Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(361,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.g (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(52.0396846251\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.667 |
Dual form | 882.4.g.r.361.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.00000 | + | 1.73205i | −0.0894427 | + | 0.154919i | −0.907276 | − | 0.420536i | \(-0.861842\pi\) |
0.817833 | + | 0.575456i | \(0.195175\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | + | 3.46410i | 0.0632456 | + | 0.109545i | ||||
\(11\) | −4.00000 | − | 6.92820i | −0.109640 | − | 0.189903i | 0.805984 | − | 0.591937i | \(-0.201637\pi\) |
−0.915625 | + | 0.402034i | \(0.868303\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 42.0000 | 0.896054 | 0.448027 | − | 0.894020i | \(-0.352127\pi\) | ||||
0.448027 | + | 0.894020i | \(0.352127\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.00000 | + | 1.73205i | 0.0142668 | + | 0.0247108i | 0.873071 | − | 0.487594i | \(-0.162125\pi\) |
−0.858804 | + | 0.512305i | \(0.828792\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −62.0000 | + | 107.387i | −0.748620 | + | 1.29665i | 0.199865 | + | 0.979824i | \(0.435950\pi\) |
−0.948484 | + | 0.316824i | \(0.897384\pi\) | |||||||
\(20\) | 8.00000 | 0.0894427 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −16.0000 | −0.155055 | ||||||||
\(23\) | 38.0000 | − | 65.8179i | 0.344502 | − | 0.596695i | −0.640761 | − | 0.767740i | \(-0.721381\pi\) |
0.985263 | + | 0.171045i | \(0.0547144\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 60.5000 | + | 104.789i | 0.484000 | + | 0.838313i | ||||
\(26\) | 42.0000 | − | 72.7461i | 0.316803 | − | 0.548719i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −254.000 | −1.62644 | −0.813218 | − | 0.581960i | \(-0.802286\pi\) | ||||
−0.813218 | + | 0.581960i | \(0.802286\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −36.0000 | − | 62.3538i | −0.208574 | − | 0.361261i | 0.742692 | − | 0.669634i | \(-0.233549\pi\) |
−0.951266 | + | 0.308373i | \(0.900216\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.00000 | 0.0201763 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −199.000 | + | 344.678i | −0.884200 | + | 1.53148i | −0.0375721 | + | 0.999294i | \(0.511962\pi\) |
−0.846628 | + | 0.532185i | \(0.821371\pi\) | |||||||
\(38\) | 124.000 | + | 214.774i | 0.529354 | + | 0.916868i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.00000 | − | 13.8564i | 0.0316228 | − | 0.0547723i | ||||
\(41\) | 462.000 | 1.75981 | 0.879906 | − | 0.475148i | \(-0.157606\pi\) | ||||
0.879906 | + | 0.475148i | \(0.157606\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 212.000 | 0.751853 | 0.375927 | − | 0.926649i | \(-0.377324\pi\) | ||||
0.375927 | + | 0.926649i | \(0.377324\pi\) | |||||||
\(44\) | −16.0000 | + | 27.7128i | −0.0548202 | + | 0.0949514i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −76.0000 | − | 131.636i | −0.243600 | − | 0.421927i | ||||
\(47\) | 132.000 | − | 228.631i | 0.409663 | − | 0.709558i | −0.585189 | − | 0.810897i | \(-0.698979\pi\) |
0.994852 | + | 0.101339i | \(0.0323128\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 242.000 | 0.684479 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −84.0000 | − | 145.492i | −0.224014 | − | 0.388003i | ||||
\(53\) | −81.0000 | − | 140.296i | −0.209928 | − | 0.363607i | 0.741763 | − | 0.670662i | \(-0.233990\pi\) |
−0.951692 | + | 0.307055i | \(0.900656\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.0000 | 0.0392262 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −254.000 | + | 439.941i | −0.575032 | + | 0.995984i | ||||
\(59\) | 386.000 | + | 668.572i | 0.851744 | + | 1.47526i | 0.879633 | + | 0.475654i | \(0.157788\pi\) |
−0.0278883 | + | 0.999611i | \(0.508878\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.0000 | − | 25.9808i | 0.0314845 | − | 0.0545327i | −0.849854 | − | 0.527018i | \(-0.823310\pi\) |
0.881338 | + | 0.472486i | \(0.156643\pi\) | |||||||
\(62\) | −144.000 | −0.294968 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −42.0000 | + | 72.7461i | −0.0801455 | + | 0.138816i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 382.000 | + | 661.643i | 0.696548 | + | 1.20646i | 0.969656 | + | 0.244473i | \(0.0786151\pi\) |
−0.273108 | + | 0.961983i | \(0.588052\pi\) | |||||||
\(68\) | 4.00000 | − | 6.92820i | 0.00713340 | − | 0.0123554i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 236.000 | 0.394480 | 0.197240 | − | 0.980355i | \(-0.436802\pi\) | ||||
0.197240 | + | 0.980355i | \(0.436802\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 209.000 | + | 361.999i | 0.335090 | + | 0.580394i | 0.983502 | − | 0.180896i | \(-0.0578998\pi\) |
−0.648412 | + | 0.761290i | \(0.724566\pi\) | |||||||
\(74\) | 398.000 | + | 689.356i | 0.625224 | + | 1.08292i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 496.000 | 0.748620 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −276.000 | + | 478.046i | −0.393069 | + | 0.680815i | −0.992853 | − | 0.119347i | \(-0.961920\pi\) |
0.599784 | + | 0.800162i | \(0.295253\pi\) | |||||||
\(80\) | −16.0000 | − | 27.7128i | −0.0223607 | − | 0.0387298i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 462.000 | − | 800.207i | 0.622187 | − | 1.07766i | ||||
\(83\) | 1036.00 | 1.37007 | 0.685035 | − | 0.728510i | \(-0.259787\pi\) | ||||
0.685035 | + | 0.728510i | \(0.259787\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | −0.00510425 | ||||||||
\(86\) | 212.000 | − | 367.195i | 0.265820 | − | 0.460414i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 32.0000 | + | 55.4256i | 0.0387638 | + | 0.0671408i | ||||
\(89\) | −15.0000 | + | 25.9808i | −0.0178651 | + | 0.0309433i | −0.874820 | − | 0.484449i | \(-0.839020\pi\) |
0.856955 | + | 0.515392i | \(0.172354\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −304.000 | −0.344502 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −264.000 | − | 457.261i | −0.289676 | − | 0.501733i | ||||
\(95\) | −124.000 | − | 214.774i | −0.133917 | − | 0.231951i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1190.00 | 1.24563 | 0.622815 | − | 0.782369i | \(-0.285989\pi\) | ||||
0.622815 | + | 0.782369i | \(0.285989\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 242.000 | − | 419.156i | 0.242000 | − | 0.419156i | ||||
\(101\) | −685.000 | − | 1186.45i | −0.674852 | − | 1.16888i | −0.976512 | − | 0.215462i | \(-0.930874\pi\) |
0.301660 | − | 0.953416i | \(-0.402459\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 232.000 | − | 401.836i | 0.221938 | − | 0.384408i | −0.733458 | − | 0.679735i | \(-0.762095\pi\) |
0.955396 | + | 0.295326i | \(0.0954283\pi\) | |||||||
\(104\) | −336.000 | −0.316803 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −324.000 | −0.296884 | ||||||||
\(107\) | −1068.00 | + | 1849.83i | −0.964930 | + | 1.67131i | −0.255125 | + | 0.966908i | \(0.582117\pi\) |
−0.709804 | + | 0.704399i | \(0.751217\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 613.000 | + | 1061.75i | 0.538667 | + | 0.932999i | 0.998976 | + | 0.0452405i | \(0.0144054\pi\) |
−0.460309 | + | 0.887759i | \(0.652261\pi\) | |||||||
\(110\) | 16.0000 | − | 27.7128i | 0.0138685 | − | 0.0240210i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −338.000 | −0.281384 | −0.140692 | − | 0.990053i | \(-0.544933\pi\) | ||||
−0.140692 | + | 0.990053i | \(0.544933\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 76.0000 | + | 131.636i | 0.0616264 | + | 0.106740i | ||||
\(116\) | 508.000 | + | 879.882i | 0.406609 | + | 0.704267i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1544.00 | 1.20455 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 633.500 | − | 1097.25i | 0.475958 | − | 0.824383i | ||||
