Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6040,2,Mod(1,6040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6040 = 2^{3} \cdot 5 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6040.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: | \(48.2296428209\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 5 x^{18} - 29 x^{17} + 165 x^{16} + 325 x^{15} - 2208 x^{14} - 1891 x^{13} + 15895 x^{12} + 6652 x^{11} - 67665 x^{10} - 17345 x^{9} + 174105 x^{8} + 41499 x^{7} + \cdots - 5628 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(-1.97307\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6040.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.97307 | 1.13915 | 0.569575 | − | 0.821939i | \(-0.307108\pi\) | ||||
0.569575 | + | 0.821939i | \(0.307108\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.188446 | −0.0712258 | −0.0356129 | − | 0.999366i | \(-0.511338\pi\) | ||||
−0.0356129 | + | 0.999366i | \(0.511338\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.892989 | 0.297663 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.45854 | 0.439767 | 0.219884 | − | 0.975526i | \(-0.429432\pi\) | ||||
0.219884 | + | 0.975526i | \(0.429432\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.70600 | −1.58256 | −0.791280 | − | 0.611454i | \(-0.790585\pi\) | ||||
−0.791280 | + | 0.611454i | \(0.790585\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.97307 | 0.509443 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.29442 | −0.799015 | −0.399507 | − | 0.916730i | \(-0.630819\pi\) | ||||
−0.399507 | + | 0.916730i | \(0.630819\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.35587 | −0.540473 | −0.270237 | − | 0.962794i | \(-0.587102\pi\) | ||||
−0.270237 | + | 0.962794i | \(0.587102\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.371816 | −0.0811369 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.811678 | −0.169247 | −0.0846233 | − | 0.996413i | \(-0.526969\pi\) | ||||
−0.0846233 | + | 0.996413i | \(0.526969\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.15727 | −0.800067 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.35299 | 1.17972 | 0.589860 | − | 0.807505i | \(-0.299183\pi\) | ||||
0.589860 | + | 0.807505i | \(0.299183\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00433 | −0.180384 | −0.0901918 | − | 0.995924i | \(-0.528748\pi\) | ||||
−0.0901918 | + | 0.995924i | \(0.528748\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.87780 | 0.500961 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.188446 | −0.0318531 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.49639 | −1.06800 | −0.534000 | − | 0.845485i | \(-0.679312\pi\) | ||||
−0.534000 | + | 0.845485i | \(0.679312\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.2583 | −1.80277 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.03633 | −1.41124 | −0.705619 | − | 0.708592i | \(-0.749331\pi\) | ||||
−0.705619 | + | 0.708592i | \(0.749331\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.4240 | −1.58965 | −0.794825 | − | 0.606839i | \(-0.792437\pi\) | ||||
−0.794825 | + | 0.606839i | \(0.792437\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.892989 | 0.133119 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.03789 | 1.02658 | 0.513291 | − | 0.858215i | \(-0.328426\pi\) | ||||
0.513291 | + | 0.858215i | \(0.328426\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.96449 | −0.994927 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.50011 | −0.910198 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.21570 | 0.716431 | 0.358216 | − | 0.933639i | \(-0.383385\pi\) | ||||
0.358216 | + | 0.933639i | \(0.383385\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.45854 | 0.196670 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.64828 | −0.615680 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.83497 | 1.02003 | 0.510013 | − | 0.860166i | \(-0.329640\pi\) | ||||
0.510013 | + | 0.860166i | \(0.329640\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.8569 | −1.51812 | −0.759059 | − | 0.651021i | \(-0.774341\pi\) | ||||
−0.759059 | + | 0.651021i | \(0.774341\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.168280 | −0.0212013 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.70600 | −0.707742 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.795991 | 0.0972458 | 0.0486229 | − | 0.998817i | \(-0.484517\pi\) | ||||
0.0486229 | + | 0.998817i | \(0.484517\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.60149 | −0.192797 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.6300 | 1.49891 | 0.749453 | − | 0.662058i | \(-0.230317\pi\) | ||||
0.749453 | + | 0.662058i | \(0.230317\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.53942 | 1.11651 | 0.558253 | − | 0.829671i | \(-0.311472\pi\) | ||||
0.558253 | + | 0.829671i | \(0.311472\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.97307 | 0.227830 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.274856 | −0.0313228 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.1002 | −1.92392 | −0.961961 | − | 0.273188i | \(-0.911922\pi\) | ||||
−0.961961 | + | 0.273188i | \(0.911922\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.8815 | −1.20906 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.51530 | 0.715147 | 0.357573 | − | 0.933885i | \(-0.383604\pi\) | ||||
0.357573 | + | 0.933885i | \(0.383604\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.29442 | −0.357330 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.5349 | 1.34388 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.05591 | −0.747925 | −0.373963 | − | 0.927444i | \(-0.622001\pi\) | ||||
−0.373963 | + | 0.927444i | \(0.622001\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.07527 | 0.112719 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.98162 | −0.205484 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.35587 | −0.241707 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.93164 | 0.602266 | 0.301133 | − | 0.953582i | \(-0.402635\pi\) | ||||
0.301133 | + | 0.953582i | \(0.402635\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.30246 | 0.130902 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.7641 | −1.66809 | −0.834045 | − | 0.551696i | \(-0.813981\pi\) | ||||
−0.834045 | + | 0.551696i | \(0.813981\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.29512 | −0.324678 | −0.162339 | − | 0.986735i | \(-0.551904\pi\) | ||||
