Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [14,5,Mod(13,14)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14.13");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.b (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: | \(1.44717948317\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.1308672.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 72x^{2} + 1278 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 13.1 | ||
Root | \(6.34371i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 14.13 |
Dual form | 14.5.b.a.13.2 |
$q$-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 \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.82843 | −0.707107 | ||||||||
\(3\) | − | 12.6874i | − | 1.40971i | −0.709350 | − | 0.704857i | \(-0.751011\pi\) | ||
0.709350 | − | 0.704857i | \(-0.248989\pi\) | |||||||
\(4\) | 8.00000 | 0.500000 | ||||||||
\(5\) | − | 23.1980i | − | 0.927921i | −0.885856 | − | 0.463960i | \(-0.846428\pi\) | ||
0.885856 | − | 0.463960i | \(-0.153572\pi\) | |||||||
\(6\) | 35.8854i | 0.996818i | ||||||||
\(7\) | 6.45584 | + | 48.5729i | 0.131752 | + | 0.991283i | ||||
\(8\) | −22.6274 | −0.353553 | ||||||||
\(9\) | −79.9706 | −0.987291 | ||||||||
\(10\) | 65.6139i | 0.656139i | ||||||||
\(11\) | 191.823 | 1.58532 | 0.792659 | − | 0.609666i | \(-0.208696\pi\) | ||||
0.792659 | + | 0.609666i | \(0.208696\pi\) | |||||||
\(12\) | − | 101.499i | − | 0.704857i | ||||||
\(13\) | − | 48.5729i | − | 0.287413i | −0.989620 | − | 0.143707i | \(-0.954098\pi\) | ||
0.989620 | − | 0.143707i | \(-0.0459022\pi\) | |||||||
\(14\) | −18.2599 | − | 137.385i | −0.0931627 | − | 0.700943i | ||||
\(15\) | −294.323 | −1.30810 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | − | 181.977i | − | 0.629680i | −0.949145 | − | 0.314840i | \(-0.898049\pi\) | ||
0.949145 | − | 0.314840i | \(-0.101951\pi\) | |||||||
\(18\) | 226.191 | 0.698120 | ||||||||
\(19\) | 599.915i | 1.66182i | 0.556410 | + | 0.830908i | \(0.312178\pi\) | ||||
−0.556410 | + | 0.830908i | \(0.687822\pi\) | |||||||
\(20\) | − | 185.584i | − | 0.463960i | ||||||
\(21\) | 616.264 | − | 81.9080i | 1.39742 | − | 0.185732i | ||||
\(22\) | −542.558 | −1.12099 | ||||||||
\(23\) | −469.529 | −0.887578 | −0.443789 | − | 0.896131i | \(-0.646366\pi\) | ||||
−0.443789 | + | 0.896131i | \(0.646366\pi\) | |||||||
\(24\) | 287.083i | 0.498409i | ||||||||
\(25\) | 86.8519 | 0.138963 | ||||||||
\(26\) | 137.385i | 0.203232i | ||||||||
\(27\) | − | 13.0609i | − | 0.0179162i | ||||||
\(28\) | 51.6468 | + | 388.583i | 0.0658760 | + | 0.495641i | ||||
\(29\) | −338.881 | −0.402951 | −0.201475 | − | 0.979494i | \(-0.564574\pi\) | ||||
−0.201475 | + | 0.979494i | \(0.564574\pi\) | |||||||
\(30\) | 832.471 | 0.924968 | ||||||||
\(31\) | 267.556i | 0.278414i | 0.990263 | + | 0.139207i | \(0.0444554\pi\) | ||||
−0.990263 | + | 0.139207i | \(0.955545\pi\) | |||||||
\(32\) | −181.019 | −0.176777 | ||||||||
\(33\) | − | 2433.74i | − | 2.23484i | ||||||
\(34\) | 514.710i | 0.445251i | ||||||||
\(35\) | 1126.79 | − | 149.763i | 0.919832 | − | 0.122255i | ||||
\(36\) | −639.765 | −0.493645 | ||||||||
\(37\) | −668.530 | −0.488334 | −0.244167 | − | 0.969733i | \(-0.578515\pi\) | ||||
−0.244167 | + | 0.969733i | \(0.578515\pi\) | |||||||
\(38\) | − | 1696.82i | − | 1.17508i | ||||||
\(39\) | −616.264 | −0.405170 | ||||||||
\(40\) | 524.911i | 0.328070i | ||||||||
\(41\) | 1323.85i | 0.787534i | 0.919210 | + | 0.393767i | \(0.128828\pi\) | ||||
−0.919210 | + | 0.393767i | \(0.871172\pi\) | |||||||
\(42\) | −1743.06 | + | 231.671i | −0.988128 | + | 0.131333i | ||||
\(43\) | 1940.23 | 1.04934 | 0.524671 | − | 0.851305i | \(-0.324188\pi\) | ||||
0.524671 | + | 0.851305i | \(0.324188\pi\) | |||||||
\(44\) | 1534.59 | 0.792659 | ||||||||
\(45\) | 1855.16i | 0.916128i | ||||||||
\(46\) | 1328.03 | 0.627613 | ||||||||
\(47\) | 2936.89i | 1.32951i | 0.747062 | + | 0.664755i | \(0.231464\pi\) | ||||
−0.747062 | + | 0.664755i | \(0.768536\pi\) | |||||||
\(48\) | − | 811.995i | − | 0.352428i | ||||||
\(49\) | −2317.64 | + | 627.158i | −0.965283 | + | 0.261207i | ||||
\(50\) | −245.654 | −0.0982618 | ||||||||
\(51\) | −2308.82 | −0.887668 | ||||||||
\(52\) | − | 388.583i | − | 0.143707i | ||||||
\(53\) | −1460.94 | −0.520091 | −0.260046 | − | 0.965596i | \(-0.583738\pi\) | ||||
−0.260046 | + | 0.965596i | \(0.583738\pi\) | |||||||
\(54\) | 36.9418i | 0.0126687i | ||||||||
\(55\) | − | 4449.92i | − | 1.47105i | ||||||
\(56\) | −146.079 | − | 1099.08i | −0.0465813 | − | 0.350471i | ||||
\(57\) | 7611.38 | 2.34268 | ||||||||
\(58\) | 958.501 | 0.284929 | ||||||||
\(59\) | − | 1730.83i | − | 0.497223i | −0.968603 | − | 0.248612i | \(-0.920026\pi\) | ||
0.968603 | − | 0.248612i | \(-0.0799743\pi\) | |||||||
\(60\) | −2354.58 | −0.654051 | ||||||||
\(61\) | 246.343i | 0.0662034i | 0.999452 | + | 0.0331017i | \(0.0105385\pi\) | ||||
−0.999452 | + | 0.0331017i | \(0.989461\pi\) | |||||||
\(62\) | − | 756.763i | − | 0.196869i | ||||||
\(63\) | −516.277 | − | 3884.40i | −0.130077 | − | 0.978684i | ||||
\(64\) | 512.000 | 0.125000 | ||||||||
\(65\) | −1126.79 | −0.266697 | ||||||||
\(66\) | 6883.67i | 1.58027i | ||||||||
\(67\) | −1076.59 | −0.239828 | −0.119914 | − | 0.992784i | \(-0.538262\pi\) | ||||
−0.119914 | + | 0.992784i | \(0.538262\pi\) | |||||||
\(68\) | − | 1455.82i | − | 0.314840i | ||||||
\(69\) | 5957.11i | 1.25123i | ||||||||
\(70\) | −3187.05 | + | 423.593i | −0.650419 | + | 0.0864476i | ||||
\(71\) | −2276.39 | −0.451574 | −0.225787 | − | 0.974177i | \(-0.572495\pi\) | ||||
−0.225787 | + | 0.974177i | \(0.572495\pi\) | |||||||
\(72\) | 1809.53 | 0.349060 | ||||||||
\(73\) | − | 7106.94i | − | 1.33363i | −0.745221 | − | 0.666817i | \(-0.767656\pi\) | ||
0.745221 | − | 0.666817i | \(-0.232344\pi\) | |||||||
\(74\) | 1890.89 | 0.345305 | ||||||||
\(75\) | − | 1101.93i | − | 0.195898i | ||||||
\(76\) | 4799.32i | 0.830908i | ||||||||
\(77\) | 1238.38 | + | 9317.41i | 0.208869 | + | 1.57150i | ||||
\(78\) | 1743.06 | 0.286499 | ||||||||
\(79\) | 7012.38 | 1.12360 | 0.561799 | − | 0.827274i | \(-0.310109\pi\) | ||||
0.561799 | + | 0.827274i | \(0.310109\pi\) | |||||||
\(80\) | − | 1484.67i | − | 0.231980i | ||||||
\(81\) | −6643.32 | −1.01255 | ||||||||
\(82\) | − | 3744.40i | − | 0.556871i | ||||||
\(83\) | − | 1448.36i | − | 0.210243i | −0.994459 | − | 0.105121i | \(-0.966477\pi\) | ||
0.994459 | − | 0.105121i | \(-0.0335231\pi\) | |||||||
\(84\) | 4930.11 | − | 655.264i | 0.698712 | − | 0.0928662i | ||||
\(85\) | −4221.52 | −0.584293 | ||||||||
\(86\) | −5487.81 | −0.741997 | ||||||||
\(87\) | 4299.53i | 0.568045i | ||||||||
\(88\) | −4340.47 | −0.560494 | ||||||||
\(89\) | − | 2133.73i | − | 0.269376i | −0.990888 | − | 0.134688i | \(-0.956997\pi\) | ||
0.990888 | − | 0.134688i | \(-0.0430032\pi\) | |||||||
\(90\) | − | 5247.18i | − | 0.647800i | ||||||
\(91\) | 2359.32 | − | 313.579i | 0.284908 | − | 0.0378673i | ||||
\(92\) | −3756.23 | −0.443789 | ||||||||
\(93\) | 3394.60 | 0.392484 | ||||||||
\(94\) | − | 8306.77i | − | 0.940105i | ||||||
\(95\) | 13916.8 | 1.54203 | ||||||||
\(96\) | 2296.67i | 0.249204i | ||||||||
\(97\) | − | 5898.76i | − | 0.626928i | −0.949600 | − | 0.313464i | \(-0.898511\pi\) | ||
0.949600 | − | 0.313464i | \(-0.101489\pi\) | |||||||
\(98\) | 6555.29 | − | 1773.87i | 0.682558 | − | 0.184701i | ||||
\(99\) | −15340.2 | −1.56517 | ||||||||
\(100\) | 694.816 | 0.0694816 | ||||||||
\(101\) | 9172.07i | 0.899135i | 0.893246 | + | 0.449567i | \(0.148422\pi\) | ||||
−0.893246 | + | 0.449567i | \(0.851578\pi\) | |||||||
\(102\) | 6530.34 | 0.627676 | ||||||||
\(103\) | 3906.46i | 0.368222i | 0.982905 | + | 0.184111i | \(0.0589406\pi\) | ||||
−0.982905 | + | 0.184111i | \(0.941059\pi\) | |||||||
\(104\) | 1099.08i | 0.101616i | ||||||||
\(105\) | −1900.10 | − | 14296.1i | −0.172345 | − | 1.29670i | ||||
\(106\) | 4132.15 | 0.367760 | ||||||||
\(107\) | −12141.3 | −1.06047 | −0.530233 | − | 0.847852i | \(-0.677896\pi\) | ||||
−0.530233 | + | 0.847852i | \(0.677896\pi\) | |||||||
\(108\) | − | 104.487i | − | 0.00895809i | ||||||
\(109\) | 6808.34 | 0.573044 | 0.286522 | − | 0.958074i | \(-0.407501\pi\) | ||||
