Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1500,2,Mod(49,1500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1500, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1500.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1500.o (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.9775603032\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 349.4 | ||
Character | \(\chi\) | \(=\) | 1500.349 |
Dual form | 1500.2.o.c.649.4 |
$q$-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 \(\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times\).
\(n\) | \(751\) | \(877\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{9}{10}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.587785 | + | 0.809017i | 0.339358 | + | 0.467086i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.80992i | 1.44001i | 0.693968 | + | 0.720006i | \(0.255861\pi\) | ||||
−0.693968 | + | 0.720006i | \(0.744139\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.309017 | + | 0.951057i | −0.103006 | + | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0589397 | + | 0.181398i | 0.0177710 | + | 0.0546935i | 0.959549 | − | 0.281542i | \(-0.0908460\pi\) |
−0.941778 | + | 0.336236i | \(0.890846\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.59724 | − | 0.518974i | −0.442994 | − | 0.143937i | 0.0790227 | − | 0.996873i | \(-0.474820\pi\) |
−0.522016 | + | 0.852935i | \(0.674820\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.70572 | + | 3.72410i | −0.656233 | + | 0.903227i | −0.999349 | − | 0.0360656i | \(-0.988517\pi\) |
0.343116 | + | 0.939293i | \(0.388517\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.13682 | − | 1.55249i | −0.490221 | − | 0.356166i | 0.315049 | − | 0.949076i | \(-0.397979\pi\) |
−0.805269 | + | 0.592909i | \(0.797979\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.08229 | + | 2.23941i | −0.672610 | + | 0.488680i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.04461 | + | 1.96401i | −1.26039 | + | 0.409525i | −0.861632 | − | 0.507533i | \(-0.830558\pi\) |
−0.398755 | + | 0.917057i | \(0.630558\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.951057 | + | 0.309017i | −0.183031 | + | 0.0594703i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.03878 | − | 1.48126i | 0.378593 | − | 0.275064i | −0.382172 | − | 0.924091i | \(-0.624824\pi\) |
0.760765 | + | 0.649027i | \(0.224824\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.03331 | − | 2.20383i | −0.544798 | − | 0.395819i | 0.281066 | − | 0.959688i | \(-0.409312\pi\) |
−0.825864 | + | 0.563870i | \(0.809312\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.112110 | + | 0.154306i | −0.0195158 | + | 0.0268612i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.2820 | + | 3.66574i | 1.85474 | + | 0.602643i | 0.995906 | + | 0.0903980i | \(0.0288139\pi\) |
0.858839 | + | 0.512245i | \(0.171186\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.518974 | − | 1.59724i | −0.0831023 | − | 0.255763i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.22169 | + | 6.83765i | −0.346969 | + | 1.06786i | 0.613552 | + | 0.789655i | \(0.289740\pi\) |
−0.960521 | + | 0.278207i | \(0.910260\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.22619i | − | 1.40698i | −0.710705 | − | 0.703491i | \(-0.751624\pi\) | ||
0.710705 | − | 0.703491i | \(-0.248376\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.67353 | − | 3.67980i | −0.389975 | − | 0.536754i | 0.568218 | − | 0.822878i | \(-0.307633\pi\) |
−0.958193 | + | 0.286124i | \(0.907633\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.51545 | −1.07364 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.60324 | −0.644583 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.54285 | − | 7.62908i | −0.761369 | − | 1.04793i | −0.997099 | − | 0.0761162i | \(-0.975748\pi\) |
0.235730 | − | 0.971819i | \(-0.424252\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.64126i | − | 0.349843i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.20656 | + | 6.79109i | −0.287269 | + | 0.884124i | 0.698440 | + | 0.715669i | \(0.253878\pi\) |
−0.985709 | + | 0.168456i | \(0.946122\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.94497 | + | 9.06368i | 0.377064 | + | 1.16049i | 0.942075 | + | 0.335402i | \(0.108872\pi\) |
−0.565011 | + | 0.825084i | \(0.691128\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.62344 | − | 1.17733i | −0.456511 | − | 0.148329i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.55709 | + | 4.89591i | −0.434567 | + | 0.598131i | −0.968994 | − | 0.247084i | \(-0.920528\pi\) |
0.534427 | + | 0.845215i | \(0.320528\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.14185 | − | 3.73577i | −0.619006 | − | 0.449734i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.7586 | + | 7.81655i | −1.27681 | + | 0.927654i | −0.999452 | − | 0.0331133i | \(-0.989458\pi\) |
−0.277355 | + | 0.960768i | \(0.589458\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.95645 | − | 1.61045i | 0.580109 | − | 0.188489i | −0.00424038 | − | 0.999991i | \(-0.501350\pi\) |
0.584349 | + | 0.811502i | \(0.301350\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.691110 | + | 0.224555i | −0.0787593 | + | 0.0255904i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.51740 | + | 1.82900i | −0.283230 | + | 0.205779i | −0.720325 | − | 0.693637i | \(-0.756007\pi\) |
0.437095 | + | 0.899415i | \(0.356007\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.74988 | − | 3.78488i | 0.301838 | − | 0.415445i | −0.630976 | − | 0.775802i | \(-0.717345\pi\) |
0.932814 | + | 0.360358i | \(0.117345\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.39673 | + | 0.778746i | 0.256957 | + | 0.0834904i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.30840 | − | 13.2599i | −0.456690 | − | 1.40555i | −0.869140 | − | 0.494566i | \(-0.835327\pi\) |
0.412451 | − | 0.910980i | \(-0.364673\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.97725 | − | 6.08534i | 0.207272 | − | 0.637917i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 3.74937i | − | 0.388792i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.93527 | + | 5.41643i | 0.399566 | + | 0.549955i | 0.960635 | − | 0.277814i | \(-0.0896099\pi\) |
−0.561069 | + | 0.827769i | \(0.689610\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.190733 | −0.0191694 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.5147 | 1.04625 | 0.523127 | − | 0.852255i | \(-0.324765\pi\) | ||||
0.523127 | + | 0.852255i | \(0.324765\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.62055 | + | 10.4888i | 0.750875 | + | 1.03349i | 0.997919 | + | 0.0644861i | \(0.0205408\pi\) |
−0.247044 | + | 0.969004i | \(0.579459\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.64606i | 0.932520i | 0.884648 | + | 0.466260i | \(0.154399\pi\) | ||||
−0.884648 | + | 0.466260i | \(0.845601\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.31798 | + | 19.4447i | −0.605153 | + | 1.86247i | −0.109414 | + | 0.993996i | \(0.534898\pi\) |
