Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6010,2,Mod(1,6010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6010, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6010 = 2 \cdot 5 \cdot 601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6010.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: | \(47.9900916148\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + \cdots - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.06059\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6010.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −3.06059 | −1.76703 | −0.883516 | − | 0.468401i | \(-0.844830\pi\) | ||||
−0.883516 | + | 0.468401i | \(0.844830\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −3.06059 | −1.24948 | ||||||||
\(7\) | 0.302669 | 0.114398 | 0.0571990 | − | 0.998363i | \(-0.481783\pi\) | ||||
0.0571990 | + | 0.998363i | \(0.481783\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 6.36721 | 2.12240 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0.393686 | 0.118701 | 0.0593505 | − | 0.998237i | \(-0.481097\pi\) | ||||
0.0593505 | + | 0.998237i | \(0.481097\pi\) | |||||||
\(12\) | −3.06059 | −0.883516 | ||||||||
\(13\) | −2.37935 | −0.659913 | −0.329956 | − | 0.943996i | \(-0.607034\pi\) | ||||
−0.329956 | + | 0.943996i | \(0.607034\pi\) | |||||||
\(14\) | 0.302669 | 0.0808916 | ||||||||
\(15\) | −3.06059 | −0.790241 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.379772 | −0.0921082 | −0.0460541 | − | 0.998939i | \(-0.514665\pi\) | ||||
−0.0460541 | + | 0.998939i | \(0.514665\pi\) | |||||||
\(18\) | 6.36721 | 1.50077 | ||||||||
\(19\) | 0.653758 | 0.149982 | 0.0749912 | − | 0.997184i | \(-0.476107\pi\) | ||||
0.0749912 | + | 0.997184i | \(0.476107\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −0.926345 | −0.202145 | ||||||||
\(22\) | 0.393686 | 0.0839342 | ||||||||
\(23\) | 0.240229 | 0.0500912 | 0.0250456 | − | 0.999686i | \(-0.492027\pi\) | ||||
0.0250456 | + | 0.999686i | \(0.492027\pi\) | |||||||
\(24\) | −3.06059 | −0.624740 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.37935 | −0.466629 | ||||||||
\(27\) | −10.3056 | −1.98332 | ||||||||
\(28\) | 0.302669 | 0.0571990 | ||||||||
\(29\) | −10.4861 | −1.94723 | −0.973613 | − | 0.228207i | \(-0.926714\pi\) | ||||
−0.973613 | + | 0.228207i | \(0.926714\pi\) | |||||||
\(30\) | −3.06059 | −0.558785 | ||||||||
\(31\) | 1.32728 | 0.238387 | 0.119193 | − | 0.992871i | \(-0.461969\pi\) | ||||
0.119193 | + | 0.992871i | \(0.461969\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.20491 | −0.209748 | ||||||||
\(34\) | −0.379772 | −0.0651303 | ||||||||
\(35\) | 0.302669 | 0.0511604 | ||||||||
\(36\) | 6.36721 | 1.06120 | ||||||||
\(37\) | 8.99410 | 1.47862 | 0.739311 | − | 0.673365i | \(-0.235152\pi\) | ||||
0.739311 | + | 0.673365i | \(0.235152\pi\) | |||||||
\(38\) | 0.653758 | 0.106054 | ||||||||
\(39\) | 7.28221 | 1.16609 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −8.36579 | −1.30652 | −0.653259 | − | 0.757135i | \(-0.726599\pi\) | ||||
−0.653259 | + | 0.757135i | \(0.726599\pi\) | |||||||
\(42\) | −0.926345 | −0.142938 | ||||||||
\(43\) | −0.545077 | −0.0831234 | −0.0415617 | − | 0.999136i | \(-0.513233\pi\) | ||||
−0.0415617 | + | 0.999136i | \(0.513233\pi\) | |||||||
\(44\) | 0.393686 | 0.0593505 | ||||||||
\(45\) | 6.36721 | 0.949167 | ||||||||
\(46\) | 0.240229 | 0.0354199 | ||||||||
\(47\) | −4.02658 | −0.587337 | −0.293668 | − | 0.955907i | \(-0.594876\pi\) | ||||
−0.293668 | + | 0.955907i | \(0.594876\pi\) | |||||||
\(48\) | −3.06059 | −0.441758 | ||||||||
\(49\) | −6.90839 | −0.986913 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 1.16233 | 0.162758 | ||||||||
\(52\) | −2.37935 | −0.329956 | ||||||||
\(53\) | −5.16043 | −0.708839 | −0.354420 | − | 0.935087i | \(-0.615322\pi\) | ||||
−0.354420 | + | 0.935087i | \(0.615322\pi\) | |||||||
\(54\) | −10.3056 | −1.40242 | ||||||||
\(55\) | 0.393686 | 0.0530847 | ||||||||
\(56\) | 0.302669 | 0.0404458 | ||||||||
\(57\) | −2.00089 | −0.265024 | ||||||||
\(58\) | −10.4861 | −1.37690 | ||||||||
\(59\) | −5.74265 | −0.747629 | −0.373815 | − | 0.927503i | \(-0.621950\pi\) | ||||
−0.373815 | + | 0.927503i | \(0.621950\pi\) | |||||||
\(60\) | −3.06059 | −0.395120 | ||||||||
\(61\) | 2.10133 | 0.269048 | 0.134524 | − | 0.990910i | \(-0.457050\pi\) | ||||
0.134524 | + | 0.990910i | \(0.457050\pi\) | |||||||
\(62\) | 1.32728 | 0.168565 | ||||||||
\(63\) | 1.92715 | 0.242799 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.37935 | −0.295122 | ||||||||
\(66\) | −1.20491 | −0.148314 | ||||||||
\(67\) | 16.1213 | 1.96953 | 0.984766 | − | 0.173882i | \(-0.0556313\pi\) | ||||
0.984766 | + | 0.173882i | \(0.0556313\pi\) | |||||||
\(68\) | −0.379772 | −0.0460541 | ||||||||
\(69\) | −0.735243 | −0.0885128 | ||||||||
\(70\) | 0.302669 | 0.0361758 | ||||||||
\(71\) | −9.79169 | −1.16206 | −0.581030 | − | 0.813882i | \(-0.697350\pi\) | ||||
−0.581030 | + | 0.813882i | \(0.697350\pi\) | |||||||
\(72\) | 6.36721 | 0.750383 | ||||||||
\(73\) | 13.1760 | 1.54213 | 0.771067 | − | 0.636754i | \(-0.219723\pi\) | ||||
0.771067 | + | 0.636754i | \(0.219723\pi\) | |||||||
\(74\) | 8.99410 | 1.04554 | ||||||||
\(75\) | −3.06059 | −0.353406 | ||||||||
\(76\) | 0.653758 | 0.0749912 | ||||||||
\(77\) | 0.119157 | 0.0135791 | ||||||||
\(78\) | 7.28221 | 0.824548 | ||||||||
\(79\) | 6.29968 | 0.708770 | 0.354385 | − | 0.935100i | \(-0.384690\pi\) | ||||
0.354385 | + | 0.935100i | \(0.384690\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 12.4397 | 1.38219 | ||||||||
\(82\) | −8.36579 | −0.923847 | ||||||||
\(83\) | 0.717328 | 0.0787370 | 0.0393685 | − | 0.999225i | \(-0.487465\pi\) | ||||
0.0393685 | + | 0.999225i | \(0.487465\pi\) | |||||||
\(84\) | −0.926345 | −0.101072 | ||||||||
\(85\) | −0.379772 | −0.0411920 | ||||||||
\(86\) | −0.545077 | −0.0587771 | ||||||||
\(87\) | 32.0937 | 3.44081 | ||||||||
\(88\) | 0.393686 | 0.0419671 | ||||||||
\(89\) | −9.68315 | −1.02641 | −0.513206 | − | 0.858266i | \(-0.671542\pi\) | ||||
−0.513206 | + | 0.858266i | \(0.671542\pi\) | |||||||
\(90\) | 6.36721 | 0.671163 | ||||||||
\(91\) | −0.720154 | −0.0754927 | ||||||||
\(92\) | 0.240229 | 0.0250456 | ||||||||
\(93\) | −4.06226 | −0.421237 | ||||||||
\(94\) | −4.02658 | −0.415310 | ||||||||
\(95\) | 0.653758 | 0.0670742 | ||||||||
\(96\) | −3.06059 | −0.312370 | ||||||||
\(97\) | −14.8895 | −1.51180 | −0.755898 | − | 0.654690i | \(-0.772799\pi\) | ||||
−0.755898 | + | 0.654690i | \(0.772799\pi\) | |||||||
\(98\) | −6.90839 | −0.697853 | ||||||||
\(99\) | 2.50668 | 0.251931 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −18.4852 | −1.83935 | −0.919675 | − | 0.392680i | \(-0.871548\pi\) | ||||
−0.919675 | + | 0.392680i | \(0.871548\pi\) | |||||||
\(102\) | 1.16233 | 0.115087 | ||||||||
\(103\) | 5.65667 | 0.557368 | 0.278684 | − | 0.960383i | \(-0.410102\pi\) | ||||
0.278684 | + | 0.960383i | \(0.410102\pi\) | |||||||
\(104\) | −2.37935 | −0.233314 | ||||||||
\(105\) | −0.926345 | −0.0904020 | ||||||||
\(106\) | −5.16043 | −0.501225 | ||||||||
\(107\) | 9.97666 | 0.964480 | 0.482240 | − | 0.876039i | \(-0.339823\pi\) | ||||
0.482240 | + | 0.876039i | \(0.339823\pi\) | |||||||
