Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(401,1600)]
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, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.l (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: |
\( x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 \)
|
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 | 1201.3 | ||
Root | \(-0.507829 - 1.31989i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1201 |
Dual form | 1600.2.l.g.401.3 |
$q$-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 | −0.688887 | − | 0.724868i | \(-0.741901\pi\) |
0.724868 | + | 0.688887i | \(0.241901\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.375877i | − | 0.142068i | −0.997474 | − | 0.0710340i | \(-0.977370\pi\) | ||
0.997474 | − | 0.0710340i | \(-0.0226299\pi\) | |||||||
\(8\) | 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 | −0.908105 | − | 0.418742i | \(-0.862471\pi\) |
0.418742 | + | 0.908105i | \(0.362471\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.64955 | −1.12768 | −0.563841 | − | 0.825883i | \(-0.690677\pi\) | ||||
−0.563841 | + | 0.825883i | \(0.690677\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.34965 | − | 2.34965i | 0.539047 | − | 0.539047i | −0.384202 | − | 0.923249i | \(-0.625524\pi\) |
0.923249 | + | 0.384202i | \(0.125524\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0234250 | − | 0.0234250i | −0.00511175 | − | 0.00511175i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.07779i | − | 0.433250i | −0.976255 | − | 0.216625i | \(-0.930495\pi\) | ||
0.976255 | − | 0.216625i | \(-0.0695048\pi\) | |||||||
\(24\) | 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 | −0.428998 | − | 0.903305i | \(-0.641133\pi\) |
0.903305 | + | 0.428998i | \(0.141133\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.51714 | −1.52972 | −0.764862 | − | 0.644194i | \(-0.777193\pi\) | ||||
−0.764862 | + | 0.644194i | \(0.777193\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.295096 | −0.0513697 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.62613 | − | 7.62613i | −1.25373 | − | 1.25373i | −0.954036 | − | 0.299691i | \(-0.903116\pi\) |
−0.299691 | − | 0.954036i | \(-0.596884\pi\) | |||||||
\(38\) | 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 | \(-0.483640\pi\) |
−0.998680 | + | 0.0513725i | \(0.983640\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.71696 | −1.41736 | −0.708682 | − | 0.705528i | \(-0.750710\pi\) | ||||
−0.708682 | + | 0.705528i | \(0.750710\pi\) | |||||||
\(48\) | 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 | \(-0.154717\pi\) |
−0.467143 | + | 0.884182i | \(0.654717\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.292864i | − | 0.0387908i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.11663 | + | 8.11663i | 1.05670 | + | 1.05670i | 0.998293 | + | 0.0584019i | \(0.0186005\pi\) |
0.0584019 | + | 0.998293i | \(0.481400\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 1.12471 | 0.141700 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.969239 | − | 0.969239i | 0.118411 | − | 0.118411i | −0.645418 | − | 0.763829i | \(-0.723317\pi\) |
0.763829 | + | 0.645418i | \(0.223317\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | − | 7.56793i | − | 0.885759i | −0.896581 | − | 0.442879i | \(-0.853957\pi\) | ||
0.896581 | − | 0.442879i | \(-0.146043\pi\) | |||||||
\(74\) | 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 | \(-0.731214\pi\) | ||||
−0.664169 | + | 0.747583i | \(0.731214\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.93015 | −0.992239 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.6393 | + | 10.6393i | −1.16782 | + | 1.16782i | −0.185101 | + | 0.982720i | \(0.559261\pi\) |
−0.982720 | + | 0.185101i | \(0.940739\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 0.318363i | − | 0.0341320i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.7111i | 1.66538i | 0.553741 | + | 0.832689i | \(0.313200\pi\) | ||||
−0.553741 | + | 0.832689i | \(0.686800\pi\) | |||||||
\(90\) | 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 | ||||||||
