Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(49,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.q (of order \(4\), degree \(2\), 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.4767670494822400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + 112 x^{2} - 128 x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 400) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 49.3 | ||
Root | \(-0.507829 + 1.31989i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.49 |
Dual form | 1600.2.q.f.849.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.0623209 | + | 0.0623209i | 0.0359810 | + | 0.0359810i | 0.724868 | − | 0.688887i | \(-0.241901\pi\) |
−0.688887 | + | 0.724868i | \(0.741901\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.375877 | −0.142068 | −0.0710340 | − | 0.997474i | \(-0.522630\pi\) | ||||
−0.0710340 | + | 0.997474i | \(0.522630\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.99223i | − | 0.997411i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.36756 | − | 2.36756i | −0.713845 | − | 0.713845i | 0.253492 | − | 0.967337i | \(-0.418421\pi\) |
−0.967337 | + | 0.253492i | \(0.918421\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.76442 | − | 1.76442i | −0.489363 | − | 0.489363i | 0.418742 | − | 0.908105i | \(-0.362471\pi\) |
−0.908105 | + | 0.418742i | \(0.862471\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.64955i | 1.12768i | 0.825883 | + | 0.563841i | \(0.190677\pi\) | ||||
−0.825883 | + | 0.563841i | \(0.809323\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.34965 | + | 2.34965i | −0.539047 | + | 0.539047i | −0.923249 | − | 0.384202i | \(-0.874476\pi\) |
0.384202 | + | 0.923249i | \(0.374476\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0234250 | − | 0.0234250i | −0.00511175 | − | 0.00511175i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.07779 | 0.433250 | 0.216625 | − | 0.976255i | \(-0.430495\pi\) | ||||
0.216625 | + | 0.976255i | \(0.430495\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.373441 | − | 0.373441i | 0.0718688 | − | 0.0718688i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.55422 | + | 2.55422i | −0.474307 | + | 0.474307i | −0.903305 | − | 0.428998i | \(-0.858867\pi\) |
0.428998 | + | 0.903305i | \(0.358867\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.51714 | −1.52972 | −0.764862 | − | 0.644194i | \(-0.777193\pi\) | ||||
−0.764862 | + | 0.644194i | \(0.777193\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.295096i | − | 0.0513697i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.62613 | + | 7.62613i | −1.25373 | + | 1.25373i | −0.299691 | + | 0.954036i | \(0.596884\pi\) |
−0.954036 | + | 0.299691i | \(0.903116\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 0.219921i | − | 0.0352155i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.77709i | 0.589882i | 0.955515 | + | 0.294941i | \(0.0953001\pi\) | ||||
−0.955515 | + | 0.294941i | \(0.904700\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.21191 | − | 6.21191i | 0.947307 | − | 0.947307i | −0.0513725 | − | 0.998680i | \(-0.516360\pi\) |
0.998680 | + | 0.0513725i | \(0.0163596\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.71696i | 1.41736i | 0.705528 | + | 0.708682i | \(0.250710\pi\) | ||||
−0.705528 | + | 0.708682i | \(0.749290\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.85872 | −0.979817 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.289764 | + | 0.289764i | −0.0405751 | + | 0.0405751i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.03609 | + | 3.03609i | −0.417040 | + | 0.417040i | −0.884182 | − | 0.467143i | \(-0.845283\pi\) |
0.467143 | + | 0.884182i | \(0.345283\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.292864 | −0.0387908 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.11663 | − | 8.11663i | −1.05670 | − | 1.05670i | −0.998293 | − | 0.0584019i | \(-0.981400\pi\) |
−0.0584019 | − | 0.998293i | \(-0.518600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.728329 | − | 0.728329i | 0.0932529 | − | 0.0932529i | −0.658941 | − | 0.752194i | \(-0.728995\pi\) |
0.752194 | + | 0.658941i | \(0.228995\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.12471i | 0.141700i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.969239 | − | 0.969239i | −0.118411 | − | 0.118411i | 0.645418 | − | 0.763829i | \(-0.276683\pi\) |
−0.763829 | + | 0.645418i | \(0.776683\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.129490 | + | 0.129490i | 0.0155887 | + | 0.0155887i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.14230i | − | 1.08499i | −0.840058 | − | 0.542496i | \(-0.817479\pi\) | ||
0.840058 | − | 0.542496i | \(-0.182521\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.56793 | 0.885759 | 0.442879 | − | 0.896581i | \(-0.353957\pi\) | ||||
0.442879 | + | 0.896581i | \(0.353957\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.889909 | + | 0.889909i | 0.101415 | + | 0.101415i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.8065 | 1.32834 | 0.664169 | − | 0.747583i | \(-0.268786\pi\) | ||||
0.664169 | + | 0.747583i | \(0.268786\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.93015 | −0.992239 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.6393 | − | 10.6393i | −1.16782 | − | 1.16782i | −0.982720 | − | 0.185101i | \(-0.940739\pi\) |
−0.185101 | − | 0.982720i | \(-0.559261\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.318363 | −0.0341320 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 15.7111i | − | 1.66538i | −0.553741 | − | 0.832689i | \(-0.686800\pi\) | ||
0.553741 | − | 0.832689i | \(-0.313200\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.663205 | + | 0.663205i | 0.0695228 | + | 0.0695228i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.530796 | − | 0.530796i | −0.0550410 | − | 0.0550410i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.86020i | 0.391943i | 0.980610 | + | 0.195972i | \(0.0627861\pi\) | ||||
−0.980610 | + | 0.195972i | \(0.937214\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.08428 | + | 7.08428i | −0.711997 | + | 0.711997i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.87437 | − | 6.87437i | −0.684026 | − | 0.684026i | 0.276879 | − | 0.960905i | \(-0.410700\pi\) |
−0.960905 | + | 0.276879i | \(0.910700\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.15407 | −0.113714 | −0.0568571 | − | 0.998382i | \(-0.518108\pi\) | ||||
−0.0568571 | + | 0.998382i | \(0.518108\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.70435 | + | 5.70435i | −0.551460 | + | 0.551460i | −0.926862 | − | 0.375402i | \(-0.877505\pi\) |
