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 | 209.21 | ||
Character | \(\chi\) | \(=\) | 252.209 |
Dual form | 252.4.x.a.41.21 |
$q$-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 | ||||||||
\(3\) | 4.66323 | + | 2.29222i | 0.897439 | + | 0.441138i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.16485 | + | 8.94579i | 0.461958 | + | 0.800135i | 0.999059 | − | 0.0433831i | \(-0.0138136\pi\) |
−0.537100 | + | 0.843518i | \(0.680480\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −17.2289 | − | 6.79448i | −0.930273 | − | 0.366867i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 16.4915 | + | 21.3783i | 0.610794 | + | 0.791789i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 27.1307 | + | 15.6639i | 0.743656 | + | 0.429350i | 0.823397 | − | 0.567466i | \(-0.192076\pi\) |
−0.0797412 | + | 0.996816i | \(0.525409\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −39.0052 | + | 22.5196i | −0.832161 | + | 0.480448i | −0.854592 | − | 0.519300i | \(-0.826193\pi\) |
0.0224312 | + | 0.999748i | \(0.492859\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.57919 | + | 53.5552i | 0.0616095 | + | 0.921860i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 62.4900 | 0.891532 | 0.445766 | − | 0.895150i | \(-0.352931\pi\) | ||||
0.445766 | + | 0.895150i | \(0.352931\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 132.928i | 1.60504i | 0.596624 | + | 0.802521i | \(0.296508\pi\) | ||||
−0.596624 | + | 0.802521i | \(0.703492\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −64.7679 | − | 71.1767i | −0.673025 | − | 0.739620i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −58.8009 | + | 33.9487i | −0.533080 | + | 0.307774i | −0.742270 | − | 0.670101i | \(-0.766251\pi\) |
0.209190 | + | 0.977875i | \(0.432917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.14862 | − | 15.8459i | 0.0731889 | − | 0.126767i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.8997 | + | 137.494i | 0.198863 | + | 0.980027i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −116.665 | − | 67.3568i | −0.747043 | − | 0.431305i | 0.0775817 | − | 0.996986i | \(-0.475280\pi\) |
−0.824624 | + | 0.565681i | \(0.808613\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −25.9914 | + | 15.0061i | −0.150587 | + | 0.0869413i | −0.573400 | − | 0.819275i | \(-0.694376\pi\) |
0.422813 | + | 0.906217i | \(0.361043\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 90.6116 | + | 135.234i | 0.477983 | + | 0.713370i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −28.2028 | − | 189.219i | −0.136204 | − | 0.913822i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 40.4778 | 0.179852 | 0.0899259 | − | 0.995948i | \(-0.471337\pi\) | ||||
0.0899259 | + | 0.995948i | \(0.471337\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −233.510 | + | 15.6059i | −0.958758 | + | 0.0640754i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 39.7514 | + | 68.8515i | 0.151418 | + | 0.262263i | 0.931749 | − | 0.363103i | \(-0.118283\pi\) |
−0.780331 | + | 0.625367i | \(0.784949\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 161.452 | − | 279.643i | 0.572586 | − | 0.991749i | −0.423713 | − | 0.905797i | \(-0.639273\pi\) |
0.996299 | − | 0.0859521i | \(-0.0273932\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −106.070 | + | 257.945i | −0.351377 | + | 0.854492i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −171.268 | + | 296.644i | −0.531531 | + | 0.920638i | 0.467792 | + | 0.883839i | \(0.345050\pi\) |
−0.999323 | + | 0.0367994i | \(0.988284\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 250.670 | + | 234.123i | 0.730817 | + | 0.682574i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 291.405 | + | 143.241i | 0.800096 | + | 0.393289i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 64.9125i | − | 0.168234i | −0.996456 | − | 0.0841172i | \(-0.973193\pi\) | ||
0.996456 | − | 0.0841172i | \(-0.0268070\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 323.607i | 0.793367i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −304.700 | + | 619.874i | −0.708045 | + | 1.44043i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 79.3800 | + | 137.490i | 0.175159 | + | 0.303385i | 0.940216 | − | 0.340578i | \(-0.110623\pi\) |
−0.765057 | + | 0.643962i | \(0.777289\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 493.640 | + | 285.003i | 1.03613 | + | 0.598212i | 0.918736 | − | 0.394873i | \(-0.129212\pi\) |
0.117397 | + | 0.993085i | \(0.462545\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −138.875 | − | 480.376i | −0.277724 | − | 0.960661i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −402.912 | − | 232.621i | −0.768847 | − | 0.443894i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 150.833 | + | 261.251i | 0.275033 | + | 0.476372i | 0.970144 | − | 0.242531i | \(-0.0779778\pi\) |
−0.695110 | + | 0.718903i | \(0.744644\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −352.020 | + | 23.5261i | −0.614178 | + | 0.0410465i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 719.100i | − | 1.20199i | −0.799252 | − | 0.600996i | \(-0.794771\pi\) | ||
0.799252 | − | 0.600996i | \(-0.205229\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 558.706i | − | 0.895775i | −0.894090 | − | 0.447888i | \(-0.852176\pi\) | ||
0.894090 | − | 0.447888i | \(-0.147824\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 78.9843 | − | 52.9223i | 0.121604 | − | 0.0814792i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −361.004 | − | 454.211i | −0.534289 | − | 0.672236i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 456.676 | − | 790.986i | 0.650381 | − | 1.12649i | −0.332650 | − | 0.943050i | \(-0.607943\pi\) |
0.983031 | − | 0.183442i | \(-0.0587239\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −185.064 | + | 705.119i | −0.253860 | + | 0.967241i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −352.348 | + | 610.285i | −0.465967 | + | 0.807078i | −0.999245 | − | 0.0388620i | \(-0.987627\pi\) |
0.533278 | + | 0.845940i | \(0.320960\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 322.751 | + | 559.022i | 0.411851 | + | 0.713346i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −389.641 | − | 581.524i | −0.480160 | − | 0.716619i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 700.133 | 0.833865 | 0.416932 | − | 0.908938i | \(-0.363105\pi\) | ||||
0.416932 | + | 0.908938i | \(0.363105\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 825.026 | − | 122.969i | 0.950398 | − | 0.141656i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −155.601 | + | 10.3991i | −0.173496 | + | 0.0115950i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1189.15 | + | 686.554i | −1.28425 | + | 0.741463i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −202.787 | − | 117.079i | −0.212267 | − | 0.122552i | 0.390098 | − | 0.920773i | \(-0.372441\pi\) |
−0.602364 | + | 0.798221i | \(0.705775\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 112.557 | + | 838.329i | 0.114266 | + | 0.851063i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 938.098 | − | 1624.83i | 0.924200 | − | 1.60076i | 0.131358 | − | 0.991335i | \(-0.458066\pi\) |
0.792843 | − | 0.609427i | \(-0.208600\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −524.507 | + | 302.824i | −0.501759 | + | 0.289691i | −0.729440 | − | 0.684045i | \(-0.760219\pi\) |
0.227681 | + | 0.973736i | \(0.426886\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 302.214 | − | 947.017i | 0.280887 | − | 0.880184i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1299.63i | − | 1.17420i | −0.809513 | − | 0.587102i | \(-0.800269\pi\) | ||
0.809513 | − | 0.587102i | \(-0.199731\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2079.24 | 1.82711 | 0.913554 | − | 0.406717i | \(-0.133326\pi\) | ||||
0.913554 | + | 0.406717i | \(0.133326\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 188.758 | + | 92.7841i | 0.161406 | + | 0.0793395i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1090.53 | − | 629.616i | 0.907860 | − | 0.524153i | 0.0281181 | − | 0.999605i | \(-0.491049\pi\) |
