Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [575,4,Mod(24,575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(575, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("575.24");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 575 = 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 575.b (of order \(2\), degree \(1\), 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: | \(33.9260982533\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{109})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 55x^{2} + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 115) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.1 | ||
Root | \(4.72015i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 575.24 |
Dual form | 575.4.b.f.24.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/575\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 3.00000i | − 1.06066i | −0.847791 | − | 0.530330i | \(-0.822068\pi\) | ||||
0.847791 | − | 0.530330i | \(-0.177932\pi\) | |||||||
\(3\) | − 3.72015i | − 0.715944i | −0.933732 | − | 0.357972i | \(-0.883468\pi\) | ||||
0.933732 | − | 0.357972i | \(-0.116532\pi\) | |||||||
\(4\) | −1.00000 | −0.125000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −11.1605 | −0.759373 | ||||||||
\(7\) | − 25.6008i | − 1.38231i | −0.722706 | − | 0.691156i | \(-0.757102\pi\) | ||||
0.722706 | − | 0.691156i | \(-0.242898\pi\) | |||||||
\(8\) | − 21.0000i | − 0.928078i | ||||||||
\(9\) | 13.1605 | 0.487424 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.6008 | 0.345389 | 0.172694 | − | 0.984975i | \(-0.444753\pi\) | ||||
0.172694 | + | 0.984975i | \(0.444753\pi\) | |||||||
\(12\) | 3.72015i | 0.0894930i | ||||||||
\(13\) | − 8.16046i | − 0.174100i | −0.996204 | − | 0.0870502i | \(-0.972256\pi\) | ||||
0.996204 | − | 0.0870502i | \(-0.0277440\pi\) | |||||||
\(14\) | −76.8023 | −1.46616 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −71.0000 | −1.10938 | ||||||||
\(17\) | − 76.0411i | − 1.08486i | −0.840100 | − | 0.542431i | \(-0.817504\pi\) | ||||
0.840100 | − | 0.542431i | \(-0.182496\pi\) | |||||||
\(18\) | − 39.4814i | − 0.516992i | ||||||||
\(19\) | 103.362 | 1.24805 | 0.624023 | − | 0.781406i | \(-0.285497\pi\) | ||||
0.624023 | + | 0.781406i | \(0.285497\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −95.2388 | −0.989657 | ||||||||
\(22\) | − 37.8023i | − 0.366340i | ||||||||
\(23\) | 23.0000i | 0.208514i | ||||||||
\(24\) | −78.1232 | −0.664451 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −24.4814 | −0.184661 | ||||||||
\(27\) | − 149.403i | − 1.06491i | ||||||||
\(28\) | 25.6008i | 0.172789i | ||||||||
\(29\) | 267.202 | 1.71097 | 0.855484 | − | 0.517829i | \(-0.173260\pi\) | ||||
0.855484 | + | 0.517829i | \(0.173260\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −63.7574 | −0.369392 | −0.184696 | − | 0.982796i | \(-0.559130\pi\) | ||||
−0.184696 | + | 0.982796i | \(0.559130\pi\) | |||||||
\(32\) | 45.0000i | 0.248592i | ||||||||
\(33\) | − 46.8768i | − 0.247279i | ||||||||
\(34\) | −228.123 | −1.15067 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −13.1605 | −0.0609281 | ||||||||
\(37\) | 112.164i | 0.498370i | 0.968456 | + | 0.249185i | \(0.0801627\pi\) | ||||
−0.968456 | + | 0.249185i | \(0.919837\pi\) | |||||||
\(38\) | − 310.086i | − 1.32375i | ||||||||
\(39\) | −30.3582 | −0.124646 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −239.078 | −0.910677 | −0.455339 | − | 0.890318i | \(-0.650482\pi\) | ||||
−0.455339 | + | 0.890318i | \(0.650482\pi\) | |||||||
\(42\) | 285.716i | 1.04969i | ||||||||
\(43\) | − 282.239i | − 1.00095i | −0.865750 | − | 0.500477i | \(-0.833158\pi\) | ||||
0.865750 | − | 0.500477i | \(-0.166842\pi\) | |||||||
\(44\) | −12.6008 | −0.0431736 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 69.0000 | 0.221163 | ||||||||
\(47\) | 577.291i | 1.79163i | 0.444427 | + | 0.895815i | \(0.353407\pi\) | ||||
−0.444427 | + | 0.895815i | \(0.646593\pi\) | |||||||
\(48\) | 264.131i | 0.794250i | ||||||||
\(49\) | −312.399 | −0.910785 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −282.884 | −0.776701 | ||||||||
\(52\) | 8.16046i | 0.0217625i | ||||||||
\(53\) | 2.31326i | 0.00599529i | 0.999996 | + | 0.00299764i | \(0.000954181\pi\) | ||||
−0.999996 | + | 0.00299764i | \(0.999046\pi\) | |||||||
\(54\) | −448.209 | −1.12951 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −537.616 | −1.28289 | ||||||||
\(57\) | − 384.522i | − 0.893531i | ||||||||
\(58\) | − 801.605i | − 1.81476i | ||||||||
\(59\) | −272.888 | −0.602153 | −0.301077 | − | 0.953600i | \(-0.597346\pi\) | ||||
−0.301077 | + | 0.953600i | \(0.597346\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 294.049 | 0.617198 | 0.308599 | − | 0.951192i | \(-0.400140\pi\) | ||||
0.308599 | + | 0.951192i | \(0.400140\pi\) | |||||||
\(62\) | 191.272i | 0.391800i | ||||||||
\(63\) | − 336.918i | − 0.673772i | ||||||||
\(64\) | −433.000 | −0.845703 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −140.630 | −0.262279 | ||||||||
\(67\) | 426.732i | 0.778113i | 0.921214 | + | 0.389056i | \(0.127199\pi\) | ||||
−0.921214 | + | 0.389056i | \(0.872801\pi\) | |||||||
\(68\) | 76.0411i | 0.135608i | ||||||||
\(69\) | 85.5635 | 0.149285 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1020.85 | −1.70638 | −0.853191 | − | 0.521598i | \(-0.825336\pi\) | ||||
−0.853191 | + | 0.521598i | \(0.825336\pi\) | |||||||
\(72\) | − 276.370i | − 0.452368i | ||||||||
\(73\) | 286.650i | 0.459586i | 0.973240 | + | 0.229793i | \(0.0738049\pi\) | ||||
−0.973240 | + | 0.229793i | \(0.926195\pi\) | |||||||
\(74\) | 336.493 | 0.528601 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −103.362 | −0.156006 | ||||||||
\(77\) | − 322.589i | − 0.477435i | ||||||||
\(78\) | 91.0745i | 0.132207i | ||||||||
\(79\) | 551.866 | 0.785947 | 0.392974 | − | 0.919550i | \(-0.371446\pi\) | ||||
0.392974 | + | 0.919550i | \(0.371446\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −200.470 | −0.274993 | ||||||||
\(82\) | 717.235i | 0.965919i | ||||||||
\(83\) | − 21.7021i | − 0.0287001i | −0.999897 | − | 0.0143501i | \(-0.995432\pi\) | ||||
0.999897 | − | 0.0143501i | \(-0.00456793\pi\) | |||||||
\(84\) | 95.2388 | 0.123707 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −846.716 | −1.06167 | ||||||||
\(87\) | − 994.031i | − 1.22496i | ||||||||
\(88\) | − 264.616i | − 0.320547i | ||||||||
\(89\) | 1049.63 | 1.25012 | 0.625058 | − | 0.780578i | \(-0.285075\pi\) | ||||
0.625058 | + | 0.780578i | \(0.285075\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −208.914 | −0.240661 | ||||||||
\(92\) | − 23.0000i | − 0.0260643i | ||||||||
\(93\) | 237.187i | 0.264464i | ||||||||
\(94\) | 1731.87 | 1.90031 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 167.407 | 0.177978 | ||||||||
\(97\) | 1729.19i | 1.81003i | 0.425381 | + | 0.905014i | \(0.360140\pi\) | ||||
−0.425381 | + | 0.905014i | \(0.639860\pi\) | |||||||
\(98\) | 937.198i | 0.966033i | ||||||||
\(99\) | 165.832 | 0.168351 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 855.874 | 0.843195 | 0.421597 | − | 0.906783i | \(-0.361470\pi\) | ||||
0.421597 | + | 0.906783i | \(0.361470\pi\) | |||||||
\(102\) | 848.653i | 0.823816i | ||||||||
