Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41590 | −1.70830 | −0.854150 | − | 0.520026i | \(-0.825922\pi\) | ||||
−0.854150 | + | 0.520026i | \(0.825922\pi\) | |||||||
\(3\) | 1.84179 | 1.06336 | 0.531680 | − | 0.846946i | \(-0.321561\pi\) | ||||
0.531680 | + | 0.846946i | \(0.321561\pi\) | |||||||
\(4\) | 3.83658 | 1.91829 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −4.44959 | −1.81654 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −4.43701 | −1.56872 | ||||||||
\(9\) | 0.392199 | 0.130733 | ||||||||
\(10\) | 2.41590 | 0.763975 | ||||||||
\(11\) | 5.68645 | 1.71453 | 0.857264 | − | 0.514877i | \(-0.172163\pi\) | ||||
0.857264 | + | 0.514877i | \(0.172163\pi\) | |||||||
\(12\) | 7.06619 | 2.03983 | ||||||||
\(13\) | −3.60089 | −0.998706 | −0.499353 | − | 0.866399i | \(-0.666429\pi\) | ||||
−0.499353 | + | 0.866399i | \(0.666429\pi\) | |||||||
\(14\) | 2.41590 | 0.645677 | ||||||||
\(15\) | −1.84179 | −0.475549 | ||||||||
\(16\) | 3.04621 | 0.761552 | ||||||||
\(17\) | 3.68593 | 0.893971 | 0.446985 | − | 0.894541i | \(-0.352498\pi\) | ||||
0.446985 | + | 0.894541i | \(0.352498\pi\) | |||||||
\(18\) | −0.947514 | −0.223331 | ||||||||
\(19\) | −1.18056 | −0.270839 | −0.135420 | − | 0.990788i | \(-0.543238\pi\) | ||||
−0.135420 | + | 0.990788i | \(0.543238\pi\) | |||||||
\(20\) | −3.83658 | −0.857886 | ||||||||
\(21\) | −1.84179 | −0.401912 | ||||||||
\(22\) | −13.7379 | −2.92893 | ||||||||
\(23\) | −1.47328 | −0.307200 | −0.153600 | − | 0.988133i | \(-0.549087\pi\) | ||||
−0.153600 | + | 0.988133i | \(0.549087\pi\) | |||||||
\(24\) | −8.17204 | −1.66811 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 8.69939 | 1.70609 | ||||||||
\(27\) | −4.80303 | −0.924343 | ||||||||
\(28\) | −3.83658 | −0.725046 | ||||||||
\(29\) | 0.109372 | 0.0203099 | 0.0101550 | − | 0.999948i | \(-0.496768\pi\) | ||||
0.0101550 | + | 0.999948i | \(0.496768\pi\) | |||||||
\(30\) | 4.44959 | 0.812380 | ||||||||
\(31\) | −0.502367 | −0.0902278 | −0.0451139 | − | 0.998982i | \(-0.514365\pi\) | ||||
−0.0451139 | + | 0.998982i | \(0.514365\pi\) | |||||||
\(32\) | 1.51468 | 0.267760 | ||||||||
\(33\) | 10.4733 | 1.82316 | ||||||||
\(34\) | −8.90486 | −1.52717 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 1.50470 | 0.250784 | ||||||||
\(37\) | −5.90785 | −0.971245 | −0.485622 | − | 0.874169i | \(-0.661407\pi\) | ||||
−0.485622 | + | 0.874169i | \(0.661407\pi\) | |||||||
\(38\) | 2.85212 | 0.462675 | ||||||||
\(39\) | −6.63208 | −1.06198 | ||||||||
\(40\) | 4.43701 | 0.701552 | ||||||||
\(41\) | −12.3065 | −1.92195 | −0.960975 | − | 0.276634i | \(-0.910781\pi\) | ||||
−0.960975 | + | 0.276634i | \(0.910781\pi\) | |||||||
\(42\) | 4.44959 | 0.686587 | ||||||||
\(43\) | 2.28127 | 0.347890 | 0.173945 | − | 0.984755i | \(-0.444349\pi\) | ||||
0.173945 | + | 0.984755i | \(0.444349\pi\) | |||||||
\(44\) | 21.8165 | 3.28896 | ||||||||
\(45\) | −0.392199 | −0.0584655 | ||||||||
\(46\) | 3.55930 | 0.524789 | ||||||||
\(47\) | 4.46248 | 0.650920 | 0.325460 | − | 0.945556i | \(-0.394481\pi\) | ||||
0.325460 | + | 0.945556i | \(0.394481\pi\) | |||||||
\(48\) | 5.61048 | 0.809803 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.41590 | −0.341660 | ||||||||
\(51\) | 6.78873 | 0.950612 | ||||||||
\(52\) | −13.8151 | −1.91581 | ||||||||
\(53\) | 10.4858 | 1.44034 | 0.720168 | − | 0.693800i | \(-0.244065\pi\) | ||||
0.720168 | + | 0.693800i | \(0.244065\pi\) | |||||||
\(54\) | 11.6036 | 1.57906 | ||||||||
\(55\) | −5.68645 | −0.766760 | ||||||||
\(56\) | 4.43701 | 0.592920 | ||||||||
\(57\) | −2.17435 | −0.287999 | ||||||||
\(58\) | −0.264233 | −0.0346955 | ||||||||
\(59\) | −4.74028 | −0.617132 | −0.308566 | − | 0.951203i | \(-0.599849\pi\) | ||||
−0.308566 | + | 0.951203i | \(0.599849\pi\) | |||||||
\(60\) | −7.06619 | −0.912241 | ||||||||
\(61\) | −10.9072 | −1.39652 | −0.698262 | − | 0.715843i | \(-0.746043\pi\) | ||||
−0.698262 | + | 0.715843i | \(0.746043\pi\) | |||||||
\(62\) | 1.21367 | 0.154136 | ||||||||
\(63\) | −0.392199 | −0.0494124 | ||||||||
\(64\) | −9.75172 | −1.21897 | ||||||||
\(65\) | 3.60089 | 0.446635 | ||||||||
\(66\) | −25.3023 | −3.11450 | ||||||||
\(67\) | 15.8281 | 1.93371 | 0.966855 | − | 0.255325i | \(-0.0821823\pi\) | ||||
0.966855 | + | 0.255325i | \(0.0821823\pi\) | |||||||
\(68\) | 14.1414 | 1.71490 | ||||||||
\(69\) | −2.71347 | −0.326664 | ||||||||
\(70\) | −2.41590 | −0.288756 | ||||||||
\(71\) | 5.08199 | 0.603122 | 0.301561 | − | 0.953447i | \(-0.402492\pi\) | ||||
0.301561 | + | 0.953447i | \(0.402492\pi\) | |||||||
\(72\) | −1.74019 | −0.205083 | ||||||||
\(73\) | 9.19853 | 1.07661 | 0.538303 | − | 0.842751i | \(-0.319066\pi\) | ||||
0.538303 | + | 0.842751i | \(0.319066\pi\) | |||||||
\(74\) | 14.2728 | 1.65918 | ||||||||
\(75\) | 1.84179 | 0.212672 | ||||||||
\(76\) | −4.52932 | −0.519549 | ||||||||
\(77\) | −5.68645 | −0.648031 | ||||||||
\(78\) | 16.0225 | 1.81419 | ||||||||
\(79\) | −2.03869 | −0.229370 | −0.114685 | − | 0.993402i | \(-0.536586\pi\) | ||||
−0.114685 | + | 0.993402i | \(0.536586\pi\) | |||||||
\(80\) | −3.04621 | −0.340576 | ||||||||
\(81\) | −10.0228 | −1.11364 | ||||||||
\(82\) | 29.7313 | 3.28327 | ||||||||
\(83\) | 11.0455 | 1.21240 | 0.606199 | − | 0.795313i | \(-0.292694\pi\) | ||||
0.606199 | + | 0.795313i | \(0.292694\pi\) | |||||||
\(84\) | −7.06619 | −0.770985 | ||||||||
\(85\) | −3.68593 | −0.399796 | ||||||||
\(86\) | −5.51132 | −0.594300 | ||||||||
\(87\) | 0.201441 | 0.0215967 | ||||||||
\(88\) | −25.2308 | −2.68961 | ||||||||
\(89\) | 7.76347 | 0.822926 | 0.411463 | − | 0.911426i | \(-0.365018\pi\) | ||||
0.411463 | + | 0.911426i | \(0.365018\pi\) | |||||||
\(90\) | 0.947514 | 0.0998767 | ||||||||
\(91\) | 3.60089 | 0.377475 | ||||||||
\(92\) | −5.65235 | −0.589299 | ||||||||
\(93\) | −0.925256 | −0.0959446 | ||||||||
\(94\) | −10.7809 | −1.11197 | ||||||||
\(95\) | 1.18056 | 0.121123 | ||||||||
\(96\) | 2.78972 | 0.284725 | ||||||||
\(97\) | 19.1651 | 1.94592 | 0.972959 | − | 0.230980i | \(-0.0741931\pi\) | ||||
0.972959 | + | 0.230980i | \(0.0741931\pi\) | |||||||
\(98\) | −2.41590 | −0.244043 | ||||||||
\(99\) | 2.23022 | 0.224145 | ||||||||
\(100\) | 3.83658 | 0.383658 | ||||||||
\(101\) | 11.0929 | 1.10378 | 0.551892 | − | 0.833916i | \(-0.313906\pi\) | ||||
0.551892 | + | 0.833916i | \(0.313906\pi\) | |||||||
\(102\) | −16.4009 | −1.62393 | ||||||||
\(103\) | 12.9130 | 1.27236 | 0.636179 | − | 0.771542i | \(-0.280514\pi\) | ||||
0.636179 | + | 0.771542i | \(0.280514\pi\) | |||||||
\(104\) | 15.9772 | 1.56669 | ||||||||
\(105\) | 1.84179 | 0.179741 | ||||||||
\(106\) | −25.3327 | −2.46053 | ||||||||
\(107\) | 2.35579 | 0.227743 | 0.113871 | − | 0.993495i | \(-0.463675\pi\) | ||||
0.113871 | + | 0.993495i | \(0.463675\pi\) | |||||||
\(108\) | −18.4272 | −1.77316 | ||||||||
\(109\) | −9.01416 | −0.863400 | −0.431700 | − | 0.902017i | \(-0.642086\pi\) | ||||
−0.431700 | + | 0.902017i | \(0.642086\pi\) | |||||||
\(110\) | 13.7379 | 1.30986 | ||||||||
\(111\) | −10.8810 | −1.03278 | ||||||||
\(112\) | −3.04621 | −0.287839 | ||||||||
\(113\) | −11.5859 | −1.08991 | −0.544954 | − | 0.838466i | \(-0.683453\pi\) | ||||