\(97\) | −3.86020 | −0.391943 | −0.195972 | − | 0.980610i | \(-0.562786\pi\) | ||||
−0.195972 | + | 0.980610i | \(0.562786\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | 1.15407i | 0.113714i | 0.998382 | + | 0.0568571i | \(0.0181079\pi\) | ||||
−0.998382 | + | 0.0568571i | \(0.981892\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.70435 | − | 5.70435i | −0.551460 | − | 0.551460i | 0.375402 | − | 0.926862i | \(-0.377505\pi\) |
−0.926862 | + | 0.375402i | \(0.877505\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.1863 | − | 11.1863i | 1.07145 | − | 1.07145i | 0.0742092 | − | 0.997243i | \(-0.476357\pi\) |
0.997243 | − | 0.0742092i | \(-0.0236433\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.950534 | −0.0902207 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.08163 | −0.383967 | −0.191984 | − | 0.981398i | \(-0.561492\pi\) | ||||
−0.191984 | + | 0.981398i | \(0.561492\pi\) | |||||||
\(114\) | 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 | ||||||||
\(127\) | −17.0918 | −1.51665 | −0.758326 | − | 0.651876i | \(-0.773982\pi\) | ||||
−0.758326 | + | 0.651876i | \(0.773982\pi\) | |||||||
\(128\) | 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 | ||||||||
\(137\) | 16.6995i | 1.42673i | 0.700792 | + | 0.713366i | \(0.252830\pi\) | ||||
−0.700792 | + | 0.713366i | \(0.747170\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.56455 | + | 7.56455i | 0.641616 | + | 0.641616i | 0.950953 | − | 0.309336i | \(-0.100107\pi\) |
−0.309336 | + | 0.950953i | \(0.600107\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.605569 | + | 0.605569i | −0.0509982 | + | 0.0509982i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.35474 | 0.698658 | ||||||||
\(144\) | 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 | 0.148810 | − | 0.988866i | \(-0.452456\pi\) |
−0.988866 | + | 0.148810i | \(0.952456\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.0430i | 1.54970i | 0.632147 | + | 0.774849i | \(0.282174\pi\) | ||||
−0.632147 | + | 0.774849i | \(0.717826\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 13.9125i | − | 1.12476i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.1335 | − | 10.1335i | 0.808741 | − | 0.808741i | −0.175702 | − | 0.984443i | \(-0.556220\pi\) |
0.984443 | + | 0.175702i | \(0.0562196\pi\) | |||||||
\(158\) | 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 | −0.357735 | − | 0.933823i | \(-0.616451\pi\) |
0.933823 | + | 0.357735i | \(0.116451\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 8.02936i | − | 0.621331i | −0.950519 | − | 0.310665i | \(-0.899448\pi\) | ||
0.950519 | − | 0.310665i | \(-0.100552\pi\) | |||||||
\(168\) | 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 | −0.982009 | − | 0.188832i | \(-0.939530\pi\) |
0.188832 | + | 0.982009i | \(0.439530\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.01167 | 0.0760418 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.30280 | − | 8.30280i | 0.620580 | − | 0.620580i | −0.325099 | − | 0.945680i | \(-0.605398\pi\) |
0.945680 | + | 0.325099i | \(0.105398\pi\) | |||||||
\(180\) | 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 | ||||||||
\(183\) | − | 0.0907802i | − | 0.00671066i | ||||||
\(184\) | 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 | ||||||||
\(193\) | −1.61403 | −0.116181 | −0.0580903 | − | 0.998311i | \(-0.518501\pi\) | ||||
−0.0580903 | + | 0.998311i | \(0.518501\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.10322 | + | 5.10322i | 0.363589 | + | 0.363589i | 0.865133 | − | 0.501543i | \(-0.167234\pi\) |
−0.501543 | + | 0.865133i | \(0.667234\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.1545i | 0.790725i | 0.918525 | + | 0.395362i | \(0.129381\pi\) | ||||
−0.918525 | + | 0.395362i | \(0.870619\pi\) | |||||||
\(200\) | 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 | ||||||||
\(207\) | 6.21724 | 0.432128 | ||||||||
\(208\) | 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 | ||||||||
\(217\) | 3.20140i | 0.217325i | ||||||||
\(218\) | 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 | ||||||||
