Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, 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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(0\) |
Dimension: | \(47\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.22 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.00179563 | −0.00103671 | −0.000518353 | − | 1.00000i | \(-0.500165\pi\) | ||||
−0.000518353 | 1.00000i | \(0.500165\pi\) | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.84522 | −1.27242 | −0.636211 | − | 0.771515i | \(-0.719499\pi\) | ||||
−0.636211 | + | 0.771515i | \(0.719499\pi\) | |||||||
\(6\) | −0.00179563 | −0.000733062 0 | ||||||||
\(7\) | 2.42071 | 0.914942 | 0.457471 | − | 0.889225i | \(-0.348755\pi\) | ||||
0.457471 | + | 0.889225i | \(0.348755\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −3.00000 | −0.999999 | ||||||||
\(10\) | −2.84522 | −0.899738 | ||||||||
\(11\) | −4.79658 | −1.44622 | −0.723111 | − | 0.690731i | \(-0.757289\pi\) | ||||
−0.723111 | + | 0.690731i | \(0.757289\pi\) | |||||||
\(12\) | −0.00179563 | −0.000518353 0 | ||||||||
\(13\) | 0.240087 | 0.0665881 | 0.0332941 | − | 0.999446i | \(-0.489400\pi\) | ||||
0.0332941 | + | 0.999446i | \(0.489400\pi\) | |||||||
\(14\) | 2.42071 | 0.646961 | ||||||||
\(15\) | 0.00510896 | 0.00131913 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.878242 | 0.213005 | 0.106502 | − | 0.994312i | \(-0.466035\pi\) | ||||
0.106502 | + | 0.994312i | \(0.466035\pi\) | |||||||
\(18\) | −3.00000 | −0.707106 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −2.84522 | −0.636211 | ||||||||
\(21\) | −0.00434669 | −0.000948525 0 | ||||||||
\(22\) | −4.79658 | −1.02263 | ||||||||
\(23\) | −5.60385 | −1.16848 | −0.584242 | − | 0.811580i | \(-0.698608\pi\) | ||||
−0.584242 | + | 0.811580i | \(0.698608\pi\) | |||||||
\(24\) | −0.00179563 | −0.000366531 0 | ||||||||
\(25\) | 3.09529 | 0.619058 | ||||||||
\(26\) | 0.240087 | 0.0470849 | ||||||||
\(27\) | 0.0107738 | 0.00207341 | ||||||||
\(28\) | 2.42071 | 0.457471 | ||||||||
\(29\) | −4.45888 | −0.827993 | −0.413997 | − | 0.910278i | \(-0.635867\pi\) | ||||
−0.413997 | + | 0.910278i | \(0.635867\pi\) | |||||||
\(30\) | 0.00510896 | 0.000932764 0 | ||||||||
\(31\) | 9.50296 | 1.70678 | 0.853391 | − | 0.521272i | \(-0.174542\pi\) | ||||
0.853391 | + | 0.521272i | \(0.174542\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.00861287 | 0.00149931 | ||||||||
\(34\) | 0.878242 | 0.150617 | ||||||||
\(35\) | −6.88745 | −1.16419 | ||||||||
\(36\) | −3.00000 | −0.499999 | ||||||||
\(37\) | 3.05886 | 0.502874 | 0.251437 | − | 0.967874i | \(-0.419097\pi\) | ||||
0.251437 | + | 0.967874i | \(0.419097\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −0.000431107 0 | −6.90323e−5 0 | ||||||||
\(40\) | −2.84522 | −0.449869 | ||||||||
\(41\) | 9.19476 | 1.43598 | 0.717990 | − | 0.696053i | \(-0.245062\pi\) | ||||
0.717990 | + | 0.696053i | \(0.245062\pi\) | |||||||
\(42\) | −0.00434669 | −0.000670709 0 | ||||||||
\(43\) | 8.02831 | 1.22431 | 0.612153 | − | 0.790740i | \(-0.290304\pi\) | ||||
0.612153 | + | 0.790740i | \(0.290304\pi\) | |||||||
\(44\) | −4.79658 | −0.723111 | ||||||||
\(45\) | 8.53566 | 1.27242 | ||||||||
\(46\) | −5.60385 | −0.826243 | ||||||||
\(47\) | −3.46726 | −0.505753 | −0.252876 | − | 0.967499i | \(-0.581377\pi\) | ||||
−0.252876 | + | 0.967499i | \(0.581377\pi\) | |||||||
\(48\) | −0.00179563 | −0.000259176 0 | ||||||||
\(49\) | −1.14017 | −0.162882 | ||||||||
\(50\) | 3.09529 | 0.437740 | ||||||||
\(51\) | −0.00157699 | −0.000220823 0 | ||||||||
\(52\) | 0.240087 | 0.0332941 | ||||||||
\(53\) | −8.34252 | −1.14593 | −0.572966 | − | 0.819579i | \(-0.694207\pi\) | ||||
−0.572966 | + | 0.819579i | \(0.694207\pi\) | |||||||
\(54\) | 0.0107738 | 0.00146612 | ||||||||
\(55\) | 13.6473 | 1.84021 | ||||||||
\(56\) | 2.42071 | 0.323481 | ||||||||
\(57\) | 0.00179563 | 0.000237837 0 | ||||||||
\(58\) | −4.45888 | −0.585479 | ||||||||
\(59\) | 5.86612 | 0.763704 | 0.381852 | − | 0.924223i | \(-0.375286\pi\) | ||||
0.381852 | + | 0.924223i | \(0.375286\pi\) | |||||||
\(60\) | 0.00510896 | 0.000659564 0 | ||||||||
\(61\) | −5.52647 | −0.707592 | −0.353796 | − | 0.935323i | \(-0.615109\pi\) | ||||
−0.353796 | + | 0.935323i | \(0.615109\pi\) | |||||||
\(62\) | 9.50296 | 1.20688 | ||||||||
\(63\) | −7.26212 | −0.914941 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.683101 | −0.0847282 | ||||||||
\(66\) | 0.00861287 | 0.00106017 | ||||||||
\(67\) | −1.60425 | −0.195991 | −0.0979954 | − | 0.995187i | \(-0.531243\pi\) | ||||
−0.0979954 | + | 0.995187i | \(0.531243\pi\) | |||||||
\(68\) | 0.878242 | 0.106502 | ||||||||
\(69\) | 0.0100624 | 0.00121137 | ||||||||
\(70\) | −6.88745 | −0.823208 | ||||||||
\(71\) | −11.9998 | −1.42412 | −0.712058 | − | 0.702121i | \(-0.752237\pi\) | ||||
−0.712058 | + | 0.702121i | \(0.752237\pi\) | |||||||
\(72\) | −3.00000 | −0.353553 | ||||||||
\(73\) | −4.81238 | −0.563246 | −0.281623 | − | 0.959525i | \(-0.590873\pi\) | ||||
−0.281623 | + | 0.959525i | \(0.590873\pi\) | |||||||
\(74\) | 3.05886 | 0.355585 | ||||||||
\(75\) | −0.00555799 | −0.000641782 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −11.6111 | −1.32321 | ||||||||
\(78\) | −0.000431107 0 | −4.88132e−5 0 | ||||||||
\(79\) | −11.5750 | −1.30229 | −0.651143 | − | 0.758955i | \(-0.725710\pi\) | ||||
−0.651143 | + | 0.758955i | \(0.725710\pi\) | |||||||
\(80\) | −2.84522 | −0.318106 | ||||||||
\(81\) | 8.99997 | 0.999997 | ||||||||
\(82\) | 9.19476 | 1.01539 | ||||||||
\(83\) | 17.6067 | 1.93258 | 0.966292 | − | 0.257447i | \(-0.0828813\pi\) | ||||
0.966292 | + | 0.257447i | \(0.0828813\pi\) | |||||||
\(84\) | −0.00434669 | −0.000474263 0 | ||||||||
\(85\) | −2.49879 | −0.271032 | ||||||||
\(86\) | 8.02831 | 0.865714 | ||||||||
\(87\) | 0.00800649 | 0.000858385 0 | ||||||||
\(88\) | −4.79658 | −0.511317 | ||||||||
\(89\) | 9.62818 | 1.02058 | 0.510292 | − | 0.860001i | \(-0.329537\pi\) | ||||
0.510292 | + | 0.860001i | \(0.329537\pi\) | |||||||
\(90\) | 8.53566 | 0.899737 | ||||||||
\(91\) | 0.581180 | 0.0609242 | ||||||||
\(92\) | −5.60385 | −0.584242 | ||||||||
\(93\) | −0.0170638 | −0.00176943 | ||||||||
\(94\) | −3.46726 | −0.357621 | ||||||||
\(95\) | 2.84522 | 0.291914 | ||||||||
\(96\) | −0.00179563 | −0.000183265 0 | ||||||||
\(97\) | 11.6368 | 1.18153 | 0.590767 | − | 0.806842i | \(-0.298825\pi\) | ||||
0.590767 | + | 0.806842i | \(0.298825\pi\) | |||||||
\(98\) | −1.14017 | −0.115175 | ||||||||
\(99\) | 14.3897 | 1.44622 | ||||||||
\(100\) | 3.09529 | 0.309529 | ||||||||
\(101\) | 14.9281 | 1.48540 | 0.742700 | − | 0.669624i | \(-0.233545\pi\) | ||||
0.742700 | + | 0.669624i | \(0.233545\pi\) | |||||||
\(102\) | −0.00157699 | −0.000156146 0 | ||||||||
\(103\) | 5.38404 | 0.530505 | 0.265253 | − | 0.964179i | \(-0.414545\pi\) | ||||
0.265253 | + | 0.964179i | \(0.414545\pi\) | |||||||
\(104\) | 0.240087 | 0.0235425 | ||||||||
\(105\) | 0.0123673 | 0.00120692 | ||||||||
\(106\) | −8.34252 | −0.810297 | ||||||||
\(107\) | 7.38286 | 0.713728 | 0.356864 | − | 0.934156i | \(-0.383846\pi\) | ||||
0.356864 | + | 0.934156i | \(0.383846\pi\) | |||||||
\(108\) | 0.0107738 | 0.00103671 | ||||||||
\(109\) | 13.4481 | 1.28809 | 0.644047 | − | 0.764986i | \(-0.277254\pi\) | ||||
0.644047 | + | 0.764986i | \(0.277254\pi\) | |||||||
\(110\) | 13.6473 | 1.30122 | ||||||||
