Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, 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("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.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: | \(32.0759064919\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.05828 | 0.748316 | 0.374158 | − | 0.927365i | \(-0.377932\pi\) | ||||
0.374158 | + | 0.927365i | \(0.377932\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.880046 | −0.440023 | ||||||||
\(5\) | −0.912505 | −0.408085 | −0.204042 | − | 0.978962i | \(-0.565408\pi\) | ||||
−0.204042 | + | 0.978962i | \(0.565408\pi\) | |||||||
\(6\) | −1.05828 | −0.432040 | ||||||||
\(7\) | −3.63309 | −1.37318 | −0.686590 | − | 0.727045i | \(-0.740893\pi\) | ||||
−0.686590 | + | 0.727045i | \(0.740893\pi\) | |||||||
\(8\) | −3.04789 | −1.07759 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.965685 | −0.305376 | ||||||||
\(11\) | −1.15222 | −0.347407 | −0.173703 | − | 0.984798i | \(-0.555573\pi\) | ||||
−0.173703 | + | 0.984798i | \(0.555573\pi\) | |||||||
\(12\) | 0.880046 | 0.254048 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −3.84483 | −1.02757 | ||||||||
\(15\) | 0.912505 | 0.235608 | ||||||||
\(16\) | −1.46543 | −0.366356 | ||||||||
\(17\) | −2.09451 | −0.507994 | −0.253997 | − | 0.967205i | \(-0.581745\pi\) | ||||
−0.253997 | + | 0.967205i | \(0.581745\pi\) | |||||||
\(18\) | 1.05828 | 0.249439 | ||||||||
\(19\) | −0.646012 | −0.148205 | −0.0741027 | − | 0.997251i | \(-0.523609\pi\) | ||||
−0.0741027 | + | 0.997251i | \(0.523609\pi\) | |||||||
\(20\) | 0.803047 | 0.179567 | ||||||||
\(21\) | 3.63309 | 0.792806 | ||||||||
\(22\) | −1.21937 | −0.259970 | ||||||||
\(23\) | −8.89813 | −1.85539 | −0.927694 | − | 0.373341i | \(-0.878212\pi\) | ||||
−0.927694 | + | 0.373341i | \(0.878212\pi\) | |||||||
\(24\) | 3.04789 | 0.622148 | ||||||||
\(25\) | −4.16733 | −0.833467 | ||||||||
\(26\) | −1.05828 | −0.207546 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.19729 | 0.604231 | ||||||||
\(29\) | 3.94970 | 0.733441 | 0.366721 | − | 0.930331i | \(-0.380480\pi\) | ||||
0.366721 | + | 0.930331i | \(0.380480\pi\) | |||||||
\(30\) | 0.965685 | 0.176309 | ||||||||
\(31\) | −4.66229 | −0.837372 | −0.418686 | − | 0.908131i | \(-0.637509\pi\) | ||||
−0.418686 | + | 0.908131i | \(0.637509\pi\) | |||||||
\(32\) | 4.54495 | 0.803442 | ||||||||
\(33\) | 1.15222 | 0.200575 | ||||||||
\(34\) | −2.21658 | −0.380140 | ||||||||
\(35\) | 3.31522 | 0.560374 | ||||||||
\(36\) | −0.880046 | −0.146674 | ||||||||
\(37\) | −1.70522 | −0.280337 | −0.140168 | − | 0.990128i | \(-0.544764\pi\) | ||||
−0.140168 | + | 0.990128i | \(0.544764\pi\) | |||||||
\(38\) | −0.683661 | −0.110904 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 2.78122 | 0.439749 | ||||||||
\(41\) | −8.06085 | −1.25889 | −0.629446 | − | 0.777044i | \(-0.716718\pi\) | ||||
−0.629446 | + | 0.777044i | \(0.716718\pi\) | |||||||
\(42\) | 3.84483 | 0.593269 | ||||||||
\(43\) | 0.912813 | 0.139203 | 0.0696013 | − | 0.997575i | \(-0.477827\pi\) | ||||
0.0696013 | + | 0.997575i | \(0.477827\pi\) | |||||||
\(44\) | 1.01401 | 0.152867 | ||||||||
\(45\) | −0.912505 | −0.136028 | ||||||||
\(46\) | −9.41670 | −1.38842 | ||||||||
\(47\) | 4.88621 | 0.712728 | 0.356364 | − | 0.934347i | \(-0.384016\pi\) | ||||
0.356364 | + | 0.934347i | \(0.384016\pi\) | |||||||
\(48\) | 1.46543 | 0.211516 | ||||||||
\(49\) | 6.19937 | 0.885625 | ||||||||
\(50\) | −4.41020 | −0.623697 | ||||||||
\(51\) | 2.09451 | 0.293291 | ||||||||
\(52\) | 0.880046 | 0.122040 | ||||||||
\(53\) | −3.15100 | −0.432823 | −0.216411 | − | 0.976302i | \(-0.569435\pi\) | ||||
−0.216411 | + | 0.976302i | \(0.569435\pi\) | |||||||
\(54\) | −1.05828 | −0.144013 | ||||||||
\(55\) | 1.05140 | 0.141771 | ||||||||
\(56\) | 11.0733 | 1.47973 | ||||||||
\(57\) | 0.646012 | 0.0855664 | ||||||||
\(58\) | 4.17989 | 0.548846 | ||||||||
\(59\) | 1.05612 | 0.137495 | 0.0687474 | − | 0.997634i | \(-0.478100\pi\) | ||||
0.0687474 | + | 0.997634i | \(0.478100\pi\) | |||||||
\(60\) | −0.803047 | −0.103673 | ||||||||
\(61\) | −4.06408 | −0.520352 | −0.260176 | − | 0.965561i | \(-0.583781\pi\) | ||||
−0.260176 | + | 0.965561i | \(0.583781\pi\) | |||||||
\(62\) | −4.93400 | −0.626619 | ||||||||
\(63\) | −3.63309 | −0.457727 | ||||||||
\(64\) | 7.74068 | 0.967585 | ||||||||
\(65\) | 0.912505 | 0.113182 | ||||||||
\(66\) | 1.21937 | 0.150094 | ||||||||
\(67\) | 3.87694 | 0.473644 | 0.236822 | − | 0.971553i | \(-0.423894\pi\) | ||||
0.236822 | + | 0.971553i | \(0.423894\pi\) | |||||||
\(68\) | 1.84327 | 0.223529 | ||||||||
\(69\) | 8.89813 | 1.07121 | ||||||||
\(70\) | 3.50842 | 0.419337 | ||||||||
\(71\) | 2.77471 | 0.329297 | 0.164649 | − | 0.986352i | \(-0.447351\pi\) | ||||
0.164649 | + | 0.986352i | \(0.447351\pi\) | |||||||
\(72\) | −3.04789 | −0.359197 | ||||||||
\(73\) | −1.56883 | −0.183617 | −0.0918085 | − | 0.995777i | \(-0.529265\pi\) | ||||
−0.0918085 | + | 0.995777i | \(0.529265\pi\) | |||||||
\(74\) | −1.80460 | −0.209780 | ||||||||
\(75\) | 4.16733 | 0.481202 | ||||||||
\(76\) | 0.568521 | 0.0652138 | ||||||||
\(77\) | 4.18612 | 0.477052 | ||||||||
\(78\) | 1.05828 | 0.119826 | ||||||||
\(79\) | 1.26952 | 0.142832 | 0.0714159 | − | 0.997447i | \(-0.477248\pi\) | ||||
0.0714159 | + | 0.997447i | \(0.477248\pi\) | |||||||
\(80\) | 1.33721 | 0.149504 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.53062 | −0.942049 | ||||||||
\(83\) | 13.3649 | 1.46699 | 0.733495 | − | 0.679695i | \(-0.237888\pi\) | ||||
0.733495 | + | 0.679695i | \(0.237888\pi\) | |||||||
\(84\) | −3.19729 | −0.348853 | ||||||||
\(85\) | 1.91125 | 0.207305 | ||||||||
\(86\) | 0.966010 | 0.104168 | ||||||||
\(87\) | −3.94970 | −0.423453 | ||||||||
\(88\) | 3.51183 | 0.374363 | ||||||||
\(89\) | −15.4734 | −1.64018 | −0.820090 | − | 0.572235i | \(-0.806077\pi\) | ||||
−0.820090 | + | 0.572235i | \(0.806077\pi\) | |||||||
\(90\) | −0.965685 | −0.101792 | ||||||||
\(91\) | 3.63309 | 0.380852 | ||||||||
\(92\) | 7.83077 | 0.816414 | ||||||||
\(93\) | 4.66229 | 0.483457 | ||||||||
\(94\) | 5.17098 | 0.533345 | ||||||||
\(95\) | 0.589489 | 0.0604803 | ||||||||
\(96\) | −4.54495 | −0.463867 | ||||||||
\(97\) | 4.91041 | 0.498577 | 0.249288 | − | 0.968429i | \(-0.419803\pi\) | ||||
0.249288 | + | 0.968429i | \(0.419803\pi\) | |||||||
\(98\) | 6.56066 | 0.662727 | ||||||||
\(99\) | −1.15222 | −0.115802 | ||||||||
\(100\) | 3.66745 | 0.366745 | ||||||||
\(101\) | 11.0928 | 1.10377 | 0.551887 | − | 0.833919i | \(-0.313908\pi\) | ||||
0.551887 | + | 0.833919i | \(0.313908\pi\) | |||||||
\(102\) | 2.21658 | 0.219474 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 3.04789 | 0.298870 | ||||||||
\(105\) | −3.31522 | −0.323532 | ||||||||
\(106\) | −3.33463 | −0.323888 | ||||||||
\(107\) | 15.3077 | 1.47985 | 0.739924 | − | 0.672691i | \(-0.234862\pi\) | ||||
0.739924 | + | 0.672691i | \(0.234862\pi\) | |||||||
\(108\) | 0.880046 | 0.0846825 | ||||||||
\(109\) | 5.50994 | 0.527756 | 0.263878 | − | 0.964556i | \(-0.414998\pi\) | ||||
0.263878 | + | 0.964556i | \(0.414998\pi\) | |||||||
\(110\) | 1.11268 | 0.106090 | ||||||||
\(111\) | 1.70522 | 0.161852 | ||||||||
\(112\) | 5.32403 | 0.503073 | ||||||||
