Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 29.4 | ||
Character | \(\chi\) | \(=\) | 76.29 |
Dual form | 76.5.j.a.21.4 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{17}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.91062 | + | 2.27699i | 0.212291 | + | 0.252999i | 0.861673 | − | 0.507464i | \(-0.169417\pi\) |
−0.649382 | + | 0.760462i | \(0.724972\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −16.1447 | − | 5.87619i | −0.645788 | − | 0.235048i | −0.00169937 | − | 0.999999i | \(-0.500541\pi\) |
−0.644088 | + | 0.764951i | \(0.722763\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 23.9804 | − | 41.5352i | 0.489396 | − | 0.847658i | −0.510530 | − | 0.859860i | \(-0.670551\pi\) |
0.999926 | + | 0.0122020i | \(0.00388410\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 12.5313 | − | 71.0685i | 0.154707 | − | 0.877389i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 41.5971 | + | 72.0483i | 0.343778 | + | 0.595440i | 0.985131 | − | 0.171805i | \(-0.0549600\pi\) |
−0.641353 | + | 0.767246i | \(0.721627\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 175.663 | − | 209.347i | 1.03943 | − | 1.23874i | 0.0689296 | − | 0.997622i | \(-0.478042\pi\) |
0.970496 | − | 0.241118i | \(-0.0775139\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −17.4664 | − | 47.9885i | −0.0776283 | − | 0.213282i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 17.7920 | + | 100.903i | 0.0615640 | + | 0.349147i | 0.999993 | + | 0.00367529i | \(0.00116988\pi\) |
−0.938429 | + | 0.345471i | \(0.887719\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −229.865 | − | 278.358i | −0.636745 | − | 0.771075i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 140.393 | − | 24.7550i | 0.318351 | − | 0.0561338i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 806.737 | − | 293.628i | 1.52502 | − | 0.555063i | 0.562626 | − | 0.826712i | \(-0.309791\pi\) |
0.962396 | + | 0.271649i | \(0.0875691\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −252.656 | − | 212.004i | −0.404250 | − | 0.339206i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 394.273 | − | 227.633i | 0.540840 | − | 0.312254i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −753.735 | − | 132.904i | −0.896237 | − | 0.158031i | −0.293489 | − | 0.955962i | \(-0.594816\pi\) |
−0.602748 | + | 0.797932i | \(0.705928\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −222.015 | − | 128.180i | −0.231025 | − | 0.133382i | 0.380020 | − | 0.924978i | \(-0.375917\pi\) |
−0.611045 | + | 0.791596i | \(0.709250\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −84.5769 | + | 232.373i | −0.0776647 | + | 0.213382i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −631.225 | + | 529.661i | −0.515286 | + | 0.432376i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2609.10i | 1.90585i | 0.303213 | + | 0.952923i | \(0.401941\pi\) | ||||
−0.303213 | + | 0.952923i | \(0.598059\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 812.306 | 0.534060 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 531.864 | + | 633.851i | 0.316397 | + | 0.377068i | 0.900680 | − | 0.434482i | \(-0.143069\pi\) |
−0.584283 | + | 0.811550i | \(0.698624\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2421.67 | − | 881.415i | −1.30972 | − | 0.476698i | −0.409568 | − | 0.912280i | \(-0.634321\pi\) |
−0.900149 | + | 0.435582i | \(0.856543\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −619.926 | + | 1073.74i | −0.306136 | + | 0.530244i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −100.427 | + | 569.549i | −0.0454626 | + | 0.257831i | −0.999065 | − | 0.0432384i | \(-0.986232\pi\) |
0.953602 | + | 0.301069i | \(0.0973436\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 50.3825 | + | 87.2650i | 0.0209840 | + | 0.0363453i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −195.762 | + | 233.300i | −0.0752642 | + | 0.0896964i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1026.07 | + | 2819.11i | 0.365280 | + | 1.00360i | 0.977133 | + | 0.212628i | \(0.0682022\pi\) |
−0.611853 | + | 0.790971i | \(0.709576\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −248.203 | − | 1407.63i | −0.0820506 | − | 0.465332i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 194.634 | − | 1055.24i | 0.0599057 | − | 0.324788i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1565.00 | − | 275.951i | 0.449583 | − | 0.0792735i | 0.0557273 | − | 0.998446i | \(-0.482252\pi\) |
0.393855 | + | 0.919172i | \(0.371141\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2684.30 | + | 977.005i | −0.721392 | + | 0.262565i | −0.676517 | − | 0.736427i | \(-0.736511\pi\) |
−0.0448755 | + | 0.998993i | \(0.514289\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2651.34 | − | 2224.74i | −0.668013 | − | 0.560529i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4066.19 | + | 2347.61i | −0.962411 | + | 0.555648i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3116.58 | + | 549.537i | 0.694270 | + | 0.122419i | 0.509638 | − | 0.860389i | \(-0.329779\pi\) |
0.184632 | + | 0.982808i | \(0.440891\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2209.96 | + | 1275.92i | 0.464179 | + | 0.267994i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2711.28 | − | 7449.18i | 0.537846 | − | 1.47772i | −0.311688 | − | 0.950185i | \(-0.600894\pi\) |
0.849534 | − | 0.527535i | \(-0.176884\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4107.82 | − | 3446.87i | 0.770843 | − | 0.646814i | −0.170082 | − | 0.985430i | \(-0.554403\pi\) |
0.940925 | + | 0.338616i | \(0.109959\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 980.354i | − | 0.174285i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3990.06 | 0.672973 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3251.34 | + | 3874.80i | 0.520965 | + | 0.620862i | 0.960809 | − | 0.277212i | \(-0.0894106\pi\) |
−0.439844 | + | 0.898074i | \(0.644966\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4221.21 | − | 1536.40i | −0.643379 | − | 0.234171i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3648.20 | − | 6318.86i | 0.529568 | − | 0.917239i | −0.469837 | − | 0.882753i | \(-0.655687\pi\) |
0.999405 | − | 0.0344859i | \(-0.0109794\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 305.681 | − | 1733.60i | 0.0423088 | − | 0.239945i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1137.48 | − | 1970.18i | −0.150282 | − | 0.260295i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2898.35 | + | 3454.12i | −0.365908 | + | 0.436072i | −0.917314 | − | 0.398165i | \(-0.869647\pi\) |
0.551406 | + | 0.834237i | \(0.314091\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4482.81 | − | 12316.4i | −0.541337 | − | 1.48731i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −132.321 | − | 750.430i | −0.0152990 | − | 0.0867649i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2075.41 | + | 5844.73i | 0.229963 | + | 0.647616i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1041.93 | + | 183.720i | −0.110737 | + | 0.0195260i | −0.228742 | − | 0.973487i | \(-0.573461\pi\) |
0.118005 | + | 0.993013i | \(0.462350\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5641.63 | − | 2053.39i | 0.575618 | − | 0.209508i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11167.0 | + | 9370.25i | 1.09470 | + | 0.918562i | 0.997057 | − | 0.0766599i | \(-0.0244256\pi\) |
0.0976419 | + | 0.995222i | \(0.468870\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1597.71 | − | 922.439i | 0.150600 | − | 0.0869487i | −0.422807 | − | 0.906220i | \(-0.638955\pi\) |
0.573406 | + | 0.819271i | \(0.305622\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2412.06 | − | 425.312i | −0.218781 | − | 0.0385770i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2023.06 | − | 1168.01i | −0.176702 | − | 0.102019i | 0.409040 | − | 0.912516i | \(-0.365864\pi\) |
−0.585742 | + | 0.810497i | \(0.699197\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −640.112 | + | 1758.69i | −0.0538770 | + | 0.148026i | −0.963712 | − | 0.266945i | \(-0.913986\pi\) |
0.909835 | + | 0.414970i | \(0.136208\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5940.90 | + | 4985.01i | −0.482177 | + | 0.404594i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9207.05i | 0.721047i | 0.932750 | + | 0.360524i | \(0.117402\pi\) | ||||
