Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2236783457\) |
Analytic rank: | \(0\) |
Dimension: | \(41\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.54858 | −1.09501 | −0.547507 | − | 0.836801i | \(-0.684423\pi\) | ||||
−0.547507 | + | 0.836801i | \(0.684423\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.398108 | 0.199054 | ||||||||
\(5\) | −1.62644 | −0.727367 | −0.363684 | − | 0.931523i | \(-0.618481\pi\) | ||||
−0.363684 | + | 0.931523i | \(0.618481\pi\) | |||||||
\(6\) | −1.54858 | −0.632206 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.48066 | 0.877046 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.51868 | 0.796477 | ||||||||
\(11\) | 0.532524 | 0.160562 | 0.0802810 | − | 0.996772i | \(-0.474418\pi\) | ||||
0.0802810 | + | 0.996772i | \(0.474418\pi\) | |||||||
\(12\) | 0.398108 | 0.114924 | ||||||||
\(13\) | 4.90309 | 1.35987 | 0.679937 | − | 0.733271i | \(-0.262007\pi\) | ||||
0.679937 | + | 0.733271i | \(0.262007\pi\) | |||||||
\(14\) | 1.54858 | 0.413876 | ||||||||
\(15\) | −1.62644 | −0.419946 | ||||||||
\(16\) | −4.63773 | −1.15943 | ||||||||
\(17\) | 5.08151 | 1.23245 | 0.616224 | − | 0.787571i | \(-0.288662\pi\) | ||||
0.616224 | + | 0.787571i | \(0.288662\pi\) | |||||||
\(18\) | −1.54858 | −0.365004 | ||||||||
\(19\) | 8.23700 | 1.88970 | 0.944849 | − | 0.327507i | \(-0.106209\pi\) | ||||
0.944849 | + | 0.327507i | \(0.106209\pi\) | |||||||
\(20\) | −0.647500 | −0.144785 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −0.824657 | −0.175818 | ||||||||
\(23\) | 5.63311 | 1.17459 | 0.587293 | − | 0.809375i | \(-0.300194\pi\) | ||||
0.587293 | + | 0.809375i | \(0.300194\pi\) | |||||||
\(24\) | 2.48066 | 0.506363 | ||||||||
\(25\) | −2.35468 | −0.470937 | ||||||||
\(26\) | −7.59285 | −1.48908 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.398108 | −0.0752353 | ||||||||
\(29\) | −0.0589117 | −0.0109396 | −0.00546982 | − | 0.999985i | \(-0.501741\pi\) | ||||
−0.00546982 | + | 0.999985i | \(0.501741\pi\) | |||||||
\(30\) | 2.51868 | 0.459846 | ||||||||
\(31\) | 0.876882 | 0.157493 | 0.0787463 | − | 0.996895i | \(-0.474908\pi\) | ||||
0.0787463 | + | 0.996895i | \(0.474908\pi\) | |||||||
\(32\) | 2.22058 | 0.392546 | ||||||||
\(33\) | 0.532524 | 0.0927005 | ||||||||
\(34\) | −7.86914 | −1.34955 | ||||||||
\(35\) | 1.62644 | 0.274919 | ||||||||
\(36\) | 0.398108 | 0.0663513 | ||||||||
\(37\) | 6.54693 | 1.07631 | 0.538154 | − | 0.842846i | \(-0.319122\pi\) | ||||
0.538154 | + | 0.842846i | \(0.319122\pi\) | |||||||
\(38\) | −12.7557 | −2.06924 | ||||||||
\(39\) | 4.90309 | 0.785124 | ||||||||
\(40\) | −4.03465 | −0.637935 | ||||||||
\(41\) | 6.91105 | 1.07932 | 0.539662 | − | 0.841882i | \(-0.318552\pi\) | ||||
0.539662 | + | 0.841882i | \(0.318552\pi\) | |||||||
\(42\) | 1.54858 | 0.238951 | ||||||||
\(43\) | −7.06674 | −1.07767 | −0.538834 | − | 0.842412i | \(-0.681135\pi\) | ||||
−0.538834 | + | 0.842412i | \(0.681135\pi\) | |||||||
\(44\) | 0.212002 | 0.0319605 | ||||||||
\(45\) | −1.62644 | −0.242456 | ||||||||
\(46\) | −8.72334 | −1.28619 | ||||||||
\(47\) | 6.26639 | 0.914046 | 0.457023 | − | 0.889455i | \(-0.348916\pi\) | ||||
0.457023 | + | 0.889455i | \(0.348916\pi\) | |||||||
\(48\) | −4.63773 | −0.669398 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.64642 | 0.515682 | ||||||||
\(51\) | 5.08151 | 0.711554 | ||||||||
\(52\) | 1.95196 | 0.270688 | ||||||||
\(53\) | 8.18967 | 1.12494 | 0.562469 | − | 0.826819i | \(-0.309852\pi\) | ||||
0.562469 | + | 0.826819i | \(0.309852\pi\) | |||||||
\(54\) | −1.54858 | −0.210735 | ||||||||
\(55\) | −0.866120 | −0.116788 | ||||||||
\(56\) | −2.48066 | −0.331492 | ||||||||
\(57\) | 8.23700 | 1.09102 | ||||||||
\(58\) | 0.0912297 | 0.0119790 | ||||||||
\(59\) | −11.6469 | −1.51630 | −0.758148 | − | 0.652082i | \(-0.773896\pi\) | ||||
−0.758148 | + | 0.652082i | \(0.773896\pi\) | |||||||
\(60\) | −0.647500 | −0.0835919 | ||||||||
\(61\) | 6.00758 | 0.769192 | 0.384596 | − | 0.923085i | \(-0.374341\pi\) | ||||
0.384596 | + | 0.923085i | \(0.374341\pi\) | |||||||
\(62\) | −1.35792 | −0.172457 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 5.83670 | 0.729588 | ||||||||
\(65\) | −7.97460 | −0.989128 | ||||||||
\(66\) | −0.824657 | −0.101508 | ||||||||
\(67\) | 15.6926 | 1.91716 | 0.958579 | − | 0.284828i | \(-0.0919363\pi\) | ||||
0.958579 | + | 0.284828i | \(0.0919363\pi\) | |||||||
\(68\) | 2.02299 | 0.245324 | ||||||||
\(69\) | 5.63311 | 0.678147 | ||||||||
\(70\) | −2.51868 | −0.301040 | ||||||||
\(71\) | 2.52323 | 0.299453 | 0.149726 | − | 0.988727i | \(-0.452161\pi\) | ||||
0.149726 | + | 0.988727i | \(0.452161\pi\) | |||||||
\(72\) | 2.48066 | 0.292349 | ||||||||
\(73\) | 12.5230 | 1.46571 | 0.732855 | − | 0.680385i | \(-0.238187\pi\) | ||||
0.732855 | + | 0.680385i | \(0.238187\pi\) | |||||||
\(74\) | −10.1385 | −1.17857 | ||||||||
\(75\) | −2.35468 | −0.271895 | ||||||||
\(76\) | 3.27922 | 0.376152 | ||||||||
\(77\) | −0.532524 | −0.0606867 | ||||||||
\(78\) | −7.59285 | −0.859721 | ||||||||
\(79\) | −11.4267 | −1.28561 | −0.642804 | − | 0.766031i | \(-0.722229\pi\) | ||||
−0.642804 | + | 0.766031i | \(0.722229\pi\) | |||||||
\(80\) | 7.54300 | 0.843333 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.7023 | −1.18187 | ||||||||
\(83\) | −4.97930 | −0.546549 | −0.273274 | − | 0.961936i | \(-0.588107\pi\) | ||||
−0.273274 | + | 0.961936i | \(0.588107\pi\) | |||||||
\(84\) | −0.398108 | −0.0434371 | ||||||||
\(85\) | −8.26479 | −0.896442 | ||||||||
\(86\) | 10.9434 | 1.18006 | ||||||||
\(87\) | −0.0589117 | −0.00631600 | ||||||||
\(88\) | 1.32101 | 0.140820 | ||||||||
\(89\) | 15.5049 | 1.64352 | 0.821760 | − | 0.569834i | \(-0.192993\pi\) | ||||
0.821760 | + | 0.569834i | \(0.192993\pi\) | |||||||
\(90\) | 2.51868 | 0.265492 | ||||||||
\(91\) | −4.90309 | −0.513984 | ||||||||
\(92\) | 2.24259 | 0.233806 | ||||||||
\(93\) | 0.876882 | 0.0909284 | ||||||||
\(94\) | −9.70402 | −1.00089 | ||||||||
\(95\) | −13.3970 | −1.37450 | ||||||||
\(96\) | 2.22058 | 0.226637 | ||||||||
\(97\) | −15.1390 | −1.53714 | −0.768568 | − | 0.639769i | \(-0.779030\pi\) | ||||
−0.768568 | + | 0.639769i | \(0.779030\pi\) | |||||||
\(98\) | −1.54858 | −0.156430 | ||||||||
\(99\) | 0.532524 | 0.0535207 | ||||||||
\(100\) | −0.937419 | −0.0937419 | ||||||||
\(101\) | 1.97335 | 0.196355 | 0.0981776 | − | 0.995169i | \(-0.468699\pi\) | ||||
0.0981776 | + | 0.995169i | \(0.468699\pi\) | |||||||
\(102\) | −7.86914 | −0.779161 | ||||||||
\(103\) | −19.1282 | −1.88476 | −0.942378 | − | 0.334550i | \(-0.891416\pi\) | ||||
−0.942378 | + | 0.334550i | \(0.891416\pi\) | |||||||
\(104\) | 12.1629 | 1.19267 | ||||||||
\(105\) | 1.62644 | 0.158725 | ||||||||
\(106\) | −12.6824 | −1.23182 | ||||||||
\(107\) | −15.8203 | −1.52941 | −0.764703 | − | 0.644383i | \(-0.777114\pi\) | ||||
−0.764703 | + | 0.644383i | \(0.777114\pi\) | |||||||
\(108\) | 0.398108 | 0.0383080 | ||||||||
\(109\) | 7.82766 | 0.749754 | 0.374877 | − | 0.927075i | \(-0.377685\pi\) | ||||
0.374877 | + | 0.927075i | \(0.377685\pi\) | |||||||
\(110\) | 1.34126 | 0.127884 | ||||||||
\(111\) | 6.54693 | 0.621407 | ||||||||
\(112\) | 4.63773 | 0.438224 | ||||||||