\(108\) | −10.3056 | −0.991661 | ||||||||
\(109\) | 16.0324 | 1.53563 | 0.767814 | − | 0.640673i | \(-0.221344\pi\) | ||||
0.767814 | + | 0.640673i | \(0.221344\pi\) | |||||||
\(110\) | 0.393686 | 0.0375365 | ||||||||
\(111\) | −27.5272 | −2.61277 | ||||||||
\(112\) | 0.302669 | 0.0285995 | ||||||||
\(113\) | −10.2264 | −0.962015 | −0.481008 | − | 0.876716i | \(-0.659729\pi\) | ||||
−0.481008 | + | 0.876716i | \(0.659729\pi\) | |||||||
\(114\) | −2.00089 | −0.187400 | ||||||||
\(115\) | 0.240229 | 0.0224015 | ||||||||
\(116\) | −10.4861 | −0.973613 | ||||||||
\(117\) | −15.1498 | −1.40060 | ||||||||
\(118\) | −5.74265 | −0.528654 | ||||||||
\(119\) | −0.114945 | −0.0105370 | ||||||||
\(120\) | −3.06059 | −0.279392 | ||||||||
\(121\) | −10.8450 | −0.985910 | ||||||||
\(122\) | 2.10133 | 0.190245 | ||||||||
\(123\) | 25.6043 | 2.30866 | ||||||||
\(124\) | 1.32728 | 0.119193 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.92715 | 0.171685 | ||||||||
\(127\) | 19.9875 | 1.77361 | 0.886803 | − | 0.462148i | \(-0.152921\pi\) | ||||
0.886803 | + | 0.462148i | \(0.152921\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.66826 | 0.146882 | ||||||||
\(130\) | −2.37935 | −0.208683 | ||||||||
\(131\) | 9.27593 | 0.810441 | 0.405221 | − | 0.914219i | \(-0.367195\pi\) | ||||
0.405221 | + | 0.914219i | \(0.367195\pi\) | |||||||
\(132\) | −1.20491 | −0.104874 | ||||||||
\(133\) | 0.197872 | 0.0171577 | ||||||||
\(134\) | 16.1213 | 1.39267 | ||||||||
\(135\) | −10.3056 | −0.886968 | ||||||||
\(136\) | −0.379772 | −0.0325652 | ||||||||
\(137\) | 0.364833 | 0.0311698 | 0.0155849 | − | 0.999879i | \(-0.495039\pi\) | ||||
0.0155849 | + | 0.999879i | \(0.495039\pi\) | |||||||
\(138\) | −0.735243 | −0.0625880 | ||||||||
\(139\) | −8.30581 | −0.704489 | −0.352245 | − | 0.935908i | \(-0.614581\pi\) | ||||
−0.352245 | + | 0.935908i | \(0.614581\pi\) | |||||||
\(140\) | 0.302669 | 0.0255802 | ||||||||
\(141\) | 12.3237 | 1.03784 | ||||||||
\(142\) | −9.79169 | −0.821701 | ||||||||
\(143\) | −0.936717 | −0.0783322 | ||||||||
\(144\) | 6.36721 | 0.530601 | ||||||||
\(145\) | −10.4861 | −0.870826 | ||||||||
\(146\) | 13.1760 | 1.09045 | ||||||||
\(147\) | 21.1438 | 1.74391 | ||||||||
\(148\) | 8.99410 | 0.739311 | ||||||||
\(149\) | 12.1058 | 0.991743 | 0.495872 | − | 0.868396i | \(-0.334849\pi\) | ||||
0.495872 | + | 0.868396i | \(0.334849\pi\) | |||||||
\(150\) | −3.06059 | −0.249896 | ||||||||
\(151\) | −20.5589 | −1.67306 | −0.836531 | − | 0.547920i | \(-0.815420\pi\) | ||||
−0.836531 | + | 0.547920i | \(0.815420\pi\) | |||||||
\(152\) | 0.653758 | 0.0530268 | ||||||||
\(153\) | −2.41809 | −0.195491 | ||||||||
\(154\) | 0.119157 | 0.00960191 | ||||||||
\(155\) | 1.32728 | 0.106610 | ||||||||
\(156\) | 7.28221 | 0.583043 | ||||||||
\(157\) | −7.47357 | −0.596456 | −0.298228 | − | 0.954495i | \(-0.596395\pi\) | ||||
−0.298228 | + | 0.954495i | \(0.596395\pi\) | |||||||
\(158\) | 6.29968 | 0.501176 | ||||||||
\(159\) | 15.7939 | 1.25254 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0.0727099 | 0.00573034 | ||||||||
\(162\) | 12.4397 | 0.977356 | ||||||||
\(163\) | −2.21871 | −0.173782 | −0.0868912 | − | 0.996218i | \(-0.527693\pi\) | ||||
−0.0868912 | + | 0.996218i | \(0.527693\pi\) | |||||||
\(164\) | −8.36579 | −0.653259 | ||||||||
\(165\) | −1.20491 | −0.0938023 | ||||||||
\(166\) | 0.717328 | 0.0556755 | ||||||||
\(167\) | −12.5368 | −0.970129 | −0.485064 | − | 0.874479i | \(-0.661204\pi\) | ||||
−0.485064 | + | 0.874479i | \(0.661204\pi\) | |||||||
\(168\) | −0.926345 | −0.0714690 | ||||||||
\(169\) | −7.33870 | −0.564515 | ||||||||
\(170\) | −0.379772 | −0.0291272 | ||||||||
\(171\) | 4.16261 | 0.318323 | ||||||||
\(172\) | −0.545077 | −0.0415617 | ||||||||
\(173\) | 7.28234 | 0.553666 | 0.276833 | − | 0.960918i | \(-0.410715\pi\) | ||||
0.276833 | + | 0.960918i | \(0.410715\pi\) | |||||||
\(174\) | 32.0937 | 2.43302 | ||||||||
\(175\) | 0.302669 | 0.0228796 | ||||||||
\(176\) | 0.393686 | 0.0296752 | ||||||||
\(177\) | 17.5759 | 1.32108 | ||||||||
\(178\) | −9.68315 | −0.725783 | ||||||||
\(179\) | 11.8959 | 0.889144 | 0.444572 | − | 0.895743i | \(-0.353356\pi\) | ||||
0.444572 | + | 0.895743i | \(0.353356\pi\) | |||||||
\(180\) | 6.36721 | 0.474584 | ||||||||
\(181\) | −20.4579 | −1.52062 | −0.760310 | − | 0.649560i | \(-0.774953\pi\) | ||||
−0.760310 | + | 0.649560i | \(0.774953\pi\) | |||||||
\(182\) | −0.720154 | −0.0533814 | ||||||||
\(183\) | −6.43131 | −0.475416 | ||||||||
\(184\) | 0.240229 | 0.0177099 | ||||||||
\(185\) | 8.99410 | 0.661259 | ||||||||
\(186\) | −4.06226 | −0.297859 | ||||||||
\(187\) | −0.149511 | −0.0109333 | ||||||||
\(188\) | −4.02658 | −0.293668 | ||||||||
\(189\) | −3.11919 | −0.226888 | ||||||||
\(190\) | 0.653758 | 0.0474286 | ||||||||
\(191\) | 9.68976 | 0.701127 | 0.350563 | − | 0.936539i | \(-0.385990\pi\) | ||||
0.350563 | + | 0.936539i | \(0.385990\pi\) | |||||||
\(192\) | −3.06059 | −0.220879 | ||||||||
\(193\) | −3.47297 | −0.249990 | −0.124995 | − | 0.992157i | \(-0.539891\pi\) | ||||
−0.124995 | + | 0.992157i | \(0.539891\pi\) | |||||||
\(194\) | −14.8895 | −1.06900 | ||||||||
\(195\) | 7.28221 | 0.521490 | ||||||||
\(196\) | −6.90839 | −0.493457 | ||||||||
\(197\) | −7.43346 | −0.529612 | −0.264806 | − | 0.964302i | \(-0.585308\pi\) | ||||
−0.264806 | + | 0.964302i | \(0.585308\pi\) | |||||||
\(198\) | 2.50668 | 0.178142 | ||||||||
\(199\) | 3.67524 | 0.260531 | 0.130265 | − | 0.991479i | \(-0.458417\pi\) | ||||
0.130265 | + | 0.991479i | \(0.458417\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −49.3407 | −3.48023 | ||||||||
\(202\) | −18.4852 | −1.30062 | ||||||||
\(203\) | −3.17382 | −0.222759 | ||||||||
\(204\) | 1.16233 | 0.0813791 | ||||||||
\(205\) | −8.36579 | −0.584292 | ||||||||
\(206\) | 5.65667 | 0.394119 | ||||||||
\(207\) | 1.52959 | 0.106314 | ||||||||
\(208\) | −2.37935 | −0.164978 | ||||||||
\(209\) | 0.257376 | 0.0178030 | ||||||||
\(210\) | −0.926345 | −0.0639239 | ||||||||
\(211\) | −20.2472 | −1.39387 | −0.696936 | − | 0.717134i | \(-0.745454\pi\) | ||||
−0.696936 | + | 0.717134i | \(0.745454\pi\) | |||||||
\(212\) | −5.16043 | −0.354420 | ||||||||
\(213\) | 29.9684 | 2.05340 | ||||||||
\(214\) | 9.97666 | 0.681990 | ||||||||
\(215\) | −0.545077 | −0.0371739 | ||||||||
\(216\) | −10.3056 | −0.701210 | ||||||||
\(217\) | 0.401726 | 0.0272710 | ||||||||
\(218\) | 16.0324 | 1.08585 | ||||||||
\(219\) | −40.3263 | −2.72500 | ||||||||
\(220\) | 0.393686 | 0.0265423 | ||||||||
\(221\) | 0.903609 | 0.0607833 | ||||||||
\(222\) | −27.5272 | −1.84751 | ||||||||
\(223\) | 10.8134 | 0.724117 | 0.362058 | − | 0.932155i | \(-0.382074\pi\) | ||||
0.362058 | + | 0.932155i | \(0.382074\pi\) | |||||||
\(224\) | 0.302669 | 0.0202229 | ||||||||
\(225\) | 6.36721 | 0.424480 | ||||||||
\(226\) | −10.2264 | −0.680247 | ||||||||
\(227\) | −27.9968 | −1.85822 | −0.929108 | − | 0.369808i | \(-0.879423\pi\) | ||||
−0.929108 | + | 0.369808i | \(0.879423\pi\) | |||||||
\(228\) | −2.00089 | −0.132512 | ||||||||
\(229\) | −21.2086 | −1.40151 | −0.700753 | − | 0.713404i | \(-0.747152\pi\) | ||||
−0.700753 | + | 0.713404i | \(0.747152\pi\) | |||||||
\(230\) | 0.240229 | 0.0158402 | ||||||||
\(231\) | −0.364689 | −0.0239948 | ||||||||
