Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1477718538\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 30x^{7} + 7x^{6} + 284x^{5} + 100x^{4} - 777x^{3} - 250x^{2} + 574x - 68 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.128459\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.871541 | 0.389765 | 0.194883 | − | 0.980827i | \(-0.437567\pi\) | ||||
0.194883 | + | 0.980827i | \(0.437567\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.79155 | 0.677142 | 0.338571 | − | 0.940941i | \(-0.390056\pi\) | ||||
0.338571 | + | 0.940941i | \(0.390056\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.871541 | 0.275606 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 6.05083 | 1.67820 | 0.839099 | − | 0.543978i | \(-0.183083\pi\) | ||||
0.839099 | + | 0.543978i | \(0.183083\pi\) | |||||||
\(14\) | 1.79155 | 0.478812 | ||||||||
\(15\) | 0.871541 | 0.225031 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.28116 | 1.03833 | 0.519167 | − | 0.854673i | \(-0.326242\pi\) | ||||
0.519167 | + | 0.854673i | \(0.326242\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −0.502442 | −0.115268 | −0.0576341 | − | 0.998338i | \(-0.518356\pi\) | ||||
−0.0576341 | + | 0.998338i | \(0.518356\pi\) | |||||||
\(20\) | 0.871541 | 0.194883 | ||||||||
\(21\) | 1.79155 | 0.390948 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −0.329122 | −0.0686266 | −0.0343133 | − | 0.999411i | \(-0.510924\pi\) | ||||
−0.0343133 | + | 0.999411i | \(0.510924\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.24042 | −0.848083 | ||||||||
\(26\) | 6.05083 | 1.18667 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.79155 | 0.338571 | ||||||||
\(29\) | 0.826208 | 0.153423 | 0.0767115 | − | 0.997053i | \(-0.475558\pi\) | ||||
0.0767115 | + | 0.997053i | \(0.475558\pi\) | |||||||
\(30\) | 0.871541 | 0.159121 | ||||||||
\(31\) | 2.54242 | 0.456632 | 0.228316 | − | 0.973587i | \(-0.426678\pi\) | ||||
0.228316 | + | 0.973587i | \(0.426678\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 4.28116 | 0.734212 | ||||||||
\(35\) | 1.56141 | 0.263926 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −11.6827 | −1.92062 | −0.960310 | − | 0.278933i | \(-0.910019\pi\) | ||||
−0.960310 | + | 0.278933i | \(0.910019\pi\) | |||||||
\(38\) | −0.502442 | −0.0815069 | ||||||||
\(39\) | 6.05083 | 0.968908 | ||||||||
\(40\) | 0.871541 | 0.137803 | ||||||||
\(41\) | 1.92808 | 0.301115 | 0.150557 | − | 0.988601i | \(-0.451893\pi\) | ||||
0.150557 | + | 0.988601i | \(0.451893\pi\) | |||||||
\(42\) | 1.79155 | 0.276442 | ||||||||
\(43\) | −4.90273 | −0.747660 | −0.373830 | − | 0.927497i | \(-0.621956\pi\) | ||||
−0.373830 | + | 0.927497i | \(0.621956\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0.871541 | 0.129922 | ||||||||
\(46\) | −0.329122 | −0.0485264 | ||||||||
\(47\) | −9.19307 | −1.34095 | −0.670474 | − | 0.741933i | \(-0.733909\pi\) | ||||
−0.670474 | + | 0.741933i | \(0.733909\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −3.79035 | −0.541479 | ||||||||
\(50\) | −4.24042 | −0.599685 | ||||||||
\(51\) | 4.28116 | 0.599482 | ||||||||
\(52\) | 6.05083 | 0.839099 | ||||||||
\(53\) | 0.198049 | 0.0272041 | 0.0136020 | − | 0.999907i | \(-0.495670\pi\) | ||||
0.0136020 | + | 0.999907i | \(0.495670\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.871541 | 0.117519 | ||||||||
\(56\) | 1.79155 | 0.239406 | ||||||||
\(57\) | −0.502442 | −0.0665501 | ||||||||
\(58\) | 0.826208 | 0.108486 | ||||||||
\(59\) | −5.77799 | −0.752230 | −0.376115 | − | 0.926573i | \(-0.622740\pi\) | ||||
−0.376115 | + | 0.926573i | \(0.622740\pi\) | |||||||
\(60\) | 0.871541 | 0.112515 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 2.54242 | 0.322888 | ||||||||
\(63\) | 1.79155 | 0.225714 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.27355 | 0.654103 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | 3.24114 | 0.395969 | 0.197984 | − | 0.980205i | \(-0.436560\pi\) | ||||
0.197984 | + | 0.980205i | \(0.436560\pi\) | |||||||
\(68\) | 4.28116 | 0.519167 | ||||||||
\(69\) | −0.329122 | −0.0396216 | ||||||||
\(70\) | 1.56141 | 0.186624 | ||||||||
\(71\) | −7.63320 | −0.905894 | −0.452947 | − | 0.891537i | \(-0.649627\pi\) | ||||
−0.452947 | + | 0.891537i | \(0.649627\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 7.93920 | 0.929213 | 0.464607 | − | 0.885517i | \(-0.346196\pi\) | ||||
0.464607 | + | 0.885517i | \(0.346196\pi\) | |||||||
\(74\) | −11.6827 | −1.35808 | ||||||||
\(75\) | −4.24042 | −0.489641 | ||||||||
\(76\) | −0.502442 | −0.0576341 | ||||||||
\(77\) | 1.79155 | 0.204166 | ||||||||
\(78\) | 6.05083 | 0.685122 | ||||||||
\(79\) | 12.1924 | 1.37176 | 0.685878 | − | 0.727717i | \(-0.259418\pi\) | ||||
0.685878 | + | 0.727717i | \(0.259418\pi\) | |||||||
\(80\) | 0.871541 | 0.0974413 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.92808 | 0.212920 | ||||||||
\(83\) | −5.33038 | −0.585085 | −0.292543 | − | 0.956252i | \(-0.594501\pi\) | ||||
−0.292543 | + | 0.956252i | \(0.594501\pi\) | |||||||
\(84\) | 1.79155 | 0.195474 | ||||||||
\(85\) | 3.73121 | 0.404706 | ||||||||
\(86\) | −4.90273 | −0.528675 | ||||||||
\(87\) | 0.826208 | 0.0885788 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −4.51300 | −0.478377 | −0.239189 | − | 0.970973i | \(-0.576881\pi\) | ||||
−0.239189 | + | 0.970973i | \(0.576881\pi\) | |||||||
\(90\) | 0.871541 | 0.0918685 | ||||||||
\(91\) | 10.8404 | 1.13638 | ||||||||
\(92\) | −0.329122 | −0.0343133 | ||||||||
\(93\) | 2.54242 | 0.263637 | ||||||||
\(94\) | −9.19307 | −0.948193 | ||||||||
\(95\) | −0.437899 | −0.0449275 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 9.53546 | 0.968179 | 0.484090 | − | 0.875018i | \(-0.339151\pi\) | ||||
0.484090 | + | 0.875018i | \(0.339151\pi\) | |||||||
\(98\) | −3.79035 | −0.382883 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −4.24042 | −0.424042 | ||||||||
\(101\) | −0.178769 | −0.0177882 | −0.00889411 | − | 0.999960i | \(-0.502831\pi\) | ||||
−0.00889411 | + | 0.999960i | \(0.502831\pi\) | |||||||
\(102\) | 4.28116 | 0.423898 | ||||||||
\(103\) | −1.56415 | −0.154120 | −0.0770600 | − | 0.997026i | \(-0.524553\pi\) | ||||
−0.0770600 | + | 0.997026i | \(0.524553\pi\) | |||||||
\(104\) | 6.05083 | 0.593333 | ||||||||
\(105\) | 1.56141 | 0.152378 | ||||||||
\(106\) | 0.198049 | 0.0192362 | ||||||||
\(107\) | −3.77496 | −0.364939 | −0.182470 | − | 0.983211i | \(-0.558409\pi\) | ||||
−0.182470 | + | 0.983211i | \(0.558409\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 0.168419 | 0.0161316 | 0.00806582 | − | 0.999967i | \(-0.497433\pi\) | ||||
0.00806582 | + | 0.999967i | \(0.497433\pi\) | |||||||
\(110\) | 0.871541 | 0.0830982 | ||||||||
\(111\) | −11.6827 | −1.10887 | ||||||||
\(112\) | 1.79155 | 0.169285 | ||||||||
\(113\) | 12.0336 | 1.13203 | 0.566013 | − | 0.824396i | \(-0.308485\pi\) | ||||
0.566013 | + | 0.824396i | \(0.308485\pi\) | |||||||
\(114\) | −0.502442 | −0.0470580 | ||||||||
\(115\) | −0.286843 | −0.0267483 | ||||||||
\(116\) | 0.826208 | 0.0767115 | ||||||||
\(117\) | 6.05083 | 0.559399 | ||||||||
