Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 | ||||||||
\(3\) | −0.510961 | −0.295003 | −0.147502 | − | 0.989062i | \(-0.547123\pi\) | ||||
−0.147502 | + | 0.989062i | \(0.547123\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.36930 | 1.05958 | 0.529791 | − | 0.848128i | \(-0.322270\pi\) | ||||
0.529791 | + | 0.848128i | \(0.322270\pi\) | |||||||
\(6\) | 0.510961 | 0.208599 | ||||||||
\(7\) | 2.78886 | 1.05409 | 0.527044 | − | 0.849838i | \(-0.323300\pi\) | ||||
0.527044 | + | 0.849838i | \(0.323300\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.73892 | −0.912973 | ||||||||
\(10\) | −2.36930 | −0.749238 | ||||||||
\(11\) | 0.898516 | 0.270913 | 0.135456 | − | 0.990783i | \(-0.456750\pi\) | ||||
0.135456 | + | 0.990783i | \(0.456750\pi\) | |||||||
\(12\) | −0.510961 | −0.147502 | ||||||||
\(13\) | 1.36209 | 0.377777 | 0.188888 | − | 0.981999i | \(-0.439512\pi\) | ||||
0.188888 | + | 0.981999i | \(0.439512\pi\) | |||||||
\(14\) | −2.78886 | −0.745353 | ||||||||
\(15\) | −1.21062 | −0.312580 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.57925 | −1.11063 | −0.555316 | − | 0.831640i | \(-0.687403\pi\) | ||||
−0.555316 | + | 0.831640i | \(0.687403\pi\) | |||||||
\(18\) | 2.73892 | 0.645569 | ||||||||
\(19\) | 3.53869 | 0.811831 | 0.405915 | − | 0.913911i | \(-0.366953\pi\) | ||||
0.405915 | + | 0.913911i | \(0.366953\pi\) | |||||||
\(20\) | 2.36930 | 0.529791 | ||||||||
\(21\) | −1.42500 | −0.310960 | ||||||||
\(22\) | −0.898516 | −0.191564 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0.510961 | 0.104299 | ||||||||
\(25\) | 0.613574 | 0.122715 | ||||||||
\(26\) | −1.36209 | −0.267129 | ||||||||
\(27\) | 2.93236 | 0.564333 | ||||||||
\(28\) | 2.78886 | 0.527044 | ||||||||
\(29\) | −9.50770 | −1.76554 | −0.882768 | − | 0.469809i | \(-0.844323\pi\) | ||||
−0.882768 | + | 0.469809i | \(0.844323\pi\) | |||||||
\(30\) | 1.21062 | 0.221028 | ||||||||
\(31\) | −7.83584 | −1.40736 | −0.703679 | − | 0.710518i | \(-0.748461\pi\) | ||||
−0.703679 | + | 0.710518i | \(0.748461\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.459106 | −0.0799202 | ||||||||
\(34\) | 4.57925 | 0.785335 | ||||||||
\(35\) | 6.60763 | 1.11689 | ||||||||
\(36\) | −2.73892 | −0.456487 | ||||||||
\(37\) | −3.08532 | −0.507224 | −0.253612 | − | 0.967306i | \(-0.581619\pi\) | ||||
−0.253612 | + | 0.967306i | \(0.581619\pi\) | |||||||
\(38\) | −3.53869 | −0.574051 | ||||||||
\(39\) | −0.695976 | −0.111445 | ||||||||
\(40\) | −2.36930 | −0.374619 | ||||||||
\(41\) | 6.50322 | 1.01563 | 0.507816 | − | 0.861465i | \(-0.330453\pi\) | ||||
0.507816 | + | 0.861465i | \(0.330453\pi\) | |||||||
\(42\) | 1.42500 | 0.219882 | ||||||||
\(43\) | −2.06915 | −0.315542 | −0.157771 | − | 0.987476i | \(-0.550431\pi\) | ||||
−0.157771 | + | 0.987476i | \(0.550431\pi\) | |||||||
\(44\) | 0.898516 | 0.135456 | ||||||||
\(45\) | −6.48932 | −0.967370 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 2.55882 | 0.373243 | 0.186621 | − | 0.982432i | \(-0.440246\pi\) | ||||
0.186621 | + | 0.982432i | \(0.440246\pi\) | |||||||
\(48\) | −0.510961 | −0.0737508 | ||||||||
\(49\) | 0.777721 | 0.111103 | ||||||||
\(50\) | −0.613574 | −0.0867724 | ||||||||
\(51\) | 2.33982 | 0.327640 | ||||||||
\(52\) | 1.36209 | 0.188888 | ||||||||
\(53\) | −0.0206505 | −0.00283657 | −0.00141828 | − | 0.999999i | \(-0.500451\pi\) | ||||
−0.00141828 | + | 0.999999i | \(0.500451\pi\) | |||||||
\(54\) | −2.93236 | −0.399044 | ||||||||
\(55\) | 2.12885 | 0.287054 | ||||||||
\(56\) | −2.78886 | −0.372677 | ||||||||
\(57\) | −1.80813 | −0.239493 | ||||||||
\(58\) | 9.50770 | 1.24842 | ||||||||
\(59\) | −3.00244 | −0.390884 | −0.195442 | − | 0.980715i | \(-0.562614\pi\) | ||||
−0.195442 | + | 0.980715i | \(0.562614\pi\) | |||||||
\(60\) | −1.21062 | −0.156290 | ||||||||
\(61\) | −8.28348 | −1.06059 | −0.530295 | − | 0.847813i | \(-0.677919\pi\) | ||||
−0.530295 | + | 0.847813i | \(0.677919\pi\) | |||||||
\(62\) | 7.83584 | 0.995153 | ||||||||
\(63\) | −7.63845 | −0.962355 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.22721 | 0.400286 | ||||||||
\(66\) | 0.459106 | 0.0565121 | ||||||||
\(67\) | −12.5193 | −1.52948 | −0.764738 | − | 0.644342i | \(-0.777132\pi\) | ||||
−0.764738 | + | 0.644342i | \(0.777132\pi\) | |||||||
\(68\) | −4.57925 | −0.555316 | ||||||||
\(69\) | 0.510961 | 0.0615124 | ||||||||
\(70\) | −6.60763 | −0.789763 | ||||||||
\(71\) | −2.24850 | −0.266848 | −0.133424 | − | 0.991059i | \(-0.542597\pi\) | ||||
−0.133424 | + | 0.991059i | \(0.542597\pi\) | |||||||
\(72\) | 2.73892 | 0.322785 | ||||||||
\(73\) | −6.70712 | −0.785009 | −0.392504 | − | 0.919750i | \(-0.628391\pi\) | ||||
−0.392504 | + | 0.919750i | \(0.628391\pi\) | |||||||
\(74\) | 3.08532 | 0.358662 | ||||||||
\(75\) | −0.313512 | −0.0362013 | ||||||||
\(76\) | 3.53869 | 0.405915 | ||||||||
\(77\) | 2.50583 | 0.285566 | ||||||||
\(78\) | 0.695976 | 0.0788038 | ||||||||
\(79\) | −5.25698 | −0.591457 | −0.295728 | − | 0.955272i | \(-0.595562\pi\) | ||||
−0.295728 | + | 0.955272i | \(0.595562\pi\) | |||||||
\(80\) | 2.36930 | 0.264896 | ||||||||
\(81\) | 6.71844 | 0.746493 | ||||||||
\(82\) | −6.50322 | −0.718161 | ||||||||
\(83\) | −6.21446 | −0.682126 | −0.341063 | − | 0.940041i | \(-0.610787\pi\) | ||||
−0.341063 | + | 0.940041i | \(0.610787\pi\) | |||||||
\(84\) | −1.42500 | −0.155480 | ||||||||
\(85\) | −10.8496 | −1.17681 | ||||||||
\(86\) | 2.06915 | 0.223122 | ||||||||
\(87\) | 4.85806 | 0.520839 | ||||||||
\(88\) | −0.898516 | −0.0957821 | ||||||||
\(89\) | −2.45122 | −0.259828 | −0.129914 | − | 0.991525i | \(-0.541470\pi\) | ||||
−0.129914 | + | 0.991525i | \(0.541470\pi\) | |||||||
\(90\) | 6.48932 | 0.684034 | ||||||||
\(91\) | 3.79868 | 0.398210 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 4.00381 | 0.415175 | ||||||||
\(94\) | −2.55882 | −0.263923 | ||||||||
\(95\) | 8.38421 | 0.860202 | ||||||||
\(96\) | 0.510961 | 0.0521497 | ||||||||
\(97\) | −8.88248 | −0.901879 | −0.450940 | − | 0.892555i | \(-0.648911\pi\) | ||||
−0.450940 | + | 0.892555i | \(0.648911\pi\) | |||||||
\(98\) | −0.777721 | −0.0785617 | ||||||||
\(99\) | −2.46096 | −0.247336 | ||||||||
\(100\) | 0.613574 | 0.0613574 | ||||||||
\(101\) | 12.4967 | 1.24347 | 0.621734 | − | 0.783229i | \(-0.286429\pi\) | ||||
0.621734 | + | 0.783229i | \(0.286429\pi\) | |||||||
\(102\) | −2.33982 | −0.231676 | ||||||||
\(103\) | −8.31273 | −0.819078 | −0.409539 | − | 0.912293i | \(-0.634310\pi\) | ||||
−0.409539 | + | 0.912293i | \(0.634310\pi\) | |||||||
\(104\) | −1.36209 | −0.133564 | ||||||||
\(105\) | −3.37624 | −0.329487 | ||||||||
\(106\) | 0.0206505 | 0.00200576 | ||||||||
\(107\) | 15.8181 | 1.52919 | 0.764597 | − | 0.644509i | \(-0.222938\pi\) | ||||
0.764597 | + | 0.644509i | \(0.222938\pi\) | |||||||
\(108\) | 2.93236 | 0.282167 | ||||||||
\(109\) | −3.38985 | −0.324689 | −0.162345 | − | 0.986734i | \(-0.551906\pi\) | ||||
−0.162345 | + | 0.986734i | \(0.551906\pi\) | |||||||
\(110\) | −2.12885 | −0.202978 | ||||||||
\(111\) | 1.57648 | 0.149633 | ||||||||
\(112\) | 2.78886 | 0.263522 | ||||||||
\(113\) | −12.8122 | −1.20527 | −0.602635 | − | 0.798017i | \(-0.705883\pi\) | ||||
