Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(41,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.41");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.x (of order \(6\), degree \(2\), 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: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 209.19 | ||
Character | \(\chi\) | \(=\) | 252.209 |
Dual form | 252.4.x.a.41.19 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.09692 | + | 3.19613i | 0.788453 | + | 0.615096i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.53447 | − | 6.12188i | −0.316132 | − | 0.547557i | 0.663545 | − | 0.748136i | \(-0.269051\pi\) |
−0.979678 | + | 0.200579i | \(0.935718\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.59538 | − | 16.8911i | 0.410112 | − | 0.912035i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.56950 | + | 26.1886i | 0.243315 | + | 0.969947i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.40072 | + | 4.27281i | 0.202855 | + | 0.117118i | 0.597986 | − | 0.801506i | \(-0.295968\pi\) |
−0.395132 | + | 0.918625i | \(0.629301\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 45.3367 | − | 26.1752i | 0.967241 | − | 0.558437i | 0.0688473 | − | 0.997627i | \(-0.478068\pi\) |
0.898394 | + | 0.439190i | \(0.144735\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.08588 | − | 36.3774i | 0.0875447 | − | 0.626174i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −38.9547 | −0.555759 | −0.277879 | − | 0.960616i | \(-0.589632\pi\) | ||||
−0.277879 | + | 0.960616i | \(0.589632\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 66.4008i | − | 0.801757i | −0.916131 | − | 0.400879i | \(-0.868705\pi\) | ||
0.916131 | − | 0.400879i | \(-0.131295\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 85.1039 | − | 44.9258i | 0.884343 | − | 0.466839i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 173.899 | − | 100.401i | 1.57654 | − | 0.910217i | 0.581204 | − | 0.813758i | \(-0.302582\pi\) |
0.995337 | − | 0.0964590i | \(-0.0307517\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 37.5151 | − | 64.9781i | 0.300121 | − | 0.519824i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −56.7874 | + | 128.289i | −0.404768 | + | 0.914419i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 52.9622 | + | 30.5777i | 0.339132 | + | 0.195798i | 0.659888 | − | 0.751364i | \(-0.270604\pi\) |
−0.320756 | + | 0.947162i | \(0.603937\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −116.401 | + | 67.2041i | −0.674395 | + | 0.389362i | −0.797740 | − | 0.603002i | \(-0.793971\pi\) |
0.123345 | + | 0.992364i | \(0.460638\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16.6637 | + | 41.1590i | 0.0879024 | + | 0.217117i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −130.251 | + | 13.2032i | −0.629041 | + | 0.0637641i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 298.967 | 1.32838 | 0.664188 | − | 0.747565i | \(-0.268777\pi\) | ||||
0.664188 | + | 0.747565i | \(0.268777\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 269.400 | + | 37.6645i | 1.10612 | + | 0.154645i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 221.278 | + | 383.265i | 0.842874 | + | 1.45990i | 0.887455 | + | 0.460895i | \(0.152472\pi\) |
−0.0445802 | + | 0.999006i | \(0.514195\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 26.1371 | − | 45.2708i | 0.0926947 | − | 0.160552i | −0.815949 | − | 0.578123i | \(-0.803785\pi\) |
0.908644 | + | 0.417571i | \(0.137119\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 137.104 | − | 132.780i | 0.454182 | − | 0.439861i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −137.682 | + | 238.472i | −0.427298 | + | 0.740101i | −0.996632 | − | 0.0820049i | \(-0.973868\pi\) |
0.569334 | + | 0.822106i | \(0.307201\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −227.620 | − | 256.589i | −0.663617 | − | 0.748073i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −159.594 | − | 124.504i | −0.438189 | − | 0.341845i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 136.637i | − | 0.354123i | −0.984200 | − | 0.177061i | \(-0.943341\pi\) | ||
0.984200 | − | 0.177061i | \(-0.0566591\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 60.4084i | − | 0.148099i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 212.226 | − | 272.039i | 0.493157 | − | 0.632147i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −191.268 | − | 331.286i | −0.422051 | − | 0.731014i | 0.574089 | − | 0.818793i | \(-0.305356\pi\) |
−0.996140 | + | 0.0877790i | \(0.972023\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −261.714 | − | 151.100i | −0.549328 | − | 0.317155i | 0.199523 | − | 0.979893i | \(-0.436061\pi\) |
−0.748851 | + | 0.662739i | \(0.769394\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 492.253 | + | 87.9458i | 0.984412 | + | 0.175875i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −320.482 | − | 185.030i | −0.611552 | − | 0.353080i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 318.940 | + | 552.420i | 0.581563 | + | 1.00730i | 0.995294 | + | 0.0968972i | \(0.0308918\pi\) |
−0.413732 | + | 0.910399i | \(0.635775\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1033.34 | + | 144.470i | 1.80290 | + | 0.252061i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 228.249i | 0.381524i | 0.981636 | + | 0.190762i | \(0.0610959\pi\) | ||||
−0.981636 | + | 0.190762i | \(0.938904\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1241.68i | − | 1.99079i | −0.0958607 | − | 0.995395i | \(-0.530560\pi\) | ||
0.0958607 | − | 0.995395i | \(-0.469440\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 361.375 | − | 146.307i | 0.556373 | − | 0.225254i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 128.384 | − | 92.5530i | 0.190009 | − | 0.136979i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −100.694 | + | 174.407i | −0.143404 | + | 0.248383i | −0.928776 | − | 0.370641i | \(-0.879138\pi\) |
0.785372 | + | 0.619024i | \(0.212472\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −642.683 | + | 344.092i | −0.881596 | + | 0.472005i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −323.452 | + | 560.235i | −0.427752 | + | 0.740889i | −0.996673 | − | 0.0815036i | \(-0.974028\pi\) |
0.568921 | + | 0.822392i | \(0.307361\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 137.684 | + | 238.476i | 0.175693 | + | 0.304310i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 119.251 | + | 294.549i | 0.146955 | + | 0.362976i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −826.042 | −0.983824 | −0.491912 | − | 0.870645i | \(-0.663702\pi\) | ||||
−0.491912 | + | 0.870645i | \(0.663702\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −97.7786 | − | 964.598i | −0.112637 | − | 1.11118i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −691.679 | − | 96.7027i | −0.771223 | − | 0.107824i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −406.497 | + | 234.691i | −0.439008 | + | 0.253461i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.0700 | + | 9.85534i | 0.0178679 | + | 0.0103161i | 0.508907 | − | 0.860821i | \(-0.330050\pi\) |
−0.491039 | + | 0.871137i | \(0.663383\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −63.2797 | + | 221.885i | −0.0642409 | + | 0.225255i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −814.290 | + | 1410.39i | −0.802226 | + | 1.38950i | 0.115921 | + | 0.993258i | \(0.463018\pi\) |
−0.918148 | + | 0.396239i | \(0.870315\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 644.110 | − | 371.877i | 0.616175 | − | 0.355749i | −0.159203 | − | 0.987246i | \(-0.550893\pi\) |
0.775378 | + | 0.631497i | \(0.217559\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −575.827 | − | 362.207i | −0.535190 | − | 0.336645i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 836.505i | − | 0.755775i | −0.925851 | − | 0.377888i | \(-0.876651\pi\) | ||
0.925851 | − | 0.377888i | \(-0.123349\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1564.06 | −1.37440 | −0.687202 | − | 0.726467i | \(-0.741161\pi\) | ||||
−0.687202 | + | 0.726467i | \(0.741161\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1224.85 | + | 955.539i | 1.04736 | + | 0.817079i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1801.80 | + | 1040.27i | −1.49999 | + | 0.866021i | −1.00000 | 7.94493e-6i | \(-0.999997\pi\) | |