0.286522 | + | 0.958074i | \(0.407501\pi\) | |||||||
\(110\) | 12586.3i | 1.04019i | ||||||||
\(111\) | 8481.92i | 0.688411i | ||||||||
\(112\) | 413.174 | + | 3108.66i | 0.0329380 | + | 0.247821i | ||||
\(113\) | −4764.20 | −0.373107 | −0.186553 | − | 0.982445i | \(-0.559732\pi\) | ||||
−0.186553 | + | 0.982445i | \(0.559732\pi\) | |||||||
\(114\) | −21528.2 | −1.65653 | ||||||||
\(115\) | 10892.1i | 0.823602i | ||||||||
\(116\) | −2711.05 | −0.201475 | ||||||||
\(117\) | 3884.40i | 0.283761i | ||||||||
\(118\) | 4895.54i | 0.351590i | ||||||||
\(119\) | 8839.17 | − | 1174.82i | 0.624191 | − | 0.0829615i | ||||
\(120\) | 6659.77 | 0.462484 | ||||||||
\(121\) | 22155.2 | 1.51323 | ||||||||
\(122\) | − | 696.763i | − | 0.0468129i | ||||||
\(123\) | 16796.2 | 1.11020 | ||||||||
\(124\) | 2140.45i | 0.139207i | ||||||||
\(125\) | − | 16513.6i | − | 1.05687i | ||||||
\(126\) | 1460.25 | + | 10986.7i | 0.0919787 | + | 0.692034i | ||||
\(127\) | −27968.9 | −1.73408 | −0.867038 | − | 0.498242i | \(-0.833979\pi\) | ||||
−0.867038 | + | 0.498242i | \(0.833979\pi\) | |||||||
\(128\) | −1448.15 | −0.0883883 | ||||||||
\(129\) | − | 24616.6i | − | 1.47927i | ||||||
\(130\) | 3187.05 | 0.188583 | ||||||||
\(131\) | − | 24016.5i | − | 1.39948i | −0.714397 | − | 0.699741i | \(-0.753299\pi\) | ||
0.714397 | − | 0.699741i | \(-0.246701\pi\) | |||||||
\(132\) | − | 19469.9i | − | 1.11742i | ||||||
\(133\) | −29139.6 | + | 3872.96i | −1.64733 | + | 0.218947i | ||||
\(134\) | 3045.05 | 0.169584 | ||||||||
\(135\) | −302.987 | −0.0166248 | ||||||||
\(136\) | 4117.68i | 0.222625i | ||||||||
\(137\) | −4162.00 | −0.221748 | −0.110874 | − | 0.993834i | \(-0.535365\pi\) | ||||
−0.110874 | + | 0.993834i | \(0.535365\pi\) | |||||||
\(138\) | − | 16849.3i | − | 0.884754i | ||||||
\(139\) | 26365.8i | 1.36462i | 0.731064 | + | 0.682309i | \(0.239024\pi\) | ||||
−0.731064 | + | 0.682309i | \(0.760976\pi\) | |||||||
\(140\) | 9014.35 | − | 1198.10i | 0.459916 | − | 0.0611277i | ||||
\(141\) | 37261.5 | 1.87423 | ||||||||
\(142\) | 6438.59 | 0.319311 | ||||||||
\(143\) | − | 9317.41i | − | 0.455641i | ||||||
\(144\) | −5118.12 | −0.246823 | ||||||||
\(145\) | 7861.38i | 0.373906i | ||||||||
\(146\) | 20101.5i | 0.943022i | ||||||||
\(147\) | 7957.01 | + | 29404.9i | 0.368227 | + | 1.36077i | ||||
\(148\) | −5348.24 | −0.244167 | ||||||||
\(149\) | −6576.57 | −0.296229 | −0.148114 | − | 0.988970i | \(-0.547320\pi\) | ||||
−0.148114 | + | 0.988970i | \(0.547320\pi\) | |||||||
\(150\) | 3116.72i | 0.138521i | ||||||||
\(151\) | −22930.4 | −1.00568 | −0.502839 | − | 0.864380i | \(-0.667711\pi\) | ||||
−0.502839 | + | 0.864380i | \(0.667711\pi\) | |||||||
\(152\) | − | 13574.5i | − | 0.587540i | ||||||
\(153\) | 14552.8i | 0.621677i | ||||||||
\(154\) | −3502.67 | − | 26353.6i | −0.147692 | − | 1.11122i | ||||
\(155\) | 6206.77 | 0.258346 | ||||||||
\(156\) | −4930.11 | −0.202585 | ||||||||
\(157\) | 37292.9i | 1.51296i | 0.654017 | + | 0.756480i | \(0.273082\pi\) | ||||
−0.654017 | + | 0.756480i | \(0.726918\pi\) | |||||||
\(158\) | −19834.0 | −0.794504 | ||||||||
\(159\) | 18535.5i | 0.733180i | ||||||||
\(160\) | 4199.29i | 0.164035i | ||||||||
\(161\) | −3031.21 | − | 22806.4i | −0.116940 | − | 0.879841i | ||||
\(162\) | 18790.2 | 0.715979 | ||||||||
\(163\) | 40854.0 | 1.53766 | 0.768828 | − | 0.639455i | \(-0.220840\pi\) | ||||
0.768828 | + | 0.639455i | \(0.220840\pi\) | |||||||
\(164\) | 10590.8i | 0.393767i | ||||||||
\(165\) | −56458.0 | −2.07376 | ||||||||
\(166\) | 4096.58i | 0.148664i | ||||||||
\(167\) | − | 34774.9i | − | 1.24690i | −0.781862 | − | 0.623452i | \(-0.785730\pi\) | ||
0.781862 | − | 0.623452i | \(-0.214270\pi\) | |||||||
\(168\) | −13944.5 | + | 1853.37i | −0.494064 | + | 0.0656663i | ||||
\(169\) | 26201.7 | 0.917394 | ||||||||
\(170\) | 11940.3 | 0.413158 | ||||||||
\(171\) | − | 47975.6i | − | 1.64070i | ||||||
\(172\) | 15521.9 | 0.524671 | ||||||||
\(173\) | 31600.1i | 1.05583i | 0.849296 | + | 0.527917i | \(0.177027\pi\) | ||||
−0.849296 | + | 0.527917i | \(0.822973\pi\) | |||||||
\(174\) | − | 12160.9i | − | 0.401668i | ||||||
\(175\) | 560.703 | + | 4218.65i | 0.0183087 | + | 0.137752i | ||||
\(176\) | 12276.7 | 0.396329 | ||||||||
\(177\) | −21959.8 | −0.700942 | ||||||||
\(178\) | 6035.09i | 0.190478i | ||||||||
\(179\) | 22750.7 | 0.710048 | 0.355024 | − | 0.934857i | \(-0.384473\pi\) | ||||
0.355024 | + | 0.934857i | \(0.384473\pi\) | |||||||
\(180\) | 14841.3i | 0.458064i | ||||||||
\(181\) | − | 55434.4i | − | 1.69208i | −0.533116 | − | 0.846042i | \(-0.678979\pi\) | ||
0.533116 | − | 0.846042i | \(-0.321021\pi\) | |||||||
\(182\) | −6673.17 | + | 886.935i | −0.201460 | + | 0.0267762i | ||||
\(183\) | 3125.45 | 0.0933278 | ||||||||
\(184\) | 10624.2 | 0.313806 | ||||||||
\(185\) | 15508.6i | 0.453136i | ||||||||
\(186\) | −9601.37 | −0.277528 | ||||||||
\(187\) | − | 34907.5i | − | 0.998242i | ||||||
\(188\) | 23495.1i | 0.664755i | ||||||||
\(189\) | 634.405 | − | 84.3191i | 0.0177600 | − | 0.00236049i | ||||
\(190\) | −39362.8 | −1.09038 | ||||||||
\(191\) | −50817.6 | −1.39299 | −0.696494 | − | 0.717562i | \(-0.745258\pi\) | ||||
−0.696494 | + | 0.717562i | \(0.745258\pi\) | |||||||
\(192\) | − | 6495.96i | − | 0.176214i | ||||||
\(193\) | −1248.34 | −0.0335134 | −0.0167567 | − | 0.999860i | \(-0.505334\pi\) | ||||
−0.0167567 | + | 0.999860i | \(0.505334\pi\) | |||||||
\(194\) | 16684.2i | 0.443305i | ||||||||
\(195\) | 14296.1i | 0.375966i | ||||||||
\(196\) | −18541.2 | + | 5017.26i | −0.482641 | + | 0.130603i | ||||
\(197\) | 64454.6 | 1.66082 | 0.830408 | − | 0.557155i | \(-0.188107\pi\) | ||||
0.830408 | + | 0.557155i | \(0.188107\pi\) | |||||||
\(198\) | 43388.7 | 1.10674 | ||||||||
\(199\) | − | 2352.60i | − | 0.0594076i | −0.999559 | − | 0.0297038i | \(-0.990544\pi\) | ||
0.999559 | − | 0.0297038i | \(-0.00945641\pi\) | |||||||
\(200\) | −1965.24 | −0.0491309 | ||||||||
\(201\) | 13659.1i | 0.338088i | ||||||||
\(202\) | − | 25942.5i | − | 0.635784i | ||||||
\(203\) | −2187.77 | − | 16460.4i | −0.0530895 | − | 0.399438i | ||||
\(204\) | −18470.6 | −0.443834 | ||||||||
\(205\) | 30710.6 | 0.730769 | ||||||||
\(206\) | − | 11049.2i | − | 0.260372i | ||||||
\(207\) | 37548.5 | 0.876298 | ||||||||
\(208\) | − | 3108.66i | − | 0.0718533i | ||||||
\(209\) | 115078.i | 2.63450i | ||||||||
\(210\) | 5374.30 | + | 40435.5i | 0.121866 | + | 0.916905i | ||||
\(211\) | −65056.4 | −1.46125 | −0.730626 | − | 0.682778i | \(-0.760772\pi\) | ||||
−0.730626 | + | 0.682778i | \(0.760772\pi\) | |||||||
\(212\) | −11687.5 | −0.260046 | ||||||||
\(213\) | 28881.5i | 0.636590i | ||||||||
\(214\) | 34340.7 | 0.749863 | ||||||||
\(215\) | − | 45009.6i | − | 0.973706i | ||||||
\(216\) | 295.534i | 0.00633433i | ||||||||
\(217\) | −12996.0 | + | 1727.30i | −0.275987 | + | 0.0366816i | ||||
\(218\) | −19256.9 | −0.405203 | ||||||||
\(219\) | −90168.7 | −1.88004 | ||||||||
\(220\) | − | 35599.4i | − | 0.735524i | ||||||
\(221\) | −8839.17 | −0.180978 | ||||||||
\(222\) | − | 23990.5i | − | 0.486780i | ||||||
\(223\) | 30412.4i | 0.611563i | 0.952102 | + | 0.305781i | \(0.0989177\pi\) | ||||
−0.952102 | + | 0.305781i | \(0.901082\pi\) | |||||||
\(224\) | −1168.63 | − | 8792.63i | −0.0232907 | − | 0.175236i | ||||
\(225\) | −6945.60 | −0.137197 | ||||||||
\(226\) | 13475.2 | 0.263826 | ||||||||
\(227\) | 52125.5i | 1.01158i | 0.862658 | + | 0.505788i | \(0.168798\pi\) | ||||
−0.862658 | + | 0.505788i | \(0.831202\pi\) | |||||||
\(228\) | 60891.0 | 1.17134 | ||||||||
\(229\) | − | 81280.2i | − | 1.54994i | −0.632000 | − | 0.774968i | \(-0.717766\pi\) | ||
0.632000 | − | 0.774968i | \(-0.282234\pi\) | |||||||
\(230\) | − | 30807.6i | − | 0.582375i | ||||||
\(231\) | 118214. | − | 15711.9i | 2.21536 | − | 0.294445i | ||||
\(232\) | 7668.01 | 0.142465 | ||||||||
\(233\) | −41718.9 | −0.768459 | −0.384229 | − | 0.923238i | \(-0.625533\pi\) | ||||
−0.384229 | + | 0.923238i | \(0.625533\pi\) | |||||||
\(234\) | − | 10986.7i | − | 0.200649i | ||||||
\(235\) | 68129.9 | 1.23368 | ||||||||
\(236\) | − | 13846.7i | − | 0.248612i | ||||||
\(237\) | − | 88968.9i | − | 1.58395i | ||||||
