Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4030,2,Mod(1,4030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4030, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4030.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4030.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: | \(32.1797120146\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.3728437.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 5x^{4} + 6x^{3} + 7x^{2} - 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.58577\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4030.1 |
$q$-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 | ||||||||
\(3\) | −1.27014 | −0.733318 | −0.366659 | − | 0.930355i | \(-0.619498\pi\) | ||||
−0.366659 | + | 0.930355i | \(0.619498\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.27014 | 0.518534 | ||||||||
\(7\) | −3.95315 | −1.49415 | −0.747074 | − | 0.664740i | \(-0.768542\pi\) | ||||
−0.747074 | + | 0.664740i | \(0.768542\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.38673 | −0.462244 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 4.66379 | 1.40619 | 0.703093 | − | 0.711098i | \(-0.251802\pi\) | ||||
0.703093 | + | 0.711098i | \(0.251802\pi\) | |||||||
\(12\) | −1.27014 | −0.366659 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 3.95315 | 1.05652 | ||||||||
\(15\) | −1.27014 | −0.327950 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.48534 | −0.360249 | −0.180124 | − | 0.983644i | \(-0.557650\pi\) | ||||
−0.180124 | + | 0.983644i | \(0.557650\pi\) | |||||||
\(18\) | 1.38673 | 0.326856 | ||||||||
\(19\) | 3.80214 | 0.872272 | 0.436136 | − | 0.899881i | \(-0.356347\pi\) | ||||
0.436136 | + | 0.899881i | \(0.356347\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 5.02107 | 1.09569 | ||||||||
\(22\) | −4.66379 | −0.994324 | ||||||||
\(23\) | −7.81311 | −1.62915 | −0.814573 | − | 0.580061i | \(-0.803029\pi\) | ||||
−0.814573 | + | 0.580061i | \(0.803029\pi\) | |||||||
\(24\) | 1.27014 | 0.259267 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 5.57178 | 1.07229 | ||||||||
\(28\) | −3.95315 | −0.747074 | ||||||||
\(29\) | 0.373984 | 0.0694470 | 0.0347235 | − | 0.999397i | \(-0.488945\pi\) | ||||
0.0347235 | + | 0.999397i | \(0.488945\pi\) | |||||||
\(30\) | 1.27014 | 0.231896 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.92369 | −1.03118 | ||||||||
\(34\) | 1.48534 | 0.254734 | ||||||||
\(35\) | −3.95315 | −0.668204 | ||||||||
\(36\) | −1.38673 | −0.231122 | ||||||||
\(37\) | −3.50437 | −0.576115 | −0.288058 | − | 0.957613i | \(-0.593009\pi\) | ||||
−0.288058 | + | 0.957613i | \(0.593009\pi\) | |||||||
\(38\) | −3.80214 | −0.616789 | ||||||||
\(39\) | −1.27014 | −0.203386 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −6.09942 | −0.952569 | −0.476284 | − | 0.879291i | \(-0.658017\pi\) | ||||
−0.476284 | + | 0.879291i | \(0.658017\pi\) | |||||||
\(42\) | −5.02107 | −0.774768 | ||||||||
\(43\) | 3.20595 | 0.488903 | 0.244451 | − | 0.969662i | \(-0.421392\pi\) | ||||
0.244451 | + | 0.969662i | \(0.421392\pi\) | |||||||
\(44\) | 4.66379 | 0.703093 | ||||||||
\(45\) | −1.38673 | −0.206722 | ||||||||
\(46\) | 7.81311 | 1.15198 | ||||||||
\(47\) | 6.40206 | 0.933837 | 0.466918 | − | 0.884300i | \(-0.345364\pi\) | ||||
0.466918 | + | 0.884300i | \(0.345364\pi\) | |||||||
\(48\) | −1.27014 | −0.183330 | ||||||||
\(49\) | 8.62737 | 1.23248 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 1.88660 | 0.264177 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 9.25929 | 1.27186 | 0.635931 | − | 0.771746i | \(-0.280616\pi\) | ||||
0.635931 | + | 0.771746i | \(0.280616\pi\) | |||||||
\(54\) | −5.57178 | −0.758224 | ||||||||
\(55\) | 4.66379 | 0.628866 | ||||||||
\(56\) | 3.95315 | 0.528261 | ||||||||
\(57\) | −4.82927 | −0.639653 | ||||||||
\(58\) | −0.373984 | −0.0491065 | ||||||||
\(59\) | 6.57218 | 0.855625 | 0.427812 | − | 0.903868i | \(-0.359284\pi\) | ||||
0.427812 | + | 0.903868i | \(0.359284\pi\) | |||||||
\(60\) | −1.27014 | −0.163975 | ||||||||
\(61\) | 4.49166 | 0.575098 | 0.287549 | − | 0.957766i | \(-0.407160\pi\) | ||||
0.287549 | + | 0.957766i | \(0.407160\pi\) | |||||||
\(62\) | 1.00000 | 0.127000 | ||||||||
\(63\) | 5.48196 | 0.690662 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 5.92369 | 0.729156 | ||||||||
\(67\) | −9.82335 | −1.20011 | −0.600057 | − | 0.799957i | \(-0.704855\pi\) | ||||
−0.600057 | + | 0.799957i | \(0.704855\pi\) | |||||||
\(68\) | −1.48534 | −0.180124 | ||||||||
\(69\) | 9.92378 | 1.19468 | ||||||||
\(70\) | 3.95315 | 0.472491 | ||||||||
\(71\) | 9.44658 | 1.12110 | 0.560552 | − | 0.828120i | \(-0.310589\pi\) | ||||
0.560552 | + | 0.828120i | \(0.310589\pi\) | |||||||
\(72\) | 1.38673 | 0.163428 | ||||||||
\(73\) | 3.09187 | 0.361876 | 0.180938 | − | 0.983495i | \(-0.442087\pi\) | ||||
0.180938 | + | 0.983495i | \(0.442087\pi\) | |||||||
\(74\) | 3.50437 | 0.407375 | ||||||||
\(75\) | −1.27014 | −0.146664 | ||||||||
\(76\) | 3.80214 | 0.436136 | ||||||||
\(77\) | −18.4367 | −2.10105 | ||||||||
\(78\) | 1.27014 | 0.143816 | ||||||||
\(79\) | 0.814856 | 0.0916785 | 0.0458392 | − | 0.998949i | \(-0.485404\pi\) | ||||
0.0458392 | + | 0.998949i | \(0.485404\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −2.91678 | −0.324086 | ||||||||
\(82\) | 6.09942 | 0.673568 | ||||||||
\(83\) | −7.28306 | −0.799420 | −0.399710 | − | 0.916642i | \(-0.630889\pi\) | ||||
−0.399710 | + | 0.916642i | \(0.630889\pi\) | |||||||
\(84\) | 5.02107 | 0.547843 | ||||||||
\(85\) | −1.48534 | −0.161108 | ||||||||
\(86\) | −3.20595 | −0.345706 | ||||||||
\(87\) | −0.475013 | −0.0509268 | ||||||||
\(88\) | −4.66379 | −0.497162 | ||||||||
\(89\) | −6.30532 | −0.668363 | −0.334181 | − | 0.942509i | \(-0.608460\pi\) | ||||
−0.334181 | + | 0.942509i | \(0.608460\pi\) | |||||||
\(90\) | 1.38673 | 0.146174 | ||||||||
\(91\) | −3.95315 | −0.414402 | ||||||||
\(92\) | −7.81311 | −0.814573 | ||||||||
\(93\) | 1.27014 | 0.131708 | ||||||||
\(94\) | −6.40206 | −0.660322 | ||||||||
\(95\) | 3.80214 | 0.390092 | ||||||||
\(96\) | 1.27014 | 0.129634 | ||||||||
\(97\) | −12.8930 | −1.30909 | −0.654543 | − | 0.756025i | \(-0.727139\pi\) | ||||
−0.654543 | + | 0.756025i | \(0.727139\pi\) | |||||||
\(98\) | −8.62737 | −0.871496 | ||||||||
\(99\) | −6.46743 | −0.650001 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −12.0537 | −1.19939 | −0.599696 | − | 0.800228i | \(-0.704712\pi\) | ||||
−0.599696 | + | 0.800228i | \(0.704712\pi\) | |||||||
\(102\) | −1.88660 | −0.186801 | ||||||||
\(103\) | −11.1145 | −1.09515 | −0.547573 | − | 0.836758i | \(-0.684448\pi\) | ||||
−0.547573 | + | 0.836758i | \(0.684448\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 5.02107 | 0.490006 | ||||||||
\(106\) | −9.25929 | −0.899342 | ||||||||
\(107\) | −4.49281 | −0.434336 | −0.217168 | − | 0.976134i | \(-0.569682\pi\) | ||||
−0.217168 | + | 0.976134i | \(0.569682\pi\) | |||||||
\(108\) | 5.57178 | 0.536145 | ||||||||
\(109\) | −14.8468 | −1.42207 | −0.711033 | − | 0.703158i | \(-0.751772\pi\) | ||||
−0.711033 | + | 0.703158i | \(0.751772\pi\) | |||||||
\(110\) | −4.66379 | −0.444675 | ||||||||