−0.499993 | + | 0.866029i | \(0.666664\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1229.28 | − | 709.725i | −0.996791 | − | 0.575498i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 983.330 | + | 1015.35i | 0.776999 | + | 0.802297i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −295.875 | + | 657.988i | −0.227923 | + | 0.506871i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −628.986 | − | 1089.44i | −0.472567 | − | 0.818509i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −318.406 | + | 2277.44i | −0.233412 | + | 1.66951i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1414.00 | −1.01178 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 774.362 | 0.541051 | 0.270526 | − | 0.962713i | \(-0.412803\pi\) | ||||
0.270526 | + | 0.962713i | \(0.412803\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 251.773 | − | 101.933i | 0.171840 | − | 0.0695715i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 402.834 | + | 697.729i | 0.268670 | + | 0.465350i | 0.968519 | − | 0.248941i | \(-0.0800826\pi\) |
−0.699849 | + | 0.714291i | \(0.746749\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1121.58 | − | 504.339i | −0.731231 | − | 0.328810i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 986.085 | − | 105.790i | 0.628657 | − | 0.0674439i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1587.40 | + | 916.484i | 0.989930 | + | 0.571537i | 0.905254 | − | 0.424872i | \(-0.139681\pi\) |
0.0846770 | + | 0.996408i | \(0.473014\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −765.487 | + | 441.954i | −0.467106 | + | 0.269684i | −0.715028 | − | 0.699096i | \(-0.753586\pi\) |
0.247921 | + | 0.968780i | \(0.420253\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1326.26 | + | 536.952i | −0.792137 | + | 0.320706i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 447.366 | 0.261613 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 432.304i | − | 0.247592i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −112.451 | − | 1778.73i | −0.0630938 | − | 0.998008i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1396.08 | + | 806.025i | −0.767590 | + | 0.443169i | −0.832014 | − | 0.554754i | \(-0.812812\pi\) |
0.0644239 | + | 0.997923i | \(0.479479\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −575.071 | + | 996.052i | −0.309925 | + | 0.536805i | −0.978346 | − | 0.206978i | \(-0.933637\pi\) |
0.668421 | + | 0.743783i | \(0.266970\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −255.913 | − | 1020.17i | −0.135224 | − | 0.539057i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 822.831 | + | 475.061i | 0.426396 | + | 0.246180i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1086.53 | − | 627.309i | 0.552322 | − | 0.318883i | −0.197736 | − | 0.980255i | \(-0.563359\pi\) |
0.750058 | + | 0.661372i | \(0.230025\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 436.709 | − | 559.790i | 0.217819 | − | 0.279209i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −375.051 | − | 3699.93i | −0.183591 | − | 1.81115i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1005.42 | 0.483131 | 0.241565 | − | 0.970385i | \(-0.422339\pi\) | ||||
0.241565 | + | 0.970385i | \(0.422339\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 193.073 | − | 247.488i | 0.0910953 | − | 0.116769i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1198.49 | + | 2075.84i | 0.555340 | + | 0.961878i | 0.997877 | + | 0.0651274i | \(0.0207454\pi\) |
−0.442536 | + | 0.896750i | \(0.645921\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 271.778 | − | 470.733i | 0.123704 | − | 0.214262i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1738.94 | − | 436.220i | 0.777662 | − | 0.195080i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.8922 | − | 27.5262i | 0.00698419 | − | 0.0120970i | −0.862512 | − | 0.506036i | \(-0.831110\pi\) |
0.869496 | + | 0.493939i | \(0.164444\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −812.611 | − | 1127.21i | −0.351015 | − | 0.486907i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 275.224 | − | 1968.57i | 0.116876 | − | 0.835972i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1553.05i | 0.648494i | 0.945972 | + | 0.324247i | \(0.105111\pi\) | ||||
−0.945972 | + | 0.324247i | \(0.894889\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3516.58i | − | 1.44412i | −0.691831 | − | 0.722059i | \(-0.743196\pi\) | ||
0.691831 | − | 0.722059i | \(-0.256804\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −589.283 | − | 1455.52i | −0.238039 | − | 0.587950i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1056.69 | − | 1830.24i | −0.419943 | − | 0.727362i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −288.293 | − | 166.446i | −0.112738 | − | 0.0650895i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1735.63 | + | 1933.61i | 0.667983 | + | 0.744177i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1971.02 | + | 1137.97i | 0.746692 | + | 0.431103i | 0.824497 | − | 0.565866i | \(-0.191458\pi\) |
−0.0778056 | + | 0.996969i | \(0.524791\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 795.313 | + | 1377.52i | 0.296621 | + | 0.513763i | 0.975361 | − | 0.220616i | \(-0.0708068\pi\) |
−0.678740 | + | 0.734379i | \(0.737473\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −721.608 | − | 1782.36i | −0.265002 | − | 0.654550i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1715.67i | − | 0.620490i | −0.950657 | − | 0.310245i | \(-0.899589\pi\) | ||
0.950657 | − | 0.310245i | \(-0.100411\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2534.03i | 0.902676i | 0.892353 | + | 0.451338i | \(0.149053\pi\) | ||||
−0.892353 | + | 0.451338i | \(0.850947\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −458.935 | + | 3282.59i | −0.161049 | + | 1.15192i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 918.760 | − | 662.342i | 0.317657 | − | 0.229001i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1564.20 | − | 2709.27i | 0.532920 | − | 0.923044i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3771.78 | + | 3894.59i | 1.26646 | + | 1.30769i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 283.718 | − | 491.414i | 0.0939004 | − | 0.162640i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2149.79 | + | 3723.55i | 0.701411 | + | 1.21488i | 0.967971 | + | 0.251061i | \(0.0807795\pi\) |
−0.266560 | + | 0.963818i | \(0.585887\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −729.515 | + | 935.120i | −0.234674 | + | 0.300814i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −369.523 | −0.117215 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 251.044 | + | 2476.58i | 0.0785345 | + | 0.774753i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3968.57 | − | 5087.06i | 1.22453 | − | 1.56964i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1766.08 | + | 1019.64i | −0.537553 | + | 0.310356i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2529.08 | − | 1460.16i | −0.759460 | − | 0.438474i | 0.0696418 | − | 0.997572i | \(-0.477814\pi\) |
−0.829102 | + | 0.559098i | \(0.811148\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1948.14 | + | 555.593i | 0.577226 | + | 0.164620i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −390.119 | + | 675.705i | −0.114066 | + | 0.197569i | −0.917406 | − | 0.397952i | \(-0.869721\pi\) |
0.803340 | + | 0.595521i | \(0.203054\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2843.34 | − | 1641.61i | 0.820495 | − | 0.473713i | −0.0300919 | − | 0.999547i | \(-0.509580\pi\) |
0.850587 | + | 0.525834i | \(0.176247\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 821.790 | + | 31.1495i | 0.234068 | + | 0.00887223i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 5223.64i | − | 1.46872i | −0.678759 | − | 0.734361i | \(-0.737482\pi\) | ||
0.678759 | − | 0.734361i | \(-0.262518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1946.53 | 0.540330 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −969.960 | + | 392.699i | −0.265847 | + | 0.107631i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −896.500 | + | 517.595i | −0.242635 | + | 0.140085i | −0.616387 | − | 0.787443i | \(-0.711404\pi\) |
