Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.22 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.5.c.a.58.19 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.850217i | 0.212554i | 0.994337 | + | 0.106277i | \(0.0338930\pi\) | ||||
−0.994337 | + | 0.106277i | \(0.966107\pi\) | |||||||
\(3\) | −5.19615 | −0.577350 | ||||||||
\(4\) | 15.2771 | 0.954821 | ||||||||
\(5\) | −11.2738 | −0.450953 | −0.225477 | − | 0.974249i | \(-0.572394\pi\) | ||||
−0.225477 | + | 0.974249i | \(0.572394\pi\) | |||||||
\(6\) | − | 4.41785i | − | 0.122718i | ||||||
\(7\) | −26.4494 | −0.539783 | −0.269892 | − | 0.962891i | \(-0.586988\pi\) | ||||
−0.269892 | + | 0.962891i | \(0.586988\pi\) | |||||||
\(8\) | 26.5923i | 0.415505i | ||||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | − | 9.58520i | − | 0.0958520i | ||||||
\(11\) | 19.9957i | 0.165254i | 0.996581 | + | 0.0826270i | \(0.0263310\pi\) | ||||
−0.996581 | + | 0.0826270i | \(0.973669\pi\) | |||||||
\(12\) | −79.3823 | −0.551266 | ||||||||
\(13\) | − | 190.208i | − | 1.12549i | −0.826630 | − | 0.562745i | \(-0.809745\pi\) | ||
0.826630 | − | 0.562745i | \(-0.190255\pi\) | |||||||
\(14\) | − | 22.4877i | − | 0.114733i | ||||||
\(15\) | 58.5805 | 0.260358 | ||||||||
\(16\) | 221.825 | 0.866503 | ||||||||
\(17\) | −159.452 | −0.551736 | −0.275868 | − | 0.961195i | \(-0.588965\pi\) | ||||
−0.275868 | + | 0.961195i | \(0.588965\pi\) | |||||||
\(18\) | 22.9558i | 0.0708514i | ||||||||
\(19\) | −294.035 | −0.814503 | −0.407251 | − | 0.913316i | \(-0.633513\pi\) | ||||
−0.407251 | + | 0.913316i | \(0.633513\pi\) | |||||||
\(20\) | −172.232 | −0.430579 | ||||||||
\(21\) | 137.435 | 0.311644 | ||||||||
\(22\) | −17.0007 | −0.0351254 | ||||||||
\(23\) | − | 165.303i | − | 0.312482i | −0.987719 | − | 0.156241i | \(-0.950062\pi\) | ||
0.987719 | − | 0.156241i | \(-0.0499376\pi\) | |||||||
\(24\) | − | 138.178i | − | 0.239892i | ||||||
\(25\) | −497.901 | −0.796641 | ||||||||
\(26\) | 161.718 | 0.239228 | ||||||||
\(27\) | −140.296 | −0.192450 | ||||||||
\(28\) | −404.071 | −0.515396 | ||||||||
\(29\) | 513.249 | 0.610284 | 0.305142 | − | 0.952307i | \(-0.401296\pi\) | ||||
0.305142 | + | 0.952307i | \(0.401296\pi\) | |||||||
\(30\) | 49.8061i | 0.0553402i | ||||||||
\(31\) | − | 1627.89i | − | 1.69396i | −0.531626 | − | 0.846979i | \(-0.678419\pi\) | ||
0.531626 | − | 0.846979i | \(-0.321581\pi\) | |||||||
\(32\) | 614.077i | 0.599684i | ||||||||
\(33\) | − | 103.901i | − | 0.0954095i | ||||||
\(34\) | − | 135.569i | − | 0.117274i | ||||||
\(35\) | 298.186 | 0.243417 | ||||||||
\(36\) | 412.483 | 0.318274 | ||||||||
\(37\) | − | 1773.75i | − | 1.29565i | −0.761787 | − | 0.647827i | \(-0.775678\pi\) | ||
0.761787 | − | 0.647827i | \(-0.224322\pi\) | |||||||
\(38\) | − | 249.994i | − | 0.173126i | ||||||
\(39\) | 988.349i | 0.649802i | ||||||||
\(40\) | − | 299.797i | − | 0.187373i | ||||||
\(41\) | −2060.39 | −1.22570 | −0.612848 | − | 0.790201i | \(-0.709976\pi\) | ||||
−0.612848 | + | 0.790201i | \(0.709976\pi\) | |||||||
\(42\) | 116.850i | 0.0662412i | ||||||||
\(43\) | − | 2180.85i | − | 1.17947i | −0.807596 | − | 0.589736i | \(-0.799232\pi\) | ||
0.807596 | − | 0.589736i | \(-0.200768\pi\) | |||||||
\(44\) | 305.478i | 0.157788i | ||||||||
\(45\) | −304.393 | −0.150318 | ||||||||
\(46\) | 140.543 | 0.0664193 | ||||||||
\(47\) | − | 4253.57i | − | 1.92557i | −0.270277 | − | 0.962783i | \(-0.587115\pi\) | ||
0.270277 | − | 0.962783i | \(-0.412885\pi\) | |||||||
\(48\) | −1152.64 | −0.500276 | ||||||||
\(49\) | −1701.43 | −0.708634 | ||||||||
\(50\) | − | 423.323i | − | 0.169329i | ||||||
\(51\) | 828.536 | 0.318545 | ||||||||
\(52\) | − | 2905.83i | − | 1.07464i | ||||||
\(53\) | 246.901 | 0.0878965 | 0.0439482 | − | 0.999034i | \(-0.486006\pi\) | ||||
0.0439482 | + | 0.999034i | \(0.486006\pi\) | |||||||
\(54\) | − | 119.282i | − | 0.0409061i | ||||||
\(55\) | − | 225.429i | − | 0.0745219i | ||||||
\(56\) | − | 703.351i | − | 0.224283i | ||||||
\(57\) | 1527.85 | 0.470253 | ||||||||
\(58\) | 436.373i | 0.129718i | ||||||||
\(59\) | −1203.62 | + | 3266.29i | −0.345769 | + | 0.938320i | ||||
\(60\) | 894.943 | 0.248595 | ||||||||
\(61\) | 1494.54i | 0.401650i | 0.979627 | + | 0.200825i | \(0.0643623\pi\) | ||||
−0.979627 | + | 0.200825i | \(0.935638\pi\) | |||||||
\(62\) | 1384.06 | 0.360058 | ||||||||
\(63\) | −714.133 | −0.179928 | ||||||||
\(64\) | 3027.10 | 0.739038 | ||||||||
\(65\) | 2144.37i | 0.507543i | ||||||||
\(66\) | 88.3383 | 0.0202797 | ||||||||
\(67\) | 3881.60i | 0.864691i | 0.901708 | + | 0.432346i | \(0.142314\pi\) | ||||
−0.901708 | + | 0.432346i | \(0.857686\pi\) | |||||||
\(68\) | −2435.97 | −0.526809 | ||||||||
\(69\) | 858.939i | 0.180412i | ||||||||
\(70\) | 253.523i | 0.0517393i | ||||||||
\(71\) | 1862.97 | 0.369564 | 0.184782 | − | 0.982780i | \(-0.440842\pi\) | ||||
0.184782 | + | 0.982780i | \(0.440842\pi\) | |||||||
\(72\) | 717.993i | 0.138502i | ||||||||
\(73\) | − | 619.232i | − | 0.116200i | −0.998311 | − | 0.0581002i | \(-0.981496\pi\) | ||
0.998311 | − | 0.0581002i | \(-0.0185043\pi\) | |||||||
\(74\) | 1508.07 | 0.275397 | ||||||||
\(75\) | 2587.17 | 0.459941 | ||||||||
\(76\) | −4492.02 | −0.777704 | ||||||||
\(77\) | − | 528.875i | − | 0.0892014i | ||||||
\(78\) | −840.311 | −0.138118 | ||||||||
\(79\) | 2372.28 | 0.380112 | 0.190056 | − | 0.981773i | \(-0.439133\pi\) | ||||
0.190056 | + | 0.981773i | \(0.439133\pi\) | |||||||
\(80\) | −2500.82 | −0.390752 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | − | 1751.78i | − | 0.260527i | ||||||
\(83\) | 4603.55i | 0.668246i | 0.942529 | + | 0.334123i | \(0.108440\pi\) | ||||
−0.942529 | + | 0.334123i | \(0.891560\pi\) | |||||||
\(84\) | 2099.61 | 0.297564 | ||||||||
\(85\) | 1797.63 | 0.248807 | ||||||||
\(86\) | 1854.19 | 0.250702 | ||||||||
\(87\) | −2666.92 | −0.352348 | ||||||||
\(88\) | −531.733 | −0.0686639 | ||||||||
\(89\) | 8914.96i | 1.12548i | 0.826633 | + | 0.562742i | \(0.190253\pi\) | ||||
−0.826633 | + | 0.562742i | \(0.809747\pi\) | |||||||
\(90\) | − | 258.800i | − | 0.0319507i | ||||||
\(91\) | 5030.88i | 0.607521i | ||||||||
\(92\) | − | 2525.36i | − | 0.298364i | ||||||
\(93\) | 8458.78i | 0.978007i | ||||||||
\(94\) | 3616.46 | 0.409287 | ||||||||
\(95\) | 3314.91 | 0.367303 | ||||||||
\(96\) | − | 3190.84i | − | 0.346228i | ||||||
\(97\) | 1374.52i | 0.146085i | 0.997329 | + | 0.0730427i | \(0.0232709\pi\) | ||||
−0.997329 | + | 0.0730427i | \(0.976729\pi\) | |||||||
\(98\) | − | 1446.58i | − | 0.150623i | ||||||
\(99\) | 539.885i | 0.0550847i | ||||||||
\(100\) | −7606.50 | −0.760650 | ||||||||
\(101\) | 3317.53i | 0.325216i | 0.986691 | + | 0.162608i | \(0.0519905\pi\) | ||||
−0.986691 | + | 0.162608i | \(0.948009\pi\) | |||||||
\(102\) | 704.435i | 0.0677081i | ||||||||
\(103\) | − | 13068.4i | − | 1.23182i | −0.787817 | − | 0.615910i | \(-0.788789\pi\) | ||
0.787817 | − | 0.615910i | \(-0.211211\pi\) | |||||||
\(104\) | 5058.07 | 0.467647 | ||||||||
\(105\) | −1549.42 | −0.140537 | ||||||||
\(106\) | 209.919i | 0.0186828i | ||||||||
\(107\) | −12221.9 | −1.06751 | −0.533754 | − | 0.845640i | \(-0.679219\pi\) | ||||
−0.533754 | + | 0.845640i | \(0.679219\pi\) | |||||||
\(108\) | −2143.32 | −0.183755 | ||||||||
\(109\) | − | 5683.83i | − | 0.478397i | −0.970971 | − | 0.239198i | \(-0.923115\pi\) | ||
0.970971 | − | 0.239198i | \(-0.0768846\pi\) | |||||||
\(110\) | 191.663 | 0.0158399 | ||||||||
\(111\) | 9216.68i | 0.748047i | ||||||||
\(112\) | −5867.13 | −0.467724 | ||||||||