\(122\) | −30.0000 | − | 51.9615i | −0.0222629 | − | 0.0385605i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −144.000 | + | 249.415i | −0.104287 | + | 0.180630i | ||||
\(125\) | −492.000 | −0.352047 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2088.00 | 1.45890 | 0.729449 | − | 0.684035i | \(-0.239777\pi\) | ||||
0.729449 | + | 0.684035i | \(0.239777\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 84.0000 | + | 145.492i | 0.0566714 | + | 0.0981578i | ||||
\(131\) | 146.000 | − | 252.879i | 0.0973747 | − | 0.168658i | −0.813223 | − | 0.581953i | \(-0.802289\pi\) |
0.910597 | + | 0.413295i | \(0.135622\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1528.00 | 0.985068 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.00000 | − | 13.8564i | −0.00504408 | − | 0.00873660i | ||||
\(137\) | 409.000 | + | 708.409i | 0.255060 | + | 0.441777i | 0.964912 | − | 0.262574i | \(-0.0845714\pi\) |
−0.709852 | + | 0.704351i | \(0.751238\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2156.00 | 1.31561 | 0.657804 | − | 0.753189i | \(-0.271485\pi\) | ||||
0.657804 | + | 0.753189i | \(0.271485\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 236.000 | − | 408.764i | 0.139470 | − | 0.241568i | ||||
\(143\) | −168.000 | − | 290.985i | −0.0982438 | − | 0.170163i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 254.000 | − | 439.941i | 0.145473 | − | 0.251966i | ||||
\(146\) | 836.000 | 0.473889 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1592.00 | 0.884200 | ||||||||
\(149\) | −1425.00 | + | 2468.17i | −0.783494 | + | 1.35705i | 0.146401 | + | 0.989225i | \(0.453231\pi\) |
−0.929895 | + | 0.367825i | \(0.880102\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −836.000 | − | 1447.99i | −0.450548 | − | 0.780372i | 0.547872 | − | 0.836562i | \(-0.315438\pi\) |
−0.998420 | + | 0.0561903i | \(0.982105\pi\) | |||||||
\(152\) | 496.000 | − | 859.097i | 0.264677 | − | 0.458434i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 144.000 | 0.0746217 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 223.000 | + | 386.247i | 0.113359 | + | 0.196343i | 0.917123 | − | 0.398605i | \(-0.130506\pi\) |
−0.803764 | + | 0.594949i | \(0.797172\pi\) | |||||||
\(158\) | 552.000 | + | 956.092i | 0.277942 | + | 0.481409i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −64.0000 | −0.0316228 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1354.00 | + | 2345.20i | −0.650635 | + | 1.12693i | 0.332334 | + | 0.943162i | \(0.392164\pi\) |
−0.982969 | + | 0.183771i | \(0.941170\pi\) | |||||||
\(164\) | −924.000 | − | 1600.41i | −0.439953 | − | 0.762021i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1036.00 | − | 1794.40i | 0.484393 | − | 0.838993i | ||||
\(167\) | 896.000 | 0.415177 | 0.207589 | − | 0.978216i | \(-0.433439\pi\) | ||||
0.207589 | + | 0.978216i | \(0.433439\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −433.000 | −0.197087 | ||||||||
\(170\) | −4.00000 | + | 6.92820i | −0.00180462 | + | 0.00312570i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −424.000 | − | 734.390i | −0.187963 | − | 0.325562i | ||||
\(173\) | −2017.00 | + | 3493.55i | −0.886414 | + | 1.53531i | −0.0423302 | + | 0.999104i | \(0.513478\pi\) |
−0.844084 | + | 0.536211i | \(0.819855\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 128.000 | 0.0548202 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 30.0000 | + | 51.9615i | 0.0126326 | + | 0.0218802i | ||||
\(179\) | −1740.00 | − | 3013.77i | −0.726557 | − | 1.25843i | −0.958330 | − | 0.285664i | \(-0.907786\pi\) |
0.231773 | − | 0.972770i | \(-0.425547\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2898.00 | 1.19009 | 0.595046 | − | 0.803692i | \(-0.297134\pi\) | ||||
0.595046 | + | 0.803692i | \(0.297134\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −304.000 | + | 526.543i | −0.121800 | + | 0.210964i | ||||
\(185\) | −398.000 | − | 689.356i | −0.158170 | − | 0.273959i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.00000 | − | 13.8564i | 0.00312844 | − | 0.00541861i | ||||
\(188\) | −1056.00 | −0.409663 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −496.000 | −0.189387 | ||||||||
\(191\) | 1326.00 | − | 2296.70i | 0.502335 | − | 0.870070i | −0.497661 | − | 0.867371i | \(-0.665808\pi\) |
0.999996 | − | 0.00269837i | \(-0.000858920\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −73.0000 | − | 126.440i | −0.0272262 | − | 0.0471571i | 0.852091 | − | 0.523393i | \(-0.175334\pi\) |
−0.879317 | + | 0.476236i | \(0.842001\pi\) | |||||||
\(194\) | 1190.00 | − | 2061.14i | 0.440397 | − | 0.762790i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2546.00 | 0.920787 | 0.460393 | − | 0.887715i | \(-0.347708\pi\) | ||||
0.460393 | + | 0.887715i | \(0.347708\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1268.00 | − | 2196.24i | −0.451689 | − | 0.782349i | 0.546802 | − | 0.837262i | \(-0.315845\pi\) |
−0.998491 | + | 0.0549134i | \(0.982512\pi\) | |||||||
\(200\) | −484.000 | − | 838.313i | −0.171120 | − | 0.296388i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2740.00 | −0.954385 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −462.000 | + | 800.207i | −0.157402 | + | 0.272629i | ||||
\(206\) | −464.000 | − | 803.672i | −0.156934 | − | 0.271818i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −336.000 | + | 581.969i | −0.112007 | + | 0.194001i | ||||
\(209\) | 992.000 | 0.328316 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1300.00 | −0.424150 | −0.212075 | − | 0.977253i | \(-0.568022\pi\) | ||||
−0.212075 | + | 0.977253i | \(0.568022\pi\) | |||||||
\(212\) | −324.000 | + | 561.184i | −0.104964 | + | 0.181803i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2136.00 | + | 3699.66i | 0.682308 | + | 1.18179i | ||||
\(215\) | −212.000 | + | 367.195i | −0.0672478 | + | 0.116477i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2452.00 | 0.761791 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −32.0000 | − | 55.4256i | −0.00980654 | − | 0.0169854i | ||||
\(221\) | 42.0000 | + | 72.7461i | 0.0127838 | + | 0.0221422i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2576.00 | −0.773550 | −0.386775 | − | 0.922174i | \(-0.626411\pi\) | ||||
−0.386775 | + | 0.922174i | \(0.626411\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −338.000 | + | 585.433i | −0.0994842 | + | 0.172312i | ||||
\(227\) | 918.000 | + | 1590.02i | 0.268413 | + | 0.464905i | 0.968452 | − | 0.249199i | \(-0.0801674\pi\) |
−0.700039 | + | 0.714105i | \(0.746834\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −937.000 | + | 1622.93i | −0.270387 | + | 0.468325i | −0.968961 | − | 0.247213i | \(-0.920485\pi\) |
0.698574 | + | 0.715538i | \(0.253818\pi\) | |||||||
\(230\) | 304.000 | 0.0871529 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2032.00 | 0.575032 | ||||||||
\(233\) | 1865.00 | − | 3230.27i | 0.524379 | − | 0.908250i | −0.475219 | − | 0.879868i | \(-0.657631\pi\) |
0.999597 | − | 0.0283826i | \(-0.00903567\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 264.000 | + | 457.261i | 0.0732828 | + | 0.126930i | ||||
\(236\) | 1544.00 | − | 2674.29i | 0.425872 | − | 0.737632i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2004.00 | −0.542377 | −0.271188 | − | 0.962526i | \(-0.587417\pi\) | ||||
−0.271188 | + | 0.962526i | \(0.587417\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −323.000 | − | 559.452i | −0.0863330 | − | 0.149533i | 0.819625 | − | 0.572900i | \(-0.194182\pi\) |
−0.905958 | + | 0.423367i | \(0.860848\pi\) | |||||||
\(242\) | −1267.00 | − | 2194.51i | −0.336553 | − | 0.582927i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −120.000 | −0.0314845 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2604.00 | + | 4510.26i | −0.670804 | + | 1.16187i | ||||