−0.544954 | + | 0.838466i | \(0.683453\pi\) | |||||||
\(114\) | 5.25301 | 0.491990 | ||||||||
\(115\) | 1.47328 | 0.137384 | ||||||||
\(116\) | 0.419616 | 0.0389604 | ||||||||
\(117\) | −1.41226 | −0.130564 | ||||||||
\(118\) | 11.4521 | 1.05425 | ||||||||
\(119\) | −3.68593 | −0.337889 | ||||||||
\(120\) | 8.17204 | 0.746002 | ||||||||
\(121\) | 21.3357 | 1.93961 | ||||||||
\(122\) | 26.3507 | 2.38568 | ||||||||
\(123\) | −22.6660 | −2.04372 | ||||||||
\(124\) | −1.92737 | −0.173083 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0.947514 | 0.0844112 | ||||||||
\(127\) | 7.09207 | 0.629320 | 0.314660 | − | 0.949204i | \(-0.398110\pi\) | ||||
0.314660 | + | 0.949204i | \(0.398110\pi\) | |||||||
\(128\) | 20.5299 | 1.81460 | ||||||||
\(129\) | 4.20162 | 0.369932 | ||||||||
\(130\) | −8.69939 | −0.762987 | ||||||||
\(131\) | 8.23872 | 0.719820 | 0.359910 | − | 0.932987i | \(-0.382807\pi\) | ||||
0.359910 | + | 0.932987i | \(0.382807\pi\) | |||||||
\(132\) | 40.1815 | 3.49735 | ||||||||
\(133\) | 1.18056 | 0.102368 | ||||||||
\(134\) | −38.2392 | −3.30336 | ||||||||
\(135\) | 4.80303 | 0.413379 | ||||||||
\(136\) | −16.3545 | −1.40239 | ||||||||
\(137\) | −22.8731 | −1.95418 | −0.977089 | − | 0.212833i | \(-0.931731\pi\) | ||||
−0.977089 | + | 0.212833i | \(0.931731\pi\) | |||||||
\(138\) | 6.55548 | 0.558040 | ||||||||
\(139\) | −20.9188 | −1.77431 | −0.887155 | − | 0.461472i | \(-0.847321\pi\) | ||||
−0.887155 | + | 0.461472i | \(0.847321\pi\) | |||||||
\(140\) | 3.83658 | 0.324250 | ||||||||
\(141\) | 8.21897 | 0.692162 | ||||||||
\(142\) | −12.2776 | −1.03031 | ||||||||
\(143\) | −20.4762 | −1.71231 | ||||||||
\(144\) | 1.19472 | 0.0995598 | ||||||||
\(145\) | −0.109372 | −0.00908287 | ||||||||
\(146\) | −22.2227 | −1.83917 | ||||||||
\(147\) | 1.84179 | 0.151908 | ||||||||
\(148\) | −22.6660 | −1.86313 | ||||||||
\(149\) | −18.5957 | −1.52342 | −0.761709 | − | 0.647920i | \(-0.775639\pi\) | ||||
−0.761709 | + | 0.647920i | \(0.775639\pi\) | |||||||
\(150\) | −4.44959 | −0.363308 | ||||||||
\(151\) | 14.5397 | 1.18322 | 0.591611 | − | 0.806223i | \(-0.298492\pi\) | ||||
0.591611 | + | 0.806223i | \(0.298492\pi\) | |||||||
\(152\) | 5.23816 | 0.424870 | ||||||||
\(153\) | 1.44562 | 0.116871 | ||||||||
\(154\) | 13.7379 | 1.10703 | ||||||||
\(155\) | 0.502367 | 0.0403511 | ||||||||
\(156\) | −25.4445 | −2.03719 | ||||||||
\(157\) | 6.38544 | 0.509614 | 0.254807 | − | 0.966992i | \(-0.417988\pi\) | ||||
0.254807 | + | 0.966992i | \(0.417988\pi\) | |||||||
\(158\) | 4.92527 | 0.391834 | ||||||||
\(159\) | 19.3127 | 1.53159 | ||||||||
\(160\) | −1.51468 | −0.119746 | ||||||||
\(161\) | 1.47328 | 0.116111 | ||||||||
\(162\) | 24.2140 | 1.90244 | ||||||||
\(163\) | 0.772563 | 0.0605118 | 0.0302559 | − | 0.999542i | \(-0.490368\pi\) | ||||
0.0302559 | + | 0.999542i | \(0.490368\pi\) | |||||||
\(164\) | −47.2149 | −3.68686 | ||||||||
\(165\) | −10.4733 | −0.815341 | ||||||||
\(166\) | −26.6848 | −2.07114 | ||||||||
\(167\) | −3.11243 | −0.240847 | −0.120424 | − | 0.992723i | \(-0.538425\pi\) | ||||
−0.120424 | + | 0.992723i | \(0.538425\pi\) | |||||||
\(168\) | 8.17204 | 0.630487 | ||||||||
\(169\) | −0.0336215 | −0.00258627 | ||||||||
\(170\) | 8.90486 | 0.682971 | ||||||||
\(171\) | −0.463014 | −0.0354076 | ||||||||
\(172\) | 8.75227 | 0.667354 | ||||||||
\(173\) | −16.6843 | −1.26849 | −0.634244 | − | 0.773133i | \(-0.718688\pi\) | ||||
−0.634244 | + | 0.773133i | \(0.718688\pi\) | |||||||
\(174\) | −0.486662 | −0.0368937 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 17.3221 | 1.30570 | ||||||||
\(177\) | −8.73062 | −0.656233 | ||||||||
\(178\) | −18.7558 | −1.40581 | ||||||||
\(179\) | 9.82181 | 0.734117 | 0.367058 | − | 0.930198i | \(-0.380365\pi\) | ||||
0.367058 | + | 0.930198i | \(0.380365\pi\) | |||||||
\(180\) | −1.50470 | −0.112154 | ||||||||
\(181\) | 10.7755 | 0.800934 | 0.400467 | − | 0.916311i | \(-0.368848\pi\) | ||||
0.400467 | + | 0.916311i | \(0.368848\pi\) | |||||||
\(182\) | −8.69939 | −0.644842 | ||||||||
\(183\) | −20.0888 | −1.48501 | ||||||||
\(184\) | 6.53694 | 0.481910 | ||||||||
\(185\) | 5.90785 | 0.434354 | ||||||||
\(186\) | 2.23533 | 0.163902 | ||||||||
\(187\) | 20.9599 | 1.53274 | ||||||||
\(188\) | 17.1207 | 1.24865 | ||||||||
\(189\) | 4.80303 | 0.349369 | ||||||||
\(190\) | −2.85212 | −0.206914 | ||||||||
\(191\) | −16.2308 | −1.17442 | −0.587211 | − | 0.809434i | \(-0.699774\pi\) | ||||
−0.587211 | + | 0.809434i | \(0.699774\pi\) | |||||||
\(192\) | −17.9606 | −1.29620 | ||||||||
\(193\) | 6.54001 | 0.470760 | 0.235380 | − | 0.971903i | \(-0.424366\pi\) | ||||
0.235380 | + | 0.971903i | \(0.424366\pi\) | |||||||
\(194\) | −46.3009 | −3.32421 | ||||||||
\(195\) | 6.63208 | 0.474933 | ||||||||
\(196\) | 3.83658 | 0.274042 | ||||||||
\(197\) | 2.73432 | 0.194812 | 0.0974060 | − | 0.995245i | \(-0.468945\pi\) | ||||
0.0974060 | + | 0.995245i | \(0.468945\pi\) | |||||||
\(198\) | −5.38798 | −0.382907 | ||||||||
\(199\) | 17.6264 | 1.24950 | 0.624752 | − | 0.780823i | \(-0.285200\pi\) | ||||
0.624752 | + | 0.780823i | \(0.285200\pi\) | |||||||
\(200\) | −4.43701 | −0.313744 | ||||||||
\(201\) | 29.1521 | 2.05623 | ||||||||
\(202\) | −26.7993 | −1.88560 | ||||||||
\(203\) | −0.109372 | −0.00767643 | ||||||||
\(204\) | 26.0455 | 1.82355 | ||||||||
\(205\) | 12.3065 | 0.859522 | ||||||||
\(206\) | −31.1966 | −2.17357 | ||||||||
\(207\) | −0.577818 | −0.0401611 | ||||||||
\(208\) | −10.9690 | −0.760566 | ||||||||
\(209\) | −6.71319 | −0.464361 | ||||||||
\(210\) | −4.44959 | −0.307051 | ||||||||
\(211\) | 20.9791 | 1.44426 | 0.722130 | − | 0.691758i | \(-0.243163\pi\) | ||||
0.722130 | + | 0.691758i | \(0.243163\pi\) | |||||||
\(212\) | 40.2297 | 2.76298 | ||||||||
\(213\) | 9.35998 | 0.641335 | ||||||||
\(214\) | −5.69136 | −0.389053 | ||||||||
\(215\) | −2.28127 | −0.155581 | ||||||||
\(216\) | 21.3111 | 1.45003 | ||||||||
\(217\) | 0.502367 | 0.0341029 | ||||||||
\(218\) | 21.7773 | 1.47495 | ||||||||
\(219\) | 16.9418 | 1.14482 | ||||||||
\(220\) | −21.8165 | −1.47087 | ||||||||
\(221\) | −13.2726 | −0.892814 | ||||||||
\(222\) | 26.2875 | 1.76430 | ||||||||
\(223\) | −6.24347 | −0.418094 | −0.209047 | − | 0.977906i | \(-0.567036\pi\) | ||||
−0.209047 | + | 0.977906i | \(0.567036\pi\) | |||||||
\(224\) | −1.51468 | −0.101204 | ||||||||
\(225\) | 0.392199 | 0.0261466 | ||||||||
\(226\) | 27.9904 | 1.86189 | ||||||||
\(227\) | −3.14486 | −0.208732 | −0.104366 | − | 0.994539i | \(-0.533281\pi\) | ||||
−0.104366 | + | 0.994539i | \(0.533281\pi\) | |||||||
\(228\) | −8.34207 | −0.552467 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | −3.55930 | −0.234693 | ||||||||
\(231\) | −10.4733 | −0.689089 | ||||||||
\(232\) | −0.485285 | −0.0318606 | ||||||||
\(233\) | 15.2893 | 1.00164 | 0.500818 | − | 0.865553i | \(-0.333033\pi\) | ||||
0.500818 | + | 0.865553i | \(0.333033\pi\) | |||||||
\(234\) | 3.41189 | 0.223042 | ||||||||
\(235\) | −4.46248 | −0.291100 | ||||||||
\(236\) | −18.1865 | −1.18384 | ||||||||
\(237\) | −3.75484 | −0.243903 | ||||||||
\(238\) | 8.90486 | 0.577216 | ||||||||