\(113\) | −9.38175 | −0.882561 | −0.441280 | − | 0.897369i | \(-0.645476\pi\) | ||||
−0.441280 | + | 0.897369i | \(0.645476\pi\) | |||||||
\(114\) | 0.683661 | 0.0640307 | ||||||||
\(115\) | 8.11959 | 0.757156 | ||||||||
\(116\) | −3.47592 | −0.322731 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 1.11767 | 0.102890 | ||||||||
\(119\) | 7.60956 | 0.697568 | ||||||||
\(120\) | −2.78122 | −0.253889 | ||||||||
\(121\) | −9.67239 | −0.879309 | ||||||||
\(122\) | −4.30093 | −0.389388 | ||||||||
\(123\) | 8.06085 | 0.726822 | ||||||||
\(124\) | 4.10303 | 0.368463 | ||||||||
\(125\) | 8.36524 | 0.748210 | ||||||||
\(126\) | −3.84483 | −0.342524 | ||||||||
\(127\) | 14.9237 | 1.32427 | 0.662134 | − | 0.749385i | \(-0.269651\pi\) | ||||
0.662134 | + | 0.749385i | \(0.269651\pi\) | |||||||
\(128\) | −0.898114 | −0.0793828 | ||||||||
\(129\) | −0.912813 | −0.0803687 | ||||||||
\(130\) | 0.965685 | 0.0846962 | ||||||||
\(131\) | −4.46081 | −0.389743 | −0.194871 | − | 0.980829i | \(-0.562429\pi\) | ||||
−0.194871 | + | 0.980829i | \(0.562429\pi\) | |||||||
\(132\) | −1.01401 | −0.0882578 | ||||||||
\(133\) | 2.34702 | 0.203513 | ||||||||
\(134\) | 4.10289 | 0.354435 | ||||||||
\(135\) | 0.912505 | 0.0785359 | ||||||||
\(136\) | 6.38385 | 0.547411 | ||||||||
\(137\) | −11.3138 | −0.966605 | −0.483302 | − | 0.875454i | \(-0.660563\pi\) | ||||
−0.483302 | + | 0.875454i | \(0.660563\pi\) | |||||||
\(138\) | 9.41670 | 0.801603 | ||||||||
\(139\) | 6.61154 | 0.560784 | 0.280392 | − | 0.959886i | \(-0.409536\pi\) | ||||
0.280392 | + | 0.959886i | \(0.409536\pi\) | |||||||
\(140\) | −2.91754 | −0.246578 | ||||||||
\(141\) | −4.88621 | −0.411493 | ||||||||
\(142\) | 2.93641 | 0.246418 | ||||||||
\(143\) | 1.15222 | 0.0963533 | ||||||||
\(144\) | −1.46543 | −0.122119 | ||||||||
\(145\) | −3.60412 | −0.299306 | ||||||||
\(146\) | −1.66025 | −0.137404 | ||||||||
\(147\) | −6.19937 | −0.511316 | ||||||||
\(148\) | 1.50067 | 0.123355 | ||||||||
\(149\) | −7.92785 | −0.649475 | −0.324737 | − | 0.945804i | \(-0.605276\pi\) | ||||
−0.324737 | + | 0.945804i | \(0.605276\pi\) | |||||||
\(150\) | 4.41020 | 0.360091 | ||||||||
\(151\) | 6.05700 | 0.492912 | 0.246456 | − | 0.969154i | \(-0.420734\pi\) | ||||
0.246456 | + | 0.969154i | \(0.420734\pi\) | |||||||
\(152\) | 1.96897 | 0.159705 | ||||||||
\(153\) | −2.09451 | −0.169331 | ||||||||
\(154\) | 4.43008 | 0.356986 | ||||||||
\(155\) | 4.25436 | 0.341719 | ||||||||
\(156\) | −0.880046 | −0.0704601 | ||||||||
\(157\) | −19.9740 | −1.59410 | −0.797051 | − | 0.603912i | \(-0.793608\pi\) | ||||
−0.797051 | + | 0.603912i | \(0.793608\pi\) | |||||||
\(158\) | 1.34350 | 0.106883 | ||||||||
\(159\) | 3.15100 | 0.249890 | ||||||||
\(160\) | −4.14729 | −0.327872 | ||||||||
\(161\) | 32.3277 | 2.54778 | ||||||||
\(162\) | 1.05828 | 0.0831462 | ||||||||
\(163\) | 14.7633 | 1.15635 | 0.578176 | − | 0.815912i | \(-0.303765\pi\) | ||||
0.578176 | + | 0.815912i | \(0.303765\pi\) | |||||||
\(164\) | 7.09392 | 0.553942 | ||||||||
\(165\) | −1.05140 | −0.0818517 | ||||||||
\(166\) | 14.1438 | 1.09777 | ||||||||
\(167\) | 8.23190 | 0.637004 | 0.318502 | − | 0.947922i | \(-0.396820\pi\) | ||||
0.318502 | + | 0.947922i | \(0.396820\pi\) | |||||||
\(168\) | −11.0733 | −0.854322 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 2.02264 | 0.155129 | ||||||||
\(171\) | −0.646012 | −0.0494018 | ||||||||
\(172\) | −0.803318 | −0.0612524 | ||||||||
\(173\) | 17.8449 | 1.35672 | 0.678362 | − | 0.734728i | \(-0.262690\pi\) | ||||
0.678362 | + | 0.734728i | \(0.262690\pi\) | |||||||
\(174\) | −4.17989 | −0.316876 | ||||||||
\(175\) | 15.1403 | 1.14450 | ||||||||
\(176\) | 1.68849 | 0.127275 | ||||||||
\(177\) | −1.05612 | −0.0793826 | ||||||||
\(178\) | −16.3752 | −1.22737 | ||||||||
\(179\) | −8.56512 | −0.640187 | −0.320093 | − | 0.947386i | \(-0.603714\pi\) | ||||
−0.320093 | + | 0.947386i | \(0.603714\pi\) | |||||||
\(180\) | 0.803047 | 0.0598556 | ||||||||
\(181\) | −18.6783 | −1.38835 | −0.694173 | − | 0.719808i | \(-0.744230\pi\) | ||||
−0.694173 | + | 0.719808i | \(0.744230\pi\) | |||||||
\(182\) | 3.84483 | 0.284997 | ||||||||
\(183\) | 4.06408 | 0.300426 | ||||||||
\(184\) | 27.1205 | 1.99935 | ||||||||
\(185\) | 1.55602 | 0.114401 | ||||||||
\(186\) | 4.93400 | 0.361779 | ||||||||
\(187\) | 2.41334 | 0.176481 | ||||||||
\(188\) | −4.30009 | −0.313617 | ||||||||
\(189\) | 3.63309 | 0.264269 | ||||||||
\(190\) | 0.623844 | 0.0452584 | ||||||||
\(191\) | −14.2339 | −1.02993 | −0.514964 | − | 0.857212i | \(-0.672195\pi\) | ||||
−0.514964 | + | 0.857212i | \(0.672195\pi\) | |||||||
\(192\) | −7.74068 | −0.558635 | ||||||||
\(193\) | 18.3968 | 1.32423 | 0.662116 | − | 0.749401i | \(-0.269658\pi\) | ||||
0.662116 | + | 0.749401i | \(0.269658\pi\) | |||||||
\(194\) | 5.19658 | 0.373093 | ||||||||
\(195\) | −0.912505 | −0.0653459 | ||||||||
\(196\) | −5.45573 | −0.389695 | ||||||||
\(197\) | −6.23250 | −0.444047 | −0.222024 | − | 0.975041i | \(-0.571266\pi\) | ||||
−0.222024 | + | 0.975041i | \(0.571266\pi\) | |||||||
\(198\) | −1.21937 | −0.0866567 | ||||||||
\(199\) | 12.6357 | 0.895719 | 0.447859 | − | 0.894104i | \(-0.352186\pi\) | ||||
0.447859 | + | 0.894104i | \(0.352186\pi\) | |||||||
\(200\) | 12.7016 | 0.898138 | ||||||||
\(201\) | −3.87694 | −0.273459 | ||||||||
\(202\) | 11.7393 | 0.825972 | ||||||||
\(203\) | −14.3496 | −1.00715 | ||||||||
\(204\) | −1.84327 | −0.129055 | ||||||||
\(205\) | 7.35556 | 0.513735 | ||||||||
\(206\) | 1.05828 | 0.0737338 | ||||||||
\(207\) | −8.89813 | −0.618463 | ||||||||
\(208\) | 1.46543 | 0.101609 | ||||||||
\(209\) | 0.744347 | 0.0514875 | ||||||||
\(210\) | −3.50842 | −0.242104 | ||||||||
\(211\) | 15.5477 | 1.07035 | 0.535175 | − | 0.844741i | \(-0.320246\pi\) | ||||
0.535175 | + | 0.844741i | \(0.320246\pi\) | |||||||
\(212\) | 2.77302 | 0.190452 | ||||||||
\(213\) | −2.77471 | −0.190120 | ||||||||
\(214\) | 16.1998 | 1.10739 | ||||||||
\(215\) | −0.832946 | −0.0568065 | ||||||||
\(216\) | 3.04789 | 0.207383 | ||||||||
\(217\) | 16.9385 | 1.14986 | ||||||||
\(218\) | 5.83105 | 0.394928 | ||||||||
\(219\) | 1.56883 | 0.106011 | ||||||||
\(220\) | −0.925285 | −0.0623827 | ||||||||
\(221\) | 2.09451 | 0.140892 | ||||||||
\(222\) | 1.80460 | 0.121117 | ||||||||
\(223\) | 1.85404 | 0.124156 | 0.0620778 | − | 0.998071i | \(-0.480227\pi\) | ||||
0.0620778 | + | 0.998071i | \(0.480227\pi\) | |||||||
\(224\) | −16.5122 | −1.10327 | ||||||||
\(225\) | −4.16733 | −0.277822 | ||||||||
\(226\) | −9.92850 | −0.660434 | ||||||||
\(227\) | 0.00619540 | 0.000411203 0 | 0.000205602 | − | 1.00000i | \(-0.499935\pi\) | ||||
0.000205602 | 1.00000i | \(0.499935\pi\) | ||||||||
\(228\) | −0.568521 | −0.0376512 | ||||||||
\(229\) | −20.8512 | −1.37789 | −0.688943 | − | 0.724815i | \(-0.741925\pi\) | ||||
−0.688943 | + | 0.724815i | \(0.741925\pi\) | |||||||
\(230\) | 8.59279 | 0.566592 | ||||||||
\(231\) | −4.18612 | −0.275426 | ||||||||
\(232\) | −12.0383 | −0.790351 | ||||||||
\(233\) | −16.4976 | −1.08080 | −0.540398 | − | 0.841409i | \(-0.681726\pi\) | ||||
−0.540398 | + | 0.841409i | \(0.681726\pi\) | |||||||
\(234\) | −1.05828 | −0.0691818 | ||||||||
\(235\) | −4.45870 | −0.290853 | ||||||||