0.375402 | + | 0.926862i | \(0.377505\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.1863 | + | 11.1863i | −1.07145 | + | 1.07145i | −0.0742092 | + | 0.997243i | \(0.523643\pi\) |
−0.997243 | + | 0.0742092i | \(0.976357\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.950534 | −0.0902207 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4.08163i | − | 0.383967i | −0.981398 | − | 0.191984i | \(-0.938508\pi\) | ||
0.981398 | − | 0.191984i | \(-0.0614920\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.27956 | + | 5.27956i | −0.488096 | + | 0.488096i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1.74766i | − | 0.160208i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.210643i | 0.0191493i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.235392 | + | 0.235392i | −0.0212245 | + | 0.0212245i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.0918i | 1.51665i | 0.651876 | + | 0.758326i | \(0.273982\pi\) | ||||
−0.651876 | + | 0.758326i | \(0.726018\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.774263 | 0.0681701 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.56424 | − | 3.56424i | 0.311409 | − | 0.311409i | −0.534046 | − | 0.845455i | \(-0.679329\pi\) |
0.845455 | + | 0.534046i | \(0.179329\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.883179 | − | 0.883179i | 0.0765813 | − | 0.0765813i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.6995 | 1.42673 | 0.713366 | − | 0.700792i | \(-0.247170\pi\) | ||||
0.713366 | + | 0.700792i | \(0.247170\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.56455 | − | 7.56455i | −0.641616 | − | 0.641616i | 0.309336 | − | 0.950953i | \(-0.399893\pi\) |
−0.950953 | + | 0.309336i | \(0.899893\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.605569 | + | 0.605569i | −0.0509982 | + | 0.0509982i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.35474i | 0.698658i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.427441 | − | 0.427441i | −0.0352548 | − | 0.0352548i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.2542 | + | 10.2542i | 0.840056 | + | 0.840056i | 0.988866 | − | 0.148810i | \(-0.0475444\pi\) |
−0.148810 | + | 0.988866i | \(0.547544\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.0430i | 1.54970i | 0.632147 | + | 0.774849i | \(0.282174\pi\) | ||||
−0.632147 | + | 0.774849i | \(0.717826\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.9125 | 1.12476 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.1335 | − | 10.1335i | −0.808741 | − | 0.808741i | 0.175702 | − | 0.984443i | \(-0.443780\pi\) |
−0.984443 | + | 0.175702i | \(0.943780\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.378424 | −0.0300110 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.780994 | −0.0615509 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.35501 | + | 7.35501i | 0.576089 | + | 0.576089i | 0.933823 | − | 0.357735i | \(-0.116451\pi\) |
−0.357735 | + | 0.933823i | \(0.616451\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.02936 | −0.621331 | −0.310665 | − | 0.950519i | \(-0.600552\pi\) | ||||
−0.310665 | + | 0.950519i | \(0.600552\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 6.77363i | − | 0.521048i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.03070 | + | 7.03070i | 0.537651 | + | 0.537651i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.4326 | − | 10.4326i | −0.793177 | − | 0.793177i | 0.188832 | − | 0.982009i | \(-0.439530\pi\) |
−0.982009 | + | 0.188832i | \(0.939530\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 1.01167i | − | 0.0760418i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.30280 | + | 8.30280i | −0.620580 | + | 0.620580i | −0.945680 | − | 0.325099i | \(-0.894602\pi\) |
0.325099 | + | 0.945680i | \(0.394602\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.4772 | − | 10.4772i | −0.778765 | − | 0.778765i | 0.200856 | − | 0.979621i | \(-0.435628\pi\) |
−0.979621 | + | 0.200856i | \(0.935628\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0907802 | 0.00671066 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.0081 | − | 11.0081i | 0.804990 | − | 0.804990i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.140368 | + | 0.140368i | −0.0102103 | + | 0.0102103i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.68079 | −0.121618 | −0.0608089 | − | 0.998149i | \(-0.519368\pi\) | ||||
−0.0608089 | + | 0.998149i | \(0.519368\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 1.61403i | − | 0.116181i | −0.998311 | − | 0.0580903i | \(-0.981499\pi\) | ||
0.998311 | − | 0.0580903i | \(-0.0185011\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.10322 | − | 5.10322i | 0.363589 | − | 0.363589i | −0.501543 | − | 0.865133i | \(-0.667234\pi\) |
0.865133 | + | 0.501543i | \(0.167234\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 11.1545i | − | 0.790725i | −0.918525 | − | 0.395362i | \(-0.870619\pi\) | ||
0.918525 | − | 0.395362i | \(-0.129381\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 0.120808i | − | 0.00852111i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.960072 | − | 0.960072i | 0.0673839 | − | 0.0673839i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.21724i | − | 0.432128i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.1259 | 0.769591 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.48377 | − | 2.48377i | 0.170989 | − | 0.170989i | −0.616425 | − | 0.787414i | \(-0.711419\pi\) |
0.787414 | + | 0.616425i | \(0.211419\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.569756 | − | 0.569756i | 0.0390391 | − | 0.0390391i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.20140 | 0.217325 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.471640 | + | 0.471640i | 0.0318705 | + | 0.0318705i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.20377 | − | 8.20377i | 0.551846 | − | 0.551846i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.1384i | 1.41553i | 0.706448 | + | 0.707765i | \(0.250297\pi\) | ||||
−0.706448 | + | 0.707765i | \(0.749703\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.4885 | − | 14.4885i | −0.961634 | − | 0.961634i | 0.0376566 | − | 0.999291i | \(-0.488011\pi\) |
−0.999291 | + | 0.0376566i | \(0.988011\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0956 | + | 10.0956i | 0.667138 | + | 0.667138i | 0.957053 | − | 0.289914i | \(-0.0936268\pi\) |
−0.289914 | + | 0.957053i | \(0.593627\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.110920i | 0.00729799i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.44995 | −0.226014 | −0.113007 | − | 0.993594i | \(-0.536048\pi\) | ||||