\(103\) | 632.534i | 0.605101i | 0.953133 | + | 0.302551i | \(0.0978381\pi\) | ||||
−0.953133 | + | 0.302551i | \(0.902162\pi\) | |||||||
\(104\) | −171.370 | −0.161579 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.93977 | 0.00635896 | ||||||||
\(107\) | 1309.62i | 1.18323i | 0.806220 | + | 0.591616i | \(0.201510\pi\) | ||||
−0.806220 | + | 0.591616i | \(0.798490\pi\) | |||||||
\(108\) | 149.403i | 0.133114i | ||||||||
\(109\) | −1726.21 | −1.51689 | −0.758443 | − | 0.651739i | \(-0.774040\pi\) | ||||
−0.758443 | + | 0.651739i | \(0.774040\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 417.268 | 0.356805 | ||||||||
\(112\) | 1817.65i | 1.53350i | ||||||||
\(113\) | 1492.24i | 1.24228i | 0.783698 | + | 0.621142i | \(0.213331\pi\) | ||||
−0.783698 | + | 0.621142i | \(0.786669\pi\) | |||||||
\(114\) | −1153.57 | −0.947732 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −267.202 | −0.213871 | ||||||||
\(117\) | − 107.395i | − 0.0848608i | ||||||||
\(118\) | 818.665i | 0.638680i | ||||||||
\(119\) | −1946.71 | −1.49962 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1172.22 | −0.880707 | ||||||||
\(122\) | − 882.146i | − 0.654637i | ||||||||
\(123\) | 889.408i | 0.651994i | ||||||||
\(124\) | 63.7574 | 0.0461741 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1010.75 | −0.714644 | ||||||||
\(127\) | − 1368.29i | − 0.956034i | −0.878351 | − | 0.478017i | \(-0.841356\pi\) | ||||
0.878351 | − | 0.478017i | \(-0.158644\pi\) | |||||||
\(128\) | 1659.00i | 1.14560i | ||||||||
\(129\) | −1049.97 | −0.716627 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1984.24 | 1.32339 | 0.661694 | − | 0.749774i | \(-0.269838\pi\) | ||||
0.661694 | + | 0.749774i | \(0.269838\pi\) | |||||||
\(132\) | 46.8768i | 0.0309098i | ||||||||
\(133\) | − 2646.15i | − 1.72519i | ||||||||
\(134\) | 1280.19 | 0.825313 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1596.86 | −1.00684 | ||||||||
\(137\) | 273.331i | 0.170455i | 0.996362 | + | 0.0852273i | \(0.0271616\pi\) | ||||
−0.996362 | + | 0.0852273i | \(0.972838\pi\) | |||||||
\(138\) | − 256.691i | − 0.158340i | ||||||||
\(139\) | 557.889 | 0.340428 | 0.170214 | − | 0.985407i | \(-0.445554\pi\) | ||||
0.170214 | + | 0.985407i | \(0.445554\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2147.61 | 1.28271 | ||||||||
\(142\) | 3062.56i | 1.80989i | ||||||||
\(143\) | − 102.828i | − 0.0601323i | ||||||||
\(144\) | −934.393 | −0.540736 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 859.949 | 0.487465 | ||||||||
\(147\) | 1162.17i | 0.652071i | ||||||||
\(148\) | − 112.164i | − 0.0622963i | ||||||||
\(149\) | 1354.16 | 0.744545 | 0.372272 | − | 0.928124i | \(-0.378579\pi\) | ||||
0.372272 | + | 0.928124i | \(0.378579\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 162.652 | 0.0876586 | 0.0438293 | − | 0.999039i | \(-0.486044\pi\) | ||||
0.0438293 | + | 0.999039i | \(0.486044\pi\) | |||||||
\(152\) | − 2170.60i | − 1.15828i | ||||||||
\(153\) | − 1000.74i | − 0.528789i | ||||||||
\(154\) | −967.768 | −0.506396 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 30.3582 | 0.0155808 | ||||||||
\(157\) | − 2364.83i | − 1.20213i | −0.799201 | − | 0.601063i | \(-0.794744\pi\) | ||||
0.799201 | − | 0.601063i | \(-0.205256\pi\) | |||||||
\(158\) | − 1655.60i | − 0.833623i | ||||||||
\(159\) | 8.60567 | 0.00429229 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 588.818 | 0.288232 | ||||||||
\(162\) | 601.410i | 0.291674i | ||||||||
\(163\) | − 471.162i | − 0.226406i | −0.993572 | − | 0.113203i | \(-0.963889\pi\) | ||||
0.993572 | − | 0.113203i | \(-0.0361111\pi\) | |||||||
\(164\) | 239.078 | 0.113835 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −65.1062 | −0.0304411 | ||||||||
\(167\) | − 3735.73i | − 1.73102i | −0.500895 | − | 0.865508i | \(-0.666996\pi\) | ||||
0.500895 | − | 0.865508i | \(-0.333004\pi\) | |||||||
\(168\) | 2000.01i | 0.918479i | ||||||||
\(169\) | 2130.41 | 0.969689 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1360.29 | 0.608328 | ||||||||
\(172\) | 282.239i | 0.125119i | ||||||||
\(173\) | 2709.33i | 1.19067i | 0.803477 | + | 0.595336i | \(0.202981\pi\) | ||||
−0.803477 | + | 0.595336i | \(0.797019\pi\) | |||||||
\(174\) | −2982.09 | −1.29926 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −894.654 | −0.383165 | ||||||||
\(177\) | 1015.19i | 0.431108i | ||||||||
\(178\) | − 3148.88i | − 1.32595i | ||||||||
\(179\) | −3300.43 | −1.37813 | −0.689066 | − | 0.724699i | \(-0.741979\pi\) | ||||
−0.689066 | + | 0.724699i | \(0.741979\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −583.868 | −0.239771 | −0.119886 | − | 0.992788i | \(-0.538253\pi\) | ||||
−0.119886 | + | 0.992788i | \(0.538253\pi\) | |||||||
\(182\) | 626.742i | 0.255259i | ||||||||
\(183\) | − 1093.91i | − 0.441879i | ||||||||
\(184\) | 483.000 | 0.193518 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 711.562 | 0.280507 | ||||||||
\(187\) | − 958.176i | − 0.374699i | ||||||||
\(188\) | − 577.291i | − 0.223954i | ||||||||
\(189\) | −3824.83 | −1.47204 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3058.98 | −1.15885 | −0.579424 | − | 0.815026i | \(-0.696722\pi\) | ||||
−0.579424 | + | 0.815026i | \(0.696722\pi\) | |||||||
\(192\) | 1610.83i | 0.605476i | ||||||||
\(193\) | 1336.93i | 0.498625i | 0.968423 | + | 0.249313i | \(0.0802046\pi\) | ||||
−0.968423 | + | 0.249313i | \(0.919795\pi\) | |||||||
\(194\) | 5187.57 | 1.91983 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 312.399 | 0.113848 | ||||||||
\(197\) | − 2449.21i | − 0.885783i | −0.896575 | − | 0.442892i | \(-0.853953\pi\) | ||||
0.896575 | − | 0.442892i | \(-0.146047\pi\) | |||||||
\(198\) | − 497.496i | − 0.178563i | ||||||||
\(199\) | −1138.66 | −0.405614 | −0.202807 | − | 0.979219i | \(-0.565006\pi\) | ||||
−0.202807 | + | 0.979219i | \(0.565006\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1587.51 | 0.557085 | ||||||||
\(202\) | − 2567.62i | − 0.894343i | ||||||||
\(203\) | − 6840.56i | − 2.36509i | ||||||||
\(204\) | 282.884 | 0.0970876 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1897.60 | 0.641807 | ||||||||
\(207\) | 302.691i | 0.101635i | ||||||||
\(208\) | 579.393i | 0.193143i | ||||||||
\(209\) | 1302.44 | 0.431061 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5596.81 | 1.82607 | 0.913034 | − | 0.407884i | \(-0.133733\pi\) | ||||
0.913034 | + | 0.407884i | \(0.133733\pi\) | |||||||
\(212\) | − 2.31326i | 0 0.000749411i | ||||||||
\(213\) | 3797.74i | 1.22167i | ||||||||
\(214\) | 3928.86 | 1.25501 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3137.46 | −0.988321 | ||||||||
\(217\) | 1632.24i | 0.510615i | ||||||||
\(218\) | 5178.62i | 1.60890i | ||||||||
\(219\) | 1066.38 | 0.329038 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −620.530 | −0.188875 | ||||||||
\(222\) | − 1251.81i | − 0.378449i | ||||||||
\(223\) | − 5580.60i | − 1.67581i | −0.545820 | − | 0.837903i | \(-0.683782\pi\) | ||||
0.545820 | − | 0.837903i | \(-0.316218\pi\) | |||||||
\(224\) | 1152.03 | 0.343632 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4476.72 | 1.31764 | ||||||||
\(227\) | − 566.323i | − 0.165587i | −0.996567 | − | 0.0827934i | \(-0.973616\pi\) | ||||