\(111\) | −0.00549258 | −0.000521332 0 | ||||||||
\(112\) | 2.42071 | 0.228735 | ||||||||
\(113\) | 5.91656 | 0.556583 | 0.278292 | − | 0.960497i | \(-0.410232\pi\) | ||||
0.278292 | + | 0.960497i | \(0.410232\pi\) | |||||||
\(114\) | 0.00179563 | 0.000168176 0 | ||||||||
\(115\) | 15.9442 | 1.48680 | ||||||||
\(116\) | −4.45888 | −0.413997 | ||||||||
\(117\) | −0.720260 | −0.0665881 | ||||||||
\(118\) | 5.86612 | 0.540021 | ||||||||
\(119\) | 2.12597 | 0.194887 | ||||||||
\(120\) | 0.00510896 | 0.000466382 0 | ||||||||
\(121\) | 12.0072 | 1.09156 | ||||||||
\(122\) | −5.52647 | −0.500343 | ||||||||
\(123\) | −0.0165104 | −0.00148869 | ||||||||
\(124\) | 9.50296 | 0.853391 | ||||||||
\(125\) | 5.41932 | 0.484719 | ||||||||
\(126\) | −7.26212 | −0.646961 | ||||||||
\(127\) | 9.34529 | 0.829260 | 0.414630 | − | 0.909990i | \(-0.363911\pi\) | ||||
0.414630 | + | 0.909990i | \(0.363911\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.0144158 | −0.00126924 | ||||||||
\(130\) | −0.683101 | −0.0599119 | ||||||||
\(131\) | −5.43634 | −0.474975 | −0.237488 | − | 0.971391i | \(-0.576324\pi\) | ||||
−0.237488 | + | 0.971391i | \(0.576324\pi\) | |||||||
\(132\) | 0.00861287 | 0.000749654 0 | ||||||||
\(133\) | −2.42071 | −0.209902 | ||||||||
\(134\) | −1.60425 | −0.138586 | ||||||||
\(135\) | −0.0306537 | −0.00263825 | ||||||||
\(136\) | 0.878242 | 0.0753086 | ||||||||
\(137\) | −4.48249 | −0.382965 | −0.191482 | − | 0.981496i | \(-0.561329\pi\) | ||||
−0.191482 | + | 0.981496i | \(0.561329\pi\) | |||||||
\(138\) | 0.0100624 | 0.000856571 0 | ||||||||
\(139\) | 12.5442 | 1.06398 | 0.531992 | − | 0.846750i | \(-0.321444\pi\) | ||||
0.531992 | + | 0.846750i | \(0.321444\pi\) | |||||||
\(140\) | −6.88745 | −0.582096 | ||||||||
\(141\) | 0.00622592 | 0.000524317 0 | ||||||||
\(142\) | −11.9998 | −1.00700 | ||||||||
\(143\) | −1.15160 | −0.0963013 | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 12.6865 | 1.05356 | ||||||||
\(146\) | −4.81238 | −0.398275 | ||||||||
\(147\) | 0.00204733 | 0.000168861 0 | ||||||||
\(148\) | 3.05886 | 0.251437 | ||||||||
\(149\) | −0.954574 | −0.0782017 | −0.0391009 | − | 0.999235i | \(-0.512449\pi\) | ||||
−0.0391009 | + | 0.999235i | \(0.512449\pi\) | |||||||
\(150\) | −0.00555799 | −0.000453808 0 | ||||||||
\(151\) | −3.99230 | −0.324889 | −0.162444 | − | 0.986718i | \(-0.551938\pi\) | ||||
−0.162444 | + | 0.986718i | \(0.551938\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −2.63472 | −0.213005 | ||||||||
\(154\) | −11.6111 | −0.935650 | ||||||||
\(155\) | −27.0380 | −2.17175 | ||||||||
\(156\) | −0.000431107 0 | −3.45162e−5 0 | ||||||||
\(157\) | 2.42485 | 0.193524 | 0.0967619 | − | 0.995308i | \(-0.469151\pi\) | ||||
0.0967619 | + | 0.995308i | \(0.469151\pi\) | |||||||
\(158\) | −11.5750 | −0.920856 | ||||||||
\(159\) | 0.0149801 | 0.00118800 | ||||||||
\(160\) | −2.84522 | −0.224935 | ||||||||
\(161\) | −13.5653 | −1.06909 | ||||||||
\(162\) | 8.99997 | 0.707105 | ||||||||
\(163\) | 15.9239 | 1.24726 | 0.623628 | − | 0.781721i | \(-0.285658\pi\) | ||||
0.623628 | + | 0.781721i | \(0.285658\pi\) | |||||||
\(164\) | 9.19476 | 0.717990 | ||||||||
\(165\) | −0.0245055 | −0.00190775 | ||||||||
\(166\) | 17.6067 | 1.36654 | ||||||||
\(167\) | 8.25446 | 0.638750 | 0.319375 | − | 0.947628i | \(-0.396527\pi\) | ||||
0.319375 | + | 0.947628i | \(0.396527\pi\) | |||||||
\(168\) | −0.00434669 | −0.000335354 0 | ||||||||
\(169\) | −12.9424 | −0.995566 | ||||||||
\(170\) | −2.49879 | −0.191649 | ||||||||
\(171\) | 3.00000 | 0.229415 | ||||||||
\(172\) | 8.02831 | 0.612153 | ||||||||
\(173\) | 3.45938 | 0.263012 | 0.131506 | − | 0.991315i | \(-0.458019\pi\) | ||||
0.131506 | + | 0.991315i | \(0.458019\pi\) | |||||||
\(174\) | 0.00800649 | 0.000606970 0 | ||||||||
\(175\) | 7.49280 | 0.566402 | ||||||||
\(176\) | −4.79658 | −0.361556 | ||||||||
\(177\) | −0.0105334 | −0.000791737 0 | ||||||||
\(178\) | 9.62818 | 0.721663 | ||||||||
\(179\) | −13.0489 | −0.975320 | −0.487660 | − | 0.873034i | \(-0.662149\pi\) | ||||
−0.487660 | + | 0.873034i | \(0.662149\pi\) | |||||||
\(180\) | 8.53566 | 0.636210 | ||||||||
\(181\) | 17.2368 | 1.28120 | 0.640602 | − | 0.767873i | \(-0.278685\pi\) | ||||
0.640602 | + | 0.767873i | \(0.278685\pi\) | |||||||
\(182\) | 0.581180 | 0.0430799 | ||||||||
\(183\) | 0.00992348 | 0.000733564 0 | ||||||||
\(184\) | −5.60385 | −0.413121 | ||||||||
\(185\) | −8.70314 | −0.639868 | ||||||||
\(186\) | −0.0170638 | −0.00125118 | ||||||||
\(187\) | −4.21256 | −0.308053 | ||||||||
\(188\) | −3.46726 | −0.252876 | ||||||||
\(189\) | 0.0260801 | 0.00189705 | ||||||||
\(190\) | 2.84522 | 0.206414 | ||||||||
\(191\) | −13.5373 | −0.979525 | −0.489762 | − | 0.871856i | \(-0.662916\pi\) | ||||
−0.489762 | + | 0.871856i | \(0.662916\pi\) | |||||||
\(192\) | −0.00179563 | −0.000129588 0 | ||||||||
\(193\) | −4.75134 | −0.342009 | −0.171004 | − | 0.985270i | \(-0.554701\pi\) | ||||
−0.171004 | + | 0.985270i | \(0.554701\pi\) | |||||||
\(194\) | 11.6368 | 0.835470 | ||||||||
\(195\) | 0.00122659 | 8.78382e−5 0 | ||||||||
\(196\) | −1.14017 | −0.0814410 | ||||||||
\(197\) | −3.71388 | −0.264603 | −0.132301 | − | 0.991210i | \(-0.542237\pi\) | ||||
−0.132301 | + | 0.991210i | \(0.542237\pi\) | |||||||
\(198\) | 14.3897 | 1.02263 | ||||||||
\(199\) | −21.9493 | −1.55594 | −0.777972 | − | 0.628298i | \(-0.783752\pi\) | ||||
−0.777972 | + | 0.628298i | \(0.783752\pi\) | |||||||
\(200\) | 3.09529 | 0.218870 | ||||||||
\(201\) | 0.00288064 | 0.000203185 0 | ||||||||
\(202\) | 14.9281 | 1.05034 | ||||||||
\(203\) | −10.7936 | −0.757565 | ||||||||
\(204\) | −0.00157699 | −0.000110412 0 | ||||||||
\(205\) | −26.1611 | −1.82717 | ||||||||
\(206\) | 5.38404 | 0.375124 | ||||||||
\(207\) | 16.8115 | 1.16848 | ||||||||
\(208\) | 0.240087 | 0.0166470 | ||||||||
\(209\) | 4.79658 | 0.331786 | ||||||||
\(210\) | 0.0123673 | 0.000853425 0 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −8.34252 | −0.572966 | ||||||||
\(213\) | 0.0215472 | 0.00147639 | ||||||||
\(214\) | 7.38286 | 0.504682 | ||||||||
\(215\) | −22.8423 | −1.55783 | ||||||||
\(216\) | 0.0107738 | 0.000733061 0 | ||||||||
\(217\) | 23.0039 | 1.56161 | ||||||||
\(218\) | 13.4481 | 0.910820 | ||||||||
\(219\) | 0.00864123 | 0.000583920 0 | ||||||||
\(220\) | 13.6473 | 0.920103 | ||||||||
\(221\) | 0.210854 | 0.0141836 | ||||||||
\(222\) | −0.00549258 | −0.000368638 0 | ||||||||
\(223\) | 10.9423 | 0.732752 | 0.366376 | − | 0.930467i | \(-0.380598\pi\) | ||||
0.366376 | + | 0.930467i | \(0.380598\pi\) | |||||||
\(224\) | 2.42071 | 0.161740 | ||||||||
\(225\) | −9.28587 | −0.619058 | ||||||||
\(226\) | 5.91656 | 0.393564 | ||||||||
\(227\) | 27.4565 | 1.82235 | 0.911175 | − | 0.412020i | \(-0.135177\pi\) | ||||
0.911175 | + | 0.412020i | \(0.135177\pi\) | |||||||
\(228\) | 0.00179563 | 0.000118918 0 | ||||||||
\(229\) | 23.5037 | 1.55317 | 0.776584 | − | 0.630014i | \(-0.216951\pi\) | ||||
0.776584 | + | 0.630014i | \(0.216951\pi\) | |||||||
\(230\) | 15.9442 | 1.05133 | ||||||||
\(231\) | 0.0208492 | 0.00137178 | ||||||||
\(232\) | −4.45888 | −0.292740 | ||||||||
\(233\) | −20.9100 | −1.36986 | −0.684930 | − | 0.728609i | \(-0.740167\pi\) | ||||
−0.684930 | + | 0.728609i | \(0.740167\pi\) | |||||||
\(234\) | −0.720260 | −0.0470849 | ||||||||
\(235\) | 9.86514 | 0.643531 | ||||||||