\(232\) | −10.4861 | −0.688448 | ||||||||
\(233\) | −29.8509 | −1.95559 | −0.977797 | − | 0.209553i | \(-0.932799\pi\) | ||||
−0.977797 | + | 0.209553i | \(0.932799\pi\) | |||||||
\(234\) | −15.1498 | −0.990374 | ||||||||
\(235\) | −4.02658 | −0.262665 | ||||||||
\(236\) | −5.74265 | −0.373815 | ||||||||
\(237\) | −19.2807 | −1.25242 | ||||||||
\(238\) | −0.114945 | −0.00745078 | ||||||||
\(239\) | −9.17427 | −0.593434 | −0.296717 | − | 0.954965i | \(-0.595892\pi\) | ||||
−0.296717 | + | 0.954965i | \(0.595892\pi\) | |||||||
\(240\) | −3.06059 | −0.197560 | ||||||||
\(241\) | 14.5645 | 0.938183 | 0.469092 | − | 0.883149i | \(-0.344581\pi\) | ||||
0.469092 | + | 0.883149i | \(0.344581\pi\) | |||||||
\(242\) | −10.8450 | −0.697144 | ||||||||
\(243\) | −7.15592 | −0.459052 | ||||||||
\(244\) | 2.10133 | 0.134524 | ||||||||
\(245\) | −6.90839 | −0.441361 | ||||||||
\(246\) | 25.6043 | 1.63247 | ||||||||
\(247\) | −1.55552 | −0.0989753 | ||||||||
\(248\) | 1.32728 | 0.0842824 | ||||||||
\(249\) | −2.19545 | −0.139131 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −15.5634 | −0.982352 | −0.491176 | − | 0.871060i | \(-0.663433\pi\) | ||||
−0.491176 | + | 0.871060i | \(0.663433\pi\) | |||||||
\(252\) | 1.92715 | 0.121399 | ||||||||
\(253\) | 0.0945750 | 0.00594588 | ||||||||
\(254\) | 19.9875 | 1.25413 | ||||||||
\(255\) | 1.16233 | 0.0727876 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.5130 | 1.03005 | 0.515026 | − | 0.857174i | \(-0.327782\pi\) | ||||
0.515026 | + | 0.857174i | \(0.327782\pi\) | |||||||
\(258\) | 1.66826 | 0.103861 | ||||||||
\(259\) | 2.72223 | 0.169151 | ||||||||
\(260\) | −2.37935 | −0.147561 | ||||||||
\(261\) | −66.7674 | −4.13280 | ||||||||
\(262\) | 9.27593 | 0.573069 | ||||||||
\(263\) | −4.57687 | −0.282222 | −0.141111 | − | 0.989994i | \(-0.545067\pi\) | ||||
−0.141111 | + | 0.989994i | \(0.545067\pi\) | |||||||
\(264\) | −1.20491 | −0.0741572 | ||||||||
\(265\) | −5.16043 | −0.317002 | ||||||||
\(266\) | 0.197872 | 0.0121323 | ||||||||
\(267\) | 29.6361 | 1.81370 | ||||||||
\(268\) | 16.1213 | 0.984766 | ||||||||
\(269\) | 28.5382 | 1.74001 | 0.870003 | − | 0.493046i | \(-0.164117\pi\) | ||||
0.870003 | + | 0.493046i | \(0.164117\pi\) | |||||||
\(270\) | −10.3056 | −0.627181 | ||||||||
\(271\) | −5.55300 | −0.337320 | −0.168660 | − | 0.985674i | \(-0.553944\pi\) | ||||
−0.168660 | + | 0.985674i | \(0.553944\pi\) | |||||||
\(272\) | −0.379772 | −0.0230270 | ||||||||
\(273\) | 2.20410 | 0.133398 | ||||||||
\(274\) | 0.364833 | 0.0220404 | ||||||||
\(275\) | 0.393686 | 0.0237402 | ||||||||
\(276\) | −0.735243 | −0.0442564 | ||||||||
\(277\) | 15.4924 | 0.930846 | 0.465423 | − | 0.885088i | \(-0.345902\pi\) | ||||
0.465423 | + | 0.885088i | \(0.345902\pi\) | |||||||
\(278\) | −8.30581 | −0.498149 | ||||||||
\(279\) | 8.45107 | 0.505952 | ||||||||
\(280\) | 0.302669 | 0.0180879 | ||||||||
\(281\) | −7.89919 | −0.471226 | −0.235613 | − | 0.971847i | \(-0.575710\pi\) | ||||
−0.235613 | + | 0.971847i | \(0.575710\pi\) | |||||||
\(282\) | 12.3237 | 0.733866 | ||||||||
\(283\) | −21.8084 | −1.29637 | −0.648187 | − | 0.761481i | \(-0.724472\pi\) | ||||
−0.648187 | + | 0.761481i | \(0.724472\pi\) | |||||||
\(284\) | −9.79169 | −0.581030 | ||||||||
\(285\) | −2.00089 | −0.118522 | ||||||||
\(286\) | −0.936717 | −0.0553892 | ||||||||
\(287\) | −2.53206 | −0.149463 | ||||||||
\(288\) | 6.36721 | 0.375191 | ||||||||
\(289\) | −16.8558 | −0.991516 | ||||||||
\(290\) | −10.4861 | −0.615767 | ||||||||
\(291\) | 45.5705 | 2.67139 | ||||||||
\(292\) | 13.1760 | 0.771067 | ||||||||
\(293\) | 22.3147 | 1.30364 | 0.651821 | − | 0.758373i | \(-0.274005\pi\) | ||||
0.651821 | + | 0.758373i | \(0.274005\pi\) | |||||||
\(294\) | 21.1438 | 1.23313 | ||||||||
\(295\) | −5.74265 | −0.334350 | ||||||||
\(296\) | 8.99410 | 0.522771 | ||||||||
\(297\) | −4.05719 | −0.235422 | ||||||||
\(298\) | 12.1058 | 0.701268 | ||||||||
\(299\) | −0.571589 | −0.0330558 | ||||||||
\(300\) | −3.06059 | −0.176703 | ||||||||
\(301\) | −0.164978 | −0.00950915 | ||||||||
\(302\) | −20.5589 | −1.18303 | ||||||||
\(303\) | 56.5757 | 3.25019 | ||||||||
\(304\) | 0.653758 | 0.0374956 | ||||||||
\(305\) | 2.10133 | 0.120322 | ||||||||
\(306\) | −2.41809 | −0.138233 | ||||||||
\(307\) | 11.9437 | 0.681661 | 0.340830 | − | 0.940125i | \(-0.389292\pi\) | ||||
0.340830 | + | 0.940125i | \(0.389292\pi\) | |||||||
\(308\) | 0.119157 | 0.00678957 | ||||||||
\(309\) | −17.3127 | −0.984887 | ||||||||
\(310\) | 1.32728 | 0.0753845 | ||||||||
\(311\) | −16.4766 | −0.934303 | −0.467151 | − | 0.884177i | \(-0.654720\pi\) | ||||
−0.467151 | + | 0.884177i | \(0.654720\pi\) | |||||||
\(312\) | 7.28221 | 0.412274 | ||||||||
\(313\) | 2.42399 | 0.137012 | 0.0685060 | − | 0.997651i | \(-0.478177\pi\) | ||||
0.0685060 | + | 0.997651i | \(0.478177\pi\) | |||||||
\(314\) | −7.47357 | −0.421758 | ||||||||
\(315\) | 1.92715 | 0.108583 | ||||||||
\(316\) | 6.29968 | 0.354385 | ||||||||
\(317\) | −29.9367 | −1.68141 | −0.840707 | − | 0.541490i | \(-0.817860\pi\) | ||||
−0.840707 | + | 0.541490i | \(0.817860\pi\) | |||||||
\(318\) | 15.7939 | 0.885680 | ||||||||
\(319\) | −4.12825 | −0.231137 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −30.5344 | −1.70427 | ||||||||
\(322\) | 0.0727099 | 0.00405196 | ||||||||
\(323\) | −0.248279 | −0.0138146 | ||||||||
\(324\) | 12.4397 | 0.691095 | ||||||||
\(325\) | −2.37935 | −0.131983 | ||||||||
\(326\) | −2.21871 | −0.122883 | ||||||||
\(327\) | −49.0687 | −2.71350 | ||||||||
\(328\) | −8.36579 | −0.461924 | ||||||||
\(329\) | −1.21872 | −0.0671902 | ||||||||
\(330\) | −1.20491 | −0.0663282 | ||||||||
\(331\) | −10.5453 | −0.579622 | −0.289811 | − | 0.957084i | \(-0.593592\pi\) | ||||
−0.289811 | + | 0.957084i | \(0.593592\pi\) | |||||||
\(332\) | 0.717328 | 0.0393685 | ||||||||
\(333\) | 57.2673 | 3.13823 | ||||||||
\(334\) | −12.5368 | −0.685984 | ||||||||
\(335\) | 16.1213 | 0.880802 | ||||||||
\(336\) | −0.926345 | −0.0505362 | ||||||||
\(337\) | −21.1632 | −1.15283 | −0.576415 | − | 0.817157i | \(-0.695549\pi\) | ||||
−0.576415 | + | 0.817157i | \(0.695549\pi\) | |||||||
\(338\) | −7.33870 | −0.399173 | ||||||||
\(339\) | 31.2987 | 1.69991 | ||||||||
\(340\) | −0.379772 | −0.0205960 | ||||||||
\(341\) | 0.522532 | 0.0282967 | ||||||||
\(342\) | 4.16261 | 0.225088 | ||||||||
\(343\) | −4.20964 | −0.227299 | ||||||||
\(344\) | −0.545077 | −0.0293886 | ||||||||
\(345\) | −0.735243 | −0.0395841 | ||||||||
\(346\) | 7.28234 | 0.391501 | ||||||||
\(347\) | −7.28255 | −0.390948 | −0.195474 | − | 0.980709i | \(-0.562625\pi\) | ||||
−0.195474 | + | 0.980709i | \(0.562625\pi\) | |||||||
\(348\) | 32.0937 | 1.72040 | ||||||||
\(349\) | 1.21409 | 0.0649887 | 0.0324944 | − | 0.999472i | \(-0.489655\pi\) | ||||
0.0324944 | + | 0.999472i | \(0.489655\pi\) | |||||||
\(350\) | 0.302669 | 0.0161783 | ||||||||
\(351\) | 24.5207 | 1.30882 | ||||||||
\(352\) | 0.393686 | 0.0209836 | ||||||||
\(353\) | −19.5750 | −1.04187 | −0.520936 | − | 0.853596i | \(-0.674417\pi\) | ||||
−0.520936 | + | 0.853596i | \(0.674417\pi\) | |||||||
\(354\) | 17.5759 | 0.934148 | ||||||||
\(355\) | −9.79169 | −0.519689 | ||||||||
\(356\) | −9.68315 | −0.513206 | ||||||||