0.373752 | + | 0.927529i | \(0.378071\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4811.53 | + | 2777.94i | 1.28605 | + | 0.742501i | 0.977947 | − | 0.208852i | \(-0.0669726\pi\) |
0.308103 | + | 0.951353i | \(0.400306\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3732.78 | − | 644.382i | −0.985425 | − | 0.170112i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −766.289 | + | 2300.37i | −0.199822 | + | 0.599858i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1738.05 | − | 3010.39i | −0.447731 | − | 0.775493i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3115.74 | + | 1261.44i | −0.792980 | + | 0.321047i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 974.838 | 0.245144 | 0.122572 | − | 0.992460i | \(-0.460886\pi\) | ||||
0.122572 | + | 0.992460i | \(0.460886\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1715.97 | 0.426412 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −198.119 | + | 1417.07i | −0.0486537 | + | 0.348002i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2406.33 | − | 4167.88i | −0.584057 | − | 1.01162i | −0.994992 | − | 0.0999520i | \(-0.968131\pi\) |
0.410935 | − | 0.911665i | \(-0.365202\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2270.77 | − | 5049.90i | 0.544783 | − | 1.21153i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −452.852 | + | 1587.89i | −0.107398 | + | 0.376581i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2132.47 | + | 1231.18i | 0.499976 | + | 0.288661i | 0.728704 | − | 0.684829i | \(-0.240123\pi\) |
−0.228728 | + | 0.973490i | \(0.573457\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −836.473 | + | 482.938i | −0.193902 | + | 0.111950i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3384.23 | − | 2640.14i | −0.775698 | − | 0.605146i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2092.97 | 0.474389 | 0.237194 | − | 0.971462i | \(-0.423772\pi\) | ||||
0.237194 | + | 0.971462i | \(0.423772\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5006.83i | 1.12230i | 0.827714 | + | 0.561150i | \(0.189641\pi\) | ||||
−0.827714 | + | 0.561150i | \(0.810359\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2682.39 | − | 4264.39i | 0.594673 | − | 0.945395i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 555.278 | − | 320.590i | 0.121762 | − | 0.0702992i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4158.94 | + | 7203.49i | −0.902117 | + | 1.56251i | −0.0773748 | + | 0.997002i | \(0.524654\pi\) |
−0.824742 | + | 0.565510i | \(0.808680\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2524.68 | − | 2606.88i | −0.541751 | − | 0.559390i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4024.77 | + | 2323.70i | 0.854440 | + | 0.493311i | 0.862146 | − | 0.506659i | \(-0.169120\pi\) |
−0.00770671 | + | 0.999970i | \(0.502453\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3970.15 | + | 2292.17i | −0.833925 | + | 0.481467i | −0.855195 | − | 0.518307i | \(-0.826563\pi\) |
0.0212695 | + | 0.999774i | \(0.493229\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2415.49 | − | 337.707i | −0.502040 | − | 0.0701895i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8154.47 | − | 826.595i | 1.67715 | − | 0.170008i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3395.53 | −0.691132 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 38.4353 | + | 94.9343i | 0.00774266 | + | 0.0191242i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1961.13 | − | 3396.77i | −0.391025 | − | 0.677275i | 0.601560 | − | 0.798828i | \(-0.294546\pi\) |
−0.992585 | + | 0.121552i | \(0.961213\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1352.06 | + | 2341.84i | −0.266848 | + | 0.462194i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −968.424 | + | 706.793i | −0.189204 | + | 0.138089i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5256.01 | − | 9103.67i | 1.01660 | − | 1.76080i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −566.154 | − | 785.334i | −0.108414 | − | 0.150385i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7843.88 | + | 3175.68i | −1.48719 | + | 0.602107i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2136.24i | 0.401051i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8034.65i | 1.49369i | 0.665000 | + | 0.746843i | \(0.268431\pi\) | ||||
−0.665000 | + | 0.746843i | \(0.731569\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3827.43 | + | 535.109i | 0.704644 | + | 0.0985154i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2215.47 | + | 3837.30i | 0.403947 | + | 0.699657i | 0.994198 | − | 0.107563i | \(-0.0343047\pi\) |
−0.590251 | + | 0.807220i | \(0.700971\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5126.22 | + | 2959.63i | 0.925723 | + | 0.534467i | 0.885456 | − | 0.464722i | \(-0.153846\pi\) |
0.0402668 | + | 0.999189i | \(0.487179\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1201.46 | − | 3324.35i | −0.214903 | − | 0.594622i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 458.040 | + | 264.450i | 0.0811549 | + | 0.0468548i | 0.540028 | − | 0.841647i | \(-0.318414\pi\) |
−0.458873 | + | 0.888502i | \(0.651747\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 261.306 | + | 452.595i | 0.0458630 | + | 0.0794371i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2673.58 | − | 3427.09i | 0.464874 | − | 0.595893i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2586.62i | 0.445583i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 3927.85i | − | 0.670394i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6407.84 | − | 4998.95i | −1.08365 | − | 0.845390i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2982.32 | + | 4136.89i | 0.499759 | + | 0.693235i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1824.88 | − | 3160.78i | 0.303035 | − | 0.524871i | −0.673787 | − | 0.738925i | \(-0.735334\pi\) |
0.976822 | + | 0.214054i | \(0.0686669\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1964.07 | + | 7829.53i | 0.323214 | + | 1.28846i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2254.56 | − | 3905.02i | 0.367701 | − | 0.636878i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3284.70 | − | 5689.26i | −0.530946 | − | 0.919625i | −0.999348 | − | 0.0361099i | \(-0.988503\pi\) |
0.468402 | − | 0.883516i | \(-0.344830\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10706.7 | − | 1496.89i | −1.71536 | − | 0.239822i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1148.60 | −0.182405 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6062.94 | + | 1895.88i | −0.954426 | + | 0.298448i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2767.89 | − | 6836.63i | −0.431937 | − | 1.06687i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10270.0 | + | 5929.38i | −1.58882 | + | 0.917307i | −0.595321 | + | 0.803488i | \(0.702975\pi\) |
−0.993501 | + | 0.113820i | \(0.963691\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.7558 | + | 17.7568i | 0.00471724 | + | 0.00272350i | 0.502357 | − | 0.864660i | \(-0.332466\pi\) |
−0.497640 | + | 0.867384i | \(0.665800\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 783.446 | + | 7302.64i | 0.119137 | + | 1.11050i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4968.07 | − | 8604.94i | 0.749075 | − | 1.29744i | −0.199191 | − | 0.979961i | \(-0.563832\pi\) |
0.948266 | − | 0.317475i | \(-0.102835\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1397.31 | − | 806.740i | 0.208906 | − | 0.120612i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3315.19 | + | 1750.07i | −0.491481 | + | 0.259450i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 10087.1i | − | 1.48295i | −0.670983 | − | 0.741473i | \(-0.734128\pi\) | ||
0.670983 | − | 0.741473i | \(-0.265872\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2449.94 | 0.357186 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 905.073 | − | 6473.65i | 0.130865 | − | 0.936030i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7601.41 | + | 4388.68i | −1.09007 | + | 0.629353i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8473.74 | + | 4892.32i | 1.20525 | + | 0.695850i | 0.961717 | − | 0.274044i | \(-0.0883612\pi\) |
