 0.923969i | \(-0.624925\pi\) | ||
0.382467 | − | 0.923969i | \(-0.375075\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −30.6364 | − | 53.0638i | −0.281068 | − | 0.486824i | 0.690580 | − | 0.723256i | \(-0.257355\pi\) |
−0.971648 | + | 0.236432i | \(0.924022\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 89.9161 | + | 68.9768i | 0.810055 | + | 0.621412i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.7705 | + | 8.52775i | 0.130712 | + | 0.0754668i | 0.563930 | − | 0.825822i | \(-0.309289\pi\) |
−0.433218 | + | 0.901289i | \(0.642622\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.56365 | − | 16.5647i | −0.0831622 | − | 0.144041i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −99.4826 | + | 99.5335i | −0.850279 | + | 0.850713i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.6285 | − | 7.86843i | −0.114525 | − | 0.0661213i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 96.4084 | − | 166.984i | 0.796764 | − | 1.38004i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 95.5737 | − | 124.587i | 0.777022 | − | 1.01290i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 89.9495i | − | 0.719596i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.0431 | + | 22.5913i | −0.102702 | + | 0.177885i | −0.912797 | − | 0.408414i | \(-0.866082\pi\) |
0.810095 | + | 0.586298i | \(0.199415\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.0328 | − | 7.05778i | 0.132038 | − | 0.0547115i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 47.2412i | 0.360619i | 0.983610 | + | 0.180310i | \(0.0577100\pi\) | ||||
−0.983610 | + | 0.180310i | \(0.942290\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.83025 | − | 13.0551i | −0.0212801 | − | 0.0981589i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −147.046 | − | 60.8426i | −1.08923 | − | 0.450686i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 199.989i | 1.45977i | 0.683568 | + | 0.729887i | \(0.260427\pi\) | ||||
−0.683568 | + | 0.729887i | \(0.739573\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 26.1789 | + | 45.3431i | 0.188337 | + | 0.326210i | 0.944696 | − | 0.327947i | \(-0.106357\pi\) |
−0.756359 | + | 0.654157i | \(0.773024\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −131.439 | + | 171.339i | −0.932188 | + | 1.21517i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 239.883 | + | 138.496i | 1.67750 | + | 0.968507i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −44.0542 | −0.303822 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −134.433 | + | 55.7042i | −0.914511 | + | 0.378940i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 95.0740i | 0.638081i | 0.947741 | + | 0.319040i | \(0.103361\pi\) | ||||
−0.947741 | + | 0.319040i | \(0.896639\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.7076 | − | 30.6705i | −0.117269 | − | 0.203116i | 0.801416 | − | 0.598108i | \(-0.204081\pi\) |
−0.918684 | + | 0.394992i | \(0.870747\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 142.481 | + | 142.408i | 0.931245 | + | 0.930770i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −43.7185 | − | 25.2409i | −0.282055 | − | 0.162844i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 52.3742 | 0.333593 | 0.166797 | − | 0.985991i | \(-0.446658\pi\) | ||||
0.166797 | + | 0.985991i | \(0.446658\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 27.1521 | + | 65.5273i | 0.170768 | + | 0.412121i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.97596 | − | 1.14082i | −0.0122731 | − | 0.00708585i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −263.493 | −1.61652 | −0.808261 | − | 0.588824i | \(-0.799591\pi\) | ||||
−0.808261 | + | 0.588824i | \(0.799591\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −40.8453 | + | 310.557i | −0.247547 | + | 1.88217i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −225.097 | + | 129.960i | −1.34789 | + | 0.778202i | −0.987950 | − | 0.154775i | \(-0.950535\pi\) |
−0.359936 | + | 0.932977i | \(0.617201\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −37.7450 | + | 65.3763i | −0.223343 | + | 0.386842i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.21430 | + | 170.803i | −0.0480369 | + | 0.998846i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 45.1264 | + | 26.0537i | 0.260846 | + | 0.150600i | 0.624721 | − | 0.780848i | \(-0.285213\pi\) |
−0.363874 | + | 0.931448i | \(0.618546\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.42350 | + | 5.92968i | 0.0195629 | + | 0.0338839i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 100.240 | − | 130.670i | 0.566330 | − | 0.738251i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 173.576i | − | 0.969697i | −0.874598 | − | 0.484849i | \(-0.838875\pi\) | ||
0.874598 | − | 0.484849i | \(-0.161125\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −116.587 | + | 201.934i | −0.644125 | + | 1.11566i | 0.340378 | + | 0.940289i | \(0.389445\pi\) |
−0.984503 | + | 0.175369i | \(0.943888\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 165.871 | + | 127.243i | 0.906398 | + | 0.695320i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 222.645i | 1.20349i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 198.256 | − | 343.389i | 1.06019 | − | 1.83630i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −18.8196 | + | 2.48499i | −0.0995748 | + | 0.0131481i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 120.700 | − | 69.6861i | 0.631936 | − | 0.364849i | −0.149565 | − | 0.988752i | \(-0.547787\pi\) |
0.781502 | + | 0.623903i | \(0.214454\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −95.5330 | −0.494990 | −0.247495 | − | 0.968889i | \(-0.579607\pi\) | ||||
−0.247495 | + | 0.968889i | \(0.579607\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −274.116 | − | 36.0524i | −1.40572 | − | 0.184884i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 310.234i | 1.57479i | 0.616446 | + | 0.787397i | \(0.288572\pi\) | ||||
−0.616446 | + | 0.787397i | \(0.711428\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 119.255 | − | 206.556i | 0.599271 | − | 1.03797i | −0.393658 | − | 0.919257i | \(-0.628791\pi\) |
0.992929 | − | 0.118711i | \(-0.0378761\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 40.1063 | − | 304.939i | 0.199534 | − | 1.51711i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.55106 | + | 2.62755i | −0.0224190 | + | 0.0129436i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 308.496 | 1.50486 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.6579 | + | 20.6473i | 0.0997965 | + | 0.0997455i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 328.941 | − | 71.3119i | 1.57388 | − | 0.341205i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.65754 | −0.0410310 | −0.0205155 | − | 0.999790i | \(-0.506531\pi\) | ||||
−0.0205155 | + | 0.999790i | \(0.506531\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24.8169 | + | 3.26398i | 0.116511 | + | 0.0153238i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 31.3697 | + | 18.1113i | 0.145906 | + | 0.0842387i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.02183 | −0.0277504 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −31.0467 | + | 236.056i | −0.141766 | + | 1.07788i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 303.095 | + | 174.992i | 1.37147 | + | 0.791818i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 151.382 | − | 262.201i | 0.678842 | − | 1.17579i | −0.296488 | − | 0.955037i | \(-0.595815\pi\) |
