Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1500,2,Mod(301,1500)]
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, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1500.301");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1500.m (of order \(5\), 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 \(\Q(\zeta_{5})\) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 1201.1 | ||
Character | \(\chi\) | \(=\) | 1500.1201 |
Dual form | 1500.2.m.c.301.1 |
$q$-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 \(\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times\).
\(n\) | \(751\) | \(877\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.309017 | + | 0.951057i | 0.178411 | + | 0.549093i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.54704 | −1.34066 | −0.670328 | − | 0.742065i | \(-0.733846\pi\) | ||||
−0.670328 | + | 0.742065i | \(0.733846\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.78482 | + | 1.29675i | 0.538145 | + | 0.390985i | 0.823396 | − | 0.567468i | \(-0.192077\pi\) |
−0.285251 | + | 0.958453i | \(0.592077\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.80689 | − | 4.21895i | 1.61054 | − | 1.17013i | 0.748773 | − | 0.662827i | \(-0.230643\pi\) |
0.861769 | − | 0.507301i | \(-0.169357\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.96699 | − | 6.05378i | 0.477066 | − | 1.46826i | −0.366086 | − | 0.930581i | \(-0.619302\pi\) |
0.843151 | − | 0.537676i | \(-0.180698\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.715151 | + | 2.20101i | −0.164067 | + | 0.504946i | −0.998966 | − | 0.0454566i | \(-0.985526\pi\) |
0.834899 | + | 0.550402i | \(0.185526\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.09610 | − | 3.37344i | −0.239188 | − | 0.736144i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.76038 | − | 1.27899i | −0.367064 | − | 0.266687i | 0.388929 | − | 0.921268i | \(-0.372845\pi\) |
−0.755992 | + | 0.654580i | \(0.772845\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.809017 | − | 0.587785i | −0.155695 | − | 0.113119i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.262008 | + | 0.806379i | 0.0486538 | + | 0.149741i | 0.972432 | − | 0.233188i | \(-0.0749156\pi\) |
−0.923778 | + | 0.382928i | \(0.874916\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.32905 | + | 4.09040i | −0.238705 | + | 0.734657i | 0.757904 | + | 0.652367i | \(0.226224\pi\) |
−0.996608 | + | 0.0822910i | \(0.973776\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.681742 | + | 2.09819i | −0.118676 | + | 0.365248i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.84918 | − | 4.24968i | 0.961599 | − | 0.698643i | 0.00807756 | − | 0.999967i | \(-0.497429\pi\) |
0.953522 | + | 0.301325i | \(0.0974288\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.80689 | + | 4.21895i | 0.929847 | + | 0.675573i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.08778 | − | 0.790317i | 0.169882 | − | 0.123427i | −0.499595 | − | 0.866259i | \(-0.666518\pi\) |
0.669478 | + | 0.742832i | \(0.266518\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.18973 | 1.24892 | 0.624461 | − | 0.781056i | \(-0.285319\pi\) | ||||
0.624461 | + | 0.781056i | \(0.285319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.87095 | + | 5.75820i | 0.272907 | + | 0.839920i | 0.989766 | + | 0.142702i | \(0.0455790\pi\) |
−0.716859 | + | 0.697218i | \(0.754421\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.58150 | 0.797357 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.36532 | 0.891323 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.69530 | + | 11.3730i | 0.507589 | + | 1.56220i | 0.796374 | + | 0.604805i | \(0.206749\pi\) |
−0.288785 | + | 0.957394i | \(0.593251\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.31428 | −0.306533 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.0896 | − | 7.33050i | 1.31355 | − | 0.954350i | 0.313561 | − | 0.949568i | \(-0.398478\pi\) |
0.999989 | − | 0.00478202i | \(-0.00152217\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.59873 | + | 4.06772i | 0.716844 | + | 0.520818i | 0.885374 | − | 0.464879i | \(-0.153902\pi\) |
−0.168530 | + | 0.985696i | \(0.553902\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.86962 | − | 2.08490i | 0.361538 | − | 0.262672i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.46291 | − | 4.50239i | 0.178723 | − | 0.550054i | −0.821060 | − | 0.570841i | \(-0.806617\pi\) |
0.999784 | + | 0.0207870i | \(0.00661719\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.672404 | − | 2.06945i | 0.0809479 | − | 0.249132i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.25799 | + | 13.1047i | 0.505330 | + | 1.55525i | 0.800214 | + | 0.599714i | \(0.204719\pi\) |
−0.294884 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.881155 | − | 0.640196i | −0.103131 | − | 0.0749293i | 0.535024 | − | 0.844837i | \(-0.320302\pi\) |
−0.638156 | + | 0.769907i | \(0.720302\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.33085 | − | 4.59963i | −0.721467 | − | 0.524176i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.80542 | − | 5.55650i | −0.203125 | − | 0.625156i | −0.999785 | − | 0.0207276i | \(-0.993402\pi\) |
0.796660 | − | 0.604428i | \(-0.206598\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.87127 | − | 11.9145i | 0.424927 | − | 1.30779i | −0.478137 | − | 0.878285i | \(-0.658688\pi\) |
0.903064 | − | 0.429505i | \(-0.141312\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.685947 | + | 0.498370i | −0.0735412 | + | 0.0534308i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.68424 | + | 4.12984i | 0.602528 | + | 0.437762i | 0.846775 | − | 0.531951i | \(-0.178541\pi\) |
−0.244247 | + | 0.969713i | \(0.578541\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −20.5973 | + | 14.9648i | −2.15918 | + | 1.56874i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.30090 | −0.445983 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.60695 | − | 17.2564i | −0.569299 | − | 1.75212i | −0.654818 | − | 0.755787i | \(-0.727255\pi\) |
0.0855183 | − | 0.996337i | \(-0.472745\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.20616 | −0.221728 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.97473 | 0.594508 | 0.297254 | − | 0.954798i | \(-0.403929\pi\) | ||||
0.297254 | + | 0.954798i | \(0.403929\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.142014 | − | 0.437076i | −0.0139931 | − | 0.0430663i | 0.943816 | − | 0.330471i | \(-0.107208\pi\) |
−0.957809 | + | 0.287405i | \(0.907208\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.47862 | 0.239617 | 0.119809 | − | 0.992797i | \(-0.461772\pi\) | ||||
0.119809 | + | 0.992797i | \(0.461772\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.70314 | − | 1.96394i | 0.258914 | − | 0.188112i | −0.450754 | − | 0.892648i | \(-0.648845\pi\) |
