Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2671,2,Mod(1,2671)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2671, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2671.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2671 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2671.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: | \(21.3280423799\) |
Analytic rank: | \(0\) |
Dimension: | \(122\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.91 | ||
Character | \(\chi\) | \(=\) | 2671.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.59269 | 1.12620 | 0.563101 | − | 0.826388i | \(-0.309608\pi\) | ||||
0.563101 | + | 0.826388i | \(0.309608\pi\) | |||||||
\(3\) | 0.133072 | 0.0768290 | 0.0384145 | − | 0.999262i | \(-0.487769\pi\) | ||||
0.0384145 | + | 0.999262i | \(0.487769\pi\) | |||||||
\(4\) | 0.536661 | 0.268331 | ||||||||
\(5\) | 3.85218 | 1.72275 | 0.861375 | − | 0.507970i | \(-0.169604\pi\) | ||||
0.861375 | + | 0.507970i | \(0.169604\pi\) | |||||||
\(6\) | 0.211942 | 0.0865250 | ||||||||
\(7\) | −3.78245 | −1.42963 | −0.714816 | − | 0.699313i | \(-0.753489\pi\) | ||||
−0.714816 | + | 0.699313i | \(0.753489\pi\) | |||||||
\(8\) | −2.33064 | −0.824007 | ||||||||
\(9\) | −2.98229 | −0.994097 | ||||||||
\(10\) | 6.13534 | 1.94016 | ||||||||
\(11\) | 3.09744 | 0.933912 | 0.466956 | − | 0.884280i | \(-0.345351\pi\) | ||||
0.466956 | + | 0.884280i | \(0.345351\pi\) | |||||||
\(12\) | 0.0714145 | 0.0206156 | ||||||||
\(13\) | 5.35946 | 1.48645 | 0.743223 | − | 0.669044i | \(-0.233296\pi\) | ||||
0.743223 | + | 0.669044i | \(0.233296\pi\) | |||||||
\(14\) | −6.02427 | −1.61005 | ||||||||
\(15\) | 0.512617 | 0.132357 | ||||||||
\(16\) | −4.78532 | −1.19633 | ||||||||
\(17\) | 4.63008 | 1.12296 | 0.561480 | − | 0.827490i | \(-0.310232\pi\) | ||||
0.561480 | + | 0.827490i | \(0.310232\pi\) | |||||||
\(18\) | −4.74987 | −1.11955 | ||||||||
\(19\) | 7.98897 | 1.83280 | 0.916398 | − | 0.400269i | \(-0.131083\pi\) | ||||
0.916398 | + | 0.400269i | \(0.131083\pi\) | |||||||
\(20\) | 2.06732 | 0.462267 | ||||||||
\(21\) | −0.503337 | −0.109837 | ||||||||
\(22\) | 4.93326 | 1.05177 | ||||||||
\(23\) | −7.87336 | −1.64171 | −0.820854 | − | 0.571138i | \(-0.806502\pi\) | ||||
−0.820854 | + | 0.571138i | \(0.806502\pi\) | |||||||
\(24\) | −0.310143 | −0.0633077 | ||||||||
\(25\) | 9.83932 | 1.96786 | ||||||||
\(26\) | 8.53596 | 1.67404 | ||||||||
\(27\) | −0.796074 | −0.153205 | ||||||||
\(28\) | −2.02990 | −0.383614 | ||||||||
\(29\) | 4.15752 | 0.772032 | 0.386016 | − | 0.922492i | \(-0.373851\pi\) | ||||
0.386016 | + | 0.922492i | \(0.373851\pi\) | |||||||
\(30\) | 0.816440 | 0.149061 | ||||||||
\(31\) | 1.46572 | 0.263251 | 0.131625 | − | 0.991300i | \(-0.457980\pi\) | ||||
0.131625 | + | 0.991300i | \(0.457980\pi\) | |||||||
\(32\) | −2.96024 | −0.523301 | ||||||||
\(33\) | 0.412181 | 0.0717516 | ||||||||
\(34\) | 7.37429 | 1.26468 | ||||||||
\(35\) | −14.5707 | −2.46290 | ||||||||
\(36\) | −1.60048 | −0.266747 | ||||||||
\(37\) | −4.72073 | −0.776083 | −0.388042 | − | 0.921642i | \(-0.626848\pi\) | ||||
−0.388042 | + | 0.921642i | \(0.626848\pi\) | |||||||
\(38\) | 12.7240 | 2.06410 | ||||||||
\(39\) | 0.713193 | 0.114202 | ||||||||
\(40\) | −8.97807 | −1.41956 | ||||||||
\(41\) | 7.47802 | 1.16787 | 0.583935 | − | 0.811800i | \(-0.301512\pi\) | ||||
0.583935 | + | 0.811800i | \(0.301512\pi\) | |||||||
\(42\) | −0.801660 | −0.123699 | ||||||||
\(43\) | −9.48799 | −1.44690 | −0.723452 | − | 0.690374i | \(-0.757446\pi\) | ||||
−0.723452 | + | 0.690374i | \(0.757446\pi\) | |||||||
\(44\) | 1.66227 | 0.250597 | ||||||||
\(45\) | −11.4883 | −1.71258 | ||||||||
\(46\) | −12.5398 | −1.84889 | ||||||||
\(47\) | 6.78344 | 0.989466 | 0.494733 | − | 0.869045i | \(-0.335266\pi\) | ||||
0.494733 | + | 0.869045i | \(0.335266\pi\) | |||||||
\(48\) | −0.636791 | −0.0919128 | ||||||||
\(49\) | 7.30693 | 1.04385 | ||||||||
\(50\) | 15.6710 | 2.21621 | ||||||||
\(51\) | 0.616134 | 0.0862760 | ||||||||
\(52\) | 2.87621 | 0.398859 | ||||||||
\(53\) | −1.40954 | −0.193615 | −0.0968074 | − | 0.995303i | \(-0.530863\pi\) | ||||
−0.0968074 | + | 0.995303i | \(0.530863\pi\) | |||||||
\(54\) | −1.26790 | −0.172539 | ||||||||
\(55\) | 11.9319 | 1.60890 | ||||||||
\(56\) | 8.81555 | 1.17803 | ||||||||
\(57\) | 1.06311 | 0.140812 | ||||||||
\(58\) | 6.62164 | 0.869464 | ||||||||
\(59\) | 6.62436 | 0.862418 | 0.431209 | − | 0.902252i | \(-0.358087\pi\) | ||||
0.431209 | + | 0.902252i | \(0.358087\pi\) | |||||||
\(60\) | 0.275102 | 0.0355155 | ||||||||
\(61\) | −0.305843 | −0.0391592 | −0.0195796 | − | 0.999808i | \(-0.506233\pi\) | ||||
−0.0195796 | + | 0.999808i | \(0.506233\pi\) | |||||||
\(62\) | 2.33443 | 0.296473 | ||||||||
\(63\) | 11.2804 | 1.42119 | ||||||||
\(64\) | 4.85589 | 0.606987 | ||||||||
\(65\) | 20.6456 | 2.56077 | ||||||||
\(66\) | 0.656477 | 0.0808068 | ||||||||
\(67\) | 13.7914 | 1.68489 | 0.842446 | − | 0.538780i | \(-0.181115\pi\) | ||||
0.842446 | + | 0.538780i | \(0.181115\pi\) | |||||||
\(68\) | 2.48479 | 0.301325 | ||||||||
\(69\) | −1.04772 | −0.126131 | ||||||||
\(70\) | −23.2066 | −2.77372 | ||||||||
\(71\) | 9.58840 | 1.13793 | 0.568967 | − | 0.822361i | \(-0.307343\pi\) | ||||
0.568967 | + | 0.822361i | \(0.307343\pi\) | |||||||
\(72\) | 6.95066 | 0.819143 | ||||||||
\(73\) | 5.49821 | 0.643517 | 0.321758 | − | 0.946822i | \(-0.395726\pi\) | ||||
0.321758 | + | 0.946822i | \(0.395726\pi\) | |||||||
\(74\) | −7.51866 | −0.874026 | ||||||||
\(75\) | 1.30934 | 0.151189 | ||||||||
\(76\) | 4.28737 | 0.491795 | ||||||||
\(77\) | −11.7159 | −1.33515 | ||||||||
\(78\) | 1.13589 | 0.128615 | ||||||||
\(79\) | −8.56076 | −0.963160 | −0.481580 | − | 0.876402i | \(-0.659937\pi\) | ||||
−0.481580 | + | 0.876402i | \(0.659937\pi\) | |||||||
\(80\) | −18.4339 | −2.06098 | ||||||||
\(81\) | 8.84094 | 0.982327 | ||||||||
\(82\) | 11.9102 | 1.31526 | ||||||||
\(83\) | 7.47403 | 0.820381 | 0.410190 | − | 0.912000i | \(-0.365462\pi\) | ||||
0.410190 | + | 0.912000i | \(0.365462\pi\) | |||||||
\(84\) | −0.270122 | −0.0294727 | ||||||||
\(85\) | 17.8359 | 1.93458 | ||||||||
\(86\) | −15.1114 | −1.62951 | ||||||||
\(87\) | 0.553249 | 0.0593145 | ||||||||
\(88\) | −7.21902 | −0.769551 | ||||||||
\(89\) | −5.28174 | −0.559863 | −0.279932 | − | 0.960020i | \(-0.590312\pi\) | ||||
−0.279932 | + | 0.960020i | \(0.590312\pi\) | |||||||
\(90\) | −18.2974 | −1.92871 | ||||||||
\(91\) | −20.2719 | −2.12507 | ||||||||
\(92\) | −4.22533 | −0.440521 | ||||||||
\(93\) | 0.195046 | 0.0202253 | ||||||||
\(94\) | 10.8039 | 1.11434 | ||||||||
\(95\) | 30.7750 | 3.15745 | ||||||||
\(96\) | −0.393924 | −0.0402047 | ||||||||
\(97\) | −8.88605 | −0.902242 | −0.451121 | − | 0.892463i | \(-0.648976\pi\) | ||||
−0.451121 | + | 0.892463i | \(0.648976\pi\) | |||||||
\(98\) | 11.6377 | 1.17558 | ||||||||
\(99\) | −9.23746 | −0.928400 | ||||||||
\(100\) | 5.28039 | 0.528039 | ||||||||
\(101\) | −3.50694 | −0.348954 | −0.174477 | − | 0.984661i | \(-0.555823\pi\) | ||||
−0.174477 | + | 0.984661i | \(0.555823\pi\) | |||||||
\(102\) | 0.981310 | 0.0971641 | ||||||||
\(103\) | −15.4205 | −1.51943 | −0.759714 | − | 0.650257i | \(-0.774661\pi\) | ||||
−0.759714 | + | 0.650257i | \(0.774661\pi\) | |||||||