0.975330 | − | 0.220753i | \(-0.0708513\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −22.7066 | − | 84.6557i | −0.100918 | − | 0.376248i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.6155 | − | 9.59297i | 0.0731961 | − | 0.0422598i | −0.462955 | − | 0.886382i | \(-0.653211\pi\) |
0.536151 | + | 0.844122i | \(0.319878\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −193.340 | + | 334.875i | −0.844281 | + | 1.46234i | 0.0419640 | + | 0.999119i | \(0.486639\pi\) |
−0.886245 | + | 0.463218i | \(0.846695\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.3032 | + | 34.5186i | 0.0619187 | + | 0.149431i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 284.002 | − | 163.969i | 1.21889 | − | 0.703728i | 0.254211 | − | 0.967149i | \(-0.418184\pi\) |
0.964681 | + | 0.263421i | \(0.0848508\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −424.261 | −1.80537 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −323.664 | + | 134.115i | −1.36567 | + | 0.565885i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 244.966 | + | 141.431i | 1.02496 | + | 0.591762i | 0.915538 | − | 0.402233i | \(-0.131766\pi\) |
0.109425 | + | 0.993995i | \(0.465099\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −237.088 | −0.983767 | −0.491884 | − | 0.870661i | \(-0.663691\pi\) | ||||
−0.491884 | + | 0.870661i | \(0.663691\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 240.941 | + | 31.5639i | 0.991528 | + | 0.129893i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −247.588 | − | 142.945i | −1.01056 | − | 0.583449i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 62.9440 | + | 290.343i | 0.254834 | + | 1.17548i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −296.499 | − | 38.9963i | −1.19076 | − | 0.156612i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 85.5177 | + | 49.3737i | 0.340708 | + | 0.196708i | 0.660585 | − | 0.750751i | \(-0.270308\pi\) |
−0.319877 | + | 0.947459i | \(0.603642\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.7445 | − | 49.7870i | 0.113615 | − | 0.196787i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −51.6085 | + | 392.393i | −0.202386 | + | 1.53879i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 129.972 | − | 75.0395i | 0.505728 | − | 0.291982i | −0.225348 | − | 0.974278i | \(-0.572352\pi\) |
0.731076 | + | 0.682296i | \(0.239018\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.2794 | + | 23.0006i | 0.0512717 | + | 0.0888053i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 64.9736 | − | 17.4274i | 0.248941 | − | 0.0667718i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −303.157 | − | 175.028i | −1.15269 | − | 0.665505i | −0.203148 | − | 0.979148i | \(-0.565117\pi\) |
−0.949541 | + | 0.313643i | \(0.898451\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −69.6763 | + | 120.683i | −0.262930 | + | 0.455407i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.40351 | − | 15.4539i | −0.0239832 | − | 0.0578796i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 86.7627 | − | 50.0925i | 0.322538 | − | 0.186217i | −0.329985 | − | 0.943986i | \(-0.607044\pi\) |
0.652523 | + | 0.757769i | \(0.273710\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 102.668 | + | 177.826i | 0.378849 | + | 0.656186i | 0.990895 | − | 0.134636i | \(-0.0429865\pi\) |
−0.612046 | + | 0.790822i | \(0.709653\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −30.4681 | + | 12.6249i | −0.111605 | + | 0.0462449i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −149.406 | + | 86.2597i | −0.543295 | + | 0.313672i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −111.754 | − | 193.564i | −0.403444 | − | 0.698786i | 0.590695 | − | 0.806895i | \(-0.298854\pi\) |
−0.994139 | + | 0.108109i | \(0.965520\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 74.4635 | + | 19.9320i | 0.266894 | + | 0.0714410i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 174.168i | 0.619817i | 0.950766 | + | 0.309908i | \(0.100298\pi\) | ||||
−0.950766 | + | 0.309908i | \(0.899702\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −421.632 | −1.48987 | −0.744933 | − | 0.667139i | \(-0.767519\pi\) | ||||
−0.744933 | + | 0.667139i | \(0.767519\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −276.072 | + | 191.442i | −0.968675 | + | 0.671726i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 31.8694 | − | 18.3998i | 0.111043 | − | 0.0641108i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 105.998 | − | 183.594i | 0.366775 | − | 0.635273i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 293.024 | − | 121.418i | 1.00695 | − | 0.417245i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −411.502 | − | 237.581i | −1.40444 | − | 0.810855i | −0.409598 | − | 0.912266i | \(-0.634331\pi\) |
−0.994845 | + | 0.101411i | \(0.967664\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 323.559 | 1.09681 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −62.6127 | − | 474.186i | −0.210817 | − | 1.59659i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 43.9449 | + | 25.3716i | 0.146973 | + | 0.0848548i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.32090 | 0.0143552 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 212.184 | − | 276.597i | 0.700279 | − | 0.912863i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 410.720i | 1.34662i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 112.818 | + | 195.406i | 0.367485 | + | 0.636503i | 0.989172 | − | 0.146763i | \(-0.0468856\pi\) |
−0.621687 | + | 0.783266i | \(0.713552\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −237.623 | + | 98.4623i | −0.769007 | + | 0.318648i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 239.811 | + | 138.455i | 0.771095 | + | 0.445192i | 0.833265 | − | 0.552874i | \(-0.186469\pi\) |
−0.0621700 | + | 0.998066i | \(0.519802\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −506.860 | −1.61936 | −0.809681 | − | 0.586870i | \(-0.800360\pi\) | ||||
−0.809681 | + | 0.586870i | \(0.800360\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −26.3783 | − | 26.3648i | −0.0837405 | − | 0.0836977i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 518.454i | − | 1.63550i | −0.575573 | − | 0.817750i | \(-0.695221\pi\) | ||
0.575573 | − | 0.817750i | \(-0.304779\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −66.2047 | − | 114.670i | −0.207538 | − | 0.359467i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −361.050 | + | 470.654i | −1.12477 | + | 1.46621i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 415.621 | − | 90.1034i | 1.28675 | − | 0.278958i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −76.1378 | − | 131.875i | −0.234270 | − | 0.405768i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23.9698 | + | 182.249i | −0.0733022 | + | 0.557336i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −43.8287 | + | 25.3045i | −0.133218 | + | 0.0769134i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 155.993 | + | 270.188i | 0.471278 | + | 0.816278i | 0.999460 | − | 0.0328536i | \(-0.0104595\pi\) |
