Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1349,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bo (of order \(6\), degree \(2\), not 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{18} - 16 x^{16} + 87 x^{14} + 91 x^{12} - 1104 x^{10} + 819 x^{8} + 7047 x^{6} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1349.7 | ||
Root | \(-1.70278 - 0.317079i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1349 |
Dual form | 2100.2.bo.g.1949.7 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 0.576792 | − | 1.63319i | 0.333011 | − | 0.942923i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.99797 | + | 1.73439i | 0.755162 | + | 0.655538i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.33462 | − | 1.88402i | −0.778208 | − | 0.628007i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.38064 | − | 1.95181i | 1.01930 | − | 0.588494i | 0.105400 | − | 0.994430i | \(-0.466388\pi\) |
0.913902 | + | 0.405936i | \(0.133054\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.06329 | 1.68166 | 0.840828 | − | 0.541303i | \(-0.182069\pi\) | ||||
0.840828 | + | 0.541303i | \(0.182069\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.65516 | + | 1.53296i | −0.643971 | + | 0.371797i | −0.786143 | − | 0.618045i | \(-0.787925\pi\) |
0.142171 | + | 0.989842i | \(0.454592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.94930 | + | 1.70278i | 0.676616 | + | 0.390645i | 0.798579 | − | 0.601890i | \(-0.205585\pi\) |
−0.121963 | + | 0.992535i | \(0.538919\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.98500 | − | 2.26269i | 0.869599 | − | 0.493759i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.43686 | − | 2.48871i | 0.299606 | − | 0.518933i | −0.676440 | − | 0.736498i | \(-0.736478\pi\) |
0.976046 | + | 0.217565i | \(0.0698114\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.42356 | + | 2.72620i | −0.851314 | + | 0.524657i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.97997i | 1.48184i | 0.671591 | + | 0.740922i | \(0.265611\pi\) | ||||
−0.671591 | + | 0.740922i | \(0.734389\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.63161 | + | 3.25141i | −1.01147 | + | 0.583971i | −0.911621 | − | 0.411032i | \(-0.865168\pi\) |
−0.0998461 | + | 0.995003i | \(0.531835\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.23776 | − | 6.64702i | −0.215466 | − | 1.15710i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.113447 | + | 0.0654987i | 0.0186506 | + | 0.0107679i | 0.509296 | − | 0.860591i | \(-0.329906\pi\) |
−0.490646 | + | 0.871359i | \(0.663239\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.49726 | − | 9.90252i | 0.560009 | − | 1.58567i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.3654 | 1.93116 | 0.965579 | − | 0.260108i | \(-0.0837583\pi\) | ||||
0.965579 | + | 0.260108i | \(0.0837583\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.43247i | 0.675945i | 0.941156 | + | 0.337972i | \(0.109741\pi\) | ||||
−0.941156 | + | 0.337972i | \(0.890259\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.71153 | − | 5.02960i | −1.27071 | − | 0.733643i | −0.295586 | − | 0.955316i | \(-0.595515\pi\) |
−0.975121 | + | 0.221674i | \(0.928848\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.983778 | + | 6.93053i | 0.140540 | + | 0.990075i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.972138 | + | 5.22058i | 0.136127 | + | 0.731028i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.67959 | − | 4.64119i | −0.368070 | − | 0.637516i | 0.621194 | − | 0.783657i | \(-0.286648\pi\) |
−0.989264 | + | 0.146141i | \(0.953315\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.48210 | − | 3.83462i | 0.593668 | − | 0.507908i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.28860 | + | 2.23193i | 0.167762 | + | 0.290572i | 0.937633 | − | 0.347628i | \(-0.113013\pi\) |
−0.769871 | + | 0.638200i | \(0.779679\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.44930 | + | 4.30086i | 0.953785 | + | 0.550668i | 0.894255 | − | 0.447558i | \(-0.147706\pi\) |
0.0595306 | + | 0.998226i | \(0.481040\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.39688 | − | 7.81337i | −0.175990 | − | 0.984392i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.8544 | − | 7.99884i | 1.69258 | − | 0.977213i | 0.740162 | − | 0.672429i | \(-0.234749\pi\) |
0.952421 | − | 0.304785i | \(-0.0985845\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.23578 | − | 3.78214i | −0.389542 | − | 0.455316i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.63245i | − | 0.431093i | −0.976494 | − | 0.215547i | \(-0.930847\pi\) | ||
0.976494 | − | 0.215547i | \(-0.0691533\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.88250 | − | 6.72468i | −0.454412 | − | 0.787064i | 0.544242 | − | 0.838928i | \(-0.316817\pi\) |
−0.998654 | + | 0.0518638i | \(0.983484\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.1396 | + | 1.96368i | 1.15552 | + | 0.223783i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.22311 | − | 2.11848i | 0.137610 | − | 0.238348i | −0.788981 | − | 0.614417i | \(-0.789391\pi\) |
0.926591 | + | 0.376069i | \(0.122725\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.90093 | + | 8.79696i | 0.211214 | + | 0.977440i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.63648i | − | 0.838213i | −0.907937 | − | 0.419106i | \(-0.862343\pi\) | ||
0.907937 | − | 0.419106i | \(-0.137657\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.0328 | + | 4.60278i | 1.39726 | + | 0.493470i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.11874 | − | 7.13387i | 0.436586 | − | 0.756189i | −0.560838 | − | 0.827926i | \(-0.689521\pi\) |
0.997424 | + | 0.0717367i | \(0.0228541\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.1143 | + | 10.5161i | 1.26992 | + | 1.10239i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.06191 | + | 11.0729i | 0.213810 | + | 1.14820i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.74985 | −0.583809 | −0.291904 | − | 0.956447i | \(-0.594289\pi\) | ||||
−0.291904 | + | 0.956447i | \(0.594289\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.5698 | − | 1.81245i | −1.16281 | − | 0.182158i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.54502 | − | 7.87220i | −0.452246 | − | 0.783313i | 0.546279 | − | 0.837603i | \(-0.316044\pi\) |
−0.998525 | + | 0.0542901i | \(0.982710\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.492615 | − | 0.853234i | 0.0485388 | − | 0.0840717i | −0.840735 | − | 0.541446i | \(-0.817877\pi\) |
0.889274 | + | 0.457375i | \(0.151210\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.645758 | + | 1.11849i | −0.0624278 | + | 0.108128i | −0.895550 | − | 0.444961i | \(-0.853218\pi\) |
0.833122 | + | 0.553089i | \(0.186551\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.68547 | − | 6.38342i | −0.353004 | − | 0.611421i | 0.633770 | − | 0.773521i | \(-0.281506\pi\) |
