Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1178522580\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 | ||||||||
\(3\) | 0.372945 | 0.215320 | 0.107660 | − | 0.994188i | \(-0.465664\pi\) | ||||
0.107660 | + | 0.994188i | \(0.465664\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.66658 | −1.19253 | −0.596266 | − | 0.802787i | \(-0.703350\pi\) | ||||
−0.596266 | + | 0.802787i | \(0.703350\pi\) | |||||||
\(6\) | −0.372945 | −0.152254 | ||||||||
\(7\) | 3.34934 | 1.26593 | 0.632966 | − | 0.774179i | \(-0.281837\pi\) | ||||
0.632966 | + | 0.774179i | \(0.281837\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.86091 | −0.953637 | ||||||||
\(10\) | 2.66658 | 0.843247 | ||||||||
\(11\) | −3.14966 | −0.949659 | −0.474829 | − | 0.880078i | \(-0.657490\pi\) | ||||
−0.474829 | + | 0.880078i | \(0.657490\pi\) | |||||||
\(12\) | 0.372945 | 0.107660 | ||||||||
\(13\) | 0.642654 | 0.178240 | 0.0891200 | − | 0.996021i | \(-0.471595\pi\) | ||||
0.0891200 | + | 0.996021i | \(0.471595\pi\) | |||||||
\(14\) | −3.34934 | −0.895149 | ||||||||
\(15\) | −0.994488 | −0.256776 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.11448 | −0.755373 | −0.377687 | − | 0.925934i | \(-0.623280\pi\) | ||||
−0.377687 | + | 0.925934i | \(0.623280\pi\) | |||||||
\(18\) | 2.86091 | 0.674323 | ||||||||
\(19\) | −0.263898 | −0.0605424 | −0.0302712 | − | 0.999542i | \(-0.509637\pi\) | ||||
−0.0302712 | + | 0.999542i | \(0.509637\pi\) | |||||||
\(20\) | −2.66658 | −0.596266 | ||||||||
\(21\) | 1.24912 | 0.272580 | ||||||||
\(22\) | 3.14966 | 0.671510 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −0.372945 | −0.0761271 | ||||||||
\(25\) | 2.11066 | 0.422131 | ||||||||
\(26\) | −0.642654 | −0.126035 | ||||||||
\(27\) | −2.18580 | −0.420657 | ||||||||
\(28\) | 3.34934 | 0.632966 | ||||||||
\(29\) | 8.24723 | 1.53147 | 0.765736 | − | 0.643155i | \(-0.222375\pi\) | ||||
0.765736 | + | 0.643155i | \(0.222375\pi\) | |||||||
\(30\) | 0.994488 | 0.181568 | ||||||||
\(31\) | 8.42877 | 1.51385 | 0.756926 | − | 0.653501i | \(-0.226700\pi\) | ||||
0.756926 | + | 0.653501i | \(0.226700\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.17465 | −0.204480 | ||||||||
\(34\) | 3.11448 | 0.534129 | ||||||||
\(35\) | −8.93129 | −1.50966 | ||||||||
\(36\) | −2.86091 | −0.476819 | ||||||||
\(37\) | −11.3608 | −1.86771 | −0.933854 | − | 0.357656i | \(-0.883576\pi\) | ||||
−0.933854 | + | 0.357656i | \(0.883576\pi\) | |||||||
\(38\) | 0.263898 | 0.0428099 | ||||||||
\(39\) | 0.239674 | 0.0383786 | ||||||||
\(40\) | 2.66658 | 0.421624 | ||||||||
\(41\) | −2.02200 | −0.315783 | −0.157892 | − | 0.987456i | \(-0.550470\pi\) | ||||
−0.157892 | + | 0.987456i | \(0.550470\pi\) | |||||||
\(42\) | −1.24912 | −0.192743 | ||||||||
\(43\) | −1.76054 | −0.268480 | −0.134240 | − | 0.990949i | \(-0.542859\pi\) | ||||
−0.134240 | + | 0.990949i | \(0.542859\pi\) | |||||||
\(44\) | −3.14966 | −0.474829 | ||||||||
\(45\) | 7.62885 | 1.13724 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −0.148071 | −0.0215984 | −0.0107992 | − | 0.999942i | \(-0.503438\pi\) | ||||
−0.0107992 | + | 0.999942i | \(0.503438\pi\) | |||||||
\(48\) | 0.372945 | 0.0538300 | ||||||||
\(49\) | 4.21809 | 0.602585 | ||||||||
\(50\) | −2.11066 | −0.298492 | ||||||||
\(51\) | −1.16153 | −0.162647 | ||||||||
\(52\) | 0.642654 | 0.0891200 | ||||||||
\(53\) | −9.49126 | −1.30373 | −0.651863 | − | 0.758337i | \(-0.726012\pi\) | ||||
−0.651863 | + | 0.758337i | \(0.726012\pi\) | |||||||
\(54\) | 2.18580 | 0.297449 | ||||||||
\(55\) | 8.39883 | 1.13250 | ||||||||
\(56\) | −3.34934 | −0.447575 | ||||||||
\(57\) | −0.0984195 | −0.0130360 | ||||||||
\(58\) | −8.24723 | −1.08291 | ||||||||
\(59\) | −3.73906 | −0.486784 | −0.243392 | − | 0.969928i | \(-0.578260\pi\) | ||||
−0.243392 | + | 0.969928i | \(0.578260\pi\) | |||||||
\(60\) | −0.994488 | −0.128388 | ||||||||
\(61\) | 5.20249 | 0.666111 | 0.333055 | − | 0.942907i | \(-0.391920\pi\) | ||||
0.333055 | + | 0.942907i | \(0.391920\pi\) | |||||||
\(62\) | −8.42877 | −1.07045 | ||||||||
\(63\) | −9.58217 | −1.20724 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.71369 | −0.212557 | ||||||||
\(66\) | 1.17465 | 0.144589 | ||||||||
\(67\) | 5.80138 | 0.708752 | 0.354376 | − | 0.935103i | \(-0.384693\pi\) | ||||
0.354376 | + | 0.935103i | \(0.384693\pi\) | |||||||
\(68\) | −3.11448 | −0.377687 | ||||||||
\(69\) | −0.372945 | −0.0448973 | ||||||||
\(70\) | 8.93129 | 1.06749 | ||||||||
\(71\) | −14.2284 | −1.68860 | −0.844301 | − | 0.535870i | \(-0.819984\pi\) | ||||
−0.844301 | + | 0.535870i | \(0.819984\pi\) | |||||||
\(72\) | 2.86091 | 0.337162 | ||||||||
\(73\) | −4.25808 | −0.498371 | −0.249185 | − | 0.968456i | \(-0.580163\pi\) | ||||
−0.249185 | + | 0.968456i | \(0.580163\pi\) | |||||||
\(74\) | 11.3608 | 1.32067 | ||||||||
\(75\) | 0.787158 | 0.0908932 | ||||||||
\(76\) | −0.263898 | −0.0302712 | ||||||||
\(77\) | −10.5493 | −1.20220 | ||||||||
\(78\) | −0.239674 | −0.0271378 | ||||||||
\(79\) | 5.78002 | 0.650303 | 0.325151 | − | 0.945662i | \(-0.394585\pi\) | ||||
0.325151 | + | 0.945662i | \(0.394585\pi\) | |||||||
\(80\) | −2.66658 | −0.298133 | ||||||||
\(81\) | 7.76755 | 0.863062 | ||||||||
\(82\) | 2.02200 | 0.223293 | ||||||||
\(83\) | 2.76081 | 0.303039 | 0.151519 | − | 0.988454i | \(-0.451583\pi\) | ||||
0.151519 | + | 0.988454i | \(0.451583\pi\) | |||||||
\(84\) | 1.24912 | 0.136290 | ||||||||
\(85\) | 8.30502 | 0.900806 | ||||||||
\(86\) | 1.76054 | 0.189844 | ||||||||
\(87\) | 3.07576 | 0.329756 | ||||||||
\(88\) | 3.14966 | 0.335755 | ||||||||
\(89\) | 12.7467 | 1.35115 | 0.675574 | − | 0.737292i | \(-0.263896\pi\) | ||||
0.675574 | + | 0.737292i | \(0.263896\pi\) | |||||||
\(90\) | −7.62885 | −0.804152 | ||||||||
\(91\) | 2.15247 | 0.225640 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 3.14347 | 0.325962 | ||||||||
\(94\) | 0.148071 | 0.0152724 | ||||||||
\(95\) | 0.703706 | 0.0721987 | ||||||||
\(96\) | −0.372945 | −0.0380635 | ||||||||
\(97\) | −3.82614 | −0.388486 | −0.194243 | − | 0.980953i | \(-0.562225\pi\) | ||||
−0.194243 | + | 0.980953i | \(0.562225\pi\) | |||||||
\(98\) | −4.21809 | −0.426092 | ||||||||
\(99\) | 9.01090 | 0.905630 | ||||||||
\(100\) | 2.11066 | 0.211066 | ||||||||
\(101\) | 16.4278 | 1.63463 | 0.817315 | − | 0.576191i | \(-0.195462\pi\) | ||||
0.817315 | + | 0.576191i | \(0.195462\pi\) | |||||||
\(102\) | 1.16153 | 0.115009 | ||||||||
\(103\) | 18.3341 | 1.80651 | 0.903255 | − | 0.429104i | \(-0.141171\pi\) | ||||
0.903255 | + | 0.429104i | \(0.141171\pi\) | |||||||
\(104\) | −0.642654 | −0.0630174 | ||||||||
\(105\) | −3.33088 | −0.325061 | ||||||||
\(106\) | 9.49126 | 0.921873 | ||||||||
\(107\) | 1.01800 | 0.0984137 | 0.0492068 | − | 0.998789i | \(-0.484331\pi\) | ||||
0.0492068 | + | 0.998789i | \(0.484331\pi\) | |||||||
\(108\) | −2.18580 | −0.210328 | ||||||||
\(109\) | 7.29920 | 0.699137 | 0.349569 | − | 0.936911i | \(-0.386328\pi\) | ||||
0.349569 | + | 0.936911i | \(0.386328\pi\) | |||||||
\(110\) | −8.39883 | −0.800797 | ||||||||
\(111\) | −4.23696 | −0.402154 | ||||||||
\(112\) | 3.34934 | 0.316483 | ||||||||
