Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,5,Mod(10,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, 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("33.10");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.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: | \(3.41120878177\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 102x^{6} + 2913x^{4} + 23292x^{2} + 41364 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 10.4 | ||
Root | \(-1.57474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.10 |
Dual form | 33.5.c.a.10.5 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.57474i | − | 0.393685i | −0.980435 | − | 0.196843i | \(-0.936931\pi\) | ||
0.980435 | − | 0.196843i | \(-0.0630688\pi\) | |||||||
\(3\) | −5.19615 | −0.577350 | ||||||||
\(4\) | 13.5202 | 0.845012 | ||||||||
\(5\) | 15.5526 | 0.622103 | 0.311051 | − | 0.950393i | \(-0.399319\pi\) | ||||
0.311051 | + | 0.950393i | \(0.399319\pi\) | |||||||
\(6\) | 8.18260i | 0.227294i | ||||||||
\(7\) | − | 93.8006i | − | 1.91430i | −0.289596 | − | 0.957149i | \(-0.593521\pi\) | ||
0.289596 | − | 0.957149i | \(-0.406479\pi\) | |||||||
\(8\) | − | 46.4867i | − | 0.726354i | ||||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | − | 24.4913i | − | 0.244913i | ||||||
\(11\) | 60.9369 | + | 104.536i | 0.503611 | + | 0.863931i | ||||
\(12\) | −70.2530 | −0.487868 | ||||||||
\(13\) | 29.4527i | 0.174276i | 0.996196 | + | 0.0871382i | \(0.0277722\pi\) | ||||
−0.996196 | + | 0.0871382i | \(0.972228\pi\) | |||||||
\(14\) | −147.712 | −0.753631 | ||||||||
\(15\) | −80.8135 | −0.359171 | ||||||||
\(16\) | 143.119 | 0.559057 | ||||||||
\(17\) | 251.915i | 0.871677i | 0.900025 | + | 0.435839i | \(0.143548\pi\) | ||||
−0.900025 | + | 0.435839i | \(0.856452\pi\) | |||||||
\(18\) | − | 42.5180i | − | 0.131228i | ||||||
\(19\) | − | 80.2497i | − | 0.222298i | −0.993804 | − | 0.111149i | \(-0.964547\pi\) | ||
0.993804 | − | 0.111149i | \(-0.0354531\pi\) | |||||||
\(20\) | 210.274 | 0.525684 | ||||||||
\(21\) | 487.402i | 1.10522i | ||||||||
\(22\) | 164.617 | − | 95.9599i | 0.340117 | − | 0.198264i | ||||
\(23\) | −702.557 | −1.32809 | −0.664043 | − | 0.747695i | \(-0.731161\pi\) | ||||
−0.664043 | + | 0.747695i | \(0.731161\pi\) | |||||||
\(24\) | 241.552i | 0.419361i | ||||||||
\(25\) | −383.118 | −0.612988 | ||||||||
\(26\) | 46.3804 | 0.0686100 | ||||||||
\(27\) | −140.296 | −0.192450 | ||||||||
\(28\) | − | 1268.20i | − | 1.61760i | ||||||
\(29\) | 1449.00i | 1.72295i | 0.507798 | + | 0.861476i | \(0.330460\pi\) | ||||
−0.507798 | + | 0.861476i | \(0.669540\pi\) | |||||||
\(30\) | 127.260i | 0.141400i | ||||||||
\(31\) | 1279.46 | 1.33138 | 0.665692 | − | 0.746227i | \(-0.268137\pi\) | ||||
0.665692 | + | 0.746227i | \(0.268137\pi\) | |||||||
\(32\) | − | 969.161i | − | 0.946447i | ||||||
\(33\) | −316.638 | − | 543.183i | −0.290760 | − | 0.498791i | ||||
\(34\) | 396.701 | 0.343167 | ||||||||
\(35\) | − | 1458.84i | − | 1.19089i | ||||||
\(36\) | 365.045 | 0.281671 | ||||||||
\(37\) | 115.552 | 0.0844063 | 0.0422031 | − | 0.999109i | \(-0.486562\pi\) | ||||
0.0422031 | + | 0.999109i | \(0.486562\pi\) | |||||||
\(38\) | −126.373 | −0.0875156 | ||||||||
\(39\) | − | 153.041i | − | 0.100618i | ||||||
\(40\) | − | 722.987i | − | 0.451867i | ||||||
\(41\) | − | 1076.75i | − | 0.640541i | −0.947326 | − | 0.320270i | \(-0.896226\pi\) | ||
0.947326 | − | 0.320270i | \(-0.103774\pi\) | |||||||
\(42\) | 767.532 | 0.435109 | ||||||||
\(43\) | 1887.47i | 1.02080i | 0.859936 | + | 0.510402i | \(0.170503\pi\) | ||||
−0.859936 | + | 0.510402i | \(0.829497\pi\) | |||||||
\(44\) | 823.879 | + | 1413.34i | 0.425557 | + | 0.730032i | ||||
\(45\) | 419.919 | 0.207368 | ||||||||
\(46\) | 1106.35i | 0.522848i | ||||||||
\(47\) | 1591.75 | 0.720575 | 0.360287 | − | 0.932841i | \(-0.382679\pi\) | ||||
0.360287 | + | 0.932841i | \(0.382679\pi\) | |||||||
\(48\) | −743.666 | −0.322772 | ||||||||
\(49\) | −6397.55 | −2.66454 | ||||||||
\(50\) | 603.311i | 0.241324i | ||||||||
\(51\) | − | 1308.99i | − | 0.503263i | ||||||
\(52\) | 398.206i | 0.147266i | ||||||||
\(53\) | 1190.69 | 0.423886 | 0.211943 | − | 0.977282i | \(-0.432021\pi\) | ||||
0.211943 | + | 0.977282i | \(0.432021\pi\) | |||||||
\(54\) | 220.930i | 0.0757648i | ||||||||
\(55\) | 947.726 | + | 1625.80i | 0.313298 | + | 0.537454i | ||||
\(56\) | −4360.48 | −1.39046 | ||||||||
\(57\) | 416.990i | 0.128344i | ||||||||
\(58\) | 2281.80 | 0.678301 | ||||||||
\(59\) | 1895.56 | 0.544544 | 0.272272 | − | 0.962220i | \(-0.412225\pi\) | ||||
0.272272 | + | 0.962220i | \(0.412225\pi\) | |||||||
\(60\) | −1092.61 | −0.303504 | ||||||||
\(61\) | 3776.15i | 1.01482i | 0.861704 | + | 0.507411i | \(0.169397\pi\) | ||||
−0.861704 | + | 0.507411i | \(0.830603\pi\) | |||||||
\(62\) | − | 2014.82i | − | 0.524146i | ||||||
\(63\) | − | 2532.62i | − | 0.638099i | ||||||
\(64\) | 763.719 | 0.186455 | ||||||||
\(65\) | 458.065i | 0.108418i | ||||||||
\(66\) | −855.373 | + | 498.622i | −0.196367 | + | 0.114468i | ||||
\(67\) | −1253.00 | −0.279127 | −0.139564 | − | 0.990213i | \(-0.544570\pi\) | ||||
−0.139564 | + | 0.990213i | \(0.544570\pi\) | |||||||
\(68\) | 3405.94i | 0.736578i | ||||||||
\(69\) | 3650.59 | 0.766770 | ||||||||
\(70\) | −2297.30 | −0.468836 | ||||||||
\(71\) | −3591.39 | −0.712437 | −0.356218 | − | 0.934403i | \(-0.615934\pi\) | ||||
−0.356218 | + | 0.934403i | \(0.615934\pi\) | |||||||
\(72\) | − | 1255.14i | − | 0.242118i | ||||||
\(73\) | 1750.75i | 0.328533i | 0.986416 | + | 0.164267i | \(0.0525257\pi\) | ||||
−0.986416 | + | 0.164267i | \(0.947474\pi\) | |||||||
\(74\) | − | 181.965i | − | 0.0332295i | ||||||
\(75\) | 1990.74 | 0.353909 | ||||||||
\(76\) | − | 1084.99i | − | 0.187845i | ||||||
\(77\) | 9805.50 | − | 5715.92i | 1.65382 | − | 0.964061i | ||||
\(78\) | −241.000 | −0.0396120 | ||||||||
\(79\) | − | 6749.08i | − | 1.08141i | −0.841212 | − | 0.540705i | \(-0.818157\pi\) | ||
0.841212 | − | 0.540705i | \(-0.181843\pi\) | |||||||
\(80\) | 2225.86 | 0.347791 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | −1695.60 | −0.252171 | ||||||||
\(83\) | − | 8616.78i | − | 1.25080i | −0.780303 | − | 0.625401i | \(-0.784935\pi\) | ||
0.780303 | − | 0.625401i | \(-0.215065\pi\) | |||||||
\(84\) | 6589.77i | 0.933924i | ||||||||
\(85\) | 3917.92i | 0.542273i | ||||||||
\(86\) | 2972.27 | 0.401876 | ||||||||
\(87\) | − | 7529.24i | − | 0.994747i | ||||||
\(88\) | 4859.51 | − | 2832.75i | 0.627520 | − | 0.365800i | ||||
\(89\) | −9334.05 | −1.17839 | −0.589196 | − | 0.807990i | \(-0.700556\pi\) | ||||
−0.589196 | + | 0.807990i | \(0.700556\pi\) | |||||||
\(90\) | − | 661.265i | − | 0.0816376i | ||||||
\(91\) | 2762.68 | 0.333617 | ||||||||
\(92\) | −9498.71 | −1.12225 | ||||||||
\(93\) | −6648.27 | −0.768675 | ||||||||
\(94\) | − | 2506.59i | − | 0.283680i | ||||||
\(95\) | − | 1248.09i | − | 0.138292i | ||||||
\(96\) | 5035.91i | 0.546431i | ||||||||
\(97\) | 11068.8 | 1.17640 | 0.588202 | − | 0.808714i | \(-0.299836\pi\) | ||||
0.588202 | + | 0.808714i | \(0.299836\pi\) | |||||||
\(98\) | 10074.5i | 1.04899i | ||||||||
\(99\) | 1645.30 | + | 2822.46i | 0.167870 | + | 0.287977i | ||||
\(100\) | −5179.82 | −0.517982 | ||||||||
\(101\) | 9732.30i | 0.954053i | 0.878889 | + | 0.477027i | \(0.158285\pi\) | ||||
−0.878889 | + | 0.477027i | \(0.841715\pi\) | |||||||
\(102\) | −2061.32 | −0.198127 | ||||||||
\(103\) | 2229.35 | 0.210138 | 0.105069 | − | 0.994465i | \(-0.466494\pi\) | ||||
0.105069 | + | 0.994465i | \(0.466494\pi\) | |||||||
\(104\) | 1369.16 | 0.126586 | ||||||||
\(105\) | 7580.36i | 0.687561i | ||||||||
\(106\) | − | 1875.04i | − | 0.166878i | ||||||
\(107\) | 8911.94i | 0.778404i | 0.921152 | + | 0.389202i | \(0.127249\pi\) | ||||
−0.921152 | + | 0.389202i | \(0.872751\pi\) | |||||||
\(108\) | −1896.83 | −0.162623 | ||||||||