\(248\) | 288.000 | + | 498.831i | 0.0737420 | + | 0.127725i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −492.000 | + | 852.169i | −0.124467 | + | 0.215584i | ||||
\(251\) | 1260.00 | 0.316855 | 0.158427 | − | 0.987371i | \(-0.449358\pi\) | ||||
0.158427 | + | 0.987371i | \(0.449358\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −608.000 | −0.151086 | ||||||||
\(254\) | 2088.00 | − | 3616.52i | 0.515798 | − | 0.893389i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −2955.00 | + | 5118.21i | −0.717229 | + | 1.24228i | 0.244865 | + | 0.969557i | \(0.421256\pi\) |
−0.962094 | + | 0.272720i | \(0.912077\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 336.000 | 0.0801455 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −292.000 | − | 505.759i | −0.0688543 | − | 0.119259i | ||||
\(263\) | 1494.00 | + | 2587.68i | 0.350281 | + | 0.606705i | 0.986299 | − | 0.164970i | \(-0.0527527\pi\) |
−0.636017 | + | 0.771675i | \(0.719419\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 324.000 | 0.0751063 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1528.00 | − | 2646.57i | 0.348274 | − | 0.603228i | ||||
\(269\) | 659.000 | + | 1141.42i | 0.149368 | + | 0.258713i | 0.930994 | − | 0.365035i | \(-0.118943\pi\) |
−0.781626 | + | 0.623747i | \(0.785609\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2820.00 | + | 4884.38i | −0.632114 | + | 1.09485i | 0.355005 | + | 0.934864i | \(0.384479\pi\) |
−0.987119 | + | 0.159989i | \(0.948854\pi\) | |||||||
\(272\) | −32.0000 | −0.00713340 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1636.00 | 0.360709 | ||||||||
\(275\) | 484.000 | − | 838.313i | 0.106132 | − | 0.183826i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3223.00 | − | 5582.40i | −0.699102 | − | 1.21088i | −0.968778 | − | 0.247929i | \(-0.920250\pi\) |
0.269676 | − | 0.962951i | \(-0.413083\pi\) | |||||||
\(278\) | 2156.00 | − | 3734.30i | 0.465138 | − | 0.805642i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4930.00 | −1.04662 | −0.523308 | − | 0.852144i | \(-0.675302\pi\) | ||||
−0.523308 | + | 0.852144i | \(0.675302\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3130.00 | − | 5421.32i | −0.657453 | − | 1.13874i | −0.981273 | − | 0.192623i | \(-0.938301\pi\) |
0.323820 | − | 0.946119i | \(-0.395033\pi\) | |||||||
\(284\) | −472.000 | − | 817.528i | −0.0986199 | − | 0.170815i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −672.000 | −0.138938 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2454.50 | − | 4251.32i | 0.499593 | − | 0.865320i | ||||
\(290\) | −508.000 | − | 879.882i | −0.102865 | − | 0.178167i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 836.000 | − | 1447.99i | 0.167545 | − | 0.290197i | ||||
\(293\) | −2310.00 | −0.460586 | −0.230293 | − | 0.973121i | \(-0.573968\pi\) | ||||
−0.230293 | + | 0.973121i | \(0.573968\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1544.00 | −0.304729 | ||||||||
\(296\) | 1592.00 | − | 2757.42i | 0.312612 | − | 0.541460i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2850.00 | + | 4936.34i | 0.554014 | + | 0.959580i | ||||
\(299\) | 1596.00 | − | 2764.35i | 0.308693 | − | 0.534671i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3344.00 | −0.637171 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −992.000 | − | 1718.19i | −0.187155 | − | 0.324162i | ||||
\(305\) | 30.0000 | + | 51.9615i | 0.00563211 | + | 0.00975511i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −196.000 | −0.0364375 | −0.0182187 | − | 0.999834i | \(-0.505800\pi\) | ||||
−0.0182187 | + | 0.999834i | \(0.505800\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 144.000 | − | 249.415i | 0.0263827 | − | 0.0456963i | ||||
\(311\) | 3368.00 | + | 5833.55i | 0.614089 | + | 1.06363i | 0.990544 | + | 0.137199i | \(0.0438099\pi\) |
−0.376454 | + | 0.926435i | \(0.622857\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 197.000 | − | 341.214i | 0.0355754 | − | 0.0616184i | −0.847690 | − | 0.530493i | \(-0.822007\pi\) |
0.883265 | + | 0.468874i | \(0.155340\pi\) | |||||||
\(314\) | 892.000 | 0.160314 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2208.00 | 0.393069 | ||||||||
\(317\) | −3357.00 | + | 5814.49i | −0.594788 | + | 1.03020i | 0.398788 | + | 0.917043i | \(0.369431\pi\) |
−0.993577 | + | 0.113161i | \(0.963903\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1016.00 | + | 1759.76i | 0.178323 | + | 0.308865i | ||||
\(320\) | −64.0000 | + | 110.851i | −0.0111803 | + | 0.0193649i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −248.000 | −0.0427216 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2541.00 | + | 4401.14i | 0.433690 | + | 0.751173i | ||||
\(326\) | 2708.00 | + | 4690.39i | 0.460068 | + | 0.796862i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3696.00 | −0.622187 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −346.000 | + | 599.290i | −0.0574558 | + | 0.0995164i | −0.893323 | − | 0.449416i | \(-0.851632\pi\) |
0.835867 | + | 0.548932i | \(0.184966\pi\) | |||||||
\(332\) | −2072.00 | − | 3588.81i | −0.342517 | − | 0.593258i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 896.000 | − | 1551.92i | 0.146787 | − | 0.254243i | ||||
\(335\) | −1528.00 | −0.249205 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1566.00 | −0.253132 | −0.126566 | − | 0.991958i | \(-0.540396\pi\) | ||||
−0.126566 | + | 0.991958i | \(0.540396\pi\) | |||||||
\(338\) | −433.000 | + | 749.978i | −0.0696808 | + | 0.120691i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.00000 | + | 13.8564i | 0.00127606 | + | 0.00221020i | ||||
\(341\) | −288.000 | + | 498.831i | −0.0457363 | + | 0.0792176i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1696.00 | −0.265820 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4034.00 | + | 6987.09i | 0.626790 | + | 1.08563i | ||||
\(347\) | −2664.00 | − | 4614.18i | −0.412135 | − | 0.713840i | 0.582988 | − | 0.812481i | \(-0.301884\pi\) |
−0.995123 | + | 0.0986415i | \(0.968550\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11326.0 | −1.73715 | −0.868577 | − | 0.495554i | \(-0.834965\pi\) | ||||
−0.868577 | + | 0.495554i | \(0.834965\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 128.000 | − | 221.703i | 0.0193819 | − | 0.0335704i | ||||
\(353\) | 1065.00 | + | 1844.63i | 0.160579 | + | 0.278130i | 0.935076 | − | 0.354446i | \(-0.115331\pi\) |
−0.774498 | + | 0.632577i | \(0.781997\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −236.000 | + | 408.764i | −0.0352833 | + | 0.0611125i | ||||
\(356\) | 120.000 | 0.0178651 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6960.00 | −1.02751 | ||||||||
\(359\) | 1522.00 | − | 2636.18i | 0.223755 | − | 0.387555i | −0.732190 | − | 0.681100i | \(-0.761502\pi\) |
0.955945 | + | 0.293545i | \(0.0948351\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4258.50 | − | 7375.94i | −0.620863 | − | 1.07537i | ||||
\(362\) | 2898.00 | − | 5019.48i | 0.420761 | − | 0.728780i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −836.000 | −0.119886 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6208.00 | + | 10752.6i | 0.882984 | + | 1.52937i | 0.848008 | + | 0.529984i | \(0.177802\pi\) |
0.0349760 | + | 0.999388i | \(0.488865\pi\) | |||||||
\(368\) | 608.000 | + | 1053.09i | 0.0861255 | + | 0.149174i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1592.00 | −0.223687 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3721.00 | − | 6444.96i | 0.516531 | − | 0.894658i | −0.483285 | − | 0.875463i | \(-0.660556\pi\) |
0.999816 | − | 0.0191948i | \(-0.00611026\pi\) | |||||||
\(374\) | −16.0000 | − | 27.7128i | −0.00221214 | − | 0.00383154i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1056.00 | + | 1829.05i | −0.144838 | + | 0.250867i | ||||