−0.528182 | + | 0.849131i | \(0.677126\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −88.0764 | − | 328.370i | −0.264494 | − | 0.986096i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 523.303 | − | 302.129i | 1.56210 | − | 0.901877i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 523.845 | 1.55444 | 0.777218 | − | 0.629232i | \(-0.216630\pi\) | ||||
0.777218 | + | 0.629232i | \(0.216630\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.5866 | − | 47.2692i | −0.0577776 | − | 0.139437i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 151.728i | − | 0.444950i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −68.5537 | −0.199865 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.48257 | + | 56.8920i | −0.0216886 | + | 0.164904i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 297.721i | − | 0.857986i | −0.903308 | − | 0.428993i | \(-0.858868\pi\) | ||
0.903308 | − | 0.428993i | \(-0.141132\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −45.0994 | − | 78.1145i | −0.129225 | − | 0.223824i | 0.794152 | − | 0.607720i | \(-0.207916\pi\) |
−0.923376 | + | 0.383896i | \(0.874582\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 418.544 | − | 55.2656i | 1.19243 | − | 0.157452i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 360.529 | − | 208.152i | 1.02133 | − | 0.589665i | 0.106841 | − | 0.994276i | \(-0.465927\pi\) |
0.914489 | + | 0.404611i | \(0.132593\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.5882 | + | 42.5880i | 0.0692626 | + | 0.119966i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.0723 | + | 43.6146i | 0.0506226 | + | 0.122170i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 53.4979 | − | 30.8870i | 0.149019 | − | 0.0860362i | −0.423636 | − | 0.905832i | \(-0.639247\pi\) |
0.572656 | + | 0.819796i | \(0.305913\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 293.764 | + | 209.819i | 0.813750 | + | 0.581215i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −534.390 | + | 221.432i | −1.47215 | + | 0.610005i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −405.094 | + | 233.881i | −1.10985 | + | 0.640770i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −314.752 | −0.857635 | −0.428818 | − | 0.903391i | \(-0.641070\pi\) | ||||
−0.428818 | + | 0.903391i | \(0.641070\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −454.987 | + | 122.038i | −1.23303 | + | 0.330726i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.6230i | 0.0448060i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 83.5260 | − | 144.671i | 0.223930 | − | 0.387859i | −0.732068 | − | 0.681232i | \(-0.761445\pi\) |
0.955998 | + | 0.293373i | \(0.0947778\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −164.246 | + | 214.106i | −0.437989 | + | 0.570950i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 101.214 | − | 58.4361i | 0.268473 | − | 0.155003i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 61.9252 | 0.163391 | 0.0816955 | − | 0.996657i | \(-0.473967\pi\) | ||||
0.0816955 | + | 0.996657i | \(0.473967\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 72.2978 | − | 29.9575i | 0.189758 | − | 0.0786287i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 612.419i | 1.59900i | 0.600663 | + | 0.799502i | \(0.294903\pi\) | ||||
−0.600663 | + | 0.799502i | \(0.705097\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −36.7042 | + | 63.5735i | −0.0953356 | + | 0.165126i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −53.4305 | − | 14.3020i | −0.138063 | − | 0.0369561i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 90.5540i | 0.232787i | 0.993203 | + | 0.116393i | \(0.0371333\pi\) | ||||
−0.993203 | + | 0.116393i | \(0.962867\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.3190 | − | 62.9064i | 0.0928876 | − | 0.160886i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 86.2614 | − | 112.448i | 0.219495 | − | 0.286127i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −596.099 | − | 344.158i | −1.50911 | − | 0.871286i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.3966 | − | 40.5241i | −0.0589335 | − | 0.102076i | 0.835053 | − | 0.550169i | \(-0.185437\pi\) |
−0.893987 | + | 0.448093i | \(0.852103\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.1016 | + | 36.2430i | −0.0428611 | + | 0.0908347i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 157.389i | 0.392491i | 0.980555 | + | 0.196245i | \(0.0628749\pi\) | ||||
−0.980555 | + | 0.196245i | \(0.937125\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 133.924 | 0.332318 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 238.916 | + | 413.327i | 0.589917 | + | 1.02056i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −579.530 | + | 334.592i | −1.42391 | + | 0.822092i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 185.625 | + | 321.512i | 0.453851 | + | 0.786094i | 0.998621 | − | 0.0524919i | \(-0.0167164\pi\) |
−0.544770 | + | 0.838586i | \(0.683383\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 365.176 | − | 476.032i | 0.888506 | − | 1.15823i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 33.4255 | − | 19.2982i | 0.0809335 | − | 0.0467270i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −293.767 | − | 508.819i | −0.707872 | − | 1.22607i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.4823 | − | 155.732i | 0.0491181 | − | 0.373458i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −587.569 | − | 339.233i | −1.40231 | − | 0.809625i | −0.407682 | − | 0.913124i | \(-0.633663\pi\) |
−0.994630 | + | 0.103499i | \(0.966996\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 254.605 | − | 440.988i | 0.604761 | − | 1.04748i | −0.387328 | − | 0.921942i | \(-0.626602\pi\) |
0.992089 | − | 0.125535i | \(-0.0400648\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 625.725 | − | 167.834i | 1.47925 | − | 0.396770i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −188.776 | + | 108.990i | −0.444180 | + | 0.256447i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.4969 | + | 42.4298i | 0.0573697 | + | 0.0993673i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −318.100 | − | 767.684i | −0.741492 | − | 1.78947i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 399.240 | + | 230.501i | 0.926311 | + | 0.534806i | 0.885643 | − | 0.464367i | \(-0.153718\pi\) |
0.0406683 | + | 0.999173i | \(0.487051\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 369.211 | − | 639.492i | 0.852681 | − | 1.47689i | −0.0260989 | − | 0.999659i | \(-0.508308\pi\) |
0.878780 | − | 0.477227i | \(-0.158358\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 104.862 | + | 80.4421i | 0.241062 | + | 0.184924i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 60.2598 | − | 13.0638i | 0.137894 | − | 0.0298944i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −259.366 | + | 449.236i | −0.590812 | + | 1.02332i | 0.403312 | + | 0.915063i | \(0.367859\pi\) |