\(111\) | 4.45106 | 0.422476 | ||||||||
\(112\) | −3.95315 | −0.373537 | ||||||||
\(113\) | 17.2057 | 1.61858 | 0.809288 | − | 0.587412i | \(-0.199853\pi\) | ||||
0.809288 | + | 0.587412i | \(0.199853\pi\) | |||||||
\(114\) | 4.82927 | 0.452303 | ||||||||
\(115\) | −7.81311 | −0.728576 | ||||||||
\(116\) | 0.373984 | 0.0347235 | ||||||||
\(117\) | −1.38673 | −0.128203 | ||||||||
\(118\) | −6.57218 | −0.605018 | ||||||||
\(119\) | 5.87178 | 0.538265 | ||||||||
\(120\) | 1.27014 | 0.115948 | ||||||||
\(121\) | 10.7510 | 0.977359 | ||||||||
\(122\) | −4.49166 | −0.406656 | ||||||||
\(123\) | 7.74714 | 0.698536 | ||||||||
\(124\) | −1.00000 | −0.0898027 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −5.48196 | −0.488371 | ||||||||
\(127\) | 13.0366 | 1.15681 | 0.578407 | − | 0.815749i | \(-0.303675\pi\) | ||||
0.578407 | + | 0.815749i | \(0.303675\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.07202 | −0.358521 | ||||||||
\(130\) | −1.00000 | −0.0877058 | ||||||||
\(131\) | 20.8577 | 1.82234 | 0.911171 | − | 0.412029i | \(-0.135180\pi\) | ||||
0.911171 | + | 0.412029i | \(0.135180\pi\) | |||||||
\(132\) | −5.92369 | −0.515591 | ||||||||
\(133\) | −15.0304 | −1.30330 | ||||||||
\(134\) | 9.82335 | 0.848609 | ||||||||
\(135\) | 5.57178 | 0.479543 | ||||||||
\(136\) | 1.48534 | 0.127367 | ||||||||
\(137\) | −8.09473 | −0.691580 | −0.345790 | − | 0.938312i | \(-0.612389\pi\) | ||||
−0.345790 | + | 0.938312i | \(0.612389\pi\) | |||||||
\(138\) | −9.92378 | −0.844768 | ||||||||
\(139\) | −8.76155 | −0.743145 | −0.371572 | − | 0.928404i | \(-0.621181\pi\) | ||||
−0.371572 | + | 0.928404i | \(0.621181\pi\) | |||||||
\(140\) | −3.95315 | −0.334102 | ||||||||
\(141\) | −8.13155 | −0.684800 | ||||||||
\(142\) | −9.44658 | −0.792740 | ||||||||
\(143\) | 4.66379 | 0.390006 | ||||||||
\(144\) | −1.38673 | −0.115561 | ||||||||
\(145\) | 0.373984 | 0.0310577 | ||||||||
\(146\) | −3.09187 | −0.255885 | ||||||||
\(147\) | −10.9580 | −0.903801 | ||||||||
\(148\) | −3.50437 | −0.288058 | ||||||||
\(149\) | −2.23059 | −0.182737 | −0.0913686 | − | 0.995817i | \(-0.529124\pi\) | ||||
−0.0913686 | + | 0.995817i | \(0.529124\pi\) | |||||||
\(150\) | 1.27014 | 0.103707 | ||||||||
\(151\) | 7.29600 | 0.593740 | 0.296870 | − | 0.954918i | \(-0.404057\pi\) | ||||
0.296870 | + | 0.954918i | \(0.404057\pi\) | |||||||
\(152\) | −3.80214 | −0.308395 | ||||||||
\(153\) | 2.05977 | 0.166523 | ||||||||
\(154\) | 18.4367 | 1.48567 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | −1.27014 | −0.101693 | ||||||||
\(157\) | −17.2073 | −1.37329 | −0.686644 | − | 0.726994i | \(-0.740917\pi\) | ||||
−0.686644 | + | 0.726994i | \(0.740917\pi\) | |||||||
\(158\) | −0.814856 | −0.0648265 | ||||||||
\(159\) | −11.7606 | −0.932679 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 30.8864 | 2.43419 | ||||||||
\(162\) | 2.91678 | 0.229164 | ||||||||
\(163\) | 11.3738 | 0.890865 | 0.445433 | − | 0.895315i | \(-0.353050\pi\) | ||||
0.445433 | + | 0.895315i | \(0.353050\pi\) | |||||||
\(164\) | −6.09942 | −0.476284 | ||||||||
\(165\) | −5.92369 | −0.461159 | ||||||||
\(166\) | 7.28306 | 0.565275 | ||||||||
\(167\) | −2.35504 | −0.182238 | −0.0911191 | − | 0.995840i | \(-0.529044\pi\) | ||||
−0.0911191 | + | 0.995840i | \(0.529044\pi\) | |||||||
\(168\) | −5.02107 | −0.387384 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 1.48534 | 0.113921 | ||||||||
\(171\) | −5.27256 | −0.403202 | ||||||||
\(172\) | 3.20595 | 0.244451 | ||||||||
\(173\) | 20.9496 | 1.59277 | 0.796385 | − | 0.604791i | \(-0.206743\pi\) | ||||
0.796385 | + | 0.604791i | \(0.206743\pi\) | |||||||
\(174\) | 0.475013 | 0.0360107 | ||||||||
\(175\) | −3.95315 | −0.298830 | ||||||||
\(176\) | 4.66379 | 0.351547 | ||||||||
\(177\) | −8.34762 | −0.627445 | ||||||||
\(178\) | 6.30532 | 0.472604 | ||||||||
\(179\) | −19.4658 | −1.45494 | −0.727470 | − | 0.686140i | \(-0.759304\pi\) | ||||
−0.727470 | + | 0.686140i | \(0.759304\pi\) | |||||||
\(180\) | −1.38673 | −0.103361 | ||||||||
\(181\) | −5.12519 | −0.380952 | −0.190476 | − | 0.981692i | \(-0.561003\pi\) | ||||
−0.190476 | + | 0.981692i | \(0.561003\pi\) | |||||||
\(182\) | 3.95315 | 0.293027 | ||||||||
\(183\) | −5.70506 | −0.421730 | ||||||||
\(184\) | 7.81311 | 0.575990 | ||||||||
\(185\) | −3.50437 | −0.257647 | ||||||||
\(186\) | −1.27014 | −0.0931315 | ||||||||
\(187\) | −6.92733 | −0.506577 | ||||||||
\(188\) | 6.40206 | 0.466918 | ||||||||
\(189\) | −22.0261 | −1.60216 | ||||||||
\(190\) | −3.80214 | −0.275836 | ||||||||
\(191\) | −4.28978 | −0.310397 | −0.155199 | − | 0.987883i | \(-0.549602\pi\) | ||||
−0.155199 | + | 0.987883i | \(0.549602\pi\) | |||||||
\(192\) | −1.27014 | −0.0916648 | ||||||||
\(193\) | −10.9142 | −0.785621 | −0.392810 | − | 0.919619i | \(-0.628497\pi\) | ||||
−0.392810 | + | 0.919619i | \(0.628497\pi\) | |||||||
\(194\) | 12.8930 | 0.925664 | ||||||||
\(195\) | −1.27014 | −0.0909570 | ||||||||
\(196\) | 8.62737 | 0.616240 | ||||||||
\(197\) | −23.8116 | −1.69650 | −0.848251 | − | 0.529594i | \(-0.822344\pi\) | ||||
−0.848251 | + | 0.529594i | \(0.822344\pi\) | |||||||
\(198\) | 6.46743 | 0.459620 | ||||||||
\(199\) | 21.3366 | 1.51251 | 0.756255 | − | 0.654277i | \(-0.227027\pi\) | ||||
0.756255 | + | 0.654277i | \(0.227027\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 12.4771 | 0.880065 | ||||||||
\(202\) | 12.0537 | 0.848098 | ||||||||
\(203\) | −1.47841 | −0.103764 | ||||||||
\(204\) | 1.88660 | 0.132088 | ||||||||
\(205\) | −6.09942 | −0.426002 | ||||||||
\(206\) | 11.1145 | 0.774385 | ||||||||
\(207\) | 10.8347 | 0.753063 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 17.7324 | 1.22658 | ||||||||
\(210\) | −5.02107 | −0.346487 | ||||||||
\(211\) | −21.8827 | −1.50647 | −0.753233 | − | 0.657753i | \(-0.771507\pi\) | ||||
−0.753233 | + | 0.657753i | \(0.771507\pi\) | |||||||
\(212\) | 9.25929 | 0.635931 | ||||||||
\(213\) | −11.9985 | −0.822125 | ||||||||
\(214\) | 4.49281 | 0.307122 | ||||||||
\(215\) | 3.20595 | 0.218644 | ||||||||
\(216\) | −5.57178 | −0.379112 | ||||||||
\(217\) | 3.95315 | 0.268357 | ||||||||
\(218\) | 14.8468 | 1.00555 | ||||||||
\(219\) | −3.92712 | −0.265370 | ||||||||
\(220\) | 4.66379 | 0.314433 | ||||||||
\(221\) | −1.48534 | −0.0999150 | ||||||||
\(222\) | −4.45106 | −0.298736 | ||||||||
\(223\) | 26.9945 | 1.80769 | 0.903843 | − | 0.427864i | \(-0.140734\pi\) | ||||
0.903843 | + | 0.427864i | \(0.140734\pi\) | |||||||
\(224\) | 3.95315 | 0.264131 | ||||||||
\(225\) | −1.38673 | −0.0924488 | ||||||||
\(226\) | −17.2057 | −1.14451 | ||||||||
\(227\) | −13.6541 | −0.906257 | −0.453128 | − | 0.891445i | \(-0.649692\pi\) | ||||
−0.453128 | + | 0.891445i | \(0.649692\pi\) | |||||||
\(228\) | −4.82927 | −0.319826 | ||||||||
\(229\) | −4.50691 | −0.297825 | −0.148913 | − | 0.988850i | \(-0.547577\pi\) | ||||
−0.148913 | + | 0.988850i | \(0.547577\pi\) | |||||||
\(230\) | 7.81311 | 0.515181 | ||||||||
\(231\) | 23.4172 | 1.54074 | ||||||||
\(232\) | −0.373984 | −0.0245532 | ||||||||
\(233\) | −4.53438 | −0.297057 | −0.148529 | − | 0.988908i | \(-0.547454\pi\) | ||||
−0.148529 | + | 0.988908i | \(0.547454\pi\) | |||||||
\(234\) | 1.38673 | 0.0906535 | ||||||||
