Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(1,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, 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("1183.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.7674048.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.10939\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.10939 | 1.49156 | 0.745781 | − | 0.666191i | \(-0.232076\pi\) | ||||
0.745781 | + | 0.666191i | \(0.232076\pi\) | |||||||
\(3\) | 2.26165 | 1.30576 | 0.652882 | − | 0.757460i | \(-0.273560\pi\) | ||||
0.652882 | + | 0.757460i | \(0.273560\pi\) | |||||||
\(4\) | 2.44952 | 1.22476 | ||||||||
\(5\) | 3.60178 | 1.61076 | 0.805382 | − | 0.592756i | \(-0.201960\pi\) | ||||
0.805382 | + | 0.592756i | \(0.201960\pi\) | |||||||
\(6\) | 4.77070 | 1.94763 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0.948212 | 0.335243 | ||||||||
\(9\) | 2.11505 | 0.705018 | ||||||||
\(10\) | 7.59755 | 2.40256 | ||||||||
\(11\) | −0.886384 | −0.267255 | −0.133627 | − | 0.991032i | \(-0.542663\pi\) | ||||
−0.133627 | + | 0.991032i | \(0.542663\pi\) | |||||||
\(12\) | 5.53995 | 1.59925 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.10939 | −0.563758 | ||||||||
\(15\) | 8.14596 | 2.10328 | ||||||||
\(16\) | −2.89889 | −0.724723 | ||||||||
\(17\) | −4.96016 | −1.20302 | −0.601508 | − | 0.798867i | \(-0.705433\pi\) | ||||
−0.601508 | + | 0.798867i | \(0.705433\pi\) | |||||||
\(18\) | 4.46147 | 1.05158 | ||||||||
\(19\) | −2.37878 | −0.545729 | −0.272864 | − | 0.962053i | \(-0.587971\pi\) | ||||
−0.272864 | + | 0.962053i | \(0.587971\pi\) | |||||||
\(20\) | 8.82263 | 1.97280 | ||||||||
\(21\) | −2.26165 | −0.493532 | ||||||||
\(22\) | −1.86973 | −0.398628 | ||||||||
\(23\) | −3.85851 | −0.804555 | −0.402278 | − | 0.915518i | \(-0.631781\pi\) | ||||
−0.402278 | + | 0.915518i | \(0.631781\pi\) | |||||||
\(24\) | 2.14452 | 0.437749 | ||||||||
\(25\) | 7.97282 | 1.59456 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.00144 | −0.385177 | ||||||||
\(28\) | −2.44952 | −0.462916 | ||||||||
\(29\) | 1.28197 | 0.238056 | 0.119028 | − | 0.992891i | \(-0.462022\pi\) | ||||
0.119028 | + | 0.992891i | \(0.462022\pi\) | |||||||
\(30\) | 17.1830 | 3.13717 | ||||||||
\(31\) | −8.46921 | −1.52111 | −0.760557 | − | 0.649271i | \(-0.775074\pi\) | ||||
−0.760557 | + | 0.649271i | \(0.775074\pi\) | |||||||
\(32\) | −8.01131 | −1.41621 | ||||||||
\(33\) | −2.00469 | −0.348972 | ||||||||
\(34\) | −10.4629 | −1.79437 | ||||||||
\(35\) | −3.60178 | −0.608812 | ||||||||
\(36\) | 5.18087 | 0.863478 | ||||||||
\(37\) | 9.63812 | 1.58450 | 0.792249 | − | 0.610198i | \(-0.208910\pi\) | ||||
0.792249 | + | 0.610198i | \(0.208910\pi\) | |||||||
\(38\) | −5.01776 | −0.813988 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.41525 | 0.539998 | ||||||||
\(41\) | 12.0841 | 1.88722 | 0.943612 | − | 0.331053i | \(-0.107404\pi\) | ||||
0.943612 | + | 0.331053i | \(0.107404\pi\) | |||||||
\(42\) | −4.77070 | −0.736134 | ||||||||
\(43\) | −3.64250 | −0.555476 | −0.277738 | − | 0.960657i | \(-0.589585\pi\) | ||||
−0.277738 | + | 0.960657i | \(0.589585\pi\) | |||||||
\(44\) | −2.17122 | −0.327323 | ||||||||
\(45\) | 7.61796 | 1.13562 | ||||||||
\(46\) | −8.13910 | −1.20004 | ||||||||
\(47\) | −2.98229 | −0.435012 | −0.217506 | − | 0.976059i | \(-0.569792\pi\) | ||||
−0.217506 | + | 0.976059i | \(0.569792\pi\) | |||||||
\(48\) | −6.55628 | −0.946317 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 16.8178 | 2.37839 | ||||||||
\(51\) | −11.2181 | −1.57085 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.92032 | 0.675858 | 0.337929 | − | 0.941172i | \(-0.390274\pi\) | ||||
0.337929 | + | 0.941172i | \(0.390274\pi\) | |||||||
\(54\) | −4.22181 | −0.574516 | ||||||||
\(55\) | −3.19256 | −0.430485 | ||||||||
\(56\) | −0.948212 | −0.126710 | ||||||||
\(57\) | −5.37995 | −0.712592 | ||||||||
\(58\) | 2.70418 | 0.355076 | ||||||||
\(59\) | 7.32746 | 0.953954 | 0.476977 | − | 0.878916i | \(-0.341732\pi\) | ||||
0.476977 | + | 0.878916i | \(0.341732\pi\) | |||||||
\(60\) | 19.9537 | 2.57601 | ||||||||
\(61\) | −1.53926 | −0.197082 | −0.0985412 | − | 0.995133i | \(-0.531418\pi\) | ||||
−0.0985412 | + | 0.995133i | \(0.531418\pi\) | |||||||
\(62\) | −17.8648 | −2.26884 | ||||||||
\(63\) | −2.11505 | −0.266472 | ||||||||
\(64\) | −11.1012 | −1.38765 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.22867 | −0.520513 | ||||||||
\(67\) | 8.42649 | 1.02946 | 0.514730 | − | 0.857352i | \(-0.327892\pi\) | ||||
0.514730 | + | 0.857352i | \(0.327892\pi\) | |||||||
\(68\) | −12.1500 | −1.47341 | ||||||||
\(69\) | −8.72660 | −1.05056 | ||||||||
\(70\) | −7.59755 | −0.908081 | ||||||||
\(71\) | 6.44888 | 0.765342 | 0.382671 | − | 0.923885i | \(-0.375004\pi\) | ||||
0.382671 | + | 0.923885i | \(0.375004\pi\) | |||||||
\(72\) | 2.00552 | 0.236353 | ||||||||
\(73\) | 7.14859 | 0.836679 | 0.418340 | − | 0.908291i | \(-0.362612\pi\) | ||||
0.418340 | + | 0.908291i | \(0.362612\pi\) | |||||||
\(74\) | 20.3305 | 2.36338 | ||||||||
\(75\) | 18.0317 | 2.08212 | ||||||||
\(76\) | −5.82686 | −0.668386 | ||||||||
\(77\) | 0.886384 | 0.101013 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.757551 | 0.0852311 | 0.0426156 | − | 0.999092i | \(-0.486431\pi\) | ||||
0.0426156 | + | 0.999092i | \(0.486431\pi\) | |||||||
\(80\) | −10.4412 | −1.16736 | ||||||||
\(81\) | −10.8717 | −1.20797 | ||||||||
\(82\) | 25.4901 | 2.81491 | ||||||||
\(83\) | 4.76766 | 0.523319 | 0.261659 | − | 0.965160i | \(-0.415730\pi\) | ||||
0.261659 | + | 0.965160i | \(0.415730\pi\) | |||||||
\(84\) | −5.53995 | −0.604458 | ||||||||
\(85\) | −17.8654 | −1.93778 | ||||||||
\(86\) | −7.68344 | −0.828527 | ||||||||
\(87\) | 2.89937 | 0.310845 | ||||||||
\(88\) | −0.840480 | −0.0895955 | ||||||||
\(89\) | −3.61884 | −0.383596 | −0.191798 | − | 0.981434i | \(-0.561432\pi\) | ||||
−0.191798 | + | 0.981434i | \(0.561432\pi\) | |||||||
\(90\) | 16.0692 | 1.69385 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.45150 | −0.985387 | ||||||||
\(93\) | −19.1544 | −1.98622 | ||||||||
\(94\) | −6.29081 | −0.648848 | ||||||||
\(95\) | −8.56783 | −0.879040 | ||||||||
\(96\) | −18.1188 | −1.84924 | ||||||||
\(97\) | 0.463300 | 0.0470409 | 0.0235205 | − | 0.999723i | \(-0.492513\pi\) | ||||
0.0235205 | + | 0.999723i | \(0.492513\pi\) | |||||||
\(98\) | 2.10939 | 0.213080 | ||||||||
\(99\) | −1.87475 | −0.188419 | ||||||||
\(100\) | 19.5296 | 1.95296 | ||||||||
\(101\) | 5.82303 | 0.579413 | 0.289707 | − | 0.957115i | \(-0.406442\pi\) | ||||
0.289707 | + | 0.957115i | \(0.406442\pi\) | |||||||
\(102\) | −23.6634 | −2.34303 | ||||||||
\(103\) | 8.23888 | 0.811801 | 0.405901 | − | 0.913917i | \(-0.366958\pi\) | ||||
0.405901 | + | 0.913917i | \(0.366958\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.14596 | −0.794964 | ||||||||
\(106\) | 10.3789 | 1.00809 | ||||||||
\(107\) | −3.83260 | −0.370511 | −0.185256 | − | 0.982690i | \(-0.559311\pi\) | ||||
−0.185256 | + | 0.982690i | \(0.559311\pi\) | |||||||
\(108\) | −4.90256 | −0.471749 | ||||||||
\(109\) | 10.4180 | 0.997867 | 0.498934 | − | 0.866640i | \(-0.333725\pi\) | ||||
0.498934 | + | 0.866640i | \(0.333725\pi\) | |||||||
\(110\) | −6.73435 | −0.642095 | ||||||||
\(111\) | 21.7980 | 2.06898 | ||||||||
\(112\) | 2.89889 | 0.273920 | ||||||||