−0.986774 | + | 0.162101i | \(0.948173\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.172407 | − | 0.147502i | 0.0163642 | − | 0.0140002i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.52778 | −0.425938 | −0.212969 | − | 0.977059i | \(-0.568313\pi\) | ||||
−0.212969 | + | 0.977059i | \(0.568313\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14.1555 | − | 11.4234i | −1.30868 | − | 1.05609i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.96368 | − | 1.54228i | −0.730030 | − | 0.141381i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.11916 | − | 3.67050i | 0.192651 | − | 0.333681i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.13229 | − | 20.1951i | 0.643097 | − | 1.82093i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.700855i | 0.0621908i | 0.999516 | + | 0.0310954i | \(0.00989957\pi\) | ||||
−0.999516 | + | 0.0310954i | \(0.990100\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.23906 | + | 2.55661i | 0.637364 | + | 0.225097i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.66028 | + | 4.60774i | −0.232430 | + | 0.402580i | −0.958523 | − | 0.285016i | \(-0.908001\pi\) |
0.726093 | + | 0.687597i | \(0.241334\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.93933 | + | 8.51735i | 0.254873 | + | 0.738548i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.96252 | − | 3.39919i | −0.167670 | − | 0.290412i | 0.769930 | − | 0.638128i | \(-0.220291\pi\) |
−0.937600 | + | 0.347715i | \(0.886958\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.1726i | 1.37174i | 0.727724 | + | 0.685870i | \(0.240578\pi\) | ||||
−0.727724 | + | 0.685870i | \(0.759422\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.2390 | + | 11.3265i | −1.11493 | + | 0.953868i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 20.4978 | − | 11.8344i | 1.71411 | − | 0.989645i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.8863 | + | 2.39077i | 0.980366 | + | 0.197188i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.4366 | − | 10.0670i | −1.42846 | − | 0.824721i | −0.431459 | − | 0.902132i | \(-0.642001\pi\) |
−0.996999 | + | 0.0774116i | \(0.975334\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.38980 | − | 4.13926i | −0.194479 | − | 0.336848i | 0.752250 | − | 0.658877i | \(-0.228968\pi\) |
−0.946730 | + | 0.322029i | \(0.895635\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.08693 | + | 1.42350i | 0.734635 | + | 0.115083i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.82658 | − | 6.62784i | −0.305395 | − | 0.528959i | 0.671955 | − | 0.740592i | \(-0.265455\pi\) |
−0.977349 | + | 0.211633i | \(0.932122\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.12551 | + | 1.69929i | −0.723700 | + | 0.134762i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.18721 | − | 2.48030i | 0.566431 | − | 0.195475i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.33954 | + | 4.23749i | 0.574877 | + | 0.331906i | 0.759095 | − | 0.650980i | \(-0.225642\pi\) |
−0.184218 | + | 0.982885i | \(0.558975\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 20.5669i | − | 1.59152i | −0.605614 | − | 0.795759i | \(-0.707072\pi\) | ||
0.605614 | − | 0.795759i | \(-0.292928\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.7635 | 1.82796 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.67743 | − | 9.53190i | −0.281220 | − | 0.728922i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.3819 | − | 8.30340i | −1.09344 | − | 0.631296i | −0.158948 | − | 0.987287i | \(-0.550810\pi\) |
−0.934489 | + | 0.355991i | \(0.884143\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.38842 | − | 0.817179i | 0.329854 | − | 0.0614229i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.336240 | + | 0.194128i | −0.0251318 | + | 0.0145098i | −0.512513 | − | 0.858679i | \(-0.671285\pi\) |
0.487381 | + | 0.873189i | \(0.337952\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.6789i | 1.53705i | 0.639820 | + | 0.768524i | \(0.279009\pi\) | ||||
−0.639820 | + | 0.768524i | \(0.720991\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.3208 | − | 9.68543i | 0.836859 | − | 0.715968i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.98410 | + | 10.3648i | −0.437601 | + | 0.757947i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.5664 | − | 2.22531i | −0.986812 | − | 0.161868i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.2933 | − | 8.82961i | −1.10659 | − | 0.638888i | −0.168644 | − | 0.985677i | \(-0.553939\pi\) |
−0.937943 | + | 0.346789i | \(0.887272\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.5161 | + | 10.6903i | −1.33282 | + | 0.769505i | −0.985731 | − | 0.168327i | \(-0.946163\pi\) |
−0.347090 | + | 0.937832i | \(0.612830\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.5070 | −1.60356 | −0.801780 | − | 0.597619i | \(-0.796114\pi\) | ||||
−0.801780 | + | 0.597619i | \(0.796114\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.48532 | − | 4.89900i | 0.601509 | − | 0.347281i | −0.168126 | − | 0.985765i | \(-0.553772\pi\) |
0.769635 | + | 0.638484i | \(0.220438\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.07253 | − | 27.2405i | −0.357789 | − | 1.92140i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.8404 | + | 15.9438i | −0.971405 | + | 1.11903i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.04332 | + | 3.10314i | −0.559049 | + | 0.215683i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.2940 | 0.919568 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.96291 | −0.135132 | −0.0675660 | − | 0.997715i | \(-0.521523\pi\) | ||||
−0.0675660 | + | 0.997715i | \(0.521523\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.93249 | − | 2.09517i | −0.406488 | − | 0.143559i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.8910 | − | 3.27118i | −1.14664 | − | 0.222062i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.2221 | + | 2.46212i | −0.893465 | + | 0.166374i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.0990 | + | 9.29478i | −1.08294 | + | 0.625234i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.78864 | −0.119776 | −0.0598882 | − | 0.998205i | \(-0.519074\pi\) | ||||
−0.0598882 | + | 0.998205i | \(0.519074\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.8990 | − | 13.7981i | 1.58623 | − | 0.915813i | 0.592315 | − | 0.805707i | \(-0.298214\pi\) |
0.993920 | − | 0.110106i | \(-0.0351191\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.37613 | + | 4.83596i | 0.553510 | + | 0.319569i | 0.750537 | − | 0.660829i | \(-0.229795\pi\) |
−0.197026 | + | 0.980398i | \(0.563128\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.05553 | − | 15.4273i | 0.595810 | − | 1.01504i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.298355 | − | 0.516767i | 0.0195459 | − | 0.0338545i | −0.856087 | − | 0.516832i | \(-0.827111\pi\) |
0.875633 | + | 0.482977i | \(0.160445\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.75441 | − | 3.21949i | −0.178918 | − | 0.209128i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.90983i | 0.576329i | 0.957581 | + | 0.288165i | \(0.0930450\pi\) | ||||
