Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(173,252)]
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, 1, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.173");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.bm (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 | 173.7 | ||
Character | \(\chi\) | \(=\) | 252.173 |
Dual form | 252.4.bm.a.185.7 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −3.15513 | + | 4.12858i | −0.607205 | + | 0.794545i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 18.3795 | 1.64392 | 0.821958 | − | 0.569549i | \(-0.192882\pi\) | ||||
0.821958 | + | 0.569549i | \(0.192882\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −11.4907 | − | 14.5246i | −0.620441 | − | 0.784253i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.09031 | − | 26.0524i | −0.262604 | − | 0.964904i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 55.3725i | − | 1.51777i | −0.651226 | − | 0.758883i | \(-0.725745\pi\) | ||
0.651226 | − | 0.758883i | \(-0.274255\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −68.0763 | + | 39.3039i | −1.45238 | + | 0.838534i | −0.998616 | − | 0.0525871i | \(-0.983253\pi\) |
−0.453766 | + | 0.891121i | \(0.649920\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −57.9898 | + | 75.8813i | −0.998193 | + | 1.30616i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −9.99021 | − | 17.3036i | −0.142528 | − | 0.246866i | 0.785920 | − | 0.618329i | \(-0.212190\pi\) |
−0.928448 | + | 0.371462i | \(0.878857\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16.7611 | − | 9.67700i | −0.202382 | − | 0.116845i | 0.395384 | − | 0.918516i | \(-0.370611\pi\) |
−0.597766 | + | 0.801671i | \(0.703945\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 96.2206 | − | 1.61341i | 0.999859 | − | 0.0167654i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 124.143i | − | 1.12546i | −0.826640 | − | 0.562731i | \(-0.809751\pi\) | ||
0.826640 | − | 0.562731i | \(-0.190249\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 212.807 | 1.70246 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 129.930 | + | 52.9258i | 0.926114 | + | 0.377243i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −48.2851 | − | 27.8774i | −0.309183 | − | 0.178507i | 0.337378 | − | 0.941369i | \(-0.390460\pi\) |
−0.646561 | + | 0.762862i | \(0.723793\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −275.387 | − | 158.995i | −1.59551 | − | 0.921170i | −0.992337 | − | 0.123562i | \(-0.960568\pi\) |
−0.603176 | − | 0.797608i | \(-0.706098\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 228.610 | + | 174.707i | 1.20593 | + | 0.921596i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −211.194 | − | 266.955i | −1.01995 | − | 1.28925i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 20.5303 | − | 35.5595i | 0.0912205 | − | 0.157999i | −0.816804 | − | 0.576915i | \(-0.804257\pi\) |
0.908025 | + | 0.418916i | \(0.137590\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 52.5205 | − | 405.067i | 0.215641 | − | 1.66315i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 53.1315 | + | 92.0264i | 0.202384 | + | 0.350539i | 0.949296 | − | 0.314383i | \(-0.101798\pi\) |
−0.746912 | + | 0.664923i | \(0.768464\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 279.238 | − | 483.655i | 0.990312 | − | 1.71527i | 0.374898 | − | 0.927066i | \(-0.377678\pi\) |
0.615414 | − | 0.788204i | \(-0.288989\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −130.317 | − | 478.831i | −0.431699 | − | 1.58622i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 73.9580 | + | 128.099i | 0.229529 | + | 0.397556i | 0.957669 | − | 0.287873i | \(-0.0929480\pi\) |
−0.728139 | + | 0.685429i | \(0.759615\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −78.9267 | + | 333.796i | −0.230107 | + | 0.973165i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 102.959 | + | 13.3496i | 0.282690 | + | 0.0366533i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 570.090 | − | 329.141i | 1.47751 | − | 0.853038i | 0.477829 | − | 0.878453i | \(-0.341424\pi\) |
0.999677 | + | 0.0254144i | \(0.00809053\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1017.72i | − | 2.49508i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 92.8356 | − | 38.6672i | 0.215726 | − | 0.0898525i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −284.255 | + | 492.343i | −0.627234 | + | 1.08640i | 0.360871 | + | 0.932616i | \(0.382480\pi\) |
−0.988104 | + | 0.153785i | \(0.950854\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −122.068 | + | 70.4757i | −0.256215 | + | 0.147926i | −0.622607 | − | 0.782535i | \(-0.713926\pi\) |
0.366391 | + | 0.930461i | \(0.380593\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −296.927 | + | 402.345i | −0.593799 | + | 0.804614i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1251.21 | + | 722.387i | −2.38759 | + | 1.37848i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 147.142 | − | 254.857i | 0.268302 | − | 0.464712i | −0.700122 | − | 0.714023i | \(-0.746871\pi\) |
0.968423 | + | 0.249312i | \(0.0802043\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 512.535 | + | 391.688i | 0.894231 | + | 0.683386i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 602.374i | 1.00688i | 0.864030 | + | 0.503441i | \(0.167933\pi\) | ||||
−0.864030 | + | 0.503441i | \(0.832067\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 541.701 | − | 312.751i | 0.868510 | − | 0.501435i | 0.00165750 | − | 0.999999i | \(-0.499472\pi\) |
0.866853 | + | 0.498564i | \(0.166139\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −671.434 | + | 878.591i | −1.03374 | + | 1.35268i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −804.262 | + | 636.270i | −1.19031 | + | 0.941684i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 267.022 | + | 462.495i | 0.380282 | + | 0.658668i | 0.991102 | − | 0.133101i | \(-0.0424935\pi\) |
−0.610820 | + | 0.791769i | \(0.709160\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −628.455 | + | 369.439i | −0.862078 | + | 0.506776i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 352.414 | − | 610.399i | 0.466054 | − | 0.807229i | −0.533195 | − | 0.845993i | \(-0.679009\pi\) |
0.999248 | + | 0.0387640i | \(0.0123420\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −183.615 | − | 318.031i | −0.234305 | − | 0.405827i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 267.440 | − | 111.392i | 0.329570 | − | 0.137270i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 38.6630 | − | 66.9663i | 0.0460480 | − | 0.0797574i | −0.842083 | − | 0.539348i | \(-0.818671\pi\) |
0.888131 | + | 0.459591i | \(0.152004\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1353.12 | + | 537.150i | 1.55874 | + | 0.618776i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1525.30 | − | 635.307i | 1.70071 | − | 0.708368i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −308.060 | − | 177.859i | −0.332698 | − | 0.192083i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −382.120 | − | 220.617i | −0.399984 | − | 0.230931i | 0.286493 | − | 0.958082i | \(-0.407510\pi\) |
−0.686477 | + | 0.727151i | \(0.740844\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1442.59 | + | 392.608i | −1.46450 | + | 0.398572i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1118.35 | −1.10179 | −0.550893 | − | 0.834576i | \(-0.685713\pi\) | ||||
−0.550893 | + | 0.834576i | \(0.685713\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 814.783i | 0.779446i | 0.920932 | + | 0.389723i | \(0.127429\pi\) | ||||
−0.920932 | + | 0.389723i | \(0.872571\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1768.49 | − | 29.6536i | 1.64368 | − | 0.0275609i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1320.94 | − | 762.645i | −1.19346 | − | 0.689044i | −0.234370 | − | 0.972147i | \(-0.575303\pi\) |
−0.959089 | + | 0.283103i | \(0.908636\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 101.432 | + | 175.685i | 0.0891319 | + | 0.154381i | 0.907144 | − | 0.420819i | \(-0.138257\pi\) |