\(239\) | −18.5392 | −1.19920 | −0.599599 | − | 0.800300i | \(-0.704673\pi\) | ||||
−0.599599 | + | 0.800300i | \(0.704673\pi\) | |||||||
\(240\) | −5.61048 | −0.362155 | ||||||||
\(241\) | 12.1978 | 0.785729 | 0.392864 | − | 0.919596i | \(-0.371484\pi\) | ||||
0.392864 | + | 0.919596i | \(0.371484\pi\) | |||||||
\(242\) | −51.5449 | −3.31343 | ||||||||
\(243\) | −4.05079 | −0.259858 | ||||||||
\(244\) | −41.8464 | −2.67894 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 54.7588 | 3.49130 | ||||||||
\(247\) | 4.25106 | 0.270489 | ||||||||
\(248\) | 2.22901 | 0.141542 | ||||||||
\(249\) | 20.3434 | 1.28921 | ||||||||
\(250\) | 2.41590 | 0.152795 | ||||||||
\(251\) | 6.83753 | 0.431581 | 0.215790 | − | 0.976440i | \(-0.430767\pi\) | ||||
0.215790 | + | 0.976440i | \(0.430767\pi\) | |||||||
\(252\) | −1.50470 | −0.0947874 | ||||||||
\(253\) | −8.37771 | −0.526702 | ||||||||
\(254\) | −17.1338 | −1.07507 | ||||||||
\(255\) | −6.78873 | −0.425127 | ||||||||
\(256\) | −30.0947 | −1.88092 | ||||||||
\(257\) | 13.8680 | 0.865062 | 0.432531 | − | 0.901619i | \(-0.357621\pi\) | ||||
0.432531 | + | 0.901619i | \(0.357621\pi\) | |||||||
\(258\) | −10.1507 | −0.631955 | ||||||||
\(259\) | 5.90785 | 0.367096 | ||||||||
\(260\) | 13.8151 | 0.856776 | ||||||||
\(261\) | 0.0428957 | 0.00265518 | ||||||||
\(262\) | −19.9039 | −1.22967 | ||||||||
\(263\) | −2.83744 | −0.174964 | −0.0874821 | − | 0.996166i | \(-0.527882\pi\) | ||||
−0.0874821 | + | 0.996166i | \(0.527882\pi\) | |||||||
\(264\) | −46.4699 | −2.86002 | ||||||||
\(265\) | −10.4858 | −0.644138 | ||||||||
\(266\) | −2.85212 | −0.174875 | ||||||||
\(267\) | 14.2987 | 0.875066 | ||||||||
\(268\) | 60.7258 | 3.70942 | ||||||||
\(269\) | −4.18748 | −0.255315 | −0.127658 | − | 0.991818i | \(-0.540746\pi\) | ||||
−0.127658 | + | 0.991818i | \(0.540746\pi\) | |||||||
\(270\) | −11.6036 | −0.706175 | ||||||||
\(271\) | −2.34290 | −0.142321 | −0.0711605 | − | 0.997465i | \(-0.522670\pi\) | ||||
−0.0711605 | + | 0.997465i | \(0.522670\pi\) | |||||||
\(272\) | 11.2281 | 0.680805 | ||||||||
\(273\) | 6.63208 | 0.401392 | ||||||||
\(274\) | 55.2591 | 3.33832 | ||||||||
\(275\) | 5.68645 | 0.342906 | ||||||||
\(276\) | −10.4105 | −0.626636 | ||||||||
\(277\) | 15.6039 | 0.937548 | 0.468774 | − | 0.883318i | \(-0.344696\pi\) | ||||
0.468774 | + | 0.883318i | \(0.344696\pi\) | |||||||
\(278\) | 50.5378 | 3.03105 | ||||||||
\(279\) | −0.197028 | −0.0117957 | ||||||||
\(280\) | −4.43701 | −0.265162 | ||||||||
\(281\) | 18.2199 | 1.08691 | 0.543455 | − | 0.839438i | \(-0.317116\pi\) | ||||
0.543455 | + | 0.839438i | \(0.317116\pi\) | |||||||
\(282\) | −19.8562 | −1.18242 | ||||||||
\(283\) | 21.2708 | 1.26442 | 0.632208 | − | 0.774799i | \(-0.282149\pi\) | ||||
0.632208 | + | 0.774799i | \(0.282149\pi\) | |||||||
\(284\) | 19.4975 | 1.15696 | ||||||||
\(285\) | 2.17435 | 0.128797 | ||||||||
\(286\) | 49.4686 | 2.92514 | ||||||||
\(287\) | 12.3065 | 0.726429 | ||||||||
\(288\) | 0.594054 | 0.0350050 | ||||||||
\(289\) | −3.41388 | −0.200817 | ||||||||
\(290\) | 0.264233 | 0.0155163 | ||||||||
\(291\) | 35.2981 | 2.06921 | ||||||||
\(292\) | 35.2909 | 2.06524 | ||||||||
\(293\) | −12.7199 | −0.743102 | −0.371551 | − | 0.928413i | \(-0.621174\pi\) | ||||
−0.371551 | + | 0.928413i | \(0.621174\pi\) | |||||||
\(294\) | −4.44959 | −0.259505 | ||||||||
\(295\) | 4.74028 | 0.275990 | ||||||||
\(296\) | 26.2132 | 1.52361 | ||||||||
\(297\) | −27.3122 | −1.58481 | ||||||||
\(298\) | 44.9253 | 2.60245 | ||||||||
\(299\) | 5.30511 | 0.306802 | ||||||||
\(300\) | 7.06619 | 0.407967 | ||||||||
\(301\) | −2.28127 | −0.131490 | ||||||||
\(302\) | −35.1264 | −2.02130 | ||||||||
\(303\) | 20.4308 | 1.17372 | ||||||||
\(304\) | −3.59623 | −0.206258 | ||||||||
\(305\) | 10.9072 | 0.624544 | ||||||||
\(306\) | −3.49247 | −0.199651 | ||||||||
\(307\) | 29.6780 | 1.69381 | 0.846906 | − | 0.531742i | \(-0.178463\pi\) | ||||
0.846906 | + | 0.531742i | \(0.178463\pi\) | |||||||
\(308\) | −21.8165 | −1.24311 | ||||||||
\(309\) | 23.7831 | 1.35297 | ||||||||
\(310\) | −1.21367 | −0.0689319 | ||||||||
\(311\) | 20.9266 | 1.18664 | 0.593318 | − | 0.804968i | \(-0.297818\pi\) | ||||
0.593318 | + | 0.804968i | \(0.297818\pi\) | |||||||
\(312\) | 29.4266 | 1.66595 | ||||||||
\(313\) | 11.7270 | 0.662849 | 0.331424 | − | 0.943482i | \(-0.392471\pi\) | ||||
0.331424 | + | 0.943482i | \(0.392471\pi\) | |||||||
\(314\) | −15.4266 | −0.870573 | ||||||||
\(315\) | 0.392199 | 0.0220979 | ||||||||
\(316\) | −7.82160 | −0.439999 | ||||||||
\(317\) | −18.6950 | −1.05001 | −0.525007 | − | 0.851098i | \(-0.675937\pi\) | ||||
−0.525007 | + | 0.851098i | \(0.675937\pi\) | |||||||
\(318\) | −46.6575 | −2.61642 | ||||||||
\(319\) | 0.621939 | 0.0348219 | ||||||||
\(320\) | 9.75172 | 0.545138 | ||||||||
\(321\) | 4.33888 | 0.242173 | ||||||||
\(322\) | −3.55930 | −0.198352 | ||||||||
\(323\) | −4.35147 | −0.242122 | ||||||||
\(324\) | −38.4532 | −2.13629 | ||||||||
\(325\) | −3.60089 | −0.199741 | ||||||||
\(326\) | −1.86644 | −0.103372 | ||||||||
\(327\) | −16.6022 | −0.918104 | ||||||||
\(328\) | 54.6040 | 3.01500 | ||||||||
\(329\) | −4.46248 | −0.246025 | ||||||||
\(330\) | 25.3023 | 1.39285 | ||||||||
\(331\) | −25.5643 | −1.40514 | −0.702570 | − | 0.711615i | \(-0.747964\pi\) | ||||
−0.702570 | + | 0.711615i | \(0.747964\pi\) | |||||||
\(332\) | 42.3768 | 2.32573 | ||||||||
\(333\) | −2.31705 | −0.126974 | ||||||||
\(334\) | 7.51933 | 0.411440 | ||||||||
\(335\) | −15.8281 | −0.864782 | ||||||||
\(336\) | −5.61048 | −0.306077 | ||||||||
\(337\) | −22.1380 | −1.20593 | −0.602966 | − | 0.797767i | \(-0.706015\pi\) | ||||
−0.602966 | + | 0.797767i | \(0.706015\pi\) | |||||||
\(338\) | 0.0812262 | 0.00441812 | ||||||||
\(339\) | −21.3388 | −1.15896 | ||||||||
\(340\) | −14.1414 | −0.766925 | ||||||||
\(341\) | −2.85668 | −0.154698 | ||||||||
\(342\) | 1.11860 | 0.0604868 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −10.1220 | −0.545741 | ||||||||
\(345\) | 2.71347 | 0.146088 | ||||||||
\(346\) | 40.3078 | 2.16696 | ||||||||
\(347\) | −2.23912 | −0.120202 | −0.0601011 | − | 0.998192i | \(-0.519142\pi\) | ||||
−0.0601011 | + | 0.998192i | \(0.519142\pi\) | |||||||
\(348\) | 0.772845 | 0.0414289 | ||||||||
\(349\) | −7.44072 | −0.398293 | −0.199146 | − | 0.979970i | \(-0.563817\pi\) | ||||
−0.199146 | + | 0.979970i | \(0.563817\pi\) | |||||||
\(350\) | 2.41590 | 0.129135 | ||||||||
\(351\) | 17.2952 | 0.923147 | ||||||||
\(352\) | 8.61312 | 0.459081 | ||||||||
\(353\) | 24.6583 | 1.31243 | 0.656215 | − | 0.754574i | \(-0.272156\pi\) | ||||
0.656215 | + | 0.754574i | \(0.272156\pi\) | |||||||
\(354\) | 21.0923 | 1.12104 | ||||||||
\(355\) | −5.08199 | −0.269724 | ||||||||
\(356\) | 29.7852 | 1.57861 | ||||||||
\(357\) | −6.78873 | −0.359298 | ||||||||
\(358\) | −23.7285 | −1.25409 | ||||||||
\(359\) | 15.3161 | 0.808353 | 0.404177 | − | 0.914681i | \(-0.367558\pi\) | ||||
0.404177 | + | 0.914681i | \(0.367558\pi\) | |||||||
\(360\) | 1.74019 | 0.0917160 | ||||||||
\(361\) | −17.6063 | −0.926646 | ||||||||
\(362\) | −26.0325 | −1.36824 | ||||||||
