Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(201,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{20} + 20 x^{18} + 261 x^{16} + 1994 x^{14} + 11074 x^{12} + 39211 x^{10} + 99376 x^{8} + 134299 x^{6} + \cdots + 4096 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 201.8 | ||
Root | \(-1.00667 - 1.74361i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.201 |
Dual form | 1900.2.i.g.501.8 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00667 | − | 1.74361i | 0.581203 | − | 1.00667i | −0.414134 | − | 0.910216i | \(-0.635915\pi\) |
0.995337 | − | 0.0964577i | \(-0.0307512\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.34403 | 0.507994 | 0.253997 | − | 0.967205i | \(-0.418255\pi\) | ||||
0.253997 | + | 0.967205i | \(0.418255\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.526784 | − | 0.912416i | −0.175595 | − | 0.304139i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.25594 | 1.58473 | 0.792363 | − | 0.610050i | \(-0.208851\pi\) | ||||
0.792363 | + | 0.610050i | \(0.208851\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.21773 | + | 2.10918i | 0.337738 | + | 0.584980i | 0.984007 | − | 0.178130i | \(-0.0570048\pi\) |
−0.646269 | + | 0.763110i | \(0.723671\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.679914 | + | 1.17765i | −0.164903 | + | 0.285621i | −0.936621 | − | 0.350344i | \(-0.886065\pi\) |
0.771718 | + | 0.635965i | \(0.219398\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.89815 | − | 3.25587i | −0.664882 | − | 0.746949i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.35300 | − | 2.34346i | 0.295248 | − | 0.511384i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.07329 | + | 7.05514i | 0.849339 | + | 1.47110i | 0.881799 | + | 0.471625i | \(0.156332\pi\) |
−0.0324603 | + | 0.999473i | \(0.510334\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.91884 | 0.754182 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.03597 | + | 1.79435i | 0.192375 | + | 0.333203i | 0.946037 | − | 0.324059i | \(-0.105048\pi\) |
−0.753662 | + | 0.657262i | \(0.771714\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.513207 | −0.0921747 | −0.0460873 | − | 0.998937i | \(-0.514675\pi\) | ||||
−0.0460873 | + | 0.998937i | \(0.514675\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.29102 | − | 9.16431i | 0.921048 | − | 1.59530i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.57175 | 0.915991 | 0.457995 | − | 0.888955i | \(-0.348568\pi\) | ||||
0.457995 | + | 0.888955i | \(0.348568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.90344 | 0.785179 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.70353 | − | 4.68265i | 0.422220 | − | 0.731307i | −0.573936 | − | 0.818900i | \(-0.694584\pi\) |
0.996156 | + | 0.0875933i | \(0.0279176\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.36221 | + | 11.0197i | −0.970228 | + | 1.68048i | −0.275369 | + | 0.961339i | \(0.588800\pi\) |
−0.694859 | + | 0.719146i | \(0.744533\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.63266 | + | 2.82785i | 0.238148 | + | 0.412485i | 0.960183 | − | 0.279372i | \(-0.0901262\pi\) |
−0.722035 | + | 0.691857i | \(0.756793\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.19359 | −0.741942 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.36890 | + | 2.37101i | 0.191685 | + | 0.332008i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.88276 | − | 10.1892i | −0.808060 | − | 1.39960i | −0.914206 | − | 0.405250i | \(-0.867185\pi\) |
0.106146 | − | 0.994351i | \(-0.466149\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.59447 | + | 1.77564i | −1.13837 | + | 0.235190i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.0175979 | + | 0.0304805i | −0.00229105 | + | 0.00396822i | −0.867169 | − | 0.498015i | \(-0.834063\pi\) |
0.864878 | + | 0.501983i | \(0.167396\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.518372 | + | 0.897846i | 0.0663707 | + | 0.114957i | 0.897301 | − | 0.441419i | \(-0.145525\pi\) |
−0.830930 | + | 0.556376i | \(0.812191\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.708011 | − | 1.22631i | −0.0892010 | − | 0.154501i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.383377 | + | 0.664028i | 0.0468369 | + | 0.0811239i | 0.888493 | − | 0.458889i | \(-0.151753\pi\) |
−0.841657 | + | 0.540013i | \(0.818419\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 16.4019 | 1.97455 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.68450 | − | 9.84583i | 0.674625 | − | 1.16849i | −0.301953 | − | 0.953323i | \(-0.597638\pi\) |
0.976578 | − | 0.215163i | \(-0.0690282\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.07635 | + | 1.86429i | −0.125977 | + | 0.218199i | −0.922115 | − | 0.386917i | \(-0.873540\pi\) |
0.796137 | + | 0.605116i | \(0.206873\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.06413 | 0.805032 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.48576 | − | 11.2337i | 0.729705 | − | 1.26389i | −0.227302 | − | 0.973824i | \(-0.572991\pi\) |
0.957008 | − | 0.290062i | \(-0.0936761\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.52535 | − | 9.57019i | 0.613928 | − | 1.06335i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.20304 | −0.461343 | −0.230672 | − | 0.973032i | \(-0.574092\pi\) | ||||
−0.230672 | + | 0.973032i | \(0.574092\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.17153 | 0.447235 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.65426 | + | 6.32937i | 0.387351 | + | 0.670912i | 0.992092 | − | 0.125510i | \(-0.0400568\pi\) |
−0.604741 | + | 0.796422i | \(0.706723\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.63667 | + | 2.83479i | 0.171569 | + | 0.297166i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.516632 | + | 0.894833i | −0.0535722 | + | 0.0927898i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.416683 | + | 0.721716i | −0.0423077 | + | 0.0732791i | −0.886404 | − | 0.462913i | \(-0.846804\pi\) |
0.844096 | + | 0.536192i | \(0.180138\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.76875 | − | 4.79561i | −0.278269 | − | 0.481977i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.40992 | − | 12.8344i | −0.737315 | − | 1.27707i | −0.953700 | − | 0.300759i | \(-0.902760\pi\) |
0.216385 | − | 0.976308i | \(-0.430573\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.40773 | 0.926971 | 0.463486 | − | 0.886104i | \(-0.346599\pi\) | ||||
0.463486 | + | 0.886104i | \(0.346599\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.8130 | −1.23868 | −0.619338 | − | 0.785124i | \(-0.712599\pi\) | ||||
−0.619338 | + | 0.785124i | \(0.712599\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.996875 | + | 1.72664i | −0.0954833 | + | 0.165382i | −0.909810 | − | 0.415025i | \(-0.863773\pi\) |