\(118\) | −5.77799 | −0.531907 | ||||||||
\(119\) | 7.66990 | 0.703099 | ||||||||
\(120\) | 0.871541 | 0.0795605 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.00000 | −0.0905357 | ||||||||
\(123\) | 1.92808 | 0.173849 | ||||||||
\(124\) | 2.54242 | 0.228316 | ||||||||
\(125\) | −8.05340 | −0.720318 | ||||||||
\(126\) | 1.79155 | 0.159604 | ||||||||
\(127\) | 13.2035 | 1.17162 | 0.585810 | − | 0.810448i | \(-0.300776\pi\) | ||||
0.585810 | + | 0.810448i | \(0.300776\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −4.90273 | −0.431661 | ||||||||
\(130\) | 5.27355 | 0.462521 | ||||||||
\(131\) | −0.292814 | −0.0255832 | −0.0127916 | − | 0.999918i | \(-0.504072\pi\) | ||||
−0.0127916 | + | 0.999918i | \(0.504072\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | −0.900150 | −0.0780529 | ||||||||
\(134\) | 3.24114 | 0.279992 | ||||||||
\(135\) | 0.871541 | 0.0750103 | ||||||||
\(136\) | 4.28116 | 0.367106 | ||||||||
\(137\) | −13.4359 | −1.14791 | −0.573954 | − | 0.818887i | \(-0.694591\pi\) | ||||
−0.573954 | + | 0.818887i | \(0.694591\pi\) | |||||||
\(138\) | −0.329122 | −0.0280167 | ||||||||
\(139\) | −18.9380 | −1.60630 | −0.803150 | − | 0.595777i | \(-0.796844\pi\) | ||||
−0.803150 | + | 0.595777i | \(0.796844\pi\) | |||||||
\(140\) | 1.56141 | 0.131963 | ||||||||
\(141\) | −9.19307 | −0.774196 | ||||||||
\(142\) | −7.63320 | −0.640564 | ||||||||
\(143\) | 6.05083 | 0.505996 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.720074 | 0.0597989 | ||||||||
\(146\) | 7.93920 | 0.657053 | ||||||||
\(147\) | −3.79035 | −0.312623 | ||||||||
\(148\) | −11.6827 | −0.960310 | ||||||||
\(149\) | 21.5424 | 1.76482 | 0.882412 | − | 0.470478i | \(-0.155918\pi\) | ||||
0.882412 | + | 0.470478i | \(0.155918\pi\) | |||||||
\(150\) | −4.24042 | −0.346228 | ||||||||
\(151\) | 7.30147 | 0.594185 | 0.297093 | − | 0.954849i | \(-0.403983\pi\) | ||||
0.297093 | + | 0.954849i | \(0.403983\pi\) | |||||||
\(152\) | −0.502442 | −0.0407535 | ||||||||
\(153\) | 4.28116 | 0.346111 | ||||||||
\(154\) | 1.79155 | 0.144367 | ||||||||
\(155\) | 2.21582 | 0.177979 | ||||||||
\(156\) | 6.05083 | 0.484454 | ||||||||
\(157\) | −16.8390 | −1.34390 | −0.671950 | − | 0.740597i | \(-0.734543\pi\) | ||||
−0.671950 | + | 0.740597i | \(0.734543\pi\) | |||||||
\(158\) | 12.1924 | 0.969978 | ||||||||
\(159\) | 0.198049 | 0.0157063 | ||||||||
\(160\) | 0.871541 | 0.0689014 | ||||||||
\(161\) | −0.589638 | −0.0464700 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 19.9962 | 1.56622 | 0.783111 | − | 0.621882i | \(-0.213632\pi\) | ||||
0.783111 | + | 0.621882i | \(0.213632\pi\) | |||||||
\(164\) | 1.92808 | 0.150557 | ||||||||
\(165\) | 0.871541 | 0.0678494 | ||||||||
\(166\) | −5.33038 | −0.413718 | ||||||||
\(167\) | −5.96323 | −0.461448 | −0.230724 | − | 0.973019i | \(-0.574109\pi\) | ||||
−0.230724 | + | 0.973019i | \(0.574109\pi\) | |||||||
\(168\) | 1.79155 | 0.138221 | ||||||||
\(169\) | 23.6126 | 1.81635 | ||||||||
\(170\) | 3.73121 | 0.286170 | ||||||||
\(171\) | −0.502442 | −0.0384227 | ||||||||
\(172\) | −4.90273 | −0.373830 | ||||||||
\(173\) | 2.13158 | 0.162061 | 0.0810307 | − | 0.996712i | \(-0.474179\pi\) | ||||
0.0810307 | + | 0.996712i | \(0.474179\pi\) | |||||||
\(174\) | 0.826208 | 0.0626347 | ||||||||
\(175\) | −7.59691 | −0.574273 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −5.77799 | −0.434300 | ||||||||
\(178\) | −4.51300 | −0.338264 | ||||||||
\(179\) | 4.23721 | 0.316704 | 0.158352 | − | 0.987383i | \(-0.449382\pi\) | ||||
0.158352 | + | 0.987383i | \(0.449382\pi\) | |||||||
\(180\) | 0.871541 | 0.0649609 | ||||||||
\(181\) | 18.4965 | 1.37483 | 0.687417 | − | 0.726263i | \(-0.258745\pi\) | ||||
0.687417 | + | 0.726263i | \(0.258745\pi\) | |||||||
\(182\) | 10.8404 | 0.803541 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | −0.329122 | −0.0242632 | ||||||||
\(185\) | −10.1819 | −0.748591 | ||||||||
\(186\) | 2.54242 | 0.186419 | ||||||||
\(187\) | 4.28116 | 0.313069 | ||||||||
\(188\) | −9.19307 | −0.670474 | ||||||||
\(189\) | 1.79155 | 0.130316 | ||||||||
\(190\) | −0.437899 | −0.0317686 | ||||||||
\(191\) | −15.3727 | −1.11233 | −0.556165 | − | 0.831072i | \(-0.687728\pi\) | ||||
−0.556165 | + | 0.831072i | \(0.687728\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 7.25371 | 0.522133 | 0.261067 | − | 0.965321i | \(-0.415926\pi\) | ||||
0.261067 | + | 0.965321i | \(0.415926\pi\) | |||||||
\(194\) | 9.53546 | 0.684606 | ||||||||
\(195\) | 5.27355 | 0.377647 | ||||||||
\(196\) | −3.79035 | −0.270739 | ||||||||
\(197\) | 2.95332 | 0.210416 | 0.105208 | − | 0.994450i | \(-0.466449\pi\) | ||||
0.105208 | + | 0.994450i | \(0.466449\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | 8.65655 | 0.613646 | 0.306823 | − | 0.951767i | \(-0.400734\pi\) | ||||
0.306823 | + | 0.951767i | \(0.400734\pi\) | |||||||
\(200\) | −4.24042 | −0.299843 | ||||||||
\(201\) | 3.24114 | 0.228613 | ||||||||
\(202\) | −0.178769 | −0.0125782 | ||||||||
\(203\) | 1.48019 | 0.103889 | ||||||||
\(204\) | 4.28116 | 0.299741 | ||||||||
\(205\) | 1.68040 | 0.117364 | ||||||||
\(206\) | −1.56415 | −0.108979 | ||||||||
\(207\) | −0.329122 | −0.0228755 | ||||||||
\(208\) | 6.05083 | 0.419550 | ||||||||
\(209\) | −0.502442 | −0.0347547 | ||||||||
\(210\) | 1.56141 | 0.107747 | ||||||||
\(211\) | −20.5222 | −1.41281 | −0.706403 | − | 0.707810i | \(-0.749683\pi\) | ||||
−0.706403 | + | 0.707810i | \(0.749683\pi\) | |||||||
\(212\) | 0.198049 | 0.0136020 | ||||||||
\(213\) | −7.63320 | −0.523018 | ||||||||
\(214\) | −3.77496 | −0.258051 | ||||||||
\(215\) | −4.27293 | −0.291412 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 4.55487 | 0.309205 | ||||||||
\(218\) | 0.168419 | 0.0114068 | ||||||||
\(219\) | 7.93920 | 0.536481 | ||||||||
\(220\) | 0.871541 | 0.0587593 | ||||||||
\(221\) | 25.9046 | 1.74253 | ||||||||
\(222\) | −11.6827 | −0.784090 | ||||||||
\(223\) | −21.0135 | −1.40717 | −0.703584 | − | 0.710612i | \(-0.748418\pi\) | ||||
−0.703584 | + | 0.710612i | \(0.748418\pi\) | |||||||
\(224\) | 1.79155 | 0.119703 | ||||||||
\(225\) | −4.24042 | −0.282694 | ||||||||
\(226\) | 12.0336 | 0.800464 | ||||||||
\(227\) | −27.1121 | −1.79949 | −0.899747 | − | 0.436412i | \(-0.856249\pi\) | ||||
−0.899747 | + | 0.436412i | \(0.856249\pi\) | |||||||
\(228\) | −0.502442 | −0.0332751 | ||||||||
\(229\) | 16.6742 | 1.10186 | 0.550932 | − | 0.834550i | \(-0.314272\pi\) | ||||
0.550932 | + | 0.834550i | \(0.314272\pi\) | |||||||
\(230\) | −0.286843 | −0.0189139 | ||||||||
\(231\) | 1.79155 | 0.117875 | ||||||||
\(232\) | 0.826208 | 0.0542432 | ||||||||
\(233\) | 7.53921 | 0.493910 | 0.246955 | − | 0.969027i | \(-0.420570\pi\) | ||||
0.246955 | + | 0.969027i | \(0.420570\pi\) | |||||||
\(234\) | 6.05083 | 0.395555 | ||||||||
\(235\) | −8.01214 | −0.522655 | ||||||||
\(236\) | −5.77799 | −0.376115 | ||||||||
\(237\) | 12.1924 | 0.791984 | ||||||||
\(238\) | 7.66990 | 0.497166 | ||||||||
\(239\) | −26.0180 | −1.68297 | −0.841483 | − | 0.540284i | \(-0.818317\pi\) | ||||
−0.841483 | + | 0.540284i | \(0.818317\pi\) | |||||||
\(240\) | 0.871541 | 0.0562577 | ||||||||