\(238\) | −25000.9 | + | 3322.89i | −0.441370 | + | 0.0586627i | ||||
\(239\) | −3936.55 | −0.0689160 | −0.0344580 | − | 0.999406i | \(-0.510970\pi\) | ||||
−0.0344580 | + | 0.999406i | \(0.510970\pi\) | |||||||
\(240\) | −18836.7 | −0.327025 | ||||||||
\(241\) | − | 70511.5i | − | 1.21402i | −0.794694 | − | 0.607010i | \(-0.792369\pi\) | ||
0.794694 | − | 0.607010i | \(-0.207631\pi\) | |||||||
\(242\) | −62664.4 | −1.07002 | ||||||||
\(243\) | 83228.7i | 1.40949i | ||||||||
\(244\) | 1970.74i | 0.0331017i | ||||||||
\(245\) | 14548.8 | + | 53764.8i | 0.242379 | + | 0.895706i | ||||
\(246\) | −47506.8 | −0.785028 | ||||||||
\(247\) | 29139.6 | 0.477628 | ||||||||
\(248\) | − | 6054.11i | − | 0.0984343i | ||||||
\(249\) | −18376.0 | −0.296382 | ||||||||
\(250\) | 46707.4i | 0.747318i | ||||||||
\(251\) | − | 72042.3i | − | 1.14351i | −0.820424 | − | 0.571755i | \(-0.806263\pi\) | ||
0.820424 | − | 0.571755i | \(-0.193737\pi\) | |||||||
\(252\) | −4130.22 | − | 31075.2i | −0.0650387 | − | 0.489342i | ||||
\(253\) | −90066.6 | −1.40709 | ||||||||
\(254\) | 79108.1 | 1.22618 | ||||||||
\(255\) | 53560.1i | 0.823685i | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 65615.5i | 0.993436i | 0.867912 | + | 0.496718i | \(0.165462\pi\) | ||||
−0.867912 | + | 0.496718i | \(0.834538\pi\) | |||||||
\(258\) | 69626.1i | 1.04600i | ||||||||
\(259\) | −4315.92 | − | 32472.4i | −0.0643390 | − | 0.484078i | ||||
\(260\) | −9014.35 | −0.133348 | ||||||||
\(261\) | 27100.5 | 0.397829 | ||||||||
\(262\) | 67929.0i | 0.989583i | ||||||||
\(263\) | −38706.1 | −0.559588 | −0.279794 | − | 0.960060i | \(-0.590266\pi\) | ||||
−0.279794 | + | 0.960060i | \(0.590266\pi\) | |||||||
\(264\) | 55069.3i | 0.790136i | ||||||||
\(265\) | 33890.8i | 0.482604i | ||||||||
\(266\) | 82419.2 | − | 10954.4i | 1.16484 | − | 0.154819i | ||||
\(267\) | −27071.5 | −0.379743 | ||||||||
\(268\) | −8612.70 | −0.119914 | ||||||||
\(269\) | − | 87226.9i | − | 1.20544i | −0.797952 | − | 0.602721i | \(-0.794083\pi\) | ||
0.797952 | − | 0.602721i | \(-0.205917\pi\) | |||||||
\(270\) | 856.977 | 0.0117555 | ||||||||
\(271\) | 105362.i | 1.43465i | 0.696739 | + | 0.717324i | \(0.254633\pi\) | ||||
−0.696739 | + | 0.717324i | \(0.745367\pi\) | |||||||
\(272\) | − | 11646.6i | − | 0.157420i | ||||||
\(273\) | −3978.50 | − | 29933.7i | −0.0533820 | − | 0.401638i | ||||
\(274\) | 11771.9 | 0.156800 | ||||||||
\(275\) | 16660.2 | 0.220301 | ||||||||
\(276\) | 47656.9i | 0.625615i | ||||||||
\(277\) | 36178.9 | 0.471515 | 0.235758 | − | 0.971812i | \(-0.424243\pi\) | ||||
0.235758 | + | 0.971812i | \(0.424243\pi\) | |||||||
\(278\) | − | 74573.7i | − | 0.964931i | ||||||
\(279\) | − | 21396.6i | − | 0.274876i | ||||||
\(280\) | −25496.4 | + | 3388.75i | −0.325210 | + | 0.0432238i | ||||
\(281\) | 99142.2 | 1.25558 | 0.627792 | − | 0.778381i | \(-0.283959\pi\) | ||||
0.627792 | + | 0.778381i | \(0.283959\pi\) | |||||||
\(282\) | −105391. | −1.32528 | ||||||||
\(283\) | − | 4153.27i | − | 0.0518581i | −0.999664 | − | 0.0259291i | \(-0.991746\pi\) | ||
0.999664 | − | 0.0259291i | \(-0.00825441\pi\) | |||||||
\(284\) | −18211.1 | −0.225787 | ||||||||
\(285\) | − | 176569.i | − | 2.17382i | ||||||
\(286\) | 26353.6i | 0.322187i | ||||||||
\(287\) | −64302.9 | + | 8546.54i | −0.780669 | + | 0.103759i | ||||
\(288\) | 14476.2 | 0.174530 | ||||||||
\(289\) | 50405.2 | 0.603503 | ||||||||
\(290\) | − | 22235.3i | − | 0.264392i | ||||||
\(291\) | −74840.1 | −0.883788 | ||||||||
\(292\) | − | 56855.5i | − | 0.666817i | ||||||
\(293\) | − | 20239.4i | − | 0.235756i | −0.993028 | − | 0.117878i | \(-0.962391\pi\) | ||
0.993028 | − | 0.117878i | \(-0.0376092\pi\) | |||||||
\(294\) | −22505.8 | − | 83169.7i | −0.260376 | − | 0.962211i | ||||
\(295\) | −40151.9 | −0.461384 | ||||||||
\(296\) | 15127.1 | 0.172652 | ||||||||
\(297\) | − | 2505.39i | − | 0.0284028i | ||||||
\(298\) | 18601.3 | 0.209465 | ||||||||
\(299\) | 22806.4i | 0.255102i | ||||||||
\(300\) | − | 8815.42i | − | 0.0979491i | ||||||
\(301\) | 12525.8 | + | 94242.7i | 0.138253 | + | 1.04019i | ||||
\(302\) | 64857.1 | 0.711121 | ||||||||
\(303\) | 116370. | 1.26752 | ||||||||
\(304\) | 38394.6i | 0.415454i | ||||||||
\(305\) | 5714.66 | 0.0614315 | ||||||||
\(306\) | − | 41161.7i | − | 0.439592i | ||||||
\(307\) | 63269.8i | 0.671305i | 0.941986 | + | 0.335652i | \(0.108957\pi\) | ||||
−0.941986 | + | 0.335652i | \(0.891043\pi\) | |||||||
\(308\) | 9907.05 | + | 74539.3i | 0.104434 | + | 0.785749i | ||||
\(309\) | 49563.0 | 0.519087 | ||||||||
\(310\) | −17555.4 | −0.182679 | ||||||||
\(311\) | − | 14375.4i | − | 0.148627i | −0.997235 | − | 0.0743137i | \(-0.976323\pi\) | ||
0.997235 | − | 0.0743137i | \(-0.0236766\pi\) | |||||||
\(312\) | 13944.5 | 0.143249 | ||||||||
\(313\) | 36763.0i | 0.375252i | 0.982241 | + | 0.187626i | \(0.0600792\pi\) | ||||
−0.982241 | + | 0.187626i | \(0.939921\pi\) | |||||||
\(314\) | − | 105480.i | − | 1.06982i | ||||||
\(315\) | −90110.3 | + | 11976.6i | −0.908142 | + | 0.120702i | ||||
\(316\) | 56099.0 | 0.561799 | ||||||||
\(317\) | −125556. | −1.24945 | −0.624726 | − | 0.780844i | \(-0.714789\pi\) | ||||
−0.624726 | + | 0.780844i | \(0.714789\pi\) | |||||||
\(318\) | − | 52426.4i | − | 0.518436i | ||||||
\(319\) | −65005.4 | −0.638804 | ||||||||
\(320\) | − | 11877.4i | − | 0.115990i | ||||||
\(321\) | 154041.i | 1.49495i | ||||||||
\(322\) | 8573.55 | + | 64506.1i | 0.0826892 | + | 0.622142i | ||||
\(323\) | 109171. | 1.04641 | ||||||||
\(324\) | −53146.6 | −0.506274 | ||||||||
\(325\) | − | 4218.65i | − | 0.0399399i | ||||||
\(326\) | −115553. | −1.08729 | ||||||||
\(327\) | − | 86380.2i | − | 0.807828i | ||||||
\(328\) | − | 29955.2i | − | 0.278435i | ||||||
\(329\) | −142653. | + | 18960.1i | −1.31792 | + | 0.175165i | ||||
\(330\) | 159687. | 1.46637 | ||||||||
\(331\) | 5376.54 | 0.0490735 | 0.0245367 | − | 0.999699i | \(-0.492189\pi\) | ||||
0.0245367 | + | 0.999699i | \(0.492189\pi\) | |||||||
\(332\) | − | 11586.9i | − | 0.105121i | ||||||
\(333\) | 53462.7 | 0.482128 | ||||||||
\(334\) | 98358.3i | 0.881694i | ||||||||
\(335\) | 24974.7i | 0.222541i | ||||||||
\(336\) | 39440.9 | − | 5242.11i | 0.349356 | − | 0.0464331i | ||||
\(337\) | 2202.27 | 0.0193914 | 0.00969572 | − | 0.999953i | \(-0.496914\pi\) | ||||
0.00969572 | + | 0.999953i | \(0.496914\pi\) | |||||||
\(338\) | −74109.5 | −0.648695 | ||||||||
\(339\) | 60445.4i | 0.525974i | ||||||||
\(340\) | −33772.1 | −0.292146 | ||||||||
\(341\) | 51323.5i | 0.441375i | ||||||||
\(342\) | 135695.i | 1.16015i | ||||||||
\(343\) | −45425.2 | − | 108526.i | −0.386108 | − | 0.922454i | ||||
\(344\) | −43902.5 | −0.370998 | ||||||||
\(345\) | 138193. | 1.16104 | ||||||||
\(346\) | − | 89378.5i | − | 0.746587i | ||||||
\(347\) | 222201. | 1.84538 | 0.922691 | − | 0.385541i | \(-0.125985\pi\) | ||||
0.922691 | + | 0.385541i | \(0.125985\pi\) | |||||||
\(348\) | 34396.2i | 0.284022i | ||||||||
\(349\) | − | 102679.i | − | 0.843006i | −0.906827 | − | 0.421503i | \(-0.861503\pi\) | ||
0.906827 | − | 0.421503i | \(-0.138497\pi\) | |||||||
\(350\) | −1585.91 | − | 11932.1i | −0.0129462 | − | 0.0974052i | ||||
\(351\) | −634.405 | −0.00514935 | ||||||||
\(352\) | −34723.7 | −0.280247 | ||||||||
\(353\) | 62595.6i | 0.502336i | 0.967943 | + | 0.251168i | \(0.0808147\pi\) | ||||
−0.967943 | + | 0.251168i | \(0.919185\pi\) | |||||||
\(354\) | 62111.8 | 0.495641 | ||||||||
\(355\) | 52807.7i | 0.419025i | ||||||||
\(356\) | − | 17069.8i | − | 0.134688i | ||||||
\(357\) | −14905.4 | − | 112146.i | −0.116952 | − | 0.879930i | ||||
\(358\) | −64348.6 | −0.502080 | ||||||||
\(359\) | 95505.9 | 0.741040 | 0.370520 | − | 0.928825i | \(-0.379180\pi\) | ||||
0.370520 | + | 0.928825i | \(0.379180\pi\) | |||||||
\(360\) | − | 41977.4i | − | 0.323900i | ||||||
\(361\) | −229577. | −1.76163 | ||||||||
\(362\) | 156792.i | 1.19648i | ||||||||
\(363\) | − | 281092.i | − | 2.13322i | ||||||
\(364\) | 18874.6 | − | 2508.63i | 0.142454 | − | 0.0189336i | ||||
\(365\) | −164867. | −1.23751 | ||||||||
\(366\) | −8840.12 | −0.0659927 | ||||||||
\(367\) | − | 82330.9i | − | 0.611267i | −0.952149 | − | 0.305633i | \(-0.901132\pi\) | ||
