Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, 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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0200112105\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 3 x^{16} - 24 x^{15} + 70 x^{14} + 228 x^{13} - 638 x^{12} - 1075 x^{11} + 2854 x^{10} + \cdots - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.24738\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-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 | ||||||||
\(3\) | −2.24738 | −1.29753 | −0.648764 | − | 0.760990i | \(-0.724714\pi\) | ||||
−0.648764 | + | 0.760990i | \(0.724714\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.24738 | 0.917491 | ||||||||
\(7\) | 2.64455 | 0.999545 | 0.499772 | − | 0.866157i | \(-0.333417\pi\) | ||||
0.499772 | + | 0.866157i | \(0.333417\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.05073 | 0.683578 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −3.63995 | −1.09749 | −0.548743 | − | 0.835991i | \(-0.684894\pi\) | ||||
−0.548743 | + | 0.835991i | \(0.684894\pi\) | |||||||
\(12\) | −2.24738 | −0.648764 | ||||||||
\(13\) | 4.23279 | 1.17396 | 0.586982 | − | 0.809600i | \(-0.300316\pi\) | ||||
0.586982 | + | 0.809600i | \(0.300316\pi\) | |||||||
\(14\) | −2.64455 | −0.706785 | ||||||||
\(15\) | 2.24738 | 0.580272 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.56021 | −0.620941 | −0.310471 | − | 0.950583i | \(-0.600487\pi\) | ||||
−0.310471 | + | 0.950583i | \(0.600487\pi\) | |||||||
\(18\) | −2.05073 | −0.483363 | ||||||||
\(19\) | 2.14346 | 0.491743 | 0.245872 | − | 0.969302i | \(-0.420926\pi\) | ||||
0.245872 | + | 0.969302i | \(0.420926\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −5.94331 | −1.29694 | ||||||||
\(22\) | 3.63995 | 0.776040 | ||||||||
\(23\) | −3.69511 | −0.770483 | −0.385242 | − | 0.922816i | \(-0.625882\pi\) | ||||
−0.385242 | + | 0.922816i | \(0.625882\pi\) | |||||||
\(24\) | 2.24738 | 0.458745 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.23279 | −0.830118 | ||||||||
\(27\) | 2.13336 | 0.410566 | ||||||||
\(28\) | 2.64455 | 0.499772 | ||||||||
\(29\) | 8.15103 | 1.51361 | 0.756804 | − | 0.653642i | \(-0.226760\pi\) | ||||
0.756804 | + | 0.653642i | \(0.226760\pi\) | |||||||
\(30\) | −2.24738 | −0.410314 | ||||||||
\(31\) | −1.65648 | −0.297513 | −0.148757 | − | 0.988874i | \(-0.547527\pi\) | ||||
−0.148757 | + | 0.988874i | \(0.547527\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 8.18037 | 1.42402 | ||||||||
\(34\) | 2.56021 | 0.439072 | ||||||||
\(35\) | −2.64455 | −0.447010 | ||||||||
\(36\) | 2.05073 | 0.341789 | ||||||||
\(37\) | −8.82225 | −1.45037 | −0.725185 | − | 0.688554i | \(-0.758246\pi\) | ||||
−0.725185 | + | 0.688554i | \(0.758246\pi\) | |||||||
\(38\) | −2.14346 | −0.347715 | ||||||||
\(39\) | −9.51270 | −1.52325 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 0.492801 | 0.0769626 | 0.0384813 | − | 0.999259i | \(-0.487748\pi\) | ||||
0.0384813 | + | 0.999259i | \(0.487748\pi\) | |||||||
\(42\) | 5.94331 | 0.917073 | ||||||||
\(43\) | 3.75914 | 0.573264 | 0.286632 | − | 0.958041i | \(-0.407464\pi\) | ||||
0.286632 | + | 0.958041i | \(0.407464\pi\) | |||||||
\(44\) | −3.63995 | −0.548743 | ||||||||
\(45\) | −2.05073 | −0.305706 | ||||||||
\(46\) | 3.69511 | 0.544814 | ||||||||
\(47\) | 10.8528 | 1.58304 | 0.791522 | − | 0.611141i | \(-0.209289\pi\) | ||||
0.791522 | + | 0.611141i | \(0.209289\pi\) | |||||||
\(48\) | −2.24738 | −0.324382 | ||||||||
\(49\) | −0.00636926 | −0.000909894 0 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 5.75377 | 0.805688 | ||||||||
\(52\) | 4.23279 | 0.586982 | ||||||||
\(53\) | −9.30244 | −1.27779 | −0.638894 | − | 0.769295i | \(-0.720608\pi\) | ||||
−0.638894 | + | 0.769295i | \(0.720608\pi\) | |||||||
\(54\) | −2.13336 | −0.290314 | ||||||||
\(55\) | 3.63995 | 0.490811 | ||||||||
\(56\) | −2.64455 | −0.353393 | ||||||||
\(57\) | −4.81718 | −0.638051 | ||||||||
\(58\) | −8.15103 | −1.07028 | ||||||||
\(59\) | 5.31155 | 0.691504 | 0.345752 | − | 0.938326i | \(-0.387624\pi\) | ||||
0.345752 | + | 0.938326i | \(0.387624\pi\) | |||||||
\(60\) | 2.24738 | 0.290136 | ||||||||
\(61\) | −2.57543 | −0.329750 | −0.164875 | − | 0.986314i | \(-0.552722\pi\) | ||||
−0.164875 | + | 0.986314i | \(0.552722\pi\) | |||||||
\(62\) | 1.65648 | 0.210374 | ||||||||
\(63\) | 5.42327 | 0.683267 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.23279 | −0.525013 | ||||||||
\(66\) | −8.18037 | −1.00693 | ||||||||
\(67\) | 12.1152 | 1.48010 | 0.740052 | − | 0.672550i | \(-0.234801\pi\) | ||||
0.740052 | + | 0.672550i | \(0.234801\pi\) | |||||||
\(68\) | −2.56021 | −0.310471 | ||||||||
\(69\) | 8.30432 | 0.999723 | ||||||||
\(70\) | 2.64455 | 0.316084 | ||||||||
\(71\) | −11.6438 | −1.38187 | −0.690933 | − | 0.722919i | \(-0.742800\pi\) | ||||
−0.690933 | + | 0.722919i | \(0.742800\pi\) | |||||||
\(72\) | −2.05073 | −0.241681 | ||||||||
\(73\) | 7.12350 | 0.833743 | 0.416872 | − | 0.908965i | \(-0.363127\pi\) | ||||
0.416872 | + | 0.908965i | \(0.363127\pi\) | |||||||
\(74\) | 8.82225 | 1.02557 | ||||||||
\(75\) | −2.24738 | −0.259506 | ||||||||
\(76\) | 2.14346 | 0.245872 | ||||||||
\(77\) | −9.62603 | −1.09699 | ||||||||
\(78\) | 9.51270 | 1.07710 | ||||||||
\(79\) | −9.66661 | −1.08758 | −0.543789 | − | 0.839222i | \(-0.683011\pi\) | ||||
−0.543789 | + | 0.839222i | \(0.683011\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −10.9467 | −1.21630 | ||||||||
\(82\) | −0.492801 | −0.0544208 | ||||||||
\(83\) | −2.87890 | −0.316000 | −0.158000 | − | 0.987439i | \(-0.550505\pi\) | ||||
−0.158000 | + | 0.987439i | \(0.550505\pi\) | |||||||
\(84\) | −5.94331 | −0.648469 | ||||||||
\(85\) | 2.56021 | 0.277693 | ||||||||
\(86\) | −3.75914 | −0.405359 | ||||||||
\(87\) | −18.3185 | −1.96395 | ||||||||
\(88\) | 3.63995 | 0.388020 | ||||||||
\(89\) | 7.00615 | 0.742650 | 0.371325 | − | 0.928503i | \(-0.378904\pi\) | ||||
0.371325 | + | 0.928503i | \(0.378904\pi\) | |||||||
\(90\) | 2.05073 | 0.216166 | ||||||||
\(91\) | 11.1938 | 1.17343 | ||||||||
\(92\) | −3.69511 | −0.385242 | ||||||||
\(93\) | 3.72275 | 0.386032 | ||||||||
\(94\) | −10.8528 | −1.11938 | ||||||||
\(95\) | −2.14346 | −0.219914 | ||||||||
\(96\) | 2.24738 | 0.229373 | ||||||||
\(97\) | 6.50997 | 0.660987 | 0.330494 | − | 0.943808i | \(-0.392785\pi\) | ||||
0.330494 | + | 0.943808i | \(0.392785\pi\) | |||||||
\(98\) | 0.00636926 | 0.000643392 0 | ||||||||
\(99\) | −7.46458 | −0.750218 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −16.0595 | −1.59798 | −0.798991 | − | 0.601343i | \(-0.794633\pi\) | ||||
−0.798991 | + | 0.601343i | \(0.794633\pi\) | |||||||
\(102\) | −5.75377 | −0.569708 | ||||||||
\(103\) | 12.6612 | 1.24755 | 0.623774 | − | 0.781605i | \(-0.285599\pi\) | ||||
0.623774 | + | 0.781605i | \(0.285599\pi\) | |||||||
\(104\) | −4.23279 | −0.415059 | ||||||||
\(105\) | 5.94331 | 0.580008 | ||||||||
\(106\) | 9.30244 | 0.903533 | ||||||||
\(107\) | 5.69611 | 0.550664 | 0.275332 | − | 0.961349i | \(-0.411212\pi\) | ||||
0.275332 | + | 0.961349i | \(0.411212\pi\) | |||||||
\(108\) | 2.13336 | 0.205283 | ||||||||