\(113\) | −4.91011 | −0.461904 | −0.230952 | − | 0.972965i | \(-0.574184\pi\) | ||||
−0.230952 | + | 0.972965i | \(0.574184\pi\) | |||||||
\(114\) | −11.3484 | −1.06288 | ||||||||
\(115\) | −13.8975 | −1.29595 | ||||||||
\(116\) | 3.14022 | 0.291562 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.4565 | 1.42288 | ||||||||
\(119\) | 4.96016 | 0.454697 | ||||||||
\(120\) | 7.72409 | 0.705110 | ||||||||
\(121\) | −10.2143 | −0.928575 | ||||||||
\(122\) | −3.24690 | −0.293961 | ||||||||
\(123\) | 27.3301 | 2.46427 | ||||||||
\(124\) | −20.7455 | −1.86300 | ||||||||
\(125\) | 10.7074 | 0.957702 | ||||||||
\(126\) | −4.46147 | −0.397459 | ||||||||
\(127\) | −12.3102 | −1.09235 | −0.546175 | − | 0.837671i | \(-0.683917\pi\) | ||||
−0.546175 | + | 0.837671i | \(0.683917\pi\) | |||||||
\(128\) | −7.39409 | −0.653551 | ||||||||
\(129\) | −8.23805 | −0.725320 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.20265 | −0.716669 | −0.358335 | − | 0.933593i | \(-0.616655\pi\) | ||||
−0.358335 | + | 0.933593i | \(0.616655\pi\) | |||||||
\(132\) | −4.91053 | −0.427406 | ||||||||
\(133\) | 2.37878 | 0.206266 | ||||||||
\(134\) | 17.7747 | 1.53550 | ||||||||
\(135\) | −7.20874 | −0.620429 | ||||||||
\(136\) | −4.70328 | −0.403303 | ||||||||
\(137\) | 7.45555 | 0.636971 | 0.318485 | − | 0.947928i | \(-0.396826\pi\) | ||||
0.318485 | + | 0.947928i | \(0.396826\pi\) | |||||||
\(138\) | −18.4078 | −1.56697 | ||||||||
\(139\) | 16.6806 | 1.41483 | 0.707413 | − | 0.706800i | \(-0.249862\pi\) | ||||
0.707413 | + | 0.706800i | \(0.249862\pi\) | |||||||
\(140\) | −8.82263 | −0.745648 | ||||||||
\(141\) | −6.74490 | −0.568023 | ||||||||
\(142\) | 13.6032 | 1.14156 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −6.13131 | −0.510943 | ||||||||
\(145\) | 4.61738 | 0.383453 | ||||||||
\(146\) | 15.0792 | 1.24796 | ||||||||
\(147\) | 2.26165 | 0.186538 | ||||||||
\(148\) | 23.6088 | 1.94063 | ||||||||
\(149\) | 2.52163 | 0.206580 | 0.103290 | − | 0.994651i | \(-0.467063\pi\) | ||||
0.103290 | + | 0.994651i | \(0.467063\pi\) | |||||||
\(150\) | 38.0359 | 3.10562 | ||||||||
\(151\) | 15.8972 | 1.29370 | 0.646849 | − | 0.762618i | \(-0.276086\pi\) | ||||
0.646849 | + | 0.762618i | \(0.276086\pi\) | |||||||
\(152\) | −2.25558 | −0.182952 | ||||||||
\(153\) | −10.4910 | −0.848148 | ||||||||
\(154\) | 1.86973 | 0.150667 | ||||||||
\(155\) | −30.5042 | −2.45016 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.9831 | 1.03616 | 0.518082 | − | 0.855331i | \(-0.326646\pi\) | ||||
0.518082 | + | 0.855331i | \(0.326646\pi\) | |||||||
\(158\) | 1.59797 | 0.127128 | ||||||||
\(159\) | 11.1280 | 0.882511 | ||||||||
\(160\) | −28.8550 | −2.28119 | ||||||||
\(161\) | 3.85851 | 0.304093 | ||||||||
\(162\) | −22.9327 | −1.80176 | ||||||||
\(163\) | −2.31948 | −0.181676 | −0.0908378 | − | 0.995866i | \(-0.528954\pi\) | ||||
−0.0908378 | + | 0.995866i | \(0.528954\pi\) | |||||||
\(164\) | 29.6003 | 2.31140 | ||||||||
\(165\) | −7.22045 | −0.562111 | ||||||||
\(166\) | 10.0569 | 0.780563 | ||||||||
\(167\) | 13.7918 | 1.06724 | 0.533622 | − | 0.845723i | \(-0.320831\pi\) | ||||
0.533622 | + | 0.845723i | \(0.320831\pi\) | |||||||
\(168\) | −2.14452 | −0.165453 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −37.6851 | −2.89031 | ||||||||
\(171\) | −5.03124 | −0.384748 | ||||||||
\(172\) | −8.92237 | −0.680324 | ||||||||
\(173\) | −3.68432 | −0.280113 | −0.140057 | − | 0.990143i | \(-0.544728\pi\) | ||||
−0.140057 | + | 0.990143i | \(0.544728\pi\) | |||||||
\(174\) | 6.11590 | 0.463645 | ||||||||
\(175\) | −7.97282 | −0.602688 | ||||||||
\(176\) | 2.56953 | 0.193686 | ||||||||
\(177\) | 16.5721 | 1.24564 | ||||||||
\(178\) | −7.63353 | −0.572157 | ||||||||
\(179\) | −5.89277 | −0.440446 | −0.220223 | − | 0.975450i | \(-0.570678\pi\) | ||||
−0.220223 | + | 0.975450i | \(0.570678\pi\) | |||||||
\(180\) | 18.6603 | 1.39086 | ||||||||
\(181\) | 2.11543 | 0.157239 | 0.0786193 | − | 0.996905i | \(-0.474949\pi\) | ||||
0.0786193 | + | 0.996905i | \(0.474949\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.48127 | −0.257343 | ||||||||
\(184\) | −3.65869 | −0.269722 | ||||||||
\(185\) | 34.7144 | 2.55225 | ||||||||
\(186\) | −40.4040 | −2.96257 | ||||||||
\(187\) | 4.39661 | 0.321512 | ||||||||
\(188\) | −7.30518 | −0.532785 | ||||||||
\(189\) | 2.00144 | 0.145583 | ||||||||
\(190\) | −18.0729 | −1.31114 | ||||||||
\(191\) | −11.3667 | −0.822462 | −0.411231 | − | 0.911531i | \(-0.634901\pi\) | ||||
−0.411231 | + | 0.911531i | \(0.634901\pi\) | |||||||
\(192\) | −25.1070 | −1.81194 | ||||||||
\(193\) | −14.0894 | −1.01417 | −0.507087 | − | 0.861895i | \(-0.669278\pi\) | ||||
−0.507087 | + | 0.861895i | \(0.669278\pi\) | |||||||
\(194\) | 0.977279 | 0.0701645 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.44952 | 0.174966 | ||||||||
\(197\) | −22.9571 | −1.63563 | −0.817814 | − | 0.575482i | \(-0.804814\pi\) | ||||
−0.817814 | + | 0.575482i | \(0.804814\pi\) | |||||||
\(198\) | −3.95458 | −0.281040 | ||||||||
\(199\) | −3.14985 | −0.223287 | −0.111643 | − | 0.993748i | \(-0.535611\pi\) | ||||
−0.111643 | + | 0.993748i | \(0.535611\pi\) | |||||||
\(200\) | 7.55992 | 0.534567 | ||||||||
\(201\) | 19.0578 | 1.34423 | ||||||||
\(202\) | 12.2830 | 0.864231 | ||||||||
\(203\) | −1.28197 | −0.0899768 | ||||||||
\(204\) | −27.4791 | −1.92392 | ||||||||
\(205\) | 43.5244 | 3.03987 | ||||||||
\(206\) | 17.3790 | 1.21085 | ||||||||
\(207\) | −8.16096 | −0.567226 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.10851 | 0.145849 | ||||||||
\(210\) | −17.1830 | −1.18574 | ||||||||
\(211\) | −14.8638 | −1.02327 | −0.511634 | − | 0.859203i | \(-0.670960\pi\) | ||||
−0.511634 | + | 0.859203i | \(0.670960\pi\) | |||||||
\(212\) | 12.0524 | 0.827764 | ||||||||
\(213\) | 14.5851 | 0.999355 | ||||||||
\(214\) | −8.08444 | −0.552641 | ||||||||
\(215\) | −13.1195 | −0.894741 | ||||||||
\(216\) | −1.89779 | −0.129128 | ||||||||
\(217\) | 8.46921 | 0.574927 | ||||||||
\(218\) | 21.9757 | 1.48838 | ||||||||
\(219\) | 16.1676 | 1.09251 | ||||||||
\(220\) | −7.82024 | −0.527241 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 45.9805 | 3.08601 | ||||||||
\(223\) | 4.38089 | 0.293366 | 0.146683 | − | 0.989184i | \(-0.453140\pi\) | ||||
0.146683 | + | 0.989184i | \(0.453140\pi\) | |||||||
\(224\) | 8.01131 | 0.535278 | ||||||||
\(225\) | 16.8629 | 1.12420 | ||||||||
\(226\) | −10.3573 | −0.688959 | ||||||||
\(227\) | −13.5663 | −0.900428 | −0.450214 | − | 0.892921i | \(-0.648652\pi\) | ||||
−0.450214 | + | 0.892921i | \(0.648652\pi\) | |||||||
\(228\) | −13.1783 | −0.872754 | ||||||||
\(229\) | −16.5180 | −1.09154 | −0.545770 | − | 0.837935i | \(-0.683763\pi\) | ||||
−0.545770 | + | 0.837935i | \(0.683763\pi\) | |||||||
\(230\) | −29.3152 | −1.93299 | ||||||||
\(231\) | 2.00469 | 0.131899 | ||||||||
\(232\) | 1.21558 | 0.0798068 | ||||||||
\(233\) | −16.5026 | −1.08112 | −0.540561 | − | 0.841305i | \(-0.681788\pi\) | ||||
−0.540561 | + | 0.841305i | \(0.681788\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.7416 | −0.700702 | ||||||||
\(236\) | 17.9488 | 1.16836 | ||||||||
\(237\) | 1.71331 | 0.111292 | ||||||||
\(238\) | 10.4629 | 0.678210 | ||||||||
\(239\) | −30.4210 | −1.96777 | −0.983886 | − | 0.178796i | \(-0.942780\pi\) | ||||
−0.983886 | + | 0.178796i | \(0.942780\pi\) | |||||||