\(363\) | 39.2959 | 2.06250 | ||||||||
\(364\) | 13.8151 | 0.724108 | ||||||||
\(365\) | −9.19853 | −0.481473 | ||||||||
\(366\) | 48.5326 | 2.53684 | ||||||||
\(367\) | −26.3431 | −1.37510 | −0.687548 | − | 0.726139i | \(-0.741313\pi\) | ||||
−0.687548 | + | 0.726139i | \(0.741313\pi\) | |||||||
\(368\) | −4.48791 | −0.233948 | ||||||||
\(369\) | −4.82659 | −0.251262 | ||||||||
\(370\) | −14.2728 | −0.742007 | ||||||||
\(371\) | −10.4858 | −0.544396 | ||||||||
\(372\) | −3.54982 | −0.184050 | ||||||||
\(373\) | −8.33152 | −0.431390 | −0.215695 | − | 0.976461i | \(-0.569202\pi\) | ||||
−0.215695 | + | 0.976461i | \(0.569202\pi\) | |||||||
\(374\) | −50.6370 | −2.61838 | ||||||||
\(375\) | −1.84179 | −0.0951097 | ||||||||
\(376\) | −19.8001 | −1.02111 | ||||||||
\(377\) | −0.393837 | −0.0202836 | ||||||||
\(378\) | −11.6036 | −0.596827 | ||||||||
\(379\) | −18.1365 | −0.931610 | −0.465805 | − | 0.884887i | \(-0.654235\pi\) | ||||
−0.465805 | + | 0.884887i | \(0.654235\pi\) | |||||||
\(380\) | 4.52932 | 0.232349 | ||||||||
\(381\) | 13.0621 | 0.669193 | ||||||||
\(382\) | 39.2121 | 2.00627 | ||||||||
\(383\) | −5.08393 | −0.259777 | −0.129888 | − | 0.991529i | \(-0.541462\pi\) | ||||
−0.129888 | + | 0.991529i | \(0.541462\pi\) | |||||||
\(384\) | 37.8117 | 1.92957 | ||||||||
\(385\) | 5.68645 | 0.289808 | ||||||||
\(386\) | −15.8000 | −0.804201 | ||||||||
\(387\) | 0.894710 | 0.0454806 | ||||||||
\(388\) | 73.5284 | 3.73284 | ||||||||
\(389\) | 13.3041 | 0.674546 | 0.337273 | − | 0.941407i | \(-0.390495\pi\) | ||||
0.337273 | + | 0.941407i | \(0.390495\pi\) | |||||||
\(390\) | −16.0225 | −0.811329 | ||||||||
\(391\) | −5.43041 | −0.274627 | ||||||||
\(392\) | −4.43701 | −0.224103 | ||||||||
\(393\) | 15.1740 | 0.765427 | ||||||||
\(394\) | −6.60584 | −0.332797 | ||||||||
\(395\) | 2.03869 | 0.102578 | ||||||||
\(396\) | 8.55641 | 0.429976 | ||||||||
\(397\) | 8.79036 | 0.441176 | 0.220588 | − | 0.975367i | \(-0.429202\pi\) | ||||
0.220588 | + | 0.975367i | \(0.429202\pi\) | |||||||
\(398\) | −42.5837 | −2.13453 | ||||||||
\(399\) | 2.17435 | 0.108854 | ||||||||
\(400\) | 3.04621 | 0.152310 | ||||||||
\(401\) | 24.2459 | 1.21078 | 0.605392 | − | 0.795928i | \(-0.293016\pi\) | ||||
0.605392 | + | 0.795928i | \(0.293016\pi\) | |||||||
\(402\) | −70.4286 | −3.51266 | ||||||||
\(403\) | 1.80897 | 0.0901111 | ||||||||
\(404\) | 42.5588 | 2.11738 | ||||||||
\(405\) | 10.0228 | 0.498036 | ||||||||
\(406\) | 0.264233 | 0.0131137 | ||||||||
\(407\) | −33.5947 | −1.66523 | ||||||||
\(408\) | −30.1216 | −1.49124 | ||||||||
\(409\) | 16.2720 | 0.804598 | 0.402299 | − | 0.915508i | \(-0.368211\pi\) | ||||
0.402299 | + | 0.915508i | \(0.368211\pi\) | |||||||
\(410\) | −29.7313 | −1.46832 | ||||||||
\(411\) | −42.1274 | −2.07799 | ||||||||
\(412\) | 49.5419 | 2.44075 | ||||||||
\(413\) | 4.74028 | 0.233254 | ||||||||
\(414\) | 1.39595 | 0.0686073 | ||||||||
\(415\) | −11.0455 | −0.542200 | ||||||||
\(416\) | −5.45418 | −0.267413 | ||||||||
\(417\) | −38.5281 | −1.88673 | ||||||||
\(418\) | 16.2184 | 0.793269 | ||||||||
\(419\) | 20.6920 | 1.01087 | 0.505435 | − | 0.862865i | \(-0.331332\pi\) | ||||
0.505435 | + | 0.862865i | \(0.331332\pi\) | |||||||
\(420\) | 7.06619 | 0.344795 | ||||||||
\(421\) | 25.8775 | 1.26119 | 0.630597 | − | 0.776110i | \(-0.282810\pi\) | ||||
0.630597 | + | 0.776110i | \(0.282810\pi\) | |||||||
\(422\) | −50.6834 | −2.46723 | ||||||||
\(423\) | 1.75018 | 0.0850967 | ||||||||
\(424\) | −46.5256 | −2.25948 | ||||||||
\(425\) | 3.68593 | 0.178794 | ||||||||
\(426\) | −22.6128 | −1.09559 | ||||||||
\(427\) | 10.9072 | 0.527836 | ||||||||
\(428\) | 9.03819 | 0.436877 | ||||||||
\(429\) | −37.7130 | −1.82080 | ||||||||
\(430\) | 5.51132 | 0.265779 | ||||||||
\(431\) | 25.0934 | 1.20871 | 0.604354 | − | 0.796716i | \(-0.293431\pi\) | ||||
0.604354 | + | 0.796716i | \(0.293431\pi\) | |||||||
\(432\) | −14.6310 | −0.703935 | ||||||||
\(433\) | 40.8732 | 1.96424 | 0.982120 | − | 0.188255i | \(-0.0602833\pi\) | ||||
0.982120 | + | 0.188255i | \(0.0602833\pi\) | |||||||
\(434\) | −1.21367 | −0.0582580 | ||||||||
\(435\) | −0.201441 | −0.00965836 | ||||||||
\(436\) | −34.5836 | −1.65625 | ||||||||
\(437\) | 1.73929 | 0.0832017 | ||||||||
\(438\) | −40.9297 | −1.95570 | ||||||||
\(439\) | 9.81138 | 0.468272 | 0.234136 | − | 0.972204i | \(-0.424774\pi\) | ||||
0.234136 | + | 0.972204i | \(0.424774\pi\) | |||||||
\(440\) | 25.2308 | 1.20283 | ||||||||
\(441\) | 0.392199 | 0.0186761 | ||||||||
\(442\) | 32.0654 | 1.52519 | ||||||||
\(443\) | −37.6513 | −1.78887 | −0.894435 | − | 0.447199i | \(-0.852422\pi\) | ||||
−0.894435 | + | 0.447199i | \(0.852422\pi\) | |||||||
\(444\) | −41.7460 | −1.98118 | ||||||||
\(445\) | −7.76347 | −0.368024 | ||||||||
\(446\) | 15.0836 | 0.714230 | ||||||||
\(447\) | −34.2494 | −1.61994 | ||||||||
\(448\) | 9.75172 | 0.460726 | ||||||||
\(449\) | 4.50308 | 0.212514 | 0.106257 | − | 0.994339i | \(-0.466113\pi\) | ||||
0.106257 | + | 0.994339i | \(0.466113\pi\) | |||||||
\(450\) | −0.947514 | −0.0446662 | ||||||||
\(451\) | −69.9802 | −3.29524 | ||||||||
\(452\) | −44.4502 | −2.09076 | ||||||||
\(453\) | 26.7791 | 1.25819 | ||||||||
\(454\) | 7.59768 | 0.356577 | ||||||||
\(455\) | −3.60089 | −0.168812 | ||||||||
\(456\) | 9.64759 | 0.451790 | ||||||||
\(457\) | −21.9985 | −1.02904 | −0.514522 | − | 0.857477i | \(-0.672031\pi\) | ||||
−0.514522 | + | 0.857477i | \(0.672031\pi\) | |||||||
\(458\) | −2.41590 | −0.112888 | ||||||||
\(459\) | −17.7036 | −0.826336 | ||||||||
\(460\) | 5.65235 | 0.263542 | ||||||||
\(461\) | 11.8084 | 0.549971 | 0.274985 | − | 0.961448i | \(-0.411327\pi\) | ||||
0.274985 | + | 0.961448i | \(0.411327\pi\) | |||||||
\(462\) | 25.3023 | 1.17717 | ||||||||
\(463\) | 19.6391 | 0.912708 | 0.456354 | − | 0.889798i | \(-0.349155\pi\) | ||||
0.456354 | + | 0.889798i | \(0.349155\pi\) | |||||||
\(464\) | 0.333171 | 0.0154671 | ||||||||
\(465\) | 0.925256 | 0.0429077 | ||||||||
\(466\) | −36.9375 | −1.71109 | ||||||||
\(467\) | 37.4721 | 1.73400 | 0.867001 | − | 0.498306i | \(-0.166044\pi\) | ||||
0.867001 | + | 0.498306i | \(0.166044\pi\) | |||||||
\(468\) | −5.41826 | −0.250459 | ||||||||
\(469\) | −15.8281 | −0.730874 | ||||||||
\(470\) | 10.7809 | 0.497287 | ||||||||
\(471\) | 11.7607 | 0.541902 | ||||||||
\(472\) | 21.0327 | 0.968107 | ||||||||
\(473\) | 12.9723 | 0.596467 | ||||||||
\(474\) | 9.07133 | 0.416660 | ||||||||
\(475\) | −1.18056 | −0.0541678 | ||||||||
\(476\) | −14.1414 | −0.648170 | ||||||||
\(477\) | 4.11252 | 0.188299 | ||||||||
\(478\) | 44.7888 | 2.04859 | ||||||||
\(479\) | 19.0649 | 0.871097 | 0.435549 | − | 0.900165i | \(-0.356554\pi\) | ||||
0.435549 | + | 0.900165i | \(0.356554\pi\) | |||||||
\(480\) | −2.78972 | −0.127333 | ||||||||
\(481\) | 21.2735 | 0.969988 | ||||||||
\(482\) | −29.4687 | −1.34226 | ||||||||
\(483\) | 2.71347 | 0.123467 | ||||||||
\(484\) | 81.8560 | 3.72073 | ||||||||
\(485\) | −19.1651 | −0.870241 | ||||||||
\(486\) | 9.78631 | 0.443916 | ||||||||
\(487\) | 43.1263 | 1.95424 | 0.977119 | − | 0.212692i | \(-0.0682231\pi\) | ||||
0.977119 | + | 0.212692i | \(0.0682231\pi\) | |||||||