−0.994123 | + | 0.108253i | \(0.965474\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 421.705 | + | 112.880i | 0.956247 | + | 0.255964i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 147.886i | 0.333828i | 0.985971 | + | 0.166914i | \(0.0533802\pi\) | ||||
−0.985971 | + | 0.166914i | \(0.946620\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.4324 | − | 28.4617i | 0.0369266 | − | 0.0639588i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 173.603 | − | 226.304i | 0.388374 | − | 0.506273i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 134.495i | − | 0.299543i | −0.988721 | − | 0.149771i | \(-0.952146\pi\) | ||
0.988721 | − | 0.149771i | \(-0.0478538\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 463.608 | + | 802.992i | 1.02795 | + | 1.78047i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.8544 | + | 105.339i | −0.0305836 | + | 0.232535i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −56.1137 | − | 32.3973i | −0.123327 | − | 0.0712028i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −144.575 | − | 250.411i | −0.316356 | − | 0.547944i | 0.663369 | − | 0.748292i | \(-0.269126\pi\) |
−0.979725 | + | 0.200348i | \(0.935793\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −79.1118 | − | 599.139i | −0.172357 | − | 1.30531i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −397.301 | − | 229.382i | −0.861824 | − | 0.497574i | 0.00279853 | − | 0.999996i | \(-0.499109\pi\) |
−0.864623 | + | 0.502422i | \(0.832443\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.5817 | − | 37.3807i | 0.0466128 | − | 0.0807358i | −0.841778 | − | 0.539824i | \(-0.818491\pi\) |
0.888390 | + | 0.459089i | \(0.151824\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 57.9735 | + | 139.910i | 0.124674 | + | 0.300881i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 41.0873i | − | 0.0879814i | −0.999032 | − | 0.0439907i | \(-0.985993\pi\) | ||
0.999032 | − | 0.0439907i | \(-0.0140072\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.0402 | − | 62.4234i | 0.0768447 | − | 0.133099i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −124.666 | − | 95.6342i | −0.264683 | − | 0.203045i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 108.871i | 0.230171i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −176.209 | − | 56.4659i | −0.370966 | − | 0.118876i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 55.0216 | − | 205.553i | 0.115349 | − | 0.430930i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 901.802i | − | 1.88268i | −0.337465 | − | 0.941338i | \(-0.609570\pi\) | ||
0.337465 | − | 0.941338i | \(-0.390430\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −295.330 | − | 511.526i | −0.613992 | − | 1.06346i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.62025 | + | 6.32356i | 0.00542495 | + | 0.0130923i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 539.668 | + | 311.577i | 1.11272 | + | 0.642428i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.53975 | 0.0154820 | 0.00774102 | − | 0.999970i | \(-0.497536\pi\) | ||||
0.00774102 | + | 0.999970i | \(0.497536\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 627.191 | + | 481.133i | 1.28260 | + | 0.983913i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 672.915i | 1.37050i | 0.728309 | + | 0.685249i | \(0.240307\pi\) | ||||
−0.728309 | + | 0.685249i | \(0.759693\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −83.6504 | − | 144.887i | −0.169676 | − | 0.293888i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 664.295 | − | 664.635i | 1.34201 | − | 1.34270i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.08021 | + | 2.93306i | 0.0102218 | + | 0.00590153i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 835.632 | 1.67461 | 0.837307 | − | 0.546733i | \(-0.184129\pi\) | ||||
0.837307 | + | 0.546733i | \(0.184129\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 773.101 | + | 101.680i | 1.54311 | + | 0.202954i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −229.542 | − | 132.526i | −0.456347 | − | 0.263472i | 0.254160 | − | 0.967162i | \(-0.418201\pi\) |
−0.710507 | + | 0.703690i | \(0.751534\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 684.895 | 1.35623 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 209.220 | − | 86.6931i | 0.412663 | − | 0.170992i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −44.0537 | + | 25.4344i | −0.0865496 | + | 0.0499694i | −0.542650 | − | 0.839959i | \(-0.682579\pi\) |
0.456101 | + | 0.889928i | \(0.349246\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.8991 | + | 48.3226i | −0.0545970 | + | 0.0945648i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 331.435 | − | 391.561i | 0.646071 | − | 0.763277i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −437.635 | − | 252.669i | −0.849777 | − | 0.490619i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −637.580 | − | 1104.32i | −1.23323 | − | 2.13602i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −59.8405 | − | 144.415i | −0.115300 | − | 0.278257i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 775.621i | 1.48872i | 0.667781 | + | 0.744358i | \(0.267244\pi\) | ||||
−0.667781 | + | 0.744358i | \(0.732756\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −422.410 | + | 731.635i | −0.807667 | + | 1.39892i | 0.106808 | + | 0.994280i | \(0.465937\pi\) |
−0.914476 | + | 0.404641i | \(0.867396\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.67854 | − | 20.3656i | 0.00510198 | − | 0.0387917i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 191.710i | − | 0.363776i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −259.234 | + | 449.007i | −0.490046 | + | 0.848784i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −477.203 | + | 127.997i | −0.898688 | + | 0.241049i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −708.767 | + | 409.207i | −1.32977 | + | 0.767743i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1165.41 | −2.17833 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −316.946 | + | 413.161i | −0.590216 | + | 0.769388i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 859.272i | − | 1.59420i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 451.156 | − | 781.425i | 0.833929 | − | 1.44441i | −0.0609701 | − | 0.998140i | \(-0.519419\pi\) |
0.894899 | − | 0.446268i | \(-0.147247\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 646.238 | − | 267.777i | 1.19012 | − | 0.493144i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −312.755 | + | 180.569i | −0.573863 | + | 0.331320i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −184.656 | −0.337580 | −0.168790 | − | 0.985652i | \(-0.553986\pi\) | ||||
−0.168790 | + | 0.985652i | \(0.553986\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −162.477 | − | 605.754i | −0.295951 | − | 1.10338i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 43.3378 | − | 135.241i | 0.0786530 | − | 0.245446i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −82.1074 | −0.148476 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 406.546 | − | 529.961i | 0.732515 | − | 0.954885i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 218.277 | + | 126.022i | 0.391880 | + | 0.226252i | 0.682974 | − | 0.730442i | \(-0.260686\pi\) |
