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 | 1.2 | ||
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 | \(-0.776705\pi\) | ||||
−0.763873 | + | 0.645366i | \(0.776705\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.66802 | 1.33401 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.16056 | −1.19458 | −0.597290 | − | 0.802026i | \(-0.703756\pi\) | ||||
−0.597290 | + | 0.802026i | \(0.703756\pi\) | |||||||
\(8\) | −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 | \(-0.759019\pi\) | ||||
−0.726857 | + | 0.686789i | \(0.759019\pi\) | |||||||
\(14\) | 6.82858 | 1.82501 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.21771 | −0.554428 | ||||||||
\(17\) | −1.29068 | −0.313037 | −0.156518 | − | 0.987675i | \(-0.550027\pi\) | ||||
−0.156518 | + | 0.987675i | \(0.550027\pi\) | |||||||
\(18\) | 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 | \(-0.265577\pi\) | ||||
0.671671 | + | 0.740850i | \(0.265577\pi\) | |||||||
\(24\) | 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 | \(-0.662895\pi\) | ||||
−0.489704 | + | 0.871889i | \(0.662895\pi\) | |||||||
\(38\) | −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 | \(-0.723943\pi\) | ||||
−0.646919 | + | 0.762559i | \(0.723943\pi\) | |||||||
\(44\) | −4.10435 | −0.618754 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.9193 | −2.05228 | ||||||||
\(47\) | −0.753070 | −0.109847 | −0.0549233 | − | 0.998491i | \(-0.517491\pi\) | ||||
−0.0549233 | + | 0.998491i | \(0.517491\pi\) | |||||||
\(48\) | 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 | \(-0.733546\pi\) | ||||
−0.669626 | + | 0.742698i | \(0.733546\pi\) | |||||||
\(54\) | 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 | \(-0.537000\pi\) | ||||
−0.115978 | + | 0.993252i | \(0.537000\pi\) | |||||||
\(68\) | −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 | \(-0.424576\pi\) | ||||
0.234739 | + | 0.972058i | \(0.424576\pi\) | |||||||
\(74\) | 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 | \(-0.756610\pi\) | ||||
−0.721636 | + | 0.692272i | \(0.756610\pi\) | |||||||
\(84\) | 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 | \(-0.326856\pi\) | ||||
0.517518 | + | 0.855673i | \(0.326856\pi\) | |||||||
\(98\) | −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 | \(-0.578216\pi\) | ||||
−0.243256 | + | 0.969962i | \(0.578216\pi\) | |||||||
\(104\) | 7.56494 | 0.741803 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21.0653 | 2.04604 | ||||||||
\(107\) | −15.3059 | −1.47967 | −0.739837 | − | 0.672786i | \(-0.765098\pi\) | ||||
−0.739837 | + | 0.672786i | \(0.765098\pi\) | |||||||
\(108\) | 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 | \(-0.361335\pi\) | ||||
0.421981 | + | 0.906605i | \(0.361335\pi\) | |||||||
\(114\) | 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 | \(-0.353382\pi\) | ||||
0.444497 | + | 0.895780i | \(0.353382\pi\) | |||||||
\(128\) | 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 | \(-0.371771\pi\) | ||||
0.392036 | + | 0.919950i | \(0.371771\pi\) | |||||||
\(138\) | 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 | \(-0.254961\pi\) | ||||
0.696001 | + | 0.718041i | \(0.254961\pi\) | |||||||
\(158\) | −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 | \(-0.719697\pi\) | ||||
−0.636689 | + | 0.771120i | \(0.719697\pi\) | |||||||
\(164\) | 22.7641 | 1.77757 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 28.4089 | 2.20496 | ||||||||
\(167\) | 11.3906 | 0.881430 | 0.440715 | − | 0.897647i | \(-0.354725\pi\) | ||||
0.440715 | + | 0.897647i | \(0.354725\pi\) | |||||||
\(168\) | 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 | \(-0.617072\pi\) | ||||
−0.359556 | + | 0.933123i | \(0.617072\pi\) | |||||||
\(174\) | 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 | \(-0.710387\pi\) | ||||
−0.613868 | + | 0.789409i | \(0.710387\pi\) | |||||||
\(194\) | −22.0246 | −1.58127 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.97508 | 0.569648 | ||||||||
