Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(1151,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.cg (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.2 | ||
Character | \(\chi\) | \(=\) | 2736.1151 |
Dual form | 2736.2.cg.a.2591.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.27729 | − | 1.31480i | −1.01844 | − | 0.587995i | −0.104786 | − | 0.994495i | \(-0.533416\pi\) |
−0.913651 | + | 0.406500i | \(0.866749\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.01718i | 1.14039i | 0.821510 | + | 0.570194i | \(0.193132\pi\) | ||||
−0.821510 | + | 0.570194i | \(0.806868\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.730663 | −0.220303 | −0.110152 | − | 0.993915i | \(-0.535134\pi\) | ||||
−0.110152 | + | 0.993915i | \(0.535134\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.20198 | + | 3.81393i | 0.610718 | + | 1.05779i | 0.991120 | + | 0.132973i | \(0.0424525\pi\) |
−0.380401 | + | 0.924821i | \(0.624214\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.35027 | − | 3.08898i | −1.29763 | − | 0.749188i | −0.317637 | − | 0.948213i | \(-0.602889\pi\) |
−0.979994 | + | 0.199025i | \(0.936223\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.91110 | + | 3.24430i | 0.667852 | + | 0.744294i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.23308 | + | 3.86781i | 0.465630 | + | 0.806494i | 0.999230 | − | 0.0392426i | \(-0.0124945\pi\) |
−0.533600 | + | 0.845737i | \(0.679161\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.957376 | + | 1.65822i | 0.191475 | + | 0.331645i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.85101 | − | 2.80073i | 0.900811 | − | 0.520083i | 0.0233476 | − | 0.999727i | \(-0.492568\pi\) |
0.877463 | + | 0.479644i | \(0.159234\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.37863i | − | 1.14564i | −0.819682 | − | 0.572818i | \(-0.805850\pi\) | ||
0.819682 | − | 0.572818i | \(-0.194150\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.96698 | − | 6.87101i | 0.670542 | − | 1.16141i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.48920 | −0.244823 | −0.122411 | − | 0.992479i | \(-0.539063\pi\) | ||||
−0.122411 | + | 0.992479i | \(0.539063\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.54789 | − | 2.04837i | −0.554087 | − | 0.319902i | 0.196682 | − | 0.980467i | \(-0.436983\pi\) |
−0.750769 | + | 0.660565i | \(0.770317\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.82401 | − | 3.93984i | −1.04065 | − | 0.600820i | −0.120634 | − | 0.992697i | \(-0.538493\pi\) |
−0.920018 | + | 0.391877i | \(0.871826\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.28368 | − | 2.22340i | −0.187244 | − | 0.324316i | 0.757087 | − | 0.653315i | \(-0.226622\pi\) |
−0.944330 | + | 0.328999i | \(0.893289\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.10340 | −0.300485 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.22041 | + | 5.32341i | −1.26652 | + | 0.731226i | −0.974328 | − | 0.225134i | \(-0.927718\pi\) |
−0.292193 | + | 0.956359i | \(0.594385\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.66393 | + | 0.960673i | 0.224365 | + | 0.129537i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.08092 | + | 1.87221i | −0.140724 | + | 0.243741i | −0.927770 | − | 0.373154i | \(-0.878276\pi\) |
0.787045 | + | 0.616895i | \(0.211610\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.26794 | − | 7.39228i | −0.546453 | − | 0.946485i | −0.998514 | − | 0.0544976i | \(-0.982644\pi\) |
0.452061 | − | 0.891987i | \(-0.350689\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 11.5806i | − | 1.43640i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.40407 | + | 4.85209i | −1.02672 | + | 0.592777i | −0.916043 | − | 0.401079i | \(-0.868635\pi\) |
−0.110677 | + | 0.993856i | \(0.535302\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.00887 | − | 8.67561i | 0.594443 | − | 1.02961i | −0.399182 | − | 0.916872i | \(-0.630706\pi\) |
0.993625 | − | 0.112734i | \(-0.0359608\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.72788 | + | 9.92098i | −0.670398 | + | 1.16116i | 0.307394 | + | 0.951582i | \(0.400543\pi\) |
−0.977791 | + | 0.209580i | \(0.932790\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.20455i | − | 0.251231i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.78342 | + | 1.02966i | 0.200650 | + | 0.115845i | 0.596959 | − | 0.802272i | \(-0.296376\pi\) |
−0.396309 | + | 0.918117i | \(0.629709\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.34096 | 0.805775 | 0.402888 | − | 0.915249i | \(-0.368007\pi\) | ||||
0.402888 | + | 0.915249i | \(0.368007\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.12276 | + | 14.0690i | 0.881037 | + | 1.52600i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.22085 | + | 1.28221i | −0.235410 | + | 0.135914i | −0.613065 | − | 0.790032i | \(-0.710064\pi\) |
0.377655 | + | 0.925946i | \(0.376730\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.5073 | + | 6.64376i | −1.20630 | + | 0.696456i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.36384 | − | 11.2157i | −0.242525 | − | 1.15071i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.80967 | + | 4.86649i | −0.285278 | + | 0.494117i | −0.972677 | − | 0.232164i | \(-0.925419\pi\) |
0.687398 | + | 0.726281i | \(0.258753\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.8914 | + | 9.75226i | −1.68076 | + | 0.970387i | −0.719601 | + | 0.694388i | \(0.755675\pi\) |
−0.961158 | + | 0.275999i | \(0.910991\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 19.6453i | − | 1.93571i | −0.251503 | − | 0.967857i | \(-0.580925\pi\) | ||
0.251503 | − | 0.967857i | \(-0.419075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.6114 | −1.41253 | −0.706267 | − | 0.707946i | \(-0.749622\pi\) | ||||
−0.706267 | + | 0.707946i | \(0.749622\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.80401 | − | 4.85669i | 0.268576 | − | 0.465187i | −0.699918 | − | 0.714223i | \(-0.746780\pi\) |
