Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,2,Mod(199,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.j (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.7798042729\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 450) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.4 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.199 |
Dual form | 1350.2.j.g.1099.4 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.85337 | − | 2.22474i | 1.45644 | − | 0.840875i | 0.457604 | − | 0.889156i | \(-0.348708\pi\) |
0.998834 | + | 0.0482818i | \(0.0153745\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.44949 | + | 4.24264i | 0.738549 | + | 1.27920i | 0.953149 | + | 0.302502i | \(0.0978220\pi\) |
−0.214600 | + | 0.976702i | \(0.568845\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.85337 | + | 2.22474i | 1.06873 | + | 0.617033i | 0.927835 | − | 0.372991i | \(-0.121668\pi\) |
0.140898 | + | 0.990024i | \(0.455001\pi\) | |||||||
\(14\) | 2.22474 | − | 3.85337i | 0.594588 | − | 1.02986i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 4.89898i | 1.18818i | 0.804400 | + | 0.594089i | \(0.202487\pi\) | ||||
−0.804400 | + | 0.594089i | \(0.797513\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.55051 | −0.585127 | −0.292564 | − | 0.956246i | \(-0.594508\pi\) | ||||
−0.292564 | + | 0.956246i | \(0.594508\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.24264 | + | 2.44949i | 0.904534 | + | 0.522233i | ||||
\(23\) | −2.12132 | − | 1.22474i | −0.442326 | − | 0.255377i | 0.262258 | − | 0.964998i | \(-0.415533\pi\) |
−0.704584 | + | 0.709621i | \(0.748866\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.44949 | 0.872617 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 4.44949i | − | 0.840875i | ||||||
\(29\) | −1.22474 | − | 2.12132i | −0.227429 | − | 0.393919i | 0.729616 | − | 0.683857i | \(-0.239699\pi\) |
−0.957046 | + | 0.289938i | \(0.906365\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.224745 | − | 0.389270i | 0.0403654 | − | 0.0699149i | −0.845137 | − | 0.534550i | \(-0.820481\pi\) |
0.885502 | + | 0.464635i | \(0.153814\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.44949 | + | 4.24264i | 0.420084 | + | 0.727607i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.34847i | 0.550485i | 0.961375 | + | 0.275242i | \(0.0887581\pi\) | ||||
−0.961375 | + | 0.275242i | \(0.911242\pi\) | |||||||
\(38\) | −2.20881 | + | 1.27526i | −0.358316 | + | 0.206874i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.50000 | − | 7.79423i | 0.702782 | − | 1.21725i | −0.264704 | − | 0.964330i | \(-0.585274\pi\) |
0.967486 | − | 0.252924i | \(-0.0813924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.45145 | + | 3.72474i | −0.983836 | + | 0.568018i | −0.903426 | − | 0.428744i | \(-0.858956\pi\) |
−0.0804103 | + | 0.996762i | \(0.525623\pi\) | |||||||
\(44\) | 4.89898 | 0.738549 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.44949 | −0.361158 | ||||||||
\(47\) | 0.953512 | − | 0.550510i | 0.139084 | − | 0.0803002i | −0.428843 | − | 0.903379i | \(-0.641079\pi\) |
0.567927 | + | 0.823079i | \(0.307745\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.39898 | − | 11.0834i | 0.914140 | − | 1.58334i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.85337 | − | 2.22474i | 0.534366 | − | 0.308517i | ||||
\(53\) | − | 8.44949i | − | 1.16063i | −0.814393 | − | 0.580313i | \(-0.802930\pi\) | ||
0.814393 | − | 0.580313i | \(-0.197070\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.22474 | − | 3.85337i | −0.297294 | − | 0.514928i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.12132 | − | 1.22474i | −0.278543 | − | 0.160817i | ||||
\(59\) | 0.275255 | − | 0.476756i | 0.0358352 | − | 0.0620683i | −0.847552 | − | 0.530713i | \(-0.821924\pi\) |
