Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(379,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("380.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.d (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: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 13x^{8} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 379.4 | ||
Root | \(-1.13320 + 0.846083i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 380.379 |
Dual form | 380.2.d.a.379.3 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.13320 | + | 0.846083i | −0.801294 | + | 0.598271i | ||||
\(3\) | − | 1.52380i | − | 0.879768i | −0.898055 | − | 0.439884i | \(-0.855020\pi\) | ||
0.898055 | − | 0.439884i | \(-0.144980\pi\) | |||||||
\(4\) | 0.568286 | − | 1.91756i | 0.284143 | − | 0.958782i | ||||
\(5\) | 2.23607 | 1.00000 | ||||||||
\(6\) | 1.28926 | + | 1.72677i | 0.526340 | + | 0.704953i | ||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0.978437 | + | 2.65380i | 0.345930 | + | 0.938260i | ||||
\(9\) | 0.678024 | 0.226008 | ||||||||
\(10\) | −2.53391 | + | 1.89190i | −0.801294 | + | 0.598271i | ||||
\(11\) | 2.92978i | 0.883361i | 0.897172 | + | 0.441680i | \(0.145618\pi\) | ||||
−0.897172 | + | 0.441680i | \(0.854382\pi\) | |||||||
\(12\) | −2.92199 | − | 0.865956i | −0.843506 | − | 0.249980i | ||||
\(13\) | 2.42350 | 0.672158 | 0.336079 | − | 0.941834i | \(-0.390899\pi\) | ||||
0.336079 | + | 0.941834i | \(0.390899\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.40733i | − | 0.879768i | ||||||
\(16\) | −3.35410 | − | 2.17945i | −0.838525 | − | 0.544862i | ||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | −0.768338 | + | 0.573665i | −0.181099 | + | 0.135214i | ||||
\(19\) | − | 4.35890i | − | 1.00000i | ||||||
\(20\) | 1.27073 | − | 4.28780i | 0.284143 | − | 0.958782i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.47884 | − | 3.32002i | −0.528489 | − | 0.707832i | ||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 4.04387 | − | 1.49094i | 0.825452 | − | 0.304338i | ||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | −2.74631 | + | 2.05048i | −0.538596 | + | 0.402133i | ||||
\(27\) | − | 5.60458i | − | 1.07860i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 2.88288 | + | 3.86118i | 0.526340 | + | 0.704953i | ||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 5.64487 | − | 0.368097i | 0.997881 | − | 0.0650709i | ||||
\(33\) | 4.46440 | 0.777153 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.385312 | − | 1.30016i | 0.0642186 | − | 0.216693i | ||||
\(37\) | 0.802795 | 0.131979 | 0.0659893 | − | 0.997820i | \(-0.478980\pi\) | ||||
0.0659893 | + | 0.997820i | \(0.478980\pi\) | |||||||
\(38\) | 3.68799 | + | 4.93951i | 0.598271 | + | 0.801294i | ||||
\(39\) | − | 3.69294i | − | 0.591343i | ||||||
\(40\) | 2.18785 | + | 5.93408i | 0.345930 | + | 0.938260i | ||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 5.61803 | + | 1.66495i | 0.846950 | + | 0.251001i | ||||
\(45\) | 1.51611 | 0.226008 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | −3.32105 | + | 5.11099i | −0.479353 | + | 0.737708i | ||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | −5.66600 | + | 4.23042i | −0.801294 | + | 0.598271i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.37724 | − | 4.64722i | 0.190989 | − | 0.644453i | ||||
\(53\) | 13.2466 | 1.81956 | 0.909781 | − | 0.415090i | \(-0.136250\pi\) | ||||
0.909781 | + | 0.415090i | \(0.136250\pi\) | |||||||
\(54\) | 4.74195 | + | 6.35112i | 0.645297 | + | 0.864278i | ||||
\(55\) | 6.55118i | 0.883361i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.64210 | −0.879768 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | −6.53377 | − | 1.93634i | −0.843506 | − | 0.249980i | ||||
\(61\) | −15.5804 | −1.99486 | −0.997430 | − | 0.0716414i | \(-0.977176\pi\) | ||||
−0.997430 | + | 0.0716414i | \(0.977176\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.08532 | + | 5.19315i | −0.760665 | + | 0.649144i | ||||
\(65\) | 5.41911 | 0.672158 | ||||||||
\(66\) | −5.05906 | + | 3.77726i | −0.622728 | + | 0.464948i | ||||
\(67\) | 3.36134i | 0.410653i | 0.978694 | + | 0.205326i | \(0.0658256\pi\) | ||||
−0.978694 | + | 0.205326i | \(0.934174\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0.663404 | + | 1.79934i | 0.0781829 | + | 0.212055i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | −0.909728 | + | 0.679231i | −0.105754 | + | 0.0789591i | ||||
\(75\) | − | 7.61901i | − | 0.879768i | ||||||
\(76\) | −8.35847 | − | 2.47710i | −0.958782 | − | 0.284143i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.12453 | + | 4.18484i | 0.353784 | + | 0.473839i | ||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | −7.50000 | − | 4.87340i | −0.838525 | − | 0.544862i | ||||
\(81\) | −6.50621 | −0.722912 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.77505 | + | 2.86660i | −0.828823 | + | 0.305581i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | −1.71806 | + | 1.28275i | −0.181099 | + | 0.135214i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 9.74679i | − | 1.00000i | ||||||
\(96\) | −0.560907 | − | 8.60166i | −0.0572473 | − | 0.877904i | ||||
\(97\) | −19.4685 | −1.97673 | −0.988364 | − | 0.152109i | \(-0.951394\pi\) | ||||
−0.988364 | + | 0.152109i | \(0.951394\pi\) | |||||||
\(98\) | 7.93240 | − | 5.92258i | 0.801294 | − | 0.598271i | ||||
\(99\) | 1.98646i | 0.199647i | ||||||||
\(100\) | 2.84143 | − | 9.58782i | 0.284143 | − | 0.958782i | ||||
