Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(185,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.185");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.cx (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: | \(4.02446026187\) |
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 | 185.2 | ||
Character | \(\chi\) | \(=\) | 504.185 |
Dual form | 504.2.cx.a.425.2 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | −1.69924 | + | 0.335557i | −0.981054 | + | 0.193734i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.64567 | −1.63039 | −0.815197 | − | 0.579183i | \(-0.803372\pi\) | ||||
−0.815197 | + | 0.579183i | \(0.803372\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.05524 | + | 2.42620i | 0.398845 | + | 0.917018i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.77480 | − | 1.14038i | 0.924934 | − | 0.380127i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.39835i | − | 0.421620i | −0.977527 | − | 0.210810i | \(-0.932390\pi\) | ||
0.977527 | − | 0.210810i | \(-0.0676101\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.97474 | − | 1.71747i | −0.825046 | − | 0.476340i | 0.0271077 | − | 0.999633i | \(-0.491370\pi\) |
−0.852153 | + | 0.523292i | \(0.824704\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.19486 | − | 1.22333i | 1.59951 | − | 0.315863i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.41670 | + | 4.18585i | −0.586137 | + | 1.01522i | 0.408596 | + | 0.912715i | \(0.366018\pi\) |
−0.994733 | + | 0.102503i | \(0.967315\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.23869 | − | 4.17926i | 1.66067 | − | 0.958787i | 0.688272 | − | 0.725453i | \(-0.258370\pi\) |
0.972397 | − | 0.233334i | \(-0.0749637\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.60724 | − | 3.76860i | −0.568946 | − | 0.822375i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 8.92741i | − | 1.86149i | −0.365665 | − | 0.930747i | \(-0.619158\pi\) | ||
0.365665 | − | 0.930747i | \(-0.380842\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.29094 | 1.65819 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.33238 | + | 2.86888i | −0.833767 | + | 0.552116i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.02182 | − | 2.89935i | 0.932529 | − | 0.538396i | 0.0449185 | − | 0.998991i | \(-0.485697\pi\) |
0.887611 | + | 0.460595i | \(0.152364\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.29782 | − | 3.05870i | 0.951516 | − | 0.549358i | 0.0579644 | − | 0.998319i | \(-0.481539\pi\) |
0.893552 | + | 0.448961i | \(0.148206\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.469228 | + | 2.37613i | 0.0816820 | + | 0.413632i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.84708 | − | 8.84514i | −0.650274 | − | 1.49510i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.89032 | − | 5.00617i | −0.475165 | − | 0.823010i | 0.524431 | − | 0.851453i | \(-0.324278\pi\) |
−0.999595 | + | 0.0284435i | \(0.990945\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.63110 | + | 1.92019i | 0.901698 | + | 0.307476i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.802159 | − | 1.38938i | 0.125276 | − | 0.216985i | −0.796565 | − | 0.604553i | \(-0.793352\pi\) |
0.921841 | + | 0.387569i | \(0.126685\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.22777 | + | 3.85862i | 0.339732 | + | 0.588434i | 0.984382 | − | 0.176044i | \(-0.0563301\pi\) |
−0.644650 | + | 0.764478i | \(0.722997\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.1160 | + | 4.15746i | −1.50801 | + | 0.619757i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.51221 | − | 2.61923i | 0.220579 | − | 0.382053i | −0.734405 | − | 0.678711i | \(-0.762539\pi\) |
0.954984 | + | 0.296658i | \(0.0958721\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.77292 | + | 5.12047i | −0.681846 | + | 0.731496i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.70196 | − | 7.92369i | 0.378350 | − | 1.10954i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.40240 | − | 2.54173i | −0.604716 | − | 0.349133i | 0.166178 | − | 0.986096i | \(-0.446857\pi\) |
−0.770895 | + | 0.636963i | \(0.780191\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.09795i | 0.687407i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.8979 | + | 9.53053i | −1.44346 | + | 1.26235i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.21233 | + | 5.56392i | 0.418210 | + | 0.724360i | 0.995759 | − | 0.0919952i | \(-0.0293244\pi\) |
−0.577550 | + | 0.816355i | \(0.695991\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.78670 | − | 4.49565i | −0.996985 | − | 0.575609i | −0.0896300 | − | 0.995975i | \(-0.528568\pi\) |
−0.907355 | + | 0.420366i | \(0.861902\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.69489 | + | 5.52886i | 0.717489 | + | 0.696570i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.8449 | + | 6.26133i | 1.34515 | + | 0.776623i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.53496 | + | 4.39068i | 0.309694 | + | 0.536407i | 0.978295 | − | 0.207215i | \(-0.0664399\pi\) |
−0.668601 | + | 0.743621i | \(0.733107\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.99565 | + | 15.1698i | 0.360634 | + | 1.82623i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.20682i | 0.499258i | 0.968342 | + | 0.249629i | \(0.0803087\pi\) | ||||
−0.968342 | + | 0.249629i | \(0.919691\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.745839 | − | 0.430610i | −0.0872938 | − | 0.0503991i | 0.455718 | − | 0.890124i | \(-0.349383\pi\) |
−0.543012 | + | 0.839725i | \(0.682716\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.0883 | + | 2.78208i | −1.62677 | + | 0.321247i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.39269 | − | 1.47561i | 0.386633 | − | 0.168161i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.31221 | + | 2.27282i | −0.147636 | + | 0.255712i | −0.930353 | − | 0.366665i | \(-0.880500\pi\) |
0.782718 | + | 0.622377i | \(0.213833\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.39906 | − | 6.32866i | 0.711007 | − | 0.703185i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.82295 | − | 6.62154i | −0.419623 | − | 0.726808i | 0.576278 | − | 0.817253i | \(-0.304504\pi\) |
−0.995901 | + | 0.0904451i | \(0.971171\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.81051 | − | 15.2603i | 0.955634 | − | 1.65521i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.56036 | + | 6.61179i | −0.810556 | + | 0.708858i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.44212 | − | 7.69398i | −0.470864 | − | 0.815560i | 0.528581 | − | 0.848883i | \(-0.322724\pi\) |
−0.999445 | + | 0.0333231i | \(0.989391\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.02785 | − | 9.02968i | 0.107748 | − | 0.946568i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.97587 | + | 6.97516i | −0.827059 | + | 0.723291i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −26.3899 | + | 15.2362i | −2.70755 | + | 1.56320i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.63985 | − | 5.56557i | 0.978778 | − | 0.565098i | 0.0768773 | − | 0.997041i | \(-0.475505\pi\) |
0.901901 | + | 0.431943i | \(0.142172\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.59466 | − | 3.88016i | −0.160269 | − | 0.389971i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.81086 | 0.578203 | 0.289101 | − | 0.957299i | \(-0.406644\pi\) | ||||
0.289101 | + | 0.957299i | \(0.406644\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.4310i | − | 1.22486i | −0.790523 | − | 0.612432i | \(-0.790191\pi\) | ||
0.790523 | − | 0.612432i | \(-0.209809\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.50514 | + | 13.7391i | 0.927606 | + | 1.34080i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.1989 | − | 5.88835i | 0.985968 | − | 0.569249i | 0.0819012 | − | 0.996640i | \(-0.473901\pi\) |
0.904067 | + | 0.427392i | \(0.140567\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.47772 | + | 7.75563i | −0.428887 | + | 0.742855i | −0.996775 | − | 0.0802516i | \(-0.974428\pi\) |
0.567887 | + | 0.823106i | \(0.307761\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.59118 | + | 7.53680i | 0.625607 | + | 0.715362i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.2381 | − | 5.91096i | −0.963117 | − | 0.556056i | −0.0659864 | − | 0.997821i | \(-0.521019\pi\) |
