Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2394,2,Mod(1063,2394)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2394, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2394.1063");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2394.e (of order \(2\), degree \(1\), 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: | \(19.1161862439\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + 2x^{10} + 54x^{8} - 114x^{7} + 120x^{6} + 46x^{5} + 9x^{4} - 4x^{3} + 8x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 798) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1063.2 | ||
Root | \(-0.301222 + 0.301222i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2394.1063 |
Dual form | 2394.2.e.b.1063.11 |
$q$-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 \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(1009\) | \(1711\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 0.602444i | − | 0.269421i | −0.990885 | − | 0.134711i | \(-0.956990\pi\) | ||
0.990885 | − | 0.134711i | \(-0.0430105\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.307956 | − | 2.62777i | −0.116396 | − | 0.993203i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.602444 | −0.190509 | ||||||||
\(11\) | −1.46816 | −0.442666 | −0.221333 | − | 0.975198i | \(-0.571041\pi\) | ||||
−0.221333 | + | 0.975198i | \(0.571041\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.60244 | 0.721788 | 0.360894 | − | 0.932607i | \(-0.382472\pi\) | ||||
0.360894 | + | 0.932607i | \(0.382472\pi\) | |||||||
\(14\) | −2.62777 | + | 0.307956i | −0.702300 | + | 0.0823047i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.08663i | 0.263547i | 0.991280 | + | 0.131774i | \(0.0420672\pi\) | ||||
−0.991280 | + | 0.131774i | \(0.957933\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00633 | − | 1.71737i | 0.919114 | − | 0.393991i | ||||
\(20\) | 0.602444i | 0.134711i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.46816i | 0.313012i | ||||||||
\(23\) | 2.83683 | 0.591520 | 0.295760 | − | 0.955262i | \(-0.404427\pi\) | ||||
0.295760 | + | 0.955262i | \(0.404427\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.63706 | 0.927412 | ||||||||
\(26\) | − | 2.60244i | − | 0.510381i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.307956 | + | 2.62777i | 0.0581982 | + | 0.496601i | ||||
\(29\) | − | 6.19185i | − | 1.14980i | −0.818224 | − | 0.574899i | \(-0.805041\pi\) | ||
0.818224 | − | 0.574899i | \(-0.194959\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.12381 | 1.27947 | 0.639737 | − | 0.768594i | \(-0.279043\pi\) | ||||
0.639737 | + | 0.768594i | \(0.279043\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.08663 | 0.186356 | ||||||||
\(35\) | −1.58308 | + | 0.185526i | −0.267590 | + | 0.0313597i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.73972i | − | 0.943605i | −0.881704 | − | 0.471802i | \(-0.843604\pi\) | ||
0.881704 | − | 0.471802i | \(-0.156396\pi\) | |||||||
\(38\) | −1.71737 | − | 4.00633i | −0.278594 | − | 0.649912i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.602444 | 0.0952547 | ||||||||
\(41\) | −9.86097 | −1.54003 | −0.770013 | − | 0.638029i | \(-0.779750\pi\) | ||||
−0.770013 | + | 0.638029i | \(0.779750\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.1295 | −1.84974 | −0.924869 | − | 0.380286i | \(-0.875826\pi\) | ||||
−0.924869 | + | 0.380286i | \(0.875826\pi\) | |||||||
\(44\) | 1.46816 | 0.221333 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 2.83683i | − | 0.418268i | ||||||
\(47\) | 0.752759i | 0.109801i | 0.998492 | + | 0.0549006i | \(0.0174842\pi\) | ||||
−0.998492 | + | 0.0549006i | \(0.982516\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.81033 | + | 1.61847i | −0.972904 | + | 0.231211i | ||||
\(50\) | − | 4.63706i | − | 0.655780i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.60244 | −0.360894 | ||||||||
\(53\) | − | 4.81882i | − | 0.661916i | −0.943645 | − | 0.330958i | \(-0.892628\pi\) | ||
0.943645 | − | 0.330958i | \(-0.107372\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.884483i | 0.119264i | ||||||||
\(56\) | 2.62777 | − | 0.307956i | 0.351150 | − | 0.0411524i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.19185 | −0.813030 | ||||||||
\(59\) | −0.799650 | −0.104106 | −0.0520528 | − | 0.998644i | \(-0.516576\pi\) | ||||
−0.0520528 | + | 0.998644i | \(0.516576\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.69481i | 1.11326i | 0.830762 | + | 0.556628i | \(0.187905\pi\) | ||||
−0.830762 | + | 0.556628i | \(0.812095\pi\) | |||||||
\(62\) | − | 7.12381i | − | 0.904725i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 1.56783i | − | 0.194465i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.90487i | − | 0.721395i | −0.932683 | − | 0.360697i | \(-0.882539\pi\) | ||
0.932683 | − | 0.360697i | \(-0.117461\pi\) | |||||||
\(68\) | − | 1.08663i | − | 0.131774i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.185526 | + | 1.58308i | 0.0221746 | + | 0.189215i | ||||
\(71\) | − | 4.75712i | − | 0.564566i | −0.959331 | − | 0.282283i | \(-0.908908\pi\) | ||
0.959331 | − | 0.282283i | \(-0.0910917\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.95747i | − | 0.931351i | −0.884956 | − | 0.465675i | \(-0.845811\pi\) | ||
0.884956 | − | 0.465675i | \(-0.154189\pi\) | |||||||
\(74\) | −5.73972 | −0.667229 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.00633 | + | 1.71737i | −0.459557 | + | 0.196996i | ||||
\(77\) | 0.452128 | + | 3.85798i | 0.0515248 | + | 0.439658i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.00299468i | 0.000336928i | 1.00000 | 0.000168464i | \(5.36238e-5\pi\) | |||||
−1.00000 | 0.000168464i | \(0.999946\pi\) | ||||||||
\(80\) | − | 0.602444i | − | 0.0673553i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.86097i | 1.08896i | ||||||||
\(83\) | 15.9162i | 1.74703i | 0.486801 | + | 0.873513i | \(0.338164\pi\) | ||||
−0.486801 | + | 0.873513i | \(0.661836\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.654635 | 0.0710051 | ||||||||
\(86\) | 12.1295i | 1.30796i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 1.46816i | − | 0.156506i | ||||||
\(89\) | 9.74408 | 1.03287 | 0.516435 | − | 0.856326i | \(-0.327259\pi\) | ||||
0.516435 | + | 0.856326i | \(0.327259\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.801438 | − | 6.83862i | −0.0840136 | − | 0.716882i | ||||
\(92\) | −2.83683 | −0.295760 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.752759 | 0.0776412 | ||||||||
\(95\) | −1.03462 | − | 2.41359i | −0.106150 | − | 0.247629i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.784815 | 0.0796859 | 0.0398430 | − | 0.999206i | \(-0.487314\pi\) | ||||
0.0398430 | + | 0.999206i | \(0.487314\pi\) | |||||||
\(98\) | 1.61847 | + | 6.81033i | 0.163491 | + | 0.687947i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.63706 | −0.463706 | ||||||||
\(101\) | − | 15.7813i | − | 1.57029i | −0.619309 | − | 0.785147i | \(-0.712587\pi\) | ||
0.619309 | − | 0.785147i | \(-0.287413\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.32160 | −0.918484 | −0.459242 | − | 0.888311i | \(-0.651879\pi\) | ||||
−0.459242 | + | 0.888311i | \(0.651879\pi\) | |||||||
\(104\) | 2.60244i | 0.255191i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.81882 | −0.468046 | ||||||||
\(107\) | − | 12.6843i | − | 1.22624i | −0.789989 | − | 0.613120i | \(-0.789914\pi\) | ||