\(109\) | −16.3994 | −1.57078 | −0.785390 | − | 0.619001i | \(-0.787538\pi\) | ||||
−0.785390 | + | 0.619001i | \(0.787538\pi\) | |||||||
\(110\) | −3.63995 | −0.347056 | ||||||||
\(111\) | 19.8270 | 1.88189 | ||||||||
\(112\) | 2.64455 | 0.249886 | ||||||||
\(113\) | −5.97011 | −0.561621 | −0.280810 | − | 0.959763i | \(-0.590603\pi\) | ||||
−0.280810 | + | 0.959763i | \(0.590603\pi\) | |||||||
\(114\) | 4.81718 | 0.451170 | ||||||||
\(115\) | 3.69511 | 0.344570 | ||||||||
\(116\) | 8.15103 | 0.756804 | ||||||||
\(117\) | 8.68032 | 0.802496 | ||||||||
\(118\) | −5.31155 | −0.488967 | ||||||||
\(119\) | −6.77059 | −0.620659 | ||||||||
\(120\) | −2.24738 | −0.205157 | ||||||||
\(121\) | 2.24925 | 0.204477 | ||||||||
\(122\) | 2.57543 | 0.233169 | ||||||||
\(123\) | −1.10751 | −0.0998611 | ||||||||
\(124\) | −1.65648 | −0.148757 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −5.42327 | −0.483143 | ||||||||
\(127\) | −14.3666 | −1.27483 | −0.637415 | − | 0.770521i | \(-0.719996\pi\) | ||||
−0.637415 | + | 0.770521i | \(0.719996\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −8.44823 | −0.743825 | ||||||||
\(130\) | 4.23279 | 0.371240 | ||||||||
\(131\) | −7.21853 | −0.630686 | −0.315343 | − | 0.948978i | \(-0.602120\pi\) | ||||
−0.315343 | + | 0.948978i | \(0.602120\pi\) | |||||||
\(132\) | 8.18037 | 0.712010 | ||||||||
\(133\) | 5.66848 | 0.491520 | ||||||||
\(134\) | −12.1152 | −1.04659 | ||||||||
\(135\) | −2.13336 | −0.183611 | ||||||||
\(136\) | 2.56021 | 0.219536 | ||||||||
\(137\) | 6.54622 | 0.559281 | 0.279641 | − | 0.960105i | \(-0.409785\pi\) | ||||
0.279641 | + | 0.960105i | \(0.409785\pi\) | |||||||
\(138\) | −8.30432 | −0.706911 | ||||||||
\(139\) | 5.72920 | 0.485945 | 0.242972 | − | 0.970033i | \(-0.421878\pi\) | ||||
0.242972 | + | 0.970033i | \(0.421878\pi\) | |||||||
\(140\) | −2.64455 | −0.223505 | ||||||||
\(141\) | −24.3904 | −2.05404 | ||||||||
\(142\) | 11.6438 | 0.977127 | ||||||||
\(143\) | −15.4071 | −1.28841 | ||||||||
\(144\) | 2.05073 | 0.170895 | ||||||||
\(145\) | −8.15103 | −0.676906 | ||||||||
\(146\) | −7.12350 | −0.589545 | ||||||||
\(147\) | 0.0143142 | 0.00118061 | ||||||||
\(148\) | −8.82225 | −0.725185 | ||||||||
\(149\) | −15.7466 | −1.29001 | −0.645007 | − | 0.764177i | \(-0.723146\pi\) | ||||
−0.645007 | + | 0.764177i | \(0.723146\pi\) | |||||||
\(150\) | 2.24738 | 0.183498 | ||||||||
\(151\) | 8.51416 | 0.692872 | 0.346436 | − | 0.938074i | \(-0.387392\pi\) | ||||
0.346436 | + | 0.938074i | \(0.387392\pi\) | |||||||
\(152\) | −2.14346 | −0.173858 | ||||||||
\(153\) | −5.25030 | −0.424462 | ||||||||
\(154\) | 9.62603 | 0.775687 | ||||||||
\(155\) | 1.65648 | 0.133052 | ||||||||
\(156\) | −9.51270 | −0.761625 | ||||||||
\(157\) | 13.8003 | 1.10139 | 0.550693 | − | 0.834708i | \(-0.314363\pi\) | ||||
0.550693 | + | 0.834708i | \(0.314363\pi\) | |||||||
\(158\) | 9.66661 | 0.769034 | ||||||||
\(159\) | 20.9062 | 1.65797 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −9.77189 | −0.770132 | ||||||||
\(162\) | 10.9467 | 0.860053 | ||||||||
\(163\) | 19.8361 | 1.55368 | 0.776841 | − | 0.629697i | \(-0.216821\pi\) | ||||
0.776841 | + | 0.629697i | \(0.216821\pi\) | |||||||
\(164\) | 0.492801 | 0.0384813 | ||||||||
\(165\) | −8.18037 | −0.636841 | ||||||||
\(166\) | 2.87890 | 0.223446 | ||||||||
\(167\) | −19.0725 | −1.47587 | −0.737936 | − | 0.674871i | \(-0.764199\pi\) | ||||
−0.737936 | + | 0.674871i | \(0.764199\pi\) | |||||||
\(168\) | 5.94331 | 0.458537 | ||||||||
\(169\) | 4.91649 | 0.378191 | ||||||||
\(170\) | −2.56021 | −0.196359 | ||||||||
\(171\) | 4.39567 | 0.336145 | ||||||||
\(172\) | 3.75914 | 0.286632 | ||||||||
\(173\) | 25.4482 | 1.93479 | 0.967397 | − | 0.253264i | \(-0.0815040\pi\) | ||||
0.967397 | + | 0.253264i | \(0.0815040\pi\) | |||||||
\(174\) | 18.3185 | 1.38872 | ||||||||
\(175\) | 2.64455 | 0.199909 | ||||||||
\(176\) | −3.63995 | −0.274372 | ||||||||
\(177\) | −11.9371 | −0.897246 | ||||||||
\(178\) | −7.00615 | −0.525133 | ||||||||
\(179\) | −10.0953 | −0.754562 | −0.377281 | − | 0.926099i | \(-0.623141\pi\) | ||||
−0.377281 | + | 0.926099i | \(0.623141\pi\) | |||||||
\(180\) | −2.05073 | −0.152853 | ||||||||
\(181\) | 1.90872 | 0.141874 | 0.0709372 | − | 0.997481i | \(-0.477401\pi\) | ||||
0.0709372 | + | 0.997481i | \(0.477401\pi\) | |||||||
\(182\) | −11.1938 | −0.829740 | ||||||||
\(183\) | 5.78798 | 0.427860 | ||||||||
\(184\) | 3.69511 | 0.272407 | ||||||||
\(185\) | 8.82225 | 0.648625 | ||||||||
\(186\) | −3.72275 | −0.272966 | ||||||||
\(187\) | 9.31903 | 0.681475 | ||||||||
\(188\) | 10.8528 | 0.791522 | ||||||||
\(189\) | 5.64178 | 0.410379 | ||||||||
\(190\) | 2.14346 | 0.155503 | ||||||||
\(191\) | 17.9529 | 1.29903 | 0.649513 | − | 0.760351i | \(-0.274973\pi\) | ||||
0.649513 | + | 0.760351i | \(0.274973\pi\) | |||||||
\(192\) | −2.24738 | −0.162191 | ||||||||
\(193\) | 6.75068 | 0.485924 | 0.242962 | − | 0.970036i | \(-0.421881\pi\) | ||||
0.242962 | + | 0.970036i | \(0.421881\pi\) | |||||||
\(194\) | −6.50997 | −0.467389 | ||||||||
\(195\) | 9.51270 | 0.681218 | ||||||||
\(196\) | −0.00636926 | −0.000454947 0 | ||||||||
\(197\) | 2.21121 | 0.157542 | 0.0787710 | − | 0.996893i | \(-0.474900\pi\) | ||||
0.0787710 | + | 0.996893i | \(0.474900\pi\) | |||||||
\(198\) | 7.46458 | 0.530484 | ||||||||
\(199\) | −16.9056 | −1.19841 | −0.599204 | − | 0.800597i | \(-0.704516\pi\) | ||||
−0.599204 | + | 0.800597i | \(0.704516\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −27.2274 | −1.92048 | ||||||||
\(202\) | 16.0595 | 1.12994 | ||||||||
\(203\) | 21.5558 | 1.51292 | ||||||||
\(204\) | 5.75377 | 0.402844 | ||||||||
\(205\) | −0.492801 | −0.0344187 | ||||||||
\(206\) | −12.6612 | −0.882149 | ||||||||
\(207\) | −7.57768 | −0.526686 | ||||||||
\(208\) | 4.23279 | 0.293491 | ||||||||
\(209\) | −7.80209 | −0.539682 | ||||||||
\(210\) | −5.94331 | −0.410128 | ||||||||
\(211\) | 26.5778 | 1.82969 | 0.914844 | − | 0.403807i | \(-0.132313\pi\) | ||||
0.914844 | + | 0.403807i | \(0.132313\pi\) | |||||||
\(212\) | −9.30244 | −0.638894 | ||||||||
\(213\) | 26.1681 | 1.79301 | ||||||||
\(214\) | −5.69611 | −0.389378 | ||||||||
\(215\) | −3.75914 | −0.256371 | ||||||||
\(216\) | −2.13336 | −0.145157 | ||||||||
\(217\) | −4.38065 | −0.297378 | ||||||||
\(218\) | 16.3994 | 1.11071 | ||||||||
\(219\) | −16.0092 | −1.08180 | ||||||||
\(220\) | 3.63995 | 0.245406 | ||||||||
\(221\) | −10.8368 | −0.728962 | ||||||||
\(222\) | −19.8270 | −1.33070 | ||||||||
\(223\) | 16.7606 | 1.12237 | 0.561187 | − | 0.827689i | \(-0.310345\pi\) | ||||
0.561187 | + | 0.827689i | \(0.310345\pi\) | |||||||
\(224\) | −2.64455 | −0.176696 | ||||||||
\(225\) | 2.05073 | 0.136716 | ||||||||
\(226\) | 5.97011 | 0.397126 | ||||||||
\(227\) | −22.5024 | −1.49354 | −0.746769 | − | 0.665084i | \(-0.768396\pi\) | ||||
−0.746769 | + | 0.665084i | \(0.768396\pi\) | |||||||
\(228\) | −4.81718 | −0.319025 | ||||||||
\(229\) | 8.15516 | 0.538908 | 0.269454 | − | 0.963013i | \(-0.413157\pi\) | ||||
0.269454 | + | 0.963013i | \(0.413157\pi\) | |||||||
\(230\) | −3.69511 | −0.243648 | ||||||||
\(231\) | 21.6334 | 1.42337 | ||||||||
\(232\) | −8.15103 | −0.535141 | ||||||||
