Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(899,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.899");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bp (of order \(6\), degree \(2\), not 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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 899.7 | ||
Character | \(\chi\) | \(=\) | 3150.899 |
Dual form | 3150.2.bp.g.1349.7 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.04195 | + | 2.43194i | 0.393821 | + | 0.919187i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.38605 | − | 0.800236i | −0.417910 | − | 0.241280i | 0.276273 | − | 0.961079i | \(-0.410901\pi\) |
−0.694183 | + | 0.719799i | \(0.744234\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.770726 | 0.213761 | 0.106880 | − | 0.994272i | \(-0.465914\pi\) | ||||
0.106880 | + | 0.994272i | \(0.465914\pi\) | |||||||
\(14\) | 1.58515 | − | 2.11833i | 0.423648 | − | 0.566147i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.05027 | − | 1.76107i | −0.739799 | − | 0.427123i | 0.0821974 | − | 0.996616i | \(-0.473806\pi\) |
−0.821996 | + | 0.569493i | \(0.807140\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.06818 | + | 1.77141i | −0.703888 | + | 0.406390i | −0.808794 | − | 0.588092i | \(-0.799879\pi\) |
0.104906 | + | 0.994482i | \(0.466546\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.60047i | 0.341222i | ||||||||
\(23\) | −1.61385 | − | 2.79527i | −0.336511 | − | 0.582854i | 0.647263 | − | 0.762267i | \(-0.275914\pi\) |
−0.983774 | + | 0.179413i | \(0.942580\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.385363 | − | 0.667468i | −0.0755759 | − | 0.130901i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.62710 | − | 0.313613i | −0.496475 | − | 0.0592674i | ||||
\(29\) | − | 0.700774i | − | 0.130131i | −0.997881 | − | 0.0650653i | \(-0.979274\pi\) | ||
0.997881 | − | 0.0650653i | \(-0.0207256\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.13725 | + | 0.656589i | 0.204255 | + | 0.117927i | 0.598639 | − | 0.801019i | \(-0.295708\pi\) |
−0.394383 | + | 0.918946i | \(0.629042\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.52215i | 0.604043i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.792101 | + | 0.457320i | −0.130221 | + | 0.0751829i | −0.563695 | − | 0.825983i | \(-0.690621\pi\) |
0.433475 | + | 0.901166i | \(0.357287\pi\) | |||||||
\(38\) | 3.06818 | + | 1.77141i | 0.497724 | + | 0.287361i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.88167 | −0.762388 | −0.381194 | − | 0.924495i | \(-0.624487\pi\) | ||||
−0.381194 | + | 0.924495i | \(0.624487\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.26963i | − | 1.41361i | −0.707411 | − | 0.706803i | \(-0.750137\pi\) | ||
0.707411 | − | 0.706803i | \(-0.249863\pi\) | |||||||
\(44\) | 1.38605 | − | 0.800236i | 0.208955 | − | 0.120640i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.61385 | + | 2.79527i | −0.237949 | + | 0.412140i | ||||
\(47\) | −2.31462 | + | 1.33635i | −0.337623 | + | 0.194926i | −0.659220 | − | 0.751950i | \(-0.729113\pi\) |
0.321598 | + | 0.946876i | \(0.395780\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.82867 | + | 5.06793i | −0.689810 | + | 0.723990i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.385363 | + | 0.667468i | −0.0534402 | + | 0.0925612i | ||||
\(53\) | 4.64520 | − | 8.04572i | 0.638067 | − | 1.10516i | −0.347789 | − | 0.937573i | \(-0.613068\pi\) |
0.985856 | − | 0.167592i | \(-0.0535991\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.04195 | + | 2.43194i | 0.139237 | + | 0.324982i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.606888 | + | 0.350387i | −0.0796883 | + | 0.0460081i | ||||
\(59\) | 1.56198 | − | 2.70542i | 0.203352 | − | 0.352216i | −0.746254 | − | 0.665661i | \(-0.768150\pi\) |
0.949606 | + | 0.313445i | \(0.101483\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.43214 | + | 5.44565i | −1.20766 | + | 0.697244i | −0.962248 | − | 0.272175i | \(-0.912257\pi\) |
−0.245414 | + | 0.969418i | \(0.578924\pi\) | |||||||
\(62\) | − | 1.31318i | − | 0.166774i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.90314 | + | 3.40818i | 0.721183 | + | 0.416375i | 0.815188 | − | 0.579196i | \(-0.196634\pi\) |
−0.0940048 | + | 0.995572i | \(0.529967\pi\) | |||||||
\(68\) | 3.05027 | − | 1.76107i | 0.369899 | − | 0.213561i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.47930i | − | 0.768951i | −0.923135 | − | 0.384475i | \(-0.874382\pi\) | ||
0.923135 | − | 0.384475i | \(-0.125618\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.51852 | − | 9.55835i | 0.645894 | − | 1.11872i | −0.338201 | − | 0.941074i | \(-0.609818\pi\) |
0.984094 | − | 0.177647i | \(-0.0568484\pi\) | |||||||
\(74\) | 0.792101 | + | 0.457320i | 0.0920799 | + | 0.0531623i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.54282i | − | 0.406390i | ||||||
\(77\) | 0.501930 | − | 4.20460i | 0.0572002 | − | 0.479158i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.45086 | + | 2.51296i | 0.163234 | + | 0.282730i | 0.936027 | − | 0.351928i | \(-0.114474\pi\) |
−0.772792 | + | 0.634659i | \(0.781141\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.44083 | + | 4.22765i | 0.269545 | + | 0.466865i | ||||
\(83\) | − | 11.9777i | − | 1.31472i | −0.753576 | − | 0.657361i | \(-0.771673\pi\) | ||
0.753576 | − | 0.657361i | \(-0.228327\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.02773 | + | 4.63481i | −0.865653 | + | 0.499785i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.38605 | − | 0.800236i | −0.147753 | − | 0.0853055i | ||||
\(89\) | 4.40369 | + | 7.62742i | 0.466791 | + | 0.808505i | 0.999280 | − | 0.0379313i | \(-0.0120768\pi\) |
−0.532490 | + | 0.846437i | \(0.678743\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.803059 | + | 1.87436i | 0.0841835 | + | 0.196486i | ||||
\(92\) | 3.22770 | 0.336511 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.31462 | + | 1.33635i | 0.238735 | + | 0.137834i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.31224 | 0.539376 | 0.269688 | − | 0.962948i | \(-0.413079\pi\) | ||||
0.269688 | + | 0.962948i | \(0.413079\pi\) | |||||||
\(98\) | 6.80329 | + | 1.64779i | 0.687236 | + | 0.166452i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.62663 | − | 8.01356i | 0.460367 | − | 0.797379i | −0.538612 | − | 0.842554i | \(-0.681051\pi\) |
0.998979 | + | 0.0451749i | \(0.0143845\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.91290 | − | 13.7055i | −0.779681 | − | 1.35045i | −0.932125 | − | 0.362136i | \(-0.882048\pi\) |
0.152444 | − | 0.988312i | \(-0.451286\pi\) | |||||||
\(104\) | 0.770726 | 0.0755759 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.29040 | −0.902363 | ||||||||
\(107\) | −6.20735 | − | 10.7514i | −0.600087 | − | 1.03938i | −0.992807 | − | 0.119724i | \(-0.961799\pi\) |
0.392720 | − | 0.919658i | \(-0.371534\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.51750 | + | 9.55659i | −0.528480 | + | 0.915355i | 0.470968 | + | 0.882150i | \(0.343905\pi\) |
−0.999449 | + | 0.0332048i | \(0.989429\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.58515 | − | 2.11833i | 0.149782 | − | 0.200163i | ||||
\(113\) | 15.0301 | 1.41391 | 0.706957 | − | 0.707256i | \(-0.250067\pi\) | ||||
0.706957 | + | 0.707256i | \(0.250067\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.606888 | + | 0.350387i | 0.0563482 | + | 0.0325326i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.12395 | −0.287583 | ||||||||
\(119\) | 1.10459 | − | 9.25303i | 0.101258 | − | 0.848223i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.21924 | − | 7.30795i | −0.383568 | − | 0.664359i | ||||
