Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.22 | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.56249 | 1.81195 | 0.905976 | − | 0.423330i | \(-0.139139\pi\) | ||||
0.905976 | + | 0.423330i | \(0.139139\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.56633 | 2.28317 | ||||||||
\(5\) | 3.89232 | 1.74070 | 0.870348 | − | 0.492437i | \(-0.163894\pi\) | ||||
0.870348 | + | 0.492437i | \(0.163894\pi\) | |||||||
\(6\) | −2.56249 | −1.04613 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 6.57620 | 2.32504 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 9.97400 | 3.15406 | ||||||||
\(11\) | 3.81355 | 1.14983 | 0.574914 | − | 0.818214i | \(-0.305035\pi\) | ||||
0.574914 | + | 0.818214i | \(0.305035\pi\) | |||||||
\(12\) | −4.56633 | −1.31819 | ||||||||
\(13\) | −6.39406 | −1.77339 | −0.886697 | − | 0.462351i | \(-0.847006\pi\) | ||||
−0.886697 | + | 0.462351i | \(0.847006\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.89232 | −1.00499 | ||||||||
\(16\) | 7.71874 | 1.92969 | ||||||||
\(17\) | −1.70351 | −0.413161 | −0.206580 | − | 0.978430i | \(-0.566233\pi\) | ||||
−0.206580 | + | 0.978430i | \(0.566233\pi\) | |||||||
\(18\) | 2.56249 | 0.603984 | ||||||||
\(19\) | 6.47548 | 1.48558 | 0.742789 | − | 0.669526i | \(-0.233503\pi\) | ||||
0.742789 | + | 0.669526i | \(0.233503\pi\) | |||||||
\(20\) | 17.7736 | 3.97430 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 9.77216 | 2.08343 | ||||||||
\(23\) | 3.51424 | 0.732771 | 0.366385 | − | 0.930463i | \(-0.380595\pi\) | ||||
0.366385 | + | 0.930463i | \(0.380595\pi\) | |||||||
\(24\) | −6.57620 | −1.34236 | ||||||||
\(25\) | 10.1501 | 2.03002 | ||||||||
\(26\) | −16.3847 | −3.21330 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.65494 | −1.60718 | −0.803591 | − | 0.595182i | \(-0.797080\pi\) | ||||
−0.803591 | + | 0.595182i | \(0.797080\pi\) | |||||||
\(30\) | −9.97400 | −1.82100 | ||||||||
\(31\) | −0.432523 | −0.0776834 | −0.0388417 | − | 0.999245i | \(-0.512367\pi\) | ||||
−0.0388417 | + | 0.999245i | \(0.512367\pi\) | |||||||
\(32\) | 6.62678 | 1.17146 | ||||||||
\(33\) | −3.81355 | −0.663854 | ||||||||
\(34\) | −4.36521 | −0.748627 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.56633 | 0.761056 | ||||||||
\(37\) | 7.97403 | 1.31092 | 0.655462 | − | 0.755229i | \(-0.272474\pi\) | ||||
0.655462 | + | 0.755229i | \(0.272474\pi\) | |||||||
\(38\) | 16.5933 | 2.69179 | ||||||||
\(39\) | 6.39406 | 1.02387 | ||||||||
\(40\) | 25.5966 | 4.04718 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.41643 | −0.978496 | −0.489248 | − | 0.872145i | \(-0.662729\pi\) | ||||
−0.489248 | + | 0.872145i | \(0.662729\pi\) | |||||||
\(44\) | 17.4139 | 2.62525 | ||||||||
\(45\) | 3.89232 | 0.580232 | ||||||||
\(46\) | 9.00520 | 1.32774 | ||||||||
\(47\) | −3.72691 | −0.543625 | −0.271813 | − | 0.962350i | \(-0.587623\pi\) | ||||
−0.271813 | + | 0.962350i | \(0.587623\pi\) | |||||||
\(48\) | −7.71874 | −1.11410 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 26.0095 | 3.67830 | ||||||||
\(51\) | 1.70351 | 0.238538 | ||||||||
\(52\) | −29.1974 | −4.04896 | ||||||||
\(53\) | 14.2446 | 1.95665 | 0.978323 | − | 0.207085i | \(-0.0663977\pi\) | ||||
0.978323 | + | 0.207085i | \(0.0663977\pi\) | |||||||
\(54\) | −2.56249 | −0.348710 | ||||||||
\(55\) | 14.8435 | 2.00150 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.47548 | −0.857699 | ||||||||
\(58\) | −22.1782 | −2.91213 | ||||||||
\(59\) | −3.38894 | −0.441203 | −0.220601 | − | 0.975364i | \(-0.570802\pi\) | ||||
−0.220601 | + | 0.975364i | \(0.570802\pi\) | |||||||
\(60\) | −17.7736 | −2.29456 | ||||||||
\(61\) | 4.40630 | 0.564169 | 0.282084 | − | 0.959390i | \(-0.408974\pi\) | ||||
0.282084 | + | 0.959390i | \(0.408974\pi\) | |||||||
\(62\) | −1.10833 | −0.140759 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.54354 | 0.192943 | ||||||||
\(65\) | −24.8877 | −3.08694 | ||||||||
\(66\) | −9.77216 | −1.20287 | ||||||||
\(67\) | 3.61186 | 0.441259 | 0.220630 | − | 0.975358i | \(-0.429189\pi\) | ||||
0.220630 | + | 0.975358i | \(0.429189\pi\) | |||||||
\(68\) | −7.77878 | −0.943315 | ||||||||
\(69\) | −3.51424 | −0.423065 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.619870 | −0.0735650 | −0.0367825 | − | 0.999323i | \(-0.511711\pi\) | ||||
−0.0367825 | + | 0.999323i | \(0.511711\pi\) | |||||||
\(72\) | 6.57620 | 0.775012 | ||||||||
\(73\) | −2.71814 | −0.318134 | −0.159067 | − | 0.987268i | \(-0.550849\pi\) | ||||
−0.159067 | + | 0.987268i | \(0.550849\pi\) | |||||||
\(74\) | 20.4334 | 2.37533 | ||||||||
\(75\) | −10.1501 | −1.17204 | ||||||||
\(76\) | 29.5692 | 3.39182 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 16.3847 | 1.85520 | ||||||||
\(79\) | 11.5546 | 1.29999 | 0.649995 | − | 0.759939i | \(-0.274771\pi\) | ||||
0.649995 | + | 0.759939i | \(0.274771\pi\) | |||||||
\(80\) | 30.0438 | 3.35900 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.56249 | 0.282979 | ||||||||
\(83\) | −5.74873 | −0.631005 | −0.315502 | − | 0.948925i | \(-0.602173\pi\) | ||||
−0.315502 | + | 0.948925i | \(0.602173\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.63058 | −0.719188 | ||||||||
\(86\) | −16.4420 | −1.77299 | ||||||||
\(87\) | 8.65494 | 0.927907 | ||||||||
\(88\) | 25.0786 | 2.67339 | ||||||||
\(89\) | −16.4936 | −1.74831 | −0.874157 | − | 0.485644i | \(-0.838585\pi\) | ||||
−0.874157 | + | 0.485644i | \(0.838585\pi\) | |||||||
\(90\) | 9.97400 | 1.05135 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 16.0472 | 1.67304 | ||||||||
\(93\) | 0.432523 | 0.0448505 | ||||||||
\(94\) | −9.55015 | −0.985022 | ||||||||
\(95\) | 25.2046 | 2.58594 | ||||||||
\(96\) | −6.62678 | −0.676343 | ||||||||
\(97\) | −2.81728 | −0.286051 | −0.143026 | − | 0.989719i | \(-0.545683\pi\) | ||||
−0.143026 | + | 0.989719i | \(0.545683\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.81355 | 0.383276 | ||||||||
\(100\) | 46.3489 | 4.63489 | ||||||||
\(101\) | −9.17978 | −0.913422 | −0.456711 | − | 0.889615i | \(-0.650973\pi\) | ||||
−0.456711 | + | 0.889615i | \(0.650973\pi\) | |||||||
\(102\) | 4.36521 | 0.432220 | ||||||||
\(103\) | 12.7010 | 1.25147 | 0.625734 | − | 0.780036i | \(-0.284799\pi\) | ||||
0.625734 | + | 0.780036i | \(0.284799\pi\) | |||||||
\(104\) | −42.0486 | −4.12321 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 36.5016 | 3.54535 | ||||||||
\(107\) | 9.75066 | 0.942632 | 0.471316 | − | 0.881964i | \(-0.343779\pi\) | ||||
0.471316 | + | 0.881964i | \(0.343779\pi\) | |||||||
\(108\) | −4.56633 | −0.439396 | ||||||||
\(109\) | −15.4367 | −1.47856 | −0.739282 | − | 0.673396i | \(-0.764835\pi\) | ||||
−0.739282 | + | 0.673396i | \(0.764835\pi\) | |||||||
\(110\) | 38.0363 | 3.62662 | ||||||||
\(111\) | −7.97403 | −0.756862 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.0865 | 1.51329 | 0.756646 | − | 0.653825i | \(-0.226837\pi\) | ||||
0.756646 | + | 0.653825i | \(0.226837\pi\) | |||||||
