Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.44400625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 11x^{4} - x^{3} + 29x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.16056\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.16056 | 1.52775 | 0.763873 | − | 0.645366i | \(-0.223295\pi\) | ||||
0.763873 | + | 0.645366i | \(0.223295\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.66802 | 1.33401 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.16056 | 1.19458 | 0.597290 | − | 0.802026i | \(-0.296244\pi\) | ||||
0.597290 | + | 0.802026i | \(0.296244\pi\) | |||||||
\(8\) | 1.44329 | 0.510282 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.53835 | −0.463830 | −0.231915 | − | 0.972736i | \(-0.574499\pi\) | ||||
−0.231915 | + | 0.972736i | \(0.574499\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.24144 | 1.45371 | 0.726857 | − | 0.686789i | \(-0.240981\pi\) | ||||
0.726857 | + | 0.686789i | \(0.240981\pi\) | |||||||
\(14\) | 6.82858 | 1.82501 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.21771 | −0.554428 | ||||||||
\(17\) | 1.29068 | 0.313037 | 0.156518 | − | 0.987675i | \(-0.449973\pi\) | ||||
0.156518 | + | 0.987675i | \(0.449973\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.44587 | 1.24937 | 0.624685 | − | 0.780877i | \(-0.285228\pi\) | ||||
0.624685 | + | 0.780877i | \(0.285228\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.32370 | −0.708615 | ||||||||
\(23\) | −6.44244 | −1.34334 | −0.671671 | − | 0.740850i | \(-0.734423\pi\) | ||||
−0.671671 | + | 0.740850i | \(0.734423\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 11.3244 | 2.22090 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8.43243 | 1.59358 | ||||||||
\(29\) | 2.36361 | 0.438912 | 0.219456 | − | 0.975622i | \(-0.429572\pi\) | ||||
0.219456 | + | 0.975622i | \(0.429572\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.46542 | −0.802014 | −0.401007 | − | 0.916075i | \(-0.631340\pi\) | ||||
−0.401007 | + | 0.916075i | \(0.631340\pi\) | |||||||
\(32\) | −7.67809 | −1.35731 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.78860 | 0.478241 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.95751 | 0.979408 | 0.489704 | − | 0.871889i | \(-0.337105\pi\) | ||||
0.489704 | + | 0.871889i | \(0.337105\pi\) | |||||||
\(38\) | 11.7661 | 1.90872 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.53219 | 1.33250 | 0.666252 | − | 0.745726i | \(-0.267897\pi\) | ||||
0.666252 | + | 0.745726i | \(0.267897\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.48426 | 1.29384 | 0.646919 | − | 0.762559i | \(-0.276057\pi\) | ||||
0.646919 | + | 0.762559i | \(0.276057\pi\) | |||||||
\(44\) | −4.10435 | −0.618754 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.9193 | −2.05228 | ||||||||
\(47\) | 0.753070 | 0.109847 | 0.0549233 | − | 0.998491i | \(-0.482509\pi\) | ||||
0.0549233 | + | 0.998491i | \(0.482509\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.98914 | 0.427020 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 13.9843 | 1.93927 | ||||||||
\(53\) | 9.74991 | 1.33925 | 0.669626 | − | 0.742698i | \(-0.266454\pi\) | ||||
0.669626 | + | 0.742698i | \(0.266454\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.56162 | 0.609572 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.10672 | 0.670546 | ||||||||
\(59\) | −4.11270 | −0.535428 | −0.267714 | − | 0.963498i | \(-0.586268\pi\) | ||||
−0.267714 | + | 0.963498i | \(0.586268\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.6939 | −1.36922 | −0.684610 | − | 0.728910i | \(-0.740027\pi\) | ||||
−0.684610 | + | 0.728910i | \(0.740027\pi\) | |||||||
\(62\) | −9.64781 | −1.22527 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.1535 | −1.51919 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.89864 | 0.231956 | 0.115978 | − | 0.993252i | \(-0.463000\pi\) | ||||
0.115978 | + | 0.993252i | \(0.463000\pi\) | |||||||
\(68\) | 3.44357 | 0.417594 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.0708774 | 0.00841160 | 0.00420580 | − | 0.999991i | \(-0.498661\pi\) | ||||
0.00420580 | + | 0.999991i | \(0.498661\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.01123 | −0.469478 | −0.234739 | − | 0.972058i | \(-0.575424\pi\) | ||||
−0.234739 | + | 0.972058i | \(0.575424\pi\) | |||||||
\(74\) | 12.8716 | 1.49629 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 14.5297 | 1.66667 | ||||||||
\(77\) | −4.86205 | −0.554082 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.61849 | 0.182094 | 0.0910472 | − | 0.995847i | \(-0.470979\pi\) | ||||
0.0910472 | + | 0.995847i | \(0.470979\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 18.4343 | 2.03573 | ||||||||
\(83\) | 13.1488 | 1.44327 | 0.721636 | − | 0.692272i | \(-0.243390\pi\) | ||||
0.721636 | + | 0.692272i | \(0.243390\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 18.3308 | 1.97666 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.22029 | −0.236684 | ||||||||
\(89\) | −7.27597 | −0.771251 | −0.385626 | − | 0.922655i | \(-0.626014\pi\) | ||||
−0.385626 | + | 0.922655i | \(0.626014\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.5659 | 1.73658 | ||||||||
\(92\) | −17.1885 | −1.79203 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.62705 | 0.167818 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.1939 | −1.03504 | −0.517518 | − | 0.855673i | \(-0.673144\pi\) | ||||
−0.517518 | + | 0.855673i | \(0.673144\pi\) | |||||||
\(98\) | 6.45821 | 0.652378 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.08759 | −0.108219 | −0.0541096 | − | 0.998535i | \(-0.517232\pi\) | ||||
−0.0541096 | + | 0.998535i | \(0.517232\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.93756 | 0.486512 | 0.243256 | − | 0.969962i | \(-0.421784\pi\) | ||||
0.243256 | + | 0.969962i | \(0.421784\pi\) | |||||||
\(104\) | 7.56494 | 0.741803 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21.0653 | 2.04604 | ||||||||
\(107\) | 15.3059 | 1.47967 | 0.739837 | − | 0.672786i | \(-0.234902\pi\) | ||||
0.739837 | + | 0.672786i | \(0.234902\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.65900 | 0.637816 | 0.318908 | − | 0.947786i | \(-0.396684\pi\) | ||||