0.789989 | − | 0.613120i | \(-0.210086\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 17.7254i | − | 1.69779i | −0.528562 | − | 0.848895i | \(-0.677269\pi\) | ||
0.528562 | − | 0.848895i | \(-0.322731\pi\) | |||||||
\(110\) | 0.884483 | 0.0843321 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.307956 | − | 2.62777i | −0.0290991 | − | 0.248301i | ||||
\(113\) | − | 9.68177i | − | 0.910785i | −0.890291 | − | 0.455392i | \(-0.849499\pi\) | ||
0.890291 | − | 0.455392i | \(-0.150501\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.70903i | − | 0.159368i | ||||||
\(116\) | 6.19185i | 0.574899i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.799650i | 0.0736138i | ||||||||
\(119\) | 2.85542 | − | 0.334635i | 0.261756 | − | 0.0306759i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.84451 | −0.804046 | ||||||||
\(122\) | 8.69481 | 0.787191 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.12381 | −0.639737 | ||||||||
\(125\) | − | 5.80579i | − | 0.519285i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.3606i | 1.71797i | 0.512000 | + | 0.858986i | \(0.328905\pi\) | ||||
−0.512000 | + | 0.858986i | \(0.671095\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.56783 | −0.137507 | ||||||||
\(131\) | 13.9458i | 1.21845i | 0.792997 | + | 0.609225i | \(0.208520\pi\) | ||||
−0.792997 | + | 0.609225i | \(0.791480\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.74662 | − | 9.99882i | −0.498295 | − | 0.867008i | ||||
\(134\) | −5.90487 | −0.510103 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.08663 | −0.0931780 | ||||||||
\(137\) | −16.2603 | −1.38921 | −0.694605 | − | 0.719392i | \(-0.744421\pi\) | ||||
−0.694605 | + | 0.719392i | \(0.744421\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 6.03418i | − | 0.511813i | −0.966702 | − | 0.255906i | \(-0.917626\pi\) | ||
0.966702 | − | 0.255906i | \(-0.0823739\pi\) | |||||||
\(140\) | 1.58308 | − | 0.185526i | 0.133795 | − | 0.0156798i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.75712 | −0.399208 | ||||||||
\(143\) | −3.82080 | −0.319511 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.73024 | −0.309780 | ||||||||
\(146\) | −7.95747 | −0.658565 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.73972i | 0.471802i | ||||||||
\(149\) | −0.944612 | −0.0773856 | −0.0386928 | − | 0.999251i | \(-0.512319\pi\) | ||||
−0.0386928 | + | 0.999251i | \(0.512319\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.62997i | 0.214024i | 0.994258 | + | 0.107012i | \(0.0341283\pi\) | ||||
−0.994258 | + | 0.107012i | \(0.965872\pi\) | |||||||
\(152\) | 1.71737 | + | 4.00633i | 0.139297 | + | 0.324956i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.85798 | − | 0.452128i | 0.310885 | − | 0.0364335i | ||||
\(155\) | − | 4.29170i | − | 0.344717i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 7.30560i | − | 0.583050i | −0.956563 | − | 0.291525i | \(-0.905837\pi\) | ||
0.956563 | − | 0.291525i | \(-0.0941627\pi\) | |||||||
\(158\) | 0.00299468 | 0.000238244 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.602444 | −0.0476274 | ||||||||
\(161\) | −0.873619 | − | 7.45453i | −0.0688508 | − | 0.587499i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.27456 | −0.491461 | −0.245731 | − | 0.969338i | \(-0.579028\pi\) | ||||
−0.245731 | + | 0.969338i | \(0.579028\pi\) | |||||||
\(164\) | 9.86097 | 0.770013 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.9162 | 1.23533 | ||||||||
\(167\) | 17.0317 | 1.31795 | 0.658975 | − | 0.752165i | \(-0.270990\pi\) | ||||
0.658975 | + | 0.752165i | \(0.270990\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.22729 | −0.479022 | ||||||||
\(170\) | − | 0.654635i | − | 0.0502082i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.1295 | 0.924869 | ||||||||
\(173\) | 12.6805 | 0.964082 | 0.482041 | − | 0.876149i | \(-0.339896\pi\) | ||||
0.482041 | + | 0.876149i | \(0.339896\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.42801 | − | 12.1851i | −0.107947 | − | 0.921109i | ||||
\(176\) | −1.46816 | −0.110667 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 9.74408i | − | 0.730350i | ||||||
\(179\) | 13.5603i | 1.01355i | 0.862079 | + | 0.506774i | \(0.169162\pi\) | ||||
−0.862079 | + | 0.506774i | \(0.830838\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.1772 | −1.05378 | −0.526891 | − | 0.849933i | \(-0.676643\pi\) | ||||
−0.526891 | + | 0.849933i | \(0.676643\pi\) | |||||||
\(182\) | −6.83862 | + | 0.801438i | −0.506912 | + | 0.0594066i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.83683i | 0.209134i | ||||||||
\(185\) | −3.45786 | −0.254227 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.59535i | − | 0.116663i | ||||||
\(188\) | − | 0.752759i | − | 0.0549006i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.41359 | + | 1.03462i | −0.175100 | + | 0.0750591i | ||||
\(191\) | −21.4891 | −1.55490 | −0.777449 | − | 0.628947i | \(-0.783486\pi\) | ||||
−0.777449 | + | 0.628947i | \(0.783486\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.87657i | 0.710931i | 0.934689 | + | 0.355466i | \(0.115678\pi\) | ||||
−0.934689 | + | 0.355466i | \(0.884322\pi\) | |||||||
\(194\) | − | 0.784815i | − | 0.0563464i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.81033 | − | 1.61847i | 0.486452 | − | 0.115605i | ||||
\(197\) | 18.6902 | 1.33162 | 0.665811 | − | 0.746120i | \(-0.268086\pi\) | ||||
0.665811 | + | 0.746120i | \(0.268086\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 14.0550i | − | 0.996329i | −0.867083 | − | 0.498165i | \(-0.834008\pi\) | ||
0.867083 | − | 0.498165i | \(-0.165992\pi\) | |||||||
\(200\) | 4.63706i | 0.327890i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.7813 | −1.11037 | ||||||||
\(203\) | −16.2707 | + | 1.90682i | −1.14198 | + | 0.133832i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.94068i | 0.414915i | ||||||||
\(206\) | 9.32160i | 0.649467i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.60244 | 0.180447 | ||||||||
\(209\) | −5.88192 | + | 2.52137i | −0.406861 | + | 0.174407i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 11.9385i | − | 0.821877i | −0.911663 | − | 0.410939i | \(-0.865201\pi\) | ||
0.911663 | − | 0.410939i | \(-0.134799\pi\) | |||||||
\(212\) | 4.81882i | 0.330958i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.6843 | −0.867083 | ||||||||
\(215\) | 7.30737i | 0.498358i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.19382 | − | 18.7197i | −0.148926 | − | 1.27078i | ||||
\(218\) | −17.7254 | −1.20052 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 0.884483i | − | 0.0596318i | ||||||
\(221\) | 2.82790i | 0.190225i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.8928 | 0.863364 | 0.431682 | − | 0.902026i | \(-0.357920\pi\) | ||||
0.431682 | + | 0.902026i | \(0.357920\pi\) | |||||||
\(224\) | −2.62777 | + | 0.307956i | −0.175575 | + | 0.0205762i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.68177 | −0.644022 | ||||||||
\(227\) | 2.30063 | 0.152698 | 0.0763491 | − | 0.997081i | \(-0.475674\pi\) | ||||
0.0763491 | + | 0.997081i | \(0.475674\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.77358i | 0.315447i | 0.987483 | + | 0.157724i | \(0.0504155\pi\) | ||||
−0.987483 | + | 0.157724i | \(0.949585\pi\) | |||||||
\(230\) | −1.70903 | −0.112690 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.19185 | 0.406515 | ||||||||
\(233\) | 24.6124 | 1.61241 | 0.806205 | − | 0.591636i | \(-0.201518\pi\) | ||||