\(197\) | 4.40523 | 0.313860 | 0.156930 | − | 0.987610i | \(-0.449840\pi\) | ||||
0.156930 | + | 0.987610i | \(0.449840\pi\) | |||||||
\(198\) | 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 | \(-0.508224\pi\) | ||||
−0.0258336 | + | 0.999666i | \(0.508224\pi\) | |||||||
\(224\) | −24.2671 | −1.62141 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.3833 | −1.28936 | ||||||||
\(227\) | −11.4314 | −0.758727 | −0.379363 | − | 0.925248i | \(-0.623857\pi\) | ||||
−0.379363 | + | 0.925248i | \(0.623857\pi\) | |||||||
\(228\) | 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 | \(-0.235882\pi\) | ||||
0.737763 | + | 0.675059i | \(0.235882\pi\) | |||||||
\(234\) | 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 | \(-0.309671\pi\) | ||||
0.562939 | + | 0.826498i | \(0.309671\pi\) | |||||||
\(258\) | 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 | \(-0.299489\pi\) | ||||
0.589083 | + | 0.808072i | \(0.299489\pi\) | |||||||
\(264\) | 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 | \(-0.660058\pi\) | ||||
−0.481913 | + | 0.876219i | \(0.660058\pi\) | |||||||
\(278\) | 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 | \(-0.510692\pi\) | ||||
−0.0335843 | + | 0.999436i | \(0.510692\pi\) | |||||||
\(284\) | 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 | \(-0.477866\pi\) | ||||
0.0694789 | + | 0.997583i | \(0.477866\pi\) | |||||||
\(294\) | 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 | \(-0.473686\pi\) | ||||
0.0825748 | + | 0.996585i | \(0.473686\pi\) | |||||||
\(308\) | 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 | \(-0.274384\pi\) | ||||
0.650918 | + | 0.759148i | \(0.274384\pi\) | |||||||
\(314\) | −37.6839 | −2.12663 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.31816 | 0.242916 | ||||||||
\(317\) | 20.7750 | 1.16684 | 0.583419 | − | 0.812171i | \(-0.301715\pi\) | ||||
0.583419 | + | 0.812171i | \(0.301715\pi\) | |||||||
\(318\) | 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 | \(-0.298649\pi\) | ||||
0.591213 | + | 0.806516i | \(0.298649\pi\) | |||||||
\(338\) | −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 | \(-0.485343\pi\) | ||||
0.0460313 | + | 0.998940i | \(0.485343\pi\) | |||||||
\(348\) | 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 | \(-0.635839\pi\) | ||||
−0.413916 | + | 0.910315i | \(0.635839\pi\) | |||||||
\(354\) | 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 | \(-0.237847\pi\) | ||||
0.733581 | + | 0.679602i | \(0.237847\pi\) | |||||||
\(368\) | −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 | \(-0.580870\pi\) | ||||
−0.251337 | + | 0.967900i | \(0.580870\pi\) | |||||||
\(374\) | −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 | \(-0.386783\pi\) | ||||
0.348229 | + | 0.937410i | \(0.386783\pi\) | |||||||
\(384\) | 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 | \(-0.311646\pi\) | ||||
0.557799 | + | 0.829976i | \(0.311646\pi\) | |||||||
\(398\) | −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 | \(-0.504204\pi\) | ||||
−0.0132079 | + | 0.999913i | \(0.504204\pi\) | |||||||
\(434\) | −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 | \(-0.163095\pi\) | ||||
0.871580 | + | 0.490253i | \(0.163095\pi\) | |||||||
\(444\) | 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 | \(-0.691320\pi\) | ||||
−0.565509 | + | 0.824742i | \(0.691320\pi\) | |||||||
\(458\) | −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 | \(-0.342533\pi\) | ||||
0.474765 | + | 0.880113i | \(0.342533\pi\) | |||||||
\(464\) | −5.24181 | −0.243345 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −48.6622 | −2.25423 | ||||||||
\(467\) | −31.2124 | −1.44434 | −0.722169 | − | 0.691716i | \(-0.756855\pi\) | ||||
−0.722169 | + | 0.691716i | \(0.756855\pi\) | |||||||
\(468\) | 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 | \(-0.448301\pi\) | ||||
0.161705 | + | 0.986839i | \(0.448301\pi\) | |||||||