0.318908 | + | 0.947786i | \(0.396684\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.00922 | −0.662309 | ||||||||
\(113\) | −8.97143 | −0.843961 | −0.421981 | − | 0.906605i | \(-0.638665\pi\) | ||||
−0.421981 | + | 0.906605i | \(0.638665\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.30616 | 0.585512 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.88573 | −0.817998 | ||||||||
\(119\) | 4.07928 | 0.373947 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.63348 | −0.784861 | ||||||||
\(122\) | −23.1049 | −2.09182 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −11.9138 | −1.06989 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0185 | −0.888995 | −0.444497 | − | 0.895780i | \(-0.646618\pi\) | ||||
−0.444497 | + | 0.895780i | \(0.646618\pi\) | |||||||
\(128\) | −10.9023 | −0.963635 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.37865 | 0.557305 | 0.278653 | − | 0.960392i | \(-0.410112\pi\) | ||||
0.278653 | + | 0.960392i | \(0.410112\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.2120 | 1.49247 | ||||||||
\(134\) | 4.10214 | 0.354371 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.86284 | 0.159737 | ||||||||
\(137\) | −9.17732 | −0.784071 | −0.392036 | − | 0.919950i | \(-0.628229\pi\) | ||||
−0.392036 | + | 0.919950i | \(0.628229\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.26539 | −0.785880 | −0.392940 | − | 0.919564i | \(-0.628542\pi\) | ||||
−0.392940 | + | 0.919564i | \(0.628542\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.153135 | 0.0128508 | ||||||||
\(143\) | −8.06317 | −0.674276 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.66649 | −0.717244 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 15.8947 | 1.30654 | ||||||||
\(149\) | 10.0817 | 0.825928 | 0.412964 | − | 0.910747i | \(-0.364494\pi\) | ||||
0.412964 | + | 0.910747i | \(0.364494\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7375 | 0.873804 | 0.436902 | − | 0.899509i | \(-0.356076\pi\) | ||||
0.436902 | + | 0.899509i | \(0.356076\pi\) | |||||||
\(152\) | 7.86000 | 0.637530 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.5048 | −0.846497 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.4417 | −1.39200 | −0.696001 | − | 0.718041i | \(-0.745039\pi\) | ||||
−0.696001 | + | 0.718041i | \(0.745039\pi\) | |||||||
\(158\) | 3.49684 | 0.278194 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.3617 | −1.60473 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.2574 | 1.27338 | 0.636689 | − | 0.771120i | \(-0.280303\pi\) | ||||
0.636689 | + | 0.771120i | \(0.280303\pi\) | |||||||
\(164\) | 22.7641 | 1.77757 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 28.4089 | 2.20496 | ||||||||
\(167\) | −11.3906 | −0.881430 | −0.440715 | − | 0.897647i | \(-0.645275\pi\) | ||||
−0.440715 | + | 0.897647i | \(0.645275\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.4727 | 1.11328 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 22.6362 | 1.72599 | ||||||||
\(173\) | 9.45845 | 0.719113 | 0.359556 | − | 0.933123i | \(-0.382928\pi\) | ||||
0.359556 | + | 0.933123i | \(0.382928\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.41162 | 0.257161 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.7202 | −1.17828 | ||||||||
\(179\) | −4.07747 | −0.304764 | −0.152382 | − | 0.988322i | \(-0.548694\pi\) | ||||
−0.152382 | + | 0.988322i | \(0.548694\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.1202 | −0.826558 | −0.413279 | − | 0.910604i | \(-0.635617\pi\) | ||||
−0.413279 | + | 0.910604i | \(0.635617\pi\) | |||||||
\(182\) | 35.7916 | 2.65305 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.29833 | −0.685482 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.98552 | −0.145196 | ||||||||
\(188\) | 2.00921 | 0.146536 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.61135 | −0.261308 | −0.130654 | − | 0.991428i | \(-0.541708\pi\) | ||||
−0.130654 | + | 0.991428i | \(0.541708\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.0562 | 1.22774 | 0.613868 | − | 0.789409i | \(-0.289613\pi\) | ||||
0.613868 | + | 0.789409i | \(0.289613\pi\) | |||||||
\(194\) | −22.0246 | −1.58127 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.97508 | 0.569648 | ||||||||
\(197\) | −4.40523 | −0.313860 | −0.156930 | − | 0.987610i | \(-0.550160\pi\) | ||||
−0.156930 | + | 0.987610i | \(0.550160\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.5956 | 1.17643 | 0.588214 | − | 0.808705i | \(-0.299831\pi\) | ||||
0.588214 | + | 0.808705i | \(0.299831\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.34980 | −0.165332 | ||||||||
\(203\) | 7.47034 | 0.524315 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.6679 | 0.743267 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −11.6240 | −0.805980 | ||||||||
\(209\) | −8.37767 | −0.579495 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.5454 | 1.27671 | 0.638357 | − | 0.769740i | \(-0.279614\pi\) | ||||
0.638357 | + | 0.769740i | \(0.279614\pi\) | |||||||
\(212\) | 26.0129 | 1.78658 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 33.0693 | 2.26057 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.1132 | −0.958069 | ||||||||
\(218\) | 14.3872 | 0.974422 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.76504 | 0.455066 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.771557 | 0.0516673 | 0.0258336 | − | 0.999666i | \(-0.491776\pi\) | ||||
0.0258336 | + | 0.999666i | \(0.491776\pi\) | |||||||
\(224\) | −24.2671 | −1.62141 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.3833 | −1.28936 | ||||||||
\(227\) | 11.4314 | 0.758727 | 0.379363 | − | 0.925248i | \(-0.376143\pi\) | ||||
0.379363 | + | 0.925248i | \(0.376143\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.2248 | 0.675671 | 0.337835 | − | 0.941205i | \(-0.390305\pi\) | ||||
0.337835 | + | 0.941205i | \(0.390305\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.41139 | 0.223969 | ||||||||
\(233\) | −22.5229 | −1.47553 | −0.737763 | − | 0.675059i | \(-0.764118\pi\) | ||||
−0.737763 | + | 0.675059i | \(0.764118\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.9728 | −0.714266 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.81353 | 0.571297 | ||||||||