−0.602635 | + | 0.798017i | \(0.705883\pi\) | |||||||
\(114\) | 1.80813 | 0.169347 | ||||||||
\(115\) | −2.36930 | −0.220938 | ||||||||
\(116\) | −9.50770 | −0.882768 | ||||||||
\(117\) | −3.73066 | −0.344900 | ||||||||
\(118\) | 3.00244 | 0.276397 | ||||||||
\(119\) | −12.7709 | −1.17070 | ||||||||
\(120\) | 1.21062 | 0.110514 | ||||||||
\(121\) | −10.1927 | −0.926606 | ||||||||
\(122\) | 8.28348 | 0.749951 | ||||||||
\(123\) | −3.32289 | −0.299615 | ||||||||
\(124\) | −7.83584 | −0.703679 | ||||||||
\(125\) | −10.3928 | −0.929556 | ||||||||
\(126\) | 7.63845 | 0.680487 | ||||||||
\(127\) | 10.3367 | 0.917234 | 0.458617 | − | 0.888634i | \(-0.348345\pi\) | ||||
0.458617 | + | 0.888634i | \(0.348345\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.05725 | 0.0930860 | ||||||||
\(130\) | −3.22721 | −0.283045 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | −0.459106 | −0.0399601 | ||||||||
\(133\) | 9.86889 | 0.855742 | ||||||||
\(134\) | 12.5193 | 1.08150 | ||||||||
\(135\) | 6.94764 | 0.597958 | ||||||||
\(136\) | 4.57925 | 0.392668 | ||||||||
\(137\) | −6.03988 | −0.516022 | −0.258011 | − | 0.966142i | \(-0.583067\pi\) | ||||
−0.258011 | + | 0.966142i | \(0.583067\pi\) | |||||||
\(138\) | −0.510961 | −0.0434959 | ||||||||
\(139\) | 7.51656 | 0.637547 | 0.318773 | − | 0.947831i | \(-0.396729\pi\) | ||||
0.318773 | + | 0.947831i | \(0.396729\pi\) | |||||||
\(140\) | 6.60763 | 0.558447 | ||||||||
\(141\) | −1.30746 | −0.110108 | ||||||||
\(142\) | 2.24850 | 0.188690 | ||||||||
\(143\) | 1.22386 | 0.102345 | ||||||||
\(144\) | −2.73892 | −0.228243 | ||||||||
\(145\) | −22.5266 | −1.87073 | ||||||||
\(146\) | 6.70712 | 0.555085 | ||||||||
\(147\) | −0.397385 | −0.0327758 | ||||||||
\(148\) | −3.08532 | −0.253612 | ||||||||
\(149\) | 9.92371 | 0.812982 | 0.406491 | − | 0.913655i | \(-0.366752\pi\) | ||||
0.406491 | + | 0.913655i | \(0.366752\pi\) | |||||||
\(150\) | 0.313512 | 0.0255982 | ||||||||
\(151\) | 0.928938 | 0.0755959 | 0.0377979 | − | 0.999285i | \(-0.487966\pi\) | ||||
0.0377979 | + | 0.999285i | \(0.487966\pi\) | |||||||
\(152\) | −3.53869 | −0.287026 | ||||||||
\(153\) | 12.5422 | 1.01398 | ||||||||
\(154\) | −2.50583 | −0.201926 | ||||||||
\(155\) | −18.5654 | −1.49121 | ||||||||
\(156\) | −0.695976 | −0.0557227 | ||||||||
\(157\) | 6.44044 | 0.514003 | 0.257001 | − | 0.966411i | \(-0.417266\pi\) | ||||
0.257001 | + | 0.966411i | \(0.417266\pi\) | |||||||
\(158\) | 5.25698 | 0.418223 | ||||||||
\(159\) | 0.0105516 | 0.000836797 0 | ||||||||
\(160\) | −2.36930 | −0.187309 | ||||||||
\(161\) | −2.78886 | −0.219793 | ||||||||
\(162\) | −6.71844 | −0.527850 | ||||||||
\(163\) | −21.0988 | −1.65258 | −0.826291 | − | 0.563243i | \(-0.809553\pi\) | ||||
−0.826291 | + | 0.563243i | \(0.809553\pi\) | |||||||
\(164\) | 6.50322 | 0.507816 | ||||||||
\(165\) | −1.08776 | −0.0846820 | ||||||||
\(166\) | 6.21446 | 0.482336 | ||||||||
\(167\) | 7.53014 | 0.582699 | 0.291350 | − | 0.956617i | \(-0.405896\pi\) | ||||
0.291350 | + | 0.956617i | \(0.405896\pi\) | |||||||
\(168\) | 1.42500 | 0.109941 | ||||||||
\(169\) | −11.1447 | −0.857285 | ||||||||
\(170\) | 10.8496 | 0.832127 | ||||||||
\(171\) | −9.69218 | −0.741180 | ||||||||
\(172\) | −2.06915 | −0.157771 | ||||||||
\(173\) | 5.61427 | 0.426845 | 0.213423 | − | 0.976960i | \(-0.431539\pi\) | ||||
0.213423 | + | 0.976960i | \(0.431539\pi\) | |||||||
\(174\) | −4.85806 | −0.368289 | ||||||||
\(175\) | 1.71117 | 0.129352 | ||||||||
\(176\) | 0.898516 | 0.0677282 | ||||||||
\(177\) | 1.53413 | 0.115312 | ||||||||
\(178\) | 2.45122 | 0.183726 | ||||||||
\(179\) | 23.9003 | 1.78639 | 0.893196 | − | 0.449667i | \(-0.148458\pi\) | ||||
0.893196 | + | 0.449667i | \(0.148458\pi\) | |||||||
\(180\) | −6.48932 | −0.483685 | ||||||||
\(181\) | −16.2641 | −1.20890 | −0.604450 | − | 0.796643i | \(-0.706607\pi\) | ||||
−0.604450 | + | 0.796643i | \(0.706607\pi\) | |||||||
\(182\) | −3.79868 | −0.281577 | ||||||||
\(183\) | 4.23253 | 0.312878 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −7.31005 | −0.537446 | ||||||||
\(186\) | −4.00381 | −0.293573 | ||||||||
\(187\) | −4.11453 | −0.300884 | ||||||||
\(188\) | 2.55882 | 0.186621 | ||||||||
\(189\) | 8.17794 | 0.594857 | ||||||||
\(190\) | −8.38421 | −0.608254 | ||||||||
\(191\) | 12.0462 | 0.871633 | 0.435816 | − | 0.900036i | \(-0.356460\pi\) | ||||
0.435816 | + | 0.900036i | \(0.356460\pi\) | |||||||
\(192\) | −0.510961 | −0.0368754 | ||||||||
\(193\) | −1.94869 | −0.140270 | −0.0701350 | − | 0.997538i | \(-0.522343\pi\) | ||||
−0.0701350 | + | 0.997538i | \(0.522343\pi\) | |||||||
\(194\) | 8.88248 | 0.637725 | ||||||||
\(195\) | −1.64898 | −0.118086 | ||||||||
\(196\) | 0.777721 | 0.0555515 | ||||||||
\(197\) | −21.5515 | −1.53548 | −0.767740 | − | 0.640761i | \(-0.778619\pi\) | ||||
−0.767740 | + | 0.640761i | \(0.778619\pi\) | |||||||
\(198\) | 2.46096 | 0.174893 | ||||||||
\(199\) | −8.18967 | −0.580550 | −0.290275 | − | 0.956943i | \(-0.593747\pi\) | ||||
−0.290275 | + | 0.956943i | \(0.593747\pi\) | |||||||
\(200\) | −0.613574 | −0.0433862 | ||||||||
\(201\) | 6.39687 | 0.451200 | ||||||||
\(202\) | −12.4967 | −0.879264 | ||||||||
\(203\) | −26.5156 | −1.86103 | ||||||||
\(204\) | 2.33982 | 0.163820 | ||||||||
\(205\) | 15.4081 | 1.07615 | ||||||||
\(206\) | 8.31273 | 0.579176 | ||||||||
\(207\) | 2.73892 | 0.190368 | ||||||||
\(208\) | 1.36209 | 0.0944442 | ||||||||
\(209\) | 3.17957 | 0.219935 | ||||||||
\(210\) | 3.37624 | 0.232983 | ||||||||
\(211\) | 3.83262 | 0.263849 | 0.131924 | − | 0.991260i | \(-0.457884\pi\) | ||||
0.131924 | + | 0.991260i | \(0.457884\pi\) | |||||||
\(212\) | −0.0206505 | −0.00141828 | ||||||||
\(213\) | 1.14890 | 0.0787211 | ||||||||
\(214\) | −15.8181 | −1.08130 | ||||||||
\(215\) | −4.90243 | −0.334343 | ||||||||
\(216\) | −2.93236 | −0.199522 | ||||||||
\(217\) | −21.8530 | −1.48348 | ||||||||
\(218\) | 3.38985 | 0.229590 | ||||||||
\(219\) | 3.42707 | 0.231580 | ||||||||
\(220\) | 2.12885 | 0.143527 | ||||||||
\(221\) | −6.23737 | −0.419571 | ||||||||
\(222\) | −1.57648 | −0.105806 | ||||||||
\(223\) | 18.0304 | 1.20741 | 0.603704 | − | 0.797209i | \(-0.293691\pi\) | ||||
0.603704 | + | 0.797209i | \(0.293691\pi\) | |||||||
\(224\) | −2.78886 | −0.186338 | ||||||||
\(225\) | −1.68053 | −0.112035 | ||||||||
\(226\) | 12.8122 | 0.852255 | ||||||||
\(227\) | 19.8771 | 1.31929 | 0.659643 | − | 0.751579i | \(-0.270707\pi\) | ||||
0.659643 | + | 0.751579i | \(0.270707\pi\) | |||||||
\(228\) | −1.80813 | −0.119746 | ||||||||
\(229\) | 12.8990 | 0.852387 | 0.426193 | − | 0.904632i | \(-0.359854\pi\) | ||||
0.426193 | + | 0.904632i | \(0.359854\pi\) | |||||||
\(230\) | 2.36930 | 0.156227 | ||||||||
\(231\) | −1.28038 | −0.0842430 | ||||||||
\(232\) | 9.50770 | 0.624211 | ||||||||
\(233\) | 13.4158 | 0.878898 | 0.439449 | − | 0.898268i | \(-0.355174\pi\) | ||||
0.439449 | + | 0.898268i | \(0.355174\pi\) | |||||||
\(234\) | 3.73066 | 0.243881 | ||||||||
\(235\) | 6.06262 | 0.395482 | ||||||||
\(236\) | −3.00244 | −0.195442 | ||||||||
\(237\) | 2.68611 | 0.174482 | ||||||||
\(238\) | 12.7709 | 0.827813 | ||||||||