0.879742 | + | 0.475451i | \(0.157715\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −607.396 | − | 350.680i | −0.492522 | − | 0.284358i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1124.68 | − | 462.483i | −0.888693 | − | 0.365441i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1076.63 | − | 424.587i | −0.829368 | − | 0.327074i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −174.783 | − | 302.734i | −0.131317 | − | 0.227448i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 27.5473 | + | 412.190i | 0.0201940 | + | 0.302162i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1480.22 | 1.05916 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1015.62 | −0.709623 | −0.354811 | − | 0.934938i | \(-0.615455\pi\) | ||||
−0.354811 | + | 0.934938i | \(0.615455\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1393.89 | − | 933.957i | 0.951359 | − | 0.637445i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1353.80 | − | 2344.85i | −0.902915 | − | 1.56390i | −0.823691 | − | 0.567039i | \(-0.808089\pi\) |
−0.0792242 | − | 0.996857i | \(-0.525244\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 903.177 | − | 2290.21i | 0.588837 | − | 1.49313i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1085.89 | + | 959.721i | −0.692288 | + | 0.611849i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2713.91 | − | 1566.88i | −1.69245 | − | 0.977135i | −0.952533 | − | 0.304435i | \(-0.901532\pi\) |
−0.739915 | − | 0.672700i | \(-0.765134\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 86.5871 | − | 49.9911i | 0.0528361 | − | 0.0305049i | −0.473349 | − | 0.880875i | \(-0.656955\pi\) |
0.526185 | + | 0.850370i | \(0.323622\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1478.63 | + | 990.737i | −0.883145 | + | 0.591738i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1410.98 | −0.825121 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1391.55i | − | 0.796980i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 632.272 | + | 1666.36i | 0.354754 | + | 0.934960i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2280.20 | − | 1316.47i | 1.25370 | − | 0.723823i | 0.281856 | − | 0.959457i | \(-0.409050\pi\) |
0.971842 | + | 0.235634i | \(0.0757167\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −944.432 | + | 1635.80i | −0.508985 | + | 0.881588i | 0.490961 | + | 0.871182i | \(0.336646\pi\) |
−0.999946 | + | 0.0104066i | \(0.996687\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1030.55 | + | 1335.93i | 0.544543 | + | 0.705905i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −268.483 | − | 155.009i | −0.139130 | − | 0.0803266i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1110.41 | − | 641.097i | 0.564462 | − | 0.325892i | −0.190472 | − | 0.981693i | \(-0.561002\pi\) |
0.754935 | + | 0.655800i | \(0.227669\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 148.794 | − | 302.702i | 0.0742146 | − | 0.150980i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1243.74 | − | 185.378i | 0.608822 | − | 0.0907442i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3558.63 | 1.71002 | 0.855011 | − | 0.518610i | \(-0.173550\pi\) | ||||
0.855011 | + | 0.518610i | \(0.173550\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −741.779 | + | 1509.06i | −0.349984 | + | 0.711999i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −471.603 | − | 816.841i | −0.218526 | − | 0.378497i | 0.735832 | − | 0.677164i | \(-0.236791\pi\) |
−0.954357 | + | 0.298667i | \(0.903458\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −84.2309 | + | 145.892i | −0.0383390 | + | 0.0664052i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2841.78 | + | 2192.18i | −1.27085 | + | 0.980351i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −489.793 | + | 848.347i | −0.215250 | + | 0.372824i | −0.953350 | − | 0.301867i | \(-0.902390\pi\) |
0.738100 | + | 0.674692i | \(0.235723\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −265.285 | + | 210.847i | −0.114592 | + | 0.0910773i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 55.0095 | + | 823.105i | 0.0233602 | + | 0.349539i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3739.96i | 1.56166i | 0.624742 | + | 0.780831i | \(0.285204\pi\) | ||||
−0.624742 | + | 0.780831i | \(0.714796\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1540.52i | 0.632631i | 0.948654 | + | 0.316316i | \(0.102446\pi\) | ||||
−0.948654 | + | 0.316316i | \(0.897554\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1648.67 | + | 2460.57i | 0.665972 | + | 0.993936i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 209.062 | + | 362.106i | 0.0830840 | + | 0.143906i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1695.40 | + | 978.838i | 0.662993 | + | 0.382779i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 453.520 | − | 2558.43i | 0.174543 | − | 0.984649i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −649.672 | − | 375.088i | −0.246118 | − | 0.142097i | 0.371867 | − | 0.928286i | \(-0.378718\pi\) |
−0.617986 | + | 0.786189i | \(0.712051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2026.03 | + | 3509.19i | 0.755632 | + | 1.30879i | 0.945060 | + | 0.326898i | \(0.106003\pi\) |
−0.189428 | + | 0.981895i | \(0.560663\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1345.65 | − | 2008.33i | −0.494175 | − | 0.737536i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 807.631i | − | 0.292088i | −0.989278 | − | 0.146044i | \(-0.953346\pi\) | ||
0.989278 | − | 0.146044i | \(-0.0466541\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4386.10i | 1.56243i | 0.624265 | + | 0.781213i | \(0.285399\pi\) | ||||
−0.624265 | + | 0.781213i | \(0.714601\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 104.526 | + | 1564.02i | 0.0366801 | + | 0.548842i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1552.36 | + | 1953.17i | 0.536722 | + | 0.675297i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −410.621 | + | 711.216i | −0.139897 | + | 0.242310i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1695.48 | − | 697.201i | −0.569295 | − | 0.234100i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2082.17 | + | 3606.43i | −0.689124 | + | 1.19360i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2132.63 | − | 3693.82i | −0.695811 | − | 1.20518i | −0.969907 | − | 0.243478i | \(-0.921712\pi\) |
0.274095 | − | 0.961702i | \(-0.411622\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1648.34 | − | 3353.33i | 0.530244 | − | 1.07871i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3335.50 | 1.05804 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 549.762 | − | 81.9413i | 0.171983 | − | 0.0256338i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1280.68 | − | 2605.38i | 0.395161 | − | 0.803904i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2437.43 | + | 1407.25i | −0.741898 | + | 0.428335i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1771.94 | − | 1023.03i | −0.532097 | − | 0.307206i | 0.209773 | − | 0.977750i | \(-0.432727\pi\) |
−0.741870 | + | 0.670544i | \(0.766061\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 489.632 | − | 65.7394i | 0.145076 | − | 0.0194784i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2797.06 | + | 4844.65i | −0.817830 | + | 1.41652i | 0.0894471 | + | 0.995992i | \(0.471490\pi\) |
−0.907278 | + | 0.420532i | \(0.861843\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −318.820 | + | 184.071i | −0.0920009 | + | 0.0531168i | −0.545295 | − | 0.838244i | \(-0.683582\pi\) |
0.453294 | + | 0.891361i | \(0.350249\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −642.293 | − | 2945.59i | −0.182943 | − | 0.838986i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 3900.42i | − | 1.09667i | −0.836258 | − | 0.548336i | \(-0.815261\pi\) | ||
0.836258 | − | 0.548336i | \(-0.184739\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3538.29 | −0.982180 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3942.70 | − | 2641.75i | 1.08062 | − | 0.724051i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2327.57 | + | 1343.82i | −0.629949 | + | 0.363701i | −0.780732 | − | 0.624866i | \(-0.785154\pi\) |