0.996567 | − | 0.0827934i | \(-0.0263841\pi\) | |||||||
\(228\) | 384.522i | 0.111691i | ||||||||
\(229\) | 693.702 | 0.200180 | 0.100090 | − | 0.994978i | \(-0.468087\pi\) | ||||
0.100090 | + | 0.994978i | \(0.468087\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1200.08 | −0.341816 | ||||||||
\(232\) | − 5611.23i | − 1.58791i | ||||||||
\(233\) | 2208.68i | 0.621011i | 0.950572 | + | 0.310506i | \(0.100498\pi\) | ||||
−0.950572 | + | 0.310506i | \(0.899502\pi\) | |||||||
\(234\) | −322.186 | −0.0900084 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 272.888 | 0.0752691 | ||||||||
\(237\) | − 2053.03i | − 0.562694i | ||||||||
\(238\) | 5840.13i | 1.59059i | ||||||||
\(239\) | 3876.79 | 1.04924 | 0.524621 | − | 0.851336i | \(-0.324207\pi\) | ||||
0.524621 | + | 0.851336i | \(0.324207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2024.57 | −0.541136 | −0.270568 | − | 0.962701i | \(-0.587211\pi\) | ||||
−0.270568 | + | 0.962701i | \(0.587211\pi\) | |||||||
\(242\) | 3516.66i | 0.934131i | ||||||||
\(243\) | − 3288.10i | − 0.868033i | ||||||||
\(244\) | −294.049 | −0.0771498 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2668.22 | 0.691544 | ||||||||
\(247\) | − 843.481i | − 0.217285i | ||||||||
\(248\) | 1338.91i | 0.342825i | ||||||||
\(249\) | −80.7350 | −0.0205477 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −733.444 | −0.184441 | −0.0922203 | − | 0.995739i | \(-0.529396\pi\) | ||||
−0.0922203 | + | 0.995739i | \(0.529396\pi\) | |||||||
\(252\) | 336.918i | 0.0842215i | ||||||||
\(253\) | 289.818i | 0.0720185i | ||||||||
\(254\) | −4104.88 | −1.01403 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1513.00 | 0.369385 | ||||||||
\(257\) | 2367.83i | 0.574713i | 0.957824 | + | 0.287356i | \(0.0927764\pi\) | ||||
−0.957824 | + | 0.287356i | \(0.907224\pi\) | |||||||
\(258\) | 3149.91i | 0.760097i | ||||||||
\(259\) | 2871.49 | 0.688903 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3516.50 | 0.833968 | ||||||||
\(262\) | − 5952.72i | − 1.40366i | ||||||||
\(263\) | − 6632.76i | − 1.55511i | −0.628816 | − | 0.777554i | \(-0.716460\pi\) | ||||
0.628816 | − | 0.777554i | \(-0.283540\pi\) | |||||||
\(264\) | −984.412 | −0.229494 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7938.44 | −1.82984 | ||||||||
\(267\) | − 3904.78i | − 0.895013i | ||||||||
\(268\) | − 426.732i | − 0.0972641i | ||||||||
\(269\) | 6092.97 | 1.38102 | 0.690511 | − | 0.723322i | \(-0.257386\pi\) | ||||
0.690511 | + | 0.723322i | \(0.257386\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1981.30 | −0.444115 | −0.222058 | − | 0.975034i | \(-0.571277\pi\) | ||||
−0.222058 | + | 0.975034i | \(0.571277\pi\) | |||||||
\(272\) | 5398.92i | 1.20352i | ||||||||
\(273\) | 777.192i | 0.172300i | ||||||||
\(274\) | 819.994 | 0.180794 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −85.5635 | −0.0186606 | ||||||||
\(277\) | − 4097.42i | − 0.888773i | −0.895835 | − | 0.444386i | \(-0.853422\pi\) | ||||
0.895835 | − | 0.444386i | \(-0.146578\pi\) | |||||||
\(278\) | − 1673.67i | − 0.361079i | ||||||||
\(279\) | −839.077 | −0.180051 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3866.40 | −0.820819 | −0.410409 | − | 0.911901i | \(-0.634614\pi\) | ||||
−0.410409 | + | 0.911901i | \(0.634614\pi\) | |||||||
\(282\) | − 6442.84i | − 1.36052i | ||||||||
\(283\) | − 3982.00i | − 0.836415i | −0.908351 | − | 0.418208i | \(-0.862658\pi\) | ||||
0.908351 | − | 0.418208i | \(-0.137342\pi\) | |||||||
\(284\) | 1020.85 | 0.213298 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −308.484 | −0.0637799 | ||||||||
\(287\) | 6120.59i | 1.25884i | ||||||||
\(288\) | 592.221i | 0.121170i | ||||||||
\(289\) | −869.245 | −0.176927 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6432.86 | 1.29588 | ||||||||
\(292\) | − 286.650i | − 0.0574483i | ||||||||
\(293\) | 7491.70i | 1.49375i | 0.664962 | + | 0.746877i | \(0.268448\pi\) | ||||
−0.664962 | + | 0.746877i | \(0.731552\pi\) | |||||||
\(294\) | 3486.52 | 0.691626 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2355.45 | 0.462526 | ||||||||
\(297\) | − 1882.59i | − 0.367809i | ||||||||
\(298\) | − 4062.48i | − 0.789709i | ||||||||
\(299\) | 187.691 | 0.0363024 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7225.53 | −1.38363 | ||||||||
\(302\) | − 487.957i | − 0.0929760i | ||||||||
\(303\) | − 3183.98i | − 0.603680i | ||||||||
\(304\) | −7338.70 | −1.38455 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3002.21 | −0.560865 | ||||||||
\(307\) | − 5813.01i | − 1.08067i | −0.841450 | − | 0.540335i | \(-0.818297\pi\) | ||||
0.841450 | − | 0.540335i | \(-0.181703\pi\) | |||||||
\(308\) | 322.589i | 0.0596793i | ||||||||
\(309\) | 2353.12 | 0.433218 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4769.43 | 0.869613 | 0.434807 | − | 0.900524i | \(-0.356817\pi\) | ||||
0.434807 | + | 0.900524i | \(0.356817\pi\) | |||||||
\(312\) | 637.521i | 0.115681i | ||||||||
\(313\) | − 7053.43i | − 1.27375i | −0.770967 | − | 0.636875i | \(-0.780227\pi\) | ||||
0.770967 | − | 0.636875i | \(-0.219773\pi\) | |||||||
\(314\) | −7094.49 | −1.27505 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −551.866 | −0.0982434 | ||||||||
\(317\) | 8845.36i | 1.56721i | 0.621261 | + | 0.783604i | \(0.286621\pi\) | ||||
−0.621261 | + | 0.783604i | \(0.713379\pi\) | |||||||
\(318\) | − 25.8170i | − 0.00455266i | ||||||||
\(319\) | 3366.94 | 0.590949 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4871.99 | 0.847127 | ||||||||
\(322\) | − 1766.45i | − 0.305716i | ||||||||
\(323\) | − 7859.76i | − 1.35396i | ||||||||
\(324\) | 200.470 | 0.0343741 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1413.48 | −0.240140 | ||||||||
\(327\) | 6421.75i | 1.08601i | ||||||||
\(328\) | 5020.64i | 0.845179i | ||||||||
\(329\) | 14779.1 | 2.47659 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4264.07 | 0.708079 | 0.354040 | − | 0.935230i | \(-0.384808\pi\) | ||||
0.354040 | + | 0.935230i | \(0.384808\pi\) | |||||||
\(332\) | 21.7021i | 0.00358752i | ||||||||
\(333\) | 1476.13i | 0.242918i | ||||||||
\(334\) | −11207.2 | −1.83602 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6761.95 | 1.09790 | ||||||||
\(337\) | − 1290.58i | − 0.208613i | −0.994545 | − | 0.104306i | \(-0.966738\pi\) | ||||
0.994545 | − | 0.104306i | \(-0.0332622\pi\) | |||||||
\(338\) | − 6391.22i | − 1.02851i | ||||||||
\(339\) | 5551.36 | 0.889405 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −803.392 | −0.127584 | ||||||||
\(342\) | − 4080.87i | − 0.645229i | ||||||||
\(343\) | − 783.403i | − 0.123323i | ||||||||
\(344\) | −5927.01 | −0.928963 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8127.98 | 1.26290 | ||||||||
\(347\) | − 1805.09i | − 0.279257i | −0.990204 | − | 0.139629i | \(-0.955409\pi\) | ||||
0.990204 | − | 0.139629i | \(-0.0445909\pi\) | |||||||
\(348\) | 994.031i | 0.153120i | ||||||||
\(349\) | 3586.81 | 0.550136 | 0.275068 | − | 0.961425i | \(-0.411300\pi\) | ||||
0.275068 | + | 0.961425i | \(0.411300\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1219.20 | −0.185402 | ||||||||
\(352\) | 567.034i | 0.0858609i | ||||||||
\(353\) | 2292.90i | 0.345719i | 0.984947 | + | 0.172859i | \(0.0553006\pi\) | ||||