0.814327 | + | 0.580406i | \(0.197106\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.60894 | − | 9.71497i | 0.532377 | − | 0.922104i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.34647 | −0.785170 | −0.392585 | − | 0.919716i | \(-0.628419\pi\) | ||||
−0.392585 | + | 0.919716i | \(0.628419\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.28296 | − | 2.22216i | 0.118610 | − | 0.205439i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.913823 | + | 1.58279i | −0.0837700 | + | 0.145094i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.6249 | 1.51136 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.44314 | − | 9.42780i | −0.490791 | − | 0.850076i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.2907 | − | 17.8240i | −0.913153 | − | 1.58163i | −0.809583 | − | 0.587005i | \(-0.800307\pi\) |
−0.103569 | − | 0.994622i | \(-0.533026\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.8093 | + | 22.1864i | 1.12780 | + | 1.95341i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.36554 | + | 9.29339i | −0.468790 | + | 0.811967i | −0.999364 | − | 0.0356712i | \(-0.988643\pi\) |
0.530574 | + | 0.847639i | \(0.321976\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.89519 | − | 4.37598i | −0.337756 | − | 0.379446i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.58931 | − | 14.8771i | −0.733834 | − | 1.27104i | −0.955233 | − | 0.295855i | \(-0.904396\pi\) |
0.221399 | − | 0.975183i | \(-0.428938\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.66394 | − | 6.34613i | −0.310771 | − | 0.538272i | 0.667758 | − | 0.744378i | \(-0.267254\pi\) |
−0.978530 | + | 0.206106i | \(0.933921\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.57423 | 0.553650 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.40033 | + | 11.0857i | 0.535223 | + | 0.927033i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.22825 | + | 9.05560i | −0.431219 | + | 0.746893i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.12292 | − | 10.6052i | 0.501609 | − | 0.868812i | −0.498389 | − | 0.866953i | \(-0.666075\pi\) |
0.999998 | − | 0.00185904i | \(-0.000591751\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.5577 | −0.940549 | −0.470274 | − | 0.882520i | \(-0.655845\pi\) | ||||
−0.470274 | + | 0.882520i | \(0.655845\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.43267 | 0.115825 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.06996 | + | 3.58528i | −0.165201 | + | 0.286137i | −0.936727 | − | 0.350062i | \(-0.886161\pi\) |
0.771526 | + | 0.636198i | \(0.219494\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −23.6881 | −1.87859 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.47460 | + | 9.48229i | 0.431459 | + | 0.747309i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.41672 | 0.737575 | 0.368787 | − | 0.929514i | \(-0.379773\pi\) | ||||
0.368787 | + | 0.929514i | \(0.379773\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.83551 | + | 11.8395i | 0.528948 | + | 0.916164i | 0.999430 | + | 0.0337550i | \(0.0107466\pi\) |
−0.470482 | + | 0.882409i | \(0.655920\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.53425 | − | 6.12151i | 0.271866 | − | 0.470885i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.44401 | + | 4.35946i | −0.110426 | + | 0.333376i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.88891 | + | 10.1999i | −0.447726 | + | 0.775484i | −0.998238 | − | 0.0593437i | \(-0.981099\pi\) |
0.550512 | + | 0.834827i | \(0.314433\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0354307 | + | 0.0613678i | 0.00266314 | + | 0.00461269i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.5727 | −1.23870 | −0.619350 | − | 0.785115i | \(-0.712604\pi\) | ||||
−0.619350 | + | 0.785115i | \(0.712604\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.19552 | + | 12.4630i | 0.534839 | + | 0.926368i | 0.999171 | + | 0.0407069i | \(0.0129610\pi\) |
−0.464332 | + | 0.885661i | \(0.653706\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.08733 | 0.154300 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.57359 | + | 6.18964i | −0.261327 | + | 0.452631i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.26703 | 0.383120 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.97170 | −0.432097 | −0.216049 | − | 0.976383i | \(-0.569317\pi\) | ||||
−0.216049 | + | 0.976383i | \(0.569317\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.14331 | − | 14.1046i | 0.586168 | − | 1.01527i | −0.408560 | − | 0.912731i | \(-0.633969\pi\) |
0.994729 | − | 0.102542i | \(-0.0326977\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.5233 | −0.820998 | −0.410499 | − | 0.911861i | \(-0.634645\pi\) | ||||
−0.410499 | + | 0.911861i | \(0.634645\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.79943 | − | 8.31285i | −0.340222 | − | 0.589283i | 0.644251 | − | 0.764814i | \(-0.277169\pi\) |
−0.984474 | + | 0.175531i | \(0.943836\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.54374 | 0.108887 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.39237 | + | 2.41166i | 0.0977253 | + | 0.169265i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.29148 | − | 7.43307i | 0.298279 | − | 0.516634i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.2325 | − | 17.1127i | −1.05366 | − | 1.18371i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.28207 | − | 12.6129i | 0.501318 | − | 0.868308i | −0.498681 | − | 0.866786i | \(-0.666182\pi\) |
0.999999 | − | 0.00152265i | \(-0.000484675\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.4449 | − | 19.8231i | −0.784189 | − | 1.35826i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.689764 | −0.0468242 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.16707 | + | 3.75347i | 0.146437 | + | 0.253636i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.31182 | −0.222777 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.78635 | + | 6.55816i | −0.253553 | + | 0.439167i | −0.964501 | − | 0.264077i | \(-0.914933\pi\) |
0.710949 | + | 0.703244i | \(0.248266\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.86640 | −0.455739 | −0.227869 | − | 0.973692i | \(-0.573176\pi\) | ||||
−0.227869 | + | 0.973692i | \(0.573176\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.1011 | 1.46048 | 0.730240 | − | 0.683191i | \(-0.239408\pi\) | ||||
0.730240 | + | 0.683191i | \(0.239408\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.11127 | − | 12.3171i | 0.467887 | − | 0.810404i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.48844 | − | 2.57806i | 0.0975111 | − | 0.168894i | −0.813143 | − | 0.582064i | \(-0.802245\pi\) |