0.709668 | + | 0.704536i | \(0.248845\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.84918 | + | 4.24968i | 0.555180 | + | 0.403362i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.2370 | + | 10.3438i | −1.33930 | + | 0.973059i | −0.339832 | + | 0.940486i | \(0.610370\pi\) |
−0.999469 | + | 0.0325728i | \(0.989630\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.21804 | + | 6.82641i | −0.205057 | + | 0.631102i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.97700 | + | 21.4730i | −0.639581 | + | 1.96843i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.89515 | − | 5.83267i | −0.172286 | − | 0.530243i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.08778 | + | 0.790317i | 0.0980816 | + | 0.0712605i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0415 | − | 7.29555i | −0.891036 | − | 0.647376i | 0.0451118 | − | 0.998982i | \(-0.485636\pi\) |
−0.936148 | + | 0.351606i | \(0.885636\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.53077 | + | 7.78890i | 0.222822 | + | 0.685774i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.88963 | − | 15.0487i | 0.427209 | − | 1.31481i | −0.473654 | − | 0.880711i | \(-0.657065\pi\) |
0.900863 | − | 0.434104i | \(-0.142935\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.53667 | − | 7.80706i | 0.219957 | − | 0.676958i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.98262 | + | 4.34663i | −0.511130 | + | 0.371358i | −0.813252 | − | 0.581912i | \(-0.802305\pi\) |
0.302122 | + | 0.953269i | \(0.402305\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.18667 | − | 2.31525i | −0.270290 | − | 0.196377i | 0.444381 | − | 0.895838i | \(-0.353424\pi\) |
−0.714671 | + | 0.699461i | \(0.753424\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.89822 | + | 3.55876i | −0.412504 | + | 0.299702i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.8352 | 1.32421 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.72478 | + | 5.30832i | 0.142257 | + | 0.437823i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.92892 | 0.321870 | 0.160935 | − | 0.986965i | \(-0.448549\pi\) | ||||
0.160935 | + | 0.986965i | \(0.448549\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.93418 | 0.645674 | 0.322837 | − | 0.946455i | \(-0.395363\pi\) | ||||
0.322837 | + | 0.946455i | \(0.395363\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.96699 | + | 6.05378i | 0.159022 | + | 0.489419i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.09738 | −0.486624 | −0.243312 | − | 0.969948i | \(-0.578234\pi\) | ||||
−0.243312 | + | 0.969948i | \(0.578234\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.67443 | + | 7.02889i | −0.767232 | + | 0.557427i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.24413 | + | 4.53662i | 0.492106 | + | 0.357536i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.00206811 | − | 0.00150257i | 0.000161987 | − | 0.000117690i | −0.587704 | − | 0.809076i | \(-0.699968\pi\) |
0.587866 | + | 0.808958i | \(0.299968\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.12128 | + | 9.60630i | −0.241532 | + | 0.743358i | 0.754656 | + | 0.656121i | \(0.227804\pi\) |
−0.996188 | + | 0.0872372i | \(0.972196\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.9032 | − | 36.6343i | 0.915631 | − | 2.81802i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.715151 | − | 2.20101i | −0.0546889 | − | 0.168315i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.99963 | + | 3.63244i | 0.380115 | + | 0.276169i | 0.761393 | − | 0.648291i | \(-0.224516\pi\) |
−0.381278 | + | 0.924460i | \(0.624516\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.0896 | + | 7.33050i | 0.758378 | + | 0.550994i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.45991 | + | 13.7262i | 0.333349 | + | 1.02594i | 0.967530 | + | 0.252758i | \(0.0813376\pi\) |
−0.634181 | + | 0.773185i | \(0.718662\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.08366 | − | 6.41283i | 0.154877 | − | 0.476662i | −0.843272 | − | 0.537488i | \(-0.819373\pi\) |
0.998148 | + | 0.0608258i | \(0.0193734\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.13853 | + | 6.58170i | −0.158084 | + | 0.486534i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.3610 | − | 8.25424i | 0.830798 | − | 0.603610i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.86962 | + | 2.08490i | 0.208734 | + | 0.151654i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.4512 | + | 9.04634i | −0.900938 | + | 0.654570i | −0.938707 | − | 0.344717i | \(-0.887975\pi\) |
0.0377687 | + | 0.999287i | \(0.487975\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.3875 | 1.17960 | 0.589799 | − | 0.807550i | \(-0.299207\pi\) | ||||
0.589799 | + | 0.807550i | \(0.299207\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.04392 | + | 9.36824i | 0.216871 | + | 0.667459i | 0.999015 | + | 0.0443625i | \(0.0141257\pi\) |
−0.782145 | + | 0.623097i | \(0.785874\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.96275 | −0.351800 | −0.175900 | − | 0.984408i | \(-0.556284\pi\) | ||||
−0.175900 | + | 0.984408i | \(0.556284\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.73409 | 0.333917 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.929355 | − | 2.86026i | −0.0652279 | − | 0.200751i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.17594 | 0.151239 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.13058 | + | 3.00104i | −0.285718 | + | 0.207586i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.83140 | − | 2.05713i | −0.194921 | − | 0.141619i | 0.486044 | − | 0.873934i | \(-0.338440\pi\) |
−0.680965 | + | 0.732316i | \(0.738440\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.1476 | + | 8.09918i | −0.763818 | + | 0.554947i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.71420 | − | 14.5088i | 0.320021 | − | 0.984923i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.336571 | − | 1.03586i | 0.0227434 | − | 0.0699969i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.1185 | − | 43.4523i | −0.949714 | − | 2.92292i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.6710 | − | 13.5653i | −1.25030 | − | 0.908397i | −0.252062 | − | 0.967711i | \(-0.581109\pi\) |
−0.998239 | + | 0.0593138i | \(0.981109\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.73323 | + | 3.43889i | 0.314155 | + | 0.228247i | 0.733677 | − | 0.679498i | \(-0.237802\pi\) |
−0.419522 | + | 0.907745i | \(0.637802\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.97484 | − | 6.07793i | −0.130501 | − | 0.401641i | 0.864362 | − | 0.502870i | \(-0.167723\pi\) |
−0.994863 | + | 0.101229i | \(0.967723\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.41817 | − | 7.44236i | 0.159104 | − | 0.489671i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.40390 | − | 4.32076i | 0.0919725 | − | 0.283062i | −0.894480 | − | 0.447107i | \(-0.852454\pi\) |
