Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(64,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.2593100598870016.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{10} + 9x^{8} - 16x^{6} + 36x^{4} - 64x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 195) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 64.1 | ||
Root | \(-1.37820 - 0.317122i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 585.64 |
Dual form | 585.2.h.g.64.2 |
$q$-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 \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.51912 | −1.78129 | −0.890643 | − | 0.454703i | \(-0.849745\pi\) | ||||
−0.890643 | + | 0.454703i | \(0.849745\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.34596 | 2.17298 | ||||||||
\(5\) | 1.45804 | − | 1.69532i | 0.652056 | − | 0.758171i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.26849 | −0.479443 | −0.239722 | − | 0.970842i | \(-0.577056\pi\) | ||||
−0.239722 | + | 0.970842i | \(0.577056\pi\) | |||||||
\(8\) | −5.90976 | −2.08942 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.67298 | + | 4.27072i | −1.16150 | + | 1.35052i | ||||
\(11\) | 2.12216i | 0.639854i | 0.947442 | + | 0.319927i | \(0.103658\pi\) | ||||
−0.947442 | + | 0.319927i | \(0.896342\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.15336 | + | 1.74823i | −0.874586 | + | 0.484871i | ||||
\(14\) | 3.19547 | 0.854025 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.19547 | 1.54887 | ||||||||
\(17\) | 7.19547i | 1.74516i | 0.488473 | + | 0.872579i | \(0.337554\pi\) | ||||
−0.488473 | + | 0.872579i | \(0.662446\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.51280i | 1.26472i | 0.774674 | + | 0.632361i | \(0.217914\pi\) | ||||
−0.774674 | + | 0.632361i | \(0.782086\pi\) | |||||||
\(20\) | 6.33660 | − | 7.36780i | 1.41691 | − | 1.64749i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 5.34596i | − | 1.13976i | ||||||
\(23\) | − | 4.00000i | − | 0.834058i | −0.908893 | − | 0.417029i | \(-0.863071\pi\) | ||
0.908893 | − | 0.417029i | \(-0.136929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.748228 | − | 4.94370i | −0.149646 | − | 0.988740i | ||||
\(26\) | 7.94370 | − | 4.40400i | 1.55789 | − | 0.863695i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.51280 | −1.04182 | ||||||||
\(29\) | −4.69193 | −0.871269 | −0.435634 | − | 0.900124i | \(-0.643476\pi\) | ||||
−0.435634 | + | 0.900124i | \(0.643476\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.97582i | 0.534474i | 0.963631 | + | 0.267237i | \(0.0861106\pi\) | ||||
−0.963631 | + | 0.267237i | \(0.913889\pi\) | |||||||
\(32\) | −3.78761 | −0.669561 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 18.1263i | − | 3.10863i | ||||||
\(35\) | −1.84951 | + | 2.15049i | −0.312624 | + | 0.363500i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.5510 | 1.73458 | 0.867290 | − | 0.497803i | \(-0.165860\pi\) | ||||
0.867290 | + | 0.497803i | \(0.165860\pi\) | |||||||
\(38\) | − | 13.8874i | − | 2.25283i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.61668 | + | 10.0189i | −1.36242 | + | 1.58413i | ||||
\(41\) | 0.853668i | 0.133321i | 0.997776 | + | 0.0666603i | \(0.0212344\pi\) | ||||
−0.997776 | + | 0.0666603i | \(0.978766\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.19547i | 0.487305i | 0.969863 | + | 0.243652i | \(0.0783456\pi\) | ||||
−0.969863 | + | 0.243652i | \(0.921654\pi\) | |||||||
\(44\) | 9.22281i | 1.39039i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.0765i | 1.48570i | ||||||||
\(47\) | 2.12216 | 0.309548 | 0.154774 | − | 0.987950i | \(-0.450535\pi\) | ||||
0.154774 | + | 0.987950i | \(0.450535\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.39094 | −0.770134 | ||||||||
\(50\) | 1.88488 | + | 12.4538i | 0.266562 | + | 1.76123i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −13.7044 | + | 7.59774i | −1.90046 | + | 1.05362i | ||||
\(53\) | 3.49646i | 0.480275i | 0.970739 | + | 0.240138i | \(0.0771926\pi\) | ||||
−0.970739 | + | 0.240138i | \(0.922807\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.59774 | + | 3.09419i | 0.485119 | + | 0.417221i | ||||
\(56\) | 7.49646 | 1.00176 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 11.8195 | 1.55198 | ||||||||
\(59\) | 8.90344i | 1.15913i | 0.814926 | + | 0.579565i | \(0.196777\pi\) | ||||
−0.814926 | + | 0.579565i | \(0.803223\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.8874 | 1.52203 | 0.761013 | − | 0.648737i | \(-0.224703\pi\) | ||||
0.761013 | + | 0.648737i | \(0.224703\pi\) | |||||||
\(62\) | − | 7.49646i | − | 0.952051i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.84951 | −0.356188 | ||||||||
\(65\) | −1.63393 | + | 7.89495i | −0.202664 | + | 0.979248i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.319369 | 0.0390172 | 0.0195086 | − | 0.999810i | \(-0.493790\pi\) | ||||
0.0195086 | + | 0.999810i | \(0.493790\pi\) | |||||||
\(68\) | 31.2713i | 3.79220i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.65913 | − | 5.41735i | 0.556872 | − | 0.647497i | ||||
\(71\) | 13.7865i | 1.63616i | 0.575108 | + | 0.818078i | \(0.304960\pi\) | ||||
−0.575108 | + | 0.818078i | \(0.695040\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.30673 | −0.738146 | −0.369073 | − | 0.929400i | \(-0.620325\pi\) | ||||
−0.369073 | + | 0.929400i | \(0.620325\pi\) | |||||||
\(74\) | −26.5793 | −3.08978 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 23.9584i | 2.74822i | ||||||||
\(77\) | − | 2.69193i | − | 0.306774i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.804530 | −0.0905167 | −0.0452583 | − | 0.998975i | \(-0.514411\pi\) | ||||
−0.0452583 | + | 0.998975i | \(0.514411\pi\) | |||||||
\(80\) | 9.03325 | − | 10.5033i | 1.00995 | − | 1.17431i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 2.15049i | − | 0.237482i | ||||||
\(83\) | 1.17304 | 0.128758 | 0.0643788 | − | 0.997926i | \(-0.479493\pi\) | ||||
0.0643788 | + | 0.997926i | \(0.479493\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.1986 | + | 10.4913i | 1.32313 | + | 1.13794i | ||||
\(86\) | − | 8.04977i | − | 0.868029i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 12.5414i | − | 1.33692i | ||||||
\(89\) | − | 7.63495i | − | 0.809303i | −0.914471 | − | 0.404652i | \(-0.867393\pi\) | ||
0.914471 | − | 0.404652i | \(-0.132607\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | − | 2.21760i | 0.419314 | − | 0.232468i | ||||
\(92\) | − | 17.3839i | − | 1.81239i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.34596 | −0.551394 | ||||||||
\(95\) | 9.34596 | + | 8.03789i | 0.958876 | + | 0.824670i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.35761 | −0.543983 | −0.271991 | − | 0.962300i | \(-0.587682\pi\) | ||||
−0.271991 | + | 0.962300i | \(0.587682\pi\) | |||||||
\(98\) | 13.5804 | 1.37183 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.25177 | − | 21.4851i | −0.325177 | − | 2.14851i | ||||
\(101\) | 8.39094 | 0.834930 | 0.417465 | − | 0.908693i | \(-0.362919\pi\) | ||||
0.417465 | + | 0.908693i | \(0.362919\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.1884i | 1.79215i | 0.443898 | + | 0.896077i | \(0.353595\pi\) | ||||
−0.443898 | + | 0.896077i | \(0.646405\pi\) | |||||||
\(104\) | 18.6356 | − | 10.3316i | 1.82737 | − | 1.01310i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 8.80799i | − | 0.855508i | ||||||
\(107\) | − | 0.300986i | − | 0.0290974i | −0.999894 | − | 0.0145487i | \(-0.995369\pi\) | ||
0.999894 | − | 0.0145487i | \(-0.00463116\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 13.3717i | − | 1.28077i | −0.768052 | − | 0.640387i | \(-0.778774\pi\) | ||