\(236\) | 5.86612 | 0.381852 | ||||||||
\(237\) | 0.0207843 | 0.00135009 | ||||||||
\(238\) | 2.12597 | 0.137806 | ||||||||
\(239\) | −5.68156 | −0.367510 | −0.183755 | − | 0.982972i | \(-0.558825\pi\) | ||||
−0.183755 | + | 0.982972i | \(0.558825\pi\) | |||||||
\(240\) | 0.00510896 | 0.000329782 0 | ||||||||
\(241\) | 9.05353 | 0.583189 | 0.291594 | − | 0.956542i | \(-0.405814\pi\) | ||||
0.291594 | + | 0.956542i | \(0.405814\pi\) | |||||||
\(242\) | 12.0072 | 0.771850 | ||||||||
\(243\) | −0.0484819 | −0.00311011 | ||||||||
\(244\) | −5.52647 | −0.353796 | ||||||||
\(245\) | 3.24405 | 0.207255 | ||||||||
\(246\) | −0.0165104 | −0.00105266 | ||||||||
\(247\) | −0.240087 | −0.0152764 | ||||||||
\(248\) | 9.50296 | 0.603438 | ||||||||
\(249\) | −0.0316150 | −0.00200352 | ||||||||
\(250\) | 5.41932 | 0.342748 | ||||||||
\(251\) | 10.5940 | 0.668690 | 0.334345 | − | 0.942451i | \(-0.391485\pi\) | ||||
0.334345 | + | 0.942451i | \(0.391485\pi\) | |||||||
\(252\) | −7.26212 | −0.457470 | ||||||||
\(253\) | 26.8793 | 1.68989 | ||||||||
\(254\) | 9.34529 | 0.586375 | ||||||||
\(255\) | 0.00448690 | 0.000280981 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −23.5918 | −1.47161 | −0.735806 | − | 0.677192i | \(-0.763197\pi\) | ||||
−0.735806 | + | 0.677192i | \(0.763197\pi\) | |||||||
\(258\) | −0.0144158 | −0.000897491 0 | ||||||||
\(259\) | 7.40461 | 0.460100 | ||||||||
\(260\) | −0.683101 | −0.0423641 | ||||||||
\(261\) | 13.3766 | 0.827992 | ||||||||
\(262\) | −5.43634 | −0.335858 | ||||||||
\(263\) | 28.7438 | 1.77242 | 0.886210 | − | 0.463285i | \(-0.153329\pi\) | ||||
0.886210 | + | 0.463285i | \(0.153329\pi\) | |||||||
\(264\) | 0.00861287 | 0.000530085 0 | ||||||||
\(265\) | 23.7363 | 1.45811 | ||||||||
\(266\) | −2.42071 | −0.148423 | ||||||||
\(267\) | −0.0172886 | −0.00105805 | ||||||||
\(268\) | −1.60425 | −0.0979954 | ||||||||
\(269\) | −14.8139 | −0.903218 | −0.451609 | − | 0.892216i | \(-0.649150\pi\) | ||||
−0.451609 | + | 0.892216i | \(0.649150\pi\) | |||||||
\(270\) | −0.0306537 | −0.00186553 | ||||||||
\(271\) | −0.836191 | −0.0507950 | −0.0253975 | − | 0.999677i | \(-0.508085\pi\) | ||||
−0.0253975 | + | 0.999677i | \(0.508085\pi\) | |||||||
\(272\) | 0.878242 | 0.0532512 | ||||||||
\(273\) | −0.00104358 | −6.31605e−5 0 | ||||||||
\(274\) | −4.48249 | −0.270797 | ||||||||
\(275\) | −14.8468 | −0.895296 | ||||||||
\(276\) | 0.0100624 | 0.000605687 0 | ||||||||
\(277\) | 12.4906 | 0.750488 | 0.375244 | − | 0.926926i | \(-0.377559\pi\) | ||||
0.375244 | + | 0.926926i | \(0.377559\pi\) | |||||||
\(278\) | 12.5442 | 0.752350 | ||||||||
\(279\) | −28.5088 | −1.70678 | ||||||||
\(280\) | −6.88745 | −0.411604 | ||||||||
\(281\) | −20.4648 | −1.22083 | −0.610414 | − | 0.792082i | \(-0.708997\pi\) | ||||
−0.610414 | + | 0.792082i | \(0.708997\pi\) | |||||||
\(282\) | 0.00622592 | 0.000370748 0 | ||||||||
\(283\) | −21.7664 | −1.29388 | −0.646938 | − | 0.762542i | \(-0.723951\pi\) | ||||
−0.646938 | + | 0.762542i | \(0.723951\pi\) | |||||||
\(284\) | −11.9998 | −0.712058 | ||||||||
\(285\) | −0.00510896 | −0.000302629 0 | ||||||||
\(286\) | −1.15160 | −0.0680953 | ||||||||
\(287\) | 22.2578 | 1.31384 | ||||||||
\(288\) | −3.00000 | −0.176777 | ||||||||
\(289\) | −16.2287 | −0.954629 | ||||||||
\(290\) | 12.6865 | 0.744977 | ||||||||
\(291\) | −0.0208953 | −0.00122490 | ||||||||
\(292\) | −4.81238 | −0.281623 | ||||||||
\(293\) | −30.4844 | −1.78092 | −0.890458 | − | 0.455065i | \(-0.849616\pi\) | ||||
−0.890458 | + | 0.455065i | \(0.849616\pi\) | |||||||
\(294\) | 0.00204733 | 0.000119403 0 | ||||||||
\(295\) | −16.6904 | −0.971754 | ||||||||
\(296\) | 3.05886 | 0.177793 | ||||||||
\(297\) | −0.0516772 | −0.00299861 | ||||||||
\(298\) | −0.954574 | −0.0552970 | ||||||||
\(299\) | −1.34541 | −0.0778072 | ||||||||
\(300\) | −0.00555799 | −0.000320891 0 | ||||||||
\(301\) | 19.4342 | 1.12017 | ||||||||
\(302\) | −3.99230 | −0.229731 | ||||||||
\(303\) | −0.0268053 | −0.00153992 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 15.7240 | 0.900355 | ||||||||
\(306\) | −2.63472 | −0.150617 | ||||||||
\(307\) | 8.11465 | 0.463128 | 0.231564 | − | 0.972820i | \(-0.425616\pi\) | ||||
0.231564 | + | 0.972820i | \(0.425616\pi\) | |||||||
\(308\) | −11.6111 | −0.661605 | ||||||||
\(309\) | −0.00966773 | −0.000549978 0 | ||||||||
\(310\) | −27.0380 | −1.53566 | ||||||||
\(311\) | 0.0140801 | 0.000798407 0 | 0.000399203 | − | 1.00000i | \(-0.499873\pi\) | ||||
0.000399203 | 1.00000i | \(0.499873\pi\) | ||||||||
\(312\) | −0.000431107 0 | −2.44066e−5 0 | ||||||||
\(313\) | 10.1958 | 0.576302 | 0.288151 | − | 0.957585i | \(-0.406959\pi\) | ||||
0.288151 | + | 0.957585i | \(0.406959\pi\) | |||||||
\(314\) | 2.42485 | 0.136842 | ||||||||
\(315\) | 20.6623 | 1.16419 | ||||||||
\(316\) | −11.5750 | −0.651143 | ||||||||
\(317\) | 2.49278 | 0.140008 | 0.0700042 | − | 0.997547i | \(-0.477699\pi\) | ||||
0.0700042 | + | 0.997547i | \(0.477699\pi\) | |||||||
\(318\) | 0.0149801 | 0.000840040 0 | ||||||||
\(319\) | 21.3874 | 1.19746 | ||||||||
\(320\) | −2.84522 | −0.159053 | ||||||||
\(321\) | −0.0132569 | −0.000739926 0 | ||||||||
\(322\) | −13.5653 | −0.755964 | ||||||||
\(323\) | −0.878242 | −0.0488667 | ||||||||
\(324\) | 8.99997 | 0.499998 | ||||||||
\(325\) | 0.743139 | 0.0412219 | ||||||||
\(326\) | 15.9239 | 0.881943 | ||||||||
\(327\) | −0.0241478 | −0.00133537 | ||||||||
\(328\) | 9.19476 | 0.507696 | ||||||||
\(329\) | −8.39323 | −0.462734 | ||||||||
\(330\) | −0.0245055 | −0.00134898 | ||||||||
\(331\) | 25.2820 | 1.38962 | 0.694811 | − | 0.719192i | \(-0.255488\pi\) | ||||
0.694811 | + | 0.719192i | \(0.255488\pi\) | |||||||
\(332\) | 17.6067 | 0.966292 | ||||||||
\(333\) | −9.17657 | −0.502873 | ||||||||
\(334\) | 8.25446 | 0.451664 | ||||||||
\(335\) | 4.56446 | 0.249383 | ||||||||
\(336\) | −0.00434669 | −0.000237131 0 | ||||||||
\(337\) | 20.4478 | 1.11386 | 0.556932 | − | 0.830558i | \(-0.311978\pi\) | ||||
0.556932 | + | 0.830558i | \(0.311978\pi\) | |||||||
\(338\) | −12.9424 | −0.703971 | ||||||||
\(339\) | −0.0106239 | −0.000577013 0 | ||||||||
\(340\) | −2.49879 | −0.135516 | ||||||||
\(341\) | −45.5817 | −2.46839 | ||||||||
\(342\) | 3.00000 | 0.162221 | ||||||||
\(343\) | −19.7050 | −1.06397 | ||||||||
\(344\) | 8.02831 | 0.432857 | ||||||||
\(345\) | −0.0286299 | −0.00154138 | ||||||||
\(346\) | 3.45938 | 0.185977 | ||||||||
\(347\) | 26.2910 | 1.41138 | 0.705688 | − | 0.708523i | \(-0.250638\pi\) | ||||
0.705688 | + | 0.708523i | \(0.250638\pi\) | |||||||
\(348\) | 0.00800649 | 0.000429193 0 | ||||||||
\(349\) | 24.8585 | 1.33065 | 0.665323 | − | 0.746556i | \(-0.268294\pi\) | ||||
0.665323 | + | 0.746556i | \(0.268294\pi\) | |||||||
\(350\) | 7.49280 | 0.400507 | ||||||||
\(351\) | 0.00258664 | 0.000138065 0 | ||||||||
\(352\) | −4.79658 | −0.255658 | ||||||||
\(353\) | 17.0158 | 0.905661 | 0.452831 | − | 0.891597i | \(-0.350414\pi\) | ||||
0.452831 | + | 0.891597i | \(0.350414\pi\) | |||||||
\(354\) | −0.0105334 | −0.000559842 0 | ||||||||
\(355\) | 34.1421 | 1.81208 | ||||||||
\(356\) | 9.62818 | 0.510292 | ||||||||
\(357\) | −0.00381744 | −0.000202041 0 | ||||||||
\(358\) | −13.0489 | −0.689656 | ||||||||
\(359\) | 10.3032 | 0.543782 | 0.271891 | − | 0.962328i | \(-0.412351\pi\) | ||||
0.271891 | + | 0.962328i | \(0.412351\pi\) | |||||||
