Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1717269744\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.220817 | 0.156142 | 0.0780708 | − | 0.996948i | \(-0.475124\pi\) | ||||
0.0780708 | + | 0.996948i | \(0.475124\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.95124 | −0.975620 | ||||||||
\(5\) | −3.79014 | −1.69500 | −0.847500 | − | 0.530795i | \(-0.821893\pi\) | ||||
−0.847500 | + | 0.530795i | \(0.821893\pi\) | |||||||
\(6\) | −0.220817 | −0.0901483 | ||||||||
\(7\) | −3.98824 | −1.50741 | −0.753707 | − | 0.657211i | \(-0.771736\pi\) | ||||
−0.753707 | + | 0.657211i | \(0.771736\pi\) | |||||||
\(8\) | −0.872503 | −0.308476 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.836928 | −0.264660 | ||||||||
\(11\) | −3.30218 | −0.995644 | −0.497822 | − | 0.867279i | \(-0.665867\pi\) | ||||
−0.497822 | + | 0.867279i | \(0.665867\pi\) | |||||||
\(12\) | 1.95124 | 0.563274 | ||||||||
\(13\) | 0.531345 | 0.147369 | 0.0736843 | − | 0.997282i | \(-0.476524\pi\) | ||||
0.0736843 | + | 0.997282i | \(0.476524\pi\) | |||||||
\(14\) | −0.880673 | −0.235370 | ||||||||
\(15\) | 3.79014 | 0.978609 | ||||||||
\(16\) | 3.70982 | 0.927454 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0.220817 | 0.0520472 | ||||||||
\(19\) | 3.84760 | 0.882700 | 0.441350 | − | 0.897335i | \(-0.354500\pi\) | ||||
0.441350 | + | 0.897335i | \(0.354500\pi\) | |||||||
\(20\) | 7.39546 | 1.65368 | ||||||||
\(21\) | 3.98824 | 0.870306 | ||||||||
\(22\) | −0.729179 | −0.155461 | ||||||||
\(23\) | 3.07235 | 0.640629 | 0.320315 | − | 0.947311i | \(-0.396211\pi\) | ||||
0.320315 | + | 0.947311i | \(0.396211\pi\) | |||||||
\(24\) | 0.872503 | 0.178099 | ||||||||
\(25\) | 9.36513 | 1.87303 | ||||||||
\(26\) | 0.117330 | 0.0230103 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 7.78201 | 1.47066 | ||||||||
\(29\) | −0.237786 | −0.0441557 | −0.0220779 | − | 0.999756i | \(-0.507028\pi\) | ||||
−0.0220779 | + | 0.999756i | \(0.507028\pi\) | |||||||
\(30\) | 0.836928 | 0.152801 | ||||||||
\(31\) | 2.26472 | 0.406755 | 0.203377 | − | 0.979100i | \(-0.434808\pi\) | ||||
0.203377 | + | 0.979100i | \(0.434808\pi\) | |||||||
\(32\) | 2.56420 | 0.453290 | ||||||||
\(33\) | 3.30218 | 0.574835 | ||||||||
\(34\) | 0.220817 | 0.0378699 | ||||||||
\(35\) | 15.1160 | 2.55507 | ||||||||
\(36\) | −1.95124 | −0.325207 | ||||||||
\(37\) | −7.01645 | −1.15350 | −0.576749 | − | 0.816922i | \(-0.695679\pi\) | ||||
−0.576749 | + | 0.816922i | \(0.695679\pi\) | |||||||
\(38\) | 0.849617 | 0.137826 | ||||||||
\(39\) | −0.531345 | −0.0850833 | ||||||||
\(40\) | 3.30690 | 0.522867 | ||||||||
\(41\) | 5.30414 | 0.828367 | 0.414183 | − | 0.910193i | \(-0.364067\pi\) | ||||
0.414183 | + | 0.910193i | \(0.364067\pi\) | |||||||
\(42\) | 0.880673 | 0.135891 | ||||||||
\(43\) | −8.66151 | −1.32087 | −0.660434 | − | 0.750884i | \(-0.729628\pi\) | ||||
−0.660434 | + | 0.750884i | \(0.729628\pi\) | |||||||
\(44\) | 6.44334 | 0.971370 | ||||||||
\(45\) | −3.79014 | −0.565000 | ||||||||
\(46\) | 0.678429 | 0.100029 | ||||||||
\(47\) | 4.19422 | 0.611790 | 0.305895 | − | 0.952065i | \(-0.401044\pi\) | ||||
0.305895 | + | 0.952065i | \(0.401044\pi\) | |||||||
\(48\) | −3.70982 | −0.535466 | ||||||||
\(49\) | 8.90607 | 1.27230 | ||||||||
\(50\) | 2.06798 | 0.292457 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −1.03678 | −0.143776 | ||||||||
\(53\) | 9.19560 | 1.26311 | 0.631556 | − | 0.775330i | \(-0.282417\pi\) | ||||
0.631556 | + | 0.775330i | \(0.282417\pi\) | |||||||
\(54\) | −0.220817 | −0.0300494 | ||||||||
\(55\) | 12.5157 | 1.68762 | ||||||||
\(56\) | 3.47975 | 0.465001 | ||||||||
\(57\) | −3.84760 | −0.509627 | ||||||||
\(58\) | −0.0525073 | −0.00689455 | ||||||||
\(59\) | −3.05737 | −0.398036 | −0.199018 | − | 0.979996i | \(-0.563775\pi\) | ||||
−0.199018 | + | 0.979996i | \(0.563775\pi\) | |||||||
\(60\) | −7.39546 | −0.954750 | ||||||||
\(61\) | −9.10515 | −1.16580 | −0.582898 | − | 0.812546i | \(-0.698081\pi\) | ||||
−0.582898 | + | 0.812546i | \(0.698081\pi\) | |||||||
\(62\) | 0.500089 | 0.0635113 | ||||||||
\(63\) | −3.98824 | −0.502471 | ||||||||
\(64\) | −6.85341 | −0.856676 | ||||||||
\(65\) | −2.01387 | −0.249790 | ||||||||
\(66\) | 0.729179 | 0.0897557 | ||||||||
\(67\) | −10.4701 | −1.27912 | −0.639561 | − | 0.768740i | \(-0.720884\pi\) | ||||
−0.639561 | + | 0.768740i | \(0.720884\pi\) | |||||||
\(68\) | −1.95124 | −0.236623 | ||||||||
\(69\) | −3.07235 | −0.369868 | ||||||||
\(70\) | 3.33787 | 0.398952 | ||||||||
\(71\) | 7.20875 | 0.855522 | 0.427761 | − | 0.903892i | \(-0.359303\pi\) | ||||
0.427761 | + | 0.903892i | \(0.359303\pi\) | |||||||
\(72\) | −0.872503 | −0.102825 | ||||||||
\(73\) | 8.40467 | 0.983693 | 0.491846 | − | 0.870682i | \(-0.336322\pi\) | ||||
0.491846 | + | 0.870682i | \(0.336322\pi\) | |||||||
\(74\) | −1.54935 | −0.180109 | ||||||||
\(75\) | −9.36513 | −1.08139 | ||||||||
\(76\) | −7.50759 | −0.861180 | ||||||||
\(77\) | 13.1699 | 1.50085 | ||||||||
\(78\) | −0.117330 | −0.0132850 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | −14.0607 | −1.57203 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.17125 | 0.129342 | ||||||||
\(83\) | −0.683764 | −0.0750528 | −0.0375264 | − | 0.999296i | \(-0.511948\pi\) | ||||
−0.0375264 | + | 0.999296i | \(0.511948\pi\) | |||||||
\(84\) | −7.78201 | −0.849087 | ||||||||
\(85\) | −3.79014 | −0.411098 | ||||||||
\(86\) | −1.91261 | −0.206242 | ||||||||
\(87\) | 0.237786 | 0.0254933 | ||||||||
\(88\) | 2.88116 | 0.307133 | ||||||||
\(89\) | −7.82109 | −0.829034 | −0.414517 | − | 0.910042i | \(-0.636049\pi\) | ||||
−0.414517 | + | 0.910042i | \(0.636049\pi\) | |||||||
\(90\) | −0.836928 | −0.0882200 | ||||||||
\(91\) | −2.11913 | −0.222145 | ||||||||
\(92\) | −5.99489 | −0.625011 | ||||||||
\(93\) | −2.26472 | −0.234840 | ||||||||
\(94\) | 0.926157 | 0.0955258 | ||||||||
\(95\) | −14.5829 | −1.49618 | ||||||||
\(96\) | −2.56420 | −0.261707 | ||||||||
\(97\) | 9.23134 | 0.937300 | 0.468650 | − | 0.883384i | \(-0.344741\pi\) | ||||
0.468650 | + | 0.883384i | \(0.344741\pi\) | |||||||
\(98\) | 1.96661 | 0.198658 | ||||||||
\(99\) | −3.30218 | −0.331881 | ||||||||
\(100\) | −18.2736 | −1.82736 | ||||||||
\(101\) | 5.24686 | 0.522082 | 0.261041 | − | 0.965328i | \(-0.415934\pi\) | ||||
0.261041 | + | 0.965328i | \(0.415934\pi\) | |||||||
\(102\) | −0.220817 | −0.0218642 | ||||||||
\(103\) | 16.9598 | 1.67110 | 0.835549 | − | 0.549416i | \(-0.185150\pi\) | ||||
0.835549 | + | 0.549416i | \(0.185150\pi\) | |||||||
\(104\) | −0.463600 | −0.0454597 | ||||||||
\(105\) | −15.1160 | −1.47517 | ||||||||
\(106\) | 2.03055 | 0.197224 | ||||||||
\(107\) | −7.74033 | −0.748286 | −0.374143 | − | 0.927371i | \(-0.622063\pi\) | ||||
−0.374143 | + | 0.927371i | \(0.622063\pi\) | |||||||
\(108\) | 1.95124 | 0.187758 | ||||||||
\(109\) | −10.0605 | −0.963618 | −0.481809 | − | 0.876276i | \(-0.660020\pi\) | ||||
−0.481809 | + | 0.876276i | \(0.660020\pi\) | |||||||
\(110\) | 2.76369 | 0.263507 | ||||||||
\(111\) | 7.01645 | 0.665972 | ||||||||
\(112\) | −14.7956 | −1.39806 | ||||||||
\(113\) | −4.81919 | −0.453352 | −0.226676 | − | 0.973970i | \(-0.572786\pi\) | ||||
