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 | 58.19 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.5.c.a.58.22 |
$q$-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 | \(-0.966107\pi\) | ||
0.994337 | − | 0.106277i | \(-0.0338930\pi\) | |||||||
\(3\) | −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 | \(-0.973669\pi\) | ||
0.996581 | − | 0.0826270i | \(-0.0263310\pi\) | |||||||
\(12\) | −79.3823 | −0.551266 | ||||||||
\(13\) | 190.208i | 1.12549i | 0.826630 | + | 0.562745i | \(0.190255\pi\) | ||||
−0.826630 | + | 0.562745i | \(0.809745\pi\) | |||||||
\(14\) | 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 | \(0.0499376\pi\) | ||||
−0.987719 | + | 0.156241i | \(0.950062\pi\) | |||||||
\(24\) | 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 | \(0.321581\pi\) | ||||
−0.531626 | + | 0.846979i | \(0.678419\pi\) | |||||||
\(32\) | − | 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 | \(0.224322\pi\) | ||||
−0.761787 | + | 0.647827i | \(0.775678\pi\) | |||||||
\(38\) | 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 | \(0.200768\pi\) | ||||
−0.807596 | + | 0.589736i | \(0.799232\pi\) | |||||||
\(44\) | − | 305.478i | − | 0.157788i | ||||||
\(45\) | −304.393 | −0.150318 | ||||||||
\(46\) | 140.543 | 0.0664193 | ||||||||
\(47\) | 4253.57i | 1.92557i | 0.270277 | + | 0.962783i | \(0.412885\pi\) | ||||
−0.270277 | + | 0.962783i | \(0.587115\pi\) | |||||||
\(48\) | −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 | \(-0.935638\pi\) | ||
0.979627 | − | 0.200825i | \(-0.0643623\pi\) | |||||||
\(62\) | 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 | \(-0.857686\pi\) | ||
0.901708 | − | 0.432346i | \(-0.142314\pi\) | |||||||
\(68\) | −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 | \(0.0185043\pi\) | ||||
−0.998311 | + | 0.0581002i | \(0.981496\pi\) | |||||||
\(74\) | 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 | \(-0.891560\pi\) | ||
0.942529 | − | 0.334123i | \(-0.108440\pi\) | |||||||
\(84\) | 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 | \(-0.809747\pi\) | ||
0.826633 | − | 0.562742i | \(-0.190253\pi\) | |||||||
\(90\) | 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 | \(-0.976729\pi\) | ||
0.997329 | − | 0.0730427i | \(-0.0232709\pi\) | |||||||
\(98\) | 1446.58i | 0.150623i | ||||||||
\(99\) | − | 539.885i | − | 0.0550847i | ||||||
\(100\) | −7606.50 | −0.760650 | ||||||||
\(101\) | − | 3317.53i | − | 0.325216i | −0.986691 | − | 0.162608i | \(-0.948009\pi\) | ||
0.986691 | − | 0.162608i | \(-0.0519905\pi\) | |||||||
\(102\) | − | 704.435i | − | 0.0677081i | ||||||
\(103\) | 13068.4i | 1.23182i | 0.787817 | + | 0.615910i | \(0.211211\pi\) | ||||
−0.787817 | + | 0.615910i | \(0.788789\pi\) | |||||||
\(104\) | 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 | \(0.0768846\pi\) | ||||
−0.970971 | + | 0.239198i | \(0.923115\pi\) | |||||||
\(110\) | 191.663 | 0.0158399 | ||||||||
\(111\) | − | 9216.68i | − | 0.748047i | ||||||
\(112\) | −5867.13 | −0.467724 | ||||||||
\(113\) | − | 16579.1i | − | 1.29839i | −0.760624 | − | 0.649193i | \(-0.775107\pi\) | ||
0.760624 | − | 0.649193i | \(-0.224893\pi\) | |||||||
\(114\) | − | 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 | \(-0.868518\pi\) | ||
0.915896 | − | 0.401416i | \(-0.131482\pi\) | |||||||
\(132\) | 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 | \(-0.837354\pi\) | ||
0.872271 | − | 0.489023i | \(-0.162646\pi\) | |||||||
\(150\) | − | 2199.65i | − | 0.0977624i | ||||||
\(151\) | − | 23115.7i | − | 1.01380i | −0.862004 | − | 0.506901i | \(-0.830791\pi\) | ||
0.862004 | − | 0.506901i | \(-0.169209\pi\) | |||||||