−0.162339 | + | 0.986735i | \(0.551904\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.371816 | −0.0362855 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.81179 | −0.851868 | −0.425934 | − | 0.904754i | \(-0.640054\pi\) | ||||
−0.425934 | + | 0.904754i | \(0.640054\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.00627 | −0.479514 | −0.239757 | − | 0.970833i | \(-0.577068\pi\) | ||||
−0.239757 | + | 0.970833i | \(0.577068\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.8178 | −1.21661 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.81571 | 0.264880 | 0.132440 | − | 0.991191i | \(-0.457719\pi\) | ||||
0.132440 | + | 0.991191i | \(0.457719\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.811678 | −0.0756893 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.09540 | −0.471070 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.620820 | 0.0569105 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.87265 | −0.806605 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.8293 | −1.60761 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.2700 | −0.911312 | −0.455656 | − | 0.890156i | \(-0.650595\pi\) | ||||
−0.455656 | + | 0.890156i | \(0.650595\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −20.5673 | −1.81085 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.76201 | −0.678170 | −0.339085 | − | 0.940756i | \(-0.610117\pi\) | ||||
−0.339085 | + | 0.940756i | \(0.610117\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.443953 | 0.0384956 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.15727 | −0.357801 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.0458 | 1.79806 | 0.899030 | − | 0.437887i | \(-0.144273\pi\) | ||||
0.899030 | + | 0.437887i | \(0.144273\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.4634 | 0.887498 | 0.443749 | − | 0.896151i | \(-0.353648\pi\) | ||||
0.443749 | + | 0.896151i | \(0.353648\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.8862 | 1.16943 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.32245 | −0.695958 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.35299 | 0.527587 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.7414 | −1.13337 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.55983 | −0.537402 | −0.268701 | − | 0.963224i | \(-0.586594\pi\) | ||||
−0.268701 | + | 0.963224i | \(0.586594\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.94188 | −0.237837 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.00433 | −0.0806700 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.86962 | −0.628064 | −0.314032 | − | 0.949412i | \(-0.601680\pi\) | ||||
−0.314032 | + | 0.949412i | \(0.601680\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.2909 | 0.816123 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.152957 | 0.0120547 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.89611 | 0.461819 | 0.230909 | − | 0.972975i | \(-0.425830\pi\) | ||||
0.230909 | + | 0.972975i | \(0.425830\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.87780 | 0.224036 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.46843 | −0.268395 | −0.134197 | − | 0.990955i | \(-0.542846\pi\) | ||||
−0.134197 | + | 0.990955i | \(0.542846\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.5585 | 1.50450 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.10376 | −0.160879 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.82521 | 0.138768 | 0.0693841 | − | 0.997590i | \(-0.477897\pi\) | ||||
0.0693841 | + | 0.997590i | \(0.477897\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.188446 | −0.0142452 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.4589 | 1.16196 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.2727 | 1.06679 | 0.533396 | − | 0.845866i | \(-0.320916\pi\) | ||||
0.533396 | + | 0.845866i | \(0.320916\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.07528 | 0.154254 | 0.0771270 | − | 0.997021i | \(-0.475425\pi\) | ||||
0.0771270 | + | 0.997021i | \(0.475425\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.3944 | −1.72937 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.49639 | −0.477624 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.80505 | −0.351380 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.783420 | 0.0569854 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.3436 | −1.11023 | −0.555113 | − | 0.831775i | \(-0.687325\pi\) | ||||
−0.555113 | + | 0.831775i | \(0.687325\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.13361 | 0.585470 | 0.292735 | − | 0.956194i | \(-0.405435\pi\) | ||||
0.292735 | + | 0.956194i | \(0.405435\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −11.2583 | −0.806225 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.89099 | 0.562209 | 0.281105 | − | 0.959677i | \(-0.409299\pi\) | ||||
0.281105 | + | 0.959677i | \(0.409299\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.71038 | −0.688351 | −0.344175 | − | 0.938905i | \(-0.611841\pi\) | ||||
−0.344175 | + | 0.938905i | \(0.611841\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.57054 | 0.110778 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.19719 | −0.0840266 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.03633 | −0.631124 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.724820 | −0.0503784 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.43613 | −0.237682 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.00745 | −0.207041 | −0.103521 | − | 0.994627i | \(-0.533011\pi\) | ||||
−0.103521 | + | 0.994627i | \(0.533011\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24.9198 | 1.70748 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.4240 | −0.710913 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.189262 | 0.0128480 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.8219 | 1.27187 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.7980 | 1.26449 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.7060 | 1.65443 | 0.827217 | − | 0.561882i | \(-0.189922\pi\) | ||||
0.827217 | + | 0.561882i | \(0.189922\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.892989 | 0.0595326 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.61489 | 0.239928 | 0.119964 | − | 0.992778i | \(-0.461722\pi\) | ||||
0.119964 | + | 0.992778i | \(0.461722\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.41310 | 0.159462 | 0.0797309 | − | 0.996816i | \(-0.474594\pi\) | ||||