−0.226676 | + | 0.973970i | \(0.572786\pi\) | |||||||
\(114\) | −0.849617 | −0.0795740 | ||||||||
\(115\) | −11.6446 | −1.08587 | ||||||||
\(116\) | 0.463977 | 0.0430792 | ||||||||
\(117\) | 0.531345 | 0.0491228 | ||||||||
\(118\) | −0.675121 | −0.0621499 | ||||||||
\(119\) | −3.98824 | −0.365601 | ||||||||
\(120\) | −3.30690 | −0.301878 | ||||||||
\(121\) | −0.0956188 | −0.00869262 | ||||||||
\(122\) | −2.01058 | −0.182029 | ||||||||
\(123\) | −5.30414 | −0.478258 | ||||||||
\(124\) | −4.41900 | −0.396838 | ||||||||
\(125\) | −16.5444 | −1.47978 | ||||||||
\(126\) | −0.880673 | −0.0784566 | ||||||||
\(127\) | 0.276862 | 0.0245675 | 0.0122838 | − | 0.999925i | \(-0.496090\pi\) | ||||
0.0122838 | + | 0.999925i | \(0.496090\pi\) | |||||||
\(128\) | −6.64175 | −0.587053 | ||||||||
\(129\) | 8.66151 | 0.762603 | ||||||||
\(130\) | −0.444697 | −0.0390025 | ||||||||
\(131\) | −7.17489 | −0.626873 | −0.313436 | − | 0.949609i | \(-0.601480\pi\) | ||||
−0.313436 | + | 0.949609i | \(0.601480\pi\) | |||||||
\(132\) | −6.44334 | −0.560821 | ||||||||
\(133\) | −15.3452 | −1.33059 | ||||||||
\(134\) | −2.31197 | −0.199724 | ||||||||
\(135\) | 3.79014 | 0.326203 | ||||||||
\(136\) | −0.872503 | −0.0748165 | ||||||||
\(137\) | 18.3482 | 1.56759 | 0.783796 | − | 0.621018i | \(-0.213281\pi\) | ||||
0.783796 | + | 0.621018i | \(0.213281\pi\) | |||||||
\(138\) | −0.678429 | −0.0577517 | ||||||||
\(139\) | −4.50301 | −0.381940 | −0.190970 | − | 0.981596i | \(-0.561163\pi\) | ||||
−0.190970 | + | 0.981596i | \(0.561163\pi\) | |||||||
\(140\) | −29.4949 | −2.49277 | ||||||||
\(141\) | −4.19422 | −0.353217 | ||||||||
\(142\) | 1.59182 | 0.133582 | ||||||||
\(143\) | −1.75460 | −0.146727 | ||||||||
\(144\) | 3.70982 | 0.309151 | ||||||||
\(145\) | 0.901241 | 0.0748440 | ||||||||
\(146\) | 1.85590 | 0.153595 | ||||||||
\(147\) | −8.90607 | −0.734560 | ||||||||
\(148\) | 13.6908 | 1.12537 | ||||||||
\(149\) | 9.59099 | 0.785724 | 0.392862 | − | 0.919597i | \(-0.371485\pi\) | ||||
0.392862 | + | 0.919597i | \(0.371485\pi\) | |||||||
\(150\) | −2.06798 | −0.168850 | ||||||||
\(151\) | 11.3043 | 0.919928 | 0.459964 | − | 0.887938i | \(-0.347862\pi\) | ||||
0.459964 | + | 0.887938i | \(0.347862\pi\) | |||||||
\(152\) | −3.35704 | −0.272292 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 2.90814 | 0.234345 | ||||||||
\(155\) | −8.58358 | −0.689450 | ||||||||
\(156\) | 1.03678 | 0.0830089 | ||||||||
\(157\) | 3.34788 | 0.267190 | 0.133595 | − | 0.991036i | \(-0.457348\pi\) | ||||
0.133595 | + | 0.991036i | \(0.457348\pi\) | |||||||
\(158\) | 0.220817 | 0.0175673 | ||||||||
\(159\) | −9.19560 | −0.729258 | ||||||||
\(160\) | −9.71866 | −0.768327 | ||||||||
\(161\) | −12.2533 | −0.965693 | ||||||||
\(162\) | 0.220817 | 0.0173491 | ||||||||
\(163\) | 21.2770 | 1.66655 | 0.833273 | − | 0.552862i | \(-0.186464\pi\) | ||||
0.833273 | + | 0.552862i | \(0.186464\pi\) | |||||||
\(164\) | −10.3496 | −0.808171 | ||||||||
\(165\) | −12.5157 | −0.974346 | ||||||||
\(166\) | −0.150987 | −0.0117189 | ||||||||
\(167\) | 14.3890 | 1.11345 | 0.556726 | − | 0.830696i | \(-0.312057\pi\) | ||||
0.556726 | + | 0.830696i | \(0.312057\pi\) | |||||||
\(168\) | −3.47975 | −0.268469 | ||||||||
\(169\) | −12.7177 | −0.978283 | ||||||||
\(170\) | −0.836928 | −0.0641895 | ||||||||
\(171\) | 3.84760 | 0.294233 | ||||||||
\(172\) | 16.9007 | 1.28866 | ||||||||
\(173\) | −9.78842 | −0.744200 | −0.372100 | − | 0.928193i | \(-0.621362\pi\) | ||||
−0.372100 | + | 0.928193i | \(0.621362\pi\) | |||||||
\(174\) | 0.0525073 | 0.00398057 | ||||||||
\(175\) | −37.3504 | −2.82342 | ||||||||
\(176\) | −12.2505 | −0.923414 | ||||||||
\(177\) | 3.05737 | 0.229806 | ||||||||
\(178\) | −1.72703 | −0.129447 | ||||||||
\(179\) | −3.00748 | −0.224789 | −0.112395 | − | 0.993664i | \(-0.535852\pi\) | ||||
−0.112395 | + | 0.993664i | \(0.535852\pi\) | |||||||
\(180\) | 7.39546 | 0.551225 | ||||||||
\(181\) | 21.9820 | 1.63391 | 0.816956 | − | 0.576701i | \(-0.195660\pi\) | ||||
0.816956 | + | 0.576701i | \(0.195660\pi\) | |||||||
\(182\) | −0.467941 | −0.0346861 | ||||||||
\(183\) | 9.10515 | 0.673072 | ||||||||
\(184\) | −2.68063 | −0.197619 | ||||||||
\(185\) | 26.5933 | 1.95518 | ||||||||
\(186\) | −0.500089 | −0.0366683 | ||||||||
\(187\) | −3.30218 | −0.241479 | ||||||||
\(188\) | −8.18393 | −0.596874 | ||||||||
\(189\) | 3.98824 | 0.290102 | ||||||||
\(190\) | −3.22017 | −0.233615 | ||||||||
\(191\) | −4.37193 | −0.316342 | −0.158171 | − | 0.987412i | \(-0.550560\pi\) | ||||
−0.158171 | + | 0.987412i | \(0.550560\pi\) | |||||||
\(192\) | 6.85341 | 0.494602 | ||||||||
\(193\) | −1.50887 | −0.108611 | −0.0543054 | − | 0.998524i | \(-0.517294\pi\) | ||||
−0.0543054 | + | 0.998524i | \(0.517294\pi\) | |||||||
\(194\) | 2.03844 | 0.146351 | ||||||||
\(195\) | 2.01387 | 0.144216 | ||||||||
\(196\) | −17.3779 | −1.24128 | ||||||||
\(197\) | 5.46718 | 0.389520 | 0.194760 | − | 0.980851i | \(-0.437607\pi\) | ||||
0.194760 | + | 0.980851i | \(0.437607\pi\) | |||||||
\(198\) | −0.729179 | −0.0518205 | ||||||||
\(199\) | 0.604992 | 0.0428868 | 0.0214434 | − | 0.999770i | \(-0.493174\pi\) | ||||
0.0214434 | + | 0.999770i | \(0.493174\pi\) | |||||||
\(200\) | −8.17110 | −0.577784 | ||||||||
\(201\) | 10.4701 | 0.738502 | ||||||||
\(202\) | 1.15860 | 0.0815187 | ||||||||
\(203\) | 0.948348 | 0.0665610 | ||||||||
\(204\) | 1.95124 | 0.136614 | ||||||||
\(205\) | −20.1034 | −1.40408 | ||||||||
\(206\) | 3.74502 | 0.260928 | ||||||||
\(207\) | 3.07235 | 0.213543 | ||||||||
\(208\) | 1.97119 | 0.136678 | ||||||||
\(209\) | −12.7055 | −0.878855 | ||||||||
\(210\) | −3.33787 | −0.230335 | ||||||||
\(211\) | −4.72652 | −0.325387 | −0.162694 | − | 0.986677i | \(-0.552018\pi\) | ||||
−0.162694 | + | 0.986677i | \(0.552018\pi\) | |||||||
\(212\) | −17.9428 | −1.23232 | ||||||||
\(213\) | −7.20875 | −0.493936 | ||||||||
\(214\) | −1.70920 | −0.116839 | ||||||||
\(215\) | 32.8283 | 2.23887 | ||||||||
\(216\) | 0.872503 | 0.0593663 | ||||||||
\(217\) | −9.03223 | −0.613148 | ||||||||
\(218\) | −2.22153 | −0.150461 | ||||||||
\(219\) | −8.40467 | −0.567935 | ||||||||
\(220\) | −24.4211 | −1.64647 | ||||||||
\(221\) | 0.531345 | 0.0357421 | ||||||||
\(222\) | 1.54935 | 0.103986 | ||||||||
\(223\) | 5.24469 | 0.351210 | 0.175605 | − | 0.984461i | \(-0.443812\pi\) | ||||
0.175605 | + | 0.984461i | \(0.443812\pi\) | |||||||
\(224\) | −10.2266 | −0.683296 | ||||||||
\(225\) | 9.36513 | 0.624342 | ||||||||
\(226\) | −1.06416 | −0.0707870 | ||||||||
\(227\) | −7.99497 | −0.530645 | −0.265323 | − | 0.964160i | \(-0.585478\pi\) | ||||
−0.265323 | + | 0.964160i | \(0.585478\pi\) | |||||||
\(228\) | 7.50759 | 0.497202 | ||||||||
\(229\) | −5.67467 | −0.374993 | −0.187496 | − | 0.982265i | \(-0.560037\pi\) | ||||
−0.187496 | + | 0.982265i | \(0.560037\pi\) | |||||||
\(230\) | −2.57134 | −0.169549 | ||||||||
\(231\) | −13.1699 | −0.866515 | ||||||||
\(232\) | 0.207469 | 0.0136210 | ||||||||
\(233\) | 25.2059 | 1.65129 | 0.825645 | − | 0.564190i | \(-0.190811\pi\) | ||||
0.825645 | + | 0.564190i | \(0.190811\pi\) | |||||||
\(234\) | 0.117330 | 0.00767012 | ||||||||
\(235\) | −15.8967 | −1.03698 | ||||||||