\(122\) | 9.43214 | + | 5.44565i | 0.853946 | + | 0.493026i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.13725 | + | 0.656589i | −0.102128 | + | 0.0589634i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.66506i | − | 0.236486i | −0.992985 | − | 0.118243i | \(-0.962274\pi\) | ||
0.992985 | − | 0.118243i | \(-0.0377262\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.10987 | − | 12.3147i | −0.621192 | − | 1.07594i | −0.989264 | − | 0.146139i | \(-0.953315\pi\) |
0.368071 | − | 0.929797i | \(-0.380018\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.50486 | − | 5.61590i | −0.650754 | − | 0.486960i | ||||
\(134\) | − | 6.81636i | − | 0.588844i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.05027 | − | 1.76107i | −0.261558 | − | 0.151011i | ||||
\(137\) | −0.0650662 | + | 0.112698i | −0.00555898 | + | 0.00962843i | −0.868792 | − | 0.495178i | \(-0.835103\pi\) |
0.863233 | + | 0.504806i | \(0.168436\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.63572i | − | 0.308378i | −0.988041 | − | 0.154189i | \(-0.950724\pi\) | ||
0.988041 | − | 0.154189i | \(-0.0492765\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.61123 | + | 3.23965i | −0.470884 | + | 0.271865i | ||||
\(143\) | −1.06826 | − | 0.616762i | −0.0893327 | − | 0.0515763i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.0370 | −0.913432 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 0.914639i | − | 0.0751829i | ||||||
\(149\) | −2.53957 | + | 1.46622i | −0.208049 | + | 0.120117i | −0.600405 | − | 0.799696i | \(-0.704994\pi\) |
0.392355 | + | 0.919814i | \(0.371660\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.56919 | + | 6.18201i | −0.290456 | + | 0.503085i | −0.973918 | − | 0.226902i | \(-0.927140\pi\) |
0.683461 | + | 0.729987i | \(0.260474\pi\) | |||||||
\(152\) | −3.06818 | + | 1.77141i | −0.248862 | + | 0.143681i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.89225 | + | 1.66762i | −0.313647 | + | 0.134380i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.15702 | − | 12.3963i | 0.571192 | − | 0.989334i | −0.425252 | − | 0.905075i | \(-0.639814\pi\) |
0.996444 | − | 0.0842589i | \(-0.0268523\pi\) | |||||||
\(158\) | 1.45086 | − | 2.51296i | 0.115424 | − | 0.199921i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.11638 | − | 6.83732i | 0.403227 | − | 0.538857i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.24313 | + | 3.60448i | −0.489000 | + | 0.282324i | −0.724160 | − | 0.689632i | \(-0.757772\pi\) |
0.235159 | + | 0.971957i | \(0.424439\pi\) | |||||||
\(164\) | 2.44083 | − | 4.22765i | 0.190597 | − | 0.330124i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.3730 | + | 5.98884i | −0.805099 | + | 0.464824i | ||||
\(167\) | 13.8952i | 1.07524i | 0.843187 | + | 0.537620i | \(0.180677\pi\) | ||||
−0.843187 | + | 0.537620i | \(0.819323\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4060 | −0.954306 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.02773 | + | 4.63481i | 0.612109 | + | 0.353401i | ||||
\(173\) | −2.05023 | + | 1.18370i | −0.155876 | + | 0.0899951i | −0.575909 | − | 0.817514i | \(-0.695352\pi\) |
0.420033 | + | 0.907509i | \(0.362018\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.60047i | 0.120640i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.40369 | − | 7.62742i | 0.330071 | − | 0.571700i | ||||
\(179\) | −15.4837 | − | 8.93953i | −1.15731 | − | 0.668172i | −0.206650 | − | 0.978415i | \(-0.566256\pi\) |
−0.950657 | + | 0.310243i | \(0.899590\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.6673i | 1.23887i | 0.785049 | + | 0.619434i | \(0.212638\pi\) | ||||
−0.785049 | + | 0.619434i | \(0.787362\pi\) | |||||||
\(182\) | 1.22171 | − | 1.63265i | 0.0905594 | − | 0.121020i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.61385 | − | 2.79527i | −0.118975 | − | 0.206070i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.81855 | + | 4.88187i | 0.206113 | + | 0.356998i | ||||
\(188\) | − | 2.67270i | − | 0.194926i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.4359 | − | 12.3760i | 1.55104 | − | 0.895496i | 0.552987 | − | 0.833190i | \(-0.313488\pi\) |
0.998057 | − | 0.0623063i | \(-0.0198456\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.8917 | − | 6.28835i | −0.784005 | − | 0.452645i | 0.0538428 | − | 0.998549i | \(-0.482853\pi\) |
−0.837848 | + | 0.545904i | \(0.816186\pi\) | |||||||
\(194\) | −2.65612 | − | 4.60054i | −0.190698 | − | 0.330299i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.97462 | − | 6.71572i | −0.141044 | − | 0.479694i | ||||
\(197\) | −19.7360 | −1.40613 | −0.703066 | − | 0.711125i | \(-0.748186\pi\) | ||||
−0.703066 | + | 0.711125i | \(0.748186\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.82275 | − | 5.67117i | −0.696316 | − | 0.402018i | 0.109658 | − | 0.993969i | \(-0.465025\pi\) |
−0.805974 | + | 0.591951i | \(0.798358\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.25326 | −0.651057 | ||||||||
\(203\) | 1.70424 | − | 0.730173i | 0.119614 | − | 0.0512481i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.91290 | + | 13.7055i | −0.551318 | + | 0.954911i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.385363 | − | 0.667468i | −0.0267201 | − | 0.0462806i | ||||
\(209\) | 5.67019 | 0.392215 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0647 | 1.10594 | 0.552970 | − | 0.833201i | \(-0.313494\pi\) | ||||
0.552970 | + | 0.833201i | \(0.313494\pi\) | |||||||
\(212\) | 4.64520 | + | 8.04572i | 0.319034 | + | 0.552582i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.20735 | + | 10.7514i | −0.424326 | + | 0.734954i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.411830 | + | 3.44985i | −0.0279569 | + | 0.234191i | ||||
\(218\) | 11.0350 | 0.747384 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.35092 | − | 1.35730i | −0.158140 | − | 0.0913022i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.00917 | 0.134544 | 0.0672720 | − | 0.997735i | \(-0.478570\pi\) | ||||
0.0672720 | + | 0.997735i | \(0.478570\pi\) | |||||||
\(224\) | −2.62710 | − | 0.313613i | −0.175530 | − | 0.0209542i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.51506 | − | 13.0165i | −0.499894 | − | 0.865842i | ||||
\(227\) | 3.38249 | + | 1.95288i | 0.224504 | + | 0.129617i | 0.608034 | − | 0.793911i | \(-0.291958\pi\) |
−0.383530 | + | 0.923528i | \(0.625292\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.5904 | + | 6.69174i | −0.765918 | + | 0.442203i | −0.831416 | − | 0.555650i | \(-0.812470\pi\) |
0.0654987 | + | 0.997853i | \(0.479136\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 0.700774i | − | 0.0460081i | ||||||
\(233\) | −5.14808 | − | 8.91673i | −0.337262 | − | 0.584154i | 0.646655 | − | 0.762783i | \(-0.276167\pi\) |
−0.983917 | + | 0.178628i | \(0.942834\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.56198 | + | 2.70542i | 0.101676 | + | 0.176108i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.56565 | + | 3.66991i | −0.555229 | + | 0.237885i | ||||
\(239\) | − | 17.5460i | − | 1.13495i | −0.823389 | − | 0.567477i | \(-0.807920\pi\) | ||
0.823389 | − | 0.567477i | \(-0.192080\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.66068 | + | 5.00024i | 0.557883 | + | 0.322094i | 0.752295 | − | 0.658826i | \(-0.228947\pi\) |
−0.194412 | + | 0.980920i | \(0.562280\pi\) | |||||||
\(242\) | −4.21924 | + | 7.30795i | −0.271223 | + | 0.469773i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 10.8913i | − | 0.697244i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.36472 | + | 1.36527i | −0.150464 | + | 0.0868702i | ||||