\(233\) | 13.1091 | 0.858807 | 0.429403 | − | 0.903113i | \(-0.358724\pi\) | ||||
0.429403 | + | 0.903113i | \(0.358724\pi\) | |||||||
\(234\) | −8.68032 | −0.567451 | ||||||||
\(235\) | −10.8528 | −0.707958 | ||||||||
\(236\) | 5.31155 | 0.345752 | ||||||||
\(237\) | 21.7246 | 1.41116 | ||||||||
\(238\) | 6.77059 | 0.438872 | ||||||||
\(239\) | 20.0607 | 1.29762 | 0.648811 | − | 0.760950i | \(-0.275267\pi\) | ||||
0.648811 | + | 0.760950i | \(0.275267\pi\) | |||||||
\(240\) | 2.24738 | 0.145068 | ||||||||
\(241\) | −9.55890 | −0.615743 | −0.307871 | − | 0.951428i | \(-0.599617\pi\) | ||||
−0.307871 | + | 0.951428i | \(0.599617\pi\) | |||||||
\(242\) | −2.24925 | −0.144587 | ||||||||
\(243\) | 18.2013 | 1.16762 | ||||||||
\(244\) | −2.57543 | −0.164875 | ||||||||
\(245\) | 0.00636926 | 0.000406917 0 | ||||||||
\(246\) | 1.10751 | 0.0706125 | ||||||||
\(247\) | 9.07281 | 0.577289 | ||||||||
\(248\) | 1.65648 | 0.105187 | ||||||||
\(249\) | 6.46999 | 0.410019 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 25.2475 | 1.59361 | 0.796805 | − | 0.604236i | \(-0.206522\pi\) | ||||
0.796805 | + | 0.604236i | \(0.206522\pi\) | |||||||
\(252\) | 5.42327 | 0.341634 | ||||||||
\(253\) | 13.4500 | 0.845595 | ||||||||
\(254\) | 14.3666 | 0.901441 | ||||||||
\(255\) | −5.75377 | −0.360315 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.9655 | 0.746389 | 0.373194 | − | 0.927753i | \(-0.378262\pi\) | ||||
0.373194 | + | 0.927753i | \(0.378262\pi\) | |||||||
\(258\) | 8.44823 | 0.525964 | ||||||||
\(259\) | −23.3309 | −1.44971 | ||||||||
\(260\) | −4.23279 | −0.262506 | ||||||||
\(261\) | 16.7156 | 1.03467 | ||||||||
\(262\) | 7.21853 | 0.445962 | ||||||||
\(263\) | −19.8387 | −1.22331 | −0.611654 | − | 0.791125i | \(-0.709496\pi\) | ||||
−0.611654 | + | 0.791125i | \(0.709496\pi\) | |||||||
\(264\) | −8.18037 | −0.503467 | ||||||||
\(265\) | 9.30244 | 0.571444 | ||||||||
\(266\) | −5.66848 | −0.347557 | ||||||||
\(267\) | −15.7455 | −0.963609 | ||||||||
\(268\) | 12.1152 | 0.740052 | ||||||||
\(269\) | −5.28011 | −0.321934 | −0.160967 | − | 0.986960i | \(-0.551461\pi\) | ||||
−0.160967 | + | 0.986960i | \(0.551461\pi\) | |||||||
\(270\) | 2.13336 | 0.129832 | ||||||||
\(271\) | 1.73009 | 0.105095 | 0.0525477 | − | 0.998618i | \(-0.483266\pi\) | ||||
0.0525477 | + | 0.998618i | \(0.483266\pi\) | |||||||
\(272\) | −2.56021 | −0.155235 | ||||||||
\(273\) | −25.1568 | −1.52256 | ||||||||
\(274\) | −6.54622 | −0.395472 | ||||||||
\(275\) | −3.63995 | −0.219497 | ||||||||
\(276\) | 8.30432 | 0.499862 | ||||||||
\(277\) | 20.7529 | 1.24692 | 0.623461 | − | 0.781855i | \(-0.285726\pi\) | ||||
0.623461 | + | 0.781855i | \(0.285726\pi\) | |||||||
\(278\) | −5.72920 | −0.343615 | ||||||||
\(279\) | −3.39701 | −0.203374 | ||||||||
\(280\) | 2.64455 | 0.158042 | ||||||||
\(281\) | 12.1586 | 0.725323 | 0.362661 | − | 0.931921i | \(-0.381868\pi\) | ||||
0.362661 | + | 0.931921i | \(0.381868\pi\) | |||||||
\(282\) | 24.3904 | 1.45243 | ||||||||
\(283\) | 25.9092 | 1.54014 | 0.770072 | − | 0.637957i | \(-0.220220\pi\) | ||||
0.770072 | + | 0.637957i | \(0.220220\pi\) | |||||||
\(284\) | −11.6438 | −0.690933 | ||||||||
\(285\) | 4.81718 | 0.285345 | ||||||||
\(286\) | 15.4071 | 0.911043 | ||||||||
\(287\) | 1.30324 | 0.0769276 | ||||||||
\(288\) | −2.05073 | −0.120841 | ||||||||
\(289\) | −10.4453 | −0.614432 | ||||||||
\(290\) | 8.15103 | 0.478645 | ||||||||
\(291\) | −14.6304 | −0.857649 | ||||||||
\(292\) | 7.12350 | 0.416872 | ||||||||
\(293\) | 21.7445 | 1.27033 | 0.635164 | − | 0.772377i | \(-0.280933\pi\) | ||||
0.635164 | + | 0.772377i | \(0.280933\pi\) | |||||||
\(294\) | −0.0143142 | −0.000834820 0 | ||||||||
\(295\) | −5.31155 | −0.309250 | ||||||||
\(296\) | 8.82225 | 0.512783 | ||||||||
\(297\) | −7.76534 | −0.450591 | ||||||||
\(298\) | 15.7466 | 0.912178 | ||||||||
\(299\) | −15.6406 | −0.904519 | ||||||||
\(300\) | −2.24738 | −0.129753 | ||||||||
\(301\) | 9.94123 | 0.573003 | ||||||||
\(302\) | −8.51416 | −0.489935 | ||||||||
\(303\) | 36.0919 | 2.07343 | ||||||||
\(304\) | 2.14346 | 0.122936 | ||||||||
\(305\) | 2.57543 | 0.147469 | ||||||||
\(306\) | 5.25030 | 0.300140 | ||||||||
\(307\) | −18.3234 | −1.04577 | −0.522887 | − | 0.852402i | \(-0.675145\pi\) | ||||
−0.522887 | + | 0.852402i | \(0.675145\pi\) | |||||||
\(308\) | −9.62603 | −0.548494 | ||||||||
\(309\) | −28.4546 | −1.61873 | ||||||||
\(310\) | −1.65648 | −0.0940819 | ||||||||
\(311\) | 26.0232 | 1.47564 | 0.737820 | − | 0.674997i | \(-0.235855\pi\) | ||||
0.737820 | + | 0.674997i | \(0.235855\pi\) | |||||||
\(312\) | 9.51270 | 0.538550 | ||||||||
\(313\) | 2.46277 | 0.139204 | 0.0696021 | − | 0.997575i | \(-0.477827\pi\) | ||||
0.0696021 | + | 0.997575i | \(0.477827\pi\) | |||||||
\(314\) | −13.8003 | −0.778798 | ||||||||
\(315\) | −5.42327 | −0.305566 | ||||||||
\(316\) | −9.66661 | −0.543789 | ||||||||
\(317\) | −9.97922 | −0.560489 | −0.280244 | − | 0.959929i | \(-0.590416\pi\) | ||||
−0.280244 | + | 0.959929i | \(0.590416\pi\) | |||||||
\(318\) | −20.9062 | −1.17236 | ||||||||
\(319\) | −29.6693 | −1.66116 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −12.8014 | −0.714502 | ||||||||
\(322\) | 9.77189 | 0.544566 | ||||||||
\(323\) | −5.48770 | −0.305344 | ||||||||
\(324\) | −10.9467 | −0.608149 | ||||||||
\(325\) | 4.23279 | 0.234793 | ||||||||
\(326\) | −19.8361 | −1.09862 | ||||||||
\(327\) | 36.8558 | 2.03813 | ||||||||
\(328\) | −0.492801 | −0.0272104 | ||||||||
\(329\) | 28.7007 | 1.58232 | ||||||||
\(330\) | 8.18037 | 0.450315 | ||||||||
\(331\) | 26.5932 | 1.46170 | 0.730848 | − | 0.682540i | \(-0.239125\pi\) | ||||
0.730848 | + | 0.682540i | \(0.239125\pi\) | |||||||
\(332\) | −2.87890 | −0.158000 | ||||||||
\(333\) | −18.0921 | −0.991441 | ||||||||
\(334\) | 19.0725 | 1.04360 | ||||||||
\(335\) | −12.1152 | −0.661923 | ||||||||
\(336\) | −5.94331 | −0.324234 | ||||||||
\(337\) | 30.2375 | 1.64714 | 0.823571 | − | 0.567213i | \(-0.191978\pi\) | ||||
0.823571 | + | 0.567213i | \(0.191978\pi\) | |||||||
\(338\) | −4.91649 | −0.267422 | ||||||||
\(339\) | 13.4171 | 0.728719 | ||||||||
\(340\) | 2.56021 | 0.138847 | ||||||||
\(341\) | 6.02952 | 0.326517 | ||||||||
\(342\) | −4.39567 | −0.237691 | ||||||||
\(343\) | −18.5287 | −1.00045 | ||||||||
\(344\) | −3.75914 | −0.202679 | ||||||||
\(345\) | −8.30432 | −0.447090 | ||||||||
\(346\) | −25.4482 | −1.36811 | ||||||||
\(347\) | 19.3462 | 1.03856 | 0.519281 | − | 0.854604i | \(-0.326200\pi\) | ||||
0.519281 | + | 0.854604i | \(0.326200\pi\) | |||||||
\(348\) | −18.3185 | −0.981974 | ||||||||
\(349\) | 16.9751 | 0.908654 | 0.454327 | − | 0.890835i | \(-0.349880\pi\) | ||||
0.454327 | + | 0.890835i | \(0.349880\pi\) | |||||||
\(350\) | −2.64455 | −0.141357 | ||||||||
\(351\) | 9.03007 | 0.481990 | ||||||||
\(352\) | 3.63995 | 0.194010 | ||||||||
\(353\) | −9.96295 | −0.530274 | −0.265137 | − | 0.964211i | \(-0.585417\pi\) | ||||
−0.265137 | + | 0.964211i | \(0.585417\pi\) | |||||||
\(354\) | 11.9371 | 0.634449 | ||||||||
\(355\) | 11.6438 | 0.617990 | ||||||||
\(356\) | 7.00615 | 0.371325 | ||||||||
\(357\) | 15.2161 | 0.805322 | ||||||||
\(358\) | 10.0953 | 0.533556 | ||||||||