\(104\) | −12.4910 | −1.22484 | ||||||||
\(105\) | −1.93895 | −0.189222 | ||||||||
\(106\) | −2.24496 | −0.218049 | ||||||||
\(107\) | −20.2044 | −1.95323 | −0.976614 | − | 0.214999i | \(-0.931025\pi\) | ||||
−0.976614 | + | 0.214999i | \(0.931025\pi\) | |||||||
\(108\) | −0.427222 | −0.0411095 | ||||||||
\(109\) | 19.6582 | 1.88291 | 0.941456 | − | 0.337135i | \(-0.109458\pi\) | ||||
0.941456 | + | 0.337135i | \(0.109458\pi\) | |||||||
\(110\) | 19.0038 | 1.81194 | ||||||||
\(111\) | −0.628196 | −0.0596257 | ||||||||
\(112\) | 18.1002 | 1.71031 | ||||||||
\(113\) | 7.21759 | 0.678974 | 0.339487 | − | 0.940611i | \(-0.389747\pi\) | ||||
0.339487 | + | 0.940611i | \(0.389747\pi\) | |||||||
\(114\) | 1.69320 | 0.158583 | ||||||||
\(115\) | −30.3296 | −2.82825 | ||||||||
\(116\) | 2.23118 | 0.207160 | ||||||||
\(117\) | −15.9835 | −1.47767 | ||||||||
\(118\) | 10.5506 | 0.971257 | ||||||||
\(119\) | −17.5131 | −1.60542 | ||||||||
\(120\) | −1.19473 | −0.109063 | ||||||||
\(121\) | −1.40589 | −0.127808 | ||||||||
\(122\) | −0.487113 | −0.0441011 | ||||||||
\(123\) | 0.995114 | 0.0897264 | ||||||||
\(124\) | 0.786594 | 0.0706382 | ||||||||
\(125\) | 18.6420 | 1.66739 | ||||||||
\(126\) | 17.9661 | 1.60055 | ||||||||
\(127\) | −4.79569 | −0.425549 | −0.212774 | − | 0.977101i | \(-0.568250\pi\) | ||||
−0.212774 | + | 0.977101i | \(0.568250\pi\) | |||||||
\(128\) | 13.6544 | 1.20689 | ||||||||
\(129\) | −1.26258 | −0.111164 | ||||||||
\(130\) | 32.8821 | 2.88395 | ||||||||
\(131\) | −16.9873 | −1.48419 | −0.742095 | − | 0.670295i | \(-0.766167\pi\) | ||||
−0.742095 | + | 0.670295i | \(0.766167\pi\) | |||||||
\(132\) | 0.221202 | 0.0192532 | ||||||||
\(133\) | −30.2179 | −2.62022 | ||||||||
\(134\) | 21.9655 | 1.89753 | ||||||||
\(135\) | −3.06662 | −0.263933 | ||||||||
\(136\) | −10.7911 | −0.925328 | ||||||||
\(137\) | 12.1572 | 1.03866 | 0.519331 | − | 0.854573i | \(-0.326181\pi\) | ||||
0.519331 | + | 0.854573i | \(0.326181\pi\) | |||||||
\(138\) | −1.66870 | −0.142049 | ||||||||
\(139\) | 13.8845 | 1.17766 | 0.588832 | − | 0.808256i | \(-0.299588\pi\) | ||||
0.588832 | + | 0.808256i | \(0.299588\pi\) | |||||||
\(140\) | −7.81953 | −0.660871 | ||||||||
\(141\) | 0.902684 | 0.0760197 | ||||||||
\(142\) | 15.2713 | 1.28154 | ||||||||
\(143\) | 16.6006 | 1.38821 | ||||||||
\(144\) | 14.2712 | 1.18927 | ||||||||
\(145\) | 16.0155 | 1.33002 | ||||||||
\(146\) | 8.75695 | 0.724730 | ||||||||
\(147\) | 0.972346 | 0.0801977 | ||||||||
\(148\) | −2.53343 | −0.208247 | ||||||||
\(149\) | 9.26574 | 0.759079 | 0.379539 | − | 0.925176i | \(-0.376082\pi\) | ||||
0.379539 | + | 0.925176i | \(0.376082\pi\) | |||||||
\(150\) | 2.08537 | 0.170269 | ||||||||
\(151\) | −6.58802 | −0.536126 | −0.268063 | − | 0.963401i | \(-0.586383\pi\) | ||||
−0.268063 | + | 0.963401i | \(0.586383\pi\) | |||||||
\(152\) | −18.6195 | −1.51024 | ||||||||
\(153\) | −13.8083 | −1.11633 | ||||||||
\(154\) | −18.6598 | −1.50365 | ||||||||
\(155\) | 5.64621 | 0.453515 | ||||||||
\(156\) | 0.382743 | 0.0306440 | ||||||||
\(157\) | −14.5013 | −1.15733 | −0.578665 | − | 0.815565i | \(-0.696426\pi\) | ||||
−0.578665 | + | 0.815565i | \(0.696426\pi\) | |||||||
\(158\) | −13.6346 | −1.08471 | ||||||||
\(159\) | −0.187570 | −0.0148752 | ||||||||
\(160\) | −11.4034 | −0.901517 | ||||||||
\(161\) | 29.7806 | 2.34704 | ||||||||
\(162\) | 14.0809 | 1.10630 | ||||||||
\(163\) | −21.8843 | −1.71411 | −0.857054 | − | 0.515226i | \(-0.827708\pi\) | ||||
−0.857054 | + | 0.515226i | \(0.827708\pi\) | |||||||
\(164\) | 4.01317 | 0.313376 | ||||||||
\(165\) | 1.58780 | 0.123610 | ||||||||
\(166\) | 11.9038 | 0.923915 | ||||||||
\(167\) | −20.0378 | −1.55057 | −0.775287 | − | 0.631609i | \(-0.782395\pi\) | ||||
−0.775287 | + | 0.631609i | \(0.782395\pi\) | |||||||
\(168\) | 1.17310 | 0.0905067 | ||||||||
\(169\) | 15.7238 | 1.20952 | ||||||||
\(170\) | 28.4071 | 2.17873 | ||||||||
\(171\) | −23.8254 | −1.82198 | ||||||||
\(172\) | −5.09184 | −0.388249 | ||||||||
\(173\) | −21.0940 | −1.60375 | −0.801875 | − | 0.597492i | \(-0.796164\pi\) | ||||
−0.801875 | + | 0.597492i | \(0.796164\pi\) | |||||||
\(174\) | 0.881154 | 0.0668001 | ||||||||
\(175\) | −37.2167 | −2.81332 | ||||||||
\(176\) | −14.8222 | −1.11727 | ||||||||
\(177\) | 0.881515 | 0.0662588 | ||||||||
\(178\) | −8.41218 | −0.630519 | ||||||||
\(179\) | 12.7991 | 0.956649 | 0.478324 | − | 0.878183i | \(-0.341244\pi\) | ||||
0.478324 | + | 0.878183i | \(0.341244\pi\) | |||||||
\(180\) | −6.16535 | −0.459538 | ||||||||
\(181\) | −8.45270 | −0.628284 | −0.314142 | − | 0.949376i | \(-0.601717\pi\) | ||||
−0.314142 | + | 0.949376i | \(0.601717\pi\) | |||||||
\(182\) | −32.2868 | −2.39326 | ||||||||
\(183\) | −0.0406991 | −0.00300856 | ||||||||
\(184\) | 18.3500 | 1.35278 | ||||||||
\(185\) | −18.1851 | −1.33700 | ||||||||
\(186\) | 0.310647 | 0.0227778 | ||||||||
\(187\) | 14.3414 | 1.04875 | ||||||||
\(188\) | 3.64041 | 0.265504 | ||||||||
\(189\) | 3.01111 | 0.219026 | ||||||||
\(190\) | 49.0150 | 3.55592 | ||||||||
\(191\) | −4.36910 | −0.316137 | −0.158069 | − | 0.987428i | \(-0.550527\pi\) | ||||
−0.158069 | + | 0.987428i | \(0.550527\pi\) | |||||||
\(192\) | 0.646182 | 0.0466342 | ||||||||
\(193\) | 18.3763 | 1.32275 | 0.661377 | − | 0.750054i | \(-0.269973\pi\) | ||||
0.661377 | + | 0.750054i | \(0.269973\pi\) | |||||||
\(194\) | −14.1527 | −1.01611 | ||||||||
\(195\) | 2.74735 | 0.196742 | ||||||||
\(196\) | 3.92135 | 0.280096 | ||||||||
\(197\) | −15.6143 | −1.11247 | −0.556237 | − | 0.831024i | \(-0.687755\pi\) | ||||
−0.556237 | + | 0.831024i | \(0.687755\pi\) | |||||||
\(198\) | −14.7124 | −1.04557 | ||||||||
\(199\) | 11.9493 | 0.847065 | 0.423533 | − | 0.905881i | \(-0.360790\pi\) | ||||
0.423533 | + | 0.905881i | \(0.360790\pi\) | |||||||
\(200\) | −22.9320 | −1.62153 | ||||||||
\(201\) | 1.83525 | 0.129449 | ||||||||
\(202\) | −5.58547 | −0.392992 | ||||||||
\(203\) | −15.7256 | −1.10372 | ||||||||
\(204\) | 0.330655 | 0.0231505 | ||||||||
\(205\) | 28.8067 | 2.01195 | ||||||||
\(206\) | −24.5601 | −1.71118 | ||||||||
\(207\) | 23.4806 | 1.63202 | ||||||||
\(208\) | −25.6467 | −1.77828 | ||||||||
\(209\) | 24.7453 | 1.71167 | ||||||||
\(210\) | −3.08814 | −0.213102 | ||||||||
\(211\) | −0.549275 | −0.0378137 | −0.0189068 | − | 0.999821i | \(-0.506019\pi\) | ||||
−0.0189068 | + | 0.999821i | \(0.506019\pi\) | |||||||
\(212\) | −0.756444 | −0.0519528 | ||||||||
\(213\) | 1.27594 | 0.0874263 | ||||||||
\(214\) | −32.1793 | −2.19973 | ||||||||
\(215\) | −36.5495 | −2.49265 | ||||||||
\(216\) | 1.85537 | 0.126242 | ||||||||
\(217\) | −5.54400 | −0.376351 | ||||||||
\(218\) | 31.3094 | 2.12054 | ||||||||
\(219\) | 0.731657 | 0.0494408 | ||||||||
\(220\) | 6.40339 | 0.431716 | ||||||||
\(221\) | 24.8147 | 1.66922 | ||||||||
\(222\) | −1.00052 | −0.0671506 | ||||||||
\(223\) | 14.9690 | 1.00240 | 0.501199 | − | 0.865332i | \(-0.332892\pi\) | ||||
0.501199 | + | 0.865332i | \(0.332892\pi\) | |||||||
\(224\) | 11.1970 | 0.748128 | ||||||||
\(225\) | −29.3437 | −1.95625 | ||||||||
\(226\) | 11.4954 | 0.764661 | ||||||||
\(227\) | 4.38784 | 0.291231 | 0.145615 | − | 0.989341i | \(-0.453484\pi\) | ||||
0.145615 | + | 0.989341i | \(0.453484\pi\) | |||||||