−0.113007 | + | 0.993594i | \(0.536048\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.735793 | + | 0.735793i | 0.0477949 | + | 0.0477949i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.0060 | 1.16471 | 0.582354 | − | 0.812935i | \(-0.302132\pi\) | ||||
0.582354 | + | 0.812935i | \(0.302132\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.6235 | 0.813154 | 0.406577 | − | 0.913617i | \(-0.366722\pi\) | ||||
0.406577 | + | 0.913617i | \(0.366722\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.67686 | − | 1.67686i | −0.107571 | − | 0.107571i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.29155 | 0.527578 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 1.32611i | − | 0.0840386i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.17919 | + | 9.17919i | 0.579386 | + | 0.579386i | 0.934734 | − | 0.355348i | \(-0.115638\pi\) |
−0.355348 | + | 0.934734i | \(0.615638\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.91929 | − | 4.91929i | −0.309273 | − | 0.309273i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 16.2897i | − | 1.01612i | −0.861321 | − | 0.508061i | \(-0.830363\pi\) | ||
0.861321 | − | 0.508061i | \(-0.169637\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.86648 | − | 2.86648i | 0.178115 | − | 0.178115i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.64282 | + | 7.64282i | 0.473079 | + | 0.473079i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.4898 | −0.646831 | −0.323416 | − | 0.946257i | \(-0.604831\pi\) | ||||
−0.323416 | + | 0.946257i | \(0.604831\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.979132 | − | 0.979132i | 0.0599219 | − | 0.0599219i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.46636 | − | 8.46636i | 0.516203 | − | 0.516203i | −0.400217 | − | 0.916420i | \(-0.631065\pi\) |
0.916420 | + | 0.400217i | \(0.131065\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.92117 | 0.541923 | 0.270961 | − | 0.962590i | \(-0.412658\pi\) | ||||
0.270961 | + | 0.962590i | \(0.412658\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0826631i | 0.00500300i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.36430 | − | 9.36430i | 0.562646 | − | 0.562646i | −0.367412 | − | 0.930058i | \(-0.619756\pi\) |
0.930058 | + | 0.367412i | \(0.119756\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 25.4853i | 1.52576i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.12921i | 0.186673i | 0.995635 | + | 0.0933365i | \(0.0297532\pi\) | ||||
−0.995635 | + | 0.0933365i | \(0.970247\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.07308 | + | 2.07308i | −0.123232 | + | 0.123232i | −0.766033 | − | 0.642801i | \(-0.777772\pi\) |
0.642801 | + | 0.766033i | \(0.277772\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1.41972i | − | 0.0838035i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.61834 | −0.271667 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.240571 | + | 0.240571i | −0.0141025 | + | 0.0141025i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.3528 | + | 12.3528i | −0.721659 | + | 0.721659i | −0.968943 | − | 0.247284i | \(-0.920462\pi\) |
0.247284 | + | 0.968943i | \(0.420462\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.76829 | −0.102606 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.66610 | − | 3.66610i | −0.212016 | − | 0.212016i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.33491 | + | 2.33491i | −0.134582 | + | 0.134582i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 0.856834i | − | 0.0492238i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.5938 | + | 10.5938i | 0.604619 | + | 0.604619i | 0.941535 | − | 0.336916i | \(-0.109384\pi\) |
−0.336916 | + | 0.941535i | \(0.609384\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.0719229 | − | 0.0719229i | −0.00409155 | − | 0.00409155i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 19.4153i | − | 1.10094i | −0.834854 | − | 0.550471i | \(-0.814448\pi\) | ||
0.834854 | − | 0.550471i | \(-0.185552\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.56569 | −0.145022 | −0.0725108 | − | 0.997368i | \(-0.523101\pi\) | ||||
−0.0725108 | + | 0.997368i | \(0.523101\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.32418 | + | 7.32418i | 0.411367 | + | 0.411367i | 0.882215 | − | 0.470848i | \(-0.156052\pi\) |
−0.470848 | + | 0.882215i | \(0.656052\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0945 | 0.677163 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.711000 | −0.0396842 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.9248 | − | 10.9248i | −0.607873 | − | 0.607873i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.39428 | −0.0771038 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 3.65238i | − | 0.201362i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.17652 | − | 4.17652i | −0.229562 | − | 0.229562i | 0.582948 | − | 0.812510i | \(-0.301899\pi\) |
−0.812510 | + | 0.582948i | \(0.801899\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 22.8191 | + | 22.8191i | 1.25048 | + | 1.25048i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 12.4540i | − | 0.678410i | −0.940712 | − | 0.339205i | \(-0.889842\pi\) | ||
0.940712 | − | 0.339205i | \(-0.110158\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.254371 | − | 0.254371i | 0.0138155 | − | 0.0138155i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.1648 | + | 20.1648i | 1.09199 | + | 1.09199i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.20917 | 0.281269 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.5107 | − | 17.5107i | 0.940024 | − | 0.940024i | −0.0582766 | − | 0.998300i | \(-0.518561\pi\) |
0.998300 | + | 0.0582766i | \(0.0185605\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.42042 | + | 8.42042i | −0.450735 | + | 0.450735i | −0.895598 | − | 0.444863i | \(-0.853252\pi\) |
0.444863 | + | 0.895598i | \(0.353252\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.31782 | −0.0703398 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.71293i | 0.516967i | 0.966016 | + | 0.258484i | \(0.0832228\pi\) | ||||
−0.966016 | + | 0.258484i | \(0.916777\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.108916 | − | 0.108916i | 0.00576443 | − | 0.00576443i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6.77551i | − | 0.357598i | −0.983886 | − | 0.178799i | \(-0.942779\pi\) | ||