\(377\) | −10668.0 | −1.45737 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 100.000 | 0.0135532 | 0.00677659 | − | 0.999977i | \(-0.497843\pi\) | ||||
0.00677659 | + | 0.999977i | \(0.497843\pi\) | |||||||
\(380\) | −496.000 | + | 859.097i | −0.0669586 | + | 0.115976i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2652.00 | − | 4593.40i | −0.355205 | − | 0.615232i | ||||
\(383\) | −4040.00 | + | 6997.49i | −0.538993 | + | 0.933563i | 0.459965 | + | 0.887937i | \(0.347862\pi\) |
−0.998959 | + | 0.0456266i | \(0.985472\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −292.000 | −0.0385036 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2380.00 | − | 4122.28i | −0.311408 | − | 0.539374i | ||||
\(389\) | −2741.00 | − | 4747.55i | −0.357260 | − | 0.618793i | 0.630242 | − | 0.776399i | \(-0.282956\pi\) |
−0.987502 | + | 0.157606i | \(0.949622\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 152.000 | 0.0196598 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2546.00 | − | 4409.80i | 0.325547 | − | 0.563864i | ||||
\(395\) | −552.000 | − | 956.092i | −0.0703143 | − | 0.121788i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5223.00 | − | 9046.50i | 0.660289 | − | 1.14365i | −0.320250 | − | 0.947333i | \(-0.603767\pi\) |
0.980540 | − | 0.196322i | \(-0.0628997\pi\) | |||||||
\(398\) | −5072.00 | −0.638785 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1936.00 | −0.242000 | ||||||||
\(401\) | −5667.00 | + | 9815.53i | −0.705727 | + | 1.22235i | 0.260702 | + | 0.965419i | \(0.416046\pi\) |
−0.966429 | + | 0.256935i | \(0.917287\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1512.00 | − | 2618.86i | −0.186894 | − | 0.323709i | ||||
\(404\) | −2740.00 | + | 4745.82i | −0.337426 | + | 0.584439i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3184.00 | 0.387776 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4297.00 | + | 7442.62i | 0.519494 | + | 0.899790i | 0.999743 | + | 0.0226578i | \(0.00721280\pi\) |
−0.480249 | + | 0.877132i | \(0.659454\pi\) | |||||||
\(410\) | 924.000 | + | 1600.41i | 0.111300 | + | 0.192778i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1856.00 | −0.221938 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1036.00 | + | 1794.40i | −0.122543 | + | 0.212250i | ||||
\(416\) | 672.000 | + | 1163.94i | 0.0792007 | + | 0.137180i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 992.000 | − | 1718.19i | 0.116077 | − | 0.201052i | ||||
\(419\) | 10500.0 | 1.22424 | 0.612122 | − | 0.790763i | \(-0.290316\pi\) | ||||
0.612122 | + | 0.790763i | \(0.290316\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12066.0 | −1.39682 | −0.698410 | − | 0.715698i | \(-0.746109\pi\) | ||||
−0.698410 | + | 0.715698i | \(0.746109\pi\) | |||||||
\(422\) | −1300.00 | + | 2251.67i | −0.149960 | + | 0.259738i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 648.000 | + | 1122.37i | 0.0742209 | + | 0.128554i | ||||
\(425\) | −121.000 | + | 209.578i | −0.0138103 | + | 0.0239201i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8544.00 | 0.964930 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 424.000 | + | 734.390i | 0.0475514 | + | 0.0823614i | ||||
\(431\) | 2166.00 | + | 3751.62i | 0.242071 | + | 0.419279i | 0.961304 | − | 0.275490i | \(-0.0888400\pi\) |
−0.719233 | + | 0.694769i | \(0.755507\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1918.00 | 0.212871 | 0.106436 | − | 0.994320i | \(-0.466056\pi\) | ||||
0.106436 | + | 0.994320i | \(0.466056\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2452.00 | − | 4246.99i | 0.269334 | − | 0.466500i | ||||
\(437\) | 4712.00 | + | 8161.42i | 0.515802 | + | 0.893395i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3996.00 | + | 6921.28i | −0.434439 | + | 0.752470i | −0.997250 | − | 0.0741155i | \(-0.976387\pi\) |
0.562811 | + | 0.826586i | \(0.309720\pi\) | |||||||
\(440\) | −128.000 | −0.0138685 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 168.000 | 0.0180791 | ||||||||
\(443\) | 1592.00 | − | 2757.42i | 0.170741 | − | 0.295732i | −0.767938 | − | 0.640524i | \(-0.778717\pi\) |
0.938679 | + | 0.344792i | \(0.112051\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.0000 | − | 51.9615i | −0.00319581 | − | 0.00553531i | ||||
\(446\) | −2576.00 | + | 4461.76i | −0.273491 | + | 0.473701i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11426.0 | −1.20095 | −0.600475 | − | 0.799644i | \(-0.705022\pi\) | ||||
−0.600475 | + | 0.799644i | \(0.705022\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1848.00 | − | 3200.83i | −0.192947 | − | 0.334193i | ||||
\(452\) | 676.000 | + | 1170.87i | 0.0703459 | + | 0.121843i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3672.00 | 0.379594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8467.00 | − | 14665.3i | 0.866673 | − | 1.50112i | 0.00129662 | − | 0.999999i | \(-0.499587\pi\) |
0.865376 | − | 0.501122i | \(-0.167079\pi\) | |||||||
\(458\) | 1874.00 | + | 3245.86i | 0.191193 | + | 0.331156i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 304.000 | − | 526.543i | 0.0308132 | − | 0.0533700i | ||||
\(461\) | −17038.0 | −1.72134 | −0.860671 | − | 0.509161i | \(-0.829956\pi\) | ||||
−0.860671 | + | 0.509161i | \(0.829956\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13592.0 | −1.36431 | −0.682153 | − | 0.731209i | \(-0.738956\pi\) | ||||
−0.682153 | + | 0.731209i | \(0.738956\pi\) | |||||||
\(464\) | 2032.00 | − | 3519.53i | 0.203304 | − | 0.352134i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3730.00 | − | 6460.55i | −0.370792 | − | 0.642230i | ||||
\(467\) | −4306.00 | + | 7458.21i | −0.426676 | + | 0.739025i | −0.996575 | − | 0.0826895i | \(-0.973649\pi\) |
0.569899 | + | 0.821715i | \(0.306982\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1056.00 | 0.103638 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3088.00 | − | 5348.57i | −0.301137 | − | 0.521585i | ||||
\(473\) | −848.000 | − | 1468.78i | −0.0824336 | − | 0.142779i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15004.0 | −1.44933 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2004.00 | + | 3471.03i | −0.191759 | + | 0.332136i | ||||
\(479\) | −3716.00 | − | 6436.30i | −0.354464 | − | 0.613950i | 0.632562 | − | 0.774510i | \(-0.282003\pi\) |
−0.987026 | + | 0.160560i | \(0.948670\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8358.00 | + | 14476.5i | −0.792291 | + | 1.37229i | ||||
\(482\) | −1292.00 | −0.122093 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5068.00 | −0.475958 | ||||||||
\(485\) | −1190.00 | + | 2061.14i | −0.111413 | + | 0.192972i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3308.00 | + | 5729.62i | 0.307802 | + | 0.533129i | 0.977881 | − | 0.209160i | \(-0.0670731\pi\) |
−0.670079 | + | 0.742290i | \(0.733740\pi\) | |||||||
\(488\) | −120.000 | + | 207.846i | −0.0111314 | + | 0.0192802i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17040.0 | −1.56620 | −0.783100 | − | 0.621896i | \(-0.786363\pi\) | ||||
−0.783100 | + | 0.621896i | \(0.786363\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −254.000 | − | 439.941i | −0.0232040 | − | 0.0401906i | ||||
\(494\) | 5208.00 | + | 9020.52i | 0.474330 | + | 0.821564i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1152.00 | 0.104287 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1474.00 | − | 2553.04i | 0.132235 | − | 0.229038i | −0.792303 | − | 0.610128i | \(-0.791118\pi\) |
0.924538 | + | 0.381090i | \(0.124451\pi\) | |||||||
\(500\) | 984.000 | + | 1704.34i | 0.0880116 | + | 0.152441i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1260.00 | − | 2182.38i | 0.112025 | − | 0.194033i | ||||