\(228\) | 0.570528 | 0.0377842 | ||||||||
\(229\) | −1.43584 | −0.0948827 | −0.0474413 | − | 0.998874i | \(-0.515107\pi\) | ||||
−0.0474413 | + | 0.998874i | \(0.515107\pi\) | |||||||
\(230\) | −48.3057 | −3.18518 | ||||||||
\(231\) | −1.55906 | −0.102578 | ||||||||
\(232\) | −9.68970 | −0.636160 | ||||||||
\(233\) | −8.51135 | −0.557597 | −0.278798 | − | 0.960350i | \(-0.589936\pi\) | ||||
−0.278798 | + | 0.960350i | \(0.589936\pi\) | |||||||
\(234\) | −25.4567 | −1.66416 | ||||||||
\(235\) | 26.1311 | 1.70460 | ||||||||
\(236\) | 3.55504 | 0.231413 | ||||||||
\(237\) | −1.13919 | −0.0739987 | ||||||||
\(238\) | −27.8929 | −1.80803 | ||||||||
\(239\) | −24.7635 | −1.60182 | −0.800908 | − | 0.598788i | \(-0.795649\pi\) | ||||
−0.800908 | + | 0.598788i | \(0.795649\pi\) | |||||||
\(240\) | −2.45304 | −0.158343 | ||||||||
\(241\) | 5.53580 | 0.356592 | 0.178296 | − | 0.983977i | \(-0.442941\pi\) | ||||
0.178296 | + | 0.983977i | \(0.442941\pi\) | |||||||
\(242\) | −2.23914 | −0.143938 | ||||||||
\(243\) | 3.56470 | 0.228676 | ||||||||
\(244\) | −0.164134 | −0.0105076 | ||||||||
\(245\) | 28.1476 | 1.79829 | ||||||||
\(246\) | 1.58491 | 0.101050 | ||||||||
\(247\) | 42.8166 | 2.72435 | ||||||||
\(248\) | −3.41607 | −0.216920 | ||||||||
\(249\) | 0.994582 | 0.0630291 | ||||||||
\(250\) | 29.6909 | 1.87782 | ||||||||
\(251\) | 13.4878 | 0.851340 | 0.425670 | − | 0.904878i | \(-0.360038\pi\) | ||||
0.425670 | + | 0.904878i | \(0.360038\pi\) | |||||||
\(252\) | 6.05374 | 0.381350 | ||||||||
\(253\) | −24.3872 | −1.53321 | ||||||||
\(254\) | −7.63805 | −0.479254 | ||||||||
\(255\) | 2.37346 | 0.148632 | ||||||||
\(256\) | 12.0355 | 0.752216 | ||||||||
\(257\) | −4.54466 | −0.283488 | −0.141744 | − | 0.989903i | \(-0.545271\pi\) | ||||
−0.141744 | + | 0.989903i | \(0.545271\pi\) | |||||||
\(258\) | −2.01090 | −0.125193 | ||||||||
\(259\) | 17.8559 | 1.10951 | ||||||||
\(260\) | 11.0797 | 0.687134 | ||||||||
\(261\) | −12.3989 | −0.767475 | ||||||||
\(262\) | −27.0555 | −1.67150 | ||||||||
\(263\) | −25.9294 | −1.59888 | −0.799438 | − | 0.600749i | \(-0.794869\pi\) | ||||
−0.799438 | + | 0.600749i | \(0.794869\pi\) | |||||||
\(264\) | −0.960648 | −0.0591238 | ||||||||
\(265\) | −5.42980 | −0.333550 | ||||||||
\(266\) | −48.1277 | −2.95090 | ||||||||
\(267\) | −0.702851 | −0.0430138 | ||||||||
\(268\) | 7.40133 | 0.452108 | ||||||||
\(269\) | 12.7042 | 0.774590 | 0.387295 | − | 0.921956i | \(-0.373409\pi\) | ||||
0.387295 | + | 0.921956i | \(0.373409\pi\) | |||||||
\(270\) | −4.88418 | −0.297242 | ||||||||
\(271\) | −18.3009 | −1.11170 | −0.555849 | − | 0.831283i | \(-0.687607\pi\) | ||||
−0.555849 | + | 0.831283i | \(0.687607\pi\) | |||||||
\(272\) | −22.1564 | −1.34343 | ||||||||
\(273\) | −2.69762 | −0.163267 | ||||||||
\(274\) | 19.3627 | 1.16974 | ||||||||
\(275\) | 30.4767 | 1.83781 | ||||||||
\(276\) | −0.562272 | −0.0338448 | ||||||||
\(277\) | −19.6057 | −1.17799 | −0.588996 | − | 0.808136i | \(-0.700477\pi\) | ||||
−0.588996 | + | 0.808136i | \(0.700477\pi\) | |||||||
\(278\) | 22.1136 | 1.32629 | ||||||||
\(279\) | −4.37120 | −0.261697 | ||||||||
\(280\) | 33.9591 | 2.02944 | ||||||||
\(281\) | −33.1876 | −1.97981 | −0.989904 | − | 0.141738i | \(-0.954731\pi\) | ||||
−0.989904 | + | 0.141738i | \(0.954731\pi\) | |||||||
\(282\) | 1.43770 | 0.0856136 | ||||||||
\(283\) | 5.71017 | 0.339434 | 0.169717 | − | 0.985493i | \(-0.445715\pi\) | ||||
0.169717 | + | 0.985493i | \(0.445715\pi\) | |||||||
\(284\) | 5.14572 | 0.305342 | ||||||||
\(285\) | 4.09528 | 0.242584 | ||||||||
\(286\) | 26.4396 | 1.56341 | ||||||||
\(287\) | −28.2852 | −1.66963 | ||||||||
\(288\) | 8.82829 | 0.520212 | ||||||||
\(289\) | 4.43768 | 0.261040 | ||||||||
\(290\) | 25.5078 | 1.49787 | ||||||||
\(291\) | −1.18248 | −0.0693184 | ||||||||
\(292\) | 2.95068 | 0.172675 | ||||||||
\(293\) | 2.84237 | 0.166053 | 0.0830265 | − | 0.996547i | \(-0.473541\pi\) | ||||
0.0830265 | + | 0.996547i | \(0.473541\pi\) | |||||||
\(294\) | 1.54865 | 0.0903188 | ||||||||
\(295\) | 25.5183 | 1.48573 | ||||||||
\(296\) | 11.0023 | 0.639498 | ||||||||
\(297\) | −2.46579 | −0.143080 | ||||||||
\(298\) | 14.7574 | 0.854876 | ||||||||
\(299\) | −42.1969 | −2.44031 | ||||||||
\(300\) | 0.702670 | 0.0405687 | ||||||||
\(301\) | 35.8878 | 2.06854 | ||||||||
\(302\) | −10.4927 | −0.603786 | ||||||||
\(303\) | −0.466675 | −0.0268098 | ||||||||
\(304\) | −38.2298 | −2.19263 | ||||||||
\(305\) | −1.17816 | −0.0674614 | ||||||||
\(306\) | −21.9923 | −1.25722 | ||||||||
\(307\) | 7.93047 | 0.452616 | 0.226308 | − | 0.974056i | \(-0.427334\pi\) | ||||
0.226308 | + | 0.974056i | \(0.427334\pi\) | |||||||
\(308\) | −6.28747 | −0.358262 | ||||||||
\(309\) | −2.05204 | −0.116736 | ||||||||
\(310\) | 8.99266 | 0.510749 | ||||||||
\(311\) | −14.6132 | −0.828637 | −0.414319 | − | 0.910132i | \(-0.635980\pi\) | ||||
−0.414319 | + | 0.910132i | \(0.635980\pi\) | |||||||
\(312\) | −1.66220 | −0.0941035 | ||||||||
\(313\) | 6.64186 | 0.375420 | 0.187710 | − | 0.982224i | \(-0.439893\pi\) | ||||
0.187710 | + | 0.982224i | \(0.439893\pi\) | |||||||
\(314\) | −23.0961 | −1.30339 | ||||||||
\(315\) | 43.4541 | 2.44836 | ||||||||
\(316\) | −4.59423 | −0.258445 | ||||||||
\(317\) | −25.4620 | −1.43009 | −0.715045 | − | 0.699079i | \(-0.753594\pi\) | ||||
−0.715045 | + | 0.699079i | \(0.753594\pi\) | |||||||
\(318\) | −0.298740 | −0.0167525 | ||||||||
\(319\) | 12.8777 | 0.721010 | ||||||||
\(320\) | 18.7058 | 1.04569 | ||||||||
\(321\) | −2.68863 | −0.150065 | ||||||||
\(322\) | 47.4312 | 2.64324 | ||||||||
\(323\) | 36.9896 | 2.05816 | ||||||||
\(324\) | 4.74459 | 0.263588 | ||||||||
\(325\) | 52.7334 | 2.92513 | ||||||||
\(326\) | −34.8549 | −1.93043 | ||||||||
\(327\) | 2.61595 | 0.144662 | ||||||||
\(328\) | −17.4286 | −0.962334 | ||||||||
\(329\) | −25.6580 | −1.41457 | ||||||||
\(330\) | 2.52887 | 0.139210 | ||||||||
\(331\) | −18.5575 | −1.02001 | −0.510005 | − | 0.860171i | \(-0.670357\pi\) | ||||
−0.510005 | + | 0.860171i | \(0.670357\pi\) | |||||||
\(332\) | 4.01102 | 0.220133 | ||||||||
\(333\) | 14.0786 | 0.771502 | ||||||||
\(334\) | −31.9141 | −1.74626 | ||||||||
\(335\) | 53.1272 | 2.90265 | ||||||||
\(336\) | 2.40863 | 0.131401 | ||||||||
\(337\) | 4.03353 | 0.219720 | 0.109860 | − | 0.993947i | \(-0.464960\pi\) | ||||
0.109860 | + | 0.993947i | \(0.464960\pi\) | |||||||
\(338\) | 25.0431 | 1.36217 | ||||||||
\(339\) | 0.960457 | 0.0521649 | ||||||||
\(340\) | 9.57186 | 0.519107 | ||||||||
\(341\) | 4.53996 | 0.245853 | ||||||||
\(342\) | −37.9465 | −2.05191 | ||||||||
\(343\) | −1.16093 | −0.0626844 | ||||||||
\(344\) | 22.1131 | 1.19226 | ||||||||
\(345\) | −4.03602 | −0.217292 | ||||||||
\(346\) | −33.5963 | −1.80615 | ||||||||
\(347\) | 6.38494 | 0.342762 | 0.171381 | − | 0.985205i | \(-0.445177\pi\) | ||||
0.171381 | + | 0.985205i | \(0.445177\pi\) | |||||||
\(348\) | 0.296907 | 0.0159159 | ||||||||
\(349\) | 6.50148 | 0.348016 | 0.174008 | − | 0.984744i | \(-0.444328\pi\) | ||||
0.174008 | + | 0.984744i | \(0.444328\pi\) | |||||||
\(350\) | −59.2747 | −3.16837 | ||||||||
\(351\) | −4.26653 | −0.227730 | ||||||||
\(352\) | −9.16915 | −0.488717 | ||||||||
\(353\) | 10.0775 | 0.536370 | 0.268185 | − | 0.963367i | \(-0.413576\pi\) | ||||