0.910654 | + | 0.413170i | \(0.135579\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.0581 | − | 22.6173i | −0.848214 | − | 1.46915i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.71289 | −0.628275 | −0.314137 | − | 0.949378i | \(-0.601715\pi\) | ||||
−0.314137 | + | 0.949378i | \(0.601715\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.34287 | + | 16.1823i | 0.601827 | + | 1.04239i | 0.992544 | + | 0.121884i | \(0.0388937\pi\) |
−0.390717 | + | 0.920511i | \(0.627773\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.24618 | − | 9.08665i | −0.336543 | − | 0.582909i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.33803 | − | 10.0775i | 0.212394 | − | 0.641216i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.23109 | + | 7.32846i | −0.268134 | + | 0.464422i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.10091 | + | 3.63888i | 0.132608 | + | 0.229684i | 0.924681 | − | 0.380742i | \(-0.124332\pi\) |
−0.792073 | + | 0.610426i | \(0.790998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.4090 | + | 37.0814i | 1.34597 | + | 2.33129i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.0842 | + | 24.3946i | 0.878548 | + | 1.52169i | 0.852934 | + | 0.522018i | \(0.174821\pi\) |
0.0256140 | + | 0.999672i | \(0.491846\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.48859 | 0.465318 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.09146 | − | 1.89047i | 0.0675599 | − | 0.117017i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.35425 | − | 2.34563i | 0.0835065 | − | 0.144637i | −0.821247 | − | 0.570572i | \(-0.806721\pi\) |
0.904754 | + | 0.425935i | \(0.140055\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.7146 | 0.900519 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.64101 | + | 9.77052i | −0.343938 | + | 0.595719i | −0.985160 | − | 0.171637i | \(-0.945094\pi\) |
0.641222 | + | 0.767356i | \(0.278428\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.16690 | + | 5.48523i | −0.192375 | + | 0.333204i | −0.946037 | − | 0.324059i | \(-0.894952\pi\) |
0.753662 | + | 0.657263i | \(0.228286\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.59035 | 0.398866 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.1435 | 0.669549 | 0.334774 | − | 0.942298i | \(-0.391340\pi\) | ||||
0.334774 | + | 0.942298i | \(0.391340\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.270349 | + | 0.468258i | 0.0161854 | + | 0.0280339i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.9061 | − | 22.3541i | −0.769916 | − | 1.33353i | −0.937608 | − | 0.347694i | \(-0.886965\pi\) |
0.167693 | − | 0.985839i | \(-0.446368\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.4304 | + | 24.9942i | −0.857799 | + | 1.48575i | 0.0162249 | + | 0.999868i | \(0.494835\pi\) |
−0.874024 | + | 0.485883i | \(0.838498\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.63361 | − | 6.29360i | 0.214485 | − | 0.371500i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.57543 | + | 13.1210i | 0.445614 | + | 0.771826i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.838927 | + | 1.45306i | 0.0491788 | + | 0.0851801i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.7742 | 1.33048 | 0.665242 | − | 0.746628i | \(-0.268328\pi\) | ||||
0.665242 | + | 0.746628i | \(0.268328\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 20.5972 | 1.19517 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.92035 | + | 17.1825i | −0.573709 | + | 0.993692i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.55098 | + | 14.8107i | −0.492870 | + | 0.853676i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −29.8375 | −1.71412 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.09880 | + | 14.0275i | −0.462223 | + | 0.800593i | −0.999071 | − | 0.0430854i | \(-0.986281\pi\) |
0.536849 | + | 0.843679i | \(0.319615\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.47052 | − | 16.4034i | 0.538759 | − | 0.933158i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.3483 | −1.60749 | −0.803743 | − | 0.594977i | \(-0.797161\pi\) | ||||
−0.803743 | + | 0.594977i | \(0.797161\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.54464 | − | 2.67539i | −0.0873081 | − | 0.151222i | 0.819064 | − | 0.573702i | \(-0.194493\pi\) |
−0.906372 | + | 0.422480i | \(0.861160\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.0225 | + | 20.8236i | 0.675251 | + | 1.16957i | 0.976395 | + | 0.215991i | \(0.0692982\pi\) |
−0.301144 | + | 0.953579i | \(0.597368\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.44500 | + | 9.43101i | 0.304861 | + | 0.528035i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.8985 | + | 22.3408i | −0.719923 | + | 1.24694i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.80476 | − | 1.19928i | 0.322986 | − | 0.0667298i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.00706 | + | 3.47632i | 0.110990 | + | 0.192241i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.19434 | + | 3.80071i | 0.120978 | + | 0.209540i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.7717 | −1.14171 | −0.570857 | − | 0.821049i | \(-0.693389\pi\) | ||||
−0.570857 | + | 0.821049i | \(0.693389\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.93511 | − | 5.08376i | −0.160843 | − | 0.278588i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.21324 | − | 2.10139i | 0.0660892 | − | 0.114470i | −0.831087 | − | 0.556142i | \(-0.812281\pi\) |
0.897177 | + | 0.441672i | \(0.145614\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.40217 | + | 14.5530i | −0.456343 | + | 0.790410i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.69739 | −0.146072 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.3885 | −0.884896 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.43664 | + | 2.48834i | −0.0771230 | + | 0.133581i | −0.902008 | − | 0.431720i | \(-0.857907\pi\) |
0.824885 | + | 0.565301i | \(0.191240\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.89385 | −0.315490 | −0.157745 | − | 0.987480i | \(-0.550422\pi\) | ||||
−0.157745 | + | 0.987480i | \(0.550422\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.77211 | + | 8.26553i | 0.254716 | + | 0.441181i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0238 | 0.639962 | 0.319981 | − | 0.947424i | \(-0.396324\pi\) | ||||
0.319981 | + | 0.947424i | \(0.396324\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.83984 | + | 3.18670i | 0.0973748 | + | 0.168658i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.26590 | − | 3.92466i | 0.119590 | − | 0.207136i | −0.800015 | − | 0.599979i | \(-0.795175\pi\) |