−0.984947 | + | 0.172859i | \(0.944699\pi\) | |||||||
\(354\) | 3045.56 | 0.457259 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1049.63 | −0.156264 | ||||||||
\(357\) | 7242.06i | 1.07364i | ||||||||
\(358\) | 9901.28i | 1.46173i | ||||||||
\(359\) | 3077.18 | 0.452388 | 0.226194 | − | 0.974082i | \(-0.427372\pi\) | ||||
0.226194 | + | 0.974082i | \(0.427372\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3824.70 | 0.557618 | ||||||||
\(362\) | 1751.60i | 0.254316i | ||||||||
\(363\) | 4360.84i | 0.630537i | ||||||||
\(364\) | 208.914 | 0.0300826 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3281.72 | −0.468684 | ||||||||
\(367\) | − 1378.56i | − 0.196076i | −0.995183 | − | 0.0980382i | \(-0.968743\pi\) | ||||
0.995183 | − | 0.0980382i | \(-0.0312567\pi\) | |||||||
\(368\) | − 1633.00i | − 0.231321i | ||||||||
\(369\) | −3146.38 | −0.443886 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 59.2211 | 0.00828736 | ||||||||
\(372\) | − 237.187i | − 0.0330580i | ||||||||
\(373\) | − 11182.3i | − 1.55227i | −0.630567 | − | 0.776135i | \(-0.717178\pi\) | ||||
0.630567 | − | 0.776135i | \(-0.282822\pi\) | |||||||
\(374\) | −2874.53 | −0.397429 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12123.1 | 1.66277 | ||||||||
\(377\) | − 2180.49i | − 0.297880i | ||||||||
\(378\) | 11474.5i | 1.56133i | ||||||||
\(379\) | −12021.9 | −1.62935 | −0.814677 | − | 0.579915i | \(-0.803086\pi\) | ||||
−0.814677 | + | 0.579915i | \(0.803086\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5090.26 | −0.684467 | ||||||||
\(382\) | 9176.93i | 1.22914i | ||||||||
\(383\) | 13274.6i | 1.77102i | 0.464617 | + | 0.885512i | \(0.346192\pi\) | ||||
−0.464617 | + | 0.885512i | \(0.653808\pi\) | |||||||
\(384\) | 6171.73 | 0.820182 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4010.80 | 0.528872 | ||||||||
\(387\) | − 3714.39i | − 0.487889i | ||||||||
\(388\) | − 1729.19i | − 0.226254i | ||||||||
\(389\) | −11016.4 | −1.43587 | −0.717934 | − | 0.696112i | \(-0.754912\pi\) | ||||
−0.717934 | + | 0.696112i | \(0.754912\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1748.94 | 0.226210 | ||||||||
\(392\) | 6560.38i | 0.845279i | ||||||||
\(393\) | − 7381.67i | − 0.947471i | ||||||||
\(394\) | −7347.64 | −0.939515 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −165.832 | −0.0210439 | ||||||||
\(397\) | − 1893.18i | − 0.239335i | −0.992814 | − | 0.119668i | \(-0.961817\pi\) | ||||
0.992814 | − | 0.119668i | \(-0.0381829\pi\) | |||||||
\(398\) | 3415.97i | 0.430219i | ||||||||
\(399\) | −9844.07 | −1.23514 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11281.8 | 1.40495 | 0.702475 | − | 0.711709i | \(-0.252078\pi\) | ||||
0.702475 | + | 0.711709i | \(0.252078\pi\) | |||||||
\(402\) | − 4762.52i | − 0.590878i | ||||||||
\(403\) | 520.290i | 0.0643113i | ||||||||
\(404\) | −855.874 | −0.105399 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20521.7 | −2.50856 | ||||||||
\(407\) | 1413.36i | 0.172131i | ||||||||
\(408\) | 5940.57i | 0.720839i | ||||||||
\(409\) | 14677.6 | 1.77447 | 0.887236 | − | 0.461316i | \(-0.152623\pi\) | ||||
0.887236 | + | 0.461316i | \(0.152623\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1016.83 | 0.122036 | ||||||||
\(412\) | − 632.534i | − 0.0756376i | ||||||||
\(413\) | 6986.15i | 0.832363i | ||||||||
\(414\) | 908.072 | 0.107800 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 367.221 | 0.0432800 | ||||||||
\(417\) | − 2075.43i | − 0.243728i | ||||||||
\(418\) | − 3907.32i | − 0.457209i | ||||||||
\(419\) | −2196.50 | −0.256100 | −0.128050 | − | 0.991768i | \(-0.540872\pi\) | ||||
−0.128050 | + | 0.991768i | \(0.540872\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6571.28 | −0.760723 | −0.380362 | − | 0.924838i | \(-0.624200\pi\) | ||||
−0.380362 | + | 0.924838i | \(0.624200\pi\) | |||||||
\(422\) | − 16790.4i | − 1.93684i | ||||||||
\(423\) | 7597.42i | 0.873284i | ||||||||
\(424\) | 48.5784 | 0.00556409 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 11393.2 | 1.29578 | ||||||||
\(427\) | − 7527.87i | − 0.853160i | ||||||||
\(428\) | − 1309.62i | − 0.147904i | ||||||||
\(429\) | −382.536 | −0.0430513 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −583.607 | −0.0652235 | −0.0326118 | − | 0.999468i | \(-0.510382\pi\) | ||||
−0.0326118 | + | 0.999468i | \(0.510382\pi\) | |||||||
\(432\) | 10607.6i | 1.18139i | ||||||||
\(433\) | 2677.60i | 0.297176i | 0.988899 | + | 0.148588i | \(0.0474728\pi\) | ||||
−0.988899 | + | 0.148588i | \(0.952527\pi\) | |||||||
\(434\) | 4896.71 | 0.541589 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1726.21 | 0.189611 | ||||||||
\(437\) | 2377.33i | 0.260236i | ||||||||
\(438\) | − 3199.14i | − 0.348997i | ||||||||
\(439\) | 5509.18 | 0.598949 | 0.299475 | − | 0.954104i | \(-0.403189\pi\) | ||||
0.299475 | + | 0.954104i | \(0.403189\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4111.32 | −0.443939 | ||||||||
\(442\) | 1861.59i | 0.200332i | ||||||||
\(443\) | 13054.6i | 1.40009i | 0.714097 | + | 0.700047i | \(0.246838\pi\) | ||||
−0.714097 | + | 0.700047i | \(0.753162\pi\) | |||||||
\(444\) | −417.268 | −0.0446006 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16741.8 | −1.77746 | ||||||||
\(447\) | − 5037.68i | − 0.533052i | ||||||||
\(448\) | 11085.1i | 1.16903i | ||||||||
\(449\) | 11819.1 | 1.24227 | 0.621135 | − | 0.783704i | \(-0.286672\pi\) | ||||
0.621135 | + | 0.783704i | \(0.286672\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3012.57 | −0.314537 | ||||||||
\(452\) | − 1492.24i | − 0.155285i | ||||||||
\(453\) | − 605.091i | − 0.0627587i | ||||||||
\(454\) | −1698.97 | −0.175631 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8074.97 | −0.829266 | ||||||||
\(457\) | − 4144.87i | − 0.424264i | −0.977241 | − | 0.212132i | \(-0.931959\pi\) | ||||
0.977241 | − | 0.212132i | \(-0.0680407\pi\) | |||||||
\(458\) | − 2081.11i | − 0.212323i | ||||||||
\(459\) | −11360.8 | −1.15528 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6061.38 | −0.612379 | −0.306189 | − | 0.951971i | \(-0.599054\pi\) | ||||
−0.306189 | + | 0.951971i | \(0.599054\pi\) | |||||||
\(462\) | 3600.24i | 0.362551i | ||||||||
\(463\) | 5729.13i | 0.575066i | 0.957771 | + | 0.287533i | \(0.0928350\pi\) | ||||
−0.957771 | + | 0.287533i | \(0.907165\pi\) | |||||||
\(464\) | −18971.3 | −1.89811 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6626.05 | 0.658682 | ||||||||
\(467\) | 8958.05i | 0.887643i | 0.896115 | + | 0.443821i | \(0.146378\pi\) | ||||
−0.896115 | + | 0.443821i | \(0.853622\pi\) | |||||||
\(468\) | 107.395i | 0.0106076i | ||||||||
\(469\) | 10924.7 | 1.07559 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8797.53 | −0.860655 | ||||||||
\(472\) | 5730.65i | 0.558845i | ||||||||
\(473\) | − 3556.42i | − 0.345718i | ||||||||
\(474\) | −6159.08 | −0.596827 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1946.71 | 0.187452 | ||||||||
\(477\) | 30.4435i | 0.00292225i | ||||||||
\(478\) | − 11630.4i | − 1.11289i | ||||||||
\(479\) | −6356.60 | −0.606347 | −0.303174 | − | 0.952935i | \(-0.598046\pi\) | ||||
−0.303174 | + | 0.952935i | \(0.598046\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 915.312 | 0.0867664 | ||||||||