0.268185 | + | 0.963367i | \(0.413576\pi\) | |||||||
\(354\) | 1.40398 | 0.0746207 | ||||||||
\(355\) | 36.9363 | 1.96037 | ||||||||
\(356\) | −2.83451 | −0.150229 | ||||||||
\(357\) | −2.33049 | −0.123343 | ||||||||
\(358\) | 20.3850 | 1.07738 | ||||||||
\(359\) | 6.31234 | 0.333153 | 0.166576 | − | 0.986029i | \(-0.446729\pi\) | ||||
0.166576 | + | 0.986029i | \(0.446729\pi\) | |||||||
\(360\) | 26.7752 | 1.41118 | ||||||||
\(361\) | 44.8237 | 2.35914 | ||||||||
\(362\) | −13.4625 | −0.707575 | ||||||||
\(363\) | −0.187084 | −0.00981936 | ||||||||
\(364\) | −10.8791 | −0.570222 | ||||||||
\(365\) | 21.1801 | 1.10862 | ||||||||
\(366\) | −0.0648210 | −0.00338825 | ||||||||
\(367\) | 5.17229 | 0.269991 | 0.134996 | − | 0.990846i | \(-0.456898\pi\) | ||||
0.134996 | + | 0.990846i | \(0.456898\pi\) | |||||||
\(368\) | 37.6765 | 1.96402 | ||||||||
\(369\) | −22.3016 | −1.16098 | ||||||||
\(370\) | −28.9633 | −1.50573 | ||||||||
\(371\) | 5.33150 | 0.276798 | ||||||||
\(372\) | 0.104673 | 0.00542706 | ||||||||
\(373\) | −6.62790 | −0.343180 | −0.171590 | − | 0.985168i | \(-0.554890\pi\) | ||||
−0.171590 | + | 0.985168i | \(0.554890\pi\) | |||||||
\(374\) | 22.8414 | 1.18110 | ||||||||
\(375\) | 2.48072 | 0.128104 | ||||||||
\(376\) | −15.8098 | −0.815327 | ||||||||
\(377\) | 22.2821 | 1.14758 | ||||||||
\(378\) | 4.79577 | 0.246668 | ||||||||
\(379\) | −22.4008 | −1.15065 | −0.575326 | − | 0.817924i | \(-0.695125\pi\) | ||||
−0.575326 | + | 0.817924i | \(0.695125\pi\) | |||||||
\(380\) | 16.5158 | 0.847240 | ||||||||
\(381\) | −0.638171 | −0.0326945 | ||||||||
\(382\) | −6.95863 | −0.356034 | ||||||||
\(383\) | 0.242974 | 0.0124154 | 0.00620768 | − | 0.999981i | \(-0.498024\pi\) | ||||
0.00620768 | + | 0.999981i | \(0.498024\pi\) | |||||||
\(384\) | 1.81702 | 0.0927242 | ||||||||
\(385\) | −45.1318 | −2.30013 | ||||||||
\(386\) | 29.2677 | 1.48969 | ||||||||
\(387\) | 28.2960 | 1.43836 | ||||||||
\(388\) | −4.76880 | −0.242099 | ||||||||
\(389\) | 17.9266 | 0.908913 | 0.454456 | − | 0.890769i | \(-0.349834\pi\) | ||||
0.454456 | + | 0.890769i | \(0.349834\pi\) | |||||||
\(390\) | 4.37568 | 0.221571 | ||||||||
\(391\) | −36.4543 | −1.84357 | ||||||||
\(392\) | −17.0298 | −0.860137 | ||||||||
\(393\) | −2.26053 | −0.114029 | ||||||||
\(394\) | −24.8688 | −1.25287 | ||||||||
\(395\) | −32.9776 | −1.65928 | ||||||||
\(396\) | −4.95739 | −0.249118 | ||||||||
\(397\) | −6.28866 | −0.315619 | −0.157809 | − | 0.987470i | \(-0.550443\pi\) | ||||
−0.157809 | + | 0.987470i | \(0.550443\pi\) | |||||||
\(398\) | 19.0316 | 0.953967 | ||||||||
\(399\) | −4.02115 | −0.201309 | ||||||||
\(400\) | −47.0843 | −2.35421 | ||||||||
\(401\) | −2.80781 | −0.140215 | −0.0701077 | − | 0.997539i | \(-0.522334\pi\) | ||||
−0.0701077 | + | 0.997539i | \(0.522334\pi\) | |||||||
\(402\) | 2.92299 | 0.145785 | ||||||||
\(403\) | 7.85545 | 0.391308 | ||||||||
\(404\) | −1.88204 | −0.0936350 | ||||||||
\(405\) | 34.0569 | 1.69230 | ||||||||
\(406\) | −25.0460 | −1.24301 | ||||||||
\(407\) | −14.6222 | −0.724794 | ||||||||
\(408\) | −1.43599 | −0.0710920 | ||||||||
\(409\) | 1.27846 | 0.0632156 | 0.0316078 | − | 0.999500i | \(-0.489937\pi\) | ||||
0.0316078 | + | 0.999500i | \(0.489937\pi\) | |||||||
\(410\) | 45.8802 | 2.26586 | ||||||||
\(411\) | 1.61778 | 0.0797994 | ||||||||
\(412\) | −8.27560 | −0.407709 | ||||||||
\(413\) | −25.0563 | −1.23294 | ||||||||
\(414\) | 37.3974 | 1.83798 | ||||||||
\(415\) | 28.7913 | 1.41331 | ||||||||
\(416\) | −15.8653 | −0.777859 | ||||||||
\(417\) | 1.84763 | 0.0904788 | ||||||||
\(418\) | 39.4116 | 1.92769 | ||||||||
\(419\) | −22.9895 | −1.12311 | −0.561555 | − | 0.827440i | \(-0.689797\pi\) | ||||
−0.561555 | + | 0.827440i | \(0.689797\pi\) | |||||||
\(420\) | −1.04056 | −0.0507741 | ||||||||
\(421\) | 11.3435 | 0.552850 | 0.276425 | − | 0.961036i | \(-0.410850\pi\) | ||||
0.276425 | + | 0.961036i | \(0.410850\pi\) | |||||||
\(422\) | −0.874825 | −0.0425858 | ||||||||
\(423\) | −20.2302 | −0.983626 | ||||||||
\(424\) | 3.28513 | 0.159540 | ||||||||
\(425\) | 45.5569 | 2.20983 | ||||||||
\(426\) | 2.03218 | 0.0984597 | ||||||||
\(427\) | 1.15684 | 0.0559832 | ||||||||
\(428\) | −10.8429 | −0.524111 | ||||||||
\(429\) | 2.20907 | 0.106655 | ||||||||
\(430\) | −58.2120 | −2.80723 | ||||||||
\(431\) | −24.3947 | −1.17505 | −0.587526 | − | 0.809205i | \(-0.699898\pi\) | ||||
−0.587526 | + | 0.809205i | \(0.699898\pi\) | |||||||
\(432\) | 3.80947 | 0.183283 | ||||||||
\(433\) | 10.9727 | 0.527315 | 0.263658 | − | 0.964616i | \(-0.415071\pi\) | ||||
0.263658 | + | 0.964616i | \(0.415071\pi\) | |||||||
\(434\) | −8.82987 | −0.423848 | ||||||||
\(435\) | 2.13122 | 0.102184 | ||||||||
\(436\) | 10.5498 | 0.505243 | ||||||||
\(437\) | −62.9000 | −3.00892 | ||||||||
\(438\) | 1.16530 | 0.0556803 | ||||||||
\(439\) | 25.3593 | 1.21034 | 0.605168 | − | 0.796098i | \(-0.293106\pi\) | ||||
0.605168 | + | 0.796098i | \(0.293106\pi\) | |||||||
\(440\) | −27.8090 | −1.32574 | ||||||||
\(441\) | −21.7914 | −1.03769 | ||||||||
\(442\) | 39.5222 | 1.87988 | ||||||||
\(443\) | 33.3777 | 1.58582 | 0.792912 | − | 0.609336i | \(-0.208564\pi\) | ||||
0.792912 | + | 0.609336i | \(0.208564\pi\) | |||||||
\(444\) | −0.337129 | −0.0159994 | ||||||||
\(445\) | −20.3462 | −0.964504 | ||||||||
\(446\) | 23.8410 | 1.12890 | ||||||||
\(447\) | 1.23301 | 0.0583193 | ||||||||
\(448\) | −18.3672 | −0.867767 | ||||||||
\(449\) | −2.75384 | −0.129962 | −0.0649808 | − | 0.997887i | \(-0.520699\pi\) | ||||
−0.0649808 | + | 0.997887i | \(0.520699\pi\) | |||||||
\(450\) | −46.7355 | −2.20313 | ||||||||
\(451\) | 23.1627 | 1.09069 | ||||||||
\(452\) | 3.87340 | 0.182189 | ||||||||
\(453\) | −0.876680 | −0.0411900 | ||||||||
\(454\) | 6.98846 | 0.327985 | ||||||||
\(455\) | −78.0910 | −3.66096 | ||||||||
\(456\) | −2.47772 | −0.116030 | ||||||||
\(457\) | 10.5646 | 0.494190 | 0.247095 | − | 0.968991i | \(-0.420524\pi\) | ||||
0.247095 | + | 0.968991i | \(0.420524\pi\) | |||||||
\(458\) | −2.28684 | −0.106857 | ||||||||
\(459\) | −3.68589 | −0.172043 | ||||||||
\(460\) | −16.2767 | −0.758907 | ||||||||
\(461\) | 2.71693 | 0.126540 | 0.0632699 | − | 0.997996i | \(-0.479847\pi\) | ||||
0.0632699 | + | 0.997996i | \(0.479847\pi\) | |||||||
\(462\) | −2.48309 | −0.115524 | ||||||||
\(463\) | −4.82893 | −0.224419 | −0.112210 | − | 0.993685i | \(-0.535793\pi\) | ||||
−0.112210 | + | 0.993685i | \(0.535793\pi\) | |||||||
\(464\) | −19.8951 | −0.923605 | ||||||||
\(465\) | 0.751351 | 0.0348431 | ||||||||
\(466\) | −13.5559 | −0.627967 | ||||||||
\(467\) | 12.3089 | 0.569588 | 0.284794 | − | 0.958589i | \(-0.408075\pi\) | ||||
0.284794 | + | 0.958589i | \(0.408075\pi\) | |||||||
\(468\) | −8.57771 | −0.396505 | ||||||||
\(469\) | −52.1654 | −2.40878 | ||||||||
\(470\) | 41.6187 | 1.91973 | ||||||||
\(471\) | −1.92971 | −0.0889165 | ||||||||
\(472\) | −15.4390 | −0.710639 | ||||||||
\(473\) | −29.3884 | −1.35128 | ||||||||
\(474\) | −1.81438 | −0.0833374 | ||||||||
\(475\) | 78.6061 | 3.60669 | ||||||||
\(476\) | −9.39858 | −0.430783 | ||||||||
\(477\) | 4.20365 | 0.192472 | ||||||||
\(478\) | −39.4405 | −1.80397 | ||||||||
\(479\) | 5.97832 | 0.273156 | 0.136578 | − | 0.990629i | \(-0.456390\pi\) | ||||
