Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, 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("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.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: | \(40.3563931816\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.19520000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 12x^{6} + 16x^{5} + 50x^{4} - 24x^{3} - 72x^{2} - 32x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.236286\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5054.1 |
$q$-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 | ||||||||
\(3\) | 0.0295377 | 0.0170536 | 0.00852679 | − | 0.999964i | \(-0.497286\pi\) | ||||
0.00852679 | + | 0.999964i | \(0.497286\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.02989 | −0.907795 | −0.453897 | − | 0.891054i | \(-0.649967\pi\) | ||||
−0.453897 | + | 0.891054i | \(0.649967\pi\) | |||||||
\(6\) | −0.0295377 | −0.0120587 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.99913 | −0.999709 | ||||||||
\(10\) | 2.02989 | 0.641908 | ||||||||
\(11\) | −2.94417 | −0.887700 | −0.443850 | − | 0.896101i | \(-0.646388\pi\) | ||||
−0.443850 | + | 0.896101i | \(0.646388\pi\) | |||||||
\(12\) | 0.0295377 | 0.00852679 | ||||||||
\(13\) | 1.18331 | 0.328190 | 0.164095 | − | 0.986445i | \(-0.447530\pi\) | ||||
0.164095 | + | 0.986445i | \(0.447530\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −0.0599583 | −0.0154812 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.65490 | 1.12898 | 0.564490 | − | 0.825440i | \(-0.309073\pi\) | ||||
0.564490 | + | 0.825440i | \(0.309073\pi\) | |||||||
\(18\) | 2.99913 | 0.706901 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −2.02989 | −0.453897 | ||||||||
\(21\) | −0.0295377 | −0.00644565 | ||||||||
\(22\) | 2.94417 | 0.627699 | ||||||||
\(23\) | 6.80976 | 1.41993 | 0.709967 | − | 0.704235i | \(-0.248710\pi\) | ||||
0.709967 | + | 0.704235i | \(0.248710\pi\) | |||||||
\(24\) | −0.0295377 | −0.00602935 | ||||||||
\(25\) | −0.879544 | −0.175909 | ||||||||
\(26\) | −1.18331 | −0.232066 | ||||||||
\(27\) | −0.177200 | −0.0341022 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −0.396447 | −0.0736184 | −0.0368092 | − | 0.999322i | \(-0.511719\pi\) | ||||
−0.0368092 | + | 0.999322i | \(0.511719\pi\) | |||||||
\(30\) | 0.0599583 | 0.0109468 | ||||||||
\(31\) | 0.265419 | 0.0476707 | 0.0238354 | − | 0.999716i | \(-0.492412\pi\) | ||||
0.0238354 | + | 0.999716i | \(0.492412\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.0869639 | −0.0151385 | ||||||||
\(34\) | −4.65490 | −0.798309 | ||||||||
\(35\) | 2.02989 | 0.343114 | ||||||||
\(36\) | −2.99913 | −0.499855 | ||||||||
\(37\) | 2.79771 | 0.459941 | 0.229971 | − | 0.973198i | \(-0.426137\pi\) | ||||
0.229971 | + | 0.973198i | \(0.426137\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0349521 | 0.00559682 | ||||||||
\(40\) | 2.02989 | 0.320954 | ||||||||
\(41\) | 5.15394 | 0.804911 | 0.402455 | − | 0.915440i | \(-0.368157\pi\) | ||||
0.402455 | + | 0.915440i | \(0.368157\pi\) | |||||||
\(42\) | 0.0295377 | 0.00455776 | ||||||||
\(43\) | −0.743718 | −0.113416 | −0.0567080 | − | 0.998391i | \(-0.518060\pi\) | ||||
−0.0567080 | + | 0.998391i | \(0.518060\pi\) | |||||||
\(44\) | −2.94417 | −0.443850 | ||||||||
\(45\) | 6.08790 | 0.907531 | ||||||||
\(46\) | −6.80976 | −1.00405 | ||||||||
\(47\) | −2.97389 | −0.433787 | −0.216893 | − | 0.976195i | \(-0.569592\pi\) | ||||
−0.216893 | + | 0.976195i | \(0.569592\pi\) | |||||||
\(48\) | 0.0295377 | 0.00426340 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.879544 | 0.124386 | ||||||||
\(51\) | 0.137495 | 0.0192532 | ||||||||
\(52\) | 1.18331 | 0.164095 | ||||||||
\(53\) | −4.60071 | −0.631957 | −0.315978 | − | 0.948766i | \(-0.602333\pi\) | ||||
−0.315978 | + | 0.948766i | \(0.602333\pi\) | |||||||
\(54\) | 0.177200 | 0.0241139 | ||||||||
\(55\) | 5.97634 | 0.805850 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.396447 | 0.0520560 | ||||||||
\(59\) | 7.11953 | 0.926884 | 0.463442 | − | 0.886127i | \(-0.346614\pi\) | ||||
0.463442 | + | 0.886127i | \(0.346614\pi\) | |||||||
\(60\) | −0.0599583 | −0.00774058 | ||||||||
\(61\) | 9.03552 | 1.15688 | 0.578440 | − | 0.815725i | \(-0.303662\pi\) | ||||
0.578440 | + | 0.815725i | \(0.303662\pi\) | |||||||
\(62\) | −0.265419 | −0.0337083 | ||||||||
\(63\) | 2.99913 | 0.377855 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.40198 | −0.297929 | ||||||||
\(66\) | 0.0869639 | 0.0107045 | ||||||||
\(67\) | −11.1770 | −1.36549 | −0.682743 | − | 0.730659i | \(-0.739213\pi\) | ||||
−0.682743 | + | 0.730659i | \(0.739213\pi\) | |||||||
\(68\) | 4.65490 | 0.564490 | ||||||||
\(69\) | 0.201145 | 0.0242150 | ||||||||
\(70\) | −2.02989 | −0.242618 | ||||||||
\(71\) | 13.9312 | 1.65333 | 0.826663 | − | 0.562697i | \(-0.190236\pi\) | ||||
0.826663 | + | 0.562697i | \(0.190236\pi\) | |||||||
\(72\) | 2.99913 | 0.353451 | ||||||||
\(73\) | 4.21053 | 0.492805 | 0.246403 | − | 0.969168i | \(-0.420751\pi\) | ||||
0.246403 | + | 0.969168i | \(0.420751\pi\) | |||||||
\(74\) | −2.79771 | −0.325228 | ||||||||
\(75\) | −0.0259797 | −0.00299988 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.94417 | 0.335519 | ||||||||
\(78\) | −0.0349521 | −0.00395755 | ||||||||
\(79\) | −2.21703 | −0.249435 | −0.124718 | − | 0.992192i | \(-0.539803\pi\) | ||||
−0.124718 | + | 0.992192i | \(0.539803\pi\) | |||||||
\(80\) | −2.02989 | −0.226949 | ||||||||
\(81\) | 8.99215 | 0.999128 | ||||||||
\(82\) | −5.15394 | −0.569158 | ||||||||
\(83\) | 12.5400 | 1.37645 | 0.688224 | − | 0.725498i | \(-0.258391\pi\) | ||||
0.688224 | + | 0.725498i | \(0.258391\pi\) | |||||||
\(84\) | −0.0295377 | −0.00322282 | ||||||||
\(85\) | −9.44895 | −1.02488 | ||||||||
\(86\) | 0.743718 | 0.0801972 | ||||||||
\(87\) | −0.0117101 | −0.00125546 | ||||||||
\(88\) | 2.94417 | 0.313849 | ||||||||
\(89\) | −16.7143 | −1.77172 | −0.885859 | − | 0.463955i | \(-0.846430\pi\) | ||||
−0.885859 | + | 0.463955i | \(0.846430\pi\) | |||||||
\(90\) | −6.08790 | −0.641721 | ||||||||
\(91\) | −1.18331 | −0.124044 | ||||||||
\(92\) | 6.80976 | 0.709967 | ||||||||
\(93\) | 0.00783987 | 0.000812957 0 | ||||||||
\(94\) | 2.97389 | 0.306734 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.0295377 | −0.00301468 | ||||||||
\(97\) | −2.11838 | −0.215089 | −0.107545 | − | 0.994200i | \(-0.534299\pi\) | ||||
−0.107545 | + | 0.994200i | \(0.534299\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 8.82994 | 0.887442 | ||||||||
\(100\) | −0.879544 | −0.0879544 | ||||||||
\(101\) | −13.3618 | −1.32955 | −0.664775 | − | 0.747043i | \(-0.731473\pi\) | ||||
−0.664775 | + | 0.747043i | \(0.731473\pi\) | |||||||
\(102\) | −0.137495 | −0.0136140 | ||||||||
\(103\) | −13.3318 | −1.31362 | −0.656811 | − | 0.754055i | \(-0.728095\pi\) | ||||
−0.656811 | + | 0.754055i | \(0.728095\pi\) | |||||||
\(104\) | −1.18331 | −0.116033 | ||||||||
\(105\) | 0.0599583 | 0.00585133 | ||||||||
\(106\) | 4.60071 | 0.446861 | ||||||||
\(107\) | −9.44616 | −0.913195 | −0.456597 | − | 0.889673i | \(-0.650932\pi\) | ||||
−0.456597 | + | 0.889673i | \(0.650932\pi\) | |||||||
\(108\) | −0.177200 | −0.0170511 | ||||||||