\(101\) | −0.868264 | −0.0863955 | −0.0431977 | − | 0.999067i | \(-0.513755\pi\) | ||||
−0.0431977 | + | 0.999067i | \(0.513755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.9447i | − | 1.66961i | −0.550548 | − | 0.834803i | \(-0.685581\pi\) | ||
0.550548 | − | 0.834803i | \(-0.314419\pi\) | |||||||
\(104\) | 2.37124 | + | 6.43149i | 0.232519 | + | 0.630659i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.0111 | + | 11.2077i | −1.45800 | + | 1.08859i | ||||
\(107\) | 16.9906i | 1.64255i | 0.570534 | + | 0.821274i | \(0.306736\pi\) | ||||
−0.570534 | + | 0.821274i | \(0.693264\pi\) | |||||||
\(108\) | −10.7471 | − | 3.18501i | −1.03414 | − | 0.306477i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | −5.54284 | − | 7.42380i | −0.528489 | − | 0.707832i | ||||
\(111\) | − | 1.22330i | − | 0.116111i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.3361 | −1.53677 | −0.768386 | − | 0.639987i | \(-0.778940\pi\) | ||||
−0.768386 | + | 0.639987i | \(0.778940\pi\) | |||||||
\(114\) | 7.52683 | − | 5.61977i | 0.704953 | − | 0.526340i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.64319 | 0.151913 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 9.04237 | − | 3.33385i | 0.825452 | − | 0.304338i | ||||
\(121\) | 2.41641 | 0.219673 | ||||||||
\(122\) | 17.6557 | − | 13.1823i | 1.59847 | − | 1.19347i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803 | 1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.7066i | 1.74868i | 0.485315 | + | 0.874339i | \(0.338705\pi\) | ||||
−0.485315 | + | 0.874339i | \(0.661295\pi\) | |||||||
\(128\) | 2.50205 | − | 11.0336i | 0.221152 | − | 0.975239i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.14094 | + | 4.58502i | −0.538596 | + | 0.402133i | ||||
\(131\) | 19.4936i | 1.70316i | 0.524222 | + | 0.851581i | \(0.324356\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 2.53706 | − | 8.56078i | 0.220823 | − | 0.745120i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.84397 | − | 3.80907i | −0.245682 | − | 0.329054i | ||||
\(135\) | − | 12.5322i | − | 1.07860i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.8917i | 1.85683i | 0.371546 | + | 0.928414i | \(0.378828\pi\) | ||||
−0.371546 | + | 0.928414i | \(0.621172\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.10031i | 0.593758i | ||||||||
\(144\) | −2.27416 | − | 1.47772i | −0.189514 | − | 0.123143i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.6666i | 0.879768i | ||||||||
\(148\) | 0.456217 | − | 1.53941i | 0.0375008 | − | 0.126539i | ||||
\(149\) | 22.9364 | 1.87902 | 0.939512 | − | 0.342516i | \(-0.111279\pi\) | ||||
0.939512 | + | 0.342516i | \(0.111279\pi\) | |||||||
\(150\) | 6.44632 | + | 8.63387i | 0.526340 | + | 0.704953i | ||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 11.5677 | − | 4.26491i | 0.938260 | − | 0.345930i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.08144 | − | 2.09864i | −0.566969 | − | 0.168026i | ||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 20.1852i | − | 1.60079i | ||||||
\(160\) | 12.6223 | − | 0.823090i | 0.997881 | − | 0.0650709i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.37284 | − | 5.50480i | 0.579265 | − | 0.432498i | ||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.98271 | 0.777153 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 25.8018i | 1.99660i | 0.0582442 | + | 0.998302i | \(0.481450\pi\) | ||||
−0.0582442 | + | 0.998302i | \(0.518550\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.12665 | −0.548204 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 2.95544i | − | 0.226008i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −25.4017 | −1.93126 | −0.965628 | − | 0.259928i | \(-0.916301\pi\) | ||||
−0.965628 | + | 0.259928i | \(0.916301\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.38530 | − | 9.82677i | 0.481310 | − | 0.740721i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0.861583 | − | 2.90724i | 0.0642186 | − | 0.216693i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.7414i | 1.75501i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.79510 | 0.131979 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.24660 | + | 11.0451i | 0.598271 | + | 0.801294i | ||||
\(191\) | − | 26.1534i | − | 1.89239i | −0.323592 | − | 0.946197i | \(-0.604891\pi\) | ||
0.323592 | − | 0.946197i | \(-0.395109\pi\) | |||||||
\(192\) | 7.91334 | + | 9.27283i | 0.571096 | + | 0.669209i | ||||
\(193\) | 17.8629 | 1.28580 | 0.642901 | − | 0.765950i | \(-0.277731\pi\) | ||||
0.642901 | + | 0.765950i | \(0.277731\pi\) | |||||||
\(194\) | 22.0617 | − | 16.4720i | 1.58394 | − | 1.18262i | ||||
\(195\) | − | 8.25766i | − | 0.591343i | ||||||
\(196\) | −3.97800 | + | 13.4229i | −0.284143 | + | 0.958782i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | −1.68071 | − | 2.25106i | −0.119443 | − | 0.159976i | ||||
\(199\) | 8.71780i | 0.617988i | 0.951064 | + | 0.308994i | \(0.0999924\pi\) | ||||
−0.951064 | + | 0.308994i | \(0.900008\pi\) | |||||||
\(200\) | 4.89218 | + | 13.2690i | 0.345930 | + | 0.938260i | ||||
\(201\) | 5.12202 | 0.361279 | ||||||||
\(202\) | 0.983917 | − | 0.734624i | 0.0692281 | − | 0.0516879i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 14.3366 | + | 19.2017i | 0.998878 | + | 1.33785i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.12866 | − | 5.28189i | −0.563621 | − | 0.366234i | ||||