\(360\) | 8.53566 | 0.449869 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 17.2368 | 0.905949 | ||||||||
\(363\) | −0.0215604 | −0.00113163 | ||||||||
\(364\) | 0.581180 | 0.0304621 | ||||||||
\(365\) | 13.6923 | 0.716687 | ||||||||
\(366\) | 0.00992348 | 0.000518708 0 | ||||||||
\(367\) | −27.4401 | −1.43236 | −0.716180 | − | 0.697915i | \(-0.754111\pi\) | ||||
−0.716180 | + | 0.697915i | \(0.754111\pi\) | |||||||
\(368\) | −5.60385 | −0.292121 | ||||||||
\(369\) | −27.5843 | −1.43598 | ||||||||
\(370\) | −8.70314 | −0.452455 | ||||||||
\(371\) | −20.1948 | −1.04846 | ||||||||
\(372\) | −0.0170638 | −0.000884715 0 | ||||||||
\(373\) | −28.9544 | −1.49920 | −0.749601 | − | 0.661890i | \(-0.769755\pi\) | ||||
−0.749601 | + | 0.661890i | \(0.769755\pi\) | |||||||
\(374\) | −4.21256 | −0.217826 | ||||||||
\(375\) | −0.00973108 | −0.000502511 0 | ||||||||
\(376\) | −3.46726 | −0.178811 | ||||||||
\(377\) | −1.07052 | −0.0551345 | ||||||||
\(378\) | 0.0260801 | 0.00134142 | ||||||||
\(379\) | 24.8584 | 1.27689 | 0.638445 | − | 0.769667i | \(-0.279578\pi\) | ||||
0.638445 | + | 0.769667i | \(0.279578\pi\) | |||||||
\(380\) | 2.84522 | 0.145957 | ||||||||
\(381\) | −0.0167807 | −0.000859699 0 | ||||||||
\(382\) | −13.5373 | −0.692629 | ||||||||
\(383\) | −20.3027 | −1.03742 | −0.518710 | − | 0.854950i | \(-0.673588\pi\) | ||||
−0.518710 | + | 0.854950i | \(0.673588\pi\) | |||||||
\(384\) | −0.00179563 | −9.16327e−5 0 | ||||||||
\(385\) | 33.0362 | 1.68368 | ||||||||
\(386\) | −4.75134 | −0.241837 | ||||||||
\(387\) | −24.0849 | −1.22430 | ||||||||
\(388\) | 11.6368 | 0.590767 | ||||||||
\(389\) | 23.5299 | 1.19301 | 0.596506 | − | 0.802608i | \(-0.296555\pi\) | ||||
0.596506 | + | 0.802608i | \(0.296555\pi\) | |||||||
\(390\) | 0.00122659 | 6.21110e−5 0 | ||||||||
\(391\) | −4.92154 | −0.248893 | ||||||||
\(392\) | −1.14017 | −0.0575875 | ||||||||
\(393\) | 0.00976164 | 0.000492409 0 | ||||||||
\(394\) | −3.71388 | −0.187102 | ||||||||
\(395\) | 32.9334 | 1.65706 | ||||||||
\(396\) | 14.3897 | 0.723111 | ||||||||
\(397\) | 10.6764 | 0.535832 | 0.267916 | − | 0.963442i | \(-0.413665\pi\) | ||||
0.267916 | + | 0.963442i | \(0.413665\pi\) | |||||||
\(398\) | −21.9493 | −1.10022 | ||||||||
\(399\) | 0.00434669 | 0.000217607 0 | ||||||||
\(400\) | 3.09529 | 0.154765 | ||||||||
\(401\) | −5.14678 | −0.257018 | −0.128509 | − | 0.991708i | \(-0.541019\pi\) | ||||
−0.128509 | + | 0.991708i | \(0.541019\pi\) | |||||||
\(402\) | 0.00288064 | 0.000143673 0 | ||||||||
\(403\) | 2.28154 | 0.113651 | ||||||||
\(404\) | 14.9281 | 0.742700 | ||||||||
\(405\) | −25.6069 | −1.27242 | ||||||||
\(406\) | −10.7936 | −0.535680 | ||||||||
\(407\) | −14.6721 | −0.727267 | ||||||||
\(408\) | −0.00157699 | −7.80729e−5 0 | ||||||||
\(409\) | 1.35507 | 0.0670037 | 0.0335018 | − | 0.999439i | \(-0.489334\pi\) | ||||
0.0335018 | + | 0.999439i | \(0.489334\pi\) | |||||||
\(410\) | −26.1611 | −1.29201 | ||||||||
\(411\) | 0.00804888 | 0.000397022 0 | ||||||||
\(412\) | 5.38404 | 0.265253 | ||||||||
\(413\) | 14.2002 | 0.698745 | ||||||||
\(414\) | 16.8115 | 0.826242 | ||||||||
\(415\) | −50.0949 | −2.45906 | ||||||||
\(416\) | 0.240087 | 0.0117712 | ||||||||
\(417\) | −0.0225247 | −0.00110304 | ||||||||
\(418\) | 4.79658 | 0.234608 | ||||||||
\(419\) | 32.8620 | 1.60541 | 0.802706 | − | 0.596375i | \(-0.203393\pi\) | ||||
0.802706 | + | 0.596375i | \(0.203393\pi\) | |||||||
\(420\) | 0.0123673 | 0.000603462 0 | ||||||||
\(421\) | 19.3852 | 0.944775 | 0.472388 | − | 0.881391i | \(-0.343392\pi\) | ||||
0.472388 | + | 0.881391i | \(0.343392\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | 10.4018 | 0.505752 | ||||||||
\(424\) | −8.34252 | −0.405148 | ||||||||
\(425\) | 2.71841 | 0.131862 | ||||||||
\(426\) | 0.0215472 | 0.00104396 | ||||||||
\(427\) | −13.3780 | −0.647405 | ||||||||
\(428\) | 7.38286 | 0.356864 | ||||||||
\(429\) | 0.00206784 | 9.98361e−5 0 | ||||||||
\(430\) | −22.8423 | −1.10155 | ||||||||
\(431\) | 19.3947 | 0.934210 | 0.467105 | − | 0.884202i | \(-0.345297\pi\) | ||||
0.467105 | + | 0.884202i | \(0.345297\pi\) | |||||||
\(432\) | 0.0107738 | 0.000518353 0 | ||||||||
\(433\) | −15.6643 | −0.752781 | −0.376390 | − | 0.926461i | \(-0.622835\pi\) | ||||
−0.376390 | + | 0.926461i | \(0.622835\pi\) | |||||||
\(434\) | 23.0039 | 1.10422 | ||||||||
\(435\) | −0.0227802 | −0.00109223 | ||||||||
\(436\) | 13.4481 | 0.644047 | ||||||||
\(437\) | 5.60385 | 0.268069 | ||||||||
\(438\) | 0.00864123 | 0.000412894 0 | ||||||||
\(439\) | 15.1152 | 0.721408 | 0.360704 | − | 0.932680i | \(-0.382536\pi\) | ||||
0.360704 | + | 0.932680i | \(0.382536\pi\) | |||||||
\(440\) | 13.6473 | 0.650611 | ||||||||
\(441\) | 3.42052 | 0.162882 | ||||||||
\(442\) | 0.210854 | 0.0100293 | ||||||||
\(443\) | 3.94271 | 0.187324 | 0.0936620 | − | 0.995604i | \(-0.470143\pi\) | ||||
0.0936620 | + | 0.995604i | \(0.470143\pi\) | |||||||
\(444\) | −0.00549258 | −0.000260666 0 | ||||||||
\(445\) | −27.3943 | −1.29861 | ||||||||
\(446\) | 10.9423 | 0.518134 | ||||||||
\(447\) | 0.00171406 | 8.10722e−5 0 | ||||||||
\(448\) | 2.42071 | 0.114368 | ||||||||
\(449\) | −4.88432 | −0.230505 | −0.115253 | − | 0.993336i | \(-0.536768\pi\) | ||||
−0.115253 | + | 0.993336i | \(0.536768\pi\) | |||||||
\(450\) | −9.28587 | −0.437740 | ||||||||
\(451\) | −44.1034 | −2.07675 | ||||||||
\(452\) | 5.91656 | 0.278292 | ||||||||
\(453\) | 0.00716869 | 0.000336814 0 | ||||||||
\(454\) | 27.4565 | 1.28860 | ||||||||
\(455\) | −1.65359 | −0.0775214 | ||||||||
\(456\) | 0.00179563 | 8.40880e−5 0 | ||||||||
\(457\) | 1.82125 | 0.0851946 | 0.0425973 | − | 0.999092i | \(-0.486437\pi\) | ||||
0.0425973 | + | 0.999092i | \(0.486437\pi\) | |||||||
\(458\) | 23.5037 | 1.09826 | ||||||||
\(459\) | 0.00946196 | 0.000441647 0 | ||||||||
\(460\) | 15.9442 | 0.743402 | ||||||||
\(461\) | −36.7344 | −1.71089 | −0.855446 | − | 0.517892i | \(-0.826717\pi\) | ||||
−0.855446 | + | 0.517892i | \(0.826717\pi\) | |||||||
\(462\) | 0.0208492 | 0.000969994 0 | ||||||||
\(463\) | 29.4545 | 1.36886 | 0.684432 | − | 0.729076i | \(-0.260050\pi\) | ||||
0.684432 | + | 0.729076i | \(0.260050\pi\) | |||||||
\(464\) | −4.45888 | −0.206998 | ||||||||
\(465\) | 0.0485502 | 0.00225146 | ||||||||
\(466\) | −20.9100 | −0.968637 | ||||||||
\(467\) | 22.3819 | 1.03571 | 0.517855 | − | 0.855468i | \(-0.326731\pi\) | ||||
0.517855 | + | 0.855468i | \(0.326731\pi\) | |||||||
\(468\) | −0.720260 | −0.0332940 | ||||||||
\(469\) | −3.88343 | −0.179320 | ||||||||
\(470\) | 9.86514 | 0.455045 | ||||||||
\(471\) | −0.00435412 | −0.000200627 0 | ||||||||
\(472\) | 5.86612 | 0.270010 | ||||||||
\(473\) | −38.5084 | −1.77062 | ||||||||
\(474\) | 0.0207843 | 0.000954656 0 | ||||||||
\(475\) | −3.09529 | −0.142022 | ||||||||
\(476\) | 2.12597 | 0.0974435 | ||||||||
\(477\) | 25.0275 | 1.14593 | ||||||||
\(478\) | −5.68156 | −0.259869 | ||||||||
\(479\) | 36.1413 | 1.65134 | 0.825669 | − | 0.564155i | \(-0.190798\pi\) | ||||
0.825669 | + | 0.564155i | \(0.190798\pi\) | |||||||
\(480\) | 0.00510896 | 0.000233191 0 | ||||||||
\(481\) | 0.734393 | 0.0334854 | ||||||||
\(482\) | 9.05353 | 0.412377 | ||||||||
\(483\) | 0.0243582 | 0.00110834 | ||||||||
\(484\) | 12.0072 | 0.545780 | ||||||||
\(485\) | −33.1092 | −1.50341 | ||||||||
\(486\) | −0.0484819 | −0.00219918 | ||||||||
\(487\) | −4.85599 | −0.220046 | −0.110023 | − | 0.993929i | \(-0.535092\pi\) | ||||