−0.495738 | + | 0.868472i | \(0.665102\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.66574 | + | 11.2820i | 0.347936 | + | 1.07084i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.84623 | − | 1.24972i | −0.361823 | − | 0.117564i | 0.122463 | − | 0.992473i | \(-0.460921\pi\) |
−0.484286 | + | 0.874910i | \(0.660921\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.987147 | − | 1.35869i | 0.0912617 | − | 0.125611i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.1885 | − | 10.3086i | −1.30066 | − | 0.944984i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.86976 | − | 6.44425i | 0.806341 | − | 0.585841i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.83765 | + | 2.22169i | −0.616530 | + | 0.200323i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.9338 | + | 5.17719i | −1.41389 | + | 0.459401i | −0.913656 | − | 0.406488i | \(-0.866753\pi\) |
−0.500236 | + | 0.865889i | \(0.666753\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.46415 | − | 5.42302i | 0.657181 | − | 0.477470i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.67583 | + | 1.94410i | 0.233788 | + | 0.169857i | 0.698511 | − | 0.715599i | \(-0.253846\pi\) |
−0.464723 | + | 0.885456i | \(0.653846\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.91486 | − | 8.14111i | 0.512884 | − | 0.705924i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.99642 | + | 0.648677i | 0.170566 | + | 0.0554202i | 0.393055 | − | 0.919515i | \(-0.371418\pi\) |
−0.222489 | + | 0.974935i | \(0.571418\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.10525 | + | 12.6347i | 0.348203 | + | 1.07166i | 0.959847 | + | 0.280525i | \(0.0905087\pi\) |
−0.611643 | + | 0.791134i | \(0.709491\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.40556 | − | 4.32586i | 0.118369 | − | 0.364303i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 0.320323i | − | 0.0267868i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.41747 | − | 6.08013i | −0.364347 | − | 0.501481i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.79913 | 0.229313 | 0.114657 | − | 0.993405i | \(-0.463423\pi\) | ||||
0.114657 | + | 0.993405i | \(0.463423\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.71330 | −0.546320 | −0.273160 | − | 0.961969i | \(-0.588069\pi\) | ||||
−0.273160 | + | 0.961969i | \(0.588069\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.70572 | − | 3.72410i | −0.218744 | − | 0.301076i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.9495i | 1.11329i | 0.830750 | + | 0.556646i | \(0.187912\pi\) | ||||
−0.830750 | + | 0.556646i | \(0.812088\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.91405 | − | 8.96852i | 0.231099 | − | 0.711250i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.48272 | − | 23.0294i | −0.589721 | − | 1.81497i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.44065 | + | 2.74253i | 0.661123 | + | 0.214812i | 0.620312 | − | 0.784355i | \(-0.287006\pi\) |
0.0408107 | + | 0.999167i | \(0.487006\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.4563 | − | 19.8973i | 1.11866 | − | 1.53970i | 0.310655 | − | 0.950523i | \(-0.399452\pi\) |
0.808003 | − | 0.589178i | \(-0.200548\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.23539 | − | 5.98336i | −0.633492 | − | 0.460259i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.13682 | − | 1.55249i | 0.163407 | − | 0.118722i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.1062 | + | 5.23322i | −1.22453 | + | 0.397874i | −0.848730 | − | 0.528826i | \(-0.822632\pi\) |
−0.375801 | + | 0.926701i | \(0.622632\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.79109 | + | 2.20656i | −0.510449 | + | 0.165855i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.9328 | − | 8.66966i | 0.891897 | − | 0.648001i | −0.0444751 | − | 0.999010i | \(-0.514162\pi\) |
0.936372 | + | 0.351010i | \(0.114162\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.89013 | + | 6.45906i | 0.660798 | + | 0.480098i | 0.866932 | − | 0.498426i | \(-0.166088\pi\) |
−0.206134 | + | 0.978524i | \(0.566088\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.60166 | + | 7.71003i | −0.414087 | + | 0.569941i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.835018 | − | 0.271314i | −0.0610625 | − | 0.0198404i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.17733 | − | 3.62344i | −0.0856380 | − | 0.263567i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.42739 | + | 22.8591i | −0.537427 | + | 1.65403i | 0.200919 | + | 0.979608i | \(0.435607\pi\) |
−0.738346 | + | 0.674422i | \(0.764393\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.50843i | 0.540469i | 0.962795 | + | 0.270234i | \(0.0871012\pi\) | ||||
−0.962795 | + | 0.270234i | \(0.912899\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.37799 | − | 10.1549i | −0.525660 | − | 0.723509i | 0.460801 | − | 0.887503i | \(-0.347562\pi\) |
−0.986461 | + | 0.163995i | \(0.947562\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.7618 | 1.40088 | 0.700440 | − | 0.713711i | \(-0.252987\pi\) | ||||
0.700440 | + | 0.713711i | \(0.252987\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.05168 | −0.426852 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.64349 | + | 7.76760i | 0.396095 | + | 0.545178i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.35567i | − | 0.441750i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.155675 | − | 0.479118i | 0.0107683 | − | 0.0331413i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.47579 | − | 10.6974i | −0.239283 | − | 0.736437i | −0.996524 | − | 0.0833021i | \(-0.973453\pi\) |
0.757241 | − | 0.653135i | \(-0.226547\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.6474 | − | 4.10941i | −0.866589 | − | 0.281572i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.39639 | − | 11.5566i | 0.569984 | − | 0.784516i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.21621 | + | 3.06326i | 0.284905 | + | 0.206996i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.25438 | − | 4.54407i | 0.420715 | − | 0.305668i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.91605 | − | 2.24716i | 0.463133 | − | 0.150481i | −0.0681508 | − | 0.997675i | \(-0.521710\pi\) |
0.531284 | + | 0.847194i | \(0.321710\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.00583 | − | 2.92617i | 0.597738 | − | 0.194217i | 0.00550660 | − | 0.999985i | \(-0.498247\pi\) |
0.592231 | + | 0.805768i | \(0.298247\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.1755 | − | 12.4787i | 1.13499 | − | 0.824617i | 0.148575 | − | 0.988901i | \(-0.452531\pi\) |
0.986413 | + | 0.164284i | \(0.0525315\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.587893 | − | 0.427129i | −0.0386805 | − | 0.0281030i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.16700 | − | 5.73538i | 0.272989 | − | 0.375737i | −0.650407 | − | 0.759586i | \(-0.725402\pi\) |
