Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.a (trivial) |
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: | yes |
Analytic conductor: | \(32.1397868136\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 14 x^{10} + 26 x^{9} + 71 x^{8} - 120 x^{7} - 162 x^{6} + 244 x^{5} + 170 x^{4} - 210 x^{3} - 81 x^{2} + 58 x + 17 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 805) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.11343\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.11343 | −0.787316 | −0.393658 | − | 0.919257i | \(-0.628791\pi\) | ||||
−0.393658 | + | 0.919257i | \(0.628791\pi\) | |||||||
\(3\) | 2.87976 | 1.66263 | 0.831314 | − | 0.555803i | \(-0.187589\pi\) | ||||
0.831314 | + | 0.555803i | \(0.187589\pi\) | |||||||
\(4\) | −0.760266 | −0.380133 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.20642 | −1.30901 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 3.07337 | 1.08660 | ||||||||
\(9\) | 5.29300 | 1.76433 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.44843 | −0.436719 | −0.218359 | − | 0.975868i | \(-0.570070\pi\) | ||||
−0.218359 | + | 0.975868i | \(0.570070\pi\) | |||||||
\(12\) | −2.18938 | −0.632020 | ||||||||
\(13\) | −2.99328 | −0.830186 | −0.415093 | − | 0.909779i | \(-0.636251\pi\) | ||||
−0.415093 | + | 0.909779i | \(0.636251\pi\) | |||||||
\(14\) | 1.11343 | 0.297578 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.90146 | −0.475366 | ||||||||
\(17\) | −0.663092 | −0.160823 | −0.0804117 | − | 0.996762i | \(-0.525624\pi\) | ||||
−0.0804117 | + | 0.996762i | \(0.525624\pi\) | |||||||
\(18\) | −5.89340 | −1.38909 | ||||||||
\(19\) | −6.91587 | −1.58661 | −0.793304 | − | 0.608825i | \(-0.791641\pi\) | ||||
−0.793304 | + | 0.608825i | \(0.791641\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.87976 | −0.628414 | ||||||||
\(22\) | 1.61273 | 0.343836 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 8.85056 | 1.80661 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.33282 | 0.653619 | ||||||||
\(27\) | 6.60327 | 1.27080 | ||||||||
\(28\) | 0.760266 | 0.143677 | ||||||||
\(29\) | 2.85250 | 0.529696 | 0.264848 | − | 0.964290i | \(-0.414678\pi\) | ||||
0.264848 | + | 0.964290i | \(0.414678\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.80140 | 1.04196 | 0.520981 | − | 0.853568i | \(-0.325566\pi\) | ||||
0.520981 | + | 0.853568i | \(0.325566\pi\) | |||||||
\(32\) | −4.02959 | −0.712338 | ||||||||
\(33\) | −4.17113 | −0.726100 | ||||||||
\(34\) | 0.738309 | 0.126619 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.02409 | −0.670681 | ||||||||
\(37\) | −1.45671 | −0.239482 | −0.119741 | − | 0.992805i | \(-0.538206\pi\) | ||||
−0.119741 | + | 0.992805i | \(0.538206\pi\) | |||||||
\(38\) | 7.70036 | 1.24916 | ||||||||
\(39\) | −8.61991 | −1.38029 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.31097 | 0.204740 | 0.102370 | − | 0.994746i | \(-0.467357\pi\) | ||||
0.102370 | + | 0.994746i | \(0.467357\pi\) | |||||||
\(42\) | 3.20642 | 0.494761 | ||||||||
\(43\) | 6.04918 | 0.922491 | 0.461246 | − | 0.887272i | \(-0.347403\pi\) | ||||
0.461246 | + | 0.887272i | \(0.347403\pi\) | |||||||
\(44\) | 1.10119 | 0.166011 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.11343 | −0.164167 | ||||||||
\(47\) | −7.26934 | −1.06034 | −0.530171 | − | 0.847891i | \(-0.677872\pi\) | ||||
−0.530171 | + | 0.847891i | \(0.677872\pi\) | |||||||
\(48\) | −5.47575 | −0.790357 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.90954 | −0.267390 | ||||||||
\(52\) | 2.27569 | 0.315581 | ||||||||
\(53\) | −7.52908 | −1.03420 | −0.517099 | − | 0.855925i | \(-0.672988\pi\) | ||||
−0.517099 | + | 0.855925i | \(0.672988\pi\) | |||||||
\(54\) | −7.35230 | −1.00052 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.07337 | −0.410697 | ||||||||
\(57\) | −19.9160 | −2.63794 | ||||||||
\(58\) | −3.17607 | −0.417038 | ||||||||
\(59\) | −1.21914 | −0.158719 | −0.0793594 | − | 0.996846i | \(-0.525287\pi\) | ||||
−0.0793594 | + | 0.996846i | \(0.525287\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.29657 | 0.166009 | 0.0830045 | − | 0.996549i | \(-0.473548\pi\) | ||||
0.0830045 | + | 0.996549i | \(0.473548\pi\) | |||||||
\(62\) | −6.45948 | −0.820354 | ||||||||
\(63\) | −5.29300 | −0.666855 | ||||||||
\(64\) | 8.28961 | 1.03620 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.64428 | 0.571671 | ||||||||
\(67\) | −6.72336 | −0.821389 | −0.410694 | − | 0.911773i | \(-0.634714\pi\) | ||||
−0.410694 | + | 0.911773i | \(0.634714\pi\) | |||||||
\(68\) | 0.504126 | 0.0611343 | ||||||||
\(69\) | 2.87976 | 0.346682 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.4619 | −1.83499 | −0.917497 | − | 0.397742i | \(-0.869794\pi\) | ||||
−0.917497 | + | 0.397742i | \(0.869794\pi\) | |||||||
\(72\) | 16.2673 | 1.91713 | ||||||||
\(73\) | −12.0554 | −1.41098 | −0.705491 | − | 0.708719i | \(-0.749273\pi\) | ||||
−0.705491 | + | 0.708719i | \(0.749273\pi\) | |||||||
\(74\) | 1.62195 | 0.188548 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.25790 | 0.603122 | ||||||||
\(77\) | 1.44843 | 0.165064 | ||||||||
\(78\) | 9.59770 | 1.08673 | ||||||||
\(79\) | −12.1005 | −1.36141 | −0.680706 | − | 0.732557i | \(-0.738327\pi\) | ||||
−0.680706 | + | 0.732557i | \(0.738327\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.13682 | 0.348536 | ||||||||
\(82\) | −1.45968 | −0.161195 | ||||||||
\(83\) | −12.8092 | −1.40599 | −0.702995 | − | 0.711194i | \(-0.748155\pi\) | ||||
−0.702995 | + | 0.711194i | \(0.748155\pi\) | |||||||
\(84\) | 2.18938 | 0.238881 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.73536 | −0.726293 | ||||||||
\(87\) | 8.21450 | 0.880687 | ||||||||
\(88\) | −4.45157 | −0.474539 | ||||||||
\(89\) | −17.4986 | −1.85485 | −0.927423 | − | 0.374013i | \(-0.877981\pi\) | ||||
−0.927423 | + | 0.374013i | \(0.877981\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.99328 | 0.313781 | ||||||||
\(92\) | −0.760266 | −0.0792632 | ||||||||
\(93\) | 16.7066 | 1.73240 | ||||||||
\(94\) | 8.09393 | 0.834825 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −11.6042 | −1.18435 | ||||||||
\(97\) | 2.17861 | 0.221204 | 0.110602 | − | 0.993865i | \(-0.464722\pi\) | ||||
0.110602 | + | 0.993865i | \(0.464722\pi\) | |||||||
\(98\) | −1.11343 | −0.112474 | ||||||||
\(99\) | −7.66654 | −0.770517 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.86707 | −0.285285 | −0.142642 | − | 0.989774i | \(-0.545560\pi\) | ||||
−0.142642 | + | 0.989774i | \(0.545560\pi\) | |||||||
\(102\) | 2.12615 | 0.210520 | ||||||||
\(103\) | 13.7697 | 1.35677 | 0.678386 | − | 0.734706i | \(-0.262680\pi\) | ||||
0.678386 | + | 0.734706i | \(0.262680\pi\) | |||||||
\(104\) | −9.19946 | −0.902081 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.38313 | 0.814241 | ||||||||
\(107\) | 7.16382 | 0.692552 | 0.346276 | − | 0.938133i | \(-0.387446\pi\) | ||||
0.346276 | + | 0.938133i | \(0.387446\pi\) | |||||||