0.952149 | − | 0.305633i | \(-0.0988682\pi\) | |||||||
\(368\) | −30049.9 | −0.221895 | ||||||||
\(369\) | − | 105869.i | − | 0.777525i | ||||||
\(370\) | − | 43864.9i | − | 0.320415i | ||||||
\(371\) | −9431.58 | − | 70961.9i | −0.0685230 | − | 0.515558i | ||||
\(372\) | 27156.8 | 0.196242 | ||||||||
\(373\) | 130223. | 0.935991 | 0.467995 | − | 0.883731i | \(-0.344976\pi\) | ||||
0.467995 | + | 0.883731i | \(0.344976\pi\) | |||||||
\(374\) | 98733.4i | 0.705864i | ||||||||
\(375\) | −209514. | −1.48988 | ||||||||
\(376\) | − | 66454.2i | − | 0.470053i | ||||||
\(377\) | 16460.4i | 0.115813i | ||||||||
\(378\) | −1794.37 | + | 238.491i | −0.0125582 | + | 0.00166912i | ||||
\(379\) | 192349. | 1.33909 | 0.669546 | − | 0.742770i | \(-0.266489\pi\) | ||||
0.669546 | + | 0.742770i | \(0.266489\pi\) | |||||||
\(380\) | 111335. | 0.771016 | ||||||||
\(381\) | 354853.i | 2.44455i | ||||||||
\(382\) | 143734. | 0.984992 | ||||||||
\(383\) | − | 101933.i | − | 0.694891i | −0.937700 | − | 0.347446i | \(-0.887049\pi\) | ||
0.937700 | − | 0.347446i | \(-0.112951\pi\) | |||||||
\(384\) | 18373.3i | 0.124602i | ||||||||
\(385\) | 216145. | − | 28728.0i | 1.45823 | − | 0.193813i | ||||
\(386\) | 3530.84 | 0.0236975 | ||||||||
\(387\) | −155162. | −1.03601 | ||||||||
\(388\) | − | 47190.1i | − | 0.313464i | ||||||
\(389\) | 191074. | 1.26271 | 0.631353 | − | 0.775495i | \(-0.282500\pi\) | ||||
0.631353 | + | 0.775495i | \(0.282500\pi\) | |||||||
\(390\) | − | 40435.5i | − | 0.265848i | ||||||
\(391\) | 85443.7i | 0.558890i | ||||||||
\(392\) | 52442.3 | − | 14191.0i | 0.341279 | − | 0.0923506i | ||||
\(393\) | −304708. | −1.97287 | ||||||||
\(394\) | −182305. | −1.17437 | ||||||||
\(395\) | − | 162673.i | − | 1.04261i | ||||||
\(396\) | −122722. | −0.782585 | ||||||||
\(397\) | 201143.i | 1.27622i | 0.769947 | + | 0.638108i | \(0.220283\pi\) | ||||
−0.769947 | + | 0.638108i | \(0.779717\pi\) | |||||||
\(398\) | 6654.16i | 0.0420076i | ||||||||
\(399\) | 49137.9 | + | 369706.i | 0.308653 | + | 2.32226i | ||||
\(400\) | 5558.52 | 0.0347408 | ||||||||
\(401\) | −39978.4 | −0.248621 | −0.124310 | − | 0.992243i | \(-0.539672\pi\) | ||||
−0.124310 | + | 0.992243i | \(0.539672\pi\) | |||||||
\(402\) | − | 38633.8i | − | 0.239065i | ||||||
\(403\) | 12996.0 | 0.0800200 | ||||||||
\(404\) | 73376.6i | 0.449567i | ||||||||
\(405\) | 154112.i | 0.939564i | ||||||||
\(406\) | 6187.93 | + | 46557.1i | 0.0375399 | + | 0.282445i | ||||
\(407\) | −128240. | −0.774165 | ||||||||
\(408\) | 52242.7 | 0.313838 | ||||||||
\(409\) | − | 80655.7i | − | 0.482157i | −0.970506 | − | 0.241078i | \(-0.922499\pi\) | ||
0.970506 | − | 0.241078i | \(-0.0775011\pi\) | |||||||
\(410\) | −86862.6 | −0.516732 | ||||||||
\(411\) | 52805.0i | 0.312602i | ||||||||
\(412\) | 31251.7i | 0.184111i | ||||||||
\(413\) | 84071.6 | − | 11174.0i | 0.492889 | − | 0.0655101i | ||||
\(414\) | −106203. | −0.619636 | ||||||||
\(415\) | −33599.1 | −0.195088 | ||||||||
\(416\) | 8792.63i | 0.0508080i | ||||||||
\(417\) | 334514. | 1.92372 | ||||||||
\(418\) | − | 325489.i | − | 1.86288i | ||||||
\(419\) | 252034.i | 1.43559i | 0.696254 | + | 0.717795i | \(0.254849\pi\) | ||||
−0.696254 | + | 0.717795i | \(0.745151\pi\) | |||||||
\(420\) | −15200.8 | − | 114369.i | −0.0861725 | − | 0.648349i | ||||
\(421\) | −84439.3 | −0.476410 | −0.238205 | − | 0.971215i | \(-0.576559\pi\) | ||||
−0.238205 | + | 0.971215i | \(0.576559\pi\) | |||||||
\(422\) | 184007. | 1.03326 | ||||||||
\(423\) | − | 234864.i | − | 1.31261i | ||||||
\(424\) | 33057.2 | 0.183880 | ||||||||
\(425\) | − | 15805.1i | − | 0.0875023i | ||||||
\(426\) | − | 81689.1i | − | 0.450137i | ||||||
\(427\) | −11965.6 | + | 1590.35i | −0.0656263 | + | 0.00872242i | ||||
\(428\) | −97130.2 | −0.530233 | ||||||||
\(429\) | −118214. | −0.642323 | ||||||||
\(430\) | 127306.i | 0.688514i | ||||||||
\(431\) | −127512. | −0.686431 | −0.343215 | − | 0.939257i | \(-0.611516\pi\) | ||||
−0.343215 | + | 0.939257i | \(0.611516\pi\) | |||||||
\(432\) | − | 835.898i | − | 0.00447905i | ||||||
\(433\) | − | 233539.i | − | 1.24562i | −0.782375 | − | 0.622808i | \(-0.785992\pi\) | ||
0.782375 | − | 0.622808i | \(-0.214008\pi\) | |||||||
\(434\) | 36758.2 | − | 4885.55i | 0.195153 | − | 0.0259378i | ||||
\(435\) | 99740.6 | 0.527100 | ||||||||
\(436\) | 54466.7 | 0.286522 | ||||||||
\(437\) | − | 281678.i | − | 1.47499i | ||||||
\(438\) | 255036. | 1.32939 | ||||||||
\(439\) | − | 304238.i | − | 1.57864i | −0.613980 | − | 0.789322i | \(-0.710432\pi\) | ||
0.613980 | − | 0.789322i | \(-0.289568\pi\) | |||||||
\(440\) | 100690.i | 0.520094i | ||||||||
\(441\) | 185343. | − | 50154.1i | 0.953015 | − | 0.257887i | ||||
\(442\) | 25000.9 | 0.127971 | ||||||||
\(443\) | −87061.0 | −0.443625 | −0.221813 | − | 0.975089i | \(-0.571197\pi\) | ||||
−0.221813 | + | 0.975089i | \(0.571197\pi\) | |||||||
\(444\) | 67855.3i | 0.344206i | ||||||||
\(445\) | −49498.2 | −0.249960 | ||||||||
\(446\) | − | 86019.3i | − | 0.432440i | ||||||
\(447\) | 83439.7i | 0.417597i | ||||||||
\(448\) | 3305.39 | + | 24869.3i | 0.0164690 | + | 0.123910i | ||||
\(449\) | −91141.4 | −0.452088 | −0.226044 | − | 0.974117i | \(-0.572579\pi\) | ||||
−0.226044 | + | 0.974117i | \(0.572579\pi\) | |||||||
\(450\) | 19645.1 | 0.0970129 | ||||||||
\(451\) | 253944.i | 1.24849i | ||||||||
\(452\) | −38113.6 | −0.186553 | ||||||||
\(453\) | 290928.i | 1.41772i | ||||||||
\(454\) | − | 147433.i | − | 0.715292i | ||||||
\(455\) | −7274.41 | − | 54731.6i | −0.0351378 | − | 0.264372i | ||||
\(456\) | −172226. | −0.828263 | ||||||||
\(457\) | −411928. | −1.97237 | −0.986187 | − | 0.165634i | \(-0.947033\pi\) | ||||
−0.986187 | + | 0.165634i | \(0.947033\pi\) | |||||||
\(458\) | 229895.i | 1.09597i | ||||||||
\(459\) | −2376.79 | −0.0112815 | ||||||||
\(460\) | 87137.1i | 0.411801i | ||||||||
\(461\) | − | 157397.i | − | 0.740617i | −0.928909 | − | 0.370309i | \(-0.879252\pi\) | ||
0.928909 | − | 0.370309i | \(-0.120748\pi\) | |||||||
\(462\) | −334359. | + | 44439.9i | −1.56650 | + | 0.208204i | ||||
\(463\) | 245557. | 1.14549 | 0.572745 | − | 0.819734i | \(-0.305879\pi\) | ||||
0.572745 | + | 0.819734i | \(0.305879\pi\) | |||||||
\(464\) | −21688.4 | −0.100738 | ||||||||
\(465\) | − | 78747.9i | − | 0.364194i | ||||||
\(466\) | 117999. | 0.543383 | ||||||||
\(467\) | − | 33069.2i | − | 0.151632i | −0.997122 | − | 0.0758158i | \(-0.975844\pi\) | ||
0.997122 | − | 0.0758158i | \(-0.0241561\pi\) | |||||||
\(468\) | 31075.2i | 0.141880i | ||||||||
\(469\) | −6950.28 | − | 52292.9i | −0.0315978 | − | 0.237737i | ||||
\(470\) | −192701. | −0.872343 | ||||||||
\(471\) | 473151. | 2.13284 | ||||||||
\(472\) | 39164.3i | 0.175795i | ||||||||
\(473\) | 372182. | 1.66354 | ||||||||
\(474\) | 251642.i | 1.12002i | ||||||||
\(475\) | 52103.8i | 0.230931i | ||||||||
\(476\) | 70713.3 | − | 9398.55i | 0.312095 | − | 0.0414808i | ||||
\(477\) | 116832. | 0.513482 | ||||||||
\(478\) | 11134.2 | 0.0487309 | ||||||||
\(479\) | 384277.i | 1.67484i | 0.546559 | + | 0.837421i | \(0.315937\pi\) | ||||
−0.546559 | + | 0.837421i | \(0.684063\pi\) | |||||||
\(480\) | 53278.1 | 0.231242 | ||||||||
\(481\) | 32472.4i | 0.140354i | ||||||||
\(482\) | 199437.i | 0.858442i | ||||||||
\(483\) | −289354. | + | 38458.2i | −1.24032 | + | 0.164852i | ||||
\(484\) | 177242. | 0.756615 | ||||||||
\(485\) | −136840. | −0.581739 | ||||||||
\(486\) | − | 235406.i | − | 0.996657i | ||||||
\(487\) | −173526. | −0.731657 | −0.365829 | − | 0.930682i | \(-0.619214\pi\) | ||||
−0.365829 | + | 0.930682i | \(0.619214\pi\) | |||||||
\(488\) | − | 5574.10i | − | 0.0234064i | ||||||
\(489\) | − | 518332.i | − | 2.16765i | ||||||
\(490\) | −41150.3 | − | 152070.i | −0.171388 | − | 0.633360i | ||||
\(491\) | −20006.3 | −0.0829858 | −0.0414929 | − | 0.999139i | \(-0.513211\pi\) | ||||
−0.0414929 | + | 0.999139i | \(0.513211\pi\) | |||||||
\(492\) | 134369. | 0.555099 | ||||||||
\(493\) | 61668.8i | 0.253730i | ||||||||
\(494\) | −82419.2 | −0.337734 | ||||||||
\(495\) | 355863.i | 1.45235i | ||||||||
\(496\) | 17123.6i | 0.0696036i | ||||||||
\(497\) | −14696.0 | − | 110571.i | −0.0594958 | − | 0.447638i | ||||