\(113\) | −18.4414 | −1.73482 | −0.867410 | − | 0.497595i | \(-0.834217\pi\) | ||||
−0.867410 | + | 0.497595i | \(0.834217\pi\) | |||||||
\(114\) | 0.0984195 | 0.00921783 | ||||||||
\(115\) | 2.66658 | 0.248660 | ||||||||
\(116\) | 8.24723 | 0.765736 | ||||||||
\(117\) | −1.83858 | −0.169976 | ||||||||
\(118\) | 3.73906 | 0.344208 | ||||||||
\(119\) | −10.4315 | −0.956251 | ||||||||
\(120\) | 0.994488 | 0.0907839 | ||||||||
\(121\) | −1.07963 | −0.0981485 | ||||||||
\(122\) | −5.20249 | −0.471011 | ||||||||
\(123\) | −0.754095 | −0.0679944 | ||||||||
\(124\) | 8.42877 | 0.756926 | ||||||||
\(125\) | 7.70467 | 0.689127 | ||||||||
\(126\) | 9.58217 | 0.853648 | ||||||||
\(127\) | −6.86305 | −0.608997 | −0.304499 | − | 0.952513i | \(-0.598489\pi\) | ||||
−0.304499 | + | 0.952513i | \(0.598489\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.656586 | −0.0578092 | ||||||||
\(130\) | 1.71369 | 0.150300 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | −1.17465 | −0.102240 | ||||||||
\(133\) | −0.883885 | −0.0766426 | ||||||||
\(134\) | −5.80138 | −0.501163 | ||||||||
\(135\) | 5.82861 | 0.501647 | ||||||||
\(136\) | 3.11448 | 0.267065 | ||||||||
\(137\) | 11.5250 | 0.984649 | 0.492325 | − | 0.870412i | \(-0.336147\pi\) | ||||
0.492325 | + | 0.870412i | \(0.336147\pi\) | |||||||
\(138\) | 0.372945 | 0.0317472 | ||||||||
\(139\) | −15.1884 | −1.28826 | −0.644132 | − | 0.764914i | \(-0.722781\pi\) | ||||
−0.644132 | + | 0.764914i | \(0.722781\pi\) | |||||||
\(140\) | −8.93129 | −0.754832 | ||||||||
\(141\) | −0.0552225 | −0.00465057 | ||||||||
\(142\) | 14.2284 | 1.19402 | ||||||||
\(143\) | −2.02414 | −0.169267 | ||||||||
\(144\) | −2.86091 | −0.238409 | ||||||||
\(145\) | −21.9919 | −1.82633 | ||||||||
\(146\) | 4.25808 | 0.352401 | ||||||||
\(147\) | 1.57312 | 0.129748 | ||||||||
\(148\) | −11.3608 | −0.933854 | ||||||||
\(149\) | 21.3323 | 1.74761 | 0.873804 | − | 0.486278i | \(-0.161646\pi\) | ||||
0.873804 | + | 0.486278i | \(0.161646\pi\) | |||||||
\(150\) | −0.787158 | −0.0642712 | ||||||||
\(151\) | 13.0219 | 1.05971 | 0.529854 | − | 0.848089i | \(-0.322247\pi\) | ||||
0.529854 | + | 0.848089i | \(0.322247\pi\) | |||||||
\(152\) | 0.263898 | 0.0214050 | ||||||||
\(153\) | 8.91026 | 0.720352 | ||||||||
\(154\) | 10.5493 | 0.850086 | ||||||||
\(155\) | −22.4760 | −1.80532 | ||||||||
\(156\) | 0.239674 | 0.0191893 | ||||||||
\(157\) | 19.0971 | 1.52412 | 0.762058 | − | 0.647509i | \(-0.224189\pi\) | ||||
0.762058 | + | 0.647509i | \(0.224189\pi\) | |||||||
\(158\) | −5.78002 | −0.459834 | ||||||||
\(159\) | −3.53972 | −0.280718 | ||||||||
\(160\) | 2.66658 | 0.210812 | ||||||||
\(161\) | −3.34934 | −0.263965 | ||||||||
\(162\) | −7.76755 | −0.610277 | ||||||||
\(163\) | −0.0511642 | −0.00400749 | −0.00200374 | − | 0.999998i | \(-0.500638\pi\) | ||||
−0.00200374 | + | 0.999998i | \(0.500638\pi\) | |||||||
\(164\) | −2.02200 | −0.157892 | ||||||||
\(165\) | 3.13230 | 0.243849 | ||||||||
\(166\) | −2.76081 | −0.214281 | ||||||||
\(167\) | 7.81925 | 0.605072 | 0.302536 | − | 0.953138i | \(-0.402167\pi\) | ||||
0.302536 | + | 0.953138i | \(0.402167\pi\) | |||||||
\(168\) | −1.24912 | −0.0963717 | ||||||||
\(169\) | −12.5870 | −0.968230 | ||||||||
\(170\) | −8.30502 | −0.636966 | ||||||||
\(171\) | 0.754989 | 0.0577355 | ||||||||
\(172\) | −1.76054 | −0.134240 | ||||||||
\(173\) | −5.91632 | −0.449810 | −0.224905 | − | 0.974381i | \(-0.572207\pi\) | ||||
−0.224905 | + | 0.974381i | \(0.572207\pi\) | |||||||
\(174\) | −3.07576 | −0.233173 | ||||||||
\(175\) | 7.06931 | 0.534389 | ||||||||
\(176\) | −3.14966 | −0.237415 | ||||||||
\(177\) | −1.39446 | −0.104814 | ||||||||
\(178\) | −12.7467 | −0.955406 | ||||||||
\(179\) | 6.28387 | 0.469679 | 0.234839 | − | 0.972034i | \(-0.424544\pi\) | ||||
0.234839 | + | 0.972034i | \(0.424544\pi\) | |||||||
\(180\) | 7.62885 | 0.568621 | ||||||||
\(181\) | 8.23941 | 0.612430 | 0.306215 | − | 0.951962i | \(-0.400937\pi\) | ||||
0.306215 | + | 0.951962i | \(0.400937\pi\) | |||||||
\(182\) | −2.15247 | −0.159551 | ||||||||
\(183\) | 1.94024 | 0.143427 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 30.2945 | 2.22730 | ||||||||
\(186\) | −3.14347 | −0.230490 | ||||||||
\(187\) | 9.80957 | 0.717347 | ||||||||
\(188\) | −0.148071 | −0.0107992 | ||||||||
\(189\) | −7.32098 | −0.532523 | ||||||||
\(190\) | −0.703706 | −0.0510522 | ||||||||
\(191\) | 8.82014 | 0.638203 | 0.319101 | − | 0.947721i | \(-0.396619\pi\) | ||||
0.319101 | + | 0.947721i | \(0.396619\pi\) | |||||||
\(192\) | 0.372945 | 0.0269150 | ||||||||
\(193\) | −7.10907 | −0.511722 | −0.255861 | − | 0.966714i | \(-0.582359\pi\) | ||||
−0.255861 | + | 0.966714i | \(0.582359\pi\) | |||||||
\(194\) | 3.82614 | 0.274701 | ||||||||
\(195\) | −0.639112 | −0.0457677 | ||||||||
\(196\) | 4.21809 | 0.301292 | ||||||||
\(197\) | −6.06136 | −0.431854 | −0.215927 | − | 0.976409i | \(-0.569277\pi\) | ||||
−0.215927 | + | 0.976409i | \(0.569277\pi\) | |||||||
\(198\) | −9.01090 | −0.640377 | ||||||||
\(199\) | −21.8539 | −1.54918 | −0.774589 | − | 0.632465i | \(-0.782043\pi\) | ||||
−0.774589 | + | 0.632465i | \(0.782043\pi\) | |||||||
\(200\) | −2.11066 | −0.149246 | ||||||||
\(201\) | 2.16360 | 0.152608 | ||||||||
\(202\) | −16.4278 | −1.15586 | ||||||||
\(203\) | 27.6228 | 1.93874 | ||||||||
\(204\) | −1.16153 | −0.0813234 | ||||||||
\(205\) | 5.39183 | 0.376581 | ||||||||
\(206\) | −18.3341 | −1.27740 | ||||||||
\(207\) | 2.86091 | 0.198847 | ||||||||
\(208\) | 0.642654 | 0.0445600 | ||||||||
\(209\) | 0.831190 | 0.0574946 | ||||||||
\(210\) | 3.33088 | 0.229853 | ||||||||
\(211\) | 8.20266 | 0.564694 | 0.282347 | − | 0.959312i | \(-0.408887\pi\) | ||||
0.282347 | + | 0.959312i | \(0.408887\pi\) | |||||||
\(212\) | −9.49126 | −0.651863 | ||||||||
\(213\) | −5.30641 | −0.363589 | ||||||||
\(214\) | −1.01800 | −0.0695890 | ||||||||
\(215\) | 4.69463 | 0.320171 | ||||||||
\(216\) | 2.18580 | 0.148725 | ||||||||
\(217\) | 28.2308 | 1.91643 | ||||||||
\(218\) | −7.29920 | −0.494365 | ||||||||
\(219\) | −1.58803 | −0.107309 | ||||||||
\(220\) | 8.39883 | 0.566249 | ||||||||
\(221\) | −2.00153 | −0.134638 | ||||||||
\(222\) | 4.23696 | 0.284366 | ||||||||
\(223\) | 5.14663 | 0.344644 | 0.172322 | − | 0.985041i | \(-0.444873\pi\) | ||||
0.172322 | + | 0.985041i | \(0.444873\pi\) | |||||||
\(224\) | −3.34934 | −0.223787 | ||||||||
\(225\) | −6.03840 | −0.402560 | ||||||||
\(226\) | 18.4414 | 1.22670 | ||||||||
\(227\) | −24.7569 | −1.64317 | −0.821585 | − | 0.570086i | \(-0.806910\pi\) | ||||
−0.821585 | + | 0.570086i | \(0.806910\pi\) | |||||||
\(228\) | −0.0984195 | −0.00651799 | ||||||||
\(229\) | 25.1048 | 1.65897 | 0.829486 | − | 0.558528i | \(-0.188634\pi\) | ||||
0.829486 | + | 0.558528i | \(0.188634\pi\) | |||||||
\(230\) | −2.66658 | −0.175829 | ||||||||
\(231\) | −3.93431 | −0.258858 | ||||||||
\(232\) | −8.24723 | −0.541457 | ||||||||
\(233\) | −7.49513 | −0.491022 | −0.245511 | − | 0.969394i | \(-0.578956\pi\) | ||||
−0.245511 | + | 0.969394i | \(0.578956\pi\) | |||||||
\(234\) | 1.83858 | 0.120191 | ||||||||
\(235\) | 0.394844 | 0.0257568 | ||||||||
\(236\) | −3.73906 | −0.243392 | ||||||||
\(237\) | 2.15563 | 0.140023 | ||||||||