0.768052 | − | 0.640387i | \(-0.221226\pi\) | |||||||
\(110\) | −9.06313 | − | 7.79464i | −0.864135 | − | 0.743190i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.85887 | −0.742594 | ||||||||
\(113\) | − | 12.5793i | − | 1.18336i | −0.806172 | − | 0.591682i | \(-0.798464\pi\) | ||
0.806172 | − | 0.591682i | \(-0.201536\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.78128 | − | 5.83217i | −0.632358 | − | 0.543852i | ||||
\(116\) | −20.3909 | −1.89325 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 22.4288i | − | 2.06474i | ||||||
\(119\) | − | 9.12736i | − | 0.836704i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.49646 | 0.590587 | ||||||||
\(122\) | −29.9458 | −2.71116 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12.9328i | 1.16140i | ||||||||
\(125\) | −9.47210 | − | 5.93963i | −0.847211 | − | 0.531257i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.3909i | 1.63193i | 0.578100 | + | 0.815966i | \(0.303794\pi\) | ||||
−0.578100 | + | 0.815966i | \(0.696206\pi\) | |||||||
\(128\) | 14.7535 | 1.30403 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.11606 | − | 19.8883i | 0.361002 | − | 1.74432i | ||||
\(131\) | −17.3839 | −1.51883 | −0.759417 | − | 0.650604i | \(-0.774516\pi\) | ||||
−0.759417 | + | 0.650604i | \(0.774516\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 6.99291i | − | 0.606362i | ||||||
\(134\) | −0.804530 | −0.0695008 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 42.5235i | − | 3.64636i | ||||||
\(137\) | −5.45306 | −0.465886 | −0.232943 | − | 0.972490i | \(-0.574836\pi\) | ||||
−0.232943 | + | 0.972490i | \(0.574836\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.3839 | −1.47448 | −0.737240 | − | 0.675631i | \(-0.763871\pi\) | ||||
−0.737240 | + | 0.675631i | \(0.763871\pi\) | |||||||
\(140\) | −8.03789 | + | 9.34596i | −0.679326 | + | 0.789878i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 34.7298i | − | 2.91446i | ||||||
\(143\) | −3.71001 | − | 6.69193i | −0.310247 | − | 0.559607i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.84103 | + | 7.95432i | −0.568116 | + | 0.660571i | ||||
\(146\) | 15.8874 | 1.31485 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 45.8544 | 3.76921 | ||||||||
\(149\) | − | 3.39064i | − | 0.277772i | −0.990308 | − | 0.138886i | \(-0.955648\pi\) | ||
0.990308 | − | 0.138886i | \(-0.0443522\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.97582i | 0.242169i | 0.992642 | + | 0.121085i | \(0.0386372\pi\) | ||||
−0.992642 | + | 0.121085i | \(0.961363\pi\) | |||||||
\(152\) | − | 32.5793i | − | 2.64253i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.78128i | 0.546452i | ||||||||
\(155\) | 5.04498 | + | 4.33888i | 0.405222 | + | 0.348507i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.00000i | − | 0.638470i | −0.947676 | − | 0.319235i | \(-0.896574\pi\) | ||
0.947676 | − | 0.319235i | \(-0.103426\pi\) | |||||||
\(158\) | 2.02671 | 0.161236 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.52249 | + | 6.42121i | −0.436591 | + | 0.507641i | ||||
\(161\) | 5.07395i | 0.399883i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.02671 | −0.158744 | −0.0793719 | − | 0.996845i | \(-0.525291\pi\) | ||||
−0.0793719 | + | 0.996845i | \(0.525291\pi\) | |||||||
\(164\) | 3.71001i | 0.289703i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.95502 | −0.229354 | ||||||||
\(167\) | 6.36647 | 0.492652 | 0.246326 | − | 0.969187i | \(-0.420777\pi\) | ||||
0.246326 | + | 0.969187i | \(0.420777\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.88740 | − | 11.0256i | 0.529800 | − | 0.848123i | ||||
\(170\) | −30.7298 | − | 26.4288i | −2.35687 | − | 2.02700i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.8874i | 1.05890i | ||||||||
\(173\) | 16.2783i | 1.23762i | 0.785541 | + | 0.618810i | \(0.212385\pi\) | ||||
−0.785541 | + | 0.618810i | \(0.787615\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.949118 | + | 6.27102i | 0.0717465 | + | 0.474044i | ||||
\(176\) | 13.1478i | 0.991049i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 19.2334i | 1.44160i | ||||||||
\(179\) | 24.3768 | 1.82201 | 0.911003 | − | 0.412401i | \(-0.135310\pi\) | ||||
0.911003 | + | 0.412401i | \(0.135310\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | −10.0765 | + | 5.58641i | −0.746918 | + | 0.414092i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 23.6390i | 1.74269i | ||||||||
\(185\) | 15.3839 | − | 17.8874i | 1.13104 | − | 1.31511i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.2699 | −1.11665 | ||||||||
\(188\) | 9.22281 | 0.672643 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −23.5436 | − | 20.2484i | −1.70803 | − | 1.46897i | ||||
\(191\) | 17.0829 | 1.23607 | 0.618036 | − | 0.786149i | \(-0.287928\pi\) | ||||
0.618036 | + | 0.786149i | \(0.287928\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.06242 | 0.148456 | 0.0742279 | − | 0.997241i | \(-0.476351\pi\) | ||||
0.0742279 | + | 0.997241i | \(0.476351\pi\) | |||||||
\(194\) | 13.4965 | 0.968989 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −23.4288 | −1.67349 | ||||||||
\(197\) | 7.99003 | 0.569266 | 0.284633 | − | 0.958637i | \(-0.408128\pi\) | ||||
0.284633 | + | 0.958637i | \(0.408128\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.20256 | 0.581464 | 0.290732 | − | 0.956805i | \(-0.406101\pi\) | ||||
0.290732 | + | 0.956805i | \(0.406101\pi\) | |||||||
\(200\) | 4.42185 | + | 29.2161i | 0.312672 | + | 2.06589i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −21.1378 | −1.48725 | ||||||||
\(203\) | 5.95165 | 0.417724 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.44724 | + | 1.24468i | 0.101080 | + | 0.0869325i | ||||
\(206\) | − | 45.8187i | − | 3.19234i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −19.5366 | + | 10.8311i | −1.35462 | + | 0.751001i | ||||
\(209\) | −11.6990 | −0.809238 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.79744 | 0.261427 | 0.130713 | − | 0.991420i | \(-0.458273\pi\) | ||||
0.130713 | + | 0.991420i | \(0.458273\pi\) | |||||||
\(212\) | 15.1955i | 1.04363i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.758219i | 0.0518308i | ||||||||
\(215\) | 5.41735 | + | 4.65913i | 0.369460 | + | 0.317750i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 3.77479i | − | 0.256250i | ||||||
\(218\) | 33.6848i | 2.28143i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 15.6356 | + | 13.4472i | 1.05415 | + | 0.906613i | ||||
\(221\) | −12.5793 | − | 22.6899i | −0.846177 | − | 1.52629i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.0754 | −1.27738 | −0.638691 | − | 0.769464i | \(-0.720524\pi\) | ||||
−0.638691 | + | 0.769464i | \(0.720524\pi\) | |||||||
\(224\) | 4.80453 | 0.321016 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 31.6888i | 2.10791i | ||||||||
\(227\) | −17.2726 | −1.14642 | −0.573211 | − | 0.819408i | \(-0.694302\pi\) | ||||
−0.573211 | + | 0.819408i | \(0.694302\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.4456i | 1.21892i | 0.792816 | + | 0.609460i | \(0.208614\pi\) | ||||
−0.792816 | + | 0.609460i | \(0.791386\pi\) | |||||||
\(230\) | 17.0829 | + | 14.6919i | 1.12641 | + | 0.968757i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 27.7282 | 1.82044 | ||||||||
\(233\) | − | 11.4965i | − | 0.753158i | −0.926385 | − | 0.376579i | \(-0.877100\pi\) | ||
0.926385 | − | 0.376579i | \(-0.122900\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.09419 | − | 3.59774i | 0.201843 | − | 0.234690i | ||||
\(236\) | 38.6940i | 2.51877i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 22.9929i | 1.49041i | ||||||||