\(113\) | 16579.1i | 1.29839i | 0.760624 | + | 0.649193i | \(0.224893\pi\) | ||||
−0.760624 | + | 0.649193i | \(0.775107\pi\) | |||||||
\(114\) | 1299.01i | 0.0999543i | ||||||||
\(115\) | 1863.60i | 0.140915i | ||||||||
\(116\) | 7840.97 | 0.582712 | ||||||||
\(117\) | − | 5135.61i | − | 0.375163i | ||||||
\(118\) | −2777.05 | − | 1023.34i | −0.199444 | − | 0.0734946i | ||||
\(119\) | 4217.40 | 0.297818 | ||||||||
\(120\) | 1557.79i | 0.108180i | ||||||||
\(121\) | 14241.2 | 0.972691 | ||||||||
\(122\) | −1270.68 | −0.0853724 | ||||||||
\(123\) | 10706.1 | 0.707655 | ||||||||
\(124\) | − | 24869.5i | − | 1.61743i | ||||||
\(125\) | 12659.4 | 0.810201 | ||||||||
\(126\) | − | 607.168i | − | 0.0382444i | ||||||
\(127\) | −10677.2 | −0.661986 | −0.330993 | − | 0.943633i | \(-0.607384\pi\) | ||||
−0.330993 | + | 0.943633i | \(0.607384\pi\) | |||||||
\(128\) | 12398.9i | 0.756770i | ||||||||
\(129\) | 11332.0i | 0.680969i | ||||||||
\(130\) | −1823.18 | −0.107880 | ||||||||
\(131\) | 13777.4i | 0.802832i | 0.915896 | + | 0.401416i | \(0.131482\pi\) | ||||
−0.915896 | + | 0.401416i | \(0.868518\pi\) | |||||||
\(132\) | − | 1587.31i | − | 0.0910990i | ||||||
\(133\) | 7777.06 | 0.439655 | ||||||||
\(134\) | −3300.20 | −0.183794 | ||||||||
\(135\) | 1581.67 | 0.0867860 | ||||||||
\(136\) | − | 4240.19i | − | 0.229249i | ||||||
\(137\) | 17518.6 | 0.933377 | 0.466689 | − | 0.884422i | \(-0.345447\pi\) | ||||
0.466689 | + | 0.884422i | \(0.345447\pi\) | |||||||
\(138\) | −730.285 | −0.0383472 | ||||||||
\(139\) | −34138.1 | −1.76689 | −0.883445 | − | 0.468535i | \(-0.844782\pi\) | ||||
−0.883445 | + | 0.468535i | \(0.844782\pi\) | |||||||
\(140\) | 4555.43 | 0.232420 | ||||||||
\(141\) | 22102.2i | 1.11173i | ||||||||
\(142\) | 1583.93i | 0.0785524i | ||||||||
\(143\) | 3803.35 | 0.185992 | ||||||||
\(144\) | 5989.27 | 0.288834 | ||||||||
\(145\) | −5786.28 | −0.275210 | ||||||||
\(146\) | 526.481 | 0.0246989 | ||||||||
\(147\) | 8840.89 | 0.409130 | ||||||||
\(148\) | − | 27097.8i | − | 1.23712i | ||||||
\(149\) | 21713.6i | 0.978045i | 0.872271 | + | 0.489023i | \(0.162646\pi\) | ||||
−0.872271 | + | 0.489023i | \(0.837354\pi\) | |||||||
\(150\) | 2199.65i | 0.0977624i | ||||||||
\(151\) | 23115.7i | 1.01380i | 0.862004 | + | 0.506901i | \(0.169209\pi\) | ||||
−0.862004 | + | 0.506901i | \(0.830791\pi\) | |||||||
\(152\) | − | 7819.09i | − | 0.338430i | ||||||
\(153\) | −4305.20 | −0.183912 | ||||||||
\(154\) | 449.658 | 0.0189601 | ||||||||
\(155\) | 18352.6i | 0.763896i | ||||||||
\(156\) | 15099.1i | 0.620445i | ||||||||
\(157\) | − | 27512.2i | − | 1.11616i | −0.829787 | − | 0.558080i | \(-0.811538\pi\) | ||
0.829787 | − | 0.558080i | \(-0.188462\pi\) | |||||||
\(158\) | 2016.95i | 0.0807944i | ||||||||
\(159\) | −1282.94 | −0.0507470 | ||||||||
\(160\) | − | 6922.99i | − | 0.270429i | ||||||
\(161\) | 4372.16i | 0.168673i | ||||||||
\(162\) | 619.808i | 0.0236171i | ||||||||
\(163\) | 28943.8 | 1.08938 | 0.544691 | − | 0.838637i | \(-0.316647\pi\) | ||||
0.544691 | + | 0.838637i | \(0.316647\pi\) | |||||||
\(164\) | −31476.9 | −1.17032 | ||||||||
\(165\) | 1171.36i | 0.0430252i | ||||||||
\(166\) | −3914.01 | −0.142039 | ||||||||
\(167\) | 15906.8 | 0.570362 | 0.285181 | − | 0.958474i | \(-0.407946\pi\) | ||||
0.285181 | + | 0.958474i | \(0.407946\pi\) | |||||||
\(168\) | 3654.72i | 0.129490i | ||||||||
\(169\) | −7618.03 | −0.266728 | ||||||||
\(170\) | 1528.38i | 0.0528850i | ||||||||
\(171\) | −7938.96 | −0.271501 | ||||||||
\(172\) | − | 33317.1i | − | 1.12619i | ||||||
\(173\) | − | 31592.5i | − | 1.05558i | −0.849375 | − | 0.527790i | \(-0.823021\pi\) | ||
0.849375 | − | 0.527790i | \(-0.176979\pi\) | |||||||
\(174\) | − | 2267.46i | − | 0.0748930i | ||||||
\(175\) | 13169.2 | 0.430014 | ||||||||
\(176\) | 4435.55i | 0.143193i | ||||||||
\(177\) | 6254.20 | − | 16972.1i | 0.199630 | − | 0.541739i | ||||
\(178\) | −7579.64 | −0.239226 | ||||||||
\(179\) | − | 61910.6i | − | 1.93223i | −0.258113 | − | 0.966115i | \(-0.583101\pi\) | ||
0.258113 | − | 0.966115i | \(-0.416899\pi\) | |||||||
\(180\) | −4650.26 | −0.143526 | ||||||||
\(181\) | 4663.31 | 0.142343 | 0.0711717 | − | 0.997464i | \(-0.477326\pi\) | ||||
0.0711717 | + | 0.997464i | \(0.477326\pi\) | |||||||
\(182\) | −4277.34 | −0.129131 | ||||||||
\(183\) | − | 7765.86i | − | 0.231893i | ||||||
\(184\) | 4395.79 | 0.129838 | ||||||||
\(185\) | 19997.0i | 0.584280i | ||||||||
\(186\) | −7191.80 | −0.207879 | ||||||||
\(187\) | − | 3188.36i | − | 0.0911767i | ||||||
\(188\) | − | 64982.4i | − | 1.83857i | ||||||
\(189\) | 3710.75 | 0.103881 | ||||||||
\(190\) | 2818.39i | 0.0780717i | ||||||||
\(191\) | − | 28272.6i | − | 0.774995i | −0.921871 | − | 0.387497i | \(-0.873340\pi\) | ||
0.921871 | − | 0.387497i | \(-0.126660\pi\) | |||||||
\(192\) | −15729.3 | −0.426684 | ||||||||
\(193\) | −20835.7 | −0.559362 | −0.279681 | − | 0.960093i | \(-0.590229\pi\) | ||||
−0.279681 | + | 0.960093i | \(0.590229\pi\) | |||||||
\(194\) | −1168.64 | −0.0310511 | ||||||||
\(195\) | − | 11142.5i | − | 0.293030i | ||||||
\(196\) | −25993.0 | −0.676618 | ||||||||
\(197\) | −51531.0 | −1.32781 | −0.663905 | − | 0.747817i | \(-0.731102\pi\) | ||||
−0.663905 | + | 0.747817i | \(0.731102\pi\) | |||||||
\(198\) | −459.019 | −0.0117085 | ||||||||
\(199\) | −32606.5 | −0.823374 | −0.411687 | − | 0.911325i | \(-0.635060\pi\) | ||||
−0.411687 | + | 0.911325i | \(0.635060\pi\) | |||||||
\(200\) | − | 13240.3i | − | 0.331009i | ||||||
\(201\) | − | 20169.4i | − | 0.499230i | ||||||
\(202\) | −2820.62 | −0.0691259 | ||||||||
\(203\) | −13575.1 | −0.329421 | ||||||||
\(204\) | 12657.6 | 0.304153 | ||||||||
\(205\) | 23228.5 | 0.552731 | ||||||||
\(206\) | 11110.9 | 0.261828 | ||||||||
\(207\) | − | 4463.18i | − | 0.104161i | ||||||
\(208\) | − | 42192.8i | − | 0.975241i | ||||||
\(209\) | − | 5879.46i | − | 0.134600i | ||||||
\(210\) | − | 1317.34i | − | 0.0298717i | ||||||
\(211\) | − | 16107.1i | − | 0.361787i | −0.983503 | − | 0.180894i | \(-0.942101\pi\) | ||
0.983503 | − | 0.180894i | \(-0.0578989\pi\) | |||||||
\(212\) | 3771.94 | 0.0839254 | ||||||||
\(213\) | −9680.29 | −0.213368 | ||||||||
\(214\) | − | 10391.3i | − | 0.226903i | ||||||
\(215\) | 24586.5i | 0.531887i | ||||||||
\(216\) | − | 3730.80i | − | 0.0799640i | ||||||
\(217\) | 43056.8i | 0.914371i | ||||||||
\(218\) | 4832.49 | 0.101685 | ||||||||
\(219\) | 3217.62i | 0.0670883i | ||||||||
\(220\) | − | 3443.90i | − | 0.0711550i | ||||||
\(221\) | 30329.0i | 0.620974i | ||||||||
\(222\) | −7836.18 | −0.159000 | ||||||||
\(223\) | 15954.1 | 0.320821 | 0.160411 | − | 0.987050i | \(-0.448718\pi\) | ||||
0.160411 | + | 0.987050i | \(0.448718\pi\) | |||||||
\(224\) | − | 16241.9i | − | 0.323700i | ||||||
\(225\) | −13443.3 | −0.265547 | ||||||||
\(226\) | −14095.8 | −0.275977 | ||||||||
\(227\) | − | 49130.8i | − | 0.953459i | −0.879050 | − | 0.476730i | \(-0.841822\pi\) | ||
0.879050 | − | 0.476730i | \(-0.158178\pi\) | |||||||
\(228\) | 23341.2 | 0.449008 | ||||||||
\(229\) | 32670.4i | 0.622993i | 0.950247 | + | 0.311496i | \(0.100830\pi\) | ||||
−0.950247 | + | 0.311496i | \(0.899170\pi\) | |||||||
\(230\) | −1584.46 | −0.0299520 | ||||||||
\(231\) | 2748.12i | 0.0515005i | ||||||||
\(232\) | 13648.5i | 0.253576i | ||||||||
\(233\) | 14015.4i | 0.258164i | 0.991634 | + | 0.129082i | \(0.0412030\pi\) | ||||
−0.991634 | + | 0.129082i | \(0.958797\pi\) | |||||||
\(234\) | 4366.38 | 0.0797425 | ||||||||
\(235\) | 47954.1i | 0.868340i | ||||||||
\(236\) | −18387.9 | + | 49899.6i | −0.330147 | + | 0.895927i | ||||