−0.957581 | + | 0.288165i | \(0.906955\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.82543 | − | 1.05391i | 0.117586 | − | 0.0678886i | −0.440053 | − | 0.897972i | \(-0.645040\pi\) |
0.557640 | + | 0.830083i | \(0.311707\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.4635 | + | 1.96943i | 0.991987 | + | 0.126339i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.8825 | + | 10.3245i | 1.13784 | + | 0.656930i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.4718 | − | 4.40466i | −0.790370 | − | 0.279134i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.8229 | 1.88241 | 0.941204 | − | 0.337840i | \(-0.109696\pi\) | ||||
0.941204 | + | 0.337840i | \(0.109696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 11.2179i | − | 0.705266i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.7518 | + | 6.78489i | 0.733055 | + | 0.423230i | 0.819539 | − | 0.573024i | \(-0.194230\pi\) |
−0.0864836 | + | 0.996253i | \(0.527563\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.113064 | + | 0.327626i | 0.00702543 | + | 0.0203577i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.0344 | − | 18.6302i | 0.930608 | − | 1.15318i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.07897 | + | 10.5291i | 0.374846 | + | 0.649252i | 0.990304 | − | 0.138918i | \(-0.0443624\pi\) |
−0.615458 | + | 0.788169i | \(0.711029\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.27532 | − | 10.8415i | −0.567640 | − | 0.663486i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.2201 | + | 19.4338i | 0.684101 | + | 1.18490i | 0.973718 | + | 0.227756i | \(0.0731388\pi\) |
−0.289617 | + | 0.957143i | \(0.593528\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.19179 | − | 4.15218i | −0.436870 | − | 0.252227i | 0.265399 | − | 0.964139i | \(-0.414496\pi\) |
−0.702269 | + | 0.711912i | \(0.747830\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 24.1622 | − | 13.7193i | 1.46237 | − | 0.830332i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.24547 | + | 3.02848i | −0.315170 | + | 0.181963i | −0.649238 | − | 0.760586i | \(-0.724912\pi\) |
0.334068 | + | 0.942549i | \(0.391579\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.2734 | + | 3.01925i | 1.15387 | + | 0.180758i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.5771i | 1.04856i | 0.851545 | + | 0.524282i | \(0.175666\pi\) | ||||
−0.851545 | + | 0.524282i | \(0.824334\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.10407 | + | 7.10845i | 0.243961 | + | 0.422554i | 0.961839 | − | 0.273616i | \(-0.0882196\pi\) |
−0.717878 | + | 0.696169i | \(0.754886\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.7058 | + | 21.4465i | 1.45834 | + | 1.26595i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.80008 | + | 6.58193i | −0.223534 | + | 0.387172i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.31647 | + | 9.39060i | −0.194415 | + | 0.550487i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.88610i | 0.227028i | 0.993536 | + | 0.113514i | \(0.0362107\pi\) | ||||
−0.993536 | + | 0.113514i | \(0.963789\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.63343 | + | 17.8503i | −0.558988 | + | 1.03578i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.71210 | − | 15.0898i | 0.503834 | − | 0.872666i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.68763 | + | 8.85594i | −0.443108 | + | 0.510448i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.4783 | + | 2.88226i | −0.889207 | + | 0.165581i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.119756 | −0.00683482 | −0.00341741 | − | 0.999994i | \(-0.501088\pi\) | ||||
−0.00341741 | + | 0.999994i | \(0.501088\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.10936 | − | 1.29667i | −0.0631092 | − | 0.0737651i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.57207 | + | 11.3832i | 0.372668 | + | 0.645480i | 0.989975 | − | 0.141243i | \(-0.0451097\pi\) |
−0.617307 | + | 0.786722i | \(0.711776\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.6346 | + | 20.1517i | −0.657625 | + | 1.13904i | 0.323604 | + | 0.946192i | \(0.395105\pi\) |
−0.981229 | + | 0.192847i | \(0.938228\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.3744 | + | 30.0933i | −0.975841 | + | 1.69021i | −0.298709 | + | 0.954344i | \(0.596556\pi\) |
−0.677132 | + | 0.735861i | \(0.736777\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.5754 | + | 26.9774i | 0.872056 | + | 1.51045i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.45423 | + | 1.69978i | 0.0811674 | + | 0.0948725i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.4412 | −0.580962 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.5511 | + | 2.33717i | −0.694077 | + | 0.129246i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.68208 | − | 25.1582i | −0.478659 | − | 1.38702i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.8024 | − | 22.1744i | 0.703684 | − | 1.21882i | −0.263481 | − | 0.964665i | \(-0.584871\pi\) |
0.967165 | − | 0.254151i | \(-0.0817961\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.141455 | − | 0.366651i | −0.00775169 | − | 0.0200924i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 26.5502i | − | 1.44628i | −0.690702 | − | 0.723140i | \(-0.742698\pi\) | ||
0.690702 | − | 0.723140i | \(-0.257302\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.61159 | + | 7.39473i | −0.141842 | + | 0.401627i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.6923 | + | 21.9837i | −0.687327 | + | 1.19048i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0547 | + | 15.5532i | −0.542902 | + | 0.839796i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.61397 | − | 16.6519i | −0.516105 | − | 0.893920i | −0.999825 | − | 0.0186975i | \(-0.994048\pi\) |
0.483720 | − | 0.875223i | \(-0.339285\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.40475i | 0.0751943i | 0.999293 | + | 0.0375972i | \(0.0119704\pi\) | ||||
−0.999293 | + | 0.0375972i | \(0.988030\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.8213 | + | 16.5297i | −1.43162 | + | 0.882292i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.3454 | + | 9.43705i | −0.869980 | + | 0.502283i | −0.867342 | − | 0.497713i | \(-0.834173\pi\) |
−0.00263867 | + | 0.999997i | \(0.500840\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.11222 | + | 12.1166i | −0.376419 | + | 0.641281i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.1592 | + | 11.0615i | 1.01118 | + | 0.583806i | 0.911537 | − | 0.411217i | \(-0.134896\pi\) |
0.0996440 | + | 0.995023i | \(0.468230\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.70108 | − | 6.41046i | −0.194794 | − | 0.337392i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.77230 | − | 5.57811i | −0.250481 | − | 0.292775i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.56047 | + | 11.3631i | 0.342454 | + | 0.593147i | 0.984888 | − | 0.173194i | \(-0.0554087\pi\) |