0.923396 | + | 0.383849i | \(0.125402\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.95939 | − | 0.961563i | −0.192233 | − | 0.0624602i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.18395 | + | 19.0323i | 0.400007 | + | 1.23109i | 0.924993 | + | 0.379983i | \(0.124070\pi\) |
−0.524987 | + | 0.851110i | \(0.675930\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.43498 | − | 19.8048i | 0.414513 | − | 1.27574i | −0.498172 | − | 0.867078i | \(-0.665995\pi\) |
0.912686 | − | 0.408662i | \(-0.134005\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.60731 | + | 3.58865i | 0.165899 | + | 0.228340i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.67837 | 0.296480 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.7741 | −1.87932 | −0.939662 | − | 0.342104i | \(-0.888861\pi\) | ||||
−0.939662 | + | 0.342104i | \(0.888861\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.712534 | − | 0.980719i | −0.0447966 | − | 0.0616573i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.2853i | 1.32774i | 0.747849 | + | 0.663869i | \(0.231087\pi\) | ||||
−0.747849 | + | 0.663869i | \(0.768913\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.9661 | + | 42.9834i | −0.867814 | + | 2.67086i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.778746 | + | 2.39673i | 0.0482032 | + | 0.148354i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.7951 | + | 6.75674i | 1.28228 | + | 0.416638i | 0.869383 | − | 0.494139i | \(-0.164517\pi\) |
0.412898 | + | 0.910777i | \(0.364517\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.19506 | − | 11.2795i | 0.501530 | − | 0.690297i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.69018 | − | 2.68108i | −0.224995 | − | 0.163468i | 0.469578 | − | 0.882891i | \(-0.344406\pi\) |
−0.694572 | + | 0.719423i | \(0.744406\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.4519 | − | 7.59377i | 0.634909 | − | 0.461288i | −0.223188 | − | 0.974775i | \(-0.571646\pi\) |
0.858097 | + | 0.513487i | \(0.171646\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.08534 | − | 1.97725i | 0.368301 | − | 0.119668i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.40278 | − | 2.73023i | 0.504874 | − | 0.164044i | −0.0454957 | − | 0.998965i | \(-0.514487\pi\) |
0.550370 | + | 0.834921i | \(0.314487\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.03331 | − | 2.20383i | 0.181599 | − | 0.131940i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.0247151 | − | 0.0179566i | −0.00147438 | − | 0.00107120i | 0.587048 | − | 0.809552i | \(-0.300290\pi\) |
−0.588522 | + | 0.808481i | \(0.700290\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.82560 | + | 3.88910i | −0.167964 | + | 0.231183i | −0.884699 | − | 0.466163i | \(-0.845636\pi\) |
0.716735 | + | 0.697346i | \(0.245636\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −26.0509 | − | 8.46444i | −1.53773 | − | 0.499640i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.29473 | − | 3.98478i | −0.0761607 | − | 0.234399i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.06889 | + | 6.36739i | −0.121281 | + | 0.373263i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.9705i | 0.874587i | 0.899319 | + | 0.437294i | \(0.144063\pi\) | ||||
−0.899319 | + | 0.437294i | \(0.855937\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.112110 | − | 0.154306i | −0.00650528 | − | 0.00895375i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.6739 | 0.617290 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 35.1510 | 2.02607 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.18040 | + | 8.50659i | 0.355055 | + | 0.488691i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.47622i | 0.255472i | 0.991808 | + | 0.127736i | \(0.0407710\pi\) | ||||
−0.991808 | + | 0.127736i | \(0.959229\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00636 | + | 12.3303i | −0.227914 | + | 0.701446i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.0915043 | + | 0.281621i | 0.00518873 | + | 0.0159693i | 0.953617 | − | 0.301021i | \(-0.0973276\pi\) |
−0.948429 | + | 0.316991i | \(0.897328\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.1214 | + | 6.53785i | 1.13733 | + | 0.369541i | 0.816357 | − | 0.577547i | \(-0.195990\pi\) |
0.320973 | + | 0.947088i | \(0.395990\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.2334 | − | 20.9670i | 0.855594 | − | 1.17762i | −0.127008 | − | 0.991902i | \(-0.540537\pi\) |
0.982602 | − | 0.185723i | \(-0.0594626\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.388863 | + | 0.282526i | 0.0217722 | + | 0.0158184i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.80383 | + | 5.66981i | −0.435567 | + | 0.316458i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.5633 | − | 3.75714i | 0.643398 | − | 0.209053i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −19.4447 | + | 6.31798i | −1.07530 | + | 0.349385i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.0197 | − | 10.1859i | 0.772932 | − | 0.561568i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.48400 | + | 1.80473i | 0.136533 | + | 0.0991969i | 0.653955 | − | 0.756533i | \(-0.273108\pi\) |
−0.517423 | + | 0.855730i | \(0.673108\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.97264 | + | 9.59702i | −0.382098 | + | 0.525913i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.8694 | + | 8.73038i | 1.46367 | + | 0.475574i | 0.929188 | − | 0.369607i | \(-0.120508\pi\) |
0.534479 | + | 0.845182i | \(0.320508\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.24972 | − | 3.84623i | −0.0678753 | − | 0.208899i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.220987 | − | 0.680128i | 0.0119671 | − | 0.0368310i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.96383i | − | 0.106037i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.9869 | − | 24.7568i | −0.965586 | − | 1.32901i | −0.944245 | − | 0.329242i | \(-0.893207\pi\) |
−0.0213401 | − | 0.999772i | \(-0.506793\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.1178 | 0.862764 | 0.431382 | − | 0.902169i | \(-0.358026\pi\) | ||||
0.431382 | + | 0.902169i | \(0.358026\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.67943 | 0.0896416 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.253341 | − | 0.348695i | −0.0134840 | − | 0.0185591i | 0.802222 | − | 0.597026i | \(-0.203651\pi\) |
−0.815706 | + | 0.578467i | \(0.803651\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 17.5380i | − | 0.928207i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.70871 | + | 17.5696i | −0.301294 | + | 0.927288i | 0.679740 | + | 0.733453i | \(0.262093\pi\) |
−0.981034 | + | 0.193835i | \(0.937907\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.71555 | − | 11.4353i | −0.195555 | − | 0.601857i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.4270 | + | 3.38795i | 0.547277 | + | 0.177821i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.03990 | − | 8.31320i | 0.315280 | − | 0.433946i | −0.621739 | − | 0.783225i | \(-0.713573\pi\) |