\(503\) | 17304.0 | 1.53389 | 0.766946 | − | 0.641712i | \(-0.221776\pi\) | ||||
0.766946 | + | 0.641712i | \(0.221776\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2740.00 | 0.241442 | ||||||||
\(506\) | −608.000 | + | 1053.09i | −0.0534168 | + | 0.0925206i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4176.00 | − | 7233.04i | −0.364724 | − | 0.631721i | ||||
\(509\) | −2325.00 | + | 4027.02i | −0.202463 | + | 0.350677i | −0.949322 | − | 0.314307i | \(-0.898228\pi\) |
0.746858 | + | 0.664983i | \(0.231561\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5910.00 | + | 10236.4i | 0.507157 | + | 0.878422i | ||||
\(515\) | 464.000 | + | 803.672i | 0.0397015 | + | 0.0687651i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2112.00 | −0.179663 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 336.000 | − | 581.969i | 0.0283357 | − | 0.0490789i | ||||
\(521\) | −8427.00 | − | 14596.0i | −0.708625 | − | 1.22737i | −0.965367 | − | 0.260894i | \(-0.915983\pi\) |
0.256742 | − | 0.966480i | \(-0.417351\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −62.0000 | + | 107.387i | −0.00518369 | + | 0.00897842i | −0.868606 | − | 0.495504i | \(-0.834983\pi\) |
0.863422 | + | 0.504482i | \(0.168317\pi\) | |||||||
\(524\) | −1168.00 | −0.0973747 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5976.00 | 0.495373 | ||||||||
\(527\) | 72.0000 | − | 124.708i | 0.00595136 | − | 0.0103081i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3195.50 | + | 5534.77i | 0.262637 | + | 0.454900i | ||||
\(530\) | 324.000 | − | 561.184i | 0.0265541 | − | 0.0459930i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19404.0 | 1.57689 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2136.00 | − | 3699.66i | −0.172612 | − | 0.298972i | ||||
\(536\) | −3056.00 | − | 5293.15i | −0.246267 | − | 0.426547i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2636.00 | 0.211238 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2691.00 | + | 4660.95i | −0.213854 | + | 0.370406i | −0.952918 | − | 0.303230i | \(-0.901935\pi\) |
0.739063 | + | 0.673636i | \(0.235268\pi\) | |||||||
\(542\) | 5640.00 | + | 9768.77i | 0.446972 | + | 0.774178i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −32.0000 | + | 55.4256i | −0.00252204 | + | 0.00436830i | ||||
\(545\) | −2452.00 | −0.192720 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17460.0 | 1.36478 | 0.682391 | − | 0.730987i | \(-0.260940\pi\) | ||||
0.682391 | + | 0.730987i | \(0.260940\pi\) | |||||||
\(548\) | 1636.00 | − | 2833.64i | 0.127530 | − | 0.220888i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −968.000 | − | 1676.63i | −0.0750467 | − | 0.129985i | ||||
\(551\) | 15748.0 | − | 27276.3i | 1.21758 | − | 2.10891i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −12892.0 | −0.988680 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4312.00 | − | 7468.60i | −0.328902 | − | 0.569675i | ||||
\(557\) | −4757.00 | − | 8239.37i | −0.361868 | − | 0.626774i | 0.626400 | − | 0.779502i | \(-0.284528\pi\) |
−0.988268 | + | 0.152728i | \(0.951194\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8904.00 | 0.673701 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4930.00 | + | 8539.01i | −0.370035 | + | 0.640919i | ||||
\(563\) | −1994.00 | − | 3453.71i | −0.149267 | − | 0.258537i | 0.781690 | − | 0.623667i | \(-0.214358\pi\) |
−0.930957 | + | 0.365130i | \(0.881025\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 338.000 | − | 585.433i | 0.0251677 | − | 0.0435918i | ||||
\(566\) | −12520.0 | −0.929779 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1888.00 | −0.139470 | ||||||||
\(569\) | 5673.00 | − | 9825.92i | 0.417969 | − | 0.723944i | −0.577766 | − | 0.816203i | \(-0.696075\pi\) |
0.995735 | + | 0.0922585i | \(0.0294086\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4218.00 | + | 7305.79i | 0.309138 | + | 0.535443i | 0.978174 | − | 0.207787i | \(-0.0666262\pi\) |
−0.669036 | + | 0.743230i | \(0.733293\pi\) | |||||||
\(572\) | −672.000 | + | 1163.94i | −0.0491219 | + | 0.0850816i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9196.00 | 0.666956 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1049.00 | + | 1816.92i | 0.0756853 | + | 0.131091i | 0.901384 | − | 0.433020i | \(-0.142552\pi\) |
−0.825699 | + | 0.564111i | \(0.809219\pi\) | |||||||
\(578\) | −4909.00 | − | 8502.64i | −0.353266 | − | 0.611874i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2032.00 | −0.145473 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −648.000 | + | 1122.37i | −0.0460333 | + | 0.0797320i | ||||
\(584\) | −1672.00 | − | 2895.99i | −0.118472 | − | 0.205200i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2310.00 | + | 4001.04i | −0.162842 | + | 0.282050i | ||||
\(587\) | 9436.00 | 0.663484 | 0.331742 | − | 0.943370i | \(-0.392364\pi\) | ||||
0.331742 | + | 0.943370i | \(0.392364\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8928.00 | 0.624570 | ||||||||
\(590\) | −1544.00 | + | 2674.29i | −0.107738 | + | 0.186608i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3184.00 | − | 5514.85i | −0.221050 | − | 0.382870i | ||||
\(593\) | 657.000 | − | 1137.96i | 0.0454971 | − | 0.0788032i | −0.842380 | − | 0.538884i | \(-0.818846\pi\) |
0.887877 | + | 0.460081i | \(0.152180\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11400.0 | 0.783494 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3192.00 | − | 5528.71i | −0.218279 | − | 0.378070i | ||||
\(599\) | −4470.00 | − | 7742.27i | −0.304907 | − | 0.528114i | 0.672334 | − | 0.740248i | \(-0.265292\pi\) |
−0.977241 | + | 0.212134i | \(0.931959\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16058.0 | −1.08988 | −0.544941 | − | 0.838474i | \(-0.683448\pi\) | ||||
−0.544941 | + | 0.838474i | \(0.683448\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3344.00 | + | 5791.98i | −0.225274 | + | 0.390186i | ||||
\(605\) | 1267.00 | + | 2194.51i | 0.0851419 | + | 0.147470i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1968.00 | − | 3408.68i | 0.131596 | − | 0.227931i | −0.792696 | − | 0.609617i | \(-0.791323\pi\) |
0.924292 | + | 0.381686i | \(0.124657\pi\) | |||||||
\(608\) | −3968.00 | −0.264677 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 120.000 | 0.00796501 | ||||||||
\(611\) | 5544.00 | − | 9602.49i | 0.367081 | − | 0.635802i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −87.0000 | − | 150.688i | −0.00573230 | − | 0.00992863i | 0.863145 | − | 0.504956i | \(-0.168491\pi\) |
−0.868877 | + | 0.495027i | \(0.835158\pi\) | |||||||
\(614\) | −196.000 | + | 339.482i | −0.0128826 | + | 0.0223133i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16018.0 | −1.04515 | −0.522577 | − | 0.852592i | \(-0.675029\pi\) | ||||
−0.522577 | + | 0.852592i | \(0.675029\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1534.00 | − | 2656.97i | −0.0996069 | − | 0.172524i | 0.811915 | − | 0.583776i | \(-0.198425\pi\) |
−0.911522 | + | 0.411251i | \(0.865092\pi\) | |||||||
\(620\) | −288.000 | − | 498.831i | −0.0186554 | − | 0.0323121i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13472.0 | 0.868453 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7070.50 | + | 12246.5i | −0.452512 | + | 0.783774i | ||||
\(626\) | −394.000 | − | 682.428i | −0.0251556 | − | 0.0435708i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 892.000 | − | 1544.99i | 0.0566794 | − | 0.0981716i | ||||
\(629\) | −796.000 | −0.0504588 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24656.0 | 1.55553 | 0.777765 | − | 0.628555i | \(-0.216353\pi\) | ||||
0.777765 | + | 0.628555i | \(0.216353\pi\) | |||||||
\(632\) | 2208.00 | − | 3824.37i | 0.138971 | − | 0.240704i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6714.00 | + | 11629.0i | 0.420579 | + | 0.728464i | ||||