0.919605 | + | 0.392844i | \(0.128509\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.20143 | + | 18.8720i | −0.115865 | + | 0.993265i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.7359 | − | 28.9874i | 0.878406 | − | 1.52144i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.2710 | + | 29.9143i | 0.901539 | + | 1.56151i | 0.825496 | + | 0.564407i | \(0.190895\pi\) |
0.0760429 | + | 0.997105i | \(0.475771\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.69670 | −0.296558 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.90659 | − | 13.6946i | −0.410490 | − | 0.710989i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.0801 | −1.24682 | −0.623411 | − | 0.781894i | \(-0.714254\pi\) | ||||
−0.623411 | + | 0.781894i | \(0.714254\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.52307 | + | 4.37008i | −0.129945 | + | 0.225071i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.1565 | 1.54904 | 0.774518 | − | 0.632552i | \(-0.217992\pi\) | ||||
0.774518 | + | 0.632552i | \(0.217992\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −41.4375 | −2.12291 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.4101 | − | 33.6192i | 0.991809 | − | 1.71786i | 0.385286 | − | 0.922797i | \(-0.374103\pi\) |
0.606522 | − | 0.795066i | \(-0.292564\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.4060 | 0.681467 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.6935 | − | 32.3781i | −0.947799 | − | 1.64164i | −0.750048 | − | 0.661383i | \(-0.769970\pi\) |
−0.197750 | − | 0.980252i | \(-0.563364\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.0779 | −0.560236 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.8027 | + | 18.7108i | 0.544924 | + | 0.943836i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.78211 | − | 13.4790i | 0.390573 | − | 0.676492i | −0.601952 | − | 0.798532i | \(-0.705610\pi\) |
0.992525 | + | 0.122040i | \(0.0389436\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.5512 | + | 2.38651i | −0.578283 | + | 0.119475i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.3113 | + | 19.5918i | −0.564860 | + | 0.978366i | 0.432203 | + | 0.901777i | \(0.357737\pi\) |
−0.997063 | + | 0.0765898i | \(0.975597\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.624949 | − | 1.08244i | −0.0311309 | − | 0.0539203i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.2848 | 1.45159 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.1239 | + | 31.3915i | 0.896169 | + | 1.55221i | 0.832351 | + | 0.554249i | \(0.186995\pi\) |
0.0638187 | + | 0.997962i | \(0.479672\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −34.5865 | −1.70603 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.0236521 | + | 0.0409666i | −0.00116384 | + | 0.00201583i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.7536 | −0.722486 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.5598 | −0.711293 | −0.355647 | − | 0.934621i | \(-0.615739\pi\) | ||||
−0.355647 | + | 0.934621i | \(0.615739\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.784161 | + | 1.35821i | −0.0382177 | + | 0.0661950i | −0.884502 | − | 0.466537i | \(-0.845501\pi\) |
0.846284 | + | 0.532732i | \(0.178835\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.72012 | − | 2.97934i | 0.0836351 | − | 0.144860i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.696705 | + | 1.20673i | 0.0337159 | + | 0.0583977i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 25.7722 | 1.24429 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.7303 | + | 22.0495i | 0.613197 | + | 1.06209i | 0.990698 | + | 0.136080i | \(0.0434503\pi\) |
−0.377500 | + | 0.926009i | \(0.623216\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.44155 | − | 14.6212i | −0.405675 | − | 0.702650i | 0.588725 | − | 0.808334i | \(-0.299630\pi\) |
−0.994400 | + | 0.105684i | \(0.966297\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.1656 | − | 33.7090i | 0.534125 | − | 1.61252i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.93240 | + | 17.2034i | −0.474048 | + | 0.821075i | −0.999558 | − | 0.0297121i | \(-0.990541\pi\) |
0.525511 | + | 0.850787i | \(0.323874\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.73590 | + | 4.73872i | 0.130281 | + | 0.225653i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.57742 | − | 4.46422i | −0.122457 | − | 0.212101i | 0.798279 | − | 0.602288i | \(-0.205744\pi\) |
−0.920736 | + | 0.390186i | \(0.872411\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.3276 | − | 21.3520i | −0.583074 | − | 1.00991i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.2207 | −1.56778 | −0.783892 | − | 0.620897i | \(-0.786768\pi\) | ||||
−0.783892 | + | 0.620897i | \(0.786768\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.2096 | − | 24.6117i | 0.669103 | − | 1.15892i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.6348 | + | 20.1520i | −0.546650 | + | 0.946826i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.7126 | −0.547894 | −0.273947 | − | 0.961745i | \(-0.588329\pi\) | ||||
−0.273947 | + | 0.961745i | \(0.588329\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.66448 | + | 4.61501i | −0.124367 | + | 0.215410i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.68501 | − | 6.38263i | 0.171628 | − | 0.297269i | −0.767361 | − | 0.641215i | \(-0.778431\pi\) |
0.938989 | + | 0.343947i | \(0.111764\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.8020 | 1.33854 | 0.669271 | − | 0.743019i | \(-0.266607\pi\) | ||||
0.669271 | + | 0.743019i | \(0.266607\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −34.1251 | −1.57912 | −0.789561 | − | 0.613673i | \(-0.789691\pi\) | ||||
−0.789561 | + | 0.613673i | \(0.789691\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.515268 | + | 0.892471i | 0.0237929 | + | 0.0412105i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.16756 | + | 7.21842i | 0.192031 | + | 0.332607i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −33.4394 | + | 57.9188i | −1.53755 | + | 2.66311i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.19789 | + | 10.7351i | −0.283782 | + | 0.491525i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.4130 | − | 24.9640i | −0.658546 | − | 1.14064i | −0.980992 | − | 0.194048i | \(-0.937838\pi\) |
0.322446 | − | 0.946588i | \(-0.395495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.78491 | + | 11.7518i | 0.309365 | + | 0.535836i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 22.0446 | 1.00306 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.5796 | −0.751294 | −0.375647 | − | 0.926763i | \(-0.622579\pi\) | ||||
−0.375647 | + | 0.926763i | \(0.622579\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.47957 | − | 16.4191i | 0.428681 | − | 0.742497i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.94615 | + | 8.56698i | −0.223217 | + | 0.386623i | −0.955783 | − | 0.294073i | \(-0.904989\pi\) |