\(239\) | −4.38008 | −0.283324 | −0.141662 | − | 0.989915i | \(-0.545245\pi\) | ||||
−0.141662 | + | 0.989915i | \(0.545245\pi\) | |||||||
\(240\) | −1.21062 | −0.0781451 | ||||||||
\(241\) | 3.61274 | 0.232717 | 0.116359 | − | 0.993207i | \(-0.462878\pi\) | ||||
0.116359 | + | 0.993207i | \(0.462878\pi\) | |||||||
\(242\) | 10.1927 | 0.655210 | ||||||||
\(243\) | −12.2299 | −0.784551 | ||||||||
\(244\) | −8.28348 | −0.530295 | ||||||||
\(245\) | 1.84265 | 0.117723 | ||||||||
\(246\) | 3.32289 | 0.211860 | ||||||||
\(247\) | 4.82002 | 0.306691 | ||||||||
\(248\) | 7.83584 | 0.497576 | ||||||||
\(249\) | 3.17534 | 0.201229 | ||||||||
\(250\) | 10.3928 | 0.657295 | ||||||||
\(251\) | −7.04420 | −0.444626 | −0.222313 | − | 0.974975i | \(-0.571361\pi\) | ||||
−0.222313 | + | 0.974975i | \(0.571361\pi\) | |||||||
\(252\) | −7.63845 | −0.481177 | ||||||||
\(253\) | −0.898516 | −0.0564892 | ||||||||
\(254\) | −10.3367 | −0.648583 | ||||||||
\(255\) | 5.54372 | 0.347162 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.26883 | −0.203904 | −0.101952 | − | 0.994789i | \(-0.532509\pi\) | ||||
−0.101952 | + | 0.994789i | \(0.532509\pi\) | |||||||
\(258\) | −1.05725 | −0.0658218 | ||||||||
\(259\) | −8.60452 | −0.534659 | ||||||||
\(260\) | 3.22721 | 0.200143 | ||||||||
\(261\) | 26.0408 | 1.61189 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | 19.8540 | 1.22425 | 0.612126 | − | 0.790760i | \(-0.290314\pi\) | ||||
0.612126 | + | 0.790760i | \(0.290314\pi\) | |||||||
\(264\) | 0.459106 | 0.0282560 | ||||||||
\(265\) | −0.0489273 | −0.00300558 | ||||||||
\(266\) | −9.86889 | −0.605101 | ||||||||
\(267\) | 1.25248 | 0.0766502 | ||||||||
\(268\) | −12.5193 | −0.764738 | ||||||||
\(269\) | 19.6024 | 1.19518 | 0.597591 | − | 0.801801i | \(-0.296125\pi\) | ||||
0.597591 | + | 0.801801i | \(0.296125\pi\) | |||||||
\(270\) | −6.94764 | −0.422820 | ||||||||
\(271\) | −3.63275 | −0.220674 | −0.110337 | − | 0.993894i | \(-0.535193\pi\) | ||||
−0.110337 | + | 0.993894i | \(0.535193\pi\) | |||||||
\(272\) | −4.57925 | −0.277658 | ||||||||
\(273\) | −1.94098 | −0.117473 | ||||||||
\(274\) | 6.03988 | 0.364883 | ||||||||
\(275\) | 0.551306 | 0.0332450 | ||||||||
\(276\) | 0.510961 | 0.0307562 | ||||||||
\(277\) | 20.3699 | 1.22391 | 0.611956 | − | 0.790892i | \(-0.290383\pi\) | ||||
0.611956 | + | 0.790892i | \(0.290383\pi\) | |||||||
\(278\) | −7.51656 | −0.450813 | ||||||||
\(279\) | 21.4617 | 1.28488 | ||||||||
\(280\) | −6.60763 | −0.394882 | ||||||||
\(281\) | −0.960400 | −0.0572927 | −0.0286463 | − | 0.999590i | \(-0.509120\pi\) | ||||
−0.0286463 | + | 0.999590i | \(0.509120\pi\) | |||||||
\(282\) | 1.30746 | 0.0778580 | ||||||||
\(283\) | −7.94276 | −0.472148 | −0.236074 | − | 0.971735i | \(-0.575861\pi\) | ||||
−0.236074 | + | 0.971735i | \(0.575861\pi\) | |||||||
\(284\) | −2.24850 | −0.133424 | ||||||||
\(285\) | −4.28400 | −0.253762 | ||||||||
\(286\) | −1.22386 | −0.0723686 | ||||||||
\(287\) | 18.1366 | 1.07057 | ||||||||
\(288\) | 2.73892 | 0.161392 | ||||||||
\(289\) | 3.96954 | 0.233502 | ||||||||
\(290\) | 22.5266 | 1.32281 | ||||||||
\(291\) | 4.53860 | 0.266057 | ||||||||
\(292\) | −6.70712 | −0.392504 | ||||||||
\(293\) | 20.7207 | 1.21052 | 0.605259 | − | 0.796029i | \(-0.293070\pi\) | ||||
0.605259 | + | 0.796029i | \(0.293070\pi\) | |||||||
\(294\) | 0.397385 | 0.0231760 | ||||||||
\(295\) | −7.11367 | −0.414174 | ||||||||
\(296\) | 3.08532 | 0.179331 | ||||||||
\(297\) | 2.63477 | 0.152885 | ||||||||
\(298\) | −9.92371 | −0.574865 | ||||||||
\(299\) | −1.36209 | −0.0787719 | ||||||||
\(300\) | −0.313512 | −0.0181006 | ||||||||
\(301\) | −5.77056 | −0.332610 | ||||||||
\(302\) | −0.928938 | −0.0534544 | ||||||||
\(303\) | −6.38532 | −0.366827 | ||||||||
\(304\) | 3.53869 | 0.202958 | ||||||||
\(305\) | −19.6260 | −1.12378 | ||||||||
\(306\) | −12.5422 | −0.716990 | ||||||||
\(307\) | −6.56579 | −0.374730 | −0.187365 | − | 0.982290i | \(-0.559995\pi\) | ||||
−0.187365 | + | 0.982290i | \(0.559995\pi\) | |||||||
\(308\) | 2.50583 | 0.142783 | ||||||||
\(309\) | 4.24748 | 0.241631 | ||||||||
\(310\) | 18.5654 | 1.05445 | ||||||||
\(311\) | −4.91478 | −0.278691 | −0.139346 | − | 0.990244i | \(-0.544500\pi\) | ||||
−0.139346 | + | 0.990244i | \(0.544500\pi\) | |||||||
\(312\) | 0.695976 | 0.0394019 | ||||||||
\(313\) | 5.15580 | 0.291423 | 0.145711 | − | 0.989327i | \(-0.453453\pi\) | ||||
0.145711 | + | 0.989327i | \(0.453453\pi\) | |||||||
\(314\) | −6.44044 | −0.363455 | ||||||||
\(315\) | −18.0978 | −1.01969 | ||||||||
\(316\) | −5.25698 | −0.295728 | ||||||||
\(317\) | −1.06135 | −0.0596112 | −0.0298056 | − | 0.999556i | \(-0.509489\pi\) | ||||
−0.0298056 | + | 0.999556i | \(0.509489\pi\) | |||||||
\(318\) | −0.0105516 | −0.000591705 0 | ||||||||
\(319\) | −8.54283 | −0.478306 | ||||||||
\(320\) | 2.36930 | 0.132448 | ||||||||
\(321\) | −8.08242 | −0.451117 | ||||||||
\(322\) | 2.78886 | 0.155417 | ||||||||
\(323\) | −16.2045 | −0.901645 | ||||||||
\(324\) | 6.71844 | 0.373246 | ||||||||
\(325\) | 0.835745 | 0.0463588 | ||||||||
\(326\) | 21.0988 | 1.16855 | ||||||||
\(327\) | 1.73208 | 0.0957844 | ||||||||
\(328\) | −6.50322 | −0.359080 | ||||||||
\(329\) | 7.13619 | 0.393431 | ||||||||
\(330\) | 1.08776 | 0.0598792 | ||||||||
\(331\) | 15.7680 | 0.866690 | 0.433345 | − | 0.901228i | \(-0.357333\pi\) | ||||
0.433345 | + | 0.901228i | \(0.357333\pi\) | |||||||
\(332\) | −6.21446 | −0.341063 | ||||||||
\(333\) | 8.45045 | 0.463082 | ||||||||
\(334\) | −7.53014 | −0.412031 | ||||||||
\(335\) | −29.6620 | −1.62061 | ||||||||
\(336\) | −1.42500 | −0.0777399 | ||||||||
\(337\) | 24.4343 | 1.33102 | 0.665510 | − | 0.746389i | \(-0.268214\pi\) | ||||
0.665510 | + | 0.746389i | \(0.268214\pi\) | |||||||
\(338\) | 11.1447 | 0.606192 | ||||||||
\(339\) | 6.54653 | 0.355559 | ||||||||
\(340\) | −10.8496 | −0.588403 | ||||||||
\(341\) | −7.04063 | −0.381271 | ||||||||
\(342\) | 9.69218 | 0.524093 | ||||||||
\(343\) | −17.3530 | −0.936976 | ||||||||
\(344\) | 2.06915 | 0.111561 | ||||||||
\(345\) | 1.21062 | 0.0651775 | ||||||||
\(346\) | −5.61427 | −0.301825 | ||||||||
\(347\) | −9.11262 | −0.489191 | −0.244596 | − | 0.969625i | \(-0.578655\pi\) | ||||
−0.244596 | + | 0.969625i | \(0.578655\pi\) | |||||||
\(348\) | 4.85806 | 0.260419 | ||||||||
\(349\) | −12.3863 | −0.663021 | −0.331511 | − | 0.943451i | \(-0.607558\pi\) | ||||
−0.331511 | + | 0.943451i | \(0.607558\pi\) | |||||||
\(350\) | −1.71117 | −0.0914659 | ||||||||
\(351\) | 3.99415 | 0.213192 | ||||||||
\(352\) | −0.898516 | −0.0478911 | ||||||||
\(353\) | −5.10072 | −0.271484 | −0.135742 | − | 0.990744i | \(-0.543342\pi\) | ||||
−0.135742 | + | 0.990744i | \(0.543342\pi\) | |||||||
\(354\) | −1.53413 | −0.0815379 | ||||||||
\(355\) | −5.32737 | −0.282748 | ||||||||
\(356\) | −2.45122 | −0.129914 | ||||||||
\(357\) | 6.52541 | 0.345362 | ||||||||
\(358\) | −23.9003 | −1.26317 | ||||||||
\(359\) | −14.3929 | −0.759627 | −0.379814 | − | 0.925063i | \(-0.624012\pi\) | ||||
−0.379814 | + | 0.925063i | \(0.624012\pi\) | |||||||
\(360\) | 6.48932 | 0.342017 | ||||||||
\(361\) | −6.47769 | −0.340931 | ||||||||
\(362\) | 16.2641 | 0.854822 | ||||||||
\(363\) | 5.20805 | 0.273352 | ||||||||