−0.932750 | + | 0.360524i | \(0.882598\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14749.9 | −1.11531 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12676.7 | − | 15107.5i | −0.926049 | − | 1.10362i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4617.71 | + | 1680.71i | 0.326086 | + | 0.118686i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3859.86 | − | 6685.48i | 0.263634 | − | 0.456627i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −427.081 | + | 2422.10i | −0.0282293 | + | 0.160096i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8202.29 | + | 14206.8i | 0.524947 | + | 0.909234i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9103.92 | + | 10849.6i | −0.564444 | + | 0.672679i | −0.970481 | − | 0.241178i | \(-0.922466\pi\) |
0.406036 | + | 0.913857i | \(0.366911\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2619.91 | − | 7198.16i | −0.157437 | − | 0.432556i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5497.76 | + | 31179.4i | 0.320364 | + | 1.81687i | 0.540430 | + | 0.841389i | \(0.318262\pi\) |
−0.220066 | + | 0.975485i | \(0.570627\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17073.9 | + | 2872.36i | −0.965228 | + | 0.162381i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7703.03 | + | 1358.25i | −0.422663 | + | 0.0745268i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3273.09 | − | 1191.31i | 0.174388 | − | 0.0634721i | −0.253351 | − | 0.967375i | \(-0.581533\pi\) |
0.427739 | + | 0.903902i | \(0.359310\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2046.85 | + | 1717.51i | 0.105939 | + | 0.0888933i | 0.694219 | − | 0.719764i | \(-0.255750\pi\) |
−0.588280 | + | 0.808658i | \(0.700195\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1488.73 | + | 859.521i | −0.0748822 | + | 0.0432333i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22390.2 | + | 3947.99i | 1.09493 | + | 0.193065i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11387.9 | + | 6574.78i | 0.541634 | + | 0.312713i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −102.440 | + | 281.451i | −0.00474060 | + | 0.0130247i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −23897.1 | + | 20052.1i | −1.07640 | + | 0.903206i | −0.995617 | − | 0.0935262i | \(-0.970186\pi\) |
−0.0807817 | + | 0.996732i | \(0.525742\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 14183.7i | − | 0.622064i | −0.950399 | − | 0.311032i | \(-0.899325\pi\) | ||
0.950399 | − | 0.311032i | \(-0.100675\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7394.01 | 0.315862 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2831.15 | + | 3374.03i | 0.117842 | + | 0.140439i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21837.4 | − | 7948.17i | −0.885935 | − | 0.322454i | −0.141333 | − | 0.989962i | \(-0.545139\pi\) |
−0.744603 | + | 0.667508i | \(0.767361\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4458.65 | + | 7722.60i | −0.176364 | + | 0.305471i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7149.94 | − | 40549.3i | 0.275836 | − | 1.56434i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2603.27 | − | 4509.00i | −0.0979816 | − | 0.169709i | 0.812867 | − | 0.582449i | \(-0.197905\pi\) |
−0.910849 | + | 0.412740i | \(0.864572\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2730.94 | − | 3254.60i | 0.100310 | − | 0.119545i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 604.919 | + | 1662.00i | 0.0216902 | + | 0.0595935i | 0.950065 | − | 0.312051i | \(-0.101016\pi\) |
−0.928375 | + | 0.371645i | \(0.878794\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8009.10 | − | 45421.9i | −0.280421 | − | 1.59035i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −22663.0 | + | 12848.0i | −0.775042 | + | 0.439382i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 50539.7 | − | 8911.52i | 1.68865 | − | 0.297755i | 0.754945 | − | 0.655788i | \(-0.227663\pi\) |
0.933709 | + | 0.358032i | \(0.116552\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14864.4 | + | 5410.20i | −0.485369 | + | 0.176660i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3618.45 | + | 3036.24i | 0.115498 | + | 0.0969147i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 38729.9 | − | 22360.7i | 1.20876 | − | 0.697878i | 0.246272 | − | 0.969201i | \(-0.420794\pi\) |
0.962488 | + | 0.271323i | \(0.0874611\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 51296.0 | + | 9044.86i | 1.56576 | + | 0.276086i | 0.888228 | − | 0.459404i | \(-0.151937\pi\) |
0.677536 | + | 0.735490i | \(0.263048\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7353.31 | − | 4245.43i | −0.219574 | − | 0.126771i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15331.6 | − | 42123.2i | 0.447964 | − | 1.23077i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6529.82 | + | 5479.17i | −0.186732 | + | 0.156687i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 21834.9i | − | 0.611264i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6618.27 | 0.181417 | 0.0907085 | − | 0.995877i | \(-0.471087\pi\) | ||||
0.0907085 | + | 0.995877i | \(0.471087\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7735.31 | − | 9218.58i | −0.207665 | − | 0.247485i | 0.652152 | − | 0.758089i | \(-0.273867\pi\) |
−0.859816 | + | 0.510603i | \(0.829422\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13114.4 | − | 4773.26i | −0.344890 | − | 0.125530i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −29311.6 | + | 50769.2i | −0.755279 | + | 1.30818i | 0.189956 | + | 0.981793i | \(0.439166\pi\) |
−0.945235 | + | 0.326390i | \(0.894168\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5197.71 | + | 29477.7i | −0.131252 | + | 0.744367i | 0.846145 | + | 0.532953i | \(0.178918\pi\) |
−0.977397 | + | 0.211414i | \(0.932193\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4703.31 | + | 8146.37i | 0.116416 | + | 0.201638i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −23595.1 | + | 28119.5i | −0.572570 | + | 0.682363i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4862.16 | − | 13358.7i | −0.115697 | − | 0.317874i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10758.3 | − | 61013.1i | −0.251074 | − | 1.42391i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10493.5 | − | 28140.3i | 0.240231 | − | 0.644222i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6244.72 | − | 1101.11i | 0.140265 | − | 0.0247324i | −0.103075 | − | 0.994674i | \(-0.532868\pi\) |
0.243340 | + | 0.969941i | \(0.421757\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 22141.9 | − | 8059.00i | 0.488041 | − | 0.177632i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 33917.7 | + | 28460.3i | 0.733753 | + | 0.615692i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10648.0 | + | 6147.63i | −0.226125 | + | 0.130553i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15697.0 | + | 2767.80i | 0.327286 | + | 0.0577094i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24249.2 | + | 14000.3i | 0.496493 | + | 0.286650i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24788.8 | − | 68106.5i | 0.498477 | − | 1.36955i | −0.394270 | − | 0.918995i | \(-0.629002\pi\) |
0.892747 | − | 0.450559i | \(-0.148775\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18232.9 | + | 15299.2i | −0.360156 | + | 0.302207i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 75365.9i | 1.46259i | 0.682060 | + | 0.731296i | \(0.261084\pi\) | ||||
−0.682060 | + | 0.731296i | \(0.738916\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −38436.8 | −0.732954 | −0.366477 | − | 0.930427i | \(-0.619436\pi\) | ||||
−0.366477 | + | 0.930427i | \(0.619436\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7623.48 | + | 9085.32i | 0.142866 | + | 0.170261i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −85629.6 | − | 31166.6i | −1.57729 | − | 0.574088i | −0.602680 | − | 0.797983i | \(-0.705900\pi\) |
−0.974613 | + | 0.223896i | \(0.928123\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4968.14 | − | 8605.06i | 0.0899617 | − | 0.155818i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2610.79 | + | 14806.5i | −0.0464810 | + | 0.263607i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 49671.9 | + | 86034.2i | 0.869590 | + | 1.50617i | 0.862416 | + | 0.506200i | \(0.168950\pi\) |