\(113\) | 9.84192 | 0.925850 | 0.462925 | − | 0.886398i | \(-0.346800\pi\) | ||||
0.462925 | + | 0.886398i | \(0.346800\pi\) | |||||||
\(114\) | −12.7557 | −1.19468 | ||||||||
\(115\) | −9.16194 | −0.854355 | ||||||||
\(116\) | −0.0234532 | −0.00217758 | ||||||||
\(117\) | 4.90309 | 0.453291 | ||||||||
\(118\) | 18.0362 | 1.66036 | ||||||||
\(119\) | −5.08151 | −0.465821 | ||||||||
\(120\) | −4.03465 | −0.368312 | ||||||||
\(121\) | −10.7164 | −0.974220 | ||||||||
\(122\) | −9.30323 | −0.842275 | ||||||||
\(123\) | 6.91105 | 0.623148 | ||||||||
\(124\) | 0.349094 | 0.0313495 | ||||||||
\(125\) | 11.9620 | 1.06991 | ||||||||
\(126\) | 1.54858 | 0.137959 | ||||||||
\(127\) | −7.22997 | −0.641556 | −0.320778 | − | 0.947154i | \(-0.603944\pi\) | ||||
−0.320778 | + | 0.947154i | \(0.603944\pi\) | |||||||
\(128\) | −13.4798 | −1.19145 | ||||||||
\(129\) | −7.06674 | −0.622192 | ||||||||
\(130\) | 12.3493 | 1.08311 | ||||||||
\(131\) | 1.58006 | 0.138050 | 0.0690252 | − | 0.997615i | \(-0.478011\pi\) | ||||
0.0690252 | + | 0.997615i | \(0.478011\pi\) | |||||||
\(132\) | 0.212002 | 0.0184524 | ||||||||
\(133\) | −8.23700 | −0.714239 | ||||||||
\(134\) | −24.3013 | −2.09931 | ||||||||
\(135\) | −1.62644 | −0.139982 | ||||||||
\(136\) | 12.6055 | 1.08091 | ||||||||
\(137\) | −9.63658 | −0.823309 | −0.411654 | − | 0.911340i | \(-0.635049\pi\) | ||||
−0.411654 | + | 0.911340i | \(0.635049\pi\) | |||||||
\(138\) | −8.72334 | −0.742580 | ||||||||
\(139\) | −17.9361 | −1.52132 | −0.760660 | − | 0.649151i | \(-0.775124\pi\) | ||||
−0.760660 | + | 0.649151i | \(0.775124\pi\) | |||||||
\(140\) | 0.647500 | 0.0547237 | ||||||||
\(141\) | 6.26639 | 0.527725 | ||||||||
\(142\) | −3.90744 | −0.327905 | ||||||||
\(143\) | 2.61102 | 0.218344 | ||||||||
\(144\) | −4.63773 | −0.386477 | ||||||||
\(145\) | 0.0958166 | 0.00795713 | ||||||||
\(146\) | −19.3929 | −1.60497 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 2.60639 | 0.214244 | ||||||||
\(149\) | 16.3820 | 1.34206 | 0.671031 | − | 0.741429i | \(-0.265852\pi\) | ||||
0.671031 | + | 0.741429i | \(0.265852\pi\) | |||||||
\(150\) | 3.64642 | 0.297729 | ||||||||
\(151\) | 17.2602 | 1.40462 | 0.702309 | − | 0.711872i | \(-0.252152\pi\) | ||||
0.702309 | + | 0.711872i | \(0.252152\pi\) | |||||||
\(152\) | 20.4332 | 1.65735 | ||||||||
\(153\) | 5.08151 | 0.410816 | ||||||||
\(154\) | 0.824657 | 0.0664528 | ||||||||
\(155\) | −1.42620 | −0.114555 | ||||||||
\(156\) | 1.95196 | 0.156282 | ||||||||
\(157\) | −12.6930 | −1.01302 | −0.506508 | − | 0.862235i | \(-0.669064\pi\) | ||||
−0.506508 | + | 0.862235i | \(0.669064\pi\) | |||||||
\(158\) | 17.6952 | 1.40776 | ||||||||
\(159\) | 8.18967 | 0.649483 | ||||||||
\(160\) | −3.61164 | −0.285525 | ||||||||
\(161\) | −5.63311 | −0.443952 | ||||||||
\(162\) | −1.54858 | −0.121668 | ||||||||
\(163\) | 8.70476 | 0.681810 | 0.340905 | − | 0.940098i | \(-0.389267\pi\) | ||||
0.340905 | + | 0.940098i | \(0.389267\pi\) | |||||||
\(164\) | 2.75134 | 0.214844 | ||||||||
\(165\) | −0.866120 | −0.0674273 | ||||||||
\(166\) | 7.71085 | 0.598478 | ||||||||
\(167\) | −15.8115 | −1.22353 | −0.611765 | − | 0.791039i | \(-0.709540\pi\) | ||||
−0.611765 | + | 0.791039i | \(0.709540\pi\) | |||||||
\(168\) | −2.48066 | −0.191387 | ||||||||
\(169\) | 11.0403 | 0.849257 | ||||||||
\(170\) | 12.7987 | 0.981616 | ||||||||
\(171\) | 8.23700 | 0.629899 | ||||||||
\(172\) | −2.81333 | −0.214514 | ||||||||
\(173\) | −5.24891 | −0.399067 | −0.199533 | − | 0.979891i | \(-0.563943\pi\) | ||||
−0.199533 | + | 0.979891i | \(0.563943\pi\) | |||||||
\(174\) | 0.0912297 | 0.00691611 | ||||||||
\(175\) | 2.35468 | 0.177997 | ||||||||
\(176\) | −2.46970 | −0.186161 | ||||||||
\(177\) | −11.6469 | −0.875434 | ||||||||
\(178\) | −24.0107 | −1.79968 | ||||||||
\(179\) | −5.54185 | −0.414217 | −0.207109 | − | 0.978318i | \(-0.566405\pi\) | ||||
−0.207109 | + | 0.978318i | \(0.566405\pi\) | |||||||
\(180\) | −0.647500 | −0.0482618 | ||||||||
\(181\) | −12.3875 | −0.920753 | −0.460376 | − | 0.887724i | \(-0.652286\pi\) | ||||
−0.460376 | + | 0.887724i | \(0.652286\pi\) | |||||||
\(182\) | 7.59285 | 0.562819 | ||||||||
\(183\) | 6.00758 | 0.444093 | ||||||||
\(184\) | 13.9739 | 1.03017 | ||||||||
\(185\) | −10.6482 | −0.782872 | ||||||||
\(186\) | −1.35792 | −0.0995678 | ||||||||
\(187\) | 2.70603 | 0.197884 | ||||||||
\(188\) | 2.49470 | 0.181945 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 20.7464 | 1.50510 | ||||||||
\(191\) | 12.1231 | 0.877199 | 0.438600 | − | 0.898683i | \(-0.355475\pi\) | ||||
0.438600 | + | 0.898683i | \(0.355475\pi\) | |||||||
\(192\) | 5.83670 | 0.421228 | ||||||||
\(193\) | −19.9176 | −1.43370 | −0.716850 | − | 0.697228i | \(-0.754417\pi\) | ||||
−0.716850 | + | 0.697228i | \(0.754417\pi\) | |||||||
\(194\) | 23.4440 | 1.68318 | ||||||||
\(195\) | −7.97460 | −0.571073 | ||||||||
\(196\) | 0.398108 | 0.0284363 | ||||||||
\(197\) | −8.45913 | −0.602688 | −0.301344 | − | 0.953515i | \(-0.597435\pi\) | ||||
−0.301344 | + | 0.953515i | \(0.597435\pi\) | |||||||
\(198\) | −0.824657 | −0.0586059 | ||||||||
\(199\) | −11.9298 | −0.845681 | −0.422841 | − | 0.906204i | \(-0.638967\pi\) | ||||
−0.422841 | + | 0.906204i | \(0.638967\pi\) | |||||||
\(200\) | −5.84117 | −0.413033 | ||||||||
\(201\) | 15.6926 | 1.10687 | ||||||||
\(202\) | −3.05589 | −0.215012 | ||||||||
\(203\) | 0.0589117 | 0.00413479 | ||||||||
\(204\) | 2.02299 | 0.141638 | ||||||||
\(205\) | −11.2404 | −0.785065 | ||||||||
\(206\) | 29.6216 | 2.06383 | ||||||||
\(207\) | 5.63311 | 0.391529 | ||||||||
\(208\) | −22.7392 | −1.57668 | ||||||||
\(209\) | 4.38640 | 0.303414 | ||||||||
\(210\) | −2.51868 | −0.173805 | ||||||||
\(211\) | 8.29673 | 0.571170 | 0.285585 | − | 0.958353i | \(-0.407812\pi\) | ||||
0.285585 | + | 0.958353i | \(0.407812\pi\) | |||||||
\(212\) | 3.26037 | 0.223923 | ||||||||
\(213\) | 2.52323 | 0.172889 | ||||||||
\(214\) | 24.4990 | 1.67472 | ||||||||
\(215\) | 11.4936 | 0.783860 | ||||||||
\(216\) | 2.48066 | 0.168788 | ||||||||
\(217\) | −0.876882 | −0.0595266 | ||||||||
\(218\) | −12.1218 | −0.820991 | ||||||||
\(219\) | 12.5230 | 0.846228 | ||||||||
\(220\) | −0.344809 | −0.0232470 | ||||||||
\(221\) | 24.9151 | 1.67597 | ||||||||
\(222\) | −10.1385 | −0.680449 | ||||||||
\(223\) | −16.8337 | −1.12727 | −0.563634 | − | 0.826025i | \(-0.690597\pi\) | ||||
−0.563634 | + | 0.826025i | \(0.690597\pi\) | |||||||
\(224\) | −2.22058 | −0.148369 | ||||||||
\(225\) | −2.35468 | −0.156979 | ||||||||
\(226\) | −15.2410 | −1.01382 | ||||||||
\(227\) | 8.26899 | 0.548832 | 0.274416 | − | 0.961611i | \(-0.411515\pi\) | ||||
0.274416 | + | 0.961611i | \(0.411515\pi\) | |||||||
\(228\) | 3.27922 | 0.217171 | ||||||||
\(229\) | −21.2886 | −1.40679 | −0.703396 | − | 0.710798i | \(-0.748334\pi\) | ||||
−0.703396 | + | 0.710798i | \(0.748334\pi\) | |||||||
\(230\) | 14.1880 | 0.935530 | ||||||||
\(231\) | −0.532524 | −0.0350375 | ||||||||
\(232\) | −0.146140 | −0.00959457 | ||||||||
\(233\) | 6.91299 | 0.452885 | 0.226442 | − | 0.974025i | \(-0.427290\pi\) | ||||
0.226442 | + | 0.974025i | \(0.427290\pi\) | |||||||
\(234\) | −7.59285 | −0.496360 | ||||||||