0.150783 | + | 0.988567i | \(0.451820\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2125.83 | + | 1227.35i | 0.568203 | + | 0.328052i | 0.756431 | − | 0.654073i | \(-0.226941\pi\) |
−0.188228 | + | 0.982125i | \(0.560274\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2479.28 | + | 2863.92i | −0.654511 | + | 0.756053i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −799.738 | + | 3451.65i | −0.208544 | + | 0.900073i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2993.49 | − | 5184.88i | −0.771139 | − | 1.33565i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3041.99 | + | 2038.24i | −0.774210 | + | 0.518748i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3096.36 | 0.778648 | 0.389324 | − | 0.921101i | \(-0.372709\pi\) | ||||
0.389324 | + | 0.921101i | \(0.372709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2127.08 | −0.528571 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 223.663 | + | 3346.67i | 0.0549268 | + | 0.821868i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1311.10 | − | 2270.89i | −0.318227 | − | 0.551185i | 0.661892 | − | 0.749600i | \(-0.269754\pi\) |
−0.980118 | + | 0.198415i | \(0.936421\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −697.389 | − | 275.026i | −0.167311 | − | 0.0659817i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −484.008 | − | 3604.92i | −0.114787 | − | 0.854939i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6179.60 | + | 3567.79i | 1.44886 | + | 0.836500i | 0.998414 | − | 0.0563032i | \(-0.0179313\pi\) |
0.450447 | + | 0.892803i | \(0.351265\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 580.693 | − | 335.263i | 0.134610 | − | 0.0777173i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3264.88 | + | 1604.86i | 0.748343 | + | 0.367849i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3846.62 | 0.871869 | 0.435934 | − | 0.899978i | \(-0.356418\pi\) | ||||
0.435934 | + | 0.899978i | \(0.356418\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 446.364i | 0.100054i | 0.998748 | + | 0.0500271i | \(0.0159308\pi\) | ||||
−0.998748 | + | 0.0500271i | \(0.984069\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4129.16 | + | 1317.71i | 0.915414 | + | 0.292129i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 496.417 | − | 286.606i | 0.108855 | − | 0.0628473i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3405.06 | + | 5897.74i | −0.738593 | + | 1.27928i | 0.214535 | + | 0.976716i | \(0.431176\pi\) |
−0.953129 | + | 0.302565i | \(0.902157\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −749.441 | − | 308.179i | −0.160817 | − | 0.0661297i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2970.96 | + | 1715.29i | 0.630722 | + | 0.364147i | 0.781031 | − | 0.624492i | \(-0.214694\pi\) |
−0.150310 | + | 0.988639i | \(0.548027\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 275.171 | − | 158.870i | 0.0577993 | − | 0.0333705i | −0.470822 | − | 0.882228i | \(-0.656043\pi\) |
0.528621 | + | 0.848858i | \(0.322709\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7119.00 | + | 475.774i | −1.47962 | + | 0.0988857i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −217.064 | − | 1456.33i | −0.0446441 | − | 0.299527i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1008.00 | −0.205171 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −677.270 | − | 1010.80i | −0.136434 | − | 0.203622i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3701.79 | − | 6411.69i | −0.738091 | − | 1.27841i | −0.953354 | − | 0.301856i | \(-0.902394\pi\) |
0.215262 | − | 0.976556i | \(-0.430939\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −819.972 | + | 1420.23i | −0.161833 | + | 0.280302i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1396.76 | + | 4167.33i | −0.272889 | + | 0.814185i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1529.03 | − | 2648.35i | 0.295739 | − | 0.512235i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4681.67 | + | 3720.96i | −0.896502 | + | 0.712534i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8099.04 | − | 5426.65i | 1.53557 | − | 1.02889i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5887.99i | 1.10540i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9692.73i | − | 1.80193i | −0.433888 | − | 0.900967i | \(-0.642859\pi\) | ||
0.433888 | − | 0.900967i | \(-0.357141\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3140.03 | + | 209.854i | −0.578092 | + | 0.0386348i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3957.20 | − | 6854.07i | −0.721518 | − | 1.24971i | −0.960391 | − | 0.278655i | \(-0.910111\pi\) |
0.238873 | − | 0.971051i | \(-0.423222\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4644.88 | + | 2681.72i | 0.838799 | + | 0.484281i | 0.856856 | − | 0.515556i | \(-0.172415\pi\) |
−0.0180566 | + | 0.999837i | \(0.505748\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3580.07 | − | 3723.42i | 0.640362 | − | 0.666002i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3741.29 | + | 2160.03i | 0.662876 | + | 0.382712i | 0.793372 | − | 0.608737i | \(-0.208324\pi\) |
−0.130496 | + | 0.991449i | \(0.541657\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2110.14 | − | 3654.88i | −0.370362 | − | 0.641485i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2979.04 | − | 6060.47i | 0.517986 | − | 1.05378i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8306.67i | 1.43095i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 824.095i | 0.140654i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9695.97 | + | 4766.07i | 1.63972 | + | 0.806007i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4966.29 | − | 3947.18i | 0.832221 | − | 0.661444i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 371.714 | − | 643.828i | 0.0617259 | − | 0.106912i | −0.833511 | − | 0.552503i | \(-0.813673\pi\) |
0.895237 | + | 0.445590i | \(0.147006\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 667.538 | + | 865.348i | 0.109852 | + | 0.142405i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1558.06 | + | 2698.65i | −0.254108 | + | 0.440128i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4874.39 | + | 8442.69i | 0.787908 | + | 1.36470i | 0.927246 | + | 0.374452i | \(0.122169\pi\) |
−0.139338 | + | 0.990245i | \(0.544497\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6528.60 | − | 436.317i | 1.04597 | − | 0.0699041i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −940.219 | −0.149313 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2728.03 | − | 5736.85i | −0.429445 | − | 0.903093i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2028.59 | − | 3027.59i | −0.316567 | − | 0.472464i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2953.16 | + | 1705.01i | −0.456870 | + | 0.263774i | −0.710727 | − | 0.703468i | \(-0.751634\pi\) |
0.253857 | + | 0.967242i | \(0.418301\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8157.38 | − | 4709.67i | −1.25116 | − | 0.722357i | −0.279820 | − | 0.960053i | \(-0.590275\pi\) |
−0.971340 | + | 0.237695i | \(0.923608\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4184.55 | − | 4734.69i | −0.636338 | − | 0.719997i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1363.14 | + | 2361.03i | −0.205532 | + | 0.355992i | −0.950302 | − | 0.311329i | \(-0.899226\pi\) |
0.744770 | + | 0.667321i | \(0.232559\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6432.91 | − | 3714.04i | 0.961756 | − | 0.555270i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4047.35 | − | 4447.83i | −0.600023 | − | 0.659395i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8978.19i | 1.31992i | 0.751302 | + | 0.659959i | \(0.229426\pi\) | ||||
−0.751302 | + | 0.659959i | \(0.770574\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10810.9 | −1.57616 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −121.123 | − | 1812.36i | −0.0175133 | − | 0.262050i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4998.06 | − | 2885.63i | 0.716742 | − | 0.413811i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6601.74 | − | 3811.52i | −0.938987 | − | 0.542124i | −0.0493444 | − | 0.998782i | \(-0.515713\pi\) |