\(108\) | −5.02024 | −0.483073 | ||||||||
\(109\) | 10.5009 | 1.00580 | 0.502902 | − | 0.864343i | \(-0.332265\pi\) | ||||
0.502902 | + | 0.864343i | \(0.332265\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.19498 | −0.398170 | ||||||||
\(112\) | 1.90146 | 0.179671 | ||||||||
\(113\) | 13.7108 | 1.28980 | 0.644901 | − | 0.764266i | \(-0.276898\pi\) | ||||
0.644901 | + | 0.764266i | \(0.276898\pi\) | |||||||
\(114\) | 22.1751 | 2.07689 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.16866 | −0.201355 | ||||||||
\(117\) | −15.8434 | −1.46472 | ||||||||
\(118\) | 1.35743 | 0.124962 | ||||||||
\(119\) | 0.663092 | 0.0607855 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.90205 | −0.809277 | ||||||||
\(122\) | −1.44365 | −0.130702 | ||||||||
\(123\) | 3.77529 | 0.340406 | ||||||||
\(124\) | −4.41061 | −0.396084 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.89340 | 0.525026 | ||||||||
\(127\) | 17.5841 | 1.56033 | 0.780166 | − | 0.625572i | \(-0.215134\pi\) | ||||
0.780166 | + | 0.625572i | \(0.215134\pi\) | |||||||
\(128\) | −1.17074 | −0.103480 | ||||||||
\(129\) | 17.4202 | 1.53376 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.10117 | −0.183580 | −0.0917901 | − | 0.995778i | \(-0.529259\pi\) | ||||
−0.0917901 | + | 0.995778i | \(0.529259\pi\) | |||||||
\(132\) | 3.17117 | 0.276015 | ||||||||
\(133\) | 6.91587 | 0.599682 | ||||||||
\(134\) | 7.48601 | 0.646693 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.03793 | −0.174751 | ||||||||
\(137\) | −3.72916 | −0.318604 | −0.159302 | − | 0.987230i | \(-0.550924\pi\) | ||||
−0.159302 | + | 0.987230i | \(0.550924\pi\) | |||||||
\(138\) | −3.20642 | −0.272948 | ||||||||
\(139\) | 7.08538 | 0.600974 | 0.300487 | − | 0.953786i | \(-0.402851\pi\) | ||||
0.300487 | + | 0.953786i | \(0.402851\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −20.9339 | −1.76296 | ||||||||
\(142\) | 17.2158 | 1.44472 | ||||||||
\(143\) | 4.33556 | 0.362558 | ||||||||
\(144\) | −10.0644 | −0.838703 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.4229 | 1.11089 | ||||||||
\(147\) | 2.87976 | 0.237518 | ||||||||
\(148\) | 1.10749 | 0.0910350 | ||||||||
\(149\) | 1.47690 | 0.120992 | 0.0604960 | − | 0.998168i | \(-0.480732\pi\) | ||||
0.0604960 | + | 0.998168i | \(0.480732\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.10228 | −0.577975 | −0.288988 | − | 0.957333i | \(-0.593319\pi\) | ||||
−0.288988 | + | 0.957333i | \(0.593319\pi\) | |||||||
\(152\) | −21.2550 | −1.72401 | ||||||||
\(153\) | −3.50974 | −0.283746 | ||||||||
\(154\) | −1.61273 | −0.129958 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.55343 | 0.524694 | ||||||||
\(157\) | −18.6138 | −1.48554 | −0.742770 | − | 0.669547i | \(-0.766488\pi\) | ||||
−0.742770 | + | 0.669547i | \(0.766488\pi\) | |||||||
\(158\) | 13.4731 | 1.07186 | ||||||||
\(159\) | −21.6819 | −1.71949 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | −3.49264 | −0.274408 | ||||||||
\(163\) | 0.205611 | 0.0161047 | 0.00805233 | − | 0.999968i | \(-0.497437\pi\) | ||||
0.00805233 | + | 0.999968i | \(0.497437\pi\) | |||||||
\(164\) | −0.996689 | −0.0778284 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.2622 | 1.10696 | ||||||||
\(167\) | 1.27677 | 0.0987995 | 0.0493997 | − | 0.998779i | \(-0.484269\pi\) | ||||
0.0493997 | + | 0.998779i | \(0.484269\pi\) | |||||||
\(168\) | −8.85056 | −0.682836 | ||||||||
\(169\) | −4.04028 | −0.310791 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −36.6057 | −2.79930 | ||||||||
\(172\) | −4.59899 | −0.350669 | ||||||||
\(173\) | 18.0714 | 1.37395 | 0.686973 | − | 0.726683i | \(-0.258939\pi\) | ||||
0.686973 | + | 0.726683i | \(0.258939\pi\) | |||||||
\(174\) | −9.14630 | −0.693379 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.75414 | 0.207601 | ||||||||
\(177\) | −3.51083 | −0.263890 | ||||||||
\(178\) | 19.4835 | 1.46035 | ||||||||
\(179\) | −8.27553 | −0.618542 | −0.309271 | − | 0.950974i | \(-0.600085\pi\) | ||||
−0.309271 | + | 0.950974i | \(0.600085\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.5703 | −1.60331 | −0.801653 | − | 0.597790i | \(-0.796046\pi\) | ||||
−0.801653 | + | 0.597790i | \(0.796046\pi\) | |||||||
\(182\) | −3.33282 | −0.247045 | ||||||||
\(183\) | 3.73381 | 0.276011 | ||||||||
\(184\) | 3.07337 | 0.226572 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −18.6017 | −1.36394 | ||||||||
\(187\) | 0.960443 | 0.0702346 | ||||||||
\(188\) | 5.52664 | 0.403071 | ||||||||
\(189\) | −6.60327 | −0.480317 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.6588 | 0.915959 | 0.457980 | − | 0.888963i | \(-0.348573\pi\) | ||||
0.457980 | + | 0.888963i | \(0.348573\pi\) | |||||||
\(192\) | 23.8721 | 1.72282 | ||||||||
\(193\) | 14.0594 | 1.01201 | 0.506007 | − | 0.862529i | \(-0.331121\pi\) | ||||
0.506007 | + | 0.862529i | \(0.331121\pi\) | |||||||
\(194\) | −2.42574 | −0.174158 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.760266 | −0.0543047 | ||||||||
\(197\) | 4.16293 | 0.296596 | 0.148298 | − | 0.988943i | \(-0.452620\pi\) | ||||
0.148298 | + | 0.988943i | \(0.452620\pi\) | |||||||
\(198\) | 8.53618 | 0.606640 | ||||||||
\(199\) | −26.7246 | −1.89446 | −0.947228 | − | 0.320561i | \(-0.896129\pi\) | ||||
−0.947228 | + | 0.320561i | \(0.896129\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.3616 | −1.36566 | ||||||||
\(202\) | 3.19230 | 0.224609 | ||||||||
\(203\) | −2.85250 | −0.200206 | ||||||||
\(204\) | 1.45176 | 0.101644 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −15.3317 | −1.06821 | ||||||||
\(207\) | 5.29300 | 0.367889 | ||||||||
\(208\) | 5.69161 | 0.394642 | ||||||||
\(209\) | 10.0172 | 0.692901 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.22635 | −0.359796 | −0.179898 | − | 0.983685i | \(-0.557577\pi\) | ||||
−0.179898 | + | 0.983685i | \(0.557577\pi\) | |||||||
\(212\) | 5.72410 | 0.393133 | ||||||||
\(213\) | −44.5266 | −3.05091 | ||||||||
\(214\) | −7.97643 | −0.545258 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 20.2943 | 1.38085 | ||||||||
\(217\) | −5.80140 | −0.393825 | ||||||||
\(218\) | −11.6921 | −0.791887 | ||||||||
\(219\) | −34.7167 | −2.34594 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.98482 | 0.133513 | ||||||||
\(222\) | 4.67083 | 0.313485 | ||||||||
\(223\) | 4.66532 | 0.312413 | 0.156206 | − | 0.987724i | \(-0.450073\pi\) | ||||
0.156206 | + | 0.987724i | \(0.450073\pi\) | |||||||
\(224\) | 4.02959 | 0.269238 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.2661 | −1.01548 | ||||||||
\(227\) | −25.0909 | −1.66534 | −0.832672 | − | 0.553767i | \(-0.813190\pi\) | ||||
−0.832672 | + | 0.553767i | \(0.813190\pi\) | |||||||
\(228\) | 15.1415 | 1.00277 | ||||||||
\(229\) | −18.2807 | −1.20802 | −0.604011 | − | 0.796976i | \(-0.706432\pi\) | ||||
−0.604011 | + | 0.796976i | \(0.706432\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.17113 | 0.274440 | ||||||||
\(232\) | 8.76679 | 0.575568 | ||||||||