\(364\) | 3.79868 | 0.199105 | ||||||||
\(365\) | −15.8912 | −0.831781 | ||||||||
\(366\) | −4.23253 | −0.221238 | ||||||||
\(367\) | 4.65866 | 0.243180 | 0.121590 | − | 0.992580i | \(-0.461201\pi\) | ||||
0.121590 | + | 0.992580i | \(0.461201\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −17.8118 | −0.927245 | ||||||||
\(370\) | 7.31005 | 0.380031 | ||||||||
\(371\) | −0.0575914 | −0.00299000 | ||||||||
\(372\) | 4.00381 | 0.207588 | ||||||||
\(373\) | 2.02497 | 0.104849 | 0.0524246 | − | 0.998625i | \(-0.483305\pi\) | ||||
0.0524246 | + | 0.998625i | \(0.483305\pi\) | |||||||
\(374\) | 4.11453 | 0.212757 | ||||||||
\(375\) | 5.31029 | 0.274222 | ||||||||
\(376\) | −2.55882 | −0.131961 | ||||||||
\(377\) | −12.9504 | −0.666979 | ||||||||
\(378\) | −8.17794 | −0.420628 | ||||||||
\(379\) | 13.2463 | 0.680418 | 0.340209 | − | 0.940350i | \(-0.389502\pi\) | ||||
0.340209 | + | 0.940350i | \(0.389502\pi\) | |||||||
\(380\) | 8.38421 | 0.430101 | ||||||||
\(381\) | −5.28165 | −0.270587 | ||||||||
\(382\) | −12.0462 | −0.616337 | ||||||||
\(383\) | −19.7135 | −1.00731 | −0.503657 | − | 0.863904i | \(-0.668012\pi\) | ||||
−0.503657 | + | 0.863904i | \(0.668012\pi\) | |||||||
\(384\) | 0.510961 | 0.0260749 | ||||||||
\(385\) | 5.93707 | 0.302581 | ||||||||
\(386\) | 1.94869 | 0.0991858 | ||||||||
\(387\) | 5.66723 | 0.288082 | ||||||||
\(388\) | −8.88248 | −0.450940 | ||||||||
\(389\) | 22.6822 | 1.15003 | 0.575016 | − | 0.818142i | \(-0.304996\pi\) | ||||
0.575016 | + | 0.818142i | \(0.304996\pi\) | |||||||
\(390\) | 1.64898 | 0.0834991 | ||||||||
\(391\) | 4.57925 | 0.231583 | ||||||||
\(392\) | −0.777721 | −0.0392809 | ||||||||
\(393\) | 0.510961 | 0.0257746 | ||||||||
\(394\) | 21.5515 | 1.08575 | ||||||||
\(395\) | −12.4554 | −0.626697 | ||||||||
\(396\) | −2.46096 | −0.123668 | ||||||||
\(397\) | 11.7673 | 0.590584 | 0.295292 | − | 0.955407i | \(-0.404583\pi\) | ||||
0.295292 | + | 0.955407i | \(0.404583\pi\) | |||||||
\(398\) | 8.18967 | 0.410511 | ||||||||
\(399\) | −5.04262 | −0.252447 | ||||||||
\(400\) | 0.613574 | 0.0306787 | ||||||||
\(401\) | −16.1699 | −0.807484 | −0.403742 | − | 0.914873i | \(-0.632291\pi\) | ||||
−0.403742 | + | 0.914873i | \(0.632291\pi\) | |||||||
\(402\) | −6.39687 | −0.319047 | ||||||||
\(403\) | −10.6731 | −0.531667 | ||||||||
\(404\) | 12.4967 | 0.621734 | ||||||||
\(405\) | 15.9180 | 0.790971 | ||||||||
\(406\) | 26.5156 | 1.31595 | ||||||||
\(407\) | −2.77221 | −0.137413 | ||||||||
\(408\) | −2.33982 | −0.115838 | ||||||||
\(409\) | 39.9690 | 1.97634 | 0.988169 | − | 0.153367i | \(-0.0490116\pi\) | ||||
0.988169 | + | 0.153367i | \(0.0490116\pi\) | |||||||
\(410\) | −15.4081 | −0.760951 | ||||||||
\(411\) | 3.08614 | 0.152228 | ||||||||
\(412\) | −8.31273 | −0.409539 | ||||||||
\(413\) | −8.37336 | −0.412026 | ||||||||
\(414\) | −2.73892 | −0.134611 | ||||||||
\(415\) | −14.7239 | −0.722768 | ||||||||
\(416\) | −1.36209 | −0.0667821 | ||||||||
\(417\) | −3.84067 | −0.188078 | ||||||||
\(418\) | −3.17957 | −0.155518 | ||||||||
\(419\) | −30.0864 | −1.46982 | −0.734908 | − | 0.678167i | \(-0.762775\pi\) | ||||
−0.734908 | + | 0.678167i | \(0.762775\pi\) | |||||||
\(420\) | −3.37624 | −0.164744 | ||||||||
\(421\) | −31.6647 | −1.54324 | −0.771622 | − | 0.636082i | \(-0.780554\pi\) | ||||
−0.771622 | + | 0.636082i | \(0.780554\pi\) | |||||||
\(422\) | −3.83262 | −0.186569 | ||||||||
\(423\) | −7.00841 | −0.340761 | ||||||||
\(424\) | 0.0206505 | 0.00100288 | ||||||||
\(425\) | −2.80971 | −0.136291 | ||||||||
\(426\) | −1.14890 | −0.0556642 | ||||||||
\(427\) | −23.1014 | −1.11796 | ||||||||
\(428\) | 15.8181 | 0.764597 | ||||||||
\(429\) | −0.625346 | −0.0301920 | ||||||||
\(430\) | 4.90243 | 0.236416 | ||||||||
\(431\) | −20.4046 | −0.982853 | −0.491426 | − | 0.870919i | \(-0.663524\pi\) | ||||
−0.491426 | + | 0.870919i | \(0.663524\pi\) | |||||||
\(432\) | 2.93236 | 0.141083 | ||||||||
\(433\) | −8.53681 | −0.410253 | −0.205126 | − | 0.978735i | \(-0.565761\pi\) | ||||
−0.205126 | + | 0.978735i | \(0.565761\pi\) | |||||||
\(434\) | 21.8530 | 1.04898 | ||||||||
\(435\) | 11.5102 | 0.551872 | ||||||||
\(436\) | −3.38985 | −0.162345 | ||||||||
\(437\) | −3.53869 | −0.169278 | ||||||||
\(438\) | −3.42707 | −0.163752 | ||||||||
\(439\) | −19.1651 | −0.914700 | −0.457350 | − | 0.889287i | \(-0.651201\pi\) | ||||
−0.457350 | + | 0.889287i | \(0.651201\pi\) | |||||||
\(440\) | −2.12885 | −0.101489 | ||||||||
\(441\) | −2.13012 | −0.101434 | ||||||||
\(442\) | 6.23737 | 0.296681 | ||||||||
\(443\) | 23.9265 | 1.13678 | 0.568392 | − | 0.822758i | \(-0.307566\pi\) | ||||
0.568392 | + | 0.822758i | \(0.307566\pi\) | |||||||
\(444\) | 1.57648 | 0.0748164 | ||||||||
\(445\) | −5.80766 | −0.275310 | ||||||||
\(446\) | −18.0304 | −0.853766 | ||||||||
\(447\) | −5.07063 | −0.239832 | ||||||||
\(448\) | 2.78886 | 0.131761 | ||||||||
\(449\) | 23.2056 | 1.09514 | 0.547571 | − | 0.836759i | \(-0.315553\pi\) | ||||
0.547571 | + | 0.836759i | \(0.315553\pi\) | |||||||
\(450\) | 1.68053 | 0.0792209 | ||||||||
\(451\) | 5.84325 | 0.275148 | ||||||||
\(452\) | −12.8122 | −0.602635 | ||||||||
\(453\) | −0.474651 | −0.0223010 | ||||||||
\(454\) | −19.8771 | −0.932876 | ||||||||
\(455\) | 9.00022 | 0.421937 | ||||||||
\(456\) | 1.80813 | 0.0846735 | ||||||||
\(457\) | −4.56956 | −0.213755 | −0.106877 | − | 0.994272i | \(-0.534085\pi\) | ||||
−0.106877 | + | 0.994272i | \(0.534085\pi\) | |||||||
\(458\) | −12.8990 | −0.602728 | ||||||||
\(459\) | −13.4280 | −0.626766 | ||||||||
\(460\) | −2.36930 | −0.110469 | ||||||||
\(461\) | −22.1990 | −1.03391 | −0.516955 | − | 0.856012i | \(-0.672935\pi\) | ||||
−0.516955 | + | 0.856012i | \(0.672935\pi\) | |||||||
\(462\) | 1.28038 | 0.0595688 | ||||||||
\(463\) | −21.1625 | −0.983507 | −0.491753 | − | 0.870735i | \(-0.663644\pi\) | ||||
−0.491753 | + | 0.870735i | \(0.663644\pi\) | |||||||
\(464\) | −9.50770 | −0.441384 | ||||||||
\(465\) | 9.48621 | 0.439913 | ||||||||
\(466\) | −13.4158 | −0.621475 | ||||||||
\(467\) | −1.89152 | −0.0875292 | −0.0437646 | − | 0.999042i | \(-0.513935\pi\) | ||||
−0.0437646 | + | 0.999042i | \(0.513935\pi\) | |||||||
\(468\) | −3.73066 | −0.172450 | ||||||||
\(469\) | −34.9145 | −1.61220 | ||||||||
\(470\) | −6.06262 | −0.279648 | ||||||||
\(471\) | −3.29081 | −0.151633 | ||||||||
\(472\) | 3.00244 | 0.138198 | ||||||||
\(473\) | −1.85916 | −0.0854845 | ||||||||
\(474\) | −2.68611 | −0.123377 | ||||||||
\(475\) | 2.17125 | 0.0996236 | ||||||||
\(476\) | −12.7709 | −0.585352 | ||||||||
\(477\) | 0.0565601 | 0.00258971 | ||||||||
\(478\) | 4.38008 | 0.200340 | ||||||||
\(479\) | −9.85969 | −0.450501 | −0.225250 | − | 0.974301i | \(-0.572320\pi\) | ||||
−0.225250 | + | 0.974301i | \(0.572320\pi\) | |||||||
\(480\) | 1.21062 | 0.0552569 | ||||||||
\(481\) | −4.20250 | −0.191617 | ||||||||
\(482\) | −3.61274 | −0.164556 | ||||||||
\(483\) | 1.42500 | 0.0648396 | ||||||||
\(484\) | −10.1927 | −0.463303 | ||||||||
\(485\) | −21.0452 | −0.955615 | ||||||||
\(486\) | 12.2299 | 0.554761 | ||||||||
\(487\) | −32.8919 | −1.49047 | −0.745237 | − | 0.666799i | \(-0.767664\pi\) | ||||