\(236\) | −0.929432 | −0.0605009 | ||||||||
\(237\) | −1.26952 | −0.0824639 | ||||||||
\(238\) | 8.05304 | 0.522001 | ||||||||
\(239\) | −11.6051 | −0.750669 | −0.375335 | − | 0.926889i | \(-0.622472\pi\) | ||||
−0.375335 | + | 0.926889i | \(0.622472\pi\) | |||||||
\(240\) | −1.33721 | −0.0863164 | ||||||||
\(241\) | −7.30272 | −0.470409 | −0.235205 | − | 0.971946i | \(-0.575576\pi\) | ||||
−0.235205 | + | 0.971946i | \(0.575576\pi\) | |||||||
\(242\) | −10.2361 | −0.658001 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.57658 | 0.228967 | ||||||||
\(245\) | −5.65696 | −0.361410 | ||||||||
\(246\) | 8.53062 | 0.543892 | ||||||||
\(247\) | 0.646012 | 0.0411048 | ||||||||
\(248\) | 14.2102 | 0.902346 | ||||||||
\(249\) | −13.3649 | −0.846967 | ||||||||
\(250\) | 8.85275 | 0.559897 | ||||||||
\(251\) | 1.05425 | 0.0665437 | 0.0332719 | − | 0.999446i | \(-0.489407\pi\) | ||||
0.0332719 | + | 0.999446i | \(0.489407\pi\) | |||||||
\(252\) | 3.19729 | 0.201410 | ||||||||
\(253\) | 10.2526 | 0.644575 | ||||||||
\(254\) | 15.7935 | 0.990971 | ||||||||
\(255\) | −1.91125 | −0.119687 | ||||||||
\(256\) | −16.4318 | −1.02699 | ||||||||
\(257\) | 1.32938 | 0.0829243 | 0.0414621 | − | 0.999140i | \(-0.486798\pi\) | ||||
0.0414621 | + | 0.999140i | \(0.486798\pi\) | |||||||
\(258\) | −0.966010 | −0.0601412 | ||||||||
\(259\) | 6.19523 | 0.384953 | ||||||||
\(260\) | −0.803047 | −0.0498029 | ||||||||
\(261\) | 3.94970 | 0.244480 | ||||||||
\(262\) | −4.72078 | −0.291651 | ||||||||
\(263\) | 11.4127 | 0.703737 | 0.351869 | − | 0.936049i | \(-0.385546\pi\) | ||||
0.351869 | + | 0.936049i | \(0.385546\pi\) | |||||||
\(264\) | −3.51183 | −0.216138 | ||||||||
\(265\) | 2.87530 | 0.176628 | ||||||||
\(266\) | 2.48380 | 0.152292 | ||||||||
\(267\) | 15.4734 | 0.946958 | ||||||||
\(268\) | −3.41189 | −0.208414 | ||||||||
\(269\) | 25.9749 | 1.58371 | 0.791857 | − | 0.610706i | \(-0.209114\pi\) | ||||
0.791857 | + | 0.610706i | \(0.209114\pi\) | |||||||
\(270\) | 0.965685 | 0.0587697 | ||||||||
\(271\) | −16.4799 | −1.00108 | −0.500542 | − | 0.865712i | \(-0.666866\pi\) | ||||
−0.500542 | + | 0.865712i | \(0.666866\pi\) | |||||||
\(272\) | 3.06935 | 0.186107 | ||||||||
\(273\) | −3.63309 | −0.219885 | ||||||||
\(274\) | −11.9732 | −0.723326 | ||||||||
\(275\) | 4.80168 | 0.289552 | ||||||||
\(276\) | −7.83077 | −0.471357 | ||||||||
\(277\) | −4.87661 | −0.293007 | −0.146503 | − | 0.989210i | \(-0.546802\pi\) | ||||
−0.146503 | + | 0.989210i | \(0.546802\pi\) | |||||||
\(278\) | 6.99686 | 0.419644 | ||||||||
\(279\) | −4.66229 | −0.279124 | ||||||||
\(280\) | −10.1044 | −0.603855 | ||||||||
\(281\) | −29.8226 | −1.77907 | −0.889533 | − | 0.456871i | \(-0.848970\pi\) | ||||
−0.889533 | + | 0.456871i | \(0.848970\pi\) | |||||||
\(282\) | −5.17098 | −0.307927 | ||||||||
\(283\) | −8.51437 | −0.506127 | −0.253063 | − | 0.967450i | \(-0.581438\pi\) | ||||
−0.253063 | + | 0.967450i | \(0.581438\pi\) | |||||||
\(284\) | −2.44187 | −0.144898 | ||||||||
\(285\) | −0.589489 | −0.0349183 | ||||||||
\(286\) | 1.21937 | 0.0721027 | ||||||||
\(287\) | 29.2858 | 1.72869 | ||||||||
\(288\) | 4.54495 | 0.267814 | ||||||||
\(289\) | −12.6130 | −0.741942 | ||||||||
\(290\) | −3.81417 | −0.223976 | ||||||||
\(291\) | −4.91041 | −0.287853 | ||||||||
\(292\) | 1.38064 | 0.0807958 | ||||||||
\(293\) | 17.9383 | 1.04796 | 0.523982 | − | 0.851729i | \(-0.324446\pi\) | ||||
0.523982 | + | 0.851729i | \(0.324446\pi\) | |||||||
\(294\) | −6.56066 | −0.382626 | ||||||||
\(295\) | −0.963713 | −0.0561095 | ||||||||
\(296\) | 5.19733 | 0.302089 | ||||||||
\(297\) | 1.15222 | 0.0668585 | ||||||||
\(298\) | −8.38987 | −0.486012 | ||||||||
\(299\) | 8.89813 | 0.514592 | ||||||||
\(300\) | −3.66745 | −0.211740 | ||||||||
\(301\) | −3.31633 | −0.191150 | ||||||||
\(302\) | 6.40999 | 0.368854 | ||||||||
\(303\) | −11.0928 | −0.637264 | ||||||||
\(304\) | 0.946682 | 0.0542960 | ||||||||
\(305\) | 3.70850 | 0.212348 | ||||||||
\(306\) | −2.21658 | −0.126713 | ||||||||
\(307\) | −13.1960 | −0.753135 | −0.376567 | − | 0.926389i | \(-0.622896\pi\) | ||||
−0.376567 | + | 0.926389i | \(0.622896\pi\) | |||||||
\(308\) | −3.68398 | −0.209914 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 4.50230 | 0.255714 | ||||||||
\(311\) | −11.8366 | −0.671194 | −0.335597 | − | 0.942006i | \(-0.608938\pi\) | ||||
−0.335597 | + | 0.942006i | \(0.608938\pi\) | |||||||
\(312\) | −3.04789 | −0.172553 | ||||||||
\(313\) | −14.8906 | −0.841666 | −0.420833 | − | 0.907138i | \(-0.638262\pi\) | ||||
−0.420833 | + | 0.907138i | \(0.638262\pi\) | |||||||
\(314\) | −21.1381 | −1.19289 | ||||||||
\(315\) | 3.31522 | 0.186791 | ||||||||
\(316\) | −1.11723 | −0.0628493 | ||||||||
\(317\) | 14.5587 | 0.817699 | 0.408849 | − | 0.912602i | \(-0.365930\pi\) | ||||
0.408849 | + | 0.912602i | \(0.365930\pi\) | |||||||
\(318\) | 3.33463 | 0.186997 | ||||||||
\(319\) | −4.55092 | −0.254802 | ||||||||
\(320\) | −7.06341 | −0.394857 | ||||||||
\(321\) | −15.3077 | −0.854390 | ||||||||
\(322\) | 34.2118 | 1.90655 | ||||||||
\(323\) | 1.35308 | 0.0752874 | ||||||||
\(324\) | −0.880046 | −0.0488915 | ||||||||
\(325\) | 4.16733 | 0.231162 | ||||||||
\(326\) | 15.6237 | 0.865317 | ||||||||
\(327\) | −5.50994 | −0.304700 | ||||||||
\(328\) | 24.5686 | 1.35657 | ||||||||
\(329\) | −17.7521 | −0.978703 | ||||||||
\(330\) | −1.11268 | −0.0612510 | ||||||||
\(331\) | 1.62408 | 0.0892673 | 0.0446337 | − | 0.999003i | \(-0.485788\pi\) | ||||
0.0446337 | + | 0.999003i | \(0.485788\pi\) | |||||||
\(332\) | −11.7617 | −0.645509 | ||||||||
\(333\) | −1.70522 | −0.0934455 | ||||||||
\(334\) | 8.71165 | 0.476680 | ||||||||
\(335\) | −3.53773 | −0.193287 | ||||||||
\(336\) | −5.32403 | −0.290450 | ||||||||
\(337\) | −4.58891 | −0.249974 | −0.124987 | − | 0.992158i | \(-0.539889\pi\) | ||||
−0.124987 | + | 0.992158i | \(0.539889\pi\) | |||||||
\(338\) | 1.05828 | 0.0575628 | ||||||||
\(339\) | 9.38175 | 0.509547 | ||||||||
\(340\) | −1.68199 | −0.0912188 | ||||||||
\(341\) | 5.37197 | 0.290909 | ||||||||
\(342\) | −0.683661 | −0.0369681 | ||||||||
\(343\) | 2.90876 | 0.157058 | ||||||||
\(344\) | −2.78215 | −0.150004 | ||||||||
\(345\) | −8.11959 | −0.437144 | ||||||||
\(346\) | 18.8849 | 1.01526 | ||||||||
\(347\) | 6.05498 | 0.325048 | 0.162524 | − | 0.986705i | \(-0.448036\pi\) | ||||
0.162524 | + | 0.986705i | \(0.448036\pi\) | |||||||
\(348\) | 3.47592 | 0.186329 | ||||||||
\(349\) | −11.2034 | −0.599705 | −0.299853 | − | 0.953986i | \(-0.596938\pi\) | ||||
−0.299853 | + | 0.953986i | \(0.596938\pi\) | |||||||
\(350\) | 16.0227 | 0.856448 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −5.23678 | −0.279121 | ||||||||
\(353\) | 18.2274 | 0.970145 | 0.485072 | − | 0.874474i | \(-0.338793\pi\) | ||||
0.485072 | + | 0.874474i | \(0.338793\pi\) | |||||||
\(354\) | −1.11767 | −0.0594033 | ||||||||
\(355\) | −2.53193 | −0.134381 | ||||||||
\(356\) | 13.6173 | 0.721717 | ||||||||
\(357\) | −7.60956 | −0.402741 | ||||||||
\(358\) | −9.06428 | −0.479062 | ||||||||
\(359\) | −33.3969 | −1.76262 | −0.881310 | − | 0.472538i | \(-0.843338\pi\) | ||||
−0.881310 | + | 0.472538i | \(0.843338\pi\) | |||||||