−0.897131 | + | 0.441764i | \(0.854353\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 32.5464i | 3.03497i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.2129 | − | 1.37330i | −0.944183 | − | 0.126962i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.7059 | − | 1.44632i | −1.16475 | − | 0.132584i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.04460 | 0.822237 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.896841 | + | 2.63005i | −0.0808654 | + | 0.237144i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.9977 | −1.07311 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.85247 | −0.608059 | −0.304029 | − | 0.952663i | \(-0.598332\pi\) | ||||
−0.304029 | + | 0.952663i | \(0.598332\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.08030 | − | 5.80916i | −0.447296 | − | 0.511468i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.689055 | −0.0602030 | −0.0301015 | − | 0.999547i | \(-0.509583\pi\) | ||||
−0.0301015 | + | 0.999547i | \(0.509583\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.7783 | + | 13.1524i | 1.54157 | + | 1.14046i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.7945 | − | 10.4590i | 1.35937 | − | 0.900167i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.47292i | 0.296712i | 0.988934 | + | 0.148356i | \(0.0473981\pi\) | ||||
−0.988934 | + | 0.148356i | \(0.952602\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.69570 | − | 4.44311i | −0.652741 | − | 0.376860i | 0.136765 | − | 0.990604i | \(-0.456330\pi\) |
−0.789505 | + | 0.613744i | \(0.789663\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.69070 | + | 4.95811i | −0.142383 | + | 0.417549i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.40163 | + | 4.15975i | −0.200835 | + | 0.347856i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.3079 | + | 10.5701i | −1.52039 | + | 0.877798i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.39211 | − | 10.3025i | 0.527212 | − | 0.849734i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 0.567607i | − | 0.0465002i | −0.999730 | − | 0.0232501i | \(-0.992599\pi\) | ||
0.999730 | − | 0.0232501i | \(-0.00740140\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.206398 | 0.0167964 | 0.00839821 | − | 0.999965i | \(-0.497327\pi\) | ||||
0.00839821 | + | 0.999965i | \(0.497327\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.93241 | + | 14.3709i | −0.156226 | + | 1.16182i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.3141 | + | 11.1510i | −1.55135 | + | 0.895671i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.69254 | − | 4.44129i | 0.613931 | − | 0.354453i | −0.160571 | − | 0.987024i | \(-0.551334\pi\) |
0.774502 | + | 0.632571i | \(0.218000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.33361 | + | 2.84174i | 0.660898 | + | 0.225364i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 21.6597 | − | 9.42060i | 1.70702 | − | 0.742447i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.351149 | − | 0.608208i | −0.0275041 | − | 0.0476386i | 0.851946 | − | 0.523630i | \(-0.175423\pi\) |
−0.879450 | + | 0.475992i | \(0.842089\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.71065 | − | 8.66261i | −0.133174 | − | 0.674383i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.24845 | − | 14.2867i | 0.638285 | − | 1.10554i | −0.347524 | − | 0.937671i | \(-0.612978\pi\) |
0.985809 | − | 0.167870i | \(-0.0536890\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.600599 | − | 1.04027i | −0.0461999 | − | 0.0800206i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.3200 | − | 19.8515i | 1.17155 | − | 1.51808i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.14623 | + | 8.91353i | −0.391261 | + | 0.677683i | −0.992616 | − | 0.121298i | \(-0.961294\pi\) |
0.601355 | + | 0.798982i | \(0.294628\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.74896 | + | 20.1155i | 0.661360 | + | 1.52059i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.32551 | − | 8.37649i | −0.550619 | − | 0.629615i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.02136 | + | 4.05378i | 0.524801 | + | 0.302994i | 0.738897 | − | 0.673819i | \(-0.235347\pi\) |
−0.214096 | + | 0.976813i | \(0.568680\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.1524i | − | 1.12627i | −0.826365 | − | 0.563134i | \(-0.809595\pi\) | ||
0.826365 | − | 0.563134i | \(-0.190405\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.7400 | + | 5.02629i | 1.08961 | + | 0.371554i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.5371 | + | 18.2509i | 0.774706 | + | 1.34183i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.85331 | + | 3.37941i | 0.428036 | + | 0.247127i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.5322 | − | 7.48387i | −0.838844 | − | 0.544371i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.49394 | + | 1.43988i | 0.180455 | + | 0.104186i | 0.587506 | − | 0.809220i | \(-0.300110\pi\) |
−0.407051 | + | 0.913405i | \(0.633443\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.03659 | − | 13.9198i | −0.578486 | − | 1.00197i | −0.995653 | − | 0.0931378i | \(-0.970310\pi\) |
0.417167 | − | 0.908830i | \(-0.363023\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −20.5292 | − | 7.00038i | −1.47012 | − | 0.501308i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.37179i | 0.453972i | 0.973898 | + | 0.226986i | \(0.0728871\pi\) | ||||
−0.973898 | + | 0.226986i | \(0.927113\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.73328 | − | 3.31011i | −0.406422 | − | 0.234648i | 0.282830 | − | 0.959170i | \(-0.408727\pi\) |
−0.689251 | + | 0.724523i | \(0.742060\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.78081 | − | 6.61017i | −0.407747 | − | 0.466246i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.3337 | + | 9.12444i | 0.865653 | + | 0.640410i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.92441 | + | 5.06522i | −0.204250 | + | 0.353771i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.1806 | − | 24.7718i | −0.707604 | − | 1.72176i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.84408 | − | 10.1223i | −0.404244 | − | 0.700171i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.13230 | − | 3.69326i | 0.146794 | − | 0.254255i | −0.783247 | − | 0.621711i | \(-0.786438\pi\) |
0.930041 | + | 0.367456i | \(0.119771\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.41163 | − | 7.14838i | −0.0967232 | − | 0.489799i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.12174 | − | 14.0673i | −0.553898 | − | 0.959380i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.0115 | + | 9.62591i | 0.883279 | + | 0.653449i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.41185 | + | 0.481437i | 0.0954040 | + | 0.0325325i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.3781 | − | 8.30123i | 0.967179 | − | 0.558401i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.338403 | + | 0.195377i | −0.0226611 | + | 0.0130834i | −0.511288 | − | 0.859410i | \(-0.670831\pi\) |
0.488627 | + | 0.872493i | \(0.337498\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 23.0057 | − | 9.45482i | 1.53371 | − | 0.630322i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.07487 | −0.137714 | −0.0688571 | − | 0.997627i | \(-0.521935\pi\) | ||||
−0.0688571 | + | 0.997627i | \(0.521935\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 14.7152i | − | 0.972411i | −0.873845 | − | 0.486205i | \(-0.838381\pi\) | ||
0.873845 | − | 0.486205i | \(-0.161619\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.26983 | + | 3.64584i | −0.346730 | + | 0.239879i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.8713 | + | 6.85389i | −0.777713 | + | 0.449013i | −0.835619 | − | 0.549309i | \(-0.814891\pi\) |
0.0579059 | + | 0.998322i | \(0.481558\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.51303 | + | 9.54884i | −0.359630 | + | 0.622898i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.46710 | − | 4.30238i | 0.0952984 | − | 0.279470i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.08032 | + | 4.66517i | 0.522672 | + | 0.301765i | 0.738027 | − | 0.674771i | \(-0.235758\pi\) |