0.986453 | + | 0.164045i | \(0.0524543\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.72664 | − | 3.43411i | 0.307029 | − | 0.223069i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.6407 | − | 13.5432i | −1.20576 | − | 0.876040i | −0.210926 | − | 0.977502i | \(-0.567648\pi\) |
−0.994839 | + | 0.101463i | \(0.967648\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.3064 | + | 9.66766i | −0.857140 | + | 0.622749i | −0.927105 | − | 0.374801i | \(-0.877711\pi\) |
0.0699655 | + | 0.997549i | \(0.477711\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.13315 | + | 15.7982i | 0.326614 | + | 1.00522i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.5277 | 0.793910 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.66327 | 0.294343 | 0.147171 | − | 0.989111i | \(-0.452983\pi\) | ||||
0.147171 | + | 0.989111i | \(0.452983\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.48343 | − | 4.56554i | −0.0932627 | − | 0.287033i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.78734 | −0.361004 | −0.180502 | − | 0.983575i | \(-0.557772\pi\) | ||||
−0.180502 | + | 0.983575i | \(0.557772\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.7473 | + | 15.0738i | −1.28917 | + | 0.936639i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.685947 | − | 0.498370i | −0.0424591 | − | 0.0308483i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.5668 | + | 13.4896i | −1.14488 | + | 0.831803i | −0.987792 | − | 0.155781i | \(-0.950210\pi\) |
−0.157087 | + | 0.987585i | \(0.550210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.17119 | + | 6.68222i | −0.132874 | + | 0.408945i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.39366 | + | 4.28923i | −0.0849727 | + | 0.261519i | −0.984511 | − | 0.175323i | \(-0.943903\pi\) |
0.899538 | + | 0.436842i | \(0.143903\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.06895 | − | 9.44525i | −0.186425 | − | 0.573758i | 0.813545 | − | 0.581502i | \(-0.197535\pi\) |
−0.999970 | + | 0.00774433i | \(0.997535\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −20.5973 | − | 14.9648i | −1.24660 | − | 0.905711i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.6197 | + | 13.5280i | 1.11875 | + | 0.812821i | 0.984019 | − | 0.178061i | \(-0.0569825\pi\) |
0.134732 | + | 0.990882i | \(0.456983\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.32905 | − | 4.09040i | −0.0795682 | − | 0.244886i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.226820 | − | 0.698080i | 0.0135309 | − | 0.0416439i | −0.944063 | − | 0.329765i | \(-0.893031\pi\) |
0.957594 | + | 0.288121i | \(0.0930305\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.64144 | − | 20.4402i | 0.394793 | − | 1.21505i | −0.534330 | − | 0.845276i | \(-0.679436\pi\) |
0.929123 | − | 0.369771i | \(-0.120564\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.85839 | + | 2.80329i | −0.227754 | + | 0.165473i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −19.0259 | − | 13.8231i | −1.11917 | − | 0.813126i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.6792 | − | 10.6651i | 0.860509 | − | 0.625196i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.5961 | −1.55376 | −0.776880 | − | 0.629649i | \(-0.783199\pi\) | ||||
−0.776880 | + | 0.629649i | \(0.783199\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.681742 | − | 2.09819i | −0.0395587 | − | 0.121749i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.6183 | −0.903230 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −29.0493 | −1.67437 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.84629 | + | 5.68231i | 0.106067 | + | 0.326440i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.1736 | 0.694785 | 0.347393 | − | 0.937720i | \(-0.387067\pi\) | ||||
0.347393 | + | 0.937720i | \(0.387067\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.371799 | − | 0.270128i | 0.0211509 | − | 0.0153670i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.0330 | + | 14.5548i | 1.13597 | + | 0.825327i | 0.986552 | − | 0.163447i | \(-0.0522614\pi\) |
0.149414 | + | 0.988775i | \(0.452261\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.0102 | + | 8.72589i | −0.678854 | + | 0.493216i | −0.872977 | − | 0.487761i | \(-0.837814\pi\) |
0.194123 | + | 0.980977i | \(0.437814\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.600207 | − | 1.84725i | 0.0337110 | − | 0.103752i | −0.932785 | − | 0.360433i | \(-0.882629\pi\) |
0.966496 | + | 0.256681i | \(0.0826290\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.578034 | + | 1.77901i | −0.0323637 | + | 0.0996052i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.765935 | + | 2.35731i | 0.0427503 | + | 0.131572i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.9177 | + | 8.65873i | 0.663120 | + | 0.481785i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.70314 | + | 1.96394i | 0.149484 | + | 0.108606i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.63635 | − | 20.4246i | −0.365874 | − | 1.12604i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.56924 | + | 26.3734i | −0.471008 | + | 1.44961i | 0.380258 | + | 0.924880i | \(0.375835\pi\) |
−0.851266 | + | 0.524734i | \(0.824165\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.23419 | + | 6.87612i | −0.122433 | + | 0.376809i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.81048 | + | 6.40119i | −0.479937 | + | 0.348695i | −0.801301 | − | 0.598261i | \(-0.795859\pi\) |
0.321364 | + | 0.946956i | \(0.395859\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.2370 | − | 10.3438i | −0.773246 | − | 0.561796i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.67636 | + | 5.57720i | −0.415698 | + | 0.302022i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.03148 | 0.271675 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.06224 | + | 21.7353i | 0.379121 | + | 1.16681i | 0.940656 | + | 0.339361i | \(0.110211\pi\) |
−0.561536 | + | 0.827453i | \(0.689789\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.8539 | −1.54451 | −0.772256 | − | 0.635311i | \(-0.780872\pi\) | ||||
−0.772256 | + | 0.635311i | \(0.780872\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.17771 | −0.383118 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.41799 | − | 25.9079i | −0.448045 | − | 1.37894i | −0.879110 | − | 0.476619i | \(-0.841862\pi\) |
0.431065 | − | 0.902321i | \(-0.358138\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −22.5781 | −1.19496 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.3648 | − | 14.0694i | 1.02204 | − | 0.742553i | 0.0553373 | − | 0.998468i | \(-0.482377\pi\) |
0.966699 | + | 0.255915i | \(0.0823766\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0383 | + | 8.01981i | 0.580965 | + | 0.422096i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.96157 | − | 3.60479i | 0.260415 | − | 0.189202i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.07450 | + | 6.38465i | −0.108288 | + | 0.333276i | −0.990488 | − | 0.137599i | \(-0.956062\pi\) |