\(359\) | 16.2723 | 0.858817 | 0.429409 | − | 0.903110i | \(-0.358722\pi\) | ||||
0.429409 | + | 0.903110i | \(0.358722\pi\) | |||||||
\(360\) | 2.05073 | 0.108083 | ||||||||
\(361\) | −14.4056 | −0.758188 | ||||||||
\(362\) | −1.90872 | −0.100320 | ||||||||
\(363\) | −5.05493 | −0.265315 | ||||||||
\(364\) | 11.1938 | 0.586715 | ||||||||
\(365\) | −7.12350 | −0.372861 | ||||||||
\(366\) | −5.78798 | −0.302543 | ||||||||
\(367\) | 7.06728 | 0.368909 | 0.184454 | − | 0.982841i | \(-0.440948\pi\) | ||||
0.184454 | + | 0.982841i | \(0.440948\pi\) | |||||||
\(368\) | −3.69511 | −0.192621 | ||||||||
\(369\) | 1.01060 | 0.0526100 | ||||||||
\(370\) | −8.82225 | −0.458647 | ||||||||
\(371\) | −24.6007 | −1.27721 | ||||||||
\(372\) | 3.72275 | 0.193016 | ||||||||
\(373\) | 20.9790 | 1.08625 | 0.543125 | − | 0.839652i | \(-0.317241\pi\) | ||||
0.543125 | + | 0.839652i | \(0.317241\pi\) | |||||||
\(374\) | −9.31903 | −0.481875 | ||||||||
\(375\) | 2.24738 | 0.116054 | ||||||||
\(376\) | −10.8528 | −0.559690 | ||||||||
\(377\) | 34.5016 | 1.77692 | ||||||||
\(378\) | −5.64178 | −0.290182 | ||||||||
\(379\) | 26.9851 | 1.38613 | 0.693065 | − | 0.720875i | \(-0.256260\pi\) | ||||
0.693065 | + | 0.720875i | \(0.256260\pi\) | |||||||
\(380\) | −2.14346 | −0.109957 | ||||||||
\(381\) | 32.2873 | 1.65413 | ||||||||
\(382\) | −17.9529 | −0.918550 | ||||||||
\(383\) | 13.1837 | 0.673657 | 0.336829 | − | 0.941566i | \(-0.390646\pi\) | ||||
0.336829 | + | 0.941566i | \(0.390646\pi\) | |||||||
\(384\) | 2.24738 | 0.114686 | ||||||||
\(385\) | 9.62603 | 0.490588 | ||||||||
\(386\) | −6.75068 | −0.343600 | ||||||||
\(387\) | 7.70900 | 0.391871 | ||||||||
\(388\) | 6.50997 | 0.330494 | ||||||||
\(389\) | 4.09900 | 0.207828 | 0.103914 | − | 0.994586i | \(-0.466863\pi\) | ||||
0.103914 | + | 0.994586i | \(0.466863\pi\) | |||||||
\(390\) | −9.51270 | −0.481694 | ||||||||
\(391\) | 9.46023 | 0.478425 | ||||||||
\(392\) | 0.00636926 | 0.000321696 0 | ||||||||
\(393\) | 16.2228 | 0.818333 | ||||||||
\(394\) | −2.21121 | −0.111399 | ||||||||
\(395\) | 9.66661 | 0.486380 | ||||||||
\(396\) | −7.46458 | −0.375109 | ||||||||
\(397\) | −9.40802 | −0.472175 | −0.236088 | − | 0.971732i | \(-0.575865\pi\) | ||||
−0.236088 | + | 0.971732i | \(0.575865\pi\) | |||||||
\(398\) | 16.9056 | 0.847402 | ||||||||
\(399\) | −12.7393 | −0.637761 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 27.2274 | 1.35798 | ||||||||
\(403\) | −7.01154 | −0.349270 | ||||||||
\(404\) | −16.0595 | −0.798991 | ||||||||
\(405\) | 10.9467 | 0.543945 | ||||||||
\(406\) | −21.5558 | −1.06979 | ||||||||
\(407\) | 32.1126 | 1.59176 | ||||||||
\(408\) | −5.75377 | −0.284854 | ||||||||
\(409\) | −30.9061 | −1.52821 | −0.764104 | − | 0.645093i | \(-0.776819\pi\) | ||||
−0.764104 | + | 0.645093i | \(0.776819\pi\) | |||||||
\(410\) | 0.492801 | 0.0243377 | ||||||||
\(411\) | −14.7119 | −0.725683 | ||||||||
\(412\) | 12.6612 | 0.623774 | ||||||||
\(413\) | 14.0466 | 0.691190 | ||||||||
\(414\) | 7.57768 | 0.372423 | ||||||||
\(415\) | 2.87890 | 0.141320 | ||||||||
\(416\) | −4.23279 | −0.207529 | ||||||||
\(417\) | −12.8757 | −0.630527 | ||||||||
\(418\) | 7.80209 | 0.381613 | ||||||||
\(419\) | 11.9442 | 0.583513 | 0.291757 | − | 0.956493i | \(-0.405760\pi\) | ||||
0.291757 | + | 0.956493i | \(0.405760\pi\) | |||||||
\(420\) | 5.94331 | 0.290004 | ||||||||
\(421\) | −17.7020 | −0.862744 | −0.431372 | − | 0.902174i | \(-0.641970\pi\) | ||||
−0.431372 | + | 0.902174i | \(0.641970\pi\) | |||||||
\(422\) | −26.5778 | −1.29379 | ||||||||
\(423\) | 22.2562 | 1.08213 | ||||||||
\(424\) | 9.30244 | 0.451766 | ||||||||
\(425\) | −2.56021 | −0.124188 | ||||||||
\(426\) | −26.1681 | −1.26785 | ||||||||
\(427\) | −6.81085 | −0.329600 | ||||||||
\(428\) | 5.69611 | 0.275332 | ||||||||
\(429\) | 34.6258 | 1.67175 | ||||||||
\(430\) | 3.75914 | 0.181282 | ||||||||
\(431\) | 11.4989 | 0.553883 | 0.276941 | − | 0.960887i | \(-0.410679\pi\) | ||||
0.276941 | + | 0.960887i | \(0.410679\pi\) | |||||||
\(432\) | 2.13336 | 0.102641 | ||||||||
\(433\) | −5.48287 | −0.263490 | −0.131745 | − | 0.991284i | \(-0.542058\pi\) | ||||
−0.131745 | + | 0.991284i | \(0.542058\pi\) | |||||||
\(434\) | 4.38065 | 0.210278 | ||||||||
\(435\) | 18.3185 | 0.878304 | ||||||||
\(436\) | −16.3994 | −0.785390 | ||||||||
\(437\) | −7.92031 | −0.378880 | ||||||||
\(438\) | 16.0092 | 0.764951 | ||||||||
\(439\) | 15.1822 | 0.724608 | 0.362304 | − | 0.932060i | \(-0.381990\pi\) | ||||
0.362304 | + | 0.932060i | \(0.381990\pi\) | |||||||
\(440\) | −3.63995 | −0.173528 | ||||||||
\(441\) | −0.0130617 | −0.000621984 0 | ||||||||
\(442\) | 10.8368 | 0.515454 | ||||||||
\(443\) | 28.2058 | 1.34010 | 0.670048 | − | 0.742318i | \(-0.266274\pi\) | ||||
0.670048 | + | 0.742318i | \(0.266274\pi\) | |||||||
\(444\) | 19.8270 | 0.940947 | ||||||||
\(445\) | −7.00615 | −0.332123 | ||||||||
\(446\) | −16.7606 | −0.793638 | ||||||||
\(447\) | 35.3887 | 1.67383 | ||||||||
\(448\) | 2.64455 | 0.124943 | ||||||||
\(449\) | 29.0535 | 1.37112 | 0.685560 | − | 0.728016i | \(-0.259557\pi\) | ||||
0.685560 | + | 0.728016i | \(0.259557\pi\) | |||||||
\(450\) | −2.05073 | −0.0966726 | ||||||||
\(451\) | −1.79377 | −0.0844654 | ||||||||
\(452\) | −5.97011 | −0.280810 | ||||||||
\(453\) | −19.1346 | −0.899021 | ||||||||
\(454\) | 22.5024 | 1.05609 | ||||||||
\(455\) | −11.1938 | −0.524774 | ||||||||
\(456\) | 4.81718 | 0.225585 | ||||||||
\(457\) | 2.42057 | 0.113230 | 0.0566148 | − | 0.998396i | \(-0.481969\pi\) | ||||
0.0566148 | + | 0.998396i | \(0.481969\pi\) | |||||||
\(458\) | −8.15516 | −0.381066 | ||||||||
\(459\) | −5.46185 | −0.254937 | ||||||||
\(460\) | 3.69511 | 0.172285 | ||||||||
\(461\) | 25.7434 | 1.19899 | 0.599496 | − | 0.800378i | \(-0.295368\pi\) | ||||
0.599496 | + | 0.800378i | \(0.295368\pi\) | |||||||
\(462\) | −21.6334 | −1.00648 | ||||||||
\(463\) | −6.11273 | −0.284083 | −0.142041 | − | 0.989861i | \(-0.545367\pi\) | ||||
−0.142041 | + | 0.989861i | \(0.545367\pi\) | |||||||
\(464\) | 8.15103 | 0.378402 | ||||||||
\(465\) | −3.72275 | −0.172639 | ||||||||
\(466\) | −13.1091 | −0.607268 | ||||||||
\(467\) | 28.5787 | 1.32246 | 0.661231 | − | 0.750182i | \(-0.270034\pi\) | ||||
0.661231 | + | 0.750182i | \(0.270034\pi\) | |||||||
\(468\) | 8.68032 | 0.401248 | ||||||||
\(469\) | 32.0391 | 1.47943 | ||||||||
\(470\) | 10.8528 | 0.500602 | ||||||||
\(471\) | −31.0147 | −1.42908 | ||||||||
\(472\) | −5.31155 | −0.244484 | ||||||||
\(473\) | −13.6831 | −0.629149 | ||||||||
\(474\) | −21.7246 | −0.997843 | ||||||||
\(475\) | 2.14346 | 0.0983487 | ||||||||
\(476\) | −6.77059 | −0.310329 | ||||||||
\(477\) | −19.0768 | −0.873468 | ||||||||
\(478\) | −20.0607 | −0.917557 | ||||||||
\(479\) | −19.7841 | −0.903957 | −0.451978 | − | 0.892029i | \(-0.649282\pi\) | ||||
−0.451978 | + | 0.892029i | \(0.649282\pi\) | |||||||
\(480\) | −2.24738 | −0.102579 | ||||||||
\(481\) | −37.3427 | −1.70268 | ||||||||
\(482\) | 9.55890 | 0.435396 | ||||||||
\(483\) | 21.9612 | 0.999268 | ||||||||
\(484\) | 2.24925 | 0.102239 | ||||||||
\(485\) | −6.50997 | −0.295603 | ||||||||
\(486\) | −18.2013 | −0.825629 | ||||||||
