Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,3,Mod(91,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2070.91");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.c (of order \(2\), degree \(1\), 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: | \(56.4034147226\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.5 | ||
Root | \(-2.26343i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.91 |
Dual form | 2070.3.c.a.91.4 |
$q$-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 \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 10.1866i | − | 1.45522i | −0.685989 | − | 0.727612i | \(-0.740630\pi\) | ||
0.685989 | − | 0.727612i | \(-0.259370\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 3.16228i | − | 0.316228i | ||||||
\(11\) | 13.0237i | 1.18397i | 0.805947 | + | 0.591987i | \(0.201657\pi\) | ||||
−0.805947 | + | 0.591987i | \(0.798343\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 23.2154 | 1.78580 | 0.892900 | − | 0.450255i | \(-0.148667\pi\) | ||||
0.892900 | + | 0.450255i | \(0.148667\pi\) | |||||||
\(14\) | 14.4060i | 1.02900i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 28.2228i | − | 1.66016i | −0.557641 | − | 0.830082i | \(-0.688293\pi\) | ||
0.557641 | − | 0.830082i | \(-0.311707\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.6665i | 0.614027i | 0.951705 | + | 0.307013i | \(0.0993297\pi\) | ||||
−0.951705 | + | 0.307013i | \(0.900670\pi\) | |||||||
\(20\) | 4.47214i | 0.223607i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 18.4183i | − | 0.837197i | ||||||
\(23\) | 17.3999 | − | 15.0414i | 0.756516 | − | 0.653976i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | −32.8315 | −1.26275 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 20.3731i | − | 0.727612i | ||||||
\(29\) | −42.4794 | −1.46481 | −0.732404 | − | 0.680870i | \(-0.761602\pi\) | ||||
−0.732404 | + | 0.680870i | \(0.761602\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18.7683 | 0.605428 | 0.302714 | − | 0.953082i | \(-0.402107\pi\) | ||||
0.302714 | + | 0.953082i | \(0.402107\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 39.9131i | 1.17391i | ||||||||
\(35\) | 22.7778 | 0.650796 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.14094i | 0.0308363i | 0.999881 | + | 0.0154182i | \(0.00490795\pi\) | ||||
−0.999881 | + | 0.0154182i | \(0.995092\pi\) | |||||||
\(38\) | − | 16.4989i | − | 0.434183i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 6.32456i | − | 0.158114i | ||||||
\(41\) | 72.8198 | 1.77609 | 0.888046 | − | 0.459755i | \(-0.152063\pi\) | ||||
0.888046 | + | 0.459755i | \(0.152063\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.96573i | 0.115482i | 0.998332 | + | 0.0577411i | \(0.0183898\pi\) | ||||
−0.998332 | + | 0.0577411i | \(0.981610\pi\) | |||||||
\(44\) | 26.0474i | 0.591987i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −24.6071 | + | 21.2718i | −0.534937 | + | 0.462431i | ||||
\(47\) | 0.813360 | 0.0173055 | 0.00865277 | − | 0.999963i | \(-0.497246\pi\) | ||||
0.00865277 | + | 0.999963i | \(0.497246\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −54.7661 | −1.11768 | ||||||||
\(50\) | 7.07107 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 46.4308 | 0.892900 | ||||||||
\(53\) | 26.7286i | 0.504313i | 0.967686 | + | 0.252157i | \(0.0811398\pi\) | ||||
−0.967686 | + | 0.252157i | \(0.918860\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −29.1219 | −0.529490 | ||||||||
\(56\) | 28.8120i | 0.514499i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 60.0750 | 1.03578 | ||||||||
\(59\) | −94.0845 | −1.59465 | −0.797326 | − | 0.603549i | \(-0.793753\pi\) | ||||
−0.797326 | + | 0.603549i | \(0.793753\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 74.5293i | 1.22179i | 0.791711 | + | 0.610896i | \(0.209191\pi\) | ||||
−0.791711 | + | 0.610896i | \(0.790809\pi\) | |||||||
\(62\) | −26.5423 | −0.428102 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 51.9112i | 0.798634i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 80.0906i | − | 1.19538i | −0.801727 | − | 0.597691i | \(-0.796085\pi\) | ||
0.801727 | − | 0.597691i | \(-0.203915\pi\) | |||||||
\(68\) | − | 56.4456i | − | 0.830082i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −32.2127 | −0.460182 | ||||||||
\(71\) | 83.5303 | 1.17648 | 0.588241 | − | 0.808686i | \(-0.299821\pi\) | ||||
0.588241 | + | 0.808686i | \(0.299821\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.98897 | −0.123137 | −0.0615683 | − | 0.998103i | \(-0.519610\pi\) | ||||
−0.0615683 | + | 0.998103i | \(0.519610\pi\) | |||||||
\(74\) | − | 1.61354i | − | 0.0218046i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 23.3330i | 0.307013i | ||||||||
\(77\) | 132.667 | 1.72295 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 80.2841i | 1.01626i | 0.861282 | + | 0.508128i | \(0.169662\pi\) | ||||
−0.861282 | + | 0.508128i | \(0.830338\pi\) | |||||||
\(80\) | 8.94427i | 0.111803i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −102.983 | −1.25589 | ||||||||
\(83\) | − | 94.6451i | − | 1.14030i | −0.821540 | − | 0.570151i | \(-0.806885\pi\) | ||
0.821540 | − | 0.570151i | \(-0.193115\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 63.1081 | 0.742448 | ||||||||
\(86\) | − | 7.02261i | − | 0.0816582i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 36.8367i | − | 0.418598i | ||||||
\(89\) | − | 136.812i | − | 1.53722i | −0.639720 | − | 0.768608i | \(-0.720950\pi\) | ||
0.639720 | − | 0.768608i | \(-0.279050\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 236.485i | − | 2.59874i | ||||||
\(92\) | 34.7997 | − | 30.0829i | 0.378258 | − | 0.326988i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.15026 | −0.0122369 | ||||||||
\(95\) | −26.0871 | −0.274601 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.32666i | 0.0239862i | 0.999928 | + | 0.0119931i | \(0.00381761\pi\) | ||||
−0.999928 | + | 0.0119931i | \(0.996182\pi\) | |||||||
\(98\) | 77.4509 | 0.790316 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | −12.9918 | −0.128632 | −0.0643161 | − | 0.997930i | \(-0.520487\pi\) | ||||
−0.0643161 | + | 0.997930i | \(0.520487\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 90.3165i | − | 0.876859i | −0.898766 | − | 0.438430i | \(-0.855535\pi\) | ||
0.898766 | − | 0.438430i | \(-0.144465\pi\) | |||||||
\(104\) | −65.6631 | −0.631376 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 37.7999i | − | 0.356603i | ||||||
\(107\) | 185.173i | 1.73059i | 0.501264 | + | 0.865294i | \(0.332869\pi\) | ||||
−0.501264 | + | 0.865294i | \(0.667131\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 13.8248i | − | 0.126833i | −0.997987 | − | 0.0634167i | \(-0.979800\pi\) | ||
0.997987 | − | 0.0634167i | \(-0.0201997\pi\) | |||||||
\(110\) | 41.1846 | 0.374406 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 40.7463i | − | 0.363806i | ||||||
\(113\) | − | 178.530i | − | 1.57991i | −0.613164 | − | 0.789956i | \(-0.710103\pi\) | ||
0.613164 | − | 0.789956i | \(-0.289897\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 33.6337 | + | 38.9073i | 0.292467 | + | 0.338324i | ||||
