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 | 13.1 | ||
Character | \(\chi\) | \(=\) | 76.13 |
Dual form | 76.5.j.a.41.1 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{18}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −4.65644 | + | 12.7935i | −0.517382 | + | 1.42150i | 0.356012 | + | 0.934481i | \(0.384136\pi\) |
−0.873394 | + | 0.487014i | \(0.838086\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.59099 | + | 37.3793i | 0.263640 | + | 1.49517i | 0.772881 | + | 0.634551i | \(0.218815\pi\) |
−0.509242 | + | 0.860623i | \(0.670074\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.00284 | − | 8.66518i | 0.102099 | − | 0.176840i | −0.810450 | − | 0.585807i | \(-0.800778\pi\) |
0.912549 | + | 0.408967i | \(0.134111\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −79.9406 | − | 67.0781i | −0.986921 | − | 0.828125i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.63671 | − | 13.2272i | −0.0631133 | − | 0.109315i | 0.832742 | − | 0.553661i | \(-0.186770\pi\) |
−0.895856 | + | 0.444345i | \(0.853436\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −22.1718 | − | 60.9166i | −0.131194 | − | 0.360453i | 0.856650 | − | 0.515897i | \(-0.172541\pi\) |
−0.987845 | + | 0.155444i | \(0.950319\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −508.902 | − | 89.7331i | −2.26179 | − | 0.398814i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −348.579 | + | 292.493i | −1.20616 | + | 1.01209i | −0.206724 | + | 0.978399i | \(0.566280\pi\) |
−0.999432 | + | 0.0336857i | \(0.989275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 281.167 | − | 226.421i | 0.778855 | − | 0.627204i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 87.5622 | + | 104.353i | 0.198554 | + | 0.236627i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 49.2696 | − | 279.422i | 0.0931372 | − | 0.528207i | −0.902165 | − | 0.431391i | \(-0.858023\pi\) |
0.995302 | − | 0.0968164i | \(-0.0308660\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −766.467 | + | 278.971i | −1.22635 | + | 0.446354i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 275.368 | − | 158.984i | 0.377734 | − | 0.218085i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −472.367 | + | 562.945i | −0.561673 | + | 0.669376i | −0.969900 | − | 0.243505i | \(-0.921703\pi\) |
0.408227 | + | 0.912881i | \(0.366147\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1430.40 | + | 825.841i | 1.48845 | + | 0.859356i | 0.999913 | − | 0.0131887i | \(-0.00419821\pi\) |
0.488535 | + | 0.872544i | \(0.337532\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 204.781 | − | 36.1084i | 0.188045 | − | 0.0331574i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 356.872 | + | 129.891i | 0.291324 | + | 0.106033i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1474.16i | − | 1.07681i | −0.842685 | − | 0.538407i | \(-0.819026\pi\) | ||
0.842685 | − | 0.538407i | \(-0.180974\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 882.576 | 0.580260 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −842.731 | + | 2315.38i | −0.501327 | + | 1.37739i | 0.388652 | + | 0.921385i | \(0.372941\pi\) |
−0.889979 | + | 0.456001i | \(0.849281\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −329.577 | − | 1869.12i | −0.178246 | − | 1.01088i | −0.934330 | − | 0.356409i | \(-0.884001\pi\) |
0.756084 | − | 0.654474i | \(-0.227110\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1980.45 | − | 3430.24i | 0.978000 | − | 1.69395i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 985.584 | + | 827.003i | 0.446167 | + | 0.374379i | 0.838011 | − | 0.545653i | \(-0.183718\pi\) |
−0.391844 | + | 0.920032i | \(0.628163\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1150.44 | + | 1992.63i | 0.479152 | + | 0.829915i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2118.86 | − | 5821.51i | −0.814631 | − | 2.23818i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3118.81 | + | 549.931i | 1.11029 | + | 0.195775i | 0.698575 | − | 0.715537i | \(-0.253818\pi\) |
0.411718 | + | 0.911311i | \(0.364929\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 444.089 | − | 372.635i | 0.146806 | − | 0.123185i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1587.47 | + | 4651.41i | 0.488603 | + | 1.43164i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 938.249 | + | 1118.16i | 0.269534 | + | 0.321218i | 0.883786 | − | 0.467892i | \(-0.154986\pi\) |
−0.614251 | + | 0.789110i | \(0.710542\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −920.289 | + | 5219.22i | −0.247323 | + | 1.40264i | 0.567712 | + | 0.823227i | \(0.307829\pi\) |
−0.815035 | + | 0.579411i | \(0.803283\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −981.174 | + | 357.118i | −0.247209 | + | 0.0899769i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2130.89 | − | 1230.27i | 0.504352 | − | 0.291188i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4064.52 | + | 4843.91i | −0.905441 | + | 1.07906i | 0.0910906 | + | 0.995843i | \(0.470965\pi\) |
−0.996531 | + | 0.0832195i | \(0.973480\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3345.35 | + | 1931.44i | 0.702657 | + | 0.405679i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9089.14 | + | 1602.66i | −1.80304 | + | 0.317925i | −0.971411 | − | 0.237402i | \(-0.923704\pi\) |
−0.831632 | + | 0.555328i | \(0.812593\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3636.99 | − | 1323.76i | −0.682491 | − | 0.248406i | −0.0225741 | − | 0.999745i | \(-0.507186\pi\) |
−0.659917 | + | 0.751339i | \(0.729408\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 11104.8i | − | 1.97418i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −152.821 | −0.0257752 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1439.36 | + | 3954.62i | −0.230630 | + | 0.633652i | −0.999987 | − | 0.00516827i | \(-0.998355\pi\) |
0.769356 | + | 0.638820i | \(0.220577\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −716.087 | − | 4061.13i | −0.109143 | − | 0.618980i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6219.89 | − | 10773.2i | 0.902873 | − | 1.56382i | 0.0791251 | − | 0.996865i | \(-0.474787\pi\) |
0.823748 | − | 0.566957i | \(-0.191879\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13230.7 | − | 11101.8i | −1.83123 | − | 1.53659i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5002.47 | − | 8664.53i | −0.660915 | − | 1.14474i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4134.29 | + | 11358.9i | 0.521940 | + | 1.43402i | 0.868358 | + | 0.495938i | \(0.165176\pi\) |
−0.346418 | + | 0.938080i | \(0.612602\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −638.775 | − | 112.633i | −0.0771374 | − | 0.0136014i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −17225.9 | + | 14454.3i | −1.99167 | + | 1.67121i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10316.6 | + | 9017.49i | 1.14312 | + | 0.999168i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1907.80 | − | 2273.62i | −0.202763 | − | 0.241643i | 0.655075 | − | 0.755564i | \(-0.272637\pi\) |
−0.857838 | + | 0.513920i | \(0.828193\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −276.771 | + | 1569.64i | −0.0282390 | + | 0.160151i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 830.282 | − | 302.198i | 0.0813923 | − | 0.0296244i | −0.301003 | − | 0.953623i | \(-0.597321\pi\) |
0.382395 | + | 0.923999i | \(0.375099\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1371.68 | + | 791.938i | −0.129294 | + | 0.0746477i | −0.563252 | − | 0.826285i | \(-0.690450\pi\) |
0.433958 | + | 0.900933i | \(0.357117\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3323.51 | + | 3960.80i | −0.301452 | + | 0.359256i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10273.8 | + | 5931.59i | 0.897355 | + | 0.518088i | 0.876341 | − | 0.481691i | \(-0.159977\pi\) |
0.0210141 | + | 0.999779i | \(0.493311\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6748.93 | − | 1190.02i | 0.568044 | − | 0.100161i | 0.117752 | − | 0.993043i | \(-0.462431\pi\) |
0.450292 | + | 0.892882i | \(0.351320\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18859.6 | + | 6864.33i | 1.53069 | + | 0.557124i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 353.475i | − | 0.0276823i | −0.999904 | − | 0.0138412i | \(-0.995594\pi\) | ||