\(152\) | 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 | \(0.188462\pi\) | ||||
−0.829787 | + | 0.558080i | \(0.811538\pi\) | |||||||
\(158\) | − | 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 | \(0.176979\pi\) | ||||
−0.849375 | + | 0.527790i | \(0.823021\pi\) | |||||||
\(174\) | 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 | \(0.416899\pi\) | ||||
−0.258113 | + | 0.966115i | \(0.583101\pi\) | |||||||
\(180\) | −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 | \(0.126660\pi\) | ||||
−0.921871 | + | 0.387497i | \(0.873340\pi\) | |||||||
\(192\) | −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 | \(0.0578989\pi\) | ||||
−0.983503 | + | 0.180894i | \(0.942101\pi\) | |||||||
\(212\) | 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 | \(0.158178\pi\) | ||||
−0.879050 | + | 0.476730i | \(0.841822\pi\) | |||||||
\(228\) | 23341.2 | 0.449008 | ||||||||
\(229\) | − | 32670.4i | − | 0.622993i | −0.950247 | − | 0.311496i | \(-0.899170\pi\) | ||
0.950247 | − | 0.311496i | \(-0.100830\pi\) | |||||||
\(230\) | −1584.46 | −0.0299520 | ||||||||
\(231\) | − | 2748.12i | − | 0.0515005i | ||||||
\(232\) | − | 13648.5i | − | 0.253576i | ||||||
\(233\) | − | 14015.4i | − | 0.258164i | −0.991634 | − | 0.129082i | \(-0.958797\pi\) | ||
0.991634 | − | 0.129082i | \(-0.0412030\pi\) | |||||||
\(234\) | 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 | \(-0.918248\pi\) | ||
0.967200 | − | 0.254018i | \(-0.0817522\pi\) | |||||||
\(270\) | − | 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 | \(0.0923040\pi\) | ||||
−0.958249 | + | 0.285935i | \(0.907696\pi\) | |||||||
\(284\) | 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 | \(-0.892322\pi\) | ||
0.943327 | − | 0.331865i | \(-0.107678\pi\) | |||||||
\(314\) | 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 | \(-0.822769\pi\) | ||
0.848956 | − | 0.528463i | \(-0.177231\pi\) | |||||||
\(338\) | 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 | \(0.276912\pi\) | ||||
−0.644869 | + | 0.764293i | \(0.723088\pi\) | |||||||
\(348\) | −40742.9 | −0.336429 | ||||||||
\(349\) | − | 179218.i | − | 1.47140i | −0.677305 | − | 0.735702i | \(-0.736852\pi\) | ||
0.677305 | − | 0.735702i | \(-0.263148\pi\) | |||||||
\(350\) | − | 11196.6i | − | 0.0914012i | ||||||
\(351\) | − | 26685.4i | − | 0.216601i | ||||||
\(352\) | −12278.9 | −0.0991002 | ||||||||
\(353\) | 124737.i | 1.00103i | 0.865728 | + | 0.500514i | \(0.166856\pi\) | ||||
−0.865728 | + | 0.500514i | \(0.833144\pi\) | |||||||
\(354\) | 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 | \(0.0504975\pi\) | ||||
−0.987443 | + | 0.157978i | \(0.949502\pi\) | |||||||
\(368\) | 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 | \(-0.969549\pi\) | ||
0.995428 | − | 0.0955181i | \(-0.0304508\pi\) | |||||||
\(398\) | 27722.5i | 0.175012i | ||||||||
\(399\) | −40410.8 | −0.253835 | ||||||||
\(400\) | −110447. | −0.690292 | ||||||||
\(401\) | − | 80257.6i | − | 0.499111i | −0.968360 | − | 0.249556i | \(-0.919715\pi\) | ||
0.968360 | − | 0.249556i | \(-0.0802846\pi\) | |||||||
\(402\) | 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 | \(0.0957018\pi\) | ||||
−0.955142 | + | 0.296147i | \(0.904298\pi\) | |||||||
\(410\) | − | 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 | \(0.346386\pi\) | ||||
−0.464078 | + | 0.885795i | \(0.653614\pi\) | |||||||
\(420\) | −23670.7 | −0.134188 | ||||||||
\(421\) | 89938.3i | 0.507435i | 0.967278 | + | 0.253718i | \(0.0816534\pi\) | ||||
−0.967278 | + | 0.253718i | \(0.918347\pi\) | |||||||
\(422\) | 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 | \(0.0632934\pi\) | ||||
