Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,6,Mod(18,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.18");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.c (of order \(3\), 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: | \(7.85880717084\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.54095201243136.19 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 102x^{6} + 320x^{5} + 4283x^{4} - 9104x^{3} - 85298x^{2} + 89904x + 714364 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 18.2 | ||
Root | \(-5.52218 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.18 |
Dual form | 49.6.c.h.30.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.40754 | − | 2.43792i | −0.248820 | − | 0.430968i | 0.714379 | − | 0.699759i | \(-0.246709\pi\) |
−0.963199 | + | 0.268791i | \(0.913376\pi\) | |||||||
\(3\) | 3.27401 | − | 5.67075i | 0.210028 | − | 0.363779i | −0.741695 | − | 0.670737i | \(-0.765978\pi\) |
0.951723 | + | 0.306958i | \(0.0993113\pi\) | |||||||
\(4\) | 12.0377 | − | 20.8499i | 0.376178 | − | 0.651559i | ||||
\(5\) | −22.9955 | − | 39.8294i | −0.411356 | − | 0.712490i | 0.583682 | − | 0.811982i | \(-0.301612\pi\) |
−0.995038 | + | 0.0994921i | \(0.968278\pi\) | |||||||
\(6\) | −18.4331 | −0.209036 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −157.856 | −0.872041 | ||||||||
\(9\) | 100.062 | + | 173.312i | 0.411777 | + | 0.713218i | ||||
\(10\) | −64.7341 | + | 112.123i | −0.204707 | + | 0.354563i | ||||
\(11\) | 275.890 | − | 477.856i | 0.687472 | − | 1.19074i | −0.285181 | − | 0.958474i | \(-0.592054\pi\) |
0.972653 | − | 0.232263i | \(-0.0746129\pi\) | |||||||
\(12\) | −78.8229 | − | 136.525i | −0.158015 | − | 0.273691i | ||||
\(13\) | −1094.10 | −1.79555 | −0.897776 | − | 0.440453i | \(-0.854818\pi\) | ||||
−0.897776 | + | 0.440453i | \(0.854818\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −301.150 | −0.345585 | ||||||||
\(16\) | −163.017 | − | 282.354i | −0.159197 | − | 0.275737i | ||||
\(17\) | −590.357 | + | 1022.53i | −0.495442 | + | 0.858130i | −0.999986 | − | 0.00525555i | \(-0.998327\pi\) |
0.504545 | + | 0.863386i | \(0.331660\pi\) | |||||||
\(18\) | 281.681 | − | 487.886i | 0.204916 | − | 0.354925i | ||||
\(19\) | −583.063 | − | 1009.89i | −0.370537 | − | 0.641789i | 0.619111 | − | 0.785303i | \(-0.287493\pi\) |
−0.989648 | + | 0.143514i | \(0.954160\pi\) | |||||||
\(20\) | −1107.25 | −0.618972 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1553.30 | −0.684226 | ||||||||
\(23\) | −22.1925 | − | 38.4386i | −0.00874757 | − | 0.0151512i | 0.861618 | − | 0.507556i | \(-0.169451\pi\) |
−0.870366 | + | 0.492405i | \(0.836118\pi\) | |||||||
\(24\) | −516.823 | + | 895.163i | −0.183153 | + | 0.317230i | ||||
\(25\) | 504.912 | − | 874.533i | 0.161572 | − | 0.279850i | ||||
\(26\) | 1539.98 | + | 2667.33i | 0.446768 | + | 0.773826i | ||||
\(27\) | 2901.58 | 0.765993 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3329.02 | 0.735057 | 0.367529 | − | 0.930012i | \(-0.380204\pi\) | ||||
0.367529 | + | 0.930012i | \(0.380204\pi\) | |||||||
\(30\) | 423.880 | + | 734.181i | 0.0859883 | + | 0.148936i | ||||
\(31\) | 4392.01 | − | 7607.18i | 0.820841 | − | 1.42174i | −0.0842165 | − | 0.996447i | \(-0.526839\pi\) |
0.905057 | − | 0.425290i | \(-0.139828\pi\) | |||||||
\(32\) | −2984.61 | + | 5169.49i | −0.515243 | + | 0.892427i | ||||
\(33\) | −1806.53 | − | 3129.01i | −0.288776 | − | 0.500175i | ||||
\(34\) | 3323.80 | 0.493102 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4818.05 | 0.619605 | ||||||||
\(37\) | 1278.56 | + | 2214.53i | 0.153539 | + | 0.265937i | 0.932526 | − | 0.361103i | \(-0.117600\pi\) |
−0.778987 | + | 0.627040i | \(0.784266\pi\) | |||||||
\(38\) | −1641.37 | + | 2842.93i | −0.184394 | + | 0.319379i | ||||
\(39\) | −3582.08 | + | 6204.35i | −0.377115 | + | 0.653183i | ||||
\(40\) | 3629.99 | + | 6287.32i | 0.358720 | + | 0.621321i | ||||
\(41\) | 12761.3 | 1.18559 | 0.592794 | − | 0.805354i | \(-0.298025\pi\) | ||||
0.592794 | + | 0.805354i | \(0.298025\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −96.7714 | −0.00798135 | −0.00399067 | − | 0.999992i | \(-0.501270\pi\) | ||||
−0.00399067 | + | 0.999992i | \(0.501270\pi\) | |||||||
\(44\) | −6642.16 | − | 11504.6i | −0.517223 | − | 0.895857i | ||||
\(45\) | 4601.94 | − | 7970.80i | 0.338774 | − | 0.586774i | ||||
\(46\) | −62.4736 | + | 108.207i | −0.00435313 | + | 0.00753985i | ||||
\(47\) | 3839.58 | + | 6650.34i | 0.253535 | + | 0.439136i | 0.964497 | − | 0.264095i | \(-0.0850732\pi\) |
−0.710961 | + | 0.703231i | \(0.751740\pi\) | |||||||
\(48\) | −2134.88 | −0.133743 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2842.73 | −0.160809 | ||||||||
\(51\) | 3865.67 | + | 6695.53i | 0.208113 | + | 0.360462i | ||||
\(52\) | −13170.4 | + | 22811.8i | −0.675446 | + | 1.16991i | ||||
\(53\) | 5976.67 | − | 10351.9i | 0.292260 | − | 0.506209i | −0.682084 | − | 0.731274i | \(-0.738926\pi\) |
0.974344 | + | 0.225065i | \(0.0722594\pi\) | |||||||
\(54\) | −4084.08 | − | 7073.83i | −0.190594 | − | 0.330119i | ||||
\(55\) | −25377.0 | −1.13118 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7635.81 | −0.311292 | ||||||||
\(58\) | −4685.71 | − | 8115.89i | −0.182897 | − | 0.316786i | ||||
\(59\) | 4928.62 | − | 8536.62i | 0.184330 | − | 0.319268i | −0.759021 | − | 0.651066i | \(-0.774322\pi\) |
0.943350 | + | 0.331798i | \(0.107655\pi\) | |||||||
\(60\) | −3625.15 | + | 6278.94i | −0.130001 | + | 0.225169i | ||||
\(61\) | −19258.9 | − | 33357.5i | −0.662686 | − | 1.14781i | −0.979907 | − | 0.199454i | \(-0.936083\pi\) |
0.317221 | − | 0.948352i | \(-0.397250\pi\) | |||||||
\(62\) | −24727.6 | −0.816965 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6370.65 | 0.194417 | ||||||||
\(65\) | 25159.4 | + | 43577.3i | 0.738612 | + | 1.27931i | ||||
\(66\) | −5085.53 | + | 8808.39i | −0.143706 | + | 0.248907i | ||||
\(67\) | 33774.5 | − | 58499.1i | 0.919182 | − | 1.59207i | 0.118521 | − | 0.992952i | \(-0.462185\pi\) |
0.800661 | − | 0.599118i | \(-0.204482\pi\) | |||||||
\(68\) | 14213.1 | + | 24617.7i | 0.372748 | + | 0.645619i | ||||
\(69\) | −290.634 | −0.00734893 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −61374.6 | −1.44492 | −0.722458 | − | 0.691415i | \(-0.756988\pi\) | ||||
−0.722458 | + | 0.691415i | \(0.756988\pi\) | |||||||
\(72\) | −15795.4 | − | 27358.4i | −0.359086 | − | 0.621955i | ||||
\(73\) | 925.199 | − | 1602.49i | 0.0203202 | − | 0.0351956i | −0.855686 | − | 0.517495i | \(-0.826865\pi\) |
0.876007 | + | 0.482299i | \(0.160198\pi\) | |||||||
\(74\) | 3599.24 | − | 6234.07i | 0.0764068 | − | 0.132340i | ||||
\(75\) | −3306.17 | − | 5726.45i | −0.0678691 | − | 0.117553i | ||||
\(76\) | −28074.9 | −0.557551 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 20167.7 | 0.375335 | ||||||||
\(79\) | 4.26456 | + | 7.38644i | 7.68788e−5 | + | 0.000133158i | 0.866064 | − | 0.499933i | \(-0.166642\pi\) |
−0.865987 | + | 0.500067i | \(0.833309\pi\) | |||||||
\(80\) | −7497.34 | + | 12985.8i | −0.130973 | + | 0.226852i | ||||
\(81\) | −14815.2 | + | 25660.7i | −0.250897 | + | 0.434566i | ||||
\(82\) | −17961.9 | − | 31111.0i | −0.294998 | − | 0.510951i | ||||
\(83\) | 95039.3 | 1.51429 | 0.757143 | − | 0.653249i | \(-0.226595\pi\) | ||||
0.757143 | + | 0.653249i | \(0.226595\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 54302.3 | 0.815212 | ||||||||
\(86\) | 136.209 | + | 235.921i | 0.00198592 | + | 0.00343971i | ||||
\(87\) | 10899.2 | − | 18878.0i | 0.154382 | − | 0.267398i | ||||
\(88\) | −43551.0 | + | 75432.6i | −0.599503 | + | 1.03837i | ||||
\(89\) | 26802.8 | + | 46423.8i | 0.358678 | + | 0.621249i | 0.987740 | − | 0.156106i | \(-0.0498942\pi\) |
−0.629062 | + | 0.777355i | \(0.716561\pi\) | |||||||
\(90\) | −25909.6 | −0.337175 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1068.59 | −0.0131626 | ||||||||
\(93\) | −28758.9 | − | 49811.9i | −0.344798 | − | 0.597208i | ||||
\(94\) | 10808.7 | − | 18721.2i | 0.126169 | − | 0.218531i | ||||
\(95\) | −26815.7 | + | 46446.1i | −0.304846 | + | 0.528008i | ||||
\(96\) | 19543.2 | + | 33849.9i | 0.216431 | + | 0.374869i | ||||
\(97\) | −3110.79 | −0.0335693 | −0.0167846 | − | 0.999859i | \(-0.505343\pi\) | ||||
−0.0167846 | + | 0.999859i | \(0.505343\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 110424. | 1.13234 | ||||||||
\(100\) | −12155.9 | − | 21054.7i | −0.121559 | − | 0.210547i | ||||
\(101\) | 10918.0 | − | 18910.4i | 0.106497 | − | 0.184458i | −0.807852 | − | 0.589386i | \(-0.799370\pi\) |
0.914349 | + | 0.404927i | \(0.132703\pi\) | |||||||
\(102\) | 10882.1 | − | 18848.4i | 0.103565 | − | 0.179380i | ||||
\(103\) | 32670.7 | + | 56587.3i | 0.303435 | + | 0.525565i | 0.976912 | − | 0.213644i | \(-0.0685332\pi\) |
−0.673477 | + | 0.739208i | \(0.735200\pi\) | |||||||
\(104\) | 172710. | 1.56579 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −33649.5 | −0.290880 | ||||||||
\(107\) | 54478.7 | + | 94359.8i | 0.460010 | + | 0.796760i | 0.998961 | − | 0.0455767i | \(-0.0145125\pi\) |
−0.538951 | + | 0.842337i | \(0.681179\pi\) | |||||||
\(108\) | 34928.3 | − | 60497.6i | 0.288150 | − | 0.499090i | ||||
\(109\) | −43364.3 | + | 75109.2i | −0.349596 | + | 0.605518i | −0.986178 | − | 0.165691i | \(-0.947014\pi\) |
0.636582 | + | 0.771209i | \(0.280348\pi\) | |||||||