\(488\) | 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 | \(-0.228387\pi\) | ||||
0.753452 | + | 0.657503i | \(0.228387\pi\) | |||||||
\(504\) | 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 | \(-0.549131\pi\) | ||||
−0.153738 | + | 0.988112i | \(0.549131\pi\) | |||||||
\(524\) | 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 | \(-0.108663\pi\) | ||||
0.942296 | + | 0.334782i | \(0.108663\pi\) | |||||||
\(548\) | 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 | \(-0.433038\pi\) | ||||
0.208820 | + | 0.977954i | \(0.433038\pi\) | |||||||
\(558\) | 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 | \(-0.415907\pi\) | ||||
0.261125 | + | 0.965305i | \(0.415907\pi\) | |||||||
\(564\) | 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 | \(-0.739234\pi\) | ||||
−0.682790 | + | 0.730614i | \(0.739234\pi\) | |||||||
\(578\) | 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 | \(-0.625684\pi\) | ||||
−0.384667 | + | 0.923055i | \(0.625684\pi\) | |||||||
\(588\) | 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 | \(-0.510190\pi\) | ||||
−0.0320064 | + | 0.999488i | \(0.510190\pi\) | |||||||
\(594\) | 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 | \(-0.331812\pi\) | ||||
0.504133 | + | 0.863626i | \(0.331812\pi\) | |||||||
\(608\) | 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 | \(-0.525390\pi\) | ||||
−0.0796802 | + | 0.996820i | \(0.525390\pi\) | |||||||
\(614\) | −6.25192 | −0.252307 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.01737 | −0.282738 | ||||||||
\(617\) | 17.4821 | 0.703801 | 0.351900 | − | 0.936037i | \(-0.385536\pi\) | ||||
0.351900 | + | 0.936037i | \(0.385536\pi\) | |||||||
\(618\) | 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 | \(-0.364603\pi\) | ||||
0.412651 | + | 0.910889i | \(0.364603\pi\) | |||||||
\(644\) | −54.3254 | −2.14072 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.1864 | 0.597499 | ||||||||
\(647\) | 1.84667 | 0.0726002 | 0.0363001 | − | 0.999341i | \(-0.488443\pi\) | ||||
0.0363001 | + | 0.999341i | \(0.488443\pi\) | |||||||
\(648\) | 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 | \(-0.382680\pi\) | ||||
0.360284 | + | 0.932843i | \(0.382680\pi\) | |||||||
\(654\) | 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 | \(-0.378077\pi\) | ||||
0.373736 | + | 0.927535i | \(0.378077\pi\) | |||||||
\(674\) | −46.8981 | −1.80645 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 38.6133 | 1.48513 | ||||||||
\(677\) | 45.6836 | 1.75576 | 0.877882 | − | 0.478876i | \(-0.158956\pi\) | ||||
0.877882 | + | 0.478876i | \(0.158956\pi\) | |||||||
\(678\) | 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 | \(-0.571169\pi\) | ||||
−0.221725 | + | 0.975109i | \(0.571169\pi\) | |||||||
\(684\) | 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 | \(-0.343667\pi\) | ||||
0.471625 | + | 0.881799i | \(0.343667\pi\) | |||||||
\(728\) | −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 | \(-0.611733\pi\) | ||||
−0.343854 | + | 0.939023i | \(0.611733\pi\) | |||||||
\(734\) | −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 | \(-0.213500\pi\) | ||||
0.783368 | + | 0.621558i | \(0.213500\pi\) | |||||||
\(744\) | 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 | \(-0.0884737\pi\) | ||||
0.961620 | + | 0.274383i | \(0.0884737\pi\) | |||||||
\(758\) | 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 | \(-0.382819\pi\) | ||||
0.359877 | + | 0.933000i | \(0.382819\pi\) | |||||||
\(774\) | 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 | \(-0.448761\pi\) | ||||
0.160278 | + | 0.987072i | \(0.448761\pi\) | |||||||
\(788\) | 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 | \(-0.266851\pi\) | ||||
0.668700 | + | 0.743533i | \(0.266851\pi\) | |||||||
\(798\) | 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 | \(-0.654743\pi\) | ||||
−0.467217 | + | 0.884143i | \(0.654743\pi\) | |||||||
\(824\) | 7.12635 | 0.248258 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −28.0839 | −0.977163 | ||||||||