\(116\) | −84.9589 | −0.732404 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 133.056 | 1.12759 | ||||||||
\(119\) | −287.493 | −2.41591 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −48.6174 | −0.401797 | ||||||||
\(122\) | − | 105.400i | − | 0.863938i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 37.5365 | 0.302714 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −112.959 | −0.889442 | −0.444721 | − | 0.895669i | \(-0.646697\pi\) | ||||
−0.444721 | + | 0.895669i | \(0.646697\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | − | 73.4135i | − | 0.564720i | ||||||
\(131\) | 12.1419 | 0.0926860 | 0.0463430 | − | 0.998926i | \(-0.485243\pi\) | ||||
0.0463430 | + | 0.998926i | \(0.485243\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 118.842 | 0.893546 | ||||||||
\(134\) | 113.265i | 0.845263i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 79.8261i | 0.586957i | ||||||||
\(137\) | 170.543i | 1.24484i | 0.782685 | + | 0.622418i | \(0.213850\pi\) | ||||
−0.782685 | + | 0.622418i | \(0.786150\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 38.5478 | 0.277322 | 0.138661 | − | 0.990340i | \(-0.455720\pi\) | ||||
0.138661 | + | 0.990340i | \(0.455720\pi\) | |||||||
\(140\) | 45.5557 | 0.325398 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −118.130 | −0.831899 | ||||||||
\(143\) | 302.351i | 2.11434i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 94.9869i | − | 0.655082i | ||||||
\(146\) | 12.7123 | 0.0870707 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.28189i | 0.0154182i | ||||||||
\(149\) | − | 81.4125i | − | 0.546393i | −0.961958 | − | 0.273196i | \(-0.911919\pi\) | ||
0.961958 | − | 0.273196i | \(-0.0880808\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 159.680 | 1.05748 | 0.528742 | − | 0.848782i | \(-0.322664\pi\) | ||||
0.528742 | + | 0.848782i | \(0.322664\pi\) | |||||||
\(152\) | − | 32.9979i | − | 0.217091i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −187.619 | −1.21831 | ||||||||
\(155\) | 41.9671i | 0.270755i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 38.5953i | − | 0.245830i | −0.992417 | − | 0.122915i | \(-0.960776\pi\) | ||
0.992417 | − | 0.122915i | \(-0.0392242\pi\) | |||||||
\(158\) | − | 113.539i | − | 0.718601i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 12.6491i | − | 0.0790569i | ||||||
\(161\) | −153.221 | − | 177.245i | −0.951681 | − | 1.10090i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 150.291 | 0.922028 | 0.461014 | − | 0.887393i | \(-0.347486\pi\) | ||||
0.461014 | + | 0.887393i | \(0.347486\pi\) | |||||||
\(164\) | 145.640 | 0.888046 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 133.848i | 0.806316i | ||||||||
\(167\) | −27.7604 | −0.166230 | −0.0831149 | − | 0.996540i | \(-0.526487\pi\) | ||||
−0.0831149 | + | 0.996540i | \(0.526487\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 369.955 | 2.18908 | ||||||||
\(170\) | −89.2483 | −0.524990 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.93146i | 0.0577411i | ||||||||
\(173\) | 24.0064 | 0.138765 | 0.0693826 | − | 0.997590i | \(-0.477897\pi\) | ||||
0.0693826 | + | 0.997590i | \(0.477897\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 50.9328i | 0.291045i | ||||||||
\(176\) | 52.0949i | 0.295994i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 193.482i | 1.08698i | ||||||||
\(179\) | 201.178 | 1.12390 | 0.561949 | − | 0.827172i | \(-0.310052\pi\) | ||||
0.561949 | + | 0.827172i | \(0.310052\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 202.358i | − | 1.11800i | −0.829168 | − | 0.558999i | \(-0.811186\pi\) | ||
0.829168 | − | 0.558999i | \(-0.188814\pi\) | |||||||
\(182\) | 334.441i | 1.83759i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −49.2142 | + | 42.5436i | −0.267469 | + | 0.231215i | ||||
\(185\) | −2.55123 | −0.0137904 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 367.566 | 1.96559 | ||||||||
\(188\) | 1.62672 | 0.00865277 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 36.8927 | 0.194172 | ||||||||
\(191\) | − | 111.302i | − | 0.582735i | −0.956611 | − | 0.291368i | \(-0.905890\pi\) | ||
0.956611 | − | 0.291368i | \(-0.0941103\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −164.081 | −0.850163 | −0.425081 | − | 0.905155i | \(-0.639754\pi\) | ||||
−0.425081 | + | 0.905155i | \(0.639754\pi\) | |||||||
\(194\) | − | 3.29040i | − | 0.0169608i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −109.532 | −0.558838 | ||||||||
\(197\) | 329.562 | 1.67290 | 0.836451 | − | 0.548042i | \(-0.184627\pi\) | ||||
0.836451 | + | 0.548042i | \(0.184627\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 337.886i | − | 1.69792i | −0.528455 | − | 0.848961i | \(-0.677229\pi\) | ||
0.528455 | − | 0.848961i | \(-0.322771\pi\) | |||||||
\(200\) | 14.1421 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 18.3732 | 0.0909566 | ||||||||
\(203\) | 432.720i | 2.13162i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 162.830i | 0.794292i | ||||||||
\(206\) | 127.727i | 0.620033i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 92.8616 | 0.446450 | ||||||||
\(209\) | −151.941 | −0.726992 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 111.656 | 0.529173 | 0.264587 | − | 0.964362i | \(-0.414765\pi\) | ||||
0.264587 | + | 0.964362i | \(0.414765\pi\) | |||||||
\(212\) | 53.4572i | 0.252157i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 261.874i | − | 1.22371i | ||||||
\(215\) | −11.1037 | −0.0516452 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 191.184i | − | 0.881032i | ||||||
\(218\) | 19.5513i | 0.0896847i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −58.2439 | −0.264745 | ||||||||
\(221\) | − | 655.204i | − | 2.96472i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −363.545 | −1.63025 | −0.815123 | − | 0.579288i | \(-0.803331\pi\) | ||||
−0.815123 | + | 0.579288i | \(0.803331\pi\) | |||||||
\(224\) | 57.6239i | 0.257250i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 252.480i | 1.11717i | ||||||||
\(227\) | − | 11.3368i | − | 0.0499418i | −0.999688 | − | 0.0249709i | \(-0.992051\pi\) | ||
0.999688 | − | 0.0249709i | \(-0.00794931\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 112.509i | − | 0.491306i | −0.969358 | − | 0.245653i | \(-0.920998\pi\) | ||
0.969358 | − | 0.245653i | \(-0.0790024\pi\) | |||||||
\(230\) | −47.5652 | − | 55.0232i | −0.206805 | − | 0.239231i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 120.150 | 0.517888 | ||||||||
\(233\) | 381.634 | 1.63791 | 0.818957 | − | 0.573855i | \(-0.194553\pi\) | ||||
0.818957 | + | 0.573855i | \(0.194553\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.81873i | 0.00773927i | ||||||||
\(236\) | −188.169 | −0.797326 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 406.577 | 1.70831 | ||||||||
\(239\) | −139.296 | −0.582828 | −0.291414 | − | 0.956597i | \(-0.594126\pi\) | ||||
−0.291414 | + | 0.956597i | \(0.594126\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 82.3347i | − | 0.341638i | −0.985302 | − | 0.170819i | \(-0.945359\pi\) | ||