\(223\) | 21.1384 | 1.41553 | 0.707765 | − | 0.706448i | \(-0.249703\pi\) | ||||
0.707765 | + | 0.706448i | \(0.249703\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.4885 | − | 14.4885i | 0.961634 | − | 0.961634i | −0.0376566 | − | 0.999291i | \(-0.511989\pi\) |
0.999291 | + | 0.0376566i | \(0.0119893\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0956 | − | 10.0956i | −0.667138 | − | 0.667138i | 0.289914 | − | 0.957053i | \(-0.406373\pi\) |
−0.957053 | + | 0.289914i | \(0.906373\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.110920i | 0.00729799i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.44995i | 0.226014i | 0.993594 | + | 0.113007i | \(0.0360482\pi\) | ||||
−0.993594 | + | 0.113007i | \(0.963952\pi\) | |||||||
\(234\) | 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 | \(-0.697868\pi\) | ||||
−0.582354 | + | 0.812935i | \(0.697868\pi\) | |||||||
\(240\) | 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 | ||||||||
\(247\) | 8.29155i | 0.527578i | ||||||||
\(248\) | 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 | ||||||||
\(257\) | 16.2897 | 1.01612 | 0.508061 | − | 0.861321i | \(-0.330363\pi\) | ||||
0.508061 | + | 0.861321i | \(0.330363\pi\) | |||||||
\(258\) | 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 | ||||||||
\(263\) | 10.4898i | 0.646831i | 0.946257 | + | 0.323416i | \(0.104831\pi\) | ||||
−0.946257 | + | 0.323416i | \(0.895169\pi\) | |||||||
\(264\) | 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 | −0.916420 | − | 0.400217i | \(-0.868935\pi\) |
0.400217 | + | 0.916420i | \(0.368935\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.92117 | 0.541923 | 0.270961 | − | 0.962590i | \(-0.412658\pi\) | ||||
0.270961 | + | 0.962590i | \(0.412658\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0826631 | 0.00500300 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.36430 | + | 9.36430i | 0.562646 | + | 0.562646i | 0.930058 | − | 0.367412i | \(-0.119756\pi\) |
−0.367412 | + | 0.930058i | \(0.619756\pi\) | |||||||
\(278\) | 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 | \(-0.222228\pi\) |
−0.642801 | + | 0.766033i | \(0.722228\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.41972 | 0.0838035 | ||||||||
\(288\) | 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 | \(-0.0795382\pi\) |
−0.247284 | + | 0.968943i | \(0.579538\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.76829i | − | 0.102606i | ||||||
\(298\) | 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 | ||||||||
\(303\) | −0.856834 | −0.0492238 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.5938 | + | 10.5938i | −0.604619 | + | 0.604619i | −0.941535 | − | 0.336916i | \(-0.890616\pi\) |
0.336916 | + | 0.941535i | \(0.390616\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | 2.56569i | 0.145022i | 0.997368 | + | 0.0725108i | \(0.0231012\pi\) | ||||
−0.997368 | + | 0.0725108i | \(0.976899\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.32418 | + | 7.32418i | −0.411367 | + | 0.411367i | −0.882215 | − | 0.470848i | \(-0.843948\pi\) |
0.470848 | + | 0.882215i | \(0.343948\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | − | 1.39428i | − | 0.0771038i | ||||||
\(328\) | 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 | ||||||||
\(337\) | 12.4540 | 0.678410 | 0.339205 | − | 0.940712i | \(-0.389842\pi\) | ||||
0.339205 | + | 0.940712i | \(0.389842\pi\) | |||||||
\(338\) | 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 | ||||||||
\(343\) | − | 5.20917i | − | 0.281269i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.5107 | + | 17.5107i | 0.940024 | + | 0.940024i | 0.998300 | − | 0.0582766i | \(-0.0185605\pi\) |
−0.0582766 | + | 0.998300i | \(0.518561\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.42042 | − | 8.42042i | 0.450735 | − | 0.450735i | −0.444863 | − | 0.895598i | \(-0.646748\pi\) |
0.895598 | + | 0.444863i | \(0.146748\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.31782 | −0.0703398 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.71293 | 0.516967 | 0.258484 | − | 0.966016i | \(-0.416777\pi\) | ||||
