Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(191,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, 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("1152.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.p (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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 16x^{14} + 178x^{12} - 1024x^{10} + 4267x^{8} - 7936x^{6} + 10594x^{4} - 2800x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 959.3 | ||
Root | \(-0.451553 + 0.260704i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.959 |
Dual form | 1152.2.p.d.191.3 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.524648 | + | 1.65068i | −0.302905 | + | 0.953021i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.86407 | + | 3.22866i | −0.833636 | + | 1.44390i | 0.0615002 | + | 0.998107i | \(0.480412\pi\) |
−0.895136 | + | 0.445793i | \(0.852922\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.39555 | − | 1.38307i | 0.905432 | − | 0.522751i | 0.0264733 | − | 0.999650i | \(-0.491572\pi\) |
0.878959 | + | 0.476898i | \(0.158239\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.44949 | − | 1.73205i | −0.816497 | − | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.21650 | + | 1.27970i | −0.668301 | + | 0.385844i | −0.795432 | − | 0.606042i | \(-0.792756\pi\) |
0.127132 | + | 0.991886i | \(0.459423\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.02619 | − | 0.592470i | −0.284613 | − | 0.164322i | 0.350897 | − | 0.936414i | \(-0.385877\pi\) |
−0.635510 | + | 0.772093i | \(0.719210\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.35150 | − | 4.77089i | −1.12355 | − | 1.23184i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.04989i | − | 0.497171i | −0.968610 | − | 0.248585i | \(-0.920034\pi\) | ||
0.968610 | − | 0.248585i | \(-0.0799657\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.66883 | −1.07110 | −0.535551 | − | 0.844503i | \(-0.679896\pi\) | ||||
−0.535551 | + | 0.844503i | \(0.679896\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.02619 | + | 4.67991i | 0.223933 | + | 1.02124i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.35150 | + | 7.53703i | −0.907351 | + | 1.57158i | −0.0896218 | + | 0.995976i | \(0.528566\pi\) |
−0.817730 | + | 0.575603i | \(0.804768\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.44949 | − | 7.70674i | −0.889898 | − | 1.54135i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.14418 | − | 3.13461i | 0.797548 | − | 0.603256i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.70195 | − | 4.67991i | −0.501739 | − | 0.869037i | −0.999998 | − | 0.00200885i | \(-0.999361\pi\) |
0.498259 | − | 0.867028i | \(-0.333973\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.26342 | + | 4.77089i | 1.48415 | + | 0.856876i | 0.999838 | − | 0.0180169i | \(-0.00573526\pi\) |
0.484316 | + | 0.874893i | \(0.339069\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.949490 | − | 4.33013i | −0.165285 | − | 0.753778i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.3125i | 1.74314i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.27238i | − | 0.866773i | −0.901208 | − | 0.433387i | \(-0.857318\pi\) | ||
0.901208 | − | 0.433387i | \(-0.142682\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.51637 | − | 1.38307i | 0.242813 | − | 0.221468i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.62372 | − | 4.40156i | −1.19063 | − | 0.687408i | −0.232177 | − | 0.972674i | \(-0.574585\pi\) |
−0.958449 | + | 0.285265i | \(0.907918\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.97697 | − | 5.15627i | −0.453984 | − | 0.786324i | 0.544645 | − | 0.838667i | \(-0.316664\pi\) |
−0.998629 | + | 0.0523430i | \(0.983331\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.1582 | − | 4.67991i | 1.51430 | − | 0.697639i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.39555 | + | 4.14921i | 0.349427 | + | 0.605224i | 0.986148 | − | 0.165870i | \(-0.0530431\pi\) |
−0.636721 | + | 0.771094i | \(0.719710\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.325765 | − | 0.564242i | 0.0465379 | − | 0.0806060i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.38371 | + | 1.07547i | 0.473814 | + | 0.150596i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.13202 | 1.25438 | 0.627190 | − | 0.778866i | \(-0.284205\pi\) | ||||
0.627190 | + | 0.778866i | \(0.284205\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 9.54177i | − | 1.28661i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.44949 | − | 7.70674i | 0.324443 | − | 1.02078i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.79045 | − | 2.18841i | −0.493474 | − | 0.284907i | 0.232541 | − | 0.972587i | \(-0.425296\pi\) |
−0.726015 | + | 0.687679i | \(0.758629\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.02619 | − | 0.592470i | 0.131390 | − | 0.0758580i | −0.432864 | − | 0.901459i | \(-0.642497\pi\) |
0.564254 | + | 0.825601i | \(0.309164\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.26342 | − | 0.761394i | −1.04109 | − | 0.0959267i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.82577 | − | 2.20881i | 0.474528 | − | 0.273969i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.60021 | − | 9.69985i | 0.684175 | − | 1.18503i | −0.289521 | − | 0.957172i | \(-0.593496\pi\) |
0.973695 | − | 0.227854i | \(-0.0731708\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.1582 | − | 11.1372i | −1.22291 | − | 1.34076i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.91191 | −0.464259 | −0.232129 | − | 0.972685i | \(-0.574569\pi\) | ||||
−0.232129 | + | 0.972685i | \(0.574569\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.44949 | −0.520773 | −0.260387 | − | 0.965504i | \(-0.583850\pi\) | ||||
−0.260387 | + | 0.965504i | \(0.583850\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 15.0558 | − | 3.30136i | 1.73849 | − | 0.381208i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.53982 | + | 6.13116i | −0.403400 | + | 0.698710i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.26342 | + | 4.77089i | −0.929707 | + | 0.536767i | −0.886719 | − | 0.462309i | \(-0.847021\pi\) |
−0.0429881 | + | 0.999076i | \(0.513688\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.00000 | + | 8.48528i | 0.333333 | + | 0.942809i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.92768 | + | 1.11295i | −0.211590 | + | 0.122162i | −0.602050 | − | 0.798458i | \(-0.705649\pi\) |
0.390460 | + | 0.920620i | \(0.372316\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.61839 | + | 3.82113i | 0.717865 | + | 0.414460i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.14260 | − | 2.00475i | 0.980190 | − | 0.214931i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 13.9993i | − | 1.48392i | −0.670444 | − | 0.741960i | \(-0.733896\pi\) | ||
0.670444 | − | 0.741960i | \(-0.266104\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.27771 | −0.343597 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.2106 | + | 11.1372i | −1.26618 | + | 1.15488i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.70301 | − | 15.0741i | 0.892910 | − | 1.54657i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.72474 | − | 2.98735i | −0.175121 | − | 0.303319i | 0.765082 | − | 0.643933i | \(-0.222698\pi\) |
−0.940203 | + | 0.340614i | \(0.889365\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.64580 | + | 0.704487i | 0.768432 | + | 0.0708036i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.59220 | − | 9.68597i | −0.556445 | − | 0.963791i | −0.997790 | − | 0.0664530i | \(-0.978832\pi\) |
0.441345 | − | 0.897338i | \(-0.354502\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.39555 | − | 1.38307i | −0.236040 | − | 0.136278i | 0.377315 | − | 0.926085i | \(-0.376847\pi\) |
−0.613355 | + | 0.789807i | \(0.710181\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −17.0227 | − | 5.41045i | −1.66125 | − | 0.528006i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.0545i | 1.06868i | 0.845270 | + | 0.534340i | \(0.179440\pi\) | ||||
−0.845270 | + | 0.534340i | \(0.820560\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.1870i | 1.74200i | 0.491283 | + | 0.871000i | \(0.336528\pi\) | ||||