\(248\) | 1.13725 | + | 0.656589i | 0.0722152 | + | 0.0416935i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.55412 | −0.224334 | −0.112167 | − | 0.993689i | \(-0.535779\pi\) | ||||
−0.112167 | + | 0.993689i | \(0.535779\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.16584i | 0.324774i | ||||||||
\(254\) | −2.30801 | + | 1.33253i | −0.144818 | + | 0.0836105i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −6.15756 | + | 3.55507i | −0.384098 | + | 0.221759i | −0.679600 | − | 0.733583i | \(-0.737847\pi\) |
0.295502 | + | 0.955342i | \(0.404513\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.93751 | − | 1.44984i | −0.120391 | − | 0.0900885i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.10987 | + | 12.3147i | −0.439249 | + | 0.760802i | ||||
\(263\) | −14.2752 | + | 24.7253i | −0.880245 | + | 1.52463i | −0.0291760 | + | 0.999574i | \(0.509288\pi\) |
−0.851069 | + | 0.525054i | \(0.824045\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.11108 | + | 9.30735i | −0.0681245 | + | 0.570670i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.90314 | + | 3.40818i | −0.360592 | + | 0.208188i | ||||
\(269\) | −12.9628 | + | 22.4523i | −0.790359 | + | 1.36894i | 0.135386 | + | 0.990793i | \(0.456772\pi\) |
−0.925745 | + | 0.378149i | \(0.876561\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.1643 | + | 13.9513i | −1.46788 | + | 0.847479i | −0.999353 | − | 0.0359726i | \(-0.988547\pi\) |
−0.468523 | + | 0.883451i | \(0.655214\pi\) | |||||||
\(272\) | 3.52215i | 0.213561i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.130132 | 0.00786158 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.98042 | + | 5.18485i | 0.539581 | + | 0.311527i | 0.744909 | − | 0.667166i | \(-0.232493\pi\) |
−0.205328 | + | 0.978693i | \(0.565826\pi\) | |||||||
\(278\) | −3.14863 | + | 1.81786i | −0.188842 | + | 0.109028i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 21.0412i | − | 1.25521i | −0.778530 | − | 0.627607i | \(-0.784035\pi\) | ||
0.778530 | − | 0.627607i | \(-0.215965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.6859 | − | 23.7046i | 0.813541 | − | 1.40909i | −0.0968293 | − | 0.995301i | \(-0.530870\pi\) |
0.910371 | − | 0.413794i | \(-0.135797\pi\) | |||||||
\(284\) | 5.61123 | + | 3.23965i | 0.332965 | + | 0.192238i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.23352i | 0.0729399i | ||||||||
\(287\) | −5.08646 | − | 11.8719i | −0.300244 | − | 0.700777i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.29724 | − | 3.97894i | −0.135132 | − | 0.234055i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.51852 | + | 9.55835i | 0.322947 | + | 0.559360i | ||||
\(293\) | − | 16.9059i | − | 0.987654i | −0.869560 | − | 0.493827i | \(-0.835598\pi\) | ||
0.869560 | − | 0.493827i | \(-0.164402\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.792101 | + | 0.457320i | −0.0460399 | + | 0.0265812i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.53957 | + | 1.46622i | 0.147113 | + | 0.0849358i | ||||
\(299\) | −1.24384 | − | 2.15439i | −0.0719328 | − | 0.124591i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.5432 | − | 9.65851i | 1.29937 | − | 0.556707i | ||||
\(302\) | 7.13837 | 0.410767 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.06818 | + | 1.77141i | 0.175972 | + | 0.101597i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.0139 | −0.799813 | −0.399906 | − | 0.916556i | \(-0.630957\pi\) | ||||
−0.399906 | + | 0.916556i | \(0.630957\pi\) | |||||||
\(308\) | 3.39032 | + | 2.53698i | 0.193182 | + | 0.144558i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.72211 | + | 11.6430i | −0.381176 | + | 0.660216i | −0.991231 | − | 0.132143i | \(-0.957814\pi\) |
0.610055 | + | 0.792359i | \(0.291147\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.12904 | + | 3.68760i | 0.120340 | + | 0.208436i | 0.919902 | − | 0.392149i | \(-0.128268\pi\) |
−0.799562 | + | 0.600584i | \(0.794935\pi\) | |||||||
\(314\) | −14.3140 | −0.807788 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.90172 | −0.163234 | ||||||||
\(317\) | −0.0987910 | − | 0.171111i | −0.00554866 | − | 0.00961055i | 0.863238 | − | 0.504798i | \(-0.168433\pi\) |
−0.868786 | + | 0.495187i | \(0.835100\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.560785 | + | 0.971308i | −0.0313979 | + | 0.0543828i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.47948 | − | 1.01225i | −0.472543 | − | 0.0564105i | ||||
\(323\) | 12.4783 | 0.694314 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.24313 | + | 3.60448i | 0.345775 | + | 0.199633i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.88167 | −0.269545 | ||||||||
\(329\) | −5.66165 | − | 4.23662i | −0.312137 | − | 0.233572i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.29740 | − | 3.97922i | −0.126277 | − | 0.218718i | 0.795955 | − | 0.605356i | \(-0.206969\pi\) |
−0.922231 | + | 0.386639i | \(0.873636\pi\) | |||||||
\(332\) | 10.3730 | + | 5.98884i | 0.569291 | + | 0.328680i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.0336 | − | 6.94758i | 0.658447 | − | 0.380155i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 6.05076i | − | 0.329606i | −0.986327 | − | 0.164803i | \(-0.947301\pi\) | ||
0.986327 | − | 0.164803i | \(-0.0526988\pi\) | |||||||
\(338\) | 6.20299 | + | 10.7439i | 0.337398 | + | 0.584391i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.05085 | − | 1.82013i | −0.0569069 | − | 0.0985656i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.3562 | − | 6.46250i | −0.937144 | − | 0.348942i | ||||
\(344\) | − | 9.26963i | − | 0.499785i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.05023 | + | 1.18370i | 0.110221 | + | 0.0636362i | ||||
\(347\) | −1.59102 | + | 2.75573i | −0.0854104 | + | 0.147935i | −0.905566 | − | 0.424205i | \(-0.860553\pi\) |
0.820156 | + | 0.572140i | \(0.193887\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 29.0573i | − | 1.55540i | −0.628636 | − | 0.777700i | \(-0.716386\pi\) | ||
0.628636 | − | 0.777700i | \(-0.283614\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.38605 | − | 0.800236i | 0.0738767 | − | 0.0426527i | ||||
\(353\) | 6.63942 | + | 3.83327i | 0.353381 | + | 0.204025i | 0.666173 | − | 0.745797i | \(-0.267931\pi\) |
−0.312792 | + | 0.949822i | \(0.601264\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8.80739 | −0.466791 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.8791i | 0.944938i | ||||||||
\(359\) | −19.6694 | + | 11.3561i | −1.03811 | + | 0.599353i | −0.919297 | − | 0.393564i | \(-0.871242\pi\) |
−0.118812 | + | 0.992917i | \(0.537909\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.22420 | + | 5.58447i | −0.169695 | + | 0.293920i | ||||
\(362\) | 14.4343 | − | 8.33363i | 0.758649 | − | 0.438006i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.02477 | − | 0.241710i | −0.106127 | − | 0.0126690i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.37433 | − | 16.2368i | 0.489336 | − | 0.847555i | −0.510589 | − | 0.859825i | \(-0.670573\pi\) |
0.999925 | + | 0.0122703i | \(0.00390585\pi\) | |||||||
\(368\) | −1.61385 | + | 2.79527i | −0.0841277 | + | 0.145713i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.4068 | + | 2.91359i | 1.26714 | + | 0.151266i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.46050 | + | 1.42057i | −0.127400 | + | 0.0735545i | −0.562346 | − | 0.826902i | \(-0.690101\pi\) |
0.434946 | + | 0.900457i | \(0.356768\pi\) | |||||||