0.00717402 | + | 0.999974i | \(0.497716\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24084.6 | + | 28702.9i | −0.414673 | + | 0.494188i | −0.932436 | − | 0.361336i | \(-0.882321\pi\) |
0.517763 | + | 0.855524i | \(0.326765\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −17179.3 | − | 47199.8i | −0.290933 | − | 0.799333i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −300.624 | − | 1704.92i | −0.00500832 | − | 0.0284036i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −98652.1 | − | 775.704i | −1.61701 | − | 0.0127146i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21358.3 | − | 3766.04i | 0.344483 | − | 0.0607416i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −61034.8 | + | 22214.8i | −0.968791 | + | 0.352611i | −0.777472 | − | 0.628917i | \(-0.783498\pi\) |
−0.191318 | + | 0.981528i | \(0.561276\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 54713.3 | + | 45909.9i | 0.854775 | + | 0.717242i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4531.44 | − | 2616.23i | 0.0696876 | − | 0.0402342i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −68176.2 | − | 12021.3i | −1.03221 | − | 0.182006i | −0.368211 | − | 0.929742i | \(-0.620029\pi\) |
−0.663995 | + | 0.747737i | \(0.731141\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 108370. | + | 62567.3i | 1.61551 | + | 0.932713i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18890.6 | + | 51901.4i | −0.277309 | + | 0.761900i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −56282.2 | + | 47226.4i | −0.813691 | + | 0.682768i | −0.951486 | − | 0.307693i | \(-0.900443\pi\) |
0.137794 | + | 0.990461i | \(0.455999\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 51543.1i | − | 0.733970i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13402.7 | −0.188004 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 38463.9 | + | 45839.5i | 0.531555 | + | 0.633483i | 0.963272 | − | 0.268526i | \(-0.0865365\pi\) |
−0.431717 | + | 0.902009i | \(0.642092\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −40217.6 | − | 14638.0i | −0.547618 | − | 0.199317i | 0.0533699 | − | 0.998575i | \(-0.483004\pi\) |
−0.600988 | + | 0.799258i | \(0.705226\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19479.4 | − | 33739.3i | 0.261367 | − | 0.452700i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4764.74 | − | 27022.2i | 0.0630048 | − | 0.357318i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 57528.5 | + | 99642.3i | 0.749762 | + | 1.29863i | 0.947936 | + | 0.318459i | \(0.103165\pi\) |
−0.198174 | + | 0.980167i | \(0.563501\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11891.7 | + | 14172.0i | −0.152769 | + | 0.182063i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −41424.5 | − | 113813.i | −0.524619 | − | 1.44138i | −0.865326 | − | 0.501210i | \(-0.832888\pi\) |
0.340706 | − | 0.940170i | \(-0.389334\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1875.66 | + | 10637.4i | 0.0234197 | + | 0.132820i | 0.994276 | − | 0.106843i | \(-0.0340743\pi\) |
−0.970856 | + | 0.239663i | \(0.922963\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9343.07 | + | 15892.8i | −0.115027 | + | 0.195663i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 39081.4 | − | 6891.11i | 0.474468 | − | 0.0836615i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 68619.1 | − | 24975.3i | 0.821579 | − | 0.299030i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2409.06 | − | 2021.44i | −0.0284486 | − | 0.0238712i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12787.0 | + | 7382.59i | −0.148948 | + | 0.0859950i | −0.572622 | − | 0.819820i | \(-0.694074\pi\) |
0.423674 | + | 0.905815i | \(0.360740\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −26887.9 | − | 4741.07i | −0.308968 | − | 0.0544794i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 32801.2 | + | 18937.8i | 0.371858 | + | 0.214692i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 80243.6 | − | 220467.i | 0.897569 | − | 2.46605i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −94682.3 | + | 79447.9i | −1.04505 | + | 0.876898i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 43330.2i | 0.471960i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 49078.3 | 0.527582 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −64298.3 | − | 76627.7i | −0.682217 | − | 0.813035i | 0.308174 | − | 0.951330i | \(-0.400282\pi\) |
−0.990391 | + | 0.138295i | \(0.955838\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5153.00 | + | 1875.54i | 0.0539689 | + | 0.0196431i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 76935.4 | − | 133256.i | 0.795437 | − | 1.37774i | −0.127125 | − | 0.991887i | \(-0.540575\pi\) |
0.922561 | − | 0.385850i | \(-0.126092\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3330.62 | + | 18888.9i | −0.0339967 | + | 0.192805i | −0.997076 | − | 0.0764118i | \(-0.975654\pi\) |
0.963080 | + | 0.269217i | \(0.0867648\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 29732.1 | + | 51497.5i | 0.299643 | + | 0.518998i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −82830.1 | + | 98713.1i | −0.824270 | + | 0.982327i | −0.999998 | − | 0.00211182i | \(-0.999328\pi\) |
0.175728 | + | 0.984439i | \(0.443772\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21777.7 | − | 59833.8i | −0.214008 | − | 0.587983i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1205.74 | − | 6838.11i | −0.0117016 | − | 0.0663630i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23997.5 | − | 28146.7i | 0.230018 | − | 0.269788i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −88764.6 | + | 15651.6i | −0.840375 | + | 0.148181i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5227.54 | + | 1902.67i | −0.0488879 | + | 0.0177938i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21248.1 | + | 17829.2i | 0.196303 | + | 0.164718i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 161743. | − | 93382.2i | 1.47628 | − | 0.852331i | 0.476638 | − | 0.879100i | \(-0.341855\pi\) |
0.999642 | + | 0.0267690i | \(0.00852186\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 185425. | + | 32695.4i | 1.67217 | + | 0.294848i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −47087.0 | − | 27185.7i | −0.419577 | − | 0.242243i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 73164.0 | − | 201016.i | 0.644225 | − | 1.76999i | 0.00619703 | − | 0.999981i | \(-0.498027\pi\) |
0.638028 | − | 0.770013i | \(-0.279750\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20964.4 | + | 17591.2i | −0.182424 | + | 0.153072i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 21327.7i | − | 0.183415i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 119987. | 1.01987 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −28181.5 | − | 33585.4i | −0.236770 | − | 0.282171i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −159826. | − | 58172.0i | −1.32736 | − | 0.483120i | −0.421551 | − | 0.906805i | \(-0.638514\pi\) |
−0.905810 | + | 0.423685i | \(0.860736\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24175.3 | + | 41872.8i | −0.198482 | + | 0.343780i | −0.948036 | − | 0.318162i | \(-0.896934\pi\) |
0.749555 | + | 0.661942i | \(0.230268\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21604.7 | − | 122527.i | 0.175362 | − | 0.994525i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26418.5 | + | 45758.2i | 0.212011 | + | 0.367214i | 0.952344 | − | 0.305027i | \(-0.0986654\pi\) |
−0.740333 | + | 0.672241i | \(0.765332\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −87545.6 | + | 104333.i | −0.694669 | + | 0.827874i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4995.73 | + | 13725.7i | 0.0391979 | + | 0.107695i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25426.8 | − | 144202.i | −0.197289 | − | 1.11888i | −0.909121 | − | 0.416531i | \(-0.863246\pi\) |