0.883387 | + | 0.468645i | \(0.155258\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | − | 6.92820i | −0.512148 | − | 0.887066i | −0.999901 | − | 0.0140840i | \(-0.995517\pi\) |
0.487753 | − | 0.872982i | \(-0.337817\pi\) | |||||||
\(62\) | − | 0.449490i | − | 0.0570853i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4261 | + | 7.17423i | 1.51809 | + | 0.876472i | 0.999773 | + | 0.0212861i | \(0.00677610\pi\) |
0.518321 | + | 0.855186i | \(0.326557\pi\) | |||||||
\(68\) | 4.24264 | + | 2.44949i | 0.514496 | + | 0.297044i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.34847 | 0.160034 | 0.0800169 | − | 0.996794i | \(-0.474503\pi\) | ||||
0.0800169 | + | 0.996794i | \(0.474503\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.00000i | 0.117041i | 0.998286 | + | 0.0585206i | \(0.0186383\pi\) | ||||
−0.998286 | + | 0.0585206i | \(0.981362\pi\) | |||||||
\(74\) | 1.67423 | + | 2.89986i | 0.194626 | + | 0.337102i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.27526 | + | 2.20881i | −0.146282 | + | 0.253368i | ||||
\(77\) | 18.8776 | + | 10.8990i | 2.15130 | + | 1.24205i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.34847 | − | 10.9959i | −0.714259 | − | 1.23713i | −0.963245 | − | 0.268625i | \(-0.913431\pi\) |
0.248986 | − | 0.968507i | \(-0.419903\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 9.00000i | − | 0.993884i | ||||||
\(83\) | −0.476756 | + | 0.275255i | −0.0523308 | + | 0.0302132i | −0.525937 | − | 0.850523i | \(-0.676285\pi\) |
0.473606 | + | 0.880737i | \(0.342952\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.72474 | + | 6.45145i | −0.401650 | + | 0.695677i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.24264 | − | 2.44949i | 0.452267 | − | 0.261116i | ||||
\(89\) | −9.00000 | −0.953998 | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.7980 | 2.07539 | ||||||||
\(92\) | −2.12132 | + | 1.22474i | −0.221163 | + | 0.127688i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.550510 | − | 0.953512i | 0.0567808 | − | 0.0983472i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.35131 | + | 5.39898i | −0.949481 | + | 0.548183i | −0.892920 | − | 0.450216i | \(-0.851347\pi\) |
−0.0565616 | + | 0.998399i | \(0.518014\pi\) | |||||||
\(98\) | − | 12.7980i | − | 1.29279i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.77526 | + | 3.07483i | 0.176644 | + | 0.305957i | 0.940729 | − | 0.339159i | \(-0.110142\pi\) |
−0.764085 | + | 0.645116i | \(0.776809\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.9959 | − | 6.34847i | −1.08346 | − | 0.625533i | −0.151629 | − | 0.988437i | \(-0.548452\pi\) |
−0.931826 | + | 0.362904i | \(0.881785\pi\) | |||||||
\(104\) | 2.22474 | − | 3.85337i | 0.218154 | − | 0.377854i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.22474 | − | 7.31747i | −0.410343 | − | 0.710736i | ||||
\(107\) | 15.2474i | 1.47403i | 0.675878 | + | 0.737013i | \(0.263764\pi\) | ||||
−0.675878 | + | 0.737013i | \(0.736236\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.4495 | −1.00088 | −0.500440 | − | 0.865771i | \(-0.666828\pi\) | ||||
−0.500440 | + | 0.865771i | \(0.666828\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.85337 | − | 2.22474i | −0.364109 | − | 0.210219i | ||||
\(113\) | 12.0369 | + | 6.94949i | 1.13233 | + | 0.653753i | 0.944521 | − | 0.328452i | \(-0.106527\pi\) |
0.187813 | + | 0.982205i | \(0.439860\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.44949 | −0.227429 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 0.550510i | − | 0.0506786i | ||||||
\(119\) | 10.8990 | + | 18.8776i | 0.999108 | + | 1.73051i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.50000 | + | 11.2583i | −0.590909 | + | 1.02348i | ||||
\(122\) | −6.92820 | − | 4.00000i | −0.627250 | − | 0.362143i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.224745 | − | 0.389270i | −0.0201827 | − | 0.0349574i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.3485i | − | 1.00701i | −0.863991 | − | 0.503507i | \(-0.832043\pi\) | ||