\(635\) | −2088.00 | + | 3616.52i | −0.130488 | + | 0.226011i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4064.00 | 0.252187 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 128.000 | + | 221.703i | 0.00790569 | + | 0.0136931i | ||||
\(641\) | 3797.00 | + | 6576.60i | 0.233966 | + | 0.405242i | 0.958972 | − | 0.283501i | \(-0.0914961\pi\) |
−0.725005 | + | 0.688743i | \(0.758163\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3724.00 | 0.228398 | 0.114199 | − | 0.993458i | \(-0.463570\pi\) | ||||
0.114199 | + | 0.993458i | \(0.463570\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −248.000 | + | 429.549i | −0.0151044 | + | 0.0261616i | ||||
\(647\) | −1896.00 | − | 3283.97i | −0.115208 | − | 0.199546i | 0.802655 | − | 0.596444i | \(-0.203420\pi\) |
−0.917863 | + | 0.396898i | \(0.870087\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3088.00 | − | 5348.57i | 0.186771 | − | 0.323497i | ||||
\(650\) | 10164.0 | 0.613331 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10832.0 | 0.650635 | ||||||||
\(653\) | 12351.0 | − | 21392.6i | 0.740171 | − | 1.28201i | −0.212245 | − | 0.977216i | \(-0.568078\pi\) |
0.952417 | − | 0.304798i | \(-0.0985890\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 292.000 | + | 505.759i | 0.0174189 | + | 0.0301704i | ||||
\(656\) | −3696.00 | + | 6401.66i | −0.219976 | + | 0.381010i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20144.0 | 1.19074 | 0.595371 | − | 0.803451i | \(-0.297005\pi\) | ||||
0.595371 | + | 0.803451i | \(0.297005\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1261.00 | − | 2184.12i | −0.0742015 | − | 0.128521i | 0.826537 | − | 0.562882i | \(-0.190307\pi\) |
−0.900739 | + | 0.434361i | \(0.856974\pi\) | |||||||
\(662\) | 692.000 | + | 1198.58i | 0.0406274 | + | 0.0703687i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8288.00 | −0.484393 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9652.00 | + | 16717.8i | −0.560310 | + | 0.970486i | ||||
\(668\) | −1792.00 | − | 3103.84i | −0.103794 | − | 0.179777i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1528.00 | + | 2646.57i | −0.0881071 | + | 0.152606i | ||||
\(671\) | −240.000 | −0.0138079 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10414.0 | −0.596479 | −0.298239 | − | 0.954491i | \(-0.596399\pi\) | ||||
−0.298239 | + | 0.954491i | \(0.596399\pi\) | |||||||
\(674\) | −1566.00 | + | 2712.39i | −0.0894956 | + | 0.155011i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 866.000 | + | 1499.96i | 0.0492717 | + | 0.0853411i | ||||
\(677\) | 11115.0 | − | 19251.7i | 0.630996 | − | 1.09292i | −0.356353 | − | 0.934352i | \(-0.615980\pi\) |
0.987348 | − | 0.158565i | \(-0.0506868\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 32.0000 | 0.00180462 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 576.000 | + | 997.661i | 0.0323404 | + | 0.0560153i | ||||
\(683\) | 9096.00 | + | 15754.7i | 0.509588 | + | 0.882633i | 0.999938 | + | 0.0111072i | \(0.00353559\pi\) |
−0.490350 | + | 0.871526i | \(0.663131\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1636.00 | −0.0912531 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1696.00 | + | 2937.56i | −0.0939817 | + | 0.162781i | ||||
\(689\) | −3402.00 | − | 5892.44i | −0.188107 | − | 0.325811i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4054.00 | − | 7021.73i | 0.223186 | − | 0.386569i | −0.732588 | − | 0.680673i | \(-0.761688\pi\) |
0.955774 | + | 0.294103i | \(0.0950210\pi\) | |||||||
\(692\) | 16136.0 | 0.886414 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10656.0 | −0.582848 | ||||||||
\(695\) | −2156.00 | + | 3734.30i | −0.117672 | + | 0.203813i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 462.000 | + | 800.207i | 0.0251069 | + | 0.0434864i | ||||
\(698\) | −11326.0 | + | 19617.2i | −0.614177 | + | 1.06379i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5794.00 | 0.312177 | 0.156089 | − | 0.987743i | \(-0.450111\pi\) | ||||
0.156089 | + | 0.987743i | \(0.450111\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24676.0 | − | 42740.1i | −1.32386 | − | 2.29299i | ||||
\(704\) | −256.000 | − | 443.405i | −0.0137051 | − | 0.0237379i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4260.00 | 0.227092 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 977.000 | − | 1692.21i | 0.0517518 | − | 0.0896367i | −0.838989 | − | 0.544148i | \(-0.816853\pi\) |
0.890741 | + | 0.454512i | \(0.150186\pi\) | |||||||
\(710\) | 472.000 | + | 817.528i | 0.0249491 | + | 0.0432131i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 120.000 | − | 207.846i | 0.00631628 | − | 0.0109401i | ||||
\(713\) | −5472.00 | −0.287417 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 672.000 | 0.0351488 | ||||||||
\(716\) | −6960.00 | + | 12055.1i | −0.363279 | + | 0.629217i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3044.00 | − | 5272.36i | −0.158219 | − | 0.274043i | ||||
\(719\) | 16008.0 | − | 27726.7i | 0.830317 | − | 1.43815i | −0.0674706 | − | 0.997721i | \(-0.521493\pi\) |
0.897787 | − | 0.440429i | \(-0.145174\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −17034.0 | −0.878033 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5796.00 | − | 10039.0i | −0.297523 | − | 0.515325i | ||||
\(725\) | −15367.0 | − | 26616.4i | −0.787195 | − | 1.36346i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23072.0 | 1.17702 | 0.588510 | − | 0.808490i | \(-0.299715\pi\) | ||||
0.588510 | + | 0.808490i | \(0.299715\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −836.000 | + | 1447.99i | −0.0423860 | + | 0.0734146i | ||||
\(731\) | 212.000 | + | 367.195i | 0.0107265 | + | 0.0185789i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15891.0 | − | 27524.0i | 0.800747 | − | 1.38693i | −0.118378 | − | 0.992969i | \(-0.537770\pi\) |
0.919125 | − | 0.393966i | \(-0.128897\pi\) | |||||||
\(734\) | 24832.0 | 1.24873 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2432.00 | 0.121800 | ||||||||
\(737\) | 3056.00 | − | 5293.15i | 0.152740 | − | 0.264553i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12198.0 | + | 21127.6i | 0.607186 | + | 1.05168i | 0.991702 | + | 0.128559i | \(0.0410352\pi\) |
−0.384516 | + | 0.923119i | \(0.625631\pi\) | |||||||
\(740\) | −1592.00 | + | 2757.42i | −0.0790852 | + | 0.136980i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32604.0 | 1.60986 | 0.804929 | − | 0.593371i | \(-0.202203\pi\) | ||||
0.804929 | + | 0.593371i | \(0.202203\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2850.00 | − | 4936.34i | −0.140156 | − | 0.242757i | ||||
\(746\) | −7442.00 | − | 12889.9i | −0.365243 | − | 0.632619i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −64.0000 | −0.00312844 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3840.00 | − | 6651.08i | 0.186583 | − | 0.323171i | −0.757526 | − | 0.652805i | \(-0.773592\pi\) |
0.944109 | + | 0.329634i | \(0.106925\pi\) | |||||||
\(752\) | 2112.00 | + | 3658.09i | 0.102416 | + | 0.177389i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10668.0 | + | 18477.5i | −0.515259 | + | 0.892456i | ||||
\(755\) | 3344.00 | 0.161193 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 366.000 | 0.0175727 | 0.00878633 | − | 0.999961i | \(-0.497203\pi\) | ||||
0.00878633 | + | 0.999961i | \(0.497203\pi\) | |||||||
\(758\) | 100.000 | − | 173.205i | 0.00479177 | − | 0.00829959i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 992.000 | + | 1718.19i | 0.0473469 | + | 0.0820072i | ||||
\(761\) | −14687.0 | + | 25438.6i | −0.699610 | + | 1.21176i | 0.268992 | + | 0.963143i | \(0.413310\pi\) |
−0.968602 | + | 0.248618i | \(0.920024\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10608.0 | −0.502335 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8080.00 | + | 13995.0i | 0.381126 | + | 0.660129i | ||||