\(239\) | − | 7.19610i | − | 0.465477i | −0.972539 | − | 0.232739i | \(-0.925231\pi\) | ||
0.972539 | − | 0.232739i | \(-0.0747687\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 15.9086i | − | 1.02477i | −0.858757 | − | 0.512383i | \(-0.828763\pi\) | ||
0.858757 | − | 0.512383i | \(-0.171237\pi\) | |||||||
\(242\) | −16.3653 | −1.05200 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 51.6622 | 3.30733 | ||||||||
\(245\) | −7.86022 | + | 9.13938i | −0.502171 | + | 0.583893i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.63763 | − | 17.3839i | −0.613228 | − | 1.10611i | ||||
\(248\) | − | 17.5864i | − | 1.11674i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 23.8614 | + | 14.9626i | 1.50913 | + | 0.946321i | ||||
\(251\) | 9.30807 | 0.587520 | 0.293760 | − | 0.955879i | \(-0.405093\pi\) | ||||
0.293760 | + | 0.955879i | \(0.405093\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.48862 | 0.533675 | ||||||||
\(254\) | − | 46.3290i | − | 2.90694i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.4667 | −1.96667 | ||||||||
\(257\) | 9.88740i | 0.616759i | 0.951263 | + | 0.308379i | \(0.0997866\pi\) | ||||
−0.951263 | + | 0.308379i | \(0.900213\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.3839 | −0.831632 | ||||||||
\(260\) | −7.10099 | + | 34.3112i | −0.440384 | + | 2.12789i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 43.7920 | 2.70548 | ||||||||
\(263\) | − | 6.69193i | − | 0.412642i | −0.978484 | − | 0.206321i | \(-0.933851\pi\) | ||
0.978484 | − | 0.206321i | \(-0.0661491\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.92762 | + | 5.09798i | 0.364131 | + | 0.313166i | ||||
\(266\) | 17.6160i | 1.08011i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.38797 | 0.0847836 | ||||||||
\(269\) | −23.6848 | −1.44409 | −0.722045 | − | 0.691846i | \(-0.756798\pi\) | ||||
−0.722045 | + | 0.691846i | \(0.756798\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3.80546i | − | 0.231165i | −0.993298 | − | 0.115583i | \(-0.963126\pi\) | ||
0.993298 | − | 0.115583i | \(-0.0368735\pi\) | |||||||
\(272\) | 44.5793i | 2.70302i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.7369 | 0.829877 | ||||||||
\(275\) | 10.4913 | − | 1.58786i | 0.632649 | − | 0.0957513i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.61615i | − | 0.157189i | −0.996907 | − | 0.0785945i | \(-0.974957\pi\) | ||
0.996907 | − | 0.0785945i | \(-0.0250432\pi\) | |||||||
\(278\) | 43.7920 | 2.62647 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 10.9301 | − | 12.7089i | 0.653201 | − | 0.759502i | ||||
\(281\) | 14.4162i | 0.860001i | 0.902829 | + | 0.430000i | \(0.141487\pi\) | ||||
−0.902829 | + | 0.430000i | \(0.858513\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 4.00000i | − | 0.237775i | −0.992908 | − | 0.118888i | \(-0.962067\pi\) | ||
0.992908 | − | 0.118888i | \(-0.0379328\pi\) | |||||||
\(284\) | 59.9156i | 3.55534i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.34596 | + | 16.8578i | 0.552638 | + | 0.996820i | ||||
\(287\) | − | 1.08287i | − | 0.0639196i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −34.7748 | −2.04558 | ||||||||
\(290\) | 17.2334 | − | 20.0379i | 1.01198 | − | 1.17667i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −27.4088 | −1.60398 | ||||||||
\(293\) | −13.1120 | −0.766014 | −0.383007 | − | 0.923746i | \(-0.625111\pi\) | ||||
−0.383007 | + | 0.923746i | \(0.625111\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.0942 | + | 12.9816i | 0.878818 | + | 0.755817i | ||||
\(296\) | −62.3541 | −3.62426 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.54143i | 0.494792i | ||||||||
\(299\) | 6.99291 | + | 12.6135i | 0.404411 | + | 0.729455i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 4.05341i | − | 0.233635i | ||||||
\(302\) | − | 7.49646i | − | 0.431373i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 34.1544i | 1.95889i | ||||||||
\(305\) | 17.3323 | − | 20.1530i | 0.992446 | − | 1.15395i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.3222 | 1.61643 | 0.808217 | − | 0.588885i | \(-0.200433\pi\) | ||||
0.808217 | + | 0.588885i | \(0.200433\pi\) | |||||||
\(308\) | − | 11.6990i | − | 0.666613i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12.7089 | − | 10.9301i | −0.721817 | − | 0.620791i | ||||
\(311\) | 2.08995 | 0.118510 | 0.0592552 | − | 0.998243i | \(-0.481127\pi\) | ||||
0.0592552 | + | 0.998243i | \(0.481127\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 16.8803i | − | 0.954131i | −0.878868 | − | 0.477066i | \(-0.841700\pi\) | ||
0.878868 | − | 0.477066i | \(-0.158300\pi\) | |||||||
\(314\) | 20.1530i | 1.13730i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.49646 | −0.196691 | ||||||||
\(317\) | 7.04091 | 0.395457 | 0.197729 | − | 0.980257i | \(-0.436644\pi\) | ||||
0.197729 | + | 0.980257i | \(0.436644\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 9.95700i | − | 0.557485i | ||||||
\(320\) | −4.15470 | + | 4.83083i | −0.232255 | + | 0.270052i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 12.7819i | − | 0.712306i | ||||||
\(323\) | −39.6672 | −2.20714 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.0021 | + | 14.2812i | 0.610289 | + | 0.792179i | ||||
\(326\) | 5.10552 | 0.282768 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 5.04498i | − | 0.278562i | ||||||
\(329\) | −2.69193 | −0.148411 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 18.8845i | − | 1.03798i | −0.854779 | − | 0.518992i | \(-0.826307\pi\) | ||
0.854779 | − | 0.518992i | \(-0.173693\pi\) | |||||||
\(332\) | 5.09798 | 0.279788 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −16.0379 | −0.877554 | ||||||||
\(335\) | 0.465654 | − | 0.541434i | 0.0254414 | − | 0.0295817i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.2713i | 0.831878i | 0.909393 | + | 0.415939i | \(0.136547\pi\) | ||||
−0.909393 | + | 0.415939i | \(0.863453\pi\) | |||||||
\(338\) | −17.3502 | + | 27.7748i | −0.943725 | + | 1.51075i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 53.0148 | + | 45.5948i | 2.87513 | + | 2.47272i | ||||
\(341\) | −6.31516 | −0.341985 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.7177 | 0.848679 | ||||||||
\(344\) | − | 18.8845i | − | 1.01818i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 41.0071i | − | 2.20455i | ||||||
\(347\) | − | 6.61615i | − | 0.355173i | −0.984105 | − | 0.177587i | \(-0.943171\pi\) | ||
0.984105 | − | 0.177587i | \(-0.0568290\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 20.1530i | − | 1.07876i | −0.842062 | − | 0.539382i | \(-0.818658\pi\) | ||
0.842062 | − | 0.539382i | \(-0.181342\pi\) | |||||||
\(350\) | −2.39094 | − | 15.7974i | −0.127801 | − | 0.844409i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 8.03789i | − | 0.428421i | ||||||
\(353\) | −18.0665 | −0.961583 | −0.480792 | − | 0.876835i | \(-0.659651\pi\) | ||||
−0.480792 | + | 0.876835i | \(0.659651\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.3725 | + | 20.1013i | 1.24049 | + | 1.06687i | ||||
\(356\) | − | 33.1812i | − | 1.75860i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −61.4080 | −3.24551 | ||||||||
\(359\) | − | 29.8860i | − | 1.57732i | −0.614827 | − | 0.788662i | \(-0.710774\pi\) | ||
0.614827 | − | 0.788662i | \(-0.289226\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.3909 | −0.599523 | ||||||||
\(362\) | 15.1147 | 0.794412 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 17.3839 | − | 9.63763i | 0.911161 | − | 0.505149i | ||||
\(365\) | −9.19547 | + | 10.6919i | −0.481313 | + | 0.559641i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.1955i | 0.584399i | 0.956357 | + | 0.292199i | \(0.0943871\pi\) | ||||