0.0797309 | + | 0.996816i | \(0.474594\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.542309 | −0.0356813 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.73549 | −0.179208 | −0.0896038 | − | 0.995977i | \(-0.528560\pi\) | ||||
−0.0896038 | + | 0.995977i | \(0.528560\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.03789 | 0.459101 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −33.7398 | −2.19164 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.1982 | 1.30651 | 0.653257 | − | 0.757136i | \(-0.273402\pi\) | ||||
0.653257 | + | 0.757136i | \(0.273402\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.1210 | 1.23169 | 0.615847 | − | 0.787865i | \(-0.288814\pi\) | ||||
0.615847 | + | 0.787865i | \(0.288814\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.99818 | −0.577233 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.96449 | −0.444945 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.4426 | 0.855331 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.8551 | 0.814660 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.2432 | −0.772784 | −0.386392 | − | 0.922335i | \(-0.626279\pi\) | ||||
−0.386392 | + | 0.922335i | \(0.626279\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.18387 | −0.0744291 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.50011 | −0.407053 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.4727 | 1.08992 | 0.544958 | − | 0.838463i | \(-0.316546\pi\) | ||||
0.544958 | + | 0.838463i | \(0.316546\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.22422 | 0.0760692 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.67315 | 0.351159 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.0884 | −1.67034 | −0.835171 | − | 0.549990i | \(-0.814631\pi\) | ||||
−0.835171 | + | 0.549990i | \(0.814631\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.21570 | 0.320398 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.9218 | −0.851999 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.8420 | −1.33173 | −0.665865 | − | 0.746072i | \(-0.731938\pi\) | ||||
−0.665865 | + | 0.746072i | \(0.731938\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.2195 | −1.53198 | −0.765989 | − | 0.642854i | \(-0.777750\pi\) | ||||
−0.765989 | + | 0.642854i | \(0.777750\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.12158 | 0.128404 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.45854 | 0.0879534 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.0957 | −1.32760 | −0.663802 | − | 0.747908i | \(-0.731058\pi\) | ||||
−0.663802 | + | 0.747908i | \(0.731058\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.896859 | −0.0536936 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.9881 | 0.774808 | 0.387404 | − | 0.921910i | \(-0.373372\pi\) | ||||
0.387404 | + | 0.921910i | \(0.373372\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.0522 | 1.13254 | 0.566268 | − | 0.824221i | \(-0.308387\pi\) | ||||
0.566268 | + | 0.824221i | \(0.308387\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.64828 | −0.275340 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.70286 | 0.100516 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.14678 | −0.361576 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.7035 | 0.686072 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.24228 | −0.364678 | −0.182339 | − | 0.983236i | \(-0.558367\pi\) | ||||
−0.182339 | + | 0.983236i | \(0.558367\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.83497 | 0.456170 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.06356 | −0.351843 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.63143 | 0.267843 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.96436 | 0.113224 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −33.0767 | −1.90021 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.8569 | −0.678923 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.96401 | −0.169165 | −0.0845825 | − | 0.996416i | \(-0.526956\pi\) | ||||
−0.0845825 | + | 0.996416i | \(0.526956\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.50149 | −0.369857 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.7783 | −1.23493 | −0.617467 | − | 0.786597i | \(-0.711841\pi\) | ||||
−0.617467 | + | 0.786597i | \(0.711841\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.27014 | −0.467456 | −0.233728 | − | 0.972302i | \(-0.575093\pi\) | ||||
−0.233728 | + | 0.972302i | \(0.575093\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.168280 | −0.00948151 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.2152 | 1.41623 | 0.708114 | − | 0.706098i | \(-0.249546\pi\) | ||||
0.708114 | + | 0.706098i | \(0.249546\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.26611 | 0.518802 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.3862 | −0.970406 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.76122 | 0.431846 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.70600 | −0.316512 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.87771 | −0.546238 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.32626 | −0.0731191 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.3441 | −0.733456 | −0.366728 | − | 0.930328i | \(-0.619522\pi\) | ||||
−0.366728 | + | 0.930328i | \(0.619522\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.80121 | −0.317904 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.795991 | 0.0434896 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.7055 | 0.910007 | 0.455004 | − | 0.890490i | \(-0.349638\pi\) | ||||
0.455004 | + | 0.890490i | \(0.349638\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.55558 | 0.301738 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.46486 | −0.0793268 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.63155 | 0.142090 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.60149 | −0.0862215 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.16196 | −0.0623774 | −0.0311887 | − | 0.999514i | \(-0.509929\pi\) | ||||
−0.0311887 | + | 0.999514i | \(0.509929\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −36.9214 | −1.97636 | −0.988180 | − | 0.153301i | \(-0.951010\pi\) | ||||
−0.988180 | + | 0.153301i | \(0.951010\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.7214 | 1.26615 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.2601 | 0.705761 | 0.352881 | − | 0.935668i | \(-0.385202\pi\) | ||||
