Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.29 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.751824 | 0.531620 | 0.265810 | − | 0.964026i | \(-0.414361\pi\) | ||||
0.265810 | + | 0.964026i | \(0.414361\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.43476 | −0.717381 | ||||||||
\(5\) | 3.06060 | 1.36874 | 0.684370 | − | 0.729135i | \(-0.260077\pi\) | ||||
0.684370 | + | 0.729135i | \(0.260077\pi\) | |||||||
\(6\) | 0.751824 | 0.306931 | ||||||||
\(7\) | −2.02078 | −0.763782 | −0.381891 | − | 0.924207i | \(-0.624727\pi\) | ||||
−0.381891 | + | 0.924207i | \(0.624727\pi\) | |||||||
\(8\) | −2.58233 | −0.912993 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.30103 | 0.727649 | ||||||||
\(11\) | −2.87419 | −0.866601 | −0.433300 | − | 0.901250i | \(-0.642651\pi\) | ||||
−0.433300 | + | 0.901250i | \(0.642651\pi\) | |||||||
\(12\) | −1.43476 | −0.414180 | ||||||||
\(13\) | −0.853656 | −0.236762 | −0.118381 | − | 0.992968i | \(-0.537770\pi\) | ||||
−0.118381 | + | 0.992968i | \(0.537770\pi\) | |||||||
\(14\) | −1.51927 | −0.406041 | ||||||||
\(15\) | 3.06060 | 0.790243 | ||||||||
\(16\) | 0.928063 | 0.232016 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0.751824 | 0.177207 | ||||||||
\(19\) | 1.01630 | 0.233155 | 0.116577 | − | 0.993182i | \(-0.462808\pi\) | ||||
0.116577 | + | 0.993182i | \(0.462808\pi\) | |||||||
\(20\) | −4.39123 | −0.981908 | ||||||||
\(21\) | −2.02078 | −0.440970 | ||||||||
\(22\) | −2.16088 | −0.460702 | ||||||||
\(23\) | 2.89886 | 0.604454 | 0.302227 | − | 0.953236i | \(-0.402270\pi\) | ||||
0.302227 | + | 0.953236i | \(0.402270\pi\) | |||||||
\(24\) | −2.58233 | −0.527117 | ||||||||
\(25\) | 4.36726 | 0.873452 | ||||||||
\(26\) | −0.641799 | −0.125867 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.89933 | 0.547922 | ||||||||
\(29\) | −7.11490 | −1.32120 | −0.660602 | − | 0.750737i | \(-0.729699\pi\) | ||||
−0.660602 | + | 0.750737i | \(0.729699\pi\) | |||||||
\(30\) | 2.30103 | 0.420109 | ||||||||
\(31\) | 1.50911 | 0.271045 | 0.135522 | − | 0.990774i | \(-0.456729\pi\) | ||||
0.135522 | + | 0.990774i | \(0.456729\pi\) | |||||||
\(32\) | 5.86241 | 1.03634 | ||||||||
\(33\) | −2.87419 | −0.500332 | ||||||||
\(34\) | −0.751824 | −0.128937 | ||||||||
\(35\) | −6.18478 | −1.04542 | ||||||||
\(36\) | −1.43476 | −0.239127 | ||||||||
\(37\) | 8.80348 | 1.44728 | 0.723642 | − | 0.690176i | \(-0.242467\pi\) | ||||
0.723642 | + | 0.690176i | \(0.242467\pi\) | |||||||
\(38\) | 0.764077 | 0.123950 | ||||||||
\(39\) | −0.853656 | −0.136694 | ||||||||
\(40\) | −7.90349 | −1.24965 | ||||||||
\(41\) | 4.79907 | 0.749489 | 0.374745 | − | 0.927128i | \(-0.377730\pi\) | ||||
0.374745 | + | 0.927128i | \(0.377730\pi\) | |||||||
\(42\) | −1.51927 | −0.234428 | ||||||||
\(43\) | −0.143371 | −0.0218639 | −0.0109319 | − | 0.999940i | \(-0.503480\pi\) | ||||
−0.0109319 | + | 0.999940i | \(0.503480\pi\) | |||||||
\(44\) | 4.12378 | 0.621683 | ||||||||
\(45\) | 3.06060 | 0.456247 | ||||||||
\(46\) | 2.17943 | 0.321339 | ||||||||
\(47\) | −6.98716 | −1.01918 | −0.509591 | − | 0.860417i | \(-0.670203\pi\) | ||||
−0.509591 | + | 0.860417i | \(0.670203\pi\) | |||||||
\(48\) | 0.928063 | 0.133954 | ||||||||
\(49\) | −2.91646 | −0.416638 | ||||||||
\(50\) | 3.28341 | 0.464344 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 1.22479 | 0.169848 | ||||||||
\(53\) | −7.81555 | −1.07355 | −0.536774 | − | 0.843726i | \(-0.680357\pi\) | ||||
−0.536774 | + | 0.843726i | \(0.680357\pi\) | |||||||
\(54\) | 0.751824 | 0.102310 | ||||||||
\(55\) | −8.79674 | −1.18615 | ||||||||
\(56\) | 5.21832 | 0.697327 | ||||||||
\(57\) | 1.01630 | 0.134612 | ||||||||
\(58\) | −5.34915 | −0.702377 | ||||||||
\(59\) | −9.82923 | −1.27966 | −0.639829 | − | 0.768518i | \(-0.720995\pi\) | ||||
−0.639829 | + | 0.768518i | \(0.720995\pi\) | |||||||
\(60\) | −4.39123 | −0.566905 | ||||||||
\(61\) | −8.44330 | −1.08105 | −0.540527 | − | 0.841327i | \(-0.681775\pi\) | ||||
−0.540527 | + | 0.841327i | \(0.681775\pi\) | |||||||
\(62\) | 1.13459 | 0.144093 | ||||||||
\(63\) | −2.02078 | −0.254594 | ||||||||
\(64\) | 2.55137 | 0.318921 | ||||||||
\(65\) | −2.61270 | −0.324065 | ||||||||
\(66\) | −2.16088 | −0.265986 | ||||||||
\(67\) | −0.210466 | −0.0257125 | −0.0128563 | − | 0.999917i | \(-0.504092\pi\) | ||||
−0.0128563 | + | 0.999917i | \(0.504092\pi\) | |||||||
\(68\) | 1.43476 | 0.173990 | ||||||||
\(69\) | 2.89886 | 0.348982 | ||||||||
\(70\) | −4.64987 | −0.555765 | ||||||||
\(71\) | −4.66633 | −0.553792 | −0.276896 | − | 0.960900i | \(-0.589306\pi\) | ||||
−0.276896 | + | 0.960900i | \(0.589306\pi\) | |||||||
\(72\) | −2.58233 | −0.304331 | ||||||||
\(73\) | 4.89518 | 0.572938 | 0.286469 | − | 0.958090i | \(-0.407518\pi\) | ||||
0.286469 | + | 0.958090i | \(0.407518\pi\) | |||||||
\(74\) | 6.61866 | 0.769404 | ||||||||
\(75\) | 4.36726 | 0.504287 | ||||||||
\(76\) | −1.45815 | −0.167261 | ||||||||
\(77\) | 5.80809 | 0.661894 | ||||||||
\(78\) | −0.641799 | −0.0726694 | ||||||||
\(79\) | 14.7425 | 1.65866 | 0.829329 | − | 0.558760i | \(-0.188723\pi\) | ||||
0.829329 | + | 0.558760i | \(0.188723\pi\) | |||||||
\(80\) | 2.84043 | 0.317569 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.60806 | 0.398443 | ||||||||
\(83\) | 2.85980 | 0.313904 | 0.156952 | − | 0.987606i | \(-0.449833\pi\) | ||||
0.156952 | + | 0.987606i | \(0.449833\pi\) | |||||||
\(84\) | 2.89933 | 0.316343 | ||||||||
\(85\) | −3.06060 | −0.331968 | ||||||||
\(86\) | −0.107790 | −0.0116233 | ||||||||
\(87\) | −7.11490 | −0.762797 | ||||||||
\(88\) | 7.42212 | 0.791200 | ||||||||
\(89\) | −14.3348 | −1.51949 | −0.759745 | − | 0.650221i | \(-0.774676\pi\) | ||||
−0.759745 | + | 0.650221i | \(0.774676\pi\) | |||||||
\(90\) | 2.30103 | 0.242550 | ||||||||
\(91\) | 1.72505 | 0.180834 | ||||||||
\(92\) | −4.15917 | −0.433623 | ||||||||
\(93\) | 1.50911 | 0.156488 | ||||||||
\(94\) | −5.25311 | −0.541817 | ||||||||
\(95\) | 3.11048 | 0.319129 | ||||||||
\(96\) | 5.86241 | 0.598330 | ||||||||
\(97\) | 11.0575 | 1.12272 | 0.561359 | − | 0.827572i | \(-0.310279\pi\) | ||||
0.561359 | + | 0.827572i | \(0.310279\pi\) | |||||||
\(98\) | −2.19267 | −0.221493 | ||||||||
\(99\) | −2.87419 | −0.288867 | ||||||||
\(100\) | −6.26597 | −0.626597 | ||||||||
\(101\) | −8.86946 | −0.882545 | −0.441272 | − | 0.897373i | \(-0.645473\pi\) | ||||
−0.441272 | + | 0.897373i | \(0.645473\pi\) | |||||||
\(102\) | −0.751824 | −0.0744416 | ||||||||
\(103\) | −16.5490 | −1.63062 | −0.815309 | − | 0.579026i | \(-0.803433\pi\) | ||||
−0.815309 | + | 0.579026i | \(0.803433\pi\) | |||||||
\(104\) | 2.20442 | 0.216162 | ||||||||
\(105\) | −6.18478 | −0.603573 | ||||||||
\(106\) | −5.87591 | −0.570719 | ||||||||
\(107\) | −7.01251 | −0.677925 | −0.338963 | − | 0.940800i | \(-0.610076\pi\) | ||||
−0.338963 | + | 0.940800i | \(0.610076\pi\) | |||||||
\(108\) | −1.43476 | −0.138060 | ||||||||
\(109\) | −12.8152 | −1.22747 | −0.613736 | − | 0.789511i | \(-0.710334\pi\) | ||||
−0.613736 | + | 0.789511i | \(0.710334\pi\) | |||||||
\(110\) | −6.61359 | −0.630581 | ||||||||
\(111\) | 8.80348 | 0.835589 | ||||||||
\(112\) | −1.87541 | −0.177209 | ||||||||