\(236\) | 5.96566 | 0.388331 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | −0.880673 | −0.0570856 | ||||||||
\(239\) | −2.86388 | −0.185249 | −0.0926247 | − | 0.995701i | \(-0.529526\pi\) | ||||
−0.0926247 | + | 0.995701i | \(0.529526\pi\) | |||||||
\(240\) | 14.0607 | 0.907615 | ||||||||
\(241\) | −25.3131 | −1.63056 | −0.815280 | − | 0.579067i | \(-0.803417\pi\) | ||||
−0.815280 | + | 0.579067i | \(0.803417\pi\) | |||||||
\(242\) | −0.0211143 | −0.00135728 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 17.7663 | 1.13737 | ||||||||
\(245\) | −33.7552 | −2.15654 | ||||||||
\(246\) | −1.17125 | −0.0746759 | ||||||||
\(247\) | 2.04440 | 0.130082 | ||||||||
\(248\) | −1.97597 | −0.125474 | ||||||||
\(249\) | 0.683764 | 0.0433318 | ||||||||
\(250\) | −3.65330 | −0.231055 | ||||||||
\(251\) | 8.09170 | 0.510743 | 0.255372 | − | 0.966843i | \(-0.417802\pi\) | ||||
0.255372 | + | 0.966843i | \(0.417802\pi\) | |||||||
\(252\) | 7.78201 | 0.490221 | ||||||||
\(253\) | −10.1454 | −0.637839 | ||||||||
\(254\) | 0.0611359 | 0.00383601 | ||||||||
\(255\) | 3.79014 | 0.237348 | ||||||||
\(256\) | 12.2402 | 0.765013 | ||||||||
\(257\) | 20.5050 | 1.27906 | 0.639532 | − | 0.768765i | \(-0.279128\pi\) | ||||
0.639532 | + | 0.768765i | \(0.279128\pi\) | |||||||
\(258\) | 1.91261 | 0.119074 | ||||||||
\(259\) | 27.9833 | 1.73880 | ||||||||
\(260\) | 3.92954 | 0.243700 | ||||||||
\(261\) | −0.237786 | −0.0147186 | ||||||||
\(262\) | −1.58434 | −0.0978809 | ||||||||
\(263\) | −5.60359 | −0.345532 | −0.172766 | − | 0.984963i | \(-0.555270\pi\) | ||||
−0.172766 | + | 0.984963i | \(0.555270\pi\) | |||||||
\(264\) | −2.88116 | −0.177323 | ||||||||
\(265\) | −34.8526 | −2.14098 | ||||||||
\(266\) | −3.38848 | −0.207761 | ||||||||
\(267\) | 7.82109 | 0.478643 | ||||||||
\(268\) | 20.4296 | 1.24794 | ||||||||
\(269\) | 10.5131 | 0.640995 | 0.320497 | − | 0.947249i | \(-0.396150\pi\) | ||||
0.320497 | + | 0.947249i | \(0.396150\pi\) | |||||||
\(270\) | 0.836928 | 0.0509338 | ||||||||
\(271\) | −25.1167 | −1.52573 | −0.762864 | − | 0.646559i | \(-0.776207\pi\) | ||||
−0.762864 | + | 0.646559i | \(0.776207\pi\) | |||||||
\(272\) | 3.70982 | 0.224941 | ||||||||
\(273\) | 2.11913 | 0.128256 | ||||||||
\(274\) | 4.05160 | 0.244766 | ||||||||
\(275\) | −30.9253 | −1.86487 | ||||||||
\(276\) | 5.99489 | 0.360850 | ||||||||
\(277\) | −11.0027 | −0.661089 | −0.330545 | − | 0.943790i | \(-0.607232\pi\) | ||||
−0.330545 | + | 0.943790i | \(0.607232\pi\) | |||||||
\(278\) | −0.994343 | −0.0596367 | ||||||||
\(279\) | 2.26472 | 0.135585 | ||||||||
\(280\) | −13.1887 | −0.788177 | ||||||||
\(281\) | 11.5593 | 0.689568 | 0.344784 | − | 0.938682i | \(-0.387952\pi\) | ||||
0.344784 | + | 0.938682i | \(0.387952\pi\) | |||||||
\(282\) | −0.926157 | −0.0551518 | ||||||||
\(283\) | −30.2843 | −1.80022 | −0.900108 | − | 0.435666i | \(-0.856513\pi\) | ||||
−0.900108 | + | 0.435666i | \(0.856513\pi\) | |||||||
\(284\) | −14.0660 | −0.834664 | ||||||||
\(285\) | 14.5829 | 0.863818 | ||||||||
\(286\) | −0.387445 | −0.0229101 | ||||||||
\(287\) | −21.1542 | −1.24869 | ||||||||
\(288\) | 2.56420 | 0.151097 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0.199010 | 0.0116863 | ||||||||
\(291\) | −9.23134 | −0.541150 | ||||||||
\(292\) | −16.3995 | −0.959710 | ||||||||
\(293\) | 13.2625 | 0.774804 | 0.387402 | − | 0.921911i | \(-0.373372\pi\) | ||||
0.387402 | + | 0.921911i | \(0.373372\pi\) | |||||||
\(294\) | −1.96661 | −0.114695 | ||||||||
\(295\) | 11.5878 | 0.674671 | ||||||||
\(296\) | 6.12187 | 0.355827 | ||||||||
\(297\) | 3.30218 | 0.191612 | ||||||||
\(298\) | 2.11786 | 0.122684 | ||||||||
\(299\) | 1.63248 | 0.0944086 | ||||||||
\(300\) | 18.2736 | 1.05503 | ||||||||
\(301\) | 34.5442 | 1.99109 | ||||||||
\(302\) | 2.49618 | 0.143639 | ||||||||
\(303\) | −5.24686 | −0.301424 | ||||||||
\(304\) | 14.2739 | 0.818664 | ||||||||
\(305\) | 34.5098 | 1.97602 | ||||||||
\(306\) | 0.220817 | 0.0126233 | ||||||||
\(307\) | 7.38733 | 0.421617 | 0.210809 | − | 0.977527i | \(-0.432390\pi\) | ||||
0.210809 | + | 0.977527i | \(0.432390\pi\) | |||||||
\(308\) | −25.6976 | −1.46426 | ||||||||
\(309\) | −16.9598 | −0.964809 | ||||||||
\(310\) | −1.89540 | −0.107652 | ||||||||
\(311\) | −28.7553 | −1.63056 | −0.815282 | − | 0.579064i | \(-0.803418\pi\) | ||||
−0.815282 | + | 0.579064i | \(0.803418\pi\) | |||||||
\(312\) | 0.463600 | 0.0262462 | ||||||||
\(313\) | −3.82591 | −0.216253 | −0.108127 | − | 0.994137i | \(-0.534485\pi\) | ||||
−0.108127 | + | 0.994137i | \(0.534485\pi\) | |||||||
\(314\) | 0.739269 | 0.0417194 | ||||||||
\(315\) | 15.1160 | 0.851689 | ||||||||
\(316\) | −1.95124 | −0.109766 | ||||||||
\(317\) | 11.4724 | 0.644354 | 0.322177 | − | 0.946679i | \(-0.395585\pi\) | ||||
0.322177 | + | 0.946679i | \(0.395585\pi\) | |||||||
\(318\) | −2.03055 | −0.113867 | ||||||||
\(319\) | 0.785212 | 0.0439634 | ||||||||
\(320\) | 25.9754 | 1.45207 | ||||||||
\(321\) | 7.74033 | 0.432023 | ||||||||
\(322\) | −2.70574 | −0.150785 | ||||||||
\(323\) | 3.84760 | 0.214086 | ||||||||
\(324\) | −1.95124 | −0.108402 | ||||||||
\(325\) | 4.97611 | 0.276025 | ||||||||
\(326\) | 4.69834 | 0.260217 | ||||||||
\(327\) | 10.0605 | 0.556345 | ||||||||
\(328\) | −4.62787 | −0.255532 | ||||||||
\(329\) | −16.7276 | −0.922220 | ||||||||
\(330\) | −2.76369 | −0.152136 | ||||||||
\(331\) | 13.6491 | 0.750222 | 0.375111 | − | 0.926980i | \(-0.377605\pi\) | ||||
0.375111 | + | 0.926980i | \(0.377605\pi\) | |||||||
\(332\) | 1.33419 | 0.0732230 | ||||||||
\(333\) | −7.01645 | −0.384499 | ||||||||
\(334\) | 3.17734 | 0.173856 | ||||||||
\(335\) | 39.6830 | 2.16811 | ||||||||
\(336\) | 14.7956 | 0.807168 | ||||||||
\(337\) | −14.0476 | −0.765224 | −0.382612 | − | 0.923909i | \(-0.624975\pi\) | ||||
−0.382612 | + | 0.923909i | \(0.624975\pi\) | |||||||
\(338\) | −2.80828 | −0.152751 | ||||||||
\(339\) | 4.81919 | 0.261743 | ||||||||
\(340\) | 7.39546 | 0.401075 | ||||||||
\(341\) | −7.47849 | −0.404983 | ||||||||
\(342\) | 0.849617 | 0.0459420 | ||||||||
\(343\) | −7.60185 | −0.410462 | ||||||||
\(344\) | 7.55719 | 0.407456 | ||||||||
\(345\) | 11.6446 | 0.626926 | ||||||||
\(346\) | −2.16145 | −0.116201 | ||||||||
\(347\) | −15.7903 | −0.847666 | −0.423833 | − | 0.905740i | \(-0.639316\pi\) | ||||
−0.423833 | + | 0.905740i | \(0.639316\pi\) | |||||||
\(348\) | −0.463977 | −0.0248718 | ||||||||
\(349\) | −7.55392 | −0.404352 | −0.202176 | − | 0.979349i | \(-0.564801\pi\) | ||||
−0.202176 | + | 0.979349i | \(0.564801\pi\) | |||||||
\(350\) | −8.24762 | −0.440854 | ||||||||
\(351\) | −0.531345 | −0.0283611 | ||||||||
\(352\) | −8.46744 | −0.451316 | ||||||||
\(353\) | 14.3700 | 0.764838 | 0.382419 | − | 0.923989i | \(-0.375091\pi\) | ||||
0.382419 | + | 0.923989i | \(0.375091\pi\) | |||||||
\(354\) | 0.675121 | 0.0358823 | ||||||||
\(355\) | −27.3222 | −1.45011 | ||||||||
\(356\) | 15.2608 | 0.808822 | ||||||||
\(357\) | 3.98824 | 0.211080 | ||||||||
\(358\) | −0.664103 | −0.0350989 | ||||||||
\(359\) | 6.63223 | 0.350036 | 0.175018 | − | 0.984565i | \(-0.444002\pi\) | ||||
0.175018 | + | 0.984565i | \(0.444002\pi\) | |||||||
\(360\) | 3.30690 | 0.174289 | ||||||||
\(361\) | −4.19597 | −0.220841 | ||||||||