\(110\) | 35719.0 | + | 61867.2i | 0.281461 | + | 0.487504i | ||||
\(111\) | 16744.1 | 0.128989 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −101496. | −0.747746 | −0.373873 | − | 0.927480i | \(-0.621970\pi\) | ||||
−0.373873 | + | 0.927480i | \(0.621970\pi\) | |||||||
\(114\) | 10747.7 | + | 18615.5i | 0.0774556 | + | 0.134157i | ||||
\(115\) | −1020.66 | + | 1767.83i | −0.00719674 | + | 0.0124651i | ||||
\(116\) | 40073.7 | − | 69409.6i | 0.276512 | − | 0.478933i | ||||
\(117\) | −109477. | − | 189620.i | −0.739366 | − | 1.28062i | ||||
\(118\) | −27748.9 | −0.183459 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 47538.4 | 0.301364 | ||||||||
\(121\) | −71705.6 | − | 124198.i | −0.445235 | − | 0.771170i | ||||
\(122\) | −54215.3 | + | 93903.7i | −0.329779 | + | 0.571193i | ||||
\(123\) | 41780.5 | − | 72365.9i | 0.249006 | − | 0.431292i | ||||
\(124\) | −105739. | − | 183146.i | −0.617564 | − | 1.06965i | ||||
\(125\) | −190165. | −1.08857 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3094.61 | −0.0170253 | −0.00851267 | − | 0.999964i | \(-0.502710\pi\) | ||||
−0.00851267 | + | 0.999964i | \(0.502710\pi\) | |||||||
\(128\) | 86540.5 | + | 149892.i | 0.466868 | + | 0.808639i | ||||
\(129\) | −316.830 | + | 548.766i | −0.00167630 | + | 0.00290344i | ||||
\(130\) | 70825.4 | − | 122673.i | 0.367562 | − | 0.636636i | ||||
\(131\) | 126715. | + | 219478.i | 0.645136 | + | 1.11741i | 0.984270 | + | 0.176671i | \(0.0565328\pi\) |
−0.339134 | + | 0.940738i | \(0.610134\pi\) | |||||||
\(132\) | −86986.0 | −0.434525 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −190155. | −0.914842 | ||||||||
\(135\) | −66723.3 | − | 115568.i | −0.315096 | − | 0.545763i | ||||
\(136\) | 93191.6 | − | 161413.i | 0.432045 | − | 0.748324i | ||||
\(137\) | 48576.4 | − | 84136.9i | 0.221118 | − | 0.382988i | −0.734030 | − | 0.679117i | \(-0.762363\pi\) |
0.955148 | + | 0.296130i | \(0.0956960\pi\) | |||||||
\(138\) | 409.078 | + | 708.544i | 0.00182856 | + | 0.00316715i | ||||
\(139\) | −210308. | −0.923249 | −0.461624 | − | 0.887076i | \(-0.652733\pi\) | ||||
−0.461624 | + | 0.887076i | \(0.652733\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 50283.2 | 0.212998 | ||||||||
\(142\) | 86387.0 | + | 149627.i | 0.359524 | + | 0.622713i | ||||
\(143\) | −301851. | + | 522822.i | −1.23439 | + | 2.13803i | ||||
\(144\) | 32623.6 | − | 56505.8i | 0.131107 | − | 0.227084i | ||||
\(145\) | −76552.5 | − | 132593.i | −0.302370 | − | 0.523721i | ||||
\(146\) | −5209.01 | −0.0202243 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 61563.7 | 0.231031 | ||||||||
\(149\) | −70203.2 | − | 121595.i | −0.259055 | − | 0.448696i | 0.706934 | − | 0.707279i | \(-0.250078\pi\) |
−0.965989 | + | 0.258584i | \(0.916744\pi\) | |||||||
\(150\) | −9307.11 | + | 16120.4i | −0.0337743 | + | 0.0584988i | ||||
\(151\) | −59847.9 | + | 103660.i | −0.213603 | + | 0.369971i | −0.952839 | − | 0.303475i | \(-0.901853\pi\) |
0.739237 | + | 0.673446i | \(0.235186\pi\) | |||||||
\(152\) | 92040.1 | + | 159418.i | 0.323123 | + | 0.559666i | ||||
\(153\) | −236289. | −0.816045 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −403986. | −1.35063 | ||||||||
\(156\) | 86240.0 | + | 149372.i | 0.283725 | + | 0.491426i | ||||
\(157\) | 48808.4 | − | 84538.7i | 0.158032 | − | 0.273720i | −0.776127 | − | 0.630577i | \(-0.782818\pi\) |
0.934159 | + | 0.356857i | \(0.116152\pi\) | |||||||
\(158\) | 12.0051 | − | 20.7934i | 3.82579e−5 | − | 6.62647e-5i | ||||
\(159\) | −39135.3 | − | 67784.3i | −0.122765 | − | 0.212636i | ||||
\(160\) | 274530. | 0.847794 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 83411.8 | 0.249712 | ||||||||
\(163\) | −91339.0 | − | 158204.i | −0.269270 | − | 0.466389i | 0.699404 | − | 0.714727i | \(-0.253449\pi\) |
−0.968673 | + | 0.248338i | \(0.920116\pi\) | |||||||
\(164\) | 153616. | − | 266071.i | 0.445992 | − | 0.772481i | ||||
\(165\) | −83084.4 | + | 143906.i | −0.237580 | + | 0.411501i | ||||
\(166\) | −133771. | − | 231699.i | −0.376784 | − | 0.652609i | ||||
\(167\) | 451674. | 1.25324 | 0.626619 | − | 0.779326i | \(-0.284438\pi\) | ||||
0.626619 | + | 0.779326i | \(0.284438\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 825757. | 2.22400 | ||||||||
\(170\) | −76432.5 | − | 132385.i | −0.202841 | − | 0.351331i | ||||
\(171\) | 116685. | − | 202104.i | 0.305157 | − | 0.528547i | ||||
\(172\) | −1164.90 | + | 2017.67i | −0.00300240 | + | 0.00520031i | ||||
\(173\) | 185824. | + | 321856.i | 0.472047 | + | 0.817610i | 0.999488 | − | 0.0319815i | \(-0.0101818\pi\) |
−0.527441 | + | 0.849592i | \(0.676848\pi\) | |||||||
\(174\) | −61364.2 | −0.153653 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −179900. | −0.437773 | ||||||||
\(177\) | −32272.7 | − | 55897.9i | −0.0774287 | − | 0.134110i | ||||
\(178\) | 75451.8 | − | 130686.i | 0.178492 | − | 0.309158i | ||||
\(179\) | −42501.7 | + | 73615.1i | −0.0991457 | + | 0.171725i | −0.911331 | − | 0.411674i | \(-0.864944\pi\) |
0.812186 | + | 0.583399i | \(0.198278\pi\) | |||||||
\(180\) | −110794. | − | 191900.i | −0.254878 | − | 0.441462i | ||||
\(181\) | 379442. | 0.860892 | 0.430446 | − | 0.902616i | \(-0.358356\pi\) | ||||
0.430446 | + | 0.902616i | \(0.358356\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −252216. | −0.556730 | ||||||||
\(184\) | 3503.23 | + | 6067.77i | 0.00762824 | + | 0.0132125i | ||||
\(185\) | 58802.4 | − | 101849.i | 0.126318 | − | 0.218789i | ||||
\(186\) | −80958.5 | + | 140224.i | −0.171585 | + | 0.297194i | ||||
\(187\) | 325748. | + | 564212.i | 0.681204 | + | 1.17988i | ||||
\(188\) | 184878. | 0.381497 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 150976. | 0.303406 | ||||||||
\(191\) | 461098. | + | 798645.i | 0.914555 | + | 1.58406i | 0.807552 | + | 0.589796i | \(0.200792\pi\) |
0.107003 | + | 0.994259i | \(0.465875\pi\) | |||||||
\(192\) | 20857.6 | − | 36126.4i | 0.0408329 | − | 0.0707247i | ||||
\(193\) | −252553. | + | 437435.i | −0.488045 | + | 0.845319i | −0.999905 | − | 0.0137498i | \(-0.995623\pi\) |
0.511860 | + | 0.859069i | \(0.328956\pi\) | |||||||
\(194\) | 4378.55 | + | 7583.88i | 0.00835269 | + | 0.0144673i | ||||
\(195\) | 329488. | 0.620516 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 251505. | 0.461723 | 0.230861 | − | 0.972987i | \(-0.425846\pi\) | ||||
0.230861 | + | 0.972987i | \(0.425846\pi\) | |||||||
\(198\) | −155426. | − | 269206.i | −0.281748 | − | 0.488002i | ||||
\(199\) | −104017. | + | 180162.i | −0.186196 | + | 0.322501i | −0.943979 | − | 0.330006i | \(-0.892949\pi\) |
0.757783 | + | 0.652507i | \(0.226283\pi\) | |||||||
\(200\) | −79703.5 | + | 138050.i | −0.140897 | + | 0.244041i | ||||
\(201\) | −221156. | − | 383053.i | −0.386107 | − | 0.668757i | ||||
\(202\) | −61469.7 | −0.105994 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 186135. | 0.313150 | ||||||||
\(205\) | −293452. | − | 508274.i | −0.487700 | − | 0.844720i | ||||
\(206\) | 91970.5 | − | 159297.i | 0.151001 | − | 0.261542i | ||||
\(207\) | 4441.25 | − | 7692.47i | 0.00720409 | − | 0.0124779i | ||||
\(208\) | 178357. | + | 308923.i | 0.285846 | + | 0.495100i | ||||
\(209\) | −643446. | −1.01893 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −640577. | −0.990525 | −0.495262 | − | 0.868744i | \(-0.664928\pi\) | ||||
−0.495262 | + | 0.868744i | \(0.664928\pi\) | |||||||
\(212\) | −143890. | − | 249225.i | −0.219883 | − | 0.380849i | ||||
\(213\) | −200941. | + | 348040.i | −0.303472 | + | 0.525630i | ||||
\(214\) | 153361. | − | 265630.i | 0.228919 | − | 0.396499i | ||||
\(215\) | 2225.31 | + | 3854.35i | 0.00328318 | + | 0.00568663i | ||||
\(216\) | −458032. | −0.667977 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 244148. | 0.347945 | ||||||||
\(219\) | −6058.22 | − | 10493.1i | −0.00853561 | − | 0.0147841i | ||||
\(220\) | −305480. | + | 529107.i | −0.425526 | + | 0.737033i | ||||
\(221\) | 645909. | − | 1.11875e6i | 0.889591 | − | 1.54082i | ||||
\(222\) | −23567.9 | − | 40820.8i | −0.0320951 | − | 0.0555903i | ||||
\(223\) | −390135. | −0.525354 | −0.262677 | − | 0.964884i | \(-0.584605\pi\) | ||||
−0.262677 | + | 0.964884i | \(0.584605\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 202089. | 0.266126 | ||||||||
\(226\) | 142860. | + | 247440.i | 0.186054 | + | 0.322255i | ||||
\(227\) | 145676. | − | 252319.i | 0.187639 | − | 0.325001i | −0.756823 | − | 0.653620i | \(-0.773250\pi\) |
0.944463 | + | 0.328618i | \(0.106583\pi\) | |||||||
\(228\) | −91917.5 | + | 159206.i | −0.117101 | + | 0.202825i | ||||
\(229\) | −615202. | − | 1.06556e6i | −0.775227 | − | 1.34273i | −0.934667 | − | 0.355526i | \(-0.884302\pi\) |
0.159439 | − | 0.987208i | \(-0.449031\pi\) | |||||||
\(230\) | 5746.45 | 0.00716276 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −525506. | −0.641000 | ||||||||
\(233\) | −57139.3 | − | 98968.1i | −0.0689517 | − | 0.119428i | 0.829488 | − | 0.558524i | \(-0.188632\pi\) |
−0.898440 | + | 0.439096i | \(0.855299\pi\) | |||||||
\(234\) | −308187. | + | 533795.i | −0.367938 | + | 0.637287i | ||||
\(235\) | 176586. | − | 305856.i | 0.208587 | − | 0.361283i | ||||
\(236\) | −118658. | − | 205522.i | −0.138681 | − | 0.240203i | ||||
\(237\) | 55.8489 | 6.45867e−5 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.14782e6 | −1.29981 | −0.649906 | − | 0.760014i | \(-0.725192\pi\) | ||||