\(357\) | 0.351800 | 0.0186192 | ||||||||
\(358\) | 11.8959 | 0.628720 | ||||||||
\(359\) | −0.360464 | −0.0190245 | −0.00951227 | − | 0.999955i | \(-0.503028\pi\) | ||||
−0.00951227 | + | 0.999955i | \(0.503028\pi\) | |||||||
\(360\) | 6.36721 | 0.335581 | ||||||||
\(361\) | −18.5726 | −0.977505 | ||||||||
\(362\) | −20.4579 | −1.07524 | ||||||||
\(363\) | 33.1921 | 1.74213 | ||||||||
\(364\) | −0.720154 | −0.0377463 | ||||||||
\(365\) | 13.1760 | 0.689664 | ||||||||
\(366\) | −6.43131 | −0.336170 | ||||||||
\(367\) | −25.9109 | −1.35254 | −0.676268 | − | 0.736656i | \(-0.736404\pi\) | ||||
−0.676268 | + | 0.736656i | \(0.736404\pi\) | |||||||
\(368\) | 0.240229 | 0.0125228 | ||||||||
\(369\) | −53.2667 | −2.77296 | ||||||||
\(370\) | 8.99410 | 0.467581 | ||||||||
\(371\) | −1.56190 | −0.0810898 | ||||||||
\(372\) | −4.06226 | −0.210618 | ||||||||
\(373\) | −28.1904 | −1.45964 | −0.729821 | − | 0.683638i | \(-0.760397\pi\) | ||||
−0.729821 | + | 0.683638i | \(0.760397\pi\) | |||||||
\(374\) | −0.149511 | −0.00773103 | ||||||||
\(375\) | −3.06059 | −0.158048 | ||||||||
\(376\) | −4.02658 | −0.207655 | ||||||||
\(377\) | 24.9502 | 1.28500 | ||||||||
\(378\) | −3.11919 | −0.160434 | ||||||||
\(379\) | 8.83096 | 0.453616 | 0.226808 | − | 0.973940i | \(-0.427171\pi\) | ||||
0.226808 | + | 0.973940i | \(0.427171\pi\) | |||||||
\(380\) | 0.653758 | 0.0335371 | ||||||||
\(381\) | −61.1736 | −3.13402 | ||||||||
\(382\) | 9.68976 | 0.495771 | ||||||||
\(383\) | −23.8392 | −1.21813 | −0.609064 | − | 0.793121i | \(-0.708455\pi\) | ||||
−0.609064 | + | 0.793121i | \(0.708455\pi\) | |||||||
\(384\) | −3.06059 | −0.156185 | ||||||||
\(385\) | 0.119157 | 0.00607278 | ||||||||
\(386\) | −3.47297 | −0.176769 | ||||||||
\(387\) | −3.47062 | −0.176421 | ||||||||
\(388\) | −14.8895 | −0.755898 | ||||||||
\(389\) | 7.53468 | 0.382023 | 0.191012 | − | 0.981588i | \(-0.438823\pi\) | ||||
0.191012 | + | 0.981588i | \(0.438823\pi\) | |||||||
\(390\) | 7.28221 | 0.368749 | ||||||||
\(391\) | −0.0912323 | −0.00461381 | ||||||||
\(392\) | −6.90839 | −0.348926 | ||||||||
\(393\) | −28.3898 | −1.43208 | ||||||||
\(394\) | −7.43346 | −0.374492 | ||||||||
\(395\) | 6.29968 | 0.316971 | ||||||||
\(396\) | 2.50668 | 0.125966 | ||||||||
\(397\) | 32.0835 | 1.61022 | 0.805112 | − | 0.593123i | \(-0.202105\pi\) | ||||
0.805112 | + | 0.593123i | \(0.202105\pi\) | |||||||
\(398\) | 3.67524 | 0.184223 | ||||||||
\(399\) | −0.605605 | −0.0303182 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −10.4304 | −0.520871 | −0.260436 | − | 0.965491i | \(-0.583866\pi\) | ||||
−0.260436 | + | 0.965491i | \(0.583866\pi\) | |||||||
\(402\) | −49.3407 | −2.46089 | ||||||||
\(403\) | −3.15806 | −0.157314 | ||||||||
\(404\) | −18.4852 | −0.919675 | ||||||||
\(405\) | 12.4397 | 0.618134 | ||||||||
\(406\) | −3.17382 | −0.157514 | ||||||||
\(407\) | 3.54085 | 0.175514 | ||||||||
\(408\) | 1.16233 | 0.0575437 | ||||||||
\(409\) | 1.01459 | 0.0501684 | 0.0250842 | − | 0.999685i | \(-0.492015\pi\) | ||||
0.0250842 | + | 0.999685i | \(0.492015\pi\) | |||||||
\(410\) | −8.36579 | −0.413157 | ||||||||
\(411\) | −1.11660 | −0.0550781 | ||||||||
\(412\) | 5.65667 | 0.278684 | ||||||||
\(413\) | −1.73812 | −0.0855273 | ||||||||
\(414\) | 1.52959 | 0.0751752 | ||||||||
\(415\) | 0.717328 | 0.0352123 | ||||||||
\(416\) | −2.37935 | −0.116657 | ||||||||
\(417\) | 25.4207 | 1.24486 | ||||||||
\(418\) | 0.257376 | 0.0125887 | ||||||||
\(419\) | 22.6659 | 1.10730 | 0.553651 | − | 0.832749i | \(-0.313234\pi\) | ||||
0.553651 | + | 0.832749i | \(0.313234\pi\) | |||||||
\(420\) | −0.926345 | −0.0452010 | ||||||||
\(421\) | −20.7214 | −1.00990 | −0.504950 | − | 0.863149i | \(-0.668489\pi\) | ||||
−0.504950 | + | 0.863149i | \(0.668489\pi\) | |||||||
\(422\) | −20.2472 | −0.985616 | ||||||||
\(423\) | −25.6381 | −1.24656 | ||||||||
\(424\) | −5.16043 | −0.250612 | ||||||||
\(425\) | −0.379772 | −0.0184216 | ||||||||
\(426\) | 29.9684 | 1.45197 | ||||||||
\(427\) | 0.636007 | 0.0307785 | ||||||||
\(428\) | 9.97666 | 0.482240 | ||||||||
\(429\) | 2.86691 | 0.138416 | ||||||||
\(430\) | −0.545077 | −0.0262859 | ||||||||
\(431\) | 9.10219 | 0.438437 | 0.219219 | − | 0.975676i | \(-0.429649\pi\) | ||||
0.219219 | + | 0.975676i | \(0.429649\pi\) | |||||||
\(432\) | −10.3056 | −0.495830 | ||||||||
\(433\) | −31.4151 | −1.50971 | −0.754856 | − | 0.655890i | \(-0.772293\pi\) | ||||
−0.754856 | + | 0.655890i | \(0.772293\pi\) | |||||||
\(434\) | 0.401726 | 0.0192835 | ||||||||
\(435\) | 32.0937 | 1.53878 | ||||||||
\(436\) | 16.0324 | 0.767814 | ||||||||
\(437\) | 0.157052 | 0.00751281 | ||||||||
\(438\) | −40.3263 | −1.92687 | ||||||||
\(439\) | −0.429760 | −0.0205113 | −0.0102557 | − | 0.999947i | \(-0.503265\pi\) | ||||
−0.0102557 | + | 0.999947i | \(0.503265\pi\) | |||||||
\(440\) | 0.393686 | 0.0187683 | ||||||||
\(441\) | −43.9872 | −2.09463 | ||||||||
\(442\) | 0.903609 | 0.0429803 | ||||||||
\(443\) | 33.5818 | 1.59552 | 0.797760 | − | 0.602975i | \(-0.206018\pi\) | ||||
0.797760 | + | 0.602975i | \(0.206018\pi\) | |||||||
\(444\) | −27.5272 | −1.30639 | ||||||||
\(445\) | −9.68315 | −0.459025 | ||||||||
\(446\) | 10.8134 | 0.512028 | ||||||||
\(447\) | −37.0508 | −1.75244 | ||||||||
\(448\) | 0.302669 | 0.0142998 | ||||||||
\(449\) | −20.7822 | −0.980772 | −0.490386 | − | 0.871505i | \(-0.663144\pi\) | ||||
−0.490386 | + | 0.871505i | \(0.663144\pi\) | |||||||
\(450\) | 6.36721 | 0.300153 | ||||||||
\(451\) | −3.29350 | −0.155085 | ||||||||
\(452\) | −10.2264 | −0.481008 | ||||||||
\(453\) | 62.9224 | 2.95635 | ||||||||
\(454\) | −27.9968 | −1.31396 | ||||||||
\(455\) | −0.720154 | −0.0337614 | ||||||||
\(456\) | −2.00089 | −0.0937000 | ||||||||
\(457\) | −1.56659 | −0.0732822 | −0.0366411 | − | 0.999328i | \(-0.511666\pi\) | ||||
−0.0366411 | + | 0.999328i | \(0.511666\pi\) | |||||||
\(458\) | −21.2086 | −0.991014 | ||||||||
\(459\) | 3.91379 | 0.182680 | ||||||||
\(460\) | 0.240229 | 0.0112007 | ||||||||
\(461\) | −7.95973 | −0.370722 | −0.185361 | − | 0.982671i | \(-0.559345\pi\) | ||||
−0.185361 | + | 0.982671i | \(0.559345\pi\) | |||||||
\(462\) | −0.364689 | −0.0169669 | ||||||||
\(463\) | −40.2680 | −1.87141 | −0.935705 | − | 0.352782i | \(-0.885236\pi\) | ||||
−0.935705 | + | 0.352782i | \(0.885236\pi\) | |||||||
\(464\) | −10.4861 | −0.486806 | ||||||||
\(465\) | −4.06226 | −0.188383 | ||||||||
\(466\) | −29.8509 | −1.38281 | ||||||||
\(467\) | −34.5397 | −1.59831 | −0.799154 | − | 0.601126i | \(-0.794719\pi\) | ||||
−0.799154 | + | 0.601126i | \(0.794719\pi\) | |||||||
\(468\) | −15.1498 | −0.700300 | ||||||||
\(469\) | 4.87942 | 0.225311 | ||||||||
\(470\) | −4.02658 | −0.185732 | ||||||||
\(471\) | 22.8735 | 1.05396 | ||||||||
\(472\) | −5.74265 | −0.264327 | ||||||||
\(473\) | −0.214589 | −0.00986682 | ||||||||
\(474\) | −19.2807 | −0.885594 | ||||||||
\(475\) | 0.653758 | 0.0299965 | ||||||||
\(476\) | −0.114945 | −0.00526850 | ||||||||
\(477\) | −32.8575 | −1.50444 | ||||||||
\(478\) | −9.17427 | −0.419621 | ||||||||
\(479\) | 2.87871 | 0.131532 | 0.0657659 | − | 0.997835i | \(-0.479051\pi\) | ||||
0.0657659 | + | 0.997835i | \(0.479051\pi\) | |||||||
\(480\) | −3.06059 | −0.139696 | ||||||||
\(481\) | −21.4001 | −0.975761 | ||||||||