\(488\) | 48.3953 | 2.19075 | ||||||||
\(489\) | 1.42290 | 0.0643458 | ||||||||
\(490\) | 2.41590 | 0.109139 | ||||||||
\(491\) | 16.3884 | 0.739599 | 0.369800 | − | 0.929112i | \(-0.379426\pi\) | ||||
0.369800 | + | 0.929112i | \(0.379426\pi\) | |||||||
\(492\) | −86.9600 | −3.92046 | ||||||||
\(493\) | 0.403139 | 0.0181565 | ||||||||
\(494\) | −10.2702 | −0.462076 | ||||||||
\(495\) | −2.23022 | −0.100241 | ||||||||
\(496\) | −1.53031 | −0.0687132 | ||||||||
\(497\) | −5.08199 | −0.227959 | ||||||||
\(498\) | −49.1478 | −2.20236 | ||||||||
\(499\) | 9.03204 | 0.404330 | 0.202165 | − | 0.979351i | \(-0.435202\pi\) | ||||
0.202165 | + | 0.979351i | \(0.435202\pi\) | |||||||
\(500\) | −3.83658 | −0.171577 | ||||||||
\(501\) | −5.73246 | −0.256107 | ||||||||
\(502\) | −16.5188 | −0.737270 | ||||||||
\(503\) | 35.9740 | 1.60400 | 0.802001 | − | 0.597323i | \(-0.203769\pi\) | ||||
0.802001 | + | 0.597323i | \(0.203769\pi\) | |||||||
\(504\) | 1.74019 | 0.0775141 | ||||||||
\(505\) | −11.0929 | −0.493627 | ||||||||
\(506\) | 20.2397 | 0.899766 | ||||||||
\(507\) | −0.0619238 | −0.00275013 | ||||||||
\(508\) | 27.2093 | 1.20722 | ||||||||
\(509\) | −28.0950 | −1.24529 | −0.622645 | − | 0.782505i | \(-0.713942\pi\) | ||||
−0.622645 | + | 0.782505i | \(0.713942\pi\) | |||||||
\(510\) | 16.4009 | 0.726244 | ||||||||
\(511\) | −9.19853 | −0.406919 | ||||||||
\(512\) | 31.6461 | 1.39857 | ||||||||
\(513\) | 5.67027 | 0.250348 | ||||||||
\(514\) | −33.5037 | −1.47779 | ||||||||
\(515\) | −12.9130 | −0.569016 | ||||||||
\(516\) | 16.1199 | 0.709637 | ||||||||
\(517\) | 25.3757 | 1.11602 | ||||||||
\(518\) | −14.2728 | −0.627110 | ||||||||
\(519\) | −30.7291 | −1.34886 | ||||||||
\(520\) | −15.9772 | −0.700644 | ||||||||
\(521\) | −31.5502 | −1.38224 | −0.691119 | − | 0.722741i | \(-0.742882\pi\) | ||||
−0.691119 | + | 0.722741i | \(0.742882\pi\) | |||||||
\(522\) | −0.103632 | −0.00453584 | ||||||||
\(523\) | 5.55677 | 0.242981 | 0.121490 | − | 0.992593i | \(-0.461233\pi\) | ||||
0.121490 | + | 0.992593i | \(0.461233\pi\) | |||||||
\(524\) | 31.6085 | 1.38082 | ||||||||
\(525\) | −1.84179 | −0.0803824 | ||||||||
\(526\) | 6.85498 | 0.298891 | ||||||||
\(527\) | −1.85169 | −0.0806610 | ||||||||
\(528\) | 31.9037 | 1.38843 | ||||||||
\(529\) | −20.8295 | −0.905628 | ||||||||
\(530\) | 25.3327 | 1.10038 | ||||||||
\(531\) | −1.85913 | −0.0806795 | ||||||||
\(532\) | 4.52932 | 0.196371 | ||||||||
\(533\) | 44.3143 | 1.91946 | ||||||||
\(534\) | −34.5442 | −1.49488 | ||||||||
\(535\) | −2.35579 | −0.101850 | ||||||||
\(536\) | −70.2294 | −3.03345 | ||||||||
\(537\) | 18.0897 | 0.780630 | ||||||||
\(538\) | 10.1165 | 0.436155 | ||||||||
\(539\) | 5.68645 | 0.244933 | ||||||||
\(540\) | 18.4272 | 0.792981 | ||||||||
\(541\) | −1.33575 | −0.0574284 | −0.0287142 | − | 0.999588i | \(-0.509141\pi\) | ||||
−0.0287142 | + | 0.999588i | \(0.509141\pi\) | |||||||
\(542\) | 5.66022 | 0.243127 | ||||||||
\(543\) | 19.8462 | 0.851681 | ||||||||
\(544\) | 5.58300 | 0.239369 | ||||||||
\(545\) | 9.01416 | 0.386124 | ||||||||
\(546\) | −16.0225 | −0.685698 | ||||||||
\(547\) | −15.9150 | −0.680475 | −0.340238 | − | 0.940340i | \(-0.610507\pi\) | ||||
−0.340238 | + | 0.940340i | \(0.610507\pi\) | |||||||
\(548\) | −87.7544 | −3.74868 | ||||||||
\(549\) | −4.27779 | −0.182572 | ||||||||
\(550\) | −13.7379 | −0.585786 | ||||||||
\(551\) | −0.129121 | −0.00550072 | ||||||||
\(552\) | 12.0397 | 0.512443 | ||||||||
\(553\) | 2.03869 | 0.0866938 | ||||||||
\(554\) | −37.6975 | −1.60161 | ||||||||
\(555\) | 10.8810 | 0.461874 | ||||||||
\(556\) | −80.2567 | −3.40364 | ||||||||
\(557\) | 6.88978 | 0.291929 | 0.145965 | − | 0.989290i | \(-0.453371\pi\) | ||||
0.145965 | + | 0.989290i | \(0.453371\pi\) | |||||||
\(558\) | 0.476000 | 0.0201507 | ||||||||
\(559\) | −8.21458 | −0.347440 | ||||||||
\(560\) | 3.04621 | 0.128726 | ||||||||
\(561\) | 38.6037 | 1.62985 | ||||||||
\(562\) | −44.0176 | −1.85677 | ||||||||
\(563\) | −16.4197 | −0.692010 | −0.346005 | − | 0.938233i | \(-0.612462\pi\) | ||||
−0.346005 | + | 0.938233i | \(0.612462\pi\) | |||||||
\(564\) | 31.5327 | 1.32777 | ||||||||
\(565\) | 11.5859 | 0.487422 | ||||||||
\(566\) | −51.3881 | −2.16000 | ||||||||
\(567\) | 10.0228 | 0.420917 | ||||||||
\(568\) | −22.5488 | −0.946128 | ||||||||
\(569\) | −45.2388 | −1.89651 | −0.948255 | − | 0.317510i | \(-0.897153\pi\) | ||||
−0.948255 | + | 0.317510i | \(0.897153\pi\) | |||||||
\(570\) | −5.25301 | −0.220024 | ||||||||
\(571\) | −4.97457 | −0.208179 | −0.104090 | − | 0.994568i | \(-0.533193\pi\) | ||||
−0.104090 | + | 0.994568i | \(0.533193\pi\) | |||||||
\(572\) | −78.5588 | −3.28471 | ||||||||
\(573\) | −29.8938 | −1.24883 | ||||||||
\(574\) | −29.7313 | −1.24096 | ||||||||
\(575\) | −1.47328 | −0.0614399 | ||||||||
\(576\) | −3.82461 | −0.159359 | ||||||||
\(577\) | −11.0207 | −0.458798 | −0.229399 | − | 0.973332i | \(-0.573676\pi\) | ||||
−0.229399 | + | 0.973332i | \(0.573676\pi\) | |||||||
\(578\) | 8.24761 | 0.343055 | ||||||||
\(579\) | 12.0453 | 0.500588 | ||||||||
\(580\) | −0.419616 | −0.0174236 | ||||||||
\(581\) | −11.0455 | −0.458243 | ||||||||
\(582\) | −85.2767 | −3.53483 | ||||||||
\(583\) | 59.6269 | 2.46950 | ||||||||
\(584\) | −40.8139 | −1.68889 | ||||||||
\(585\) | 1.41226 | 0.0583899 | ||||||||
\(586\) | 30.7299 | 1.26944 | ||||||||
\(587\) | 20.6143 | 0.850845 | 0.425423 | − | 0.904995i | \(-0.360125\pi\) | ||||
0.425423 | + | 0.904995i | \(0.360125\pi\) | |||||||
\(588\) | 7.06619 | 0.291405 | ||||||||
\(589\) | 0.593075 | 0.0244372 | ||||||||
\(590\) | −11.4521 | −0.471474 | ||||||||
\(591\) | 5.03604 | 0.207155 | ||||||||
\(592\) | −17.9965 | −0.739653 | ||||||||
\(593\) | −13.3783 | −0.549382 | −0.274691 | − | 0.961533i | \(-0.588576\pi\) | ||||
−0.274691 | + | 0.961533i | \(0.588576\pi\) | |||||||
\(594\) | 65.9835 | 2.70734 | ||||||||
\(595\) | 3.68593 | 0.151109 | ||||||||
\(596\) | −71.3439 | −2.92236 | ||||||||
\(597\) | 32.4642 | 1.32867 | ||||||||
\(598\) | −12.8166 | −0.524110 | ||||||||
\(599\) | −43.1644 | −1.76365 | −0.881825 | − | 0.471576i | \(-0.843685\pi\) | ||||
−0.881825 | + | 0.471576i | \(0.843685\pi\) | |||||||
\(600\) | −8.17204 | −0.333622 | ||||||||
\(601\) | −8.81945 | −0.359753 | −0.179876 | − | 0.983689i | \(-0.557570\pi\) | ||||
−0.179876 | + | 0.983689i | \(0.557570\pi\) | |||||||
\(602\) | 5.51132 | 0.224624 | ||||||||
\(603\) | 6.20776 | 0.252800 | ||||||||
\(604\) | 55.7827 | 2.26977 | ||||||||
\(605\) | −21.3357 | −0.867418 | ||||||||
\(606\) | −49.3588 | −2.00507 | ||||||||
\(607\) | 2.72131 | 0.110455 | 0.0552273 | − | 0.998474i | \(-0.482412\pi\) | ||||
0.0552273 | + | 0.998474i | \(0.482412\pi\) | |||||||
\(608\) | −1.78817 | −0.0725198 | ||||||||
\(609\) | −0.201441 | −0.00816280 | ||||||||
\(610\) | −26.3507 | −1.06691 | ||||||||
\(611\) | −16.0689 | −0.650078 | ||||||||
\(612\) | 5.54624 | 0.224193 | ||||||||
\(613\) | −15.7229 | −0.635042 | −0.317521 | − | 0.948251i | \(-0.602850\pi\) | ||||
−0.317521 | + | 0.948251i | \(0.602850\pi\) | |||||||
\(614\) | −71.6991 | −2.89354 | ||||||||
\(615\) | 22.6660 | 0.913981 | ||||||||