−0.818013 | + | 0.575200i | \(0.804924\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 82.0345 | + | 196.956i | 0.0701475 | + | 0.168416i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −75.2101 | + | 43.4226i | −0.0626121 | + | 0.0361491i | −0.530979 | − | 0.847385i | \(-0.678176\pi\) |
0.468367 | + | 0.883534i | \(0.344842\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2281.69i | − | 1.85016i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1506.64 | + | 1494.87i | 1.19051 | + | 1.18121i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −136.532 | + | 343.934i | −0.105175 | + | 0.264944i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1735.11 | −1.30362 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −547.575 | − | 70.9978i | −0.401408 | − | 0.0520460i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1613.85 | 1.15478 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −486.709 | −0.340066 | −0.170033 | − | 0.985438i | \(-0.554388\pi\) | ||||
−0.170033 | + | 0.985438i | \(0.554388\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1115.77 | + | 2678.85i | 0.761538 | + | 1.82837i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 801.955 | 0.534864 | 0.267432 | − | 0.963577i | \(-0.413825\pi\) | ||||
0.267432 | + | 0.963577i | \(0.413825\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 52.0423 | + | 354.643i | 0.0339296 | + | 0.231214i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2388.06 | + | 972.751i | 1.52245 | + | 0.620156i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 918.829i | 0.572999i | 0.958080 | + | 0.286500i | \(0.0924917\pi\) | ||||
−0.958080 | + | 0.286500i | \(0.907508\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 159.738 | − | 92.2248i | 0.0974734 | − | 0.0562763i | −0.450471 | − | 0.892791i | \(-0.648744\pi\) |
0.547944 | + | 0.836515i | \(0.315411\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −762.213 | − | 98.8276i | −0.455248 | − | 0.0590268i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2176.35 | + | 3769.56i | 1.27270 | + | 2.20438i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −887.457 | − | 512.374i | −0.508271 | − | 0.293450i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1129.08 | − | 1379.02i | −0.633502 | − | 0.773741i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2240.73i | − | 1.23200i | −0.787748 | − | 0.615998i | \(-0.788753\pi\) | ||
0.787748 | − | 0.615998i | \(-0.211247\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2129.10 | −1.14744 | −0.573721 | − | 0.819051i | \(-0.694501\pi\) | ||||
−0.573721 | + | 0.819051i | \(0.694501\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −379.965 | + | 382.957i | −0.200774 | + | 0.202354i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5061.48 | − | 2922.25i | −2.62289 | − | 1.51433i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2403.02 | + | 1387.38i | 1.22154 | + | 0.705256i | 0.965246 | − | 0.261343i | \(-0.0841653\pi\) |
0.256294 | + | 0.966599i | \(0.417499\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −439.821 | + | 3392.14i | −0.219371 | + | 1.69191i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1803.13 | + | 1426.49i | −0.882648 | + | 0.698282i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −536.860 | + | 929.870i | −0.257976 | + | 0.446828i | −0.965700 | − | 0.259661i | \(-0.916389\pi\) |
0.707723 | + | 0.706490i | \(0.249722\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4201.74 | + | 3211.04i | 1.98245 | + | 1.51503i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.8325 | + | 39.5471i | 0.0105798 | + | 0.0183248i | 0.871267 | − | 0.490810i | \(-0.163299\pi\) |
−0.860687 | + | 0.509134i | \(0.829966\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1991.09 | − | 3448.67i | 0.906277 | − | 1.56972i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −133.268 | + | 505.279i | −0.0595980 | + | 0.225963i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 454.541 | + | 787.289i | 0.199758 | + | 0.345991i | 0.948450 | − | 0.316927i | \(-0.102651\pi\) |
−0.748692 | + | 0.662918i | \(0.769318\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2445.31 | − | 3090.93i | −1.05627 | − | 1.33516i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1135.82 | − | 2726.97i | −0.482335 | − | 1.15803i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3140.15 | + | 1812.96i | −1.31120 | + | 0.757024i | −0.982296 | − | 0.187338i | \(-0.940014\pi\) |
−0.328909 | + | 0.944362i | \(0.606681\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1659.16i | − | 0.681351i | −0.940181 | − | 0.340676i | \(-0.889344\pi\) | ||
0.940181 | − | 0.340676i | \(-0.110656\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 94.1743 | − | 726.325i | 0.0380414 | − | 0.293396i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 377.337 | − | 653.567i | 0.149959 | − | 0.259736i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −958.141 | + | 553.183i | −0.374686 | + | 0.216325i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −724.267 | − | 2495.34i | −0.278744 | − | 0.960365i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1333.96 | + | 770.160i | −0.505349 | + | 0.291763i | −0.730920 | − | 0.682463i | \(-0.760909\pi\) |
0.225571 | + | 0.974227i | \(0.427575\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1450.05 | − | 2511.55i | 0.540811 | − | 0.936713i | −0.458046 | − | 0.888928i | \(-0.651451\pi\) |
0.998858 | − | 0.0477845i | \(-0.0152161\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 965.302 | − | 7444.95i | 0.354496 | − | 2.73407i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2096.85i | − | 0.758347i | −0.925326 | − | 0.379173i | \(-0.876208\pi\) | ||
0.925326 | − | 0.379173i | \(-0.123792\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3937.78 | − | 2273.48i | 1.40272 | − | 0.809862i | 0.408051 | − | 0.912959i | \(-0.366209\pi\) |
0.994671 | + | 0.103097i | \(0.0328752\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 587.945 | + | 1411.59i | 0.206321 | + | 0.495353i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 149.923 | + | 1021.65i | 0.0518351 | + | 0.353231i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 976.532 | + | 1691.40i | 0.332702 | + | 0.576257i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3234.23 | + | 880.214i | −1.08596 | + | 0.295551i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −535.840 | + | 928.102i | −0.177344 | + | 0.307168i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1506.32 | + | 2609.03i | 0.491467 | + | 0.851245i | 0.999952 | − | 0.00982544i | \(-0.00312758\pi\) |
−0.508485 | + | 0.861071i | \(0.669794\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2486.95 | − | 1900.57i | −0.800013 | − | 0.611384i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5132.26 | − | 8889.34i | 1.62799 | − | 2.81976i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 855.062 | + | 5826.84i | 0.267490 | + | 1.82282i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −417.919 | + | 3223.22i | −0.128951 | + | 0.994545i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1360.19 | + | 785.308i | 0.414012 | + | 0.239030i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −230.173 | − | 132.890i | −0.0691188 | − | 0.0399058i | 0.465042 | − | 0.885288i | \(-0.346039\pi\) |
−0.534161 | + | 0.845383i | \(0.679372\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1508.87 | − | 5544.14i | −0.447072 | − | 1.64271i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1158.84 | −0.338834 | −0.169417 | − | 0.985544i | \(-0.554188\pi\) | ||||
−0.169417 | + | 0.985544i | \(0.554188\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1142.85i | 0.329790i | 0.986311 | + | 0.164895i | \(0.0527285\pi\) | ||||
−0.986311 | + | 0.164895i | \(0.947272\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −89.3383 | − | 5327.97i | −0.0254460 | − | 1.51755i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4943.19 | + | 2853.95i | 1.38987 | + | 0.802440i | 0.993300 | − | 0.115565i | \(-0.0368680\pi\) |