\(209\) | 12.7706 | 0.883361 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | 7.52786 | − | 25.4012i | 0.517016 | − | 1.74456i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.3755 | − | 19.2538i | −0.982689 | − | 1.31616i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.8735 | − | 5.48373i | 1.01201 | − | 0.373121i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 12.5623 | + | 3.72294i | 0.846950 | + | 0.251001i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.03501 | + | 1.38625i | 0.0694657 | + | 0.0930387i | ||||
\(223\) | − | 28.8494i | − | 1.93190i | −0.258728 | − | 0.965950i | \(-0.583303\pi\) | ||
0.258728 | − | 0.965950i | \(-0.416697\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.39012 | 0.226008 | ||||||||
\(226\) | 18.5121 | − | 13.8217i | 1.23140 | − | 0.919406i | ||||
\(227\) | 3.45331i | 0.229205i | 0.993411 | + | 0.114602i | \(0.0365594\pi\) | ||||
−0.993411 | + | 0.114602i | \(0.963441\pi\) | |||||||
\(228\) | −3.77461 | + | 12.7367i | −0.249980 | + | 0.843506i | ||||
\(229\) | −6.48779 | −0.428725 | −0.214362 | − | 0.976754i | \(-0.568767\pi\) | ||||
−0.214362 | + | 0.976754i | \(0.568767\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(234\) | −1.86207 | + | 1.39028i | −0.121727 | + | 0.0908853i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 19.4936i | − | 1.26094i | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||
0.776215 | − | 0.630468i | \(-0.217137\pi\) | |||||||
\(240\) | −7.42610 | + | 11.4285i | −0.479353 | + | 0.737708i | ||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | −2.73827 | + | 2.04448i | −0.176023 | + | 0.131424i | ||||
\(243\) | − | 6.89957i | − | 0.442608i | ||||||
\(244\) | −8.85410 | + | 29.8763i | −0.566826 | + | 1.91264i | ||||
\(245\) | −15.6525 | −1.00000 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 10.5638i | − | 0.672158i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.6696 | + | 9.45950i | −0.801294 | + | 0.598271i | ||||
\(251\) | 26.1534i | 1.65079i | 0.564557 | + | 0.825394i | \(0.309047\pi\) | ||||
−0.564557 | + | 0.825394i | \(0.690953\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −16.6734 | − | 22.3315i | −1.04618 | − | 1.40121i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.50000 | + | 14.6202i | 0.406250 | + | 0.913762i | ||||
\(257\) | −31.9123 | −1.99064 | −0.995318 | − | 0.0966558i | \(-0.969185\pi\) | ||||
−0.995318 | + | 0.0966558i | \(0.969185\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.07960 | − | 10.3915i | 0.190989 | − | 0.644453i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −16.4932 | − | 22.0901i | −1.01895 | − | 1.36473i | ||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 4.36814 | + | 11.8476i | 0.268840 | + | 0.729172i | ||||
\(265\) | 29.6203 | 1.81956 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.44558 | + | 1.91020i | 0.393727 | + | 0.116684i | ||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 10.6033 | + | 14.2015i | 0.645297 | + | 0.864278i | ||||
\(271\) | − | 24.1298i | − | 1.46578i | −0.680345 | − | 0.732892i | \(-0.738170\pi\) | ||
0.680345 | − | 0.732892i | \(-0.261830\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.6489i | 0.883361i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | −18.5222 | − | 24.8077i | −1.11089 | − | 1.48787i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14.8522 | −0.879768 | ||||||||
\(286\) | −6.00746 | − | 8.04608i | −0.355228 | − | 0.475774i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.82736 | − | 0.249579i | 0.225529 | − | 0.0147066i | ||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 29.6662i | 1.73906i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.0848 | −1.40705 | −0.703525 | − | 0.710670i | \(-0.748392\pi\) | ||||
−0.703525 | + | 0.710670i | \(0.748392\pi\) | |||||||
\(294\) | −9.02485 | − | 12.0874i | −0.526340 | − | 0.704953i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.785484 | + | 2.13046i | 0.0456553 | + | 0.123830i | ||||
\(297\) | 16.4202 | 0.952796 | ||||||||
\(298\) | −25.9915 | + | 19.4061i | −1.50565 | + | 1.12417i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −14.6099 | − | 4.32978i | −0.843506 | − | 0.249980i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.32306i | 0.0760080i | ||||||||
\(304\) | −9.50000 | + | 14.6202i | −0.544862 | + | 0.838525i | ||||
\(305\) | −34.8387 | −1.99486 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 23.8053i | − | 1.35864i | −0.733842 | − | 0.679320i | \(-0.762275\pi\) | ||
0.733842 | − | 0.679320i | \(-0.237725\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.8203 | −1.46887 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 31.3726i | − | 1.77898i | −0.456955 | − | 0.889490i | \(-0.651060\pi\) | ||
0.456955 | − | 0.889490i | \(-0.348940\pi\) | |||||||
\(312\) | 9.80032 | − | 3.61330i | 0.554834 | − | 0.204563i | ||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.8607 | 0.609998 | 0.304999 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304999 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(318\) | 17.0784 | + | 22.8739i | 0.957708 | + | 1.28270i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −13.6072 | + | 11.6122i | −0.760665 | + | 0.649144i | ||||
\(321\) | 25.8904 | 1.44506 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −3.69739 | + | 12.4761i | −0.205410 | + | 0.693115i | ||||
\(325\) | 12.1175 | 0.672158 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −11.3124 | + | 8.44620i | −0.622728 | + | 0.464948i | ||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.544315 | 0.0298283 | ||||||||
\(334\) | −21.8305 | − | 29.2386i | −1.19451 | − | 1.59987i | ||||