\(374\) | 2.81855 | − | 4.88187i | 0.145744 | − | 0.252435i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.31462 | + | 1.33635i | −0.119368 | + | 0.0689169i | ||||
\(377\) | − | 0.540105i | − | 0.0278168i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.2750 | 1.40102 | 0.700510 | − | 0.713642i | \(-0.252956\pi\) | ||||
0.700510 | + | 0.713642i | \(0.252956\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21.4359 | − | 12.3760i | −1.09675 | − | 0.633211i | ||||
\(383\) | −26.1843 | + | 15.1175i | −1.33796 | + | 0.772469i | −0.986504 | − | 0.163737i | \(-0.947645\pi\) |
−0.351451 | + | 0.936206i | \(0.614312\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.5767i | 0.640137i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.65612 | + | 4.60054i | −0.134844 | + | 0.233557i | ||||
\(389\) | 4.29588 | + | 2.48023i | 0.217810 | + | 0.125752i | 0.604936 | − | 0.796274i | \(-0.293199\pi\) |
−0.387126 | + | 0.922027i | \(0.626532\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.3684i | 0.574926i | ||||||||
\(392\) | −4.82867 | + | 5.06793i | −0.243885 | + | 0.255969i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.86800 | + | 17.0919i | 0.497143 | + | 0.861077i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.30213 | + | 12.6477i | 0.366483 | + | 0.634768i | 0.989013 | − | 0.147828i | \(-0.0472283\pi\) |
−0.622530 | + | 0.782596i | \(0.713895\pi\) | |||||||
\(398\) | 11.3423i | 0.568540i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.5622 | − | 10.1395i | 0.877014 | − | 0.506345i | 0.00734158 | − | 0.999973i | \(-0.497663\pi\) |
0.869673 | + | 0.493629i | \(0.164330\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.876505 | + | 0.506050i | 0.0436618 | + | 0.0252082i | ||||
\(404\) | 4.62663 | + | 8.01356i | 0.230183 | + | 0.398689i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.48447 | − | 1.11083i | −0.0736730 | − | 0.0551296i | ||||
\(407\) | 1.46385 | 0.0725606 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.26877 | − | 2.46458i | −0.211077 | − | 0.121865i | 0.390735 | − | 0.920503i | \(-0.372221\pi\) |
−0.601812 | + | 0.798638i | \(0.705554\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.8258 | 0.779681 | ||||||||
\(413\) | 8.20693 | + | 0.979714i | 0.403837 | + | 0.0482086i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.385363 | + | 0.667468i | −0.0188940 | + | 0.0327253i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.83510 | − | 4.91053i | −0.138669 | − | 0.240182i | ||||
\(419\) | −24.0686 | −1.17583 | −0.587913 | − | 0.808924i | \(-0.700050\pi\) | ||||
−0.587913 | + | 0.808924i | \(0.700050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0657 | 0.782995 | 0.391498 | − | 0.920179i | \(-0.371957\pi\) | ||||
0.391498 | + | 0.920179i | \(0.371957\pi\) | |||||||
\(422\) | −8.03236 | − | 13.9125i | −0.391009 | − | 0.677248i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.64520 | − | 8.04572i | 0.225591 | − | 0.390735i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.0713 | − | 17.2643i | −1.11650 | − | 0.835478i | ||||
\(428\) | 12.4147 | 0.600087 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.373691 | + | 0.215751i | 0.0180001 | + | 0.0103923i | 0.508973 | − | 0.860782i | \(-0.330025\pi\) |
−0.490973 | + | 0.871175i | \(0.663359\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.5287 | 1.46711 | 0.733557 | − | 0.679628i | \(-0.237859\pi\) | ||||
0.733557 | + | 0.679628i | \(0.237859\pi\) | |||||||
\(434\) | 3.19357 | − | 1.36827i | 0.153296 | − | 0.0656790i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.51750 | − | 9.55659i | −0.264240 | − | 0.457677i | ||||
\(437\) | 9.90315 | + | 5.71759i | 0.473732 | + | 0.273509i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.9059 | − | 18.9982i | 1.57051 | − | 0.906735i | 0.574406 | − | 0.818571i | \(-0.305233\pi\) |
0.996106 | − | 0.0881648i | \(-0.0281002\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.71461i | 0.129121i | ||||||||
\(443\) | −11.6503 | − | 20.1789i | −0.553522 | − | 0.958728i | −0.998017 | − | 0.0629464i | \(-0.979950\pi\) |
0.444495 | − | 0.895781i | \(-0.353383\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.00459 | − | 1.73999i | −0.0475685 | − | 0.0823911i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.04195 | + | 2.43194i | 0.0492276 | + | 0.114898i | ||||
\(449\) | 21.9119i | 1.03409i | 0.855960 | + | 0.517043i | \(0.172967\pi\) | ||||
−0.855960 | + | 0.517043i | \(0.827033\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.76623 | + | 3.90648i | 0.318609 | + | 0.183949i | ||||
\(452\) | −7.51506 | + | 13.0165i | −0.353479 | + | 0.612243i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 3.90576i | − | 0.183306i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.0904 | + | 19.6821i | −1.59468 | + | 0.920691i | −0.602195 | + | 0.798349i | \(0.705707\pi\) |
−0.992488 | + | 0.122341i | \(0.960960\pi\) | |||||||
\(458\) | 11.5904 | + | 6.69174i | 0.541586 | + | 0.312685i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.35282 | −0.109582 | −0.0547909 | − | 0.998498i | \(-0.517449\pi\) | ||||
−0.0547909 | + | 0.998498i | \(0.517449\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2.24550i | − | 0.104357i | −0.998638 | − | 0.0521787i | \(-0.983383\pi\) | ||
0.998638 | − | 0.0521787i | \(-0.0166165\pi\) | |||||||
\(464\) | −0.606888 | + | 0.350387i | −0.0281741 | + | 0.0162663i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.14808 | + | 8.91673i | −0.238480 | + | 0.413059i | ||||
\(467\) | −27.8740 | + | 16.0931i | −1.28986 | + | 0.744699i | −0.978628 | − | 0.205636i | \(-0.934074\pi\) |
−0.311228 | + | 0.950335i | \(0.600740\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.13770 | + | 17.9072i | −0.0987099 | + | 0.826880i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.56198 | − | 2.70542i | 0.0718958 | − | 0.124527i | ||||
\(473\) | −7.41789 | + | 12.8482i | −0.341075 | + | 0.590759i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.46106 | + | 5.58312i | 0.341977 | + | 0.255902i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −15.1952 | + | 8.77298i | −0.695014 | + | 0.401267i | ||||
\(479\) | −3.30556 | + | 5.72539i | −0.151035 | + | 0.261600i | −0.931608 | − | 0.363464i | \(-0.881594\pi\) |
0.780573 | + | 0.625064i | \(0.214927\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.610493 | + | 0.352468i | −0.0278361 | + | 0.0160712i | ||||
\(482\) | − | 10.0005i | − | 0.455510i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.43849 | 0.383568 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.99120 | + | 2.88167i | 0.226173 | + | 0.130581i | 0.608805 | − | 0.793320i | \(-0.291649\pi\) |
−0.382632 | + | 0.923901i | \(0.624982\pi\) | |||||||
\(488\) | −9.43214 | + | 5.44565i | −0.426973 | + | 0.246513i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.90529i | 0.131114i | 0.997849 | + | 0.0655570i | \(0.0208824\pi\) | ||||
−0.997849 | + | 0.0655570i | \(0.979118\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.23411 | + | 2.13755i | −0.0555817 | + | 0.0962704i | ||||
\(494\) | 2.36472 | + | 1.36527i | 0.106394 | + | 0.0614265i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 1.31318i | − | 0.0589634i | ||||||
\(497\) | 15.7573 | − | 6.75111i | 0.706810 | − | 0.302829i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.14104 | + | 1.97634i | 0.0510800 | + | 0.0884732i | 0.890435 | − | 0.455111i | \(-0.150400\pi\) |
−0.839355 | + | 0.543584i | \(0.817067\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.77706 | + | 3.07796i | 0.0793141 | + | 0.137376i | ||||