\(235\) | 6.40206 | 0.417625 | ||||||||
\(236\) | 6.57218 | 0.427812 | ||||||||
\(237\) | −1.03499 | −0.0672295 | ||||||||
\(238\) | −5.87178 | −0.380611 | ||||||||
\(239\) | −19.0123 | −1.22981 | −0.614903 | − | 0.788603i | \(-0.710805\pi\) | ||||
−0.614903 | + | 0.788603i | \(0.710805\pi\) | |||||||
\(240\) | −1.27014 | −0.0819875 | ||||||||
\(241\) | −26.6169 | −1.71455 | −0.857274 | − | 0.514861i | \(-0.827844\pi\) | ||||
−0.857274 | + | 0.514861i | \(0.827844\pi\) | |||||||
\(242\) | −10.7510 | −0.691097 | ||||||||
\(243\) | −13.0106 | −0.834632 | ||||||||
\(244\) | 4.49166 | 0.287549 | ||||||||
\(245\) | 8.62737 | 0.551182 | ||||||||
\(246\) | −7.74714 | −0.493940 | ||||||||
\(247\) | 3.80214 | 0.241925 | ||||||||
\(248\) | 1.00000 | 0.0635001 | ||||||||
\(249\) | 9.25055 | 0.586230 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −22.7877 | −1.43835 | −0.719173 | − | 0.694831i | \(-0.755479\pi\) | ||||
−0.719173 | + | 0.694831i | \(0.755479\pi\) | |||||||
\(252\) | 5.48196 | 0.345331 | ||||||||
\(253\) | −36.4387 | −2.29088 | ||||||||
\(254\) | −13.0366 | −0.817991 | ||||||||
\(255\) | 1.88660 | 0.118144 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.3418 | −0.645101 | −0.322550 | − | 0.946552i | \(-0.604540\pi\) | ||||
−0.322550 | + | 0.946552i | \(0.604540\pi\) | |||||||
\(258\) | 4.07202 | 0.253513 | ||||||||
\(259\) | 13.8533 | 0.860802 | ||||||||
\(260\) | 1.00000 | 0.0620174 | ||||||||
\(261\) | −0.518615 | −0.0321015 | ||||||||
\(262\) | −20.8577 | −1.28859 | ||||||||
\(263\) | −13.4039 | −0.826521 | −0.413260 | − | 0.910613i | \(-0.635610\pi\) | ||||
−0.413260 | + | 0.910613i | \(0.635610\pi\) | |||||||
\(264\) | 5.92369 | 0.364578 | ||||||||
\(265\) | 9.25929 | 0.568794 | ||||||||
\(266\) | 15.0304 | 0.921575 | ||||||||
\(267\) | 8.00867 | 0.490123 | ||||||||
\(268\) | −9.82335 | −0.600057 | ||||||||
\(269\) | −30.8839 | −1.88303 | −0.941514 | − | 0.336974i | \(-0.890596\pi\) | ||||
−0.941514 | + | 0.336974i | \(0.890596\pi\) | |||||||
\(270\) | −5.57178 | −0.339088 | ||||||||
\(271\) | 5.83820 | 0.354645 | 0.177323 | − | 0.984153i | \(-0.443256\pi\) | ||||
0.177323 | + | 0.984153i | \(0.443256\pi\) | |||||||
\(272\) | −1.48534 | −0.0900622 | ||||||||
\(273\) | 5.02107 | 0.303889 | ||||||||
\(274\) | 8.09473 | 0.489021 | ||||||||
\(275\) | 4.66379 | 0.281237 | ||||||||
\(276\) | 9.92378 | 0.597341 | ||||||||
\(277\) | 21.3108 | 1.28044 | 0.640219 | − | 0.768192i | \(-0.278843\pi\) | ||||
0.640219 | + | 0.768192i | \(0.278843\pi\) | |||||||
\(278\) | 8.76155 | 0.525483 | ||||||||
\(279\) | 1.38673 | 0.0830215 | ||||||||
\(280\) | 3.95315 | 0.236246 | ||||||||
\(281\) | −20.7103 | −1.23547 | −0.617737 | − | 0.786385i | \(-0.711950\pi\) | ||||
−0.617737 | + | 0.786385i | \(0.711950\pi\) | |||||||
\(282\) | 8.13155 | 0.484227 | ||||||||
\(283\) | −2.82014 | −0.167640 | −0.0838199 | − | 0.996481i | \(-0.526712\pi\) | ||||
−0.0838199 | + | 0.996481i | \(0.526712\pi\) | |||||||
\(284\) | 9.44658 | 0.560552 | ||||||||
\(285\) | −4.82927 | −0.286061 | ||||||||
\(286\) | −4.66379 | −0.275776 | ||||||||
\(287\) | 24.1119 | 1.42328 | ||||||||
\(288\) | 1.38673 | 0.0817140 | ||||||||
\(289\) | −14.7938 | −0.870221 | ||||||||
\(290\) | −0.373984 | −0.0219611 | ||||||||
\(291\) | 16.3760 | 0.959977 | ||||||||
\(292\) | 3.09187 | 0.180938 | ||||||||
\(293\) | 15.1264 | 0.883693 | 0.441846 | − | 0.897091i | \(-0.354324\pi\) | ||||
0.441846 | + | 0.897091i | \(0.354324\pi\) | |||||||
\(294\) | 10.9580 | 0.639084 | ||||||||
\(295\) | 6.57218 | 0.382647 | ||||||||
\(296\) | 3.50437 | 0.203687 | ||||||||
\(297\) | 25.9856 | 1.50784 | ||||||||
\(298\) | 2.23059 | 0.129215 | ||||||||
\(299\) | −7.81311 | −0.451844 | ||||||||
\(300\) | −1.27014 | −0.0733318 | ||||||||
\(301\) | −12.6736 | −0.730493 | ||||||||
\(302\) | −7.29600 | −0.419837 | ||||||||
\(303\) | 15.3100 | 0.879536 | ||||||||
\(304\) | 3.80214 | 0.218068 | ||||||||
\(305\) | 4.49166 | 0.257192 | ||||||||
\(306\) | −2.05977 | −0.117749 | ||||||||
\(307\) | 11.7199 | 0.668889 | 0.334445 | − | 0.942415i | \(-0.391451\pi\) | ||||
0.334445 | + | 0.942415i | \(0.391451\pi\) | |||||||
\(308\) | −18.4367 | −1.05053 | ||||||||
\(309\) | 14.1171 | 0.803091 | ||||||||
\(310\) | 1.00000 | 0.0567962 | ||||||||
\(311\) | −10.8823 | −0.617078 | −0.308539 | − | 0.951212i | \(-0.599840\pi\) | ||||
−0.308539 | + | 0.951212i | \(0.599840\pi\) | |||||||
\(312\) | 1.27014 | 0.0719078 | ||||||||
\(313\) | −21.9056 | −1.23818 | −0.619090 | − | 0.785320i | \(-0.712498\pi\) | ||||
−0.619090 | + | 0.785320i | \(0.712498\pi\) | |||||||
\(314\) | 17.2073 | 0.971061 | ||||||||
\(315\) | 5.48196 | 0.308873 | ||||||||
\(316\) | 0.814856 | 0.0458392 | ||||||||
\(317\) | 9.03617 | 0.507522 | 0.253761 | − | 0.967267i | \(-0.418332\pi\) | ||||
0.253761 | + | 0.967267i | \(0.418332\pi\) | |||||||
\(318\) | 11.7606 | 0.659504 | ||||||||
\(319\) | 1.74418 | 0.0976555 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 5.70652 | 0.318507 | ||||||||
\(322\) | −30.8864 | −1.72123 | ||||||||
\(323\) | −5.64749 | −0.314235 | ||||||||
\(324\) | −2.91678 | −0.162043 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | −11.3738 | −0.629937 | ||||||||
\(327\) | 18.8576 | 1.04283 | ||||||||
\(328\) | 6.09942 | 0.336784 | ||||||||
\(329\) | −25.3083 | −1.39529 | ||||||||
\(330\) | 5.92369 | 0.326088 | ||||||||
\(331\) | −2.78825 | −0.153256 | −0.0766280 | − | 0.997060i | \(-0.524415\pi\) | ||||
−0.0766280 | + | 0.997060i | \(0.524415\pi\) | |||||||
\(332\) | −7.28306 | −0.399710 | ||||||||
\(333\) | 4.85963 | 0.266306 | ||||||||
\(334\) | 2.35504 | 0.128862 | ||||||||
\(335\) | −9.82335 | −0.536707 | ||||||||
\(336\) | 5.02107 | 0.273922 | ||||||||
\(337\) | −3.80184 | −0.207099 | −0.103550 | − | 0.994624i | \(-0.533020\pi\) | ||||
−0.103550 | + | 0.994624i | \(0.533020\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −21.8537 | −1.18693 | ||||||||
\(340\) | −1.48534 | −0.0805541 | ||||||||
\(341\) | −4.66379 | −0.252558 | ||||||||
\(342\) | 5.27256 | 0.285107 | ||||||||
\(343\) | −6.43321 | −0.347361 | ||||||||
\(344\) | −3.20595 | −0.172853 | ||||||||
\(345\) | 9.92378 | 0.534278 | ||||||||
\(346\) | −20.9496 | −1.12626 | ||||||||
\(347\) | −32.7754 | −1.75947 | −0.879737 | − | 0.475462i | \(-0.842281\pi\) | ||||
−0.879737 | + | 0.475462i | \(0.842281\pi\) | |||||||
\(348\) | −0.475013 | −0.0254634 | ||||||||
\(349\) | 23.5163 | 1.25880 | 0.629398 | − | 0.777083i | \(-0.283301\pi\) | ||||
0.629398 | + | 0.777083i | \(0.283301\pi\) | |||||||
\(350\) | 3.95315 | 0.211305 | ||||||||
\(351\) | 5.57178 | 0.297400 | ||||||||
\(352\) | −4.66379 | −0.248581 | ||||||||
\(353\) | −18.9683 | −1.00958 | −0.504792 | − | 0.863241i | \(-0.668431\pi\) | ||||
−0.504792 | + | 0.863241i | \(0.668431\pi\) | |||||||
\(354\) | 8.34762 | 0.443671 | ||||||||
\(355\) | 9.44658 | 0.501373 | ||||||||
\(356\) | −6.30532 | −0.334181 | ||||||||
\(357\) | −7.45801 | −0.394720 | ||||||||
\(358\) | 19.4658 | 1.02880 | ||||||||
\(359\) | 17.0190 | 0.898227 | 0.449113 | − | 0.893475i | \(-0.351740\pi\) | ||||
0.449113 | + | 0.893475i | \(0.351740\pi\) | |||||||