\(235\) | −10.1919 | −0.664847 | ||||||||
\(236\) | −4.63672 | −0.301825 | ||||||||
\(237\) | −11.4267 | −0.742246 | ||||||||
\(238\) | 7.86914 | 0.510081 | ||||||||
\(239\) | 8.17338 | 0.528692 | 0.264346 | − | 0.964428i | \(-0.414844\pi\) | ||||
0.264346 | + | 0.964428i | \(0.414844\pi\) | |||||||
\(240\) | 7.54300 | 0.486898 | ||||||||
\(241\) | −8.16882 | −0.526200 | −0.263100 | − | 0.964769i | \(-0.584745\pi\) | ||||
−0.263100 | + | 0.964769i | \(0.584745\pi\) | |||||||
\(242\) | 16.5953 | 1.06678 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 2.39167 | 0.153111 | ||||||||
\(245\) | −1.62644 | −0.103910 | ||||||||
\(246\) | −10.7023 | −0.682356 | ||||||||
\(247\) | 40.3868 | 2.56975 | ||||||||
\(248\) | 2.17525 | 0.138128 | ||||||||
\(249\) | −4.97930 | −0.315550 | ||||||||
\(250\) | −18.5241 | −1.17157 | ||||||||
\(251\) | −5.03779 | −0.317982 | −0.158991 | − | 0.987280i | \(-0.550824\pi\) | ||||
−0.158991 | + | 0.987280i | \(0.550824\pi\) | |||||||
\(252\) | −0.398108 | −0.0250784 | ||||||||
\(253\) | 2.99977 | 0.188594 | ||||||||
\(254\) | 11.1962 | 0.702512 | ||||||||
\(255\) | −8.26479 | −0.517561 | ||||||||
\(256\) | 9.20113 | 0.575071 | ||||||||
\(257\) | 13.8553 | 0.864271 | 0.432135 | − | 0.901809i | \(-0.357760\pi\) | ||||
0.432135 | + | 0.901809i | \(0.357760\pi\) | |||||||
\(258\) | 10.9434 | 0.681308 | ||||||||
\(259\) | −6.54693 | −0.406807 | ||||||||
\(260\) | −3.17475 | −0.196890 | ||||||||
\(261\) | −0.0589117 | −0.00364655 | ||||||||
\(262\) | −2.44685 | −0.151167 | ||||||||
\(263\) | −17.6071 | −1.08570 | −0.542849 | − | 0.839830i | \(-0.682655\pi\) | ||||
−0.542849 | + | 0.839830i | \(0.682655\pi\) | |||||||
\(264\) | 1.32101 | 0.0813027 | ||||||||
\(265\) | −13.3200 | −0.818243 | ||||||||
\(266\) | 12.7557 | 0.782101 | ||||||||
\(267\) | 15.5049 | 0.948886 | ||||||||
\(268\) | 6.24735 | 0.381618 | ||||||||
\(269\) | −20.5693 | −1.25414 | −0.627068 | − | 0.778965i | \(-0.715745\pi\) | ||||
−0.627068 | + | 0.778965i | \(0.715745\pi\) | |||||||
\(270\) | 2.51868 | 0.153282 | ||||||||
\(271\) | 16.2853 | 0.989263 | 0.494632 | − | 0.869103i | \(-0.335303\pi\) | ||||
0.494632 | + | 0.869103i | \(0.335303\pi\) | |||||||
\(272\) | −23.5667 | −1.42894 | ||||||||
\(273\) | −4.90309 | −0.296749 | ||||||||
\(274\) | 14.9230 | 0.901534 | ||||||||
\(275\) | −1.25393 | −0.0756146 | ||||||||
\(276\) | 2.24259 | 0.134988 | ||||||||
\(277\) | 0.403491 | 0.0242434 | 0.0121217 | − | 0.999927i | \(-0.496141\pi\) | ||||
0.0121217 | + | 0.999927i | \(0.496141\pi\) | |||||||
\(278\) | 27.7755 | 1.66586 | ||||||||
\(279\) | 0.876882 | 0.0524975 | ||||||||
\(280\) | 4.03465 | 0.241117 | ||||||||
\(281\) | 25.3008 | 1.50932 | 0.754658 | − | 0.656118i | \(-0.227803\pi\) | ||||
0.754658 | + | 0.656118i | \(0.227803\pi\) | |||||||
\(282\) | −9.70402 | −0.577866 | ||||||||
\(283\) | −9.98933 | −0.593804 | −0.296902 | − | 0.954908i | \(-0.595953\pi\) | ||||
−0.296902 | + | 0.954908i | \(0.595953\pi\) | |||||||
\(284\) | 1.00452 | 0.0596073 | ||||||||
\(285\) | −13.3970 | −0.793570 | ||||||||
\(286\) | −4.04337 | −0.239090 | ||||||||
\(287\) | −6.91105 | −0.407946 | ||||||||
\(288\) | 2.22058 | 0.130849 | ||||||||
\(289\) | 8.82176 | 0.518927 | ||||||||
\(290\) | −0.148380 | −0.00871317 | ||||||||
\(291\) | −15.1390 | −0.887465 | ||||||||
\(292\) | 4.98552 | 0.291755 | ||||||||
\(293\) | −3.63791 | −0.212529 | −0.106265 | − | 0.994338i | \(-0.533889\pi\) | ||||
−0.106265 | + | 0.994338i | \(0.533889\pi\) | |||||||
\(294\) | −1.54858 | −0.0903152 | ||||||||
\(295\) | 18.9430 | 1.10290 | ||||||||
\(296\) | 16.2407 | 0.943973 | ||||||||
\(297\) | 0.532524 | 0.0309002 | ||||||||
\(298\) | −25.3688 | −1.46958 | ||||||||
\(299\) | 27.6197 | 1.59729 | ||||||||
\(300\) | −0.937419 | −0.0541219 | ||||||||
\(301\) | 7.06674 | 0.407320 | ||||||||
\(302\) | −26.7289 | −1.53808 | ||||||||
\(303\) | 1.97335 | 0.113366 | ||||||||
\(304\) | −38.2010 | −2.19097 | ||||||||
\(305\) | −9.77098 | −0.559485 | ||||||||
\(306\) | −7.86914 | −0.449849 | ||||||||
\(307\) | 10.6335 | 0.606885 | 0.303442 | − | 0.952850i | \(-0.401864\pi\) | ||||
0.303442 | + | 0.952850i | \(0.401864\pi\) | |||||||
\(308\) | −0.212002 | −0.0120799 | ||||||||
\(309\) | −19.1282 | −1.08816 | ||||||||
\(310\) | 2.20859 | 0.125439 | ||||||||
\(311\) | 11.5142 | 0.652909 | 0.326454 | − | 0.945213i | \(-0.394146\pi\) | ||||
0.326454 | + | 0.945213i | \(0.394146\pi\) | |||||||
\(312\) | 12.1629 | 0.688590 | ||||||||
\(313\) | 22.5354 | 1.27378 | 0.636889 | − | 0.770955i | \(-0.280221\pi\) | ||||
0.636889 | + | 0.770955i | \(0.280221\pi\) | |||||||
\(314\) | 19.6562 | 1.10927 | ||||||||
\(315\) | 1.62644 | 0.0916397 | ||||||||
\(316\) | −4.54908 | −0.255905 | ||||||||
\(317\) | 7.99031 | 0.448780 | 0.224390 | − | 0.974499i | \(-0.427961\pi\) | ||||
0.224390 | + | 0.974499i | \(0.427961\pi\) | |||||||
\(318\) | −12.6824 | −0.711192 | ||||||||
\(319\) | −0.0313719 | −0.00175649 | ||||||||
\(320\) | −9.49307 | −0.530678 | ||||||||
\(321\) | −15.8203 | −0.883003 | ||||||||
\(322\) | 8.72334 | 0.486133 | ||||||||
\(323\) | 41.8564 | 2.32895 | ||||||||
\(324\) | 0.398108 | 0.0221171 | ||||||||
\(325\) | −11.5452 | −0.640415 | ||||||||
\(326\) | −13.4800 | −0.746591 | ||||||||
\(327\) | 7.82766 | 0.432871 | ||||||||
\(328\) | 17.1440 | 0.946618 | ||||||||
\(329\) | −6.26639 | −0.345477 | ||||||||
\(330\) | 1.34126 | 0.0738338 | ||||||||
\(331\) | 23.4689 | 1.28997 | 0.644984 | − | 0.764196i | \(-0.276864\pi\) | ||||
0.644984 | + | 0.764196i | \(0.276864\pi\) | |||||||
\(332\) | −1.98230 | −0.108793 | ||||||||
\(333\) | 6.54693 | 0.358770 | ||||||||
\(334\) | 24.4854 | 1.33978 | ||||||||
\(335\) | −25.5231 | −1.39448 | ||||||||
\(336\) | 4.63773 | 0.253009 | ||||||||
\(337\) | −5.40122 | −0.294223 | −0.147112 | − | 0.989120i | \(-0.546998\pi\) | ||||
−0.147112 | + | 0.989120i | \(0.546998\pi\) | |||||||
\(338\) | −17.0969 | −0.929948 | ||||||||
\(339\) | 9.84192 | 0.534540 | ||||||||
\(340\) | −3.29028 | −0.178440 | ||||||||
\(341\) | 0.466961 | 0.0252873 | ||||||||
\(342\) | −12.7557 | −0.689748 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −17.5302 | −0.945165 | ||||||||
\(345\) | −9.16194 | −0.493262 | ||||||||
\(346\) | 8.12836 | 0.436984 | ||||||||
\(347\) | 35.3855 | 1.89959 | 0.949796 | − | 0.312871i | \(-0.101291\pi\) | ||||
0.949796 | + | 0.312871i | \(0.101291\pi\) | |||||||
\(348\) | −0.0234532 | −0.00125723 | ||||||||
\(349\) | 0.416052 | 0.0222708 | 0.0111354 | − | 0.999938i | \(-0.496455\pi\) | ||||
0.0111354 | + | 0.999938i | \(0.496455\pi\) | |||||||
\(350\) | −3.64642 | −0.194909 | ||||||||
\(351\) | 4.90309 | 0.261708 | ||||||||
\(352\) | 1.18251 | 0.0630281 | ||||||||
\(353\) | 9.79867 | 0.521531 | 0.260765 | − | 0.965402i | \(-0.416025\pi\) | ||||
0.260765 | + | 0.965402i | \(0.416025\pi\) | |||||||
\(354\) | 18.0362 | 0.958612 | ||||||||
\(355\) | −4.10390 | −0.217812 | ||||||||
\(356\) | 6.17264 | 0.327149 | ||||||||
\(357\) | −5.08151 | −0.268942 | ||||||||
\(358\) | 8.58201 | 0.453573 | ||||||||
\(359\) | 22.0624 | 1.16441 | 0.582205 | − | 0.813042i | \(-0.302190\pi\) | ||||
0.582205 | + | 0.813042i | \(0.302190\pi\) | |||||||
