Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,12,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.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: | \(151.363606570\) |
Analytic rank: | \(0\) |
Dimension: | \(92\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −79.8918 | −1.76537 | −0.882687 | − | 0.469960i | \(-0.844268\pi\) | ||||
−0.882687 | + | 0.469960i | \(0.844268\pi\) | |||||||
\(3\) | 101.497 | 0.241150 | 0.120575 | − | 0.992704i | \(-0.461526\pi\) | ||||
0.120575 | + | 0.992704i | \(0.461526\pi\) | |||||||
\(4\) | 4334.69 | 2.11655 | ||||||||
\(5\) | 1864.60 | 0.266840 | 0.133420 | − | 0.991060i | \(-0.457404\pi\) | ||||
0.133420 | + | 0.991060i | \(0.457404\pi\) | |||||||
\(6\) | −8108.77 | −0.425719 | ||||||||
\(7\) | 52018.3 | 1.16981 | 0.584907 | − | 0.811100i | \(-0.301131\pi\) | ||||
0.584907 | + | 0.811100i | \(0.301131\pi\) | |||||||
\(8\) | −182688. | −1.97113 | ||||||||
\(9\) | −166845. | −0.941847 | ||||||||
\(10\) | −148966. | −0.471072 | ||||||||
\(11\) | −81826.4 | −0.153191 | −0.0765956 | − | 0.997062i | \(-0.524405\pi\) | ||||
−0.0765956 | + | 0.997062i | \(0.524405\pi\) | |||||||
\(12\) | 439958. | 0.510405 | ||||||||
\(13\) | 1.50884e6 | 1.12708 | 0.563541 | − | 0.826088i | \(-0.309439\pi\) | ||||
0.563541 | + | 0.826088i | \(0.309439\pi\) | |||||||
\(14\) | −4.15583e6 | −2.06516 | ||||||||
\(15\) | 189251. | 0.0643483 | ||||||||
\(16\) | 5.71780e6 | 1.36323 | ||||||||
\(17\) | −9.93022e6 | −1.69625 | −0.848125 | − | 0.529796i | \(-0.822268\pi\) | ||||
−0.848125 | + | 0.529796i | \(0.822268\pi\) | |||||||
\(18\) | 1.33296e7 | 1.66271 | ||||||||
\(19\) | −1.66012e7 | −1.53813 | −0.769067 | − | 0.639168i | \(-0.779279\pi\) | ||||
−0.769067 | + | 0.639168i | \(0.779279\pi\) | |||||||
\(20\) | 8.08246e6 | 0.564779 | ||||||||
\(21\) | 5.27970e6 | 0.282100 | ||||||||
\(22\) | 6.53725e6 | 0.270440 | ||||||||
\(23\) | −4.11960e7 | −1.33460 | −0.667302 | − | 0.744788i | \(-0.732551\pi\) | ||||
−0.667302 | + | 0.744788i | \(0.732551\pi\) | |||||||
\(24\) | −1.85423e7 | −0.475336 | ||||||||
\(25\) | −4.53514e7 | −0.928797 | ||||||||
\(26\) | −1.20544e8 | −1.98972 | ||||||||
\(27\) | −3.49142e7 | −0.468275 | ||||||||
\(28\) | 2.25483e8 | 2.47597 | ||||||||
\(29\) | −2.29850e7 | −0.208092 | −0.104046 | − | 0.994573i | \(-0.533179\pi\) | ||||
−0.104046 | + | 0.994573i | \(0.533179\pi\) | |||||||
\(30\) | −1.51196e7 | −0.113599 | ||||||||
\(31\) | 1.81442e7 | 0.113828 | 0.0569138 | − | 0.998379i | \(-0.481874\pi\) | ||||
0.0569138 | + | 0.998379i | \(0.481874\pi\) | |||||||
\(32\) | −8.26606e7 | −0.435485 | ||||||||
\(33\) | −8.30513e6 | −0.0369420 | ||||||||
\(34\) | 7.93343e8 | 2.99452 | ||||||||
\(35\) | 9.69932e7 | 0.312153 | ||||||||
\(36\) | −7.23223e8 | −1.99347 | ||||||||
\(37\) | −5.49903e8 | −1.30370 | −0.651849 | − | 0.758349i | \(-0.726006\pi\) | ||||
−0.651849 | + | 0.758349i | \(0.726006\pi\) | |||||||
\(38\) | 1.32630e9 | 2.71538 | ||||||||
\(39\) | 1.53143e8 | 0.271795 | ||||||||
\(40\) | −3.40640e8 | −0.525975 | ||||||||
\(41\) | 8.19172e7 | 0.110424 | 0.0552121 | − | 0.998475i | \(-0.482417\pi\) | ||||
0.0552121 | + | 0.998475i | \(0.482417\pi\) | |||||||
\(42\) | −4.21805e8 | −0.498012 | ||||||||
\(43\) | 1.43469e9 | 1.48827 | 0.744134 | − | 0.668030i | \(-0.232862\pi\) | ||||
0.744134 | + | 0.668030i | \(0.232862\pi\) | |||||||
\(44\) | −3.54692e8 | −0.324236 | ||||||||
\(45\) | −3.11100e8 | −0.251322 | ||||||||
\(46\) | 3.29122e9 | 2.35607 | ||||||||
\(47\) | −5.29515e8 | −0.336775 | −0.168388 | − | 0.985721i | \(-0.553856\pi\) | ||||
−0.168388 | + | 0.985721i | \(0.553856\pi\) | |||||||
\(48\) | 5.80340e8 | 0.328742 | ||||||||
\(49\) | 7.28575e8 | 0.368464 | ||||||||
\(50\) | 3.62320e9 | 1.63967 | ||||||||
\(51\) | −1.00789e9 | −0.409050 | ||||||||
\(52\) | 6.54037e9 | 2.38552 | ||||||||
\(53\) | 1.88546e9 | 0.619297 | 0.309648 | − | 0.950851i | \(-0.399789\pi\) | ||||
0.309648 | + | 0.950851i | \(0.399789\pi\) | |||||||
\(54\) | 2.78936e9 | 0.826682 | ||||||||
\(55\) | −1.52573e8 | −0.0408775 | ||||||||
\(56\) | −9.50311e9 | −2.30585 | ||||||||
\(57\) | −1.68497e9 | −0.370920 | ||||||||
\(58\) | 1.83631e9 | 0.367360 | ||||||||
\(59\) | 9.68096e9 | 1.76292 | 0.881460 | − | 0.472259i | \(-0.156561\pi\) | ||||
0.881460 | + | 0.472259i | \(0.156561\pi\) | |||||||
\(60\) | 8.20346e8 | 0.136196 | ||||||||
\(61\) | 2.66854e9 | 0.404539 | 0.202269 | − | 0.979330i | \(-0.435168\pi\) | ||||
0.202269 | + | 0.979330i | \(0.435168\pi\) | |||||||
\(62\) | −1.44957e9 | −0.200948 | ||||||||
\(63\) | −8.67901e9 | −1.10179 | ||||||||
\(64\) | −5.10616e9 | −0.594436 | ||||||||
\(65\) | 2.81339e9 | 0.300750 | ||||||||
\(66\) | 6.63512e8 | 0.0652164 | ||||||||
\(67\) | 1.03086e10 | 0.932804 | 0.466402 | − | 0.884573i | \(-0.345550\pi\) | ||||
0.466402 | + | 0.884573i | \(0.345550\pi\) | |||||||
\(68\) | −4.30445e10 | −3.59020 | ||||||||
\(69\) | −4.18127e9 | −0.321839 | ||||||||
\(70\) | −7.74896e9 | −0.551067 | ||||||||
\(71\) | −2.60268e10 | −1.71199 | −0.855993 | − | 0.516988i | \(-0.827053\pi\) | ||||
−0.855993 | + | 0.516988i | \(0.827053\pi\) | |||||||
\(72\) | 3.04806e10 | 1.85650 | ||||||||
\(73\) | 3.05024e10 | 1.72210 | 0.861051 | − | 0.508518i | \(-0.169807\pi\) | ||||
0.861051 | + | 0.508518i | \(0.169807\pi\) | |||||||
\(74\) | 4.39327e10 | 2.30152 | ||||||||
\(75\) | −4.60303e9 | −0.223979 | ||||||||
\(76\) | −7.19610e10 | −3.25554 | ||||||||
\(77\) | −4.25647e9 | −0.179205 | ||||||||
\(78\) | −1.22349e10 | −0.479821 | ||||||||
\(79\) | 3.22798e10 | 1.18027 | 0.590135 | − | 0.807305i | \(-0.299074\pi\) | ||||
0.590135 | + | 0.807305i | \(0.299074\pi\) | |||||||
\(80\) | 1.06614e10 | 0.363764 | ||||||||
\(81\) | 2.60125e10 | 0.828923 | ||||||||
\(82\) | −6.54451e9 | −0.194940 | ||||||||
\(83\) | −5.02186e10 | −1.39938 | −0.699690 | − | 0.714447i | \(-0.746678\pi\) | ||||
−0.699690 | + | 0.714447i | \(0.746678\pi\) | |||||||
\(84\) | 2.28859e10 | 0.597079 | ||||||||
\(85\) | −1.85159e10 | −0.452627 | ||||||||
\(86\) | −1.14620e11 | −2.62735 | ||||||||
\(87\) | −2.33291e9 | −0.0501812 | ||||||||
\(88\) | 1.49487e10 | 0.301959 | ||||||||
\(89\) | 2.94603e10 | 0.559232 | 0.279616 | − | 0.960112i | \(-0.409793\pi\) | ||||
0.279616 | + | 0.960112i | \(0.409793\pi\) | |||||||
\(90\) | 2.48543e10 | 0.443678 | ||||||||
\(91\) | 7.84874e10 | 1.31848 | ||||||||
\(92\) | −1.78572e11 | −2.82475 | ||||||||
\(93\) | 1.84158e9 | 0.0274495 | ||||||||
\(94\) | 4.23039e10 | 0.594534 | ||||||||
\(95\) | −3.09545e10 | −0.410435 | ||||||||
\(96\) | −8.38980e9 | −0.105017 | ||||||||
\(97\) | 4.41143e10 | 0.521597 | 0.260798 | − | 0.965393i | \(-0.416014\pi\) | ||||
0.260798 | + | 0.965393i | \(0.416014\pi\) | |||||||
\(98\) | −5.82071e10 | −0.650478 | ||||||||
\(99\) | 1.36524e10 | 0.144283 | ||||||||
\(100\) | −1.96584e11 | −1.96584 | ||||||||
\(101\) | 1.99545e10 | 0.188918 | 0.0944591 | − | 0.995529i | \(-0.469888\pi\) | ||||
0.0944591 | + | 0.995529i | \(0.469888\pi\) | |||||||
\(102\) | 8.05219e10 | 0.722126 | ||||||||
\(103\) | −2.97252e9 | −0.0252650 | −0.0126325 | − | 0.999920i | \(-0.504021\pi\) | ||||
−0.0126325 | + | 0.999920i | \(0.504021\pi\) | |||||||
\(104\) | −2.75647e11 | −2.22162 | ||||||||
\(105\) | 9.84452e9 | 0.0752755 | ||||||||
\(106\) | −1.50632e11 | −1.09329 | ||||||||
\(107\) | −1.57952e11 | −1.08872 | −0.544359 | − | 0.838852i | \(-0.683227\pi\) | ||||
−0.544359 | + | 0.838852i | \(0.683227\pi\) | |||||||
\(108\) | −1.51342e11 | −0.991128 | ||||||||
\(109\) | 4.62875e10 | 0.288150 | 0.144075 | − | 0.989567i | \(-0.453979\pi\) | ||||