0.352881 | + | 0.935668i | \(0.385202\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.6300 | 0.670331 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.22492 | 0.0648296 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.26636 | −0.383504 | −0.191752 | − | 0.981443i | \(-0.561417\pi\) | ||||
−0.191752 | + | 0.981443i | \(0.561417\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.4499 | −0.707889 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.5063 | −0.918844 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.53942 | 0.499316 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.3390 | −0.957286 | −0.478643 | − | 0.878010i | \(-0.658871\pi\) | ||||
−0.478643 | + | 0.878010i | \(0.658871\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.06934 | −0.420073 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.982876 | −0.0510284 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.5544 | 1.16782 | 0.583911 | − | 0.811817i | \(-0.301522\pi\) | ||||
0.583911 | + | 0.811817i | \(0.301522\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.97307 | 0.101889 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −36.2502 | −1.86698 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.9228 | 1.12610 | 0.563049 | − | 0.826423i | \(-0.309628\pi\) | ||||
0.563049 | + | 0.826423i | \(0.309628\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.2633 | −1.03812 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.6390 | 1.61668 | 0.808340 | − | 0.588716i | \(-0.200366\pi\) | ||||
0.808340 | + | 0.588716i | \(0.200366\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.274856 | −0.0140080 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.30855 | −0.473180 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.4167 | 1.44079 | 0.720393 | − | 0.693567i | \(-0.243962\pi\) | ||||
0.720393 | + | 0.693567i | \(0.243962\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.67401 | 0.135230 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.3150 | −0.772538 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.1002 | −0.860404 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.4172 | −0.874146 | −0.437073 | − | 0.899426i | \(-0.643985\pi\) | ||||
−0.437073 | + | 0.899426i | \(0.643985\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.875949 | 0.0438523 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.6095 | −0.929314 | −0.464657 | − | 0.885491i | \(-0.653822\pi\) | ||||
−0.464657 | + | 0.885491i | \(0.653822\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.73073 | 0.285468 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.8815 | −0.540708 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.47526 | −0.469671 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.2564 | 1.34774 | 0.673871 | − | 0.738849i | \(-0.264631\pi\) | ||||
0.673871 | + | 0.738849i | \(0.264631\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 41.5247 | 2.04826 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.47647 | −0.0726522 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.51530 | 0.319823 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.6451 | 1.01099 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.3451 | 1.18934 | 0.594669 | − | 0.803971i | \(-0.297283\pi\) | ||||
0.594669 | + | 0.803971i | \(0.297283\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.6110 | 1.24820 | 0.624102 | − | 0.781343i | \(-0.285465\pi\) | ||||
0.624102 | + | 0.781343i | \(0.285465\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.28476 | 0.305575 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.29442 | −0.159803 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.23438 | 0.108129 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16.4207 | −0.792800 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.10491 | 0.438568 | 0.219284 | − | 0.975661i | \(-0.429628\pi\) | ||||
0.219284 | + | 0.975661i | \(0.429628\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.1652 | 1.54576 | 0.772880 | − | 0.634552i | \(-0.218815\pi\) | ||||
0.772880 | + | 0.634552i | \(0.218815\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.5349 | 0.601001 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.91221 | 0.0914732 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.6927 | 0.653515 | 0.326757 | − | 0.945108i | \(-0.394044\pi\) | ||||
0.326757 | + | 0.945108i | \(0.394044\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.21921 | −0.296153 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.4325 | −1.63594 | −0.817969 | − | 0.575263i | \(-0.804900\pi\) | ||||
−0.817969 | + | 0.575263i | \(0.804900\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.05591 | −0.334482 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.9430 | −0.612182 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.2783 | 1.19296 | 0.596479 | − | 0.802628i | \(-0.296566\pi\) | ||||
0.596479 | + | 0.802628i | \(0.296566\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.1799 | −0.620616 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.97307 | 0.0927027 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.07527 | 0.0504095 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.9143 | −1.44611 | −0.723056 | − | 0.690790i | \(-0.757263\pi\) | ||||
−0.723056 | + | 0.690790i | \(0.757263\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.6958 | 0.639265 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.7687 | 1.66592 | 0.832958 | − | 0.553336i | \(-0.186645\pi\) | ||||
0.832958 | + | 0.553336i | \(0.186645\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.8482 | −1.52659 | −0.763293 | − | 0.646053i | \(-0.776419\pi\) | ||||
−0.763293 | + | 0.646053i | \(0.776419\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.98162 | −0.0918953 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.0429 | 1.15885 | 0.579423 | − | 0.815027i | \(-0.303278\pi\) | ||||
0.579423 | + | 0.815027i | \(0.303278\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.150001 | −0.00692641 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.5273 | −0.715459 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.2039 | −0.699076 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.35587 | −0.108095 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.65756 | 0.213255 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.9908 | −1.05048 | −0.525238 | − | 0.850955i | \(-0.676024\pi\) | ||||