\(109\) | −9.67812 | −0.926996 | −0.463498 | − | 0.886098i | \(-0.653406\pi\) | ||||
−0.463498 | + | 0.886098i | \(0.653406\pi\) | |||||||
\(110\) | −5.97634 | −0.569822 | ||||||||
\(111\) | 0.0826380 | 0.00784365 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −8.76641 | −0.824675 | −0.412337 | − | 0.911031i | \(-0.635287\pi\) | ||||
−0.412337 | + | 0.911031i | \(0.635287\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.8231 | −1.28901 | ||||||||
\(116\) | −0.396447 | −0.0368092 | ||||||||
\(117\) | −3.54889 | −0.328095 | ||||||||
\(118\) | −7.11953 | −0.655406 | ||||||||
\(119\) | −4.65490 | −0.426714 | ||||||||
\(120\) | 0.0599583 | 0.00547341 | ||||||||
\(121\) | −2.33187 | −0.211988 | ||||||||
\(122\) | −9.03552 | −0.818038 | ||||||||
\(123\) | 0.152236 | 0.0137266 | ||||||||
\(124\) | 0.265419 | 0.0238354 | ||||||||
\(125\) | 11.9348 | 1.06748 | ||||||||
\(126\) | −2.99913 | −0.267184 | ||||||||
\(127\) | −17.1303 | −1.52007 | −0.760033 | − | 0.649884i | \(-0.774818\pi\) | ||||
−0.760033 | + | 0.649884i | \(0.774818\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.0219677 | −0.00193415 | ||||||||
\(130\) | 2.40198 | 0.210668 | ||||||||
\(131\) | 6.67961 | 0.583600 | 0.291800 | − | 0.956479i | \(-0.405746\pi\) | ||||
0.291800 | + | 0.956479i | \(0.405746\pi\) | |||||||
\(132\) | −0.0869639 | −0.00756924 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.1770 | 0.965544 | ||||||||
\(135\) | 0.359697 | 0.0309578 | ||||||||
\(136\) | −4.65490 | −0.399155 | ||||||||
\(137\) | 7.13250 | 0.609371 | 0.304685 | − | 0.952453i | \(-0.401449\pi\) | ||||
0.304685 | + | 0.952453i | \(0.401449\pi\) | |||||||
\(138\) | −0.201145 | −0.0171226 | ||||||||
\(139\) | 17.3500 | 1.47161 | 0.735803 | − | 0.677195i | \(-0.236805\pi\) | ||||
0.735803 | + | 0.677195i | \(0.236805\pi\) | |||||||
\(140\) | 2.02989 | 0.171557 | ||||||||
\(141\) | −0.0878419 | −0.00739762 | ||||||||
\(142\) | −13.9312 | −1.16908 | ||||||||
\(143\) | −3.48386 | −0.291335 | ||||||||
\(144\) | −2.99913 | −0.249927 | ||||||||
\(145\) | 0.804744 | 0.0668304 | ||||||||
\(146\) | −4.21053 | −0.348466 | ||||||||
\(147\) | 0.0295377 | 0.00243623 | ||||||||
\(148\) | 2.79771 | 0.229971 | ||||||||
\(149\) | 10.6622 | 0.873480 | 0.436740 | − | 0.899588i | \(-0.356133\pi\) | ||||
0.436740 | + | 0.899588i | \(0.356133\pi\) | |||||||
\(150\) | 0.0259797 | 0.00212123 | ||||||||
\(151\) | 4.50841 | 0.366889 | 0.183445 | − | 0.983030i | \(-0.441275\pi\) | ||||
0.183445 | + | 0.983030i | \(0.441275\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.9607 | −1.12865 | ||||||||
\(154\) | −2.94417 | −0.237248 | ||||||||
\(155\) | −0.538772 | −0.0432752 | ||||||||
\(156\) | 0.0349521 | 0.00279841 | ||||||||
\(157\) | −1.30678 | −0.104293 | −0.0521463 | − | 0.998639i | \(-0.516606\pi\) | ||||
−0.0521463 | + | 0.998639i | \(0.516606\pi\) | |||||||
\(158\) | 2.21703 | 0.176377 | ||||||||
\(159\) | −0.135894 | −0.0107771 | ||||||||
\(160\) | 2.02989 | 0.160477 | ||||||||
\(161\) | −6.80976 | −0.536685 | ||||||||
\(162\) | −8.99215 | −0.706490 | ||||||||
\(163\) | −12.8874 | −1.00942 | −0.504710 | − | 0.863289i | \(-0.668401\pi\) | ||||
−0.504710 | + | 0.863289i | \(0.668401\pi\) | |||||||
\(164\) | 5.15394 | 0.402455 | ||||||||
\(165\) | 0.176527 | 0.0137426 | ||||||||
\(166\) | −12.5400 | −0.973296 | ||||||||
\(167\) | −17.2129 | −1.33198 | −0.665988 | − | 0.745963i | \(-0.731990\pi\) | ||||
−0.665988 | + | 0.745963i | \(0.731990\pi\) | |||||||
\(168\) | 0.0295377 | 0.00227888 | ||||||||
\(169\) | −11.5998 | −0.892291 | ||||||||
\(170\) | 9.44895 | 0.724701 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.743718 | −0.0567080 | ||||||||
\(173\) | −12.2229 | −0.929291 | −0.464646 | − | 0.885497i | \(-0.653818\pi\) | ||||
−0.464646 | + | 0.885497i | \(0.653818\pi\) | |||||||
\(174\) | 0.0117101 | 0.000887742 0 | ||||||||
\(175\) | 0.879544 | 0.0664873 | ||||||||
\(176\) | −2.94417 | −0.221925 | ||||||||
\(177\) | 0.210294 | 0.0158067 | ||||||||
\(178\) | 16.7143 | 1.25279 | ||||||||
\(179\) | 10.7092 | 0.800445 | 0.400222 | − | 0.916418i | \(-0.368933\pi\) | ||||
0.400222 | + | 0.916418i | \(0.368933\pi\) | |||||||
\(180\) | 6.08790 | 0.453765 | ||||||||
\(181\) | −21.8663 | −1.62531 | −0.812653 | − | 0.582748i | \(-0.801978\pi\) | ||||
−0.812653 | + | 0.582748i | \(0.801978\pi\) | |||||||
\(182\) | 1.18331 | 0.0877126 | ||||||||
\(183\) | 0.266888 | 0.0197290 | ||||||||
\(184\) | −6.80976 | −0.502023 | ||||||||
\(185\) | −5.67905 | −0.417532 | ||||||||
\(186\) | −0.00783987 | −0.000574847 0 | ||||||||
\(187\) | −13.7048 | −1.00220 | ||||||||
\(188\) | −2.97389 | −0.216893 | ||||||||
\(189\) | 0.177200 | 0.0128894 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.1654 | −1.38676 | −0.693380 | − | 0.720572i | \(-0.743879\pi\) | ||||
−0.693380 | + | 0.720572i | \(0.743879\pi\) | |||||||
\(192\) | 0.0295377 | 0.00213170 | ||||||||
\(193\) | 12.9081 | 0.929145 | 0.464572 | − | 0.885535i | \(-0.346208\pi\) | ||||
0.464572 | + | 0.885535i | \(0.346208\pi\) | |||||||
\(194\) | 2.11838 | 0.152091 | ||||||||
\(195\) | −0.0709490 | −0.00508077 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 23.6787 | 1.68704 | 0.843520 | − | 0.537098i | \(-0.180479\pi\) | ||||
0.843520 | + | 0.537098i | \(0.180479\pi\) | |||||||
\(198\) | −8.82994 | −0.627516 | ||||||||
\(199\) | −6.56540 | −0.465409 | −0.232705 | − | 0.972547i | \(-0.574758\pi\) | ||||
−0.232705 | + | 0.972547i | \(0.574758\pi\) | |||||||
\(200\) | 0.879544 | 0.0621932 | ||||||||
\(201\) | −0.330142 | −0.0232864 | ||||||||
\(202\) | 13.3618 | 0.940134 | ||||||||
\(203\) | 0.396447 | 0.0278251 | ||||||||
\(204\) | 0.137495 | 0.00962658 | ||||||||
\(205\) | −10.4619 | −0.730694 | ||||||||
\(206\) | 13.3318 | 0.928871 | ||||||||
\(207\) | −20.4234 | −1.41952 | ||||||||
\(208\) | 1.18331 | 0.0820476 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.0599583 | −0.00413751 | ||||||||
\(211\) | 11.9730 | 0.824255 | 0.412128 | − | 0.911126i | \(-0.364786\pi\) | ||||
0.412128 | + | 0.911126i | \(0.364786\pi\) | |||||||
\(212\) | −4.60071 | −0.315978 | ||||||||
\(213\) | 0.411495 | 0.0281951 | ||||||||
\(214\) | 9.44616 | 0.645726 | ||||||||
\(215\) | 1.50967 | 0.102958 | ||||||||
\(216\) | 0.177200 | 0.0120570 | ||||||||
\(217\) | −0.265419 | −0.0180178 | ||||||||
\(218\) | 9.67812 | 0.655485 | ||||||||
\(219\) | 0.124369 | 0.00840410 | ||||||||
\(220\) | 5.97634 | 0.402925 | ||||||||
\(221\) | 5.50818 | 0.370520 | ||||||||
\(222\) | −0.0826380 | −0.00554630 | ||||||||
\(223\) | −8.47530 | −0.567548 | −0.283774 | − | 0.958891i | \(-0.591587\pi\) | ||||
−0.283774 | + | 0.958891i | \(0.591587\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 2.63787 | 0.175858 | ||||||||
\(226\) | 8.76641 | 0.583133 | ||||||||
\(227\) | −2.19728 | −0.145839 | −0.0729193 | − | 0.997338i | \(-0.523232\pi\) | ||||
−0.0729193 | + | 0.997338i | \(0.523232\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.5591 | −0.962089 | −0.481045 | − | 0.876696i | \(-0.659743\pi\) | ||||
−0.481045 | + | 0.876696i | \(0.659743\pi\) | |||||||
\(230\) | 13.8231 | 0.911467 | ||||||||
\(231\) | 0.0869639 | 0.00572181 | ||||||||
\(232\) | 0.396447 | 0.0260280 | ||||||||
\(233\) | −17.7732 | −1.16436 | −0.582179 | − | 0.813060i | \(-0.697800\pi\) | ||||