−0.110023 | + | 0.993929i | \(0.535092\pi\) | |||||||
\(488\) | −5.52647 | −0.250171 | ||||||||
\(489\) | −0.0285934 | −0.00129304 | ||||||||
\(490\) | 3.24405 | 0.146551 | ||||||||
\(491\) | 34.0613 | 1.53717 | 0.768583 | − | 0.639750i | \(-0.220962\pi\) | ||||
0.768583 | + | 0.639750i | \(0.220962\pi\) | |||||||
\(492\) | −0.0165104 | −0.000744345 0 | ||||||||
\(493\) | −3.91597 | −0.176367 | ||||||||
\(494\) | −0.240087 | −0.0108020 | ||||||||
\(495\) | −40.9420 | −1.84020 | ||||||||
\(496\) | 9.50296 | 0.426695 | ||||||||
\(497\) | −29.0480 | −1.30298 | ||||||||
\(498\) | −0.0316150 | −0.00141670 | ||||||||
\(499\) | −35.6636 | −1.59652 | −0.798260 | − | 0.602312i | \(-0.794246\pi\) | ||||
−0.798260 | + | 0.602312i | \(0.794246\pi\) | |||||||
\(500\) | 5.41932 | 0.242359 | ||||||||
\(501\) | −0.0148219 | −0.000662196 0 | ||||||||
\(502\) | 10.5940 | 0.472835 | ||||||||
\(503\) | 18.6709 | 0.832493 | 0.416247 | − | 0.909252i | \(-0.363345\pi\) | ||||
0.416247 | + | 0.909252i | \(0.363345\pi\) | |||||||
\(504\) | −7.26212 | −0.323480 | ||||||||
\(505\) | −42.4737 | −1.89006 | ||||||||
\(506\) | 26.8793 | 1.19493 | ||||||||
\(507\) | 0.0232397 | 0.00103211 | ||||||||
\(508\) | 9.34529 | 0.414630 | ||||||||
\(509\) | 10.5431 | 0.467315 | 0.233658 | − | 0.972319i | \(-0.424931\pi\) | ||||
0.233658 | + | 0.972319i | \(0.424931\pi\) | |||||||
\(510\) | 0.00448690 | 0.000198683 0 | ||||||||
\(511\) | −11.6494 | −0.515337 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.0107738 | −0.000475673 0 | ||||||||
\(514\) | −23.5918 | −1.04059 | ||||||||
\(515\) | −15.3188 | −0.675027 | ||||||||
\(516\) | −0.0144158 | −0.000634622 0 | ||||||||
\(517\) | 16.6310 | 0.731431 | ||||||||
\(518\) | 7.40461 | 0.325340 | ||||||||
\(519\) | −0.00621176 | −0.000272666 0 | ||||||||
\(520\) | −0.683101 | −0.0299559 | ||||||||
\(521\) | −19.2105 | −0.841627 | −0.420814 | − | 0.907147i | \(-0.638255\pi\) | ||||
−0.420814 | + | 0.907147i | \(0.638255\pi\) | |||||||
\(522\) | 13.3766 | 0.585479 | ||||||||
\(523\) | −32.8940 | −1.43835 | −0.719177 | − | 0.694827i | \(-0.755481\pi\) | ||||
−0.719177 | + | 0.694827i | \(0.755481\pi\) | |||||||
\(524\) | −5.43634 | −0.237488 | ||||||||
\(525\) | −0.0134543 | −0.000587193 0 | ||||||||
\(526\) | 28.7438 | 1.25329 | ||||||||
\(527\) | 8.34589 | 0.363553 | ||||||||
\(528\) | 0.00861287 | 0.000374827 0 | ||||||||
\(529\) | 8.40316 | 0.365355 | ||||||||
\(530\) | 23.7363 | 1.03104 | ||||||||
\(531\) | −17.5984 | −0.763704 | ||||||||
\(532\) | −2.42071 | −0.104951 | ||||||||
\(533\) | 2.20754 | 0.0956192 | ||||||||
\(534\) | −0.0172886 | −0.000748152 0 | ||||||||
\(535\) | −21.0059 | −0.908163 | ||||||||
\(536\) | −1.60425 | −0.0692932 | ||||||||
\(537\) | 0.0234310 | 0.00101112 | ||||||||
\(538\) | −14.8139 | −0.638672 | ||||||||
\(539\) | 5.46893 | 0.235564 | ||||||||
\(540\) | −0.0306537 | −0.00131913 | ||||||||
\(541\) | 38.9807 | 1.67591 | 0.837955 | − | 0.545740i | \(-0.183751\pi\) | ||||
0.837955 | + | 0.545740i | \(0.183751\pi\) | |||||||
\(542\) | −0.836191 | −0.0359175 | ||||||||
\(543\) | −0.0309510 | −0.00132823 | ||||||||
\(544\) | 0.878242 | 0.0376543 | ||||||||
\(545\) | −38.2628 | −1.63900 | ||||||||
\(546\) | −0.00104358 | −4.46612e−5 0 | ||||||||
\(547\) | 0.492857 | 0.0210730 | 0.0105365 | − | 0.999944i | \(-0.496646\pi\) | ||||
0.0105365 | + | 0.999944i | \(0.496646\pi\) | |||||||
\(548\) | −4.48249 | −0.191482 | ||||||||
\(549\) | 16.5794 | 0.707591 | ||||||||
\(550\) | −14.8468 | −0.633070 | ||||||||
\(551\) | 4.45888 | 0.189955 | ||||||||
\(552\) | 0.0100624 | 0.000428285 0 | ||||||||
\(553\) | −28.0196 | −1.19152 | ||||||||
\(554\) | 12.4906 | 0.530675 | ||||||||
\(555\) | 0.0156276 | 0.000663355 0 | ||||||||
\(556\) | 12.5442 | 0.531992 | ||||||||
\(557\) | −12.5752 | −0.532828 | −0.266414 | − | 0.963859i | \(-0.585839\pi\) | ||||
−0.266414 | + | 0.963859i | \(0.585839\pi\) | |||||||
\(558\) | −28.5088 | −1.20688 | ||||||||
\(559\) | 1.92749 | 0.0815242 | ||||||||
\(560\) | −6.88745 | −0.291048 | ||||||||
\(561\) | 0.00756418 | 0.000319360 0 | ||||||||
\(562\) | −20.4648 | −0.863256 | ||||||||
\(563\) | −25.9381 | −1.09316 | −0.546580 | − | 0.837407i | \(-0.684071\pi\) | ||||
−0.546580 | + | 0.837407i | \(0.684071\pi\) | |||||||
\(564\) | 0.00622592 | 0.000262158 0 | ||||||||
\(565\) | −16.8339 | −0.708209 | ||||||||
\(566\) | −21.7664 | −0.914909 | ||||||||
\(567\) | 21.7863 | 0.914939 | ||||||||
\(568\) | −11.9998 | −0.503501 | ||||||||
\(569\) | 6.72278 | 0.281833 | 0.140917 | − | 0.990021i | \(-0.454995\pi\) | ||||
0.140917 | + | 0.990021i | \(0.454995\pi\) | |||||||
\(570\) | −0.00510896 | −0.000213991 0 | ||||||||
\(571\) | −16.7539 | −0.701129 | −0.350564 | − | 0.936539i | \(-0.614010\pi\) | ||||
−0.350564 | + | 0.936539i | \(0.614010\pi\) | |||||||
\(572\) | −1.15160 | −0.0481506 | ||||||||
\(573\) | 0.0243079 | 0.00101548 | ||||||||
\(574\) | 22.2578 | 0.929024 | ||||||||
\(575\) | −17.3456 | −0.723360 | ||||||||
\(576\) | −3.00000 | −0.125000 | ||||||||
\(577\) | −35.7934 | −1.49010 | −0.745049 | − | 0.667010i | \(-0.767574\pi\) | ||||
−0.745049 | + | 0.667010i | \(0.767574\pi\) | |||||||
\(578\) | −16.2287 | −0.675025 | ||||||||
\(579\) | 0.00853164 | 0.000354563 0 | ||||||||
\(580\) | 12.6865 | 0.526778 | ||||||||
\(581\) | 42.6206 | 1.76820 | ||||||||
\(582\) | −0.0208953 | −0.000866137 0 | ||||||||
\(583\) | 40.0155 | 1.65727 | ||||||||
\(584\) | −4.81238 | −0.199138 | ||||||||
\(585\) | 2.04930 | 0.0847281 | ||||||||
\(586\) | −30.4844 | −1.25930 | ||||||||
\(587\) | −5.08519 | −0.209888 | −0.104944 | − | 0.994478i | \(-0.533466\pi\) | ||||
−0.104944 | + | 0.994478i | \(0.533466\pi\) | |||||||
\(588\) | 0.00204733 | 8.44304e−5 0 | ||||||||
\(589\) | −9.50296 | −0.391562 | ||||||||
\(590\) | −16.6904 | −0.687134 | ||||||||
\(591\) | 0.00666874 | 0.000274315 0 | ||||||||
\(592\) | 3.05886 | 0.125718 | ||||||||
\(593\) | 2.28232 | 0.0937238 | 0.0468619 | − | 0.998901i | \(-0.485078\pi\) | ||||
0.0468619 | + | 0.998901i | \(0.485078\pi\) | |||||||
\(594\) | −0.0516772 | −0.00212034 | ||||||||
\(595\) | −6.04885 | −0.247979 | ||||||||
\(596\) | −0.954574 | −0.0391009 | ||||||||
\(597\) | 0.0394128 | 0.00161306 | ||||||||
\(598\) | −1.34541 | −0.0550180 | ||||||||
\(599\) | −20.9805 | −0.857238 | −0.428619 | − | 0.903485i | \(-0.641000\pi\) | ||||
−0.428619 | + | 0.903485i | \(0.641000\pi\) | |||||||
\(600\) | −0.00555799 | −0.000226904 0 | ||||||||
\(601\) | 39.4205 | 1.60800 | 0.803998 | − | 0.594632i | \(-0.202702\pi\) | ||||
0.803998 | + | 0.594632i | \(0.202702\pi\) | |||||||
\(602\) | 19.4342 | 0.792078 | ||||||||
\(603\) | 4.81276 | 0.195991 | ||||||||
\(604\) | −3.99230 | −0.162444 | ||||||||
\(605\) | −34.1631 | −1.38893 | ||||||||
\(606\) | −0.0268053 | −0.00108889 | ||||||||
\(607\) | 27.7390 | 1.12589 | 0.562946 | − | 0.826494i | \(-0.309668\pi\) | ||||
0.562946 | + | 0.826494i | \(0.309668\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0.0193814 | 0.000785372 0 | ||||||||
\(610\) | 15.7240 | 0.636647 | ||||||||
\(611\) | −0.832445 | −0.0336771 | ||||||||
\(612\) | −2.63472 | −0.106502 | ||||||||
\(613\) | 25.5132 | 1.03047 | 0.515235 | − | 0.857049i | \(-0.327705\pi\) | ||||
0.515235 | + | 0.857049i | \(0.327705\pi\) | |||||||
\(614\) | 8.11465 | 0.327481 | ||||||||