\(360\) | 1.38673 | 0.0730872 | ||||||||
\(361\) | −4.54370 | −0.239142 | ||||||||
\(362\) | 5.12519 | 0.269374 | ||||||||
\(363\) | −13.6553 | −0.716715 | ||||||||
\(364\) | −3.95315 | −0.207201 | ||||||||
\(365\) | 3.09187 | 0.161836 | ||||||||
\(366\) | 5.70506 | 0.298208 | ||||||||
\(367\) | −27.4066 | −1.43061 | −0.715305 | − | 0.698812i | \(-0.753712\pi\) | ||||
−0.715305 | + | 0.698812i | \(0.753712\pi\) | |||||||
\(368\) | −7.81311 | −0.407286 | ||||||||
\(369\) | 8.45826 | 0.440319 | ||||||||
\(370\) | 3.50437 | 0.182184 | ||||||||
\(371\) | −36.6033 | −1.90035 | ||||||||
\(372\) | 1.27014 | 0.0658539 | ||||||||
\(373\) | −14.4935 | −0.750447 | −0.375224 | − | 0.926934i | \(-0.622434\pi\) | ||||
−0.375224 | + | 0.926934i | \(0.622434\pi\) | |||||||
\(374\) | 6.92733 | 0.358204 | ||||||||
\(375\) | −1.27014 | −0.0655900 | ||||||||
\(376\) | −6.40206 | −0.330161 | ||||||||
\(377\) | 0.373984 | 0.0192611 | ||||||||
\(378\) | 22.0261 | 1.13290 | ||||||||
\(379\) | 5.12722 | 0.263368 | 0.131684 | − | 0.991292i | \(-0.457962\pi\) | ||||
0.131684 | + | 0.991292i | \(0.457962\pi\) | |||||||
\(380\) | 3.80214 | 0.195046 | ||||||||
\(381\) | −16.5584 | −0.848313 | ||||||||
\(382\) | 4.28978 | 0.219484 | ||||||||
\(383\) | −4.34716 | −0.222130 | −0.111065 | − | 0.993813i | \(-0.535426\pi\) | ||||
−0.111065 | + | 0.993813i | \(0.535426\pi\) | |||||||
\(384\) | 1.27014 | 0.0648168 | ||||||||
\(385\) | −18.4367 | −0.939619 | ||||||||
\(386\) | 10.9142 | 0.555518 | ||||||||
\(387\) | −4.44579 | −0.225992 | ||||||||
\(388\) | −12.8930 | −0.654543 | ||||||||
\(389\) | 16.4912 | 0.836135 | 0.418068 | − | 0.908416i | \(-0.362708\pi\) | ||||
0.418068 | + | 0.908416i | \(0.362708\pi\) | |||||||
\(390\) | 1.27014 | 0.0643163 | ||||||||
\(391\) | 11.6051 | 0.586898 | ||||||||
\(392\) | −8.62737 | −0.435748 | ||||||||
\(393\) | −26.4922 | −1.33636 | ||||||||
\(394\) | 23.8116 | 1.19961 | ||||||||
\(395\) | 0.814856 | 0.0409999 | ||||||||
\(396\) | −6.46743 | −0.325001 | ||||||||
\(397\) | −9.92346 | −0.498044 | −0.249022 | − | 0.968498i | \(-0.580109\pi\) | ||||
−0.249022 | + | 0.968498i | \(0.580109\pi\) | |||||||
\(398\) | −21.3366 | −1.06951 | ||||||||
\(399\) | 19.0908 | 0.955736 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 29.1905 | 1.45770 | 0.728852 | − | 0.684671i | \(-0.240054\pi\) | ||||
0.728852 | + | 0.684671i | \(0.240054\pi\) | |||||||
\(402\) | −12.4771 | −0.622300 | ||||||||
\(403\) | −1.00000 | −0.0498135 | ||||||||
\(404\) | −12.0537 | −0.599696 | ||||||||
\(405\) | −2.91678 | −0.144936 | ||||||||
\(406\) | 1.47841 | 0.0733724 | ||||||||
\(407\) | −16.3437 | −0.810125 | ||||||||
\(408\) | −1.88660 | −0.0934007 | ||||||||
\(409\) | −13.9128 | −0.687946 | −0.343973 | − | 0.938980i | \(-0.611773\pi\) | ||||
−0.343973 | + | 0.938980i | \(0.611773\pi\) | |||||||
\(410\) | 6.09942 | 0.301229 | ||||||||
\(411\) | 10.2815 | 0.507148 | ||||||||
\(412\) | −11.1145 | −0.547573 | ||||||||
\(413\) | −25.9808 | −1.27843 | ||||||||
\(414\) | −10.8347 | −0.532496 | ||||||||
\(415\) | −7.28306 | −0.357512 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 11.1284 | 0.544962 | ||||||||
\(418\) | −17.7324 | −0.867320 | ||||||||
\(419\) | −19.0311 | −0.929729 | −0.464864 | − | 0.885382i | \(-0.653897\pi\) | ||||
−0.464864 | + | 0.885382i | \(0.653897\pi\) | |||||||
\(420\) | 5.02107 | 0.245003 | ||||||||
\(421\) | 11.0709 | 0.539561 | 0.269781 | − | 0.962922i | \(-0.413049\pi\) | ||||
0.269781 | + | 0.962922i | \(0.413049\pi\) | |||||||
\(422\) | 21.8827 | 1.06523 | ||||||||
\(423\) | −8.87795 | −0.431661 | ||||||||
\(424\) | −9.25929 | −0.449671 | ||||||||
\(425\) | −1.48534 | −0.0720497 | ||||||||
\(426\) | 11.9985 | 0.581330 | ||||||||
\(427\) | −17.7562 | −0.859282 | ||||||||
\(428\) | −4.49281 | −0.217168 | ||||||||
\(429\) | −5.92369 | −0.285998 | ||||||||
\(430\) | −3.20595 | −0.154605 | ||||||||
\(431\) | 28.2467 | 1.36059 | 0.680297 | − | 0.732936i | \(-0.261851\pi\) | ||||
0.680297 | + | 0.732936i | \(0.261851\pi\) | |||||||
\(432\) | 5.57178 | 0.268073 | ||||||||
\(433\) | −10.7500 | −0.516612 | −0.258306 | − | 0.966063i | \(-0.583164\pi\) | ||||
−0.258306 | + | 0.966063i | \(0.583164\pi\) | |||||||
\(434\) | −3.95315 | −0.189757 | ||||||||
\(435\) | −0.475013 | −0.0227752 | ||||||||
\(436\) | −14.8468 | −0.711033 | ||||||||
\(437\) | −29.7066 | −1.42106 | ||||||||
\(438\) | 3.92712 | 0.187645 | ||||||||
\(439\) | −17.5758 | −0.838846 | −0.419423 | − | 0.907791i | \(-0.637768\pi\) | ||||
−0.419423 | + | 0.907791i | \(0.637768\pi\) | |||||||
\(440\) | −4.66379 | −0.222338 | ||||||||
\(441\) | −11.9638 | −0.569707 | ||||||||
\(442\) | 1.48534 | 0.0706506 | ||||||||
\(443\) | −9.28428 | −0.441109 | −0.220555 | − | 0.975375i | \(-0.570787\pi\) | ||||
−0.220555 | + | 0.975375i | \(0.570787\pi\) | |||||||
\(444\) | 4.45106 | 0.211238 | ||||||||
\(445\) | −6.30532 | −0.298901 | ||||||||
\(446\) | −26.9945 | −1.27823 | ||||||||
\(447\) | 2.83317 | 0.134005 | ||||||||
\(448\) | −3.95315 | −0.186769 | ||||||||
\(449\) | −8.32815 | −0.393030 | −0.196515 | − | 0.980501i | \(-0.562962\pi\) | ||||
−0.196515 | + | 0.980501i | \(0.562962\pi\) | |||||||
\(450\) | 1.38673 | 0.0653712 | ||||||||
\(451\) | −28.4464 | −1.33949 | ||||||||
\(452\) | 17.2057 | 0.809288 | ||||||||
\(453\) | −9.26697 | −0.435400 | ||||||||
\(454\) | 13.6541 | 0.640820 | ||||||||
\(455\) | −3.95315 | −0.185326 | ||||||||
\(456\) | 4.82927 | 0.226151 | ||||||||
\(457\) | −41.2452 | −1.92937 | −0.964685 | − | 0.263405i | \(-0.915154\pi\) | ||||
−0.964685 | + | 0.263405i | \(0.915154\pi\) | |||||||
\(458\) | 4.50691 | 0.210594 | ||||||||
\(459\) | −8.27601 | −0.386291 | ||||||||
\(460\) | −7.81311 | −0.364288 | ||||||||
\(461\) | −24.8401 | −1.15692 | −0.578460 | − | 0.815711i | \(-0.696346\pi\) | ||||
−0.578460 | + | 0.815711i | \(0.696346\pi\) | |||||||
\(462\) | −23.4172 | −1.08947 | ||||||||
\(463\) | 21.8812 | 1.01691 | 0.508453 | − | 0.861090i | \(-0.330217\pi\) | ||||
0.508453 | + | 0.861090i | \(0.330217\pi\) | |||||||
\(464\) | 0.373984 | 0.0173618 | ||||||||
\(465\) | 1.27014 | 0.0589015 | ||||||||
\(466\) | 4.53438 | 0.210051 | ||||||||
\(467\) | 2.00619 | 0.0928355 | 0.0464177 | − | 0.998922i | \(-0.485219\pi\) | ||||
0.0464177 | + | 0.998922i | \(0.485219\pi\) | |||||||
\(468\) | −1.38673 | −0.0641017 | ||||||||
\(469\) | 38.8332 | 1.79315 | ||||||||
\(470\) | −6.40206 | −0.295305 | ||||||||
\(471\) | 21.8557 | 1.00706 | ||||||||
\(472\) | −6.57218 | −0.302509 | ||||||||
\(473\) | 14.9519 | 0.687488 | ||||||||
\(474\) | 1.03499 | 0.0475384 | ||||||||
\(475\) | 3.80214 | 0.174454 | ||||||||
\(476\) | 5.87178 | 0.269133 | ||||||||
\(477\) | −12.8402 | −0.587910 | ||||||||
\(478\) | 19.0123 | 0.869604 | ||||||||
\(479\) | 11.5411 | 0.527328 | 0.263664 | − | 0.964615i | \(-0.415069\pi\) | ||||
0.263664 | + | 0.964615i | \(0.415069\pi\) | |||||||
\(480\) | 1.27014 | 0.0579739 | ||||||||
\(481\) | −3.50437 | −0.159786 | ||||||||
\(482\) | 26.6169 | 1.21237 | ||||||||
\(483\) | −39.2301 | −1.78503 | ||||||||
\(484\) | 10.7510 | 0.488680 | ||||||||
\(485\) | −12.8930 | −0.585441 | ||||||||
\(486\) | 13.0106 | 0.590174 | ||||||||