\(360\) | 2.78122 | 0.146583 | ||||||||
\(361\) | −18.5827 | −0.978035 | ||||||||
\(362\) | −19.7668 | −1.03892 | ||||||||
\(363\) | 9.67239 | 0.507669 | ||||||||
\(364\) | −3.19729 | −0.167584 | ||||||||
\(365\) | 1.43156 | 0.0749313 | ||||||||
\(366\) | 4.30093 | 0.224813 | ||||||||
\(367\) | −2.69579 | −0.140719 | −0.0703596 | − | 0.997522i | \(-0.522415\pi\) | ||||
−0.0703596 | + | 0.997522i | \(0.522415\pi\) | |||||||
\(368\) | 13.0395 | 0.679733 | ||||||||
\(369\) | −8.06085 | −0.419631 | ||||||||
\(370\) | 1.64671 | 0.0856082 | ||||||||
\(371\) | 11.4479 | 0.594344 | ||||||||
\(372\) | −4.10303 | −0.212732 | ||||||||
\(373\) | 29.4584 | 1.52530 | 0.762649 | − | 0.646813i | \(-0.223898\pi\) | ||||
0.762649 | + | 0.646813i | \(0.223898\pi\) | |||||||
\(374\) | 2.55398 | 0.132063 | ||||||||
\(375\) | −8.36524 | −0.431979 | ||||||||
\(376\) | −14.8926 | −0.768030 | ||||||||
\(377\) | −3.94970 | −0.203420 | ||||||||
\(378\) | 3.84483 | 0.197756 | ||||||||
\(379\) | −27.9528 | −1.43584 | −0.717920 | − | 0.696126i | \(-0.754906\pi\) | ||||
−0.717920 | + | 0.696126i | \(0.754906\pi\) | |||||||
\(380\) | −0.518778 | −0.0266127 | ||||||||
\(381\) | −14.9237 | −0.764567 | ||||||||
\(382\) | −15.0634 | −0.770711 | ||||||||
\(383\) | −5.24706 | −0.268112 | −0.134056 | − | 0.990974i | \(-0.542800\pi\) | ||||
−0.134056 | + | 0.990974i | \(0.542800\pi\) | |||||||
\(384\) | 0.898114 | 0.0458317 | ||||||||
\(385\) | −3.81985 | −0.194678 | ||||||||
\(386\) | 19.4690 | 0.990945 | ||||||||
\(387\) | 0.912813 | 0.0464009 | ||||||||
\(388\) | −4.32139 | −0.219385 | ||||||||
\(389\) | −2.70325 | −0.137060 | −0.0685302 | − | 0.997649i | \(-0.521831\pi\) | ||||
−0.0685302 | + | 0.997649i | \(0.521831\pi\) | |||||||
\(390\) | −0.965685 | −0.0488993 | ||||||||
\(391\) | 18.6373 | 0.942526 | ||||||||
\(392\) | −18.8950 | −0.954342 | ||||||||
\(393\) | 4.46081 | 0.225018 | ||||||||
\(394\) | −6.59572 | −0.332288 | ||||||||
\(395\) | −1.15844 | −0.0582874 | ||||||||
\(396\) | 1.01401 | 0.0509557 | ||||||||
\(397\) | −0.742341 | −0.0372570 | −0.0186285 | − | 0.999826i | \(-0.505930\pi\) | ||||
−0.0186285 | + | 0.999826i | \(0.505930\pi\) | |||||||
\(398\) | 13.3721 | 0.670281 | ||||||||
\(399\) | −2.34702 | −0.117498 | ||||||||
\(400\) | 6.10692 | 0.305346 | ||||||||
\(401\) | 2.65955 | 0.132812 | 0.0664059 | − | 0.997793i | \(-0.478847\pi\) | ||||
0.0664059 | + | 0.997793i | \(0.478847\pi\) | |||||||
\(402\) | −4.10289 | −0.204633 | ||||||||
\(403\) | 4.66229 | 0.232245 | ||||||||
\(404\) | −9.76218 | −0.485686 | ||||||||
\(405\) | −0.912505 | −0.0453427 | ||||||||
\(406\) | −15.1859 | −0.753664 | ||||||||
\(407\) | 1.96479 | 0.0973908 | ||||||||
\(408\) | −6.38385 | −0.316048 | ||||||||
\(409\) | 15.2361 | 0.753379 | 0.376689 | − | 0.926340i | \(-0.377062\pi\) | ||||
0.376689 | + | 0.926340i | \(0.377062\pi\) | |||||||
\(410\) | 7.78424 | 0.384436 | ||||||||
\(411\) | 11.3138 | 0.558069 | ||||||||
\(412\) | −0.880046 | −0.0433568 | ||||||||
\(413\) | −3.83697 | −0.188805 | ||||||||
\(414\) | −9.41670 | −0.462806 | ||||||||
\(415\) | −12.1955 | −0.598656 | ||||||||
\(416\) | −4.54495 | −0.222835 | ||||||||
\(417\) | −6.61154 | −0.323769 | ||||||||
\(418\) | 0.787726 | 0.0385289 | ||||||||
\(419\) | 32.2369 | 1.57487 | 0.787437 | − | 0.616395i | \(-0.211407\pi\) | ||||
0.787437 | + | 0.616395i | \(0.211407\pi\) | |||||||
\(420\) | 2.91754 | 0.142362 | ||||||||
\(421\) | −1.92093 | −0.0936202 | −0.0468101 | − | 0.998904i | \(-0.514906\pi\) | ||||
−0.0468101 | + | 0.998904i | \(0.514906\pi\) | |||||||
\(422\) | 16.4538 | 0.800959 | ||||||||
\(423\) | 4.88621 | 0.237576 | ||||||||
\(424\) | 9.60390 | 0.466406 | ||||||||
\(425\) | 8.72854 | 0.423396 | ||||||||
\(426\) | −2.93641 | −0.142270 | ||||||||
\(427\) | 14.7652 | 0.714538 | ||||||||
\(428\) | −13.4714 | −0.651167 | ||||||||
\(429\) | −1.15222 | −0.0556296 | ||||||||
\(430\) | −0.881489 | −0.0425092 | ||||||||
\(431\) | 8.99846 | 0.433441 | 0.216720 | − | 0.976234i | \(-0.430464\pi\) | ||||
0.216720 | + | 0.976234i | \(0.430464\pi\) | |||||||
\(432\) | 1.46543 | 0.0705053 | ||||||||
\(433\) | −14.4505 | −0.694447 | −0.347224 | − | 0.937782i | \(-0.612876\pi\) | ||||
−0.347224 | + | 0.937782i | \(0.612876\pi\) | |||||||
\(434\) | 17.9257 | 0.860461 | ||||||||
\(435\) | 3.60412 | 0.172805 | ||||||||
\(436\) | −4.84900 | −0.232225 | ||||||||
\(437\) | 5.74830 | 0.274978 | ||||||||
\(438\) | 1.66025 | 0.0793300 | ||||||||
\(439\) | −4.41182 | −0.210565 | −0.105282 | − | 0.994442i | \(-0.533575\pi\) | ||||
−0.105282 | + | 0.994442i | \(0.533575\pi\) | |||||||
\(440\) | −3.20457 | −0.152772 | ||||||||
\(441\) | 6.19937 | 0.295208 | ||||||||
\(442\) | 2.21658 | 0.105432 | ||||||||
\(443\) | 14.7710 | 0.701792 | 0.350896 | − | 0.936414i | \(-0.385877\pi\) | ||||
0.350896 | + | 0.936414i | \(0.385877\pi\) | |||||||
\(444\) | −1.50067 | −0.0712188 | ||||||||
\(445\) | 14.1196 | 0.669332 | ||||||||
\(446\) | 1.96209 | 0.0929077 | ||||||||
\(447\) | 7.92785 | 0.374974 | ||||||||
\(448\) | −28.1226 | −1.32867 | ||||||||
\(449\) | −25.5819 | −1.20728 | −0.603642 | − | 0.797256i | \(-0.706284\pi\) | ||||
−0.603642 | + | 0.797256i | \(0.706284\pi\) | |||||||
\(450\) | −4.41020 | −0.207899 | ||||||||
\(451\) | 9.28785 | 0.437348 | ||||||||
\(452\) | 8.25637 | 0.388347 | ||||||||
\(453\) | −6.05700 | −0.284583 | ||||||||
\(454\) | 0.00655646 | 0.000307710 0 | ||||||||
\(455\) | −3.31522 | −0.155420 | ||||||||
\(456\) | −1.96897 | −0.0922057 | ||||||||
\(457\) | −18.8643 | −0.882433 | −0.441217 | − | 0.897401i | \(-0.645453\pi\) | ||||
−0.441217 | + | 0.897401i | \(0.645453\pi\) | |||||||
\(458\) | −22.0664 | −1.03109 | ||||||||
\(459\) | 2.09451 | 0.0977635 | ||||||||
\(460\) | −7.14562 | −0.333166 | ||||||||
\(461\) | 7.17280 | 0.334071 | 0.167035 | − | 0.985951i | \(-0.446581\pi\) | ||||
0.167035 | + | 0.985951i | \(0.446581\pi\) | |||||||
\(462\) | −4.43008 | −0.206106 | ||||||||
\(463\) | −23.5859 | −1.09613 | −0.548066 | − | 0.836435i | \(-0.684636\pi\) | ||||
−0.548066 | + | 0.836435i | \(0.684636\pi\) | |||||||
\(464\) | −5.78799 | −0.268701 | ||||||||
\(465\) | −4.25436 | −0.197291 | ||||||||
\(466\) | −17.4591 | −0.808777 | ||||||||
\(467\) | −33.7926 | −1.56373 | −0.781867 | − | 0.623445i | \(-0.785733\pi\) | ||||
−0.781867 | + | 0.623445i | \(0.785733\pi\) | |||||||
\(468\) | 0.880046 | 0.0406802 | ||||||||
\(469\) | −14.0853 | −0.650399 | ||||||||
\(470\) | −4.71854 | −0.217650 | ||||||||
\(471\) | 19.9740 | 0.920355 | ||||||||
\(472\) | −3.21893 | −0.148163 | ||||||||
\(473\) | −1.05176 | −0.0483599 | ||||||||
\(474\) | −1.34350 | −0.0617091 | ||||||||
\(475\) | 2.69215 | 0.123524 | ||||||||
\(476\) | −6.69677 | −0.306946 | ||||||||
\(477\) | −3.15100 | −0.144274 | ||||||||
\(478\) | −12.2814 | −0.561738 | ||||||||
\(479\) | −19.2375 | −0.878983 | −0.439491 | − | 0.898247i | \(-0.644841\pi\) | ||||
−0.439491 | + | 0.898247i | \(0.644841\pi\) | |||||||
\(480\) | 4.14729 | 0.189297 | ||||||||
\(481\) | 1.70522 | 0.0777514 | ||||||||
\(482\) | −7.72831 | −0.352015 | ||||||||
\(483\) | −32.3277 | −1.47096 | ||||||||
\(484\) | 8.51216 | 0.386916 | ||||||||
\(485\) | −4.48077 | −0.203461 | ||||||||