0.258484 | + | 0.966016i | \(0.416777\pi\) | |||||||
\(354\) | 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 | \(0.0572212\pi\) | ||||
−0.983886 | + | 0.178799i | \(0.942779\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | 34.4591 | 1.79875 | 0.899376 | − | 0.437176i | \(-0.144021\pi\) | ||||
0.899376 | + | 0.437176i | \(0.144021\pi\) | |||||||
\(368\) | 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 | \(-0.208488\pi\) |
−0.609148 | + | 0.793057i | \(0.708488\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.01345i | 0.464216i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.4464 | − | 26.4464i | −1.35846 | − | 1.35846i | −0.875817 | − | 0.482644i | \(-0.839677\pi\) |
−0.482644 | − | 0.875817i | \(-0.660323\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.06518 | + | 1.06518i | −0.0545706 | + | 0.0545706i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.8614 | −1.57695 | −0.788473 | − | 0.615069i | \(-0.789128\pi\) | ||||
−0.788473 | + | 0.615069i | \(0.789128\pi\) | |||||||
\(384\) | 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 | 0.905819 | − | 0.423664i | \(-0.139256\pi\) |
−0.423664 | + | 0.905819i | \(0.639256\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.66080i | 0.488568i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 0.444253i | − | 0.0224096i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.8540 | − | 24.8540i | 1.24739 | − | 1.24739i | 0.290518 | − | 0.956870i | \(-0.406172\pi\) |
0.956870 | − | 0.290518i | \(-0.0938276\pi\) | |||||||
\(398\) | 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 | ||||||||
\(407\) | 36.1106i | 1.78993i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 28.2641i | − | 1.39757i | −0.715331 | − | 0.698786i | \(-0.753724\pi\) | ||
0.715331 | − | 0.698786i | \(-0.246276\pi\) | |||||||
\(410\) | 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 | ||||||||
\(417\) | 0.942858 | 0.0461720 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.0355 | + | 23.0355i | −1.12536 | + | 1.12536i | −0.134433 | + | 0.990923i | \(0.542921\pi\) |
−0.990923 | + | 0.134433i | \(0.957079\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | − | 29.0754i | − | 1.41369i | ||||||
\(424\) | 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 | ||||||||
\(433\) | 23.8511 | 1.14621 | 0.573104 | − | 0.819482i | \(-0.305739\pi\) | ||||
0.573104 | + | 0.819482i | \(0.305739\pi\) | |||||||
\(434\) | 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 | \(0.0354617\pi\) | ||||
−0.993801 | + | 0.111176i | \(0.964538\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.5229i | 0.977280i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.74048 | + | 8.74048i | 0.415273 | + | 0.415273i | 0.883571 | − | 0.468298i | \(-0.155133\pi\) |
−0.468298 | + | 0.883571i | \(0.655133\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.27810 | −0.0604520 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.28525 | −0.343812 | −0.171906 | − | 0.985113i | \(-0.554993\pi\) | ||||
−0.171906 | + | 0.985113i | \(0.554993\pi\) | |||||||
\(450\) | 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 | ||||||||
\(457\) | − | 25.2194i | − | 1.17971i | −0.807508 | − | 0.589857i | \(-0.799184\pi\) | ||
0.807508 | − | 0.589857i | \(-0.200816\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 2.77045 | 0.128754 | 0.0643768 | − | 0.997926i | \(-0.479494\pi\) | ||||
0.0643768 | + | 0.997926i | \(0.479494\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.9587 | + | 17.9587i | −0.831031 | + | 0.831031i | −0.987658 | − | 0.156627i | \(-0.949938\pi\) |
0.156627 | + | 0.987658i | \(0.449938\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.364314 | − | 0.364314i | −0.0168225 | − | 0.0168225i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 1.26306i | − | 0.0581986i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 29.4141i | 1.35246i | ||||||||
\(474\) | 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 | \(-0.328543\pi\) | ||||
0.512975 | + | 0.858403i | \(0.328543\pi\) | |||||||