\(113\) | −1.53869 | −0.144748 | −0.0723741 | − | 0.997378i | \(-0.523058\pi\) | ||||
−0.0723741 | + | 0.997378i | \(0.523058\pi\) | |||||||
\(114\) | 0.764077 | 0.0715624 | ||||||||
\(115\) | 8.87224 | 0.827341 | ||||||||
\(116\) | 10.2082 | 0.947806 | ||||||||
\(117\) | −0.853656 | −0.0789205 | ||||||||
\(118\) | −7.38985 | −0.680291 | ||||||||
\(119\) | 2.02078 | 0.185244 | ||||||||
\(120\) | −7.90349 | −0.721486 | ||||||||
\(121\) | −2.73904 | −0.249003 | ||||||||
\(122\) | −6.34787 | −0.574709 | ||||||||
\(123\) | 4.79907 | 0.432718 | ||||||||
\(124\) | −2.16522 | −0.194442 | ||||||||
\(125\) | −1.93657 | −0.173212 | ||||||||
\(126\) | −1.51927 | −0.135347 | ||||||||
\(127\) | 8.04162 | 0.713579 | 0.356789 | − | 0.934185i | \(-0.383871\pi\) | ||||
0.356789 | + | 0.934185i | \(0.383871\pi\) | |||||||
\(128\) | −9.80664 | −0.866792 | ||||||||
\(129\) | −0.143371 | −0.0126231 | ||||||||
\(130\) | −1.96429 | −0.172279 | ||||||||
\(131\) | −18.0424 | −1.57638 | −0.788188 | − | 0.615435i | \(-0.788981\pi\) | ||||
−0.788188 | + | 0.615435i | \(0.788981\pi\) | |||||||
\(132\) | 4.12378 | 0.358929 | ||||||||
\(133\) | −2.05371 | −0.178079 | ||||||||
\(134\) | −0.158233 | −0.0136693 | ||||||||
\(135\) | 3.06060 | 0.263414 | ||||||||
\(136\) | 2.58233 | 0.221433 | ||||||||
\(137\) | −17.1264 | −1.46321 | −0.731604 | − | 0.681730i | \(-0.761228\pi\) | ||||
−0.731604 | + | 0.681730i | \(0.761228\pi\) | |||||||
\(138\) | 2.17943 | 0.185525 | ||||||||
\(139\) | 7.56541 | 0.641690 | 0.320845 | − | 0.947132i | \(-0.396033\pi\) | ||||
0.320845 | + | 0.947132i | \(0.396033\pi\) | |||||||
\(140\) | 8.87369 | 0.749963 | ||||||||
\(141\) | −6.98716 | −0.588425 | ||||||||
\(142\) | −3.50826 | −0.294407 | ||||||||
\(143\) | 2.45357 | 0.205178 | ||||||||
\(144\) | 0.928063 | 0.0773386 | ||||||||
\(145\) | −21.7758 | −1.80838 | ||||||||
\(146\) | 3.68032 | 0.304585 | ||||||||
\(147\) | −2.91646 | −0.240546 | ||||||||
\(148\) | −12.6309 | −1.03825 | ||||||||
\(149\) | −18.9859 | −1.55538 | −0.777691 | − | 0.628646i | \(-0.783609\pi\) | ||||
−0.777691 | + | 0.628646i | \(0.783609\pi\) | |||||||
\(150\) | 3.28341 | 0.268089 | ||||||||
\(151\) | −14.7577 | −1.20096 | −0.600482 | − | 0.799638i | \(-0.705025\pi\) | ||||
−0.600482 | + | 0.799638i | \(0.705025\pi\) | |||||||
\(152\) | −2.62442 | −0.212869 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 4.36666 | 0.351876 | ||||||||
\(155\) | 4.61879 | 0.370990 | ||||||||
\(156\) | 1.22479 | 0.0980619 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | 11.0837 | 0.881775 | ||||||||
\(159\) | −7.81555 | −0.619813 | ||||||||
\(160\) | 17.9425 | 1.41848 | ||||||||
\(161\) | −5.85794 | −0.461671 | ||||||||
\(162\) | 0.751824 | 0.0590688 | ||||||||
\(163\) | −11.2197 | −0.878793 | −0.439396 | − | 0.898293i | \(-0.644808\pi\) | ||||
−0.439396 | + | 0.898293i | \(0.644808\pi\) | |||||||
\(164\) | −6.88552 | −0.537669 | ||||||||
\(165\) | −8.79674 | −0.684825 | ||||||||
\(166\) | 2.15007 | 0.166877 | ||||||||
\(167\) | 10.9725 | 0.849075 | 0.424538 | − | 0.905410i | \(-0.360437\pi\) | ||||
0.424538 | + | 0.905410i | \(0.360437\pi\) | |||||||
\(168\) | 5.21832 | 0.402602 | ||||||||
\(169\) | −12.2713 | −0.943944 | ||||||||
\(170\) | −2.30103 | −0.176481 | ||||||||
\(171\) | 1.01630 | 0.0777183 | ||||||||
\(172\) | 0.205703 | 0.0156847 | ||||||||
\(173\) | −2.30294 | −0.175089 | −0.0875447 | − | 0.996161i | \(-0.527902\pi\) | ||||
−0.0875447 | + | 0.996161i | \(0.527902\pi\) | |||||||
\(174\) | −5.34915 | −0.405518 | ||||||||
\(175\) | −8.82525 | −0.667126 | ||||||||
\(176\) | −2.66743 | −0.201065 | ||||||||
\(177\) | −9.82923 | −0.738811 | ||||||||
\(178\) | −10.7773 | −0.807790 | ||||||||
\(179\) | 25.8243 | 1.93020 | 0.965101 | − | 0.261879i | \(-0.0843420\pi\) | ||||
0.965101 | + | 0.261879i | \(0.0843420\pi\) | |||||||
\(180\) | −4.39123 | −0.327303 | ||||||||
\(181\) | −15.4193 | −1.14611 | −0.573053 | − | 0.819518i | \(-0.694241\pi\) | ||||
−0.573053 | + | 0.819518i | \(0.694241\pi\) | |||||||
\(182\) | 1.29693 | 0.0961349 | ||||||||
\(183\) | −8.44330 | −0.624146 | ||||||||
\(184\) | −7.48582 | −0.551862 | ||||||||
\(185\) | 26.9439 | 1.98096 | ||||||||
\(186\) | 1.13459 | 0.0831919 | ||||||||
\(187\) | 2.87419 | 0.210182 | ||||||||
\(188\) | 10.0249 | 0.731141 | ||||||||
\(189\) | −2.02078 | −0.146990 | ||||||||
\(190\) | 2.33853 | 0.169655 | ||||||||
\(191\) | −15.4712 | −1.11945 | −0.559727 | − | 0.828677i | \(-0.689094\pi\) | ||||
−0.559727 | + | 0.828677i | \(0.689094\pi\) | |||||||
\(192\) | 2.55137 | 0.184129 | ||||||||
\(193\) | 1.92958 | 0.138894 | 0.0694471 | − | 0.997586i | \(-0.477877\pi\) | ||||
0.0694471 | + | 0.997586i | \(0.477877\pi\) | |||||||
\(194\) | 8.31329 | 0.596859 | ||||||||
\(195\) | −2.61270 | −0.187099 | ||||||||
\(196\) | 4.18443 | 0.298888 | ||||||||
\(197\) | 25.7976 | 1.83800 | 0.919002 | − | 0.394252i | \(-0.128996\pi\) | ||||
0.919002 | + | 0.394252i | \(0.128996\pi\) | |||||||
\(198\) | −2.16088 | −0.153567 | ||||||||
\(199\) | 13.7262 | 0.973028 | 0.486514 | − | 0.873673i | \(-0.338268\pi\) | ||||
0.486514 | + | 0.873673i | \(0.338268\pi\) | |||||||
\(200\) | −11.2777 | −0.797455 | ||||||||
\(201\) | −0.210466 | −0.0148451 | ||||||||
\(202\) | −6.66827 | −0.469178 | ||||||||
\(203\) | 14.3776 | 1.00911 | ||||||||
\(204\) | 1.43476 | 0.100453 | ||||||||
\(205\) | 14.6880 | 1.02586 | ||||||||
\(206\) | −12.4419 | −0.866868 | ||||||||
\(207\) | 2.89886 | 0.201485 | ||||||||
\(208\) | −0.792246 | −0.0549324 | ||||||||
\(209\) | −2.92103 | −0.202052 | ||||||||
\(210\) | −4.64987 | −0.320871 | ||||||||
\(211\) | −15.1204 | −1.04093 | −0.520466 | − | 0.853882i | \(-0.674242\pi\) | ||||
−0.520466 | + | 0.853882i | \(0.674242\pi\) | |||||||
\(212\) | 11.2134 | 0.770143 | ||||||||
\(213\) | −4.66633 | −0.319732 | ||||||||
\(214\) | −5.27217 | −0.360398 | ||||||||
\(215\) | −0.438801 | −0.0299260 | ||||||||
\(216\) | −2.58233 | −0.175706 | ||||||||
\(217\) | −3.04958 | −0.207019 | ||||||||
\(218\) | −9.63476 | −0.652549 | ||||||||
\(219\) | 4.89518 | 0.330786 | ||||||||
\(220\) | 12.6212 | 0.850922 | ||||||||
\(221\) | 0.853656 | 0.0574231 | ||||||||
\(222\) | 6.61866 | 0.444216 | ||||||||
\(223\) | 4.57697 | 0.306496 | 0.153248 | − | 0.988188i | \(-0.451027\pi\) | ||||
0.153248 | + | 0.988188i | \(0.451027\pi\) | |||||||
\(224\) | −11.8466 | −0.791535 | ||||||||
\(225\) | 4.36726 | 0.291151 | ||||||||
\(226\) | −1.15683 | −0.0769510 | ||||||||
\(227\) | −12.2361 | −0.812137 | −0.406069 | − | 0.913843i | \(-0.633101\pi\) | ||||
−0.406069 | + | 0.913843i | \(0.633101\pi\) | |||||||
\(228\) | −1.45815 | −0.0965681 | ||||||||
\(229\) | −18.7988 | −1.24226 | −0.621129 | − | 0.783708i | \(-0.713326\pi\) | ||||
−0.621129 | + | 0.783708i | \(0.713326\pi\) | |||||||
\(230\) | 6.67036 | 0.439830 | ||||||||
\(231\) | 5.80809 | 0.382144 | ||||||||
\(232\) | 18.3730 | 1.20625 | ||||||||
\(233\) | −0.383971 | −0.0251548 | −0.0125774 | − | 0.999921i | \(-0.504004\pi\) | ||||
−0.0125774 | + | 0.999921i | \(0.504004\pi\) | |||||||
\(234\) | −0.641799 | −0.0419557 | ||||||||
\(235\) | −21.3849 | −1.39500 | ||||||||
\(236\) | 14.1026 | 0.918001 | ||||||||