0.968494 | + | 0.249036i | \(0.0801137\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.55408i | − | 0.522484i | −0.965273 | − | 0.261242i | \(-0.915868\pi\) | ||
0.965273 | − | 0.261242i | \(-0.0841320\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 11.7442i | − | 1.09515i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.32002 | − | 16.1427i | 0.854365 | − | 1.47980i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4661 | −0.951466 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.11294i | 0.725644i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.99683 | − | 1.15287i | 0.177190 | − | 0.102301i | −0.408782 | − | 0.912632i | \(-0.634046\pi\) |
0.585972 | + | 0.810331i | \(0.300713\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.24465 | − | 7.35196i | 0.370857 | − | 0.642343i | −0.618840 | − | 0.785517i | \(-0.712397\pi\) |
0.989698 | + | 0.143173i | \(0.0457306\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.78865 | + | 8.78333i | −0.848784 | + | 0.761611i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.68866 | + | 3.86170i | −0.571450 | + | 0.329927i | −0.757728 | − | 0.652570i | \(-0.773691\pi\) |
0.186278 | + | 0.982497i | \(0.440357\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.66344 | + | 5.00184i | −0.734824 | + | 0.424251i | −0.820184 | − | 0.572099i | \(-0.806129\pi\) |
0.0853606 | + | 0.996350i | \(0.472796\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.60890 | − | 2.78670i | −0.134543 | − | 0.233036i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.7296 | −1.22322 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.897686 | + | 0.518279i | 0.0735413 | + | 0.0424591i | 0.536320 | − | 0.844015i | \(-0.319814\pi\) |
−0.462778 | + | 0.886474i | \(0.653147\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 21.5740i | − | 1.75567i | −0.478965 | − | 0.877834i | \(-0.658988\pi\) | ||
0.478965 | − | 0.877834i | \(-0.341012\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.38660 | + | 14.5260i | −0.673628 | + | 1.16676i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.79444 | + | 13.5004i | −0.622064 | + | 1.07745i | 0.367036 | + | 0.930207i | \(0.380372\pi\) |
−0.989101 | + | 0.147240i | \(0.952961\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.6699 | + | 6.73762i | −0.919717 | + | 0.530999i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.2536i | 1.42973i | 0.699261 | + | 0.714867i | \(0.253513\pi\) | ||||
−0.699261 | + | 0.714867i | \(0.746487\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.74585 | + | 3.02390i | 0.135098 | + | 0.233997i | 0.925635 | − | 0.378418i | \(-0.123532\pi\) |
−0.790537 | + | 0.612414i | \(0.790198\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.19739 | + | 5.53805i | −0.245953 | + | 0.426004i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.9620 | − | 6.32893i | −0.833428 | − | 0.481180i | 0.0215969 | − | 0.999767i | \(-0.493125\pi\) |
−0.855025 | + | 0.518587i | \(0.826458\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.00317 | + | 2.88858i | −0.378204 | + | 0.218356i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.95556 | 0.146165 | 0.0730826 | − | 0.997326i | \(-0.476716\pi\) | ||||
0.0730826 | + | 0.997326i | \(0.476716\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.90914 | − | 6.77082i | −0.290564 | − | 0.503271i | 0.683379 | − | 0.730064i | \(-0.260510\pi\) |
−0.973943 | + | 0.226792i | \(0.927176\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.39134 | + | 1.95799i | 0.249336 | + | 0.143954i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.90925 | + | 2.25700i | 0.285872 | + | 0.165048i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.37771 | 0.0996879 | 0.0498439 | − | 0.998757i | \(-0.484128\pi\) | ||||
0.0498439 | + | 0.998757i | \(0.484128\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.67422 | − | 4.63188i | 0.192494 | − | 0.333410i | −0.753582 | − | 0.657354i | \(-0.771676\pi\) |
0.946076 | + | 0.323944i | \(0.105009\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 21.1527i | − | 1.50707i | −0.657409 | − | 0.753534i | \(-0.728348\pi\) | ||
0.657409 | − | 0.753534i | \(-0.271652\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.22547 | − | 4.74898i | 0.583088 | − | 0.336646i | −0.179272 | − | 0.983800i | \(-0.557374\pi\) |
0.762360 | + | 0.647154i | \(0.224041\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.45033 | + | 14.6364i | 0.593097 | + | 1.02727i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.38639 | + | 9.32950i | 0.376202 | + | 0.651601i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.12703 | − | 2.37049i | −0.147130 | − | 0.163970i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.6313 | + | 14.2209i | 1.69569 | + | 0.979006i | 0.949759 | + | 0.312981i | \(0.101328\pi\) |
0.745929 | + | 0.666025i | \(0.232006\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.3602 | + | 17.9444i | 0.706558 | + | 1.22379i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.2455 | 1.30647 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 27.2074i | − | 1.83017i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.0576 | − | 8.69352i | −1.00833 | − | 0.582161i | −0.0976300 | − | 0.995223i | \(-0.531126\pi\) |
−0.910703 | + | 0.413061i | \(0.864459\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.9603 | −1.78942 | −0.894708 | − | 0.446652i | \(-0.852616\pi\) | ||||
−0.894708 | + | 0.446652i | \(0.852616\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.645395 | −0.0426489 | −0.0213245 | − | 0.999773i | \(-0.506788\pi\) | ||||
−0.0213245 | + | 0.999773i | \(0.506788\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.3758 | − | 11.1866i | −1.26935 | − | 0.732862i | −0.294488 | − | 0.955655i | \(-0.595149\pi\) |