\(239\) | 0.589074 | 0.0381040 | 0.0190520 | − | 0.999818i | \(-0.493935\pi\) | ||||
0.0190520 | + | 0.999818i | \(0.493935\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.50937 | 0.0972270 | 0.0486135 | − | 0.998818i | \(-0.484520\pi\) | ||||
0.0486135 | + | 0.998818i | \(0.484520\pi\) | |||||||
\(242\) | −18.6531 | −1.19907 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −28.5317 | −1.82655 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 28.5442 | 1.81622 | ||||||||
\(248\) | −6.44492 | −0.409253 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.8953 | −0.750823 | −0.375412 | − | 0.926858i | \(-0.622499\pi\) | ||||
−0.375412 | + | 0.926858i | \(0.622499\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.91073 | 0.623082 | ||||||||
\(254\) | −21.6455 | −1.35816 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.752056 | 0.0470035 | ||||||||
\(257\) | −18.0492 | −1.12588 | −0.562939 | − | 0.826498i | \(-0.690329\pi\) | ||||
−0.562939 | + | 0.826498i | \(0.690329\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.8291 | 1.16998 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.7815 | 0.851421 | ||||||||
\(263\) | −19.1066 | −1.17817 | −0.589083 | − | 0.808072i | \(-0.700511\pi\) | ||||
−0.589083 | + | 0.808072i | \(0.700511\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 37.1876 | 2.28012 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.06562 | 0.309432 | ||||||||
\(269\) | 22.2250 | 1.35508 | 0.677542 | − | 0.735484i | \(-0.263045\pi\) | ||||
0.677542 | + | 0.735484i | \(0.263045\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.2107 | 1.22772 | 0.613858 | − | 0.789417i | \(-0.289617\pi\) | ||||
0.613858 | + | 0.789417i | \(0.289617\pi\) | |||||||
\(272\) | −2.86237 | −0.173556 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.8281 | −1.19786 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.0413 | 0.963826 | 0.481913 | − | 0.876219i | \(-0.339942\pi\) | ||||
0.481913 | + | 0.876219i | \(0.339942\pi\) | |||||||
\(278\) | −20.0184 | −1.20063 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.37308 | −0.499496 | −0.249748 | − | 0.968311i | \(-0.580348\pi\) | ||||
−0.249748 | + | 0.968311i | \(0.580348\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.12995 | 0.0671685 | 0.0335843 | − | 0.999436i | \(-0.489308\pi\) | ||||
0.0335843 | + | 0.999436i | \(0.489308\pi\) | |||||||
\(284\) | 0.189102 | 0.0112211 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −17.4210 | −1.03012 | ||||||||
\(287\) | 26.9665 | 1.59178 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.3341 | −0.902008 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.7020 | −0.626289 | ||||||||
\(293\) | −2.37857 | −0.138958 | −0.0694789 | − | 0.997583i | \(-0.522134\pi\) | ||||
−0.0694789 | + | 0.997583i | \(0.522134\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.59844 | 0.499774 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 21.7822 | 1.26181 | ||||||||
\(299\) | −33.7676 | −1.95283 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.8150 | 1.54559 | ||||||||
\(302\) | 23.1990 | 1.33495 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −12.0774 | −0.692686 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.89366 | −0.165150 | −0.0825748 | − | 0.996585i | \(-0.526314\pi\) | ||||
−0.0825748 | + | 0.996585i | \(0.526314\pi\) | |||||||
\(308\) | −12.9720 | −0.739151 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.14545 | 0.405181 | 0.202591 | − | 0.979264i | \(-0.435064\pi\) | ||||
0.202591 | + | 0.979264i | \(0.435064\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.0318 | −1.30184 | −0.650918 | − | 0.759148i | \(-0.725616\pi\) | ||||
−0.650918 | + | 0.759148i | \(0.725616\pi\) | |||||||
\(314\) | −37.6839 | −2.12663 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.31816 | 0.242916 | ||||||||
\(317\) | −20.7750 | −1.16684 | −0.583419 | − | 0.812171i | \(-0.698285\pi\) | ||||
−0.583419 | + | 0.812171i | \(0.698285\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.63606 | −0.203581 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −43.9927 | −2.45162 | ||||||||
\(323\) | 7.02890 | 0.391098 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 35.1251 | 1.94540 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 12.3145 | 0.679953 | ||||||||
\(329\) | 2.38012 | 0.131220 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.2504 | −1.05810 | −0.529048 | − | 0.848592i | \(-0.677451\pi\) | ||||
−0.529048 | + | 0.848592i | \(0.677451\pi\) | |||||||
\(332\) | 35.0814 | 1.92534 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −24.6100 | −1.34660 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.7064 | −1.18243 | −0.591213 | − | 0.806516i | \(-0.701351\pi\) | ||||
−0.591213 | + | 0.806516i | \(0.701351\pi\) | |||||||
\(338\) | 31.2690 | 1.70081 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.86939 | 0.371998 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.6766 | −0.684470 | ||||||||
\(344\) | 12.2453 | 0.660221 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.4356 | 1.09862 | ||||||||
\(347\) | −1.71494 | −0.0920626 | −0.0460313 | − | 0.998940i | \(-0.514657\pi\) | ||||
−0.0460313 | + | 0.998940i | \(0.514657\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.5553 | −0.832654 | −0.416327 | − | 0.909215i | \(-0.636683\pi\) | ||||
−0.416327 | + | 0.909215i | \(0.636683\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.8116 | 0.629560 | ||||||||
\(353\) | 15.5536 | 0.827833 | 0.413916 | − | 0.910315i | \(-0.364161\pi\) | ||||
0.413916 | + | 0.910315i | \(0.364161\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −19.4124 | −1.02886 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.80961 | −0.465602 | ||||||||
\(359\) | 24.5371 | 1.29502 | 0.647508 | − | 0.762059i | \(-0.275811\pi\) | ||||
0.647508 | + | 0.762059i | \(0.275811\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.6575 | 0.560924 | ||||||||
\(362\) | −24.0259 | −1.26277 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 44.1981 | 2.31661 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.1068 | −1.46716 | −0.733581 | − | 0.679602i | \(-0.762153\pi\) | ||||