\(360\) | −4.03465 | −0.212645 | ||||||||
\(361\) | 48.8482 | 2.57096 | ||||||||
\(362\) | 19.1830 | 1.00824 | ||||||||
\(363\) | −10.7164 | −0.562466 | ||||||||
\(364\) | −1.95196 | −0.102311 | ||||||||
\(365\) | −20.3680 | −1.06611 | ||||||||
\(366\) | −9.30323 | −0.486288 | ||||||||
\(367\) | −25.5898 | −1.33578 | −0.667888 | − | 0.744262i | \(-0.732802\pi\) | ||||
−0.667888 | + | 0.744262i | \(0.732802\pi\) | |||||||
\(368\) | −26.1248 | −1.36185 | ||||||||
\(369\) | 6.91105 | 0.359775 | ||||||||
\(370\) | 16.4896 | 0.857255 | ||||||||
\(371\) | −8.18967 | −0.425186 | ||||||||
\(372\) | 0.349094 | 0.0180997 | ||||||||
\(373\) | 12.9959 | 0.672901 | 0.336451 | − | 0.941701i | \(-0.390773\pi\) | ||||
0.336451 | + | 0.941701i | \(0.390773\pi\) | |||||||
\(374\) | −4.19051 | −0.216686 | ||||||||
\(375\) | 11.9620 | 0.617714 | ||||||||
\(376\) | 15.5448 | 0.801661 | ||||||||
\(377\) | −0.288850 | −0.0148765 | ||||||||
\(378\) | 1.54858 | 0.0796505 | ||||||||
\(379\) | −15.5549 | −0.799003 | −0.399502 | − | 0.916733i | \(-0.630817\pi\) | ||||
−0.399502 | + | 0.916733i | \(0.630817\pi\) | |||||||
\(380\) | −5.33346 | −0.273601 | ||||||||
\(381\) | −7.22997 | −0.370403 | ||||||||
\(382\) | −18.7737 | −0.960545 | ||||||||
\(383\) | −1.00000 | −0.0510976 | ||||||||
\(384\) | −13.4798 | −0.687887 | ||||||||
\(385\) | 0.866120 | 0.0441416 | ||||||||
\(386\) | 30.8440 | 1.56992 | ||||||||
\(387\) | −7.06674 | −0.359223 | ||||||||
\(388\) | −6.02697 | −0.305973 | ||||||||
\(389\) | −21.1533 | −1.07251 | −0.536257 | − | 0.844055i | \(-0.680162\pi\) | ||||
−0.536257 | + | 0.844055i | \(0.680162\pi\) | |||||||
\(390\) | 12.3493 | 0.625333 | ||||||||
\(391\) | 28.6247 | 1.44762 | ||||||||
\(392\) | 2.48066 | 0.125292 | ||||||||
\(393\) | 1.58006 | 0.0797034 | ||||||||
\(394\) | 13.0997 | 0.659951 | ||||||||
\(395\) | 18.5849 | 0.935109 | ||||||||
\(396\) | 0.212002 | 0.0106535 | ||||||||
\(397\) | 37.1404 | 1.86403 | 0.932013 | − | 0.362425i | \(-0.118051\pi\) | ||||
0.932013 | + | 0.362425i | \(0.118051\pi\) | |||||||
\(398\) | 18.4743 | 0.926032 | ||||||||
\(399\) | −8.23700 | −0.412366 | ||||||||
\(400\) | 10.9204 | 0.546019 | ||||||||
\(401\) | −9.97826 | −0.498290 | −0.249145 | − | 0.968466i | \(-0.580150\pi\) | ||||
−0.249145 | + | 0.968466i | \(0.580150\pi\) | |||||||
\(402\) | −24.3013 | −1.21204 | ||||||||
\(403\) | 4.29943 | 0.214170 | ||||||||
\(404\) | 0.785605 | 0.0390853 | ||||||||
\(405\) | −1.62644 | −0.0808186 | ||||||||
\(406\) | −0.0912297 | −0.00452765 | ||||||||
\(407\) | 3.48640 | 0.172814 | ||||||||
\(408\) | 12.6055 | 0.624066 | ||||||||
\(409\) | 5.83605 | 0.288574 | 0.144287 | − | 0.989536i | \(-0.453911\pi\) | ||||
0.144287 | + | 0.989536i | \(0.453911\pi\) | |||||||
\(410\) | 17.4067 | 0.859657 | ||||||||
\(411\) | −9.63658 | −0.475338 | ||||||||
\(412\) | −7.61508 | −0.375168 | ||||||||
\(413\) | 11.6469 | 0.573106 | ||||||||
\(414\) | −8.72334 | −0.428729 | ||||||||
\(415\) | 8.09854 | 0.397542 | ||||||||
\(416\) | 10.8877 | 0.533814 | ||||||||
\(417\) | −17.9361 | −0.878334 | ||||||||
\(418\) | −6.79270 | −0.332242 | ||||||||
\(419\) | −34.4415 | −1.68258 | −0.841288 | − | 0.540586i | \(-0.818202\pi\) | ||||
−0.841288 | + | 0.540586i | \(0.818202\pi\) | |||||||
\(420\) | 0.647500 | 0.0315948 | ||||||||
\(421\) | 33.7371 | 1.64425 | 0.822123 | − | 0.569310i | \(-0.192790\pi\) | ||||
0.822123 | + | 0.569310i | \(0.192790\pi\) | |||||||
\(422\) | −12.8482 | −0.625439 | ||||||||
\(423\) | 6.26639 | 0.304682 | ||||||||
\(424\) | 20.3158 | 0.986622 | ||||||||
\(425\) | −11.9654 | −0.580405 | ||||||||
\(426\) | −3.90744 | −0.189316 | ||||||||
\(427\) | −6.00758 | −0.290727 | ||||||||
\(428\) | −6.29819 | −0.304434 | ||||||||
\(429\) | 2.61102 | 0.126061 | ||||||||
\(430\) | −17.7989 | −0.858337 | ||||||||
\(431\) | 26.7297 | 1.28752 | 0.643762 | − | 0.765226i | \(-0.277373\pi\) | ||||
0.643762 | + | 0.765226i | \(0.277373\pi\) | |||||||
\(432\) | −4.63773 | −0.223133 | ||||||||
\(433\) | −14.6626 | −0.704640 | −0.352320 | − | 0.935880i | \(-0.614607\pi\) | ||||
−0.352320 | + | 0.935880i | \(0.614607\pi\) | |||||||
\(434\) | 1.35792 | 0.0651824 | ||||||||
\(435\) | 0.0958166 | 0.00459405 | ||||||||
\(436\) | 3.11626 | 0.149242 | ||||||||
\(437\) | 46.4000 | 2.21961 | ||||||||
\(438\) | −19.3929 | −0.926631 | ||||||||
\(439\) | −20.1759 | −0.962944 | −0.481472 | − | 0.876462i | \(-0.659898\pi\) | ||||
−0.481472 | + | 0.876462i | \(0.659898\pi\) | |||||||
\(440\) | −2.14855 | −0.102428 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −38.5831 | −1.83521 | ||||||||
\(443\) | −18.3348 | −0.871113 | −0.435556 | − | 0.900161i | \(-0.643448\pi\) | ||||
−0.435556 | + | 0.900161i | \(0.643448\pi\) | |||||||
\(444\) | 2.60639 | 0.123694 | ||||||||
\(445\) | −25.2179 | −1.19544 | ||||||||
\(446\) | 26.0684 | 1.23437 | ||||||||
\(447\) | 16.3820 | 0.774840 | ||||||||
\(448\) | −5.83670 | −0.275758 | ||||||||
\(449\) | −16.9010 | −0.797608 | −0.398804 | − | 0.917036i | \(-0.630575\pi\) | ||||
−0.398804 | + | 0.917036i | \(0.630575\pi\) | |||||||
\(450\) | 3.64642 | 0.171894 | ||||||||
\(451\) | 3.68030 | 0.173299 | ||||||||
\(452\) | 3.91815 | 0.184294 | ||||||||
\(453\) | 17.2602 | 0.810957 | ||||||||
\(454\) | −12.8052 | −0.600978 | ||||||||
\(455\) | 7.97460 | 0.373855 | ||||||||
\(456\) | 20.4332 | 0.956873 | ||||||||
\(457\) | −10.5701 | −0.494449 | −0.247224 | − | 0.968958i | \(-0.579518\pi\) | ||||
−0.247224 | + | 0.968958i | \(0.579518\pi\) | |||||||
\(458\) | 32.9672 | 1.54046 | ||||||||
\(459\) | 5.08151 | 0.237185 | ||||||||
\(460\) | −3.64744 | −0.170063 | ||||||||
\(461\) | −21.0826 | −0.981913 | −0.490957 | − | 0.871184i | \(-0.663353\pi\) | ||||
−0.490957 | + | 0.871184i | \(0.663353\pi\) | |||||||
\(462\) | 0.824657 | 0.0383665 | ||||||||
\(463\) | −28.0464 | −1.30342 | −0.651712 | − | 0.758466i | \(-0.725949\pi\) | ||||
−0.651712 | + | 0.758466i | \(0.725949\pi\) | |||||||
\(464\) | 0.273217 | 0.0126838 | ||||||||
\(465\) | −1.42620 | −0.0661384 | ||||||||
\(466\) | −10.7053 | −0.495915 | ||||||||
\(467\) | 32.5560 | 1.50651 | 0.753255 | − | 0.657728i | \(-0.228483\pi\) | ||||
0.753255 | + | 0.657728i | \(0.228483\pi\) | |||||||
\(468\) | 1.95196 | 0.0902294 | ||||||||
\(469\) | −15.6926 | −0.724617 | ||||||||
\(470\) | 15.7830 | 0.728017 | ||||||||
\(471\) | −12.6930 | −0.584865 | ||||||||
\(472\) | −28.8920 | −1.32986 | ||||||||
\(473\) | −3.76321 | −0.173033 | ||||||||
\(474\) | 17.6952 | 0.812770 | ||||||||
\(475\) | −19.3955 | −0.889928 | ||||||||
\(476\) | −2.02299 | −0.0927236 | ||||||||
\(477\) | 8.18967 | 0.374979 | ||||||||
\(478\) | −12.6571 | −0.578924 | ||||||||
\(479\) | 20.3345 | 0.929106 | 0.464553 | − | 0.885545i | \(-0.346215\pi\) | ||||
0.464553 | + | 0.885545i | \(0.346215\pi\) | |||||||
\(480\) | −3.61164 | −0.164848 | ||||||||
\(481\) | 32.1002 | 1.46364 | ||||||||
\(482\) | 12.6501 | 0.576196 | ||||||||
\(483\) | −5.63311 | −0.256316 | ||||||||
\(484\) | −4.26629 | −0.193922 | ||||||||
\(485\) | 24.6228 | 1.11806 | ||||||||
\(486\) | −1.54858 | −0.0702451 | ||||||||
\(487\) | −9.03081 | −0.409225 | −0.204613 | − | 0.978843i | \(-0.565593\pi\) | ||||