−0.582179 | + | 0.813060i | \(0.697800\pi\) | |||||||
\(234\) | 3.54889 | 0.231998 | ||||||||
\(235\) | 6.03668 | 0.393789 | ||||||||
\(236\) | 7.11953 | 0.463442 | ||||||||
\(237\) | −0.0654859 | −0.00425377 | ||||||||
\(238\) | 4.65490 | 0.301733 | ||||||||
\(239\) | −18.9372 | −1.22495 | −0.612473 | − | 0.790492i | \(-0.709825\pi\) | ||||
−0.612473 | + | 0.790492i | \(0.709825\pi\) | |||||||
\(240\) | −0.0599583 | −0.00387029 | ||||||||
\(241\) | 19.6449 | 1.26544 | 0.632720 | − | 0.774380i | \(-0.281938\pi\) | ||||
0.632720 | + | 0.774380i | \(0.281938\pi\) | |||||||
\(242\) | 2.33187 | 0.149898 | ||||||||
\(243\) | 0.797208 | 0.0511409 | ||||||||
\(244\) | 9.03552 | 0.578440 | ||||||||
\(245\) | −2.02989 | −0.129685 | ||||||||
\(246\) | −0.152236 | −0.00970618 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.265419 | −0.0168541 | ||||||||
\(249\) | 0.370404 | 0.0234734 | ||||||||
\(250\) | −11.9348 | −0.754825 | ||||||||
\(251\) | 23.0399 | 1.45426 | 0.727132 | − | 0.686497i | \(-0.240853\pi\) | ||||
0.727132 | + | 0.686497i | \(0.240853\pi\) | |||||||
\(252\) | 2.99913 | 0.188927 | ||||||||
\(253\) | −20.0491 | −1.26048 | ||||||||
\(254\) | 17.1303 | 1.07485 | ||||||||
\(255\) | −0.279100 | −0.0174779 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.0390 | −1.18762 | −0.593811 | − | 0.804604i | \(-0.702377\pi\) | ||||
−0.593811 | + | 0.804604i | \(0.702377\pi\) | |||||||
\(258\) | 0.0219677 | 0.00136765 | ||||||||
\(259\) | −2.79771 | −0.173842 | ||||||||
\(260\) | −2.40198 | −0.148965 | ||||||||
\(261\) | 1.18900 | 0.0735970 | ||||||||
\(262\) | −6.67961 | −0.412668 | ||||||||
\(263\) | 15.3994 | 0.949569 | 0.474785 | − | 0.880102i | \(-0.342526\pi\) | ||||
0.474785 | + | 0.880102i | \(0.342526\pi\) | |||||||
\(264\) | 0.0869639 | 0.00535226 | ||||||||
\(265\) | 9.33895 | 0.573687 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.493703 | −0.0302141 | ||||||||
\(268\) | −11.1770 | −0.682743 | ||||||||
\(269\) | 15.8634 | 0.967207 | 0.483603 | − | 0.875287i | \(-0.339328\pi\) | ||||
0.483603 | + | 0.875287i | \(0.339328\pi\) | |||||||
\(270\) | −0.359697 | −0.0218905 | ||||||||
\(271\) | −23.1622 | −1.40701 | −0.703503 | − | 0.710692i | \(-0.748382\pi\) | ||||
−0.703503 | + | 0.710692i | \(0.748382\pi\) | |||||||
\(272\) | 4.65490 | 0.282245 | ||||||||
\(273\) | −0.0349521 | −0.00211540 | ||||||||
\(274\) | −7.13250 | −0.430890 | ||||||||
\(275\) | 2.58953 | 0.156154 | ||||||||
\(276\) | 0.201145 | 0.0121075 | ||||||||
\(277\) | 0.153840 | 0.00924332 | 0.00462166 | − | 0.999989i | \(-0.498529\pi\) | ||||
0.00462166 | + | 0.999989i | \(0.498529\pi\) | |||||||
\(278\) | −17.3500 | −1.04058 | ||||||||
\(279\) | −0.796026 | −0.0476569 | ||||||||
\(280\) | −2.02989 | −0.121309 | ||||||||
\(281\) | −12.5517 | −0.748770 | −0.374385 | − | 0.927273i | \(-0.622146\pi\) | ||||
−0.374385 | + | 0.927273i | \(0.622146\pi\) | |||||||
\(282\) | 0.0878419 | 0.00523091 | ||||||||
\(283\) | −0.132478 | −0.00787500 | −0.00393750 | − | 0.999992i | \(-0.501253\pi\) | ||||
−0.00393750 | + | 0.999992i | \(0.501253\pi\) | |||||||
\(284\) | 13.9312 | 0.826663 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.48386 | 0.206005 | ||||||||
\(287\) | −5.15394 | −0.304228 | ||||||||
\(288\) | 2.99913 | 0.176725 | ||||||||
\(289\) | 4.66813 | 0.274596 | ||||||||
\(290\) | −0.804744 | −0.0472562 | ||||||||
\(291\) | −0.0625721 | −0.00366804 | ||||||||
\(292\) | 4.21053 | 0.246403 | ||||||||
\(293\) | 31.7197 | 1.85308 | 0.926542 | − | 0.376191i | \(-0.122766\pi\) | ||||
0.926542 | + | 0.376191i | \(0.122766\pi\) | |||||||
\(294\) | −0.0295377 | −0.00172267 | ||||||||
\(295\) | −14.4519 | −0.841421 | ||||||||
\(296\) | −2.79771 | −0.162614 | ||||||||
\(297\) | 0.521708 | 0.0302725 | ||||||||
\(298\) | −10.6622 | −0.617644 | ||||||||
\(299\) | 8.05804 | 0.466009 | ||||||||
\(300\) | −0.0259797 | −0.00149994 | ||||||||
\(301\) | 0.743718 | 0.0428672 | ||||||||
\(302\) | −4.50841 | −0.259430 | ||||||||
\(303\) | −0.394677 | −0.0226736 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.3411 | −1.05021 | ||||||||
\(306\) | 13.9607 | 0.798077 | ||||||||
\(307\) | −6.49152 | −0.370491 | −0.185245 | − | 0.982692i | \(-0.559308\pi\) | ||||
−0.185245 | + | 0.982692i | \(0.559308\pi\) | |||||||
\(308\) | 2.94417 | 0.167760 | ||||||||
\(309\) | −0.393790 | −0.0224020 | ||||||||
\(310\) | 0.538772 | 0.0306002 | ||||||||
\(311\) | 15.9813 | 0.906218 | 0.453109 | − | 0.891455i | \(-0.350315\pi\) | ||||
0.453109 | + | 0.891455i | \(0.350315\pi\) | |||||||
\(312\) | −0.0349521 | −0.00197878 | ||||||||
\(313\) | 2.85203 | 0.161207 | 0.0806033 | − | 0.996746i | \(-0.474315\pi\) | ||||
0.0806033 | + | 0.996746i | \(0.474315\pi\) | |||||||
\(314\) | 1.30678 | 0.0737460 | ||||||||
\(315\) | −6.08790 | −0.343014 | ||||||||
\(316\) | −2.21703 | −0.124718 | ||||||||
\(317\) | 16.9449 | 0.951720 | 0.475860 | − | 0.879521i | \(-0.342137\pi\) | ||||
0.475860 | + | 0.879521i | \(0.342137\pi\) | |||||||
\(318\) | 0.135894 | 0.00762058 | ||||||||
\(319\) | 1.16721 | 0.0653510 | ||||||||
\(320\) | −2.02989 | −0.113474 | ||||||||
\(321\) | −0.279018 | −0.0155732 | ||||||||
\(322\) | 6.80976 | 0.379493 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 8.99215 | 0.499564 | ||||||||
\(325\) | −1.04077 | −0.0577316 | ||||||||
\(326\) | 12.8874 | 0.713767 | ||||||||
\(327\) | −0.285869 | −0.0158086 | ||||||||
\(328\) | −5.15394 | −0.284579 | ||||||||
\(329\) | 2.97389 | 0.163956 | ||||||||
\(330\) | −0.176527 | −0.00971750 | ||||||||
\(331\) | −21.8016 | −1.19832 | −0.599162 | − | 0.800628i | \(-0.704499\pi\) | ||||
−0.599162 | + | 0.800628i | \(0.704499\pi\) | |||||||
\(332\) | 12.5400 | 0.688224 | ||||||||
\(333\) | −8.39070 | −0.459808 | ||||||||
\(334\) | 17.2129 | 0.941849 | ||||||||
\(335\) | 22.6880 | 1.23958 | ||||||||
\(336\) | −0.0295377 | −0.00161141 | ||||||||
\(337\) | 24.5605 | 1.33790 | 0.668949 | − | 0.743309i | \(-0.266745\pi\) | ||||
0.668949 | + | 0.743309i | \(0.266745\pi\) | |||||||
\(338\) | 11.5998 | 0.630945 | ||||||||
\(339\) | −0.258939 | −0.0140637 | ||||||||
\(340\) | −9.44895 | −0.512441 | ||||||||
\(341\) | −0.781439 | −0.0423173 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0.743718 | 0.0400986 | ||||||||
\(345\) | −0.408302 | −0.0219822 | ||||||||
\(346\) | 12.2229 | 0.657108 | ||||||||
\(347\) | −22.6149 | −1.21403 | −0.607015 | − | 0.794690i | \(-0.707633\pi\) | ||||
−0.607015 | + | 0.794690i | \(0.707633\pi\) | |||||||
\(348\) | −0.0117101 | −0.000627729 0 | ||||||||
\(349\) | −28.8834 | −1.54609 | −0.773046 | − | 0.634350i | \(-0.781268\pi\) | ||||
−0.773046 | + | 0.634350i | \(0.781268\pi\) | |||||||
\(350\) | −0.879544 | −0.0470136 | ||||||||
\(351\) | −0.209682 | −0.0111920 | ||||||||
\(352\) | 2.94417 | 0.156925 | ||||||||
\(353\) | −21.9422 | −1.16787 | −0.583933 | − | 0.811802i | \(-0.698487\pi\) | ||||
−0.583933 | + | 0.811802i | \(0.698487\pi\) | |||||||
\(354\) | −0.210294 | −0.0111770 | ||||||||
\(355\) | −28.2788 | −1.50088 | ||||||||
\(356\) | −16.7143 | −0.885859 | ||||||||
\(357\) | −0.137495 | −0.00727701 | ||||||||
\(358\) | −10.7092 | −0.566000 | ||||||||