−0.215355 | + | 0.976536i | \(0.569091\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 17.1500i | − | 1.10473i | −0.833604 | − | 0.552363i | \(-0.813726\pi\) | ||
0.833604 | − | 0.552363i | \(-0.186274\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.74989 | + | 12.9011i | −0.561306 | + | 0.827608i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.4005 | − | 18.6676i | 1.11168 | − | 1.19263i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.7110 | −1.82684 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.71799 | + | 9.96874i | 0.552480 | + | 0.631743i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.53124 | 0.601606 | 0.300803 | − | 0.953686i | \(-0.402745\pi\) | ||||
0.300803 | + | 0.953686i | \(0.402745\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.4837 | −0.784843 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.85045 | + | 28.8872i | −0.616859 | + | 1.80899i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.6663 | 1.47626 | 0.738131 | − | 0.674658i | \(-0.235709\pi\) | ||||
0.738131 | + | 0.674658i | \(0.235709\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.09600 | − | 12.2952i | 0.565198 | − | 0.763988i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.6282 | − | 13.7719i | 0.657869 | − | 0.852460i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 18.8037i | − | 1.15949i | −0.814799 | − | 0.579744i | \(-0.803153\pi\) | ||
0.814799 | − | 0.579744i | \(-0.196847\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.0497 | + | 9.26631i | 0.985926 | + | 0.569225i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.1300 | + | 11.5833i | 0.619944 | + | 0.708886i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.16840 | + | 2.02372i | −0.0712383 | + | 0.123388i | −0.899444 | − | 0.437035i | \(-0.856028\pi\) |
0.828206 | + | 0.560424i | \(0.189362\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.9051 | + | 11.4922i | −1.20915 | + | 0.698103i | −0.962574 | − | 0.271021i | \(-0.912639\pi\) |
−0.246576 | + | 0.969123i | \(0.579306\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.28342 | + | 15.6885i | 0.0776759 | + | 0.949509i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 11.5937i | − | 0.699125i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.9918 | −1.86211 | −0.931057 | − | 0.364873i | \(-0.881113\pi\) | ||||
−0.931057 | + | 0.364873i | \(0.881113\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.2123 | − | 14.5288i | 0.671264 | − | 0.869817i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.29924 | + | 4.21422i | −0.435436 | + | 0.251399i | −0.701660 | − | 0.712512i | \(-0.747557\pi\) |
0.266224 | + | 0.963911i | \(0.414224\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.6948 | − | 10.7935i | 1.11129 | − | 0.641604i | 0.172128 | − | 0.985075i | \(-0.444936\pi\) |
0.939163 | + | 0.343471i | \(0.111603\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 39.7300 | − | 34.7452i | 2.35340 | − | 2.05813i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.21739 | + | 0.480065i | 0.248945 | + | 0.0283373i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.18091 | − | 5.50950i | −0.187112 | − | 0.324088i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.5128 | + | 12.6919i | −0.850756 | + | 0.744014i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.7083 | + | 22.0114i | −0.742427 | + | 1.28592i | 0.208960 | + | 0.977924i | \(0.432992\pi\) |
−0.951387 | + | 0.307998i | \(0.900341\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.7111 | − | 20.2842i | −0.681847 | − | 1.18099i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.01171 | + | 6.05821i | 0.232783 | + | 0.351533i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.3326 | + | 26.5568i | −0.886704 | + | 1.53582i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.01095 | + | 9.47682i | −0.404104 | + | 0.546235i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.87403 | + | 1.94988i | −0.567248 | + | 0.112017i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 28.3878 | + | 16.3897i | 1.62548 | + | 0.938471i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.44895i | 0.539280i | 0.962961 | + | 0.269640i | \(0.0869047\pi\) | ||||
−0.962961 | + | 0.269640i | \(0.913095\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.17131 | + | 21.1232i | 0.237298 | + | 1.20166i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.73567 | − | 8.20242i | −0.268535 | − | 0.465117i | 0.699949 | − | 0.714193i | \(-0.253206\pi\) |
−0.968484 | + | 0.249077i | \(0.919873\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.90654 | + | 3.41015i | 0.333858 | + | 0.192753i | 0.657552 | − | 0.753409i | \(-0.271592\pi\) |
−0.323695 | + | 0.946162i | \(0.604925\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −20.7617 | − | 20.1564i | −1.16979 | − | 1.13568i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.8540 | + | 14.3494i | 1.39594 | + | 0.805945i | 0.993964 | − | 0.109706i | \(-0.0349910\pi\) |
0.401974 | + | 0.915651i | \(0.368324\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.05432 | − | 7.02229i | −0.226998 | − | 0.393173i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.3545 | + | 13.4280i | −0.857005 | + | 0.749479i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 40.4001i | 2.24792i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.6634 | − | 14.2394i | −1.36808 | − | 0.789862i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.00624 | − | 14.6812i | 0.276846 | − | 0.811871i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.95052 | + | 0.905007i | 0.438327 | + | 0.0498947i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.600666 | + | 1.04038i | −0.0330156 | + | 0.0571847i | −0.882061 | − | 0.471135i | \(-0.843844\pi\) |
0.849045 | + | 0.528320i | \(0.177178\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.7290 | − | 10.5951i | −0.752344 | − | 0.580607i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.24163 | − | 16.0070i | −0.504924 | − | 0.874554i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.34451 | − | 5.79285i | 0.182187 | − | 0.315557i | −0.760438 | − | 0.649410i | \(-0.775016\pi\) |
0.942625 | + | 0.333854i | \(0.108349\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.3804 | + | 6.60865i | 1.05260 | + | 0.358933i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.27714 | − | 7.40823i | −0.231620 | − | 0.401178i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.4599 | − | 6.17672i | −0.942746 | − | 0.333512i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.9212 | − | 55.3040i | −0.587976 | − | 2.97747i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.14577 | + | 0.661512i | −0.0615083 | + | 0.0355118i | −0.530439 | − | 0.847723i | \(-0.677973\pi\) |
0.468930 | + | 0.883235i | \(0.344639\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.25327 | + | 1.87828i | −0.174144 | + | 0.100542i | −0.584538 | − | 0.811366i | \(-0.698724\pi\) |
0.410395 | + | 0.911908i | \(0.365391\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.8149 | − | 1.09345i | 0.950891 | − | 0.0583640i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.7059 | 0.623040 | 0.311520 | − | 0.950240i | \(-0.399162\pi\) | ||||
0.311520 | + | 0.950240i | \(0.399162\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 15.3367i | − | 0.813988i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 22.0757 | − | 1.80593i | 1.16837 | − | 0.0955802i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.0847 | − | 13.3280i | 1.21836 | − | 0.703423i | 0.253797 | − | 0.967258i | \(-0.418321\pi\) |
0.964568 | + | 0.263835i | \(0.0849873\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.4324 | − | 44.0502i | 1.33855 | − | 2.31843i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.3689 | + | 3.03498i | −0.806659 | + | 0.159295i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.71909 | + | 1.56986i | 0.142323 | + | 0.0821705i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.0815i | 1.41364i | 0.707392 | + | 0.706821i | \(0.249872\pi\) | ||||