\(487\) | −4.44801 | −0.201559 | −0.100779 | − | 0.994909i | \(-0.532134\pi\) | ||||
−0.100779 | + | 0.994909i | \(0.532134\pi\) | |||||||
\(488\) | 2.57543 | 0.116584 | ||||||||
\(489\) | −44.5793 | −2.01595 | ||||||||
\(490\) | −0.00636926 | −0.000287734 0 | ||||||||
\(491\) | 32.7380 | 1.47745 | 0.738723 | − | 0.674009i | \(-0.235429\pi\) | ||||
0.738723 | + | 0.674009i | \(0.235429\pi\) | |||||||
\(492\) | −1.10751 | −0.0499305 | ||||||||
\(493\) | −20.8683 | −0.939861 | ||||||||
\(494\) | −9.07281 | −0.408205 | ||||||||
\(495\) | 7.46458 | 0.335508 | ||||||||
\(496\) | −1.65648 | −0.0743783 | ||||||||
\(497\) | −30.7926 | −1.38124 | ||||||||
\(498\) | −6.46999 | −0.289927 | ||||||||
\(499\) | −33.3590 | −1.49336 | −0.746678 | − | 0.665186i | \(-0.768352\pi\) | ||||
−0.746678 | + | 0.665186i | \(0.768352\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 42.8632 | 1.91498 | ||||||||
\(502\) | −25.2475 | −1.12685 | ||||||||
\(503\) | −19.6160 | −0.874634 | −0.437317 | − | 0.899307i | \(-0.644071\pi\) | ||||
−0.437317 | + | 0.899307i | \(0.644071\pi\) | |||||||
\(504\) | −5.42327 | −0.241571 | ||||||||
\(505\) | 16.0595 | 0.714639 | ||||||||
\(506\) | −13.4500 | −0.597926 | ||||||||
\(507\) | −11.0492 | −0.490714 | ||||||||
\(508\) | −14.3666 | −0.637415 | ||||||||
\(509\) | −35.9119 | −1.59177 | −0.795885 | − | 0.605448i | \(-0.792994\pi\) | ||||
−0.795885 | + | 0.605448i | \(0.792994\pi\) | |||||||
\(510\) | 5.75377 | 0.254781 | ||||||||
\(511\) | 18.8384 | 0.833364 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.57278 | 0.201893 | ||||||||
\(514\) | −11.9655 | −0.527776 | ||||||||
\(515\) | −12.6612 | −0.557920 | ||||||||
\(516\) | −8.44823 | −0.371913 | ||||||||
\(517\) | −39.5037 | −1.73737 | ||||||||
\(518\) | 23.3309 | 1.02510 | ||||||||
\(519\) | −57.1920 | −2.51045 | ||||||||
\(520\) | 4.23279 | 0.185620 | ||||||||
\(521\) | −27.8298 | −1.21925 | −0.609624 | − | 0.792691i | \(-0.708680\pi\) | ||||
−0.609624 | + | 0.792691i | \(0.708680\pi\) | |||||||
\(522\) | −16.7156 | −0.731622 | ||||||||
\(523\) | 24.3758 | 1.06588 | 0.532940 | − | 0.846153i | \(-0.321087\pi\) | ||||
0.532940 | + | 0.846153i | \(0.321087\pi\) | |||||||
\(524\) | −7.21853 | −0.315343 | ||||||||
\(525\) | −5.94331 | −0.259387 | ||||||||
\(526\) | 19.8387 | 0.865010 | ||||||||
\(527\) | 4.24094 | 0.184738 | ||||||||
\(528\) | 8.18037 | 0.356005 | ||||||||
\(529\) | −9.34619 | −0.406356 | ||||||||
\(530\) | −9.30244 | −0.404072 | ||||||||
\(531\) | 10.8926 | 0.472697 | ||||||||
\(532\) | 5.66848 | 0.245760 | ||||||||
\(533\) | 2.08592 | 0.0903513 | ||||||||
\(534\) | 15.7455 | 0.681375 | ||||||||
\(535\) | −5.69611 | −0.246264 | ||||||||
\(536\) | −12.1152 | −0.523296 | ||||||||
\(537\) | 22.6881 | 0.979065 | ||||||||
\(538\) | 5.28011 | 0.227642 | ||||||||
\(539\) | 0.0231838 | 0.000998597 0 | ||||||||
\(540\) | −2.13336 | −0.0918053 | ||||||||
\(541\) | −4.03656 | −0.173545 | −0.0867726 | − | 0.996228i | \(-0.527655\pi\) | ||||
−0.0867726 | + | 0.996228i | \(0.527655\pi\) | |||||||
\(542\) | −1.73009 | −0.0743136 | ||||||||
\(543\) | −4.28964 | −0.184086 | ||||||||
\(544\) | 2.56021 | 0.109768 | ||||||||
\(545\) | 16.3994 | 0.702474 | ||||||||
\(546\) | 25.1568 | 1.07661 | ||||||||
\(547\) | −34.1299 | −1.45929 | −0.729644 | − | 0.683827i | \(-0.760314\pi\) | ||||
−0.729644 | + | 0.683827i | \(0.760314\pi\) | |||||||
\(548\) | 6.54622 | 0.279641 | ||||||||
\(549\) | −5.28153 | −0.225410 | ||||||||
\(550\) | 3.63995 | 0.155208 | ||||||||
\(551\) | 17.4714 | 0.744307 | ||||||||
\(552\) | −8.30432 | −0.353456 | ||||||||
\(553\) | −25.5638 | −1.08708 | ||||||||
\(554\) | −20.7529 | −0.881707 | ||||||||
\(555\) | −19.8270 | −0.841609 | ||||||||
\(556\) | 5.72920 | 0.242972 | ||||||||
\(557\) | 17.3035 | 0.733174 | 0.366587 | − | 0.930384i | \(-0.380526\pi\) | ||||
0.366587 | + | 0.930384i | \(0.380526\pi\) | |||||||
\(558\) | 3.39701 | 0.143807 | ||||||||
\(559\) | 15.9116 | 0.672991 | ||||||||
\(560\) | −2.64455 | −0.111753 | ||||||||
\(561\) | −20.9434 | −0.884232 | ||||||||
\(562\) | −12.1586 | −0.512881 | ||||||||
\(563\) | 37.8047 | 1.59328 | 0.796638 | − | 0.604457i | \(-0.206610\pi\) | ||||
0.796638 | + | 0.604457i | \(0.206610\pi\) | |||||||
\(564\) | −24.3904 | −1.02702 | ||||||||
\(565\) | 5.97011 | 0.251164 | ||||||||
\(566\) | −25.9092 | −1.08905 | ||||||||
\(567\) | −28.9490 | −1.21575 | ||||||||
\(568\) | 11.6438 | 0.488564 | ||||||||
\(569\) | −2.56225 | −0.107415 | −0.0537076 | − | 0.998557i | \(-0.517104\pi\) | ||||
−0.0537076 | + | 0.998557i | \(0.517104\pi\) | |||||||
\(570\) | −4.81718 | −0.201769 | ||||||||
\(571\) | 13.8184 | 0.578280 | 0.289140 | − | 0.957287i | \(-0.406631\pi\) | ||||
0.289140 | + | 0.957287i | \(0.406631\pi\) | |||||||
\(572\) | −15.4071 | −0.644205 | ||||||||
\(573\) | −40.3470 | −1.68552 | ||||||||
\(574\) | −1.30324 | −0.0543960 | ||||||||
\(575\) | −3.69511 | −0.154097 | ||||||||
\(576\) | 2.05073 | 0.0854473 | ||||||||
\(577\) | −32.3766 | −1.34786 | −0.673928 | − | 0.738797i | \(-0.735394\pi\) | ||||
−0.673928 | + | 0.738797i | \(0.735394\pi\) | |||||||
\(578\) | 10.4453 | 0.434469 | ||||||||
\(579\) | −15.1714 | −0.630500 | ||||||||
\(580\) | −8.15103 | −0.338453 | ||||||||
\(581\) | −7.61339 | −0.315857 | ||||||||
\(582\) | 14.6304 | 0.606450 | ||||||||
\(583\) | 33.8604 | 1.40236 | ||||||||
\(584\) | −7.12350 | −0.294773 | ||||||||
\(585\) | −8.68032 | −0.358887 | ||||||||
\(586\) | −21.7445 | −0.898258 | ||||||||
\(587\) | 1.41582 | 0.0584372 | 0.0292186 | − | 0.999573i | \(-0.490698\pi\) | ||||
0.0292186 | + | 0.999573i | \(0.490698\pi\) | |||||||
\(588\) | 0.0143142 | 0.000590307 0 | ||||||||
\(589\) | −3.55061 | −0.146300 | ||||||||
\(590\) | 5.31155 | 0.218673 | ||||||||
\(591\) | −4.96943 | −0.204415 | ||||||||
\(592\) | −8.82225 | −0.362592 | ||||||||
\(593\) | −33.3084 | −1.36781 | −0.683906 | − | 0.729570i | \(-0.739720\pi\) | ||||
−0.683906 | + | 0.729570i | \(0.739720\pi\) | |||||||
\(594\) | 7.76534 | 0.318616 | ||||||||
\(595\) | 6.77059 | 0.277567 | ||||||||
\(596\) | −15.7466 | −0.645007 | ||||||||
\(597\) | 37.9934 | 1.55497 | ||||||||
\(598\) | 15.6406 | 0.639592 | ||||||||
\(599\) | −25.0294 | −1.02267 | −0.511337 | − | 0.859380i | \(-0.670850\pi\) | ||||
−0.511337 | + | 0.859380i | \(0.670850\pi\) | |||||||
\(600\) | 2.24738 | 0.0917491 | ||||||||
\(601\) | −42.0536 | −1.71540 | −0.857701 | − | 0.514149i | \(-0.828108\pi\) | ||||
−0.857701 | + | 0.514149i | \(0.828108\pi\) | |||||||
\(602\) | −9.94123 | −0.405174 | ||||||||
\(603\) | 24.8450 | 1.01177 | ||||||||
\(604\) | 8.51416 | 0.346436 | ||||||||
\(605\) | −2.24925 | −0.0914451 | ||||||||
\(606\) | −36.0919 | −1.46613 | ||||||||
\(607\) | 35.6597 | 1.44738 | 0.723691 | − | 0.690125i | \(-0.242444\pi\) | ||||
0.723691 | + | 0.690125i | \(0.242444\pi\) | |||||||
\(608\) | −2.14346 | −0.0869288 | ||||||||
\(609\) | −48.4441 | −1.96305 | ||||||||
\(610\) | −2.57543 | −0.104276 | ||||||||
\(611\) | 45.9376 | 1.85844 | ||||||||
\(612\) | −5.25030 | −0.212231 | ||||||||
\(613\) | 23.9140 | 0.965878 | 0.482939 | − | 0.875654i | \(-0.339569\pi\) | ||||
0.482939 | + | 0.875654i | \(0.339569\pi\) | |||||||