−0.204613 | + | 0.978843i | \(0.565593\pi\) | |||||||
\(488\) | 14.9028 | 0.674617 | ||||||||
\(489\) | 8.70476 | 0.393643 | ||||||||
\(490\) | 2.51868 | 0.113782 | ||||||||
\(491\) | −2.83301 | −0.127852 | −0.0639260 | − | 0.997955i | \(-0.520362\pi\) | ||||
−0.0639260 | + | 0.997955i | \(0.520362\pi\) | |||||||
\(492\) | 2.75134 | 0.124040 | ||||||||
\(493\) | −0.299361 | −0.0134825 | ||||||||
\(494\) | −62.5423 | −2.81391 | ||||||||
\(495\) | −0.866120 | −0.0389292 | ||||||||
\(496\) | −4.06674 | −0.182602 | ||||||||
\(497\) | −2.52323 | −0.113183 | ||||||||
\(498\) | 7.71085 | 0.345532 | ||||||||
\(499\) | −27.5225 | −1.23208 | −0.616039 | − | 0.787716i | \(-0.711264\pi\) | ||||
−0.616039 | + | 0.787716i | \(0.711264\pi\) | |||||||
\(500\) | 4.76216 | 0.212970 | ||||||||
\(501\) | −15.8115 | −0.706406 | ||||||||
\(502\) | 7.80143 | 0.348195 | ||||||||
\(503\) | 33.3770 | 1.48821 | 0.744104 | − | 0.668064i | \(-0.232877\pi\) | ||||
0.744104 | + | 0.668064i | \(0.232877\pi\) | |||||||
\(504\) | −2.48066 | −0.110497 | ||||||||
\(505\) | −3.20953 | −0.142822 | ||||||||
\(506\) | −4.64539 | −0.206513 | ||||||||
\(507\) | 11.0403 | 0.490319 | ||||||||
\(508\) | −2.87831 | −0.127704 | ||||||||
\(509\) | −9.06947 | −0.401997 | −0.200999 | − | 0.979592i | \(-0.564419\pi\) | ||||
−0.200999 | + | 0.979592i | \(0.564419\pi\) | |||||||
\(510\) | 12.7987 | 0.566736 | ||||||||
\(511\) | −12.5230 | −0.553986 | ||||||||
\(512\) | 12.7108 | 0.561745 | ||||||||
\(513\) | 8.23700 | 0.363672 | ||||||||
\(514\) | −21.4561 | −0.946388 | ||||||||
\(515\) | 31.1109 | 1.37091 | ||||||||
\(516\) | −2.81333 | −0.123850 | ||||||||
\(517\) | 3.33700 | 0.146761 | ||||||||
\(518\) | 10.1385 | 0.445459 | ||||||||
\(519\) | −5.24891 | −0.230401 | ||||||||
\(520\) | −19.7823 | −0.867511 | ||||||||
\(521\) | 14.4705 | 0.633965 | 0.316982 | − | 0.948431i | \(-0.397330\pi\) | ||||
0.316982 | + | 0.948431i | \(0.397330\pi\) | |||||||
\(522\) | 0.0912297 | 0.00399302 | ||||||||
\(523\) | 29.6323 | 1.29573 | 0.647865 | − | 0.761755i | \(-0.275662\pi\) | ||||
0.647865 | + | 0.761755i | \(0.275662\pi\) | |||||||
\(524\) | 0.629034 | 0.0274795 | ||||||||
\(525\) | 2.35468 | 0.102767 | ||||||||
\(526\) | 27.2660 | 1.18885 | ||||||||
\(527\) | 4.45588 | 0.194101 | ||||||||
\(528\) | −2.46970 | −0.107480 | ||||||||
\(529\) | 8.73198 | 0.379651 | ||||||||
\(530\) | 20.6272 | 0.895986 | ||||||||
\(531\) | −11.6469 | −0.505432 | ||||||||
\(532\) | −3.27922 | −0.142172 | ||||||||
\(533\) | 33.8855 | 1.46774 | ||||||||
\(534\) | −24.0107 | −1.03904 | ||||||||
\(535\) | 25.7308 | 1.11244 | ||||||||
\(536\) | 38.9281 | 1.68144 | ||||||||
\(537\) | −5.54185 | −0.239148 | ||||||||
\(538\) | 31.8533 | 1.37329 | ||||||||
\(539\) | 0.532524 | 0.0229374 | ||||||||
\(540\) | −0.647500 | −0.0278640 | ||||||||
\(541\) | 2.02251 | 0.0869545 | 0.0434773 | − | 0.999054i | \(-0.486156\pi\) | ||||
0.0434773 | + | 0.999054i | \(0.486156\pi\) | |||||||
\(542\) | −25.2192 | −1.08326 | ||||||||
\(543\) | −12.3875 | −0.531597 | ||||||||
\(544\) | 11.2839 | 0.483793 | ||||||||
\(545\) | −12.7312 | −0.545347 | ||||||||
\(546\) | 7.59285 | 0.324944 | ||||||||
\(547\) | 10.0940 | 0.431589 | 0.215795 | − | 0.976439i | \(-0.430766\pi\) | ||||
0.215795 | + | 0.976439i | \(0.430766\pi\) | |||||||
\(548\) | −3.83640 | −0.163883 | ||||||||
\(549\) | 6.00758 | 0.256397 | ||||||||
\(550\) | 1.94181 | 0.0827990 | ||||||||
\(551\) | −0.485256 | −0.0206726 | ||||||||
\(552\) | 13.9739 | 0.594767 | ||||||||
\(553\) | 11.4267 | 0.485914 | ||||||||
\(554\) | −0.624839 | −0.0265469 | ||||||||
\(555\) | −10.6482 | −0.451991 | ||||||||
\(556\) | −7.14050 | −0.302825 | ||||||||
\(557\) | −20.8793 | −0.884682 | −0.442341 | − | 0.896847i | \(-0.645852\pi\) | ||||
−0.442341 | + | 0.896847i | \(0.645852\pi\) | |||||||
\(558\) | −1.35792 | −0.0574855 | ||||||||
\(559\) | −34.6489 | −1.46549 | ||||||||
\(560\) | −7.54300 | −0.318750 | ||||||||
\(561\) | 2.70603 | 0.114249 | ||||||||
\(562\) | −39.1803 | −1.65272 | ||||||||
\(563\) | 28.7929 | 1.21348 | 0.606738 | − | 0.794902i | \(-0.292478\pi\) | ||||
0.606738 | + | 0.794902i | \(0.292478\pi\) | |||||||
\(564\) | 2.49470 | 0.105046 | ||||||||
\(565\) | −16.0073 | −0.673433 | ||||||||
\(566\) | 15.4693 | 0.650223 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 6.25929 | 0.262634 | ||||||||
\(569\) | 29.9344 | 1.25491 | 0.627457 | − | 0.778651i | \(-0.284096\pi\) | ||||
0.627457 | + | 0.778651i | \(0.284096\pi\) | |||||||
\(570\) | 20.7464 | 0.868970 | ||||||||
\(571\) | −43.2703 | −1.81080 | −0.905402 | − | 0.424555i | \(-0.860431\pi\) | ||||
−0.905402 | + | 0.424555i | \(0.860431\pi\) | |||||||
\(572\) | 1.03947 | 0.0434623 | ||||||||
\(573\) | 12.1231 | 0.506451 | ||||||||
\(574\) | 10.7023 | 0.446707 | ||||||||
\(575\) | −13.2642 | −0.553156 | ||||||||
\(576\) | 5.83670 | 0.243196 | ||||||||
\(577\) | −4.00163 | −0.166590 | −0.0832949 | − | 0.996525i | \(-0.526544\pi\) | ||||
−0.0832949 | + | 0.996525i | \(0.526544\pi\) | |||||||
\(578\) | −13.6612 | −0.568232 | ||||||||
\(579\) | −19.9176 | −0.827747 | ||||||||
\(580\) | 0.0381453 | 0.00158390 | ||||||||
\(581\) | 4.97930 | 0.206576 | ||||||||
\(582\) | 23.4440 | 0.971786 | ||||||||
\(583\) | 4.36119 | 0.180622 | ||||||||
\(584\) | 31.0654 | 1.28550 | ||||||||
\(585\) | −7.97460 | −0.329709 | ||||||||
\(586\) | 5.63361 | 0.232722 | ||||||||
\(587\) | −30.1078 | −1.24268 | −0.621342 | − | 0.783540i | \(-0.713412\pi\) | ||||
−0.621342 | + | 0.783540i | \(0.713412\pi\) | |||||||
\(588\) | 0.398108 | 0.0164177 | ||||||||
\(589\) | 7.22288 | 0.297613 | ||||||||
\(590\) | −29.3348 | −1.20770 | ||||||||
\(591\) | −8.45913 | −0.347962 | ||||||||
\(592\) | −30.3629 | −1.24791 | ||||||||
\(593\) | −21.0063 | −0.862624 | −0.431312 | − | 0.902203i | \(-0.641949\pi\) | ||||
−0.431312 | + | 0.902203i | \(0.641949\pi\) | |||||||
\(594\) | −0.824657 | −0.0338361 | ||||||||
\(595\) | 8.26479 | 0.338823 | ||||||||
\(596\) | 6.52179 | 0.267143 | ||||||||
\(597\) | −11.9298 | −0.488254 | ||||||||
\(598\) | −42.7714 | −1.74905 | ||||||||
\(599\) | 38.6936 | 1.58098 | 0.790490 | − | 0.612475i | \(-0.209826\pi\) | ||||
0.790490 | + | 0.612475i | \(0.209826\pi\) | |||||||
\(600\) | −5.84117 | −0.238465 | ||||||||
\(601\) | −6.29247 | −0.256675 | −0.128338 | − | 0.991731i | \(-0.540964\pi\) | ||||
−0.128338 | + | 0.991731i | \(0.540964\pi\) | |||||||
\(602\) | −10.9434 | −0.446021 | ||||||||
\(603\) | 15.6926 | 0.639053 | ||||||||
\(604\) | 6.87144 | 0.279595 | ||||||||
\(605\) | 17.4296 | 0.708616 | ||||||||
\(606\) | −3.05589 | −0.124137 | ||||||||
\(607\) | −32.0932 | −1.30262 | −0.651310 | − | 0.758811i | \(-0.725780\pi\) | ||||
−0.651310 | + | 0.758811i | \(0.725780\pi\) | |||||||
\(608\) | 18.2909 | 0.741794 | ||||||||
\(609\) | 0.0589117 | 0.00238722 | ||||||||
\(610\) | 15.1312 | 0.612643 | ||||||||
\(611\) | 30.7247 | 1.24299 | ||||||||
\(612\) | 2.02299 | 0.0817745 | ||||||||
\(613\) | −20.5436 | −0.829748 | −0.414874 | − | 0.909879i | \(-0.636174\pi\) | ||||
−0.414874 | + | 0.909879i | \(0.636174\pi\) | |||||||
\(614\) | −16.4668 | −0.664547 | ||||||||