\(482\) | 6073.70i | 0.573961i | ||||||||
\(483\) | − 2190.49i | − 0.206358i | ||||||||
\(484\) | 1172.22 | 0.110088 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9864.31 | −0.920688 | ||||||||
\(487\) | 13991.2i | 1.30185i | 0.759141 | + | 0.650926i | \(0.225619\pi\) | ||||
−0.759141 | + | 0.650926i | \(0.774381\pi\) | |||||||
\(488\) | − 6175.02i | − 0.572808i | ||||||||
\(489\) | −1752.79 | −0.162094 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5301.96 | −0.487320 | −0.243660 | − | 0.969861i | \(-0.578348\pi\) | ||||
−0.243660 | + | 0.969861i | \(0.578348\pi\) | |||||||
\(492\) | − 889.408i | − 0.0814992i | ||||||||
\(493\) | − 20318.3i | − 1.85617i | ||||||||
\(494\) | −2530.44 | −0.230466 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4526.78 | 0.409795 | ||||||||
\(497\) | 26134.7i | 2.35875i | ||||||||
\(498\) | 242.205i | 0.0217941i | ||||||||
\(499\) | 8013.45 | 0.718900 | 0.359450 | − | 0.933164i | \(-0.382964\pi\) | ||||
0.359450 | + | 0.933164i | \(0.382964\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13897.5 | −1.23931 | ||||||||
\(502\) | 2200.33i | 0.195629i | ||||||||
\(503\) | 11881.9i | 1.05325i | 0.850097 | + | 0.526627i | \(0.176544\pi\) | ||||
−0.850097 | + | 0.526627i | \(0.823456\pi\) | |||||||
\(504\) | −7075.27 | −0.625313 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 869.453 | 0.0763871 | ||||||||
\(507\) | − 7925.44i | − 0.694243i | ||||||||
\(508\) | 1368.29i | 0.119504i | ||||||||
\(509\) | 12113.8 | 1.05488 | 0.527441 | − | 0.849592i | \(-0.323152\pi\) | ||||
0.527441 | + | 0.849592i | \(0.323152\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7338.45 | 0.635291 | ||||||||
\(512\) | 8733.00i | 0.753804i | ||||||||
\(513\) | − 15442.6i | − 1.32906i | ||||||||
\(514\) | 7103.49 | 0.609575 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1049.97 | 0.0895783 | ||||||||
\(517\) | 7274.31i | 0.618808i | ||||||||
\(518\) | − 8614.48i | − 0.730692i | ||||||||
\(519\) | 10079.1 | 0.852454 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15327.6 | −1.28890 | −0.644449 | − | 0.764647i | \(-0.722913\pi\) | ||||
−0.644449 | + | 0.764647i | \(0.722913\pi\) | |||||||
\(522\) | − 10549.5i | − 0.884556i | ||||||||
\(523\) | − 14545.8i | − 1.21614i | −0.793883 | − | 0.608070i | \(-0.791944\pi\) | ||||
0.793883 | − | 0.608070i | \(-0.208056\pi\) | |||||||
\(524\) | −1984.24 | −0.165423 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19898.3 | −1.64944 | ||||||||
\(527\) | 4848.18i | 0.400740i | ||||||||
\(528\) | 3328.25i | 0.274325i | ||||||||
\(529\) | −529.000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3591.34 | −0.293504 | ||||||||
\(532\) | 2646.15i | 0.215648i | ||||||||
\(533\) | 1950.99i | 0.158549i | ||||||||
\(534\) | −11714.3 | −0.949304 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8961.36 | 0.722149 | ||||||||
\(537\) | 12278.1i | 0.986665i | ||||||||
\(538\) | − 18278.9i | − 1.46479i | ||||||||
\(539\) | −3936.47 | −0.314575 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5468.93 | −0.434617 | −0.217308 | − | 0.976103i | \(-0.569728\pi\) | ||||
−0.217308 | + | 0.976103i | \(0.569728\pi\) | |||||||
\(542\) | 5943.89i | 0.471055i | ||||||||
\(543\) | 2172.08i | 0.171663i | ||||||||
\(544\) | 3421.85 | 0.269688 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2331.58 | 0.182751 | ||||||||
\(547\) | − 19566.3i | − 1.52943i | −0.644371 | − | 0.764713i | \(-0.722881\pi\) | ||||
0.644371 | − | 0.764713i | \(-0.277119\pi\) | |||||||
\(548\) | − 273.331i | − 0.0213068i | ||||||||
\(549\) | 3869.82 | 0.300837 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27618.5 | 2.13537 | ||||||||
\(552\) | − 1796.83i | − 0.138548i | ||||||||
\(553\) | − 14128.2i | − 1.08642i | ||||||||
\(554\) | −12292.3 | −0.942686 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −557.889 | −0.0425536 | ||||||||
\(557\) | − 9803.11i | − 0.745729i | −0.927886 | − | 0.372865i | \(-0.878376\pi\) | ||||
0.927886 | − | 0.372865i | \(-0.121624\pi\) | |||||||
\(558\) | 2517.23i | 0.190973i | ||||||||
\(559\) | −2303.20 | −0.174266 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3564.56 | −0.268264 | ||||||||
\(562\) | 11599.2i | 0.870610i | ||||||||
\(563\) | 4909.73i | 0.367532i | 0.982970 | + | 0.183766i | \(0.0588288\pi\) | ||||
−0.982970 | + | 0.183766i | \(0.941171\pi\) | |||||||
\(564\) | −2147.61 | −0.160338 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11946.0 | −0.887153 | ||||||||
\(567\) | 5132.18i | 0.380126i | ||||||||
\(568\) | 21438.0i | 1.58366i | ||||||||
\(569\) | −11498.2 | −0.847155 | −0.423578 | − | 0.905860i | \(-0.639226\pi\) | ||||
−0.423578 | + | 0.905860i | \(0.639226\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14766.6 | 1.08225 | 0.541124 | − | 0.840943i | \(-0.317999\pi\) | ||||
0.541124 | + | 0.840943i | \(0.317999\pi\) | |||||||
\(572\) | 102.828i | 0.00751653i | ||||||||
\(573\) | 11379.9i | 0.829670i | ||||||||
\(574\) | 18361.8 | 1.33520 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5698.48 | −0.412216 | ||||||||
\(577\) | 13364.0i | 0.964212i | 0.876113 | + | 0.482106i | \(0.160128\pi\) | ||||
−0.876113 | + | 0.482106i | \(0.839872\pi\) | |||||||
\(578\) | 2607.73i | 0.187660i | ||||||||
\(579\) | 4973.60 | 0.356988 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −555.590 | −0.0396725 | ||||||||
\(582\) | − 19298.6i | − 1.37449i | ||||||||
\(583\) | 29.1488i | 0.00207070i | ||||||||
\(584\) | 6019.64 | 0.426532 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22475.1 | 1.58437 | ||||||||
\(587\) | 12524.7i | 0.880664i | 0.897835 | + | 0.440332i | \(0.145139\pi\) | ||||
−0.897835 | + | 0.440332i | \(0.854861\pi\) | |||||||
\(588\) | − 1162.17i | − 0.0815089i | ||||||||
\(589\) | −6590.09 | −0.461019 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9111.45 | −0.634171 | ||||||||
\(592\) | − 7963.66i | − 0.552879i | ||||||||
\(593\) | 17938.6i | 1.24224i | 0.783714 | + | 0.621121i | \(0.213323\pi\) | ||||
−0.783714 | + | 0.621121i | \(0.786677\pi\) | |||||||
\(594\) | −5647.78 | −0.390120 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1354.16 | −0.0930681 | ||||||||
\(597\) | 4235.98i | 0.290397i | ||||||||
\(598\) | − 563.072i | − 0.0385045i | ||||||||
\(599\) | 26735.8 | 1.82370 | 0.911848 | − | 0.410528i | \(-0.134656\pi\) | ||||
0.911848 | + | 0.410528i | \(0.134656\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21043.6 | −1.42826 | −0.714131 | − | 0.700012i | \(-0.753178\pi\) | ||||
−0.714131 | + | 0.700012i | \(0.753178\pi\) | |||||||
\(602\) | 21676.6i | 1.46756i | ||||||||
\(603\) | 5615.98i | 0.379271i | ||||||||
\(604\) | −162.652 | −0.0109573 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9551.95 | −0.640299 | ||||||||
\(607\) | 5098.83i | 0.340947i | 0.985362 | + | 0.170474i | \(0.0545298\pi\) | ||||
−0.985362 | + | 0.170474i | \(0.945470\pi\) | |||||||
\(608\) | 4651.29i | 0.310254i | ||||||||
\(609\) | −25447.9 | −1.69327 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4710.96 | 0.311923 | ||||||||
\(612\) | 1000.74i | 0.0660986i | ||||||||
\(613\) | 12784.8i | 0.842369i | 0.906975 | + | 0.421185i | \(0.138386\pi\) | ||||
−0.906975 | + | 0.421185i | \(0.861614\pi\) | |||||||