\(480\) | 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 | ||||||||
\(487\) | − | 27.7615i | − | 1.25799i | −0.777408 | − | 0.628997i | \(-0.783466\pi\) | ||
0.777408 | − | 0.628997i | \(-0.216534\pi\) | |||||||
\(488\) | 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 | ||||||||
\(497\) | −3.43638 | −0.154143 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.81950 | − | 1.81950i | 0.0814520 | − | 0.0814520i | −0.665207 | − | 0.746659i | \(-0.731657\pi\) |
0.746659 | + | 0.665207i | \(0.231657\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.500397 | − | 0.500397i | −0.0223561 | − | 0.0223561i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 42.2076i | 1.88195i | 0.338482 | + | 0.940973i | \(0.390087\pi\) | ||||
−0.338482 | + | 0.940973i | \(0.609913\pi\) | |||||||
\(504\) | 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 | −0.999680 | − | 0.0252980i | \(-0.991947\pi\) |
0.0252980 | + | 0.999680i | \(0.491947\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.84461 | −0.125838 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.75491 | 0.0774812 | ||||||||
\(514\) | 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 | \(-0.345732\pi\) |
−0.884840 | + | 0.465895i | \(0.845732\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39.6009 | 1.72504 | ||||||||
\(528\) | 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 | ||||||||
\(537\) | − | 1.03488i | − | 0.0446582i | ||||||
\(538\) | 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 | ||||||||
\(543\) | −1.30590 | −0.0560415 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.6627 | + | 10.6627i | −0.455902 | + | 0.455902i | −0.897308 | − | 0.441406i | \(-0.854480\pi\) |
0.441406 | + | 0.897308i | \(0.354480\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.17933 | + | 2.17933i | 0.0930115 | + | 0.0930115i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 12.0030i | − | 0.511347i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.43780i | 0.188714i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.8060 | + | 22.8060i | −0.966320 | + | 0.966320i | −0.999451 | − | 0.0331307i | \(-0.989452\pi\) |
0.0331307 | + | 0.999451i | \(0.489452\pi\) | |||||||
\(558\) | 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 | −0.716994 | − | 0.697080i | \(-0.754482\pi\) |
0.697080 | + | 0.716994i | \(0.254482\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.35664i | 0.140965i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 3.14792i | − | 0.131967i | −0.997821 | − | 0.0659837i | \(-0.978981\pi\) | ||
0.997821 | − | 0.0659837i | \(-0.0210185\pi\) | |||||||
\(570\) | 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 | ||||||||
\(577\) | −29.0110 | −1.20774 | −0.603872 | − | 0.797081i | \(-0.706376\pi\) | ||||
−0.603872 | + | 0.797081i | \(0.706376\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | − | 14.3762i | − | 0.595403i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.4099 | − | 20.4099i | −0.842408 | − | 0.842408i | 0.146764 | − | 0.989172i | \(-0.453114\pi\) |
−0.989172 | + | 0.146764i | \(0.953114\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.0123 | + | 20.0123i | −0.824592 | + | 0.824592i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.636074 | 0.0261646 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.9098 | −1.18718 | −0.593592 | − | 0.804766i | \(-0.702291\pi\) | ||||
−0.593592 | + | 0.804766i | \(0.702291\pi\) | |||||||
\(594\) | 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 | \(-0.922574\pi\) | ||
0.970563 | − | 0.240848i | \(-0.0774256\pi\) | |||||||
\(600\) | 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 | ||||||||
\(607\) | −25.8393 | −1.04878 | −0.524392 | − | 0.851477i | \(-0.675707\pi\) | ||||
−0.524392 | + | 0.851477i | \(0.675707\pi\) | |||||||
\(608\) | 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 | −0.944006 | − | 0.329929i | \(-0.892975\pi\) |
−0.329929 | − | 0.944006i | \(-0.607025\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 15.0637i | − | 0.606440i | −0.952921 | − | 0.303220i | \(-0.901938\pi\) | ||