\(114\) | −16.5933 | −1.55411 | ||||||||
\(115\) | 13.6786 | 1.27553 | ||||||||
\(116\) | −39.5213 | −3.66946 | ||||||||
\(117\) | −6.39406 | −0.591131 | ||||||||
\(118\) | −8.68412 | −0.799438 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −25.5966 | −2.33664 | ||||||||
\(121\) | 3.54315 | 0.322105 | ||||||||
\(122\) | 11.2911 | 1.02225 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −1.97504 | −0.177364 | ||||||||
\(125\) | 20.0459 | 1.79296 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.4222 | −1.19103 | −0.595515 | − | 0.803344i | \(-0.703052\pi\) | ||||
−0.595515 | + | 0.803344i | \(0.703052\pi\) | |||||||
\(128\) | −9.29825 | −0.821857 | ||||||||
\(129\) | 6.41643 | 0.564935 | ||||||||
\(130\) | −63.7744 | −5.59339 | ||||||||
\(131\) | 3.10894 | 0.271630 | 0.135815 | − | 0.990734i | \(-0.456635\pi\) | ||||
0.135815 | + | 0.990734i | \(0.456635\pi\) | |||||||
\(132\) | −17.4139 | −1.51569 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 9.25535 | 0.799540 | ||||||||
\(135\) | −3.89232 | −0.334997 | ||||||||
\(136\) | −11.2026 | −0.960614 | ||||||||
\(137\) | −12.3063 | −1.05140 | −0.525700 | − | 0.850670i | \(-0.676196\pi\) | ||||
−0.525700 | + | 0.850670i | \(0.676196\pi\) | |||||||
\(138\) | −9.00520 | −0.766574 | ||||||||
\(139\) | −10.9403 | −0.927944 | −0.463972 | − | 0.885850i | \(-0.653576\pi\) | ||||
−0.463972 | + | 0.885850i | \(0.653576\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.72691 | 0.313862 | ||||||||
\(142\) | −1.58841 | −0.133296 | ||||||||
\(143\) | −24.3841 | −2.03910 | ||||||||
\(144\) | 7.71874 | 0.643229 | ||||||||
\(145\) | −33.6877 | −2.79762 | ||||||||
\(146\) | −6.96519 | −0.576443 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 36.4121 | 2.99306 | ||||||||
\(149\) | 10.0711 | 0.825057 | 0.412529 | − | 0.910945i | \(-0.364646\pi\) | ||||
0.412529 | + | 0.910945i | \(0.364646\pi\) | |||||||
\(150\) | −26.0095 | −2.12367 | ||||||||
\(151\) | −17.6807 | −1.43883 | −0.719416 | − | 0.694579i | \(-0.755590\pi\) | ||||
−0.719416 | + | 0.694579i | \(0.755590\pi\) | |||||||
\(152\) | 42.5841 | 3.45402 | ||||||||
\(153\) | −1.70351 | −0.137720 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.68352 | −0.135223 | ||||||||
\(156\) | 29.1974 | 2.33767 | ||||||||
\(157\) | −9.27189 | −0.739977 | −0.369989 | − | 0.929036i | \(-0.620638\pi\) | ||||
−0.369989 | + | 0.929036i | \(0.620638\pi\) | |||||||
\(158\) | 29.6084 | 2.35552 | ||||||||
\(159\) | −14.2446 | −1.12967 | ||||||||
\(160\) | 25.7935 | 2.03916 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.56249 | 0.201328 | ||||||||
\(163\) | −21.2183 | −1.66195 | −0.830974 | − | 0.556312i | \(-0.812216\pi\) | ||||
−0.830974 | + | 0.556312i | \(0.812216\pi\) | |||||||
\(164\) | 4.56633 | 0.356571 | ||||||||
\(165\) | −14.8435 | −1.15557 | ||||||||
\(166\) | −14.7310 | −1.14335 | ||||||||
\(167\) | 15.0869 | 1.16746 | 0.583731 | − | 0.811947i | \(-0.301592\pi\) | ||||
0.583731 | + | 0.811947i | \(0.301592\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.8841 | 2.14493 | ||||||||
\(170\) | −16.9908 | −1.30313 | ||||||||
\(171\) | 6.47548 | 0.495193 | ||||||||
\(172\) | −29.2996 | −2.23407 | ||||||||
\(173\) | 3.21775 | 0.244641 | 0.122320 | − | 0.992491i | \(-0.460966\pi\) | ||||
0.122320 | + | 0.992491i | \(0.460966\pi\) | |||||||
\(174\) | 22.1782 | 1.68132 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 29.4358 | 2.21881 | ||||||||
\(177\) | 3.38894 | 0.254729 | ||||||||
\(178\) | −42.2645 | −3.16786 | ||||||||
\(179\) | −3.09693 | −0.231475 | −0.115738 | − | 0.993280i | \(-0.536923\pi\) | ||||
−0.115738 | + | 0.993280i | \(0.536923\pi\) | |||||||
\(180\) | 17.7736 | 1.32477 | ||||||||
\(181\) | 0.106111 | 0.00788716 | 0.00394358 | − | 0.999992i | \(-0.498745\pi\) | ||||
0.00394358 | + | 0.999992i | \(0.498745\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.40630 | −0.325723 | ||||||||
\(184\) | 23.1104 | 1.70372 | ||||||||
\(185\) | 31.0375 | 2.28192 | ||||||||
\(186\) | 1.10833 | 0.0812670 | ||||||||
\(187\) | −6.49640 | −0.475064 | ||||||||
\(188\) | −17.0183 | −1.24119 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 64.5865 | 4.68560 | ||||||||
\(191\) | −11.2353 | −0.812957 | −0.406478 | − | 0.913660i | \(-0.633243\pi\) | ||||
−0.406478 | + | 0.913660i | \(0.633243\pi\) | |||||||
\(192\) | −1.54354 | −0.111396 | ||||||||
\(193\) | −8.99177 | −0.647242 | −0.323621 | − | 0.946187i | \(-0.604900\pi\) | ||||
−0.323621 | + | 0.946187i | \(0.604900\pi\) | |||||||
\(194\) | −7.21924 | −0.518311 | ||||||||
\(195\) | 24.8877 | 1.78225 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.416020 | 0.0296402 | 0.0148201 | − | 0.999890i | \(-0.495282\pi\) | ||||
0.0148201 | + | 0.999890i | \(0.495282\pi\) | |||||||
\(198\) | 9.77216 | 0.694477 | ||||||||
\(199\) | 7.21407 | 0.511392 | 0.255696 | − | 0.966757i | \(-0.417695\pi\) | ||||
0.255696 | + | 0.966757i | \(0.417695\pi\) | |||||||
\(200\) | 66.7492 | 4.71988 | ||||||||
\(201\) | −3.61186 | −0.254761 | ||||||||
\(202\) | −23.5231 | −1.65508 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.77878 | 0.544623 | ||||||||
\(205\) | 3.89232 | 0.271851 | ||||||||
\(206\) | 32.5462 | 2.26760 | ||||||||
\(207\) | 3.51424 | 0.244257 | ||||||||
\(208\) | −49.3541 | −3.42209 | ||||||||
\(209\) | 24.6946 | 1.70816 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.7020 | −0.805599 | −0.402800 | − | 0.915288i | \(-0.631963\pi\) | ||||
−0.402800 | + | 0.915288i | \(0.631963\pi\) | |||||||
\(212\) | 65.0456 | 4.46735 | ||||||||
\(213\) | 0.619870 | 0.0424728 | ||||||||
\(214\) | 24.9859 | 1.70800 | ||||||||
\(215\) | −24.9748 | −1.70327 | ||||||||
\(216\) | −6.57620 | −0.447454 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −39.5562 | −2.67909 | ||||||||
\(219\) | 2.71814 | 0.183675 | ||||||||
\(220\) | 67.7805 | 4.56976 | ||||||||
\(221\) | 10.8923 | 0.732697 | ||||||||
\(222\) | −20.4334 | −1.37140 | ||||||||
\(223\) | 8.90948 | 0.596623 | 0.298311 | − | 0.954469i | \(-0.403577\pi\) | ||||
0.298311 | + | 0.954469i | \(0.403577\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.1501 | 0.676675 | ||||||||
\(226\) | 41.2215 | 2.74201 | ||||||||
\(227\) | 14.3864 | 0.954861 | 0.477431 | − | 0.878669i | \(-0.341568\pi\) | ||||
0.477431 | + | 0.878669i | \(0.341568\pi\) | |||||||
\(228\) | −29.5692 | −1.95827 | ||||||||
\(229\) | 4.19714 | 0.277355 | 0.138677 | − | 0.990338i | \(-0.455715\pi\) | ||||
0.138677 | + | 0.990338i | \(0.455715\pi\) | |||||||
\(230\) | 35.0511 | 2.31120 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −56.9166 | −3.73676 | ||||||||
\(233\) | −4.56437 | −0.299022 | −0.149511 | − | 0.988760i | \(-0.547770\pi\) | ||||
−0.149511 | + | 0.988760i | \(0.547770\pi\) | |||||||
\(234\) | −16.3847 | −1.07110 | ||||||||
\(235\) | −14.5063 | −0.946287 | ||||||||
\(236\) | −15.4750 | −1.00734 | ||||||||