0.144075 | + | 0.989567i | \(0.453979\pi\) | |||||||
\(110\) | 1.21894e10 | 0.0721641 | ||||||||
\(111\) | −5.58135e10 | −0.314386 | ||||||||
\(112\) | 2.97430e11 | 1.59473 | ||||||||
\(113\) | −1.93933e11 | −0.990196 | −0.495098 | − | 0.868837i | \(-0.664868\pi\) | ||||
−0.495098 | + | 0.868837i | \(0.664868\pi\) | |||||||
\(114\) | 1.34615e11 | 0.654813 | ||||||||
\(115\) | −7.68141e10 | −0.356125 | ||||||||
\(116\) | −9.96327e10 | −0.440436 | ||||||||
\(117\) | −2.51743e11 | −1.06154 | ||||||||
\(118\) | −7.73429e11 | −3.11221 | ||||||||
\(119\) | −5.16553e11 | −1.98430 | ||||||||
\(120\) | −3.45739e10 | −0.126839 | ||||||||
\(121\) | −2.78616e11 | −0.976532 | ||||||||
\(122\) | −2.13195e11 | −0.714163 | ||||||||
\(123\) | 8.31436e9 | 0.0266287 | ||||||||
\(124\) | 7.86494e10 | 0.240922 | ||||||||
\(125\) | −1.75607e11 | −0.514680 | ||||||||
\(126\) | 6.93381e11 | 1.94506 | ||||||||
\(127\) | −6.97597e10 | −0.187363 | −0.0936816 | − | 0.995602i | \(-0.529864\pi\) | ||||
−0.0936816 | + | 0.995602i | \(0.529864\pi\) | |||||||
\(128\) | 5.77229e11 | 1.48489 | ||||||||
\(129\) | 1.45617e11 | 0.358895 | ||||||||
\(130\) | −2.24766e11 | −0.530937 | ||||||||
\(131\) | 6.20880e11 | 1.40610 | 0.703049 | − | 0.711141i | \(-0.251821\pi\) | ||||
0.703049 | + | 0.711141i | \(0.251821\pi\) | |||||||
\(132\) | −3.60002e10 | −0.0781895 | ||||||||
\(133\) | −8.63565e11 | −1.79933 | ||||||||
\(134\) | −8.23576e11 | −1.64675 | ||||||||
\(135\) | −6.51010e10 | −0.124954 | ||||||||
\(136\) | 1.81413e12 | 3.34353 | ||||||||
\(137\) | 8.34982e11 | 1.47813 | 0.739067 | − | 0.673632i | \(-0.235267\pi\) | ||||
0.739067 | + | 0.673632i | \(0.235267\pi\) | |||||||
\(138\) | 3.34049e11 | 0.568166 | ||||||||
\(139\) | 6.64732e11 | 1.08659 | 0.543294 | − | 0.839543i | \(-0.317177\pi\) | ||||
0.543294 | + | 0.839543i | \(0.317177\pi\) | |||||||
\(140\) | 4.20436e11 | 0.660687 | ||||||||
\(141\) | −5.37442e10 | −0.0812132 | ||||||||
\(142\) | 2.07933e12 | 3.02230 | ||||||||
\(143\) | −1.23463e11 | −0.172659 | ||||||||
\(144\) | −9.53989e11 | −1.28395 | ||||||||
\(145\) | −4.28577e10 | −0.0555271 | ||||||||
\(146\) | −2.43689e12 | −3.04016 | ||||||||
\(147\) | 7.39482e10 | 0.0888550 | ||||||||
\(148\) | −2.38366e12 | −2.75934 | ||||||||
\(149\) | 4.71677e11 | 0.526163 | 0.263082 | − | 0.964774i | \(-0.415261\pi\) | ||||
0.263082 | + | 0.964774i | \(0.415261\pi\) | |||||||
\(150\) | 3.67744e11 | 0.395407 | ||||||||
\(151\) | 1.52329e12 | 1.57910 | 0.789552 | − | 0.613684i | \(-0.210313\pi\) | ||||
0.789552 | + | 0.613684i | \(0.210313\pi\) | |||||||
\(152\) | 3.03283e12 | 3.03186 | ||||||||
\(153\) | 1.65681e12 | 1.59761 | ||||||||
\(154\) | 3.40057e11 | 0.316364 | ||||||||
\(155\) | 3.38316e10 | 0.0303737 | ||||||||
\(156\) | 6.63828e11 | 0.575268 | ||||||||
\(157\) | 5.90539e11 | 0.494083 | 0.247042 | − | 0.969005i | \(-0.420542\pi\) | ||||
0.247042 | + | 0.969005i | \(0.420542\pi\) | |||||||
\(158\) | −2.57889e12 | −2.08362 | ||||||||
\(159\) | 1.91368e11 | 0.149343 | ||||||||
\(160\) | −1.54129e11 | −0.116205 | ||||||||
\(161\) | −2.14295e12 | −1.56124 | ||||||||
\(162\) | −2.07818e12 | −1.46336 | ||||||||
\(163\) | 1.00470e11 | 0.0683919 | 0.0341960 | − | 0.999415i | \(-0.489113\pi\) | ||||
0.0341960 | + | 0.999415i | \(0.489113\pi\) | |||||||
\(164\) | 3.55086e11 | 0.233718 | ||||||||
\(165\) | −1.54857e10 | −0.00985758 | ||||||||
\(166\) | 4.01206e12 | 2.47043 | ||||||||
\(167\) | 2.72062e12 | 1.62079 | 0.810396 | − | 0.585883i | \(-0.199252\pi\) | ||||
0.810396 | + | 0.585883i | \(0.199252\pi\) | |||||||
\(168\) | −9.64537e11 | −0.556055 | ||||||||
\(169\) | 4.84445e11 | 0.270313 | ||||||||
\(170\) | 1.47927e12 | 0.799056 | ||||||||
\(171\) | 2.76983e12 | 1.44869 | ||||||||
\(172\) | 6.21894e12 | 3.14999 | ||||||||
\(173\) | −6.77593e11 | −0.332442 | −0.166221 | − | 0.986089i | \(-0.553156\pi\) | ||||
−0.166221 | + | 0.986089i | \(0.553156\pi\) | |||||||
\(174\) | 1.86380e11 | 0.0885887 | ||||||||
\(175\) | −2.35910e12 | −1.08652 | ||||||||
\(176\) | −4.67867e11 | −0.208835 | ||||||||
\(177\) | 9.82589e11 | 0.425127 | ||||||||
\(178\) | −2.35363e12 | −0.987254 | ||||||||
\(179\) | 3.55100e12 | 1.44431 | 0.722153 | − | 0.691734i | \(-0.243153\pi\) | ||||
0.722153 | + | 0.691734i | \(0.243153\pi\) | |||||||
\(180\) | −1.34852e12 | −0.531936 | ||||||||
\(181\) | 1.88616e12 | 0.721684 | 0.360842 | − | 0.932627i | \(-0.382489\pi\) | ||||
0.360842 | + | 0.932627i | \(0.382489\pi\) | |||||||
\(182\) | −6.27049e12 | −2.32760 | ||||||||
\(183\) | 2.70849e11 | 0.0975544 | ||||||||
\(184\) | 7.52601e12 | 2.63067 | ||||||||
\(185\) | −1.02535e12 | −0.347878 | ||||||||
\(186\) | −1.47127e11 | −0.0484586 | ||||||||
\(187\) | 8.12554e11 | 0.259850 | ||||||||
\(188\) | −2.29528e12 | −0.712801 | ||||||||
\(189\) | −1.81618e12 | −0.547795 | ||||||||
\(190\) | 2.47301e12 | 0.724572 | ||||||||
\(191\) | −5.40642e12 | −1.53896 | −0.769478 | − | 0.638673i | \(-0.779484\pi\) | ||||
−0.769478 | + | 0.638673i | \(0.779484\pi\) | |||||||
\(192\) | −5.18260e11 | −0.143348 | ||||||||
\(193\) | 1.98890e12 | 0.534624 | 0.267312 | − | 0.963610i | \(-0.413865\pi\) | ||||
0.267312 | + | 0.963610i | \(0.413865\pi\) | |||||||
\(194\) | −3.52437e12 | −0.920814 | ||||||||
\(195\) | 2.85550e11 | 0.0725258 | ||||||||
\(196\) | 3.15815e12 | 0.779873 | ||||||||
\(197\) | −2.96709e11 | −0.0712470 | ||||||||
\(198\) | −1.09071e12 | −0.254713 | ||||||||
\(199\) | 2.02691e11 | 0.0460408 | 0.0230204 | − | 0.999735i | \(-0.492672\pi\) | ||||
0.0230204 | + | 0.999735i | \(0.492672\pi\) | |||||||
\(200\) | 8.28515e12 | 1.83078 | ||||||||
\(201\) | 1.04630e12 | 0.224945 | ||||||||
\(202\) | −1.59420e12 | −0.333512 | ||||||||
\(203\) | −1.19564e12 | −0.243429 | ||||||||
\(204\) | −4.36888e12 | −0.865774 | ||||||||
\(205\) | 1.52743e11 | 0.0294656 | ||||||||
\(206\) | 2.37479e11 | 0.0446022 | ||||||||
\(207\) | 6.87336e12 | 1.25699 | ||||||||
\(208\) | 8.62726e12 | 1.53647 | ||||||||
\(209\) | 1.35841e12 | 0.235628 | ||||||||
\(210\) | −7.86496e11 | −0.132889 | ||||||||
\(211\) | −1.23239e12 | −0.202860 | −0.101430 | − | 0.994843i | \(-0.532342\pi\) | ||||
−0.101430 | + | 0.994843i | \(0.532342\pi\) | |||||||
\(212\) | 8.17287e12 | 1.31077 | ||||||||
\(213\) | −2.64164e12 | −0.412844 | ||||||||
\(214\) | 1.26191e13 | 1.92200 | ||||||||
\(215\) | 2.67512e12 | 0.397129 | ||||||||
\(216\) | 6.37840e12 | 0.923031 | ||||||||
\(217\) | 9.43828e11 | 0.133157 | ||||||||
\(218\) | −3.69799e12 | −0.508693 | ||||||||
\(219\) | 3.09591e12 | 0.415284 | ||||||||
\(220\) | −6.61359e11 | −0.0865192 | ||||||||
\(221\) | −1.49831e13 | −1.91181 | ||||||||
\(222\) | 4.45904e12 | 0.555009 | ||||||||
\(223\) | −9.78719e12 | −1.18845 | −0.594226 | − | 0.804298i | \(-0.702541\pi\) | ||||
−0.594226 | + | 0.804298i | \(0.702541\pi\) | |||||||
\(224\) | −4.29986e12 | −0.509437 | ||||||||
\(225\) | 7.56667e12 | 0.874784 | ||||||||
\(226\) | 1.54937e13 | 1.74807 | ||||||||
\(227\) | −9.47252e12 | −1.04309 | −0.521547 | − | 0.853223i | \(-0.674645\pi\) | ||||
−0.521547 | + | 0.853223i | \(0.674645\pi\) | |||||||
\(228\) | −7.30383e12 | −0.785071 | ||||||||
\(229\) | −1.05546e13 | −1.10751 | −0.553753 | − | 0.832681i | \(-0.686805\pi\) | ||||
−0.553753 | + | 0.832681i | \(0.686805\pi\) | |||||||
\(230\) | 6.13681e12 | 0.628694 | ||||||||
\(231\) | −4.32019e11 | −0.0432152 | ||||||||
\(232\) | 4.19907e12 | 0.410175 | ||||||||
\(233\) | 1.58697e13 | 1.51395 | 0.756973 | − | 0.653447i | \(-0.226678\pi\) | ||||
0.756973 | + | 0.653447i | \(0.226678\pi\) | |||||||