0.732566 | + | 0.680696i | \(0.238322\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.81748 | −0.126893 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.64011 | − | 13.2331i | 0.342706 | − | 0.593584i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.4949 | − | 26.8380i | 0.693649 | − | 1.20144i | −0.276985 | − | 0.960874i | \(-0.589335\pi\) |
0.970634 | − | 0.240561i | \(-0.0773315\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 27.5245 | 1.22970 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.43203 | − | 11.1406i | −0.286790 | − | 0.496735i | 0.686252 | − | 0.727364i | \(-0.259255\pi\) |
−0.973042 | + | 0.230629i | \(0.925922\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.11568 | − | 12.3247i | −0.316018 | − | 0.547360i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.35312 | + | 12.7360i | 0.325921 | + | 0.564512i | 0.981698 | − | 0.190442i | \(-0.0609922\pi\) |
−0.655777 | + | 0.754955i | \(0.727659\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.44664 | + | 2.50566i | −0.0639957 | + | 0.110844i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11.3574 | − | 12.7593i | −0.501442 | − | 0.563335i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.58118 | + | 14.8630i | 0.377400 | + | 0.653676i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.8564 | + | 20.5359i | 0.520439 | + | 0.901427i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.35528 | 0.234619 | 0.117310 | − | 0.993095i | \(-0.462573\pi\) | ||||
0.117310 | + | 0.993095i | \(0.462573\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.98981 | + | 13.8388i | 0.349370 | + | 0.605127i | 0.986138 | − | 0.165929i | \(-0.0530623\pi\) |
−0.636768 | + | 0.771056i | \(0.719729\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.348937 | − | 0.604376i | 0.0151999 | − | 0.0263270i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6833 | + | 37.5566i | −0.942753 | + | 1.63290i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.0370812 | 0.00160919 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.1687 | 0.570400 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.6833 | + | 28.8963i | −0.719937 | + | 1.24697i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −27.2972 | −1.17577 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.9500 | − | 31.0904i | −0.771732 | − | 1.33668i | −0.936613 | − | 0.350366i | \(-0.886057\pi\) |
0.164881 | − | 0.986313i | \(-0.447276\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 28.9742 | 1.24340 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.0754 | − | 22.6473i | −0.559064 | − | 0.968327i | −0.997575 | − | 0.0696011i | \(-0.977827\pi\) |
0.438511 | − | 0.898726i | \(-0.355506\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.546140 | − | 0.945942i | 0.0233087 | − | 0.0403718i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.83979 | − | 8.57329i | 0.120979 | − | 0.365235i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.71704 | − | 15.0983i | 0.370686 | − | 0.642047i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.10412 | − | 3.64444i | −0.0891543 | − | 0.154420i | 0.818000 | − | 0.575219i | \(-0.195083\pi\) |
−0.907154 | + | 0.420799i | \(0.861750\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −30.9899 | −1.31073 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.19488 | + | 12.4619i | 0.303768 | + | 0.526142i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −40.5225 | −1.70782 | −0.853909 | − | 0.520422i | \(-0.825775\pi\) | ||||
−0.853909 | + | 0.520422i | \(0.825775\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.42622 | − | 12.8626i | 0.311872 | − | 0.540178i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.9522 | 1.00413 | 0.502064 | − | 0.864831i | \(-0.332574\pi\) | ||||
0.502064 | + | 0.864831i | \(0.332574\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.78949 | −0.325980 | −0.162990 | − | 0.986628i | \(-0.552114\pi\) | ||||
−0.162990 | + | 0.986628i | \(0.552114\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.01155 | + | 10.4123i | −0.251136 | + | 0.434981i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.1385 | −1.42121 | −0.710603 | − | 0.703593i | \(-0.751578\pi\) | ||||
−0.710603 | + | 0.703593i | \(0.751578\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.3953 | − | 28.3975i | −0.681366 | − | 1.18016i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.64899 | −0.234360 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.9195 | − | 53.5541i | −1.28055 | − | 2.21798i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.0700 | + | 19.1737i | −0.456906 | + | 0.791384i | −0.998796 | − | 0.0490654i | \(-0.984376\pi\) |
0.541890 | + | 0.840450i | \(0.317709\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.48735 | + | 1.67094i | 0.0612853 | + | 0.0688498i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.6002 | + | 20.0921i | −0.477167 | + | 0.826477i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.6767 | + | 35.8131i | 0.849089 | + | 1.47067i | 0.882022 | + | 0.471208i | \(0.156182\pi\) |
−0.0329325 | + | 0.999458i | \(0.510485\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.3258 | −0.790954 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.8243 | − | 29.1406i | −0.687423 | − | 1.19065i | −0.972669 | − | 0.232197i | \(-0.925409\pi\) |
0.285246 | − | 0.958454i | \(-0.407925\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.4939 | 1.57020 | 0.785100 | − | 0.619369i | \(-0.212611\pi\) | ||||
0.785100 | + | 0.619369i | \(0.212611\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.403913 | − | 0.699598i | 0.0164486 | − | 0.0284899i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.1827 | 0.900367 | 0.450183 | − | 0.892936i | \(-0.351359\pi\) | ||||
0.450183 | + | 0.892936i | \(0.351359\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.60665 | 0.227193 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.97629 | + | 6.88714i | −0.160864 | + | 0.278624i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.38703 | − | 4.13445i | 0.0964111 | − | 0.166989i | −0.813786 | − | 0.581165i | \(-0.802597\pi\) |
0.910197 | + | 0.414176i | \(0.135930\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.09317 | − | 14.0178i | −0.325819 | − | 0.564335i | 0.655859 | − | 0.754883i | \(-0.272307\pi\) |
−0.981678 | + | 0.190549i | \(0.938973\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.4892 | 0.542176 | 0.271088 | − | 0.962555i | \(-0.412617\pi\) | ||||