\(241\) | −23.7245 | −1.52823 | −0.764114 | − | 0.645082i | \(-0.776823\pi\) | ||||
−0.764114 | + | 0.645082i | \(0.776823\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | −3.30345 | −0.211050 | ||||||||
\(246\) | 1.92808 | 0.122930 | ||||||||
\(247\) | −3.04019 | −0.193443 | ||||||||
\(248\) | 2.54242 | 0.161444 | ||||||||
\(249\) | −5.33038 | −0.337799 | ||||||||
\(250\) | −8.05340 | −0.509342 | ||||||||
\(251\) | 17.2264 | 1.08732 | 0.543661 | − | 0.839305i | \(-0.317038\pi\) | ||||
0.543661 | + | 0.839305i | \(0.317038\pi\) | |||||||
\(252\) | 1.79155 | 0.112857 | ||||||||
\(253\) | −0.329122 | −0.0206917 | ||||||||
\(254\) | 13.2035 | 0.828461 | ||||||||
\(255\) | 3.73121 | 0.233657 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.9836 | 0.934649 | 0.467325 | − | 0.884086i | \(-0.345218\pi\) | ||||
0.467325 | + | 0.884086i | \(0.345218\pi\) | |||||||
\(258\) | −4.90273 | −0.305231 | ||||||||
\(259\) | −20.9301 | −1.30053 | ||||||||
\(260\) | 5.27355 | 0.327052 | ||||||||
\(261\) | 0.826208 | 0.0511410 | ||||||||
\(262\) | −0.292814 | −0.0180901 | ||||||||
\(263\) | 6.28404 | 0.387490 | 0.193745 | − | 0.981052i | \(-0.437936\pi\) | ||||
0.193745 | + | 0.981052i | \(0.437936\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | 0.172607 | 0.0106032 | ||||||||
\(266\) | −0.900150 | −0.0551918 | ||||||||
\(267\) | −4.51300 | −0.276191 | ||||||||
\(268\) | 3.24114 | 0.197984 | ||||||||
\(269\) | −19.9982 | −1.21931 | −0.609655 | − | 0.792666i | \(-0.708692\pi\) | ||||
−0.609655 | + | 0.792666i | \(0.708692\pi\) | |||||||
\(270\) | 0.871541 | 0.0530403 | ||||||||
\(271\) | 5.33390 | 0.324011 | 0.162006 | − | 0.986790i | \(-0.448204\pi\) | ||||
0.162006 | + | 0.986790i | \(0.448204\pi\) | |||||||
\(272\) | 4.28116 | 0.259583 | ||||||||
\(273\) | 10.8404 | 0.656089 | ||||||||
\(274\) | −13.4359 | −0.811694 | ||||||||
\(275\) | −4.24042 | −0.255707 | ||||||||
\(276\) | −0.329122 | −0.0198108 | ||||||||
\(277\) | −13.2945 | −0.798791 | −0.399396 | − | 0.916779i | \(-0.630780\pi\) | ||||
−0.399396 | + | 0.916779i | \(0.630780\pi\) | |||||||
\(278\) | −18.9380 | −1.13583 | ||||||||
\(279\) | 2.54242 | 0.152211 | ||||||||
\(280\) | 1.56141 | 0.0933120 | ||||||||
\(281\) | 0.315638 | 0.0188294 | 0.00941471 | − | 0.999956i | \(-0.497003\pi\) | ||||
0.00941471 | + | 0.999956i | \(0.497003\pi\) | |||||||
\(282\) | −9.19307 | −0.547440 | ||||||||
\(283\) | 0.146911 | 0.00873297 | 0.00436648 | − | 0.999990i | \(-0.498610\pi\) | ||||
0.00436648 | + | 0.999990i | \(0.498610\pi\) | |||||||
\(284\) | −7.63320 | −0.452947 | ||||||||
\(285\) | −0.437899 | −0.0259389 | ||||||||
\(286\) | 6.05083 | 0.357793 | ||||||||
\(287\) | 3.45424 | 0.203898 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.32831 | 0.0781358 | ||||||||
\(290\) | 0.720074 | 0.0422842 | ||||||||
\(291\) | 9.53546 | 0.558979 | ||||||||
\(292\) | 7.93920 | 0.464607 | ||||||||
\(293\) | −31.8915 | −1.86312 | −0.931560 | − | 0.363587i | \(-0.881552\pi\) | ||||
−0.931560 | + | 0.363587i | \(0.881552\pi\) | |||||||
\(294\) | −3.79035 | −0.221058 | ||||||||
\(295\) | −5.03576 | −0.293193 | ||||||||
\(296\) | −11.6827 | −0.679042 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 21.5424 | 1.24792 | ||||||||
\(299\) | −1.99146 | −0.115169 | ||||||||
\(300\) | −4.24042 | −0.244821 | ||||||||
\(301\) | −8.78349 | −0.506272 | ||||||||
\(302\) | 7.30147 | 0.420152 | ||||||||
\(303\) | −0.178769 | −0.0102700 | ||||||||
\(304\) | −0.502442 | −0.0288170 | ||||||||
\(305\) | −0.871541 | −0.0499043 | ||||||||
\(306\) | 4.28116 | 0.244737 | ||||||||
\(307\) | 3.27266 | 0.186781 | 0.0933903 | − | 0.995630i | \(-0.470230\pi\) | ||||
0.0933903 | + | 0.995630i | \(0.470230\pi\) | |||||||
\(308\) | 1.79155 | 0.102083 | ||||||||
\(309\) | −1.56415 | −0.0889812 | ||||||||
\(310\) | 2.21582 | 0.125850 | ||||||||
\(311\) | 11.1080 | 0.629877 | 0.314938 | − | 0.949112i | \(-0.398016\pi\) | ||||
0.314938 | + | 0.949112i | \(0.398016\pi\) | |||||||
\(312\) | 6.05083 | 0.342561 | ||||||||
\(313\) | −21.1941 | −1.19796 | −0.598981 | − | 0.800763i | \(-0.704428\pi\) | ||||
−0.598981 | + | 0.800763i | \(0.704428\pi\) | |||||||
\(314\) | −16.8390 | −0.950280 | ||||||||
\(315\) | 1.56141 | 0.0879754 | ||||||||
\(316\) | 12.1924 | 0.685878 | ||||||||
\(317\) | −10.5636 | −0.593310 | −0.296655 | − | 0.954985i | \(-0.595871\pi\) | ||||
−0.296655 | + | 0.954985i | \(0.595871\pi\) | |||||||
\(318\) | 0.198049 | 0.0111060 | ||||||||
\(319\) | 0.826208 | 0.0462588 | ||||||||
\(320\) | 0.871541 | 0.0487206 | ||||||||
\(321\) | −3.77496 | −0.210698 | ||||||||
\(322\) | −0.589638 | −0.0328592 | ||||||||
\(323\) | −2.15104 | −0.119687 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −25.6580 | −1.42325 | ||||||||
\(326\) | 19.9962 | 1.10749 | ||||||||
\(327\) | 0.168419 | 0.00931360 | ||||||||
\(328\) | 1.92808 | 0.106460 | ||||||||
\(329\) | −16.4698 | −0.908012 | ||||||||
\(330\) | 0.871541 | 0.0479768 | ||||||||
\(331\) | 26.7220 | 1.46877 | 0.734387 | − | 0.678731i | \(-0.237470\pi\) | ||||
0.734387 | + | 0.678731i | \(0.237470\pi\) | |||||||
\(332\) | −5.33038 | −0.292543 | ||||||||
\(333\) | −11.6827 | −0.640207 | ||||||||
\(334\) | −5.96323 | −0.326293 | ||||||||
\(335\) | 2.82479 | 0.154335 | ||||||||
\(336\) | 1.79155 | 0.0977370 | ||||||||
\(337\) | 14.8452 | 0.808669 | 0.404335 | − | 0.914611i | \(-0.367503\pi\) | ||||
0.404335 | + | 0.914611i | \(0.367503\pi\) | |||||||
\(338\) | 23.6126 | 1.28435 | ||||||||
\(339\) | 12.0336 | 0.653576 | ||||||||
\(340\) | 3.73121 | 0.202353 | ||||||||
\(341\) | 2.54242 | 0.137680 | ||||||||
\(342\) | −0.502442 | −0.0271690 | ||||||||
\(343\) | −19.3314 | −1.04380 | ||||||||
\(344\) | −4.90273 | −0.264338 | ||||||||
\(345\) | −0.286843 | −0.0154431 | ||||||||
\(346\) | 2.13158 | 0.114595 | ||||||||
\(347\) | 32.2966 | 1.73377 | 0.866887 | − | 0.498504i | \(-0.166117\pi\) | ||||
0.866887 | + | 0.498504i | \(0.166117\pi\) | |||||||
\(348\) | 0.826208 | 0.0442894 | ||||||||
\(349\) | 19.0687 | 1.02073 | 0.510363 | − | 0.859959i | \(-0.329511\pi\) | ||||
0.510363 | + | 0.859959i | \(0.329511\pi\) | |||||||
\(350\) | −7.59691 | −0.406072 | ||||||||
\(351\) | 6.05083 | 0.322969 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −24.7218 | −1.31581 | −0.657905 | − | 0.753101i | \(-0.728557\pi\) | ||||
−0.657905 | + | 0.753101i | \(0.728557\pi\) | |||||||
\(354\) | −5.77799 | −0.307097 | ||||||||
\(355\) | −6.65265 | −0.353086 | ||||||||
\(356\) | −4.51300 | −0.239189 | ||||||||
\(357\) | 7.66990 | 0.405934 | ||||||||
\(358\) | 4.23721 | 0.223944 | ||||||||
\(359\) | 29.6397 | 1.56432 | 0.782162 | − | 0.623075i | \(-0.214117\pi\) | ||||
0.782162 | + | 0.623075i | \(0.214117\pi\) | |||||||
\(360\) | 0.871541 | 0.0459343 | ||||||||
\(361\) | −18.7476 | −0.986713 | ||||||||
\(362\) | 18.4965 | 0.972154 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 10.8404 | 0.568189 | ||||||||
\(365\) | 6.91934 | 0.362175 | ||||||||
\(366\) | −1.00000 | −0.0522708 | ||||||||
\(367\) | −2.72541 | −0.142265 | −0.0711325 | − | 0.997467i | \(-0.522661\pi\) | ||||