−0.525238 | + | 0.850955i | \(0.676024\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 37.0684 | 1.69017 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.301795 | 0.0137321 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.93164 | 0.269342 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.1531 | −1.18511 | −0.592555 | − | 0.805530i | \(-0.701881\pi\) | ||||
−0.592555 | + | 0.805530i | \(0.701881\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.6334 | 0.526081 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.1841 | −0.685247 | −0.342623 | − | 0.939473i | \(-0.611316\pi\) | ||||
−0.342623 | + | 0.939473i | \(0.611316\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.9294 | −0.942614 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.30246 | 0.0585413 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.38007 | −0.106761 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.95963 | −0.0877250 | −0.0438625 | − | 0.999038i | \(-0.513966\pi\) | ||||
−0.0438625 | + | 0.999038i | \(0.513966\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.84343 | −0.305742 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.7556 | 1.68344 | 0.841718 | − | 0.539917i | \(-0.181544\pi\) | ||||
0.841718 | + | 0.539917i | \(0.181544\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.7641 | −0.745993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 38.5901 | 1.71385 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.1891 | 1.51541 | 0.757703 | − | 0.652600i | \(-0.226322\pi\) | ||||
0.757703 | + | 0.652600i | \(0.226322\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.79766 | −0.0795240 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.79398 | 0.432415 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.29512 | −0.145200 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.2651 | 0.451457 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.60126 | 0.158078 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.2394 | −0.755272 | −0.377636 | − | 0.925954i | \(-0.623263\pi\) | ||||
−0.377636 | + | 0.925954i | \(0.623263\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.7547 | 1.25735 | 0.628677 | − | 0.777666i | \(-0.283597\pi\) | ||||
0.628677 | + | 0.777666i | \(0.283597\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.371816 | −0.0162274 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.30870 | 0.144129 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3412 | −0.971356 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.99655 | 0.303624 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 51.5613 | 2.23337 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.81179 | −0.380967 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 28.1610 | 1.21524 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.1580 | −0.437536 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.4085 | −1.39335 | −0.696676 | − | 0.717386i | \(-0.745338\pi\) | ||||
−0.696676 | + | 0.717386i | \(0.745338\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.09466 | 0.175718 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.00627 | −0.214445 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.8456 | −1.53265 | −0.766323 | − | 0.642456i | \(-0.777916\pi\) | ||||
−0.766323 | + | 0.642456i | \(0.777916\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.5881 | −0.451888 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.9668 | −0.637607 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.22246 | 0.137033 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.8178 | −0.544086 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −33.2005 | −1.40675 | −0.703375 | − | 0.710819i | \(-0.748325\pi\) | ||||
−0.703375 | + | 0.710819i | \(0.748325\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 59.4795 | 2.51572 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.48069 | −0.400275 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.48206 | 0.231041 | 0.115521 | − | 0.993305i | \(-0.463146\pi\) | ||||
0.115521 | + | 0.993305i | \(0.463146\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.81571 | 0.118458 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.05058 | 0.0861163 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.11243 | 0.130480 | 0.0652399 | − | 0.997870i | \(-0.479219\pi\) | ||||
0.0652399 | + | 0.997870i | \(0.479219\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.7084 | −1.45250 | −0.726252 | − | 0.687429i | \(-0.758739\pi\) | ||||
−0.726252 | + | 0.687429i | \(0.758739\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −30.2740 | −1.26471 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.811678 | −0.0338493 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.4814 | 0.894284 | 0.447142 | − | 0.894463i | \(-0.352442\pi\) | ||||
0.447142 | + | 0.894463i | \(0.352442\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.0482 | 0.666938 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.22778 | −0.0509369 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.60732 | 0.315063 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.09540 | −0.210669 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.03865 | 0.290516 | 0.145258 | − | 0.989394i | \(-0.453599\pi\) | ||||
0.145258 | + | 0.989394i | \(0.453599\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.36608 | 0.0974925 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.5694 | 0.640441 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.63627 | −0.190389 | −0.0951943 | − | 0.995459i | \(-0.530347\pi\) | ||||
−0.0951943 | + | 0.995459i | \(0.530347\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.620820 | 0.0254511 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.1592 | −0.784135 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.8199 | −0.809820 | −0.404910 | − | 0.914357i | \(-0.632697\pi\) | ||||
−0.404910 | + | 0.914357i | \(0.632697\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.5664 | 0.838923 | 0.419461 | − | 0.907773i | \(-0.362219\pi\) | ||||
0.419461 | + | 0.907773i | \(0.362219\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.710811 | 0.0289465 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.87265 | −0.360725 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −45.1910 | −1.83424 | −0.917122 | − | 0.398606i | \(-0.869494\pi\) | ||||
−0.917122 | + | 0.398606i | \(0.869494\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.36214 | −0.0957189 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −40.1582 | −1.62463 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.56705 | 0.0632927 | 0.0316463 | − | 0.999499i | \(-0.489925\pi\) | ||||