\(237\) | −11.5546 | −0.750549 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.7068 | −1.72752 | −0.863761 | − | 0.503902i | \(-0.831897\pi\) | ||||
−0.863761 | + | 0.503902i | \(0.831897\pi\) | |||||||
\(240\) | −30.0438 | −1.93932 | ||||||||
\(241\) | −10.9960 | −0.708316 | −0.354158 | − | 0.935186i | \(-0.615233\pi\) | ||||
−0.354158 | + | 0.935186i | \(0.615233\pi\) | |||||||
\(242\) | 9.07927 | 0.583638 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 20.1206 | 1.28809 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.56249 | −0.163378 | ||||||||
\(247\) | −41.4047 | −2.63452 | ||||||||
\(248\) | −2.84436 | −0.180617 | ||||||||
\(249\) | 5.74873 | 0.364311 | ||||||||
\(250\) | 51.3673 | 3.24876 | ||||||||
\(251\) | 19.7095 | 1.24405 | 0.622026 | − | 0.782997i | \(-0.286310\pi\) | ||||
0.622026 | + | 0.782997i | \(0.286310\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.4017 | 0.842560 | ||||||||
\(254\) | −34.3943 | −2.15809 | ||||||||
\(255\) | 6.63058 | 0.415223 | ||||||||
\(256\) | −26.9137 | −1.68211 | ||||||||
\(257\) | 31.9263 | 1.99151 | 0.995754 | − | 0.0920522i | \(-0.0293427\pi\) | ||||
0.995754 | + | 0.0920522i | \(0.0293427\pi\) | |||||||
\(258\) | 16.4420 | 1.02363 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −113.646 | −7.04800 | ||||||||
\(261\) | −8.65494 | −0.535727 | ||||||||
\(262\) | 7.96662 | 0.492180 | ||||||||
\(263\) | 17.2241 | 1.06208 | 0.531042 | − | 0.847345i | \(-0.321801\pi\) | ||||
0.531042 | + | 0.847345i | \(0.321801\pi\) | |||||||
\(264\) | −25.0786 | −1.54348 | ||||||||
\(265\) | 55.4445 | 3.40593 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.4936 | 1.00939 | ||||||||
\(268\) | 16.4930 | 1.00747 | ||||||||
\(269\) | −10.3538 | −0.631282 | −0.315641 | − | 0.948879i | \(-0.602220\pi\) | ||||
−0.315641 | + | 0.948879i | \(0.602220\pi\) | |||||||
\(270\) | −9.97400 | −0.606999 | ||||||||
\(271\) | −27.4283 | −1.66615 | −0.833076 | − | 0.553158i | \(-0.813423\pi\) | ||||
−0.833076 | + | 0.553158i | \(0.813423\pi\) | |||||||
\(272\) | −13.1489 | −0.797271 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −31.5348 | −1.90508 | ||||||||
\(275\) | 38.7080 | 2.33418 | ||||||||
\(276\) | −16.0472 | −0.965929 | ||||||||
\(277\) | 11.9690 | 0.719149 | 0.359574 | − | 0.933116i | \(-0.382922\pi\) | ||||
0.359574 | + | 0.933116i | \(0.382922\pi\) | |||||||
\(278\) | −28.0344 | −1.68139 | ||||||||
\(279\) | −0.432523 | −0.0258945 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.1762 | 0.607063 | 0.303531 | − | 0.952821i | \(-0.401834\pi\) | ||||
0.303531 | + | 0.952821i | \(0.401834\pi\) | |||||||
\(282\) | 9.55015 | 0.568703 | ||||||||
\(283\) | 6.37817 | 0.379143 | 0.189572 | − | 0.981867i | \(-0.439290\pi\) | ||||
0.189572 | + | 0.981867i | \(0.439290\pi\) | |||||||
\(284\) | −2.83053 | −0.167961 | ||||||||
\(285\) | −25.2046 | −1.49299 | ||||||||
\(286\) | −62.4838 | −3.69475 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.62678 | 0.390487 | ||||||||
\(289\) | −14.0981 | −0.829298 | ||||||||
\(290\) | −86.3244 | −5.06914 | ||||||||
\(291\) | 2.81728 | 0.165152 | ||||||||
\(292\) | −12.4119 | −0.726353 | ||||||||
\(293\) | −31.5877 | −1.84537 | −0.922687 | − | 0.385550i | \(-0.874012\pi\) | ||||
−0.922687 | + | 0.385550i | \(0.874012\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.1908 | −0.768000 | ||||||||
\(296\) | 52.4388 | 3.04794 | ||||||||
\(297\) | −3.81355 | −0.221285 | ||||||||
\(298\) | 25.8071 | 1.49496 | ||||||||
\(299\) | −22.4703 | −1.29949 | ||||||||
\(300\) | −46.3489 | −2.67595 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −45.3065 | −2.60709 | ||||||||
\(303\) | 9.17978 | 0.527364 | ||||||||
\(304\) | 49.9826 | 2.86670 | ||||||||
\(305\) | 17.1507 | 0.982046 | ||||||||
\(306\) | −4.36521 | −0.249542 | ||||||||
\(307\) | 4.13968 | 0.236264 | 0.118132 | − | 0.992998i | \(-0.462309\pi\) | ||||
0.118132 | + | 0.992998i | \(0.462309\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.7010 | −0.722536 | ||||||||
\(310\) | −4.31398 | −0.245018 | ||||||||
\(311\) | −14.6828 | −0.832587 | −0.416293 | − | 0.909230i | \(-0.636671\pi\) | ||||
−0.416293 | + | 0.909230i | \(0.636671\pi\) | |||||||
\(312\) | 42.0486 | 2.38053 | ||||||||
\(313\) | 32.5963 | 1.84245 | 0.921225 | − | 0.389031i | \(-0.127190\pi\) | ||||
0.921225 | + | 0.389031i | \(0.127190\pi\) | |||||||
\(314\) | −23.7591 | −1.34080 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 52.7620 | 2.96809 | ||||||||
\(317\) | −0.374845 | −0.0210534 | −0.0105267 | − | 0.999945i | \(-0.503351\pi\) | ||||
−0.0105267 | + | 0.999945i | \(0.503351\pi\) | |||||||
\(318\) | −36.5016 | −2.04691 | ||||||||
\(319\) | −33.0060 | −1.84798 | ||||||||
\(320\) | 6.00795 | 0.335855 | ||||||||
\(321\) | −9.75066 | −0.544229 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.0310 | −0.613782 | ||||||||
\(324\) | 4.56633 | 0.253685 | ||||||||
\(325\) | −64.9005 | −3.60003 | ||||||||
\(326\) | −54.3717 | −3.01137 | ||||||||
\(327\) | 15.4367 | 0.853650 | ||||||||
\(328\) | 6.57620 | 0.363110 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −38.0363 | −2.09383 | ||||||||
\(331\) | −2.42663 | −0.133379 | −0.0666897 | − | 0.997774i | \(-0.521244\pi\) | ||||
−0.0666897 | + | 0.997774i | \(0.521244\pi\) | |||||||
\(332\) | −26.2506 | −1.44069 | ||||||||
\(333\) | 7.97403 | 0.436974 | ||||||||
\(334\) | 38.6601 | 2.11539 | ||||||||
\(335\) | 14.0585 | 0.768098 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.6106 | −1.23168 | −0.615840 | − | 0.787871i | \(-0.711183\pi\) | ||||
−0.615840 | + | 0.787871i | \(0.711183\pi\) | |||||||
\(338\) | 71.4525 | 3.88650 | ||||||||
\(339\) | −16.0865 | −0.873699 | ||||||||
\(340\) | −30.2775 | −1.64203 | ||||||||
\(341\) | −1.64945 | −0.0893225 | ||||||||
\(342\) | 16.5933 | 0.897265 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −42.1957 | −2.27504 | ||||||||
\(345\) | −13.6786 | −0.736428 | ||||||||
\(346\) | 8.24544 | 0.443277 | ||||||||
\(347\) | −32.2232 | −1.72983 | −0.864916 | − | 0.501916i | \(-0.832629\pi\) | ||||
−0.864916 | + | 0.501916i | \(0.832629\pi\) | |||||||
\(348\) | 39.5213 | 2.11857 | ||||||||
\(349\) | −9.93257 | −0.531678 | −0.265839 | − | 0.964017i | \(-0.585649\pi\) | ||||
−0.265839 | + | 0.964017i | \(0.585649\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.39406 | 0.341290 | ||||||||
\(352\) | 25.2715 | 1.34698 | ||||||||
\(353\) | −0.470477 | −0.0250410 | −0.0125205 | − | 0.999922i | \(-0.503985\pi\) | ||||
−0.0125205 | + | 0.999922i | \(0.503985\pi\) | |||||||
\(354\) | 8.68412 | 0.461556 | ||||||||
\(355\) | −2.41273 | −0.128054 | ||||||||
\(356\) | −75.3151 | −3.99169 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.93584 | −0.419422 | ||||||||
\(359\) | −3.78654 | −0.199846 | −0.0999230 | − | 0.994995i | \(-0.531860\pi\) | ||||
−0.0999230 | + | 0.994995i | \(0.531860\pi\) | |||||||
\(360\) | 25.5966 | 1.34906 | ||||||||
\(361\) | 22.9319 | 1.20694 | ||||||||
\(362\) | 0.271908 | 0.0142912 | ||||||||