\(237\) | 14.7425 | 0.957627 | ||||||||
\(238\) | 1.51927 | 0.0984795 | ||||||||
\(239\) | 3.09443 | 0.200162 | 0.100081 | − | 0.994979i | \(-0.468090\pi\) | ||||
0.100081 | + | 0.994979i | \(0.468090\pi\) | |||||||
\(240\) | 2.84043 | 0.183349 | ||||||||
\(241\) | −15.0686 | −0.970654 | −0.485327 | − | 0.874333i | \(-0.661300\pi\) | ||||
−0.485327 | + | 0.874333i | \(0.661300\pi\) | |||||||
\(242\) | −2.05927 | −0.132375 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 12.1141 | 0.775527 | ||||||||
\(245\) | −8.92612 | −0.570269 | ||||||||
\(246\) | 3.60806 | 0.230041 | ||||||||
\(247\) | −0.867569 | −0.0552021 | ||||||||
\(248\) | −3.89703 | −0.247462 | ||||||||
\(249\) | 2.85980 | 0.181233 | ||||||||
\(250\) | −1.45596 | −0.0920829 | ||||||||
\(251\) | 26.3654 | 1.66417 | 0.832083 | − | 0.554651i | \(-0.187148\pi\) | ||||
0.832083 | + | 0.554651i | \(0.187148\pi\) | |||||||
\(252\) | 2.89933 | 0.182641 | ||||||||
\(253\) | −8.33187 | −0.523820 | ||||||||
\(254\) | 6.04588 | 0.379352 | ||||||||
\(255\) | −3.06060 | −0.191662 | ||||||||
\(256\) | −12.4756 | −0.779725 | ||||||||
\(257\) | −11.1381 | −0.694776 | −0.347388 | − | 0.937721i | \(-0.612931\pi\) | ||||
−0.347388 | + | 0.937721i | \(0.612931\pi\) | |||||||
\(258\) | −0.107790 | −0.00671070 | ||||||||
\(259\) | −17.7899 | −1.10541 | ||||||||
\(260\) | 3.74860 | 0.232478 | ||||||||
\(261\) | −7.11490 | −0.440401 | ||||||||
\(262\) | −13.5647 | −0.838032 | ||||||||
\(263\) | 9.87268 | 0.608776 | 0.304388 | − | 0.952548i | \(-0.401548\pi\) | ||||
0.304388 | + | 0.952548i | \(0.401548\pi\) | |||||||
\(264\) | 7.42212 | 0.456800 | ||||||||
\(265\) | −23.9203 | −1.46941 | ||||||||
\(266\) | −1.54403 | −0.0946705 | ||||||||
\(267\) | −14.3348 | −0.877278 | ||||||||
\(268\) | 0.301969 | 0.0184457 | ||||||||
\(269\) | 21.1237 | 1.28794 | 0.643968 | − | 0.765053i | \(-0.277287\pi\) | ||||
0.643968 | + | 0.765053i | \(0.277287\pi\) | |||||||
\(270\) | 2.30103 | 0.140036 | ||||||||
\(271\) | 19.6114 | 1.19131 | 0.595653 | − | 0.803242i | \(-0.296893\pi\) | ||||
0.595653 | + | 0.803242i | \(0.296893\pi\) | |||||||
\(272\) | −0.928063 | −0.0562721 | ||||||||
\(273\) | 1.72505 | 0.104405 | ||||||||
\(274\) | −12.8760 | −0.777869 | ||||||||
\(275\) | −12.5523 | −0.756934 | ||||||||
\(276\) | −4.15917 | −0.250353 | ||||||||
\(277\) | 5.34480 | 0.321138 | 0.160569 | − | 0.987025i | \(-0.448667\pi\) | ||||
0.160569 | + | 0.987025i | \(0.448667\pi\) | |||||||
\(278\) | 5.68785 | 0.341135 | ||||||||
\(279\) | 1.50911 | 0.0903482 | ||||||||
\(280\) | 15.9712 | 0.954460 | ||||||||
\(281\) | 11.3948 | 0.679759 | 0.339879 | − | 0.940469i | \(-0.389614\pi\) | ||||
0.339879 | + | 0.940469i | \(0.389614\pi\) | |||||||
\(282\) | −5.25311 | −0.312818 | ||||||||
\(283\) | 17.5218 | 1.04156 | 0.520781 | − | 0.853690i | \(-0.325641\pi\) | ||||
0.520781 | + | 0.853690i | \(0.325641\pi\) | |||||||
\(284\) | 6.69507 | 0.397280 | ||||||||
\(285\) | 3.11048 | 0.184249 | ||||||||
\(286\) | 1.84465 | 0.109076 | ||||||||
\(287\) | −9.69785 | −0.572446 | ||||||||
\(288\) | 5.86241 | 0.345446 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −16.3716 | −0.961373 | ||||||||
\(291\) | 11.0575 | 0.648202 | ||||||||
\(292\) | −7.02342 | −0.411015 | ||||||||
\(293\) | −23.2569 | −1.35868 | −0.679342 | − | 0.733822i | \(-0.737735\pi\) | ||||
−0.679342 | + | 0.733822i | \(0.737735\pi\) | |||||||
\(294\) | −2.19267 | −0.127879 | ||||||||
\(295\) | −30.0833 | −1.75152 | ||||||||
\(296\) | −22.7335 | −1.32136 | ||||||||
\(297\) | −2.87419 | −0.166777 | ||||||||
\(298\) | −14.2740 | −0.826872 | ||||||||
\(299\) | −2.47463 | −0.143111 | ||||||||
\(300\) | −6.26597 | −0.361766 | ||||||||
\(301\) | 0.289721 | 0.0166992 | ||||||||
\(302\) | −11.0952 | −0.638456 | ||||||||
\(303\) | −8.86946 | −0.509537 | ||||||||
\(304\) | 0.943189 | 0.0540956 | ||||||||
\(305\) | −25.8415 | −1.47968 | ||||||||
\(306\) | −0.751824 | −0.0429789 | ||||||||
\(307\) | −14.5309 | −0.829320 | −0.414660 | − | 0.909976i | \(-0.636099\pi\) | ||||
−0.414660 | + | 0.909976i | \(0.636099\pi\) | |||||||
\(308\) | −8.33323 | −0.474830 | ||||||||
\(309\) | −16.5490 | −0.941438 | ||||||||
\(310\) | 3.47251 | 0.197225 | ||||||||
\(311\) | 8.72286 | 0.494628 | 0.247314 | − | 0.968935i | \(-0.420452\pi\) | ||||
0.247314 | + | 0.968935i | \(0.420452\pi\) | |||||||
\(312\) | 2.20442 | 0.124801 | ||||||||
\(313\) | −2.16307 | −0.122264 | −0.0611319 | − | 0.998130i | \(-0.519471\pi\) | ||||
−0.0611319 | + | 0.998130i | \(0.519471\pi\) | |||||||
\(314\) | 0.751824 | 0.0424279 | ||||||||
\(315\) | −6.18478 | −0.348473 | ||||||||
\(316\) | −21.1519 | −1.18989 | ||||||||
\(317\) | 23.8411 | 1.33905 | 0.669525 | − | 0.742790i | \(-0.266498\pi\) | ||||
0.669525 | + | 0.742790i | \(0.266498\pi\) | |||||||
\(318\) | −5.87591 | −0.329505 | ||||||||
\(319\) | 20.4496 | 1.14496 | ||||||||
\(320\) | 7.80872 | 0.436521 | ||||||||
\(321\) | −7.01251 | −0.391400 | ||||||||
\(322\) | −4.40414 | −0.245433 | ||||||||
\(323\) | −1.01630 | −0.0565484 | ||||||||
\(324\) | −1.43476 | −0.0797090 | ||||||||
\(325\) | −3.72813 | −0.206800 | ||||||||
\(326\) | −8.43521 | −0.467183 | ||||||||
\(327\) | −12.8152 | −0.708682 | ||||||||
\(328\) | −12.3928 | −0.684279 | ||||||||
\(329\) | 14.1195 | 0.778432 | ||||||||
\(330\) | −6.61359 | −0.364066 | ||||||||
\(331\) | 14.2207 | 0.781638 | 0.390819 | − | 0.920468i | \(-0.372192\pi\) | ||||
0.390819 | + | 0.920468i | \(0.372192\pi\) | |||||||
\(332\) | −4.10313 | −0.225189 | ||||||||
\(333\) | 8.80348 | 0.482428 | ||||||||
\(334\) | 8.24936 | 0.451385 | ||||||||
\(335\) | −0.644152 | −0.0351938 | ||||||||
\(336\) | −1.87541 | −0.102312 | ||||||||
\(337\) | −12.6902 | −0.691277 | −0.345639 | − | 0.938368i | \(-0.612338\pi\) | ||||
−0.345639 | + | 0.938368i | \(0.612338\pi\) | |||||||
\(338\) | −9.22583 | −0.501819 | ||||||||
\(339\) | −1.53869 | −0.0835704 | ||||||||
\(340\) | 4.39123 | 0.238148 | ||||||||
\(341\) | −4.33748 | −0.234887 | ||||||||
\(342\) | 0.764077 | 0.0413166 | ||||||||
\(343\) | 20.0390 | 1.08200 | ||||||||
\(344\) | 0.370232 | 0.0199616 | ||||||||
\(345\) | 8.87224 | 0.477665 | ||||||||
\(346\) | −1.73141 | −0.0930809 | ||||||||
\(347\) | 20.6787 | 1.11009 | 0.555046 | − | 0.831819i | \(-0.312701\pi\) | ||||
0.555046 | + | 0.831819i | \(0.312701\pi\) | |||||||
\(348\) | 10.2082 | 0.547216 | ||||||||
\(349\) | 32.4140 | 1.73508 | 0.867540 | − | 0.497367i | \(-0.165700\pi\) | ||||
0.867540 | + | 0.497367i | \(0.165700\pi\) | |||||||
\(350\) | −6.63503 | −0.354657 | ||||||||
\(351\) | −0.853656 | −0.0455648 | ||||||||
\(352\) | −16.8497 | −0.898090 | ||||||||
\(353\) | 1.31973 | 0.0702419 | 0.0351210 | − | 0.999383i | \(-0.488818\pi\) | ||||
0.0351210 | + | 0.999383i | \(0.488818\pi\) | |||||||
\(354\) | −7.38985 | −0.392766 | ||||||||
\(355\) | −14.2818 | −0.757997 | ||||||||
\(356\) | 20.5671 | 1.09005 | ||||||||
\(357\) | 2.02078 | 0.106951 | ||||||||
\(358\) | 19.4153 | 1.02613 | ||||||||
\(359\) | 15.0592 | 0.794793 | 0.397397 | − | 0.917647i | \(-0.369914\pi\) | ||||
0.397397 | + | 0.917647i | \(0.369914\pi\) | |||||||
\(360\) | −7.90349 | −0.416550 | ||||||||
\(361\) | −17.9671 | −0.945639 | ||||||||