−0.291095 | + | 0.956694i | \(0.594019\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −96.0957 | −0.171906 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1098.93 | + | 455.355i | −1.95887 | + | 0.811685i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −561.132 | − | 323.970i | −0.996683 | − | 0.575435i | −0.0894175 | − | 0.995994i | \(-0.528501\pi\) |
−0.907265 | + | 0.420559i | \(0.861834\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 50.2622 | − | 87.0566i | 0.0889596 | − | 0.154083i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 49.3338 | + | 28.4493i | 0.0870085 | + | 0.0501751i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −154.886 | + | 89.4234i | −0.272207 | + | 0.157159i | −0.629890 | − | 0.776684i | \(-0.716900\pi\) |
0.357683 | + | 0.933843i | \(0.383567\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 291.759 | − | 505.342i | 0.510962 | − | 0.885012i | −0.488958 | − | 0.872308i | \(-0.662623\pi\) |
0.999919 | − | 0.0127040i | \(-0.00404393\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −414.546 | − | 54.5222i | −0.723467 | − | 0.0951521i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −27.3702 | + | 15.8022i | −0.0476003 | + | 0.0274821i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 536.087 | 0.929094 | 0.464547 | − | 0.885549i | \(-0.346217\pi\) | ||||
0.464547 | + | 0.885549i | \(0.346217\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 227.397 | + | 174.441i | 0.392740 | + | 0.301280i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −60.6957 | − | 35.0427i | −0.104468 | − | 0.0603144i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −418.839 | −0.718420 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 586.645 | + | 586.346i | 1.00281 | + | 1.00230i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −382.920 | − | 221.079i | −0.652334 | − | 0.376625i | 0.137016 | − | 0.990569i | \(-0.456249\pi\) |
−0.789350 | + | 0.613944i | \(0.789582\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 120.494 | − | 109.380i | 0.204574 | − | 0.185704i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 566.482 | − | 738.449i | 0.958514 | − | 1.24949i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −410.110 | − | 236.777i | −0.691585 | − | 0.399287i | 0.112621 | − | 0.993638i | \(-0.464076\pi\) |
−0.804205 | + | 0.594351i | \(0.797409\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −46.3762 | + | 80.3259i | −0.0779431 | + | 0.135001i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −661.028 | + | 273.906i | −1.10725 | + | 0.458804i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 774.211 | − | 446.991i | 1.29251 | − | 0.746228i | 0.313407 | − | 0.949619i | \(-0.398529\pi\) |
0.979098 | + | 0.203391i | \(0.0651961\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.3132 | + | 73.2886i | 0.0704047 | + | 0.121944i | 0.899079 | − | 0.437787i | \(-0.144238\pi\) |
−0.828674 | + | 0.559731i | \(0.810904\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −652.277 | + | 652.611i | −1.08172 | + | 1.08227i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −984.198 | − | 568.227i | −1.62677 | − | 0.939218i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −444.617 | + | 770.099i | −0.732483 | + | 1.26870i | 0.223336 | + | 0.974741i | \(0.428305\pi\) |
−0.955819 | + | 0.293956i | \(0.905028\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.6307 | + | 2.05579i | 0.0256662 | + | 0.00337568i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 974.738 | − | 562.765i | 1.59532 | − | 0.921056i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 329.622 | + | 570.923i | 0.537720 | + | 0.931359i | 0.999026 | + | 0.0441175i | \(0.0140476\pi\) |
−0.461306 | + | 0.887241i | \(0.652619\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −734.310 | − | 563.307i | −1.19400 | − | 0.915946i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −179.946 | + | 103.892i | −0.291646 | + | 0.168382i | −0.638684 | − | 0.769469i | \(-0.720521\pi\) |
0.347038 | + | 0.937851i | \(0.387188\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 403.579 | + | 699.019i | 0.651985 | + | 1.12927i | 0.982641 | + | 0.185520i | \(0.0593968\pi\) |
−0.330656 | + | 0.943751i | \(0.607270\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.4702 | − | 86.8675i | −0.0184706 | − | 0.139883i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 3.92034i | − | 0.00629269i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −773.625 | −1.23780 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −913.191 | − | 430.897i | −1.45645 | − | 0.687237i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −732.242 | + | 422.760i | −1.16414 | + | 0.672115i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −496.871 | + | 860.606i | −0.787435 | + | 1.36388i | 0.140099 | + | 0.990138i | \(0.455258\pi\) |
−0.927534 | + | 0.373740i | \(0.878075\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.6075 | + | 15.8085i | 0.0325553 | + | 0.0249739i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 133.152 | + | 76.8755i | 0.209689 | + | 0.121064i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 758.444 | 1.19065 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −53.1115 | − | 53.0844i | −0.0831166 | − | 0.0830741i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −751.727 | − | 434.010i | −1.17274 | − | 0.677083i | −0.218417 | − | 0.975855i | \(-0.570089\pi\) |
−0.954324 | + | 0.298773i | \(0.903423\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 209.372 | 0.325617 | 0.162808 | − | 0.986658i | \(-0.447945\pi\) | ||||
0.162808 | + | 0.986658i | \(0.447945\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −41.5982 | − | 100.391i | −0.0644934 | − | 0.155645i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 570.098i | − | 0.881140i | −0.897718 | − | 0.440570i | \(-0.854776\pi\) | ||
0.897718 | − | 0.440570i | \(-0.145224\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 486.245 | + | 842.201i | 0.749221 | + | 1.29769i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.3337 | + | 10.9957i | 0.0220180 | + | 0.0168905i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 343.712 | + | 198.442i | 0.526358 | + | 0.303893i | 0.739532 | − | 0.673121i | \(-0.235047\pi\) |
−0.213174 | + | 0.977014i | \(0.568380\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 278.437 | 0.425095 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 504.935 | − | 505.193i | 0.768546 | − | 0.768939i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 395.517i | 0.600178i | 0.953911 | + | 0.300089i | \(0.0970164\pi\) | ||||
−0.953911 | + | 0.300089i | \(0.902984\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 209.238 | + | 362.411i | 0.316548 | + | 0.548278i | 0.979765 | − | 0.200149i | \(-0.0641428\pi\) |