\(482\) | 14.5645 | 0.663396 | ||||||||
\(483\) | −0.222535 | −0.0101257 | ||||||||
\(484\) | −10.8450 | −0.492955 | ||||||||
\(485\) | −14.8895 | −0.676096 | ||||||||
\(486\) | −7.15592 | −0.324599 | ||||||||
\(487\) | −4.69576 | −0.212785 | −0.106393 | − | 0.994324i | \(-0.533930\pi\) | ||||
−0.106393 | + | 0.994324i | \(0.533930\pi\) | |||||||
\(488\) | 2.10133 | 0.0951227 | ||||||||
\(489\) | 6.79055 | 0.307079 | ||||||||
\(490\) | −6.90839 | −0.312089 | ||||||||
\(491\) | 4.22768 | 0.190793 | 0.0953964 | − | 0.995439i | \(-0.469588\pi\) | ||||
0.0953964 | + | 0.995439i | \(0.469588\pi\) | |||||||
\(492\) | 25.6043 | 1.15433 | ||||||||
\(493\) | 3.98234 | 0.179355 | ||||||||
\(494\) | −1.55552 | −0.0699861 | ||||||||
\(495\) | 2.50668 | 0.112667 | ||||||||
\(496\) | 1.32728 | 0.0595967 | ||||||||
\(497\) | −2.96364 | −0.132937 | ||||||||
\(498\) | −2.19545 | −0.0983803 | ||||||||
\(499\) | 33.4020 | 1.49528 | 0.747639 | − | 0.664105i | \(-0.231187\pi\) | ||||
0.747639 | + | 0.664105i | \(0.231187\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 38.3701 | 1.71425 | ||||||||
\(502\) | −15.5634 | −0.694628 | ||||||||
\(503\) | 20.2165 | 0.901408 | 0.450704 | − | 0.892673i | \(-0.351173\pi\) | ||||
0.450704 | + | 0.892673i | \(0.351173\pi\) | |||||||
\(504\) | 1.92715 | 0.0858423 | ||||||||
\(505\) | −18.4852 | −0.822582 | ||||||||
\(506\) | 0.0945750 | 0.00420437 | ||||||||
\(507\) | 22.4608 | 0.997517 | ||||||||
\(508\) | 19.9875 | 0.886803 | ||||||||
\(509\) | −30.5279 | −1.35313 | −0.676563 | − | 0.736384i | \(-0.736532\pi\) | ||||
−0.676563 | + | 0.736384i | \(0.736532\pi\) | |||||||
\(510\) | 1.16233 | 0.0514686 | ||||||||
\(511\) | 3.98796 | 0.176417 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.73739 | −0.297463 | ||||||||
\(514\) | 16.5130 | 0.728357 | ||||||||
\(515\) | 5.65667 | 0.249263 | ||||||||
\(516\) | 1.66826 | 0.0734409 | ||||||||
\(517\) | −1.58521 | −0.0697174 | ||||||||
\(518\) | 2.72223 | 0.119608 | ||||||||
\(519\) | −22.2882 | −0.978345 | ||||||||
\(520\) | −2.37935 | −0.104341 | ||||||||
\(521\) | 24.1994 | 1.06019 | 0.530096 | − | 0.847937i | \(-0.322156\pi\) | ||||
0.530096 | + | 0.847937i | \(0.322156\pi\) | |||||||
\(522\) | −66.7674 | −2.92233 | ||||||||
\(523\) | 12.2653 | 0.536325 | 0.268162 | − | 0.963374i | \(-0.413584\pi\) | ||||
0.268162 | + | 0.963374i | \(0.413584\pi\) | |||||||
\(524\) | 9.27593 | 0.405221 | ||||||||
\(525\) | −0.926345 | −0.0404290 | ||||||||
\(526\) | −4.57687 | −0.199561 | ||||||||
\(527\) | −0.504064 | −0.0219574 | ||||||||
\(528\) | −1.20491 | −0.0524371 | ||||||||
\(529\) | −22.9423 | −0.997491 | ||||||||
\(530\) | −5.16043 | −0.224155 | ||||||||
\(531\) | −36.5646 | −1.58677 | ||||||||
\(532\) | 0.197872 | 0.00857885 | ||||||||
\(533\) | 19.9051 | 0.862187 | ||||||||
\(534\) | 29.6361 | 1.28248 | ||||||||
\(535\) | 9.97666 | 0.431328 | ||||||||
\(536\) | 16.1213 | 0.696335 | ||||||||
\(537\) | −36.4086 | −1.57115 | ||||||||
\(538\) | 28.5382 | 1.23037 | ||||||||
\(539\) | −2.71974 | −0.117147 | ||||||||
\(540\) | −10.3056 | −0.443484 | ||||||||
\(541\) | −2.98187 | −0.128200 | −0.0641002 | − | 0.997943i | \(-0.520418\pi\) | ||||
−0.0641002 | + | 0.997943i | \(0.520418\pi\) | |||||||
\(542\) | −5.55300 | −0.238522 | ||||||||
\(543\) | 62.6131 | 2.68698 | ||||||||
\(544\) | −0.379772 | −0.0162826 | ||||||||
\(545\) | 16.0324 | 0.686754 | ||||||||
\(546\) | 2.20410 | 0.0943266 | ||||||||
\(547\) | 0.380513 | 0.0162696 | 0.00813478 | − | 0.999967i | \(-0.497411\pi\) | ||||
0.00813478 | + | 0.999967i | \(0.497411\pi\) | |||||||
\(548\) | 0.364833 | 0.0155849 | ||||||||
\(549\) | 13.3796 | 0.571028 | ||||||||
\(550\) | 0.393686 | 0.0167868 | ||||||||
\(551\) | −6.85539 | −0.292050 | ||||||||
\(552\) | −0.735243 | −0.0312940 | ||||||||
\(553\) | 1.90672 | 0.0810819 | ||||||||
\(554\) | 15.4924 | 0.658208 | ||||||||
\(555\) | −27.5272 | −1.16847 | ||||||||
\(556\) | −8.30581 | −0.352245 | ||||||||
\(557\) | 37.7655 | 1.60018 | 0.800088 | − | 0.599882i | \(-0.204786\pi\) | ||||
0.800088 | + | 0.599882i | \(0.204786\pi\) | |||||||
\(558\) | 8.45107 | 0.357762 | ||||||||
\(559\) | 1.29693 | 0.0548542 | ||||||||
\(560\) | 0.302669 | 0.0127901 | ||||||||
\(561\) | 0.457592 | 0.0193195 | ||||||||
\(562\) | −7.89919 | −0.333207 | ||||||||
\(563\) | 24.6905 | 1.04058 | 0.520291 | − | 0.853989i | \(-0.325824\pi\) | ||||
0.520291 | + | 0.853989i | \(0.325824\pi\) | |||||||
\(564\) | 12.3237 | 0.518921 | ||||||||
\(565\) | −10.2264 | −0.430226 | ||||||||
\(566\) | −21.8084 | −0.916675 | ||||||||
\(567\) | 3.76511 | 0.158120 | ||||||||
\(568\) | −9.79169 | −0.410850 | ||||||||
\(569\) | 39.8520 | 1.67068 | 0.835341 | − | 0.549732i | \(-0.185270\pi\) | ||||
0.835341 | + | 0.549732i | \(0.185270\pi\) | |||||||
\(570\) | −2.00089 | −0.0838079 | ||||||||
\(571\) | 37.8580 | 1.58431 | 0.792154 | − | 0.610322i | \(-0.208960\pi\) | ||||
0.792154 | + | 0.610322i | \(0.208960\pi\) | |||||||
\(572\) | −0.936717 | −0.0391661 | ||||||||
\(573\) | −29.6564 | −1.23891 | ||||||||
\(574\) | −2.53206 | −0.105686 | ||||||||
\(575\) | 0.240229 | 0.0100182 | ||||||||
\(576\) | 6.36721 | 0.265300 | ||||||||
\(577\) | 26.4122 | 1.09955 | 0.549777 | − | 0.835312i | \(-0.314713\pi\) | ||||
0.549777 | + | 0.835312i | \(0.314713\pi\) | |||||||
\(578\) | −16.8558 | −0.701108 | ||||||||
\(579\) | 10.6293 | 0.441740 | ||||||||
\(580\) | −10.4861 | −0.435413 | ||||||||
\(581\) | 0.217113 | 0.00900736 | ||||||||
\(582\) | 45.5705 | 1.88896 | ||||||||
\(583\) | −2.03159 | −0.0841398 | ||||||||
\(584\) | 13.1760 | 0.545227 | ||||||||
\(585\) | −15.1498 | −0.626367 | ||||||||
\(586\) | 22.3147 | 0.921814 | ||||||||
\(587\) | −42.1756 | −1.74077 | −0.870387 | − | 0.492368i | \(-0.836132\pi\) | ||||
−0.870387 | + | 0.492368i | \(0.836132\pi\) | |||||||
\(588\) | 21.1438 | 0.871954 | ||||||||
\(589\) | 0.867721 | 0.0357538 | ||||||||
\(590\) | −5.74265 | −0.236421 | ||||||||
\(591\) | 22.7508 | 0.935841 | ||||||||
\(592\) | 8.99410 | 0.369655 | ||||||||
\(593\) | 20.6911 | 0.849683 | 0.424841 | − | 0.905268i | \(-0.360330\pi\) | ||||
0.424841 | + | 0.905268i | \(0.360330\pi\) | |||||||
\(594\) | −4.05719 | −0.166468 | ||||||||
\(595\) | −0.114945 | −0.00471229 | ||||||||
\(596\) | 12.1058 | 0.495872 | ||||||||
\(597\) | −11.2484 | −0.460366 | ||||||||
\(598\) | −0.571589 | −0.0233740 | ||||||||
\(599\) | −32.8420 | −1.34189 | −0.670943 | − | 0.741509i | \(-0.734111\pi\) | ||||
−0.670943 | + | 0.741509i | \(0.734111\pi\) | |||||||
\(600\) | −3.06059 | −0.124948 | ||||||||
\(601\) | −1.00000 | −0.0407909 | ||||||||
\(602\) | −0.164978 | −0.00672399 | ||||||||
\(603\) | 102.648 | 4.18014 | ||||||||
\(604\) | −20.5589 | −0.836531 | ||||||||
\(605\) | −10.8450 | −0.440912 | ||||||||
\(606\) | 56.5757 | 2.29823 | ||||||||
\(607\) | −4.05152 | −0.164446 | −0.0822231 | − | 0.996614i | \(-0.526202\pi\) | ||||
−0.0822231 | + | 0.996614i | \(0.526202\pi\) | |||||||
\(608\) | 0.653758 | 0.0265134 | ||||||||
\(609\) | 9.71377 | 0.393622 | ||||||||
\(610\) | 2.10133 | 0.0850804 | ||||||||
\(611\) | 9.58063 | 0.387591 | ||||||||
\(612\) | −2.41809 | −0.0977453 | ||||||||
\(613\) | 30.3621 | 1.22631 | 0.613157 | − | 0.789961i | \(-0.289899\pi\) | ||||