0.952921 | − | 0.303220i | \(-0.0980618\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.4975 | + | 10.4975i | 0.421929 | + | 0.421929i | 0.885868 | − | 0.463938i | \(-0.153564\pi\) |
−0.463938 | + | 0.885868i | \(0.653564\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.775933 | − | 0.775933i | 0.0311371 | − | 0.0311371i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.90545 | 0.236597 | ||||||||
\(624\) | 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 | ||||||||
\(633\) | − | 0.309581i | − | 0.0123047i | ||||||
\(634\) | 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 | 0.213857 | − | 0.976865i | \(-0.431397\pi\) |
0.976865 | − | 0.213857i | \(-0.0686027\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 15.7474i | − | 0.619096i | −0.950884 | − | 0.309548i | \(-0.899822\pi\) | ||
0.950884 | − | 0.309548i | \(-0.100178\pi\) | |||||||
\(648\) | 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 | −0.584314 | − | 0.811528i | \(-0.698636\pi\) |
0.811528 | + | 0.584314i | \(0.198636\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.6450 | 0.883465 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.76782 | + | 1.76782i | −0.0688647 | + | 0.0688647i | −0.740700 | − | 0.671836i | \(-0.765506\pi\) |
0.671836 | + | 0.740700i | \(0.265506\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | − | 1.02253i | − | 0.0397119i | ||||||
\(664\) | 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 | ||||||||
\(673\) | −14.1113 | −0.543950 | −0.271975 | − | 0.962304i | \(-0.587677\pi\) | ||||
−0.271975 | + | 0.962304i | \(0.587677\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.31191 | − | 8.31191i | −0.319453 | − | 0.319453i | 0.529104 | − | 0.848557i | \(-0.322528\pi\) |
−0.848557 | + | 0.529104i | \(0.822528\pi\) | |||||||
\(678\) | 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 | 0.986348 | + | 0.164673i | \(0.0526570\pi\) |
0.164673 | + | 0.986348i | \(0.447343\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.25834 | −0.0480086 | ||||||||
\(688\) | 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 | ||||||||
\(697\) | − | 17.5618i | − | 0.665200i | ||||||
\(698\) | 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 | ||||||||
\(703\) | −35.8375 | −1.35164 | ||||||||
\(704\) | 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 | 0.613890 | − | 0.789392i | \(-0.289604\pi\) |
−0.789392 | + | 0.613890i | \(0.789604\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 35.3279i | − | 1.32490i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.6968i | 0.662752i | ||||||||
\(714\) | 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 | \(-0.355392\pi\) | ||||
0.438833 | + | 0.898568i | \(0.355392\pi\) | |||||||
\(720\) | 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 | ||||||||
\(727\) | − | 16.6692i | − | 0.618226i | −0.951025 | − | 0.309113i | \(-0.899968\pi\) | ||
0.951025 | − | 0.309113i | \(-0.100032\pi\) | |||||||
\(728\) | 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 | 0.0146760 | − | 0.999892i | \(-0.495328\pi\) |
0.999892 | − | 0.0146760i | \(-0.00467168\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.58945 | −0.169055 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.7939 | + | 22.7939i | −0.838486 | + | 0.838486i | −0.988660 | − | 0.150174i | \(-0.952017\pi\) |
0.150174 | + | 0.988660i | \(0.452017\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.516736 | + | 0.516736i | 0.0189828 | + | 0.0189828i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 16.4964i | − | 0.605196i | −0.953118 | − | 0.302598i | \(-0.902146\pi\) | ||
0.953118 | − | 0.302598i | \(-0.0978539\pi\) | |||||||
\(744\) | 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 | ||||||||
\(753\) | 1.14411 | 0.0416937 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.73819 | − | 1.73819i | −0.0631757 | − | 0.0631757i | 0.674813 | − | 0.737989i | \(-0.264224\pi\) |
−0.737989 | + | 0.674813i | \(0.764224\pi\) | |||||||
\(758\) | 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 | ||||||||