\(614\) | −17439.0 | −1.14622 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6774.37 | −0.443096 | ||||||||
\(617\) | − 8940.73i | − 0.583372i | −0.956514 | − | 0.291686i | \(-0.905784\pi\) | ||||
0.956514 | − | 0.291686i | \(-0.0942162\pi\) | |||||||
\(618\) | − 7059.37i | − 0.459498i | ||||||||
\(619\) | −1333.26 | −0.0865725 | −0.0432863 | − | 0.999063i | \(-0.513783\pi\) | ||||
−0.0432863 | + | 0.999063i | \(0.513783\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3436.27 | 0.222050 | ||||||||
\(622\) | − 14308.3i | − 0.922364i | ||||||||
\(623\) | − 26871.3i | − 1.72805i | ||||||||
\(624\) | 2155.43 | 0.138279 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −21160.3 | −1.35102 | ||||||||
\(627\) | − 4845.28i | − 0.308615i | ||||||||
\(628\) | 2364.83i | 0.150266i | ||||||||
\(629\) | 8529.09 | 0.540663 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16667.9 | −1.05157 | −0.525784 | − | 0.850618i | \(-0.676228\pi\) | ||||
−0.525784 | + | 0.850618i | \(0.676228\pi\) | |||||||
\(632\) | − 11589.2i | − 0.729420i | ||||||||
\(633\) | − 20821.0i | − 1.30736i | ||||||||
\(634\) | 26536.1 | 1.66228 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.60567 | −0.000536536 0 | ||||||||
\(637\) | 2549.32i | 0.158568i | ||||||||
\(638\) | − 10100.8i | − 0.626796i | ||||||||
\(639\) | −13434.9 | −0.831733 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27431.9 | 1.69032 | 0.845158 | − | 0.534516i | \(-0.179506\pi\) | ||||
0.845158 | + | 0.534516i | \(0.179506\pi\) | |||||||
\(642\) | − 14616.0i | − 0.898514i | ||||||||
\(643\) | − 9618.00i | − 0.589886i | −0.955515 | − | 0.294943i | \(-0.904699\pi\) | ||||
0.955515 | − | 0.294943i | \(-0.0953007\pi\) | |||||||
\(644\) | −588.818 | −0.0360290 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −23579.3 | −1.43609 | ||||||||
\(647\) | − 12548.6i | − 0.762496i | −0.924473 | − | 0.381248i | \(-0.875494\pi\) | ||||
0.924473 | − | 0.381248i | \(-0.124506\pi\) | |||||||
\(648\) | 4209.87i | 0.255215i | ||||||||
\(649\) | −3438.60 | −0.207977 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6072.18 | 0.365572 | ||||||||
\(652\) | 471.162i | 0.0283008i | ||||||||
\(653\) | 8829.79i | 0.529152i | 0.964365 | + | 0.264576i | \(0.0852320\pi\) | ||||
−0.964365 | + | 0.264576i | \(0.914768\pi\) | |||||||
\(654\) | 19265.3 | 1.15188 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 16974.6 | 1.01028 | ||||||||
\(657\) | 3772.44i | 0.224014i | ||||||||
\(658\) | − 44337.3i | − 2.62682i | ||||||||
\(659\) | −5935.56 | −0.350860 | −0.175430 | − | 0.984492i | \(-0.556132\pi\) | ||||
−0.175430 | + | 0.984492i | \(0.556132\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1182.03 | −0.0695549 | −0.0347775 | − | 0.999395i | \(-0.511072\pi\) | ||||
−0.0347775 | + | 0.999395i | \(0.511072\pi\) | |||||||
\(662\) | − 12792.2i | − 0.751032i | ||||||||
\(663\) | 2308.47i | 0.135224i | ||||||||
\(664\) | −455.743 | −0.0266360 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4428.40 | 0.257653 | ||||||||
\(667\) | 6145.64i | 0.356762i | ||||||||
\(668\) | 3735.73i | 0.216377i | ||||||||
\(669\) | −20760.7 | −1.19978 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3705.24 | 0.213173 | ||||||||
\(672\) | − 4285.74i | − 0.246021i | ||||||||
\(673\) | 6053.25i | 0.346710i | 0.984859 | + | 0.173355i | \(0.0554608\pi\) | ||||
−0.984859 | + | 0.173355i | \(0.944539\pi\) | |||||||
\(674\) | −3871.74 | −0.221267 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2130.41 | −0.121211 | ||||||||
\(677\) | 16694.2i | 0.947728i | 0.880598 | + | 0.473864i | \(0.157141\pi\) | ||||
−0.880598 | + | 0.473864i | \(0.842859\pi\) | |||||||
\(678\) | − 16654.1i | − 0.943357i | ||||||||
\(679\) | 44268.6 | 2.50202 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2106.81 | −0.118551 | ||||||||
\(682\) | 2410.18i | 0.135323i | ||||||||
\(683\) | 4150.03i | 0.232499i | 0.993220 | + | 0.116249i | \(0.0370871\pi\) | ||||
−0.993220 | + | 0.116249i | \(0.962913\pi\) | |||||||
\(684\) | −1360.29 | −0.0760410 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2350.21 | −0.130804 | ||||||||
\(687\) | − 2580.68i | − 0.143317i | ||||||||
\(688\) | 20039.0i | 1.11043i | ||||||||
\(689\) | 18.8772 | 0.00104378 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33382.4 | 1.83781 | 0.918904 | − | 0.394481i | \(-0.129076\pi\) | ||||
0.918904 | + | 0.394481i | \(0.129076\pi\) | |||||||
\(692\) | − 2709.33i | − 0.148834i | ||||||||
\(693\) | − 4245.42i | − 0.232713i | ||||||||
\(694\) | −5415.27 | −0.296197 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −20874.6 | −1.13686 | ||||||||
\(697\) | 18179.8i | 0.987960i | ||||||||
\(698\) | − 10760.4i | − 0.583508i | ||||||||
\(699\) | 8216.64 | 0.444609 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29528.7 | −1.59099 | −0.795494 | − | 0.605961i | \(-0.792789\pi\) | ||||
−0.795494 | + | 0.605961i | \(0.792789\pi\) | |||||||
\(702\) | 3657.59i | 0.196648i | ||||||||
\(703\) | 11593.5i | 0.621989i | ||||||||
\(704\) | −5456.13 | −0.292096 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6878.69 | 0.366690 | ||||||||
\(707\) | − 21911.0i | − 1.16556i | ||||||||
\(708\) | − 1015.19i | − 0.0538885i | ||||||||
\(709\) | −27016.3 | −1.43106 | −0.715529 | − | 0.698583i | \(-0.753814\pi\) | ||||
−0.715529 | + | 0.698583i | \(0.753814\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7262.82 | 0.383090 | ||||||||
\(712\) | − 22042.2i | − 1.16020i | ||||||||
\(713\) | − 1466.42i | − 0.0770237i | ||||||||
\(714\) | 21726.2 | 1.13877 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3300.43 | 0.172266 | ||||||||
\(717\) | − 14422.3i | − 0.751198i | ||||||||
\(718\) | − 9231.54i | − 0.479830i | ||||||||
\(719\) | −24752.9 | −1.28390 | −0.641952 | − | 0.766745i | \(-0.721875\pi\) | ||||
−0.641952 | + | 0.766745i | \(0.721875\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16193.4 | 0.836438 | ||||||||
\(722\) | − 11474.1i | − 0.591443i | ||||||||
\(723\) | 7531.69i | 0.387423i | ||||||||
\(724\) | 583.868 | 0.0299714 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 13082.5 | 0.668785 | ||||||||
\(727\) | − 17574.5i | − 0.896565i | −0.893892 | − | 0.448283i | \(-0.852036\pi\) | ||||
0.893892 | − | 0.448283i | \(-0.147964\pi\) | |||||||
\(728\) | 4387.19i | 0.223352i | ||||||||
\(729\) | −17644.9 | −0.896456 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21461.7 | −1.08590 | ||||||||
\(732\) | 1093.91i | 0.0552349i | ||||||||
\(733\) | − 27739.6i | − 1.39780i | −0.715221 | − | 0.698898i | \(-0.753674\pi\) | ||||
0.715221 | − | 0.698898i | \(-0.246326\pi\) | |||||||
\(734\) | −4135.67 | −0.207970 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1035.00 | −0.0518351 | ||||||||
\(737\) | 5377.15i | 0.268751i | ||||||||
\(738\) | 9439.14i | 0.470812i | ||||||||
\(739\) | 3140.78 | 0.156340 | 0.0781701 | − | 0.996940i | \(-0.475092\pi\) | ||||
0.0781701 | + | 0.996940i | \(0.475092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3137.88 | −0.155564 | ||||||||
\(742\) | − 177.663i | − 0.00879007i | ||||||||
\(743\) | 35881.5i | 1.77169i | 0.463984 | + | 0.885844i | \(0.346420\pi\) | ||||
−0.463984 | + | 0.885844i | \(0.653580\pi\) | |||||||