0.985302 | − | 0.170819i | \(-0.0546413\pi\) | |||||||
\(242\) | 68.7554 | 0.284113 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 149.059i | 0.610896i | ||||||||
\(245\) | − | 122.461i | − | 0.499840i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 270.843i | 1.09653i | ||||||||
\(248\) | −53.0846 | −0.214051 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 15.8114i | 0.0632456i | ||||||||
\(251\) | 323.924i | 1.29054i | 0.763957 | + | 0.645268i | \(0.223254\pi\) | ||||
−0.763957 | + | 0.645268i | \(0.776746\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 195.896 | + | 226.611i | 0.774291 | + | 0.895695i | ||||
\(254\) | 159.748 | 0.628931 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 250.796 | 0.975858 | 0.487929 | − | 0.872883i | \(-0.337752\pi\) | ||||
0.487929 | + | 0.872883i | \(0.337752\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.6223 | 0.0448737 | ||||||||
\(260\) | 103.822i | 0.399317i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −17.1712 | −0.0655389 | ||||||||
\(263\) | − | 276.878i | − | 1.05277i | −0.850247 | − | 0.526384i | \(-0.823548\pi\) | ||
0.850247 | − | 0.526384i | \(-0.176452\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −59.7670 | −0.225536 | ||||||||
\(266\) | −168.067 | −0.631833 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 160.181i | − | 0.597691i | ||||||
\(269\) | 78.1002 | 0.290335 | 0.145168 | − | 0.989407i | \(-0.453628\pi\) | ||||
0.145168 | + | 0.989407i | \(0.453628\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 331.551 | 1.22343 | 0.611717 | − | 0.791076i | \(-0.290479\pi\) | ||||
0.611717 | + | 0.791076i | \(0.290479\pi\) | |||||||
\(272\) | − | 112.891i | − | 0.415041i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 241.184i | − | 0.880232i | ||||||
\(275\) | − | 65.1186i | − | 0.236795i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −355.974 | −1.28511 | −0.642553 | − | 0.766241i | \(-0.722125\pi\) | ||||
−0.642553 | + | 0.766241i | \(0.722125\pi\) | |||||||
\(278\) | −54.5148 | −0.196097 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −64.4255 | −0.230091 | ||||||||
\(281\) | − | 391.437i | − | 1.39301i | −0.717550 | − | 0.696507i | \(-0.754736\pi\) | ||
0.717550 | − | 0.696507i | \(-0.245264\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 133.616i | 0.472143i | 0.971736 | + | 0.236071i | \(0.0758599\pi\) | ||||
−0.971736 | + | 0.236071i | \(0.924140\pi\) | |||||||
\(284\) | 167.061 | 0.588241 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 427.589i | − | 1.49507i | ||||||
\(287\) | − | 741.783i | − | 2.58461i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −507.527 | −1.75615 | ||||||||
\(290\) | 134.332i | 0.463213i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −17.9779 | −0.0615683 | ||||||||
\(293\) | − | 533.454i | − | 1.82066i | −0.413880 | − | 0.910331i | \(-0.635827\pi\) | ||
0.413880 | − | 0.910331i | \(-0.364173\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 210.379i | − | 0.713150i | ||||||
\(296\) | − | 3.22708i | − | 0.0109023i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 115.135i | 0.386358i | ||||||||
\(299\) | 403.945 | − | 349.193i | 1.35099 | − | 1.16787i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 50.5837 | 0.168052 | ||||||||
\(302\) | −225.822 | −0.747755 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 46.6660i | 0.153507i | ||||||||
\(305\) | −166.653 | −0.546402 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 282.656 | 0.920705 | 0.460352 | − | 0.887736i | \(-0.347723\pi\) | ||||
0.460352 | + | 0.887736i | \(0.347723\pi\) | |||||||
\(308\) | 265.334 | 0.861474 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 59.3504i | − | 0.191453i | ||||||
\(311\) | 193.206 | 0.621241 | 0.310620 | − | 0.950534i | \(-0.399463\pi\) | ||||
0.310620 | + | 0.950534i | \(0.399463\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 399.279i | − | 1.27565i | −0.770181 | − | 0.637826i | \(-0.779834\pi\) | ||
0.770181 | − | 0.637826i | \(-0.220166\pi\) | |||||||
\(314\) | 54.5820i | 0.173828i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 160.568i | 0.508128i | ||||||||
\(317\) | 36.5297 | 0.115236 | 0.0576178 | − | 0.998339i | \(-0.481650\pi\) | ||||
0.0576178 | + | 0.998339i | \(0.481650\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 553.241i | − | 1.73430i | ||||||
\(320\) | 17.8885i | 0.0559017i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 216.687 | + | 250.662i | 0.672940 | + | 0.778453i | ||||
\(323\) | 329.262 | 1.01939 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −116.077 | −0.357160 | ||||||||
\(326\) | −212.543 | −0.651973 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −205.965 | −0.627943 | ||||||||
\(329\) | − | 8.28534i | − | 0.0251834i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 85.9406 | 0.259639 | 0.129820 | − | 0.991538i | \(-0.458560\pi\) | ||||
0.129820 | + | 0.991538i | \(0.458560\pi\) | |||||||
\(332\) | − | 189.290i | − | 0.570151i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 39.2591 | 0.117542 | ||||||||
\(335\) | 179.088 | 0.534591 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 548.713i | − | 1.62823i | −0.580706 | − | 0.814114i | \(-0.697223\pi\) | ||
0.580706 | − | 0.814114i | \(-0.302777\pi\) | |||||||
\(338\) | −523.195 | −1.54791 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 126.216 | 0.371224 | ||||||||
\(341\) | 244.433i | 0.716811i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 58.7366i | 0.171244i | ||||||||
\(344\) | − | 14.0452i | − | 0.0408291i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −33.9502 | −0.0981219 | ||||||||
\(347\) | −62.0036 | −0.178685 | −0.0893424 | − | 0.996001i | \(-0.528477\pi\) | ||||
−0.0893424 | + | 0.996001i | \(0.528477\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −131.393 | −0.376485 | −0.188242 | − | 0.982123i | \(-0.560279\pi\) | ||||
−0.188242 | + | 0.982123i | \(0.560279\pi\) | |||||||
\(350\) | − | 72.0299i | − | 0.205800i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 73.6733i | − | 0.209299i | ||||||
\(353\) | 176.990 | 0.501389 | 0.250694 | − | 0.968066i | \(-0.419341\pi\) | ||||
0.250694 | + | 0.968066i | \(0.419341\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 186.779i | 0.526139i | ||||||||
\(356\) | − | 273.624i | − | 0.768608i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −284.508 | −0.794716 | ||||||||
\(359\) | − | 187.851i | − | 0.523260i | −0.965168 | − | 0.261630i | \(-0.915740\pi\) | ||
0.965168 | − | 0.261630i | \(-0.0842601\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 224.893 | 0.622971 | ||||||||
\(362\) | 286.177i | 0.790544i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 472.970i | − | 1.29937i | ||||||
\(365\) | − | 20.0999i | − | 0.0550684i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 128.510i | 0.350162i | 0.984554 | + | 0.175081i | \(0.0560188\pi\) | ||||
−0.984554 | + | 0.175081i | \(0.943981\pi\) | |||||||