0.0316463 | + | 0.999499i | \(0.489925\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −17.8293 | −0.718945 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.9257 | −0.560630 | −0.280315 | − | 0.959908i | \(-0.590439\pi\) | ||||
−0.280315 | + | 0.959908i | \(0.590439\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.2910 | −0.614596 | −0.307298 | − | 0.951613i | \(-0.599425\pi\) | ||||
−0.307298 | + | 0.951613i | \(0.599425\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.37436 | 0.135409 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.32966 | 0.0532716 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.77972 | −0.270756 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.4018 | 0.853348 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.6021 | −1.33768 | −0.668840 | − | 0.743406i | \(-0.733209\pi\) | ||||
−0.668840 | + | 0.743406i | \(0.733209\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.93389 | −0.235851 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.2700 | −0.407551 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 39.7394 | 1.57453 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.2785 | 0.446169 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.98940 | −0.236567 | −0.118283 | − | 0.992980i | \(-0.537739\pi\) | ||||
−0.118283 | + | 0.992980i | \(0.537739\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.3369 | 0.683699 | 0.341850 | − | 0.939755i | \(-0.388947\pi\) | ||||
0.341850 | + | 0.939755i | \(0.388947\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20.5673 | −0.809837 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −39.0043 | −1.53342 | −0.766708 | − | 0.641996i | \(-0.778106\pi\) | ||||
−0.766708 | + | 0.641996i | \(0.778106\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.4276 | 0.448574 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.373427 | 0.0146358 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.5523 | 0.843407 | 0.421704 | − | 0.906734i | \(-0.361432\pi\) | ||||
0.421704 | + | 0.906734i | \(0.361432\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.76201 | −0.303287 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.51860 | 0.332342 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.2891 | 0.712441 | 0.356221 | − | 0.934402i | \(-0.384065\pi\) | ||||
0.356221 | + | 0.934402i | \(0.384065\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.2982 | −0.633926 | −0.316963 | − | 0.948438i | \(-0.602663\pi\) | ||||
−0.316963 | + | 0.948438i | \(0.602663\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 37.0896 | 1.44044 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.443953 | 0.0172158 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.15658 | −0.199664 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 48.7465 | 1.88465 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.2938 | −0.667619 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.35910 | 0.283672 | 0.141836 | − | 0.989890i | \(-0.454699\pi\) | ||||
0.141836 | + | 0.989890i | \(0.454699\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.15727 | −0.160013 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.9604 | 0.805574 | 0.402787 | − | 0.915294i | \(-0.368042\pi\) | ||||
0.402787 | + | 0.915294i | \(0.368042\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.11779 | −0.0428969 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.13241 | 0.273315 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.9997 | −1.10964 | −0.554822 | − | 0.831969i | \(-0.687214\pi\) | ||||
−0.554822 | + | 0.831969i | \(0.687214\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.0458 | 0.804117 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.76120 | 0.181651 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −29.7608 | −1.13380 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.84746 | −0.108323 | −0.0541613 | − | 0.998532i | \(-0.517249\pi\) | ||||
−0.0541613 | + | 0.998532i | \(0.517249\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.245444 | −0.00932363 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.4634 | 0.396901 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.7695 | 1.12760 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.39729 | −0.204144 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.7745 | −0.558024 | −0.279012 | − | 0.960288i | \(-0.590007\pi\) | ||||
−0.279012 | + | 0.960288i | \(0.590007\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.3046 | 0.577225 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.8862 | 0.522985 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.15913 | 0.118811 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.381680 | 0.0143343 | 0.00716714 | − | 0.999974i | \(-0.497719\pi\) | ||||
0.00716714 | + | 0.999974i | \(0.497719\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.2703 | −0.572680 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.815195 | 0.0305293 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.32245 | −0.311242 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 39.8524 | 1.48832 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.8978 | 1.07771 | 0.538853 | − | 0.842400i | \(-0.318858\pi\) | ||||
0.538853 | + | 0.842400i | \(0.318858\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.620952 | 0.0231255 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 37.7271 | 1.40309 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.35299 | 0.235944 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.75757 | −0.139361 | −0.0696803 | − | 0.997569i | \(-0.522198\pi\) | ||||
−0.0696803 | + | 0.997569i | \(0.522198\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.8906 | 0.551504 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34.3411 | 1.27015 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.1481 | 0.670317 | 0.335158 | − | 0.942162i | \(-0.391210\pi\) | ||||
0.335158 | + | 0.942162i | \(0.391210\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.7414 | −0.506859 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.16099 | 0.0427655 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.9893 | −0.992817 | −0.496409 | − | 0.868089i | \(-0.665348\pi\) | ||||