−0.980296 | + | 0.197534i | \(0.936707\pi\) | |||||||
\(432\) | −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 | \(0.0160054\pi\) | ||||
−0.998736 | + | 0.0502611i | \(0.983995\pi\) | |||||||
\(444\) | − | 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 | \(-0.846463\pi\) | ||
0.885906 | − | 0.463864i | \(-0.153537\pi\) | |||||||
\(458\) | −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 | \(-0.828905\pi\) | ||
0.858985 | − | 0.512000i | \(-0.171095\pi\) | |||||||
\(464\) | 113851. | 0.528813 | ||||||||
\(465\) | 95362.9i | 0.441035i | ||||||||
\(466\) | −11916.2 | −0.0548737 | ||||||||
\(467\) | 321723.i | 1.47519i | 0.675243 | + | 0.737596i | \(0.264039\pi\) | ||||
−0.675243 | + | 0.737596i | \(0.735961\pi\) | |||||||
\(468\) | 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 | \(0.243779\pi\) | ||||
−0.720791 | + | 0.693152i | \(0.756221\pi\) | |||||||
\(504\) | 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 | \(-0.941297\pi\) | ||
0.983043 | − | 0.183378i | \(-0.0587031\pi\) | |||||||
\(510\) | 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 | \(0.217478\pi\) | ||||
−0.775539 | + | 0.631300i | \(0.782522\pi\) | |||||||
\(542\) | − | 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 | \(0.210200\pi\) | ||||
−0.789771 | + | 0.613402i | \(0.789800\pi\) | |||||||
\(564\) | − | 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 | \(-0.761316\pi\) | ||
0.731792 | − | 0.681528i | \(-0.238684\pi\) | |||||||
\(570\) | 14644.8i | 0.0450747i | ||||||||
\(571\) | − | 18999.3i | − | 0.0582726i | −0.999575 | − | 0.0291363i | \(-0.990724\pi\) | ||
0.999575 | − | 0.0291363i | \(-0.00927569\pi\) | |||||||
\(572\) | 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 | \(-0.843247\pi\) | ||
0.881175 | − | 0.472790i | \(-0.156753\pi\) | |||||||
\(588\) | 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 | \(0.101640\pi\) | ||||
−0.949452 | + | 0.313913i | \(0.898360\pi\) | |||||||
\(602\) | −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 | \(0.123312\pi\) | ||||
−0.925896 | + | 0.377779i | \(0.876688\pi\) | |||||||
\(614\) | − | 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 | \(-0.747466\pi\) | ||
0.701456 | − | 0.712713i | \(-0.252534\pi\) | |||||||
\(660\) | − | 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 | \(-0.815298\pi\) | ||
0.836321 | − | 0.548240i | \(-0.184702\pi\) | |||||||
\(674\) | −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 | \(0.0274919\pi\) | ||||
−0.996273 | + | 0.0862609i | \(0.972508\pi\) | |||||||
\(684\) | −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 | \(0.261969\pi\) | ||||
−0.680025 | + | 0.733189i | \(0.738031\pi\) | |||||||
\(692\) | 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 | \(0.148354\pi\) | ||||
−0.893342 | + | 0.449377i | \(0.851646\pi\) | |||||||
\(702\) | −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 | \(0.0204353\pi\) | ||||
−0.997940 | + | 0.0641551i | \(0.979565\pi\) | |||||||
\(720\) | −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 | \(0.0132684\pi\) | ||||
−0.999131 | + | 0.0416719i | \(0.986732\pi\) | |||||||
\(740\) | − | 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 | \(0.0961140\pi\) | ||||
−0.954758 | + | 0.297383i | \(0.903886\pi\) | |||||||
\(752\) | 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 | \(-0.799056\pi\) | ||
0.807271 | − | 0.590181i | \(-0.200944\pi\) | |||||||
\(770\) | −5069.37 | −0.00855013 | ||||||||
\(771\) | −183052. | −0.307940 | ||||||||
\(772\) | −318310. | −0.534091 | ||||||||
\(773\) | 531513.i | 0.889519i | 0.895650 | + | 0.444759i | \(0.146711\pi\) | ||||