−0.0711325 | + | 0.997467i | \(0.522661\pi\) | |||||||
\(368\) | −0.329122 | −0.0171567 | ||||||||
\(369\) | 1.92808 | 0.100372 | ||||||||
\(370\) | −10.1819 | −0.529334 | ||||||||
\(371\) | 0.354814 | 0.0184210 | ||||||||
\(372\) | 2.54242 | 0.131818 | ||||||||
\(373\) | 25.8653 | 1.33926 | 0.669628 | − | 0.742696i | \(-0.266453\pi\) | ||||
0.669628 | + | 0.742696i | \(0.266453\pi\) | |||||||
\(374\) | 4.28116 | 0.221373 | ||||||||
\(375\) | −8.05340 | −0.415876 | ||||||||
\(376\) | −9.19307 | −0.474097 | ||||||||
\(377\) | 4.99924 | 0.257474 | ||||||||
\(378\) | 1.79155 | 0.0921474 | ||||||||
\(379\) | −29.8825 | −1.53496 | −0.767479 | − | 0.641074i | \(-0.778489\pi\) | ||||
−0.767479 | + | 0.641074i | \(0.778489\pi\) | |||||||
\(380\) | −0.437899 | −0.0224638 | ||||||||
\(381\) | 13.2035 | 0.676435 | ||||||||
\(382\) | −15.3727 | −0.786536 | ||||||||
\(383\) | −32.6319 | −1.66741 | −0.833705 | − | 0.552210i | \(-0.813785\pi\) | ||||
−0.833705 | + | 0.552210i | \(0.813785\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 1.56141 | 0.0795768 | ||||||||
\(386\) | 7.25371 | 0.369204 | ||||||||
\(387\) | −4.90273 | −0.249220 | ||||||||
\(388\) | 9.53546 | 0.484090 | ||||||||
\(389\) | −24.7562 | −1.25519 | −0.627595 | − | 0.778540i | \(-0.715961\pi\) | ||||
−0.627595 | + | 0.778540i | \(0.715961\pi\) | |||||||
\(390\) | 5.27355 | 0.267037 | ||||||||
\(391\) | −1.40902 | −0.0712573 | ||||||||
\(392\) | −3.79035 | −0.191442 | ||||||||
\(393\) | −0.292814 | −0.0147705 | ||||||||
\(394\) | 2.95332 | 0.148786 | ||||||||
\(395\) | 10.6262 | 0.534663 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | −8.25865 | −0.414490 | −0.207245 | − | 0.978289i | \(-0.566450\pi\) | ||||
−0.207245 | + | 0.978289i | \(0.566450\pi\) | |||||||
\(398\) | 8.65655 | 0.433914 | ||||||||
\(399\) | −0.900150 | −0.0450639 | ||||||||
\(400\) | −4.24042 | −0.212021 | ||||||||
\(401\) | 10.5654 | 0.527613 | 0.263807 | − | 0.964576i | \(-0.415022\pi\) | ||||
0.263807 | + | 0.964576i | \(0.415022\pi\) | |||||||
\(402\) | 3.24114 | 0.161653 | ||||||||
\(403\) | 15.3837 | 0.766319 | ||||||||
\(404\) | −0.178769 | −0.00889411 | ||||||||
\(405\) | 0.871541 | 0.0433072 | ||||||||
\(406\) | 1.48019 | 0.0734607 | ||||||||
\(407\) | −11.6827 | −0.579089 | ||||||||
\(408\) | 4.28116 | 0.211949 | ||||||||
\(409\) | 31.0066 | 1.53318 | 0.766590 | − | 0.642137i | \(-0.221952\pi\) | ||||
0.766590 | + | 0.642137i | \(0.221952\pi\) | |||||||
\(410\) | 1.68040 | 0.0829889 | ||||||||
\(411\) | −13.4359 | −0.662745 | ||||||||
\(412\) | −1.56415 | −0.0770600 | ||||||||
\(413\) | −10.3516 | −0.509367 | ||||||||
\(414\) | −0.329122 | −0.0161755 | ||||||||
\(415\) | −4.64565 | −0.228046 | ||||||||
\(416\) | 6.05083 | 0.296666 | ||||||||
\(417\) | −18.9380 | −0.927397 | ||||||||
\(418\) | −0.502442 | −0.0245753 | ||||||||
\(419\) | −6.83731 | −0.334024 | −0.167012 | − | 0.985955i | \(-0.553412\pi\) | ||||
−0.167012 | + | 0.985955i | \(0.553412\pi\) | |||||||
\(420\) | 1.56141 | 0.0761890 | ||||||||
\(421\) | 27.9306 | 1.36125 | 0.680627 | − | 0.732630i | \(-0.261707\pi\) | ||||
0.680627 | + | 0.732630i | \(0.261707\pi\) | |||||||
\(422\) | −20.5222 | −0.999004 | ||||||||
\(423\) | −9.19307 | −0.446982 | ||||||||
\(424\) | 0.198049 | 0.00961809 | ||||||||
\(425\) | −18.1539 | −0.880593 | ||||||||
\(426\) | −7.63320 | −0.369830 | ||||||||
\(427\) | −1.79155 | −0.0866991 | ||||||||
\(428\) | −3.77496 | −0.182470 | ||||||||
\(429\) | 6.05083 | 0.292137 | ||||||||
\(430\) | −4.27293 | −0.206059 | ||||||||
\(431\) | −39.8994 | −1.92189 | −0.960943 | − | 0.276746i | \(-0.910744\pi\) | ||||
−0.960943 | + | 0.276746i | \(0.910744\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 40.2106 | 1.93240 | 0.966200 | − | 0.257795i | \(-0.0829959\pi\) | ||||
0.966200 | + | 0.257795i | \(0.0829959\pi\) | |||||||
\(434\) | 4.55487 | 0.218641 | ||||||||
\(435\) | 0.720074 | 0.0345249 | ||||||||
\(436\) | 0.168419 | 0.00806582 | ||||||||
\(437\) | 0.165365 | 0.00791047 | ||||||||
\(438\) | 7.93920 | 0.379350 | ||||||||
\(439\) | 3.05387 | 0.145753 | 0.0728767 | − | 0.997341i | \(-0.476782\pi\) | ||||
0.0728767 | + | 0.997341i | \(0.476782\pi\) | |||||||
\(440\) | 0.871541 | 0.0415491 | ||||||||
\(441\) | −3.79035 | −0.180493 | ||||||||
\(442\) | 25.9046 | 1.23215 | ||||||||
\(443\) | 24.4029 | 1.15942 | 0.579709 | − | 0.814824i | \(-0.303166\pi\) | ||||
0.579709 | + | 0.814824i | \(0.303166\pi\) | |||||||
\(444\) | −11.6827 | −0.554435 | ||||||||
\(445\) | −3.93327 | −0.186455 | ||||||||
\(446\) | −21.0135 | −0.995018 | ||||||||
\(447\) | 21.5424 | 1.01892 | ||||||||
\(448\) | 1.79155 | 0.0846427 | ||||||||
\(449\) | 20.0453 | 0.945995 | 0.472998 | − | 0.881064i | \(-0.343172\pi\) | ||||
0.472998 | + | 0.881064i | \(0.343172\pi\) | |||||||
\(450\) | −4.24042 | −0.199895 | ||||||||
\(451\) | 1.92808 | 0.0907895 | ||||||||
\(452\) | 12.0336 | 0.566013 | ||||||||
\(453\) | 7.30147 | 0.343053 | ||||||||
\(454\) | −27.1121 | −1.27243 | ||||||||
\(455\) | 9.44782 | 0.442921 | ||||||||
\(456\) | −0.502442 | −0.0235290 | ||||||||
\(457\) | −19.3350 | −0.904451 | −0.452226 | − | 0.891904i | \(-0.649370\pi\) | ||||
−0.452226 | + | 0.891904i | \(0.649370\pi\) | |||||||
\(458\) | 16.6742 | 0.779136 | ||||||||
\(459\) | 4.28116 | 0.199827 | ||||||||
\(460\) | −0.286843 | −0.0133741 | ||||||||
\(461\) | −33.8556 | −1.57681 | −0.788406 | − | 0.615155i | \(-0.789093\pi\) | ||||
−0.788406 | + | 0.615155i | \(0.789093\pi\) | |||||||
\(462\) | 1.79155 | 0.0833504 | ||||||||
\(463\) | 24.0563 | 1.11799 | 0.558996 | − | 0.829170i | \(-0.311187\pi\) | ||||
0.558996 | + | 0.829170i | \(0.311187\pi\) | |||||||
\(464\) | 0.826208 | 0.0383557 | ||||||||
\(465\) | 2.21582 | 0.102756 | ||||||||
\(466\) | 7.53921 | 0.349247 | ||||||||
\(467\) | 34.5776 | 1.60006 | 0.800030 | − | 0.599960i | \(-0.204817\pi\) | ||||
0.800030 | + | 0.599960i | \(0.204817\pi\) | |||||||
\(468\) | 6.05083 | 0.279700 | ||||||||
\(469\) | 5.80667 | 0.268127 | ||||||||
\(470\) | −8.01214 | −0.369573 | ||||||||
\(471\) | −16.8390 | −0.775901 | ||||||||
\(472\) | −5.77799 | −0.265953 | ||||||||
\(473\) | −4.90273 | −0.225428 | ||||||||
\(474\) | 12.1924 | 0.560017 | ||||||||
\(475\) | 2.13056 | 0.0977570 | ||||||||
\(476\) | 7.66990 | 0.351549 | ||||||||
\(477\) | 0.198049 | 0.00906802 | ||||||||
\(478\) | −26.0180 | −1.19004 | ||||||||
\(479\) | 15.7430 | 0.719315 | 0.359657 | − | 0.933084i | \(-0.382894\pi\) | ||||
0.359657 | + | 0.933084i | \(0.382894\pi\) | |||||||
\(480\) | 0.871541 | 0.0397802 | ||||||||
\(481\) | −70.6899 | −3.22318 | ||||||||
\(482\) | −23.7245 | −1.08062 | ||||||||
\(483\) | −0.589638 | −0.0268295 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 8.31055 | 0.377363 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 3.71321 | 0.168262 | 0.0841308 | − | 0.996455i | \(-0.473189\pi\) | ||||
0.0841308 | + | 0.996455i | \(0.473189\pi\) | |||||||
\(488\) | −1.00000 | −0.0452679 | ||||||||
\(489\) | 19.9962 | 0.904259 | ||||||||
\(490\) | −3.30345 | −0.149235 | ||||||||
\(491\) | −34.7263 | −1.56718 | −0.783588 | − | 0.621281i | \(-0.786613\pi\) | ||||