\(498\) | 51975.1 | 0.209574 | ||||||||
\(499\) | −428368. | −1.72035 | −0.860174 | − | 0.510000i | \(-0.829645\pi\) | ||||
−0.860174 | + | 0.510000i | \(0.829645\pi\) | |||||||
\(500\) | − | 132108.i | − | 0.528434i | ||||||
\(501\) | −441204. | −1.75778 | ||||||||
\(502\) | 203766.i | 0.808584i | ||||||||
\(503\) | 36793.4i | 0.145423i | 0.997353 | + | 0.0727116i | \(0.0231653\pi\) | ||||
−0.997353 | + | 0.0727116i | \(0.976835\pi\) | |||||||
\(504\) | 11682.0 | + | 87893.9i | 0.0459893 | + | 0.346017i | ||||
\(505\) | 212774. | 0.834326 | ||||||||
\(506\) | 254747. | 0.994965 | ||||||||
\(507\) | − | 332432.i | − | 1.29326i | ||||||
\(508\) | −223751. | −0.867038 | ||||||||
\(509\) | − | 137334.i | − | 0.530080i | −0.964237 | − | 0.265040i | \(-0.914615\pi\) | ||
0.964237 | − | 0.265040i | \(-0.0853852\pi\) | |||||||
\(510\) | − | 151491.i | − | 0.582434i | ||||||
\(511\) | 345204. | − | 45881.3i | 1.32201 | − | 0.175709i | ||||
\(512\) | −11585.2 | −0.0441942 | ||||||||
\(513\) | 7835.43 | 0.0297734 | ||||||||
\(514\) | − | 185589.i | − | 0.702466i | ||||||
\(515\) | 90622.2 | 0.341681 | ||||||||
\(516\) | − | 196932.i | − | 0.739636i | ||||||
\(517\) | 563363.i | 2.10769i | ||||||||
\(518\) | 12207.3 | + | 91845.8i | 0.0454945 | + | 0.342294i | ||||
\(519\) | 400923. | 1.48842 | ||||||||
\(520\) | 25496.4 | 0.0942916 | ||||||||
\(521\) | 102775.i | 0.378629i | 0.981916 | + | 0.189315i | \(0.0606266\pi\) | ||||
−0.981916 | + | 0.189315i | \(0.939373\pi\) | |||||||
\(522\) | −76651.9 | −0.281308 | ||||||||
\(523\) | − | 314194.i | − | 1.14867i | −0.818621 | − | 0.574334i | \(-0.805261\pi\) | ||
0.818621 | − | 0.574334i | \(-0.194739\pi\) | |||||||
\(524\) | − | 192132.i | − | 0.699741i | ||||||
\(525\) | 53523.7 | − | 7113.87i | 0.194190 | − | 0.0258100i | ||||
\(526\) | 109478. | 0.395689 | ||||||||
\(527\) | 48689.2 | 0.175312 | ||||||||
\(528\) | − | 155760.i | − | 0.558711i | ||||||
\(529\) | −59383.5 | −0.212204 | ||||||||
\(530\) | − | 95857.8i | − | 0.341252i | ||||||
\(531\) | 138416.i | 0.490904i | ||||||||
\(532\) | −233117. | + | 30983.7i | −0.823664 | + | 0.109474i | ||||
\(533\) | 64302.9 | 0.226348 | ||||||||
\(534\) | 76569.7 | 0.268519 | ||||||||
\(535\) | 281654.i | 0.984029i | ||||||||
\(536\) | 24360.4 | 0.0847919 | ||||||||
\(537\) | − | 288647.i | − | 1.00096i | ||||||
\(538\) | 246715.i | 0.852376i | ||||||||
\(539\) | −444578. | + | 120303.i | −1.53028 | + | 0.414096i | ||||
\(540\) | −2423.90 | −0.00831240 | ||||||||
\(541\) | 298384. | 1.01948 | 0.509742 | − | 0.860327i | \(-0.329741\pi\) | ||||
0.509742 | + | 0.860327i | \(0.329741\pi\) | |||||||
\(542\) | − | 298009.i | − | 1.01445i | ||||||
\(543\) | −703319. | −2.38535 | ||||||||
\(544\) | 32941.4i | 0.111313i | ||||||||
\(545\) | − | 157940.i | − | 0.531740i | ||||||
\(546\) | 11252.9 | + | 84665.3i | 0.0377468 | + | 0.284001i | ||||
\(547\) | 361462. | 1.20806 | 0.604029 | − | 0.796963i | \(-0.293561\pi\) | ||||
0.604029 | + | 0.796963i | \(0.293561\pi\) | |||||||
\(548\) | −33296.0 | −0.110874 | ||||||||
\(549\) | − | 19700.2i | − | 0.0653620i | ||||||
\(550\) | −47122.3 | −0.155776 | ||||||||
\(551\) | − | 203300.i | − | 0.669629i | ||||||
\(552\) | − | 134794.i | − | 0.442377i | ||||||
\(553\) | 45270.8 | + | 340611.i | 0.148036 | + | 1.11380i | ||||
\(554\) | −102329. | −0.333412 | ||||||||
\(555\) | 196764. | 0.638791 | ||||||||
\(556\) | 210926.i | 0.682309i | ||||||||
\(557\) | 112424. | 0.362367 | 0.181183 | − | 0.983449i | \(-0.442007\pi\) | ||||
0.181183 | + | 0.983449i | \(0.442007\pi\) | |||||||
\(558\) | 60518.8i | 0.194367i | ||||||||
\(559\) | − | 94242.7i | − | 0.301595i | ||||||
\(560\) | 72114.8 | − | 9584.82i | 0.229958 | − | 0.0305638i | ||||
\(561\) | −442886. | −1.40724 | ||||||||
\(562\) | −280416. | −0.887832 | ||||||||
\(563\) | 441530.i | 1.39298i | 0.717569 | + | 0.696488i | \(0.245255\pi\) | ||||
−0.717569 | + | 0.696488i | \(0.754745\pi\) | |||||||
\(564\) | 298092. | 0.937113 | ||||||||
\(565\) | 110520.i | 0.346214i | ||||||||
\(566\) | 11747.2i | 0.0366692i | ||||||||
\(567\) | −42888.3 | − | 322685.i | −0.133405 | − | 1.00372i | ||||
\(568\) | 51508.8 | 0.159656 | ||||||||
\(569\) | 397273. | 1.22706 | 0.613529 | − | 0.789673i | \(-0.289750\pi\) | ||||
0.613529 | + | 0.789673i | \(0.289750\pi\) | |||||||
\(570\) | 499412.i | 1.53713i | ||||||||
\(571\) | −67235.8 | −0.206219 | −0.103109 | − | 0.994670i | \(-0.532879\pi\) | ||||
−0.103109 | + | 0.994670i | \(0.532879\pi\) | |||||||
\(572\) | − | 74539.3i | − | 0.227821i | ||||||
\(573\) | 644744.i | 1.96371i | ||||||||
\(574\) | 181876. | − | 24173.3i | 0.552016 | − | 0.0733688i | ||||
\(575\) | −40779.5 | −0.123341 | ||||||||
\(576\) | −40944.9 | −0.123411 | ||||||||
\(577\) | − | 64756.1i | − | 0.194504i | −0.995260 | − | 0.0972521i | \(-0.968995\pi\) | ||
0.995260 | − | 0.0972521i | \(-0.0310053\pi\) | |||||||
\(578\) | −142567. | −0.426741 | ||||||||
\(579\) | 15838.2i | 0.0472443i | ||||||||
\(580\) | 62891.0i | 0.186953i | ||||||||
\(581\) | 70351.0 | − | 9350.39i | 0.208410 | − | 0.0276999i | ||||
\(582\) | 211680. | 0.624933 | ||||||||
\(583\) | −280242. | −0.824510 | ||||||||
\(584\) | 160812.i | 0.471511i | ||||||||
\(585\) | 90110.3 | 0.263307 | ||||||||
\(586\) | 57245.8i | 0.166705i | ||||||||
\(587\) | − | 338967.i | − | 0.983741i | −0.870668 | − | 0.491870i | \(-0.836313\pi\) | ||
0.870668 | − | 0.491870i | \(-0.163687\pi\) | |||||||
\(588\) | 63656.1 | + | 235239.i | 0.184113 | + | 0.680386i | ||||
\(589\) | −160511. | −0.462673 | ||||||||
\(590\) | 113567. | 0.326248 | ||||||||
\(591\) | − | 817763.i | − | 2.34128i | ||||||
\(592\) | −42785.9 | −0.122084 | ||||||||
\(593\) | 255668.i | 0.727054i | 0.931584 | + | 0.363527i | \(0.118428\pi\) | ||||
−0.931584 | + | 0.363527i | \(0.881572\pi\) | |||||||
\(594\) | 7086.30i | 0.0200838i | ||||||||
\(595\) | −27253.5 | − | 205051.i | −0.0769817 | − | 0.579200i | ||||
\(596\) | −52612.6 | −0.148114 | ||||||||
\(597\) | −29848.4 | −0.0837477 | ||||||||
\(598\) | − | 64506.1i | − | 0.180384i | ||||||
\(599\) | 129521. | 0.360982 | 0.180491 | − | 0.983577i | \(-0.442231\pi\) | ||||
0.180491 | + | 0.983577i | \(0.442231\pi\) | |||||||
\(600\) | 24933.8i | 0.0692604i | ||||||||
\(601\) | − | 377277.i | − | 1.04451i | −0.852790 | − | 0.522254i | \(-0.825091\pi\) | ||
0.852790 | − | 0.522254i | \(-0.174909\pi\) | |||||||
\(602\) | −35428.4 | − | 266559.i | −0.0977595 | − | 0.735529i | ||||
\(603\) | 86095.3 | 0.236780 | ||||||||
\(604\) | −183444. | −0.502839 | ||||||||
\(605\) | − | 513957.i | − | 1.40416i | ||||||
\(606\) | −329144. | −0.896274 | ||||||||
\(607\) | 421091.i | 1.14287i | 0.820646 | + | 0.571437i | \(0.193614\pi\) | ||||
−0.820646 | + | 0.571437i | \(0.806386\pi\) | |||||||
\(608\) | − | 108596.i | − | 0.293770i | ||||||
\(609\) | −208840. | + | 27757.1i | −0.563093 | + | 0.0748410i | ||||
\(610\) | −16163.5 | −0.0434386 | ||||||||
\(611\) | 142653. | 0.382119 | ||||||||
\(612\) | 116423.i | 0.310839i | ||||||||
\(613\) | 412173. | 1.09688 | 0.548440 | − | 0.836190i | \(-0.315222\pi\) | ||||
0.548440 | + | 0.836190i | \(0.315222\pi\) | |||||||
\(614\) | − | 178954.i | − | 0.474684i | ||||||
\(615\) | − | 389638.i | − | 1.03018i | ||||||
\(616\) | −28021.4 | − | 210829.i | −0.0738462 | − | 0.555608i | ||||
\(617\) | −262676. | −0.690002 | −0.345001 | − | 0.938602i | \(-0.612121\pi\) | ||||
−0.345001 | + | 0.938602i | \(0.612121\pi\) | |||||||
\(618\) | −140185. | −0.367050 | ||||||||
\(619\) | − | 373975.i | − | 0.976026i | −0.872836 | − | 0.488013i | \(-0.837722\pi\) | ||
0.872836 | − | 0.488013i | \(-0.162278\pi\) | |||||||
\(620\) | 49654.2 | 0.129173 | ||||||||
\(621\) | 6132.47i | 0.0159020i | ||||||||
\(622\) | 40659.7i | 0.105095i | ||||||||
\(623\) | 103641. | − | 13775.0i | 0.267028 | − | 0.0354908i | ||||
\(624\) | −39440.9 | −0.101293 | ||||||||
\(625\) | −328799. | −0.841726 | ||||||||
\(626\) | − | 103982.i | − | 0.265343i | ||||||
\(627\) | 1.46004e6 | 3.71389 | ||||||||
\(628\) | 298344.i | 0.756480i | ||||||||
\(629\) | 121657.i | 0.307494i | ||||||||
\(630\) | 254871. | − | 33875.0i | 0.642153 | − | 0.0853489i | ||||