0.243530 | + | 0.969893i | \(0.421695\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8583.48 | + | 8312.82i | −1.21094 | + | 1.17276i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2307.95 | − | 1037.81i | −0.322972 | − | 0.145230i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3884.31 | + | 6727.82i | 0.539201 | + | 0.933923i | 0.998947 | + | 0.0458729i | \(0.0146069\pi\) |
−0.459747 | + | 0.888050i | \(0.652060\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5793.04 | − | 4519.33i | −0.797737 | − | 0.622339i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3201.51 | 0.437364 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10683.1 | −1.44789 | −0.723947 | − | 0.689856i | \(-0.757674\pi\) | ||||
−0.723947 | + | 0.689856i | \(0.757674\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3172.50 | + | 2474.96i | 0.426593 | + | 0.332798i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6456.89 | − | 11183.7i | −0.861440 | − | 1.49206i | −0.870539 | − | 0.492100i | \(-0.836230\pi\) |
0.00909866 | − | 0.999959i | \(-0.497104\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1020.37 | − | 458.825i | −0.135072 | − | 0.0607373i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1357.29 | + | 387.087i | 0.178281 | + | 0.0508443i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9760.56 | + | 5635.26i | 1.27218 | + | 0.734496i | 0.975399 | − | 0.220448i | \(-0.0707518\pi\) |
0.296786 | + | 0.954944i | \(0.404085\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6774.18 | + | 3911.07i | −0.876176 | + | 0.505861i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −579.654 | + | 4146.05i | −0.0744012 | + | 0.532164i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1423.59 | 0.181339 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4908.58i | 0.620540i | 0.950648 | + | 0.310270i | \(0.100419\pi\) | ||||
−0.950648 | + | 0.310270i | \(0.899581\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2983.11 | − | 5650.97i | −0.374291 | − | 0.709028i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4193.64 | + | 2421.20i | −0.522246 | + | 0.301519i | −0.737853 | − | 0.674961i | \(-0.764160\pi\) |
0.215607 | + | 0.976480i | \(0.430827\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3518.16 | + | 6093.63i | −0.434868 | + | 0.753214i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4378.03 | + | 2718.25i | 0.537151 | + | 0.333508i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2212.58 | + | 1277.43i | 0.269468 | + | 0.155577i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −421.586 | + | 243.403i | −0.0509684 | + | 0.0294266i | −0.525268 | − | 0.850937i | \(-0.676035\pi\) |
0.474299 | + | 0.880364i | \(0.342701\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3574.24 | + | 8828.29i | 0.428964 | + | 1.05953i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7048.56 | + | 714.492i | −0.839799 | + | 0.0851280i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4572.92 | 0.540905 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4548.68 | − | 635.946i | −0.534173 | − | 0.0746820i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6580.88 | + | 11398.4i | 0.767296 | + | 1.32900i | 0.939024 | + | 0.343851i | \(0.111732\pi\) |
−0.171728 | + | 0.985144i | \(0.554935\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −848.070 | + | 1468.90i | −0.0981767 | + | 0.170047i | −0.910930 | − | 0.412561i | \(-0.864634\pi\) |
0.812753 | + | 0.582608i | \(0.197968\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7149.75 | − | 2039.05i | −0.821827 | − | 0.234378i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1461.39 | + | 2531.20i | −0.166795 | + | 0.288897i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4540.07 | + | 3272.97i | −0.514542 | + | 0.370937i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1832.82 | + | 1429.84i | 0.206269 | + | 0.160917i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 3662.97i | − | 0.409372i | −0.978828 | − | 0.204686i | \(-0.934383\pi\) | ||
0.978828 | − | 0.204686i | \(-0.0656173\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5695.06i | − | 0.632071i | −0.948747 | − | 0.316036i | \(-0.897648\pi\) | ||
0.948747 | − | 0.316036i | \(-0.102352\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1381.70 | − | 1771.11i | 0.152293 | − | 0.195215i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6666.68 | − | 11547.0i | −0.729773 | − | 1.26400i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12705.5 | + | 7335.54i | 1.38132 | + | 0.797508i | 0.992316 | − | 0.123726i | \(-0.0394845\pi\) |
0.389008 | + | 0.921234i | \(0.372818\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5224.35 | − | 7646.72i | 0.564124 | − | 0.825690i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3537.20 | + | 2042.20i | 0.379362 | + | 0.219025i | 0.677541 | − | 0.735485i | \(-0.263046\pi\) |
−0.298179 | + | 0.954510i | \(0.596379\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2919.62 | + | 5056.93i | 0.311018 | + | 0.538700i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8295.77 | − | 1159.82i | −0.877800 | − | 0.122724i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 17057.8i | − | 1.79289i | −0.443160 | − | 0.896443i | \(-0.646143\pi\) | ||
0.443160 | − | 0.896443i | \(-0.353857\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3781.92i | 0.394864i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5539.53 | + | 2242.74i | −0.574547 | + | 0.232612i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5559.56 | + | 4007.93i | −0.572826 | + | 0.412955i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1850.19 | + | 3204.63i | −0.189384 | + | 0.328022i | −0.945045 | − | 0.326940i | \(-0.893982\pi\) |
0.755661 | + | 0.654963i | \(0.227316\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2212.13 | − | 4997.48i | 0.224953 | − | 0.508196i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6736.65 | + | 11668.2i | −0.680601 | + | 1.17884i | 0.294197 | + | 0.955745i | \(0.404948\pi\) |
−0.974798 | + | 0.223091i | \(0.928385\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1550.96 | − | 2686.34i | −0.155678 | − | 0.269643i | 0.777627 | − | 0.628725i | \(-0.216423\pi\) |
−0.933306 | + | 0.359082i | \(0.883090\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1852.71 | + | 4576.16i | 0.184769 | + | 0.456375i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12591.3 | 1.24766 | 0.623828 | − | 0.781561i | \(-0.285576\pi\) | ||||
0.623828 | + | 0.781561i | \(0.285576\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11753.5 | − | 1191.41i | 1.15720 | − | 0.117302i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6456.39 | + | 902.660i | 0.631624 | + | 0.0883065i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 386.867 | − | 223.358i | 0.0376071 | − | 0.0217125i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4314.59 | − | 2491.03i | −0.416773 | − | 0.240624i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3578.32 | − | 897.635i | 0.343480 | − | 0.0861633i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2640.55 | − | 4573.56i | 0.251878 | − | 0.436266i | −0.712165 | − | 0.702012i | \(-0.752285\pi\) |
0.964043 | + | 0.265747i | \(0.0856184\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13554.2 | − | 7825.52i | 1.28486 | − | 0.741815i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10288.9 | − | 16357.0i | 0.969278 | − | 1.54093i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 139.333i | − | 0.0130450i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 945.042 | 0.0879341 | 0.0439671 | − | 0.999033i | \(-0.486000\pi\) | ||||
0.0439671 | + | 0.999033i | \(0.486000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4119.11 | + | 3213.44i | 0.380926 | + | 0.297171i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1326.45 | + | 765.828i | −0.121919 | + | 0.0703897i | −0.559719 | − | 0.828682i | \(-0.689091\pi\) |