−0.707392 | + | 0.706821i | \(0.750128\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.641411 | − | 4.77002i | 0.0333905 | − | 0.248317i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.52114 | − | 13.3633i | 0.0789736 | − | 0.693786i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.60898 | 0.445756 | 0.222878 | − | 0.974846i | \(-0.428455\pi\) | ||||
0.222878 | + | 0.974846i | \(0.428455\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.3869 | − | 4.02591i | 1.05278 | − | 0.207897i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.9182 | −1.02584 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.49028 | 0.127917 | 0.0639585 | − | 0.997953i | \(-0.479627\pi\) | ||||
0.0639585 | + | 0.997953i | \(0.479627\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.6440 | − | 2.29940i | 0.596539 | − | 0.117802i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.2597 | 1.03522 | 0.517612 | − | 0.855616i | \(-0.326821\pi\) | ||||
0.517612 | + | 0.855616i | \(0.326821\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.3687 | + | 5.37958i | −0.630365 | + | 0.274169i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.5819 | + | 8.16640i | 0.537910 | + | 0.415121i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.60894i | 0.182980i | 0.995806 | + | 0.0914902i | \(0.0291630\pi\) | ||||
−0.995806 | + | 0.0914902i | \(0.970837\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.3688 | + | 21.5749i | 1.88982 | + | 1.09109i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.17087 | − | 0.231217i | 0.0590624 | − | 0.0116634i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.78390 | − | 8.28597i | 0.240704 | − | 0.416912i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.3076 | + | 9.41521i | −0.818456 | + | 0.472536i | −0.849884 | − | 0.526970i | \(-0.823328\pi\) |
0.0314275 | + | 0.999506i | \(0.489995\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −34.6229 | − | 16.3834i | −1.73331 | − | 0.820194i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 14.3026i | − | 0.714239i | −0.934059 | − | 0.357119i | \(-0.883759\pi\) | ||
0.934059 | − | 0.357119i | \(-0.116241\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.0129 | −1.04673 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −23.3289 | + | 23.0722i | −1.15922 | + | 1.14647i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.00041 | + | 4.04169i | −0.346997 | + | 0.200339i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.3685 | + | 17.5332i | −1.50162 | + | 0.866963i | −0.501626 | + | 0.865085i | \(0.667265\pi\) |
−0.999998 | + | 0.00187827i | \(0.999402\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.16536 | − | 5.90131i | −0.0574831 | − | 0.291090i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.1094 | + | 13.6650i | −0.497451 | + | 0.672413i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.9372 | + | 24.1400i | 0.684151 | + | 1.18498i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.5677 | + | 4.96755i | 0.713384 | + | 0.243262i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.83034 | + | 10.0984i | −0.284831 | + | 0.493341i | −0.972568 | − | 0.232618i | \(-0.925271\pi\) |
0.687737 | + | 0.725959i | \(0.258604\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.42981 | + | 2.47650i | 0.0696845 | + | 0.120697i | 0.898762 | − | 0.438436i | \(-0.144467\pi\) |
−0.829078 | + | 0.559133i | \(0.811134\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.20917 | − | 8.99233i | 0.0587920 | − | 0.437222i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.0367 | + | 34.7046i | −0.971925 | + | 1.68342i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.69050 | − | 23.6361i | 0.130202 | − | 1.14383i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.68511 | − | 7.87428i | 0.129638 | − | 0.380174i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.720513 | − | 0.415989i | −0.0347059 | − | 0.0200375i | 0.482547 | − | 0.875870i | \(-0.339712\pi\) |
−0.517253 | + | 0.855833i | \(0.673045\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 41.2560i | 1.98264i | 0.131479 | + | 0.991319i | \(0.458027\pi\) | ||||
−0.131479 | + | 0.991319i | \(0.541973\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 27.5626 | − | 24.1044i | 1.32153 | − | 1.15572i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −37.3099 | − | 64.6227i | −1.78478 | − | 3.09132i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.72695 | − | 2.15175i | −0.177877 | − | 0.102698i | 0.408418 | − | 0.912795i | \(-0.366081\pi\) |
−0.586295 | + | 0.810098i | \(0.699414\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.40463 | + | 19.6512i | −0.352601 | + | 0.935774i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.98795 | + | 5.18919i | 0.427030 | + | 0.246546i | 0.698081 | − | 0.716019i | \(-0.254038\pi\) |
−0.271050 | + | 0.962565i | \(0.587371\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.1945 | + | 28.0497i | 0.767694 | + | 1.32968i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.190464 | + | 0.964498i | 0.00900866 | + | 0.0456192i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.5119i | 1.39275i | 0.717677 | + | 0.696376i | \(0.245205\pi\) | ||||
−0.717677 | + | 0.696376i | \(0.754795\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.94285 | − | 1.12170i | −0.0914850 | − | 0.0528189i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.350719 | + | 0.0692583i | −0.0164782 | + | 0.00325404i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.74720 | + | 32.9193i | −0.175671 | + | 1.54328i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.11805 | + | 1.93652i | −0.0523001 | + | 0.0905864i | −0.890990 | − | 0.454023i | \(-0.849989\pi\) |
0.838690 | + | 0.544609i | \(0.183322\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.53863 | − | 25.0679i | −0.0718169 | − | 1.17007i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.62018 | − | 9.73443i | −0.261758 | − | 0.453378i | 0.704951 | − | 0.709256i | \(-0.250969\pi\) |
−0.966709 | + | 0.255878i | \(0.917635\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.58576 | + | 4.47867i | −0.120170 | + | 0.208141i | −0.919835 | − | 0.392306i | \(-0.871677\pi\) |
0.799664 | + | 0.600447i | \(0.205011\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 29.0774 | − | 25.4292i | 1.34843 | − | 1.17925i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.9873 | + | 25.9587i | 0.693528 | + | 1.20123i | 0.970674 | + | 0.240398i | \(0.0772780\pi\) |
−0.277146 | + | 0.960828i | \(0.589389\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.97767 | + | 10.7836i | −0.368375 | + | 0.497938i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.5811 | + | 10.1281i | −0.533630 | + | 0.466677i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.39572 | − | 3.11522i | 0.248095 | − | 0.143238i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 60.0155 | − | 34.6500i | 2.75370 | − | 1.58985i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15.1143 | − | 2.03238i | −0.692038 | − | 0.0930563i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.2436 | 1.61032 | 0.805159 | − | 0.593058i | \(-0.202080\pi\) | ||||
0.805159 | + | 0.593058i | \(0.202080\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.8561i | 0.905361i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −33.6438 | + | 23.2759i | −1.53085 | + | 1.05909i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −35.1437 | + | 20.2903i | −1.59580 | + | 0.921333i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.3984 | + | 21.4747i | −0.561826 | + | 0.973111i | 0.435511 | + | 0.900183i | \(0.356568\pi\) |
−0.997337 | + | 0.0729280i | \(0.976766\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.800774 | + | 0.915659i | 0.0362122 | + | 0.0414075i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.4696 | − | 10.0860i | −0.788390 | − | 0.455177i | 0.0510056 | − | 0.998698i | \(-0.483757\pi\) |
−0.839395 | + | 0.543521i | \(0.817091\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.0275i | 1.26229i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.81360 | + | 14.1458i | 0.261302 | + | 0.635806i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.2066 | + | 4.43922i | −0.457829 | + | 0.199126i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.5961 | −1.23537 | −0.617687 | − | 0.786424i | \(-0.711930\pi\) | ||||