\(503\) | − | 1.32664i | − | 0.0591520i | −0.999563 | − | 0.0295760i | \(-0.990584\pi\) | ||
0.999563 | − | 0.0295760i | \(-0.00941571\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.47375 | − | 2.58292i | 0.198882 | − | 0.114825i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.30801 | + | 1.33253i | 0.102402 | + | 0.0591215i | ||||
\(509\) | 21.5053 | + | 37.2483i | 0.953207 | + | 1.65100i | 0.738419 | + | 0.674342i | \(0.235573\pi\) |
0.214788 | + | 0.976661i | \(0.431094\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.9954 | + | 3.46136i | 1.28268 | + | 0.153122i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.15756 | + | 3.55507i | 0.271598 | + | 0.156807i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.27758 | 0.188128 | ||||||||
\(518\) | −0.286843 | + | 2.40285i | −0.0126032 | + | 0.105575i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.8838 | + | 34.4397i | −0.871124 | + | 1.50883i | −0.0102890 | + | 0.999947i | \(0.503275\pi\) |
−0.860835 | + | 0.508884i | \(0.830058\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.8804 | + | 34.4338i | 0.869307 | + | 1.50568i | 0.862706 | + | 0.505706i | \(0.168768\pi\) |
0.00660128 | + | 0.999978i | \(0.497899\pi\) | |||||||
\(524\) | 14.2197 | 0.621192 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.5503 | 1.24485 | ||||||||
\(527\) | −2.31260 | − | 4.00555i | −0.100739 | − | 0.174484i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.29098 | − | 10.8963i | 0.273521 | − | 0.473752i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.61594 | − | 3.69145i | 0.373548 | − | 0.160045i | ||||
\(533\) | −3.76242 | −0.162969 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.90314 | + | 3.40818i | 0.254977 | + | 0.147211i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 25.9257 | 1.11774 | ||||||||
\(539\) | 10.7483 | − | 3.16033i | 0.462963 | − | 0.136125i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.1006 | − | 17.4947i | −0.434258 | − | 0.752157i | 0.562977 | − | 0.826473i | \(-0.309656\pi\) |
−0.997235 | + | 0.0743161i | \(0.976323\pi\) | |||||||
\(542\) | 24.1643 | + | 13.9513i | 1.03795 | + | 0.599258i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.05027 | − | 1.76107i | 0.130779 | − | 0.0755054i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 34.5631i | − | 1.47781i | −0.673810 | − | 0.738905i | \(-0.735343\pi\) | ||
0.673810 | − | 0.738905i | \(-0.264657\pi\) | |||||||
\(548\) | −0.0650662 | − | 0.112698i | −0.00277949 | − | 0.00481422i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.24136 | + | 2.15010i | 0.0528837 | + | 0.0915973i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.59965 | + | 6.14679i | −0.195597 | + | 0.261388i | ||||
\(554\) | − | 10.3697i | − | 0.440566i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.14863 | + | 1.81786i | 0.133532 | + | 0.0770945i | ||||
\(557\) | 16.2396 | − | 28.1278i | 0.688094 | − | 1.19181i | −0.284360 | − | 0.958718i | \(-0.591781\pi\) |
0.972454 | − | 0.233096i | \(-0.0748856\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.14434i | − | 0.302173i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.2222 | + | 10.5206i | −0.768658 | + | 0.443785i | ||||
\(563\) | −12.4603 | − | 7.19395i | −0.525139 | − | 0.303189i | 0.213896 | − | 0.976856i | \(-0.431385\pi\) |
−0.739035 | + | 0.673668i | \(0.764718\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −27.3718 | −1.15052 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 6.47930i | − | 0.271865i | ||||||
\(569\) | 6.84504 | − | 3.95199i | 0.286959 | − | 0.165676i | −0.349611 | − | 0.936895i | \(-0.613686\pi\) |
0.636570 | + | 0.771219i | \(0.280353\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.3198 | − | 31.7309i | 0.766661 | − | 1.32789i | −0.172704 | − | 0.984974i | \(-0.555250\pi\) |
0.939364 | − | 0.342921i | \(-0.111416\pi\) | |||||||
\(572\) | 1.06826 | − | 0.616762i | 0.0446664 | − | 0.0257881i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.73815 | + | 10.3410i | −0.322984 | + | 0.431624i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.6961 | − | 20.2583i | 0.486916 | − | 0.843363i | −0.512971 | − | 0.858406i | \(-0.671455\pi\) |
0.999887 | + | 0.0150431i | \(0.00478854\pi\) | |||||||
\(578\) | −2.29724 | + | 3.97894i | −0.0955527 | + | 0.165502i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.1290 | − | 12.4802i | 1.20848 | − | 0.517765i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.8770 | + | 7.43451i | −0.533309 | + | 0.307906i | ||||
\(584\) | 5.51852 | − | 9.55835i | 0.228358 | − | 0.395527i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.6409 | + | 8.45295i | −0.604812 | + | 0.349188i | ||||
\(587\) | 23.7776i | 0.981407i | 0.871327 | + | 0.490704i | \(0.163260\pi\) | ||||
−0.871327 | + | 0.490704i | \(0.836740\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.65236 | −0.191697 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.792101 | + | 0.457320i | 0.0325551 | + | 0.0187957i | ||||
\(593\) | −33.6979 | + | 19.4555i | −1.38381 | + | 0.798942i | −0.992608 | − | 0.121364i | \(-0.961273\pi\) |
−0.391200 | + | 0.920306i | \(0.627940\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 2.93244i | − | 0.120117i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.24384 | + | 2.15439i | −0.0508642 | + | 0.0880994i | ||||
\(599\) | 3.09380 | + | 1.78621i | 0.126409 | + | 0.0729824i | 0.561871 | − | 0.827225i | \(-0.310082\pi\) |
−0.435462 | + | 0.900207i | \(0.643415\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 21.3183i | − | 0.869591i | −0.900529 | − | 0.434795i | \(-0.856821\pi\) | ||
0.900529 | − | 0.434795i | \(-0.143179\pi\) | |||||||
\(602\) | −19.6361 | − | 14.6937i | −0.800308 | − | 0.598871i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.56919 | − | 6.18201i | −0.145228 | − | 0.251543i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.285402 | + | 0.494331i | 0.0115841 | + | 0.0200643i | 0.871759 | − | 0.489934i | \(-0.162979\pi\) |
−0.860175 | + | 0.509999i | \(0.829646\pi\) | |||||||
\(608\) | − | 3.54282i | − | 0.143681i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.78394 | + | 1.02996i | −0.0721705 | + | 0.0416676i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.5954 | + | 17.0869i | 1.19535 | + | 0.690134i | 0.959514 | − | 0.281659i | \(-0.0908848\pi\) |
0.235833 | + | 0.971794i | \(0.424218\pi\) | |||||||
\(614\) | 7.00693 | + | 12.1364i | 0.282777 | + | 0.489783i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.501930 | − | 4.20460i | 0.0202233 | − | 0.169408i | ||||
\(617\) | 20.1713 | 0.812066 | 0.406033 | − | 0.913858i | \(-0.366912\pi\) | ||||
0.406033 | + | 0.913858i | \(0.366912\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.9621 | − | 8.06104i | −0.561186 | − | 0.324001i | 0.192436 | − | 0.981310i | \(-0.438361\pi\) |
−0.753621 | + | 0.657309i | \(0.771695\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.4442 | 0.539064 | ||||||||
\(623\) | −13.9610 | + | 18.6569i | −0.559336 | + | 0.747474i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.12904 | − | 3.68760i | 0.0850935 | − | 0.147386i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.15702 | + | 12.3963i | 0.285596 | + | 0.494667i | ||||
\(629\) | 3.22149 | 0.128449 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.10655 | 0.123670 | 0.0618350 | − | 0.998086i | \(-0.480305\pi\) | ||||
0.0618350 | + | 0.998086i | \(0.480305\pi\) | |||||||