−0.491283 | + | 0.871000i | \(0.663472\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.70301 | + | 2.76614i | 0.826053 | + | 0.262550i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.39898 | + | 1.96240i | 0.319749 | + | 0.184607i | 0.651281 | − | 0.758837i | \(-0.274232\pi\) |
−0.331532 | + | 0.943444i | \(0.607565\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.2230 | − | 28.0990i | −1.51280 | − | 2.62025i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.48745 | + | 3.22866i | 0.137515 | + | 0.298490i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.83514 | − | 4.91060i | −0.259897 | − | 0.450154i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.22474 | + | 3.85337i | −0.202250 | + | 0.350306i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.2653 | − | 10.2751i | 1.01576 | − | 0.926471i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 14.5359 | 1.30013 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.53228i | 0.490910i | 0.969408 | + | 0.245455i | \(0.0789374\pi\) | ||||
−0.969408 | + | 0.245455i | \(0.921063\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.0732 | − | 2.20881i | 0.886897 | − | 0.194475i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.9342 | + | 9.19959i | 1.39217 | + | 0.803772i | 0.993556 | − | 0.113345i | \(-0.0361564\pi\) |
0.398619 | + | 0.917117i | \(0.369490\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.1844 | + | 6.45732i | −0.969811 | + | 0.559920i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.39555 | + | 19.2233i | 0.206176 | + | 1.65447i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.7247 | + | 6.76928i | −1.00171 | + | 0.578339i | −0.908755 | − | 0.417331i | \(-0.862966\pi\) |
−0.0929580 | + | 0.995670i | \(0.529632\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.31139 | + | 9.19959i | −0.450506 | + | 0.780299i | −0.998417 | − | 0.0562370i | \(-0.982090\pi\) |
0.547911 | + | 0.836536i | \(0.315423\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.10584 | + | 1.77741i | −0.682635 | + | 0.149685i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.03273 | 0.253610 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.1464 | 1.67307 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.760471 | + | 0.833763i | 0.0627226 | + | 0.0687676i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.70195 | + | 4.67991i | −0.221352 | + | 0.383393i | −0.955219 | − | 0.295901i | \(-0.904380\pi\) |
0.733867 | + | 0.679293i | \(0.237714\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.0545 | + | 7.53703i | −1.06236 | + | 0.613354i | −0.926084 | − | 0.377316i | \(-0.876847\pi\) |
−0.136277 | + | 0.990671i | \(0.543514\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.55051 | + | 5.02118i | −0.287042 | + | 0.405938i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −30.8071 | + | 17.7865i | −2.47449 | + | 1.42865i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.6718 | − | 7.31610i | −1.01132 | − | 0.583888i | −0.0997447 | − | 0.995013i | \(-0.531803\pi\) |
−0.911579 | + | 0.411125i | \(0.865136\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.79110 | + | 15.0741i | −0.379959 | + | 1.19545i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.0737i | 1.89728i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.4362 | −0.895756 | −0.447878 | − | 0.894095i | \(-0.647820\pi\) | ||||
−0.447878 | + | 0.894095i | \(0.647820\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 15.7504 | + | 5.00607i | 1.22617 | + | 0.389722i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.30746 | − | 10.9248i | 0.488086 | − | 0.845390i | −0.511820 | − | 0.859093i | \(-0.671029\pi\) |
0.999906 | + | 0.0137030i | \(0.00436193\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.79796 | − | 10.0424i | −0.445997 | − | 0.772489i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.4362 | + | 8.08665i | 0.874552 | + | 0.618401i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.86407 | − | 3.22866i | −0.141722 | − | 0.245470i | 0.786423 | − | 0.617688i | \(-0.211931\pi\) |
−0.928145 | + | 0.372218i | \(0.878597\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.3179 | − | 12.3079i | −1.61148 | − | 0.930391i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.60102 | − | 5.10867i | 0.420998 | − | 0.383991i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.5384i | 0.937166i | 0.883419 | + | 0.468583i | \(0.155235\pi\) | ||||
−0.883419 | + | 0.468583i | \(0.844765\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 10.0121i | − | 0.744196i | −0.928193 | − | 0.372098i | \(-0.878638\pi\) | ||
0.928193 | − | 0.372098i | \(-0.121362\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.439591 | + | 2.00475i | 0.0324955 | + | 0.148195i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.0227 | + | 9.82806i | 1.25153 | + | 0.722574i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.62324 | + | 4.54358i | 0.191830 | + | 0.332260i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.59220 | − | 13.2408i | 0.406773 | − | 0.963126i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.30746 | − | 10.9248i | −0.456392 | − | 0.790494i | 0.542375 | − | 0.840136i | \(-0.317525\pi\) |
−0.998767 | + | 0.0496426i | \(0.984192\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.6237 | + | 21.8649i | −0.908676 | + | 1.57387i | −0.0927696 | + | 0.995688i | \(0.529572\pi\) |
−0.815906 | + | 0.578185i | \(0.803761\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.63885 | + | 7.47396i | 0.117361 | + | 0.535221i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.35152 | −0.238786 | −0.119393 | − | 0.992847i | \(-0.538095\pi\) | ||||
−0.119393 | + | 0.992847i | \(0.538095\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.3079i | 0.872485i | 0.899829 | + | 0.436242i | \(0.143691\pi\) | ||||
−0.899829 | + | 0.436242i | \(0.856309\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.0732 | + | 14.3332i | 0.922113 | + | 1.01098i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.9453 | − | 7.47396i | −0.908580 | − | 0.524569i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28.4223 | − | 16.4096i | 1.98510 | − | 1.14610i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 23.7135 | − | 10.9248i | 1.64820 | − | 0.759329i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.3485 | − | 5.97469i | 0.715819 | − | 0.413278i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.5049 | − | 18.1950i | 0.723185 | − | 1.25259i | −0.236532 | − | 0.971624i | \(-0.576011\pi\) |
0.959717 | − | 0.280969i | \(-0.0906558\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.05238 | − | 6.45732i | 0.140626 | − | 0.442448i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 22.1971 | 1.51383 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 26.3939 | 1.79173 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.33441 | − | 7.34468i | 0.157745 | − | 0.496308i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.21450 | + | 2.10357i | −0.0816959 | + | 0.141501i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.1313 | − | 8.15870i | 0.946301 | − | 0.546347i | 0.0543710 | − | 0.998521i | \(-0.482685\pi\) |
0.891930 | + | 0.452174i | \(0.149351\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.44949 | + | 26.5843i | −0.163299 | + | 1.77229i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.64210 | + | 4.98952i | −0.573596 | + | 0.331166i | −0.758584 | − | 0.651575i | \(-0.774109\pi\) |
0.184988 | + | 0.982741i | \(0.440775\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.6718 | + | 7.31610i | 0.837379 | + | 0.483461i | 0.856373 | − | 0.516358i | \(-0.172713\pi\) |
−0.0189932 | + | 0.999820i | \(0.506046\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.26342 | − | 9.05981i | −0.543693 | − | 0.596092i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.09978i | 0.268585i | 0.990942 | + | 0.134293i | \(0.0428762\pi\) | ||||
−0.990942 | + | 0.134293i | \(0.957124\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.8618 | −1.16518 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.53982 | − | 16.1433i | −0.229936 | − | 1.04862i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.1753 | + | 21.0883i | −0.787557 | + | 1.36409i | 0.139903 | + | 0.990165i | \(0.455321\pi\) |