−0.649906 | + | 0.760014i | \(0.725192\pi\) | |||||||
\(240\) | 49092.7 | + | 85031.1i | 0.0550160 | + | 0.0952905i | ||||
\(241\) | 406354. | − | 703825.i | 0.450673 | − | 0.780589i | −0.547755 | − | 0.836639i | \(-0.684517\pi\) |
0.998428 | + | 0.0560501i | \(0.0178507\pi\) | |||||||
\(242\) | −201856. | + | 349626.i | −0.221567 | + | 0.383764i | ||||
\(243\) | 449552. | + | 778647.i | 0.488387 | + | 0.845912i | ||||
\(244\) | −927332. | −0.997150 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −235230. | −0.247831 | ||||||||
\(247\) | 637928. | + | 1.10492e6i | 0.665318 | + | 1.15236i | ||||
\(248\) | −693306. | + | 1.20084e6i | −0.715806 | + | 1.23981i | ||||
\(249\) | 311159. | − | 538944.i | 0.318042 | − | 0.550865i | ||||
\(250\) | 267664. | + | 463608.i | 0.270857 | + | 0.469138i | ||||
\(251\) | 406772. | 0.407537 | 0.203768 | − | 0.979019i | \(-0.434681\pi\) | ||||
0.203768 | + | 0.979019i | \(0.434681\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24490.8 | −0.0240548 | ||||||||
\(254\) | 4355.77 | + | 7544.41i | 0.00423624 | + | 0.00733738i | ||||
\(255\) | 177786. | − | 307935.i | 0.171217 | − | 0.296557i | ||||
\(256\) | 345548. | − | 598507.i | 0.329540 | − | 0.570781i | ||||
\(257\) | −848562. | − | 1.46975e6i | −0.801403 | − | 1.38807i | −0.918693 | − | 0.394973i | \(-0.870754\pi\) |
0.117290 | − | 0.993098i | \(-0.462579\pi\) | |||||||
\(258\) | 1783.80 | 0.00166839 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.21144e6 | 1.11140 | ||||||||
\(261\) | 333107. | + | 576959.i | 0.302679 | + | 0.524256i | ||||
\(262\) | 356713. | − | 617846.i | 0.321045 | − | 0.556067i | ||||
\(263\) | −102847. | + | 178136.i | −0.0916859 | + | 0.158805i | −0.908221 | − | 0.418492i | \(-0.862559\pi\) |
0.816535 | + | 0.577296i | \(0.195892\pi\) | |||||||
\(264\) | 285173. | + | 493934.i | 0.251825 | + | 0.436173i | ||||
\(265\) | −549746. | −0.480892 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 351010. | 0.301330 | ||||||||
\(268\) | −813133. | − | 1.40839e6i | −0.691551 | − | 1.19780i | ||||
\(269\) | 867123. | − | 1.50190e6i | 0.730635 | − | 1.26550i | −0.225978 | − | 0.974132i | \(-0.572558\pi\) |
0.956612 | − | 0.291364i | \(-0.0941090\pi\) | |||||||
\(270\) | −187831. | + | 325333.i | −0.156804 | + | 0.271593i | ||||
\(271\) | 184521. | + | 319600.i | 0.152624 | + | 0.264352i | 0.932191 | − | 0.361966i | \(-0.117894\pi\) |
−0.779567 | + | 0.626318i | \(0.784561\pi\) | |||||||
\(272\) | 384954. | 0.315491 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −273492. | −0.220074 | ||||||||
\(275\) | −278601. | − | 482550.i | −0.222152 | − | 0.384779i | ||||
\(276\) | −3498.56 | + | 6059.69i | −0.00276450 | + | 0.00478826i | ||||
\(277\) | −613835. | + | 1.06319e6i | −0.480676 | + | 0.832554i | −0.999754 | − | 0.0221720i | \(-0.992942\pi\) |
0.519079 | + | 0.854727i | \(0.326275\pi\) | |||||||
\(278\) | 296016. | + | 512715.i | 0.229722 | + | 0.397891i | ||||
\(279\) | 1.75789e6 | 1.35201 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00671e6 | 1.51607 | 0.758035 | − | 0.652214i | \(-0.226159\pi\) | ||||
0.758035 | + | 0.652214i | \(0.226159\pi\) | |||||||
\(282\) | −70775.4 | − | 122587.i | −0.0529980 | − | 0.0917953i | ||||
\(283\) | −892905. | + | 1.54656e6i | −0.662734 | + | 1.14789i | 0.317160 | + | 0.948372i | \(0.397271\pi\) |
−0.979894 | + | 0.199517i | \(0.936063\pi\) | |||||||
\(284\) | −738808. | + | 1.27965e6i | −0.543545 | + | 0.941448i | ||||
\(285\) | 175589. | + | 304130.i | 0.128052 | + | 0.221793i | ||||
\(286\) | 1.69947e6 | 1.22856 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.19458e6 | −0.848660 | ||||||||
\(289\) | 12885.4 | + | 22318.1i | 0.00907513 | + | 0.0157186i | ||||
\(290\) | −215501. | + | 373258.i | −0.150471 | + | 0.260624i | ||||
\(291\) | −10184.8 | + | 17640.5i | −0.00705047 | + | 0.0122118i | ||||
\(292\) | −22274.5 | − | 38580.6i | −0.0152880 | − | 0.0264796i | ||||
\(293\) | −853248. | −0.580639 | −0.290319 | − | 0.956930i | \(-0.593762\pi\) | ||||
−0.290319 | + | 0.956930i | \(0.593762\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −453345. | −0.303301 | ||||||||
\(296\) | −201829. | − | 349578.i | −0.133892 | − | 0.231908i | ||||
\(297\) | 800518. | − | 1.38654e6i | 0.526599 | − | 0.912096i | ||||
\(298\) | −197627. | + | 342300.i | −0.128916 | + | 0.223289i | ||||
\(299\) | 24280.8 | + | 42055.6i | 0.0157067 | + | 0.0272048i | ||||
\(300\) | −159194. | −0.102123 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 336952. | 0.212594 | ||||||||
\(303\) | −71490.9 | − | 123826.i | −0.0447347 | − | 0.0774827i | ||||
\(304\) | −190099. | + | 329261.i | −0.117977 | + | 0.204341i | ||||
\(305\) | −885739. | + | 1.53414e6i | −0.545200 | + | 0.944315i | ||||
\(306\) | 332585. | + | 576054.i | 0.203048 | + | 0.351690i | ||||
\(307\) | 1.96068e6 | 1.18730 | 0.593652 | − | 0.804722i | \(-0.297686\pi\) | ||||
0.593652 | + | 0.804722i | \(0.297686\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 427857. | 0.254919 | ||||||||
\(310\) | 568625. | + | 984888.i | 0.336064 | + | 0.582080i | ||||
\(311\) | 431802. | − | 747903.i | 0.253153 | − | 0.438474i | −0.711239 | − | 0.702950i | \(-0.751866\pi\) |
0.964392 | + | 0.264476i | \(0.0851990\pi\) | |||||||
\(312\) | 565454. | − | 979396.i | 0.328860 | − | 0.569602i | ||||
\(313\) | 550235. | + | 953035.i | 0.317459 | + | 0.549855i | 0.979957 | − | 0.199209i | \(-0.0638372\pi\) |
−0.662498 | + | 0.749063i | \(0.730504\pi\) | |||||||
\(314\) | −274799. | −0.157286 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 205.342 | 0.000115680 | ||||||||
\(317\) | −747954. | − | 1.29549e6i | −0.418048 | − | 0.724081i | 0.577695 | − | 0.816253i | \(-0.303952\pi\) |
−0.995743 | + | 0.0921719i | \(0.970619\pi\) | |||||||
\(318\) | −110169. | + | 190818.i | −0.0610929 | + | 0.105816i | ||||
\(319\) | 918444. | − | 1.59079e6i | 0.505331 | − | 0.875259i | ||||
\(320\) | −146496. | − | 253739.i | −0.0799746 | − | 0.138520i | ||||
\(321\) | 713454. | 0.386459 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.37686e6 | 0.734318 | ||||||||
\(324\) | 356682. | + | 617791.i | 0.188764 | + | 0.326948i | ||||
\(325\) | −552423. | + | 956824.i | −0.290110 | + | 0.502486i | ||||
\(326\) | −257126. | + | 445355.i | −0.133999 | + | 0.232093i | ||||
\(327\) | 283950. | + | 491816.i | 0.146850 | + | 0.254351i | ||||
\(328\) | −2.01445e6 | −1.03388 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 467777. | 0.236458 | ||||||||
\(331\) | 1.37008e6 | + | 2.37304e6i | 0.687345 | + | 1.19052i | 0.972694 | + | 0.232093i | \(0.0745573\pi\) |
−0.285348 | + | 0.958424i | \(0.592109\pi\) | |||||||
\(332\) | 1.14405e6 | − | 1.98156e6i | 0.569640 | − | 0.986646i | ||||
\(333\) | −255870. | + | 443180.i | −0.126447 | + | 0.219013i | ||||
\(334\) | −635747. | − | 1.10115e6i | −0.311830 | − | 0.540106i | ||||
\(335\) | −3.10665e6 | −1.51245 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.31353e6 | −1.10968 | −0.554842 | − | 0.831956i | \(-0.687221\pi\) | ||||
−0.554842 | + | 0.831956i | \(0.687221\pi\) | |||||||
\(338\) | −1.16228e6 | − | 2.01313e6i | −0.553376 | − | 0.958475i | ||||
\(339\) | −332300. | + | 575560.i | −0.157047 | + | 0.272014i | ||||
\(340\) | 653674. | − | 1.13220e6i | 0.306665 | − | 0.531159i | ||||
\(341\) | −2.42343e6 | − | 4.19750e6i | −1.12861 | − | 1.95481i | ||||
\(342\) | −656951. | −0.303716 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 15276.0 | 0.00696006 | ||||||||
\(345\) | 6683.29 | + | 11575.8i | 0.00302303 | + | 0.00523604i | ||||
\(346\) | 523107. | − | 906048.i | 0.234909 | − | 0.406875i | ||||
\(347\) | 1.52963e6 | − | 2.64940e6i | 0.681966 | − | 1.18120i | −0.292414 | − | 0.956292i | \(-0.594459\pi\) |
0.974380 | − | 0.224908i | \(-0.0722081\pi\) | |||||||
\(348\) | −262403. | − | 454495.i | −0.116150 | − | 0.201178i | ||||
\(349\) | 210232. | 0.0923921 | 0.0461961 | − | 0.998932i | \(-0.485290\pi\) | ||||
0.0461961 | + | 0.998932i | \(0.485290\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.17461e6 | −1.37538 | ||||||||
\(352\) | 1.64685e6 | + | 2.85243e6i | 0.708430 | + | 1.22704i | ||||
\(353\) | −1.88395e6 | + | 3.26310e6i | −0.804697 | + | 1.39378i | 0.111798 | + | 0.993731i | \(0.464339\pi\) |
−0.916495 | + | 0.400045i | \(0.868994\pi\) | |||||||
\(354\) | −90850.0 | + | 157357.i | −0.0385316 | + | 0.0667386i | ||||
\(355\) | 1.41134e6 | + | 2.44451e6i | 0.594376 | + | 1.02949i | ||||
\(356\) | 1.29057e6 | 0.539707 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 239291. | 0.0986776 | ||||||||
\(359\) | −503608. | − | 872275.i | −0.206232 | − | 0.357205i | 0.744292 | − | 0.667854i | \(-0.232787\pi\) |
−0.950525 | + | 0.310649i | \(0.899454\pi\) | |||||||
\(360\) | −726446. | + | 1.25824e6i | −0.295425 | + | 0.511691i | ||||
\(361\) | 558124. | − | 966700.i | 0.225405 | − | 0.390412i | ||||
\(362\) | −534078. | − | 925050.i | −0.214207 | − | 0.371017i | ||||
\(363\) | −939058. | −0.374047 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −85101.8 | −0.0334354 | ||||||||
\(366\) | 355003. | + | 614883.i | 0.138525 | + | 0.239933i | ||||
\(367\) | −763248. | + | 1.32198e6i | −0.295802 | + | 0.512343i | −0.975171 | − | 0.221453i | \(-0.928920\pi\) |
0.679369 | + | 0.733796i | \(0.262253\pi\) | |||||||