0.863991 | − | 0.503507i | \(-0.167957\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.89898 | − | 13.6814i | 0.690137 | − | 1.19535i | −0.281656 | − | 0.959516i | \(-0.590884\pi\) |
0.971793 | − | 0.235837i | \(-0.0757831\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.82806 | + | 5.67423i | −0.852201 | + | 0.492019i | ||||
\(134\) | 14.3485 | 1.23952 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.89898 | 0.420084 | ||||||||
\(137\) | −2.59808 | + | 1.50000i | −0.221969 | + | 0.128154i | −0.606861 | − | 0.794808i | \(-0.707572\pi\) |
0.384893 | + | 0.922961i | \(0.374238\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.00000 | + | 3.46410i | −0.169638 | + | 0.293821i | −0.938293 | − | 0.345843i | \(-0.887593\pi\) |
0.768655 | + | 0.639664i | \(0.220926\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.16781 | − | 0.674235i | 0.0980003 | − | 0.0565805i | ||||
\(143\) | 21.7980i | 1.82284i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.500000 | + | 0.866025i | 0.0413803 | + | 0.0716728i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.89986 | + | 1.67423i | 0.238367 | + | 0.137621i | ||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.0000 | − | 17.3205i | −0.813788 | − | 1.40952i | −0.910195 | − | 0.414181i | \(-0.864068\pi\) |
0.0964061 | − | 0.995342i | \(-0.469265\pi\) | |||||||
\(152\) | 2.55051i | 0.206874i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 21.7980 | 1.75653 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.174973 | + | 0.101021i | 0.0139643 | + | 0.00806231i | 0.506966 | − | 0.861966i | \(-0.330767\pi\) |
−0.493002 | + | 0.870028i | \(0.664100\pi\) | |||||||
\(158\) | −10.9959 | − | 6.34847i | −0.874785 | − | 0.505057i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.8990 | −0.858960 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.55051i | − | 0.199771i | −0.994999 | − | 0.0998857i | \(-0.968152\pi\) | ||
0.994999 | − | 0.0998857i | \(-0.0318477\pi\) | |||||||
\(164\) | −4.50000 | − | 7.79423i | −0.351391 | − | 0.608627i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.275255 | + | 0.476756i | −0.0213639 | + | 0.0370034i | ||||
\(167\) | −16.9706 | − | 9.79796i | −1.31322 | − | 0.758189i | −0.330593 | − | 0.943773i | \(-0.607249\pi\) |
−0.982628 | + | 0.185584i | \(0.940582\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.39898 | + | 5.88721i | 0.261460 | + | 0.452862i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.44949i | 0.568018i | ||||||||
\(173\) | −8.48528 | + | 4.89898i | −0.645124 | + | 0.372463i | −0.786586 | − | 0.617481i | \(-0.788153\pi\) |
0.141462 | + | 0.989944i | \(0.454820\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.44949 | − | 4.24264i | 0.184637 | − | 0.319801i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.79423 | + | 4.50000i | −0.584202 | + | 0.337289i | ||||
\(179\) | −15.2474 | −1.13965 | −0.569824 | − | 0.821767i | \(-0.692989\pi\) | ||||
−0.569824 | + | 0.821767i | \(0.692989\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.79796 | −0.133641 | −0.0668206 | − | 0.997765i | \(-0.521286\pi\) | ||||
−0.0668206 | + | 0.997765i | \(0.521286\pi\) | |||||||
\(182\) | 17.1455 | − | 9.89898i | 1.27091 | − | 0.733761i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.22474 | + | 2.12132i | −0.0902894 | + | 0.156386i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.7846 | + | 12.0000i | −1.51992 | + | 0.877527i | ||||
\(188\) | − | 1.10102i | − | 0.0803002i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.44949 | − | 9.43879i | −0.394311 | − | 0.682967i | 0.598702 | − | 0.800972i | \(-0.295683\pi\) |
−0.993013 | + | 0.118005i | \(0.962350\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.3205 | + | 10.0000i | 1.24676 | + | 0.719816i | 0.970461 | − | 0.241257i | \(-0.0775596\pi\) |