0.396567 | + | 0.918006i | \(0.370201\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1359.31 | + | 2354.40i | 0.377327 | + | 0.653549i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2751.94 | − | 356.812i | −0.754251 | − | 0.0977952i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 310.843 | − | 179.466i | 0.0841288 | − | 0.0485718i | −0.457345 | − | 0.889289i | \(-0.651200\pi\) |
0.541474 | + | 0.840717i | \(0.317866\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4439.82i | − | 1.18670i | −0.804946 | − | 0.593349i | \(-0.797806\pi\) | ||
0.804946 | − | 0.593349i | \(-0.202194\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 457.597 | − | 3760.25i | 0.120802 | − | 0.992677i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1450.64 | + | 6135.01i | −0.378277 | + | 1.59980i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1521.38 | 0.391914 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1408.17 | + | 3380.86i | 0.358390 | + | 0.860454i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3438.88 | 0.864782 | 0.432391 | − | 0.901686i | \(-0.357670\pi\) | ||||
0.432391 | + | 0.901686i | \(0.357670\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6874.12 | −1.70819 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1892.35 | + | 245.359i | 0.464719 | + | 0.0602549i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1821.67 | −0.442150 | −0.221075 | − | 0.975257i | \(-0.570957\pi\) | ||||
−0.221075 | + | 0.975257i | \(0.570957\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −752.395 | + | 110.411i | −0.180508 | + | 0.0264887i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −383.917 | + | 1455.60i | −0.0910493 | + | 0.345209i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4243.16i | − | 0.994845i | −0.867508 | − | 0.497422i | \(-0.834280\pi\) | ||
0.867508 | − | 0.497422i | \(-0.165720\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10478.0 | − | 6049.46i | 2.42889 | − | 1.40232i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 154.489 | + | 370.910i | 0.0354103 | + | 0.0850163i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1538.72 | + | 2665.14i | 0.348763 | + | 0.604075i | 0.986030 | − | 0.166568i | \(-0.0532685\pi\) |
−0.637267 | + | 0.770643i | \(0.719935\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −623.012 | − | 359.696i | −0.139651 | − | 0.0806273i | 0.428547 | − | 0.903520i | \(-0.359026\pi\) |
−0.568197 | + | 0.822892i | \(0.692359\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6486.93 | + | 3891.68i | −1.43812 | + | 0.862766i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 11783.7i | − | 2.58393i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −911.179 | −0.197644 | −0.0988221 | − | 0.995105i | \(-0.531507\pi\) | ||||
−0.0988221 | + | 0.995105i | \(0.531507\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2189.61 | + | 8301.81i | −0.469852 | + | 1.78142i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4142.21 | + | 2391.50i | 0.879372 | + | 0.507705i | 0.870451 | − | 0.492255i | \(-0.163827\pi\) |
0.00892043 | + | 0.999960i | \(0.497161\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3471.59 | − | 2004.33i | −0.729204 | − | 0.421006i | 0.0889266 | − | 0.996038i | \(-0.471656\pi\) |
−0.818131 | + | 0.575032i | \(0.804990\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1706.27 | − | 710.684i | 0.354635 | − | 0.147710i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 726.126 | − | 1829.16i | 0.149344 | − | 0.376209i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2256.89 | − | 3909.05i | 0.459371 | − | 0.795654i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2116.48 | − | 881.538i | 0.426357 | − | 0.177583i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3758.85 | − | 6510.51i | −0.749468 | − | 1.29812i | −0.948078 | − | 0.318038i | \(-0.896976\pi\) |
0.198610 | − | 0.980079i | \(-0.436357\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5224.47 | + | 9049.04i | −1.03112 | + | 1.78595i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2930.63 | − | 7194.56i | 0.572567 | − | 1.40563i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4879.31 | + | 8451.21i | 0.943738 | + | 1.63460i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10233.5 | + | 1501.72i | −1.95964 | + | 0.287568i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3528.55 | − | 4617.21i | 0.669009 | − | 0.875418i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2243.54 | + | 1295.31i | −0.421196 | + | 0.243178i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6149.80i | 1.14328i | 0.820504 | + | 0.571641i | \(0.193693\pi\) | ||||
−0.820504 | + | 0.571641i | \(0.806307\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3363.90 | − | 2570.75i | −0.619305 | − | 0.473284i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1059.67 | − | 1835.41i | 0.193211 | − | 0.334650i | −0.753102 | − | 0.657904i | \(-0.771443\pi\) |
0.946312 | + | 0.323253i | \(0.104777\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −126.231 | + | 72.8795i | −0.0227955 | + | 0.0131610i | −0.511354 | − | 0.859370i | \(-0.670856\pi\) |
0.488559 | + | 0.872531i | \(0.337523\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5457.38 | + | 7394.91i | −0.976155 | + | 1.32272i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2257.86 | − | 1303.58i | 0.400044 | − | 0.230966i | −0.286459 | − | 0.958093i | \(-0.592478\pi\) |
0.686503 | + | 0.727127i | \(0.259145\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1543.64 | + | 2673.67i | −0.270932 | + | 0.469268i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7316.38 | − | 3047.36i | 1.27215 | − | 0.529866i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 386.701i | 0.0666150i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14487.1 | + | 8364.15i | −2.47262 | + | 1.42757i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1045.36 | − | 135.540i | −0.176784 | − | 0.0229216i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1010.75 | − | 2546.16i | 0.169376 | − | 0.426669i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5445.02 | + | 9431.04i | 0.904185 | + | 1.56609i | 0.822008 | + | 0.569476i | \(0.192854\pi\) |
0.0821769 | + | 0.996618i | \(0.473813\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1071.98 | − | 282.735i | −0.176408 | − | 0.0465279i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2704.39 | − | 4684.15i | 0.441065 | − | 0.763947i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1171.50 | + | 2029.09i | 0.189364 | + | 0.327987i | 0.945038 | − | 0.326960i | \(-0.106024\pi\) |
−0.755675 | + | 0.654947i | \(0.772691\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 58.0241 | − | 447.514i | 0.00929628 | − | 0.0716981i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8803.93 | + | 15248.8i | −1.39812 | + | 2.42162i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5755.17 | − | 2689.18i | 0.905976 | − | 0.423329i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9420.15 | + | 7199.04i | 1.47004 | + | 1.12343i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3380.66 | − | 1951.83i | −0.523007 | − | 0.301958i | 0.215157 | − | 0.976579i | \(-0.430974\pi\) |
−0.738164 | + | 0.674621i | \(0.764307\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1985.23 | − | 1146.17i | −0.304490 | − | 0.175797i | 0.339968 | − | 0.940437i | \(-0.389584\pi\) |
−0.644458 | + | 0.764640i | \(0.722917\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10925.4 | + | 1503.77i | −1.66140 | + | 0.228676i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7745.90 | 1.16791 | 0.583956 | − | 0.811785i | \(-0.301504\pi\) | ||||
0.583956 | + | 0.811785i | \(0.301504\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11071.3i | 1.65523i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −989.182 | − | 1648.84i | −0.146647 | − | 0.244442i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5235.74 | + | 3022.86i | 0.769727 | + | 0.444402i | 0.832777 | − | 0.553608i | \(-0.186749\pi\) |