\(234\) | 2.01122e13 | 1.87401 | ||||||||
\(235\) | −9.87333e11 | −0.0898650 | ||||||||
\(236\) | 4.19640e13 | 3.73131 | ||||||||
\(237\) | 3.27630e12 | 0.284622 | ||||||||
\(238\) | 4.12683e13 | 3.50303 | ||||||||
\(239\) | 1.88903e13 | 1.56694 | 0.783468 | − | 0.621432i | \(-0.213449\pi\) | ||||
0.783468 | + | 0.621432i | \(0.213449\pi\) | |||||||
\(240\) | 1.08210e12 | 0.0877215 | ||||||||
\(241\) | −8.31011e12 | −0.658435 | −0.329218 | − | 0.944254i | \(-0.606785\pi\) | ||||
−0.329218 | + | 0.944254i | \(0.606785\pi\) | |||||||
\(242\) | 2.22591e13 | 1.72395 | ||||||||
\(243\) | 8.82513e12 | 0.668170 | ||||||||
\(244\) | 1.15673e13 | 0.856226 | ||||||||
\(245\) | 1.35850e12 | 0.0983210 | ||||||||
\(246\) | −6.64248e11 | −0.0470097 | ||||||||
\(247\) | −2.50486e13 | −1.73360 | ||||||||
\(248\) | −3.31472e12 | −0.224369 | ||||||||
\(249\) | −5.09704e12 | −0.337460 | ||||||||
\(250\) | 1.40296e13 | 0.908602 | ||||||||
\(251\) | 7.87031e12 | 0.498639 | 0.249320 | − | 0.968421i | \(-0.419793\pi\) | ||||
0.249320 | + | 0.968421i | \(0.419793\pi\) | |||||||
\(252\) | −3.76208e13 | −2.33198 | ||||||||
\(253\) | 3.37092e12 | 0.204449 | ||||||||
\(254\) | 5.57323e12 | 0.330766 | ||||||||
\(255\) | −1.87931e12 | −0.109151 | ||||||||
\(256\) | −3.56584e13 | −2.02695 | ||||||||
\(257\) | −1.12626e13 | −0.626625 | −0.313313 | − | 0.949650i | \(-0.601439\pi\) | ||||
−0.313313 | + | 0.949650i | \(0.601439\pi\) | |||||||
\(258\) | −1.16336e13 | −0.633585 | ||||||||
\(259\) | −2.86050e13 | −1.52508 | ||||||||
\(260\) | 1.21952e13 | 0.636552 | ||||||||
\(261\) | 3.83493e12 | 0.195991 | ||||||||
\(262\) | −4.96032e13 | −2.48229 | ||||||||
\(263\) | −2.15206e13 | −1.05462 | −0.527311 | − | 0.849672i | \(-0.676800\pi\) | ||||
−0.527311 | + | 0.849672i | \(0.676800\pi\) | |||||||
\(264\) | 1.51725e12 | 0.0728173 | ||||||||
\(265\) | 3.51562e12 | 0.165253 | ||||||||
\(266\) | 6.89917e13 | 3.17649 | ||||||||
\(267\) | 2.99013e12 | 0.134858 | ||||||||
\(268\) | 4.46848e13 | 1.97432 | ||||||||
\(269\) | 1.15303e13 | 0.499117 | 0.249559 | − | 0.968360i | \(-0.419714\pi\) | ||||
0.249559 | + | 0.968360i | \(0.419714\pi\) | |||||||
\(270\) | 5.20103e12 | 0.220592 | ||||||||
\(271\) | 5.46846e11 | 0.0227266 | 0.0113633 | − | 0.999935i | \(-0.496383\pi\) | ||||
0.0113633 | + | 0.999935i | \(0.496383\pi\) | |||||||
\(272\) | −5.67790e13 | −2.31238 | ||||||||
\(273\) | 7.96624e12 | 0.317950 | ||||||||
\(274\) | −6.67082e13 | −2.60946 | ||||||||
\(275\) | 3.71094e12 | 0.142283 | ||||||||
\(276\) | −1.81245e13 | −0.681188 | ||||||||
\(277\) | 1.85877e13 | 0.684836 | 0.342418 | − | 0.939548i | \(-0.388754\pi\) | ||||
0.342418 | + | 0.939548i | \(0.388754\pi\) | |||||||
\(278\) | −5.31066e13 | −1.91824 | ||||||||
\(279\) | −3.02727e12 | −0.107208 | ||||||||
\(280\) | −1.77195e13 | −0.615293 | ||||||||
\(281\) | 5.53087e13 | 1.88325 | 0.941626 | − | 0.336661i | \(-0.109298\pi\) | ||||
0.941626 | + | 0.336661i | \(0.109298\pi\) | |||||||
\(282\) | 4.29372e12 | 0.143372 | ||||||||
\(283\) | −7.89731e12 | −0.258615 | −0.129308 | − | 0.991605i | \(-0.541275\pi\) | ||||
−0.129308 | + | 0.991605i | \(0.541275\pi\) | |||||||
\(284\) | −1.12818e14 | −3.62350 | ||||||||
\(285\) | −3.14179e12 | −0.0989762 | ||||||||
\(286\) | 9.86368e12 | 0.304808 | ||||||||
\(287\) | 4.26119e12 | 0.129176 | ||||||||
\(288\) | 1.37915e13 | 0.410160 | ||||||||
\(289\) | 6.43374e13 | 1.87726 | ||||||||
\(290\) | 3.42398e12 | 0.0980262 | ||||||||
\(291\) | 4.47747e12 | 0.125783 | ||||||||
\(292\) | 1.32219e14 | 3.64491 | ||||||||
\(293\) | −6.80152e13 | −1.84007 | −0.920034 | − | 0.391838i | \(-0.871839\pi\) | ||||
−0.920034 | + | 0.391838i | \(0.871839\pi\) | |||||||
\(294\) | −5.90785e12 | −0.156862 | ||||||||
\(295\) | 1.80511e13 | 0.470417 | ||||||||
\(296\) | 1.00461e14 | 2.56975 | ||||||||
\(297\) | 2.85690e12 | 0.0717356 | ||||||||
\(298\) | −3.76831e13 | −0.928876 | ||||||||
\(299\) | −6.21583e13 | −1.50421 | ||||||||
\(300\) | −1.99527e13 | −0.474062 | ||||||||
\(301\) | 7.46301e13 | 1.74100 | ||||||||
\(302\) | −1.21699e14 | −2.78771 | ||||||||
\(303\) | 2.02532e12 | 0.0455575 | ||||||||
\(304\) | −9.49223e13 | −2.09683 | ||||||||
\(305\) | 4.97577e12 | 0.107947 | ||||||||
\(306\) | −1.32366e14 | −2.82038 | ||||||||
\(307\) | 6.64088e13 | 1.38984 | 0.694920 | − | 0.719087i | \(-0.255440\pi\) | ||||
0.694920 | + | 0.719087i | \(0.255440\pi\) | |||||||
\(308\) | −1.84505e13 | −0.379296 | ||||||||
\(309\) | −3.01701e11 | −0.00609264 | ||||||||
\(310\) | −2.70286e12 | −0.0536210 | ||||||||
\(311\) | 9.69704e12 | 0.188998 | 0.0944989 | − | 0.995525i | \(-0.469875\pi\) | ||||
0.0944989 | + | 0.995525i | \(0.469875\pi\) | |||||||
\(312\) | −2.79774e13 | −0.535743 | ||||||||
\(313\) | 3.17670e13 | 0.597698 | 0.298849 | − | 0.954300i | \(-0.403397\pi\) | ||||
0.298849 | + | 0.954300i | \(0.403397\pi\) | |||||||
\(314\) | −4.71792e13 | −0.872242 | ||||||||
\(315\) | −1.61829e13 | −0.294000 | ||||||||
\(316\) | 1.39923e14 | 2.49810 | ||||||||
\(317\) | −9.96377e13 | −1.74823 | −0.874113 | − | 0.485722i | \(-0.838557\pi\) | ||||
−0.874113 | + | 0.485722i | \(0.838557\pi\) | |||||||
\(318\) | −1.52887e13 | −0.263647 | ||||||||
\(319\) | 1.88078e12 | 0.0318778 | ||||||||
\(320\) | −9.52095e12 | −0.158619 | ||||||||
\(321\) | −1.60317e13 | −0.262544 | ||||||||
\(322\) | 1.71204e14 | 2.75617 | ||||||||
\(323\) | 1.64853e14 | 2.60906 | ||||||||
\(324\) | 1.12756e14 | 1.75446 | ||||||||
\(325\) | −6.84281e13 | −1.04683 | ||||||||
\(326\) | −8.02673e12 | −0.120737 | ||||||||
\(327\) | 4.69805e12 | 0.0694872 | ||||||||
\(328\) | −1.49653e13 | −0.217660 | ||||||||
\(329\) | −2.75445e13 | −0.393964 | ||||||||
\(330\) | 1.23718e12 | 0.0174023 | ||||||||
\(331\) | −1.85492e13 | −0.256608 | −0.128304 | − | 0.991735i | \(-0.540953\pi\) | ||||
−0.128304 | + | 0.991735i | \(0.540953\pi\) | |||||||
\(332\) | −2.17682e14 | −2.96185 | ||||||||
\(333\) | 9.17488e13 | 1.22788 | ||||||||
\(334\) | −2.17355e14 | −2.86130 | ||||||||
\(335\) | 1.92215e13 | 0.248909 | ||||||||
\(336\) | 3.01883e13 | 0.384567 | ||||||||
\(337\) | 3.17248e13 | 0.397589 | 0.198794 | − | 0.980041i | \(-0.436297\pi\) | ||||
0.198794 | + | 0.980041i | \(0.436297\pi\) | |||||||
\(338\) | −3.87032e13 | −0.477205 | ||||||||
\(339\) | −1.96837e13 | −0.238785 | ||||||||
\(340\) | −8.02606e13 | −0.958007 | ||||||||
\(341\) | −1.48467e12 | −0.0174374 | ||||||||
\(342\) | −2.21287e14 | −2.55748 | ||||||||
\(343\) | −6.49579e13 | −0.738779 | ||||||||
\(344\) | −2.62100e14 | −2.93357 | ||||||||
\(345\) | −7.79640e12 | −0.0858794 | ||||||||
\(346\) | 5.41341e13 | 0.586884 | ||||||||
\(347\) | −2.83475e13 | −0.302484 | −0.151242 | − | 0.988497i | \(-0.548327\pi\) | ||||
−0.151242 | + | 0.988497i | \(0.548327\pi\) | |||||||
\(348\) | −1.01124e13 | −0.106211 | ||||||||
\(349\) | 3.64436e13 | 0.376774 | 0.188387 | − | 0.982095i | \(-0.439674\pi\) | ||||
0.188387 | + | 0.982095i | \(0.439674\pi\) | |||||||
\(350\) | 1.88473e14 | 1.91811 | ||||||||
\(351\) | −5.26800e13 | −0.527785 | ||||||||
\(352\) | 6.76381e12 | 0.0667125 | ||||||||
\(353\) | −4.91177e13 | −0.476955 | −0.238478 | − | 0.971148i | \(-0.576648\pi\) | ||||
−0.238478 | + | 0.971148i | \(0.576648\pi\) | |||||||
\(354\) | −7.85007e13 | −0.750509 | ||||||||
\(355\) | −4.85296e13 | −0.456826 | ||||||||
\(356\) | 1.27701e14 | 1.18364 | ||||||||
\(357\) | −5.24286e13 | −0.478512 | ||||||||
\(358\) | −2.83696e14 | −2.54974 | ||||||||
\(359\) | 1.78482e14 | 1.57970 | 0.789850 | − | 0.613300i | \(-0.210158\pi\) | ||||