\(109\) | − | 8075.42i | − | 0.679692i | −0.940481 | − | 0.339846i | \(-0.889625\pi\) | ||
0.940481 | − | 0.339846i | \(-0.110375\pi\) | |||||||
\(110\) | 2560.21 | − | 1492.42i | 0.211588 | − | 0.123341i | ||||
\(111\) | −600.427 | −0.0487320 | ||||||||
\(112\) | − | 13424.6i | − | 1.07020i | ||||||
\(113\) | −16548.3 | −1.29597 | −0.647987 | − | 0.761652i | \(-0.724389\pi\) | ||||
−0.647987 | + | 0.761652i | \(0.724389\pi\) | |||||||
\(114\) | 656.651 | 0.0505272 | ||||||||
\(115\) | −10926.6 | −0.826206 | ||||||||
\(116\) | 19590.8i | 1.45592i | ||||||||
\(117\) | 795.223i | 0.0580921i | ||||||||
\(118\) | − | 2985.01i | − | 0.214379i | ||||||
\(119\) | 23629.8 | 1.66865 | ||||||||
\(120\) | 3756.75i | 0.260886i | ||||||||
\(121\) | −7214.38 | + | 12740.2i | −0.492752 | + | 0.870170i | ||||
\(122\) | 5946.46 | 0.399520 | ||||||||
\(123\) | 5594.95i | 0.369816i | ||||||||
\(124\) | 17298.5 | 1.12503 | ||||||||
\(125\) | −15678.8 | −1.00344 | ||||||||
\(126\) | −3988.22 | −0.251210 | ||||||||
\(127\) | 2165.25i | 0.134246i | 0.997745 | + | 0.0671228i | \(0.0213819\pi\) | ||||
−0.997745 | + | 0.0671228i | \(0.978618\pi\) | |||||||
\(128\) | − | 16709.2i | − | 1.01985i | ||||||
\(129\) | − | 9807.56i | − | 0.589361i | ||||||
\(130\) | 721.334 | 0.0426825 | ||||||||
\(131\) | − | 15267.4i | − | 0.889658i | −0.895616 | − | 0.444829i | \(-0.853264\pi\) | ||
0.895616 | − | 0.444829i | \(-0.146736\pi\) | |||||||
\(132\) | −4281.00 | − | 7343.94i | −0.245696 | − | 0.421484i | ||||
\(133\) | −7527.47 | −0.425545 | ||||||||
\(134\) | 1973.16i | 0.109888i | ||||||||
\(135\) | −2181.97 | −0.119724 | ||||||||
\(136\) | 11710.7 | 0.633146 | ||||||||
\(137\) | 10391.2 | 0.553636 | 0.276818 | − | 0.960922i | \(-0.410720\pi\) | ||||
0.276818 | + | 0.960922i | \(0.410720\pi\) | |||||||
\(138\) | − | 5748.74i | − | 0.301866i | ||||||
\(139\) | − | 21983.9i | − | 1.13782i | −0.822399 | − | 0.568911i | \(-0.807365\pi\) | ||
0.822399 | − | 0.568911i | \(-0.192635\pi\) | |||||||
\(140\) | − | 19723.8i | − | 1.00632i | ||||||
\(141\) | −8270.98 | −0.416024 | ||||||||
\(142\) | 5655.52i | 0.280476i | ||||||||
\(143\) | −3078.86 | + | 1794.76i | −0.150563 | + | 0.0877675i | ||||
\(144\) | 3864.20 | 0.186352 | ||||||||
\(145\) | 22535.7i | 1.07185i | ||||||||
\(146\) | 2756.98 | 0.129339 | ||||||||
\(147\) | 33242.7 | 1.53837 | ||||||||
\(148\) | 1562.29 | 0.0713243 | ||||||||
\(149\) | − | 10316.9i | − | 0.464705i | −0.972632 | − | 0.232353i | \(-0.925358\pi\) | ||
0.972632 | − | 0.232353i | \(-0.0746423\pi\) | |||||||
\(150\) | − | 3134.90i | − | 0.139329i | ||||||
\(151\) | 20057.9i | 0.879694i | 0.898073 | + | 0.439847i | \(0.144967\pi\) | ||||
−0.898073 | + | 0.439847i | \(0.855033\pi\) | |||||||
\(152\) | −3730.54 | −0.161467 | ||||||||
\(153\) | 6801.70i | 0.290559i | ||||||||
\(154\) | −9001.10 | − | 15441.1i | −0.379537 | − | 0.651085i | ||||
\(155\) | 19898.9 | 0.828258 | ||||||||
\(156\) | − | 2069.14i | − | 0.0850238i | ||||||
\(157\) | −5742.18 | −0.232958 | −0.116479 | − | 0.993193i | \(-0.537161\pi\) | ||||
−0.116479 | + | 0.993193i | \(0.537161\pi\) | |||||||
\(158\) | −10628.1 | −0.425735 | ||||||||
\(159\) | −6187.03 | −0.244730 | ||||||||
\(160\) | − | 15073.0i | − | 0.588787i | ||||||
\(161\) | 65900.3i | 2.54235i | ||||||||
\(162\) | − | 1147.99i | − | 0.0437428i | ||||||
\(163\) | −24660.6 | −0.928174 | −0.464087 | − | 0.885790i | \(-0.653617\pi\) | ||||
−0.464087 | + | 0.885790i | \(0.653617\pi\) | |||||||
\(164\) | − | 14557.8i | − | 0.541265i | ||||||
\(165\) | −4924.53 | − | 8447.89i | −0.180883 | − | 0.310299i | ||||
\(166\) | −13569.2 | −0.492423 | ||||||||
\(167\) | − | 47391.6i | − | 1.69930i | −0.527351 | − | 0.849648i | \(-0.676815\pi\) | ||
0.527351 | − | 0.849648i | \(-0.323185\pi\) | |||||||
\(168\) | 22657.7 | 0.802781 | ||||||||
\(169\) | 27693.5 | 0.969628 | ||||||||
\(170\) | 6169.71 | 0.213485 | ||||||||
\(171\) | − | 2166.74i | − | 0.0740995i | ||||||
\(172\) | 25518.9i | 0.862591i | ||||||||
\(173\) | − | 1326.29i | − | 0.0443147i | −0.999754 | − | 0.0221573i | \(-0.992947\pi\) | ||
0.999754 | − | 0.0221573i | \(-0.00705347\pi\) | |||||||
\(174\) | −11856.6 | −0.391617 | ||||||||
\(175\) | 35936.7i | 1.17344i | ||||||||
\(176\) | 8721.21 | + | 14961.0i | 0.281547 | + | 0.482986i | ||||
\(177\) | −9849.60 | −0.314392 | ||||||||
\(178\) | 14698.7i | 0.463916i | ||||||||
\(179\) | −53822.7 | −1.67981 | −0.839903 | − | 0.542736i | \(-0.817388\pi\) | ||||
−0.839903 | + | 0.542736i | \(0.817388\pi\) | |||||||
\(180\) | 5677.39 | 0.175228 | ||||||||
\(181\) | 9961.35 | 0.304061 | 0.152031 | − | 0.988376i | \(-0.451419\pi\) | ||||
0.152031 | + | 0.988376i | \(0.451419\pi\) | |||||||
\(182\) | − | 4350.51i | − | 0.131340i | ||||||
\(183\) | − | 19621.5i | − | 0.585907i | ||||||
\(184\) | 32659.5i | 0.964660i | ||||||||
\(185\) | 1797.13 | 0.0525094 | ||||||||
\(186\) | 10469.3i | 0.302616i | ||||||||
\(187\) | −26334.1 | + | 15350.9i | −0.753069 | + | 0.438986i | ||||
\(188\) | 21520.8 | 0.608894 | ||||||||
\(189\) | 13159.9i | 0.368407i | ||||||||
\(190\) | −1965.42 | −0.0544437 | ||||||||
\(191\) | −54964.8 | −1.50667 | −0.753335 | − | 0.657637i | \(-0.771556\pi\) | ||||
−0.753335 | + | 0.657637i | \(0.771556\pi\) | |||||||
\(192\) | −3968.40 | −0.107650 | ||||||||
\(193\) | − | 1722.76i | − | 0.0462498i | −0.999733 | − | 0.0231249i | \(-0.992638\pi\) | ||
0.999733 | − | 0.0231249i | \(-0.00736154\pi\) | |||||||
\(194\) | − | 17430.5i | − | 0.463133i | ||||||
\(195\) | − | 2380.18i | − | 0.0625950i | ||||||
\(196\) | −86496.1 | −2.25156 | ||||||||
\(197\) | − | 10387.5i | − | 0.267656i | −0.991005 | − | 0.133828i | \(-0.957273\pi\) | ||
0.991005 | − | 0.133828i | \(-0.0427270\pi\) | |||||||
\(198\) | 4444.65 | − | 2590.92i | 0.113372 | − | 0.0660881i | ||||
\(199\) | 50964.3 | 1.28695 | 0.643473 | − | 0.765469i | \(-0.277493\pi\) | ||||
0.643473 | + | 0.765469i | \(0.277493\pi\) | |||||||
\(200\) | 17809.9i | 0.445246i | ||||||||
\(201\) | 6510.79 | 0.161154 | ||||||||
\(202\) | 15325.9 | 0.375597 | ||||||||
\(203\) | 135917. | 3.29824 | ||||||||
\(204\) | − | 17697.8i | − | 0.425263i | ||||||
\(205\) | − | 16746.2i | − | 0.398482i | ||||||
\(206\) | − | 3510.66i | − | 0.0827283i | ||||||
\(207\) | −18969.0 | −0.442695 | ||||||||
\(208\) | 4215.23i | 0.0974304i | ||||||||
\(209\) | 8388.95 | − | 4890.17i | 0.192050 | − | 0.111952i | ||||
\(210\) | 11937.1 | 0.270683 | ||||||||
\(211\) | − | 68681.5i | − | 1.54268i | −0.636426 | − | 0.771338i | \(-0.719588\pi\) | ||
0.636426 | − | 0.771338i | \(-0.280412\pi\) | |||||||
\(212\) | 16098.4 | 0.358188 | ||||||||
\(213\) | 18661.4 | 0.411326 | ||||||||
\(214\) | 14034.0 | 0.306446 | ||||||||
\(215\) | 29355.0i | 0.635045i | ||||||||
\(216\) | 6521.90i | 0.139787i | ||||||||
\(217\) | − | 120014.i | − | 2.54866i | ||||||
\(218\) | −12716.7 | −0.267585 | ||||||||
\(219\) | − | 9097.18i | − | 0.189679i | ||||||
\(220\) | 12813.4 | + | 21981.1i | 0.264740 | + | 0.454155i | ||||
\(221\) | −7419.57 | −0.151913 | ||||||||
\(222\) | 945.517i | 0.0191851i | ||||||||
\(223\) | −1628.89 | −0.0327553 | −0.0163777 | − | 0.999866i | \(-0.505213\pi\) | ||||
−0.0163777 | + | 0.999866i | \(0.505213\pi\) | |||||||
\(224\) | −90907.9 | −1.81178 | ||||||||
\(225\) | −10344.2 | −0.204329 | ||||||||
\(226\) | 26059.3i | 0.510206i | ||||||||
\(227\) | − | 42599.1i | − | 0.826701i | −0.910572 | − | 0.413351i | \(-0.864358\pi\) | ||
0.910572 | − | 0.413351i | \(-0.135642\pi\) | |||||||
\(228\) | 5637.78i | 0.108452i | ||||||||
\(229\) | 32387.8 | 0.617605 | 0.308802 | − | 0.951126i | \(-0.400072\pi\) | ||||
0.308802 | + | 0.951126i | \(0.400072\pi\) | |||||||
\(230\) | 17206.5i | 0.325265i | ||||||||
\(231\) | −50950.9 | + | 29700.8i | −0.954834 | + | 0.556601i | ||||
\(232\) | 67359.3 | 1.25147 | ||||||||