\(359\) | −14.3290 | −0.756257 | −0.378128 | − | 0.925753i | \(-0.623432\pi\) | ||||
−0.378128 | + | 0.925753i | \(0.623432\pi\) | |||||||
\(360\) | −6.08790 | −0.320861 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 21.8663 | 1.14927 | ||||||||
\(363\) | −0.0688780 | −0.00361516 | ||||||||
\(364\) | −1.18331 | −0.0620221 | ||||||||
\(365\) | −8.54692 | −0.447366 | ||||||||
\(366\) | −0.266888 | −0.0139505 | ||||||||
\(367\) | −4.90373 | −0.255973 | −0.127986 | − | 0.991776i | \(-0.540851\pi\) | ||||
−0.127986 | + | 0.991776i | \(0.540851\pi\) | |||||||
\(368\) | 6.80976 | 0.354984 | ||||||||
\(369\) | −15.4573 | −0.804677 | ||||||||
\(370\) | 5.67905 | 0.295240 | ||||||||
\(371\) | 4.60071 | 0.238857 | ||||||||
\(372\) | 0.00783987 | 0.000406478 0 | ||||||||
\(373\) | −27.4511 | −1.42137 | −0.710683 | − | 0.703512i | \(-0.751614\pi\) | ||||
−0.710683 | + | 0.703512i | \(0.751614\pi\) | |||||||
\(374\) | 13.7048 | 0.708660 | ||||||||
\(375\) | 0.352527 | 0.0182044 | ||||||||
\(376\) | 2.97389 | 0.153367 | ||||||||
\(377\) | −0.469119 | −0.0241608 | ||||||||
\(378\) | −0.177200 | −0.00911420 | ||||||||
\(379\) | −3.03127 | −0.155706 | −0.0778528 | − | 0.996965i | \(-0.524806\pi\) | ||||
−0.0778528 | + | 0.996965i | \(0.524806\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.505989 | −0.0259226 | ||||||||
\(382\) | 19.1654 | 0.980588 | ||||||||
\(383\) | 1.79284 | 0.0916098 | 0.0458049 | − | 0.998950i | \(-0.485415\pi\) | ||||
0.0458049 | + | 0.998950i | \(0.485415\pi\) | |||||||
\(384\) | −0.0295377 | −0.00150734 | ||||||||
\(385\) | −5.97634 | −0.304583 | ||||||||
\(386\) | −12.9081 | −0.657005 | ||||||||
\(387\) | 2.23051 | 0.113383 | ||||||||
\(388\) | −2.11838 | −0.107545 | ||||||||
\(389\) | −30.3079 | −1.53667 | −0.768335 | − | 0.640048i | \(-0.778915\pi\) | ||||
−0.768335 | + | 0.640048i | \(0.778915\pi\) | |||||||
\(390\) | 0.0709490 | 0.00359264 | ||||||||
\(391\) | 31.6988 | 1.60308 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0.197300 | 0.00995247 | ||||||||
\(394\) | −23.6787 | −1.19292 | ||||||||
\(395\) | 4.50033 | 0.226436 | ||||||||
\(396\) | 8.82994 | 0.443721 | ||||||||
\(397\) | 39.1611 | 1.96544 | 0.982719 | − | 0.185102i | \(-0.0592614\pi\) | ||||
0.982719 | + | 0.185102i | \(0.0592614\pi\) | |||||||
\(398\) | 6.56540 | 0.329094 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.879544 | −0.0439772 | ||||||||
\(401\) | 0.123230 | 0.00615384 | 0.00307692 | − | 0.999995i | \(-0.499021\pi\) | ||||
0.00307692 | + | 0.999995i | \(0.499021\pi\) | |||||||
\(402\) | 0.330142 | 0.0164660 | ||||||||
\(403\) | 0.314073 | 0.0156451 | ||||||||
\(404\) | −13.3618 | −0.664775 | ||||||||
\(405\) | −18.2531 | −0.907003 | ||||||||
\(406\) | −0.396447 | −0.0196753 | ||||||||
\(407\) | −8.23694 | −0.408290 | ||||||||
\(408\) | −0.137495 | −0.00680702 | ||||||||
\(409\) | −29.4542 | −1.45642 | −0.728208 | − | 0.685356i | \(-0.759647\pi\) | ||||
−0.728208 | + | 0.685356i | \(0.759647\pi\) | |||||||
\(410\) | 10.4619 | 0.516678 | ||||||||
\(411\) | 0.210678 | 0.0103920 | ||||||||
\(412\) | −13.3318 | −0.656811 | ||||||||
\(413\) | −7.11953 | −0.350329 | ||||||||
\(414\) | 20.4234 | 1.00375 | ||||||||
\(415\) | −25.4549 | −1.24953 | ||||||||
\(416\) | −1.18331 | −0.0580164 | ||||||||
\(417\) | 0.512478 | 0.0250962 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.1094 | 0.786996 | 0.393498 | − | 0.919325i | \(-0.371265\pi\) | ||||
0.393498 | + | 0.919325i | \(0.371265\pi\) | |||||||
\(420\) | 0.0599583 | 0.00292566 | ||||||||
\(421\) | −28.9033 | −1.40866 | −0.704329 | − | 0.709873i | \(-0.748752\pi\) | ||||
−0.704329 | + | 0.709873i | \(0.748752\pi\) | |||||||
\(422\) | −11.9730 | −0.582837 | ||||||||
\(423\) | 8.91908 | 0.433661 | ||||||||
\(424\) | 4.60071 | 0.223430 | ||||||||
\(425\) | −4.09419 | −0.198598 | ||||||||
\(426\) | −0.411495 | −0.0199370 | ||||||||
\(427\) | −9.03552 | −0.437260 | ||||||||
\(428\) | −9.44616 | −0.456597 | ||||||||
\(429\) | −0.102905 | −0.00496830 | ||||||||
\(430\) | −1.50967 | −0.0728026 | ||||||||
\(431\) | 39.7770 | 1.91599 | 0.957996 | − | 0.286781i | \(-0.0925852\pi\) | ||||
0.957996 | + | 0.286781i | \(0.0925852\pi\) | |||||||
\(432\) | −0.177200 | −0.00852555 | ||||||||
\(433\) | −26.9114 | −1.29328 | −0.646641 | − | 0.762795i | \(-0.723827\pi\) | ||||
−0.646641 | + | 0.762795i | \(0.723827\pi\) | |||||||
\(434\) | 0.265419 | 0.0127405 | ||||||||
\(435\) | 0.0237703 | 0.00113970 | ||||||||
\(436\) | −9.67812 | −0.463498 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −0.124369 | −0.00594260 | ||||||||
\(439\) | 0.705775 | 0.0336848 | 0.0168424 | − | 0.999858i | \(-0.494639\pi\) | ||||
0.0168424 | + | 0.999858i | \(0.494639\pi\) | |||||||
\(440\) | −5.97634 | −0.284911 | ||||||||
\(441\) | −2.99913 | −0.142816 | ||||||||
\(442\) | −5.50818 | −0.261997 | ||||||||
\(443\) | 15.2248 | 0.723350 | 0.361675 | − | 0.932304i | \(-0.382205\pi\) | ||||
0.361675 | + | 0.932304i | \(0.382205\pi\) | |||||||
\(444\) | 0.0826380 | 0.00392183 | ||||||||
\(445\) | 33.9283 | 1.60836 | ||||||||
\(446\) | 8.47530 | 0.401317 | ||||||||
\(447\) | 0.314936 | 0.0148960 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 16.0822 | 0.758968 | 0.379484 | − | 0.925198i | \(-0.376102\pi\) | ||||
0.379484 | + | 0.925198i | \(0.376102\pi\) | |||||||
\(450\) | −2.63787 | −0.124350 | ||||||||
\(451\) | −15.1741 | −0.714520 | ||||||||
\(452\) | −8.76641 | −0.412337 | ||||||||
\(453\) | 0.133168 | 0.00625678 | ||||||||
\(454\) | 2.19728 | 0.103124 | ||||||||
\(455\) | 2.40198 | 0.112607 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.39979 | −0.0654794 | −0.0327397 | − | 0.999464i | \(-0.510423\pi\) | ||||
−0.0327397 | + | 0.999464i | \(0.510423\pi\) | |||||||
\(458\) | 14.5591 | 0.680300 | ||||||||
\(459\) | −0.824850 | −0.0385007 | ||||||||
\(460\) | −13.8231 | −0.644504 | ||||||||
\(461\) | 15.4887 | 0.721380 | 0.360690 | − | 0.932686i | \(-0.382541\pi\) | ||||
0.360690 | + | 0.932686i | \(0.382541\pi\) | |||||||
\(462\) | −0.0869639 | −0.00404593 | ||||||||
\(463\) | −1.80796 | −0.0840229 | −0.0420115 | − | 0.999117i | \(-0.513377\pi\) | ||||
−0.0420115 | + | 0.999117i | \(0.513377\pi\) | |||||||
\(464\) | −0.396447 | −0.0184046 | ||||||||
\(465\) | −0.0159141 | −0.000737998 0 | ||||||||
\(466\) | 17.7732 | 0.823326 | ||||||||
\(467\) | 11.8566 | 0.548659 | 0.274330 | − | 0.961636i | \(-0.411544\pi\) | ||||
0.274330 | + | 0.961636i | \(0.411544\pi\) | |||||||
\(468\) | −3.54889 | −0.164047 | ||||||||
\(469\) | 11.1770 | 0.516105 | ||||||||
\(470\) | −6.03668 | −0.278451 | ||||||||
\(471\) | −0.0385993 | −0.00177856 | ||||||||
\(472\) | −7.11953 | −0.327703 | ||||||||
\(473\) | 2.18963 | 0.100679 | ||||||||
\(474\) | 0.0654859 | 0.00300787 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.65490 | −0.213357 | ||||||||
\(477\) | 13.7981 | 0.631773 | ||||||||
\(478\) | 18.9372 | 0.866167 | ||||||||
\(479\) | 2.75396 | 0.125831 | 0.0629157 | − | 0.998019i | \(-0.479960\pi\) | ||||
0.0629157 | + | 0.998019i | \(0.479960\pi\) | |||||||
\(480\) | 0.0599583 | 0.00273671 | ||||||||
\(481\) | 3.31056 | 0.150948 | ||||||||
\(482\) | −19.6449 | −0.894802 | ||||||||
\(483\) | −0.201145 | −0.00915240 | ||||||||
\(484\) | −2.33187 | −0.105994 | ||||||||