\(487\) | 21.5414 | 0.976132 | 0.488066 | − | 0.872807i | \(-0.337703\pi\) | ||||
0.488066 | + | 0.872807i | \(0.337703\pi\) | |||||||
\(488\) | −4.49166 | −0.203328 | ||||||||
\(489\) | −14.4464 | −0.653288 | ||||||||
\(490\) | −8.62737 | −0.389745 | ||||||||
\(491\) | 7.25724 | 0.327515 | 0.163757 | − | 0.986501i | \(-0.447639\pi\) | ||||
0.163757 | + | 0.986501i | \(0.447639\pi\) | |||||||
\(492\) | 7.74714 | 0.349268 | ||||||||
\(493\) | −0.555494 | −0.0250182 | ||||||||
\(494\) | −3.80214 | −0.171067 | ||||||||
\(495\) | −6.46743 | −0.290689 | ||||||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | −37.3437 | −1.67509 | ||||||||
\(498\) | −9.25055 | −0.414527 | ||||||||
\(499\) | 14.8212 | 0.663488 | 0.331744 | − | 0.943369i | \(-0.392363\pi\) | ||||
0.331744 | + | 0.943369i | \(0.392363\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 2.99124 | 0.133639 | ||||||||
\(502\) | 22.7877 | 1.01706 | ||||||||
\(503\) | 20.3670 | 0.908122 | 0.454061 | − | 0.890971i | \(-0.349975\pi\) | ||||
0.454061 | + | 0.890971i | \(0.349975\pi\) | |||||||
\(504\) | −5.48196 | −0.244186 | ||||||||
\(505\) | −12.0537 | −0.536384 | ||||||||
\(506\) | 36.4387 | 1.61990 | ||||||||
\(507\) | −1.27014 | −0.0564091 | ||||||||
\(508\) | 13.0366 | 0.578407 | ||||||||
\(509\) | −3.57242 | −0.158345 | −0.0791723 | − | 0.996861i | \(-0.525228\pi\) | ||||
−0.0791723 | + | 0.996861i | \(0.525228\pi\) | |||||||
\(510\) | −1.88660 | −0.0835401 | ||||||||
\(511\) | −12.2226 | −0.540696 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 21.1847 | 0.935328 | ||||||||
\(514\) | 10.3418 | 0.456155 | ||||||||
\(515\) | −11.1145 | −0.489764 | ||||||||
\(516\) | −4.07202 | −0.179261 | ||||||||
\(517\) | 29.8579 | 1.31315 | ||||||||
\(518\) | −13.8533 | −0.608679 | ||||||||
\(519\) | −26.6090 | −1.16801 | ||||||||
\(520\) | −1.00000 | −0.0438529 | ||||||||
\(521\) | −37.6544 | −1.64967 | −0.824834 | − | 0.565375i | \(-0.808731\pi\) | ||||
−0.824834 | + | 0.565375i | \(0.808731\pi\) | |||||||
\(522\) | 0.518615 | 0.0226992 | ||||||||
\(523\) | 33.1986 | 1.45167 | 0.725837 | − | 0.687867i | \(-0.241453\pi\) | ||||
0.725837 | + | 0.687867i | \(0.241453\pi\) | |||||||
\(524\) | 20.8577 | 0.911171 | ||||||||
\(525\) | 5.02107 | 0.219137 | ||||||||
\(526\) | 13.4039 | 0.584439 | ||||||||
\(527\) | 1.48534 | 0.0647026 | ||||||||
\(528\) | −5.92369 | −0.257796 | ||||||||
\(529\) | 38.0447 | 1.65412 | ||||||||
\(530\) | −9.25929 | −0.402198 | ||||||||
\(531\) | −9.11385 | −0.395508 | ||||||||
\(532\) | −15.0304 | −0.651652 | ||||||||
\(533\) | −6.09942 | −0.264195 | ||||||||
\(534\) | −8.00867 | −0.346569 | ||||||||
\(535\) | −4.49281 | −0.194241 | ||||||||
\(536\) | 9.82335 | 0.424304 | ||||||||
\(537\) | 24.7243 | 1.06693 | ||||||||
\(538\) | 30.8839 | 1.33150 | ||||||||
\(539\) | 40.2362 | 1.73310 | ||||||||
\(540\) | 5.57178 | 0.239771 | ||||||||
\(541\) | 2.77824 | 0.119446 | 0.0597229 | − | 0.998215i | \(-0.480978\pi\) | ||||
0.0597229 | + | 0.998215i | \(0.480978\pi\) | |||||||
\(542\) | −5.83820 | −0.250772 | ||||||||
\(543\) | 6.50973 | 0.279359 | ||||||||
\(544\) | 1.48534 | 0.0636836 | ||||||||
\(545\) | −14.8468 | −0.635967 | ||||||||
\(546\) | −5.02107 | −0.214882 | ||||||||
\(547\) | −17.7341 | −0.758254 | −0.379127 | − | 0.925345i | \(-0.623776\pi\) | ||||
−0.379127 | + | 0.925345i | \(0.623776\pi\) | |||||||
\(548\) | −8.09473 | −0.345790 | ||||||||
\(549\) | −6.22873 | −0.265836 | ||||||||
\(550\) | −4.66379 | −0.198865 | ||||||||
\(551\) | 1.42194 | 0.0605767 | ||||||||
\(552\) | −9.92378 | −0.422384 | ||||||||
\(553\) | −3.22125 | −0.136981 | ||||||||
\(554\) | −21.3108 | −0.905407 | ||||||||
\(555\) | 4.45106 | 0.188937 | ||||||||
\(556\) | −8.76155 | −0.371572 | ||||||||
\(557\) | −18.7270 | −0.793487 | −0.396744 | − | 0.917929i | \(-0.629860\pi\) | ||||
−0.396744 | + | 0.917929i | \(0.629860\pi\) | |||||||
\(558\) | −1.38673 | −0.0587051 | ||||||||
\(559\) | 3.20595 | 0.135597 | ||||||||
\(560\) | −3.95315 | −0.167051 | ||||||||
\(561\) | 8.79871 | 0.371482 | ||||||||
\(562\) | 20.7103 | 0.873612 | ||||||||
\(563\) | −7.49091 | −0.315704 | −0.157852 | − | 0.987463i | \(-0.550457\pi\) | ||||
−0.157852 | + | 0.987463i | \(0.550457\pi\) | |||||||
\(564\) | −8.13155 | −0.342400 | ||||||||
\(565\) | 17.2057 | 0.723849 | ||||||||
\(566\) | 2.82014 | 0.118539 | ||||||||
\(567\) | 11.5304 | 0.484233 | ||||||||
\(568\) | −9.44658 | −0.396370 | ||||||||
\(569\) | −26.4785 | −1.11004 | −0.555018 | − | 0.831838i | \(-0.687289\pi\) | ||||
−0.555018 | + | 0.831838i | \(0.687289\pi\) | |||||||
\(570\) | 4.82927 | 0.202276 | ||||||||
\(571\) | 17.3569 | 0.726362 | 0.363181 | − | 0.931719i | \(-0.381691\pi\) | ||||
0.363181 | + | 0.931719i | \(0.381691\pi\) | |||||||
\(572\) | 4.66379 | 0.195003 | ||||||||
\(573\) | 5.44864 | 0.227620 | ||||||||
\(574\) | −24.1119 | −1.00641 | ||||||||
\(575\) | −7.81311 | −0.325829 | ||||||||
\(576\) | −1.38673 | −0.0577805 | ||||||||
\(577\) | −6.32021 | −0.263114 | −0.131557 | − | 0.991309i | \(-0.541998\pi\) | ||||
−0.131557 | + | 0.991309i | \(0.541998\pi\) | |||||||
\(578\) | 14.7938 | 0.615339 | ||||||||
\(579\) | 13.8626 | 0.576110 | ||||||||
\(580\) | 0.373984 | 0.0155288 | ||||||||
\(581\) | 28.7910 | 1.19445 | ||||||||
\(582\) | −16.3760 | −0.678806 | ||||||||
\(583\) | 43.1834 | 1.78847 | ||||||||
\(584\) | −3.09187 | −0.127942 | ||||||||
\(585\) | −1.38673 | −0.0573343 | ||||||||
\(586\) | −15.1264 | −0.624865 | ||||||||
\(587\) | −19.0343 | −0.785629 | −0.392815 | − | 0.919618i | \(-0.628499\pi\) | ||||
−0.392815 | + | 0.919618i | \(0.628499\pi\) | |||||||
\(588\) | −10.9580 | −0.451900 | ||||||||
\(589\) | −3.80214 | −0.156665 | ||||||||
\(590\) | −6.57218 | −0.270572 | ||||||||
\(591\) | 30.2441 | 1.24408 | ||||||||
\(592\) | −3.50437 | −0.144029 | ||||||||
\(593\) | −34.4793 | −1.41590 | −0.707948 | − | 0.706265i | \(-0.750379\pi\) | ||||
−0.707948 | + | 0.706265i | \(0.750379\pi\) | |||||||
\(594\) | −25.9856 | −1.06620 | ||||||||
\(595\) | 5.87178 | 0.240719 | ||||||||
\(596\) | −2.23059 | −0.0913686 | ||||||||
\(597\) | −27.1005 | −1.10915 | ||||||||
\(598\) | 7.81311 | 0.319502 | ||||||||
\(599\) | −0.626472 | −0.0255969 | −0.0127985 | − | 0.999918i | \(-0.504074\pi\) | ||||
−0.0127985 | + | 0.999918i | \(0.504074\pi\) | |||||||
\(600\) | 1.27014 | 0.0518534 | ||||||||
\(601\) | 1.01389 | 0.0413575 | 0.0206788 | − | 0.999786i | \(-0.493417\pi\) | ||||
0.0206788 | + | 0.999786i | \(0.493417\pi\) | |||||||
\(602\) | 12.6736 | 0.516537 | ||||||||
\(603\) | 13.6224 | 0.554746 | ||||||||
\(604\) | 7.29600 | 0.296870 | ||||||||
\(605\) | 10.7510 | 0.437088 | ||||||||
\(606\) | −15.3100 | −0.621926 | ||||||||
\(607\) | 23.2688 | 0.944450 | 0.472225 | − | 0.881478i | \(-0.343451\pi\) | ||||
0.472225 | + | 0.881478i | \(0.343451\pi\) | |||||||
\(608\) | −3.80214 | −0.154197 | ||||||||
\(609\) | 1.87780 | 0.0760922 | ||||||||
\(610\) | −4.49166 | −0.181862 | ||||||||
\(611\) | 6.40206 | 0.259000 | ||||||||
\(612\) | 2.05977 | 0.0832614 | ||||||||
\(613\) | 10.7274 | 0.433276 | 0.216638 | − | 0.976252i | \(-0.430491\pi\) | ||||