\(335\) | 7.51618i | 0.410653i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.7733 | −1.34949 | −0.674744 | − | 0.738052i | \(-0.735746\pi\) | ||||
−0.674744 | + | 0.738052i | \(0.735746\pi\) | |||||||
\(338\) | 8.07592 | − | 6.02974i | 0.439272 | − | 0.327975i | ||||
\(339\) | 24.8930i | 1.35200i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.50055 | + | 3.34911i | 0.135214 | + | 0.181099i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 28.7852 | − | 21.4920i | 1.54750 | − | 1.15541i | ||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.4164 | −0.718164 | −0.359082 | − | 0.933306i | \(-0.616910\pi\) | ||||
−0.359082 | + | 0.933306i | \(0.616910\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 13.5827i | − | 0.724991i | ||||||
\(352\) | 1.07844 | + | 16.5382i | 0.0574811 | + | 0.881489i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.5131i | 1.34653i | 0.739401 | + | 0.673265i | \(0.235109\pi\) | ||||
−0.739401 | + | 0.673265i | \(0.764891\pi\) | |||||||
\(360\) | 1.48342 | + | 4.02345i | 0.0781829 | + | 0.212055i | ||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 3.68213i | − | 0.193262i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −20.0872 | − | 26.9038i | −1.04997 | − | 1.40628i | ||||
\(367\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.03421 | + | 1.51881i | −0.105754 | + | 0.0789591i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 38.1342 | 1.97452 | 0.987258 | − | 0.159130i | \(-0.0508689\pi\) | ||||
0.987258 | + | 0.159130i | \(0.0508689\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 17.0366i | − | 0.879768i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | −18.6901 | − | 5.53897i | −0.958782 | − | 0.284143i | ||||
\(381\) | 30.0290 | 1.53843 | ||||||||
\(382\) | 22.1280 | + | 29.6370i | 1.13216 | + | 1.51636i | ||||
\(383\) | − | 3.31535i | − | 0.169407i | −0.996406 | − | 0.0847033i | \(-0.973006\pi\) | ||
0.996406 | − | 0.0847033i | \(-0.0269942\pi\) | |||||||
\(384\) | −16.8130 | − | 3.81263i | −0.857984 | − | 0.194562i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −20.2423 | + | 15.1135i | −1.03030 | + | 0.769258i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.0637 | + | 37.3321i | −0.561673 | + | 1.89525i | ||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 6.98666 | + | 9.35758i | 0.353784 | + | 0.473839i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −6.84906 | − | 18.5766i | −0.345930 | − | 0.938260i | ||||
\(393\) | 29.7044 | 1.49839 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.80916 | + | 1.12888i | 0.191418 | + | 0.0567282i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | −7.37598 | − | 9.87901i | −0.369725 | − | 0.495190i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.7705 | − | 10.8972i | −0.838525 | − | 0.544862i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | −5.80427 | + | 4.33365i | −0.289491 | + | 0.216143i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.493422 | + | 1.66495i | −0.0245487 | + | 0.0828344i | ||||
\(405\) | −14.5483 | −0.722912 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.35201i | 0.116585i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −32.4925 | − | 9.62941i | −1.60079 | − | 0.474407i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 13.6803 | − | 0.892083i | 0.670733 | − | 0.0437379i | ||||
\(417\) | 33.3586 | 1.63358 | ||||||||
\(418\) | −14.4716 | + | 10.8050i | −0.707832 | + | 0.528489i | ||||
\(419\) | 19.4936i | 0.952324i | 0.879358 | + | 0.476162i | \(0.157972\pi\) | ||||
−0.879358 | + | 0.476162i | \(0.842028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.9610 | + | 35.1539i | 0.629440 | + | 1.70722i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 32.5807 | + | 9.65555i | 1.57485 | + | 0.466719i | ||||
\(429\) | 10.8195 | 0.522369 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | −12.2149 | + | 18.7983i | −0.587690 | + | 0.904436i | ||||
\(433\) | 39.3143 | 1.88932 | 0.944662 | − | 0.328044i | \(-0.106389\pi\) | ||||
0.944662 | + | 0.328044i | \(0.106389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | −17.3855 | + | 6.40992i | −0.828823 | + | 0.305581i | ||||
\(441\) | −4.74617 | −0.226008 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | −2.34576 | − | 0.695185i | −0.111325 | − | 0.0329920i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 24.4090 | + | 32.6922i | 1.15580 | + | 1.54802i | ||||
\(447\) | − | 34.9506i | − | 1.65311i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | −3.84169 | + | 2.86833i | −0.181099 | + | 0.135214i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −9.28358 | + | 31.3255i | −0.436663 | + | 1.47343i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.92179 | − | 3.91330i | −0.137126 | − | 0.183660i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.49888 | − | 17.6268i | −0.304338 | − | 0.825452i | ||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | 7.35196 | − | 5.48921i | 0.343535 | − | 0.256494i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 0.933803 | − | 3.15093i | 0.0431651 | − | 0.145652i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 21.7945i | − | 1.00000i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.98152 | 0.411236 | ||||||||
\(478\) | 16.4932 | + | 22.0901i | 0.754381 | + | 1.01038i | ||||
\(479\) | − | 43.0918i | − | 1.96891i | −0.175630 | − | 0.984456i | \(-0.556196\pi\) | ||
0.175630 | − | 0.984456i | \(-0.443804\pi\) | |||||||
\(480\) | −1.25423 | − | 19.2339i | −0.0572473 | − | 0.877904i | ||||