\(368\) | 69.5994 | − | 60.1658i | 0.189129 | − | 0.163494i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.60798 | 0.00975130 | ||||||||
\(371\) | 272.273 | 0.733888 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 79.2928i | 0.212581i | 0.994335 | + | 0.106291i | \(0.0338974\pi\) | ||||
−0.994335 | + | 0.106291i | \(0.966103\pi\) | |||||||
\(374\) | −519.817 | −1.38988 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.30053 | −0.00611843 | ||||||||
\(377\) | −986.177 | −2.61585 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 402.569i | 1.06219i | 0.847313 | + | 0.531094i | \(0.178219\pi\) | ||||
−0.847313 | + | 0.531094i | \(0.821781\pi\) | |||||||
\(380\) | −52.1742 | −0.137301 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 157.405i | 0.412056i | ||||||||
\(383\) | 370.198i | 0.966575i | 0.875462 | + | 0.483288i | \(0.160557\pi\) | ||||
−0.875462 | + | 0.483288i | \(0.839443\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 296.652i | 0.770526i | ||||||||
\(386\) | 232.046 | 0.601156 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.65332i | 0.0119931i | ||||||||
\(389\) | − | 12.0598i | − | 0.0310021i | −0.999880 | − | 0.0155011i | \(-0.995066\pi\) | ||
0.999880 | − | 0.0155011i | \(-0.00493434\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −424.512 | − | 491.073i | −1.08571 | − | 1.25594i | ||||
\(392\) | 154.902 | 0.395158 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −466.071 | −1.18292 | ||||||||
\(395\) | −179.521 | −0.454483 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 233.543 | 0.588270 | 0.294135 | − | 0.955764i | \(-0.404968\pi\) | ||||
0.294135 | + | 0.955764i | \(0.404968\pi\) | |||||||
\(398\) | 477.844i | 1.20061i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | − | 114.072i | − | 0.284469i | −0.989833 | − | 0.142235i | \(-0.954571\pi\) | ||
0.989833 | − | 0.142235i | \(-0.0454287\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 435.713 | 1.08117 | ||||||||
\(404\) | −25.9837 | −0.0643161 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 611.958i | − | 1.50729i | ||||||
\(407\) | −14.8593 | −0.0365094 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 125.952 | 0.307950 | 0.153975 | − | 0.988075i | \(-0.450792\pi\) | ||||
0.153975 | + | 0.988075i | \(0.450792\pi\) | |||||||
\(410\) | − | 230.276i | − | 0.561650i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 180.633i | − | 0.438430i | ||||||
\(413\) | 958.397i | 2.32057i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 211.633 | 0.509959 | ||||||||
\(416\) | −131.326 | −0.315688 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 214.878 | 0.514061 | ||||||||
\(419\) | 135.868i | 0.324268i | 0.986769 | + | 0.162134i | \(0.0518377\pi\) | ||||
−0.986769 | + | 0.162134i | \(0.948162\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 194.111i | − | 0.461070i | −0.973064 | − | 0.230535i | \(-0.925952\pi\) | ||
0.973064 | − | 0.230535i | \(-0.0740477\pi\) | |||||||
\(422\) | −157.905 | −0.374182 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 75.5999i | − | 0.178302i | ||||||
\(425\) | 141.114i | 0.332033i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 759.198 | 1.77798 | ||||||||
\(428\) | 370.346i | 0.865294i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.7030 | 0.0365187 | ||||||||
\(431\) | 421.699i | 0.978420i | 0.872166 | + | 0.489210i | \(0.162715\pi\) | ||||
−0.872166 | + | 0.489210i | \(0.837285\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.78505i | − | 0.00874144i | −0.999990 | − | 0.00437072i | \(-0.998609\pi\) | ||
0.999990 | − | 0.00437072i | \(-0.00139125\pi\) | |||||||
\(434\) | 270.375i | 0.622984i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 27.6497i | − | 0.0634167i | ||||||
\(437\) | 175.481 | + | 202.996i | 0.401559 | + | 0.464521i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.17744 | −0.0140716 | −0.00703581 | − | 0.999975i | \(-0.502240\pi\) | ||||
−0.00703581 | + | 0.999975i | \(0.502240\pi\) | |||||||
\(440\) | 82.3693 | 0.187203 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 926.598i | 2.09638i | ||||||||
\(443\) | 406.821 | 0.918331 | 0.459166 | − | 0.888351i | \(-0.348148\pi\) | ||||
0.459166 | + | 0.888351i | \(0.348148\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 305.921 | 0.687464 | ||||||||
\(446\) | 514.130 | 1.15276 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 81.4925i | − | 0.181903i | ||||||
\(449\) | 289.981 | 0.645837 | 0.322918 | − | 0.946427i | \(-0.395336\pi\) | ||||
0.322918 | + | 0.946427i | \(0.395336\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 948.385i | 2.10285i | ||||||||
\(452\) | − | 357.060i | − | 0.789956i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.0326i | 0.0353142i | ||||||||
\(455\) | 528.797 | 1.16219 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 224.430i | − | 0.491094i | −0.969385 | − | 0.245547i | \(-0.921032\pi\) | ||
0.969385 | − | 0.245547i | \(-0.0789676\pi\) | |||||||
\(458\) | 159.112i | 0.347406i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 67.2674 | + | 77.8145i | 0.146233 | + | 0.169162i | ||||
\(461\) | −534.660 | −1.15978 | −0.579891 | − | 0.814694i | \(-0.696905\pi\) | ||||
−0.579891 | + | 0.814694i | \(0.696905\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 166.226 | 0.359019 | 0.179509 | − | 0.983756i | \(-0.442549\pi\) | ||||
0.179509 | + | 0.983756i | \(0.442549\pi\) | |||||||
\(464\) | −169.918 | −0.366202 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −539.712 | −1.15818 | ||||||||
\(467\) | − | 113.755i | − | 0.243587i | −0.992555 | − | 0.121794i | \(-0.961135\pi\) | ||
0.992555 | − | 0.121794i | \(-0.0388646\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −815.848 | −1.73955 | ||||||||
\(470\) | − | 2.57207i | − | 0.00547249i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 266.111 | 0.563795 | ||||||||
\(473\) | −64.6723 | −0.136728 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 58.3326i | − | 0.122805i | ||||||
\(476\) | −574.987 | −1.20796 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 196.994 | 0.412121 | ||||||||
\(479\) | 156.314i | 0.326334i | 0.986598 | + | 0.163167i | \(0.0521710\pi\) | ||||
−0.986598 | + | 0.163167i | \(0.947829\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.4875i | 0.0550675i | ||||||||
\(482\) | 116.439i | 0.241574i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −97.2348 | −0.200898 | ||||||||
\(485\) | −5.20257 | −0.0107270 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −207.919 | −0.426938 | −0.213469 | − | 0.976950i | \(-0.568476\pi\) | ||||
−0.213469 | + | 0.976950i | \(0.568476\pi\) | |||||||
\(488\) | − | 210.801i | − | 0.431969i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 173.186i | 0.353440i | ||||||||
\(491\) | 463.345 | 0.943676 | 0.471838 | − | 0.881685i | \(-0.343591\pi\) | ||||
0.471838 | + | 0.881685i | \(0.343591\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1198.89i | 2.43182i | ||||||||
\(494\) | − | 383.029i | − | 0.775363i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 75.0730 | 0.151357 | ||||||||