0.999904 | − | 0.0138412i | \(-0.00440592\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10769.3 | 0.814317 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2313.74 | + | 6356.96i | −0.169022 | + | 0.464384i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 790.614 | + | 4483.79i | 0.0558304 | + | 0.316630i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7203.86 | − | 12477.5i | 0.492033 | − | 0.852227i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −25697.7 | − | 21562.9i | −1.69857 | − | 1.42527i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3618.28 | − | 6267.05i | −0.231570 | − | 0.401091i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 761.552 | + | 2092.35i | 0.0472163 | + | 0.129726i | 0.961060 | − | 0.276341i | \(-0.0891221\pi\) |
−0.913843 | + | 0.406067i | \(0.866900\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 25447.2 | + | 4487.03i | 1.52919 | + | 0.269637i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20343.3 | − | 17070.1i | 1.18544 | − | 0.994700i | 0.185510 | − | 0.982642i | \(-0.440606\pi\) |
0.999927 | − | 0.0120581i | \(-0.00383830\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −555.343 | − | 3569.11i | −0.0313948 | − | 0.201770i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7757.67 | + | 9245.23i | 0.425661 | + | 0.507283i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 612.283 | − | 3472.43i | 0.0326221 | − | 0.185009i | −0.964143 | − | 0.265385i | \(-0.914501\pi\) |
0.996765 | + | 0.0803760i | \(0.0256121\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13225.7 | − | 4813.75i | 0.684522 | − | 0.249146i | 0.0237343 | − | 0.999718i | \(-0.492444\pi\) |
0.660788 | + | 0.750573i | \(0.270222\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15169.5 | + | 8758.14i | −0.763017 | + | 0.440528i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −636.434 | + | 758.472i | −0.0311230 | + | 0.0370909i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −24155.9 | − | 13946.4i | −1.14891 | − | 0.663325i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −30849.6 | + | 5439.61i | −1.42763 | + | 0.251729i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 33951.2 | + | 12357.2i | 1.52927 | + | 0.556607i | 0.963442 | − | 0.267918i | \(-0.0863357\pi\) |
0.565825 | + | 0.824526i | \(0.308558\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 22405.3i | − | 0.982644i | −0.870978 | − | 0.491322i | \(-0.836514\pi\) | ||
0.870978 | − | 0.491322i | \(-0.163486\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 47485.5 | 2.02851 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21441.7 | + | 58910.5i | −0.892473 | + | 2.45205i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8341.26 | − | 47305.7i | −0.338402 | − | 1.91917i | −0.390654 | − | 0.920538i | \(-0.627751\pi\) |
0.0522519 | − | 0.998634i | \(-0.483360\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −21558.1 | + | 37339.7i | −0.852738 | + | 1.47699i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2174.75 | − | 1824.83i | −0.0838992 | − | 0.0703998i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5852.63 | + | 10137.0i | 0.220280 | + | 0.381537i | 0.954893 | − | 0.296950i | \(-0.0959695\pi\) |
−0.734613 | + | 0.678487i | \(0.762636\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2699.42 | + | 7416.59i | 0.0991522 | + | 0.272418i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11805.3 | + | 2081.60i | 0.423297 | + | 0.0746387i | 0.381239 | − | 0.924476i | \(-0.375497\pi\) |
0.0420580 | + | 0.999115i | \(0.486609\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18659.8 | − | 15657.4i | 0.653330 | − | 0.548209i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −37664.5 | − | 759.921i | −1.28807 | − | 0.0259882i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12729.2 | − | 15170.1i | −0.425315 | − | 0.506870i | 0.510250 | − | 0.860026i | \(-0.329553\pi\) |
−0.935564 | + | 0.353156i | \(0.885108\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1417.18 | + | 8037.22i | −0.0462752 | + | 0.262440i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18674.1 | + | 6796.80i | −0.596063 | + | 0.216949i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12656.1 | − | 7306.98i | 0.394996 | − | 0.228051i | −0.289327 | − | 0.957230i | \(-0.593431\pi\) |
0.684322 | + | 0.729179i | \(0.260098\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19336.0 | + | 23043.8i | −0.590215 | + | 0.703391i | −0.975647 | − | 0.219345i | \(-0.929608\pi\) |
0.385432 | + | 0.922736i | \(0.374052\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −62486.6 | − | 36076.6i | −1.86588 | − | 1.07727i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 55103.1 | − | 9716.16i | 1.61002 | − | 0.283891i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6530.84 | + | 2377.03i | 0.186761 | + | 0.0679754i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 3181.49i | − | 0.0890649i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −26426.2 | −0.724383 | −0.362191 | − | 0.932104i | \(-0.617971\pi\) | ||||
−0.362191 | + | 0.932104i | \(0.617971\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11007.9 | + | 30243.9i | −0.295521 | + | 0.811938i | 0.699713 | + | 0.714424i | \(0.253311\pi\) |
−0.995234 | + | 0.0975137i | \(0.968911\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5817.05 | + | 32990.1i | 0.152980 | + | 0.867590i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22446.5 | + | 38878.6i | −0.578385 | + | 1.00179i | 0.417280 | + | 0.908778i | \(0.362984\pi\) |
−0.995665 | + | 0.0930142i | \(0.970350\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4917.74 | − | 4126.47i | −0.124182 | − | 0.104201i | 0.578582 | − | 0.815625i | \(-0.303606\pi\) |
−0.702764 | + | 0.711423i | \(0.748051\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −43044.2 | − | 74554.7i | −1.06542 | − | 1.84537i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2514.84 | + | 6909.47i | 0.0610265 | + | 0.167669i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −92102.0 | − | 16240.1i | −2.19160 | − | 0.386438i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −22681.7 | + | 19032.2i | −0.529341 | + | 0.444170i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5142.09 | − | 1989.93i | −0.117719 | − | 0.0455559i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 32561.2 | + | 38804.9i | 0.731367 | + | 0.871609i | 0.995682 | − | 0.0928271i | \(-0.0295904\pi\) |
−0.264315 | + | 0.964436i | \(0.585146\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21819.5 | − | 123744.i | 0.480933 | − | 2.72751i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 67694.4 | − | 24638.7i | 1.46445 | − | 0.533018i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14312.1 | − | 8263.10i | 0.303937 | − | 0.175478i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 33870.9 | − | 40365.7i | 0.706217 | − | 0.841637i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25546.3 | + | 14749.2i | 0.523050 | + | 0.301983i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2412.23 | − | 425.340i | 0.0485074 | − | 0.00855317i | −0.149342 | − | 0.988786i | \(-0.547715\pi\) |
0.197849 | + | 0.980232i | \(0.436604\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 79984.7 | + | 29112.0i | 1.57994 | + | 0.575053i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 35918.6i | 0.697056i | 0.937298 | + | 0.348528i | \(0.113318\pi\) | ||||
−0.937298 | + | 0.348528i | \(0.886682\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −33051.1 | −0.630253 | −0.315126 | − | 0.949050i | \(-0.602047\pi\) | ||||
−0.315126 | + | 0.949050i | \(0.602047\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 711.601 | − | 1955.11i | 0.0133356 | − | 0.0366393i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3363.41 | − | 19074.9i | −0.0619539 | − | 0.351358i | −0.999988 | − | 0.00481606i | \(-0.998467\pi\) |
0.938035 | − | 0.346542i | \(-0.112644\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24416.9 | + | 42291.2i | −0.442134 | + | 0.765799i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −43891.0 | − | 36828.9i | −0.781409 | − | 0.655680i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28728.8 | + | 49759.7i | 0.502946 | + | 0.871127i | 0.999994 | + | 0.00340461i | \(0.00108372\pi\) |