−0.783588 | + | 0.621281i | \(0.786613\pi\) | |||||||
\(492\) | 1.92808 | 0.0869244 | ||||||||
\(493\) | 3.53713 | 0.159304 | ||||||||
\(494\) | −3.04019 | −0.136785 | ||||||||
\(495\) | 0.871541 | 0.0391729 | ||||||||
\(496\) | 2.54242 | 0.114158 | ||||||||
\(497\) | −13.6753 | −0.613419 | ||||||||
\(498\) | −5.33038 | −0.238860 | ||||||||
\(499\) | 8.45034 | 0.378289 | 0.189145 | − | 0.981949i | \(-0.439429\pi\) | ||||
0.189145 | + | 0.981949i | \(0.439429\pi\) | |||||||
\(500\) | −8.05340 | −0.360159 | ||||||||
\(501\) | −5.96323 | −0.266417 | ||||||||
\(502\) | 17.2264 | 0.768853 | ||||||||
\(503\) | −8.67082 | −0.386613 | −0.193306 | − | 0.981138i | \(-0.561921\pi\) | ||||
−0.193306 | + | 0.981138i | \(0.561921\pi\) | |||||||
\(504\) | 1.79155 | 0.0798019 | ||||||||
\(505\) | −0.155805 | −0.00693323 | ||||||||
\(506\) | −0.329122 | −0.0146312 | ||||||||
\(507\) | 23.6126 | 1.04867 | ||||||||
\(508\) | 13.2035 | 0.585810 | ||||||||
\(509\) | −30.2899 | −1.34258 | −0.671288 | − | 0.741197i | \(-0.734258\pi\) | ||||
−0.671288 | + | 0.741197i | \(0.734258\pi\) | |||||||
\(510\) | 3.73121 | 0.165221 | ||||||||
\(511\) | 14.2235 | 0.629209 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.502442 | −0.0221834 | ||||||||
\(514\) | 14.9836 | 0.660897 | ||||||||
\(515\) | −1.36322 | −0.0600706 | ||||||||
\(516\) | −4.90273 | −0.215831 | ||||||||
\(517\) | −9.19307 | −0.404311 | ||||||||
\(518\) | −20.9301 | −0.919616 | ||||||||
\(519\) | 2.13158 | 0.0935662 | ||||||||
\(520\) | 5.27355 | 0.231260 | ||||||||
\(521\) | −30.7393 | −1.34671 | −0.673356 | − | 0.739318i | \(-0.735148\pi\) | ||||
−0.673356 | + | 0.739318i | \(0.735148\pi\) | |||||||
\(522\) | 0.826208 | 0.0361621 | ||||||||
\(523\) | 31.2904 | 1.36823 | 0.684117 | − | 0.729373i | \(-0.260188\pi\) | ||||
0.684117 | + | 0.729373i | \(0.260188\pi\) | |||||||
\(524\) | −0.292814 | −0.0127916 | ||||||||
\(525\) | −7.59691 | −0.331557 | ||||||||
\(526\) | 6.28404 | 0.273997 | ||||||||
\(527\) | 10.8845 | 0.474136 | ||||||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | −22.8917 | −0.995290 | ||||||||
\(530\) | 0.172607 | 0.00749759 | ||||||||
\(531\) | −5.77799 | −0.250743 | ||||||||
\(532\) | −0.900150 | −0.0390265 | ||||||||
\(533\) | 11.6665 | 0.505331 | ||||||||
\(534\) | −4.51300 | −0.195297 | ||||||||
\(535\) | −3.29003 | −0.142241 | ||||||||
\(536\) | 3.24114 | 0.139996 | ||||||||
\(537\) | 4.23721 | 0.182849 | ||||||||
\(538\) | −19.9982 | −0.862183 | ||||||||
\(539\) | −3.79035 | −0.163262 | ||||||||
\(540\) | 0.871541 | 0.0375052 | ||||||||
\(541\) | 8.22017 | 0.353413 | 0.176706 | − | 0.984264i | \(-0.443456\pi\) | ||||
0.176706 | + | 0.984264i | \(0.443456\pi\) | |||||||
\(542\) | 5.33390 | 0.229111 | ||||||||
\(543\) | 18.4965 | 0.793760 | ||||||||
\(544\) | 4.28116 | 0.183553 | ||||||||
\(545\) | 0.146784 | 0.00628755 | ||||||||
\(546\) | 10.8404 | 0.463925 | ||||||||
\(547\) | −31.2358 | −1.33555 | −0.667773 | − | 0.744365i | \(-0.732752\pi\) | ||||
−0.667773 | + | 0.744365i | \(0.732752\pi\) | |||||||
\(548\) | −13.4359 | −0.573954 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | −4.24042 | −0.180812 | ||||||||
\(551\) | −0.415122 | −0.0176848 | ||||||||
\(552\) | −0.329122 | −0.0140084 | ||||||||
\(553\) | 21.8433 | 0.928874 | ||||||||
\(554\) | −13.2945 | −0.564831 | ||||||||
\(555\) | −10.1819 | −0.432199 | ||||||||
\(556\) | −18.9380 | −0.803150 | ||||||||
\(557\) | −12.4285 | −0.526613 | −0.263307 | − | 0.964712i | \(-0.584813\pi\) | ||||
−0.263307 | + | 0.964712i | \(0.584813\pi\) | |||||||
\(558\) | 2.54242 | 0.107629 | ||||||||
\(559\) | −29.6656 | −1.25472 | ||||||||
\(560\) | 1.56141 | 0.0659816 | ||||||||
\(561\) | 4.28116 | 0.180751 | ||||||||
\(562\) | 0.315638 | 0.0133144 | ||||||||
\(563\) | −4.07195 | −0.171612 | −0.0858062 | − | 0.996312i | \(-0.527347\pi\) | ||||
−0.0858062 | + | 0.996312i | \(0.527347\pi\) | |||||||
\(564\) | −9.19307 | −0.387098 | ||||||||
\(565\) | 10.4878 | 0.441225 | ||||||||
\(566\) | 0.146911 | 0.00617514 | ||||||||
\(567\) | 1.79155 | 0.0752380 | ||||||||
\(568\) | −7.63320 | −0.320282 | ||||||||
\(569\) | 36.9313 | 1.54824 | 0.774120 | − | 0.633039i | \(-0.218193\pi\) | ||||
0.774120 | + | 0.633039i | \(0.218193\pi\) | |||||||
\(570\) | −0.437899 | −0.0183416 | ||||||||
\(571\) | −22.1626 | −0.927478 | −0.463739 | − | 0.885972i | \(-0.653492\pi\) | ||||
−0.463739 | + | 0.885972i | \(0.653492\pi\) | |||||||
\(572\) | 6.05083 | 0.252998 | ||||||||
\(573\) | −15.3727 | −0.642204 | ||||||||
\(574\) | 3.45424 | 0.144177 | ||||||||
\(575\) | 1.39561 | 0.0582011 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −21.4524 | −0.893074 | −0.446537 | − | 0.894765i | \(-0.647343\pi\) | ||||
−0.446537 | + | 0.894765i | \(0.647343\pi\) | |||||||
\(578\) | 1.32831 | 0.0552503 | ||||||||
\(579\) | 7.25371 | 0.301454 | ||||||||
\(580\) | 0.720074 | 0.0298995 | ||||||||
\(581\) | −9.54964 | −0.396186 | ||||||||
\(582\) | 9.53546 | 0.395258 | ||||||||
\(583\) | 0.198049 | 0.00820233 | ||||||||
\(584\) | 7.93920 | 0.328526 | ||||||||
\(585\) | 5.27355 | 0.218034 | ||||||||
\(586\) | −31.8915 | −1.31743 | ||||||||
\(587\) | 41.7377 | 1.72270 | 0.861350 | − | 0.508012i | \(-0.169620\pi\) | ||||
0.861350 | + | 0.508012i | \(0.169620\pi\) | |||||||
\(588\) | −3.79035 | −0.156311 | ||||||||
\(589\) | −1.27742 | −0.0526351 | ||||||||
\(590\) | −5.03576 | −0.207319 | ||||||||
\(591\) | 2.95332 | 0.121484 | ||||||||
\(592\) | −11.6827 | −0.480155 | ||||||||
\(593\) | 5.41312 | 0.222290 | 0.111145 | − | 0.993804i | \(-0.464548\pi\) | ||||
0.111145 | + | 0.993804i | \(0.464548\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 6.68464 | 0.274043 | ||||||||
\(596\) | 21.5424 | 0.882412 | ||||||||
\(597\) | 8.65655 | 0.354289 | ||||||||
\(598\) | −1.99146 | −0.0814369 | ||||||||
\(599\) | −19.5160 | −0.797401 | −0.398700 | − | 0.917081i | \(-0.630539\pi\) | ||||
−0.398700 | + | 0.917081i | \(0.630539\pi\) | |||||||
\(600\) | −4.24042 | −0.173114 | ||||||||
\(601\) | 23.3839 | 0.953850 | 0.476925 | − | 0.878944i | \(-0.341751\pi\) | ||||
0.476925 | + | 0.878944i | \(0.341751\pi\) | |||||||
\(602\) | −8.78349 | −0.357988 | ||||||||
\(603\) | 3.24114 | 0.131990 | ||||||||
\(604\) | 7.30147 | 0.297093 | ||||||||
\(605\) | 0.871541 | 0.0354332 | ||||||||
\(606\) | −0.178769 | −0.00726201 | ||||||||
\(607\) | −5.66519 | −0.229943 | −0.114971 | − | 0.993369i | \(-0.536678\pi\) | ||||
−0.114971 | + | 0.993369i | \(0.536678\pi\) | |||||||
\(608\) | −0.502442 | −0.0203767 | ||||||||
\(609\) | 1.48019 | 0.0599804 | ||||||||
\(610\) | −0.871541 | −0.0352877 | ||||||||
\(611\) | −55.6257 | −2.25038 | ||||||||
\(612\) | 4.28116 | 0.173056 | ||||||||
\(613\) | 30.1541 | 1.21791 | 0.608956 | − | 0.793204i | \(-0.291588\pi\) | ||||
0.608956 | + | 0.793204i | \(0.291588\pi\) | |||||||
\(614\) | 3.27266 | 0.132074 | ||||||||
\(615\) | 1.68040 | 0.0677602 | ||||||||
\(616\) | 1.79155 | 0.0721836 | ||||||||
\(617\) | 15.7985 | 0.636026 | 0.318013 | − | 0.948086i | \(-0.396984\pi\) | ||||