\(827\) | 21.3649 | 0.742929 | 0.371465 | − | 0.928447i | \(-0.378856\pi\) | ||||
0.371465 | + | 0.928447i | \(0.378856\pi\) | |||||||
\(828\) | 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 | \(-0.972998\pi\) | ||||
−0.996404 | + | 0.0847260i | \(0.972998\pi\) | |||||||
\(854\) | −73.0245 | −2.49885 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22.0909 | 0.755051 | ||||||||
\(857\) | 3.22045 | 0.110008 | 0.0550042 | − | 0.998486i | \(-0.482483\pi\) | ||||
0.0550042 | + | 0.998486i | \(0.482483\pi\) | |||||||
\(858\) | 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 | \(-0.619207\pi\) | ||||
−0.365806 | + | 0.930691i | \(0.619207\pi\) | |||||||
\(864\) | 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 | \(-0.416389\pi\) | ||||
0.259661 | + | 0.965700i | \(0.416389\pi\) | |||||||
\(878\) | 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 | \(-0.466102\pi\) | ||||
0.106293 | + | 0.994335i | \(0.466102\pi\) | |||||||
\(884\) | 18.0492 | 0.607062 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −79.2694 | −2.66311 | ||||||||
\(887\) | −0.0721586 | −0.00242285 | −0.00121142 | − | 0.999999i | \(-0.500386\pi\) | ||||
−0.00121142 | + | 0.999999i | \(0.500386\pi\) | |||||||
\(888\) | 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 | \(-0.639120\pi\) | ||||
−0.423275 | + | 0.906001i | \(0.639120\pi\) | |||||||
\(908\) | −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 | \(-0.326573\pi\) | ||||
0.518280 | + | 0.855211i | \(0.326573\pi\) | |||||||
\(938\) | −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 | \(-0.449006\pi\) | ||||
0.159519 | + | 0.987195i | \(0.449006\pi\) | |||||||
\(948\) | 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 | \(-0.829680\pi\) | ||||
−0.860230 | + | 0.509906i | \(0.829680\pi\) | |||||||
\(954\) | 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 | \(-0.512529\pi\) | ||||
−0.0393502 | + | 0.999225i | \(0.512529\pi\) | |||||||
\(968\) | 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 | \(-0.623744\pi\) | ||||
−0.379035 | + | 0.925382i | \(0.623744\pi\) | |||||||
\(978\) | 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 | \(-0.566217\pi\) | ||||
−0.206529 | + | 0.978441i | \(0.566217\pi\) | |||||||
\(984\) | 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 | \(-0.842232\pi\) | ||||
−0.879663 | + | 0.475597i | \(0.842232\pi\) | |||||||
\(998\) | −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.p.1.2 | 6 | ||
3.2 | odd | 2 | 1875.2.a.j.1.5 | 6 | |||
5.4 | even | 2 | 5625.2.a.q.1.5 | 6 | |||
15.2 | even | 4 | 1875.2.b.f.1249.10 | 12 | |||
15.8 | even | 4 | 1875.2.b.f.1249.3 | 12 | |||
15.14 | odd | 2 | 1875.2.a.k.1.2 | 6 | |||
25.6 | even | 5 | 225.2.h.d.136.3 | 12 | |||
25.21 | even | 5 | 225.2.h.d.91.3 | 12 | |||
75.8 | even | 20 | 375.2.i.d.199.6 | 24 | |||
75.17 | even | 20 | 375.2.i.d.199.1 | 24 | |||
75.29 | odd | 10 | 375.2.g.c.76.3 | 12 | |||
75.44 | odd | 10 | 375.2.g.c.301.3 | 12 | |||
75.47 | even | 20 | 375.2.i.d.49.6 | 24 | |||
75.53 | even | 20 | 375.2.i.d.49.1 | 24 | |||
75.56 | odd | 10 | 75.2.g.c.61.1 | yes | 12 | ||
75.71 | odd | 10 | 75.2.g.c.16.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.16.1 | ✓ | 12 | 75.71 | odd | 10 | ||
75.2.g.c.61.1 | yes | 12 | 75.56 | odd | 10 | ||
225.2.h.d.91.3 | 12 | 25.21 | even | 5 | |||
225.2.h.d.136.3 | 12 | 25.6 | even | 5 | |||
375.2.g.c.76.3 | 12 | 75.29 | odd | 10 | |||
375.2.g.c.301.3 | 12 | 75.44 | odd | 10 | |||
375.2.i.d.49.1 | 24 | 75.53 | even | 20 | |||
375.2.i.d.49.6 | 24 | 75.47 | even | 20 | |||
375.2.i.d.199.1 | 24 | 75.17 | even | 20 | |||
375.2.i.d.199.6 | 24 | 75.8 | even | 20 | |||
1875.2.a.j.1.5 | 6 | 3.2 | odd | 2 | |||
1875.2.a.k.1.2 | 6 | 15.14 | odd | 2 | |||
1875.2.b.f.1249.3 | 12 | 15.8 | even | 4 | |||
1875.2.b.f.1249.10 | 12 | 15.2 | even | 4 | |||
5625.2.a.p.1.2 | 6 | 1.1 | even | 1 | trivial | ||
5625.2.a.q.1.5 | 6 | 5.4 | even | 2 |