\(481\) | 1.94557 | 0.0887105 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.37321 | − | 4.63362i | 0.0624187 | − | 0.210619i | ||||
\(485\) | −43.5329 | −1.97673 | ||||||||
\(486\) | 5.83761 | + | 7.81860i | 0.264800 | + | 0.354659i | ||||
\(487\) | − | 44.1113i | − | 1.99887i | −0.0335531 | − | 0.999437i | \(-0.510682\pi\) | ||
0.0335531 | − | 0.999437i | \(-0.489318\pi\) | |||||||
\(488\) | −15.2444 | − | 41.3472i | −0.690082 | − | 1.87170i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 17.7374 | − | 13.2433i | 0.801294 | − | 0.598271i | ||||
\(491\) | 26.1534i | 1.18029i | 0.807299 | + | 0.590143i | \(0.200929\pi\) | ||||
−0.807299 | + | 0.590143i | \(0.799071\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 8.93785 | + | 11.9709i | 0.402133 | + | 0.538596i | ||||
\(495\) | 4.44186i | 0.199647i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 4.31303i | − | 0.193078i | −0.995329 | − | 0.0965389i | \(-0.969223\pi\) | ||
0.995329 | − | 0.0965389i | \(-0.0307772\pi\) | |||||||
\(500\) | 6.35363 | − | 21.4390i | 0.284143 | − | 0.958782i | ||||
\(501\) | 39.3169 | 1.75655 | ||||||||
\(502\) | −22.1280 | − | 29.6370i | −0.987619 | − | 1.32277i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.94150 | −0.0863955 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.8596i | 0.482292i | ||||||||
\(508\) | 37.7887 | + | 11.1990i | 1.67660 | + | 0.496875i | ||||
\(509\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −19.7357 | − | 11.0681i | −0.872203 | − | 0.489144i | ||||
\(513\) | −24.4298 | −1.07860 | ||||||||
\(514\) | 36.1631 | − | 27.0005i | 1.59508 | − | 1.19094i | ||||
\(515\) | − | 37.8894i | − | 1.66961i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 38.7072i | 1.69906i | ||||||||
\(520\) | 5.30226 | + | 14.3812i | 0.232519 | + | 0.630659i | ||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 43.9846i | − | 1.92331i | −0.274256 | − | 0.961657i | \(-0.588432\pi\) | ||
0.274256 | − | 0.961657i | \(-0.411568\pi\) | |||||||
\(524\) | 37.3802 | + | 11.0779i | 1.63296 | + | 0.483942i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −14.9741 | − | 9.72994i | −0.651662 | − | 0.423441i | ||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | −33.5657 | + | 25.0612i | −1.45800 | + | 1.08859i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 37.9922i | 1.64255i | ||||||||
\(536\) | −8.92033 | + | 3.28886i | −0.385299 | + | 0.142057i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 20.5084i | − | 0.883361i | ||||||
\(540\) | −24.0314 | − | 7.12189i | −1.03414 | − | 0.306477i | ||||
\(541\) | 37.6485 | 1.61864 | 0.809318 | − | 0.587371i | \(-0.199837\pi\) | ||||
0.809318 | + | 0.587371i | \(0.199837\pi\) | |||||||
\(542\) | 20.4159 | + | 27.3439i | 0.876936 | + | 1.17452i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.8418i | 1.48973i | 0.667216 | + | 0.744864i | \(0.267486\pi\) | ||||
−0.667216 | + | 0.744864i | \(0.732514\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.5639 | −0.450855 | ||||||||
\(550\) | −12.3942 | − | 16.6001i | −0.528489 | − | 0.707832i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 2.73539i | − | 0.116111i | ||||||
\(556\) | 41.9787 | + | 12.4407i | 1.78029 | + | 0.527605i | ||||
\(557\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 47.0322i | 1.98217i | 0.133223 | + | 0.991086i | \(0.457467\pi\) | ||||
−0.133223 | + | 0.991086i | \(0.542533\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −36.5286 | −1.53677 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 16.8305 | − | 12.5662i | 0.704953 | − | 0.526340i | ||||
\(571\) | − | 39.4704i | − | 1.65178i | −0.563829 | − | 0.825891i | \(-0.690672\pi\) | ||
0.563829 | − | 0.825891i | \(-0.309328\pi\) | |||||||
\(572\) | 13.6153 | + | 4.03501i | 0.569284 | + | 0.168712i | ||||
\(573\) | −39.8526 | −1.66487 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.12600 | + | 3.52109i | −0.171917 | + | 0.146712i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | −19.2644 | + | 14.3834i | −0.801294 | + | 0.598271i | ||||
\(579\) | − | 27.2196i | − | 1.13121i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −25.1001 | − | 33.6177i | −1.04043 | − | 1.39350i | ||||
\(583\) | 38.8096i | 1.60733i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.67429 | 0.151913 | ||||||||
\(586\) | 27.2929 | − | 20.3778i | 1.12746 | − | 0.841798i | ||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 20.4539 | + | 6.06169i | 0.843506 | + | 0.249980i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.69266 | − | 1.74965i | −0.110667 | − | 0.0719102i | ||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | −18.6074 | + | 13.8928i | −0.763469 | + | 0.570030i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 13.0344 | − | 43.9820i | 0.533912 | − | 1.80157i | ||||
\(597\) | 13.2842 | 0.543686 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 20.2194 | − | 7.45472i | 0.825452 | − | 0.304338i | ||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.27907i | 0.0928109i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.40325 | 0.219673 | ||||||||
\(606\) | −1.11942 | − | 1.49930i | −0.0454734 | − | 0.0609047i | ||||
\(607\) | 23.6673i | 0.960628i | 0.877097 | + | 0.480314i | \(0.159477\pi\) | ||||
−0.877097 | + | 0.480314i | \(0.840523\pi\) | |||||||
\(608\) | −1.60450 | − | 24.6054i | −0.0650709 | − | 0.997881i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 39.4793 | − | 29.4765i | 1.59847 | − | 1.19347i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 20.1413 | + | 26.9762i | 0.812835 | + | 1.08867i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 29.2596 | − | 21.8461i | 1.17699 | − | 0.878781i | ||||