\(615\) | −11.2404 | −0.453258 | ||||||||
\(616\) | −1.32101 | −0.0532251 | ||||||||
\(617\) | −40.6182 | −1.63523 | −0.817613 | − | 0.575768i | \(-0.804703\pi\) | ||||
−0.817613 | + | 0.575768i | \(0.804703\pi\) | |||||||
\(618\) | 29.6216 | 1.19155 | ||||||||
\(619\) | 2.50189 | 0.100559 | 0.0502797 | − | 0.998735i | \(-0.483989\pi\) | ||||
0.0502797 | + | 0.998735i | \(0.483989\pi\) | |||||||
\(620\) | −0.567781 | −0.0228026 | ||||||||
\(621\) | 5.63311 | 0.226049 | ||||||||
\(622\) | −17.8307 | −0.714944 | ||||||||
\(623\) | −15.5049 | −0.621192 | ||||||||
\(624\) | −22.7392 | −0.910297 | ||||||||
\(625\) | −7.68204 | −0.307282 | ||||||||
\(626\) | −34.8980 | −1.39480 | ||||||||
\(627\) | 4.38640 | 0.175176 | ||||||||
\(628\) | −5.05320 | −0.201645 | ||||||||
\(629\) | 33.2683 | 1.32649 | ||||||||
\(630\) | −2.51868 | −0.100347 | ||||||||
\(631\) | −39.9728 | −1.59129 | −0.795646 | − | 0.605761i | \(-0.792869\pi\) | ||||
−0.795646 | + | 0.605761i | \(0.792869\pi\) | |||||||
\(632\) | −28.3459 | −1.12754 | ||||||||
\(633\) | 8.29673 | 0.329765 | ||||||||
\(634\) | −12.3736 | −0.491420 | ||||||||
\(635\) | 11.7591 | 0.466647 | ||||||||
\(636\) | 3.26037 | 0.129282 | ||||||||
\(637\) | 4.90309 | 0.194268 | ||||||||
\(638\) | 0.0485820 | 0.00192338 | ||||||||
\(639\) | 2.52323 | 0.0998176 | ||||||||
\(640\) | 21.9241 | 0.866625 | ||||||||
\(641\) | 19.5537 | 0.772323 | 0.386161 | − | 0.922431i | \(-0.373801\pi\) | ||||
0.386161 | + | 0.922431i | \(0.373801\pi\) | |||||||
\(642\) | 24.4990 | 0.966900 | ||||||||
\(643\) | −39.9311 | −1.57473 | −0.787364 | − | 0.616489i | \(-0.788555\pi\) | ||||
−0.787364 | + | 0.616489i | \(0.788555\pi\) | |||||||
\(644\) | −2.24259 | −0.0883703 | ||||||||
\(645\) | 11.4936 | 0.452562 | ||||||||
\(646\) | −64.8181 | −2.55023 | ||||||||
\(647\) | 33.3241 | 1.31011 | 0.655053 | − | 0.755583i | \(-0.272646\pi\) | ||||
0.655053 | + | 0.755583i | \(0.272646\pi\) | |||||||
\(648\) | 2.48066 | 0.0974496 | ||||||||
\(649\) | −6.20225 | −0.243460 | ||||||||
\(650\) | 17.8788 | 0.701262 | ||||||||
\(651\) | −0.876882 | −0.0343677 | ||||||||
\(652\) | 3.46544 | 0.135717 | ||||||||
\(653\) | 34.0377 | 1.33200 | 0.666000 | − | 0.745952i | \(-0.268005\pi\) | ||||
0.666000 | + | 0.745952i | \(0.268005\pi\) | |||||||
\(654\) | −12.1218 | −0.473999 | ||||||||
\(655\) | −2.56988 | −0.100413 | ||||||||
\(656\) | −32.0515 | −1.25140 | ||||||||
\(657\) | 12.5230 | 0.488570 | ||||||||
\(658\) | 9.70402 | 0.378302 | ||||||||
\(659\) | 18.5205 | 0.721457 | 0.360729 | − | 0.932671i | \(-0.382528\pi\) | ||||
0.360729 | + | 0.932671i | \(0.382528\pi\) | |||||||
\(660\) | −0.344809 | −0.0134217 | ||||||||
\(661\) | −22.0614 | −0.858087 | −0.429044 | − | 0.903284i | \(-0.641149\pi\) | ||||
−0.429044 | + | 0.903284i | \(0.641149\pi\) | |||||||
\(662\) | −36.3436 | −1.41253 | ||||||||
\(663\) | 24.9151 | 0.967624 | ||||||||
\(664\) | −12.3520 | −0.479349 | ||||||||
\(665\) | 13.3970 | 0.519514 | ||||||||
\(666\) | −10.1385 | −0.392858 | ||||||||
\(667\) | −0.331857 | −0.0128495 | ||||||||
\(668\) | −6.29469 | −0.243549 | ||||||||
\(669\) | −16.8337 | −0.650828 | ||||||||
\(670\) | 39.5247 | 1.52697 | ||||||||
\(671\) | 3.19918 | 0.123503 | ||||||||
\(672\) | −2.22058 | −0.0856606 | ||||||||
\(673\) | 41.0041 | 1.58059 | 0.790297 | − | 0.612724i | \(-0.209926\pi\) | ||||
0.790297 | + | 0.612724i | \(0.209926\pi\) | |||||||
\(674\) | 8.36424 | 0.322179 | ||||||||
\(675\) | −2.35468 | −0.0906318 | ||||||||
\(676\) | 4.39525 | 0.169048 | ||||||||
\(677\) | 31.3599 | 1.20526 | 0.602630 | − | 0.798021i | \(-0.294120\pi\) | ||||
0.602630 | + | 0.798021i | \(0.294120\pi\) | |||||||
\(678\) | −15.2410 | −0.585328 | ||||||||
\(679\) | 15.1390 | 0.580982 | ||||||||
\(680\) | −20.5021 | −0.786221 | ||||||||
\(681\) | 8.26899 | 0.316868 | ||||||||
\(682\) | −0.723127 | −0.0276900 | ||||||||
\(683\) | −51.2962 | −1.96279 | −0.981397 | − | 0.191990i | \(-0.938506\pi\) | ||||
−0.981397 | + | 0.191990i | \(0.938506\pi\) | |||||||
\(684\) | 3.27922 | 0.125384 | ||||||||
\(685\) | 15.6733 | 0.598848 | ||||||||
\(686\) | 1.54858 | 0.0591252 | ||||||||
\(687\) | −21.2886 | −0.812212 | ||||||||
\(688\) | 32.7736 | 1.24948 | ||||||||
\(689\) | 40.1547 | 1.52977 | ||||||||
\(690\) | 14.1880 | 0.540129 | ||||||||
\(691\) | 48.6136 | 1.84935 | 0.924675 | − | 0.380757i | \(-0.124337\pi\) | ||||
0.924675 | + | 0.380757i | \(0.124337\pi\) | |||||||
\(692\) | −2.08963 | −0.0794359 | ||||||||
\(693\) | −0.532524 | −0.0202289 | ||||||||
\(694\) | −54.7973 | −2.08008 | ||||||||
\(695\) | 29.1720 | 1.10656 | ||||||||
\(696\) | −0.146140 | −0.00553943 | ||||||||
\(697\) | 35.1186 | 1.33021 | ||||||||
\(698\) | −0.644291 | −0.0243868 | ||||||||
\(699\) | 6.91299 | 0.261473 | ||||||||
\(700\) | 0.937419 | 0.0354311 | ||||||||
\(701\) | −42.0716 | −1.58902 | −0.794512 | − | 0.607249i | \(-0.792273\pi\) | ||||
−0.794512 | + | 0.607249i | \(0.792273\pi\) | |||||||
\(702\) | −7.59285 | −0.286574 | ||||||||
\(703\) | 53.9271 | 2.03390 | ||||||||
\(704\) | 3.10819 | 0.117144 | ||||||||
\(705\) | −10.1919 | −0.383850 | ||||||||
\(706\) | −15.1740 | −0.571083 | ||||||||
\(707\) | −1.97335 | −0.0742153 | ||||||||
\(708\) | −4.63672 | −0.174259 | ||||||||
\(709\) | −17.4595 | −0.655706 | −0.327853 | − | 0.944729i | \(-0.606325\pi\) | ||||
−0.327853 | + | 0.944729i | \(0.606325\pi\) | |||||||
\(710\) | 6.35522 | 0.238507 | ||||||||
\(711\) | −11.4267 | −0.428536 | ||||||||
\(712\) | 38.4625 | 1.44144 | ||||||||
\(713\) | 4.93958 | 0.184989 | ||||||||
\(714\) | 7.86914 | 0.294495 | ||||||||
\(715\) | −4.24667 | −0.158816 | ||||||||
\(716\) | −2.20625 | −0.0824516 | ||||||||
\(717\) | 8.17338 | 0.305240 | ||||||||
\(718\) | −34.1655 | −1.27504 | ||||||||
\(719\) | 20.4883 | 0.764084 | 0.382042 | − | 0.924145i | \(-0.375221\pi\) | ||||
0.382042 | + | 0.924145i | \(0.375221\pi\) | |||||||
\(720\) | 7.54300 | 0.281111 | ||||||||
\(721\) | 19.1282 | 0.712371 | ||||||||
\(722\) | −75.6454 | −2.81523 | ||||||||
\(723\) | −8.16882 | −0.303802 | ||||||||
\(724\) | −4.93155 | −0.183280 | ||||||||
\(725\) | 0.138719 | 0.00515188 | ||||||||
\(726\) | 16.5953 | 0.615908 | ||||||||
\(727\) | 9.06133 | 0.336066 | 0.168033 | − | 0.985781i | \(-0.446258\pi\) | ||||
0.168033 | + | 0.985781i | \(0.446258\pi\) | |||||||
\(728\) | −12.1629 | −0.450788 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 31.5415 | 1.16740 | ||||||||
\(731\) | −35.9097 | −1.32817 | ||||||||
\(732\) | 2.39167 | 0.0883985 | ||||||||
\(733\) | −10.7353 | −0.396518 | −0.198259 | − | 0.980150i | \(-0.563529\pi\) | ||||
−0.198259 | + | 0.980150i | \(0.563529\pi\) | |||||||
\(734\) | 39.6279 | 1.46269 | ||||||||
\(735\) | −1.62644 | −0.0599922 | ||||||||
\(736\) | 12.5088 | 0.461079 | ||||||||
\(737\) | 8.35669 | 0.307823 | ||||||||
\(738\) | −10.7023 | −0.393958 | ||||||||
\(739\) | −4.89606 | −0.180104 | −0.0900522 | − | 0.995937i | \(-0.528703\pi\) | ||||
−0.0900522 | + | 0.995937i | \(0.528703\pi\) | |||||||
\(740\) | −4.23914 | −0.155834 | ||||||||
\(741\) | 40.3868 | 1.48365 | ||||||||
\(742\) | 12.6824 | 0.465585 | ||||||||
\(743\) | 5.10457 | 0.187269 | 0.0936343 | − | 0.995607i | \(-0.470152\pi\) | ||||