0.937019 | + | 0.349279i | \(0.113573\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.81645 | − | 4.22590i | −0.302792 | − | 0.219992i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 29.0662 | − | 21.1178i | 1.50904 | − | 1.09638i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.9266 | − | 4.52503i | 0.721092 | − | 0.234297i | 0.0745954 | − | 0.997214i | \(-0.476233\pi\) |
0.646497 | + | 0.762917i | \(0.276233\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.02516 | + | 1.30785i | −0.207306 | + | 0.0673579i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.66061 | + | 6.29230i | −0.444866 | + | 0.323214i | −0.787565 | − | 0.616231i | \(-0.788659\pi\) |
0.342700 | + | 0.939445i | \(0.388659\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.5541 | − | 9.84760i | −0.694396 | − | 0.504508i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.4690 | + | 21.2912i | −0.790428 | + | 1.08793i | 0.203627 | + | 0.979049i | \(0.434727\pi\) |
−0.994055 | + | 0.108882i | \(0.965273\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.77463 | + | 2.85105i | 0.446040 | + | 0.144927i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.0901650 | − | 0.277499i | −0.00457155 | − | 0.0140698i | 0.948745 | − | 0.316043i | \(-0.102355\pi\) |
−0.953316 | + | 0.301974i | \(0.902355\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.04082 | − | 27.8248i | 0.457214 | − | 1.40716i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.30750i | 0.166841i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.18504 | − | 1.63106i | −0.0594753 | − | 0.0818608i | 0.778243 | − | 0.627963i | \(-0.216111\pi\) |
−0.837719 | + | 0.546102i | \(0.816111\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.0630 | 0.503778 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.88760 | 0.493763 | 0.246882 | − | 0.969046i | \(-0.420594\pi\) | ||||
0.246882 | + | 0.969046i | \(0.420594\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.70118 | + | 5.09424i | 0.184369 | + | 0.253762i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.26258i | 0.112152i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.6440 | − | 35.8367i | 0.575761 | − | 1.77201i | −0.0578124 | − | 0.998327i | \(-0.518413\pi\) |
0.633573 | − | 0.773683i | \(-0.281587\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.648677 | + | 1.99642i | 0.0319969 | + | 0.0984762i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −25.8735 | − | 8.40680i | −1.27315 | − | 0.413672i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.80866 | + | 10.7477i | −0.382392 | + | 0.526317i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.6641 | − | 9.20102i | −0.618682 | − | 0.449499i | 0.233779 | − | 0.972290i | \(-0.424891\pi\) |
−0.852461 | + | 0.522791i | \(0.824891\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.7531 | + | 8.53916i | −0.572813 | + | 0.416173i | −0.836126 | − | 0.548537i | \(-0.815185\pi\) |
0.263313 | + | 0.964711i | \(0.415185\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.32586 | − | 1.40556i | 0.210331 | − | 0.0683406i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −34.5318 | + | 11.2201i | −1.67111 | + | 0.542978i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.259147 | − | 0.188281i | 0.0125117 | − | 0.00909030i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.2150 | + | 7.42161i | 0.492038 | + | 0.357486i | 0.805967 | − | 0.591960i | \(-0.201646\pi\) |
−0.313930 | + | 0.949446i | \(0.601646\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.05145 | − | 2.82358i | 0.0985864 | − | 0.135693i | −0.756874 | − | 0.653561i | \(-0.773274\pi\) |
0.855460 | + | 0.517868i | \(0.173274\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.9654 | + | 5.18746i | 0.763727 | + | 0.248150i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.04528 | + | 18.6055i | 0.288526 | + | 0.887991i | 0.985320 | + | 0.170719i | \(0.0546092\pi\) |
−0.696794 | + | 0.717271i | \(0.745391\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.32240 | − | 7.14762i | 0.110591 | − | 0.340363i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.77485i | 0.131837i | 0.997825 | + | 0.0659185i | \(0.0209977\pi\) | ||||
−0.997825 | + | 0.0659185i | \(0.979002\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.64529 | + | 2.26454i | 0.0778194 | + | 0.107109i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.4261 | 1.81344 | 0.906721 | − | 0.421732i | \(-0.138578\pi\) | ||||
0.906721 | + | 0.421732i | \(0.138578\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.37128 | −0.0645710 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.94598 | − | 5.43117i | −0.185398 | − | 0.255179i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 36.0296i | − | 1.68539i | −0.538389 | − | 0.842696i | \(-0.680967\pi\) | ||
0.538389 | − | 0.842696i | \(-0.319033\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.42248 | − | 4.37794i | 0.0663957 | − | 0.204345i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.265011 | + | 0.815619i | 0.0123428 | + | 0.0379871i | 0.957038 | − | 0.289962i | \(-0.0936426\pi\) |
−0.944695 | + | 0.327949i | \(0.893643\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.89742 | − | 3.21587i | −0.459972 | − | 0.149454i | 0.0698596 | − | 0.997557i | \(-0.477745\pi\) |
−0.529832 | + | 0.848103i | \(0.677745\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.0910 | + | 16.6419i | −0.559506 | + | 0.770094i | −0.991264 | − | 0.131895i | \(-0.957894\pi\) |
0.431757 | + | 0.901990i | \(0.357894\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.6530 | − | 13.5522i | −0.861316 | − | 0.625782i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.2854 | + | 8.19931i | −0.520003 | + | 0.377804i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.67361 | − | 0.543789i | 0.0769527 | − | 0.0250034i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.96852 | − | 2.91405i | 0.410640 | − | 0.133425i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.8384 | − | 18.7727i | 1.18059 | − | 0.857747i | 0.188350 | − | 0.982102i | \(-0.439686\pi\) |
0.992238 | + | 0.124355i | \(0.0396861\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.1176 | − | 11.7101i | −0.734898 | − | 0.533934i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.2330 | − | 19.5900i | 0.647623 | − | 0.891376i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.9140 | + | 4.84587i | 0.675820 | + | 0.219587i | 0.626764 | − | 0.779209i | \(-0.284379\pi\) |
0.0490554 | + | 0.998796i | \(0.484379\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.74253 | + | 8.44065i | 0.124022 | + | 0.381699i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.09354 | − | 15.6763i | 0.229868 | − | 0.707462i | −0.767892 | − | 0.640579i | \(-0.778694\pi\) |