0.276296 | + | 0.961073i | \(0.410893\pi\) | |||||||
\(194\) | −5.39898 | + | 9.35131i | −0.387624 | + | 0.671385i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.39898 | − | 11.0834i | −0.457070 | − | 0.791668i | ||||
\(197\) | − | 24.2474i | − | 1.72756i | −0.503870 | − | 0.863780i | \(-0.668091\pi\) | ||
0.503870 | − | 0.863780i | \(-0.331909\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.79796 | −0.411006 | −0.205503 | − | 0.978656i | \(-0.565883\pi\) | ||||
−0.205503 | + | 0.978656i | \(0.565883\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.07483 | + | 1.77526i | 0.216344 | + | 0.124907i | ||||
\(203\) | −9.43879 | − | 5.44949i | −0.662473 | − | 0.382479i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.6969 | −0.884638 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 4.44949i | − | 0.308517i | ||||||
\(209\) | −6.24745 | − | 10.8209i | −0.432145 | − | 0.748497i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.724745 | + | 1.25529i | −0.0498935 | + | 0.0864181i | −0.889894 | − | 0.456168i | \(-0.849222\pi\) |
0.840000 | + | 0.542586i | \(0.182555\pi\) | |||||||
\(212\) | −7.31747 | − | 4.22474i | −0.502566 | − | 0.290157i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.62372 | + | 13.2047i | 0.521147 | + | 0.902653i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.00000i | − | 0.135769i | ||||||
\(218\) | −9.04952 | + | 5.22474i | −0.612911 | + | 0.353864i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.8990 | + | 18.8776i | −0.733145 | + | 1.26984i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.55708 | − | 0.898979i | 0.104270 | − | 0.0602001i | −0.446958 | − | 0.894555i | \(-0.647493\pi\) |
0.551228 | + | 0.834355i | \(0.314159\pi\) | |||||||
\(224\) | −4.44949 | −0.297294 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.8990 | 0.924546 | ||||||||
\(227\) | −24.5505 | + | 14.1742i | −1.62947 | + | 0.940777i | −0.645224 | + | 0.763994i | \(0.723236\pi\) |
−0.984250 | + | 0.176783i | \(0.943431\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.5732 | + | 18.3133i | −0.698698 | + | 1.21018i | 0.270221 | + | 0.962798i | \(0.412903\pi\) |
−0.968918 | + | 0.247381i | \(0.920430\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.12132 | + | 1.22474i | −0.139272 | + | 0.0804084i | ||||
\(233\) | 5.69694i | 0.373219i | 0.982434 | + | 0.186609i | \(0.0597499\pi\) | ||||
−0.982434 | + | 0.186609i | \(0.940250\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.275255 | − | 0.476756i | −0.0179176 | − | 0.0310342i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 18.8776 | + | 10.8990i | 1.22365 | + | 0.706476i | ||||
\(239\) | −4.77526 | + | 8.27098i | −0.308886 | + | 0.535006i | −0.978119 | − | 0.208047i | \(-0.933289\pi\) |
0.669233 | + | 0.743052i | \(0.266623\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.3990 | + | 19.7436i | 0.734273 | + | 1.27180i | 0.955042 | + | 0.296472i | \(0.0958100\pi\) |
−0.220769 | + | 0.975326i | \(0.570857\pi\) | |||||||
\(242\) | 13.0000i | 0.835672i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.00000 | −0.512148 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.82806 | − | 5.67423i | −0.625345 | − | 0.361043i | ||||
\(248\) | −0.389270 | − | 0.224745i | −0.0247186 | − | 0.0142713i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.44949 | 0.343969 | 0.171984 | − | 0.985100i | \(-0.444982\pi\) | ||||
0.171984 | + | 0.985100i | \(0.444982\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 12.0000i | − | 0.754434i | ||||||
\(254\) | −5.67423 | − | 9.82806i | −0.356033 | − | 0.616667i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 5.88721 | + | 3.39898i | 0.367234 | + | 0.212023i | 0.672249 | − | 0.740325i | \(-0.265328\pi\) |