\(497\) | − | 850.886i | − | 1.71204i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −50.7777 | −0.101759 | −0.0508794 | − | 0.998705i | \(-0.516202\pi\) | ||||
−0.0508794 | + | 0.998705i | \(0.516202\pi\) | |||||||
\(500\) | − | 22.3607i | − | 0.0447214i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 458.098i | − | 0.912546i | ||||||
\(503\) | 91.1857i | 0.181284i | 0.995884 | + | 0.0906419i | \(0.0288919\pi\) | ||||
−0.995884 | + | 0.0906419i | \(0.971108\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 29.0506i | − | 0.0575260i | ||||||
\(506\) | −277.038 | − | 320.476i | −0.547506 | − | 0.633352i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −225.918 | −0.444721 | ||||||||
\(509\) | −317.681 | −0.624128 | −0.312064 | − | 0.950061i | \(-0.601020\pi\) | ||||
−0.312064 | + | 0.950061i | \(0.601020\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 91.5667i | 0.179191i | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −354.678 | −0.690036 | ||||||||
\(515\) | 201.954 | 0.392143 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.5930i | 0.0204893i | ||||||||
\(518\) | −16.4364 | −0.0317305 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | − | 146.827i | − | 0.282360i | ||||||
\(521\) | 522.346i | 1.00258i | 0.865279 | + | 0.501291i | \(0.167142\pi\) | ||||
−0.865279 | + | 0.501291i | \(0.832858\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 245.926i | 0.470221i | 0.971969 | + | 0.235111i | \(0.0755452\pi\) | ||||
−0.971969 | + | 0.235111i | \(0.924455\pi\) | |||||||
\(524\) | 24.2837 | 0.0463430 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 391.564i | 0.744419i | ||||||||
\(527\) | − | 529.693i | − | 1.00511i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 76.5101 | − | 523.438i | 0.144632 | − | 0.989486i | ||||
\(530\) | 84.5232 | 0.159478 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 237.683 | 0.446773 | ||||||||
\(533\) | 1690.54 | 3.17174 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −414.059 | −0.773943 | ||||||||
\(536\) | 226.530i | 0.422631i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −110.450 | −0.205298 | ||||||||
\(539\) | − | 713.258i | − | 1.32330i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −307.138 | −0.567723 | −0.283861 | − | 0.958865i | \(-0.591616\pi\) | ||||
−0.283861 | + | 0.958865i | \(0.591616\pi\) | |||||||
\(542\) | −468.884 | −0.865099 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 159.652i | 0.293478i | ||||||||
\(545\) | 30.9133 | 0.0567216 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −712.547 | −1.30265 | −0.651323 | − | 0.758801i | \(-0.725786\pi\) | ||||
−0.651323 | + | 0.758801i | \(0.725786\pi\) | |||||||
\(548\) | 341.085i | 0.622418i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 92.0916i | 0.167439i | ||||||||
\(551\) | − | 495.587i | − | 0.899432i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 817.820 | 1.47888 | ||||||||
\(554\) | 503.424 | 0.908707 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 77.0956 | 0.138661 | ||||||||
\(557\) | 1.17109i | 0.00210250i | 0.999999 | + | 0.00105125i | \(0.000334623\pi\) | ||||
−0.999999 | + | 0.00105125i | \(0.999665\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 115.281i | 0.206228i | ||||||||
\(560\) | 91.1114 | 0.162699 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 553.575i | 0.985010i | ||||||||
\(563\) | 900.058i | 1.59868i | 0.600878 | + | 0.799341i | \(0.294818\pi\) | ||||
−0.600878 | + | 0.799341i | \(0.705182\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 399.205 | 0.706558 | ||||||||
\(566\) | − | 188.962i | − | 0.333855i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −236.259 | −0.415949 | ||||||||
\(569\) | − | 589.836i | − | 1.03662i | −0.855193 | − | 0.518309i | \(-0.826562\pi\) | ||
0.855193 | − | 0.518309i | \(-0.173438\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 117.755i | − | 0.206225i | −0.994670 | − | 0.103113i | \(-0.967120\pi\) | ||
0.994670 | − | 0.103113i | \(-0.0328802\pi\) | |||||||
\(572\) | 604.702i | 1.05717i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1049.04i | 1.82760i | ||||||||
\(575\) | −86.9993 | + | 75.2072i | −0.151303 | + | 0.130795i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −403.533 | −0.699365 | −0.349682 | − | 0.936868i | \(-0.613710\pi\) | ||||
−0.349682 | + | 0.936868i | \(0.613710\pi\) | |||||||
\(578\) | 717.751 | 1.24178 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 189.974i | − | 0.327541i | ||||||
\(581\) | −964.109 | −1.65940 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −348.106 | −0.597094 | ||||||||
\(584\) | 25.4246 | 0.0435354 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 754.418i | 1.28740i | ||||||||
\(587\) | −607.731 | −1.03532 | −0.517659 | − | 0.855587i | \(-0.673196\pi\) | ||||
−0.517659 | + | 0.855587i | \(0.673196\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 218.960i | 0.371749i | ||||||||
\(590\) | 297.521i | 0.504273i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.56377i | 0.00770908i | ||||||||
\(593\) | −428.555 | −0.722690 | −0.361345 | − | 0.932432i | \(-0.617682\pi\) | ||||
−0.361345 | + | 0.932432i | \(0.617682\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 642.855i | − | 1.08043i | ||||||
\(596\) | − | 162.825i | − | 0.273196i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −571.264 | + | 493.834i | −0.955291 | + | 0.825809i | ||||
\(599\) | 162.171 | 0.270736 | 0.135368 | − | 0.990795i | \(-0.456778\pi\) | ||||
0.135368 | + | 0.990795i | \(0.456778\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 957.407 | 1.59302 | 0.796512 | − | 0.604623i | \(-0.206676\pi\) | ||||
0.796512 | + | 0.604623i | \(0.206676\pi\) | |||||||
\(602\) | −71.5362 | −0.118831 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 319.360 | 0.528742 | ||||||||
\(605\) | − | 108.712i | − | 0.179689i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −989.893 | −1.63080 | −0.815398 | − | 0.578901i | \(-0.803482\pi\) | ||||
−0.815398 | + | 0.578901i | \(0.803482\pi\) | |||||||
\(608\) | − | 65.9958i | − | 0.108546i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 235.682 | 0.386365 | ||||||||
\(611\) | 18.8825 | 0.0309042 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 134.181i | 0.218892i | 0.993993 | + | 0.109446i | \(0.0349076\pi\) | ||||
−0.993993 | + | 0.109446i | \(0.965092\pi\) | |||||||
\(614\) | −399.736 | −0.651037 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −375.239 | −0.609154 | ||||||||
\(617\) | 151.269i | 0.245168i | 0.992458 | + | 0.122584i | \(0.0391181\pi\) | ||||
−0.992458 | + | 0.122584i | \(0.960882\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 115.852i | 0.187159i | 0.995612 | + | 0.0935797i | \(0.0298310\pi\) | ||||
−0.995612 | + | 0.0935797i | \(0.970169\pi\) | |||||||
\(620\) | 83.9342i | 0.135378i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −273.234 | −0.439284 | ||||||||
\(623\) | −1393.65 | −2.23699 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 564.665i | 0.902022i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 77.1906i | − | 0.122915i | ||||||