−0.733581 | + | 0.679602i | \(0.762153\pi\) | |||||||
\(368\) | 14.2875 | 0.744786 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 30.8152 | 1.59984 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.70825 | 0.502674 | 0.251337 | − | 0.967900i | \(-0.419130\pi\) | ||||
0.251337 | + | 0.967900i | \(0.419130\pi\) | |||||||
\(374\) | −4.28984 | −0.221823 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.08690 | 0.0560527 | ||||||||
\(377\) | 12.3887 | 0.638052 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.2665 | −1.14375 | −0.571875 | − | 0.820340i | \(-0.693784\pi\) | ||||
−0.571875 | + | 0.820340i | \(0.693784\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.80253 | −0.399212 | ||||||||
\(383\) | −13.6299 | −0.696458 | −0.348229 | − | 0.937410i | \(-0.613217\pi\) | ||||
−0.348229 | + | 0.937410i | \(0.613217\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 36.8510 | 1.87567 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −27.1976 | −1.38075 | ||||||||
\(389\) | −19.2304 | −0.975021 | −0.487510 | − | 0.873117i | \(-0.662095\pi\) | ||||
−0.487510 | + | 0.873117i | \(0.662095\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.31515 | −0.420515 | ||||||||
\(392\) | 4.31421 | 0.217900 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.51777 | −0.479498 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.2281 | −1.11560 | −0.557799 | − | 0.829976i | \(-0.688354\pi\) | ||||
−0.557799 | + | 0.829976i | \(0.688354\pi\) | |||||||
\(398\) | 35.8557 | 1.79729 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.71728 | −0.235570 | −0.117785 | − | 0.993039i | \(-0.537579\pi\) | ||||
−0.117785 | + | 0.993039i | \(0.537579\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.4052 | −1.16590 | ||||||||
\(404\) | −2.90171 | −0.144365 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.1401 | 0.801020 | ||||||||
\(407\) | −9.16474 | −0.454279 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.4807 | −0.617130 | −0.308565 | − | 0.951203i | \(-0.599849\pi\) | ||||
−0.308565 | + | 0.951203i | \(0.599849\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.1735 | 0.649012 | ||||||||
\(413\) | −12.9984 | −0.639611 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −40.2442 | −1.97314 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −18.1005 | −0.885322 | ||||||||
\(419\) | −34.9484 | −1.70734 | −0.853669 | − | 0.520815i | \(-0.825628\pi\) | ||||
−0.853669 | + | 0.520815i | \(0.825628\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.5601 | −1.92804 | −0.964020 | − | 0.265829i | \(-0.914354\pi\) | ||||
−0.964020 | + | 0.265829i | \(0.914354\pi\) | |||||||
\(422\) | 40.0683 | 1.95050 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 14.0720 | 0.683396 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −33.7989 | −1.63564 | ||||||||
\(428\) | 40.8364 | 1.97390 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.0584 | 0.677170 | 0.338585 | − | 0.940936i | \(-0.390052\pi\) | ||||
0.338585 | + | 0.940936i | \(0.390052\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.549678 | 0.0264158 | 0.0132079 | − | 0.999913i | \(-0.495796\pi\) | ||||
0.0132079 | + | 0.999913i | \(0.495796\pi\) | |||||||
\(434\) | −30.4925 | −1.46369 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.7663 | 0.850853 | ||||||||
\(437\) | −35.0847 | −1.67833 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.97377 | −0.141930 | −0.0709651 | − | 0.997479i | \(-0.522608\pi\) | ||||
−0.0709651 | + | 0.997479i | \(0.522608\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.6163 | 0.695225 | ||||||||
\(443\) | −36.6893 | −1.74316 | −0.871580 | − | 0.490253i | \(-0.836905\pi\) | ||||
−0.871580 | + | 0.490253i | \(0.836905\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.66700 | 0.0789345 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −38.4120 | −1.81480 | ||||||||
\(449\) | 17.8432 | 0.842071 | 0.421036 | − | 0.907044i | \(-0.361667\pi\) | ||||
0.421036 | + | 0.907044i | \(0.361667\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.1255 | −0.618056 | ||||||||
\(452\) | −23.9359 | −1.12585 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 24.6982 | 1.15914 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.1784 | 1.13102 | 0.565509 | − | 0.824742i | \(-0.308680\pi\) | ||||
0.565509 | + | 0.824742i | \(0.308680\pi\) | |||||||
\(458\) | 22.0912 | 1.03225 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.3874 | 1.74130 | 0.870651 | − | 0.491901i | \(-0.163698\pi\) | ||||
0.870651 | + | 0.491901i | \(0.163698\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.4314 | −0.949530 | −0.474765 | − | 0.880113i | \(-0.657467\pi\) | ||||
−0.474765 | + | 0.880113i | \(0.657467\pi\) | |||||||
\(464\) | −5.24181 | −0.243345 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −48.6622 | −2.25423 | ||||||||
\(467\) | 31.2124 | 1.44434 | 0.722169 | − | 0.691716i | \(-0.243145\pi\) | ||||
0.722169 | + | 0.691716i | \(0.243145\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.00078 | 0.277090 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.93584 | −0.273219 | ||||||||
\(473\) | −13.0518 | −0.600121 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10.8836 | 0.498849 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.27273 | 0.0582133 | ||||||||
\(479\) | −11.0970 | −0.507033 | −0.253516 | − | 0.967331i | \(-0.581587\pi\) | ||||
−0.253516 | + | 0.967331i | \(0.581587\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.2259 | 1.42378 | ||||||||
\(482\) | 3.26108 | 0.148538 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −23.0343 | −1.04701 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.13702 | −0.323409 | −0.161705 | − | 0.986839i | \(-0.551699\pi\) | ||||
−0.161705 | + | 0.986839i | \(0.551699\pi\) | |||||||
\(488\) | −15.4345 | −0.698688 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.23348 | −0.326442 | −0.163221 | − | 0.986590i | \(-0.552188\pi\) | ||||
−0.163221 | + | 0.986590i | \(0.552188\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.05067 | 0.137395 | ||||||||
\(494\) | 61.6715 | 2.77473 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.90303 | 0.444659 | ||||||||