−0.745237 | + | 0.666799i | \(0.767664\pi\) | |||||||
\(488\) | 8.28348 | 0.374976 | ||||||||
\(489\) | 10.7806 | 0.487517 | ||||||||
\(490\) | −1.84265 | −0.0832426 | ||||||||
\(491\) | −21.7901 | −0.983372 | −0.491686 | − | 0.870773i | \(-0.663619\pi\) | ||||
−0.491686 | + | 0.870773i | \(0.663619\pi\) | |||||||
\(492\) | −3.32289 | −0.149808 | ||||||||
\(493\) | 43.5382 | 1.96086 | ||||||||
\(494\) | −4.82002 | −0.216863 | ||||||||
\(495\) | −5.83076 | −0.262073 | ||||||||
\(496\) | −7.83584 | −0.351840 | ||||||||
\(497\) | −6.27075 | −0.281282 | ||||||||
\(498\) | −3.17534 | −0.142291 | ||||||||
\(499\) | 11.1791 | 0.500443 | 0.250222 | − | 0.968189i | \(-0.419497\pi\) | ||||
0.250222 | + | 0.968189i | \(0.419497\pi\) | |||||||
\(500\) | −10.3928 | −0.464778 | ||||||||
\(501\) | −3.84760 | −0.171898 | ||||||||
\(502\) | 7.04420 | 0.314398 | ||||||||
\(503\) | −38.2699 | −1.70637 | −0.853185 | − | 0.521609i | \(-0.825332\pi\) | ||||
−0.853185 | + | 0.521609i | \(0.825332\pi\) | |||||||
\(504\) | 7.63845 | 0.340244 | ||||||||
\(505\) | 29.6084 | 1.31756 | ||||||||
\(506\) | 0.898516 | 0.0399439 | ||||||||
\(507\) | 5.69450 | 0.252902 | ||||||||
\(508\) | 10.3367 | 0.458617 | ||||||||
\(509\) | 13.0436 | 0.578148 | 0.289074 | − | 0.957307i | \(-0.406653\pi\) | ||||
0.289074 | + | 0.957307i | \(0.406653\pi\) | |||||||
\(510\) | −5.54372 | −0.245480 | ||||||||
\(511\) | −18.7052 | −0.827469 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 10.3767 | 0.458143 | ||||||||
\(514\) | 3.26883 | 0.144182 | ||||||||
\(515\) | −19.6953 | −0.867881 | ||||||||
\(516\) | 1.05725 | 0.0465430 | ||||||||
\(517\) | 2.29915 | 0.101116 | ||||||||
\(518\) | 8.60452 | 0.378061 | ||||||||
\(519\) | −2.86867 | −0.125921 | ||||||||
\(520\) | −3.22721 | −0.141522 | ||||||||
\(521\) | 12.1415 | 0.531927 | 0.265963 | − | 0.963983i | \(-0.414310\pi\) | ||||
0.265963 | + | 0.963983i | \(0.414310\pi\) | |||||||
\(522\) | −26.0408 | −1.13978 | ||||||||
\(523\) | −5.14171 | −0.224831 | −0.112416 | − | 0.993661i | \(-0.535859\pi\) | ||||
−0.112416 | + | 0.993661i | \(0.535859\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | −0.874340 | −0.0381593 | ||||||||
\(526\) | −19.8540 | −0.865677 | ||||||||
\(527\) | 35.8823 | 1.56306 | ||||||||
\(528\) | −0.459106 | −0.0199800 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0.0489273 | 0.00212526 | ||||||||
\(531\) | 8.22343 | 0.356866 | ||||||||
\(532\) | 9.86889 | 0.427871 | ||||||||
\(533\) | 8.85800 | 0.383683 | ||||||||
\(534\) | −1.25248 | −0.0541999 | ||||||||
\(535\) | 37.4778 | 1.62031 | ||||||||
\(536\) | 12.5193 | 0.540751 | ||||||||
\(537\) | −12.2121 | −0.526992 | ||||||||
\(538\) | −19.6024 | −0.845121 | ||||||||
\(539\) | 0.698795 | 0.0300992 | ||||||||
\(540\) | 6.94764 | 0.298979 | ||||||||
\(541\) | 1.01304 | 0.0435539 | 0.0217769 | − | 0.999763i | \(-0.493068\pi\) | ||||
0.0217769 | + | 0.999763i | \(0.493068\pi\) | |||||||
\(542\) | 3.63275 | 0.156040 | ||||||||
\(543\) | 8.31032 | 0.356630 | ||||||||
\(544\) | 4.57925 | 0.196334 | ||||||||
\(545\) | −8.03157 | −0.344035 | ||||||||
\(546\) | 1.94098 | 0.0830662 | ||||||||
\(547\) | −27.2628 | −1.16567 | −0.582837 | − | 0.812589i | \(-0.698057\pi\) | ||||
−0.582837 | + | 0.812589i | \(0.698057\pi\) | |||||||
\(548\) | −6.03988 | −0.258011 | ||||||||
\(549\) | 22.6878 | 0.968291 | ||||||||
\(550\) | −0.551306 | −0.0235078 | ||||||||
\(551\) | −33.6448 | −1.43332 | ||||||||
\(552\) | −0.510961 | −0.0217479 | ||||||||
\(553\) | −14.6610 | −0.623448 | ||||||||
\(554\) | −20.3699 | −0.865436 | ||||||||
\(555\) | 3.73515 | 0.158548 | ||||||||
\(556\) | 7.51656 | 0.318773 | ||||||||
\(557\) | 3.16273 | 0.134009 | 0.0670046 | − | 0.997753i | \(-0.478656\pi\) | ||||
0.0670046 | + | 0.997753i | \(0.478656\pi\) | |||||||
\(558\) | −21.4617 | −0.908548 | ||||||||
\(559\) | −2.81838 | −0.119205 | ||||||||
\(560\) | 6.60763 | 0.279223 | ||||||||
\(561\) | 2.10236 | 0.0887619 | ||||||||
\(562\) | 0.960400 | 0.0405120 | ||||||||
\(563\) | −19.7409 | −0.831978 | −0.415989 | − | 0.909370i | \(-0.636565\pi\) | ||||
−0.415989 | + | 0.909370i | \(0.636565\pi\) | |||||||
\(564\) | −1.30746 | −0.0550539 | ||||||||
\(565\) | −30.3559 | −1.27708 | ||||||||
\(566\) | 7.94276 | 0.333859 | ||||||||
\(567\) | 18.7368 | 0.786870 | ||||||||
\(568\) | 2.24850 | 0.0943451 | ||||||||
\(569\) | 9.48894 | 0.397797 | 0.198898 | − | 0.980020i | \(-0.436264\pi\) | ||||
0.198898 | + | 0.980020i | \(0.436264\pi\) | |||||||
\(570\) | 4.28400 | 0.179437 | ||||||||
\(571\) | 45.8540 | 1.91893 | 0.959465 | − | 0.281826i | \(-0.0909402\pi\) | ||||
0.959465 | + | 0.281826i | \(0.0909402\pi\) | |||||||
\(572\) | 1.22386 | 0.0511723 | ||||||||
\(573\) | −6.15514 | −0.257135 | ||||||||
\(574\) | −18.1366 | −0.757005 | ||||||||
\(575\) | −0.613574 | −0.0255878 | ||||||||
\(576\) | −2.73892 | −0.114122 | ||||||||
\(577\) | 10.6861 | 0.444870 | 0.222435 | − | 0.974948i | \(-0.428599\pi\) | ||||
0.222435 | + | 0.974948i | \(0.428599\pi\) | |||||||
\(578\) | −3.96954 | −0.165111 | ||||||||
\(579\) | 0.995705 | 0.0413801 | ||||||||
\(580\) | −22.5266 | −0.935365 | ||||||||
\(581\) | −17.3312 | −0.719021 | ||||||||
\(582\) | −4.53860 | −0.188131 | ||||||||
\(583\) | −0.0185548 | −0.000768463 0 | ||||||||
\(584\) | 6.70712 | 0.277543 | ||||||||
\(585\) | −8.83906 | −0.365450 | ||||||||
\(586\) | −20.7207 | −0.855965 | ||||||||
\(587\) | −2.26704 | −0.0935706 | −0.0467853 | − | 0.998905i | \(-0.514898\pi\) | ||||
−0.0467853 | + | 0.998905i | \(0.514898\pi\) | |||||||
\(588\) | −0.397385 | −0.0163879 | ||||||||
\(589\) | −27.7286 | −1.14254 | ||||||||
\(590\) | 7.11367 | 0.292865 | ||||||||
\(591\) | 11.0120 | 0.452972 | ||||||||
\(592\) | −3.08532 | −0.126806 | ||||||||
\(593\) | −19.8737 | −0.816115 | −0.408057 | − | 0.912956i | \(-0.633794\pi\) | ||||
−0.408057 | + | 0.912956i | \(0.633794\pi\) | |||||||
\(594\) | −2.63477 | −0.108106 | ||||||||
\(595\) | −30.2580 | −1.24046 | ||||||||
\(596\) | 9.92371 | 0.406491 | ||||||||
\(597\) | 4.18460 | 0.171264 | ||||||||
\(598\) | 1.36209 | 0.0557002 | ||||||||
\(599\) | −30.7323 | −1.25569 | −0.627843 | − | 0.778340i | \(-0.716062\pi\) | ||||
−0.627843 | + | 0.778340i | \(0.716062\pi\) | |||||||
\(600\) | 0.313512 | 0.0127991 | ||||||||
\(601\) | −22.8624 | −0.932576 | −0.466288 | − | 0.884633i | \(-0.654409\pi\) | ||||
−0.466288 | + | 0.884633i | \(0.654409\pi\) | |||||||
\(602\) | 5.77056 | 0.235191 | ||||||||
\(603\) | 34.2893 | 1.39637 | ||||||||
\(604\) | 0.928938 | 0.0377979 | ||||||||
\(605\) | −24.1495 | −0.981816 | ||||||||
\(606\) | 6.38532 | 0.259386 | ||||||||
\(607\) | −24.2688 | −0.985042 | −0.492521 | − | 0.870301i | \(-0.663925\pi\) | ||||
−0.492521 | + | 0.870301i | \(0.663925\pi\) | |||||||
\(608\) | −3.53869 | −0.143513 | ||||||||
\(609\) | 13.5484 | 0.549010 | ||||||||
\(610\) | 19.6260 | 0.794635 | ||||||||
\(611\) | 3.48536 | 0.141003 | ||||||||
\(612\) | 12.5422 | 0.506988 | ||||||||
\(613\) | −27.8346 | −1.12423 | −0.562115 | − | 0.827059i | \(-0.690012\pi\) | ||||
−0.562115 | + | 0.827059i | \(0.690012\pi\) | |||||||
\(614\) | 6.56579 | 0.264974 | ||||||||
\(615\) | −7.87292 | −0.317467 | ||||||||