0.613157 | + | 0.789961i | \(0.289899\pi\) | |||||||
\(614\) | 11.9437 | 0.482007 | ||||||||
\(615\) | 25.6043 | 1.03246 | ||||||||
\(616\) | 0.119157 | 0.00480095 | ||||||||
\(617\) | −18.9474 | −0.762792 | −0.381396 | − | 0.924412i | \(-0.624556\pi\) | ||||
−0.381396 | + | 0.924412i | \(0.624556\pi\) | |||||||
\(618\) | −17.3127 | −0.696420 | ||||||||
\(619\) | 26.6354 | 1.07057 | 0.535283 | − | 0.844673i | \(-0.320205\pi\) | ||||
0.535283 | + | 0.844673i | \(0.320205\pi\) | |||||||
\(620\) | 1.32728 | 0.0533049 | ||||||||
\(621\) | −2.47572 | −0.0993470 | ||||||||
\(622\) | −16.4766 | −0.660652 | ||||||||
\(623\) | −2.93079 | −0.117419 | ||||||||
\(624\) | 7.28221 | 0.291522 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 2.42399 | 0.0968820 | ||||||||
\(627\) | −0.787721 | −0.0314586 | ||||||||
\(628\) | −7.47357 | −0.298228 | ||||||||
\(629\) | −3.41571 | −0.136193 | ||||||||
\(630\) | 1.92715 | 0.0767797 | ||||||||
\(631\) | 50.1155 | 1.99507 | 0.997533 | − | 0.0701957i | \(-0.0223624\pi\) | ||||
0.997533 | + | 0.0701957i | \(0.0223624\pi\) | |||||||
\(632\) | 6.29968 | 0.250588 | ||||||||
\(633\) | 61.9682 | 2.46302 | ||||||||
\(634\) | −29.9367 | −1.18894 | ||||||||
\(635\) | 19.9875 | 0.793181 | ||||||||
\(636\) | 15.7939 | 0.626271 | ||||||||
\(637\) | 16.4375 | 0.651276 | ||||||||
\(638\) | −4.12825 | −0.163439 | ||||||||
\(639\) | −62.3457 | −2.46636 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 3.86427 | 0.152630 | 0.0763148 | − | 0.997084i | \(-0.475685\pi\) | ||||
0.0763148 | + | 0.997084i | \(0.475685\pi\) | |||||||
\(642\) | −30.5344 | −1.20510 | ||||||||
\(643\) | −21.3635 | −0.842496 | −0.421248 | − | 0.906946i | \(-0.638408\pi\) | ||||
−0.421248 | + | 0.906946i | \(0.638408\pi\) | |||||||
\(644\) | 0.0727099 | 0.00286517 | ||||||||
\(645\) | 1.66826 | 0.0656875 | ||||||||
\(646\) | −0.248279 | −0.00976840 | ||||||||
\(647\) | 19.5335 | 0.767941 | 0.383971 | − | 0.923345i | \(-0.374556\pi\) | ||||
0.383971 | + | 0.923345i | \(0.374556\pi\) | |||||||
\(648\) | 12.4397 | 0.488678 | ||||||||
\(649\) | −2.26080 | −0.0887442 | ||||||||
\(650\) | −2.37935 | −0.0933257 | ||||||||
\(651\) | −1.22952 | −0.0481887 | ||||||||
\(652\) | −2.21871 | −0.0868912 | ||||||||
\(653\) | −42.5938 | −1.66682 | −0.833411 | − | 0.552653i | \(-0.813615\pi\) | ||||
−0.833411 | + | 0.552653i | \(0.813615\pi\) | |||||||
\(654\) | −49.0687 | −1.91874 | ||||||||
\(655\) | 9.27593 | 0.362440 | ||||||||
\(656\) | −8.36579 | −0.326629 | ||||||||
\(657\) | 83.8943 | 3.27303 | ||||||||
\(658\) | −1.21872 | −0.0475106 | ||||||||
\(659\) | 3.46889 | 0.135129 | 0.0675644 | − | 0.997715i | \(-0.478477\pi\) | ||||
0.0675644 | + | 0.997715i | \(0.478477\pi\) | |||||||
\(660\) | −1.20491 | −0.0469011 | ||||||||
\(661\) | 10.5580 | 0.410659 | 0.205329 | − | 0.978693i | \(-0.434173\pi\) | ||||
0.205329 | + | 0.978693i | \(0.434173\pi\) | |||||||
\(662\) | −10.5453 | −0.409855 | ||||||||
\(663\) | −2.76558 | −0.107406 | ||||||||
\(664\) | 0.717328 | 0.0278377 | ||||||||
\(665\) | 0.197872 | 0.00767315 | ||||||||
\(666\) | 57.2673 | 2.21906 | ||||||||
\(667\) | −2.51907 | −0.0975390 | ||||||||
\(668\) | −12.5368 | −0.485064 | ||||||||
\(669\) | −33.0953 | −1.27954 | ||||||||
\(670\) | 16.1213 | 0.622821 | ||||||||
\(671\) | 0.827265 | 0.0319362 | ||||||||
\(672\) | −0.926345 | −0.0357345 | ||||||||
\(673\) | −28.4403 | −1.09629 | −0.548147 | − | 0.836382i | \(-0.684667\pi\) | ||||
−0.548147 | + | 0.836382i | \(0.684667\pi\) | |||||||
\(674\) | −21.1632 | −0.815174 | ||||||||
\(675\) | −10.3056 | −0.396664 | ||||||||
\(676\) | −7.33870 | −0.282258 | ||||||||
\(677\) | −0.161383 | −0.00620246 | −0.00310123 | − | 0.999995i | \(-0.500987\pi\) | ||||
−0.00310123 | + | 0.999995i | \(0.500987\pi\) | |||||||
\(678\) | 31.2987 | 1.20202 | ||||||||
\(679\) | −4.50657 | −0.172946 | ||||||||
\(680\) | −0.379772 | −0.0145636 | ||||||||
\(681\) | 85.6869 | 3.28353 | ||||||||
\(682\) | 0.522532 | 0.0200088 | ||||||||
\(683\) | −20.8736 | −0.798707 | −0.399353 | − | 0.916797i | \(-0.630765\pi\) | ||||
−0.399353 | + | 0.916797i | \(0.630765\pi\) | |||||||
\(684\) | 4.16261 | 0.159162 | ||||||||
\(685\) | 0.364833 | 0.0139396 | ||||||||
\(686\) | −4.20964 | −0.160725 | ||||||||
\(687\) | 64.9109 | 2.47651 | ||||||||
\(688\) | −0.545077 | −0.0207808 | ||||||||
\(689\) | 12.2785 | 0.467772 | ||||||||
\(690\) | −0.735243 | −0.0279902 | ||||||||
\(691\) | 12.3797 | 0.470946 | 0.235473 | − | 0.971881i | \(-0.424336\pi\) | ||||
0.235473 | + | 0.971881i | \(0.424336\pi\) | |||||||
\(692\) | 7.28234 | 0.276833 | ||||||||
\(693\) | 0.758694 | 0.0288204 | ||||||||
\(694\) | −7.28255 | −0.276442 | ||||||||
\(695\) | −8.30581 | −0.315057 | ||||||||
\(696\) | 32.0937 | 1.21651 | ||||||||
\(697\) | 3.17709 | 0.120341 | ||||||||
\(698\) | 1.21409 | 0.0459540 | ||||||||
\(699\) | 91.3612 | 3.45560 | ||||||||
\(700\) | 0.302669 | 0.0114398 | ||||||||
\(701\) | −9.45537 | −0.357124 | −0.178562 | − | 0.983929i | \(-0.557145\pi\) | ||||
−0.178562 | + | 0.983929i | \(0.557145\pi\) | |||||||
\(702\) | 24.5207 | 0.925474 | ||||||||
\(703\) | 5.87997 | 0.221767 | ||||||||
\(704\) | 0.393686 | 0.0148376 | ||||||||
\(705\) | 12.3237 | 0.464137 | ||||||||
\(706\) | −19.5750 | −0.736714 | ||||||||
\(707\) | −5.59490 | −0.210418 | ||||||||
\(708\) | 17.5759 | 0.660542 | ||||||||
\(709\) | 25.5181 | 0.958354 | 0.479177 | − | 0.877718i | \(-0.340935\pi\) | ||||
0.479177 | + | 0.877718i | \(0.340935\pi\) | |||||||
\(710\) | −9.79169 | −0.367476 | ||||||||
\(711\) | 40.1114 | 1.50429 | ||||||||
\(712\) | −9.68315 | −0.362891 | ||||||||
\(713\) | 0.318852 | 0.0119411 | ||||||||
\(714\) | 0.351800 | 0.0131658 | ||||||||
\(715\) | −0.936717 | −0.0350312 | ||||||||
\(716\) | 11.8959 | 0.444572 | ||||||||
\(717\) | 28.0787 | 1.04862 | ||||||||
\(718\) | −0.360464 | −0.0134524 | ||||||||
\(719\) | −6.07987 | −0.226741 | −0.113370 | − | 0.993553i | \(-0.536165\pi\) | ||||
−0.113370 | + | 0.993553i | \(0.536165\pi\) | |||||||
\(720\) | 6.36721 | 0.237292 | ||||||||
\(721\) | 1.71210 | 0.0637618 | ||||||||
\(722\) | −18.5726 | −0.691201 | ||||||||
\(723\) | −44.5760 | −1.65780 | ||||||||
\(724\) | −20.4579 | −0.760310 | ||||||||
\(725\) | −10.4861 | −0.389445 | ||||||||
\(726\) | 33.1921 | 1.23188 | ||||||||
\(727\) | −42.1326 | −1.56261 | −0.781305 | − | 0.624149i | \(-0.785446\pi\) | ||||
−0.781305 | + | 0.624149i | \(0.785446\pi\) | |||||||
\(728\) | −0.720154 | −0.0266907 | ||||||||
\(729\) | −15.4178 | −0.571029 | ||||||||
\(730\) | 13.1760 | 0.487666 | ||||||||
\(731\) | 0.207005 | 0.00765635 | ||||||||
\(732\) | −6.43131 | −0.237708 | ||||||||
\(733\) | 39.4881 | 1.45852 | 0.729262 | − | 0.684234i | \(-0.239863\pi\) | ||||
0.729262 | + | 0.684234i | \(0.239863\pi\) | |||||||
\(734\) | −25.9109 | −0.956387 | ||||||||
\(735\) | 21.1438 | 0.779899 | ||||||||
\(736\) | 0.240229 | 0.00885497 | ||||||||
\(737\) | 6.34674 | 0.233785 | ||||||||
\(738\) | −53.2667 | −1.96078 | ||||||||
\(739\) | 9.43579 | 0.347101 | 0.173551 | − | 0.984825i | \(-0.444476\pi\) | ||||
0.173551 | + | 0.984825i | \(0.444476\pi\) | |||||||
\(740\) | 8.99410 | 0.330630 | ||||||||
\(741\) | 4.76080 | 0.174892 | ||||||||