\(614\) | 18.3234 | 0.739473 | ||||||||
\(615\) | 1.10751 | 0.0446592 | ||||||||
\(616\) | 9.62603 | 0.387844 | ||||||||
\(617\) | 13.0895 | 0.526963 | 0.263482 | − | 0.964664i | \(-0.415129\pi\) | ||||
0.263482 | + | 0.964664i | \(0.415129\pi\) | |||||||
\(618\) | 28.4546 | 1.14461 | ||||||||
\(619\) | 39.7102 | 1.59609 | 0.798043 | − | 0.602600i | \(-0.205869\pi\) | ||||
0.798043 | + | 0.602600i | \(0.205869\pi\) | |||||||
\(620\) | 1.65648 | 0.0665260 | ||||||||
\(621\) | −7.88300 | −0.316334 | ||||||||
\(622\) | −26.0232 | −1.04344 | ||||||||
\(623\) | 18.5281 | 0.742312 | ||||||||
\(624\) | −9.51270 | −0.380813 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −2.46277 | −0.0984322 | ||||||||
\(627\) | 17.5343 | 0.700252 | ||||||||
\(628\) | 13.8003 | 0.550693 | ||||||||
\(629\) | 22.5868 | 0.900594 | ||||||||
\(630\) | 5.42327 | 0.216068 | ||||||||
\(631\) | −14.9622 | −0.595635 | −0.297818 | − | 0.954623i | \(-0.596259\pi\) | ||||
−0.297818 | + | 0.954623i | \(0.596259\pi\) | |||||||
\(632\) | 9.66661 | 0.384517 | ||||||||
\(633\) | −59.7304 | −2.37407 | ||||||||
\(634\) | 9.97922 | 0.396325 | ||||||||
\(635\) | 14.3666 | 0.570121 | ||||||||
\(636\) | 20.9062 | 0.828983 | ||||||||
\(637\) | −0.0269597 | −0.00106818 | ||||||||
\(638\) | 29.6693 | 1.17462 | ||||||||
\(639\) | −23.8784 | −0.944614 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 12.1796 | 0.481066 | 0.240533 | − | 0.970641i | \(-0.422678\pi\) | ||||
0.240533 | + | 0.970641i | \(0.422678\pi\) | |||||||
\(642\) | 12.8014 | 0.505229 | ||||||||
\(643\) | −35.9622 | −1.41821 | −0.709106 | − | 0.705102i | \(-0.750901\pi\) | ||||
−0.709106 | + | 0.705102i | \(0.750901\pi\) | |||||||
\(644\) | −9.77189 | −0.385066 | ||||||||
\(645\) | 8.44823 | 0.332649 | ||||||||
\(646\) | 5.48770 | 0.215911 | ||||||||
\(647\) | 3.02867 | 0.119069 | 0.0595346 | − | 0.998226i | \(-0.481038\pi\) | ||||
0.0595346 | + | 0.998226i | \(0.481038\pi\) | |||||||
\(648\) | 10.9467 | 0.430027 | ||||||||
\(649\) | −19.3338 | −0.758917 | ||||||||
\(650\) | −4.23279 | −0.166024 | ||||||||
\(651\) | 9.84500 | 0.385856 | ||||||||
\(652\) | 19.8361 | 0.776841 | ||||||||
\(653\) | −47.6835 | −1.86600 | −0.933000 | − | 0.359877i | \(-0.882819\pi\) | ||||
−0.933000 | + | 0.359877i | \(0.882819\pi\) | |||||||
\(654\) | −36.8558 | −1.44118 | ||||||||
\(655\) | 7.21853 | 0.282051 | ||||||||
\(656\) | 0.492801 | 0.0192406 | ||||||||
\(657\) | 14.6084 | 0.569929 | ||||||||
\(658\) | −28.7007 | −1.11887 | ||||||||
\(659\) | −5.83074 | −0.227133 | −0.113567 | − | 0.993530i | \(-0.536228\pi\) | ||||
−0.113567 | + | 0.993530i | \(0.536228\pi\) | |||||||
\(660\) | −8.18037 | −0.318420 | ||||||||
\(661\) | 26.5689 | 1.03341 | 0.516705 | − | 0.856163i | \(-0.327158\pi\) | ||||
0.516705 | + | 0.856163i | \(0.327158\pi\) | |||||||
\(662\) | −26.5932 | −1.03358 | ||||||||
\(663\) | 24.3545 | 0.945849 | ||||||||
\(664\) | 2.87890 | 0.111723 | ||||||||
\(665\) | −5.66848 | −0.219814 | ||||||||
\(666\) | 18.0921 | 0.701055 | ||||||||
\(667\) | −30.1189 | −1.16621 | ||||||||
\(668\) | −19.0725 | −0.737936 | ||||||||
\(669\) | −37.6675 | −1.45631 | ||||||||
\(670\) | 12.1152 | 0.468050 | ||||||||
\(671\) | 9.37445 | 0.361896 | ||||||||
\(672\) | 5.94331 | 0.229268 | ||||||||
\(673\) | 6.76895 | 0.260924 | 0.130462 | − | 0.991453i | \(-0.458354\pi\) | ||||
0.130462 | + | 0.991453i | \(0.458354\pi\) | |||||||
\(674\) | −30.2375 | −1.16471 | ||||||||
\(675\) | 2.13336 | 0.0821132 | ||||||||
\(676\) | 4.91649 | 0.189096 | ||||||||
\(677\) | 27.0777 | 1.04068 | 0.520339 | − | 0.853960i | \(-0.325805\pi\) | ||||
0.520339 | + | 0.853960i | \(0.325805\pi\) | |||||||
\(678\) | −13.4171 | −0.515282 | ||||||||
\(679\) | 17.2159 | 0.660687 | ||||||||
\(680\) | −2.56021 | −0.0981794 | ||||||||
\(681\) | 50.5716 | 1.93791 | ||||||||
\(682\) | −6.02952 | −0.230882 | ||||||||
\(683\) | −11.6449 | −0.445578 | −0.222789 | − | 0.974867i | \(-0.571516\pi\) | ||||
−0.222789 | + | 0.974867i | \(0.571516\pi\) | |||||||
\(684\) | 4.39567 | 0.168073 | ||||||||
\(685\) | −6.54622 | −0.250118 | ||||||||
\(686\) | 18.5287 | 0.707428 | ||||||||
\(687\) | −18.3278 | −0.699249 | ||||||||
\(688\) | 3.75914 | 0.143316 | ||||||||
\(689\) | −39.3752 | −1.50008 | ||||||||
\(690\) | 8.30432 | 0.316140 | ||||||||
\(691\) | 18.4079 | 0.700271 | 0.350135 | − | 0.936699i | \(-0.386136\pi\) | ||||
0.350135 | + | 0.936699i | \(0.386136\pi\) | |||||||
\(692\) | 25.4482 | 0.967397 | ||||||||
\(693\) | −19.7404 | −0.749877 | ||||||||
\(694\) | −19.3462 | −0.734374 | ||||||||
\(695\) | −5.72920 | −0.217321 | ||||||||
\(696\) | 18.3185 | 0.694360 | ||||||||
\(697\) | −1.26167 | −0.0477892 | ||||||||
\(698\) | −16.9751 | −0.642515 | ||||||||
\(699\) | −29.4612 | −1.11433 | ||||||||
\(700\) | 2.64455 | 0.0999545 | ||||||||
\(701\) | 41.6674 | 1.57376 | 0.786879 | − | 0.617108i | \(-0.211696\pi\) | ||||
0.786879 | + | 0.617108i | \(0.211696\pi\) | |||||||
\(702\) | −9.03007 | −0.340818 | ||||||||
\(703\) | −18.9101 | −0.713210 | ||||||||
\(704\) | −3.63995 | −0.137186 | ||||||||
\(705\) | 24.3904 | 0.918596 | ||||||||
\(706\) | 9.96295 | 0.374960 | ||||||||
\(707\) | −42.4702 | −1.59725 | ||||||||
\(708\) | −11.9371 | −0.448623 | ||||||||
\(709\) | 6.39902 | 0.240320 | 0.120160 | − | 0.992755i | \(-0.461659\pi\) | ||||
0.120160 | + | 0.992755i | \(0.461659\pi\) | |||||||
\(710\) | −11.6438 | −0.436985 | ||||||||
\(711\) | −19.8236 | −0.743445 | ||||||||
\(712\) | −7.00615 | −0.262566 | ||||||||
\(713\) | 6.12088 | 0.229229 | ||||||||
\(714\) | −15.2161 | −0.569448 | ||||||||
\(715\) | 15.4071 | 0.576194 | ||||||||
\(716\) | −10.0953 | −0.377281 | ||||||||
\(717\) | −45.0842 | −1.68370 | ||||||||
\(718\) | −16.2723 | −0.607276 | ||||||||
\(719\) | 1.15175 | 0.0429529 | 0.0214764 | − | 0.999769i | \(-0.493163\pi\) | ||||
0.0214764 | + | 0.999769i | \(0.493163\pi\) | |||||||
\(720\) | −2.05073 | −0.0764264 | ||||||||
\(721\) | 33.4832 | 1.24698 | ||||||||
\(722\) | 14.4056 | 0.536120 | ||||||||
\(723\) | 21.4825 | 0.798943 | ||||||||
\(724\) | 1.90872 | 0.0709372 | ||||||||
\(725\) | 8.15103 | 0.302721 | ||||||||
\(726\) | 5.05493 | 0.187606 | ||||||||
\(727\) | 22.5219 | 0.835290 | 0.417645 | − | 0.908610i | \(-0.362856\pi\) | ||||
0.417645 | + | 0.908610i | \(0.362856\pi\) | |||||||
\(728\) | −11.1938 | −0.414870 | ||||||||
\(729\) | −8.06530 | −0.298715 | ||||||||
\(730\) | 7.12350 | 0.263653 | ||||||||
\(731\) | −9.62417 | −0.355963 | ||||||||
\(732\) | 5.78798 | 0.213930 | ||||||||
\(733\) | −14.1577 | −0.522928 | −0.261464 | − | 0.965213i | \(-0.584205\pi\) | ||||
−0.261464 | + | 0.965213i | \(0.584205\pi\) | |||||||
\(734\) | −7.06728 | −0.260858 | ||||||||
\(735\) | −0.0143142 | −0.000527986 0 | ||||||||
\(736\) | 3.69511 | 0.136203 | ||||||||
\(737\) | −44.0986 | −1.62439 | ||||||||
\(738\) | −1.01060 | −0.0372009 | ||||||||
\(739\) | 13.9682 | 0.513830 | 0.256915 | − | 0.966434i | \(-0.417294\pi\) | ||||
0.256915 | + | 0.966434i | \(0.417294\pi\) | |||||||
\(740\) | 8.82225 | 0.324312 | ||||||||
\(741\) | −20.3901 | −0.749049 | ||||||||
\(742\) | 24.6007 | 0.903121 | ||||||||
\(743\) | −20.0697 | −0.736286 | −0.368143 | − | 0.929769i | \(-0.620006\pi\) | ||||