\(238\) | 10.4315 | 0.676172 | ||||||||
\(239\) | −18.7569 | −1.21328 | −0.606641 | − | 0.794976i | \(-0.707483\pi\) | ||||
−0.606641 | + | 0.794976i | \(0.707483\pi\) | |||||||
\(240\) | −0.994488 | −0.0641939 | ||||||||
\(241\) | −21.4904 | −1.38432 | −0.692159 | − | 0.721745i | \(-0.743340\pi\) | ||||
−0.692159 | + | 0.721745i | \(0.743340\pi\) | |||||||
\(242\) | 1.07963 | 0.0694014 | ||||||||
\(243\) | 9.45426 | 0.606491 | ||||||||
\(244\) | 5.20249 | 0.333055 | ||||||||
\(245\) | −11.2479 | −0.718601 | ||||||||
\(246\) | 0.754095 | 0.0480793 | ||||||||
\(247\) | −0.169595 | −0.0107911 | ||||||||
\(248\) | −8.42877 | −0.535227 | ||||||||
\(249\) | 1.02963 | 0.0652502 | ||||||||
\(250\) | −7.70467 | −0.487286 | ||||||||
\(251\) | −3.62925 | −0.229076 | −0.114538 | − | 0.993419i | \(-0.536539\pi\) | ||||
−0.114538 | + | 0.993419i | \(0.536539\pi\) | |||||||
\(252\) | −9.58217 | −0.603620 | ||||||||
\(253\) | 3.14966 | 0.198018 | ||||||||
\(254\) | 6.86305 | 0.430626 | ||||||||
\(255\) | 3.09732 | 0.193961 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.7861 | −1.35898 | −0.679489 | − | 0.733686i | \(-0.737798\pi\) | ||||
−0.679489 | + | 0.733686i | \(0.737798\pi\) | |||||||
\(258\) | 0.656586 | 0.0408773 | ||||||||
\(259\) | −38.0513 | −2.36439 | ||||||||
\(260\) | −1.71369 | −0.106278 | ||||||||
\(261\) | −23.5946 | −1.46047 | ||||||||
\(262\) | −1.00000 | −0.0617802 | ||||||||
\(263\) | 4.41684 | 0.272354 | 0.136177 | − | 0.990685i | \(-0.456518\pi\) | ||||
0.136177 | + | 0.990685i | \(0.456518\pi\) | |||||||
\(264\) | 1.17465 | 0.0722947 | ||||||||
\(265\) | 25.3092 | 1.55473 | ||||||||
\(266\) | 0.883885 | 0.0541945 | ||||||||
\(267\) | 4.75382 | 0.290929 | ||||||||
\(268\) | 5.80138 | 0.354376 | ||||||||
\(269\) | 22.9534 | 1.39949 | 0.699747 | − | 0.714390i | \(-0.253296\pi\) | ||||
0.699747 | + | 0.714390i | \(0.253296\pi\) | |||||||
\(270\) | −5.82861 | −0.354718 | ||||||||
\(271\) | 15.9775 | 0.970563 | 0.485282 | − | 0.874358i | \(-0.338717\pi\) | ||||
0.485282 | + | 0.874358i | \(0.338717\pi\) | |||||||
\(272\) | −3.11448 | −0.188843 | ||||||||
\(273\) | 0.802752 | 0.0485848 | ||||||||
\(274\) | −11.5250 | −0.696252 | ||||||||
\(275\) | −6.64785 | −0.400880 | ||||||||
\(276\) | −0.372945 | −0.0224486 | ||||||||
\(277\) | 16.4329 | 0.987355 | 0.493678 | − | 0.869645i | \(-0.335652\pi\) | ||||
0.493678 | + | 0.869645i | \(0.335652\pi\) | |||||||
\(278\) | 15.1884 | 0.910940 | ||||||||
\(279\) | −24.1140 | −1.44367 | ||||||||
\(280\) | 8.93129 | 0.533747 | ||||||||
\(281\) | 7.52356 | 0.448818 | 0.224409 | − | 0.974495i | \(-0.427955\pi\) | ||||
0.224409 | + | 0.974495i | \(0.427955\pi\) | |||||||
\(282\) | 0.0552225 | 0.00328845 | ||||||||
\(283\) | 28.4605 | 1.69180 | 0.845902 | − | 0.533338i | \(-0.179063\pi\) | ||||
0.845902 | + | 0.533338i | \(0.179063\pi\) | |||||||
\(284\) | −14.2284 | −0.844301 | ||||||||
\(285\) | 0.262444 | 0.0155458 | ||||||||
\(286\) | 2.02414 | 0.119690 | ||||||||
\(287\) | −6.77237 | −0.399760 | ||||||||
\(288\) | 2.86091 | 0.168581 | ||||||||
\(289\) | −7.29999 | −0.429411 | ||||||||
\(290\) | 21.9919 | 1.29141 | ||||||||
\(291\) | −1.42694 | −0.0836487 | ||||||||
\(292\) | −4.25808 | −0.249185 | ||||||||
\(293\) | 15.6896 | 0.916599 | 0.458299 | − | 0.888798i | \(-0.348459\pi\) | ||||
0.458299 | + | 0.888798i | \(0.348459\pi\) | |||||||
\(294\) | −1.57312 | −0.0917460 | ||||||||
\(295\) | 9.97051 | 0.580505 | ||||||||
\(296\) | 11.3608 | 0.660334 | ||||||||
\(297\) | 6.88452 | 0.399481 | ||||||||
\(298\) | −21.3323 | −1.23575 | ||||||||
\(299\) | −0.642654 | −0.0371656 | ||||||||
\(300\) | 0.787158 | 0.0454466 | ||||||||
\(301\) | −5.89666 | −0.339878 | ||||||||
\(302\) | −13.0219 | −0.749327 | ||||||||
\(303\) | 6.12668 | 0.351968 | ||||||||
\(304\) | −0.263898 | −0.0151356 | ||||||||
\(305\) | −13.8729 | −0.794358 | ||||||||
\(306\) | −8.91026 | −0.509366 | ||||||||
\(307\) | 25.3152 | 1.44481 | 0.722406 | − | 0.691469i | \(-0.243036\pi\) | ||||
0.722406 | + | 0.691469i | \(0.243036\pi\) | |||||||
\(308\) | −10.5493 | −0.601102 | ||||||||
\(309\) | 6.83760 | 0.388978 | ||||||||
\(310\) | 22.4760 | 1.27655 | ||||||||
\(311\) | −23.3532 | −1.32424 | −0.662119 | − | 0.749399i | \(-0.730343\pi\) | ||||
−0.662119 | + | 0.749399i | \(0.730343\pi\) | |||||||
\(312\) | −0.239674 | −0.0135689 | ||||||||
\(313\) | 23.9573 | 1.35415 | 0.677073 | − | 0.735916i | \(-0.263248\pi\) | ||||
0.677073 | + | 0.735916i | \(0.263248\pi\) | |||||||
\(314\) | −19.0971 | −1.07771 | ||||||||
\(315\) | 25.5516 | 1.43967 | ||||||||
\(316\) | 5.78002 | 0.325151 | ||||||||
\(317\) | 18.3402 | 1.03009 | 0.515043 | − | 0.857164i | \(-0.327776\pi\) | ||||
0.515043 | + | 0.857164i | \(0.327776\pi\) | |||||||
\(318\) | 3.53972 | 0.198498 | ||||||||
\(319\) | −25.9760 | −1.45438 | ||||||||
\(320\) | −2.66658 | −0.149066 | ||||||||
\(321\) | 0.379658 | 0.0211904 | ||||||||
\(322\) | 3.34934 | 0.186652 | ||||||||
\(323\) | 0.821906 | 0.0457321 | ||||||||
\(324\) | 7.76755 | 0.431531 | ||||||||
\(325\) | 1.35642 | 0.0752407 | ||||||||
\(326\) | 0.0511642 | 0.00283372 | ||||||||
\(327\) | 2.72220 | 0.150538 | ||||||||
\(328\) | 2.02200 | 0.111646 | ||||||||
\(329\) | −0.495942 | −0.0273422 | ||||||||
\(330\) | −3.13230 | −0.172427 | ||||||||
\(331\) | 33.1619 | 1.82275 | 0.911373 | − | 0.411582i | \(-0.135024\pi\) | ||||
0.911373 | + | 0.411582i | \(0.135024\pi\) | |||||||
\(332\) | 2.76081 | 0.151519 | ||||||||
\(333\) | 32.5023 | 1.78112 | ||||||||
\(334\) | −7.81925 | −0.427850 | ||||||||
\(335\) | −15.4699 | −0.845209 | ||||||||
\(336\) | 1.24912 | 0.0681451 | ||||||||
\(337\) | 22.6883 | 1.23591 | 0.617956 | − | 0.786213i | \(-0.287961\pi\) | ||||
0.617956 | + | 0.786213i | \(0.287961\pi\) | |||||||
\(338\) | 12.5870 | 0.684642 | ||||||||
\(339\) | −6.87762 | −0.373541 | ||||||||
\(340\) | 8.30502 | 0.450403 | ||||||||
\(341\) | −26.5478 | −1.43764 | ||||||||
\(342\) | −0.754989 | −0.0408251 | ||||||||
\(343\) | −9.31756 | −0.503101 | ||||||||
\(344\) | 1.76054 | 0.0949222 | ||||||||
\(345\) | 0.994488 | 0.0535414 | ||||||||
\(346\) | 5.91632 | 0.318064 | ||||||||
\(347\) | −23.2997 | −1.25079 | −0.625397 | − | 0.780306i | \(-0.715063\pi\) | ||||
−0.625397 | + | 0.780306i | \(0.715063\pi\) | |||||||
\(348\) | 3.07576 | 0.164878 | ||||||||
\(349\) | 22.2842 | 1.19285 | 0.596424 | − | 0.802670i | \(-0.296588\pi\) | ||||
0.596424 | + | 0.802670i | \(0.296588\pi\) | |||||||
\(350\) | −7.06931 | −0.377870 | ||||||||
\(351\) | −1.40471 | −0.0749779 | ||||||||
\(352\) | 3.14966 | 0.167878 | ||||||||
\(353\) | 13.2432 | 0.704865 | 0.352432 | − | 0.935837i | \(-0.385355\pi\) | ||||
0.352432 | + | 0.935837i | \(0.385355\pi\) | |||||||
\(354\) | 1.39446 | 0.0741149 | ||||||||
\(355\) | 37.9412 | 2.01371 | ||||||||
\(356\) | 12.7467 | 0.675574 | ||||||||
\(357\) | −3.89036 | −0.205900 | ||||||||
\(358\) | −6.28387 | −0.332113 | ||||||||
\(359\) | 28.2912 | 1.49315 | 0.746577 | − | 0.665299i | \(-0.231696\pi\) | ||||
0.746577 | + | 0.665299i | \(0.231696\pi\) | |||||||
\(360\) | −7.62885 | −0.402076 | ||||||||
\(361\) | −18.9304 | −0.996335 | ||||||||
\(362\) | −8.23941 | −0.433054 | ||||||||