0.882200 | + | 0.470875i | \(0.156062\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.415494 | + | 1.27876i | −0.0216298 | + | 0.0665696i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.1074 | − | 40.3404i | −0.680502 | − | 2.09437i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0100 | − | 7.99923i | −0.570076 | − | 0.414184i | 0.265057 | − | 0.964233i | \(-0.414609\pi\) |
−0.835133 | + | 0.550048i | \(0.814609\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.92353 | + | 3.57715i | 0.253575 | + | 0.184233i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.137272 | + | 0.422481i | 0.00705120 | + | 0.0217014i | 0.954520 | − | 0.298146i | \(-0.0963683\pi\) |
−0.947469 | + | 0.319848i | \(0.896368\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.83550 | − | 11.8045i | 0.196499 | − | 0.604760i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.16140 | − | 9.72980i | 0.161540 | − | 0.497170i | −0.837224 | − | 0.546859i | \(-0.815823\pi\) |
0.998765 | + | 0.0496897i | \(0.0158232\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.62563 | + | 4.81380i | −0.336800 | + | 0.244699i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.5834 | + | 14.2282i | 0.992919 | + | 0.721398i | 0.960558 | − | 0.278078i | \(-0.0896975\pi\) |
0.0323607 | + | 0.999476i | \(0.489697\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.2054 | + | 8.14117i | −0.566679 | + | 0.411717i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.8232 | 0.798174 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.841124 | + | 2.58871i | 0.0422148 | + | 0.129924i | 0.969943 | − | 0.243333i | \(-0.0782409\pi\) |
−0.927728 | + | 0.373257i | \(0.878241\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.20883 | 0.410956 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.3538 | 1.56573 | 0.782867 | − | 0.622189i | \(-0.213756\pi\) | ||||
0.782867 | + | 0.622189i | \(0.213756\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.53955 | + | 29.3597i | 0.475199 | + | 1.46251i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.9505 | 0.790639 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.68805 | + | 1.95298i | −0.132916 | + | 0.0965688i | −0.652256 | − | 0.757998i | \(-0.726177\pi\) |
0.519341 | + | 0.854567i | \(0.326177\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.98262 | − | 4.34663i | −0.295101 | − | 0.214404i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −35.7881 | + | 26.0016i | −1.76102 | + | 1.27945i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.21720 | − | 3.74615i | 0.0596065 | − | 0.183450i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.41347 | + | 10.5056i | −0.166759 | + | 0.513231i | −0.999162 | − | 0.0409399i | \(-0.986965\pi\) |
0.832403 | + | 0.554171i | \(0.186965\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.56044 | − | 23.2686i | −0.368473 | − | 1.13404i | −0.947777 | − | 0.318932i | \(-0.896676\pi\) |
0.579304 | − | 0.815111i | \(-0.303324\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.89822 | − | 3.55876i | −0.238160 | − | 0.173033i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.8589 | − | 14.4284i | −0.961041 | − | 0.698237i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.89335 | + | 15.0602i | 0.236253 | + | 0.727113i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.354621 | − | 1.09141i | 0.0170815 | − | 0.0525715i | −0.942152 | − | 0.335185i | \(-0.891201\pi\) |
0.959234 | + | 0.282613i | \(0.0912013\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.80916 | − | 5.56802i | 0.0869427 | − | 0.267582i | −0.898128 | − | 0.439735i | \(-0.855072\pi\) |
0.985070 | + | 0.172153i | \(0.0550723\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.07400 | − | 2.95993i | 0.194886 | − | 0.141593i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.4473 | + | 11.9497i | 0.784988 | + | 0.570328i | 0.906472 | − | 0.422266i | \(-0.138765\pi\) |
−0.121484 | + | 0.992593i | \(0.538765\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.51553 | + | 3.28072i | −0.215025 | + | 0.156225i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.5912 | −0.835783 | −0.417891 | − | 0.908497i | \(-0.637231\pi\) | ||||
−0.417891 | + | 0.908497i | \(0.637231\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.21410 | + | 3.73662i | 0.0574251 | + | 0.176736i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.83956 | −0.134007 | −0.0670037 | − | 0.997753i | \(-0.521344\pi\) | ||||
−0.0670037 | + | 0.997753i | \(0.521344\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.96634 | 0.139679 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.45180 | + | 7.54585i | 0.115195 | + | 0.354535i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.12004 | 0.379840 | 0.189920 | − | 0.981800i | \(-0.439177\pi\) | ||||
0.189920 | + | 0.981800i | \(0.439177\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.14965 | + | 3.74144i | −0.240365 | + | 0.174636i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.5629 | − | 10.5806i | −0.678261 | − | 0.492786i | 0.194519 | − | 0.980899i | \(-0.437685\pi\) |
−0.872780 | + | 0.488113i | \(0.837685\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.1960 | − | 16.8529i | 1.07801 | − | 0.783219i | 0.100674 | − | 0.994919i | \(-0.467900\pi\) |
0.977335 | + | 0.211700i | \(0.0679001\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.19421 | + | 19.0638i | −0.286634 | + | 0.882169i | 0.699270 | + | 0.714858i | \(0.253509\pi\) |
−0.985904 | + | 0.167311i | \(0.946491\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.18902 | + | 15.9702i | −0.239607 | + | 0.737433i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.88419 | − | 5.79896i | −0.0868191 | − | 0.267202i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.6172 | + | 10.6200i | 0.672101 | + | 0.488310i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.67443 | − | 7.02889i | −0.442962 | − | 0.321831i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.78232 | − | 14.7185i | −0.218510 | − | 0.672505i | −0.998886 | − | 0.0471937i | \(-0.984972\pi\) |
0.780376 | − | 0.625311i | \(-0.215028\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0364 | − | 49.3548i | 0.731195 | − | 2.25039i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.38504 | + | 7.34041i | −0.108523 | + | 0.334000i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.3110 | + | 22.0222i | −1.37352 | + | 0.997923i | −0.376070 | + | 0.926591i | \(0.622725\pi\) |
−0.997453 | + | 0.0713312i | \(0.977275\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.00206811 | + | 0.00150257i | 9.35232e−5 | + | 6.79486e-5i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.3517 | + | 23.5049i | −1.46001 | + | 1.06076i | −0.476651 | + | 0.879093i | \(0.658149\pi\) |