\(362\) | −11.5926 | −0.609292 | ||||||||
\(363\) | −2.73904 | −0.143762 | ||||||||
\(364\) | −2.47503 | −0.129727 | ||||||||
\(365\) | 14.9822 | 0.784204 | ||||||||
\(366\) | −6.34787 | −0.331808 | ||||||||
\(367\) | −28.1666 | −1.47028 | −0.735142 | − | 0.677913i | \(-0.762885\pi\) | ||||
−0.735142 | + | 0.677913i | \(0.762885\pi\) | |||||||
\(368\) | 2.69032 | 0.140243 | ||||||||
\(369\) | 4.79907 | 0.249830 | ||||||||
\(370\) | 20.2571 | 1.05311 | ||||||||
\(371\) | 15.7935 | 0.819957 | ||||||||
\(372\) | −2.16522 | −0.112261 | ||||||||
\(373\) | 7.41684 | 0.384029 | 0.192015 | − | 0.981392i | \(-0.438498\pi\) | ||||
0.192015 | + | 0.981392i | \(0.438498\pi\) | |||||||
\(374\) | 2.16088 | 0.111737 | ||||||||
\(375\) | −1.93657 | −0.100004 | ||||||||
\(376\) | 18.0432 | 0.930506 | ||||||||
\(377\) | 6.07367 | 0.312810 | ||||||||
\(378\) | −1.51927 | −0.0781427 | ||||||||
\(379\) | 13.0462 | 0.670136 | 0.335068 | − | 0.942194i | \(-0.391241\pi\) | ||||
0.335068 | + | 0.942194i | \(0.391241\pi\) | |||||||
\(380\) | −4.46280 | −0.228937 | ||||||||
\(381\) | 8.04162 | 0.411985 | ||||||||
\(382\) | −11.6316 | −0.595124 | ||||||||
\(383\) | 25.6727 | 1.31181 | 0.655907 | − | 0.754842i | \(-0.272286\pi\) | ||||
0.655907 | + | 0.754842i | \(0.272286\pi\) | |||||||
\(384\) | −9.80664 | −0.500443 | ||||||||
\(385\) | 17.7762 | 0.905961 | ||||||||
\(386\) | 1.45070 | 0.0738388 | ||||||||
\(387\) | −0.143371 | −0.00728796 | ||||||||
\(388\) | −15.8649 | −0.805417 | ||||||||
\(389\) | −25.2878 | −1.28214 | −0.641070 | − | 0.767482i | \(-0.721509\pi\) | ||||
−0.641070 | + | 0.767482i | \(0.721509\pi\) | |||||||
\(390\) | −1.96429 | −0.0994655 | ||||||||
\(391\) | −2.89886 | −0.146602 | ||||||||
\(392\) | 7.53128 | 0.380387 | ||||||||
\(393\) | −18.0424 | −0.910121 | ||||||||
\(394\) | 19.3953 | 0.977119 | ||||||||
\(395\) | 45.1208 | 2.27027 | ||||||||
\(396\) | 4.12378 | 0.207228 | ||||||||
\(397\) | 8.37457 | 0.420308 | 0.210154 | − | 0.977668i | \(-0.432604\pi\) | ||||
0.210154 | + | 0.977668i | \(0.432604\pi\) | |||||||
\(398\) | 10.3197 | 0.517281 | ||||||||
\(399\) | −2.05371 | −0.102814 | ||||||||
\(400\) | 4.05309 | 0.202654 | ||||||||
\(401\) | −21.8688 | −1.09207 | −0.546037 | − | 0.837761i | \(-0.683864\pi\) | ||||
−0.546037 | + | 0.837761i | \(0.683864\pi\) | |||||||
\(402\) | −0.158233 | −0.00789196 | ||||||||
\(403\) | −1.28826 | −0.0641729 | ||||||||
\(404\) | 12.7256 | 0.633120 | ||||||||
\(405\) | 3.06060 | 0.152082 | ||||||||
\(406\) | 10.8094 | 0.536463 | ||||||||
\(407\) | −25.3029 | −1.25422 | ||||||||
\(408\) | 2.58233 | 0.127845 | ||||||||
\(409\) | −16.1805 | −0.800076 | −0.400038 | − | 0.916499i | \(-0.631003\pi\) | ||||
−0.400038 | + | 0.916499i | \(0.631003\pi\) | |||||||
\(410\) | 11.0428 | 0.545365 | ||||||||
\(411\) | −17.1264 | −0.844783 | ||||||||
\(412\) | 23.7438 | 1.16977 | ||||||||
\(413\) | 19.8627 | 0.977379 | ||||||||
\(414\) | 2.17943 | 0.107113 | ||||||||
\(415\) | 8.75270 | 0.429653 | ||||||||
\(416\) | −5.00448 | −0.245365 | ||||||||
\(417\) | 7.56541 | 0.370480 | ||||||||
\(418\) | −2.19610 | −0.107415 | ||||||||
\(419\) | −26.4661 | −1.29295 | −0.646476 | − | 0.762934i | \(-0.723758\pi\) | ||||
−0.646476 | + | 0.762934i | \(0.723758\pi\) | |||||||
\(420\) | 8.87369 | 0.432992 | ||||||||
\(421\) | −17.0950 | −0.833160 | −0.416580 | − | 0.909099i | \(-0.636771\pi\) | ||||
−0.416580 | + | 0.909099i | \(0.636771\pi\) | |||||||
\(422\) | −11.3679 | −0.553380 | ||||||||
\(423\) | −6.98716 | −0.339727 | ||||||||
\(424\) | 20.1824 | 0.980142 | ||||||||
\(425\) | −4.36726 | −0.211843 | ||||||||
\(426\) | −3.50826 | −0.169976 | ||||||||
\(427\) | 17.0620 | 0.825689 | ||||||||
\(428\) | 10.0613 | 0.486330 | ||||||||
\(429\) | 2.45357 | 0.118459 | ||||||||
\(430\) | −0.329901 | −0.0159092 | ||||||||
\(431\) | −0.112786 | −0.00543270 | −0.00271635 | − | 0.999996i | \(-0.500865\pi\) | ||||
−0.00271635 | + | 0.999996i | \(0.500865\pi\) | |||||||
\(432\) | 0.928063 | 0.0446514 | ||||||||
\(433\) | 19.1178 | 0.918744 | 0.459372 | − | 0.888244i | \(-0.348075\pi\) | ||||
0.459372 | + | 0.888244i | \(0.348075\pi\) | |||||||
\(434\) | −2.29275 | −0.110055 | ||||||||
\(435\) | −21.7758 | −1.04407 | ||||||||
\(436\) | 18.3867 | 0.880565 | ||||||||
\(437\) | 2.94611 | 0.140931 | ||||||||
\(438\) | 3.68032 | 0.175852 | ||||||||
\(439\) | 10.6889 | 0.510155 | 0.255078 | − | 0.966921i | \(-0.417899\pi\) | ||||
0.255078 | + | 0.966921i | \(0.417899\pi\) | |||||||
\(440\) | 22.7161 | 1.08295 | ||||||||
\(441\) | −2.91646 | −0.138879 | ||||||||
\(442\) | 0.641799 | 0.0305272 | ||||||||
\(443\) | −18.4793 | −0.877979 | −0.438990 | − | 0.898492i | \(-0.644664\pi\) | ||||
−0.438990 | + | 0.898492i | \(0.644664\pi\) | |||||||
\(444\) | −12.6309 | −0.599436 | ||||||||
\(445\) | −43.8732 | −2.07979 | ||||||||
\(446\) | 3.44107 | 0.162939 | ||||||||
\(447\) | −18.9859 | −0.898001 | ||||||||
\(448\) | −5.15575 | −0.243586 | ||||||||
\(449\) | 1.83557 | 0.0866259 | 0.0433130 | − | 0.999062i | \(-0.486209\pi\) | ||||
0.0433130 | + | 0.999062i | \(0.486209\pi\) | |||||||
\(450\) | 3.28341 | 0.154781 | ||||||||
\(451\) | −13.7934 | −0.649508 | ||||||||
\(452\) | 2.20766 | 0.103840 | ||||||||
\(453\) | −14.7577 | −0.693377 | ||||||||
\(454\) | −9.19937 | −0.431748 | ||||||||
\(455\) | 5.27968 | 0.247515 | ||||||||
\(456\) | −2.62442 | −0.122900 | ||||||||
\(457\) | 10.1289 | 0.473811 | 0.236905 | − | 0.971533i | \(-0.423867\pi\) | ||||
0.236905 | + | 0.971533i | \(0.423867\pi\) | |||||||
\(458\) | −14.1334 | −0.660409 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −12.7295 | −0.593518 | ||||||||
\(461\) | 26.6053 | 1.23913 | 0.619565 | − | 0.784945i | \(-0.287309\pi\) | ||||
0.619565 | + | 0.784945i | \(0.287309\pi\) | |||||||
\(462\) | 4.36666 | 0.203155 | ||||||||
\(463\) | −21.5160 | −0.999932 | −0.499966 | − | 0.866045i | \(-0.666654\pi\) | ||||
−0.499966 | + | 0.866045i | \(0.666654\pi\) | |||||||
\(464\) | −6.60307 | −0.306540 | ||||||||
\(465\) | 4.61879 | 0.214191 | ||||||||
\(466\) | −0.288678 | −0.0133728 | ||||||||
\(467\) | 40.6119 | 1.87930 | 0.939648 | − | 0.342142i | \(-0.111152\pi\) | ||||
0.939648 | + | 0.342142i | \(0.111152\pi\) | |||||||
\(468\) | 1.22479 | 0.0566160 | ||||||||
\(469\) | 0.425305 | 0.0196388 | ||||||||
\(470\) | −16.0777 | −0.741607 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 25.3824 | 1.16832 | ||||||||
\(473\) | 0.412076 | 0.0189473 | ||||||||
\(474\) | 11.0837 | 0.509093 | ||||||||
\(475\) | 4.43844 | 0.203650 | ||||||||
\(476\) | −2.89933 | −0.132891 | ||||||||
\(477\) | −7.81555 | −0.357849 | ||||||||
\(478\) | 2.32646 | 0.106410 | ||||||||
\(479\) | −31.9712 | −1.46080 | −0.730401 | − | 0.683019i | \(-0.760667\pi\) | ||||
−0.730401 | + | 0.683019i | \(0.760667\pi\) | |||||||
\(480\) | 17.9425 | 0.818958 | ||||||||
\(481\) | −7.51514 | −0.342661 | ||||||||
\(482\) | −11.3289 | −0.516019 | ||||||||
\(483\) | −5.85794 | −0.266546 | ||||||||
\(484\) | 3.92986 | 0.178630 | ||||||||
\(485\) | 33.8425 | 1.53671 | ||||||||
\(486\) | 0.751824 | 0.0341034 | ||||||||
\(487\) | 10.0548 | 0.455625 | 0.227812 | − | 0.973705i | \(-0.426843\pi\) | ||||