\(233\) | 57867.1i | 1.06591i | 0.846144 | + | 0.532954i | \(0.178918\pi\) | ||||
−0.846144 | + | 0.532954i | \(0.821082\pi\) | |||||||
\(234\) | 1252.27 | 0.0228700 | ||||||||
\(235\) | 24755.8 | 0.448272 | ||||||||
\(236\) | 25628.3 | 0.460146 | ||||||||
\(237\) | 35069.3i | 0.624352i | ||||||||
\(238\) | − | 37210.8i | − | 0.656923i | ||||||
\(239\) | 3758.46i | 0.0657982i | 0.999459 | + | 0.0328991i | \(0.0104740\pi\) | ||||
−0.999459 | + | 0.0328991i | \(0.989526\pi\) | |||||||
\(240\) | −11565.9 | −0.200797 | ||||||||
\(241\) | − | 53393.2i | − | 0.919288i | −0.888103 | − | 0.459644i | \(-0.847977\pi\) | ||
0.888103 | − | 0.459644i | \(-0.152023\pi\) | |||||||
\(242\) | 20062.5 | + | 11360.8i | 0.342573 | + | 0.193989i | ||||
\(243\) | −3788.00 | −0.0641500 | ||||||||
\(244\) | 51054.3i | 0.857536i | ||||||||
\(245\) | −99498.4 | −1.65762 | ||||||||
\(246\) | 8810.60 | 0.145591 | ||||||||
\(247\) | 2363.57 | 0.0387414 | ||||||||
\(248\) | − | 59477.8i | − | 0.967056i | ||||||
\(249\) | 44774.1i | 0.722151i | ||||||||
\(250\) | 24690.1i | 0.395041i | ||||||||
\(251\) | 1857.31 | 0.0294807 | 0.0147403 | − | 0.999891i | \(-0.495308\pi\) | ||||
0.0147403 | + | 0.999891i | \(0.495308\pi\) | |||||||
\(252\) | − | 34241.5i | − | 0.539201i | ||||||
\(253\) | −42811.7 | − | 73442.2i | −0.668838 | − | 1.14737i | ||||
\(254\) | 3409.70 | 0.0528505 | ||||||||
\(255\) | − | 20358.1i | − | 0.313081i | ||||||
\(256\) | −14093.2 | −0.215046 | ||||||||
\(257\) | −1262.77 | −0.0191187 | −0.00955933 | − | 0.999954i | \(-0.503043\pi\) | ||||
−0.00955933 | + | 0.999954i | \(0.503043\pi\) | |||||||
\(258\) | −15444.4 | −0.232023 | ||||||||
\(259\) | − | 10838.9i | − | 0.161579i | ||||||
\(260\) | 6193.13i | 0.0916143i | ||||||||
\(261\) | 39123.1i | 0.574317i | ||||||||
\(262\) | −24042.2 | −0.350245 | ||||||||
\(263\) | 118343.i | 1.71092i | 0.517870 | + | 0.855459i | \(0.326725\pi\) | ||||
−0.517870 | + | 0.855459i | \(0.673275\pi\) | |||||||
\(264\) | −25250.8 | + | 14719.4i | −0.362299 | + | 0.211195i | ||||
\(265\) | 18518.4 | 0.263700 | ||||||||
\(266\) | 11853.8i | 0.167531i | ||||||||
\(267\) | 48501.1 | 0.680345 | ||||||||
\(268\) | −16940.8 | −0.235866 | ||||||||
\(269\) | 100514. | 1.38906 | 0.694528 | − | 0.719465i | \(-0.255613\pi\) | ||||
0.694528 | + | 0.719465i | \(0.255613\pi\) | |||||||
\(270\) | 3436.03i | 0.0471335i | ||||||||
\(271\) | 138354.i | 1.88389i | 0.335773 | + | 0.941943i | \(0.391003\pi\) | ||||
−0.335773 | + | 0.941943i | \(0.608997\pi\) | |||||||
\(272\) | 36053.7i | 0.487317i | ||||||||
\(273\) | −14355.3 | −0.192614 | ||||||||
\(274\) | − | 16363.5i | − | 0.217958i | ||||||
\(275\) | −23346.0 | − | 40049.4i | −0.308707 | − | 0.529579i | ||||
\(276\) | 49356.7 | 0.647930 | ||||||||
\(277\) | − | 40696.2i | − | 0.530388i | −0.964195 | − | 0.265194i | \(-0.914564\pi\) | ||
0.964195 | − | 0.265194i | \(-0.0854360\pi\) | |||||||
\(278\) | −34618.9 | −0.447944 | ||||||||
\(279\) | 34545.4 | 0.443795 | ||||||||
\(280\) | −67816.6 | −0.865008 | ||||||||
\(281\) | − | 17381.6i | − | 0.220129i | −0.993924 | − | 0.110065i | \(-0.964894\pi\) | ||
0.993924 | − | 0.110065i | \(-0.0351058\pi\) | |||||||
\(282\) | 13024.6i | 0.163783i | ||||||||
\(283\) | 102799.i | 1.28355i | 0.766891 | + | 0.641777i | \(0.221802\pi\) | ||||
−0.766891 | + | 0.641777i | \(0.778198\pi\) | |||||||
\(284\) | −48556.3 | −0.602018 | ||||||||
\(285\) | 6485.26i | 0.0798432i | ||||||||
\(286\) | 2826.28 | + | 4848.40i | 0.0345528 | + | 0.0592743i | ||||
\(287\) | −101000. | −1.22619 | ||||||||
\(288\) | − | 26167.4i | − | 0.315482i | ||||||
\(289\) | 20059.9 | 0.240178 | ||||||||
\(290\) | 35487.9 | 0.421973 | ||||||||
\(291\) | −57515.1 | −0.679197 | ||||||||
\(292\) | 23670.5i | 0.277614i | ||||||||
\(293\) | − | 106779.i | − | 1.24380i | −0.783098 | − | 0.621898i | \(-0.786362\pi\) | ||
0.783098 | − | 0.621898i | \(-0.213638\pi\) | |||||||
\(294\) | − | 52348.6i | − | 0.605634i | ||||||
\(295\) | 29480.8 | 0.338762 | ||||||||
\(296\) | − | 5371.64i | − | 0.0613088i | ||||||
\(297\) | −8549.21 | − | 14665.9i | −0.0969200 | − | 0.166264i | ||||
\(298\) | −16246.5 | −0.182948 | ||||||||
\(299\) | − | 20692.2i | − | 0.231454i | ||||||
\(300\) | 26915.1 | 0.299057 | ||||||||
\(301\) | 177045. | 1.95412 | ||||||||
\(302\) | 31586.0 | 0.346322 | ||||||||
\(303\) | − | 50570.5i | − | 0.550823i | ||||||
\(304\) | − | 11485.2i | − | 0.124277i | ||||||
\(305\) | 58728.8i | 0.631323i | ||||||||
\(306\) | 10710.9 | 0.114389 | ||||||||
\(307\) | − | 78416.1i | − | 0.832010i | −0.909362 | − | 0.416005i | \(-0.863430\pi\) | ||
0.909362 | − | 0.416005i | \(-0.136570\pi\) | |||||||
\(308\) | 132572. | − | 77280.3i | 1.39750 | − | 0.814643i | ||||
\(309\) | −11584.1 | −0.121323 | ||||||||
\(310\) | − | 31335.6i | − | 0.326073i | ||||||
\(311\) | −60684.2 | −0.627415 | −0.313707 | − | 0.949520i | \(-0.601571\pi\) | ||||
−0.313707 | + | 0.949520i | \(0.601571\pi\) | |||||||
\(312\) | −7114.35 | −0.0730846 | ||||||||
\(313\) | −85739.0 | −0.875165 | −0.437582 | − | 0.899178i | \(-0.644165\pi\) | ||||
−0.437582 | + | 0.899178i | \(0.644165\pi\) | |||||||
\(314\) | 9042.45i | 0.0917121i | ||||||||
\(315\) | − | 39388.7i | − | 0.396963i | ||||||
\(316\) | − | 91248.9i | − | 0.913804i | ||||||
\(317\) | 117644. | 1.17071 | 0.585357 | − | 0.810776i | \(-0.300955\pi\) | ||||
0.585357 | + | 0.810776i | \(0.300955\pi\) | |||||||
\(318\) | 9742.97i | 0.0963468i | ||||||||
\(319\) | −151472. | + | 88297.8i | −1.48851 | + | 0.867698i | ||||
\(320\) | 11877.8 | 0.115994 | ||||||||
\(321\) | − | 46307.8i | − | 0.449412i | ||||||
\(322\) | 103776. | 1.00089 | ||||||||
\(323\) | 20216.1 | 0.193773 | ||||||||
\(324\) | 9856.22 | 0.0938902 | ||||||||
\(325\) | − | 11283.8i | − | 0.106829i | ||||||
\(326\) | 38834.1i | 0.365408i | ||||||||
\(327\) | 41961.1i | 0.392420i | ||||||||
\(328\) | −50054.5 | −0.465259 | ||||||||
\(329\) | − | 149307.i | − | 1.37940i | ||||||
\(330\) | −13303.2 | + | 7754.86i | −0.122160 | + | 0.0712108i | ||||
\(331\) | −109718. | −1.00143 | −0.500717 | − | 0.865611i | \(-0.666930\pi\) | ||||
−0.500717 | + | 0.865611i | \(0.666930\pi\) | |||||||
\(332\) | − | 116501.i | − | 1.05694i | ||||||
\(333\) | 3119.91 | 0.0281354 | ||||||||
\(334\) | −74629.6 | −0.668988 | ||||||||
\(335\) | −19487.4 | −0.173646 | ||||||||
\(336\) | 69756.3i | 0.617881i | ||||||||
\(337\) | − | 73221.5i | − | 0.644731i | −0.946615 | − | 0.322365i | \(-0.895522\pi\) | ||
0.946615 | − | 0.322365i | \(-0.104478\pi\) | |||||||
\(338\) | − | 43610.2i | − | 0.381728i | ||||||
\(339\) | 85987.4 | 0.748230 | ||||||||
\(340\) | 52971.1i | 0.458227i | ||||||||
\(341\) | 77966.3 | + | 133749.i | 0.670499 | + | 1.15022i | ||||
\(342\) | −3412.06 | −0.0291719 | ||||||||
\(343\) | 374879.i | 3.18642i | ||||||||
\(344\) | 87742.0 | 0.741465 | ||||||||
\(345\) | 56776.1 | 0.477010 | ||||||||
\(346\) | −2088.57 | −0.0174460 | ||||||||
\(347\) | 160256.i | 1.33093i | 0.746428 | + | 0.665466i | \(0.231767\pi\) | ||||
−0.746428 | + | 0.665466i | \(0.768233\pi\) | |||||||
\(348\) | − | 101797.i | − | 0.840573i | ||||||
\(349\) | − | 24791.6i | − | 0.203542i | −0.994808 | − | 0.101771i | \(-0.967549\pi\) | ||
0.994808 | − | 0.101771i | \(-0.0324509\pi\) | |||||||
\(350\) | 56590.9 | 0.461967 | ||||||||
\(351\) | − | 4132.10i | − | 0.0335395i | ||||||
\(352\) | 101312. | − | 59057.7i | 0.817664 | − | 0.476641i | ||||
\(353\) | −140695. | −1.12909 | −0.564547 | − | 0.825401i | \(-0.690949\pi\) | ||||
−0.564547 | + | 0.825401i | \(0.690949\pi\) | |||||||
\(354\) | 15510.6i | 0.123772i | ||||||||
\(355\) | −55855.4 | −0.443209 | ||||||||
\(356\) | −126198. | −0.995756 | ||||||||
\(357\) | −122784. | −0.963396 | ||||||||
\(358\) | 84756.8i | 0.661315i | ||||||||
\(359\) | 14603.5i | 0.113310i | 0.998394 | + | 0.0566552i | \(0.0180436\pi\) | ||||