−0.895650 | + | 0.444759i | \(0.853289\pi\) | |||||||
\(774\) | 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 | \(-0.855551\pi\) | ||
0.898788 | − | 0.438384i | \(-0.144449\pi\) | |||||||
\(798\) | 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 | \(-0.952572\pi\) | ||
0.988920 | − | 0.148449i | \(-0.0474280\pi\) | |||||||
\(810\) | 6987.61i | 0.0106502i | ||||||||
\(811\) | 830609.i | 1.26286i | 0.775433 | + | 0.631430i | \(0.217531\pi\) | ||||
−0.775433 | + | 0.631430i | \(0.782469\pi\) | |||||||
\(812\) | −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 | \(0.149207\pi\) | ||||
−0.892134 | + | 0.451771i | \(0.850793\pi\) | |||||||
\(822\) | 77394.5i | 0.114542i | ||||||||
\(823\) | 612312.i | 0.904010i | 0.892015 | + | 0.452005i | \(0.149291\pi\) | ||||
−0.892015 | + | 0.452005i | \(0.850709\pi\) | |||||||
\(824\) | 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 | \(-0.618238\pi\) | ||
0.362971 | − | 0.931800i | \(-0.381762\pi\) | |||||||
\(840\) | 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 | \(-0.883572\pi\) | ||
0.933849 | − | 0.357667i | \(-0.116428\pi\) | |||||||
\(858\) | 16802.6i | 0.0228246i | ||||||||
\(859\) | − | 93378.3i | − | 0.126549i | −0.997996 | − | 0.0632747i | \(-0.979846\pi\) | ||
0.997996 | − | 0.0632747i | \(-0.0201544\pi\) | |||||||
\(860\) | − | 375611.i | − | 0.507857i | ||||||
\(861\) | −283170. | −0.381981 | ||||||||
\(862\) | 62396.0 | 0.0839734 | ||||||||
\(863\) | 865885.i | 1.16262i | 0.813681 | + | 0.581311i | \(0.197460\pi\) | ||||
−0.813681 | + | 0.581311i | \(0.802540\pi\) | |||||||
\(864\) | 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 | \(0.152437\pi\) | ||||
−0.887504 | + | 0.460800i | \(0.847563\pi\) | |||||||
\(882\) | 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 | \(0.360852\pi\) | ||||
−0.423355 | + | 0.905964i | \(0.639148\pi\) | |||||||
\(888\) | −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 | \(0.00554188\pi\) | ||||
−0.999848 | + | 0.0174094i | \(0.994458\pi\) | |||||||
\(920\) | −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 | \(-0.751740\pi\) | ||
0.710961 | − | 0.703232i | \(-0.248260\pi\) | |||||||
\(930\) | 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 | \(-0.891565\pi\) | ||
0.942535 | − | 0.334108i | \(-0.108435\pi\) | |||||||
\(938\) | 87288.3 | 0.0992088 | ||||||||
\(939\) | 337880.i | 0.383205i | ||||||||
\(940\) | − | 732601.i | − | 0.829109i | ||||||
\(941\) | − | 565854.i | − | 0.639035i | −0.947580 | − | 0.319518i | \(-0.896479\pi\) | ||
0.947580 | − | 0.319518i | \(-0.103521\pi\) | |||||||
\(942\) | −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 | \(-0.853709\pi\) | ||
0.896236 | − | 0.443577i | \(-0.146291\pi\) | |||||||
\(968\) | − | 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 | \(-0.759476\pi\) | ||
0.727840 | − | 0.685747i | \(-0.240524\pi\) | |||||||
\(978\) | 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 | \(-0.997915\pi\) | ||
0.999979 | − | 0.00655140i | \(-0.00208539\pi\) | |||||||
\(984\) | − | 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 | \(0.132313\pi\) | ||||
−0.914845 | + | 0.403805i | \(0.867687\pi\) | |||||||
\(992\) | 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.58.19 | ✓ | 40 | |
3.2 | odd | 2 | 531.5.c.d.235.22 | 40 | |||
59.58 | odd | 2 | inner | 177.5.c.a.58.22 | yes | 40 | |
177.176 | even | 2 | 531.5.c.d.235.19 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.c.a.58.19 | ✓ | 40 | 1.1 | even | 1 | trivial | |
177.5.c.a.58.22 | yes | 40 | 59.58 | odd | 2 | inner | |
531.5.c.d.235.19 | 40 | 177.176 | even | 2 | |||
531.5.c.d.235.22 | 40 | 3.2 | odd | 2 |