−0.927460 | + | 0.373923i | \(0.878012\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0505103 | + | 0.0874863i | 0.00325365 | + | 0.00563549i | 0.867648 | − | 0.497180i | \(-0.165631\pi\) |
−0.864394 | + | 0.502815i | \(0.832298\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5804 | + | 0.500258i | −0.999485 | + | 0.0320915i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.21450 | + | 2.10357i | 0.0775914 | + | 0.134392i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.79110 | + | 2.76614i | 0.304850 | + | 0.176005i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.825765 | − | 3.76588i | −0.0523308 | − | 0.238653i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.75366i | 0.552526i | 0.961082 | + | 0.276263i | \(0.0890961\pi\) | ||||
−0.961082 | + | 0.276263i | \(0.910904\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 22.2744i | − | 1.40038i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.77978 | + | 8.92010i | −0.612434 | + | 0.558598i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.94949 | − | 5.74434i | −0.620632 | − | 0.358322i | 0.156483 | − | 0.987681i | \(-0.449984\pi\) |
−0.777115 | + | 0.629359i | \(0.783318\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.29207 | − | 12.6302i | −0.453107 | − | 0.784804i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.48745 | + | 16.1433i | −0.0920708 | + | 0.999245i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.47232 | − | 6.01424i | −0.214113 | − | 0.370854i | 0.738885 | − | 0.673831i | \(-0.235353\pi\) |
−0.952998 | + | 0.302978i | \(0.902019\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.0227 | + | 29.4842i | −1.04570 | + | 1.81120i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 23.1083 | + | 7.34468i | 1.41421 | + | 0.449487i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.5883 | −1.01141 | −0.505703 | − | 0.862708i | \(-0.668767\pi\) | ||||
−0.505703 | + | 0.862708i | \(0.668767\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 11.0646i | − | 0.672124i | −0.941840 | − | 0.336062i | \(-0.890905\pi\) | ||
0.941840 | − | 0.336062i | \(-0.109095\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.71964 | − | 5.41045i | 0.104077 | − | 0.327455i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.7246 | + | 11.3880i | 1.18944 | + | 0.686723i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.7766 | + | 9.68597i | −1.00801 | + | 0.581974i | −0.910608 | − | 0.413271i | \(-0.864386\pi\) |
−0.0974004 | + | 0.995245i | \(0.531053\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.9777 | − | 25.9989i | −0.717088 | − | 1.55651i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.92679 | + | 1.11243i | −0.114942 | + | 0.0663620i | −0.556369 | − | 0.830935i | \(-0.687806\pi\) |
0.441427 | + | 0.897297i | \(0.354473\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.21280 | + | 5.56473i | −0.190981 | + | 0.330789i | −0.945576 | − | 0.325402i | \(-0.894500\pi\) |
0.754595 | + | 0.656191i | \(0.227834\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 20.3164 | + | 22.2744i | 1.20344 | + | 1.31942i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −24.3507 | −1.43737 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.7980 | 0.752821 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.83604 | − | 1.27970i | 0.342114 | − | 0.0750172i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.86407 | − | 3.22866i | 0.108900 | − | 0.188620i | −0.806425 | − | 0.591336i | \(-0.798601\pi\) |
0.915325 | + | 0.402716i | \(0.131934\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.1313 | − | 8.15870i | 0.822755 | − | 0.475018i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.17423 | + | 12.2512i | −0.300240 | + | 0.710885i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.93092 | − | 5.15627i | 0.516489 | − | 0.298195i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.2630 | − | 8.23473i | −0.822104 | − | 0.474642i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.9224 | − | 4.14921i | 1.08706 | − | 0.238366i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.41761i | 0.252952i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.33766 | −0.532928 | −0.266464 | − | 0.963845i | \(-0.585855\pi\) | ||||
−0.266464 | + | 0.963845i | \(0.585855\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.53982 | − | 3.22866i | 0.201374 | − | 0.183672i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.23069 | + | 9.05981i | −0.296605 | + | 0.513735i | −0.975357 | − | 0.220633i | \(-0.929188\pi\) |
0.678752 | + | 0.734368i | \(0.262521\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.94949 | + | 5.10867i | 0.166715 | + | 0.288759i | 0.937263 | − | 0.348623i | \(-0.113351\pi\) |
−0.770548 | + | 0.637382i | \(0.780017\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 17.8618 | − | 25.2605i | 1.00640 | − | 1.42327i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.8340 | + | 20.4970i | 0.664662 | + | 1.15123i | 0.979377 | + | 0.202042i | \(0.0647578\pi\) |
−0.314715 | + | 0.949186i | \(0.601909\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.9777 | + | 6.91535i | 0.670625 | + | 0.387185i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.2474 | − | 5.79972i | −1.01847 | − | 0.323709i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.57058i | 0.532521i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.5448i | 0.584918i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −30.0209 | − | 9.54177i | −1.66016 | − | 0.527661i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.4773 | + | 6.62642i | 0.632764 | + | 0.365326i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.07927 | + | 7.06550i | 0.224217 | + | 0.388355i | 0.956084 | − | 0.293092i | \(-0.0946843\pi\) |
−0.731867 | + | 0.681447i | \(0.761351\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.13202 | + | 12.9146i | −0.500432 | + | 0.707718i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20.8783 | + | 36.1623i | 1.14071 | + | 1.97576i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.94949 | + | 8.57277i | −0.269616 | + | 0.466988i | −0.968763 | − | 0.247990i | \(-0.920230\pi\) |
0.699147 | + | 0.714978i | \(0.253563\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.02256 | + | 4.58106i | −0.272788 | + | 0.248809i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.4212 | −1.32248 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.5608i | 0.948192i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 54.8939 | − | 12.0369i | 2.95539 | − | 0.648043i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.7932 | − | 10.8503i | −1.00887 | − | 0.582473i | −0.0980117 | − | 0.995185i | \(-0.531248\pi\) |
−0.910862 | + | 0.412712i | \(0.864582\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.8039 | + | 12.5885i | −1.16713 | + | 0.673845i | −0.953003 | − | 0.302959i | \(-0.902025\pi\) |
−0.214131 | + | 0.976805i | \(0.568692\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.10987 | + | 0.761394i | −0.326121 | + | 0.0406402i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.62372 | − | 4.40156i | 0.405770 | − | 0.234271i | −0.283201 | − | 0.959061i | \(-0.591396\pi\) |
0.688971 | + | 0.724789i | \(0.258063\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.29207 | − | 12.6302i | 0.387023 | − | 0.670343i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.59329 | − | 2.10357i | 0.507731 | − | 0.111333i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.75836 | −0.0928029 | −0.0464015 | − | 0.998923i | \(-0.514775\pi\) | ||||
−0.0464015 | + | 0.998923i | \(0.514775\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.79796 | 0.147261 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.19348 | − | 5.69400i | −0.272587 | − | 0.298858i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.29415 | − | 14.3659i | 0.434135 | − | 0.751945i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.8456 | − | 10.3032i | 0.931533 | − | 0.537821i | 0.0442370 | − | 0.999021i | \(-0.485914\pi\) |