−0.305016 | + | 0.952347i | \(0.598662\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.44949 | + | 12.9029i | 0.462889 | + | 0.801747i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 15.7980i | − | 0.976001i | ||||||
\(263\) | 13.4671 | − | 7.77526i | 0.830419 | − | 0.479443i | −0.0235770 | − | 0.999722i | \(-0.507505\pi\) |
0.853996 | + | 0.520279i | \(0.174172\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.67423 | + | 9.82806i | −0.347910 | + | 0.602597i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.4261 | − | 7.17423i | 0.759047 | − | 0.438236i | ||||
\(269\) | 9.55051 | 0.582305 | 0.291152 | − | 0.956677i | \(-0.405961\pi\) | ||||
0.291152 | + | 0.956677i | \(0.405961\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.651531 | 0.0395777 | 0.0197888 | − | 0.999804i | \(-0.493701\pi\) | ||||
0.0197888 | + | 0.999804i | \(0.493701\pi\) | |||||||
\(272\) | 4.24264 | − | 2.44949i | 0.257248 | − | 0.148522i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.50000 | + | 2.59808i | −0.0906183 | + | 0.156956i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.58542 | + | 3.22474i | −0.335595 | + | 0.193756i | −0.658323 | − | 0.752736i | \(-0.728734\pi\) |
0.322727 | + | 0.946492i | \(0.395400\pi\) | |||||||
\(278\) | 4.00000i | 0.239904i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.4495 | + | 25.0273i | 0.861984 | + | 1.49300i | 0.870011 | + | 0.493033i | \(0.164112\pi\) |
−0.00802643 | + | 0.999968i | \(0.502555\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.74058 | + | 5.62372i | 0.579017 | + | 0.334296i | 0.760743 | − | 0.649054i | \(-0.224835\pi\) |
−0.181726 | + | 0.983349i | \(0.558168\pi\) | |||||||
\(284\) | 0.674235 | − | 1.16781i | 0.0400085 | − | 0.0692967i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.8990 | + | 18.8776i | 0.644470 | + | 1.11626i | ||||
\(287\) | − | 40.0454i | − | 2.36381i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.866025 | + | 0.500000i | 0.0506803 | + | 0.0292603i | ||||
\(293\) | 24.2880 | + | 14.0227i | 1.41892 | + | 0.819215i | 0.996204 | − | 0.0870462i | \(-0.0277428\pi\) |
0.422718 | + | 0.906261i | \(0.361076\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.34847 | 0.194626 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 6.00000i | − | 0.347571i | ||||||
\(299\) | −5.44949 | − | 9.43879i | −0.315152 | − | 0.545859i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.5732 | + | 28.7056i | −0.955264 | + | 1.65457i | ||||
\(302\) | −17.3205 | − | 10.0000i | −0.996683 | − | 0.575435i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.27526 | + | 2.20881i | 0.0731409 | + | 0.126684i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6.69694i | − | 0.382214i | −0.981569 | − | 0.191107i | \(-0.938792\pi\) | ||
0.981569 | − | 0.191107i | \(-0.0612078\pi\) | |||||||
\(308\) | 18.8776 | − | 10.8990i | 1.07565 | − | 0.621027i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.44949 | + | 9.43879i | −0.309012 | + | 0.535225i | −0.978147 | − | 0.207917i | \(-0.933332\pi\) |
0.669134 | + | 0.743141i | \(0.266665\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.37662 | + | 1.94949i | −0.190858 | + | 0.110192i | −0.592384 | − | 0.805656i | \(-0.701813\pi\) |
0.401526 | + | 0.915847i | \(0.368480\pi\) | |||||||
\(314\) | 0.202041 | 0.0114018 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.6969 | −0.714259 | ||||||||
\(317\) | 14.8492 | − | 8.57321i | 0.834017 | − | 0.481520i | −0.0212094 | − | 0.999775i | \(-0.506752\pi\) |
0.855226 | + | 0.518255i | \(0.173418\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.00000 | − | 10.3923i | 0.335936 | − | 0.581857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.43879 | + | 5.44949i | −0.526003 | + | 0.303688i | ||||
\(323\) | − | 12.4949i | − | 0.695235i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.27526 | − | 2.20881i | −0.0706298 | − | 0.122334i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.79423 | − | 4.50000i | −0.430364 | − | 0.248471i | ||||