−0.663217 | + | 0.748427i | \(0.730809\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −401.923 | − | 969.977i | −0.606218 | − | 1.46301i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −76.9464 | + | 16.6814i | −0.115709 | + | 0.0250848i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.1282 | − | 21.0067i | −0.0181833 | − | 0.0314943i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −839.107 | + | 347.695i | −1.25427 | + | 0.519724i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1069.08 | + | 617.231i | −1.59326 | + | 0.919867i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 197.751 | + | 342.514i | 0.293835 | + | 0.508936i | 0.974713 | − | 0.223460i | \(-0.0717352\pi\) |
−0.680879 | + | 0.732396i | \(0.738402\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −100.531 | + | 242.967i | −0.148935 | + | 0.359952i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 592.263 | − | 341.943i | 0.874835 | − | 0.505086i | 0.00588308 | − | 0.999983i | \(-0.498127\pi\) |
0.868952 | + | 0.494896i | \(0.164794\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 74.3345 | 0.109476 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −57.0664 | − | 7.50551i | −0.0837979 | − | 0.0110213i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 692.506i | 1.01392i | 0.861970 | + | 0.506959i | \(0.169230\pi\) | ||||
−0.861970 | + | 0.506959i | \(0.830770\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1178.73 | 1.72077 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1071.68 | − | 444.066i | 1.55994 | − | 0.646384i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 369.691i | − | 0.536562i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 672.752 | + | 1165.24i | 0.973591 | + | 1.68631i | 0.684507 | + | 0.729006i | \(0.260017\pi\) |
0.289084 | + | 0.957304i | \(0.406649\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 28.9843 | − | 108.282i | 0.0418244 | − | 0.156251i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 267.250 | − | 154.297i | 0.384533 | − | 0.222010i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 585.773 | + | 1014.59i | 0.840421 | + | 1.45565i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −975.411 | − | 128.289i | −1.39544 | − | 0.183531i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −208.828 | + | 120.567i | −0.297900 | + | 0.171993i | −0.641499 | − | 0.767124i | \(-0.721687\pi\) |
0.343599 | + | 0.939116i | \(0.388354\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −683.493 | − | 219.025i | −0.972252 | − | 0.311557i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1009.87 | + | 774.693i | 1.43243 | + | 1.09885i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 70.7537 | − | 40.8497i | 0.100076 | − | 0.0577789i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 238.357 | 0.336187 | 0.168093 | − | 0.985771i | \(-0.446239\pi\) | ||||
0.168093 | + | 0.985771i | \(0.446239\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1015.31 | + | 271.773i | 1.42800 | + | 0.382240i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 27.7955i | − | 0.0389839i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 816.292 | − | 1413.86i | 1.14167 | − | 1.97742i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −324.841 | − | 783.951i | −0.453055 | − | 1.09338i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 101.612 | − | 58.6655i | 0.141324 | − | 0.0815933i | −0.427671 | − | 0.903934i | \(-0.640666\pi\) |
0.568995 | + | 0.822341i | \(0.307332\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −60.2804 | −0.0836066 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 564.339 | + | 432.918i | 0.780551 | + | 0.598780i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 72.7915i | 0.100402i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −123.015 | + | 213.068i | −0.169209 | + | 0.293078i | −0.938142 | − | 0.346251i | \(-0.887455\pi\) |
0.768933 | + | 0.639329i | \(0.220788\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −515.876 | − | 515.085i | −0.707649 | − | 0.706564i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 137.559i | 0.188180i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −573.658 | + | 993.605i | −0.782617 | + | 1.35553i | 0.147796 | + | 0.989018i | \(0.452782\pi\) |
−0.930412 | + | 0.366514i | \(0.880551\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 328.318 | + | 792.342i | 0.446691 | + | 1.07802i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1572.84 | + | 908.079i | 2.13411 | + | 1.23213i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −331.543 | − | 574.249i | −0.448637 | − | 0.777062i | 0.549661 | − | 0.835388i | \(-0.314757\pi\) |
−0.998298 | + | 0.0583262i | \(0.981424\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 380.335 | − | 806.036i | 0.513273 | − | 1.08777i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 895.276i | − | 1.20495i | −0.798139 | − | 0.602474i | \(-0.794182\pi\) | ||
0.798139 | − | 0.602474i | \(-0.205818\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 560.362 | 0.752163 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 634.548 | + | 634.224i | 0.849462 | + | 0.849028i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −120.393 | + | 69.5092i | −0.160739 | + | 0.0928027i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 659.782 | + | 1142.78i | 0.878538 | + | 1.52167i | 0.852946 | + | 0.522000i | \(0.174814\pi\) |
0.0255919 | + | 0.999672i | \(0.491853\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −113.402 | − | 273.677i | −0.150600 | − | 0.363449i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −180.770 | + | 104.368i | −0.239431 | + | 0.138236i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 571.887 | + | 990.537i | 0.755465 | + | 1.30850i | 0.945143 | + | 0.326657i | \(0.105922\pi\) |
−0.189678 | + | 0.981846i | \(0.560744\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −159.330 | + | 66.0207i | −0.209922 | + | 0.0869838i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 228.476 | + | 131.910i | 0.300231 | + | 0.173338i | 0.642547 | − | 0.766247i | \(-0.277878\pi\) |
−0.342316 | + | 0.939585i | \(0.611211\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.5396 | + | 37.3078i | −0.0282302 | + | 0.0488961i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 839.344 | − | 839.774i | 1.09718 | − | 1.09774i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −743.375 | + | 429.188i | −0.969198 | + | 0.559567i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 197.800 | + | 342.599i | 0.257217 | + | 0.445512i | 0.965495 | − | 0.260421i | \(-0.0838613\pi\) |
−0.708279 | + | 0.705933i | \(0.750528\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −446.393 | − | 58.7107i | −0.578979 | − | 0.0761487i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1281.12 | + | 739.656i | 1.65734 | + | 0.956864i | 0.973937 | + | 0.226820i | \(0.0728330\pi\) |
0.683400 | + | 0.730044i | \(0.260500\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −41.7059 | + | 72.2367i | −0.0538141 | + | 0.0932087i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.3897 | − | 78.9960i | 0.0133716 | − | 0.101668i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −303.479 | + | 947.043i | −0.389575 | + | 1.21572i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −73.9024 | + | 128.003i | −0.0946253 | + | 0.163896i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −186.478 | − | 77.1582i | −0.238159 | − | 0.0985417i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 308.691i | − | 0.393237i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −454.543 | + | 787.291i | −0.577564 | + | 1.00037i | 0.418194 | + | 0.908358i | \(0.362663\pi\) |