0.0936343 | + | 0.995607i | \(0.470152\pi\) | |||||||
\(744\) | 2.17525 | 0.0797484 | ||||||||
\(745\) | −26.6443 | −0.976172 | ||||||||
\(746\) | −20.1252 | −0.736836 | ||||||||
\(747\) | −4.97930 | −0.182183 | ||||||||
\(748\) | 1.07729 | 0.0393897 | ||||||||
\(749\) | 15.8203 | 0.578061 | ||||||||
\(750\) | −18.5241 | −0.676405 | ||||||||
\(751\) | 2.87503 | 0.104911 | 0.0524557 | − | 0.998623i | \(-0.483295\pi\) | ||||
0.0524557 | + | 0.998623i | \(0.483295\pi\) | |||||||
\(752\) | −29.0618 | −1.05977 | ||||||||
\(753\) | −5.03779 | −0.183587 | ||||||||
\(754\) | 0.447308 | 0.0162900 | ||||||||
\(755\) | −28.0728 | −1.02167 | ||||||||
\(756\) | −0.398108 | −0.0144790 | ||||||||
\(757\) | −2.44746 | −0.0889543 | −0.0444772 | − | 0.999010i | \(-0.514162\pi\) | ||||
−0.0444772 | + | 0.999010i | \(0.514162\pi\) | |||||||
\(758\) | 24.0881 | 0.874919 | ||||||||
\(759\) | 2.99977 | 0.108885 | ||||||||
\(760\) | −33.2335 | −1.20550 | ||||||||
\(761\) | 6.98471 | 0.253196 | 0.126598 | − | 0.991954i | \(-0.459594\pi\) | ||||
0.126598 | + | 0.991954i | \(0.459594\pi\) | |||||||
\(762\) | 11.1962 | 0.405596 | ||||||||
\(763\) | −7.82766 | −0.283380 | ||||||||
\(764\) | 4.82632 | 0.174610 | ||||||||
\(765\) | −8.26479 | −0.298814 | ||||||||
\(766\) | 1.54858 | 0.0559526 | ||||||||
\(767\) | −57.1058 | −2.06197 | ||||||||
\(768\) | 9.20113 | 0.332017 | ||||||||
\(769\) | 44.7197 | 1.61263 | 0.806317 | − | 0.591484i | \(-0.201458\pi\) | ||||
0.806317 | + | 0.591484i | \(0.201458\pi\) | |||||||
\(770\) | −1.34126 | −0.0483356 | ||||||||
\(771\) | 13.8553 | 0.498987 | ||||||||
\(772\) | −7.92935 | −0.285384 | ||||||||
\(773\) | 13.2121 | 0.475208 | 0.237604 | − | 0.971362i | \(-0.423638\pi\) | ||||
0.237604 | + | 0.971362i | \(0.423638\pi\) | |||||||
\(774\) | 10.9434 | 0.393353 | ||||||||
\(775\) | −2.06478 | −0.0741691 | ||||||||
\(776\) | −37.5548 | −1.34814 | ||||||||
\(777\) | −6.54693 | −0.234870 | ||||||||
\(778\) | 32.7576 | 1.17442 | ||||||||
\(779\) | 56.9263 | 2.03960 | ||||||||
\(780\) | −3.17475 | −0.113674 | ||||||||
\(781\) | 1.34368 | 0.0480808 | ||||||||
\(782\) | −44.3278 | −1.58516 | ||||||||
\(783\) | −0.0589117 | −0.00210533 | ||||||||
\(784\) | −4.63773 | −0.165633 | ||||||||
\(785\) | 20.6445 | 0.736834 | ||||||||
\(786\) | −2.44685 | −0.0872763 | ||||||||
\(787\) | −22.7415 | −0.810646 | −0.405323 | − | 0.914174i | \(-0.632841\pi\) | ||||
−0.405323 | + | 0.914174i | \(0.632841\pi\) | |||||||
\(788\) | −3.36765 | −0.119967 | ||||||||
\(789\) | −17.6071 | −0.626828 | ||||||||
\(790\) | −28.7803 | −1.02396 | ||||||||
\(791\) | −9.84192 | −0.349938 | ||||||||
\(792\) | 1.32101 | 0.0469401 | ||||||||
\(793\) | 29.4557 | 1.04600 | ||||||||
\(794\) | −57.5151 | −2.04113 | ||||||||
\(795\) | −13.3200 | −0.472413 | ||||||||
\(796\) | −4.74935 | −0.168336 | ||||||||
\(797\) | 35.0326 | 1.24092 | 0.620459 | − | 0.784239i | \(-0.286946\pi\) | ||||
0.620459 | + | 0.784239i | \(0.286946\pi\) | |||||||
\(798\) | 12.7557 | 0.451546 | ||||||||
\(799\) | 31.8427 | 1.12651 | ||||||||
\(800\) | −5.22876 | −0.184865 | ||||||||
\(801\) | 15.5049 | 0.547840 | ||||||||
\(802\) | 15.4522 | 0.545634 | ||||||||
\(803\) | 6.66881 | 0.235337 | ||||||||
\(804\) | 6.24735 | 0.220327 | ||||||||
\(805\) | 9.16194 | 0.322916 | ||||||||
\(806\) | −6.65803 | −0.234519 | ||||||||
\(807\) | −20.5693 | −0.724075 | ||||||||
\(808\) | 4.89520 | 0.172213 | ||||||||
\(809\) | −13.2260 | −0.465001 | −0.232501 | − | 0.972596i | \(-0.574691\pi\) | ||||
−0.232501 | + | 0.972596i | \(0.574691\pi\) | |||||||
\(810\) | 2.51868 | 0.0884974 | ||||||||
\(811\) | −35.3500 | −1.24131 | −0.620653 | − | 0.784085i | \(-0.713133\pi\) | ||||
−0.620653 | + | 0.784085i | \(0.713133\pi\) | |||||||
\(812\) | 0.0234532 | 0.000823047 0 | ||||||||
\(813\) | 16.2853 | 0.571151 | ||||||||
\(814\) | −5.39898 | −0.189234 | ||||||||
\(815\) | −14.1578 | −0.495926 | ||||||||
\(816\) | −23.5667 | −0.824998 | ||||||||
\(817\) | −58.2087 | −2.03647 | ||||||||
\(818\) | −9.03761 | −0.315993 | ||||||||
\(819\) | −4.90309 | −0.171328 | ||||||||
\(820\) | −4.47490 | −0.156270 | ||||||||
\(821\) | −20.0595 | −0.700082 | −0.350041 | − | 0.936734i | \(-0.613832\pi\) | ||||
−0.350041 | + | 0.936734i | \(0.613832\pi\) | |||||||
\(822\) | 14.9230 | 0.520501 | ||||||||
\(823\) | 6.63964 | 0.231443 | 0.115722 | − | 0.993282i | \(-0.463082\pi\) | ||||
0.115722 | + | 0.993282i | \(0.463082\pi\) | |||||||
\(824\) | −47.4506 | −1.65302 | ||||||||
\(825\) | −1.25393 | −0.0436561 | ||||||||
\(826\) | −18.0362 | −0.627559 | ||||||||
\(827\) | 7.61754 | 0.264888 | 0.132444 | − | 0.991190i | \(-0.457718\pi\) | ||||
0.132444 | + | 0.991190i | \(0.457718\pi\) | |||||||
\(828\) | 2.24259 | 0.0779353 | ||||||||
\(829\) | −38.5832 | −1.34005 | −0.670026 | − | 0.742338i | \(-0.733717\pi\) | ||||
−0.670026 | + | 0.742338i | \(0.733717\pi\) | |||||||
\(830\) | −12.5413 | −0.435314 | ||||||||
\(831\) | 0.403491 | 0.0139970 | ||||||||
\(832\) | 28.6179 | 0.992148 | ||||||||
\(833\) | 5.08151 | 0.176064 | ||||||||
\(834\) | 27.7755 | 0.961788 | ||||||||
\(835\) | 25.7165 | 0.889956 | ||||||||
\(836\) | 1.74626 | 0.0603957 | ||||||||
\(837\) | 0.876882 | 0.0303095 | ||||||||
\(838\) | 53.3355 | 1.84244 | ||||||||
\(839\) | −28.3458 | −0.978604 | −0.489302 | − | 0.872114i | \(-0.662748\pi\) | ||||
−0.489302 | + | 0.872114i | \(0.662748\pi\) | |||||||
\(840\) | 4.03465 | 0.139209 | ||||||||
\(841\) | −28.9965 | −0.999880 | ||||||||
\(842\) | −52.2447 | −1.80047 | ||||||||
\(843\) | 25.3008 | 0.871404 | ||||||||
\(844\) | 3.30299 | 0.113694 | ||||||||
\(845\) | −17.9565 | −0.617722 | ||||||||
\(846\) | −9.70402 | −0.333631 | ||||||||
\(847\) | 10.7164 | 0.368220 | ||||||||
\(848\) | −37.9814 | −1.30429 | ||||||||
\(849\) | −9.98933 | −0.342833 | ||||||||
\(850\) | 18.5293 | 0.635551 | ||||||||
\(851\) | 36.8796 | 1.26422 | ||||||||
\(852\) | 1.00452 | 0.0344143 | ||||||||
\(853\) | 29.9905 | 1.02685 | 0.513427 | − | 0.858133i | \(-0.328376\pi\) | ||||
0.513427 | + | 0.858133i | \(0.328376\pi\) | |||||||
\(854\) | 9.30323 | 0.318350 | ||||||||
\(855\) | −13.3970 | −0.458168 | ||||||||
\(856\) | −39.2448 | −1.34136 | ||||||||
\(857\) | −40.1009 | −1.36982 | −0.684910 | − | 0.728627i | \(-0.740159\pi\) | ||||
−0.684910 | + | 0.728627i | \(0.740159\pi\) | |||||||
\(858\) | −4.04337 | −0.138038 | ||||||||
\(859\) | −30.5786 | −1.04333 | −0.521664 | − | 0.853151i | \(-0.674689\pi\) | ||||
−0.521664 | + | 0.853151i | \(0.674689\pi\) | |||||||
\(860\) | 4.57571 | 0.156031 | ||||||||
\(861\) | −6.91105 | −0.235528 | ||||||||
\(862\) | −41.3931 | −1.40986 | ||||||||
\(863\) | −18.5672 | −0.632035 | −0.316017 | − | 0.948753i | \(-0.602346\pi\) | ||||
−0.316017 | + | 0.948753i | \(0.602346\pi\) | |||||||
\(864\) | 2.22058 | 0.0755456 | ||||||||
\(865\) | 8.53704 | 0.290268 | ||||||||
\(866\) | 22.7063 | 0.771591 | ||||||||
\(867\) | 8.82176 | 0.299603 | ||||||||
\(868\) | −0.349094 | −0.0118490 | ||||||||
\(869\) | −6.08501 | −0.206420 | ||||||||
\(870\) | −0.148380 | −0.00503055 | ||||||||
\(871\) | 76.9424 | 2.60709 | ||||||||
\(872\) | 19.4178 | 0.657569 | ||||||||