0.711832 | − | 0.702349i | \(-0.247866\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −24645.4 | + | 127969.i | −0.189113 | + | 0.981955i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22597.5 | − | 3984.55i | 0.171493 | − | 0.0302389i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −86574.0 | + | 31510.4i | −0.649833 | + | 0.236520i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14232.8 | + | 11942.7i | 0.105672 | + | 0.0886689i | 0.694093 | − | 0.719886i | \(-0.255806\pi\) |
−0.588421 | + | 0.808555i | \(0.700250\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 51711.8 | − | 29855.8i | 0.379784 | − | 0.219268i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 141698. | + | 24985.2i | 1.02948 | + | 0.181524i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 89208.0 | + | 51504.2i | 0.641189 | + | 0.370191i | 0.785072 | − | 0.619404i | \(-0.212626\pi\) |
−0.143884 | + | 0.989595i | \(0.545959\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −16677.2 | + | 45820.3i | −0.118594 | + | 0.325833i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −160226. | + | 134446.i | −1.12733 | + | 0.945943i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 22793.2i | − | 0.158682i | −0.996848 | − | 0.0793408i | \(-0.974718\pi\) | ||
0.996848 | − | 0.0793408i | \(-0.0252815\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −42098.6 | −0.290013 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 77114.8 | + | 91901.8i | 0.525702 | + | 0.626508i | 0.961919 | − | 0.273334i | \(-0.0881264\pi\) |
−0.436217 | + | 0.899842i | \(0.643682\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −64418.3 | − | 23446.3i | −0.434598 | − | 0.158181i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −92987.4 | + | 161059.i | −0.620872 | + | 1.07538i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25924.3 | − | 147024.i | 0.171320 | − | 0.971604i | −0.770986 | − | 0.636852i | \(-0.780236\pi\) |
0.942306 | − | 0.334752i | \(-0.108653\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 43981.5 | + | 76178.2i | 0.287685 | + | 0.498285i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −60490.9 | + | 72090.3i | −0.391656 | + | 0.466758i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −29722.9 | − | 81663.0i | −0.190501 | − | 0.523397i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17085.6 | + | 96897.4i | 0.108405 | + | 0.614796i | 0.989805 | + | 0.142426i | \(0.0454902\pi\) |
−0.881400 | + | 0.472370i | \(0.843399\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −39162.1 | − | 33389.1i | −0.245991 | − | 0.209729i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −137641. | + | 24269.8i | −0.855970 | + | 0.150931i | −0.584378 | − | 0.811482i | \(-0.698661\pi\) |
−0.271592 | + | 0.962412i | \(0.587550\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −65834.0 | + | 23961.6i | −0.405359 | + | 0.147539i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 59122.0 | + | 49609.3i | 0.360445 | + | 0.302449i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −187981. | + | 108531.i | −1.13482 | + | 0.655187i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 216667. | + | 38204.3i | 1.29523 | + | 0.228384i | 0.778434 | − | 0.627726i | \(-0.216014\pi\) |
0.516794 | + | 0.856110i | \(0.327125\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8966.22 | + | 5176.65i | 0.0530794 | + | 0.0306454i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26067.5 | − | 71619.9i | 0.152827 | − | 0.419888i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −96029.8 | + | 80578.6i | −0.557584 | + | 0.467868i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7942.15i | 0.0456737i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1845.34 | −0.0105111 | −0.00525554 | − | 0.999986i | \(-0.501673\pi\) | ||||
−0.00525554 | + | 0.999986i | \(0.501673\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 86.2612 | + | 102.802i | 0.000486689 | + | 0.000580013i | 0.766288 | − | 0.642498i | \(-0.222102\pi\) |
−0.765801 | + | 0.643078i | \(0.777657\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 39218.5 | + | 14274.4i | 0.219185 | + | 0.0797767i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16896.6 | − | 29265.8i | 0.0935454 | − | 0.162025i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23790.4 | + | 134922.i | −0.130481 | + | 0.739992i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 33789.6 | + | 58525.2i | 0.183598 | + | 0.318001i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −59624.7 | + | 71057.9i | −0.320975 | + | 0.382523i | −0.902271 | − | 0.431169i | \(-0.858101\pi\) |
0.581296 | + | 0.813692i | \(0.302546\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −44616.5 | − | 122583.i | −0.237969 | − | 0.653813i | −0.999980 | − | 0.00625025i | \(-0.998010\pi\) |
0.762012 | − | 0.647563i | \(-0.224212\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6787.17 | + | 38491.9i | 0.0358682 | + | 0.203419i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −267174. | − | 157067.i | −1.39904 | − | 0.822473i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 365653. | − | 64474.5i | 1.89732 | − | 0.334549i | 0.902044 | − | 0.431644i | \(-0.142066\pi\) |
0.995275 | + | 0.0970952i | \(0.0309551\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6833.15 | − | 2487.06i | 0.0351353 | − | 0.0127882i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −156372. | − | 131211.i | −0.796802 | − | 0.668596i | 0.150617 | − | 0.988592i | \(-0.451874\pi\) |
−0.947419 | + | 0.319996i | \(0.896318\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 67090.1 | − | 38734.5i | 0.338796 | − | 0.195604i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −91316.7 | − | 16101.6i | −0.457020 | − | 0.0805849i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 49892.5 | + | 28805.4i | 0.247481 | + | 0.142883i | 0.618610 | − | 0.785698i | \(-0.287696\pi\) |
−0.371129 | + | 0.928581i | \(0.621029\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23543.9 | + | 64686.2i | −0.115751 | + | 0.318023i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 32296.1 | − | 27099.6i | 0.157381 | − | 0.132059i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 225187.i | 1.08773i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −306928. | −1.46962 | −0.734808 | − | 0.678275i | \(-0.762728\pi\) | ||||
−0.734808 | + | 0.678275i | \(0.762728\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 29983.9 | + | 35733.4i | 0.142319 | + | 0.169609i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −115079. | − | 41885.4i | −0.541495 | − | 0.197088i | 0.0567687 | − | 0.998387i | \(-0.481920\pi\) |
−0.598264 | + | 0.801299i | \(0.704142\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 42930.7 | − | 74358.2i | 0.200266 | − | 0.346870i | −0.748348 | − | 0.663306i | \(-0.769153\pi\) |
0.948614 | + | 0.316436i | \(0.102486\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2273.38 | + | 12893.0i | −0.0105140 | + | 0.0596277i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 40903.8 | + | 70847.4i | 0.187555 | + | 0.324856i | 0.944435 | − | 0.328699i | \(-0.106610\pi\) |
−0.756879 | + | 0.653555i | \(0.773277\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 97561.9 | − | 116270.i | 0.443542 | − | 0.528592i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23625.1 | − | 64909.5i | −0.106496 | − | 0.292595i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −37229.9 | − | 211141.i | −0.166406 | − | 0.943737i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −936.180 | + | 119061.i | −0.00414927 | + | 0.527694i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 213208. | − | 37594.3i | 0.937058 | − | 0.165229i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 323177. | − | 117627.i | 1.40854 | − | 0.512667i | 0.477839 | − | 0.878447i | \(-0.341420\pi\) |
0.930701 | + | 0.365780i | \(0.119198\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 546208. | + | 458323.i | 2.36085 | + | 1.98098i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 105991. | − | 61194.0i | 0.454334 | − | 0.262310i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17901.2 | + | 3156.46i | 0.0761024 | + | 0.0134189i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11216.3 | + | 6475.72i | 0.0472923 | + | 0.0273042i | 0.523460 | − | 0.852050i | \(-0.324641\pi\) |