\(497\) | 0.224012 | 0.0100483 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.0169 | 0.717014 | 0.358507 | − | 0.933527i | \(-0.383286\pi\) | ||||
0.358507 | + | 0.933527i | \(0.383286\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −25.7005 | −1.14707 | ||||||||
\(503\) | −33.7963 | −1.50690 | −0.753452 | − | 0.657503i | \(-0.771613\pi\) | ||||
−0.753452 | + | 0.657503i | \(0.771613\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 21.4127 | 0.951912 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −26.7294 | −1.18593 | ||||||||
\(509\) | 36.4270 | 1.61460 | 0.807300 | − | 0.590142i | \(-0.200928\pi\) | ||||
0.807300 | + | 0.590142i | \(0.200928\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.6777 | −0.560829 | ||||||||
\(512\) | 23.4294 | 1.03544 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −38.9964 | −1.72006 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.15849 | −0.0509502 | ||||||||
\(518\) | 40.6813 | 1.78743 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.4993 | −1.11714 | −0.558572 | − | 0.829456i | \(-0.688651\pi\) | ||||
−0.558572 | + | 0.829456i | \(0.688651\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.03174 | 0.307477 | 0.153738 | − | 0.988112i | \(-0.450869\pi\) | ||||
0.153738 | + | 0.988112i | \(0.450869\pi\) | |||||||
\(524\) | 17.0184 | 0.743450 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −41.2811 | −1.79994 | ||||||||
\(527\) | −5.76345 | −0.251060 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.5050 | 0.804565 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 45.9220 | 1.99097 | ||||||||
\(533\) | 44.7210 | 1.93708 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.74030 | 0.118363 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 48.0185 | 2.07022 | ||||||||
\(539\) | −4.59834 | −0.198065 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.1476 | −1.16717 | −0.583584 | − | 0.812053i | \(-0.698350\pi\) | ||||
−0.583584 | + | 0.812053i | \(0.698350\pi\) | |||||||
\(542\) | 43.6665 | 1.87564 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.90999 | −0.424887 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −44.0769 | −1.88459 | −0.942296 | − | 0.334782i | \(-0.891337\pi\) | ||||
−0.942296 | + | 0.334782i | \(0.891337\pi\) | |||||||
\(548\) | −24.4853 | −1.04596 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.8719 | 0.548363 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.11533 | 0.217526 | ||||||||
\(554\) | 34.6581 | 1.47248 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −24.7202 | −1.04837 | ||||||||
\(557\) | −9.85667 | −0.417641 | −0.208820 | − | 0.977954i | \(-0.566962\pi\) | ||||
−0.208820 | + | 0.977954i | \(0.566962\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 44.4697 | 1.88087 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.0905 | −0.763103 | ||||||||
\(563\) | −12.3917 | −0.522249 | −0.261125 | − | 0.965305i | \(-0.584093\pi\) | ||||
−0.261125 | + | 0.965305i | \(0.584093\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.44132 | 0.102616 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.102297 | 0.00429228 | ||||||||
\(569\) | 11.7158 | 0.491150 | 0.245575 | − | 0.969378i | \(-0.421023\pi\) | ||||
0.245575 | + | 0.969378i | \(0.421023\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.9797 | 1.21276 | 0.606382 | − | 0.795173i | \(-0.292620\pi\) | ||||
0.606382 | + | 0.795173i | \(0.292620\pi\) | |||||||
\(572\) | −21.5127 | −0.899491 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 58.2628 | 2.43184 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.8024 | 1.36558 | 0.682790 | − | 0.730614i | \(-0.260766\pi\) | ||||
0.682790 | + | 0.730614i | \(0.260766\pi\) | |||||||
\(578\) | −33.1303 | −1.37804 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 41.5577 | 1.72410 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.9988 | −0.621186 | ||||||||
\(584\) | −5.78938 | −0.239566 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.13905 | −0.212292 | ||||||||
\(587\) | 18.6395 | 0.769334 | 0.384667 | − | 0.923055i | \(-0.374316\pi\) | ||||
0.384667 | + | 0.923055i | \(0.374316\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.3181 | −1.00201 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −13.2120 | −0.543012 | ||||||||
\(593\) | 1.55882 | 0.0640129 | 0.0320064 | − | 0.999488i | \(-0.489810\pi\) | ||||
0.0320064 | + | 0.999488i | \(0.489810\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 26.8983 | 1.10180 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −72.9570 | −2.98343 | ||||||||
\(599\) | 31.5470 | 1.28898 | 0.644489 | − | 0.764614i | \(-0.277070\pi\) | ||||
0.644489 | + | 0.764614i | \(0.277070\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.3999 | −1.32162 | −0.660809 | − | 0.750554i | \(-0.729787\pi\) | ||||
−0.660809 | + | 0.750554i | \(0.729787\pi\) | |||||||
\(602\) | 57.9354 | 2.36127 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 28.6478 | 1.16566 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.8410 | −1.00827 | −0.504133 | − | 0.863626i | \(-0.668188\pi\) | ||||
−0.504133 | + | 0.863626i | \(0.668188\pi\) | |||||||
\(608\) | −41.8139 | −1.69578 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.94717 | 0.159685 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.94558 | 0.159360 | 0.0796802 | − | 0.996820i | \(-0.474610\pi\) | ||||
0.0796802 | + | 0.996820i | \(0.474610\pi\) | |||||||
\(614\) | −6.25192 | −0.252307 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.01737 | −0.282738 | ||||||||
\(617\) | −17.4821 | −0.703801 | −0.351900 | − | 0.936037i | \(-0.614464\pi\) | ||||
−0.351900 | + | 0.936037i | \(0.614464\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.3869 | −0.578260 | −0.289130 | − | 0.957290i | \(-0.593366\pi\) | ||||
−0.289130 | + | 0.957290i | \(0.593366\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.4382 | 0.619014 | ||||||||
\(623\) | −22.9961 | −0.921321 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −49.7617 | −1.98888 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −46.5349 | −1.85694 | ||||||||