0.136578 | + | 0.990629i | \(0.456390\pi\) | |||||||
\(480\) | −1.51747 | −0.0692626 | ||||||||
\(481\) | −25.3006 | −1.15361 | ||||||||
\(482\) | 8.81682 | 0.401595 | ||||||||
\(483\) | 3.96295 | 0.180321 | ||||||||
\(484\) | −0.754486 | −0.0342948 | ||||||||
\(485\) | −34.2307 | −1.55434 | ||||||||
\(486\) | 5.67747 | 0.257535 | ||||||||
\(487\) | −32.6657 | −1.48022 | −0.740112 | − | 0.672484i | \(-0.765228\pi\) | ||||
−0.740112 | + | 0.672484i | \(0.765228\pi\) | |||||||
\(488\) | 0.712811 | 0.0322674 | ||||||||
\(489\) | −2.91218 | −0.131693 | ||||||||
\(490\) | 44.8304 | 2.02523 | ||||||||
\(491\) | 7.55392 | 0.340904 | 0.170452 | − | 0.985366i | \(-0.445477\pi\) | ||||
0.170452 | + | 0.985366i | \(0.445477\pi\) | |||||||
\(492\) | 0.534039 | 0.0240763 | ||||||||
\(493\) | 19.2497 | 0.866962 | ||||||||
\(494\) | 68.1935 | 3.06817 | ||||||||
\(495\) | −35.5844 | −1.59940 | ||||||||
\(496\) | −7.01392 | −0.314934 | ||||||||
\(497\) | −36.2676 | −1.62683 | ||||||||
\(498\) | 1.58406 | 0.0709835 | ||||||||
\(499\) | −19.9072 | −0.891169 | −0.445585 | − | 0.895240i | \(-0.647004\pi\) | ||||
−0.445585 | + | 0.895240i | \(0.647004\pi\) | |||||||
\(500\) | 10.0044 | 0.447411 | ||||||||
\(501\) | −2.66647 | −0.119129 | ||||||||
\(502\) | 21.4818 | 0.958781 | ||||||||
\(503\) | −22.0686 | −0.983991 | −0.491996 | − | 0.870598i | \(-0.663732\pi\) | ||||
−0.491996 | + | 0.870598i | \(0.663732\pi\) | |||||||
\(504\) | −26.2905 | −1.17107 | ||||||||
\(505\) | −13.5094 | −0.601160 | ||||||||
\(506\) | −38.8413 | −1.72671 | ||||||||
\(507\) | 2.09239 | 0.0929264 | ||||||||
\(508\) | −2.57366 | −0.114188 | ||||||||
\(509\) | 18.8213 | 0.834239 | 0.417119 | − | 0.908852i | \(-0.363040\pi\) | ||||
0.417119 | + | 0.908852i | \(0.363040\pi\) | |||||||
\(510\) | 3.78019 | 0.167389 | ||||||||
\(511\) | −20.7967 | −0.919992 | ||||||||
\(512\) | −8.14007 | −0.359744 | ||||||||
\(513\) | −6.35981 | −0.280793 | ||||||||
\(514\) | −7.23823 | −0.319265 | ||||||||
\(515\) | −59.4027 | −2.61759 | ||||||||
\(516\) | −0.677580 | −0.0298288 | ||||||||
\(517\) | 21.0113 | 0.924075 | ||||||||
\(518\) | 28.4389 | 1.24954 | ||||||||
\(519\) | −2.80702 | −0.123215 | ||||||||
\(520\) | −48.1176 | −2.11010 | ||||||||
\(521\) | −29.7858 | −1.30494 | −0.652470 | − | 0.757814i | \(-0.726267\pi\) | ||||
−0.652470 | + | 0.757814i | \(0.726267\pi\) | |||||||
\(522\) | −19.7477 | −0.864332 | ||||||||
\(523\) | 9.68696 | 0.423581 | 0.211790 | − | 0.977315i | \(-0.432071\pi\) | ||||
0.211790 | + | 0.977315i | \(0.432071\pi\) | |||||||
\(524\) | −9.11644 | −0.398254 | ||||||||
\(525\) | −4.95250 | −0.216145 | ||||||||
\(526\) | −41.2975 | −1.80066 | ||||||||
\(527\) | 6.78639 | 0.295620 | ||||||||
\(528\) | −1.97242 | −0.0858385 | ||||||||
\(529\) | 38.9897 | 1.69521 | ||||||||
\(530\) | −8.64798 | −0.375644 | ||||||||
\(531\) | −19.7558 | −0.857328 | ||||||||
\(532\) | −16.2168 | −0.703086 | ||||||||
\(533\) | 40.0781 | 1.73598 | ||||||||
\(534\) | −1.11942 | −0.0484422 | ||||||||
\(535\) | −77.8309 | −3.36492 | ||||||||
\(536\) | −32.1429 | −1.38836 | ||||||||
\(537\) | 1.70320 | 0.0734984 | ||||||||
\(538\) | 20.2339 | 0.872345 | ||||||||
\(539\) | 22.6327 | 0.974861 | ||||||||
\(540\) | −1.64574 | −0.0708213 | ||||||||
\(541\) | 27.3382 | 1.17536 | 0.587680 | − | 0.809094i | \(-0.300041\pi\) | ||||
0.587680 | + | 0.809094i | \(0.300041\pi\) | |||||||
\(542\) | −29.1476 | −1.25200 | ||||||||
\(543\) | −1.12482 | −0.0482705 | ||||||||
\(544\) | −13.7062 | −0.587646 | ||||||||
\(545\) | 75.7270 | 3.24379 | ||||||||
\(546\) | −4.29646 | −0.183872 | ||||||||
\(547\) | 5.26107 | 0.224947 | 0.112473 | − | 0.993655i | \(-0.464123\pi\) | ||||
0.112473 | + | 0.993655i | \(0.464123\pi\) | |||||||
\(548\) | 6.52432 | 0.278705 | ||||||||
\(549\) | 0.912113 | 0.0389280 | ||||||||
\(550\) | 48.5399 | 2.06975 | ||||||||
\(551\) | 33.2143 | 1.41498 | ||||||||
\(552\) | 2.44187 | 0.103933 | ||||||||
\(553\) | 32.3806 | 1.37696 | ||||||||
\(554\) | −31.2258 | −1.32666 | ||||||||
\(555\) | −2.41993 | −0.102720 | ||||||||
\(556\) | 7.45125 | 0.316003 | ||||||||
\(557\) | −8.87242 | −0.375936 | −0.187968 | − | 0.982175i | \(-0.560190\pi\) | ||||
−0.187968 | + | 0.982175i | \(0.560190\pi\) | |||||||
\(558\) | −6.96196 | −0.294723 | ||||||||
\(559\) | −50.8505 | −2.15075 | ||||||||
\(560\) | 69.7254 | 2.94644 | ||||||||
\(561\) | 1.90843 | 0.0805742 | ||||||||
\(562\) | −52.8576 | −2.22966 | ||||||||
\(563\) | 37.0268 | 1.56049 | 0.780246 | − | 0.625473i | \(-0.215094\pi\) | ||||
0.780246 | + | 0.625473i | \(0.215094\pi\) | |||||||
\(564\) | 0.484436 | 0.0203984 | ||||||||
\(565\) | 27.8035 | 1.16970 | ||||||||
\(566\) | 9.09453 | 0.382272 | ||||||||
\(567\) | −33.4404 | −1.40437 | ||||||||
\(568\) | −22.3471 | −0.937665 | ||||||||
\(569\) | −2.28965 | −0.0959870 | −0.0479935 | − | 0.998848i | \(-0.515283\pi\) | ||||
−0.0479935 | + | 0.998848i | \(0.515283\pi\) | |||||||
\(570\) | 6.52252 | 0.273198 | ||||||||
\(571\) | 16.1987 | 0.677896 | 0.338948 | − | 0.940805i | \(-0.389929\pi\) | ||||
0.338948 | + | 0.940805i | \(0.389929\pi\) | |||||||
\(572\) | 8.90889 | 0.372499 | ||||||||
\(573\) | −0.581404 | −0.0242885 | ||||||||
\(574\) | −45.0496 | −1.88033 | ||||||||
\(575\) | −77.4685 | −3.23066 | ||||||||
\(576\) | −14.4817 | −0.603404 | ||||||||
\(577\) | −22.1486 | −0.922057 | −0.461028 | − | 0.887385i | \(-0.652519\pi\) | ||||
−0.461028 | + | 0.887385i | \(0.652519\pi\) | |||||||
\(578\) | 7.06785 | 0.293984 | ||||||||
\(579\) | 2.44536 | 0.101626 | ||||||||
\(580\) | 8.59492 | 0.356885 | ||||||||
\(581\) | −28.2701 | −1.17284 | ||||||||
\(582\) | −1.88333 | −0.0780665 | ||||||||
\(583\) | −4.36595 | −0.180819 | ||||||||
\(584\) | −12.8144 | −0.530263 | ||||||||
\(585\) | −61.5713 | −2.54566 | ||||||||
\(586\) | 4.52701 | 0.187009 | ||||||||
\(587\) | −38.2594 | −1.57914 | −0.789568 | − | 0.613663i | \(-0.789695\pi\) | ||||
−0.789568 | + | 0.613663i | \(0.789695\pi\) | |||||||
\(588\) | 0.521820 | 0.0215195 | ||||||||
\(589\) | 11.7096 | 0.482484 | ||||||||
\(590\) | 40.6427 | 1.67323 | ||||||||
\(591\) | −2.07783 | −0.0854703 | ||||||||
\(592\) | 22.5902 | 0.928451 | ||||||||
\(593\) | −16.2128 | −0.665781 | −0.332890 | − | 0.942965i | \(-0.608024\pi\) | ||||
−0.332890 | + | 0.942965i | \(0.608024\pi\) | |||||||
\(594\) | −3.92724 | −0.161137 | ||||||||
\(595\) | −67.4635 | −2.76574 | ||||||||
\(596\) | 4.97257 | 0.203684 | ||||||||
\(597\) | 1.59012 | 0.0650792 | ||||||||
\(598\) | −67.2066 | −2.74828 | ||||||||
\(599\) | 17.4063 | 0.711201 | 0.355600 | − | 0.934638i | \(-0.384276\pi\) | ||||
0.355600 | + | 0.934638i | \(0.384276\pi\) | |||||||
\(600\) | −3.05160 | −0.124581 | ||||||||
\(601\) | −7.31569 | −0.298413 | −0.149207 | − | 0.988806i | \(-0.547672\pi\) | ||||
−0.149207 | + | 0.988806i | \(0.547672\pi\) | |||||||
\(602\) | 57.1582 | 2.32959 | ||||||||
\(603\) | −41.1301 | −1.67495 | ||||||||
\(604\) | −3.53554 | −0.143859 | ||||||||
\(605\) | −5.41574 | −0.220181 | ||||||||
\(606\) | −0.743269 | −0.0301932 | ||||||||
\(607\) | −7.70672 | −0.312806 | −0.156403 | − | 0.987693i | \(-0.549990\pi\) | ||||
−0.156403 | + | 0.987693i | \(0.549990\pi\) | |||||||
\(608\) | −23.6493 | −0.959104 | ||||||||
\(609\) | −2.09264 | −0.0847979 | ||||||||