−0.0630502 | + | 0.998010i | \(0.520083\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3242.21 | − | 5615.67i | −0.472694 | − | 0.818731i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5474.51 | − | 7163.55i | 0.791562 | − | 1.03578i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9956.20 | − | 5748.22i | 1.42776 | − | 0.824316i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10933.5i | 1.55510i | 0.628820 | + | 0.777551i | \(0.283538\pi\) | ||||
−0.628820 | + | 0.777551i | \(0.716462\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2020.79 | − | 2036.70i | 0.285090 | − | 0.287334i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11331.4 | − | 4498.24i | −1.58570 | − | 0.629480i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2865.12 | 0.397722 | 0.198861 | − | 0.980028i | \(-0.436276\pi\) | ||||
0.198861 | + | 0.980028i | \(0.436276\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5091.92 | + | 6662.92i | −0.701188 | + | 0.917525i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4382.76 | 0.598737 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2071.78 | −0.280792 | −0.140396 | − | 0.990095i | \(-0.544838\pi\) | ||||
−0.140396 | + | 0.990095i | \(0.544838\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1535.63 | − | 2009.42i | 0.206490 | − | 0.270198i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7428.00 | 0.991001 | 0.495500 | − | 0.868608i | \(-0.334985\pi\) | ||||
0.495500 | + | 0.868608i | \(0.334985\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14782.0 | + | 11694.3i | −1.95678 | + | 1.54805i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −14580.2 | − | 3845.56i | −1.91513 | − | 0.505118i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7584.01i | 0.988496i | 0.869321 | + | 0.494248i | \(0.164556\pi\) | ||||
−0.869321 | + | 0.494248i | \(0.835444\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2148.12 | + | 1240.22i | −0.277839 | + | 0.160410i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2530.27 | + | 3310.94i | −0.324772 | + | 0.424973i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4907.74 | + | 8500.45i | 0.625152 | + | 1.08279i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1031.73 | + | 595.671i | 0.130431 | + | 0.0753044i | 0.563796 | − | 0.825914i | \(-0.309340\pi\) |
−0.433365 | + | 0.901219i | \(0.642674\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1628.37 | − | 904.084i | −0.204312 | − | 0.113436i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6457.05i | 0.804114i | 0.915615 | + | 0.402057i | \(0.131705\pi\) | ||||
−0.915615 | + | 0.402057i | \(0.868295\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24996.4 | 3.08973 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11550.7 | + | 6790.12i | −1.41718 | + | 0.833096i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1969.02 | − | 1136.81i | −0.239805 | − | 0.138451i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1642.41 | − | 948.247i | −0.198563 | − | 0.114640i | 0.397422 | − | 0.917636i | \(-0.369905\pi\) |
−0.595985 | + | 0.802996i | \(0.703238\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3793.46 | − | 2899.03i | −0.455274 | − | 0.347928i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10417.4 | − | 1528.70i | 1.24117 | − | 0.182137i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6477.20 | − | 11218.8i | 0.766153 | − | 1.32702i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −123.237 | + | 950.473i | −0.0144723 | + | 0.111618i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7002.37 | − | 12128.5i | −0.816440 | − | 1.41412i | −0.908289 | − | 0.418342i | \(-0.862611\pi\) |
0.0918495 | − | 0.995773i | \(-0.470722\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4485.43 | − | 7769.00i | 0.519256 | − | 0.899377i | −0.480494 | − | 0.876998i | \(-0.659543\pi\) |
0.999750 | − | 0.0223789i | \(-0.00712403\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2812.90 | − | 2835.04i | 0.323328 | − | 0.325874i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2125.99 | − | 3682.32i | −0.242648 | − | 0.420279i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2426.27 | + | 963.162i | 0.274978 | + | 0.109159i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −22429.6 | − | 2908.19i | −2.52427 | − | 0.327293i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8722.70 | − | 5036.05i | 0.974844 | − | 0.562826i | 0.0741343 | − | 0.997248i | \(-0.476381\pi\) |
0.900709 | + | 0.434422i | \(0.143047\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10574.2i | − | 1.17358i | −0.809738 | − | 0.586791i | \(-0.800391\pi\) | ||
0.809738 | − | 0.586791i | \(-0.199609\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4915.42 | − | 2047.33i | 0.541784 | − | 0.225660i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1201.33 | + | 2080.77i | −0.131505 | + | 0.227773i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7842.45 | − | 4527.84i | 0.852619 | − | 0.492260i | −0.00891464 | − | 0.999960i | \(-0.502838\pi\) |
0.861534 | + | 0.507700i | \(0.169504\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9255.79 | − | 310.486i | 0.999438 | − | 0.0335262i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3071.48 | + | 1773.32i | −0.329414 | + | 0.190187i | −0.655581 | − | 0.755125i | \(-0.727576\pi\) |
0.326167 | + | 0.945312i | \(0.394243\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 710.608 | − | 1230.81i | 0.0756989 | − | 0.131114i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9251.01 | + | 7069.78i | 0.978876 | + | 0.748074i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 200.727i | − | 0.0210977i | −0.999944 | − | 0.0105489i | \(-0.996642\pi\) | ||
0.999944 | − | 0.0105489i | \(-0.00335787\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5095.73 | − | 2942.02i | 0.532037 | − | 0.307172i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6717.59 | − | 8790.16i | 0.696732 | − | 0.911694i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 24869.7 | + | 9872.56i | 2.56244 | + | 1.01722i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4292.02 | + | 7434.00i | 0.439327 | + | 0.760936i | 0.997638 | − | 0.0686955i | \(-0.0218837\pi\) |
−0.558311 | + | 0.829632i | \(0.688550\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −382.226 | − | 2776.99i | −0.0388688 | − | 0.282394i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5807.63 | + | 10059.1i | −0.586742 | + | 1.01627i | 0.407913 | + | 0.913021i | \(0.366257\pi\) |
−0.994656 | + | 0.103247i | \(0.967077\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5426.15 | + | 9398.36i | 0.544653 | + | 0.943367i | 0.998629 | + | 0.0523527i | \(0.0166720\pi\) |
−0.453976 | + | 0.891014i | \(0.649995\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 28034.3 | − | 11676.6i | 2.79583 | − | 1.16450i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3071.32 | + | 5319.68i | −0.304333 | + | 0.527120i | −0.977113 | − | 0.212723i | \(-0.931767\pi\) |
0.672780 | + | 0.739843i | \(0.265100\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5392.45 | + | 791.317i | −0.530917 | + | 0.0779097i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13309.8 | + | 5543.67i | −1.30208 | + | 0.542333i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −26781.2 | − | 15462.1i | −2.60338 | − | 1.50306i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3566.87 | − | 2059.34i | −0.344546 | − | 0.198924i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12617.0 | − | 12518.5i | −1.21110 | − | 1.20164i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15213.6 | −1.45121 | −0.725603 | − | 0.688113i | \(-0.758439\pi\) | ||||
−0.725603 | + | 0.688113i | \(0.758439\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3227.68i | 0.305966i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −200.293 | − | 11945.1i | −0.0188689 | − | 1.12530i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7023.19 | − | 4054.84i | −0.657540 | − | 0.379631i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −780.525 | − | 1351.91i | −0.0726262 | − | 0.125792i | 0.827425 | − | 0.561576i | \(-0.189805\pi\) |
−0.900052 | + | 0.435783i | \(0.856471\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2145.17 | − | 5150.33i | −0.198381 | − | 0.476290i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5107.22 | − | 2948.66i | 0.469421 | − | 0.271020i | −0.246576 | − | 0.969123i | \(-0.579306\pi\) |