\(767\) | 16212.0 | + | 28080.0i | 0.763209 | + | 1.32192i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38990.0 | 1.82837 | 0.914184 | − | 0.405299i | \(-0.132833\pi\) | ||||
0.914184 | + | 0.405299i | \(0.132833\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −292.000 | + | 505.759i | −0.0136131 | + | 0.0235786i | ||||
\(773\) | 10235.0 | + | 17727.5i | 0.476232 | + | 0.824858i | 0.999629 | − | 0.0272308i | \(-0.00866890\pi\) |
−0.523397 | + | 0.852089i | \(0.675336\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4356.00 | − | 7544.81i | 0.201900 | − | 0.349700i | ||||
\(776\) | −9520.00 | −0.440397 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10964.0 | −0.505242 | ||||||||
\(779\) | −28644.0 | + | 49612.9i | −1.31743 | + | 2.28186i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −944.000 | − | 1635.06i | −0.0432509 | − | 0.0749128i | ||||
\(782\) | 152.000 | − | 263.272i | 0.00695078 | − | 0.0120391i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −892.000 | −0.0405565 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14958.0 | + | 25908.0i | 0.677503 | + | 1.17347i | 0.975730 | + | 0.218975i | \(0.0702714\pi\) |
−0.298227 | + | 0.954495i | \(0.596395\pi\) | |||||||
\(788\) | −5092.00 | − | 8819.60i | −0.230197 | − | 0.398712i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2208.00 | −0.0994394 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 630.000 | − | 1091.19i | 0.0282118 | − | 0.0488643i | ||||
\(794\) | −10446.0 | − | 18093.0i | −0.466895 | − | 0.808686i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5072.00 | + | 8784.96i | −0.225845 | + | 0.391174i | ||||
\(797\) | 4914.00 | 0.218398 | 0.109199 | − | 0.994020i | \(-0.465172\pi\) | ||||
0.109199 | + | 0.994020i | \(0.465172\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 528.000 | 0.0233783 | ||||||||
\(800\) | −1936.00 | + | 3353.25i | −0.0855599 | + | 0.148194i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11334.0 | + | 19631.1i | 0.499024 | + | 0.864335i | ||||
\(803\) | 1672.00 | − | 2895.99i | 0.0734790 | − | 0.127269i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6048.00 | −0.264307 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5480.00 | + | 9491.64i | 0.238596 | + | 0.413261i | ||||
\(809\) | 17125.0 | + | 29661.4i | 0.744231 | + | 1.28905i | 0.950553 | + | 0.310562i | \(0.100517\pi\) |
−0.206322 | + | 0.978484i | \(0.566149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41804.0 | 1.81003 | 0.905017 | − | 0.425376i | \(-0.139858\pi\) | ||||
0.905017 | + | 0.425376i | \(0.139858\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3184.00 | − | 5514.85i | 0.137100 | − | 0.237464i | ||||
\(815\) | −2708.00 | − | 4690.39i | −0.116389 | − | 0.201592i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13144.0 | + | 22766.1i | −0.562852 | + | 0.974889i | ||||
\(818\) | 17188.0 | 0.734675 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3696.00 | 0.157402 | ||||||||
\(821\) | 15431.0 | − | 26727.3i | 0.655963 | − | 1.13616i | −0.325688 | − | 0.945477i | \(-0.605596\pi\) |
0.981651 | − | 0.190684i | \(-0.0610706\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5288.00 | − | 9159.08i | −0.223971 | − | 0.387929i | 0.732039 | − | 0.681262i | \(-0.238569\pi\) |
−0.956010 | + | 0.293333i | \(0.905235\pi\) | |||||||
\(824\) | −1856.00 | + | 3214.69i | −0.0784670 | + | 0.135909i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10680.0 | 0.449069 | 0.224534 | − | 0.974466i | \(-0.427914\pi\) | ||||
0.224534 | + | 0.974466i | \(0.427914\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −589.000 | − | 1020.18i | −0.0246765 | − | 0.0427409i | 0.853423 | − | 0.521218i | \(-0.174522\pi\) |
−0.878100 | + | 0.478477i | \(0.841189\pi\) | |||||||
\(830\) | 2072.00 | + | 3588.81i | 0.0866508 | + | 0.150084i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2688.00 | 0.112007 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −896.000 | + | 1551.92i | −0.0371346 | + | 0.0643189i | ||||
\(836\) | −1984.00 | − | 3436.39i | −0.0820790 | − | 0.142165i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10500.0 | − | 18186.5i | 0.432836 | − | 0.749694i | ||||
\(839\) | −5600.00 | −0.230433 | −0.115217 | − | 0.993340i | \(-0.536756\pi\) | ||||
−0.115217 | + | 0.993340i | \(0.536756\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 40127.0 | 1.64529 | ||||||||
\(842\) | −12066.0 | + | 20898.9i | −0.493850 | + | 0.855374i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2600.00 | + | 4503.33i | 0.106038 | + | 0.183662i | ||||
\(845\) | 433.000 | − | 749.978i | 0.0176280 | − | 0.0305326i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2592.00 | 0.104964 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 242.000 | + | 419.156i | 0.00976533 | + | 0.0169140i | ||||
\(851\) | 15124.0 | + | 26195.5i | 0.609217 | + | 1.05520i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 826.000 | 0.0331556 | 0.0165778 | − | 0.999863i | \(-0.494723\pi\) | ||||
0.0165778 | + | 0.999863i | \(0.494723\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8544.00 | − | 14798.6i | 0.341154 | − | 0.590896i | ||||
\(857\) | −22959.0 | − | 39766.2i | −0.915128 | − | 1.58505i | −0.806714 | − | 0.590942i | \(-0.798756\pi\) |
−0.108414 | − | 0.994106i | \(-0.534577\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21190.0 | − | 36702.2i | 0.841669 | − | 1.45781i | −0.0468143 | − | 0.998904i | \(-0.514907\pi\) |
0.888483 | − | 0.458909i | \(-0.151760\pi\) | |||||||
\(860\) | 1696.00 | 0.0672478 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8664.00 | 0.342340 | ||||||||
\(863\) | −13262.0 | + | 22970.5i | −0.523110 | + | 0.906053i | 0.476529 | + | 0.879159i | \(0.341895\pi\) |
−0.999638 | + | 0.0268937i | \(0.991438\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4034.00 | − | 6987.09i | −0.158567 | − | 0.274645i | ||||
\(866\) | 1918.00 | − | 3322.07i | 0.0752613 | − | 0.130356i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4416.00 | 0.172385 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16044.0 | + | 27789.0i | 0.624145 | + | 1.08105i | ||||
\(872\) | −4904.00 | − | 8493.98i | −0.190448 | − | 0.329865i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18848.0 | 0.729454 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10307.0 | + | 17852.2i | −0.396856 | + | 0.687375i | −0.993336 | − | 0.115253i | \(-0.963232\pi\) |
0.596480 | + | 0.802628i | \(0.296565\pi\) | |||||||
\(878\) | 7992.00 | + | 13842.6i | 0.307195 | + | 0.532077i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −128.000 | + | 221.703i | −0.00490327 | + | 0.00849272i | ||||
\(881\) | −23730.0 | −0.907473 | −0.453737 | − | 0.891136i | \(-0.649909\pi\) | ||||
−0.453737 | + | 0.891136i | \(0.649909\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9028.00 | −0.344073 | −0.172036 | − | 0.985091i | \(-0.555035\pi\) | ||||
−0.172036 | + | 0.985091i | \(0.555035\pi\) | |||||||
\(884\) | 168.000 | − | 290.985i | 0.00639191 | − | 0.0110711i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3184.00 | − | 5514.85i | −0.120732 | − | 0.209114i | ||||
\(887\) | −18600.0 | + | 32216.1i | −0.704089 | + | 1.21952i | 0.262930 | + | 0.964815i | \(0.415311\pi\) |
−0.967019 | + | 0.254703i | \(0.918022\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −120.000 | −0.00451956 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5152.00 | + | 8923.53i | 0.193388 | + | 0.334957i | ||||
\(893\) | 16368.0 | + | 28350.2i | 0.613364 | + | 1.06238i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6960.00 | 0.259941 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11426.0 | + | 19790.4i | −0.424600 | + | 0.735428i | ||||