\(233\) | 18.7459 | 1.22809 | 0.614044 | − | 0.789272i | \(-0.289542\pi\) | ||||
0.614044 | + | 0.789272i | \(0.289542\pi\) | |||||||
\(234\) | 17.6406 | 1.15320 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.926872 | 0.0603342 | ||||||||
\(237\) | −34.8465 | −2.26352 | ||||||||
\(238\) | −0.738309 | −0.0478575 | ||||||||
\(239\) | −18.2568 | −1.18094 | −0.590468 | − | 0.807061i | \(-0.701057\pi\) | ||||
−0.590468 | + | 0.807061i | \(0.701057\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.4641 | 1.18937 | 0.594687 | − | 0.803957i | \(-0.297276\pi\) | ||||
0.594687 | + | 0.803957i | \(0.297276\pi\) | |||||||
\(242\) | 9.91184 | 0.637157 | ||||||||
\(243\) | −10.7765 | −0.691315 | ||||||||
\(244\) | −0.985740 | −0.0631055 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.20353 | −0.268007 | ||||||||
\(247\) | 20.7011 | 1.31718 | ||||||||
\(248\) | 17.8299 | 1.13220 | ||||||||
\(249\) | −36.8873 | −2.33764 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.5229 | 0.916679 | 0.458339 | − | 0.888777i | \(-0.348444\pi\) | ||||
0.458339 | + | 0.888777i | \(0.348444\pi\) | |||||||
\(252\) | 4.02409 | 0.253494 | ||||||||
\(253\) | −1.44843 | −0.0910621 | ||||||||
\(254\) | −19.5787 | −1.22848 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.2757 | −0.954730 | ||||||||
\(257\) | 12.9024 | 0.804828 | 0.402414 | − | 0.915458i | \(-0.368171\pi\) | ||||
0.402414 | + | 0.915458i | \(0.368171\pi\) | |||||||
\(258\) | −19.3962 | −1.20755 | ||||||||
\(259\) | 1.45671 | 0.0905157 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.0983 | 0.934559 | ||||||||
\(262\) | 2.33951 | 0.144536 | ||||||||
\(263\) | −8.31789 | −0.512903 | −0.256452 | − | 0.966557i | \(-0.582553\pi\) | ||||
−0.256452 | + | 0.966557i | \(0.582553\pi\) | |||||||
\(264\) | −12.8194 | −0.788982 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.70036 | −0.472139 | ||||||||
\(267\) | −50.3917 | −3.08392 | ||||||||
\(268\) | 5.11154 | 0.312237 | ||||||||
\(269\) | 12.4137 | 0.756877 | 0.378439 | − | 0.925626i | \(-0.376461\pi\) | ||||
0.378439 | + | 0.925626i | \(0.376461\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.28170 | −0.442331 | −0.221166 | − | 0.975236i | \(-0.570986\pi\) | ||||
−0.221166 | + | 0.975236i | \(0.570986\pi\) | |||||||
\(272\) | 1.26085 | 0.0764500 | ||||||||
\(273\) | 8.61991 | 0.521701 | ||||||||
\(274\) | 4.15217 | 0.250842 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.18938 | −0.131785 | ||||||||
\(277\) | −4.12299 | −0.247726 | −0.123863 | − | 0.992299i | \(-0.539528\pi\) | ||||
−0.123863 | + | 0.992299i | \(0.539528\pi\) | |||||||
\(278\) | −7.88910 | −0.473157 | ||||||||
\(279\) | 30.7068 | 1.83837 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.3317 | 0.795305 | 0.397653 | − | 0.917536i | \(-0.369825\pi\) | ||||
0.397653 | + | 0.917536i | \(0.369825\pi\) | |||||||
\(282\) | 23.3085 | 1.38800 | ||||||||
\(283\) | −6.86438 | −0.408045 | −0.204023 | − | 0.978966i | \(-0.565402\pi\) | ||||
−0.204023 | + | 0.978966i | \(0.565402\pi\) | |||||||
\(284\) | 11.7552 | 0.697542 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.82736 | −0.285448 | ||||||||
\(287\) | −1.31097 | −0.0773844 | ||||||||
\(288\) | −21.3286 | −1.25680 | ||||||||
\(289\) | −16.5603 | −0.974136 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.27387 | 0.367781 | ||||||||
\(292\) | 9.16533 | 0.536361 | ||||||||
\(293\) | −31.1708 | −1.82102 | −0.910508 | − | 0.413492i | \(-0.864309\pi\) | ||||
−0.910508 | + | 0.413492i | \(0.864309\pi\) | |||||||
\(294\) | −3.20642 | −0.187002 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.47702 | −0.260221 | ||||||||
\(297\) | −9.56439 | −0.554982 | ||||||||
\(298\) | −1.64442 | −0.0952590 | ||||||||
\(299\) | −2.99328 | −0.173106 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.04918 | −0.348669 | ||||||||
\(302\) | 7.90792 | 0.455049 | ||||||||
\(303\) | −8.25648 | −0.474322 | ||||||||
\(304\) | 13.1503 | 0.754219 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.90787 | 0.223398 | ||||||||
\(307\) | 30.3088 | 1.72981 | 0.864907 | − | 0.501933i | \(-0.167378\pi\) | ||||
0.864907 | + | 0.501933i | \(0.167378\pi\) | |||||||
\(308\) | −1.10119 | −0.0627463 | ||||||||
\(309\) | 39.6535 | 2.25581 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.7717 | −0.667514 | −0.333757 | − | 0.942659i | \(-0.608317\pi\) | ||||
−0.333757 | + | 0.942659i | \(0.608317\pi\) | |||||||
\(312\) | −26.4922 | −1.49983 | ||||||||
\(313\) | −24.4892 | −1.38421 | −0.692106 | − | 0.721795i | \(-0.743317\pi\) | ||||
−0.692106 | + | 0.721795i | \(0.743317\pi\) | |||||||
\(314\) | 20.7252 | 1.16959 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.19959 | 0.517517 | ||||||||
\(317\) | −4.07739 | −0.229009 | −0.114505 | − | 0.993423i | \(-0.536528\pi\) | ||||
−0.114505 | + | 0.993423i | \(0.536528\pi\) | |||||||
\(318\) | 24.1414 | 1.35378 | ||||||||
\(319\) | −4.13165 | −0.231328 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.6301 | 1.15146 | ||||||||
\(322\) | 1.11343 | 0.0620492 | ||||||||
\(323\) | 4.58586 | 0.255164 | ||||||||
\(324\) | −2.38482 | −0.132490 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.228934 | −0.0126795 | ||||||||
\(327\) | 30.2401 | 1.67228 | ||||||||
\(328\) | 4.02911 | 0.222470 | ||||||||
\(329\) | 7.26934 | 0.400772 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.69263 | 0.257930 | 0.128965 | − | 0.991649i | \(-0.458835\pi\) | ||||
0.128965 | + | 0.991649i | \(0.458835\pi\) | |||||||
\(332\) | 9.73839 | 0.534464 | ||||||||
\(333\) | −7.71037 | −0.422526 | ||||||||
\(334\) | −1.42160 | −0.0777864 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.47575 | 0.298727 | ||||||||
\(337\) | 21.4035 | 1.16592 | 0.582960 | − | 0.812501i | \(-0.301894\pi\) | ||||
0.582960 | + | 0.812501i | \(0.301894\pi\) | |||||||
\(338\) | 4.49858 | 0.244691 | ||||||||
\(339\) | 39.4837 | 2.14446 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.40293 | −0.455044 | ||||||||
\(342\) | 40.7580 | 2.20394 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 18.5914 | 1.00238 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.1214 | −1.08173 | ||||||||
\(347\) | 28.5572 | 1.53303 | 0.766515 | − | 0.642226i | \(-0.221989\pi\) | ||||
0.766515 | + | 0.642226i | \(0.221989\pi\) | |||||||
\(348\) | −6.24521 | −0.334778 | ||||||||
\(349\) | 9.75879 | 0.522376 | 0.261188 | − | 0.965288i | \(-0.415886\pi\) | ||||
0.261188 | + | 0.965288i | \(0.415886\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.7654 | −1.05500 | ||||||||
\(352\) | 5.83659 | 0.311091 | ||||||||
\(353\) | 37.2666 | 1.98350 | 0.991750 | − | 0.128191i | \(-0.0409170\pi\) | ||||
0.991750 | + | 0.128191i | \(0.0409170\pi\) | |||||||
\(354\) | 3.90908 | 0.207765 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.3036 | 0.705089 | ||||||||
\(357\) | 1.90954 | 0.101064 | ||||||||
\(358\) | 9.21425 | 0.486988 | ||||||||