\(363\) | −3.54315 | −0.185967 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.5799 | −0.553775 | ||||||||
\(366\) | −11.2911 | −0.590194 | ||||||||
\(367\) | 5.50525 | 0.287372 | 0.143686 | − | 0.989623i | \(-0.454105\pi\) | ||||
0.143686 | + | 0.989623i | \(0.454105\pi\) | |||||||
\(368\) | 27.1256 | 1.41402 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 79.5331 | 4.13473 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.97504 | 0.102401 | ||||||||
\(373\) | 18.8594 | 0.976505 | 0.488252 | − | 0.872703i | \(-0.337635\pi\) | ||||
0.488252 | + | 0.872703i | \(0.337635\pi\) | |||||||
\(374\) | −16.6469 | −0.860793 | ||||||||
\(375\) | −20.0459 | −1.03517 | ||||||||
\(376\) | −24.5089 | −1.26395 | ||||||||
\(377\) | 55.3402 | 2.85017 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.70498 | 0.241678 | 0.120839 | − | 0.992672i | \(-0.461441\pi\) | ||||
0.120839 | + | 0.992672i | \(0.461441\pi\) | |||||||
\(380\) | 115.093 | 5.90413 | ||||||||
\(381\) | 13.4222 | 0.687642 | ||||||||
\(382\) | −28.7903 | −1.47304 | ||||||||
\(383\) | −9.31366 | −0.475906 | −0.237953 | − | 0.971277i | \(-0.576476\pi\) | ||||
−0.237953 | + | 0.971277i | \(0.576476\pi\) | |||||||
\(384\) | 9.29825 | 0.474500 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.0413 | −1.17277 | ||||||||
\(387\) | −6.41643 | −0.326165 | ||||||||
\(388\) | −12.8646 | −0.653103 | ||||||||
\(389\) | 11.8547 | 0.601056 | 0.300528 | − | 0.953773i | \(-0.402837\pi\) | ||||
0.300528 | + | 0.953773i | \(0.402837\pi\) | |||||||
\(390\) | 63.7744 | 3.22934 | ||||||||
\(391\) | −5.98654 | −0.302752 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.10894 | −0.156825 | ||||||||
\(394\) | 1.06605 | 0.0537066 | ||||||||
\(395\) | 44.9740 | 2.26289 | ||||||||
\(396\) | 17.4139 | 0.875083 | ||||||||
\(397\) | 24.0952 | 1.20930 | 0.604652 | − | 0.796490i | \(-0.293312\pi\) | ||||
0.604652 | + | 0.796490i | \(0.293312\pi\) | |||||||
\(398\) | 18.4860 | 0.926617 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 78.3462 | 3.91731 | ||||||||
\(401\) | 28.0444 | 1.40047 | 0.700234 | − | 0.713913i | \(-0.253079\pi\) | ||||
0.700234 | + | 0.713913i | \(0.253079\pi\) | |||||||
\(402\) | −9.25535 | −0.461615 | ||||||||
\(403\) | 2.76558 | 0.137763 | ||||||||
\(404\) | −41.9179 | −2.08550 | ||||||||
\(405\) | 3.89232 | 0.193411 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 30.4094 | 1.50734 | ||||||||
\(408\) | 11.2026 | 0.554611 | ||||||||
\(409\) | 17.0017 | 0.840682 | 0.420341 | − | 0.907366i | \(-0.361911\pi\) | ||||
0.420341 | + | 0.907366i | \(0.361911\pi\) | |||||||
\(410\) | 9.97400 | 0.492581 | ||||||||
\(411\) | 12.3063 | 0.607026 | ||||||||
\(412\) | 57.9971 | 2.85731 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 9.00520 | 0.442582 | ||||||||
\(415\) | −22.3759 | −1.09839 | ||||||||
\(416\) | −42.3721 | −2.07746 | ||||||||
\(417\) | 10.9403 | 0.535749 | ||||||||
\(418\) | 63.2795 | 3.09510 | ||||||||
\(419\) | 34.5411 | 1.68744 | 0.843722 | − | 0.536781i | \(-0.180360\pi\) | ||||
0.843722 | + | 0.536781i | \(0.180360\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.26526 | −0.354087 | −0.177044 | − | 0.984203i | \(-0.556653\pi\) | ||||
−0.177044 | + | 0.984203i | \(0.556653\pi\) | |||||||
\(422\) | −29.9862 | −1.45971 | ||||||||
\(423\) | −3.72691 | −0.181208 | ||||||||
\(424\) | 93.6753 | 4.54927 | ||||||||
\(425\) | −17.2908 | −0.838726 | ||||||||
\(426\) | 1.58841 | 0.0769586 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 44.5248 | 2.15219 | ||||||||
\(429\) | 24.3841 | 1.17727 | ||||||||
\(430\) | −63.9975 | −3.08623 | ||||||||
\(431\) | −8.73640 | −0.420818 | −0.210409 | − | 0.977613i | \(-0.567480\pi\) | ||||
−0.210409 | + | 0.977613i | \(0.567480\pi\) | |||||||
\(432\) | −7.71874 | −0.371368 | ||||||||
\(433\) | −25.5753 | −1.22907 | −0.614534 | − | 0.788890i | \(-0.710656\pi\) | ||||
−0.614534 | + | 0.788890i | \(0.710656\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 33.6877 | 1.61520 | ||||||||
\(436\) | −70.4890 | −3.37581 | ||||||||
\(437\) | 22.7564 | 1.08859 | ||||||||
\(438\) | 6.96519 | 0.332810 | ||||||||
\(439\) | 30.0329 | 1.43339 | 0.716697 | − | 0.697385i | \(-0.245653\pi\) | ||||
0.716697 | + | 0.697385i | \(0.245653\pi\) | |||||||
\(440\) | 97.6140 | 4.65357 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 27.9114 | 1.32761 | ||||||||
\(443\) | 11.8190 | 0.561538 | 0.280769 | − | 0.959775i | \(-0.409411\pi\) | ||||
0.280769 | + | 0.959775i | \(0.409411\pi\) | |||||||
\(444\) | −36.4121 | −1.72804 | ||||||||
\(445\) | −64.1981 | −3.04328 | ||||||||
\(446\) | 22.8304 | 1.08105 | ||||||||
\(447\) | −10.0711 | −0.476347 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.74219 | 0.223798 | 0.111899 | − | 0.993720i | \(-0.464307\pi\) | ||||
0.111899 | + | 0.993720i | \(0.464307\pi\) | |||||||
\(450\) | 26.0095 | 1.22610 | ||||||||
\(451\) | 3.81355 | 0.179573 | ||||||||
\(452\) | 73.4564 | 3.45510 | ||||||||
\(453\) | 17.6807 | 0.830710 | ||||||||
\(454\) | 36.8650 | 1.73016 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −42.5841 | −1.99418 | ||||||||
\(457\) | −4.79322 | −0.224217 | −0.112109 | − | 0.993696i | \(-0.535760\pi\) | ||||
−0.112109 | + | 0.993696i | \(0.535760\pi\) | |||||||
\(458\) | 10.7551 | 0.502553 | ||||||||
\(459\) | 1.70351 | 0.0795128 | ||||||||
\(460\) | 62.4608 | 2.91225 | ||||||||
\(461\) | −0.478050 | −0.0222650 | −0.0111325 | − | 0.999938i | \(-0.503544\pi\) | ||||
−0.0111325 | + | 0.999938i | \(0.503544\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.36341 | −0.202785 | −0.101392 | − | 0.994847i | \(-0.532330\pi\) | ||||
−0.101392 | + | 0.994847i | \(0.532330\pi\) | |||||||
\(464\) | −66.8052 | −3.10136 | ||||||||
\(465\) | 1.68352 | 0.0780711 | ||||||||
\(466\) | −11.6961 | −0.541813 | ||||||||
\(467\) | −34.5418 | −1.59841 | −0.799203 | − | 0.601062i | \(-0.794745\pi\) | ||||
−0.799203 | + | 0.601062i | \(0.794745\pi\) | |||||||
\(468\) | −29.1974 | −1.34965 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −37.1722 | −1.71463 | ||||||||
\(471\) | 9.27189 | 0.427226 | ||||||||
\(472\) | −22.2864 | −1.02581 | ||||||||
\(473\) | −24.4694 | −1.12510 | ||||||||
\(474\) | −29.6084 | −1.35996 | ||||||||
\(475\) | 65.7269 | 3.01576 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.2446 | 0.652215 | ||||||||
\(478\) | −68.4359 | −3.13018 | ||||||||
\(479\) | −41.9564 | −1.91704 | −0.958518 | − | 0.285032i | \(-0.907996\pi\) | ||||
−0.958518 | + | 0.285032i | \(0.907996\pi\) | |||||||
\(480\) | −25.7935 | −1.17731 | ||||||||
\(481\) | −50.9865 | −2.32478 | ||||||||
\(482\) | −28.1772 | −1.28343 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.1792 | 0.735419 | ||||||||
\(485\) | −10.9657 | −0.497929 | ||||||||
\(486\) | −2.56249 | −0.116237 | ||||||||
\(487\) | 12.9603 | 0.587287 | 0.293644 | − | 0.955915i | \(-0.405132\pi\) | ||||
0.293644 | + | 0.955915i | \(0.405132\pi\) | |||||||