−0.974866 | + | 0.222794i | \(0.928482\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.75110i | 0.440393i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.37564 | 0.347721 | 0.173861 | − | 0.984770i | \(-0.444376\pi\) | ||||
0.173861 | + | 0.984770i | \(0.444376\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.0588490 | − | 0.101929i | −0.00379080 | − | 0.00656585i | 0.864124 | − | 0.503279i | \(-0.167873\pi\) |
−0.867915 | + | 0.496713i | \(0.834540\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.79005 | + | 2.76554i | 0.306025 | + | 0.176684i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.96338 | + | 18.2466i | −0.379441 | + | 1.16100i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.16780 | − | 8.95089i | −0.326188 | − | 0.564975i | 0.655564 | − | 0.755140i | \(-0.272431\pi\) |
−0.981752 | + | 0.190165i | \(0.939098\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.63163 | − | 2.82607i | −0.102580 | − | 0.177673i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.7958 | − | 10.8518i | 1.17245 | − | 0.676914i | 0.218194 | − | 0.975905i | \(-0.429983\pi\) |
0.954256 | + | 0.298991i | \(0.0966501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 4.49319i | − | 0.279193i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.5325 | − | 23.4391i | 0.834453 | − | 1.44531i | −0.0600228 | − | 0.998197i | \(-0.519117\pi\) |
0.894475 | − | 0.447117i | \(-0.147549\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.9968 | 1.71983 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.93328 | + | 2.84823i | 0.300787 | + | 0.173660i | 0.642796 | − | 0.766037i | \(-0.277774\pi\) |
−0.342009 | + | 0.939697i | \(0.611107\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.59990 | − | 1.50105i | −0.157933 | − | 0.0911824i | 0.418951 | − | 0.908009i | \(-0.362398\pi\) |
−0.576883 | + | 0.816827i | \(0.695731\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.699519 | − | 1.21160i | −0.0421826 | − | 0.0730624i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.08132 | 0.0649703 | 0.0324851 | − | 0.999472i | \(-0.489658\pi\) | ||||
0.0324851 | + | 0.999472i | \(0.489658\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.6773 | + | 9.05127i | −0.935227 | + | 0.539954i | −0.888461 | − | 0.458952i | \(-0.848225\pi\) |
−0.0467662 | + | 0.998906i | \(0.514892\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.62115 | + | 0.935971i | 0.0963674 | + | 0.0556377i | 0.547409 | − | 0.836865i | \(-0.315614\pi\) |
−0.451042 | + | 0.892503i | \(0.648947\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.18032 | − | 10.7046i | 0.364813 | − | 0.631875i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.5836 | + | 18.3313i | 0.622564 | + | 1.07831i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.51284i | 0.0883812i | 0.999023 | + | 0.0441906i | \(0.0140709\pi\) | ||||
−0.999023 | + | 0.0441906i | \(0.985929\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.92316 | − | 2.84239i | 0.286637 | − | 0.165490i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.83438 | + | 17.0337i | −0.568737 | + | 0.985082i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.8872 | − | 20.5893i | 0.685169 | − | 1.18675i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.4459i | 1.28525i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.715534 | + | 0.413114i | 0.0408377 | + | 0.0235776i | 0.520280 | − | 0.853996i | \(-0.325828\pi\) |
−0.479442 | + | 0.877573i | \(0.659161\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.4749 | 1.50126 | 0.750628 | − | 0.660725i | \(-0.229751\pi\) | ||||
0.750628 | + | 0.660725i | \(0.229751\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.36483 | − | 9.29215i | −0.303238 | − | 0.525223i | 0.673630 | − | 0.739069i | \(-0.264734\pi\) |
−0.976867 | + | 0.213846i | \(0.931401\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.5225 | + | 8.96192i | −0.871830 | + | 0.503351i | −0.867956 | − | 0.496641i | \(-0.834567\pi\) |
−0.00387421 | + | 0.999992i | \(0.501233\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.54446 | + | 2.04639i | −0.198452 | + | 0.114576i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.55360 | − | 26.3502i | −0.309010 | − | 1.46617i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.21624 | + | 7.30274i | −0.233875 | + | 0.405083i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.70839 | − | 3.87309i | 0.369846 | − | 0.213531i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 17.6283i | − | 0.968936i | −0.874809 | − | 0.484468i | \(-0.839013\pi\) | ||
0.874809 | − | 0.484468i | \(-0.160987\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 25.5180 | 1.39420 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.5924 | − | 20.0786i | 0.631477 | − | 1.09375i | −0.355773 | − | 0.934572i | \(-0.615782\pi\) |
0.987250 | − | 0.159178i | \(-0.0508843\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.66063i | 0.252387i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.7739i | 0.797718i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.11621 | − | 1.93333i | 0.0599211 | − | 0.103786i | −0.834509 | − | 0.550995i | \(-0.814248\pi\) |
0.894430 | + | 0.447208i | \(0.147582\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.8456 | −1.70466 | −0.852329 | − | 0.523007i | \(-0.824810\pi\) | ||||
−0.852329 | + | 0.523007i | \(0.824810\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.5384i | 0.560901i | 0.959868 | + | 0.280451i | \(0.0904839\pi\) | ||||
−0.959868 | + | 0.280451i | \(0.909516\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.8133 | + | 13.1713i | −1.21080 | + | 0.699059i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.3642 | + | 30.0756i | −0.916446 | + | 1.58733i | −0.111677 | + | 0.993745i | \(0.535622\pi\) |