\(486\) | −1.05828 | −0.0480045 | ||||||||
\(487\) | 24.5015 | 1.11027 | 0.555134 | − | 0.831761i | \(-0.312667\pi\) | ||||
0.555134 | + | 0.831761i | \(0.312667\pi\) | |||||||
\(488\) | 12.3869 | 0.560728 | ||||||||
\(489\) | −14.7633 | −0.667620 | ||||||||
\(490\) | −5.98664 | −0.270449 | ||||||||
\(491\) | 28.8003 | 1.29974 | 0.649870 | − | 0.760046i | \(-0.274823\pi\) | ||||
0.649870 | + | 0.760046i | \(0.274823\pi\) | |||||||
\(492\) | −7.09392 | −0.319819 | ||||||||
\(493\) | −8.27270 | −0.372584 | ||||||||
\(494\) | 0.683661 | 0.0307593 | ||||||||
\(495\) | 1.05140 | 0.0472571 | ||||||||
\(496\) | 6.83224 | 0.306777 | ||||||||
\(497\) | −10.0808 | −0.452184 | ||||||||
\(498\) | −14.1438 | −0.633799 | ||||||||
\(499\) | −5.77561 | −0.258552 | −0.129276 | − | 0.991609i | \(-0.541265\pi\) | ||||
−0.129276 | + | 0.991609i | \(0.541265\pi\) | |||||||
\(500\) | −7.36180 | −0.329230 | ||||||||
\(501\) | −8.23190 | −0.367774 | ||||||||
\(502\) | 1.11569 | 0.0497957 | ||||||||
\(503\) | 27.8274 | 1.24076 | 0.620381 | − | 0.784301i | \(-0.286978\pi\) | ||||
0.620381 | + | 0.784301i | \(0.286978\pi\) | |||||||
\(504\) | 11.0733 | 0.493243 | ||||||||
\(505\) | −10.1222 | −0.450433 | ||||||||
\(506\) | 10.8501 | 0.482345 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −13.1336 | −0.582709 | ||||||||
\(509\) | −5.90413 | −0.261696 | −0.130848 | − | 0.991402i | \(-0.541770\pi\) | ||||
−0.130848 | + | 0.991402i | \(0.541770\pi\) | |||||||
\(510\) | −2.02264 | −0.0895640 | ||||||||
\(511\) | 5.69969 | 0.252139 | ||||||||
\(512\) | −15.5932 | −0.689129 | ||||||||
\(513\) | 0.646012 | 0.0285221 | ||||||||
\(514\) | 1.40685 | 0.0620536 | ||||||||
\(515\) | −0.912505 | −0.0402098 | ||||||||
\(516\) | 0.803318 | 0.0353641 | ||||||||
\(517\) | −5.62998 | −0.247606 | ||||||||
\(518\) | 6.55628 | 0.288066 | ||||||||
\(519\) | −17.8449 | −0.783305 | ||||||||
\(520\) | −2.78122 | −0.121964 | ||||||||
\(521\) | 2.91277 | 0.127611 | 0.0638053 | − | 0.997962i | \(-0.479676\pi\) | ||||
0.0638053 | + | 0.997962i | \(0.479676\pi\) | |||||||
\(522\) | 4.17989 | 0.182949 | ||||||||
\(523\) | −19.4860 | −0.852063 | −0.426032 | − | 0.904708i | \(-0.640089\pi\) | ||||
−0.426032 | + | 0.904708i | \(0.640089\pi\) | |||||||
\(524\) | 3.92572 | 0.171496 | ||||||||
\(525\) | −15.1403 | −0.660778 | ||||||||
\(526\) | 12.0778 | 0.526618 | ||||||||
\(527\) | 9.76523 | 0.425380 | ||||||||
\(528\) | −1.68849 | −0.0734821 | ||||||||
\(529\) | 56.1767 | 2.44247 | ||||||||
\(530\) | 3.04287 | 0.132174 | ||||||||
\(531\) | 1.05612 | 0.0458316 | ||||||||
\(532\) | −2.06549 | −0.0895503 | ||||||||
\(533\) | 8.06085 | 0.349154 | ||||||||
\(534\) | 16.3752 | 0.708624 | ||||||||
\(535\) | −13.9683 | −0.603903 | ||||||||
\(536\) | −11.8165 | −0.510395 | ||||||||
\(537\) | 8.56512 | 0.369612 | ||||||||
\(538\) | 27.4886 | 1.18512 | ||||||||
\(539\) | −7.14303 | −0.307672 | ||||||||
\(540\) | −0.803047 | −0.0345576 | ||||||||
\(541\) | 13.7847 | 0.592652 | 0.296326 | − | 0.955087i | \(-0.404238\pi\) | ||||
0.296326 | + | 0.955087i | \(0.404238\pi\) | |||||||
\(542\) | −17.4404 | −0.749128 | ||||||||
\(543\) | 18.6783 | 0.801562 | ||||||||
\(544\) | −9.51947 | −0.408144 | ||||||||
\(545\) | −5.02784 | −0.215369 | ||||||||
\(546\) | −3.84483 | −0.164543 | ||||||||
\(547\) | 41.0007 | 1.75306 | 0.876531 | − | 0.481345i | \(-0.159851\pi\) | ||||
0.876531 | + | 0.481345i | \(0.159851\pi\) | |||||||
\(548\) | 9.95668 | 0.425328 | ||||||||
\(549\) | −4.06408 | −0.173451 | ||||||||
\(550\) | 5.08151 | 0.216676 | ||||||||
\(551\) | −2.55156 | −0.108700 | ||||||||
\(552\) | −27.1205 | −1.15433 | ||||||||
\(553\) | −4.61227 | −0.196134 | ||||||||
\(554\) | −5.16081 | −0.219262 | ||||||||
\(555\) | −1.55602 | −0.0660495 | ||||||||
\(556\) | −5.81847 | −0.246758 | ||||||||
\(557\) | 36.6413 | 1.55254 | 0.776271 | − | 0.630400i | \(-0.217109\pi\) | ||||
0.776271 | + | 0.630400i | \(0.217109\pi\) | |||||||
\(558\) | −4.93400 | −0.208873 | ||||||||
\(559\) | −0.912813 | −0.0386079 | ||||||||
\(560\) | −4.85820 | −0.205297 | ||||||||
\(561\) | −2.41334 | −0.101891 | ||||||||
\(562\) | −31.5606 | −1.33130 | ||||||||
\(563\) | 30.7776 | 1.29712 | 0.648562 | − | 0.761162i | \(-0.275371\pi\) | ||||
0.648562 | + | 0.761162i | \(0.275371\pi\) | |||||||
\(564\) | 4.30009 | 0.181067 | ||||||||
\(565\) | 8.56090 | 0.360160 | ||||||||
\(566\) | −9.01057 | −0.378743 | ||||||||
\(567\) | −3.63309 | −0.152576 | ||||||||
\(568\) | −8.45700 | −0.354848 | ||||||||
\(569\) | −23.4563 | −0.983340 | −0.491670 | − | 0.870782i | \(-0.663613\pi\) | ||||
−0.491670 | + | 0.870782i | \(0.663613\pi\) | |||||||
\(570\) | −0.623844 | −0.0261299 | ||||||||
\(571\) | −12.9784 | −0.543127 | −0.271564 | − | 0.962421i | \(-0.587541\pi\) | ||||
−0.271564 | + | 0.962421i | \(0.587541\pi\) | |||||||
\(572\) | −1.01401 | −0.0423977 | ||||||||
\(573\) | 14.2339 | 0.594629 | ||||||||
\(574\) | 30.9925 | 1.29360 | ||||||||
\(575\) | 37.0815 | 1.54640 | ||||||||
\(576\) | 7.74068 | 0.322528 | ||||||||
\(577\) | −21.5678 | −0.897880 | −0.448940 | − | 0.893562i | \(-0.648198\pi\) | ||||
−0.448940 | + | 0.893562i | \(0.648198\pi\) | |||||||
\(578\) | −13.3481 | −0.555207 | ||||||||
\(579\) | −18.3968 | −0.764546 | ||||||||
\(580\) | 3.17180 | 0.131702 | ||||||||
\(581\) | −48.5560 | −2.01444 | ||||||||
\(582\) | −5.19658 | −0.215405 | ||||||||
\(583\) | 3.63063 | 0.150366 | ||||||||
\(584\) | 4.78161 | 0.197864 | ||||||||
\(585\) | 0.912505 | 0.0377274 | ||||||||
\(586\) | 18.9837 | 0.784208 | ||||||||
\(587\) | −26.5715 | −1.09672 | −0.548362 | − | 0.836241i | \(-0.684748\pi\) | ||||
−0.548362 | + | 0.836241i | \(0.684748\pi\) | |||||||
\(588\) | 5.45573 | 0.224991 | ||||||||
\(589\) | 3.01189 | 0.124103 | ||||||||
\(590\) | −1.01988 | −0.0419876 | ||||||||
\(591\) | 6.23250 | 0.256371 | ||||||||
\(592\) | 2.49887 | 0.102703 | ||||||||
\(593\) | 2.89906 | 0.119050 | 0.0595250 | − | 0.998227i | \(-0.481041\pi\) | ||||
0.0595250 | + | 0.998227i | \(0.481041\pi\) | |||||||
\(594\) | 1.21937 | 0.0500313 | ||||||||
\(595\) | −6.94377 | −0.284667 | ||||||||
\(596\) | 6.97688 | 0.285784 | ||||||||
\(597\) | −12.6357 | −0.517144 | ||||||||
\(598\) | 9.41670 | 0.385078 | ||||||||
\(599\) | 31.1460 | 1.27259 | 0.636295 | − | 0.771446i | \(-0.280466\pi\) | ||||
0.636295 | + | 0.771446i | \(0.280466\pi\) | |||||||
\(600\) | −12.7016 | −0.518540 | ||||||||
\(601\) | 34.4732 | 1.40619 | 0.703095 | − | 0.711096i | \(-0.251801\pi\) | ||||
0.703095 | + | 0.711096i | \(0.251801\pi\) | |||||||
\(602\) | −3.50961 | −0.143041 | ||||||||
\(603\) | 3.87694 | 0.157881 | ||||||||
\(604\) | −5.33044 | −0.216893 | ||||||||
\(605\) | 8.82611 | 0.358832 | ||||||||
\(606\) | −11.7393 | −0.476875 | ||||||||
\(607\) | 6.91780 | 0.280785 | 0.140393 | − | 0.990096i | \(-0.455164\pi\) | ||||
0.140393 | + | 0.990096i | \(0.455164\pi\) | |||||||
\(608\) | −2.93610 | −0.119074 | ||||||||
\(609\) | 14.3496 | 0.581477 | ||||||||
\(610\) | 3.92462 | 0.158903 | ||||||||
\(611\) | −4.88621 | −0.197675 | ||||||||
\(612\) | 1.84327 | 0.0745097 | ||||||||
\(613\) | −22.7641 | −0.919432 | −0.459716 | − | 0.888066i | \(-0.652049\pi\) | ||||
−0.459716 | + | 0.888066i | \(0.652049\pi\) | |||||||