0.997761 | − | 0.0668834i | \(-0.0213055\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.6005i | 0.522461i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −29.7804 | − | 40.9892i | −1.33583 | − | 1.83862i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.4339 | −0.556618 | −0.278309 | − | 0.960492i | \(-0.589774\pi\) | ||||
−0.278309 | + | 0.960492i | \(0.589774\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.5944 | 1.09880 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.54703 | + | 3.50569i | 0.113567 | + | 0.156311i | 0.862016 | − | 0.506881i | \(-0.169201\pi\) |
−0.748450 | + | 0.663191i | \(0.769201\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 10.1795i | − | 0.452088i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.32995 | + | 13.3262i | −0.191922 | + | 0.590674i | 0.808077 | + | 0.589077i | \(0.200508\pi\) |
−0.999999 | + | 0.00159734i | \(0.999492\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.13568 | + | 18.8837i | 0.271426 | + | 0.835364i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.51198 | + | 0.816193i | 0.110907 | + | 0.0360358i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.509930 | − | 0.701859i | 0.0224267 | − | 0.0308677i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.7007 | − | 9.95417i | −0.601396 | − | 0.436940i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.56002 | + | 1.13342i | −0.0683458 | + | 0.0496561i | −0.621434 | − | 0.783467i | \(-0.713449\pi\) |
0.553088 | + | 0.833123i | \(0.313449\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.86306 | + | 0.605344i | −0.0814659 | + | 0.0264699i | −0.349466 | − | 0.936949i | \(-0.613637\pi\) |
0.268001 | + | 0.963419i | \(0.413637\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.4145 | − | 5.33341i | 0.715029 | − | 0.232327i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.0725 | − | 10.2243i | 0.611849 | − | 0.444534i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.77684 | − | 4.19712i | −0.250694 | − | 0.182140i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.09712 | − | 9.76835i | 0.307410 | − | 0.423114i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.0278 | + | 4.55791i | 0.605345 | + | 0.196688i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.442958 | − | 1.36329i | −0.0190796 | − | 0.0587209i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.6961 | + | 32.9191i | −0.459860 | + | 1.41530i | 0.405473 | + | 0.914107i | \(0.367107\pi\) |
−0.865333 | + | 0.501197i | \(0.832893\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.9888i | 0.471575i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.37482 | − | 12.9033i | −0.400838 | − | 0.551706i | 0.560116 | − | 0.828414i | \(-0.310757\pi\) |
−0.960954 | + | 0.276708i | \(0.910757\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.53012 | −0.406735 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.65617 | −0.283562 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.96834 | − | 9.59110i | −0.296324 | − | 0.407855i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 43.0343i | 1.82342i | 0.410831 | + | 0.911711i | \(0.365239\pi\) | ||||
−0.410831 | + | 0.911711i | \(0.634761\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.78815 | + | 14.7364i | −0.202517 | + | 0.623284i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.271314 | − | 0.835018i | −0.0114549 | − | 0.0352545i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.9331 | − | 5.82682i | −0.755791 | − | 0.245571i | −0.0943197 | − | 0.995542i | \(-0.530068\pi\) |
−0.661471 | + | 0.749971i | \(0.730068\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.23941 | − | 3.08229i | 0.0940465 | − | 0.129444i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.7119 | − | 14.3215i | −0.826364 | − | 0.600389i | 0.0921644 | − | 0.995744i | \(-0.470621\pi\) |
−0.918528 | + | 0.395355i | \(0.870621\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.4096 | + | 9.01612i | −0.519327 | + | 0.377313i | −0.816350 | − | 0.577557i | \(-0.804006\pi\) |
0.297023 | + | 0.954870i | \(0.404006\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.8591 | + | 7.42739i | −0.954955 | + | 0.310284i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.6382 | + | 4.43133i | −0.567767 | + | 0.184479i | −0.578813 | − | 0.815460i | \(-0.696484\pi\) |
0.0110462 | + | 0.999939i | \(0.496484\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.07445 | + | 4.41335i | −0.252446 | + | 0.183412i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.4201 | + | 10.4768i | 0.598245 | + | 0.434651i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.05720 | − | 1.45512i | 0.0437849 | − | 0.0602648i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.1788 | − | 3.30729i | −0.420123 | − | 0.136506i | 0.0913234 | − | 0.995821i | \(-0.470890\pi\) |
−0.511447 | + | 0.859315i | \(0.670890\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.06021 | + | 9.41837i | 0.126094 | + | 0.388077i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.87884 | − | 11.9378i | 0.159554 | − | 0.491057i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 23.5756i | − | 0.968135i | −0.875031 | − | 0.484067i | \(-0.839159\pi\) | ||
0.875031 | − | 0.484067i | \(-0.160841\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.6157 | + | 15.9877i | 0.475400 | + | 0.654332i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.8055 | −0.564078 | −0.282039 | − | 0.959403i | \(-0.591011\pi\) | ||||
−0.282039 | + | 0.959403i | \(0.591011\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.61536 | 0.392219 | 0.196109 | − | 0.980582i | \(-0.437169\pi\) | ||||
0.196109 | + | 0.980582i | \(0.437169\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.55709 | − | 4.89591i | −0.144856 | − | 0.199377i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.7884i | 0.965539i | 0.875747 | + | 0.482770i | \(0.160369\pi\) | ||||
−0.875747 | + | 0.482770i | \(0.839631\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.96696 | + | 9.13136i | −0.120227 | + | 0.370021i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.36054 | + | 7.26500i | 0.0954973 | + | 0.293911i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.2850 | + | 4.96640i | 0.617356 | + | 0.200591i | 0.600966 | − | 0.799275i | \(-0.294783\pi\) |
0.0163900 | + | 0.999866i | \(0.494783\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.49341 | + | 7.56104i | −0.221157 | + | 0.304396i | −0.905150 | − | 0.425092i | \(-0.860242\pi\) |
0.683994 | + | 0.729488i | \(0.260242\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.9480 | − | 10.8604i | −0.600813 | − | 0.436516i | 0.245354 | − | 0.969433i | \(-0.421096\pi\) |