−0.983360 | + | 0.181667i | \(0.941851\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.39701 | 0.243069 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.1033 | − | 46.4831i | −0.677474 | − | 2.08505i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.3040 | 1.26706 | 0.633530 | − | 0.773718i | \(-0.281605\pi\) | ||||
0.633530 | + | 0.773718i | \(0.281605\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.1007 | −0.451264 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.0998 | + | 31.0839i | 0.450327 | + | 1.38596i | 0.876535 | + | 0.481338i | \(0.159849\pi\) |
−0.426208 | + | 0.904625i | \(0.640151\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 38.5196 | 1.71071 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.8620 | + | 10.0713i | −0.614422 | + | 0.446404i | −0.850969 | − | 0.525217i | \(-0.823984\pi\) |
0.236547 | + | 0.971620i | \(0.423984\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.12549 | + | 2.27080i | 0.138264 | + | 0.100454i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.87229 | − | 1.36030i | 0.0826636 | − | 0.0600586i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.12763 | + | 12.7035i | −0.181533 | + | 0.558701i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.90969 | + | 5.87741i | −0.0838260 | + | 0.257990i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.22259 | + | 19.1512i | 0.272617 | + | 0.839028i | 0.989840 | + | 0.142185i | \(0.0454128\pi\) |
−0.717223 | + | 0.696843i | \(0.754587\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.5777 | − | 16.4036i | −0.987253 | − | 0.717281i | −0.0279349 | − | 0.999610i | \(-0.508893\pi\) |
−0.959318 | + | 0.282329i | \(0.908893\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.1482 | + | 16.0916i | 0.964789 | + | 0.700960i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.64428 | − | 17.3713i | −0.245403 | − | 0.755274i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.85387 | + | 11.8610i | −0.167244 | + | 0.514724i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.98230 | − | 9.17857i | 0.129178 | − | 0.397568i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.6762 | + | 8.48325i | −0.503865 | + | 0.366079i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.96200 | + | 7.23781i | 0.429094 | + | 0.311755i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.00089 | − | 6.53953i | 0.386979 | − | 0.281156i | −0.377238 | − | 0.926116i | \(-0.623126\pi\) |
0.764216 | + | 0.644960i | \(0.223126\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.74285 | 0.289363 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.60009 | − | 26.4684i | −0.367713 | − | 1.13171i | −0.948264 | − | 0.317482i | \(-0.897163\pi\) |
0.580551 | − | 0.814224i | \(-0.302837\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.92041 | −0.295356 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.96222 | −0.0835935 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.40389 | + | 19.7091i | 0.272321 | + | 0.838118i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.36580 | 0.269728 | 0.134864 | − | 0.990864i | \(-0.456940\pi\) | ||||
0.134864 | + | 0.990864i | \(0.456940\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 47.5569 | − | 34.5521i | 2.01144 | − | 1.46140i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.3610 | + | 8.25424i | 0.479661 | + | 0.348494i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.8569 | − | 10.0676i | 0.584000 | − | 0.424301i | −0.256164 | − | 0.966633i | \(-0.582459\pi\) |
0.840164 | + | 0.542333i | \(0.182459\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.09610 | + | 3.37344i | −0.0460317 | + | 0.141671i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.75461 | − | 14.6332i | 0.199324 | − | 0.613455i | −0.800575 | − | 0.599232i | \(-0.795473\pi\) |
0.999899 | − | 0.0142229i | \(-0.00452743\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.63760 | + | 8.11770i | 0.110380 | + | 0.339715i | 0.990955 | − | 0.134191i | \(-0.0428435\pi\) |
−0.880575 | + | 0.473906i | \(0.842844\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.4512 | − | 9.04634i | −0.520157 | − | 0.377916i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.86491 | − | 1.35494i | −0.0776374 | − | 0.0564068i | 0.548290 | − | 0.836289i | \(-0.315279\pi\) |
−0.625927 | + | 0.779882i | \(0.715279\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.06402 | + | 15.5854i | 0.210453 | + | 0.647709i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.7315 | + | 42.2614i | −0.569681 | + | 1.75330i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.15245 | + | 25.0907i | −0.337640 | + | 1.03915i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.743663 | − | 0.540303i | 0.0306943 | − | 0.0223007i | −0.572332 | − | 0.820022i | \(-0.693961\pi\) |
0.603027 | + | 0.797721i | \(0.293961\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.05253 | − | 5.85051i | −0.331799 | − | 0.241066i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.96910 | + | 5.78989i | −0.327805 | + | 0.238164i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.5925 | 1.05096 | 0.525478 | − | 0.850807i | \(-0.323886\pi\) | ||||
0.525478 | + | 0.850807i | \(0.323886\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.53357 | − | 4.71985i | −0.0627650 | − | 0.193171i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.0204 | −1.51261 | −0.756307 | − | 0.654217i | \(-0.772998\pi\) | ||||
−0.756307 | + | 0.654217i | \(0.772998\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.4191 | 1.36319 | 0.681597 | − | 0.731728i | \(-0.261286\pi\) | ||||
0.681597 | + | 0.731728i | \(0.261286\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.46291 | + | 4.50239i | 0.0595745 | + | 0.183351i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.34502 | −0.176359 | −0.0881795 | − | 0.996105i | \(-0.528105\pi\) | ||||
−0.0881795 | + | 0.996105i | \(0.528105\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.43308 | − | 1.76774i | 0.0985935 | − | 0.0716323i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.1580 | + | 25.5438i | 1.42234 | + | 1.03339i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.20367 | − | 2.32761i | 0.129395 | − | 0.0940111i | −0.521205 | − | 0.853431i | \(-0.674517\pi\) |
0.650600 | + | 0.759420i | \(0.274517\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.26189 | + | 19.2721i | −0.252094 | + | 0.775866i | 0.742294 | + | 0.670074i | \(0.233738\pi\) |
−0.994388 | + | 0.105792i | \(0.966262\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.65930 | + | 14.3398i | −0.187273 | + | 0.576367i | −0.999980 | − | 0.00630532i | \(-0.997993\pi\) |