0.437801 | + | 0.899072i | \(0.355758\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2063.12 | − | 1191.15i | −0.188476 | − | 0.108816i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1582.01 | − | 396.853i | 0.143649 | − | 0.0360348i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3855.39 | + | 1733.64i | 0.347964 | + | 0.156468i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6853.72 | − | 11871.0i | −0.614859 | − | 1.06497i | −0.990409 | − | 0.138165i | \(-0.955879\pi\) |
0.375550 | − | 0.926802i | \(-0.377454\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1724.55 | + | 12335.1i | −0.153787 | + | 1.09998i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17261.6 | 1.53013 | 0.765065 | − | 0.643953i | \(-0.222707\pi\) | ||||
0.765065 | + | 0.643953i | \(0.222707\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11512.3 | 1.01444 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2617.97 | − | 1059.92i | 0.229326 | − | 0.0928453i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6542.31 | − | 11331.6i | −0.569711 | − | 0.986768i | −0.996594 | − | 0.0824613i | \(-0.973722\pi\) |
0.426884 | − | 0.904307i | \(-0.359611\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20973.4 | − | 9431.03i | −1.81567 | − | 0.816446i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8518.52 | + | 3770.73i | 0.733142 | + | 0.324526i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4553.17 | − | 2628.77i | −0.389586 | − | 0.224927i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2037.89 | + | 1176.58i | −0.173359 | + | 0.100089i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 153.087 | − | 61.9789i | 0.0129475 | − | 0.00524195i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12720.6 | −1.06967 | −0.534835 | − | 0.844956i | \(-0.679626\pi\) | ||||
−0.534835 | + | 0.844956i | \(0.679626\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1352.20i | 0.113055i | 0.998401 | + | 0.0565274i | \(0.0180028\pi\) | ||||
−0.998401 | + | 0.0565274i | \(0.981997\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 273.491 | − | 7215.28i | 0.0227355 | − | 0.599811i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4534.36 | − | 2617.91i | 0.374801 | − | 0.216391i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14077.1 | − | 24382.2i | 1.15699 | − | 2.00396i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7419.38 | − | 7185.43i | 0.606354 | − | 0.587234i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20064.0 | + | 11584.0i | 1.63053 | + | 0.941385i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5120.98 | + | 2956.60i | −0.413830 | + | 0.238925i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4963.75 | + | 6362.72i | −0.398886 | + | 0.511307i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −588.200 | − | 2871.52i | −0.0470048 | − | 0.229472i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8023.06 | −0.637594 | −0.318797 | − | 0.947823i | \(-0.603279\pi\) | ||||
−0.318797 | + | 0.947823i | \(0.603279\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11239.5 | − | 14407.1i | 0.888271 | − | 1.13862i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5528.13 | + | 9574.99i | 0.434493 | + | 0.752565i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 966.417 | − | 1673.88i | 0.0755411 | − | 0.130841i | −0.825780 | − | 0.563992i | \(-0.809265\pi\) |
0.901321 | + | 0.433151i | \(0.142598\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2237.78 | − | 7846.56i | 0.173964 | − | 0.609988i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2030.39 | − | 3516.73i | 0.156982 | − | 0.271902i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2181.12 | + | 3025.51i | 0.167722 | + | 0.232654i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1520.51 | − | 10875.7i | 0.116292 | − | 0.831796i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3185.91i | 0.242354i | 0.992631 | + | 0.121177i | \(0.0386669\pi\) | ||||
−0.992631 | + | 0.121177i | \(0.961333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2736.57i | − | 0.207057i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −649.130 | − | 1603.34i | −0.0488525 | − | 0.120665i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5544.17 | + | 9602.79i | 0.415025 | + | 0.718844i | 0.995431 | − | 0.0954828i | \(-0.0304395\pi\) |
−0.580406 | + | 0.814327i | \(0.697106\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12736.8 | + | 7353.60i | 0.948392 | + | 0.547555i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 930.679 | + | 13469.2i | 0.0689327 | + | 0.997621i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4166.78 | + | 2405.69i | 0.306995 | + | 0.177244i | 0.645581 | − | 0.763692i | \(-0.276615\pi\) |
−0.338586 | + | 0.940936i | \(0.609949\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1711.30 | + | 2964.07i | 0.125422 | + | 0.217237i | 0.921898 | − | 0.387433i | \(-0.126638\pi\) |
−0.796476 | + | 0.604670i | \(0.793305\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4438.02 | + | 10961.8i | 0.323562 | + | 0.799191i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 15066.2i | − | 1.09270i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 15586.3i | − | 1.12455i | −0.826950 | − | 0.562275i | \(-0.809926\pi\) | ||
0.826950 | − | 0.562275i | \(-0.190074\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1144.41 | + | 8185.52i | −0.0821415 | + | 0.587528i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7006.26 | + | 9718.66i | 0.500290 | + | 0.693973i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 583.823 | − | 1011.21i | 0.0414742 | − | 0.0718354i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2740.28 | − | 9608.53i | 0.193669 | − | 0.679083i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12308.5 | + | 21319.0i | −0.865465 | + | 1.49903i | 0.00111897 | + | 0.999999i | \(0.499644\pi\) |
−0.866584 | + | 0.499031i | \(0.833690\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4462.41 | + | 7729.12i | 0.312174 | + | 0.540701i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5483.51 | − | 7028.97i | 0.381661 | − | 0.489227i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25080.0 | −1.73678 | −0.868392 | − | 0.495878i | \(-0.834846\pi\) | ||||
−0.868392 | + | 0.495878i | \(0.834846\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5073.88 | − | 514.325i | 0.349595 | − | 0.0354374i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8099.09 | + | 10381.7i | −0.555232 | + | 0.711718i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11208.0 | − | 6470.92i | 0.764516 | − | 0.441394i | −0.0663988 | − | 0.997793i | \(-0.521151\pi\) |
0.830915 | + | 0.556400i | \(0.187818\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11568.5 | − | 6679.10i | −0.785176 | − | 0.453321i | 0.0530857 | − | 0.998590i | \(-0.483094\pi\) |
−0.838261 | + | 0.545269i | \(0.816428\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12371.8 | + | 11981.7i | −0.835521 | + | 0.809175i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4446.26 | + | 7701.15i | −0.298787 | + | 0.517514i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9551.96 | − | 5514.83i | 0.638718 | − | 0.368764i | −0.145402 | − | 0.989373i | \(-0.546448\pi\) |
0.784121 | + | 0.620608i | \(0.213114\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5881.02 | + | 222.917i | 0.391315 | + | 0.0148326i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14415.4i | 0.954475i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9716.71 | −0.640219 | −0.320109 | − | 0.947381i | \(-0.603720\pi\) | ||||
−0.320109 | + | 0.947381i | \(0.603720\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15067.6 | − | 6100.29i | 0.987942 | − | 0.399980i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19367.5 | − | 11181.9i | 1.26371 | − | 0.729602i | 0.289918 | − | 0.957051i | \(-0.406372\pi\) |
0.973790 | + | 0.227449i | \(0.0730386\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5030.74 | − | 2904.50i | −0.326660 | − | 0.188597i | 0.327697 | − | 0.944783i | \(-0.393727\pi\) |