\(742\) | −1.56190 | −0.0573391 | ||||||||
\(743\) | 9.27233 | 0.340169 | 0.170084 | − | 0.985429i | \(-0.445596\pi\) | ||||
0.170084 | + | 0.985429i | \(0.445596\pi\) | |||||||
\(744\) | −4.06226 | −0.148930 | ||||||||
\(745\) | 12.1058 | 0.443521 | ||||||||
\(746\) | −28.1904 | −1.03212 | ||||||||
\(747\) | 4.56738 | 0.167112 | ||||||||
\(748\) | −0.149511 | −0.00546666 | ||||||||
\(749\) | 3.01962 | 0.110335 | ||||||||
\(750\) | −3.06059 | −0.111757 | ||||||||
\(751\) | 30.1938 | 1.10179 | 0.550894 | − | 0.834575i | \(-0.314287\pi\) | ||||
0.550894 | + | 0.834575i | \(0.314287\pi\) | |||||||
\(752\) | −4.02658 | −0.146834 | ||||||||
\(753\) | 47.6331 | 1.73585 | ||||||||
\(754\) | 24.9502 | 0.908631 | ||||||||
\(755\) | −20.5589 | −0.748216 | ||||||||
\(756\) | −3.11919 | −0.113444 | ||||||||
\(757\) | −8.16053 | −0.296600 | −0.148300 | − | 0.988942i | \(-0.547380\pi\) | ||||
−0.148300 | + | 0.988942i | \(0.547380\pi\) | |||||||
\(758\) | 8.83096 | 0.320755 | ||||||||
\(759\) | −0.289455 | −0.0105066 | ||||||||
\(760\) | 0.653758 | 0.0237143 | ||||||||
\(761\) | −6.29743 | −0.228282 | −0.114141 | − | 0.993465i | \(-0.536411\pi\) | ||||
−0.114141 | + | 0.993465i | \(0.536411\pi\) | |||||||
\(762\) | −61.1736 | −2.21609 | ||||||||
\(763\) | 4.85252 | 0.175673 | ||||||||
\(764\) | 9.68976 | 0.350563 | ||||||||
\(765\) | −2.41809 | −0.0874261 | ||||||||
\(766\) | −23.8392 | −0.861346 | ||||||||
\(767\) | 13.6638 | 0.493370 | ||||||||
\(768\) | −3.06059 | −0.110440 | ||||||||
\(769\) | −14.2318 | −0.513213 | −0.256606 | − | 0.966516i | \(-0.582604\pi\) | ||||
−0.256606 | + | 0.966516i | \(0.582604\pi\) | |||||||
\(770\) | 0.119157 | 0.00429410 | ||||||||
\(771\) | −50.5395 | −1.82014 | ||||||||
\(772\) | −3.47297 | −0.124995 | ||||||||
\(773\) | −31.3779 | −1.12858 | −0.564291 | − | 0.825576i | \(-0.690851\pi\) | ||||
−0.564291 | + | 0.825576i | \(0.690851\pi\) | |||||||
\(774\) | −3.47062 | −0.124749 | ||||||||
\(775\) | 1.32728 | 0.0476773 | ||||||||
\(776\) | −14.8895 | −0.534500 | ||||||||
\(777\) | −8.33164 | −0.298896 | ||||||||
\(778\) | 7.53468 | 0.270131 | ||||||||
\(779\) | −5.46921 | −0.195955 | ||||||||
\(780\) | 7.28221 | 0.260745 | ||||||||
\(781\) | −3.85486 | −0.137938 | ||||||||
\(782\) | −0.0912323 | −0.00326246 | ||||||||
\(783\) | 108.066 | 3.86197 | ||||||||
\(784\) | −6.90839 | −0.246728 | ||||||||
\(785\) | −7.47357 | −0.266743 | ||||||||
\(786\) | −28.3898 | −1.01263 | ||||||||
\(787\) | 16.1594 | 0.576019 | 0.288009 | − | 0.957628i | \(-0.407007\pi\) | ||||
0.288009 | + | 0.957628i | \(0.407007\pi\) | |||||||
\(788\) | −7.43346 | −0.264806 | ||||||||
\(789\) | 14.0079 | 0.498695 | ||||||||
\(790\) | 6.29968 | 0.224133 | ||||||||
\(791\) | −3.09520 | −0.110053 | ||||||||
\(792\) | 2.50668 | 0.0890711 | ||||||||
\(793\) | −4.99980 | −0.177548 | ||||||||
\(794\) | 32.0835 | 1.13860 | ||||||||
\(795\) | 15.7939 | 0.560154 | ||||||||
\(796\) | 3.67524 | 0.130265 | ||||||||
\(797\) | −25.9997 | −0.920957 | −0.460478 | − | 0.887671i | \(-0.652322\pi\) | ||||
−0.460478 | + | 0.887671i | \(0.652322\pi\) | |||||||
\(798\) | −0.605605 | −0.0214382 | ||||||||
\(799\) | 1.52918 | 0.0540985 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −61.6546 | −2.17846 | ||||||||
\(802\) | −10.4304 | −0.368311 | ||||||||
\(803\) | 5.18721 | 0.183053 | ||||||||
\(804\) | −49.3407 | −1.74011 | ||||||||
\(805\) | 0.0727099 | 0.00256269 | ||||||||
\(806\) | −3.15806 | −0.111238 | ||||||||
\(807\) | −87.3438 | −3.07465 | ||||||||
\(808\) | −18.4852 | −0.650309 | ||||||||
\(809\) | 34.8638 | 1.22575 | 0.612873 | − | 0.790181i | \(-0.290014\pi\) | ||||
0.612873 | + | 0.790181i | \(0.290014\pi\) | |||||||
\(810\) | 12.4397 | 0.437087 | ||||||||
\(811\) | 17.2743 | 0.606582 | 0.303291 | − | 0.952898i | \(-0.401915\pi\) | ||||
0.303291 | + | 0.952898i | \(0.401915\pi\) | |||||||
\(812\) | −3.17382 | −0.111379 | ||||||||
\(813\) | 16.9954 | 0.596056 | ||||||||
\(814\) | 3.54085 | 0.124107 | ||||||||
\(815\) | −2.21871 | −0.0777179 | ||||||||
\(816\) | 1.16233 | 0.0406895 | ||||||||
\(817\) | −0.356348 | −0.0124670 | ||||||||
\(818\) | 1.01459 | 0.0354744 | ||||||||
\(819\) | −4.58537 | −0.160226 | ||||||||
\(820\) | −8.36579 | −0.292146 | ||||||||
\(821\) | 34.9707 | 1.22049 | 0.610243 | − | 0.792214i | \(-0.291072\pi\) | ||||
0.610243 | + | 0.792214i | \(0.291072\pi\) | |||||||
\(822\) | −1.11660 | −0.0389461 | ||||||||
\(823\) | −24.5645 | −0.856265 | −0.428133 | − | 0.903716i | \(-0.640828\pi\) | ||||
−0.428133 | + | 0.903716i | \(0.640828\pi\) | |||||||
\(824\) | 5.65667 | 0.197059 | ||||||||
\(825\) | −1.20491 | −0.0419497 | ||||||||
\(826\) | −1.73812 | −0.0604769 | ||||||||
\(827\) | 21.7667 | 0.756901 | 0.378451 | − | 0.925621i | \(-0.376457\pi\) | ||||
0.378451 | + | 0.925621i | \(0.376457\pi\) | |||||||
\(828\) | 1.52959 | 0.0531569 | ||||||||
\(829\) | −41.9351 | −1.45647 | −0.728233 | − | 0.685330i | \(-0.759658\pi\) | ||||
−0.728233 | + | 0.685330i | \(0.759658\pi\) | |||||||
\(830\) | 0.717328 | 0.0248988 | ||||||||
\(831\) | −47.4158 | −1.64484 | ||||||||
\(832\) | −2.37935 | −0.0824891 | ||||||||
\(833\) | 2.62361 | 0.0909028 | ||||||||
\(834\) | 25.4207 | 0.880245 | ||||||||
\(835\) | −12.5368 | −0.433855 | ||||||||
\(836\) | 0.257376 | 0.00890152 | ||||||||
\(837\) | −13.6785 | −0.472797 | ||||||||
\(838\) | 22.6659 | 0.782981 | ||||||||
\(839\) | 1.34936 | 0.0465851 | 0.0232926 | − | 0.999729i | \(-0.492585\pi\) | ||||
0.0232926 | + | 0.999729i | \(0.492585\pi\) | |||||||
\(840\) | −0.926345 | −0.0319619 | ||||||||
\(841\) | 80.9589 | 2.79169 | ||||||||
\(842\) | −20.7214 | −0.714107 | ||||||||
\(843\) | 24.1762 | 0.832672 | ||||||||
\(844\) | −20.2472 | −0.696936 | ||||||||
\(845\) | −7.33870 | −0.252459 | ||||||||
\(846\) | −25.6381 | −0.881454 | ||||||||
\(847\) | −3.28245 | −0.112786 | ||||||||
\(848\) | −5.16043 | −0.177210 | ||||||||
\(849\) | 66.7465 | 2.29073 | ||||||||
\(850\) | −0.379772 | −0.0130261 | ||||||||
\(851\) | 2.16065 | 0.0740660 | ||||||||
\(852\) | 29.9684 | 1.02670 | ||||||||
\(853\) | 38.6294 | 1.32265 | 0.661323 | − | 0.750101i | \(-0.269995\pi\) | ||||
0.661323 | + | 0.750101i | \(0.269995\pi\) | |||||||
\(854\) | 0.636007 | 0.0217637 | ||||||||
\(855\) | 4.16261 | 0.142358 | ||||||||
\(856\) | 9.97666 | 0.340995 | ||||||||
\(857\) | −50.7150 | −1.73239 | −0.866196 | − | 0.499704i | \(-0.833442\pi\) | ||||
−0.866196 | + | 0.499704i | \(0.833442\pi\) | |||||||
\(858\) | 2.86691 | 0.0978746 | ||||||||
\(859\) | 42.3999 | 1.44667 | 0.723333 | − | 0.690499i | \(-0.242609\pi\) | ||||
0.723333 | + | 0.690499i | \(0.242609\pi\) | |||||||
\(860\) | −0.545077 | −0.0185870 | ||||||||
\(861\) | 7.74961 | 0.264106 | ||||||||
\(862\) | 9.10219 | 0.310022 | ||||||||
\(863\) | 40.2068 | 1.36866 | 0.684328 | − | 0.729174i | \(-0.260096\pi\) | ||||
0.684328 | + | 0.729174i | \(0.260096\pi\) | |||||||
\(864\) | −10.3056 | −0.350605 | ||||||||
\(865\) | 7.28234 | 0.247607 | ||||||||
\(866\) | −31.4151 | −1.06753 | ||||||||
\(867\) | 51.5886 | 1.75204 | ||||||||
\(868\) | 0.401726 | 0.0136355 | ||||||||
\(869\) | 2.48010 | 0.0841316 | ||||||||
\(870\) | 32.0937 | 1.08808 | ||||||||
\(871\) | −38.3582 | −1.29972 | ||||||||