−0.998394 | + | 0.0566552i | \(0.981956\pi\) | |||||||
\(360\) | − | 19520.7i | − | 0.150622i | ||||||
\(361\) | 123881. | 0.950583 | ||||||||
\(362\) | − | 15686.5i | − | 0.119704i | ||||||
\(363\) | 37487.0 | − | 66199.8i | 0.284491 | − | 0.502393i | ||||
\(364\) | 37352.0 | 0.281910 | ||||||||
\(365\) | 27228.7i | 0.204381i | ||||||||
\(366\) | −30898.7 | −0.230663 | ||||||||
\(367\) | −168034. | −1.24757 | −0.623785 | − | 0.781596i | \(-0.714406\pi\) | ||||
−0.623785 | + | 0.781596i | \(0.714406\pi\) | |||||||
\(368\) | −100549. | −0.742475 | ||||||||
\(369\) | − | 29072.2i | − | 0.213514i | ||||||
\(370\) | − | 2830.02i | − | 0.0206722i | ||||||
\(371\) | − | 111688.i | − | 0.811443i | ||||||
\(372\) | −89885.8 | −0.649539 | ||||||||
\(373\) | 179739.i | 1.29189i | 0.763385 | + | 0.645944i | \(0.223536\pi\) | ||||
−0.763385 | + | 0.645944i | \(0.776464\pi\) | |||||||
\(374\) | 24173.7 | + | 41469.3i | 0.172822 | + | 0.296472i | ||||
\(375\) | 81469.5 | 0.579339 | ||||||||
\(376\) | − | 73995.2i | − | 0.523393i | ||||||
\(377\) | −42677.0 | −0.300270 | ||||||||
\(378\) | 20723.4 | 0.145036 | ||||||||
\(379\) | −88424.0 | −0.615590 | −0.307795 | − | 0.951453i | \(-0.599591\pi\) | ||||
−0.307795 | + | 0.951453i | \(0.599591\pi\) | |||||||
\(380\) | − | 16874.4i | − | 0.116859i | ||||||
\(381\) | − | 11251.0i | − | 0.0775067i | ||||||
\(382\) | 86555.4i | 0.593154i | ||||||||
\(383\) | 95956.7 | 0.654151 | 0.327075 | − | 0.944998i | \(-0.393937\pi\) | ||||
0.327075 | + | 0.944998i | \(0.393937\pi\) | |||||||
\(384\) | 86823.8i | 0.588811i | ||||||||
\(385\) | 152501. | − | 88897.3i | 1.02885 | − | 0.599745i | ||||
\(386\) | −2712.90 | −0.0182079 | ||||||||
\(387\) | 50961.6i | 0.340268i | ||||||||
\(388\) | 149652. | 0.994075 | ||||||||
\(389\) | −118749. | −0.784747 | −0.392373 | − | 0.919806i | \(-0.628346\pi\) | ||||
−0.392373 | + | 0.919806i | \(0.628346\pi\) | |||||||
\(390\) | −3748.16 | −0.0246428 | ||||||||
\(391\) | − | 176985.i | − | 1.15766i | ||||||
\(392\) | 297401.i | 1.93540i | ||||||||
\(393\) | 79331.8i | 0.513644i | ||||||||
\(394\) | −16357.6 | −0.105372 | ||||||||
\(395\) | − | 104966.i | − | 0.672748i | ||||||
\(396\) | 22244.7 | + | 38160.2i | 0.141852 | + | 0.243344i | ||||
\(397\) | −159427. | −1.01154 | −0.505768 | − | 0.862670i | \(-0.668791\pi\) | ||||
−0.505768 | + | 0.862670i | \(0.668791\pi\) | |||||||
\(398\) | − | 80255.6i | − | 0.506652i | ||||||
\(399\) | 39113.9 | 0.245689 | ||||||||
\(400\) | −54831.2 | −0.342695 | ||||||||
\(401\) | −41646.5 | −0.258994 | −0.129497 | − | 0.991580i | \(-0.541336\pi\) | ||||
−0.129497 | + | 0.991580i | \(0.541336\pi\) | |||||||
\(402\) | − | 10252.8i | − | 0.0634441i | ||||||
\(403\) | 37683.5i | 0.232029i | ||||||||
\(404\) | 131583.i | 0.806186i | ||||||||
\(405\) | 11337.8 | 0.0691225 | ||||||||
\(406\) | − | 214035.i | − | 1.29847i | ||||||
\(407\) | 7041.40 | + | 12079.3i | 0.0425079 | + | 0.0729212i | ||||
\(408\) | −60850.5 | −0.365547 | ||||||||
\(409\) | − | 265054.i | − | 1.58449i | −0.610206 | − | 0.792243i | \(-0.708913\pi\) | ||
0.610206 | − | 0.792243i | \(-0.291087\pi\) | |||||||
\(410\) | −26371.0 | −0.156877 | ||||||||
\(411\) | −53994.3 | −0.319642 | ||||||||
\(412\) | 30141.3 | 0.177569 | ||||||||
\(413\) | − | 177804.i | − | 1.04242i | ||||||
\(414\) | 29871.3i | 0.174283i | ||||||||
\(415\) | − | 134013.i | − | 0.778128i | ||||||
\(416\) | 28544.4 | 0.164943 | ||||||||
\(417\) | 114232.i | 0.656922i | ||||||||
\(418\) | −7700.76 | − | 13210.4i | −0.0440738 | − | 0.0756074i | ||||
\(419\) | 255711. | 1.45654 | 0.728270 | − | 0.685291i | \(-0.240325\pi\) | ||||
0.728270 | + | 0.685291i | \(0.240325\pi\) | |||||||
\(420\) | 102488.i | 0.580997i | ||||||||
\(421\) | 189209. | 1.06753 | 0.533763 | − | 0.845634i | \(-0.320778\pi\) | ||||
0.533763 | + | 0.845634i | \(0.320778\pi\) | |||||||
\(422\) | −108156. | −0.607329 | ||||||||
\(423\) | 42977.3 | 0.240192 | ||||||||
\(424\) | − | 55351.4i | − | 0.307891i | ||||||
\(425\) | − | 96513.0i | − | 0.534328i | ||||||
\(426\) | − | 29386.9i | − | 0.161933i | ||||||
\(427\) | 354205. | 1.94267 | ||||||||
\(428\) | 120491.i | 0.657760i | ||||||||
\(429\) | 15998.2 | − | 9325.83i | 0.0869274 | − | 0.0506726i | ||||
\(430\) | 46226.5 | 0.250008 | ||||||||
\(431\) | − | 110749.i | − | 0.596190i | −0.954536 | − | 0.298095i | \(-0.903649\pi\) | ||
0.954536 | − | 0.298095i | \(-0.0963512\pi\) | |||||||
\(432\) | −20079.0 | −0.107591 | ||||||||
\(433\) | 172877. | 0.922062 | 0.461031 | − | 0.887384i | \(-0.347480\pi\) | ||||
0.461031 | + | 0.887384i | \(0.347480\pi\) | |||||||
\(434\) | −188991. | −1.00337 | ||||||||
\(435\) | − | 117099.i | − | 0.618835i | ||||||
\(436\) | − | 109181.i | − | 0.574348i | ||||||
\(437\) | 56380.0i | 0.295231i | ||||||||
\(438\) | −14325.7 | −0.0746737 | ||||||||
\(439\) | 155214.i | 0.805383i | 0.915336 | + | 0.402691i | \(0.131925\pi\) | ||||
−0.915336 | + | 0.402691i | \(0.868075\pi\) | |||||||
\(440\) | 75577.9 | − | 44056.6i | 0.390382 | − | 0.227565i | ||||
\(441\) | −172734. | −0.888179 | ||||||||
\(442\) | 11683.9i | 0.0598058i | ||||||||
\(443\) | 104175. | 0.530828 | 0.265414 | − | 0.964134i | \(-0.414491\pi\) | ||||
0.265414 | + | 0.964134i | \(0.414491\pi\) | |||||||
\(444\) | −8117.88 | −0.0411791 | ||||||||
\(445\) | −145168. | −0.733082 | ||||||||
\(446\) | 2565.08i | 0.0128953i | ||||||||
\(447\) | 53608.3i | 0.268298i | ||||||||
\(448\) | − | 71637.3i | − | 0.356930i | ||||||
\(449\) | 88086.4 | 0.436934 | 0.218467 | − | 0.975844i | \(-0.429894\pi\) | ||||
0.218467 | + | 0.975844i | \(0.429894\pi\) | |||||||
\(450\) | 16289.4i | 0.0804415i | ||||||||
\(451\) | 112559. | − | 65613.8i | 0.553383 | − | 0.322583i | ||||
\(452\) | −223736. | −1.09511 | ||||||||
\(453\) | − | 104224.i | − | 0.507891i | ||||||
\(454\) | −67082.5 | −0.325460 | ||||||||
\(455\) | 42966.8 | 0.207544 | ||||||||
\(456\) | 19384.5 | 0.0932232 | ||||||||
\(457\) | 77946.3i | 0.373219i | 0.982434 | + | 0.186609i | \(0.0597499\pi\) | ||||
−0.982434 | + | 0.186609i | \(0.940250\pi\) | |||||||
\(458\) | − | 51002.4i | − | 0.243142i | ||||||
\(459\) | − | 35342.7i | − | 0.167754i | ||||||
\(460\) | −147729. | −0.698154 | ||||||||
\(461\) | 115963.i | 0.545653i | 0.962063 | + | 0.272827i | \(0.0879586\pi\) | ||||
−0.962063 | + | 0.272827i | \(0.912041\pi\) | |||||||
\(462\) | 46771.1 | + | 80234.5i | 0.219126 | + | 0.375904i | ||||
\(463\) | −313839. | −1.46401 | −0.732007 | − | 0.681297i | \(-0.761416\pi\) | ||||
−0.732007 | + | 0.681297i | \(0.761416\pi\) | |||||||
\(464\) | 207379.i | 0.963228i | ||||||||
\(465\) | −103398. | −0.478195 | ||||||||
\(466\) | 91125.7 | 0.419632 | ||||||||
\(467\) | −96033.3 | −0.440340 | −0.220170 | − | 0.975462i | \(-0.570661\pi\) | ||||
−0.220170 | + | 0.975462i | \(0.570661\pi\) | |||||||
\(468\) | 10751.6i | 0.0490885i | ||||||||
\(469\) | 117532.i | 0.534333i | ||||||||
\(470\) | − | 38984.0i | − | 0.176478i | ||||||
\(471\) | 29837.2 | 0.134498 | ||||||||
\(472\) | − | 88118.1i | − | 0.395532i | ||||||
\(473\) | −197307. | + | 115016.i | −0.881904 | + | 0.514088i | ||||
\(474\) | 55225.0 | 0.245798 | ||||||||
\(475\) | 30745.1i | 0.136266i | ||||||||
\(476\) | 319479. | 1.41003 | ||||||||
\(477\) | 32148.7 | 0.141295 | ||||||||
\(478\) | 5918.60 | 0.0259038 | ||||||||
\(479\) | 215693.i | 0.940082i | 0.882645 | + | 0.470041i | \(0.155761\pi\) | ||||
−0.882645 | + | 0.470041i | \(0.844239\pi\) | |||||||
\(480\) | 78321.4i | 0.339936i | ||||||||
\(481\) | 3403.32i | 0.0147100i | ||||||||
\(482\) | −84080.5 | −0.361910 | ||||||||
\(483\) | − | 342428.i | − | 1.46783i | ||||||
\(484\) | −97539.8 | + | 172249.i | −0.416381 | + | 0.735304i | ||||
\(485\) | 172148. | 0.731844 | ||||||||
\(486\) | 5965.11i | 0.0252549i | ||||||||