\(615\) | 0.0469757 | 0.00189424 | ||||||||
\(616\) | −11.6111 | −0.467825 | ||||||||
\(617\) | −3.27412 | −0.131811 | −0.0659056 | − | 0.997826i | \(-0.520994\pi\) | ||||
−0.0659056 | + | 0.997826i | \(0.520994\pi\) | |||||||
\(618\) | −0.00966773 | −0.000388893 0 | ||||||||
\(619\) | −1.84005 | −0.0739578 | −0.0369789 | − | 0.999316i | \(-0.511773\pi\) | ||||
−0.0369789 | + | 0.999316i | \(0.511773\pi\) | |||||||
\(620\) | −27.0380 | −1.08587 | ||||||||
\(621\) | −0.0603746 | −0.00242275 | ||||||||
\(622\) | 0.0140801 | 0.000564559 0 | ||||||||
\(623\) | 23.3070 | 0.933776 | ||||||||
\(624\) | −0.000431107 0 | −1.72581e−5 0 | ||||||||
\(625\) | −30.8956 | −1.23583 | ||||||||
\(626\) | 10.1958 | 0.407507 | ||||||||
\(627\) | −0.00861287 | −0.000343965 0 | ||||||||
\(628\) | 2.42485 | 0.0967619 | ||||||||
\(629\) | 2.68642 | 0.107115 | ||||||||
\(630\) | 20.6623 | 0.823207 | ||||||||
\(631\) | 40.3974 | 1.60819 | 0.804097 | − | 0.594498i | \(-0.202649\pi\) | ||||
0.804097 | + | 0.594498i | \(0.202649\pi\) | |||||||
\(632\) | −11.5750 | −0.460428 | ||||||||
\(633\) | 0.00179563 | 7.13698e−5 0 | ||||||||
\(634\) | 2.49278 | 0.0990009 | ||||||||
\(635\) | −26.5894 | −1.05517 | ||||||||
\(636\) | 0.0149801 | 0.000593998 0 | ||||||||
\(637\) | −0.273741 | −0.0108460 | ||||||||
\(638\) | 21.3874 | 0.846734 | ||||||||
\(639\) | 35.9994 | 1.42411 | ||||||||
\(640\) | −2.84522 | −0.112467 | ||||||||
\(641\) | −38.7155 | −1.52917 | −0.764586 | − | 0.644522i | \(-0.777057\pi\) | ||||
−0.764586 | + | 0.644522i | \(0.777057\pi\) | |||||||
\(642\) | −0.0132569 | −0.000523207 0 | ||||||||
\(643\) | 41.7031 | 1.64461 | 0.822306 | − | 0.569046i | \(-0.192687\pi\) | ||||
0.822306 | + | 0.569046i | \(0.192687\pi\) | |||||||
\(644\) | −13.5653 | −0.534547 | ||||||||
\(645\) | 0.0410163 | 0.00161501 | ||||||||
\(646\) | −0.878242 | −0.0345540 | ||||||||
\(647\) | −42.4389 | −1.66844 | −0.834222 | − | 0.551429i | \(-0.814083\pi\) | ||||
−0.834222 | + | 0.551429i | \(0.814083\pi\) | |||||||
\(648\) | 8.99997 | 0.353552 | ||||||||
\(649\) | −28.1373 | −1.10449 | ||||||||
\(650\) | 0.743139 | 0.0291483 | ||||||||
\(651\) | −0.0413064 | −0.00161893 | ||||||||
\(652\) | 15.9239 | 0.623628 | ||||||||
\(653\) | 23.9430 | 0.936962 | 0.468481 | − | 0.883474i | \(-0.344802\pi\) | ||||
0.468481 | + | 0.883474i | \(0.344802\pi\) | |||||||
\(654\) | −0.0241478 | −0.000944252 0 | ||||||||
\(655\) | 15.4676 | 0.604369 | ||||||||
\(656\) | 9.19476 | 0.358995 | ||||||||
\(657\) | 14.4371 | 0.563245 | ||||||||
\(658\) | −8.39323 | −0.327202 | ||||||||
\(659\) | −35.3540 | −1.37719 | −0.688597 | − | 0.725144i | \(-0.741773\pi\) | ||||
−0.688597 | + | 0.725144i | \(0.741773\pi\) | |||||||
\(660\) | −0.0245055 | −0.000953876 0 | ||||||||
\(661\) | 17.0210 | 0.662041 | 0.331021 | − | 0.943624i | \(-0.392607\pi\) | ||||
0.331021 | + | 0.943624i | \(0.392607\pi\) | |||||||
\(662\) | 25.2820 | 0.982612 | ||||||||
\(663\) | −0.000378616 0 | −1.47042e−5 0 | ||||||||
\(664\) | 17.6067 | 0.683272 | ||||||||
\(665\) | 6.88745 | 0.267084 | ||||||||
\(666\) | −9.17657 | −0.355585 | ||||||||
\(667\) | 24.9869 | 0.967497 | ||||||||
\(668\) | 8.25446 | 0.319375 | ||||||||
\(669\) | −0.0196483 | −0.000759648 0 | ||||||||
\(670\) | 4.56446 | 0.176341 | ||||||||
\(671\) | 26.5081 | 1.02334 | ||||||||
\(672\) | −0.00434669 | −0.000167677 0 | ||||||||
\(673\) | −50.3333 | −1.94021 | −0.970104 | − | 0.242691i | \(-0.921970\pi\) | ||||
−0.970104 | + | 0.242691i | \(0.921970\pi\) | |||||||
\(674\) | 20.4478 | 0.787621 | ||||||||
\(675\) | 0.0333479 | 0.00128356 | ||||||||
\(676\) | −12.9424 | −0.497783 | ||||||||
\(677\) | −4.24362 | −0.163095 | −0.0815477 | − | 0.996669i | \(-0.525986\pi\) | ||||
−0.0815477 | + | 0.996669i | \(0.525986\pi\) | |||||||
\(678\) | −0.0106239 | −0.000408010 0 | ||||||||
\(679\) | 28.1692 | 1.08103 | ||||||||
\(680\) | −2.49879 | −0.0958243 | ||||||||
\(681\) | −0.0493016 | −0.00188924 | ||||||||
\(682\) | −45.5817 | −1.74541 | ||||||||
\(683\) | 17.5799 | 0.672676 | 0.336338 | − | 0.941741i | \(-0.390812\pi\) | ||||
0.336338 | + | 0.941741i | \(0.390812\pi\) | |||||||
\(684\) | 3.00000 | 0.114708 | ||||||||
\(685\) | 12.7537 | 0.487293 | ||||||||
\(686\) | −19.7050 | −0.752340 | ||||||||
\(687\) | −0.0422039 | −0.00161018 | ||||||||
\(688\) | 8.02831 | 0.306076 | ||||||||
\(689\) | −2.00293 | −0.0763055 | ||||||||
\(690\) | −0.0286299 | −0.00108992 | ||||||||
\(691\) | 21.3157 | 0.810886 | 0.405443 | − | 0.914120i | \(-0.367117\pi\) | ||||
0.405443 | + | 0.914120i | \(0.367117\pi\) | |||||||
\(692\) | 3.45938 | 0.131506 | ||||||||
\(693\) | 34.8333 | 1.32321 | ||||||||
\(694\) | 26.2910 | 0.997993 | ||||||||
\(695\) | −35.6910 | −1.35384 | ||||||||
\(696\) | 0.00800649 | 0.000303485 0 | ||||||||
\(697\) | 8.07522 | 0.305871 | ||||||||
\(698\) | 24.8585 | 0.940909 | ||||||||
\(699\) | 0.0375466 | 0.00142014 | ||||||||
\(700\) | 7.49280 | 0.283201 | ||||||||
\(701\) | 49.4369 | 1.86721 | 0.933603 | − | 0.358309i | \(-0.116647\pi\) | ||||
0.933603 | + | 0.358309i | \(0.116647\pi\) | |||||||
\(702\) | 0.00258664 | 9.76264e−5 0 | ||||||||
\(703\) | −3.05886 | −0.115367 | ||||||||
\(704\) | −4.79658 | −0.180778 | ||||||||
\(705\) | −0.0177141 | −0.000667152 0 | ||||||||
\(706\) | 17.0158 | 0.640399 | ||||||||
\(707\) | 36.1365 | 1.35905 | ||||||||
\(708\) | −0.0105334 | −0.000395868 0 | ||||||||
\(709\) | −26.2836 | −0.987103 | −0.493551 | − | 0.869717i | \(-0.664302\pi\) | ||||
−0.493551 | + | 0.869717i | \(0.664302\pi\) | |||||||
\(710\) | 34.1421 | 1.28133 | ||||||||
\(711\) | 34.7249 | 1.30228 | ||||||||
\(712\) | 9.62818 | 0.360831 | ||||||||
\(713\) | −53.2532 | −1.99435 | ||||||||
\(714\) | −0.00381744 | −0.000142864 0 | ||||||||
\(715\) | 3.27655 | 0.122536 | ||||||||
\(716\) | −13.0489 | −0.487660 | ||||||||
\(717\) | 0.0102020 | 0.000381000 0 | ||||||||
\(718\) | 10.3032 | 0.384512 | ||||||||
\(719\) | −18.7008 | −0.697422 | −0.348711 | − | 0.937230i | \(-0.613380\pi\) | ||||
−0.348711 | + | 0.937230i | \(0.613380\pi\) | |||||||
\(720\) | 8.53566 | 0.318105 | ||||||||
\(721\) | 13.0332 | 0.485381 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −0.0162568 | −0.000604595 0 | ||||||||
\(724\) | 17.2368 | 0.640602 | ||||||||
\(725\) | −13.8015 | −0.512576 | ||||||||
\(726\) | −0.0215604 | −0.000800181 0 | ||||||||
\(727\) | −17.2064 | −0.638149 | −0.319074 | − | 0.947730i | \(-0.603372\pi\) | ||||
−0.319074 | + | 0.947730i | \(0.603372\pi\) | |||||||
\(728\) | 0.581180 | 0.0215400 | ||||||||
\(729\) | −26.9998 | −0.999994 | ||||||||
\(730\) | 13.6923 | 0.506774 | ||||||||
\(731\) | 7.05079 | 0.260783 | ||||||||
\(732\) | 0.00992348 | 0.000366782 0 | ||||||||
\(733\) | −51.7474 | −1.91133 | −0.955667 | − | 0.294449i | \(-0.904864\pi\) | ||||
−0.955667 | + | 0.294449i | \(0.904864\pi\) | |||||||
\(734\) | −27.4401 | −1.01283 | ||||||||
\(735\) | −0.00582510 | −0.000214862 0 | ||||||||
\(736\) | −5.60385 | −0.206561 | ||||||||
\(737\) | 7.69493 | 0.283446 | ||||||||
\(738\) | −27.5843 | −1.01539 | ||||||||
\(739\) | −22.1750 | −0.815721 | −0.407860 | − | 0.913044i | \(-0.633725\pi\) | ||||
−0.407860 | + | 0.913044i | \(0.633725\pi\) | |||||||
\(740\) | −8.70314 | −0.319934 | ||||||||
\(741\) | 0.000431107 0 | 1.58371e−5 0 | ||||||||
\(742\) | −20.1948 | −0.741374 | ||||||||
\(743\) | −2.68077 | −0.0983477 | −0.0491739 | − | 0.998790i | \(-0.515659\pi\) | ||||