0.271088 | + | 0.962555i | \(0.412617\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.9626 | + | 27.6480i | 0.640556 | + | 1.10948i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.91143 | + | 8.50684i | 0.196772 | + | 0.340819i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −45.1720 | + | 9.33268i | −1.80400 | + | 0.372711i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.78832 | + | 6.56156i | −0.151050 | + | 0.261626i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.2207 | + | 22.8989i | 0.526308 | + | 0.911592i | 0.999530 | + | 0.0306488i | \(0.00975735\pi\) |
−0.473222 | + | 0.880943i | \(0.656909\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.6613 | − | 25.3942i | −0.582735 | − | 1.00933i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.32441 | − | 10.9542i | −0.250582 | − | 0.434021i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.9780 | −0.473842 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.27817 | + | 7.41000i | −0.168977 | + | 0.292677i | −0.938061 | − | 0.346471i | \(-0.887380\pi\) |
0.769083 | + | 0.639149i | \(0.220713\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.0112 | + | 24.2681i | −0.552548 | + | 0.957042i | 0.445541 | + | 0.895261i | \(0.353011\pi\) |
−0.998090 | + | 0.0617804i | \(0.980322\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.57376 | 0.376383 | 0.188192 | − | 0.982132i | \(-0.439737\pi\) | ||||
0.188192 | + | 0.982132i | \(0.439737\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.0924936 | + | 0.160204i | −0.00363069 | + | 0.00628854i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.694367 | + | 1.20268i | −0.0272144 | + | 0.0471367i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.4168 | −0.642439 | −0.321219 | − | 0.947005i | \(-0.604093\pi\) | ||||
−0.321219 | + | 0.947005i | \(0.604093\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.26801 | 0.0884837 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.08162 | − | 12.2657i | −0.275861 | − | 0.477805i | 0.694491 | − | 0.719501i | \(-0.255629\pi\) |
−0.970352 | + | 0.241697i | \(0.922296\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.5170 | − | 32.0724i | −0.720229 | − | 1.24747i | −0.960908 | − | 0.276868i | \(-0.910704\pi\) |
0.240679 | − | 0.970605i | \(-0.422630\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.33392 | + | 5.77452i | −0.129479 | + | 0.224264i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.43960 | + | 14.6178i | −0.326783 | + | 0.566004i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.62324 | + | 13.2038i | 0.294732 | + | 0.510490i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.72453 | + | 4.71903i | 0.105179 | + | 0.182176i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.3293 | 1.63167 | 0.815837 | − | 0.578282i | \(-0.196277\pi\) | ||||
0.815837 | + | 0.578282i | \(0.196277\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.9856 | 0.537510 | 0.268755 | − | 0.963209i | \(-0.413388\pi\) | ||||
0.268755 | + | 0.963209i | \(0.413388\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.560033 | + | 0.970005i | −0.0214921 | + | 0.0372254i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.91222 | + | 11.9723i | −0.264877 | + | 0.458780i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.6668 | −0.446416 | −0.223208 | − | 0.974771i | \(-0.571653\pi\) | ||||
−0.223208 | + | 0.974771i | \(0.571653\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.2486 | − | 38.5356i | 0.848835 | − | 1.47023i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.3273 | − | 24.8156i | 0.545825 | − | 0.945397i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.7886 | −0.600627 | −0.300313 | − | 0.953841i | \(-0.597091\pi\) | ||||
−0.300313 | + | 0.953841i | \(0.597091\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.72127 | − | 6.44542i | −0.141359 | − | 0.244841i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.67633 | + | 6.36760i | 0.139251 | + | 0.241190i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.99675 | − | 5.19053i | −0.113348 | − | 0.196324i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.64450 | − | 4.58042i | 0.0998816 | − | 0.173000i | −0.811754 | − | 0.584000i | \(-0.801487\pi\) |
0.911635 | + | 0.411000i | \(0.134820\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.1478 | − | 18.1409i | −0.609025 | − | 0.684198i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.95913 | − | 17.2497i | −0.374552 | − | 0.648743i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.2529 | + | 21.2226i | 0.460166 | + | 0.797031i | 0.998969 | − | 0.0454011i | \(-0.0144566\pi\) |
−0.538803 | + | 0.842432i | \(0.681123\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.6664 | −0.512529 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.09044 | − | 3.62075i | −0.0782875 | − | 0.135598i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.77771 | + | 16.9355i | −0.365155 | + | 0.632467i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.4239 | + | 38.8393i | −0.836269 | + | 1.44846i | 0.0567236 | + | 0.998390i | \(0.481935\pi\) |
−0.892993 | + | 0.450071i | \(0.851399\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.6442 | 0.470896 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 37.6209 | 1.39914 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.2453 | − | 28.1376i | 0.602504 | − | 1.04357i | −0.389937 | − | 0.920842i | \(-0.627503\pi\) |
0.992441 | − | 0.122726i | \(-0.0391635\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.0273 | 0.445457 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.65152 | − | 14.9849i | −0.319988 | − | 0.554235i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.1969 | 0.413568 | 0.206784 | − | 0.978387i | \(-0.433700\pi\) | ||||
0.206784 | + | 0.978387i | \(0.433700\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.01501 | + | 3.49009i | 0.0742237 | + | 0.128559i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.466361 | + | 0.807761i | −0.0171554 | + | 0.0297140i | −0.874476 | − | 0.485069i | \(-0.838794\pi\) |
0.857320 | + | 0.514783i | \(0.172128\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.2109 | − | 15.9650i | −0.522051 | − | 0.586488i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.4736 | + | 23.3370i | −0.494300 | + | 0.856153i | −0.999978 | − | 0.00656939i | \(-0.997909\pi\) |
0.505678 | + | 0.862722i | \(0.331242\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.21409 | + | 3.83492i | 0.0810094 | + | 0.140312i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.2210 | −0.629240 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.33645 | + | 4.04686i | 0.0852584 | + | 0.147672i | 0.905501 | − | 0.424343i | \(-0.139495\pi\) |
−0.820243 | + | 0.572015i | \(0.806162\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.45971 | 0.308289 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.4140 | + | 37.0902i | −0.778306 | + | 1.34807i | 0.154612 | + | 0.987975i | \(0.450587\pi\) |