−0.956357 | + | 0.292199i | \(0.905613\pi\) | |||||||
\(368\) | − | 24.7819i | − | 1.29184i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −38.7538 | + | 45.0605i | −2.01471 | + | 2.34258i | ||||
\(371\) | − | 4.43521i | − | 0.230265i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 26.8945i | − | 1.39254i | −0.717778 | − | 0.696272i | \(-0.754841\pi\) | ||
0.717778 | − | 0.696272i | \(-0.245159\pi\) | |||||||
\(374\) | 38.4667 | 1.98907 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.5414 | −0.646775 | ||||||||
\(377\) | 14.7953 | − | 8.20256i | 0.761999 | − | 0.422453i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.2027i | 1.44868i | 0.689445 | + | 0.724338i | \(0.257855\pi\) | ||||
−0.689445 | + | 0.724338i | \(0.742145\pi\) | |||||||
\(380\) | 40.6172 | + | 34.9324i | 2.08362 | + | 1.79199i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −43.0338 | −2.20180 | ||||||||
\(383\) | −13.7865 | −0.704457 | −0.352228 | − | 0.935914i | \(-0.614576\pi\) | ||||
−0.352228 | + | 0.935914i | \(0.614576\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.56368 | − | 3.92494i | −0.232587 | − | 0.200034i | ||||
\(386\) | −5.19547 | −0.264442 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −23.2840 | −1.18206 | ||||||||
\(389\) | −15.6848 | −0.795253 | −0.397626 | − | 0.917547i | \(-0.630166\pi\) | ||||
−0.397626 | + | 0.917547i | \(0.630166\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.7819 | 1.45556 | ||||||||
\(392\) | 31.8592 | 1.60913 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −20.1278 | −1.01403 | ||||||||
\(395\) | −1.17304 | + | 1.36394i | −0.0590219 | + | 0.0686271i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.59939 | 0.230837 | 0.115418 | − | 0.993317i | \(-0.463179\pi\) | ||||
0.115418 | + | 0.993317i | \(0.463179\pi\) | |||||||
\(398\) | −20.6632 | −1.03575 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.63563 | − | 30.6285i | −0.231781 | − | 1.53143i | ||||
\(401\) | 11.0016i | 0.549392i | 0.961531 | + | 0.274696i | \(0.0885772\pi\) | ||||
−0.961531 | + | 0.274696i | \(0.911423\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.20242 | − | 9.38385i | −0.259151 | − | 0.467443i | ||||
\(404\) | 36.4667 | 1.81429 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.9929 | −0.744086 | ||||||||
\(407\) | 22.3909i | 1.10988i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 28.8325i | − | 1.42567i | −0.701330 | − | 0.712837i | \(-0.747410\pi\) | ||
0.701330 | − | 0.712837i | \(-0.252590\pi\) | |||||||
\(410\) | −3.64578 | − | 3.13551i | −0.180052 | − | 0.154852i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 79.0460i | 3.89432i | ||||||||
\(413\) | − | 11.2939i | − | 0.555736i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.71034 | − | 1.98868i | 0.0839572 | − | 0.0976203i | ||||
\(416\) | 11.9437 | − | 6.62160i | 0.585588 | − | 0.324651i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 29.4712 | 1.44148 | ||||||||
\(419\) | −24.3768 | −1.19088 | −0.595441 | − | 0.803399i | \(-0.703023\pi\) | ||||
−0.595441 | + | 0.803399i | \(0.703023\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.95700i | 0.485274i | 0.970117 | + | 0.242637i | \(0.0780125\pi\) | ||||
−0.970117 | + | 0.242637i | \(0.921988\pi\) | |||||||
\(422\) | −9.56621 | −0.465676 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 20.6632i | − | 1.00349i | ||||||
\(425\) | 35.5722 | − | 5.38385i | 1.72551 | − | 0.261155i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.0790 | −0.729724 | ||||||||
\(428\) | − | 1.30807i | − | 0.0632281i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.6469 | − | 11.7369i | −0.658114 | − | 0.566004i | ||||
\(431\) | 4.65913i | 0.224422i | 0.993684 | + | 0.112211i | \(0.0357933\pi\) | ||||
−0.993684 | + | 0.112211i | \(0.964207\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.89448i | 0.139100i | 0.997578 | + | 0.0695500i | \(0.0221563\pi\) | ||||
−0.997578 | + | 0.0695500i | \(0.977844\pi\) | |||||||
\(434\) | 9.50916i | 0.456454i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 58.1128i | − | 2.78310i | ||||||
\(437\) | 22.0512 | 1.05485 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.38385 | 0.256957 | 0.128479 | − | 0.991712i | \(-0.458991\pi\) | ||||
0.128479 | + | 0.991712i | \(0.458991\pi\) | |||||||
\(440\) | −21.2618 | − | 18.2859i | −1.01361 | − | 0.871748i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 31.6888 | + | 57.1586i | 1.50728 | + | 2.71876i | ||||
\(443\) | − | 7.29390i | − | 0.346544i | −0.984874 | − | 0.173272i | \(-0.944566\pi\) | ||
0.984874 | − | 0.173272i | \(-0.0554339\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.9437 | − | 11.1321i | −0.613590 | − | 0.527711i | ||||
\(446\) | 48.0531 | 2.27538 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.61456 | 0.170772 | ||||||||
\(449\) | 22.4750i | 1.06066i | 0.847791 | + | 0.530330i | \(0.177932\pi\) | ||||
−0.847791 | + | 0.530330i | \(0.822068\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.81162 | −0.0853057 | ||||||||
\(452\) | − | 54.6693i | − | 2.57143i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 43.5117 | 2.04211 | ||||||||
\(455\) | 2.07262 | − | 10.0146i | 0.0971657 | − | 0.469494i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.5080 | 0.959325 | 0.479663 | − | 0.877453i | \(-0.340759\pi\) | ||||
0.479663 | + | 0.877453i | \(0.340759\pi\) | |||||||
\(458\) | − | 46.4667i | − | 2.17125i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −29.4712 | − | 25.3464i | −1.37410 | − | 1.18178i | ||||
\(461\) | − | 1.68331i | − | 0.0783994i | −0.999231 | − | 0.0391997i | \(-0.987519\pi\) | ||
0.999231 | − | 0.0391997i | \(-0.0124808\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.80546 | −0.176855 | −0.0884274 | − | 0.996083i | \(-0.528184\pi\) | ||||
−0.0884274 | + | 0.996083i | \(0.528184\pi\) | |||||||
\(464\) | −29.0687 | −1.34948 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.9609i | 1.34159i | ||||||||
\(467\) | − | 15.7748i | − | 0.729970i | −0.931013 | − | 0.364985i | \(-0.881074\pi\) | ||
0.931013 | − | 0.364985i | \(-0.118926\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.405116 | −0.0187065 | ||||||||
\(470\) | −7.79464 | + | 9.06313i | −0.359540 | + | 0.418051i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 52.6172i | − | 2.42190i | ||||||
\(473\) | −6.78128 | −0.311804 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27.2536 | − | 4.12483i | 1.25048 | − | 0.189260i | ||||
\(476\) | − | 39.6672i | − | 1.81814i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.1278i | 0.829148i | ||||||||
\(479\) | − | 26.5194i | − | 1.21170i | −0.795578 | − | 0.605852i | \(-0.792832\pi\) | ||
0.795578 | − | 0.605852i | \(-0.207168\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.2713 | + | 18.4456i | −1.51704 | + | 0.841048i | ||||
\(482\) | 40.0758i | 1.82540i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 28.2334 | 1.28333 | ||||||||
\(485\) | −7.81162 | + | 9.08287i | −0.354707 | + | 0.412432i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.1771 | −0.778370 | −0.389185 | − | 0.921160i | \(-0.627243\pi\) | ||||
−0.389185 | + | 0.921160i | \(0.627243\pi\) | |||||||
\(488\) | −70.2517 | −3.18014 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 19.8008 | − | 23.0232i | 0.894510 | − | 1.04008i | ||||
\(491\) | −16.7061 | −0.753936 | −0.376968 | − | 0.926226i | \(-0.623033\pi\) | ||||
−0.376968 | + | 0.926226i | \(0.623033\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 33.7606i | − | 1.52050i | ||||||