\(632\) | 1.45086 | + | 2.51296i | 0.0577121 | + | 0.0999603i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.0987910 | + | 0.171111i | −0.00392349 | + | 0.00679569i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.72158 | + | 3.90598i | −0.147454 | + | 0.154761i | ||||
\(638\) | 1.12157 | 0.0444034 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.9248 | − | 10.9262i | −0.747483 | − | 0.431559i | 0.0773008 | − | 0.997008i | \(-0.475370\pi\) |
−0.824784 | + | 0.565448i | \(0.808703\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.4873 | 1.00512 | 0.502560 | − | 0.864542i | \(-0.332391\pi\) | ||||
0.502560 | + | 0.864542i | \(0.332391\pi\) | |||||||
\(644\) | 3.36311 | + | 7.84957i | 0.132525 | + | 0.309317i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.23917 | − | 10.8066i | −0.245477 | − | 0.425179i | ||||
\(647\) | −41.5745 | − | 24.0030i | −1.63446 | − | 0.943657i | −0.982694 | − | 0.185239i | \(-0.940694\pi\) |
−0.651768 | − | 0.758418i | \(-0.725973\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.32995 | + | 2.49990i | −0.169966 | + | 0.0981296i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 7.20895i | − | 0.282324i | ||||||
\(653\) | −23.0213 | − | 39.8741i | −0.900894 | − | 1.56039i | −0.826336 | − | 0.563177i | \(-0.809579\pi\) |
−0.0745575 | − | 0.997217i | \(-0.523754\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.44083 | + | 4.22765i | 0.0952985 | + | 0.165062i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.838194 | + | 7.02144i | −0.0326762 | + | 0.273724i | ||||
\(659\) | − | 14.8751i | − | 0.579453i | −0.957109 | − | 0.289727i | \(-0.906436\pi\) | ||
0.957109 | − | 0.289727i | \(-0.0935644\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.7957 | + | 21.2440i | 1.43119 | + | 0.826296i | 0.997211 | − | 0.0746297i | \(-0.0237775\pi\) |
0.433974 | + | 0.900925i | \(0.357111\pi\) | |||||||
\(662\) | −2.29740 | + | 3.97922i | −0.0892911 | + | 0.154657i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 11.9777i | − | 0.464824i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.95885 | + | 1.13094i | −0.0758471 | + | 0.0437903i | ||||
\(668\) | −12.0336 | − | 6.94758i | −0.465593 | − | 0.268810i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.4312 | 0.672925 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 50.6101i | 1.95088i | 0.220270 | + | 0.975439i | \(0.429306\pi\) | ||||
−0.220270 | + | 0.975439i | \(0.570694\pi\) | |||||||
\(674\) | −5.24011 | + | 3.02538i | −0.201841 | + | 0.116533i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.20299 | − | 10.7439i | 0.238577 | − | 0.413227i | ||||
\(677\) | 29.9259 | − | 17.2777i | 1.15015 | − | 0.664037i | 0.201223 | − | 0.979545i | \(-0.435508\pi\) |
0.948923 | + | 0.315508i | \(0.102175\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.53510 | + | 12.9191i | 0.212418 | + | 0.495788i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.05085 | + | 1.82013i | −0.0402392 | + | 0.0696964i | ||||
\(683\) | −8.57731 | + | 14.8563i | −0.328202 | + | 0.568462i | −0.982155 | − | 0.188073i | \(-0.939776\pi\) |
0.653953 | + | 0.756535i | \(0.273109\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.08138 | + | 18.2621i | 0.117648 | + | 0.697251i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.02773 | + | 4.63481i | −0.306055 | + | 0.176701i | ||||
\(689\) | 3.58017 | − | 6.20104i | 0.136394 | − | 0.236241i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.8635 | + | 17.8190i | −1.17410 | + | 0.677869i | −0.954643 | − | 0.297753i | \(-0.903763\pi\) |
−0.219460 | + | 0.975622i | \(0.570429\pi\) | |||||||
\(692\) | − | 2.36740i | − | 0.0899951i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.18204 | 0.120788 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.8904 | + | 8.59697i | 0.564014 | + | 0.325633i | ||||
\(698\) | −25.1643 | + | 14.5286i | −0.952484 | + | 0.549917i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.0808i | 0.871751i | 0.900007 | + | 0.435876i | \(0.143561\pi\) | ||||
−0.900007 | + | 0.435876i | \(0.856439\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.62020 | − | 2.80627i | 0.0611071 | − | 0.105841i | ||||
\(704\) | −1.38605 | − | 0.800236i | −0.0522387 | − | 0.0301600i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 7.66655i | − | 0.288534i | ||||||
\(707\) | 24.3092 | + | 2.90195i | 0.914243 | + | 0.109139i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.08362 | + | 7.07303i | 0.153363 | + | 0.265633i | 0.932462 | − | 0.361268i | \(-0.117656\pi\) |
−0.779098 | + | 0.626902i | \(0.784323\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.40369 | + | 7.62742i | 0.165035 | + | 0.285850i | ||||
\(713\) | − | 4.23854i | − | 0.158735i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.4837 | − | 8.93953i | 0.578654 | − | 0.334086i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.6694 | + | 11.3561i | 0.734054 | + | 0.423806i | ||||
\(719\) | 0.377499 | + | 0.653847i | 0.0140783 | + | 0.0243844i | 0.872979 | − | 0.487758i | \(-0.162185\pi\) |
−0.858900 | + | 0.512143i | \(0.828852\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.0862 | − | 33.5242i | 0.934260 | − | 1.24851i | ||||
\(722\) | 6.44839 | 0.239984 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.4343 | − | 8.33363i | −0.536446 | − | 0.309717i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.27807 | −0.158665 | −0.0793325 | − | 0.996848i | \(-0.525279\pi\) | ||||
−0.0793325 | + | 0.996848i | \(0.525279\pi\) | |||||||
\(728\) | 0.803059 | + | 1.87436i | 0.0297634 | + | 0.0694684i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.3245 | + | 28.2749i | −0.603783 | + | 1.04578i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.7810 | + | 29.0656i | 0.619822 | + | 1.07356i | 0.989518 | + | 0.144410i | \(0.0461286\pi\) |
−0.369696 | + | 0.929153i | \(0.620538\pi\) | |||||||
\(734\) | −18.7487 | −0.692026 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.22770 | 0.118975 | ||||||||
\(737\) | −5.45470 | − | 9.44781i | −0.200926 | − | 0.348015i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.3726 | − | 30.0902i | 0.639060 | − | 1.10688i | −0.346579 | − | 0.938021i | \(-0.612657\pi\) |
0.985639 | − | 0.168864i | \(-0.0540099\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.68015 | − | 22.5937i | −0.355369 | − | 0.829441i | ||||
\(743\) | −14.3040 | −0.524762 | −0.262381 | − | 0.964964i | \(-0.584508\pi\) | ||||
−0.262381 | + | 0.964964i | \(0.584508\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.46050 | + | 1.42057i | 0.0900854 | + | 0.0520109i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.63710 | −0.206113 | ||||||||
\(749\) | 19.6791 | − | 26.2984i | 0.719060 | − | 0.960923i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.3172 | − | 36.9224i | −0.777874 | − | 1.34732i | −0.933165 | − | 0.359449i | \(-0.882965\pi\) |
0.155290 | − | 0.987869i | \(-0.450369\pi\) | |||||||
\(752\) | 2.31462 | + | 1.33635i | 0.0844056 | + | 0.0487316i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.467744 | + | 0.270052i | −0.0170342 | + | 0.00983473i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.92253i | − | 0.106221i | −0.998589 | − | 0.0531107i | \(-0.983086\pi\) | ||
0.998589 | − | 0.0531107i | \(-0.0169136\pi\) | |||||||
\(758\) | −13.6375 | − | 23.6208i | −0.495336 | − | 0.857946i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.2447 | − | 26.4046i | −0.552621 | − | 0.957167i | −0.998084 | − | 0.0618669i | \(-0.980295\pi\) |
0.445464 | − | 0.895300i | \(-0.353039\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28.9900 | − | 3.46072i | −1.04951 | − | 0.125287i | ||||