\(485\) | 4.30008 | 0.195257 | ||||||||
\(486\) | −0.797208 | −0.0361621 | ||||||||
\(487\) | −11.6214 | −0.526615 | −0.263307 | − | 0.964712i | \(-0.584813\pi\) | ||||
−0.263307 | + | 0.964712i | \(0.584813\pi\) | |||||||
\(488\) | −9.03552 | −0.409019 | ||||||||
\(489\) | −0.380664 | −0.0172142 | ||||||||
\(490\) | 2.02989 | 0.0917011 | ||||||||
\(491\) | −20.5701 | −0.928317 | −0.464158 | − | 0.885752i | \(-0.653643\pi\) | ||||
−0.464158 | + | 0.885752i | \(0.653643\pi\) | |||||||
\(492\) | 0.152236 | 0.00686331 | ||||||||
\(493\) | −1.84542 | −0.0831137 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −17.9238 | −0.805615 | ||||||||
\(496\) | 0.265419 | 0.0119177 | ||||||||
\(497\) | −13.9312 | −0.624899 | ||||||||
\(498\) | −0.370404 | −0.0165982 | ||||||||
\(499\) | −13.7051 | −0.613522 | −0.306761 | − | 0.951787i | \(-0.599245\pi\) | ||||
−0.306761 | + | 0.951787i | \(0.599245\pi\) | |||||||
\(500\) | 11.9348 | 0.533742 | ||||||||
\(501\) | −0.508429 | −0.0227150 | ||||||||
\(502\) | −23.0399 | −1.02832 | ||||||||
\(503\) | −3.42219 | −0.152588 | −0.0762939 | − | 0.997085i | \(-0.524309\pi\) | ||||
−0.0762939 | + | 0.997085i | \(0.524309\pi\) | |||||||
\(504\) | −2.99913 | −0.133592 | ||||||||
\(505\) | 27.1230 | 1.20696 | ||||||||
\(506\) | 20.0491 | 0.891291 | ||||||||
\(507\) | −0.342631 | −0.0152168 | ||||||||
\(508\) | −17.1303 | −0.760033 | ||||||||
\(509\) | −29.8042 | −1.32105 | −0.660524 | − | 0.750805i | \(-0.729666\pi\) | ||||
−0.660524 | + | 0.750805i | \(0.729666\pi\) | |||||||
\(510\) | 0.279100 | 0.0123588 | ||||||||
\(511\) | −4.21053 | −0.186263 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 19.0390 | 0.839776 | ||||||||
\(515\) | 27.0621 | 1.19250 | ||||||||
\(516\) | −0.0219677 | −0.000967074 0 | ||||||||
\(517\) | 8.75564 | 0.385073 | ||||||||
\(518\) | 2.79771 | 0.122925 | ||||||||
\(519\) | −0.361037 | −0.0158477 | ||||||||
\(520\) | 2.40198 | 0.105334 | ||||||||
\(521\) | −19.6327 | −0.860125 | −0.430062 | − | 0.902799i | \(-0.641508\pi\) | ||||
−0.430062 | + | 0.902799i | \(0.641508\pi\) | |||||||
\(522\) | −1.18900 | −0.0520409 | ||||||||
\(523\) | −25.6599 | −1.12203 | −0.561016 | − | 0.827805i | \(-0.689589\pi\) | ||||
−0.561016 | + | 0.827805i | \(0.689589\pi\) | |||||||
\(524\) | 6.67961 | 0.291800 | ||||||||
\(525\) | 0.0259797 | 0.00113385 | ||||||||
\(526\) | −15.3994 | −0.671447 | ||||||||
\(527\) | 1.23550 | 0.0538193 | ||||||||
\(528\) | −0.0869639 | −0.00378462 | ||||||||
\(529\) | 23.3729 | 1.01621 | ||||||||
\(530\) | −9.33895 | −0.405658 | ||||||||
\(531\) | −21.3524 | −0.926615 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.09870 | 0.264164 | ||||||||
\(534\) | 0.493703 | 0.0213646 | ||||||||
\(535\) | 19.1747 | 0.828993 | ||||||||
\(536\) | 11.1770 | 0.482772 | ||||||||
\(537\) | 0.316326 | 0.0136505 | ||||||||
\(538\) | −15.8634 | −0.683919 | ||||||||
\(539\) | −2.94417 | −0.126814 | ||||||||
\(540\) | 0.359697 | 0.0154789 | ||||||||
\(541\) | −8.99925 | −0.386908 | −0.193454 | − | 0.981109i | \(-0.561969\pi\) | ||||
−0.193454 | + | 0.981109i | \(0.561969\pi\) | |||||||
\(542\) | 23.1622 | 0.994903 | ||||||||
\(543\) | −0.645879 | −0.0277173 | ||||||||
\(544\) | −4.65490 | −0.199577 | ||||||||
\(545\) | 19.6455 | 0.841522 | ||||||||
\(546\) | 0.0349521 | 0.00149581 | ||||||||
\(547\) | 21.8354 | 0.933616 | 0.466808 | − | 0.884359i | \(-0.345404\pi\) | ||||
0.466808 | + | 0.884359i | \(0.345404\pi\) | |||||||
\(548\) | 7.13250 | 0.304685 | ||||||||
\(549\) | −27.0987 | −1.15654 | ||||||||
\(550\) | −2.58953 | −0.110418 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −0.201145 | −0.00856128 | ||||||||
\(553\) | 2.21703 | 0.0942777 | ||||||||
\(554\) | −0.153840 | −0.00653602 | ||||||||
\(555\) | −0.167746 | −0.00712043 | ||||||||
\(556\) | 17.3500 | 0.735803 | ||||||||
\(557\) | −14.1210 | −0.598324 | −0.299162 | − | 0.954202i | \(-0.596707\pi\) | ||||
−0.299162 | + | 0.954202i | \(0.596707\pi\) | |||||||
\(558\) | 0.796026 | 0.0336985 | ||||||||
\(559\) | −0.880047 | −0.0372220 | ||||||||
\(560\) | 2.02989 | 0.0857785 | ||||||||
\(561\) | −0.404809 | −0.0170910 | ||||||||
\(562\) | 12.5517 | 0.529461 | ||||||||
\(563\) | −25.8400 | −1.08903 | −0.544513 | − | 0.838752i | \(-0.683286\pi\) | ||||
−0.544513 | + | 0.838752i | \(0.683286\pi\) | |||||||
\(564\) | −0.0878419 | −0.00369881 | ||||||||
\(565\) | 17.7949 | 0.748635 | ||||||||
\(566\) | 0.132478 | 0.00556847 | ||||||||
\(567\) | −8.99215 | −0.377635 | ||||||||
\(568\) | −13.9312 | −0.584539 | ||||||||
\(569\) | 27.5260 | 1.15395 | 0.576976 | − | 0.816761i | \(-0.304233\pi\) | ||||
0.576976 | + | 0.816761i | \(0.304233\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.9105 | 0.916928 | 0.458464 | − | 0.888713i | \(-0.348400\pi\) | ||||
0.458464 | + | 0.888713i | \(0.348400\pi\) | |||||||
\(572\) | −3.48386 | −0.145667 | ||||||||
\(573\) | −0.566102 | −0.0236492 | ||||||||
\(574\) | 5.15394 | 0.215121 | ||||||||
\(575\) | −5.98949 | −0.249779 | ||||||||
\(576\) | −2.99913 | −0.124964 | ||||||||
\(577\) | −46.9112 | −1.95294 | −0.976469 | − | 0.215659i | \(-0.930810\pi\) | ||||
−0.976469 | + | 0.215659i | \(0.930810\pi\) | |||||||
\(578\) | −4.66813 | −0.194169 | ||||||||
\(579\) | 0.381275 | 0.0158452 | ||||||||
\(580\) | 0.804744 | 0.0334152 | ||||||||
\(581\) | −12.5400 | −0.520249 | ||||||||
\(582\) | 0.0625721 | 0.00259370 | ||||||||
\(583\) | 13.5453 | 0.560988 | ||||||||
\(584\) | −4.21053 | −0.174233 | ||||||||
\(585\) | 7.20386 | 0.297843 | ||||||||
\(586\) | −31.7197 | −1.31033 | ||||||||
\(587\) | 20.2603 | 0.836234 | 0.418117 | − | 0.908393i | \(-0.362690\pi\) | ||||
0.418117 | + | 0.908393i | \(0.362690\pi\) | |||||||
\(588\) | 0.0295377 | 0.00121811 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 14.4519 | 0.594974 | ||||||||
\(591\) | 0.699415 | 0.0287701 | ||||||||
\(592\) | 2.79771 | 0.114985 | ||||||||
\(593\) | −30.8939 | −1.26866 | −0.634330 | − | 0.773062i | \(-0.718724\pi\) | ||||
−0.634330 | + | 0.773062i | \(0.718724\pi\) | |||||||
\(594\) | −0.521708 | −0.0214059 | ||||||||
\(595\) | 9.44895 | 0.387369 | ||||||||
\(596\) | 10.6622 | 0.436740 | ||||||||
\(597\) | −0.193927 | −0.00793689 | ||||||||
\(598\) | −8.05804 | −0.329518 | ||||||||
\(599\) | 30.1902 | 1.23354 | 0.616769 | − | 0.787144i | \(-0.288441\pi\) | ||||
0.616769 | + | 0.787144i | \(0.288441\pi\) | |||||||
\(600\) | 0.0259797 | 0.00106062 | ||||||||
\(601\) | −42.7945 | −1.74562 | −0.872812 | − | 0.488057i | \(-0.837706\pi\) | ||||
−0.872812 | + | 0.488057i | \(0.837706\pi\) | |||||||
\(602\) | −0.743718 | −0.0303117 | ||||||||
\(603\) | 33.5212 | 1.36509 | ||||||||
\(604\) | 4.50841 | 0.183445 | ||||||||
\(605\) | 4.73344 | 0.192442 | ||||||||
\(606\) | 0.394677 | 0.0160327 | ||||||||
\(607\) | −25.8352 | −1.04862 | −0.524309 | − | 0.851528i | \(-0.675676\pi\) | ||||
−0.524309 | + | 0.851528i | \(0.675676\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.0117101 | 0.000474518 0 | ||||||||
\(610\) | 18.3411 | 0.742610 | ||||||||
\(611\) | −3.51903 | −0.142365 | ||||||||
\(612\) | −13.9607 | −0.564326 | ||||||||
\(613\) | 8.26177 | 0.333690 | 0.166845 | − | 0.985983i | \(-0.446642\pi\) | ||||