0.715997 | + | 0.698103i | \(0.245972\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1114.00i | 0.101769i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −26514.1 | + | 7215.96i | −2.40751 | + | 0.655219i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8749.22 | − | 6921.71i | 0.789651 | − | 0.624710i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11691.6 | −1.04888 | −0.524438 | − | 0.851449i | \(-0.675724\pi\) | ||||
−0.524438 | + | 0.851449i | \(0.675724\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −235.313 | − | 30.5103i | −0.0209840 | − | 0.00272076i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2180.14 | −0.193255 | −0.0966277 | − | 0.995321i | \(-0.530806\pi\) | ||||
−0.0966277 | + | 0.995321i | \(0.530806\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20554.8 | −1.81124 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7955.96 | + | 19101.4i | 0.696916 | + | 1.67322i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1595.05 | −0.138899 | −0.0694494 | − | 0.997585i | \(-0.522124\pi\) | ||||
−0.0694494 | + | 0.997585i | \(0.522124\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10767.1 | − | 4274.24i | −0.932111 | − | 0.370022i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1665.61 | − | 2144.43i | −0.143349 | − | 0.184559i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14975.3i | 1.28134i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7093.16 | − | 4095.24i | 0.603398 | − | 0.348372i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4684.52 | − | 607.389i | −0.396200 | − | 0.0513707i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2974.63 | − | 5152.20i | −0.250136 | − | 0.433248i | 0.713427 | − | 0.700729i | \(-0.247142\pi\) |
−0.963563 | + | 0.267481i | \(0.913809\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12106.0 | + | 6989.39i | 1.01216 | + | 0.584369i | 0.911822 | − | 0.410585i | \(-0.134675\pi\) |
0.100334 | + | 0.994954i | \(0.468009\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20476.4 | − | 343.344i | 1.70222 | − | 0.0285424i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6353.56i | 0.525171i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3244.52 | −0.266665 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14842.2 | + | 3914.64i | 1.21299 | + | 0.319927i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7233.99 | − | 4176.55i | −0.587878 | − | 0.339412i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24278.3 | − | 14017.1i | −1.96195 | − | 1.13273i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2422.60 | − | 18684.5i | 0.194680 | − | 1.50148i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18483.1 | + | 4370.37i | 1.47704 | + | 0.349249i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6174.78 | − | 10695.0i | 0.490710 | − | 0.849935i | −0.509232 | − | 0.860629i | \(-0.670071\pi\) |
0.999943 | + | 0.0106936i | \(0.00340395\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6849.98 | + | 5234.87i | 0.541364 | + | 0.413720i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1864.26 | + | 3229.00i | 0.146525 | + | 0.253789i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8771.44 | − | 15192.6i | 0.685630 | − | 1.18755i | −0.287609 | − | 0.957748i | \(-0.592860\pi\) |
0.973238 | − | 0.229798i | \(-0.0738064\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2701.56 | + | 2680.46i | 0.210018 | + | 0.208377i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 539.540 | + | 934.510i | 0.0417154 | + | 0.0722531i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3649.28 | − | 9192.78i | 0.280620 | − | 0.706902i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1507.76 | + | 3619.95i | 0.115316 | + | 0.276862i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19166.8 | + | 11065.9i | −1.45803 | + | 0.841794i | −0.998914 | − | 0.0465824i | \(-0.985167\pi\) |
−0.459116 | + | 0.888376i | \(0.651834\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43900.6i | 3.32164i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 739.200 | − | 5701.12i | 0.0556311 | − | 0.429058i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4808.10 | − | 8327.88i | 0.359924 | − | 0.623407i | −0.628024 | − | 0.778194i | \(-0.716136\pi\) |
0.987948 | + | 0.154787i | \(0.0494692\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1382.33 | + | 798.086i | −0.102929 | + | 0.0594261i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12587.3 | + | 4882.92i | 0.932309 | + | 0.361664i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9884.02 | − | 5706.54i | 0.728225 | − | 0.420441i | −0.0895477 | − | 0.995983i | \(-0.528542\pi\) |
0.817772 | + | 0.575542i | \(0.195209\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9591.91 | − | 16613.7i | 0.702993 | − | 1.21762i | −0.264418 | − | 0.964408i | \(-0.585180\pi\) |
0.967411 | − | 0.253211i | \(-0.0814868\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1029.14 | − | 7937.30i | 0.0750312 | − | 0.578683i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 26418.5i | − | 1.91605i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9697.32 | − | 5598.75i | 0.699661 | − | 0.403950i | −0.107560 | − | 0.994199i | \(-0.534304\pi\) |
0.807221 | + | 0.590249i | \(0.200970\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5794.06 | + | 13910.9i | 0.415877 | + | 0.998476i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12915.3 | + | 1895.26i | −0.922230 | + | 0.135333i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18225.4 | − | 31567.3i | −1.29471 | − | 2.24251i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 27691.4 | + | 27475.1i | 1.95709 | + | 1.94180i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5285.80 | − | 9155.27i | 0.371666 | − | 0.643745i | −0.618156 | − | 0.786056i | \(-0.712120\pi\) |
0.989822 | + | 0.142311i | \(0.0454532\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3077.18 | + | 5329.84i | 0.215268 | + | 0.372856i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8657.01 | + | 6615.83i | 0.602541 | + | 0.460472i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7667.36 | − | 13280.3i | 0.530963 | − | 0.919655i | −0.468384 | − | 0.883525i | \(-0.655164\pi\) |
0.999347 | − | 0.0361297i | \(-0.0115029\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2509.40 | + | 6321.34i | −0.172900 | + | 0.435546i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3037.97 | + | 23430.5i | −0.208268 | + | 1.60628i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7727.40 | − | 4461.42i | −0.527100 | − | 0.304321i | 0.212735 | − | 0.977110i | \(-0.431763\pi\) |
−0.739835 | + | 0.672789i | \(0.765096\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6221.25 | − | 3591.84i | −0.422246 | − | 0.243784i | 0.273792 | − | 0.961789i | \(-0.411722\pi\) |
−0.696038 | + | 0.718005i | \(0.745055\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7682.91 | − | 2026.38i | −0.518859 | − | 0.136850i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −31890.6 | −2.14303 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 5512.13i | − | 0.368584i | −0.982872 | − | 0.184292i | \(-0.941001\pi\) | ||
0.982872 | − | 0.184292i | \(-0.0589992\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4691.00 | − | 2604.48i | −0.312133 | − | 0.173298i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10069.6 | − | 5813.67i | −0.666729 | − | 0.384936i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12611.1 | − | 21843.0i | −0.830925 | − | 1.43920i | −0.897306 | − | 0.441410i | \(-0.854478\pi\) |
0.0663806 | − | 0.997794i | \(-0.478855\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10064.2 | − | 1304.91i | −0.659881 | − | 0.0855592i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22013.2 | − | 12709.3i | 1.43633 | − | 0.829268i | 0.438741 | − | 0.898613i | \(-0.355424\pi\) |
0.997593 | + | 0.0693457i | \(0.0220912\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10829.0i | − | 0.703155i | −0.936159 | − | 0.351577i | \(-0.885645\pi\) | ||