−0.889643 | + | 0.456657i | \(0.849047\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −816.370 | + | 1985.28i | −0.115172 | + | 0.280080i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −441.047 | + | 1118.37i | −0.0617197 | + | 0.156504i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1255.32 | − | 2174.28i | −0.174258 | − | 0.301823i | 0.765646 | − | 0.643262i | \(-0.222419\pi\) |
−0.939904 | + | 0.341438i | \(0.889086\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6902.60 | + | 3392.99i | 0.950530 | + | 0.467235i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6067.41 | 0.828879 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7234.68 | −0.980529 | −0.490265 | − | 0.871574i | \(-0.663100\pi\) | ||||
−0.490265 | + | 0.871574i | \(0.663100\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4736.09 | − | 2328.04i | −0.636844 | − | 0.313042i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6219.05 | − | 10771.7i | −0.829710 | − | 1.43710i | −0.898266 | − | 0.439452i | \(-0.855173\pi\) |
0.0685562 | − | 0.997647i | \(-0.478161\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2198.74 | − | 5575.40i | 0.291060 | − | 0.738048i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8640.88 | − | 1160.15i | 1.13499 | − | 0.152387i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2593.05 | − | 1497.10i | −0.337976 | − | 0.195131i | 0.321400 | − | 0.946943i | \(-0.395846\pi\) |
−0.659377 | + | 0.751813i | \(0.729180\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3674.47 | + | 2121.46i | −0.475258 | + | 0.274390i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −938.168 | − | 14037.8i | −0.120418 | − | 1.80181i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9434.66 | 1.20180 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3404.67i | 0.430417i | 0.976568 | + | 0.215208i | \(0.0690430\pi\) | ||||
−0.976568 | + | 0.215208i | \(0.930957\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9461.38 | − | 8609.48i | 1.18712 | − | 1.08023i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2674.32 | − | 1544.02i | 0.333040 | − | 0.192281i | −0.324150 | − | 0.946006i | \(-0.605078\pi\) |
0.657190 | + | 0.753725i | \(0.271745\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 675.866 | − | 1170.63i | 0.0835416 | − | 0.144698i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7263.67 | + | 1986.29i | −0.891196 | + | 0.243703i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1098.19 | + | 634.041i | 0.133748 | + | 0.0772193i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8924.66 | − | 5152.66i | 1.07896 | − | 0.622940i | 0.148347 | − | 0.988935i | \(-0.452605\pi\) |
0.930617 | + | 0.365995i | \(0.119271\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9063.98 | − | 13527.6i | −1.08782 | − | 1.62352i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −433.456 | − | 2908.15i | −0.0516440 | − | 0.346491i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7279.31 | −0.861029 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 518.366 | − | 34.6433i | 0.0608741 | − | 0.00406832i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5734.36 | + | 9932.20i | 0.668596 | + | 1.15804i | 0.978297 | + | 0.207208i | \(0.0664378\pi\) |
−0.309701 | + | 0.950834i | \(0.600229\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3002.26 | + | 5200.07i | −0.347557 | + | 0.601986i | −0.985815 | − | 0.167837i | \(-0.946322\pi\) |
0.638258 | + | 0.769822i | \(0.279655\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9166.20 | + | 1230.68i | −1.05361 | + | 0.141460i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 571.697 | − | 990.208i | 0.0652503 | − | 0.113017i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6568.43 | − | 8264.32i | −0.744422 | − | 0.936624i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6579.74 | − | 3234.29i | −0.740496 | − | 0.363992i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8312.17i | 0.928963i | 0.885583 | + | 0.464481i | \(0.153759\pi\) | ||||
−0.885583 | + | 0.464481i | \(0.846241\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4419.65i | 0.490519i | 0.969458 | + | 0.245259i | \(0.0788731\pi\) | ||||
−0.969458 | + | 0.245259i | \(0.921127\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3189.74 | − | 6489.13i | 0.351578 | − | 0.715241i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4512.74 | − | 7816.30i | −0.493990 | − | 0.855616i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14013.5 | + | 8090.72i | 1.52353 | + | 0.879610i | 0.999612 | + | 0.0278416i | \(0.00886340\pi\) |
0.523918 | + | 0.851769i | \(0.324470\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −871.235 | + | 9219.93i | −0.0940757 | + | 0.995565i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2983.47 | + | 1722.51i | 0.319976 | + | 0.184738i | 0.651382 | − | 0.758750i | \(-0.274190\pi\) |
−0.331406 | + | 0.943488i | \(0.607523\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3616.08 | + | 6263.24i | 0.385211 | + | 0.667205i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13650.7 | − | 912.300i | 1.44442 | − | 0.0965332i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3345.89i | − | 0.351675i | −0.984419 | − | 0.175838i | \(-0.943737\pi\) | ||
0.984419 | − | 0.175838i | \(-0.0562634\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2490.65i | 0.260045i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8153.73 | + | 5463.29i | −0.845686 | + | 0.566639i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5361.19 | + | 6745.39i | 0.552388 | + | 0.695008i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2817.23 | − | 4879.58i | 0.288368 | − | 0.499469i | −0.685052 | − | 0.728494i | \(-0.740221\pi\) |
0.973420 | + | 0.229025i | \(0.0735539\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1743.45 | + | 8592.00i | 0.177292 | + | 0.873726i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8810.53 | + | 15260.3i | −0.890124 | + | 1.54174i | −0.0503981 | + | 0.998729i | \(0.516049\pi\) |
−0.839726 | + | 0.543011i | \(0.817284\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1050.86 | + | 1820.15i | 0.105481 | + | 0.182699i | 0.913935 | − | 0.405861i | \(-0.133028\pi\) |
−0.808454 | + | 0.588560i | \(0.799695\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −896.685 | − | 1338.27i | −0.0894253 | − | 0.133464i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4439.19 | −0.439874 | −0.219937 | − | 0.975514i | \(-0.570585\pi\) | ||||
−0.219937 | + | 0.975514i | \(0.570585\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −823.629 | − | 5525.91i | −0.0810910 | − | 0.544057i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6647.65 | − | 444.273i | 0.650334 | − | 0.0434629i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8760.62 | − | 5057.94i | 0.851614 | − | 0.491680i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2106.36 | + | 1216.11i | 0.203466 | + | 0.117471i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1387.72 | − | 1070.50i | 0.133206 | − | 0.102757i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1192.77 | + | 2065.94i | −0.113777 | + | 0.197067i | −0.917290 | − | 0.398220i | \(-0.869628\pi\) |
0.803513 | + | 0.595287i | \(0.202961\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1578.85 | + | 911.547i | −0.149666 | + | 0.0864095i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6224.77 | + | 1986.47i | 0.586412 | + | 0.187137i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 2418.78i | − | 0.226456i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1032.17 | −0.0960409 | −0.0480205 | − | 0.998846i | \(-0.515291\pi\) | ||||
−0.0480205 | + | 0.998846i | \(0.515291\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16594.7 | + | 8157.17i | 1.53464 | + | 0.754356i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18322.5 | + | 10578.5i | −1.68408 | + | 0.972305i | −0.725183 | + | 0.688556i | \(0.758245\pi\) |