\(363\) | −0.402644 | −0.0211333 | ||||||||
\(364\) | 2.15247 | 0.112820 | ||||||||
\(365\) | 11.3545 | 0.594323 | ||||||||
\(366\) | −1.94024 | −0.101418 | ||||||||
\(367\) | 32.3605 | 1.68921 | 0.844603 | − | 0.535394i | \(-0.179837\pi\) | ||||
0.844603 | + | 0.535394i | \(0.179837\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 5.78476 | 0.301143 | ||||||||
\(370\) | −30.2945 | −1.57494 | ||||||||
\(371\) | −31.7895 | −1.65043 | ||||||||
\(372\) | 3.14347 | 0.162981 | ||||||||
\(373\) | 30.1838 | 1.56286 | 0.781428 | − | 0.623995i | \(-0.214491\pi\) | ||||
0.781428 | + | 0.623995i | \(0.214491\pi\) | |||||||
\(374\) | −9.80957 | −0.507241 | ||||||||
\(375\) | 2.87342 | 0.148383 | ||||||||
\(376\) | 0.148071 | 0.00763620 | ||||||||
\(377\) | 5.30012 | 0.272970 | ||||||||
\(378\) | 7.32098 | 0.376551 | ||||||||
\(379\) | −27.3705 | −1.40593 | −0.702965 | − | 0.711225i | \(-0.748141\pi\) | ||||
−0.702965 | + | 0.711225i | \(0.748141\pi\) | |||||||
\(380\) | 0.703706 | 0.0360993 | ||||||||
\(381\) | −2.55954 | −0.131129 | ||||||||
\(382\) | −8.82014 | −0.451277 | ||||||||
\(383\) | −4.70135 | −0.240228 | −0.120114 | − | 0.992760i | \(-0.538326\pi\) | ||||
−0.120114 | + | 0.992760i | \(0.538326\pi\) | |||||||
\(384\) | −0.372945 | −0.0190318 | ||||||||
\(385\) | 28.1305 | 1.43367 | ||||||||
\(386\) | 7.10907 | 0.361842 | ||||||||
\(387\) | 5.03676 | 0.256033 | ||||||||
\(388\) | −3.82614 | −0.194243 | ||||||||
\(389\) | 25.4451 | 1.29012 | 0.645059 | − | 0.764133i | \(-0.276833\pi\) | ||||
0.645059 | + | 0.764133i | \(0.276833\pi\) | |||||||
\(390\) | 0.639112 | 0.0323627 | ||||||||
\(391\) | 3.11448 | 0.157506 | ||||||||
\(392\) | −4.21809 | −0.213046 | ||||||||
\(393\) | 0.372945 | 0.0188126 | ||||||||
\(394\) | 6.06136 | 0.305367 | ||||||||
\(395\) | −15.4129 | −0.775506 | ||||||||
\(396\) | 9.01090 | 0.452815 | ||||||||
\(397\) | −22.2238 | −1.11538 | −0.557689 | − | 0.830050i | \(-0.688312\pi\) | ||||
−0.557689 | + | 0.830050i | \(0.688312\pi\) | |||||||
\(398\) | 21.8539 | 1.09543 | ||||||||
\(399\) | −0.329640 | −0.0165027 | ||||||||
\(400\) | 2.11066 | 0.105533 | ||||||||
\(401\) | 25.6445 | 1.28063 | 0.640313 | − | 0.768114i | \(-0.278805\pi\) | ||||
0.640313 | + | 0.768114i | \(0.278805\pi\) | |||||||
\(402\) | −2.16360 | −0.107910 | ||||||||
\(403\) | 5.41678 | 0.269829 | ||||||||
\(404\) | 16.4278 | 0.817315 | ||||||||
\(405\) | −20.7128 | −1.02923 | ||||||||
\(406\) | −27.6228 | −1.37090 | ||||||||
\(407\) | 35.7827 | 1.77368 | ||||||||
\(408\) | 1.16153 | 0.0575043 | ||||||||
\(409\) | −13.3226 | −0.658761 | −0.329381 | − | 0.944197i | \(-0.606840\pi\) | ||||
−0.329381 | + | 0.944197i | \(0.606840\pi\) | |||||||
\(410\) | −5.39183 | −0.266283 | ||||||||
\(411\) | 4.29820 | 0.212015 | ||||||||
\(412\) | 18.3341 | 0.903255 | ||||||||
\(413\) | −12.5234 | −0.616236 | ||||||||
\(414\) | −2.86091 | −0.140606 | ||||||||
\(415\) | −7.36193 | −0.361383 | ||||||||
\(416\) | −0.642654 | −0.0315087 | ||||||||
\(417\) | −5.66444 | −0.277389 | ||||||||
\(418\) | −0.831190 | −0.0406548 | ||||||||
\(419\) | 11.9710 | 0.584820 | 0.292410 | − | 0.956293i | \(-0.405543\pi\) | ||||
0.292410 | + | 0.956293i | \(0.405543\pi\) | |||||||
\(420\) | −3.33088 | −0.162530 | ||||||||
\(421\) | 27.0823 | 1.31991 | 0.659955 | − | 0.751305i | \(-0.270575\pi\) | ||||
0.659955 | + | 0.751305i | \(0.270575\pi\) | |||||||
\(422\) | −8.20266 | −0.399299 | ||||||||
\(423\) | 0.423619 | 0.0205971 | ||||||||
\(424\) | 9.49126 | 0.460936 | ||||||||
\(425\) | −6.57360 | −0.318866 | ||||||||
\(426\) | 5.30641 | 0.257097 | ||||||||
\(427\) | 17.4249 | 0.843251 | ||||||||
\(428\) | 1.01800 | 0.0492068 | ||||||||
\(429\) | −0.754894 | −0.0364466 | ||||||||
\(430\) | −4.69463 | −0.226395 | ||||||||
\(431\) | −36.5228 | −1.75924 | −0.879622 | − | 0.475674i | \(-0.842204\pi\) | ||||
−0.879622 | + | 0.475674i | \(0.842204\pi\) | |||||||
\(432\) | −2.18580 | −0.105164 | ||||||||
\(433\) | −2.46789 | −0.118599 | −0.0592997 | − | 0.998240i | \(-0.518887\pi\) | ||||
−0.0592997 | + | 0.998240i | \(0.518887\pi\) | |||||||
\(434\) | −28.2308 | −1.35512 | ||||||||
\(435\) | −8.20177 | −0.393245 | ||||||||
\(436\) | 7.29920 | 0.349569 | ||||||||
\(437\) | 0.263898 | 0.0126240 | ||||||||
\(438\) | 1.58803 | 0.0758790 | ||||||||
\(439\) | 6.81768 | 0.325390 | 0.162695 | − | 0.986676i | \(-0.447981\pi\) | ||||
0.162695 | + | 0.986676i | \(0.447981\pi\) | |||||||
\(440\) | −8.39883 | −0.400398 | ||||||||
\(441\) | −12.0676 | −0.574647 | ||||||||
\(442\) | 2.00153 | 0.0952033 | ||||||||
\(443\) | −13.8361 | −0.657371 | −0.328686 | − | 0.944439i | \(-0.606606\pi\) | ||||
−0.328686 | + | 0.944439i | \(0.606606\pi\) | |||||||
\(444\) | −4.23696 | −0.201077 | ||||||||
\(445\) | −33.9901 | −1.61129 | ||||||||
\(446\) | −5.14663 | −0.243700 | ||||||||
\(447\) | 7.95576 | 0.376295 | ||||||||
\(448\) | 3.34934 | 0.158242 | ||||||||
\(449\) | −15.1134 | −0.713245 | −0.356623 | − | 0.934249i | \(-0.616072\pi\) | ||||
−0.356623 | + | 0.934249i | \(0.616072\pi\) | |||||||
\(450\) | 6.03840 | 0.284653 | ||||||||
\(451\) | 6.36861 | 0.299886 | ||||||||
\(452\) | −18.4414 | −0.867410 | ||||||||
\(453\) | 4.85646 | 0.228176 | ||||||||
\(454\) | 24.7569 | 1.16190 | ||||||||
\(455\) | −5.73973 | −0.269083 | ||||||||
\(456\) | 0.0984195 | 0.00460891 | ||||||||
\(457\) | −27.9887 | −1.30926 | −0.654628 | − | 0.755951i | \(-0.727175\pi\) | ||||
−0.654628 | + | 0.755951i | \(0.727175\pi\) | |||||||
\(458\) | −25.1048 | −1.17307 | ||||||||
\(459\) | 6.80763 | 0.317753 | ||||||||
\(460\) | 2.66658 | 0.124330 | ||||||||
\(461\) | 34.7688 | 1.61935 | 0.809673 | − | 0.586882i | \(-0.199645\pi\) | ||||
0.809673 | + | 0.586882i | \(0.199645\pi\) | |||||||
\(462\) | 3.93431 | 0.183040 | ||||||||
\(463\) | −1.10173 | −0.0512015 | −0.0256008 | − | 0.999672i | \(-0.508150\pi\) | ||||
−0.0256008 | + | 0.999672i | \(0.508150\pi\) | |||||||
\(464\) | 8.24723 | 0.382868 | ||||||||
\(465\) | −8.38231 | −0.388720 | ||||||||
\(466\) | 7.49513 | 0.347205 | ||||||||
\(467\) | −19.7907 | −0.915807 | −0.457903 | − | 0.889002i | \(-0.651399\pi\) | ||||
−0.457903 | + | 0.889002i | \(0.651399\pi\) | |||||||
\(468\) | −1.83858 | −0.0849882 | ||||||||
\(469\) | 19.4308 | 0.897232 | ||||||||
\(470\) | −0.394844 | −0.0182128 | ||||||||
\(471\) | 7.12217 | 0.328172 | ||||||||
\(472\) | 3.73906 | 0.172104 | ||||||||
\(473\) | 5.54512 | 0.254965 | ||||||||
\(474\) | −2.15563 | −0.0990113 | ||||||||
\(475\) | −0.556998 | −0.0255568 | ||||||||
\(476\) | −10.4315 | −0.478126 | ||||||||
\(477\) | 27.1537 | 1.24328 | ||||||||
\(478\) | 18.7569 | 0.857919 | ||||||||
\(479\) | 23.6862 | 1.08225 | 0.541125 | − | 0.840942i | \(-0.317998\pi\) | ||||
0.541125 | + | 0.840942i | \(0.317998\pi\) | |||||||
\(480\) | 0.994488 | 0.0453920 | ||||||||
\(481\) | −7.30107 | −0.332900 | ||||||||
\(482\) | 21.4904 | 0.978861 | ||||||||
\(483\) | −1.24912 | −0.0568369 | ||||||||
\(484\) | −1.07963 | −0.0490742 | ||||||||
\(485\) | 10.2027 | 0.463281 | ||||||||
\(486\) | −9.45426 | −0.428854 | ||||||||
\(487\) | −21.7382 | −0.985052 | −0.492526 | − | 0.870298i | \(-0.663926\pi\) | ||||