−0.995758 | + | 0.0920122i | \(0.970670\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 402.006 | + | 970.177i | 0.509513 | + | 1.22963i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 11.9913i | − | 0.0151596i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −544.804 | − | 943.628i | −0.687016 | − | 1.18995i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 386.215 | − | 160.033i | 0.485805 | − | 0.201300i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 196.814 | + | 113.631i | 0.246944 | + | 0.142573i | 0.618364 | − | 0.785892i | \(-0.287796\pi\) |
−0.371420 | + | 0.928465i | \(0.621129\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −805.590 | − | 1395.32i | −1.00825 | − | 1.74634i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.9762 | + | 48.4774i | −0.0162000 | + | 0.0605211i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1217.55 | − | 702.954i | −1.51625 | − | 0.875410i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.72395 | + | 11.6462i | −0.00835274 | + | 0.0144674i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −297.988 | − | 39.1922i | −0.369255 | − | 0.0485653i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1244.41i | 1.53820i | 0.639127 | + | 0.769101i | \(0.279296\pi\) | ||||
−0.639127 | + | 0.769101i | \(0.720704\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −668.064 | + | 1157.12i | −0.823753 | + | 1.42678i | 0.0791151 | + | 0.996865i | \(0.474791\pi\) |
−0.902868 | + | 0.429917i | \(0.858543\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 80.3272 | − | 610.749i | 0.0988035 | − | 0.751229i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1553.02i | 1.90554i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −86.4591 | + | 78.4843i | −0.105825 | + | 0.0960640i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 95.5757 | + | 25.5833i | 0.116698 | + | 0.0312372i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1101.94i | 1.34219i | 0.741373 | + | 0.671094i | \(0.234175\pi\) | ||||
−0.741373 | + | 0.671094i | \(0.765825\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 125.920 | + | 218.099i | 0.153001 | + | 0.265005i | 0.932329 | − | 0.361610i | \(-0.117773\pi\) |
−0.779328 | + | 0.626616i | \(0.784440\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 513.139 | + | 67.4893i | 0.621987 | + | 0.0818052i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −152.841 | − | 88.2427i | −0.184814 | − | 0.106702i | 0.404739 | − | 0.914432i | \(-0.367362\pi\) |
−0.589552 | + | 0.807730i | \(0.700696\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1408.64 | −1.69920 | −0.849602 | − | 0.527424i | \(-0.823158\pi\) | ||||
−0.849602 | + | 0.527424i | \(0.823158\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −87.4360 | + | 664.799i | −0.105218 | + | 0.799999i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1085.70i | − | 1.30336i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 765.977 | + | 1326.71i | 0.917337 | + | 1.58887i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −140.850 | − | 183.413i | −0.168279 | − | 0.219132i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −151.349 | − | 87.3816i | −0.180393 | − | 0.104150i | 0.407084 | − | 0.913391i | \(-0.366545\pi\) |
−0.587477 | + | 0.809241i | \(0.699879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 785.132 | 0.933570 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 318.028 | − | 414.572i | 0.377258 | − | 0.491782i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 385.325 | + | 222.467i | 0.456006 | + | 0.263275i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −135.565 | −0.160053 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1003.61 | + | 769.892i | 1.18211 | + | 0.906822i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −106.166 | + | 61.2949i | −0.124754 | + | 0.0720269i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −336.670 | + | 583.130i | −0.394690 | + | 0.683622i | −0.993062 | − | 0.117596i | \(-0.962481\pi\) |
0.598372 | + | 0.801218i | \(0.295815\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1006.70 | + | 48.4147i | 1.17743 | + | 0.0566254i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 227.664 | + | 131.442i | 0.265652 | + | 0.153374i | 0.626910 | − | 0.779092i | \(-0.284319\pi\) |
−0.361258 | + | 0.932466i | \(0.617653\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −277.678 | − | 480.952i | −0.323257 | − | 0.559897i | 0.657901 | − | 0.753104i | \(-0.271444\pi\) |
−0.981158 | + | 0.193207i | \(0.938111\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −109.456 | − | 14.3960i | −0.127127 | − | 0.0167200i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 923.240i | 1.06980i | 0.844914 | + | 0.534902i | \(0.179651\pi\) | ||||
−0.844914 | + | 0.534902i | \(0.820349\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 153.559 | − | 265.973i | 0.177525 | − | 0.307483i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −587.545 | + | 243.457i | −0.677676 | + | 0.280804i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2068.80i | − | 2.38067i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −801.523 | + | 1388.28i | −0.920234 | + | 1.59389i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −919.190 | − | 246.044i | −1.05291 | − | 0.281838i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −54.7685 | + | 31.6206i | −0.0625925 | + | 0.0361378i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1178.10 | −1.34333 | −0.671666 | − | 0.740854i | \(-0.734421\pi\) | ||||
−0.671666 | + | 0.740854i | \(0.734421\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 545.677 | + | 1316.91i | 0.620793 | + | 1.49819i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 140.552i | 0.159537i | 0.996813 | + | 0.0797684i | \(0.0254181\pi\) | ||||
−0.996813 | + | 0.0797684i | \(0.974582\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 384.661 | − | 666.252i | 0.435629 | − | 0.754532i | −0.561717 | − | 0.827329i | \(-0.689859\pi\) |
0.997347 | + | 0.0727970i | \(0.0231925\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −770.165 | − | 590.812i | −0.870243 | − | 0.667584i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −773.195 | + | 446.405i | −0.871697 | + | 0.503275i | −0.867912 | − | 0.496718i | \(-0.834538\pi\) |
−0.00378525 | + | 0.999993i | \(0.501205\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.3405 | 0.0206305 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −716.817 | + | 1243.03i | −0.804509 | + | 1.39510i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 417.362 | − | 1302.43i | 0.467371 | − | 1.45849i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1023.05 | −1.14307 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −58.2737 | − | 140.634i | −0.0649651 | − | 0.156783i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −55.4420 | − | 32.0095i | −0.0616708 | − | 0.0356056i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −529.207 | −0.587355 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.2850 | − | 7.88988i | −0.0113898 | − | 0.00873741i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1190.19 | + | 687.156i | 1.31513 | + | 0.759288i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.4713 | − | 35.4573i | 0.0225703 | − | 0.0390929i | −0.854520 | − | 0.519419i | \(-0.826148\pi\) |