0.216638 | + | 0.976252i | \(0.430491\pi\) | |||||||
\(614\) | −11.7199 | −0.472976 | ||||||||
\(615\) | 7.74714 | 0.312395 | ||||||||
\(616\) | 18.4367 | 0.742834 | ||||||||
\(617\) | 21.4576 | 0.863852 | 0.431926 | − | 0.901909i | \(-0.357834\pi\) | ||||
0.431926 | + | 0.901909i | \(0.357834\pi\) | |||||||
\(618\) | −14.1171 | −0.567871 | ||||||||
\(619\) | 0.293212 | 0.0117852 | 0.00589258 | − | 0.999983i | \(-0.498124\pi\) | ||||
0.00589258 | + | 0.999983i | \(0.498124\pi\) | |||||||
\(620\) | −1.00000 | −0.0401610 | ||||||||
\(621\) | −43.5330 | −1.74692 | ||||||||
\(622\) | 10.8823 | 0.436340 | ||||||||
\(623\) | 24.9259 | 0.998633 | ||||||||
\(624\) | −1.27014 | −0.0508465 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 21.9056 | 0.875525 | ||||||||
\(627\) | −22.5227 | −0.899471 | ||||||||
\(628\) | −17.2073 | −0.686644 | ||||||||
\(629\) | 5.20520 | 0.207545 | ||||||||
\(630\) | −5.48196 | −0.218406 | ||||||||
\(631\) | −23.2622 | −0.926053 | −0.463027 | − | 0.886344i | \(-0.653237\pi\) | ||||
−0.463027 | + | 0.886344i | \(0.653237\pi\) | |||||||
\(632\) | −0.814856 | −0.0324132 | ||||||||
\(633\) | 27.7942 | 1.10472 | ||||||||
\(634\) | −9.03617 | −0.358872 | ||||||||
\(635\) | 13.0366 | 0.517343 | ||||||||
\(636\) | −11.7606 | −0.466340 | ||||||||
\(637\) | 8.62737 | 0.341829 | ||||||||
\(638\) | −1.74418 | −0.0690528 | ||||||||
\(639\) | −13.0999 | −0.518223 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −12.2104 | −0.482281 | −0.241140 | − | 0.970490i | \(-0.577521\pi\) | ||||
−0.241140 | + | 0.970490i | \(0.577521\pi\) | |||||||
\(642\) | −5.70652 | −0.225218 | ||||||||
\(643\) | 0.445546 | 0.0175706 | 0.00878531 | − | 0.999961i | \(-0.497204\pi\) | ||||
0.00878531 | + | 0.999961i | \(0.497204\pi\) | |||||||
\(644\) | 30.8864 | 1.21709 | ||||||||
\(645\) | −4.07202 | −0.160336 | ||||||||
\(646\) | 5.64749 | 0.222197 | ||||||||
\(647\) | −32.2420 | −1.26757 | −0.633783 | − | 0.773511i | \(-0.718499\pi\) | ||||
−0.633783 | + | 0.773511i | \(0.718499\pi\) | |||||||
\(648\) | 2.91678 | 0.114582 | ||||||||
\(649\) | 30.6513 | 1.20317 | ||||||||
\(650\) | −1.00000 | −0.0392232 | ||||||||
\(651\) | −5.02107 | −0.196791 | ||||||||
\(652\) | 11.3738 | 0.445433 | ||||||||
\(653\) | −9.25671 | −0.362243 | −0.181121 | − | 0.983461i | \(-0.557973\pi\) | ||||
−0.181121 | + | 0.983461i | \(0.557973\pi\) | |||||||
\(654\) | −18.8576 | −0.737390 | ||||||||
\(655\) | 20.8577 | 0.814976 | ||||||||
\(656\) | −6.09942 | −0.238142 | ||||||||
\(657\) | −4.28759 | −0.167275 | ||||||||
\(658\) | 25.3083 | 0.986620 | ||||||||
\(659\) | −38.8000 | −1.51143 | −0.755717 | − | 0.654899i | \(-0.772711\pi\) | ||||
−0.755717 | + | 0.654899i | \(0.772711\pi\) | |||||||
\(660\) | −5.92369 | −0.230579 | ||||||||
\(661\) | 35.4376 | 1.37836 | 0.689181 | − | 0.724589i | \(-0.257971\pi\) | ||||
0.689181 | + | 0.724589i | \(0.257971\pi\) | |||||||
\(662\) | 2.78825 | 0.108368 | ||||||||
\(663\) | 1.88660 | 0.0732695 | ||||||||
\(664\) | 7.28306 | 0.282638 | ||||||||
\(665\) | −15.0304 | −0.582855 | ||||||||
\(666\) | −4.85963 | −0.188307 | ||||||||
\(667\) | −2.92198 | −0.113139 | ||||||||
\(668\) | −2.35504 | −0.0911191 | ||||||||
\(669\) | −34.2869 | −1.32561 | ||||||||
\(670\) | 9.82335 | 0.379509 | ||||||||
\(671\) | 20.9482 | 0.808695 | ||||||||
\(672\) | −5.02107 | −0.193692 | ||||||||
\(673\) | −23.2486 | −0.896168 | −0.448084 | − | 0.893991i | \(-0.647894\pi\) | ||||
−0.448084 | + | 0.893991i | \(0.647894\pi\) | |||||||
\(674\) | 3.80184 | 0.146441 | ||||||||
\(675\) | 5.57178 | 0.214458 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −40.6547 | −1.56249 | −0.781243 | − | 0.624227i | \(-0.785414\pi\) | ||||
−0.781243 | + | 0.624227i | \(0.785414\pi\) | |||||||
\(678\) | 21.8537 | 0.839287 | ||||||||
\(679\) | 50.9679 | 1.95597 | ||||||||
\(680\) | 1.48534 | 0.0569603 | ||||||||
\(681\) | 17.3427 | 0.664575 | ||||||||
\(682\) | 4.66379 | 0.178586 | ||||||||
\(683\) | −2.20624 | −0.0844194 | −0.0422097 | − | 0.999109i | \(-0.513440\pi\) | ||||
−0.0422097 | + | 0.999109i | \(0.513440\pi\) | |||||||
\(684\) | −5.27256 | −0.201601 | ||||||||
\(685\) | −8.09473 | −0.309284 | ||||||||
\(686\) | 6.43321 | 0.245621 | ||||||||
\(687\) | 5.72443 | 0.218401 | ||||||||
\(688\) | 3.20595 | 0.122226 | ||||||||
\(689\) | 9.25929 | 0.352751 | ||||||||
\(690\) | −9.92378 | −0.377792 | ||||||||
\(691\) | 42.3349 | 1.61050 | 0.805248 | − | 0.592938i | \(-0.202032\pi\) | ||||
0.805248 | + | 0.592938i | \(0.202032\pi\) | |||||||
\(692\) | 20.9496 | 0.796385 | ||||||||
\(693\) | 25.5667 | 0.971199 | ||||||||
\(694\) | 32.7754 | 1.24414 | ||||||||
\(695\) | −8.76155 | −0.332344 | ||||||||
\(696\) | 0.475013 | 0.0180053 | ||||||||
\(697\) | 9.05973 | 0.343162 | ||||||||
\(698\) | −23.5163 | −0.890104 | ||||||||
\(699\) | 5.75932 | 0.217838 | ||||||||
\(700\) | −3.95315 | −0.149415 | ||||||||
\(701\) | −27.5771 | −1.04157 | −0.520786 | − | 0.853687i | \(-0.674361\pi\) | ||||
−0.520786 | + | 0.853687i | \(0.674361\pi\) | |||||||
\(702\) | −5.57178 | −0.210293 | ||||||||
\(703\) | −13.3241 | −0.502529 | ||||||||
\(704\) | 4.66379 | 0.175773 | ||||||||
\(705\) | −8.13155 | −0.306252 | ||||||||
\(706\) | 18.9683 | 0.713883 | ||||||||
\(707\) | 47.6502 | 1.79207 | ||||||||
\(708\) | −8.34762 | −0.313723 | ||||||||
\(709\) | 37.4283 | 1.40565 | 0.702824 | − | 0.711364i | \(-0.251922\pi\) | ||||
0.702824 | + | 0.711364i | \(0.251922\pi\) | |||||||
\(710\) | −9.44658 | −0.354524 | ||||||||
\(711\) | −1.12999 | −0.0423778 | ||||||||
\(712\) | 6.30532 | 0.236302 | ||||||||
\(713\) | 7.81311 | 0.292603 | ||||||||
\(714\) | 7.45801 | 0.279109 | ||||||||
\(715\) | 4.66379 | 0.174416 | ||||||||
\(716\) | −19.4658 | −0.727470 | ||||||||
\(717\) | 24.1484 | 0.901839 | ||||||||
\(718\) | −17.0190 | −0.635142 | ||||||||
\(719\) | −10.3837 | −0.387246 | −0.193623 | − | 0.981076i | \(-0.562024\pi\) | ||||
−0.193623 | + | 0.981076i | \(0.562024\pi\) | |||||||
\(720\) | −1.38673 | −0.0516805 | ||||||||
\(721\) | 43.9373 | 1.63631 | ||||||||
\(722\) | 4.54370 | 0.169099 | ||||||||
\(723\) | 33.8074 | 1.25731 | ||||||||
\(724\) | −5.12519 | −0.190476 | ||||||||
\(725\) | 0.373984 | 0.0138894 | ||||||||
\(726\) | 13.6553 | 0.506794 | ||||||||
\(727\) | 46.3517 | 1.71909 | 0.859544 | − | 0.511061i | \(-0.170747\pi\) | ||||
0.859544 | + | 0.511061i | \(0.170747\pi\) | |||||||
\(728\) | 3.95315 | 0.146513 | ||||||||
\(729\) | 25.2757 | 0.936137 | ||||||||
\(730\) | −3.09187 | −0.114435 | ||||||||
\(731\) | −4.76193 | −0.176127 | ||||||||
\(732\) | −5.70506 | −0.210865 | ||||||||
\(733\) | −37.4186 | −1.38209 | −0.691043 | − | 0.722814i | \(-0.742849\pi\) | ||||
−0.691043 | + | 0.722814i | \(0.742849\pi\) | |||||||
\(734\) | 27.4066 | 1.01159 | ||||||||
\(735\) | −10.9580 | −0.404192 | ||||||||
\(736\) | 7.81311 | 0.287995 | ||||||||
\(737\) | −45.8141 | −1.68758 | ||||||||
\(738\) | −8.45826 | −0.311353 | ||||||||
\(739\) | −42.5966 | −1.56694 | −0.783471 | − | 0.621429i | \(-0.786552\pi\) | ||||
−0.783471 | + | 0.621429i | \(0.786552\pi\) | |||||||
\(740\) | −3.50437 | −0.128823 | ||||||||
\(741\) | −4.82927 | −0.177408 | ||||||||
\(742\) | 36.6033 | 1.34375 | ||||||||