\(764\) | 24.7520i | 0.895496i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.1843 | + | 15.1175i | 0.946077 | + | 0.546218i | ||||
\(767\) | 1.20386 | − | 2.08514i | 0.0434687 | − | 0.0752900i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.7989i | 1.54337i | 0.636005 | + | 0.771685i | \(0.280586\pi\) | ||||
−0.636005 | + | 0.771685i | \(0.719414\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10.8917 | − | 6.28835i | 0.392002 | − | 0.226323i | ||||
\(773\) | 34.9867 | + | 20.1996i | 1.25838 | + | 0.726529i | 0.972760 | − | 0.231813i | \(-0.0744657\pi\) |
0.285624 | + | 0.958342i | \(0.407799\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.31224 | 0.190698 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 4.96045i | − | 0.177841i | ||||||
\(779\) | 14.9778 | − | 8.64744i | 0.536636 | − | 0.309827i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.18497 | + | 8.98062i | −0.185533 | + | 0.321352i | ||||
\(782\) | 9.84535 | − | 5.68421i | 0.352069 | − | 0.203267i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.80329 | + | 1.64779i | 0.242975 | + | 0.0588495i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.8780 | − | 27.5015i | 0.565990 | − | 0.980323i | −0.430967 | − | 0.902368i | \(-0.641827\pi\) |
0.996957 | − | 0.0779556i | \(-0.0248392\pi\) | |||||||
\(788\) | 9.86800 | − | 17.0919i | 0.351533 | − | 0.608873i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.6607 | + | 36.5524i | 0.556829 | + | 1.29965i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.26959 | + | 4.19710i | −0.258151 | + | 0.149043i | ||||
\(794\) | 7.30213 | − | 12.6477i | 0.259143 | − | 0.448849i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.82275 | − | 5.67117i | 0.348158 | − | 0.201009i | ||||
\(797\) | − | 2.25420i | − | 0.0798477i | −0.999203 | − | 0.0399239i | \(-0.987288\pi\) | ||
0.999203 | − | 0.0399239i | \(-0.0127115\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.41363 | 0.333030 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17.5622 | − | 10.1395i | −0.620143 | − | 0.358040i | ||||
\(803\) | −15.2979 | + | 8.83223i | −0.539850 | + | 0.311683i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 1.01210i | − | 0.0356497i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.62663 | − | 8.01356i | 0.162764 | − | 0.281916i | ||||
\(809\) | 43.6911 | + | 25.2251i | 1.53610 | + | 0.886867i | 0.999062 | + | 0.0433083i | \(0.0137898\pi\) |
0.537037 | + | 0.843559i | \(0.319544\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.2828i | 0.431308i | 0.976470 | + | 0.215654i | \(0.0691883\pi\) | ||||
−0.976470 | + | 0.215654i | \(0.930812\pi\) | |||||||
\(812\) | −0.219772 | + | 1.84100i | −0.00771250 | + | 0.0646065i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.731927 | − | 1.26774i | −0.0256540 | − | 0.0444341i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.4203 | + | 28.4409i | 0.574475 | + | 0.995020i | ||||
\(818\) | 4.92915i | 0.172344i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.8702 | − | 18.4003i | 1.11228 | − | 0.642174i | 0.172859 | − | 0.984947i | \(-0.444699\pi\) |
0.939418 | + | 0.342773i | \(0.111366\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.9608 | + | 8.06030i | 0.486644 | + | 0.280964i | 0.723181 | − | 0.690658i | \(-0.242679\pi\) |
−0.236537 | + | 0.971622i | \(0.576012\pi\) | |||||||
\(824\) | −7.91290 | − | 13.7055i | −0.275659 | − | 0.477455i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.25501 | − | 7.59727i | −0.113256 | − | 0.264343i | ||||
\(827\) | −35.1713 | −1.22302 | −0.611512 | − | 0.791235i | \(-0.709438\pi\) | ||||
−0.611512 | + | 0.791235i | \(0.709438\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.89744 | − | 2.25019i | −0.135364 | − | 0.0781522i | 0.430789 | − | 0.902453i | \(-0.358235\pi\) |
−0.566152 | + | 0.824301i | \(0.691569\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.770726 | 0.0267201 | ||||||||
\(833\) | 23.6537 | − | 6.95490i | 0.819554 | − | 0.240973i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.83510 | + | 4.91053i | −0.0980539 | + | 0.169834i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.0343 | + | 20.8440i | 0.415718 | + | 0.720044i | ||||
\(839\) | 37.7067 | 1.30178 | 0.650891 | − | 0.759172i | \(-0.274396\pi\) | ||||
0.650891 | + | 0.759172i | \(0.274396\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.5089 | 0.983066 | ||||||||
\(842\) | −8.03286 | − | 13.9133i | −0.276831 | − | 0.479485i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.03236 | + | 13.9125i | −0.276485 | + | 0.478886i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.3762 | − | 17.8755i | 0.459613 | − | 0.614209i | ||||
\(848\) | −9.29040 | −0.319034 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.55666 | + | 1.47609i | 0.0876413 | + | 0.0505997i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.4928 | 1.14677 | 0.573386 | − | 0.819285i | \(-0.305629\pi\) | ||||
0.573386 | + | 0.819285i | \(0.305629\pi\) | |||||||
\(854\) | −3.41566 | + | 28.6125i | −0.116881 | + | 0.979100i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.20735 | − | 10.7514i | −0.212163 | − | 0.367477i | ||||
\(857\) | 38.7373 | + | 22.3650i | 1.32324 | + | 0.763973i | 0.984244 | − | 0.176815i | \(-0.0565793\pi\) |
0.338996 | + | 0.940788i | \(0.389913\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.4154 | − | 15.2509i | 0.901281 | − | 0.520355i | 0.0236654 | − | 0.999720i | \(-0.492466\pi\) |
0.877616 | + | 0.479365i | \(0.159133\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 0.431501i | − | 0.0146970i | ||||||
\(863\) | 11.8770 | + | 20.5715i | 0.404297 | + | 0.700262i | 0.994239 | − | 0.107183i | \(-0.0341830\pi\) |
−0.589943 | + | 0.807445i | \(0.700850\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −15.2643 | − | 26.4386i | −0.518703 | − | 0.898420i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.78174 | − | 2.08158i | −0.0944185 | − | 0.0706534i | ||||
\(869\) | − | 4.64412i | − | 0.157541i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.54970 | + | 2.62677i | 0.154161 | + | 0.0890047i | ||||
\(872\) | −5.51750 | + | 9.55659i | −0.186846 | + | 0.323627i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 11.4352i | − | 0.386800i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.8940 | + | 6.86700i | −0.401632 | + | 0.231882i | −0.687188 | − | 0.726480i | \(-0.741155\pi\) |
0.285556 | + | 0.958362i | \(0.407822\pi\) | |||||||
\(878\) | −32.9059 | − | 18.9982i | −1.11052 | − | 0.641159i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.0753 | −1.51863 | −0.759313 | − | 0.650726i | \(-0.774465\pi\) | ||||
−0.759313 | + | 0.650726i | \(0.774465\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.61116i | 0.188831i | 0.995533 | + | 0.0944153i | \(0.0300981\pi\) | ||||
−0.995533 | + | 0.0944153i | \(0.969902\pi\) | |||||||
\(884\) | 2.35092 | − | 1.35730i | 0.0790700 | − | 0.0456511i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.6503 | + | 20.1789i | −0.391399 | + | 0.677923i | ||||
\(887\) | −11.9041 | + | 6.87285i | −0.399701 | + | 0.230768i | −0.686355 | − | 0.727267i | \(-0.740790\pi\) |
0.286654 | + | 0.958034i | \(0.407457\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.48128 | − | 2.77687i | 0.217375 | − | 0.0931332i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.00459 | + | 1.73999i | −0.0336360 | + | 0.0582593i | ||||
\(893\) | 4.73445 | − | 8.20031i | 0.158432 | − | 0.274413i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.58515 | − | 2.11833i | 0.0529560 | − | 0.0707683i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.9762 | − | 10.9559i | 0.633245 | − | 0.365604i | ||||