−0.617687 | + | 0.786424i | \(0.711930\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.22205 | + | 27.0444i | −0.412011 | + | 1.20825i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.9512 | −1.24628 | −0.623142 | − | 0.782109i | \(-0.714144\pi\) | ||||
−0.623142 | + | 0.782109i | \(0.714144\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.1845 | −0.942699 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.36963 | + | 1.56612i | 0.0608273 | + | 0.0695540i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −43.1118 | −1.91090 | −0.955448 | − | 0.295160i | \(-0.904627\pi\) | ||||
−0.955448 | + | 0.295160i | \(0.904627\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.257706 | − | 2.26396i | 0.0114002 | − | 0.100151i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.3710 | + | 38.8731i | −0.855249 | + | 1.71629i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 45.3194i | 1.99701i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.66261 | − | 2.11461i | −0.161081 | − | 0.0930003i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.75366 | − | 16.8730i | 0.252558 | − | 0.740645i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.06052 | − | 5.30098i | 0.134084 | − | 0.232240i | −0.791163 | − | 0.611605i | \(-0.790524\pi\) |
0.925247 | + | 0.379365i | \(0.123857\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.1647 | − | 7.60065i | 0.575652 | − | 0.332353i | −0.183751 | − | 0.982973i | \(-0.558824\pi\) |
0.759404 | + | 0.650620i | \(0.225491\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −21.6164 | − | 31.2452i | −0.943419 | − | 1.36365i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 29.5678i | 1.28800i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −56.6986 | −2.46516 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.2586 | + | 11.7755i | 0.662165 | + | 0.511013i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.77243 | + | 2.75537i | −0.206717 | + | 0.119348i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −37.1820 | + | 21.4670i | −1.60752 | + | 0.928100i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.2912 | − | 4.53227i | −0.573558 | − | 0.195582i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.16024 | + | 6.67424i | 0.308413 | + | 0.287480i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.9995 | + | 22.5159i | 0.558894 | + | 0.968033i | 0.997589 | + | 0.0693968i | \(0.0221074\pi\) |
−0.438695 | + | 0.898636i | \(0.644559\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.08449 | + | 25.7475i | 0.218196 | + | 1.10493i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.3243 | − | 28.2745i | 0.699256 | − | 1.21115i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.7120 | − | 27.2139i | −0.671794 | − | 1.16358i | −0.977395 | − | 0.211422i | \(-0.932190\pi\) |
0.305600 | − | 0.952160i | \(-0.401143\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −26.7333 | − | 3.59475i | −1.14095 | − | 0.153420i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.2343 | − | 41.9750i | 1.03241 | − | 1.78819i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.89903 | − | 0.785316i | −0.293377 | − | 0.0333950i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −24.0293 | − | 27.4767i | −1.01999 | − | 1.16632i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.8867 | + | 19.5645i | 1.43582 | + | 0.828974i | 0.997556 | − | 0.0698707i | \(-0.0222587\pi\) |
0.438268 | + | 0.898844i | \(0.355592\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 15.3045i | − | 0.647313i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.0801 | − | 3.77829i | −0.467804 | − | 0.159520i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.6402 | + | 25.3576i | 0.617012 | + | 1.06870i | 0.990028 | + | 0.140871i | \(0.0449902\pi\) |
−0.373016 | + | 0.927825i | \(0.621676\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.3247 | + | 21.5494i | 1.57026 | + | 0.906591i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 22.1072 | + | 8.84715i | 0.928415 | + | 0.371545i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.3754 | + | 16.3825i | 1.18956 | + | 0.686791i | 0.958206 | − | 0.286079i | \(-0.0923521\pi\) |
0.231351 | + | 0.972870i | \(0.425685\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.5170 | − | 18.2160i | −0.440123 | − | 0.762315i | 0.557576 | − | 0.830126i | \(-0.311732\pi\) |
−0.997698 | + | 0.0678114i | \(0.978398\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.72095 | − | 1.60983i | −0.197220 | − | 0.0672516i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 74.0166i | − | 3.08671i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.9926 | + | 8.65597i | 0.624149 | + | 0.360353i | 0.778483 | − | 0.627666i | \(-0.215990\pi\) |
−0.154334 | + | 0.988019i | \(0.549323\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.3269 | + | 20.9563i | 0.761641 | + | 0.870912i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0311 | − | 16.2626i | 0.499132 | − | 0.674686i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.55424 | + | 6.15612i | −0.147201 | + | 0.254960i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 37.2329 | + | 5.00660i | 1.53939 | + | 0.206997i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.95712 | − | 15.5142i | −0.369700 | − | 0.640339i | 0.619819 | − | 0.784745i | \(-0.287206\pi\) |
−0.989518 | + | 0.144406i | \(0.953873\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.5662 | − | 44.2819i | 1.05343 | − | 1.82460i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.13810 | − | 10.8272i | −0.0879497 | − | 0.445371i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.6799 | − | 30.6225i | −0.726028 | − | 1.25752i | −0.958550 | − | 0.284926i | \(-0.908031\pi\) |
0.232522 | − | 0.972591i | \(-0.425302\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 46.3217 | + | 5.27280i | 1.89901 | + | 0.216164i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.8529 | + | 3.70082i | 0.444181 | + | 0.151464i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.773338 | + | 0.446487i | −0.0315977 | + | 0.0182430i | −0.515716 | − | 0.856760i | \(-0.672474\pi\) |
0.484118 | + | 0.875003i | \(0.339141\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.7713 | − | 13.7244i | 0.969653 | − | 0.559829i | 0.0705225 | − | 0.997510i | \(-0.477533\pi\) |
0.899130 | + | 0.437681i | \(0.144200\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.0411 | + | 9.29245i | 0.490350 | + | 0.378418i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −32.9737 | −1.34057 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 20.3891i | − | 0.827568i | −0.910375 | − | 0.413784i | \(-0.864207\pi\) | ||
0.910375 | − | 0.413784i | \(-0.135793\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24.0196 | − | 11.3659i | −0.973322 | − | 0.460570i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.99688 | + | 5.19435i | −0.363975 | + | 0.210141i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.6541 | − | 28.8457i | 0.672652 | − | 1.16507i | −0.304497 | − | 0.952513i | \(-0.598488\pi\) |
0.977149 | − | 0.212554i | \(-0.0681783\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.26959 | − | 9.58832i | 0.131843 | − | 0.386638i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.6812 | − | 15.9817i | −1.11440 | − | 0.643401i | −0.174437 | − | 0.984668i | \(-0.555810\pi\) |
−0.939966 | + | 0.341268i | \(0.889144\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 4.39913i | − | 0.176816i | −0.996084 | − | 0.0884079i | \(-0.971822\pi\) | ||
0.996084 | − | 0.0884079i | \(-0.0281779\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 25.6117 | + | 38.6769i | 1.02776 | + | 1.55205i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.9796 | − | 18.8965i | 0.560082 | − | 0.757072i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.28497 | 0.0913990 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.3271 | + | 15.2391i | 0.532232 | + | 0.608590i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.9401 | 1.11405 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.0749 | −0.719549 | −0.359775 | − | 0.933039i | \(-0.617146\pi\) | ||||