\(631\) | −408746. | −1.02659 | −0.513293 | − | 0.858214i | \(-0.671574\pi\) | ||||
−0.513293 | + | 0.858214i | \(0.671574\pi\) | |||||||
\(632\) | −158672. | −0.397252 | ||||||||
\(633\) | 825397.i | 2.05995i | ||||||||
\(634\) | 355126. | 0.883495 | ||||||||
\(635\) | 648824.i | 1.60909i | ||||||||
\(636\) | 148284.i | 0.366590i | ||||||||
\(637\) | 30462.8 | + | 112575.i | 0.0750743 | + | 0.277435i | ||||
\(638\) | 183863. | 0.451703 | ||||||||
\(639\) | 182044. | 0.445835 | ||||||||
\(640\) | 33594.3i | 0.0820174i | ||||||||
\(641\) | −528074. | −1.28522 | −0.642612 | − | 0.766192i | \(-0.722149\pi\) | ||||
−0.642612 | + | 0.766192i | \(0.722149\pi\) | |||||||
\(642\) | − | 435695.i | − | 1.05709i | ||||||
\(643\) | − | 323445.i | − | 0.782310i | −0.920325 | − | 0.391155i | \(-0.872076\pi\) | ||
0.920325 | − | 0.391155i | \(-0.127924\pi\) | |||||||
\(644\) | −24249.6 | − | 182451.i | −0.0584701 | − | 0.439921i | ||||
\(645\) | −571055. | −1.37265 | ||||||||
\(646\) | −308782. | −0.739925 | ||||||||
\(647\) | 592372.i | 1.41510i | 0.706665 | + | 0.707548i | \(0.250199\pi\) | ||||
−0.706665 | + | 0.707548i | \(0.749801\pi\) | |||||||
\(648\) | 150321. | 0.357990 | ||||||||
\(649\) | − | 332015.i | − | 0.788257i | ||||||
\(650\) | 11932.1i | 0.0282417i | ||||||||
\(651\) | 21915.0 | + | 164885.i | 0.0517106 | + | 0.389063i | ||||
\(652\) | 326832. | 0.768828 | ||||||||
\(653\) | −329810. | −0.773459 | −0.386730 | − | 0.922193i | \(-0.626395\pi\) | ||||
−0.386730 | + | 0.922193i | \(0.626395\pi\) | |||||||
\(654\) | 244320.i | 0.571221i | ||||||||
\(655\) | −557135. | −1.29861 | ||||||||
\(656\) | 84726.1i | 0.196884i | ||||||||
\(657\) | 568346.i | 1.31669i | ||||||||
\(658\) | 403483. | − | 53627.2i | 0.931910 | − | 0.123861i | ||||
\(659\) | −526737. | −1.21290 | −0.606448 | − | 0.795123i | \(-0.707406\pi\) | ||||
−0.606448 | + | 0.795123i | \(0.707406\pi\) | |||||||
\(660\) | −451664. | −1.03688 | ||||||||
\(661\) | − | 144047.i | − | 0.329686i | −0.986320 | − | 0.164843i | \(-0.947288\pi\) | ||
0.986320 | − | 0.164843i | \(-0.0527117\pi\) | |||||||
\(662\) | −15207.2 | −0.0347002 | ||||||||
\(663\) | 112146.i | 0.255128i | ||||||||
\(664\) | 32772.7i | 0.0743320i | ||||||||
\(665\) | 89845.0 | + | 675981.i | 0.203166 | + | 1.52859i | ||||
\(666\) | −151215. | −0.340916 | ||||||||
\(667\) | 159115. | 0.357650 | ||||||||
\(668\) | − | 278199.i | − | 0.623452i | ||||||
\(669\) | 385855. | 0.862128 | ||||||||
\(670\) | − | 70639.1i | − | 0.157360i | ||||||
\(671\) | 47254.3i | 0.104953i | ||||||||
\(672\) | −111556. | + | 14826.9i | −0.247032 | + | 0.0328332i | ||||
\(673\) | 620117. | 1.36913 | 0.684563 | − | 0.728953i | \(-0.259993\pi\) | ||||
0.684563 | + | 0.728953i | \(0.259993\pi\) | |||||||
\(674\) | −6228.95 | −0.0137118 | ||||||||
\(675\) | − | 1134.36i | − | 0.00248969i | ||||||
\(676\) | 209613. | 0.458697 | ||||||||
\(677\) | − | 626172.i | − | 1.36621i | −0.730322 | − | 0.683103i | \(-0.760630\pi\) | ||
0.730322 | − | 0.683103i | \(-0.239370\pi\) | |||||||
\(678\) | − | 170965.i | − | 0.371920i | ||||||
\(679\) | 286520. | − | 38081.5i | 0.621463 | − | 0.0825989i | ||||
\(680\) | 95522.0 | 0.206579 | ||||||||
\(681\) | 661338. | 1.42603 | ||||||||
\(682\) | − | 145165.i | − | 0.312099i | ||||||
\(683\) | 185558. | 0.397775 | 0.198888 | − | 0.980022i | \(-0.436267\pi\) | ||||
0.198888 | + | 0.980022i | \(0.436267\pi\) | |||||||
\(684\) | − | 383805.i | − | 0.820348i | ||||||
\(685\) | 96550.1i | 0.205765i | ||||||||
\(686\) | 128482. | + | 306957.i | 0.273019 | + | 0.652273i | ||||
\(687\) | −1.03124e6 | −2.18497 | ||||||||
\(688\) | 124175. | 0.262336 | ||||||||
\(689\) | 70961.9i | 0.149481i | ||||||||
\(690\) | −390869. | −0.820981 | ||||||||
\(691\) | − | 548881.i | − | 1.14953i | −0.818317 | − | 0.574767i | \(-0.805093\pi\) | ||
0.818317 | − | 0.574767i | \(-0.194907\pi\) | |||||||
\(692\) | 252800.i | 0.527917i | ||||||||
\(693\) | −99034.1 | − | 745118.i | −0.206214 | − | 1.55153i | ||||
\(694\) | −628478. | −1.30488 | ||||||||
\(695\) | 611634. | 1.26626 | ||||||||
\(696\) | − | 97287.2i | − | 0.200834i | ||||||
\(697\) | 240910. | 0.495894 | ||||||||
\(698\) | 290420.i | 0.596095i | ||||||||
\(699\) | 529305.i | 1.08331i | ||||||||
\(700\) | 4485.62 | + | 33749.2i | 0.00915433 | + | 0.0688759i | ||||
\(701\) | 517501. | 1.05311 | 0.526556 | − | 0.850140i | \(-0.323483\pi\) | ||||
0.526556 | + | 0.850140i | \(0.323483\pi\) | |||||||
\(702\) | 1794.37 | 0.00364114 | ||||||||
\(703\) | − | 401061.i | − | 0.811522i | ||||||
\(704\) | 98213.6 | 0.198165 | ||||||||
\(705\) | − | 864393.i | − | 1.73913i | ||||||
\(706\) | − | 177047.i | − | 0.355205i | ||||||
\(707\) | −445514. | + | 59213.5i | −0.891297 | + | 0.118463i | ||||
\(708\) | −175679. | −0.350471 | ||||||||
\(709\) | 6035.96 | 0.0120075 | 0.00600377 | − | 0.999982i | \(-0.498089\pi\) | ||||
0.00600377 | + | 0.999982i | \(0.498089\pi\) | |||||||
\(710\) | − | 149363.i | − | 0.296296i | ||||||
\(711\) | −560784. | −1.10932 | ||||||||
\(712\) | 48280.7i | 0.0952388i | ||||||||
\(713\) | − | 125625.i | − | 0.247115i | ||||||
\(714\) | 42158.9 | + | 317197.i | 0.0826975 | + | 0.622204i | ||||
\(715\) | −216145. | −0.422799 | ||||||||
\(716\) | 182005. | 0.355024 | ||||||||
\(717\) | 49944.6i | 0.0971517i | ||||||||
\(718\) | −270132. | −0.523994 | ||||||||
\(719\) | 748658.i | 1.44819i | 0.689700 | + | 0.724095i | \(0.257742\pi\) | ||||
−0.689700 | + | 0.724095i | \(0.742258\pi\) | |||||||
\(720\) | 118730.i | 0.229032i | ||||||||
\(721\) | −189748. | + | 25219.5i | −0.365012 | + | 0.0485139i | ||||
\(722\) | 649343. | 1.24566 | ||||||||
\(723\) | −894609. | −1.71142 | ||||||||
\(724\) | − | 443475.i | − | 0.846042i | ||||||
\(725\) | −29432.5 | −0.0559953 | ||||||||
\(726\) | 795049.i | 1.50841i | ||||||||
\(727\) | − | 370335.i | − | 0.700691i | −0.936621 | − | 0.350345i | \(-0.886064\pi\) | ||
0.936621 | − | 0.350345i | \(-0.113936\pi\) | |||||||
\(728\) | −53385.4 | + | 7095.48i | −0.100730 | + | 0.0133881i | ||||
\(729\) | 517848. | 0.974422 | ||||||||
\(730\) | 466314. | 0.875050 | ||||||||
\(731\) | − | 353079.i | − | 0.660750i | ||||||
\(732\) | 25003.6 | 0.0466639 | ||||||||
\(733\) | 144545.i | 0.269027i | 0.990912 | + | 0.134513i | \(0.0429471\pi\) | ||||
−0.990912 | + | 0.134513i | \(0.957053\pi\) | |||||||
\(734\) | 232867.i | 0.432231i | ||||||||
\(735\) | 682136. | − | 184587.i | 1.26269 | − | 0.341685i | ||||
\(736\) | 84993.8 | 0.156903 | ||||||||
\(737\) | −206515. | −0.380203 | ||||||||
\(738\) | 299442.i | 0.549793i | ||||||||
\(739\) | 4650.26 | 0.00851506 | 0.00425753 | − | 0.999991i | \(-0.498645\pi\) | ||||
0.00425753 | + | 0.999991i | \(0.498645\pi\) | |||||||
\(740\) | 124069.i | 0.226568i | ||||||||
\(741\) | − | 369706.i | − | 0.673318i | ||||||
\(742\) | 26676.5 | + | 200710.i | 0.0484531 | + | 0.364554i | ||||
\(743\) | 500204. | 0.906087 | 0.453043 | − | 0.891489i | \(-0.350338\pi\) | ||||
0.453043 | + | 0.891489i | \(0.350338\pi\) | |||||||
\(744\) | −76811.0 | −0.138764 | ||||||||
\(745\) | 152563.i | 0.274877i | ||||||||
\(746\) | −368327. | −0.661845 | ||||||||
\(747\) | 115826.i | 0.207571i | ||||||||
\(748\) | − | 279260.i | − | 0.499121i | ||||||
\(749\) | −78382.2 | − | 589737.i | −0.139718 | − | 1.05122i | ||||
\(750\) | 592596. | 1.05350 | ||||||||
\(751\) | 944576. | 1.67478 | 0.837389 | − | 0.546608i | \(-0.184081\pi\) | ||||
0.837389 | + | 0.546608i | \(0.184081\pi\) | |||||||
\(752\) | 187961.i | 0.332377i | ||||||||
\(753\) | −914031. | −1.61202 | ||||||||
\(754\) | − | 46557.1i | − | 0.0818924i | ||||||
\(755\) | 531941.i | 0.933189i | ||||||||
\(756\) | 5075.24 | − | 674.553i | 0.00888000 | − | 0.00118025i | ||||
\(757\) | −654028. | −1.14131 | −0.570656 | − | 0.821189i | \(-0.693311\pi\) | ||||
−0.570656 | + | 0.821189i | \(0.693311\pi\) | |||||||
\(758\) | −544044. | −0.946881 | ||||||||
\(759\) | 1.14271e6i | 1.98360i | ||||||||
\(760\) | −314902. | −0.545191 | ||||||||
\(761\) | 643673.i | 1.11147i | 0.831361 | + | 0.555733i | \(0.187562\pi\) | ||||
−0.831361 | + | 0.555733i | \(0.812438\pi\) | |||||||
\(762\) | − | 1.00368e6i | − | 1.72856i | ||||||