\(767\) | −28.6423 | −1.03421 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.4731 | 0.557976 | 0.278988 | − | 0.960295i | \(-0.410001\pi\) | ||||
0.278988 | + | 0.960295i | \(0.410001\pi\) | |||||||
\(770\) | 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 | \(-0.203705\pi\) |
−0.597161 | + | 0.802121i | \(0.703705\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.357284i | 0.0128175i | ||||||||
\(778\) | 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 | ||||||||
\(783\) | 1.90770 | 0.0681757 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.1351 | + | 18.1351i | −0.646448 | + | 0.646448i | −0.952133 | − | 0.305685i | \(-0.901115\pi\) |
0.305685 | + | 0.952133i | \(0.401115\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.653736 | + | 0.653736i | 0.0232736 | + | 0.0232736i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.53419i | 0.0545495i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.57016i | 0.0912690i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.51575 | − | 4.51575i | 0.159956 | − | 0.159956i | −0.622591 | − | 0.782547i | \(-0.713920\pi\) |
0.782547 | + | 0.622591i | \(0.213920\pi\) | |||||||
\(798\) | 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 | ||||||||
\(807\) | 1.05526i | 0.0371470i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 3.33368i | − | 0.117206i | −0.998281 | − | 0.0586030i | \(-0.981335\pi\) | ||
0.998281 | − | 0.0586030i | \(-0.0186646\pi\) | |||||||
\(810\) | 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 | ||||||||
\(817\) | −29.1916 | −1.02129 | ||||||||
\(818\) | 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 | ||||||||
\(823\) | 16.8858i | 0.588603i | 0.955713 | + | 0.294301i | \(0.0950870\pi\) | ||||
−0.955713 | + | 0.294301i | \(0.904913\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.5765 | − | 11.5765i | −0.402556 | − | 0.402556i | 0.476577 | − | 0.879133i | \(-0.341877\pi\) |
−0.879133 | + | 0.476577i | \(0.841877\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.97296 | − | 5.97296i | 0.207449 | − | 0.207449i | −0.595733 | − | 0.803182i | \(-0.703138\pi\) |
0.803182 | + | 0.595733i | \(0.203138\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.16718 | 0.0404891 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −31.8900 | −1.10492 | ||||||||
\(834\) | 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 | \(0.156172\pi\) | ||||
−0.882037 | + | 0.471181i | \(0.843828\pi\) | |||||||
\(840\) | 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 | ||||||||
\(847\) | 0.0791757 | 0.00272051 | ||||||||
\(848\) | 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 | \(-0.499027\pi\) |
−0.999995 | + | 0.00305738i | \(0.999027\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 22.0170i | − | 0.752087i | −0.926602 | − | 0.376044i | \(-0.877284\pi\) | ||
0.926602 | − | 0.376044i | \(-0.122716\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.8910 | − | 16.8910i | −0.576312 | − | 0.576312i | 0.357573 | − | 0.933885i | \(-0.383604\pi\) |
−0.933885 | + | 0.357573i | \(0.883604\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0884782 | − | 0.0884782i | 0.00301533 | − | 0.00301533i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.2073 | −1.57292 | −0.786458 | − | 0.617644i | \(-0.788087\pi\) | ||||
−0.786458 | + | 0.617644i | \(0.788087\pi\) | |||||||
\(864\) | 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 | ||||||||
\(873\) | − | 11.5506i | − | 0.390929i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.6380 | + | 21.6380i | −0.730664 | + | 0.730664i | −0.970751 | − | 0.240087i | \(-0.922824\pi\) |
0.240087 | + | 0.970751i | \(0.422824\pi\) | |||||||
\(878\) | 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 | −0.937959 | − | 0.346746i | \(-0.887287\pi\) |
0.346746 | + | 0.937959i | \(0.387287\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.2454i | 1.72065i | 0.509744 | + | 0.860326i | \(0.329740\pi\) | ||||
−0.509744 | + | 0.860326i | \(0.670260\pi\) | |||||||
\(888\) | 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 | ||||||||
\(897\) | 0.456949 | 0.0152571 | ||||||||
\(898\) | 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 | ||||||||