0.887296 | + | 0.461200i | \(0.152581\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.0505 | + | 23.9863i | 0.575267 | + | 1.24867i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.8762 | − | 12.6302i | 1.13576 | − | 0.655729i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.10584 | − | 4.67991i | −0.419704 | − | 0.242316i | 0.275246 | − | 0.961374i | \(-0.411241\pi\) |
−0.694951 | + | 0.719057i | \(0.744574\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.62623 | + | 23.9941i | −0.393817 | + | 1.23905i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.40329i | 0.329786i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.2594 | 1.70842 | 0.854212 | − | 0.519926i | \(-0.174040\pi\) | ||||
0.854212 | + | 0.519926i | \(0.174040\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.13202 | − | 2.90250i | −0.467848 | − | 0.148699i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.18664 | + | 12.4476i | −0.367220 | + | 0.636044i | −0.989130 | − | 0.147045i | \(-0.953024\pi\) |
0.621910 | + | 0.783089i | \(0.286357\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.1969 | − | 22.8578i | −0.672578 | − | 1.16494i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.63885 | + | 17.7865i | −0.0833077 | + | 0.904139i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.6718 | + | 21.9483i | 0.642488 | + | 1.11282i | 0.984876 | + | 0.173263i | \(0.0554312\pi\) |
−0.342387 | + | 0.939559i | \(0.611235\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.4501 | + | 8.92010i | 0.781343 | + | 0.451109i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23.5454 | + | 21.4757i | −1.18771 | + | 1.08330i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 35.5730i | − | 1.78987i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.4715i | 1.67989i | 0.542673 | + | 0.839944i | \(0.317412\pi\) | ||||
−0.542673 | + | 0.839944i | \(0.682588\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.79110 | − | 21.8497i | −0.239855 | − | 1.09385i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.37628 | − | 2.52664i | −0.218541 | − | 0.126175i | 0.386734 | − | 0.922191i | \(-0.373603\pi\) |
−0.605274 | + | 0.796017i | \(0.706937\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.65321 | − | 9.79165i | −0.281607 | − | 0.487757i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −32.9883 | − | 6.13116i | −1.63920 | − | 0.304660i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.74705 | + | 11.6862i | 0.334439 | + | 0.579265i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.60102 | − | 13.1654i | 0.375846 | − | 0.650985i | −0.614607 | − | 0.788833i | \(-0.710685\pi\) |
0.990453 | + | 0.137849i | \(0.0440187\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.02256 | − | 22.9053i | −0.247745 | − | 1.12983i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.1069 | −0.595743 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 8.29842i | − | 0.407353i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.3990 | − | 13.5939i | −0.607181 | − | 0.665698i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.94204 | + | 3.43064i | 0.290287 | + | 0.167598i | 0.638071 | − | 0.769977i | \(-0.279732\pi\) |
−0.347784 | + | 0.937575i | \(0.613066\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.5270 | − | 18.7795i | 1.58527 | − | 0.915256i | 0.591198 | − | 0.806526i | \(-0.298655\pi\) |
0.994071 | − | 0.108730i | \(-0.0346783\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.31877 | − | 14.3127i | 0.0641210 | − | 0.695905i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.7980 | + | 9.12096i | −0.766314 | + | 0.442431i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.63885 | − | 2.83858i | 0.0793097 | − | 0.137368i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.59111 | + | 5.00607i | −0.0768197 | + | 0.241695i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.4060 | −0.838418 | −0.419209 | − | 0.907890i | \(-0.637693\pi\) | ||||
−0.419209 | + | 0.907890i | \(0.637693\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.75255 | −0.0842222 | −0.0421111 | − | 0.999113i | \(-0.513408\pi\) | ||||
−0.0421111 | + | 0.999113i | \(0.513408\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.5698 | + | 33.2553i | −0.506782 | + | 1.59447i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.3164 | − | 35.1891i | 0.971866 | − | 1.68332i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.8456 | − | 10.3032i | 0.851724 | − | 0.491743i | −0.00950794 | − | 0.999955i | \(-0.503027\pi\) |
0.861232 | + | 0.508212i | \(0.169693\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.77526 | + | 0.817863i | −0.0845360 | + | 0.0389459i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.80110 | + | 5.08132i | −0.418153 | + | 0.241421i | −0.694287 | − | 0.719699i | \(-0.744280\pi\) |
0.276134 | + | 0.961119i | \(0.410947\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 45.1989 | + | 26.0956i | 2.14263 | + | 1.23705i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.30746 | − | 6.91535i | −0.298333 | − | 0.327085i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 10.1852i | − | 0.480670i | −0.970690 | − | 0.240335i | \(-0.922743\pi\) | ||
0.970690 | − | 0.240335i | \(-0.0772574\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.5307 | 1.06093 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.59220 | − | 25.5031i | −0.262744 | − | 1.19824i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.10987 | − | 10.5826i | 0.286435 | − | 0.496120i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.07321 | − | 8.78706i | −0.237315 | − | 0.411042i | 0.722628 | − | 0.691237i | \(-0.242934\pi\) |
−0.959943 | + | 0.280196i | \(0.909601\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.42559 | − | 8.49511i | −0.299921 | − | 0.396518i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.02619 | − | 1.77741i | −0.0477943 | − | 0.0827822i | 0.841139 | − | 0.540820i | \(-0.181886\pi\) |
−0.888933 | + | 0.458037i | \(0.848553\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.26342 | − | 4.77089i | −0.384034 | − | 0.221722i | 0.295538 | − | 0.955331i | \(-0.404501\pi\) |
−0.679572 | + | 0.733609i | \(0.737834\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.1969 | − | 60.1843i | −0.611993 | − | 2.79098i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 0.667010i | − | 0.0308656i | −0.999881 | − | 0.0154328i | \(-0.995087\pi\) | ||
0.999881 | − | 0.0154328i | \(-0.00491260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 30.9819i | − | 1.43061i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.7248 | − | 17.0788i | 0.862793 | − | 0.786949i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.1969 | + | 7.61926i | 0.606796 | + | 0.350334i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 20.7739 | + | 35.9815i | 0.953172 | + | 1.65094i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22.3688 | − | 15.8171i | −1.02420 | − | 0.724217i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.9664 | − | 29.3867i | −0.775216 | − | 1.34271i | −0.934673 | − | 0.355508i | \(-0.884308\pi\) |
0.159457 | − | 0.987205i | \(-0.449026\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.12372 | + | 5.41045i | −0.142430 | + | 0.246695i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −39.7380 | − | 12.6302i | −1.80814 | − | 0.574695i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.8602 | 0.583950 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.0646i | 0.501383i | 0.968067 | + | 0.250692i | \(0.0806580\pi\) | ||||
−0.968067 | + | 0.250692i | \(0.919342\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.00000 | − | 18.8776i | 0.271329 | − | 0.853674i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.21280 | − | 1.85491i | −0.144992 | − | 0.0837109i | 0.425749 | − | 0.904841i | \(-0.360011\pi\) |
−0.570741 | + | 0.821130i | \(0.693344\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.59329 | + | 5.53869i | −0.432060 | + | 0.249450i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.5268 | + | 23.3725i | −0.742826 | + | 1.05051i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.37117 | + | 5.41045i | −0.420355 | + | 0.242692i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.6104 | + | 32.2342i | −0.833116 | + | 1.44300i | 0.0624392 | + | 0.998049i | \(0.480112\pi\) |