\(237\) | −12326.7 | −0.219458 | ||||||||
\(238\) | 3585.70i | 0.0633025i | ||||||||
\(239\) | 100221. | 1.75454 | 0.877271 | − | 0.479996i | \(-0.159362\pi\) | ||||
0.877271 | + | 0.479996i | \(0.159362\pi\) | |||||||
\(240\) | 12994.6 | 0.225601 | ||||||||
\(241\) | 29390.7 | 0.506030 | 0.253015 | − | 0.967462i | \(-0.418578\pi\) | ||||
0.253015 | + | 0.967462i | \(0.418578\pi\) | |||||||
\(242\) | 12108.1i | 0.206750i | ||||||||
\(243\) | −3788.00 | −0.0641500 | ||||||||
\(244\) | 22832.3i | 0.383504i | ||||||||
\(245\) | 19181.6 | 0.319561 | ||||||||
\(246\) | 9102.52i | 0.150415i | ||||||||
\(247\) | 55927.8i | 0.916715i | ||||||||
\(248\) | 43289.5 | 0.703849 | ||||||||
\(249\) | − | 23920.7i | − | 0.385812i | ||||||
\(250\) | 10763.2i | 0.172212i | ||||||||
\(251\) | −100346. | −1.59277 | −0.796385 | − | 0.604790i | \(-0.793257\pi\) | ||||
−0.796385 | + | 0.604790i | \(0.793257\pi\) | |||||||
\(252\) | −10909.9 | −0.171799 | ||||||||
\(253\) | 3305.36 | 0.0516389 | ||||||||
\(254\) | − | 9077.91i | − | 0.140708i | ||||||
\(255\) | −9340.77 | −0.143649 | ||||||||
\(256\) | 37891.8 | 0.578184 | ||||||||
\(257\) | 35228.4 | 0.533367 | 0.266684 | − | 0.963784i | \(-0.414072\pi\) | ||||
0.266684 | + | 0.963784i | \(0.414072\pi\) | |||||||
\(258\) | −9634.66 | −0.144743 | ||||||||
\(259\) | 46914.6i | 0.699373i | ||||||||
\(260\) | 32759.8i | 0.484613i | ||||||||
\(261\) | 13857.7 | 0.203428 | ||||||||
\(262\) | −11713.8 | −0.170645 | ||||||||
\(263\) | −118656. | −1.71545 | −0.857725 | − | 0.514109i | \(-0.828123\pi\) | ||||
−0.857725 | + | 0.514109i | \(0.828123\pi\) | |||||||
\(264\) | 2762.97 | 0.0396431 | ||||||||
\(265\) | −2783.52 | −0.0396372 | ||||||||
\(266\) | 6612.18i | 0.0934505i | ||||||||
\(267\) | − | 46323.5i | − | 0.649798i | ||||||
\(268\) | 59299.7i | 0.825625i | ||||||||
\(269\) | 36762.0i | 0.508035i | 0.967200 | + | 0.254018i | \(0.0817522\pi\) | ||||
−0.967200 | + | 0.254018i | \(0.918248\pi\) | |||||||
\(270\) | 1344.77i | 0.0184467i | ||||||||
\(271\) | 91224.9 | 1.24215 | 0.621076 | − | 0.783750i | \(-0.286696\pi\) | ||||
0.621076 | + | 0.783750i | \(0.286696\pi\) | |||||||
\(272\) | −35370.4 | −0.478081 | ||||||||
\(273\) | − | 26141.2i | − | 0.350752i | ||||||
\(274\) | 14894.6i | 0.198393i | ||||||||
\(275\) | − | 9955.90i | − | 0.131648i | ||||||
\(276\) | 13122.1i | 0.172261i | ||||||||
\(277\) | 81627.4 | 1.06384 | 0.531920 | − | 0.846794i | \(-0.321471\pi\) | ||||
0.531920 | + | 0.846794i | \(0.321471\pi\) | |||||||
\(278\) | − | 29024.8i | − | 0.375560i | ||||||
\(279\) | − | 43953.1i | − | 0.564653i | ||||||
\(280\) | 7929.46i | 0.101141i | ||||||||
\(281\) | 58538.2 | 0.741355 | 0.370678 | − | 0.928762i | \(-0.379125\pi\) | ||||
0.370678 | + | 0.928762i | \(0.379125\pi\) | |||||||
\(282\) | −18791.7 | −0.236302 | ||||||||
\(283\) | − | 45800.4i | − | 0.571869i | −0.958249 | − | 0.285935i | \(-0.907696\pi\) | ||
0.958249 | − | 0.285935i | \(-0.0923040\pi\) | |||||||
\(284\) | 28460.9 | 0.352867 | ||||||||
\(285\) | −17224.8 | −0.212062 | ||||||||
\(286\) | 3233.67i | 0.0395333i | ||||||||
\(287\) | 54496.1 | 0.661610 | ||||||||
\(288\) | 16580.1i | 0.199895i | ||||||||
\(289\) | −58096.1 | −0.695587 | ||||||||
\(290\) | − | 4919.59i | − | 0.0584969i | ||||||
\(291\) | − | 7142.20i | − | 0.0843425i | ||||||
\(292\) | − | 9460.09i | − | 0.110951i | ||||||
\(293\) | −85610.9 | −0.997226 | −0.498613 | − | 0.866825i | \(-0.666157\pi\) | ||||
−0.498613 | + | 0.866825i | \(0.666157\pi\) | |||||||
\(294\) | 7516.67i | 0.0869623i | ||||||||
\(295\) | 13569.4 | − | 36823.6i | 0.155925 | − | 0.423138i | ||||
\(296\) | 47168.2 | 0.538351 | ||||||||
\(297\) | − | 2805.32i | − | 0.0318032i | ||||||
\(298\) | −18461.2 | −0.207888 | ||||||||
\(299\) | −31441.9 | −0.351695 | ||||||||
\(300\) | 39524.5 | 0.439161 | ||||||||
\(301\) | 57682.0i | 0.636660i | ||||||||
\(302\) | −19653.3 | −0.215488 | ||||||||
\(303\) | − | 17238.4i | − | 0.187763i | ||||||
\(304\) | −65224.4 | −0.705769 | ||||||||
\(305\) | − | 16849.2i | − | 0.181125i | ||||||
\(306\) | − | 3660.35i | − | 0.0390913i | ||||||
\(307\) | 121584. | 1.29002 | 0.645012 | − | 0.764172i | \(-0.276852\pi\) | ||||
0.645012 | + | 0.764172i | \(0.276852\pi\) | |||||||
\(308\) | − | 8079.70i | − | 0.0851714i | ||||||
\(309\) | 67905.3i | 0.711191i | ||||||||
\(310\) | −15603.7 | −0.162369 | ||||||||
\(311\) | −17980.2 | −0.185898 | −0.0929488 | − | 0.995671i | \(-0.529629\pi\) | ||||
−0.0929488 | + | 0.995671i | \(0.529629\pi\) | |||||||
\(312\) | −26282.5 | −0.269996 | ||||||||
\(313\) | 65025.1i | 0.663731i | 0.943327 | + | 0.331865i | \(0.107678\pi\) | ||||
−0.943327 | + | 0.331865i | \(0.892322\pi\) | |||||||
\(314\) | 23391.3 | 0.237244 | ||||||||
\(315\) | 8051.02 | 0.0811390 | ||||||||
\(316\) | 36241.6 | 0.362939 | ||||||||
\(317\) | −6089.75 | −0.0606011 | −0.0303006 | − | 0.999541i | \(-0.509646\pi\) | ||||
−0.0303006 | + | 0.999541i | \(0.509646\pi\) | |||||||
\(318\) | − | 1090.77i | − | 0.0107865i | ||||||
\(319\) | 10262.8i | 0.100852i | ||||||||
\(320\) | −34127.0 | −0.333272 | ||||||||
\(321\) | 63506.8 | 0.616326 | ||||||||
\(322\) | −3717.28 | −0.0358521 | ||||||||
\(323\) | 46884.5 | 0.449391 | ||||||||
\(324\) | 11137.0 | 0.106091 | ||||||||
\(325\) | 94704.6i | 0.896612i | ||||||||
\(326\) | 24608.5i | 0.231553i | ||||||||
\(327\) | 29534.1i | 0.276203i | ||||||||
\(328\) | − | 54790.7i | − | 0.509283i | ||||||
\(329\) | 112504.i | 1.03939i | ||||||||
\(330\) | −995.911 | −0.00914519 | ||||||||
\(331\) | −159934. | −1.45977 | −0.729884 | − | 0.683571i | \(-0.760426\pi\) | ||||
−0.729884 | + | 0.683571i | \(0.760426\pi\) | |||||||
\(332\) | 70329.0i | 0.638055i | ||||||||
\(333\) | − | 47891.3i | − | 0.431885i | ||||||
\(334\) | 13524.3i | 0.121233i | ||||||||
\(335\) | − | 43760.5i | − | 0.389935i | ||||||
\(336\) | 30486.5 | 0.270041 | ||||||||
\(337\) | 120034.i | 1.05693i | 0.848956 | + | 0.528463i | \(0.177231\pi\) | ||||
−0.848956 | + | 0.528463i | \(0.822769\pi\) | |||||||
\(338\) | − | 6476.98i | − | 0.0566942i | ||||||
\(339\) | − | 86147.5i | − | 0.749623i | ||||||
\(340\) | 27462.7 | 0.237566 | ||||||||
\(341\) | 32550.9 | 0.279933 | ||||||||
\(342\) | − | 6749.83i | − | 0.0577086i | ||||||
\(343\) | 108507. | 0.922292 | ||||||||
\(344\) | 57993.8 | 0.490077 | ||||||||
\(345\) | − | 9683.54i | − | 0.0813572i | ||||||
\(346\) | 26860.4 | 0.224368 | ||||||||
\(347\) | − | 184056.i | − | 1.52859i | −0.644869 | − | 0.764293i | \(-0.723088\pi\) | ||
0.644869 | − | 0.764293i | \(-0.276912\pi\) | |||||||
\(348\) | −40742.9 | −0.336429 | ||||||||
\(349\) | 179218.i | 1.47140i | 0.677305 | + | 0.735702i | \(0.263148\pi\) | ||||
−0.677305 | + | 0.735702i | \(0.736852\pi\) | |||||||
\(350\) | 11196.6i | 0.0914012i | ||||||||
\(351\) | 26685.4i | 0.216601i | ||||||||
\(352\) | −12278.9 | −0.0991002 | ||||||||
\(353\) | − | 124737.i | − | 1.00103i | −0.865728 | − | 0.500514i | \(-0.833144\pi\) | ||
0.865728 | − | 0.500514i | \(-0.166856\pi\) | |||||||
\(354\) | 14430.0 | + | 5317.42i | 0.115149 | + | 0.0424321i | ||||
\(355\) | −21002.8 | −0.166656 | ||||||||
\(356\) | 136195.i | 1.07464i | ||||||||
\(357\) | −21914.3 | −0.171945 | ||||||||
\(358\) | 52637.4 | 0.410703 | ||||||||
\(359\) | −77449.2 | −0.600936 | −0.300468 | − | 0.953792i | \(-0.597143\pi\) | ||||
−0.300468 | + | 0.953792i | \(0.597143\pi\) | |||||||
\(360\) | − | 8094.53i | − | 0.0624578i | ||||||
\(361\) | −43864.2 | −0.336586 | ||||||||
\(362\) | 3964.83i | 0.0302557i | ||||||||