\(763\) | 43953.6 | + | 330700.i | 0.0754997 | + | 0.568049i | ||||
\(764\) | −406541. | −0.696494 | ||||||||
\(765\) | 337597. | 0.576867 | ||||||||
\(766\) | 288310.i | 0.491362i | ||||||||
\(767\) | −84071.6 | −0.142909 | ||||||||
\(768\) | − | 51967.7i | − | 0.0881071i | ||||||
\(769\) | − | 103697.i | − | 0.175354i | −0.996149 | − | 0.0876768i | \(-0.972056\pi\) | ||
0.996149 | − | 0.0876768i | \(-0.0279443\pi\) | |||||||
\(770\) | −611352. | + | 81255.1i | −1.03112 | + | 0.137047i | ||||
\(771\) | 832491. | 1.40046 | ||||||||
\(772\) | −9986.72 | −0.0167567 | ||||||||
\(773\) | − | 796380.i | − | 1.33279i | −0.745599 | − | 0.666394i | \(-0.767837\pi\) | ||
0.745599 | − | 0.666394i | \(-0.232163\pi\) | |||||||
\(774\) | 438863. | 0.732567 | ||||||||
\(775\) | 23237.8i | 0.0386893i | ||||||||
\(776\) | 133474.i | 0.221652i | ||||||||
\(777\) | −411991. | + | 54757.9i | −0.682410 | + | 0.0906995i | ||||
\(778\) | −540439. | −0.892868 | ||||||||
\(779\) | −794195. | −1.30874 | ||||||||
\(780\) | 114369.i | 0.187983i | ||||||||
\(781\) | −436664. | −0.715889 | ||||||||
\(782\) | − | 241671.i | − | 0.395195i | ||||||
\(783\) | 4426.10i | 0.00721934i | ||||||||
\(784\) | −148329. | + | 40138.1i | −0.241321 | + | 0.0653017i | ||||
\(785\) | 865122. | 1.40391 | ||||||||
\(786\) | 861843. | 1.39503 | ||||||||
\(787\) | 1.16895e6i | 1.88733i | 0.330905 | + | 0.943664i | \(0.392646\pi\) | ||||
−0.330905 | + | 0.943664i | \(0.607354\pi\) | |||||||
\(788\) | 515637. | 0.830408 | ||||||||
\(789\) | 491081.i | 0.788859i | ||||||||
\(790\) | 460109.i | 0.737237i | ||||||||
\(791\) | −30756.9 | − | 231411.i | −0.0491575 | − | 0.369854i | ||||
\(792\) | 347110. | 0.553371 | ||||||||
\(793\) | 11965.6 | 0.0190277 | ||||||||
\(794\) | − | 568919.i | − | 0.902421i | ||||||
\(795\) | 429987. | 0.680333 | ||||||||
\(796\) | − | 18820.8i | − | 0.0297038i | ||||||
\(797\) | − | 808048.i | − | 1.27210i | −0.771649 | − | 0.636049i | \(-0.780568\pi\) | ||
0.771649 | − | 0.636049i | \(-0.219432\pi\) | |||||||
\(798\) | −138983. | − | 1.04569e6i | −0.218251 | − | 1.64209i | ||||
\(799\) | 534447. | 0.837165 | ||||||||
\(800\) | −15721.9 | −0.0245654 | ||||||||
\(801\) | 170635.i | 0.265952i | ||||||||
\(802\) | 113076. | 0.175801 | ||||||||
\(803\) | − | 1.36328e6i | − | 2.11423i | ||||||
\(804\) | 109273.i | 0.169044i | ||||||||
\(805\) | −529062. | + | 70318.0i | −0.816423 | + | 0.108511i | ||||
\(806\) | −36758.2 | −0.0565827 | ||||||||
\(807\) | −1.10668e6 | −1.69933 | ||||||||
\(808\) | − | 207540.i | − | 0.317892i | ||||||
\(809\) | −692708. | −1.05841 | −0.529204 | − | 0.848495i | \(-0.677509\pi\) | ||||
−0.529204 | + | 0.848495i | \(0.677509\pi\) | |||||||
\(810\) | − | 435894.i | − | 0.664372i | ||||||
\(811\) | 382267.i | 0.581200i | 0.956845 | + | 0.290600i | \(0.0938548\pi\) | ||||
−0.956845 | + | 0.290600i | \(0.906145\pi\) | |||||||
\(812\) | −17502.1 | − | 131683.i | −0.0265448 | − | 0.199719i | ||||
\(813\) | 1.33677e6 | 2.02244 | ||||||||
\(814\) | 362717. | 0.547417 | ||||||||
\(815\) | − | 947732.i | − | 1.42682i | ||||||
\(816\) | −147765. | −0.221917 | ||||||||
\(817\) | 1.16398e6i | 1.74381i | ||||||||
\(818\) | 228129.i | 0.340936i | ||||||||
\(819\) | −188676. | + | 25077.1i | −0.281287 | + | 0.0373860i | ||||
\(820\) | 245685. | 0.365385 | ||||||||
\(821\) | 116392. | 0.172678 | 0.0863392 | − | 0.996266i | \(-0.472483\pi\) | ||||
0.0863392 | + | 0.996266i | \(0.472483\pi\) | |||||||
\(822\) | − | 149355.i | − | 0.221043i | ||||||
\(823\) | 640526. | 0.945665 | 0.472832 | − | 0.881152i | \(-0.343232\pi\) | ||||
0.472832 | + | 0.881152i | \(0.343232\pi\) | |||||||
\(824\) | − | 88393.2i | − | 0.130186i | ||||||
\(825\) | − | 211375.i | − | 0.310561i | ||||||
\(826\) | −237790. | + | 31604.8i | −0.348525 | + | 0.0463227i | ||||
\(827\) | −158299. | −0.231455 | −0.115727 | − | 0.993281i | \(-0.536920\pi\) | ||||
−0.115727 | + | 0.993281i | \(0.536920\pi\) | |||||||
\(828\) | 300388. | 0.438149 | ||||||||
\(829\) | − | 680501.i | − | 0.990192i | −0.868838 | − | 0.495096i | \(-0.835133\pi\) | ||
0.868838 | − | 0.495096i | \(-0.164867\pi\) | |||||||
\(830\) | 95032.6 | 0.137948 | ||||||||
\(831\) | − | 459017.i | − | 0.664701i | ||||||
\(832\) | − | 24869.3i | − | 0.0359267i | ||||||
\(833\) | 114129. | + | 421759.i | 0.164477 | + | 0.607819i | ||||
\(834\) | −946148. | −1.36028 | ||||||||
\(835\) | −806709. | −1.15703 | ||||||||
\(836\) | 920622.i | 1.31725i | ||||||||
\(837\) | 3494.53 | 0.00498812 | ||||||||
\(838\) | − | 712859.i | − | 1.01512i | ||||||
\(839\) | 622397.i | 0.884186i | 0.896969 | + | 0.442093i | \(0.145764\pi\) | ||||
−0.896969 | + | 0.442093i | \(0.854236\pi\) | |||||||
\(840\) | 42994.4 | + | 323484.i | 0.0609331 | + | 0.458452i | ||||
\(841\) | −592440. | −0.837631 | ||||||||
\(842\) | 238831. | 0.336873 | ||||||||
\(843\) | − | 1.25786e6i | − | 1.77001i | ||||||
\(844\) | −520451. | −0.730626 | ||||||||
\(845\) | − | 607827.i | − | 0.851269i | ||||||
\(846\) | 664297.i | 0.928157i | ||||||||
\(847\) | 143031. | + | 1.07614e6i | 0.199371 | + | 1.50004i | ||||
\(848\) | −93500.0 | −0.130023 | ||||||||
\(849\) | −52694.2 | −0.0731051 | ||||||||
\(850\) | 44703.6i | 0.0618735i | ||||||||
\(851\) | 313894. | 0.433435 | ||||||||
\(852\) | 231052.i | 0.318295i | ||||||||
\(853\) | 826596.i | 1.13604i | 0.823013 | + | 0.568022i | \(0.192291\pi\) | ||||
−0.823013 | + | 0.568022i | \(0.807709\pi\) | |||||||
\(854\) | 33843.7 | − | 4498.19i | 0.0464048 | − | 0.00616768i | ||||
\(855\) | −1.11294e6 | −1.52243 | ||||||||
\(856\) | 274726. | 0.374931 | ||||||||
\(857\) | 539076.i | 0.733987i | 0.930223 | + | 0.366994i | \(0.119613\pi\) | ||||
−0.930223 | + | 0.366994i | \(0.880387\pi\) | |||||||
\(858\) | 334359. | 0.454191 | ||||||||
\(859\) | 499964.i | 0.677567i | 0.940864 | + | 0.338783i | \(0.110015\pi\) | ||||
−0.940864 | + | 0.338783i | \(0.889985\pi\) | |||||||
\(860\) | − | 360077.i | − | 0.486853i | ||||||
\(861\) | 108433. | + | 815838.i | 0.146271 | + | 1.10052i | ||||
\(862\) | 360659. | 0.485380 | ||||||||
\(863\) | 1.16944e6 | 1.57021 | 0.785103 | − | 0.619365i | \(-0.212610\pi\) | ||||
0.785103 | + | 0.619365i | \(0.212610\pi\) | |||||||
\(864\) | 2364.28i | 0.00316716i | ||||||||
\(865\) | 733059. | 0.979730 | ||||||||
\(866\) | 660548.i | 0.880783i | ||||||||
\(867\) | − | 639512.i | − | 0.850766i | ||||||
\(868\) | −103968. | + | 13818.4i | −0.137994 | + | 0.0183408i | ||||
\(869\) | 1.34514e6 | 1.78126 | ||||||||
\(870\) | −282109. | −0.372716 | ||||||||
\(871\) | 52292.9i | 0.0689297i | ||||||||
\(872\) | −154055. | −0.202602 | ||||||||
\(873\) | 471727.i | 0.618960i | ||||||||
\(874\) | 796705.i | 1.04298i | ||||||||
\(875\) | 802110. | − | 106609.i | 1.04765 | − | 0.139244i | ||||
\(876\) | −721350. | −0.940021 | ||||||||
\(877\) | 187496. | 0.243777 | 0.121888 | − | 0.992544i | \(-0.461105\pi\) | ||||
0.121888 | + | 0.992544i | \(0.461105\pi\) | |||||||
\(878\) | 860515.i | 1.11627i | ||||||||
\(879\) | −256786. | −0.332349 | ||||||||
\(880\) | − | 284795.i | − | 0.367762i | ||||||
\(881\) | − | 179673.i | − | 0.231489i | −0.993279 | − | 0.115745i | \(-0.963075\pi\) | ||
0.993279 | − | 0.115745i | \(-0.0369254\pi\) | |||||||
\(882\) | −524230. | + | 141857.i | −0.673883 | + | 0.182354i | ||||
\(883\) | −1.04658e6 | −1.34231 | −0.671155 | − | 0.741317i | \(-0.734201\pi\) | ||||
−0.671155 | + | 0.741317i | \(0.734201\pi\) | |||||||
\(884\) | −70713.3 | −0.0904892 | ||||||||
\(885\) | 509424.i | 0.650419i | ||||||||
\(886\) | 246246. | 0.313691 | ||||||||
\(887\) | − | 1.30029e6i | − | 1.65270i | −0.563158 | − | 0.826349i | \(-0.690414\pi\) | ||
0.563158 | − | 0.826349i | \(-0.309586\pi\) | |||||||
\(888\) | − | 191924.i | − | 0.243390i | ||||||
\(889\) | −180563. | − | 1.35853e6i | −0.228468 | − | 1.71896i | ||||
\(890\) | 140002. | 0.176748 | ||||||||
\(891\) | −1.27434e6 | −1.60521 | ||||||||
\(892\) | 243299.i | 0.305781i | ||||||||
\(893\) | −1.76188e6 | −2.20940 | ||||||||
\(894\) | − | 236003.i | − | 0.295286i | ||||||
\(895\) | − | 527770.i | − | 0.658868i | ||||||
\(896\) | −9349.06 | − | 70341.0i | −0.0116453 | − | 0.0876178i | ||||
\(897\) | 289354. | 0.359620 | ||||||||