−0.368143 | + | 0.929769i | \(0.620006\pi\) | |||||||
\(744\) | −3.72275 | −0.136483 | ||||||||
\(745\) | 15.7466 | 0.576912 | ||||||||
\(746\) | −20.9790 | −0.768095 | ||||||||
\(747\) | −5.90386 | −0.216011 | ||||||||
\(748\) | 9.31903 | 0.340737 | ||||||||
\(749\) | 15.0636 | 0.550413 | ||||||||
\(750\) | −2.24738 | −0.0820629 | ||||||||
\(751\) | −0.144520 | −0.00527362 | −0.00263681 | − | 0.999997i | \(-0.500839\pi\) | ||||
−0.00263681 | + | 0.999997i | \(0.500839\pi\) | |||||||
\(752\) | 10.8528 | 0.395761 | ||||||||
\(753\) | −56.7409 | −2.06775 | ||||||||
\(754\) | −34.5016 | −1.25647 | ||||||||
\(755\) | −8.51416 | −0.309862 | ||||||||
\(756\) | 5.64178 | 0.205190 | ||||||||
\(757\) | −9.76780 | −0.355017 | −0.177508 | − | 0.984119i | \(-0.556804\pi\) | ||||
−0.177508 | + | 0.984119i | \(0.556804\pi\) | |||||||
\(758\) | −26.9851 | −0.980142 | ||||||||
\(759\) | −30.2273 | −1.09718 | ||||||||
\(760\) | 2.14346 | 0.0777515 | ||||||||
\(761\) | 27.4102 | 0.993618 | 0.496809 | − | 0.867860i | \(-0.334505\pi\) | ||||
0.496809 | + | 0.867860i | \(0.334505\pi\) | |||||||
\(762\) | −32.2873 | −1.16964 | ||||||||
\(763\) | −43.3691 | −1.57007 | ||||||||
\(764\) | 17.9529 | 0.649513 | ||||||||
\(765\) | 5.25030 | 0.189825 | ||||||||
\(766\) | −13.1837 | −0.476348 | ||||||||
\(767\) | 22.4826 | 0.811801 | ||||||||
\(768\) | −2.24738 | −0.0810955 | ||||||||
\(769\) | −7.46809 | −0.269306 | −0.134653 | − | 0.990893i | \(-0.542992\pi\) | ||||
−0.134653 | + | 0.990893i | \(0.542992\pi\) | |||||||
\(770\) | −9.62603 | −0.346898 | ||||||||
\(771\) | −26.8911 | −0.968460 | ||||||||
\(772\) | 6.75068 | 0.242962 | ||||||||
\(773\) | 38.9756 | 1.40186 | 0.700928 | − | 0.713232i | \(-0.252769\pi\) | ||||
0.700928 | + | 0.713232i | \(0.252769\pi\) | |||||||
\(774\) | −7.70900 | −0.277094 | ||||||||
\(775\) | −1.65648 | −0.0595026 | ||||||||
\(776\) | −6.50997 | −0.233694 | ||||||||
\(777\) | 52.4334 | 1.88104 | ||||||||
\(778\) | −4.09900 | −0.146956 | ||||||||
\(779\) | 1.05630 | 0.0378459 | ||||||||
\(780\) | 9.51270 | 0.340609 | ||||||||
\(781\) | 42.3829 | 1.51658 | ||||||||
\(782\) | −9.46023 | −0.338297 | ||||||||
\(783\) | 17.3891 | 0.621436 | ||||||||
\(784\) | −0.00636926 | −0.000227474 0 | ||||||||
\(785\) | −13.8003 | −0.492555 | ||||||||
\(786\) | −16.2228 | −0.578649 | ||||||||
\(787\) | 24.4377 | 0.871111 | 0.435555 | − | 0.900162i | \(-0.356552\pi\) | ||||
0.435555 | + | 0.900162i | \(0.356552\pi\) | |||||||
\(788\) | 2.21121 | 0.0787710 | ||||||||
\(789\) | 44.5853 | 1.58728 | ||||||||
\(790\) | −9.66661 | −0.343922 | ||||||||
\(791\) | −15.7882 | −0.561365 | ||||||||
\(792\) | 7.46458 | 0.265242 | ||||||||
\(793\) | −10.9013 | −0.387115 | ||||||||
\(794\) | 9.40802 | 0.333878 | ||||||||
\(795\) | −20.9062 | −0.741465 | ||||||||
\(796\) | −16.9056 | −0.599204 | ||||||||
\(797\) | −32.5269 | −1.15216 | −0.576081 | − | 0.817393i | \(-0.695419\pi\) | ||||
−0.576081 | + | 0.817393i | \(0.695419\pi\) | |||||||
\(798\) | 12.7393 | 0.450965 | ||||||||
\(799\) | −27.7854 | −0.982977 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 14.3678 | 0.507659 | ||||||||
\(802\) | −1.00000 | −0.0353112 | ||||||||
\(803\) | −25.9292 | −0.915022 | ||||||||
\(804\) | −27.2274 | −0.960238 | ||||||||
\(805\) | 9.77189 | 0.344414 | ||||||||
\(806\) | 7.01154 | 0.246971 | ||||||||
\(807\) | 11.8664 | 0.417718 | ||||||||
\(808\) | 16.0595 | 0.564972 | ||||||||
\(809\) | −20.9475 | −0.736474 | −0.368237 | − | 0.929732i | \(-0.620038\pi\) | ||||
−0.368237 | + | 0.929732i | \(0.620038\pi\) | |||||||
\(810\) | −10.9467 | −0.384628 | ||||||||
\(811\) | −4.40294 | −0.154608 | −0.0773041 | − | 0.997008i | \(-0.524631\pi\) | ||||
−0.0773041 | + | 0.997008i | \(0.524631\pi\) | |||||||
\(812\) | 21.5558 | 0.756459 | ||||||||
\(813\) | −3.88817 | −0.136364 | ||||||||
\(814\) | −32.1126 | −1.12555 | ||||||||
\(815\) | −19.8361 | −0.694828 | ||||||||
\(816\) | 5.75377 | 0.201422 | ||||||||
\(817\) | 8.05757 | 0.281899 | ||||||||
\(818\) | 30.9061 | 1.08061 | ||||||||
\(819\) | 22.9555 | 0.802131 | ||||||||
\(820\) | −0.492801 | −0.0172094 | ||||||||
\(821\) | 24.4861 | 0.854571 | 0.427286 | − | 0.904117i | \(-0.359470\pi\) | ||||
0.427286 | + | 0.904117i | \(0.359470\pi\) | |||||||
\(822\) | 14.7119 | 0.513135 | ||||||||
\(823\) | 36.6232 | 1.27661 | 0.638303 | − | 0.769786i | \(-0.279637\pi\) | ||||
0.638303 | + | 0.769786i | \(0.279637\pi\) | |||||||
\(824\) | −12.6612 | −0.441075 | ||||||||
\(825\) | 8.18037 | 0.284804 | ||||||||
\(826\) | −14.0466 | −0.488745 | ||||||||
\(827\) | 21.0412 | 0.731674 | 0.365837 | − | 0.930679i | \(-0.380783\pi\) | ||||
0.365837 | + | 0.930679i | \(0.380783\pi\) | |||||||
\(828\) | −7.57768 | −0.263343 | ||||||||
\(829\) | 32.3549 | 1.12373 | 0.561867 | − | 0.827228i | \(-0.310083\pi\) | ||||
0.561867 | + | 0.827228i | \(0.310083\pi\) | |||||||
\(830\) | −2.87890 | −0.0999281 | ||||||||
\(831\) | −46.6398 | −1.61792 | ||||||||
\(832\) | 4.23279 | 0.146745 | ||||||||
\(833\) | 0.0163066 | 0.000564991 0 | ||||||||
\(834\) | 12.8757 | 0.445850 | ||||||||
\(835\) | 19.0725 | 0.660030 | ||||||||
\(836\) | −7.80209 | −0.269841 | ||||||||
\(837\) | −3.53388 | −0.122149 | ||||||||
\(838\) | −11.9442 | −0.412606 | ||||||||
\(839\) | 39.5482 | 1.36536 | 0.682678 | − | 0.730719i | \(-0.260815\pi\) | ||||
0.682678 | + | 0.730719i | \(0.260815\pi\) | |||||||
\(840\) | −5.94331 | −0.205064 | ||||||||
\(841\) | 37.4392 | 1.29101 | ||||||||
\(842\) | 17.7020 | 0.610052 | ||||||||
\(843\) | −27.3251 | −0.941127 | ||||||||
\(844\) | 26.5778 | 0.914844 | ||||||||
\(845\) | −4.91649 | −0.169132 | ||||||||
\(846\) | −22.2562 | −0.765184 | ||||||||
\(847\) | 5.94825 | 0.204384 | ||||||||
\(848\) | −9.30244 | −0.319447 | ||||||||
\(849\) | −58.2280 | −1.99838 | ||||||||
\(850\) | 2.56021 | 0.0878143 | ||||||||
\(851\) | 32.5992 | 1.11748 | ||||||||
\(852\) | 26.1681 | 0.896505 | ||||||||
\(853\) | −4.47754 | −0.153308 | −0.0766540 | − | 0.997058i | \(-0.524424\pi\) | ||||
−0.0766540 | + | 0.997058i | \(0.524424\pi\) | |||||||
\(854\) | 6.81085 | 0.233062 | ||||||||
\(855\) | −4.39567 | −0.150329 | ||||||||
\(856\) | −5.69611 | −0.194689 | ||||||||
\(857\) | −29.8856 | −1.02087 | −0.510436 | − | 0.859916i | \(-0.670516\pi\) | ||||
−0.510436 | + | 0.859916i | \(0.670516\pi\) | |||||||
\(858\) | −34.6258 | −1.18210 | ||||||||
\(859\) | −46.5935 | −1.58975 | −0.794875 | − | 0.606773i | \(-0.792464\pi\) | ||||
−0.794875 | + | 0.606773i | \(0.792464\pi\) | |||||||
\(860\) | −3.75914 | −0.128186 | ||||||||
\(861\) | −2.92887 | −0.0998157 | ||||||||
\(862\) | −11.4989 | −0.391654 | ||||||||
\(863\) | −37.0533 | −1.26131 | −0.630654 | − | 0.776064i | \(-0.717213\pi\) | ||||
−0.630654 | + | 0.776064i | \(0.717213\pi\) | |||||||
\(864\) | −2.13336 | −0.0725785 | ||||||||
\(865\) | −25.4482 | −0.865266 | ||||||||
\(866\) | 5.48287 | 0.186315 | ||||||||
\(867\) | 23.4747 | 0.797243 | ||||||||
\(868\) | −4.38065 | −0.148689 | ||||||||
\(869\) | 35.1860 | 1.19360 | ||||||||
\(870\) | −18.3185 | −0.621055 | ||||||||
\(871\) | 51.2809 | 1.73759 | ||||||||
\(872\) | 16.3994 | 0.555355 | ||||||||