−0.359775 | + | 0.933039i | \(0.617146\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.38399 | + | 6.99123i | −0.0947551 | + | 0.277876i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.9819 | 0.991376 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.9925 | − | 7.03475i | 0.910995 | − | 0.278727i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.79738 | + | 11.6731i | 0.189781 | + | 0.461781i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4.10040i | − | 0.161956i | −0.996716 | − | 0.0809779i | \(-0.974196\pi\) | ||
0.996716 | − | 0.0809779i | \(-0.0258043\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.12890 | + | 4.11587i | 0.281136 | + | 0.162314i | 0.633938 | − | 0.773384i | \(-0.281438\pi\) |
−0.352801 | + | 0.935698i | \(0.614771\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.5211 | + | 21.1783i | 0.729268 | + | 0.833895i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.07138 | − | 12.2480i | 0.278004 | − | 0.481518i | −0.692884 | − | 0.721049i | \(-0.743660\pi\) |
0.970889 | + | 0.239531i | \(0.0769937\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.78033 | − | 4.49198i | 0.305405 | − | 0.176325i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −25.3397 | − | 11.9906i | −0.993139 | − | 0.469948i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.0473i | 0.901911i | 0.892546 | + | 0.450956i | \(0.148917\pi\) | ||||
−0.892546 | + | 0.450956i | \(0.851083\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.51207 | 0.0981547 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.56062 | − | 0.344319i | −0.0998991 | − | 0.0134332i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.09924 | − | 4.09875i | 0.276547 | − | 0.159665i | −0.355312 | − | 0.934748i | \(-0.615625\pi\) |
0.631859 | + | 0.775083i | \(0.282292\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.3464 | − | 15.2111i | 1.02476 | − | 0.591643i | 0.109277 | − | 0.994011i | \(-0.465146\pi\) |
0.915478 | + | 0.402369i | \(0.131813\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −21.6463 | + | 18.9304i | −0.840674 | + | 0.735197i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −64.8139 | − | 47.9493i | −2.51338 | − | 1.85939i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.8837 | − | 44.8319i | −1.00222 | − | 1.73590i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.509466 | − | 0.445545i | 0.0196971 | − | 0.0172258i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.28652 | + | 10.8886i | −0.242688 | + | 0.420349i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.44406 | + | 4.23323i | 0.0942115 | + | 0.163179i | 0.909279 | − | 0.416187i | \(-0.136634\pi\) |
−0.815068 | + | 0.579366i | \(0.803300\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −35.9195 | + | 23.7857i | −1.38254 | + | 0.915512i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.7121 | − | 18.5539i | 0.411699 | − | 0.713083i | −0.583377 | − | 0.812202i | \(-0.698269\pi\) |
0.995076 | + | 0.0991185i | \(0.0316023\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.6756 | + | 17.5152i | 0.908586 | + | 0.672171i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.52570 | − | 0.696238i | 0.135105 | − | 0.0266799i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.49101 | − | 2.01553i | −0.133580 | − | 0.0771222i | 0.431721 | − | 0.902007i | \(-0.357906\pi\) |
−0.565301 | + | 0.824885i | \(0.691240\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 12.6611i | − | 0.483757i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.93780 | + | 25.0047i | 0.188389 | + | 0.953988i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.73068 | + | 15.1220i | 0.332612 | + | 0.576101i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.0272 | − | 17.3362i | −1.14229 | − | 0.659500i | −0.195291 | − | 0.980745i | \(-0.562565\pi\) |
−0.946996 | + | 0.321246i | \(0.895899\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.73130 | − | 7.96348i | 0.293688 | − | 0.302507i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28.0560 | + | 16.1981i | 1.06422 | + | 0.614431i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.87716 | + | 6.71544i | 0.146858 | + | 0.254365i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.8722 | − | 15.6299i | 0.675990 | − | 0.591176i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.1575i | 1.17680i | 0.808569 | + | 0.588401i | \(0.200242\pi\) | ||||
−0.808569 | + | 0.588401i | \(0.799758\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −41.8442 | − | 24.1587i | −1.57818 | − | 0.911164i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.16375 | − | 18.0757i | 0.232140 | − | 0.680769i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.13188 | + | 14.0983i | 0.230613 | + | 0.530222i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.1925 | + | 24.5821i | −0.533009 | + | 0.923199i | 0.466248 | + | 0.884654i | \(0.345606\pi\) |
−0.999257 | + | 0.0385448i | \(0.987728\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.04925 | + | 7.80306i | −0.0393501 | + | 0.292637i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.3062 | − | 47.2958i | −1.02263 | − | 1.77124i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.75557 | − | 15.1651i | 0.327440 | − | 0.567142i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.2958 | − | 5.21582i | −0.571232 | − | 0.194788i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.8969 | + | 25.8022i | 0.555561 | + | 0.962259i | 0.997860 | + | 0.0653917i | \(0.0208297\pi\) |
−0.442299 | + | 0.896868i | \(0.645837\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.1602 | − | 13.1178i | 1.12322 | − | 0.488531i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.75479 | + | 29.1418i | 0.214023 | + | 1.08380i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 41.6356 | − | 24.0383i | 1.54631 | − | 0.892762i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.8231 | − | 21.2598i | 1.36569 | − | 0.788484i | 0.375320 | − | 0.926895i | \(-0.377533\pi\) |
0.990375 | + | 0.138411i | \(0.0441996\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.5391 | − | 24.8582i | 0.390336 | − | 0.920673i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.5355 | −0.796519 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.9920i | 1.36633i | 0.730263 | + | 0.683166i | \(0.239398\pi\) | ||||
−0.730263 | + | 0.683166i | \(0.760602\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −23.3035 | + | 37.5595i | −0.859564 | + | 1.38540i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.13972 | − | 3.54477i | 0.226160 | − | 0.130573i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.3127 | − | 29.9864i | 0.636857 | − | 1.10307i | −0.349261 | − | 0.937025i | \(-0.613567\pi\) |
0.986118 | − | 0.166044i | \(-0.0530993\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 48.7867 | − | 9.63417i | 1.79222 | − | 0.353920i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.1788 | − | 12.2276i | −0.776976 | − | 0.448587i | 0.0583814 | − | 0.998294i | \(-0.481406\pi\) |
−0.835358 | + | 0.549707i | \(0.814739\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.06931i | 0.0758136i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.1590 | − | 14.0139i | −0.664403 | − | 0.512740i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.0487 | + | 18.5310i | 0.915260 | + | 0.677109i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.19662 | −0.153137 | −0.0765685 | − | 0.997064i | \(-0.524396\pi\) | ||||
−0.0765685 | + | 0.997064i | \(0.524396\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.1958 | + | 3.19827i | −0.590208 | + | 0.116552i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.752460 | −0.0273848 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.3020 | 0.701545 | 0.350772 | − | 0.936461i | \(-0.385919\pi\) | ||||
0.350772 | + | 0.936461i | \(0.385919\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 21.2127 | − | 4.18899i | 0.769973 | − | 0.152051i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.7261 | −0.533821 | −0.266910 | − | 0.963721i | \(-0.586003\pi\) | ||||