−0.497049 | + | 0.867723i | \(0.665583\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19044.5 | + | 52324.4i | 0.327896 | + | 0.900887i | 0.988644 | + | 0.150279i | \(0.0480171\pi\) |
−0.660748 | + | 0.750608i | \(0.729761\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 80654.5 | + | 14221.6i | 1.36589 | + | 0.240843i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −66900.5 | + | 56136.2i | −1.11454 | + | 0.935213i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20026.8 | − | 12107.5i | −0.328259 | − | 0.198455i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 108864. | + | 129739.i | 1.75584 | + | 2.09252i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2649.04 | + | 15023.4i | −0.0420476 | + | 0.238464i | −0.998587 | − | 0.0531390i | \(-0.983077\pi\) |
0.956540 | + | 0.291603i | \(0.0941885\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4072.21 | + | 1482.16i | −0.0636194 | + | 0.0231556i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 203639. | − | 117571.i | 3.13170 | − | 1.80809i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6421.48 | + | 7652.82i | −0.0972230 | + | 0.115866i | −0.812462 | − | 0.583014i | \(-0.801873\pi\) |
0.715239 | + | 0.698880i | \(0.246318\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12773.8 | − | 7374.98i | −0.190424 | − | 0.109941i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 75522.6 | − | 13316.7i | 1.10865 | − | 0.195486i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −33819.4 | − | 12309.2i | −0.488938 | − | 0.177959i | 0.0857740 | − | 0.996315i | \(-0.472664\pi\) |
−0.574712 | + | 0.818356i | \(0.694886\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 120204.i | 1.71169i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −164570. | −2.30849 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 43070.1 | − | 118334.i | 0.595211 | − | 1.63533i | −0.165478 | − | 0.986214i | \(-0.552917\pi\) |
0.760689 | − | 0.649116i | \(-0.224861\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12760.4 | − | 72368.0i | −0.173751 | − | 0.985389i | −0.939576 | − | 0.342340i | \(-0.888780\pi\) |
0.765825 | − | 0.643049i | \(-0.222331\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4415.39 | − | 7647.67i | 0.0592439 | − | 0.102613i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9543.28 | + | 8007.76i | 0.126192 | + | 0.105888i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3268.44 | − | 5661.10i | −0.0425971 | − | 0.0737804i | 0.843941 | − | 0.536436i | \(-0.180230\pi\) |
−0.886538 | + | 0.462656i | \(0.846897\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −58951.1 | − | 161967.i | −0.757327 | − | 2.08074i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23883.9 | + | 4211.38i | 0.302477 | + | 0.0533349i | 0.322827 | − | 0.946458i | \(-0.395367\pi\) |
−0.0203497 | + | 0.999793i | \(0.506478\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 50567.4 | − | 42431.1i | 0.631390 | − | 0.529799i | −0.269970 | − | 0.962869i | \(-0.587014\pi\) |
0.901361 | + | 0.433069i | \(0.142569\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −163404. | + | 89996.0i | −2.01174 | + | 1.10798i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15847.2 | + | 18885.9i | 0.192392 | + | 0.229284i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21452.2 | − | 121661.i | 0.256848 | − | 1.45666i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 37971.1 | − | 13820.3i | 0.448401 | − | 0.163205i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 94398.8 | − | 54501.2i | 1.09959 | − | 0.634849i | 0.163478 | − | 0.986547i | \(-0.447729\pi\) |
0.936114 | + | 0.351698i | \(0.114396\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −35612.2 | + | 42440.9i | −0.409218 | + | 0.487686i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4205.82 | − | 2428.23i | −0.0476801 | − | 0.0275281i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18113.8 | + | 3193.95i | −0.202613 | + | 0.0357262i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17845.1 | − | 6495.09i | −0.196964 | − | 0.0716889i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12029.4i | 0.131026i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −201157. | −2.16239 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33364.0 | + | 91666.9i | −0.353999 | + | 0.972603i | 0.627073 | + | 0.778960i | \(0.284253\pi\) |
−0.981072 | + | 0.193643i | \(0.937970\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3744.50 | − | 21236.1i | −0.0392172 | − | 0.222412i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28528.3 | + | 49412.5i | −0.294955 | + | 0.510876i | −0.974974 | − | 0.222317i | \(-0.928638\pi\) |
0.680020 | + | 0.733194i | \(0.261971\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 126121. | + | 105828.i | 1.28735 | + | 1.08022i | 0.992185 | + | 0.124772i | \(0.0398201\pi\) |
0.295168 | + | 0.955445i | \(0.404624\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −19815.8 | − | 34321.9i | −0.199705 | − | 0.345900i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1581.86 | − | 4346.13i | −0.0157416 | − | 0.0432498i | 0.931573 | − | 0.363554i | \(-0.118437\pi\) |
−0.947315 | + | 0.320305i | \(0.896215\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11053.5 | + | 1949.03i | 0.108622 | + | 0.0191530i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −123725. | + | 103818.i | −1.20074 | + | 1.00754i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −31782.4 | + | 161165.i | −0.304636 | + | 1.54477i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 33987.9 | + | 40505.2i | 0.321779 | + | 0.383482i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16201.5 | + | 91883.4i | −0.151517 | + | 0.859293i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12096.8 | − | 4402.89i | 0.111758 | − | 0.0406767i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 153760. | − | 88773.4i | 1.40342 | − | 0.810264i | 0.408677 | − | 0.912679i | \(-0.365990\pi\) |
0.994742 | + | 0.102415i | \(0.0326570\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −98883.8 | + | 117845.i | −0.891737 | + | 1.06273i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −207851. | − | 120003.i | −1.85210 | − | 1.06931i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 81386.6 | − | 14350.7i | 0.716627 | − | 0.126361i | 0.196567 | − | 0.980490i | \(-0.437021\pi\) |
0.520060 | + | 0.854130i | \(0.325910\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4522.17 | + | 1645.94i | 0.0393503 | + | 0.0143223i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 25226.8i | − | 0.216947i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 47045.6 | 0.399881 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −50146.8 | + | 137777.i | −0.421313 | + | 1.15755i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27172.5 | − | 154103.i | −0.225668 | − | 1.27983i | −0.861404 | − | 0.507921i | \(-0.830414\pi\) |
0.635735 | − | 0.771907i | \(-0.280697\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −53851.5 | + | 93273.5i | −0.442127 | + | 0.765786i | −0.997847 | − | 0.0655833i | \(-0.979109\pi\) |
0.555720 | + | 0.831369i | \(0.312443\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15790.2 | − | 13249.5i | −0.128166 | − | 0.107544i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −38337.3 | − | 66402.2i | −0.307661 | − | 0.532884i | 0.670189 | − | 0.742190i | \(-0.266213\pi\) |
−0.977850 | + | 0.209306i | \(0.932880\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −119813. | − | 329183.i | −0.950707 | − | 2.61205i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −61044.7 | − | 10763.8i | −0.478973 | − | 0.0844559i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34087.3 | + | 28602.6i | −0.264486 | + | 0.221931i | −0.765380 | − | 0.643578i | \(-0.777449\pi\) |