0.166845 | + | 0.985983i | \(0.446642\pi\) | |||||||
\(614\) | 6.49152 | 0.261977 | ||||||||
\(615\) | −0.309021 | −0.0124609 | ||||||||
\(616\) | −2.94417 | −0.118624 | ||||||||
\(617\) | 14.5351 | 0.585163 | 0.292581 | − | 0.956241i | \(-0.405486\pi\) | ||||
0.292581 | + | 0.956241i | \(0.405486\pi\) | |||||||
\(618\) | 0.393790 | 0.0158406 | ||||||||
\(619\) | −42.9334 | −1.72564 | −0.862819 | − | 0.505513i | \(-0.831303\pi\) | ||||
−0.862819 | + | 0.505513i | \(0.831303\pi\) | |||||||
\(620\) | −0.538772 | −0.0216376 | ||||||||
\(621\) | −1.20669 | −0.0484229 | ||||||||
\(622\) | −15.9813 | −0.640793 | ||||||||
\(623\) | 16.7143 | 0.669646 | ||||||||
\(624\) | 0.0349521 | 0.00139921 | ||||||||
\(625\) | −19.8287 | −0.793147 | ||||||||
\(626\) | −2.85203 | −0.113990 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.30678 | −0.0521463 | ||||||||
\(629\) | 13.0231 | 0.519265 | ||||||||
\(630\) | 6.08790 | 0.242548 | ||||||||
\(631\) | 11.4310 | 0.455062 | 0.227531 | − | 0.973771i | \(-0.426935\pi\) | ||||
0.227531 | + | 0.973771i | \(0.426935\pi\) | |||||||
\(632\) | 2.21703 | 0.0881887 | ||||||||
\(633\) | 0.353655 | 0.0140565 | ||||||||
\(634\) | −16.9449 | −0.672968 | ||||||||
\(635\) | 34.7726 | 1.37991 | ||||||||
\(636\) | −0.135894 | −0.00538856 | ||||||||
\(637\) | 1.18331 | 0.0468843 | ||||||||
\(638\) | −1.16721 | −0.0462102 | ||||||||
\(639\) | −41.7814 | −1.65285 | ||||||||
\(640\) | 2.02989 | 0.0802385 | ||||||||
\(641\) | 15.4233 | 0.609184 | 0.304592 | − | 0.952483i | \(-0.401480\pi\) | ||||
0.304592 | + | 0.952483i | \(0.401480\pi\) | |||||||
\(642\) | 0.279018 | 0.0110119 | ||||||||
\(643\) | 25.3895 | 1.00126 | 0.500632 | − | 0.865660i | \(-0.333101\pi\) | ||||
0.500632 | + | 0.865660i | \(0.333101\pi\) | |||||||
\(644\) | −6.80976 | −0.268342 | ||||||||
\(645\) | 0.0445920 | 0.00175581 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.4239 | 0.724318 | 0.362159 | − | 0.932116i | \(-0.382040\pi\) | ||||
0.362159 | + | 0.932116i | \(0.382040\pi\) | |||||||
\(648\) | −8.99215 | −0.353245 | ||||||||
\(649\) | −20.9611 | −0.822796 | ||||||||
\(650\) | 1.04077 | 0.0408224 | ||||||||
\(651\) | −0.00783987 | −0.000307269 0 | ||||||||
\(652\) | −12.8874 | −0.504710 | ||||||||
\(653\) | 25.5335 | 0.999205 | 0.499602 | − | 0.866255i | \(-0.333479\pi\) | ||||
0.499602 | + | 0.866255i | \(0.333479\pi\) | |||||||
\(654\) | 0.285869 | 0.0111784 | ||||||||
\(655\) | −13.5589 | −0.529789 | ||||||||
\(656\) | 5.15394 | 0.201228 | ||||||||
\(657\) | −12.6279 | −0.492662 | ||||||||
\(658\) | −2.97389 | −0.115934 | ||||||||
\(659\) | 4.27377 | 0.166482 | 0.0832412 | − | 0.996529i | \(-0.473473\pi\) | ||||
0.0832412 | + | 0.996529i | \(0.473473\pi\) | |||||||
\(660\) | 0.176527 | 0.00687131 | ||||||||
\(661\) | −18.0211 | −0.700941 | −0.350470 | − | 0.936574i | \(-0.613978\pi\) | ||||
−0.350470 | + | 0.936574i | \(0.613978\pi\) | |||||||
\(662\) | 21.8016 | 0.847343 | ||||||||
\(663\) | 0.162699 | 0.00631870 | ||||||||
\(664\) | −12.5400 | −0.486648 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.39070 | 0.325133 | ||||||||
\(667\) | −2.69971 | −0.104533 | ||||||||
\(668\) | −17.2129 | −0.665988 | ||||||||
\(669\) | −0.250341 | −0.00967873 | ||||||||
\(670\) | −22.6880 | −0.876516 | ||||||||
\(671\) | −26.6021 | −1.02696 | ||||||||
\(672\) | 0.0295377 | 0.00113944 | ||||||||
\(673\) | 12.0784 | 0.465587 | 0.232793 | − | 0.972526i | \(-0.425213\pi\) | ||||
0.232793 | + | 0.972526i | \(0.425213\pi\) | |||||||
\(674\) | −24.5605 | −0.946036 | ||||||||
\(675\) | 0.155856 | 0.00599888 | ||||||||
\(676\) | −11.5998 | −0.446146 | ||||||||
\(677\) | 18.5172 | 0.711674 | 0.355837 | − | 0.934548i | \(-0.384196\pi\) | ||||
0.355837 | + | 0.934548i | \(0.384196\pi\) | |||||||
\(678\) | 0.258939 | 0.00994451 | ||||||||
\(679\) | 2.11838 | 0.0812960 | ||||||||
\(680\) | 9.44895 | 0.362351 | ||||||||
\(681\) | −0.0649026 | −0.00248707 | ||||||||
\(682\) | 0.781439 | 0.0299229 | ||||||||
\(683\) | −40.1450 | −1.53611 | −0.768053 | − | 0.640386i | \(-0.778774\pi\) | ||||
−0.768053 | + | 0.640386i | \(0.778774\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.4782 | −0.553184 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −0.430041 | −0.0164071 | ||||||||
\(688\) | −0.743718 | −0.0283540 | ||||||||
\(689\) | −5.44406 | −0.207402 | ||||||||
\(690\) | 0.408302 | 0.0155438 | ||||||||
\(691\) | −37.9320 | −1.44300 | −0.721501 | − | 0.692414i | \(-0.756547\pi\) | ||||
−0.721501 | + | 0.692414i | \(0.756547\pi\) | |||||||
\(692\) | −12.2229 | −0.464646 | ||||||||
\(693\) | −8.82994 | −0.335422 | ||||||||
\(694\) | 22.6149 | 0.858449 | ||||||||
\(695\) | −35.2186 | −1.33592 | ||||||||
\(696\) | 0.0117101 | 0.000443871 0 | ||||||||
\(697\) | 23.9911 | 0.908728 | ||||||||
\(698\) | 28.8834 | 1.09325 | ||||||||
\(699\) | −0.524978 | −0.0198565 | ||||||||
\(700\) | 0.879544 | 0.0332436 | ||||||||
\(701\) | −9.19991 | −0.347476 | −0.173738 | − | 0.984792i | \(-0.555585\pi\) | ||||
−0.173738 | + | 0.984792i | \(0.555585\pi\) | |||||||
\(702\) | 0.209682 | 0.00791395 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −2.94417 | −0.110963 | ||||||||
\(705\) | 0.178309 | 0.00671552 | ||||||||
\(706\) | 21.9422 | 0.825806 | ||||||||
\(707\) | 13.3618 | 0.502523 | ||||||||
\(708\) | 0.210294 | 0.00790335 | ||||||||
\(709\) | 40.5184 | 1.52170 | 0.760850 | − | 0.648928i | \(-0.224782\pi\) | ||||
0.760850 | + | 0.648928i | \(0.224782\pi\) | |||||||
\(710\) | 28.2788 | 1.06128 | ||||||||
\(711\) | 6.64915 | 0.249363 | ||||||||
\(712\) | 16.7143 | 0.626397 | ||||||||
\(713\) | 1.80744 | 0.0676893 | ||||||||
\(714\) | 0.137495 | 0.00514562 | ||||||||
\(715\) | 7.07185 | 0.264472 | ||||||||
\(716\) | 10.7092 | 0.400222 | ||||||||
\(717\) | −0.559361 | −0.0208897 | ||||||||
\(718\) | 14.3290 | 0.534754 | ||||||||
\(719\) | −47.7082 | −1.77921 | −0.889607 | − | 0.456727i | \(-0.849022\pi\) | ||||
−0.889607 | + | 0.456727i | \(0.849022\pi\) | |||||||
\(720\) | 6.08790 | 0.226883 | ||||||||
\(721\) | 13.3318 | 0.496502 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.580265 | 0.0215803 | ||||||||
\(724\) | −21.8663 | −0.812653 | ||||||||
\(725\) | 0.348693 | 0.0129501 | ||||||||
\(726\) | 0.0688780 | 0.00255630 | ||||||||
\(727\) | 1.93893 | 0.0719108 | 0.0359554 | − | 0.999353i | \(-0.488553\pi\) | ||||
0.0359554 | + | 0.999353i | \(0.488553\pi\) | |||||||
\(728\) | 1.18331 | 0.0438563 | ||||||||
\(729\) | −26.9529 | −0.998255 | ||||||||
\(730\) | 8.54692 | 0.316336 | ||||||||
\(731\) | −3.46194 | −0.128044 | ||||||||
\(732\) | 0.266888 | 0.00986448 | ||||||||
\(733\) | 43.0842 | 1.59135 | 0.795676 | − | 0.605723i | \(-0.207116\pi\) | ||||
0.795676 | + | 0.605723i | \(0.207116\pi\) | |||||||
\(734\) | 4.90373 | 0.181000 | ||||||||
\(735\) | −0.0599583 | −0.00221159 | ||||||||
\(736\) | −6.80976 | −0.251011 | ||||||||
\(737\) | 32.9069 | 1.21214 | ||||||||
\(738\) | 15.4573 | 0.568992 | ||||||||
\(739\) | 23.6580 | 0.870273 | 0.435137 | − | 0.900364i | \(-0.356700\pi\) | ||||
0.435137 | + | 0.900364i | \(0.356700\pi\) | |||||||
\(740\) | −5.67905 | −0.208766 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.60071 | −0.168898 | ||||||||
\(743\) | −25.8480 | −0.948270 | −0.474135 | − | 0.880452i | \(-0.657239\pi\) | ||||