\(629\) | 32.2006 | 0.0511934 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 730.187i | 1.15719i | 0.815615 | + | 0.578595i | \(0.196399\pi\) | ||||
−0.815615 | + | 0.578595i | \(0.803601\pi\) | |||||||
\(632\) | − | 227.078i | − | 0.359300i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −51.6608 | −0.0814839 | ||||||||
\(635\) | − | 252.584i | − | 0.397771i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1271.42 | −1.99594 | ||||||||
\(638\) | 782.400i | 1.22633i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 25.2982i | − | 0.0395285i | ||||||
\(641\) | 725.551i | 1.13190i | 0.824438 | + | 0.565952i | \(0.191491\pi\) | ||||
−0.824438 | + | 0.565952i | \(0.808509\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 505.908i | 0.786792i | 0.919369 | + | 0.393396i | \(0.128700\pi\) | ||||
−0.919369 | + | 0.393396i | \(0.871300\pi\) | |||||||
\(644\) | −306.441 | − | 354.490i | −0.475840 | − | 0.550450i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −465.646 | −0.720815 | ||||||||
\(647\) | 324.943 | 0.502230 | 0.251115 | − | 0.967957i | \(-0.419203\pi\) | ||||
0.251115 | + | 0.967957i | \(0.419203\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1225.33i | − | 1.88803i | ||||||
\(650\) | 164.158 | 0.252550 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 300.581 | 0.461014 | ||||||||
\(653\) | 146.801 | 0.224810 | 0.112405 | − | 0.993662i | \(-0.464145\pi\) | ||||
0.112405 | + | 0.993662i | \(0.464145\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.1500i | 0.0414504i | ||||||||
\(656\) | 291.279 | 0.444023 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11.7172i | 0.0178074i | ||||||||
\(659\) | − | 366.667i | − | 0.556399i | −0.960523 | − | 0.278200i | \(-0.910262\pi\) | ||
0.960523 | − | 0.278200i | \(-0.0897377\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1241.87i | 1.87878i | 0.342852 | + | 0.939389i | \(0.388607\pi\) | ||||
−0.342852 | + | 0.939389i | \(0.611393\pi\) | |||||||
\(662\) | −121.538 | −0.183593 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 267.697i | 0.403158i | ||||||||
\(665\) | 265.738i | 0.399606i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −739.136 | + | 638.952i | −1.10815 | + | 0.957949i | ||||
\(668\) | −55.5208 | −0.0831149 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −253.269 | −0.378013 | ||||||||
\(671\) | −970.649 | −1.44657 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 812.966 | 1.20797 | 0.603987 | − | 0.796994i | \(-0.293578\pi\) | ||||
0.603987 | + | 0.796994i | \(0.293578\pi\) | |||||||
\(674\) | 775.997i | 1.15133i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 739.910 | 1.09454 | ||||||||
\(677\) | 1053.03i | 1.55544i | 0.628610 | + | 0.777721i | \(0.283624\pi\) | ||||
−0.628610 | + | 0.777721i | \(0.716376\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.7007 | 0.0349053 | ||||||||
\(680\) | −178.497 | −0.262495 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 345.680i | − | 0.506862i | ||||||
\(683\) | −947.718 | −1.38758 | −0.693791 | − | 0.720177i | \(-0.744061\pi\) | ||||
−0.693791 | + | 0.720177i | \(0.744061\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −381.345 | −0.556708 | ||||||||
\(686\) | − | 83.0661i | − | 0.121088i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 19.8629i | 0.0288705i | ||||||||
\(689\) | 620.515i | 0.900602i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −600.541 | −0.869090 | −0.434545 | − | 0.900650i | \(-0.643091\pi\) | ||||
−0.434545 | + | 0.900650i | \(0.643091\pi\) | |||||||
\(692\) | 48.0128 | 0.0693826 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 87.6863 | 0.126349 | ||||||||
\(695\) | 86.1955i | 0.124022i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2055.18i | − | 2.94861i | ||||||
\(698\) | 185.818 | 0.266215 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 101.866i | 0.145522i | ||||||||
\(701\) | − | 907.376i | − | 1.29440i | −0.762319 | − | 0.647201i | \(-0.775939\pi\) | ||
0.762319 | − | 0.647201i | \(-0.224061\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.3108 | −0.0189343 | ||||||||
\(704\) | 104.190i | 0.147997i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −250.302 | −0.354536 | ||||||||
\(707\) | 132.342i | 0.187188i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 657.300i | 0.927081i | 0.886076 | + | 0.463540i | \(0.153421\pi\) | ||||
−0.886076 | + | 0.463540i | \(0.846579\pi\) | |||||||
\(710\) | − | 264.146i | − | 0.372036i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 386.963i | 0.543488i | ||||||||
\(713\) | 326.565 | − | 282.302i | 0.458015 | − | 0.395935i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −676.077 | −0.945563 | ||||||||
\(716\) | 402.356 | 0.561949 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 265.661i | 0.370001i | ||||||||
\(719\) | −1095.72 | −1.52395 | −0.761975 | − | 0.647606i | \(-0.775770\pi\) | ||||
−0.761975 | + | 0.647606i | \(0.775770\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −920.015 | −1.27603 | ||||||||
\(722\) | −318.046 | −0.440507 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 404.715i | − | 0.558999i | ||||||
\(725\) | 212.397 | 0.292962 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 814.942i | 1.12097i | 0.828166 | + | 0.560483i | \(0.189384\pi\) | ||||
−0.828166 | + | 0.560483i | \(0.810616\pi\) | |||||||
\(728\) | 668.881i | 0.918793i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 28.4256i | 0.0389392i | ||||||||
\(731\) | 140.147 | 0.191719 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 742.293i | − | 1.01268i | −0.862335 | − | 0.506339i | \(-0.830999\pi\) | ||
0.862335 | − | 0.506339i | \(-0.169001\pi\) | |||||||
\(734\) | − | 181.740i | − | 0.247602i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −98.4285 | + | 85.0872i | −0.133734 | + | 0.115608i | ||||
\(737\) | 1043.08 | 1.41530 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −288.013 | −0.389733 | −0.194866 | − | 0.980830i | \(-0.562427\pi\) | ||||
−0.194866 | + | 0.980830i | \(0.562427\pi\) | |||||||
\(740\) | −5.10245 | −0.00689521 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −385.052 | −0.518937 | ||||||||
\(743\) | − | 199.651i | − | 0.268709i | −0.990933 | − | 0.134354i | \(-0.957104\pi\) | ||
0.990933 | − | 0.134354i | \(-0.0428961\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 182.044 | 0.244354 | ||||||||
\(746\) | − | 112.137i | − | 0.150318i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 735.132 | 0.982797 | ||||||||
\(749\) | 1886.28 | 2.51839 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 610.667i | 0.813138i | 0.913620 | + | 0.406569i | \(0.133275\pi\) | ||||
−0.913620 | + | 0.406569i | \(0.866725\pi\) | |||||||
\(752\) | 3.25344 | 0.00432638 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1394.67 | 1.84969 | ||||||||
\(755\) | 357.056i | 0.472922i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 241.235i | 0.318672i | 0.987224 | + | 0.159336i | \(0.0509354\pi\) | ||||
−0.987224 | + | 0.159336i | \(0.949065\pi\) | |||||||