\(363\) | −73999.3 | −0.561583 | ||||||||
\(364\) | 76857.4i | 0.580074i | ||||||||
\(365\) | 6981.12i | 0.0524009i | ||||||||
\(366\) | 6602.66 | 0.0492898 | ||||||||
\(367\) | − | 42555.8i | − | 0.315956i | −0.987443 | − | 0.157978i | \(-0.949502\pi\) | ||
0.987443 | − | 0.157978i | \(-0.0504975\pi\) | |||||||
\(368\) | − | 36668.3i | − | 0.270767i | ||||||
\(369\) | −55630.6 | −0.408565 | ||||||||
\(370\) | −17001.8 | −0.124191 | ||||||||
\(371\) | −6530.38 | −0.0474451 | ||||||||
\(372\) | 129226.i | 0.933822i | ||||||||
\(373\) | 86818.1 | 0.624012 | 0.312006 | − | 0.950080i | \(-0.398999\pi\) | ||||
0.312006 | + | 0.950080i | \(0.398999\pi\) | |||||||
\(374\) | 2710.79 | 0.0193800 | ||||||||
\(375\) | −65780.1 | −0.467770 | ||||||||
\(376\) | 113112. | 0.800082 | ||||||||
\(377\) | − | 97624.0i | − | 0.686869i | ||||||
\(378\) | 3154.94i | 0.0220804i | ||||||||
\(379\) | 45077.2 | 0.313819 | 0.156909 | − | 0.987613i | \(-0.449847\pi\) | ||||
0.156909 | + | 0.987613i | \(0.449847\pi\) | |||||||
\(380\) | 50642.2 | 0.350708 | ||||||||
\(381\) | 55480.2 | 0.382198 | ||||||||
\(382\) | 24037.8 | 0.164728 | ||||||||
\(383\) | −275505. | −1.87815 | −0.939077 | − | 0.343707i | \(-0.888317\pi\) | ||||
−0.939077 | + | 0.343707i | \(0.888317\pi\) | |||||||
\(384\) | − | 64426.7i | − | 0.436921i | ||||||
\(385\) | 5962.45i | 0.0402257i | ||||||||
\(386\) | − | 17714.8i | − | 0.118895i | ||||||
\(387\) | − | 58882.8i | − | 0.393158i | ||||||
\(388\) | 20998.7i | 0.139485i | ||||||||
\(389\) | 104159. | 0.688333 | 0.344167 | − | 0.938909i | \(-0.388161\pi\) | ||||
0.344167 | + | 0.938909i | \(0.388161\pi\) | |||||||
\(390\) | 9473.52 | 0.0622848 | ||||||||
\(391\) | 26357.9i | 0.172408i | ||||||||
\(392\) | − | 45245.0i | − | 0.294441i | ||||||
\(393\) | − | 71589.5i | − | 0.463516i | ||||||
\(394\) | − | 43812.5i | − | 0.282232i | ||||||
\(395\) | −26744.7 | −0.171413 | ||||||||
\(396\) | 8247.89i | 0.0525960i | ||||||||
\(397\) | 30109.0i | 0.191036i | 0.995428 | + | 0.0955181i | \(0.0304508\pi\) | ||||
−0.995428 | + | 0.0955181i | \(0.969549\pi\) | |||||||
\(398\) | − | 27722.5i | − | 0.175012i | ||||||
\(399\) | −40410.8 | −0.253835 | ||||||||
\(400\) | −110447. | −0.690292 | ||||||||
\(401\) | 80257.6i | 0.499111i | 0.968360 | + | 0.249556i | \(0.0802846\pi\) | ||||
−0.968360 | + | 0.249556i | \(0.919715\pi\) | |||||||
\(402\) | 17148.3 | 0.106113 | ||||||||
\(403\) | −309638. | −1.90653 | ||||||||
\(404\) | 50682.3i | 0.310523i | ||||||||
\(405\) | −8218.62 | −0.0501059 | ||||||||
\(406\) | − | 11541.8i | − | 0.0700199i | ||||||
\(407\) | 35467.5 | 0.214112 | ||||||||
\(408\) | 22032.7i | 0.132357i | ||||||||
\(409\) | − | 99079.5i | − | 0.592294i | −0.955142 | − | 0.296147i | \(-0.904298\pi\) | ||
0.955142 | − | 0.296147i | \(-0.0957018\pi\) | |||||||
\(410\) | 19749.3i | 0.117485i | ||||||||
\(411\) | −91029.1 | −0.538886 | ||||||||
\(412\) | − | 199647.i | − | 1.17617i | ||||||
\(413\) | 31835.0 | − | 86391.4i | 0.186640 | − | 0.506489i | ||||
\(414\) | 3794.67 | 0.0221398 | ||||||||
\(415\) | − | 51899.6i | − | 0.301348i | ||||||
\(416\) | 116802. | 0.674939 | ||||||||
\(417\) | 177387. | 1.02011 | ||||||||
\(418\) | 4998.81 | 0.0286098 | ||||||||
\(419\) | − | 311022.i | − | 1.77159i | −0.464078 | − | 0.885795i | \(-0.653614\pi\) | ||
0.464078 | − | 0.885795i | \(-0.346386\pi\) | |||||||
\(420\) | −23670.7 | −0.134188 | ||||||||
\(421\) | − | 89938.3i | − | 0.507435i | −0.967278 | − | 0.253718i | \(-0.918347\pi\) | ||
0.967278 | − | 0.253718i | \(-0.0816534\pi\) | |||||||
\(422\) | 13694.5 | 0.0768993 | ||||||||
\(423\) | − | 114846.i | − | 0.641855i | ||||||
\(424\) | 6565.68i | 0.0365214i | ||||||||
\(425\) | 79391.2 | 0.439536 | ||||||||
\(426\) | − | 8230.34i | − | 0.0453522i | ||||||
\(427\) | − | 39529.7i | − | 0.216804i | ||||||
\(428\) | −186715. | −1.01928 | ||||||||
\(429\) | −19762.8 | −0.107382 | ||||||||
\(430\) | −20903.8 | −0.113055 | ||||||||
\(431\) | − | 73388.3i | − | 0.395068i | −0.980296 | − | 0.197534i | \(-0.936707\pi\) | ||
0.980296 | − | 0.197534i | \(-0.0632934\pi\) | |||||||
\(432\) | −31121.2 | −0.166759 | ||||||||
\(433\) | 68075.2 | 0.363089 | 0.181545 | − | 0.983383i | \(-0.441890\pi\) | ||||
0.181545 | + | 0.983383i | \(0.441890\pi\) | |||||||
\(434\) | −36607.6 | −0.194353 | ||||||||
\(435\) | 30066.4 | 0.158892 | ||||||||
\(436\) | − | 86832.7i | − | 0.456783i | ||||||
\(437\) | 48604.9i | 0.254517i | ||||||||
\(438\) | −2735.68 | −0.0142599 | ||||||||
\(439\) | 137778. | 0.714909 | 0.357454 | − | 0.933931i | \(-0.383645\pi\) | ||||
0.357454 | + | 0.933931i | \(0.383645\pi\) | |||||||
\(440\) | 5994.67 | 0.0309642 | ||||||||
\(441\) | −45938.6 | −0.236211 | ||||||||
\(442\) | −25786.2 | −0.131991 | ||||||||
\(443\) | − | 19727.4i | − | 0.100522i | −0.998736 | − | 0.0502611i | \(-0.983995\pi\) | ||
0.998736 | − | 0.0502611i | \(-0.0160054\pi\) | |||||||
\(444\) | 140804.i | 0.714251i | ||||||||
\(445\) | − | 100506.i | − | 0.507540i | ||||||
\(446\) | 13564.5i | 0.0681919i | ||||||||
\(447\) | − | 112827.i | − | 0.564675i | ||||||
\(448\) | −80064.9 | −0.398920 | ||||||||
\(449\) | −279194. | −1.38489 | −0.692443 | − | 0.721473i | \(-0.743466\pi\) | ||||
−0.692443 | + | 0.721473i | \(0.743466\pi\) | |||||||
\(450\) | − | 11429.7i | − | 0.0564431i | ||||||
\(451\) | − | 41199.1i | − | 0.202551i | ||||||
\(452\) | 253281.i | 1.23973i | ||||||||
\(453\) | − | 120113.i | − | 0.585318i | ||||||
\(454\) | 41771.8 | 0.202662 | ||||||||
\(455\) | − | 56717.3i | − | 0.273964i | ||||||
\(456\) | 40629.2i | 0.195393i | ||||||||
\(457\) | 193755.i | 0.927728i | 0.885906 | + | 0.463864i | \(0.153537\pi\) | ||||
−0.885906 | + | 0.463864i | \(0.846463\pi\) | |||||||
\(458\) | −27776.9 | −0.132420 | ||||||||
\(459\) | 22370.5 | 0.106182 | ||||||||
\(460\) | 28470.4i | 0.134548i | ||||||||
\(461\) | 40358.7 | 0.189905 | 0.0949524 | − | 0.995482i | \(-0.469730\pi\) | ||||
0.0949524 | + | 0.995482i | \(0.469730\pi\) | |||||||
\(462\) | −2336.49 | −0.0109466 | ||||||||
\(463\) | 219514.i | 1.02400i | 0.858985 | + | 0.512000i | \(0.171095\pi\) | ||||
−0.858985 | + | 0.512000i | \(0.828905\pi\) | |||||||
\(464\) | 113851. | 0.528813 | ||||||||
\(465\) | − | 95362.9i | − | 0.441035i | ||||||
\(466\) | −11916.2 | −0.0548737 | ||||||||
\(467\) | − | 321723.i | − | 1.47519i | −0.675243 | − | 0.737596i | \(-0.735961\pi\) | ||
0.675243 | − | 0.737596i | \(-0.264039\pi\) | |||||||
\(468\) | − | 78457.4i | − | 0.358214i | ||||||
\(469\) | − | 102666.i | − | 0.466746i | ||||||
\(470\) | −40771.3 | −0.184569 | ||||||||
\(471\) | 142958.i | 0.644415i | ||||||||
\(472\) | −86858.3 | − | 32007.1i | −0.389877 | − | 0.143669i | ||||
\(473\) | 43607.6 | 0.194913 | ||||||||
\(474\) | − | 10480.4i | − | 0.0466467i | ||||||
\(475\) | 146400. | 0.648866 | ||||||||
\(476\) | 64429.8 | 0.284363 | ||||||||
\(477\) | 6666.33 | 0.0292988 | ||||||||
\(478\) | 85209.7i | 0.372935i | ||||||||
\(479\) | 42962.3 | 0.187248 | 0.0936238 | − | 0.995608i | \(-0.470155\pi\) | ||||
0.0936238 | + | 0.995608i | \(0.470155\pi\) | |||||||
\(480\) | 35972.9i | 0.156133i | ||||||||
\(481\) | −337381. | −1.45825 | ||||||||
\(482\) | 24988.5i | 0.107559i | ||||||||
\(483\) | − | 22718.4i | − | 0.0973832i | ||||||
\(484\) | 217564. | 0.928746 | ||||||||
\(485\) | − | 15496.1i | − | 0.0658777i | ||||||
\(486\) | − | 3220.62i | − | 0.0136354i | ||||||
\(487\) | −268645. | −1.13271 | −0.566357 | − | 0.824160i | \(-0.691648\pi\) | ||||
−0.566357 | + | 0.824160i | \(0.691648\pi\) | |||||||