−0.895555 | + | 0.444950i | \(0.853221\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.7242 | + | 16.1433i | 0.657830 | + | 0.721229i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.5596 | −0.872118 | −0.436059 | − | 0.899918i | \(-0.643626\pi\) | ||||
−0.436059 | + | 0.899918i | \(0.643626\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 41.6969 | 1.85549 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.6186 | − | 4.30188i | 0.871293 | − | 0.191053i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.2106 | − | 21.1494i | 0.541225 | − | 0.937429i | −0.457609 | − | 0.889153i | \(-0.651294\pi\) |
0.998834 | − | 0.0482755i | \(-0.0153725\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.6590 | + | 6.15396i | −0.471525 | + | 0.272235i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.3485 | + | 14.6349i | −0.854256 | + | 0.646149i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.93092 | − | 5.15627i | 0.393543 | − | 0.227212i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.6195 | − | 6.13116i | −0.467044 | − | 0.269648i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.30746 | − | 1.38307i | 0.276867 | − | 0.0607100i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 21.4203i | − | 0.938440i | −0.883081 | − | 0.469220i | \(-0.844535\pi\) | ||
0.883081 | − | 0.469220i | \(-0.155465\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.3162 | −1.41309 | −0.706543 | − | 0.707670i | \(-0.749746\pi\) | ||||
−0.706543 | + | 0.707670i | \(0.749746\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 31.5008 | − | 28.7318i | 1.37481 | − | 1.25396i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.77978 | − | 16.9391i | 0.426014 | − | 0.737878i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −26.3712 | − | 45.6762i | −1.14657 | − | 1.98592i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.49421 | + | 11.9257i | 0.238428 | + | 0.517533i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.21558 | + | 9.03365i | 0.225912 | + | 0.391291i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −35.6912 | − | 20.6063i | −1.54307 | − | 0.890889i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.6969 | − | 6.57826i | −0.893139 | − | 0.283873i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.66753i | 0.0718254i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.43512i | 0.147687i | 0.997270 | + | 0.0738436i | \(0.0235266\pi\) | ||||
−0.997270 | + | 0.0738436i | \(0.976473\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.5268 | + | 5.25284i | 0.709234 | + | 0.225421i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −58.7196 | − | 33.9018i | −2.51527 | − | 1.45219i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.26580 | + | 5.65653i | 0.139635 | + | 0.241856i | 0.927359 | − | 0.374174i | \(-0.122074\pi\) |
−0.787723 | + | 0.616029i | \(0.788740\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.53982 | − | 0.326161i | −0.151076 | − | 0.0139202i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.6149 | + | 21.8497i | 0.537414 | + | 0.930828i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.1969 | + | 22.8578i | −0.561191 | + | 0.972011i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −25.1539 | + | 22.9428i | −1.06772 | + | 0.973866i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.78051 | 0.244928 | 0.122464 | − | 0.992473i | \(-0.460920\pi\) | ||||
0.122464 | + | 0.992473i | \(0.460920\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.05507i | 0.298398i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.87628 | + | 1.94635i | −0.374757 | + | 0.0821749i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.07186 | − | 3.50559i | −0.255898 | − | 0.147743i | 0.366564 | − | 0.930393i | \(-0.380534\pi\) |
−0.622462 | + | 0.782650i | \(0.713868\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.6718 | + | 7.31610i | −0.533109 | + | 0.307790i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.9224 | + | 16.1777i | 0.794665 | + | 0.679399i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.2980 | − | 20.3793i | 1.47977 | − | 0.854344i | 0.480030 | − | 0.877252i | \(-0.340626\pi\) |
0.999738 | + | 0.0229080i | \(0.00729249\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.1244 | + | 24.4642i | −0.591088 | + | 1.02379i | 0.402999 | + | 0.915201i | \(0.367968\pi\) |
−0.994086 | + | 0.108593i | \(0.965365\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.3426 | − | 4.67991i | 0.891600 | − | 0.195506i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 77.4479 | 3.22980 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.55051 | −0.0645486 | −0.0322743 | − | 0.999479i | \(-0.510275\pi\) | ||||
−0.0322743 | + | 0.999479i | \(0.510275\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −29.4690 | − | 32.3091i | −1.22469 | − | 1.34272i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.07856 | + | 5.33223i | −0.127720 | + | 0.221218i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.2412 | + | 11.6862i | −0.838303 | + | 0.483994i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.1969 | − | 1.21597i | −0.545626 | − | 0.0502742i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.8002 | − | 14.3184i | 1.02361 | − | 0.590983i | 0.108464 | − | 0.994100i | \(-0.465407\pi\) |
0.915148 | + | 0.403117i | \(0.132073\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −38.5805 | − | 22.2744i | −1.58968 | − | 0.917803i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.75836 | − | 5.53228i | 0.0723295 | − | 0.227568i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 4.87832i | − | 0.200328i | −0.994971 | − | 0.100164i | \(-0.968063\pi\) | ||
0.994971 | − | 0.100164i | \(-0.0319368\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.1396 | 0.866637 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.3164 | − | 6.45732i | −0.831496 | − | 0.264280i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.30746 | − | 10.9248i | 0.257716 | − | 0.446377i | −0.707914 | − | 0.706299i | \(-0.750363\pi\) |
0.965630 | + | 0.259922i | \(0.0836968\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.2753 | − | 24.7255i | −0.582300 | − | 1.00857i | −0.995206 | − | 0.0977994i | \(-0.968820\pi\) |
0.412906 | − | 0.910773i | \(-0.364514\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −30.5183 | + | 14.0598i | −1.24280 | + | 0.572561i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.29415 | − | 14.3659i | −0.337205 | − | 0.584056i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.54910 | + | 2.62642i | 0.184642 | + | 0.106603i | 0.589472 | − | 0.807789i | \(-0.299336\pi\) |
−0.404830 | + | 0.914392i | \(0.632669\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.1288 | − | 17.4473i | 0.775139 | − | 0.707001i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 5.67716i | − | 0.229673i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.7318i | 1.16047i | 0.814451 | + | 0.580233i | \(0.197038\pi\) | ||||
−0.814451 | + | 0.580233i | \(0.802962\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.1753 | + | 55.5253i | 0.490957 | + | 2.23900i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.6237 | + | 13.0618i | 0.910797 | + | 0.525849i | 0.880687 | − | 0.473698i | \(-0.157081\pi\) |
0.0301094 | + | 0.999547i | \(0.490414\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.30768 | + | 10.9252i | 0.253527 | + | 0.439122i | 0.964494 | − | 0.264103i | \(-0.0850759\pi\) |
−0.710967 | + | 0.703225i | \(0.751743\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.59220 | + | 44.8751i | 0.224407 | + | 1.80077i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.3620 | − | 33.5359i | −0.775721 | − | 1.34359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.84847 | + | 8.39780i | −0.193939 | + | 0.335912i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.43300 | + | 20.2166i | 0.177037 | + | 0.807374i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.8078 | −0.430935 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 27.1025i | − | 1.07893i | −0.842007 | − | 0.539467i | \(-0.818626\pi\) | ||