\(368\) | −7235.54 | + | 12532.3i | −0.00278517 | + | 0.00482405i | ||||
\(369\) | 1.27691e6 | + | 2.21168e6i | 0.488198 | + | 0.845583i | ||||
\(370\) | −331066. | −0.125722 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.38476e6 | −0.518822 | ||||||||
\(373\) | −2.43149e6 | − | 4.21146e6i | −0.904898 | − | 1.56733i | −0.821054 | − | 0.570850i | \(-0.806614\pi\) |
−0.0838438 | − | 0.996479i | \(-0.526720\pi\) | |||||||
\(374\) | 917004. | − | 1.58830e6i | 0.338994 | − | 0.587155i | ||||
\(375\) | −622601. | + | 1.07838e6i | −0.228629 | + | 0.395997i | ||||
\(376\) | −606101. | − | 1.04980e6i | −0.221093 | − | 0.382945i | ||||
\(377\) | −3.64227e6 | −1.31983 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 630878. | 0.225604 | 0.112802 | − | 0.993617i | \(-0.464017\pi\) | ||||
0.112802 | + | 0.993617i | \(0.464017\pi\) | |||||||
\(380\) | 645597. | + | 1.11821e6i | 0.229352 | + | 0.397249i | ||||
\(381\) | −10131.8 | + | 17548.7i | −0.00357579 | + | 0.00619346i | ||||
\(382\) | 1.29802e6 | − | 2.24824e6i | 0.455118 | − | 0.788288i | ||||
\(383\) | 282822. | + | 489862.i | 0.0985182 | + | 0.170639i | 0.911072 | − | 0.412248i | \(-0.135256\pi\) |
−0.812553 | + | 0.582887i | \(0.801923\pi\) | |||||||
\(384\) | 1.13334e6 | 0.392221 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.42191e6 | 0.485741 | ||||||||
\(387\) | −9683.12 | − | 16771.7i | −0.00328653 | − | 0.00569244i | ||||
\(388\) | −37446.7 | + | 64859.7i | −0.0126280 | + | 0.0218723i | ||||
\(389\) | −296106. | + | 512870.i | −0.0992140 | + | 0.171844i | −0.911360 | − | 0.411611i | \(-0.864966\pi\) |
0.812146 | + | 0.583455i | \(0.198300\pi\) | |||||||
\(390\) | −463766. | − | 803266.i | −0.154396 | − | 0.267423i | ||||
\(391\) | 52406.1 | 0.0173356 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.65947e6 | 0.541986 | ||||||||
\(394\) | −354003. | − | 613151.i | −0.114886 | − | 0.198988i | ||||
\(395\) | 196.132 | − | 339.710i | 6.32492e−5 | − | 0.000109551i | ||||
\(396\) | 1.32925e6 | − | 2.30233e6i | 0.425961 | − | 0.737786i | ||||
\(397\) | 671558. | + | 1.16317e6i | 0.213849 | + | 0.370397i | 0.952916 | − | 0.303235i | \(-0.0980666\pi\) |
−0.739067 | + | 0.673632i | \(0.764733\pi\) | |||||||
\(398\) | 585629. | 0.185317 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −329238. | −0.102887 | ||||||||
\(401\) | 1.84358e6 | + | 3.19318e6i | 0.572534 | + | 0.991658i | 0.996305 | + | 0.0858884i | \(0.0273729\pi\) |
−0.423771 | + | 0.905769i | \(0.639294\pi\) | |||||||
\(402\) | −622569. | + | 1.07832e6i | −0.192142 | + | 0.332800i | ||||
\(403\) | −4.80529e6 | + | 8.32300e6i | −1.47386 | + | 2.55280i | ||||
\(404\) | −262854. | − | 455276.i | −0.0801236 | − | 0.138778i | ||||
\(405\) | 1.36273e6 | 0.412832 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.41097e6 | 0.422214 | ||||||||
\(408\) | −610220. | − | 1.05693e6i | −0.181483 | − | 0.314338i | ||||
\(409\) | 728151. | − | 1.26119e6i | 0.215235 | − | 0.372798i | −0.738110 | − | 0.674680i | \(-0.764282\pi\) |
0.953345 | + | 0.301882i | \(0.0976149\pi\) | |||||||
\(410\) | −826089. | + | 1.43083e6i | −0.242698 | + | 0.420366i | ||||
\(411\) | −318079. | − | 550929.i | −0.0928818 | − | 0.160876i | ||||
\(412\) | 1.57312e6 | 0.456582 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −25004.9 | −0.00717008 | ||||||||
\(415\) | −2.18548e6 | − | 3.78536e6i | −0.622911 | − | 1.07891i | ||||
\(416\) | 3.26545e6 | − | 5.65593e6i | 0.925145 | − | 1.60240i | ||||
\(417\) | −688550. | + | 1.19260e6i | −0.193908 | + | 0.335858i | ||||
\(418\) | 905674. | + | 1.56867e6i | 0.253531 | + | 0.439129i | ||||
\(419\) | 2.92192e6 | 0.813080 | 0.406540 | − | 0.913633i | \(-0.366735\pi\) | ||||
0.406540 | + | 0.913633i | \(0.366735\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.01999e6 | 0.555450 | 0.277725 | − | 0.960661i | \(-0.410420\pi\) | ||||
0.277725 | + | 0.960661i | \(0.410420\pi\) | |||||||
\(422\) | 901636. | + | 1.56168e6i | 0.246462 | + | 0.426885i | ||||
\(423\) | −768389. | + | 1.33089e6i | −0.208800 | + | 0.361652i | ||||
\(424\) | −943454. | + | 1.63411e6i | −0.254863 | + | 0.441435i | ||||
\(425\) | 596156. | + | 1.03257e6i | 0.160099 | + | 0.277299i | ||||
\(426\) | 1.13133e6 | 0.302040 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.62319e6 | 0.692182 | ||||||||
\(429\) | 1.97653e6 | + | 3.42344e6i | 0.518513 | + | 0.898090i | ||||
\(430\) | 6264.41 | − | 10850.3i | 0.00163384 | − | 0.00282989i | ||||
\(431\) | 2.71900e6 | − | 4.70944e6i | 0.705043 | − | 1.22117i | −0.261633 | − | 0.965167i | \(-0.584261\pi\) |
0.966676 | − | 0.256003i | \(-0.0824057\pi\) | |||||||
\(432\) | −473008. | − | 819274.i | −0.121944 | − | 0.211213i | ||||
\(433\) | 3.77335e6 | 0.967179 | 0.483590 | − | 0.875295i | \(-0.339333\pi\) | ||||
0.483590 | + | 0.875295i | \(0.339333\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.00253e6 | −0.254025 | ||||||||
\(436\) | 1.04401e6 | + | 1.80828e6i | 0.263020 | + | 0.455565i | ||||
\(437\) | −25879.3 | + | 44824.3i | −0.00648260 | + | 0.0112282i | ||||
\(438\) | −17054.3 | + | 29539.0i | −0.00424766 | + | 0.00735716i | ||||
\(439\) | 1.17575e6 | + | 2.03646e6i | 0.291175 | + | 0.504330i | 0.974088 | − | 0.226170i | \(-0.0726205\pi\) |
−0.682913 | + | 0.730500i | \(0.739287\pi\) | |||||||
\(440\) | 4.00591e6 | 0.986439 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.63656e6 | −0.885391 | ||||||||
\(443\) | −2.40188e6 | − | 4.16019e6i | −0.581491 | − | 1.00717i | −0.995303 | − | 0.0968092i | \(-0.969136\pi\) |
0.413812 | − | 0.910362i | \(-0.364197\pi\) | |||||||
\(444\) | 201560. | − | 349112.i | 0.0485229 | − | 0.0840441i | ||||
\(445\) | 1.23269e6 | − | 2.13508e6i | 0.295089 | − | 0.511110i | ||||
\(446\) | 549129. | + | 951119.i | 0.130718 | + | 0.226411i | ||||
\(447\) | −919383. | −0.217634 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.76805e6 | −0.647975 | −0.323987 | − | 0.946061i | \(-0.605024\pi\) | ||||
−0.323987 | + | 0.946061i | \(0.605024\pi\) | |||||||
\(450\) | −284448. | − | 492679.i | −0.0662174 | − | 0.114692i | ||||
\(451\) | 3.52071e6 | − | 6.09805e6i | 0.815059 | − | 1.41172i | ||||
\(452\) | −1.22178e6 | + | 2.11619e6i | −0.281285 | + | 0.487201i | ||||
\(453\) | 391885. | + | 678765.i | 0.0897249 | + | 0.155408i | ||||
\(454\) | −820179. | −0.186754 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.20536e6 | 0.271459 | ||||||||
\(457\) | −120783. | − | 209203.i | −0.0270530 | − | 0.0468573i | 0.852182 | − | 0.523246i | \(-0.175279\pi\) |
−0.879235 | + | 0.476388i | \(0.841946\pi\) | |||||||
\(458\) | −1.73184e6 | + | 2.99963e6i | −0.385784 | + | 0.668197i | ||||
\(459\) | −1.71297e6 | + | 2.96695e6i | −0.379505 | + | 0.657322i | ||||
\(460\) | 24572.7 | + | 42561.2i | 0.00541450 | + | 0.00937819i | ||||
\(461\) | −990579. | −0.217088 | −0.108544 | − | 0.994092i | \(-0.534619\pi\) | ||||
−0.108544 | + | 0.994092i | \(0.534619\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.20488e6 | 1.34518 | 0.672591 | − | 0.740014i | \(-0.265181\pi\) | ||||
0.672591 | + | 0.740014i | \(0.265181\pi\) | |||||||
\(464\) | −542688. | − | 939963.i | −0.117019 | − | 0.202682i | ||||
\(465\) | −1.32265e6 | + | 2.29090e6i | −0.283670 | + | 0.491331i | ||||
\(466\) | −160851. | + | 278602.i | −0.0343131 | + | 0.0594320i | ||||
\(467\) | −3.44249e6 | − | 5.96256e6i | −0.730432 | − | 1.26515i | −0.956699 | − | 0.291080i | \(-0.905985\pi\) |
0.226266 | − | 0.974066i | \(-0.427348\pi\) | |||||||
\(468\) | −5.27141e6 | −1.11253 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −994206. | −0.207602 | ||||||||
\(471\) | −319598. | − | 553561.i | −0.0663823 | − | 0.114978i | ||||
\(472\) | −778014. | + | 1.34756e6i | −0.160743 | + | 0.278415i | ||||
\(473\) | −26698.3 | + | 46242.8i | −0.00548695 | + | 0.00950368i | ||||
\(474\) | −78.6093 | − | 136.155i | −1.60705e−5 | − | 2.78348e-5i | ||||
\(475\) | −1.17758e6 | −0.239473 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.39214e6 | 0.481383 | ||||||||
\(478\) | 1.61561e6 | + | 2.79831e6i | 0.323419 | + | 0.560178i | ||||
\(479\) | −2.70644e6 | + | 4.68769e6i | −0.538963 | + | 0.933512i | 0.459997 | + | 0.887921i | \(0.347851\pi\) |
−0.998960 | + | 0.0455914i | \(0.985483\pi\) | |||||||
\(480\) | 898814. | − | 1.55679e6i | 0.178060 | − | 0.308409i | ||||
\(481\) | −1.39887e6 | − | 2.42292e6i | −0.275686 | − | 0.477503i | ||||
\(482\) | −2.28783e6 | −0.448545 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.45268e6 | −0.669950 | ||||||||
\(485\) | 71534.3 | + | 123901.i | 0.0138089 | + | 0.0239178i | ||||
\(486\) | 1.26552e6 | − | 2.19195e6i | 0.243041 | − | 0.420959i | ||||
\(487\) | 1.50521e6 | − | 2.60711e6i | 0.287591 | − | 0.498122i | −0.685643 | − | 0.727938i | \(-0.740479\pi\) |
0.973234 | + | 0.229815i | \(0.0738122\pi\) | |||||||
\(488\) | 3.04014e6 | + | 5.26568e6i | 0.577889 | + | 1.00093i | ||||
\(489\) | −1.19618e6 | −0.226216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.24498e6 | −1.35623 | −0.678115 | − | 0.734956i | \(-0.737203\pi\) | ||||
−0.678115 | + | 0.734956i | \(0.737203\pi\) | |||||||
\(492\) | −1.00588e6 | − | 1.74224e6i | −0.187341 | − | 0.324485i | ||||
\(493\) | −1.96531e6 | + | 3.40402e6i | −0.364178 | + | 0.630775i | ||||
\(494\) | 1.79581e6 | − | 3.11044e6i | 0.331088 | − | 0.573462i | ||||