\(488\) | −39743.3 | −0.166888 | ||||||||
\(489\) | −150396. | −0.628955 | ||||||||
\(490\) | 16308.5i | 0.0679239i | ||||||||
\(491\) | 331744. | 1.37607 | 0.688034 | − | 0.725678i | \(-0.258474\pi\) | ||||
0.688034 | + | 0.725678i | \(0.258474\pi\) | |||||||
\(492\) | 163559. | 0.675684 | ||||||||
\(493\) | −81838.5 | −0.336716 | ||||||||
\(494\) | −47550.8 | −0.194852 | ||||||||
\(495\) | − | 6086.57i | − | 0.0248406i | ||||||
\(496\) | − | 361107.i | − | 1.46782i | ||||||
\(497\) | −49274.5 | −0.199485 | ||||||||
\(498\) | 20337.8 | 0.0820060 | ||||||||
\(499\) | 112576. | 0.452111 | 0.226055 | − | 0.974114i | \(-0.427417\pi\) | ||||
0.226055 | + | 0.974114i | \(0.427417\pi\) | |||||||
\(500\) | 193399. | 0.773597 | ||||||||
\(501\) | −82654.3 | −0.329299 | ||||||||
\(502\) | − | 85315.9i | − | 0.338550i | ||||||
\(503\) | − | 350747.i | − | 1.38630i | −0.720791 | − | 0.693152i | \(-0.756221\pi\) | ||
0.720791 | − | 0.693152i | \(-0.243779\pi\) | |||||||
\(504\) | − | 18990.5i | − | 0.0747609i | ||||||
\(505\) | − | 37401.2i | − | 0.146657i | ||||||
\(506\) | 2810.27i | 0.0109761i | ||||||||
\(507\) | 39584.5 | 0.153996 | ||||||||
\(508\) | −163117. | −0.632078 | ||||||||
\(509\) | 95019.3i | 0.366755i | 0.983043 | + | 0.183378i | \(0.0587031\pi\) | ||||
−0.983043 | + | 0.183378i | \(0.941297\pi\) | |||||||
\(510\) | − | 7941.68i | − | 0.0305332i | ||||||
\(511\) | 16378.3i | 0.0627231i | ||||||||
\(512\) | 230599.i | 0.879665i | ||||||||
\(513\) | 41252.0 | 0.156751 | ||||||||
\(514\) | 29951.7i | 0.113369i | ||||||||
\(515\) | 147331.i | 0.555493i | ||||||||
\(516\) | 173121.i | 0.650203i | ||||||||
\(517\) | 85053.4 | 0.318208 | ||||||||
\(518\) | −39887.6 | −0.148655 | ||||||||
\(519\) | 164159.i | 0.609440i | ||||||||
\(520\) | −57023.8 | −0.210887 | ||||||||
\(521\) | −131693. | −0.485161 | −0.242581 | − | 0.970131i | \(-0.577994\pi\) | ||||
−0.242581 | + | 0.970131i | \(0.577994\pi\) | |||||||
\(522\) | 11782.1i | 0.0432395i | ||||||||
\(523\) | 432940. | 1.58280 | 0.791398 | − | 0.611302i | \(-0.209354\pi\) | ||||
0.791398 | + | 0.611302i | \(0.209354\pi\) | |||||||
\(524\) | 210479.i | 0.766561i | ||||||||
\(525\) | −68429.0 | −0.248269 | ||||||||
\(526\) | − | 100883.i | − | 0.364626i | ||||||
\(527\) | 259571.i | 0.934618i | ||||||||
\(528\) | − | 23047.8i | − | 0.0826726i | ||||||
\(529\) | 252516. | 0.902355 | ||||||||
\(530\) | − | 2366.60i | − | 0.00842505i | ||||||
\(531\) | −32497.8 | + | 88189.9i | −0.115256 | + | 0.312773i | ||||
\(532\) | 118811. | 0.419792 | ||||||||
\(533\) | 391903.i | 1.37951i | ||||||||
\(534\) | 39385.0 | 0.138117 | ||||||||
\(535\) | 137788. | 0.481396 | ||||||||
\(536\) | −103221. | −0.359284 | ||||||||
\(537\) | 321697.i | 1.11557i | ||||||||
\(538\) | −31255.6 | −0.107985 | ||||||||
\(539\) | − | 34021.4i | − | 0.117105i | ||||||
\(540\) | 24163.5 | 0.0828651 | ||||||||
\(541\) | − | 369539.i | − | 1.26260i | −0.775539 | − | 0.631300i | \(-0.782522\pi\) | ||
0.775539 | − | 0.631300i | \(-0.217478\pi\) | |||||||
\(542\) | 77560.9i | 0.264024i | ||||||||
\(543\) | −24231.3 | −0.0821820 | ||||||||
\(544\) | − | 97915.6i | − | 0.330867i | ||||||
\(545\) | 64078.6i | 0.215735i | ||||||||
\(546\) | 22225.7 | 0.0745539 | ||||||||
\(547\) | −145339. | −0.485745 | −0.242873 | − | 0.970058i | \(-0.578090\pi\) | ||||
−0.242873 | + | 0.970058i | \(0.578090\pi\) | |||||||
\(548\) | 267633. | 0.891208 | ||||||||
\(549\) | 40352.6i | 0.133883i | ||||||||
\(550\) | 8464.67 | 0.0279824 | ||||||||
\(551\) | −150913. | −0.497078 | ||||||||
\(552\) | −22841.2 | −0.0749619 | ||||||||
\(553\) | −62745.4 | −0.205178 | ||||||||
\(554\) | 69401.0i | 0.226124i | ||||||||
\(555\) | − | 103907.i | − | 0.337334i | ||||||
\(556\) | −521532. | −1.68706 | ||||||||
\(557\) | 120254. | 0.387604 | 0.193802 | − | 0.981041i | \(-0.437918\pi\) | ||||
0.193802 | + | 0.981041i | \(0.437918\pi\) | |||||||
\(558\) | 37369.7 | 0.120019 | ||||||||
\(559\) | −414814. | −1.32749 | ||||||||
\(560\) | 66145.0 | 0.210922 | ||||||||
\(561\) | 16567.2i | 0.0526409i | ||||||||
\(562\) | 49770.1i | 0.157578i | ||||||||
\(563\) | − | 388859.i | − | 1.22680i | −0.789771 | − | 0.613402i | \(-0.789800\pi\) | ||
0.789771 | − | 0.613402i | \(-0.210200\pi\) | |||||||
\(564\) | 337658.i | 1.06150i | ||||||||
\(565\) | − | 186910.i | − | 0.585511i | ||||||
\(566\) | 38940.3 | 0.121553 | ||||||||
\(567\) | −19281.6 | −0.0599759 | ||||||||
\(568\) | 49540.8i | 0.153556i | ||||||||
\(569\) | 441305.i | 1.36306i | 0.731792 | + | 0.681528i | \(0.238684\pi\) | ||||
−0.731792 | + | 0.681528i | \(0.761316\pi\) | |||||||
\(570\) | − | 14644.8i | − | 0.0450747i | ||||||
\(571\) | 18999.3i | 0.0582726i | 0.999575 | + | 0.0291363i | \(0.00927569\pi\) | ||||
−0.999575 | + | 0.0291363i | \(0.990724\pi\) | |||||||
\(572\) | 58104.2 | 0.177589 | ||||||||
\(573\) | 146909.i | 0.447444i | ||||||||
\(574\) | 46333.5i | 0.140628i | ||||||||
\(575\) | 82304.5i | 0.248936i | ||||||||
\(576\) | 81731.7 | 0.246346 | ||||||||
\(577\) | 70278.9 | 0.211093 | 0.105546 | − | 0.994414i | \(-0.466341\pi\) | ||||
0.105546 | + | 0.994414i | \(0.466341\pi\) | |||||||
\(578\) | − | 49394.3i | − | 0.147850i | ||||||
\(579\) | 108265. | 0.322948 | ||||||||
\(580\) | −88397.8 | −0.262776 | ||||||||
\(581\) | − | 121761.i | − | 0.360708i | ||||||
\(582\) | 6072.42 | 0.0179273 | ||||||||
\(583\) | 4936.97i | 0.0145252i | ||||||||
\(584\) | 16466.8 | 0.0482819 | ||||||||
\(585\) | 57898.0i | 0.169181i | ||||||||
\(586\) | − | 72787.8i | − | 0.211965i | ||||||
\(587\) | 325818.i | 0.945581i | 0.881175 | + | 0.472790i | \(0.156753\pi\) | ||||
−0.881175 | + | 0.472790i | \(0.843247\pi\) | |||||||
\(588\) | 135063. | 0.390646 | ||||||||
\(589\) | 478658.i | 1.37973i | ||||||||
\(590\) | 31308.0 | + | 11536.9i | 0.0899398 | + | 0.0331426i | ||||
\(591\) | 267763. | 0.766612 | ||||||||
\(592\) | − | 393462.i | − | 1.12269i | ||||||
\(593\) | 607064. | 1.72634 | 0.863168 | − | 0.504917i | \(-0.168477\pi\) | ||||
0.863168 | + | 0.504917i | \(0.168477\pi\) | |||||||
\(594\) | 2385.13 | 0.00675989 | ||||||||
\(595\) | −47546.3 | −0.134302 | ||||||||
\(596\) | 331721.i | 0.933858i | ||||||||
\(597\) | 169428. | 0.475375 | ||||||||
\(598\) | − | 26732.4i | − | 0.0747543i | ||||||
\(599\) | 23980.8 | 0.0668360 | 0.0334180 | − | 0.999441i | \(-0.489361\pi\) | ||||
0.0334180 | + | 0.999441i | \(0.489361\pi\) | |||||||
\(600\) | 68798.8i | 0.191108i | ||||||||
\(601\) | − | 226771.i | − | 0.627825i | −0.949452 | − | 0.313913i | \(-0.898360\pi\) | ||
0.949452 | − | 0.313913i | \(-0.101640\pi\) | |||||||
\(602\) | −49042.2 | −0.135325 | ||||||||
\(603\) | 104803.i | 0.288230i | ||||||||
\(604\) | 353141.i | 0.967999i | ||||||||
\(605\) | −160553. | −0.438638 | ||||||||
\(606\) | 14656.3 | 0.0399099 | ||||||||
\(607\) | −172250. | −0.467499 | −0.233749 | − | 0.972297i | \(-0.575100\pi\) | ||||
−0.233749 | + | 0.972297i | \(0.575100\pi\) | |||||||
\(608\) | − | 180560.i | − | 0.488444i | ||||||
\(609\) | 70538.4 | 0.190191 | ||||||||
\(610\) | 14325.5 | 0.0384989 | ||||||||
\(611\) | −809063. | −2.16721 | ||||||||
\(612\) | −65771.1 | −0.175603 | ||||||||
\(613\) | − | 283915.i | − | 0.755559i | −0.925896 | − | 0.377779i | \(-0.876688\pi\) | ||
0.925896 | − | 0.377779i | \(-0.123312\pi\) | |||||||
\(614\) | 103372.i | 0.274200i | ||||||||
\(615\) | −120699. | −0.319119 | ||||||||
\(616\) | 14064.0 | 0.0370637 | ||||||||
\(617\) | −117535. | −0.308743 | −0.154372 | − | 0.988013i | \(-0.549335\pi\) | ||||