\(362\) | 4.85401 | 0.255121 | ||||||||
\(363\) | 0.0956188 | 0.00501869 | ||||||||
\(364\) | 4.13493 | 0.216729 | ||||||||
\(365\) | −31.8549 | −1.66736 | ||||||||
\(366\) | 2.01058 | 0.105095 | ||||||||
\(367\) | −37.2812 | −1.94606 | −0.973031 | − | 0.230676i | \(-0.925906\pi\) | ||||
−0.973031 | + | 0.230676i | \(0.925906\pi\) | |||||||
\(368\) | 11.3979 | 0.594154 | ||||||||
\(369\) | 5.30414 | 0.276122 | ||||||||
\(370\) | 5.87226 | 0.305284 | ||||||||
\(371\) | −36.6743 | −1.90403 | ||||||||
\(372\) | 4.41900 | 0.229115 | ||||||||
\(373\) | 30.2400 | 1.56577 | 0.782885 | − | 0.622167i | \(-0.213747\pi\) | ||||
0.782885 | + | 0.622167i | \(0.213747\pi\) | |||||||
\(374\) | −0.729179 | −0.0377049 | ||||||||
\(375\) | 16.5444 | 0.854351 | ||||||||
\(376\) | −3.65947 | −0.188723 | ||||||||
\(377\) | −0.126346 | −0.00650717 | ||||||||
\(378\) | 0.880673 | 0.0452969 | ||||||||
\(379\) | −27.8518 | −1.43065 | −0.715324 | − | 0.698793i | \(-0.753721\pi\) | ||||
−0.715324 | + | 0.698793i | \(0.753721\pi\) | |||||||
\(380\) | 28.4548 | 1.45970 | ||||||||
\(381\) | −0.276862 | −0.0141841 | ||||||||
\(382\) | −0.965398 | −0.0493941 | ||||||||
\(383\) | −19.4345 | −0.993057 | −0.496528 | − | 0.868021i | \(-0.665392\pi\) | ||||
−0.496528 | + | 0.868021i | \(0.665392\pi\) | |||||||
\(384\) | 6.64175 | 0.338935 | ||||||||
\(385\) | −49.9156 | −2.54394 | ||||||||
\(386\) | −0.333185 | −0.0169586 | ||||||||
\(387\) | −8.66151 | −0.440289 | ||||||||
\(388\) | −18.0125 | −0.914449 | ||||||||
\(389\) | −9.68047 | −0.490819 | −0.245410 | − | 0.969419i | \(-0.578922\pi\) | ||||
−0.245410 | + | 0.969419i | \(0.578922\pi\) | |||||||
\(390\) | 0.444697 | 0.0225181 | ||||||||
\(391\) | 3.07235 | 0.155375 | ||||||||
\(392\) | −7.77057 | −0.392473 | ||||||||
\(393\) | 7.17489 | 0.361925 | ||||||||
\(394\) | 1.20725 | 0.0608203 | ||||||||
\(395\) | −3.79014 | −0.190702 | ||||||||
\(396\) | 6.44334 | 0.323790 | ||||||||
\(397\) | 8.94257 | 0.448815 | 0.224407 | − | 0.974495i | \(-0.427955\pi\) | ||||
0.224407 | + | 0.974495i | \(0.427955\pi\) | |||||||
\(398\) | 0.133593 | 0.00669640 | ||||||||
\(399\) | 15.3452 | 0.768219 | ||||||||
\(400\) | 34.7429 | 1.73715 | ||||||||
\(401\) | −3.51241 | −0.175401 | −0.0877007 | − | 0.996147i | \(-0.527952\pi\) | ||||
−0.0877007 | + | 0.996147i | \(0.527952\pi\) | |||||||
\(402\) | 2.31197 | 0.115311 | ||||||||
\(403\) | 1.20334 | 0.0599429 | ||||||||
\(404\) | −10.2379 | −0.509354 | ||||||||
\(405\) | −3.79014 | −0.188333 | ||||||||
\(406\) | 0.209412 | 0.0103929 | ||||||||
\(407\) | 23.1696 | 1.14847 | ||||||||
\(408\) | 0.872503 | 0.0431953 | ||||||||
\(409\) | −0.0543466 | −0.00268727 | −0.00134363 | − | 0.999999i | \(-0.500428\pi\) | ||||
−0.00134363 | + | 0.999999i | \(0.500428\pi\) | |||||||
\(410\) | −4.43918 | −0.219236 | ||||||||
\(411\) | −18.3482 | −0.905050 | ||||||||
\(412\) | −33.0926 | −1.63036 | ||||||||
\(413\) | 12.1935 | 0.600004 | ||||||||
\(414\) | 0.678429 | 0.0333429 | ||||||||
\(415\) | 2.59156 | 0.127215 | ||||||||
\(416\) | 1.36247 | 0.0668007 | ||||||||
\(417\) | 4.50301 | 0.220513 | ||||||||
\(418\) | −2.80559 | −0.137226 | ||||||||
\(419\) | 17.7182 | 0.865590 | 0.432795 | − | 0.901492i | \(-0.357527\pi\) | ||||
0.432795 | + | 0.901492i | \(0.357527\pi\) | |||||||
\(420\) | 29.4949 | 1.43920 | ||||||||
\(421\) | −9.83293 | −0.479228 | −0.239614 | − | 0.970868i | \(-0.577021\pi\) | ||||
−0.239614 | + | 0.970868i | \(0.577021\pi\) | |||||||
\(422\) | −1.04370 | −0.0508064 | ||||||||
\(423\) | 4.19422 | 0.203930 | ||||||||
\(424\) | −8.02318 | −0.389640 | ||||||||
\(425\) | 9.36513 | 0.454276 | ||||||||
\(426\) | −1.59182 | −0.0771239 | ||||||||
\(427\) | 36.3135 | 1.75734 | ||||||||
\(428\) | 15.1032 | 0.730043 | ||||||||
\(429\) | 1.75460 | 0.0847127 | ||||||||
\(430\) | 7.24906 | 0.349581 | ||||||||
\(431\) | −17.6583 | −0.850570 | −0.425285 | − | 0.905060i | \(-0.639826\pi\) | ||||
−0.425285 | + | 0.905060i | \(0.639826\pi\) | |||||||
\(432\) | −3.70982 | −0.178489 | ||||||||
\(433\) | −15.1622 | −0.728649 | −0.364325 | − | 0.931272i | \(-0.618700\pi\) | ||||
−0.364325 | + | 0.931272i | \(0.618700\pi\) | |||||||
\(434\) | −1.99447 | −0.0957378 | ||||||||
\(435\) | −0.901241 | −0.0432112 | ||||||||
\(436\) | 19.6304 | 0.940124 | ||||||||
\(437\) | 11.8212 | 0.565484 | ||||||||
\(438\) | −1.85590 | −0.0886783 | ||||||||
\(439\) | −9.11027 | −0.434809 | −0.217405 | − | 0.976082i | \(-0.569759\pi\) | ||||
−0.217405 | + | 0.976082i | \(0.569759\pi\) | |||||||
\(440\) | −10.9200 | −0.520590 | ||||||||
\(441\) | 8.90607 | 0.424098 | ||||||||
\(442\) | 0.117330 | 0.00558083 | ||||||||
\(443\) | −0.939933 | −0.0446576 | −0.0223288 | − | 0.999751i | \(-0.507108\pi\) | ||||
−0.0223288 | + | 0.999751i | \(0.507108\pi\) | |||||||
\(444\) | −13.6908 | −0.649735 | ||||||||
\(445\) | 29.6430 | 1.40521 | ||||||||
\(446\) | 1.15812 | 0.0548385 | ||||||||
\(447\) | −9.59099 | −0.453638 | ||||||||
\(448\) | 27.3331 | 1.29137 | ||||||||
\(449\) | 20.6971 | 0.976759 | 0.488379 | − | 0.872631i | \(-0.337588\pi\) | ||||
0.488379 | + | 0.872631i | \(0.337588\pi\) | |||||||
\(450\) | 2.06798 | 0.0974857 | ||||||||
\(451\) | −17.5152 | −0.824759 | ||||||||
\(452\) | 9.40340 | 0.442299 | ||||||||
\(453\) | −11.3043 | −0.531121 | ||||||||
\(454\) | −1.76543 | −0.0828557 | ||||||||
\(455\) | 8.03180 | 0.376536 | ||||||||
\(456\) | 3.35704 | 0.157208 | ||||||||
\(457\) | −28.1998 | −1.31913 | −0.659566 | − | 0.751647i | \(-0.729260\pi\) | ||||
−0.659566 | + | 0.751647i | \(0.729260\pi\) | |||||||
\(458\) | −1.25307 | −0.0585519 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 22.7215 | 1.05939 | ||||||||
\(461\) | 3.50436 | 0.163214 | 0.0816072 | − | 0.996665i | \(-0.473995\pi\) | ||||
0.0816072 | + | 0.996665i | \(0.473995\pi\) | |||||||
\(462\) | −2.90814 | −0.135299 | ||||||||
\(463\) | 41.1642 | 1.91306 | 0.956532 | − | 0.291629i | \(-0.0941972\pi\) | ||||
0.956532 | + | 0.291629i | \(0.0941972\pi\) | |||||||
\(464\) | −0.882142 | −0.0409524 | ||||||||
\(465\) | 8.58358 | 0.398054 | ||||||||
\(466\) | 5.56589 | 0.257835 | ||||||||
\(467\) | 16.5020 | 0.763620 | 0.381810 | − | 0.924241i | \(-0.375301\pi\) | ||||
0.381810 | + | 0.924241i | \(0.375301\pi\) | |||||||
\(468\) | −1.03678 | −0.0479252 | ||||||||
\(469\) | 41.7572 | 1.92817 | ||||||||
\(470\) | −3.51026 | −0.161916 | ||||||||
\(471\) | −3.34788 | −0.154262 | ||||||||
\(472\) | 2.66756 | 0.122785 | ||||||||
\(473\) | 28.6018 | 1.31511 | ||||||||
\(474\) | −0.220817 | −0.0101425 | ||||||||
\(475\) | 36.0333 | 1.65332 | ||||||||
\(476\) | 7.78201 | 0.356688 | ||||||||
\(477\) | 9.19560 | 0.421037 | ||||||||
\(478\) | −0.632396 | −0.0289251 | ||||||||
\(479\) | −21.4126 | −0.978368 | −0.489184 | − | 0.872181i | \(-0.662705\pi\) | ||||
−0.489184 | + | 0.872181i | \(0.662705\pi\) | |||||||
\(480\) | 9.71866 | 0.443594 | ||||||||
\(481\) | −3.72815 | −0.169989 | ||||||||
\(482\) | −5.58957 | −0.254598 | ||||||||
\(483\) | 12.2533 | 0.557543 | ||||||||
\(484\) | 0.186575 | 0.00848069 | ||||||||
\(485\) | −34.9880 | −1.58872 | ||||||||
\(486\) | −0.220817 | −0.0100165 | ||||||||