−0.642434 | + | 0.766341i | \(0.722075\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −28.8687 | − | 23.2968i | −1.50284 | − | 1.21278i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.69589 | − | 13.9204i | 0.139964 | − | 0.722712i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.7826 | − | 7.38003i | −0.661857 | − | 0.382123i | 0.131127 | − | 0.991366i | \(-0.458140\pi\) |
−0.792984 | + | 0.609242i | \(0.791474\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 48.3849i | 2.49195i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.9980 | −1.54089 | −0.770447 | − | 0.637505i | \(-0.779967\pi\) | ||||
−0.770447 | + | 0.637505i | \(0.779967\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.14463 | + | 0.404247i | 0.0586411 | + | 0.0207102i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.3723 | + | 7.72052i | 0.683294 | + | 0.394500i | 0.801095 | − | 0.598537i | \(-0.204251\pi\) |
−0.117801 | + | 0.993037i | \(0.537584\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.35086 | − | 10.3481i | 0.424498 | − | 0.526025i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.53666 | + | 4.35129i | −0.382124 | + | 0.220619i | −0.678742 | − | 0.734377i | \(-0.737475\pi\) |
0.296618 | + | 0.954996i | \(0.404141\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.81059i | 0.445570i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.99089 | + | 7.00245i | 0.302201 | + | 0.353227i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.5044 | − | 23.3904i | 0.677768 | − | 1.17393i | −0.297883 | − | 0.954602i | \(-0.596281\pi\) |
0.975651 | − | 0.219327i | \(-0.0703861\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.6058 | + | 0.112241i | 0.781269 | + | 0.00561909i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.30215 | − | 2.48385i | −0.214839 | − | 0.124037i | 0.388719 | − | 0.921356i | \(-0.372918\pi\) |
−0.603558 | + | 0.797319i | \(0.706251\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −34.1461 | + | 19.7143i | −1.70094 | + | 0.982037i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.511365 | 0.0253474 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.00387 | − | 4.04369i | 0.346319 | − | 0.199947i | −0.316744 | − | 0.948511i | \(-0.602590\pi\) |
0.663063 | + | 0.748564i | \(0.269256\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.68349 | + | 1.24455i | −0.329672 | + | 0.0613891i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.29644 | + | 6.69427i | −0.0637937 | + | 0.329403i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 26.4129 | + | 9.32820i | 1.29345 | + | 0.456804i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.60294 | −0.371428 | −0.185714 | − | 0.982604i | \(-0.559460\pi\) | ||||
−0.185714 | + | 0.982604i | \(0.559460\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.43892 | −0.216340 | −0.108170 | − | 0.994132i | \(-0.534499\pi\) | ||||
−0.108170 | + | 0.994132i | \(0.534499\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.8623 | + | 28.1549i | 0.528141 | + | 1.36894i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.42413 | + | 21.5130i | 0.359279 | + | 1.04109i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.50490 | − | 40.3029i | −0.362340 | − | 1.94584i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.24065 | + | 2.44834i | −0.204265 | + | 0.117932i | −0.598643 | − | 0.801016i | \(-0.704293\pi\) |
0.394378 | + | 0.918948i | \(0.370960\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.6390 | −0.895732 | −0.447866 | − | 0.894101i | \(-0.647816\pi\) | ||||
−0.447866 | + | 0.894101i | \(0.647816\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.47547 | − | 4.89331i | 0.405437 | − | 0.234079i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.87038 | + | 1.65722i | 0.136996 | + | 0.0790946i | 0.566932 | − | 0.823765i | \(-0.308130\pi\) |
−0.429936 | + | 0.902860i | \(0.641464\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.7605 | − | 18.0336i | 0.512405 | − | 0.858744i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.408581 | + | 0.707683i | −0.0194123 | + | 0.0336231i | −0.875568 | − | 0.483094i | \(-0.839513\pi\) |
0.856156 | + | 0.516717i | \(0.172846\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −26.4986 | + | 22.6707i | −1.25334 | + | 1.07229i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.17892i | − | 0.244408i | −0.992505 | − | 0.122204i | \(-0.961004\pi\) | ||
0.992505 | − | 0.122204i | \(-0.0389962\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 41.8032 | − | 24.1351i | 1.96843 | − | 1.13648i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.13862 | + | 1.51551i | −0.382386 | + | 0.0712051i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.4250 | + | 6.01889i | 0.487662 | + | 0.281552i | 0.723604 | − | 0.690215i | \(-0.242484\pi\) |
−0.235942 | + | 0.971767i | \(0.575817\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.56611 | − | 14.0196i | 0.353156 | − | 0.654380i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.0451 | −1.07332 | −0.536658 | − | 0.843800i | \(-0.680314\pi\) | ||||
−0.536658 | + | 0.843800i | \(0.680314\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.8549i | 1.29453i | 0.762267 | + | 0.647263i | \(0.224086\pi\) | ||||
−0.762267 | + | 0.647263i | \(0.775914\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.91950 | − | 1.10822i | −0.0888240 | − | 0.0512825i | 0.454930 | − | 0.890527i | \(-0.349664\pi\) |
−0.543754 | + | 0.839245i | \(0.682998\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 41.5538 | + | 8.04748i | 1.91878 | + | 0.371598i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.0317 | + | 2.42666i | −0.600467 | + | 0.111815i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.65135 | + | 14.9846i | 0.397790 | + | 0.688992i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.48826 | + | 15.8838i | −0.113930 | + | 0.727271i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.53276 | − | 6.11892i | −0.161416 | − | 0.279581i | 0.773961 | − | 0.633234i | \(-0.218273\pi\) |
−0.935377 | + | 0.353653i | \(0.884939\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.687863 | + | 0.397138i | 0.0313638 | + | 0.0181079i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.0947128 | − | 13.1687i | 0.00430958 | − | 0.599197i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.00270 | + | 4.62036i | −0.362637 | + | 0.209368i | −0.670237 | − | 0.742147i | \(-0.733807\pi\) |
0.307600 | + | 0.951516i | \(0.400474\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.1540 | − | 9.54273i | 0.504402 | − | 0.431537i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.0713i | 0.635031i | 0.948253 | + | 0.317515i | \(0.102848\pi\) | ||||
−0.948253 | + | 0.317515i | \(0.897152\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.2330 | − | 21.1881i | −0.550945 | − | 0.954265i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.30010 | − | 7.25754i | 0.282598 | − | 0.325545i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.50255 | − | 11.2627i | 0.291094 | − | 0.504190i | −0.682975 | − | 0.730442i | \(-0.739314\pi\) |