\(614\) | −13.9650 | −0.563583 | ||||||||
\(615\) | −7.35556 | −0.296605 | ||||||||
\(616\) | −12.7588 | −0.514068 | ||||||||
\(617\) | 23.5136 | 0.946623 | 0.473312 | − | 0.880895i | \(-0.343058\pi\) | ||||
0.473312 | + | 0.880895i | \(0.343058\pi\) | |||||||
\(618\) | −1.05828 | −0.0425702 | ||||||||
\(619\) | −28.0906 | −1.12906 | −0.564529 | − | 0.825413i | \(-0.690942\pi\) | ||||
−0.564529 | + | 0.825413i | \(0.690942\pi\) | |||||||
\(620\) | −3.74404 | −0.150364 | ||||||||
\(621\) | 8.89813 | 0.357070 | ||||||||
\(622\) | −12.5265 | −0.502265 | ||||||||
\(623\) | 56.2164 | 2.25226 | ||||||||
\(624\) | −1.46543 | −0.0586640 | ||||||||
\(625\) | 13.2033 | 0.528134 | ||||||||
\(626\) | −15.7584 | −0.629832 | ||||||||
\(627\) | −0.744347 | −0.0297263 | ||||||||
\(628\) | 17.5781 | 0.701442 | ||||||||
\(629\) | 3.57161 | 0.142409 | ||||||||
\(630\) | 3.50842 | 0.139779 | ||||||||
\(631\) | −37.4438 | −1.49062 | −0.745308 | − | 0.666721i | \(-0.767697\pi\) | ||||
−0.745308 | + | 0.666721i | \(0.767697\pi\) | |||||||
\(632\) | −3.86935 | −0.153914 | ||||||||
\(633\) | −15.5477 | −0.617966 | ||||||||
\(634\) | 15.4072 | 0.611897 | ||||||||
\(635\) | −13.6180 | −0.540414 | ||||||||
\(636\) | −2.77302 | −0.109958 | ||||||||
\(637\) | −6.19937 | −0.245628 | ||||||||
\(638\) | −4.81614 | −0.190673 | ||||||||
\(639\) | 2.77471 | 0.109766 | ||||||||
\(640\) | 0.819534 | 0.0323949 | ||||||||
\(641\) | 34.9305 | 1.37967 | 0.689836 | − | 0.723966i | \(-0.257683\pi\) | ||||
0.689836 | + | 0.723966i | \(0.257683\pi\) | |||||||
\(642\) | −16.1998 | −0.639354 | ||||||||
\(643\) | 35.9677 | 1.41843 | 0.709214 | − | 0.704993i | \(-0.249050\pi\) | ||||
0.709214 | + | 0.704993i | \(0.249050\pi\) | |||||||
\(644\) | −28.4499 | −1.12108 | ||||||||
\(645\) | 0.832946 | 0.0327972 | ||||||||
\(646\) | 1.43194 | 0.0563388 | ||||||||
\(647\) | 49.3445 | 1.93993 | 0.969967 | − | 0.243237i | \(-0.0782092\pi\) | ||||
0.969967 | + | 0.243237i | \(0.0782092\pi\) | |||||||
\(648\) | −3.04789 | −0.119732 | ||||||||
\(649\) | −1.21688 | −0.0477666 | ||||||||
\(650\) | 4.41020 | 0.172982 | ||||||||
\(651\) | −16.9385 | −0.663874 | ||||||||
\(652\) | −12.9924 | −0.508822 | ||||||||
\(653\) | 16.8876 | 0.660864 | 0.330432 | − | 0.943830i | \(-0.392806\pi\) | ||||
0.330432 | + | 0.943830i | \(0.392806\pi\) | |||||||
\(654\) | −5.83105 | −0.228012 | ||||||||
\(655\) | 4.07051 | 0.159048 | ||||||||
\(656\) | 11.8126 | 0.461203 | ||||||||
\(657\) | −1.56883 | −0.0612057 | ||||||||
\(658\) | −18.7866 | −0.732379 | ||||||||
\(659\) | −29.5954 | −1.15287 | −0.576437 | − | 0.817142i | \(-0.695557\pi\) | ||||
−0.576437 | + | 0.817142i | \(0.695557\pi\) | |||||||
\(660\) | 0.925285 | 0.0360167 | ||||||||
\(661\) | −26.7152 | −1.03910 | −0.519550 | − | 0.854440i | \(-0.673901\pi\) | ||||
−0.519550 | + | 0.854440i | \(0.673901\pi\) | |||||||
\(662\) | 1.71873 | 0.0668002 | ||||||||
\(663\) | −2.09451 | −0.0813442 | ||||||||
\(664\) | −40.7348 | −1.58082 | ||||||||
\(665\) | −2.14167 | −0.0830504 | ||||||||
\(666\) | −1.80460 | −0.0699268 | ||||||||
\(667\) | −35.1450 | −1.36082 | ||||||||
\(668\) | −7.24446 | −0.280296 | ||||||||
\(669\) | −1.85404 | −0.0716813 | ||||||||
\(670\) | −3.74391 | −0.144640 | ||||||||
\(671\) | 4.68271 | 0.180774 | ||||||||
\(672\) | 16.5122 | 0.636974 | ||||||||
\(673\) | 15.7330 | 0.606461 | 0.303230 | − | 0.952917i | \(-0.401935\pi\) | ||||
0.303230 | + | 0.952917i | \(0.401935\pi\) | |||||||
\(674\) | −4.85634 | −0.187059 | ||||||||
\(675\) | 4.16733 | 0.160401 | ||||||||
\(676\) | −0.880046 | −0.0338479 | ||||||||
\(677\) | −0.416439 | −0.0160051 | −0.00800253 | − | 0.999968i | \(-0.502547\pi\) | ||||
−0.00800253 | + | 0.999968i | \(0.502547\pi\) | |||||||
\(678\) | 9.92850 | 0.381302 | ||||||||
\(679\) | −17.8400 | −0.684636 | ||||||||
\(680\) | −5.82530 | −0.223390 | ||||||||
\(681\) | −0.00619540 | −0.000237408 0 | ||||||||
\(682\) | 5.68504 | 0.217692 | ||||||||
\(683\) | 14.8619 | 0.568675 | 0.284337 | − | 0.958724i | \(-0.408226\pi\) | ||||
0.284337 | + | 0.958724i | \(0.408226\pi\) | |||||||
\(684\) | 0.568521 | 0.0217379 | ||||||||
\(685\) | 10.3239 | 0.394457 | ||||||||
\(686\) | 3.07828 | 0.117529 | ||||||||
\(687\) | 20.8512 | 0.795523 | ||||||||
\(688\) | −1.33766 | −0.0509978 | ||||||||
\(689\) | 3.15100 | 0.120043 | ||||||||
\(690\) | −8.59279 | −0.327122 | ||||||||
\(691\) | −30.7192 | −1.16862 | −0.584308 | − | 0.811532i | \(-0.698634\pi\) | ||||
−0.584308 | + | 0.811532i | \(0.698634\pi\) | |||||||
\(692\) | −15.7044 | −0.596990 | ||||||||
\(693\) | 4.18612 | 0.159017 | ||||||||
\(694\) | 6.40786 | 0.243239 | ||||||||
\(695\) | −6.03307 | −0.228847 | ||||||||
\(696\) | 12.0383 | 0.456309 | ||||||||
\(697\) | 16.8835 | 0.639510 | ||||||||
\(698\) | −11.8563 | −0.448769 | ||||||||
\(699\) | 16.4976 | 0.623998 | ||||||||
\(700\) | −13.3242 | −0.503607 | ||||||||
\(701\) | 36.6486 | 1.38420 | 0.692098 | − | 0.721803i | \(-0.256686\pi\) | ||||
0.692098 | + | 0.721803i | \(0.256686\pi\) | |||||||
\(702\) | 1.05828 | 0.0399422 | ||||||||
\(703\) | 1.10159 | 0.0415474 | ||||||||
\(704\) | −8.91895 | −0.336146 | ||||||||
\(705\) | 4.45870 | 0.167924 | ||||||||
\(706\) | 19.2896 | 0.725975 | ||||||||
\(707\) | −40.3012 | −1.51568 | ||||||||
\(708\) | 0.929432 | 0.0349302 | ||||||||
\(709\) | −9.79318 | −0.367791 | −0.183895 | − | 0.982946i | \(-0.558871\pi\) | ||||
−0.183895 | + | 0.982946i | \(0.558871\pi\) | |||||||
\(710\) | −2.67949 | −0.100560 | ||||||||
\(711\) | 1.26952 | 0.0476106 | ||||||||
\(712\) | 47.1613 | 1.76744 | ||||||||
\(713\) | 41.4857 | 1.55365 | ||||||||
\(714\) | −8.05304 | −0.301377 | ||||||||
\(715\) | −1.05140 | −0.0393203 | ||||||||
\(716\) | 7.53770 | 0.281697 | ||||||||
\(717\) | 11.6051 | 0.433399 | ||||||||
\(718\) | −35.3432 | −1.31900 | ||||||||
\(719\) | 10.8265 | 0.403760 | 0.201880 | − | 0.979410i | \(-0.435295\pi\) | ||||
0.201880 | + | 0.979410i | \(0.435295\pi\) | |||||||
\(720\) | 1.33721 | 0.0498348 | ||||||||
\(721\) | −3.63309 | −0.135303 | ||||||||
\(722\) | −19.6656 | −0.731879 | ||||||||
\(723\) | 7.30272 | 0.271591 | ||||||||
\(724\) | 16.4378 | 0.610904 | ||||||||
\(725\) | −16.4597 | −0.611299 | ||||||||
\(726\) | 10.2361 | 0.379897 | ||||||||
\(727\) | −27.5127 | −1.02039 | −0.510194 | − | 0.860059i | \(-0.670426\pi\) | ||||
−0.510194 | + | 0.860059i | \(0.670426\pi\) | |||||||
\(728\) | −11.0733 | −0.410403 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.51499 | 0.0560723 | ||||||||
\(731\) | −1.91190 | −0.0707141 | ||||||||
\(732\) | −3.57658 | −0.132194 | ||||||||
\(733\) | 3.65073 | 0.134843 | 0.0674215 | − | 0.997725i | \(-0.478523\pi\) | ||||
0.0674215 | + | 0.997725i | \(0.478523\pi\) | |||||||
\(734\) | −2.85290 | −0.105302 | ||||||||
\(735\) | 5.65696 | 0.208660 | ||||||||
\(736\) | −40.4416 | −1.49070 | ||||||||
\(737\) | −4.46708 | −0.164547 | ||||||||
\(738\) | −8.53062 | −0.314016 | ||||||||
\(739\) | −22.1767 | −0.815783 | −0.407892 | − | 0.913030i | \(-0.633736\pi\) | ||||
−0.407892 | + | 0.913030i | \(0.633736\pi\) | |||||||
\(740\) | −1.36937 | −0.0503391 | ||||||||
\(741\) | −0.646012 | −0.0237318 | ||||||||
\(742\) | 12.1150 | 0.444757 | ||||||||