−0.932918 | + | 0.360090i | \(0.882746\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 86.2073 | 3.12913 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.7169 | −0.605987 | −0.302994 | − | 0.952993i | \(-0.597986\pi\) | ||||
−0.302994 | + | 0.952993i | \(0.597986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.33983 | + | 2.32065i | −0.0485050 | + | 0.0840131i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.0857182 | −0.00309511 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.70852 | + | 13.3516i | 0.277976 | + | 0.481469i | 0.970882 | − | 0.239559i | \(-0.0770029\pi\) |
−0.692905 | + | 0.721029i | \(0.743670\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 56.7128 | 2.04246 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.5897 | − | 28.7343i | −0.596691 | − | 1.03350i | −0.993306 | − | 0.115514i | \(-0.963148\pi\) |
0.396615 | − | 0.917985i | \(-0.370185\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.53856 | − | 13.0572i | 0.270444 | − | 0.468423i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.0813 | + | 4.76868i | −0.826975 | + | 0.170856i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.8774 | − | 51.7491i | 1.06910 | − | 1.85173i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.05980 | + | 7.03179i | 0.145086 | + | 0.251296i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.8318 | 0.457405 | 0.228702 | − | 0.973496i | \(-0.426552\pi\) | ||||
0.228702 | + | 0.973496i | \(0.426552\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.72657 | − | 4.72256i | −0.0970685 | − | 0.168128i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.2179 | −0.398862 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.26248 | + | 2.18667i | −0.0448319 | + | 0.0776511i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.28485 | 0.0809336 | 0.0404668 | − | 0.999181i | \(-0.487115\pi\) | ||||
0.0404668 | + | 0.999181i | \(0.487115\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.44028 | −0.157086 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.85001 | − | 6.66842i | 0.136034 | − | 0.235617i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.65723 | + | 9.79861i | −0.199639 | + | 0.345786i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.3573 | + | 19.6714i | 0.399796 | + | 0.692468i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.3304 | 0.609305 | 0.304652 | − | 0.952464i | \(-0.401460\pi\) | ||||
0.304652 | + | 0.952464i | \(0.401460\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.7926 | − | 42.9420i | −0.870586 | − | 1.50790i | −0.861392 | − | 0.507941i | \(-0.830407\pi\) |
−0.00919378 | − | 0.999958i | \(-0.502927\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.37606 | + | 11.0437i | 0.223618 | + | 0.387318i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 54.3173 | − | 11.2221i | 1.90032 | − | 0.392612i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.72434 | − | 2.98664i | 0.0602532 | − | 0.104362i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.1029 | − | 19.2308i | −0.387495 | − | 0.671160i | 0.604617 | − | 0.796516i | \(-0.293326\pi\) |
−0.992112 | + | 0.125356i | \(0.959993\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.56519 | + | 16.5674i | 0.333422 | + | 0.577503i | 0.983180 | − | 0.182637i | \(-0.0584634\pi\) |
−0.649759 | + | 0.760141i | \(0.725130\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.52461 | + | 13.0330i | 0.261656 | + | 0.453202i | 0.966682 | − | 0.255980i | \(-0.0823980\pi\) |
−0.705026 | + | 0.709182i | \(0.749065\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.62995 | 0.126074 | 0.0630368 | − | 0.998011i | \(-0.479921\pi\) | ||||
0.0630368 | + | 0.998011i | \(0.479921\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.2179 | − | 19.4299i | 0.389144 | − | 0.674017i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.53120 | − | 6.11621i | 0.122349 | − | 0.211914i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.01118 | −0.0695165 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.47453 | − | 16.4104i | 0.327097 | − | 0.566549i | −0.654838 | − | 0.755770i | \(-0.727263\pi\) |
0.981935 | + | 0.189221i | \(0.0605963\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.3535 | − | 21.3969i | 0.425984 | − | 0.737826i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −51.9691 | −1.78991 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.3443 | 0.767761 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.0534 | + | 50.3220i | 0.997111 | + | 1.72705i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.6954 | + | 39.3095i | 0.777987 | + | 1.34751i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.3785 | − | 37.0287i | 0.731987 | − | 1.26784i | −0.224045 | − | 0.974579i | \(-0.571926\pi\) |
0.956033 | − | 0.293260i | \(-0.0947403\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.57024 | − | 2.71973i | 0.0536383 | − | 0.0929043i | −0.837960 | − | 0.545732i | \(-0.816252\pi\) |
0.891598 | + | 0.452828i | \(0.149585\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.53437 | − | 6.12170i | −0.120591 | − | 0.208870i | 0.799410 | − | 0.600786i | \(-0.205146\pi\) |
−0.920001 | + | 0.391916i | \(0.871812\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.31572 | − | 12.6712i | −0.249319 | − | 0.431834i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.464328 | 0.0158059 | 0.00790296 | − | 0.999969i | \(-0.497484\pi\) | ||||
0.00790296 | + | 0.999969i | \(0.497484\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 30.5040 | 1.03597 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.0888 | − | 59.0435i | 1.15638 | − | 2.00291i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.933701 | + | 1.61722i | −0.0316373 | + | 0.0547973i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.878007 | 0.0297160 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.463552 | + | 0.802896i | −0.0156530 | + | 0.0271119i | −0.873746 | − | 0.486383i | \(-0.838316\pi\) |
0.858093 | + | 0.513495i | \(0.171649\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.9262 | − | 39.7094i | 0.773282 | − | 1.33936i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.50850 | 0.151895 | 0.0759477 | − | 0.997112i | \(-0.475802\pi\) | ||||
0.0759477 | + | 0.997112i | \(0.475802\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.1245 | − | 29.6605i | −0.576286 | − | 0.998156i | −0.995901 | − | 0.0904542i | \(-0.971168\pi\) |
0.419615 | − | 0.907702i | \(-0.362165\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.2791 | − | 24.7321i | −0.479445 | − | 0.830423i | 0.520277 | − | 0.853997i | \(-0.325829\pi\) |