\(744\) | 4980.93 | 0.245443 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −33546.9 | −1.64643 | ||||||||
\(747\) | − 285.609i | − 0.0139891i | ||||||||
\(748\) | 958.176i | 0.0468374i | ||||||||
\(749\) | 33527.3 | 1.63559 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7009.03 | −0.340563 | −0.170282 | − | 0.985395i | \(-0.554468\pi\) | ||||
−0.170282 | + | 0.985395i | \(0.554468\pi\) | |||||||
\(752\) | − 40987.7i | − 1.98759i | ||||||||
\(753\) | 2728.52i | 0.132049i | ||||||||
\(754\) | −6541.46 | −0.315950 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3824.83 | 0.184005 | ||||||||
\(757\) | 29998.3i | 1.44030i | 0.693818 | + | 0.720150i | \(0.255927\pi\) | ||||
−0.693818 | + | 0.720150i | \(0.744073\pi\) | |||||||
\(758\) | 36065.8i | 1.72819i | ||||||||
\(759\) | 1078.17 | 0.0515612 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5283.49 | 0.251677 | 0.125839 | − | 0.992051i | \(-0.459838\pi\) | ||||
0.125839 | + | 0.992051i | \(0.459838\pi\) | |||||||
\(762\) | 15270.8i | 0.725987i | ||||||||
\(763\) | 44192.2i | 2.09681i | ||||||||
\(764\) | 3058.98 | 0.144856 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 39823.9 | 1.87845 | ||||||||
\(767\) | 2226.89i | 0.104835i | ||||||||
\(768\) | − 5628.59i | − 0.264459i | ||||||||
\(769\) | 15216.2 | 0.713538 | 0.356769 | − | 0.934193i | \(-0.383878\pi\) | ||||
0.356769 | + | 0.934193i | \(0.383878\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8808.69 | 0.411462 | ||||||||
\(772\) | − 1336.93i | − 0.0623281i | ||||||||
\(773\) | − 15651.3i | − 0.728250i | −0.931350 | − | 0.364125i | \(-0.881368\pi\) | ||||
0.931350 | − | 0.364125i | \(-0.118632\pi\) | |||||||
\(774\) | −11143.2 | −0.517485 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 36313.0 | 1.67985 | ||||||||
\(777\) | − 10682.4i | − 0.493216i | ||||||||
\(778\) | 33049.1i | 1.52297i | ||||||||
\(779\) | −24711.6 | −1.13657 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12863.6 | −0.589365 | ||||||||
\(782\) | − 5246.83i | − 0.239931i | ||||||||
\(783\) | − 39920.7i | − 1.82203i | ||||||||
\(784\) | 22180.3 | 1.01040 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −22145.0 | −1.00494 | ||||||||
\(787\) | 9401.09i | 0.425810i | 0.977073 | + | 0.212905i | \(0.0682925\pi\) | ||||
−0.977073 | + | 0.212905i | \(0.931707\pi\) | |||||||
\(788\) | 2449.21i | 0.110723i | ||||||||
\(789\) | −24674.9 | −1.11337 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38202.5 | 1.71722 | ||||||||
\(792\) | − 3482.47i | − 0.156243i | ||||||||
\(793\) | − 2399.57i | − 0.107454i | ||||||||
\(794\) | −5679.55 | −0.253854 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1138.66 | 0.0507018 | ||||||||
\(797\) | 37388.5i | 1.66169i | 0.556504 | + | 0.830845i | \(0.312143\pi\) | ||||
−0.556504 | + | 0.830845i | \(0.687857\pi\) | |||||||
\(798\) | 29532.2i | 1.31006i | ||||||||
\(799\) | 43897.9 | 1.94367 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13813.6 | 0.609337 | ||||||||
\(802\) | − 33845.3i | − 1.49017i | ||||||||
\(803\) | 3612.00i | 0.158736i | ||||||||
\(804\) | −1587.51 | −0.0696356 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1560.87 | 0.0682125 | ||||||||
\(807\) | − 22666.8i | − 0.988734i | ||||||||
\(808\) | − 17973.4i | − 0.782550i | ||||||||
\(809\) | −24390.6 | −1.05999 | −0.529993 | − | 0.848002i | \(-0.677805\pi\) | ||||
−0.529993 | + | 0.848002i | \(0.677805\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23750.8 | 1.02836 | 0.514181 | − | 0.857682i | \(-0.328096\pi\) | ||||
0.514181 | + | 0.857682i | \(0.328096\pi\) | |||||||
\(812\) | 6840.56i | 0.295636i | ||||||||
\(813\) | 7370.73i | 0.317962i | ||||||||
\(814\) | 4240.07 | 0.182573 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 20084.8 | 0.861653 | ||||||||
\(817\) | − 29172.8i | − 1.24924i | ||||||||
\(818\) | − 44032.7i | − 1.88211i | ||||||||
\(819\) | −2749.40 | −0.117304 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3041.59 | 0.129296 | 0.0646481 | − | 0.997908i | \(-0.479408\pi\) | ||||
0.0646481 | + | 0.997908i | \(0.479408\pi\) | |||||||
\(822\) | − 3050.50i | − 0.129439i | ||||||||
\(823\) | − 28411.6i | − 1.20336i | −0.798737 | − | 0.601681i | \(-0.794498\pi\) | ||||
0.798737 | − | 0.601681i | \(-0.205502\pi\) | |||||||
\(824\) | 13283.2 | 0.561581 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 20958.4 | 0.882854 | ||||||||
\(827\) | − 24351.5i | − 1.02392i | −0.859008 | − | 0.511962i | \(-0.828919\pi\) | ||||
0.859008 | − | 0.511962i | \(-0.171081\pi\) | |||||||
\(828\) | − 302.691i | − 0.0127044i | ||||||||
\(829\) | 47240.8 | 1.97918 | 0.989590 | − | 0.143914i | \(-0.0459688\pi\) | ||||
0.989590 | + | 0.143914i | \(0.0459688\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15243.0 | −0.636311 | ||||||||
\(832\) | 3533.48i | 0.147237i | ||||||||
\(833\) | 23755.2i | 0.988077i | ||||||||
\(834\) | −6226.30 | −0.258512 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1302.44 | −0.0538826 | ||||||||
\(837\) | 9525.55i | 0.393371i | ||||||||
\(838\) | 6589.49i | 0.271635i | ||||||||
\(839\) | −2646.33 | −0.108893 | −0.0544466 | − | 0.998517i | \(-0.517339\pi\) | ||||
−0.0544466 | + | 0.998517i | \(0.517339\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47007.7 | 1.92741 | ||||||||
\(842\) | 19713.8i | 0.806869i | ||||||||
\(843\) | 14383.6i | 0.587660i | ||||||||
\(844\) | −5596.81 | −0.228258 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 22792.3 | 0.926258 | ||||||||
\(847\) | 30009.7i | 1.21741i | ||||||||
\(848\) | − 164.241i | − 0.00665102i | ||||||||
\(849\) | −14813.7 | −0.598827 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2579.78 | −0.103917 | ||||||||
\(852\) | − 3797.74i | − 0.152709i | ||||||||
\(853\) | 40826.4i | 1.63877i | 0.573244 | + | 0.819385i | \(0.305685\pi\) | ||||
−0.573244 | + | 0.819385i | \(0.694315\pi\) | |||||||
\(854\) | −22583.6 | −0.904913 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 27502.0 | 1.09813 | ||||||||
\(857\) | 1516.61i | 0.0604510i | 0.999543 | + | 0.0302255i | \(0.00962254\pi\) | ||||
−0.999543 | + | 0.0302255i | \(0.990377\pi\) | |||||||
\(858\) | 1147.61i | 0.0456628i | ||||||||
\(859\) | −6514.74 | −0.258766 | −0.129383 | − | 0.991595i | \(-0.541300\pi\) | ||||
−0.129383 | + | 0.991595i | \(0.541300\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22769.5 | 0.901258 | ||||||||
\(862\) | 1750.82i | 0.0691800i | ||||||||
\(863\) | 7120.18i | 0.280850i | 0.990091 | + | 0.140425i | \(0.0448469\pi\) | ||||
−0.990091 | + | 0.140425i | \(0.955153\pi\) | |||||||
\(864\) | 6723.14 | 0.264729 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8032.79 | 0.315202 | ||||||||
\(867\) | 3233.72i | 0.126670i | ||||||||
\(868\) | − 1632.24i | − 0.0638269i | ||||||||
\(869\) | 6953.94 | 0.271457 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3482.33 | 0.135470 | ||||||||
\(872\) | 36250.3i | 1.40779i | ||||||||
\(873\) | 22757.0i | 0.882252i | ||||||||
\(874\) | 7131.98 | 0.276021 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1066.38 | −0.0411297 | ||||||||
\(877\) | − 34013.4i | − 1.30964i | −0.755787 | − | 0.654818i | \(-0.772745\pi\) | ||||
0.755787 | − | 0.654818i | \(-0.227255\pi\) | |||||||