\(329\) | 2.44949 | − | 4.24264i | 0.135045 | − | 0.233904i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.17423 | + | 7.22999i | 0.229437 | + | 0.397396i | 0.957641 | − | 0.287964i | \(-0.0929783\pi\) |
−0.728205 | + | 0.685360i | \(0.759645\pi\) | |||||||
\(332\) | 0.550510i | 0.0302132i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.5959 | −1.07224 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.61377 | + | 5.55051i | 0.523695 | + | 0.302356i | 0.738445 | − | 0.674313i | \(-0.235560\pi\) |
−0.214750 | + | 0.976669i | \(0.568894\pi\) | |||||||
\(338\) | 5.88721 | + | 3.39898i | 0.320222 | + | 0.184880i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.20204 | 0.119247 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 25.7980i | − | 1.39296i | ||||||
\(344\) | 3.72474 | + | 6.45145i | 0.200825 | + | 0.347839i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.89898 | + | 8.48528i | −0.263371 | + | 0.456172i | ||||
\(347\) | 10.3923 | + | 6.00000i | 0.557888 | + | 0.322097i | 0.752297 | − | 0.658824i | \(-0.228946\pi\) |
−0.194409 | + | 0.980921i | \(0.562279\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.00000 | + | 12.1244i | 0.374701 | + | 0.649002i | 0.990282 | − | 0.139072i | \(-0.0444119\pi\) |
−0.615581 | + | 0.788074i | \(0.711079\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 4.89898i | − | 0.261116i | ||||||
\(353\) | −7.79423 | + | 4.50000i | −0.414845 | + | 0.239511i | −0.692869 | − | 0.721063i | \(-0.743654\pi\) |
0.278024 | + | 0.960574i | \(0.410320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.50000 | + | 7.79423i | −0.238500 | + | 0.413093i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.2047 | + | 7.62372i | −0.697889 | + | 0.402926i | ||||
\(359\) | −33.7980 | −1.78379 | −0.891894 | − | 0.452244i | \(-0.850623\pi\) | ||||
−0.891894 | + | 0.452244i | \(0.850623\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.4949 | −0.657626 | ||||||||
\(362\) | −1.55708 | + | 0.898979i | −0.0818382 | + | 0.0472493i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.89898 | − | 17.1455i | 0.518848 | − | 0.898670i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.4600 | − | 8.34847i | 0.754804 | − | 0.435787i | −0.0726228 | − | 0.997359i | \(-0.523137\pi\) |
0.827427 | + | 0.561573i | \(0.189804\pi\) | |||||||
\(368\) | 2.44949i | 0.127688i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.7980 | − | 32.5590i | −0.975941 | − | 1.69038i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.5065 | + | 7.79796i | 0.699338 | + | 0.403763i | 0.807101 | − | 0.590414i | \(-0.201035\pi\) |
−0.107763 | + | 0.994177i | \(0.534369\pi\) | |||||||
\(374\) | −12.0000 | + | 20.7846i | −0.620505 | + | 1.07475i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.550510 | − | 0.953512i | −0.0283904 | − | 0.0491736i | ||||
\(377\) | − | 10.8990i | − | 0.561326i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.898979 | −0.0461775 | −0.0230887 | − | 0.999733i | \(-0.507350\pi\) | ||||
−0.0230887 | + | 0.999733i | \(0.507350\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.43879 | − | 5.44949i | −0.482931 | − | 0.278820i | ||||
\(383\) | −22.9059 | − | 13.2247i | −1.17044 | − | 0.675753i | −0.216655 | − | 0.976248i | \(-0.569515\pi\) |
−0.953783 | + | 0.300495i | \(0.902848\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.0000 | 1.01797 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.7980i | 0.548183i | ||||||||
\(389\) | 6.79796 | + | 11.7744i | 0.344670 | + | 0.596986i | 0.985294 | − | 0.170869i | \(-0.0546574\pi\) |
−0.640624 | + | 0.767855i | \(0.721324\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.00000 | − | 10.3923i | 0.303433 | − | 0.525561i | ||||