−0.804770 | + | 0.593587i | \(0.797711\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.05098 | + | 18.8890i | −0.107946 | + | 0.994157i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.0881 | − | 15.0620i | 1.36551 | − | 0.788380i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.0717 | + | 7.54694i | −0.682337 | + | 0.393947i | −0.800735 | − | 0.599019i | \(-0.795557\pi\) |
0.118398 | + | 0.992966i | \(0.462224\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.0617 | − | 27.8197i | −0.833882 | − | 1.44433i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.2927 | 1.62027 | 0.810136 | − | 0.586242i | \(-0.199393\pi\) | ||||
0.810136 | + | 0.586242i | \(0.199393\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.3636 | + | 12.3343i | 1.10028 | + | 0.635249i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.6109i | 0.699146i | 0.936909 | + | 0.349573i | \(0.113673\pi\) | ||||
−0.936909 | + | 0.349573i | \(0.886327\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.2735 | + | 24.7223i | −0.729339 | + | 1.26325i | 0.227824 | + | 0.973702i | \(0.426839\pi\) |
−0.957163 | + | 0.289550i | \(0.906494\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.89853 | + | 5.02040i | −0.147723 | + | 0.255863i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.3036 | − | 6.52612i | 0.573114 | − | 0.330887i | −0.185278 | − | 0.982686i | \(-0.559319\pi\) |
0.758392 | + | 0.651799i | \(0.225985\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 27.5918i | − | 1.39538i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.70757 | − | 4.68965i | −0.136233 | − | 0.235962i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.22502 | − | 5.58590i | 0.161859 | − | 0.280348i | −0.773676 | − | 0.633581i | \(-0.781584\pi\) |
0.935535 | + | 0.353233i | \(0.114918\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.8231 | + | 16.0637i | 1.38942 | + | 0.802181i | 0.993250 | − | 0.115996i | \(-0.0370061\pi\) |
0.396169 | + | 0.918178i | \(0.370339\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.3277 | − | 14.0456i | 1.21185 | − | 0.699661i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.08810 | 0.0539353 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.7369 | − | 23.7930i | −0.679247 | − | 1.17649i | −0.975208 | − | 0.221290i | \(-0.928973\pi\) |
0.295961 | − | 0.955200i | \(-0.404360\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.64881 | − | 3.26134i | −0.277960 | − | 0.160480i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.7175 | − | 9.65186i | −0.820631 | − | 0.473791i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.7384 | −0.817723 | −0.408861 | − | 0.912597i | \(-0.634074\pi\) | ||||
−0.408861 | + | 0.912597i | \(0.634074\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.37905 | − | 9.31679i | 0.262159 | − | 0.454072i | −0.704657 | − | 0.709549i | \(-0.748899\pi\) |
0.966815 | + | 0.255476i | \(0.0822322\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 11.8293i | − | 0.573803i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.3039 | − | 12.8771i | 1.07936 | − | 0.623169i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.9070 | + | 18.8915i | 0.525373 | + | 0.909972i | 0.999563 | + | 0.0295500i | \(0.00940743\pi\) |
−0.474191 | + | 0.880422i | \(0.657259\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.6446 | − | 21.9010i | −0.607659 | − | 1.05250i | −0.991625 | − | 0.129149i | \(-0.958776\pi\) |
0.383967 | − | 0.923347i | \(-0.374558\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.04762 | + | 18.5044i | −0.289297 | + | 0.885185i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.0701 | + | 15.6289i | 1.29198 | + | 0.745927i | 0.979006 | − | 0.203833i | \(-0.0653401\pi\) |
0.312978 | + | 0.949760i | \(0.398673\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.86303 | − | 10.1551i | −0.278561 | − | 0.482482i | 0.692466 | − | 0.721450i | \(-0.256524\pi\) |
−0.971027 | + | 0.238968i | \(0.923191\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.74337 | 0.319667 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 19.3531i | − | 0.913329i | −0.889639 | − | 0.456664i | \(-0.849044\pi\) | ||
0.889639 | − | 0.456664i | \(-0.150956\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.59231 | + | 1.49667i | 0.122067 | + | 0.0704755i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 34.9408 | 1.63805 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.43069 | −0.347593 | −0.173796 | − | 0.984782i | \(-0.555603\pi\) | ||||
−0.173796 | + | 0.984782i | \(0.555603\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.0829 | + | 17.3684i | 1.40110 | + | 0.808925i | 0.994506 | − | 0.104684i | \(-0.0333832\pi\) |
0.406594 | + | 0.913609i | \(0.366716\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.95687i | 0.416261i | 0.978101 | + | 0.208130i | \(0.0667378\pi\) | ||||
−0.978101 | + | 0.208130i | \(0.933262\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.282420 | −0.0130689 | −0.00653443 | − | 0.999979i | \(-0.502080\pi\) | ||||
−0.00653443 | + | 0.999979i | \(0.502080\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.6397 | − | 25.3566i | −0.675996 | − | 1.17086i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.98605 | + | 2.87870i | 0.229259 | + | 0.132363i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.59276 | + | 7.93327i | −0.118964 | + | 0.364004i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.93957 | − | 10.2876i | −0.271386 | − | 0.470054i | 0.697831 | − | 0.716263i | \(-0.254149\pi\) |
−0.969217 | + | 0.246208i | \(0.920815\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.27918 | − | 5.67971i | −0.149518 | − | 0.258972i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.7969 | − | 7.38828i | 0.581076 | − | 0.335484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.04436i | − | 0.273896i | −0.990578 | − | 0.136948i | \(-0.956271\pi\) | ||