−0.846167 | + | 0.532917i | \(0.821096\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.14185 | − | 3.73577i | 0.206335 | − | 0.149911i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 50.5191 | − | 16.4146i | 2.02400 | − | 0.657639i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.479118 | − | 0.155675i | 0.0191341 | − | 0.00621706i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −44.1774 | + | 32.0968i | −1.76147 | + | 1.27978i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.2030 | − | 22.6703i | −1.24217 | − | 0.902491i | −0.244431 | − | 0.969667i | \(-0.578601\pi\) |
−0.997741 | + | 0.0671762i | \(0.978601\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.61134 | − | 9.09973i | 0.262777 | − | 0.361682i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.0040 | + | 3.90032i | 0.475614 | + | 0.154536i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.10941 | − | 12.6474i | −0.162566 | − | 0.500325i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.96965 | + | 12.2173i | −0.156792 | + | 0.482556i | −0.998338 | − | 0.0576293i | \(-0.981646\pi\) |
0.841546 | + | 0.540185i | \(0.181646\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.1030i | 0.792784i | 0.918081 | + | 0.396392i | \(0.129738\pi\) | ||||
−0.918081 | + | 0.396392i | \(0.870262\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.0350 | + | 31.7050i | 0.905600 | + | 1.24645i | 0.968647 | + | 0.248441i | \(0.0799183\pi\) |
−0.0630466 | + | 0.998011i | \(0.520082\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.36194 | −0.0534609 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.2848 | 0.559865 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.2762 | − | 21.0259i | −0.597804 | − | 0.822806i | 0.397701 | − | 0.917515i | \(-0.369808\pi\) |
−0.995505 | + | 0.0947087i | \(0.969808\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.21152i | 0.203321i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.98499 | − | 6.10917i | 0.0773242 | − | 0.237980i | −0.904921 | − | 0.425579i | \(-0.860071\pi\) |
0.982246 | + | 0.187599i | \(0.0600706\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.67091 | + | 20.5310i | 0.259468 | + | 0.798562i | 0.992916 | + | 0.118816i | \(0.0379098\pi\) |
−0.733448 | + | 0.679746i | \(0.762090\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.35247 | + | 2.38896i | 0.285546 | + | 0.0927796i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.41443 | + | 12.9578i | −0.364528 | + | 0.501730i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.88314 | + | 4.27435i | 0.227455 | + | 0.165256i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.47055 | + | 1.06842i | −0.0567701 | + | 0.0412459i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.64965 | + | 1.83568i | −0.217778 | + | 0.0707604i | −0.415874 | − | 0.909422i | \(-0.636524\pi\) |
0.198096 | + | 0.980183i | \(0.436524\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.3587 | − | 11.4888i | 1.35895 | − | 0.441549i | 0.463256 | − | 0.886225i | \(-0.346681\pi\) |
0.895691 | + | 0.444676i | \(0.146681\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.6361 | + | 14.9930i | −0.791942 | + | 0.575380i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.66082 | + | 5.56591i | 0.293563 | + | 0.213286i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.5106 | + | 36.4886i | −1.01440 | + | 1.39620i | −0.0983404 | + | 0.995153i | \(0.531353\pi\) |
−0.916058 | + | 0.401046i | \(0.868647\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.1910 | + | 6.56045i | 0.770334 | + | 0.250297i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.89395 | + | 15.0620i | 0.186445 | + | 0.573818i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.82903 | + | 27.1730i | −0.335872 | + | 1.03371i | 0.630419 | + | 0.776255i | \(0.282883\pi\) |
−0.966291 | + | 0.257453i | \(0.917117\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 0.726676i | − | 0.0276041i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.4528 | − | 26.7745i | −0.736829 | − | 1.01416i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.08932 | 0.268143 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.2636 | −1.67181 | −0.835907 | − | 0.548871i | \(-0.815058\pi\) | ||||
−0.835907 | + | 0.548871i | \(0.815058\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.4165 | − | 25.3482i | −0.694593 | − | 0.956025i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 40.0602i | 1.50662i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.25711 | + | 16.1797i | −0.197435 | + | 0.607643i | 0.802505 | + | 0.596646i | \(0.203500\pi\) |
−0.999940 | + | 0.0109965i | \(0.996500\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.961563 | − | 2.95939i | −0.0360614 | − | 0.110986i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.6635 | + | 7.36381i | 0.848754 | + | 0.275777i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.7626 | + | 16.1898i | −0.439282 | + | 0.604619i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.71076 | + | 4.87565i | 0.250269 | + | 0.181831i | 0.705846 | − | 0.708365i | \(-0.250567\pi\) |
−0.455577 | + | 0.890196i | \(0.650567\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39.9614 | + | 29.0336i | −1.48824 | + | 1.08127i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.8048 | − | 6.43498i | 0.736549 | − | 0.239319i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.09791 | + | 2.30625i | −0.263247 | + | 0.0855342i | −0.437667 | − | 0.899137i | \(-0.644195\pi\) |
0.174420 | + | 0.984671i | \(0.444195\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.809017 | − | 0.587785i | 0.0299636 | − | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34.3593 | + | 24.9635i | 1.27082 | + | 0.923308i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.06525 | + | 9.72449i | −0.260961 | + | 0.359182i | −0.919312 | − | 0.393529i | \(-0.871254\pi\) |
0.658351 | + | 0.752711i | \(0.271254\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.09776 | − | 0.356684i | −0.0404365 | − | 0.0131386i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.82848 | − | 24.0936i | −0.287975 | − | 0.886297i | −0.985491 | − | 0.169728i | \(-0.945711\pi\) |
0.697516 | − | 0.716570i | \(-0.254289\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.37074 | + | 4.21871i | −0.0503555 | + | 0.154978i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 21.0959i | − | 0.773935i | −0.922093 | − | 0.386968i | \(-0.873523\pi\) | ||
0.922093 | − | 0.386968i | \(-0.126477\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.74988 | + | 3.78488i | 0.100613 | + | 0.138482i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −36.7507 | −1.34284 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.3897 | −1.25490 | −0.627449 | − | 0.778658i | \(-0.715901\pi\) | ||||
−0.627449 | + | 0.778658i | \(0.715901\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17.5008 | − | 24.0877i | −0.637764 | − | 0.877806i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 33.9762i | − | 1.23488i | −0.786616 | − | 0.617442i | \(-0.788169\pi\) | ||