−0.654357 | + | 0.756186i | \(0.727061\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3005.08 | + | 28010.9i | 0.194186 | + | 1.81005i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6274.10 | + | 13952.8i | −0.403478 | + | 0.897282i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 308.348 | + | 534.075i | 0.0197343 | + | 0.0341808i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2732.99 | − | 1106.48i | 0.174075 | − | 0.0704764i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11646.2 | −0.738257 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11462.0 | −0.723128 | −0.361564 | − | 0.932347i | \(-0.617757\pi\) | ||||
−0.361564 | + | 0.932347i | \(0.617757\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3093.42 | + | 22126.1i | −0.194238 | + | 1.38931i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2736.96 | − | 4740.55i | −0.171044 | − | 0.296257i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17035.8 | − | 5674.90i | −1.05963 | − | 0.352979i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5977.53 | + | 1499.49i | −0.370058 | + | 0.0928306i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22256.6 | − | 12849.8i | −1.37142 | − | 0.791791i | −0.380315 | − | 0.924857i | \(-0.624184\pi\) |
−0.991107 | + | 0.133066i | \(0.957518\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14555.9 | + | 8403.85i | −0.892735 | + | 0.515421i | −0.874836 | − | 0.484419i | \(-0.839031\pi\) |
−0.0178986 | + | 0.999840i | \(0.505698\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1513.91 | − | 1181.04i | −0.0924186 | − | 0.0720985i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14607.3 | −0.887595 | −0.443798 | − | 0.896127i | \(-0.646369\pi\) | ||||
−0.443798 | + | 0.896127i | \(0.646369\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 3269.01i | − | 0.197720i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6886.98 | + | 10948.7i | −0.414627 | + | 0.659163i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23324.4 | + | 13466.4i | −1.39779 | + | 0.807013i | −0.994161 | − | 0.107911i | \(-0.965584\pi\) |
−0.403627 | + | 0.914924i | \(0.632251\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2847.61 | − | 4932.20i | 0.169870 | − | 0.294224i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 32517.8 | − | 8157.22i | 1.93096 | − | 0.484389i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21546.5 | − | 12439.9i | −1.27364 | − | 0.735339i | −0.297973 | − | 0.954574i | \(-0.596310\pi\) |
−0.975672 | + | 0.219235i | \(0.929644\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24869.6 | − | 14358.5i | 1.46341 | − | 0.844902i | 0.464247 | − | 0.885706i | \(-0.346325\pi\) |
0.999167 | + | 0.0408035i | \(0.0129918\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10494.4 | − | 1467.21i | −0.614734 | − | 0.0859451i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 876.701 | + | 8648.77i | 0.0511233 | + | 0.504338i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12280.1 | 0.712874 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5694.56 | − | 14065.4i | −0.329095 | − | 0.812857i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1291.25 | − | 2236.51i | −0.0742892 | − | 0.128673i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −487.441 | + | 844.272i | −0.0279190 | + | 0.0483570i | −0.879647 | − | 0.475627i | \(-0.842221\pi\) |
0.851728 | + | 0.523984i | \(0.175555\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6205.62 | + | 8502.73i | 0.353858 | + | 0.484845i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10639.0 | − | 18427.4i | 0.603976 | − | 1.04612i | −0.388236 | − | 0.921560i | \(-0.626916\pi\) |
0.992212 | − | 0.124557i | \(-0.0397511\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 296.121 | − | 213.476i | 0.0167365 | − | 0.0120655i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3757.93 | + | 1521.44i | −0.211460 | + | 0.0856120i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6554.78i | 0.367221i | 0.982999 | + | 0.183610i | \(0.0587785\pi\) | ||||
−0.982999 | + | 0.183610i | \(0.941222\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 12957.1i | − | 0.722725i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16895.7 | + | 2362.17i | 0.938301 | + | 0.131183i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3576.49 | − | 6194.66i | −0.197755 | − | 0.342522i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7567.47 | − | 4369.08i | −0.416614 | − | 0.240532i | 0.277014 | − | 0.960866i | \(-0.410655\pi\) |
−0.693627 | + | 0.720334i | \(0.743989\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3267.25 | + | 2754.16i | 0.179095 | + | 0.150970i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5411.18 | + | 3124.15i | 0.295335 | + | 0.170512i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8619.82 | − | 14930.0i | −0.468435 | − | 0.811353i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16695.4 | − | 21400.8i | 0.903404 | − | 1.15802i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9016.22i | 0.485789i | 0.970053 | + | 0.242894i | \(0.0780969\pi\) | ||||
−0.970053 | + | 0.242894i | \(0.921903\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 19851.7i | − | 1.06504i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7974.78 | + | 6221.36i | 0.426025 | + | 0.332355i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17638.3 | + | 24466.7i | 0.938268 | + | 1.30151i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14131.7 | + | 24476.8i | −0.748557 | + | 1.29654i | 0.199958 | + | 0.979804i | \(0.435919\pi\) |
−0.948515 | + | 0.316734i | \(0.897414\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5228.97 | − | 1491.26i | −0.275811 | − | 0.0786591i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13494.7 | + | 23373.5i | −0.708807 | + | 1.22769i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1581.20 | − | 2738.72i | −0.0827042 | − | 0.143248i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5327.19 | − | 744.788i | −0.277472 | − | 0.0387930i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23753.1 | −1.23205 | −0.616023 | − | 0.787728i | \(-0.711257\pi\) | ||||
−0.616023 | + | 0.787728i | \(0.711257\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1389.16 | − | 13704.3i | −0.0717548 | − | 0.707870i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10833.8 | + | 26759.3i | 0.557280 | + | 1.37647i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3973.76 | − | 2294.25i | 0.203561 | − | 0.117526i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23109.1 | − | 13342.1i | −1.17891 | − | 0.680645i | −0.223150 | − | 0.974784i | \(-0.571634\pi\) |
−0.955763 | + | 0.294139i | \(0.904967\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13233.4 | − | 14570.4i | −0.672326 | − | 0.740255i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1018.16 | + | 1763.51i | −0.0515159 | + | 0.0892281i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29171.7 | − | 16842.3i | 1.46996 | − | 0.848684i | 0.470531 | − | 0.882383i | \(-0.344062\pi\) |
0.999432 | + | 0.0337000i | \(0.0107291\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10491.7 | + | 6975.27i | −0.526520 | + | 0.350050i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5451.08i | 0.272446i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1602.94 | 0.0797905 | 0.0398952 | − | 0.999204i | \(-0.487298\pi\) | ||||
0.0398952 | + | 0.999204i | \(0.487298\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2500.95 | − | 17888.4i | 0.123987 | − | 0.886836i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33905.7 | + | 19575.5i | −1.67413 | + | 0.966560i | −0.708846 | + | 0.705363i | \(0.750784\pi\) |
−0.965285 | + | 0.261197i | \(0.915883\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9868.76 | + | 5697.73i | 0.485320 | + | 0.280200i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16796.7 | − | 4790.28i | −0.822702 | − | 0.234628i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14129.5 | − | 6353.57i | −0.689294 | − | 0.309952i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10417.9 | + | 18044.4i | 0.506199 | + | 0.876762i | 0.999974 | + | 0.00717280i | \(0.00228319\pi\) |
−0.493775 | + | 0.869590i | \(0.664383\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3993.83 | + | 3115.71i | 0.193285 | + | 0.150787i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8130.28 | 0.391909 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1105.00 | 0.0530538 | 0.0265269 | − | 0.999648i | \(-0.491555\pi\) | ||||