−0.492526 | + | 0.870298i | \(0.663926\pi\) | |||||||
\(488\) | −5.20249 | −0.235506 | ||||||||
\(489\) | −0.0190814 | −0.000862892 0 | ||||||||
\(490\) | 11.2479 | 0.508128 | ||||||||
\(491\) | 2.54218 | 0.114727 | 0.0573635 | − | 0.998353i | \(-0.481731\pi\) | ||||
0.0573635 | + | 0.998353i | \(0.481731\pi\) | |||||||
\(492\) | −0.754095 | −0.0339972 | ||||||||
\(493\) | −25.6859 | −1.15683 | ||||||||
\(494\) | 0.169595 | 0.00763045 | ||||||||
\(495\) | −24.0283 | −1.07999 | ||||||||
\(496\) | 8.42877 | 0.378463 | ||||||||
\(497\) | −47.6558 | −2.13765 | ||||||||
\(498\) | −1.02963 | −0.0461389 | ||||||||
\(499\) | 34.6773 | 1.55237 | 0.776185 | − | 0.630505i | \(-0.217152\pi\) | ||||
0.776185 | + | 0.630505i | \(0.217152\pi\) | |||||||
\(500\) | 7.70467 | 0.344563 | ||||||||
\(501\) | 2.91615 | 0.130284 | ||||||||
\(502\) | 3.62925 | 0.161981 | ||||||||
\(503\) | −0.127885 | −0.00570212 | −0.00285106 | − | 0.999996i | \(-0.500908\pi\) | ||||
−0.00285106 | + | 0.999996i | \(0.500908\pi\) | |||||||
\(504\) | 9.58217 | 0.426824 | ||||||||
\(505\) | −43.8061 | −1.94935 | ||||||||
\(506\) | −3.14966 | −0.140020 | ||||||||
\(507\) | −4.69426 | −0.208479 | ||||||||
\(508\) | −6.86305 | −0.304499 | ||||||||
\(509\) | −2.20831 | −0.0978815 | −0.0489407 | − | 0.998802i | \(-0.515585\pi\) | ||||
−0.0489407 | + | 0.998802i | \(0.515585\pi\) | |||||||
\(510\) | −3.09732 | −0.137151 | ||||||||
\(511\) | −14.2618 | −0.630903 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.576828 | 0.0254676 | ||||||||
\(514\) | 21.7861 | 0.960942 | ||||||||
\(515\) | −48.8893 | −2.15432 | ||||||||
\(516\) | −0.656586 | −0.0289046 | ||||||||
\(517\) | 0.466375 | 0.0205111 | ||||||||
\(518\) | 38.0513 | 1.67188 | ||||||||
\(519\) | −2.20646 | −0.0968530 | ||||||||
\(520\) | 1.71369 | 0.0751502 | ||||||||
\(521\) | 31.5433 | 1.38194 | 0.690969 | − | 0.722885i | \(-0.257184\pi\) | ||||
0.690969 | + | 0.722885i | \(0.257184\pi\) | |||||||
\(522\) | 23.5946 | 1.03271 | ||||||||
\(523\) | −1.43055 | −0.0625538 | −0.0312769 | − | 0.999511i | \(-0.509957\pi\) | ||||
−0.0312769 | + | 0.999511i | \(0.509957\pi\) | |||||||
\(524\) | 1.00000 | 0.0436852 | ||||||||
\(525\) | 2.63646 | 0.115065 | ||||||||
\(526\) | −4.41684 | −0.192583 | ||||||||
\(527\) | −26.2513 | −1.14352 | ||||||||
\(528\) | −1.17465 | −0.0511201 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −25.3092 | −1.09936 | ||||||||
\(531\) | 10.6971 | 0.464216 | ||||||||
\(532\) | −0.883885 | −0.0383213 | ||||||||
\(533\) | −1.29945 | −0.0562852 | ||||||||
\(534\) | −4.75382 | −0.205718 | ||||||||
\(535\) | −2.71458 | −0.117361 | ||||||||
\(536\) | −5.80138 | −0.250582 | ||||||||
\(537\) | 2.34354 | 0.101131 | ||||||||
\(538\) | −22.9534 | −0.989592 | ||||||||
\(539\) | −13.2856 | −0.572250 | ||||||||
\(540\) | 5.82861 | 0.250823 | ||||||||
\(541\) | −26.2537 | −1.12874 | −0.564368 | − | 0.825523i | \(-0.690880\pi\) | ||||
−0.564368 | + | 0.825523i | \(0.690880\pi\) | |||||||
\(542\) | −15.9775 | −0.686292 | ||||||||
\(543\) | 3.07285 | 0.131868 | ||||||||
\(544\) | 3.11448 | 0.133532 | ||||||||
\(545\) | −19.4639 | −0.833743 | ||||||||
\(546\) | −0.802752 | −0.0343546 | ||||||||
\(547\) | −28.5549 | −1.22092 | −0.610459 | − | 0.792048i | \(-0.709015\pi\) | ||||
−0.610459 | + | 0.792048i | \(0.709015\pi\) | |||||||
\(548\) | 11.5250 | 0.492325 | ||||||||
\(549\) | −14.8839 | −0.635228 | ||||||||
\(550\) | 6.64785 | 0.283465 | ||||||||
\(551\) | −2.17643 | −0.0927190 | ||||||||
\(552\) | 0.372945 | 0.0158736 | ||||||||
\(553\) | 19.3593 | 0.823239 | ||||||||
\(554\) | −16.4329 | −0.698165 | ||||||||
\(555\) | 11.2982 | 0.479582 | ||||||||
\(556\) | −15.1884 | −0.644132 | ||||||||
\(557\) | 36.3515 | 1.54026 | 0.770132 | − | 0.637885i | \(-0.220190\pi\) | ||||
0.770132 | + | 0.637885i | \(0.220190\pi\) | |||||||
\(558\) | 24.1140 | 1.02083 | ||||||||
\(559\) | −1.13142 | −0.0478540 | ||||||||
\(560\) | −8.93129 | −0.377416 | ||||||||
\(561\) | 3.65843 | 0.154459 | ||||||||
\(562\) | −7.52356 | −0.317362 | ||||||||
\(563\) | 6.27585 | 0.264496 | 0.132248 | − | 0.991217i | \(-0.457781\pi\) | ||||
0.132248 | + | 0.991217i | \(0.457781\pi\) | |||||||
\(564\) | −0.0552225 | −0.00232529 | ||||||||
\(565\) | 49.1754 | 2.06883 | ||||||||
\(566\) | −28.4605 | −1.19629 | ||||||||
\(567\) | 26.0162 | 1.09258 | ||||||||
\(568\) | 14.2284 | 0.597011 | ||||||||
\(569\) | 30.1215 | 1.26276 | 0.631379 | − | 0.775475i | \(-0.282489\pi\) | ||||
0.631379 | + | 0.775475i | \(0.282489\pi\) | |||||||
\(570\) | −0.262444 | −0.0109925 | ||||||||
\(571\) | 18.0098 | 0.753686 | 0.376843 | − | 0.926277i | \(-0.377010\pi\) | ||||
0.376843 | + | 0.926277i | \(0.377010\pi\) | |||||||
\(572\) | −2.02414 | −0.0846336 | ||||||||
\(573\) | 3.28943 | 0.137418 | ||||||||
\(574\) | 6.77237 | 0.282673 | ||||||||
\(575\) | −2.11066 | −0.0880204 | ||||||||
\(576\) | −2.86091 | −0.119205 | ||||||||
\(577\) | 38.5114 | 1.60325 | 0.801625 | − | 0.597827i | \(-0.203969\pi\) | ||||
0.801625 | + | 0.597827i | \(0.203969\pi\) | |||||||
\(578\) | 7.29999 | 0.303640 | ||||||||
\(579\) | −2.65129 | −0.110184 | ||||||||
\(580\) | −21.9919 | −0.913165 | ||||||||
\(581\) | 9.24691 | 0.383626 | ||||||||
\(582\) | 1.42694 | 0.0591485 | ||||||||
\(583\) | 29.8943 | 1.23809 | ||||||||
\(584\) | 4.25808 | 0.176201 | ||||||||
\(585\) | 4.90271 | 0.202702 | ||||||||
\(586\) | −15.6896 | −0.648133 | ||||||||
\(587\) | 28.4959 | 1.17615 | 0.588075 | − | 0.808806i | \(-0.299886\pi\) | ||||
0.588075 | + | 0.808806i | \(0.299886\pi\) | |||||||
\(588\) | 1.57312 | 0.0648742 | ||||||||
\(589\) | −2.22434 | −0.0916522 | ||||||||
\(590\) | −9.97051 | −0.410479 | ||||||||
\(591\) | −2.26055 | −0.0929868 | ||||||||
\(592\) | −11.3608 | −0.466927 | ||||||||
\(593\) | −0.996844 | −0.0409355 | −0.0204677 | − | 0.999791i | \(-0.506516\pi\) | ||||
−0.0204677 | + | 0.999791i | \(0.506516\pi\) | |||||||
\(594\) | −6.88452 | −0.282475 | ||||||||
\(595\) | 27.8164 | 1.14036 | ||||||||
\(596\) | 21.3323 | 0.873804 | ||||||||
\(597\) | −8.15028 | −0.333569 | ||||||||
\(598\) | 0.642654 | 0.0262801 | ||||||||
\(599\) | 14.8959 | 0.608630 | 0.304315 | − | 0.952571i | \(-0.401572\pi\) | ||||
0.304315 | + | 0.952571i | \(0.401572\pi\) | |||||||
\(600\) | −0.787158 | −0.0321356 | ||||||||
\(601\) | 1.70680 | 0.0696217 | 0.0348108 | − | 0.999394i | \(-0.488917\pi\) | ||||
0.0348108 | + | 0.999394i | \(0.488917\pi\) | |||||||
\(602\) | 5.89666 | 0.240330 | ||||||||
\(603\) | −16.5972 | −0.675892 | ||||||||
\(604\) | 13.0219 | 0.529854 | ||||||||
\(605\) | 2.87893 | 0.117045 | ||||||||
\(606\) | −6.12668 | −0.248879 | ||||||||
\(607\) | 5.75840 | 0.233726 | 0.116863 | − | 0.993148i | \(-0.462716\pi\) | ||||
0.116863 | + | 0.993148i | \(0.462716\pi\) | |||||||
\(608\) | 0.263898 | 0.0107025 | ||||||||
\(609\) | 10.3018 | 0.417449 | ||||||||
\(610\) | 13.8729 | 0.561696 | ||||||||
\(611\) | −0.0951586 | −0.00384971 | ||||||||
\(612\) | 8.91026 | 0.360176 | ||||||||
\(613\) | 16.4947 | 0.666214 | 0.333107 | − | 0.942889i | \(-0.391903\pi\) | ||||
0.333107 | + | 0.942889i | \(0.391903\pi\) | |||||||
\(614\) | −25.3152 | −1.02164 | ||||||||
\(615\) | 2.01085 | 0.0810855 | ||||||||