0.974069 | + | 0.226252i | \(0.0726474\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −33.5897 | − | 11.8628i | −1.50068 | − | 0.529993i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.580122i | 0.0258664i | 0.999916 | + | 0.0129332i | \(0.00411687\pi\) | ||||
−0.999916 | + | 0.0129332i | \(0.995883\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.7066 | − | 38.8104i | 0.608732 | − | 1.72363i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.86251 | − | 17.0824i | 0.437148 | − | 0.757163i | −0.560320 | − | 0.828276i | \(-0.689322\pi\) |
0.997468 | + | 0.0711133i | \(0.0226552\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.90611 | − | 20.1695i | 0.172796 | − | 0.892245i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17.6885 | + | 0.508034i | −0.780967 | + | 0.0224302i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −39.2674 | −1.72698 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.8564 | + | 18.6991i | −0.959390 | + | 0.820799i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.0051 | − | 31.1857i | −0.788818 | − | 1.36627i | −0.926692 | − | 0.375822i | \(-0.877360\pi\) |
0.137874 | − | 0.990450i | \(-0.455973\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.7033 | − | 18.5387i | 0.468023 | − | 0.810640i | −0.531309 | − | 0.847178i | \(-0.678300\pi\) |
0.999332 | + | 0.0365378i | \(0.0116329\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.96855 | − | 17.2660i | 0.434237 | − | 0.752121i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.37087 | + | 12.7667i | 0.320472 | + | 0.555075i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.19659 | − | 7.63846i | 0.0519277 | − | 0.331481i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 74.9754 | 3.24754 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.123108 | + | 0.661116i | 0.00531251 | + | 0.0285293i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.8529 | + | 21.5095i | 0.725906 | + | 0.926479i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.32759 | + | 4.03151i | −0.100071 | + | 0.173328i | −0.911714 | − | 0.410826i | \(-0.865240\pi\) |
0.811643 | + | 0.584154i | \(0.198574\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 33.7725 | + | 11.9274i | 1.44932 | + | 0.511854i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 7.34057i | − | 0.313860i | −0.987610 | − | 0.156930i | \(-0.949840\pi\) | ||
0.987610 | − | 0.156930i | \(-0.0501597\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.28841 | − | 24.0755i | −0.396420 | − | 1.02752i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.5881 | + | 23.5353i | −0.578874 | + | 1.00264i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.11800 | − | 2.11132i | 0.260164 | − | 0.0897825i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.1169 | − | 27.9154i | −0.682897 | − | 1.18281i | −0.974093 | − | 0.226149i | \(-0.927386\pi\) |
0.291196 | − | 0.956663i | \(-0.405947\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.8753i | 1.13671i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.4761 | + | 15.7515i | 0.568960 | + | 0.665028i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.8892 | + | 11.4830i | −0.838230 | + | 0.483952i | −0.856662 | − | 0.515878i | \(-0.827466\pi\) |
0.0184324 | + | 0.999830i | \(0.494132\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.4594 | + | 20.8730i | −0.481248 | + | 0.876585i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.0347 | − | 9.25765i | −0.672211 | − | 0.388101i | 0.124703 | − | 0.992194i | \(-0.460202\pi\) |
−0.796914 | + | 0.604093i | \(0.793535\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.9408 | − | 38.0025i | −0.918193 | − | 1.59036i | −0.802158 | − | 0.597112i | \(-0.796315\pi\) |
−0.116035 | − | 0.993245i | \(-0.537019\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23.2415 | + | 19.8841i | −0.970928 | + | 0.830670i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.46761 | − | 14.6663i | −0.352511 | − | 0.610568i | 0.634177 | − | 0.773188i | \(-0.281339\pi\) |
−0.986689 | + | 0.162620i | \(0.948006\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.77934 | + | 36.4065i | 0.281740 | + | 1.51300i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.2446 | − | 15.2575i | 0.549480 | − | 0.632987i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.1175 | − | 10.4601i | −0.750349 | − | 0.433214i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.3959i | 0.635456i | 0.948182 | + | 0.317728i | \(0.102920\pi\) | ||||
−0.948182 | + | 0.317728i | \(0.897080\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.1458 | −0.912500 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.9819 | + | 36.7583i | −0.534003 | + | 1.51203i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.11363 | − | 2.37500i | −0.168926 | − | 0.0975297i | 0.413153 | − | 0.910662i | \(-0.364427\pi\) |
−0.582079 | + | 0.813132i | \(0.697761\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.10674 | − | 16.6839i | −0.127151 | − | 0.682825i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.2300 | + | 11.1024i | −0.785716 | + | 0.453634i | −0.838452 | − | 0.544975i | \(-0.816539\pi\) |
0.0527360 | + | 0.998608i | \(0.483206\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.5924i | 1.73738i | 0.495357 | + | 0.868689i | \(0.335037\pi\) | ||||
−0.495357 | + | 0.868689i | \(0.664963\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −47.4148 | − | 7.42770i | −1.93088 | − | 0.302479i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.40283 | − | 16.2862i | 0.381649 | − | 0.661035i | −0.609649 | − | 0.792671i | \(-0.708690\pi\) |
0.991298 | + | 0.131636i | \(0.0420230\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.0562 | + | 31.8002i | 0.731673 | + | 1.28861i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −52.8205 | − | 30.4960i | −2.13689 | − | 1.23373i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.4196 | − | 7.74783i | 0.542014 | − | 0.312932i | −0.203881 | − | 0.978996i | \(-0.565355\pi\) |
0.745895 | + | 0.666064i | \(0.232022\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.7219 | −0.713459 | −0.356729 | − | 0.934208i | \(-0.616108\pi\) | ||||
−0.356729 | + | 0.934208i | \(0.616108\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.96204 | + | 3.44219i | −0.239635 | + | 0.138353i | −0.615009 | − | 0.788520i | \(-0.710848\pi\) |
0.375374 | + | 0.926873i | \(0.377514\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.428695 | + | 14.9261i | 0.0172029 | + | 0.598965i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.6021 | − | 7.10976i | 0.825404 | − | 0.284847i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.66789 | − | 21.7117i | 0.306226 | − | 0.867082i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.401627 | −0.0160139 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −49.6754 | −1.97755 | −0.988774 | − | 0.149421i | \(-0.952259\pi\) | ||||