0.936159 | − | 0.351577i | \(-0.114355\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6570.37 | − | 16129.9i | 0.424573 | − | 1.04231i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1416.92 | + | 207.927i | −0.0911200 | + | 0.0133715i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3060.98 | 0.195903 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2141.10 | − | 5140.54i | −0.136375 | − | 0.327422i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −820.408 | −0.0520061 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25750.8 | 1.62460 | 0.812301 | − | 0.583239i | \(-0.198215\pi\) | ||||
0.812301 | + | 0.583239i | \(0.198215\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15524.2 | − | 2012.85i | −0.974774 | − | 0.126388i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8945.48 | −0.559040 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7746.43 | − | 25825.7i | −0.481828 | − | 1.60636i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15693.3 | − | 4271.02i | 0.971544 | − | 0.264411i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 7576.45i | − | 0.466851i | −0.972375 | − | 0.233426i | \(-0.925006\pi\) | ||
0.972375 | − | 0.233426i | \(-0.0749936\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15581.8 | − | 8996.16i | 0.955655 | − | 0.551748i | 0.0608220 | − | 0.998149i | \(-0.480628\pi\) |
0.894833 | + | 0.446401i | \(0.147294\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20507.4 | + | 49236.0i | 1.25190 | + | 3.00568i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8457.22 | + | 14648.3i | 0.513891 | + | 0.890086i | 0.999870 | + | 0.0161153i | \(0.00512987\pi\) |
−0.485979 | + | 0.873971i | \(0.661537\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27262.3 | + | 15739.9i | 1.64890 | + | 0.951995i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26754.4 | − | 14854.2i | −1.61073 | − | 0.894291i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17449.4i | 1.04571i | 0.852422 | + | 0.522854i | \(0.175133\pi\) | ||||
−0.852422 | + | 0.522854i | \(0.824867\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14739.6 | 0.879271 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11988.7 | − | 11895.1i | −0.711911 | − | 0.706350i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1730.83 | − | 999.298i | −0.102312 | − | 0.0590700i | 0.447971 | − | 0.894048i | \(-0.352147\pi\) |
−0.550283 | + | 0.834978i | \(0.685480\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29006.3 | − | 16746.8i | −1.70683 | − | 0.985440i | −0.938428 | − | 0.345476i | \(-0.887718\pi\) |
−0.768404 | − | 0.639964i | \(-0.778949\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7533.80 | + | 3137.92i | −0.441310 | + | 0.183811i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 956.513 | + | 6518.17i | 0.0557774 | + | 0.380096i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3460.79 | + | 5994.26i | −0.200903 | + | 0.347974i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1274.87 | − | 531.000i | 0.0736762 | − | 0.0306870i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3902.42 | + | 6759.18i | 0.224517 | + | 0.388875i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16342.6 | + | 28306.3i | −0.936051 | + | 1.62129i | −0.163303 | + | 0.986576i | \(0.552215\pi\) |
−0.772749 | + | 0.634712i | \(0.781119\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 27650.1 | + | 11263.0i | 1.57667 | + | 0.642241i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3663.87 | − | 6346.00i | −0.207997 | − | 0.360261i | 0.743087 | − | 0.669195i | \(-0.233361\pi\) |
−0.951083 | + | 0.308934i | \(0.900028\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1186.46 | + | 8085.19i | 0.0670579 | + | 0.456968i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3656.31 | − | 4784.38i | 0.205741 | − | 0.269219i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12311.2 | − | 7107.88i | 0.689715 | − | 0.398207i | −0.113790 | − | 0.993505i | \(-0.536299\pi\) |
0.803505 | + | 0.595298i | \(0.202966\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16887.7i | 0.941962i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4718.36 | − | 3605.85i | −0.262033 | − | 0.200250i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25873.1 | + | 44813.5i | −1.43060 | + | 2.47788i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12403.5 | + | 7161.17i | −0.682854 | + | 0.394246i | −0.800929 | − | 0.598759i | \(-0.795661\pi\) |
0.118076 | + | 0.993005i | \(0.462328\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 22278.8 | + | 16441.6i | 1.22122 | + | 0.901248i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2935.91 | − | 1695.05i | 0.160238 | − | 0.0925135i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1061.59 | − | 1838.73i | 0.0576909 | − | 0.0999236i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −27379.2 | + | 11403.8i | −1.48151 | + | 0.617067i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3371.89i | 0.181675i | 0.995866 | + | 0.0908377i | \(0.0289544\pi\) | ||||
−0.995866 | + | 0.0908377i | \(0.971046\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −688.219 | + | 397.344i | −0.0369227 | + | 0.0213173i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14009.1 | − | 1816.40i | −0.748389 | − | 0.0970351i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12850.7 | + | 16243.6i | 0.683592 | + | 0.864079i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15358.4 | + | 26601.6i | 0.813537 | + | 1.40909i | 0.910374 | + | 0.413787i | \(0.135794\pi\) |
−0.0968372 | + | 0.995300i | \(0.530873\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10155.8 | − | 10235.8i | 0.535688 | − | 0.539905i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19738.1 | + | 34187.4i | −1.03674 | + | 1.79569i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 40000.4 | + | 69282.7i | 2.09221 | + | 3.62381i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −239.814 | + | 1849.58i | −0.0124910 | + | 0.0963372i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5218.17 | + | 9038.14i | −0.270661 | + | 0.468798i | −0.969031 | − | 0.246939i | \(-0.920575\pi\) |
0.698371 | + | 0.715736i | \(0.253909\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11834.4 | − | 9362.45i | 0.611284 | − | 0.483600i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18330.1 | + | 14008.2i | 0.942884 | + | 0.720568i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10275.4 | − | 5932.51i | −0.526371 | − | 0.303901i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22053.0 | − | 12732.3i | −1.12503 | − | 0.649538i | −0.182352 | − | 0.983233i | \(-0.558371\pi\) |
−0.942681 | + | 0.333696i | \(0.891704\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14080.7 | + | 13753.3i | 0.715375 | + | 0.698741i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11158.6 | −0.564590 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 10275.7i | − | 0.517793i | −0.965905 | − | 0.258896i | \(-0.916641\pi\) | ||
0.965905 | − | 0.258896i | \(-0.0833588\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −20751.9 | − | 25345.8i | −1.04142 | − | 1.27197i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14112.1 | − | 8147.60i | −0.705324 | − | 0.407219i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8232.96 | − | 14259.9i | −0.409816 | − | 0.709823i | 0.585053 | − | 0.810995i | \(-0.301074\pi\) |
−0.994869 | + | 0.101173i | \(0.967741\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4800.14 | + | 6281.12i | −0.237972 | + | 0.311394i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34426.3 | + | 19876.0i | −1.69984 | + | 0.981400i | −0.753932 | + | 0.656953i | \(0.771845\pi\) |
−0.945904 | + | 0.324448i | \(0.894822\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 41183.5i | − | 2.02530i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18401.1 | − | 4853.31i | −0.901285 | − | 0.237715i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4101.46 | + | 27949.5i | 0.200085 | + | 1.36349i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18477.7 | 0.897818 | 0.448909 | − | 0.893578i | \(-0.351813\pi\) | ||||