0.789850 | + | 0.613300i | \(0.210158\pi\) | |||||||
\(360\) | 5.68341e13 | 0.495388 | ||||||||
\(361\) | 1.59109e14 | 1.36586 | ||||||||
\(362\) | −1.50689e14 | −1.27404 | ||||||||
\(363\) | −2.82787e13 | −0.235490 | ||||||||
\(364\) | 3.40219e14 | 2.79062 | ||||||||
\(365\) | 5.68748e13 | 0.459525 | ||||||||
\(366\) | −2.16386e13 | −0.172220 | ||||||||
\(367\) | 1.53021e14 | 1.19974 | 0.599871 | − | 0.800097i | \(-0.295218\pi\) | ||||
0.599871 | + | 0.800097i | \(0.295218\pi\) | |||||||
\(368\) | −2.35551e14 | −1.81937 | ||||||||
\(369\) | −1.36675e13 | −0.104003 | ||||||||
\(370\) | 8.19169e13 | 0.614136 | ||||||||
\(371\) | 9.80781e13 | 0.724462 | ||||||||
\(372\) | 7.98267e12 | 0.0580981 | ||||||||
\(373\) | 1.58375e14 | 1.13576 | 0.567880 | − | 0.823111i | \(-0.307764\pi\) | ||||
0.567880 | + | 0.823111i | \(0.307764\pi\) | |||||||
\(374\) | −6.49164e13 | −0.458733 | ||||||||
\(375\) | −1.78236e13 | −0.124115 | ||||||||
\(376\) | 9.67360e13 | 0.663827 | ||||||||
\(377\) | −3.46807e13 | −0.234536 | ||||||||
\(378\) | 1.45098e14 | 0.967064 | ||||||||
\(379\) | −2.62873e14 | −1.72675 | −0.863377 | − | 0.504559i | \(-0.831655\pi\) | ||||
−0.863377 | + | 0.504559i | \(0.831655\pi\) | |||||||
\(380\) | −1.34178e14 | −0.868706 | ||||||||
\(381\) | −7.08040e12 | −0.0451825 | ||||||||
\(382\) | 4.31928e14 | 2.71683 | ||||||||
\(383\) | −2.35961e13 | −0.146301 | −0.0731504 | − | 0.997321i | \(-0.523305\pi\) | ||||
−0.0731504 | + | 0.997321i | \(0.523305\pi\) | |||||||
\(384\) | 5.85870e13 | 0.358080 | ||||||||
\(385\) | −7.93661e12 | −0.0478190 | ||||||||
\(386\) | −1.58897e14 | −0.943811 | ||||||||
\(387\) | −2.39371e14 | −1.40172 | ||||||||
\(388\) | 1.91222e14 | 1.10399 | ||||||||
\(389\) | 3.02235e13 | 0.172037 | 0.0860185 | − | 0.996294i | \(-0.472586\pi\) | ||||
0.0860185 | + | 0.996294i | \(0.472586\pi\) | |||||||
\(390\) | −2.28131e13 | −0.128035 | ||||||||
\(391\) | 4.09086e14 | 2.26382 | ||||||||
\(392\) | −1.33102e14 | −0.726290 | ||||||||
\(393\) | 6.30175e13 | 0.339080 | ||||||||
\(394\) | 2.37046e13 | 0.125778 | ||||||||
\(395\) | 6.01888e13 | 0.314943 | ||||||||
\(396\) | 5.91787e13 | 0.305381 | ||||||||
\(397\) | 1.16590e14 | 0.593352 | 0.296676 | − | 0.954978i | \(-0.404122\pi\) | ||||
0.296676 | + | 0.954978i | \(0.404122\pi\) | |||||||
\(398\) | −1.61933e13 | −0.0812792 | ||||||||
\(399\) | −8.76492e13 | −0.433908 | ||||||||
\(400\) | −2.59310e14 | −1.26616 | ||||||||
\(401\) | 8.37630e13 | 0.403421 | 0.201710 | − | 0.979445i | \(-0.435350\pi\) | ||||
0.201710 | + | 0.979445i | \(0.435350\pi\) | |||||||
\(402\) | −8.35905e13 | −0.397113 | ||||||||
\(403\) | 2.73767e13 | 0.128293 | ||||||||
\(404\) | 8.64967e13 | 0.399855 | ||||||||
\(405\) | 4.85028e13 | 0.221189 | ||||||||
\(406\) | 9.55216e13 | 0.429743 | ||||||||
\(407\) | 4.49966e13 | 0.199715 | ||||||||
\(408\) | 1.84129e14 | 0.806289 | ||||||||
\(409\) | −2.31783e14 | −1.00139 | −0.500695 | − | 0.865624i | \(-0.666922\pi\) | ||||
−0.500695 | + | 0.865624i | \(0.666922\pi\) | |||||||
\(410\) | −1.22029e13 | −0.0520177 | ||||||||
\(411\) | 8.47482e13 | 0.356451 | ||||||||
\(412\) | −1.28849e13 | −0.0534746 | ||||||||
\(413\) | 5.03587e14 | 2.06229 | ||||||||
\(414\) | −5.49125e14 | −2.21906 | ||||||||
\(415\) | −9.36376e13 | −0.373410 | ||||||||
\(416\) | −1.24722e14 | −0.490827 | ||||||||
\(417\) | 6.74683e13 | 0.262030 | ||||||||
\(418\) | −1.08526e14 | −0.415973 | ||||||||
\(419\) | 4.51676e14 | 1.70864 | 0.854318 | − | 0.519750i | \(-0.173975\pi\) | ||||
0.854318 | + | 0.519750i | \(0.173975\pi\) | |||||||
\(420\) | 4.26730e13 | 0.159324 | ||||||||
\(421\) | 1.04417e14 | 0.384786 | 0.192393 | − | 0.981318i | \(-0.438375\pi\) | ||||
0.192393 | + | 0.981318i | \(0.438375\pi\) | |||||||
\(422\) | 9.84582e13 | 0.358124 | ||||||||
\(423\) | 8.83471e13 | 0.317191 | ||||||||
\(424\) | −3.44450e14 | −1.22071 | ||||||||
\(425\) | 4.50349e14 | 1.57547 | ||||||||
\(426\) | 2.11046e14 | 0.728825 | ||||||||
\(427\) | 1.38813e14 | 0.473235 | ||||||||
\(428\) | −6.84675e14 | −2.30432 | ||||||||
\(429\) | −1.25311e13 | −0.0416366 | ||||||||
\(430\) | −2.13720e14 | −0.701082 | ||||||||
\(431\) | −3.92866e14 | −1.27239 | −0.636194 | − | 0.771529i | \(-0.719492\pi\) | ||||
−0.636194 | + | 0.771529i | \(0.719492\pi\) | |||||||
\(432\) | −1.99632e14 | −0.638367 | ||||||||
\(433\) | 1.57318e14 | 0.496702 | 0.248351 | − | 0.968670i | \(-0.420111\pi\) | ||||
0.248351 | + | 0.968670i | \(0.420111\pi\) | |||||||
\(434\) | −7.54041e13 | −0.235072 | ||||||||
\(435\) | −4.34993e12 | −0.0133903 | ||||||||
\(436\) | 2.00642e14 | 0.609883 | ||||||||
\(437\) | 6.83902e14 | 2.05280 | ||||||||
\(438\) | −2.47337e14 | −0.733132 | ||||||||
\(439\) | −3.44490e13 | −0.100837 | −0.0504187 | − | 0.998728i | \(-0.516056\pi\) | ||||
−0.0504187 | + | 0.998728i | \(0.516056\pi\) | |||||||
\(440\) | 2.78733e13 | 0.0805747 | ||||||||
\(441\) | −1.21559e14 | −0.347037 | ||||||||
\(442\) | 1.19703e15 | 3.37507 | ||||||||
\(443\) | 6.48442e13 | 0.180572 | 0.0902860 | − | 0.995916i | \(-0.471222\pi\) | ||||
0.0902860 | + | 0.995916i | \(0.471222\pi\) | |||||||
\(444\) | −2.41935e14 | −0.665413 | ||||||||
\(445\) | 5.49316e13 | 0.149225 | ||||||||
\(446\) | 7.81916e14 | 2.09806 | ||||||||
\(447\) | 4.78739e13 | 0.126884 | ||||||||
\(448\) | −2.65614e14 | −0.695379 | ||||||||
\(449\) | −4.44984e14 | −1.15077 | −0.575386 | − | 0.817882i | \(-0.695148\pi\) | ||||
−0.575386 | + | 0.817882i | \(0.695148\pi\) | |||||||
\(450\) | −6.04514e14 | −1.54432 | ||||||||
\(451\) | −6.70299e12 | −0.0169160 | ||||||||
\(452\) | −8.40641e14 | −2.09580 | ||||||||
\(453\) | 1.54610e14 | 0.380800 | ||||||||
\(454\) | 7.56776e14 | 1.84145 | ||||||||
\(455\) | 1.46348e14 | 0.351822 | ||||||||
\(456\) | 3.07824e14 | 0.731131 | ||||||||
\(457\) | 6.04598e14 | 1.41882 | 0.709410 | − | 0.704796i | \(-0.248961\pi\) | ||||
0.709410 | + | 0.704796i | \(0.248961\pi\) | |||||||
\(458\) | 8.43225e14 | 1.95516 | ||||||||
\(459\) | 3.46706e14 | 0.794312 | ||||||||
\(460\) | −3.32965e14 | −0.753756 | ||||||||
\(461\) | −2.44475e14 | −0.546864 | −0.273432 | − | 0.961891i | \(-0.588159\pi\) | ||||
−0.273432 | + | 0.961891i | \(0.588159\pi\) | |||||||
\(462\) | 3.45147e13 | 0.0762911 | ||||||||
\(463\) | −3.72317e14 | −0.813239 | −0.406619 | − | 0.913598i | \(-0.633292\pi\) | ||||
−0.406619 | + | 0.913598i | \(0.633292\pi\) | |||||||
\(464\) | −1.31423e14 | −0.283677 | ||||||||
\(465\) | 3.43381e12 | 0.00732461 | ||||||||
\(466\) | −1.26786e15 | −2.67268 | ||||||||
\(467\) | −5.42981e14 | −1.13121 | −0.565603 | − | 0.824678i | \(-0.691357\pi\) | ||||
−0.565603 | + | 0.824678i | \(0.691357\pi\) | |||||||
\(468\) | −1.09123e15 | −2.24680 | ||||||||
\(469\) | 5.36238e14 | 1.09121 | ||||||||
\(470\) | 7.88798e13 | 0.158645 | ||||||||
\(471\) | 5.99379e13 | 0.119148 | ||||||||
\(472\) | −1.76859e15 | −3.47494 | ||||||||
\(473\) | −1.17395e14 | −0.227990 | ||||||||
\(474\) | −2.61749e14 | −0.502464 | ||||||||
\(475\) | 7.52887e14 | 1.42861 | ||||||||
\(476\) | −2.23910e15 | −4.19986 | ||||||||
\(477\) | −3.14579e14 | −0.583283 | ||||||||
\(478\) | −1.50918e15 | −2.76623 | ||||||||
\(479\) | −1.96268e14 | −0.355635 | −0.177817 | − | 0.984063i | \(-0.556904\pi\) | ||||
−0.177817 | + | 0.984063i | \(0.556904\pi\) | |||||||
\(480\) | −1.56436e13 | −0.0280227 | ||||||||
\(481\) | −8.29717e14 | −1.46937 | ||||||||
\(482\) | 6.63909e14 | 1.16239 | ||||||||
\(483\) | −2.17503e14 | −0.376492 | ||||||||
\(484\) | −1.20772e15 | −2.06688 | ||||||||
\(485\) | 8.22555e13 | 0.139183 | ||||||||