−0.988774 | + | 0.149421i | \(0.952259\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.13219 | + | 3.20580i | −0.0450004 | + | 0.127419i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.96493 | + | 42.0218i | 0.236339 | + | 1.66496i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.84362 | + | 8.48041i | −0.270729 | + | 0.335480i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.3007 | − | 13.4527i | 0.920324 | − | 0.531349i | 0.0365856 | − | 0.999331i | \(-0.488352\pi\) |
0.883738 | + | 0.467981i | \(0.155019\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.9638 | 0.550679 | 0.275339 | − | 0.961347i | \(-0.411210\pi\) | ||||
0.275339 | + | 0.961347i | \(0.411210\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −26.5656 | + | 15.3377i | −1.04440 | + | 0.602985i | −0.921077 | − | 0.389381i | \(-0.872689\pi\) |
−0.123324 | + | 0.992366i | \(0.539356\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.71262 | + | 5.03023i | 0.342000 | + | 0.197454i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.0851 | + | 25.6994i | −0.591230 | + | 1.00724i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.55879 | + | 11.3602i | −0.256665 | + | 0.444557i | −0.965347 | − | 0.260971i | \(-0.915957\pi\) |
0.708681 | + | 0.705529i | \(0.249290\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.60527 | + | 23.0143i | −0.140655 | + | 0.897873i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.1306i | 1.44640i | 0.690638 | + | 0.723201i | \(0.257330\pi\) | ||||
−0.690638 | + | 0.723201i | \(0.742670\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.41297 | − | 2.54783i | 0.171645 | − | 0.0990992i | −0.411716 | − | 0.911312i | \(-0.635071\pi\) |
0.583361 | + | 0.812213i | \(0.301737\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.89436 | + | 31.6539i | 0.228918 | + | 1.22934i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.8599 | + | 11.4661i | 0.768977 | + | 0.443969i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.03168 | + | 2.92120i | −0.0398869 | + | 0.112940i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33.5779 | 1.29626 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.0339i | 1.11918i | 0.828771 | + | 0.559588i | \(0.189040\pi\) | ||||
−0.828771 | + | 0.559588i | \(0.810960\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.6131 | − | 12.4783i | −0.830658 | − | 0.479581i | 0.0234197 | − | 0.999726i | \(-0.492545\pi\) |
−0.854078 | + | 0.520145i | \(0.825878\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.4880 | − | 9.97249i | −0.440870 | − | 0.382709i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.75019 | − | 46.9903i | −0.335308 | − | 1.80067i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.9226 | + | 29.3107i | 0.647524 | + | 1.12154i | 0.983712 | + | 0.179749i | \(0.0575287\pi\) |
−0.336189 | + | 0.941795i | \(0.609138\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.7293 | − | 10.8905i | 0.485654 | − | 0.415498i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.2472 | − | 28.1409i | −0.618967 | − | 1.07208i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.82503 | + | 5.67249i | 0.373762 | + | 0.215792i | 0.675101 | − | 0.737726i | \(-0.264100\pi\) |
−0.301339 | + | 0.953517i | \(0.597434\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −19.9726 | − | 23.6878i | −0.758696 | − | 0.899823i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.8323 | + | 18.9557i | −1.24361 | + | 0.717999i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.671890 | − | 0.785338i | −0.0254132 | − | 0.0297042i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.1947i | 0.876052i | 0.898962 | + | 0.438026i | \(0.144322\pi\) | ||||
−0.898962 | + | 0.438026i | \(0.855678\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.223060 | + | 0.386351i | 0.00841285 | + | 0.0145715i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.57266 | − | 23.6113i | 0.171972 | − | 0.887993i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.29490 | + | 12.6351i | −0.273966 | + | 0.474522i | −0.969874 | − | 0.243609i | \(-0.921669\pi\) |
0.695908 | + | 0.718131i | \(0.255002\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.84675 | + | 2.64150i | −0.256773 | + | 0.0990639i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.6873i | 0.699844i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.5515 | + | 5.13912i | 0.543434 | + | 0.191924i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.35171 | + | 16.1976i | −0.348760 | + | 0.604070i | −0.986029 | − | 0.166571i | \(-0.946730\pi\) |
0.637270 | + | 0.770641i | \(0.280064\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.46407 | − | 0.850351i | 0.0917668 | − | 0.0316687i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.668348 | − | 3.58917i | −0.0248561 | − | 0.133483i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.0483 | 0.854815 | 0.427407 | − | 0.904059i | \(-0.359427\pi\) | ||||
0.427407 | + | 0.904059i | \(0.359427\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.1357 | − | 24.1190i | 0.449470 | − | 0.893295i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.79479 | − | 11.7689i | −0.251314 | − | 0.435289i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.89746 | + | 15.4109i | −0.328635 | + | 0.569213i | −0.982241 | − | 0.187622i | \(-0.939922\pi\) |
0.653606 | + | 0.756835i | \(0.273255\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31.2245 | − | 54.0824i | 1.15017 | − | 1.99215i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.97258 | − | 12.0769i | −0.256491 | − | 0.444255i | 0.708809 | − | 0.705401i | \(-0.249233\pi\) |
−0.965299 | + | 0.261146i | \(0.915900\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 27.1763 | − | 23.2504i | 0.998345 | − | 0.854127i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.8975 | −1.13352 | −0.566760 | − | 0.823883i | \(-0.691803\pi\) | ||||
−0.566760 | + | 0.823883i | \(0.691803\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.3873 | + | 17.8283i | −0.526404 | + | 0.652304i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.23010 | + | 1.11471i | −0.118025 | + | 0.0407305i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.7085 | + | 20.2797i | −0.427249 | + | 0.740017i | −0.996628 | − | 0.0820583i | \(-0.973851\pi\) |
0.569378 | + | 0.822076i | \(0.307184\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.2016 | − | 48.7065i | 0.626862 | − | 1.77497i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 25.7901i | − | 0.937357i | −0.883369 | − | 0.468679i | \(-0.844730\pi\) | ||
0.883369 | − | 0.468679i | \(-0.155270\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.3210 | − | 6.47041i | −0.665011 | − | 0.234861i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.03119 | − | 15.6425i | 0.327380 | − | 0.567039i | −0.654611 | − | 0.755966i | \(-0.727168\pi\) |
0.981991 | + | 0.188927i | \(0.0605008\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.70788 | − | 19.1459i | 0.134234 | − | 0.693129i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.81318 | + | 13.5328i | 0.282118 | + | 0.488642i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 46.2208i | − | 1.66677i | −0.552696 | − | 0.833383i | \(-0.686401\pi\) | ||