\(758\) | − | 569.319i | − | 0.751080i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 73.7855 | 0.0970862 | ||||||||
\(761\) | −568.126 | −0.746552 | −0.373276 | − | 0.927720i | \(-0.621765\pi\) | ||||
−0.373276 | + | 0.927720i | \(0.621765\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −140.828 | −0.184571 | ||||||||
\(764\) | − | 222.605i | − | 0.291368i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 523.539i | − | 0.683472i | ||||||
\(767\) | −2184.21 | −2.84773 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 425.966i | − | 0.553922i | −0.960881 | − | 0.276961i | \(-0.910673\pi\) | ||
0.960881 | − | 0.276961i | \(-0.0893273\pi\) | |||||||
\(770\) | − | 419.530i | − | 0.544844i | ||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −328.163 | −0.425081 | ||||||||
\(773\) | − | 849.417i | − | 1.09886i | −0.835540 | − | 0.549429i | \(-0.814845\pi\) | ||
0.835540 | − | 0.549429i | \(-0.185155\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −93.8413 | −0.121086 | ||||||||
\(776\) | − | 6.58079i | − | 0.00848040i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.0552i | 0.0219218i | ||||||||
\(779\) | 849.553i | 1.09057i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1087.87i | 1.39293i | ||||||||
\(782\) | 600.350 | + | 694.482i | 0.767711 | + | 0.888084i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −219.064 | −0.279419 | ||||||||
\(785\) | 86.3017 | 0.109938 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1448.81i | − | 1.84093i | −0.390828 | − | 0.920464i | \(-0.627811\pi\) | ||
0.390828 | − | 0.920464i | \(-0.372189\pi\) | |||||||
\(788\) | 659.123 | 0.836451 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 253.881 | 0.321368 | ||||||||
\(791\) | −1818.61 | −2.29912 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1730.23i | 2.18188i | ||||||||
\(794\) | −330.280 | −0.415970 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 675.773i | − | 0.848961i | ||||||
\(797\) | − | 405.786i | − | 0.509141i | −0.967054 | − | 0.254571i | \(-0.918066\pi\) | ||
0.967054 | − | 0.254571i | \(-0.0819342\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 22.9553i | − | 0.0287300i | ||||||
\(800\) | 28.2843 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 161.322i | 0.201150i | ||||||||
\(803\) | − | 117.070i | − | 0.145791i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 396.331 | − | 342.612i | 0.492337 | − | 0.425605i | ||||
\(806\) | −616.191 | −0.764504 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 36.7465 | 0.0454783 | ||||||||
\(809\) | −755.183 | −0.933477 | −0.466739 | − | 0.884395i | \(-0.654571\pi\) | ||||
−0.466739 | + | 0.884395i | \(0.654571\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1132.66 | −1.39662 | −0.698311 | − | 0.715795i | \(-0.746065\pi\) | ||||
−0.698311 | + | 0.715795i | \(0.746065\pi\) | |||||||
\(812\) | 865.439i | 1.06581i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 21.0143 | 0.0258161 | ||||||||
\(815\) | 336.060i | 0.412344i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −57.9328 | −0.0709091 | ||||||||
\(818\) | −178.122 | −0.217754 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 325.660i | 0.397146i | ||||||||
\(821\) | −167.684 | −0.204244 | −0.102122 | − | 0.994772i | \(-0.532563\pi\) | ||||
−0.102122 | + | 0.994772i | \(0.532563\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −403.176 | −0.489886 | −0.244943 | − | 0.969538i | \(-0.578769\pi\) | ||||
−0.244943 | + | 0.969538i | \(0.578769\pi\) | |||||||
\(824\) | 255.454i | 0.310016i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 1355.38i | − | 1.64089i | ||||||
\(827\) | 901.234i | 1.08976i | 0.838513 | + | 0.544881i | \(0.183425\pi\) | ||||
−0.838513 | + | 0.544881i | \(0.816575\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −455.150 | −0.549034 | −0.274517 | − | 0.961582i | \(-0.588518\pi\) | ||||
−0.274517 | + | 0.961582i | \(0.588518\pi\) | |||||||
\(830\) | −299.294 | −0.360595 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 185.723 | 0.223225 | ||||||||
\(833\) | 1545.65i | 1.85553i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 62.0741i | − | 0.0743402i | ||||||
\(836\) | −303.883 | −0.363496 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 192.147i | − | 0.229292i | ||||||
\(839\) | − | 150.136i | − | 0.178946i | −0.995989 | − | 0.0894730i | \(-0.971482\pi\) | ||
0.995989 | − | 0.0894730i | \(-0.0285183\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 963.503 | 1.14566 | ||||||||
\(842\) | 274.514i | 0.326026i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 223.311 | 0.264587 | ||||||||
\(845\) | 827.244i | 0.978987i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 495.244i | 0.584704i | ||||||||
\(848\) | 106.914i | 0.126078i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 199.565i | − | 0.234783i | ||||||
\(851\) | 17.1614 | + | 19.8523i | 0.0201662 | + | 0.0233281i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 582.826 | 0.683266 | 0.341633 | − | 0.939833i | \(-0.389020\pi\) | ||||
0.341633 | + | 0.939833i | \(0.389020\pi\) | |||||||
\(854\) | −1073.67 | −1.25722 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 523.748i | − | 0.611856i | ||||||
\(857\) | 435.647 | 0.508339 | 0.254170 | − | 0.967160i | \(-0.418198\pi\) | ||||
0.254170 | + | 0.967160i | \(0.418198\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −427.848 | −0.498076 | −0.249038 | − | 0.968494i | \(-0.580114\pi\) | ||||
−0.249038 | + | 0.968494i | \(0.580114\pi\) | |||||||
\(860\) | −22.2074 | −0.0258226 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 596.373i | − | 0.691848i | ||||||
\(863\) | 698.719 | 0.809640 | 0.404820 | − | 0.914396i | \(-0.367334\pi\) | ||||
0.404820 | + | 0.914396i | \(0.367334\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 53.6799i | 0.0620577i | ||||||||
\(866\) | 5.35286i | 0.00618113i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 382.368i | − | 0.440516i | ||||||
\(869\) | −1045.60 | −1.20322 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1859.34i | − | 2.13471i | ||||||
\(872\) | 39.1025i | 0.0448424i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −248.168 | − | 287.079i | −0.283945 | − | 0.328466i | ||||
\(875\) | −113.889 | −0.130159 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 779.272 | 0.888566 | 0.444283 | − | 0.895887i | \(-0.353459\pi\) | ||||
0.444283 | + | 0.895887i | \(0.353459\pi\) | |||||||
\(878\) | 8.73622 | 0.00995014 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −116.488 | −0.132372 | ||||||||
\(881\) | − | 1612.85i | − | 1.83070i | −0.402659 | − | 0.915350i | \(-0.631914\pi\) | ||
0.402659 | − | 0.915350i | \(-0.368086\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −336.489 | −0.381075 | −0.190537 | − | 0.981680i | \(-0.561023\pi\) | ||||
−0.190537 | + | 0.981680i | \(0.561023\pi\) | |||||||
\(884\) | − | 1310.41i | − | 1.48236i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −575.331 | −0.649358 | ||||||||
\(887\) | 12.5177 | 0.0141124 | 0.00705619 | − | 0.999975i | \(-0.497754\pi\) | ||||