0.500894 | + | 0.865509i | \(0.333005\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27788.3 | − | 127324.i | 0.213230 | − | 0.977002i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 126085. | + | 150263.i | 0.956868 | + | 1.14035i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25509.8 | − | 144673.i | 0.191479 | − | 1.08593i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −105525. | + | 38408.0i | −0.783473 | + | 0.285161i | −0.702620 | − | 0.711565i | \(-0.747987\pi\) |
−0.0808531 | + | 0.996726i | \(0.525764\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 222680. | − | 128564.i | 1.63542 | − | 0.944209i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20368.2 | − | 24273.8i | 0.147980 | − | 0.176356i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 135345. | + | 78141.6i | 0.972804 | + | 0.561649i | 0.900090 | − | 0.435704i | \(-0.143501\pi\) |
0.0727141 | + | 0.997353i | \(0.476834\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 97025.6 | − | 17108.2i | 0.689960 | − | 0.121659i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 44765.9 | + | 16293.5i | 0.314967 | + | 0.114639i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 180715.i | − | 1.25810i | −0.777364 | − | 0.629051i | \(-0.783443\pi\) | ||
0.777364 | − | 0.629051i | \(-0.216557\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −30314.5 | −0.208834 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11888.3 | − | 32662.7i | 0.0810439 | − | 0.222666i | −0.892552 | − | 0.450944i | \(-0.851087\pi\) |
0.973596 | + | 0.228278i | \(0.0733095\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1007.24 | − | 5712.35i | −0.00679535 | − | 0.0385383i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −99030.7 | + | 171526.i | −0.661223 | + | 1.14527i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −179821. | − | 150888.i | −1.18834 | − | 0.997137i | −0.999887 | − | 0.0150555i | \(-0.995208\pi\) |
−0.188455 | − | 0.982082i | \(-0.560348\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 64554.4 | + | 111812.i | 0.422253 | + | 0.731363i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 123658. | + | 339747.i | 0.800638 | + | 2.19973i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −157308. | − | 27737.6i | −1.00822 | − | 0.177777i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −164819. | + | 138300.i | −1.04575 | + | 0.877487i | −0.992640 | − | 0.121102i | \(-0.961357\pi\) |
−0.0531080 | + | 0.998589i | \(0.516913\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 48247.1 | + | 9514.56i | 0.303058 | + | 0.0597644i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 118155. | + | 140811.i | 0.734789 | + | 0.875688i | 0.995978 | − | 0.0895999i | \(-0.0285588\pi\) |
−0.261188 | + | 0.965288i | \(0.584114\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18592.9 | − | 105445.i | 0.114482 | − | 0.649258i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 147083. | − | 53533.7i | 0.896709 | − | 0.326375i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19498.9 | + | 11257.7i | −0.117712 | + | 0.0679612i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 161880. | − | 192921.i | 0.967714 | − | 1.15328i | −0.0204371 | − | 0.999791i | \(-0.506506\pi\) |
0.988151 | − | 0.153485i | \(-0.0490498\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 41573.4 | + | 24002.4i | 0.246111 | + | 0.142092i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14383.0 | − | 2536.11i | 0.0843235 | − | 0.0148685i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 443689. | + | 161490.i | 2.57622 | + | 0.937667i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 191617.i | 1.10195i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 155593. | 0.886261 | 0.443130 | − | 0.896457i | \(-0.353868\pi\) | ||||
0.443130 | + | 0.896457i | \(0.353868\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −113197. | + | 311006.i | −0.638661 | + | 1.75471i | 0.0172286 | + | 0.999852i | \(0.494516\pi\) |
−0.655890 | + | 0.754856i | \(0.727707\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −23314.4 | − | 132222.i | −0.130299 | − | 0.738965i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 185577. | − | 321429.i | 1.02742 | − | 1.77954i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 40621.4 | + | 34085.4i | 0.222792 | + | 0.186944i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6739.97 | − | 11674.0i | −0.0366221 | − | 0.0634314i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11427.4 | + | 31396.5i | 0.0615166 | + | 0.169016i | 0.966643 | − | 0.256127i | \(-0.0824464\pi\) |
−0.905127 | + | 0.425142i | \(0.860224\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −87468.3 | − | 15423.0i | −0.466525 | − | 0.0822609i | −0.0645556 | − | 0.997914i | \(-0.520563\pi\) |
−0.401969 | + | 0.915653i | \(0.631674\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 290903. | − | 244097.i | 1.53734 | − | 1.28998i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −49413.9 | − | 89719.7i | −0.258754 | − | 0.469813i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11796.9 | − | 14059.0i | −0.0612124 | − | 0.0729501i | 0.734569 | − | 0.678534i | \(-0.237384\pi\) |
−0.795782 | + | 0.605583i | \(0.792940\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 41694.5 | − | 236461.i | 0.214389 | − | 1.21586i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5871.78 | + | 2137.15i | −0.0299201 | + | 0.0108900i | −0.356937 | − | 0.934129i | \(-0.616179\pi\) |
0.327017 | + | 0.945019i | \(0.393957\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −397338. | + | 229403.i | −2.00650 | + | 1.15846i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −316184. | + | 376813.i | −1.58243 | + | 1.88587i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −86468.3 | − | 49922.5i | −0.428908 | − | 0.247630i | 0.269973 | − | 0.962868i | \(-0.412985\pi\) |
−0.698881 | + | 0.715238i | \(0.746319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 37061.7 | − | 6534.97i | 0.182210 | − | 0.0321285i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 286641. | + | 104329.i | 1.39682 | + | 0.508402i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 24619.4i | − | 0.118920i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 304377. | 1.45740 | 0.728700 | − | 0.684833i | \(-0.240125\pi\) | ||||
0.728700 | + | 0.684833i | \(0.240125\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −49486.0 | + | 135962.i | −0.234886 | + | 0.645344i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8793.03 | + | 49867.7i | 0.0413749 | + | 0.234648i | 0.998482 | − | 0.0550872i | \(-0.0175437\pi\) |
−0.957107 | + | 0.289736i | \(0.906433\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38991.0 | + | 67534.3i | −0.181887 | + | 0.315038i | −0.942523 | − | 0.334141i | \(-0.891554\pi\) |
0.760636 | + | 0.649179i | \(0.224887\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −653827. | − | 548626.i | −3.02383 | − | 2.53729i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −187480. | − | 324725.i | −0.859649 | − | 1.48896i | −0.872264 | − | 0.489035i | \(-0.837349\pi\) |
0.0126152 | − | 0.999920i | \(-0.495984\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21639.2 | + | 59453.1i | 0.0983773 | + | 0.270289i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 644044. | + | 113562.i | 2.90318 | + | 0.511908i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22206.3 | + | 18633.3i | −0.0992554 | + | 0.0832852i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −152340. | + | 251981.i | −0.675191 | + | 1.11681i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −212431. | − | 253166.i | −0.933646 | − | 1.11268i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −45381.3 | + | 257370.i | −0.197791 | + | 1.12173i | 0.710597 | + | 0.703599i | \(0.248425\pi\) |
−0.908388 | + | 0.418128i | \(0.862686\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −89800.7 | + | 32684.8i | −0.388141 | + | 0.141272i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 33472.5 | − | 19325.4i | 0.143481 | − | 0.0828387i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 72412.3 | − | 86297.6i | 0.307843 | − | 0.366873i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −276196. | − | 159462.i | −1.16455 | − | 0.672355i | −0.212162 | − | 0.977235i | \(-0.568050\pi\) |