0.806205 | + | 0.591636i | \(0.201518\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.453495 | 0.0295828 | ||||||||
\(236\) | 0.799650 | 0.0520528 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.334635 | − | 2.85542i | −0.0216912 | − | 0.185089i | ||||
\(239\) | 14.1110 | 0.912762 | 0.456381 | − | 0.889785i | \(-0.349145\pi\) | ||||
0.456381 | + | 0.889785i | \(0.349145\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.19261 | 0.141239 | 0.0706193 | − | 0.997503i | \(-0.477502\pi\) | ||||
0.0706193 | + | 0.997503i | \(0.477502\pi\) | |||||||
\(242\) | 8.84451i | 0.568547i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 8.69481i | − | 0.556628i | ||||||
\(245\) | 0.975040 | + | 4.10284i | 0.0622930 | + | 0.262121i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.4262 | − | 4.46935i | 0.663406 | − | 0.284378i | ||||
\(248\) | 7.12381i | 0.452363i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.80579 | −0.367190 | ||||||||
\(251\) | − | 15.5451i | − | 0.981198i | −0.871385 | − | 0.490599i | \(-0.836778\pi\) | ||
0.871385 | − | 0.490599i | \(-0.163222\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.16492 | −0.261846 | ||||||||
\(254\) | 19.3606 | 1.21479 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.27531 | 0.329065 | 0.164532 | − | 0.986372i | \(-0.447389\pi\) | ||||
0.164532 | + | 0.986372i | \(0.447389\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.0827 | + | 1.76758i | −0.937191 | + | 0.109832i | ||||
\(260\) | 1.56783i | 0.0972325i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.9458 | 0.861575 | ||||||||
\(263\) | −26.3265 | −1.62336 | −0.811681 | − | 0.584101i | \(-0.801447\pi\) | ||||
−0.811681 | + | 0.584101i | \(0.801447\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.90307 | −0.178334 | ||||||||
\(266\) | −9.99882 | + | 5.74662i | −0.613067 | + | 0.352348i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.90487i | 0.360697i | ||||||||
\(269\) | 11.7926 | 0.719004 | 0.359502 | − | 0.933144i | \(-0.382946\pi\) | ||||
0.359502 | + | 0.933144i | \(0.382946\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.03439i | 0.427309i | 0.976909 | + | 0.213654i | \(0.0685366\pi\) | ||||
−0.976909 | + | 0.213654i | \(0.931463\pi\) | |||||||
\(272\) | 1.08663i | 0.0658868i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.2603i | 0.982319i | ||||||||
\(275\) | −6.80794 | −0.410534 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.79468 | −0.107832 | −0.0539158 | − | 0.998545i | \(-0.517170\pi\) | ||||
−0.0539158 | + | 0.998545i | \(0.517170\pi\) | |||||||
\(278\) | −6.03418 | −0.361906 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.185526 | − | 1.58308i | −0.0110873 | − | 0.0946073i | ||||
\(281\) | − | 11.6228i | − | 0.693357i | −0.937984 | − | 0.346678i | \(-0.887310\pi\) | ||
0.937984 | − | 0.346678i | \(-0.112690\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 3.48005i | − | 0.206867i | −0.994636 | − | 0.103434i | \(-0.967017\pi\) | ||
0.994636 | − | 0.103434i | \(-0.0329830\pi\) | |||||||
\(284\) | 4.75712i | 0.282283i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.82080i | 0.225929i | ||||||||
\(287\) | 3.03675 | + | 25.9123i | 0.179253 | + | 1.52956i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.8192 | 0.930543 | ||||||||
\(290\) | 3.73024i | 0.219047i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.95747i | 0.465675i | ||||||||
\(293\) | 7.09787 | 0.414662 | 0.207331 | − | 0.978271i | \(-0.433522\pi\) | ||||
0.207331 | + | 0.978271i | \(0.433522\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.481744i | 0.0280482i | ||||||||
\(296\) | 5.73972 | 0.333615 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.944612i | 0.0547199i | ||||||||
\(299\) | 7.38269 | 0.426952 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.73537 | + | 31.8736i | 0.215303 | + | 1.83717i | ||||
\(302\) | 2.62997 | 0.151338 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.00633 | − | 1.71737i | 0.229779 | − | 0.0984978i | ||||
\(305\) | 5.23813 | 0.299935 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.10840 | −0.177405 | −0.0887027 | − | 0.996058i | \(-0.528272\pi\) | ||||
−0.0887027 | + | 0.996058i | \(0.528272\pi\) | |||||||
\(308\) | −0.452128 | − | 3.85798i | −0.0257624 | − | 0.219829i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.29170 | −0.243752 | ||||||||
\(311\) | − | 1.56565i | − | 0.0887797i | −0.999014 | − | 0.0443899i | \(-0.985866\pi\) | ||
0.999014 | − | 0.0443899i | \(-0.0141344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.4848i | 0.875253i | 0.899157 | + | 0.437626i | \(0.144181\pi\) | ||||
−0.899157 | + | 0.437626i | \(0.855819\pi\) | |||||||
\(314\) | −7.30560 | −0.412279 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 0.00299468i | − | 0.000168464i | ||||||
\(317\) | − | 23.4743i | − | 1.31845i | −0.751946 | − | 0.659225i | \(-0.770885\pi\) | ||
0.751946 | − | 0.659225i | \(-0.229115\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.09062i | 0.508977i | ||||||||
\(320\) | 0.602444i | 0.0336776i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.45453 | + | 0.873619i | −0.415425 | + | 0.0486849i | ||||
\(323\) | 1.86615 | + | 4.35340i | 0.103835 | + | 0.242230i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.0677 | 0.669395 | ||||||||
\(326\) | 6.27456i | 0.347516i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 9.86097i | − | 0.544481i | ||||||
\(329\) | 1.97808 | − | 0.231817i | 0.109055 | − | 0.0127805i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.3550i | 1.17378i | 0.809668 | + | 0.586888i | \(0.199647\pi\) | ||||
−0.809668 | + | 0.586888i | \(0.800353\pi\) | |||||||
\(332\) | − | 15.9162i | − | 0.873513i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 17.0317i | − | 0.931932i | ||||||
\(335\) | −3.55735 | −0.194359 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.1349i | 0.878924i | 0.898261 | + | 0.439462i | \(0.144831\pi\) | ||||
−0.898261 | + | 0.439462i | \(0.855169\pi\) | |||||||
\(338\) | 6.22729i | 0.338720i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.654635 | −0.0355026 | ||||||||
\(341\) | −10.4589 | −0.566380 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.35025 | + | 17.3975i | 0.342882 | + | 0.939379i | ||||
\(344\) | − | 12.1295i | − | 0.653981i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 12.6805i | − | 0.681709i | ||||||
\(347\) | 18.8578 | 1.01234 | 0.506169 | − | 0.862434i | \(-0.331061\pi\) | ||||
0.506169 | + | 0.862434i | \(0.331061\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.0310i | 0.858120i | 0.903276 | + | 0.429060i | \(0.141155\pi\) | ||||
−0.903276 | + | 0.429060i | \(0.858845\pi\) | |||||||
\(350\) | −12.1851 | + | 1.42801i | −0.651322 | + | 0.0763304i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.46816i | 0.0782531i | ||||||||
\(353\) | − | 11.0403i | − | 0.587615i | −0.955865 | − | 0.293808i | \(-0.905078\pi\) | ||
0.955865 | − | 0.293808i | \(-0.0949225\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.86590 | −0.152106 | ||||||||
\(356\) | −9.74408 | −0.516435 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.5603 | 0.716686 | ||||||||
\(359\) | 7.24265 | 0.382253 | 0.191126 | − | 0.981565i | \(-0.438786\pi\) | ||||
0.191126 | + | 0.981565i | \(0.438786\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.1013 | − | 13.7607i | 0.689542 | − | 0.724246i | ||||