\(616\) | 25.2308 | 1.01658 | ||||||||
\(617\) | −19.4975 | −0.784941 | −0.392471 | − | 0.919765i | \(-0.628380\pi\) | ||||
−0.392471 | + | 0.919765i | \(0.628380\pi\) | |||||||
\(618\) | −57.4577 | −2.31129 | ||||||||
\(619\) | 26.6453 | 1.07096 | 0.535482 | − | 0.844547i | \(-0.320130\pi\) | ||||
0.535482 | + | 0.844547i | \(0.320130\pi\) | |||||||
\(620\) | 1.92737 | 0.0774052 | ||||||||
\(621\) | 7.07620 | 0.283958 | ||||||||
\(622\) | −50.5565 | −2.02713 | ||||||||
\(623\) | −7.76347 | −0.311037 | ||||||||
\(624\) | −20.2027 | −0.808755 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −28.3313 | −1.13235 | ||||||||
\(627\) | −12.3643 | −0.493783 | ||||||||
\(628\) | 24.4983 | 0.977588 | ||||||||
\(629\) | −21.7760 | −0.868264 | ||||||||
\(630\) | −0.947514 | −0.0377499 | ||||||||
\(631\) | −23.7433 | −0.945205 | −0.472603 | − | 0.881276i | \(-0.656685\pi\) | ||||
−0.472603 | + | 0.881276i | \(0.656685\pi\) | |||||||
\(632\) | 9.04567 | 0.359818 | ||||||||
\(633\) | 38.6391 | 1.53577 | ||||||||
\(634\) | 45.1652 | 1.79374 | ||||||||
\(635\) | −7.09207 | −0.281440 | ||||||||
\(636\) | 74.0947 | 2.93805 | ||||||||
\(637\) | −3.60089 | −0.142672 | ||||||||
\(638\) | −1.50254 | −0.0594863 | ||||||||
\(639\) | 1.99315 | 0.0788479 | ||||||||
\(640\) | −20.5299 | −0.811514 | ||||||||
\(641\) | 12.2448 | 0.483642 | 0.241821 | − | 0.970321i | \(-0.422255\pi\) | ||||
0.241821 | + | 0.970321i | \(0.422255\pi\) | |||||||
\(642\) | −10.4823 | −0.413704 | ||||||||
\(643\) | 46.9824 | 1.85281 | 0.926403 | − | 0.376535i | \(-0.122884\pi\) | ||||
0.926403 | + | 0.376535i | \(0.122884\pi\) | |||||||
\(644\) | 5.65235 | 0.222734 | ||||||||
\(645\) | −4.20162 | −0.165439 | ||||||||
\(646\) | 10.5127 | 0.413618 | ||||||||
\(647\) | 17.5500 | 0.689963 | 0.344981 | − | 0.938610i | \(-0.387885\pi\) | ||||
0.344981 | + | 0.938610i | \(0.387885\pi\) | |||||||
\(648\) | 44.4711 | 1.74699 | ||||||||
\(649\) | −26.9554 | −1.05809 | ||||||||
\(650\) | 8.69939 | 0.341218 | ||||||||
\(651\) | 0.925256 | 0.0362637 | ||||||||
\(652\) | 2.96400 | 0.116079 | ||||||||
\(653\) | −28.3693 | −1.11018 | −0.555089 | − | 0.831791i | \(-0.687316\pi\) | ||||
−0.555089 | + | 0.831791i | \(0.687316\pi\) | |||||||
\(654\) | 40.1093 | 1.56840 | ||||||||
\(655\) | −8.23872 | −0.321913 | ||||||||
\(656\) | −37.4881 | −1.46366 | ||||||||
\(657\) | 3.60765 | 0.140748 | ||||||||
\(658\) | 10.7809 | 0.420284 | ||||||||
\(659\) | −18.2749 | −0.711887 | −0.355944 | − | 0.934507i | \(-0.615840\pi\) | ||||
−0.355944 | + | 0.934507i | \(0.615840\pi\) | |||||||
\(660\) | −40.1815 | −1.56406 | ||||||||
\(661\) | 11.1886 | 0.435188 | 0.217594 | − | 0.976039i | \(-0.430179\pi\) | ||||
0.217594 | + | 0.976039i | \(0.430179\pi\) | |||||||
\(662\) | 61.7608 | 2.40040 | ||||||||
\(663\) | −24.4454 | −0.949382 | ||||||||
\(664\) | −49.0088 | −1.90191 | ||||||||
\(665\) | −1.18056 | −0.0457802 | ||||||||
\(666\) | 5.59777 | 0.216909 | ||||||||
\(667\) | −0.161136 | −0.00623920 | ||||||||
\(668\) | −11.9411 | −0.462015 | ||||||||
\(669\) | −11.4992 | −0.444584 | ||||||||
\(670\) | 38.2392 | 1.47731 | ||||||||
\(671\) | −62.0232 | −2.39438 | ||||||||
\(672\) | −2.78972 | −0.107616 | ||||||||
\(673\) | 2.56259 | 0.0987807 | 0.0493904 | − | 0.998780i | \(-0.484272\pi\) | ||||
0.0493904 | + | 0.998780i | \(0.484272\pi\) | |||||||
\(674\) | 53.4832 | 2.06010 | ||||||||
\(675\) | −4.80303 | −0.184869 | ||||||||
\(676\) | −0.128992 | −0.00496121 | ||||||||
\(677\) | −21.7010 | −0.834036 | −0.417018 | − | 0.908898i | \(-0.636925\pi\) | ||||
−0.417018 | + | 0.908898i | \(0.636925\pi\) | |||||||
\(678\) | 51.5524 | 1.97986 | ||||||||
\(679\) | −19.1651 | −0.735488 | ||||||||
\(680\) | 16.3545 | 0.627167 | ||||||||
\(681\) | −5.79218 | −0.221957 | ||||||||
\(682\) | 6.90147 | 0.264271 | ||||||||
\(683\) | 20.1403 | 0.770649 | 0.385324 | − | 0.922781i | \(-0.374090\pi\) | ||||
0.385324 | + | 0.922781i | \(0.374090\pi\) | |||||||
\(684\) | −1.77639 | −0.0679221 | ||||||||
\(685\) | 22.8731 | 0.873935 | ||||||||
\(686\) | 2.41590 | 0.0922396 | ||||||||
\(687\) | 1.84179 | 0.0702688 | ||||||||
\(688\) | 6.94921 | 0.264936 | ||||||||
\(689\) | −37.7582 | −1.43847 | ||||||||
\(690\) | −6.55548 | −0.249563 | ||||||||
\(691\) | 7.24524 | 0.275622 | 0.137811 | − | 0.990459i | \(-0.455993\pi\) | ||||
0.137811 | + | 0.990459i | \(0.455993\pi\) | |||||||
\(692\) | −64.0109 | −2.43333 | ||||||||
\(693\) | −2.23022 | −0.0847189 | ||||||||
\(694\) | 5.40950 | 0.205342 | ||||||||
\(695\) | 20.9188 | 0.793495 | ||||||||
\(696\) | −0.893795 | −0.0338792 | ||||||||
\(697\) | −45.3609 | −1.71817 | ||||||||
\(698\) | 17.9761 | 0.680404 | ||||||||
\(699\) | 28.1597 | 1.06510 | ||||||||
\(700\) | −3.83658 | −0.145009 | ||||||||
\(701\) | 1.56344 | 0.0590505 | 0.0295253 | − | 0.999564i | \(-0.490600\pi\) | ||||
0.0295253 | + | 0.999564i | \(0.490600\pi\) | |||||||
\(702\) | −41.7834 | −1.57701 | ||||||||
\(703\) | 6.97458 | 0.263051 | ||||||||
\(704\) | −55.4526 | −2.08995 | ||||||||
\(705\) | −8.21897 | −0.309544 | ||||||||
\(706\) | −59.5721 | −2.24203 | ||||||||
\(707\) | −11.0929 | −0.417191 | ||||||||
\(708\) | −33.4957 | −1.25885 | ||||||||
\(709\) | −1.00811 | −0.0378602 | −0.0189301 | − | 0.999821i | \(-0.506026\pi\) | ||||
−0.0189301 | + | 0.999821i | \(0.506026\pi\) | |||||||
\(710\) | 12.2776 | 0.460770 | ||||||||
\(711\) | −0.799571 | −0.0299863 | ||||||||
\(712\) | −34.4466 | −1.29094 | ||||||||
\(713\) | 0.740127 | 0.0277180 | ||||||||
\(714\) | 16.4009 | 0.613788 | ||||||||
\(715\) | 20.4762 | 0.765768 | ||||||||
\(716\) | 37.6822 | 1.40825 | ||||||||
\(717\) | −34.1453 | −1.27518 | ||||||||
\(718\) | −37.0022 | −1.38091 | ||||||||
\(719\) | 7.23617 | 0.269863 | 0.134932 | − | 0.990855i | \(-0.456918\pi\) | ||||
0.134932 | + | 0.990855i | \(0.456918\pi\) | |||||||
\(720\) | −1.19472 | −0.0445245 | ||||||||
\(721\) | −12.9130 | −0.480906 | ||||||||
\(722\) | 42.5350 | 1.58299 | ||||||||
\(723\) | 22.4658 | 0.835512 | ||||||||
\(724\) | 41.3410 | 1.53643 | ||||||||
\(725\) | 0.109372 | 0.00406198 | ||||||||
\(726\) | −94.9349 | −3.52337 | ||||||||
\(727\) | −15.9774 | −0.592567 | −0.296284 | − | 0.955100i | \(-0.595747\pi\) | ||||
−0.296284 | + | 0.955100i | \(0.595747\pi\) | |||||||
\(728\) | −15.9772 | −0.592153 | ||||||||
\(729\) | 22.6076 | 0.837319 | ||||||||
\(730\) | 22.2227 | 0.822501 | ||||||||
\(731\) | 8.40860 | 0.311003 | ||||||||
\(732\) | −77.0723 | −2.84868 | ||||||||
\(733\) | −4.46744 | −0.165009 | −0.0825043 | − | 0.996591i | \(-0.526292\pi\) | ||||
−0.0825043 | + | 0.996591i | \(0.526292\pi\) | |||||||
\(734\) | 63.6422 | 2.34908 | ||||||||
\(735\) | −1.84179 | −0.0679355 | ||||||||
\(736\) | −2.23154 | −0.0822556 | ||||||||
\(737\) | 90.0057 | 3.31540 | ||||||||
\(738\) | 11.6606 | 0.429231 | ||||||||
\(739\) | 25.5916 | 0.941404 | 0.470702 | − | 0.882292i | \(-0.344001\pi\) | ||||
0.470702 | + | 0.882292i | \(0.344001\pi\) | |||||||
\(740\) | 22.6660 | 0.833217 | ||||||||
\(741\) | 7.82958 | 0.287627 | ||||||||
\(742\) | 25.3327 | 0.929992 | ||||||||
\(743\) | −2.45997 | −0.0902477 | −0.0451239 | − | 0.998981i | \(-0.514368\pi\) | ||||