−0.0491739 | + | 0.998790i | \(0.515659\pi\) | |||||||
\(744\) | −0.0170638 | −0.000625588 0 | ||||||||
\(745\) | 2.71598 | 0.0995056 | ||||||||
\(746\) | −28.9544 | −1.06010 | ||||||||
\(747\) | −52.8200 | −1.93258 | ||||||||
\(748\) | −4.21256 | −0.154026 | ||||||||
\(749\) | 17.8717 | 0.653019 | ||||||||
\(750\) | −0.00973108 | −0.000355329 0 | ||||||||
\(751\) | −21.4368 | −0.782240 | −0.391120 | − | 0.920340i | \(-0.627912\pi\) | ||||
−0.391120 | + | 0.920340i | \(0.627912\pi\) | |||||||
\(752\) | −3.46726 | −0.126438 | ||||||||
\(753\) | −0.0190229 | −0.000693235 0 | ||||||||
\(754\) | −1.07052 | −0.0389860 | ||||||||
\(755\) | 11.3590 | 0.413396 | ||||||||
\(756\) | 0.0260801 | 0.000948525 0 | ||||||||
\(757\) | 13.3428 | 0.484952 | 0.242476 | − | 0.970157i | \(-0.422040\pi\) | ||||
0.242476 | + | 0.970157i | \(0.422040\pi\) | |||||||
\(758\) | 24.8584 | 0.902898 | ||||||||
\(759\) | −0.0482652 | −0.00175192 | ||||||||
\(760\) | 2.84522 | 0.103207 | ||||||||
\(761\) | 44.2849 | 1.60533 | 0.802664 | − | 0.596432i | \(-0.203415\pi\) | ||||
0.802664 | + | 0.596432i | \(0.203415\pi\) | |||||||
\(762\) | −0.0167807 | −0.000607899 0 | ||||||||
\(763\) | 32.5539 | 1.17853 | ||||||||
\(764\) | −13.5373 | −0.489762 | ||||||||
\(765\) | 7.49637 | 0.271032 | ||||||||
\(766\) | −20.3027 | −0.733567 | ||||||||
\(767\) | 1.40838 | 0.0508536 | ||||||||
\(768\) | −0.00179563 | −6.47941e−5 0 | ||||||||
\(769\) | 3.60467 | 0.129988 | 0.0649939 | − | 0.997886i | \(-0.479297\pi\) | ||||
0.0649939 | + | 0.997886i | \(0.479297\pi\) | |||||||
\(770\) | 33.0362 | 1.19054 | ||||||||
\(771\) | 0.0423620 | 0.00152563 | ||||||||
\(772\) | −4.75134 | −0.171004 | ||||||||
\(773\) | −7.12506 | −0.256271 | −0.128135 | − | 0.991757i | \(-0.540899\pi\) | ||||
−0.128135 | + | 0.991757i | \(0.540899\pi\) | |||||||
\(774\) | −24.0849 | −0.865714 | ||||||||
\(775\) | 29.4144 | 1.05660 | ||||||||
\(776\) | 11.6368 | 0.417735 | ||||||||
\(777\) | −0.0132959 | −0.000476988 0 | ||||||||
\(778\) | 23.5299 | 0.843587 | ||||||||
\(779\) | −9.19476 | −0.329436 | ||||||||
\(780\) | 0.00122659 | 4.39191e−5 0 | ||||||||
\(781\) | 57.5580 | 2.05959 | ||||||||
\(782\) | −4.92154 | −0.175994 | ||||||||
\(783\) | −0.0480389 | −0.00171677 | ||||||||
\(784\) | −1.14017 | −0.0407205 | ||||||||
\(785\) | −6.89923 | −0.246244 | ||||||||
\(786\) | 0.00976164 | 0.000348186 0 | ||||||||
\(787\) | 22.8348 | 0.813971 | 0.406986 | − | 0.913435i | \(-0.366580\pi\) | ||||
0.406986 | + | 0.913435i | \(0.366580\pi\) | |||||||
\(788\) | −3.71388 | −0.132301 | ||||||||
\(789\) | −0.0516132 | −0.00183748 | ||||||||
\(790\) | 32.9334 | 1.17172 | ||||||||
\(791\) | 14.3223 | 0.509241 | ||||||||
\(792\) | 14.3897 | 0.511316 | ||||||||
\(793\) | −1.32683 | −0.0471172 | ||||||||
\(794\) | 10.6764 | 0.378890 | ||||||||
\(795\) | −0.0426216 | −0.00151163 | ||||||||
\(796\) | −21.9493 | −0.777972 | ||||||||
\(797\) | −18.7724 | −0.664952 | −0.332476 | − | 0.943112i | \(-0.607884\pi\) | ||||
−0.332476 | + | 0.943112i | \(0.607884\pi\) | |||||||
\(798\) | 0.00434669 | 0.000153871 0 | ||||||||
\(799\) | −3.04510 | −0.107728 | ||||||||
\(800\) | 3.09529 | 0.109435 | ||||||||
\(801\) | −28.8845 | −1.02058 | ||||||||
\(802\) | −5.14678 | −0.181739 | ||||||||
\(803\) | 23.0829 | 0.814579 | ||||||||
\(804\) | 0.00288064 | 0.000101592 0 | ||||||||
\(805\) | 38.5963 | 1.36034 | ||||||||
\(806\) | 2.28154 | 0.0803636 | ||||||||
\(807\) | 0.0266002 | 0.000936372 0 | ||||||||
\(808\) | 14.9281 | 0.525168 | ||||||||
\(809\) | 26.7279 | 0.939704 | 0.469852 | − | 0.882745i | \(-0.344307\pi\) | ||||
0.469852 | + | 0.882745i | \(0.344307\pi\) | |||||||
\(810\) | −25.6069 | −0.899736 | ||||||||
\(811\) | 8.06370 | 0.283155 | 0.141577 | − | 0.989927i | \(-0.454783\pi\) | ||||
0.141577 | + | 0.989927i | \(0.454783\pi\) | |||||||
\(812\) | −10.7936 | −0.378783 | ||||||||
\(813\) | 0.00150149 | 5.26595e−5 0 | ||||||||
\(814\) | −14.6721 | −0.514256 | ||||||||
\(815\) | −45.3070 | −1.58704 | ||||||||
\(816\) | −0.00157699 | −5.52059e−5 0 | ||||||||
\(817\) | −8.02831 | −0.280875 | ||||||||
\(818\) | 1.35507 | 0.0473787 | ||||||||
\(819\) | −1.74354 | −0.0609242 | ||||||||
\(820\) | −26.1611 | −0.913587 | ||||||||
\(821\) | −20.8937 | −0.729195 | −0.364597 | − | 0.931165i | \(-0.618793\pi\) | ||||
−0.364597 | + | 0.931165i | \(0.618793\pi\) | |||||||
\(822\) | 0.00804888 | 0.000280737 0 | ||||||||
\(823\) | −9.56812 | −0.333524 | −0.166762 | − | 0.985997i | \(-0.553331\pi\) | ||||
−0.166762 | + | 0.985997i | \(0.553331\pi\) | |||||||
\(824\) | 5.38404 | 0.187562 | ||||||||
\(825\) | 0.0266593 | 0.000928159 0 | ||||||||
\(826\) | 14.2002 | 0.494087 | ||||||||
\(827\) | −16.1182 | −0.560486 | −0.280243 | − | 0.959929i | \(-0.590415\pi\) | ||||
−0.280243 | + | 0.959929i | \(0.590415\pi\) | |||||||
\(828\) | 16.8115 | 0.584241 | ||||||||
\(829\) | 3.99510 | 0.138756 | 0.0693778 | − | 0.997590i | \(-0.477899\pi\) | ||||
0.0693778 | + | 0.997590i | \(0.477899\pi\) | |||||||
\(830\) | −50.0949 | −1.73882 | ||||||||
\(831\) | −0.0224285 | −0.000778036 0 | ||||||||
\(832\) | 0.240087 | 0.00832352 | ||||||||
\(833\) | −1.00135 | −0.0346947 | ||||||||
\(834\) | −0.0225247 | −0.000779966 0 | ||||||||
\(835\) | −23.4858 | −0.812759 | ||||||||
\(836\) | 4.79658 | 0.165893 | ||||||||
\(837\) | 0.102383 | 0.00353886 | ||||||||
\(838\) | 32.8620 | 1.13520 | ||||||||
\(839\) | −51.3694 | −1.77347 | −0.886734 | − | 0.462280i | \(-0.847031\pi\) | ||||
−0.886734 | + | 0.462280i | \(0.847031\pi\) | |||||||
\(840\) | 0.0123673 | 0.000426712 0 | ||||||||
\(841\) | −9.11840 | −0.314428 | ||||||||
\(842\) | 19.3852 | 0.668057 | ||||||||
\(843\) | 0.0367472 | 0.00126564 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | 36.8239 | 1.26678 | ||||||||
\(846\) | 10.4018 | 0.357621 | ||||||||
\(847\) | 29.0658 | 0.998714 | ||||||||
\(848\) | −8.34252 | −0.286483 | ||||||||
\(849\) | 0.0390843 | 0.00134137 | ||||||||
\(850\) | 2.71841 | 0.0932409 | ||||||||
\(851\) | −17.1414 | −0.587600 | ||||||||
\(852\) | 0.0215472 | 0.000738195 0 | ||||||||
\(853\) | 36.6607 | 1.25524 | 0.627619 | − | 0.778521i | \(-0.284030\pi\) | ||||
0.627619 | + | 0.778521i | \(0.284030\pi\) | |||||||
\(854\) | −13.3780 | −0.457784 | ||||||||
\(855\) | −8.53566 | −0.291913 | ||||||||
\(856\) | 7.38286 | 0.252341 | ||||||||
\(857\) | −7.94393 | −0.271359 | −0.135680 | − | 0.990753i | \(-0.543322\pi\) | ||||
−0.135680 | + | 0.990753i | \(0.543322\pi\) | |||||||
\(858\) | 0.00206784 | 7.05948e−5 0 | ||||||||
\(859\) | 14.3412 | 0.489316 | 0.244658 | − | 0.969609i | \(-0.421324\pi\) | ||||
0.244658 | + | 0.969609i | \(0.421324\pi\) | |||||||
\(860\) | −22.8423 | −0.778917 | ||||||||
\(861\) | −0.0399668 | −0.00136206 | ||||||||
\(862\) | 19.3947 | 0.660586 | ||||||||
\(863\) | −32.4626 | −1.10504 | −0.552520 | − | 0.833500i | \(-0.686334\pi\) | ||||
−0.552520 | + | 0.833500i | \(0.686334\pi\) | |||||||
\(864\) | 0.0107738 | 0.000366531 0 | ||||||||
\(865\) | −9.84270 | −0.334662 | ||||||||
\(866\) | −15.6643 | −0.532296 | ||||||||
\(867\) | 0.0291407 | 0.000989670 0 | ||||||||
\(868\) | 23.0039 | 0.780803 | ||||||||
\(869\) | 55.5203 | 1.88340 | ||||||||
\(870\) | −0.0227802 | −0.000772322 0 | ||||||||
\(871\) | −0.385160 | −0.0130507 | ||||||||
\(872\) | 13.4481 | 0.455410 | ||||||||