−0.154372 | + | 0.988013i | \(0.549335\pi\) | |||||||
\(618\) | −57734.2 | −0.151167 | ||||||||
\(619\) | 232785. | 0.607537 | 0.303769 | − | 0.952746i | \(-0.401755\pi\) | ||||
0.303769 | + | 0.952746i | \(0.401755\pi\) | |||||||
\(620\) | 280375.i | 0.729384i | ||||||||
\(621\) | 23191.4i | 0.0601372i | ||||||||
\(622\) | − | 15287.1i | − | 0.0395133i | ||||||
\(623\) | − | 235795.i | − | 0.607517i | ||||||
\(624\) | 219240.i | 0.563056i | ||||||||
\(625\) | 168468. | 0.431278 | ||||||||
\(626\) | −55285.4 | −0.141079 | ||||||||
\(627\) | 30550.6i | 0.0777113i | ||||||||
\(628\) | − | 420308.i | − | 1.06573i | ||||||
\(629\) | 282828.i | 0.714860i | ||||||||
\(630\) | 6845.11i | 0.0172464i | ||||||||
\(631\) | 58189.1 | 0.146145 | 0.0730723 | − | 0.997327i | \(-0.476720\pi\) | ||||
0.0730723 | + | 0.997327i | \(0.476720\pi\) | |||||||
\(632\) | 63084.5i | 0.157939i | ||||||||
\(633\) | 83695.1i | 0.208878i | ||||||||
\(634\) | − | 5177.60i | − | 0.0128810i | ||||||
\(635\) | 120373. | 0.298525 | ||||||||
\(636\) | −19599.6 | −0.0484543 | ||||||||
\(637\) | 323625.i | 0.797561i | ||||||||
\(638\) | −8725.60 | −0.0214365 | ||||||||
\(639\) | 50300.3 | 0.123188 | ||||||||
\(640\) | − | 139783.i | − | 0.341268i | ||||||
\(641\) | 774979. | 1.88614 | 0.943070 | − | 0.332595i | \(-0.107924\pi\) | ||||
0.943070 | + | 0.332595i | \(0.107924\pi\) | |||||||
\(642\) | 53994.5i | 0.131003i | ||||||||
\(643\) | −69007.6 | −0.166907 | −0.0834536 | − | 0.996512i | \(-0.526595\pi\) | ||||
−0.0834536 | + | 0.996512i | \(0.526595\pi\) | |||||||
\(644\) | 66794.1i | 0.161052i | ||||||||
\(645\) | − | 127755.i | − | 0.307085i | ||||||
\(646\) | 39861.9i | 0.0955198i | ||||||||
\(647\) | 278274. | 0.664760 | 0.332380 | − | 0.943146i | \(-0.392148\pi\) | ||||
0.332380 | + | 0.943146i | \(0.392148\pi\) | |||||||
\(648\) | 19385.8i | 0.0461672i | ||||||||
\(649\) | −65311.9 | − | 24067.3i | −0.155061 | − | 0.0571397i | ||||
\(650\) | −80519.5 | −0.190579 | ||||||||
\(651\) | − | 223730.i | − | 0.527912i | ||||||
\(652\) | 442178. | 1.04017 | ||||||||
\(653\) | −158117. | −0.370811 | −0.185406 | − | 0.982662i | \(-0.559360\pi\) | ||||
−0.185406 | + | 0.982662i | \(0.559360\pi\) | |||||||
\(654\) | −25110.3 | −0.0587080 | ||||||||
\(655\) | − | 155324.i | − | 0.362040i | ||||||
\(656\) | −457046. | −1.06207 | ||||||||
\(657\) | − | 16719.3i | − | 0.0387335i | ||||||
\(658\) | −95653.1 | −0.220926 | ||||||||
\(659\) | 619035.i | 1.42543i | 0.701456 | + | 0.712713i | \(0.252534\pi\) | ||||
−0.701456 | + | 0.712713i | \(0.747466\pi\) | |||||||
\(660\) | 17895.0i | 0.0410814i | ||||||||
\(661\) | −109703. | −0.251081 | −0.125541 | − | 0.992088i | \(-0.540067\pi\) | ||||
−0.125541 | + | 0.992088i | \(0.540067\pi\) | |||||||
\(662\) | − | 135978.i | − | 0.310280i | ||||||
\(663\) | − | 157594.i | − | 0.358519i | ||||||
\(664\) | −122419. | −0.277660 | ||||||||
\(665\) | −87677.2 | −0.198264 | ||||||||
\(666\) | 40718.0 | 0.0917989 | ||||||||
\(667\) | − | 84841.6i | − | 0.190703i | ||||||
\(668\) | 243011. | 0.544594 | ||||||||
\(669\) | −82900.1 | −0.185226 | ||||||||
\(670\) | 37205.9 | 0.0828824 | ||||||||
\(671\) | −29884.4 | −0.0663743 | ||||||||
\(672\) | 84395.6i | 0.186888i | ||||||||
\(673\) | 496628.i | 1.09648i | 0.836321 | + | 0.548240i | \(0.184702\pi\) | ||||
−0.836321 | + | 0.548240i | \(0.815298\pi\) | |||||||
\(674\) | −102055. | −0.224654 | ||||||||
\(675\) | 69853.5 | 0.153314 | ||||||||
\(676\) | −116382. | −0.254678 | ||||||||
\(677\) | −273451. | −0.596626 | −0.298313 | − | 0.954468i | \(-0.596424\pi\) | ||||
−0.298313 | + | 0.954468i | \(0.596424\pi\) | |||||||
\(678\) | 73244.0 | 0.159336 | ||||||||
\(679\) | − | 36355.2i | − | 0.0788545i | ||||||
\(680\) | 47803.2i | 0.103381i | ||||||||
\(681\) | 255291.i | 0.550480i | ||||||||
\(682\) | 27675.4i | 0.0595010i | ||||||||
\(683\) | − | 80479.6i | − | 0.172522i | −0.996273 | − | 0.0862609i | \(-0.972508\pi\) | ||
0.996273 | − | 0.0862609i | \(-0.0274919\pi\) | |||||||
\(684\) | −121284. | −0.259235 | ||||||||
\(685\) | −197501. | −0.420910 | ||||||||
\(686\) | 92254.2i | 0.196037i | ||||||||
\(687\) | − | 169760.i | − | 0.359685i | ||||||
\(688\) | − | 483766.i | − | 1.02202i | ||||||
\(689\) | − | 46962.5i | − | 0.0989266i | ||||||
\(690\) | 8233.10 | 0.0172928 | ||||||||
\(691\) | − | 700168.i | − | 1.46638i | −0.680025 | − | 0.733189i | \(-0.738031\pi\) | ||
0.680025 | − | 0.733189i | \(-0.261969\pi\) | |||||||
\(692\) | − | 482642.i | − | 1.00789i | ||||||
\(693\) | − | 14279.6i | − | 0.0297338i | ||||||
\(694\) | 156487. | 0.324907 | ||||||||
\(695\) | 384867. | 0.796785 | ||||||||
\(696\) | − | 70919.6i | − | 0.146402i | ||||||
\(697\) | 328533. | 0.676260 | ||||||||
\(698\) | −152375. | −0.312753 | ||||||||
\(699\) | − | 72826.4i | − | 0.149051i | ||||||
\(700\) | 201187. | 0.410586 | ||||||||
\(701\) | − | 441649.i | − | 0.898754i | −0.893342 | − | 0.449377i | \(-0.851646\pi\) | ||
0.893342 | − | 0.449377i | \(-0.148354\pi\) | |||||||
\(702\) | −22688.4 | −0.0460394 | ||||||||
\(703\) | 521546.i | 1.05531i | ||||||||
\(704\) | 60529.1i | 0.122129i | ||||||||
\(705\) | − | 249177.i | − | 0.501336i | ||||||
\(706\) | 106054. | 0.212773 | ||||||||
\(707\) | − | 87746.5i | − | 0.175546i | ||||||
\(708\) | 95546.2 | − | 259286.i | 0.190610 | − | 0.517264i | ||||
\(709\) | 110109. | 0.219043 | 0.109522 | − | 0.993984i | \(-0.465068\pi\) | ||||
0.109522 | + | 0.993984i | \(0.465068\pi\) | |||||||
\(710\) | − | 17857.0i | − | 0.0354234i | ||||||
\(711\) | 64051.6 | 0.126704 | ||||||||
\(712\) | −237069. | −0.467644 | ||||||||
\(713\) | −269096. | −0.529331 | ||||||||
\(714\) | − | 18631.9i | − | 0.0365477i | ||||||
\(715\) | −42878.3 | −0.0838736 | ||||||||
\(716\) | − | 945816.i | − | 1.84493i | ||||||
\(717\) | −520764. | −1.01298 | ||||||||
\(718\) | − | 65848.6i | − | 0.127731i | ||||||
\(719\) | − | 66331.4i | − | 0.128310i | −0.997940 | − | 0.0641551i | \(-0.979565\pi\) | ||
0.997940 | − | 0.0641551i | \(-0.0204353\pi\) | |||||||
\(720\) | −67522.0 | −0.130251 | ||||||||
\(721\) | 345651.i | 0.664916i | ||||||||
\(722\) | − | 37294.0i | − | 0.0715427i | ||||||
\(723\) | −152719. | −0.292156 | ||||||||
\(724\) | 71242.0 | 0.135912 | ||||||||
\(725\) | −255547. | −0.486178 | ||||||||
\(726\) | − | 62915.4i | − | 0.119367i | ||||||
\(727\) | −199842. | −0.378110 | −0.189055 | − | 0.981967i | \(-0.560542\pi\) | ||||
−0.189055 | + | 0.981967i | \(0.560542\pi\) | |||||||
\(728\) | −133783. | −0.252428 | ||||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | −5935.46 | −0.0111380 | ||||||||
\(731\) | 347740.i | 0.650758i | ||||||||
\(732\) | − | 118640.i | − | 0.221416i | ||||||
\(733\) | −582907. | −1.08490 | −0.542452 | − | 0.840087i | \(-0.682504\pi\) | ||||
−0.542452 | + | 0.840087i | \(0.682504\pi\) | |||||||
\(734\) | 36181.7 | 0.0671578 | ||||||||
\(735\) | −99670.7 | −0.184498 | ||||||||
\(736\) | 101509. | 0.187390 | ||||||||
\(737\) | −77615.5 | −0.142894 | ||||||||
\(738\) | − | 47298.1i | − | 0.0868422i | ||||||
\(739\) | − | 45515.8i | − | 0.0833438i | −0.999131 | − | 0.0416719i | \(-0.986732\pi\) | ||
0.999131 | − | 0.0416719i | \(-0.0132684\pi\) | |||||||
\(740\) | 305496.i | 0.557882i | ||||||||
\(741\) | − | 290610.i | − | 0.529265i | ||||||
\(742\) | − | 5552.24i | − | 0.0100846i | ||||||
\(743\) | −156217. | −0.282977 | −0.141488 | − | 0.989940i | \(-0.545189\pi\) | ||||
−0.141488 | + | 0.989940i | \(0.545189\pi\) | |||||||
\(744\) | −224939. | −0.406367 | ||||||||
\(745\) | − | 244795.i | − | 0.441053i | ||||||