0.227812 | + | 0.973705i | \(0.426843\pi\) | |||||||
\(488\) | 21.8034 | 0.986994 | ||||||||
\(489\) | −11.2197 | −0.507371 | ||||||||
\(490\) | −6.71087 | −0.303166 | ||||||||
\(491\) | −41.8781 | −1.88993 | −0.944966 | − | 0.327168i | \(-0.893906\pi\) | ||||
−0.944966 | + | 0.327168i | \(0.893906\pi\) | |||||||
\(492\) | −6.88552 | −0.310423 | ||||||||
\(493\) | 7.11490 | 0.320439 | ||||||||
\(494\) | −0.652259 | −0.0293465 | ||||||||
\(495\) | −8.79674 | −0.395384 | ||||||||
\(496\) | 1.40055 | 0.0628866 | ||||||||
\(497\) | 9.42961 | 0.422976 | ||||||||
\(498\) | 2.15007 | 0.0963468 | ||||||||
\(499\) | −0.922947 | −0.0413168 | −0.0206584 | − | 0.999787i | \(-0.506576\pi\) | ||||
−0.0206584 | + | 0.999787i | \(0.506576\pi\) | |||||||
\(500\) | 2.77852 | 0.124259 | ||||||||
\(501\) | 10.9725 | 0.490214 | ||||||||
\(502\) | 19.8221 | 0.884703 | ||||||||
\(503\) | 4.32910 | 0.193025 | 0.0965126 | − | 0.995332i | \(-0.469231\pi\) | ||||
0.0965126 | + | 0.995332i | \(0.469231\pi\) | |||||||
\(504\) | 5.21832 | 0.232442 | ||||||||
\(505\) | −27.1459 | −1.20797 | ||||||||
\(506\) | −6.26409 | −0.278473 | ||||||||
\(507\) | −12.2713 | −0.544986 | ||||||||
\(508\) | −11.5378 | −0.511908 | ||||||||
\(509\) | −10.0863 | −0.447069 | −0.223535 | − | 0.974696i | \(-0.571760\pi\) | ||||
−0.223535 | + | 0.974696i | \(0.571760\pi\) | |||||||
\(510\) | −2.30103 | −0.101891 | ||||||||
\(511\) | −9.89207 | −0.437600 | ||||||||
\(512\) | 10.2338 | 0.452275 | ||||||||
\(513\) | 1.01630 | 0.0448707 | ||||||||
\(514\) | −8.37389 | −0.369357 | ||||||||
\(515\) | −50.6497 | −2.23189 | ||||||||
\(516\) | 0.205703 | 0.00905559 | ||||||||
\(517\) | 20.0824 | 0.883224 | ||||||||
\(518\) | −13.3748 | −0.587657 | ||||||||
\(519\) | −2.30294 | −0.101088 | ||||||||
\(520\) | 6.74686 | 0.295869 | ||||||||
\(521\) | −26.0480 | −1.14118 | −0.570591 | − | 0.821235i | \(-0.693286\pi\) | ||||
−0.570591 | + | 0.821235i | \(0.693286\pi\) | |||||||
\(522\) | −5.34915 | −0.234126 | ||||||||
\(523\) | 14.5362 | 0.635625 | 0.317812 | − | 0.948154i | \(-0.397052\pi\) | ||||
0.317812 | + | 0.948154i | \(0.397052\pi\) | |||||||
\(524\) | 25.8866 | 1.13086 | ||||||||
\(525\) | −8.82525 | −0.385166 | ||||||||
\(526\) | 7.42252 | 0.323637 | ||||||||
\(527\) | −1.50911 | −0.0657380 | ||||||||
\(528\) | −2.66743 | −0.116085 | ||||||||
\(529\) | −14.5966 | −0.634636 | ||||||||
\(530\) | −17.9838 | −0.781167 | ||||||||
\(531\) | −9.82923 | −0.426552 | ||||||||
\(532\) | 2.94659 | 0.127751 | ||||||||
\(533\) | −4.09676 | −0.177450 | ||||||||
\(534\) | −10.7773 | −0.466378 | ||||||||
\(535\) | −21.4625 | −0.927904 | ||||||||
\(536\) | 0.543494 | 0.0234754 | ||||||||
\(537\) | 25.8243 | 1.11440 | ||||||||
\(538\) | 15.8813 | 0.684692 | ||||||||
\(539\) | 8.38247 | 0.361058 | ||||||||
\(540\) | −4.39123 | −0.188968 | ||||||||
\(541\) | 34.6129 | 1.48813 | 0.744063 | − | 0.668110i | \(-0.232896\pi\) | ||||
0.744063 | + | 0.668110i | \(0.232896\pi\) | |||||||
\(542\) | 14.7443 | 0.633321 | ||||||||
\(543\) | −15.4193 | −0.661704 | ||||||||
\(544\) | −5.86241 | −0.251349 | ||||||||
\(545\) | −39.2221 | −1.68009 | ||||||||
\(546\) | 1.29693 | 0.0555035 | ||||||||
\(547\) | −2.33926 | −0.100020 | −0.0500098 | − | 0.998749i | \(-0.515925\pi\) | ||||
−0.0500098 | + | 0.998749i | \(0.515925\pi\) | |||||||
\(548\) | 24.5723 | 1.04968 | ||||||||
\(549\) | −8.44330 | −0.360351 | ||||||||
\(550\) | −9.43713 | −0.402401 | ||||||||
\(551\) | −7.23086 | −0.308045 | ||||||||
\(552\) | −7.48582 | −0.318618 | ||||||||
\(553\) | −29.7913 | −1.26685 | ||||||||
\(554\) | 4.01835 | 0.170723 | ||||||||
\(555\) | 26.9439 | 1.14371 | ||||||||
\(556\) | −10.8546 | −0.460336 | ||||||||
\(557\) | −15.0977 | −0.639711 | −0.319855 | − | 0.947466i | \(-0.603634\pi\) | ||||
−0.319855 | + | 0.947466i | \(0.603634\pi\) | |||||||
\(558\) | 1.13459 | 0.0480309 | ||||||||
\(559\) | 0.122390 | 0.00517653 | ||||||||
\(560\) | −5.73987 | −0.242554 | ||||||||
\(561\) | 2.87419 | 0.121348 | ||||||||
\(562\) | 8.56690 | 0.361373 | ||||||||
\(563\) | 20.9076 | 0.881150 | 0.440575 | − | 0.897716i | \(-0.354775\pi\) | ||||
0.440575 | + | 0.897716i | \(0.354775\pi\) | |||||||
\(564\) | 10.0249 | 0.422125 | ||||||||
\(565\) | −4.70933 | −0.198123 | ||||||||
\(566\) | 13.1733 | 0.553715 | ||||||||
\(567\) | −2.02078 | −0.0848646 | ||||||||
\(568\) | 12.0500 | 0.505608 | ||||||||
\(569\) | 32.0864 | 1.34513 | 0.672566 | − | 0.740037i | \(-0.265192\pi\) | ||||
0.672566 | + | 0.740037i | \(0.265192\pi\) | |||||||
\(570\) | 2.33853 | 0.0979504 | ||||||||
\(571\) | −15.3995 | −0.644449 | −0.322225 | − | 0.946663i | \(-0.604431\pi\) | ||||
−0.322225 | + | 0.946663i | \(0.604431\pi\) | |||||||
\(572\) | −3.52028 | −0.147191 | ||||||||
\(573\) | −15.4712 | −0.646317 | ||||||||
\(574\) | −7.29107 | −0.304324 | ||||||||
\(575\) | 12.6601 | 0.527961 | ||||||||
\(576\) | 2.55137 | 0.106307 | ||||||||
\(577\) | 38.3801 | 1.59778 | 0.798892 | − | 0.601474i | \(-0.205420\pi\) | ||||
0.798892 | + | 0.601474i | \(0.205420\pi\) | |||||||
\(578\) | 0.751824 | 0.0312717 | ||||||||
\(579\) | 1.92958 | 0.0801906 | ||||||||
\(580\) | 31.2431 | 1.29730 | ||||||||
\(581\) | −5.77902 | −0.239754 | ||||||||
\(582\) | 8.31329 | 0.344597 | ||||||||
\(583\) | 22.4634 | 0.930338 | ||||||||
\(584\) | −12.6410 | −0.523088 | ||||||||
\(585\) | −2.61270 | −0.108022 | ||||||||
\(586\) | −17.4851 | −0.722303 | ||||||||
\(587\) | −26.6605 | −1.10040 | −0.550198 | − | 0.835034i | \(-0.685448\pi\) | ||||
−0.550198 | + | 0.835034i | \(0.685448\pi\) | |||||||
\(588\) | 4.18443 | 0.172563 | ||||||||
\(589\) | 1.53371 | 0.0631954 | ||||||||
\(590\) | −22.6174 | −0.931142 | ||||||||
\(591\) | 25.7976 | 1.06117 | ||||||||
\(592\) | 8.17018 | 0.335792 | ||||||||
\(593\) | −8.89584 | −0.365308 | −0.182654 | − | 0.983177i | \(-0.558469\pi\) | ||||
−0.182654 | + | 0.983177i | \(0.558469\pi\) | |||||||
\(594\) | −2.16088 | −0.0886621 | ||||||||
\(595\) | 6.18478 | 0.253551 | ||||||||
\(596\) | 27.2402 | 1.11580 | ||||||||
\(597\) | 13.7262 | 0.561778 | ||||||||
\(598\) | −1.86048 | −0.0760808 | ||||||||
\(599\) | −17.6084 | −0.719461 | −0.359731 | − | 0.933056i | \(-0.617131\pi\) | ||||
−0.359731 | + | 0.933056i | \(0.617131\pi\) | |||||||
\(600\) | −11.2777 | −0.460411 | ||||||||
\(601\) | 30.6700 | 1.25106 | 0.625528 | − | 0.780202i | \(-0.284884\pi\) | ||||
0.625528 | + | 0.780202i | \(0.284884\pi\) | |||||||
\(602\) | 0.217819 | 0.00887764 | ||||||||
\(603\) | −0.210466 | −0.00857084 | ||||||||
\(604\) | 21.1738 | 0.861549 | ||||||||
\(605\) | −8.38309 | −0.340821 | ||||||||
\(606\) | −6.66827 | −0.270880 | ||||||||
\(607\) | 18.0284 | 0.731749 | 0.365874 | − | 0.930664i | \(-0.380770\pi\) | ||||
0.365874 | + | 0.930664i | \(0.380770\pi\) | |||||||
\(608\) | 5.95796 | 0.241627 | ||||||||
\(609\) | 14.3776 | 0.582610 | ||||||||
\(610\) | −19.4283 | −0.786628 | ||||||||
\(611\) | 5.96463 | 0.241303 | ||||||||
\(612\) | 1.43476 | 0.0579968 | ||||||||
\(613\) | 16.7268 | 0.675588 | 0.337794 | − | 0.941220i | \(-0.390319\pi\) | ||||
0.337794 | + | 0.941220i | \(0.390319\pi\) | |||||||
\(614\) | −10.9246 | −0.440883 | ||||||||