0.448909 | + | 0.893578i | \(0.351813\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10850.1 | + | 14197.7i | −0.525100 | + | 0.687109i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −39131.9 | −1.88630 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14830.5 | 0.712053 | 0.356026 | − | 0.934476i | \(-0.384131\pi\) | ||||
0.356026 | + | 0.934476i | \(0.384131\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 21688.7 | − | 28380.3i | 1.03722 | − | 1.35723i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5974.38 | −0.284587 | −0.142294 | − | 0.989824i | \(-0.545448\pi\) | ||||
−0.142294 | + | 0.989824i | \(0.545448\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1386.22 | − | 3491.99i | 0.0657728 | − | 0.165686i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6983.59 | + | 7038.56i | −0.330055 | + | 0.332653i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 44689.2i | − | 2.10383i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16782.8 | − | 9689.54i | 0.786999 | − | 0.454374i | −0.0519057 | − | 0.998652i | \(-0.516530\pi\) |
0.838905 | + | 0.544278i | \(0.183196\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5747.60 | − | 7520.91i | 0.268476 | − | 0.351308i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8932.67 | + | 15471.8i | 0.415635 | + | 0.719900i | 0.995495 | − | 0.0948156i | \(-0.0302261\pi\) |
−0.579860 | + | 0.814716i | \(0.696893\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −58604.3 | − | 33835.2i | −2.71629 | − | 1.56825i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1918.06 | − | 3454.68i | 0.0885588 | − | 0.159506i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 2056.61i | − | 0.0945903i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33354.9 | 1.52821 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4798.26 | − | 6177.64i | −0.218998 | − | 0.281955i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 44166.3 | + | 25499.5i | 2.00811 | + | 1.15938i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10416.8 | − | 6014.14i | −0.471816 | − | 0.272403i | 0.245184 | − | 0.969477i | \(-0.421152\pi\) |
−0.716999 | + | 0.697074i | \(0.754485\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17518.2 | + | 13387.7i | 0.790449 | + | 0.604075i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1494.91 | + | 593.438i | 0.0671972 | + | 0.0266754i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5539.94 | − | 9595.45i | 0.248082 | − | 0.429691i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8083.70 | + | 62346.0i | −0.360628 | + | 2.78136i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13117.1 | + | 22719.5i | 0.582976 | + | 1.00974i | 0.995124 | + | 0.0986270i | \(0.0314451\pi\) |
−0.412149 | + | 0.911117i | \(0.635222\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1477.71 | − | 2559.47i | 0.0654289 | − | 0.113326i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2018.76 | − | 532.452i | −0.0890506 | − | 0.0234872i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17317.8 | − | 29995.3i | −0.761061 | − | 1.31820i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −33140.6 | + | 26218.3i | −1.45100 | + | 1.14792i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15858.1 | − | 2056.14i | −0.691736 | − | 0.0896895i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24743.3 | + | 14285.5i | −1.07531 | + | 0.620832i | −0.929628 | − | 0.368499i | \(-0.879872\pi\) |
−0.145684 | + | 0.989331i | \(0.546538\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 36790.7i | − | 1.59297i | −0.604661 | − | 0.796483i | \(-0.706692\pi\) | ||
0.604661 | − | 0.796483i | \(-0.293308\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3450.72 | − | 1437.27i | 0.148859 | − | 0.0620014i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9867.24 | + | 17090.6i | −0.424091 | + | 0.734548i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9360.65 | + | 5404.38i | −0.400842 | + | 0.231426i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4400.01 | − | 39060.5i | 0.187728 | − | 1.66653i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23764.4 | − | 13720.4i | 1.01021 | − | 0.583246i | 0.0989586 | − | 0.995092i | \(-0.468449\pi\) |
0.911254 | + | 0.411845i | \(0.135116\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14717.5 | − | 25491.5i | 0.623354 | − | 1.07968i | −0.365503 | − | 0.930810i | \(-0.619103\pi\) |
0.988857 | − | 0.148871i | \(-0.0475638\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 48649.8 | + | 37179.0i | 2.05305 | + | 1.56898i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9108.48i | 0.382990i | 0.981494 | + | 0.191495i | \(0.0613336\pi\) | ||||
−0.981494 | + | 0.191495i | \(0.938666\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 745.006 | − | 430.129i | 0.0312124 | − | 0.0180205i | −0.484313 | − | 0.874895i | \(-0.660930\pi\) |
0.515525 | + | 0.856875i | \(0.327597\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2874.89 | − | 3761.88i | 0.120011 | − | 0.157037i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6564.35 | − | 1968.98i | 0.273039 | − | 0.0818980i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 419.651 | + | 726.856i | 0.0173923 | + | 0.0301244i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −27366.1 | − | 35233.3i | −1.13012 | − | 1.45501i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13869.3 | + | 24022.3i | −0.570704 | + | 0.988488i | 0.425790 | + | 0.904822i | \(0.359996\pi\) |
−0.996494 | + | 0.0836658i | \(0.973337\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10640.2 | − | 18429.4i | −0.436270 | − | 0.755643i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22942.7 | + | 9555.92i | −0.937354 | + | 0.390419i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 36595.3 | − | 63384.9i | 1.48984 | − | 2.58048i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19937.7 | + | 25201.8i | 0.808816 | + | 1.02237i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19228.3 | − | 8008.84i | 0.777285 | − | 0.323749i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4414.47 | − | 2548.70i | −0.177821 | − | 0.102665i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13605.1 | + | 7854.94i | 0.546109 | + | 0.315296i | 0.747551 | − | 0.664204i | \(-0.231229\pi\) |
−0.201442 | + | 0.979500i | \(0.564563\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2449.40 | + | 9286.79i | −0.0979740 | + | 0.371464i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41065.2 | 1.63683 | 0.818414 | − | 0.574629i | \(-0.194854\pi\) | ||||
0.818414 | + | 0.574629i | \(0.194854\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 3839.19i | − | 0.152493i | −0.997089 | − | 0.0762466i | \(-0.975706\pi\) | ||
0.997089 | − | 0.0762466i | \(-0.0242936\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5260.82 | + | 8769.11i | 0.208233 | + | 0.347097i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24681.4 | − | 14249.8i | −0.973540 | − | 0.562074i | −0.0732263 | − | 0.997315i | \(-0.523330\pi\) |
−0.900314 | + | 0.435242i | \(0.856663\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8354.26 | + | 14470.0i | 0.328385 | + | 0.568780i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9018.04 | + | 21651.3i | 0.353251 | + | 0.848117i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25609.5 | − | 14785.7i | 0.999705 | − | 0.577180i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23132.9i | 0.899919i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3038.26 | + | 11519.4i | −0.117789 | + | 0.446589i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18544.3 | − | 23440.5i | −0.716472 | − | 0.905640i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4008.65 | −0.154347 | −0.0771737 | − | 0.997018i | \(-0.524590\pi\) | ||||
−0.0771737 | + | 0.997018i | \(0.524590\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 38738.8 | + | 5022.82i | 1.48649 | + | 0.192737i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20416.0 | 0.780742 | 0.390371 | − | 0.920658i | \(-0.372347\pi\) | ||||