\(873\) | −15.1390 | −0.512378 | ||||||||
\(874\) | −71.8542 | −2.43050 | ||||||||
\(875\) | −11.9620 | −0.404388 | ||||||||
\(876\) | 4.98552 | 0.168445 | ||||||||
\(877\) | −32.4123 | −1.09448 | −0.547242 | − | 0.836974i | \(-0.684322\pi\) | ||||
−0.547242 | + | 0.836974i | \(0.684322\pi\) | |||||||
\(878\) | 31.2441 | 1.05444 | ||||||||
\(879\) | −3.63791 | −0.122704 | ||||||||
\(880\) | 4.01683 | 0.135407 | ||||||||
\(881\) | −11.6118 | −0.391211 | −0.195605 | − | 0.980683i | \(-0.562667\pi\) | ||||
−0.195605 | + | 0.980683i | \(0.562667\pi\) | |||||||
\(882\) | −1.54858 | −0.0521435 | ||||||||
\(883\) | 9.68838 | 0.326040 | 0.163020 | − | 0.986623i | \(-0.447877\pi\) | ||||
0.163020 | + | 0.986623i | \(0.447877\pi\) | |||||||
\(884\) | 9.91891 | 0.333609 | ||||||||
\(885\) | 18.9430 | 0.636762 | ||||||||
\(886\) | 28.3930 | 0.953880 | ||||||||
\(887\) | 32.0555 | 1.07632 | 0.538160 | − | 0.842843i | \(-0.319120\pi\) | ||||
0.538160 | + | 0.842843i | \(0.319120\pi\) | |||||||
\(888\) | 16.2407 | 0.545003 | ||||||||
\(889\) | 7.22997 | 0.242485 | ||||||||
\(890\) | 39.0520 | 1.30902 | ||||||||
\(891\) | 0.532524 | 0.0178402 | ||||||||
\(892\) | −6.70163 | −0.224387 | ||||||||
\(893\) | 51.6162 | 1.72727 | ||||||||
\(894\) | −25.3688 | −0.848460 | ||||||||
\(895\) | 9.01350 | 0.301288 | ||||||||
\(896\) | 13.4798 | 0.450328 | ||||||||
\(897\) | 27.6197 | 0.922195 | ||||||||
\(898\) | 26.1726 | 0.873391 | ||||||||
\(899\) | −0.0516586 | −0.00172291 | ||||||||
\(900\) | −0.937419 | −0.0312473 | ||||||||
\(901\) | 41.6159 | 1.38643 | ||||||||
\(902\) | −5.69925 | −0.189764 | ||||||||
\(903\) | 7.06674 | 0.235166 | ||||||||
\(904\) | 24.4145 | 0.812013 | ||||||||
\(905\) | 20.1475 | 0.669725 | ||||||||
\(906\) | −26.7289 | −0.888009 | ||||||||
\(907\) | −16.4128 | −0.544977 | −0.272489 | − | 0.962159i | \(-0.587847\pi\) | ||||
−0.272489 | + | 0.962159i | \(0.587847\pi\) | |||||||
\(908\) | 3.29195 | 0.109247 | ||||||||
\(909\) | 1.97335 | 0.0654517 | ||||||||
\(910\) | −12.3493 | −0.409376 | ||||||||
\(911\) | −46.0638 | −1.52616 | −0.763080 | − | 0.646304i | \(-0.776314\pi\) | ||||
−0.763080 | + | 0.646304i | \(0.776314\pi\) | |||||||
\(912\) | −38.2010 | −1.26496 | ||||||||
\(913\) | −2.65160 | −0.0877550 | ||||||||
\(914\) | 16.3687 | 0.541428 | ||||||||
\(915\) | −9.77098 | −0.323019 | ||||||||
\(916\) | −8.47518 | −0.280028 | ||||||||
\(917\) | −1.58006 | −0.0521781 | ||||||||
\(918\) | −7.86914 | −0.259720 | ||||||||
\(919\) | −25.1784 | −0.830558 | −0.415279 | − | 0.909694i | \(-0.636316\pi\) | ||||
−0.415279 | + | 0.909694i | \(0.636316\pi\) | |||||||
\(920\) | −22.7277 | −0.749309 | ||||||||
\(921\) | 10.6335 | 0.350385 | ||||||||
\(922\) | 32.6481 | 1.07521 | ||||||||
\(923\) | 12.3717 | 0.407218 | ||||||||
\(924\) | −0.212002 | −0.00697436 | ||||||||
\(925\) | −15.4160 | −0.506873 | ||||||||
\(926\) | 43.4321 | 1.42727 | ||||||||
\(927\) | −19.1282 | −0.628252 | ||||||||
\(928\) | −0.130818 | −0.00429431 | ||||||||
\(929\) | 12.7155 | 0.417181 | 0.208590 | − | 0.978003i | \(-0.433112\pi\) | ||||
0.208590 | + | 0.978003i | \(0.433112\pi\) | |||||||
\(930\) | 2.20859 | 0.0724224 | ||||||||
\(931\) | 8.23700 | 0.269957 | ||||||||
\(932\) | 2.75212 | 0.0901485 | ||||||||
\(933\) | 11.5142 | 0.376957 | ||||||||
\(934\) | −50.4156 | −1.64965 | ||||||||
\(935\) | −4.40120 | −0.143935 | ||||||||
\(936\) | 12.1629 | 0.397558 | ||||||||
\(937\) | −37.7721 | −1.23396 | −0.616980 | − | 0.786978i | \(-0.711644\pi\) | ||||
−0.616980 | + | 0.786978i | \(0.711644\pi\) | |||||||
\(938\) | 24.3013 | 0.793466 | ||||||||
\(939\) | 22.5354 | 0.735416 | ||||||||
\(940\) | −4.05748 | −0.132341 | ||||||||
\(941\) | 37.9554 | 1.23731 | 0.618655 | − | 0.785663i | \(-0.287678\pi\) | ||||
0.618655 | + | 0.785663i | \(0.287678\pi\) | |||||||
\(942\) | 19.6562 | 0.640435 | ||||||||
\(943\) | 38.9307 | 1.26776 | ||||||||
\(944\) | 54.0151 | 1.75804 | ||||||||
\(945\) | 1.62644 | 0.0529082 | ||||||||
\(946\) | 5.82764 | 0.189473 | ||||||||
\(947\) | −49.3020 | −1.60210 | −0.801050 | − | 0.598597i | \(-0.795725\pi\) | ||||
−0.801050 | + | 0.598597i | \(0.795725\pi\) | |||||||
\(948\) | −4.54908 | −0.147747 | ||||||||
\(949\) | 61.4016 | 1.99318 | ||||||||
\(950\) | 30.0356 | 0.974483 | ||||||||
\(951\) | 7.99031 | 0.259103 | ||||||||
\(952\) | −12.6055 | −0.408547 | ||||||||
\(953\) | 11.4742 | 0.371686 | 0.185843 | − | 0.982579i | \(-0.440498\pi\) | ||||
0.185843 | + | 0.982579i | \(0.440498\pi\) | |||||||
\(954\) | −12.6824 | −0.410607 | ||||||||
\(955\) | −19.7176 | −0.638046 | ||||||||
\(956\) | 3.25389 | 0.105238 | ||||||||
\(957\) | −0.0313719 | −0.00101411 | ||||||||
\(958\) | −31.4896 | −1.01738 | ||||||||
\(959\) | 9.63658 | 0.311181 | ||||||||
\(960\) | −9.49307 | −0.306387 | ||||||||
\(961\) | −30.2311 | −0.975196 | ||||||||
\(962\) | −49.7099 | −1.60271 | ||||||||
\(963\) | −15.8203 | −0.509802 | ||||||||
\(964\) | −3.25207 | −0.104742 | ||||||||
\(965\) | 32.3948 | 1.04283 | ||||||||
\(966\) | 8.72334 | 0.280669 | ||||||||
\(967\) | −23.6001 | −0.758927 | −0.379464 | − | 0.925207i | \(-0.623891\pi\) | ||||
−0.379464 | + | 0.925207i | \(0.623891\pi\) | |||||||
\(968\) | −26.5838 | −0.854436 | ||||||||
\(969\) | 41.8564 | 1.34462 | ||||||||
\(970\) | −38.1304 | −1.22429 | ||||||||
\(971\) | 5.66897 | 0.181926 | 0.0909630 | − | 0.995854i | \(-0.471006\pi\) | ||||
0.0909630 | + | 0.995854i | \(0.471006\pi\) | |||||||
\(972\) | 0.398108 | 0.0127693 | ||||||||
\(973\) | 17.9361 | 0.575005 | ||||||||
\(974\) | 13.9850 | 0.448107 | ||||||||
\(975\) | −11.5452 | −0.369744 | ||||||||
\(976\) | −27.8615 | −0.891825 | ||||||||
\(977\) | −43.7258 | −1.39891 | −0.699456 | − | 0.714676i | \(-0.746574\pi\) | ||||
−0.699456 | + | 0.714676i | \(0.746574\pi\) | |||||||
\(978\) | −13.4800 | −0.431044 | ||||||||
\(979\) | 8.25675 | 0.263887 | ||||||||
\(980\) | −0.647500 | −0.0206836 | ||||||||
\(981\) | 7.82766 | 0.249918 | ||||||||
\(982\) | 4.38715 | 0.140000 | ||||||||
\(983\) | −2.67540 | −0.0853319 | −0.0426660 | − | 0.999089i | \(-0.513585\pi\) | ||||
−0.0426660 | + | 0.999089i | \(0.513585\pi\) | |||||||
\(984\) | 17.1440 | 0.546530 | ||||||||
\(985\) | 13.7583 | 0.438376 | ||||||||
\(986\) | 0.463585 | 0.0147635 | ||||||||
\(987\) | −6.26639 | −0.199461 | ||||||||
\(988\) | 16.0783 | 0.511519 | ||||||||
\(989\) | −39.8078 | −1.26581 | ||||||||
\(990\) | 1.34126 | 0.0426280 | ||||||||
\(991\) | −46.9775 | −1.49229 | −0.746145 | − | 0.665783i | \(-0.768098\pi\) | ||||
−0.746145 | + | 0.665783i | \(0.768098\pi\) | |||||||
\(992\) | 1.94718 | 0.0618232 | ||||||||
\(993\) | 23.4689 | 0.744764 | ||||||||
\(994\) | 3.90744 | 0.123936 | ||||||||
\(995\) | 19.4031 | 0.615121 | ||||||||
\(996\) | −1.98230 | −0.0628115 | ||||||||
\(997\) | 3.13084 | 0.0991548 | 0.0495774 | − | 0.998770i | \(-0.484213\pi\) | ||||
0.0495774 | + | 0.998770i | \(0.484213\pi\) | |||||||
\(998\) | 42.6209 | 1.34914 | ||||||||
\(999\) | 6.54693 | 0.207136 |
(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 | 8043.2.a.p.1.11 | ✓ | 41 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.p.1.11 | ✓ | 41 | 1.1 | even | 1 | trivial |