0.983886 | − | 0.178799i | \(-0.0572212\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.95830i | 0.418858i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.0131274 | + | 0.0131274i | −0.000689012 | + | 0.000689012i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 34.4591i | − | 1.79875i | −0.437176 | − | 0.899376i | \(-0.644021\pi\) | ||
0.437176 | − | 0.899376i | \(-0.355979\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.3019 | 0.588355 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.14120 | − | 1.14120i | 0.0592480 | − | 0.0592480i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.55187 | + | 3.55187i | −0.183909 | + | 0.183909i | −0.793057 | − | 0.609148i | \(-0.791512\pi\) |
0.609148 | + | 0.793057i | \(0.291512\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.01345 | 0.464216 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.4464 | + | 26.4464i | 1.35846 | + | 1.35846i | 0.875817 | + | 0.482644i | \(0.160323\pi\) |
0.482644 | + | 0.875817i | \(0.339677\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.06518 | + | 1.06518i | −0.0545706 | + | 0.0545706i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 30.8614i | − | 1.57695i | −0.615069 | − | 0.788473i | \(-0.710872\pi\) | ||
0.615069 | − | 0.788473i | \(-0.289128\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.5875 | − | 18.5875i | −0.944854 | − | 0.944854i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.50959 | − | 9.50959i | −0.482155 | − | 0.482155i | 0.423664 | − | 0.905819i | \(-0.360744\pi\) |
−0.905819 | + | 0.423664i | \(0.860744\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.66080i | 0.488568i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.444253 | 0.0224096 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.8540 | − | 24.8540i | −1.24739 | − | 1.24739i | −0.956870 | − | 0.290518i | \(-0.906172\pi\) |
−0.290518 | − | 0.956870i | \(-0.593828\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.110081 | 0.00551094 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.69303 | 0.234359 | 0.117179 | − | 0.993111i | \(-0.462615\pi\) | ||||
0.117179 | + | 0.993111i | \(0.462615\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.0278 | + | 15.0278i | 0.748590 | + | 0.748590i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 36.1106 | 1.78993 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.2641i | 1.39757i | 0.715331 | + | 0.698786i | \(0.246276\pi\) | ||||
−0.715331 | + | 0.698786i | \(0.753724\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.04073 | + | 1.04073i | 0.0513352 | + | 0.0513352i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.05085 | + | 3.05085i | 0.150123 | + | 0.150123i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 0.942858i | − | 0.0461720i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.0355 | − | 23.0355i | 1.12536 | − | 1.12536i | 0.134433 | − | 0.990923i | \(-0.457079\pi\) |
0.990923 | − | 0.134433i | \(-0.0429213\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.40760 | + | 5.40760i | 0.263550 | + | 0.263550i | 0.826495 | − | 0.562945i | \(-0.190332\pi\) |
−0.562945 | + | 0.826495i | \(0.690332\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 29.0754 | 1.41369 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.273762 | + | 0.273762i | −0.0132483 | + | 0.0132483i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.520675 | + | 0.520675i | −0.0251384 | + | 0.0251384i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.6839 | 0.610961 | 0.305481 | − | 0.952198i | \(-0.401183\pi\) | ||||
0.305481 | + | 0.952198i | \(0.401183\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.8511i | 1.14621i | 0.819482 | + | 0.573104i | \(0.194261\pi\) | ||||
−0.819482 | + | 0.573104i | \(0.805739\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.88208 | + | 4.88208i | −0.233542 | + | 0.233542i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.65878i | − | 0.222352i | −0.993801 | − | 0.111176i | \(-0.964538\pi\) | ||
0.993801 | − | 0.111176i | \(-0.0354617\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.5229i | 0.977280i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.74048 | + | 8.74048i | −0.415273 | + | 0.415273i | −0.883571 | − | 0.468298i | \(-0.844867\pi\) |
0.468298 | + | 0.883571i | \(0.344867\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.27810i | 0.0604520i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.28525 | 0.343812 | 0.171906 | − | 0.985113i | \(-0.445007\pi\) | ||||
0.171906 | + | 0.985113i | \(0.445007\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.94247 | − | 8.94247i | 0.421085 | − | 0.421085i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.18678 | + | 1.18678i | −0.0557596 | + | 0.0557596i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.2194 | −1.17971 | −0.589857 | − | 0.807508i | \(-0.700816\pi\) | ||||
−0.589857 | + | 0.807508i | \(0.700816\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.73633 | + | 1.73633i | 0.0810451 | + | 0.0810451i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.6698 | − | 13.6698i | 0.636667 | − | 0.636667i | −0.313064 | − | 0.949732i | \(-0.601356\pi\) |
0.949732 | + | 0.313064i | \(0.101356\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.77045i | 0.128754i | 0.997926 | + | 0.0643768i | \(0.0205060\pi\) | ||||
−0.997926 | + | 0.0643768i | \(0.979494\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.9587 | + | 17.9587i | 0.831031 | + | 0.831031i | 0.987658 | − | 0.156627i | \(-0.0500621\pi\) |
−0.156627 | + | 0.987658i | \(0.550062\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.364314 | + | 0.364314i | 0.0168225 | + | 0.0168225i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 1.26306i | − | 0.0581986i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −29.4141 | −1.35246 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.08470 | + | 9.08470i | 0.415960 | + | 0.415960i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.4540 | −1.02595 | −0.512975 | − | 0.858403i | \(-0.671457\pi\) | ||||
−0.512975 | + | 0.858403i | \(0.671457\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.9114 | 1.22705 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.0486722 | − | 0.0486722i | −0.00221466 | − | 0.00221466i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.7615 | −1.25799 | −0.628997 | − | 0.777408i | \(-0.716534\pi\) | ||||
−0.628997 | + | 0.777408i | \(0.716534\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.916741i | 0.0414565i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.8993 | − | 16.8993i | −0.762656 | − | 0.762656i | 0.214146 | − | 0.976802i | \(-0.431303\pi\) |