\(615\) | 14.6880 | 0.592279 | ||||||||
\(616\) | −14.9984 | −0.604304 | ||||||||
\(617\) | 43.9538 | 1.76951 | 0.884757 | − | 0.466052i | \(-0.154324\pi\) | ||||
0.884757 | + | 0.466052i | \(0.154324\pi\) | |||||||
\(618\) | −12.4419 | −0.500487 | ||||||||
\(619\) | −6.86592 | −0.275965 | −0.137982 | − | 0.990435i | \(-0.544062\pi\) | ||||
−0.137982 | + | 0.990435i | \(0.544062\pi\) | |||||||
\(620\) | −6.62686 | −0.266141 | ||||||||
\(621\) | 2.89886 | 0.116327 | ||||||||
\(622\) | 6.55805 | 0.262954 | ||||||||
\(623\) | 28.9675 | 1.16056 | ||||||||
\(624\) | −0.792246 | −0.0317152 | ||||||||
\(625\) | −27.7633 | −1.11053 | ||||||||
\(626\) | −1.62624 | −0.0649978 | ||||||||
\(627\) | −2.92103 | −0.116655 | ||||||||
\(628\) | −1.43476 | −0.0572532 | ||||||||
\(629\) | −8.80348 | −0.351018 | ||||||||
\(630\) | −4.64987 | −0.185255 | ||||||||
\(631\) | −3.02352 | −0.120364 | −0.0601822 | − | 0.998187i | \(-0.519168\pi\) | ||||
−0.0601822 | + | 0.998187i | \(0.519168\pi\) | |||||||
\(632\) | −38.0700 | −1.51434 | ||||||||
\(633\) | −15.1204 | −0.600982 | ||||||||
\(634\) | 17.9243 | 0.711865 | ||||||||
\(635\) | 24.6122 | 0.976704 | ||||||||
\(636\) | 11.2134 | 0.444642 | ||||||||
\(637\) | 2.48966 | 0.0986437 | ||||||||
\(638\) | 15.3745 | 0.608681 | ||||||||
\(639\) | −4.66633 | −0.184597 | ||||||||
\(640\) | −30.0142 | −1.18641 | ||||||||
\(641\) | −23.6079 | −0.932455 | −0.466228 | − | 0.884665i | \(-0.654387\pi\) | ||||
−0.466228 | + | 0.884665i | \(0.654387\pi\) | |||||||
\(642\) | −5.27217 | −0.208076 | ||||||||
\(643\) | 10.5165 | 0.414729 | 0.207365 | − | 0.978264i | \(-0.433511\pi\) | ||||
0.207365 | + | 0.978264i | \(0.433511\pi\) | |||||||
\(644\) | 8.40475 | 0.331194 | ||||||||
\(645\) | −0.438801 | −0.0172778 | ||||||||
\(646\) | −0.764077 | −0.0300622 | ||||||||
\(647\) | −12.8500 | −0.505185 | −0.252592 | − | 0.967573i | \(-0.581283\pi\) | ||||
−0.252592 | + | 0.967573i | \(0.581283\pi\) | |||||||
\(648\) | −2.58233 | −0.101444 | ||||||||
\(649\) | 28.2511 | 1.10895 | ||||||||
\(650\) | −2.80290 | −0.109939 | ||||||||
\(651\) | −3.04958 | −0.119522 | ||||||||
\(652\) | 16.0976 | 0.630429 | ||||||||
\(653\) | 36.2697 | 1.41934 | 0.709671 | − | 0.704534i | \(-0.248844\pi\) | ||||
0.709671 | + | 0.704534i | \(0.248844\pi\) | |||||||
\(654\) | −9.63476 | −0.376749 | ||||||||
\(655\) | −55.2207 | −2.15765 | ||||||||
\(656\) | 4.45384 | 0.173893 | ||||||||
\(657\) | 4.89518 | 0.190979 | ||||||||
\(658\) | 10.6154 | 0.413830 | ||||||||
\(659\) | 27.0551 | 1.05392 | 0.526959 | − | 0.849891i | \(-0.323332\pi\) | ||||
0.526959 | + | 0.849891i | \(0.323332\pi\) | |||||||
\(660\) | 12.6212 | 0.491280 | ||||||||
\(661\) | −32.8042 | −1.27593 | −0.637967 | − | 0.770063i | \(-0.720224\pi\) | ||||
−0.637967 | + | 0.770063i | \(0.720224\pi\) | |||||||
\(662\) | 10.6914 | 0.415534 | ||||||||
\(663\) | 0.853656 | 0.0331532 | ||||||||
\(664\) | −7.38496 | −0.286592 | ||||||||
\(665\) | −6.28559 | −0.243745 | ||||||||
\(666\) | 6.61866 | 0.256468 | ||||||||
\(667\) | −20.6251 | −0.798606 | ||||||||
\(668\) | −15.7429 | −0.609110 | ||||||||
\(669\) | 4.57697 | 0.176956 | ||||||||
\(670\) | −0.484289 | −0.0187097 | ||||||||
\(671\) | 24.2676 | 0.936842 | ||||||||
\(672\) | −11.8466 | −0.456993 | ||||||||
\(673\) | 13.7099 | 0.528478 | 0.264239 | − | 0.964457i | \(-0.414879\pi\) | ||||
0.264239 | + | 0.964457i | \(0.414879\pi\) | |||||||
\(674\) | −9.54076 | −0.367497 | ||||||||
\(675\) | 4.36726 | 0.168096 | ||||||||
\(676\) | 17.6063 | 0.677167 | ||||||||
\(677\) | 39.3539 | 1.51249 | 0.756247 | − | 0.654286i | \(-0.227031\pi\) | ||||
0.756247 | + | 0.654286i | \(0.227031\pi\) | |||||||
\(678\) | −1.15683 | −0.0444277 | ||||||||
\(679\) | −22.3447 | −0.857512 | ||||||||
\(680\) | 7.90349 | 0.303085 | ||||||||
\(681\) | −12.2361 | −0.468888 | ||||||||
\(682\) | −3.26102 | −0.124871 | ||||||||
\(683\) | −9.69517 | −0.370975 | −0.185488 | − | 0.982647i | \(-0.559386\pi\) | ||||
−0.185488 | + | 0.982647i | \(0.559386\pi\) | |||||||
\(684\) | −1.45815 | −0.0557536 | ||||||||
\(685\) | −52.4170 | −2.00275 | ||||||||
\(686\) | 15.0658 | 0.575213 | ||||||||
\(687\) | −18.7988 | −0.717218 | ||||||||
\(688\) | −0.133057 | −0.00507277 | ||||||||
\(689\) | 6.67179 | 0.254175 | ||||||||
\(690\) | 6.67036 | 0.253936 | ||||||||
\(691\) | −3.36504 | −0.128012 | −0.0640060 | − | 0.997950i | \(-0.520388\pi\) | ||||
−0.0640060 | + | 0.997950i | \(0.520388\pi\) | |||||||
\(692\) | 3.30417 | 0.125606 | ||||||||
\(693\) | 5.80809 | 0.220631 | ||||||||
\(694\) | 15.5468 | 0.590147 | ||||||||
\(695\) | 23.1547 | 0.878307 | ||||||||
\(696\) | 18.3730 | 0.696428 | ||||||||
\(697\) | −4.79907 | −0.181778 | ||||||||
\(698\) | 24.3696 | 0.922403 | ||||||||
\(699\) | −0.383971 | −0.0145231 | ||||||||
\(700\) | 12.6621 | 0.478583 | ||||||||
\(701\) | −38.0574 | −1.43741 | −0.718704 | − | 0.695316i | \(-0.755264\pi\) | ||||
−0.718704 | + | 0.695316i | \(0.755264\pi\) | |||||||
\(702\) | −0.641799 | −0.0242231 | ||||||||
\(703\) | 8.94697 | 0.337441 | ||||||||
\(704\) | −7.33312 | −0.276377 | ||||||||
\(705\) | −21.3849 | −0.805401 | ||||||||
\(706\) | 0.992201 | 0.0373420 | ||||||||
\(707\) | 17.9232 | 0.674071 | ||||||||
\(708\) | 14.1026 | 0.530008 | ||||||||
\(709\) | −48.8365 | −1.83409 | −0.917046 | − | 0.398782i | \(-0.869433\pi\) | ||||
−0.917046 | + | 0.398782i | \(0.869433\pi\) | |||||||
\(710\) | −10.7374 | −0.402966 | ||||||||
\(711\) | 14.7425 | 0.552886 | ||||||||
\(712\) | 37.0173 | 1.38728 | ||||||||
\(713\) | 4.37470 | 0.163834 | ||||||||
\(714\) | 1.51927 | 0.0568571 | ||||||||
\(715\) | 7.50938 | 0.280835 | ||||||||
\(716\) | −37.0518 | −1.38469 | ||||||||
\(717\) | 3.09443 | 0.115564 | ||||||||
\(718\) | 11.3218 | 0.422528 | ||||||||
\(719\) | 44.2936 | 1.65187 | 0.825936 | − | 0.563764i | \(-0.190647\pi\) | ||||
0.825936 | + | 0.563764i | \(0.190647\pi\) | |||||||
\(720\) | 2.84043 | 0.105856 | ||||||||
\(721\) | 33.4418 | 1.24544 | ||||||||
\(722\) | −13.5081 | −0.502720 | ||||||||
\(723\) | −15.0686 | −0.560408 | ||||||||
\(724\) | 22.1230 | 0.822194 | ||||||||
\(725\) | −31.0726 | −1.15401 | ||||||||
\(726\) | −2.05927 | −0.0764268 | ||||||||
\(727\) | −47.8295 | −1.77390 | −0.886950 | − | 0.461866i | \(-0.847180\pi\) | ||||
−0.886950 | + | 0.461866i | \(0.847180\pi\) | |||||||
\(728\) | −4.45465 | −0.165100 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 11.2640 | 0.416898 | ||||||||
\(731\) | 0.143371 | 0.00530277 | ||||||||
\(732\) | 12.1141 | 0.447751 | ||||||||
\(733\) | −33.2681 | −1.22878 | −0.614392 | − | 0.789001i | \(-0.710599\pi\) | ||||
−0.614392 | + | 0.789001i | \(0.710599\pi\) | |||||||
\(734\) | −21.1763 | −0.781632 | ||||||||
\(735\) | −8.92612 | −0.329245 | ||||||||
\(736\) | 16.9943 | 0.626418 | ||||||||
\(737\) | 0.604919 | 0.0222825 | ||||||||
\(738\) | 3.60806 | 0.132814 | ||||||||
\(739\) | 6.69262 | 0.246192 | 0.123096 | − | 0.992395i | \(-0.460718\pi\) | ||||
0.123096 | + | 0.992395i | \(0.460718\pi\) | |||||||
\(740\) | −38.6581 | −1.42110 | ||||||||
\(741\) | −0.867569 | −0.0318710 | ||||||||
\(742\) | 11.8739 | 0.435905 | ||||||||