\(878\) | − 16527.5i | − 0.635282i | ||||||||
\(879\) | 27870.3 | 1.06944 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6704.11 | 0.256376 | 0.128188 | − | 0.991750i | \(-0.459084\pi\) | ||||
0.128188 | + | 0.991750i | \(0.459084\pi\) | |||||||
\(882\) | 12334.0i | 0.470868i | ||||||||
\(883\) | − 47808.5i | − 1.82207i | −0.412333 | − | 0.911033i | \(-0.635286\pi\) | ||||
0.412333 | − | 0.911033i | \(-0.364714\pi\) | |||||||
\(884\) | 620.530 | 0.0236094 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 39163.7 | 1.48502 | ||||||||
\(887\) | − 38955.7i | − 1.47464i | −0.675544 | − | 0.737320i | \(-0.736091\pi\) | ||||
0.675544 | − | 0.737320i | \(-0.263909\pi\) | |||||||
\(888\) | − 8762.64i | − 0.331143i | ||||||||
\(889\) | −35029.3 | −1.32154 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2526.07 | −0.0949794 | ||||||||
\(892\) | 5580.60i | 0.209476i | ||||||||
\(893\) | 59670.0i | 2.23604i | ||||||||
\(894\) | −15113.1 | −0.565387 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 42471.7 | 1.58357 | ||||||||
\(897\) | − 698.238i | − 0.0259905i | ||||||||
\(898\) | − 35457.4i | − 1.31763i | ||||||||
\(899\) | −17036.1 | −0.632019 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 175.903 | 0.00650407 | ||||||||
\(902\) | 9037.71i | 0.333617i | ||||||||
\(903\) | 26880.1i | 0.990601i | ||||||||
\(904\) | 31337.0 | 1.15294 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1815.27 | −0.0665656 | ||||||||
\(907\) | 7725.66i | 0.282830i | 0.989950 | + | 0.141415i | \(0.0451651\pi\) | ||||
−0.989950 | + | 0.141415i | \(0.954835\pi\) | |||||||
\(908\) | 566.323i | 0.0206983i | ||||||||
\(909\) | 11263.7 | 0.410994 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13150.7 | −0.478269 | −0.239135 | − | 0.970986i | \(-0.576864\pi\) | ||||
−0.239135 | + | 0.970986i | \(0.576864\pi\) | |||||||
\(912\) | 27301.1i | 0.991260i | ||||||||
\(913\) | − 273.463i | − 0.00991270i | ||||||||
\(914\) | −12434.6 | −0.450000 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −693.702 | −0.0250224 | ||||||||
\(917\) | − 50798.0i | − 1.82933i | ||||||||
\(918\) | 34082.3i | 1.22536i | ||||||||
\(919\) | −33083.7 | −1.18752 | −0.593759 | − | 0.804643i | \(-0.702357\pi\) | ||||
−0.593759 | + | 0.804643i | \(0.702357\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21625.3 | −0.773699 | ||||||||
\(922\) | 18184.1i | 0.649526i | ||||||||
\(923\) | 8330.65i | 0.297082i | ||||||||
\(924\) | 1200.08 | 0.0427270 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17187.4 | 0.609949 | ||||||||
\(927\) | 8324.44i | 0.294941i | ||||||||
\(928\) | 12024.1i | 0.425333i | ||||||||
\(929\) | 1310.12 | 0.0462686 | 0.0231343 | − | 0.999732i | \(-0.492635\pi\) | ||||
0.0231343 | + | 0.999732i | \(0.492635\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32290.2 | −1.13670 | ||||||||
\(932\) | − 2208.68i | − 0.0776264i | ||||||||
\(933\) | − 17743.0i | − 0.622594i | ||||||||
\(934\) | 26874.1 | 0.941487 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2255.30 | −0.0787574 | ||||||||
\(937\) | 40623.1i | 1.41633i | 0.706049 | + | 0.708163i | \(0.250476\pi\) | ||||
−0.706049 | + | 0.708163i | \(0.749524\pi\) | |||||||
\(938\) | − 32774.0i | − 1.14084i | ||||||||
\(939\) | −26239.8 | −0.911933 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10434.0 | −0.361466 | −0.180733 | − | 0.983532i | \(-0.557847\pi\) | ||||
−0.180733 | + | 0.983532i | \(0.557847\pi\) | |||||||
\(942\) | 26392.6i | 0.912863i | ||||||||
\(943\) | − 5498.80i | − 0.189889i | ||||||||
\(944\) | 19375.1 | 0.668013 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10669.3 | −0.366689 | ||||||||
\(947\) | − 51333.4i | − 1.76147i | −0.473612 | − | 0.880734i | \(-0.657050\pi\) | ||||
0.473612 | − | 0.880734i | \(-0.342950\pi\) | |||||||
\(948\) | 2053.03i | 0.0703367i | ||||||||
\(949\) | 2339.19 | 0.0800141 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32906.1 | 1.12203 | ||||||||
\(952\) | 40880.9i | 1.39176i | ||||||||
\(953\) | − 40263.6i | − 1.36859i | −0.729206 | − | 0.684294i | \(-0.760110\pi\) | ||||
0.729206 | − | 0.684294i | \(-0.239890\pi\) | |||||||
\(954\) | 91.3306 | 0.00309951 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3876.79 | −0.131155 | ||||||||
\(957\) | − 12525.5i | − 0.423086i | ||||||||
\(958\) | 19069.8i | 0.643128i | ||||||||
\(959\) | 6997.49 | 0.235621 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25726.0 | −0.863549 | ||||||||
\(962\) | − 2745.94i | − 0.0920297i | ||||||||
\(963\) | 17235.2i | 0.576736i | ||||||||
\(964\) | 2024.57 | 0.0676420 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6571.48 | −0.218876 | ||||||||
\(967\) | − 8353.12i | − 0.277785i | −0.990307 | − | 0.138893i | \(-0.955646\pi\) | ||||
0.990307 | − | 0.138893i | \(-0.0443543\pi\) | |||||||
\(968\) | 24616.6i | 0.817364i | ||||||||
\(969\) | −29239.5 | −0.969358 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28020.1 | −0.926063 | −0.463032 | − | 0.886342i | \(-0.653238\pi\) | ||||
−0.463032 | + | 0.886342i | \(0.653238\pi\) | |||||||
\(972\) | 3288.10i | 0.108504i | ||||||||
\(973\) | − 14282.4i | − 0.470578i | ||||||||
\(974\) | 41973.6 | 1.38082 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20877.5 | −0.684704 | ||||||||
\(977\) | − 50115.3i | − 1.64107i | −0.571593 | − | 0.820537i | \(-0.693674\pi\) | ||||
0.571593 | − | 0.820537i | \(-0.306326\pi\) | |||||||
\(978\) | 5258.38i | 0.171927i | ||||||||
\(979\) | 13226.1 | 0.431776 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −22717.7 | −0.739367 | ||||||||
\(982\) | 15905.9i | 0.516881i | ||||||||
\(983\) | 38113.0i | 1.23664i | 0.785926 | + | 0.618320i | \(0.212186\pi\) | ||||
−0.785926 | + | 0.618320i | \(0.787814\pi\) | |||||||
\(984\) | 18677.6 | 0.605101 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −60954.9 | −1.96876 | ||||||||
\(987\) | − 54980.5i | − 1.77310i | ||||||||
\(988\) | 843.481i | 0.0271606i | ||||||||
\(989\) | 6491.49 | 0.208713 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5245.02 | −0.168127 | −0.0840634 | − | 0.996460i | \(-0.526790\pi\) | ||||
−0.0840634 | + | 0.996460i | \(0.526790\pi\) | |||||||
\(992\) | − 2869.08i | − 0.0918281i | ||||||||
\(993\) | − 15863.0i | − 0.506945i | ||||||||
\(994\) | 78404.0 | 2.50183 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 80.7350 | 0.00256846 | ||||||||
\(997\) | 21896.1i | 0.695544i | 0.937579 | + | 0.347772i | \(0.113062\pi\) | ||||
−0.937579 | + | 0.347772i | \(0.886938\pi\) | |||||||
\(998\) | − 24040.3i | − 0.762509i | ||||||||
\(999\) | 16757.7 | 0.530721 |
(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 | 575.4.b.f.24.1 | 4 | ||
5.2 | odd | 4 | 575.4.a.h.1.1 | 2 | |||
5.3 | odd | 4 | 115.4.a.c.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 575.4.b.f.24.4 | 4 | ||
15.8 | even | 4 | 1035.4.a.g.1.1 | 2 | |||
20.3 | even | 4 | 1840.4.a.h.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.4.a.c.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
575.4.a.h.1.1 | 2 | 5.2 | odd | 4 | |||
575.4.b.f.24.1 | 4 | 1.1 | even | 1 | trivial | ||
575.4.b.f.24.4 | 4 | 5.4 | even | 2 | inner | ||
1035.4.a.g.1.1 | 2 | 15.8 | even | 4 | |||
1840.4.a.h.1.1 | 2 | 20.3 | even | 4 |