\(487\) | −1.58896 | −0.0720024 | −0.0360012 | − | 0.999352i | \(-0.511462\pi\) | ||||
−0.0360012 | + | 0.999352i | \(0.511462\pi\) | |||||||
\(488\) | 7.94427 | 0.359620 | ||||||||
\(489\) | −21.2770 | −0.962180 | ||||||||
\(490\) | −7.45374 | −0.336726 | ||||||||
\(491\) | −2.28991 | −0.103342 | −0.0516711 | − | 0.998664i | \(-0.516455\pi\) | ||||
−0.0516711 | + | 0.998664i | \(0.516455\pi\) | |||||||
\(492\) | 10.3496 | 0.466598 | ||||||||
\(493\) | −0.237786 | −0.0107093 | ||||||||
\(494\) | 0.451440 | 0.0203112 | ||||||||
\(495\) | 12.5157 | 0.562539 | ||||||||
\(496\) | 8.40168 | 0.377246 | ||||||||
\(497\) | −28.7502 | −1.28962 | ||||||||
\(498\) | 0.150987 | 0.00676589 | ||||||||
\(499\) | 37.6406 | 1.68503 | 0.842513 | − | 0.538677i | \(-0.181076\pi\) | ||||
0.842513 | + | 0.538677i | \(0.181076\pi\) | |||||||
\(500\) | 32.2822 | 1.44370 | ||||||||
\(501\) | −14.3890 | −0.642852 | ||||||||
\(502\) | 1.78679 | 0.0797482 | ||||||||
\(503\) | 31.3737 | 1.39888 | 0.699442 | − | 0.714690i | \(-0.253432\pi\) | ||||
0.699442 | + | 0.714690i | \(0.253432\pi\) | |||||||
\(504\) | 3.47975 | 0.155000 | ||||||||
\(505\) | −19.8863 | −0.884929 | ||||||||
\(506\) | −2.24029 | −0.0995931 | ||||||||
\(507\) | 12.7177 | 0.564812 | ||||||||
\(508\) | −0.540224 | −0.0239686 | ||||||||
\(509\) | 23.9734 | 1.06260 | 0.531302 | − | 0.847182i | \(-0.321703\pi\) | ||||
0.531302 | + | 0.847182i | \(0.321703\pi\) | |||||||
\(510\) | 0.836928 | 0.0370598 | ||||||||
\(511\) | −33.5199 | −1.48283 | ||||||||
\(512\) | 15.9863 | 0.706503 | ||||||||
\(513\) | −3.84760 | −0.169876 | ||||||||
\(514\) | 4.52785 | 0.199715 | ||||||||
\(515\) | −64.2799 | −2.83251 | ||||||||
\(516\) | −16.9007 | −0.744011 | ||||||||
\(517\) | −13.8501 | −0.609125 | ||||||||
\(518\) | 6.17920 | 0.271498 | ||||||||
\(519\) | 9.78842 | 0.429664 | ||||||||
\(520\) | 1.75711 | 0.0770542 | ||||||||
\(521\) | 0.743064 | 0.0325542 | 0.0162771 | − | 0.999868i | \(-0.494819\pi\) | ||||
0.0162771 | + | 0.999868i | \(0.494819\pi\) | |||||||
\(522\) | −0.0525073 | −0.00229818 | ||||||||
\(523\) | −28.7566 | −1.25744 | −0.628718 | − | 0.777633i | \(-0.716420\pi\) | ||||
−0.628718 | + | 0.777633i | \(0.716420\pi\) | |||||||
\(524\) | 13.9999 | 0.611590 | ||||||||
\(525\) | 37.3504 | 1.63011 | ||||||||
\(526\) | −1.23737 | −0.0539519 | ||||||||
\(527\) | 2.26472 | 0.0986526 | ||||||||
\(528\) | 12.2505 | 0.533133 | ||||||||
\(529\) | −13.5607 | −0.589594 | ||||||||
\(530\) | −7.69605 | −0.334295 | ||||||||
\(531\) | −3.05737 | −0.132679 | ||||||||
\(532\) | 29.9421 | 1.29815 | ||||||||
\(533\) | 2.81833 | 0.122075 | ||||||||
\(534\) | 1.72703 | 0.0747360 | ||||||||
\(535\) | 29.3369 | 1.26835 | ||||||||
\(536\) | 9.13517 | 0.394579 | ||||||||
\(537\) | 3.00748 | 0.129782 | ||||||||
\(538\) | 2.32147 | 0.100086 | ||||||||
\(539\) | −29.4094 | −1.26675 | ||||||||
\(540\) | −7.39546 | −0.318250 | ||||||||
\(541\) | 43.4358 | 1.86745 | 0.933725 | − | 0.357991i | \(-0.116538\pi\) | ||||
0.933725 | + | 0.357991i | \(0.116538\pi\) | |||||||
\(542\) | −5.54620 | −0.238229 | ||||||||
\(543\) | −21.9820 | −0.943339 | ||||||||
\(544\) | 2.56420 | 0.109939 | ||||||||
\(545\) | 38.1305 | 1.63333 | ||||||||
\(546\) | 0.467941 | 0.0200260 | ||||||||
\(547\) | −40.9703 | −1.75176 | −0.875881 | − | 0.482526i | \(-0.839719\pi\) | ||||
−0.875881 | + | 0.482526i | \(0.839719\pi\) | |||||||
\(548\) | −35.8017 | −1.52937 | ||||||||
\(549\) | −9.10515 | −0.388598 | ||||||||
\(550\) | −6.82885 | −0.291183 | ||||||||
\(551\) | −0.914905 | −0.0389763 | ||||||||
\(552\) | 2.68063 | 0.114095 | ||||||||
\(553\) | −3.98824 | −0.169597 | ||||||||
\(554\) | −2.42959 | −0.103223 | ||||||||
\(555\) | −26.5933 | −1.12882 | ||||||||
\(556\) | 8.78645 | 0.372629 | ||||||||
\(557\) | 24.5464 | 1.04006 | 0.520031 | − | 0.854147i | \(-0.325920\pi\) | ||||
0.520031 | + | 0.854147i | \(0.325920\pi\) | |||||||
\(558\) | 0.500089 | 0.0211704 | ||||||||
\(559\) | −4.60225 | −0.194654 | ||||||||
\(560\) | 56.0775 | 2.36971 | ||||||||
\(561\) | 3.30218 | 0.139418 | ||||||||
\(562\) | 2.55249 | 0.107670 | ||||||||
\(563\) | −13.2567 | −0.558703 | −0.279352 | − | 0.960189i | \(-0.590120\pi\) | ||||
−0.279352 | + | 0.960189i | \(0.590120\pi\) | |||||||
\(564\) | 8.18393 | 0.344605 | ||||||||
\(565\) | 18.2654 | 0.768431 | ||||||||
\(566\) | −6.68731 | −0.281089 | ||||||||
\(567\) | −3.98824 | −0.167490 | ||||||||
\(568\) | −6.28966 | −0.263908 | ||||||||
\(569\) | −42.1699 | −1.76785 | −0.883927 | − | 0.467624i | \(-0.845110\pi\) | ||||
−0.883927 | + | 0.467624i | \(0.845110\pi\) | |||||||
\(570\) | 3.22017 | 0.134878 | ||||||||
\(571\) | −36.3594 | −1.52159 | −0.760796 | − | 0.648991i | \(-0.775191\pi\) | ||||
−0.760796 | + | 0.648991i | \(0.775191\pi\) | |||||||
\(572\) | 3.42364 | 0.143149 | ||||||||
\(573\) | 4.37193 | 0.182640 | ||||||||
\(574\) | −4.67121 | −0.194973 | ||||||||
\(575\) | 28.7730 | 1.19992 | ||||||||
\(576\) | −6.85341 | −0.285559 | ||||||||
\(577\) | −26.6084 | −1.10772 | −0.553860 | − | 0.832610i | \(-0.686846\pi\) | ||||
−0.553860 | + | 0.832610i | \(0.686846\pi\) | |||||||
\(578\) | 0.220817 | 0.00918479 | ||||||||
\(579\) | 1.50887 | 0.0627064 | ||||||||
\(580\) | −1.75854 | −0.0730193 | ||||||||
\(581\) | 2.72702 | 0.113136 | ||||||||
\(582\) | −2.03844 | −0.0844960 | ||||||||
\(583\) | −30.3655 | −1.25761 | ||||||||
\(584\) | −7.33310 | −0.303446 | ||||||||
\(585\) | −2.01387 | −0.0832632 | ||||||||
\(586\) | 2.92859 | 0.120979 | ||||||||
\(587\) | −33.1488 | −1.36820 | −0.684099 | − | 0.729389i | \(-0.739805\pi\) | ||||
−0.684099 | + | 0.729389i | \(0.739805\pi\) | |||||||
\(588\) | 17.3779 | 0.716651 | ||||||||
\(589\) | 8.71372 | 0.359043 | ||||||||
\(590\) | 2.55880 | 0.105344 | ||||||||
\(591\) | −5.46718 | −0.224890 | ||||||||
\(592\) | −26.0297 | −1.06982 | ||||||||
\(593\) | 27.9810 | 1.14904 | 0.574521 | − | 0.818490i | \(-0.305188\pi\) | ||||
0.574521 | + | 0.818490i | \(0.305188\pi\) | |||||||
\(594\) | 0.729179 | 0.0299186 | ||||||||
\(595\) | 15.1160 | 0.619695 | ||||||||
\(596\) | −18.7143 | −0.766568 | ||||||||
\(597\) | −0.604992 | −0.0247607 | ||||||||
\(598\) | 0.360480 | 0.0147411 | ||||||||
\(599\) | −9.38607 | −0.383504 | −0.191752 | − | 0.981443i | \(-0.561417\pi\) | ||||
−0.191752 | + | 0.981443i | \(0.561417\pi\) | |||||||
\(600\) | 8.17110 | 0.333584 | ||||||||
\(601\) | −42.7674 | −1.74452 | −0.872260 | − | 0.489043i | \(-0.837346\pi\) | ||||
−0.872260 | + | 0.489043i | \(0.837346\pi\) | |||||||
\(602\) | 7.62796 | 0.310892 | ||||||||
\(603\) | −10.4701 | −0.426374 | ||||||||
\(604\) | −22.0573 | −0.897500 | ||||||||
\(605\) | 0.362408 | 0.0147340 | ||||||||
\(606\) | −1.15860 | −0.0470648 | ||||||||
\(607\) | −5.27631 | −0.214159 | −0.107079 | − | 0.994250i | \(-0.534150\pi\) | ||||
−0.107079 | + | 0.994250i | \(0.534150\pi\) | |||||||
\(608\) | 9.86601 | 0.400119 | ||||||||
\(609\) | −0.948348 | −0.0384290 | ||||||||
\(610\) | 7.62036 | 0.308539 | ||||||||
\(611\) | 2.22858 | 0.0901586 | ||||||||
\(612\) | −1.95124 | −0.0788742 | ||||||||
\(613\) | −26.5735 | −1.07329 | −0.536646 | − | 0.843808i | \(-0.680309\pi\) | ||||
−0.536646 | + | 0.843808i | \(0.680309\pi\) | |||||||