\(359\) | −5.15223 | −0.271924 | −0.135962 | − | 0.990714i | \(-0.543413\pi\) | ||||
−0.135962 | + | 0.990714i | \(0.543413\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 28.8292 | 1.51733 | ||||||||
\(362\) | 24.0171 | 1.26231 | ||||||||
\(363\) | −25.6357 | −1.34553 | ||||||||
\(364\) | −2.27569 | −0.119278 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.15735 | −0.217308 | ||||||||
\(367\) | −23.3715 | −1.21998 | −0.609990 | − | 0.792409i | \(-0.708827\pi\) | ||||
−0.609990 | + | 0.792409i | \(0.708827\pi\) | |||||||
\(368\) | −1.90146 | −0.0991206 | ||||||||
\(369\) | 6.93898 | 0.361229 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.52908 | 0.390890 | ||||||||
\(372\) | −12.7015 | −0.658541 | ||||||||
\(373\) | 31.2466 | 1.61789 | 0.808943 | − | 0.587888i | \(-0.200040\pi\) | ||||
0.808943 | + | 0.587888i | \(0.200040\pi\) | |||||||
\(374\) | −1.06939 | −0.0552968 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −22.3414 | −1.15217 | ||||||||
\(377\) | −8.53833 | −0.439746 | ||||||||
\(378\) | 7.35230 | 0.378162 | ||||||||
\(379\) | 20.5672 | 1.05647 | 0.528233 | − | 0.849099i | \(-0.322855\pi\) | ||||
0.528233 | + | 0.849099i | \(0.322855\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 50.6378 | 2.59425 | ||||||||
\(382\) | −14.0947 | −0.721150 | ||||||||
\(383\) | −21.5957 | −1.10349 | −0.551743 | − | 0.834014i | \(-0.686037\pi\) | ||||
−0.551743 | + | 0.834014i | \(0.686037\pi\) | |||||||
\(384\) | −3.37145 | −0.172049 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.6542 | −0.796775 | ||||||||
\(387\) | 32.0183 | 1.62758 | ||||||||
\(388\) | −1.65632 | −0.0840871 | ||||||||
\(389\) | −19.3475 | −0.980957 | −0.490478 | − | 0.871453i | \(-0.663178\pi\) | ||||
−0.490478 | + | 0.871453i | \(0.663178\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.663092 | −0.0335340 | ||||||||
\(392\) | 3.07337 | 0.155229 | ||||||||
\(393\) | −6.05086 | −0.305226 | ||||||||
\(394\) | −4.63514 | −0.233515 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.82861 | 0.292899 | ||||||||
\(397\) | −32.1676 | −1.61445 | −0.807223 | − | 0.590247i | \(-0.799030\pi\) | ||||
−0.807223 | + | 0.590247i | \(0.799030\pi\) | |||||||
\(398\) | 29.7560 | 1.49154 | ||||||||
\(399\) | 19.9160 | 0.997048 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.7719 | −1.18711 | −0.593556 | − | 0.804793i | \(-0.702276\pi\) | ||||
−0.593556 | + | 0.804793i | \(0.702276\pi\) | |||||||
\(402\) | 21.5579 | 1.07521 | ||||||||
\(403\) | −17.3652 | −0.865023 | ||||||||
\(404\) | 2.17974 | 0.108446 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.17607 | 0.157626 | ||||||||
\(407\) | 2.10995 | 0.104586 | ||||||||
\(408\) | −5.86874 | −0.290546 | ||||||||
\(409\) | −9.99727 | −0.494333 | −0.247166 | − | 0.968973i | \(-0.579499\pi\) | ||||
−0.247166 | + | 0.968973i | \(0.579499\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.7391 | −0.529719 | ||||||||
\(412\) | −10.4687 | −0.515754 | ||||||||
\(413\) | 1.21914 | 0.0599900 | ||||||||
\(414\) | −5.89340 | −0.289645 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 12.0617 | 0.591373 | ||||||||
\(417\) | 20.4042 | 0.999196 | ||||||||
\(418\) | −11.1534 | −0.545532 | ||||||||
\(419\) | −16.2626 | −0.794482 | −0.397241 | − | 0.917714i | \(-0.630032\pi\) | ||||
−0.397241 | + | 0.917714i | \(0.630032\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.62211 | −0.322742 | −0.161371 | − | 0.986894i | \(-0.551592\pi\) | ||||
−0.161371 | + | 0.986894i | \(0.551592\pi\) | |||||||
\(422\) | 5.81919 | 0.283274 | ||||||||
\(423\) | −38.4766 | −1.87080 | ||||||||
\(424\) | −23.1397 | −1.12376 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 49.5774 | 2.40203 | ||||||||
\(427\) | −1.29657 | −0.0627455 | ||||||||
\(428\) | −5.44641 | −0.263262 | ||||||||
\(429\) | 12.4854 | 0.602799 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.1629 | 0.778540 | 0.389270 | − | 0.921124i | \(-0.372727\pi\) | ||||
0.389270 | + | 0.921124i | \(0.372727\pi\) | |||||||
\(432\) | −12.5559 | −0.604095 | ||||||||
\(433\) | 2.34223 | 0.112561 | 0.0562803 | − | 0.998415i | \(-0.482076\pi\) | ||||
0.0562803 | + | 0.998415i | \(0.482076\pi\) | |||||||
\(434\) | 6.45948 | 0.310065 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.98349 | −0.382340 | ||||||||
\(437\) | −6.91587 | −0.330831 | ||||||||
\(438\) | 38.6547 | 1.84699 | ||||||||
\(439\) | −28.8480 | −1.37684 | −0.688421 | − | 0.725311i | \(-0.741696\pi\) | ||||
−0.688421 | + | 0.725311i | \(0.741696\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.29300 | 0.252047 | ||||||||
\(442\) | −2.20996 | −0.105117 | ||||||||
\(443\) | −27.5171 | −1.30737 | −0.653687 | − | 0.756765i | \(-0.726779\pi\) | ||||
−0.653687 | + | 0.756765i | \(0.726779\pi\) | |||||||
\(444\) | 3.18930 | 0.151357 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.19452 | −0.245968 | ||||||||
\(447\) | 4.25310 | 0.201165 | ||||||||
\(448\) | −8.28961 | −0.391647 | ||||||||
\(449\) | −0.919843 | −0.0434101 | −0.0217050 | − | 0.999764i | \(-0.506909\pi\) | ||||
−0.0217050 | + | 0.999764i | \(0.506909\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.89886 | −0.0894137 | ||||||||
\(452\) | −10.4239 | −0.490297 | ||||||||
\(453\) | −20.4528 | −0.960958 | ||||||||
\(454\) | 27.9371 | 1.31115 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −61.2093 | −2.86639 | ||||||||
\(457\) | −1.00887 | −0.0471930 | −0.0235965 | − | 0.999722i | \(-0.507512\pi\) | ||||
−0.0235965 | + | 0.999722i | \(0.507512\pi\) | |||||||
\(458\) | 20.3543 | 0.951096 | ||||||||
\(459\) | −4.37858 | −0.204374 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.4967 | 0.721754 | 0.360877 | − | 0.932613i | \(-0.382477\pi\) | ||||
0.360877 | + | 0.932613i | \(0.382477\pi\) | |||||||
\(462\) | −4.64428 | −0.216071 | ||||||||
\(463\) | −41.6691 | −1.93653 | −0.968265 | − | 0.249927i | \(-0.919593\pi\) | ||||
−0.968265 | + | 0.249927i | \(0.919593\pi\) | |||||||
\(464\) | −5.42392 | −0.251799 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.8724 | −0.966894 | ||||||||
\(467\) | 4.55326 | 0.210700 | 0.105350 | − | 0.994435i | \(-0.466404\pi\) | ||||
0.105350 | + | 0.994435i | \(0.466404\pi\) | |||||||
\(468\) | 12.0452 | 0.556790 | ||||||||
\(469\) | 6.72336 | 0.310456 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −53.6031 | −2.46990 | ||||||||
\(472\) | −3.74688 | −0.172464 | ||||||||
\(473\) | −8.76182 | −0.402869 | ||||||||
\(474\) | 38.7992 | 1.78211 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.504126 | −0.0231066 | ||||||||
\(477\) | −39.8514 | −1.82467 | ||||||||
\(478\) | 20.3278 | 0.929771 | ||||||||
\(479\) | 10.1748 | 0.464899 | 0.232450 | − | 0.972608i | \(-0.425326\pi\) | ||||
0.232450 | + | 0.972608i | \(0.425326\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.36035 | 0.198815 | ||||||||
\(482\) | −20.5585 | −0.936414 | ||||||||
\(483\) | −2.87976 | −0.131033 | ||||||||
\(484\) | 6.76792 | 0.307633 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 11.9989 | 0.544283 | ||||||||