\(899\) | 0.460121 | − | 0.796953i | 0.0153459 | − | 0.0265799i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.3382 | + | 16.3611i | −0.944083 | + | 0.545066i | ||||
\(902\) | − | 7.81297i | − | 0.260143i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.0301 | 0.499894 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.01644 | − | 2.89624i | −0.166568 | − | 0.0961681i | 0.414399 | − | 0.910096i | \(-0.363992\pi\) |
−0.580967 | + | 0.813927i | \(0.697325\pi\) | |||||||
\(908\) | −3.38249 | + | 1.95288i | −0.112252 | + | 0.0648086i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.9139i | 0.494120i | 0.969000 | + | 0.247060i | \(0.0794645\pi\) | ||||
−0.969000 | + | 0.247060i | \(0.920535\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.58497 | + | 16.6017i | −0.317216 | + | 0.549435i | ||||
\(914\) | 34.0904 | + | 19.6821i | 1.12761 | + | 0.651027i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 13.3835i | − | 0.442203i | ||||||
\(917\) | 22.5404 | − | 30.1221i | 0.744349 | − | 0.994719i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.3387 | + | 47.3520i | 0.901821 | + | 1.56200i | 0.825129 | + | 0.564945i | \(0.191103\pi\) |
0.0766921 | + | 0.997055i | \(0.475564\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.17641 | + | 2.03760i | 0.0387430 | + | 0.0671049i | ||||
\(923\) | − | 4.99376i | − | 0.164372i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.94466 | + | 1.12275i | −0.0639056 | + | 0.0368959i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.606888 | + | 0.350387i | 0.0199221 | + | 0.0115020i | ||||
\(929\) | 24.6920 | + | 42.7678i | 0.810118 | + | 1.40317i | 0.912781 | + | 0.408449i | \(0.133930\pi\) |
−0.102663 | + | 0.994716i | \(0.532736\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.83782 | − | 24.1029i | 0.191327 | − | 0.789940i | ||||
\(932\) | 10.2962 | 0.337262 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 27.8740 | + | 16.0931i | 0.912066 | + | 0.526582i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.4762 | −0.407578 | −0.203789 | − | 0.979015i | \(-0.565326\pi\) | ||||
−0.203789 | + | 0.979015i | \(0.565326\pi\) | |||||||
\(938\) | 16.5770 | − | 7.10232i | 0.541258 | − | 0.231899i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.11387 | + | 10.5895i | −0.199307 | + | 0.345209i | −0.948304 | − | 0.317364i | \(-0.897202\pi\) |
0.748997 | + | 0.662573i | \(0.230536\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.87827 | + | 13.6456i | 0.256552 | + | 0.444361i | ||||
\(944\) | −3.12395 | −0.101676 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.8358 | 0.482353 | ||||||||
\(947\) | 0.915974 | + | 1.58651i | 0.0297652 | + | 0.0515548i | 0.880524 | − | 0.474001i | \(-0.157191\pi\) |
−0.850759 | + | 0.525556i | \(0.823857\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.25326 | − | 7.36687i | 0.138067 | − | 0.239139i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.10459 | − | 9.25303i | 0.0358001 | − | 0.299892i | ||||
\(953\) | 42.7813 | 1.38582 | 0.692911 | − | 0.721023i | \(-0.256328\pi\) | ||||
0.692911 | + | 0.721023i | \(0.256328\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 15.1952 | + | 8.77298i | 0.491449 | + | 0.283738i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.61111 | 0.213595 | ||||||||
\(959\) | −0.341870 | − | 0.0408113i | −0.0110396 | − | 0.00131786i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.6378 | − | 25.3534i | −0.472186 | − | 0.817851i | ||||
\(962\) | 0.610493 | + | 0.352468i | 0.0196831 | + | 0.0113640i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.66068 | + | 5.00024i | −0.278942 | + | 0.161047i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 24.5160i | − | 0.788380i | −0.919029 | − | 0.394190i | \(-0.871025\pi\) | ||
0.919029 | − | 0.394190i | \(-0.128975\pi\) | |||||||
\(968\) | −4.21924 | − | 7.30795i | −0.135612 | − | 0.234886i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.5704 | + | 20.0405i | 0.371312 | + | 0.643131i | 0.989768 | − | 0.142688i | \(-0.0455747\pi\) |
−0.618456 | + | 0.785820i | \(0.712241\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.84186 | − | 3.78825i | 0.283457 | − | 0.121446i | ||||
\(974\) | − | 5.76335i | − | 0.184669i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.43214 | + | 5.44565i | 0.301915 | + | 0.174311i | ||||
\(977\) | 23.3254 | − | 40.4007i | 0.746244 | − | 1.29253i | −0.203367 | − | 0.979103i | \(-0.565188\pi\) |
0.949611 | − | 0.313430i | \(-0.101478\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 14.0960i | − | 0.450510i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.51606 | − | 1.45265i | 0.0802906 | − | 0.0463558i | ||||
\(983\) | −4.26934 | − | 2.46490i | −0.136171 | − | 0.0786182i | 0.430367 | − | 0.902654i | \(-0.358384\pi\) |
−0.566538 | + | 0.824036i | \(0.691717\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.46823 | 0.0786044 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 2.73055i | − | 0.0868702i | ||||||
\(989\) | −25.9111 | + | 14.9598i | −0.823925 | + | 0.475694i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.0708 | + | 19.1752i | −0.351676 | + | 0.609121i | −0.986543 | − | 0.163500i | \(-0.947722\pi\) |
0.634867 | + | 0.772621i | \(0.281055\pi\) | |||||||
\(992\) | −1.13725 | + | 0.656589i | −0.0361076 | + | 0.0208467i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −13.7253 | − | 10.2706i | −0.435339 | − | 0.325765i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.94487 | − | 12.0289i | 0.219946 | − | 0.380958i | −0.734845 | − | 0.678235i | \(-0.762745\pi\) |
0.954791 | + | 0.297277i | \(0.0960785\pi\) | |||||||
\(998\) | 1.14104 | − | 1.97634i | 0.0361190 | − | 0.0625600i | ||||
\(999\) | 0 | 0 |
(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 | 3150.2.bp.g.899.7 | 24 | ||
3.2 | odd | 2 | 3150.2.bp.h.899.7 | 24 | |||
5.2 | odd | 4 | 3150.2.bf.d.1151.8 | yes | 24 | ||
5.3 | odd | 4 | 3150.2.bf.e.1151.5 | yes | 24 | ||
5.4 | even | 2 | 3150.2.bp.h.899.6 | 24 | |||
7.5 | odd | 6 | inner | 3150.2.bp.g.1349.6 | 24 | ||
15.2 | even | 4 | 3150.2.bf.d.1151.5 | ✓ | 24 | ||
15.8 | even | 4 | 3150.2.bf.e.1151.8 | yes | 24 | ||
15.14 | odd | 2 | inner | 3150.2.bp.g.899.6 | 24 | ||
21.5 | even | 6 | 3150.2.bp.h.1349.6 | 24 | |||
35.12 | even | 12 | 3150.2.bf.d.1601.5 | yes | 24 | ||
35.19 | odd | 6 | 3150.2.bp.h.1349.7 | 24 | |||
35.33 | even | 12 | 3150.2.bf.e.1601.8 | yes | 24 | ||
105.47 | odd | 12 | 3150.2.bf.d.1601.8 | yes | 24 | ||
105.68 | odd | 12 | 3150.2.bf.e.1601.5 | yes | 24 | ||
105.89 | even | 6 | inner | 3150.2.bp.g.1349.7 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.bf.d.1151.5 | ✓ | 24 | 15.2 | even | 4 | ||
3150.2.bf.d.1151.8 | yes | 24 | 5.2 | odd | 4 | ||
3150.2.bf.d.1601.5 | yes | 24 | 35.12 | even | 12 | ||
3150.2.bf.d.1601.8 | yes | 24 | 105.47 | odd | 12 | ||
3150.2.bf.e.1151.5 | yes | 24 | 5.3 | odd | 4 | ||
3150.2.bf.e.1151.8 | yes | 24 | 15.8 | even | 4 | ||
3150.2.bf.e.1601.5 | yes | 24 | 105.68 | odd | 12 | ||
3150.2.bf.e.1601.8 | yes | 24 | 35.33 | even | 12 | ||
3150.2.bp.g.899.6 | 24 | 15.14 | odd | 2 | inner | ||
3150.2.bp.g.899.7 | 24 | 1.1 | even | 1 | trivial | ||
3150.2.bp.g.1349.6 | 24 | 7.5 | odd | 6 | inner | ||
3150.2.bp.g.1349.7 | 24 | 105.89 | even | 6 | inner | ||
3150.2.bp.h.899.6 | 24 | 5.4 | even | 2 | |||
3150.2.bp.h.899.7 | 24 | 3.2 | odd | 2 | |||
3150.2.bp.h.1349.6 | 24 | 21.5 | even | 6 | |||
3150.2.bp.h.1349.7 | 24 | 35.19 | odd | 6 |