−0.952391 | + | 0.304880i | \(0.901384\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −156940. | + | 27672.8i | −0.656322 | + | 0.115727i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −370318. | − | 134785.i | −1.53607 | − | 0.559085i | −0.570973 | − | 0.820969i | \(-0.693434\pi\) |
−0.965099 | + | 0.261884i | \(0.915656\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 334395.i | − | 1.37583i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −60496.5 | −0.246899 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −31584.2 | + | 86776.9i | −0.127867 | + | 0.351310i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13867.0 | − | 78643.7i | −0.0556906 | − | 0.315837i | 0.944219 | − | 0.329320i | \(-0.106819\pi\) |
−0.999909 | + | 0.0134826i | \(0.995708\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −81601.7 | + | 141338.i | −0.325105 | + | 0.563098i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 86261.9 | + | 72382.4i | 0.340944 | + | 0.286086i | 0.797142 | − | 0.603793i | \(-0.206344\pi\) |
−0.456197 | + | 0.889879i | \(0.650789\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16768.3 | + | 29043.6i | 0.0657518 | + | 0.113885i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 113424. | + | 311631.i | 0.441255 | + | 1.21234i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 161578. | + | 28490.6i | 0.623658 | + | 0.109968i | 0.476542 | − | 0.879151i | \(-0.341890\pi\) |
0.147116 | + | 0.989119i | \(0.453001\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29665.9 | + | 24892.6i | −0.113610 | + | 0.0953299i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 41427.1 | − | 107050.i | 0.157416 | − | 0.406773i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −38642.8 | − | 46052.7i | −0.145698 | − | 0.173636i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3412.29 | − | 19352.1i | 0.0127663 | − | 0.0724012i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 253351. | − | 92212.3i | 0.940564 | − | 0.342337i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −165547. | + | 95578.7i | −0.609883 | + | 0.352116i | −0.772919 | − | 0.634504i | \(-0.781204\pi\) |
0.163037 | + | 0.986620i | \(0.447871\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 53445.8 | − | 63694.2i | 0.195393 | − | 0.232861i | −0.659448 | − | 0.751750i | \(-0.729210\pi\) |
0.854841 | + | 0.518889i | \(0.173654\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −96224.8 | − | 55555.4i | −0.349115 | − | 0.201562i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −740159. | + | 130510.i | −2.66504 | + | 0.469919i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 187316. | + | 68177.3i | 0.669364 | + | 0.243629i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 152323.i | − | 0.540225i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 159730. | 0.562254 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −154004. | + | 423124.i | −0.538054 | + | 1.47829i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34549.4 | + | 195939.i | 0.119810 | + | 0.679474i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17571.2 | − | 30434.2i | 0.0604817 | − | 0.104757i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −47919.3 | − | 40209.1i | −0.163725 | − | 0.137382i | 0.557244 | − | 0.830349i | \(-0.311859\pi\) |
−0.720969 | + | 0.692967i | \(0.756303\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −204773. | − | 354677.i | −0.694500 | − | 1.20291i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 88964.2 | + | 244427.i | 0.299518 | + | 0.822918i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36797.9 | + | 6488.47i | 0.122984 | + | 0.0216854i | 0.234801 | − | 0.972043i | \(-0.424556\pi\) |
−0.111817 | + | 0.993729i | \(0.535667\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 423664. | − | 355496.i | 1.40565 | − | 1.17948i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5351.39 | + | 265235.i | −0.0176264 | + | 0.873630i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27066.6 | + | 32256.7i | 0.0885081 | + | 0.105480i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −132281. | + | 750202.i | −0.429448 | + | 2.43552i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 449858. | − | 163735.i | 1.44999 | − | 0.527753i | 0.507402 | − | 0.861709i | \(-0.330606\pi\) |
0.942589 | + | 0.333956i | \(0.108384\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −106553. | + | 61518.6i | −0.340991 | + | 0.196871i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −60820.9 | + | 72483.6i | −0.193254 | + | 0.230311i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 158180. | + | 91325.4i | 0.499040 | + | 0.288121i | 0.728317 | − | 0.685240i | \(-0.240303\pi\) |
−0.229277 | + | 0.973361i | \(0.573636\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13212.7 | − | 2329.75i | 0.0413899 | − | 0.00729815i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −38772.9 | − | 14112.2i | −0.120604 | − | 0.0438963i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 307756.i | − | 0.950565i | −0.879833 | − | 0.475283i | \(-0.842346\pi\) | ||
0.879833 | − | 0.475283i | \(-0.157654\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 474577. | 1.45557 | 0.727787 | − | 0.685803i | \(-0.240549\pi\) | ||||
0.727787 | + | 0.685803i | \(0.240549\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 123052. | − | 338083.i | 0.374783 | − | 1.02971i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 40187.1 | + | 227912.i | 0.121549 | + | 0.689338i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15494.2 | + | 26836.7i | −0.0465390 | + | 0.0806078i | −0.888357 | − | 0.459154i | \(-0.848152\pi\) |
0.841818 | + | 0.539762i | \(0.181486\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −335666. | − | 281657.i | −1.00127 | − | 0.840164i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −62234.2 | − | 107793.i | −0.184364 | − | 0.319329i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16543.4 | − | 45452.7i | −0.0486730 | − | 0.133728i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −252869. | − | 44587.6i | −0.738896 | − | 0.130287i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −355861. | + | 298603.i | −1.03277 | + | 0.866598i | −0.991178 | − | 0.132536i | \(-0.957688\pi\) |
−0.0415934 | + | 0.999135i | \(0.513243\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 589168. | − | 91673.0i | 1.69828 | − | 0.264247i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −392870. | − | 468205.i | −1.12480 | − | 1.34048i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −483.474 | + | 2741.92i | −0.00137488 | + | 0.00779731i | −0.985487 | − | 0.169748i | \(-0.945705\pi\) |
0.984113 | + | 0.177545i | \(0.0568157\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −162390. | + | 59105.3i | −0.458697 | + | 0.166952i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 75691.0 | − | 43700.2i | 0.212371 | − | 0.122613i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18966.7 | + | 22603.6i | −0.0528613 | + | 0.0629976i | −0.791827 | − | 0.610745i | \(-0.790870\pi\) |
0.738966 | + | 0.673743i | \(0.235314\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20074.7 | − | 11590.2i | −0.0555777 | − | 0.0320878i | 0.471954 | − | 0.881623i | \(-0.343549\pi\) |
−0.527531 | + | 0.849536i | \(0.676882\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 649841. | − | 114585.i | 1.78720 | − | 0.315131i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 513880. | + | 187037.i | 1.40395 | + | 0.510995i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 199091.i | − | 0.540350i | −0.962811 | − | 0.270175i | \(-0.912918\pi\) | ||
0.962811 | − | 0.270175i | \(-0.0870815\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −100106. | −0.269915 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28526.0 | − | 78374.6i | 0.0764115 | − | 0.209939i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −73960.7 | − | 419452.i | −0.196825 | − | 1.11625i | −0.909796 | − | 0.415056i | \(-0.863762\pi\) |
0.712971 | − | 0.701194i | \(-0.247349\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 636634. | − | 1.10268e6i | 1.68322 | − | 2.91541i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5407.03 | − | 4537.04i | −0.0142033 | − | 0.0119180i | 0.635658 | − | 0.771971i | \(-0.280729\pi\) |