−0.958899 | + | 0.283748i | \(0.908422\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7290.42 | − | 4209.13i | −0.666012 | − | 0.384522i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6918.17 | + | 5336.75i | −0.628179 | + | 0.484584i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4885.91 | + | 12389.3i | −0.440972 | + | 1.11818i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5302.31 | + | 9183.86i | 0.475679 | + | 0.823900i | 0.999612 | − | 0.0278593i | \(-0.00886904\pi\) |
−0.523933 | + | 0.851760i | \(0.675536\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −326.816 | − | 4890.14i | −0.0291438 | − | 0.436078i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4721.95 | −0.418572 | −0.209286 | − | 0.977855i | \(-0.567114\pi\) | ||||
−0.209286 | + | 0.977855i | \(0.567114\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19380.5 | 1.70777 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −727.205 | + | 487.253i | −0.0637008 | + | 0.0426818i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6295.97 | − | 10904.9i | −0.548259 | − | 0.949613i | −0.998394 | − | 0.0566522i | \(-0.981957\pi\) |
0.450135 | − | 0.892961i | \(-0.351376\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3796.12 | + | 9625.89i | −0.328631 | + | 0.833316i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18276.8 | + | 3708.65i | −1.57298 | + | 0.319183i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5418.00 | − | 3128.08i | −0.463583 | − | 0.267650i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9293.22 | + | 5365.44i | −0.790552 | + | 0.456425i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4228.62 | + | 2833.32i | −0.357641 | + | 0.239632i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11584.6 | 0.974145 | 0.487072 | − | 0.873362i | \(-0.338065\pi\) | ||||
0.487072 | + | 0.873362i | \(0.338065\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3526.37i | 0.294833i | 0.989075 | + | 0.147416i | \(0.0470957\pi\) | ||||
−0.989075 | + | 0.147416i | \(0.952904\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1720.39 | + | 375.136i | −0.143017 | + | 0.0311853i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1624.20 | + | 937.733i | −0.134253 | + | 0.0775110i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3778.47 | + | 6544.50i | −0.310550 | + | 0.537889i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1630.22 | + | 3964.42i | −0.133230 | + | 0.323995i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3101.02 | − | 1790.38i | −0.252008 | − | 0.145497i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11626.2 | − | 6712.39i | 0.939523 | − | 0.542434i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8572.81 | + | 17440.3i | −0.688909 | + | 1.40150i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3133.58 | + | 10278.4i | 0.250413 | + | 0.821376i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7849.84 | 0.623828 | 0.311914 | − | 0.950110i | \(-0.399030\pi\) | ||||
0.311914 | + | 0.950110i | \(0.399030\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3531.22 | + | 7183.82i | −0.279078 | + | 0.567748i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10739.0 | + | 18600.4i | 0.844048 | + | 1.46193i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7842.27 | − | 13583.2i | 0.613001 | − | 1.06175i | −0.377731 | − | 0.925915i | \(-0.623296\pi\) |
0.990732 | − | 0.135833i | \(-0.0433710\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2047.95 | + | 15253.3i | 0.159207 | + | 1.18578i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8953.62 | − | 15508.1i | 0.692263 | − | 1.19903i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13242.4 | + | 10524.9i | −1.01831 | + | 0.809342i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 144.878 | + | 2167.80i | 0.0110806 | + | 0.165798i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 21036.4i | − | 1.60025i | −0.599833 | − | 0.800126i | \(-0.704766\pi\) | ||
0.599833 | − | 0.800126i | \(-0.295234\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14543.4i | 1.10039i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5662.32 | + | 8450.77i | 0.426137 | + | 0.635992i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6347.02 | − | 10993.4i | −0.475124 | − | 0.822939i | 0.524470 | − | 0.851429i | \(-0.324264\pi\) |
−0.999594 | + | 0.0284899i | \(0.990930\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11264.8 | + | 6503.75i | 0.838787 | + | 0.484274i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7979.36 | − | 10891.0i | 0.591008 | − | 0.806665i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15753.0 | − | 9095.03i | −1.16064 | − | 0.670094i | −0.209180 | − | 0.977877i | \(-0.567079\pi\) |
−0.951456 | + | 0.307783i | \(0.900413\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10146.0 | − | 17573.3i | −0.743599 | − | 1.28795i | −0.950846 | − | 0.309663i | \(-0.899784\pi\) |
0.207247 | − | 0.978289i | \(-0.433550\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2169.79 | − | 3238.32i | −0.158192 | − | 0.236095i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1242.34i | 0.0901026i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12356.1i | 0.891494i | 0.895159 | + | 0.445747i | \(0.147062\pi\) | ||||
−0.895159 | + | 0.445747i | \(0.852938\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1404.02 | + | 21008.3i | 0.100775 | + | 1.50790i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10217.1 | − | 8120.52i | 0.729567 | − | 0.579855i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1016.78 | − | 1761.12i | 0.0722314 | − | 0.125108i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1671.55 | − | 12449.8i | −0.118137 | − | 0.879893i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1434.42 | + | 2484.50i | −0.100860 | + | 0.174695i | −0.912039 | − | 0.410103i | \(-0.865493\pi\) |
0.811179 | + | 0.584798i | \(0.198826\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1994.74 | − | 3454.99i | −0.139544 | − | 0.241698i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1851.27 | − | 3766.17i | 0.128851 | − | 0.262131i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3259.99 | 0.225754 | 0.112877 | − | 0.993609i | \(-0.463993\pi\) | ||||
0.112877 | + | 0.993609i | \(0.463993\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1762.39 | − | 11824.3i | −0.121430 | − | 0.814702i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10053.9 | + | 20453.4i | −0.689245 | + | 1.40218i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19971.2 | − | 11530.4i | 1.36227 | − | 0.786509i | 0.372348 | − | 0.928093i | \(-0.378553\pi\) |
0.989926 | + | 0.141584i | \(0.0452195\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10827.8 | − | 6251.41i | −0.734897 | − | 0.424293i | 0.0853138 | − | 0.996354i | \(-0.472811\pi\) |
−0.820211 | + | 0.572061i | \(0.806144\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3097.65 | + | 7532.97i | −0.209197 | + | 0.508734i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1805.46 | − | 3127.15i | 0.121326 | − | 0.210143i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6638.81 | − | 3832.92i | 0.443923 | − | 0.256299i | −0.261338 | − | 0.965247i | \(-0.584164\pi\) |
0.705260 | + | 0.708949i | \(0.250830\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2761.94 | + | 12666.4i | 0.183776 | + | 0.842807i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 15427.5i | − | 1.02149i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20585.4 | 1.35634 | 0.678170 | − | 0.734905i | \(-0.262773\pi\) | ||||
0.678170 | + | 0.734905i | \(0.262773\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3545.08 | + | 2375.33i | −0.232441 | + | 0.155744i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14174.2 | + | 8183.50i | −0.924852 | + | 0.533963i | −0.885180 | − | 0.465249i | \(-0.845965\pi\) |
−0.0396720 | + | 0.999213i | \(0.512631\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6056.80 | + | 3496.90i | 0.393285 | + | 0.227063i | 0.683583 | − | 0.729873i | \(-0.260421\pi\) |