\(495\) | −2.53927e6 | − | 4.39814e6i | −0.465795 | − | 0.806781i | ||||
\(496\) | −2.86389e6 | −0.522700 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.75187e6 | −0.316540 | ||||||||
\(499\) | 2.56394e6 | + | 4.44088e6i | 0.460953 | + | 0.798394i | 0.999009 | − | 0.0445152i | \(-0.0141743\pi\) |
−0.538056 | + | 0.842909i | \(0.680841\pi\) | |||||||
\(500\) | −2.28914e6 | + | 3.96491e6i | −0.409495 | + | 0.709265i | ||||
\(501\) | 1.47878e6 | − | 2.56133e6i | 0.263215 | − | 0.455901i | ||||
\(502\) | −572546. | − | 991679.i | −0.101403 | − | 0.175635i | ||||
\(503\) | −1.05978e7 | −1.86766 | −0.933830 | − | 0.357718i | \(-0.883555\pi\) | ||||
−0.933830 | + | 0.357718i | \(0.883555\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.00426e6 | −0.175233 | ||||||||
\(506\) | 34471.7 | + | 59706.8i | 0.00598531 | + | 0.0103669i | ||||
\(507\) | 2.70354e6 | − | 4.68266e6i | 0.467103 | − | 0.809045i | ||||
\(508\) | −37251.9 | + | 64522.1i | −0.00640455 | + | 0.0110930i | ||||
\(509\) | 4.39420e6 | + | 7.61097e6i | 0.751770 | + | 1.30210i | 0.946964 | + | 0.321340i | \(0.104133\pi\) |
−0.195194 | + | 0.980765i | \(0.562534\pi\) | |||||||
\(510\) | −1.00096e6 | −0.170409 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3.59310e6 | 0.605752 | ||||||||
\(513\) | −1.69180e6 | − | 2.93029e6i | −0.283829 | − | 0.491606i | ||||
\(514\) | −2.38877e6 | + | 4.13746e6i | −0.398810 | + | 0.690759i | ||||
\(515\) | 1.50256e6 | − | 2.60251e6i | 0.249640 | − | 0.432389i | ||||
\(516\) | 7627.81 | + | 13211.8i | 0.00126118 | + | 0.00218442i | ||||
\(517\) | 4.23721e6 | 0.697194 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.43355e6 | 0.396572 | ||||||||
\(520\) | −3.97156e6 | − | 6.87895e6i | −0.644099 | − | 1.11561i | ||||
\(521\) | 81066.4 | − | 140411.i | 0.0130842 | − | 0.0226625i | −0.859409 | − | 0.511288i | \(-0.829168\pi\) |
0.872493 | + | 0.488626i | \(0.162502\pi\) | |||||||
\(522\) | 937721. | − | 1.62418e6i | 0.150625 | − | 0.260890i | ||||
\(523\) | −3.57422e6 | − | 6.19073e6i | −0.571383 | − | 0.989664i | −0.996424 | − | 0.0844904i | \(-0.973074\pi\) |
0.425041 | − | 0.905174i | \(-0.360260\pi\) | |||||||
\(524\) | 6.10144e6 | 0.970743 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 579044. | 0.0912530 | ||||||||
\(527\) | 5.18571e6 | + | 8.98191e6i | 0.813357 | + | 1.40878i | ||||
\(528\) | −588993. | + | 1.02017e6i | −0.0919445 | + | 0.159252i | ||||
\(529\) | 3.21719e6 | − | 5.57233e6i | 0.499847 | − | 0.865760i | ||||
\(530\) | 773788. | + | 1.34024e6i | 0.119655 | + | 0.207249i | ||||
\(531\) | 1.97267e6 | 0.303611 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.39621e7 | −2.12879 | ||||||||
\(534\) | −494060. | − | 855737.i | −0.0749767 | − | 0.129863i | ||||
\(535\) | 2.50553e6 | − | 4.33971e6i | 0.378456 | − | 0.655505i | ||||
\(536\) | −5.33151e6 | + | 9.23445e6i | −0.801564 | + | 1.38835i | ||||
\(537\) | 278302. | + | 482033.i | 0.0416467 | + | 0.0721342i | ||||
\(538\) | −4.88203e6 | −0.727185 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.21278e6 | −0.474129 | ||||||||
\(541\) | 2.41802e6 | + | 4.18813e6i | 0.355195 | + | 0.615216i | 0.987151 | − | 0.159788i | \(-0.0510811\pi\) |
−0.631956 | + | 0.775004i | \(0.717748\pi\) | |||||||
\(542\) | 519440. | − | 899696.i | 0.0759516 | − | 0.131552i | ||||
\(543\) | 1.24230e6 | − | 2.15172e6i | 0.180811 | − | 0.313174i | ||||
\(544\) | −3.52397e6 | − | 6.10369e6i | −0.510546 | − | 0.884291i | ||||
\(545\) | 3.98874e6 | 0.575234 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.98777e6 | 1.42725 | 0.713626 | − | 0.700527i | \(-0.247052\pi\) | ||||
0.713626 | + | 0.700527i | \(0.247052\pi\) | |||||||
\(548\) | −1.16950e6 | − | 2.02563e6i | −0.166359 | − | 0.288143i | ||||
\(549\) | 3.85417e6 | − | 6.67561e6i | 0.545757 | − | 0.945279i | ||||
\(550\) | −784281. | + | 1.35841e6i | −0.110552 | + | 0.191481i | ||||
\(551\) | −1.94103e6 | − | 3.36196e6i | −0.272366 | − | 0.471751i | ||||
\(552\) | 45878.4 | 0.00640856 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.45598e6 | 0.478406 | ||||||||
\(555\) | −385039. | − | 666907.i | −0.0530606 | − | 0.0919037i | ||||
\(556\) | −2.53162e6 | + | 4.38490e6i | −0.347305 | + | 0.601551i | ||||
\(557\) | −873096. | + | 1.51225e6i | −0.119241 | + | 0.206531i | −0.919467 | − | 0.393167i | \(-0.871379\pi\) |
0.800226 | + | 0.599698i | \(0.204713\pi\) | |||||||
\(558\) | −2.47429e6 | − | 4.28560e6i | −0.336407 | − | 0.582674i | ||||
\(559\) | 105877. | 0.0143309 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.26600e6 | 0.572287 | ||||||||
\(562\) | −2.82452e6 | − | 4.89221e6i | −0.377228 | − | 0.653378i | ||||
\(563\) | −377609. | + | 654038.i | −0.0502078 | + | 0.0869625i | −0.890037 | − | 0.455888i | \(-0.849322\pi\) |
0.839829 | + | 0.542851i | \(0.182655\pi\) | |||||||
\(564\) | 605293. | − | 1.04840e6i | 0.0801250 | − | 0.138781i | ||||
\(565\) | 2.33396e6 | + | 4.04254e6i | 0.307590 | + | 0.532762i | ||||
\(566\) | 5.02719e6 | 0.659605 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.68836e6 | 1.26003 | ||||||||
\(569\) | 2.19767e6 | + | 3.80648e6i | 0.284565 | + | 0.492882i | 0.972504 | − | 0.232888i | \(-0.0748174\pi\) |
−0.687938 | + | 0.725769i | \(0.741484\pi\) | |||||||
\(570\) | 494297. | − | 856148.i | 0.0637237 | − | 0.110373i | ||||
\(571\) | −5.80520e6 | + | 1.00549e7i | −0.745121 | + | 1.29059i | 0.205018 | + | 0.978758i | \(0.434275\pi\) |
−0.950138 | + | 0.311829i | \(0.899059\pi\) | |||||||
\(572\) | 7.26718e6 | + | 1.25871e7i | 0.928700 | + | 1.60856i | ||||
\(573\) | 6.03855e6 | 0.768327 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −44821.1 | −0.00565344 | ||||||||
\(576\) | 637458. | + | 1.10411e6i | 0.0800563 | + | 0.138662i | ||||
\(577\) | 5.33214e6 | − | 9.23554e6i | 0.666748 | − | 1.15484i | −0.312060 | − | 0.950062i | \(-0.601019\pi\) |
0.978808 | − | 0.204779i | \(-0.0656477\pi\) | |||||||
\(578\) | 36273.3 | − | 62827.2i | 0.00451614 | − | 0.00782218i | ||||
\(579\) | 1.65372e6 | + | 2.86433e6i | 0.205006 | + | 0.355081i | ||||
\(580\) | −3.68606e6 | −0.454980 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 57341.7 | 0.00701719 | ||||||||
\(583\) | −3.29781e6 | − | 5.71197e6i | −0.401841 | − | 0.696009i | ||||
\(584\) | −146049. | + | 252963.i | −0.0177201 | + | 0.0306920i | ||||
\(585\) | −5.03498e6 | + | 8.72084e6i | −0.608286 | + | 1.05358i | ||||
\(586\) | 1.20098e6 | + | 2.08015e6i | 0.144474 | + | 0.250237i | ||||
\(587\) | 1.39482e7 | 1.67079 | 0.835396 | − | 0.549648i | \(-0.185238\pi\) | ||||
0.835396 | + | 0.549648i | \(0.185238\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.02433e7 | −1.21661 | ||||||||
\(590\) | 638099. | + | 1.10522e6i | 0.0754672 | + | 0.130713i | ||||
\(591\) | 823430. | − | 1.42622e6i | 0.0969746 | − | 0.167965i | ||||
\(592\) | 416856. | − | 722015.i | 0.0488857 | − | 0.0846724i | ||||
\(593\) | 5.89663e6 | + | 1.02133e7i | 0.688600 | + | 1.19269i | 0.972291 | + | 0.233774i | \(0.0751076\pi\) |
−0.283691 | + | 0.958916i | \(0.591559\pi\) | |||||||
\(594\) | −4.50703e6 | −0.524113 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.38033e6 | −0.389802 | ||||||||
\(597\) | 681102. | + | 1.17970e6i | 0.0782125 | + | 0.135468i | ||||
\(598\) | 68352.3 | − | 118390.i | 0.00781628 | − | 0.0135382i | ||||
\(599\) | 2.19029e6 | − | 3.79369e6i | 0.249421 | − | 0.432011i | −0.713944 | − | 0.700203i | \(-0.753093\pi\) |
0.963365 | + | 0.268192i | \(0.0864262\pi\) | |||||||
\(600\) | 521899. | + | 903956.i | 0.0591846 | + | 0.102511i | ||||
\(601\) | −688570. | −0.0777610 | −0.0388805 | − | 0.999244i | \(-0.512379\pi\) | ||||
−0.0388805 | + | 0.999244i | \(0.512379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.35181e7 | 1.51399 | ||||||||
\(604\) | 1.44086e6 | + | 2.49564e6i | 0.160705 | + | 0.278349i | ||||
\(605\) | −3.29781e6 | + | 5.71198e6i | −0.366301 | + | 0.634451i | ||||
\(606\) | −201252. | + | 348579.i | −0.0222617 | + | 0.0385584i | ||||
\(607\) | −4.68660e6 | − | 8.11742e6i | −0.516281 | − | 0.894224i | −0.999821 | − | 0.0189023i | \(-0.993983\pi\) |
0.483541 | − | 0.875322i | \(-0.339350\pi\) | |||||||
\(608\) | 6.96085e6 | 0.763666 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.98684e6 | 0.542626 | ||||||||
\(611\) | −4.20087e6 | − | 7.27612e6i | −0.455236 | − | 0.788492i | ||||
\(612\) | −2.84437e6 | + | 4.92659e6i | −0.306978 | + | 0.531701i | ||||
\(613\) | 1.08342e6 | − | 1.87655e6i | 0.116452 | − | 0.201701i | −0.801907 | − | 0.597449i | \(-0.796181\pi\) |
0.918359 | + | 0.395748i | \(0.129515\pi\) | |||||||
\(614\) | −2.75974e6 | − | 4.78000e6i | −0.295424 | − | 0.511690i | ||||
\(615\) | −3.84306e6 | −0.409722 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.07951e6 | −0.537166 | −0.268583 | − | 0.963256i | \(-0.586555\pi\) | ||||
−0.268583 | + | 0.963256i | \(0.586555\pi\) | |||||||
\(618\) | −602224. | − | 1.04308e6i | −0.0634288 | − | 0.109862i | ||||
\(619\) | −1.09517e6 | + | 1.89689e6i | −0.114883 | + | 0.198983i | −0.917733 | − | 0.397198i | \(-0.869983\pi\) |
0.802850 | + | 0.596181i | \(0.203316\pi\) | |||||||
\(620\) | −4.86306e6 | + | 8.42306e6i | −0.508078 | + | 0.880016i | ||||
\(621\) | −64393.4 | − | 111533.i | −0.00670058 | − | 0.0116057i | ||||
\(622\) | −2.43111e6 | −0.251958 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.33577e6 | 0.240142 | ||||||||