0.552696 | − | 0.833383i | \(-0.313599\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.8593 | − | 15.2794i | 0.643188 | − | 0.550275i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.52734 | − | 2.03651i | 0.126870 | − | 0.0732482i | −0.435222 | − | 0.900323i | \(-0.643330\pi\) |
0.562092 | + | 0.827075i | \(0.309997\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.600290 | + | 0.00431744i | 0.0215353 | + | 0.000154887i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 36.4694 | + | 21.0556i | 1.30665 | + | 0.754397i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.08988 | − | 12.2800i | −0.253696 | − | 0.439414i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.7550 | − | 35.2998i | −0.777459 | − | 1.26151i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.82407 | − | 10.0876i | −0.207606 | − | 0.359584i | 0.743354 | − | 0.668898i | \(-0.233234\pi\) |
−0.950960 | + | 0.309314i | \(0.899900\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.7023 | − | 3.85503i | 0.737022 | − | 0.137243i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.04638 | − | 7.85295i | −0.321652 | − | 0.279219i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45.1673 | + | 26.0774i | 1.60394 | + | 0.926034i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36.7250i | 1.30087i | 0.759564 | + | 0.650433i | \(0.225412\pi\) | ||||
−0.759564 | + | 0.650433i | \(0.774588\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.8407 | 1.09106 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −23.0561 | + | 8.89511i | −0.814647 | + | 0.314293i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −26.2507 | − | 15.1558i | −0.926366 | − | 0.534837i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 38.2107 | − | 7.11532i | 1.34508 | − | 0.250471i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.1224 | + | 19.7006i | −1.19968 | + | 0.692635i | −0.960484 | − | 0.278336i | \(-0.910217\pi\) |
−0.239196 | + | 0.970971i | \(0.576884\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.4733i | 1.77236i | 0.463345 | + | 0.886178i | \(0.346649\pi\) | ||||
−0.463345 | + | 0.886178i | \(0.653351\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.9295 | + | 9.35062i | −0.383313 | + | 0.327941i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.54752 | + | 13.0727i | −0.264054 | + | 0.457355i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.46970 | − | 47.3748i | −0.295955 | − | 1.65541i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.6817 | − | 13.6726i | −0.826498 | − | 0.477179i | 0.0261543 | − | 0.999658i | \(-0.491674\pi\) |
−0.852652 | + | 0.522479i | \(0.825007\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.8603 | + | 12.0437i | −0.727144 | + | 0.419817i | −0.817377 | − | 0.576104i | \(-0.804572\pi\) |
0.0902322 | + | 0.995921i | \(0.471239\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.4026 | −0.744242 | −0.372121 | − | 0.928184i | \(-0.621369\pi\) | ||||
−0.372121 | + | 0.928184i | \(0.621369\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.3957 | + | 15.8169i | −0.951494 | + | 0.549345i | −0.893545 | − | 0.448974i | \(-0.851789\pi\) |
−0.0579490 | + | 0.998320i | \(0.518456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.92053 | + | 10.3137i | 0.0666225 | + | 0.357777i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.2363 | − | 16.8936i | −0.458610 | − | 0.585328i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.0478 | − | 29.7357i | 0.554691 | − | 1.02782i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.4562 | 1.39670 | 0.698351 | − | 0.715755i | \(-0.253917\pi\) | ||||
0.698351 | + | 0.715755i | \(0.253917\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34.6799 | −1.19586 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.7068 | + | 10.1383i | 0.988716 | + | 0.349183i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.6001 | − | 3.65809i | 0.364224 | − | 0.125693i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.9766 | − | 2.60263i | 0.479677 | − | 0.0893220i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.326015 | − | 0.188225i | 0.0111756 | − | 0.00645226i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.7681 | 1.56707 | 0.783536 | − | 0.621347i | \(-0.213414\pi\) | ||||
0.783536 | + | 0.621347i | \(0.213414\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.12566 | − | 2.95930i | 0.175089 | − | 0.101088i | −0.409894 | − | 0.912133i | \(-0.634434\pi\) |
0.584983 | + | 0.811045i | \(0.301101\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.8859 | − | 10.9038i | −0.644377 | − | 0.372031i | 0.141921 | − | 0.989878i | \(-0.454672\pi\) |
−0.786299 | + | 0.617847i | \(0.788005\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 49.2764 | − | 27.9791i | 1.67933 | − | 0.953526i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.9429 | − | 32.8100i | 0.644823 | − | 1.11687i | −0.339519 | − | 0.940599i | \(-0.610264\pi\) |
0.984342 | − | 0.176267i | \(-0.0564023\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.55769 | + | 10.0027i | 0.290634 | + | 0.339708i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 9.54910i | − | 0.323931i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 84.0032 | − | 48.4993i | 2.84634 | − | 1.64334i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.4237 | + | 10.8328i | 0.454325 | + | 0.366636i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.4929 | − | 26.8427i | −1.56995 | − | 0.906412i | −0.996173 | − | 0.0874025i | \(-0.972143\pi\) |
−0.573779 | − | 0.819010i | \(-0.694523\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.34674 | + | 2.24147i | 0.214070 | + | 0.0756029i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.12570 | −0.0379259 | −0.0189630 | − | 0.999820i | \(-0.506036\pi\) | ||||
−0.0189630 | + | 0.999820i | \(0.506036\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 48.0889i | − | 1.61832i | −0.587587 | − | 0.809161i | \(-0.699922\pi\) | ||
0.587587 | − | 0.809161i | \(-0.300078\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.9352 | + | 25.9434i | 1.50878 | + | 0.871093i | 0.999948 | + | 0.0102253i | \(0.00325487\pi\) |
0.508829 | + | 0.860867i | \(0.330078\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.21556 | + | 1.40029i | −0.0407684 | + | 0.0469641i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.5964 | + | 26.0291i | 0.790509 | + | 0.872008i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.1286 | − | 29.6676i | −0.573187 | − | 0.992789i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.6195 | − | 22.9322i | −0.655075 | − | 0.765684i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −25.9462 | − | 44.9401i | −0.865353 | − | 1.49884i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.2295 | + | 8.21540i | 0.474053 | + | 0.273695i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.0293 | + | 17.6634i | 0.333754 | + | 0.587801i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.18747 | − | 3.57234i | 0.205452 | − | 0.118618i | −0.393744 | − | 0.919220i | \(-0.628820\pi\) |