\(487\) | −281250. | −1.18587 | −0.592933 | − | 0.805252i | \(-0.702030\pi\) | ||||
−0.592933 | + | 0.805252i | \(0.702030\pi\) | |||||||
\(488\) | 175541. | 0.737120 | ||||||||
\(489\) | 128140. | 0.535881 | ||||||||
\(490\) | 156684.i | 0.652579i | ||||||||
\(491\) | − | 229094.i | − | 0.950279i | −0.879910 | − | 0.475139i | \(-0.842398\pi\) | ||
0.879910 | − | 0.475139i | \(-0.157602\pi\) | |||||||
\(492\) | 75644.8i | 0.312499i | ||||||||
\(493\) | −365025. | −1.50186 | ||||||||
\(494\) | − | 3722.01i | − | 0.0152519i | ||||||
\(495\) | 25588.6 | + | 43896.5i | 0.104433 | + | 0.179151i | ||||
\(496\) | 183114. | 0.744319 | ||||||||
\(497\) | 336875.i | 1.36382i | ||||||||
\(498\) | 70507.6 | 0.284300 | ||||||||
\(499\) | 37652.6 | 0.151215 | 0.0756073 | − | 0.997138i | \(-0.475910\pi\) | ||||
0.0756073 | + | 0.997138i | \(0.475910\pi\) | |||||||
\(500\) | −211981. | −0.847922 | ||||||||
\(501\) | 246254.i | 0.981088i | ||||||||
\(502\) | − | 2924.79i | − | 0.0116061i | ||||||
\(503\) | − | 353544.i | − | 1.39736i | −0.715435 | − | 0.698679i | \(-0.753772\pi\) | ||
0.715435 | − | 0.698679i | \(-0.246228\pi\) | |||||||
\(504\) | −117733. | −0.463486 | ||||||||
\(505\) | 151362.i | 0.593519i | ||||||||
\(506\) | −115653. | + | 67417.3i | −0.451704 | + | 0.263312i | ||||
\(507\) | −143900. | −0.559815 | ||||||||
\(508\) | 29274.6i | 0.113439i | ||||||||
\(509\) | −240356. | −0.927727 | −0.463864 | − | 0.885907i | \(-0.653537\pi\) | ||||
−0.463864 | + | 0.885907i | \(0.653537\pi\) | |||||||
\(510\) | −32058.8 | −0.123256 | ||||||||
\(511\) | 164222. | 0.628910 | ||||||||
\(512\) | − | 245155.i | − | 0.935191i | ||||||
\(513\) | 11258.7i | 0.0427814i | ||||||||
\(514\) | 1988.53i | 0.00752673i | ||||||||
\(515\) | 34672.2 | 0.130727 | ||||||||
\(516\) | − | 132600.i | − | 0.498017i | ||||||
\(517\) | 96996.4 | + | 166395.i | 0.362889 | + | 0.622527i | ||||
\(518\) | −17068.4 | −0.0636112 | ||||||||
\(519\) | 6891.62i | 0.0255851i | ||||||||
\(520\) | 21293.9 | 0.0787497 | ||||||||
\(521\) | 484627. | 1.78539 | 0.892693 | − | 0.450666i | \(-0.148813\pi\) | ||||
0.892693 | + | 0.450666i | \(0.148813\pi\) | |||||||
\(522\) | 61608.7 | 0.226100 | ||||||||
\(523\) | 188211.i | 0.688084i | 0.938954 | + | 0.344042i | \(0.111796\pi\) | ||||
−0.938954 | + | 0.344042i | \(0.888204\pi\) | |||||||
\(524\) | − | 206418.i | − | 0.751771i | ||||||
\(525\) | − | 186732.i | − | 0.677487i | ||||||
\(526\) | 186359. | 0.673564 | ||||||||
\(527\) | 322315.i | 1.16054i | ||||||||
\(528\) | −45316.7 | − | 77739.6i | −0.162551 | − | 0.278852i | ||||
\(529\) | 213746. | 0.763811 | ||||||||
\(530\) | − | 29161.6i | − | 0.103815i | ||||||
\(531\) | 51180.0 | 0.181515 | ||||||||
\(532\) | −101773. | −0.359591 | ||||||||
\(533\) | 31713.2 | 0.111631 | ||||||||
\(534\) | − | 76376.8i | − | 0.267842i | ||||||
\(535\) | 138604.i | 0.484247i | ||||||||
\(536\) | 58247.9i | 0.202745i | ||||||||
\(537\) | 279671. | 0.969837 | ||||||||
\(538\) | − | 158283.i | − | 0.546851i | ||||||
\(539\) | −389847. | − | 668772.i | −1.34189 | − | 2.30197i | ||||
\(540\) | −29500.6 | −0.101168 | ||||||||
\(541\) | − | 329143.i | − | 1.12458i | −0.826940 | − | 0.562290i | \(-0.809920\pi\) | ||
0.826940 | − | 0.562290i | \(-0.190080\pi\) | |||||||
\(542\) | 217873. | 0.741658 | ||||||||
\(543\) | −51760.7 | −0.175550 | ||||||||
\(544\) | 244146. | 0.824996 | ||||||||
\(545\) | − | 125594.i | − | 0.422838i | ||||||
\(546\) | 22605.9i | 0.0758292i | ||||||||
\(547\) | 201214.i | 0.672486i | 0.941775 | + | 0.336243i | \(0.109156\pi\) | ||||
−0.941775 | + | 0.336243i | \(0.890844\pi\) | |||||||
\(548\) | 140491. | 0.467829 | ||||||||
\(549\) | 101956.i | 0.338274i | ||||||||
\(550\) | −63067.5 | + | 36763.9i | −0.208488 | + | 0.121534i | ||||
\(551\) | 116282. | 0.383010 | ||||||||
\(552\) | − | 169704.i | − | 0.556947i | ||||||
\(553\) | −633068. | −2.07014 | ||||||||
\(554\) | −64085.9 | −0.208806 | ||||||||
\(555\) | −9338.18 | −0.0303163 | ||||||||
\(556\) | − | 297226.i | − | 0.961474i | ||||||
\(557\) | 52859.7i | 0.170378i | 0.996365 | + | 0.0851892i | \(0.0271495\pi\) | ||||
−0.996365 | + | 0.0851892i | \(0.972851\pi\) | |||||||
\(558\) | − | 54400.1i | − | 0.174715i | ||||||
\(559\) | −55591.0 | −0.177902 | ||||||||
\(560\) | − | 208787.i | − | 0.665775i | ||||||
\(561\) | 136836. | − | 79765.7i | 0.434784 | − | 0.253449i | ||||
\(562\) | −27371.5 | −0.0866616 | ||||||||
\(563\) | − | 143681.i | − | 0.453295i | −0.973977 | − | 0.226648i | \(-0.927223\pi\) | ||
0.973977 | − | 0.226648i | \(-0.0727766\pi\) | |||||||
\(564\) | −111825. | −0.351545 | ||||||||
\(565\) | −257368. | −0.806229 | ||||||||
\(566\) | 161881. | 0.505316 | ||||||||
\(567\) | − | 68380.6i | − | 0.212700i | ||||||
\(568\) | 166952.i | 0.517481i | ||||||||
\(569\) | 568025.i | 1.75446i | 0.480071 | + | 0.877230i | \(0.340611\pi\) | ||||
−0.480071 | + | 0.877230i | \(0.659389\pi\) | |||||||
\(570\) | 10212.6 | 0.0314331 | ||||||||
\(571\) | − | 165896.i | − | 0.508818i | −0.967097 | − | 0.254409i | \(-0.918119\pi\) | ||
0.967097 | − | 0.254409i | \(-0.0818810\pi\) | |||||||
\(572\) | −41626.7 | + | 24265.5i | −0.127227 | + | 0.0741645i | ||||
\(573\) | 285606. | 0.869876 | ||||||||
\(574\) | 159048.i | 0.482731i | ||||||||
\(575\) | 269162. | 0.814100 | ||||||||
\(576\) | 20620.4 | 0.0621516 | ||||||||
\(577\) | 157238. | 0.472286 | 0.236143 | − | 0.971718i | \(-0.424117\pi\) | ||||
0.236143 | + | 0.971718i | \(0.424117\pi\) | |||||||
\(578\) | − | 31589.2i | − | 0.0945547i | ||||||
\(579\) | 8951.72i | 0.0267023i | ||||||||
\(580\) | 304687.i | 0.905729i | ||||||||
\(581\) | −808259. | −2.39441 | ||||||||
\(582\) | 90571.4i | 0.267390i | ||||||||
\(583\) | 72557.3 | + | 124470.i | 0.213473 | + | 0.366208i | ||||
\(584\) | 81386.6 | 0.238631 | ||||||||
\(585\) | 12367.8i | 0.0361393i | ||||||||
\(586\) | −168149. | −0.489664 | ||||||||
\(587\) | 9552.74 | 0.0277237 | 0.0138619 | − | 0.999904i | \(-0.495587\pi\) | ||||
0.0138619 | + | 0.999904i | \(0.495587\pi\) | |||||||
\(588\) | 449447. | 1.29994 | ||||||||
\(589\) | − | 102676.i | − | 0.295964i | ||||||
\(590\) | − | 46424.6i | − | 0.133366i | ||||||
\(591\) | 53974.9i | 0.154531i | ||||||||
\(592\) | 16537.7 | 0.0471879 | ||||||||
\(593\) | − | 164511.i | − | 0.467827i | −0.972257 | − | 0.233913i | \(-0.924847\pi\) | ||
0.972257 | − | 0.233913i | \(-0.0751532\pi\) | |||||||
\(594\) | −23095.1 | + | 13462.8i | −0.0654555 | + | 0.0381560i | ||||
\(595\) | 367503. | 1.03807 | ||||||||
\(596\) | − | 139487.i | − | 0.392681i | ||||||
\(597\) | −264818. | −0.743018 | ||||||||
\(598\) | −32584.9 | −0.0911200 | ||||||||
\(599\) | 318614. | 0.887996 | 0.443998 | − | 0.896028i | \(-0.353560\pi\) | ||||
0.443998 | + | 0.896028i | \(0.353560\pi\) | |||||||
\(600\) | − | 92542.7i | − | 0.257063i | ||||||
\(601\) | − | 385872.i | − | 1.06830i | −0.845389 | − | 0.534151i | \(-0.820631\pi\) | ||
0.845389 | − | 0.534151i | \(-0.179369\pi\) | |||||||
\(602\) | − | 278801.i | − | 0.769310i | ||||||
\(603\) | −33831.1 | −0.0930425 | ||||||||
\(604\) | 271187.i | 0.743351i | ||||||||
\(605\) | −112202. | + | 198142.i | −0.306542 | + | 0.541335i | ||||
\(606\) | −79635.5 | −0.216851 | ||||||||
\(607\) | 218753.i | 0.593712i | 0.954922 | + | 0.296856i | \(0.0959381\pi\) | ||||
−0.954922 | + | 0.296856i | \(0.904062\pi\) | |||||||
\(608\) | −77774.9 | −0.210394 | ||||||||
\(609\) | −706247. | −1.90424 | ||||||||
\(610\) | 92482.7 | 0.248543 | ||||||||
\(611\) | 46881.3i | 0.125579i | ||||||||
\(612\) | 91960.3i | 0.245526i | ||||||||
\(613\) | 348766.i | 0.928140i | 0.885799 | + | 0.464070i | \(0.153611\pi\) | ||||
−0.885799 | + | 0.464070i | \(0.846389\pi\) | |||||||
\(614\) | −123485. | −0.327550 | ||||||||
\(615\) | 87015.9i | 0.230064i | ||||||||
\(616\) | −265714. | − | 455825.i | −0.700250 | − | 1.20126i | ||||