−0.476167 | + | 0.879355i | \(0.657974\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5293.08 | − | 14542.6i | 0.0221356 | − | 0.0608170i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19005.8 | − | 15947.7i | 0.0788356 | − | 0.0661509i | −0.602518 | − | 0.798105i | \(-0.705836\pi\) |
0.681354 | + | 0.731954i | \(0.261391\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 78419.1i | − | 0.322647i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −103148. | −0.420971 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −244386. | − | 291248.i | −0.989381 | − | 1.17910i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −178513. | − | 64973.3i | −0.716916 | − | 0.260936i | −0.0422999 | − | 0.999105i | \(-0.513469\pi\) |
−0.674616 | + | 0.738169i | \(0.735691\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2628.59 | + | 4552.85i | −0.0104724 | + | 0.0181388i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2082.98 | + | 11813.1i | −0.00823281 | + | 0.0466906i | −0.988647 | − | 0.150254i | \(-0.951991\pi\) |
0.980415 | + | 0.196945i | \(0.0631019\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −125227. | − | 216899.i | −0.491038 | − | 0.850502i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 88122.7 | − | 105021.i | 0.342825 | − | 0.408563i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18369.4 | − | 50469.5i | −0.0709021 | − | 0.194802i | 0.899180 | − | 0.437579i | \(-0.144164\pi\) |
−0.970082 | + | 0.242777i | \(0.921942\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −44659.5 | − | 253277.i | −0.171030 | − | 0.969959i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −153993. | − | 57424.1i | −0.585149 | − | 0.218202i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −31215.0 | + | 5504.04i | −0.117692 | + | 0.0207524i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −45212.5 | + | 16456.0i | −0.169152 | + | 0.0615663i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 116854. | + | 98051.9i | 0.433818 | + | 0.364017i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 252445. | − | 145749.i | 0.930018 | − | 0.536946i | 0.0432004 | − | 0.999066i | \(-0.486245\pi\) |
0.886817 | + | 0.462121i | \(0.152911\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −320281. | − | 56474.2i | −1.17092 | − | 0.206465i | −0.445830 | − | 0.895117i | \(-0.647092\pi\) |
−0.725092 | + | 0.688652i | \(0.758203\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −40719.2 | − | 23509.3i | −0.147734 | − | 0.0852944i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8983.75 | − | 24682.7i | 0.0323472 | − | 0.0888731i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 350236. | − | 293883.i | 1.25155 | − | 1.05018i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 114680.i | − | 0.406723i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 226123. | 0.795960 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25798.2 | + | 30745.1i | 0.0901326 | + | 0.107416i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 124913. | + | 45464.7i | 0.433171 | + | 0.157661i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4191.53 | + | 7259.95i | −0.0144276 | + | 0.0249894i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3332.67 | + | 18900.5i | −0.0113867 | + | 0.0645772i | −0.989972 | − | 0.141266i | \(-0.954883\pi\) |
0.978585 | + | 0.205843i | \(0.0659938\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 77412.1 | + | 134082.i | 0.262548 | + | 0.454747i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20668.8 | − | 24632.2i | 0.0695862 | − | 0.0829296i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 47200.9 | + | 129684.i | 0.157752 | + | 0.433421i | 0.993239 | − | 0.116090i | \(-0.0370361\pi\) |
−0.835486 | + | 0.549511i | \(0.814814\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 35796.6 | + | 203012.i | 0.118767 | + | 0.673562i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 136262. | + | 240358.i | 0.448820 | + | 0.791691i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 238909. | − | 42126.1i | 0.781237 | − | 0.137753i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 125207. | − | 45571.6i | 0.406483 | − | 0.147948i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −432127. | − | 362598.i | −1.39284 | − | 1.16873i | −0.964175 | − | 0.265268i | \(-0.914540\pi\) |
−0.428665 | − | 0.903464i | \(-0.641016\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −609919. | + | 352137.i | −1.95186 | + | 1.12691i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24952.0 | − | 4399.72i | −0.0792830 | − | 0.0139797i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 303151. | + | 175025.i | 0.956407 | + | 0.552182i | 0.895065 | − | 0.445935i | \(-0.147129\pi\) |
0.0613417 | + | 0.998117i | \(0.480462\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 54102.4 | − | 148645.i | 0.169480 | − | 0.465644i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −165041. | + | 138486.i | −0.513364 | + | 0.430763i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 21199.4i | − | 0.0654786i | −0.999464 | − | 0.0327393i | \(-0.989577\pi\) | ||
0.999464 | − | 0.0327393i | \(-0.0104231\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10357.8 | 0.0317682 | 0.0158841 | − | 0.999874i | \(-0.494944\pi\) | ||||
0.0158841 | + | 0.999874i | \(0.494944\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12645.0 | + | 15069.7i | 0.0385132 | + | 0.0458983i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −266077. | − | 96844.2i | −0.804770 | − | 0.292912i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −196044. | + | 339559.i | −0.588847 | + | 1.01991i | 0.405537 | + | 0.914079i | \(0.367085\pi\) |
−0.994384 | + | 0.105834i | \(0.966249\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6211.37 | − | 35226.4i | 0.0185281 | − | 0.105078i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −174970. | − | 303057.i | −0.518337 | − | 0.897786i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −160430. | + | 191194.i | −0.472008 | + | 0.562518i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 115887. | + | 318396.i | 0.338628 | + | 0.930372i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 78897.2 | + | 447448.i | 0.228973 | + | 1.29857i | 0.854942 | + | 0.518724i | \(0.173593\pi\) |
−0.625968 | + | 0.779849i | \(0.715296\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15353.4 | + | 91263.8i | 0.0442561 | + | 0.263068i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −171604. | + | 30258.5i | −0.491308 | + | 0.0866308i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −276794. | + | 100745.i | −0.787132 | + | 0.286493i | −0.704144 | − | 0.710058i | \(-0.748669\pi\) |
−0.0829890 | + | 0.996550i | \(0.526447\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −64675.3 | − | 54269.0i | −0.182686 | − | 0.153292i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −77051.2 | + | 44485.5i | −0.216188 | + | 0.124816i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 440740. | + | 77714.4i | 1.22837 | + | 0.216595i | 0.749925 | − | 0.661523i | \(-0.230090\pi\) |
0.478445 | + | 0.878118i | \(0.341201\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −135466. | − | 78211.5i | −0.375044 | − | 0.216532i | 0.300616 | − | 0.953745i | \(-0.402808\pi\) |
−0.675660 | + | 0.737214i | \(0.736141\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 78109.5 | − | 214604.i | 0.214817 | − | 0.590206i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −101601. | + | 85253.7i | −0.277581 | + | 0.232918i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 239177.i | − | 0.649144i | −0.945861 | − | 0.324572i | \(-0.894780\pi\) | ||
0.945861 | − | 0.324572i | \(-0.105220\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −109109. | −0.294189 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 101592. | + | 121073.i | 0.272130 | + | 0.324312i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 269735. | + | 98175.6i | 0.717822 | + | 0.261266i | 0.675001 | − | 0.737817i | \(-0.264143\pi\) |
0.0428211 | + | 0.999083i | \(0.486365\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 21127.8 | − | 36594.4i | 0.0558604 | − | 0.0967530i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −92784.5 | + | 526207.i | −0.243728 | + | 1.38225i | 0.579701 | + | 0.814829i | \(0.303169\pi\) |