−0.0451239 | + | 0.998981i | \(0.514368\pi\) | |||||||
\(744\) | 4.10537 | 0.150510 | ||||||||
\(745\) | 18.5957 | 0.681293 | ||||||||
\(746\) | 20.1281 | 0.736944 | ||||||||
\(747\) | 4.33202 | 0.158500 | ||||||||
\(748\) | 80.4143 | 2.94024 | ||||||||
\(749\) | −2.35579 | −0.0860787 | ||||||||
\(750\) | 4.44959 | 0.162476 | ||||||||
\(751\) | 50.2396 | 1.83327 | 0.916635 | − | 0.399725i | \(-0.130894\pi\) | ||||
0.916635 | + | 0.399725i | \(0.130894\pi\) | |||||||
\(752\) | 13.5936 | 0.495709 | ||||||||
\(753\) | 12.5933 | 0.458926 | ||||||||
\(754\) | 0.951472 | 0.0346506 | ||||||||
\(755\) | −14.5397 | −0.529153 | ||||||||
\(756\) | 18.4272 | 0.670191 | ||||||||
\(757\) | −28.9065 | −1.05063 | −0.525313 | − | 0.850909i | \(-0.676052\pi\) | ||||
−0.525313 | + | 0.850909i | \(0.676052\pi\) | |||||||
\(758\) | 43.8160 | 1.59147 | ||||||||
\(759\) | −15.4300 | −0.560074 | ||||||||
\(760\) | −5.23816 | −0.190008 | ||||||||
\(761\) | −5.39044 | −0.195403 | −0.0977017 | − | 0.995216i | \(-0.531149\pi\) | ||||
−0.0977017 | + | 0.995216i | \(0.531149\pi\) | |||||||
\(762\) | −31.5568 | −1.14318 | ||||||||
\(763\) | 9.01416 | 0.326335 | ||||||||
\(764\) | −62.2710 | −2.25289 | ||||||||
\(765\) | −1.44562 | −0.0522665 | ||||||||
\(766\) | 12.2823 | 0.443777 | ||||||||
\(767\) | 17.0692 | 0.616334 | ||||||||
\(768\) | −55.4281 | −2.00009 | ||||||||
\(769\) | 50.7622 | 1.83053 | 0.915266 | − | 0.402849i | \(-0.131980\pi\) | ||||
0.915266 | + | 0.402849i | \(0.131980\pi\) | |||||||
\(770\) | −13.7379 | −0.495079 | ||||||||
\(771\) | 25.5420 | 0.919872 | ||||||||
\(772\) | 25.0913 | 0.903056 | ||||||||
\(773\) | 47.8152 | 1.71979 | 0.859897 | − | 0.510468i | \(-0.170528\pi\) | ||||
0.859897 | + | 0.510468i | \(0.170528\pi\) | |||||||
\(774\) | −2.16153 | −0.0776946 | ||||||||
\(775\) | −0.502367 | −0.0180456 | ||||||||
\(776\) | −85.0355 | −3.05260 | ||||||||
\(777\) | 10.8810 | 0.390355 | ||||||||
\(778\) | −32.1415 | −1.15233 | ||||||||
\(779\) | 14.5286 | 0.520540 | ||||||||
\(780\) | 25.4445 | 0.911061 | ||||||||
\(781\) | 28.8985 | 1.03407 | ||||||||
\(782\) | 13.1193 | 0.469146 | ||||||||
\(783\) | −0.525318 | −0.0187733 | ||||||||
\(784\) | 3.04621 | 0.108793 | ||||||||
\(785\) | −6.38544 | −0.227906 | ||||||||
\(786\) | −36.6589 | −1.30758 | ||||||||
\(787\) | 9.88872 | 0.352495 | 0.176247 | − | 0.984346i | \(-0.443604\pi\) | ||||
0.176247 | + | 0.984346i | \(0.443604\pi\) | |||||||
\(788\) | 10.4904 | 0.373706 | ||||||||
\(789\) | −5.22598 | −0.186050 | ||||||||
\(790\) | −4.92527 | −0.175233 | ||||||||
\(791\) | 11.5859 | 0.411947 | ||||||||
\(792\) | −9.89548 | −0.351621 | ||||||||
\(793\) | 39.2756 | 1.39472 | ||||||||
\(794\) | −21.2367 | −0.753661 | ||||||||
\(795\) | −19.3127 | −0.684950 | ||||||||
\(796\) | 67.6253 | 2.39691 | ||||||||
\(797\) | −35.0166 | −1.24035 | −0.620176 | − | 0.784463i | \(-0.712939\pi\) | ||||
−0.620176 | + | 0.784463i | \(0.712939\pi\) | |||||||
\(798\) | −5.25301 | −0.185955 | ||||||||
\(799\) | 16.4484 | 0.581903 | ||||||||
\(800\) | 1.51468 | 0.0535519 | ||||||||
\(801\) | 3.04482 | 0.107584 | ||||||||
\(802\) | −58.5758 | −2.06838 | ||||||||
\(803\) | 52.3069 | 1.84587 | ||||||||
\(804\) | 111.844 | 3.94445 | ||||||||
\(805\) | −1.47328 | −0.0519262 | ||||||||
\(806\) | −4.37029 | −0.153937 | ||||||||
\(807\) | −7.71247 | −0.271492 | ||||||||
\(808\) | −49.2192 | −1.73153 | ||||||||
\(809\) | 31.1080 | 1.09370 | 0.546849 | − | 0.837231i | \(-0.315827\pi\) | ||||
0.546849 | + | 0.837231i | \(0.315827\pi\) | |||||||
\(810\) | −24.2140 | −0.850795 | ||||||||
\(811\) | 35.2043 | 1.23619 | 0.618094 | − | 0.786104i | \(-0.287905\pi\) | ||||
0.618094 | + | 0.786104i | \(0.287905\pi\) | |||||||
\(812\) | −0.419616 | −0.0147256 | ||||||||
\(813\) | −4.31513 | −0.151338 | ||||||||
\(814\) | 81.1614 | 2.84471 | ||||||||
\(815\) | −0.772563 | −0.0270617 | ||||||||
\(816\) | 20.6799 | 0.723940 | ||||||||
\(817\) | −2.69317 | −0.0942222 | ||||||||
\(818\) | −39.3115 | −1.37450 | ||||||||
\(819\) | 1.41226 | 0.0493485 | ||||||||
\(820\) | 47.2149 | 1.64881 | ||||||||
\(821\) | −19.5393 | −0.681926 | −0.340963 | − | 0.940077i | \(-0.610753\pi\) | ||||
−0.340963 | + | 0.940077i | \(0.610753\pi\) | |||||||
\(822\) | 101.776 | 3.54984 | ||||||||
\(823\) | 21.9467 | 0.765013 | 0.382507 | − | 0.923953i | \(-0.375061\pi\) | ||||
0.382507 | + | 0.923953i | \(0.375061\pi\) | |||||||
\(824\) | −57.2952 | −1.99597 | ||||||||
\(825\) | 10.4733 | 0.364632 | ||||||||
\(826\) | −11.4521 | −0.398468 | ||||||||
\(827\) | 10.8659 | 0.377844 | 0.188922 | − | 0.981992i | \(-0.439501\pi\) | ||||
0.188922 | + | 0.981992i | \(0.439501\pi\) | |||||||
\(828\) | −2.21685 | −0.0770407 | ||||||||
\(829\) | 47.4450 | 1.64783 | 0.823916 | − | 0.566712i | \(-0.191785\pi\) | ||||
0.823916 | + | 0.566712i | \(0.191785\pi\) | |||||||
\(830\) | 26.6848 | 0.926241 | ||||||||
\(831\) | 28.7392 | 0.996950 | ||||||||
\(832\) | 35.1148 | 1.21739 | ||||||||
\(833\) | 3.68593 | 0.127710 | ||||||||
\(834\) | 93.0801 | 3.22310 | ||||||||
\(835\) | 3.11243 | 0.107710 | ||||||||
\(836\) | −25.7557 | −0.890781 | ||||||||
\(837\) | 2.41288 | 0.0834015 | ||||||||
\(838\) | −49.9899 | −1.72687 | ||||||||
\(839\) | 53.9888 | 1.86390 | 0.931950 | − | 0.362586i | \(-0.118106\pi\) | ||||
0.931950 | + | 0.362586i | \(0.118106\pi\) | |||||||
\(840\) | −8.17204 | −0.281962 | ||||||||
\(841\) | −28.9880 | −0.999588 | ||||||||
\(842\) | −62.5176 | −2.15450 | ||||||||
\(843\) | 33.5573 | 1.15578 | ||||||||
\(844\) | 80.4880 | 2.77051 | ||||||||
\(845\) | 0.0336215 | 0.00115661 | ||||||||
\(846\) | −4.22826 | −0.145371 | ||||||||
\(847\) | −21.3357 | −0.733102 | ||||||||
\(848\) | 31.9419 | 1.09689 | ||||||||
\(849\) | 39.1763 | 1.34453 | ||||||||
\(850\) | −8.90486 | −0.305434 | ||||||||
\(851\) | 8.70391 | 0.298366 | ||||||||
\(852\) | 35.9103 | 1.23027 | ||||||||
\(853\) | 2.20747 | 0.0755823 | 0.0377911 | − | 0.999286i | \(-0.487968\pi\) | ||||
0.0377911 | + | 0.999286i | \(0.487968\pi\) | |||||||
\(854\) | −26.3507 | −0.901703 | ||||||||
\(855\) | 0.463014 | 0.0158348 | ||||||||
\(856\) | −10.4527 | −0.357265 | ||||||||
\(857\) | −53.6896 | −1.83400 | −0.917001 | − | 0.398884i | \(-0.869398\pi\) | ||||
−0.917001 | + | 0.398884i | \(0.869398\pi\) | |||||||
\(858\) | 91.1109 | 3.11047 | ||||||||
\(859\) | 12.9934 | 0.443328 | 0.221664 | − | 0.975123i | \(-0.428851\pi\) | ||||
0.221664 | + | 0.975123i | \(0.428851\pi\) | |||||||
\(860\) | −8.75227 | −0.298450 | ||||||||
\(861\) | 22.6660 | 0.772455 | ||||||||
\(862\) | −60.6233 | −2.06484 | ||||||||
\(863\) | −4.35114 | −0.148114 | −0.0740572 | − | 0.997254i | \(-0.523595\pi\) | ||||
−0.0740572 | + | 0.997254i | \(0.523595\pi\) | |||||||
\(864\) | −7.27503 | −0.247502 | ||||||||
\(865\) | 16.6843 | 0.567285 | ||||||||
\(866\) | −98.7456 | −3.35551 | ||||||||
\(867\) | −6.28766 | −0.213540 | ||||||||
\(868\) | 1.92737 | 0.0654194 | ||||||||
\(869\) | −11.5929 | −0.393262 | ||||||||
\(870\) | 0.486662 | 0.0164994 | ||||||||
\(871\) | −56.9952 | −1.93121 | ||||||||
\(872\) | 39.9959 | 1.35443 | ||||||||