−0.266910 | + | 0.963721i | \(0.586003\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.5418 | − | 2.67976i | −0.852271 | − | 0.0970139i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.04494 | − | 52.3915i | 0.254710 | − | 1.89422i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 22.0683i | − | 0.796840i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −43.6719 | − | 25.2140i | −1.57485 | − | 0.909240i | −0.995561 | − | 0.0941181i | \(-0.969997\pi\) |
−0.579289 | − | 0.815122i | \(-0.696670\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40.2146 | + | 7.94138i | −1.44829 | + | 0.286002i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.54706 | − | 16.5360i | 0.343384 | − | 0.594758i | −0.641675 | − | 0.766977i | \(-0.721760\pi\) |
0.985059 | + | 0.172218i | \(0.0550935\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 43.9239 | − | 25.3595i | 1.57779 | − | 0.910939i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.3305 | + | 23.9447i | −0.406480 | + | 0.859012i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 13.4097i | − | 0.480453i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.88263 | 0.210497 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.4386 | + | 26.9681i | −0.480255 | + | 0.963761i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28.0445 | + | 16.1915i | −1.00095 | + | 0.577899i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.0297 | − | 24.8432i | 1.53384 | − | 0.885566i | 0.534665 | − | 0.845064i | \(-0.320438\pi\) |
0.999179 | − | 0.0405015i | \(-0.0128956\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.30972 | + | 31.9520i | 0.224632 | + | 1.13752i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.53751 | − | 31.0772i | 0.125779 | − | 1.10498i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.4423 | + | 26.7468i | 0.548372 | + | 0.949808i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −30.3816 | − | 10.3600i | −1.07753 | − | 0.367433i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.17665 | + | 8.96621i | −0.183366 | + | 0.317600i | −0.943025 | − | 0.332723i | \(-0.892033\pi\) |
0.759659 | + | 0.650322i | \(0.225366\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.30913 | + | 12.6598i | 0.258578 | + | 0.447871i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −21.1001 | − | 16.2836i | −0.745534 | − | 0.575351i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.602146 | + | 1.04295i | −0.0212493 | + | 0.0368048i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −78.9642 | + | 34.3444i | −2.78312 | + | 1.21048i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.30631 | − | 3.83084i | 0.0459841 | − | 0.134852i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41.5520 | − | 23.9901i | −1.46089 | − | 0.843446i | −0.461838 | − | 0.886964i | \(-0.652810\pi\) |
−0.999053 | + | 0.0435184i | \(0.986143\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.79426i | 0.168349i | 0.996451 | + | 0.0841745i | \(0.0268253\pi\) | ||||
−0.996451 | + | 0.0841745i | \(0.973175\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.9672 | − | 26.2073i | 1.05100 | − | 0.919130i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.28018 | + | 2.21733i | 0.0448426 | + | 0.0776697i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 32.2523 | + | 18.6209i | 1.12837 | + | 0.651462i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.44520 | − | 26.2277i | −0.260156 | − | 0.916471i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.3923 | − | 14.0829i | −0.851296 | − | 0.491496i | 0.00979179 | − | 0.999952i | \(-0.496883\pi\) |
−0.861088 | + | 0.508456i | \(0.830216\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.6428 | + | 49.6107i | 0.998424 | + | 1.72932i | 0.547813 | + | 0.836601i | \(0.315460\pi\) |
0.450611 | + | 0.892720i | \(0.351206\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.89034 | + | 19.7004i | 0.135444 | + | 0.685879i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 27.9805i | − | 0.972976i | −0.873687 | − | 0.486488i | \(-0.838278\pi\) | ||
0.873687 | − | 0.486488i | \(-0.161722\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.6428 | + | 25.7745i | 1.55051 | + | 0.895186i | 0.998100 | + | 0.0616119i | \(0.0196241\pi\) |
0.552408 | + | 0.833574i | \(0.313709\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 52.6623 | − | 10.3995i | 1.82684 | − | 0.360755i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.89881 | − | 32.3534i | −0.342973 | − | 1.12098i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.0712 | + | 52.0848i | −1.04066 | + | 1.80247i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14.1771 | + | 28.4502i | −0.490033 | + | 0.983384i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.64286 | + | 8.04167i | 0.160289 | + | 0.277629i | 0.934972 | − | 0.354720i | \(-0.115424\pi\) |
−0.774683 | + | 0.632350i | \(0.782091\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.31247 | − | 4.00531i | 0.0797403 | − | 0.138114i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.9890 | − | 9.61027i | 0.378482 | − | 0.330995i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.18959 | + | 3.79248i | 0.0753241 | + | 0.130465i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.54426 | + | 21.9440i | 0.327945 | + | 0.754006i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.1451 | + | 24.6138i | −0.965936 | + | 0.844743i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −44.6922 | + | 25.8030i | −1.53203 | + | 0.884516i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.5591 | − | 12.4471i | 0.738168 | − | 0.426181i | −0.0832349 | − | 0.996530i | \(-0.526525\pi\) |
0.821403 | + | 0.570349i | \(0.193192\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −55.8517 | + | 72.3720i | −1.91009 | + | 2.47507i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.4238 | 1.14174 | 0.570868 | − | 0.821042i | \(-0.306607\pi\) | ||||
0.570868 | + | 0.821042i | \(0.306607\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.7864i | 1.15278i | 0.817175 | + | 0.576389i | \(0.195539\pi\) | ||||
−0.817175 | + | 0.576389i | \(0.804461\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.32743 | + | 0.599431i | −0.249718 | + | 0.0204285i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.74739 | − | 5.62766i | 0.331805 | − | 0.191568i | −0.324837 | − | 0.945770i | \(-0.605309\pi\) |
0.656642 | + | 0.754202i | \(0.271976\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.7615 | − | 32.4958i | 0.637910 | − | 1.10489i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.25386 | + | 8.29456i | 0.246354 | + | 0.281698i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.17821 | + | 1.83494i | 0.107813 | + | 0.0622461i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 17.4149i | − | 0.590080i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.4018 | − | 26.4365i | 0.690497 | − | 0.894738i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.6605 | − | 29.1088i | −0.428003 | − | 0.984058i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.7801 | −1.41081 | −0.705407 | − | 0.708803i | \(-0.749236\pi\) | ||||
−0.705407 | + | 0.708803i | \(0.749236\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.2083 | − | 41.6670i | 0.479235 | − | 1.40539i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.2845 | 0.649710 | 0.324855 | − | 0.945764i | \(-0.394685\pi\) | ||||
0.324855 | + | 0.945764i | \(0.394685\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.1130 | 1.85470 | 0.927350 | − | 0.374195i | \(-0.122081\pi\) | ||||
0.927350 | + | 0.374195i | \(0.122081\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 26.7064 | + | 30.5379i | 0.897727 | + | 1.02652i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.9546 | 0.837892 | 0.418946 | − | 0.908011i | \(-0.362400\pi\) | ||||