−0.823429 | + | 0.567419i | \(0.807942\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 54937.5 | + | 95154.5i | 0.143380 | + | 0.248341i | 0.928767 | − | 0.370664i | \(-0.120870\pi\) |
−0.785388 | + | 0.619004i | \(0.787536\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 251235. | − | 299410.i | 0.651473 | − | 0.776395i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 73964.2 | + | 203215.i | 0.190566 | + | 0.523576i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13146.4 | − | 74557.1i | −0.0336549 | − | 0.190866i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 84124.1 | − | 29871.7i | 0.213986 | − | 0.0759845i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −263267. | + | 46421.1i | −0.665420 | + | 0.117331i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −535576. | + | 194934.i | −1.34512 | + | 0.489585i | −0.911423 | − | 0.411471i | \(-0.865015\pi\) |
−0.433702 | + | 0.901056i | \(0.642793\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14438.5 | + | 12115.4i | 0.0360342 | + | 0.0302363i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 210735. | − | 121668.i | 0.522623 | − | 0.301736i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27119.0 | + | 4781.81i | 0.0668336 | + | 0.0117846i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −495426. | − | 286035.i | −1.21333 | − | 0.700514i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −279930. | + | 769102.i | −0.681293 | + | 1.87184i | −0.256507 | + | 0.966542i | \(0.582572\pi\) |
−0.424785 | + | 0.905294i | \(0.639650\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 140685. | − | 118049.i | 0.340272 | − | 0.285522i | −0.456597 | − | 0.889673i | \(-0.650932\pi\) |
0.796870 | + | 0.604151i | \(0.206488\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 131607.i | 0.316344i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 554623. | 1.32492 | 0.662459 | − | 0.749098i | \(-0.269513\pi\) | ||||
0.662459 | + | 0.749098i | \(0.269513\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 84981.1 | + | 101277.i | 0.201759 | + | 0.240447i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −34342.4 | − | 12499.6i | −0.0810342 | − | 0.0294940i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 117261. | − | 203101.i | 0.274995 | − | 0.476306i | −0.695139 | − | 0.718876i | \(-0.744657\pi\) |
0.970134 | + | 0.242570i | \(0.0779903\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 94456.1 | − | 535687.i | 0.220165 | − | 1.24862i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −193488. | − | 335131.i | −0.448252 | − | 0.776396i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −104774. | + | 124864.i | −0.241257 | + | 0.287519i | −0.873063 | − | 0.487608i | \(-0.837870\pi\) |
0.631805 | + | 0.775127i | \(0.282314\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −51551.4 | − | 141636.i | −0.117988 | − | 0.324169i | 0.866614 | − | 0.498979i | \(-0.166291\pi\) |
−0.984602 | + | 0.174809i | \(0.944069\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 14452.5 | + | 81964.4i | 0.0328789 | + | 0.186465i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 292532. | + | 53956.2i | 0.661500 | + | 0.122011i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −647090. | + | 114099.i | −1.45450 | + | 0.256467i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 202440. | − | 73682.0i | 0.452318 | − | 0.164630i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −182051. | − | 152759.i | −0.404341 | − | 0.339282i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −109990. | + | 63502.7i | −0.242841 | + | 0.140205i | −0.616482 | − | 0.787369i | \(-0.711443\pi\) |
0.373641 | + | 0.927574i | \(0.378109\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −147875. | − | 26074.3i | −0.324553 | − | 0.0572275i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23991.9 | − | 13851.8i | −0.0523465 | − | 0.0302223i | 0.473598 | − | 0.880741i | \(-0.342955\pi\) |
−0.525945 | + | 0.850519i | \(0.676288\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17355.0 | + | 47682.4i | −0.0376431 | + | 0.103423i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −171607. | + | 143996.i | −0.370034 | + | 0.310495i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 597143.i | 1.28008i | 0.768342 | + | 0.640040i | \(0.221082\pi\) | ||||
−0.768342 | + | 0.640040i | \(0.778918\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −59843.4 | −0.127537 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −73438.2 | − | 87520.2i | −0.155600 | − | 0.185436i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 770415. | + | 280408.i | 1.62288 | + | 0.590680i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 388563. | − | 673011.i | 0.813777 | − | 1.40950i | −0.0964250 | − | 0.995340i | \(-0.530741\pi\) |
0.910202 | − | 0.414164i | \(-0.135926\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 50000.6 | − | 283567.i | 0.104114 | − | 0.590459i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22953.3 | − | 39756.3i | −0.0475199 | − | 0.0823069i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −54494.8 | + | 64944.4i | −0.112173 | + | 0.133683i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −92639.6 | − | 254525.i | −0.189602 | − | 0.520927i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20302.7 | − | 115143.i | −0.0413160 | − | 0.234315i | 0.957156 | − | 0.289572i | \(-0.0935131\pi\) |
−0.998472 | + | 0.0552576i | \(0.982402\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 726265. | − | 599741.i | 1.46955 | − | 1.21354i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 29085.9 | − | 5128.62i | 0.0585199 | − | 0.0103186i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 656985. | − | 239123.i | 1.31437 | − | 0.478390i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −349377. | − | 293162.i | −0.695028 | − | 0.583198i | 0.225326 | − | 0.974283i | \(-0.427655\pi\) |
−0.920354 | + | 0.391086i | \(0.872100\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 316120. | − | 182512.i | 0.625335 | − | 0.361037i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −216745. | − | 38218.0i | −0.426354 | − | 0.0751776i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −338283. | − | 195308.i | −0.661711 | − | 0.382039i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −100995. | + | 277481.i | −0.196454 | + | 0.539753i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 737375. | − | 618731.i | 1.42637 | − | 1.19686i | 0.478543 | − | 0.878064i | \(-0.341165\pi\) |
0.947822 | − | 0.318799i | \(-0.103279\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 88481.7i | − | 0.170209i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −111373. | −0.213060 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 162260. | + | 193374.i | 0.308699 | + | 0.367893i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 642267. | + | 233766.i | 1.21520 | + | 0.442296i | 0.868504 | − | 0.495683i | \(-0.165082\pi\) |
0.346694 | + | 0.937978i | \(0.387304\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −107281. | + | 185815.i | −0.201867 | + | 0.349644i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45851.5 | − | 260037.i | 0.0858062 | − | 0.486631i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10194.9 | + | 17658.1i | 0.0189747 | + | 0.0328651i | 0.875357 | − | 0.483477i | \(-0.160626\pi\) |
−0.856382 | + | 0.516343i | \(0.827293\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3307.72 | − | 3941.98i | 0.00612285 | − | 0.00729693i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 90047.4 | + | 247403.i | 0.165782 | + | 0.455481i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 63505.2 | + | 360156.i | 0.116284 | + | 0.659480i | 0.986106 | + | 0.166115i | \(0.0531222\pi\) |
−0.869822 | + | 0.493365i | \(0.835767\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −186720. | − | 226112.i | −0.340060 | − | 0.411800i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −610254. | + | 107604.i | −1.10543 | + | 0.194918i | −0.696437 | − | 0.717617i | \(-0.745233\pi\) |