\(487\) | 31.1690 | 1.41240 | 0.706202 | − | 0.708010i | \(-0.250407\pi\) | ||||
0.706202 | + | 0.708010i | \(0.250407\pi\) | |||||||
\(488\) | 3.98485 | 0.180386 | ||||||||
\(489\) | 0.592109 | 0.0267761 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.3052 | 0.600456 | 0.300228 | − | 0.953867i | \(-0.402937\pi\) | ||||
0.300228 | + | 0.953867i | \(0.402937\pi\) | |||||||
\(492\) | −2.87022 | −0.129400 | ||||||||
\(493\) | −1.89147 | −0.0851875 | ||||||||
\(494\) | −23.0493 | −1.03704 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.0312 | −0.495313 | ||||||||
\(497\) | 15.4619 | 0.693563 | ||||||||
\(498\) | 41.0716 | 1.84046 | ||||||||
\(499\) | −39.3655 | −1.76224 | −0.881121 | − | 0.472890i | \(-0.843211\pi\) | ||||
−0.881121 | + | 0.472890i | \(0.843211\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.67679 | 0.164267 | ||||||||
\(502\) | −16.1703 | −0.721716 | ||||||||
\(503\) | 6.98352 | 0.311380 | 0.155690 | − | 0.987806i | \(-0.450240\pi\) | ||||
0.155690 | + | 0.987806i | \(0.450240\pi\) | |||||||
\(504\) | −16.2673 | −0.724605 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.61273 | 0.0716947 | ||||||||
\(507\) | −11.6350 | −0.516729 | ||||||||
\(508\) | −13.3686 | −0.593134 | ||||||||
\(509\) | 30.8880 | 1.36908 | 0.684542 | − | 0.728973i | \(-0.260002\pi\) | ||||
0.684542 | + | 0.728973i | \(0.260002\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0554 | 0.533301 | ||||||||
\(512\) | 19.3499 | 0.855154 | ||||||||
\(513\) | −45.6673 | −2.01626 | ||||||||
\(514\) | −14.3659 | −0.633654 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −13.2440 | −0.583033 | ||||||||
\(517\) | 10.5291 | 0.463071 | ||||||||
\(518\) | −1.62195 | −0.0712645 | ||||||||
\(519\) | 52.0414 | 2.28436 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.1013 | 1.66925 | 0.834623 | − | 0.550821i | \(-0.185685\pi\) | ||||
0.834623 | + | 0.550821i | \(0.185685\pi\) | |||||||
\(522\) | −16.8109 | −0.735794 | ||||||||
\(523\) | 13.0908 | 0.572421 | 0.286210 | − | 0.958167i | \(-0.407604\pi\) | ||||
0.286210 | + | 0.958167i | \(0.407604\pi\) | |||||||
\(524\) | 1.59745 | 0.0697849 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.26142 | 0.403817 | ||||||||
\(527\) | −3.84686 | −0.167572 | ||||||||
\(528\) | 7.93125 | 0.345163 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.45291 | −0.280033 | ||||||||
\(532\) | −5.25790 | −0.227959 | ||||||||
\(533\) | −3.92411 | −0.169972 | ||||||||
\(534\) | 56.1078 | 2.42802 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −20.6634 | −0.892522 | ||||||||
\(537\) | −23.8315 | −1.02841 | ||||||||
\(538\) | −13.8218 | −0.595902 | ||||||||
\(539\) | −1.44843 | −0.0623884 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.8575 | 0.853742 | 0.426871 | − | 0.904312i | \(-0.359616\pi\) | ||||
0.426871 | + | 0.904312i | \(0.359616\pi\) | |||||||
\(542\) | 8.10768 | 0.348255 | ||||||||
\(543\) | −62.1171 | −2.66570 | ||||||||
\(544\) | 2.67199 | 0.114561 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −9.59770 | −0.410744 | ||||||||
\(547\) | −2.33451 | −0.0998163 | −0.0499081 | − | 0.998754i | \(-0.515893\pi\) | ||||
−0.0499081 | + | 0.998754i | \(0.515893\pi\) | |||||||
\(548\) | 2.83515 | 0.121112 | ||||||||
\(549\) | 6.86275 | 0.292895 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.7275 | −0.840420 | ||||||||
\(552\) | 8.85056 | 0.376705 | ||||||||
\(553\) | 12.1005 | 0.514565 | ||||||||
\(554\) | 4.59067 | 0.195039 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.38677 | −0.228450 | ||||||||
\(557\) | 3.11889 | 0.132152 | 0.0660759 | − | 0.997815i | \(-0.478952\pi\) | ||||
0.0660759 | + | 0.997815i | \(0.478952\pi\) | |||||||
\(558\) | −34.1900 | −1.44738 | ||||||||
\(559\) | −18.1069 | −0.765840 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.76584 | 0.116774 | ||||||||
\(562\) | −14.8440 | −0.626157 | ||||||||
\(563\) | 33.1239 | 1.39601 | 0.698003 | − | 0.716094i | \(-0.254072\pi\) | ||||
0.698003 | + | 0.716094i | \(0.254072\pi\) | |||||||
\(564\) | 15.9154 | 0.670158 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.64304 | 0.321261 | ||||||||
\(567\) | −3.13682 | −0.131734 | ||||||||
\(568\) | −47.5203 | −1.99391 | ||||||||
\(569\) | −36.2581 | −1.52002 | −0.760008 | − | 0.649913i | \(-0.774805\pi\) | ||||
−0.760008 | + | 0.649913i | \(0.774805\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.4478 | −1.02311 | −0.511554 | − | 0.859251i | \(-0.670930\pi\) | ||||
−0.511554 | + | 0.859251i | \(0.670930\pi\) | |||||||
\(572\) | −3.29618 | −0.137820 | ||||||||
\(573\) | 36.4543 | 1.52290 | ||||||||
\(574\) | 1.45968 | 0.0609260 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 43.8769 | 1.82820 | ||||||||
\(577\) | 41.1613 | 1.71357 | 0.856784 | − | 0.515675i | \(-0.172459\pi\) | ||||
0.856784 | + | 0.515675i | \(0.172459\pi\) | |||||||
\(578\) | 18.4388 | 0.766953 | ||||||||
\(579\) | 40.4875 | 1.68260 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.8092 | 0.531415 | ||||||||
\(582\) | −6.98554 | −0.289560 | ||||||||
\(583\) | 10.9054 | 0.451654 | ||||||||
\(584\) | −37.0508 | −1.53317 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 34.7066 | 1.43372 | ||||||||
\(587\) | 44.9204 | 1.85406 | 0.927031 | − | 0.374984i | \(-0.122352\pi\) | ||||
0.927031 | + | 0.374984i | \(0.122352\pi\) | |||||||
\(588\) | −2.18938 | −0.0902886 | ||||||||
\(589\) | −40.1217 | −1.65319 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.9882 | 0.493130 | ||||||||
\(592\) | 2.76988 | 0.113842 | ||||||||
\(593\) | −32.4937 | −1.33436 | −0.667178 | − | 0.744898i | \(-0.732498\pi\) | ||||
−0.667178 | + | 0.744898i | \(0.732498\pi\) | |||||||
\(594\) | 10.6493 | 0.436946 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.12283 | −0.0459931 | ||||||||
\(597\) | −76.9603 | −3.14978 | ||||||||
\(598\) | 3.33282 | 0.136289 | ||||||||
\(599\) | 27.3234 | 1.11640 | 0.558201 | − | 0.829706i | \(-0.311492\pi\) | ||||
0.558201 | + | 0.829706i | \(0.311492\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.51397 | 0.224920 | 0.112460 | − | 0.993656i | \(-0.464127\pi\) | ||||
0.112460 | + | 0.993656i | \(0.464127\pi\) | |||||||
\(602\) | 6.73536 | 0.274513 | ||||||||
\(603\) | −35.5867 | −1.44920 | ||||||||
\(604\) | 5.39962 | 0.219708 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.19303 | 0.373442 | ||||||||
\(607\) | 7.96719 | 0.323378 | 0.161689 | − | 0.986842i | \(-0.448306\pi\) | ||||
0.161689 | + | 0.986842i | \(0.448306\pi\) | |||||||
\(608\) | 27.8681 | 1.13020 | ||||||||
\(609\) | −8.21450 | −0.332868 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.7592 | 0.880282 | ||||||||
\(612\) | 2.66834 | 0.107861 | ||||||||
\(613\) | 6.29976 | 0.254445 | 0.127222 | − | 0.991874i | \(-0.459394\pi\) | ||||
0.127222 | + | 0.991874i | \(0.459394\pi\) | |||||||
\(614\) | −33.7468 | −1.36191 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.45157 | 0.179359 | ||||||||