\(240\) | −23.6143 | −1.52429 | ||||||||
\(241\) | −29.5143 | −1.90119 | −0.950593 | − | 0.310440i | \(-0.899524\pi\) | ||||
−0.950593 | + | 0.310440i | \(0.899524\pi\) | |||||||
\(242\) | −21.5460 | −1.38503 | ||||||||
\(243\) | −18.5837 | −1.19214 | ||||||||
\(244\) | −3.77046 | −0.241379 | ||||||||
\(245\) | 3.60178 | 0.230109 | ||||||||
\(246\) | 57.6497 | 3.67561 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −8.03060 | −0.509944 | ||||||||
\(249\) | 10.7828 | 0.683331 | ||||||||
\(250\) | 22.5861 | 1.42847 | ||||||||
\(251\) | −12.9827 | −0.819459 | −0.409730 | − | 0.912207i | \(-0.634377\pi\) | ||||
−0.409730 | + | 0.912207i | \(0.634377\pi\) | |||||||
\(252\) | −5.18087 | −0.326364 | ||||||||
\(253\) | 3.42012 | 0.215021 | ||||||||
\(254\) | −25.9669 | −1.62931 | ||||||||
\(255\) | −40.4053 | −2.53028 | ||||||||
\(256\) | 6.60537 | 0.412836 | ||||||||
\(257\) | −4.58521 | −0.286018 | −0.143009 | − | 0.989721i | \(-0.545678\pi\) | ||||
−0.143009 | + | 0.989721i | \(0.545678\pi\) | |||||||
\(258\) | −17.3772 | −1.08186 | ||||||||
\(259\) | −9.63812 | −0.598884 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.71144 | 0.167834 | ||||||||
\(262\) | −17.3026 | −1.06896 | ||||||||
\(263\) | −2.66499 | −0.164330 | −0.0821652 | − | 0.996619i | \(-0.526184\pi\) | ||||
−0.0821652 | + | 0.996619i | \(0.526184\pi\) | |||||||
\(264\) | −1.90087 | −0.116990 | ||||||||
\(265\) | 17.7219 | 1.08865 | ||||||||
\(266\) | 5.01776 | 0.307659 | ||||||||
\(267\) | −8.18453 | −0.500885 | ||||||||
\(268\) | 20.6409 | 1.26084 | ||||||||
\(269\) | 11.9256 | 0.727119 | 0.363559 | − | 0.931571i | \(-0.381561\pi\) | ||||
0.363559 | + | 0.931571i | \(0.381561\pi\) | |||||||
\(270\) | −15.2060 | −0.925409 | ||||||||
\(271\) | 13.0283 | 0.791414 | 0.395707 | − | 0.918377i | \(-0.370500\pi\) | ||||
0.395707 | + | 0.918377i | \(0.370500\pi\) | |||||||
\(272\) | 14.3790 | 0.871853 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.7267 | 0.950082 | ||||||||
\(275\) | −7.06698 | −0.426155 | ||||||||
\(276\) | −21.3760 | −1.28668 | ||||||||
\(277\) | 21.3649 | 1.28369 | 0.641846 | − | 0.766833i | \(-0.278169\pi\) | ||||
0.641846 | + | 0.766833i | \(0.278169\pi\) | |||||||
\(278\) | 35.1858 | 2.11030 | ||||||||
\(279\) | −17.9128 | −1.07241 | ||||||||
\(280\) | −3.41525 | −0.204100 | ||||||||
\(281\) | −17.2678 | −1.03011 | −0.515054 | − | 0.857158i | \(-0.672228\pi\) | ||||
−0.515054 | + | 0.857158i | \(0.672228\pi\) | |||||||
\(282\) | −14.2276 | −0.847242 | ||||||||
\(283\) | −21.2402 | −1.26260 | −0.631299 | − | 0.775539i | \(-0.717478\pi\) | ||||
−0.631299 | + | 0.775539i | \(0.717478\pi\) | |||||||
\(284\) | 15.7967 | 0.937360 | ||||||||
\(285\) | −19.3774 | −1.14782 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0841 | −0.713304 | ||||||||
\(288\) | −16.9444 | −0.998456 | ||||||||
\(289\) | 7.60320 | 0.447247 | ||||||||
\(290\) | 9.73985 | 0.571944 | ||||||||
\(291\) | 1.04782 | 0.0614243 | ||||||||
\(292\) | 17.5106 | 1.02473 | ||||||||
\(293\) | −0.420060 | −0.0245402 | −0.0122701 | − | 0.999925i | \(-0.503906\pi\) | ||||
−0.0122701 | + | 0.999925i | \(0.503906\pi\) | |||||||
\(294\) | 4.77070 | 0.278233 | ||||||||
\(295\) | 26.3919 | 1.53660 | ||||||||
\(296\) | 9.13898 | 0.531192 | ||||||||
\(297\) | 1.77404 | 0.102940 | ||||||||
\(298\) | 5.31910 | 0.308127 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 44.1690 | 2.55010 | ||||||||
\(301\) | 3.64250 | 0.209950 | ||||||||
\(302\) | 33.5335 | 1.92963 | ||||||||
\(303\) | 13.1696 | 0.756577 | ||||||||
\(304\) | 6.89581 | 0.395502 | ||||||||
\(305\) | −5.54409 | −0.317453 | ||||||||
\(306\) | −22.1296 | −1.26507 | ||||||||
\(307\) | 14.0807 | 0.803628 | 0.401814 | − | 0.915721i | \(-0.368380\pi\) | ||||
0.401814 | + | 0.915721i | \(0.368380\pi\) | |||||||
\(308\) | 2.17122 | 0.123717 | ||||||||
\(309\) | 18.6335 | 1.06002 | ||||||||
\(310\) | −64.3453 | −3.65456 | ||||||||
\(311\) | 10.3848 | 0.588867 | 0.294434 | − | 0.955672i | \(-0.404869\pi\) | ||||
0.294434 | + | 0.955672i | \(0.404869\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.84759 | 0.387048 | 0.193524 | − | 0.981096i | \(-0.438008\pi\) | ||||
0.193524 | + | 0.981096i | \(0.438008\pi\) | |||||||
\(314\) | 27.3864 | 1.54550 | ||||||||
\(315\) | −7.61796 | −0.429223 | ||||||||
\(316\) | 1.85564 | 0.104388 | ||||||||
\(317\) | 0.701249 | 0.0393861 | 0.0196930 | − | 0.999806i | \(-0.493731\pi\) | ||||
0.0196930 | + | 0.999806i | \(0.493731\pi\) | |||||||
\(318\) | 23.4734 | 1.31632 | ||||||||
\(319\) | −1.13632 | −0.0636217 | ||||||||
\(320\) | −39.9840 | −2.23518 | ||||||||
\(321\) | −8.66799 | −0.483800 | ||||||||
\(322\) | 8.13910 | 0.453574 | ||||||||
\(323\) | 11.7991 | 0.656520 | ||||||||
\(324\) | −26.6305 | −1.47947 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.89268 | −0.270980 | ||||||||
\(327\) | 23.5619 | 1.30298 | ||||||||
\(328\) | 11.4583 | 0.632680 | ||||||||
\(329\) | 2.98229 | 0.164419 | ||||||||
\(330\) | −15.2307 | −0.838424 | ||||||||
\(331\) | −4.19865 | −0.230778 | −0.115389 | − | 0.993320i | \(-0.536812\pi\) | ||||
−0.115389 | + | 0.993320i | \(0.536812\pi\) | |||||||
\(332\) | 11.6785 | 0.640940 | ||||||||
\(333\) | 20.3851 | 1.11710 | ||||||||
\(334\) | 29.0923 | 1.59186 | ||||||||
\(335\) | 30.3504 | 1.65822 | ||||||||
\(336\) | 6.55628 | 0.357674 | ||||||||
\(337\) | 20.4278 | 1.11278 | 0.556388 | − | 0.830923i | \(-0.312187\pi\) | ||||
0.556388 | + | 0.830923i | \(0.312187\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.1049 | −0.603138 | ||||||||
\(340\) | −43.7617 | −2.37331 | ||||||||
\(341\) | 7.50697 | 0.406525 | ||||||||
\(342\) | −10.6128 | −0.573876 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −3.45386 | −0.186220 | ||||||||
\(345\) | −31.4313 | −1.69220 | ||||||||
\(346\) | −7.77165 | −0.417807 | ||||||||
\(347\) | 7.97000 | 0.427852 | 0.213926 | − | 0.976850i | \(-0.431375\pi\) | ||||
0.213926 | + | 0.976850i | \(0.431375\pi\) | |||||||
\(348\) | 7.10207 | 0.380711 | ||||||||
\(349\) | −21.5972 | −1.15607 | −0.578037 | − | 0.816011i | \(-0.696181\pi\) | ||||
−0.578037 | + | 0.816011i | \(0.696181\pi\) | |||||||
\(350\) | −16.8178 | −0.898947 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.10110 | 0.378490 | ||||||||
\(353\) | 21.6176 | 1.15059 | 0.575295 | − | 0.817946i | \(-0.304887\pi\) | ||||
0.575295 | + | 0.817946i | \(0.304887\pi\) | |||||||
\(354\) | 34.9571 | 1.85795 | ||||||||
\(355\) | 23.2275 | 1.23279 | ||||||||
\(356\) | −8.86441 | −0.469813 | ||||||||
\(357\) | 11.2181 | 0.593727 | ||||||||
\(358\) | −12.4301 | −0.656953 | ||||||||
\(359\) | −13.6834 | −0.722180 | −0.361090 | − | 0.932531i | \(-0.617595\pi\) | ||||
−0.361090 | + | 0.932531i | \(0.617595\pi\) | |||||||
\(360\) | 7.22344 | 0.380708 | ||||||||
\(361\) | −13.3414 | −0.702180 | ||||||||
\(362\) | 4.46226 | 0.234531 | ||||||||
\(363\) | −23.1012 | −1.21250 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.7477 | 1.34769 | ||||||||
\(366\) | −7.34335 | −0.383843 | ||||||||
\(367\) | −11.4128 | −0.595741 | −0.297871 | − | 0.954606i | \(-0.596276\pi\) | ||||
−0.297871 | + | 0.954606i | \(0.596276\pi\) | |||||||
\(368\) | 11.1854 | 0.583080 | ||||||||
\(369\) | 25.5586 | 1.33053 | ||||||||
\(370\) | 73.2261 | 3.80685 | ||||||||
\(371\) | −4.92032 | −0.255450 | ||||||||
\(372\) | −46.9190 | −2.43264 | ||||||||
\(373\) | −31.2808 | −1.61966 | −0.809830 | − | 0.586664i | \(-0.800441\pi\) | ||||
−0.809830 | + | 0.586664i | \(0.800441\pi\) | |||||||
\(374\) | 9.27416 | 0.479555 | ||||||||
\(375\) | 24.2164 | 1.25053 | ||||||||
\(376\) | −2.82784 | −0.145835 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4.22181 | 0.217146 | ||||||||
\(379\) | 27.4151 | 1.40822 | 0.704108 | − | 0.710093i | \(-0.251347\pi\) | ||||
0.704108 | + | 0.710093i | \(0.251347\pi\) | |||||||
\(380\) | −20.9871 | −1.07661 | ||||||||
\(381\) | −27.8412 | −1.42635 | ||||||||
\(382\) | −23.9767 | −1.22675 | ||||||||
\(383\) | −16.1006 | −0.822705 | −0.411352 | − | 0.911476i | \(-0.634943\pi\) | ||||
−0.411352 | + | 0.911476i | \(0.634943\pi\) | |||||||
\(384\) | −16.7228 | −0.853383 | ||||||||
\(385\) | 3.19256 | 0.162708 | ||||||||
\(386\) | −29.7199 | −1.51271 | ||||||||
\(387\) | −7.70408 | −0.391620 | ||||||||
\(388\) | 1.13486 | 0.0576139 | ||||||||
\(389\) | 21.1380 | 1.07174 | 0.535870 | − | 0.844301i | \(-0.319984\pi\) | ||||
0.535870 | + | 0.844301i | \(0.319984\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.1388 | 0.967893 | ||||||||
\(392\) | 0.948212 | 0.0478919 | ||||||||
\(393\) | −18.5515 | −0.935800 | ||||||||
\(394\) | −48.4255 | −2.43964 | ||||||||
\(395\) | 2.72853 | 0.137287 | ||||||||
\(396\) | −4.59224 | −0.230769 | ||||||||
\(397\) | 13.0984 | 0.657390 | 0.328695 | − | 0.944436i | \(-0.393391\pi\) | ||||
0.328695 | + | 0.944436i | \(0.393391\pi\) | |||||||
\(398\) | −6.64426 | −0.333046 | ||||||||
\(399\) | 5.37995 | 0.269335 | ||||||||
\(400\) | −23.1123 | −1.15562 | ||||||||
\(401\) | −19.4447 | −0.971022 | −0.485511 | − | 0.874230i | \(-0.661367\pi\) | ||||
−0.485511 | + | 0.874230i | \(0.661367\pi\) | |||||||
\(402\) | 40.2002 | 2.00501 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 14.2636 | 0.709642 | ||||||||
\(405\) | −39.1575 | −1.94575 | ||||||||
\(406\) | −2.70418 | −0.134206 | ||||||||
\(407\) | −8.54308 | −0.423465 | ||||||||
\(408\) | −10.6372 | −0.526618 | ||||||||
\(409\) | −24.0559 | −1.18949 | −0.594743 | − | 0.803916i | \(-0.702746\pi\) | ||||
−0.594743 | + | 0.803916i | \(0.702746\pi\) | |||||||
\(410\) | 91.8098 | 4.53416 | ||||||||
\(411\) | 16.8618 | 0.831733 | ||||||||
\(412\) | 20.1813 | 0.994261 | ||||||||
\(413\) | −7.32746 | −0.360561 | ||||||||
\(414\) | −17.2146 | −0.846053 | ||||||||
\(415\) | 17.1721 | 0.842944 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 37.7256 | 1.84743 | ||||||||
\(418\) | 4.44767 | 0.217542 | ||||||||
\(419\) | 39.0238 | 1.90644 | 0.953218 | − | 0.302283i | \(-0.0977487\pi\) | ||||
0.953218 | + | 0.302283i | \(0.0977487\pi\) | |||||||
\(420\) | −19.9537 | −0.973640 | ||||||||
\(421\) | −22.0284 | −1.07360 | −0.536799 | − | 0.843710i | \(-0.680367\pi\) | ||||
−0.536799 | + | 0.843710i | \(0.680367\pi\) | |||||||
\(422\) | −31.3536 | −1.52627 | ||||||||
\(423\) | −6.30771 | −0.306691 | ||||||||
\(424\) | 4.66551 | 0.226577 | ||||||||
\(425\) | −39.5465 | −1.91828 | ||||||||
\(426\) | 30.7657 | 1.49060 | ||||||||
\(427\) | 1.53926 | 0.0744902 | ||||||||
\(428\) | −9.38803 | −0.453787 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −27.6741 | −1.33456 | ||||||||
\(431\) | −35.8797 | −1.72826 | −0.864131 | − | 0.503267i | \(-0.832131\pi\) | ||||
−0.864131 | + | 0.503267i | \(0.832131\pi\) | |||||||
\(432\) | 5.80195 | 0.279147 | ||||||||
\(433\) | 12.2136 | 0.586946 | 0.293473 | − | 0.955967i | \(-0.405189\pi\) | ||||
0.293473 | + | 0.955967i | \(0.405189\pi\) | |||||||
\(434\) | 17.8648 | 0.857540 | ||||||||
\(435\) | 10.4429 | 0.500699 | ||||||||
\(436\) | 25.5192 | 1.22215 | ||||||||
\(437\) | 9.17853 | 0.439069 | ||||||||
\(438\) | 34.1037 | 1.62954 | ||||||||
\(439\) | −15.7553 | −0.751960 | −0.375980 | − | 0.926628i | \(-0.622694\pi\) | ||||
−0.375980 | + | 0.926628i | \(0.622694\pi\) | |||||||
\(440\) | −3.02722 | −0.144317 | ||||||||
\(441\) | 2.11505 | 0.100717 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.0706 | −0.716028 | −0.358014 | − | 0.933716i | \(-0.616546\pi\) | ||||
−0.358014 | + | 0.933716i | \(0.616546\pi\) | |||||||
\(444\) | 53.3947 | 2.53400 | ||||||||
\(445\) | −13.0342 | −0.617883 | ||||||||
\(446\) | 9.24099 | 0.437574 | ||||||||
\(447\) | 5.70305 | 0.269745 | ||||||||
\(448\) | 11.1012 | 0.524482 | ||||||||
\(449\) | 30.7826 | 1.45272 | 0.726360 | − | 0.687315i | \(-0.241211\pi\) | ||||
0.726360 | + | 0.687315i | \(0.241211\pi\) | |||||||
\(450\) | 35.5705 | 1.67681 | ||||||||
\(451\) | −10.7112 | −0.504370 | ||||||||
\(452\) | −12.0274 | −0.565722 | ||||||||
\(453\) | 35.9540 | 1.68926 | ||||||||
\(454\) | −28.6166 | −1.34304 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.10133 | −0.238892 | ||||||||
\(457\) | −7.75597 | −0.362809 | −0.181405 | − | 0.983409i | \(-0.558064\pi\) | ||||
−0.181405 | + | 0.983409i | \(0.558064\pi\) | |||||||
\(458\) | −34.8429 | −1.62810 | ||||||||
\(459\) | 9.92745 | 0.463374 | ||||||||
\(460\) | −34.0422 | −1.58723 | ||||||||
\(461\) | −1.47222 | −0.0685681 | −0.0342840 | − | 0.999412i | \(-0.510915\pi\) | ||||
−0.0342840 | + | 0.999412i | \(0.510915\pi\) | |||||||
\(462\) | 4.22867 | 0.196735 | ||||||||
\(463\) | 14.0366 | 0.652335 | 0.326168 | − | 0.945312i | \(-0.394243\pi\) | ||||
0.326168 | + | 0.945312i | \(0.394243\pi\) | |||||||
\(464\) | −3.71630 | −0.172525 | ||||||||
\(465\) | −68.9898 | −3.19933 | ||||||||
\(466\) | −34.8104 | −1.61256 | ||||||||
\(467\) | 31.3806 | 1.45212 | 0.726060 | − | 0.687631i | \(-0.241349\pi\) | ||||
0.726060 | + | 0.687631i | \(0.241349\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.42649 | −0.389099 | ||||||||
\(470\) | −22.6581 | −1.04514 | ||||||||
\(471\) | 29.3632 | 1.35298 | ||||||||
\(472\) | 6.94798 | 0.319807 | ||||||||
\(473\) | 3.22865 | 0.148454 | ||||||||
\(474\) | 3.61404 | 0.165999 | ||||||||
\(475\) | −18.9655 | −0.870199 | ||||||||
\(476\) | 12.1500 | 0.556895 | ||||||||
\(477\) | 10.4067 | 0.476492 | ||||||||
\(478\) | −64.1698 | −2.93506 | ||||||||
\(479\) | −41.1951 | −1.88225 | −0.941125 | − | 0.338059i | \(-0.890230\pi\) | ||||
−0.941125 | + | 0.338059i | \(0.890230\pi\) | |||||||
\(480\) | −65.2598 | −2.97869 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −62.2572 | −2.83574 | ||||||||
\(483\) | 8.72660 | 0.397074 | ||||||||
\(484\) | −25.0202 | −1.13728 | ||||||||
\(485\) | 1.66870 | 0.0757719 | ||||||||
\(486\) | −39.2002 | −1.77816 | ||||||||
\(487\) | −28.3265 | −1.28360 | −0.641798 | − | 0.766874i | \(-0.721811\pi\) | ||||
−0.641798 | + | 0.766874i | \(0.721811\pi\) | |||||||
\(488\) | −1.45955 | −0.0660706 | ||||||||
\(489\) | −5.24584 | −0.237225 | ||||||||
\(490\) | 7.59755 | 0.343222 | ||||||||
\(491\) | 34.7863 | 1.56988 | 0.784941 | − | 0.619571i | \(-0.212693\pi\) | ||||
0.784941 | + | 0.619571i | \(0.212693\pi\) | |||||||
\(492\) | 66.9455 | 3.01814 | ||||||||
\(493\) | −6.35879 | −0.286386 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.75244 | −0.303499 | ||||||||
\(496\) | 24.5513 | 1.10239 | ||||||||
\(497\) | −6.44888 | −0.289272 | ||||||||
\(498\) | 22.7451 | 1.01923 | ||||||||
\(499\) | −0.0694885 | −0.00311073 | −0.00155537 | − | 0.999999i | \(-0.500495\pi\) | ||||
−0.00155537 | + | 0.999999i | \(0.500495\pi\) | |||||||
\(500\) | 26.2281 | 1.17295 | ||||||||
\(501\) | 31.1923 | 1.39357 | ||||||||
\(502\) | −27.3855 | −1.22228 | ||||||||
\(503\) | 25.7372 | 1.14756 | 0.573782 | − | 0.819008i | \(-0.305476\pi\) | ||||
0.573782 | + | 0.819008i | \(0.305476\pi\) | |||||||
\(504\) | −2.00552 | −0.0893329 | ||||||||
\(505\) | 20.9733 | 0.933299 | ||||||||
\(506\) | 7.21437 | 0.320718 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −30.1540 | −1.33787 | ||||||||
\(509\) | −7.04000 | −0.312042 | −0.156021 | − | 0.987754i | \(-0.549867\pi\) | ||||
−0.156021 | + | 0.987754i | \(0.549867\pi\) | |||||||
\(510\) | −85.2304 | −3.77407 | ||||||||
\(511\) | −7.14859 | −0.316235 | ||||||||
\(512\) | 28.7215 | 1.26932 | ||||||||
\(513\) | 4.76097 | 0.210202 | ||||||||
\(514\) | −9.67199 | −0.426613 | ||||||||
\(515\) | 29.6746 | 1.30762 | ||||||||
\(516\) | −20.1793 | −0.888342 | ||||||||
\(517\) | 2.64346 | 0.116259 | ||||||||
\(518\) | −20.3305 | −0.893273 | ||||||||
\(519\) | −8.33263 | −0.365762 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.3253 | 0.715225 | 0.357613 | − | 0.933870i | \(-0.383591\pi\) | ||||
0.357613 | + | 0.933870i | \(0.383591\pi\) | |||||||
\(522\) | 5.71948 | 0.250335 | ||||||||
\(523\) | −7.08946 | −0.310000 | −0.155000 | − | 0.987914i | \(-0.549538\pi\) | ||||
−0.155000 | + | 0.987914i | \(0.549538\pi\) | |||||||
\(524\) | −20.0926 | −0.877748 | ||||||||
\(525\) | −18.0317 | −0.786968 | ||||||||
\(526\) | −5.62150 | −0.245109 | ||||||||
\(527\) | 42.0086 | 1.82993 | ||||||||
\(528\) | 5.81138 | 0.252908 | ||||||||
\(529\) | −8.11189 | −0.352691 | ||||||||
\(530\) | 37.3824 | 1.62379 | ||||||||
\(531\) | 15.4980 | 0.672555 | ||||||||
\(532\) | 5.82686 | 0.252626 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −17.2644 | −0.747102 | ||||||||
\(535\) | −13.8042 | −0.596807 | ||||||||
\(536\) | 7.99010 | 0.345120 | ||||||||
\(537\) | −13.3274 | −0.575118 | ||||||||
\(538\) | 25.1558 | 1.08454 | ||||||||
\(539\) | −0.886384 | −0.0381793 | ||||||||
\(540\) | −17.6579 | −0.759877 | ||||||||
\(541\) | 25.5162 | 1.09703 | 0.548515 | − | 0.836141i | \(-0.315194\pi\) | ||||
0.548515 | + | 0.836141i | \(0.315194\pi\) | |||||||
\(542\) | 27.4818 | 1.18044 | ||||||||
\(543\) | 4.78436 | 0.205316 | ||||||||
\(544\) | 39.7374 | 1.70373 | ||||||||
\(545\) | 37.5235 | 1.60733 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.3073 | −0.568978 | −0.284489 | − | 0.958679i | \(-0.591824\pi\) | ||||
−0.284489 | + | 0.958679i | \(0.591824\pi\) | |||||||
\(548\) | 18.2625 | 0.780136 | ||||||||
\(549\) | −3.25562 | −0.138947 | ||||||||
\(550\) | −14.9070 | −0.635637 | ||||||||
\(551\) | −3.04952 | −0.129914 | ||||||||
\(552\) | −8.27466 | −0.352193 | ||||||||
\(553\) | −0.757551 | −0.0322143 | ||||||||
\(554\) | 45.0669 | 1.91471 | ||||||||
\(555\) | 78.5118 | 3.33264 | ||||||||
\(556\) | 40.8594 | 1.73282 | ||||||||
\(557\) | 17.0071 | 0.720612 | 0.360306 | − | 0.932834i | \(-0.382672\pi\) | ||||
0.360306 | + | 0.932834i | \(0.382672\pi\) | |||||||
\(558\) | −37.7851 | −1.59957 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 10.4412 | 0.441220 | ||||||||
\(561\) | 9.94358 | 0.419818 | ||||||||
\(562\) | −36.4244 | −1.53647 | ||||||||
\(563\) | −24.9193 | −1.05022 | −0.525111 | − | 0.851034i | \(-0.675976\pi\) | ||||
−0.525111 | + | 0.851034i | \(0.675976\pi\) | |||||||
\(564\) | −16.5218 | −0.695691 | ||||||||
\(565\) | −17.6851 | −0.744019 | ||||||||
\(566\) | −44.8038 | −1.88325 | ||||||||
\(567\) | 10.8717 | 0.456569 | ||||||||
\(568\) | 6.11491 | 0.256576 | ||||||||
\(569\) | 5.88129 | 0.246557 | 0.123278 | − | 0.992372i | \(-0.460659\pi\) | ||||
0.123278 | + | 0.992372i | \(0.460659\pi\) | |||||||
\(570\) | −40.8745 | −1.71204 | ||||||||
\(571\) | 8.92622 | 0.373551 | 0.186775 | − | 0.982403i | \(-0.440196\pi\) | ||||
0.186775 | + | 0.982403i | \(0.440196\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.7074 | −1.07394 | ||||||||
\(574\) | −25.4901 | −1.06394 | ||||||||
\(575\) | −30.7632 | −1.28291 | ||||||||
\(576\) | −23.4796 | −0.978317 | ||||||||
\(577\) | 36.1933 | 1.50675 | 0.753374 | − | 0.657592i | \(-0.228425\pi\) | ||||
0.753374 | + | 0.657592i | \(0.228425\pi\) | |||||||
\(578\) | 16.0381 | 0.667097 | ||||||||
\(579\) | −31.8652 | −1.32427 | ||||||||
\(580\) | 11.3104 | 0.469638 | ||||||||
\(581\) | −4.76766 | −0.197796 | ||||||||
\(582\) | 2.21026 | 0.0916183 | ||||||||
\(583\) | −4.36130 | −0.180626 | ||||||||
\(584\) | 6.77838 | 0.280491 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.886069 | −0.0366032 | ||||||||
\(587\) | 36.4895 | 1.50608 | 0.753041 | − | 0.657974i | \(-0.228586\pi\) | ||||
0.753041 | + | 0.657974i | \(0.228586\pi\) | |||||||
\(588\) | 5.53995 | 0.228464 | ||||||||
\(589\) | 20.1463 | 0.830116 | ||||||||
\(590\) | 55.6708 | 2.29193 | ||||||||
\(591\) | −51.9210 | −2.13574 | ||||||||
\(592\) | −27.9399 | −1.14832 | ||||||||
\(593\) | 34.9930 | 1.43699 | 0.718495 | − | 0.695533i | \(-0.244832\pi\) | ||||
0.718495 | + | 0.695533i | \(0.244832\pi\) | |||||||
\(594\) | 3.74215 | 0.153542 | ||||||||
\(595\) | 17.8654 | 0.732410 | ||||||||
\(596\) | 6.17679 | 0.253011 | ||||||||
\(597\) | −7.12385 | −0.291560 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.5052 | −1.32812 | −0.664062 | − | 0.747677i | \(-0.731169\pi\) | ||||
−0.664062 | + | 0.747677i | \(0.731169\pi\) | |||||||
\(600\) | 17.0979 | 0.698018 | ||||||||
\(601\) | 20.0780 | 0.819000 | 0.409500 | − | 0.912310i | \(-0.365703\pi\) | ||||
0.409500 | + | 0.912310i | \(0.365703\pi\) | |||||||
\(602\) | 7.68344 | 0.313154 | ||||||||
\(603\) | 17.8225 | 0.725788 | ||||||||
\(604\) | 38.9406 | 1.58447 | ||||||||
\(605\) | −36.7897 | −1.49572 | ||||||||
\(606\) | 27.7799 | 1.12848 | ||||||||
\(607\) | 9.71601 | 0.394361 | 0.197180 | − | 0.980367i | \(-0.436822\pi\) | ||||
0.197180 | + | 0.980367i | \(0.436822\pi\) | |||||||
\(608\) | 19.0571 | 0.772868 | ||||||||
\(609\) | −2.89937 | −0.117488 | ||||||||
\(610\) | −11.6946 | −0.473502 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −25.6979 | −1.03878 | ||||||||
\(613\) | −11.8816 | −0.479893 | −0.239947 | − | 0.970786i | \(-0.577130\pi\) | ||||
−0.239947 | + | 0.970786i | \(0.577130\pi\) | |||||||
\(614\) | 29.7017 | 1.19866 | ||||||||
\(615\) | 98.4368 | 3.96936 | ||||||||
\(616\) | 0.840480 | 0.0338639 | ||||||||
\(617\) | 19.9884 | 0.804705 | 0.402352 | − | 0.915485i | \(-0.368193\pi\) | ||||
0.402352 | + | 0.915485i | \(0.368193\pi\) | |||||||
\(618\) | 39.3052 | 1.58109 | ||||||||
\(619\) | 41.7176 | 1.67677 | 0.838386 | − | 0.545078i | \(-0.183500\pi\) | ||||
0.838386 | + | 0.545078i | \(0.183500\pi\) | |||||||
\(620\) | −74.7207 | −3.00086 | ||||||||
\(621\) | 7.72257 | 0.309896 | ||||||||
\(622\) | 21.9056 | 0.878333 | ||||||||
\(623\) | 3.61884 | 0.144986 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.29828 | −0.0519312 | ||||||||
\(626\) | 14.4442 | 0.577307 | ||||||||
\(627\) | 4.76871 | 0.190444 | ||||||||
\(628\) | 31.8023 | 1.26905 | ||||||||
\(629\) | −47.8066 | −1.90618 | ||||||||
\(630\) | −16.0692 | −0.640213 | ||||||||
\(631\) | 17.6415 | 0.702296 | 0.351148 | − | 0.936320i | \(-0.385791\pi\) | ||||
0.351148 | + | 0.936320i | \(0.385791\pi\) | |||||||
\(632\) | 0.718319 | 0.0285732 | ||||||||
\(633\) | −33.6168 | −1.33615 | ||||||||
\(634\) | 1.47921 | 0.0587468 | ||||||||
\(635\) | −44.3385 | −1.75952 | ||||||||
\(636\) | 27.2584 | 1.08086 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.39694 | −0.0948958 | ||||||||
\(639\) | 13.6397 | 0.539580 | ||||||||
\(640\) | −26.6319 | −1.05272 | ||||||||
\(641\) | −10.9202 | −0.431324 | −0.215662 | − | 0.976468i | \(-0.569191\pi\) | ||||
−0.215662 | + | 0.976468i | \(0.569191\pi\) | |||||||
\(642\) | −18.2842 | −0.721618 | ||||||||
\(643\) | −17.6351 | −0.695462 | −0.347731 | − | 0.937594i | \(-0.613048\pi\) | ||||
−0.347731 | + | 0.937594i | \(0.613048\pi\) | |||||||
\(644\) | 9.45150 | 0.372441 | ||||||||
\(645\) | −29.6716 | −1.16832 | ||||||||
\(646\) | 24.8889 | 0.979241 | ||||||||
\(647\) | 16.6726 | 0.655469 | 0.327735 | − | 0.944770i | \(-0.393715\pi\) | ||||
0.327735 | + | 0.944770i | \(0.393715\pi\) | |||||||
\(648\) | −10.3087 | −0.404963 | ||||||||
\(649\) | −6.49495 | −0.254949 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.1544 | 0.750719 | ||||||||
\(652\) | −5.68161 | −0.222509 | ||||||||
\(653\) | −6.77329 | −0.265059 | −0.132530 | − | 0.991179i | \(-0.542310\pi\) | ||||
−0.132530 | + | 0.991179i | \(0.542310\pi\) | |||||||
\(654\) | 49.7013 | 1.94347 | ||||||||
\(655\) | −29.5441 | −1.15439 | ||||||||
\(656\) | −35.0306 | −1.36772 | ||||||||
\(657\) | 15.1197 | 0.589874 | ||||||||
\(658\) | 6.29081 | 0.245241 | ||||||||
\(659\) | 33.5361 | 1.30638 | 0.653190 | − | 0.757194i | \(-0.273430\pi\) | ||||
0.653190 | + | 0.757194i | \(0.273430\pi\) | |||||||
\(660\) | −17.6866 | −0.688451 | ||||||||
\(661\) | 25.1661 | 0.978848 | 0.489424 | − | 0.872046i | \(-0.337207\pi\) | ||||
0.489424 | + | 0.872046i | \(0.337207\pi\) | |||||||
\(662\) | −8.85657 | −0.344221 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.52075 | 0.175439 | ||||||||
\(665\) | 8.56783 | 0.332246 | ||||||||
\(666\) | 43.0002 | 1.66622 | ||||||||
\(667\) | −4.94651 | −0.191529 | ||||||||
\(668\) | 33.7833 | 1.30712 | ||||||||
\(669\) | 9.90802 | 0.383066 | ||||||||
\(670\) | 64.0207 | 2.47334 | ||||||||
\(671\) | 1.36438 | 0.0526713 | ||||||||
\(672\) | 18.1188 | 0.698947 | ||||||||
\(673\) | −1.85468 | −0.0714927 | −0.0357464 | − | 0.999361i | \(-0.511381\pi\) | ||||
−0.0357464 | + | 0.999361i | \(0.511381\pi\) | |||||||
\(674\) | 43.0902 | 1.65977 | ||||||||
\(675\) | −15.9571 | −0.614189 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.7209 | −0.565770 | −0.282885 | − | 0.959154i | \(-0.591291\pi\) | ||||
−0.282885 | + | 0.959154i | \(0.591291\pi\) | |||||||
\(678\) | −23.4246 | −0.899618 | ||||||||
\(679\) | −0.463300 | −0.0177798 | ||||||||
\(680\) | −16.9402 | −0.649627 | ||||||||
\(681\) | −30.6822 | −1.17575 | ||||||||
\(682\) | 15.8351 | 0.606358 | ||||||||
\(683\) | 7.94353 | 0.303951 | 0.151975 | − | 0.988384i | \(-0.451437\pi\) | ||||
0.151975 | + | 0.988384i | \(0.451437\pi\) | |||||||
\(684\) | −12.3241 | −0.471224 | ||||||||
\(685\) | 26.8533 | 1.02601 | ||||||||
\(686\) | −2.10939 | −0.0805368 | ||||||||
\(687\) | −37.3579 | −1.42529 | ||||||||
\(688\) | 10.5592 | 0.402566 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −66.3008 | −2.52403 | ||||||||
\(691\) | 10.2307 | 0.389193 | 0.194597 | − | 0.980883i | \(-0.437660\pi\) | ||||
0.194597 | + | 0.980883i | \(0.437660\pi\) | |||||||
\(692\) | −9.02481 | −0.343072 | ||||||||
\(693\) | 1.87475 | 0.0712159 | ||||||||
\(694\) | 16.8118 | 0.638168 | ||||||||
\(695\) | 60.0797 | 2.27895 | ||||||||
\(696\) | 2.74922 | 0.104209 | ||||||||
\(697\) | −59.9392 | −2.27036 | ||||||||
\(698\) | −45.5570 | −1.72436 | ||||||||
\(699\) | −37.3231 | −1.41169 | ||||||||
\(700\) | −19.5296 | −0.738148 | ||||||||
\(701\) | 16.5978 | 0.626891 | 0.313445 | − | 0.949606i | \(-0.398517\pi\) | ||||
0.313445 | + | 0.949606i | \(0.398517\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.9269 | −0.864706 | ||||||||
\(704\) | 9.83992 | 0.370856 | ||||||||
\(705\) | −24.2936 | −0.914951 | ||||||||
\(706\) | 45.5999 | 1.71618 | ||||||||
\(707\) | −5.82303 | −0.218998 | ||||||||
\(708\) | 40.5938 | 1.52561 | ||||||||
\(709\) | 47.8659 | 1.79764 | 0.898820 | − | 0.438318i | \(-0.144426\pi\) | ||||
0.898820 | + | 0.438318i | \(0.144426\pi\) | |||||||
\(710\) | 48.9957 | 1.83878 | ||||||||
\(711\) | 1.60226 | 0.0600895 | ||||||||
\(712\) | −3.43142 | −0.128598 | ||||||||
\(713\) | 32.6785 | 1.22382 | ||||||||
\(714\) | 23.6634 | 0.885581 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −14.4344 | −0.539441 | ||||||||
\(717\) | −68.8017 | −2.56944 | ||||||||
\(718\) | −28.8635 | −1.07718 | ||||||||
\(719\) | −38.0922 | −1.42060 | −0.710300 | − | 0.703899i | \(-0.751441\pi\) | ||||
−0.710300 | + | 0.703899i | \(0.751441\pi\) | |||||||
\(720\) | −22.0836 | −0.823009 | ||||||||
\(721\) | −8.23888 | −0.306832 | ||||||||
\(722\) | −28.1423 | −1.04735 | ||||||||
\(723\) | −66.7511 | −2.48250 | ||||||||
\(724\) | 5.18179 | 0.192580 | ||||||||
\(725\) | 10.2209 | 0.379596 | ||||||||
\(726\) | −48.7294 | −1.80852 | ||||||||
\(727\) | −15.4059 | −0.571374 | −0.285687 | − | 0.958323i | \(-0.592222\pi\) | ||||
−0.285687 | + | 0.958323i | \(0.592222\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.41460 | −0.348689 | ||||||||
\(730\) | 54.3118 | 2.01017 | ||||||||
\(731\) | 18.0674 | 0.668246 | ||||||||
\(732\) | −8.52744 | −0.315183 | ||||||||
\(733\) | −11.6298 | −0.429557 | −0.214778 | − | 0.976663i | \(-0.568903\pi\) | ||||
−0.214778 | + | 0.976663i | \(0.568903\pi\) | |||||||
\(734\) | −24.0740 | −0.888586 | ||||||||
\(735\) | 8.14596 | 0.300468 | ||||||||
\(736\) | 30.9117 | 1.13942 | ||||||||
\(737\) | −7.46911 | −0.275128 | ||||||||
\(738\) | 53.9130 | 1.98456 | ||||||||
\(739\) | −2.68901 | −0.0989168 | −0.0494584 | − | 0.998776i | \(-0.515750\pi\) | ||||
−0.0494584 | + | 0.998776i | \(0.515750\pi\) | |||||||
\(740\) | 85.0336 | 3.12590 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.3789 | −0.381020 | ||||||||
\(743\) | −2.46720 | −0.0905126 | −0.0452563 | − | 0.998975i | \(-0.514410\pi\) | ||||
−0.0452563 | + | 0.998975i | \(0.514410\pi\) | |||||||
\(744\) | −18.1624 | −0.665866 | ||||||||
\(745\) | 9.08236 | 0.332752 | ||||||||
\(746\) | −65.9835 | −2.41583 | ||||||||
\(747\) | 10.0839 | 0.368949 | ||||||||
\(748\) | 10.7696 | 0.393775 | ||||||||
\(749\) | 3.83260 | 0.140040 | ||||||||
\(750\) | 51.0819 | 1.86525 | ||||||||
\(751\) | −37.9185 | −1.38366 | −0.691832 | − | 0.722058i | \(-0.743196\pi\) | ||||
−0.691832 | + | 0.722058i | \(0.743196\pi\) | |||||||
\(752\) | 8.64534 | 0.315263 | ||||||||
\(753\) | −29.3623 | −1.07002 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 57.2583 | 2.08384 | ||||||||
\(756\) | 4.90256 | 0.178304 | ||||||||
\(757\) | 34.6451 | 1.25920 | 0.629598 | − | 0.776921i | \(-0.283219\pi\) | ||||
0.629598 | + | 0.776921i | \(0.283219\pi\) | |||||||
\(758\) | 57.8290 | 2.10044 | ||||||||
\(759\) | 7.73512 | 0.280767 | ||||||||
\(760\) | −8.12411 | −0.294692 | ||||||||
\(761\) | 22.8595 | 0.828655 | 0.414328 | − | 0.910128i | \(-0.364017\pi\) | ||||
0.414328 | + | 0.910128i | \(0.364017\pi\) | |||||||
\(762\) | −58.7280 | −2.12749 | ||||||||
\(763\) | −10.4180 | −0.377158 | ||||||||
\(764\) | −27.8428 | −1.00732 | ||||||||
\(765\) | −37.7863 | −1.36617 | ||||||||
\(766\) | −33.9625 | −1.22712 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 14.9390 | 0.539065 | ||||||||
\(769\) | −51.8275 | −1.86895 | −0.934473 | − | 0.356034i | \(-0.884129\pi\) | ||||
−0.934473 | + | 0.356034i | \(0.884129\pi\) | |||||||
\(770\) | 6.73435 | 0.242689 | ||||||||
\(771\) | −10.3701 | −0.373471 | ||||||||
\(772\) | −34.5122 | −1.24212 | ||||||||
\(773\) | 5.69966 | 0.205003 | 0.102501 | − | 0.994733i | \(-0.467315\pi\) | ||||
0.102501 | + | 0.994733i | \(0.467315\pi\) | |||||||
\(774\) | −16.2509 | −0.584126 | ||||||||
\(775\) | −67.5234 | −2.42551 | ||||||||
\(776\) | 0.439306 | 0.0157702 | ||||||||
\(777\) | −21.7980 | −0.782001 | ||||||||
\(778\) | 44.5883 | 1.59857 | ||||||||
\(779\) | −28.7454 | −1.02991 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.71619 | −0.204541 | ||||||||
\(782\) | 40.3712 | 1.44367 | ||||||||
\(783\) | −2.56579 | −0.0916938 | ||||||||
\(784\) | −2.89889 | −0.103532 | ||||||||
\(785\) | 46.7622 | 1.66902 | ||||||||
\(786\) | −39.1324 | −1.39580 | ||||||||
\(787\) | −16.8141 | −0.599358 | −0.299679 | − | 0.954040i | \(-0.596880\pi\) | ||||
−0.299679 | + | 0.954040i | \(0.596880\pi\) | |||||||
\(788\) | −56.2340 | −2.00325 | ||||||||
\(789\) | −6.02727 | −0.214577 | ||||||||
\(790\) | 5.75553 | 0.204773 | ||||||||
\(791\) | 4.91011 | 0.174583 | ||||||||
\(792\) | −1.77766 | −0.0631664 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 27.6296 | 0.980539 | ||||||||
\(795\) | 40.0807 | 1.42152 | ||||||||
\(796\) | −7.71562 | −0.273473 | ||||||||
\(797\) | 42.1301 | 1.49233 | 0.746163 | − | 0.665764i | \(-0.231894\pi\) | ||||
0.746163 | + | 0.665764i | \(0.231894\pi\) | |||||||
\(798\) | 11.3484 | 0.401729 | ||||||||
\(799\) | 14.7926 | 0.523326 | ||||||||
\(800\) | −63.8727 | −2.25824 | ||||||||
\(801\) | −7.65403 | −0.270442 | ||||||||
\(802\) | −41.0164 | −1.44834 | ||||||||
\(803\) | −6.33640 | −0.223607 | ||||||||
\(804\) | 46.6824 | 1.64636 | ||||||||
\(805\) | 13.8975 | 0.489823 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.9716 | 0.949445 | ||||||||
\(808\) | 5.52147 | 0.194245 | ||||||||
\(809\) | −30.1686 | −1.06067 | −0.530336 | − | 0.847787i | \(-0.677934\pi\) | ||||
−0.530336 | + | 0.847787i | \(0.677934\pi\) | |||||||
\(810\) | −82.5984 | −2.90221 | ||||||||
\(811\) | 23.7929 | 0.835480 | 0.417740 | − | 0.908567i | \(-0.362822\pi\) | ||||
0.417740 | + | 0.908567i | \(0.362822\pi\) | |||||||
\(812\) | −3.14022 | −0.110200 | ||||||||
\(813\) | 29.4655 | 1.03340 | ||||||||
\(814\) | −18.0207 | −0.631624 | ||||||||
\(815\) | −8.35425 | −0.292637 | ||||||||
\(816\) | 32.5202 | 1.13843 | ||||||||
\(817\) | 8.66468 | 0.303139 | ||||||||
\(818\) | −50.7432 | −1.77419 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 106.614 | 3.72312 | ||||||||
\(821\) | −35.8847 | −1.25239 | −0.626193 | − | 0.779668i | \(-0.715388\pi\) | ||||
−0.626193 | + | 0.779668i | \(0.715388\pi\) | |||||||
\(822\) | 35.5682 | 1.24058 | ||||||||
\(823\) | −12.2346 | −0.426470 | −0.213235 | − | 0.977001i | \(-0.568400\pi\) | ||||
−0.213235 | + | 0.977001i | \(0.568400\pi\) | |||||||
\(824\) | 7.81220 | 0.272151 | ||||||||
\(825\) | −15.9830 | −0.556457 | ||||||||
\(826\) | −15.4565 | −0.537799 | ||||||||
\(827\) | 27.3474 | 0.950962 | 0.475481 | − | 0.879726i | \(-0.342274\pi\) | ||||
0.475481 | + | 0.879726i | \(0.342274\pi\) | |||||||
\(828\) | −19.9904 | −0.694715 | ||||||||
\(829\) | 23.5738 | 0.818751 | 0.409376 | − | 0.912366i | \(-0.365747\pi\) | ||||
0.409376 | + | 0.912366i | \(0.365747\pi\) | |||||||
\(830\) | 36.2226 | 1.25730 | ||||||||
\(831\) | 48.3199 | 1.67620 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.96016 | −0.171859 | ||||||||
\(834\) | 79.5779 | 2.75556 | ||||||||
\(835\) | 49.6751 | 1.71908 | ||||||||
\(836\) | 5.16483 | 0.178630 | ||||||||
\(837\) | 16.9506 | 0.585898 | ||||||||
\(838\) | 82.3163 | 2.84357 | ||||||||
\(839\) | 10.5883 | 0.365549 | 0.182775 | − | 0.983155i | \(-0.441492\pi\) | ||||
0.182775 | + | 0.983155i | \(0.441492\pi\) | |||||||
\(840\) | −7.72409 | −0.266507 | ||||||||
\(841\) | −27.3565 | −0.943329 | ||||||||
\(842\) | −46.4664 | −1.60134 | ||||||||
\(843\) | −39.0536 | −1.34508 | ||||||||
\(844\) | −36.4092 | −1.25326 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −13.3054 | −0.457449 | ||||||||
\(847\) | 10.2143 | 0.350968 | ||||||||
\(848\) | −14.2635 | −0.489810 | ||||||||
\(849\) | −48.0379 | −1.64866 | ||||||||
\(850\) | −83.4188 | −2.86124 | ||||||||
\(851\) | −37.1888 | −1.27482 | ||||||||
\(852\) | 35.7265 | 1.22397 | ||||||||
\(853\) | 21.3925 | 0.732464 | 0.366232 | − | 0.930524i | \(-0.380648\pi\) | ||||
0.366232 | + | 0.930524i | \(0.380648\pi\) | |||||||
\(854\) | 3.24690 | 0.111107 | ||||||||
\(855\) | −18.1214 | −0.619739 | ||||||||
\(856\) | −3.63412 | −0.124212 | ||||||||
\(857\) | 7.22129 | 0.246675 | 0.123337 | − | 0.992365i | \(-0.460640\pi\) | ||||
0.123337 | + | 0.992365i | \(0.460640\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 57.1073 | 1.94848 | 0.974238 | − | 0.225524i | \(-0.0724095\pi\) | ||||
0.974238 | + | 0.225524i | \(0.0724095\pi\) | |||||||
\(860\) | −32.1364 | −1.09584 | ||||||||
\(861\) | −27.3301 | −0.931406 | ||||||||
\(862\) | −75.6841 | −2.57781 | ||||||||
\(863\) | 51.3361 | 1.74750 | 0.873751 | − | 0.486374i | \(-0.161681\pi\) | ||||
0.873751 | + | 0.486374i | \(0.161681\pi\) | |||||||
\(864\) | 16.0341 | 0.545493 | ||||||||
\(865\) | −13.2701 | −0.451197 | ||||||||
\(866\) | 25.7631 | 0.875467 | ||||||||
\(867\) | 17.1958 | 0.583999 | ||||||||
\(868\) | 20.7455 | 0.704148 | ||||||||
\(869\) | −0.671481 | −0.0227784 | ||||||||
\(870\) | 22.0281 | 0.746823 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 9.87851 | 0.334528 | ||||||||
\(873\) | 0.979903 | 0.0331647 | ||||||||
\(874\) | 19.3611 | 0.654899 | ||||||||
\(875\) | −10.7074 | −0.361977 | ||||||||
\(876\) | 39.6029 | 1.33806 | ||||||||
\(877\) | 21.4277 | 0.723563 | 0.361781 | − | 0.932263i | \(-0.382169\pi\) | ||||
0.361781 | + | 0.932263i | \(0.382169\pi\) | |||||||
\(878\) | −33.2341 | −1.12160 | ||||||||
\(879\) | −0.950027 | −0.0320436 | ||||||||
\(880\) | 9.25489 | 0.311982 | ||||||||
\(881\) | 29.0619 | 0.979120 | 0.489560 | − | 0.871970i | \(-0.337157\pi\) | ||||
0.489560 | + | 0.871970i | \(0.337157\pi\) | |||||||
\(882\) | 4.46147 | 0.150225 | ||||||||
\(883\) | −4.83594 | −0.162742 | −0.0813711 | − | 0.996684i | \(-0.525930\pi\) | ||||
−0.0813711 | + | 0.996684i | \(0.525930\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 59.6892 | 2.00643 | ||||||||
\(886\) | −31.7899 | −1.06800 | ||||||||
\(887\) | −24.9898 | −0.839075 | −0.419538 | − | 0.907738i | \(-0.637808\pi\) | ||||
−0.419538 | + | 0.907738i | \(0.637808\pi\) | |||||||
\(888\) | 20.6692 | 0.693612 | ||||||||
\(889\) | 12.3102 | 0.412869 | ||||||||
\(890\) | −27.4943 | −0.921611 | ||||||||
\(891\) | 9.63651 | 0.322835 | ||||||||
\(892\) | 10.7311 | 0.359303 | ||||||||
\(893\) | 7.09420 | 0.237398 | ||||||||
\(894\) | 12.0299 | 0.402341 | ||||||||
\(895\) | −21.2244 | −0.709455 | ||||||||
\(896\) | 7.39409 | 0.247019 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 64.9324 | 2.16682 | ||||||||
\(899\) | −10.8573 | −0.362111 | ||||||||
\(900\) | 41.3061 | 1.37687 | ||||||||
\(901\) | −24.4056 | −0.813068 | ||||||||
\(902\) | −22.5940 | −0.752300 | ||||||||
\(903\) | 8.23805 | 0.274145 | ||||||||
\(904\) | −4.65582 | −0.154850 | ||||||||
\(905\) | 7.61931 | 0.253274 | ||||||||
\(906\) | 75.8409 | 2.51964 | ||||||||
\(907\) | 15.0412 | 0.499435 | 0.249717 | − | 0.968319i | \(-0.419662\pi\) | ||||
0.249717 | + | 0.968319i | \(0.419662\pi\) | |||||||
\(908\) | −33.2310 | −1.10281 | ||||||||
\(909\) | 12.3160 | 0.408497 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.22150 | −0.305522 | −0.152761 | − | 0.988263i | \(-0.548816\pi\) | ||||
−0.152761 | + | 0.988263i | \(0.548816\pi\) | |||||||
\(912\) | 15.5959 | 0.516432 | ||||||||
\(913\) | −4.22598 | −0.139860 | ||||||||
\(914\) | −16.3604 | −0.541153 | ||||||||
\(915\) | −12.5388 | −0.414519 | ||||||||
\(916\) | −40.4612 | −1.33687 | ||||||||
\(917\) | 8.20265 | 0.270875 | ||||||||
\(918\) | 20.9409 | 0.691151 | ||||||||
\(919\) | −45.0803 | −1.48706 | −0.743531 | − | 0.668701i | \(-0.766851\pi\) | ||||
−0.743531 | + | 0.668701i | \(0.766851\pi\) | |||||||
\(920\) | −13.1778 | −0.434459 | ||||||||
\(921\) | 31.8456 | 1.04935 | ||||||||
\(922\) | −3.10548 | −0.102274 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 4.91053 | 0.161544 | ||||||||
\(925\) | 76.8430 | 2.52658 | ||||||||
\(926\) | 29.6086 | 0.972999 | ||||||||
\(927\) | 17.4257 | 0.572334 | ||||||||
\(928\) | −10.2703 | −0.337139 | ||||||||
\(929\) | 46.9169 | 1.53929 | 0.769647 | − | 0.638469i | \(-0.220432\pi\) | ||||
0.769647 | + | 0.638469i | \(0.220432\pi\) | |||||||
\(930\) | −145.526 | −4.77200 | ||||||||
\(931\) | −2.37878 | −0.0779612 | ||||||||
\(932\) | −40.4235 | −1.32412 | ||||||||
\(933\) | 23.4867 | 0.768921 | ||||||||
\(934\) | 66.1939 | 2.16593 | ||||||||
\(935\) | 15.8356 | 0.517880 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.3912 | −0.927501 | −0.463750 | − | 0.885966i | \(-0.653497\pi\) | ||||
−0.463750 | + | 0.885966i | \(0.653497\pi\) | |||||||
\(938\) | −17.7747 | −0.580366 | ||||||||
\(939\) | 15.4868 | 0.505394 | ||||||||
\(940\) | −26.3117 | −0.858192 | ||||||||
\(941\) | 17.8718 | 0.582603 | 0.291302 | − | 0.956631i | \(-0.405912\pi\) | ||||
0.291302 | + | 0.956631i | \(0.405912\pi\) | |||||||
\(942\) | 61.9384 | 2.01806 | ||||||||
\(943\) | −46.6268 | −1.51838 | ||||||||
\(944\) | −21.2415 | −0.691353 | ||||||||
\(945\) | 7.20874 | 0.234500 | ||||||||
\(946\) | 6.81048 | 0.221428 | ||||||||
\(947\) | −9.52234 | −0.309435 | −0.154717 | − | 0.987959i | \(-0.549447\pi\) | ||||
−0.154717 | + | 0.987959i | \(0.549447\pi\) | |||||||
\(948\) | 4.19680 | 0.136306 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −40.0057 | −1.29796 | ||||||||
\(951\) | 1.58598 | 0.0514289 | ||||||||
\(952\) | 4.70328 | 0.152434 | ||||||||
\(953\) | −13.4180 | −0.434652 | −0.217326 | − | 0.976099i | \(-0.569733\pi\) | ||||
−0.217326 | + | 0.976099i | \(0.569733\pi\) | |||||||
\(954\) | 21.9519 | 0.710718 | ||||||||
\(955\) | −40.9402 | −1.32479 | ||||||||
\(956\) | −74.5169 | −2.41005 | ||||||||
\(957\) | −2.56996 | −0.0830749 | ||||||||
\(958\) | −86.8964 | −2.80749 | ||||||||
\(959\) | −7.45555 | −0.240752 | ||||||||
\(960\) | −90.4298 | −2.91861 | ||||||||
\(961\) | 40.7275 | 1.31379 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.10615 | −0.261217 | ||||||||
\(964\) | −72.2960 | −2.32850 | ||||||||
\(965\) | −50.7468 | −1.63360 | ||||||||
\(966\) | 18.4078 | 0.592261 | ||||||||
\(967\) | −12.9316 | −0.415851 | −0.207926 | − | 0.978145i | \(-0.566671\pi\) | ||||
−0.207926 | + | 0.978145i | \(0.566671\pi\) | |||||||
\(968\) | −9.68534 | −0.311299 | ||||||||
\(969\) | 26.6854 | 0.857260 | ||||||||
\(970\) | 3.51994 | 0.113019 | ||||||||
\(971\) | 47.5213 | 1.52503 | 0.762516 | − | 0.646969i | \(-0.223964\pi\) | ||||
0.762516 | + | 0.646969i | \(0.223964\pi\) | |||||||
\(972\) | −45.5211 | −1.46009 | ||||||||
\(973\) | −16.6806 | −0.534754 | ||||||||
\(974\) | −59.7515 | −1.91456 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.46216 | 0.142830 | ||||||||
\(977\) | 36.4942 | 1.16755 | 0.583776 | − | 0.811915i | \(-0.301575\pi\) | ||||
0.583776 | + | 0.811915i | \(0.301575\pi\) | |||||||
\(978\) | −11.0655 | −0.353836 | ||||||||
\(979\) | 3.20768 | 0.102518 | ||||||||
\(980\) | 8.82263 | 0.281829 | ||||||||
\(981\) | 22.0347 | 0.703514 | ||||||||
\(982\) | 73.3777 | 2.34158 | ||||||||
\(983\) | −44.1843 | −1.40926 | −0.704629 | − | 0.709576i | \(-0.748887\pi\) | ||||
−0.704629 | + | 0.709576i | \(0.748887\pi\) | |||||||
\(984\) | 25.9147 | 0.826130 | ||||||||
\(985\) | −82.6865 | −2.63461 | ||||||||
\(986\) | −13.4132 | −0.427162 | ||||||||
\(987\) | 6.74490 | 0.214692 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.0546 | 0.446911 | ||||||||
\(990\) | −14.2435 | −0.452689 | ||||||||
\(991\) | −50.7097 | −1.61085 | −0.805424 | − | 0.592699i | \(-0.798062\pi\) | ||||
−0.805424 | + | 0.592699i | \(0.798062\pi\) | |||||||
\(992\) | 67.8495 | 2.15422 | ||||||||
\(993\) | −9.49586 | −0.301342 | ||||||||
\(994\) | −13.6032 | −0.431467 | ||||||||
\(995\) | −11.3451 | −0.359663 | ||||||||
\(996\) | 26.4126 | 0.836916 | ||||||||
\(997\) | −50.2768 | −1.59228 | −0.796141 | − | 0.605111i | \(-0.793129\pi\) | ||||
−0.796141 | + | 0.605111i | \(0.793129\pi\) | |||||||
\(998\) | −0.146578 | −0.00463985 | ||||||||
\(999\) | −19.2901 | −0.610312 |
(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 | 1183.2.a.p.1.5 | 6 | ||
7.6 | odd | 2 | 8281.2.a.ch.1.5 | 6 | |||
13.2 | odd | 12 | 91.2.q.a.43.6 | yes | 12 | ||
13.5 | odd | 4 | 1183.2.c.i.337.2 | 12 | |||
13.7 | odd | 12 | 91.2.q.a.36.6 | ✓ | 12 | ||
13.8 | odd | 4 | 1183.2.c.i.337.11 | 12 | |||
13.12 | even | 2 | 1183.2.a.m.1.2 | 6 | |||
39.2 | even | 12 | 819.2.ct.a.316.1 | 12 | |||
39.20 | even | 12 | 819.2.ct.a.127.1 | 12 | |||
52.7 | even | 12 | 1456.2.cc.c.673.5 | 12 | |||
52.15 | even | 12 | 1456.2.cc.c.225.5 | 12 | |||
91.2 | odd | 12 | 637.2.k.h.459.1 | 12 | |||
91.20 | even | 12 | 637.2.q.h.491.6 | 12 | |||
91.33 | even | 12 | 637.2.u.i.361.1 | 12 | |||
91.41 | even | 12 | 637.2.q.h.589.6 | 12 | |||
91.46 | odd | 12 | 637.2.k.h.569.6 | 12 | |||
91.54 | even | 12 | 637.2.k.g.459.1 | 12 | |||
91.59 | even | 12 | 637.2.k.g.569.6 | 12 | |||
91.67 | odd | 12 | 637.2.u.h.30.1 | 12 | |||
91.72 | odd | 12 | 637.2.u.h.361.1 | 12 | |||
91.80 | even | 12 | 637.2.u.i.30.1 | 12 | |||
91.90 | odd | 2 | 8281.2.a.by.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.q.a.36.6 | ✓ | 12 | 13.7 | odd | 12 | ||
91.2.q.a.43.6 | yes | 12 | 13.2 | odd | 12 | ||
637.2.k.g.459.1 | 12 | 91.54 | even | 12 | |||
637.2.k.g.569.6 | 12 | 91.59 | even | 12 | |||
637.2.k.h.459.1 | 12 | 91.2 | odd | 12 | |||
637.2.k.h.569.6 | 12 | 91.46 | odd | 12 | |||
637.2.q.h.491.6 | 12 | 91.20 | even | 12 | |||
637.2.q.h.589.6 | 12 | 91.41 | even | 12 | |||
637.2.u.h.30.1 | 12 | 91.67 | odd | 12 | |||
637.2.u.h.361.1 | 12 | 91.72 | odd | 12 | |||
637.2.u.i.30.1 | 12 | 91.80 | even | 12 | |||
637.2.u.i.361.1 | 12 | 91.33 | even | 12 | |||
819.2.ct.a.127.1 | 12 | 39.20 | even | 12 | |||
819.2.ct.a.316.1 | 12 | 39.2 | even | 12 | |||
1183.2.a.m.1.2 | 6 | 13.12 | even | 2 | |||
1183.2.a.p.1.5 | 6 | 1.1 | even | 1 | trivial | ||
1183.2.c.i.337.2 | 12 | 13.5 | odd | 4 | |||
1183.2.c.i.337.11 | 12 | 13.8 | odd | 4 | |||
1456.2.cc.c.225.5 | 12 | 52.15 | even | 12 | |||
1456.2.cc.c.673.5 | 12 | 52.7 | even | 12 | |||
8281.2.a.by.1.2 | 6 | 91.90 | odd | 2 | |||
8281.2.a.ch.1.5 | 6 | 7.6 | odd | 2 |