\(494\) | 24.2783 | + | 43.7920i | 1.09233 | + | 1.97030i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.4366i | 0.827829i | ||||||||
\(497\) | − | 17.4880i | − | 0.784443i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.390787i | 0.0174940i | 0.999962 | + | 0.00874702i | \(0.00278430\pi\) | ||||
−0.999962 | + | 0.00874702i | \(0.997216\pi\) | |||||||
\(500\) | −41.1654 | − | 25.8134i | −1.84097 | − | 1.15441i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −23.4481 | −1.04654 | ||||||||
\(503\) | 43.4738i | 1.93840i | 0.246272 | + | 0.969201i | \(0.420794\pi\) | ||||
−0.246272 | + | 0.969201i | \(0.579206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.2343 | − | 14.2253i | 0.544421 | − | 0.633019i | ||||
\(506\) | −21.3839 | −0.950628 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 79.9264i | 3.54616i | ||||||||
\(509\) | − | 6.80532i | − | 0.301640i | −0.988561 | − | 0.150820i | \(-0.951809\pi\) | ||
0.988561 | − | 0.150820i | \(-0.0481914\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.00000 | 0.353899 | ||||||||
\(512\) | 49.7615 | 2.19917 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 24.9075i | − | 1.09862i | ||||||
\(515\) | 30.8352 | + | 26.5194i | 1.35876 | + | 1.16859i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.50354i | 0.198066i | ||||||||
\(518\) | 33.7155 | 1.48138 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.65612 | − | 46.6573i | 0.423449 | − | 2.04606i | ||||
\(521\) | 14.7061 | 0.644286 | 0.322143 | − | 0.946691i | \(-0.395597\pi\) | ||||
0.322143 | + | 0.946691i | \(0.395597\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 18.5935i | − | 0.813037i | −0.913643 | − | 0.406518i | \(-0.866743\pi\) | ||
0.913643 | − | 0.406518i | \(-0.133257\pi\) | |||||||
\(524\) | −75.5496 | −3.30040 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.8578i | 0.735033i | ||||||||
\(527\) | −21.4125 | −0.932741 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | −14.9324 | − | 12.8424i | −0.648621 | − | 0.557839i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 30.3909i | − | 1.31761i | ||||||
\(533\) | −1.49241 | − | 2.69193i | −0.0646433 | − | 0.116600i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.510268 | − | 0.438850i | −0.0220608 | − | 0.0189731i | ||||
\(536\) | −1.88740 | −0.0815231 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 59.6649 | 2.57234 | ||||||||
\(539\) | − | 11.4404i | − | 0.492774i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.6469i | 1.40360i | 0.712374 | + | 0.701801i | \(0.247620\pi\) | ||||
−0.712374 | + | 0.701801i | \(0.752380\pi\) | |||||||
\(542\) | 9.58641i | 0.411772i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 27.2536i | − | 1.16849i | ||||||
\(545\) | −22.6693 | − | 19.4965i | −0.971045 | − | 0.835136i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 18.5935i | − | 0.795001i | −0.917602 | − | 0.397500i | \(-0.869878\pi\) | ||
0.917602 | − | 0.397500i | \(-0.130122\pi\) | |||||||
\(548\) | −23.6988 | −1.01236 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −26.4288 | + | 4.00000i | −1.12693 | + | 0.170561i | ||||
\(551\) | − | 25.8656i | − | 1.10191i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.02054 | 0.0433976 | ||||||||
\(554\) | 6.59039i | 0.279999i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −75.5496 | −3.20402 | ||||||||
\(557\) | −8.22899 | −0.348674 | −0.174337 | − | 0.984686i | \(-0.555778\pi\) | ||||
−0.174337 | + | 0.984686i | \(0.555778\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.58641 | − | 10.0765i | −0.236280 | − | 0.426190i | ||||
\(560\) | −11.4586 | + | 13.3233i | −0.484213 | + | 0.563013i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 36.3162i | − | 1.53191i | ||||||
\(563\) | 21.0829i | 0.888537i | 0.895894 | + | 0.444268i | \(0.146536\pi\) | ||||
−0.895894 | + | 0.444268i | \(0.853464\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.3260 | − | 18.3412i | −0.897191 | − | 0.771619i | ||||
\(566\) | 10.0765i | 0.423546i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 81.4749i | − | 3.41861i | ||||||
\(569\) | 24.3909 | 1.02252 | 0.511261 | − | 0.859426i | \(-0.329179\pi\) | ||||
0.511261 | + | 0.859426i | \(0.329179\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.7974 | −0.493708 | −0.246854 | − | 0.969053i | \(-0.579397\pi\) | ||||
−0.246854 | + | 0.969053i | \(0.579397\pi\) | |||||||
\(572\) | −16.1236 | − | 29.0829i | −0.674161 | − | 1.21602i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.72787i | 0.113859i | ||||||||
\(575\) | −19.7748 | + | 2.99291i | −0.824666 | + | 0.124813i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.2868 | 0.927811 | 0.463906 | − | 0.885885i | \(-0.346448\pi\) | ||||
0.463906 | + | 0.885885i | \(0.346448\pi\) | |||||||
\(578\) | 87.6019 | 3.64376 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −29.7308 | + | 34.5692i | −1.23451 | + | 1.43541i | ||||
\(581\) | −1.48798 | −0.0617319 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.42002 | −0.307306 | ||||||||
\(584\) | 37.2713 | 1.54230 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 33.0308 | 1.36449 | ||||||||
\(587\) | 39.9625 | 1.64943 | 0.824715 | − | 0.565549i | \(-0.191336\pi\) | ||||
0.824715 | + | 0.565549i | \(0.191336\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.4051 | −0.675961 | ||||||||
\(590\) | −38.0241 | − | 32.7022i | −1.56543 | − | 1.34633i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 65.3686 | 2.68663 | ||||||||
\(593\) | 31.6291 | 1.29885 | 0.649425 | − | 0.760425i | \(-0.275010\pi\) | ||||
0.649425 | + | 0.760425i | \(0.275010\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.4738 | − | 13.3081i | −0.634364 | − | 0.545578i | ||||
\(596\) | − | 14.7356i | − | 0.603594i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −17.6160 | − | 31.7748i | −0.720371 | − | 1.29937i | ||||
\(599\) | 20.3768 | 0.832572 | 0.416286 | − | 0.909234i | \(-0.363331\pi\) | ||||
0.416286 | + | 0.909234i | \(0.363331\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.49646 | −0.0610417 | −0.0305209 | − | 0.999534i | \(-0.509717\pi\) | ||||
−0.0305209 | + | 0.999534i | \(0.509717\pi\) | |||||||
\(602\) | 10.2110i | 0.416171i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.9328i | 0.526229i | ||||||||
\(605\) | 9.47210 | − | 11.0136i | 0.385096 | − | 0.447766i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.20256i | 0.170577i | 0.996356 | + | 0.0852883i | \(0.0271811\pi\) | ||||
−0.996356 | + | 0.0852883i | \(0.972819\pi\) | |||||||
\(608\) | − | 20.8803i | − | 0.846808i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −43.6622 | + | 50.7677i | −1.76783 | + | 2.05552i | ||||
\(611\) | −6.69193 | + | 3.71001i | −0.270726 | + | 0.150091i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.11583 | −0.247016 | −0.123508 | − | 0.992344i | \(-0.539414\pi\) | ||||
−0.123508 | + | 0.992344i | \(0.539414\pi\) | |||||||
\(614\) | −71.3470 | −2.87933 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15.9086i | 0.640978i | ||||||||
\(617\) | 21.6721 | 0.872485 | 0.436243 | − | 0.899829i | \(-0.356309\pi\) | ||||
0.436243 | + | 0.899829i | \(0.356309\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.4214i | 0.861001i | 0.902590 | + | 0.430500i | \(0.141663\pi\) | ||||
−0.902590 | + | 0.430500i | \(0.858337\pi\) | |||||||
\(620\) | 21.9253 | + | 18.8566i | 0.880541 | + | 0.757299i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.26485 | −0.211101 | ||||||||
\(623\) | 9.68484i | 0.388015i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.8803 | + | 7.39803i | −0.955212 | + | 0.295921i | ||||