\(614\) | 1.63125 | 0.0658320 | ||||||||
\(615\) | 20.1034 | 0.810647 | ||||||||
\(616\) | −11.4908 | −0.462976 | ||||||||
\(617\) | −3.48150 | −0.140160 | −0.0700799 | − | 0.997541i | \(-0.522325\pi\) | ||||
−0.0700799 | + | 0.997541i | \(0.522325\pi\) | |||||||
\(618\) | −3.74502 | −0.150647 | ||||||||
\(619\) | 15.9692 | 0.641858 | 0.320929 | − | 0.947103i | \(-0.396005\pi\) | ||||
0.320929 | + | 0.947103i | \(0.396005\pi\) | |||||||
\(620\) | 16.7486 | 0.672641 | ||||||||
\(621\) | −3.07235 | −0.123289 | ||||||||
\(622\) | −6.34968 | −0.254599 | ||||||||
\(623\) | 31.1924 | 1.24970 | ||||||||
\(624\) | −1.97119 | −0.0789108 | ||||||||
\(625\) | 15.8800 | 0.635201 | ||||||||
\(626\) | −0.844828 | −0.0337661 | ||||||||
\(627\) | 12.7055 | 0.507407 | ||||||||
\(628\) | −6.53251 | −0.260675 | ||||||||
\(629\) | −7.01645 | −0.279764 | ||||||||
\(630\) | 3.33787 | 0.132984 | ||||||||
\(631\) | 35.6288 | 1.41836 | 0.709180 | − | 0.705028i | \(-0.249065\pi\) | ||||
0.709180 | + | 0.705028i | \(0.249065\pi\) | |||||||
\(632\) | −0.872503 | −0.0347063 | ||||||||
\(633\) | 4.72652 | 0.187862 | ||||||||
\(634\) | 2.53331 | 0.100610 | ||||||||
\(635\) | −1.04934 | −0.0416419 | ||||||||
\(636\) | 17.9428 | 0.711479 | ||||||||
\(637\) | 4.73219 | 0.187496 | ||||||||
\(638\) | 0.173388 | 0.00686451 | ||||||||
\(639\) | 7.20875 | 0.285174 | ||||||||
\(640\) | 25.1731 | 0.995055 | ||||||||
\(641\) | 42.8299 | 1.69168 | 0.845839 | − | 0.533438i | \(-0.179100\pi\) | ||||
0.845839 | + | 0.533438i | \(0.179100\pi\) | |||||||
\(642\) | 1.70920 | 0.0674567 | ||||||||
\(643\) | −30.2662 | −1.19358 | −0.596791 | − | 0.802396i | \(-0.703558\pi\) | ||||
−0.596791 | + | 0.802396i | \(0.703558\pi\) | |||||||
\(644\) | 23.9091 | 0.942150 | ||||||||
\(645\) | −32.8283 | −1.29261 | ||||||||
\(646\) | 0.849617 | 0.0334277 | ||||||||
\(647\) | −29.7954 | −1.17138 | −0.585689 | − | 0.810536i | \(-0.699176\pi\) | ||||
−0.585689 | + | 0.810536i | \(0.699176\pi\) | |||||||
\(648\) | −0.872503 | −0.0342751 | ||||||||
\(649\) | 10.0960 | 0.396302 | ||||||||
\(650\) | 1.09881 | 0.0430990 | ||||||||
\(651\) | 9.03223 | 0.354001 | ||||||||
\(652\) | −41.5166 | −1.62591 | ||||||||
\(653\) | −11.7167 | −0.458512 | −0.229256 | − | 0.973366i | \(-0.573629\pi\) | ||||
−0.229256 | + | 0.973366i | \(0.573629\pi\) | |||||||
\(654\) | 2.22153 | 0.0868685 | ||||||||
\(655\) | 27.1938 | 1.06255 | ||||||||
\(656\) | 19.6774 | 0.768272 | ||||||||
\(657\) | 8.40467 | 0.327898 | ||||||||
\(658\) | −3.69374 | −0.143997 | ||||||||
\(659\) | 35.0881 | 1.36684 | 0.683419 | − | 0.730026i | \(-0.260492\pi\) | ||||
0.683419 | + | 0.730026i | \(0.260492\pi\) | |||||||
\(660\) | 24.4211 | 0.950592 | ||||||||
\(661\) | 19.2793 | 0.749879 | 0.374939 | − | 0.927049i | \(-0.377664\pi\) | ||||
0.374939 | + | 0.927049i | \(0.377664\pi\) | |||||||
\(662\) | 3.01396 | 0.117141 | ||||||||
\(663\) | −0.531345 | −0.0206357 | ||||||||
\(664\) | 0.596586 | 0.0231520 | ||||||||
\(665\) | 58.1602 | 2.25536 | ||||||||
\(666\) | −1.54935 | −0.0600363 | ||||||||
\(667\) | −0.730562 | −0.0282875 | ||||||||
\(668\) | −28.0764 | −1.08631 | ||||||||
\(669\) | −5.24469 | −0.202771 | ||||||||
\(670\) | 8.76270 | 0.338533 | ||||||||
\(671\) | 30.0668 | 1.16072 | ||||||||
\(672\) | 10.2266 | 0.394501 | ||||||||
\(673\) | 11.0711 | 0.426761 | 0.213380 | − | 0.976969i | \(-0.431553\pi\) | ||||
0.213380 | + | 0.976969i | \(0.431553\pi\) | |||||||
\(674\) | −3.10196 | −0.119483 | ||||||||
\(675\) | −9.36513 | −0.360464 | ||||||||
\(676\) | 24.8152 | 0.954432 | ||||||||
\(677\) | 9.63412 | 0.370269 | 0.185135 | − | 0.982713i | \(-0.440728\pi\) | ||||
0.185135 | + | 0.982713i | \(0.440728\pi\) | |||||||
\(678\) | 1.06416 | 0.0408689 | ||||||||
\(679\) | −36.8168 | −1.41290 | ||||||||
\(680\) | 3.30690 | 0.126814 | ||||||||
\(681\) | 7.99497 | 0.306368 | ||||||||
\(682\) | −1.65138 | −0.0632347 | ||||||||
\(683\) | 1.77907 | 0.0680741 | 0.0340370 | − | 0.999421i | \(-0.489164\pi\) | ||||
0.0340370 | + | 0.999421i | \(0.489164\pi\) | |||||||
\(684\) | −7.50759 | −0.287060 | ||||||||
\(685\) | −69.5422 | −2.65707 | ||||||||
\(686\) | −1.67862 | −0.0640901 | ||||||||
\(687\) | 5.67467 | 0.216502 | ||||||||
\(688\) | −32.1326 | −1.22504 | ||||||||
\(689\) | 4.88603 | 0.186143 | ||||||||
\(690\) | 2.57134 | 0.0978891 | ||||||||
\(691\) | −13.8838 | −0.528164 | −0.264082 | − | 0.964500i | \(-0.585069\pi\) | ||||
−0.264082 | + | 0.964500i | \(0.585069\pi\) | |||||||
\(692\) | 19.0996 | 0.726056 | ||||||||
\(693\) | 13.1699 | 0.500282 | ||||||||
\(694\) | −3.48677 | −0.132356 | ||||||||
\(695\) | 17.0670 | 0.647389 | ||||||||
\(696\) | −0.207469 | −0.00786409 | ||||||||
\(697\) | 5.30414 | 0.200909 | ||||||||
\(698\) | −1.66804 | −0.0631362 | ||||||||
\(699\) | −25.2059 | −0.953373 | ||||||||
\(700\) | 72.8796 | 2.75459 | ||||||||
\(701\) | −19.7699 | −0.746701 | −0.373350 | − | 0.927690i | \(-0.621791\pi\) | ||||
−0.373350 | + | 0.927690i | \(0.621791\pi\) | |||||||
\(702\) | −0.117330 | −0.00442834 | ||||||||
\(703\) | −26.9965 | −1.01819 | ||||||||
\(704\) | 22.6312 | 0.852945 | ||||||||
\(705\) | 15.8967 | 0.598703 | ||||||||
\(706\) | 3.17315 | 0.119423 | ||||||||
\(707\) | −20.9257 | −0.786994 | ||||||||
\(708\) | −5.96566 | −0.224203 | ||||||||
\(709\) | 6.58904 | 0.247456 | 0.123728 | − | 0.992316i | \(-0.460515\pi\) | ||||
0.123728 | + | 0.992316i | \(0.460515\pi\) | |||||||
\(710\) | −6.03321 | −0.226422 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | 6.82392 | 0.255737 | ||||||||
\(713\) | 6.95800 | 0.260579 | ||||||||
\(714\) | 0.880673 | 0.0329584 | ||||||||
\(715\) | 6.65016 | 0.248702 | ||||||||
\(716\) | 5.86831 | 0.219309 | ||||||||
\(717\) | 2.86388 | 0.106954 | ||||||||
\(718\) | 1.46451 | 0.0546551 | ||||||||
\(719\) | −19.0540 | −0.710595 | −0.355298 | − | 0.934753i | \(-0.615620\pi\) | ||||
−0.355298 | + | 0.934753i | \(0.615620\pi\) | |||||||
\(720\) | −14.0607 | −0.524012 | ||||||||
\(721\) | −67.6397 | −2.51904 | ||||||||
\(722\) | −0.926543 | −0.0344824 | ||||||||
\(723\) | 25.3131 | 0.941404 | ||||||||
\(724\) | −42.8922 | −1.59408 | ||||||||
\(725\) | −2.22690 | −0.0827049 | ||||||||
\(726\) | 0.0211143 | 0.000783625 0 | ||||||||
\(727\) | −16.8288 | −0.624145 | −0.312072 | − | 0.950058i | \(-0.601023\pi\) | ||||
−0.312072 | + | 0.950058i | \(0.601023\pi\) | |||||||
\(728\) | 1.84895 | 0.0685266 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −7.03411 | −0.260344 | ||||||||
\(731\) | −8.66151 | −0.320357 | ||||||||
\(732\) | −17.7663 | −0.656663 | ||||||||
\(733\) | −15.8786 | −0.586488 | −0.293244 | − | 0.956038i | \(-0.594735\pi\) | ||||
−0.293244 | + | 0.956038i | \(0.594735\pi\) | |||||||
\(734\) | −8.23233 | −0.303861 | ||||||||
\(735\) | 33.7552 | 1.24508 | ||||||||
\(736\) | 7.87811 | 0.290391 | ||||||||
\(737\) | 34.5740 | 1.27355 | ||||||||
\(738\) | 1.17125 | 0.0431142 | ||||||||
\(739\) | 44.8738 | 1.65071 | 0.825355 | − | 0.564614i | \(-0.190975\pi\) | ||||
0.825355 | + | 0.564614i | \(0.190975\pi\) | |||||||
\(740\) | −51.8899 | −1.90751 | ||||||||
\(741\) | −2.04440 | −0.0751030 | ||||||||
\(742\) | −8.09831 | −0.297298 | ||||||||