−0.474135 | + | 0.880452i | \(0.657239\pi\) | |||||||
\(744\) | −0.00783987 | −0.000287424 0 | ||||||||
\(745\) | −21.6431 | −0.792941 | ||||||||
\(746\) | 27.4511 | 1.00506 | ||||||||
\(747\) | −37.6092 | −1.37605 | ||||||||
\(748\) | −13.7048 | −0.501098 | ||||||||
\(749\) | 9.44616 | 0.345155 | ||||||||
\(750\) | −0.352527 | −0.0128725 | ||||||||
\(751\) | 23.4711 | 0.856472 | 0.428236 | − | 0.903667i | \(-0.359135\pi\) | ||||
0.428236 | + | 0.903667i | \(0.359135\pi\) | |||||||
\(752\) | −2.97389 | −0.108447 | ||||||||
\(753\) | 0.680545 | 0.0248004 | ||||||||
\(754\) | 0.469119 | 0.0170843 | ||||||||
\(755\) | −9.15158 | −0.333060 | ||||||||
\(756\) | 0.177200 | 0.00644471 | ||||||||
\(757\) | −21.0205 | −0.764005 | −0.382002 | − | 0.924161i | \(-0.624765\pi\) | ||||
−0.382002 | + | 0.924161i | \(0.624765\pi\) | |||||||
\(758\) | 3.03127 | 0.110101 | ||||||||
\(759\) | −0.592204 | −0.0214956 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.0214 | 1.23327 | 0.616637 | − | 0.787248i | \(-0.288495\pi\) | ||||
0.616637 | + | 0.787248i | \(0.288495\pi\) | |||||||
\(762\) | 0.505989 | 0.0183300 | ||||||||
\(763\) | 9.67812 | 0.350371 | ||||||||
\(764\) | −19.1654 | −0.693380 | ||||||||
\(765\) | 28.3386 | 1.02458 | ||||||||
\(766\) | −1.79284 | −0.0647779 | ||||||||
\(767\) | 8.42460 | 0.304194 | ||||||||
\(768\) | 0.0295377 | 0.00106585 | ||||||||
\(769\) | 37.4225 | 1.34949 | 0.674745 | − | 0.738051i | \(-0.264254\pi\) | ||||
0.674745 | + | 0.738051i | \(0.264254\pi\) | |||||||
\(770\) | 5.97634 | 0.215372 | ||||||||
\(771\) | −0.562369 | −0.0202532 | ||||||||
\(772\) | 12.9081 | 0.464572 | ||||||||
\(773\) | 20.7862 | 0.747627 | 0.373814 | − | 0.927504i | \(-0.378050\pi\) | ||||
0.373814 | + | 0.927504i | \(0.378050\pi\) | |||||||
\(774\) | −2.23051 | −0.0801739 | ||||||||
\(775\) | −0.233448 | −0.00838570 | ||||||||
\(776\) | 2.11838 | 0.0760455 | ||||||||
\(777\) | −0.0826380 | −0.00296462 | ||||||||
\(778\) | 30.3079 | 1.08659 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.0709490 | −0.00254038 | ||||||||
\(781\) | −41.0157 | −1.46766 | ||||||||
\(782\) | −31.6988 | −1.13355 | ||||||||
\(783\) | 0.0702505 | 0.00251055 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 2.65263 | 0.0946763 | ||||||||
\(786\) | −0.197300 | −0.00703746 | ||||||||
\(787\) | 33.4364 | 1.19188 | 0.595939 | − | 0.803029i | \(-0.296780\pi\) | ||||
0.595939 | + | 0.803029i | \(0.296780\pi\) | |||||||
\(788\) | 23.6787 | 0.843520 | ||||||||
\(789\) | 0.454863 | 0.0161936 | ||||||||
\(790\) | −4.50033 | −0.160114 | ||||||||
\(791\) | 8.76641 | 0.311698 | ||||||||
\(792\) | −8.82994 | −0.313758 | ||||||||
\(793\) | 10.6918 | 0.379677 | ||||||||
\(794\) | −39.1611 | −1.38978 | ||||||||
\(795\) | 0.275851 | 0.00978342 | ||||||||
\(796\) | −6.56540 | −0.232705 | ||||||||
\(797\) | −26.0945 | −0.924316 | −0.462158 | − | 0.886798i | \(-0.652925\pi\) | ||||
−0.462158 | + | 0.886798i | \(0.652925\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.8432 | −0.489737 | ||||||||
\(800\) | 0.879544 | 0.0310966 | ||||||||
\(801\) | 50.1285 | 1.77120 | ||||||||
\(802\) | −0.123230 | −0.00435142 | ||||||||
\(803\) | −12.3965 | −0.437464 | ||||||||
\(804\) | −0.330142 | −0.0116432 | ||||||||
\(805\) | 13.8231 | 0.487199 | ||||||||
\(806\) | −0.314073 | −0.0110627 | ||||||||
\(807\) | 0.468567 | 0.0164943 | ||||||||
\(808\) | 13.3618 | 0.470067 | ||||||||
\(809\) | −40.7851 | −1.43393 | −0.716964 | − | 0.697110i | \(-0.754469\pi\) | ||||
−0.716964 | + | 0.697110i | \(0.754469\pi\) | |||||||
\(810\) | 18.2531 | 0.641348 | ||||||||
\(811\) | −14.5813 | −0.512017 | −0.256009 | − | 0.966674i | \(-0.582408\pi\) | ||||
−0.256009 | + | 0.966674i | \(0.582408\pi\) | |||||||
\(812\) | 0.396447 | 0.0139126 | ||||||||
\(813\) | −0.684159 | −0.0239945 | ||||||||
\(814\) | 8.23694 | 0.288705 | ||||||||
\(815\) | 26.1600 | 0.916346 | ||||||||
\(816\) | 0.137495 | 0.00481329 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 29.4542 | 1.02984 | ||||||||
\(819\) | 3.54889 | 0.124008 | ||||||||
\(820\) | −10.4619 | −0.365347 | ||||||||
\(821\) | −20.1502 | −0.703246 | −0.351623 | − | 0.936142i | \(-0.614370\pi\) | ||||
−0.351623 | + | 0.936142i | \(0.614370\pi\) | |||||||
\(822\) | −0.210678 | −0.00734822 | ||||||||
\(823\) | 49.4504 | 1.72373 | 0.861866 | − | 0.507136i | \(-0.169296\pi\) | ||||
0.861866 | + | 0.507136i | \(0.169296\pi\) | |||||||
\(824\) | 13.3318 | 0.464435 | ||||||||
\(825\) | 0.0764886 | 0.00266299 | ||||||||
\(826\) | 7.11953 | 0.247720 | ||||||||
\(827\) | −35.7637 | −1.24363 | −0.621813 | − | 0.783166i | \(-0.713603\pi\) | ||||
−0.621813 | + | 0.783166i | \(0.713603\pi\) | |||||||
\(828\) | −20.4234 | −0.709761 | ||||||||
\(829\) | −26.6486 | −0.925544 | −0.462772 | − | 0.886477i | \(-0.653145\pi\) | ||||
−0.462772 | + | 0.886477i | \(0.653145\pi\) | |||||||
\(830\) | 25.4549 | 0.883553 | ||||||||
\(831\) | 0.00454406 | 0.000157632 0 | ||||||||
\(832\) | 1.18331 | 0.0410238 | ||||||||
\(833\) | 4.65490 | 0.161283 | ||||||||
\(834\) | −0.512478 | −0.0177457 | ||||||||
\(835\) | 34.9403 | 1.20916 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.0470324 | −0.00162568 | ||||||||
\(838\) | −16.1094 | −0.556491 | ||||||||
\(839\) | 13.0277 | 0.449766 | 0.224883 | − | 0.974386i | \(-0.427800\pi\) | ||||
0.224883 | + | 0.974386i | \(0.427800\pi\) | |||||||
\(840\) | −0.0599583 | −0.00206876 | ||||||||
\(841\) | −28.8428 | −0.994580 | ||||||||
\(842\) | 28.9033 | 0.996072 | ||||||||
\(843\) | −0.370747 | −0.0127692 | ||||||||
\(844\) | 11.9730 | 0.412128 | ||||||||
\(845\) | 23.5463 | 0.810017 | ||||||||
\(846\) | −8.91908 | −0.306644 | ||||||||
\(847\) | 2.33187 | 0.0801240 | ||||||||
\(848\) | −4.60071 | −0.157989 | ||||||||
\(849\) | −0.00391309 | −0.000134297 0 | ||||||||
\(850\) | 4.09419 | 0.140430 | ||||||||
\(851\) | 19.0518 | 0.653087 | ||||||||
\(852\) | 0.411495 | 0.0140976 | ||||||||
\(853\) | 25.8812 | 0.886156 | 0.443078 | − | 0.896483i | \(-0.353886\pi\) | ||||
0.443078 | + | 0.896483i | \(0.353886\pi\) | |||||||
\(854\) | 9.03552 | 0.309189 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.44616 | 0.322863 | ||||||||
\(857\) | −30.2522 | −1.03340 | −0.516698 | − | 0.856168i | \(-0.672839\pi\) | ||||
−0.516698 | + | 0.856168i | \(0.672839\pi\) | |||||||
\(858\) | 0.102905 | 0.00351312 | ||||||||
\(859\) | −7.90397 | −0.269680 | −0.134840 | − | 0.990867i | \(-0.543052\pi\) | ||||
−0.134840 | + | 0.990867i | \(0.543052\pi\) | |||||||
\(860\) | 1.50967 | 0.0514792 | ||||||||
\(861\) | −0.152236 | −0.00518817 | ||||||||
\(862\) | −39.7770 | −1.35481 | ||||||||
\(863\) | 52.7257 | 1.79480 | 0.897402 | − | 0.441214i | \(-0.145452\pi\) | ||||
0.897402 | + | 0.441214i | \(0.145452\pi\) | |||||||
\(864\) | 0.177200 | 0.00602848 | ||||||||
\(865\) | 24.8112 | 0.843606 | ||||||||
\(866\) | 26.9114 | 0.914488 | ||||||||
\(867\) | 0.137886 | 0.00468284 | ||||||||
\(868\) | −0.265419 | −0.00900892 | ||||||||
\(869\) | 6.52731 | 0.221424 | ||||||||
\(870\) | −0.0237703 | −0.000805888 0 | ||||||||
\(871\) | −13.2258 | −0.448139 | ||||||||
\(872\) | 9.67812 | 0.327742 | ||||||||