\(899\) | 9144.00 | + | 15837.9i | 0.339232 | + | 0.587567i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 162.000 | − | 280.592i | 0.00599001 | − | 0.0103750i | ||||
\(902\) | −7392.00 | −0.272868 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2704.00 | 0.0994842 | ||||||||
\(905\) | −2898.00 | + | 5019.48i | −0.106445 | + | 0.184368i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11994.0 | − | 20774.2i | −0.439090 | − | 0.760525i | 0.558530 | − | 0.829484i | \(-0.311366\pi\) |
−0.997619 | + | 0.0689589i | \(0.978032\pi\) | |||||||
\(908\) | 3672.00 | − | 6360.09i | 0.134207 | − | 0.232453i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15276.0 | −0.555561 | −0.277781 | − | 0.960645i | \(-0.589599\pi\) | ||||
−0.277781 | + | 0.960645i | \(0.589599\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4144.00 | − | 7177.62i | −0.150215 | − | 0.260180i | ||||
\(914\) | −16934.0 | − | 29330.5i | −0.612830 | − | 1.06145i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7496.00 | 0.270387 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5380.00 | − | 9318.43i | 0.193112 | − | 0.334480i | −0.753168 | − | 0.657828i | \(-0.771475\pi\) |
0.946280 | + | 0.323349i | \(0.104809\pi\) | |||||||
\(920\) | −608.000 | − | 1053.09i | −0.0217882 | − | 0.0377383i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17038.0 | + | 29510.7i | −0.608586 | + | 1.05410i | ||||
\(923\) | 9912.00 | 0.353475 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −48158.0 | −1.71181 | ||||||||
\(926\) | −13592.0 | + | 23542.0i | −0.482355 | + | 0.835464i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4064.00 | − | 7039.05i | −0.143758 | − | 0.248996i | ||||
\(929\) | 26445.0 | − | 45804.1i | 0.933942 | − | 1.61764i | 0.157433 | − | 0.987530i | \(-0.449678\pi\) |
0.776509 | − | 0.630106i | \(-0.216988\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −14920.0 | −0.524379 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8612.00 | + | 14916.4i | 0.301706 | + | 0.522570i | ||||
\(935\) | 16.0000 | + | 27.7128i | 0.000559632 | + | 0.000969311i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6118.00 | 0.213305 | 0.106652 | − | 0.994296i | \(-0.465987\pi\) | ||||
0.106652 | + | 0.994296i | \(0.465987\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1056.00 | − | 1829.05i | 0.0366414 | − | 0.0634648i | ||||
\(941\) | 16115.0 | + | 27912.0i | 0.558272 | + | 0.966956i | 0.997641 | + | 0.0686488i | \(0.0218688\pi\) |
−0.439369 | + | 0.898307i | \(0.644798\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17556.0 | − | 30407.9i | 0.606259 | − | 1.05007i | ||||
\(944\) | −12352.0 | −0.425872 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3392.00 | −0.116579 | ||||||||
\(947\) | −9272.00 | + | 16059.6i | −0.318162 | + | 0.551073i | −0.980105 | − | 0.198482i | \(-0.936399\pi\) |
0.661942 | + | 0.749555i | \(0.269732\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8778.00 | + | 15203.9i | 0.300259 | + | 0.520064i | ||||
\(950\) | −15004.0 | + | 25987.7i | −0.512415 | + | 0.887528i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25930.0 | −0.881380 | −0.440690 | − | 0.897659i | \(-0.645266\pi\) | ||||
−0.440690 | + | 0.897659i | \(0.645266\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2652.00 | + | 4593.40i | 0.0898604 | + | 0.155643i | ||||
\(956\) | 4008.00 | + | 6942.06i | 0.135594 | + | 0.234856i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −14864.0 | −0.501288 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12303.5 | − | 21310.3i | 0.412994 | − | 0.715326i | ||||
\(962\) | 16716.0 | + | 28953.0i | 0.560234 | + | 0.970354i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1292.00 | + | 2237.81i | −0.0431665 | + | 0.0747666i | ||||
\(965\) | 292.000 | 0.00974074 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8192.00 | 0.272427 | 0.136214 | − | 0.990680i | \(-0.456507\pi\) | ||||
0.136214 | + | 0.990680i | \(0.456507\pi\) | |||||||
\(968\) | −5068.00 | + | 8778.03i | −0.168277 | + | 0.291464i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2380.00 | + | 4122.28i | 0.0787806 | + | 0.136452i | ||||
\(971\) | 27222.0 | − | 47149.9i | 0.899686 | − | 1.55830i | 0.0717914 | − | 0.997420i | \(-0.477128\pi\) |
0.827895 | − | 0.560883i | \(-0.189538\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 13232.0 | 0.435298 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 240.000 | + | 415.692i | 0.00787112 | + | 0.0136332i | ||||
\(977\) | −12723.0 | − | 22036.9i | −0.416627 | − | 0.721620i | 0.578970 | − | 0.815348i | \(-0.303455\pi\) |
−0.995598 | + | 0.0937289i | \(0.970121\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 240.000 | 0.00783497 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17040.0 | + | 29514.1i | −0.553735 | + | 0.959098i | ||||
\(983\) | −16596.0 | − | 28745.1i | −0.538484 | − | 0.932682i | −0.998986 | − | 0.0450235i | \(-0.985664\pi\) |
0.460502 | − | 0.887659i | \(-0.347670\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2546.00 | + | 4409.80i | −0.0823577 | + | 0.142648i | ||||
\(986\) | −1016.00 | −0.0328154 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20832.0 | 0.670804 | ||||||||
\(989\) | 8056.00 | − | 13953.4i | 0.259015 | − | 0.448627i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5512.00 | − | 9547.06i | −0.176685 | − | 0.306027i | 0.764058 | − | 0.645147i | \(-0.223204\pi\) |
−0.940743 | + | 0.339120i | \(0.889871\pi\) | |||||||
\(992\) | 1152.00 | − | 1995.32i | 0.0368710 | − | 0.0638625i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5072.00 | 0.161601 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20357.0 | − | 35259.4i | −0.646653 | − | 1.12004i | −0.983917 | − | 0.178625i | \(-0.942835\pi\) |
0.337265 | − | 0.941410i | \(-0.390498\pi\) | |||||||
\(998\) | −2948.00 | − | 5106.09i | −0.0935043 | − | 0.161954i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 882.4.g.r.667.1 | 2 | ||
3.2 | odd | 2 | 294.4.e.d.79.1 | 2 | |||
7.2 | even | 3 | 882.4.a.d.1.1 | 1 | |||
7.3 | odd | 6 | 882.4.g.s.361.1 | 2 | |||
7.4 | even | 3 | inner | 882.4.g.r.361.1 | 2 | ||
7.5 | odd | 6 | 126.4.a.c.1.1 | 1 | |||
7.6 | odd | 2 | 882.4.g.s.667.1 | 2 | |||
21.2 | odd | 6 | 294.4.a.h.1.1 | 1 | |||
21.5 | even | 6 | 42.4.a.b.1.1 | ✓ | 1 | ||
21.11 | odd | 6 | 294.4.e.d.67.1 | 2 | |||
21.17 | even | 6 | 294.4.e.a.67.1 | 2 | |||
21.20 | even | 2 | 294.4.e.a.79.1 | 2 | |||
28.19 | even | 6 | 1008.4.a.j.1.1 | 1 | |||
84.23 | even | 6 | 2352.4.a.ba.1.1 | 1 | |||
84.47 | odd | 6 | 336.4.a.d.1.1 | 1 | |||
105.47 | odd | 12 | 1050.4.g.n.799.2 | 2 | |||
105.68 | odd | 12 | 1050.4.g.n.799.1 | 2 | |||
105.89 | even | 6 | 1050.4.a.d.1.1 | 1 | |||
168.5 | even | 6 | 1344.4.a.f.1.1 | 1 | |||
168.131 | odd | 6 | 1344.4.a.t.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.a.b.1.1 | ✓ | 1 | 21.5 | even | 6 | ||
126.4.a.c.1.1 | 1 | 7.5 | odd | 6 | |||
294.4.a.h.1.1 | 1 | 21.2 | odd | 6 | |||
294.4.e.a.67.1 | 2 | 21.17 | even | 6 | |||
294.4.e.a.79.1 | 2 | 21.20 | even | 2 | |||
294.4.e.d.67.1 | 2 | 21.11 | odd | 6 | |||
294.4.e.d.79.1 | 2 | 3.2 | odd | 2 | |||
336.4.a.d.1.1 | 1 | 84.47 | odd | 6 | |||
882.4.a.d.1.1 | 1 | 7.2 | even | 3 | |||
882.4.g.r.361.1 | 2 | 7.4 | even | 3 | inner | ||
882.4.g.r.667.1 | 2 | 1.1 | even | 1 | trivial | ||
882.4.g.s.361.1 | 2 | 7.3 | odd | 6 | |||
882.4.g.s.667.1 | 2 | 7.6 | odd | 2 | |||
1008.4.a.j.1.1 | 1 | 28.19 | even | 6 | |||
1050.4.a.d.1.1 | 1 | 105.89 | even | 6 | |||
1050.4.g.n.799.1 | 2 | 105.68 | odd | 12 | |||
1050.4.g.n.799.2 | 2 | 105.47 | odd | 12 | |||
1344.4.a.f.1.1 | 1 | 168.5 | even | 6 | |||
1344.4.a.t.1.1 | 1 | 168.131 | odd | 6 | |||
2352.4.a.ba.1.1 | 1 | 84.23 | even | 6 |