\(362\) | 14.1772i | 0.745137i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.801438 | + | 6.83862i | 0.0420068 | + | 0.358441i | ||||
\(365\) | −4.79393 | −0.250926 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4.37658i | − | 0.228456i | −0.993455 | − | 0.114228i | \(-0.963561\pi\) | ||
0.993455 | − | 0.114228i | \(-0.0364394\pi\) | |||||||
\(368\) | 2.83683 | 0.147880 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.45786i | 0.179766i | ||||||||
\(371\) | −12.6627 | + | 1.48399i | −0.657417 | + | 0.0770447i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.14709i | 0.214728i | 0.994220 | + | 0.107364i | \(0.0342410\pi\) | ||||
−0.994220 | + | 0.107364i | \(0.965759\pi\) | |||||||
\(374\) | −1.59535 | −0.0824935 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.752759 | −0.0388206 | ||||||||
\(377\) | − | 16.1139i | − | 0.829911i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 23.2482i | − | 1.19418i | −0.802174 | − | 0.597091i | \(-0.796323\pi\) | ||
0.802174 | − | 0.597091i | \(-0.203677\pi\) | |||||||
\(380\) | 1.03462 | + | 2.41359i | 0.0530748 | + | 0.123814i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.4891i | 1.09948i | ||||||||
\(383\) | −17.7789 | −0.908457 | −0.454228 | − | 0.890885i | \(-0.650085\pi\) | ||||
−0.454228 | + | 0.890885i | \(0.650085\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.32422 | − | 0.272382i | 0.118453 | − | 0.0138819i | ||||
\(386\) | 9.87657 | 0.502704 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.784815 | −0.0398430 | ||||||||
\(389\) | 4.77920 | 0.242315 | 0.121157 | − | 0.992633i | \(-0.461339\pi\) | ||||
0.121157 | + | 0.992633i | \(0.461339\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.08259i | 0.155893i | ||||||||
\(392\) | −1.61847 | − | 6.81033i | −0.0817453 | − | 0.343973i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 18.6902i | − | 0.941600i | ||||||
\(395\) | 0.00180413 | 9.07755e−5 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.0306i | 1.65776i | 0.559427 | + | 0.828880i | \(0.311021\pi\) | ||||
−0.559427 | + | 0.828880i | \(0.688979\pi\) | |||||||
\(398\) | −14.0550 | −0.704511 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.63706 | 0.231853 | ||||||||
\(401\) | 6.66991i | 0.333080i | 0.986035 | + | 0.166540i | \(0.0532594\pi\) | ||||
−0.986035 | + | 0.166540i | \(0.946741\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.5393 | 0.923509 | ||||||||
\(404\) | 15.7813i | 0.785147i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.90682 | + | 16.2707i | 0.0946338 | + | 0.807504i | ||||
\(407\) | 8.42682i | 0.417702i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.36786 | −0.265423 | −0.132712 | − | 0.991155i | \(-0.542368\pi\) | ||||
−0.132712 | + | 0.991155i | \(0.542368\pi\) | |||||||
\(410\) | 5.94068 | 0.293389 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.32160 | 0.459242 | ||||||||
\(413\) | 0.246257 | + | 2.10130i | 0.0121175 | + | 0.103398i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.58859 | 0.470685 | ||||||||
\(416\) | − | 2.60244i | − | 0.127595i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.52137 | + | 5.88192i | 0.123324 | + | 0.287694i | ||||
\(419\) | − | 18.5084i | − | 0.904193i | −0.891969 | − | 0.452096i | \(-0.850676\pi\) | ||
0.891969 | − | 0.452096i | \(-0.149324\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.7310i | 1.49774i | 0.662719 | + | 0.748868i | \(0.269403\pi\) | ||||
−0.662719 | + | 0.748868i | \(0.730597\pi\) | |||||||
\(422\) | −11.9385 | −0.581155 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.81882 | 0.234023 | ||||||||
\(425\) | 5.03878i | 0.244417i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.8479 | − | 2.67762i | 1.10569 | − | 0.129579i | ||||
\(428\) | 12.6843i | 0.613120i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.30737 | 0.352393 | ||||||||
\(431\) | 3.63136i | 0.174917i | 0.996168 | + | 0.0874583i | \(0.0278744\pi\) | ||||
−0.996168 | + | 0.0874583i | \(0.972126\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.3433 | 0.737352 | 0.368676 | − | 0.929558i | \(-0.379811\pi\) | ||||
0.368676 | + | 0.929558i | \(0.379811\pi\) | |||||||
\(434\) | −18.7197 | + | 2.19382i | −0.898575 | + | 0.105307i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.7254i | 0.848895i | ||||||||
\(437\) | 11.3653 | − | 4.87188i | 0.543674 | − | 0.233054i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.5479 | 1.83979 | 0.919895 | − | 0.392164i | \(-0.128273\pi\) | ||||
0.919895 | + | 0.392164i | \(0.128273\pi\) | |||||||
\(440\) | −0.884483 | −0.0421661 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.82790 | 0.134509 | ||||||||
\(443\) | −19.0232 | −0.903817 | −0.451909 | − | 0.892064i | \(-0.649257\pi\) | ||||
−0.451909 | + | 0.892064i | \(0.649257\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 5.87026i | − | 0.278277i | ||||||
\(446\) | − | 12.8928i | − | 0.610491i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.307956 | + | 2.62777i | 0.0145496 | + | 0.124150i | ||||
\(449\) | − | 27.5946i | − | 1.30227i | −0.758962 | − | 0.651134i | \(-0.774293\pi\) | ||
0.758962 | − | 0.651134i | \(-0.225707\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.4775 | 0.681718 | ||||||||
\(452\) | 9.68177i | 0.455392i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 2.30063i | − | 0.107974i | ||||||
\(455\) | −4.11988 | + | 0.482822i | −0.193143 | + | 0.0226350i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.7393 | 1.43792 | 0.718962 | − | 0.695050i | \(-0.244618\pi\) | ||||
0.718962 | + | 0.695050i | \(0.244618\pi\) | |||||||
\(458\) | 4.77358 | 0.223055 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.70903i | 0.0796840i | ||||||||
\(461\) | − | 20.6499i | − | 0.961760i | −0.876786 | − | 0.480880i | \(-0.840317\pi\) | ||
0.876786 | − | 0.480880i | \(-0.159683\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.0039 | −1.76619 | −0.883095 | − | 0.469193i | \(-0.844545\pi\) | ||||
−0.883095 | + | 0.469193i | \(0.844545\pi\) | |||||||
\(464\) | − | 6.19185i | − | 0.287450i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 24.6124i | − | 1.14015i | ||||||
\(467\) | 16.0408i | 0.742279i | 0.928577 | + | 0.371139i | \(0.121033\pi\) | ||||
−0.928577 | + | 0.371139i | \(0.878967\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.5166 | + | 1.81844i | −0.716491 | + | 0.0839678i | ||||
\(470\) | − | 0.453495i | − | 0.0209182i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 0.799650i | − | 0.0368069i | ||||||
\(473\) | 17.8081 | 0.818817 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.5776 | − | 7.96354i | 0.852398 | − | 0.365392i | ||||
\(476\) | −2.85542 | + | 0.334635i | −0.130878 | + | 0.0153380i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 14.1110i | − | 0.645420i | ||||||
\(479\) | − | 19.4280i | − | 0.887690i | −0.896104 | − | 0.443845i | \(-0.853614\pi\) | ||
0.896104 | − | 0.443845i | \(-0.146386\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 14.9373i | − | 0.681083i | ||||||
\(482\) | − | 2.19261i | − | 0.0998708i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.84451 | 0.402023 | ||||||||
\(485\) | − | 0.472807i | − | 0.0214691i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.60382i | 0.0726760i | 0.999340 | + | 0.0363380i | \(0.0115693\pi\) | ||||
−0.999340 | + | 0.0363380i | \(0.988431\pi\) | |||||||