\(873\) | 6.35330 | 0.215027 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.9348 | −0.403471 | ||||||||
\(876\) | 0.124369 | 0.00420205 | ||||||||
\(877\) | −19.6747 | −0.664369 | −0.332184 | − | 0.943214i | \(-0.607786\pi\) | ||||
−0.332184 | + | 0.943214i | \(0.607786\pi\) | |||||||
\(878\) | −0.705775 | −0.0238188 | ||||||||
\(879\) | 0.936926 | 0.0316017 | ||||||||
\(880\) | 5.97634 | 0.201462 | ||||||||
\(881\) | −45.4201 | −1.53024 | −0.765121 | − | 0.643887i | \(-0.777321\pi\) | ||||
−0.765121 | + | 0.643887i | \(0.777321\pi\) | |||||||
\(882\) | 2.99913 | 0.100986 | ||||||||
\(883\) | 23.3127 | 0.784534 | 0.392267 | − | 0.919851i | \(-0.371691\pi\) | ||||
0.392267 | + | 0.919851i | \(0.371691\pi\) | |||||||
\(884\) | 5.50818 | 0.185260 | ||||||||
\(885\) | −0.426875 | −0.0143492 | ||||||||
\(886\) | −15.2248 | −0.511486 | ||||||||
\(887\) | −54.4206 | −1.82727 | −0.913633 | − | 0.406541i | \(-0.866735\pi\) | ||||
−0.913633 | + | 0.406541i | \(0.866735\pi\) | |||||||
\(888\) | −0.0826380 | −0.00277315 | ||||||||
\(889\) | 17.1303 | 0.574531 | ||||||||
\(890\) | −33.9283 | −1.13728 | ||||||||
\(891\) | −26.4744 | −0.886926 | ||||||||
\(892\) | −8.47530 | −0.283774 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −0.314936 | −0.0105330 | ||||||||
\(895\) | −21.7386 | −0.726640 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0.238016 | 0.00794712 | ||||||||
\(898\) | −16.0822 | −0.536671 | ||||||||
\(899\) | −0.105225 | −0.00350944 | ||||||||
\(900\) | 2.63787 | 0.0879288 | ||||||||
\(901\) | −21.4159 | −0.713467 | ||||||||
\(902\) | 15.1741 | 0.505242 | ||||||||
\(903\) | 0.0219677 | 0.000731040 0 | ||||||||
\(904\) | 8.76641 | 0.291566 | ||||||||
\(905\) | 44.3861 | 1.47544 | ||||||||
\(906\) | −0.133168 | −0.00442421 | ||||||||
\(907\) | −40.9915 | −1.36110 | −0.680550 | − | 0.732702i | \(-0.738259\pi\) | ||||
−0.680550 | + | 0.732702i | \(0.738259\pi\) | |||||||
\(908\) | −2.19728 | −0.0729193 | ||||||||
\(909\) | 40.0738 | 1.32916 | ||||||||
\(910\) | −2.40198 | −0.0796250 | ||||||||
\(911\) | −25.5209 | −0.845544 | −0.422772 | − | 0.906236i | \(-0.638943\pi\) | ||||
−0.422772 | + | 0.906236i | \(0.638943\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.9200 | −1.22187 | ||||||||
\(914\) | 1.39979 | 0.0463009 | ||||||||
\(915\) | −0.541754 | −0.0179098 | ||||||||
\(916\) | −14.5591 | −0.481045 | ||||||||
\(917\) | −6.67961 | −0.220580 | ||||||||
\(918\) | 0.824850 | 0.0272241 | ||||||||
\(919\) | −6.80969 | −0.224631 | −0.112315 | − | 0.993673i | \(-0.535827\pi\) | ||||
−0.112315 | + | 0.993673i | \(0.535827\pi\) | |||||||
\(920\) | 13.8231 | 0.455733 | ||||||||
\(921\) | −0.191745 | −0.00631820 | ||||||||
\(922\) | −15.4887 | −0.510093 | ||||||||
\(923\) | 16.4849 | 0.542606 | ||||||||
\(924\) | 0.0869639 | 0.00286090 | ||||||||
\(925\) | −2.46071 | −0.0809078 | ||||||||
\(926\) | 1.80796 | 0.0594132 | ||||||||
\(927\) | 39.9838 | 1.31324 | ||||||||
\(928\) | 0.396447 | 0.0130140 | ||||||||
\(929\) | −11.7047 | −0.384018 | −0.192009 | − | 0.981393i | \(-0.561500\pi\) | ||||
−0.192009 | + | 0.981393i | \(0.561500\pi\) | |||||||
\(930\) | 0.0159141 | 0.000521843 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −17.7732 | −0.582179 | ||||||||
\(933\) | 0.472051 | 0.0154543 | ||||||||
\(934\) | −11.8566 | −0.387961 | ||||||||
\(935\) | 27.8193 | 0.909788 | ||||||||
\(936\) | 3.54889 | 0.115999 | ||||||||
\(937\) | −9.26878 | −0.302798 | −0.151399 | − | 0.988473i | \(-0.548378\pi\) | ||||
−0.151399 | + | 0.988473i | \(0.548378\pi\) | |||||||
\(938\) | −11.1770 | −0.364941 | ||||||||
\(939\) | 0.0842425 | 0.00274915 | ||||||||
\(940\) | 6.03668 | 0.196895 | ||||||||
\(941\) | 14.0020 | 0.456451 | 0.228226 | − | 0.973608i | \(-0.426708\pi\) | ||||
0.228226 | + | 0.973608i | \(0.426708\pi\) | |||||||
\(942\) | 0.0385993 | 0.00125763 | ||||||||
\(943\) | 35.0971 | 1.14292 | ||||||||
\(944\) | 7.11953 | 0.231721 | ||||||||
\(945\) | −0.359697 | −0.0117010 | ||||||||
\(946\) | −2.18963 | −0.0711911 | ||||||||
\(947\) | −32.5246 | −1.05691 | −0.528453 | − | 0.848962i | \(-0.677228\pi\) | ||||
−0.528453 | + | 0.848962i | \(0.677228\pi\) | |||||||
\(948\) | −0.0654859 | −0.00212688 | ||||||||
\(949\) | 4.98235 | 0.161734 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.500513 | 0.0162302 | ||||||||
\(952\) | 4.65490 | 0.150866 | ||||||||
\(953\) | −5.75300 | −0.186358 | −0.0931790 | − | 0.995649i | \(-0.529703\pi\) | ||||
−0.0931790 | + | 0.995649i | \(0.529703\pi\) | |||||||
\(954\) | −13.7981 | −0.446731 | ||||||||
\(955\) | 38.9037 | 1.25889 | ||||||||
\(956\) | −18.9372 | −0.612473 | ||||||||
\(957\) | 0.0344766 | 0.00111447 | ||||||||
\(958\) | −2.75396 | −0.0889763 | ||||||||
\(959\) | −7.13250 | −0.230321 | ||||||||
\(960\) | −0.0599583 | −0.00193514 | ||||||||
\(961\) | −30.9296 | −0.997728 | ||||||||
\(962\) | −3.31056 | −0.106737 | ||||||||
\(963\) | 28.3302 | 0.912929 | ||||||||
\(964\) | 19.6449 | 0.632720 | ||||||||
\(965\) | −26.2020 | −0.843473 | ||||||||
\(966\) | 0.201145 | 0.00647172 | ||||||||
\(967\) | 54.9793 | 1.76802 | 0.884008 | − | 0.467471i | \(-0.154835\pi\) | ||||
0.884008 | + | 0.467471i | \(0.154835\pi\) | |||||||
\(968\) | 2.33187 | 0.0749491 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.30008 | −0.138067 | ||||||||
\(971\) | −33.7559 | −1.08328 | −0.541639 | − | 0.840611i | \(-0.682196\pi\) | ||||
−0.541639 | + | 0.840611i | \(0.682196\pi\) | |||||||
\(972\) | 0.797208 | 0.0255705 | ||||||||
\(973\) | −17.3500 | −0.556215 | ||||||||
\(974\) | 11.6214 | 0.372373 | ||||||||
\(975\) | −0.0307420 | −0.000984531 0 | ||||||||
\(976\) | 9.03552 | 0.289220 | ||||||||
\(977\) | −21.6915 | −0.693973 | −0.346987 | − | 0.937870i | \(-0.612795\pi\) | ||||
−0.346987 | + | 0.937870i | \(0.612795\pi\) | |||||||
\(978\) | 0.380664 | 0.0121723 | ||||||||
\(979\) | 49.2099 | 1.57275 | ||||||||
\(980\) | −2.02989 | −0.0648425 | ||||||||
\(981\) | 29.0259 | 0.926726 | ||||||||
\(982\) | 20.5701 | 0.656419 | ||||||||
\(983\) | −8.62213 | −0.275003 | −0.137502 | − | 0.990502i | \(-0.543907\pi\) | ||||
−0.137502 | + | 0.990502i | \(0.543907\pi\) | |||||||
\(984\) | −0.152236 | −0.00485309 | ||||||||
\(985\) | −48.0652 | −1.53149 | ||||||||
\(986\) | 1.84542 | 0.0587702 | ||||||||
\(987\) | 0.0878419 | 0.00279604 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.06455 | −0.161043 | ||||||||
\(990\) | 17.9238 | 0.569656 | ||||||||
\(991\) | −10.2995 | −0.327176 | −0.163588 | − | 0.986529i | \(-0.552307\pi\) | ||||
−0.163588 | + | 0.986529i | \(0.552307\pi\) | |||||||
\(992\) | −0.265419 | −0.00842707 | ||||||||
\(993\) | −0.643969 | −0.0204357 | ||||||||
\(994\) | 13.9312 | 0.441870 | ||||||||
\(995\) | 13.3270 | 0.422496 | ||||||||
\(996\) | 0.370404 | 0.0117367 | ||||||||
\(997\) | 22.2647 | 0.705129 | 0.352565 | − | 0.935787i | \(-0.385310\pi\) | ||||
0.352565 | + | 0.935787i | \(0.385310\pi\) | |||||||
\(998\) | 13.7051 | 0.433826 | ||||||||
\(999\) | −0.495756 | −0.0156850 |
(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 | 5054.2.a.bf.1.5 | ✓ | 8 | |
19.18 | odd | 2 | 5054.2.a.bi.1.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5054.2.a.bf.1.5 | ✓ | 8 | 1.1 | even | 1 | trivial | |
5054.2.a.bi.1.4 | yes | 8 | 19.18 | odd | 2 |