−0.976802 | + | 0.214146i | \(0.931303\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.8760 | − | 11.8760i | −0.534867 | − | 0.534867i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.43638i | 0.154143i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.81950 | + | 1.81950i | −0.0814520 | + | 0.0814520i | −0.746659 | − | 0.665207i | \(-0.768343\pi\) |
0.665207 | + | 0.746659i | \(0.268343\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.500397 | − | 0.500397i | −0.0223561 | − | 0.0223561i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −42.2076 | −1.88195 | −0.940973 | − | 0.338482i | \(-0.890087\pi\) | ||||
−0.940973 | + | 0.338482i | \(0.890087\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.422139 | − | 0.422139i | 0.0187478 | − | 0.0187478i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.9831 | − | 21.9831i | 0.974382 | − | 0.974382i | −0.0252980 | − | 0.999680i | \(-0.508053\pi\) |
0.999680 | + | 0.0252980i | \(0.00805345\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.84461 | −0.125838 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.75491i | 0.0774812i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.0054 | − | 23.0054i | 1.01178 | − | 1.01178i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 1.30034i | − | 0.0570786i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 28.1418i | − | 1.23291i | −0.787388 | − | 0.616457i | \(-0.788567\pi\) | ||
0.787388 | − | 0.616457i | \(-0.211433\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.58093 | − | 9.58093i | 0.418945 | − | 0.418945i | −0.465895 | − | 0.884840i | \(-0.654268\pi\) |
0.884840 | + | 0.465895i | \(0.154268\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 39.6009i | − | 1.72504i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.6828 | −0.812295 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −24.2868 | + | 24.2868i | −1.05396 | + | 1.05396i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.66438 | − | 6.66438i | 0.288666 | − | 0.288666i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.03488 | −0.0446582 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.2384 | + | 16.2384i | 0.699437 | + | 0.699437i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.9128 | + | 26.9128i | −1.15707 | + | 1.15707i | −0.171972 | + | 0.985102i | \(0.555014\pi\) |
−0.985102 | + | 0.171972i | \(0.944986\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1.30590i | − | 0.0560415i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.6627 | + | 10.6627i | 0.455902 | + | 0.455902i | 0.897308 | − | 0.441406i | \(-0.145520\pi\) |
−0.441406 | + | 0.897308i | \(0.645520\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.17933 | − | 2.17933i | −0.0930115 | − | 0.0930115i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 12.0030i | − | 0.511347i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.43780 | −0.188714 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.8060 | + | 22.8060i | 0.966320 | + | 0.966320i | 0.999451 | − | 0.0331307i | \(-0.0105477\pi\) |
−0.0331307 | + | 0.999451i | \(0.510548\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.9209 | −0.927153 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.37207 | 0.0579287 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.472513 | − | 0.472513i | −0.0199140 | − | 0.0199140i | 0.697080 | − | 0.716994i | \(-0.254482\pi\) |
−0.716994 | + | 0.697080i | \(0.754482\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.35664 | 0.140965 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.14792i | 0.131967i | 0.997821 | + | 0.0659837i | \(0.0210185\pi\) | ||||
−0.997821 | + | 0.0659837i | \(0.978981\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.78162 | − | 5.78162i | −0.241953 | − | 0.241953i | 0.575704 | − | 0.817658i | \(-0.304728\pi\) |
−0.817658 | + | 0.575704i | \(0.804728\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.104748 | − | 0.104748i | −0.00437593 | − | 0.00437593i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.0110i | 1.20774i | 0.797081 | + | 0.603872i | \(0.206376\pi\) | ||||
−0.797081 | + | 0.603872i | \(0.793624\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.100588 | − | 0.100588i | 0.00418029 | − | 0.00418029i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.99908 | + | 3.99908i | 0.165910 | + | 0.165910i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.3762 | 0.595403 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.4099 | + | 20.4099i | −0.842408 | + | 0.842408i | −0.989172 | − | 0.146764i | \(-0.953114\pi\) |
0.146764 | + | 0.989172i | \(0.453114\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.0123 | − | 20.0123i | 0.824592 | − | 0.824592i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.636074 | 0.0261646 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 28.9098i | − | 1.18718i | −0.804766 | − | 0.593592i | \(-0.797709\pi\) | ||
0.804766 | − | 0.593592i | \(-0.202291\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.695161 | − | 0.695161i | 0.0284511 | − | 0.0284511i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.7893i | 0.481696i | 0.970563 | + | 0.240848i | \(0.0774256\pi\) | ||||
−0.970563 | + | 0.240848i | \(0.922574\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 17.7398i | − | 0.723621i | −0.932252 | − | 0.361810i | \(-0.882159\pi\) | ||
0.932252 | − | 0.361810i | \(-0.117841\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.90019 | + | 2.90019i | −0.118105 | + | 0.118105i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.8393i | 1.04878i | 0.851477 | + | 0.524392i | \(0.175707\pi\) | ||||
−0.851477 | + | 0.524392i | \(0.824293\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.119665 | 0.00484907 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.1448 | − | 17.1448i | 0.693605 | − | 0.693605i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.5411 | − | 31.5411i | 1.27393 | − | 1.27393i | 0.329929 | − | 0.944006i | \(-0.392975\pi\) |
0.944006 | − | 0.329929i | \(-0.107025\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.0637 | −0.606440 | −0.303220 | − | 0.952921i | \(-0.598062\pi\) | ||||
−0.303220 | + | 0.952921i | \(0.598062\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.4975 | − | 10.4975i | −0.421929 | − | 0.421929i | 0.463938 | − | 0.885868i | \(-0.346436\pi\) |