\(488\) | 28.9767 | 1.31171 | ||||||||
\(489\) | 21.2183 | 0.959526 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.3306 | −1.32367 | −0.661835 | − | 0.749650i | \(-0.730222\pi\) | ||||
−0.661835 | + | 0.749650i | \(0.730222\pi\) | |||||||
\(492\) | −4.56633 | −0.205866 | ||||||||
\(493\) | 14.7437 | 0.664024 | ||||||||
\(494\) | −106.099 | −4.77361 | ||||||||
\(495\) | 14.8435 | 0.667167 | ||||||||
\(496\) | −3.33853 | −0.149905 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 14.7310 | 0.660114 | ||||||||
\(499\) | 29.3644 | 1.31453 | 0.657265 | − | 0.753659i | \(-0.271713\pi\) | ||||
0.657265 | + | 0.753659i | \(0.271713\pi\) | |||||||
\(500\) | 91.5363 | 4.09363 | ||||||||
\(501\) | −15.0869 | −0.674035 | ||||||||
\(502\) | 50.5053 | 2.25416 | ||||||||
\(503\) | 14.3799 | 0.641166 | 0.320583 | − | 0.947220i | \(-0.396121\pi\) | ||||
0.320583 | + | 0.947220i | \(0.396121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −35.7306 | −1.58999 | ||||||||
\(506\) | 34.3418 | 1.52668 | ||||||||
\(507\) | −27.8841 | −1.23837 | ||||||||
\(508\) | −61.2904 | −2.71932 | ||||||||
\(509\) | 22.5208 | 0.998216 | 0.499108 | − | 0.866540i | \(-0.333661\pi\) | ||||
0.499108 | + | 0.866540i | \(0.333661\pi\) | |||||||
\(510\) | 16.9908 | 0.752364 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −50.3696 | −2.22604 | ||||||||
\(513\) | −6.47548 | −0.285900 | ||||||||
\(514\) | 81.8107 | 3.60852 | ||||||||
\(515\) | 49.4364 | 2.17843 | ||||||||
\(516\) | 29.2996 | 1.28984 | ||||||||
\(517\) | −14.2127 | −0.625076 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.21775 | −0.141243 | ||||||||
\(520\) | −163.667 | −7.17725 | ||||||||
\(521\) | 19.3136 | 0.846144 | 0.423072 | − | 0.906096i | \(-0.360952\pi\) | ||||
0.423072 | + | 0.906096i | \(0.360952\pi\) | |||||||
\(522\) | −22.1782 | −0.970712 | ||||||||
\(523\) | 2.22956 | 0.0974918 | 0.0487459 | − | 0.998811i | \(-0.484478\pi\) | ||||
0.0487459 | + | 0.998811i | \(0.484478\pi\) | |||||||
\(524\) | 14.1965 | 0.620176 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 44.1366 | 1.92445 | ||||||||
\(527\) | 0.736805 | 0.0320957 | ||||||||
\(528\) | −29.4358 | −1.28103 | ||||||||
\(529\) | −10.6501 | −0.463047 | ||||||||
\(530\) | 142.076 | 6.17137 | ||||||||
\(531\) | −3.38894 | −0.147068 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.39406 | −0.276958 | ||||||||
\(534\) | 42.2645 | 1.82896 | ||||||||
\(535\) | 37.9527 | 1.64084 | ||||||||
\(536\) | 23.7523 | 1.02594 | ||||||||
\(537\) | 3.09693 | 0.133642 | ||||||||
\(538\) | −26.5315 | −1.14385 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −17.7736 | −0.764855 | ||||||||
\(541\) | −22.6192 | −0.972473 | −0.486237 | − | 0.873827i | \(-0.661631\pi\) | ||||
−0.486237 | + | 0.873827i | \(0.661631\pi\) | |||||||
\(542\) | −70.2847 | −3.01899 | ||||||||
\(543\) | −0.106111 | −0.00455366 | ||||||||
\(544\) | −11.2888 | −0.484001 | ||||||||
\(545\) | −60.0844 | −2.57373 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.0174 | −1.28345 | −0.641725 | − | 0.766935i | \(-0.721781\pi\) | ||||
−0.641725 | + | 0.766935i | \(0.721781\pi\) | |||||||
\(548\) | −56.1947 | −2.40052 | ||||||||
\(549\) | 4.40630 | 0.188056 | ||||||||
\(550\) | 99.1887 | 4.22942 | ||||||||
\(551\) | −56.0449 | −2.38759 | ||||||||
\(552\) | −23.1104 | −0.983643 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 30.6705 | 1.30306 | ||||||||
\(555\) | −31.0375 | −1.31747 | ||||||||
\(556\) | −49.9571 | −2.11865 | ||||||||
\(557\) | 7.24842 | 0.307125 | 0.153563 | − | 0.988139i | \(-0.450925\pi\) | ||||
0.153563 | + | 0.988139i | \(0.450925\pi\) | |||||||
\(558\) | −1.10833 | −0.0469195 | ||||||||
\(559\) | 41.0271 | 1.73526 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.49640 | 0.274278 | ||||||||
\(562\) | 26.0764 | 1.09997 | ||||||||
\(563\) | −22.1704 | −0.934372 | −0.467186 | − | 0.884159i | \(-0.654732\pi\) | ||||
−0.467186 | + | 0.884159i | \(0.654732\pi\) | |||||||
\(564\) | 17.0183 | 0.716600 | ||||||||
\(565\) | 62.6138 | 2.63418 | ||||||||
\(566\) | 16.3440 | 0.686989 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.07639 | −0.171041 | ||||||||
\(569\) | −31.1263 | −1.30488 | −0.652440 | − | 0.757840i | \(-0.726255\pi\) | ||||
−0.652440 | + | 0.757840i | \(0.726255\pi\) | |||||||
\(570\) | −64.5865 | −2.70523 | ||||||||
\(571\) | −18.3057 | −0.766068 | −0.383034 | − | 0.923734i | \(-0.625121\pi\) | ||||
−0.383034 | + | 0.923734i | \(0.625121\pi\) | |||||||
\(572\) | −111.346 | −4.65560 | ||||||||
\(573\) | 11.2353 | 0.469361 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 35.6700 | 1.48754 | ||||||||
\(576\) | 1.54354 | 0.0643143 | ||||||||
\(577\) | 4.86103 | 0.202367 | 0.101184 | − | 0.994868i | \(-0.467737\pi\) | ||||
0.101184 | + | 0.994868i | \(0.467737\pi\) | |||||||
\(578\) | −36.1261 | −1.50265 | ||||||||
\(579\) | 8.99177 | 0.373685 | ||||||||
\(580\) | −153.830 | −6.38742 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.21924 | 0.299247 | ||||||||
\(583\) | 54.3225 | 2.24981 | ||||||||
\(584\) | −17.8750 | −0.739673 | ||||||||
\(585\) | −24.8877 | −1.02898 | ||||||||
\(586\) | −80.9431 | −3.34373 | ||||||||
\(587\) | 28.6682 | 1.18326 | 0.591632 | − | 0.806208i | \(-0.298484\pi\) | ||||
0.591632 | + | 0.806208i | \(0.298484\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.80079 | −0.115405 | ||||||||
\(590\) | −33.8013 | −1.39158 | ||||||||
\(591\) | −0.416020 | −0.0171128 | ||||||||
\(592\) | 61.5495 | 2.52967 | ||||||||
\(593\) | 21.9738 | 0.902354 | 0.451177 | − | 0.892434i | \(-0.351004\pi\) | ||||
0.451177 | + | 0.892434i | \(0.351004\pi\) | |||||||
\(594\) | −9.77216 | −0.400957 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 45.9881 | 1.88374 | ||||||||
\(597\) | −7.21407 | −0.295252 | ||||||||
\(598\) | −57.5799 | −2.35462 | ||||||||
\(599\) | 31.3230 | 1.27982 | 0.639911 | − | 0.768449i | \(-0.278971\pi\) | ||||
0.639911 | + | 0.768449i | \(0.278971\pi\) | |||||||
\(600\) | −66.7492 | −2.72502 | ||||||||
\(601\) | 6.15788 | 0.251185 | 0.125593 | − | 0.992082i | \(-0.459917\pi\) | ||||
0.125593 | + | 0.992082i | \(0.459917\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.61186 | 0.147086 | ||||||||
\(604\) | −80.7358 | −3.28509 | ||||||||
\(605\) | 13.7911 | 0.560686 | ||||||||
\(606\) | 23.5231 | 0.955559 | ||||||||
\(607\) | 12.7567 | 0.517779 | 0.258889 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258889 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(608\) | 42.9116 | 1.74029 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 43.9484 | 1.77942 | ||||||||
\(611\) | 23.8301 | 0.964062 | ||||||||
\(612\) | −7.77878 | −0.314438 | ||||||||
\(613\) | −43.0140 | −1.73732 | −0.868659 | − | 0.495410i | \(-0.835018\pi\) | ||||
−0.868659 | + | 0.495410i | \(0.835018\pi\) | |||||||
\(614\) | 10.6079 | 0.428099 | ||||||||