\(743\) | −32.5742 | −1.19503 | −0.597515 | − | 0.801858i | \(-0.703845\pi\) | ||||
−0.597515 | + | 0.801858i | \(0.703845\pi\) | |||||||
\(744\) | −14.2102 | −0.520969 | ||||||||
\(745\) | 7.23420 | 0.265041 | ||||||||
\(746\) | 31.1752 | 1.14140 | ||||||||
\(747\) | 13.3649 | 0.488996 | ||||||||
\(748\) | −2.12385 | −0.0776555 | ||||||||
\(749\) | −55.6142 | −2.03210 | ||||||||
\(750\) | −8.85275 | −0.323257 | ||||||||
\(751\) | 20.8635 | 0.761321 | 0.380660 | − | 0.924715i | \(-0.375697\pi\) | ||||
0.380660 | + | 0.924715i | \(0.375697\pi\) | |||||||
\(752\) | −7.16038 | −0.261112 | ||||||||
\(753\) | −1.05425 | −0.0384190 | ||||||||
\(754\) | −4.17989 | −0.152222 | ||||||||
\(755\) | −5.52704 | −0.201150 | ||||||||
\(756\) | −3.19729 | −0.116284 | ||||||||
\(757\) | 8.93766 | 0.324845 | 0.162422 | − | 0.986721i | \(-0.448069\pi\) | ||||
0.162422 | + | 0.986721i | \(0.448069\pi\) | |||||||
\(758\) | −29.5819 | −1.07446 | ||||||||
\(759\) | −10.2526 | −0.372145 | ||||||||
\(760\) | −1.79670 | −0.0651731 | ||||||||
\(761\) | −51.8674 | −1.88019 | −0.940096 | − | 0.340910i | \(-0.889265\pi\) | ||||
−0.940096 | + | 0.340910i | \(0.889265\pi\) | |||||||
\(762\) | −15.7935 | −0.572138 | ||||||||
\(763\) | −20.0181 | −0.724704 | ||||||||
\(764\) | 12.5265 | 0.453192 | ||||||||
\(765\) | 1.91125 | 0.0691015 | ||||||||
\(766\) | −5.55285 | −0.200633 | ||||||||
\(767\) | −1.05612 | −0.0381342 | ||||||||
\(768\) | 16.4318 | 0.592932 | ||||||||
\(769\) | −13.1951 | −0.475826 | −0.237913 | − | 0.971286i | \(-0.576463\pi\) | ||||
−0.237913 | + | 0.971286i | \(0.576463\pi\) | |||||||
\(770\) | −4.04247 | −0.145680 | ||||||||
\(771\) | −1.32938 | −0.0478764 | ||||||||
\(772\) | −16.1901 | −0.582693 | ||||||||
\(773\) | 1.09411 | 0.0393524 | 0.0196762 | − | 0.999806i | \(-0.493736\pi\) | ||||
0.0196762 | + | 0.999806i | \(0.493736\pi\) | |||||||
\(774\) | 0.966010 | 0.0347225 | ||||||||
\(775\) | 19.4293 | 0.697922 | ||||||||
\(776\) | −14.9664 | −0.537262 | ||||||||
\(777\) | −6.19523 | −0.222253 | ||||||||
\(778\) | −2.86079 | −0.102564 | ||||||||
\(779\) | 5.20740 | 0.186575 | ||||||||
\(780\) | 0.803047 | 0.0287537 | ||||||||
\(781\) | −3.19707 | −0.114400 | ||||||||
\(782\) | 19.7234 | 0.705308 | ||||||||
\(783\) | −3.94970 | −0.141151 | ||||||||
\(784\) | −9.08472 | −0.324454 | ||||||||
\(785\) | 18.2264 | 0.650529 | ||||||||
\(786\) | 4.72078 | 0.168385 | ||||||||
\(787\) | 47.3597 | 1.68819 | 0.844096 | − | 0.536193i | \(-0.180138\pi\) | ||||
0.844096 | + | 0.536193i | \(0.180138\pi\) | |||||||
\(788\) | 5.48489 | 0.195391 | ||||||||
\(789\) | −11.4127 | −0.406303 | ||||||||
\(790\) | −1.22595 | −0.0436174 | ||||||||
\(791\) | 34.0848 | 1.21192 | ||||||||
\(792\) | 3.51183 | 0.124788 | ||||||||
\(793\) | 4.06408 | 0.144320 | ||||||||
\(794\) | −0.785604 | −0.0278800 | ||||||||
\(795\) | −2.87530 | −0.101976 | ||||||||
\(796\) | −11.1200 | −0.394137 | ||||||||
\(797\) | −32.5906 | −1.15442 | −0.577209 | − | 0.816596i | \(-0.695858\pi\) | ||||
−0.577209 | + | 0.816596i | \(0.695858\pi\) | |||||||
\(798\) | −2.48380 | −0.0879257 | ||||||||
\(799\) | −10.2342 | −0.362061 | ||||||||
\(800\) | −18.9403 | −0.669642 | ||||||||
\(801\) | −15.4734 | −0.546727 | ||||||||
\(802\) | 2.81455 | 0.0993851 | ||||||||
\(803\) | 1.80763 | 0.0637898 | ||||||||
\(804\) | 3.41189 | 0.120328 | ||||||||
\(805\) | −29.4992 | −1.03971 | ||||||||
\(806\) | 4.93400 | 0.173793 | ||||||||
\(807\) | −25.9749 | −0.914358 | ||||||||
\(808\) | −33.8096 | −1.18942 | ||||||||
\(809\) | −1.17356 | −0.0412601 | −0.0206301 | − | 0.999787i | \(-0.506567\pi\) | ||||
−0.0206301 | + | 0.999787i | \(0.506567\pi\) | |||||||
\(810\) | −0.965685 | −0.0339307 | ||||||||
\(811\) | −24.8317 | −0.871959 | −0.435980 | − | 0.899957i | \(-0.643598\pi\) | ||||
−0.435980 | + | 0.899957i | \(0.643598\pi\) | |||||||
\(812\) | 12.6283 | 0.443168 | ||||||||
\(813\) | 16.4799 | 0.577976 | ||||||||
\(814\) | 2.07929 | 0.0728791 | ||||||||
\(815\) | −13.4716 | −0.471890 | ||||||||
\(816\) | −3.06935 | −0.107449 | ||||||||
\(817\) | −0.589688 | −0.0206306 | ||||||||
\(818\) | 16.1241 | 0.563765 | ||||||||
\(819\) | 3.63309 | 0.126951 | ||||||||
\(820\) | −6.47324 | −0.226055 | ||||||||
\(821\) | 49.4197 | 1.72476 | 0.862380 | − | 0.506261i | \(-0.168973\pi\) | ||||
0.862380 | + | 0.506261i | \(0.168973\pi\) | |||||||
\(822\) | 11.9732 | 0.417612 | ||||||||
\(823\) | −44.0564 | −1.53571 | −0.767854 | − | 0.640625i | \(-0.778675\pi\) | ||||
−0.767854 | + | 0.640625i | \(0.778675\pi\) | |||||||
\(824\) | −3.04789 | −0.106178 | ||||||||
\(825\) | −4.80168 | −0.167173 | ||||||||
\(826\) | −4.06059 | −0.141286 | ||||||||
\(827\) | −4.83406 | −0.168097 | −0.0840484 | − | 0.996462i | \(-0.526785\pi\) | ||||
−0.0840484 | + | 0.996462i | \(0.526785\pi\) | |||||||
\(828\) | 7.83077 | 0.272138 | ||||||||
\(829\) | 12.7858 | 0.444071 | 0.222035 | − | 0.975039i | \(-0.428730\pi\) | ||||
0.222035 | + | 0.975039i | \(0.428730\pi\) | |||||||
\(830\) | −12.9063 | −0.447984 | ||||||||
\(831\) | 4.87661 | 0.169168 | ||||||||
\(832\) | −7.74068 | −0.268360 | ||||||||
\(833\) | −12.9847 | −0.449892 | ||||||||
\(834\) | −6.99686 | −0.242281 | ||||||||
\(835\) | −7.51165 | −0.259951 | ||||||||
\(836\) | −0.655059 | −0.0226557 | ||||||||
\(837\) | 4.66229 | 0.161152 | ||||||||
\(838\) | 34.1156 | 1.17850 | ||||||||
\(839\) | −18.6518 | −0.643932 | −0.321966 | − | 0.946751i | \(-0.604344\pi\) | ||||
−0.321966 | + | 0.946751i | \(0.604344\pi\) | |||||||
\(840\) | 10.1044 | 0.348636 | ||||||||
\(841\) | −13.3998 | −0.462064 | ||||||||
\(842\) | −2.03287 | −0.0700575 | ||||||||
\(843\) | 29.8226 | 1.02714 | ||||||||
\(844\) | −13.6827 | −0.470978 | ||||||||
\(845\) | −0.912505 | −0.0313911 | ||||||||
\(846\) | 5.17098 | 0.177782 | ||||||||
\(847\) | 35.1407 | 1.20745 | ||||||||
\(848\) | 4.61755 | 0.158567 | ||||||||
\(849\) | 8.51437 | 0.292212 | ||||||||
\(850\) | 9.23722 | 0.316834 | ||||||||
\(851\) | 15.1733 | 0.520133 | ||||||||
\(852\) | 2.44187 | 0.0836571 | ||||||||
\(853\) | −43.9046 | −1.50326 | −0.751632 | − | 0.659582i | \(-0.770733\pi\) | ||||
−0.751632 | + | 0.659582i | \(0.770733\pi\) | |||||||
\(854\) | 15.6257 | 0.534700 | ||||||||
\(855\) | 0.589489 | 0.0201601 | ||||||||
\(856\) | −46.6561 | −1.59467 | ||||||||
\(857\) | 18.5751 | 0.634515 | 0.317257 | − | 0.948339i | \(-0.397238\pi\) | ||||
0.317257 | + | 0.948339i | \(0.397238\pi\) | |||||||
\(858\) | −1.21937 | −0.0416285 | ||||||||
\(859\) | −55.1525 | −1.88178 | −0.940890 | − | 0.338712i | \(-0.890009\pi\) | ||||
−0.940890 | + | 0.338712i | \(0.890009\pi\) | |||||||
\(860\) | 0.733032 | 0.0249962 | ||||||||
\(861\) | −29.2858 | −0.998058 | ||||||||
\(862\) | 9.52288 | 0.324351 | ||||||||
\(863\) | 11.8656 | 0.403911 | 0.201955 | − | 0.979395i | \(-0.435270\pi\) | ||||
0.201955 | + | 0.979395i | \(0.435270\pi\) | |||||||
\(864\) | −4.54495 | −0.154622 | ||||||||
\(865\) | −16.2836 | −0.553658 | ||||||||
\(866\) | −15.2927 | −0.519666 | ||||||||
\(867\) | 12.6130 | 0.428360 | ||||||||
\(868\) | −14.9067 | −0.505966 | ||||||||
\(869\) | −1.46276 | −0.0496207 | ||||||||
\(870\) | 3.81417 | 0.129312 | ||||||||
\(871\) | −3.87694 | −0.131365 | ||||||||