\(872\) | 16.0324 | 0.542927 | ||||||||
\(873\) | −94.8043 | −3.20864 | ||||||||
\(874\) | 0.157052 | 0.00531236 | ||||||||
\(875\) | 0.302669 | 0.0102321 | ||||||||
\(876\) | −40.3263 | −1.36250 | ||||||||
\(877\) | 2.34974 | 0.0793450 | 0.0396725 | − | 0.999213i | \(-0.487369\pi\) | ||||
0.0396725 | + | 0.999213i | \(0.487369\pi\) | |||||||
\(878\) | −0.429760 | −0.0145037 | ||||||||
\(879\) | −68.2963 | −2.30358 | ||||||||
\(880\) | 0.393686 | 0.0132712 | ||||||||
\(881\) | 7.06575 | 0.238051 | 0.119026 | − | 0.992891i | \(-0.462023\pi\) | ||||
0.119026 | + | 0.992891i | \(0.462023\pi\) | |||||||
\(882\) | −43.9872 | −1.48112 | ||||||||
\(883\) | 53.2309 | 1.79136 | 0.895681 | − | 0.444696i | \(-0.146688\pi\) | ||||
0.895681 | + | 0.444696i | \(0.146688\pi\) | |||||||
\(884\) | 0.903609 | 0.0303917 | ||||||||
\(885\) | 17.5759 | 0.590807 | ||||||||
\(886\) | 33.5818 | 1.12820 | ||||||||
\(887\) | −29.9113 | −1.00432 | −0.502162 | − | 0.864774i | \(-0.667462\pi\) | ||||
−0.502162 | + | 0.864774i | \(0.667462\pi\) | |||||||
\(888\) | −27.5272 | −0.923754 | ||||||||
\(889\) | 6.04960 | 0.202897 | ||||||||
\(890\) | −9.68315 | −0.324580 | ||||||||
\(891\) | 4.89734 | 0.164067 | ||||||||
\(892\) | 10.8134 | 0.362058 | ||||||||
\(893\) | −2.63241 | −0.0880902 | ||||||||
\(894\) | −37.0508 | −1.23916 | ||||||||
\(895\) | 11.8959 | 0.397637 | ||||||||
\(896\) | 0.302669 | 0.0101115 | ||||||||
\(897\) | 1.74940 | 0.0584107 | ||||||||
\(898\) | −20.7822 | −0.693510 | ||||||||
\(899\) | −13.9180 | −0.464193 | ||||||||
\(900\) | 6.36721 | 0.212240 | ||||||||
\(901\) | 1.95978 | 0.0652899 | ||||||||
\(902\) | −3.29350 | −0.109662 | ||||||||
\(903\) | 0.504929 | 0.0168030 | ||||||||
\(904\) | −10.2264 | −0.340124 | ||||||||
\(905\) | −20.4579 | −0.680042 | ||||||||
\(906\) | 62.9224 | 2.09046 | ||||||||
\(907\) | −5.96352 | −0.198015 | −0.0990077 | − | 0.995087i | \(-0.531567\pi\) | ||||
−0.0990077 | + | 0.995087i | \(0.531567\pi\) | |||||||
\(908\) | −27.9968 | −0.929108 | ||||||||
\(909\) | −117.699 | −3.90384 | ||||||||
\(910\) | −0.720154 | −0.0238729 | ||||||||
\(911\) | −29.5363 | −0.978581 | −0.489290 | − | 0.872121i | \(-0.662744\pi\) | ||||
−0.489290 | + | 0.872121i | \(0.662744\pi\) | |||||||
\(912\) | −2.00089 | −0.0662559 | ||||||||
\(913\) | 0.282402 | 0.00934615 | ||||||||
\(914\) | −1.56659 | −0.0518183 | ||||||||
\(915\) | −6.43131 | −0.212612 | ||||||||
\(916\) | −21.2086 | −0.700753 | ||||||||
\(917\) | 2.80753 | 0.0927129 | ||||||||
\(918\) | 3.91379 | 0.129174 | ||||||||
\(919\) | 2.98568 | 0.0984886 | 0.0492443 | − | 0.998787i | \(-0.484319\pi\) | ||||
0.0492443 | + | 0.998787i | \(0.484319\pi\) | |||||||
\(920\) | 0.240229 | 0.00792012 | ||||||||
\(921\) | −36.5547 | −1.20452 | ||||||||
\(922\) | −7.95973 | −0.262140 | ||||||||
\(923\) | 23.2978 | 0.766858 | ||||||||
\(924\) | −0.364689 | −0.0119974 | ||||||||
\(925\) | 8.99410 | 0.295724 | ||||||||
\(926\) | −40.2680 | −1.32329 | ||||||||
\(927\) | 36.0172 | 1.18296 | ||||||||
\(928\) | −10.4861 | −0.344224 | ||||||||
\(929\) | 18.5062 | 0.607170 | 0.303585 | − | 0.952804i | \(-0.401816\pi\) | ||||
0.303585 | + | 0.952804i | \(0.401816\pi\) | |||||||
\(930\) | −4.06226 | −0.133207 | ||||||||
\(931\) | −4.51642 | −0.148020 | ||||||||
\(932\) | −29.8509 | −0.977797 | ||||||||
\(933\) | 50.4281 | 1.65094 | ||||||||
\(934\) | −34.5397 | −1.13017 | ||||||||
\(935\) | −0.149511 | −0.00488953 | ||||||||
\(936\) | −15.1498 | −0.495187 | ||||||||
\(937\) | −24.6054 | −0.803822 | −0.401911 | − | 0.915679i | \(-0.631654\pi\) | ||||
−0.401911 | + | 0.915679i | \(0.631654\pi\) | |||||||
\(938\) | 4.87942 | 0.159319 | ||||||||
\(939\) | −7.41883 | −0.242104 | ||||||||
\(940\) | −4.02658 | −0.131332 | ||||||||
\(941\) | −21.6435 | −0.705558 | −0.352779 | − | 0.935707i | \(-0.614763\pi\) | ||||
−0.352779 | + | 0.935707i | \(0.614763\pi\) | |||||||
\(942\) | 22.8735 | 0.745259 | ||||||||
\(943\) | −2.00971 | −0.0654451 | ||||||||
\(944\) | −5.74265 | −0.186907 | ||||||||
\(945\) | −3.11919 | −0.101467 | ||||||||
\(946\) | −0.214589 | −0.00697690 | ||||||||
\(947\) | 43.9424 | 1.42794 | 0.713968 | − | 0.700178i | \(-0.246896\pi\) | ||||
0.713968 | + | 0.700178i | \(0.246896\pi\) | |||||||
\(948\) | −19.2807 | −0.626209 | ||||||||
\(949\) | −31.3503 | −1.01767 | ||||||||
\(950\) | 0.653758 | 0.0212107 | ||||||||
\(951\) | 91.6240 | 2.97111 | ||||||||
\(952\) | −0.114945 | −0.00372539 | ||||||||
\(953\) | 52.7051 | 1.70728 | 0.853642 | − | 0.520860i | \(-0.174389\pi\) | ||||
0.853642 | + | 0.520860i | \(0.174389\pi\) | |||||||
\(954\) | −32.8575 | −1.06380 | ||||||||
\(955\) | 9.68976 | 0.313553 | ||||||||
\(956\) | −9.17427 | −0.296717 | ||||||||
\(957\) | 12.6349 | 0.408427 | ||||||||
\(958\) | 2.87871 | 0.0930071 | ||||||||
\(959\) | 0.110424 | 0.00356576 | ||||||||
\(960\) | −3.06059 | −0.0987801 | ||||||||
\(961\) | −29.2383 | −0.943172 | ||||||||
\(962\) | −21.4001 | −0.689967 | ||||||||
\(963\) | 63.5234 | 2.04701 | ||||||||
\(964\) | 14.5645 | 0.469092 | ||||||||
\(965\) | −3.47297 | −0.111799 | ||||||||
\(966\) | −0.222535 | −0.00715995 | ||||||||
\(967\) | 30.6050 | 0.984190 | 0.492095 | − | 0.870542i | \(-0.336231\pi\) | ||||
0.492095 | + | 0.870542i | \(0.336231\pi\) | |||||||
\(968\) | −10.8450 | −0.348572 | ||||||||
\(969\) | 0.759880 | 0.0244109 | ||||||||
\(970\) | −14.8895 | −0.478072 | ||||||||
\(971\) | 0.654697 | 0.0210102 | 0.0105051 | − | 0.999945i | \(-0.496656\pi\) | ||||
0.0105051 | + | 0.999945i | \(0.496656\pi\) | |||||||
\(972\) | −7.15592 | −0.229526 | ||||||||
\(973\) | −2.51391 | −0.0805922 | ||||||||
\(974\) | −4.69576 | −0.150462 | ||||||||
\(975\) | 7.28221 | 0.233217 | ||||||||
\(976\) | 2.10133 | 0.0672619 | ||||||||
\(977\) | 50.6299 | 1.61979 | 0.809896 | − | 0.586573i | \(-0.199523\pi\) | ||||
0.809896 | + | 0.586573i | \(0.199523\pi\) | |||||||
\(978\) | 6.79055 | 0.217138 | ||||||||
\(979\) | −3.81212 | −0.121836 | ||||||||
\(980\) | −6.90839 | −0.220680 | ||||||||
\(981\) | 102.082 | 3.25922 | ||||||||
\(982\) | 4.22768 | 0.134911 | ||||||||
\(983\) | −30.6793 | −0.978516 | −0.489258 | − | 0.872139i | \(-0.662732\pi\) | ||||
−0.489258 | + | 0.872139i | \(0.662732\pi\) | |||||||
\(984\) | 25.6043 | 0.816234 | ||||||||
\(985\) | −7.43346 | −0.236850 | ||||||||
\(986\) | 3.98234 | 0.126823 | ||||||||
\(987\) | 3.73000 | 0.118727 | ||||||||
\(988\) | −1.55552 | −0.0494876 | ||||||||
\(989\) | −0.130943 | −0.00416375 | ||||||||
\(990\) | 2.50668 | 0.0796676 | ||||||||
\(991\) | 28.0894 | 0.892288 | 0.446144 | − | 0.894961i | \(-0.352797\pi\) | ||||
0.446144 | + | 0.894961i | \(0.352797\pi\) | |||||||
\(992\) | 1.32728 | 0.0421412 | ||||||||
\(993\) | 32.2748 | 1.02421 | ||||||||
\(994\) | −2.96364 | −0.0940009 | ||||||||
\(995\) | 3.67524 | 0.116513 | ||||||||
\(996\) | −2.19545 | −0.0695654 | ||||||||
\(997\) | 14.8062 | 0.468916 | 0.234458 | − | 0.972126i | \(-0.424669\pi\) | ||||
0.234458 | + | 0.972126i | \(0.424669\pi\) | |||||||
\(998\) | 33.4020 | 1.05732 | ||||||||
\(999\) | −92.6900 | −2.93258 |
(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 | 6010.2.a.c.1.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6010.2.a.c.1.1 | ✓ | 16 | 1.1 | even | 1 | trivial |