\(615\) | −3.89232 | −0.156953 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.6914 | −1.39662 | −0.698312 | − | 0.715793i | \(-0.746065\pi\) | ||||
−0.698312 | + | 0.715793i | \(0.746065\pi\) | |||||||
\(618\) | −32.5462 | −1.30920 | ||||||||
\(619\) | −3.93932 | −0.158335 | −0.0791673 | − | 0.996861i | \(-0.525226\pi\) | ||||
−0.0791673 | + | 0.996861i | \(0.525226\pi\) | |||||||
\(620\) | −7.68749 | −0.308737 | ||||||||
\(621\) | −3.51424 | −0.141022 | ||||||||
\(622\) | −37.6246 | −1.50861 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 49.3541 | 1.97575 | ||||||||
\(625\) | 27.2744 | 1.09097 | ||||||||
\(626\) | 83.5275 | 3.33843 | ||||||||
\(627\) | −24.6946 | −0.986206 | ||||||||
\(628\) | −42.3385 | −1.68949 | ||||||||
\(629\) | −13.5838 | −0.541622 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.68087 | 0.0669144 | 0.0334572 | − | 0.999440i | \(-0.489348\pi\) | ||||
0.0334572 | + | 0.999440i | \(0.489348\pi\) | |||||||
\(632\) | 75.9850 | 3.02252 | ||||||||
\(633\) | 11.7020 | 0.465113 | ||||||||
\(634\) | −0.960534 | −0.0381477 | ||||||||
\(635\) | −52.2436 | −2.07322 | ||||||||
\(636\) | −65.0456 | −2.57923 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −84.5775 | −3.34845 | ||||||||
\(639\) | −0.619870 | −0.0245217 | ||||||||
\(640\) | −36.1917 | −1.43060 | ||||||||
\(641\) | 21.8935 | 0.864740 | 0.432370 | − | 0.901696i | \(-0.357678\pi\) | ||||
0.432370 | + | 0.901696i | \(0.357678\pi\) | |||||||
\(642\) | −24.9859 | −0.986116 | ||||||||
\(643\) | −47.8257 | −1.88606 | −0.943031 | − | 0.332705i | \(-0.892039\pi\) | ||||
−0.943031 | + | 0.332705i | \(0.892039\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.9748 | 0.983381 | ||||||||
\(646\) | −28.2668 | −1.11214 | ||||||||
\(647\) | −13.4095 | −0.527181 | −0.263591 | − | 0.964635i | \(-0.584907\pi\) | ||||
−0.263591 | + | 0.964635i | \(0.584907\pi\) | |||||||
\(648\) | 6.57620 | 0.258337 | ||||||||
\(649\) | −12.9239 | −0.507307 | ||||||||
\(650\) | −166.307 | −6.52309 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −96.8900 | −3.79450 | ||||||||
\(653\) | 4.31746 | 0.168955 | 0.0844775 | − | 0.996425i | \(-0.473078\pi\) | ||||
0.0844775 | + | 0.996425i | \(0.473078\pi\) | |||||||
\(654\) | 39.5562 | 1.54677 | ||||||||
\(655\) | 12.1010 | 0.472825 | ||||||||
\(656\) | 7.71874 | 0.301366 | ||||||||
\(657\) | −2.71814 | −0.106045 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.7187 | 1.07977 | 0.539883 | − | 0.841740i | \(-0.318468\pi\) | ||||
0.539883 | + | 0.841740i | \(0.318468\pi\) | |||||||
\(660\) | −67.7805 | −2.63835 | ||||||||
\(661\) | 24.2825 | 0.944481 | 0.472241 | − | 0.881470i | \(-0.343445\pi\) | ||||
0.472241 | + | 0.881470i | \(0.343445\pi\) | |||||||
\(662\) | −6.21820 | −0.241677 | ||||||||
\(663\) | −10.8923 | −0.423023 | ||||||||
\(664\) | −37.8048 | −1.46711 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 20.4334 | 0.791776 | ||||||||
\(667\) | −30.4156 | −1.17770 | ||||||||
\(668\) | 68.8920 | 2.66551 | ||||||||
\(669\) | −8.90948 | −0.344460 | ||||||||
\(670\) | 36.0247 | 1.39176 | ||||||||
\(671\) | 16.8036 | 0.648697 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.8664 | 0.650152 | 0.325076 | − | 0.945688i | \(-0.394610\pi\) | ||||
0.325076 | + | 0.945688i | \(0.394610\pi\) | |||||||
\(674\) | −57.9395 | −2.23174 | ||||||||
\(675\) | −10.1501 | −0.390678 | ||||||||
\(676\) | 127.328 | 4.89723 | ||||||||
\(677\) | 36.5414 | 1.40440 | 0.702200 | − | 0.711980i | \(-0.252201\pi\) | ||||
0.702200 | + | 0.711980i | \(0.252201\pi\) | |||||||
\(678\) | −41.2215 | −1.58310 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −43.6040 | −1.67214 | ||||||||
\(681\) | −14.3864 | −0.551289 | ||||||||
\(682\) | −4.22668 | −0.161848 | ||||||||
\(683\) | −19.6855 | −0.753244 | −0.376622 | − | 0.926367i | \(-0.622914\pi\) | ||||
−0.376622 | + | 0.926367i | \(0.622914\pi\) | |||||||
\(684\) | 29.5692 | 1.13061 | ||||||||
\(685\) | −47.9001 | −1.83017 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.19714 | −0.160131 | ||||||||
\(688\) | −49.5268 | −1.88819 | ||||||||
\(689\) | −91.0809 | −3.46990 | ||||||||
\(690\) | −35.0511 | −1.33437 | ||||||||
\(691\) | 11.0941 | 0.422041 | 0.211020 | − | 0.977482i | \(-0.432321\pi\) | ||||
0.211020 | + | 0.977482i | \(0.432321\pi\) | |||||||
\(692\) | 14.6933 | 0.558556 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −82.5715 | −3.13437 | ||||||||
\(695\) | −42.5831 | −1.61527 | ||||||||
\(696\) | 56.9166 | 2.15742 | ||||||||
\(697\) | −1.70351 | −0.0645249 | ||||||||
\(698\) | −25.4521 | −0.963375 | ||||||||
\(699\) | 4.56437 | 0.172640 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.7923 | 1.12524 | 0.562620 | − | 0.826716i | \(-0.309794\pi\) | ||||
0.562620 | + | 0.826716i | \(0.309794\pi\) | |||||||
\(702\) | 16.3847 | 0.618401 | ||||||||
\(703\) | 51.6357 | 1.94748 | ||||||||
\(704\) | 5.88637 | 0.221851 | ||||||||
\(705\) | 14.5063 | 0.546339 | ||||||||
\(706\) | −1.20559 | −0.0453730 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 15.4750 | 0.581588 | ||||||||
\(709\) | 36.5747 | 1.37359 | 0.686795 | − | 0.726851i | \(-0.259017\pi\) | ||||
0.686795 | + | 0.726851i | \(0.259017\pi\) | |||||||
\(710\) | −6.18258 | −0.232028 | ||||||||
\(711\) | 11.5546 | 0.433330 | ||||||||
\(712\) | −108.465 | −4.06489 | ||||||||
\(713\) | −1.51999 | −0.0569241 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −94.9105 | −3.54945 | ||||||||
\(716\) | −14.1416 | −0.528497 | ||||||||
\(717\) | 26.7068 | 0.997385 | ||||||||
\(718\) | −9.70296 | −0.362111 | ||||||||
\(719\) | −34.8891 | −1.30114 | −0.650572 | − | 0.759444i | \(-0.725471\pi\) | ||||
−0.650572 | + | 0.759444i | \(0.725471\pi\) | |||||||
\(720\) | 30.0438 | 1.11967 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 58.7626 | 2.18692 | ||||||||
\(723\) | 10.9960 | 0.408947 | ||||||||
\(724\) | 0.484538 | 0.0180077 | ||||||||
\(725\) | −87.8487 | −3.26262 | ||||||||
\(726\) | −9.07927 | −0.336963 | ||||||||
\(727\) | 5.29173 | 0.196259 | 0.0981296 | − | 0.995174i | \(-0.468714\pi\) | ||||
0.0981296 | + | 0.995174i | \(0.468714\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −27.1107 | −1.00341 | ||||||||
\(731\) | 10.9304 | 0.404276 | ||||||||
\(732\) | −20.1206 | −0.743680 | ||||||||
\(733\) | −10.9375 | −0.403986 | −0.201993 | − | 0.979387i | \(-0.564742\pi\) | ||||
−0.201993 | + | 0.979387i | \(0.564742\pi\) | |||||||
\(734\) | 14.1071 | 0.520703 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 23.2881 | 0.858412 | ||||||||
\(737\) | 13.7740 | 0.507372 | ||||||||
\(738\) | 2.56249 | 0.0943264 | ||||||||
\(739\) | 14.0490 | 0.516802 | 0.258401 | − | 0.966038i | \(-0.416805\pi\) | ||||
0.258401 | + | 0.966038i | \(0.416805\pi\) | |||||||
\(740\) | 141.727 | 5.21000 | ||||||||
\(741\) | 41.4047 | 1.52104 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −47.8936 | −1.75704 | −0.878522 | − | 0.477701i | \(-0.841470\pi\) | ||||
−0.878522 | + | 0.477701i | \(0.841470\pi\) | |||||||