\(626\) | 42.5235i | 1.69958i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 34.7677i | − | 1.38738i | ||||||
\(629\) | 75.9197i | 3.02712i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.6123i | 0.860374i | 0.902740 | + | 0.430187i | \(0.141552\pi\) | ||||
−0.902740 | + | 0.430187i | \(0.858448\pi\) | |||||||
\(632\) | 4.75458 | 0.189127 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −17.7369 | −0.704422 | ||||||||
\(635\) | 31.1786 | + | 26.8148i | 1.23728 | + | 1.06411i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.9996 | − | 9.42459i | 0.673548 | − | 0.373416i | ||||
\(638\) | 25.0829i | 0.993040i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 21.5112 | − | 25.0119i | 0.850303 | − | 0.988680i | ||||
\(641\) | 3.91005 | 0.154437 | 0.0772187 | − | 0.997014i | \(-0.475396\pi\) | ||||
0.0772187 | + | 0.997014i | \(0.475396\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.9609 | 1.14211 | 0.571054 | − | 0.820912i | \(-0.306535\pi\) | ||||
0.571054 | + | 0.820912i | \(0.306535\pi\) | |||||||
\(644\) | 22.0512i | 0.868939i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 99.9264 | 3.93155 | ||||||||
\(647\) | 18.4667i | 0.726002i | 0.931789 | + | 0.363001i | \(0.118248\pi\) | ||||
−0.931789 | + | 0.363001i | \(0.881752\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.8945 | −0.741673 | ||||||||
\(650\) | −27.7157 | − | 35.9761i | −1.08710 | − | 1.41110i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.80799 | −0.344948 | ||||||||
\(653\) | − | 31.3470i | − | 1.22670i | −0.789810 | − | 0.613352i | \(-0.789821\pi\) | ||
0.789810 | − | 0.613352i | \(-0.210179\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.3464 | + | 29.4712i | −0.990365 | + | 1.15154i | ||||
\(656\) | 5.28888i | 0.206496i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.78128 | 0.264362 | ||||||||
\(659\) | −32.8577 | −1.27995 | −0.639976 | − | 0.768395i | \(-0.721056\pi\) | ||||
−0.639976 | + | 0.768395i | \(0.721056\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 3.17571i | − | 0.123521i | −0.998091 | − | 0.0617605i | \(-0.980329\pi\) | ||
0.998091 | − | 0.0617605i | \(-0.0196715\pi\) | |||||||
\(662\) | 47.5722i | 1.84895i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.93237 | −0.269028 | ||||||||
\(665\) | −11.8552 | − | 10.1960i | −0.459726 | − | 0.395382i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.7677i | 0.726688i | ||||||||
\(668\) | 27.6684 | 1.07052 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.17304 | + | 1.36394i | −0.0453184 | + | 0.0526935i | ||||
\(671\) | 25.2269i | 0.973874i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.3909i | 1.17148i | 0.810497 | + | 0.585742i | \(0.199197\pi\) | ||||
−0.810497 | + | 0.585742i | \(0.800803\pi\) | |||||||
\(674\) | − | 38.4701i | − | 1.48181i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 29.9324 | − | 47.9168i | 1.15125 | − | 1.84296i | ||||
\(677\) | 14.2642i | 0.548216i | 0.961699 | + | 0.274108i | \(0.0883826\pi\) | ||||
−0.961699 | + | 0.274108i | \(0.911617\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.79606 | 0.260809 | ||||||||
\(680\) | −72.0910 | − | 62.0011i | −2.76456 | − | 2.37763i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 15.9086 | 0.609174 | ||||||||
\(683\) | 15.6133 | 0.597427 | 0.298713 | − | 0.954343i | \(-0.403443\pi\) | ||||
0.298713 | + | 0.954343i | \(0.403443\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.95079 | + | 9.24468i | −0.303784 | + | 0.353221i | ||||
\(686\) | −39.5949 | −1.51174 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 19.7974i | 0.754770i | ||||||||
\(689\) | −6.11260 | − | 11.0256i | −0.232872 | − | 0.420042i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 5.70370i | − | 0.216979i | −0.994098 | − | 0.108489i | \(-0.965399\pi\) | ||
0.994098 | − | 0.108489i | \(-0.0346014\pi\) | |||||||
\(692\) | 70.7451i | 2.68932i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.6669i | 0.632666i | ||||||||
\(695\) | −25.3464 | + | 29.4712i | −0.961443 | + | 1.11791i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.14255 | −0.232666 | ||||||||
\(698\) | 50.7677i | 1.92159i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.12483 | + | 27.2536i | 0.155904 | + | 1.03009i | ||||
\(701\) | 17.0687 | 0.644676 | 0.322338 | − | 0.946625i | \(-0.395531\pi\) | ||||
0.322338 | + | 0.946625i | \(0.395531\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 58.1657i | 2.19376i | ||||||||
\(704\) | − | 6.04710i | − | 0.227909i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 45.5117 | 1.71286 | ||||||||
\(707\) | −10.6438 | −0.400301 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 22.4990i | − | 0.844969i | −0.906370 | − | 0.422484i | \(-0.861158\pi\) | ||
0.906370 | − | 0.422484i | \(-0.138842\pi\) | |||||||
\(710\) | −58.8782 | − | 50.6375i | −2.20966 | − | 1.90039i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 45.1208i | 1.69097i | ||||||||
\(713\) | 11.9033 | 0.445782 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.7543 | − | 3.46745i | −0.626576 | − | 0.129675i | ||||
\(716\) | 105.941 | 3.95918 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 75.2865i | 2.80967i | ||||||||
\(719\) | 25.0829 | 0.935433 | 0.467717 | − | 0.883879i | \(-0.345077\pi\) | ||||
0.467717 | + | 0.883879i | \(0.345077\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 23.0717i | − | 0.859236i | ||||||
\(722\) | 28.6951 | 1.06792 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −26.0758 | −0.969099 | ||||||||
\(725\) | 3.51063 | + | 23.1955i | 0.130382 | + | 0.861458i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.376766i | 0.0139735i | 0.999976 | + | 0.00698673i | \(0.00222396\pi\) | ||||
−0.999976 | + | 0.00698673i | \(0.997776\pi\) | |||||||
\(728\) | −23.6390 | + | 13.1055i | −0.876121 | + | 0.485723i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 23.1645 | − | 26.9342i | 0.857356 | − | 0.996881i | ||||
\(731\) | −22.9929 | −0.850424 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.45937 | 0.127775 | 0.0638874 | − | 0.997957i | \(-0.479650\pi\) | ||||
0.0638874 | + | 0.997957i | \(0.479650\pi\) | |||||||
\(734\) | − | 28.2027i | − | 1.04098i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.1504i | 0.558452i | ||||||||
\(737\) | 0.677751i | 0.0249653i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.5488i | 1.12376i | 0.827220 | + | 0.561878i | \(0.189921\pi\) | ||||
−0.827220 | + | 0.561878i | \(0.810079\pi\) | |||||||
\(740\) | 66.8577 | − | 77.7380i | 2.45774 | − | 2.85770i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.1728i | 0.410167i | ||||||||
\(743\) | 9.73308 | 0.357072 | 0.178536 | − | 0.983933i | \(-0.442864\pi\) | ||||
0.178536 | + | 0.983933i | \(0.442864\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.74823 | − | 4.94370i | −0.210599 | − | 0.181123i | ||||
\(746\) | 67.7504i | 2.48052i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −66.3625 | −2.42645 | ||||||||
\(749\) | 0.381797i | 0.0139505i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.7677 | 1.26869 | 0.634346 | − | 0.773049i | \(-0.281270\pi\) | ||||
0.634346 | + | 0.773049i | \(0.281270\pi\) | |||||||
\(752\) | 13.1478 | 0.479449 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −37.2713 | + | 20.6632i | −1.35734 | + | 0.752510i | ||||
\(755\) | 5.04498 | + | 4.33888i | 0.183606 | + | 0.157908i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 30.6693i | − | 1.11469i | −0.830280 | − | 0.557347i | \(-0.811819\pi\) | ||
0.830280 | − | 0.557347i | \(-0.188181\pi\) | |||||||
\(758\) | − | 71.0460i | − | 2.58051i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −55.2324 | − | 47.5020i | −2.00349 | − | 1.72308i | ||||