\(746\) | 73814.2i | 0.132636i | ||||||||
\(747\) | 124296.i | 0.222749i | ||||||||
\(748\) | − | 48708.9i | − | 0.0870574i | ||||||
\(749\) | 323262. | 0.576223 | ||||||||
\(750\) | − | 55927.4i | − | 0.0994264i | ||||||
\(751\) | − | 335449.i | − | 0.594767i | −0.954758 | − | 0.297383i | \(-0.903886\pi\) | ||
0.954758 | − | 0.297383i | \(-0.0961140\pi\) | |||||||
\(752\) | − | 943548.i | − | 1.66851i | ||||||
\(753\) | 521414. | 0.919586 | ||||||||
\(754\) | 83001.5 | 0.145997 | ||||||||
\(755\) | − | 260602.i | − | 0.457177i | ||||||
\(756\) | 56689.6 | 0.0991881 | ||||||||
\(757\) | 797908. | 1.39239 | 0.696196 | − | 0.717852i | \(-0.254875\pi\) | ||||
0.696196 | + | 0.717852i | \(0.254875\pi\) | |||||||
\(758\) | 38325.4i | 0.0667035i | ||||||||
\(759\) | −17175.1 | −0.0298137 | ||||||||
\(760\) | 88151.1i | 0.152616i | ||||||||
\(761\) | −23661.3 | −0.0408572 | −0.0204286 | − | 0.999791i | \(-0.506503\pi\) | ||||
−0.0204286 | + | 0.999791i | \(0.506503\pi\) | |||||||
\(762\) | 47170.2i | 0.0812377i | ||||||||
\(763\) | 150334.i | 0.258231i | ||||||||
\(764\) | − | 431924.i | − | 0.739981i | ||||||
\(765\) | 48536.1 | 0.0829357 | ||||||||
\(766\) | − | 234239.i | − | 0.399209i | ||||||
\(767\) | 621274. | + | 228938.i | 1.05607 | + | 0.389159i | ||||
\(768\) | −196892. | −0.333814 | ||||||||
\(769\) | 698020.i | 1.18036i | 0.807271 | + | 0.590181i | \(0.200944\pi\) | ||||
−0.807271 | + | 0.590181i | \(0.799056\pi\) | |||||||
\(770\) | −5069.37 | −0.00855013 | ||||||||
\(771\) | −183052. | −0.307940 | ||||||||
\(772\) | −318310. | −0.534091 | ||||||||
\(773\) | − | 531513.i | − | 0.889519i | −0.895650 | − | 0.444759i | \(-0.853289\pi\) | ||
0.895650 | − | 0.444759i | \(-0.146711\pi\) | |||||||
\(774\) | 50063.2 | 0.0835673 | ||||||||
\(775\) | 810530.i | 1.34948i | ||||||||
\(776\) | −36551.6 | −0.0606993 | ||||||||
\(777\) | − | 243776.i | − | 0.403783i | ||||||
\(778\) | 88558.0i | 0.146308i | ||||||||
\(779\) | 605829. | 0.998332 | ||||||||
\(780\) | − | 170225.i | − | 0.279791i | ||||||
\(781\) | 37251.5i | 0.0610720i | ||||||||
\(782\) | −22409.9 | −0.0366460 | ||||||||
\(783\) | −72006.8 | −0.117449 | ||||||||
\(784\) | −377419. | −0.614034 | ||||||||
\(785\) | 310168.i | 0.503336i | ||||||||
\(786\) | 60866.6 | 0.0985221 | ||||||||
\(787\) | −127904. | −0.206506 | −0.103253 | − | 0.994655i | \(-0.532925\pi\) | ||||
−0.103253 | + | 0.994655i | \(0.532925\pi\) | |||||||
\(788\) | −787246. | −1.26782 | ||||||||
\(789\) | 616554. | 0.990415 | ||||||||
\(790\) | − | 22738.8i | − | 0.0364345i | ||||||
\(791\) | − | 438507.i | − | 0.700847i | ||||||
\(792\) | −14356.8 | −0.0228880 | ||||||||
\(793\) | 284273. | 0.452053 | ||||||||
\(794\) | −25599.2 | −0.0406055 | ||||||||
\(795\) | 14463.6 | 0.0228845 | ||||||||
\(796\) | −498133. | −0.786175 | ||||||||
\(797\) | 556931.i | 0.876769i | 0.898788 | + | 0.438384i | \(0.144449\pi\) | ||||
−0.898788 | + | 0.438384i | \(0.855551\pi\) | |||||||
\(798\) | − | 34357.9i | − | 0.0539537i | ||||||
\(799\) | 678240.i | 1.06240i | ||||||||
\(800\) | − | 305749.i | − | 0.477733i | ||||||
\(801\) | 240704.i | 0.375161i | ||||||||
\(802\) | −68236.4 | −0.106088 | ||||||||
\(803\) | 12382.0 | 0.0192026 | ||||||||
\(804\) | − | 308130.i | − | 0.476675i | ||||||
\(805\) | − | 49291.0i | − | 0.0760634i | ||||||
\(806\) | − | 263260.i | − | 0.405242i | ||||||
\(807\) | − | 191021.i | − | 0.293314i | ||||||
\(808\) | −88220.8 | −0.135129 | ||||||||
\(809\) | 194314.i | 0.296898i | 0.988920 | + | 0.148449i | \(0.0474280\pi\) | ||||
−0.988920 | + | 0.148449i | \(0.952572\pi\) | |||||||
\(810\) | − | 6987.61i | − | 0.0106502i | ||||||
\(811\) | − | 830609.i | − | 1.26286i | −0.775433 | − | 0.631430i | \(-0.782469\pi\) | ||
0.775433 | − | 0.631430i | \(-0.217531\pi\) | |||||||
\(812\) | −207389. | −0.314538 | ||||||||
\(813\) | −474018. | −0.717157 | ||||||||
\(814\) | 30155.0i | 0.0455104i | ||||||||
\(815\) | −326308. | −0.491261 | ||||||||
\(816\) | 183790. | 0.276020 | ||||||||
\(817\) | 641246.i | 0.960684i | ||||||||
\(818\) | 84239.0 | 0.125895 | ||||||||
\(819\) | 135834.i | 0.202507i | ||||||||
\(820\) | 354865. | 0.527759 | ||||||||
\(821\) | − | 609024.i | − | 0.903541i | −0.892134 | − | 0.451771i | \(-0.850793\pi\) | ||
0.892134 | − | 0.451771i | \(-0.149207\pi\) | |||||||
\(822\) | − | 77394.5i | − | 0.114542i | ||||||
\(823\) | − | 612312.i | − | 0.904010i | −0.892015 | − | 0.452005i | \(-0.850709\pi\) | ||
0.892015 | − | 0.452005i | \(-0.149291\pi\) | |||||||
\(824\) | 347519. | 0.511827 | ||||||||
\(825\) | 51732.3i | 0.0760071i | ||||||||
\(826\) | 73451.4 | + | 27066.7i | 0.107656 | + | 0.0396711i | ||||
\(827\) | −1.10592e6 | −1.61701 | −0.808507 | − | 0.588487i | \(-0.799724\pi\) | ||||
−0.808507 | + | 0.588487i | \(0.799724\pi\) | |||||||
\(828\) | − | 68184.6i | − | 0.0994548i | ||||||
\(829\) | 272661. | 0.396747 | 0.198374 | − | 0.980126i | \(-0.436434\pi\) | ||||
0.198374 | + | 0.980126i | \(0.436434\pi\) | |||||||
\(830\) | 44125.9 | 0.0640527 | ||||||||
\(831\) | −424149. | −0.614209 | ||||||||
\(832\) | − | 575778.i | − | 0.831780i | ||||||
\(833\) | 271296. | 0.390979 | ||||||||
\(834\) | 150817.i | 0.216830i | ||||||||
\(835\) | −179331. | −0.257207 | ||||||||
\(836\) | − | 89821.2i | − | 0.128519i | ||||||
\(837\) | 228387.i | 0.326002i | ||||||||
\(838\) | 264436. | 0.376559 | ||||||||
\(839\) | 1.31183e6i | 1.86360i | 0.362971 | + | 0.931800i | \(0.381762\pi\) | ||||
−0.362971 | + | 0.931800i | \(0.618238\pi\) | |||||||
\(840\) | − | 41202.7i | − | 0.0583938i | ||||||
\(841\) | −443856. | −0.627553 | ||||||||
\(842\) | 76467.0 | 0.107857 | ||||||||
\(843\) | −304173. | −0.428022 | ||||||||
\(844\) | − | 246071.i | − | 0.345442i | ||||||
\(845\) | 85884.4 | 0.120282 | ||||||||
\(846\) | 97644.4 | 0.136429 | ||||||||
\(847\) | −376670. | −0.525043 | ||||||||
\(848\) | 54768.8 | 0.0761626 | ||||||||
\(849\) | 237986.i | 0.330169i | ||||||||
\(850\) | 67499.7i | 0.0934252i | ||||||||
\(851\) | −293206. | −0.404869 | ||||||||
\(852\) | −147887. | −0.203728 | ||||||||
\(853\) | 326685. | 0.448984 | 0.224492 | − | 0.974476i | \(-0.427928\pi\) | ||||
0.224492 | + | 0.974476i | \(0.427928\pi\) | |||||||
\(854\) | 33608.8 | 0.0460826 | ||||||||
\(855\) | 89502.4 | 0.122434 | ||||||||
\(856\) | − | 325009.i | − | 0.443555i | ||||||
\(857\) | 525376.i | 0.715334i | 0.933849 | + | 0.357667i | \(0.116428\pi\) | ||||
−0.933849 | + | 0.357667i | \(0.883572\pi\) | |||||||
\(858\) | − | 16802.6i | − | 0.0228246i | ||||||
\(859\) | 93378.3i | 0.126549i | 0.997996 | + | 0.0632747i | \(0.0201544\pi\) | ||||
−0.997996 | + | 0.0632747i | \(0.979846\pi\) | |||||||
\(860\) | 375611.i | 0.507857i | ||||||||
\(861\) | −283170. | −0.381981 | ||||||||
\(862\) | 62396.0 | 0.0839734 | ||||||||
\(863\) | − | 865885.i | − | 1.16262i | −0.813681 | − | 0.581311i | \(-0.802540\pi\) | ||
0.813681 | − | 0.581311i | \(-0.197460\pi\) | |||||||
\(864\) | − | 86152.6i | − | 0.115409i | ||||||
\(865\) | 356168.i | 0.476018i | ||||||||
\(866\) | 57878.7i | 0.0771761i | ||||||||
\(867\) | 301876. | 0.401597 | ||||||||
\(868\) | 657784.i | 0.873060i | ||||||||
\(869\) | 47435.5i | 0.0628151i | ||||||||
\(870\) | 25563.0i | 0.0337732i | ||||||||
\(871\) | 738311. | 0.973202 | ||||||||
\(872\) | 151146. | 0.198776 | ||||||||
\(873\) | 37112.0i | 0.0486951i | ||||||||
\(874\) | −41324.7 | −0.0540987 | ||||||||
\(875\) | −334833. | −0.437333 | ||||||||
\(876\) | 49156.1i | 0.0640573i | ||||||||