\(744\) | 2.84436 | 0.104279 | ||||||||
\(745\) | 39.1999 | 1.43617 | ||||||||
\(746\) | 48.3270 | 1.76938 | ||||||||
\(747\) | −5.74873 | −0.210335 | ||||||||
\(748\) | −29.6647 | −1.08465 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −51.3673 | −1.87567 | ||||||||
\(751\) | −30.9737 | −1.13025 | −0.565124 | − | 0.825006i | \(-0.691172\pi\) | ||||
−0.565124 | + | 0.825006i | \(0.691172\pi\) | |||||||
\(752\) | −28.7670 | −1.04903 | ||||||||
\(753\) | −19.7095 | −0.718254 | ||||||||
\(754\) | 141.809 | 5.16436 | ||||||||
\(755\) | −68.8187 | −2.50457 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.1123 | 0.730995 | 0.365497 | − | 0.930812i | \(-0.380899\pi\) | ||||
0.365497 | + | 0.930812i | \(0.380899\pi\) | |||||||
\(758\) | 12.0564 | 0.437909 | ||||||||
\(759\) | −13.4017 | −0.486452 | ||||||||
\(760\) | 165.751 | 6.01240 | ||||||||
\(761\) | −13.6838 | −0.496038 | −0.248019 | − | 0.968755i | \(-0.579780\pi\) | ||||
−0.248019 | + | 0.968755i | \(0.579780\pi\) | |||||||
\(762\) | 34.3943 | 1.24597 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −51.3041 | −1.85612 | ||||||||
\(765\) | −6.63058 | −0.239729 | ||||||||
\(766\) | −23.8661 | −0.862318 | ||||||||
\(767\) | 21.6691 | 0.782427 | ||||||||
\(768\) | 26.9137 | 0.971166 | ||||||||
\(769\) | 1.06746 | 0.0384937 | 0.0192468 | − | 0.999815i | \(-0.493873\pi\) | ||||
0.0192468 | + | 0.999815i | \(0.493873\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.9263 | −1.14980 | ||||||||
\(772\) | −41.0594 | −1.47776 | ||||||||
\(773\) | 2.94940 | 0.106082 | 0.0530412 | − | 0.998592i | \(-0.483109\pi\) | ||||
0.0530412 | + | 0.998592i | \(0.483109\pi\) | |||||||
\(774\) | −16.4420 | −0.590996 | ||||||||
\(775\) | −4.39016 | −0.157699 | ||||||||
\(776\) | −18.5270 | −0.665080 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 30.3774 | 1.08908 | ||||||||
\(779\) | 6.47548 | 0.232008 | ||||||||
\(780\) | 113.646 | 4.06917 | ||||||||
\(781\) | −2.36390 | −0.0845871 | ||||||||
\(782\) | −15.3404 | −0.548572 | ||||||||
\(783\) | 8.65494 | 0.309302 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.0891 | −1.28808 | ||||||||
\(786\) | −7.96662 | −0.284160 | ||||||||
\(787\) | 0.0995646 | 0.00354910 | 0.00177455 | − | 0.999998i | \(-0.499435\pi\) | ||||
0.00177455 | + | 0.999998i | \(0.499435\pi\) | |||||||
\(788\) | 1.89969 | 0.0676735 | ||||||||
\(789\) | −17.2241 | −0.613195 | ||||||||
\(790\) | 115.245 | 4.10024 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 25.0786 | 0.891131 | ||||||||
\(793\) | −28.1741 | −1.00049 | ||||||||
\(794\) | 61.7437 | 2.19120 | ||||||||
\(795\) | −55.4445 | −1.96641 | ||||||||
\(796\) | 32.9419 | 1.16759 | ||||||||
\(797\) | 18.5859 | 0.658346 | 0.329173 | − | 0.944270i | \(-0.393230\pi\) | ||||
0.329173 | + | 0.944270i | \(0.393230\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.34881 | 0.224605 | ||||||||
\(800\) | 67.2626 | 2.37809 | ||||||||
\(801\) | −16.4936 | −0.582771 | ||||||||
\(802\) | 71.8633 | 2.53758 | ||||||||
\(803\) | −10.3657 | −0.365799 | ||||||||
\(804\) | −16.4930 | −0.581662 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.08676 | 0.249620 | ||||||||
\(807\) | 10.3538 | 0.364471 | ||||||||
\(808\) | −60.3680 | −2.12374 | ||||||||
\(809\) | −37.1832 | −1.30729 | −0.653645 | − | 0.756801i | \(-0.726761\pi\) | ||||
−0.653645 | + | 0.756801i | \(0.726761\pi\) | |||||||
\(810\) | 9.97400 | 0.350451 | ||||||||
\(811\) | −15.1429 | −0.531738 | −0.265869 | − | 0.964009i | \(-0.585659\pi\) | ||||
−0.265869 | + | 0.964009i | \(0.585659\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.4283 | 0.961954 | ||||||||
\(814\) | 77.9236 | 2.73122 | ||||||||
\(815\) | −82.5884 | −2.89295 | ||||||||
\(816\) | 13.1489 | 0.460304 | ||||||||
\(817\) | −41.5495 | −1.45363 | ||||||||
\(818\) | 43.5667 | 1.52327 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.7736 | 0.620682 | ||||||||
\(821\) | −9.35104 | −0.326354 | −0.163177 | − | 0.986597i | \(-0.552174\pi\) | ||||
−0.163177 | + | 0.986597i | \(0.552174\pi\) | |||||||
\(822\) | 31.5348 | 1.09990 | ||||||||
\(823\) | 4.99218 | 0.174017 | 0.0870083 | − | 0.996208i | \(-0.472269\pi\) | ||||
0.0870083 | + | 0.996208i | \(0.472269\pi\) | |||||||
\(824\) | 83.5244 | 2.90971 | ||||||||
\(825\) | −38.7080 | −1.34764 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.42913 | 0.223563 | 0.111781 | − | 0.993733i | \(-0.464344\pi\) | ||||
0.111781 | + | 0.993733i | \(0.464344\pi\) | |||||||
\(828\) | 16.0472 | 0.557679 | ||||||||
\(829\) | −18.3653 | −0.637853 | −0.318926 | − | 0.947779i | \(-0.603322\pi\) | ||||
−0.318926 | + | 0.947779i | \(0.603322\pi\) | |||||||
\(830\) | −57.3378 | −1.99023 | ||||||||
\(831\) | −11.9690 | −0.415201 | ||||||||
\(832\) | −9.86951 | −0.342164 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 28.0344 | 0.970750 | ||||||||
\(835\) | 58.7231 | 2.03220 | ||||||||
\(836\) | 112.764 | 3.90001 | ||||||||
\(837\) | 0.432523 | 0.0149502 | ||||||||
\(838\) | 88.5111 | 3.05756 | ||||||||
\(839\) | −54.3366 | −1.87591 | −0.937954 | − | 0.346760i | \(-0.887282\pi\) | ||||
−0.937954 | + | 0.346760i | \(0.887282\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 45.9079 | 1.58303 | ||||||||
\(842\) | −18.6171 | −0.641589 | ||||||||
\(843\) | −10.1762 | −0.350488 | ||||||||
\(844\) | −53.4353 | −1.83932 | ||||||||
\(845\) | 108.534 | 3.73367 | ||||||||
\(846\) | −9.55015 | −0.328341 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 109.950 | 3.77571 | ||||||||
\(849\) | −6.37817 | −0.218898 | ||||||||
\(850\) | −44.3074 | −1.51973 | ||||||||
\(851\) | 28.0227 | 0.960606 | ||||||||
\(852\) | 2.83053 | 0.0969725 | ||||||||
\(853\) | 23.5896 | 0.807692 | 0.403846 | − | 0.914827i | \(-0.367673\pi\) | ||||
0.403846 | + | 0.914827i | \(0.367673\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 25.2046 | 0.861980 | ||||||||
\(856\) | 64.1223 | 2.19165 | ||||||||
\(857\) | 45.5365 | 1.55550 | 0.777749 | − | 0.628575i | \(-0.216362\pi\) | ||||
0.777749 | + | 0.628575i | \(0.216362\pi\) | |||||||
\(858\) | 62.4838 | 2.13316 | ||||||||
\(859\) | −46.3999 | −1.58314 | −0.791572 | − | 0.611075i | \(-0.790737\pi\) | ||||
−0.791572 | + | 0.611075i | \(0.790737\pi\) | |||||||
\(860\) | −114.043 | −3.88884 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.3869 | −0.762501 | ||||||||
\(863\) | −28.2733 | −0.962433 | −0.481217 | − | 0.876602i | \(-0.659805\pi\) | ||||
−0.481217 | + | 0.876602i | \(0.659805\pi\) | |||||||
\(864\) | −6.62678 | −0.225448 | ||||||||
\(865\) | 12.5245 | 0.425846 | ||||||||
\(866\) | −65.5362 | −2.22701 | ||||||||
\(867\) | 14.0981 | 0.478796 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 44.0639 | 1.49476 | ||||||||
\(870\) | 86.3244 | 2.92667 | ||||||||
\(871\) | −23.0945 | −0.782527 | ||||||||
\(872\) | −101.515 | −3.43772 | ||||||||
\(873\) | −2.81728 | −0.0953504 | ||||||||