0.812707 | + | 0.582672i | \(0.197993\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.672404 | + | 2.06945i | 0.0269826 | + | 0.0830440i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −20.1622 | − | 14.6487i | −0.807782 | − | 0.586888i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.13058 | − | 3.00104i | −0.164959 | − | 0.119850i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.2213 | − | 43.7687i | −0.567041 | − | 1.74517i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.755761 | + | 2.32599i | −0.0300864 | + | 0.0925963i | −0.964972 | − | 0.262352i | \(-0.915502\pi\) |
0.934886 | + | 0.354949i | \(0.115502\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.08150 | − | 3.32851i | 0.0429857 | − | 0.132296i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.4112 | − | 23.5481i | 1.28418 | − | 0.933009i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.1476 | − | 8.09918i | −0.440991 | − | 0.320399i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.8353 | + | 7.87228i | −0.427967 | + | 0.310936i | −0.780836 | − | 0.624737i | \(-0.785206\pi\) |
0.352868 | + | 0.935673i | \(0.385206\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.4836 | −1.39934 | −0.699669 | − | 0.714467i | \(-0.746669\pi\) | ||||
−0.699669 | + | 0.714467i | \(0.746669\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.91707 | − | 21.2886i | −0.271938 | − | 0.836940i | −0.990013 | − | 0.140974i | \(-0.954977\pi\) |
0.718075 | − | 0.695966i | \(-0.245023\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.5140 | 1.08002 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.2555 | 0.597909 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.84923 | − | 18.0021i | −0.228898 | − | 0.704476i | −0.997872 | − | 0.0651961i | \(-0.979233\pi\) |
0.768974 | − | 0.639279i | \(-0.220767\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.08917 | 0.0424925 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.58371 | + | 3.33026i | −0.178556 | + | 0.129729i | −0.673473 | − | 0.739212i | \(-0.735198\pi\) |
0.494917 | + | 0.868940i | \(0.335198\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.4225 | + | 14.8378i | 0.794342 | + | 0.577123i | 0.909249 | − | 0.416253i | \(-0.136657\pi\) |
−0.114907 | + | 0.993376i | \(0.536657\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 36.9627 | − | 26.8550i | 1.43551 | − | 1.04296i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.570116 | − | 1.75464i | 0.0220750 | − | 0.0679398i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.13168 | − | 21.9491i | 0.275727 | − | 0.848600i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.71794 | + | 14.5203i | 0.182134 | + | 0.560551i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.6538 | − | 7.74044i | −0.410674 | − | 0.298372i | 0.363201 | − | 0.931711i | \(-0.381684\pi\) |
−0.773875 | + | 0.633339i | \(0.781684\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.8139 | − | 15.8487i | −0.838375 | − | 0.609115i | 0.0835409 | − | 0.996504i | \(-0.473377\pi\) |
−0.921916 | + | 0.387389i | \(0.873377\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.8881 | + | 61.2092i | 0.763234 | + | 2.34899i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.80793 | + | 5.56424i | −0.0692801 | + | 0.213222i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.0008 | − | 49.2454i | 0.612254 | − | 1.88432i | 0.176356 | − | 0.984326i | \(-0.443569\pi\) |
0.435897 | − | 0.899996i | \(-0.356431\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.17019 | − | 3.75637i | 0.197255 | − | 0.143314i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 69.4403 | + | 50.4513i | 2.64546 | + | 1.92204i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.00647 | − | 2.18432i | 0.114371 | − | 0.0830956i | −0.529129 | − | 0.848541i | \(-0.677481\pi\) |
0.643501 | + | 0.765446i | \(0.277481\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.82536 | 0.297261 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.64475 | − | 8.13972i | −0.100177 | − | 0.308314i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.54311 | 0.171836 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.4299 | −1.07378 | −0.536890 | − | 0.843652i | \(-0.680401\pi\) | ||||
−0.536890 | + | 0.843652i | \(0.680401\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.17053 | + | 15.9132i | 0.195010 | + | 0.600180i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.1926 | −0.797030 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.1126 | + | 24.0577i | −1.24357 | + | 0.903507i | −0.997831 | − | 0.0658288i | \(-0.979031\pi\) |
−0.245740 | + | 0.969336i | \(0.579031\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.72664 | + | 3.43411i | 0.177263 | + | 0.128789i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.57120 | − | 5.50080i | 0.283544 | − | 0.206007i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.12010 | − | 21.9134i | 0.265905 | − | 0.818372i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.46368 | − | 4.50475i | 0.0545861 | − | 0.167999i | −0.920047 | − | 0.391809i | \(-0.871849\pi\) |
0.974633 | + | 0.223810i | \(0.0718495\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.503731 | + | 1.55032i | 0.0187599 | + | 0.0577371i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.3064 | − | 9.66766i | −0.494870 | − | 0.359544i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.50692 | + | 3.27447i | 0.167153 | + | 0.121443i | 0.668217 | − | 0.743967i | \(-0.267058\pi\) |
−0.501064 | + | 0.865410i | \(0.667058\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.1091 | − | 49.5788i | 0.595818 | − | 1.83374i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.38166 | + | 28.8738i | −0.346520 | + | 1.06648i | 0.614246 | + | 0.789115i | \(0.289460\pi\) |
−0.960765 | + | 0.277363i | \(0.910540\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.44952 | − | 6.13894i | 0.311242 | − | 0.226131i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.6127 | − | 28.7803i | −1.45718 | − | 1.05870i | −0.984087 | − | 0.177686i | \(-0.943139\pi\) |
−0.473089 | − | 0.881015i | \(-0.656861\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.4388 | + | 9.76383i | −0.493685 | + | 0.358683i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.5953 | 1.67273 | 0.836364 | − | 0.548174i | \(-0.184677\pi\) | ||||
0.836364 | + | 0.548174i | \(0.184677\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.87127 | + | 11.9145i | 0.141642 | + | 0.435930i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.79176 | −0.321244 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.9100 | −1.01845 | −0.509225 | − | 0.860633i | \(-0.670068\pi\) | ||||
−0.509225 | + | 0.860633i | \(0.670068\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.44103 | + | 4.43503i | 0.0525140 | + | 0.161621i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.6680 | 1.00561 | 0.502804 | − | 0.864400i | \(-0.332302\pi\) | ||||