\(743\) | 39.5168 | 1.44973 | 0.724865 | − | 0.688891i | \(-0.241902\pi\) | ||||
0.724865 | + | 0.688891i | \(0.241902\pi\) | |||||||
\(744\) | 1.97597 | 0.0724426 | ||||||||
\(745\) | −36.3511 | −1.33180 | ||||||||
\(746\) | 6.67753 | 0.244482 | ||||||||
\(747\) | −0.683764 | −0.0250176 | ||||||||
\(748\) | 6.44334 | 0.235592 | ||||||||
\(749\) | 30.8703 | 1.12798 | ||||||||
\(750\) | 3.65330 | 0.133400 | ||||||||
\(751\) | 27.1773 | 0.991712 | 0.495856 | − | 0.868405i | \(-0.334854\pi\) | ||||
0.495856 | + | 0.868405i | \(0.334854\pi\) | |||||||
\(752\) | 15.5598 | 0.567407 | ||||||||
\(753\) | −8.09170 | −0.294878 | ||||||||
\(754\) | −0.0278995 | −0.00101604 | ||||||||
\(755\) | −42.8447 | −1.55928 | ||||||||
\(756\) | −7.78201 | −0.283029 | ||||||||
\(757\) | 16.4403 | 0.597535 | 0.298767 | − | 0.954326i | \(-0.403425\pi\) | ||||
0.298767 | + | 0.954326i | \(0.403425\pi\) | |||||||
\(758\) | −6.15015 | −0.223384 | ||||||||
\(759\) | 10.1454 | 0.368256 | ||||||||
\(760\) | 12.7236 | 0.461535 | ||||||||
\(761\) | −38.4468 | −1.39369 | −0.696847 | − | 0.717219i | \(-0.745415\pi\) | ||||
−0.696847 | + | 0.717219i | \(0.745415\pi\) | |||||||
\(762\) | −0.0611359 | −0.00221472 | ||||||||
\(763\) | 40.1236 | 1.45257 | ||||||||
\(764\) | 8.53068 | 0.308629 | ||||||||
\(765\) | −3.79014 | −0.137033 | ||||||||
\(766\) | −4.29148 | −0.155057 | ||||||||
\(767\) | −1.62452 | −0.0586579 | ||||||||
\(768\) | −12.2402 | −0.441681 | ||||||||
\(769\) | 15.4682 | 0.557798 | 0.278899 | − | 0.960320i | \(-0.410030\pi\) | ||||
0.278899 | + | 0.960320i | \(0.410030\pi\) | |||||||
\(770\) | −11.0222 | −0.397214 | ||||||||
\(771\) | −20.5050 | −0.738468 | ||||||||
\(772\) | 2.94416 | 0.105963 | ||||||||
\(773\) | 18.7785 | 0.675415 | 0.337708 | − | 0.941251i | \(-0.390348\pi\) | ||||
0.337708 | + | 0.941251i | \(0.390348\pi\) | |||||||
\(774\) | −1.91261 | −0.0687474 | ||||||||
\(775\) | 21.2094 | 0.761863 | ||||||||
\(776\) | −8.05436 | −0.289135 | ||||||||
\(777\) | −27.9833 | −1.00390 | ||||||||
\(778\) | −2.13762 | −0.0766373 | ||||||||
\(779\) | 20.4082 | 0.731200 | ||||||||
\(780\) | −3.92954 | −0.140700 | ||||||||
\(781\) | −23.8046 | −0.851795 | ||||||||
\(782\) | 0.678429 | 0.0242606 | ||||||||
\(783\) | 0.237786 | 0.00849778 | ||||||||
\(784\) | 33.0399 | 1.18000 | ||||||||
\(785\) | −12.6889 | −0.452886 | ||||||||
\(786\) | 1.58434 | 0.0565116 | ||||||||
\(787\) | −18.5493 | −0.661210 | −0.330605 | − | 0.943769i | \(-0.607253\pi\) | ||||
−0.330605 | + | 0.943769i | \(0.607253\pi\) | |||||||
\(788\) | −10.6678 | −0.380024 | ||||||||
\(789\) | 5.60359 | 0.199493 | ||||||||
\(790\) | −0.836928 | −0.0297766 | ||||||||
\(791\) | 19.2201 | 0.683388 | ||||||||
\(792\) | 2.88116 | 0.102378 | ||||||||
\(793\) | −4.83798 | −0.171802 | ||||||||
\(794\) | 1.97468 | 0.0700786 | ||||||||
\(795\) | 34.8526 | 1.23609 | ||||||||
\(796\) | −1.18049 | −0.0418412 | ||||||||
\(797\) | −36.7610 | −1.30214 | −0.651071 | − | 0.759017i | \(-0.725680\pi\) | ||||
−0.651071 | + | 0.759017i | \(0.725680\pi\) | |||||||
\(798\) | 3.38848 | 0.119951 | ||||||||
\(799\) | 4.19422 | 0.148381 | ||||||||
\(800\) | 24.0140 | 0.849025 | ||||||||
\(801\) | −7.82109 | −0.276345 | ||||||||
\(802\) | −0.775602 | −0.0273874 | ||||||||
\(803\) | −27.7537 | −0.979408 | ||||||||
\(804\) | −20.4296 | −0.720497 | ||||||||
\(805\) | 46.4416 | 1.63685 | ||||||||
\(806\) | 0.265720 | 0.00935957 | ||||||||
\(807\) | −10.5131 | −0.370079 | ||||||||
\(808\) | −4.57790 | −0.161050 | ||||||||
\(809\) | −38.9655 | −1.36995 | −0.684977 | − | 0.728564i | \(-0.740188\pi\) | ||||
−0.684977 | + | 0.728564i | \(0.740188\pi\) | |||||||
\(810\) | −0.836928 | −0.0294067 | ||||||||
\(811\) | −24.6889 | −0.866946 | −0.433473 | − | 0.901167i | \(-0.642712\pi\) | ||||
−0.433473 | + | 0.901167i | \(0.642712\pi\) | |||||||
\(812\) | −1.85045 | −0.0649382 | ||||||||
\(813\) | 25.1167 | 0.880880 | ||||||||
\(814\) | 5.11624 | 0.179324 | ||||||||
\(815\) | −80.6428 | −2.82479 | ||||||||
\(816\) | −3.70982 | −0.129870 | ||||||||
\(817\) | −33.3260 | −1.16593 | ||||||||
\(818\) | −0.0120007 | −0.000419594 0 | ||||||||
\(819\) | −2.11913 | −0.0740484 | ||||||||
\(820\) | 39.2266 | 1.36985 | ||||||||
\(821\) | −32.3845 | −1.13023 | −0.565114 | − | 0.825013i | \(-0.691168\pi\) | ||||
−0.565114 | + | 0.825013i | \(0.691168\pi\) | |||||||
\(822\) | −4.05160 | −0.141316 | ||||||||
\(823\) | −10.6531 | −0.371343 | −0.185671 | − | 0.982612i | \(-0.559446\pi\) | ||||
−0.185671 | + | 0.982612i | \(0.559446\pi\) | |||||||
\(824\) | −14.7975 | −0.515494 | ||||||||
\(825\) | 30.9253 | 1.07668 | ||||||||
\(826\) | 2.69254 | 0.0936856 | ||||||||
\(827\) | 40.3174 | 1.40197 | 0.700987 | − | 0.713174i | \(-0.252743\pi\) | ||||
0.700987 | + | 0.713174i | \(0.252743\pi\) | |||||||
\(828\) | −5.99489 | −0.208337 | ||||||||
\(829\) | −6.24535 | −0.216910 | −0.108455 | − | 0.994101i | \(-0.534590\pi\) | ||||
−0.108455 | + | 0.994101i | \(0.534590\pi\) | |||||||
\(830\) | 0.572261 | 0.0198635 | ||||||||
\(831\) | 11.0027 | 0.381680 | ||||||||
\(832\) | −3.64152 | −0.126247 | ||||||||
\(833\) | 8.90607 | 0.308577 | ||||||||
\(834\) | 0.994343 | 0.0344313 | ||||||||
\(835\) | −54.5362 | −1.88730 | ||||||||
\(836\) | 24.7914 | 0.857429 | ||||||||
\(837\) | −2.26472 | −0.0782800 | ||||||||
\(838\) | 3.91248 | 0.135155 | ||||||||
\(839\) | 33.7878 | 1.16648 | 0.583242 | − | 0.812298i | \(-0.301784\pi\) | ||||
0.583242 | + | 0.812298i | \(0.301784\pi\) | |||||||
\(840\) | 13.1887 | 0.455054 | ||||||||
\(841\) | −28.9435 | −0.998050 | ||||||||
\(842\) | −2.17128 | −0.0748274 | ||||||||
\(843\) | −11.5593 | −0.398122 | ||||||||
\(844\) | 9.22257 | 0.317454 | ||||||||
\(845\) | 48.2017 | 1.65819 | ||||||||
\(846\) | 0.926157 | 0.0318419 | ||||||||
\(847\) | 0.381351 | 0.0131034 | ||||||||
\(848\) | 34.1140 | 1.17148 | ||||||||
\(849\) | 30.2843 | 1.03936 | ||||||||
\(850\) | 2.06798 | 0.0709313 | ||||||||
\(851\) | −21.5570 | −0.738964 | ||||||||
\(852\) | 14.0660 | 0.481893 | ||||||||
\(853\) | 27.1455 | 0.929445 | 0.464723 | − | 0.885456i | \(-0.346154\pi\) | ||||
0.464723 | + | 0.885456i | \(0.346154\pi\) | |||||||
\(854\) | 8.01866 | 0.274393 | ||||||||
\(855\) | −14.5829 | −0.498726 | ||||||||
\(856\) | 6.75346 | 0.230828 | ||||||||
\(857\) | −42.5769 | −1.45440 | −0.727200 | − | 0.686426i | \(-0.759179\pi\) | ||||
−0.727200 | + | 0.686426i | \(0.759179\pi\) | |||||||
\(858\) | 0.387445 | 0.0132272 | ||||||||
\(859\) | 13.6077 | 0.464288 | 0.232144 | − | 0.972681i | \(-0.425426\pi\) | ||||
0.232144 | + | 0.972681i | \(0.425426\pi\) | |||||||
\(860\) | −64.0559 | −2.18429 | ||||||||
\(861\) | 21.1542 | 0.720932 | ||||||||
\(862\) | −3.89926 | −0.132809 | ||||||||
\(863\) | −46.2225 | −1.57343 | −0.786716 | − | 0.617315i | \(-0.788220\pi\) | ||||
−0.786716 | + | 0.617315i | \(0.788220\pi\) | |||||||
\(864\) | −2.56420 | −0.0872358 | ||||||||
\(865\) | 37.0995 | 1.26142 | ||||||||
\(866\) | −3.34808 | −0.113772 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 17.6240 | 0.598199 | ||||||||
\(869\) | −3.30218 | −0.112019 | ||||||||
\(870\) | −0.199010 | −0.00674706 | ||||||||
\(871\) | −5.56322 | −0.188502 | ||||||||
\(872\) | 8.77778 | 0.297253 | ||||||||