\(873\) | 13.3502 | 0.451837 | ||||||||
\(874\) | 7.92031 | 0.267909 | ||||||||
\(875\) | −2.64455 | −0.0894020 | ||||||||
\(876\) | −16.0092 | −0.540902 | ||||||||
\(877\) | −13.9198 | −0.470038 | −0.235019 | − | 0.971991i | \(-0.575515\pi\) | ||||
−0.235019 | + | 0.971991i | \(0.575515\pi\) | |||||||
\(878\) | −15.1822 | −0.512375 | ||||||||
\(879\) | −48.8683 | −1.64829 | ||||||||
\(880\) | 3.63995 | 0.122703 | ||||||||
\(881\) | −21.3258 | −0.718483 | −0.359242 | − | 0.933245i | \(-0.616965\pi\) | ||||
−0.359242 | + | 0.933245i | \(0.616965\pi\) | |||||||
\(882\) | 0.0130617 | 0.000439809 0 | ||||||||
\(883\) | −8.85142 | −0.297874 | −0.148937 | − | 0.988847i | \(-0.547585\pi\) | ||||
−0.148937 | + | 0.988847i | \(0.547585\pi\) | |||||||
\(884\) | −10.8368 | −0.364481 | ||||||||
\(885\) | 11.9371 | 0.401261 | ||||||||
\(886\) | −28.2058 | −0.947591 | ||||||||
\(887\) | −26.4880 | −0.889379 | −0.444689 | − | 0.895685i | \(-0.646686\pi\) | ||||
−0.444689 | + | 0.895685i | \(0.646686\pi\) | |||||||
\(888\) | −19.8270 | −0.665350 | ||||||||
\(889\) | −37.9932 | −1.27425 | ||||||||
\(890\) | 7.00615 | 0.234847 | ||||||||
\(891\) | 39.8454 | 1.33487 | ||||||||
\(892\) | 16.7606 | 0.561187 | ||||||||
\(893\) | 23.2625 | 0.778451 | ||||||||
\(894\) | −35.3887 | −1.18358 | ||||||||
\(895\) | 10.0953 | 0.337450 | ||||||||
\(896\) | −2.64455 | −0.0883481 | ||||||||
\(897\) | 35.1504 | 1.17364 | ||||||||
\(898\) | −29.0535 | −0.969528 | ||||||||
\(899\) | −13.5020 | −0.450318 | ||||||||
\(900\) | 2.05073 | 0.0683578 | ||||||||
\(901\) | 23.8162 | 0.793431 | ||||||||
\(902\) | 1.79377 | 0.0597261 | ||||||||
\(903\) | −22.3418 | −0.743487 | ||||||||
\(904\) | 5.97011 | 0.198563 | ||||||||
\(905\) | −1.90872 | −0.0634481 | ||||||||
\(906\) | 19.1346 | 0.635704 | ||||||||
\(907\) | 24.3462 | 0.808403 | 0.404202 | − | 0.914670i | \(-0.367549\pi\) | ||||
0.404202 | + | 0.914670i | \(0.367549\pi\) | |||||||
\(908\) | −22.5024 | −0.746769 | ||||||||
\(909\) | −32.9338 | −1.09235 | ||||||||
\(910\) | 11.1938 | 0.371071 | ||||||||
\(911\) | −5.34248 | −0.177004 | −0.0885021 | − | 0.996076i | \(-0.528208\pi\) | ||||
−0.0885021 | + | 0.996076i | \(0.528208\pi\) | |||||||
\(912\) | −4.81718 | −0.159513 | ||||||||
\(913\) | 10.4791 | 0.346806 | ||||||||
\(914\) | −2.42057 | −0.0800655 | ||||||||
\(915\) | −5.78798 | −0.191345 | ||||||||
\(916\) | 8.15516 | 0.269454 | ||||||||
\(917\) | −19.0897 | −0.630399 | ||||||||
\(918\) | 5.46185 | 0.180268 | ||||||||
\(919\) | 30.1191 | 0.993537 | 0.496768 | − | 0.867883i | \(-0.334520\pi\) | ||||
0.496768 | + | 0.867883i | \(0.334520\pi\) | |||||||
\(920\) | −3.69511 | −0.121824 | ||||||||
\(921\) | 41.1798 | 1.35692 | ||||||||
\(922\) | −25.7434 | −0.847815 | ||||||||
\(923\) | −49.2858 | −1.62226 | ||||||||
\(924\) | 21.6334 | 0.711686 | ||||||||
\(925\) | −8.82225 | −0.290074 | ||||||||
\(926\) | 6.11273 | 0.200877 | ||||||||
\(927\) | 25.9648 | 0.852796 | ||||||||
\(928\) | −8.15103 | −0.267571 | ||||||||
\(929\) | 38.5146 | 1.26362 | 0.631812 | − | 0.775122i | \(-0.282311\pi\) | ||||
0.631812 | + | 0.775122i | \(0.282311\pi\) | |||||||
\(930\) | 3.72275 | 0.122074 | ||||||||
\(931\) | −0.0136523 | −0.000447435 0 | ||||||||
\(932\) | 13.1091 | 0.429403 | ||||||||
\(933\) | −58.4841 | −1.91468 | ||||||||
\(934\) | −28.5787 | −0.935122 | ||||||||
\(935\) | −9.31903 | −0.304765 | ||||||||
\(936\) | −8.68032 | −0.283725 | ||||||||
\(937\) | 5.34984 | 0.174772 | 0.0873858 | − | 0.996175i | \(-0.472149\pi\) | ||||
0.0873858 | + | 0.996175i | \(0.472149\pi\) | |||||||
\(938\) | −32.0391 | −1.04612 | ||||||||
\(939\) | −5.53480 | −0.180621 | ||||||||
\(940\) | −10.8528 | −0.353979 | ||||||||
\(941\) | −4.09505 | −0.133495 | −0.0667474 | − | 0.997770i | \(-0.521262\pi\) | ||||
−0.0667474 | + | 0.997770i | \(0.521262\pi\) | |||||||
\(942\) | 31.0147 | 1.01051 | ||||||||
\(943\) | −1.82095 | −0.0592984 | ||||||||
\(944\) | 5.31155 | 0.172876 | ||||||||
\(945\) | −5.64178 | −0.183527 | ||||||||
\(946\) | 13.6831 | 0.444876 | ||||||||
\(947\) | −49.5429 | −1.60993 | −0.804964 | − | 0.593324i | \(-0.797815\pi\) | ||||
−0.804964 | + | 0.593324i | \(0.797815\pi\) | |||||||
\(948\) | 21.7246 | 0.705581 | ||||||||
\(949\) | 30.1523 | 0.978784 | ||||||||
\(950\) | −2.14346 | −0.0695430 | ||||||||
\(951\) | 22.4271 | 0.727250 | ||||||||
\(952\) | 6.77059 | 0.219436 | ||||||||
\(953\) | 41.4007 | 1.34110 | 0.670551 | − | 0.741864i | \(-0.266058\pi\) | ||||
0.670551 | + | 0.741864i | \(0.266058\pi\) | |||||||
\(954\) | 19.0768 | 0.617635 | ||||||||
\(955\) | −17.9529 | −0.580942 | ||||||||
\(956\) | 20.0607 | 0.648811 | ||||||||
\(957\) | 66.6784 | 2.15541 | ||||||||
\(958\) | 19.7841 | 0.639194 | ||||||||
\(959\) | 17.3118 | 0.559027 | ||||||||
\(960\) | 2.24738 | 0.0725340 | ||||||||
\(961\) | −28.2561 | −0.911486 | ||||||||
\(962\) | 37.3427 | 1.20398 | ||||||||
\(963\) | 11.6812 | 0.376422 | ||||||||
\(964\) | −9.55890 | −0.307871 | ||||||||
\(965\) | −6.75068 | −0.217312 | ||||||||
\(966\) | −21.9612 | −0.706589 | ||||||||
\(967\) | 31.6390 | 1.01744 | 0.508720 | − | 0.860932i | \(-0.330119\pi\) | ||||
0.508720 | + | 0.860932i | \(0.330119\pi\) | |||||||
\(968\) | −2.24925 | −0.0722937 | ||||||||
\(969\) | 12.3330 | 0.396192 | ||||||||
\(970\) | 6.50997 | 0.209023 | ||||||||
\(971\) | −1.51187 | −0.0485182 | −0.0242591 | − | 0.999706i | \(-0.507723\pi\) | ||||
−0.0242591 | + | 0.999706i | \(0.507723\pi\) | |||||||
\(972\) | 18.2013 | 0.583808 | ||||||||
\(973\) | 15.1512 | 0.485724 | ||||||||
\(974\) | 4.44801 | 0.142523 | ||||||||
\(975\) | −9.51270 | −0.304650 | ||||||||
\(976\) | −2.57543 | −0.0824375 | ||||||||
\(977\) | 37.9954 | 1.21558 | 0.607791 | − | 0.794097i | \(-0.292056\pi\) | ||||
0.607791 | + | 0.794097i | \(0.292056\pi\) | |||||||
\(978\) | 44.5793 | 1.42549 | ||||||||
\(979\) | −25.5020 | −0.815049 | ||||||||
\(980\) | 0.00636926 | 0.000203459 0 | ||||||||
\(981\) | −33.6309 | −1.07375 | ||||||||
\(982\) | −32.7380 | −1.04471 | ||||||||
\(983\) | −39.8909 | −1.27232 | −0.636160 | − | 0.771557i | \(-0.719478\pi\) | ||||
−0.636160 | + | 0.771557i | \(0.719478\pi\) | |||||||
\(984\) | 1.10751 | 0.0353062 | ||||||||
\(985\) | −2.21121 | −0.0704550 | ||||||||
\(986\) | 20.8683 | 0.664582 | ||||||||
\(987\) | −64.5016 | −2.05311 | ||||||||
\(988\) | 9.07281 | 0.288645 | ||||||||
\(989\) | −13.8904 | −0.441690 | ||||||||
\(990\) | −7.46458 | −0.237240 | ||||||||
\(991\) | 19.2149 | 0.610380 | 0.305190 | − | 0.952291i | \(-0.401280\pi\) | ||||
0.305190 | + | 0.952291i | \(0.401280\pi\) | |||||||
\(992\) | 1.65648 | 0.0525934 | ||||||||
\(993\) | −59.7652 | −1.89659 | ||||||||
\(994\) | 30.7926 | 0.976683 | ||||||||
\(995\) | 16.9056 | 0.535944 | ||||||||
\(996\) | 6.46999 | 0.205010 | ||||||||
\(997\) | −9.66377 | −0.306055 | −0.153027 | − | 0.988222i | \(-0.548902\pi\) | ||||
−0.153027 | + | 0.988222i | \(0.548902\pi\) | |||||||
\(998\) | 33.3590 | 1.05596 | ||||||||
\(999\) | −18.8211 | −0.595472 |
(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 | 4010.2.a.l.1.3 | ✓ | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.l.1.3 | ✓ | 17 | 1.1 | even | 1 | trivial |