−0.649862 | + | 0.760053i | \(0.725173\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 267202. | + | 462808.i | 0.697362 | + | 1.20787i | 0.969378 | + | 0.245574i | \(0.0789765\pi\) |
−0.272015 | + | 0.962293i | \(0.587690\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −30856.3 | − | 84777.0i | −0.0800130 | − | 0.219834i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 119110. | + | 21002.3i | 0.306882 | + | 0.0541115i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −180108. | + | 151129.i | −0.461077 | + | 0.386889i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 49401.9 | − | 56519.2i | 0.125663 | − | 0.143767i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 431180. | + | 513861.i | 1.08983 | + | 1.29881i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 130960. | − | 742708.i | 0.328911 | − | 1.86535i | −0.151720 | − | 0.988424i | \(-0.548481\pi\) |
0.480631 | − | 0.876923i | \(-0.340408\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −648068. | + | 235878.i | −1.61738 | + | 0.588680i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −73191.2 | + | 42257.0i | −0.181515 | + | 0.104797i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 95876.6 | − | 114261.i | 0.236284 | − | 0.281592i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 834095. | + | 481565.i | 2.04274 | + | 1.17938i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −45355.0 | + | 7997.30i | −0.110385 | + | 0.0194638i | −0.228568 | − | 0.973528i | \(-0.573404\pi\) |
0.118183 | + | 0.992992i | \(0.462293\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −610909. | − | 222353.i | −1.47759 | − | 0.537800i | −0.527442 | − | 0.849591i | \(-0.676849\pi\) |
−0.950151 | + | 0.311791i | \(0.899071\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 980774.i | 2.35749i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −156389. | −0.373592 | −0.186796 | − | 0.982399i | \(-0.559810\pi\) | ||||
−0.186796 | + | 0.982399i | \(0.559810\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7624.97 | − | 20949.4i | 0.0181029 | − | 0.0497374i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 39070.2 | + | 221578.i | 0.0921900 | + | 0.522835i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −161708. | + | 280086.i | −0.379232 | + | 0.656849i | −0.990951 | − | 0.134226i | \(-0.957145\pi\) |
0.611719 | + | 0.791075i | \(0.290478\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 772150. | + | 647911.i | 1.79978 | + | 1.51019i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 201948. | + | 349785.i | 0.467853 | + | 0.810345i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23712.1 | + | 65148.5i | 0.0546009 | + | 0.150015i | 0.963995 | − | 0.265922i | \(-0.0856762\pi\) |
−0.909394 | + | 0.415936i | \(0.863454\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −730123. | − | 128740.i | −1.67106 | − | 0.294653i | −0.743616 | − | 0.668607i | \(-0.766891\pi\) |
−0.927447 | + | 0.373954i | \(0.878002\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −307647. | + | 258147.i | −0.699884 | + | 0.587273i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 129751. | − | 44282.3i | 0.293404 | − | 0.100135i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 134026. | + | 159726.i | 0.301257 | + | 0.359024i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5790.80 | + | 32841.3i | −0.0129386 | + | 0.0733783i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 76063.4 | − | 27684.8i | 0.168939 | − | 0.0614889i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −555858. | + | 320925.i | −1.22725 | + | 0.708554i | −0.966454 | − | 0.256839i | \(-0.917319\pi\) |
−0.260798 | + | 0.965393i | \(0.583986\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −166709. | + | 198676.i | −0.365890 | + | 0.436051i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 276698. | + | 159752.i | 0.603711 | + | 0.348552i | 0.770500 | − | 0.637440i | \(-0.220007\pi\) |
−0.166789 | + | 0.985993i | \(0.553340\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29245.8 | + | 5156.82i | −0.0634342 | + | 0.0111852i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −459523. | − | 167253.i | −0.990862 | − | 0.360644i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 368384.i | − | 0.789694i | −0.918747 | − | 0.394847i | \(-0.870798\pi\) | ||
0.918747 | − | 0.394847i | \(-0.129202\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 133833. | 0.285221 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 153900. | − | 422838.i | 0.326081 | − | 0.895902i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −35649.9 | − | 202180.i | −0.0750964 | − | 0.425893i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 165830. | − | 287226.i | 0.347302 | − | 0.601544i | −0.638467 | − | 0.769649i | \(-0.720431\pi\) |
0.985769 | + | 0.168105i | \(0.0537647\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12216.6 | + | 10250.9i | 0.0254381 | + | 0.0213451i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 267105. | + | 462639.i | 0.552983 | + | 0.957795i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −383474. | − | 1.05359e6i | −0.789352 | − | 2.16873i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 259695. | + | 45791.3i | 0.531508 | + | 0.0937191i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24515.3 | − | 20570.8i | 0.0498885 | − | 0.0418615i | −0.617502 | − | 0.786569i | \(-0.711855\pi\) |
0.667391 | + | 0.744707i | \(0.267411\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −333780. | − | 414484.i | −0.675382 | − | 0.838682i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −427356. | − | 509303.i | −0.859827 | − | 1.02470i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1535.17 | − | 8706.39i | 0.00307127 | − | 0.0174180i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −867795. | + | 315852.i | −1.72633 | + | 0.628334i | −0.998359 | − | 0.0572695i | \(-0.981761\pi\) |
−0.727975 | + | 0.685604i | \(0.759538\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 380332. | − | 219585.i | 0.752357 | − | 0.434373i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 301233. | − | 358996.i | 0.592548 | − | 0.706171i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −32545.9 | − | 18790.4i | −0.0636626 | − | 0.0367556i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −770372. | + | 135837.i | −1.49852 | + | 0.264229i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −656850. | − | 239074.i | −1.27060 | − | 0.462460i | −0.383287 | − | 0.923629i | \(-0.625208\pi\) |
−0.887312 | + | 0.461169i | \(0.847430\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15847.8i | 0.0304858i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −758090. | −1.45025 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 205008. | − | 563255.i | 0.390027 | − | 1.07159i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −97044.7 | − | 550368.i | −0.183613 | − | 1.04132i | −0.927725 | − | 0.373265i | \(-0.878238\pi\) |
0.744112 | − | 0.668055i | \(-0.232873\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −390492. | + | 676353.i | −0.734780 | + | 1.27268i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 661588. | + | 555138.i | 1.23809 | + | 1.03888i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 93102.8 | + | 161259.i | 0.173283 | + | 0.300134i | 0.939566 | − | 0.342369i | \(-0.111229\pi\) |
−0.766283 | + | 0.642503i | \(0.777896\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −406658. | − | 1.11728e6i | −0.752757 | − | 2.06818i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 95110.8 | + | 16770.6i | 0.175103 | + | 0.0308755i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 620269. | − | 520467.i | 1.13577 | − | 0.953025i | 0.136479 | − | 0.990643i | \(-0.456421\pi\) |
0.999292 | + | 0.0376175i | \(0.0119769\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 248151. | − | 199833.i | 0.451938 | − | 0.363942i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −315238. | − | 375686.i | −0.571032 | − | 0.680530i | 0.400810 | − | 0.916161i | \(-0.368729\pi\) |