0.318013 | + | 0.948086i | \(0.396984\pi\) | |||||||
\(618\) | −1.56415 | −0.0629192 | ||||||||
\(619\) | −40.3515 | −1.62186 | −0.810931 | − | 0.585142i | \(-0.801039\pi\) | ||||
−0.810931 | + | 0.585142i | \(0.801039\pi\) | |||||||
\(620\) | 2.21582 | 0.0889896 | ||||||||
\(621\) | −0.329122 | −0.0132072 | ||||||||
\(622\) | 11.1080 | 0.445390 | ||||||||
\(623\) | −8.08527 | −0.323929 | ||||||||
\(624\) | 6.05083 | 0.242227 | ||||||||
\(625\) | 14.1832 | 0.567328 | ||||||||
\(626\) | −21.1941 | −0.847087 | ||||||||
\(627\) | −0.502442 | −0.0200656 | ||||||||
\(628\) | −16.8390 | −0.671950 | ||||||||
\(629\) | −50.0154 | −1.99424 | ||||||||
\(630\) | 1.56141 | 0.0622080 | ||||||||
\(631\) | 15.3245 | 0.610060 | 0.305030 | − | 0.952343i | \(-0.401333\pi\) | ||||
0.305030 | + | 0.952343i | \(0.401333\pi\) | |||||||
\(632\) | 12.1924 | 0.484989 | ||||||||
\(633\) | −20.5222 | −0.815684 | ||||||||
\(634\) | −10.5636 | −0.419533 | ||||||||
\(635\) | 11.5074 | 0.456657 | ||||||||
\(636\) | 0.198049 | 0.00785314 | ||||||||
\(637\) | −22.9348 | −0.908709 | ||||||||
\(638\) | 0.826208 | 0.0327099 | ||||||||
\(639\) | −7.63320 | −0.301965 | ||||||||
\(640\) | 0.871541 | 0.0344507 | ||||||||
\(641\) | −4.60133 | −0.181741 | −0.0908707 | − | 0.995863i | \(-0.528965\pi\) | ||||
−0.0908707 | + | 0.995863i | \(0.528965\pi\) | |||||||
\(642\) | −3.77496 | −0.148986 | ||||||||
\(643\) | 26.3732 | 1.04006 | 0.520028 | − | 0.854149i | \(-0.325921\pi\) | ||||
0.520028 | + | 0.854149i | \(0.325921\pi\) | |||||||
\(644\) | −0.589638 | −0.0232350 | ||||||||
\(645\) | −4.27293 | −0.168247 | ||||||||
\(646\) | −2.15104 | −0.0846313 | ||||||||
\(647\) | −14.3028 | −0.562300 | −0.281150 | − | 0.959664i | \(-0.590716\pi\) | ||||
−0.281150 | + | 0.959664i | \(0.590716\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −5.77799 | −0.226806 | ||||||||
\(650\) | −25.6580 | −1.00639 | ||||||||
\(651\) | 4.55487 | 0.178519 | ||||||||
\(652\) | 19.9962 | 0.783111 | ||||||||
\(653\) | −12.7098 | −0.497371 | −0.248686 | − | 0.968584i | \(-0.579999\pi\) | ||||
−0.248686 | + | 0.968584i | \(0.579999\pi\) | |||||||
\(654\) | 0.168419 | 0.00658571 | ||||||||
\(655\) | −0.255199 | −0.00997146 | ||||||||
\(656\) | 1.92808 | 0.0752787 | ||||||||
\(657\) | 7.93920 | 0.309738 | ||||||||
\(658\) | −16.4698 | −0.642061 | ||||||||
\(659\) | −40.4796 | −1.57686 | −0.788430 | − | 0.615124i | \(-0.789106\pi\) | ||||
−0.788430 | + | 0.615124i | \(0.789106\pi\) | |||||||
\(660\) | 0.871541 | 0.0339247 | ||||||||
\(661\) | 18.5910 | 0.723104 | 0.361552 | − | 0.932352i | \(-0.382247\pi\) | ||||
0.361552 | + | 0.932352i | \(0.382247\pi\) | |||||||
\(662\) | 26.7220 | 1.03858 | ||||||||
\(663\) | 25.9046 | 1.00605 | ||||||||
\(664\) | −5.33038 | −0.206859 | ||||||||
\(665\) | −0.784518 | −0.0304223 | ||||||||
\(666\) | −11.6827 | −0.452695 | ||||||||
\(667\) | −0.271923 | −0.0105289 | ||||||||
\(668\) | −5.96323 | −0.230724 | ||||||||
\(669\) | −21.0135 | −0.812429 | ||||||||
\(670\) | 2.82479 | 0.109131 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 1.79155 | 0.0691105 | ||||||||
\(673\) | −13.3367 | −0.514091 | −0.257045 | − | 0.966399i | \(-0.582749\pi\) | ||||
−0.257045 | + | 0.966399i | \(0.582749\pi\) | |||||||
\(674\) | 14.8452 | 0.571815 | ||||||||
\(675\) | −4.24042 | −0.163214 | ||||||||
\(676\) | 23.6126 | 0.908175 | ||||||||
\(677\) | 25.7955 | 0.991402 | 0.495701 | − | 0.868493i | \(-0.334911\pi\) | ||||
0.495701 | + | 0.868493i | \(0.334911\pi\) | |||||||
\(678\) | 12.0336 | 0.462148 | ||||||||
\(679\) | 17.0832 | 0.655595 | ||||||||
\(680\) | 3.73121 | 0.143085 | ||||||||
\(681\) | −27.1121 | −1.03894 | ||||||||
\(682\) | 2.54242 | 0.0973543 | ||||||||
\(683\) | −2.30888 | −0.0883468 | −0.0441734 | − | 0.999024i | \(-0.514065\pi\) | ||||
−0.0441734 | + | 0.999024i | \(0.514065\pi\) | |||||||
\(684\) | −0.502442 | −0.0192114 | ||||||||
\(685\) | −11.7100 | −0.447415 | ||||||||
\(686\) | −19.3314 | −0.738078 | ||||||||
\(687\) | 16.6742 | 0.636162 | ||||||||
\(688\) | −4.90273 | −0.186915 | ||||||||
\(689\) | 1.19836 | 0.0456538 | ||||||||
\(690\) | −0.286843 | −0.0109199 | ||||||||
\(691\) | 23.5170 | 0.894630 | 0.447315 | − | 0.894376i | \(-0.352380\pi\) | ||||
0.447315 | + | 0.894376i | \(0.352380\pi\) | |||||||
\(692\) | 2.13158 | 0.0810307 | ||||||||
\(693\) | 1.79155 | 0.0680553 | ||||||||
\(694\) | 32.2966 | 1.22596 | ||||||||
\(695\) | −16.5052 | −0.626080 | ||||||||
\(696\) | 0.826208 | 0.0313173 | ||||||||
\(697\) | 8.25440 | 0.312658 | ||||||||
\(698\) | 19.0687 | 0.721762 | ||||||||
\(699\) | 7.53921 | 0.285159 | ||||||||
\(700\) | −7.59691 | −0.287136 | ||||||||
\(701\) | 4.93652 | 0.186450 | 0.0932249 | − | 0.995645i | \(-0.470282\pi\) | ||||
0.0932249 | + | 0.995645i | \(0.470282\pi\) | |||||||
\(702\) | 6.05083 | 0.228374 | ||||||||
\(703\) | 5.86987 | 0.221387 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −8.01214 | −0.301755 | ||||||||
\(706\) | −24.7218 | −0.930419 | ||||||||
\(707\) | −0.320274 | −0.0120451 | ||||||||
\(708\) | −5.77799 | −0.217150 | ||||||||
\(709\) | −15.8317 | −0.594572 | −0.297286 | − | 0.954788i | \(-0.596082\pi\) | ||||
−0.297286 | + | 0.954788i | \(0.596082\pi\) | |||||||
\(710\) | −6.65265 | −0.249670 | ||||||||
\(711\) | 12.1924 | 0.457252 | ||||||||
\(712\) | −4.51300 | −0.169132 | ||||||||
\(713\) | −0.836766 | −0.0313371 | ||||||||
\(714\) | 7.66990 | 0.287039 | ||||||||
\(715\) | 5.27355 | 0.197220 | ||||||||
\(716\) | 4.23721 | 0.158352 | ||||||||
\(717\) | −26.0180 | −0.971661 | ||||||||
\(718\) | 29.6397 | 1.10614 | ||||||||
\(719\) | −9.24628 | −0.344828 | −0.172414 | − | 0.985025i | \(-0.555157\pi\) | ||||
−0.172414 | + | 0.985025i | \(0.555157\pi\) | |||||||
\(720\) | 0.871541 | 0.0324804 | ||||||||
\(721\) | −2.80225 | −0.104361 | ||||||||
\(722\) | −18.7476 | −0.697712 | ||||||||
\(723\) | −23.7245 | −0.882323 | ||||||||
\(724\) | 18.4965 | 0.687417 | ||||||||
\(725\) | −3.50347 | −0.130115 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | 22.9494 | 0.851147 | 0.425574 | − | 0.904924i | \(-0.360072\pi\) | ||||
0.425574 | + | 0.904924i | \(0.360072\pi\) | |||||||
\(728\) | 10.8404 | 0.401771 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.91934 | 0.256096 | ||||||||
\(731\) | −20.9894 | −0.776320 | ||||||||
\(732\) | −1.00000 | −0.0369611 | ||||||||
\(733\) | 25.1109 | 0.927491 | 0.463745 | − | 0.885969i | \(-0.346505\pi\) | ||||
0.463745 | + | 0.885969i | \(0.346505\pi\) | |||||||
\(734\) | −2.72541 | −0.100597 | ||||||||
\(735\) | −3.30345 | −0.121849 | ||||||||
\(736\) | −0.329122 | −0.0121316 | ||||||||
\(737\) | 3.24114 | 0.119389 | ||||||||
\(738\) | 1.92808 | 0.0709735 | ||||||||
\(739\) | −45.7398 | −1.68257 | −0.841283 | − | 0.540595i | \(-0.818199\pi\) | ||||
−0.841283 | + | 0.540595i | \(0.818199\pi\) | |||||||
\(740\) | −10.1819 | −0.374296 | ||||||||
\(741\) | −3.04019 | −0.111684 | ||||||||
\(742\) | 0.354814 | 0.0130256 | ||||||||
\(743\) | −29.0108 | −1.06430 | −0.532152 | − | 0.846649i | \(-0.678617\pi\) | ||||
−0.532152 | + | 0.846649i | \(0.678617\pi\) | |||||||