\(873\) | 9.23134 | 0.312433 | ||||||||
\(874\) | 2.61032 | 0.0882955 | ||||||||
\(875\) | 65.9832 | 2.23064 | ||||||||
\(876\) | 16.3995 | 0.554089 | ||||||||
\(877\) | 4.66961 | 0.157682 | 0.0788408 | − | 0.996887i | \(-0.474878\pi\) | ||||
0.0788408 | + | 0.996887i | \(0.474878\pi\) | |||||||
\(878\) | −2.01171 | −0.0678918 | ||||||||
\(879\) | −13.2625 | −0.447334 | ||||||||
\(880\) | 46.4310 | 1.56519 | ||||||||
\(881\) | −14.7489 | −0.496905 | −0.248452 | − | 0.968644i | \(-0.579922\pi\) | ||||
−0.248452 | + | 0.968644i | \(0.579922\pi\) | |||||||
\(882\) | 1.96661 | 0.0662194 | ||||||||
\(883\) | −12.4240 | −0.418100 | −0.209050 | − | 0.977905i | \(-0.567037\pi\) | ||||
−0.209050 | + | 0.977905i | \(0.567037\pi\) | |||||||
\(884\) | −1.03678 | −0.0348707 | ||||||||
\(885\) | −11.5878 | −0.389521 | ||||||||
\(886\) | −0.207554 | −0.00697290 | ||||||||
\(887\) | 25.7699 | 0.865267 | 0.432634 | − | 0.901570i | \(-0.357584\pi\) | ||||
0.432634 | + | 0.901570i | \(0.357584\pi\) | |||||||
\(888\) | −6.12187 | −0.205437 | ||||||||
\(889\) | −1.10419 | −0.0370334 | ||||||||
\(890\) | 6.54569 | 0.219412 | ||||||||
\(891\) | −3.30218 | −0.110627 | ||||||||
\(892\) | −10.2336 | −0.342648 | ||||||||
\(893\) | 16.1377 | 0.540027 | ||||||||
\(894\) | −2.11786 | −0.0708317 | ||||||||
\(895\) | 11.3987 | 0.381018 | ||||||||
\(896\) | 26.4889 | 0.884932 | ||||||||
\(897\) | −1.63248 | −0.0545068 | ||||||||
\(898\) | 4.57029 | 0.152513 | ||||||||
\(899\) | −0.538518 | −0.0179606 | ||||||||
\(900\) | −18.2736 | −0.609120 | ||||||||
\(901\) | 9.19560 | 0.306350 | ||||||||
\(902\) | −3.86766 | −0.128779 | ||||||||
\(903\) | −34.5442 | −1.14956 | ||||||||
\(904\) | 4.20476 | 0.139848 | ||||||||
\(905\) | −83.3149 | −2.76948 | ||||||||
\(906\) | −2.49618 | −0.0829300 | ||||||||
\(907\) | 49.0820 | 1.62974 | 0.814870 | − | 0.579644i | \(-0.196808\pi\) | ||||
0.814870 | + | 0.579644i | \(0.196808\pi\) | |||||||
\(908\) | 15.6001 | 0.517708 | ||||||||
\(909\) | 5.24686 | 0.174027 | ||||||||
\(910\) | 1.77356 | 0.0587930 | ||||||||
\(911\) | −6.76367 | −0.224090 | −0.112045 | − | 0.993703i | \(-0.535740\pi\) | ||||
−0.112045 | + | 0.993703i | \(0.535740\pi\) | |||||||
\(912\) | −14.2739 | −0.472656 | ||||||||
\(913\) | 2.25791 | 0.0747259 | ||||||||
\(914\) | −6.22701 | −0.205971 | ||||||||
\(915\) | −34.5098 | −1.14086 | ||||||||
\(916\) | 11.0726 | 0.365850 | ||||||||
\(917\) | 28.6152 | 0.944957 | ||||||||
\(918\) | −0.220817 | −0.00728806 | ||||||||
\(919\) | −6.36750 | −0.210044 | −0.105022 | − | 0.994470i | \(-0.533491\pi\) | ||||
−0.105022 | + | 0.994470i | \(0.533491\pi\) | |||||||
\(920\) | 10.1600 | 0.334964 | ||||||||
\(921\) | −7.38733 | −0.243421 | ||||||||
\(922\) | 0.773824 | 0.0254845 | ||||||||
\(923\) | 3.83033 | 0.126077 | ||||||||
\(924\) | 25.6976 | 0.845389 | ||||||||
\(925\) | −65.7100 | −2.16053 | ||||||||
\(926\) | 9.08978 | 0.298709 | ||||||||
\(927\) | 16.9598 | 0.557033 | ||||||||
\(928\) | −0.609730 | −0.0200154 | ||||||||
\(929\) | −27.4767 | −0.901481 | −0.450741 | − | 0.892655i | \(-0.648840\pi\) | ||||
−0.450741 | + | 0.892655i | \(0.648840\pi\) | |||||||
\(930\) | 1.89540 | 0.0621527 | ||||||||
\(931\) | 34.2670 | 1.12306 | ||||||||
\(932\) | −49.1827 | −1.61103 | ||||||||
\(933\) | 28.7553 | 0.941407 | ||||||||
\(934\) | 3.64392 | 0.119233 | ||||||||
\(935\) | 12.5157 | 0.409307 | ||||||||
\(936\) | −0.463600 | −0.0151532 | ||||||||
\(937\) | 48.2679 | 1.57684 | 0.788422 | − | 0.615135i | \(-0.210899\pi\) | ||||
0.788422 | + | 0.615135i | \(0.210899\pi\) | |||||||
\(938\) | 9.22071 | 0.301067 | ||||||||
\(939\) | 3.82591 | 0.124854 | ||||||||
\(940\) | 31.0182 | 1.01170 | ||||||||
\(941\) | −44.3429 | −1.44554 | −0.722769 | − | 0.691090i | \(-0.757131\pi\) | ||||
−0.722769 | + | 0.691090i | \(0.757131\pi\) | |||||||
\(942\) | −0.739269 | −0.0240867 | ||||||||
\(943\) | 16.2962 | 0.530676 | ||||||||
\(944\) | −11.3423 | −0.369160 | ||||||||
\(945\) | −15.1160 | −0.491723 | ||||||||
\(946\) | 6.31578 | 0.205344 | ||||||||
\(947\) | 36.1218 | 1.17380 | 0.586901 | − | 0.809659i | \(-0.300348\pi\) | ||||
0.586901 | + | 0.809659i | \(0.300348\pi\) | |||||||
\(948\) | 1.95124 | 0.0633733 | ||||||||
\(949\) | 4.46578 | 0.144965 | ||||||||
\(950\) | 7.95678 | 0.258152 | ||||||||
\(951\) | −11.4724 | −0.372018 | ||||||||
\(952\) | 3.47975 | 0.112779 | ||||||||
\(953\) | 26.5522 | 0.860110 | 0.430055 | − | 0.902803i | \(-0.358494\pi\) | ||||
0.430055 | + | 0.902803i | \(0.358494\pi\) | |||||||
\(954\) | 2.03055 | 0.0657414 | ||||||||
\(955\) | 16.5702 | 0.536199 | ||||||||
\(956\) | 5.58813 | 0.180733 | ||||||||
\(957\) | −0.785212 | −0.0253823 | ||||||||
\(958\) | −4.72828 | −0.152764 | ||||||||
\(959\) | −73.1770 | −2.36301 | ||||||||
\(960\) | −25.9754 | −0.838351 | ||||||||
\(961\) | −25.8711 | −0.834550 | ||||||||
\(962\) | −0.823242 | −0.0265424 | ||||||||
\(963\) | −7.74033 | −0.249429 | ||||||||
\(964\) | 49.3919 | 1.59081 | ||||||||
\(965\) | 5.71882 | 0.184095 | ||||||||
\(966\) | 2.70574 | 0.0870556 | ||||||||
\(967\) | 45.9715 | 1.47834 | 0.739172 | − | 0.673516i | \(-0.235217\pi\) | ||||
0.739172 | + | 0.673516i | \(0.235217\pi\) | |||||||
\(968\) | 0.0834277 | 0.00268147 | ||||||||
\(969\) | −3.84760 | −0.123603 | ||||||||
\(970\) | −7.72596 | −0.248066 | ||||||||
\(971\) | 30.5637 | 0.980835 | 0.490417 | − | 0.871488i | \(-0.336844\pi\) | ||||
0.490417 | + | 0.871488i | \(0.336844\pi\) | |||||||
\(972\) | 1.95124 | 0.0625860 | ||||||||
\(973\) | 17.9591 | 0.575742 | ||||||||
\(974\) | −0.350869 | −0.0112426 | ||||||||
\(975\) | −4.97611 | −0.159363 | ||||||||
\(976\) | −33.7784 | −1.08122 | ||||||||
\(977\) | −5.05977 | −0.161876 | −0.0809382 | − | 0.996719i | \(-0.525792\pi\) | ||||
−0.0809382 | + | 0.996719i | \(0.525792\pi\) | |||||||
\(978\) | −4.69834 | −0.150236 | ||||||||
\(979\) | 25.8266 | 0.825423 | ||||||||
\(980\) | 65.8645 | 2.10396 | ||||||||
\(981\) | −10.0605 | −0.321206 | ||||||||
\(982\) | −0.505652 | −0.0161360 | ||||||||
\(983\) | 9.89839 | 0.315710 | 0.157855 | − | 0.987462i | \(-0.449542\pi\) | ||||
0.157855 | + | 0.987462i | \(0.449542\pi\) | |||||||
\(984\) | 4.62787 | 0.147531 | ||||||||
\(985\) | −20.7213 | −0.660237 | ||||||||
\(986\) | −0.0525073 | −0.00167217 | ||||||||
\(987\) | 16.7276 | 0.532444 | ||||||||
\(988\) | −3.98912 | −0.126911 | ||||||||
\(989\) | −26.6112 | −0.846186 | ||||||||
\(990\) | 2.76369 | 0.0878357 | ||||||||
\(991\) | −41.1991 | −1.30873 | −0.654366 | − | 0.756178i | \(-0.727064\pi\) | ||||
−0.654366 | + | 0.756178i | \(0.727064\pi\) | |||||||
\(992\) | 5.80718 | 0.184378 | ||||||||
\(993\) | −13.6491 | −0.433141 | ||||||||
\(994\) | −6.34856 | −0.201364 | ||||||||
\(995\) | −2.29300 | −0.0726931 | ||||||||
\(996\) | −1.33419 | −0.0422753 | ||||||||
\(997\) | 8.76429 | 0.277568 | 0.138784 | − | 0.990323i | \(-0.455681\pi\) | ||||
0.138784 | + | 0.990323i | \(0.455681\pi\) | |||||||
\(998\) | 8.31170 | 0.263102 | ||||||||
\(999\) | 7.01645 | 0.221991 |
(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 | 4029.2.a.f.1.12 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.f.1.12 | ✓ | 22 | 1.1 | even | 1 | trivial |