\(616\) | 10.5493 | 0.425043 | ||||||||
\(617\) | −28.4796 | −1.14654 | −0.573272 | − | 0.819365i | \(-0.694326\pi\) | ||||
−0.573272 | + | 0.819365i | \(0.694326\pi\) | |||||||
\(618\) | −6.83760 | −0.275049 | ||||||||
\(619\) | −32.0452 | −1.28801 | −0.644003 | − | 0.765023i | \(-0.722728\pi\) | ||||
−0.644003 | + | 0.765023i | \(0.722728\pi\) | |||||||
\(620\) | −22.4760 | −0.902658 | ||||||||
\(621\) | 2.18580 | 0.0877130 | ||||||||
\(622\) | 23.3532 | 0.936377 | ||||||||
\(623\) | 42.6931 | 1.71046 | ||||||||
\(624\) | 0.239674 | 0.00959466 | ||||||||
\(625\) | −31.0984 | −1.24394 | ||||||||
\(626\) | −23.9573 | −0.957526 | ||||||||
\(627\) | 0.309988 | 0.0123797 | ||||||||
\(628\) | 19.0971 | 0.762058 | ||||||||
\(629\) | 35.3831 | 1.41082 | ||||||||
\(630\) | −25.5516 | −1.01800 | ||||||||
\(631\) | −29.2285 | −1.16357 | −0.581783 | − | 0.813344i | \(-0.697645\pi\) | ||||
−0.581783 | + | 0.813344i | \(0.697645\pi\) | |||||||
\(632\) | −5.78002 | −0.229917 | ||||||||
\(633\) | 3.05914 | 0.121590 | ||||||||
\(634\) | −18.3402 | −0.728381 | ||||||||
\(635\) | 18.3009 | 0.726248 | ||||||||
\(636\) | −3.53972 | −0.140359 | ||||||||
\(637\) | 2.71077 | 0.107405 | ||||||||
\(638\) | 25.9760 | 1.02840 | ||||||||
\(639\) | 40.7062 | 1.61031 | ||||||||
\(640\) | 2.66658 | 0.105406 | ||||||||
\(641\) | 3.39538 | 0.134110 | 0.0670548 | − | 0.997749i | \(-0.478640\pi\) | ||||
0.0670548 | + | 0.997749i | \(0.478640\pi\) | |||||||
\(642\) | −0.379658 | −0.0149839 | ||||||||
\(643\) | 44.4694 | 1.75370 | 0.876852 | − | 0.480761i | \(-0.159640\pi\) | ||||
0.876852 | + | 0.480761i | \(0.159640\pi\) | |||||||
\(644\) | −3.34934 | −0.131983 | ||||||||
\(645\) | 1.75084 | 0.0689393 | ||||||||
\(646\) | −0.821906 | −0.0323375 | ||||||||
\(647\) | 27.0705 | 1.06425 | 0.532125 | − | 0.846666i | \(-0.321394\pi\) | ||||
0.532125 | + | 0.846666i | \(0.321394\pi\) | |||||||
\(648\) | −7.76755 | −0.305138 | ||||||||
\(649\) | 11.7768 | 0.462279 | ||||||||
\(650\) | −1.35642 | −0.0532032 | ||||||||
\(651\) | 10.5285 | 0.412646 | ||||||||
\(652\) | −0.0511642 | −0.00200374 | ||||||||
\(653\) | −23.6357 | −0.924937 | −0.462468 | − | 0.886636i | \(-0.653036\pi\) | ||||
−0.462468 | + | 0.886636i | \(0.653036\pi\) | |||||||
\(654\) | −2.72220 | −0.106447 | ||||||||
\(655\) | −2.66658 | −0.104192 | ||||||||
\(656\) | −2.02200 | −0.0789458 | ||||||||
\(657\) | 12.1820 | 0.475265 | ||||||||
\(658\) | 0.495942 | 0.0193338 | ||||||||
\(659\) | −40.8700 | −1.59207 | −0.796035 | − | 0.605251i | \(-0.793073\pi\) | ||||
−0.796035 | + | 0.605251i | \(0.793073\pi\) | |||||||
\(660\) | 3.13230 | 0.121925 | ||||||||
\(661\) | 7.49141 | 0.291382 | 0.145691 | − | 0.989330i | \(-0.453459\pi\) | ||||
0.145691 | + | 0.989330i | \(0.453459\pi\) | |||||||
\(662\) | −33.1619 | −1.28888 | ||||||||
\(663\) | −0.746462 | −0.0289902 | ||||||||
\(664\) | −2.76081 | −0.107140 | ||||||||
\(665\) | 2.35695 | 0.0913987 | ||||||||
\(666\) | −32.5023 | −1.25944 | ||||||||
\(667\) | −8.24723 | −0.319334 | ||||||||
\(668\) | 7.81925 | 0.302536 | ||||||||
\(669\) | 1.91941 | 0.0742087 | ||||||||
\(670\) | 15.4699 | 0.597653 | ||||||||
\(671\) | −16.3861 | −0.632578 | ||||||||
\(672\) | −1.24912 | −0.0481859 | ||||||||
\(673\) | 7.18704 | 0.277040 | 0.138520 | − | 0.990360i | \(-0.455765\pi\) | ||||
0.138520 | + | 0.990360i | \(0.455765\pi\) | |||||||
\(674\) | −22.6883 | −0.873921 | ||||||||
\(675\) | −4.61347 | −0.177572 | ||||||||
\(676\) | −12.5870 | −0.484115 | ||||||||
\(677\) | 25.2307 | 0.969694 | 0.484847 | − | 0.874599i | \(-0.338875\pi\) | ||||
0.484847 | + | 0.874599i | \(0.338875\pi\) | |||||||
\(678\) | 6.87762 | 0.264133 | ||||||||
\(679\) | −12.8150 | −0.491796 | ||||||||
\(680\) | −8.30502 | −0.318483 | ||||||||
\(681\) | −9.23294 | −0.353807 | ||||||||
\(682\) | 26.5478 | 1.01657 | ||||||||
\(683\) | −38.0767 | −1.45697 | −0.728483 | − | 0.685064i | \(-0.759774\pi\) | ||||
−0.728483 | + | 0.685064i | \(0.759774\pi\) | |||||||
\(684\) | 0.754989 | 0.0288677 | ||||||||
\(685\) | −30.7324 | −1.17423 | ||||||||
\(686\) | 9.31756 | 0.355746 | ||||||||
\(687\) | 9.36271 | 0.357210 | ||||||||
\(688\) | −1.76054 | −0.0671201 | ||||||||
\(689\) | −6.09960 | −0.232376 | ||||||||
\(690\) | −0.994488 | −0.0378595 | ||||||||
\(691\) | −11.3114 | −0.430305 | −0.215152 | − | 0.976581i | \(-0.569025\pi\) | ||||
−0.215152 | + | 0.976581i | \(0.569025\pi\) | |||||||
\(692\) | −5.91632 | −0.224905 | ||||||||
\(693\) | 30.1806 | 1.14647 | ||||||||
\(694\) | 23.2997 | 0.884445 | ||||||||
\(695\) | 40.5011 | 1.53630 | ||||||||
\(696\) | −3.07576 | −0.116587 | ||||||||
\(697\) | 6.29748 | 0.238534 | ||||||||
\(698\) | −22.2842 | −0.843471 | ||||||||
\(699\) | −2.79527 | −0.105727 | ||||||||
\(700\) | 7.06931 | 0.267195 | ||||||||
\(701\) | 4.62190 | 0.174567 | 0.0872834 | − | 0.996184i | \(-0.472181\pi\) | ||||
0.0872834 | + | 0.996184i | \(0.472181\pi\) | |||||||
\(702\) | 1.40471 | 0.0530174 | ||||||||
\(703\) | 2.99810 | 0.113075 | ||||||||
\(704\) | −3.14966 | −0.118707 | ||||||||
\(705\) | 0.147255 | 0.00554595 | ||||||||
\(706\) | −13.2432 | −0.498415 | ||||||||
\(707\) | 55.0224 | 2.06933 | ||||||||
\(708\) | −1.39446 | −0.0524072 | ||||||||
\(709\) | 25.1846 | 0.945829 | 0.472914 | − | 0.881108i | \(-0.343202\pi\) | ||||
0.472914 | + | 0.881108i | \(0.343202\pi\) | |||||||
\(710\) | −37.9412 | −1.42391 | ||||||||
\(711\) | −16.5361 | −0.620153 | ||||||||
\(712\) | −12.7467 | −0.477703 | ||||||||
\(713\) | −8.42877 | −0.315660 | ||||||||
\(714\) | 3.89036 | 0.145593 | ||||||||
\(715\) | 5.39754 | 0.201857 | ||||||||
\(716\) | 6.28387 | 0.234839 | ||||||||
\(717\) | −6.99528 | −0.261244 | ||||||||
\(718\) | −28.2912 | −1.05582 | ||||||||
\(719\) | −10.4039 | −0.388000 | −0.194000 | − | 0.981002i | \(-0.562146\pi\) | ||||
−0.194000 | + | 0.981002i | \(0.562146\pi\) | |||||||
\(720\) | 7.62885 | 0.284311 | ||||||||
\(721\) | 61.4071 | 2.28692 | ||||||||
\(722\) | 18.9304 | 0.704515 | ||||||||
\(723\) | −8.01474 | −0.298071 | ||||||||
\(724\) | 8.23941 | 0.306215 | ||||||||
\(725\) | 17.4071 | 0.646482 | ||||||||
\(726\) | 0.402644 | 0.0149435 | ||||||||
\(727\) | 16.1748 | 0.599890 | 0.299945 | − | 0.953957i | \(-0.403032\pi\) | ||||
0.299945 | + | 0.953957i | \(0.403032\pi\) | |||||||
\(728\) | −2.15247 | −0.0797757 | ||||||||
\(729\) | −19.7767 | −0.732472 | ||||||||
\(730\) | −11.3545 | −0.420249 | ||||||||
\(731\) | 5.48318 | 0.202803 | ||||||||
\(732\) | 1.94024 | 0.0717134 | ||||||||
\(733\) | −18.2603 | −0.674461 | −0.337231 | − | 0.941422i | \(-0.609490\pi\) | ||||
−0.337231 | + | 0.941422i | \(0.609490\pi\) | |||||||
\(734\) | −32.3605 | −1.19445 | ||||||||
\(735\) | −4.19484 | −0.154729 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −18.2724 | −0.673072 | ||||||||
\(738\) | −5.78476 | −0.212940 | ||||||||
\(739\) | −47.7774 | −1.75752 | −0.878761 | − | 0.477263i | \(-0.841629\pi\) | ||||
−0.878761 | + | 0.477263i | \(0.841629\pi\) | |||||||
\(740\) | 30.2945 | 1.11365 | ||||||||
\(741\) | −0.0632497 | −0.00232353 | ||||||||
\(742\) | 31.7895 | 1.16703 | ||||||||
\(743\) | 34.8801 | 1.27963 | 0.639814 | − | 0.768530i | \(-0.279011\pi\) | ||||