\(617\) | 222234. | 0.583767 | 0.291884 | − | 0.956454i | \(-0.405718\pi\) | ||||
0.291884 | + | 0.956454i | \(0.405718\pi\) | |||||||
\(618\) | 18241.9i | 0.0477632i | ||||||||
\(619\) | 478523. | 1.24888 | 0.624441 | − | 0.781072i | \(-0.285327\pi\) | ||||
0.624441 | + | 0.781072i | \(0.285327\pi\) | |||||||
\(620\) | 269037. | 0.699888 | ||||||||
\(621\) | 98566.0 | 0.255590 | ||||||||
\(622\) | 95561.9i | 0.247004i | ||||||||
\(623\) | 875539.i | 2.25579i | ||||||||
\(624\) | − | 21903.0i | − | 0.0562515i | ||||||
\(625\) | −4397.54 | −0.0112577 | ||||||||
\(626\) | 135017.i | 0.344539i | ||||||||
\(627\) | −43590.3 | + | 25410.1i | −0.110880 | + | 0.0646355i | ||||
\(628\) | −77635.4 | −0.196852 | ||||||||
\(629\) | 29109.3i | 0.0735750i | ||||||||
\(630\) | −62027.0 | −0.156279 | ||||||||
\(631\) | −332157. | −0.834229 | −0.417115 | − | 0.908854i | \(-0.636959\pi\) | ||||
−0.417115 | + | 0.908854i | \(0.636959\pi\) | |||||||
\(632\) | −313742. | −0.785487 | ||||||||
\(633\) | 356879.i | 0.890664i | ||||||||
\(634\) | − | 185259.i | − | 0.460893i | ||||||
\(635\) | 33675.2i | 0.0835146i | ||||||||
\(636\) | −83649.8 | −0.206800 | ||||||||
\(637\) | − | 188425.i | − | 0.464366i | ||||||
\(638\) | 139046. | + | 238530.i | 0.341600 | + | 0.586005i | ||||
\(639\) | −96967.6 | −0.237479 | ||||||||
\(640\) | − | 259872.i | − | 0.634452i | ||||||
\(641\) | −194677. | −0.473803 | −0.236902 | − | 0.971534i | \(-0.576132\pi\) | ||||
−0.236902 | + | 0.971534i | \(0.576132\pi\) | |||||||
\(642\) | −72922.8 | −0.176927 | ||||||||
\(643\) | 598433. | 1.44742 | 0.723709 | − | 0.690106i | \(-0.242436\pi\) | ||||
0.723709 | + | 0.690106i | \(0.242436\pi\) | |||||||
\(644\) | 890984.i | 2.14832i | ||||||||
\(645\) | − | 152533.i | − | 0.366643i | ||||||
\(646\) | − | 31835.1i | − | 0.0762854i | ||||||
\(647\) | −789504. | −1.88602 | −0.943008 | − | 0.332769i | \(-0.892017\pi\) | ||||
−0.943008 | + | 0.332769i | \(0.892017\pi\) | |||||||
\(648\) | − | 33888.8i | − | 0.0807060i | ||||||
\(649\) | 115509. | + | 198153.i | 0.274238 | + | 0.470448i | ||||
\(650\) | −17769.1 | −0.0420571 | ||||||||
\(651\) | 623611.i | 1.47147i | ||||||||
\(652\) | −333417. | −0.784318 | ||||||||
\(653\) | 704147. | 1.65134 | 0.825671 | − | 0.564151i | \(-0.190797\pi\) | ||||
0.825671 | + | 0.564151i | \(0.190797\pi\) | |||||||
\(654\) | 66077.9 | 0.154490 | ||||||||
\(655\) | − | 237448.i | − | 0.553459i | ||||||
\(656\) | − | 154103.i | − | 0.358099i | ||||||
\(657\) | 47270.3i | 0.109511i | ||||||||
\(658\) | −235120. | −0.543048 | ||||||||
\(659\) | − | 603395.i | − | 1.38941i | −0.719294 | − | 0.694706i | \(-0.755535\pi\) | ||
0.719294 | − | 0.694706i | \(-0.244465\pi\) | |||||||
\(660\) | −66580.6 | − | 114217.i | −0.152848 | − | 0.262206i | ||||
\(661\) | 257502. | 0.589356 | 0.294678 | − | 0.955597i | \(-0.404788\pi\) | ||||
0.294678 | + | 0.955597i | \(0.404788\pi\) | |||||||
\(662\) | 172778.i | 0.394250i | ||||||||
\(663\) | 38553.2 | 0.0877069 | ||||||||
\(664\) | −400565. | −0.908526 | ||||||||
\(665\) | −117072. | −0.264733 | ||||||||
\(666\) | − | 4913.05i | − | 0.0110765i | ||||||
\(667\) | − | 1.01801e6i | − | 2.28823i | ||||||
\(668\) | − | 640744.i | − | 1.43592i | ||||||
\(669\) | 8463.96 | 0.0189113 | ||||||||
\(670\) | 30687.6i | 0.0683619i | ||||||||
\(671\) | −394742. | + | 230107.i | −0.876735 | + | 0.511075i | ||||
\(672\) | 472371. | 1.04603 | ||||||||
\(673\) | − | 10491.1i | − | 0.0231629i | −0.999933 | − | 0.0115814i | \(-0.996313\pi\) | ||
0.999933 | − | 0.0115814i | \(-0.00368656\pi\) | |||||||
\(674\) | −115305. | −0.253821 | ||||||||
\(675\) | 53749.9 | 0.117970 | ||||||||
\(676\) | 374422. | 0.819347 | ||||||||
\(677\) | − | 243377.i | − | 0.531008i | −0.964110 | − | 0.265504i | \(-0.914462\pi\) | ||
0.964110 | − | 0.265504i | \(-0.0855384\pi\) | |||||||
\(678\) | − | 135408.i | − | 0.294567i | ||||||
\(679\) | − | 1.03826e6i | − | 2.25199i | ||||||
\(680\) | 182131. | 0.393882 | ||||||||
\(681\) | 221351.i | 0.477296i | ||||||||
\(682\) | 210620. | − | 122777.i | 0.452826 | − | 0.263966i | ||||
\(683\) | 94210.5 | 0.201957 | 0.100978 | − | 0.994889i | \(-0.467803\pi\) | ||||
0.100978 | + | 0.994889i | \(0.467803\pi\) | |||||||
\(684\) | − | 29294.8i | − | 0.0626149i | ||||||
\(685\) | 161610. | 0.344419 | ||||||||
\(686\) | 590337. | 1.25445 | ||||||||
\(687\) | −168292. | −0.356574 | ||||||||
\(688\) | 270131.i | 0.570687i | ||||||||
\(689\) | 35069.2i | 0.0738732i | ||||||||
\(690\) | − | 89407.7i | − | 0.187792i | ||||||
\(691\) | −49743.2 | −0.104178 | −0.0520892 | − | 0.998642i | \(-0.516588\pi\) | ||||
−0.0520892 | + | 0.998642i | \(0.516588\pi\) | |||||||
\(692\) | − | 17931.7i | − | 0.0374464i | ||||||
\(693\) | 264749. | − | 154330.i | 0.551273 | − | 0.321354i | ||||
\(694\) | 252362. | 0.523968 | ||||||||
\(695\) | − | 341906.i | − | 0.707843i | ||||||
\(696\) | −350009. | −0.722539 | ||||||||
\(697\) | 271249. | 0.558345 | ||||||||
\(698\) | −39040.3 | −0.0801314 | ||||||||
\(699\) | − | 300686.i | − | 0.615402i | ||||||
\(700\) | 485870.i | 0.991572i | ||||||||
\(701\) | 337972.i | 0.687772i | 0.939011 | + | 0.343886i | \(0.111743\pi\) | ||||
−0.939011 | + | 0.343886i | \(0.888257\pi\) | |||||||
\(702\) | −6506.99 | −0.0132040 | ||||||||
\(703\) | − | 9273.03i | − | 0.0187634i | ||||||
\(704\) | 46538.7 | + | 79835.8i | 0.0939006 | + | 0.161084i | ||||
\(705\) | −128635. | −0.258810 | ||||||||
\(706\) | 221558.i | 0.444507i | ||||||||
\(707\) | 912895. | 1.82634 | ||||||||
\(708\) | −133168. | −0.265665 | ||||||||
\(709\) | 209306. | 0.416379 | 0.208189 | − | 0.978089i | \(-0.433243\pi\) | ||||
0.208189 | + | 0.978089i | \(0.433243\pi\) | |||||||
\(710\) | 87957.8i | 0.174485i | ||||||||
\(711\) | − | 182225.i | − | 0.360470i | ||||||
\(712\) | 433909.i | 0.855930i | ||||||||
\(713\) | −898894. | −1.76819 | ||||||||
\(714\) | 193353.i | 0.379275i | ||||||||
\(715\) | −47884.1 | + | 27913.1i | −0.0936655 | + | 0.0546004i | ||||
\(716\) | −727693. | −1.41946 | ||||||||
\(717\) | − | 19529.5i | − | 0.0379886i | ||||||
\(718\) | 22996.8 | 0.0446086 | ||||||||
\(719\) | 382242. | 0.739403 | 0.369701 | − | 0.929151i | \(-0.379460\pi\) | ||||
0.369701 | + | 0.929151i | \(0.379460\pi\) | |||||||
\(720\) | 60098.3 | 0.115930 | ||||||||
\(721\) | − | 209115.i | − | 0.402267i | ||||||
\(722\) | − | 195081.i | − | 0.374231i | ||||||
\(723\) | 277439.i | 0.530751i | ||||||||
\(724\) | 134679. | 0.256935 | ||||||||
\(725\) | − | 555138.i | − | 1.05615i | ||||||
\(726\) | −104248. | − | 59032.4i | −0.197785 | − | 0.112000i | ||||
\(727\) | −573664. | −1.08540 | −0.542698 | − | 0.839928i | \(-0.682597\pi\) | ||||
−0.542698 | + | 0.839928i | \(0.682597\pi\) | |||||||
\(728\) | − | 128428.i | − | 0.242324i | ||||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | 42878.2 | 0.0804619 | ||||||||
\(731\) | −475481. | −0.889812 | ||||||||
\(732\) | − | 265286.i | − | 0.495099i | ||||||
\(733\) | 898874.i | 1.67298i | 0.547982 | + | 0.836490i | \(0.315396\pi\) | ||||
−0.547982 | + | 0.836490i | \(0.684604\pi\) | |||||||
\(734\) | 264610.i | 0.491150i | ||||||||
\(735\) | 517009. | 0.957025 | ||||||||
\(736\) | 680891.i | 1.25696i | ||||||||
\(737\) | −76354.1 | − | 130983.i | −0.140572 | − | 0.241147i | ||||
\(738\) | −45781.2 | −0.0840572 | ||||||||
\(739\) | − | 716712.i | − | 1.31237i | −0.754601 | − | 0.656184i | \(-0.772170\pi\) | ||
0.754601 | − | 0.656184i | \(-0.227830\pi\) | |||||||
\(740\) | 24297.6 | 0.0443711 | ||||||||
\(741\) | −12281.5 | −0.0223673 | ||||||||
\(742\) | −175879. | −0.319453 | ||||||||
\(743\) | − | 327330.i | − | 0.592937i | −0.955043 | − | 0.296468i | \(-0.904191\pi\) | ||
0.955043 | − | 0.296468i | \(-0.0958089\pi\) | |||||||
\(744\) | 309056.i | 0.558330i | ||||||||
\(745\) | − | 160455.i | − | 0.289094i | ||||||
\(746\) | 283043. | 0.508597 | ||||||||