\(619\) | − | 34.9941i | − | 1.40653i | −0.710928 | − | 0.703265i | \(-0.751725\pi\) | ||
0.710928 | − | 0.703265i | \(-0.248275\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.5439 | + | 35.5515i | 1.06431 | + | 1.42549i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −8.04857 | + | 12.3865i | −0.322201 | + | 0.495856i | ||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 19.4599i | − | 0.777153i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.0275i | 0.438997i | 0.975613 | + | 0.219499i | \(0.0704421\pi\) | ||||
−0.975613 | + | 0.219499i | \(0.929558\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.3074 | + | 9.18906i | −0.488788 | + | 0.364944i | ||||
\(635\) | 44.0653i | 1.74868i | ||||||||
\(636\) | −38.7064 | − | 11.4710i | −1.53481 | − | 0.454854i | ||||
\(637\) | −16.9645 | −0.672158 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.59475 | − | 24.6718i | 0.221152 | − | 0.975239i | ||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | −29.3390 | + | 21.9054i | −1.15792 | + | 0.864539i | ||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | −6.36591 | − | 17.2662i | −0.250077 | − | 0.678280i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −13.7316 | + | 10.2524i | −0.538596 | + | 0.402133i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 43.5890i | 1.70316i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 5.67303 | − | 19.1425i | 0.220823 | − | 0.745120i | ||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.616818 | + | 0.460536i | −0.0239012 | + | 0.0178454i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 49.4766 | + | 14.6628i | 1.91431 | + | 0.567321i | ||||
\(669\) | −43.9608 | −1.69962 | ||||||||
\(670\) | −6.35932 | − | 8.51734i | −0.245682 | − | 0.329054i | ||||
\(671\) | − | 45.6470i | − | 1.76218i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.1613 | −1.70229 | −0.851147 | − | 0.524928i | \(-0.824092\pi\) | ||||
−0.851147 | + | 0.524928i | \(0.824092\pi\) | |||||||
\(674\) | 28.0731 | − | 20.9603i | 1.08134 | − | 0.807360i | ||||
\(675\) | − | 28.0229i | − | 1.07860i | ||||||
\(676\) | −4.04998 | + | 13.6658i | −0.155768 | + | 0.525608i | ||||
\(677\) | 50.5780 | 1.94387 | 0.971936 | − | 0.235246i | \(-0.0755896\pi\) | ||||
0.971936 | + | 0.235246i | \(0.0755896\pi\) | |||||||
\(678\) | −21.0616 | − | 28.2088i | −0.808864 | − | 1.08335i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.26217 | 0.201647 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.7466i | 1.09996i | 0.835179 | + | 0.549979i | \(0.185364\pi\) | ||||
−0.835179 | + | 0.549979i | \(0.814636\pi\) | |||||||
\(684\) | −5.66725 | − | 1.67954i | −0.216693 | − | 0.0642186i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.88611i | 0.377178i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 32.1031 | 1.22303 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 52.5727i | 1.99996i | 0.00630823 | + | 0.999980i | \(0.497992\pi\) | ||||
−0.00630823 | + | 0.999980i | \(0.502008\pi\) | |||||||
\(692\) | −14.4354 | + | 48.7094i | −0.548753 | + | 1.85165i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 48.9513i | 1.85683i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 15.2035 | − | 11.3514i | 0.575460 | − | 0.429657i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.1999 | −0.800709 | −0.400354 | − | 0.916360i | \(-0.631113\pi\) | ||||
−0.400354 | + | 0.916360i | \(0.631113\pi\) | |||||||
\(702\) | 11.4921 | + | 15.3919i | 0.433741 | + | 0.580931i | ||||
\(703\) | − | 3.49930i | − | 0.131979i | ||||||
\(704\) | −15.2148 | − | 17.8286i | −0.573429 | − | 0.671942i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.2492 | 1.51159 | 0.755796 | − | 0.654808i | \(-0.227250\pi\) | ||||
0.755796 | + | 0.654808i | \(0.227250\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.8768i | 0.593758i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −29.7044 | −1.10933 | ||||||||
\(718\) | −21.5862 | − | 28.9114i | −0.805590 | − | 1.07897i | ||||
\(719\) | 13.7940i | 0.514429i | 0.966354 | + | 0.257214i | \(0.0828047\pi\) | ||||
−0.966354 | + | 0.257214i | \(0.917195\pi\) | |||||||
\(720\) | −5.08518 | − | 3.30428i | −0.189514 | − | 0.123143i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 21.5308 | − | 16.0756i | 0.801294 | − | 0.598271i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.11539 | + | 4.17259i | 0.115623 | + | 0.154859i | ||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −30.0322 | −1.11230 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 45.5257 | + | 13.4919i | 1.68268 | + | 0.498675i | ||||
\(733\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 23.8513i | 0.879768i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.84797 | −0.362755 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 8.71780i | − | 0.320689i | −0.987061 | − | 0.160345i | \(-0.948739\pi\) | ||
0.987061 | − | 0.160345i | \(-0.0512606\pi\) | |||||||
\(740\) | 1.02013 | − | 3.44223i | 0.0375008 | − | 0.126539i | ||||
\(741\) | −16.0971 | −0.591343 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.62663i | 0.0596754i | 0.999555 | + | 0.0298377i | \(0.00949905\pi\) | ||||
−0.999555 | + | 0.0298377i | \(0.990501\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 51.2874 | 1.87902 | ||||||||