0.990578 | − | 0.136948i | \(-0.0437294\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.76957 | + | 11.7252i | −0.305506 | + | 0.529153i | −0.977374 | − | 0.211519i | \(-0.932159\pi\) |
0.671868 | + | 0.740671i | \(0.265492\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.6056 | −1.55856 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 26.1759 | + | 15.1127i | 1.17415 | + | 0.677896i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.1361 | + | 12.7803i | 0.990950 | + | 0.572125i | 0.905558 | − | 0.424222i | \(-0.139453\pi\) |
0.0853915 | + | 0.996347i | \(0.472786\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.234869 | − | 0.406806i | −0.0104723 | − | 0.0181386i | 0.860742 | − | 0.509042i | \(-0.170000\pi\) |
−0.871214 | + | 0.490903i | \(0.836667\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 51.2889 | 2.28233 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.39853 | − | 3.11684i | 0.239285 | − | 0.138152i | −0.375563 | − | 0.926797i | \(-0.622551\pi\) |
0.614848 | + | 0.788645i | \(0.289217\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.9334 | − | 17.2821i | −1.32418 | − | 0.764514i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.8296 | + | 44.7382i | −1.13819 | + | 1.97140i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.937937 | + | 1.62455i | 0.0412504 | + | 0.0714478i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.7521i | 1.08441i | 0.840247 | + | 0.542204i | \(0.182410\pi\) | ||||
−0.840247 | + | 0.542204i | \(0.817590\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.9312 | − | 9.77523i | 0.740350 | − | 0.427441i | −0.0818469 | − | 0.996645i | \(-0.526082\pi\) |
0.822196 | + | 0.569204i | \(0.192749\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.7035 | + | 34.1274i | −0.858297 | + | 1.48661i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.52669 | − | 2.64430i | 0.0663778 | − | 0.114970i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 18.0419i | − | 0.781481i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.2743 | + | 19.2109i | 1.43858 | + | 0.830562i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.53688 | 0.0661979 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.43658 | + | 11.1485i | 0.276730 | + | 0.479311i | 0.970570 | − | 0.240819i | \(-0.0774159\pi\) |
−0.693840 | + | 0.720129i | \(0.744083\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.7711 | + | 7.37341i | −0.547055 | + | 0.315842i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.74630 | + | 3.31763i | −0.245694 | + | 0.141852i | −0.617791 | − | 0.786342i | \(-0.711972\pi\) |
0.372097 | + | 0.928194i | \(0.378639\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.2082 | + | 7.58493i | 0.988703 | + | 0.323129i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.10666 | + | 5.38089i | −0.132109 | + | 0.228819i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.8855 | + | 14.3676i | −1.05443 | + | 0.608776i | −0.923887 | − | 0.382666i | \(-0.875006\pi\) |
−0.130545 | + | 0.991442i | \(0.541673\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 34.7018i | − | 1.46773i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35.7237 | −1.50558 | −0.752788 | − | 0.658263i | \(-0.771291\pi\) | ||||
−0.752788 | + | 0.658263i | \(0.771291\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.30248 | + | 12.6483i | −0.307218 | + | 0.532116i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.2818i | 0.976023i | 0.872837 | + | 0.488011i | \(0.162278\pi\) | ||||
−0.872837 | + | 0.488011i | \(0.837722\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.1334i | 0.968102i | 0.875040 | + | 0.484051i | \(0.160835\pi\) | ||||
−0.875040 | + | 0.484051i | \(0.839165\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.27580 | + | 7.40590i | −0.178313 | + | 0.308847i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.6533 | −0.610023 | −0.305012 | − | 0.952349i | \(-0.598660\pi\) | ||||
−0.305012 | + | 0.952349i | \(0.598660\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.1490i | 0.918897i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.73701 | − | 3.88962i | 0.279019 | − | 0.161091i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.1867 | + | 22.8401i | −0.544275 | + | 0.942712i | 0.454377 | + | 0.890810i | \(0.349862\pi\) |
−0.998652 | + | 0.0519029i | \(0.983471\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.6942 | − | 18.5688i | 0.852690 | − | 0.765116i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.8529 | − | 18.9676i | 1.34911 | − | 0.778908i | 0.360985 | − | 0.932572i | \(-0.382441\pi\) |
0.988123 | + | 0.153664i | \(0.0491072\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −42.4488 | + | 24.5078i | −1.74023 | + | 1.00472i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.55133 | + | 2.68698i | 0.0633856 | + | 0.109787i | 0.895977 | − | 0.444101i | \(-0.146477\pi\) |
−0.832591 | + | 0.553888i | \(0.813144\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −43.4637 | −1.77292 | −0.886460 | − | 0.462805i | \(-0.846843\pi\) | ||||
−0.886460 | + | 0.462805i | \(0.846843\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.8344 | + | 13.7608i | 0.969008 | + | 0.559457i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.19694i | − | 0.0891708i | −0.999006 | − | 0.0445854i | \(-0.985803\pi\) | ||
0.999006 | − | 0.0445854i | \(-0.0141967\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.65326 | − | 9.79173i | 0.228706 | − | 0.396131i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.82963 | − | 4.90107i | 0.114288 | − | 0.197952i | −0.803207 | − | 0.595700i | \(-0.796875\pi\) |
0.917495 | + | 0.397748i | \(0.130208\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.6435 | + | 10.1865i | −0.710302 | + | 0.410093i | −0.811173 | − | 0.584807i | \(-0.801170\pi\) |
0.100871 | + | 0.994900i | \(0.467837\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 40.3661i | − | 1.62245i | −0.584735 | − | 0.811224i | \(-0.698801\pi\) | ||