\(629\) | 7.68926 | 0.306591 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.6758 | −0.703664 | −0.351832 | − | 0.936063i | \(-0.614441\pi\) | ||||
−0.351832 | + | 0.936063i | \(0.614441\pi\) | |||||||
\(632\) | 2.33596 | 0.0929194 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −44.8855 | −1.78263 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.6674 | 0.620764 | ||||||||
\(638\) | −7.85594 | −0.311019 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.74127 | 0.108274 | 0.0541369 | − | 0.998534i | \(-0.482759\pi\) | ||||
0.0541369 | + | 0.998534i | \(0.482759\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.9276 | −0.825303 | −0.412651 | − | 0.910889i | \(-0.635397\pi\) | ||||
−0.412651 | + | 0.910889i | \(0.635397\pi\) | |||||||
\(644\) | −54.3254 | −2.14072 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.1864 | 0.597499 | ||||||||
\(647\) | −1.84667 | −0.0726002 | −0.0363001 | − | 0.999341i | \(-0.511557\pi\) | ||||
−0.0363001 | + | 0.999341i | \(0.511557\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.32678 | 0.248348 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 43.3751 | 1.69870 | ||||||||
\(653\) | −18.4133 | −0.720567 | −0.360284 | − | 0.932843i | \(-0.617320\pi\) | ||||
−0.360284 | + | 0.932843i | \(0.617320\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −18.9220 | −0.738778 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.14240 | 0.200472 | ||||||||
\(659\) | 13.3800 | 0.521210 | 0.260605 | − | 0.965446i | \(-0.416078\pi\) | ||||
0.260605 | + | 0.965446i | \(0.416078\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.1834 | 1.52406 | 0.762030 | − | 0.647542i | \(-0.224203\pi\) | ||||
0.762030 | + | 0.647542i | \(0.224203\pi\) | |||||||
\(662\) | −41.5915 | −1.61650 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18.9776 | 0.736476 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.2274 | −0.589608 | ||||||||
\(668\) | −30.3903 | −1.17584 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.4510 | 0.635086 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.3911 | −0.747473 | −0.373736 | − | 0.927535i | \(-0.621923\pi\) | ||||
−0.373736 | + | 0.927535i | \(0.621923\pi\) | |||||||
\(674\) | −46.8981 | −1.80645 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 38.6133 | 1.48513 | ||||||||
\(677\) | −45.6836 | −1.75576 | −0.877882 | − | 0.478876i | \(-0.841044\pi\) | ||||
−0.877882 | + | 0.478876i | \(0.841044\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32.2185 | −1.23643 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 14.8417 | 0.568319 | ||||||||
\(683\) | 11.5893 | 0.443451 | 0.221725 | − | 0.975109i | \(-0.428831\pi\) | ||||
0.221725 | + | 0.975109i | \(0.428831\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −27.3885 | −1.04570 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18.8157 | −0.717340 | ||||||||
\(689\) | 51.1035 | 1.94689 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.6424 | −0.823317 | −0.411658 | − | 0.911338i | \(-0.635050\pi\) | ||||
−0.411658 | + | 0.911338i | \(0.635050\pi\) | |||||||
\(692\) | 25.2353 | 0.959303 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.70522 | −0.140648 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.0124 | 0.417123 | ||||||||
\(698\) | −33.6081 | −1.27208 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.61904 | 0.325537 | 0.162768 | − | 0.986664i | \(-0.447958\pi\) | ||||
0.162768 | + | 0.986664i | \(0.447958\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.4438 | 1.22364 | ||||||||
\(704\) | 18.6964 | 0.704648 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 33.6044 | 1.26472 | ||||||||
\(707\) | −3.43739 | −0.129276 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.0001 | 0.600895 | 0.300447 | − | 0.953798i | \(-0.402864\pi\) | ||||
0.300447 | + | 0.953798i | \(0.402864\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.5014 | −0.393555 | ||||||||
\(713\) | 28.7682 | 1.07738 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10.8788 | −0.406558 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 53.0138 | 1.97846 | ||||||||
\(719\) | 48.5838 | 1.81187 | 0.905935 | − | 0.423416i | \(-0.139169\pi\) | ||||
0.905935 | + | 0.423416i | \(0.139169\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.6055 | 0.581177 | ||||||||
\(722\) | 23.0263 | 0.856949 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −29.6689 | −1.10264 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.4328 | −0.943251 | −0.471625 | − | 0.881799i | \(-0.656333\pi\) | ||||
−0.471625 | + | 0.881799i | \(0.656333\pi\) | |||||||
\(728\) | 23.9094 | 0.886143 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.9505 | 0.405019 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.6190 | 0.687708 | 0.343854 | − | 0.939023i | \(-0.388267\pi\) | ||||
0.343854 | + | 0.939023i | \(0.388267\pi\) | |||||||
\(734\) | −60.7264 | −2.24145 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 49.4656 | 1.82333 | ||||||||
\(737\) | −2.92078 | −0.107588 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.8872 | 1.72478 | 0.862388 | − | 0.506249i | \(-0.168968\pi\) | ||||
0.862388 | + | 0.506249i | \(0.168968\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 66.5780 | 2.44416 | ||||||||
\(743\) | −42.7061 | −1.56674 | −0.783368 | − | 0.621558i | \(-0.786500\pi\) | ||||
−0.783368 | + | 0.621558i | \(0.786500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 20.9753 | 0.767959 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.29742 | −0.193693 | ||||||||
\(749\) | 48.3751 | 1.76759 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.64893 | −0.0966608 | −0.0483304 | − | 0.998831i | \(-0.515390\pi\) | ||||
−0.0483304 | + | 0.998831i | \(0.515390\pi\) | |||||||
\(752\) | −1.67009 | −0.0609021 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 26.7666 | 0.974781 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −52.9153 | −1.92324 | −0.961620 | − | 0.274383i | \(-0.911526\pi\) | ||||
−0.961620 | + | 0.274383i | \(0.911526\pi\) | |||||||
\(758\) | −48.1080 | −1.74736 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −50.7787 | −1.84073 | −0.920363 | − | 0.391064i | \(-0.872107\pi\) | ||||