\(747\) | − | 232653.i | − | 0.416934i | ||||||
\(748\) | −356042. | + | 207547.i | −0.636352 | + | 0.370949i | ||||
\(749\) | 835946. | 1.49010 | ||||||||
\(750\) | − | 128293.i | − | 0.228077i | ||||||
\(751\) | 473695. | 0.839883 | 0.419941 | − | 0.907551i | \(-0.362051\pi\) | ||||
0.419941 | + | 0.907551i | \(0.362051\pi\) | |||||||
\(752\) | 227809. | 0.402842 | ||||||||
\(753\) | −9650.88 | −0.0170207 | ||||||||
\(754\) | 67205.3i | 0.118212i | ||||||||
\(755\) | 311952.i | 0.547260i | ||||||||
\(756\) | 177924.i | 0.311308i | ||||||||
\(757\) | 168385. | 0.293841 | 0.146920 | − | 0.989148i | \(-0.453064\pi\) | ||||
0.146920 | + | 0.989148i | \(0.453064\pi\) | |||||||
\(758\) | 139245.i | 0.242349i | ||||||||
\(759\) | 222456. | + | 381617.i | 0.386154 | + | 0.662436i | ||||
\(760\) | −58019.5 | −0.100449 | ||||||||
\(761\) | 216244.i | 0.373400i | 0.982417 | + | 0.186700i | \(0.0597792\pi\) | ||||
−0.982417 | + | 0.186700i | \(0.940221\pi\) | |||||||
\(762\) | −17717.3 | −0.0305133 | ||||||||
\(763\) | −757479. | −1.30113 | ||||||||
\(764\) | −743135. | −1.27315 | ||||||||
\(765\) | 105784.i | 0.180758i | ||||||||
\(766\) | − | 151107.i | − | 0.257530i | ||||||
\(767\) | 55829.3i | 0.0949011i | ||||||||
\(768\) | 73230.6 | 0.124157 | ||||||||
\(769\) | 356784.i | 0.603328i | 0.953414 | + | 0.301664i | \(0.0975420\pi\) | ||||
−0.953414 | + | 0.301664i | \(0.902458\pi\) | |||||||
\(770\) | −139990. | − | 240149.i | −0.236111 | − | 0.405042i | ||||
\(771\) | 6561.53 | 0.0110382 | ||||||||
\(772\) | − | 23292.0i | − | 0.0390816i | ||||||
\(773\) | −91587.2 | −0.153277 | −0.0766383 | − | 0.997059i | \(-0.524419\pi\) | ||||
−0.0766383 | + | 0.997059i | \(0.524419\pi\) | |||||||
\(774\) | 80251.3 | 0.133959 | ||||||||
\(775\) | −490183. | −0.816122 | ||||||||
\(776\) | − | 514551.i | − | 0.854486i | ||||||
\(777\) | 56320.4i | 0.0932875i | ||||||||
\(778\) | 186998.i | 0.308943i | ||||||||
\(779\) | −86408.8 | −0.142391 | ||||||||
\(780\) | − | 32180.4i | − | 0.0528936i | ||||||
\(781\) | −218849. | − | 375429.i | −0.358791 | − | 0.615496i | ||||
\(782\) | −278705. | −0.455755 | ||||||||
\(783\) | − | 203289.i | − | 0.331582i | ||||||
\(784\) | −915608. | −1.48963 | ||||||||
\(785\) | −89305.7 | −0.144924 | ||||||||
\(786\) | 124927. | 0.202214 | ||||||||
\(787\) | 77739.6i | 0.125514i | 0.998029 | + | 0.0627571i | \(0.0199894\pi\) | ||||
−0.998029 | + | 0.0627571i | \(0.980011\pi\) | |||||||
\(788\) | − | 140441.i | − | 0.226173i | ||||||
\(789\) | − | 614926.i | − | 0.987799i | ||||||
\(790\) | −165294. | −0.264851 | ||||||||
\(791\) | 1.55224e6i | 2.48088i | ||||||||
\(792\) | 131207. | − | 76484.4i | 0.209173 | − | 0.121933i | ||||
\(793\) | −111218. | −0.176859 | ||||||||
\(794\) | 251056.i | 0.398227i | ||||||||
\(795\) | −96224.2 | −0.152247 | ||||||||
\(796\) | 689047. | 1.08748 | ||||||||
\(797\) | 125376. | 0.197377 | 0.0986887 | − | 0.995118i | \(-0.468535\pi\) | ||||
0.0986887 | + | 0.995118i | \(0.468535\pi\) | |||||||
\(798\) | − | 61594.3i | − | 0.0967241i | ||||||
\(799\) | 400985.i | 0.628109i | ||||||||
\(800\) | 371303.i | 0.580160i | ||||||||
\(801\) | −252019. | −0.392798 | ||||||||
\(802\) | 65582.5i | 0.101962i | ||||||||
\(803\) | −183016. | + | 106685.i | −0.283830 | + | 0.165453i | ||||
\(804\) | 88027.2 | 0.136177 | ||||||||
\(805\) | 1.02492e6i | 1.58160i | ||||||||
\(806\) | 59341.8 | 0.0913463 | ||||||||
\(807\) | −522284. | −0.801972 | ||||||||
\(808\) | 452422. | 0.692981 | ||||||||
\(809\) | − | 466047.i | − | 0.712087i | −0.934469 | − | 0.356044i | \(-0.884125\pi\) | ||
0.934469 | − | 0.356044i | \(-0.115875\pi\) | |||||||
\(810\) | − | 17854.1i | − | 0.0272125i | ||||||
\(811\) | 1.07207e6i | 1.62998i | 0.579473 | + | 0.814992i | \(0.303259\pi\) | ||||
−0.579473 | + | 0.814992i | \(0.696741\pi\) | |||||||
\(812\) | 1.83763e6 | 2.78706 | ||||||||
\(813\) | − | 718911.i | − | 1.08766i | ||||||
\(814\) | 19021.8 | − | 11088.4i | 0.0287080 | − | 0.0167347i | ||||
\(815\) | −383536. | −0.577420 | ||||||||
\(816\) | − | 187340.i | − | 0.281353i | ||||||
\(817\) | 151469. | 0.226923 | ||||||||
\(818\) | −417392. | −0.623789 | ||||||||
\(819\) | 74592.4 | 0.111206 | ||||||||
\(820\) | − | 226412.i | − | 0.336722i | ||||||
\(821\) | − | 423155.i | − | 0.627789i | −0.949458 | − | 0.313894i | \(-0.898366\pi\) | ||
0.949458 | − | 0.313894i | \(-0.101634\pi\) | |||||||
\(822\) | 85027.0i | 0.125838i | ||||||||
\(823\) | 1.01630e6 | 1.50045 | 0.750227 | − | 0.661180i | \(-0.229944\pi\) | ||||
0.750227 | + | 0.661180i | \(0.229944\pi\) | |||||||
\(824\) | − | 103635.i | − | 0.152635i | ||||||
\(825\) | 121309. | + | 208103.i | 0.178232 | + | 0.305753i | ||||
\(826\) | −279996. | −0.410385 | ||||||||
\(827\) | − | 83099.6i | − | 0.121503i | −0.998153 | − | 0.0607517i | \(-0.980650\pi\) | ||
0.998153 | − | 0.0607517i | \(-0.0193498\pi\) | |||||||
\(828\) | −256465. | −0.374083 | ||||||||
\(829\) | −293001. | −0.426343 | −0.213172 | − | 0.977015i | \(-0.568379\pi\) | ||||
−0.213172 | + | 0.977015i | \(0.568379\pi\) | |||||||
\(830\) | −211036. | −0.306338 | ||||||||
\(831\) | 211463.i | 0.306220i | ||||||||
\(832\) | 22493.6i | 0.0324946i | ||||||||
\(833\) | − | 1.61164e6i | − | 2.32262i | ||||||
\(834\) | 179885. | 0.258621 | ||||||||
\(835\) | − | 737062.i | − | 1.05714i | ||||||
\(836\) | 113420. | − | 66116.1i | 0.162285 | − | 0.0946007i | ||||
\(837\) | −179503. | −0.256225 | ||||||||
\(838\) | − | 402679.i | − | 0.573418i | ||||||
\(839\) | 426202. | 0.605468 | 0.302734 | − | 0.953075i | \(-0.402101\pi\) | ||||
0.302734 | + | 0.953075i | \(0.402101\pi\) | |||||||
\(840\) | 352386. | 0.499413 | ||||||||
\(841\) | −1.39233e6 | −1.96856 | ||||||||
\(842\) | − | 297956.i | − | 0.420269i | ||||||
\(843\) | 90317.5i | 0.127092i | ||||||||
\(844\) | − | 928587.i | − | 1.30358i | ||||||
\(845\) | 430706. | 0.603208 | ||||||||
\(846\) | − | 67678.1i | − | 0.0945599i | ||||||
\(847\) | 1.19503e6 | + | 676713.i | 1.66576 | + | 0.943274i | ||||
\(848\) | 170410. | 0.236976 | ||||||||
\(849\) | − | 534157.i | − | 0.741060i | ||||||
\(850\) | −151983. | −0.210357 | ||||||||
\(851\) | −81182.0 | −0.112099 | ||||||||
\(852\) | 252306. | 0.347575 | ||||||||
\(853\) | 1.33250e6i | 1.83134i | 0.401926 | + | 0.915672i | \(0.368341\pi\) | ||||
−0.401926 | + | 0.915672i | \(0.631659\pi\) | |||||||
\(854\) | − | 557781.i | − | 0.764801i | ||||||
\(855\) | − | 33698.4i | − | 0.0460975i | ||||||
\(856\) | 414287. | 0.565397 | ||||||||
\(857\) | 295654.i | 0.402552i | 0.979535 | + | 0.201276i | \(0.0645088\pi\) | ||||
−0.979535 | + | 0.201276i | \(0.935491\pi\) | |||||||
\(858\) | −14685.8 | − | 25193.0i | −0.0199490 | − | 0.0342220i | ||||
\(859\) | −931988. | −1.26306 | −0.631530 | − | 0.775352i | \(-0.717573\pi\) | ||||
−0.631530 | + | 0.775352i | \(0.717573\pi\) | |||||||
\(860\) | 396885.i | 0.536621i | ||||||||
\(861\) | 524810. | 0.707939 | ||||||||
\(862\) | −174401. | −0.234711 | ||||||||
\(863\) | 159744. | 0.214488 | 0.107244 | − | 0.994233i | \(-0.465797\pi\) | ||||
0.107244 | + | 0.994233i | \(0.465797\pi\) | |||||||
\(864\) | 135970.i | 0.182144i | ||||||||
\(865\) | − | 20627.3i | − | 0.0275683i | ||||||
\(866\) | − | 272236.i | − | 0.363002i | ||||||
\(867\) | −104235. | −0.138667 | ||||||||
\(868\) | − | 1.62261e6i | − | 2.15365i | ||||||
\(869\) | 705519. | − | 411268.i | 0.934263 | − | 0.544610i | ||||
\(870\) | −184401. | −0.243626 | ||||||||
\(871\) | − | 36904.3i | − | 0.0486453i | ||||||
\(872\) | −375399. | −0.493697 | ||||||||
\(873\) | 298857. | 0.392135 | ||||||||
\(874\) | 88784.0 | 0.116228 | ||||||||
\(875\) | 1.47068e6i | 1.92089i | ||||||||
\(876\) | − | 122996.i | − | 0.160281i | ||||||
\(877\) | − | 1.43711e6i | − | 1.86849i | −0.356636 | − | 0.934244i | \(-0.616076\pi\) | ||
0.356636 | − | 0.934244i | \(-0.383924\pi\) | |||||||