\(743\) | 33.0581 | 1.21278 | 0.606392 | − | 0.795166i | \(-0.292616\pi\) | ||||
0.606392 | + | 0.795166i | \(0.292616\pi\) | |||||||
\(744\) | −1.27014 | −0.0465658 | ||||||||
\(745\) | −2.23059 | −0.0817226 | ||||||||
\(746\) | 14.4935 | 0.530646 | ||||||||
\(747\) | 10.0997 | 0.369527 | ||||||||
\(748\) | −6.92733 | −0.253288 | ||||||||
\(749\) | 17.7607 | 0.648963 | ||||||||
\(750\) | 1.27014 | 0.0463791 | ||||||||
\(751\) | −12.7191 | −0.464125 | −0.232063 | − | 0.972701i | \(-0.574547\pi\) | ||||
−0.232063 | + | 0.972701i | \(0.574547\pi\) | |||||||
\(752\) | 6.40206 | 0.233459 | ||||||||
\(753\) | 28.9437 | 1.05477 | ||||||||
\(754\) | −0.373984 | −0.0136197 | ||||||||
\(755\) | 7.29600 | 0.265528 | ||||||||
\(756\) | −22.0261 | −0.801081 | ||||||||
\(757\) | 16.7647 | 0.609325 | 0.304662 | − | 0.952460i | \(-0.401456\pi\) | ||||
0.304662 | + | 0.952460i | \(0.401456\pi\) | |||||||
\(758\) | −5.12722 | −0.186229 | ||||||||
\(759\) | 46.2824 | 1.67995 | ||||||||
\(760\) | −3.80214 | −0.137918 | ||||||||
\(761\) | 39.7382 | 1.44051 | 0.720254 | − | 0.693710i | \(-0.244025\pi\) | ||||
0.720254 | + | 0.693710i | \(0.244025\pi\) | |||||||
\(762\) | 16.5584 | 0.599848 | ||||||||
\(763\) | 58.6916 | 2.12478 | ||||||||
\(764\) | −4.28978 | −0.155199 | ||||||||
\(765\) | 2.05977 | 0.0744713 | ||||||||
\(766\) | 4.34716 | 0.157069 | ||||||||
\(767\) | 6.57218 | 0.237308 | ||||||||
\(768\) | −1.27014 | −0.0458324 | ||||||||
\(769\) | 18.6585 | 0.672842 | 0.336421 | − | 0.941712i | \(-0.390783\pi\) | ||||
0.336421 | + | 0.941712i | \(0.390783\pi\) | |||||||
\(770\) | 18.4367 | 0.664411 | ||||||||
\(771\) | 13.1355 | 0.473064 | ||||||||
\(772\) | −10.9142 | −0.392810 | ||||||||
\(773\) | 17.3426 | 0.623770 | 0.311885 | − | 0.950120i | \(-0.399040\pi\) | ||||
0.311885 | + | 0.950120i | \(0.399040\pi\) | |||||||
\(774\) | 4.44579 | 0.159801 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 12.8930 | 0.462832 | ||||||||
\(777\) | −17.5957 | −0.631242 | ||||||||
\(778\) | −16.4912 | −0.591237 | ||||||||
\(779\) | −23.1909 | −0.830899 | ||||||||
\(780\) | −1.27014 | −0.0454785 | ||||||||
\(781\) | 44.0569 | 1.57648 | ||||||||
\(782\) | −11.6051 | −0.414999 | ||||||||
\(783\) | 2.08376 | 0.0744674 | ||||||||
\(784\) | 8.62737 | 0.308120 | ||||||||
\(785\) | −17.2073 | −0.614153 | ||||||||
\(786\) | 26.4922 | 0.944947 | ||||||||
\(787\) | −10.9153 | −0.389088 | −0.194544 | − | 0.980894i | \(-0.562323\pi\) | ||||
−0.194544 | + | 0.980894i | \(0.562323\pi\) | |||||||
\(788\) | −23.8116 | −0.848251 | ||||||||
\(789\) | 17.0249 | 0.606103 | ||||||||
\(790\) | −0.814856 | −0.0289913 | ||||||||
\(791\) | −68.0166 | −2.41839 | ||||||||
\(792\) | 6.46743 | 0.229810 | ||||||||
\(793\) | 4.49166 | 0.159503 | ||||||||
\(794\) | 9.92346 | 0.352170 | ||||||||
\(795\) | −11.7606 | −0.417107 | ||||||||
\(796\) | 21.3366 | 0.756255 | ||||||||
\(797\) | −32.2537 | −1.14249 | −0.571243 | − | 0.820781i | \(-0.693538\pi\) | ||||
−0.571243 | + | 0.820781i | \(0.693538\pi\) | |||||||
\(798\) | −19.0908 | −0.675808 | ||||||||
\(799\) | −9.50926 | −0.336414 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 8.74379 | 0.308947 | ||||||||
\(802\) | −29.1905 | −1.03075 | ||||||||
\(803\) | 14.4198 | 0.508865 | ||||||||
\(804\) | 12.4771 | 0.440033 | ||||||||
\(805\) | 30.8864 | 1.08860 | ||||||||
\(806\) | 1.00000 | 0.0352235 | ||||||||
\(807\) | 39.2271 | 1.38086 | ||||||||
\(808\) | 12.0537 | 0.424049 | ||||||||
\(809\) | −26.4704 | −0.930650 | −0.465325 | − | 0.885140i | \(-0.654062\pi\) | ||||
−0.465325 | + | 0.885140i | \(0.654062\pi\) | |||||||
\(810\) | 2.91678 | 0.102485 | ||||||||
\(811\) | 11.9476 | 0.419536 | 0.209768 | − | 0.977751i | \(-0.432729\pi\) | ||||
0.209768 | + | 0.977751i | \(0.432729\pi\) | |||||||
\(812\) | −1.47841 | −0.0518821 | ||||||||
\(813\) | −7.41536 | −0.260068 | ||||||||
\(814\) | 16.3437 | 0.572845 | ||||||||
\(815\) | 11.3738 | 0.398407 | ||||||||
\(816\) | 1.88660 | 0.0660442 | ||||||||
\(817\) | 12.1895 | 0.426456 | ||||||||
\(818\) | 13.9128 | 0.486451 | ||||||||
\(819\) | 5.48196 | 0.191555 | ||||||||
\(820\) | −6.09942 | −0.213001 | ||||||||
\(821\) | 39.7075 | 1.38580 | 0.692901 | − | 0.721033i | \(-0.256332\pi\) | ||||
0.692901 | + | 0.721033i | \(0.256332\pi\) | |||||||
\(822\) | −10.2815 | −0.358608 | ||||||||
\(823\) | 49.0554 | 1.70996 | 0.854982 | − | 0.518658i | \(-0.173568\pi\) | ||||
0.854982 | + | 0.518658i | \(0.173568\pi\) | |||||||
\(824\) | 11.1145 | 0.387193 | ||||||||
\(825\) | −5.92369 | −0.206236 | ||||||||
\(826\) | 25.9808 | 0.903987 | ||||||||
\(827\) | 45.3421 | 1.57670 | 0.788349 | − | 0.615228i | \(-0.210936\pi\) | ||||
0.788349 | + | 0.615228i | \(0.210936\pi\) | |||||||
\(828\) | 10.8347 | 0.376532 | ||||||||
\(829\) | 28.1278 | 0.976918 | 0.488459 | − | 0.872587i | \(-0.337559\pi\) | ||||
0.488459 | + | 0.872587i | \(0.337559\pi\) | |||||||
\(830\) | 7.28306 | 0.252799 | ||||||||
\(831\) | −27.0677 | −0.938969 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −12.8146 | −0.444000 | ||||||||
\(834\) | −11.1284 | −0.385346 | ||||||||
\(835\) | −2.35504 | −0.0814994 | ||||||||
\(836\) | 17.7324 | 0.613288 | ||||||||
\(837\) | −5.57178 | −0.192589 | ||||||||
\(838\) | 19.0311 | 0.657417 | ||||||||
\(839\) | 23.0958 | 0.797354 | 0.398677 | − | 0.917091i | \(-0.369469\pi\) | ||||
0.398677 | + | 0.917091i | \(0.369469\pi\) | |||||||
\(840\) | −5.02107 | −0.173243 | ||||||||
\(841\) | −28.8601 | −0.995177 | ||||||||
\(842\) | −11.0709 | −0.381527 | ||||||||
\(843\) | 26.3051 | 0.905995 | ||||||||
\(844\) | −21.8827 | −0.753233 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 8.87795 | 0.305230 | ||||||||
\(847\) | −42.5001 | −1.46032 | ||||||||
\(848\) | 9.25929 | 0.317965 | ||||||||
\(849\) | 3.58199 | 0.122933 | ||||||||
\(850\) | 1.48534 | 0.0509469 | ||||||||
\(851\) | 27.3800 | 0.938576 | ||||||||
\(852\) | −11.9985 | −0.411063 | ||||||||
\(853\) | −15.9738 | −0.546932 | −0.273466 | − | 0.961882i | \(-0.588170\pi\) | ||||
−0.273466 | + | 0.961882i | \(0.588170\pi\) | |||||||
\(854\) | 17.7562 | 0.607604 | ||||||||
\(855\) | −5.27256 | −0.180318 | ||||||||
\(856\) | 4.49281 | 0.153561 | ||||||||
\(857\) | 25.0465 | 0.855572 | 0.427786 | − | 0.903880i | \(-0.359294\pi\) | ||||
0.427786 | + | 0.903880i | \(0.359294\pi\) | |||||||
\(858\) | 5.92369 | 0.202231 | ||||||||
\(859\) | 7.00985 | 0.239173 | 0.119586 | − | 0.992824i | \(-0.461843\pi\) | ||||
0.119586 | + | 0.992824i | \(0.461843\pi\) | |||||||
\(860\) | 3.20595 | 0.109322 | ||||||||
\(861\) | −30.6256 | −1.04372 | ||||||||
\(862\) | −28.2467 | −0.962086 | ||||||||
\(863\) | 18.1111 | 0.616508 | 0.308254 | − | 0.951304i | \(-0.400255\pi\) | ||||
0.308254 | + | 0.951304i | \(0.400255\pi\) | |||||||
\(864\) | −5.57178 | −0.189556 | ||||||||
\(865\) | 20.9496 | 0.712308 | ||||||||
\(866\) | 10.7500 | 0.365300 | ||||||||
\(867\) | 18.7902 | 0.638149 | ||||||||
\(868\) | 3.95315 | 0.134179 | ||||||||
\(869\) | 3.80032 | 0.128917 | ||||||||
\(870\) | 0.475013 | 0.0161045 | ||||||||
\(871\) | −9.82335 | −0.332852 | ||||||||
\(872\) | 14.8468 | 0.502776 | ||||||||