\(874\) | 58.3130 | 1.97247 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.4119 | 0.419360 | ||||||||
\(877\) | 25.1433 | 0.849030 | 0.424515 | − | 0.905421i | \(-0.360445\pi\) | ||||
0.424515 | + | 0.905421i | \(0.360445\pi\) | |||||||
\(878\) | 76.9590 | 2.59724 | ||||||||
\(879\) | 31.5877 | 1.06543 | ||||||||
\(880\) | 114.573 | 3.86227 | ||||||||
\(881\) | −25.6604 | −0.864519 | −0.432260 | − | 0.901749i | \(-0.642284\pi\) | ||||
−0.432260 | + | 0.901749i | \(0.642284\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −50.6683 | −1.70512 | −0.852562 | − | 0.522627i | \(-0.824952\pi\) | ||||
−0.852562 | + | 0.522627i | \(0.824952\pi\) | |||||||
\(884\) | 49.7380 | 1.67287 | ||||||||
\(885\) | 13.1908 | 0.443405 | ||||||||
\(886\) | 30.2860 | 1.01748 | ||||||||
\(887\) | 23.1852 | 0.778483 | 0.389242 | − | 0.921136i | \(-0.372737\pi\) | ||||
0.389242 | + | 0.921136i | \(0.372737\pi\) | |||||||
\(888\) | −52.4388 | −1.75973 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −164.507 | −5.51428 | ||||||||
\(891\) | 3.81355 | 0.127759 | ||||||||
\(892\) | 40.6836 | 1.36219 | ||||||||
\(893\) | −24.1335 | −0.807598 | ||||||||
\(894\) | −25.8071 | −0.863118 | ||||||||
\(895\) | −12.0542 | −0.402928 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.4703 | 0.750262 | ||||||||
\(898\) | 12.1518 | 0.405511 | ||||||||
\(899\) | 3.74346 | 0.124851 | ||||||||
\(900\) | 46.3489 | 1.54496 | ||||||||
\(901\) | −24.2658 | −0.808409 | ||||||||
\(902\) | 9.77216 | 0.325377 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 105.788 | 3.51846 | ||||||||
\(905\) | 0.413017 | 0.0137292 | ||||||||
\(906\) | 45.3065 | 1.50521 | ||||||||
\(907\) | 33.2474 | 1.10396 | 0.551981 | − | 0.833856i | \(-0.313872\pi\) | ||||
0.551981 | + | 0.833856i | \(0.313872\pi\) | |||||||
\(908\) | 65.6933 | 2.18011 | ||||||||
\(909\) | −9.17978 | −0.304474 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.5992 | 0.516825 | 0.258412 | − | 0.966035i | \(-0.416801\pi\) | ||||
0.258412 | + | 0.966035i | \(0.416801\pi\) | |||||||
\(912\) | −49.9826 | −1.65509 | ||||||||
\(913\) | −21.9231 | −0.725547 | ||||||||
\(914\) | −12.2826 | −0.406271 | ||||||||
\(915\) | −17.1507 | −0.566985 | ||||||||
\(916\) | 19.1655 | 0.633247 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.36521 | 0.144073 | ||||||||
\(919\) | −4.50305 | −0.148542 | −0.0742709 | − | 0.997238i | \(-0.523663\pi\) | ||||
−0.0742709 | + | 0.997238i | \(0.523663\pi\) | |||||||
\(920\) | 89.9528 | 2.96566 | ||||||||
\(921\) | −4.13968 | −0.136407 | ||||||||
\(922\) | −1.22500 | −0.0403431 | ||||||||
\(923\) | 3.96349 | 0.130460 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 80.9374 | 2.66121 | ||||||||
\(926\) | −11.1812 | −0.367437 | ||||||||
\(927\) | 12.7010 | 0.417156 | ||||||||
\(928\) | −57.3544 | −1.88275 | ||||||||
\(929\) | 4.26219 | 0.139838 | 0.0699190 | − | 0.997553i | \(-0.477726\pi\) | ||||
0.0699190 | + | 0.997553i | \(0.477726\pi\) | |||||||
\(930\) | 4.31398 | 0.141461 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −20.8424 | −0.682717 | ||||||||
\(933\) | 14.6828 | 0.480694 | ||||||||
\(934\) | −88.5130 | −2.89623 | ||||||||
\(935\) | −25.2860 | −0.826942 | ||||||||
\(936\) | −42.0486 | −1.37440 | ||||||||
\(937\) | 25.6728 | 0.838695 | 0.419347 | − | 0.907826i | \(-0.362259\pi\) | ||||
0.419347 | + | 0.907826i | \(0.362259\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.5963 | −1.06374 | ||||||||
\(940\) | −66.2406 | −2.16053 | ||||||||
\(941\) | −25.1298 | −0.819210 | −0.409605 | − | 0.912263i | \(-0.634333\pi\) | ||||
−0.409605 | + | 0.912263i | \(0.634333\pi\) | |||||||
\(942\) | 23.7591 | 0.774113 | ||||||||
\(943\) | 3.51424 | 0.114440 | ||||||||
\(944\) | −26.1584 | −0.851383 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −62.7024 | −2.03863 | ||||||||
\(947\) | 1.84065 | 0.0598131 | 0.0299065 | − | 0.999553i | \(-0.490479\pi\) | ||||
0.0299065 | + | 0.999553i | \(0.490479\pi\) | |||||||
\(948\) | −52.7620 | −1.71363 | ||||||||
\(949\) | 17.3799 | 0.564177 | ||||||||
\(950\) | 168.424 | 5.46441 | ||||||||
\(951\) | 0.374845 | 0.0121552 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.9038 | −0.839107 | −0.419554 | − | 0.907731i | \(-0.637813\pi\) | ||||
−0.419554 | + | 0.907731i | \(0.637813\pi\) | |||||||
\(954\) | 36.5016 | 1.18178 | ||||||||
\(955\) | −43.7313 | −1.41511 | ||||||||
\(956\) | −121.952 | −3.94422 | ||||||||
\(957\) | 33.0060 | 1.06693 | ||||||||
\(958\) | −107.513 | −3.47358 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −6.00795 | −0.193906 | ||||||||
\(961\) | −30.8129 | −0.993965 | ||||||||
\(962\) | −130.652 | −4.21240 | ||||||||
\(963\) | 9.75066 | 0.314211 | ||||||||
\(964\) | −50.2115 | −1.61720 | ||||||||
\(965\) | −34.9988 | −1.12665 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.7879 | −0.572019 | −0.286009 | − | 0.958227i | \(-0.592329\pi\) | ||||
−0.286009 | + | 0.958227i | \(0.592329\pi\) | |||||||
\(968\) | 23.3005 | 0.748905 | ||||||||
\(969\) | 11.0310 | 0.354367 | ||||||||
\(970\) | −28.0996 | −0.902222 | ||||||||
\(971\) | −53.5532 | −1.71860 | −0.859302 | − | 0.511468i | \(-0.829102\pi\) | ||||
−0.859302 | + | 0.511468i | \(0.829102\pi\) | |||||||
\(972\) | −4.56633 | −0.146465 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 33.2106 | 1.06414 | ||||||||
\(975\) | 64.9005 | 2.07848 | ||||||||
\(976\) | 34.0111 | 1.08867 | ||||||||
\(977\) | 31.9422 | 1.02192 | 0.510961 | − | 0.859604i | \(-0.329290\pi\) | ||||
0.510961 | + | 0.859604i | \(0.329290\pi\) | |||||||
\(978\) | 54.3717 | 1.73861 | ||||||||
\(979\) | −62.8990 | −2.01026 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.4367 | −0.492855 | ||||||||
\(982\) | −75.1591 | −2.39842 | ||||||||
\(983\) | −26.2569 | −0.837466 | −0.418733 | − | 0.908109i | \(-0.637526\pi\) | ||||
−0.418733 | + | 0.908109i | \(0.637526\pi\) | |||||||
\(984\) | −6.57620 | −0.209642 | ||||||||
\(985\) | 1.61928 | 0.0515946 | ||||||||
\(986\) | 37.7806 | 1.20318 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −189.068 | −6.01504 | ||||||||
\(989\) | −22.5489 | −0.717014 | ||||||||
\(990\) | 38.0363 | 1.20887 | ||||||||
\(991\) | −59.4449 | −1.88833 | −0.944164 | − | 0.329475i | \(-0.893128\pi\) | ||||
−0.944164 | + | 0.329475i | \(0.893128\pi\) | |||||||
\(992\) | −2.86623 | −0.0910030 | ||||||||
\(993\) | 2.42663 | 0.0770066 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.0794 | 0.890178 | ||||||||
\(996\) | 26.2506 | 0.831783 | ||||||||
\(997\) | 6.34221 | 0.200860 | 0.100430 | − | 0.994944i | \(-0.467978\pi\) | ||||
0.100430 | + | 0.994944i | \(0.467978\pi\) | |||||||
\(998\) | 75.2458 | 2.38187 | ||||||||
\(999\) | −7.97403 | −0.252287 |
(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 | 6027.2.a.bn.1.22 | ✓ | 24 | |
7.6 | odd | 2 | 6027.2.a.bo.1.22 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bn.1.22 | ✓ | 24 | 1.1 | even | 1 | trivial | |
6027.2.a.bo.1.22 | yes | 24 | 7.6 | odd | 2 |