0.786616 | − | 0.617442i | \(-0.211831\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.374601 | − | 1.15290i | 0.0135972 | − | 0.0418478i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.13686 | − | 12.7319i | −0.149961 | − | 0.461533i | 0.847654 | − | 0.530549i | \(-0.178014\pi\) |
−0.997616 | + | 0.0690159i | \(0.978014\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −74.0828 | − | 24.0710i | −2.68198 | − | 0.871427i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.04879 | − | 9.70183i | 0.254517 | − | 0.350313i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.80948 | − | 3.49429i | −0.173434 | − | 0.126007i | 0.497682 | − | 0.867360i | \(-0.334185\pi\) |
−0.671116 | + | 0.741352i | \(0.734185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.2201 | + | 12.5112i | −0.620168 | + | 0.450579i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.4278 | + | 10.5364i | −1.16635 | + | 0.378969i | −0.827278 | − | 0.561793i | \(-0.810112\pi\) |
−0.339068 | + | 0.940762i | \(0.610112\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −42.9834 | + | 13.9661i | −1.54202 | + | 0.501032i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.3628 | − | 11.1617i | 0.550428 | − | 0.399909i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.05201 | − | 1.49087i | −0.0734267 | − | 0.0533476i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.48126 | + | 2.03878i | −0.0529360 | + | 0.0728602i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.87644 | + | 0.609693i | 0.0668879 | + | 0.0217332i | 0.342270 | − | 0.939602i | \(-0.388804\pi\) |
−0.275382 | + | 0.961335i | \(0.588804\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.75674 | + | 20.7951i | 0.240546 | + | 0.740325i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.76132 | − | 14.6538i | 0.169293 | − | 0.521030i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 16.0052i | − | 0.568361i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.3698 | + | 23.9075i | 0.615269 | + | 0.846845i | 0.996998 | − | 0.0774291i | \(-0.0246711\pi\) |
−0.381729 | + | 0.924274i | \(0.624671\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.9378 | 0.740725 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.9423 | 0.492626 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.584264 | + | 0.804170i | 0.0206182 | + | 0.0283785i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 4.56132i | − | 0.160566i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.45516 | + | 7.55621i | −0.0863189 | + | 0.265662i | −0.984894 | − | 0.173157i | \(-0.944603\pi\) |
0.898575 | + | 0.438819i | \(0.144603\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.71747 | + | 17.5966i | 0.200768 | + | 0.617899i | 0.999861 | + | 0.0166920i | \(0.00531347\pi\) |
−0.799093 | + | 0.601207i | \(0.794687\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.2870 | + | 3.99228i | 0.430923 | + | 0.140015i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.3236 | + | 19.7147i | −0.501119 | + | 0.689731i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.17650 | + | 3.76094i | 0.180881 | + | 0.131418i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.4784 | − | 9.06610i | 0.435500 | − | 0.316409i | −0.348345 | − | 0.937367i | \(-0.613256\pi\) |
0.783844 | + | 0.620958i | \(0.213256\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.5494 | + | 12.8504i | −1.37860 | + | 0.447936i | −0.902210 | − | 0.431296i | \(-0.858056\pi\) |
−0.476394 | + | 0.879232i | \(0.658056\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.1783 | − | 10.7803i | 1.15372 | − | 0.374867i | 0.331177 | − | 0.943569i | \(-0.392554\pi\) |
0.822544 | + | 0.568702i | \(0.192554\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.7079 | − | 27.3964i | 1.30965 | − | 0.951516i | 0.309649 | − | 0.950851i | \(-0.399788\pi\) |
1.00000 | 0.000664954i | \(-0.000211661\pi\) | ||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.14783 | + | 5.19320i | 0.247956 | + | 0.180150i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.3347 | − | 27.9883i | 0.704555 | − | 0.969737i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.56587 | + | 1.15862i | 0.123254 | + | 0.0400478i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.1009 | − | 40.3203i | −0.452292 | − | 1.39201i | −0.874285 | − | 0.485414i | \(-0.838669\pi\) |
0.421992 | − | 0.906599i | \(-0.361331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.99899 | + | 21.5407i | −0.241345 | + | 0.742782i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 0.0305495i | − | 0.00105218i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.5521 | + | 33.7930i | 0.843619 | + | 1.16114i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.80719 | −0.164982 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −75.3946 | −2.58449 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.20116 | − | 3.02964i | −0.0753663 | − | 0.103733i | 0.769670 | − | 0.638442i | \(-0.220421\pi\) |
−0.845036 | + | 0.534710i | \(0.820421\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.9648i | 1.36517i | 0.730806 | + | 0.682586i | \(0.239145\pi\) | ||||
−0.730806 | + | 0.682586i | \(0.760855\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.3383 | − | 53.3617i | 0.591574 | − | 1.82068i | 0.0204824 | − | 0.999790i | \(-0.493480\pi\) |
0.571091 | − | 0.820887i | \(-0.306520\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.46444 | − | 26.0509i | −0.288467 | − | 0.887811i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.6827 | − | 5.74547i | −0.601927 | − | 0.195578i | −0.00782756 | − | 0.999969i | \(-0.502492\pi\) |
−0.594100 | + | 0.804391i | \(0.702492\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.46273 | − | 3.38965i | 0.0836386 | − | 0.115119i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.480152 | − | 0.348851i | −0.0162880 | − | 0.0118339i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.22236 | − | 5.97389i | 0.278604 | − | 0.202418i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.36739 | + | 2.06889i | −0.215504 | + | 0.0700214i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.3467 | + | 3.36186i | −0.349385 | + | 0.113522i | −0.478452 | − | 0.878114i | \(-0.658802\pi\) |
0.129067 | + | 0.991636i | \(0.458802\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.1114 | + | 8.79945i | −0.408508 | + | 0.296798i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.5016 | − | 19.9811i | −0.926552 | − | 0.673180i | 0.0185939 | − | 0.999827i | \(-0.494081\pi\) |
−0.945146 | + | 0.326647i | \(0.894081\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.96658 | + | 12.3414i | −0.301749 | + | 0.415322i | −0.932786 | − | 0.360431i | \(-0.882630\pi\) |
0.631037 | + | 0.775753i | \(0.282630\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.1095 | − | 8.80840i | −0.910247 | − | 0.295757i | −0.183787 | − | 0.982966i | \(-0.558836\pi\) |