\(878\) | 244422. | 0.317067 | ||||||||
\(879\) | 554838.i | 0.718106i | ||||||||
\(880\) | 135637. | + | 232682.i | 0.175151 | + | 0.300467i | ||||
\(881\) | 478465. | 0.616451 | 0.308225 | − | 0.951313i | \(-0.400265\pi\) | ||||
0.308225 | + | 0.951313i | \(0.400265\pi\) | |||||||
\(882\) | 272011.i | 0.349663i | ||||||||
\(883\) | 280446. | 0.359689 | 0.179845 | − | 0.983695i | \(-0.442440\pi\) | ||||
0.179845 | + | 0.983695i | \(0.442440\pi\) | |||||||
\(884\) | −100314. | −0.128368 | ||||||||
\(885\) | −153187. | −0.195584 | ||||||||
\(886\) | − | 164048.i | − | 0.208979i | ||||||
\(887\) | − | 1.20382e6i | − | 1.53008i | −0.643982 | − | 0.765041i | \(-0.722719\pi\) | ||
0.643982 | − | 0.765041i | \(-0.277281\pi\) | |||||||
\(888\) | 27911.8i | 0.0353967i | ||||||||
\(889\) | 203101. | 0.256986 | ||||||||
\(890\) | 228603.i | 0.288603i | ||||||||
\(891\) | 44423.0 | + | 76206.5i | 0.0559568 | + | 0.0959923i | ||||
\(892\) | −22022.9 | −0.0276786 | ||||||||
\(893\) | − | 127738.i | − | 0.160183i | ||||||
\(894\) | 84419.2 | 0.105625 | ||||||||
\(895\) | −837081. | −1.04501 | ||||||||
\(896\) | −1.56734e6 | −1.95230 | ||||||||
\(897\) | 107520.i | 0.133630i | ||||||||
\(898\) | − | 138713.i | − | 0.172015i | ||||||
\(899\) | 1.85394e6i | 2.29391i | ||||||||
\(900\) | −139855. | −0.172661 | ||||||||
\(901\) | 299954.i | 0.369491i | ||||||||
\(902\) | −103325. | − | 177251.i | −0.126996 | − | 0.217859i | ||||
\(903\) | −919955. | −1.12821 | ||||||||
\(904\) | 769274.i | 0.941335i | ||||||||
\(905\) | 154925. | 0.189157 | ||||||||
\(906\) | −164126. | −0.199949 | ||||||||
\(907\) | 224182. | 0.272512 | 0.136256 | − | 0.990674i | \(-0.456493\pi\) | ||||
0.136256 | + | 0.990674i | \(0.456493\pi\) | |||||||
\(908\) | − | 575948.i | − | 0.698572i | ||||||
\(909\) | 262772.i | 0.318018i | ||||||||
\(910\) | − | 67661.6i | − | 0.0817070i | ||||||
\(911\) | −815416. | −0.982522 | −0.491261 | − | 0.871012i | \(-0.663464\pi\) | ||||
−0.491261 | + | 0.871012i | \(0.663464\pi\) | |||||||
\(912\) | 59679.0i | 0.0717516i | ||||||||
\(913\) | 900760. | − | 525080.i | 1.08061 | − | 0.629918i | ||||
\(914\) | 122745. | 0.146931 | ||||||||
\(915\) | − | 305164.i | − | 0.364495i | ||||||
\(916\) | 437889. | 0.521883 | ||||||||
\(917\) | −1.43209e6 | −1.70307 | ||||||||
\(918\) | −55655.6 | −0.0660424 | ||||||||
\(919\) | − | 858763.i | − | 1.01682i | −0.861116 | − | 0.508408i | \(-0.830234\pi\) | ||
0.861116 | − | 0.508408i | \(-0.169766\pi\) | |||||||
\(920\) | 507940.i | 0.600118i | ||||||||
\(921\) | 407462.i | 0.480361i | ||||||||
\(922\) | 182611. | 0.214816 | ||||||||
\(923\) | − | 105776.i | − | 0.124161i | ||||||
\(924\) | −688866. | + | 401560.i | −0.806846 | + | 0.470335i | ||||
\(925\) | −44270.1 | −0.0517400 | ||||||||
\(926\) | 494215.i | 0.576361i | ||||||||
\(927\) | 60192.6 | 0.0700460 | ||||||||
\(928\) | 1.40432e6 | 1.63068 | ||||||||
\(929\) | 489087. | 0.566702 | 0.283351 | − | 0.959016i | \(-0.408554\pi\) | ||||
0.283351 | + | 0.959016i | \(0.408554\pi\) | |||||||
\(930\) | 162825.i | 0.188258i | ||||||||
\(931\) | 513402.i | 0.592322i | ||||||||
\(932\) | 782374.i | 0.900705i | ||||||||
\(933\) | 315324. | 0.362238 | ||||||||
\(934\) | 151228.i | 0.173355i | ||||||||
\(935\) | −409562. | + | 238746.i | −0.468486 | + | 0.273095i | ||||
\(936\) | 36967.3 | 0.0421954 | ||||||||
\(937\) | − | 276854.i | − | 0.315335i | −0.987492 | − | 0.157667i | \(-0.949603\pi\) | ||
0.987492 | − | 0.157667i | \(-0.0503974\pi\) | |||||||
\(938\) | 185083. | 0.210359 | ||||||||
\(939\) | 445513. | 0.505277 | ||||||||
\(940\) | 334703. | 0.378795 | ||||||||
\(941\) | 61582.8i | 0.0695472i | 0.999395 | + | 0.0347736i | \(0.0110710\pi\) | ||||
−0.999395 | + | 0.0347736i | \(0.988929\pi\) | |||||||
\(942\) | − | 46985.9i | − | 0.0529500i | ||||||
\(943\) | 756478.i | 0.850693i | ||||||||
\(944\) | 271289. | 0.304431 | ||||||||
\(945\) | 204670.i | 0.229187i | ||||||||
\(946\) | 181121. | + | 310708.i | 0.202389 | + | 0.347193i | ||||
\(947\) | −1.23913e6 | −1.38171 | −0.690856 | − | 0.722992i | \(-0.742766\pi\) | ||||
−0.690856 | + | 0.722992i | \(0.742766\pi\) | |||||||
\(948\) | 474143.i | 0.527585i | ||||||||
\(949\) | −51564.4 | −0.0572555 | ||||||||
\(950\) | 48415.5 | 0.0536460 | ||||||||
\(951\) | −611295. | −0.675912 | ||||||||
\(952\) | − | 1.09847e6i | − | 1.21203i | ||||||
\(953\) | 1.44690e6i | 1.59314i | 0.604548 | + | 0.796569i | \(0.293354\pi\) | ||||
−0.604548 | + | 0.796569i | \(0.706646\pi\) | |||||||
\(954\) | − | 50626.0i | − | 0.0556258i | ||||||
\(955\) | −854844. | −0.937303 | ||||||||
\(956\) | 50815.1i | 0.0556002i | ||||||||
\(957\) | 787074. | − | 458809.i | 0.859392 | − | 0.500966i | ||||
\(958\) | 339661. | 0.370096 | ||||||||
\(959\) | − | 974701.i | − | 1.05982i | ||||||
\(960\) | −61718.8 | −0.0669692 | ||||||||
\(961\) | 713496. | 0.772582 | ||||||||
\(962\) | 5359.35 | 0.00579112 | ||||||||
\(963\) | 240622.i | 0.259468i | ||||||||
\(964\) | − | 721886.i | − | 0.776810i | ||||||
\(965\) | − | 26793.3i | − | 0.0287721i | ||||||
\(966\) | −539235. | −0.577862 | ||||||||
\(967\) | 382759.i | 0.409328i | 0.978832 | + | 0.204664i | \(0.0656102\pi\) | ||||
−0.978832 | + | 0.204664i | \(0.934390\pi\) | |||||||
\(968\) | 592247. | + | 335373.i | 0.632051 | + | 0.357912i | ||||
\(969\) | −105046. | −0.111875 | ||||||||
\(970\) | − | 271089.i | − | 0.288116i | ||||||
\(971\) | 571623. | 0.606277 | 0.303138 | − | 0.952947i | \(-0.401966\pi\) | ||||
0.303138 | + | 0.952947i | \(0.401966\pi\) | |||||||
\(972\) | −51214.4 | −0.0542075 | ||||||||
\(973\) | −2.06210e6 | −2.17813 | ||||||||
\(974\) | 442897.i | 0.466858i | ||||||||
\(975\) | 58632.6i | 0.0616779i | ||||||||
\(976\) | 540437.i | 0.567343i | ||||||||
\(977\) | 1.22248e6 | 1.28072 | 0.640360 | − | 0.768075i | \(-0.278785\pi\) | ||||
0.640360 | + | 0.768075i | \(0.278785\pi\) | |||||||
\(978\) | − | 201788.i | − | 0.210969i | ||||||
\(979\) | −568788. | − | 975740.i | −0.593451 | − | 1.01805i | ||||
\(980\) | −1.34524e6 | −1.40071 | ||||||||
\(981\) | − | 218036.i | − | 0.226564i | ||||||
\(982\) | −360764. | −0.374111 | ||||||||
\(983\) | −1.01427e6 | −1.04966 | −0.524829 | − | 0.851208i | \(-0.675871\pi\) | ||||
−0.524829 | + | 0.851208i | \(0.675871\pi\) | |||||||
\(984\) | 260091. | 0.268618 | ||||||||
\(985\) | − | 161552.i | − | 0.166510i | ||||||
\(986\) | 574820.i | 0.591260i | ||||||||
\(987\) | 775822.i | 0.796394i | ||||||||
\(988\) | 31955.9 | 0.0327369 | ||||||||
\(989\) | − | 1.32605e6i | − | 1.35571i | ||||||
\(990\) | 69125.7 | − | 40295.4i | 0.0705292 | − | 0.0411136i | ||||
\(991\) | 609717. | 0.620842 | 0.310421 | − | 0.950599i | \(-0.399530\pi\) | ||||
0.310421 | + | 0.950599i | \(0.399530\pi\) | |||||||
\(992\) | − | 1.24000e6i | − | 1.26008i | ||||||
\(993\) | 570112. | 0.578178 | ||||||||
\(994\) | 530491. | 0.536914 | ||||||||
\(995\) | 792626. | 0.800612 | ||||||||
\(996\) | 605354.i | 0.610226i | ||||||||
\(997\) | 134059.i | 0.134867i | 0.997724 | + | 0.0674335i | \(0.0214811\pi\) | ||||
−0.997724 | + | 0.0674335i | \(0.978519\pi\) | |||||||
\(998\) | − | 59293.1i | − | 0.0595310i | ||||||
\(999\) | −16211.5 | −0.0162440 |
(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 | 33.5.c.a.10.4 | ✓ | 8 | |
3.2 | odd | 2 | 99.5.c.c.10.5 | 8 | |||
4.3 | odd | 2 | 528.5.j.a.241.8 | 8 | |||
11.10 | odd | 2 | inner | 33.5.c.a.10.5 | yes | 8 | |
33.32 | even | 2 | 99.5.c.c.10.4 | 8 | |||
44.43 | even | 2 | 528.5.j.a.241.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.5.c.a.10.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
33.5.c.a.10.5 | yes | 8 | 11.10 | odd | 2 | inner | |
99.5.c.c.10.4 | 8 | 33.32 | even | 2 | |||
99.5.c.c.10.5 | 8 | 3.2 | odd | 2 | |||
528.5.j.a.241.7 | 8 | 44.43 | even | 2 | |||
528.5.j.a.241.8 | 8 | 4.3 | odd | 2 |