\(872\) | −16.7937 | −0.568706 | ||||||||
\(873\) | 4.91041 | 0.166192 | ||||||||
\(874\) | 6.08330 | 0.205771 | ||||||||
\(875\) | −30.3917 | −1.02743 | ||||||||
\(876\) | −1.38064 | −0.0466475 | ||||||||
\(877\) | −13.7934 | −0.465771 | −0.232886 | − | 0.972504i | \(-0.574817\pi\) | ||||
−0.232886 | + | 0.972504i | \(0.574817\pi\) | |||||||
\(878\) | −4.66893 | −0.157569 | ||||||||
\(879\) | −17.9383 | −0.605042 | ||||||||
\(880\) | −1.54076 | −0.0519388 | ||||||||
\(881\) | 35.0062 | 1.17939 | 0.589694 | − | 0.807627i | \(-0.299248\pi\) | ||||
0.589694 | + | 0.807627i | \(0.299248\pi\) | |||||||
\(882\) | 6.56066 | 0.220909 | ||||||||
\(883\) | 7.56853 | 0.254701 | 0.127351 | − | 0.991858i | \(-0.459353\pi\) | ||||
0.127351 | + | 0.991858i | \(0.459353\pi\) | |||||||
\(884\) | −1.84327 | −0.0619958 | ||||||||
\(885\) | 0.963713 | 0.0323948 | ||||||||
\(886\) | 15.6318 | 0.525162 | ||||||||
\(887\) | −38.7055 | −1.29960 | −0.649801 | − | 0.760104i | \(-0.725148\pi\) | ||||
−0.649801 | + | 0.760104i | \(0.725148\pi\) | |||||||
\(888\) | −5.19733 | −0.174411 | ||||||||
\(889\) | −54.2194 | −1.81846 | ||||||||
\(890\) | 14.9424 | 0.500872 | ||||||||
\(891\) | −1.15222 | −0.0386007 | ||||||||
\(892\) | −1.63164 | −0.0546314 | ||||||||
\(893\) | −3.15655 | −0.105630 | ||||||||
\(894\) | 8.38987 | 0.280599 | ||||||||
\(895\) | 7.81571 | 0.261250 | ||||||||
\(896\) | 3.26293 | 0.109007 | ||||||||
\(897\) | −8.89813 | −0.297100 | ||||||||
\(898\) | −27.0727 | −0.903429 | ||||||||
\(899\) | −18.4147 | −0.614163 | ||||||||
\(900\) | 3.66745 | 0.122248 | ||||||||
\(901\) | 6.59980 | 0.219871 | ||||||||
\(902\) | 9.82913 | 0.327274 | ||||||||
\(903\) | 3.31633 | 0.110361 | ||||||||
\(904\) | 28.5946 | 0.951041 | ||||||||
\(905\) | 17.0440 | 0.566563 | ||||||||
\(906\) | −6.40999 | −0.212958 | ||||||||
\(907\) | −36.4509 | −1.21033 | −0.605167 | − | 0.796099i | \(-0.706894\pi\) | ||||
−0.605167 | + | 0.796099i | \(0.706894\pi\) | |||||||
\(908\) | −0.00545224 | −0.000180939 0 | ||||||||
\(909\) | 11.0928 | 0.367925 | ||||||||
\(910\) | −3.50842 | −0.116303 | ||||||||
\(911\) | −18.2314 | −0.604032 | −0.302016 | − | 0.953303i | \(-0.597660\pi\) | ||||
−0.302016 | + | 0.953303i | \(0.597660\pi\) | |||||||
\(912\) | −0.946682 | −0.0313478 | ||||||||
\(913\) | −15.3993 | −0.509642 | ||||||||
\(914\) | −19.9636 | −0.660339 | ||||||||
\(915\) | −3.70850 | −0.122599 | ||||||||
\(916\) | 18.3500 | 0.606302 | ||||||||
\(917\) | 16.2065 | 0.535187 | ||||||||
\(918\) | 2.21658 | 0.0731580 | ||||||||
\(919\) | 20.6215 | 0.680239 | 0.340120 | − | 0.940382i | \(-0.389532\pi\) | ||||
0.340120 | + | 0.940382i | \(0.389532\pi\) | |||||||
\(920\) | −24.7476 | −0.815905 | ||||||||
\(921\) | 13.1960 | 0.434822 | ||||||||
\(922\) | 7.59082 | 0.249990 | ||||||||
\(923\) | −2.77471 | −0.0913306 | ||||||||
\(924\) | 3.68398 | 0.121194 | ||||||||
\(925\) | 7.10623 | 0.233651 | ||||||||
\(926\) | −24.9605 | −0.820253 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 17.9512 | 0.589278 | ||||||||
\(929\) | 28.0681 | 0.920884 | 0.460442 | − | 0.887690i | \(-0.347691\pi\) | ||||
0.460442 | + | 0.887690i | \(0.347691\pi\) | |||||||
\(930\) | −4.50230 | −0.147636 | ||||||||
\(931\) | −4.00487 | −0.131254 | ||||||||
\(932\) | 14.5187 | 0.475575 | ||||||||
\(933\) | 11.8366 | 0.387514 | ||||||||
\(934\) | −35.7620 | −1.17017 | ||||||||
\(935\) | −2.20218 | −0.0720190 | ||||||||
\(936\) | 3.04789 | 0.0996234 | ||||||||
\(937\) | −37.8188 | −1.23549 | −0.617743 | − | 0.786380i | \(-0.711953\pi\) | ||||
−0.617743 | + | 0.786380i | \(0.711953\pi\) | |||||||
\(938\) | −14.9062 | −0.486704 | ||||||||
\(939\) | 14.8906 | 0.485936 | ||||||||
\(940\) | 3.92386 | 0.127982 | ||||||||
\(941\) | 21.1615 | 0.689846 | 0.344923 | − | 0.938631i | \(-0.387905\pi\) | ||||
0.344923 | + | 0.938631i | \(0.387905\pi\) | |||||||
\(942\) | 21.1381 | 0.688717 | ||||||||
\(943\) | 71.7265 | 2.33574 | ||||||||
\(944\) | −1.54766 | −0.0503721 | ||||||||
\(945\) | −3.31522 | −0.107844 | ||||||||
\(946\) | −1.11305 | −0.0361885 | ||||||||
\(947\) | 29.6597 | 0.963811 | 0.481905 | − | 0.876223i | \(-0.339945\pi\) | ||||
0.481905 | + | 0.876223i | \(0.339945\pi\) | |||||||
\(948\) | 1.11723 | 0.0362860 | ||||||||
\(949\) | 1.56883 | 0.0509262 | ||||||||
\(950\) | 2.84904 | 0.0924351 | ||||||||
\(951\) | −14.5587 | −0.472099 | ||||||||
\(952\) | −23.1931 | −0.751693 | ||||||||
\(953\) | −11.5483 | −0.374086 | −0.187043 | − | 0.982352i | \(-0.559890\pi\) | ||||
−0.187043 | + | 0.982352i | \(0.559890\pi\) | |||||||
\(954\) | −3.33463 | −0.107963 | ||||||||
\(955\) | 12.9885 | 0.420298 | ||||||||
\(956\) | 10.2130 | 0.330312 | ||||||||
\(957\) | 4.55092 | 0.147110 | ||||||||
\(958\) | −20.3586 | −0.657757 | ||||||||
\(959\) | 41.1042 | 1.32732 | ||||||||
\(960\) | 7.06341 | 0.227971 | ||||||||
\(961\) | −9.26306 | −0.298808 | ||||||||
\(962\) | 1.80460 | 0.0581826 | ||||||||
\(963\) | 15.3077 | 0.493282 | ||||||||
\(964\) | 6.42673 | 0.206991 | ||||||||
\(965\) | −16.7872 | −0.540399 | ||||||||
\(966\) | −34.2118 | −1.10075 | ||||||||
\(967\) | 52.3562 | 1.68366 | 0.841831 | − | 0.539741i | \(-0.181478\pi\) | ||||
0.841831 | + | 0.539741i | \(0.181478\pi\) | |||||||
\(968\) | 29.4804 | 0.947536 | ||||||||
\(969\) | −1.35308 | −0.0434672 | ||||||||
\(970\) | −4.74191 | −0.152253 | ||||||||
\(971\) | −13.0417 | −0.418527 | −0.209264 | − | 0.977859i | \(-0.567107\pi\) | ||||
−0.209264 | + | 0.977859i | \(0.567107\pi\) | |||||||
\(972\) | 0.880046 | 0.0282275 | ||||||||
\(973\) | −24.0204 | −0.770057 | ||||||||
\(974\) | 25.9294 | 0.830831 | ||||||||
\(975\) | −4.16733 | −0.133462 | ||||||||
\(976\) | 5.95561 | 0.190634 | ||||||||
\(977\) | −35.6600 | −1.14087 | −0.570433 | − | 0.821344i | \(-0.693225\pi\) | ||||
−0.570433 | + | 0.821344i | \(0.693225\pi\) | |||||||
\(978\) | −15.6237 | −0.499591 | ||||||||
\(979\) | 17.8288 | 0.569809 | ||||||||
\(980\) | 4.97839 | 0.159029 | ||||||||
\(981\) | 5.50994 | 0.175919 | ||||||||
\(982\) | 30.4787 | 0.972616 | ||||||||
\(983\) | 42.1476 | 1.34430 | 0.672150 | − | 0.740415i | \(-0.265371\pi\) | ||||
0.672150 | + | 0.740415i | \(0.265371\pi\) | |||||||
\(984\) | −24.5686 | −0.783218 | ||||||||
\(985\) | 5.68719 | 0.181209 | ||||||||
\(986\) | −8.75483 | −0.278810 | ||||||||
\(987\) | 17.7521 | 0.565055 | ||||||||
\(988\) | −0.568521 | −0.0180870 | ||||||||
\(989\) | −8.12233 | −0.258275 | ||||||||
\(990\) | 1.11268 | 0.0353633 | ||||||||
\(991\) | 8.97040 | 0.284954 | 0.142477 | − | 0.989798i | \(-0.454493\pi\) | ||||
0.142477 | + | 0.989798i | \(0.454493\pi\) | |||||||
\(992\) | −21.1899 | −0.672780 | ||||||||
\(993\) | −1.62408 | −0.0515385 | ||||||||
\(994\) | −10.6683 | −0.338377 | ||||||||
\(995\) | −11.5301 | −0.365529 | ||||||||
\(996\) | 11.7617 | 0.372685 | ||||||||
\(997\) | 1.39992 | 0.0443358 | 0.0221679 | − | 0.999754i | \(-0.492943\pi\) | ||||
0.0221679 | + | 0.999754i | \(0.492943\pi\) | |||||||
\(998\) | −6.11220 | −0.193478 | ||||||||
\(999\) | 1.70522 | 0.0539508 |
(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 | 4017.2.a.g.1.16 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.g.1.16 | ✓ | 24 | 1.1 | even | 1 | trivial |