0.00705619 | + | 0.999975i | \(0.497754\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1150.67i | 1.29434i | ||||||||
\(890\) | −432.638 | −0.486110 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −727.090 | −0.815123 | ||||||||
\(893\) | 9.48907i | 0.0106261i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 449.847i | 0.502623i | ||||||||
\(896\) | 115.248i | 0.128625i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −410.095 | −0.456676 | ||||||||
\(899\) | −797.265 | −0.886835 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 754.356 | 0.837243 | ||||||||
\(902\) | − | 1341.22i | − | 1.48694i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 504.959i | 0.558583i | ||||||||
\(905\) | 452.485 | 0.499984 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1320.74i | 1.45616i | 0.685492 | + | 0.728080i | \(0.259587\pi\) | ||||
−0.685492 | + | 0.728080i | \(0.740413\pi\) | |||||||
\(908\) | − | 22.6736i | − | 0.0249709i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −747.832 | −0.821793 | ||||||||
\(911\) | 1388.64i | 1.52430i | 0.647398 | + | 0.762152i | \(0.275857\pi\) | ||||
−0.647398 | + | 0.762152i | \(0.724143\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1232.63 | 1.35009 | ||||||||
\(914\) | 317.392i | 0.347256i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 225.018i | − | 0.245653i | ||||||
\(917\) | − | 123.684i | − | 0.134879i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 814.108i | − | 0.885863i | −0.896555 | − | 0.442932i | \(-0.853938\pi\) | ||
0.896555 | − | 0.442932i | \(-0.146062\pi\) | |||||||
\(920\) | −95.1304 | − | 110.046i | −0.103403 | − | 0.119616i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 756.123 | 0.820090 | ||||||||
\(923\) | 1939.19 | 2.10096 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 5.70472i | − | 0.00616726i | ||||||
\(926\) | −235.078 | −0.253864 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 240.300 | 0.258944 | ||||||||
\(929\) | −951.041 | −1.02373 | −0.511863 | − | 0.859067i | \(-0.671044\pi\) | ||||
−0.511863 | + | 0.859067i | \(0.671044\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 638.929i | − | 0.686283i | ||||||
\(932\) | 763.268 | 0.818957 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 160.874i | 0.172242i | ||||||||
\(935\) | 821.903i | 0.879040i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 25.4596i | − | 0.0271713i | −0.999908 | − | 0.0135857i | \(-0.995675\pi\) | ||
0.999908 | − | 0.0135857i | \(-0.00432459\pi\) | |||||||
\(938\) | 1153.78 | 1.23005 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.63746i | 0.00386963i | ||||||||
\(941\) | − | 1304.69i | − | 1.38650i | −0.720698 | − | 0.693249i | \(-0.756179\pi\) | ||
0.720698 | − | 0.693249i | \(-0.243821\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1267.05 | − | 1095.31i | 1.34364 | − | 1.16152i | ||||
\(944\) | −376.338 | −0.398663 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 91.4605 | 0.0966813 | ||||||||
\(947\) | 25.1178 | 0.0265236 | 0.0132618 | − | 0.999912i | \(-0.495779\pi\) | ||||
0.0132618 | + | 0.999912i | \(0.495779\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −208.683 | −0.219897 | ||||||||
\(950\) | 82.4947i | 0.0868365i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 813.154 | 0.854153 | ||||||||
\(953\) | 663.560i | 0.696286i | 0.937442 | + | 0.348143i | \(0.113188\pi\) | ||||
−0.937442 | + | 0.348143i | \(0.886812\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 248.880 | 0.260607 | ||||||||
\(956\) | −278.592 | −0.291414 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 221.061i | − | 0.230753i | ||||||
\(959\) | 1737.24 | 1.81152 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −608.753 | −0.633457 | ||||||||
\(962\) | − | 37.4589i | − | 0.0389386i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 164.669i | − | 0.170819i | ||||||
\(965\) | − | 366.897i | − | 0.380204i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −661.312 | −0.683880 | −0.341940 | − | 0.939722i | \(-0.611084\pi\) | ||||
−0.341940 | + | 0.939722i | \(0.611084\pi\) | |||||||
\(968\) | 137.511 | 0.142057 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.35755 | 0.00758510 | ||||||||
\(971\) | 1198.53i | 1.23433i | 0.786834 | + | 0.617165i | \(0.211719\pi\) | ||||
−0.786834 | + | 0.617165i | \(0.788281\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 392.670i | − | 0.403566i | ||||||
\(974\) | 294.042 | 0.301891 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 298.117i | 0.305448i | ||||||||
\(977\) | − | 1156.31i | − | 1.18353i | −0.806110 | − | 0.591765i | \(-0.798431\pi\) | ||
0.806110 | − | 0.591765i | \(-0.201569\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1781.80 | 1.82002 | ||||||||
\(980\) | − | 244.921i | − | 0.249920i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −655.268 | −0.667279 | ||||||||
\(983\) | − | 534.831i | − | 0.544080i | −0.962286 | − | 0.272040i | \(-0.912302\pi\) | ||
0.962286 | − | 0.272040i | \(-0.0876983\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 736.922i | 0.748144i | ||||||||
\(986\) | − | 1695.48i | − | 1.71956i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 541.685i | 0.548265i | ||||||||
\(989\) | 74.6918 | + | 86.4030i | 0.0755225 | + | 0.0873640i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −217.485 | −0.219461 | −0.109730 | − | 0.993961i | \(-0.534999\pi\) | ||||
−0.109730 | + | 0.993961i | \(0.534999\pi\) | |||||||
\(992\) | −106.169 | −0.107025 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1203.33i | 1.21060i | ||||||||
\(995\) | 755.537 | 0.759334 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −248.055 | −0.248801 | −0.124400 | − | 0.992232i | \(-0.539701\pi\) | ||||
−0.124400 | + | 0.992232i | \(0.539701\pi\) | |||||||
\(998\) | 71.8105 | 0.0719544 | ||||||||
\(999\) | 0 | 0 |
(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 | 2070.3.c.a.91.5 | 16 | ||
3.2 | odd | 2 | 230.3.d.a.91.13 | ✓ | 16 | ||
12.11 | even | 2 | 1840.3.k.d.321.7 | 16 | |||
15.2 | even | 4 | 1150.3.c.c.1149.32 | 32 | |||
15.8 | even | 4 | 1150.3.c.c.1149.1 | 32 | |||
15.14 | odd | 2 | 1150.3.d.b.551.4 | 16 | |||
23.22 | odd | 2 | inner | 2070.3.c.a.91.4 | 16 | ||
69.68 | even | 2 | 230.3.d.a.91.14 | yes | 16 | ||
276.275 | odd | 2 | 1840.3.k.d.321.8 | 16 | |||
345.68 | odd | 4 | 1150.3.c.c.1149.31 | 32 | |||
345.137 | odd | 4 | 1150.3.c.c.1149.2 | 32 | |||
345.344 | even | 2 | 1150.3.d.b.551.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.d.a.91.13 | ✓ | 16 | 3.2 | odd | 2 | ||
230.3.d.a.91.14 | yes | 16 | 69.68 | even | 2 | ||
1150.3.c.c.1149.1 | 32 | 15.8 | even | 4 | |||
1150.3.c.c.1149.2 | 32 | 345.137 | odd | 4 | |||
1150.3.c.c.1149.31 | 32 | 345.68 | odd | 4 | |||
1150.3.c.c.1149.32 | 32 | 15.2 | even | 4 | |||
1150.3.d.b.551.3 | 16 | 345.344 | even | 2 | |||
1150.3.d.b.551.4 | 16 | 15.14 | odd | 2 | |||
1840.3.k.d.321.7 | 16 | 12.11 | even | 2 | |||
1840.3.k.d.321.8 | 16 | 276.275 | odd | 2 | |||
2070.3.c.a.91.4 | 16 | 23.22 | odd | 2 | inner | ||
2070.3.c.a.91.5 | 16 | 1.1 | even | 1 | trivial |