−0.971842 | + | 0.235631i | \(0.924284\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −238133. | + | 1.35052e6i | −0.429050 | + | 2.43326i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.21987e6 | + | 443995.i | −2.18610 | + | 0.795677i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 102797. | − | 59349.6i | 0.183238 | − | 0.105792i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −374067. | + | 445796.i | −0.663239 | + | 0.790418i | −0.987847 | − | 0.155431i | \(-0.950323\pi\) |
0.324608 | + | 0.945849i | \(0.394768\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −179867. | − | 103846.i | −0.317220 | − | 0.183147i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 837494. | − | 147673.i | 1.46922 | − | 0.259064i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 186518. | + | 67886.8i | 0.325483 | + | 0.118466i | 0.499593 | − | 0.866260i | \(-0.333483\pi\) |
−0.174111 | + | 0.984726i | \(0.555705\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 58999.3i | − | 0.102415i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −325873. | −0.562703 | −0.281352 | − | 0.959605i | \(-0.590783\pi\) | ||||
−0.281352 | + | 0.959605i | \(0.590783\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23452.1 | − | 64434.1i | 0.0402840 | − | 0.110679i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 312976. | + | 1.77498e6i | 0.534797 | + | 3.03298i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 47311.9 | − | 81946.6i | 0.0804229 | − | 0.139296i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 512619. | + | 430138.i | 0.866845 | + | 0.727370i | 0.963431 | − | 0.267955i | \(-0.0863478\pi\) |
−0.0965860 | + | 0.995325i | \(0.530792\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −68004.9 | − | 117788.i | −0.114401 | − | 0.198149i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 156644. | + | 430375.i | 0.262152 | + | 0.720257i | 0.999022 | + | 0.0442223i | \(0.0140810\pi\) |
−0.736870 | + | 0.676035i | \(0.763697\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.32674e6 | − | 233940.i | −2.20893 | − | 0.389494i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 153832. | − | 129080.i | 0.254803 | − | 0.213805i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 287303. | + | 841821.i | 0.473441 | + | 1.38722i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 90609.7 | + | 107984.i | 0.148550 | + | 0.177035i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −40575.7 | + | 230116.i | −0.0661824 | + | 0.375339i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.71328e6 | − | 623582.i | 2.78028 | − | 1.01194i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 405172. | − | 233926.i | 0.654169 | − | 0.377685i | −0.135883 | − | 0.990725i | \(-0.543387\pi\) |
0.790052 | + | 0.613040i | \(0.210054\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 314955. | − | 375349.i | 0.505936 | − | 0.602950i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3062.93 | − | 1768.38i | −0.00489535 | − | 0.00282633i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 338341. | − | 59658.7i | 0.538033 | − | 0.0948697i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.53782e6 | − | 559721.i | −2.43317 | − | 0.885600i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 649953.i | 1.02321i | 0.859221 | + | 0.511605i | \(0.170949\pi\) | ||||
−0.859221 | + | 0.511605i | \(0.829051\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −585446. | −0.917051 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 431434. | − | 1.18536e6i | 0.672433 | − | 1.84750i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10265.1 | + | 58216.2i | 0.0159196 | + | 0.0902845i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 53877.3 | − | 93318.2i | 0.0831408 | − | 0.144004i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.31335e6 | + | 1.10203e6i | 2.01666 | + | 1.69218i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 263790. | + | 456898.i | 0.403052 | + | 0.698107i | 0.994093 | − | 0.108535i | \(-0.0346160\pi\) |
−0.591041 | + | 0.806642i | \(0.701283\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25742.5 | + | 70727.0i | 0.0391390 | + | 0.107533i | 0.957723 | − | 0.287693i | \(-0.0928883\pi\) |
−0.918584 | + | 0.395227i | \(0.870666\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 985255. | + | 173727.i | 1.49062 | + | 0.262837i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −340342. | + | 285581.i | −0.512389 | + | 0.429945i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −515874. | − | 450912.i | −0.772858 | − | 0.675535i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 43508.8 | + | 51851.8i | 0.0648649 | + | 0.0773030i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14296.0 | + | 81076.9i | −0.0212094 | + | 0.120285i | −0.993574 | − | 0.113182i | \(-0.963896\pi\) |
0.972365 | + | 0.233466i | \(0.0750069\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 928191. | − | 337834.i | 1.37037 | − | 0.498774i | 0.451125 | − | 0.892461i | \(-0.351023\pi\) |
0.919244 | + | 0.393687i | \(0.128801\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −146885. | + | 84803.9i | −0.215808 | + | 0.124597i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 526428. | − | 627373.i | 0.769712 | − | 0.917306i | −0.228709 | − | 0.973495i | \(-0.573450\pi\) |
0.998420 | + | 0.0561884i | \(0.0178948\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −584819. | − | 337646.i | −0.850967 | − | 0.491306i | 0.0100101 | − | 0.999950i | \(-0.496814\pi\) |
−0.860977 | + | 0.508644i | \(0.830147\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 87644.3 | − | 15454.1i | 0.126918 | − | 0.0223790i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −983849. | − | 358092.i | −1.41788 | − | 0.516065i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 454996.i | 0.652581i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 525182. | 0.749651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 290197. | − | 797310.i | 0.412258 | − | 1.13267i | −0.543729 | − | 0.839261i | \(-0.682988\pi\) |
0.955987 | − | 0.293409i | \(-0.0947897\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29041.5 | + | 164703.i | 0.0410608 | + | 0.232867i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −165092. | + | 285948.i | −0.232312 | + | 0.402375i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 708249. | + | 594292.i | 0.991911 | + | 0.832312i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −72079.6 | − | 124845.i | −0.100472 | − | 0.174023i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 307377. | + | 844510.i | 0.426437 | + | 1.17163i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −411912. | − | 72631.2i | −0.568781 | − | 0.100291i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 674237. | − | 565752.i | 0.926647 | − | 0.777549i | −0.0485653 | − | 0.998820i | \(-0.515465\pi\) |
0.975212 | + | 0.221271i | \(0.0710205\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −219841. | − | 1.41288e6i | −0.300730 | − | 1.93274i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −839806. | − | 1.00084e6i | −1.14345 | − | 1.36271i | −0.921838 | − | 0.387577i | \(-0.873312\pi\) |
−0.221613 | − | 0.975135i | \(-0.571132\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 207717. | − | 1.17802e6i | 0.281505 | − | 1.59649i | −0.436006 | − | 0.899944i | \(-0.643607\pi\) |
0.717510 | − | 0.696548i | \(-0.245282\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −315408. | + | 114799.i | −0.425467 | + | 0.154857i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −140092. | + | 80882.2i | −0.188101 | + | 0.108600i | −0.591093 | − | 0.806603i | \(-0.701304\pi\) |
0.402992 | + | 0.915203i | \(0.367970\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 483151. | − | 575797.i | 0.645729 | − | 0.769550i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.45658e6 | + | 840957.i | 1.93774 | + | 1.11876i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 63300.4 | − | 11161.6i | 0.0838237 | − | 0.0147804i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 385192. | + | 140199.i | 0.507740 | + | 0.184802i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 309726.i | 0.406396i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −72406.8 | −0.0945721 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 195670. | − | 537599.i | 0.254405 | − | 0.698972i | −0.745083 | − | 0.666972i | \(-0.767590\pi\) |