−0.290298 | + | 0.956936i | \(0.593754\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6308.28 | − | 7137.62i | −0.407637 | − | 0.461228i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12062.5 | − | 4757.04i | −0.775722 | − | 0.305918i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6501.53 | + | 11261.0i | 0.416098 | + | 0.720703i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17976.4 | + | 12044.8i | −1.14499 | + | 0.767183i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2529.46 | 0.160344 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8776.78 | 0.553721 | 0.276861 | − | 0.960910i | \(-0.410706\pi\) | ||||
0.276861 | + | 0.960910i | \(0.410706\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1477.89 | − | 22113.6i | −0.0927974 | − | 1.38852i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5245.55 | − | 9085.56i | −0.327816 | − | 0.567794i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15049.8 | − | 3487.00i | −0.936098 | − | 0.216891i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15373.1 | − | 11859.0i | 0.951724 | − | 0.734170i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2562.09 | − | 1479.23i | −0.157873 | − | 0.0911481i | 0.418982 | − | 0.907994i | \(-0.362387\pi\) |
−0.576855 | + | 0.816846i | \(0.695720\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11590.6 | + | 6691.85i | −0.710870 | + | 0.410421i | −0.811383 | − | 0.584515i | \(-0.801285\pi\) |
0.100513 | + | 0.994936i | \(0.467952\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15554.2 | + | 7645.71i | 0.949530 | + | 0.466744i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20353.0 | −1.23672 | −0.618362 | − | 0.785893i | \(-0.712203\pi\) | ||||
−0.618362 | + | 0.785893i | \(0.712203\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4973.61i | 0.300818i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2751.49 | + | 878.064i | 0.165652 | + | 0.0528634i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13525.8 | + | 7809.11i | −0.810574 | + | 0.467985i | −0.847155 | − | 0.531346i | \(-0.821687\pi\) |
0.0365814 | + | 0.999331i | \(0.488353\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13984.3 | − | 24221.6i | 0.834219 | − | 1.44491i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11944.2 | − | 9213.87i | 0.709265 | − | 0.547135i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5847.81 | − | 3376.24i | −0.345673 | − | 0.199574i | 0.317105 | − | 0.948390i | \(-0.397289\pi\) |
−0.662778 | + | 0.748816i | \(0.730623\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8658.65 | + | 4999.07i | −0.509504 | + | 0.294162i | −0.732630 | − | 0.680627i | \(-0.761707\pi\) |
0.223126 | + | 0.974790i | \(0.428374\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14592.0 | + | 975.210i | −0.854763 | + | 0.0571252i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 25152.5 | − | 3748.94i | 1.46672 | − | 0.218613i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9146.72 | 0.530978 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5917.94 | − | 8832.28i | −0.342004 | − | 0.510427i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8928.53 | + | 15464.7i | 0.513684 | + | 0.889727i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.7088 | + | 54.9213i | −0.00181617 | + | 0.00314570i | −0.866932 | − | 0.498426i | \(-0.833911\pi\) |
0.865116 | + | 0.501572i | \(0.167245\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2433.96 | + | 815.786i | 0.138790 | + | 0.0465180i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8874.33 | − | 15370.8i | 0.503793 | − | 0.872596i | −0.496197 | − | 0.868210i | \(-0.665271\pi\) |
0.999990 | − | 0.00438565i | \(-0.00139600\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2698.30 | + | 3394.97i | 0.152506 | + | 0.191881i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24148.4 | + | 16180.3i | −1.35884 | + | 0.910468i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 8356.42i | − | 0.468155i | −0.972218 | − | 0.234077i | \(-0.924793\pi\) | ||
0.972218 | − | 0.234077i | \(-0.0752069\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 32370.8i | − | 1.80558i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1908.66 | + | 127.559i | −0.105997 | + | 0.00708396i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1461.81 | + | 2531.92i | 0.0808279 | + | 0.139998i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25237.8 | + | 14571.1i | 1.38942 | + | 0.802185i | 0.993250 | − | 0.115991i | \(-0.0370042\pi\) |
0.396174 | + | 0.918175i | \(0.370338\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3756.78 | − | 15208.3i | 0.205928 | − | 0.833642i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 894.419 | + | 516.393i | 0.0488162 | + | 0.0281840i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2484.07 | + | 4302.53i | 0.134994 | + | 0.233816i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8940.61 | − | 18188.5i | 0.483784 | − | 0.984197i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 30359.4i | − | 1.63574i | −0.575400 | − | 0.817872i | \(-0.695154\pi\) | ||
0.575400 | − | 0.817872i | \(-0.304846\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5380.64i | 0.288670i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16499.8 | − | 8110.53i | −0.881447 | − | 0.433277i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27202.3 | + | 21620.2i | −1.44703 | + | 1.15009i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6063.83 | + | 10502.9i | −0.321202 | + | 0.556338i | −0.980736 | − | 0.195337i | \(-0.937420\pi\) |
0.659535 | + | 0.751674i | \(0.270753\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24441.2 | − | 3281.55i | 1.28919 | − | 0.173091i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1018.88 | − | 1764.75i | 0.0535166 | − | 0.0926934i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7287.52 | − | 12622.4i | −0.381172 | − | 0.660209i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13934.3 | + | 931.254i | −0.725783 | + | 0.0485053i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9928.20 | 0.514964 | 0.257482 | − | 0.966283i | \(-0.417107\pi\) | ||||
0.257482 | + | 0.966283i | \(0.417107\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11094.2 | − | 1653.58i | 0.573051 | − | 0.0854125i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7099.90 | + | 10596.3i | 0.365212 | + | 0.545063i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2134.66 | + | 1232.44i | −0.109351 | + | 0.0631335i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26251.7 | − | 15156.4i | −1.33923 | − | 0.773204i | −0.352536 | − | 0.935798i | \(-0.614681\pi\) |
−0.986693 | + | 0.162594i | \(0.948014\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18126.2 | + | 7672.07i | −0.920907 | + | 0.389782i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10089.1 | − | 17474.9i | 0.510479 | − | 0.884176i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16344.8 | − | 9436.67i | 0.823613 | − | 0.475513i | −0.0280476 | − | 0.999607i | \(-0.508929\pi\) |
0.851661 | + | 0.524093i | \(0.175596\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11641.3 | + | 14262.7i | −0.584212 | + | 0.715764i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9450.57i | 0.472342i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24825.4 | 1.23575 | 0.617873 | − | 0.786278i | \(-0.287995\pi\) | ||||
0.617873 | + | 0.786278i | \(0.287995\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2074.46 | − | 31040.1i | −0.102844 | − | 1.53885i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22599.1 | − | 13047.6i | 1.11586 | − | 0.644241i | 0.175517 | − | 0.984476i | \(-0.443840\pi\) |
0.940340 | + | 0.340236i | \(0.110507\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23553.7 | + | 13598.8i | 1.15831 | + | 0.668752i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18857.6 | + | 2531.88i | −0.923646 | + | 0.124011i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8830.30 | + | 22391.2i | −0.430777 | + | 1.09233i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13211.2 | + | 22882.5i | 0.641922 | + | 1.11184i | 0.985003 | + | 0.172536i | \(0.0551962\pi\) |
−0.343081 | + | 0.939306i | \(0.611470\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14439.1 | + | 7097.54i | 0.698789 | + | 0.343491i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19511.4 | −0.940520 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28263.9 | 1.35703 | 0.678513 | − | 0.734588i | \(-0.262625\pi\) | ||||