−0.408998 | + | 0.912535i | \(0.634122\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 503642. | − | 183311.i | 0.907421 | − | 0.330274i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −403355. | − | 338455.i | −0.722847 | − | 0.606541i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −97027.5 | + | 56018.8i | −0.172954 | + | 0.0998552i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −687250. | − | 121181.i | −1.21853 | − | 0.214859i | −0.472835 | − | 0.881151i | \(-0.656769\pi\) |
−0.745691 | + | 0.666292i | \(0.767881\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −167197. | − | 96531.4i | −0.294876 | − | 0.170247i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −83346.0 | + | 228991.i | −0.146215 | + | 0.401721i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 137490. | − | 115368.i | 0.239928 | − | 0.201323i | −0.514893 | − | 0.857255i | \(-0.672168\pi\) |
0.754821 | + | 0.655931i | \(0.227724\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 212298.i | 0.368521i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −202495. | −0.349659 | −0.174830 | − | 0.984599i | \(-0.555937\pi\) | ||||
−0.174830 | + | 0.984599i | \(0.555937\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 57697.6 | + | 68761.4i | 0.0991081 | + | 0.118112i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −119374. | − | 43448.6i | −0.203980 | − | 0.0742426i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 217142. | − | 376102.i | 0.369108 | − | 0.639314i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −90273.7 | + | 511967.i | −0.152654 | + | 0.865744i | 0.808245 | + | 0.588846i | \(0.200418\pi\) |
−0.960899 | + | 0.276898i | \(0.910694\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −102886. | − | 178205.i | −0.173081 | − | 0.299785i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 458750. | − | 546717.i | 0.767745 | − | 0.914963i | −0.230566 | − | 0.973057i | \(-0.574058\pi\) |
0.998311 | + | 0.0580935i | \(0.0185022\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28918.7 | + | 79453.6i | 0.0481477 | + | 0.132285i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 64588.4 | + | 366299.i | 0.106982 | + | 0.606727i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 54180.7 | − | 293749.i | 0.0892831 | − | 0.484062i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 649482. | − | 114521.i | 1.06479 | − | 0.187752i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −327431. | + | 119175.i | −0.534067 | + | 0.194384i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 305853. | + | 256642.i | 0.496334 | + | 0.416474i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −340466. | + | 196568.i | −0.549699 | + | 0.317369i | −0.749001 | − | 0.662569i | \(-0.769466\pi\) |
0.199302 | + | 0.979938i | \(0.436133\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −215068. | − | 37922.3i | −0.345479 | − | 0.0609173i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 382417. | + | 220789.i | 0.611201 | + | 0.352877i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −266999. | + | 733574.i | −0.424584 | + | 1.16653i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 117363. | − | 98479.2i | 0.185694 | − | 0.155815i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1.00661e6i | − | 1.58470i | −0.610069 | − | 0.792348i | \(-0.708858\pi\) | ||
0.610069 | − | 0.792348i | \(-0.291142\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −59256.2 | −0.0928197 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 209159. | + | 249266.i | 0.325996 | + | 0.388507i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 419215. | + | 152582.i | 0.650138 | + | 0.236631i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −353709. | + | 612642.i | −0.545826 | + | 0.945399i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30886.1 | + | 175164.i | −0.0474259 | + | 0.268966i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8996.82 | + | 15583.0i | 0.0137465 | + | 0.0238096i | 0.872817 | − | 0.488048i | \(-0.162291\pi\) |
−0.859070 | + | 0.511858i | \(0.828958\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 746604. | − | 889768.i | 1.13514 | − | 1.35280i | 0.207980 | − | 0.978133i | \(-0.433311\pi\) |
0.927158 | − | 0.374672i | \(-0.122245\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −43510.0 | − | 119543.i | −0.0658276 | − | 0.180860i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15533.3 | + | 88093.8i | 0.0233856 | + | 0.132626i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 311307. | + | 876697.i | 0.466385 | + | 1.31342i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −931485. | + | 164246.i | −1.38870 | + | 0.244865i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.04409e6 | + | 380018.i | −1.54900 | + | 0.563790i | −0.968183 | − | 0.250243i | \(-0.919489\pi\) |
−0.580818 | + | 0.814033i | \(0.697267\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −725280. | − | 608582.i | −1.07079 | − | 0.898503i | −0.0756704 | − | 0.997133i | \(-0.524110\pi\) |
−0.995124 | + | 0.0986295i | \(0.968554\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 70632.8 | − | 40779.9i | 0.103776 | − | 0.0599153i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −639418. | − | 112747.i | −0.934919 | − | 0.164851i | −0.314621 | − | 0.949217i | \(-0.601877\pi\) |
−0.620298 | + | 0.784366i | \(0.712988\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −410154. | − | 236802.i | −0.596812 | − | 0.344570i | 0.170974 | − | 0.985275i | \(-0.445308\pi\) |
−0.767786 | + | 0.640706i | \(0.778642\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −116969. | + | 321370.i | −0.169383 | + | 0.465376i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7908.94 | + | 6636.39i | −0.0113980 | + | 0.00956404i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 30387.1i | − | 0.0435830i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −116713. | −0.166597 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 336199. | + | 400667.i | 0.477609 | + | 0.569193i | 0.950021 | − | 0.312185i | \(-0.101061\pi\) |
−0.472412 | + | 0.881378i | \(0.656617\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −114173. | − | 41555.6i | −0.161425 | − | 0.0587541i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 180004. | − | 311776.i | 0.253295 | − | 0.438720i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −137603. | + | 780385.i | −0.192715 | + | 1.09294i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −185122. | − | 320641.i | −0.258042 | − | 0.446943i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20637.5 | + | 24594.9i | −0.0286314 | + | 0.0341216i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 766106. | + | 2.10486e6i | 1.05786 | + | 2.90646i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13993.6 | − | 79361.7i | −0.0192323 | − | 0.109072i | 0.973680 | − | 0.227918i | \(-0.0731917\pi\) |
−0.992913 | + | 0.118846i | \(0.962081\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 441384. | − | 74254.4i | 0.603788 | − | 0.101576i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 778857. | − | 137334.i | 1.06046 | − | 0.186989i | 0.383902 | − | 0.923374i | \(-0.374580\pi\) |
0.676563 | + | 0.736385i | \(0.263469\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −370189. | + | 134738.i | −0.501692 | + | 0.182601i | −0.580455 | − | 0.814293i | \(-0.697125\pi\) |
0.0787631 | + | 0.996893i | \(0.474903\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 90360.8 | + | 75821.7i | 0.121892 | + | 0.102279i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −560672. | + | 323704.i | −0.752813 | + | 0.434637i | −0.826709 | − | 0.562629i | \(-0.809790\pi\) |
0.0738965 | + | 0.997266i | \(0.476457\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −868314. | − | 153107.i | −1.16050 | − | 0.204627i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 187974. | + | 108527.i | 0.250068 | + | 0.144377i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −143926. | + | 395434.i | −0.190590 | + | 0.523642i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 662511. | − | 555913.i | 0.873286 | − | 0.732774i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 76350.6i | 0.100181i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 786776. | 1.02763 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −779669. | − | 929173.i | −1.01370 | − | 1.20808i | −0.977975 | − | 0.208723i | \(-0.933069\pi\) |