\(616\) | −2.50583 | −0.100963 | ||||||||
\(617\) | −18.6085 | −0.749150 | −0.374575 | − | 0.927197i | \(-0.622211\pi\) | ||||
−0.374575 | + | 0.927197i | \(0.622211\pi\) | |||||||
\(618\) | −4.24748 | −0.170859 | ||||||||
\(619\) | −43.8186 | −1.76122 | −0.880610 | − | 0.473842i | \(-0.842867\pi\) | ||||
−0.880610 | + | 0.473842i | \(0.842867\pi\) | |||||||
\(620\) | −18.5654 | −0.745606 | ||||||||
\(621\) | −2.93236 | −0.117672 | ||||||||
\(622\) | 4.91478 | 0.197065 | ||||||||
\(623\) | −6.83609 | −0.273882 | ||||||||
\(624\) | −0.695976 | −0.0278614 | ||||||||
\(625\) | −27.6914 | −1.10766 | ||||||||
\(626\) | −5.15580 | −0.206067 | ||||||||
\(627\) | −1.62463 | −0.0648817 | ||||||||
\(628\) | 6.44044 | 0.257001 | ||||||||
\(629\) | 14.1285 | 0.563339 | ||||||||
\(630\) | 18.0978 | 0.721033 | ||||||||
\(631\) | 36.3020 | 1.44516 | 0.722579 | − | 0.691288i | \(-0.242956\pi\) | ||||
0.722579 | + | 0.691288i | \(0.242956\pi\) | |||||||
\(632\) | 5.25698 | 0.209112 | ||||||||
\(633\) | −1.95832 | −0.0778362 | ||||||||
\(634\) | 1.06135 | 0.0421515 | ||||||||
\(635\) | 24.4907 | 0.971885 | ||||||||
\(636\) | 0.0105516 | 0.000418399 0 | ||||||||
\(637\) | 1.05933 | 0.0419722 | ||||||||
\(638\) | 8.54283 | 0.338214 | ||||||||
\(639\) | 6.15847 | 0.243625 | ||||||||
\(640\) | −2.36930 | −0.0936547 | ||||||||
\(641\) | 5.87055 | 0.231873 | 0.115936 | − | 0.993257i | \(-0.463013\pi\) | ||||
0.115936 | + | 0.993257i | \(0.463013\pi\) | |||||||
\(642\) | 8.08242 | 0.318988 | ||||||||
\(643\) | 24.4460 | 0.964057 | 0.482028 | − | 0.876156i | \(-0.339900\pi\) | ||||
0.482028 | + | 0.876156i | \(0.339900\pi\) | |||||||
\(644\) | −2.78886 | −0.109896 | ||||||||
\(645\) | 2.50495 | 0.0986323 | ||||||||
\(646\) | 16.2045 | 0.637559 | ||||||||
\(647\) | −6.93673 | −0.272711 | −0.136356 | − | 0.990660i | \(-0.543539\pi\) | ||||
−0.136356 | + | 0.990660i | \(0.543539\pi\) | |||||||
\(648\) | −6.71844 | −0.263925 | ||||||||
\(649\) | −2.69774 | −0.105895 | ||||||||
\(650\) | −0.835745 | −0.0327806 | ||||||||
\(651\) | 11.1660 | 0.437632 | ||||||||
\(652\) | −21.0988 | −0.826291 | ||||||||
\(653\) | 38.2599 | 1.49723 | 0.748613 | − | 0.663008i | \(-0.230720\pi\) | ||||
0.748613 | + | 0.663008i | \(0.230720\pi\) | |||||||
\(654\) | −1.73208 | −0.0677298 | ||||||||
\(655\) | −2.36930 | −0.0925761 | ||||||||
\(656\) | 6.50322 | 0.253908 | ||||||||
\(657\) | 18.3703 | 0.716692 | ||||||||
\(658\) | −7.13619 | −0.278198 | ||||||||
\(659\) | −35.4568 | −1.38120 | −0.690599 | − | 0.723237i | \(-0.742653\pi\) | ||||
−0.690599 | + | 0.723237i | \(0.742653\pi\) | |||||||
\(660\) | −1.08776 | −0.0423410 | ||||||||
\(661\) | 33.2645 | 1.29384 | 0.646920 | − | 0.762558i | \(-0.276057\pi\) | ||||
0.646920 | + | 0.762558i | \(0.276057\pi\) | |||||||
\(662\) | −15.7680 | −0.612842 | ||||||||
\(663\) | 3.18705 | 0.123775 | ||||||||
\(664\) | 6.21446 | 0.241168 | ||||||||
\(665\) | 23.3824 | 0.906729 | ||||||||
\(666\) | −8.45045 | −0.327448 | ||||||||
\(667\) | 9.50770 | 0.368140 | ||||||||
\(668\) | 7.53014 | 0.291350 | ||||||||
\(669\) | −9.21285 | −0.356189 | ||||||||
\(670\) | 29.6620 | 1.14594 | ||||||||
\(671\) | −7.44284 | −0.287328 | ||||||||
\(672\) | 1.42500 | 0.0549704 | ||||||||
\(673\) | −17.5508 | −0.676535 | −0.338267 | − | 0.941050i | \(-0.609841\pi\) | ||||
−0.338267 | + | 0.941050i | \(0.609841\pi\) | |||||||
\(674\) | −24.4343 | −0.941174 | ||||||||
\(675\) | 1.79922 | 0.0692520 | ||||||||
\(676\) | −11.1447 | −0.428642 | ||||||||
\(677\) | 42.2559 | 1.62403 | 0.812013 | − | 0.583639i | \(-0.198372\pi\) | ||||
0.812013 | + | 0.583639i | \(0.198372\pi\) | |||||||
\(678\) | −6.54653 | −0.251418 | ||||||||
\(679\) | −24.7720 | −0.950661 | ||||||||
\(680\) | 10.8496 | 0.416064 | ||||||||
\(681\) | −10.1564 | −0.389194 | ||||||||
\(682\) | 7.04063 | 0.269600 | ||||||||
\(683\) | −21.5436 | −0.824344 | −0.412172 | − | 0.911106i | \(-0.635230\pi\) | ||||
−0.412172 | + | 0.911106i | \(0.635230\pi\) | |||||||
\(684\) | −9.69218 | −0.370590 | ||||||||
\(685\) | −14.3103 | −0.546768 | ||||||||
\(686\) | 17.3530 | 0.662542 | ||||||||
\(687\) | −6.59086 | −0.251457 | ||||||||
\(688\) | −2.06915 | −0.0788856 | ||||||||
\(689\) | −0.0281280 | −0.00107159 | ||||||||
\(690\) | −1.21062 | −0.0460874 | ||||||||
\(691\) | −16.9878 | −0.646248 | −0.323124 | − | 0.946357i | \(-0.604733\pi\) | ||||
−0.323124 | + | 0.946357i | \(0.604733\pi\) | |||||||
\(692\) | 5.61427 | 0.213423 | ||||||||
\(693\) | −6.86327 | −0.260714 | ||||||||
\(694\) | 9.11262 | 0.345910 | ||||||||
\(695\) | 17.8090 | 0.675533 | ||||||||
\(696\) | −4.85806 | −0.184144 | ||||||||
\(697\) | −29.7799 | −1.12799 | ||||||||
\(698\) | 12.3863 | 0.468827 | ||||||||
\(699\) | −6.85494 | −0.259278 | ||||||||
\(700\) | 1.71117 | 0.0646761 | ||||||||
\(701\) | 2.96122 | 0.111844 | 0.0559218 | − | 0.998435i | \(-0.482190\pi\) | ||||
0.0559218 | + | 0.998435i | \(0.482190\pi\) | |||||||
\(702\) | −3.99415 | −0.150750 | ||||||||
\(703\) | −10.9180 | −0.411780 | ||||||||
\(704\) | 0.898516 | 0.0338641 | ||||||||
\(705\) | −3.09776 | −0.116668 | ||||||||
\(706\) | 5.10072 | 0.191968 | ||||||||
\(707\) | 34.8515 | 1.31072 | ||||||||
\(708\) | 1.53413 | 0.0576560 | ||||||||
\(709\) | 0.271298 | 0.0101888 | 0.00509440 | − | 0.999987i | \(-0.498378\pi\) | ||||
0.00509440 | + | 0.999987i | \(0.498378\pi\) | |||||||
\(710\) | 5.32737 | 0.199933 | ||||||||
\(711\) | 14.3985 | 0.539984 | ||||||||
\(712\) | 2.45122 | 0.0918632 | ||||||||
\(713\) | 7.83584 | 0.293455 | ||||||||
\(714\) | −6.52541 | −0.244208 | ||||||||
\(715\) | 2.89970 | 0.108443 | ||||||||
\(716\) | 23.9003 | 0.893196 | ||||||||
\(717\) | 2.23805 | 0.0835815 | ||||||||
\(718\) | 14.3929 | 0.537138 | ||||||||
\(719\) | −27.9379 | −1.04191 | −0.520953 | − | 0.853585i | \(-0.674423\pi\) | ||||
−0.520953 | + | 0.853585i | \(0.674423\pi\) | |||||||
\(720\) | −6.48932 | −0.241843 | ||||||||
\(721\) | −23.1830 | −0.863381 | ||||||||
\(722\) | 6.47769 | 0.241074 | ||||||||
\(723\) | −1.84597 | −0.0686524 | ||||||||
\(724\) | −16.2641 | −0.604450 | ||||||||
\(725\) | −5.83368 | −0.216657 | ||||||||
\(726\) | −5.20805 | −0.193289 | ||||||||
\(727\) | −22.5350 | −0.835778 | −0.417889 | − | 0.908498i | \(-0.637230\pi\) | ||||
−0.417889 | + | 0.908498i | \(0.637230\pi\) | |||||||
\(728\) | −3.79868 | −0.140789 | ||||||||
\(729\) | −13.9063 | −0.515048 | ||||||||
\(730\) | 15.8912 | 0.588158 | ||||||||
\(731\) | 9.47515 | 0.350451 | ||||||||
\(732\) | 4.23253 | 0.156439 | ||||||||
\(733\) | −48.9736 | −1.80888 | −0.904440 | − | 0.426600i | \(-0.859711\pi\) | ||||
−0.904440 | + | 0.426600i | \(0.859711\pi\) | |||||||
\(734\) | −4.65866 | −0.171954 | ||||||||
\(735\) | −0.941524 | −0.0347286 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −11.2488 | −0.414355 | ||||||||
\(738\) | 17.8118 | 0.655662 | ||||||||
\(739\) | −3.91778 | −0.144118 | −0.0720589 | − | 0.997400i | \(-0.522957\pi\) | ||||
−0.0720589 | + | 0.997400i | \(0.522957\pi\) | |||||||
\(740\) | −7.31005 | −0.268723 | ||||||||
\(741\) | −2.46284 | −0.0904748 | ||||||||
\(742\) | 0.0575914 | 0.00211425 | ||||||||
\(743\) | 1.74544 | 0.0640340 | 0.0320170 | − | 0.999487i | \(-0.489807\pi\) | ||||