0.584735 | − | 0.811224i | \(-0.301199\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.86866 | − | 6.70072i | −0.154995 | − | 0.268459i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.4537 | − | 26.7667i | 0.618150 | − | 1.07067i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.96762 | + | 4.60011i | 0.317690 | + | 0.183418i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0420 | − | 18.4995i | 1.27557 | − | 0.736452i | 0.299541 | − | 0.954083i | \(-0.403166\pi\) |
0.976031 | + | 0.217631i | \(0.0698330\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.06315 | −0.240609 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.63163 | − | 8.02222i | −0.183512 | − | 0.317852i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.37740 | − | 4.83669i | −0.330887 | − | 0.191038i | 0.325348 | − | 0.945594i | \(-0.394519\pi\) |
−0.656235 | + | 0.754557i | \(0.727852\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.6351 | + | 18.2645i | 1.24757 | + | 0.720282i | 0.970623 | − | 0.240604i | \(-0.0773457\pi\) |
0.276942 | + | 0.960887i | \(0.410679\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.0388 | −1.18095 | −0.590474 | − | 0.807057i | \(-0.701059\pi\) | ||||
−0.590474 | + | 0.807057i | \(0.701059\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.789791 | − | 1.36796i | 0.0310020 | − | 0.0536970i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.2628i | 1.37994i | 0.723838 | + | 0.689970i | \(0.242376\pi\) | ||||
−0.723838 | + | 0.689970i | \(0.757624\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.3326 | + | 11.1617i | −0.755389 | + | 0.436124i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.8773 | + | 27.5002i | 0.618490 | + | 1.07126i | 0.989761 | + | 0.142732i | \(0.0455886\pi\) |
−0.371272 | + | 0.928524i | \(0.621078\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.1533 | + | 17.5861i | 0.394919 | + | 0.684020i | 0.993091 | − | 0.117348i | \(-0.0374394\pi\) |
−0.598172 | + | 0.801368i | \(0.704106\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 33.8399 | − | 7.13213i | 1.31226 | − | 0.276572i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.6654 | + | 12.5085i | 0.838889 | + | 0.484333i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.11842 | + | 5.40127i | 0.120385 | + | 0.208514i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.6513 | −1.41280 | −0.706402 | − | 0.707811i | \(-0.749683\pi\) | ||||
−0.706402 | + | 0.707811i | \(0.749683\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.6921i | 0.910562i | 0.890348 | + | 0.455281i | \(0.150461\pi\) | ||||
−0.890348 | + | 0.455281i | \(0.849539\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.6831 | − | 8.47728i | −0.563485 | − | 0.325328i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.59785 | −0.175932 | −0.0879659 | − | 0.996123i | \(-0.528037\pi\) | ||||
−0.0879659 | + | 0.996123i | \(0.528037\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.3094 | 0.775981 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −40.6062 | − | 23.4440i | −1.54697 | − | 0.893146i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.3184i | 1.26749i | 0.773542 | + | 0.633745i | \(0.218483\pi\) | ||||
−0.773542 | + | 0.633745i | \(0.781517\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 26.3056 | 0.997828 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.6548 | + | 21.9187i | 0.479334 | + | 0.830231i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.9031 | + | 9.18164i | 0.600651 | + | 0.346786i | 0.769297 | − | 0.638891i | \(-0.220606\pi\) |
−0.168647 | + | 0.985677i | \(0.553940\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.33521 | − | 4.83141i | −0.163506 | − | 0.182220i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.4244 | − | 50.9645i | −1.10662 | − | 1.91672i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.5671 | − | 33.8913i | −0.734860 | − | 1.27281i | −0.954785 | − | 0.297298i | \(-0.903915\pi\) |
0.219925 | − | 0.975517i | \(-0.429419\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.6714 | − | 14.2440i | 0.923949 | − | 0.533442i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.46151i | 0.316443i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.0577 | − | 22.6166i | 0.486969 | − | 0.843455i | −0.512919 | − | 0.858437i | \(-0.671436\pi\) |
0.999888 | + | 0.0149819i | \(0.00476905\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 59.2736 | 2.20746 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.28849 | + | 5.36271i | 0.344966 | + | 0.199166i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.3018 | + | 20.3815i | 1.30927 | + | 0.755907i | 0.981974 | − | 0.189015i | \(-0.0605295\pi\) |
0.327295 | + | 0.944922i | \(0.393863\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.3402 | + | 42.1584i | 0.900254 | + | 1.55929i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.0259 | 0.850482 | 0.425241 | − | 0.905080i | \(-0.360189\pi\) | ||||
0.425241 | + | 0.905080i | \(0.360189\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.14055 | − | 3.54525i | 0.226190 | − | 0.130591i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.72833 | − | 3.88460i | −0.247505 | − | 0.142897i | 0.371116 | − | 0.928587i | \(-0.378975\pi\) |
−0.618621 | + | 0.785689i | \(0.712309\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.661917 | − | 1.14647i | 0.0242834 | − | 0.0420600i | −0.853628 | − | 0.520883i | \(-0.825603\pi\) |
0.877912 | + | 0.478823i | \(0.158936\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.36286 | − | 2.36055i | −0.0499314 | − | 0.0864838i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 44.0851i | − | 1.61084i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.5737 | + | 6.10474i | −0.385841 | + | 0.222765i | −0.680356 | − | 0.732881i | \(-0.738175\pi\) |