−0.496409 | + | 0.868089i | \(0.665348\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26.5231 | 0.974351 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.4932 | −0.715136 | −0.357568 | − | 0.933887i | \(-0.616394\pi\) | ||||
−0.357568 | + | 0.933887i | \(0.616394\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.55983 | −0.240334 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.81809 | 0.212873 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.66054 | 0.0606750 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.248167 | 0.00905574 | 0.00452787 | − | 0.999990i | \(-0.498559\pi\) | ||||
0.00452787 | + | 0.999990i | \(0.498559\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24.1567 | −0.880317 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.00000 | 0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.1317 | 0.986120 | 0.493060 | − | 0.869995i | \(-0.335878\pi\) | ||||
0.493060 | + | 0.869995i | \(0.335878\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.33585 | −0.0847859 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.3758 | −0.484873 | −0.242436 | − | 0.970167i | \(-0.577947\pi\) | ||||
−0.242436 | + | 0.970167i | \(0.577947\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.943411 | 0.0341538 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.94188 | −0.106364 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −44.7064 | −1.61425 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.6141 | 0.995791 | 0.497896 | − | 0.867237i | \(-0.334106\pi\) | ||||
0.497896 | + | 0.867237i | \(0.334106\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 34.4748 | 1.24158 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.5348 | 0.378912 | 0.189456 | − | 0.981889i | \(-0.439328\pi\) | ||||
0.189456 | + | 0.981889i | \(0.439328\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00433 | −0.0360767 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.41546 | 0.0866542 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21.2884 | 0.762736 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.4214 | 0.659169 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −26.4111 | −0.943856 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.86962 | −0.280879 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.4949 | −0.766209 | −0.383105 | − | 0.923705i | \(-0.625145\pi\) | ||||
−0.383105 | + | 0.923705i | \(0.625145\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −53.4472 | −1.90277 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.530608 | −0.0188663 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 67.6554 | 2.40251 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.2909 | 0.364981 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39.6938 | −1.40603 | −0.703013 | − | 0.711177i | \(-0.748163\pi\) | ||||
−0.703013 | + | 0.711177i | \(0.748163\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.1858 | −0.820254 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.30085 | −0.222630 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.9137 | 0.491002 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.152957 | 0.00539103 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −43.0957 | −1.51704 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.9520 | 1.15853 | 0.579265 | − | 0.815140i | \(-0.303340\pi\) | ||||
0.579265 | + | 0.815140i | \(0.303340\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.7754 | −1.15090 | −0.575450 | − | 0.817837i | \(-0.695173\pi\) | ||||
−0.575450 | + | 0.817837i | \(0.695173\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −49.7598 | −1.74515 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.89611 | 0.206532 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.5576 | 0.859163 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.960206 | 0.0335523 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 50.6760 | 1.76861 | 0.884303 | − | 0.466914i | \(-0.154634\pi\) | ||||
0.884303 | + | 0.466914i | \(0.154634\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.91318 | 0.206121 | 0.103060 | − | 0.994675i | \(-0.467137\pi\) | ||||
0.103060 | + | 0.994675i | \(0.467137\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.87780 | 0.100192 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 51.9688 | 1.80713 | 0.903566 | − | 0.428448i | \(-0.140940\pi\) | ||||
0.903566 | + | 0.428448i | \(0.140940\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.38328 | 0.221700 | 0.110850 | − | 0.993837i | \(-0.464643\pi\) | ||||
0.110850 | + | 0.993837i | \(0.464643\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −43.5964 | −1.51234 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22.9440 | 0.794961 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.46843 | −0.120030 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.17529 | 0.144319 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −54.0976 | −1.86766 | −0.933829 | − | 0.357720i | \(-0.883554\pi\) | ||||
−0.933829 | + | 0.357720i | \(0.883554\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.3605 | 0.391741 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.6265 | 0.882622 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.5585 | 0.672831 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.67201 | 0.0574511 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 37.5912 | 1.29013 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.27298 | 0.180755 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.6041 | 0.602753 | 0.301377 | − | 0.953505i | \(-0.402554\pi\) | ||||
0.301377 | + | 0.953505i | \(0.402554\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.10376 | −0.0719472 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.4769 | 0.392042 | 0.196021 | − | 0.980600i | \(-0.437198\pi\) | ||||
0.196021 | + | 0.980600i | \(0.437198\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.3629 | −0.626533 | −0.313266 | − | 0.949665i | \(-0.601423\pi\) | ||||
−0.313266 | + | 0.949665i | \(0.601423\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.35985 | 0.114503 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −56.7078 | −1.93035 | −0.965177 | − | 0.261597i | \(-0.915751\pi\) | ||||
−0.965177 | + | 0.261597i | \(0.915751\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.82521 | 0.0620590 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.1280 | −0.411889 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.9414 | −0.846077 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.54193 | −0.153897 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.29689 | 0.179272 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.188446 | −0.00637063 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.0790 | −0.475413 | −0.237706 | − | 0.971337i | \(-0.576396\pi\) | ||||