\(743\) | −43.5418 | −1.59739 | −0.798697 | − | 0.601733i | \(-0.794477\pi\) | ||||
−0.798697 | + | 0.601733i | \(0.794477\pi\) | |||||||
\(744\) | −3.89703 | −0.142872 | ||||||||
\(745\) | −58.1081 | −2.12892 | ||||||||
\(746\) | 5.57615 | 0.204157 | ||||||||
\(747\) | 2.85980 | 0.104635 | ||||||||
\(748\) | −4.12378 | −0.150780 | ||||||||
\(749\) | 14.1707 | 0.517787 | ||||||||
\(750\) | −1.45596 | −0.0531641 | ||||||||
\(751\) | 1.41177 | 0.0515162 | 0.0257581 | − | 0.999668i | \(-0.491800\pi\) | ||||
0.0257581 | + | 0.999668i | \(0.491800\pi\) | |||||||
\(752\) | −6.48452 | −0.236466 | ||||||||
\(753\) | 26.3654 | 0.960807 | ||||||||
\(754\) | 4.56633 | 0.166296 | ||||||||
\(755\) | −45.1674 | −1.64381 | ||||||||
\(756\) | 2.89933 | 0.105448 | ||||||||
\(757\) | −2.95780 | −0.107503 | −0.0537516 | − | 0.998554i | \(-0.517118\pi\) | ||||
−0.0537516 | + | 0.998554i | \(0.517118\pi\) | |||||||
\(758\) | 9.80841 | 0.356257 | ||||||||
\(759\) | −8.33187 | −0.302428 | ||||||||
\(760\) | −8.03230 | −0.291362 | ||||||||
\(761\) | 17.3738 | 0.629798 | 0.314899 | − | 0.949125i | \(-0.398029\pi\) | ||||
0.314899 | + | 0.949125i | \(0.398029\pi\) | |||||||
\(762\) | 6.04588 | 0.219019 | ||||||||
\(763\) | 25.8966 | 0.937521 | ||||||||
\(764\) | 22.1974 | 0.803075 | ||||||||
\(765\) | −3.06060 | −0.110656 | ||||||||
\(766\) | 19.3013 | 0.697386 | ||||||||
\(767\) | 8.39078 | 0.302974 | ||||||||
\(768\) | −12.4756 | −0.450175 | ||||||||
\(769\) | −12.3801 | −0.446438 | −0.223219 | − | 0.974768i | \(-0.571656\pi\) | ||||
−0.223219 | + | 0.974768i | \(0.571656\pi\) | |||||||
\(770\) | 13.3646 | 0.481626 | ||||||||
\(771\) | −11.1381 | −0.401129 | ||||||||
\(772\) | −2.76848 | −0.0996400 | ||||||||
\(773\) | 7.23875 | 0.260360 | 0.130180 | − | 0.991490i | \(-0.458445\pi\) | ||||
0.130180 | + | 0.991490i | \(0.458445\pi\) | |||||||
\(774\) | −0.107790 | −0.00387442 | ||||||||
\(775\) | 6.59068 | 0.236744 | ||||||||
\(776\) | −28.5542 | −1.02503 | ||||||||
\(777\) | −17.7899 | −0.638208 | ||||||||
\(778\) | −19.0119 | −0.681611 | ||||||||
\(779\) | 4.87729 | 0.174747 | ||||||||
\(780\) | 3.74860 | 0.134221 | ||||||||
\(781\) | 13.4119 | 0.479916 | ||||||||
\(782\) | −2.17943 | −0.0779363 | ||||||||
\(783\) | −7.11490 | −0.254266 | ||||||||
\(784\) | −2.70666 | −0.0966665 | ||||||||
\(785\) | 3.06060 | 0.109237 | ||||||||
\(786\) | −13.5647 | −0.483838 | ||||||||
\(787\) | 5.70181 | 0.203248 | 0.101624 | − | 0.994823i | \(-0.467596\pi\) | ||||
0.101624 | + | 0.994823i | \(0.467596\pi\) | |||||||
\(788\) | −37.0134 | −1.31855 | ||||||||
\(789\) | 9.87268 | 0.351477 | ||||||||
\(790\) | 33.9229 | 1.20692 | ||||||||
\(791\) | 3.10936 | 0.110556 | ||||||||
\(792\) | 7.42212 | 0.263733 | ||||||||
\(793\) | 7.20767 | 0.255952 | ||||||||
\(794\) | 6.29620 | 0.223444 | ||||||||
\(795\) | −23.9203 | −0.848364 | ||||||||
\(796\) | −19.6939 | −0.698031 | ||||||||
\(797\) | −30.4071 | −1.07708 | −0.538538 | − | 0.842602i | \(-0.681023\pi\) | ||||
−0.538538 | + | 0.842602i | \(0.681023\pi\) | |||||||
\(798\) | −1.54403 | −0.0546580 | ||||||||
\(799\) | 6.98716 | 0.247188 | ||||||||
\(800\) | 25.6026 | 0.905190 | ||||||||
\(801\) | −14.3348 | −0.506497 | ||||||||
\(802\) | −16.4415 | −0.580568 | ||||||||
\(803\) | −14.0697 | −0.496508 | ||||||||
\(804\) | 0.301969 | 0.0106496 | ||||||||
\(805\) | −17.9288 | −0.631908 | ||||||||
\(806\) | −0.968546 | −0.0341156 | ||||||||
\(807\) | 21.1237 | 0.743590 | ||||||||
\(808\) | 22.9039 | 0.805757 | ||||||||
\(809\) | 4.41526 | 0.155232 | 0.0776161 | − | 0.996983i | \(-0.475269\pi\) | ||||
0.0776161 | + | 0.996983i | \(0.475269\pi\) | |||||||
\(810\) | 2.30103 | 0.0808499 | ||||||||
\(811\) | 52.0026 | 1.82606 | 0.913030 | − | 0.407893i | \(-0.133736\pi\) | ||||
0.913030 | + | 0.407893i | \(0.133736\pi\) | |||||||
\(812\) | −20.6284 | −0.723917 | ||||||||
\(813\) | 19.6114 | 0.687801 | ||||||||
\(814\) | −19.0233 | −0.666766 | ||||||||
\(815\) | −34.3389 | −1.20284 | ||||||||
\(816\) | −0.928063 | −0.0324887 | ||||||||
\(817\) | −0.145708 | −0.00509767 | ||||||||
\(818\) | −12.1649 | −0.425336 | ||||||||
\(819\) | 1.72505 | 0.0602780 | ||||||||
\(820\) | −21.0738 | −0.735930 | ||||||||
\(821\) | −53.0794 | −1.85249 | −0.926243 | − | 0.376928i | \(-0.876980\pi\) | ||||
−0.926243 | + | 0.376928i | \(0.876980\pi\) | |||||||
\(822\) | −12.8760 | −0.449103 | ||||||||
\(823\) | 21.6924 | 0.756150 | 0.378075 | − | 0.925775i | \(-0.376586\pi\) | ||||
0.378075 | + | 0.925775i | \(0.376586\pi\) | |||||||
\(824\) | 42.7350 | 1.48874 | ||||||||
\(825\) | −12.5523 | −0.437016 | ||||||||
\(826\) | 14.9332 | 0.519594 | ||||||||
\(827\) | −29.6985 | −1.03272 | −0.516359 | − | 0.856372i | \(-0.672713\pi\) | ||||
−0.516359 | + | 0.856372i | \(0.672713\pi\) | |||||||
\(828\) | −4.15917 | −0.144541 | ||||||||
\(829\) | 43.3733 | 1.50642 | 0.753209 | − | 0.657781i | \(-0.228505\pi\) | ||||
0.753209 | + | 0.657781i | \(0.228505\pi\) | |||||||
\(830\) | 6.58049 | 0.228412 | ||||||||
\(831\) | 5.34480 | 0.185409 | ||||||||
\(832\) | −2.17799 | −0.0755083 | ||||||||
\(833\) | 2.91646 | 0.101049 | ||||||||
\(834\) | 5.68785 | 0.196954 | ||||||||
\(835\) | 33.5823 | 1.16216 | ||||||||
\(836\) | 4.19099 | 0.144948 | ||||||||
\(837\) | 1.50911 | 0.0521626 | ||||||||
\(838\) | −19.8978 | −0.687359 | ||||||||
\(839\) | −13.8906 | −0.479557 | −0.239779 | − | 0.970828i | \(-0.577075\pi\) | ||||
−0.239779 | + | 0.970828i | \(0.577075\pi\) | |||||||
\(840\) | 15.9712 | 0.551058 | ||||||||
\(841\) | 21.6218 | 0.745578 | ||||||||
\(842\) | −12.8524 | −0.442924 | ||||||||
\(843\) | 11.3948 | 0.392459 | ||||||||
\(844\) | 21.6942 | 0.746745 | ||||||||
\(845\) | −37.5574 | −1.29201 | ||||||||
\(846\) | −5.25311 | −0.180606 | ||||||||
\(847\) | 5.53498 | 0.190184 | ||||||||
\(848\) | −7.25332 | −0.249080 | ||||||||
\(849\) | 17.5218 | 0.601346 | ||||||||
\(850\) | −3.28341 | −0.112620 | ||||||||
\(851\) | 25.5200 | 0.874816 | ||||||||
\(852\) | 6.69507 | 0.229369 | ||||||||
\(853\) | 21.0813 | 0.721810 | 0.360905 | − | 0.932603i | \(-0.382468\pi\) | ||||
0.360905 | + | 0.932603i | \(0.382468\pi\) | |||||||
\(854\) | 12.8276 | 0.438952 | ||||||||
\(855\) | 3.11048 | 0.106376 | ||||||||
\(856\) | 18.1087 | 0.618941 | ||||||||
\(857\) | −25.1539 | −0.859242 | −0.429621 | − | 0.903009i | \(-0.641353\pi\) | ||||
−0.429621 | + | 0.903009i | \(0.641353\pi\) | |||||||
\(858\) | 1.84465 | 0.0629753 | ||||||||
\(859\) | 26.6151 | 0.908096 | 0.454048 | − | 0.890977i | \(-0.349980\pi\) | ||||
0.454048 | + | 0.890977i | \(0.349980\pi\) | |||||||
\(860\) | 0.629575 | 0.0214683 | ||||||||
\(861\) | −9.69785 | −0.330502 | ||||||||
\(862\) | −0.0847950 | −0.00288813 | ||||||||
\(863\) | 1.47149 | 0.0500901 | 0.0250450 | − | 0.999686i | \(-0.492027\pi\) | ||||
0.0250450 | + | 0.999686i | \(0.492027\pi\) | |||||||
\(864\) | 5.86241 | 0.199443 | ||||||||
\(865\) | −7.04838 | −0.239652 | ||||||||
\(866\) | 14.3732 | 0.488422 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 4.37542 | 0.148511 | ||||||||
\(869\) | −42.3727 | −1.43739 | ||||||||
\(870\) | −16.3716 | −0.555049 | ||||||||
\(871\) | 0.179666 | 0.00608774 | ||||||||
\(872\) | 33.0931 | 1.12067 | ||||||||