\(617\) | 22.2397 | 0.895336 | 0.447668 | − | 0.894200i | \(-0.352255\pi\) | ||||
0.447668 | + | 0.894200i | \(0.352255\pi\) | |||||||
\(618\) | −44.1515 | −1.77603 | ||||||||
\(619\) | 6.07253 | 0.244076 | 0.122038 | − | 0.992525i | \(-0.461057\pi\) | ||||
0.122038 | + | 0.992525i | \(0.461057\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.60327 | 0.264980 | ||||||||
\(622\) | 13.1071 | 0.525545 | ||||||||
\(623\) | 17.4986 | 0.701066 | ||||||||
\(624\) | 16.3905 | 0.656143 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 27.2671 | 1.08981 | ||||||||
\(627\) | 28.8470 | 1.15204 | ||||||||
\(628\) | 14.1514 | 0.564703 | ||||||||
\(629\) | 0.965934 | 0.0385143 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −48.3297 | −1.92398 | −0.961988 | − | 0.273093i | \(-0.911953\pi\) | ||||
−0.961988 | + | 0.273093i | \(0.911953\pi\) | |||||||
\(632\) | −37.1893 | −1.47931 | ||||||||
\(633\) | −15.0506 | −0.598208 | ||||||||
\(634\) | 4.53990 | 0.180303 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 16.4840 | 0.653634 | ||||||||
\(637\) | −2.99328 | −0.118598 | ||||||||
\(638\) | 4.60032 | 0.182128 | ||||||||
\(639\) | −81.8400 | −3.23754 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.7883 | 0.702595 | 0.351297 | − | 0.936264i | \(-0.385741\pi\) | ||||
0.351297 | + | 0.936264i | \(0.385741\pi\) | |||||||
\(642\) | −22.9702 | −0.906561 | ||||||||
\(643\) | 29.4888 | 1.16292 | 0.581462 | − | 0.813573i | \(-0.302481\pi\) | ||||
0.581462 | + | 0.813573i | \(0.302481\pi\) | |||||||
\(644\) | 0.760266 | 0.0299587 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.10604 | −0.200895 | ||||||||
\(647\) | −2.00709 | −0.0789067 | −0.0394534 | − | 0.999221i | \(-0.512562\pi\) | ||||
−0.0394534 | + | 0.999221i | \(0.512562\pi\) | |||||||
\(648\) | 9.64063 | 0.378720 | ||||||||
\(649\) | 1.76584 | 0.0693154 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.7066 | −0.654784 | ||||||||
\(652\) | −0.156319 | −0.00612192 | ||||||||
\(653\) | 5.44963 | 0.213260 | 0.106630 | − | 0.994299i | \(-0.465994\pi\) | ||||
0.106630 | + | 0.994299i | \(0.465994\pi\) | |||||||
\(654\) | −33.6703 | −1.31661 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.49277 | −0.0973263 | ||||||||
\(657\) | −63.8094 | −2.48944 | ||||||||
\(658\) | −8.09393 | −0.315534 | ||||||||
\(659\) | 5.72411 | 0.222980 | 0.111490 | − | 0.993766i | \(-0.464438\pi\) | ||||
0.111490 | + | 0.993766i | \(0.464438\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.634951 | −0.0246967 | −0.0123484 | − | 0.999924i | \(-0.503931\pi\) | ||||
−0.0123484 | + | 0.999924i | \(0.503931\pi\) | |||||||
\(662\) | −5.22493 | −0.203073 | ||||||||
\(663\) | 5.71580 | 0.221983 | ||||||||
\(664\) | −39.3674 | −1.52775 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.58499 | 0.332661 | ||||||||
\(667\) | 2.85250 | 0.110449 | ||||||||
\(668\) | −0.970685 | −0.0375569 | ||||||||
\(669\) | 13.4350 | 0.519426 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.87800 | −0.0724992 | ||||||||
\(672\) | 11.6042 | 0.447643 | ||||||||
\(673\) | 27.6288 | 1.06501 | 0.532506 | − | 0.846426i | \(-0.321250\pi\) | ||||
0.532506 | + | 0.846426i | \(0.321250\pi\) | |||||||
\(674\) | −23.8313 | −0.917948 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.07169 | 0.118142 | ||||||||
\(677\) | −13.9294 | −0.535351 | −0.267676 | − | 0.963509i | \(-0.586256\pi\) | ||||
−0.267676 | + | 0.963509i | \(0.586256\pi\) | |||||||
\(678\) | −43.9625 | −1.68837 | ||||||||
\(679\) | −2.17861 | −0.0836074 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −72.2557 | −2.76885 | ||||||||
\(682\) | 9.35611 | 0.358264 | ||||||||
\(683\) | 22.8605 | 0.874732 | 0.437366 | − | 0.899284i | \(-0.355911\pi\) | ||||
0.437366 | + | 0.899284i | \(0.355911\pi\) | |||||||
\(684\) | 27.8300 | 1.06411 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.11343 | 0.0425111 | ||||||||
\(687\) | −52.6440 | −2.00849 | ||||||||
\(688\) | −11.5023 | −0.438521 | ||||||||
\(689\) | 22.5366 | 0.858577 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.1913 | 0.920282 | 0.460141 | − | 0.887846i | \(-0.347799\pi\) | ||||
0.460141 | + | 0.887846i | \(0.347799\pi\) | |||||||
\(692\) | −13.7391 | −0.522283 | ||||||||
\(693\) | 7.66654 | 0.291228 | ||||||||
\(694\) | −31.7965 | −1.20698 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 25.2462 | 0.956956 | ||||||||
\(697\) | −0.869297 | −0.0329270 | ||||||||
\(698\) | −10.8658 | −0.411275 | ||||||||
\(699\) | 53.9838 | 2.04185 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.5742 | 1.04146 | 0.520731 | − | 0.853721i | \(-0.325659\pi\) | ||||
0.520731 | + | 0.853721i | \(0.325659\pi\) | |||||||
\(702\) | 22.0075 | 0.830619 | ||||||||
\(703\) | 10.0744 | 0.379964 | ||||||||
\(704\) | −12.0069 | −0.452528 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −41.4938 | −1.56164 | ||||||||
\(707\) | 2.86707 | 0.107827 | ||||||||
\(708\) | 2.66917 | 0.100313 | ||||||||
\(709\) | 37.7172 | 1.41650 | 0.708249 | − | 0.705963i | \(-0.249485\pi\) | ||||
0.708249 | + | 0.705963i | \(0.249485\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −64.0479 | −2.40198 | ||||||||
\(712\) | −53.7797 | −2.01548 | ||||||||
\(713\) | 5.80140 | 0.217264 | ||||||||
\(714\) | −2.12615 | −0.0795691 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.29161 | 0.235128 | ||||||||
\(717\) | −52.5752 | −1.96346 | ||||||||
\(718\) | 5.73667 | 0.214091 | ||||||||
\(719\) | −28.5538 | −1.06488 | −0.532438 | − | 0.846469i | \(-0.678724\pi\) | ||||
−0.532438 | + | 0.846469i | \(0.678724\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.7697 | −0.512811 | ||||||||
\(722\) | −32.0994 | −1.19462 | ||||||||
\(723\) | 53.1720 | 1.97749 | ||||||||
\(724\) | 16.3991 | 0.609469 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 28.5437 | 1.05935 | ||||||||
\(727\) | −2.95773 | −0.109696 | −0.0548480 | − | 0.998495i | \(-0.517467\pi\) | ||||
−0.0548480 | + | 0.998495i | \(0.517467\pi\) | |||||||
\(728\) | 9.19946 | 0.340955 | ||||||||
\(729\) | −40.4442 | −1.49793 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.01116 | −0.148358 | ||||||||
\(732\) | −2.83869 | −0.104921 | ||||||||
\(733\) | −29.3085 | −1.08254 | −0.541268 | − | 0.840850i | \(-0.682055\pi\) | ||||
−0.541268 | + | 0.840850i | \(0.682055\pi\) | |||||||
\(734\) | 26.0226 | 0.960510 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.02959 | −0.148533 | ||||||||
\(737\) | 9.73832 | 0.358716 | ||||||||
\(738\) | −7.72609 | −0.284401 | ||||||||
\(739\) | 15.4678 | 0.568993 | 0.284497 | − | 0.958677i | \(-0.408174\pi\) | ||||
0.284497 | + | 0.958677i | \(0.408174\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 59.6142 | 2.18998 | ||||||||
\(742\) | −8.38313 | −0.307754 | ||||||||
\(743\) | 7.62875 | 0.279872 | 0.139936 | − | 0.990161i | \(-0.455310\pi\) | ||||
0.139936 | + | 0.990161i | \(0.455310\pi\) | |||||||