−0.920363 | + | 0.391064i | \(0.872107\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.0462 | 0.761922 | ||||||||
\(764\) | −9.63514 | −0.348587 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −29.4483 | −1.06401 | ||||||||
\(767\) | −21.5565 | −0.778358 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.5805 | 0.886396 | 0.443198 | − | 0.896424i | \(-0.353844\pi\) | ||||
0.443198 | + | 0.896424i | \(0.353844\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 45.5064 | 1.63781 | ||||||||
\(773\) | −20.0112 | −0.719754 | −0.359877 | − | 0.933000i | \(-0.617181\pi\) | ||||
−0.359877 | + | 0.933000i | \(0.617181\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.7128 | −0.528159 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −41.5485 | −1.48958 | ||||||||
\(779\) | 46.4653 | 1.66479 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.109034 | −0.00390155 | ||||||||
\(782\) | −17.9654 | −0.642441 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.62905 | −0.236752 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.99272 | −0.320556 | −0.160278 | − | 0.987072i | \(-0.551239\pi\) | ||||
−0.160278 | + | 0.987072i | \(0.551239\pi\) | |||||||
\(788\) | −11.7532 | −0.418692 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −28.3547 | −1.00818 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −56.0517 | −1.99045 | ||||||||
\(794\) | −48.0252 | −1.70435 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 44.2773 | 1.56937 | ||||||||
\(797\) | −37.7564 | −1.33740 | −0.668700 | − | 0.743533i | \(-0.733149\pi\) | ||||
−0.668700 | + | 0.743533i | \(0.733149\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.971976 | 0.0343860 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.1920 | −0.359891 | ||||||||
\(803\) | 6.17067 | 0.217758 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −50.5684 | −1.78120 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.56971 | −0.0552223 | ||||||||
\(809\) | 48.9001 | 1.71924 | 0.859618 | − | 0.510937i | \(-0.170702\pi\) | ||||
0.859618 | + | 0.510937i | \(0.170702\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.0551 | −0.633999 | −0.317000 | − | 0.948426i | \(-0.602675\pi\) | ||||
−0.317000 | + | 0.948426i | \(0.602675\pi\) | |||||||
\(812\) | 19.9310 | 0.699441 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −19.8010 | −0.694024 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 46.2042 | 1.61648 | ||||||||
\(818\) | −26.9653 | −0.942819 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −50.6097 | −1.76629 | −0.883146 | − | 0.469099i | \(-0.844579\pi\) | ||||
−0.883146 | + | 0.469099i | \(0.844579\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.8070 | 0.934433 | 0.467217 | − | 0.884143i | \(-0.345257\pi\) | ||||
0.467217 | + | 0.884143i | \(0.345257\pi\) | |||||||
\(824\) | 7.12635 | 0.248258 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.0839 | −0.977163 | ||||||||
\(827\) | −21.3649 | −0.742929 | −0.371465 | − | 0.928447i | \(-0.621144\pi\) | ||||
−0.371465 | + | 0.928447i | \(0.621144\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −48.1123 | −1.67101 | −0.835504 | − | 0.549484i | \(-0.814824\pi\) | ||||
−0.835504 | + | 0.549484i | \(0.814824\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −63.7021 | −2.20847 | ||||||||
\(833\) | 3.85803 | 0.133673 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −22.3518 | −0.773052 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −75.5080 | −2.60838 | ||||||||
\(839\) | 41.8540 | 1.44496 | 0.722481 | − | 0.691391i | \(-0.243002\pi\) | ||||
0.722481 | + | 0.691391i | \(0.243002\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4133 | −0.807357 | ||||||||
\(842\) | −85.4719 | −2.94556 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 49.4794 | 1.70315 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.2866 | −0.937579 | ||||||||
\(848\) | −21.6225 | −0.742520 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38.3809 | −1.31568 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 58.2023 | 1.99281 | 0.996404 | − | 0.0847260i | \(-0.0270015\pi\) | ||||
0.996404 | + | 0.0847260i | \(0.0270015\pi\) | |||||||
\(854\) | −73.0245 | −2.49885 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22.0909 | 0.755051 | ||||||||
\(857\) | −3.22045 | −0.110008 | −0.0550042 | − | 0.998486i | \(-0.517517\pi\) | ||||
−0.0550042 | + | 0.998486i | \(0.517517\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.4431 | 1.68698 | 0.843488 | − | 0.537147i | \(-0.180498\pi\) | ||||
0.843488 | + | 0.537147i | \(0.180498\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.3740 | 1.03454 | ||||||||
\(863\) | 21.4924 | 0.731611 | 0.365806 | − | 0.930691i | \(-0.380793\pi\) | ||||
0.365806 | + | 0.930691i | \(0.380793\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.18761 | 0.0403567 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −37.6544 | −1.27807 | ||||||||
\(869\) | −2.48981 | −0.0844609 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.95163 | 0.337198 | ||||||||
\(872\) | 9.61090 | 0.325466 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −75.8026 | −2.56406 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.3793 | −0.519321 | −0.259661 | − | 0.965700i | \(-0.583611\pi\) | ||||
−0.259661 | + | 0.965700i | \(0.583611\pi\) | |||||||
\(878\) | −6.42501 | −0.216833 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.9275 | −0.637682 | −0.318841 | − | 0.947808i | \(-0.603294\pi\) | ||||
−0.318841 | + | 0.947808i | \(0.603294\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.31708 | −0.212587 | −0.106293 | − | 0.994335i | \(-0.533898\pi\) | ||||
−0.106293 | + | 0.994335i | \(0.533898\pi\) | |||||||
\(884\) | 18.0492 | 0.607062 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −79.2694 | −2.66311 | ||||||||
\(887\) | 0.0721586 | 0.00242285 | 0.00121142 | − | 0.999999i | \(-0.499614\pi\) | ||||
0.00121142 | + | 0.999999i | \(0.499614\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.6639 | −1.06197 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.05853 | 0.0689246 | ||||||||
\(893\) | 4.10113 | 0.137239 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −34.4573 | −1.15114 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 38.5512 | 1.28647 | ||||||||