−0.885868 | + | 0.463938i | \(0.846436\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.775933 | − | 0.775933i | 0.0311371 | − | 0.0311371i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.90545i | 0.236597i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.693373 | + | 0.693373i | 0.0276906 | + | 0.0276906i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −35.4581 | − | 35.4581i | −1.41381 | − | 1.41381i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.6349i | 1.73708i | 0.495621 | + | 0.868539i | \(0.334940\pi\) | ||||
−0.495621 | + | 0.868539i | \(0.665060\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.309581 | 0.0123047 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.1017 | + | 12.1017i | 0.479486 | + | 0.479486i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27.3559 | −1.08218 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.2710 | −1.35362 | −0.676812 | − | 0.736156i | \(-0.736639\pi\) | ||||
−0.676812 | + | 0.736156i | \(0.736639\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.1937 | + | 30.1937i | 1.19072 | + | 1.19072i | 0.976865 | + | 0.213857i | \(0.0686027\pi\) |
0.213857 | + | 0.976865i | \(0.431397\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.7474 | −0.619096 | −0.309548 | − | 0.950884i | \(-0.600178\pi\) | ||||
−0.309548 | + | 0.950884i | \(0.600178\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 38.4331i | 1.50863i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.199514 | + | 0.199514i | 0.00781956 | + | 0.00781956i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.80619 | + | 5.80619i | 0.227214 | + | 0.227214i | 0.811528 | − | 0.584314i | \(-0.198636\pi\) |
−0.584314 | + | 0.811528i | \(0.698636\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 22.6450i | − | 0.883465i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.76782 | − | 1.76782i | 0.0688647 | − | 0.0688647i | −0.671836 | − | 0.740700i | \(-0.734494\pi\) |
0.740700 | + | 0.671836i | \(0.234494\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.4824 | − | 12.4824i | −0.485509 | − | 0.485509i | 0.421377 | − | 0.906886i | \(-0.361547\pi\) |
−0.906886 | + | 0.421377i | \(0.861547\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.02253 | 0.0397119 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.30714 | + | 5.30714i | −0.205493 | + | 0.205493i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.31736 | + | 1.31736i | −0.0509322 | + | 0.0509322i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.44872 | −0.133136 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 14.1113i | − | 0.543950i | −0.962304 | − | 0.271975i | \(-0.912323\pi\) | ||
0.962304 | − | 0.271975i | \(-0.0876768\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.31191 | + | 8.31191i | −0.319453 | + | 0.319453i | −0.848557 | − | 0.529104i | \(-0.822528\pi\) |
0.529104 | + | 0.848557i | \(0.322528\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.45096i | − | 0.0556827i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 1.80587i | − | 0.0692011i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.0811 | + | 30.0811i | −1.15102 | + | 1.15102i | −0.164673 | + | 0.986348i | \(0.552657\pi\) |
−0.986348 | + | 0.164673i | \(0.947343\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.25834i | 0.0480086i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.7139 | 0.408167 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.0212 | + | 24.0212i | −0.913810 | + | 0.913810i | −0.996570 | − | 0.0827600i | \(-0.973627\pi\) |
0.0827600 | + | 0.996570i | \(0.473627\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.66282 | − | 2.66282i | 0.101152 | − | 0.101152i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.5618 | −0.665200 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.215004 | − | 0.215004i | −0.00813219 | − | 0.00813219i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.0971 | − | 10.0971i | 0.381363 | − | 0.381363i | −0.490230 | − | 0.871593i | \(-0.663087\pi\) |
0.871593 | + | 0.490230i | \(0.163087\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 35.8375i | − | 1.35164i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.58392 | + | 2.58392i | 0.0971782 | + | 0.0971782i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.67310 | + | 4.67310i | 0.175502 | + | 0.175502i | 0.789392 | − | 0.613890i | \(-0.210396\pi\) |
−0.613890 | + | 0.789392i | \(0.710396\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 35.3279i | − | 1.32490i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.6968 | −0.662752 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.12215 | + | 1.12215i | 0.0419074 | + | 0.0419074i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.5339 | −0.877667 | −0.438833 | − | 0.898568i | \(-0.644608\pi\) | ||||
−0.438833 | + | 0.898568i | \(0.644608\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.433789 | 0.0161552 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.786710 | + | 0.786710i | 0.0292581 | + | 0.0292581i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.6692 | −0.618226 | −0.309113 | − | 0.951025i | \(-0.600032\pi\) | ||||
−0.309113 | + | 0.951025i | \(0.600032\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.5814i | 0.984498i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.8826 | + | 28.8826i | 1.06826 | + | 1.06826i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.4684 | + | 27.4684i | 1.01457 | + | 1.01457i | 0.999892 | + | 0.0146760i | \(0.00467168\pi\) |
0.0146760 | + | 0.999892i | \(0.495328\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.58945i | 0.169055i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.7939 | − | 22.7939i | 0.838486 | − | 0.838486i | −0.150174 | − | 0.988660i | \(-0.547983\pi\) |
0.988660 | + | 0.150174i | \(0.0479832\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.516736 | + | 0.516736i | 0.0189828 | + | 0.0189828i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.4964 | 0.605196 | 0.302598 | − | 0.953118i | \(-0.402146\pi\) | ||||
0.302598 | + | 0.953118i | \(0.402146\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −31.8354 | + | 31.8354i | −1.16480 | + | 1.16480i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.14413 | − | 2.14413i | 0.0783449 | − | 0.0783449i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.6997 | 0.791833 | 0.395917 | − | 0.918286i | \(-0.370427\pi\) | ||||
0.395917 | + | 0.918286i | \(0.370427\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.14411i | 0.0416937i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.73819 | + | 1.73819i | −0.0631757 | + | 0.0631757i | −0.737989 | − | 0.674813i | \(-0.764224\pi\) |
0.674813 | + | 0.737989i | \(0.264224\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 0.613149i | − | 0.0222559i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 46.5311i | − | 1.68675i | −0.537323 | − | 0.843376i | \(-0.680565\pi\) | ||