\(486\) | −7.05055e14 | −1.17957 | ||||||||
\(487\) | −1.06344e15 | −1.75915 | −0.879576 | − | 0.475758i | \(-0.842174\pi\) | ||||
−0.879576 | + | 0.475758i | \(0.842174\pi\) | |||||||
\(488\) | −4.87511e14 | −0.797398 | ||||||||
\(489\) | 1.01974e13 | 0.0164927 | ||||||||
\(490\) | −1.08533e14 | −0.173573 | ||||||||
\(491\) | −2.56729e14 | −0.406000 | −0.203000 | − | 0.979179i | \(-0.565069\pi\) | ||||
−0.203000 | + | 0.979179i | \(0.565069\pi\) | |||||||
\(492\) | 3.60402e13 | 0.0563610 | ||||||||
\(493\) | 2.28246e14 | 0.352976 | ||||||||
\(494\) | 2.00117e15 | 3.06046 | ||||||||
\(495\) | 2.54562e13 | 0.0385003 | ||||||||
\(496\) | 1.03745e14 | 0.155173 | ||||||||
\(497\) | −1.35387e15 | −2.00270 | ||||||||
\(498\) | 4.07212e14 | 0.595743 | ||||||||
\(499\) | 6.69840e14 | 0.969210 | 0.484605 | − | 0.874733i | \(-0.338963\pi\) | ||||
0.484605 | + | 0.874733i | \(0.338963\pi\) | |||||||
\(500\) | −7.61203e14 | −1.08934 | ||||||||
\(501\) | 2.76135e14 | 0.390853 | ||||||||
\(502\) | −6.28773e14 | −0.880285 | ||||||||
\(503\) | −1.36310e15 | −1.88757 | −0.943784 | − | 0.330563i | \(-0.892762\pi\) | ||||
−0.943784 | + | 0.330563i | \(0.892762\pi\) | |||||||
\(504\) | 1.58555e15 | 2.17176 | ||||||||
\(505\) | 3.72072e13 | 0.0504109 | ||||||||
\(506\) | −2.69309e14 | −0.360930 | ||||||||
\(507\) | 4.91697e13 | 0.0651859 | ||||||||
\(508\) | −3.02387e14 | −0.396563 | ||||||||
\(509\) | −1.04561e15 | −1.35651 | −0.678254 | − | 0.734827i | \(-0.737263\pi\) | ||||
−0.678254 | + | 0.734827i | \(0.737263\pi\) | |||||||
\(510\) | 1.50141e14 | 0.192692 | ||||||||
\(511\) | 1.58668e15 | 2.01454 | ||||||||
\(512\) | 1.66665e15 | 2.09343 | ||||||||
\(513\) | 5.79617e14 | 0.720270 | ||||||||
\(514\) | 8.99792e14 | 1.10623 | ||||||||
\(515\) | −5.54255e12 | −0.00674171 | ||||||||
\(516\) | 6.31204e14 | 0.759619 | ||||||||
\(517\) | 4.33283e13 | 0.0515910 | ||||||||
\(518\) | 2.28531e15 | 2.69234 | ||||||||
\(519\) | −6.87737e13 | −0.0801681 | ||||||||
\(520\) | −5.13971e14 | −0.592817 | ||||||||
\(521\) | 1.08874e15 | 1.24256 | 0.621280 | − | 0.783589i | \(-0.286613\pi\) | ||||
0.621280 | + | 0.783589i | \(0.286613\pi\) | |||||||
\(522\) | −3.06380e14 | −0.345997 | ||||||||
\(523\) | 9.45122e14 | 1.05616 | 0.528078 | − | 0.849196i | \(-0.322913\pi\) | ||||
0.528078 | + | 0.849196i | \(0.322913\pi\) | |||||||
\(524\) | 2.69132e15 | 2.97608 | ||||||||
\(525\) | −2.39442e14 | −0.262014 | ||||||||
\(526\) | 1.71931e15 | 1.86180 | ||||||||
\(527\) | −1.80176e14 | −0.193080 | ||||||||
\(528\) | −4.74871e13 | −0.0503604 | ||||||||
\(529\) | 7.44302e14 | 0.781165 | ||||||||
\(530\) | −2.80869e14 | −0.291734 | ||||||||
\(531\) | −1.61522e15 | −1.66040 | ||||||||
\(532\) | −3.74329e15 | −3.80837 | ||||||||
\(533\) | 1.23600e14 | 0.124457 | ||||||||
\(534\) | −2.38887e14 | −0.238076 | ||||||||
\(535\) | −2.94518e14 | −0.290513 | ||||||||
\(536\) | −1.88326e15 | −1.83867 | ||||||||
\(537\) | 3.60416e14 | 0.348294 | ||||||||
\(538\) | −9.21175e14 | −0.881129 | ||||||||
\(539\) | −5.96166e13 | −0.0564455 | ||||||||
\(540\) | −2.82193e14 | −0.264472 | ||||||||
\(541\) | 1.11380e15 | 1.03329 | 0.516646 | − | 0.856199i | \(-0.327180\pi\) | ||||
0.516646 | + | 0.856199i | \(0.327180\pi\) | |||||||
\(542\) | −4.36885e13 | −0.0401209 | ||||||||
\(543\) | 1.91440e14 | 0.174034 | ||||||||
\(544\) | 8.20838e14 | 0.738692 | ||||||||
\(545\) | 8.63077e13 | 0.0768898 | ||||||||
\(546\) | −6.36437e14 | −0.561301 | ||||||||
\(547\) | −1.97274e15 | −1.72242 | −0.861212 | − | 0.508245i | \(-0.830294\pi\) | ||||
−0.861212 | + | 0.508245i | \(0.830294\pi\) | |||||||
\(548\) | 3.61939e15 | 3.12854 | ||||||||
\(549\) | −4.45234e14 | −0.381014 | ||||||||
\(550\) | −2.96474e14 | −0.251184 | ||||||||
\(551\) | 3.81577e14 | 0.320073 | ||||||||
\(552\) | 7.63868e14 | 0.634385 | ||||||||
\(553\) | 1.67914e15 | 1.38070 | ||||||||
\(554\) | −1.48500e15 | −1.20899 | ||||||||
\(555\) | −1.04070e14 | −0.0838907 | ||||||||
\(556\) | 2.88141e15 | 2.29982 | ||||||||
\(557\) | 2.40646e15 | 1.90184 | 0.950921 | − | 0.309433i | \(-0.100139\pi\) | ||||
0.950921 | + | 0.309433i | \(0.100139\pi\) | |||||||
\(558\) | 2.41854e14 | 0.189263 | ||||||||
\(559\) | 2.16472e15 | 1.67740 | ||||||||
\(560\) | 5.54588e14 | 0.425536 | ||||||||
\(561\) | 8.24718e13 | 0.0626628 | ||||||||
\(562\) | −4.41871e15 | −3.32465 | ||||||||
\(563\) | 2.55477e14 | 0.190351 | 0.0951757 | − | 0.995460i | \(-0.469659\pi\) | ||||
0.0951757 | + | 0.995460i | \(0.469659\pi\) | |||||||
\(564\) | −2.32965e14 | −0.171892 | ||||||||
\(565\) | −3.61608e14 | −0.264223 | ||||||||
\(566\) | 6.30930e14 | 0.456553 | ||||||||
\(567\) | 1.35312e15 | 0.969685 | ||||||||
\(568\) | 4.75478e15 | 3.37454 | ||||||||
\(569\) | 1.06022e15 | 0.745207 | 0.372603 | − | 0.927991i | \(-0.378465\pi\) | ||||
0.372603 | + | 0.927991i | \(0.378465\pi\) | |||||||
\(570\) | 2.51003e14 | 0.174730 | ||||||||
\(571\) | −1.82875e15 | −1.26083 | −0.630413 | − | 0.776260i | \(-0.717114\pi\) | ||||
−0.630413 | + | 0.776260i | \(0.717114\pi\) | |||||||
\(572\) | −5.35175e14 | −0.365441 | ||||||||
\(573\) | −5.48735e14 | −0.371119 | ||||||||
\(574\) | −3.40434e14 | −0.228044 | ||||||||
\(575\) | 1.86830e15 | 1.23957 | ||||||||
\(576\) | 8.51940e14 | 0.559867 | ||||||||
\(577\) | 2.95605e15 | 1.92418 | 0.962089 | − | 0.272737i | \(-0.0879290\pi\) | ||||
0.962089 | + | 0.272737i | \(0.0879290\pi\) | |||||||
\(578\) | −5.14003e15 | −3.31408 | ||||||||
\(579\) | 2.01868e14 | 0.128924 | ||||||||
\(580\) | −1.85775e14 | −0.117526 | ||||||||
\(581\) | −2.61229e15 | −1.63701 | ||||||||
\(582\) | −3.57713e14 | −0.222054 | ||||||||
\(583\) | −1.54280e14 | −0.0948708 | ||||||||
\(584\) | −5.57243e15 | −3.39448 | ||||||||
\(585\) | −4.69400e14 | −0.283261 | ||||||||
\(586\) | 5.43385e15 | 3.24841 | ||||||||
\(587\) | −1.26309e15 | −0.748038 | −0.374019 | − | 0.927421i | \(-0.622021\pi\) | ||||
−0.374019 | + | 0.927421i | \(0.622021\pi\) | |||||||
\(588\) | 3.20543e14 | 0.188066 | ||||||||
\(589\) | −3.01214e14 | −0.175082 | ||||||||
\(590\) | −1.44214e15 | −0.830462 | ||||||||
\(591\) | −3.01151e13 | −0.0171812 | ||||||||
\(592\) | −3.14424e15 | −1.77724 | ||||||||
\(593\) | 2.38619e15 | 1.33630 | 0.668150 | − | 0.744027i | \(-0.267087\pi\) | ||||
0.668150 | + | 0.744027i | \(0.267087\pi\) | |||||||
\(594\) | −2.28243e14 | −0.126640 | ||||||||
\(595\) | −9.63164e14 | −0.529489 | ||||||||
\(596\) | 2.04458e15 | 1.11365 | ||||||||
\(597\) | 2.05725e13 | 0.0111027 | ||||||||
\(598\) | 4.96594e15 | 2.65549 | ||||||||
\(599\) | −2.33823e15 | −1.23891 | −0.619454 | − | 0.785033i | \(-0.712646\pi\) | ||||
−0.619454 | + | 0.785033i | \(0.712646\pi\) | |||||||
\(600\) | 8.40918e14 | 0.441491 | ||||||||
\(601\) | 1.24352e14 | 0.0646909 | 0.0323454 | − | 0.999477i | \(-0.489702\pi\) | ||||
0.0323454 | + | 0.999477i | \(0.489702\pi\) | |||||||
\(602\) | −5.96233e15 | −3.07351 | ||||||||
\(603\) | −1.71995e15 | −0.878558 | ||||||||
\(604\) | 6.60301e15 | 3.34225 | ||||||||
\(605\) | −5.19507e14 | −0.260578 | ||||||||
\(606\) | −1.61807e14 | −0.0804261 | ||||||||
\(607\) | 2.17760e15 | 1.07261 | 0.536304 | − | 0.844025i | \(-0.319820\pi\) | ||||
0.536304 | + | 0.844025i | \(0.319820\pi\) | |||||||
\(608\) | 1.37226e15 | 0.669835 | ||||||||
\(609\) | −1.21354e14 | −0.0587027 | ||||||||
\(610\) | −3.97523e14 | −0.190567 | ||||||||
\(611\) | −7.98955e14 | −0.379573 | ||||||||
\(612\) | 7.18177e15 | 3.38142 | ||||||||
\(613\) | 2.76949e15 | 1.29231 | 0.646157 | − | 0.763205i | \(-0.276375\pi\) | ||||
0.646157 | + | 0.763205i | \(0.276375\pi\) | |||||||