\(903\) | 0.291028i | 0.00968479i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.6745 | − | 29.6745i | −0.985324 | − | 0.985324i | 0.0145695 | − | 0.999894i | \(-0.495362\pi\) |
−0.999894 | + | 0.0145695i | \(0.995362\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | 50.3785 | 1.66729 | ||||||||
\(914\) | 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 | \(0.0833429\pi\) | ||||
−0.965918 | + | 0.258848i | \(0.916657\pi\) | |||||||
\(920\) | 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 | ||||||||
\(927\) | −3.45326 | −0.113420 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.00598 | 0.197050 | 0.0985249 | − | 0.995135i | \(-0.468588\pi\) | ||||
0.0985249 | + | 0.995135i | \(0.468588\pi\) | |||||||
\(930\) | 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 | ||||||||
\(937\) | 4.83037i | 0.157801i | 0.996882 | + | 0.0789006i | \(0.0251410\pi\) | ||||
−0.996882 | + | 0.0789006i | \(0.974859\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | 7.84801 | 0.255566 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.7720 | + | 34.7720i | −1.12994 | + | 1.12994i | −0.139751 | + | 0.990187i | \(0.544630\pi\) |
−0.990187 | + | 0.139751i | \(0.955370\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.3530 | + | 13.3530i | 0.433457 | + | 0.433457i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.912899i | 0.0296028i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.89827i | − | 0.0614910i | −0.999527 | − | 0.0307455i | \(-0.990212\pi\) | ||
0.999527 | − | 0.0307455i | \(-0.00978813\pi\) | |||||||
\(954\) | 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 | ||||||||
\(967\) | − | 61.5753i | − | 1.98013i | −0.140616 | − | 0.990064i | \(-0.544908\pi\) | ||
0.140616 | − | 0.990064i | \(-0.455092\pi\) | |||||||
\(968\) | 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 | ||||||||
\(977\) | −25.3240 | −0.810186 | −0.405093 | − | 0.914276i | \(-0.632761\pi\) | ||||
−0.405093 | + | 0.914276i | \(0.632761\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | 5.01686i | 0.160013i | 0.996794 | + | 0.0800065i | \(0.0254941\pi\) | ||||
−0.996794 | + | 0.0800065i | \(0.974506\pi\) | |||||||
\(984\) | 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 | ||||||||
\(993\) | −0.520569 | −0.0165198 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.23850 | + | 1.23850i | 0.0392235 | + | 0.0392235i | 0.726447 | − | 0.687223i | \(-0.241170\pi\) |
−0.687223 | + | 0.726447i | \(0.741170\pi\) | |||||||
\(998\) | 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.l.g.1201.3 | 12 | ||
4.3 | odd | 2 | 400.2.l.f.101.5 | ✓ | 12 | ||
5.2 | odd | 4 | 1600.2.q.e.49.4 | 12 | |||
5.3 | odd | 4 | 1600.2.q.f.49.3 | 12 | |||
5.4 | even | 2 | 1600.2.l.f.1201.4 | 12 | |||
16.3 | odd | 4 | 400.2.l.f.301.5 | yes | 12 | ||
16.13 | even | 4 | inner | 1600.2.l.g.401.3 | 12 | ||
20.3 | even | 4 | 400.2.q.f.149.6 | 12 | |||
20.7 | even | 4 | 400.2.q.e.149.1 | 12 | |||
20.19 | odd | 2 | 400.2.l.g.101.2 | yes | 12 | ||
80.3 | even | 4 | 400.2.q.e.349.1 | 12 | |||
80.13 | odd | 4 | 1600.2.q.e.849.4 | 12 | |||
80.19 | odd | 4 | 400.2.l.g.301.2 | yes | 12 | ||
80.29 | even | 4 | 1600.2.l.f.401.4 | 12 | |||
80.67 | even | 4 | 400.2.q.f.349.6 | 12 | |||
80.77 | odd | 4 | 1600.2.q.f.849.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.5 | ✓ | 12 | 4.3 | odd | 2 | ||
400.2.l.f.301.5 | yes | 12 | 16.3 | odd | 4 | ||
400.2.l.g.101.2 | yes | 12 | 20.19 | odd | 2 | ||
400.2.l.g.301.2 | yes | 12 | 80.19 | odd | 4 | ||
400.2.q.e.149.1 | 12 | 20.7 | even | 4 | |||
400.2.q.e.349.1 | 12 | 80.3 | even | 4 | |||
400.2.q.f.149.6 | 12 | 20.3 | even | 4 | |||
400.2.q.f.349.6 | 12 | 80.67 | even | 4 | |||
1600.2.l.f.401.4 | 12 | 80.29 | even | 4 | |||
1600.2.l.f.1201.4 | 12 | 5.4 | even | 2 | |||
1600.2.l.g.401.3 | 12 | 16.13 | even | 4 | inner | ||
1600.2.l.g.1201.3 | 12 | 1.1 | even | 1 | trivial | ||
1600.2.q.e.49.4 | 12 | 5.2 | odd | 4 | |||
1600.2.q.e.849.4 | 12 | 80.13 | odd | 4 | |||
1600.2.q.f.49.3 | 12 | 5.3 | odd | 4 | |||
1600.2.q.f.849.3 | 12 | 80.77 | odd | 4 |