0.0320170 | + | 0.999487i | \(0.489807\pi\) | |||||||
\(744\) | −4.00381 | −0.146787 | ||||||||
\(745\) | 23.5122 | 0.861421 | ||||||||
\(746\) | −2.02497 | −0.0741395 | ||||||||
\(747\) | 17.0209 | 0.622762 | ||||||||
\(748\) | −4.11453 | −0.150442 | ||||||||
\(749\) | 44.1144 | 1.61191 | ||||||||
\(750\) | −5.31029 | −0.193904 | ||||||||
\(751\) | 17.7952 | 0.649355 | 0.324677 | − | 0.945825i | \(-0.394744\pi\) | ||||
0.324677 | + | 0.945825i | \(0.394744\pi\) | |||||||
\(752\) | 2.55882 | 0.0933107 | ||||||||
\(753\) | 3.59931 | 0.131166 | ||||||||
\(754\) | 12.9504 | 0.471625 | ||||||||
\(755\) | 2.20093 | 0.0801001 | ||||||||
\(756\) | 8.17794 | 0.297429 | ||||||||
\(757\) | 42.4155 | 1.54162 | 0.770809 | − | 0.637067i | \(-0.219852\pi\) | ||||
0.770809 | + | 0.637067i | \(0.219852\pi\) | |||||||
\(758\) | −13.2463 | −0.481128 | ||||||||
\(759\) | 0.459106 | 0.0166645 | ||||||||
\(760\) | −8.38421 | −0.304127 | ||||||||
\(761\) | −8.81019 | −0.319369 | −0.159685 | − | 0.987168i | \(-0.551048\pi\) | ||||
−0.159685 | + | 0.987168i | \(0.551048\pi\) | |||||||
\(762\) | 5.28165 | 0.191334 | ||||||||
\(763\) | −9.45382 | −0.342251 | ||||||||
\(764\) | 12.0462 | 0.435816 | ||||||||
\(765\) | 29.7162 | 1.07439 | ||||||||
\(766\) | 19.7135 | 0.712278 | ||||||||
\(767\) | −4.08960 | −0.147667 | ||||||||
\(768\) | −0.510961 | −0.0184377 | ||||||||
\(769\) | −44.1256 | −1.59121 | −0.795604 | − | 0.605817i | \(-0.792846\pi\) | ||||
−0.795604 | + | 0.605817i | \(0.792846\pi\) | |||||||
\(770\) | −5.93707 | −0.213957 | ||||||||
\(771\) | 1.67024 | 0.0601523 | ||||||||
\(772\) | −1.94869 | −0.0701350 | ||||||||
\(773\) | 13.3700 | 0.480885 | 0.240443 | − | 0.970663i | \(-0.422707\pi\) | ||||
0.240443 | + | 0.970663i | \(0.422707\pi\) | |||||||
\(774\) | −5.66723 | −0.203704 | ||||||||
\(775\) | −4.80787 | −0.172704 | ||||||||
\(776\) | 8.88248 | 0.318862 | ||||||||
\(777\) | 4.39657 | 0.157726 | ||||||||
\(778\) | −22.6822 | −0.813195 | ||||||||
\(779\) | 23.0129 | 0.824522 | ||||||||
\(780\) | −1.64898 | −0.0590428 | ||||||||
\(781\) | −2.02032 | −0.0722926 | ||||||||
\(782\) | −4.57925 | −0.163754 | ||||||||
\(783\) | −27.8800 | −0.996351 | ||||||||
\(784\) | 0.777721 | 0.0277758 | ||||||||
\(785\) | 15.2593 | 0.544628 | ||||||||
\(786\) | −0.510961 | −0.0182254 | ||||||||
\(787\) | −26.7837 | −0.954734 | −0.477367 | − | 0.878704i | \(-0.658409\pi\) | ||||
−0.477367 | + | 0.878704i | \(0.658409\pi\) | |||||||
\(788\) | −21.5515 | −0.767740 | ||||||||
\(789\) | −10.1446 | −0.361159 | ||||||||
\(790\) | 12.4554 | 0.443142 | ||||||||
\(791\) | −35.7314 | −1.27046 | ||||||||
\(792\) | 2.46096 | 0.0874465 | ||||||||
\(793\) | −11.2829 | −0.400667 | ||||||||
\(794\) | −11.7673 | −0.417606 | ||||||||
\(795\) | 0.0249999 | 0.000886655 0 | ||||||||
\(796\) | −8.18967 | −0.290275 | ||||||||
\(797\) | −23.4686 | −0.831299 | −0.415650 | − | 0.909525i | \(-0.636446\pi\) | ||||
−0.415650 | + | 0.909525i | \(0.636446\pi\) | |||||||
\(798\) | 5.04262 | 0.178507 | ||||||||
\(799\) | −11.7175 | −0.414535 | ||||||||
\(800\) | −0.613574 | −0.0216931 | ||||||||
\(801\) | 6.71368 | 0.237216 | ||||||||
\(802\) | 16.1699 | 0.570977 | ||||||||
\(803\) | −6.02645 | −0.212669 | ||||||||
\(804\) | 6.39687 | 0.225600 | ||||||||
\(805\) | −6.60763 | −0.232888 | ||||||||
\(806\) | 10.6731 | 0.375946 | ||||||||
\(807\) | −10.0161 | −0.352583 | ||||||||
\(808\) | −12.4967 | −0.439632 | ||||||||
\(809\) | 30.1944 | 1.06158 | 0.530789 | − | 0.847504i | \(-0.321895\pi\) | ||||
0.530789 | + | 0.847504i | \(0.321895\pi\) | |||||||
\(810\) | −15.9180 | −0.559301 | ||||||||
\(811\) | 34.2559 | 1.20289 | 0.601443 | − | 0.798916i | \(-0.294593\pi\) | ||||
0.601443 | + | 0.798916i | \(0.294593\pi\) | |||||||
\(812\) | −26.5156 | −0.930516 | ||||||||
\(813\) | 1.85619 | 0.0650995 | ||||||||
\(814\) | 2.77221 | 0.0971660 | ||||||||
\(815\) | −49.9893 | −1.75105 | ||||||||
\(816\) | 2.33982 | 0.0819100 | ||||||||
\(817\) | −7.32207 | −0.256167 | ||||||||
\(818\) | −39.9690 | −1.39748 | ||||||||
\(819\) | −10.4043 | −0.363555 | ||||||||
\(820\) | 15.4081 | 0.538073 | ||||||||
\(821\) | −25.4104 | −0.886829 | −0.443415 | − | 0.896317i | \(-0.646233\pi\) | ||||
−0.443415 | + | 0.896317i | \(0.646233\pi\) | |||||||
\(822\) | −3.08614 | −0.107642 | ||||||||
\(823\) | −18.8329 | −0.656474 | −0.328237 | − | 0.944595i | \(-0.606454\pi\) | ||||
−0.328237 | + | 0.944595i | \(0.606454\pi\) | |||||||
\(824\) | 8.31273 | 0.289588 | ||||||||
\(825\) | −0.281696 | −0.00980739 | ||||||||
\(826\) | 8.37336 | 0.291347 | ||||||||
\(827\) | 55.5970 | 1.93330 | 0.966649 | − | 0.256105i | \(-0.0824391\pi\) | ||||
0.966649 | + | 0.256105i | \(0.0824391\pi\) | |||||||
\(828\) | 2.73892 | 0.0951840 | ||||||||
\(829\) | −26.6216 | −0.924607 | −0.462304 | − | 0.886722i | \(-0.652977\pi\) | ||||
−0.462304 | + | 0.886722i | \(0.652977\pi\) | |||||||
\(830\) | 14.7239 | 0.511074 | ||||||||
\(831\) | −10.4082 | −0.361058 | ||||||||
\(832\) | 1.36209 | 0.0472221 | ||||||||
\(833\) | −3.56138 | −0.123395 | ||||||||
\(834\) | 3.84067 | 0.132991 | ||||||||
\(835\) | 17.8411 | 0.617418 | ||||||||
\(836\) | 3.17957 | 0.109968 | ||||||||
\(837\) | −22.9775 | −0.794219 | ||||||||
\(838\) | 30.0864 | 1.03932 | ||||||||
\(839\) | −40.8399 | −1.40995 | −0.704975 | − | 0.709232i | \(-0.749042\pi\) | ||||
−0.704975 | + | 0.709232i | \(0.749042\pi\) | |||||||
\(840\) | 3.37624 | 0.116491 | ||||||||
\(841\) | 61.3964 | 2.11712 | ||||||||
\(842\) | 31.6647 | 1.09124 | ||||||||
\(843\) | 0.490727 | 0.0169015 | ||||||||
\(844\) | 3.83262 | 0.131924 | ||||||||
\(845\) | −26.4051 | −0.908364 | ||||||||
\(846\) | 7.00841 | 0.240954 | ||||||||
\(847\) | −28.4259 | −0.976725 | ||||||||
\(848\) | −0.0206505 | −0.000709142 0 | ||||||||
\(849\) | 4.05844 | 0.139285 | ||||||||
\(850\) | 2.80971 | 0.0963722 | ||||||||
\(851\) | 3.08532 | 0.105764 | ||||||||
\(852\) | 1.14890 | 0.0393606 | ||||||||
\(853\) | 35.7169 | 1.22292 | 0.611461 | − | 0.791275i | \(-0.290582\pi\) | ||||
0.611461 | + | 0.791275i | \(0.290582\pi\) | |||||||
\(854\) | 23.1014 | 0.790515 | ||||||||
\(855\) | −22.9637 | −0.785341 | ||||||||
\(856\) | −15.8181 | −0.540651 | ||||||||
\(857\) | 7.36730 | 0.251662 | 0.125831 | − | 0.992052i | \(-0.459840\pi\) | ||||
0.125831 | + | 0.992052i | \(0.459840\pi\) | |||||||
\(858\) | 0.625346 | 0.0213490 | ||||||||
\(859\) | −3.24579 | −0.110745 | −0.0553724 | − | 0.998466i | \(-0.517635\pi\) | ||||
−0.0553724 | + | 0.998466i | \(0.517635\pi\) | |||||||
\(860\) | −4.90243 | −0.167172 | ||||||||
\(861\) | −9.26707 | −0.315821 | ||||||||
\(862\) | 20.4046 | 0.694982 | ||||||||
\(863\) | 16.0169 | 0.545222 | 0.272611 | − | 0.962124i | \(-0.412113\pi\) | ||||
0.272611 | + | 0.962124i | \(0.412113\pi\) | |||||||
\(864\) | −2.93236 | −0.0997610 | ||||||||
\(865\) | 13.3019 | 0.452277 | ||||||||
\(866\) | 8.53681 | 0.290093 | ||||||||
\(867\) | −2.02828 | −0.0688840 | ||||||||
\(868\) | −21.8530 | −0.741740 | ||||||||
\(869\) | −4.72348 | −0.160233 | ||||||||
\(870\) | −11.5102 | −0.390232 | ||||||||
\(871\) | −17.0525 | −0.577800 | ||||||||