0.537323 | − | 0.843376i | \(-0.319435\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.20467 | − | 4.20467i | 0.152219 | − | 0.152219i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.6423i | 1.03421i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.4731 | −0.557976 | −0.278988 | − | 0.960295i | \(-0.589999\pi\) | ||||
−0.278988 | + | 0.960295i | \(0.589999\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.01519 | − | 1.01519i | 0.0365610 | − | 0.0365610i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.69848 | + | 5.69848i | −0.204960 | + | 0.204960i | −0.802121 | − | 0.597161i | \(-0.796295\pi\) |
0.597161 | + | 0.802121i | \(0.296295\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.357284 | 0.0128175 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.87484 | − | 8.87484i | −0.317974 | − | 0.317974i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.6449 | + | 21.6449i | −0.774516 | + | 0.774516i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.90770i | 0.0681757i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.1351 | + | 18.1351i | 0.646448 | + | 0.646448i | 0.952133 | − | 0.305685i | \(-0.0988855\pi\) |
−0.305685 | + | 0.952133i | \(0.598885\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.653736 | − | 0.653736i | −0.0232736 | − | 0.0232736i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.53419i | 0.0545495i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.57016 | −0.0912690 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.51575 | − | 4.51575i | −0.159956 | − | 0.159956i | 0.622591 | − | 0.782547i | \(-0.286080\pi\) |
−0.782547 | + | 0.622591i | \(0.786080\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −45.1795 | −1.59834 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −47.0114 | −1.66107 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.9175 | − | 17.9175i | −0.632294 | − | 0.632294i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.05526 | 0.0371470 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.33368i | 0.117206i | 0.998281 | + | 0.0586030i | \(0.0186646\pi\) | ||||
−0.998281 | + | 0.0586030i | \(0.981335\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.1948 | − | 37.1948i | −1.30609 | − | 1.30609i | −0.924215 | − | 0.381873i | \(-0.875279\pi\) |
−0.381873 | − | 0.924215i | \(-0.624721\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.555975 | + | 0.555975i | 0.0194989 | + | 0.0194989i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.1916i | 1.02129i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.98446 | − | 1.98446i | 0.0693428 | − | 0.0693428i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.5278 | − | 25.5278i | −0.890926 | − | 0.890926i | 0.103684 | − | 0.994610i | \(-0.466937\pi\) |
−0.994610 | + | 0.103684i | \(0.966937\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.8858 | −0.588603 | −0.294301 | − | 0.955713i | \(-0.595087\pi\) | ||||
−0.294301 | + | 0.955713i | \(0.595087\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.5765 | + | 11.5765i | −0.402556 | + | 0.402556i | −0.879133 | − | 0.476577i | \(-0.841877\pi\) |
0.476577 | + | 0.879133i | \(0.341877\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.97296 | + | 5.97296i | −0.207449 | + | 0.207449i | −0.803182 | − | 0.595733i | \(-0.796862\pi\) |
0.595733 | + | 0.803182i | \(0.296862\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.16718 | 0.0404891 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 31.8900i | − | 1.10492i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.18065 | + | 3.18065i | −0.109939 | + | 0.109939i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 27.2960i | − | 0.942362i | −0.882037 | − | 0.471181i | \(-0.843828\pi\) | ||
0.882037 | − | 0.471181i | \(-0.156172\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.9519i | 0.550066i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.195015 | + | 0.195015i | −0.00671668 | + | 0.00671668i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 0.0791757i | − | 0.00272051i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.258392 | −0.00886799 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.8455 | + | 15.8455i | −0.543177 | + | 0.543177i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.1167 | − | 29.1167i | 0.996938 | − | 0.996938i | −0.00305738 | − | 0.999995i | \(-0.500973\pi\) |
0.999995 | + | 0.00305738i | \(0.000973195\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.0170 | −0.752087 | −0.376044 | − | 0.926602i | \(-0.622716\pi\) | ||||
−0.376044 | + | 0.926602i | \(0.622716\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.8910 | + | 16.8910i | 0.576312 | + | 0.576312i | 0.933885 | − | 0.357573i | \(-0.116396\pi\) |
−0.357573 | + | 0.933885i | \(0.616396\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0884782 | − | 0.0884782i | 0.00301533 | − | 0.00301533i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 46.2073i | − | 1.57292i | −0.617644 | − | 0.786458i | \(-0.711913\pi\) | ||
0.617644 | − | 0.786458i | \(-0.288087\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.287819 | − | 0.287819i | −0.00977484 | − | 0.00977484i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.9526 | − | 27.9526i | −0.948227 | − | 0.948227i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.42029i | 0.115892i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.5506 | 0.390929 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.6380 | + | 21.6380i | 0.730664 | + | 0.730664i | 0.970751 | − | 0.240087i | \(-0.0771760\pi\) |
−0.240087 | + | 0.970751i | \(0.577176\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.53968 | −0.0519320 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.6649 | −1.20158 | −0.600790 | − | 0.799407i | \(-0.705147\pi\) | ||||
−0.600790 | + | 0.799407i | \(0.705147\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.5681 | − | 17.5681i | −0.591213 | − | 0.591213i | 0.346746 | − | 0.937959i | \(-0.387287\pi\) |
−0.937959 | + | 0.346746i | \(0.887287\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.2454 | 1.72065 | 0.860326 | − | 0.509744i | \(-0.170260\pi\) | ||||