0.599196 | + | 0.800602i | \(0.295487\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.22049 | + | 26.9415i | −0.139985 | + | 0.893594i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.4884i | 1.27518i | 0.770377 | + | 0.637589i | \(0.220068\pi\) | ||||
−0.770377 | + | 0.637589i | \(0.779932\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.9050 | − | 25.8162i | −0.493283 | − | 0.854392i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.3068 | + | 4.59217i | −0.439429 | + | 0.151647i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.0403 | − | 46.8351i | 0.891976 | − | 1.54495i | 0.0544730 | − | 0.998515i | \(-0.482652\pi\) |
0.837503 | − | 0.546433i | \(-0.184015\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.0690741 | + | 0.195584i | −0.00227607 | + | 0.00644471i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 22.0246i | − | 0.724950i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.75758 | + | 1.06388i | −0.0905709 | + | 0.0349425i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.8140 | + | 32.5869i | −0.617269 | + | 1.06914i | 0.372713 | + | 0.927947i | \(0.378427\pi\) |
−0.989982 | + | 0.141194i | \(0.954906\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.89970 | + | 22.1154i | −0.291676 | + | 0.724802i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.3816 | − | 4.16773i | 0.732740 | − | 0.136445i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.05652 | 0.0998522 | 0.0499261 | − | 0.998753i | \(-0.484101\pi\) | ||||
0.0499261 | + | 0.998753i | \(0.484101\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.2008 | + | 30.6248i | 0.855030 | + | 0.999402i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.3577 | + | 47.3849i | 0.891835 | + | 1.54470i | 0.837674 | + | 0.546171i | \(0.183915\pi\) |
0.0541612 | + | 0.998532i | \(0.482752\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.7674 | − | 30.7741i | 0.578587 | − | 1.00214i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.58341 | + | 6.20664i | −0.116445 | + | 0.201689i | −0.918356 | − | 0.395754i | \(-0.870483\pi\) |
0.801911 | + | 0.597443i | \(0.203817\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.5407 | − | 40.7737i | −0.764164 | − | 1.32357i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 39.1266 | + | 45.7332i | 1.26877 | + | 1.48300i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.140553 | 0.00455295 | 0.00227648 | − | 0.999997i | \(-0.499275\pi\) | ||||
0.00227648 | + | 0.999997i | \(0.499275\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 53.0431 | − | 9.87729i | 1.71464 | − | 0.319287i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.97446 | − | 10.1953i | 0.0637586 | − | 0.329222i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.64335 | − | 9.77457i | 0.182043 | − | 0.315309i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.61485 | − | 1.39462i | 0.116487 | − | 0.0449410i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 21.4958i | − | 0.691258i | −0.938371 | − | 0.345629i | \(-0.887666\pi\) | ||
0.938371 | − | 0.345629i | \(-0.112334\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.02238 | + | 17.0524i | −0.193467 | + | 0.547802i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.37642 | − | 12.7763i | 0.236721 | − | 0.410012i | −0.723051 | − | 0.690795i | \(-0.757261\pi\) |
0.959771 | + | 0.280783i | \(0.0905940\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.0496 | + | 32.3123i | −0.899228 | + | 1.03589i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.621141 | + | 1.07585i | 0.0198720 | + | 0.0344194i | 0.875790 | − | 0.482692i | \(-0.160341\pi\) |
−0.855918 | + | 0.517111i | \(0.827007\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 32.1561i | − | 1.02771i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.42232 | + | 21.8464i | −0.109266 | + | 0.697501i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.4680 | − | 6.04373i | 0.333879 | − | 0.192765i | −0.323683 | − | 0.946166i | \(-0.604921\pi\) |
0.657562 | + | 0.753401i | \(0.271588\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −46.0959 | − | 0.331534i | −1.46725 | − | 0.0105528i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.0311 | + | 6.36883i | 0.350770 | + | 0.202517i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.50767 | − | 7.80752i | −0.143191 | − | 0.248014i | 0.785506 | − | 0.618854i | \(-0.212403\pi\) |
−0.928697 | + | 0.370841i | \(0.879070\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −28.8307 | − | 33.6988i | −0.914915 | − | 1.06940i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.5205 | + | 37.2746i | 0.681562 | + | 1.18050i | 0.974504 | + | 0.224370i | \(0.0720323\pi\) |
−0.292942 | + | 0.956130i | \(0.594634\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.680401 | + | 0.0195419i | −0.0215270 | + | 0.000618278i |
(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 | 2100.2.bo.g.1349.7 | 20 | ||
3.2 | odd | 2 | 2100.2.bo.h.1349.1 | 20 | |||
5.2 | odd | 4 | 420.2.bh.b.341.1 | yes | 10 | ||
5.3 | odd | 4 | 2100.2.bi.j.1601.5 | 10 | |||
5.4 | even | 2 | inner | 2100.2.bo.g.1349.4 | 20 | ||
7.3 | odd | 6 | 2100.2.bo.h.1949.10 | 20 | |||
15.2 | even | 4 | 420.2.bh.a.341.3 | yes | 10 | ||
15.8 | even | 4 | 2100.2.bi.k.1601.3 | 10 | |||
15.14 | odd | 2 | 2100.2.bo.h.1349.10 | 20 | |||
21.17 | even | 6 | inner | 2100.2.bo.g.1949.4 | 20 | ||
35.2 | odd | 12 | 2940.2.d.a.881.9 | 10 | |||
35.3 | even | 12 | 2100.2.bi.k.101.3 | 10 | |||
35.12 | even | 12 | 2940.2.d.b.881.2 | 10 | |||
35.17 | even | 12 | 420.2.bh.a.101.3 | ✓ | 10 | ||
35.24 | odd | 6 | 2100.2.bo.h.1949.1 | 20 | |||
105.2 | even | 12 | 2940.2.d.b.881.1 | 10 | |||
105.17 | odd | 12 | 420.2.bh.b.101.1 | yes | 10 | ||
105.38 | odd | 12 | 2100.2.bi.j.101.5 | 10 | |||
105.47 | odd | 12 | 2940.2.d.a.881.10 | 10 | |||
105.59 | even | 6 | inner | 2100.2.bo.g.1949.7 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bh.a.101.3 | ✓ | 10 | 35.17 | even | 12 | ||
420.2.bh.a.341.3 | yes | 10 | 15.2 | even | 4 | ||
420.2.bh.b.101.1 | yes | 10 | 105.17 | odd | 12 | ||
420.2.bh.b.341.1 | yes | 10 | 5.2 | odd | 4 | ||
2100.2.bi.j.101.5 | 10 | 105.38 | odd | 12 | |||
2100.2.bi.j.1601.5 | 10 | 5.3 | odd | 4 | |||
2100.2.bi.k.101.3 | 10 | 35.3 | even | 12 | |||
2100.2.bi.k.1601.3 | 10 | 15.8 | even | 4 | |||
2100.2.bo.g.1349.4 | 20 | 5.4 | even | 2 | inner | ||
2100.2.bo.g.1349.7 | 20 | 1.1 | even | 1 | trivial | ||
2100.2.bo.g.1949.4 | 20 | 21.17 | even | 6 | inner | ||
2100.2.bo.g.1949.7 | 20 | 105.59 | even | 6 | inner | ||
2100.2.bo.h.1349.1 | 20 | 3.2 | odd | 2 | |||
2100.2.bo.h.1349.10 | 20 | 15.14 | odd | 2 | |||
2100.2.bo.h.1949.1 | 20 | 35.24 | odd | 6 | |||
2100.2.bo.h.1949.10 | 20 | 7.3 | odd | 6 | |||
2940.2.d.a.881.9 | 10 | 35.2 | odd | 12 | |||
2940.2.d.a.881.10 | 10 | 105.47 | odd | 12 | |||
2940.2.d.b.881.1 | 10 | 105.2 | even | 12 | |||
2940.2.d.b.881.2 | 10 | 35.12 | even | 12 |