\(744\) | 2.54242 | 0.0932096 | ||||||||
\(745\) | 18.7751 | 0.687867 | ||||||||
\(746\) | 25.8653 | 0.946997 | ||||||||
\(747\) | −5.33038 | −0.195028 | ||||||||
\(748\) | 4.28116 | 0.156535 | ||||||||
\(749\) | −6.76303 | −0.247116 | ||||||||
\(750\) | −8.05340 | −0.294069 | ||||||||
\(751\) | −17.1099 | −0.624350 | −0.312175 | − | 0.950025i | \(-0.601057\pi\) | ||||
−0.312175 | + | 0.950025i | \(0.601057\pi\) | |||||||
\(752\) | −9.19307 | −0.335237 | ||||||||
\(753\) | 17.2264 | 0.627766 | ||||||||
\(754\) | 4.99924 | 0.182062 | ||||||||
\(755\) | 6.36353 | 0.231593 | ||||||||
\(756\) | 1.79155 | 0.0651580 | ||||||||
\(757\) | 51.1697 | 1.85980 | 0.929898 | − | 0.367819i | \(-0.119895\pi\) | ||||
0.929898 | + | 0.367819i | \(0.119895\pi\) | |||||||
\(758\) | −29.8825 | −1.08538 | ||||||||
\(759\) | −0.329122 | −0.0119464 | ||||||||
\(760\) | −0.437899 | −0.0158843 | ||||||||
\(761\) | −4.71107 | −0.170776 | −0.0853881 | − | 0.996348i | \(-0.527213\pi\) | ||||
−0.0853881 | + | 0.996348i | \(0.527213\pi\) | |||||||
\(762\) | 13.2035 | 0.478312 | ||||||||
\(763\) | 0.301731 | 0.0109234 | ||||||||
\(764\) | −15.3727 | −0.556165 | ||||||||
\(765\) | 3.73121 | 0.134902 | ||||||||
\(766\) | −32.6319 | −1.17904 | ||||||||
\(767\) | −34.9616 | −1.26239 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 43.7160 | 1.57644 | 0.788220 | − | 0.615394i | \(-0.211003\pi\) | ||||
0.788220 | + | 0.615394i | \(0.211003\pi\) | |||||||
\(770\) | 1.56141 | 0.0562693 | ||||||||
\(771\) | 14.9836 | 0.539620 | ||||||||
\(772\) | 7.25371 | 0.261067 | ||||||||
\(773\) | 11.7670 | 0.423229 | 0.211615 | − | 0.977353i | \(-0.432128\pi\) | ||||
0.211615 | + | 0.977353i | \(0.432128\pi\) | |||||||
\(774\) | −4.90273 | −0.176225 | ||||||||
\(775\) | −10.7809 | −0.387262 | ||||||||
\(776\) | 9.53546 | 0.342303 | ||||||||
\(777\) | −20.9301 | −0.750863 | ||||||||
\(778\) | −24.7562 | −0.887554 | ||||||||
\(779\) | −0.968747 | −0.0347090 | ||||||||
\(780\) | 5.27355 | 0.188823 | ||||||||
\(781\) | −7.63320 | −0.273137 | ||||||||
\(782\) | −1.40902 | −0.0503865 | ||||||||
\(783\) | 0.826208 | 0.0295263 | ||||||||
\(784\) | −3.79035 | −0.135370 | ||||||||
\(785\) | −14.6759 | −0.523805 | ||||||||
\(786\) | −0.292814 | −0.0104443 | ||||||||
\(787\) | −1.27956 | −0.0456114 | −0.0228057 | − | 0.999740i | \(-0.507260\pi\) | ||||
−0.0228057 | + | 0.999740i | \(0.507260\pi\) | |||||||
\(788\) | 2.95332 | 0.105208 | ||||||||
\(789\) | 6.28404 | 0.223718 | ||||||||
\(790\) | 10.6262 | 0.378064 | ||||||||
\(791\) | 21.5588 | 0.766543 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | −6.05083 | −0.214871 | ||||||||
\(794\) | −8.25865 | −0.293088 | ||||||||
\(795\) | 0.172607 | 0.00612176 | ||||||||
\(796\) | 8.65655 | 0.306823 | ||||||||
\(797\) | −28.8178 | −1.02078 | −0.510390 | − | 0.859943i | \(-0.670499\pi\) | ||||
−0.510390 | + | 0.859943i | \(0.670499\pi\) | |||||||
\(798\) | −0.900150 | −0.0318650 | ||||||||
\(799\) | −39.3570 | −1.39235 | ||||||||
\(800\) | −4.24042 | −0.149921 | ||||||||
\(801\) | −4.51300 | −0.159459 | ||||||||
\(802\) | 10.5654 | 0.373079 | ||||||||
\(803\) | 7.93920 | 0.280168 | ||||||||
\(804\) | 3.24114 | 0.114306 | ||||||||
\(805\) | −0.513894 | −0.0181124 | ||||||||
\(806\) | 15.3837 | 0.541869 | ||||||||
\(807\) | −19.9982 | −0.703970 | ||||||||
\(808\) | −0.178769 | −0.00628908 | ||||||||
\(809\) | 15.0691 | 0.529800 | 0.264900 | − | 0.964276i | \(-0.414661\pi\) | ||||
0.264900 | + | 0.964276i | \(0.414661\pi\) | |||||||
\(810\) | 0.871541 | 0.0306228 | ||||||||
\(811\) | −28.7549 | −1.00972 | −0.504861 | − | 0.863201i | \(-0.668456\pi\) | ||||
−0.504861 | + | 0.863201i | \(0.668456\pi\) | |||||||
\(812\) | 1.48019 | 0.0519446 | ||||||||
\(813\) | 5.33390 | 0.187068 | ||||||||
\(814\) | −11.6827 | −0.409478 | ||||||||
\(815\) | 17.4275 | 0.610459 | ||||||||
\(816\) | 4.28116 | 0.149870 | ||||||||
\(817\) | 2.46334 | 0.0861814 | ||||||||
\(818\) | 31.0066 | 1.08412 | ||||||||
\(819\) | 10.8404 | 0.378793 | ||||||||
\(820\) | 1.68040 | 0.0586820 | ||||||||
\(821\) | 41.2780 | 1.44061 | 0.720307 | − | 0.693656i | \(-0.244001\pi\) | ||||
0.720307 | + | 0.693656i | \(0.244001\pi\) | |||||||
\(822\) | −13.4359 | −0.468632 | ||||||||
\(823\) | −33.0229 | −1.15111 | −0.575554 | − | 0.817764i | \(-0.695213\pi\) | ||||
−0.575554 | + | 0.817764i | \(0.695213\pi\) | |||||||
\(824\) | −1.56415 | −0.0544896 | ||||||||
\(825\) | −4.24042 | −0.147632 | ||||||||
\(826\) | −10.3516 | −0.360177 | ||||||||
\(827\) | 21.1263 | 0.734632 | 0.367316 | − | 0.930096i | \(-0.380277\pi\) | ||||
0.367316 | + | 0.930096i | \(0.380277\pi\) | |||||||
\(828\) | −0.329122 | −0.0114378 | ||||||||
\(829\) | 20.0800 | 0.697409 | 0.348704 | − | 0.937233i | \(-0.386622\pi\) | ||||
0.348704 | + | 0.937233i | \(0.386622\pi\) | |||||||
\(830\) | −4.64565 | −0.161253 | ||||||||
\(831\) | −13.2945 | −0.461182 | ||||||||
\(832\) | 6.05083 | 0.209775 | ||||||||
\(833\) | −16.2271 | −0.562235 | ||||||||
\(834\) | −18.9380 | −0.655769 | ||||||||
\(835\) | −5.19720 | −0.179856 | ||||||||
\(836\) | −0.502442 | −0.0173773 | ||||||||
\(837\) | 2.54242 | 0.0878789 | ||||||||
\(838\) | −6.83731 | −0.236191 | ||||||||
\(839\) | 11.8308 | 0.408443 | 0.204222 | − | 0.978925i | \(-0.434534\pi\) | ||||
0.204222 | + | 0.978925i | \(0.434534\pi\) | |||||||
\(840\) | 1.56141 | 0.0538737 | ||||||||
\(841\) | −28.3174 | −0.976461 | ||||||||
\(842\) | 27.9306 | 0.962552 | ||||||||
\(843\) | 0.315638 | 0.0108712 | ||||||||
\(844\) | −20.5222 | −0.706403 | ||||||||
\(845\) | 20.5793 | 0.707950 | ||||||||
\(846\) | −9.19307 | −0.316064 | ||||||||
\(847\) | 1.79155 | 0.0615584 | ||||||||
\(848\) | 0.198049 | 0.00680102 | ||||||||
\(849\) | 0.146911 | 0.00504198 | ||||||||
\(850\) | −18.1539 | −0.622673 | ||||||||
\(851\) | 3.84503 | 0.131806 | ||||||||
\(852\) | −7.63320 | −0.261509 | ||||||||
\(853\) | 8.86844 | 0.303650 | 0.151825 | − | 0.988407i | \(-0.451485\pi\) | ||||
0.151825 | + | 0.988407i | \(0.451485\pi\) | |||||||
\(854\) | −1.79155 | −0.0613056 | ||||||||
\(855\) | −0.437899 | −0.0149758 | ||||||||
\(856\) | −3.77496 | −0.129025 | ||||||||
\(857\) | 37.6326 | 1.28551 | 0.642753 | − | 0.766074i | \(-0.277792\pi\) | ||||
0.642753 | + | 0.766074i | \(0.277792\pi\) | |||||||
\(858\) | 6.05083 | 0.206572 | ||||||||
\(859\) | 43.4331 | 1.48192 | 0.740960 | − | 0.671550i | \(-0.234371\pi\) | ||||
0.740960 | + | 0.671550i | \(0.234371\pi\) | |||||||
\(860\) | −4.27293 | −0.145706 | ||||||||
\(861\) | 3.45424 | 0.117720 | ||||||||
\(862\) | −39.8994 | −1.35898 | ||||||||
\(863\) | −31.7604 | −1.08114 | −0.540568 | − | 0.841301i | \(-0.681790\pi\) | ||||
−0.540568 | + | 0.841301i | \(0.681790\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 1.85776 | 0.0631659 | ||||||||
\(866\) | 40.2106 | 1.36641 | ||||||||
\(867\) | 1.32831 | 0.0451117 | ||||||||
\(868\) | 4.55487 | 0.154602 | ||||||||
\(869\) | 12.1924 | 0.413600 | ||||||||
\(870\) | 0.720074 | 0.0244128 | ||||||||
\(871\) | 19.6116 | 0.664514 | ||||||||
\(872\) | 0.168419 | 0.00570339 | ||||||||
\(873\) | 9.53546 | 0.322726 | ||||||||