\(488\) | −8.69481 | −0.393596 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.10284 | − | 0.975040i | 0.185347 | − | 0.0440478i | ||||
\(491\) | 35.6125 | 1.60717 | 0.803586 | − | 0.595189i | \(-0.202923\pi\) | ||||
0.803586 | + | 0.595189i | \(0.202923\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.72827 | 0.303026 | ||||||||
\(494\) | −4.46935 | − | 10.4262i | −0.201086 | − | 0.469099i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.12381 | 0.319869 | ||||||||
\(497\) | −12.5006 | + | 1.46498i | −0.560728 | + | 0.0657135i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.89620 | 0.129652 | 0.0648258 | − | 0.997897i | \(-0.479351\pi\) | ||||
0.0648258 | + | 0.997897i | \(0.479351\pi\) | |||||||
\(500\) | 5.80579i | 0.259643i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.5451 | −0.693812 | ||||||||
\(503\) | 34.7741i | 1.55050i | 0.631654 | + | 0.775250i | \(0.282376\pi\) | ||||
−0.631654 | + | 0.775250i | \(0.717624\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.50732 | −0.423070 | ||||||||
\(506\) | 4.16492i | 0.185153i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 19.3606i | − | 0.858986i | ||||||
\(509\) | 37.1924 | 1.64852 | 0.824262 | − | 0.566208i | \(-0.191590\pi\) | ||||
0.824262 | + | 0.566208i | \(0.191590\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.9104 | + | 2.45055i | −0.925020 | + | 0.108406i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 5.27531i | − | 0.232684i | ||||||
\(515\) | 5.61574i | 0.247459i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.10517i | − | 0.0486053i | ||||||
\(518\) | 1.76758 | + | 15.0827i | 0.0776631 | + | 0.662694i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.56783 | 0.0687537 | ||||||||
\(521\) | −16.9681 | −0.743384 | −0.371692 | − | 0.928356i | \(-0.621222\pi\) | ||||
−0.371692 | + | 0.928356i | \(0.621222\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.64279 | 0.0718340 | 0.0359170 | − | 0.999355i | \(-0.488565\pi\) | ||||
0.0359170 | + | 0.999355i | \(0.488565\pi\) | |||||||
\(524\) | − | 13.9458i | − | 0.609225i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.3265i | 1.14789i | ||||||||
\(527\) | 7.74096i | 0.337202i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.9524 | −0.650104 | ||||||||
\(530\) | 2.90307i | 0.126101i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.74662 | + | 9.99882i | 0.249147 | + | 0.433504i | ||||
\(533\) | −25.6626 | −1.11157 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.64160 | −0.330375 | ||||||||
\(536\) | 5.90487 | 0.255052 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 11.7926i | − | 0.508413i | ||||||
\(539\) | 9.99864 | − | 2.37618i | 0.430672 | − | 0.102349i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.5601 | 0.883947 | 0.441974 | − | 0.897028i | \(-0.354278\pi\) | ||||
0.441974 | + | 0.897028i | \(0.354278\pi\) | |||||||
\(542\) | 7.03439 | 0.302153 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.08663 | 0.0465890 | ||||||||
\(545\) | −10.6786 | −0.457420 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.9504i | 0.981287i | 0.871360 | + | 0.490644i | \(0.163238\pi\) | ||||
−0.871360 | + | 0.490644i | \(0.836762\pi\) | |||||||
\(548\) | 16.2603 | 0.694605 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.80794i | 0.290292i | ||||||||
\(551\) | −10.6337 | − | 24.8066i | −0.453010 | − | 1.05680i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.00786933 | 0.000922231i | 0.000334638 | 3.92172e-5i | ||||||
\(554\) | 1.79468i | 0.0762484i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.03418i | 0.255906i | ||||||||
\(557\) | 9.90274 | 0.419593 | 0.209796 | − | 0.977745i | \(-0.432720\pi\) | ||||
0.209796 | + | 0.977745i | \(0.432720\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.5665 | −1.33512 | ||||||||
\(560\) | −1.58308 | + | 0.185526i | −0.0668974 | + | 0.00783991i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.6228 | −0.490277 | ||||||||
\(563\) | −11.3791 | −0.479571 | −0.239786 | − | 0.970826i | \(-0.577077\pi\) | ||||
−0.239786 | + | 0.970826i | \(0.577077\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.83272 | −0.245385 | ||||||||
\(566\) | −3.48005 | −0.146277 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.75712 | 0.199604 | ||||||||
\(569\) | − | 34.7575i | − | 1.45711i | −0.684987 | − | 0.728555i | \(-0.740192\pi\) | ||
0.684987 | − | 0.728555i | \(-0.259808\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.9139 | 1.29371 | 0.646854 | − | 0.762614i | \(-0.276084\pi\) | ||||
0.646854 | + | 0.762614i | \(0.276084\pi\) | |||||||
\(572\) | 3.82080 | 0.159756 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 25.9123 | − | 3.03675i | 1.08156 | − | 0.126751i | ||||
\(575\) | 13.1546 | 0.548583 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 39.8992i | − | 1.66102i | −0.557001 | − | 0.830512i | \(-0.688048\pi\) | ||
0.557001 | − | 0.830512i | \(-0.311952\pi\) | |||||||
\(578\) | − | 15.8192i | − | 0.657993i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.73024 | 0.154890 | ||||||||
\(581\) | 41.8240 | − | 4.90148i | 1.73515 | − | 0.203348i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.07480i | 0.293008i | ||||||||
\(584\) | 7.95747 | 0.329282 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 7.09787i | − | 0.293210i | ||||||
\(587\) | 28.8180i | 1.18945i | 0.803930 | + | 0.594724i | \(0.202739\pi\) | ||||
−0.803930 | + | 0.594724i | \(0.797261\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.5403 | − | 12.2342i | 1.17598 | − | 0.504102i | ||||
\(590\) | 0.481744 | 0.0198331 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 5.73972i | − | 0.235901i | ||||||
\(593\) | 41.1324i | 1.68911i | 0.535472 | + | 0.844553i | \(0.320134\pi\) | ||||
−0.535472 | + | 0.844553i | \(0.679866\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.201599 | − | 1.72023i | −0.00826474 | − | 0.0705225i | ||||
\(596\) | 0.944612 | 0.0386928 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 7.38269i | − | 0.301901i | ||||||
\(599\) | 2.29940i | 0.0939511i | 0.998896 | + | 0.0469755i | \(0.0149583\pi\) | ||||
−0.998896 | + | 0.0469755i | \(0.985042\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.48455 | −0.182928 | −0.0914642 | − | 0.995808i | \(-0.529155\pi\) | ||||
−0.0914642 | + | 0.995808i | \(0.529155\pi\) | |||||||
\(602\) | 31.8736 | − | 3.73537i | 1.29907 | − | 0.152242i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 2.62997i | − | 0.107012i | ||||||
\(605\) | 5.32832i | 0.216627i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.0487 | −0.935517 | −0.467758 | − | 0.883856i | \(-0.654938\pi\) | ||||
−0.467758 | + | 0.883856i | \(0.654938\pi\) | |||||||
\(608\) | −1.71737 | − | 4.00633i | −0.0696485 | − | 0.162478i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 5.23813i | − | 0.212086i | ||||||
\(611\) | 1.95901i | 0.0792532i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.5731 | −1.19445 | −0.597224 | − | 0.802075i | \(-0.703729\pi\) | ||||
−0.597224 | + | 0.802075i | \(0.703729\pi\) | |||||||
\(614\) | 3.10840i | 0.125445i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.85798 | + | 0.452128i | −0.155442 | + | 0.0182168i | ||||
\(617\) | −11.9663 | −0.481745 | −0.240873 | − | 0.970557i | \(-0.577434\pi\) | ||||
−0.240873 | + | 0.970557i | \(0.577434\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 38.3335i | − | 1.54075i | −0.637590 | − | 0.770376i | \(-0.720069\pi\) | ||