\(873\) | 17.8792 | 0.605118 | ||||||||
\(874\) | 29.7066 | 1.00484 | ||||||||
\(875\) | −3.95315 | −0.133641 | ||||||||
\(876\) | −3.92712 | −0.132685 | ||||||||
\(877\) | −30.0882 | −1.01601 | −0.508003 | − | 0.861355i | \(-0.669616\pi\) | ||||
−0.508003 | + | 0.861355i | \(0.669616\pi\) | |||||||
\(878\) | 17.5758 | 0.593154 | ||||||||
\(879\) | −19.2127 | −0.648028 | ||||||||
\(880\) | 4.66379 | 0.157216 | ||||||||
\(881\) | −20.0590 | −0.675804 | −0.337902 | − | 0.941181i | \(-0.609717\pi\) | ||||
−0.337902 | + | 0.941181i | \(0.609717\pi\) | |||||||
\(882\) | 11.9638 | 0.402844 | ||||||||
\(883\) | 53.5511 | 1.80214 | 0.901070 | − | 0.433675i | \(-0.142783\pi\) | ||||
0.901070 | + | 0.433675i | \(0.142783\pi\) | |||||||
\(884\) | −1.48534 | −0.0499575 | ||||||||
\(885\) | −8.34762 | −0.280602 | ||||||||
\(886\) | 9.28428 | 0.311911 | ||||||||
\(887\) | −55.5046 | −1.86366 | −0.931831 | − | 0.362891i | \(-0.881790\pi\) | ||||
−0.931831 | + | 0.362891i | \(0.881790\pi\) | |||||||
\(888\) | −4.45106 | −0.149368 | ||||||||
\(889\) | −51.5357 | −1.72845 | ||||||||
\(890\) | 6.30532 | 0.211355 | ||||||||
\(891\) | −13.6032 | −0.455725 | ||||||||
\(892\) | 26.9945 | 0.903843 | ||||||||
\(893\) | 24.3416 | 0.814559 | ||||||||
\(894\) | −2.83317 | −0.0947555 | ||||||||
\(895\) | −19.4658 | −0.650669 | ||||||||
\(896\) | 3.95315 | 0.132065 | ||||||||
\(897\) | 9.92378 | 0.331345 | ||||||||
\(898\) | 8.32815 | 0.277914 | ||||||||
\(899\) | −0.373984 | −0.0124731 | ||||||||
\(900\) | −1.38673 | −0.0462244 | ||||||||
\(901\) | −13.7532 | −0.458186 | ||||||||
\(902\) | 28.4464 | 0.947162 | ||||||||
\(903\) | 16.0973 | 0.535684 | ||||||||
\(904\) | −17.2057 | −0.572253 | ||||||||
\(905\) | −5.12519 | −0.170367 | ||||||||
\(906\) | 9.26697 | 0.307874 | ||||||||
\(907\) | 48.5593 | 1.61239 | 0.806193 | − | 0.591652i | \(-0.201524\pi\) | ||||
0.806193 | + | 0.591652i | \(0.201524\pi\) | |||||||
\(908\) | −13.6541 | −0.453128 | ||||||||
\(909\) | 16.7153 | 0.554412 | ||||||||
\(910\) | 3.95315 | 0.131046 | ||||||||
\(911\) | 28.9992 | 0.960785 | 0.480393 | − | 0.877054i | \(-0.340494\pi\) | ||||
0.480393 | + | 0.877054i | \(0.340494\pi\) | |||||||
\(912\) | −4.82927 | −0.159913 | ||||||||
\(913\) | −33.9667 | −1.12413 | ||||||||
\(914\) | 41.2452 | 1.36427 | ||||||||
\(915\) | −5.70506 | −0.188603 | ||||||||
\(916\) | −4.50691 | −0.148913 | ||||||||
\(917\) | −82.4534 | −2.72285 | ||||||||
\(918\) | 8.27601 | 0.273149 | ||||||||
\(919\) | −25.7246 | −0.848577 | −0.424289 | − | 0.905527i | \(-0.639476\pi\) | ||||
−0.424289 | + | 0.905527i | \(0.639476\pi\) | |||||||
\(920\) | 7.81311 | 0.257591 | ||||||||
\(921\) | −14.8859 | −0.490509 | ||||||||
\(922\) | 24.8401 | 0.818066 | ||||||||
\(923\) | 9.44658 | 0.310938 | ||||||||
\(924\) | 23.4172 | 0.770370 | ||||||||
\(925\) | −3.50437 | −0.115223 | ||||||||
\(926\) | −21.8812 | −0.719061 | ||||||||
\(927\) | 15.4129 | 0.506225 | ||||||||
\(928\) | −0.373984 | −0.0122766 | ||||||||
\(929\) | −5.02671 | −0.164921 | −0.0824605 | − | 0.996594i | \(-0.526278\pi\) | ||||
−0.0824605 | + | 0.996594i | \(0.526278\pi\) | |||||||
\(930\) | −1.27014 | −0.0416497 | ||||||||
\(931\) | 32.8025 | 1.07506 | ||||||||
\(932\) | −4.53438 | −0.148529 | ||||||||
\(933\) | 13.8221 | 0.452515 | ||||||||
\(934\) | −2.00619 | −0.0656446 | ||||||||
\(935\) | −6.92733 | −0.226548 | ||||||||
\(936\) | 1.38673 | 0.0453268 | ||||||||
\(937\) | 36.0203 | 1.17673 | 0.588366 | − | 0.808595i | \(-0.299771\pi\) | ||||
0.588366 | + | 0.808595i | \(0.299771\pi\) | |||||||
\(938\) | −38.8332 | −1.26795 | ||||||||
\(939\) | 27.8233 | 0.907979 | ||||||||
\(940\) | 6.40206 | 0.208812 | ||||||||
\(941\) | 37.8548 | 1.23403 | 0.617015 | − | 0.786951i | \(-0.288342\pi\) | ||||
0.617015 | + | 0.786951i | \(0.288342\pi\) | |||||||
\(942\) | −21.8557 | −0.712097 | ||||||||
\(943\) | 47.6554 | 1.55187 | ||||||||
\(944\) | 6.57218 | 0.213906 | ||||||||
\(945\) | −22.0261 | −0.716508 | ||||||||
\(946\) | −14.9519 | −0.486127 | ||||||||
\(947\) | −3.56214 | −0.115754 | −0.0578770 | − | 0.998324i | \(-0.518433\pi\) | ||||
−0.0578770 | + | 0.998324i | \(0.518433\pi\) | |||||||
\(948\) | −1.03499 | −0.0336148 | ||||||||
\(949\) | 3.09187 | 0.100366 | ||||||||
\(950\) | −3.80214 | −0.123358 | ||||||||
\(951\) | −11.4772 | −0.372175 | ||||||||
\(952\) | −5.87178 | −0.190305 | ||||||||
\(953\) | 27.6781 | 0.896583 | 0.448291 | − | 0.893887i | \(-0.352033\pi\) | ||||
0.448291 | + | 0.893887i | \(0.352033\pi\) | |||||||
\(954\) | 12.8402 | 0.415715 | ||||||||
\(955\) | −4.28978 | −0.138814 | ||||||||
\(956\) | −19.0123 | −0.614903 | ||||||||
\(957\) | −2.21536 | −0.0716125 | ||||||||
\(958\) | −11.5411 | −0.372877 | ||||||||
\(959\) | 31.9997 | 1.03332 | ||||||||
\(960\) | −1.27014 | −0.0409937 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 3.50437 | 0.112985 | ||||||||
\(963\) | 6.23033 | 0.200769 | ||||||||
\(964\) | −26.6169 | −0.857274 | ||||||||
\(965\) | −10.9142 | −0.351340 | ||||||||
\(966\) | 39.2301 | 1.26221 | ||||||||
\(967\) | −26.6772 | −0.857880 | −0.428940 | − | 0.903333i | \(-0.641113\pi\) | ||||
−0.428940 | + | 0.903333i | \(0.641113\pi\) | |||||||
\(968\) | −10.7510 | −0.345549 | ||||||||
\(969\) | 7.17313 | 0.230434 | ||||||||
\(970\) | 12.8930 | 0.413970 | ||||||||
\(971\) | −29.3861 | −0.943043 | −0.471522 | − | 0.881854i | \(-0.656295\pi\) | ||||
−0.471522 | + | 0.881854i | \(0.656295\pi\) | |||||||
\(972\) | −13.0106 | −0.417316 | ||||||||
\(973\) | 34.6357 | 1.11037 | ||||||||
\(974\) | −21.5414 | −0.690230 | ||||||||
\(975\) | −1.27014 | −0.0406772 | ||||||||
\(976\) | 4.49166 | 0.143775 | ||||||||
\(977\) | −28.5134 | −0.912224 | −0.456112 | − | 0.889922i | \(-0.650758\pi\) | ||||
−0.456112 | + | 0.889922i | \(0.650758\pi\) | |||||||
\(978\) | 14.4464 | 0.461944 | ||||||||
\(979\) | −29.4067 | −0.939842 | ||||||||
\(980\) | 8.62737 | 0.275591 | ||||||||
\(981\) | 20.5886 | 0.657342 | ||||||||
\(982\) | −7.25724 | −0.231588 | ||||||||
\(983\) | −49.5439 | −1.58021 | −0.790103 | − | 0.612974i | \(-0.789973\pi\) | ||||
−0.790103 | + | 0.612974i | \(0.789973\pi\) | |||||||
\(984\) | −7.74714 | −0.246970 | ||||||||
\(985\) | −23.8116 | −0.758699 | ||||||||
\(986\) | 0.555494 | 0.0176905 | ||||||||
\(987\) | 32.1452 | 1.02319 | ||||||||
\(988\) | 3.80214 | 0.120962 | ||||||||
\(989\) | −25.0484 | −0.796494 | ||||||||
\(990\) | 6.46743 | 0.205548 | ||||||||
\(991\) | 2.03355 | 0.0645979 | 0.0322989 | − | 0.999478i | \(-0.489717\pi\) | ||||
0.0322989 | + | 0.999478i | \(0.489717\pi\) | |||||||
\(992\) | 1.00000 | 0.0317500 | ||||||||
\(993\) | 3.54148 | 0.112385 | ||||||||
\(994\) | 37.3437 | 1.18447 | ||||||||
\(995\) | 21.3366 | 0.676415 | ||||||||
\(996\) | 9.25055 | 0.293115 | ||||||||
\(997\) | 9.50217 | 0.300937 | 0.150468 | − | 0.988615i | \(-0.451922\pi\) | ||||
0.150468 | + | 0.988615i | \(0.451922\pi\) | |||||||
\(998\) | −14.8212 | −0.469157 | ||||||||
\(999\) | −19.5256 | −0.617763 |
(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 | 4030.2.a.d.1.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4030.2.a.d.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial |