Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, 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("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.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: | \(32.1876970548\) |
Analytic rank: | \(1\) |
Dimension: | \(59\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.19361 | −1.55112 | −0.775560 | − | 0.631274i | \(-0.782532\pi\) | ||||
−0.775560 | + | 0.631274i | \(0.782532\pi\) | |||||||
\(3\) | −1.71235 | −0.988628 | −0.494314 | − | 0.869283i | \(-0.664581\pi\) | ||||
−0.494314 | + | 0.869283i | \(0.664581\pi\) | |||||||
\(4\) | 2.81195 | 1.40597 | ||||||||
\(5\) | −2.23633 | −1.00012 | −0.500058 | − | 0.865992i | \(-0.666688\pi\) | ||||
−0.500058 | + | 0.865992i | \(0.666688\pi\) | |||||||
\(6\) | 3.75624 | 1.53348 | ||||||||
\(7\) | −3.04720 | −1.15173 | −0.575867 | − | 0.817543i | \(-0.695336\pi\) | ||||
−0.575867 | + | 0.817543i | \(0.695336\pi\) | |||||||
\(8\) | −1.78110 | −0.629713 | ||||||||
\(9\) | −0.0678453 | −0.0226151 | ||||||||
\(10\) | 4.90564 | 1.55130 | ||||||||
\(11\) | −1.23615 | −0.372712 | −0.186356 | − | 0.982482i | \(-0.559668\pi\) | ||||
−0.186356 | + | 0.982482i | \(0.559668\pi\) | |||||||
\(12\) | −4.81505 | −1.38998 | ||||||||
\(13\) | 4.62416 | 1.28251 | 0.641256 | − | 0.767327i | \(-0.278414\pi\) | ||||
0.641256 | + | 0.767327i | \(0.278414\pi\) | |||||||
\(14\) | 6.68439 | 1.78648 | ||||||||
\(15\) | 3.82938 | 0.988742 | ||||||||
\(16\) | −1.71685 | −0.429213 | ||||||||
\(17\) | −2.82011 | −0.683977 | −0.341989 | − | 0.939704i | \(-0.611100\pi\) | ||||
−0.341989 | + | 0.939704i | \(0.611100\pi\) | |||||||
\(18\) | 0.148826 | 0.0350787 | ||||||||
\(19\) | −2.42496 | −0.556324 | −0.278162 | − | 0.960534i | \(-0.589725\pi\) | ||||
−0.278162 | + | 0.960534i | \(0.589725\pi\) | |||||||
\(20\) | −6.28843 | −1.40614 | ||||||||
\(21\) | 5.21789 | 1.13864 | ||||||||
\(22\) | 2.71163 | 0.578121 | ||||||||
\(23\) | −1.68438 | −0.351217 | −0.175608 | − | 0.984460i | \(-0.556189\pi\) | ||||
−0.175608 | + | 0.984460i | \(0.556189\pi\) | |||||||
\(24\) | 3.04987 | 0.622552 | ||||||||
\(25\) | 0.00115310 | 0.000230620 0 | ||||||||
\(26\) | −10.1436 | −1.98933 | ||||||||
\(27\) | 5.25324 | 1.01099 | ||||||||
\(28\) | −8.56857 | −1.61931 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −8.40019 | −1.53366 | ||||||||
\(31\) | −3.83960 | −0.689613 | −0.344806 | − | 0.938674i | \(-0.612055\pi\) | ||||
−0.344806 | + | 0.938674i | \(0.612055\pi\) | |||||||
\(32\) | 7.32830 | 1.29547 | ||||||||
\(33\) | 2.11672 | 0.368473 | ||||||||
\(34\) | 6.18624 | 1.06093 | ||||||||
\(35\) | 6.81454 | 1.15187 | ||||||||
\(36\) | −0.190777 | −0.0317962 | ||||||||
\(37\) | −11.7579 | −1.93298 | −0.966491 | − | 0.256700i | \(-0.917365\pi\) | ||||
−0.966491 | + | 0.256700i | \(0.917365\pi\) | |||||||
\(38\) | 5.31943 | 0.862925 | ||||||||
\(39\) | −7.91820 | −1.26793 | ||||||||
\(40\) | 3.98311 | 0.629786 | ||||||||
\(41\) | 5.64161 | 0.881071 | 0.440536 | − | 0.897735i | \(-0.354789\pi\) | ||||
0.440536 | + | 0.897735i | \(0.354789\pi\) | |||||||
\(42\) | −11.4460 | −1.76616 | ||||||||
\(43\) | 1.28438 | 0.195867 | 0.0979334 | − | 0.995193i | \(-0.468777\pi\) | ||||
0.0979334 | + | 0.995193i | \(0.468777\pi\) | |||||||
\(44\) | −3.47598 | −0.524023 | ||||||||
\(45\) | 0.151724 | 0.0226177 | ||||||||
\(46\) | 3.69487 | 0.544779 | ||||||||
\(47\) | 2.94154 | 0.429067 | 0.214534 | − | 0.976717i | \(-0.431177\pi\) | ||||
0.214534 | + | 0.976717i | \(0.431177\pi\) | |||||||
\(48\) | 2.93986 | 0.424332 | ||||||||
\(49\) | 2.28545 | 0.326493 | ||||||||
\(50\) | −0.00252946 | −0.000357720 0 | ||||||||
\(51\) | 4.82903 | 0.676199 | ||||||||
\(52\) | 13.0029 | 1.80318 | ||||||||
\(53\) | 6.00738 | 0.825177 | 0.412589 | − | 0.910917i | \(-0.364625\pi\) | ||||
0.412589 | + | 0.910917i | \(0.364625\pi\) | |||||||
\(54\) | −11.5236 | −1.56816 | ||||||||
\(55\) | 2.76442 | 0.372755 | ||||||||
\(56\) | 5.42737 | 0.725262 | ||||||||
\(57\) | 4.15239 | 0.549997 | ||||||||
\(58\) | −2.19361 | −0.288036 | ||||||||
\(59\) | −2.00477 | −0.260999 | −0.130500 | − | 0.991448i | \(-0.541658\pi\) | ||||
−0.130500 | + | 0.991448i | \(0.541658\pi\) | |||||||
\(60\) | 10.7680 | 1.39014 | ||||||||
\(61\) | −0.627562 | −0.0803511 | −0.0401756 | − | 0.999193i | \(-0.512792\pi\) | ||||
−0.0401756 | + | 0.999193i | \(0.512792\pi\) | |||||||
\(62\) | 8.42261 | 1.06967 | ||||||||
\(63\) | 0.206738 | 0.0260466 | ||||||||
\(64\) | −12.6418 | −1.58022 | ||||||||
\(65\) | −10.3411 | −1.28266 | ||||||||
\(66\) | −4.64327 | −0.571546 | ||||||||
\(67\) | −0.175788 | −0.0214759 | −0.0107380 | − | 0.999942i | \(-0.503418\pi\) | ||||
−0.0107380 | + | 0.999942i | \(0.503418\pi\) | |||||||
\(68\) | −7.93000 | −0.961654 | ||||||||
\(69\) | 2.88425 | 0.347222 | ||||||||
\(70\) | −14.9485 | −1.78668 | ||||||||
\(71\) | 10.5450 | 1.25146 | 0.625728 | − | 0.780041i | \(-0.284802\pi\) | ||||
0.625728 | + | 0.780041i | \(0.284802\pi\) | |||||||
\(72\) | 0.120839 | 0.0142410 | ||||||||
\(73\) | 8.86291 | 1.03733 | 0.518663 | − | 0.854979i | \(-0.326430\pi\) | ||||
0.518663 | + | 0.854979i | \(0.326430\pi\) | |||||||
\(74\) | 25.7922 | 2.99829 | ||||||||
\(75\) | −0.00197452 | −0.000227998 0 | ||||||||
\(76\) | −6.81886 | −0.782177 | ||||||||
\(77\) | 3.76679 | 0.429265 | ||||||||
\(78\) | 17.3695 | 1.96671 | ||||||||
\(79\) | 12.9873 | 1.46119 | 0.730593 | − | 0.682813i | \(-0.239244\pi\) | ||||
0.730593 | + | 0.682813i | \(0.239244\pi\) | |||||||
\(80\) | 3.83944 | 0.429262 | ||||||||
\(81\) | −8.79186 | −0.976873 | ||||||||
\(82\) | −12.3755 | −1.36665 | ||||||||
\(83\) | 6.51740 | 0.715377 | 0.357689 | − | 0.933841i | \(-0.383565\pi\) | ||||
0.357689 | + | 0.933841i | \(0.383565\pi\) | |||||||
\(84\) | 14.6724 | 1.60089 | ||||||||
\(85\) | 6.30668 | 0.684056 | ||||||||
\(86\) | −2.81744 | −0.303813 | ||||||||
\(87\) | −1.71235 | −0.183584 | ||||||||
\(88\) | 2.20170 | 0.234702 | ||||||||
\(89\) | 6.91860 | 0.733370 | 0.366685 | − | 0.930345i | \(-0.380493\pi\) | ||||
0.366685 | + | 0.930345i | \(0.380493\pi\) | |||||||
\(90\) | −0.332824 | −0.0350828 | ||||||||
\(91\) | −14.0908 | −1.47711 | ||||||||
\(92\) | −4.73637 | −0.493801 | ||||||||
\(93\) | 6.57475 | 0.681770 | ||||||||
\(94\) | −6.45260 | −0.665535 | ||||||||
\(95\) | 5.42300 | 0.556388 | ||||||||
\(96\) | −12.5486 | −1.28074 | ||||||||
\(97\) | −6.03515 | −0.612776 | −0.306388 | − | 0.951907i | \(-0.599121\pi\) | ||||
−0.306388 | + | 0.951907i | \(0.599121\pi\) | |||||||
\(98\) | −5.01339 | −0.506429 | ||||||||
\(99\) | 0.0838666 | 0.00842892 | ||||||||
\(100\) | 0.00324246 | 0.000324246 0 | ||||||||
\(101\) | 0.315225 | 0.0313660 | 0.0156830 | − | 0.999877i | \(-0.495008\pi\) | ||||
0.0156830 | + | 0.999877i | \(0.495008\pi\) | |||||||
\(102\) | −10.5930 | −1.04887 | ||||||||
\(103\) | −1.62823 | −0.160434 | −0.0802170 | − | 0.996777i | \(-0.525561\pi\) | ||||
−0.0802170 | + | 0.996777i | \(0.525561\pi\) | |||||||
\(104\) | −8.23608 | −0.807614 | ||||||||
\(105\) | −11.6689 | −1.13877 | ||||||||
\(106\) | −13.1779 | −1.27995 | ||||||||
\(107\) | 16.3813 | 1.58364 | 0.791818 | − | 0.610757i | \(-0.209135\pi\) | ||||
0.791818 | + | 0.610757i | \(0.209135\pi\) | |||||||
\(108\) | 14.7718 | 1.42142 | ||||||||
\(109\) | 0.606072 | 0.0580511 | 0.0290256 | − | 0.999579i | \(-0.490760\pi\) | ||||
0.0290256 | + | 0.999579i | \(0.490760\pi\) | |||||||
\(110\) | −6.06408 | −0.578188 | ||||||||
\(111\) | 20.1336 | 1.91100 | ||||||||
\(112\) | 5.23159 | 0.494339 | ||||||||
\(113\) | −8.91723 | −0.838862 | −0.419431 | − | 0.907787i | \(-0.637770\pi\) | ||||
−0.419431 | + | 0.907787i | \(0.637770\pi\) | |||||||
\(114\) | −9.10874 | −0.853112 | ||||||||
\(115\) | 3.76681 | 0.351257 | ||||||||
\(116\) | 2.81195 | 0.261083 | ||||||||
\(117\) | −0.313727 | −0.0290041 | ||||||||
\(118\) | 4.39770 | 0.404841 | ||||||||
\(119\) | 8.59345 | 0.787760 | ||||||||
\(120\) | −6.82050 | −0.622624 | ||||||||
\(121\) | −9.47194 | −0.861086 | ||||||||
\(122\) | 1.37663 | 0.124634 | ||||||||
\(123\) | −9.66043 | −0.871052 | ||||||||
\(124\) | −10.7968 | −0.969577 | ||||||||
\(125\) | 11.1791 | 0.999885 | ||||||||
\(126\) | −0.453504 | −0.0404014 | ||||||||
\(127\) | 10.0274 | 0.889789 | 0.444894 | − | 0.895583i | \(-0.353241\pi\) | ||||
0.444894 | + | 0.895583i | \(0.353241\pi\) | |||||||
\(128\) | 13.0746 | 1.15564 | ||||||||
\(129\) | −2.19932 | −0.193639 | ||||||||
\(130\) | 22.6845 | 1.98956 | ||||||||
\(131\) | −6.75402 | −0.590102 | −0.295051 | − | 0.955482i | \(-0.595337\pi\) | ||||
−0.295051 | + | 0.955482i | \(0.595337\pi\) | |||||||
\(132\) | 5.95210 | 0.518064 | ||||||||
\(133\) | 7.38935 | 0.640738 | ||||||||
\(134\) | 0.385611 | 0.0333117 | ||||||||
\(135\) | −11.7479 | −1.01110 | ||||||||
\(136\) | 5.02289 | 0.430709 | ||||||||
\(137\) | 1.75918 | 0.150297 | 0.0751486 | − | 0.997172i | \(-0.476057\pi\) | ||||
0.0751486 | + | 0.997172i | \(0.476057\pi\) | |||||||
\(138\) | −6.32693 | −0.538584 | ||||||||
\(139\) | 1.00000 | 0.0848189 | ||||||||
\(140\) | 19.1621 | 1.61949 | ||||||||
\(141\) | −5.03695 | −0.424188 | ||||||||
\(142\) | −23.1316 | −1.94116 | ||||||||
\(143\) | −5.71614 | −0.478007 | ||||||||
\(144\) | 0.116480 | 0.00970668 | ||||||||
\(145\) | −2.23633 | −0.185717 | ||||||||
\(146\) | −19.4418 | −1.60902 | ||||||||
\(147\) | −3.91349 | −0.322780 | ||||||||
\(148\) | −33.0625 | −2.71772 | ||||||||
\(149\) | −10.9341 | −0.895760 | −0.447880 | − | 0.894094i | \(-0.647821\pi\) | ||||
−0.447880 | + | 0.894094i | \(0.647821\pi\) | |||||||
\(150\) | 0.00433133 | 0.000353652 0 | ||||||||
\(151\) | 7.42367 | 0.604129 | 0.302065 | − | 0.953287i | \(-0.402324\pi\) | ||||
0.302065 | + | 0.953287i | \(0.402324\pi\) | |||||||
\(152\) | 4.31909 | 0.350324 | ||||||||
\(153\) | 0.191331 | 0.0154682 | ||||||||
\(154\) | −8.26288 | −0.665842 | ||||||||
\(155\) | 8.58660 | 0.689692 | ||||||||
\(156\) | −22.2655 | −1.78267 | ||||||||
\(157\) | −0.334951 | −0.0267320 | −0.0133660 | − | 0.999911i | \(-0.504255\pi\) | ||||
−0.0133660 | + | 0.999911i | \(0.504255\pi\) | |||||||
\(158\) | −28.4891 | −2.26647 | ||||||||
\(159\) | −10.2868 | −0.815793 | ||||||||
\(160\) | −16.3885 | −1.29562 | ||||||||
\(161\) | 5.13263 | 0.404508 | ||||||||
\(162\) | 19.2860 | 1.51525 | ||||||||
\(163\) | 10.5105 | 0.823244 | 0.411622 | − | 0.911355i | \(-0.364962\pi\) | ||||
0.411622 | + | 0.911355i | \(0.364962\pi\) | |||||||
\(164\) | 15.8639 | 1.23876 | ||||||||
\(165\) | −4.73367 | −0.368516 | ||||||||
\(166\) | −14.2967 | −1.10964 | ||||||||
\(167\) | 8.16987 | 0.632203 | 0.316102 | − | 0.948725i | \(-0.397626\pi\) | ||||
0.316102 | + | 0.948725i | \(0.397626\pi\) | |||||||
\(168\) | −9.29357 | −0.717014 | ||||||||
\(169\) | 8.38286 | 0.644835 | ||||||||
\(170\) | −13.8344 | −1.06105 | ||||||||
\(171\) | 0.164522 | 0.0125813 | ||||||||
\(172\) | 3.61162 | 0.275383 | ||||||||
\(173\) | −1.36012 | −0.103408 | −0.0517040 | − | 0.998662i | \(-0.516465\pi\) | ||||
−0.0517040 | + | 0.998662i | \(0.516465\pi\) | |||||||
\(174\) | 3.75624 | 0.284760 | ||||||||
\(175\) | −0.00351373 | −0.000265613 0 | ||||||||
\(176\) | 2.12228 | 0.159973 | ||||||||
\(177\) | 3.43288 | 0.258031 | ||||||||
\(178\) | −15.1767 | −1.13754 | ||||||||
\(179\) | 14.6215 | 1.09286 | 0.546431 | − | 0.837504i | \(-0.315986\pi\) | ||||
0.546431 | + | 0.837504i | \(0.315986\pi\) | |||||||
\(180\) | 0.426640 | 0.0317999 | ||||||||
\(181\) | −20.3589 | −1.51327 | −0.756634 | − | 0.653838i | \(-0.773158\pi\) | ||||
−0.756634 | + | 0.653838i | \(0.773158\pi\) | |||||||
\(182\) | 30.9097 | 2.29118 | ||||||||
\(183\) | 1.07461 | 0.0794373 | ||||||||
\(184\) | 3.00004 | 0.221166 | ||||||||
\(185\) | 26.2944 | 1.93321 | ||||||||
\(186\) | −14.4225 | −1.05751 | ||||||||
\(187\) | 3.48607 | 0.254926 | ||||||||
\(188\) | 8.27145 | 0.603257 | ||||||||
\(189\) | −16.0077 | −1.16439 | ||||||||
\(190\) | −11.8960 | −0.863025 | ||||||||
\(191\) | 4.13976 | 0.299542 | 0.149771 | − | 0.988721i | \(-0.452146\pi\) | ||||
0.149771 | + | 0.988721i | \(0.452146\pi\) | |||||||
\(192\) | 21.6472 | 1.56225 | ||||||||
\(193\) | 13.4746 | 0.969922 | 0.484961 | − | 0.874536i | \(-0.338834\pi\) | ||||
0.484961 | + | 0.874536i | \(0.338834\pi\) | |||||||
\(194\) | 13.2388 | 0.950490 | ||||||||
\(195\) | 17.7077 | 1.26807 | ||||||||
\(196\) | 6.42656 | 0.459040 | ||||||||
\(197\) | 9.49257 | 0.676318 | 0.338159 | − | 0.941089i | \(-0.390196\pi\) | ||||
0.338159 | + | 0.941089i | \(0.390196\pi\) | |||||||
\(198\) | −0.183971 | −0.0130743 | ||||||||
\(199\) | −18.3412 | −1.30017 | −0.650085 | − | 0.759861i | \(-0.725267\pi\) | ||||
−0.650085 | + | 0.759861i | \(0.725267\pi\) | |||||||
\(200\) | −0.00205379 | −0.000145225 0 | ||||||||
\(201\) | 0.301011 | 0.0212317 | ||||||||
\(202\) | −0.691482 | −0.0486525 | ||||||||
\(203\) | −3.04720 | −0.213872 | ||||||||
\(204\) | 13.5790 | 0.950717 | ||||||||
\(205\) | −12.6165 | −0.881173 | ||||||||
\(206\) | 3.57170 | 0.248852 | ||||||||
\(207\) | 0.114277 | 0.00794279 | ||||||||
\(208\) | −7.93899 | −0.550470 | ||||||||
\(209\) | 2.99760 | 0.207349 | ||||||||
\(210\) | 25.5971 | 1.76637 | ||||||||
\(211\) | 0.812851 | 0.0559590 | 0.0279795 | − | 0.999608i | \(-0.491093\pi\) | ||||
0.0279795 | + | 0.999608i | \(0.491093\pi\) | |||||||
\(212\) | 16.8924 | 1.16018 | ||||||||
\(213\) | −18.0567 | −1.23722 | ||||||||
\(214\) | −35.9342 | −2.45641 | ||||||||
\(215\) | −2.87230 | −0.195889 | ||||||||
\(216\) | −9.35653 | −0.636631 | ||||||||
\(217\) | 11.7000 | 0.794251 | ||||||||
\(218\) | −1.32949 | −0.0900443 | ||||||||
\(219\) | −15.1764 | −1.02553 | ||||||||
\(220\) | 7.77341 | 0.524083 | ||||||||
\(221\) | −13.0406 | −0.877208 | ||||||||
\(222\) | −44.1654 | −2.96419 | ||||||||
\(223\) | 28.8515 | 1.93204 | 0.966021 | − | 0.258464i | \(-0.0832162\pi\) | ||||
0.966021 | + | 0.258464i | \(0.0832162\pi\) | |||||||
\(224\) | −22.3308 | −1.49204 | ||||||||
\(225\) | −7.82325e−5 0 | −5.21550e−6 0 | ||||||||
\(226\) | 19.5610 | 1.30118 | ||||||||
\(227\) | 7.40465 | 0.491464 | 0.245732 | − | 0.969338i | \(-0.420972\pi\) | ||||
0.245732 | + | 0.969338i | \(0.420972\pi\) | |||||||
\(228\) | 11.6763 | 0.773281 | ||||||||
\(229\) | −7.08862 | −0.468429 | −0.234215 | − | 0.972185i | \(-0.575252\pi\) | ||||
−0.234215 | + | 0.972185i | \(0.575252\pi\) | |||||||
\(230\) | −8.26294 | −0.544842 | ||||||||
\(231\) | −6.45007 | −0.424384 | ||||||||
\(232\) | −1.78110 | −0.116935 | ||||||||
\(233\) | 27.9754 | 1.83273 | 0.916363 | − | 0.400348i | \(-0.131111\pi\) | ||||
0.916363 | + | 0.400348i | \(0.131111\pi\) | |||||||
\(234\) | 0.688197 | 0.0449889 | ||||||||
\(235\) | −6.57824 | −0.429117 | ||||||||
\(236\) | −5.63731 | −0.366958 | ||||||||
\(237\) | −22.2389 | −1.44457 | ||||||||
\(238\) | −18.8507 | −1.22191 | ||||||||
\(239\) | −17.3927 | −1.12504 | −0.562519 | − | 0.826784i | \(-0.690168\pi\) | ||||
−0.562519 | + | 0.826784i | \(0.690168\pi\) | |||||||
\(240\) | −6.57447 | −0.424380 | ||||||||
\(241\) | −0.628817 | −0.0405056 | −0.0202528 | − | 0.999795i | \(-0.506447\pi\) | ||||
−0.0202528 | + | 0.999795i | \(0.506447\pi\) | |||||||
\(242\) | 20.7778 | 1.33565 | ||||||||
\(243\) | −0.704933 | −0.0452214 | ||||||||
\(244\) | −1.76467 | −0.112972 | ||||||||
\(245\) | −5.11101 | −0.326530 | ||||||||
\(246\) | 21.1913 | 1.35111 | ||||||||
\(247\) | −11.2134 | −0.713492 | ||||||||
\(248\) | 6.83870 | 0.434258 | ||||||||
\(249\) | −11.1601 | −0.707242 | ||||||||
\(250\) | −24.5225 | −1.55094 | ||||||||
\(251\) | −6.75212 | −0.426190 | −0.213095 | − | 0.977031i | \(-0.568354\pi\) | ||||
−0.213095 | + | 0.977031i | \(0.568354\pi\) | |||||||
\(252\) | 0.581337 | 0.0366208 | ||||||||
\(253\) | 2.08213 | 0.130903 | ||||||||
\(254\) | −21.9963 | −1.38017 | ||||||||
\(255\) | −10.7993 | −0.676277 | ||||||||
\(256\) | −3.39704 | −0.212315 | ||||||||
\(257\) | −10.3738 | −0.647101 | −0.323550 | − | 0.946211i | \(-0.604877\pi\) | ||||
−0.323550 | + | 0.946211i | \(0.604877\pi\) | |||||||
\(258\) | 4.82446 | 0.300358 | ||||||||
\(259\) | 35.8286 | 2.22628 | ||||||||
\(260\) | −29.0787 | −1.80338 | ||||||||
\(261\) | −0.0678453 | −0.00419952 | ||||||||
\(262\) | 14.8157 | 0.915319 | ||||||||
\(263\) | 22.7679 | 1.40393 | 0.701964 | − | 0.712212i | \(-0.252307\pi\) | ||||
0.701964 | + | 0.712212i | \(0.252307\pi\) | |||||||
\(264\) | −3.77008 | −0.232033 | ||||||||
\(265\) | −13.4345 | −0.825272 | ||||||||
\(266\) | −16.2094 | −0.993861 | ||||||||
\(267\) | −11.8471 | −0.725030 | ||||||||
\(268\) | −0.494307 | −0.0301946 | ||||||||
\(269\) | 20.4883 | 1.24919 | 0.624596 | − | 0.780948i | \(-0.285264\pi\) | ||||
0.624596 | + | 0.780948i | \(0.285264\pi\) | |||||||
\(270\) | 25.7705 | 1.56834 | ||||||||
\(271\) | −6.49749 | −0.394694 | −0.197347 | − | 0.980334i | \(-0.563233\pi\) | ||||
−0.197347 | + | 0.980334i | \(0.563233\pi\) | |||||||
\(272\) | 4.84171 | 0.293572 | ||||||||
\(273\) | 24.1284 | 1.46031 | ||||||||
\(274\) | −3.85897 | −0.233129 | ||||||||
\(275\) | −0.00142540 | −8.59549e−5 0 | ||||||||
\(276\) | 8.11035 | 0.488185 | ||||||||
\(277\) | −12.2209 | −0.734283 | −0.367142 | − | 0.930165i | \(-0.619664\pi\) | ||||
−0.367142 | + | 0.930165i | \(0.619664\pi\) | |||||||
\(278\) | −2.19361 | −0.131564 | ||||||||
\(279\) | 0.260499 | 0.0155957 | ||||||||
\(280\) | −12.1374 | −0.725346 | ||||||||
\(281\) | 7.61619 | 0.454344 | 0.227172 | − | 0.973855i | \(-0.427052\pi\) | ||||
0.227172 | + | 0.973855i | \(0.427052\pi\) | |||||||
\(282\) | 11.0491 | 0.657966 | ||||||||
\(283\) | 14.9057 | 0.886052 | 0.443026 | − | 0.896509i | \(-0.353905\pi\) | ||||
0.443026 | + | 0.896509i | \(0.353905\pi\) | |||||||
\(284\) | 29.6518 | 1.75951 | ||||||||
\(285\) | −9.28609 | −0.550061 | ||||||||
\(286\) | 12.5390 | 0.741447 | ||||||||
\(287\) | −17.1911 | −1.01476 | ||||||||
\(288\) | −0.497191 | −0.0292973 | ||||||||
\(289\) | −9.04698 | −0.532175 | ||||||||
\(290\) | 4.90564 | 0.288069 | ||||||||
\(291\) | 10.3343 | 0.605808 | ||||||||
\(292\) | 24.9220 | 1.45845 | ||||||||
\(293\) | −6.27915 | −0.366832 | −0.183416 | − | 0.983035i | \(-0.558716\pi\) | ||||
−0.183416 | + | 0.983035i | \(0.558716\pi\) | |||||||
\(294\) | 8.58470 | 0.500670 | ||||||||
\(295\) | 4.48332 | 0.261029 | ||||||||
\(296\) | 20.9419 | 1.21722 | ||||||||
\(297\) | −6.49376 | −0.376806 | ||||||||
\(298\) | 23.9853 | 1.38943 | ||||||||
\(299\) | −7.78882 | −0.450439 | ||||||||
\(300\) | −0.00555224 | −0.000320558 0 | ||||||||
\(301\) | −3.91378 | −0.225587 | ||||||||
\(302\) | −16.2847 | −0.937077 | ||||||||
\(303\) | −0.539776 | −0.0310093 | ||||||||
\(304\) | 4.16329 | 0.238781 | ||||||||
\(305\) | 1.40343 | 0.0803604 | ||||||||
\(306\) | −0.419707 | −0.0239930 | ||||||||
\(307\) | −21.7635 | −1.24211 | −0.621055 | − | 0.783767i | \(-0.713296\pi\) | ||||
−0.621055 | + | 0.783767i | \(0.713296\pi\) | |||||||
\(308\) | 10.5920 | 0.603535 | ||||||||
\(309\) | 2.78810 | 0.158609 | ||||||||
\(310\) | −18.8357 | −1.06980 | ||||||||
\(311\) | −25.6032 | −1.45182 | −0.725912 | − | 0.687787i | \(-0.758582\pi\) | ||||
−0.725912 | + | 0.687787i | \(0.758582\pi\) | |||||||
\(312\) | 14.1031 | 0.798430 | ||||||||
\(313\) | −3.84534 | −0.217351 | −0.108676 | − | 0.994077i | \(-0.534661\pi\) | ||||
−0.108676 | + | 0.994077i | \(0.534661\pi\) | |||||||
\(314\) | 0.734753 | 0.0414645 | ||||||||
\(315\) | −0.462334 | −0.0260496 | ||||||||
\(316\) | 36.5196 | 2.05439 | ||||||||
\(317\) | −15.4804 | −0.869464 | −0.434732 | − | 0.900560i | \(-0.643157\pi\) | ||||
−0.434732 | + | 0.900560i | \(0.643157\pi\) | |||||||
\(318\) | 22.5652 | 1.26539 | ||||||||
\(319\) | −1.23615 | −0.0692109 | ||||||||
\(320\) | 28.2711 | 1.58040 | ||||||||
\(321\) | −28.0505 | −1.56563 | ||||||||
\(322\) | −11.2590 | −0.627441 | ||||||||
\(323\) | 6.83865 | 0.380513 | ||||||||
\(324\) | −24.7222 | −1.37346 | ||||||||
\(325\) | 0.00533212 | 0.000295773 0 | ||||||||
\(326\) | −23.0559 | −1.27695 | ||||||||
\(327\) | −1.03781 | −0.0573910 | ||||||||
\(328\) | −10.0483 | −0.554822 | ||||||||
\(329\) | −8.96346 | −0.494172 | ||||||||
\(330\) | 10.3839 | 0.571612 | ||||||||
\(331\) | −29.2569 | −1.60810 | −0.804052 | − | 0.594559i | \(-0.797327\pi\) | ||||
−0.804052 | + | 0.594559i | \(0.797327\pi\) | |||||||
\(332\) | 18.3266 | 1.00580 | ||||||||
\(333\) | 0.797716 | 0.0437146 | ||||||||
\(334\) | −17.9215 | −0.980623 | ||||||||
\(335\) | 0.393119 | 0.0214784 | ||||||||
\(336\) | −8.95834 | −0.488717 | ||||||||
\(337\) | −5.85699 | −0.319050 | −0.159525 | − | 0.987194i | \(-0.550996\pi\) | ||||
−0.159525 | + | 0.987194i | \(0.550996\pi\) | |||||||
\(338\) | −18.3888 | −1.00022 | ||||||||
\(339\) | 15.2694 | 0.829322 | ||||||||
\(340\) | 17.7341 | 0.961764 | ||||||||
\(341\) | 4.74631 | 0.257027 | ||||||||
\(342\) | −0.360898 | −0.0195151 | ||||||||
\(343\) | 14.3662 | 0.775702 | ||||||||
\(344\) | −2.28761 | −0.123340 | ||||||||
\(345\) | −6.45011 | −0.347262 | ||||||||
\(346\) | 2.98358 | 0.160398 | ||||||||
\(347\) | −6.63929 | −0.356416 | −0.178208 | − | 0.983993i | \(-0.557030\pi\) | ||||
−0.178208 | + | 0.983993i | \(0.557030\pi\) | |||||||
\(348\) | −4.81505 | −0.258114 | ||||||||
\(349\) | 24.0057 | 1.28499 | 0.642497 | − | 0.766288i | \(-0.277899\pi\) | ||||
0.642497 | + | 0.766288i | \(0.277899\pi\) | |||||||
\(350\) | 0.00770778 | 0.000411998 0 | ||||||||
\(351\) | 24.2918 | 1.29660 | ||||||||
\(352\) | −9.05885 | −0.482838 | ||||||||
\(353\) | −22.1705 | −1.18001 | −0.590007 | − | 0.807398i | \(-0.700875\pi\) | ||||
−0.590007 | + | 0.807398i | \(0.700875\pi\) | |||||||
\(354\) | −7.53041 | −0.400237 | ||||||||
\(355\) | −23.5819 | −1.25160 | ||||||||
\(356\) | 19.4547 | 1.03110 | ||||||||
\(357\) | −14.7150 | −0.778802 | ||||||||
\(358\) | −32.0739 | −1.69516 | ||||||||
\(359\) | −6.91733 | −0.365083 | −0.182541 | − | 0.983198i | \(-0.558432\pi\) | ||||
−0.182541 | + | 0.983198i | \(0.558432\pi\) | |||||||
\(360\) | −0.270236 | −0.0142427 | ||||||||
\(361\) | −13.1196 | −0.690504 | ||||||||
\(362\) | 44.6597 | 2.34726 | ||||||||
\(363\) | 16.2193 | 0.851293 | ||||||||
\(364\) | −39.6224 | −2.07678 | ||||||||
\(365\) | −19.8204 | −1.03744 | ||||||||
\(366\) | −2.35728 | −0.123217 | ||||||||
\(367\) | −4.41163 | −0.230285 | −0.115143 | − | 0.993349i | \(-0.536733\pi\) | ||||
−0.115143 | + | 0.993349i | \(0.536733\pi\) | |||||||
\(368\) | 2.89182 | 0.150747 | ||||||||
\(369\) | −0.382757 | −0.0199255 | ||||||||
\(370\) | −57.6799 | −2.99863 | ||||||||
\(371\) | −18.3057 | −0.950385 | ||||||||
\(372\) | 18.4879 | 0.958551 | ||||||||
\(373\) | −23.0975 | −1.19594 | −0.597972 | − | 0.801517i | \(-0.704027\pi\) | ||||
−0.597972 | + | 0.801517i | \(0.704027\pi\) | |||||||
\(374\) | −7.64709 | −0.395422 | ||||||||
\(375\) | −19.1425 | −0.988514 | ||||||||
\(376\) | −5.23917 | −0.270189 | ||||||||
\(377\) | 4.62416 | 0.238156 | ||||||||
\(378\) | 35.1147 | 1.80610 | ||||||||
\(379\) | 3.94939 | 0.202866 | 0.101433 | − | 0.994842i | \(-0.467657\pi\) | ||||
0.101433 | + | 0.994842i | \(0.467657\pi\) | |||||||
\(380\) | 15.2492 | 0.782267 | ||||||||
\(381\) | −17.1705 | −0.879670 | ||||||||
\(382\) | −9.08103 | −0.464626 | ||||||||
\(383\) | −14.7771 | −0.755076 | −0.377538 | − | 0.925994i | \(-0.623229\pi\) | ||||
−0.377538 | + | 0.925994i | \(0.623229\pi\) | |||||||
\(384\) | −22.3883 | −1.14250 | ||||||||
\(385\) | −8.42376 | −0.429315 | ||||||||
\(386\) | −29.5580 | −1.50446 | ||||||||
\(387\) | −0.0871394 | −0.00442954 | ||||||||
\(388\) | −16.9705 | −0.861547 | ||||||||
\(389\) | 15.5718 | 0.789522 | 0.394761 | − | 0.918784i | \(-0.370827\pi\) | ||||
0.394761 | + | 0.918784i | \(0.370827\pi\) | |||||||
\(390\) | −38.8438 | −1.96693 | ||||||||
\(391\) | 4.75012 | 0.240224 | ||||||||
\(392\) | −4.07061 | −0.205597 | ||||||||
\(393\) | 11.5653 | 0.583391 | ||||||||
\(394\) | −20.8230 | −1.04905 | ||||||||
\(395\) | −29.0438 | −1.46135 | ||||||||
\(396\) | 0.235829 | 0.0118508 | ||||||||
\(397\) | 0.931099 | 0.0467305 | 0.0233653 | − | 0.999727i | \(-0.492562\pi\) | ||||
0.0233653 | + | 0.999727i | \(0.492562\pi\) | |||||||
\(398\) | 40.2334 | 2.01672 | ||||||||
\(399\) | −12.6532 | −0.633451 | ||||||||
\(400\) | −0.00197970 | −9.89851e−5 0 | ||||||||
\(401\) | 3.06120 | 0.152869 | 0.0764346 | − | 0.997075i | \(-0.475646\pi\) | ||||
0.0764346 | + | 0.997075i | \(0.475646\pi\) | |||||||
\(402\) | −0.660303 | −0.0329329 | ||||||||
\(403\) | −17.7549 | −0.884436 | ||||||||
\(404\) | 0.886395 | 0.0440998 | ||||||||
\(405\) | 19.6615 | 0.976986 | ||||||||
\(406\) | 6.68439 | 0.331741 | ||||||||
\(407\) | 14.5344 | 0.720446 | ||||||||
\(408\) | −8.60097 | −0.425811 | ||||||||
\(409\) | −16.0618 | −0.794207 | −0.397103 | − | 0.917774i | \(-0.629985\pi\) | ||||
−0.397103 | + | 0.917774i | \(0.629985\pi\) | |||||||
\(410\) | 27.6757 | 1.36680 | ||||||||
\(411\) | −3.01234 | −0.148588 | ||||||||
\(412\) | −4.57849 | −0.225566 | ||||||||
\(413\) | 6.10895 | 0.300602 | ||||||||
\(414\) | −0.250680 | −0.0123202 | ||||||||
\(415\) | −14.5750 | −0.715460 | ||||||||
\(416\) | 33.8873 | 1.66146 | ||||||||
\(417\) | −1.71235 | −0.0838543 | ||||||||
\(418\) | −6.57559 | −0.321623 | ||||||||
\(419\) | −10.4654 | −0.511271 | −0.255635 | − | 0.966773i | \(-0.582285\pi\) | ||||
−0.255635 | + | 0.966773i | \(0.582285\pi\) | |||||||
\(420\) | −32.8123 | −1.60108 | ||||||||
\(421\) | −36.7832 | −1.79271 | −0.896353 | − | 0.443341i | \(-0.853793\pi\) | ||||
−0.896353 | + | 0.443341i | \(0.853793\pi\) | |||||||
\(422\) | −1.78308 | −0.0867991 | ||||||||
\(423\) | −0.199569 | −0.00970340 | ||||||||
\(424\) | −10.6997 | −0.519625 | ||||||||
\(425\) | −0.00325187 | −0.000157739 0 | ||||||||
\(426\) | 39.6094 | 1.91908 | ||||||||
\(427\) | 1.91231 | 0.0925432 | ||||||||
\(428\) | 46.0632 | 2.22655 | ||||||||
\(429\) | 9.78804 | 0.472571 | ||||||||
\(430\) | 6.30072 | 0.303848 | ||||||||
\(431\) | −11.8286 | −0.569761 | −0.284881 | − | 0.958563i | \(-0.591954\pi\) | ||||
−0.284881 | + | 0.958563i | \(0.591954\pi\) | |||||||
\(432\) | −9.01902 | −0.433928 | ||||||||
\(433\) | −14.7847 | −0.710506 | −0.355253 | − | 0.934770i | \(-0.615605\pi\) | ||||
−0.355253 | + | 0.934770i | \(0.615605\pi\) | |||||||
\(434\) | −25.6654 | −1.23198 | ||||||||
\(435\) | 3.82938 | 0.183605 | ||||||||
\(436\) | 1.70424 | 0.0816183 | ||||||||
\(437\) | 4.08454 | 0.195390 | ||||||||
\(438\) | 33.2913 | 1.59072 | ||||||||
\(439\) | −5.68147 | −0.271162 | −0.135581 | − | 0.990766i | \(-0.543290\pi\) | ||||
−0.135581 | + | 0.990766i | \(0.543290\pi\) | |||||||
\(440\) | −4.92371 | −0.234729 | ||||||||
\(441\) | −0.155057 | −0.00738366 | ||||||||
\(442\) | 28.6061 | 1.36066 | ||||||||
\(443\) | −28.8245 | −1.36950 | −0.684748 | − | 0.728780i | \(-0.740088\pi\) | ||||
−0.684748 | + | 0.728780i | \(0.740088\pi\) | |||||||
\(444\) | 56.6147 | 2.68681 | ||||||||
\(445\) | −15.4722 | −0.733455 | ||||||||
\(446\) | −63.2892 | −2.99683 | ||||||||
\(447\) | 18.7231 | 0.885573 | ||||||||
\(448\) | 38.5221 | 1.82000 | ||||||||
\(449\) | −6.84205 | −0.322897 | −0.161448 | − | 0.986881i | \(-0.551616\pi\) | ||||
−0.161448 | + | 0.986881i | \(0.551616\pi\) | |||||||
\(450\) | 0.000171612 0 | 8.08986e−6 0 | ||||||||
\(451\) | −6.97385 | −0.328386 | ||||||||
\(452\) | −25.0748 | −1.17942 | ||||||||
\(453\) | −12.7119 | −0.597259 | ||||||||
\(454\) | −16.2430 | −0.762320 | ||||||||
\(455\) | 31.5115 | 1.47728 | ||||||||
\(456\) | −7.39581 | −0.346341 | ||||||||
\(457\) | 35.6615 | 1.66818 | 0.834088 | − | 0.551631i | \(-0.185994\pi\) | ||||
0.834088 | + | 0.551631i | \(0.185994\pi\) | |||||||
\(458\) | 15.5497 | 0.726590 | ||||||||
\(459\) | −14.8147 | −0.691491 | ||||||||
\(460\) | 10.5921 | 0.493858 | ||||||||
\(461\) | −26.9967 | −1.25736 | −0.628681 | − | 0.777663i | \(-0.716405\pi\) | ||||
−0.628681 | + | 0.777663i | \(0.716405\pi\) | |||||||
\(462\) | 14.1490 | 0.658270 | ||||||||
\(463\) | 16.1665 | 0.751321 | 0.375660 | − | 0.926757i | \(-0.377416\pi\) | ||||
0.375660 | + | 0.926757i | \(0.377416\pi\) | |||||||
\(464\) | −1.71685 | −0.0797028 | ||||||||
\(465\) | −14.7033 | −0.681849 | ||||||||
\(466\) | −61.3672 | −2.84278 | ||||||||
\(467\) | 0.339338 | 0.0157027 | 0.00785135 | − | 0.999969i | \(-0.497501\pi\) | ||||
0.00785135 | + | 0.999969i | \(0.497501\pi\) | |||||||
\(468\) | −0.882185 | −0.0407790 | ||||||||
\(469\) | 0.535662 | 0.0247346 | ||||||||
\(470\) | 14.4301 | 0.665612 | ||||||||
\(471\) | 0.573554 | 0.0264280 | ||||||||
\(472\) | 3.57069 | 0.164355 | ||||||||
\(473\) | −1.58769 | −0.0730019 | ||||||||
\(474\) | 48.7835 | 2.24070 | ||||||||
\(475\) | −0.00279622 | −0.000128300 0 | ||||||||
\(476\) | 24.1643 | 1.10757 | ||||||||
\(477\) | −0.407572 | −0.0186615 | ||||||||
\(478\) | 38.1528 | 1.74507 | ||||||||
\(479\) | 12.9319 | 0.590876 | 0.295438 | − | 0.955362i | \(-0.404534\pi\) | ||||
0.295438 | + | 0.955362i | \(0.404534\pi\) | |||||||
\(480\) | 28.0629 | 1.28089 | ||||||||
\(481\) | −54.3703 | −2.47907 | ||||||||
\(482\) | 1.37938 | 0.0628291 | ||||||||
\(483\) | −8.78888 | −0.399908 | ||||||||
\(484\) | −26.6346 | −1.21066 | ||||||||
\(485\) | 13.4966 | 0.612847 | ||||||||
\(486\) | 1.54635 | 0.0701439 | ||||||||
\(487\) | −5.19086 | −0.235220 | −0.117610 | − | 0.993060i | \(-0.537523\pi\) | ||||
−0.117610 | + | 0.993060i | \(0.537523\pi\) | |||||||
\(488\) | 1.11775 | 0.0505981 | ||||||||
\(489\) | −17.9977 | −0.813882 | ||||||||
\(490\) | 11.2116 | 0.506488 | ||||||||
\(491\) | −26.8894 | −1.21350 | −0.606752 | − | 0.794891i | \(-0.707528\pi\) | ||||
−0.606752 | + | 0.794891i | \(0.707528\pi\) | |||||||
\(492\) | −27.1646 | −1.22468 | ||||||||
\(493\) | −2.82011 | −0.127011 | ||||||||
\(494\) | 24.5979 | 1.10671 | ||||||||
\(495\) | −0.187553 | −0.00842989 | ||||||||
\(496\) | 6.59202 | 0.295991 | ||||||||
\(497\) | −32.1326 | −1.44134 | ||||||||
\(498\) | 24.4809 | 1.09702 | ||||||||
\(499\) | −5.81465 | −0.260299 | −0.130150 | − | 0.991494i | \(-0.541546\pi\) | ||||
−0.130150 | + | 0.991494i | \(0.541546\pi\) | |||||||
\(500\) | 31.4349 | 1.40581 | ||||||||
\(501\) | −13.9897 | −0.625014 | ||||||||
\(502\) | 14.8116 | 0.661072 | ||||||||
\(503\) | 14.1721 | 0.631902 | 0.315951 | − | 0.948775i | \(-0.397676\pi\) | ||||
0.315951 | + | 0.948775i | \(0.397676\pi\) | |||||||
\(504\) | −0.368221 | −0.0164019 | ||||||||
\(505\) | −0.704946 | −0.0313697 | ||||||||
\(506\) | −4.56740 | −0.203046 | ||||||||
\(507\) | −14.3544 | −0.637502 | ||||||||
\(508\) | 28.1965 | 1.25102 | ||||||||
\(509\) | −27.1766 | −1.20458 | −0.602292 | − | 0.798276i | \(-0.705746\pi\) | ||||
−0.602292 | + | 0.798276i | \(0.705746\pi\) | |||||||
\(510\) | 23.6894 | 1.04899 | ||||||||
\(511\) | −27.0071 | −1.19472 | ||||||||
\(512\) | −18.6974 | −0.826314 | ||||||||
\(513\) | −12.7389 | −0.562436 | ||||||||
\(514\) | 22.7562 | 1.00373 | ||||||||
\(515\) | 3.64125 | 0.160452 | ||||||||
\(516\) | −6.18437 | −0.272252 | ||||||||
\(517\) | −3.63617 | −0.159919 | ||||||||
\(518\) | −78.5942 | −3.45323 | ||||||||
\(519\) | 2.32900 | 0.102232 | ||||||||
\(520\) | 18.4186 | 0.807707 | ||||||||
\(521\) | −36.5787 | −1.60254 | −0.801271 | − | 0.598301i | \(-0.795843\pi\) | ||||
−0.801271 | + | 0.598301i | \(0.795843\pi\) | |||||||
\(522\) | 0.148826 | 0.00651396 | ||||||||
\(523\) | 16.1921 | 0.708031 | 0.354016 | − | 0.935240i | \(-0.384816\pi\) | ||||
0.354016 | + | 0.935240i | \(0.384816\pi\) | |||||||
\(524\) | −18.9920 | −0.829667 | ||||||||
\(525\) | 0.00601675 | 0.000262593 0 | ||||||||
\(526\) | −49.9440 | −2.17766 | ||||||||
\(527\) | 10.8281 | 0.471679 | ||||||||
\(528\) | −3.63409 | −0.158153 | ||||||||
\(529\) | −20.1629 | −0.876647 | ||||||||
\(530\) | 29.4700 | 1.28010 | ||||||||
\(531\) | 0.136014 | 0.00590252 | ||||||||
\(532\) | 20.7784 | 0.900860 | ||||||||
\(533\) | 26.0877 | 1.12998 | ||||||||
\(534\) | 25.9879 | 1.12461 | ||||||||
\(535\) | −36.6338 | −1.58382 | ||||||||
\(536\) | 0.313096 | 0.0135237 | ||||||||
\(537\) | −25.0372 | −1.08043 | ||||||||
\(538\) | −44.9434 | −1.93765 | ||||||||
\(539\) | −2.82515 | −0.121688 | ||||||||
\(540\) | −33.0346 | −1.42158 | ||||||||
\(541\) | 12.8529 | 0.552588 | 0.276294 | − | 0.961073i | \(-0.410894\pi\) | ||||
0.276294 | + | 0.961073i | \(0.410894\pi\) | |||||||
\(542\) | 14.2530 | 0.612218 | ||||||||
\(543\) | 34.8617 | 1.49606 | ||||||||
\(544\) | −20.6666 | −0.886074 | ||||||||
\(545\) | −1.35537 | −0.0580578 | ||||||||
\(546\) | −52.9283 | −2.26512 | ||||||||
\(547\) | −2.73862 | −0.117095 | −0.0585476 | − | 0.998285i | \(-0.518647\pi\) | ||||
−0.0585476 | + | 0.998285i | \(0.518647\pi\) | |||||||
\(548\) | 4.94673 | 0.211314 | ||||||||
\(549\) | 0.0425771 | 0.00181715 | ||||||||
\(550\) | 0.00312678 | 0.000133326 0 | ||||||||
\(551\) | −2.42496 | −0.103307 | ||||||||
\(552\) | −5.13712 | −0.218651 | ||||||||
\(553\) | −39.5750 | −1.68290 | ||||||||
\(554\) | 26.8080 | 1.13896 | ||||||||
\(555\) | −45.0254 | −1.91122 | ||||||||
\(556\) | 2.81195 | 0.119253 | ||||||||
\(557\) | 17.8413 | 0.755959 | 0.377979 | − | 0.925814i | \(-0.376619\pi\) | ||||
0.377979 | + | 0.925814i | \(0.376619\pi\) | |||||||
\(558\) | −0.571434 | −0.0241907 | ||||||||
\(559\) | 5.93920 | 0.251201 | ||||||||
\(560\) | −11.6995 | −0.494396 | ||||||||
\(561\) | −5.96938 | −0.252027 | ||||||||
\(562\) | −16.7070 | −0.704741 | ||||||||
\(563\) | −7.04099 | −0.296742 | −0.148371 | − | 0.988932i | \(-0.547403\pi\) | ||||
−0.148371 | + | 0.988932i | \(0.547403\pi\) | |||||||
\(564\) | −14.1636 | −0.596397 | ||||||||
\(565\) | 19.9418 | 0.838959 | ||||||||
\(566\) | −32.6974 | −1.37437 | ||||||||
\(567\) | 26.7906 | 1.12510 | ||||||||
\(568\) | −18.7816 | −0.788058 | ||||||||
\(569\) | 15.8440 | 0.664213 | 0.332107 | − | 0.943242i | \(-0.392241\pi\) | ||||
0.332107 | + | 0.943242i | \(0.392241\pi\) | |||||||
\(570\) | 20.3701 | 0.853210 | ||||||||
\(571\) | 46.5722 | 1.94899 | 0.974494 | − | 0.224415i | \(-0.0720470\pi\) | ||||
0.974494 | + | 0.224415i | \(0.0720470\pi\) | |||||||
\(572\) | −16.0735 | −0.672065 | ||||||||
\(573\) | −7.08873 | −0.296136 | ||||||||
\(574\) | 37.7107 | 1.57401 | ||||||||
\(575\) | −0.00194226 | −8.09976e−5 0 | ||||||||
\(576\) | 0.857685 | 0.0357369 | ||||||||
\(577\) | −11.0696 | −0.460834 | −0.230417 | − | 0.973092i | \(-0.574009\pi\) | ||||
−0.230417 | + | 0.973092i | \(0.574009\pi\) | |||||||
\(578\) | 19.8456 | 0.825468 | ||||||||
\(579\) | −23.0732 | −0.958891 | ||||||||
\(580\) | −6.28843 | −0.261113 | ||||||||
\(581\) | −19.8598 | −0.823925 | ||||||||
\(582\) | −22.6695 | −0.939680 | ||||||||
\(583\) | −7.42600 | −0.307553 | ||||||||
\(584\) | −15.7857 | −0.653217 | ||||||||
\(585\) | 0.701597 | 0.0290075 | ||||||||
\(586\) | 13.7740 | 0.569000 | ||||||||
\(587\) | 36.0609 | 1.48839 | 0.744195 | − | 0.667962i | \(-0.232833\pi\) | ||||
0.744195 | + | 0.667962i | \(0.232833\pi\) | |||||||
\(588\) | −11.0045 | −0.453819 | ||||||||
\(589\) | 9.31088 | 0.383648 | ||||||||
\(590\) | −9.83469 | −0.404888 | ||||||||
\(591\) | −16.2546 | −0.668626 | ||||||||
\(592\) | 20.1865 | 0.829661 | ||||||||
\(593\) | 14.7547 | 0.605905 | 0.302952 | − | 0.953006i | \(-0.402028\pi\) | ||||
0.302952 | + | 0.953006i | \(0.402028\pi\) | |||||||
\(594\) | 14.2448 | 0.584472 | ||||||||
\(595\) | −19.2178 | −0.787851 | ||||||||
\(596\) | −30.7462 | −1.25941 | ||||||||
\(597\) | 31.4066 | 1.28538 | ||||||||
\(598\) | 17.0857 | 0.698685 | ||||||||
\(599\) | −0.544719 | −0.0222566 | −0.0111283 | − | 0.999938i | \(-0.503542\pi\) | ||||
−0.0111283 | + | 0.999938i | \(0.503542\pi\) | |||||||
\(600\) | 0.00351681 | 0.000143573 0 | ||||||||
\(601\) | 15.8966 | 0.648437 | 0.324219 | − | 0.945982i | \(-0.394899\pi\) | ||||
0.324219 | + | 0.945982i | \(0.394899\pi\) | |||||||
\(602\) | 8.58533 | 0.349912 | ||||||||
\(603\) | 0.0119264 | 0.000485680 0 | ||||||||
\(604\) | 20.8750 | 0.849390 | ||||||||
\(605\) | 21.1824 | 0.861185 | ||||||||
\(606\) | 1.18406 | 0.0480992 | ||||||||
\(607\) | −6.41339 | −0.260312 | −0.130156 | − | 0.991494i | \(-0.541548\pi\) | ||||
−0.130156 | + | 0.991494i | \(0.541548\pi\) | |||||||
\(608\) | −17.7708 | −0.720703 | ||||||||
\(609\) | 5.21789 | 0.211440 | ||||||||
\(610\) | −3.07859 | −0.124649 | ||||||||
\(611\) | 13.6021 | 0.550284 | ||||||||
\(612\) | 0.538013 | 0.0217479 | ||||||||
\(613\) | 18.1907 | 0.734715 | 0.367357 | − | 0.930080i | \(-0.380263\pi\) | ||||
0.367357 | + | 0.930080i | \(0.380263\pi\) | |||||||
\(614\) | 47.7408 | 1.92666 | ||||||||
\(615\) | 21.6039 | 0.871152 | ||||||||
\(616\) | −6.70902 | −0.270314 | ||||||||
\(617\) | 27.4921 | 1.10679 | 0.553395 | − | 0.832919i | \(-0.313332\pi\) | ||||
0.553395 | + | 0.832919i | \(0.313332\pi\) | |||||||
\(618\) | −6.11602 | −0.246022 | ||||||||
\(619\) | 1.55256 | 0.0624026 | 0.0312013 | − | 0.999513i | \(-0.490067\pi\) | ||||
0.0312013 | + | 0.999513i | \(0.490067\pi\) | |||||||
\(620\) | 24.1451 | 0.969689 | ||||||||
\(621\) | −8.84842 | −0.355075 | ||||||||
\(622\) | 56.1636 | 2.25195 | ||||||||
\(623\) | −21.0824 | −0.844648 | ||||||||
\(624\) | 13.5944 | 0.544210 | ||||||||
\(625\) | −25.0058 | −1.00023 | ||||||||
\(626\) | 8.43519 | 0.337138 | ||||||||
\(627\) | −5.13296 | −0.204991 | ||||||||
\(628\) | −0.941863 | −0.0375844 | ||||||||
\(629\) | 33.1585 | 1.32212 | ||||||||
\(630\) | 1.01418 | 0.0404060 | ||||||||
\(631\) | 2.38646 | 0.0950035 | 0.0475017 | − | 0.998871i | \(-0.484874\pi\) | ||||
0.0475017 | + | 0.998871i | \(0.484874\pi\) | |||||||
\(632\) | −23.1317 | −0.920128 | ||||||||
\(633\) | −1.39189 | −0.0553226 | ||||||||
\(634\) | 33.9579 | 1.34864 | ||||||||
\(635\) | −22.4246 | −0.889891 | ||||||||
\(636\) | −28.9258 | −1.14698 | ||||||||
\(637\) | 10.5683 | 0.418730 | ||||||||
\(638\) | 2.71163 | 0.107354 | ||||||||
\(639\) | −0.715425 | −0.0283018 | ||||||||
\(640\) | −29.2390 | −1.15577 | ||||||||
\(641\) | −12.4619 | −0.492217 | −0.246108 | − | 0.969242i | \(-0.579152\pi\) | ||||
−0.246108 | + | 0.969242i | \(0.579152\pi\) | |||||||
\(642\) | 61.5320 | 2.42847 | ||||||||
\(643\) | 30.3287 | 1.19605 | 0.598024 | − | 0.801478i | \(-0.295953\pi\) | ||||
0.598024 | + | 0.801478i | \(0.295953\pi\) | |||||||
\(644\) | 14.4327 | 0.568728 | ||||||||
\(645\) | 4.91840 | 0.193662 | ||||||||
\(646\) | −15.0014 | −0.590221 | ||||||||
\(647\) | 1.67157 | 0.0657163 | 0.0328582 | − | 0.999460i | \(-0.489539\pi\) | ||||
0.0328582 | + | 0.999460i | \(0.489539\pi\) | |||||||
\(648\) | 15.6592 | 0.615150 | ||||||||
\(649\) | 2.47819 | 0.0972775 | ||||||||
\(650\) | −0.0116966 | −0.000458779 0 | ||||||||
\(651\) | −20.0346 | −0.785218 | ||||||||
\(652\) | 29.5549 | 1.15746 | ||||||||
\(653\) | 1.68651 | 0.0659982 | 0.0329991 | − | 0.999455i | \(-0.489494\pi\) | ||||
0.0329991 | + | 0.999455i | \(0.489494\pi\) | |||||||
\(654\) | 2.27655 | 0.0890203 | ||||||||
\(655\) | 15.1042 | 0.590170 | ||||||||
\(656\) | −9.68580 | −0.378167 | ||||||||
\(657\) | −0.601307 | −0.0234592 | ||||||||
\(658\) | 19.6624 | 0.766520 | ||||||||
\(659\) | −7.66163 | −0.298455 | −0.149227 | − | 0.988803i | \(-0.547679\pi\) | ||||
−0.149227 | + | 0.988803i | \(0.547679\pi\) | |||||||
\(660\) | −13.3108 | −0.518123 | ||||||||
\(661\) | −24.5560 | −0.955117 | −0.477559 | − | 0.878600i | \(-0.658478\pi\) | ||||
−0.477559 | + | 0.878600i | \(0.658478\pi\) | |||||||
\(662\) | 64.1784 | 2.49436 | ||||||||
\(663\) | 22.3302 | 0.867233 | ||||||||
\(664\) | −11.6081 | −0.450482 | ||||||||
\(665\) | −16.5250 | −0.640811 | ||||||||
\(666\) | −1.74988 | −0.0678066 | ||||||||
\(667\) | −1.68438 | −0.0652193 | ||||||||
\(668\) | 22.9732 | 0.888861 | ||||||||
\(669\) | −49.4040 | −1.91007 | ||||||||
\(670\) | −0.862353 | −0.0333156 | ||||||||
\(671\) | 0.775758 | 0.0299478 | ||||||||
\(672\) | 38.2383 | 1.47507 | ||||||||
\(673\) | −14.1036 | −0.543654 | −0.271827 | − | 0.962346i | \(-0.587628\pi\) | ||||
−0.271827 | + | 0.962346i | \(0.587628\pi\) | |||||||
\(674\) | 12.8480 | 0.494886 | ||||||||
\(675\) | 0.00605751 | 0.000233154 0 | ||||||||
\(676\) | 23.5721 | 0.906621 | ||||||||
\(677\) | 35.5685 | 1.36701 | 0.683504 | − | 0.729947i | \(-0.260455\pi\) | ||||
0.683504 | + | 0.729947i | \(0.260455\pi\) | |||||||
\(678\) | −33.4953 | −1.28638 | ||||||||
\(679\) | 18.3903 | 0.705756 | ||||||||
\(680\) | −11.2328 | −0.430759 | ||||||||
\(681\) | −12.6794 | −0.485875 | ||||||||
\(682\) | −10.4116 | −0.398680 | ||||||||
\(683\) | 10.4193 | 0.398682 | 0.199341 | − | 0.979930i | \(-0.436120\pi\) | ||||
0.199341 | + | 0.979930i | \(0.436120\pi\) | |||||||
\(684\) | 0.462627 | 0.0176890 | ||||||||
\(685\) | −3.93411 | −0.150315 | ||||||||
\(686\) | −31.5139 | −1.20321 | ||||||||
\(687\) | 12.1382 | 0.463102 | ||||||||
\(688\) | −2.20510 | −0.0840685 | ||||||||
\(689\) | 27.7791 | 1.05830 | ||||||||
\(690\) | 14.1491 | 0.538646 | ||||||||
\(691\) | 37.1399 | 1.41287 | 0.706435 | − | 0.707778i | \(-0.250302\pi\) | ||||
0.706435 | + | 0.707778i | \(0.250302\pi\) | |||||||
\(692\) | −3.82458 | −0.145389 | ||||||||
\(693\) | −0.255559 | −0.00970787 | ||||||||
\(694\) | 14.5640 | 0.552843 | ||||||||
\(695\) | −2.23633 | −0.0848287 | ||||||||
\(696\) | 3.04987 | 0.115605 | ||||||||
\(697\) | −15.9100 | −0.602633 | ||||||||
\(698\) | −52.6592 | −1.99318 | ||||||||
\(699\) | −47.9037 | −1.81188 | ||||||||
\(700\) | −0.00988043 | −0.000373445 0 | ||||||||
\(701\) | −22.8356 | −0.862490 | −0.431245 | − | 0.902235i | \(-0.641926\pi\) | ||||
−0.431245 | + | 0.902235i | \(0.641926\pi\) | |||||||
\(702\) | −53.2869 | −2.01118 | ||||||||
\(703\) | 28.5124 | 1.07536 | ||||||||
\(704\) | 15.6271 | 0.588968 | ||||||||
\(705\) | 11.2643 | 0.424237 | ||||||||
\(706\) | 48.6335 | 1.83034 | ||||||||
\(707\) | −0.960554 | −0.0361254 | ||||||||
\(708\) | 9.65307 | 0.362785 | ||||||||
\(709\) | 45.5934 | 1.71230 | 0.856149 | − | 0.516730i | \(-0.172851\pi\) | ||||
0.856149 | + | 0.516730i | \(0.172851\pi\) | |||||||
\(710\) | 51.7297 | 1.94138 | ||||||||
\(711\) | −0.881127 | −0.0330448 | ||||||||
\(712\) | −12.3227 | −0.461813 | ||||||||
\(713\) | 6.46733 | 0.242203 | ||||||||
\(714\) | 32.2791 | 1.20801 | ||||||||
\(715\) | 12.7831 | 0.478062 | ||||||||
\(716\) | 41.1148 | 1.53653 | ||||||||
\(717\) | 29.7824 | 1.11224 | ||||||||
\(718\) | 15.1740 | 0.566287 | ||||||||
\(719\) | 22.2633 | 0.830280 | 0.415140 | − | 0.909758i | \(-0.363733\pi\) | ||||
0.415140 | + | 0.909758i | \(0.363733\pi\) | |||||||
\(720\) | −0.260488 | −0.00970780 | ||||||||
\(721\) | 4.96154 | 0.184777 | ||||||||
\(722\) | 28.7793 | 1.07105 | ||||||||
\(723\) | 1.07676 | 0.0400450 | ||||||||
\(724\) | −57.2483 | −2.12761 | ||||||||
\(725\) | 0.00115310 | 4.28251e−5 0 | ||||||||
\(726\) | −35.5789 | −1.32046 | ||||||||
\(727\) | −37.4973 | −1.39070 | −0.695350 | − | 0.718672i | \(-0.744750\pi\) | ||||
−0.695350 | + | 0.718672i | \(0.744750\pi\) | |||||||
\(728\) | 25.0970 | 0.930157 | ||||||||
\(729\) | 27.5827 | 1.02158 | ||||||||
\(730\) | 43.4782 | 1.60920 | ||||||||
\(731\) | −3.62210 | −0.133968 | ||||||||
\(732\) | 3.02174 | 0.111687 | ||||||||
\(733\) | −10.8492 | −0.400725 | −0.200363 | − | 0.979722i | \(-0.564212\pi\) | ||||
−0.200363 | + | 0.979722i | \(0.564212\pi\) | |||||||
\(734\) | 9.67743 | 0.357200 | ||||||||
\(735\) | 8.75185 | 0.322817 | ||||||||
\(736\) | −12.3436 | −0.454992 | ||||||||
\(737\) | 0.217300 | 0.00800434 | ||||||||
\(738\) | 0.839620 | 0.0309069 | ||||||||
\(739\) | 0.762676 | 0.0280555 | 0.0140277 | − | 0.999902i | \(-0.495535\pi\) | ||||
0.0140277 | + | 0.999902i | \(0.495535\pi\) | |||||||
\(740\) | 73.9385 | 2.71803 | ||||||||
\(741\) | 19.2013 | 0.705378 | ||||||||
\(742\) | 40.1557 | 1.47416 | ||||||||
\(743\) | −8.51803 | −0.312496 | −0.156248 | − | 0.987718i | \(-0.549940\pi\) | ||||
−0.156248 | + | 0.987718i | \(0.549940\pi\) | |||||||
\(744\) | −11.7103 | −0.429320 | ||||||||
\(745\) | 24.4523 | 0.895863 | ||||||||
\(746\) | 50.6670 | 1.85505 | ||||||||
\(747\) | −0.442175 | −0.0161783 | ||||||||
\(748\) | 9.80263 | 0.358420 | ||||||||
\(749\) | −49.9170 | −1.82393 | ||||||||
\(750\) | 41.9912 | 1.53330 | ||||||||
\(751\) | 30.0749 | 1.09745 | 0.548724 | − | 0.836003i | \(-0.315114\pi\) | ||||
0.548724 | + | 0.836003i | \(0.315114\pi\) | |||||||
\(752\) | −5.05018 | −0.184161 | ||||||||
\(753\) | 11.5620 | 0.421344 | ||||||||
\(754\) | −10.1436 | −0.369409 | ||||||||
\(755\) | −16.6017 | −0.604199 | ||||||||
\(756\) | −45.0127 | −1.63710 | ||||||||
\(757\) | −38.6729 | −1.40559 | −0.702796 | − | 0.711392i | \(-0.748065\pi\) | ||||
−0.702796 | + | 0.711392i | \(0.748065\pi\) | |||||||
\(758\) | −8.66343 | −0.314670 | ||||||||
\(759\) | −3.56535 | −0.129414 | ||||||||
\(760\) | −9.65889 | −0.350365 | ||||||||
\(761\) | −13.9600 | −0.506049 | −0.253025 | − | 0.967460i | \(-0.581425\pi\) | ||||
−0.253025 | + | 0.967460i | \(0.581425\pi\) | |||||||
\(762\) | 37.6654 | 1.36447 | ||||||||
\(763\) | −1.84682 | −0.0668595 | ||||||||
\(764\) | 11.6408 | 0.421148 | ||||||||
\(765\) | −0.427879 | −0.0154700 | ||||||||
\(766\) | 32.4153 | 1.17121 | ||||||||
\(767\) | −9.27039 | −0.334734 | ||||||||
\(768\) | 5.81694 | 0.209901 | ||||||||
\(769\) | −43.0406 | −1.55208 | −0.776041 | − | 0.630682i | \(-0.782775\pi\) | ||||
−0.776041 | + | 0.630682i | \(0.782775\pi\) | |||||||
\(770\) | 18.4785 | 0.665919 | ||||||||
\(771\) | 17.7636 | 0.639742 | ||||||||
\(772\) | 37.8898 | 1.36368 | ||||||||
\(773\) | 9.81779 | 0.353121 | 0.176561 | − | 0.984290i | \(-0.443503\pi\) | ||||
0.176561 | + | 0.984290i | \(0.443503\pi\) | |||||||
\(774\) | 0.191150 | 0.00687076 | ||||||||
\(775\) | −0.00442745 | −0.000159039 0 | ||||||||
\(776\) | 10.7492 | 0.385873 | ||||||||
\(777\) | −61.3513 | −2.20097 | ||||||||
\(778\) | −34.1585 | −1.22464 | ||||||||
\(779\) | −13.6807 | −0.490161 | ||||||||
\(780\) | 49.7930 | 1.78288 | ||||||||
\(781\) | −13.0351 | −0.466432 | ||||||||
\(782\) | −10.4199 | −0.372616 | ||||||||
\(783\) | 5.25324 | 0.187735 | ||||||||
\(784\) | −3.92377 | −0.140135 | ||||||||
\(785\) | 0.749059 | 0.0267351 | ||||||||
\(786\) | −25.3698 | −0.904909 | ||||||||
\(787\) | −18.1905 | −0.648421 | −0.324210 | − | 0.945985i | \(-0.605099\pi\) | ||||
−0.324210 | + | 0.945985i | \(0.605099\pi\) | |||||||
\(788\) | 26.6926 | 0.950884 | ||||||||
\(789\) | −38.9867 | −1.38796 | ||||||||
\(790\) | 63.7110 | 2.26674 | ||||||||
\(791\) | 27.1726 | 0.966146 | ||||||||
\(792\) | −0.149375 | −0.00530780 | ||||||||
\(793\) | −2.90195 | −0.103051 | ||||||||
\(794\) | −2.04247 | −0.0724846 | ||||||||
\(795\) | 23.0045 | 0.815887 | ||||||||
\(796\) | −51.5744 | −1.82800 | ||||||||
\(797\) | 23.9899 | 0.849767 | 0.424884 | − | 0.905248i | \(-0.360315\pi\) | ||||
0.424884 | + | 0.905248i | \(0.360315\pi\) | |||||||
\(798\) | 27.7562 | 0.982558 | ||||||||
\(799\) | −8.29546 | −0.293472 | ||||||||
\(800\) | 0.00845028 | 0.000298762 0 | ||||||||
\(801\) | −0.469394 | −0.0165852 | ||||||||
\(802\) | −6.71510 | −0.237118 | ||||||||
\(803\) | −10.9558 | −0.386624 | ||||||||
\(804\) | 0.846428 | 0.0298512 | ||||||||
\(805\) | −11.4782 | −0.404555 | ||||||||
\(806\) | 38.9475 | 1.37187 | ||||||||
\(807\) | −35.0832 | −1.23499 | ||||||||
\(808\) | −0.561446 | −0.0197516 | ||||||||
\(809\) | −21.2688 | −0.747771 | −0.373886 | − | 0.927475i | \(-0.621975\pi\) | ||||
−0.373886 | + | 0.927475i | \(0.621975\pi\) | |||||||
\(810\) | −43.1297 | −1.51542 | ||||||||
\(811\) | 24.1280 | 0.847250 | 0.423625 | − | 0.905838i | \(-0.360757\pi\) | ||||
0.423625 | + | 0.905838i | \(0.360757\pi\) | |||||||
\(812\) | −8.56857 | −0.300698 | ||||||||
\(813\) | 11.1260 | 0.390206 | ||||||||
\(814\) | −31.8830 | −1.11750 | ||||||||
\(815\) | −23.5049 | −0.823339 | ||||||||
\(816\) | −8.29072 | −0.290233 | ||||||||
\(817\) | −3.11458 | −0.108965 | ||||||||
\(818\) | 35.2335 | 1.23191 | ||||||||
\(819\) | 0.955991 | 0.0334050 | ||||||||
\(820\) | −35.4769 | −1.23891 | ||||||||
\(821\) | 46.8952 | 1.63665 | 0.818326 | − | 0.574754i | \(-0.194902\pi\) | ||||
0.818326 | + | 0.574754i | \(0.194902\pi\) | |||||||
\(822\) | 6.60792 | 0.230478 | ||||||||
\(823\) | −20.4049 | −0.711272 | −0.355636 | − | 0.934625i | \(-0.615736\pi\) | ||||
−0.355636 | + | 0.934625i | \(0.615736\pi\) | |||||||
\(824\) | 2.90003 | 0.101027 | ||||||||
\(825\) | 0.00244079 | 8.49774e−5 0 | ||||||||
\(826\) | −13.4007 | −0.466269 | ||||||||
\(827\) | 8.64849 | 0.300737 | 0.150369 | − | 0.988630i | \(-0.451954\pi\) | ||||
0.150369 | + | 0.988630i | \(0.451954\pi\) | |||||||
\(828\) | 0.321341 | 0.0111674 | ||||||||
\(829\) | 16.5277 | 0.574030 | 0.287015 | − | 0.957926i | \(-0.407337\pi\) | ||||
0.287015 | + | 0.957926i | \(0.407337\pi\) | |||||||
\(830\) | 31.9720 | 1.10976 | ||||||||
\(831\) | 20.9265 | 0.725933 | ||||||||
\(832\) | −58.4576 | −2.02665 | ||||||||
\(833\) | −6.44521 | −0.223313 | ||||||||
\(834\) | 3.75624 | 0.130068 | ||||||||
\(835\) | −18.2705 | −0.632276 | ||||||||
\(836\) | 8.42910 | 0.291527 | ||||||||
\(837\) | −20.1703 | −0.697189 | ||||||||
\(838\) | 22.9572 | 0.793042 | ||||||||
\(839\) | −6.84408 | −0.236284 | −0.118142 | − | 0.992997i | \(-0.537694\pi\) | ||||
−0.118142 | + | 0.992997i | \(0.537694\pi\) | |||||||
\(840\) | 20.7835 | 0.717097 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 80.6883 | 2.78070 | ||||||||
\(843\) | −13.0416 | −0.449177 | ||||||||
\(844\) | 2.28569 | 0.0786768 | ||||||||
\(845\) | −18.7468 | −0.644909 | ||||||||
\(846\) | 0.437779 | 0.0150511 | ||||||||
\(847\) | 28.8629 | 0.991742 | ||||||||
\(848\) | −10.3138 | −0.354176 | ||||||||
\(849\) | −25.5238 | −0.875976 | ||||||||
\(850\) | 0.00713336 | 0.000244672 0 | ||||||||
\(851\) | 19.8047 | 0.678895 | ||||||||
\(852\) | −50.7744 | −1.73950 | ||||||||
\(853\) | −18.3716 | −0.629033 | −0.314517 | − | 0.949252i | \(-0.601842\pi\) | ||||
−0.314517 | + | 0.949252i | \(0.601842\pi\) | |||||||
\(854\) | −4.19487 | −0.143546 | ||||||||
\(855\) | −0.367925 | −0.0125828 | ||||||||
\(856\) | −29.1766 | −0.997236 | ||||||||
\(857\) | 12.4559 | 0.425487 | 0.212743 | − | 0.977108i | \(-0.431760\pi\) | ||||
0.212743 | + | 0.977108i | \(0.431760\pi\) | |||||||
\(858\) | −21.4712 | −0.733015 | ||||||||
\(859\) | −30.2817 | −1.03320 | −0.516600 | − | 0.856227i | \(-0.672803\pi\) | ||||
−0.516600 | + | 0.856227i | \(0.672803\pi\) | |||||||
\(860\) | −8.07676 | −0.275415 | ||||||||
\(861\) | 29.4373 | 1.00322 | ||||||||
\(862\) | 25.9473 | 0.883768 | ||||||||
\(863\) | 16.3159 | 0.555399 | 0.277699 | − | 0.960668i | \(-0.410428\pi\) | ||||
0.277699 | + | 0.960668i | \(0.410428\pi\) | |||||||
\(864\) | 38.4973 | 1.30971 | ||||||||
\(865\) | 3.04167 | 0.103420 | ||||||||
\(866\) | 32.4319 | 1.10208 | ||||||||
\(867\) | 15.4916 | 0.526123 | ||||||||
\(868\) | 32.8999 | 1.11670 | ||||||||
\(869\) | −16.0542 | −0.544601 | ||||||||
\(870\) | −8.40019 | −0.284793 | ||||||||
\(871\) | −0.812872 | −0.0275431 | ||||||||
\(872\) | −1.07947 | −0.0365556 | ||||||||
\(873\) | 0.409456 | 0.0138580 | ||||||||
\(874\) | −8.95991 | −0.303074 | ||||||||
\(875\) | −34.0648 | −1.15160 | ||||||||
\(876\) | −42.6753 | −1.44187 | ||||||||
\(877\) | 23.7024 | 0.800374 | 0.400187 | − | 0.916433i | \(-0.368945\pi\) | ||||
0.400187 | + | 0.916433i | \(0.368945\pi\) | |||||||
\(878\) | 12.4630 | 0.420605 | ||||||||
\(879\) | 10.7521 | 0.362660 | ||||||||
\(880\) | −4.74610 | −0.159991 | ||||||||
\(881\) | 18.9059 | 0.636955 | 0.318477 | − | 0.947930i | \(-0.396828\pi\) | ||||
0.318477 | + | 0.947930i | \(0.396828\pi\) | |||||||
\(882\) | 0.340135 | 0.0114529 | ||||||||
\(883\) | 23.7780 | 0.800193 | 0.400097 | − | 0.916473i | \(-0.368977\pi\) | ||||
0.400097 | + | 0.916473i | \(0.368977\pi\) | |||||||
\(884\) | −36.6696 | −1.23333 | ||||||||
\(885\) | −7.67704 | −0.258061 | ||||||||
\(886\) | 63.2299 | 2.12425 | ||||||||
\(887\) | 16.1515 | 0.542315 | 0.271157 | − | 0.962535i | \(-0.412594\pi\) | ||||
0.271157 | + | 0.962535i | \(0.412594\pi\) | |||||||
\(888\) | −35.8600 | −1.20338 | ||||||||
\(889\) | −30.5556 | −1.02480 | ||||||||
\(890\) | 33.9401 | 1.13768 | ||||||||
\(891\) | 10.8680 | 0.364092 | ||||||||
\(892\) | 81.1290 | 2.71640 | ||||||||
\(893\) | −7.13311 | −0.238700 | ||||||||
\(894\) | −41.0713 | −1.37363 | ||||||||
\(895\) | −32.6984 | −1.09299 | ||||||||
\(896\) | −39.8409 | −1.33099 | ||||||||
\(897\) | 13.3372 | 0.445317 | ||||||||
\(898\) | 15.0088 | 0.500851 | ||||||||
\(899\) | −3.83960 | −0.128058 | ||||||||
\(900\) | −0.000219985 0 | −7.33285e−6 0 | ||||||||
\(901\) | −16.9415 | −0.564402 | ||||||||
\(902\) | 15.2979 | 0.509366 | ||||||||
\(903\) | 6.70177 | 0.223021 | ||||||||
\(904\) | 15.8824 | 0.528242 | ||||||||
\(905\) | 45.5292 | 1.51344 | ||||||||
\(906\) | 27.8851 | 0.926421 | ||||||||
\(907\) | −34.7712 | −1.15456 | −0.577280 | − | 0.816546i | \(-0.695886\pi\) | ||||
−0.577280 | + | 0.816546i | \(0.695886\pi\) | |||||||
\(908\) | 20.8215 | 0.690985 | ||||||||
\(909\) | −0.0213865 | −0.000709346 0 | ||||||||
\(910\) | −69.1241 | −2.29144 | ||||||||
\(911\) | −52.5178 | −1.73999 | −0.869996 | − | 0.493059i | \(-0.835879\pi\) | ||||
−0.869996 | + | 0.493059i | \(0.835879\pi\) | |||||||
\(912\) | −7.12903 | −0.236066 | ||||||||
\(913\) | −8.05645 | −0.266630 | ||||||||
\(914\) | −78.2277 | −2.58754 | ||||||||
\(915\) | −2.40317 | −0.0794465 | ||||||||
\(916\) | −19.9328 | −0.658599 | ||||||||
\(917\) | 20.5809 | 0.679641 | ||||||||
\(918\) | 32.4978 | 1.07259 | ||||||||
\(919\) | −19.6793 | −0.649159 | −0.324579 | − | 0.945858i | \(-0.605223\pi\) | ||||
−0.324579 | + | 0.945858i | \(0.605223\pi\) | |||||||
\(920\) | −6.70906 | −0.221191 | ||||||||
\(921\) | 37.2668 | 1.22798 | ||||||||
\(922\) | 59.2204 | 1.95032 | ||||||||
\(923\) | 48.7615 | 1.60501 | ||||||||
\(924\) | −18.1373 | −0.596672 | ||||||||
\(925\) | −0.0135580 | −0.000445785 0 | ||||||||
\(926\) | −35.4631 | −1.16539 | ||||||||
\(927\) | 0.110467 | 0.00362823 | ||||||||
\(928\) | 7.32830 | 0.240563 | ||||||||
\(929\) | 52.0527 | 1.70780 | 0.853898 | − | 0.520441i | \(-0.174232\pi\) | ||||
0.853898 | + | 0.520441i | \(0.174232\pi\) | |||||||
\(930\) | 32.2534 | 1.05763 | ||||||||
\(931\) | −5.54212 | −0.181636 | ||||||||
\(932\) | 78.6652 | 2.57676 | ||||||||
\(933\) | 43.8417 | 1.43531 | ||||||||
\(934\) | −0.744378 | −0.0243568 | ||||||||
\(935\) | −7.79598 | −0.254956 | ||||||||
\(936\) | 0.558779 | 0.0182643 | ||||||||
\(937\) | −24.0301 | −0.785028 | −0.392514 | − | 0.919746i | \(-0.628395\pi\) | ||||
−0.392514 | + | 0.919746i | \(0.628395\pi\) | |||||||
\(938\) | −1.17504 | −0.0383663 | ||||||||
\(939\) | 6.58458 | 0.214880 | ||||||||
\(940\) | −18.4976 | −0.603327 | ||||||||
\(941\) | −48.0339 | −1.56586 | −0.782930 | − | 0.622110i | \(-0.786276\pi\) | ||||
−0.782930 | + | 0.622110i | \(0.786276\pi\) | |||||||
\(942\) | −1.25816 | −0.0409930 | ||||||||
\(943\) | −9.50259 | −0.309447 | ||||||||
\(944\) | 3.44189 | 0.112024 | ||||||||
\(945\) | 35.7984 | 1.16452 | ||||||||
\(946\) | 3.48277 | 0.113235 | ||||||||
\(947\) | −2.76166 | −0.0897419 | −0.0448710 | − | 0.998993i | \(-0.514288\pi\) | ||||
−0.0448710 | + | 0.998993i | \(0.514288\pi\) | |||||||
\(948\) | −62.5345 | −2.03102 | ||||||||
\(949\) | 40.9835 | 1.33038 | ||||||||
\(950\) | 0.00613384 | 0.000199008 0 | ||||||||
\(951\) | 26.5078 | 0.859576 | ||||||||
\(952\) | −15.3058 | −0.496063 | ||||||||
\(953\) | −12.5120 | −0.405305 | −0.202652 | − | 0.979251i | \(-0.564956\pi\) | ||||
−0.202652 | + | 0.979251i | \(0.564956\pi\) | |||||||
\(954\) | 0.894057 | 0.0289462 | ||||||||
\(955\) | −9.25784 | −0.299577 | ||||||||
\(956\) | −48.9072 | −1.58177 | ||||||||
\(957\) | 2.11672 | 0.0684238 | ||||||||
\(958\) | −28.3677 | −0.916519 | ||||||||
\(959\) | −5.36059 | −0.173102 | ||||||||
\(960\) | −48.4102 | −1.56243 | ||||||||
\(961\) | −16.2575 | −0.524434 | ||||||||
\(962\) | 119.267 | 3.84534 | ||||||||
\(963\) | −1.11139 | −0.0358141 | ||||||||
\(964\) | −1.76820 | −0.0569498 | ||||||||
\(965\) | −30.1336 | −0.970033 | ||||||||
\(966\) | 19.2794 | 0.620305 | ||||||||
\(967\) | −18.6051 | −0.598299 | −0.299150 | − | 0.954206i | \(-0.596703\pi\) | ||||
−0.299150 | + | 0.954206i | \(0.596703\pi\) | |||||||
\(968\) | 16.8705 | 0.542237 | ||||||||
\(969\) | −11.7102 | −0.376186 | ||||||||
\(970\) | −29.6062 | −0.950599 | ||||||||
\(971\) | 41.4220 | 1.32930 | 0.664648 | − | 0.747157i | \(-0.268582\pi\) | ||||
0.664648 | + | 0.747157i | \(0.268582\pi\) | |||||||
\(972\) | −1.98223 | −0.0635801 | ||||||||
\(973\) | −3.04720 | −0.0976889 | ||||||||
\(974\) | 11.3867 | 0.364855 | ||||||||
\(975\) | −0.00913048 | −0.000292409 0 | ||||||||
\(976\) | 1.07743 | 0.0344877 | ||||||||
\(977\) | −47.5754 | −1.52207 | −0.761036 | − | 0.648709i | \(-0.775309\pi\) | ||||
−0.761036 | + | 0.648709i | \(0.775309\pi\) | |||||||
\(978\) | 39.4799 | 1.26243 | ||||||||
\(979\) | −8.55240 | −0.273336 | ||||||||
\(980\) | −14.3719 | −0.459093 | ||||||||
\(981\) | −0.0411191 | −0.00131283 | ||||||||
\(982\) | 58.9851 | 1.88229 | ||||||||
\(983\) | 31.3046 | 0.998461 | 0.499231 | − | 0.866469i | \(-0.333616\pi\) | ||||
0.499231 | + | 0.866469i | \(0.333616\pi\) | |||||||
\(984\) | 17.2062 | 0.548513 | ||||||||
\(985\) | −21.2285 | −0.676396 | ||||||||
\(986\) | 6.18624 | 0.197010 | ||||||||
\(987\) | 15.3486 | 0.488552 | ||||||||
\(988\) | −31.5315 | −1.00315 | ||||||||
\(989\) | −2.16339 | −0.0687916 | ||||||||
\(990\) | 0.411419 | 0.0130758 | ||||||||
\(991\) | −36.6547 | −1.16437 | −0.582187 | − | 0.813055i | \(-0.697803\pi\) | ||||
−0.582187 | + | 0.813055i | \(0.697803\pi\) | |||||||
\(992\) | −28.1378 | −0.893375 | ||||||||
\(993\) | 50.0982 | 1.58982 | ||||||||
\(994\) | 70.4866 | 2.23570 | ||||||||
\(995\) | 41.0168 | 1.30032 | ||||||||
\(996\) | −31.3816 | −0.994363 | ||||||||
\(997\) | 11.6378 | 0.368574 | 0.184287 | − | 0.982872i | \(-0.441002\pi\) | ||||
0.184287 | + | 0.982872i | \(0.441002\pi\) | |||||||
\(998\) | 12.7551 | 0.403755 | ||||||||
\(999\) | −61.7669 | −1.95422 |
(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 | 4031.2.a.b.1.8 | ✓ | 59 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.b.1.8 | ✓ | 59 | 1.1 | even | 1 | trivial |