\(625\) | 2.79509e6 | + | 4.84124e6i | 0.286217 | + | 0.495743i | ||||
\(626\) | 1.54895e6 | − | 2.68286e6i | 0.157980 | − | 0.273629i | ||||
\(627\) | −2.10665e6 | + | 3.64882e6i | −0.214005 | + | 0.370667i | ||||
\(628\) | −1.17508e6 | − | 2.03530e6i | −0.118896 | − | 0.205935i | ||||
\(629\) | −3.01923e6 | −0.304278 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.18693e6 | −0.718572 | −0.359286 | − | 0.933228i | \(-0.616980\pi\) | ||||
−0.359286 | + | 0.933228i | \(0.616980\pi\) | |||||||
\(632\) | −673.188 | − | 1166.00i | −6.70415e−5 | − | 0.000116119i | ||||
\(633\) | −2.09725e6 | + | 3.63255e6i | −0.208038 | + | 0.360332i | ||||
\(634\) | −2.10554e6 | + | 3.64691e6i | −0.208037 | + | 0.360331i | ||||
\(635\) | 71162.1 | + | 123256.i | 0.00700349 | + | 0.0121304i | ||||
\(636\) | −1.88439e6 | −0.184726 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.17097e6 | −0.502945 | ||||||||
\(639\) | −6.14125e6 | − | 1.06370e7i | −0.594983 | − | 1.03054i | ||||
\(640\) | 3.98009e6 | − | 6.89371e6i | 0.384098 | − | 0.665278i | ||||
\(641\) | 8.82500e6 | − | 1.52854e7i | 0.848340 | − | 1.46937i | −0.0343490 | − | 0.999410i | \(-0.510936\pi\) |
0.882689 | − | 0.469958i | \(-0.155731\pi\) | |||||||
\(642\) | −1.00421e6 | − | 1.73935e6i | −0.0961586 | − | 0.166552i | ||||
\(643\) | −898309. | −0.0856837 | −0.0428419 | − | 0.999082i | \(-0.513641\pi\) | ||||
−0.0428419 | + | 0.999082i | \(0.513641\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 29142.7 | 0.00275823 | ||||||||
\(646\) | −1.93798e6 | − | 3.35669e6i | −0.182713 | − | 0.316468i | ||||
\(647\) | −693210. | + | 1.20068e6i | −0.0651035 | + | 0.112763i | −0.896740 | − | 0.442558i | \(-0.854071\pi\) |
0.831636 | + | 0.555321i | \(0.187404\pi\) | |||||||
\(648\) | 2.33867e6 | − | 4.05070e6i | 0.218792 | − | 0.378959i | ||||
\(649\) | −2.71952e6 | − | 4.71034e6i | −0.253443 | − | 0.438976i | ||||
\(650\) | 3.11022e6 | 0.288741 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.39804e6 | −0.405173 | ||||||||
\(653\) | 8.77125e6 | + | 1.51923e7i | 0.804968 | + | 1.39425i | 0.916313 | + | 0.400464i | \(0.131151\pi\) |
−0.111345 | + | 0.993782i | \(0.535516\pi\) | |||||||
\(654\) | 799341. | − | 1.38450e6i | 0.0730782 | − | 0.126575i | ||||
\(655\) | 5.82778e6 | − | 1.00940e7i | 0.530762 | − | 0.919307i | ||||
\(656\) | −2.08031e6 | − | 3.60320e6i | −0.188742 | − | 0.326910i | ||||
\(657\) | 370308. | 0.0334696 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.87522e6 | 0.885795 | 0.442898 | − | 0.896572i | \(-0.353950\pi\) | ||||
0.442898 | + | 0.896572i | \(0.353950\pi\) | |||||||
\(660\) | 2.00029e6 | + | 3.46460e6i | 0.178744 | + | 0.309595i | ||||
\(661\) | −4.03396e6 | + | 6.98702e6i | −0.359110 | + | 0.621997i | −0.987812 | − | 0.155649i | \(-0.950253\pi\) |
0.628702 | + | 0.777646i | \(0.283586\pi\) | |||||||
\(662\) | 3.85687e6 | − | 6.68029e6i | 0.342050 | − | 0.592448i | ||||
\(663\) | −4.22942e6 | − | 7.32557e6i | −0.373677 | − | 0.647228i | ||||
\(664\) | −1.50025e7 | −1.32052 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.44059e6 | 0.125850 | ||||||||
\(667\) | −73879.3 | − | 127963.i | −0.00642996 | − | 0.0111370i | ||||
\(668\) | 5.43710e6 | − | 9.41734e6i | 0.471440 | − | 0.816558i | ||||
\(669\) | −1.27730e6 | + | 2.21236e6i | −0.110339 | + | 0.191113i | ||||
\(670\) | 4.37272e6 | + | 7.57377e6i | 0.376326 | + | 0.651816i | ||||
\(671\) | −2.12534e7 | −1.82231 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.12772e7 | −0.959762 | −0.479881 | − | 0.877334i | \(-0.659320\pi\) | ||||
−0.479881 | + | 0.877334i | \(0.659320\pi\) | |||||||
\(674\) | 3.25637e6 | + | 5.64020e6i | 0.276111 | + | 0.478239i | ||||
\(675\) | 1.46504e6 | − | 2.53753e6i | 0.123763 | − | 0.214364i | ||||
\(676\) | 9.94020e6 | − | 1.72169e7i | 0.836621 | − | 1.44907i | ||||
\(677\) | 2.60186e6 | + | 4.50655e6i | 0.218179 | + | 0.377897i | 0.954251 | − | 0.299006i | \(-0.0966551\pi\) |
−0.736073 | + | 0.676903i | \(0.763322\pi\) | |||||||
\(678\) | 1.87090e6 | 0.156306 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −8.57196e6 | −0.710899 | ||||||||
\(681\) | −953891. | − | 1.65219e6i | −0.0788190 | − | 0.136518i | ||||
\(682\) | −6.82212e6 | + | 1.18163e7i | −0.561640 | + | 0.972790i | ||||
\(683\) | −3.02957e6 | + | 5.24737e6i | −0.248502 | + | 0.430418i | −0.963110 | − | 0.269107i | \(-0.913272\pi\) |
0.714608 | + | 0.699525i | \(0.246605\pi\) | |||||||
\(684\) | −2.80922e6 | − | 4.86572e6i | −0.229586 | − | 0.397655i | ||||
\(685\) | −4.46816e6 | −0.363833 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.05671e6 | −0.651277 | ||||||||
\(688\) | 15775.4 | + | 27323.8i | 0.00127060 | + | 0.00220075i | ||||
\(689\) | −6.53906e6 | + | 1.13260e7i | −0.524768 | + | 0.908924i | ||||
\(690\) | 18813.9 | − | 32586.7i | 0.00150438 | − | 0.00260566i | ||||
\(691\) | 3.68249e6 | + | 6.37826e6i | 0.293391 | + | 0.508168i | 0.974609 | − | 0.223912i | \(-0.0718830\pi\) |
−0.681219 | + | 0.732080i | \(0.738550\pi\) | |||||||
\(692\) | 8.94754e6 | 0.710295 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.61204e6 | −0.678746 | ||||||||
\(695\) | 4.83614e6 | + | 8.37644e6i | 0.379784 | + | 0.657806i | ||||
\(696\) | −1.72051e6 | + | 2.98001e6i | −0.134628 | + | 0.233182i | ||||
\(697\) | −7.53370e6 | + | 1.30488e7i | −0.587390 | + | 1.01739i | ||||
\(698\) | −295909. | − | 512529.i | −0.0229890 | − | 0.0398181i | ||||
\(699\) | −748298. | −0.0579271 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.80919e6 | 0.600221 | 0.300110 | − | 0.953904i | \(-0.402977\pi\) | ||||
0.300110 | + | 0.953904i | \(0.402977\pi\) | |||||||
\(702\) | 4.46838e6 | + | 7.73946e6i | 0.342222 | + | 0.592745i | ||||
\(703\) | 1.49096e6 | − | 2.58243e6i | 0.113783 | − | 0.197079i | ||||
\(704\) | 1.75760e6 | − | 3.04426e6i | 0.133656 | − | 0.231499i | ||||
\(705\) | −1.15629e6 | − | 2.00275e6i | −0.0876180 | − | 0.151759i | ||||
\(706\) | 1.06069e7 | 0.800898 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.55395e6 | −0.116508 | ||||||||
\(709\) | −8.78251e6 | − | 1.52118e7i | −0.656150 | − | 1.13649i | −0.981604 | − | 0.190927i | \(-0.938851\pi\) |
0.325454 | − | 0.945558i | \(-0.394483\pi\) | |||||||
\(710\) | 3.97303e6 | − | 6.88149e6i | 0.295785 | − | 0.512314i | ||||
\(711\) | −853.439 | + | 1478.20i | −6.33138e−5 | + | 0.000109663i | ||||
\(712\) | −4.23099e6 | − | 7.32829e6i | −0.312782 | − | 0.541755i | ||||
\(713\) | −389879. | −0.0287214 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.77649e7 | 2.03110 | ||||||||
\(716\) | 1.02324e6 | + | 1.77231e6i | 0.0745928 | + | 0.129198i | ||||
\(717\) | −3.75799e6 | + | 6.50902e6i | −0.272997 | + | 0.472844i | ||||
\(718\) | −1.41769e6 | + | 2.45552e6i | −0.102629 | + | 0.177759i | ||||
\(719\) | −4.04610e6 | − | 7.00805e6i | −0.291887 | − | 0.505563i | 0.682369 | − | 0.731008i | \(-0.260950\pi\) |
−0.974256 | + | 0.225445i | \(0.927616\pi\) | |||||||
\(720\) | −3.00079e6 | −0.215727 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.14232e6 | −0.224341 | ||||||||
\(723\) | −2.66081e6 | − | 4.60866e6i | −0.189308 | − | 0.327890i | ||||
\(724\) | 4.56760e6 | − | 7.91131e6i | 0.323848 | − | 0.560922i | ||||
\(725\) | 1.68086e6 | − | 2.91133e6i | 0.118764 | − | 0.205706i | ||||
\(726\) | 1.32176e6 | + | 2.28935e6i | 0.0930702 | + | 0.161202i | ||||
\(727\) | −1.51986e7 | −1.06652 | −0.533258 | − | 0.845952i | \(-0.679033\pi\) | ||||
−0.533258 | + | 0.845952i | \(0.679033\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.31285e6 | −0.0914944 | ||||||||
\(730\) | 119784. | + | 207472.i | 0.00831938 | + | 0.0144096i | ||||
\(731\) | 57129.7 | − | 98951.6i | 0.00395429 | − | 0.00684903i | ||||
\(732\) | −3.03609e6 | + | 5.25866e6i | −0.209429 | + | 0.362742i | ||||
\(733\) | 2.91701e6 | + | 5.05241e6i | 0.200530 | + | 0.347327i | 0.948699 | − | 0.316180i | \(-0.102400\pi\) |
−0.748170 | + | 0.663507i | \(0.769067\pi\) | |||||||
\(734\) | 4.29720e6 | 0.294405 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 264944. | 0.0180285 | ||||||||
\(737\) | −1.86361e7 | − | 3.22787e7i | −1.26382 | − | 2.18901i | ||||
\(738\) | 3.59461e6 | − | 6.22604e6i | 0.242946 | − | 0.420796i | ||||
\(739\) | −3.23860e6 | + | 5.60941e6i | −0.218145 | + | 0.377838i | −0.954241 | − | 0.299039i | \(-0.903334\pi\) |
0.736096 | + | 0.676877i | \(0.236667\pi\) | |||||||
\(740\) | −1.41569e6 | − | 2.45205e6i | −0.0950361 | − | 0.164607i | ||||
\(741\) | 8.35433e6 | 0.558941 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.50899e7 | −1.00280 | −0.501401 | − | 0.865215i | \(-0.667182\pi\) | ||||
−0.501401 | + | 0.865215i | \(0.667182\pi\) | |||||||
\(744\) | 4.53978e6 | + | 7.86312e6i | 0.300678 | + | 0.520790i | ||||
\(745\) | −3.22872e6 | + | 5.59230e6i | −0.213127 | + | 0.369148i | ||||
\(746\) | −6.84481e6 | + | 1.18556e7i | −0.450313 | + | 0.779965i | ||||
\(747\) | 9.50979e6 | + | 1.64714e7i | 0.623548 | + | 1.08002i | ||||
\(748\) | 1.56850e7 | 1.02502 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.50534e6 | 0.227550 | ||||||||
\(751\) | 1.06998e6 | + | 1.85327e6i | 0.0692273 | + | 0.119905i | 0.898561 | − | 0.438848i | \(-0.144613\pi\) |
−0.829334 | + | 0.558753i | \(0.811280\pi\) | |||||||
\(752\) | 1.25184e6 | − | 2.16824e6i | 0.0807240 | − | 0.139818i | ||||