\(610\) | −1.87645 | −0.0759752 | ||||||||
\(611\) | 36.3556 | 1.47079 | ||||||||
\(612\) | −7.41036 | −0.299546 | ||||||||
\(613\) | −6.42614 | −0.259549 | −0.129775 | − | 0.991544i | \(-0.541425\pi\) | ||||
−0.129775 | + | 0.991544i | \(0.541425\pi\) | |||||||
\(614\) | 12.6308 | 0.509737 | ||||||||
\(615\) | 3.83336 | 0.154576 | ||||||||
\(616\) | 27.3056 | 1.10017 | ||||||||
\(617\) | 44.7049 | 1.79975 | 0.899877 | − | 0.436144i | \(-0.143656\pi\) | ||||
0.899877 | + | 0.436144i | \(0.143656\pi\) | |||||||
\(618\) | −3.26826 | −0.131469 | ||||||||
\(619\) | 14.6653 | 0.589450 | 0.294725 | − | 0.955582i | \(-0.404772\pi\) | ||||
0.294725 | + | 0.955582i | \(0.404772\pi\) | |||||||
\(620\) | 3.03010 | 0.121692 | ||||||||
\(621\) | 6.26778 | 0.251517 | ||||||||
\(622\) | −23.2743 | −0.933213 | ||||||||
\(623\) | 19.9779 | 0.800398 | ||||||||
\(624\) | −3.41285 | −0.136623 | ||||||||
\(625\) | 22.6157 | 0.904627 | ||||||||
\(626\) | 10.5784 | 0.422799 | ||||||||
\(627\) | 3.29291 | 0.131506 | ||||||||
\(628\) | −7.78229 | −0.310547 | ||||||||
\(629\) | −21.8574 | −0.871511 | ||||||||
\(630\) | 69.2088 | 2.75735 | ||||||||
\(631\) | 17.7486 | 0.706561 | 0.353280 | − | 0.935517i | \(-0.385066\pi\) | ||||
0.353280 | + | 0.935517i | \(0.385066\pi\) | |||||||
\(632\) | 19.9521 | 0.793651 | ||||||||
\(633\) | −0.0730931 | −0.00290519 | ||||||||
\(634\) | −40.5531 | −1.61057 | ||||||||
\(635\) | −18.4739 | −0.733114 | ||||||||
\(636\) | −0.100661 | −0.00399148 | ||||||||
\(637\) | 39.1612 | 1.55162 | ||||||||
\(638\) | 20.5101 | 0.812003 | ||||||||
\(639\) | −28.5954 | −1.13122 | ||||||||
\(640\) | 52.5993 | 2.07917 | ||||||||
\(641\) | −4.16534 | −0.164521 | −0.0822605 | − | 0.996611i | \(-0.526214\pi\) | ||||
−0.0822605 | + | 0.996611i | \(0.526214\pi\) | |||||||
\(642\) | −4.28215 | −0.169003 | ||||||||
\(643\) | −32.4839 | −1.28104 | −0.640520 | − | 0.767941i | \(-0.721281\pi\) | ||||
−0.640520 | + | 0.767941i | \(0.721281\pi\) | |||||||
\(644\) | 15.9821 | 0.629782 | ||||||||
\(645\) | −4.86371 | −0.191508 | ||||||||
\(646\) | 58.9130 | 2.31790 | ||||||||
\(647\) | −20.5270 | −0.806998 | −0.403499 | − | 0.914980i | \(-0.632206\pi\) | ||||
−0.403499 | + | 0.914980i | \(0.632206\pi\) | |||||||
\(648\) | −20.6051 | −0.809444 | ||||||||
\(649\) | 20.5185 | 0.805423 | ||||||||
\(650\) | 83.9880 | 3.29428 | ||||||||
\(651\) | −0.737750 | −0.0289147 | ||||||||
\(652\) | −11.7444 | −0.459948 | ||||||||
\(653\) | 9.24507 | 0.361788 | 0.180894 | − | 0.983503i | \(-0.442101\pi\) | ||||
0.180894 | + | 0.983503i | \(0.442101\pi\) | |||||||
\(654\) | 4.16640 | 0.162919 | ||||||||
\(655\) | −65.4383 | −2.55689 | ||||||||
\(656\) | −35.7847 | −1.39716 | ||||||||
\(657\) | −16.3973 | −0.639718 | ||||||||
\(658\) | −40.8653 | −1.59309 | ||||||||
\(659\) | −0.114905 | −0.00447606 | −0.00223803 | − | 0.999997i | \(-0.500712\pi\) | ||||
−0.00223803 | + | 0.999997i | \(0.500712\pi\) | |||||||
\(660\) | 0.852110 | 0.0331684 | ||||||||
\(661\) | −10.9411 | −0.425560 | −0.212780 | − | 0.977100i | \(-0.568252\pi\) | ||||
−0.212780 | + | 0.977100i | \(0.568252\pi\) | |||||||
\(662\) | −29.5563 | −1.14874 | ||||||||
\(663\) | 3.30214 | 0.128245 | ||||||||
\(664\) | −17.4193 | −0.676000 | ||||||||
\(665\) | −116.405 | −4.51399 | ||||||||
\(666\) | 22.4228 | 0.868867 | ||||||||
\(667\) | −32.7336 | −1.26745 | ||||||||
\(668\) | −10.7535 | −0.416067 | ||||||||
\(669\) | 1.99195 | 0.0770133 | ||||||||
\(670\) | 84.6151 | 3.26897 | ||||||||
\(671\) | −0.947329 | −0.0365712 | ||||||||
\(672\) | 1.49000 | 0.0574779 | ||||||||
\(673\) | 44.8362 | 1.72831 | 0.864154 | − | 0.503228i | \(-0.167854\pi\) | ||||
0.864154 | + | 0.503228i | \(0.167854\pi\) | |||||||
\(674\) | 6.42417 | 0.247450 | ||||||||
\(675\) | −7.83283 | −0.301486 | ||||||||
\(676\) | 8.43835 | 0.324552 | ||||||||
\(677\) | 12.2871 | 0.472232 | 0.236116 | − | 0.971725i | \(-0.424125\pi\) | ||||
0.236116 | + | 0.971725i | \(0.424125\pi\) | |||||||
\(678\) | 1.52971 | 0.0587482 | ||||||||
\(679\) | 33.6110 | 1.28987 | ||||||||
\(680\) | −41.5692 | −1.59411 | ||||||||
\(681\) | 0.583897 | 0.0223750 | ||||||||
\(682\) | 7.23076 | 0.276880 | ||||||||
\(683\) | 15.7722 | 0.603506 | 0.301753 | − | 0.953386i | \(-0.402428\pi\) | ||||
0.301753 | + | 0.953386i | \(0.402428\pi\) | |||||||
\(684\) | −12.7862 | −0.488892 | ||||||||
\(685\) | 46.8319 | 1.78935 | ||||||||
\(686\) | −1.84900 | −0.0705953 | ||||||||
\(687\) | −0.191069 | −0.00728975 | ||||||||
\(688\) | 45.4030 | 1.73097 | ||||||||
\(689\) | −7.55436 | −0.287798 | ||||||||
\(690\) | −6.42812 | −0.244714 | ||||||||
\(691\) | −24.7877 | −0.942968 | −0.471484 | − | 0.881875i | \(-0.656281\pi\) | ||||
−0.471484 | + | 0.881875i | \(0.656281\pi\) | |||||||
\(692\) | −11.3204 | −0.430335 | ||||||||
\(693\) | 34.9402 | 1.32727 | ||||||||
\(694\) | 10.1692 | 0.386019 | ||||||||
\(695\) | 53.4855 | 2.02882 | ||||||||
\(696\) | −1.28943 | −0.0488756 | ||||||||
\(697\) | 34.6239 | 1.31147 | ||||||||
\(698\) | 10.3548 | 0.391936 | ||||||||
\(699\) | −1.13262 | −0.0428396 | ||||||||
\(700\) | −19.9728 | −0.754901 | ||||||||
\(701\) | −22.4515 | −0.847980 | −0.423990 | − | 0.905667i | \(-0.639371\pi\) | ||||
−0.423990 | + | 0.905667i | \(0.639371\pi\) | |||||||
\(702\) | −6.79525 | −0.256470 | ||||||||
\(703\) | −37.7138 | −1.42240 | ||||||||
\(704\) | 15.0408 | 0.566872 | ||||||||
\(705\) | 3.47731 | 0.130963 | ||||||||
\(706\) | 16.0503 | 0.604061 | ||||||||
\(707\) | 13.2648 | 0.498875 | ||||||||
\(708\) | 0.473075 | 0.0177793 | ||||||||
\(709\) | 6.09525 | 0.228912 | 0.114456 | − | 0.993428i | \(-0.463487\pi\) | ||||
0.114456 | + | 0.993428i | \(0.463487\pi\) | |||||||
\(710\) | 58.8280 | 2.20778 | ||||||||
\(711\) | 25.5307 | 0.957475 | ||||||||
\(712\) | 12.3099 | 0.461332 | ||||||||
\(713\) | −11.5401 | −0.432180 | ||||||||
\(714\) | −3.71175 | −0.138909 | ||||||||
\(715\) | 63.9485 | 2.39154 | ||||||||
\(716\) | 6.86878 | 0.256698 | ||||||||
\(717\) | −3.29532 | −0.123066 | ||||||||
\(718\) | 10.0536 | 0.375197 | ||||||||
\(719\) | 50.3385 | 1.87731 | 0.938655 | − | 0.344857i | \(-0.112073\pi\) | ||||
0.938655 | + | 0.344857i | \(0.112073\pi\) | |||||||
\(720\) | 54.9753 | 2.04881 | ||||||||
\(721\) | 58.3273 | 2.17222 | ||||||||
\(722\) | 71.3902 | 2.65687 | ||||||||
\(723\) | 0.736659 | 0.0273966 | ||||||||
\(724\) | −4.53624 | −0.168588 | ||||||||
\(725\) | 40.9072 | 1.51926 | ||||||||
\(726\) | −0.297967 | −0.0110586 | ||||||||
\(727\) | 3.07810 | 0.114160 | 0.0570802 | − | 0.998370i | \(-0.481821\pi\) | ||||
0.0570802 | + | 0.998370i | \(0.481821\pi\) | |||||||
\(728\) | 47.2466 | 1.75107 | ||||||||
\(729\) | −26.0485 | −0.964758 | ||||||||
\(730\) | 33.7334 | 1.24853 | ||||||||
\(731\) | −43.9302 | −1.62482 | ||||||||
\(732\) | −0.0218416 | −0.000807289 0 | ||||||||
\(733\) | 29.9429 | 1.10596 | 0.552982 | − | 0.833193i | \(-0.313490\pi\) | ||||
0.552982 | + | 0.833193i | \(0.313490\pi\) | |||||||
\(734\) | 8.23785 | 0.304065 | ||||||||
\(735\) | 3.74565 | 0.138161 | ||||||||
\(736\) | 23.3070 | 0.859108 | ||||||||
\(737\) | 42.7181 | 1.57354 | ||||||||
\(738\) | −35.5196 | −1.30749 | ||||||||
\(739\) | 50.0635 | 1.84162 | 0.920808 | − | 0.390016i | \(-0.127530\pi\) | ||||