0.639814 | + | 0.768530i | \(0.279011\pi\) | |||||||
\(744\) | −3.14347 | −0.115245 | ||||||||
\(745\) | −56.8842 | −2.08408 | ||||||||
\(746\) | −30.1838 | −1.10511 | ||||||||
\(747\) | −7.89844 | −0.288989 | ||||||||
\(748\) | 9.80957 | 0.358673 | ||||||||
\(749\) | 3.40963 | 0.124585 | ||||||||
\(750\) | −2.87342 | −0.104922 | ||||||||
\(751\) | −36.0545 | −1.31565 | −0.657823 | − | 0.753172i | \(-0.728523\pi\) | ||||
−0.657823 | + | 0.753172i | \(0.728523\pi\) | |||||||
\(752\) | −0.148071 | −0.00539961 | ||||||||
\(753\) | −1.35351 | −0.0493246 | ||||||||
\(754\) | −5.30012 | −0.193019 | ||||||||
\(755\) | −34.7240 | −1.26374 | ||||||||
\(756\) | −7.32098 | −0.266262 | ||||||||
\(757\) | −47.7211 | −1.73445 | −0.867227 | − | 0.497913i | \(-0.834100\pi\) | ||||
−0.867227 | + | 0.497913i | \(0.834100\pi\) | |||||||
\(758\) | 27.3705 | 0.994142 | ||||||||
\(759\) | 1.17465 | 0.0426371 | ||||||||
\(760\) | −0.703706 | −0.0255261 | ||||||||
\(761\) | 16.8366 | 0.610327 | 0.305164 | − | 0.952300i | \(-0.401289\pi\) | ||||
0.305164 | + | 0.952300i | \(0.401289\pi\) | |||||||
\(762\) | 2.55954 | 0.0927224 | ||||||||
\(763\) | 24.4475 | 0.885060 | ||||||||
\(764\) | 8.82014 | 0.319101 | ||||||||
\(765\) | −23.7599 | −0.859042 | ||||||||
\(766\) | 4.70135 | 0.169867 | ||||||||
\(767\) | −2.40292 | −0.0867645 | ||||||||
\(768\) | 0.372945 | 0.0134575 | ||||||||
\(769\) | 18.6237 | 0.671589 | 0.335794 | − | 0.941935i | \(-0.390995\pi\) | ||||
0.335794 | + | 0.941935i | \(0.390995\pi\) | |||||||
\(770\) | −28.1305 | −1.01375 | ||||||||
\(771\) | −8.12500 | −0.292615 | ||||||||
\(772\) | −7.10907 | −0.255861 | ||||||||
\(773\) | 49.4999 | 1.78039 | 0.890193 | − | 0.455583i | \(-0.150569\pi\) | ||||
0.890193 | + | 0.455583i | \(0.150569\pi\) | |||||||
\(774\) | −5.03676 | −0.181043 | ||||||||
\(775\) | 17.7902 | 0.639044 | ||||||||
\(776\) | 3.82614 | 0.137350 | ||||||||
\(777\) | −14.1910 | −0.509100 | ||||||||
\(778\) | −25.4451 | −0.912251 | ||||||||
\(779\) | 0.533602 | 0.0191183 | ||||||||
\(780\) | −0.639112 | −0.0228839 | ||||||||
\(781\) | 44.8147 | 1.60359 | ||||||||
\(782\) | −3.11448 | −0.111374 | ||||||||
\(783\) | −18.0268 | −0.644225 | ||||||||
\(784\) | 4.21809 | 0.150646 | ||||||||
\(785\) | −50.9240 | −1.81756 | ||||||||
\(786\) | −0.372945 | −0.0133025 | ||||||||
\(787\) | −13.5743 | −0.483871 | −0.241936 | − | 0.970292i | \(-0.577782\pi\) | ||||
−0.241936 | + | 0.970292i | \(0.577782\pi\) | |||||||
\(788\) | −6.06136 | −0.215927 | ||||||||
\(789\) | 1.64724 | 0.0586432 | ||||||||
\(790\) | 15.4129 | 0.548366 | ||||||||
\(791\) | −61.7665 | −2.19616 | ||||||||
\(792\) | −9.01090 | −0.320189 | ||||||||
\(793\) | 3.34340 | 0.118728 | ||||||||
\(794\) | 22.2238 | 0.788692 | ||||||||
\(795\) | 9.43895 | 0.334765 | ||||||||
\(796\) | −21.8539 | −0.774589 | ||||||||
\(797\) | −9.25510 | −0.327832 | −0.163916 | − | 0.986474i | \(-0.552413\pi\) | ||||
−0.163916 | + | 0.986474i | \(0.552413\pi\) | |||||||
\(798\) | 0.329640 | 0.0116691 | ||||||||
\(799\) | 0.461166 | 0.0163149 | ||||||||
\(800\) | −2.11066 | −0.0746229 | ||||||||
\(801\) | −36.4672 | −1.28851 | ||||||||
\(802\) | −25.6445 | −0.905539 | ||||||||
\(803\) | 13.4115 | 0.473282 | ||||||||
\(804\) | 2.16360 | 0.0763042 | ||||||||
\(805\) | 8.93129 | 0.314787 | ||||||||
\(806\) | −5.41678 | −0.190798 | ||||||||
\(807\) | 8.56036 | 0.301339 | ||||||||
\(808\) | −16.4278 | −0.577929 | ||||||||
\(809\) | −13.0959 | −0.460426 | −0.230213 | − | 0.973140i | \(-0.573942\pi\) | ||||
−0.230213 | + | 0.973140i | \(0.573942\pi\) | |||||||
\(810\) | 20.7128 | 0.727774 | ||||||||
\(811\) | −27.1252 | −0.952496 | −0.476248 | − | 0.879311i | \(-0.658003\pi\) | ||||
−0.476248 | + | 0.879311i | \(0.658003\pi\) | |||||||
\(812\) | 27.6228 | 0.969370 | ||||||||
\(813\) | 5.95872 | 0.208982 | ||||||||
\(814\) | −35.7827 | −1.25418 | ||||||||
\(815\) | 0.136433 | 0.00477905 | ||||||||
\(816\) | −1.16153 | −0.0406617 | ||||||||
\(817\) | 0.464604 | 0.0162544 | ||||||||
\(818\) | 13.3226 | 0.465815 | ||||||||
\(819\) | −6.15802 | −0.215179 | ||||||||
\(820\) | 5.39183 | 0.188291 | ||||||||
\(821\) | 33.7355 | 1.17738 | 0.588688 | − | 0.808360i | \(-0.299645\pi\) | ||||
0.588688 | + | 0.808360i | \(0.299645\pi\) | |||||||
\(822\) | −4.29820 | −0.149917 | ||||||||
\(823\) | 37.8037 | 1.31775 | 0.658877 | − | 0.752251i | \(-0.271032\pi\) | ||||
0.658877 | + | 0.752251i | \(0.271032\pi\) | |||||||
\(824\) | −18.3341 | −0.638698 | ||||||||
\(825\) | −2.47928 | −0.0863175 | ||||||||
\(826\) | 12.5234 | 0.435745 | ||||||||
\(827\) | −42.9560 | −1.49373 | −0.746864 | − | 0.664977i | \(-0.768441\pi\) | ||||
−0.746864 | + | 0.664977i | \(0.768441\pi\) | |||||||
\(828\) | 2.86091 | 0.0994236 | ||||||||
\(829\) | −34.3874 | −1.19432 | −0.597162 | − | 0.802121i | \(-0.703705\pi\) | ||||
−0.597162 | + | 0.802121i | \(0.703705\pi\) | |||||||
\(830\) | 7.36193 | 0.255536 | ||||||||
\(831\) | 6.12855 | 0.212597 | ||||||||
\(832\) | 0.642654 | 0.0222800 | ||||||||
\(833\) | −13.1372 | −0.455176 | ||||||||
\(834\) | 5.66444 | 0.196144 | ||||||||
\(835\) | −20.8507 | −0.721567 | ||||||||
\(836\) | 0.831190 | 0.0287473 | ||||||||
\(837\) | −18.4236 | −0.636812 | ||||||||
\(838\) | −11.9710 | −0.413530 | ||||||||
\(839\) | −28.8928 | −0.997490 | −0.498745 | − | 0.866749i | \(-0.666206\pi\) | ||||
−0.498745 | + | 0.866749i | \(0.666206\pi\) | |||||||
\(840\) | 3.33088 | 0.114926 | ||||||||
\(841\) | 39.0168 | 1.34541 | ||||||||
\(842\) | −27.0823 | −0.933317 | ||||||||
\(843\) | 2.80587 | 0.0966394 | ||||||||
\(844\) | 8.20266 | 0.282347 | ||||||||
\(845\) | 33.5642 | 1.15465 | ||||||||
\(846\) | −0.423619 | −0.0145643 | ||||||||
\(847\) | −3.61606 | −0.124249 | ||||||||
\(848\) | −9.49126 | −0.325931 | ||||||||
\(849\) | 10.6142 | 0.364279 | ||||||||
\(850\) | 6.57360 | 0.225473 | ||||||||
\(851\) | 11.3608 | 0.389444 | ||||||||
\(852\) | −5.30641 | −0.181795 | ||||||||
\(853\) | −45.5351 | −1.55909 | −0.779546 | − | 0.626345i | \(-0.784550\pi\) | ||||
−0.779546 | + | 0.626345i | \(0.784550\pi\) | |||||||
\(854\) | −17.4249 | −0.596269 | ||||||||
\(855\) | −2.01324 | −0.0688514 | ||||||||
\(856\) | −1.01800 | −0.0347945 | ||||||||
\(857\) | −22.7173 | −0.776010 | −0.388005 | − | 0.921657i | \(-0.626836\pi\) | ||||
−0.388005 | + | 0.921657i | \(0.626836\pi\) | |||||||
\(858\) | 0.754894 | 0.0257716 | ||||||||
\(859\) | 40.1664 | 1.37046 | 0.685230 | − | 0.728327i | \(-0.259702\pi\) | ||||
0.685230 | + | 0.728327i | \(0.259702\pi\) | |||||||
\(860\) | 4.69463 | 0.160086 | ||||||||
\(861\) | −2.52572 | −0.0860763 | ||||||||
\(862\) | 36.5228 | 1.24397 | ||||||||
\(863\) | 36.2600 | 1.23430 | 0.617152 | − | 0.786844i | \(-0.288286\pi\) | ||||
0.617152 | + | 0.786844i | \(0.288286\pi\) | |||||||
\(864\) | 2.18580 | 0.0743623 | ||||||||
\(865\) | 15.7764 | 0.536412 | ||||||||
\(866\) | 2.46789 | 0.0838624 | ||||||||
\(867\) | −2.72250 | −0.0924608 | ||||||||
\(868\) | 28.2308 | 0.958217 | ||||||||
\(869\) | −18.2051 | −0.617566 | ||||||||
\(870\) | 8.20177 | 0.278066 | ||||||||
\(871\) | 3.72828 | 0.126328 | ||||||||
\(872\) | −7.29920 | −0.247182 | ||||||||