0.502804 | + | 0.864400i | \(0.332302\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.88368 | − | 2.82166i | 0.140969 | − | 0.102420i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.80362 | + | 7.12275i | 0.355381 | + | 0.258199i | 0.751123 | − | 0.660162i | \(-0.229513\pi\) |
−0.395742 | + | 0.918362i | \(0.629513\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.58814 | + | 6.96619i | −0.347114 | + | 0.252193i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.6620 | − | 85.1349i | 0.998817 | − | 3.07404i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.13398 | + | 9.64540i | −0.113014 | + | 0.347822i | −0.991528 | − | 0.129896i | \(-0.958536\pi\) |
0.878513 | + | 0.477718i | \(0.158536\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.78839 | − | 5.50409i | −0.0644071 | − | 0.198225i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.5906 | + | 29.4908i | 1.45994 | + | 1.06071i | 0.983378 | + | 0.181569i | \(0.0581177\pi\) |
0.476563 | + | 0.879140i | \(0.341882\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −20.7473 | − | 15.0738i | −0.744304 | − | 0.540769i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.961568 | + | 2.95940i | 0.0344518 | + | 0.106032i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.39383 | + | 28.9112i | −0.336138 | + | 1.03453i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.262008 | − | 0.806379i | 0.00936342 | − | 0.0288176i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.5059 | + | 9.08606i | −0.445787 | + | 0.323883i | −0.787930 | − | 0.615765i | \(-0.788847\pi\) |
0.342143 | + | 0.939648i | \(0.388847\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.5668 | − | 13.4896i | −0.660996 | − | 0.480242i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 50.4991 | − | 36.6897i | 1.79554 | − | 1.30454i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.6727 | 1.76393 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.77110 | + | 5.45087i | 0.0627354 | + | 0.193080i | 0.977512 | − | 0.210881i | \(-0.0676332\pi\) |
−0.914776 | + | 0.403961i | \(0.867633\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.5390 | 1.36341 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.02611 | −0.248255 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.742531 | − | 2.28528i | −0.0262034 | − | 0.0806457i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.50997 | −0.158758 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.9907 | − | 16.7038i | 0.808312 | − | 0.587273i | −0.105029 | − | 0.994469i | \(-0.533494\pi\) |
0.913341 | + | 0.407196i | \(0.133494\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.86048 | + | 7.16406i | 0.346248 | + | 0.251564i | 0.747293 | − | 0.664494i | \(-0.231353\pi\) |
−0.401045 | + | 0.916058i | \(0.631353\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.03461 | − | 5.83748i | 0.281786 | − | 0.204730i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.85689 | + | 18.0257i | −0.204907 | + | 0.630638i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.86746 | − | 24.2136i | 0.274911 | − | 0.846090i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.51854 | + | 13.9066i | 0.157698 | + | 0.485345i | 0.998424 | − | 0.0561157i | \(-0.0178716\pi\) |
−0.840726 | + | 0.541461i | \(0.817872\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.5077 | + | 12.7201i | 0.610280 | + | 0.443394i | 0.849513 | − | 0.527568i | \(-0.176896\pi\) |
−0.239233 | + | 0.970962i | \(0.576896\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.03038 | + | 6.56096i | 0.314017 | + | 0.228147i | 0.733618 | − | 0.679562i | \(-0.237830\pi\) |
−0.419601 | + | 0.907709i | \(0.637830\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.60563 | + | 26.4854i | 0.298886 | + | 0.919876i | 0.981888 | + | 0.189460i | \(0.0606738\pi\) |
−0.683003 | + | 0.730416i | \(0.739326\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.11211 | + | 21.8888i | −0.246716 | + | 0.759315i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.9788 | − | 33.7892i | 0.380392 | − | 1.17073i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.47950 | − | 2.52801i | 0.120269 | − | 0.0873807i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.3556 | + | 11.1565i | 0.530133 | + | 0.385164i | 0.820408 | − | 0.571779i | \(-0.193747\pi\) |
−0.290274 | + | 0.956943i | \(0.593747\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.8799 | − | 16.6232i | 0.788962 | − | 0.573214i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.734004 | 0.0252804 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.72218 | + | 20.6887i | 0.230977 | + | 0.710873i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.4921 | 0.737609 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.7320 | −0.539287 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.10082 | + | 15.6987i | 0.174649 | + | 0.537513i | 0.999617 | − | 0.0276653i | \(-0.00880727\pi\) |
−0.824969 | + | 0.565179i | \(0.808807\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.7615 | −0.982475 | −0.491237 | − | 0.871026i | \(-0.663455\pi\) | ||||
−0.491237 | + | 0.871026i | \(0.663455\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.2446 | − | 8.89622i | 0.417780 | − | 0.303535i | −0.358964 | − | 0.933351i | \(-0.616870\pi\) |
0.776744 | + | 0.629816i | \(0.216870\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.85839 | − | 2.80329i | −0.131494 | − | 0.0955357i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34.8258 | + | 25.3024i | −1.18549 | + | 0.861305i | −0.992780 | − | 0.119951i | \(-0.961726\pi\) |
−0.192705 | + | 0.981257i | \(0.561726\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.26725 | − | 22.3663i | 0.246809 | − | 0.759600i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.98305 | − | 12.2586i | 0.135116 | − | 0.415843i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.5004 | − | 32.3168i | −0.355792 | − | 1.09501i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.6792 | + | 10.6651i | 0.496815 | + | 0.360957i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.0134 | + | 29.7980i | 1.38492 | + | 1.00621i | 0.996401 | + | 0.0847668i | \(0.0270145\pi\) |
0.388523 | + | 0.921439i | \(0.372985\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.21864 | − | 25.2944i | −0.277208 | − | 0.853158i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.818966 | + | 2.52052i | −0.0275917 | + | 0.0849184i | −0.963904 | − | 0.266250i | \(-0.914215\pi\) |
0.936312 | + | 0.351168i | \(0.114215\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.4361 | + | 32.1189i | −0.351201 | + | 1.08089i | 0.606978 | + | 0.794719i | \(0.292382\pi\) |
−0.958179 | + | 0.286168i | \(0.907618\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.49811 | − | 2.54153i | 0.117455 | − | 0.0853361i | −0.527507 | − | 0.849551i | \(-0.676873\pi\) |