\(872\) | 3.38985 | 0.114795 | ||||||||
\(873\) | 24.3284 | 0.823391 | ||||||||
\(874\) | 3.53869 | 0.119698 | ||||||||
\(875\) | −28.9839 | −0.979834 | ||||||||
\(876\) | 3.42707 | 0.115790 | ||||||||
\(877\) | 47.0961 | 1.59032 | 0.795161 | − | 0.606399i | \(-0.207387\pi\) | ||||
0.795161 | + | 0.606399i | \(0.207387\pi\) | |||||||
\(878\) | 19.1651 | 0.646791 | ||||||||
\(879\) | −10.5875 | −0.357107 | ||||||||
\(880\) | 2.12885 | 0.0717636 | ||||||||
\(881\) | 30.9668 | 1.04330 | 0.521649 | − | 0.853160i | \(-0.325317\pi\) | ||||
0.521649 | + | 0.853160i | \(0.325317\pi\) | |||||||
\(882\) | 2.13012 | 0.0717247 | ||||||||
\(883\) | 4.05885 | 0.136591 | 0.0682955 | − | 0.997665i | \(-0.478244\pi\) | ||||
0.0682955 | + | 0.997665i | \(0.478244\pi\) | |||||||
\(884\) | −6.23737 | −0.209785 | ||||||||
\(885\) | 3.63480 | 0.122183 | ||||||||
\(886\) | −23.9265 | −0.803827 | ||||||||
\(887\) | −33.6774 | −1.13078 | −0.565388 | − | 0.824825i | \(-0.691273\pi\) | ||||
−0.565388 | + | 0.824825i | \(0.691273\pi\) | |||||||
\(888\) | −1.57648 | −0.0529032 | ||||||||
\(889\) | 28.8276 | 0.966846 | ||||||||
\(890\) | 5.80766 | 0.194673 | ||||||||
\(891\) | 6.03662 | 0.202234 | ||||||||
\(892\) | 18.0304 | 0.603704 | ||||||||
\(893\) | 9.05488 | 0.303010 | ||||||||
\(894\) | 5.07063 | 0.169587 | ||||||||
\(895\) | 56.6269 | 1.89283 | ||||||||
\(896\) | −2.78886 | −0.0931692 | ||||||||
\(897\) | 0.695976 | 0.0232380 | ||||||||
\(898\) | −23.2056 | −0.774382 | ||||||||
\(899\) | 74.5008 | 2.48474 | ||||||||
\(900\) | −1.68053 | −0.0560176 | ||||||||
\(901\) | 0.0945640 | 0.00315038 | ||||||||
\(902\) | −5.84325 | −0.194559 | ||||||||
\(903\) | 2.94853 | 0.0981209 | ||||||||
\(904\) | 12.8122 | 0.426128 | ||||||||
\(905\) | −38.5345 | −1.28093 | ||||||||
\(906\) | 0.474651 | 0.0157692 | ||||||||
\(907\) | 22.6180 | 0.751020 | 0.375510 | − | 0.926818i | \(-0.377468\pi\) | ||||
0.375510 | + | 0.926818i | \(0.377468\pi\) | |||||||
\(908\) | 19.8771 | 0.659643 | ||||||||
\(909\) | −34.2274 | −1.13525 | ||||||||
\(910\) | −9.00022 | −0.298354 | ||||||||
\(911\) | −36.0075 | −1.19298 | −0.596490 | − | 0.802620i | \(-0.703439\pi\) | ||||
−0.596490 | + | 0.802620i | \(0.703439\pi\) | |||||||
\(912\) | −1.80813 | −0.0598732 | ||||||||
\(913\) | −5.58379 | −0.184797 | ||||||||
\(914\) | 4.56956 | 0.151148 | ||||||||
\(915\) | 10.0281 | 0.331520 | ||||||||
\(916\) | 12.8990 | 0.426193 | ||||||||
\(917\) | −2.78886 | −0.0920962 | ||||||||
\(918\) | 13.4280 | 0.443191 | ||||||||
\(919\) | −34.7315 | −1.14569 | −0.572843 | − | 0.819665i | \(-0.694159\pi\) | ||||
−0.572843 | + | 0.819665i | \(0.694159\pi\) | |||||||
\(920\) | 2.36930 | 0.0781134 | ||||||||
\(921\) | 3.35486 | 0.110546 | ||||||||
\(922\) | 22.1990 | 0.731085 | ||||||||
\(923\) | −3.06267 | −0.100809 | ||||||||
\(924\) | −1.28038 | −0.0421215 | ||||||||
\(925\) | −1.89307 | −0.0622439 | ||||||||
\(926\) | 21.1625 | 0.695444 | ||||||||
\(927\) | 22.7679 | 0.747796 | ||||||||
\(928\) | 9.50770 | 0.312106 | ||||||||
\(929\) | 15.8472 | 0.519930 | 0.259965 | − | 0.965618i | \(-0.416289\pi\) | ||||
0.259965 | + | 0.965618i | \(0.416289\pi\) | |||||||
\(930\) | −9.48621 | −0.311065 | ||||||||
\(931\) | 2.75211 | 0.0901969 | ||||||||
\(932\) | 13.4158 | 0.439449 | ||||||||
\(933\) | 2.51126 | 0.0822149 | ||||||||
\(934\) | 1.89152 | 0.0618925 | ||||||||
\(935\) | −9.74855 | −0.318812 | ||||||||
\(936\) | 3.73066 | 0.121941 | ||||||||
\(937\) | −6.50109 | −0.212381 | −0.106191 | − | 0.994346i | \(-0.533865\pi\) | ||||
−0.106191 | + | 0.994346i | \(0.533865\pi\) | |||||||
\(938\) | 34.9145 | 1.14000 | ||||||||
\(939\) | −2.63441 | −0.0859707 | ||||||||
\(940\) | 6.06262 | 0.197741 | ||||||||
\(941\) | −30.9520 | −1.00901 | −0.504503 | − | 0.863410i | \(-0.668324\pi\) | ||||
−0.504503 | + | 0.863410i | \(0.668324\pi\) | |||||||
\(942\) | 3.29081 | 0.107220 | ||||||||
\(943\) | −6.50322 | −0.211774 | ||||||||
\(944\) | −3.00244 | −0.0977210 | ||||||||
\(945\) | 19.3760 | 0.630300 | ||||||||
\(946\) | 1.85916 | 0.0604466 | ||||||||
\(947\) | −3.25183 | −0.105670 | −0.0528351 | − | 0.998603i | \(-0.516826\pi\) | ||||
−0.0528351 | + | 0.998603i | \(0.516826\pi\) | |||||||
\(948\) | 2.68611 | 0.0872408 | ||||||||
\(949\) | −9.13572 | −0.296558 | ||||||||
\(950\) | −2.17125 | −0.0704445 | ||||||||
\(951\) | 0.542307 | 0.0175855 | ||||||||
\(952\) | 12.7709 | 0.413906 | ||||||||
\(953\) | 36.9112 | 1.19567 | 0.597836 | − | 0.801618i | \(-0.296027\pi\) | ||||
0.597836 | + | 0.801618i | \(0.296027\pi\) | |||||||
\(954\) | −0.0565601 | −0.00183120 | ||||||||
\(955\) | 28.5410 | 0.923567 | ||||||||
\(956\) | −4.38008 | −0.141662 | ||||||||
\(957\) | 4.36505 | 0.141102 | ||||||||
\(958\) | 9.85969 | 0.318552 | ||||||||
\(959\) | −16.8444 | −0.543933 | ||||||||
\(960\) | −1.21062 | −0.0390725 | ||||||||
\(961\) | 30.4004 | 0.980658 | ||||||||
\(962\) | 4.20250 | 0.135494 | ||||||||
\(963\) | −43.3245 | −1.39611 | ||||||||
\(964\) | 3.61274 | 0.116359 | ||||||||
\(965\) | −4.61703 | −0.148628 | ||||||||
\(966\) | −1.42500 | −0.0458485 | ||||||||
\(967\) | 41.6289 | 1.33870 | 0.669348 | − | 0.742949i | \(-0.266574\pi\) | ||||
0.669348 | + | 0.742949i | \(0.266574\pi\) | |||||||
\(968\) | 10.1927 | 0.327605 | ||||||||
\(969\) | 8.27988 | 0.265988 | ||||||||
\(970\) | 21.0452 | 0.675722 | ||||||||
\(971\) | 42.7414 | 1.37164 | 0.685819 | − | 0.727773i | \(-0.259444\pi\) | ||||
0.685819 | + | 0.727773i | \(0.259444\pi\) | |||||||
\(972\) | −12.2299 | −0.392276 | ||||||||
\(973\) | 20.9626 | 0.672031 | ||||||||
\(974\) | 32.8919 | 1.05392 | ||||||||
\(975\) | −0.427033 | −0.0136760 | ||||||||
\(976\) | −8.28348 | −0.265148 | ||||||||
\(977\) | 21.1898 | 0.677921 | 0.338960 | − | 0.940801i | \(-0.389925\pi\) | ||||
0.338960 | + | 0.940801i | \(0.389925\pi\) | |||||||
\(978\) | −10.7806 | −0.344727 | ||||||||
\(979\) | −2.20246 | −0.0703908 | ||||||||
\(980\) | 1.84265 | 0.0588614 | ||||||||
\(981\) | 9.28454 | 0.296432 | ||||||||
\(982\) | 21.7901 | 0.695349 | ||||||||
\(983\) | −3.06058 | −0.0976173 | −0.0488087 | − | 0.998808i | \(-0.515542\pi\) | ||||
−0.0488087 | + | 0.998808i | \(0.515542\pi\) | |||||||
\(984\) | 3.32289 | 0.105930 | ||||||||
\(985\) | −51.0619 | −1.62697 | ||||||||
\(986\) | −43.5382 | −1.38654 | ||||||||
\(987\) | −3.64631 | −0.116063 | ||||||||
\(988\) | 4.82002 | 0.153345 | ||||||||
\(989\) | 2.06915 | 0.0657951 | ||||||||
\(990\) | 5.83076 | 0.185314 | ||||||||
\(991\) | −29.5613 | −0.939044 | −0.469522 | − | 0.882921i | \(-0.655574\pi\) | ||||
−0.469522 | + | 0.882921i | \(0.655574\pi\) | |||||||
\(992\) | 7.83584 | 0.248788 | ||||||||
\(993\) | −8.05685 | −0.255676 | ||||||||
\(994\) | 6.27075 | 0.198896 | ||||||||
\(995\) | −19.4038 | −0.615141 | ||||||||
\(996\) | 3.17534 | 0.100615 | ||||||||
\(997\) | 35.0113 | 1.10882 | 0.554410 | − | 0.832244i | \(-0.312944\pi\) | ||||
0.554410 | + | 0.832244i | \(0.312944\pi\) | |||||||
\(998\) | −11.1791 | −0.353867 | ||||||||
\(999\) | −9.04728 | −0.286243 |
(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 | 6026.2.a.h.1.13 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.h.1.13 | ✓ | 24 | 1.1 | even | 1 | trivial |