\(873\) | 7.51651 | 0.254395 | ||||||||
\(874\) | −4.20196 | −0.142134 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 64.9985 | 2.19610 | ||||||||
\(877\) | −2.50039 | −0.0844321 | −0.0422161 | − | 0.999109i | \(-0.513442\pi\) | ||||
−0.0422161 | + | 0.999109i | \(0.513442\pi\) | |||||||
\(878\) | −23.7033 | −0.799949 | ||||||||
\(879\) | −23.4273 | −0.790184 | ||||||||
\(880\) | −17.3221 | −0.583927 | ||||||||
\(881\) | 48.3556 | 1.62914 | 0.814570 | − | 0.580065i | \(-0.196973\pi\) | ||||
0.814570 | + | 0.580065i | \(0.196973\pi\) | |||||||
\(882\) | −0.947514 | −0.0319044 | ||||||||
\(883\) | 26.7698 | 0.900874 | 0.450437 | − | 0.892808i | \(-0.351268\pi\) | ||||
0.450437 | + | 0.892808i | \(0.351268\pi\) | |||||||
\(884\) | −50.9216 | −1.71268 | ||||||||
\(885\) | 8.73062 | 0.293476 | ||||||||
\(886\) | 90.9620 | 3.05593 | ||||||||
\(887\) | 42.9236 | 1.44123 | 0.720617 | − | 0.693333i | \(-0.243859\pi\) | ||||
0.720617 | + | 0.693333i | \(0.243859\pi\) | |||||||
\(888\) | 48.2792 | 1.62014 | ||||||||
\(889\) | −7.09207 | −0.237861 | ||||||||
\(890\) | 18.7558 | 0.628695 | ||||||||
\(891\) | −56.9940 | −1.90937 | ||||||||
\(892\) | −23.9536 | −0.802026 | ||||||||
\(893\) | −5.26823 | −0.176295 | ||||||||
\(894\) | 82.7431 | 2.76734 | ||||||||
\(895\) | −9.82181 | −0.328307 | ||||||||
\(896\) | −20.5299 | −0.685854 | ||||||||
\(897\) | 9.77090 | 0.326241 | ||||||||
\(898\) | −10.8790 | −0.363037 | ||||||||
\(899\) | −0.0549451 | −0.00183252 | ||||||||
\(900\) | 1.50470 | 0.0501568 | ||||||||
\(901\) | 38.6500 | 1.28762 | ||||||||
\(902\) | 169.065 | 5.62926 | ||||||||
\(903\) | −4.20162 | −0.139821 | ||||||||
\(904\) | 51.4067 | 1.70976 | ||||||||
\(905\) | −10.7755 | −0.358189 | ||||||||
\(906\) | −64.6956 | −2.14937 | ||||||||
\(907\) | 11.3109 | 0.375572 | 0.187786 | − | 0.982210i | \(-0.439869\pi\) | ||||
0.187786 | + | 0.982210i | \(0.439869\pi\) | |||||||
\(908\) | −12.0655 | −0.400409 | ||||||||
\(909\) | 4.35062 | 0.144301 | ||||||||
\(910\) | 8.69939 | 0.288382 | ||||||||
\(911\) | 46.6223 | 1.54467 | 0.772333 | − | 0.635218i | \(-0.219090\pi\) | ||||
0.772333 | + | 0.635218i | \(0.219090\pi\) | |||||||
\(912\) | −6.62351 | −0.219326 | ||||||||
\(913\) | 62.8094 | 2.07869 | ||||||||
\(914\) | 53.1461 | 1.75792 | ||||||||
\(915\) | 20.0888 | 0.664115 | ||||||||
\(916\) | 3.83658 | 0.126764 | ||||||||
\(917\) | −8.23872 | −0.272066 | ||||||||
\(918\) | 42.7703 | 1.41163 | ||||||||
\(919\) | 1.64331 | 0.0542077 | 0.0271038 | − | 0.999633i | \(-0.491372\pi\) | ||||
0.0271038 | + | 0.999633i | \(0.491372\pi\) | |||||||
\(920\) | −6.53694 | −0.215517 | ||||||||
\(921\) | 54.6607 | 1.80113 | ||||||||
\(922\) | −28.5279 | −0.939515 | ||||||||
\(923\) | −18.2997 | −0.602341 | ||||||||
\(924\) | −40.1815 | −1.32187 | ||||||||
\(925\) | −5.90785 | −0.194249 | ||||||||
\(926\) | −47.4462 | −1.55918 | ||||||||
\(927\) | 5.06447 | 0.166339 | ||||||||
\(928\) | 0.165664 | 0.00543817 | ||||||||
\(929\) | −21.3327 | −0.699903 | −0.349952 | − | 0.936768i | \(-0.613802\pi\) | ||||
−0.349952 | + | 0.936768i | \(0.613802\pi\) | |||||||
\(930\) | −2.23533 | −0.0732993 | ||||||||
\(931\) | −1.18056 | −0.0386913 | ||||||||
\(932\) | 58.6587 | 1.92143 | ||||||||
\(933\) | 38.5424 | 1.26182 | ||||||||
\(934\) | −90.5290 | −2.96220 | ||||||||
\(935\) | −20.9599 | −0.685461 | ||||||||
\(936\) | 6.26622 | 0.204818 | ||||||||
\(937\) | 27.7518 | 0.906611 | 0.453306 | − | 0.891355i | \(-0.350245\pi\) | ||||
0.453306 | + | 0.891355i | \(0.350245\pi\) | |||||||
\(938\) | 38.2392 | 1.24855 | ||||||||
\(939\) | 21.5987 | 0.704846 | ||||||||
\(940\) | −17.1207 | −0.558415 | ||||||||
\(941\) | −10.2245 | −0.333308 | −0.166654 | − | 0.986015i | \(-0.553296\pi\) | ||||
−0.166654 | + | 0.986015i | \(0.553296\pi\) | |||||||
\(942\) | −28.4126 | −0.925732 | ||||||||
\(943\) | 18.1309 | 0.590423 | ||||||||
\(944\) | −14.4399 | −0.469978 | ||||||||
\(945\) | −4.80303 | −0.156243 | ||||||||
\(946\) | −31.3398 | −1.01894 | ||||||||
\(947\) | −3.85369 | −0.125228 | −0.0626140 | − | 0.998038i | \(-0.519944\pi\) | ||||
−0.0626140 | + | 0.998038i | \(0.519944\pi\) | |||||||
\(948\) | −14.4058 | −0.467877 | ||||||||
\(949\) | −33.1228 | −1.07521 | ||||||||
\(950\) | 2.85212 | 0.0925350 | ||||||||
\(951\) | −34.4322 | −1.11654 | ||||||||
\(952\) | 16.3545 | 0.530053 | ||||||||
\(953\) | −8.38095 | −0.271486 | −0.135743 | − | 0.990744i | \(-0.543342\pi\) | ||||
−0.135743 | + | 0.990744i | \(0.543342\pi\) | |||||||
\(954\) | −9.93544 | −0.321672 | ||||||||
\(955\) | 16.2308 | 0.525218 | ||||||||
\(956\) | −71.1270 | −2.30041 | ||||||||
\(957\) | 1.14548 | 0.0370282 | ||||||||
\(958\) | −46.0589 | −1.48810 | ||||||||
\(959\) | 22.8731 | 0.738610 | ||||||||
\(960\) | 17.9606 | 0.579677 | ||||||||
\(961\) | −30.7476 | −0.991859 | ||||||||
\(962\) | −51.3947 | −1.65703 | ||||||||
\(963\) | 0.923938 | 0.0297735 | ||||||||
\(964\) | 46.7978 | 1.50726 | ||||||||
\(965\) | −6.54001 | −0.210530 | ||||||||
\(966\) | −6.55548 | −0.210919 | ||||||||
\(967\) | 2.09521 | 0.0673776 | 0.0336888 | − | 0.999432i | \(-0.489275\pi\) | ||||
0.0336888 | + | 0.999432i | \(0.489275\pi\) | |||||||
\(968\) | −94.6664 | −3.04269 | ||||||||
\(969\) | −8.01450 | −0.257463 | ||||||||
\(970\) | 46.3009 | 1.48663 | ||||||||
\(971\) | −0.737084 | −0.0236542 | −0.0118271 | − | 0.999930i | \(-0.503765\pi\) | ||||
−0.0118271 | + | 0.999930i | \(0.503765\pi\) | |||||||
\(972\) | −15.5412 | −0.498484 | ||||||||
\(973\) | 20.9188 | 0.670626 | ||||||||
\(974\) | −104.189 | −3.33843 | ||||||||
\(975\) | −6.63208 | −0.212397 | ||||||||
\(976\) | −33.2256 | −1.06352 | ||||||||
\(977\) | −24.4738 | −0.782988 | −0.391494 | − | 0.920181i | \(-0.628042\pi\) | ||||
−0.391494 | + | 0.920181i | \(0.628042\pi\) | |||||||
\(978\) | −3.43759 | −0.109922 | ||||||||
\(979\) | 44.1465 | 1.41093 | ||||||||
\(980\) | −3.83658 | −0.122555 | ||||||||
\(981\) | −3.53534 | −0.112875 | ||||||||
\(982\) | −39.5928 | −1.26346 | ||||||||
\(983\) | 21.2441 | 0.677582 | 0.338791 | − | 0.940862i | \(-0.389982\pi\) | ||||
0.338791 | + | 0.940862i | \(0.389982\pi\) | |||||||
\(984\) | 100.569 | 3.20603 | ||||||||
\(985\) | −2.73432 | −0.0871225 | ||||||||
\(986\) | −0.973945 | −0.0310167 | ||||||||
\(987\) | −8.21897 | −0.261613 | ||||||||
\(988\) | 16.3096 | 0.518876 | ||||||||
\(989\) | −3.36094 | −0.106872 | ||||||||
\(990\) | 5.38798 | 0.171241 | ||||||||
\(991\) | 24.7706 | 0.786865 | 0.393433 | − | 0.919353i | \(-0.371287\pi\) | ||||
0.393433 | + | 0.919353i | \(0.371287\pi\) | |||||||
\(992\) | −0.760924 | −0.0241594 | ||||||||
\(993\) | −47.0841 | −1.49417 | ||||||||
\(994\) | 12.2776 | 0.389422 | ||||||||
\(995\) | −17.6264 | −0.558795 | ||||||||
\(996\) | 78.0493 | 2.47309 | ||||||||
\(997\) | −46.3714 | −1.46860 | −0.734299 | − | 0.678827i | \(-0.762489\pi\) | ||||
−0.734299 | + | 0.678827i | \(0.762489\pi\) | |||||||
\(998\) | −21.8205 | −0.690717 | ||||||||
\(999\) | 28.3756 | 0.897763 |
(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 | 8015.2.a.l.1.5 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.5 | ✓ | 62 | 1.1 | even | 1 | trivial |