\(744\) | 51.3457 | 1.88242 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −34.7910 | −1.27379 | ||||||||
\(747\) | −67.7990 | −2.48063 | ||||||||
\(748\) | −0.730193 | −0.0266985 | ||||||||
\(749\) | −7.16382 | −0.261760 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.82336 | −0.176007 | −0.0880034 | − | 0.996120i | \(-0.528049\pi\) | ||||
−0.0880034 | + | 0.996120i | \(0.528049\pi\) | |||||||
\(752\) | 13.8224 | 0.504051 | ||||||||
\(753\) | 41.8225 | 1.52410 | ||||||||
\(754\) | 9.50686 | 0.346219 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.02024 | 0.182584 | ||||||||
\(757\) | −4.81593 | −0.175038 | −0.0875190 | − | 0.996163i | \(-0.527894\pi\) | ||||
−0.0875190 | + | 0.996163i | \(0.527894\pi\) | |||||||
\(758\) | −22.9002 | −0.831773 | ||||||||
\(759\) | −4.17113 | −0.151402 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0293 | 0.762311 | 0.381156 | − | 0.924511i | \(-0.375526\pi\) | ||||
0.381156 | + | 0.924511i | \(0.375526\pi\) | |||||||
\(762\) | −56.3818 | −2.04250 | ||||||||
\(763\) | −10.5009 | −0.380159 | ||||||||
\(764\) | −9.62406 | −0.348186 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0453 | 0.868793 | ||||||||
\(767\) | 3.64923 | 0.131766 | ||||||||
\(768\) | −43.9902 | −1.58736 | ||||||||
\(769\) | −26.7473 | −0.964533 | −0.482267 | − | 0.876024i | \(-0.660186\pi\) | ||||
−0.482267 | + | 0.876024i | \(0.660186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.1557 | 1.33813 | ||||||||
\(772\) | −10.6888 | −0.384700 | ||||||||
\(773\) | −18.0588 | −0.649530 | −0.324765 | − | 0.945795i | \(-0.605285\pi\) | ||||
−0.324765 | + | 0.945795i | \(0.605285\pi\) | |||||||
\(774\) | −35.6502 | −1.28142 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.69568 | 0.240361 | ||||||||
\(777\) | 4.19498 | 0.150494 | ||||||||
\(778\) | 21.5421 | 0.772323 | ||||||||
\(779\) | −9.06652 | −0.324842 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.3956 | 0.801376 | ||||||||
\(782\) | 0.738309 | 0.0264019 | ||||||||
\(783\) | 18.8358 | 0.673138 | ||||||||
\(784\) | −1.90146 | −0.0679094 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.73723 | 0.240309 | ||||||||
\(787\) | −30.6722 | −1.09335 | −0.546674 | − | 0.837346i | \(-0.684106\pi\) | ||||
−0.546674 | + | 0.837346i | \(0.684106\pi\) | |||||||
\(788\) | −3.16493 | −0.112746 | ||||||||
\(789\) | −23.9535 | −0.852767 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.7108 | −0.487500 | ||||||||
\(792\) | −23.5621 | −0.837244 | ||||||||
\(793\) | −3.88100 | −0.137818 | ||||||||
\(794\) | 35.8165 | 1.27108 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.3178 | 0.720145 | ||||||||
\(797\) | −8.87753 | −0.314458 | −0.157229 | − | 0.987562i | \(-0.550256\pi\) | ||||
−0.157229 | + | 0.987562i | \(0.550256\pi\) | |||||||
\(798\) | −22.1751 | −0.784992 | ||||||||
\(799\) | 4.82024 | 0.170528 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −92.6200 | −3.27257 | ||||||||
\(802\) | 26.4684 | 0.934633 | ||||||||
\(803\) | 17.4615 | 0.616202 | ||||||||
\(804\) | 14.7200 | 0.519134 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 19.3350 | 0.681047 | ||||||||
\(807\) | 35.7485 | 1.25841 | ||||||||
\(808\) | −8.81159 | −0.309991 | ||||||||
\(809\) | −45.1721 | −1.58817 | −0.794083 | − | 0.607810i | \(-0.792048\pi\) | ||||
−0.794083 | + | 0.607810i | \(0.792048\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.7969 | 1.64326 | 0.821630 | − | 0.570021i | \(-0.193065\pi\) | ||||
0.821630 | + | 0.570021i | \(0.193065\pi\) | |||||||
\(812\) | 2.16866 | 0.0761050 | ||||||||
\(813\) | −20.9695 | −0.735433 | ||||||||
\(814\) | −2.34929 | −0.0823424 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.63093 | 0.127108 | ||||||||
\(817\) | −41.8353 | −1.46363 | ||||||||
\(818\) | 11.1313 | 0.389196 | ||||||||
\(819\) | 15.8434 | 0.553614 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.9685 | −1.32511 | −0.662555 | − | 0.749013i | \(-0.730528\pi\) | ||||
−0.662555 | + | 0.749013i | \(0.730528\pi\) | |||||||
\(822\) | 11.9572 | 0.417057 | ||||||||
\(823\) | −48.8194 | −1.70174 | −0.850869 | − | 0.525378i | \(-0.823924\pi\) | ||||
−0.850869 | + | 0.525378i | \(0.823924\pi\) | |||||||
\(824\) | 42.3195 | 1.47427 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.35743 | −0.0472311 | ||||||||
\(827\) | 30.1297 | 1.04771 | 0.523855 | − | 0.851807i | \(-0.324493\pi\) | ||||
0.523855 | + | 0.851807i | \(0.324493\pi\) | |||||||
\(828\) | −4.02409 | −0.139847 | ||||||||
\(829\) | 13.5220 | 0.469638 | 0.234819 | − | 0.972039i | \(-0.424550\pi\) | ||||
0.234819 | + | 0.972039i | \(0.424550\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.8732 | −0.411877 | ||||||||
\(832\) | −24.8131 | −0.860240 | ||||||||
\(833\) | −0.663092 | −0.0229748 | ||||||||
\(834\) | −22.7187 | −0.786683 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.61571 | −0.263395 | ||||||||
\(837\) | 38.3082 | 1.32413 | ||||||||
\(838\) | 18.1074 | 0.625508 | ||||||||
\(839\) | 34.4251 | 1.18849 | 0.594243 | − | 0.804285i | \(-0.297452\pi\) | ||||
0.594243 | + | 0.804285i | \(0.297452\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.8632 | −0.719422 | ||||||||
\(842\) | 7.37328 | 0.254100 | ||||||||
\(843\) | 38.3922 | 1.32230 | ||||||||
\(844\) | 3.97341 | 0.136771 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 42.8411 | 1.47291 | ||||||||
\(847\) | 8.90205 | 0.305878 | ||||||||
\(848\) | 14.3163 | 0.491623 | ||||||||
\(849\) | −19.7678 | −0.678428 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.45671 | −0.0499355 | ||||||||
\(852\) | 33.8521 | 1.15975 | ||||||||
\(853\) | 31.0886 | 1.06445 | 0.532226 | − | 0.846602i | \(-0.321356\pi\) | ||||
0.532226 | + | 0.846602i | \(0.321356\pi\) | |||||||
\(854\) | 1.44365 | 0.0494006 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22.0171 | 0.752528 | ||||||||
\(857\) | 23.5785 | 0.805427 | 0.402714 | − | 0.915326i | \(-0.368067\pi\) | ||||
0.402714 | + | 0.915326i | \(0.368067\pi\) | |||||||
\(858\) | −13.9016 | −0.474593 | ||||||||
\(859\) | −31.9744 | −1.09095 | −0.545476 | − | 0.838126i | \(-0.683651\pi\) | ||||
−0.545476 | + | 0.838126i | \(0.683651\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.77529 | −0.128661 | ||||||||
\(862\) | −17.9963 | −0.612957 | ||||||||
\(863\) | −27.5084 | −0.936397 | −0.468198 | − | 0.883623i | \(-0.655097\pi\) | ||||
−0.468198 | + | 0.883623i | \(0.655097\pi\) | |||||||
\(864\) | −26.6085 | −0.905239 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.60792 | −0.0886208 | ||||||||
\(867\) | −47.6897 | −1.61963 | ||||||||
\(868\) | 4.41061 | 0.149706 | ||||||||
\(869\) | 17.5267 | 0.594554 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.1249 | 0.681906 | ||||||||
\(872\) | 32.2732 | 1.09291 | ||||||||
\(873\) | 11.5314 | 0.390278 | ||||||||
\(874\) | 7.70036 | 0.260468 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 26.3939 | 0.891768 | ||||||||