−0.0357286 | − | 0.999362i | \(-0.511375\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −41241.2 | − | 15010.6i | −0.0533769 | − | 0.0194276i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −685461. | + | 1.18725e6i | −0.883142 | + | 1.52965i | −0.0353145 | + | 0.999376i | \(0.511243\pi\) |
−0.847828 | + | 0.530271i | \(0.822090\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −203932. | + | 1.15656e6i | −0.261556 | + | 1.48335i | 0.517112 | + | 0.855918i | \(0.327007\pi\) |
−0.778667 | + | 0.627437i | \(0.784104\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −40577.3 | − | 70281.9i | −0.0518080 | − | 0.0897340i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14389.9 | − | 17149.2i | 0.0182898 | − | 0.0217969i | −0.756822 | − | 0.653621i | \(-0.773249\pi\) |
0.775112 | + | 0.631824i | \(0.217693\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 232327. | + | 638312.i | 0.293965 | + | 0.807662i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −64895.5 | − | 368041.i | −0.0817446 | − | 0.463597i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 181623. | − | 102965.i | 0.227755 | − | 0.129117i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −756678. | + | 133423.i | −0.944637 | + | 0.166565i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 655317. | − | 238516.i | 0.814454 | − | 0.296437i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 150305. | + | 126121.i | 0.185975 | + | 0.156051i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −266202. | + | 153692.i | −0.327915 | + | 0.189322i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −361804. | − | 63795.8i | −0.443708 | − | 0.0782377i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −775009. | − | 447451.i | −0.946257 | − | 0.546322i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 224981. | − | 618129.i | 0.273483 | − | 0.751388i | −0.724581 | − | 0.689190i | \(-0.757967\pi\) |
0.998064 | − | 0.0621985i | \(-0.0198112\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 805867. | − | 676203.i | 0.975294 | − | 0.818369i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 73478.6i | 0.0885369i | 0.999020 | + | 0.0442685i | \(0.0140957\pi\) | ||||
−0.999020 | + | 0.0442685i | \(0.985904\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 607017. | 0.728215 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 93770.0 | + | 111751.i | 0.112001 | + | 0.133477i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.42688e6 | + | 519342.i | 1.69687 | + | 0.617611i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −405049. | + | 701566.i | −0.479598 | + | 0.830687i | −0.999726 | − | 0.0234006i | \(-0.992551\pi\) |
0.520129 | + | 0.854088i | \(0.325884\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 51630.8 | − | 292813.i | 0.0608681 | − | 0.345200i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.08319e6 | − | 1.87614e6i | −1.27146 | − | 2.20223i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 553139. | − | 659206.i | 0.646474 | − | 0.770438i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −45535.0 | − | 125106.i | −0.0529890 | − | 0.145586i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −170453. | − | 966688.i | −0.197503 | − | 1.12010i | −0.908809 | − | 0.417213i | \(-0.863007\pi\) |
0.711306 | − | 0.702883i | \(-0.248104\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12709.8 | − | 34083.5i | 0.0146635 | − | 0.0393229i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 450417. | − | 79420.7i | 0.517430 | − | 0.0912369i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 137619. | − | 50089.1i | 0.157418 | − | 0.0572954i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 175639. | + | 147379.i | 0.200052 | + | 0.167864i | 0.737310 | − | 0.675554i | \(-0.236096\pi\) |
−0.537258 | + | 0.843418i | \(0.680540\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −49373.4 | + | 28505.7i | −0.0559966 | + | 0.0323296i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 256738. | + | 45269.8i | 0.289941 | + | 0.0511245i | 0.316727 | − | 0.948517i | \(-0.397416\pi\) |
−0.0267857 | + | 0.999641i | \(0.508527\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 615191. | + | 355180.i | 0.691809 | + | 0.399416i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −128306. | + | 352519.i | −0.143676 | + | 0.394747i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −366887. | + | 307854.i | −0.409102 | + | 0.343278i | −0.823999 | − | 0.566591i | \(-0.808262\pi\) |
0.414897 | + | 0.909868i | \(0.363818\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.46545e6i | − | 1.62719i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −383025. | −0.423513 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −656124. | − | 781939.i | −0.722438 | − | 0.860968i | 0.272427 | − | 0.962176i | \(-0.412174\pi\) |
−0.994865 | + | 0.101209i | \(0.967729\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −106850. | − | 38890.2i | −0.117157 | − | 0.0426416i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 94631.9 | − | 163907.i | 0.103327 | − | 0.178967i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29008.7 | − | 164517.i | 0.0315421 | − | 0.178884i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −428900. | − | 742877.i | −0.464418 | − | 0.804396i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −108361. | + | 129139.i | −0.116847 | + | 0.139253i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 70714.1 | + | 194285.i | 0.0759366 | + | 0.208634i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 126048. | + | 714852.i | 0.134797 | + | 0.764474i | 0.975001 | + | 0.222202i | \(0.0713246\pi\) |
−0.840203 | + | 0.542272i | \(0.817564\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 109940. | + | 864.459i | 0.117087 | + | 0.000920655i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.34327e6 | − | 236855.i | 1.42471 | − | 0.251214i | 0.592451 | − | 0.805607i | \(-0.298160\pi\) |
0.832255 | + | 0.554393i | \(0.187049\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 120421. | − | 43829.7i | 0.127197 | − | 0.0462960i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −205234. | − | 172212.i | −0.215894 | − | 0.181156i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.05630e6 | − | 609857.i | 1.10662 | − | 0.638909i | 0.168670 | − | 0.985673i | \(-0.446053\pi\) |
0.937952 | + | 0.346764i | \(0.112719\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −369427. | − | 65139.9i | −0.385445 | − | 0.0679644i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 116966. | + | 67530.5i | 0.121541 | + | 0.0701717i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −395219. | + | 1.08586e6i | −0.409007 | + | 1.12374i | 0.548707 | + | 0.836015i | \(0.315120\pi\) |
−0.957714 | + | 0.287723i | \(0.907102\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 771557. | − | 647413.i | 0.795235 | − | 0.667282i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 82446.5i | 0.0846327i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.21246e6 | −2.26194 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 826730. | + | 985258.i | 0.841814 | + | 1.00324i | 0.999875 | + | 0.0158057i | \(0.00503131\pi\) |
−0.158061 | + | 0.987429i | \(0.550524\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 521659. | + | 189868.i | 0.529040 | + | 0.192555i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 257132. | − | 445366.i | 0.259723 | − | 0.449853i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 223996. | − | 1.27034e6i | 0.225346 | − | 1.27800i | −0.636677 | − | 0.771130i | \(-0.719692\pi\) |
0.862023 | − | 0.506869i | \(-0.169197\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 593919. | + | 1.02870e6i | 0.595109 | + | 1.03076i |
(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 | 76.5.j.a.29.4 | yes | 42 | |
19.2 | odd | 18 | inner | 76.5.j.a.21.4 | ✓ | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.j.a.21.4 | ✓ | 42 | 19.2 | odd | 18 | inner | |
76.5.j.a.29.4 | yes | 42 | 1.1 | even | 1 | trivial |