\(873\) | −34.9102 | −1.18153 | ||||||||
\(874\) | 5.60385 | 0.189553 | ||||||||
\(875\) | 13.1186 | 0.443489 | ||||||||
\(876\) | 0.00864123 | 0.000291960 0 | ||||||||
\(877\) | 23.1183 | 0.780649 | 0.390324 | − | 0.920677i | \(-0.372363\pi\) | ||||
0.390324 | + | 0.920677i | \(0.372363\pi\) | |||||||
\(878\) | 15.1152 | 0.510112 | ||||||||
\(879\) | 0.0547386 | 0.00184629 | ||||||||
\(880\) | 13.6473 | 0.460052 | ||||||||
\(881\) | 10.2682 | 0.345944 | 0.172972 | − | 0.984927i | \(-0.444663\pi\) | ||||
0.172972 | + | 0.984927i | \(0.444663\pi\) | |||||||
\(882\) | 3.42052 | 0.115175 | ||||||||
\(883\) | 0.913466 | 0.0307406 | 0.0153703 | − | 0.999882i | \(-0.495107\pi\) | ||||
0.0153703 | + | 0.999882i | \(0.495107\pi\) | |||||||
\(884\) | 0.210854 | 0.00709180 | ||||||||
\(885\) | 0.0299698 | 0.00100742 | ||||||||
\(886\) | 3.94271 | 0.132458 | ||||||||
\(887\) | 48.0970 | 1.61494 | 0.807469 | − | 0.589910i | \(-0.200837\pi\) | ||||
0.807469 | + | 0.589910i | \(0.200837\pi\) | |||||||
\(888\) | −0.00549258 | −0.000184319 0 | ||||||||
\(889\) | 22.6222 | 0.758724 | ||||||||
\(890\) | −27.3943 | −0.918259 | ||||||||
\(891\) | −43.1691 | −1.44622 | ||||||||
\(892\) | 10.9423 | 0.366376 | ||||||||
\(893\) | 3.46726 | 0.116028 | ||||||||
\(894\) | 0.00171406 | 5.73267e−5 0 | ||||||||
\(895\) | 37.1270 | 1.24102 | ||||||||
\(896\) | 2.42071 | 0.0808702 | ||||||||
\(897\) | 0.00241586 | 8.06631e−5 0 | ||||||||
\(898\) | −4.88432 | −0.162992 | ||||||||
\(899\) | −42.3725 | −1.41320 | ||||||||
\(900\) | −9.28587 | −0.309529 | ||||||||
\(901\) | −7.32675 | −0.244089 | ||||||||
\(902\) | −44.1034 | −1.46848 | ||||||||
\(903\) | −0.0348965 | −0.00116128 | ||||||||
\(904\) | 5.91656 | 0.196782 | ||||||||
\(905\) | −49.0427 | −1.63023 | ||||||||
\(906\) | 0.00716869 | 0.000238164 0 | ||||||||
\(907\) | −11.6383 | −0.386444 | −0.193222 | − | 0.981155i | \(-0.561894\pi\) | ||||
−0.193222 | + | 0.981155i | \(0.561894\pi\) | |||||||
\(908\) | 27.4565 | 0.911175 | ||||||||
\(909\) | −44.7842 | −1.48540 | ||||||||
\(910\) | −1.65359 | −0.0548159 | ||||||||
\(911\) | 3.53423 | 0.117094 | 0.0585471 | − | 0.998285i | \(-0.481353\pi\) | ||||
0.0585471 | + | 0.998285i | \(0.481353\pi\) | |||||||
\(912\) | 0.00179563 | 5.94592e−5 0 | ||||||||
\(913\) | −84.4518 | −2.79495 | ||||||||
\(914\) | 1.82125 | 0.0602417 | ||||||||
\(915\) | −0.0282345 | −0.000933404 0 | ||||||||
\(916\) | 23.5037 | 0.776584 | ||||||||
\(917\) | −13.1598 | −0.434574 | ||||||||
\(918\) | 0.00946196 | 0.000312291 0 | ||||||||
\(919\) | −2.87305 | −0.0947732 | −0.0473866 | − | 0.998877i | \(-0.515089\pi\) | ||||
−0.0473866 | + | 0.998877i | \(0.515089\pi\) | |||||||
\(920\) | 15.9442 | 0.525665 | ||||||||
\(921\) | −0.0145709 | −0.000480127 0 | ||||||||
\(922\) | −36.7344 | −1.20978 | ||||||||
\(923\) | −2.88100 | −0.0948292 | ||||||||
\(924\) | 0.0208492 | 0.000685889 0 | ||||||||
\(925\) | 9.46807 | 0.311308 | ||||||||
\(926\) | 29.4545 | 0.967934 | ||||||||
\(927\) | −16.1521 | −0.530505 | ||||||||
\(928\) | −4.45888 | −0.146370 | ||||||||
\(929\) | −15.3309 | −0.502992 | −0.251496 | − | 0.967858i | \(-0.580922\pi\) | ||||
−0.251496 | + | 0.967858i | \(0.580922\pi\) | |||||||
\(930\) | 0.0485502 | 0.00159202 | ||||||||
\(931\) | 1.14017 | 0.0373677 | ||||||||
\(932\) | −20.9100 | −0.684930 | ||||||||
\(933\) | −2.52825e−5 0 | −8.27713e−7 0 | ||||||||
\(934\) | 22.3819 | 0.732357 | ||||||||
\(935\) | 11.9857 | 0.391973 | ||||||||
\(936\) | −0.720260 | −0.0235424 | ||||||||
\(937\) | −16.5432 | −0.540443 | −0.270221 | − | 0.962798i | \(-0.587097\pi\) | ||||
−0.270221 | + | 0.962798i | \(0.587097\pi\) | |||||||
\(938\) | −3.88343 | −0.126799 | ||||||||
\(939\) | −0.0183079 | −0.000597456 0 | ||||||||
\(940\) | 9.86514 | 0.321765 | ||||||||
\(941\) | −27.8624 | −0.908289 | −0.454145 | − | 0.890928i | \(-0.650055\pi\) | ||||
−0.454145 | + | 0.890928i | \(0.650055\pi\) | |||||||
\(942\) | −0.00435412 | −0.000141865 0 | ||||||||
\(943\) | −51.5261 | −1.67792 | ||||||||
\(944\) | 5.86612 | 0.190926 | ||||||||
\(945\) | −0.0742038 | −0.00241385 | ||||||||
\(946\) | −38.5084 | −1.25202 | ||||||||
\(947\) | −0.522227 | −0.0169701 | −0.00848505 | − | 0.999964i | \(-0.502701\pi\) | ||||
−0.00848505 | + | 0.999964i | \(0.502701\pi\) | |||||||
\(948\) | 0.0207843 | 0.000675044 0 | ||||||||
\(949\) | −1.15539 | −0.0375055 | ||||||||
\(950\) | −3.09529 | −0.100425 | ||||||||
\(951\) | −0.00447610 | −0.000145148 0 | ||||||||
\(952\) | 2.12597 | 0.0689030 | ||||||||
\(953\) | 25.0170 | 0.810379 | 0.405190 | − | 0.914233i | \(-0.367205\pi\) | ||||
0.405190 | + | 0.914233i | \(0.367205\pi\) | |||||||
\(954\) | 25.0275 | 0.810296 | ||||||||
\(955\) | 38.5166 | 1.24637 | ||||||||
\(956\) | −5.68156 | −0.183755 | ||||||||
\(957\) | −0.0384037 | −0.00124142 | ||||||||
\(958\) | 36.1413 | 1.16767 | ||||||||
\(959\) | −10.8508 | −0.350390 | ||||||||
\(960\) | 0.00510896 | 0.000164891 0 | ||||||||
\(961\) | 59.3062 | 1.91310 | ||||||||
\(962\) | 0.734393 | 0.0236778 | ||||||||
\(963\) | −22.1486 | −0.713727 | ||||||||
\(964\) | 9.05353 | 0.291594 | ||||||||
\(965\) | 13.5186 | 0.435180 | ||||||||
\(966\) | 0.0243582 | 0.000783712 0 | ||||||||
\(967\) | −17.6698 | −0.568222 | −0.284111 | − | 0.958791i | \(-0.591698\pi\) | ||||
−0.284111 | + | 0.958791i | \(0.591698\pi\) | |||||||
\(968\) | 12.0072 | 0.385925 | ||||||||
\(969\) | 0.00157699 | 5.06604e−5 0 | ||||||||
\(970\) | −33.1092 | −1.06307 | ||||||||
\(971\) | 3.42041 | 0.109766 | 0.0548831 | − | 0.998493i | \(-0.482521\pi\) | ||||
0.0548831 | + | 0.998493i | \(0.482521\pi\) | |||||||
\(972\) | −0.0484819 | −0.00155506 | ||||||||
\(973\) | 30.3658 | 0.973483 | ||||||||
\(974\) | −4.85599 | −0.155596 | ||||||||
\(975\) | −0.00133440 | −4.27350e−5 0 | ||||||||
\(976\) | −5.52647 | −0.176898 | ||||||||
\(977\) | 25.7862 | 0.824974 | 0.412487 | − | 0.910963i | \(-0.364660\pi\) | ||||
0.412487 | + | 0.910963i | \(0.364660\pi\) | |||||||
\(978\) | −0.0285934 | −0.000914316 0 | ||||||||
\(979\) | −46.1823 | −1.47599 | ||||||||
\(980\) | 3.24405 | 0.103627 | ||||||||
\(981\) | −40.3442 | −1.28809 | ||||||||
\(982\) | 34.0613 | 1.08694 | ||||||||
\(983\) | 20.1953 | 0.644129 | 0.322064 | − | 0.946718i | \(-0.395623\pi\) | ||||
0.322064 | + | 0.946718i | \(0.395623\pi\) | |||||||
\(984\) | −0.0165104 | −0.000526331 0 | ||||||||
\(985\) | 10.5668 | 0.336686 | ||||||||
\(986\) | −3.91597 | −0.124710 | ||||||||
\(987\) | 0.0150711 | 0.000479719 0 | ||||||||
\(988\) | −0.240087 | −0.00763818 | ||||||||
\(989\) | −44.9894 | −1.43058 | ||||||||
\(990\) | −40.9420 | −1.30122 | ||||||||
\(991\) | 55.2073 | 1.75372 | 0.876860 | − | 0.480747i | \(-0.159634\pi\) | ||||
0.876860 | + | 0.480747i | \(0.159634\pi\) | |||||||
\(992\) | 9.50296 | 0.301719 | ||||||||
\(993\) | −0.0453970 | −0.00144063 | ||||||||
\(994\) | −29.0480 | −0.921348 | ||||||||
\(995\) | 62.4507 | 1.97982 | ||||||||
\(996\) | −0.0316150 | −0.00100176 | ||||||||
\(997\) | −22.2158 | −0.703582 | −0.351791 | − | 0.936079i | \(-0.614427\pi\) | ||||
−0.351791 | + | 0.936079i | \(0.614427\pi\) | |||||||
\(998\) | −35.6636 | −1.12891 | ||||||||
\(999\) | 0.0329554 | 0.00104266 |
(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 | 8018.2.a.j.1.22 | ✓ | 47 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.j.1.22 | ✓ | 47 | 1.1 | even | 1 | trivial |