\(761\) | 2.51294i | 0.0910941i | 0.998962 | + | 0.0455470i | \(0.0145031\pi\) | ||||
−0.998962 | + | 0.0455470i | \(0.985497\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.9618i | 0.614058i | ||||||||
\(764\) | 74.2415 | 2.68596 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34.7298 | 1.25484 | ||||||||
\(767\) | −15.5652 | − | 28.0758i | −0.562028 | − | 1.01376i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 32.8378i | − | 1.18416i | −0.805878 | − | 0.592081i | \(-0.798306\pi\) | ||
0.805878 | − | 0.592081i | \(-0.201694\pi\) | |||||||
\(770\) | 11.4965 | + | 9.88740i | 0.414304 | + | 0.356317i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.96318 | 0.322592 | ||||||||
\(773\) | −28.3339 | −1.01910 | −0.509550 | − | 0.860441i | \(-0.670188\pi\) | ||||
−0.509550 | + | 0.860441i | \(0.670188\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.7116 | − | 2.22660i | 0.528455 | − | 0.0799817i | ||||
\(776\) | 31.6622 | 1.13661 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 39.5120 | 1.41657 | ||||||||
\(779\) | −4.70610 | −0.168614 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.2571 | −1.04690 | ||||||||
\(782\) | −72.5050 | −2.59277 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −33.3994 | −1.19284 | ||||||||
\(785\) | −13.5626 | − | 11.6643i | −0.484069 | − | 0.416318i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.8336 | 0.706991 | 0.353496 | − | 0.935436i | \(-0.384993\pi\) | ||||
0.353496 | + | 0.935436i | \(0.384993\pi\) | |||||||
\(788\) | 34.7244 | 1.23700 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.95502 | − | 3.43592i | 0.105135 | − | 0.122244i | ||||
\(791\) | 15.9567i | 0.567355i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −37.4853 | + | 20.7819i | −1.33114 | + | 0.737986i | ||||
\(794\) | −11.5864 | −0.411186 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 35.6480 | 1.26351 | ||||||||
\(797\) | − | 26.3683i | − | 0.934013i | −0.884254 | − | 0.467006i | \(-0.845332\pi\) | ||
0.884254 | − | 0.467006i | \(-0.154668\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.2699i | 0.540210i | ||||||||
\(800\) | 2.83399 | + | 18.7248i | 0.100197 | + | 0.662021i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 27.7143i | − | 0.978624i | ||||||
\(803\) | − | 13.3839i | − | 0.472306i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.60197 | + | 7.39803i | 0.303180 | + | 0.260746i | ||||
\(806\) | 13.1055 | + | 23.6390i | 0.461622 | + | 0.832650i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −49.5885 | −1.74452 | ||||||||
\(809\) | −15.6848 | −0.551450 | −0.275725 | − | 0.961237i | \(-0.588918\pi\) | ||||
−0.275725 | + | 0.961237i | \(0.588918\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.6174i | 1.11024i | 0.831771 | + | 0.555119i | \(0.187327\pi\) | ||||
−0.831771 | + | 0.555119i | \(0.812673\pi\) | |||||||
\(812\) | 25.8656 | 0.907706 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 56.4055i | − | 1.97701i | ||||||
\(815\) | −2.95502 | + | 3.43592i | −0.103510 | + | 0.120355i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.6160 | −0.616305 | ||||||||
\(818\) | 72.6325i | 2.53953i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.28966 | + | 5.40935i | 0.219645 | + | 0.188903i | ||||
\(821\) | − | 13.5385i | − | 0.472498i | −0.971693 | − | 0.236249i | \(-0.924082\pi\) | ||
0.971693 | − | 0.236249i | \(-0.0759181\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 30.3683i | − | 1.05857i | −0.848443 | − | 0.529286i | \(-0.822460\pi\) | ||
0.848443 | − | 0.529286i | \(-0.177540\pi\) | |||||||
\(824\) | − | 107.489i | − | 3.74456i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 28.4507i | 0.989926i | ||||||||
\(827\) | −36.9777 | −1.28584 | −0.642920 | − | 0.765933i | \(-0.722277\pi\) | ||||
−0.642920 | + | 0.765933i | \(0.722277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 49.6764 | 1.72533 | 0.862666 | − | 0.505774i | \(-0.168793\pi\) | ||||
0.862666 | + | 0.505774i | \(0.168793\pi\) | |||||||
\(830\) | −4.30855 | + | 5.00971i | −0.149552 | + | 0.173890i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.98553 | − | 4.98159i | 0.311517 | − | 0.172706i | ||||
\(833\) | − | 38.7904i | − | 1.34401i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.28257 | − | 10.7932i | 0.321237 | − | 0.373514i | ||||
\(836\) | −50.8435 | −1.75846 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 61.4080 | 2.12130 | ||||||||
\(839\) | 35.8377i | 1.23725i | 0.785685 | + | 0.618627i | \(0.212311\pi\) | ||||
−0.785685 | + | 0.618627i | \(0.787689\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.98582 | −0.240891 | ||||||||
\(842\) | − | 25.0829i | − | 0.864413i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16.5035 | 0.568075 | ||||||||
\(845\) | −8.64981 | − | 27.7521i | −0.297563 | − | 0.954702i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.24067 | −0.283153 | ||||||||
\(848\) | 21.6622i | 0.743883i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −89.6107 | + | 13.5626i | −3.07362 | + | 0.465192i | ||||
\(851\) | − | 42.2041i | − | 1.44674i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.1898 | 0.383131 | 0.191565 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191565 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(854\) | 37.9858 | 1.29985 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.77875i | 0.0607966i | ||||||||
\(857\) | 15.1197i | 0.516479i | 0.966081 | + | 0.258239i | \(0.0831423\pi\) | ||||
−0.966081 | + | 0.258239i | \(0.916858\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.5722 | −0.804274 | −0.402137 | − | 0.915579i | \(-0.631733\pi\) | ||||
−0.402137 | + | 0.915579i | \(0.631733\pi\) | |||||||
\(860\) | 23.5436 | + | 20.2484i | 0.802830 | + | 0.690465i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 11.7369i | − | 0.399761i | ||||||
\(863\) | 39.2524 | 1.33617 | 0.668083 | − | 0.744087i | \(-0.267115\pi\) | ||||
0.668083 | + | 0.744087i | \(0.267115\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27.5970 | + | 23.7345i | 0.938327 | + | 0.806997i | ||||
\(866\) | − | 7.29155i | − | 0.247777i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 16.4051i | − | 0.556826i | ||||||
\(869\) | − | 1.70734i | − | 0.0579174i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.00709 | + | 0.558331i | −0.0341239 | + | 0.0189183i | ||||
\(872\) | 79.0234i | 2.67607i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −55.5496 | −1.87899 | ||||||||
\(875\) | 12.0152 | + | 7.53435i | 0.406189 | + | 0.254707i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.8541 | −0.771728 | −0.385864 | − | 0.922556i | \(-0.626097\pi\) | ||||
−0.385864 | + | 0.922556i | \(0.626097\pi\) | |||||||
\(878\) | −13.5626 | −0.457715 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 22.2897 | + | 19.1700i | 0.751384 | + | 0.646220i | ||||
\(881\) | 27.1586 | 0.914998 | 0.457499 | − | 0.889210i | \(-0.348745\pi\) | ||||
0.457499 | + | 0.889210i | \(0.348745\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 36.1516i | − | 1.21660i | −0.793708 | − | 0.608298i | \(-0.791852\pi\) | ||
0.793708 | − | 0.608298i | \(-0.208148\pi\) | |||||||
\(884\) | −54.6693 | − | 98.6096i | −1.83873 | − | 3.31660i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.3742i | 0.617293i | ||||||||
\(887\) | 2.99291i | 0.100492i | 0.998737 | + | 0.0502461i | \(0.0160006\pi\) | ||||
−0.998737 | + | 0.0502461i | \(0.983999\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 23.3287i | − | 0.782418i | ||||||