0.637590 | − | 0.770376i | \(-0.279931\pi\) | |||||||
\(620\) | 4.29170i | 0.172359i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.56565 | −0.0627767 | ||||||||
\(623\) | −3.00075 | − | 25.6052i | −0.120222 | − | 1.02585i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.6876 | 0.787506 | ||||||||
\(626\) | 15.4848 | 0.618897 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.30560i | 0.291525i | ||||||||
\(629\) | 6.23697 | 0.248684 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.5444 | 0.698431 | 0.349215 | − | 0.937042i | \(-0.386448\pi\) | ||||
0.349215 | + | 0.937042i | \(0.386448\pi\) | |||||||
\(632\) | −0.00299468 | −0.000119122 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −23.4743 | −0.932285 | ||||||||
\(635\) | 11.6636 | 0.462858 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.7235 | + | 4.21199i | −0.702230 | + | 0.166885i | ||||
\(638\) | 9.09062 | 0.359901 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.602444 | 0.0238137 | ||||||||
\(641\) | − | 14.9850i | − | 0.591871i | −0.955208 | − | 0.295935i | \(-0.904369\pi\) | ||
0.955208 | − | 0.295935i | \(-0.0956313\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.1996i | 0.481105i | 0.970636 | + | 0.240553i | \(0.0773287\pi\) | ||||
−0.970636 | + | 0.240553i | \(0.922671\pi\) | |||||||
\(644\) | 0.873619 | + | 7.45453i | 0.0344254 | + | 0.293750i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.35340 | − | 1.86615i | 0.171282 | − | 0.0734226i | ||||
\(647\) | 18.9604i | 0.745412i | 0.927950 | + | 0.372706i | \(0.121570\pi\) | ||||
−0.927950 | + | 0.372706i | \(0.878430\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.17401 | 0.0460841 | ||||||||
\(650\) | − | 12.0677i | − | 0.473334i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.27456 | 0.245731 | ||||||||
\(653\) | −11.9475 | −0.467540 | −0.233770 | − | 0.972292i | \(-0.575106\pi\) | ||||
−0.233770 | + | 0.972292i | \(0.575106\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.40156 | 0.328276 | ||||||||
\(656\) | −9.86097 | −0.385006 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.231817 | − | 1.97808i | −0.00903716 | − | 0.0771135i | ||||
\(659\) | 14.6240i | 0.569671i | 0.958576 | + | 0.284836i | \(0.0919390\pi\) | ||||
−0.958576 | + | 0.284836i | \(0.908061\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.4941 | 1.49725 | 0.748623 | − | 0.662996i | \(-0.230716\pi\) | ||||
0.748623 | + | 0.662996i | \(0.230716\pi\) | |||||||
\(662\) | 21.3550 | 0.829984 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.9162 | −0.617667 | ||||||||
\(665\) | −6.02373 | + | 3.46201i | −0.233590 | + | 0.134251i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 17.5652i | − | 0.680128i | ||||||
\(668\) | −17.0317 | −0.658975 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.55735i | 0.137433i | ||||||||
\(671\) | − | 12.7654i | − | 0.492801i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 39.1709i | − | 1.50993i | −0.655767 | − | 0.754963i | \(-0.727655\pi\) | ||
0.655767 | − | 0.754963i | \(-0.272345\pi\) | |||||||
\(674\) | 16.1349 | 0.621493 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.22729 | 0.239511 | ||||||||
\(677\) | 13.6204 | 0.523476 | 0.261738 | − | 0.965139i | \(-0.415704\pi\) | ||||
0.261738 | + | 0.965139i | \(0.415704\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.241689 | − | 2.06231i | −0.00927516 | − | 0.0791443i | ||||
\(680\) | 0.654635i | 0.0251041i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.4589i | 0.400491i | ||||||||
\(683\) | 44.7869i | 1.71372i | 0.515545 | + | 0.856862i | \(0.327589\pi\) | ||||
−0.515545 | + | 0.856862i | \(0.672411\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.79590i | 0.374282i | ||||||||
\(686\) | 17.3975 | − | 6.35025i | 0.664241 | − | 0.242454i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −12.1295 | −0.462435 | ||||||||
\(689\) | − | 12.5407i | − | 0.477763i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.8900i | 1.32728i | 0.748053 | + | 0.663639i | \(0.230989\pi\) | ||||
−0.748053 | + | 0.663639i | \(0.769011\pi\) | |||||||
\(692\) | −12.6805 | −0.482041 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 18.8578i | − | 0.715831i | ||||||
\(695\) | −3.63526 | −0.137893 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 10.7153i | − | 0.405869i | ||||||
\(698\) | 16.0310 | 0.606783 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.42801 | + | 12.1851i | 0.0539737 | + | 0.460554i | ||||
\(701\) | 27.2769 | 1.03024 | 0.515118 | − | 0.857119i | \(-0.327748\pi\) | ||||
0.515118 | + | 0.857119i | \(0.327748\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.85722 | − | 22.9952i | −0.371772 | − | 0.867281i | ||||
\(704\) | 1.46816 | 0.0553333 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.0403 | −0.415507 | ||||||||
\(707\) | −41.4695 | + | 4.85993i | −1.55962 | + | 0.182777i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.36116 | −0.238899 | −0.119449 | − | 0.992840i | \(-0.538113\pi\) | ||||
−0.119449 | + | 0.992840i | \(0.538113\pi\) | |||||||
\(710\) | 2.86590i | 0.107555i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.74408i | 0.365175i | ||||||||
\(713\) | 20.2090 | 0.756835 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.30182i | 0.0860831i | ||||||||
\(716\) | − | 13.5603i | − | 0.506774i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 7.24265i | − | 0.270293i | ||||||
\(719\) | 5.38127i | 0.200687i | 0.994953 | + | 0.100344i | \(0.0319943\pi\) | ||||
−0.994953 | + | 0.100344i | \(0.968006\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.87064 | + | 24.4950i | 0.106908 | + | 0.912241i | ||||
\(722\) | −13.7607 | − | 13.1013i | −0.512119 | − | 0.487580i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.1772 | 0.526891 | ||||||||
\(725\) | − | 28.7120i | − | 1.06634i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 27.6598i | − | 1.02584i | −0.858435 | − | 0.512922i | \(-0.828563\pi\) | ||
0.858435 | − | 0.512922i | \(-0.171437\pi\) | |||||||
\(728\) | 6.83862 | − | 0.801438i | 0.253456 | − | 0.0297033i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.79393i | 0.177431i | ||||||||
\(731\) | − | 13.1804i | − | 0.487493i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.25771i | 0.120326i | 0.998189 | + | 0.0601632i | \(0.0191621\pi\) | ||||
−0.998189 | + | 0.0601632i | \(0.980838\pi\) | |||||||
\(734\) | −4.37658 | −0.161543 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 2.83683i | − | 0.104567i | ||||||
\(737\) | 8.66928i | 0.319337i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.12780 | 0.188629 | 0.0943147 | − | 0.995542i | \(-0.469934\pi\) | ||||
0.0943147 | + | 0.995542i | \(0.469934\pi\) | |||||||
\(740\) | 3.45786 | 0.127114 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.48399 | + | 12.6627i | 0.0544788 | + | 0.464864i | ||||
\(743\) | 28.9581i | 1.06237i | 0.847256 | + | 0.531184i | \(0.178253\pi\) | ||||
−0.847256 | + | 0.531184i | \(0.821747\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.569075i | 0.0208493i | ||||||||
\(746\) | 4.14709 | 0.151836 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.59535i | 0.0583317i | ||||||||
\(749\) | −33.3315 | + | 3.90622i | −1.21791 | + | 0.142730i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.2740i | 1.46962i | 0.678274 | + | 0.734809i | \(0.262728\pi\) | ||||