0.294516 | + | 0.955647i | \(0.404842\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.3654 | + | 49.1303i | −1.03232 | + | 1.78804i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.3695 | − | 17.9606i | 0.376888 | − | 0.652788i | −0.613720 | − | 0.789524i | \(-0.710328\pi\) |
0.990608 | + | 0.136735i | \(0.0436610\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 41.6236i | − | 1.50886i | −0.656383 | − | 0.754428i | \(-0.727914\pi\) | ||
0.656383 | − | 0.754428i | \(-0.272086\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.6535 | + | 8.46022i | 0.530494 | + | 0.306281i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.52066 | −0.343771 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.74896 | − | 3.02929i | −0.0630692 | − | 0.109239i | 0.832767 | − | 0.553624i | \(-0.186756\pi\) |
−0.895836 | + | 0.444385i | \(0.853422\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.20851 | + | 0.697735i | −0.0434672 | + | 0.0250958i | −0.521576 | − | 0.853205i | \(-0.674656\pi\) |
0.478109 | + | 0.878301i | \(0.341322\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.5772 | − | 6.10675i | 0.379944 | − | 0.219361i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.68272 | − | 17.4734i | −0.131947 | − | 0.626051i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.65979 | + | 6.33895i | −0.130958 | + | 0.226825i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 35.5005 | − | 20.4962i | 1.26707 | − | 0.731541i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.6125i | 0.449586i | 0.974407 | + | 0.224793i | \(0.0721706\pi\) | ||||
−0.974407 | + | 0.224793i | \(0.927829\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.7577 | 0.595834 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.7958 | − | 32.5552i | 0.667458 | − | 1.15607i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.6012i | 0.481780i | 0.970552 | + | 0.240890i | \(0.0774393\pi\) | ||||
−0.970552 | + | 0.240890i | \(0.922561\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.8610i | 0.561123i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.18515 | − | 7.24889i | 0.147691 | − | 0.255808i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 35.4344 | 1.24890 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.53063i | 0.299921i | 0.988692 | + | 0.149960i | \(0.0479146\pi\) | ||||
−0.988692 | + | 0.149960i | \(0.952085\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.3271 | − | 26.1696i | 1.59165 | − | 0.918939i | 0.598624 | − | 0.801030i | \(-0.295714\pi\) |
0.993024 | − | 0.117908i | \(-0.0376189\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.9998 | − | 41.5688i | 0.840675 | − | 1.45609i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.08334 | − | 33.6084i | −0.247815 | − | 1.17581i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.3083 | − | 15.1891i | 0.918165 | − | 0.530103i | 0.0351160 | − | 0.999383i | \(-0.488820\pi\) |
0.883049 | + | 0.469280i | \(0.155487\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.4836 | + | 18.1770i | −1.09745 | + | 0.633612i | −0.935550 | − | 0.353195i | \(-0.885095\pi\) |
−0.161899 | + | 0.986807i | \(0.551762\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.2908 | + | 31.6806i | 0.636033 | + | 1.10164i | 0.986295 | + | 0.164989i | \(0.0527590\pi\) |
−0.350263 | + | 0.936652i | \(0.613908\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.1047 | 0.455147 | 0.227573 | − | 0.973761i | \(-0.426921\pi\) | ||||
0.227573 | + | 0.973761i | \(0.426921\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.2537 | + | 6.49735i | 0.389919 | + | 0.225120i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 9.18175i | − | 0.317748i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.94545 | − | 15.4940i | 0.308831 | − | 0.534911i | −0.669276 | − | 0.743014i | \(-0.733396\pi\) |
0.978107 | + | 0.208103i | \(0.0667289\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.18823 | − | 2.05807i | 0.0409733 | − | 0.0709679i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.5628 | − | 8.40784i | 0.500976 | − | 0.289238i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 31.5782i | − | 1.08504i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.32550 | − | 5.75994i | −0.113997 | − | 0.197448i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.15772 | + | 8.93344i | −0.176597 | + | 0.305875i | −0.940713 | − | 0.339204i | \(-0.889842\pi\) |
0.764116 | + | 0.645079i | \(0.223176\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.34720 | − | 4.81926i | −0.285135 | − | 0.164623i | 0.350611 | − | 0.936521i | \(-0.385974\pi\) |
−0.635746 | + | 0.771898i | \(0.719307\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.1615 | + | 22.0326i | −1.30205 | + | 0.751741i | −0.980756 | − | 0.195237i | \(-0.937452\pi\) |
−0.321298 | + | 0.946978i | \(0.604119\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 51.0749 | 1.73861 | 0.869306 | − | 0.494275i | \(-0.164566\pi\) | ||||
0.869306 | + | 0.494275i | \(0.164566\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.6425 | + | 28.8257i | 0.565862 | + | 0.980102i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.30308 | − | 0.752331i | −0.0442038 | − | 0.0255211i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.0111 | − | 21.3684i | −1.25407 | − | 0.724040i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.4782 | −0.827515 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.91775 | − | 10.2498i | 0.199828 | − | 0.346112i | −0.748644 | − | 0.662972i | \(-0.769295\pi\) |
0.948473 | + | 0.316859i | \(0.102628\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.4075i | 0.586475i | 0.956040 | + | 0.293237i | \(0.0947326\pi\) | ||||
−0.956040 | + | 0.293237i | \(0.905267\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.2311 | + | 19.1860i | −1.11831 | + | 0.645659i | −0.940970 | − | 0.338490i | \(-0.890084\pi\) |