−0.999722 | + | 0.0235747i | \(0.992495\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.8310 | − | 23.9560i | −0.463876 | − | 0.803457i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 29.0409 | − | 50.3003i | 0.972907 | − | 1.68512i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.47544 | − | 13.5113i | 0.149765 | − | 0.452138i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.9731 | + | 34.5944i | 0.666883 | + | 1.15507i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.531667 | − | 0.920874i | −0.0177321 | − | 0.0307129i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.9991 | 0.533007 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.2161 | + | 29.8191i | 0.572916 | + | 0.992319i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.85765 | + | 13.6098i | −0.260909 | + | 0.451907i | −0.966484 | − | 0.256728i | \(-0.917356\pi\) |
0.705575 | + | 0.708635i | \(0.250689\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.80686 | + | 13.5219i | −0.258937 | + | 0.448492i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.7125 | 0.686237 | 0.343119 | − | 0.939292i | \(-0.388517\pi\) | ||||
0.343119 | + | 0.939292i | \(0.388517\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.0909 | −0.731103 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.21143 | + | 12.4906i | −0.238142 | + | 0.412475i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.6628 | 1.01147 | 0.505737 | − | 0.862688i | \(-0.331221\pi\) | ||||
0.505737 | + | 0.862688i | \(0.331221\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.3057 | + | 28.2423i | 0.537291 | + | 0.930615i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.6888 | 0.911388 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.95584 | − | 8.58377i | −0.162771 | − | 0.281928i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.65011 | − | 13.2504i | 0.250992 | − | 0.434731i | −0.712807 | − | 0.701360i | \(-0.752577\pi\) |
0.963799 | + | 0.266629i | \(0.0859099\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.0518 | + | 16.9097i | 0.493303 | + | 0.554193i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28.5375 | + | 49.4284i | −0.934276 | + | 1.61821i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.21623 | + | 3.83862i | 0.0724011 | + | 0.125402i | 0.899953 | − | 0.435987i | \(-0.143601\pi\) |
−0.827552 | + | 0.561389i | \(0.810267\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.21978 | −0.202975 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.3400 | − | 30.0338i | −0.565268 | − | 0.979073i | −0.997025 | − | 0.0770825i | \(-0.975440\pi\) |
0.431757 | − | 0.901990i | \(-0.357894\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44.0490 | 1.43443 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.603945 | − | 1.04606i | 0.0196256 | − | 0.0339925i | −0.856046 | − | 0.516900i | \(-0.827086\pi\) |
0.875671 | + | 0.482907i | \(0.160419\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.24283 | −0.170189 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 48.4110 | 1.56983 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.6627 | − | 51.3773i | 0.960868 | − | 1.66427i | 0.240540 | − | 0.970639i | \(-0.422676\pi\) |
0.720329 | − | 0.693633i | \(-0.243991\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21.9253 | 0.708746 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.5443 | − | 19.9952i | −0.372784 | − | 0.645680i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7366 | −0.991504 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.74966 | + | 11.6908i | 0.217505 | + | 0.376729i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.7736 | + | 39.4450i | −0.732350 | + | 1.26847i | 0.223527 | + | 0.974698i | \(0.428243\pi\) |
−0.955876 | + | 0.293769i | \(0.905090\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.75242 | − | 11.3285i | 0.120545 | − | 0.363925i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.738715 | + | 1.27949i | −0.0237065 | + | 0.0410608i | −0.877635 | − | 0.479329i | \(-0.840880\pi\) |
0.853929 | + | 0.520390i | \(0.174213\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.92443 | − | 8.52937i | −0.157870 | − | 0.273439i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46.8443 | 1.49868 | 0.749341 | − | 0.662184i | \(-0.230370\pi\) | ||||
0.749341 | + | 0.662184i | \(0.230370\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.2066 | + | 33.2668i | 0.613846 | + | 1.06321i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.10055 | 0.0670654 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.0466 | − | 17.4012i | 0.320436 | − | 0.555011i | −0.660142 | − | 0.751141i | \(-0.729504\pi\) |
0.980578 | + | 0.196130i | \(0.0628373\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.83595 | 0.281251 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −103.660 | −3.29621 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.95274 | + | 15.5066i | −0.284393 | + | 0.492583i | −0.972462 | − | 0.233062i | \(-0.925125\pi\) |
0.688069 | + | 0.725646i | \(0.258459\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.9103 | + | 36.2177i | −0.663568 | + | 1.14933i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.989838 | + | 1.71445i | 0.0313485 | + | 0.0542972i | 0.881274 | − | 0.472606i | \(-0.156686\pi\) |
−0.849926 | + | 0.526903i | \(0.823353\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21.8348 | 0.690824 |
(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 | 1900.2.i.g.201.8 | 20 | ||
5.2 | odd | 4 | 380.2.r.a.49.3 | ✓ | 20 | ||
5.3 | odd | 4 | 380.2.r.a.49.8 | yes | 20 | ||
5.4 | even | 2 | inner | 1900.2.i.g.201.3 | 20 | ||
15.2 | even | 4 | 3420.2.bj.c.1189.8 | 20 | |||
15.8 | even | 4 | 3420.2.bj.c.1189.6 | 20 | |||
19.7 | even | 3 | inner | 1900.2.i.g.501.8 | 20 | ||
95.7 | odd | 12 | 380.2.r.a.349.8 | yes | 20 | ||
95.64 | even | 6 | inner | 1900.2.i.g.501.3 | 20 | ||
95.83 | odd | 12 | 380.2.r.a.349.3 | yes | 20 | ||
285.83 | even | 12 | 3420.2.bj.c.2629.8 | 20 | |||
285.197 | even | 12 | 3420.2.bj.c.2629.6 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.r.a.49.3 | ✓ | 20 | 5.2 | odd | 4 | ||
380.2.r.a.49.8 | yes | 20 | 5.3 | odd | 4 | ||
380.2.r.a.349.3 | yes | 20 | 95.83 | odd | 12 | ||
380.2.r.a.349.8 | yes | 20 | 95.7 | odd | 12 | ||
1900.2.i.g.201.3 | 20 | 5.4 | even | 2 | inner | ||
1900.2.i.g.201.8 | 20 | 1.1 | even | 1 | trivial | ||
1900.2.i.g.501.3 | 20 | 95.64 | even | 6 | inner | ||
1900.2.i.g.501.8 | 20 | 19.7 | even | 3 | inner | ||
3420.2.bj.c.1189.6 | 20 | 15.8 | even | 4 | |||
3420.2.bj.c.1189.8 | 20 | 15.2 | even | 4 | |||
3420.2.bj.c.2629.6 | 20 | 285.197 | even | 12 | |||
3420.2.bj.c.2629.8 | 20 | 285.83 | even | 12 |