\(614\) | −5.30552e15 | −2.45359 | ||||||||
\(615\) | 1.55029e13 | 0.00710560 | ||||||||
\(616\) | 7.77605e14 | 0.353236 | ||||||||
\(617\) | −6.64877e14 | −0.299346 | −0.149673 | − | 0.988736i | \(-0.547822\pi\) | ||||
−0.149673 | + | 0.988736i | \(0.547822\pi\) | |||||||
\(618\) | 2.41035e13 | 0.0107558 | ||||||||
\(619\) | −1.19536e15 | −0.528689 | −0.264345 | − | 0.964428i | \(-0.585156\pi\) | ||||
−0.264345 | + | 0.964428i | \(0.585156\pi\) | |||||||
\(620\) | 1.46650e14 | 0.0642875 | ||||||||
\(621\) | 1.43833e15 | 0.624962 | ||||||||
\(622\) | −7.74713e14 | −0.333652 | ||||||||
\(623\) | 1.53247e15 | 0.654197 | ||||||||
\(624\) | 8.75641e14 | 0.370520 | ||||||||
\(625\) | 1.88699e15 | 0.791460 | ||||||||
\(626\) | −2.53792e15 | −1.05516 | ||||||||
\(627\) | 1.37875e14 | 0.0568217 | ||||||||
\(628\) | 2.55980e15 | 1.04575 | ||||||||
\(629\) | 5.46066e15 | 2.21140 | ||||||||
\(630\) | 1.29288e15 | 0.519020 | ||||||||
\(631\) | −1.02104e15 | −0.406334 | −0.203167 | − | 0.979144i | \(-0.565123\pi\) | ||||
−0.203167 | + | 0.979144i | \(0.565123\pi\) | |||||||
\(632\) | −5.89712e15 | −2.32646 | ||||||||
\(633\) | −1.25084e14 | −0.0489196 | ||||||||
\(634\) | 7.96023e15 | 3.08628 | ||||||||
\(635\) | −1.30074e14 | −0.0499959 | ||||||||
\(636\) | 8.29522e14 | 0.316092 | ||||||||
\(637\) | 1.09930e15 | 0.415290 | ||||||||
\(638\) | −1.50258e14 | −0.0562763 | ||||||||
\(639\) | 4.34245e15 | 1.61243 | ||||||||
\(640\) | 1.07630e15 | 0.396227 | ||||||||
\(641\) | −3.93885e15 | −1.43764 | −0.718820 | − | 0.695197i | \(-0.755317\pi\) | ||||
−0.718820 | + | 0.695197i | \(0.755317\pi\) | |||||||
\(642\) | 1.28080e15 | 0.463488 | ||||||||
\(643\) | −2.41123e15 | −0.865123 | −0.432561 | − | 0.901604i | \(-0.642390\pi\) | ||||
−0.432561 | + | 0.901604i | \(0.642390\pi\) | |||||||
\(644\) | −9.28901e15 | −3.30443 | ||||||||
\(645\) | 2.71517e14 | 0.0957675 | ||||||||
\(646\) | −1.31704e16 | −4.60597 | ||||||||
\(647\) | 2.50673e15 | 0.869230 | 0.434615 | − | 0.900616i | \(-0.356884\pi\) | ||||
0.434615 | + | 0.900616i | \(0.356884\pi\) | |||||||
\(648\) | −4.75216e15 | −1.63391 | ||||||||
\(649\) | −7.92158e14 | −0.270064 | ||||||||
\(650\) | 5.46684e15 | 1.84805 | ||||||||
\(651\) | 9.57957e13 | 0.0321108 | ||||||||
\(652\) | 4.35507e14 | 0.144755 | ||||||||
\(653\) | 8.01060e14 | 0.264023 | 0.132012 | − | 0.991248i | \(-0.457856\pi\) | ||||
0.132012 | + | 0.991248i | \(0.457856\pi\) | |||||||
\(654\) | −3.75335e14 | −0.122671 | ||||||||
\(655\) | 1.15769e15 | 0.375203 | ||||||||
\(656\) | 4.68387e14 | 0.150534 | ||||||||
\(657\) | −5.08919e15 | −1.62196 | ||||||||
\(658\) | 2.20058e15 | 0.695495 | ||||||||
\(659\) | 1.23234e13 | 0.00386243 | 0.00193122 | − | 0.999998i | \(-0.499385\pi\) | ||||
0.00193122 | + | 0.999998i | \(0.499385\pi\) | |||||||
\(660\) | −6.71259e13 | −0.0208641 | ||||||||
\(661\) | 3.29931e14 | 0.101699 | 0.0508493 | − | 0.998706i | \(-0.483807\pi\) | ||||
0.0508493 | + | 0.998706i | \(0.483807\pi\) | |||||||
\(662\) | 1.48193e15 | 0.453010 | ||||||||
\(663\) | −1.52074e15 | −0.461033 | ||||||||
\(664\) | 9.17434e15 | 2.75836 | ||||||||
\(665\) | −1.61020e15 | −0.480133 | ||||||||
\(666\) | −7.32997e15 | −2.16767 | ||||||||
\(667\) | 9.46889e14 | 0.277720 | ||||||||
\(668\) | 1.17930e16 | 3.43048 | ||||||||
\(669\) | −9.93371e14 | −0.286594 | ||||||||
\(670\) | −1.53564e15 | −0.439418 | ||||||||
\(671\) | −2.18357e14 | −0.0619718 | ||||||||
\(672\) | −4.36423e14 | −0.122850 | ||||||||
\(673\) | −8.60530e14 | −0.240261 | −0.120131 | − | 0.992758i | \(-0.538331\pi\) | ||||
−0.120131 | + | 0.992758i | \(0.538331\pi\) | |||||||
\(674\) | −2.53455e15 | −0.701893 | ||||||||
\(675\) | 1.58341e15 | 0.434933 | ||||||||
\(676\) | 2.09992e15 | 0.572132 | ||||||||
\(677\) | 2.19254e14 | 0.0592530 | 0.0296265 | − | 0.999561i | \(-0.490568\pi\) | ||||
0.0296265 | + | 0.999561i | \(0.490568\pi\) | |||||||
\(678\) | 1.57256e15 | 0.421545 | ||||||||
\(679\) | 2.29475e15 | 0.610171 | ||||||||
\(680\) | 3.38263e15 | 0.892185 | ||||||||
\(681\) | −9.61433e14 | −0.251542 | ||||||||
\(682\) | 1.18613e14 | 0.0307835 | ||||||||
\(683\) | −4.08440e15 | −1.05151 | −0.525756 | − | 0.850635i | \(-0.676217\pi\) | ||||
−0.525756 | + | 0.850635i | \(0.676217\pi\) | |||||||
\(684\) | 1.20064e16 | 3.06622 | ||||||||
\(685\) | 1.55691e15 | 0.394425 | ||||||||
\(686\) | 5.18960e15 | 1.30422 | ||||||||
\(687\) | −1.07126e15 | −0.267075 | ||||||||
\(688\) | 8.20327e15 | 2.02885 | ||||||||
\(689\) | 2.84485e15 | 0.697998 | ||||||||
\(690\) | 6.22868e14 | 0.151609 | ||||||||
\(691\) | −5.97418e15 | −1.44261 | −0.721305 | − | 0.692618i | \(-0.756457\pi\) | ||||
−0.721305 | + | 0.692618i | \(0.756457\pi\) | |||||||
\(692\) | −2.93716e15 | −0.703629 | ||||||||
\(693\) | 7.10172e14 | 0.168784 | ||||||||
\(694\) | 2.26473e15 | 0.533998 | ||||||||
\(695\) | 1.23946e15 | 0.289945 | ||||||||
\(696\) | 4.26193e14 | 0.0989136 | ||||||||
\(697\) | −8.13456e14 | −0.187307 | ||||||||
\(698\) | −2.91154e15 | −0.665148 | ||||||||
\(699\) | 1.61072e15 | 0.365087 | ||||||||
\(700\) | −1.02260e16 | −2.29967 | ||||||||
\(701\) | −6.07856e15 | −1.35629 | −0.678144 | − | 0.734929i | \(-0.737215\pi\) | ||||
−0.678144 | + | 0.734929i | \(0.737215\pi\) | |||||||
\(702\) | 4.20870e15 | 0.931738 | ||||||||
\(703\) | 9.12904e15 | 2.00526 | ||||||||
\(704\) | 4.17819e14 | 0.0910622 | ||||||||
\(705\) | −1.00211e14 | −0.0216709 | ||||||||
\(706\) | 3.92410e15 | 0.842005 | ||||||||
\(707\) | 1.03800e15 | 0.220999 | ||||||||
\(708\) | 4.25922e15 | 0.899802 | ||||||||
\(709\) | −3.49835e15 | −0.733345 | −0.366673 | − | 0.930350i | \(-0.619503\pi\) | ||||
−0.366673 | + | 0.930350i | \(0.619503\pi\) | |||||||
\(710\) | 3.87711e15 | 0.806469 | ||||||||
\(711\) | −5.38573e15 | −1.11163 | ||||||||
\(712\) | −5.38204e15 | −1.10232 | ||||||||
\(713\) | −7.47467e14 | −0.151915 | ||||||||
\(714\) | 4.18861e15 | 0.844754 | ||||||||
\(715\) | −2.30209e14 | −0.0460723 | ||||||||
\(716\) | 1.53925e16 | 3.05694 | ||||||||
\(717\) | 1.91731e15 | 0.377866 | ||||||||
\(718\) | −1.42592e16 | −2.78876 | ||||||||
\(719\) | 1.02063e16 | 1.98088 | 0.990441 | − | 0.137939i | \(-0.0440479\pi\) | ||||
0.990441 | + | 0.137939i | \(0.0440479\pi\) | |||||||
\(720\) | −1.77881e15 | −0.342610 | ||||||||
\(721\) | −1.54625e14 | −0.0295553 | ||||||||
\(722\) | −1.27115e16 | −2.41125 | ||||||||
\(723\) | −8.43452e14 | −0.158781 | ||||||||
\(724\) | 8.17593e15 | 1.52748 | ||||||||
\(725\) | 1.04240e15 | 0.193275 | ||||||||
\(726\) | 2.25924e15 | 0.415729 | ||||||||
\(727\) | 8.11473e15 | 1.48195 | 0.740977 | − | 0.671531i | \(-0.234363\pi\) | ||||
0.740977 | + | 0.671531i | \(0.234363\pi\) | |||||||
\(728\) | −1.43387e16 | −2.59888 | ||||||||
\(729\) | −3.71231e15 | −0.667794 | ||||||||
\(730\) | −4.54383e15 | −0.811234 | ||||||||
\(731\) | −1.42468e16 | −2.52448 | ||||||||
\(732\) | 1.17405e15 | 0.206479 | ||||||||
\(733\) | −1.00244e16 | −1.74980 | −0.874898 | − | 0.484307i | \(-0.839072\pi\) | ||||
−0.874898 | + | 0.484307i | \(0.839072\pi\) | |||||||
\(734\) | −1.22251e16 | −2.11800 | ||||||||
\(735\) | 1.37884e14 | 0.0237101 | ||||||||
\(736\) | 3.40529e15 | 0.581200 | ||||||||
\(737\) | −8.43519e14 | −0.142897 | ||||||||
\(738\) | 1.09192e15 | 0.183604 | ||||||||
\(739\) | 5.65116e15 | 0.943176 | 0.471588 | − | 0.881819i | \(-0.343681\pi\) | ||||
0.471588 | + | 0.881819i | \(0.343681\pi\) | |||||||
\(740\) | −4.44457e15 | −0.736301 | ||||||||
\(741\) | −2.54235e15 | −0.418057 | ||||||||
\(742\) | −7.83563e15 | −1.27895 | ||||||||