\(873\) | 10.9462 | 0.370474 | ||||||||
\(874\) | −0.263898 | −0.00892649 | ||||||||
\(875\) | 25.8056 | 0.872388 | ||||||||
\(876\) | −1.58803 | −0.0536545 | ||||||||
\(877\) | −11.5298 | −0.389335 | −0.194667 | − | 0.980869i | \(-0.562363\pi\) | ||||
−0.194667 | + | 0.980869i | \(0.562363\pi\) | |||||||
\(878\) | −6.81768 | −0.230086 | ||||||||
\(879\) | 5.85137 | 0.197362 | ||||||||
\(880\) | 8.39883 | 0.283124 | ||||||||
\(881\) | 19.3724 | 0.652673 | 0.326337 | − | 0.945254i | \(-0.394186\pi\) | ||||
0.326337 | + | 0.945254i | \(0.394186\pi\) | |||||||
\(882\) | 12.0676 | 0.406337 | ||||||||
\(883\) | −47.8898 | −1.61162 | −0.805810 | − | 0.592174i | \(-0.798270\pi\) | ||||
−0.805810 | + | 0.592174i | \(0.798270\pi\) | |||||||
\(884\) | −2.00153 | −0.0673189 | ||||||||
\(885\) | 3.71845 | 0.124994 | ||||||||
\(886\) | 13.8361 | 0.464832 | ||||||||
\(887\) | 37.1370 | 1.24694 | 0.623470 | − | 0.781847i | \(-0.285722\pi\) | ||||
0.623470 | + | 0.781847i | \(0.285722\pi\) | |||||||
\(888\) | 4.23696 | 0.142183 | ||||||||
\(889\) | −22.9867 | −0.770949 | ||||||||
\(890\) | 33.9901 | 1.13935 | ||||||||
\(891\) | −24.4652 | −0.819614 | ||||||||
\(892\) | 5.14663 | 0.172322 | ||||||||
\(893\) | 0.0390758 | 0.00130762 | ||||||||
\(894\) | −7.95576 | −0.266081 | ||||||||
\(895\) | −16.7565 | −0.560107 | ||||||||
\(896\) | −3.34934 | −0.111894 | ||||||||
\(897\) | −0.239674 | −0.00800250 | ||||||||
\(898\) | 15.1134 | 0.504340 | ||||||||
\(899\) | 69.5140 | 2.31842 | ||||||||
\(900\) | −6.03840 | −0.201280 | ||||||||
\(901\) | 29.5604 | 0.984799 | ||||||||
\(902\) | −6.36861 | −0.212052 | ||||||||
\(903\) | −2.19913 | −0.0731825 | ||||||||
\(904\) | 18.4414 | 0.613351 | ||||||||
\(905\) | −21.9710 | −0.730342 | ||||||||
\(906\) | −4.85646 | −0.161345 | ||||||||
\(907\) | 19.3501 | 0.642510 | 0.321255 | − | 0.946993i | \(-0.395895\pi\) | ||||
0.321255 | + | 0.946993i | \(0.395895\pi\) | |||||||
\(908\) | −24.7569 | −0.821585 | ||||||||
\(909\) | −46.9986 | −1.55884 | ||||||||
\(910\) | 5.73973 | 0.190270 | ||||||||
\(911\) | 38.2539 | 1.26741 | 0.633704 | − | 0.773576i | \(-0.281534\pi\) | ||||
0.633704 | + | 0.773576i | \(0.281534\pi\) | |||||||
\(912\) | −0.0984195 | −0.00325899 | ||||||||
\(913\) | −8.69563 | −0.287783 | ||||||||
\(914\) | 27.9887 | 0.925783 | ||||||||
\(915\) | −5.17382 | −0.171041 | ||||||||
\(916\) | 25.1048 | 0.829486 | ||||||||
\(917\) | 3.34934 | 0.110605 | ||||||||
\(918\) | −6.80763 | −0.224685 | ||||||||
\(919\) | 24.1599 | 0.796962 | 0.398481 | − | 0.917177i | \(-0.369538\pi\) | ||||
0.398481 | + | 0.917177i | \(0.369538\pi\) | |||||||
\(920\) | −2.66658 | −0.0879146 | ||||||||
\(921\) | 9.44116 | 0.311097 | ||||||||
\(922\) | −34.7688 | −1.14505 | ||||||||
\(923\) | −9.14394 | −0.300976 | ||||||||
\(924\) | −3.93431 | −0.129429 | ||||||||
\(925\) | −23.9788 | −0.788417 | ||||||||
\(926\) | 1.10173 | 0.0362050 | ||||||||
\(927\) | −52.4522 | −1.72276 | ||||||||
\(928\) | −8.24723 | −0.270729 | ||||||||
\(929\) | −54.5778 | −1.79064 | −0.895320 | − | 0.445424i | \(-0.853053\pi\) | ||||
−0.895320 | + | 0.445424i | \(0.853053\pi\) | |||||||
\(930\) | 8.38231 | 0.274867 | ||||||||
\(931\) | −1.11315 | −0.0364819 | ||||||||
\(932\) | −7.49513 | −0.245511 | ||||||||
\(933\) | −8.70945 | −0.285135 | ||||||||
\(934\) | 19.7907 | 0.647573 | ||||||||
\(935\) | −26.1580 | −0.855458 | ||||||||
\(936\) | 1.83858 | 0.0600957 | ||||||||
\(937\) | −23.1848 | −0.757415 | −0.378708 | − | 0.925516i | \(-0.623631\pi\) | ||||
−0.378708 | + | 0.925516i | \(0.623631\pi\) | |||||||
\(938\) | −19.4308 | −0.634439 | ||||||||
\(939\) | 8.93475 | 0.291575 | ||||||||
\(940\) | 0.394844 | 0.0128784 | ||||||||
\(941\) | −46.5073 | −1.51610 | −0.758048 | − | 0.652199i | \(-0.773847\pi\) | ||||
−0.758048 | + | 0.652199i | \(0.773847\pi\) | |||||||
\(942\) | −7.12217 | −0.232053 | ||||||||
\(943\) | 2.02200 | 0.0658454 | ||||||||
\(944\) | −3.73906 | −0.121696 | ||||||||
\(945\) | 19.5220 | 0.635051 | ||||||||
\(946\) | −5.54512 | −0.180287 | ||||||||
\(947\) | 40.1595 | 1.30501 | 0.652504 | − | 0.757786i | \(-0.273719\pi\) | ||||
0.652504 | + | 0.757786i | \(0.273719\pi\) | |||||||
\(948\) | 2.15563 | 0.0700116 | ||||||||
\(949\) | −2.73647 | −0.0888296 | ||||||||
\(950\) | 0.556998 | 0.0180714 | ||||||||
\(951\) | 6.83987 | 0.221798 | ||||||||
\(952\) | 10.4315 | 0.338086 | ||||||||
\(953\) | 53.9001 | 1.74600 | 0.872998 | − | 0.487724i | \(-0.162173\pi\) | ||||
0.872998 | + | 0.487724i | \(0.162173\pi\) | |||||||
\(954\) | −27.1537 | −0.879132 | ||||||||
\(955\) | −23.5196 | −0.761077 | ||||||||
\(956\) | −18.7569 | −0.606641 | ||||||||
\(957\) | −9.68761 | −0.313156 | ||||||||
\(958\) | −23.6862 | −0.765267 | ||||||||
\(959\) | 38.6012 | 1.24650 | ||||||||
\(960\) | −0.994488 | −0.0320970 | ||||||||
\(961\) | 40.0441 | 1.29175 | ||||||||
\(962\) | 7.30107 | 0.235396 | ||||||||
\(963\) | −2.91241 | −0.0938510 | ||||||||
\(964\) | −21.4904 | −0.692159 | ||||||||
\(965\) | 18.9569 | 0.610245 | ||||||||
\(966\) | 1.24912 | 0.0401898 | ||||||||
\(967\) | 42.3787 | 1.36281 | 0.681404 | − | 0.731908i | \(-0.261370\pi\) | ||||
0.681404 | + | 0.731908i | \(0.261370\pi\) | |||||||
\(968\) | 1.07963 | 0.0347007 | ||||||||
\(969\) | 0.306526 | 0.00984703 | ||||||||
\(970\) | −10.2027 | −0.327589 | ||||||||
\(971\) | 31.3681 | 1.00665 | 0.503326 | − | 0.864097i | \(-0.332110\pi\) | ||||
0.503326 | + | 0.864097i | \(0.332110\pi\) | |||||||
\(972\) | 9.45426 | 0.303246 | ||||||||
\(973\) | −50.8712 | −1.63085 | ||||||||
\(974\) | 21.7382 | 0.696537 | ||||||||
\(975\) | 0.505870 | 0.0162008 | ||||||||
\(976\) | 5.20249 | 0.166528 | ||||||||
\(977\) | 14.4098 | 0.461011 | 0.230505 | − | 0.973071i | \(-0.425962\pi\) | ||||
0.230505 | + | 0.973071i | \(0.425962\pi\) | |||||||
\(978\) | 0.0190814 | 0.000610157 0 | ||||||||
\(979\) | −40.1478 | −1.28313 | ||||||||
\(980\) | −11.2479 | −0.359300 | ||||||||
\(981\) | −20.8824 | −0.666723 | ||||||||
\(982\) | −2.54218 | −0.0811242 | ||||||||
\(983\) | 10.4402 | 0.332992 | 0.166496 | − | 0.986042i | \(-0.446755\pi\) | ||||
0.166496 | + | 0.986042i | \(0.446755\pi\) | |||||||
\(984\) | 0.754095 | 0.0240397 | ||||||||
\(985\) | 16.1631 | 0.515000 | ||||||||
\(986\) | 25.6859 | 0.818005 | ||||||||
\(987\) | −0.184959 | −0.00588731 | ||||||||
\(988\) | −0.169595 | −0.00539554 | ||||||||
\(989\) | 1.76054 | 0.0559820 | ||||||||
\(990\) | 24.0283 | 0.763670 | ||||||||
\(991\) | 30.2499 | 0.960920 | 0.480460 | − | 0.877017i | \(-0.340470\pi\) | ||||
0.480460 | + | 0.877017i | \(0.340470\pi\) | |||||||
\(992\) | −8.42877 | −0.267614 | ||||||||
\(993\) | 12.3676 | 0.392473 | ||||||||
\(994\) | 47.6558 | 1.51155 | ||||||||
\(995\) | 58.2751 | 1.84744 | ||||||||
\(996\) | 1.02963 | 0.0326251 | ||||||||
\(997\) | −27.4843 | −0.870438 | −0.435219 | − | 0.900325i | \(-0.643329\pi\) | ||||
−0.435219 | + | 0.900325i | \(0.643329\pi\) | |||||||
\(998\) | −34.6773 | −1.09769 | ||||||||
\(999\) | 24.8324 | 0.785664 |
(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 | 6026.2.a.l.1.19 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.l.1.19 | ✓ | 36 | 1.1 | even | 1 | trivial |