0.678513 | + | 0.734588i | \(0.262625\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9919.07 | − | 4875.74i | −0.474360 | − | 0.233173i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19195.4 | − | 33247.5i | −0.914369 | − | 1.58373i | −0.807823 | − | 0.589425i | \(-0.799354\pi\) |
−0.106545 | − | 0.994308i | \(-0.533979\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35823.0 | − | 14127.3i | −1.69971 | − | 0.670307i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6628.30 | + | 16119.0i | −0.313264 | + | 0.761807i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6192.46 | − | 3575.22i | −0.291521 | − | 0.168310i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26820.3 | − | 15484.7i | 1.25769 | − | 0.726129i | 0.285067 | − | 0.958508i | \(-0.407984\pi\) |
0.972625 | + | 0.232378i | \(0.0746507\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −908.579 | − | 13595.0i | −0.0424405 | − | 0.635037i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28691.6 | −1.33501 | −0.667507 | − | 0.744604i | \(-0.732638\pi\) | ||||
−0.667507 | + | 0.744604i | \(0.732638\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 549.142i | 0.0254526i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2621.67 | − | 2881.08i | −0.121045 | − | 0.133022i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9152.30 | + | 5284.08i | −0.420944 | + | 0.243032i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11263.9 | − | 19509.7i | 0.516075 | − | 0.893868i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6006.24 | − | 17920.0i | 0.274132 | − | 0.817893i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11470.2 | + | 6622.34i | 0.521516 | + | 0.301097i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19658.2 | − | 11349.7i | 0.890392 | − | 0.514068i | 0.0163216 | − | 0.999867i | \(-0.494804\pi\) |
0.874071 | + | 0.485798i | \(0.161471\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20638.7 | + | 30802.4i | 0.931252 | + | 1.38986i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23066.5 | + | 3438.03i | −1.03685 | + | 0.154542i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25672.7 | −1.14964 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3476.41 | − | 232.334i | 0.155089 | − | 0.0103648i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4945.60 | − | 8566.03i | −0.219802 | − | 0.380708i | 0.734945 | − | 0.678126i | \(-0.237208\pi\) |
−0.954747 | + | 0.297418i | \(0.903874\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10702.5 | + | 18537.3i | −0.473877 | + | 0.820778i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11546.2 | + | 14967.7i | 0.509320 | + | 0.660245i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8751.53 | − | 15158.1i | 0.384601 | − | 0.666149i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8082.08 | + | 10168.8i | 0.353858 | + | 0.445220i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17937.7 | + | 8817.31i | 0.782449 | + | 0.384614i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 15328.4i | − | 0.666155i | −0.942900 | − | 0.333077i | \(-0.891913\pi\) | ||
0.942900 | − | 0.333077i | \(-0.108087\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 4463.96i | − | 0.193281i | −0.995319 | − | 0.0966406i | \(-0.969190\pi\) | ||
0.995319 | − | 0.0966406i | \(-0.0308097\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1023.16 | + | 2081.50i | −0.0441377 | + | 0.0897925i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18379.8 | + | 31834.8i | 0.789959 | + | 1.36825i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37172.4 | + | 21461.5i | 1.59180 | + | 0.919025i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16234.7 | + | 15609.7i | 0.692659 | + | 0.665992i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13660.6 | + | 7886.94i | 0.580704 | + | 0.335269i | 0.761413 | − | 0.648267i | \(-0.224506\pi\) |
−0.180709 | + | 0.983537i | \(0.557839\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −960.810 | − | 1664.17i | −0.0406947 | − | 0.0704853i | 0.844961 | − | 0.534828i | \(-0.179624\pi\) |
−0.885655 | + | 0.464343i | \(0.846290\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2971.87 | − | 198.615i | 0.125415 | − | 0.00838168i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 28140.7i | − | 1.18325i | −0.806214 | − | 0.591624i | \(-0.798487\pi\) | ||
0.806214 | − | 0.591624i | \(-0.201513\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13305.9i | 0.557460i | 0.960370 | + | 0.278730i | \(0.0899134\pi\) | ||||
−0.960370 | + | 0.278730i | \(0.910087\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29397.5 | + | 19697.4i | −1.22718 | + | 0.822256i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15664.4 | + | 14630.3i | 0.651547 | + | 0.608536i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4871.52 | − | 8437.73i | 0.201899 | − | 0.349700i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2788.40 | − | 3154.99i | −0.115151 | − | 0.130290i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8913.20 | − | 15438.1i | 0.366767 | − | 0.635260i | −0.622291 | − | 0.782786i | \(-0.713798\pi\) |
0.989058 | + | 0.147526i | \(0.0471311\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3120.61 | − | 5405.06i | −0.127952 | − | 0.221619i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9922.47 | + | 14808.9i | 0.405395 | + | 0.605035i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1740.16 | −0.0708442 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 954.409 | + | 6403.33i | 0.0387177 | + | 0.259765i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1647.35 | − | 110.095i | 0.0665924 | − | 0.00445048i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2380.14 | + | 1374.17i | −0.0958754 | + | 0.0553537i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35437.7 | − | 20459.9i | −1.42247 | − | 0.821261i | −0.425956 | − | 0.904744i | \(-0.640062\pi\) |
−0.996509 | + | 0.0834834i | \(0.973395\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −34288.1 | − | 14099.7i | −1.37150 | − | 0.563975i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14081.4 | − | 24389.8i | 0.561275 | − | 0.972157i | −0.436110 | − | 0.899893i | \(-0.643644\pi\) |
0.997386 | − | 0.0722641i | \(-0.0230225\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3110.46 | + | 1795.83i | −0.123548 | + | 0.0713304i | −0.560500 | − | 0.828154i | \(-0.689391\pi\) |
0.436952 | + | 0.899485i | \(0.356058\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2326.00 | − | 7288.74i | 0.0920673 | − | 0.288501i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18091.2i | 0.713593i | 0.934182 | + | 0.356796i | \(0.116131\pi\) | ||||
−0.934182 | + | 0.356796i | \(0.883869\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10118.8 | −0.397747 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4700.55 | − | 2310.57i | −0.184128 | − | 0.0905085i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24779.9 | − | 14306.7i | 0.967319 | − | 0.558482i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11766.6 | − | 6793.43i | −0.457744 | − | 0.264279i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −841.296 | − | 6266.03i | −0.0326158 | − | 0.242925i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −25502.5 | − | 10057.3i | −0.985306 | − | 0.388570i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23215.3 | − | 40210.1i | −0.893871 | − | 1.54823i | −0.835195 | − | 0.549954i | \(-0.814645\pi\) |
−0.0586762 | − | 0.998277i | \(-0.518688\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2565.30 | − | 38384.5i | −0.0984362 | − | 1.47290i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5007.33 | 0.191488 | 0.0957441 | − | 0.995406i | \(-0.469477\pi\) | ||||
0.0957441 | + | 0.995406i | \(0.469477\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49999.0 | −1.90555 | −0.952775 | − | 0.303677i | \(-0.901786\pi\) | ||||
−0.952775 | + | 0.303677i | \(0.901786\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7079.20 | + | 4743.32i | −0.268887 | + | 0.180164i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1730.41 | + | 2997.16i | 0.0655034 | + | 0.113455i | 0.896917 | − | 0.442199i | \(-0.145801\pi\) |