0.860326 | + | 0.509744i | \(0.170260\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 6.42441i | − | 0.215468i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.1426 | + | 21.1426i | 0.708305 | + | 0.708305i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.8315 | − | 22.8315i | −0.764025 | − | 0.764025i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 0.456949i | − | 0.0152571i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.7547 | − | 21.7547i | 0.725559 | − | 0.725559i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.1165 | − | 14.1165i | −0.470288 | − | 0.470288i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.291028 | −0.00968479 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.6745 | + | 29.6745i | −0.985324 | + | 0.985324i | −0.999894 | − | 0.0145695i | \(-0.995362\pi\) |
0.0145695 | + | 0.999894i | \(0.495362\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −20.5697 | + | 20.5697i | −0.682255 | + | 0.682255i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.9064 | 0.825187 | 0.412593 | − | 0.910915i | \(-0.364623\pi\) | ||||
0.412593 | + | 0.910915i | \(0.364623\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 50.3785i | 1.66729i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.33971 | + | 1.33971i | −0.0442413 | + | 0.0442413i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 15.6940i | − | 0.517696i | −0.965918 | − | 0.258848i | \(-0.916657\pi\) | ||
0.965918 | − | 0.258848i | \(-0.0833429\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.32043i | 0.0435096i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.1309 | + | 16.1309i | −0.530954 | + | 0.530954i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.45326i | 0.113420i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.00598 | −0.197050 | −0.0985249 | − | 0.995135i | \(-0.531412\pi\) | ||||
−0.0985249 | + | 0.995135i | \(0.531412\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.1156 | − | 16.1156i | 0.528167 | − | 0.528167i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.20998 | − | 1.20998i | 0.0396130 | − | 0.0396130i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.83037 | 0.157801 | 0.0789006 | − | 0.996882i | \(-0.474859\pi\) | ||||
0.0789006 | + | 0.996882i | \(0.474859\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.159896 | − | 0.159896i | −0.00521802 | − | 0.00521802i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.63878 | + | 3.63878i | −0.118621 | + | 0.118621i | −0.763925 | − | 0.645305i | \(-0.776730\pi\) |
0.645305 | + | 0.763925i | \(0.276730\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.84801i | 0.255566i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.7720 | + | 34.7720i | 1.12994 | + | 1.12994i | 0.990187 | + | 0.139751i | \(0.0446302\pi\) |
0.139751 | + | 0.990187i | \(0.455370\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.3530 | − | 13.3530i | −0.433457 | − | 0.433457i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.912899i | 0.0296028i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.89827 | 0.0614910 | 0.0307455 | − | 0.999527i | \(-0.490212\pi\) | ||||
0.0307455 | + | 0.999527i | \(0.490212\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.753741 | + | 0.753741i | 0.0243650 | + | 0.0243650i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.27694 | −0.202693 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.5417 | 1.34006 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.0687 | + | 17.0687i | 0.550033 | + | 0.550033i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −61.5753 | −1.98013 | −0.990064 | − | 0.140616i | \(-0.955092\pi\) | ||||
−0.990064 | + | 0.140616i | \(0.955092\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1.36169i | − | 0.0437437i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.6595 | − | 22.6595i | −0.727179 | − | 0.727179i | 0.242878 | − | 0.970057i | \(-0.421909\pi\) |
−0.970057 | + | 0.242878i | \(0.921909\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.84334 | + | 2.84334i | 0.0911532 | + | 0.0911532i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.3240i | 0.810186i | 0.914276 | + | 0.405093i | \(0.132761\pi\) | ||||
−0.914276 | + | 0.405093i | \(0.867239\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −37.1970 | + | 37.1970i | −1.18882 | + | 1.18882i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.4720 | + | 33.4720i | 1.06868 | + | 1.06868i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.01686 | −0.160013 | −0.0800065 | − | 0.996794i | \(-0.525494\pi\) | ||||
−0.0800065 | + | 0.996794i | \(0.525494\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.227620 | − | 0.227620i | 0.00724521 | − | 0.00724521i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.9071 | − | 12.9071i | 0.410420 | − | 0.410420i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.2998 | −1.31193 | −0.655965 | − | 0.754791i | \(-0.727738\pi\) | ||||
−0.655965 | + | 0.754791i | \(0.727738\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 0.520569i | − | 0.0165198i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.23850 | − | 1.23850i | 0.0392235 | − | 0.0392235i | −0.687223 | − | 0.726447i | \(-0.741170\pi\) |
0.726447 | + | 0.687223i | \(0.241170\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.69582i | 0.180208i |
(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 | 1600.2.q.f.49.3 | 12 | ||
4.3 | odd | 2 | 400.2.q.f.149.6 | 12 | |||
5.2 | odd | 4 | 1600.2.l.g.1201.3 | 12 | |||
5.3 | odd | 4 | 1600.2.l.f.1201.4 | 12 | |||
5.4 | even | 2 | 1600.2.q.e.49.4 | 12 | |||
16.3 | odd | 4 | 400.2.q.e.349.1 | 12 | |||
16.13 | even | 4 | 1600.2.q.e.849.4 | 12 | |||
20.3 | even | 4 | 400.2.l.g.101.2 | yes | 12 | ||
20.7 | even | 4 | 400.2.l.f.101.5 | ✓ | 12 | ||
20.19 | odd | 2 | 400.2.q.e.149.1 | 12 | |||
80.3 | even | 4 | 400.2.l.g.301.2 | yes | 12 | ||
80.13 | odd | 4 | 1600.2.l.f.401.4 | 12 | |||
80.19 | odd | 4 | 400.2.q.f.349.6 | 12 | |||
80.29 | even | 4 | inner | 1600.2.q.f.849.3 | 12 | ||
80.67 | even | 4 | 400.2.l.f.301.5 | yes | 12 | ||
80.77 | odd | 4 | 1600.2.l.g.401.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.5 | ✓ | 12 | 20.7 | even | 4 | ||
400.2.l.f.301.5 | yes | 12 | 80.67 | even | 4 | ||
400.2.l.g.101.2 | yes | 12 | 20.3 | even | 4 | ||
400.2.l.g.301.2 | yes | 12 | 80.3 | even | 4 | ||
400.2.q.e.149.1 | 12 | 20.19 | odd | 2 | |||
400.2.q.e.349.1 | 12 | 16.3 | odd | 4 | |||
400.2.q.f.149.6 | 12 | 4.3 | odd | 2 | |||
400.2.q.f.349.6 | 12 | 80.19 | odd | 4 | |||
1600.2.l.f.401.4 | 12 | 80.13 | odd | 4 | |||
1600.2.l.f.1201.4 | 12 | 5.3 | odd | 4 | |||
1600.2.l.g.401.3 | 12 | 80.77 | odd | 4 | |||
1600.2.l.g.1201.3 | 12 | 5.2 | odd | 4 | |||
1600.2.q.e.49.4 | 12 | 5.4 | even | 2 | |||
1600.2.q.e.849.4 | 12 | 16.13 | even | 4 | |||
1600.2.q.f.49.3 | 12 | 1.1 | even | 1 | trivial | ||
1600.2.q.f.849.3 | 12 | 80.29 | even | 4 | inner |