−0.678274 | + | 0.734809i | \(0.737272\pi\) | |||||||
\(752\) | 0.752759i | 0.0274503i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16.1139 | −0.586835 | ||||||||
\(755\) | 1.58441 | 0.0576625 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.0198 | 0.909358 | 0.454679 | − | 0.890655i | \(-0.349754\pi\) | ||||
0.454679 | + | 0.890655i | \(0.349754\pi\) | |||||||
\(758\) | −23.2482 | −0.844414 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.41359 | − | 1.03462i | 0.0875500 | − | 0.0375295i | ||||
\(761\) | 24.3619i | 0.883119i | 0.897232 | + | 0.441560i | \(0.145575\pi\) | ||||
−0.897232 | + | 0.441560i | \(0.854425\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −46.5783 | + | 5.45866i | −1.68625 | + | 0.197617i | ||||
\(764\) | 21.4891 | 0.777449 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.7789i | 0.642376i | ||||||||
\(767\) | −2.08105 | −0.0751422 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 9.31118i | − | 0.335770i | −0.985807 | − | 0.167885i | \(-0.946306\pi\) | ||
0.985807 | − | 0.167885i | \(-0.0536937\pi\) | |||||||
\(770\) | −0.272382 | − | 2.32422i | −0.00981596 | − | 0.0837589i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 9.87657i | − | 0.355466i | ||||||
\(773\) | 44.0350 | 1.58383 | 0.791914 | − | 0.610633i | \(-0.209085\pi\) | ||||
0.791914 | + | 0.610633i | \(0.209085\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33.0336 | 1.18660 | ||||||||
\(776\) | 0.784815i | 0.0281732i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 4.77920i | − | 0.171342i | ||||||
\(779\) | −39.5063 | + | 16.9349i | −1.41546 | + | 0.606756i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.98420i | 0.249914i | ||||||||
\(782\) | 3.08259 | 0.110233 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.81033 | + | 1.61847i | −0.243226 | + | 0.0578026i | ||||
\(785\) | −4.40121 | −0.157086 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.21088 | −0.0431631 | −0.0215816 | − | 0.999767i | \(-0.506870\pi\) | ||||
−0.0215816 | + | 0.999767i | \(0.506870\pi\) | |||||||
\(788\) | −18.6902 | −0.665811 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 0.00180413i | − | 6.41880e-5i | ||||||
\(791\) | −25.4415 | + | 2.98156i | −0.904594 | + | 0.106012i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.6278i | 0.803535i | ||||||||
\(794\) | 33.0306 | 1.17221 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.0550i | 0.498165i | ||||||||
\(797\) | 19.0026 | 0.673107 | 0.336554 | − | 0.941664i | \(-0.390739\pi\) | ||||
0.336554 | + | 0.941664i | \(0.390739\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.817973 | −0.0289378 | ||||||||
\(800\) | − | 4.63706i | − | 0.163945i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.66991 | 0.235523 | ||||||||
\(803\) | 11.6828i | 0.412278i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.49094 | + | 0.526306i | −0.158285 | + | 0.0185499i | ||||
\(806\) | − | 18.5393i | − | 0.653020i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15.7813 | 0.555183 | ||||||||
\(809\) | 28.0122 | 0.984858 | 0.492429 | − | 0.870353i | \(-0.336109\pi\) | ||||
0.492429 | + | 0.870353i | \(0.336109\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.6270 | 0.654081 | 0.327041 | − | 0.945010i | \(-0.393949\pi\) | ||||
0.327041 | + | 0.945010i | \(0.393949\pi\) | |||||||
\(812\) | 16.2707 | − | 1.90682i | 0.570991 | − | 0.0669162i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.42682 | 0.295360 | ||||||||
\(815\) | 3.78007i | 0.132410i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −48.5949 | + | 20.8309i | −1.70012 | + | 0.728781i | ||||
\(818\) | 5.36786i | 0.187683i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 5.94068i | − | 0.207458i | ||||||
\(821\) | −29.2267 | −1.02002 | −0.510009 | − | 0.860169i | \(-0.670358\pi\) | ||||
−0.510009 | + | 0.860169i | \(0.670358\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.0198 | −0.662989 | −0.331495 | − | 0.943457i | \(-0.607553\pi\) | ||||
−0.331495 | + | 0.943457i | \(0.607553\pi\) | |||||||
\(824\) | − | 9.32160i | − | 0.324733i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.10130 | − | 0.246257i | 0.0731134 | − | 0.00856838i | ||||
\(827\) | − | 10.8091i | − | 0.375870i | −0.982181 | − | 0.187935i | \(-0.939821\pi\) | ||
0.982181 | − | 0.187935i | \(-0.0601794\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.7073 | −1.58748 | −0.793739 | − | 0.608258i | \(-0.791869\pi\) | ||||
−0.793739 | + | 0.608258i | \(0.791869\pi\) | |||||||
\(830\) | − | 9.58859i | − | 0.332825i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.60244 | −0.0902235 | ||||||||
\(833\) | −1.75869 | − | 7.40032i | −0.0609349 | − | 0.256406i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 10.2606i | − | 0.355084i | ||||||
\(836\) | 5.88192 | − | 2.52137i | 0.203430 | − | 0.0872033i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −18.5084 | −0.639361 | ||||||||
\(839\) | 31.5684 | 1.08986 | 0.544931 | − | 0.838481i | \(-0.316556\pi\) | ||||
0.544931 | + | 0.838481i | \(0.316556\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.33903 | −0.322036 | ||||||||
\(842\) | 30.7310 | 1.05906 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.9385i | 0.410939i | ||||||||
\(845\) | 3.75159i | 0.129059i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.72372 | + | 23.2413i | 0.0935882 | + | 0.798581i | ||||
\(848\) | − | 4.81882i | − | 0.165479i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.03878 | 0.172829 | ||||||||
\(851\) | − | 16.2826i | − | 0.558161i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 28.1651i | − | 0.964355i | −0.876074 | − | 0.482178i | \(-0.839846\pi\) | ||
0.876074 | − | 0.482178i | \(-0.160154\pi\) | |||||||
\(854\) | −2.67762 | − | 22.8479i | −0.0916262 | − | 0.781840i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.6843 | 0.433542 | ||||||||
\(857\) | −0.355917 | −0.0121579 | −0.00607895 | − | 0.999982i | \(-0.501935\pi\) | ||||
−0.00607895 | + | 0.999982i | \(0.501935\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.3548i | 0.967454i | 0.875219 | + | 0.483727i | \(0.160717\pi\) | ||||
−0.875219 | + | 0.483727i | \(0.839283\pi\) | |||||||
\(860\) | − | 7.30737i | − | 0.249179i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.63136 | 0.123685 | ||||||||
\(863\) | 26.9169i | 0.916264i | 0.888884 | + | 0.458132i | \(0.151481\pi\) | ||||
−0.888884 | + | 0.458132i | \(0.848519\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 7.63930i | − | 0.259744i | ||||||
\(866\) | − | 15.3433i | − | 0.521387i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.19382 | + | 18.7197i | 0.0744631 | + | 0.635389i | ||||
\(869\) | − | 0.00439667i | − | 0.000149147i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 15.3671i | − | 0.520694i | ||||||
\(872\) | 17.7254 | 0.600259 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.87188 | − | 11.3653i | −0.164794 | − | 0.384436i | ||||
\(875\) | −15.2563 | + | 1.78793i | −0.515756 | + | 0.0604430i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 27.5902i | − | 0.931656i | −0.884875 | − | 0.465828i | \(-0.845757\pi\) | ||
0.884875 | − | 0.465828i | \(-0.154243\pi\) | |||||||
\(878\) | − | 38.5479i | − | 1.30093i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.884483i | 0.0298159i | ||||||||
\(881\) | 50.3489i | 1.69630i | 0.529759 | + | 0.848148i | \(0.322282\pi\) | ||||