0.842007 | − | 0.539467i | \(-0.181374\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.5227 | + | 26.8861i | 0.974690 | + | 1.06863i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.8618 | − | 10.3125i | −0.708826 | − | 0.409241i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.668593 | + | 0.386012i | −0.0264906 | + | 0.0152944i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.58219 | + | 6.77563i | 0.379066 | + | 0.268040i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.70204 | − | 5.60148i | 0.383208 | − | 0.221245i | −0.296005 | − | 0.955186i | \(-0.595655\pi\) |
0.679213 | + | 0.733941i | \(0.262321\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.40303 | − | 2.43012i | 0.0553301 | − | 0.0958346i | −0.837034 | − | 0.547151i | \(-0.815712\pi\) |
0.892364 | + | 0.451317i | \(0.149046\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.6457 | + | 36.6403i | −0.458547 | + | 1.44271i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.7466 | −1.13014 | −0.565072 | − | 0.825041i | \(-0.691152\pi\) | ||||
−0.565072 | + | 0.825041i | \(0.691152\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.2020 | 0.439719 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.8475 | + | 43.5678i | −0.542726 | + | 1.70756i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.64458 | + | 13.2408i | −0.299155 | + | 0.518152i | −0.975943 | − | 0.218026i | \(-0.930038\pi\) |
0.676788 | + | 0.736178i | \(0.263372\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −59.4047 | + | 34.2973i | −2.32113 | + | 1.34011i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.8990 | + | 7.70674i | 0.425210 | + | 0.300669i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.6657 | − | 24.0557i | 1.62307 | − | 0.937078i | 0.636972 | − | 0.770887i | \(-0.280186\pi\) |
0.986094 | − | 0.166191i | \(-0.0531468\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.8835 | + | 16.6759i | 1.12344 | + | 0.648618i | 0.942277 | − | 0.334836i | \(-0.108681\pi\) |
0.181162 | + | 0.983453i | \(0.442014\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.83514 | − | 3.10838i | −0.110108 | − | 0.120719i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 48.1475i | − | 1.86708i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 47.0301 | 1.82101 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.05346 | + | 27.6067i | 0.234040 | + | 1.06734i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.51637 | + | 2.62642i | −0.0585386 | + | 0.101392i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.0732 | − | 26.1076i | −0.581030 | − | 1.00637i | −0.995358 | − | 0.0962453i | \(-0.969317\pi\) |
0.414328 | − | 0.910128i | \(-0.364017\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −42.5971 | − | 17.9907i | −1.63956 | − | 0.692463i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.64458 | + | 13.2408i | 0.293805 | + | 0.508885i | 0.974706 | − | 0.223490i | \(-0.0717451\pi\) |
−0.680901 | + | 0.732375i | \(0.738412\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.26342 | − | 4.77089i | −0.317121 | − | 0.183090i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.70204 | − | 16.8831i | −0.141863 | − | 0.646961i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 37.4654i | − | 1.43357i | −0.697293 | − | 0.716787i | \(-0.745612\pi\) | ||
0.697293 | − | 0.716787i | \(-0.254388\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 50.4736i | − | 1.92850i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.7248 | + | 17.0788i | −0.714395 | + | 0.651597i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.37117 | − | 5.41045i | −0.357013 | − | 0.206122i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.6490 | + | 25.3729i | 0.557276 | + | 0.965230i | 0.997723 | + | 0.0674514i | \(0.0214868\pi\) |
−0.440447 | + | 0.897779i | \(0.645180\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 19.2902 | − | 8.88705i | 0.732776 | − | 0.337591i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.8016 | − | 34.2973i | −0.751116 | − | 1.30097i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.02270 | + | 15.6278i | −0.341759 | + | 0.591944i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.76742 | − | 2.15094i | −0.255967 | − | 0.0813559i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.0618 | −1.62642 | −0.813212 | − | 0.581968i | \(-0.802283\pi\) | ||||
−0.813212 | + | 0.581968i | \(0.802283\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.6158i | 0.928403i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.37117 | − | 29.4842i | 0.352939 | − | 1.11044i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −26.7928 | − | 15.4688i | −1.00765 | − | 0.581764i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.53982 | − | 2.04372i | 0.132941 | − | 0.0767535i | −0.432055 | − | 0.901847i | \(-0.642211\pi\) |
0.564996 | + | 0.825094i | \(0.308878\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 28.5046 | + | 2.62642i | 1.06900 | + | 0.0984985i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −71.9166 | + | 41.5211i | −2.69330 | + | 1.55498i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.65321 | + | 9.79165i | −0.211418 | + | 0.366187i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −28.4223 | − | 31.1615i | −1.06145 | − | 1.16375i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.1644 | 0.714711 | 0.357355 | − | 0.933968i | \(-0.383678\pi\) | ||||
0.357355 | + | 0.933968i | \(0.383678\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.65153 | −0.284958 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.170912 | + | 0.0374768i | −0.00635629 | + | 0.00139378i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24.0446 | + | 41.6464i | −0.892992 | + | 1.54671i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.9992 | + | 11.5465i | −0.741728 | + | 0.428237i | −0.822697 | − | 0.568480i | \(-0.807532\pi\) |
0.0809695 | + | 0.996717i | \(0.474198\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.34847 | − | 25.9808i | 0.272166 | − | 0.962250i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.5698 | + | 6.10246i | −0.390937 | + | 0.225708i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.2902 | + | 11.1372i | 0.712501 | + | 0.411363i | 0.811986 | − | 0.583676i | \(-0.198386\pi\) |
−0.0994853 | + | 0.995039i | \(0.531720\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.10950 | + | 0.901113i | −0.151581 | + | 0.0332380i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.6663i | 1.05594i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.18977 | 0.227694 | 0.113847 | − | 0.993498i | \(-0.463683\pi\) | ||||
0.113847 | + | 0.993498i | \(0.463683\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.07965 | + | 6.45732i | −0.260077 | + | 0.237215i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.39555 | − | 4.14921i | 0.0878841 | − | 0.152220i | −0.818732 | − | 0.574175i | \(-0.805323\pi\) |
0.906617 | + | 0.421955i | \(0.138656\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.0732 | − | 17.4473i | −0.369054 | − | 0.639220i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.64951 | + | 0.612688i | 0.243293 | + | 0.0224171i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.2892 | + | 26.4816i | 0.558653 | + | 0.967616i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.2403 | + | 23.2328i | 1.46839 | + | 0.847775i | 0.999373 | − | 0.0354139i | \(-0.0112750\pi\) |
0.469017 | + | 0.883189i | \(0.344608\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.4495 | − | 4.59259i | −0.526569 | − | 0.167363i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 56.1981i | − | 2.04526i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.4393i | 1.36075i | 0.732863 | + | 0.680376i | \(0.238184\pi\) | ||||
−0.732863 | + | 0.680376i | \(0.761816\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 36.7680 | + | 11.6862i | 1.33459 | + | 0.424183i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.97219 | − | 3.44805i | −0.216492 | − | 0.124992i | 0.387833 | − | 0.921730i | \(-0.373224\pi\) |