\(873\) | 11.0575 | 0.374240 | ||||||||
\(874\) | 2.21495 | 0.0749219 | ||||||||
\(875\) | 3.91337 | 0.132296 | ||||||||
\(876\) | −7.02342 | −0.237299 | ||||||||
\(877\) | −49.4100 | −1.66846 | −0.834228 | − | 0.551420i | \(-0.814086\pi\) | ||||
−0.834228 | + | 0.551420i | \(0.814086\pi\) | |||||||
\(878\) | 8.03619 | 0.271208 | ||||||||
\(879\) | −23.2569 | −0.784436 | ||||||||
\(880\) | −8.16392 | −0.275206 | ||||||||
\(881\) | −40.5718 | −1.36690 | −0.683449 | − | 0.729998i | \(-0.739521\pi\) | ||||
−0.683449 | + | 0.729998i | \(0.739521\pi\) | |||||||
\(882\) | −2.19267 | −0.0738309 | ||||||||
\(883\) | 48.6389 | 1.63683 | 0.818415 | − | 0.574627i | \(-0.194853\pi\) | ||||
0.818415 | + | 0.574627i | \(0.194853\pi\) | |||||||
\(884\) | −1.22479 | −0.0411942 | ||||||||
\(885\) | −30.0833 | −1.01124 | ||||||||
\(886\) | −13.8932 | −0.466751 | ||||||||
\(887\) | −5.97463 | −0.200609 | −0.100304 | − | 0.994957i | \(-0.531982\pi\) | ||||
−0.100304 | + | 0.994957i | \(0.531982\pi\) | |||||||
\(888\) | −22.7335 | −0.762887 | ||||||||
\(889\) | −16.2503 | −0.545018 | ||||||||
\(890\) | −32.9849 | −1.10566 | ||||||||
\(891\) | −2.87419 | −0.0962890 | ||||||||
\(892\) | −6.56685 | −0.219875 | ||||||||
\(893\) | −7.10104 | −0.237627 | ||||||||
\(894\) | −14.2740 | −0.477395 | ||||||||
\(895\) | 79.0379 | 2.64195 | ||||||||
\(896\) | 19.8170 | 0.662040 | ||||||||
\(897\) | −2.47463 | −0.0826254 | ||||||||
\(898\) | 1.38003 | 0.0460520 | ||||||||
\(899\) | −10.7372 | −0.358105 | ||||||||
\(900\) | −6.26597 | −0.208866 | ||||||||
\(901\) | 7.81555 | 0.260374 | ||||||||
\(902\) | −10.3702 | −0.345291 | ||||||||
\(903\) | 0.289721 | 0.00964131 | ||||||||
\(904\) | 3.97342 | 0.132154 | ||||||||
\(905\) | −47.1922 | −1.56872 | ||||||||
\(906\) | −11.0952 | −0.368613 | ||||||||
\(907\) | −31.7784 | −1.05519 | −0.527593 | − | 0.849497i | \(-0.676905\pi\) | ||||
−0.527593 | + | 0.849497i | \(0.676905\pi\) | |||||||
\(908\) | 17.5559 | 0.582612 | ||||||||
\(909\) | −8.86946 | −0.294182 | ||||||||
\(910\) | 3.96938 | 0.131584 | ||||||||
\(911\) | −9.13900 | −0.302788 | −0.151394 | − | 0.988473i | \(-0.548376\pi\) | ||||
−0.151394 | + | 0.988473i | \(0.548376\pi\) | |||||||
\(912\) | 0.943189 | 0.0312321 | ||||||||
\(913\) | −8.21961 | −0.272029 | ||||||||
\(914\) | 7.61516 | 0.251887 | ||||||||
\(915\) | −25.8415 | −0.854295 | ||||||||
\(916\) | 26.9718 | 0.891172 | ||||||||
\(917\) | 36.4597 | 1.20401 | ||||||||
\(918\) | −0.751824 | −0.0248139 | ||||||||
\(919\) | −16.2553 | −0.536212 | −0.268106 | − | 0.963389i | \(-0.586398\pi\) | ||||
−0.268106 | + | 0.963389i | \(0.586398\pi\) | |||||||
\(920\) | −22.9111 | −0.755356 | ||||||||
\(921\) | −14.5309 | −0.478808 | ||||||||
\(922\) | 20.0025 | 0.658746 | ||||||||
\(923\) | 3.98344 | 0.131117 | ||||||||
\(924\) | −8.33323 | −0.274143 | ||||||||
\(925\) | 38.4471 | 1.26413 | ||||||||
\(926\) | −16.1762 | −0.531583 | ||||||||
\(927\) | −16.5490 | −0.543539 | ||||||||
\(928\) | −41.7104 | −1.36921 | ||||||||
\(929\) | 24.6580 | 0.809003 | 0.404501 | − | 0.914537i | \(-0.367445\pi\) | ||||
0.404501 | + | 0.914537i | \(0.367445\pi\) | |||||||
\(930\) | 3.47251 | 0.113868 | ||||||||
\(931\) | −2.96400 | −0.0971411 | ||||||||
\(932\) | 0.550907 | 0.0180455 | ||||||||
\(933\) | 8.72286 | 0.285573 | ||||||||
\(934\) | 30.5330 | 0.999071 | ||||||||
\(935\) | 8.79674 | 0.287684 | ||||||||
\(936\) | 2.20442 | 0.0720539 | ||||||||
\(937\) | −12.1762 | −0.397781 | −0.198890 | − | 0.980022i | \(-0.563734\pi\) | ||||
−0.198890 | + | 0.980022i | \(0.563734\pi\) | |||||||
\(938\) | 0.319754 | 0.0104403 | ||||||||
\(939\) | −2.16307 | −0.0705890 | ||||||||
\(940\) | 30.6822 | 1.00074 | ||||||||
\(941\) | 19.3439 | 0.630592 | 0.315296 | − | 0.948993i | \(-0.397896\pi\) | ||||
0.315296 | + | 0.948993i | \(0.397896\pi\) | |||||||
\(942\) | 0.751824 | 0.0244957 | ||||||||
\(943\) | 13.9118 | 0.453032 | ||||||||
\(944\) | −9.12215 | −0.296901 | ||||||||
\(945\) | −6.18478 | −0.201191 | ||||||||
\(946\) | 0.309808 | 0.0100727 | ||||||||
\(947\) | 42.2358 | 1.37248 | 0.686239 | − | 0.727376i | \(-0.259260\pi\) | ||||
0.686239 | + | 0.727376i | \(0.259260\pi\) | |||||||
\(948\) | −21.1519 | −0.686983 | ||||||||
\(949\) | −4.17880 | −0.135650 | ||||||||
\(950\) | 3.33692 | 0.108264 | ||||||||
\(951\) | 23.8411 | 0.773101 | ||||||||
\(952\) | −5.21832 | −0.169127 | ||||||||
\(953\) | −9.78065 | −0.316826 | −0.158413 | − | 0.987373i | \(-0.550638\pi\) | ||||
−0.158413 | + | 0.987373i | \(0.550638\pi\) | |||||||
\(954\) | −5.87591 | −0.190240 | ||||||||
\(955\) | −47.3510 | −1.53224 | ||||||||
\(956\) | −4.43977 | −0.143592 | ||||||||
\(957\) | 20.4496 | 0.661040 | ||||||||
\(958\) | −24.0367 | −0.776591 | ||||||||
\(959\) | 34.6086 | 1.11757 | ||||||||
\(960\) | 7.80872 | 0.252025 | ||||||||
\(961\) | −28.7226 | −0.926535 | ||||||||
\(962\) | −5.65006 | −0.182165 | ||||||||
\(963\) | −7.01251 | −0.225975 | ||||||||
\(964\) | 21.6199 | 0.696329 | ||||||||
\(965\) | 5.90566 | 0.190110 | ||||||||
\(966\) | −4.40414 | −0.141701 | ||||||||
\(967\) | −46.3642 | −1.49097 | −0.745487 | − | 0.666520i | \(-0.767783\pi\) | ||||
−0.745487 | + | 0.666520i | \(0.767783\pi\) | |||||||
\(968\) | 7.07311 | 0.227338 | ||||||||
\(969\) | −1.01630 | −0.0326482 | ||||||||
\(970\) | 25.4436 | 0.816946 | ||||||||
\(971\) | −13.1383 | −0.421630 | −0.210815 | − | 0.977526i | \(-0.567612\pi\) | ||||
−0.210815 | + | 0.977526i | \(0.567612\pi\) | |||||||
\(972\) | −1.43476 | −0.0460200 | ||||||||
\(973\) | −15.2880 | −0.490111 | ||||||||
\(974\) | 7.55941 | 0.242219 | ||||||||
\(975\) | −3.72813 | −0.119396 | ||||||||
\(976\) | −7.83591 | −0.250821 | ||||||||
\(977\) | −35.9138 | −1.14898 | −0.574492 | − | 0.818510i | \(-0.694801\pi\) | ||||
−0.574492 | + | 0.818510i | \(0.694801\pi\) | |||||||
\(978\) | −8.43521 | −0.269728 | ||||||||
\(979\) | 41.2010 | 1.31679 | ||||||||
\(980\) | 12.8069 | 0.409100 | ||||||||
\(981\) | −12.8152 | −0.409158 | ||||||||
\(982\) | −31.4849 | −1.00472 | ||||||||
\(983\) | 0.197517 | 0.00629982 | 0.00314991 | − | 0.999995i | \(-0.498997\pi\) | ||||
0.00314991 | + | 0.999995i | \(0.498997\pi\) | |||||||
\(984\) | −12.3928 | −0.395068 | ||||||||
\(985\) | 78.9562 | 2.51575 | ||||||||
\(986\) | 5.34915 | 0.170352 | ||||||||
\(987\) | 14.1195 | 0.449428 | ||||||||
\(988\) | 1.24475 | 0.0396009 | ||||||||
\(989\) | −0.415613 | −0.0132157 | ||||||||
\(990\) | −6.61359 | −0.210194 | ||||||||
\(991\) | 9.28548 | 0.294963 | 0.147481 | − | 0.989065i | \(-0.452883\pi\) | ||||
0.147481 | + | 0.989065i | \(0.452883\pi\) | |||||||
\(992\) | 8.84704 | 0.280894 | ||||||||
\(993\) | 14.2207 | 0.451279 | ||||||||
\(994\) | 7.08941 | 0.224862 | ||||||||
\(995\) | 42.0105 | 1.33182 | ||||||||
\(996\) | −4.10313 | −0.130013 | ||||||||
\(997\) | −47.3535 | −1.49970 | −0.749850 | − | 0.661608i | \(-0.769874\pi\) | ||||
−0.749850 | + | 0.661608i | \(0.769874\pi\) | |||||||
\(998\) | −0.693894 | −0.0219648 | ||||||||
\(999\) | 8.80348 | 0.278530 |
(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 | 8007.2.a.e.1.29 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.e.1.29 | ✓ | 46 | 1.1 | even | 1 | trivial |