\(877\) | −36.4417 | −1.23055 | −0.615274 | − | 0.788314i | \(-0.710955\pi\) | ||||
−0.615274 | + | 0.788314i | \(0.710955\pi\) | |||||||
\(878\) | 32.1204 | 1.08401 | ||||||||
\(879\) | −89.7642 | −3.02767 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.9049 | −1.34443 | −0.672216 | − | 0.740355i | \(-0.734657\pi\) | ||||
−0.672216 | + | 0.740355i | \(0.734657\pi\) | |||||||
\(882\) | −5.89340 | −0.198441 | ||||||||
\(883\) | 52.5102 | 1.76711 | 0.883555 | − | 0.468327i | \(-0.155143\pi\) | ||||
0.883555 | + | 0.468327i | \(0.155143\pi\) | |||||||
\(884\) | −1.50899 | −0.0507529 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.6384 | 1.02932 | ||||||||
\(887\) | 2.24783 | 0.0754748 | 0.0377374 | − | 0.999288i | \(-0.487985\pi\) | ||||
0.0377374 | + | 0.999288i | \(0.487985\pi\) | |||||||
\(888\) | −12.8927 | −0.432651 | ||||||||
\(889\) | −17.5841 | −0.589750 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.54347 | −0.152212 | ||||||||
\(892\) | −3.54688 | −0.118758 | ||||||||
\(893\) | 50.2738 | 1.68235 | ||||||||
\(894\) | −4.73554 | −0.158380 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.17074 | 0.0391118 | ||||||||
\(897\) | −8.61991 | −0.287811 | ||||||||
\(898\) | 1.02418 | 0.0341774 | ||||||||
\(899\) | 16.5485 | 0.551923 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.99247 | 0.166323 | ||||||||
\(902\) | 2.11425 | 0.0703968 | ||||||||
\(903\) | −17.4202 | −0.579707 | ||||||||
\(904\) | 42.1384 | 1.40150 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 22.7729 | 0.756578 | ||||||||
\(907\) | 19.1127 | 0.634625 | 0.317313 | − | 0.948321i | \(-0.397220\pi\) | ||||
0.317313 | + | 0.948321i | \(0.397220\pi\) | |||||||
\(908\) | 19.0758 | 0.633052 | ||||||||
\(909\) | −15.1754 | −0.503337 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.7484 | 1.35006 | 0.675028 | − | 0.737792i | \(-0.264131\pi\) | ||||
0.675028 | + | 0.737792i | \(0.264131\pi\) | |||||||
\(912\) | 37.8696 | 1.25399 | ||||||||
\(913\) | 18.5532 | 0.614022 | ||||||||
\(914\) | 1.12331 | 0.0371558 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.8982 | 0.459209 | ||||||||
\(917\) | 2.10117 | 0.0693868 | ||||||||
\(918\) | 4.87525 | 0.160907 | ||||||||
\(919\) | 38.7070 | 1.27683 | 0.638414 | − | 0.769693i | \(-0.279591\pi\) | ||||
0.638414 | + | 0.769693i | \(0.279591\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 87.2819 | 2.87604 | ||||||||
\(922\) | −17.2546 | −0.568249 | ||||||||
\(923\) | 46.2819 | 1.52339 | ||||||||
\(924\) | −3.17117 | −0.104324 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 46.3958 | 1.52466 | ||||||||
\(927\) | 72.8831 | 2.39380 | ||||||||
\(928\) | −11.4944 | −0.377322 | ||||||||
\(929\) | 49.9855 | 1.63997 | 0.819986 | − | 0.572384i | \(-0.193981\pi\) | ||||
0.819986 | + | 0.572384i | \(0.193981\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.91587 | −0.226658 | ||||||||
\(932\) | −14.2519 | −0.466837 | ||||||||
\(933\) | −33.8998 | −1.10983 | ||||||||
\(934\) | −5.06975 | −0.165887 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −48.6927 | −1.59157 | ||||||||
\(937\) | −12.5826 | −0.411056 | −0.205528 | − | 0.978651i | \(-0.565891\pi\) | ||||
−0.205528 | + | 0.978651i | \(0.565891\pi\) | |||||||
\(938\) | −7.48601 | −0.244427 | ||||||||
\(939\) | −70.5230 | −2.30143 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.761460 | 0.0248229 | 0.0124114 | − | 0.999923i | \(-0.496049\pi\) | ||||
0.0124114 | + | 0.999923i | \(0.496049\pi\) | |||||||
\(942\) | 59.6835 | 1.94459 | ||||||||
\(943\) | 1.31097 | 0.0426912 | ||||||||
\(944\) | 2.31815 | 0.0754495 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.75571 | 0.317185 | ||||||||
\(947\) | −50.8324 | −1.65183 | −0.825915 | − | 0.563795i | \(-0.809341\pi\) | ||||
−0.825915 | + | 0.563795i | \(0.809341\pi\) | |||||||
\(948\) | 26.4926 | 0.860439 | ||||||||
\(949\) | 36.0853 | 1.17138 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.7419 | −0.380757 | ||||||||
\(952\) | 2.03793 | 0.0660496 | ||||||||
\(953\) | −10.3471 | −0.335174 | −0.167587 | − | 0.985857i | \(-0.553597\pi\) | ||||
−0.167587 | + | 0.985857i | \(0.553597\pi\) | |||||||
\(954\) | 44.3719 | 1.43659 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.8801 | 0.448913 | ||||||||
\(957\) | −11.8981 | −0.384612 | ||||||||
\(958\) | −11.3290 | −0.366023 | ||||||||
\(959\) | 3.72916 | 0.120421 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.65627 | 0.0856861 | ||||||||
\(962\) | −4.85496 | −0.156530 | ||||||||
\(963\) | 37.9181 | 1.22189 | ||||||||
\(964\) | −14.0376 | −0.452121 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.20642 | 0.103165 | ||||||||
\(967\) | 15.7145 | 0.505345 | 0.252673 | − | 0.967552i | \(-0.418690\pi\) | ||||
0.252673 | + | 0.967552i | \(0.418690\pi\) | |||||||
\(968\) | −27.3593 | −0.879361 | ||||||||
\(969\) | 13.2061 | 0.424243 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.1348 | −0.678248 | −0.339124 | − | 0.940742i | \(-0.610131\pi\) | ||||
−0.339124 | + | 0.940742i | \(0.610131\pi\) | |||||||
\(972\) | 8.19303 | 0.262792 | ||||||||
\(973\) | −7.08538 | −0.227147 | ||||||||
\(974\) | −34.7046 | −1.11201 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.46538 | −0.0789150 | ||||||||
\(977\) | 42.8162 | 1.36981 | 0.684906 | − | 0.728632i | \(-0.259843\pi\) | ||||
0.684906 | + | 0.728632i | \(0.259843\pi\) | |||||||
\(978\) | −0.659273 | −0.0210812 | ||||||||
\(979\) | 25.3455 | 0.810046 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 55.5813 | 1.77457 | ||||||||
\(982\) | −14.8145 | −0.472749 | ||||||||
\(983\) | 17.9746 | 0.573300 | 0.286650 | − | 0.958035i | \(-0.407458\pi\) | ||||
0.286650 | + | 0.958035i | \(0.407458\pi\) | |||||||
\(984\) | 11.6029 | 0.369886 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.10603 | 0.0670695 | ||||||||
\(987\) | 20.9339 | 0.666335 | ||||||||
\(988\) | −15.7384 | −0.500704 | ||||||||
\(989\) | 6.04918 | 0.192353 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.0706 | −0.732862 | −0.366431 | − | 0.930445i | \(-0.619420\pi\) | ||||
−0.366431 | + | 0.930445i | \(0.619420\pi\) | |||||||
\(992\) | −23.3773 | −0.742230 | ||||||||
\(993\) | 13.5136 | 0.428842 | ||||||||
\(994\) | −17.2158 | −0.546053 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 28.0442 | 0.888614 | ||||||||
\(997\) | 33.9230 | 1.07435 | 0.537176 | − | 0.843470i | \(-0.319491\pi\) | ||||
0.537176 | + | 0.843470i | \(0.319491\pi\) | |||||||
\(998\) | 43.8309 | 1.38744 | ||||||||
\(999\) | −9.61907 | −0.304334 |
(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 | 4025.2.a.y.1.4 | 12 | ||
5.2 | odd | 4 | 805.2.c.b.484.9 | ✓ | 24 | ||
5.3 | odd | 4 | 805.2.c.b.484.16 | yes | 24 | ||
5.4 | even | 2 | 4025.2.a.x.1.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
805.2.c.b.484.9 | ✓ | 24 | 5.2 | odd | 4 | ||
805.2.c.b.484.16 | yes | 24 | 5.3 | odd | 4 | ||
4025.2.a.x.1.9 | 12 | 5.4 | even | 2 | |||
4025.2.a.y.1.4 | 12 | 1.1 | even | 1 | trivial |