−0.604325 | + | 0.796738i | \(0.706557\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.1539 | + | 43.5678i | 0.910633 | + | 1.57726i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.59329 | − | 20.8232i | −0.346846 | − | 0.752864i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.59314 | + | 4.49145i | 0.0936328 | + | 0.162177i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.60102 | − | 6.23715i | 0.129856 | − | 0.224917i | −0.793765 | − | 0.608225i | \(-0.791882\pi\) |
0.923621 | + | 0.383308i | \(0.125215\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.7020 | − | 13.4097i | 0.529481 | − | 0.482937i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.5883 | −0.596639 | −0.298320 | − | 0.954466i | \(-0.596426\pi\) | ||||
−0.298320 | + | 0.954466i | \(0.596426\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 84.9120i | − | 3.05013i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.6742 | − | 5.41045i | 0.885183 | − | 0.194099i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35.5939 | + | 20.5501i | 1.27528 | + | 0.736285i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.67076 | − | 5.00607i | 0.310264 | − | 0.179131i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −25.8670 | − | 10.9248i | −0.924412 | − | 0.390422i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 47.2423 | − | 27.2754i | 1.68615 | − | 0.973500i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.6490 | − | 25.3729i | 0.522182 | − | 0.904446i | −0.477485 | − | 0.878640i | \(-0.658451\pi\) |
0.999667 | − | 0.0258059i | \(-0.00821519\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.7493 | − | 2.57634i | 0.418287 | − | 0.0917200i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.8566 | 0.386015 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.40408 | −0.0498604 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −39.7380 | − | 43.5678i | −1.40936 | − | 1.54519i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.37770 | + | 7.58240i | −0.155066 | + | 0.268583i | −0.933083 | − | 0.359661i | \(-0.882892\pi\) |
0.778017 | + | 0.628243i | \(0.216226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.50542 | − | 4.91060i | 0.300900 | − | 0.173725i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.2474 | + | 34.2911i | −0.856741 | + | 1.21162i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.86230 | − | 5.69400i | 0.348033 | − | 0.200937i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −77.7259 | − | 44.8751i | −2.73948 | − | 1.58164i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.70301 | − | 27.3820i | 0.306360 | − | 0.963891i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 20.6417i | − | 0.725725i | −0.931843 | − | 0.362863i | \(-0.881799\pi\) | ||
0.931843 | − | 0.362863i | \(-0.118201\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.683648 | −0.0240061 | −0.0120031 | − | 0.999928i | \(-0.503821\pi\) | ||||
−0.0120031 | + | 0.999928i | \(0.503821\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.2640 | + | 5.80500i | 0.640548 | + | 0.203590i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.3179 | − | 36.9237i | 0.746734 | − | 1.29338i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.8990 | + | 24.0737i | 0.486264 | + | 0.842234i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.02871 | + | 5.67716i | 0.280546 | + | 0.198376i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.8340 | − | 20.4970i | −0.413008 | − | 0.715352i | 0.582209 | − | 0.813039i | \(-0.302189\pi\) |
−0.995217 | + | 0.0976878i | \(0.968855\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.4278 | + | 15.8354i | 0.956073 | + | 0.551989i | 0.894962 | − | 0.446142i | \(-0.147202\pi\) |
0.0611107 | + | 0.998131i | \(0.480536\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −29.1464 | + | 26.5843i | −1.01475 | + | 0.925548i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.63487i | 0.126397i | 0.998001 | + | 0.0631983i | \(0.0201301\pi\) | ||||
−0.998001 | + | 0.0631983i | \(0.979870\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 28.7318i | − | 0.997895i | −0.866632 | − | 0.498948i | \(-0.833720\pi\) | ||
0.866632 | − | 0.498948i | \(-0.166280\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.18664 | − | 32.7745i | −0.249302 | − | 1.13694i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.15663 | − | 0.667783i | −0.0400750 | − | 0.0231373i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.5151 | + | 40.7293i | 0.813772 | + | 1.40949i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 49.1999 | − | 6.13116i | 1.70060 | − | 0.211924i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.9777 | + | 20.7461i | 0.413517 | + | 0.716233i | 0.995272 | − | 0.0971315i | \(-0.0309667\pi\) |
−0.581754 | + | 0.813365i | \(0.697633\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.101021 | + | 0.174973i | −0.00348347 | + | 0.00603354i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.825383 | − | 3.76414i | −0.0284277 | − | 0.129644i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 43.2311 | 1.48720 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.3079i | 0.422905i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.50000 | − | 8.22282i | −0.257399 | − | 0.282207i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.7380 | + | 22.9428i | 1.36220 | + | 0.786468i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.6863 | − | 26.9544i | 1.59851 | − | 0.922900i | 0.606734 | − | 0.794905i | \(-0.292479\pi\) |
0.991775 | − | 0.127995i | \(-0.0408540\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −47.4270 | + | 21.8497i | −1.62197 | + | 0.747243i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.67934 | + | 2.70162i | −0.159843 | + | 0.0922855i | −0.577788 | − | 0.816187i | \(-0.696084\pi\) |
0.417945 | + | 0.908472i | \(0.362751\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.74485 | − | 3.02218i | 0.0595337 | − | 0.103115i | −0.834722 | − | 0.550671i | \(-0.814372\pi\) |
0.894256 | + | 0.447555i | \(0.147705\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.7755 | − | 40.1951i | 0.435388 | − | 1.36985i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.4060 | −0.592508 | −0.296254 | − | 0.955109i | \(-0.595737\pi\) | ||||
−0.296254 | + | 0.955109i | \(0.595737\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.8990 | 0.472579 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.71442 | + | 21.1253i | −0.228034 | + | 0.717454i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.2106 | − | 21.1494i | 0.414216 | − | 0.717443i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.4937 | + | 6.63591i | −0.389450 | + | 0.224849i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.949490 | + | 10.3048i | −0.0321354 | + | 0.348765i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 34.8215 | − | 20.1042i | 1.17718 | − | 0.679646i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.4997 | + | 15.8770i | 0.928600 | + | 0.536128i | 0.886369 | − | 0.462980i | \(-0.153220\pi\) |
0.0422317 | + | 0.999108i | \(0.486553\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.35150 | + | 4.77089i | 0.146773 | + | 0.160918i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.0416i | 0.809983i | 0.914320 | + | 0.404992i | \(0.132726\pi\) | ||||
−0.914320 | + | 0.404992i | \(0.867274\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.0632 | −0.439611 | −0.219806 | − | 0.975544i | \(-0.570542\pi\) | ||||
−0.219806 | + | 0.975544i | \(0.570542\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.05346 | + | 27.6067i | 0.203485 | + | 0.927988i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.8783 | + | 36.1623i | −0.701026 | + | 1.21421i | 0.267081 | + | 0.963674i | \(0.413941\pi\) |