\(898\) | 257787. | 0.319675 | ||||||||
\(899\) | − | 90669.8i | − | 0.112187i | ||||||
\(900\) | −55564.8 | −0.0685985 | ||||||||
\(901\) | 265858.i | 0.327491i | ||||||||
\(902\) | − | 718263.i | − | 0.882817i | ||||||
\(903\) | 1.19570e6 | − | 158921.i | 1.46638 | − | 0.194897i | ||||
\(904\) | 107802. | 0.131913 | ||||||||
\(905\) | −1.28597e6 | −1.57012 | ||||||||
\(906\) | − | 822869.i | − | 1.00248i | ||||||
\(907\) | 1.18388e6 | 1.43911 | 0.719556 | − | 0.694435i | \(-0.244346\pi\) | ||||
0.719556 | + | 0.694435i | \(0.244346\pi\) | |||||||
\(908\) | 417004.i | 0.505788i | ||||||||
\(909\) | − | 733496.i | − | 0.887708i | ||||||
\(910\) | 20575.1 | + | 154804.i | 0.0248462 | + | 0.186939i | ||||
\(911\) | −1.30731e6 | −1.57522 | −0.787612 | − | 0.616172i | \(-0.788683\pi\) | ||||
−0.787612 | + | 0.616172i | \(0.788683\pi\) | |||||||
\(912\) | 487128. | 0.585671 | ||||||||
\(913\) | − | 277830.i | − | 0.333301i | ||||||
\(914\) | 1.16511e6 | 1.39468 | ||||||||
\(915\) | − | 72504.3i | − | 0.0866008i | ||||||
\(916\) | − | 650242.i | − | 0.774968i | ||||||
\(917\) | 1.16655e6 | − | 155047.i | 1.38728 | − | 0.184384i | ||||
\(918\) | 6722.58 | 0.00797720 | ||||||||
\(919\) | 698775. | 0.827382 | 0.413691 | − | 0.910417i | \(-0.364239\pi\) | ||||
0.413691 | + | 0.910417i | \(0.364239\pi\) | |||||||
\(920\) | − | 246461.i | − | 0.291187i | ||||||
\(921\) | 802730. | 0.946347 | ||||||||
\(922\) | 445185.i | 0.523696i | ||||||||
\(923\) | 110571.i | 0.129789i | ||||||||
\(924\) | 945711. | − | 125695.i | 1.10768 | − | 0.147222i | ||||
\(925\) | −58063.1 | −0.0678605 | ||||||||
\(926\) | −694541. | −0.809984 | ||||||||
\(927\) | − | 312402.i | − | 0.363542i | ||||||
\(928\) | 61344.1 | 0.0712323 | ||||||||
\(929\) | 1.39460e6i | 1.61591i | 0.589244 | + | 0.807955i | \(0.299426\pi\) | ||||
−0.589244 | + | 0.807955i | \(0.700574\pi\) | |||||||
\(930\) | 222733.i | 0.257524i | ||||||||
\(931\) | −376241. | − | 1.39039e6i | −0.434077 | − | 1.60412i | ||||
\(932\) | −333751. | −0.384229 | ||||||||
\(933\) | −182387. | −0.209522 | ||||||||
\(934\) | 93533.8i | 0.107220i | ||||||||
\(935\) | −809786. | −0.926290 | ||||||||
\(936\) | − | 87893.9i | − | 0.100325i | ||||||
\(937\) | 509380.i | 0.580180i | 0.956999 | + | 0.290090i | \(0.0936852\pi\) | ||||
−0.956999 | + | 0.290090i | \(0.906315\pi\) | |||||||
\(938\) | 19658.4 | + | 147907.i | 0.0223430 | + | 0.168106i | ||||
\(939\) | 466428. | 0.528997 | ||||||||
\(940\) | 545040. | 0.616840 | ||||||||
\(941\) | 1.62505e6i | 1.83522i | 0.397486 | + | 0.917608i | \(0.369883\pi\) | ||||
−0.397486 | + | 0.917608i | \(0.630117\pi\) | |||||||
\(942\) | −1.33827e6 | −1.50814 | ||||||||
\(943\) | − | 621584.i | − | 0.698998i | ||||||
\(944\) | − | 110773.i | − | 0.124306i | ||||||
\(945\) | −1956.04 | − | 14716.9i | −0.00219035 | − | 0.0164799i | ||||
\(946\) | −1.05269e6 | −1.17630 | ||||||||
\(947\) | 1.22462e6 | 1.36553 | 0.682763 | − | 0.730640i | \(-0.260778\pi\) | ||||
0.682763 | + | 0.730640i | \(0.260778\pi\) | |||||||
\(948\) | − | 711752.i | − | 0.791976i | ||||||
\(949\) | −345204. | −0.383304 | ||||||||
\(950\) | − | 147372.i | − | 0.163293i | ||||||
\(951\) | 1.59298e6i | 1.76137i | ||||||||
\(952\) | −200007. | + | 26583.1i | −0.220685 | + | 0.0293313i | ||||
\(953\) | −1.14847e6 | −1.26454 | −0.632269 | − | 0.774749i | \(-0.717876\pi\) | ||||
−0.632269 | + | 0.774749i | \(0.717876\pi\) | |||||||
\(954\) | −330451. | −0.363086 | ||||||||
\(955\) | 1.17887e6i | 1.29258i | ||||||||
\(956\) | −31492.4 | −0.0344580 | ||||||||
\(957\) | 824750.i | 0.900531i | ||||||||
\(958\) | − | 1.08690e6i | − | 1.18429i | ||||||
\(959\) | −26869.2 | − | 202160.i | −0.0292158 | − | 0.219815i | ||||
\(960\) | −150693. | −0.163513 | ||||||||
\(961\) | 851935. | 0.922485 | ||||||||
\(962\) | − | 91845.8i | − | 0.0992451i | ||||||
\(963\) | 970945. | 1.04699 | ||||||||
\(964\) | − | 564092.i | − | 0.607010i | ||||||
\(965\) | 28959.0i | 0.0310978i | ||||||||
\(966\) | 818416. | − | 108776.i | 0.877041 | − | 0.116568i | ||||
\(967\) | −733668. | −0.784597 | −0.392298 | − | 0.919838i | \(-0.628320\pi\) | ||||
−0.392298 | + | 0.919838i | \(0.628320\pi\) | |||||||
\(968\) | −501315. | −0.535008 | ||||||||
\(969\) | − | 1.38510e6i | − | 1.47514i | ||||||
\(970\) | 387041. | 0.411352 | ||||||||
\(971\) | 786749.i | 0.834445i | 0.908804 | + | 0.417223i | \(0.136996\pi\) | ||||
−0.908804 | + | 0.417223i | \(0.863004\pi\) | |||||||
\(972\) | 665830.i | 0.704743i | ||||||||
\(973\) | −1.28066e6 | + | 170213.i | −1.35272 | + | 0.179791i | ||||
\(974\) | 490807. | 0.517360 | ||||||||
\(975\) | −53523.7 | −0.0563037 | ||||||||
\(976\) | 15765.9i | 0.0165508i | ||||||||
\(977\) | 837039. | 0.876913 | 0.438457 | − | 0.898752i | \(-0.355525\pi\) | ||||
0.438457 | + | 0.898752i | \(0.355525\pi\) | |||||||
\(978\) | 1.46606e6i | 1.53276i | ||||||||
\(979\) | − | 409299.i | − | 0.427046i | ||||||
\(980\) | 116390. | + | 430118.i | 0.121190 | + | 0.447853i | ||||
\(981\) | −544467. | −0.565761 | ||||||||
\(982\) | 56586.3 | 0.0586798 | ||||||||
\(983\) | 644129.i | 0.666600i | 0.942821 | + | 0.333300i | \(0.108162\pi\) | ||||
−0.942821 | + | 0.333300i | \(0.891838\pi\) | |||||||
\(984\) | −380054. | −0.392514 | ||||||||
\(985\) | − | 1.49522e6i | − | 1.54111i | ||||||
\(986\) | − | 174426.i | − | 0.179414i | ||||||
\(987\) | 240554. | + | 1.80990e6i | 0.246933 | + | 1.85789i | ||||
\(988\) | 233117. | 0.238814 | ||||||||
\(989\) | −910996. | −0.931374 | ||||||||
\(990\) | − | 1.00653e6i | − | 1.02697i | ||||||
\(991\) | 92517.5 | 0.0942056 | 0.0471028 | − | 0.998890i | \(-0.485001\pi\) | ||||
0.0471028 | + | 0.998890i | \(0.485001\pi\) | |||||||
\(992\) | − | 48432.8i | − | 0.0492172i | ||||||
\(993\) | − | 68214.4i | − | 0.0691795i | ||||||
\(994\) | 41566.6 | + | 312741.i | 0.0420699 | + | 0.316528i | ||||
\(995\) | −54575.7 | −0.0551256 | ||||||||
\(996\) | −147008. | −0.148191 | ||||||||
\(997\) | 366383.i | 0.368591i | 0.982871 | + | 0.184295i | \(0.0590003\pi\) | ||||
−0.982871 | + | 0.184295i | \(0.941000\pi\) | |||||||
\(998\) | 1.21161e6 | 1.21647 | ||||||||
\(999\) | 8731.60i | 0.00874909i |
(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 | 14.5.b.a.13.1 | ✓ | 4 | |
3.2 | odd | 2 | 126.5.c.a.55.4 | 4 | |||
4.3 | odd | 2 | 112.5.c.c.97.4 | 4 | |||
5.2 | odd | 4 | 350.5.d.a.349.1 | 8 | |||
5.3 | odd | 4 | 350.5.d.a.349.8 | 8 | |||
5.4 | even | 2 | 350.5.b.a.251.4 | 4 | |||
7.2 | even | 3 | 98.5.d.d.31.4 | 8 | |||
7.3 | odd | 6 | 98.5.d.d.19.4 | 8 | |||
7.4 | even | 3 | 98.5.d.d.19.3 | 8 | |||
7.5 | odd | 6 | 98.5.d.d.31.3 | 8 | |||
7.6 | odd | 2 | inner | 14.5.b.a.13.2 | yes | 4 | |
8.3 | odd | 2 | 448.5.c.f.321.1 | 4 | |||
8.5 | even | 2 | 448.5.c.e.321.4 | 4 | |||
12.11 | even | 2 | 1008.5.f.h.433.3 | 4 | |||
21.20 | even | 2 | 126.5.c.a.55.3 | 4 | |||
28.27 | even | 2 | 112.5.c.c.97.1 | 4 | |||
35.13 | even | 4 | 350.5.d.a.349.5 | 8 | |||
35.27 | even | 4 | 350.5.d.a.349.4 | 8 | |||
35.34 | odd | 2 | 350.5.b.a.251.3 | 4 | |||
56.13 | odd | 2 | 448.5.c.e.321.1 | 4 | |||
56.27 | even | 2 | 448.5.c.f.321.4 | 4 | |||
84.83 | odd | 2 | 1008.5.f.h.433.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.5.b.a.13.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
14.5.b.a.13.2 | yes | 4 | 7.6 | odd | 2 | inner | |
98.5.d.d.19.3 | 8 | 7.4 | even | 3 | |||
98.5.d.d.19.4 | 8 | 7.3 | odd | 6 | |||
98.5.d.d.31.3 | 8 | 7.5 | odd | 6 | |||
98.5.d.d.31.4 | 8 | 7.2 | even | 3 | |||
112.5.c.c.97.1 | 4 | 28.27 | even | 2 | |||
112.5.c.c.97.4 | 4 | 4.3 | odd | 2 | |||
126.5.c.a.55.3 | 4 | 21.20 | even | 2 | |||
126.5.c.a.55.4 | 4 | 3.2 | odd | 2 | |||
350.5.b.a.251.3 | 4 | 35.34 | odd | 2 | |||
350.5.b.a.251.4 | 4 | 5.4 | even | 2 | |||
350.5.d.a.349.1 | 8 | 5.2 | odd | 4 | |||
350.5.d.a.349.4 | 8 | 35.27 | even | 4 | |||
350.5.d.a.349.5 | 8 | 35.13 | even | 4 | |||
350.5.d.a.349.8 | 8 | 5.3 | odd | 4 | |||
448.5.c.e.321.1 | 4 | 56.13 | odd | 2 | |||
448.5.c.e.321.4 | 4 | 8.5 | even | 2 | |||
448.5.c.f.321.1 | 4 | 8.3 | odd | 2 | |||
448.5.c.f.321.4 | 4 | 56.27 | even | 2 | |||
1008.5.f.h.433.2 | 4 | 84.83 | odd | 2 | |||
1008.5.f.h.433.3 | 4 | 12.11 | even | 2 |