\(899\) | −10.5545 | −0.352013 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.5840 | 0.419235 | ||||||||
\(902\) | −28.3584 | −0.944233 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.9484 | −0.430658 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.4951 | 0.846550 | 0.423275 | − | 0.906001i | \(-0.360880\pi\) | ||||
0.423275 | + | 0.906001i | \(0.360880\pi\) | |||||||
\(908\) | 30.4991 | 1.01215 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.55803 | −0.117883 | −0.0589414 | − | 0.998261i | \(-0.518773\pi\) | ||||
−0.0589414 | + | 0.998261i | \(0.518773\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.2275 | −0.669434 | ||||||||
\(914\) | 52.2389 | 1.72791 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 27.2798 | 0.901351 | ||||||||
\(917\) | 20.1601 | 0.665745 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.96968 | 0.262896 | 0.131448 | − | 0.991323i | \(-0.458037\pi\) | ||||
0.131448 | + | 0.991323i | \(0.458037\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 80.7776 | 2.66027 | ||||||||
\(923\) | 0.371499 | 0.0122280 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −44.1434 | −1.45064 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −18.1480 | −0.595738 | ||||||||
\(929\) | −48.5424 | −1.59263 | −0.796313 | − | 0.604885i | \(-0.793219\pi\) | ||||
−0.796313 | + | 0.604885i | \(0.793219\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.2785 | 0.533505 | ||||||||
\(932\) | −60.0916 | −1.96837 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 67.4363 | 2.20658 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.7296 | −1.03656 | −0.518280 | − | 0.855211i | \(-0.673427\pi\) | ||||
−0.518280 | + | 0.855211i | \(0.673427\pi\) | |||||||
\(938\) | 12.9650 | 0.423324 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.0068 | −1.33678 | −0.668392 | − | 0.743809i | \(-0.733017\pi\) | ||||
−0.668392 | + | 0.743809i | \(0.733017\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −54.9681 | −1.79001 | ||||||||
\(944\) | 9.12079 | 0.296856 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −28.1991 | −0.916833 | ||||||||
\(947\) | −9.81789 | −0.319038 | −0.159519 | − | 0.987195i | \(-0.550994\pi\) | ||||
−0.159519 | + | 0.987195i | \(0.550994\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.0246 | −0.682487 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.88761 | 0.190818 | ||||||||
\(953\) | 53.1118 | 1.72046 | 0.860230 | − | 0.509906i | \(-0.170320\pi\) | ||||
0.860230 | + | 0.509906i | \(0.170320\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.57166 | 0.0508311 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −23.9756 | −0.774618 | ||||||||
\(959\) | −29.0055 | −0.936635 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.0600 | −0.356774 | ||||||||
\(962\) | 67.4654 | 2.17517 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.02702 | 0.129702 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.44732 | 0.0787004 | 0.0393502 | − | 0.999225i | \(-0.487471\pi\) | ||||
0.0393502 | + | 0.999225i | \(0.487471\pi\) | |||||||
\(968\) | −12.4606 | −0.400500 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.9683 | 1.53938 | 0.769688 | − | 0.638421i | \(-0.220412\pi\) | ||||
0.769688 | + | 0.638421i | \(0.220412\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29.2838 | −0.938796 | ||||||||
\(974\) | −15.4200 | −0.494088 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 23.7161 | 0.759134 | ||||||||
\(977\) | 23.6950 | 0.758070 | 0.379035 | − | 0.925382i | \(-0.376256\pi\) | ||||
0.379035 | + | 0.925382i | \(0.376256\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.1930 | 0.357730 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.6284 | −0.498721 | ||||||||
\(983\) | 12.9505 | 0.413057 | 0.206529 | − | 0.978441i | \(-0.433783\pi\) | ||||
0.206529 | + | 0.978441i | \(0.433783\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.59116 | 0.209905 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 76.1565 | 2.42286 | ||||||||
\(989\) | −54.6593 | −1.73807 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.4967 | 1.41348 | 0.706742 | − | 0.707471i | \(-0.250164\pi\) | ||||
0.706742 | + | 0.707471i | \(0.250164\pi\) | |||||||
\(992\) | 34.2859 | 1.08858 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.483992 | 0.0153513 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 55.5513 | 1.75933 | 0.879663 | − | 0.475597i | \(-0.157768\pi\) | ||||
0.879663 | + | 0.475597i | \(0.157768\pi\) | |||||||
\(998\) | 34.6054 | 1.09542 | ||||||||
\(999\) | 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 | 5625.2.a.q.1.5 | 6 | ||
3.2 | odd | 2 | 1875.2.a.k.1.2 | 6 | |||
5.4 | even | 2 | 5625.2.a.p.1.2 | 6 | |||
15.2 | even | 4 | 1875.2.b.f.1249.3 | 12 | |||
15.8 | even | 4 | 1875.2.b.f.1249.10 | 12 | |||
15.14 | odd | 2 | 1875.2.a.j.1.5 | 6 | |||
25.4 | even | 10 | 225.2.h.d.91.3 | 12 | |||
25.19 | even | 10 | 225.2.h.d.136.3 | 12 | |||
75.8 | even | 20 | 375.2.i.d.199.1 | 24 | |||
75.17 | even | 20 | 375.2.i.d.199.6 | 24 | |||
75.29 | odd | 10 | 75.2.g.c.16.1 | ✓ | 12 | ||
75.44 | odd | 10 | 75.2.g.c.61.1 | yes | 12 | ||
75.47 | even | 20 | 375.2.i.d.49.1 | 24 | |||
75.53 | even | 20 | 375.2.i.d.49.6 | 24 | |||
75.56 | odd | 10 | 375.2.g.c.301.3 | 12 | |||
75.71 | odd | 10 | 375.2.g.c.76.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.16.1 | ✓ | 12 | 75.29 | odd | 10 | ||
75.2.g.c.61.1 | yes | 12 | 75.44 | odd | 10 | ||
225.2.h.d.91.3 | 12 | 25.4 | even | 10 | |||
225.2.h.d.136.3 | 12 | 25.19 | even | 10 | |||
375.2.g.c.76.3 | 12 | 75.71 | odd | 10 | |||
375.2.g.c.301.3 | 12 | 75.56 | odd | 10 | |||
375.2.i.d.49.1 | 24 | 75.47 | even | 20 | |||
375.2.i.d.49.6 | 24 | 75.53 | even | 20 | |||
375.2.i.d.199.1 | 24 | 75.8 | even | 20 | |||
375.2.i.d.199.6 | 24 | 75.17 | even | 20 | |||
1875.2.a.j.1.5 | 6 | 15.14 | odd | 2 | |||
1875.2.a.k.1.2 | 6 | 3.2 | odd | 2 | |||
1875.2.b.f.1249.3 | 12 | 15.2 | even | 4 | |||
1875.2.b.f.1249.10 | 12 | 15.8 | even | 4 | |||
5625.2.a.p.1.2 | 6 | 5.4 | even | 2 | |||
5625.2.a.q.1.5 | 6 | 1.1 | even | 1 | trivial |