−0.726460 | + | 0.687209i | \(0.758836\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.7247 | − | 60.7063i | −0.661544 | − | 2.03602i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.0589397 | − | 0.181398i | 0.00197455 | − | 0.00607705i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.0137i | 0.402024i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.27398 | + | 8.63540i | 0.209482 | + | 0.288327i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.44871 | −0.315132 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.4089 | 1.44616 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.6612 | + | 28.4378i | 0.687563 | + | 0.946350i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 22.1919i | − | 0.736868i | −0.929654 | − | 0.368434i | \(-0.879894\pi\) | ||
0.929654 | − | 0.368434i | \(-0.120106\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.24923 | + | 10.0001i | −0.107770 | + | 0.331682i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.5476 | + | 38.6174i | 0.415719 | + | 1.27945i | 0.911606 | + | 0.411064i | \(0.134843\pi\) |
−0.495887 | + | 0.868387i | \(0.665157\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.848645 | + | 0.275742i | 0.0280861 | + | 0.00912572i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.40686 | + | 10.1947i | −0.244596 | + | 0.336658i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.1543 | + | 7.37751i | 0.334958 | + | 0.243361i | 0.742532 | − | 0.669811i | \(-0.233625\pi\) |
−0.407573 | + | 0.913173i | \(0.633625\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.62134 | + | 2.63106i | −0.119327 | + | 0.0866963i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.2406 | − | 6.90148i | 0.699141 | − | 0.227165i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.3303 | + | 4.00636i | −0.404980 | + | 0.131586i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.6390 | + | 33.1587i | −1.49737 | + | 1.08790i | −0.525953 | + | 0.850513i | \(0.676291\pi\) |
−0.971415 | + | 0.237388i | \(0.923709\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.0592 | + | 11.6677i | 0.526319 | + | 0.382393i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.174051 | + | 0.239561i | −0.00569819 | + | 0.00784288i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.0630 | − | 13.0173i | −1.30880 | − | 0.425255i | −0.430166 | − | 0.902750i | \(-0.641545\pi\) |
−0.878635 | + | 0.477494i | \(0.841545\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.53785 | + | 20.1214i | 0.213355 | + | 0.656638i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.51260 | + | 29.2768i | −0.310102 | + | 0.954395i | 0.667622 | + | 0.744500i | \(0.267312\pi\) |
−0.977724 | + | 0.209895i | \(0.932688\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 45.6943i | − | 1.48801i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.435973 | − | 0.600065i | −0.0141672 | − | 0.0194995i | 0.801875 | − | 0.597492i | \(-0.203836\pi\) |
−0.816042 | + | 0.577993i | \(0.803836\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.75241 | −0.284115 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.9166 | 0.840405 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.1037 | + | 31.7995i | 0.748401 | + | 1.03009i | 0.998091 | + | 0.0617601i | \(0.0196714\pi\) |
−0.249690 | + | 0.968326i | \(0.580329\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.480661i | 0.0155376i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.47140 | + | 7.60620i | −0.0798058 | + | 0.245617i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.23543 | − | 16.1130i | −0.168885 | − | 0.519774i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.17395 | − | 2.98080i | −0.295626 | − | 0.0960548i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.6718 | − | 39.4633i | 0.922022 | − | 1.26905i | −0.0408691 | − | 0.999165i | \(-0.513013\pi\) |
0.962891 | − | 0.269890i | \(-0.0869873\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.83631 | + | 7.14650i | 0.315988 | + | 0.229579i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.5659 | − | 36.0118i | 1.59065 | − | 1.15567i | 0.687635 | − | 0.726056i | \(-0.258649\pi\) |
0.903011 | − | 0.429616i | \(-0.141351\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −48.1370 | + | 15.6407i | −1.54320 | + | 0.501417i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.6181 | + | 3.45004i | −0.339704 | + | 0.110377i | −0.473901 | − | 0.880578i | \(-0.657155\pi\) |
0.134197 | + | 0.990955i | \(0.457155\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.15138 | − | 1.56307i | 0.0687583 | − | 0.0499559i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.5407 | − | 12.0175i | −0.528103 | − | 0.383690i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.2257 | − | 25.0855i | 0.581310 | − | 0.800104i | −0.412528 | − | 0.910945i | \(-0.635354\pi\) |
0.993838 | + | 0.110840i | \(0.0353543\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.4812 | + | 5.35506i | 0.524602 | + | 0.170453i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.1203 | + | 55.7687i | 0.576194 | + | 1.77334i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.13378 | − | 28.1109i | 0.290144 | − | 0.892972i | −0.694665 | − | 0.719333i | \(-0.744447\pi\) |
0.984809 | − | 0.173639i | \(-0.0555526\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.07039i | 0.0974358i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.7701 | + | 43.7278i | 1.00617 | + | 1.38487i | 0.921462 | + | 0.388469i | \(0.126996\pi\) |
0.0847083 | + | 0.996406i | \(0.473004\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.8626 | −0.375315 |
(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 | 1500.2.o.c.349.4 | 24 | ||
5.2 | odd | 4 | 1500.2.m.d.901.2 | 24 | |||
5.3 | odd | 4 | 1500.2.m.c.901.5 | 24 | |||
5.4 | even | 2 | 300.2.o.a.169.3 | ✓ | 24 | ||
15.14 | odd | 2 | 900.2.w.c.469.1 | 24 | |||
25.2 | odd | 20 | 7500.2.a.m.1.3 | 12 | |||
25.3 | odd | 20 | 1500.2.m.c.601.5 | 24 | |||
25.4 | even | 10 | inner | 1500.2.o.c.649.4 | 24 | ||
25.11 | even | 5 | 7500.2.d.g.1249.10 | 24 | |||
25.14 | even | 10 | 7500.2.d.g.1249.15 | 24 | |||
25.21 | even | 5 | 300.2.o.a.229.3 | yes | 24 | ||
25.22 | odd | 20 | 1500.2.m.d.601.2 | 24 | |||
25.23 | odd | 20 | 7500.2.a.n.1.10 | 12 | |||
75.71 | odd | 10 | 900.2.w.c.829.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.169.3 | ✓ | 24 | 5.4 | even | 2 | ||
300.2.o.a.229.3 | yes | 24 | 25.21 | even | 5 | ||
900.2.w.c.469.1 | 24 | 15.14 | odd | 2 | |||
900.2.w.c.829.1 | 24 | 75.71 | odd | 10 | |||
1500.2.m.c.601.5 | 24 | 25.3 | odd | 20 | |||
1500.2.m.c.901.5 | 24 | 5.3 | odd | 4 | |||
1500.2.m.d.601.2 | 24 | 25.22 | odd | 20 | |||
1500.2.m.d.901.2 | 24 | 5.2 | odd | 4 | |||
1500.2.o.c.349.4 | 24 | 1.1 | even | 1 | trivial | ||
1500.2.o.c.649.4 | 24 | 25.4 | even | 10 | inner | ||
7500.2.a.m.1.3 | 12 | 25.2 | odd | 20 | |||
7500.2.a.n.1.10 | 12 | 25.23 | odd | 20 | |||
7500.2.d.g.1249.10 | 24 | 25.11 | even | 5 | |||
7500.2.d.g.1249.15 | 24 | 25.14 | even | 10 |