0.877090 | + | 0.480326i | \(0.159482\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1010.12 | + | 270.938i | −1.11125 | + | 0.298062i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 196.890 | − | 113.674i | 0.216125 | − | 0.124780i | −0.388030 | − | 0.921647i | \(-0.626844\pi\) |
0.604155 | + | 0.796867i | \(0.293511\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 882.946 | − | 1529.31i | 0.967082 | − | 1.67504i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 749.967 | − | 977.635i | 0.819636 | − | 1.06845i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.7642 | − | 16.6070i | 0.0313677 | − | 0.0181102i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −211.772 | −0.230438 | −0.115219 | − | 0.993340i | \(-0.536757\pi\) | ||||
−0.115219 | + | 0.993340i | \(0.536757\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 88.2684 | − | 671.128i | 0.0958397 | − | 0.728694i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −112.983 | − | 65.2305i | −0.122408 | − | 0.0706723i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 367.880 | 0.397709 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 745.403 | + | 199.526i | 0.804102 | + | 0.215238i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −139.817 | − | 80.7233i | −0.150502 | − | 0.0868926i | 0.422858 | − | 0.906196i | \(-0.361027\pi\) |
−0.573360 | + | 0.819304i | \(0.694360\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 682.386 | − | 619.444i | 0.732960 | − | 0.665354i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −318.004 | − | 767.452i | −0.340840 | − | 0.822564i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2023.92 | − | 1168.51i | −2.16462 | − | 1.24974i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 381.188 | − | 660.237i | 0.406817 | − | 0.704628i | −0.587714 | − | 0.809069i | \(-0.699972\pi\) |
0.994531 | + | 0.104441i | \(0.0333052\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1206.48 | + | 925.517i | 1.28485 | + | 0.985641i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1251.65 | + | 722.643i | −1.33013 | + | 0.767952i | −0.985320 | − | 0.170719i | \(-0.945391\pi\) |
−0.344813 | + | 0.938671i | \(0.612058\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 84.9297 | + | 147.103i | 0.0900633 | + | 0.155994i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.6464 | + | 110.922i | 0.0154989 | + | 0.117378i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 576.543 | + | 332.867i | 0.608810 | + | 0.351496i | 0.772499 | − | 0.635015i | \(-0.219006\pi\) |
−0.163690 | + | 0.986512i | \(0.552340\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 620.468 | − | 1074.68i | 0.653812 | − | 1.13244i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −946.686 | + | 1234.07i | −0.995464 | + | 1.29766i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 346.885 | − | 200.274i | 0.363992 | − | 0.210151i | −0.306838 | − | 0.951762i | \(-0.599271\pi\) |
0.670831 | + | 0.741611i | \(0.265938\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −410.726 | − | 711.399i | −0.430080 | − | 0.744920i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −51.7983 | + | 393.836i | −0.0541258 | + | 0.411532i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 121.769 | − | 70.3035i | 0.126975 | − | 0.0733092i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 443.820 | + | 768.719i | 0.461832 | + | 0.799916i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1718.81 | − | 461.025i | 1.78485 | − | 0.478738i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 563.067i | 0.583489i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.4178 | −0.0107733 | −0.00538664 | − | 0.999985i | \(-0.501715\pi\) | ||||
−0.00538664 | + | 0.999985i | \(0.501715\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1153.83 | − | 544.443i | −1.19074 | − | 0.561861i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −112.459 | + | 64.9283i | −0.115818 | + | 0.0668675i | −0.556790 | − | 0.830653i | \(-0.687967\pi\) |
0.440972 | + | 0.897521i | \(0.354634\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.4057 | − | 31.8796i | 0.0189164 | − | 0.0327642i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −59.5700 | + | 452.926i | −0.0610974 | + | 0.464540i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −509.607 | − | 294.222i | −0.521604 | − | 0.301148i | 0.215987 | − | 0.976396i | \(-0.430703\pi\) |
−0.737591 | + | 0.675248i | \(0.764037\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 98.7783 | 0.100897 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 389.838 | − | 390.037i | 0.397388 | − | 0.397591i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −706.945 | − | 408.155i | −0.719171 | − | 0.415213i | 0.0952766 | − | 0.995451i | \(-0.469626\pi\) |
−0.814447 | + | 0.580237i | \(0.802960\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1828.51 | 1.85635 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 150.531 | + | 19.7982i | 0.152513 | + | 0.0200589i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.9444i | 0.0201662i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.6772 | − | 41.0101i | −0.0238922 | − | 0.0413826i | 0.853832 | − | 0.520549i | \(-0.174273\pi\) |
−0.877724 | + | 0.479166i | \(0.840939\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 122.048 | − | 927.967i | 0.122909 | − | 0.934508i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1217.43 | − | 702.883i | −1.22355 | − | 0.706415i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1782.01 | −1.78737 | −0.893686 | − | 0.448693i | \(-0.851890\pi\) | ||||
−0.893686 | + | 0.448693i | \(0.851890\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −389.949 | + | 942.443i | −0.390340 | + | 0.943386i |
(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 | 684.3.m.a.653.9 | yes | 80 | |
3.2 | odd | 2 | 2052.3.m.a.881.35 | 80 | |||
9.2 | odd | 6 | 684.3.be.a.425.19 | yes | 80 | ||
9.7 | even | 3 | 2052.3.be.a.197.35 | 80 | |||
19.11 | even | 3 | 684.3.be.a.581.19 | yes | 80 | ||
57.11 | odd | 6 | 2052.3.be.a.125.35 | 80 | |||
171.11 | odd | 6 | inner | 684.3.m.a.353.9 | ✓ | 80 | |
171.106 | even | 3 | 2052.3.m.a.1493.6 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.m.a.353.9 | ✓ | 80 | 171.11 | odd | 6 | inner | |
684.3.m.a.653.9 | yes | 80 | 1.1 | even | 1 | trivial | |
684.3.be.a.425.19 | yes | 80 | 9.2 | odd | 6 | ||
684.3.be.a.581.19 | yes | 80 | 19.11 | even | 3 | ||
2052.3.m.a.881.35 | 80 | 3.2 | odd | 2 | |||
2052.3.m.a.1493.6 | 80 | 171.106 | even | 3 | |||
2052.3.be.a.125.35 | 80 | 57.11 | odd | 6 | |||
2052.3.be.a.197.35 | 80 | 9.7 | even | 3 |