0.920808 | + | 0.390016i | \(0.127530\pi\) | |||||||
\(740\) | −9.75925 | −0.358757 | ||||||||
\(741\) | 5.69768 | 0.209309 | ||||||||
\(742\) | 8.49143 | 0.311730 | ||||||||
\(743\) | 21.8551 | 0.801785 | 0.400892 | − | 0.916125i | \(-0.368700\pi\) | ||||
0.400892 | + | 0.916125i | \(0.368700\pi\) | |||||||
\(744\) | −0.454582 | −0.0166658 | ||||||||
\(745\) | 35.6933 | 1.30770 | ||||||||
\(746\) | −10.5562 | −0.386490 | ||||||||
\(747\) | −22.2897 | −0.815538 | ||||||||
\(748\) | 7.69647 | 0.281411 | ||||||||
\(749\) | 76.4220 | 2.79240 | ||||||||
\(750\) | 3.95102 | 0.144271 | ||||||||
\(751\) | 15.5073 | 0.565869 | 0.282935 | − | 0.959139i | \(-0.408692\pi\) | ||||
0.282935 | + | 0.959139i | \(0.408692\pi\) | |||||||
\(752\) | −32.4609 | −1.18373 | ||||||||
\(753\) | 1.79484 | 0.0654076 | ||||||||
\(754\) | 35.4884 | 1.29241 | ||||||||
\(755\) | −25.3783 | −0.923610 | ||||||||
\(756\) | 1.61595 | 0.0587714 | ||||||||
\(757\) | 28.7870 | 1.04628 | 0.523140 | − | 0.852247i | \(-0.324760\pi\) | ||||
0.523140 | + | 0.852247i | \(0.324760\pi\) | |||||||
\(758\) | −35.6776 | −1.29587 | ||||||||
\(759\) | −3.24525 | −0.117795 | ||||||||
\(760\) | −71.7256 | −2.60176 | ||||||||
\(761\) | 33.2039 | 1.20364 | 0.601819 | − | 0.798632i | \(-0.294443\pi\) | ||||
0.601819 | + | 0.798632i | \(0.294443\pi\) | |||||||
\(762\) | −1.01641 | −0.0368206 | ||||||||
\(763\) | −74.3561 | −2.69187 | ||||||||
\(764\) | −2.34473 | −0.0848293 | ||||||||
\(765\) | −53.1920 | −1.92316 | ||||||||
\(766\) | 0.386981 | 0.0139822 | ||||||||
\(767\) | 35.5030 | 1.28194 | ||||||||
\(768\) | 1.60158 | 0.0577920 | ||||||||
\(769\) | −42.5825 | −1.53557 | −0.767783 | − | 0.640710i | \(-0.778640\pi\) | ||||
−0.767783 | + | 0.640710i | \(0.778640\pi\) | |||||||
\(770\) | −71.8810 | −2.59041 | ||||||||
\(771\) | −0.604766 | −0.0217801 | ||||||||
\(772\) | 9.86184 | 0.354935 | ||||||||
\(773\) | 12.3322 | 0.443559 | 0.221779 | − | 0.975097i | \(-0.428814\pi\) | ||||
0.221779 | + | 0.975097i | \(0.428814\pi\) | |||||||
\(774\) | 45.0667 | 1.61989 | ||||||||
\(775\) | 14.4217 | 0.518041 | ||||||||
\(776\) | 20.7102 | 0.743454 | ||||||||
\(777\) | 2.37612 | 0.0852428 | ||||||||
\(778\) | 28.5515 | 1.02362 | ||||||||
\(779\) | 59.7417 | 2.14047 | ||||||||
\(780\) | 1.47440 | 0.0527919 | ||||||||
\(781\) | 29.6994 | 1.06273 | ||||||||
\(782\) | −58.0604 | −2.07624 | ||||||||
\(783\) | −3.30970 | −0.118279 | ||||||||
\(784\) | −34.9660 | −1.24878 | ||||||||
\(785\) | −55.8617 | −1.99379 | ||||||||
\(786\) | −3.60033 | −0.128419 | ||||||||
\(787\) | −25.7076 | −0.916377 | −0.458189 | − | 0.888855i | \(-0.651502\pi\) | ||||
−0.458189 | + | 0.888855i | \(0.651502\pi\) | |||||||
\(788\) | −8.37961 | −0.298511 | ||||||||
\(789\) | −3.45047 | −0.122840 | ||||||||
\(790\) | −52.5231 | −1.86869 | ||||||||
\(791\) | −27.3002 | −0.970682 | ||||||||
\(792\) | 21.5292 | 0.765008 | ||||||||
\(793\) | −1.63915 | −0.0582080 | ||||||||
\(794\) | −10.0159 | −0.355450 | ||||||||
\(795\) | −0.722553 | −0.0256263 | ||||||||
\(796\) | 6.41274 | 0.227294 | ||||||||
\(797\) | 21.7793 | 0.771461 | 0.385730 | − | 0.922612i | \(-0.373949\pi\) | ||||
0.385730 | + | 0.922612i | \(0.373949\pi\) | |||||||
\(798\) | −6.40444 | −0.226715 | ||||||||
\(799\) | 31.4079 | 1.11113 | ||||||||
\(800\) | −29.1267 | −1.02979 | ||||||||
\(801\) | 15.7517 | 0.556559 | ||||||||
\(802\) | −4.47197 | −0.157911 | ||||||||
\(803\) | 17.0304 | 0.600988 | ||||||||
\(804\) | 0.984909 | 0.0347351 | ||||||||
\(805\) | 114.720 | 4.04336 | ||||||||
\(806\) | 12.5113 | 0.440692 | ||||||||
\(807\) | 1.69057 | 0.0595110 | ||||||||
\(808\) | 8.17343 | 0.287540 | ||||||||
\(809\) | −36.5836 | −1.28621 | −0.643105 | − | 0.765778i | \(-0.722354\pi\) | ||||
−0.643105 | + | 0.765778i | \(0.722354\pi\) | |||||||
\(810\) | 54.2421 | 1.90587 | ||||||||
\(811\) | −3.31224 | −0.116308 | −0.0581542 | − | 0.998308i | \(-0.518521\pi\) | ||||
−0.0581542 | + | 0.998308i | \(0.518521\pi\) | |||||||
\(812\) | −8.43933 | −0.296162 | ||||||||
\(813\) | −2.43533 | −0.0854107 | ||||||||
\(814\) | −23.2886 | −0.816264 | ||||||||
\(815\) | −84.3023 | −2.95298 | ||||||||
\(816\) | −2.94839 | −0.103214 | ||||||||
\(817\) | −75.7993 | −2.65188 | ||||||||
\(818\) | 2.03618 | 0.0711935 | ||||||||
\(819\) | 60.4567 | 2.11253 | ||||||||
\(820\) | 15.4595 | 0.539868 | ||||||||
\(821\) | −20.4794 | −0.714736 | −0.357368 | − | 0.933964i | \(-0.616326\pi\) | ||||
−0.357368 | + | 0.933964i | \(0.616326\pi\) | |||||||
\(822\) | 2.57663 | 0.0898702 | ||||||||
\(823\) | −25.5204 | −0.889586 | −0.444793 | − | 0.895633i | \(-0.646723\pi\) | ||||
−0.444793 | + | 0.895633i | \(0.646723\pi\) | |||||||
\(824\) | 35.9397 | 1.25202 | ||||||||
\(825\) | 4.05559 | 0.141197 | ||||||||
\(826\) | −39.9069 | −1.38854 | ||||||||
\(827\) | −9.88107 | −0.343598 | −0.171799 | − | 0.985132i | \(-0.554958\pi\) | ||||
−0.171799 | + | 0.985132i | \(0.554958\pi\) | |||||||
\(828\) | 12.6012 | 0.437920 | ||||||||
\(829\) | −13.3413 | −0.463363 | −0.231682 | − | 0.972792i | \(-0.574423\pi\) | ||||
−0.231682 | + | 0.972792i | \(0.574423\pi\) | |||||||
\(830\) | 45.8557 | 1.59167 | ||||||||
\(831\) | −2.60897 | −0.0905040 | ||||||||
\(832\) | 26.0250 | 0.902253 | ||||||||
\(833\) | 33.8317 | 1.17220 | ||||||||
\(834\) | 2.94270 | 0.101897 | ||||||||
\(835\) | −77.1894 | −2.67125 | ||||||||
\(836\) | 13.2799 | 0.459294 | ||||||||
\(837\) | −1.16682 | −0.0403312 | ||||||||
\(838\) | −36.6151 | −1.26485 | ||||||||
\(839\) | −2.87114 | −0.0991228 | −0.0495614 | − | 0.998771i | \(-0.515782\pi\) | ||||
−0.0495614 | + | 0.998771i | \(0.515782\pi\) | |||||||
\(840\) | 4.51900 | 0.155920 | ||||||||
\(841\) | −11.7150 | −0.403966 | ||||||||
\(842\) | 18.0667 | 0.622621 | ||||||||
\(843\) | −4.41634 | −0.152107 | ||||||||
\(844\) | −0.294775 | −0.0101466 | ||||||||
\(845\) | 60.5709 | 2.08370 | ||||||||
\(846\) | −32.2204 | −1.10776 | ||||||||
\(847\) | 5.31770 | 0.182718 | ||||||||
\(848\) | 6.74508 | 0.231627 | ||||||||
\(849\) | 0.759862 | 0.0260784 | ||||||||
\(850\) | 72.5580 | 2.48872 | ||||||||
\(851\) | 37.1680 | 1.27410 | ||||||||
\(852\) | 0.684750 | 0.0234592 | ||||||||
\(853\) | −19.3900 | −0.663902 | −0.331951 | − | 0.943297i | \(-0.607707\pi\) | ||||
−0.331951 | + | 0.943297i | \(0.607707\pi\) | |||||||
\(854\) | 1.84248 | 0.0630484 | ||||||||
\(855\) | −91.7800 | −3.13881 | ||||||||
\(856\) | 47.0892 | 1.60947 | ||||||||
\(857\) | −42.5804 | −1.45452 | −0.727259 | − | 0.686363i | \(-0.759206\pi\) | ||||
−0.727259 | + | 0.686363i | \(0.759206\pi\) | |||||||
\(858\) | 3.51836 | 0.120115 | ||||||||
\(859\) | 36.4148 | 1.24246 | 0.621228 | − | 0.783630i | \(-0.286634\pi\) | ||||
0.621228 | + | 0.783630i | \(0.286634\pi\) | |||||||
\(860\) | −19.6147 | −0.668856 | ||||||||
\(861\) | −3.76397 | −0.128276 | ||||||||
\(862\) | −38.8532 | −1.32335 | ||||||||
\(863\) | −32.8207 | −1.11723 | −0.558615 | − | 0.829427i | \(-0.688667\pi\) | ||||
−0.558615 | + | 0.829427i | \(0.688667\pi\) | |||||||
\(864\) | 2.35657 | 0.0801721 | ||||||||
\(865\) | −81.2581 | −2.76286 | ||||||||
\(866\) | 17.4761 | 0.593863 | ||||||||
\(867\) | 0.590530 | 0.0200554 | ||||||||
\(868\) | −2.97525 | −0.100987 | ||||||||
\(869\) | −26.5164 | −0.899507 | ||||||||