−0.831414 | + | 0.555654i | \(0.812468\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17498.1 | + | 6900.64i | 0.660143 | + | 0.260337i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16065.8 | + | 16231.5i | −0.604069 | + | 0.610299i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −39432.3 | − | 22766.3i | −1.47766 | − | 0.853129i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33456.9 | + | 19316.3i | −1.24954 | + | 0.721423i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13200.8 | − | 8845.01i | 0.491374 | − | 0.329238i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4043.06 | 0.149993 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 4056.38i | − | 0.149986i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30361.0 | + | 6620.29i | −1.11888 | + | 0.243975i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13781.2 | + | 7956.58i | −0.506191 | + | 0.292249i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14546.9 | − | 25196.0i | 0.532550 | − | 0.922404i | −0.466727 | − | 0.884401i | \(-0.654567\pi\) |
0.999278 | − | 0.0380031i | \(-0.0120997\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 50206.8 | − | 6740.91i | 1.83196 | − | 0.245965i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28776.2 | + | 16613.9i | 1.04654 | + | 0.604220i | 0.921679 | − | 0.387954i | \(-0.126818\pi\) |
0.124861 | + | 0.992174i | \(0.460151\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19118.9 | + | 11038.3i | −0.693038 | + | 0.400126i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13496.6 | + | 27457.1i | −0.487632 | + | 0.992025i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7392.44 | + | 49597.5i | 0.266216 | + | 1.78610i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11642.5 | −0.417902 | −0.208951 | − | 0.977926i | \(-0.567005\pi\) | ||||
−0.208951 | + | 0.977926i | \(0.567005\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22217.9 | − | 45199.5i | 0.794901 | − | 1.61713i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16193.9 | + | 28048.6i | 0.577495 | + | 1.00025i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 370.316 | − | 641.407i | 0.0131632 | − | 0.0227993i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15123.7 | − | 6219.06i | −0.535845 | − | 0.220346i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19057.0 | − | 33007.6i | 0.673024 | − | 1.16571i | −0.304019 | − | 0.952666i | \(-0.598329\pi\) |
0.977042 | − | 0.213045i | \(-0.0683381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31121.5 | + | 33321.1i | −1.09556 | + | 1.17299i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2742.29 | − | 41032.9i | −0.0962258 | − | 1.43982i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20222.2i | 0.707312i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22454.2i | 0.782869i | 0.920206 | + | 0.391435i | \(0.128021\pi\) | ||||
−0.920206 | + | 0.391435i | \(0.871979\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15513.1 | + | 23152.6i | 0.539137 | + | 0.804639i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6159.92 | + | 10669.3i | 0.213398 | + | 0.369616i | 0.952776 | − | 0.303675i | \(-0.0982135\pi\) |
−0.739378 | + | 0.673291i | \(0.764880\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4674.84 | − | 2699.02i | −0.161436 | − | 0.0932049i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 25229.6 | − | 9156.85i | 0.868485 | − | 0.315209i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13396.5 | + | 7734.46i | 0.459691 | + | 0.265403i | 0.711914 | − | 0.702266i | \(-0.247828\pi\) |
−0.252223 | + | 0.967669i | \(0.581162\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12581.9 | + | 21792.4i | 0.430374 | + | 0.745429i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12495.2 | + | 18648.6i | 0.426062 | + | 0.635880i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5267.67i | 0.179052i | 0.995984 | + | 0.0895260i | \(0.0285352\pi\) | ||||
−0.995984 | + | 0.0895260i | \(0.971465\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 7749.10i | − | 0.262571i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1462.31 | − | 21880.4i | −0.0493936 | − | 0.739075i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36111.6 | + | 45435.2i | 1.21596 | + | 1.52991i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14445.1 | + | 25019.7i | −0.484882 | + | 0.839841i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 27783.9 | − | 21432.8i | 0.929723 | − | 0.717198i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20928.3 | + | 36248.9i | −0.698141 | + | 1.20922i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6237.09 | + | 10803.0i | 0.207416 | + | 0.359255i | 0.950900 | − | 0.309499i | \(-0.100161\pi\) |
−0.743484 | + | 0.668754i | \(0.766828\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −19040.7 | + | 38735.9i | −0.631245 | + | 1.28419i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −57914.6 | −1.91407 | −0.957037 | − | 0.289964i | \(-0.906357\pi\) | ||||
−0.957037 | + | 0.289964i | \(0.906357\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1831.46 | + | 272.977i | −0.0603433 | + | 0.00899409i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1889.01 | + | 3842.94i | −0.0620478 | + | 0.126228i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15954.7 | − | 9211.48i | 0.522454 | − | 0.301639i | −0.215484 | − | 0.976507i | \(-0.569133\pi\) |
0.737938 | + | 0.674868i | \(0.235800\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18995.1 | + | 10966.8i | 0.620108 | + | 0.358020i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 34289.6 | + | 44450.6i | 1.11599 | + | 1.44668i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4293.70 | + | 7436.90i | −0.139316 | + | 0.241302i | −0.927238 | − | 0.374473i | \(-0.877824\pi\) |
0.787922 | + | 0.615775i | \(0.211157\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7224.90 | − | 4171.30i | 0.233710 | − | 0.134933i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 32206.8 | − | 7022.77i | 1.03866 | − | 0.226481i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21924.4i | 0.704909i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17639.5 | −0.565426 | −0.282713 | − | 0.959205i | \(-0.591234\pi\) | ||||
−0.282713 | + | 0.959205i | \(0.591234\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3209.19 | − | 2150.27i | 0.102558 | − | 0.0687177i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39237.1 | + | 22653.6i | −1.25015 | + | 0.721776i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4180.85 | + | 2413.82i | 0.132807 | + | 0.0766764i | 0.564932 | − | 0.825138i | \(-0.308903\pi\) |
−0.432124 | + | 0.901814i | \(0.642236\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1129.32 | + | 5565.46i | 0.0357658 | + | 0.176260i |
(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.209.21 | yes | 48 | |
3.2 | odd | 2 | 756.4.x.a.629.7 | 48 | |||
7.6 | odd | 2 | inner | 252.4.x.a.209.4 | yes | 48 | |
9.2 | odd | 6 | 2268.4.f.a.1133.36 | 48 | |||
9.4 | even | 3 | 756.4.x.a.125.18 | 48 | |||
9.5 | odd | 6 | inner | 252.4.x.a.41.4 | ✓ | 48 | |
9.7 | even | 3 | 2268.4.f.a.1133.13 | 48 | |||
21.20 | even | 2 | 756.4.x.a.629.18 | 48 | |||
63.13 | odd | 6 | 756.4.x.a.125.7 | 48 | |||
63.20 | even | 6 | 2268.4.f.a.1133.14 | 48 | |||
63.34 | odd | 6 | 2268.4.f.a.1133.35 | 48 | |||
63.41 | even | 6 | inner | 252.4.x.a.41.21 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.x.a.41.4 | ✓ | 48 | 9.5 | odd | 6 | inner | |
252.4.x.a.41.21 | yes | 48 | 63.41 | even | 6 | inner | |
252.4.x.a.209.4 | yes | 48 | 7.6 | odd | 2 | inner | |
252.4.x.a.209.21 | yes | 48 | 1.1 | even | 1 | trivial | |
756.4.x.a.125.7 | 48 | 63.13 | odd | 6 | |||
756.4.x.a.125.18 | 48 | 9.4 | even | 3 | |||
756.4.x.a.629.7 | 48 | 3.2 | odd | 2 | |||
756.4.x.a.629.18 | 48 | 21.20 | even | 2 | |||
2268.4.f.a.1133.13 | 48 | 9.7 | even | 3 | |||
2268.4.f.a.1133.14 | 48 | 63.20 | even | 6 | |||
2268.4.f.a.1133.35 | 48 | 63.34 | odd | 6 | |||
2268.4.f.a.1133.36 | 48 | 9.2 | odd | 6 |