0.999488 | − | 0.0320000i | \(-0.0101876\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 257696. | + | 1.46147e6i | 0.333527 | + | 1.89152i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −339561. | + | 588138.i | −0.437488 | + | 0.757752i | −0.997495 | − | 0.0707360i | \(-0.977465\pi\) |
0.560007 | + | 0.828488i | \(0.310799\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −267811. | − | 224720.i | −0.343484 | − | 0.288217i | 0.454683 | − | 0.890653i | \(-0.349752\pi\) |
−0.798167 | + | 0.602436i | \(0.794197\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −377140. | − | 653226.i | −0.481522 | − | 0.834021i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 404343. | + | 1.11092e6i | 0.513929 | + | 1.41201i | 0.877110 | + | 0.480289i | \(0.159468\pi\) |
−0.363182 | + | 0.931718i | \(0.618310\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21940.5 | + | 3868.70i | 0.0277615 | + | 0.00489510i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −48248.7 | + | 40485.4i | −0.0607757 | + | 0.0509969i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 464364. | + | 9369.02i | 0.582312 | + | 0.0117487i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 356546. | + | 424915.i | 0.445112 | + | 0.530464i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 43484.1 | − | 246611.i | 0.0540438 | − | 0.306498i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.14058e6 | + | 415136.i | −1.41125 | + | 0.513654i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.24800e6 | + | 720535.i | −1.53733 | + | 0.887576i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 166189. | − | 198057.i | 0.203811 | − | 0.242892i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −988805. | − | 570887.i | −1.20730 | − | 0.697032i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −671641. | + | 118428.i | −0.816436 | + | 0.143960i | −0.566245 | − | 0.824237i | \(-0.691605\pi\) |
−0.250191 | + | 0.968196i | \(0.580493\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −86644.2 | − | 31535.9i | −0.104860 | − | 0.0381661i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.56668e6i | 1.88774i | 0.330312 | + | 0.943872i | \(0.392846\pi\) | ||||
−0.330312 | + | 0.943872i | \(0.607154\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −189998. | −0.227933 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 936673. | − | 2.57349e6i | 1.11878 | − | 3.07383i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −46140.7 | − | 261677.i | −0.0548714 | − | 0.311191i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 174963. | − | 303045.i | 0.207165 | − | 0.358820i | −0.743656 | − | 0.668563i | \(-0.766910\pi\) |
0.950820 | + | 0.309743i | \(0.100243\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.01738e6 | − | 853683.i | −1.19940 | − | 1.00642i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 299151. | + | 518145.i | 0.351146 | + | 0.608203i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 411247. | + | 1.12989e6i | 0.480640 | + | 1.32055i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 162774. | + | 28701.5i | 0.189420 | + | 0.0333999i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 227850. | − | 191189.i | 0.264009 | − | 0.221530i | −0.501168 | − | 0.865350i | \(-0.667096\pi\) |
0.765177 | + | 0.643820i | \(0.222652\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 774638. | + | 299776.i | 0.893716 | + | 0.345857i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −499316. | − | 595062.i | −0.573604 | − | 0.683595i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −45807.2 | + | 259786.i | −0.0523975 | + | 0.297161i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.20985e6 | − | 440350.i | 1.37801 | − | 0.501556i | 0.456438 | − | 0.889755i | \(-0.349125\pi\) |
0.921575 | + | 0.388200i | \(0.126903\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.94118e6 | + | 1.12074e6i | −2.20158 | + | 1.27108i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 869893. | − | 1.03670e6i | 0.982396 | − | 1.17077i | −0.00291337 | − | 0.999996i | \(-0.500927\pi\) |
0.985309 | − | 0.170778i | \(-0.0546282\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 605448. | + | 349555.i | 0.680853 | + | 0.393091i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 118922. | − | 20969.1i | 0.133168 | − | 0.0234810i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.43236e6 | + | 521336.i | 1.59717 | + | 0.581323i | 0.978846 | − | 0.204598i | \(-0.0655888\pi\) |
0.618326 | + | 0.785921i | \(0.287811\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 250903.i | 0.278595i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 62967.8 | 0.0696238 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −526703. | + | 1.44710e6i | −0.579936 | + | 1.59336i | 0.208352 | + | 0.978054i | \(0.433190\pi\) |
−0.788288 | + | 0.615307i | \(0.789032\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −174175. | − | 987794.i | −0.190976 | − | 1.08308i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −76404.7 | + | 132337.i | −0.0834250 | + | 0.144496i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27026.1 | − | 22677.6i | −0.0293864 | − | 0.0246581i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 902266. | + | 1.56277e6i | 0.976985 | + | 1.69219i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −423415. | − | 1.16332e6i | −0.456577 | − | 1.25444i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.20305e6 | − | 212130.i | −1.29190 | − | 0.227797i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −871233. | + | 731051.i | −0.931711 | + | 0.781798i | −0.976124 | − | 0.217215i | \(-0.930303\pi\) |
0.0444127 | + | 0.999013i | \(0.485858\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.91386e6 | − | 1.15706e6i | −2.03828 | − | 1.23228i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 75845.2 | + | 90388.8i | 0.0804433 | + | 0.0958686i | 0.804765 | − | 0.593594i | \(-0.202291\pi\) |
−0.724322 | + | 0.689462i | \(0.757847\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24453.9 | − | 138685.i | 0.0258299 | − | 0.146489i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −676465. | + | 246213.i | −0.711600 | + | 0.259001i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −402008. | + | 232099.i | −0.421158 | + | 0.243156i | −0.695573 | − | 0.718456i | \(-0.744849\pi\) |
0.274414 | + | 0.961612i | \(0.411516\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 118673. | − | 141429.i | 0.123819 | − | 0.147562i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −619338. | − | 357575.i | −0.643561 | − | 0.371560i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −905562. | + | 159675.i | −0.937154 | + | 0.165246i | −0.621310 | − | 0.783565i | \(-0.713399\pi\) |
−0.315845 | + | 0.948811i | \(0.602288\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.60120e6 | − | 582789.i | −1.65034 | − | 0.600674i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 175262.i | 0.179910i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −538512. | −0.550557 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −301131. | + | 827349.i | −0.306625 | + | 0.842445i | 0.686684 | + | 0.726956i | \(0.259066\pi\) |
−0.993309 | + | 0.115489i | \(0.963157\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 419745. | + | 2.38049e6i | 0.425683 | + | 2.41417i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 121832. | − | 211019.i | 0.123060 | − | 0.213145i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.09217e6 | + | 916438.i | 1.09875 | + | 0.921961i | 0.997340 | − | 0.0728834i | \(-0.0232201\pi\) |
0.101410 | + | 0.994845i | \(0.467665\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −234368. | − | 405937.i | −0.234837 | − | 0.406750i |
(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.13.1 | ✓ | 42 | |
19.3 | odd | 18 | inner | 76.5.j.a.41.1 | yes | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.j.a.13.1 | ✓ | 42 | 1.1 | even | 1 | trivial | |
76.5.j.a.41.1 | yes | 42 | 19.3 | odd | 18 | inner |