\(877\) | 951741. | 1.23743 | 0.618714 | − | 0.785616i | \(-0.287654\pi\) | ||||
0.618714 | + | 0.785616i | \(0.287654\pi\) | |||||||
\(878\) | 117141.i | 0.151957i | ||||||||
\(879\) | 444847. | 0.575749 | ||||||||
\(880\) | − | 50005.7i | − | 0.0645734i | ||||||
\(881\) | − | 715309.i | − | 0.921599i | −0.887504 | − | 0.460800i | \(-0.847563\pi\) | ||
0.887504 | − | 0.460800i | \(-0.152437\pi\) | |||||||
\(882\) | − | 39057.8i | − | 0.0502077i | ||||||
\(883\) | −941299. | −1.20727 | −0.603637 | − | 0.797259i | \(-0.706283\pi\) | ||||
−0.603637 | + | 0.797259i | \(0.706283\pi\) | |||||||
\(884\) | 463340.i | 0.592919i | ||||||||
\(885\) | −70508.7 | + | 191341.i | −0.0900236 | + | 0.244299i | ||||
\(886\) | 16772.6 | 0.0213664 | ||||||||
\(887\) | − | 1.42557e6i | − | 1.81193i | −0.423355 | − | 0.905964i | \(-0.639148\pi\) | ||
0.423355 | − | 0.905964i | \(-0.360852\pi\) | |||||||
\(888\) | −245093. | −0.310817 | ||||||||
\(889\) | 282405. | 0.357329 | ||||||||
\(890\) | 85451.6 | 0.107880 | ||||||||
\(891\) | 14576.9i | 0.0183616i | ||||||||
\(892\) | 243733. | 0.306327 | ||||||||
\(893\) | 1.25070e6i | 1.56838i | ||||||||
\(894\) | 95927.5 | 0.120024 | ||||||||
\(895\) | 697969.i | 0.871345i | ||||||||
\(896\) | − | 327944.i | − | 0.408492i | ||||||
\(897\) | 163377. | 0.203051 | ||||||||
\(898\) | − | 237376.i | − | 0.294363i | ||||||
\(899\) | − | 835515.i | − | 1.03380i | ||||||
\(900\) | −205375. | −0.253550 | ||||||||
\(901\) | −39368.8 | −0.0484957 | ||||||||
\(902\) | 35028.2 | 0.0430531 | ||||||||
\(903\) | − | 299725.i | − | 0.367576i | ||||||
\(904\) | −440877. | −0.539486 | ||||||||
\(905\) | −52573.4 | −0.0641902 | ||||||||
\(906\) | 102122. | 0.124412 | ||||||||
\(907\) | 173366. | 0.210741 | 0.105371 | − | 0.994433i | \(-0.466397\pi\) | ||||
0.105371 | + | 0.994433i | \(0.466397\pi\) | |||||||
\(908\) | − | 750578.i | − | 0.910383i | ||||||
\(909\) | 89573.2i | 0.108405i | ||||||||
\(910\) | 48222.0 | 0.0582321 | ||||||||
\(911\) | 1.07058e6 | 1.28998 | 0.644989 | − | 0.764191i | \(-0.276862\pi\) | ||||
0.644989 | + | 0.764191i | \(0.276862\pi\) | |||||||
\(912\) | 338916. | 0.407476 | ||||||||
\(913\) | −92051.4 | −0.110430 | ||||||||
\(914\) | −164734. | −0.197192 | ||||||||
\(915\) | 87550.9i | 0.104573i | ||||||||
\(916\) | 499109.i | 0.594846i | ||||||||
\(917\) | − | 364404.i | − | 0.433356i | ||||||
\(918\) | 19019.7i | 0.0225694i | ||||||||
\(919\) | − | 29406.7i | − | 0.0348189i | −0.999848 | − | 0.0174094i | \(-0.994458\pi\) | ||
0.999848 | − | 0.0174094i | \(-0.00554188\pi\) | |||||||
\(920\) | −49557.4 | −0.0585508 | ||||||||
\(921\) | −631767. | −0.744796 | ||||||||
\(922\) | 34313.7i | 0.0403650i | ||||||||
\(923\) | − | 354352.i | − | 0.415941i | ||||||
\(924\) | 41983.3i | 0.0491737i | ||||||||
\(925\) | 883152.i | 1.03217i | ||||||||
\(926\) | −186634. | −0.217655 | ||||||||
\(927\) | − | 352846.i | − | 0.410607i | ||||||
\(928\) | 315174.i | 0.365978i | ||||||||
\(929\) | 1.21384e6i | 1.40646i | 0.710961 | + | 0.703232i | \(0.248260\pi\) | ||||
−0.710961 | + | 0.703232i | \(0.751740\pi\) | |||||||
\(930\) | 81079.1 | 0.0937439 | ||||||||
\(931\) | 500281. | 0.577184 | ||||||||
\(932\) | 214116.i | 0.246500i | ||||||||
\(933\) | 93427.8 | 0.107328 | ||||||||
\(934\) | 273534. | 0.313558 | ||||||||
\(935\) | 35945.0i | 0.0411164i | ||||||||
\(936\) | 136568. | 0.155882 | ||||||||
\(937\) | 586673.i | 0.668216i | 0.942535 | + | 0.334108i | \(0.108435\pi\) | ||||
−0.942535 | + | 0.334108i | \(0.891565\pi\) | |||||||
\(938\) | 87288.3 | 0.0992088 | ||||||||
\(939\) | − | 337880.i | − | 0.383205i | ||||||
\(940\) | 732601.i | 0.829109i | ||||||||
\(941\) | 565854.i | 0.639035i | 0.947580 | + | 0.319518i | \(0.103521\pi\) | ||||
−0.947580 | + | 0.319518i | \(0.896479\pi\) | |||||||
\(942\) | −121545. | −0.136973 | ||||||||
\(943\) | 340589.i | 0.383008i | ||||||||
\(944\) | −266993. | + | 724545.i | −0.299610 | + | 0.813057i | ||||
\(945\) | −41834.3 | −0.0468456 | ||||||||
\(946\) | 37075.9i | 0.0414295i | ||||||||
\(947\) | −108724. | −0.121235 | −0.0606174 | − | 0.998161i | \(-0.519307\pi\) | ||||
−0.0606174 | + | 0.998161i | \(0.519307\pi\) | |||||||
\(948\) | −188317. | −0.209543 | ||||||||
\(949\) | −117783. | −0.130782 | ||||||||
\(950\) | 124472.i | 0.137919i | ||||||||
\(951\) | 31643.3 | 0.0349881 | ||||||||
\(952\) | 112151.i | 0.123745i | ||||||||
\(953\) | −329400. | −0.362691 | −0.181346 | − | 0.983419i | \(-0.558045\pi\) | ||||
−0.181346 | + | 0.983419i | \(0.558045\pi\) | |||||||
\(954\) | 5667.82i | 0.00622758i | ||||||||
\(955\) | 318740.i | 0.349486i | ||||||||
\(956\) | 1.53109e6 | 1.67527 | ||||||||
\(957\) | − | 53327.0i | − | 0.0582269i | ||||||
\(958\) | 36527.2i | 0.0398002i | ||||||||
\(959\) | −463355. | −0.503822 | ||||||||
\(960\) | 177329. | 0.192414 | ||||||||
\(961\) | −1.72652e6 | −1.86949 | ||||||||
\(962\) | − | 286847.i | − | 0.309956i | ||||||
\(963\) | −329991. | −0.355836 | ||||||||
\(964\) | 449006. | 0.483168 | ||||||||
\(965\) | 234898. | 0.252246 | ||||||||
\(966\) | 19315.6 | 0.0206992 | ||||||||
\(967\) | 829568.i | 0.887154i | 0.896236 | + | 0.443577i | \(0.146291\pi\) | ||||
−0.896236 | + | 0.443577i | \(0.853709\pi\) | |||||||
\(968\) | 378706.i | 0.404158i | ||||||||
\(969\) | −243619. | −0.259456 | ||||||||
\(970\) | 13175.0 | 0.0140026 | ||||||||
\(971\) | 681484. | 0.722798 | 0.361399 | − | 0.932411i | \(-0.382299\pi\) | ||||
0.361399 | + | 0.932411i | \(0.382299\pi\) | |||||||
\(972\) | −57869.7 | −0.0612518 | ||||||||
\(973\) | 902932. | 0.953738 | ||||||||
\(974\) | − | 228406.i | − | 0.240763i | ||||||
\(975\) | − | 492100.i | − | 0.517659i | ||||||
\(976\) | 331526.i | 0.348031i | ||||||||
\(977\) | 1.30913e6i | 1.37149i | 0.727840 | + | 0.685747i | \(0.240524\pi\) | ||||
−0.727840 | + | 0.685747i | \(0.759476\pi\) | |||||||
\(978\) | − | 127870.i | − | 0.133687i | ||||||
\(979\) | −178261. | −0.185991 | ||||||||
\(980\) | 293040. | 0.305123 | ||||||||
\(981\) | − | 153463.i | − | 0.159466i | ||||||
\(982\) | 282054.i | 0.292489i | ||||||||
\(983\) | 12661.1i | 0.0131028i | 0.999979 | + | 0.00655140i | \(0.00208539\pi\) | ||||
−0.999979 | + | 0.00655140i | \(0.997915\pi\) | |||||||
\(984\) | 284701.i | 0.294035i | ||||||||
\(985\) | 580952. | 0.598780 | ||||||||
\(986\) | − | 69580.4i | − | 0.0715704i | ||||||
\(987\) | − | 584590.i | − | 0.600091i | ||||||
\(988\) | 854417.i | 0.875298i | ||||||||
\(989\) | −360500. | −0.368564 | ||||||||
\(990\) | 5174.90 | 0.00527998 | ||||||||
\(991\) | − | 793139.i | − | 0.807610i | −0.914845 | − | 0.403805i | \(-0.867687\pi\) | ||
0.914845 | − | 0.403805i | \(-0.132313\pi\) | |||||||
\(992\) | 999651. | 1.01584 | ||||||||
\(993\) | 831039. | 0.842797 | ||||||||
\(994\) | − | 41894.0i | − | 0.0424013i | ||||||
\(995\) | 367600. | 0.371303 | ||||||||
\(996\) | − | 365440.i | − | 0.368381i | ||||||
\(997\) | 73242.3 | 0.0736838 | 0.0368419 | − | 0.999321i | \(-0.488270\pi\) | ||||
0.0368419 | + | 0.999321i | \(0.488270\pi\) | |||||||
\(998\) | 95714.0i | 0.0960981i | ||||||||
\(999\) | 248850.i | 0.249349i |
(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 | 177.5.c.a.58.22 | yes | 40 | |
3.2 | odd | 2 | 531.5.c.d.235.19 | 40 | |||
59.58 | odd | 2 | inner | 177.5.c.a.58.19 | ✓ | 40 | |
177.176 | even | 2 | 531.5.c.d.235.22 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.19 | ✓ | 40 | 59.58 | odd | 2 | inner | |
177.5.c.a.58.22 | yes | 40 | 1.1 | even | 1 | trivial | |
531.5.c.d.235.19 | 40 | 3.2 | odd | 2 | |||
531.5.c.d.235.22 | 40 | 177.176 | even | 2 |