\(874\) | 0.165365 | 0.00559355 | ||||||||
\(875\) | −14.4281 | −0.487758 | ||||||||
\(876\) | 7.93920 | 0.268241 | ||||||||
\(877\) | −45.6417 | −1.54121 | −0.770605 | − | 0.637313i | \(-0.780046\pi\) | ||||
−0.770605 | + | 0.637313i | \(0.780046\pi\) | |||||||
\(878\) | 3.05387 | 0.103063 | ||||||||
\(879\) | −31.8915 | −1.07567 | ||||||||
\(880\) | 0.871541 | 0.0293797 | ||||||||
\(881\) | −42.3932 | −1.42826 | −0.714132 | − | 0.700011i | \(-0.753179\pi\) | ||||
−0.714132 | + | 0.700011i | \(0.753179\pi\) | |||||||
\(882\) | −3.79035 | −0.127628 | ||||||||
\(883\) | −9.14185 | −0.307648 | −0.153824 | − | 0.988098i | \(-0.549159\pi\) | ||||
−0.153824 | + | 0.988098i | \(0.549159\pi\) | |||||||
\(884\) | 25.9046 | 0.871265 | ||||||||
\(885\) | −5.03576 | −0.169275 | ||||||||
\(886\) | 24.4029 | 0.819832 | ||||||||
\(887\) | −27.1358 | −0.911131 | −0.455565 | − | 0.890202i | \(-0.650563\pi\) | ||||
−0.455565 | + | 0.890202i | \(0.650563\pi\) | |||||||
\(888\) | −11.6827 | −0.392045 | ||||||||
\(889\) | 23.6547 | 0.793353 | ||||||||
\(890\) | −3.93327 | −0.131843 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −21.0135 | −0.703584 | ||||||||
\(893\) | 4.61899 | 0.154569 | ||||||||
\(894\) | 21.5424 | 0.720486 | ||||||||
\(895\) | 3.69290 | 0.123440 | ||||||||
\(896\) | 1.79155 | 0.0598515 | ||||||||
\(897\) | −1.99146 | −0.0664929 | ||||||||
\(898\) | 20.0453 | 0.668920 | ||||||||
\(899\) | 2.10057 | 0.0700578 | ||||||||
\(900\) | −4.24042 | −0.141347 | ||||||||
\(901\) | 0.847877 | 0.0282469 | ||||||||
\(902\) | 1.92808 | 0.0641979 | ||||||||
\(903\) | −8.78349 | −0.292296 | ||||||||
\(904\) | 12.0336 | 0.400232 | ||||||||
\(905\) | 16.1205 | 0.535862 | ||||||||
\(906\) | 7.30147 | 0.242575 | ||||||||
\(907\) | −34.4559 | −1.14409 | −0.572045 | − | 0.820222i | \(-0.693850\pi\) | ||||
−0.572045 | + | 0.820222i | \(0.693850\pi\) | |||||||
\(908\) | −27.1121 | −0.899747 | ||||||||
\(909\) | −0.178769 | −0.00592941 | ||||||||
\(910\) | 9.44782 | 0.313192 | ||||||||
\(911\) | 45.0367 | 1.49213 | 0.746067 | − | 0.665871i | \(-0.231940\pi\) | ||||
0.746067 | + | 0.665871i | \(0.231940\pi\) | |||||||
\(912\) | −0.502442 | −0.0166375 | ||||||||
\(913\) | −5.33038 | −0.176410 | ||||||||
\(914\) | −19.3350 | −0.639544 | ||||||||
\(915\) | −0.871541 | −0.0288123 | ||||||||
\(916\) | 16.6742 | 0.550932 | ||||||||
\(917\) | −0.524590 | −0.0173235 | ||||||||
\(918\) | 4.28116 | 0.141299 | ||||||||
\(919\) | −5.52206 | −0.182156 | −0.0910780 | − | 0.995844i | \(-0.529031\pi\) | ||||
−0.0910780 | + | 0.995844i | \(0.529031\pi\) | |||||||
\(920\) | −0.286843 | −0.00945694 | ||||||||
\(921\) | 3.27266 | 0.107838 | ||||||||
\(922\) | −33.8556 | −1.11497 | ||||||||
\(923\) | −46.1872 | −1.52027 | ||||||||
\(924\) | 1.79155 | 0.0589376 | ||||||||
\(925\) | 49.5394 | 1.62885 | ||||||||
\(926\) | 24.0563 | 0.790540 | ||||||||
\(927\) | −1.56415 | −0.0513733 | ||||||||
\(928\) | 0.826208 | 0.0271216 | ||||||||
\(929\) | −11.5449 | −0.378777 | −0.189388 | − | 0.981902i | \(-0.560650\pi\) | ||||
−0.189388 | + | 0.981902i | \(0.560650\pi\) | |||||||
\(930\) | 2.21582 | 0.0726597 | ||||||||
\(931\) | 1.90443 | 0.0624153 | ||||||||
\(932\) | 7.53921 | 0.246955 | ||||||||
\(933\) | 11.1080 | 0.363660 | ||||||||
\(934\) | 34.5776 | 1.13141 | ||||||||
\(935\) | 3.73121 | 0.122023 | ||||||||
\(936\) | 6.05083 | 0.197778 | ||||||||
\(937\) | 18.9532 | 0.619176 | 0.309588 | − | 0.950871i | \(-0.399809\pi\) | ||||
0.309588 | + | 0.950871i | \(0.399809\pi\) | |||||||
\(938\) | 5.80667 | 0.189594 | ||||||||
\(939\) | −21.1941 | −0.691644 | ||||||||
\(940\) | −8.01214 | −0.261327 | ||||||||
\(941\) | −32.9889 | −1.07541 | −0.537704 | − | 0.843133i | \(-0.680708\pi\) | ||||
−0.537704 | + | 0.843133i | \(0.680708\pi\) | |||||||
\(942\) | −16.8390 | −0.548645 | ||||||||
\(943\) | −0.634572 | −0.0206645 | ||||||||
\(944\) | −5.77799 | −0.188058 | ||||||||
\(945\) | 1.56141 | 0.0507926 | ||||||||
\(946\) | −4.90273 | −0.159402 | ||||||||
\(947\) | 32.9216 | 1.06981 | 0.534904 | − | 0.844913i | \(-0.320348\pi\) | ||||
0.534904 | + | 0.844913i | \(0.320348\pi\) | |||||||
\(948\) | 12.1924 | 0.395992 | ||||||||
\(949\) | 48.0388 | 1.55940 | ||||||||
\(950\) | 2.13056 | 0.0691246 | ||||||||
\(951\) | −10.5636 | −0.342547 | ||||||||
\(952\) | 7.66990 | 0.248583 | ||||||||
\(953\) | 38.5330 | 1.24821 | 0.624103 | − | 0.781342i | \(-0.285465\pi\) | ||||
0.624103 | + | 0.781342i | \(0.285465\pi\) | |||||||
\(954\) | 0.198049 | 0.00641206 | ||||||||
\(955\) | −13.3979 | −0.433547 | ||||||||
\(956\) | −26.0180 | −0.841483 | ||||||||
\(957\) | 0.826208 | 0.0267075 | ||||||||
\(958\) | 15.7430 | 0.508632 | ||||||||
\(959\) | −24.0711 | −0.777297 | ||||||||
\(960\) | 0.871541 | 0.0281289 | ||||||||
\(961\) | −24.5361 | −0.791487 | ||||||||
\(962\) | −70.6899 | −2.27913 | ||||||||
\(963\) | −3.77496 | −0.121646 | ||||||||
\(964\) | −23.7245 | −0.764114 | ||||||||
\(965\) | 6.32191 | 0.203509 | ||||||||
\(966\) | −0.589638 | −0.0189713 | ||||||||
\(967\) | 28.0347 | 0.901535 | 0.450767 | − | 0.892641i | \(-0.351150\pi\) | ||||
0.450767 | + | 0.892641i | \(0.351150\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −2.15104 | −0.0691012 | ||||||||
\(970\) | 8.31055 | 0.266836 | ||||||||
\(971\) | −17.3290 | −0.556115 | −0.278057 | − | 0.960565i | \(-0.589690\pi\) | ||||
−0.278057 | + | 0.960565i | \(0.589690\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −33.9283 | −1.08769 | ||||||||
\(974\) | 3.71321 | 0.118979 | ||||||||
\(975\) | −25.6580 | −0.821715 | ||||||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | −2.32402 | −0.0743521 | −0.0371761 | − | 0.999309i | \(-0.511836\pi\) | ||||
−0.0371761 | + | 0.999309i | \(0.511836\pi\) | |||||||
\(978\) | 19.9962 | 0.639408 | ||||||||
\(979\) | −4.51300 | −0.144236 | ||||||||
\(980\) | −3.30345 | −0.105525 | ||||||||
\(981\) | 0.168419 | 0.00537721 | ||||||||
\(982\) | −34.7263 | −1.10816 | ||||||||
\(983\) | −23.4849 | −0.749052 | −0.374526 | − | 0.927216i | \(-0.622195\pi\) | ||||
−0.374526 | + | 0.927216i | \(0.622195\pi\) | |||||||
\(984\) | 1.92808 | 0.0614648 | ||||||||
\(985\) | 2.57394 | 0.0820127 | ||||||||
\(986\) | 3.53713 | 0.112645 | ||||||||
\(987\) | −16.4698 | −0.524241 | ||||||||
\(988\) | −3.04019 | −0.0967215 | ||||||||
\(989\) | 1.61360 | 0.0513094 | ||||||||
\(990\) | 0.871541 | 0.0276994 | ||||||||
\(991\) | 5.88572 | 0.186966 | 0.0934830 | − | 0.995621i | \(-0.470200\pi\) | ||||
0.0934830 | + | 0.995621i | \(0.470200\pi\) | |||||||
\(992\) | 2.54242 | 0.0807219 | ||||||||
\(993\) | 26.7220 | 0.847997 | ||||||||
\(994\) | −13.6753 | −0.433753 | ||||||||
\(995\) | 7.54454 | 0.239178 | ||||||||
\(996\) | −5.33038 | −0.168900 | ||||||||
\(997\) | 52.4312 | 1.66051 | 0.830256 | − | 0.557382i | \(-0.188194\pi\) | ||||
0.830256 | + | 0.557382i | \(0.188194\pi\) | |||||||
\(998\) | 8.45034 | 0.267491 | ||||||||
\(999\) | −11.6827 | −0.369624 |
(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 | 4026.2.a.bc.1.5 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.bc.1.5 | ✓ | 9 | 1.1 | even | 1 | trivial |