−0.968107 | + | 0.250538i | \(0.919392\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.65153 | + | 13.2528i | 0.256624 | + | 0.444486i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.5081 | − | 14.9686i | −0.586544 | − | 0.501465i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.1844 | − | 19.3719i | −0.374272 | − | 0.648258i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −40.4823 | − | 23.3725i | −1.35317 | − | 0.781256i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.82577 | + | 17.4473i | 0.127739 | + | 0.582549i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 51.5627i | − | 1.71971i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 18.7196i | − | 0.623641i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.0759 | − | 19.2233i | 0.701363 | − | 0.639710i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 32.3258 | + | 18.6633i | 1.07454 | + | 0.620389i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.7509 | − | 41.1377i | −0.788635 | − | 1.36596i | −0.926803 | − | 0.375547i | \(-0.877455\pi\) |
0.138168 | − | 0.990409i | \(-0.455878\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.07856 | + | 33.4117i | −0.102110 | + | 1.10820i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.31877 | + | 2.28418i | 0.0436929 | + | 0.0756783i | 0.887045 | − | 0.461683i | \(-0.152754\pi\) |
−0.843352 | + | 0.537362i | \(0.819421\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.84847 | − | 4.93369i | 0.0942706 | − | 0.163281i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.29207 | − | 2.31769i | −0.241068 | − | 0.0766205i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 50.8947 | 1.68069 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.6804i | 1.17699i | 0.808502 | + | 0.588494i | \(0.200279\pi\) | ||||
−0.808502 | + | 0.588494i | \(0.799721\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.89898 | − | 15.4135i | 0.161427 | − | 0.507892i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.01436 | + | 2.31769i | 0.132134 | + | 0.0762877i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.6329 | + | 23.4594i | −1.33600 | + | 0.771340i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.47232 | + | 7.53703i | 0.114046 | + | 0.247548i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.0278 | − | 12.1404i | 0.689900 | − | 0.398314i | −0.113675 | − | 0.993518i | \(-0.536262\pi\) |
0.803575 | + | 0.595204i | \(0.202929\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.52094 | + | 2.63435i | −0.0498469 | + | 0.0863373i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.2106 | − | 13.3874i | −0.399757 | − | 0.438284i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −19.5596 | −0.639666 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.85357 | −0.0932221 | −0.0466111 | − | 0.998913i | \(-0.514842\pi\) | ||||
−0.0466111 | + | 0.998913i | \(0.514842\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.98022 | + | 2.18841i | −0.325692 | + | 0.0714162i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.26796 | − | 12.5885i | 0.236929 | − | 0.410372i | −0.722903 | − | 0.690950i | \(-0.757193\pi\) |
0.959831 | + | 0.280577i | \(0.0905259\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 66.3493 | − | 38.3068i | 2.16063 | − | 1.24744i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 32.3258 | + | 42.7370i | 1.05156 | + | 1.39024i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.3741 | + | 15.2271i | −0.857044 | + | 0.494814i | −0.863021 | − | 0.505168i | \(-0.831431\pi\) |
0.00597754 | + | 0.999982i | \(0.498097\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.56601 | + | 2.63619i | 0.148219 | + | 0.0855743i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −40.0427 | + | 8.78038i | −1.29847 | + | 0.284723i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.7121i | 1.35119i | 0.737274 | + | 0.675593i | \(0.236113\pi\) | ||||
−0.737274 | + | 0.675593i | \(0.763887\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 47.0301 | 1.52186 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −17.6991 | + | 16.1433i | −0.572131 | + | 0.521839i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.7248 | + | 32.4323i | −0.604655 | + | 1.04729i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.0227 | + | 52.0008i | 0.968474 | + | 1.67745i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19.1470 | − | 27.0779i | 0.617002 | − | 0.872573i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −47.0629 | − | 81.5154i | −1.51501 | − | 2.62407i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.2081 | + | 8.78038i | 0.489058 | + | 0.282358i | 0.724184 | − | 0.689607i | \(-0.242217\pi\) |
−0.235125 | + | 0.971965i | \(0.575550\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.7980 | − | 5.02118i | −0.507504 | − | 0.161304i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 49.5204i | − | 1.58919i | −0.607143 | − | 0.794593i | \(-0.707684\pi\) | ||
0.607143 | − | 0.794593i | \(-0.292316\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.3841i | 0.942011i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −17.4060 | − | 5.53228i | −0.557439 | − | 0.177175i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.05051 | − | 2.91591i | −0.161580 | − | 0.0932883i | 0.417029 | − | 0.908893i | \(-0.363071\pi\) |
−0.578610 | + | 0.815605i | \(0.696405\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.9148 | + | 31.0294i | 0.572561 | + | 0.991704i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 31.5008 | − | 44.5489i | 1.00574 | − | 1.42234i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.9664 | + | 29.3867i | 0.541145 | + | 0.937290i | 0.998839 | + | 0.0481806i | \(0.0153423\pi\) |
−0.457694 | + | 0.889110i | \(0.651324\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.24745 | − | 10.8209i | 0.199060 | − | 0.344782i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.9596 | + | 15.4688i | −0.539831 | + | 0.492378i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 51.8173 | 1.64769 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 2.48670i | − | 0.0789927i | −0.999220 | − | 0.0394964i | \(-0.987425\pi\) | ||
0.999220 | − | 0.0394964i | \(-0.0125754\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.8031 | + | 3.02667i | −0.438027 | + | 0.0960485i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39.7380 | − | 22.9428i | −1.25978 | − | 0.727335i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.56710 | + | 4.94622i | −0.271323 | + | 0.156648i | −0.629489 | − | 0.777010i | \(-0.716736\pi\) |
0.358166 | + | 0.933658i | \(0.383402\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.5268 | − | 21.8497i | −0.522886 | − | 0.691293i |
(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 | 1152.2.p.d.959.3 | yes | 16 | |
3.2 | odd | 2 | 3456.2.p.d.2879.8 | 16 | |||
4.3 | odd | 2 | inner | 1152.2.p.d.959.5 | yes | 16 | |
8.3 | odd | 2 | inner | 1152.2.p.d.959.4 | yes | 16 | |
8.5 | even | 2 | inner | 1152.2.p.d.959.6 | yes | 16 | |
9.2 | odd | 6 | inner | 1152.2.p.d.191.4 | yes | 16 | |
9.7 | even | 3 | 3456.2.p.d.575.1 | 16 | |||
12.11 | even | 2 | 3456.2.p.d.2879.7 | 16 | |||
24.5 | odd | 2 | 3456.2.p.d.2879.2 | 16 | |||
24.11 | even | 2 | 3456.2.p.d.2879.1 | 16 | |||
36.7 | odd | 6 | 3456.2.p.d.575.2 | 16 | |||
36.11 | even | 6 | inner | 1152.2.p.d.191.6 | yes | 16 | |
72.11 | even | 6 | inner | 1152.2.p.d.191.3 | ✓ | 16 | |
72.29 | odd | 6 | inner | 1152.2.p.d.191.5 | yes | 16 | |
72.43 | odd | 6 | 3456.2.p.d.575.8 | 16 | |||
72.61 | even | 6 | 3456.2.p.d.575.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.p.d.191.3 | ✓ | 16 | 72.11 | even | 6 | inner | |
1152.2.p.d.191.4 | yes | 16 | 9.2 | odd | 6 | inner | |
1152.2.p.d.191.5 | yes | 16 | 72.29 | odd | 6 | inner | |
1152.2.p.d.191.6 | yes | 16 | 36.11 | even | 6 | inner | |
1152.2.p.d.959.3 | yes | 16 | 1.1 | even | 1 | trivial | |
1152.2.p.d.959.4 | yes | 16 | 8.3 | odd | 2 | inner | |
1152.2.p.d.959.5 | yes | 16 | 4.3 | odd | 2 | inner | |
1152.2.p.d.959.6 | yes | 16 | 8.5 | even | 2 | inner | |
3456.2.p.d.575.1 | 16 | 9.7 | even | 3 | |||
3456.2.p.d.575.2 | 16 | 36.7 | odd | 6 | |||
3456.2.p.d.575.7 | 16 | 72.61 | even | 6 | |||
3456.2.p.d.575.8 | 16 | 72.43 | odd | 6 | |||
3456.2.p.d.2879.1 | 16 | 24.11 | even | 2 | |||
3456.2.p.d.2879.2 | 16 | 24.5 | odd | 2 | |||
3456.2.p.d.2879.7 | 16 | 12.11 | even | 2 | |||
3456.2.p.d.2879.8 | 16 | 3.2 | odd | 2 |