0.418946 | + | 0.908011i | \(0.362400\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.23103 | − | 16.6255i | −0.242521 | − | 0.557601i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.84972 | − | 8.94816i | −0.296477 | − | 0.299775i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 25.2797i | − | 0.845952i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.5976 | − | 14.7788i | −0.855633 | − | 0.494000i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.1423 | − | 50.2711i | 0.572365 | − | 1.67850i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.7365 | − | 30.7205i | 0.591544 | − | 1.02458i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.2786 | − | 12.2852i | 0.708893 | − | 0.409279i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.73324 | − | 18.4559i | 0.290624 | − | 0.614174i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 55.2407i | 1.83626i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 58.8709 | 1.95478 | 0.977388 | − | 0.211452i | \(-0.0678192\pi\) | ||||
0.977388 | + | 0.211452i | \(0.0678192\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.1240 | − | 6.62660i | 0.534799 | − | 0.219790i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.6533 | + | 21.1618i | −1.21438 | + | 0.701121i | −0.963710 | − | 0.266952i | \(-0.913983\pi\) |
−0.250668 | + | 0.968073i | \(0.580650\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.25926 | + | 5.34584i | −0.306437 | + | 0.176921i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −53.7372 | − | 18.3242i | −1.77650 | − | 0.605780i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.727121 | − | 1.67179i | −0.0240117 | − | 0.0552073i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.9879 | + | 29.4239i | 0.560379 | + | 0.970605i | 0.997463 | + | 0.0711842i | \(0.0226778\pi\) |
−0.437084 | + | 0.899421i | \(0.643989\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.17066 | − | 16.0560i | −0.104477 | − | 0.529063i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.22509 | − | 12.5142i | 0.237817 | − | 0.411911i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.9634 | − | 41.5059i | −0.787913 | − | 1.36470i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.1761 | − | 34.4936i | −0.465604 | − | 1.13292i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.41930 | + | 11.1185i | −0.210610 | + | 0.364788i | −0.951906 | − | 0.306391i | \(-0.900878\pi\) |
0.741295 | + | 0.671179i | \(0.234212\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.1499 | + | 57.0127i | −0.430970 | + | 1.86852i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.7994 | + | 12.3488i | 0.353556 | + | 0.404280i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21.3393 | − | 12.3202i | −0.697868 | − | 0.402914i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.2886i | 0.924149i | 0.886841 | + | 0.462075i | \(0.152895\pi\) | ||||
−0.886841 | + | 0.462075i | \(0.847105\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.1809 | − | 3.81266i | −0.364875 | − | 0.124421i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.8901 | + | 22.3263i | 0.420205 | + | 0.727817i | 0.995959 | − | 0.0898059i | \(-0.0286247\pi\) |
−0.575754 | + | 0.817623i | \(0.695291\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.4036 | − | 7.16120i | −0.403915 | − | 0.233201i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 42.0427 | + | 27.2837i | 1.36765 | + | 0.887540i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −52.3308 | − | 30.2132i | −1.70052 | − | 0.981798i | −0.945227 | − | 0.326415i | \(-0.894159\pi\) |
−0.755297 | − | 0.655383i | \(-0.772507\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.47912 | + | 2.56191i | 0.0480143 | + | 0.0831631i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −47.0478 | − | 16.0432i | −1.52563 | − | 0.520235i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.83769i | − | 0.124315i | −0.998066 | − | 0.0621575i | \(-0.980202\pi\) | ||
0.998066 | − | 0.0621575i | \(-0.0197981\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.09208 | − | 5.24932i | −0.294213 | − | 0.169864i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.24562 | + | 10.5721i | 0.298869 | + | 0.341746i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.42601 | + | 3.66478i | −0.272090 | + | 0.118342i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.21124 | − | 5.56203i | 0.103588 | − | 0.179420i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.5851 | − | 27.9697i | 0.695569 | − | 0.901311i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29.2988 | + | 50.7470i | 0.943161 | + | 1.63360i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.68243 | + | 6.37816i | −0.118419 | + | 0.205108i | −0.919141 | − | 0.393928i | \(-0.871116\pi\) |
0.800722 | + | 0.599036i | \(0.204449\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.5565 | − | 68.6493i | −0.435499 | − | 2.20533i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.6276 | + | 46.1204i | 0.854521 | + | 1.48007i | 0.877089 | + | 0.480328i | \(0.159482\pi\) |
−0.0225686 | + | 0.999745i | \(0.507184\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.65905 | − | 23.3599i | 0.0852454 | − | 0.748884i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 46.6871 | + | 15.9202i | 1.49518 | + | 0.509853i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −50.5473 | + | 29.1835i | −1.61715 | + | 0.933663i | −0.629500 | + | 0.777001i | \(0.716740\pi\) |
−0.987652 | + | 0.156662i | \(0.949927\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.7589 | + | 6.21166i | −0.343856 | + | 0.198525i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.58041 | + | 26.6266i | −0.114314 | + | 0.850123i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56.9508 | −1.81645 | −0.908224 | − | 0.418485i | \(-0.862561\pi\) | ||||
−0.908224 | + | 0.418485i | \(0.862561\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 23.2295i | − | 0.740153i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.8135 | + | 1.13003i | −0.439688 | + | 0.0359693i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.4475 | − | 19.8883i | 1.09537 | − | 0.632410i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.39894 | + | 12.8153i | −0.235035 | + | 0.407093i | −0.959283 | − | 0.282447i | \(-0.908854\pi\) |
0.724248 | + | 0.689540i | \(0.242187\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.671565 | − | 1.96942i | 0.0213115 | − | 0.0624975i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.9017 | + | 12.0676i | 0.662628 | + | 0.382568i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 39.0440i | − | 1.23654i | −0.785967 | − | 0.618268i | \(-0.787835\pi\) | ||
0.785967 | − | 0.618268i | \(-0.212165\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 26.8841 | + | 13.3967i | 0.850574 | + | 0.423852i |
(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 | 504.2.cx.a.185.2 | yes | 48 | |
3.2 | odd | 2 | 1512.2.cx.a.17.23 | 48 | |||
4.3 | odd | 2 | 1008.2.df.e.689.23 | 48 | |||
7.5 | odd | 6 | 504.2.bs.a.257.9 | ✓ | 48 | ||
9.2 | odd | 6 | 504.2.bs.a.353.9 | yes | 48 | ||
9.7 | even | 3 | 1512.2.bs.a.521.23 | 48 | |||
12.11 | even | 2 | 3024.2.df.e.17.23 | 48 | |||
21.5 | even | 6 | 1512.2.bs.a.1097.23 | 48 | |||
28.19 | even | 6 | 1008.2.ca.e.257.16 | 48 | |||
36.7 | odd | 6 | 3024.2.ca.e.2033.23 | 48 | |||
36.11 | even | 6 | 1008.2.ca.e.353.16 | 48 | |||
63.47 | even | 6 | inner | 504.2.cx.a.425.2 | yes | 48 | |
63.61 | odd | 6 | 1512.2.cx.a.89.23 | 48 | |||
84.47 | odd | 6 | 3024.2.ca.e.2609.23 | 48 | |||
252.47 | odd | 6 | 1008.2.df.e.929.23 | 48 | |||
252.187 | even | 6 | 3024.2.df.e.1601.23 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bs.a.257.9 | ✓ | 48 | 7.5 | odd | 6 | ||
504.2.bs.a.353.9 | yes | 48 | 9.2 | odd | 6 | ||
504.2.cx.a.185.2 | yes | 48 | 1.1 | even | 1 | trivial | |
504.2.cx.a.425.2 | yes | 48 | 63.47 | even | 6 | inner | |
1008.2.ca.e.257.16 | 48 | 28.19 | even | 6 | |||
1008.2.ca.e.353.16 | 48 | 36.11 | even | 6 | |||
1008.2.df.e.689.23 | 48 | 4.3 | odd | 2 | |||
1008.2.df.e.929.23 | 48 | 252.47 | odd | 6 | |||
1512.2.bs.a.521.23 | 48 | 9.7 | even | 3 | |||
1512.2.bs.a.1097.23 | 48 | 21.5 | even | 6 | |||
1512.2.cx.a.17.23 | 48 | 3.2 | odd | 2 | |||
1512.2.cx.a.89.23 | 48 | 63.61 | odd | 6 | |||
3024.2.ca.e.2033.23 | 48 | 36.7 | odd | 6 | |||
3024.2.ca.e.2609.23 | 48 | 84.47 | odd | 6 | |||
3024.2.df.e.17.23 | 48 | 12.11 | even | 2 | |||
3024.2.df.e.1601.23 | 48 | 252.187 | even | 6 |