\(753\) | 1.33177e6 | − | 2.30670e6i | 0.0855940 | − | 0.148253i | ||||
\(754\) | 5.12663e6 | + | 8.87958e6i | 0.328400 | + | 0.568806i | ||||
\(755\) | 5.50494e6 | 0.351467 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.10943e7 | 1.33791 | 0.668954 | − | 0.743304i | \(-0.266742\pi\) | ||||
0.668954 | + | 0.743304i | \(0.266742\pi\) | |||||||
\(758\) | −887984. | − | 1.53803e6i | −0.0561348 | − | 0.0972283i | ||||
\(759\) | −80183.2 | + | 138881.i | −0.00505218 | + | 0.00875063i | ||||
\(760\) | 4.23302e6 | − | 7.33181e6i | 0.265838 | − | 0.460444i | ||||
\(761\) | 4.89979e6 | + | 8.48669e6i | 0.306701 | + | 0.531222i | 0.977639 | − | 0.210292i | \(-0.0674414\pi\) |
−0.670937 | + | 0.741514i | \(0.734108\pi\) | |||||||
\(762\) | 57043.3 | 0.00355891 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.22022e7 | 1.37614 | ||||||||
\(765\) | 5.43358e6 | + | 9.41124e6i | 0.335686 | + | 0.581424i | ||||
\(766\) | 796165. | − | 1.37900e6i | 0.0490265 | − | 0.0849164i | ||||
\(767\) | −5.39239e6 | + | 9.33990e6i | −0.330973 | + | 0.573263i | ||||
\(768\) | −2.26265e6 | − | 3.91903e6i | −0.138425 | − | 0.239759i | ||||
\(769\) | 3.23493e7 | 1.97265 | 0.986323 | − | 0.164825i | \(-0.0527060\pi\) | ||||
0.986323 | + | 0.164825i | \(0.0527060\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.11128e7 | −0.673267 | ||||||||
\(772\) | 6.08031e6 | + | 1.05314e7i | 0.367183 | + | 0.635980i | ||||
\(773\) | 4.59856e6 | − | 7.96495e6i | 0.276805 | − | 0.479440i | −0.693784 | − | 0.720183i | \(-0.744058\pi\) |
0.970589 | + | 0.240743i | \(0.0773912\pi\) | |||||||
\(774\) | −27258.7 | + | 47213.4i | −0.00163551 | + | 0.00283278i | ||||
\(775\) | −4.43515e6 | − | 7.68191e6i | −0.265249 | − | 0.459425i | ||||
\(776\) | 491058. | 0.0292738 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.66712e6 | 0.0987456 | ||||||||
\(779\) | −7.44062e6 | − | 1.28875e7i | −0.439304 | − | 0.760898i | ||||
\(780\) | 3.96627e6 | − | 6.86978e6i | 0.233424 | − | 0.404302i | ||||
\(781\) | −1.69327e7 | + | 2.93282e7i | −0.993339 | + | 1.72051i | ||||
\(782\) | −73763.5 | − | 127762.i | −0.00431345 | − | 0.00747111i | ||||
\(783\) | 9.65941e6 | 0.563049 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.48950e6 | −0.260030 | ||||||||
\(786\) | −2.33576e6 | − | 4.04566e6i | −0.134857 | − | 0.233579i | ||||
\(787\) | 7.34749e6 | − | 1.27262e7i | 0.422866 | − | 0.732425i | −0.573353 | − | 0.819309i | \(-0.694358\pi\) |
0.996218 | + | 0.0868838i | \(0.0276909\pi\) | |||||||
\(788\) | 3.02754e6 | − | 5.24385e6i | 0.173690 | − | 0.300839i | ||||
\(789\) | 673444. | + | 1.16644e6i | 0.0385132 | + | 0.0667068i | ||||
\(790\) | −1104.25 | −6.29506e−5 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.74312e7 | −0.987446 | ||||||||
\(793\) | 2.10712e7 | + | 3.64963e7i | 1.18989 | + | 2.06094i | ||||
\(794\) | 1.89048e6 | − | 3.27442e6i | 0.106420 | − | 0.184324i | ||||
\(795\) | −1.79987e6 | + | 3.11747e6i | −0.101001 | + | 0.174938i | ||||
\(796\) | 2.50424e6 | + | 4.33747e6i | 0.140085 | + | 0.242635i | ||||
\(797\) | −2.33344e7 | −1.30122 | −0.650610 | − | 0.759412i | \(-0.725487\pi\) | ||||
−0.650610 | + | 0.759412i | \(0.725487\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.06688e6 | −0.502448 | ||||||||
\(800\) | 3.01392e6 | + | 5.22027e6i | 0.166497 | + | 0.288382i | ||||
\(801\) | −5.36387e6 | + | 9.29050e6i | −0.295391 | + | 0.511632i | ||||
\(802\) | 5.18981e6 | − | 8.98902e6i | 0.284915 | − | 0.493488i | ||||
\(803\) | −510507. | − | 884225.i | −0.0279391 | − | 0.0483920i | ||||
\(804\) | −1.06488e7 | −0.580980 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.70545e7 | 1.46690 | ||||||||
\(807\) | −5.67794e6 | − | 9.83448e6i | −0.306907 | − | 0.531578i | ||||
\(808\) | −1.72347e6 | + | 2.98513e6i | −0.0928698 | + | 0.160855i | ||||
\(809\) | −846503. | + | 1.46619e6i | −0.0454734 | + | 0.0787622i | −0.887866 | − | 0.460102i | \(-0.847813\pi\) |
0.842393 | + | 0.538864i | \(0.181146\pi\) | |||||||
\(810\) | −1.91810e6 | − | 3.32224e6i | −0.102721 | − | 0.177918i | ||||
\(811\) | 2.12400e7 | 1.13397 | 0.566987 | − | 0.823727i | \(-0.308109\pi\) | ||||
0.566987 | + | 0.823727i | \(0.308109\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.41649e6 | 0.128221 | ||||||||
\(814\) | −1.98599e6 | − | 3.43984e6i | −0.105055 | − | 0.181961i | ||||
\(815\) | −4.20078e6 | + | 7.27596e6i | −0.221532 | + | 0.383704i | ||||
\(816\) | 1.26034e6 | − | 2.18298e6i | 0.0662618 | − | 0.114769i | ||||
\(817\) | 56423.9 | + | 97729.0i | 0.00295738 | + | 0.00512234i | ||||
\(818\) | −4.09960e6 | −0.214219 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.41299e7 | −0.733847 | ||||||||
\(821\) | −4.36775e6 | − | 7.56517e6i | −0.226152 | − | 0.391706i | 0.730513 | − | 0.682899i | \(-0.239281\pi\) |
−0.956664 | + | 0.291193i | \(0.905948\pi\) | |||||||
\(822\) | −895416. | + | 1.55091e6i | −0.0462217 | + | 0.0800583i | ||||
\(823\) | 1.63982e7 | − | 2.84025e7i | 0.843910 | − | 1.46170i | −0.0426542 | − | 0.999090i | \(-0.513581\pi\) |
0.886564 | − | 0.462605i | \(-0.153085\pi\) | |||||||
\(824\) | −5.15728e6 | − | 8.93266e6i | −0.264608 | − | 0.458314i | ||||
\(825\) | −3.64856e6 | −0.186632 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.31248e7 | 0.667311 | 0.333656 | − | 0.942695i | \(-0.391718\pi\) | ||||
0.333656 | + | 0.942695i | \(0.391718\pi\) | |||||||
\(828\) | −106925. | − | 185199.i | −0.00542004 | − | 0.00938778i | ||||
\(829\) | 1.02701e7 | − | 1.77884e7i | 0.519026 | − | 0.898979i | −0.480730 | − | 0.876869i | \(-0.659628\pi\) |
0.999756 | − | 0.0221101i | \(-0.00703844\pi\) | |||||||
\(830\) | −6.15228e6 | + | 1.06561e7i | −0.309985 | + | 0.536910i | ||||
\(831\) | 4.01940e6 | + | 6.96180e6i | 0.201910 | + | 0.349719i | ||||
\(832\) | −6.97012e6 | −0.349085 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.87664e6 | 0.192992 | ||||||||
\(835\) | −1.03865e7 | − | 1.79899e7i | −0.515528 | − | 0.892920i | ||||
\(836\) | −7.74560e6 | + | 1.34158e7i | −0.383300 | + | 0.663896i | ||||
\(837\) | 1.27438e7 | − | 2.20728e7i | 0.628758 | − | 1.08904i | ||||
\(838\) | −4.11271e6 | − | 7.12343e6i | −0.202310 | − | 0.350412i | ||||
\(839\) | −2.83736e7 | −1.39159 | −0.695793 | − | 0.718243i | \(-0.744947\pi\) | ||||
−0.695793 | + | 0.718243i | \(0.744947\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.42879e6 | −0.459691 | ||||||||
\(842\) | −2.84322e6 | − | 4.92459e6i | −0.138207 | − | 0.239381i | ||||
\(843\) | 6.56999e6 | − | 1.13796e7i | 0.318417 | − | 0.551514i | ||||
\(844\) | −7.71106e6 | + | 1.33560e7i | −0.372613 | + | 0.645385i | ||||
\(845\) | −1.89887e7 | − | 3.28894e7i | −0.914859 | − | 1.58458i | ||||
\(846\) | 4.32614e6 | 0.207814 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.89720e6 | −0.186107 | ||||||||
\(849\) | 5.84676e6 | + | 1.01269e7i | 0.278385 | + | 0.482177i | ||||
\(850\) | 1.67822e6 | − | 2.90677e6i | 0.0796714 | − | 0.137995i | ||||
\(851\) | 56749.1 | − | 98292.3i | 0.00268618 | − | 0.00465260i | ||||
\(852\) | 4.83772e6 | + | 8.37919e6i | 0.228319 | + | 0.395460i | ||||
\(853\) | −1.02093e7 | −0.480424 | −0.240212 | − | 0.970720i | \(-0.577217\pi\) | ||||
−0.240212 | + | 0.970720i | \(0.577217\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.07329e7 | −0.502113 | ||||||||
\(856\) | −8.59980e6 | − | 1.48953e7i | −0.401147 | − | 0.694808i | ||||
\(857\) | −4.16603e6 | + | 7.21577e6i | −0.193763 | + | 0.335607i | −0.946494 | − | 0.322721i | \(-0.895403\pi\) |
0.752732 | + | 0.658328i | \(0.228736\pi\) | |||||||
\(858\) | 5.56406e6 | − | 9.63724e6i | 0.258032 | − | 0.446925i | ||||
\(859\) | 1.56383e7 | + | 2.70863e7i | 0.723113 | + | 1.25247i | 0.959746 | + | 0.280870i | \(0.0906229\pi\) |
−0.236633 | + | 0.971599i | \(0.576044\pi\) | |||||||
\(860\) | 107150. | 0.00494023 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.53084e7 | −0.701714 | ||||||||
\(863\) | 1.86787e7 | + | 3.23524e7i | 0.853726 | + | 1.47870i | 0.877822 | + | 0.478988i | \(0.158996\pi\) |
−0.0240955 | + | 0.999710i | \(0.507671\pi\) | |||||||
\(864\) | −8.66007e6 | + | 1.49997e7i | −0.394673 | + | 0.683593i | ||||
\(865\) | 8.54622e6 | − | 1.48025e7i | 0.388360 | − | 0.672658i | ||||
\(866\) | −5.31112e6 | − | 9.19913e6i | −0.240653 | − | 0.416823i | ||||
\(867\) | 168747. | 0.00762411 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4706.21 | 0.000211408 | ||||||||
\(870\) | 1.41110e6 | + | 2.44410e6i | 0.0632063 | + | 0.109477i | ||||
\(871\) | −3.69526e7 | + | 6.40037e7i | −1.65044 | + | 2.85864i | ||||
\(872\) | 6.84533e6 | − | 1.18565e7i | 0.304862 | − | 0.528036i | ||||
\(873\) | −311271. | − | 539138.i | −0.0138230 | − | 0.0239422i | ||||
\(874\) | 145704. | 0.00645199 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −291708. | −0.0128436 | ||||||||
\(877\) | −19498.3 | − | 33772.1i | −0.000856049 | − | 0.00148272i | 0.865597 | − | 0.500741i | \(-0.166939\pi\) |
−0.866453 | + | 0.499258i | \(0.833606\pi\) | |||||||
\(878\) | 3.30982e6 | − | 5.73278e6i | 0.144900 | − | 0.250974i | ||||
\(879\) | −2.79354e6 | + | 4.83855e6i | −0.121950 | + | 0.211224i | ||||
\(880\) | 4.13689e6 | + | 7.16530e6i | 0.180081 | + | 0.311909i | ||||
\(881\) | −3.15554e7 | −1.36973 | −0.684864 | − | 0.728671i | \(-0.740138\pi\) | ||||
−0.684864 | + | 0.728671i | \(0.740138\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.42253e7 | −1.47722 | −0.738611 | − | 0.674132i | \(-0.764518\pi\) | ||||