\(743\) | 8.50764e15 | 1.37839 | 0.689193 | − | 0.724578i | \(-0.257965\pi\) | ||||
0.689193 | + | 0.724578i | \(0.257965\pi\) | |||||||
\(744\) | −3.36434e14 | −0.0541064 | ||||||||
\(745\) | 8.79489e14 | 0.140401 | ||||||||
\(746\) | −1.26528e16 | −2.00504 | ||||||||
\(747\) | 8.37875e15 | 1.31800 | ||||||||
\(748\) | 3.52217e15 | 0.549986 | ||||||||
\(749\) | −8.21641e15 | −1.27360 | ||||||||
\(750\) | 1.42396e15 | 0.219109 | ||||||||
\(751\) | −1.00126e16 | −1.52942 | −0.764712 | − | 0.644372i | \(-0.777119\pi\) | ||||
−0.764712 | + | 0.644372i | \(0.777119\pi\) | |||||||
\(752\) | −3.02766e15 | −0.459102 | ||||||||
\(753\) | 7.98813e14 | 0.120247 | ||||||||
\(754\) | 2.77070e15 | 0.414045 | ||||||||
\(755\) | 2.84033e15 | 0.421367 | ||||||||
\(756\) | −7.87257e15 | −1.15944 | ||||||||
\(757\) | 8.17216e15 | 1.19484 | 0.597420 | − | 0.801929i | \(-0.296193\pi\) | ||||
0.597420 | + | 0.801929i | \(0.296193\pi\) | |||||||
\(758\) | 2.10014e16 | 3.04837 | ||||||||
\(759\) | 3.42138e14 | 0.0493029 | ||||||||
\(760\) | 5.65502e15 | 0.809020 | ||||||||
\(761\) | −9.13630e15 | −1.29764 | −0.648820 | − | 0.760942i | \(-0.724737\pi\) | ||||
−0.648820 | + | 0.760942i | \(0.724737\pi\) | |||||||
\(762\) | 5.65666e14 | 0.0797641 | ||||||||
\(763\) | 2.40780e15 | 0.337082 | ||||||||
\(764\) | −2.34352e16 | −3.25728 | ||||||||
\(765\) | 3.08929e15 | 0.426305 | ||||||||
\(766\) | 1.88513e15 | 0.258276 | ||||||||
\(767\) | 1.46070e16 | 1.98695 | ||||||||
\(768\) | −3.61922e15 | −0.488797 | ||||||||
\(769\) | 7.92063e15 | 1.06210 | 0.531049 | − | 0.847341i | \(-0.321798\pi\) | ||||
0.531049 | + | 0.847341i | \(0.321798\pi\) | |||||||
\(770\) | 6.34069e14 | 0.0844185 | ||||||||
\(771\) | −1.14312e15 | −0.151110 | ||||||||
\(772\) | 8.62128e15 | 1.13156 | ||||||||
\(773\) | −1.11311e16 | −1.45061 | −0.725306 | − | 0.688426i | \(-0.758302\pi\) | ||||
−0.725306 | + | 0.688426i | \(0.758302\pi\) | |||||||
\(774\) | 1.91238e16 | 2.47456 | ||||||||
\(775\) | −8.22863e14 | −0.105723 | ||||||||
\(776\) | −8.05915e15 | −1.02813 | ||||||||
\(777\) | −2.90332e15 | −0.367773 | ||||||||
\(778\) | −2.41461e15 | −0.303710 | ||||||||
\(779\) | −1.35992e15 | −0.169847 | ||||||||
\(780\) | 1.23777e15 | 0.153504 | ||||||||
\(781\) | 2.12968e15 | 0.262261 | ||||||||
\(782\) | −3.26826e16 | −3.99649 | ||||||||
\(783\) | 8.02502e14 | 0.0974442 | ||||||||
\(784\) | 4.16585e15 | 0.502302 | ||||||||
\(785\) | 1.10112e15 | 0.131841 | ||||||||
\(786\) | −5.03458e15 | −0.598603 | ||||||||
\(787\) | −1.89021e14 | −0.0223177 | −0.0111588 | − | 0.999938i | \(-0.503552\pi\) | ||||
−0.0111588 | + | 0.999938i | \(0.503552\pi\) | |||||||
\(788\) | −1.28614e15 | −0.150798 | ||||||||
\(789\) | −2.18427e15 | −0.254322 | ||||||||
\(790\) | −4.80859e15 | −0.555992 | ||||||||
\(791\) | −1.00881e16 | −1.15834 | ||||||||
\(792\) | −2.49412e15 | −0.284399 | ||||||||
\(793\) | 4.02641e15 | 0.455949 | ||||||||
\(794\) | −9.31456e15 | −1.04749 | ||||||||
\(795\) | 3.56825e14 | 0.0398507 | ||||||||
\(796\) | 8.78603e14 | 0.0974475 | ||||||||
\(797\) | 8.56639e15 | 0.943576 | 0.471788 | − | 0.881712i | \(-0.343609\pi\) | ||||
0.471788 | + | 0.881712i | \(0.343609\pi\) | |||||||
\(798\) | 7.00245e15 | 0.766010 | ||||||||
\(799\) | 5.25820e15 | 0.571255 | ||||||||
\(800\) | 3.74877e15 | 0.404477 | ||||||||
\(801\) | −4.91531e15 | −0.526711 | ||||||||
\(802\) | −6.69197e15 | −0.712189 | ||||||||
\(803\) | −2.49590e15 | −0.263811 | ||||||||
\(804\) | 4.53538e15 | 0.476107 | ||||||||
\(805\) | −3.99574e15 | −0.416600 | ||||||||
\(806\) | −2.18717e15 | −0.226485 | ||||||||
\(807\) | 1.17029e15 | 0.120362 | ||||||||
\(808\) | −3.64545e15 | −0.372382 | ||||||||
\(809\) | −9.97290e15 | −1.01182 | −0.505911 | − | 0.862585i | \(-0.668844\pi\) | ||||
−0.505911 | + | 0.862585i | \(0.668844\pi\) | |||||||
\(810\) | −3.87498e15 | −0.390482 | ||||||||
\(811\) | −6.57801e15 | −0.658384 | −0.329192 | − | 0.944263i | \(-0.606776\pi\) | ||||
−0.329192 | + | 0.944263i | \(0.606776\pi\) | |||||||
\(812\) | −5.18272e15 | −0.515228 | ||||||||
\(813\) | 5.55032e13 | 0.00548050 | ||||||||
\(814\) | −3.59486e15 | −0.352572 | ||||||||
\(815\) | 1.87336e14 | 0.0182497 | ||||||||
\(816\) | −5.76290e15 | −0.557629 | ||||||||
\(817\) | −2.38175e16 | −2.28916 | ||||||||
\(818\) | 1.85176e16 | 1.76783 | ||||||||
\(819\) | −1.30953e16 | −1.24180 | ||||||||
\(820\) | 6.62093e14 | 0.0623653 | ||||||||
\(821\) | 8.28416e14 | 0.0775106 | 0.0387553 | − | 0.999249i | \(-0.487661\pi\) | ||||
0.0387553 | + | 0.999249i | \(0.487661\pi\) | |||||||
\(822\) | −6.77068e15 | −0.629270 | ||||||||
\(823\) | 9.26342e15 | 0.855209 | 0.427604 | − | 0.903966i | \(-0.359358\pi\) | ||||
0.427604 | + | 0.903966i | \(0.359358\pi\) | |||||||
\(824\) | 5.43042e14 | 0.0498005 | ||||||||
\(825\) | 3.76649e14 | 0.0343116 | ||||||||
\(826\) | −4.02324e16 | −3.64071 | ||||||||
\(827\) | −3.87100e14 | −0.0347971 | −0.0173986 | − | 0.999849i | \(-0.505538\pi\) | ||||
−0.0173986 | + | 0.999849i | \(0.505538\pi\) | |||||||
\(828\) | 2.97939e16 | 2.66048 | ||||||||
\(829\) | 2.75678e15 | 0.244541 | 0.122271 | − | 0.992497i | \(-0.460982\pi\) | ||||
0.122271 | + | 0.992497i | \(0.460982\pi\) | |||||||
\(830\) | 7.48087e15 | 0.659209 | ||||||||
\(831\) | 1.88660e15 | 0.165148 | ||||||||
\(832\) | −7.70440e15 | −0.669978 | ||||||||
\(833\) | −7.23491e15 | −0.625008 | ||||||||
\(834\) | −5.39016e15 | −0.462581 | ||||||||
\(835\) | 5.07286e15 | 0.432491 | ||||||||
\(836\) | 5.88831e15 | 0.498719 | ||||||||
\(837\) | −6.33489e14 | −0.0533027 | ||||||||
\(838\) | −3.60852e16 | −3.01638 | ||||||||
\(839\) | −1.04464e16 | −0.867510 | −0.433755 | − | 0.901031i | \(-0.642812\pi\) | ||||
−0.433755 | + | 0.901031i | \(0.642812\pi\) | |||||||
\(840\) | −1.79847e15 | −0.148378 | ||||||||
\(841\) | −1.16722e16 | −0.956698 | ||||||||
\(842\) | −8.34205e15 | −0.679292 | ||||||||
\(843\) | 5.61366e15 | 0.454145 | ||||||||
\(844\) | −5.34205e15 | −0.429363 | ||||||||
\(845\) | 9.03296e14 | 0.0721304 | ||||||||
\(846\) | −7.05821e15 | −0.559960 | ||||||||
\(847\) | −1.44931e16 | −1.14236 | ||||||||
\(848\) | 1.07807e16 | 0.844244 | ||||||||
\(849\) | −8.01554e14 | −0.0623649 | ||||||||
\(850\) | −3.59792e16 | −2.78130 | ||||||||
\(851\) | 2.26538e16 | 1.73992 | ||||||||
\(852\) | −1.14507e16 | −0.873806 | ||||||||
\(853\) | 8.43783e14 | 0.0639751 | 0.0319875 | − | 0.999488i | \(-0.489816\pi\) | ||||
0.0319875 | + | 0.999488i | \(0.489816\pi\) | |||||||
\(854\) | −1.10900e16 | −0.835438 | ||||||||
\(855\) | 5.16462e15 | 0.386567 | ||||||||
\(856\) | 2.88560e16 | 2.14600 | ||||||||
\(857\) | −5.87956e14 | −0.0434460 | −0.0217230 | − | 0.999764i | \(-0.506915\pi\) | ||||
−0.0217230 | + | 0.999764i | \(0.506915\pi\) | |||||||
\(858\) | 1.00113e15 | 0.0735042 | ||||||||
\(859\) | −9.88023e15 | −0.720783 | −0.360392 | − | 0.932801i | \(-0.617357\pi\) | ||||
−0.360392 | + | 0.932801i | \(0.617357\pi\) | |||||||
\(860\) | 1.15958e16 | 0.840543 | ||||||||
\(861\) | 4.32499e14 | 0.0311507 | ||||||||
\(862\) | 3.13868e16 | 2.24624 | ||||||||
\(863\) | 2.99589e15 | 0.213042 | 0.106521 | − | 0.994310i | \(-0.466029\pi\) | ||||
0.106521 | + | 0.994310i | \(0.466029\pi\) | |||||||
\(864\) | 2.88603e15 | 0.203927 | ||||||||
\(865\) | −1.26344e15 | −0.0887086 | ||||||||
\(866\) | −1.25684e16 | −0.876864 | ||||||||
\(867\) | 6.53005e15 | 0.452701 | ||||||||
\(868\) | 4.09120e15 | 0.281834 | ||||||||
\(869\) | −2.64134e15 | −0.180807 | ||||||||
\(870\) | 3.47524e14 | 0.0236390 | ||||||||
\(871\) | 1.55541e16 | 1.05135 | ||||||||