−0.237706 | + | 0.971337i | \(0.576396\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.3164 | −0.415423 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.2110 | −0.950454 | −0.475227 | − | 0.879863i | \(-0.657634\pi\) | ||||
−0.475227 | + | 0.879863i | \(0.657634\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.9124 | −1.04028 | −0.520142 | − | 0.854080i | \(-0.674121\pi\) | ||||
−0.520142 | + | 0.854080i | \(0.674121\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.4589 | 0.519646 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.2352 | 0.780163 | 0.390082 | − | 0.920780i | \(-0.372447\pi\) | ||||
0.390082 | + | 0.920780i | \(0.372447\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.93533 | 0.0649090 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.8712 | −0.531705 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.5803 | −0.554840 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.2727 | 0.477084 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.13813 | 0.305113 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.38052 | −0.212802 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.1827 | −0.572439 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.87582 | 0.128979 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.07528 | 0.0689845 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.7548 | 0.788765 | 0.394382 | − | 0.918946i | \(-0.370959\pi\) | ||||
0.394382 | + | 0.918946i | \(0.370959\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.9702 | −0.496529 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.0249 | −0.530930 | −0.265465 | − | 0.964121i | \(-0.585525\pi\) | ||||
−0.265465 | + | 0.964121i | \(0.585525\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.50284 | 0.314498 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23.3944 | −0.773396 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.46272 | 0.0483032 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.0903 | 1.61934 | 0.809670 | − | 0.586885i | \(-0.199646\pi\) | ||||
0.809670 | + | 0.586885i | \(0.199646\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.84819 | −0.192704 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −72.0668 | −2.37211 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.49639 | −0.213600 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.94251 | −0.0966447 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −54.0620 | −1.77372 | −0.886858 | − | 0.462042i | \(-0.847117\pi\) | ||||
−0.886858 | + | 0.462042i | \(0.847117\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.4074 | 0.537731 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −42.9700 | −1.40678 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.80505 | −0.157142 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.2934 | 0.826301 | 0.413150 | − | 0.910663i | \(-0.364428\pi\) | ||||
0.413150 | + | 0.910663i | \(0.364428\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.3175 | −0.532502 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.1481 | −1.43919 | −0.719593 | − | 0.694396i | \(-0.755671\pi\) | ||||
−0.719593 | + | 0.694396i | \(0.755671\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.33459 | 0.238847 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.783420 | 0.0254847 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.5571 | −0.668017 | −0.334008 | − | 0.942570i | \(-0.608401\pi\) | ||||
−0.334008 | + | 0.942570i | \(0.608401\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −54.4320 | −1.76694 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 49.7513 | 1.61330 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.33150 | −0.107918 | −0.0539590 | − | 0.998543i | \(-0.517184\pi\) | ||||
−0.0539590 | + | 0.998543i | \(0.517184\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.3436 | −0.496508 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.2826 | 0.590994 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.96598 | −0.128068 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.9913 | −0.967462 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.86884 | −0.253570 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.13361 | 0.261830 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.3673 | 0.558496 | 0.279248 | − | 0.960219i | \(-0.409915\pi\) | ||||
0.279248 | + | 0.960219i | \(0.409915\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.3134 | 0.491937 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.6022 | −0.917890 | −0.458945 | − | 0.888465i | \(-0.651772\pi\) | ||||
−0.458945 | + | 0.888465i | \(0.651772\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.97179 | −0.0632127 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.2583 | −0.360555 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.1725 | −0.933310 | −0.466655 | − | 0.884440i | \(-0.654541\pi\) | ||||
−0.466655 | + | 0.884440i | \(0.654541\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.2913 | −0.328913 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.47055 | −0.142734 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.10404 | 0.194689 | 0.0973443 | − | 0.995251i | \(-0.468965\pi\) | ||||
0.0973443 | + | 0.995251i | \(0.468965\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.89099 | 0.251428 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.61680 | −0.0832936 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.46095 | 0.269043 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.6212 | −0.813883 | −0.406942 | − | 0.913454i | \(-0.633405\pi\) | ||||
−0.406942 | + | 0.913454i | \(0.633405\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.3287 | −0.835517 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.71038 | −0.307840 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.2770 | 0.642181 | 0.321090 | − | 0.947049i | \(-0.395951\pi\) | ||||
0.321090 | + | 0.947049i | \(0.395951\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 27.0073 | 0.854472 |
(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 | 6040.2.a.p.1.16 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6040.2.a.p.1.16 | ✓ | 19 | 1.1 | even | 1 | trivial |