−0.177344 | + | 0.984149i | \(0.556751\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.0878 | + | 19.2046i | 0.372292 | + | 0.644828i | 0.989918 | − | 0.141644i | \(-0.0452387\pi\) |
−0.617626 | + | 0.786472i | \(0.711905\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.47842 | + | 6.02480i | 0.116662 | + | 0.202065i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.47645 | − | 10.6372i | 0.116335 | − | 0.355959i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.45338 | − | 2.57116i | −0.148860 | − | 0.0859443i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.8649 | − | 30.9428i | −0.595826 | − | 1.03200i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 65.7756 | 2.19130 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.5589i | 0.683400i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.09253 | − | 1.78547i | −0.102686 | − | 0.0592856i | 0.447778 | − | 0.894145i | \(-0.352216\pi\) |
−0.550463 | + | 0.834859i | \(0.685549\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.2094 | 1.10028 | 0.550138 | − | 0.835074i | \(-0.314575\pi\) | ||||
0.550138 | + | 0.835074i | \(0.314575\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.36377 | −0.177515 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.1822 | + | 12.8069i | 0.732521 | + | 0.422921i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.5957i | 0.415493i | 0.978183 | + | 0.207746i | \(0.0666128\pi\) | ||||
−0.978183 | + | 0.207746i | \(0.933387\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 44.1176 | 1.45215 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.42572 | − | 2.46943i | −0.0468775 | − | 0.0811942i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.2298 | − | 19.1853i | −1.09024 | − | 0.629448i | −0.156596 | − | 0.987663i | \(-0.550052\pi\) |
−0.933639 | + | 0.358215i | \(0.883386\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.12320 | − | 6.82406i | −0.200680 | − | 0.223649i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.93500 | − | 10.2797i | −0.194095 | − | 0.336183i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.0371 | − | 48.5617i | −0.915932 | − | 1.58644i | −0.805530 | − | 0.592555i | \(-0.798119\pi\) |
−0.110402 | − | 0.993887i | \(-0.535214\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.3546 | + | 6.55556i | −0.370148 | + | 0.213705i | −0.673523 | − | 0.739166i | \(-0.735220\pi\) |
0.303375 | + | 0.952871i | \(0.401887\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 18.2968i | − | 0.595824i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.3590 | − | 42.1910i | 0.791560 | − | 1.37102i | −0.133441 | − | 0.991057i | \(-0.542603\pi\) |
0.925001 | − | 0.379965i | \(-0.124064\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −50.4506 | −1.63770 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.6474 | − | 7.87933i | −0.442083 | − | 0.255237i | 0.262398 | − | 0.964960i | \(-0.415487\pi\) |
−0.704481 | + | 0.709723i | \(0.748820\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.13746 | − | 1.81141i | −0.101526 | − | 0.0586159i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.6515 | − | 20.1809i | −0.376245 | − | 0.651675i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.68697 | −0.312483 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.1800 | + | 7.03210i | −0.392086 | + | 0.226371i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.7997 | + | 24.7104i | 1.37635 | + | 0.794633i | 0.991718 | − | 0.128438i | \(-0.0409964\pi\) |
0.384628 | + | 0.923072i | \(0.374330\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.95664 | + | 15.5134i | −0.287432 | + | 0.497848i | −0.973196 | − | 0.229977i | \(-0.926135\pi\) |
0.685764 | + | 0.727824i | \(0.259468\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.0915 | − | 26.1392i | −0.483810 | − | 0.837984i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46.2005i | 1.47808i | 0.673660 | + | 0.739042i | \(0.264721\pi\) | ||||
−0.673660 | + | 0.739042i | \(0.735279\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.62269 | − | 0.936863i | 0.0518615 | − | 0.0299423i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.8820 | + | 43.0970i | −0.793614 | + | 1.37458i | 0.130102 | + | 0.991501i | \(0.458470\pi\) |
−0.923716 | + | 0.383079i | \(0.874864\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.8115 | + | 48.1709i | −0.886147 | + | 1.53485i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 35.1920i | − | 1.11904i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.8014 | + | 7.39089i | 0.406650 | + | 0.234779i | 0.689349 | − | 0.724429i | \(-0.257897\pi\) |
−0.282699 | + | 0.959209i | \(0.591230\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.9757 | −0.791784 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.77321 | − | 3.07130i | −0.0561582 | − | 0.0972689i | 0.836580 | − | 0.547845i | \(-0.184552\pi\) |
−0.892738 | + | 0.450576i | \(0.851218\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2736.2.cg.a.1151.2 | ✓ | 24 | |
3.2 | odd | 2 | inner | 2736.2.cg.a.1151.11 | yes | 24 | |
4.3 | odd | 2 | 2736.2.cg.b.1151.2 | yes | 24 | ||
12.11 | even | 2 | 2736.2.cg.b.1151.11 | yes | 24 | ||
19.7 | even | 3 | 2736.2.cg.b.2591.11 | yes | 24 | ||
57.26 | odd | 6 | 2736.2.cg.b.2591.2 | yes | 24 | ||
76.7 | odd | 6 | inner | 2736.2.cg.a.2591.11 | yes | 24 | |
228.83 | even | 6 | inner | 2736.2.cg.a.2591.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2736.2.cg.a.1151.2 | ✓ | 24 | 1.1 | even | 1 | trivial | |
2736.2.cg.a.1151.11 | yes | 24 | 3.2 | odd | 2 | inner | |
2736.2.cg.a.2591.2 | yes | 24 | 228.83 | even | 6 | inner | |
2736.2.cg.a.2591.11 | yes | 24 | 76.7 | odd | 6 | inner | |
2736.2.cg.b.1151.2 | yes | 24 | 4.3 | odd | 2 | ||
2736.2.cg.b.1151.11 | yes | 24 | 12.11 | even | 2 | ||
2736.2.cg.b.2591.2 | yes | 24 | 57.26 | odd | 6 | ||
2736.2.cg.b.2591.11 | yes | 24 | 19.7 | even | 3 |