−0.529759 | + | 0.848148i | \(0.677718\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.3680 | 0.517175 | 0.258587 | − | 0.965988i | \(-0.416743\pi\) | ||||
0.258587 | + | 0.965988i | \(0.416743\pi\) | |||||||
\(884\) | − | 2.82790i | − | 0.0951126i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19.0232i | 0.639095i | ||||||||
\(887\) | −17.5241 | −0.588402 | −0.294201 | − | 0.955744i | \(-0.595054\pi\) | ||||
−0.294201 | + | 0.955744i | \(0.595054\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 50.8750 | − | 5.96220i | 1.70629 | − | 0.199966i | ||||
\(890\) | −5.87026 | −0.196772 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.8928 | −0.431682 | ||||||||
\(893\) | 1.29276 | + | 3.01580i | 0.0432607 | + | 0.100920i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.16934 | 0.273071 | ||||||||
\(896\) | 2.62777 | − | 0.307956i | 0.0877876 | − | 0.0102881i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −27.5946 | −0.920843 | ||||||||
\(899\) | − | 44.1096i | − | 1.47114i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.23629 | 0.174446 | ||||||||
\(902\) | − | 14.4775i | − | 0.482047i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.68177 | 0.322011 | ||||||||
\(905\) | 8.54097i | 0.283911i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.6312i | 1.51516i | 0.652743 | + | 0.757579i | \(0.273618\pi\) | ||||
−0.652743 | + | 0.757579i | \(0.726382\pi\) | |||||||
\(908\) | −2.30063 | −0.0763491 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.482822 | + | 4.11988i | 0.0160054 | + | 0.136573i | ||||
\(911\) | 36.4617i | 1.20803i | 0.796973 | + | 0.604015i | \(0.206433\pi\) | ||||
−0.796973 | + | 0.604015i | \(0.793567\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 23.3674i | − | 0.773350i | ||||||
\(914\) | − | 30.7393i | − | 1.01677i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 4.77358i | − | 0.157724i | ||||||
\(917\) | 36.6463 | − | 4.29470i | 1.21017 | − | 0.141823i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.9016 | −1.11831 | −0.559155 | − | 0.829063i | \(-0.688874\pi\) | ||||
−0.559155 | + | 0.829063i | \(0.688874\pi\) | |||||||
\(920\) | 1.70903 | 0.0563451 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20.6499 | −0.680067 | ||||||||
\(923\) | − | 12.3801i | − | 0.407497i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 26.6155i | − | 0.875111i | ||||||
\(926\) | 38.0039i | 1.24889i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.19185 | −0.203258 | ||||||||
\(929\) | 25.2468i | 0.828322i | 0.910204 | + | 0.414161i | \(0.135925\pi\) | ||||
−0.910204 | + | 0.414161i | \(0.864075\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.5049 | + | 18.1800i | −0.803115 | + | 0.595824i | ||||
\(932\) | −24.6124 | −0.806205 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16.0408 | 0.524870 | ||||||||
\(935\) | −0.961108 | −0.0314316 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 60.7106i | − | 1.98333i | −0.128843 | − | 0.991665i | \(-0.541126\pi\) | ||
0.128843 | − | 0.991665i | \(-0.458874\pi\) | |||||||
\(938\) | 1.81844 | + | 15.5166i | 0.0593742 | + | 0.506636i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.453495 | −0.0147914 | ||||||||
\(941\) | −33.8435 | −1.10327 | −0.551633 | − | 0.834087i | \(-0.685995\pi\) | ||||
−0.551633 | + | 0.834087i | \(0.685995\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.9739 | −0.910956 | ||||||||
\(944\) | −0.799650 | −0.0260264 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 17.8081i | − | 0.578991i | ||||||
\(947\) | 1.14059 | 0.0370642 | 0.0185321 | − | 0.999828i | \(-0.494101\pi\) | ||||
0.0185321 | + | 0.999828i | \(0.494101\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 20.7089i | − | 0.672238i | ||||||
\(950\) | −7.96354 | − | 18.5776i | −0.258371 | − | 0.602736i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.334635 | + | 2.85542i | 0.0108456 | + | 0.0925446i | ||||
\(953\) | 37.0477i | 1.20009i | 0.799965 | + | 0.600046i | \(0.204851\pi\) | ||||
−0.799965 | + | 0.600046i | \(0.795149\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.9460i | 0.418922i | ||||||||
\(956\) | −14.1110 | −0.456381 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −19.4280 | −0.627691 | ||||||||
\(959\) | 5.00745 | + | 42.7282i | 0.161699 | + | 1.37977i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.7487 | 0.637055 | ||||||||
\(962\) | −14.9373 | −0.481598 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.19261 | −0.0706193 | ||||||||
\(965\) | 5.95008 | 0.191540 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.4696 | −0.593944 | −0.296972 | − | 0.954886i | \(-0.595977\pi\) | ||||
−0.296972 | + | 0.954886i | \(0.595977\pi\) | |||||||
\(968\) | − | 8.84451i | − | 0.284273i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.472807 | −0.0151809 | ||||||||
\(971\) | −13.1599 | −0.422320 | −0.211160 | − | 0.977452i | \(-0.567724\pi\) | ||||
−0.211160 | + | 0.977452i | \(0.567724\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.8564 | + | 1.85826i | −0.508334 | + | 0.0595732i | ||||
\(974\) | 1.60382 | 0.0513897 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.69481i | 0.278314i | ||||||||
\(977\) | 15.4551i | 0.494452i | 0.968958 | + | 0.247226i | \(0.0795190\pi\) | ||||
−0.968958 | + | 0.247226i | \(0.920481\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.3059 | −0.457217 | ||||||||
\(980\) | −0.975040 | − | 4.10284i | −0.0311465 | − | 0.131060i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 35.6125i | − | 1.13644i | ||||||
\(983\) | 49.5309 | 1.57979 | 0.789895 | − | 0.613242i | \(-0.210135\pi\) | ||||
0.789895 | + | 0.613242i | \(0.210135\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 11.2598i | − | 0.358767i | ||||||
\(986\) | − | 6.72827i | − | 0.214272i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.4262 | + | 4.46935i | −0.331703 | + | 0.142189i | ||||
\(989\) | −34.4095 | −1.09416 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.3846i | 0.520474i | 0.965545 | + | 0.260237i | \(0.0838007\pi\) | ||||
−0.965545 | + | 0.260237i | \(0.916199\pi\) | |||||||
\(992\) | − | 7.12381i | − | 0.226181i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.46498 | + | 12.5006i | 0.0464664 | + | 0.396495i | ||||
\(995\) | −8.46732 | −0.268432 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.77042i | 0.182751i | 0.995817 | + | 0.0913755i | \(0.0291263\pi\) | ||||
−0.995817 | + | 0.0913755i | \(0.970874\pi\) | |||||||
\(998\) | − | 2.89620i | − | 0.0916775i | ||||||
\(999\) | 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 | 2394.2.e.b.1063.2 | 12 | ||
3.2 | odd | 2 | 798.2.e.b.265.11 | yes | 12 | ||
7.6 | odd | 2 | 2394.2.e.a.1063.5 | 12 | |||
19.18 | odd | 2 | 2394.2.e.a.1063.8 | 12 | |||
21.20 | even | 2 | 798.2.e.a.265.8 | yes | 12 | ||
57.56 | even | 2 | 798.2.e.a.265.5 | ✓ | 12 | ||
133.132 | even | 2 | inner | 2394.2.e.b.1063.11 | 12 | ||
399.398 | odd | 2 | 798.2.e.b.265.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
798.2.e.a.265.5 | ✓ | 12 | 57.56 | even | 2 | ||
798.2.e.a.265.8 | yes | 12 | 21.20 | even | 2 | ||
798.2.e.b.265.2 | yes | 12 | 399.398 | odd | 2 | ||
798.2.e.b.265.11 | yes | 12 | 3.2 | odd | 2 | ||
2394.2.e.a.1063.5 | 12 | 7.6 | odd | 2 | |||
2394.2.e.a.1063.8 | 12 | 19.18 | odd | 2 | |||
2394.2.e.b.1063.2 | 12 | 1.1 | even | 1 | trivial | ||
2394.2.e.b.1063.11 | 12 | 133.132 | even | 2 | inner |