\(870\) | 3.39437 | 0.115080 | ||||||||
\(871\) | 73.9146 | 2.50450 | ||||||||
\(872\) | −45.8162 | −1.55153 | ||||||||
\(873\) | 26.5008 | 0.896916 | ||||||||
\(874\) | −100.180 | −3.38865 | ||||||||
\(875\) | −70.5123 | −2.38375 | ||||||||
\(876\) | 0.392652 | 0.0132665 | ||||||||
\(877\) | −6.13368 | −0.207120 | −0.103560 | − | 0.994623i | \(-0.533023\pi\) | ||||
−0.103560 | + | 0.994623i | \(0.533023\pi\) | |||||||
\(878\) | 40.3896 | 1.36308 | ||||||||
\(879\) | 0.378239 | 0.0127577 | ||||||||
\(880\) | −57.0979 | −1.92477 | ||||||||
\(881\) | −4.37391 | −0.147361 | −0.0736803 | − | 0.997282i | \(-0.523474\pi\) | ||||
−0.0736803 | + | 0.997282i | \(0.523474\pi\) | |||||||
\(882\) | −34.7069 | −1.16864 | ||||||||
\(883\) | 28.8998 | 0.972555 | 0.486278 | − | 0.873804i | \(-0.338354\pi\) | ||||
0.486278 | + | 0.873804i | \(0.338354\pi\) | |||||||
\(884\) | 13.3171 | 0.447903 | ||||||||
\(885\) | 3.39576 | 0.114147 | ||||||||
\(886\) | 53.1604 | 1.78596 | ||||||||
\(887\) | −29.8072 | −1.00083 | −0.500414 | − | 0.865787i | \(-0.666819\pi\) | ||||
−0.500414 | + | 0.865787i | \(0.666819\pi\) | |||||||
\(888\) | 1.46410 | 0.0491320 | ||||||||
\(889\) | 18.1395 | 0.608378 | ||||||||
\(890\) | −32.4053 | −1.08623 | ||||||||
\(891\) | 27.3843 | 0.917407 | ||||||||
\(892\) | 8.03329 | 0.268974 | ||||||||
\(893\) | 54.1927 | 1.81349 | ||||||||
\(894\) | 1.96380 | 0.0656793 | ||||||||
\(895\) | 49.3044 | 1.64807 | ||||||||
\(896\) | −51.6471 | −1.72541 | ||||||||
\(897\) | −5.61522 | −0.187487 | ||||||||
\(898\) | −4.38601 | −0.146363 | ||||||||
\(899\) | 6.09375 | 0.203238 | ||||||||
\(900\) | −15.7477 | −0.524922 | ||||||||
\(901\) | −6.52628 | −0.217422 | ||||||||
\(902\) | 36.8910 | 1.22834 | ||||||||
\(903\) | 4.77566 | 0.158924 | ||||||||
\(904\) | −16.8216 | −0.559479 | ||||||||
\(905\) | −32.5614 | −1.08238 | ||||||||
\(906\) | −1.39628 | −0.0463883 | ||||||||
\(907\) | 27.7853 | 0.922596 | 0.461298 | − | 0.887245i | \(-0.347384\pi\) | ||||
0.461298 | + | 0.887245i | \(0.347384\pi\) | |||||||
\(908\) | 2.35478 | 0.0781462 | ||||||||
\(909\) | 10.4587 | 0.346894 | ||||||||
\(910\) | −124.375 | −4.12298 | ||||||||
\(911\) | −23.1095 | −0.765651 | −0.382825 | − | 0.923821i | \(-0.625049\pi\) | ||||
−0.382825 | + | 0.923821i | \(0.625049\pi\) | |||||||
\(912\) | −5.08730 | −0.168457 | ||||||||
\(913\) | 23.1503 | 0.766164 | ||||||||
\(914\) | 16.8261 | 0.556558 | ||||||||
\(915\) | −0.156780 | −0.00518300 | ||||||||
\(916\) | −0.770558 | −0.0254599 | ||||||||
\(917\) | 64.2537 | 2.12184 | ||||||||
\(918\) | −5.87048 | −0.193755 | ||||||||
\(919\) | −10.9408 | −0.360905 | −0.180452 | − | 0.983584i | \(-0.557756\pi\) | ||||
−0.180452 | + | 0.983584i | \(0.557756\pi\) | |||||||
\(920\) | 70.6876 | 2.33050 | ||||||||
\(921\) | 1.05532 | 0.0347740 | ||||||||
\(922\) | 4.32722 | 0.142509 | ||||||||
\(923\) | 51.3886 | 1.69148 | ||||||||
\(924\) | −0.836685 | −0.0275249 | ||||||||
\(925\) | −46.4488 | −1.52723 | ||||||||
\(926\) | −7.69098 | −0.252741 | ||||||||
\(927\) | 45.9885 | 1.51046 | ||||||||
\(928\) | −12.3073 | −0.404005 | ||||||||
\(929\) | −40.4546 | −1.32727 | −0.663637 | − | 0.748055i | \(-0.730988\pi\) | ||||
−0.663637 | + | 0.748055i | \(0.730988\pi\) | |||||||
\(930\) | 1.19667 | 0.0392404 | ||||||||
\(931\) | 58.3748 | 1.91316 | ||||||||
\(932\) | −4.56771 | −0.149620 | ||||||||
\(933\) | −1.94460 | −0.0636634 | ||||||||
\(934\) | 19.6043 | 0.641471 | ||||||||
\(935\) | 55.2457 | 1.80673 | ||||||||
\(936\) | 37.2518 | 1.21761 | ||||||||
\(937\) | 9.08113 | 0.296668 | 0.148334 | − | 0.988937i | \(-0.452609\pi\) | ||||
0.148334 | + | 0.988937i | \(0.452609\pi\) | |||||||
\(938\) | −83.0834 | −2.71277 | ||||||||
\(939\) | 0.883845 | 0.0288432 | ||||||||
\(940\) | 14.0235 | 0.457397 | ||||||||
\(941\) | 12.8520 | 0.418964 | 0.209482 | − | 0.977812i | \(-0.432822\pi\) | ||||
0.209482 | + | 0.977812i | \(0.432822\pi\) | |||||||
\(942\) | −3.07344 | −0.100138 | ||||||||
\(943\) | −58.8771 | −1.91730 | ||||||||
\(944\) | −31.6997 | −1.03174 | ||||||||
\(945\) | 11.5994 | 0.377327 | ||||||||
\(946\) | −46.8067 | −1.52182 | ||||||||
\(947\) | 44.6938 | 1.45235 | 0.726177 | − | 0.687508i | \(-0.241295\pi\) | ||||
0.726177 | + | 0.687508i | \(0.241295\pi\) | |||||||
\(948\) | −0.611362 | −0.0198561 | ||||||||
\(949\) | 29.4674 | 0.956553 | ||||||||
\(950\) | 125.195 | 4.06187 | ||||||||
\(951\) | −3.38828 | −0.109872 | ||||||||
\(952\) | 40.8167 | 1.32288 | ||||||||
\(953\) | −9.11417 | −0.295237 | −0.147618 | − | 0.989044i | \(-0.547161\pi\) | ||||
−0.147618 | + | 0.989044i | \(0.547161\pi\) | |||||||
\(954\) | 6.69511 | 0.216762 | ||||||||
\(955\) | −16.8306 | −0.544625 | ||||||||
\(956\) | −13.2896 | −0.429816 | ||||||||
\(957\) | 1.71365 | 0.0553945 | ||||||||
\(958\) | 9.52161 | 0.307629 | ||||||||
\(959\) | −45.9841 | −1.48490 | ||||||||
\(960\) | 2.48921 | 0.0803390 | ||||||||
\(961\) | −28.8517 | −0.930699 | ||||||||
\(962\) | −40.2959 | −1.29919 | ||||||||
\(963\) | 60.2553 | 1.94170 | ||||||||
\(964\) | 2.97085 | 0.0956847 | ||||||||
\(965\) | 70.7888 | 2.27877 | ||||||||
\(966\) | 6.31176 | 0.203077 | ||||||||
\(967\) | 39.3216 | 1.26450 | 0.632249 | − | 0.774765i | \(-0.282132\pi\) | ||||
0.632249 | + | 0.774765i | \(0.282132\pi\) | |||||||
\(968\) | 3.27662 | 0.105315 | ||||||||
\(969\) | 4.92227 | 0.158126 | ||||||||
\(970\) | −54.5189 | −1.75050 | ||||||||
\(971\) | 32.9797 | 1.05837 | 0.529184 | − | 0.848507i | \(-0.322498\pi\) | ||||
0.529184 | + | 0.848507i | \(0.322498\pi\) | |||||||
\(972\) | 1.91304 | 0.0613607 | ||||||||
\(973\) | −52.5172 | −1.68363 | ||||||||
\(974\) | −52.0263 | −1.66703 | ||||||||
\(975\) | 7.01733 | 0.224735 | ||||||||
\(976\) | 1.46356 | 0.0468473 | ||||||||
\(977\) | 34.8469 | 1.11485 | 0.557425 | − | 0.830227i | \(-0.311789\pi\) | ||||
0.557425 | + | 0.830227i | \(0.311789\pi\) | |||||||
\(978\) | −4.63820 | −0.148313 | ||||||||
\(979\) | −16.3599 | −0.522863 | ||||||||
\(980\) | 15.1057 | 0.482535 | ||||||||
\(981\) | −58.6264 | −1.87180 | ||||||||
\(982\) | 12.0310 | 0.383926 | ||||||||
\(983\) | −1.47944 | −0.0471868 | −0.0235934 | − | 0.999722i | \(-0.507511\pi\) | ||||
−0.0235934 | + | 0.999722i | \(0.507511\pi\) | |||||||
\(984\) | −2.31926 | −0.0739352 | ||||||||
\(985\) | −60.1493 | −1.91651 | ||||||||
\(986\) | 30.6588 | 0.976374 | ||||||||
\(987\) | −3.41436 | −0.108680 | ||||||||
\(988\) | 22.9780 | 0.731027 | ||||||||
\(989\) | 74.7023 | 2.37540 | ||||||||
\(990\) | −56.6749 | −1.80125 | ||||||||
\(991\) | −48.6649 | −1.54589 | −0.772946 | − | 0.634472i | \(-0.781217\pi\) | ||||
−0.772946 | + | 0.634472i | \(0.781217\pi\) | |||||||
\(992\) | −4.33887 | −0.137759 | ||||||||
\(993\) | −2.46948 | −0.0783665 | ||||||||
\(994\) | −57.7631 | −1.83213 | ||||||||
\(995\) | 46.0310 | 1.45928 | ||||||||
\(996\) | 0.533754 | 0.0169126 | ||||||||
\(997\) | 17.8052 | 0.563897 | 0.281949 | − | 0.959430i | \(-0.409019\pi\) | ||||
0.281949 | + | 0.959430i | \(0.409019\pi\) | |||||||
\(998\) | −31.7060 | −1.00364 | ||||||||
\(999\) | 3.75805 | 0.118899 |
(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 | 2671.2.a.b.1.91 | ✓ | 122 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2671.2.a.b.1.91 | ✓ | 122 | 1.1 | even | 1 | trivial |