0.0265269 | + | 0.999648i | \(0.491555\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7030.20 | + | 5484.47i | 0.336206 | + | 0.262284i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13772.2 | − | 23854.2i | −0.656036 | − | 1.13629i | −0.981633 | − | 0.190779i | \(-0.938899\pi\) |
0.325597 | − | 0.945508i | \(-0.394435\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11879.6 | + | 26418.8i | −0.563659 | + | 1.25350i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5340.82 | + | 5172.41i | −0.252415 | + | 0.244456i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17342.9 | − | 10013.0i | −0.816451 | − | 0.471378i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10418.2 | + | 6014.95i | −0.488543 | + | 0.282060i | −0.723970 | − | 0.689832i | \(-0.757685\pi\) |
0.235427 | + | 0.971892i | \(0.424351\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3462.56 | − | 24766.4i | 0.161740 | − | 1.15686i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20325.9 | 0.945758 | 0.472879 | − | 0.881127i | \(-0.343215\pi\) | ||||
0.472879 | + | 0.881127i | \(0.343215\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10084.7i | 0.467422i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 25443.3 | − | 13431.3i | 1.17474 | − | 0.620138i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25449.1 | − | 14693.0i | 1.17049 | − | 0.675780i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −975.266 | + | 1689.21i | −0.0446834 | + | 0.0773940i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6930.39 | + | 5058.06i | −0.316311 | + | 0.230856i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7680.61 | − | 4434.40i | −0.349214 | − | 0.201619i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22900.0 | + | 13221.3i | −1.03722 | + | 0.598842i | −0.919046 | − | 0.394151i | \(-0.871039\pi\) |
−0.118178 | + | 0.992992i | \(0.537705\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4801.54 | + | 11859.7i | 0.216653 | + | 0.535129i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3885.98 | + | 38335.7i | 0.174677 | + | 1.72321i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15820.3 | −0.708443 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4970.49 | − | 694.919i | −0.221742 | − | 0.0310015i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13176.4 | + | 22822.2i | 0.585612 | + | 1.01431i | 0.994799 | + | 0.101859i | \(0.0324792\pi\) |
−0.409187 | + | 0.912451i | \(0.634187\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5363.36 | − | 9289.61i | 0.237474 | − | 0.411318i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5426.69 | − | 21632.9i | −0.239379 | − | 0.954257i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5305.46 | − | 9189.33i | 0.233158 | − | 0.403841i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21324.9 | + | 15373.3i | −0.933670 | + | 0.673090i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8574.72 | + | 6689.40i | 0.374033 | + | 0.291794i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 36209.0i | − | 1.57360i | −0.617211 | − | 0.786798i | \(-0.711737\pi\) | ||
0.617211 | − | 0.786798i | \(-0.288263\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 12130.9i | − | 0.525245i | −0.964899 | − | 0.262622i | \(-0.915413\pi\) | ||
0.964899 | − | 0.262622i | \(-0.0845874\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16002.5 | + | 20512.6i | −0.690322 | + | 0.884880i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3553.61 | − | 6155.03i | −0.152733 | − | 0.264542i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3006.02 | − | 1735.53i | −0.128724 | − | 0.0743186i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 24619.1 | − | 8897.61i | 1.05038 | − | 0.379619i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16661.5 | − | 9619.52i | −0.708271 | − | 0.408920i | 0.102150 | − | 0.994769i | \(-0.467428\pi\) |
−0.810420 | + | 0.585849i | \(0.800761\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −987.266 | − | 1710.00i | −0.0418152 | − | 0.0724261i | 0.844360 | − | 0.535776i | \(-0.179981\pi\) |
−0.886176 | + | 0.463350i | \(0.846647\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3299.57 | + | 461.309i | 0.139244 | + | 0.0194676i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18657.5i | 0.784506i | 0.919857 | + | 0.392253i | \(0.128304\pi\) | ||||
−0.919857 | + | 0.392253i | \(0.871696\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39035.0i | 1.63539i | 0.575650 | + | 0.817696i | \(0.304749\pi\) | ||||
−0.575650 | + | 0.817696i | \(0.695251\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −40062.1 | + | 16219.6i | −1.67237 | + | 0.677079i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8866.88 | + | 9995.34i | 0.368811 | + | 0.415748i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8472.04 | − | 14674.0i | 0.351122 | − | 0.608161i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2011.48 | − | 18749.4i | −0.0830668 | − | 0.774281i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7645.68 | − | 13242.7i | 0.314610 | − | 0.544921i | −0.664744 | − | 0.747071i | \(-0.731459\pi\) |
0.979355 | + | 0.202150i | \(0.0647928\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10324.5 | − | 17882.6i | −0.423326 | − | 0.733223i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9062.30 | + | 22383.7i | 0.370252 | + | 0.914514i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3842.36 | −0.156427 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23179.2 | + | 2349.61i | −0.940315 | + | 0.0953170i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23591.4 | − | 3298.29i | −0.953659 | − | 0.133330i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 51990.1 | − | 30016.5i | 2.09424 | − | 1.20911i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24102.9 | − | 13915.8i | −0.967486 | − | 0.558579i | −0.0690174 | − | 0.997615i | \(-0.521986\pi\) |
−0.898469 | + | 0.439037i | \(0.855320\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8816.72 | − | 9103.78i | −0.352661 | − | 0.364144i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12190.5 | + | 21114.6i | −0.485905 | + | 0.841613i | −0.999869 | − | 0.0161994i | \(-0.994843\pi\) |
0.513963 | + | 0.857812i | \(0.328177\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23886.7 | − | 13791.0i | 0.948781 | − | 0.547779i | 0.0560791 | − | 0.998426i | \(-0.482140\pi\) |
0.892702 | + | 0.450647i | \(0.148807\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 36050.1 | + | 22676.3i | 1.42693 | + | 0.897566i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26388.4i | 1.04087i | 0.853901 | + | 0.520436i | \(0.174230\pi\) | ||||
−0.853901 | + | 0.520436i | \(0.825770\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −224.682 | −0.00883171 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13911.2 | − | 10852.6i | −0.544925 | − | 0.425112i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1490.41 | + | 860.490i | −0.0581804 | + | 0.0335905i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28919.4 | + | 16696.6i | 1.12502 | + | 0.649532i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −145.956 | + | 511.782i | −0.00565850 | + | 0.0198410i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10739.9 | + | 23884.1i | −0.414941 | + | 0.922775i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15753.5 | + | 27285.8i | 0.606564 | + | 1.05060i | 0.991802 | + | 0.127782i | \(0.0407859\pi\) |
−0.385238 | + | 0.922817i | \(0.625881\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2821.95 | − | 20184.3i | 0.108284 | − | 0.774517i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1153.83 | 0.0441243 | 0.0220621 | − | 0.999757i | \(-0.492977\pi\) | ||||
0.0220621 | + | 0.999757i | \(0.492977\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22903.1 | 0.872877 | 0.436439 | − | 0.899734i | \(-0.356240\pi\) | ||||
0.436439 | + | 0.899734i | \(0.356240\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13024.1 | + | 5272.97i | −0.494691 | + | 0.200281i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14902.5 | − | 25811.9i | −0.564123 | − | 0.977090i | −0.997131 | − | 0.0756994i | \(-0.975881\pi\) |