\(746\) | −43.2137 | + | 32.2647i | −1.58217 | + | 1.18130i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 14.4144 | + | 19.3059i | 0.526340 | + | 0.704953i | ||||
\(751\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 39.8526 | 1.45231 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 25.8661 | − | 9.53662i | 0.938260 | − | 0.345930i | ||||
\(761\) | 9.29755 | 0.337036 | 0.168518 | − | 0.985699i | \(-0.446102\pi\) | ||||
0.168518 | + | 0.985699i | \(0.446102\pi\) | |||||||
\(762\) | −34.0289 | + | 25.4070i | −1.23274 | + | 0.920399i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −50.1508 | − | 14.8626i | −1.81439 | − | 0.537710i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.80506 | + | 3.75696i | 0.101351 | + | 0.135744i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 22.2783 | − | 9.90472i | 0.803899 | − | 0.357406i | ||||
\(769\) | −29.2192 | −1.05367 | −0.526836 | − | 0.849967i | \(-0.676622\pi\) | ||||
−0.526836 | + | 0.849967i | \(0.676622\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 48.6281i | 1.75130i | ||||||||
\(772\) | 10.1512 | − | 34.2533i | 0.365351 | − | 1.23280i | ||||
\(773\) | 28.9919 | 1.04277 | 0.521383 | − | 0.853323i | \(-0.325416\pi\) | ||||
0.521383 | + | 0.853323i | \(0.325416\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −19.0487 | − | 51.6656i | −0.683809 | − | 1.85469i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.79920 | + | 5.07650i | −0.243763 | + | 0.182001i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −15.8346 | − | 4.69271i | −0.566969 | − | 0.168026i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 23.4787 | + | 15.2561i | 0.838525 | + | 0.544862i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −33.6610 | + | 25.1324i | −1.20065 | + | 0.896443i | ||||
\(787\) | − | 25.6990i | − | 0.916070i | −0.888934 | − | 0.458035i | \(-0.848553\pi\) | ||
0.888934 | − | 0.458035i | \(-0.151447\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.27167 | + | 1.94363i | −0.187321 | + | 0.0690637i | ||||
\(793\) | −37.7590 | −1.34086 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 45.1355i | − | 1.60079i | ||||||
\(796\) | 16.7169 | + | 4.95420i | 0.592516 | + | 0.175597i | ||||
\(797\) | 28.9016 | 1.02375 | 0.511873 | − | 0.859061i | \(-0.328952\pi\) | ||||
0.511873 | + | 0.859061i | \(0.328952\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 28.2243 | − | 1.84048i | 0.997881 | − | 0.0650709i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 2.91077 | − | 9.82180i | 0.102655 | − | 0.346388i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.849541 | − | 2.30420i | −0.0298868 | − | 0.0810615i | ||||
\(809\) | −22.3607 | −0.786160 | −0.393080 | − | 0.919504i | \(-0.628590\pi\) | ||||
−0.393080 | + | 0.919504i | \(0.628590\pi\) | |||||||
\(810\) | 16.4862 | − | 12.3091i | 0.579265 | − | 0.432498i | ||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −36.7691 | −1.28955 | ||||||||
\(814\) | −1.99000 | − | 2.66530i | −0.0697493 | − | 0.0934187i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.0000 | −1.46581 | −0.732905 | − | 0.680331i | \(-0.761836\pi\) | ||||
−0.732905 | + | 0.680331i | \(0.761836\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(824\) | 44.9678 | − | 16.5793i | 1.56653 | − | 0.577567i | ||||
\(825\) | 22.3220 | 0.777153 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 56.1750i | − | 1.95340i | −0.214614 | − | 0.976699i | \(-0.568849\pi\) | ||
0.214614 | − | 0.976699i | \(-0.431151\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −14.7478 | + | 12.5856i | −0.511287 | + | 0.436327i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −37.8020 | + | 28.2242i | −1.30898 | + | 0.977323i | ||||
\(835\) | 57.6946i | 1.99660i | ||||||||
\(836\) | 7.25735 | − | 24.4884i | 0.251001 | − | 0.846950i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.4932 | − | 22.0901i | −0.569748 | − | 0.763091i | ||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.9357 | −0.548204 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −44.4305 | − | 28.8703i | −1.52575 | − | 0.991410i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 6.60857i | − | 0.226008i | ||||||
\(856\) | −45.0898 | + | 16.6243i | −1.54114 | + | 0.568206i | ||||
\(857\) | −10.2359 | −0.349651 | −0.174825 | − | 0.984599i | \(-0.555936\pi\) | ||||
−0.174825 | + | 0.984599i | \(0.555936\pi\) | |||||||
\(858\) | −12.2606 | + | 9.15418i | −0.418571 | + | 0.312519i | ||||
\(859\) | − | 58.4808i | − | 1.99534i | −0.0682391 | − | 0.997669i | \(-0.521738\pi\) | ||
0.0682391 | − | 0.997669i | \(-0.478262\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.0875i | 1.50075i | 0.661010 | + | 0.750377i | \(0.270128\pi\) | ||||
−0.661010 | + | 0.750377i | \(0.729872\pi\) | |||||||
\(864\) | −2.06303 | − | 31.6371i | −0.0701857 | − | 1.07632i | ||||
\(865\) | −56.7999 | −1.93126 | ||||||||
\(866\) | −44.5510 | + | 33.2632i | −1.51390 | + | 1.13033i | ||||
\(867\) | − | 25.9047i | − | 0.879768i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.14620i | 0.276024i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.2001 | −0.446757 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.3454 | 1.39614 | 0.698068 | − | 0.716032i | \(-0.254044\pi\) | ||||
0.698068 | + | 0.716032i | \(0.254044\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 36.7005i | 1.23788i | ||||||||
\(880\) | 14.2780 | − | 21.9733i | 0.481310 | − | 0.740721i | ||||
\(881\) | −58.6434 | −1.97575 | −0.987874 | − | 0.155261i | \(-0.950378\pi\) | ||||
−0.987874 | + | 0.155261i | \(0.950378\pi\) | |||||||