\(890\) | 32.6067 | + | 28.0430i | 1.09298 | + | 0.940005i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −82.9008 | −2.77573 | ||||||||
\(893\) | 11.6990i | 0.391493i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 35.5423 | − | 41.3264i | 1.18805 | − | 1.38139i | ||||
\(896\) | −18.7146 | −0.625210 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 56.6172i | − | 1.88934i | ||||||
\(899\) | − | 13.9623i | − | 0.465670i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25.1586 | −0.838156 | ||||||||
\(902\) | 4.56368 | 0.151954 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 74.3408i | 2.47254i | ||||||||
\(905\) | −8.74825 | + | 10.1719i | −0.290802 | + | 0.338126i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 22.1657i | − | 0.736001i | −0.929826 | − | 0.368001i | \(-0.880042\pi\) | ||
0.929826 | − | 0.368001i | \(-0.119958\pi\) | |||||||
\(908\) | −75.0660 | −2.49115 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.22117 | + | 25.2281i | −0.173080 | + | 0.836303i | ||||
\(911\) | 14.9171 | 0.494227 | 0.247113 | − | 0.968987i | \(-0.420518\pi\) | ||||
0.247113 | + | 0.968987i | \(0.420518\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.48937i | 0.0823861i | ||||||||
\(914\) | −51.6622 | −1.70883 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 80.1640i | 2.64869i | ||||||||
\(917\) | 22.0512 | 0.728195 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.804530 | −0.0265390 | −0.0132695 | − | 0.999912i | \(-0.504224\pi\) | ||||
−0.0132695 | + | 0.999912i | \(0.504224\pi\) | |||||||
\(920\) | 40.0758 | + | 34.4667i | 1.32126 | + | 1.13633i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.24045i | 0.139652i | ||||||||
\(923\) | −24.1019 | − | 43.4738i | −0.793325 | − | 1.43096i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.89458 | − | 52.1611i | −0.259572 | − | 1.71505i | ||||
\(926\) | 9.58641 | 0.315029 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 17.7712 | 0.583367 | ||||||||
\(929\) | 22.9049i | 0.751484i | 0.926724 | + | 0.375742i | \(0.122612\pi\) | ||||
−0.926724 | + | 0.375742i | \(0.877388\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 29.7192i | − | 0.974006i | ||||||
\(932\) | − | 49.9632i | − | 1.63660i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 39.7386i | 1.30029i | ||||||||
\(935\) | −22.2642 | + | 25.8874i | −0.728116 | + | 0.846608i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.6622i | 0.969022i | 0.874785 | + | 0.484511i | \(0.161002\pi\) | ||||
−0.874785 | + | 0.484511i | \(0.838998\pi\) | |||||||
\(938\) | 1.02054 | 0.0333217 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 13.4472 | − | 15.6356i | 0.438601 | − | 0.509978i | ||||
\(941\) | − | 49.2004i | − | 1.60389i | −0.597401 | − | 0.801943i | \(-0.703800\pi\) | ||
0.597401 | − | 0.801943i | \(-0.296200\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.41467 | 0.111197 | ||||||||
\(944\) | 55.1610i | 1.79534i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.0829 | 0.555412 | ||||||||
\(947\) | −46.5529 | −1.51277 | −0.756383 | − | 0.654129i | \(-0.773035\pi\) | ||||
−0.756383 | + | 0.654129i | \(0.773035\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.8874 | − | 11.0256i | 0.645572 | − | 0.357906i | ||||
\(950\) | −68.6551 | + | 10.3909i | −2.22747 | + | 0.337127i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 53.9405i | 1.74822i | ||||||||
\(953\) | − | 16.8803i | − | 0.546807i | −0.961899 | − | 0.273403i | \(-0.911851\pi\) | ||
0.961899 | − | 0.273403i | \(-0.0881494\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.9075 | − | 28.9609i | 0.805989 | − | 0.937154i | ||||
\(956\) | − | 31.2740i | − | 1.01147i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 66.8056i | 2.15839i | ||||||||
\(959\) | 6.91713 | 0.223366 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.1445 | 0.714338 | ||||||||
\(962\) | 83.8143 | − | 46.4667i | 2.70228 | − | 1.49815i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 69.1384i | − | 2.22680i | ||||||
\(965\) | 3.00709 | − | 3.49646i | 0.0968016 | − | 0.112555i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.9531 | 0.641647 | 0.320824 | − | 0.947139i | \(-0.396040\pi\) | ||||
0.320824 | + | 0.947139i | \(0.396040\pi\) | |||||||
\(968\) | −38.3925 | −1.23398 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 19.6784 | − | 22.8808i | 0.631835 | − | 0.734659i | ||||
\(971\) | 44.4809 | 1.42746 | 0.713730 | − | 0.700421i | \(-0.247004\pi\) | ||||
0.713730 | + | 0.700421i | \(0.247004\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.0512 | 0.706929 | ||||||||
\(974\) | 43.2713 | 1.38650 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 73.6480 | 2.35742 | ||||||||
\(977\) | 17.1174 | 0.547634 | 0.273817 | − | 0.961782i | \(-0.411714\pi\) | ||||
0.273817 | + | 0.961782i | \(0.411714\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.2026 | 0.517836 | ||||||||
\(980\) | −34.1602 | + | 39.7194i | −1.09121 | + | 1.26879i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 42.0847 | 1.34298 | ||||||||
\(983\) | −57.2501 | −1.82600 | −0.912998 | − | 0.407964i | \(-0.866239\pi\) | ||||
−0.912998 | + | 0.407964i | \(0.866239\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.6498 | − | 13.5457i | 0.371193 | − | 0.431601i | ||||
\(986\) | 85.0470i | 2.70845i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −41.8848 | − | 75.5496i | −1.33253 | − | 2.40355i | ||||
\(989\) | 12.7819 | 0.406440 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.9858 | −0.698403 | −0.349201 | − | 0.937048i | \(-0.613547\pi\) | ||||
−0.349201 | + | 0.937048i | \(0.613547\pi\) | |||||||
\(992\) | − | 11.2713i | − | 0.357863i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 44.0543i | 1.39732i | ||||||||
\(995\) | 11.9597 | − | 13.9060i | 0.379147 | − | 0.440849i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.1586i | 1.55687i | 0.627725 | + | 0.778435i | \(0.283986\pi\) | ||||
−0.627725 | + | 0.778435i | \(0.716014\pi\) | |||||||
\(998\) | − | 0.984439i | − | 0.0311619i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 585.2.h.g.64.1 | 12 | ||
3.2 | odd | 2 | 195.2.h.c.64.11 | yes | 12 | ||
5.4 | even | 2 | inner | 585.2.h.g.64.11 | 12 | ||
12.11 | even | 2 | 3120.2.r.n.2209.8 | 12 | |||
13.12 | even | 2 | inner | 585.2.h.g.64.12 | 12 | ||
15.2 | even | 4 | 975.2.b.j.376.6 | 6 | |||
15.8 | even | 4 | 975.2.b.l.376.1 | 6 | |||
15.14 | odd | 2 | 195.2.h.c.64.2 | yes | 12 | ||
39.38 | odd | 2 | 195.2.h.c.64.1 | ✓ | 12 | ||
60.59 | even | 2 | 3120.2.r.n.2209.5 | 12 | |||
65.64 | even | 2 | inner | 585.2.h.g.64.2 | 12 | ||
156.155 | even | 2 | 3120.2.r.n.2209.11 | 12 | |||
195.38 | even | 4 | 975.2.b.l.376.6 | 6 | |||
195.77 | even | 4 | 975.2.b.j.376.1 | 6 | |||
195.194 | odd | 2 | 195.2.h.c.64.12 | yes | 12 | ||
780.779 | even | 2 | 3120.2.r.n.2209.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.h.c.64.1 | ✓ | 12 | 39.38 | odd | 2 | ||
195.2.h.c.64.2 | yes | 12 | 15.14 | odd | 2 | ||
195.2.h.c.64.11 | yes | 12 | 3.2 | odd | 2 | ||
195.2.h.c.64.12 | yes | 12 | 195.194 | odd | 2 | ||
585.2.h.g.64.1 | 12 | 1.1 | even | 1 | trivial | ||
585.2.h.g.64.2 | 12 | 65.64 | even | 2 | inner | ||
585.2.h.g.64.11 | 12 | 5.4 | even | 2 | inner | ||
585.2.h.g.64.12 | 12 | 13.12 | even | 2 | inner | ||
975.2.b.j.376.1 | 6 | 195.77 | even | 4 | |||
975.2.b.j.376.6 | 6 | 15.2 | even | 4 | |||
975.2.b.l.376.1 | 6 | 15.8 | even | 4 | |||
975.2.b.l.376.6 | 6 | 195.38 | even | 4 | |||
3120.2.r.n.2209.2 | 12 | 780.779 | even | 2 | |||
3120.2.r.n.2209.5 | 12 | 60.59 | even | 2 | |||
3120.2.r.n.2209.8 | 12 | 12.11 | even | 2 | |||
3120.2.r.n.2209.11 | 12 | 156.155 | even | 2 |