−0.738611 | + | 0.674132i | \(0.764518\pi\) | |||||||
\(884\) | −1.55505e7 | − | 2.69342e7i | −0.669288 | − | 1.15924i | ||||
\(885\) | −1.48425e6 | + | 2.57080e6i | −0.0637016 | + | 0.110334i | ||||
\(886\) | −6.76148e6 | + | 1.17112e7i | −0.289373 | + | 0.501208i | ||||
\(887\) | −1.34943e7 | − | 2.33728e7i | −0.575892 | − | 0.997474i | −0.995944 | − | 0.0899741i | \(-0.971322\pi\) |
0.420052 | − | 0.907500i | \(-0.362012\pi\) | |||||||
\(888\) | −2.64316e6 | −0.112484 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6.94022e6 | −0.293696 | ||||||||
\(891\) | 8.17475e6 | + | 1.41591e7i | 0.344969 | + | 0.597504i | ||||
\(892\) | −4.69632e6 | + | 8.13426e6i | −0.197627 | + | 0.342299i | ||||
\(893\) | 4.47743e6 | − | 7.75514e6i | 0.187888 | − | 0.325432i | ||||
\(894\) | 1.29407e6 | + | 2.24139e6i | 0.0541517 | + | 0.0937935i | ||||
\(895\) | 3.90940e6 | 0.163137 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 317982. | 0.0131954 | ||||||||
\(898\) | 3.89613e6 | + | 6.74830e6i | 0.161229 | + | 0.279257i | ||||
\(899\) | 1.46211e7 | − | 2.53244e7i | 0.603365 | − | 1.04506i | ||||
\(900\) | 2.43269e6 | − | 4.21354e6i | 0.100111 | − | 0.173397i | ||||
\(901\) | 7.05673e6 | + | 1.22226e7i | 0.289595 | + | 0.501594i | ||||
\(902\) | −1.98221e7 | −0.811211 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.60218e7 | 0.652065 | ||||||||
\(905\) | −8.72546e6 | − | 1.51129e7i | −0.354133 | − | 0.613377i | ||||
\(906\) | 1.10318e6 | − | 1.91077e6i | 0.0446506 | − | 0.0773372i | ||||
\(907\) | −9.60513e6 | + | 1.66366e7i | −0.387690 | + | 0.671499i | −0.992138 | − | 0.125145i | \(-0.960060\pi\) |
0.604448 | + | 0.796644i | \(0.293394\pi\) | |||||||
\(908\) | −3.50721e6 | − | 6.07467e6i | −0.141172 | − | 0.244516i | ||||
\(909\) | 4.36988e6 | 0.175412 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.86013e7 | 1.14180 | 0.570899 | − | 0.821020i | \(-0.306595\pi\) | ||||
0.570899 | + | 0.821020i | \(0.306595\pi\) | |||||||
\(912\) | 1.24477e6 | + | 2.15601e6i | 0.0495567 | + | 0.0858347i | ||||
\(913\) | 2.62204e7 | − | 4.54151e7i | 1.04103 | − | 1.80311i | ||||
\(914\) | −340014. | + | 588921.i | −0.0134627 | + | 0.0233180i | ||||
\(915\) | 5.79983e6 | + | 1.00456e7i | 0.229014 | + | 0.396664i | ||||
\(916\) | −2.96224e7 | −1.16649 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 9.64426e6 | 0.377713 | ||||||||
\(919\) | 2.10877e7 | + | 3.65249e7i | 0.823645 | + | 1.42660i | 0.902950 | + | 0.429745i | \(0.141396\pi\) |
−0.0793054 | + | 0.996850i | \(0.525270\pi\) | |||||||
\(920\) | 161117. | − | 279063.i | 0.00627585 | − | 0.0108701i | ||||
\(921\) | 6.41930e6 | − | 1.11185e7i | 0.249367 | − | 0.431916i | ||||
\(922\) | 1.39428e6 | + | 2.41496e6i | 0.0540159 | + | 0.0935582i | ||||
\(923\) | 6.71498e7 | 2.59442 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.58224e6 | 0.0992299 | ||||||||
\(926\) | −8.73360e6 | − | 1.51270e7i | −0.334708 | − | 0.579731i | ||||
\(927\) | −6.53818e6 | + | 1.13245e7i | −0.249895 | + | 0.432831i | ||||
\(928\) | −9.93580e6 | + | 1.72093e7i | −0.378733 | + | 0.655985i | ||||
\(929\) | −1.50943e7 | − | 2.61441e7i | −0.573817 | − | 0.993881i | −0.996169 | − | 0.0874487i | \(-0.972129\pi\) |
0.422352 | − | 0.906432i | \(-0.361205\pi\) | |||||||
\(930\) | 7.44673e6 | 0.282331 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.75130e6 | −0.103752 | ||||||||
\(933\) | −2.82745e6 | − | 4.89728e6i | −0.106338 | − | 0.184184i | ||||
\(934\) | −9.69085e6 | + | 1.67850e7i | −0.363492 | + | 0.629586i | ||||
\(935\) | 1.49815e7 | − | 2.59487e7i | 0.560436 | − | 0.970703i | ||||
\(936\) | 1.72817e7 | + | 2.99328e7i | 0.644758 | + | 1.11675i | ||||
\(937\) | 3.64068e6 | 0.135467 | 0.0677335 | − | 0.997703i | \(-0.478423\pi\) | ||||
0.0677335 | + | 0.997703i | \(0.478423\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.20589e6 | 0.266701 | ||||||||
\(940\) | −4.25138e6 | − | 7.36360e6i | −0.156931 | − | 0.271813i | ||||
\(941\) | 9.43004e6 | − | 1.63333e7i | 0.347168 | − | 0.601312i | −0.638577 | − | 0.769558i | \(-0.720477\pi\) |
0.985745 | + | 0.168245i | \(0.0538101\pi\) | |||||||
\(942\) | −899693. | + | 1.55831e6i | −0.0330344 | + | 0.0572173i | ||||
\(943\) | −283205. | − | 490525.i | −0.0103710 | − | 0.0179631i | ||||
\(944\) | −3.21380e6 | −0.117379 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 150315. | 0.00546104 | ||||||||
\(947\) | 9.10858e6 | + | 1.57765e7i | 0.330047 | + | 0.571658i | 0.982521 | − | 0.186153i | \(-0.0596021\pi\) |
−0.652474 | + | 0.757811i | \(0.726269\pi\) | |||||||
\(948\) | 672.291 | − | 1164.44i | 2.42961e−5 | − | 4.20821e-5i | ||||
\(949\) | −1.01226e6 | + | 1.75328e6i | −0.0364860 | + | 0.0631956i | ||||
\(950\) | 1.65749e6 | + | 2.87085e6i | 0.0595856 | + | 0.103205i | ||||
\(951\) | −9.79522e6 | −0.351207 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.76898e7 | 0.987616 | 0.493808 | − | 0.869571i | \(-0.335604\pi\) | ||||
0.493808 | + | 0.869571i | \(0.335604\pi\) | |||||||
\(954\) | −3.36703e6 | − | 5.83186e6i | −0.119778 | − | 0.207461i | ||||
\(955\) | 2.12064e7 | − | 3.67305e7i | 0.752416 | − | 1.30322i | ||||
\(956\) | −1.38171e7 | + | 2.39320e7i | −0.488960 | + | 0.846904i | ||||
\(957\) | −6.01399e6 | − | 1.04165e7i | −0.212267 | − | 0.367657i | ||||
\(958\) | 1.52376e7 | 0.536419 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.91852e6 | −0.0671875 | ||||||||
\(961\) | −2.42649e7 | − | 4.20280e7i | −0.847559 | − | 1.46801i | ||||
\(962\) | −3.93793e6 | + | 6.82069e6i | −0.137192 | + | 0.237624i | ||||
\(963\) | −1.09025e7 | + | 1.88836e7i | −0.378843 | + | 0.656175i | ||||
\(964\) | −9.78311e6 | − | 1.69449e7i | −0.339066 | − | 0.587280i | ||||
\(965\) | 2.32304e7 | 0.803042 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.44768e7 | −0.841761 | −0.420881 | − | 0.907116i | \(-0.638279\pi\) | ||||
−0.420881 | + | 0.907116i | \(0.638279\pi\) | |||||||
\(968\) | 1.13192e7 | + | 1.96054e7i | 0.388263 | + | 0.672492i | ||||
\(969\) | 4.50786e6 | − | 7.80784e6i | 0.154227 | − | 0.267129i | ||||
\(970\) | 201374. | − | 348791.i | 0.00687187 | − | 0.0119024i | ||||
\(971\) | 4.75076e6 | + | 8.22855e6i | 0.161702 | + | 0.280076i | 0.935479 | − | 0.353382i | \(-0.114968\pi\) |
−0.773777 | + | 0.633458i | \(0.781635\pi\) | |||||||
\(972\) | 2.16463e7 | 0.734881 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −8.47457e6 | −0.286233 | ||||||||
\(975\) | 3.61727e6 | + | 6.26530e6i | 0.121862 | + | 0.211072i | ||||
\(976\) | −6.27908e6 | + | 1.08757e7i | −0.210995 | + | 0.365454i | ||||
\(977\) | −2.34506e7 | + | 4.06176e7i | −0.785991 | + | 1.36138i | 0.142414 | + | 0.989807i | \(0.454514\pi\) |
−0.928405 | + | 0.371570i | \(0.878820\pi\) | |||||||
\(978\) | 1.68366e6 | + | 2.91619e6i | 0.0562870 | + | 0.0974920i | ||||
\(979\) | 2.95785e7 | 0.986325 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.73564e7 | −0.575822 | ||||||||
\(982\) | 1.01976e7 | + | 1.76627e7i | 0.337457 | + | 0.584492i | ||||
\(983\) | 1.17691e7 | − | 2.03847e7i | 0.388473 | − | 0.672854i | −0.603772 | − | 0.797157i | \(-0.706336\pi\) |
0.992244 | + | 0.124303i | \(0.0396695\pi\) | |||||||
\(984\) | −6.59531e6 | + | 1.14234e7i | −0.217144 | + | 0.376104i | ||||
\(985\) | −5.78349e6 | − | 1.00173e7i | −0.189933 | − | 0.328973i | ||||
\(986\) | 1.10650e7 | 0.362458 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.07167e7 | 1.00111 | ||||||||
\(989\) | 2147.60 | + | 3719.76i | 6.98174e−5 | + | 0.000120927i | ||||
\(990\) | −7.14822e6 | + | 1.23811e7i | −0.231798 | + | 0.401486i | ||||
\(991\) | 1.32052e7 | − | 2.28721e7i | 0.427130 | − | 0.739812i | −0.569486 | − | 0.822001i | \(-0.692858\pi\) |
0.996617 | + | 0.0821892i | \(0.0261912\pi\) | |||||||
\(992\) | 2.62168e7 | + | 4.54089e7i | 0.845865 | + | 1.46508i | ||||
\(993\) | 1.79426e7 | 0.577446 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.56766e6 | 0.306371 | ||||||||
\(996\) | −7.49127e6 | − | 1.29753e7i | −0.239280 | − | 0.414446i | ||||
\(997\) | −9.75818e6 | + | 1.69017e7i | −0.310907 | + | 0.538507i | −0.978559 | − | 0.205966i | \(-0.933966\pi\) |
0.667652 | + | 0.744474i | \(0.267300\pi\) | |||||||
\(998\) | 7.21768e6 | − | 1.25014e7i | 0.229388 | − | 0.397312i | ||||
\(999\) | 3.70985e6 | + | 6.42565e6i | 0.117610 | + | 0.203706i |
(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 | 49.6.c.h.18.2 | 8 | ||
7.2 | even | 3 | inner | 49.6.c.h.30.2 | 8 | ||
7.3 | odd | 6 | 49.6.a.g.1.4 | yes | 4 | ||
7.4 | even | 3 | 49.6.a.g.1.3 | ✓ | 4 | ||
7.5 | odd | 6 | inner | 49.6.c.h.30.1 | 8 | ||
7.6 | odd | 2 | inner | 49.6.c.h.18.1 | 8 | ||
21.11 | odd | 6 | 441.6.a.z.1.1 | 4 | |||
21.17 | even | 6 | 441.6.a.z.1.2 | 4 | |||
28.3 | even | 6 | 784.6.a.bf.1.2 | 4 | |||
28.11 | odd | 6 | 784.6.a.bf.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.6.a.g.1.3 | ✓ | 4 | 7.4 | even | 3 | ||
49.6.a.g.1.4 | yes | 4 | 7.3 | odd | 6 | ||
49.6.c.h.18.1 | 8 | 7.6 | odd | 2 | inner | ||
49.6.c.h.18.2 | 8 | 1.1 | even | 1 | trivial | ||
49.6.c.h.30.1 | 8 | 7.5 | odd | 6 | inner | ||
49.6.c.h.30.2 | 8 | 7.2 | even | 3 | inner | ||
441.6.a.z.1.1 | 4 | 21.11 | odd | 6 | |||
441.6.a.z.1.2 | 4 | 21.17 | even | 6 | |||
784.6.a.bf.1.2 | 4 | 28.3 | even | 6 | |||
784.6.a.bf.1.3 | 4 | 28.11 | odd | 6 |