0.390371 | + | 0.920658i | \(0.372347\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16822.4 | 0.641133 | 0.320566 | − | 0.947226i | \(-0.396127\pi\) | ||||
0.320566 | + | 0.947226i | \(0.396127\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20875.8 | − | 50120.5i | −0.792918 | − | 1.90371i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31455.3 | 1.19072 | 0.595358 | − | 0.803461i | \(-0.297010\pi\) | ||||
0.595358 | + | 0.803461i | \(0.297010\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5592.64 | + | 7069.24i | 0.210991 | + | 0.266698i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20456.8 | + | 34799.1i | 0.769167 | + | 1.30843i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 2862.77i | − | 0.107278i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −57714.4 | + | 33321.4i | −2.15551 | + | 1.24448i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −50286.3 | − | 6520.06i | −1.87181 | − | 0.242696i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8864.71 | + | 15354.1i | 0.328871 | + | 0.569621i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11390.6 | − | 6576.38i | −0.421173 | − | 0.243164i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 26088.1 | − | 46988.0i | 0.961415 | − | 1.73163i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 30494.6i | − | 1.12008i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −216.082 | −0.00791058 | −0.00395529 | − | 0.999992i | \(-0.501259\pi\) | ||||
−0.00395529 | + | 0.999992i | \(0.501259\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7929.48 | + | 29135.8i | 0.289333 | + | 1.06312i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9169.28 | + | 5293.88i | 0.333471 | + | 0.192529i | 0.657381 | − | 0.753558i | \(-0.271664\pi\) |
−0.323910 | + | 0.946088i | \(0.604998\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33799.3 | − | 19514.0i | −1.22518 | − | 0.707361i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1730.88 | − | 13349.5i | 0.0625368 | − | 0.482318i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9215.04 | − | 11648.1i | −0.331851 | − | 0.419469i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14001.8 | + | 24251.8i | −0.502586 | + | 0.870504i | 0.497410 | + | 0.867516i | \(0.334285\pi\) |
−0.999996 | + | 0.00298831i | \(0.999049\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25389.9 | − | 19403.4i | −0.908390 | − | 0.694207i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23675.6 | − | 41007.4i | −0.844304 | − | 1.46238i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4368.99 | − | 7567.32i | 0.155299 | − | 0.268986i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 21227.1 | − | 5777.07i | 0.752091 | − | 0.204686i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13648.2 | + | 23639.4i | 0.482007 | + | 0.834860i | 0.999787 | − | 0.0206539i | \(-0.00657480\pi\) |
−0.517780 | + | 0.855514i | \(0.673241\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4553.04 | − | 4831.00i | 0.160279 | − | 0.170064i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4234.21 | + | 10165.9i | 0.148577 | + | 0.356716i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17610.2 | + | 10167.2i | −0.615951 | + | 0.355620i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6443.03i | 0.224637i | 0.993672 | + | 0.112318i | \(0.0358277\pi\) | ||||
−0.993672 | + | 0.112318i | \(0.964172\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 97.3864 | − | 751.098i | 0.00338454 | − | 0.0261035i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17839.1 | + | 30898.2i | −0.617999 | + | 1.07041i | 0.371851 | + | 0.928292i | \(0.378723\pi\) |
−0.989850 | + | 0.142114i | \(0.954610\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11424.5 | − | 6595.91i | 0.394519 | − | 0.227776i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13311.7 | − | 45863.1i | −0.458232 | − | 1.57876i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4451.12 | + | 2569.86i | −0.152737 | + | 0.0881828i | −0.574421 | − | 0.818560i | \(-0.694773\pi\) |
0.421684 | + | 0.906743i | \(0.361439\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24584.7 | + | 42581.9i | −0.840940 | + | 1.45655i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1741.93 | + | 13434.7i | −0.0593962 | + | 0.458097i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 12018.0i | − | 0.408502i | −0.978919 | − | 0.204251i | \(-0.934524\pi\) | ||
0.978919 | − | 0.204251i | \(-0.0654758\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24517.5 | + | 14155.2i | −0.830751 | + | 0.479634i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6168.05 | − | 14808.8i | −0.208343 | − | 0.500210i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13345.6 | − | 10558.0i | 0.449377 | − | 0.355512i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35663.1 | + | 61770.2i | 1.19711 | + | 2.07345i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10502.9 | + | 39821.1i | −0.351454 | + | 1.33252i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26651.2 | − | 46161.2i | 0.889048 | − | 1.53988i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7474.18 | + | 12945.7i | 0.248556 | + | 0.430511i | 0.963125 | − | 0.269053i | \(-0.0867108\pi\) |
−0.714570 | + | 0.699564i | \(0.753377\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1596.53 | − | 1220.09i | −0.0529286 | − | 0.0404489i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21188.3 | − | 36699.3i | 0.700274 | − | 1.21291i | −0.268096 | − | 0.963392i | \(-0.586395\pi\) |
0.968370 | − | 0.249518i | \(-0.0802721\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3175.03 | − | 1260.40i | −0.104611 | − | 0.0415278i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11176.7 | − | 86201.2i | 0.367120 | − | 2.83143i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13715.1 | + | 7918.44i | 0.449116 | + | 0.259297i | 0.707457 | − | 0.706757i | \(-0.249842\pi\) |
−0.258341 | + | 0.966054i | \(0.583176\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3708.09 | − | 2140.87i | −0.121053 | − | 0.0698901i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3857.82 | − | 3888.19i | 0.125556 | − | 0.126545i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14254.8 | 0.462519 | 0.231260 | − | 0.972892i | \(-0.425715\pi\) | ||||
0.231260 | + | 0.972892i | \(0.425715\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 38539.1i | − | 1.24666i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7322.95 | + | 12206.4i | 0.236162 | + | 0.393652i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −60042.4 | − | 34665.5i | −1.93047 | − | 1.11456i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1262.03 | + | 2185.91i | 0.0404539 | + | 0.0700682i | 0.885543 | − | 0.464557i | \(-0.153786\pi\) |
−0.845090 | + | 0.534625i | \(0.820453\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −56116.5 | − | 7275.99i | −1.79336 | − | 0.232524i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 72374.5 | − | 41785.5i | 2.30596 | − | 1.33134i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 50024.6i | − | 1.58906i | −0.607224 | − | 0.794531i | \(-0.707717\pi\) | ||
0.607224 | − | 0.794531i | \(-0.292283\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4549.52 | − | 3533.67i | 0.144085 | − | 0.111912i |
(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.bm.a.173.7 | yes | 48 | |
3.2 | odd | 2 | 756.4.bm.a.89.2 | 48 | |||
7.3 | odd | 6 | 252.4.w.a.101.2 | yes | 48 | ||
9.4 | even | 3 | 756.4.w.a.341.2 | 48 | |||
9.5 | odd | 6 | 252.4.w.a.5.2 | ✓ | 48 | ||
21.17 | even | 6 | 756.4.w.a.521.2 | 48 | |||
63.31 | odd | 6 | 756.4.bm.a.17.2 | 48 | |||
63.59 | even | 6 | inner | 252.4.bm.a.185.7 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.w.a.5.2 | ✓ | 48 | 9.5 | odd | 6 | ||
252.4.w.a.101.2 | yes | 48 | 7.3 | odd | 6 | ||
252.4.bm.a.173.7 | yes | 48 | 1.1 | even | 1 | trivial | |
252.4.bm.a.185.7 | yes | 48 | 63.59 | even | 6 | inner | |
756.4.w.a.341.2 | 48 | 9.4 | even | 3 | |||
756.4.w.a.521.2 | 48 | 21.17 | even | 6 | |||
756.4.bm.a.17.2 | 48 | 63.31 | odd | 6 | |||
756.4.bm.a.89.2 | 48 | 3.2 | odd | 2 |