0.433008 | − | 0.901390i | \(-0.357452\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5881.57 | − | 13079.8i | 0.221892 | − | 0.493458i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6226.56 | − | 199.534i | −0.234116 | − | 0.00750239i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15834.7 | + | 9142.19i | 0.593381 | + | 0.342589i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9507.58 | − | 5489.20i | 0.355087 | − | 0.205010i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 50629.9 | − | 20498.1i | 1.88460 | − | 0.763001i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8219.80 | −0.304945 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5322.64i | 0.196807i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 190.544 | − | 5026.95i | 0.00702204 | − | 0.185256i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21528.1 | + | 12429.2i | −0.790737 | + | 0.456532i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10173.5 | − | 17621.0i | 0.372442 | − | 0.645089i | −0.617499 | − | 0.786572i | \(-0.711854\pi\) |
0.989941 | + | 0.141483i | \(0.0451872\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −42285.6 | − | 12059.5i | −1.54293 | − | 0.440032i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26966.9 | + | 15569.4i | 0.980740 | + | 0.566231i | 0.902494 | − | 0.430703i | \(-0.141735\pi\) |
0.0782466 | + | 0.996934i | \(0.475068\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4787.55 | + | 2764.10i | −0.173543 | + | 0.100195i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6827.69 | + | 8751.99i | −0.246685 | + | 0.316210i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14845.1 | − | 1504.81i | 0.534600 | − | 0.0541909i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18807.6 | 0.675089 | 0.337545 | − | 0.941310i | \(-0.390404\pi\) | ||||
0.337545 | + | 0.941310i | \(0.390404\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25679.8 | + | 32917.3i | −0.918760 | + | 1.17770i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5974.46 | + | 10348.1i | 0.213057 | + | 0.369026i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11215.8 | − | 19426.3i | 0.398674 | − | 0.690523i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13970.4 | + | 14425.3i | 0.494982 | + | 0.511098i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13698.8 | − | 23727.0i | 0.483791 | − | 0.837951i | −0.516035 | − | 0.856567i | \(-0.672593\pi\) |
0.999827 | + | 0.0186161i | \(0.00592603\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17037.7 | + | 15114.2i | −0.599773 | + | 0.532059i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3187.92 | + | 22802.0i | −0.111863 | + | 0.800112i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2353.19i | 0.0823075i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 27022.7i | − | 0.942149i | −0.882093 | − | 0.471075i | \(-0.843866\pi\) | ||
0.882093 | − | 0.471075i | \(-0.156134\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11542.4 | + | 28509.4i | 0.401141 | + | 0.990810i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8024.19 | − | 13898.3i | −0.277982 | − | 0.481479i | 0.692901 | − | 0.721033i | \(-0.256332\pi\) |
−0.970883 | + | 0.239554i | \(0.922999\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 76960.1 | + | 44432.9i | 2.65765 | + | 1.53440i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5702.78 | − | 17459.6i | 0.196309 | − | 0.601017i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3053.61 | − | 1763.00i | −0.104782 | − | 0.0604962i | 0.446693 | − | 0.894687i | \(-0.352602\pi\) |
−0.551475 | + | 0.834191i | \(0.685935\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32501.2 | − | 56293.7i | −1.11173 | − | 1.92557i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1031.34 | + | 2547.39i | 0.0351666 | + | 0.0868609i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 31452.5i | − | 1.06909i | −0.845139 | − | 0.534547i | \(-0.820482\pi\) | ||
0.845139 | − | 0.534547i | \(-0.179518\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 16088.5i | − | 0.545142i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −376.003 | + | 2689.41i | −0.0127006 | + | 0.0908426i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27537.3 | − | 19851.9i | 0.927244 | − | 0.668458i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5862.71 | + | 10154.5i | −0.196795 | + | 0.340858i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21906.9 | − | 5495.42i | 0.733062 | − | 0.183891i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5622.01 | − | 9737.61i | 0.187543 | − | 0.324834i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4935.48 | + | 8548.51i | 0.164131 | + | 0.284283i | 0.936346 | − | 0.351078i | \(-0.114185\pi\) |
−0.772215 | + | 0.635361i | \(0.780851\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8267.18 | + | 10597.2i | −0.274076 | + | 0.351321i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9155.66 | 0.302594 | 0.151297 | − | 0.988488i | \(-0.451655\pi\) | ||||
0.151297 | + | 0.988488i | \(0.451655\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1650.94 | + | 16286.8i | 0.0543954 | + | 0.536618i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12553.9 | − | 16092.1i | 0.412357 | − | 0.528574i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11814.1 | − | 6820.88i | 0.386865 | − | 0.223356i | −0.293936 | − | 0.955825i | \(-0.594965\pi\) |
0.680801 | + | 0.732469i | \(0.261632\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6113.31 | − | 3529.52i | −0.199573 | − | 0.115224i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10275.1 | − | 40960.6i | −0.334413 | − | 1.33310i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28836.8 | − | 49946.9i | 0.935659 | − | 1.62061i | 0.162203 | − | 0.986757i | \(-0.448140\pi\) |
0.773455 | − | 0.633851i | \(-0.218527\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10503.1 | + | 6063.98i | −0.339754 | + | 0.196157i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1003.72 | + | 26480.4i | −0.0323697 | + | 0.853982i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 10496.7i | − | 0.337489i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28668.4 | 0.918953 | 0.459476 | − | 0.888190i | \(-0.348037\pi\) | ||||
0.459476 | + | 0.888190i | \(0.348037\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17578.7 | − | 7116.93i | 0.561774 | − | 0.227441i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15513.0 | − | 8956.44i | 0.494267 | − | 0.285365i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3928.31 | + | 2268.01i | 0.124785 | + | 0.0720448i | 0.561093 | − | 0.827753i | \(-0.310381\pi\) |
−0.436308 | + | 0.899797i | \(0.643714\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16977.6 | + | 38354.4i | −0.537684 | + | 1.21469i |
(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 | 252.4.x.a.209.19 | yes | 48 | |
3.2 | odd | 2 | 756.4.x.a.629.17 | 48 | |||
7.6 | odd | 2 | inner | 252.4.x.a.209.6 | yes | 48 | |
9.2 | odd | 6 | 2268.4.f.a.1133.16 | 48 | |||
9.4 | even | 3 | 756.4.x.a.125.8 | 48 | |||
9.5 | odd | 6 | inner | 252.4.x.a.41.6 | ✓ | 48 | |
9.7 | even | 3 | 2268.4.f.a.1133.33 | 48 | |||
21.20 | even | 2 | 756.4.x.a.629.8 | 48 | |||
63.13 | odd | 6 | 756.4.x.a.125.17 | 48 | |||
63.20 | even | 6 | 2268.4.f.a.1133.34 | 48 | |||
63.34 | odd | 6 | 2268.4.f.a.1133.15 | 48 | |||
63.41 | even | 6 | inner | 252.4.x.a.41.19 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.x.a.41.6 | ✓ | 48 | 9.5 | odd | 6 | inner | |
252.4.x.a.41.19 | yes | 48 | 63.41 | even | 6 | inner | |
252.4.x.a.209.6 | yes | 48 | 7.6 | odd | 2 | inner | |
252.4.x.a.209.19 | yes | 48 | 1.1 | even | 1 | trivial | |
756.4.x.a.125.8 | 48 | 9.4 | even | 3 | |||
756.4.x.a.125.17 | 48 | 63.13 | odd | 6 | |||
756.4.x.a.629.8 | 48 | 21.20 | even | 2 | |||
756.4.x.a.629.17 | 48 | 3.2 | odd | 2 | |||
2268.4.f.a.1133.15 | 48 | 63.34 | odd | 6 | |||
2268.4.f.a.1133.16 | 48 | 9.2 | odd | 6 | |||
2268.4.f.a.1133.33 | 48 | 9.7 | even | 3 | |||
2268.4.f.a.1133.34 | 48 | 63.20 | even | 6 |