\(872\) | −8.45617e15 | −0.567980 | ||||||||
\(873\) | −7.36027e15 | −0.491264 | ||||||||
\(874\) | −5.46382e16 | −3.62396 | ||||||||
\(875\) | −9.13478e15 | −0.602079 | ||||||||
\(876\) | 1.34198e16 | 0.878969 | ||||||||
\(877\) | 2.29142e16 | 1.49144 | 0.745721 | − | 0.666258i | \(-0.232105\pi\) | ||||
0.745721 | + | 0.666258i | \(0.232105\pi\) | |||||||
\(878\) | 2.75219e15 | 0.178016 | ||||||||
\(879\) | −6.90334e15 | −0.443732 | ||||||||
\(880\) | −8.72384e14 | −0.0557254 | ||||||||
\(881\) | 2.25902e16 | 1.43401 | 0.717007 | − | 0.697066i | \(-0.245511\pi\) | ||||
0.717007 | + | 0.697066i | \(0.245511\pi\) | |||||||
\(882\) | 9.71159e15 | 0.612651 | ||||||||
\(883\) | 1.66067e16 | 1.04111 | 0.520557 | − | 0.853827i | \(-0.325724\pi\) | ||||
0.520557 | + | 0.853827i | \(0.325724\pi\) | |||||||
\(884\) | −6.49473e16 | −4.04644 | ||||||||
\(885\) | 1.83213e15 | 0.113441 | ||||||||
\(886\) | −5.18051e15 | −0.318777 | ||||||||
\(887\) | 2.34470e16 | 1.43386 | 0.716932 | − | 0.697143i | \(-0.245546\pi\) | ||||
0.716932 | + | 0.697143i | \(0.245546\pi\) | |||||||
\(888\) | 1.01965e16 | 0.619695 | ||||||||
\(889\) | −3.62878e15 | −0.219180 | ||||||||
\(890\) | −4.38858e15 | −0.263439 | ||||||||
\(891\) | −2.12851e15 | −0.126984 | ||||||||
\(892\) | −4.24245e16 | −2.51542 | ||||||||
\(893\) | 8.79057e15 | 0.518005 | ||||||||
\(894\) | −3.82473e15 | −0.223998 | ||||||||
\(895\) | 6.62119e15 | 0.385398 | ||||||||
\(896\) | 3.00265e16 | 1.73704 | ||||||||
\(897\) | −6.30888e15 | −0.362739 | ||||||||
\(898\) | 3.55505e16 | 2.03154 | ||||||||
\(899\) | −4.17043e14 | −0.0236866 | ||||||||
\(900\) | 3.27992e16 | 1.85152 | ||||||||
\(901\) | −1.87230e16 | −1.05048 | ||||||||
\(902\) | 5.35514e14 | 0.0298631 | ||||||||
\(903\) | 7.57473e15 | 0.419841 | ||||||||
\(904\) | 3.54293e16 | 1.95180 | ||||||||
\(905\) | 3.51694e15 | 0.192574 | ||||||||
\(906\) | −1.23520e16 | −0.672255 | ||||||||
\(907\) | 1.82286e16 | 0.986083 | 0.493041 | − | 0.870006i | \(-0.335885\pi\) | ||||
0.493041 | + | 0.870006i | \(0.335885\pi\) | |||||||
\(908\) | −4.10605e16 | −2.20776 | ||||||||
\(909\) | −3.32932e15 | −0.177932 | ||||||||
\(910\) | −1.16920e16 | −0.621097 | ||||||||
\(911\) | 3.20443e16 | 1.69200 | 0.845999 | − | 0.533184i | \(-0.179005\pi\) | ||||
0.845999 | + | 0.533184i | \(0.179005\pi\) | |||||||
\(912\) | −9.63433e15 | −0.505650 | ||||||||
\(913\) | 4.10921e15 | 0.214372 | ||||||||
\(914\) | −4.83024e16 | −2.50475 | ||||||||
\(915\) | 5.05025e14 | 0.0260314 | ||||||||
\(916\) | −4.57509e16 | −2.34409 | ||||||||
\(917\) | 3.22971e16 | 1.64487 | ||||||||
\(918\) | −2.76989e16 | −1.40226 | ||||||||
\(919\) | 1.73607e16 | 0.873641 | 0.436820 | − | 0.899549i | \(-0.356105\pi\) | ||||
0.436820 | + | 0.899549i | \(0.356105\pi\) | |||||||
\(920\) | 1.40330e16 | 0.701968 | ||||||||
\(921\) | 6.74030e15 | 0.335159 | ||||||||
\(922\) | 1.95316e16 | 0.965421 | ||||||||
\(923\) | −3.92704e16 | −1.92955 | ||||||||
\(924\) | −1.87267e15 | −0.0914671 | ||||||||
\(925\) | 2.49389e16 | 1.21087 | ||||||||
\(926\) | 2.97451e16 | 1.43567 | ||||||||
\(927\) | 4.95950e14 | 0.0237958 | ||||||||
\(928\) | 1.89995e15 | 0.0906209 | ||||||||
\(929\) | 1.50305e15 | 0.0712670 | 0.0356335 | − | 0.999365i | \(-0.488655\pi\) | ||||
0.0356335 | + | 0.999365i | \(0.488655\pi\) | |||||||
\(930\) | −2.74333e14 | −0.0129307 | ||||||||
\(931\) | −1.20952e16 | −0.566748 | ||||||||
\(932\) | 6.87901e16 | 3.20434 | ||||||||
\(933\) | 9.84220e14 | 0.0455767 | ||||||||
\(934\) | 4.33797e16 | 1.99700 | ||||||||
\(935\) | 1.51509e15 | 0.0693384 | ||||||||
\(936\) | 4.59904e16 | 2.09243 | ||||||||
\(937\) | −3.61465e13 | −0.00163493 | −0.000817463 | − | 1.00000i | \(-0.500260\pi\) | ||||
−0.000817463 | 1.00000i | \(0.500260\pi\) | ||||||||
\(938\) | −4.28410e16 | −1.92639 | ||||||||
\(939\) | 3.22425e15 | 0.144135 | ||||||||
\(940\) | −4.27979e15 | −0.190204 | ||||||||
\(941\) | −1.70143e16 | −0.751747 | −0.375873 | − | 0.926671i | \(-0.622657\pi\) | ||||
−0.375873 | + | 0.926671i | \(0.622657\pi\) | |||||||
\(942\) | −4.78854e15 | −0.210341 | ||||||||
\(943\) | −3.37466e15 | −0.147372 | ||||||||
\(944\) | 5.53538e16 | 2.40327 | ||||||||
\(945\) | −3.38644e15 | −0.146173 | ||||||||
\(946\) | 9.37893e15 | 0.402487 | ||||||||
\(947\) | −3.45643e16 | −1.47470 | −0.737350 | − | 0.675511i | \(-0.763923\pi\) | ||||
−0.737350 | + | 0.675511i | \(0.763923\pi\) | |||||||
\(948\) | 1.42018e16 | 0.602416 | ||||||||
\(949\) | 4.60234e16 | 1.94095 | ||||||||
\(950\) | −6.01494e16 | −2.52204 | ||||||||
\(951\) | −1.01129e16 | −0.421584 | ||||||||
\(952\) | 9.43680e16 | 3.91130 | ||||||||
\(953\) | 5.69537e15 | 0.234699 | 0.117350 | − | 0.993091i | \(-0.462560\pi\) | ||||
0.117350 | + | 0.993091i | \(0.462560\pi\) | |||||||
\(954\) | 2.51323e16 | 1.02971 | ||||||||
\(955\) | −1.00808e16 | −0.410655 | ||||||||
\(956\) | 8.18838e16 | 3.31650 | ||||||||
\(957\) | 1.90893e14 | 0.00768732 | ||||||||
\(958\) | 1.56802e16 | 0.627829 | ||||||||
\(959\) | 4.34343e16 | 1.72914 | ||||||||
\(960\) | −9.66348e14 | −0.0382509 | ||||||||
\(961\) | −2.50793e16 | −0.987043 | ||||||||
\(962\) | 6.62876e16 | 2.59400 | ||||||||
\(963\) | 2.63536e16 | 1.02541 | ||||||||
\(964\) | −3.60218e16 | −1.39361 | ||||||||
\(965\) | 3.70850e15 | 0.142659 | ||||||||
\(966\) | 1.73767e16 | 0.664649 | ||||||||
\(967\) | −2.15504e16 | −0.819616 | −0.409808 | − | 0.912172i | \(-0.634404\pi\) | ||||
−0.409808 | + | 0.912172i | \(0.634404\pi\) | |||||||
\(968\) | 5.08998e16 | 1.92487 | ||||||||
\(969\) | 1.67321e16 | 0.629173 | ||||||||
\(970\) | −6.57154e15 | −0.245710 | ||||||||
\(971\) | −2.48494e15 | −0.0923869 | −0.0461934 | − | 0.998933i | \(-0.514709\pi\) | ||||
−0.0461934 | + | 0.998933i | \(0.514709\pi\) | |||||||
\(972\) | 3.82542e16 | 1.41421 | ||||||||
\(973\) | 3.45782e16 | 1.27111 | ||||||||
\(974\) | 8.49600e16 | 3.10556 | ||||||||
\(975\) | −6.94525e15 | −0.252442 | ||||||||
\(976\) | 1.52582e16 | 0.551480 | ||||||||
\(977\) | 1.81086e16 | 0.650827 | 0.325414 | − | 0.945572i | \(-0.394496\pi\) | ||||
0.325414 | + | 0.945572i | \(0.394496\pi\) | |||||||
\(978\) | −8.14689e14 | −0.0291158 | ||||||||
\(979\) | −2.41063e15 | −0.0856693 | ||||||||
\(980\) | 5.88868e15 | 0.208101 | ||||||||
\(981\) | −7.72286e15 | −0.271393 | ||||||||
\(982\) | 2.05105e16 | 0.716743 | ||||||||
\(983\) | −1.41651e16 | −0.492240 | −0.246120 | − | 0.969239i | \(-0.579156\pi\) | ||||
−0.246120 | + | 0.969239i | \(0.579156\pi\) | |||||||
\(984\) | −1.51893e15 | −0.0524886 | ||||||||
\(985\) | −5.53244e14 | −0.0190115 | ||||||||
\(986\) | −1.82350e16 | −0.623134 | ||||||||
\(987\) | −2.79568e15 | −0.0950043 | ||||||||
\(988\) | −1.08578e17 | −3.66925 | ||||||||
\(989\) | −5.91035e16 | −1.98625 | ||||||||
\(990\) | −2.03374e15 | −0.0679675 | ||||||||
\(991\) | −2.72321e16 | −0.905058 | −0.452529 | − | 0.891750i | \(-0.649478\pi\) | ||||
−0.452529 | + | 0.891750i | \(0.649478\pi\) | |||||||
\(992\) | −1.49981e15 | −0.0495702 | ||||||||
\(993\) | −1.88269e15 | −0.0618810 | ||||||||
\(994\) | 1.08163e17 | 3.53552 | ||||||||
\(995\) | 3.77937e14 | 0.0122855 | ||||||||
\(996\) | −2.20941e16 | −0.714250 | ||||||||
\(997\) | −1.09742e16 | −0.352817 | −0.176408 | − | 0.984317i | \(-0.556448\pi\) | ||||
−0.176408 | + | 0.984317i | \(0.556448\pi\) | |||||||
\(998\) | −5.35147e16 | −1.71102 | ||||||||
\(999\) | 1.91994e16 | 0.610490 |
(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 | 197.12.a.b.1.6 | ✓ | 92 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.12.a.b.1.6 | ✓ | 92 | 1.1 | even | 1 | trivial |