0.644962 | + | 0.764215i | \(0.276873\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.6175 | + | 25.8776i | 1.19457 | + | 0.867908i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.78482 | − | 1.29675i | 0.0597939 | − | 0.0434428i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.0119 | −0.468889 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.82632 | − | 14.8539i | −0.161146 | − | 0.495957i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.64664 | −0.121622 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 76.1182 | 2.53586 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.97673 | − | 27.6275i | −0.298727 | − | 0.919387i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47.2507 | −1.56893 | −0.784467 | − | 0.620171i | \(-0.787063\pi\) | ||||
−0.784467 | + | 0.620171i | \(0.787063\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.83366 | + | 3.51186i | −0.160322 | + | 0.116481i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.1586 | − | 29.9035i | −1.36365 | − | 0.990747i | −0.998204 | − | 0.0599132i | \(-0.980918\pi\) |
−0.365443 | − | 0.930834i | \(-0.619082\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.3597 | − | 16.2453i | 0.739999 | − | 0.537641i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.3437 | + | 53.3785i | −0.572740 | + | 1.76271i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.3396 | + | 34.8998i | −0.374060 | + | 1.15124i | 0.570051 | + | 0.821610i | \(0.306924\pi\) |
−0.944111 | + | 0.329629i | \(0.893076\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.76186 | + | 11.5778i | 0.123957 | + | 0.381502i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 80.0140 | + | 58.1336i | 2.63369 | + | 1.91349i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.371799 | + | 0.270128i | 0.0122115 | + | 0.00887215i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.9269 | + | 45.9401i | 0.489734 | + | 1.50725i | 0.825005 | + | 0.565125i | \(0.191172\pi\) |
−0.335271 | + | 0.942122i | \(0.608828\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.99161 | + | 12.2849i | −0.130820 | + | 0.402622i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.65191 | + | 23.5502i | −0.250512 | + | 0.770998i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.67223 | + | 5.57420i | −0.250641 | + | 0.182101i | −0.706011 | − | 0.708201i | \(-0.749507\pi\) |
0.455370 | + | 0.890302i | \(0.349507\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.0102 | − | 8.72589i | −0.391937 | − | 0.284759i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.2272 | − | 12.5163i | 0.561590 | − | 0.408019i | −0.270450 | − | 0.962734i | \(-0.587173\pi\) |
0.832041 | + | 0.554715i | \(0.187173\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.92570 | −0.0952740 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.73768 | − | 29.9695i | −0.316432 | − | 0.973877i | −0.975161 | − | 0.221497i | \(-0.928906\pi\) |
0.658729 | − | 0.752380i | \(-0.271094\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.81773 | −0.253774 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.94231 | 0.0629837 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.46513 | − | 10.6646i | −0.112247 | − | 0.345460i | 0.879116 | − | 0.476608i | \(-0.158134\pi\) |
−0.991363 | + | 0.131148i | \(0.958134\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.87056 | −0.0604665 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.2206 | − | 15.4177i | 0.685249 | − | 0.497863i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.1145 | + | 7.34864i | 0.326275 | + | 0.237053i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.00524 | + | 1.45689i | −0.0646181 | + | 0.0469478i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.0077 | − | 33.8782i | 0.353984 | − | 1.08945i | −0.602612 | − | 0.798034i | \(-0.705873\pi\) |
0.956596 | − | 0.291417i | \(-0.0941266\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.55217 | + | 14.0101i | −0.146237 | + | 0.450070i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.2227 | + | 40.6953i | 0.424337 | + | 1.30598i | 0.903628 | + | 0.428319i | \(0.140894\pi\) |
−0.479290 | + | 0.877656i | \(0.659106\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.3032 | + | 8.21228i | 0.362365 | + | 0.263274i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.9119 | − | 23.9119i | −1.05294 | − | 0.765009i | −0.0801740 | − | 0.996781i | \(-0.525548\pi\) |
−0.972770 | + | 0.231772i | \(0.925548\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.78999 | + | 14.7421i | 0.153089 | + | 0.471159i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.03251 | + | 3.17773i | −0.0329654 | + | 0.101457i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.1319 | − | 46.5713i | 0.482634 | − | 1.48539i | −0.352746 | − | 0.935719i | \(-0.614752\pi\) |
0.835379 | − | 0.549674i | \(-0.185248\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17.3742 | − | 12.6231i | 0.553026 | − | 0.401797i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.4170 | − | 10.4746i | −0.458434 | − | 0.333072i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.99334 | − | 1.44825i | 0.0633206 | − | 0.0460051i | −0.555675 | − | 0.831400i | \(-0.687540\pi\) |
0.618995 | + | 0.785395i | \(0.287540\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.7307 | −0.880006 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.7650 | + | 51.5975i | 0.530954 | + | 1.63411i | 0.752232 | + | 0.658899i | \(0.228977\pi\) |
−0.221277 | + | 0.975211i | \(0.571023\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.22998 | −0.228747 |
(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.m.c.1201.1 | 24 | ||
5.2 | odd | 4 | 300.2.o.a.109.4 | ✓ | 24 | ||
5.3 | odd | 4 | 1500.2.o.c.49.3 | 24 | |||
5.4 | even | 2 | 1500.2.m.d.1201.6 | 24 | |||
15.2 | even | 4 | 900.2.w.c.109.5 | 24 | |||
25.2 | odd | 20 | 1500.2.o.c.949.3 | 24 | |||
25.6 | even | 5 | 7500.2.a.n.1.2 | 12 | |||
25.8 | odd | 20 | 7500.2.d.g.1249.23 | 24 | |||
25.11 | even | 5 | inner | 1500.2.m.c.301.1 | 24 | ||
25.14 | even | 10 | 1500.2.m.d.301.6 | 24 | |||
25.17 | odd | 20 | 7500.2.d.g.1249.2 | 24 | |||
25.19 | even | 10 | 7500.2.a.m.1.11 | 12 | |||
25.23 | odd | 20 | 300.2.o.a.289.4 | yes | 24 | ||
75.23 | even | 20 | 900.2.w.c.289.5 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.109.4 | ✓ | 24 | 5.2 | odd | 4 | ||
300.2.o.a.289.4 | yes | 24 | 25.23 | odd | 20 | ||
900.2.w.c.109.5 | 24 | 15.2 | even | 4 | |||
900.2.w.c.289.5 | 24 | 75.23 | even | 20 | |||
1500.2.m.c.301.1 | 24 | 25.11 | even | 5 | inner | ||
1500.2.m.c.1201.1 | 24 | 1.1 | even | 1 | trivial | ||
1500.2.m.d.301.6 | 24 | 25.14 | even | 10 | |||
1500.2.m.d.1201.6 | 24 | 5.4 | even | 2 | |||
1500.2.o.c.49.3 | 24 | 5.3 | odd | 4 | |||
1500.2.o.c.949.3 | 24 | 25.2 | odd | 20 | |||
7500.2.a.m.1.11 | 12 | 25.19 | even | 10 | |||
7500.2.a.n.1.2 | 12 | 25.6 | even | 5 | |||
7500.2.d.g.1249.2 | 24 | 25.17 | odd | 20 | |||
7500.2.d.g.1249.23 | 24 | 25.8 | odd | 20 |