\(882\) | 5.37836 | − | 4.01566i | 0.181099 | − | 0.135214i | ||||
\(883\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 16.8527i | − | 0.565858i | −0.959141 | − | 0.282929i | \(-0.908694\pi\) | ||
0.959141 | − | 0.282929i | \(-0.0913060\pi\) | |||||||
\(888\) | 3.24640 | − | 1.19692i | 0.108942 | − | 0.0401661i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 19.0617i | − | 0.638592i | ||||||
\(892\) | −55.3206 | − | 16.3947i | −1.85227 | − | 0.548936i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 29.5711 | + | 39.6060i | 0.989005 | + | 1.32462i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.92656 | − | 6.50078i | 0.0642186 | − | 0.216693i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.9838 | − | 43.3528i | −0.531615 | − | 1.44189i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.0826i | 0.567219i | 0.958940 | + | 0.283610i | \(0.0915320\pi\) | ||||
−0.958940 | + | 0.283610i | \(0.908468\pi\) | |||||||
\(908\) | 6.62195 | + | 1.96247i | 0.219757 | + | 0.0651269i | ||||
\(909\) | −0.588704 | −0.0195261 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 22.2783 | + | 14.4761i | 0.737708 | + | 0.479353i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 53.0874i | 1.75501i | ||||||||
\(916\) | −3.68692 | + | 12.4407i | −0.121819 | + | 0.411054i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 58.4808i | 1.92910i | 0.263896 | + | 0.964551i | \(0.414993\pi\) | ||||
−0.263896 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −36.2746 | −1.19529 | ||||||||
\(922\) | 20.3976 | − | 15.2295i | 0.671759 | − | 0.501557i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.01397 | 0.131979 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 11.4889i | − | 0.377345i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.3050 | 1.02708 | 0.513541 | − | 0.858065i | \(-0.328333\pi\) | ||||
0.513541 | + | 0.858065i | \(0.328333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.5123i | 1.00000i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −47.8057 | −1.56509 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.60776 | + | 4.36071i | 0.0525513 | + | 0.142534i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 18.4400 | + | 24.6975i | 0.598271 | + | 0.801294i | ||||
\(951\) | − | 16.5496i | − | 0.536657i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.5673 | −1.54086 | −0.770428 | − | 0.637527i | \(-0.779957\pi\) | ||||
−0.770428 | + | 0.637527i | \(0.779957\pi\) | |||||||
\(954\) | −10.1779 | + | 7.59912i | −0.329521 | + | 0.246030i | ||||
\(955\) | − | 58.4808i | − | 1.89239i | ||||||
\(956\) | −37.3802 | − | 11.0779i | −1.20896 | − | 0.358286i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 36.4592 | + | 48.8316i | 1.17794 | + | 1.57768i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 17.6948 | + | 20.7347i | 0.571096 | + | 0.669209i | ||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | −2.20472 | + | 1.64612i | −0.0710832 | + | 0.0530729i | ||||
\(963\) | 11.5201i | 0.371229i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 39.9427 | 1.28580 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(968\) | 2.36430 | + | 6.41267i | 0.0759916 | + | 0.206111i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 49.3315 | − | 36.8325i | 1.58394 | − | 1.18262i | ||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | −13.2304 | − | 3.92093i | −0.424364 | − | 0.125764i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 37.3218 | + | 49.9869i | 1.19587 | + | 1.60168i | ||||
\(975\) | − | 18.4647i | − | 0.591343i | ||||||
\(976\) | 52.2581 | + | 33.9566i | 1.67274 | + | 1.08692i | ||||
\(977\) | 30.8771 | 0.987846 | 0.493923 | − | 0.869506i | \(-0.335562\pi\) | ||||
0.493923 | + | 0.869506i | \(0.335562\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −8.89508 | + | 30.0146i | −0.284143 | + | 0.958782i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −22.1280 | − | 29.6370i | −0.706131 | − | 0.945756i | ||||
\(983\) | − | 44.2033i | − | 1.40987i | −0.709274 | − | 0.704933i | \(-0.750977\pi\) | ||
0.709274 | − | 0.704933i | \(-0.249023\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −20.2567 | − | 6.00325i | −0.644453 | − | 0.190989i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −3.75818 | − | 5.03352i | −0.119443 | − | 0.159976i | ||||
\(991\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.4936i | 0.617988i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(998\) | 3.64918 | + | 4.88753i | 0.115513 | + | 0.154712i | ||||
\(999\) | − | 4.49933i | − | 0.142353i |
(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 | 380.2.d.a.379.4 | yes | 16 | |
4.3 | odd | 2 | inner | 380.2.d.a.379.3 | ✓ | 16 | |
5.4 | even | 2 | inner | 380.2.d.a.379.13 | yes | 16 | |
19.18 | odd | 2 | inner | 380.2.d.a.379.13 | yes | 16 | |
20.19 | odd | 2 | inner | 380.2.d.a.379.14 | yes | 16 | |
76.75 | even | 2 | inner | 380.2.d.a.379.14 | yes | 16 | |
95.94 | odd | 2 | CM | 380.2.d.a.379.4 | yes | 16 | |
380.379 | even | 2 | inner | 380.2.d.a.379.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.d.a.379.3 | ✓ | 16 | 4.3 | odd | 2 | inner | |
380.2.d.a.379.3 | ✓ | 16 | 380.379 | even | 2 | inner | |
380.2.d.a.379.4 | yes | 16 | 1.1 | even | 1 | trivial | |
380.2.d.a.379.4 | yes | 16 | 95.94 | odd | 2 | CM | |
380.2.d.a.379.13 | yes | 16 | 5.4 | even | 2 | inner | |
380.2.d.a.379.13 | yes | 16 | 19.18 | odd | 2 | inner | |
380.2.d.a.379.14 | yes | 16 | 20.19 | odd | 2 | inner | |
380.2.d.a.379.14 | yes | 16 | 76.75 | even | 2 | inner |