\(392\) | −11.0834 | − | 6.39898i | −0.559794 | − | 0.323197i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.1237 | − | 20.9989i | −0.610784 | − | 1.05791i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.5959i | 1.08387i | 0.840421 | + | 0.541934i | \(0.182308\pi\) | ||||
−0.840421 | + | 0.541934i | \(0.817692\pi\) | |||||||
\(398\) | −5.02118 | + | 2.89898i | −0.251689 | + | 0.145313i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.65153 | − | 8.05669i | 0.232286 | − | 0.402332i | −0.726194 | − | 0.687490i | \(-0.758713\pi\) |
0.958481 | + | 0.285158i | \(0.0920460\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.73205 | − | 1.00000i | 0.0862796 | − | 0.0498135i | ||||
\(404\) | 3.55051 | 0.176644 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.8990 | −0.540907 | ||||||||
\(407\) | −14.2064 | + | 8.20204i | −0.704183 | + | 0.406560i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.94949 | − | 8.57277i | 0.244737 | − | 0.423896i | −0.717321 | − | 0.696743i | \(-0.754632\pi\) |
0.962058 | + | 0.272847i | \(0.0879652\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.9959 | + | 6.34847i | −0.541728 | + | 0.312767i | ||||
\(413\) | − | 2.44949i | − | 0.120532i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.22474 | − | 3.85337i | −0.109077 | − | 0.188927i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.8209 | − | 6.24745i | −0.529267 | − | 0.305573i | ||||
\(419\) | −4.07321 | + | 7.05501i | −0.198990 | + | 0.344660i | −0.948201 | − | 0.317671i | \(-0.897099\pi\) |
0.749212 | + | 0.662331i | \(0.230433\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.02270 | − | 15.6278i | −0.439740 | − | 0.761651i | 0.557929 | − | 0.829888i | \(-0.311596\pi\) |
−0.997669 | + | 0.0682369i | \(0.978263\pi\) | |||||||
\(422\) | 1.44949i | 0.0705601i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.44949 | −0.410343 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.8270 | − | 17.7980i | −1.49182 | − | 0.861304i | ||||
\(428\) | 13.2047 | + | 7.62372i | 0.638272 | + | 0.368507i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.6515 | −0.513066 | −0.256533 | − | 0.966535i | \(-0.582580\pi\) | ||||
−0.256533 | + | 0.966535i | \(0.582580\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.5959i | 1.42229i | 0.703046 | + | 0.711145i | \(0.251823\pi\) | ||||
−0.703046 | + | 0.711145i | \(0.748177\pi\) | |||||||
\(434\) | −1.00000 | − | 1.73205i | −0.0480015 | − | 0.0831411i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.22474 | + | 9.04952i | −0.250220 | + | 0.433394i | ||||
\(437\) | 5.41045 | + | 3.12372i | 0.258817 | + | 0.149428i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.67423 | − | 9.82806i | −0.270816 | − | 0.469068i | 0.698255 | − | 0.715849i | \(-0.253960\pi\) |
−0.969071 | + | 0.246782i | \(0.920627\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 21.7980i | 1.03682i | ||||||||
\(443\) | 24.0737 | − | 13.8990i | 1.14378 | − | 0.660360i | 0.196415 | − | 0.980521i | \(-0.437070\pi\) |
0.947363 | + | 0.320161i | \(0.103737\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.898979 | − | 1.55708i | 0.0425679 | − | 0.0737298i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.85337 | + | 2.22474i | −0.182055 | + | 0.105109i | ||||
\(449\) | 10.5959 | 0.500052 | 0.250026 | − | 0.968239i | \(-0.419561\pi\) | ||||
0.250026 | + | 0.968239i | \(0.419561\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 44.0908 | 2.07616 | ||||||||
\(452\) | 12.0369 | − | 6.94949i | 0.566167 | − | 0.326877i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −14.1742 | + | 24.5505i | −0.665230 | + | 1.15221i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.5939 | + | 7.84847i | −0.635898 | + | 0.367136i | −0.783033 | − | 0.621981i | \(-0.786328\pi\) |
0.147135 | + | 0.989116i | \(0.452995\pi\) | |||||||
\(458\) | 21.1464i | 0.988108i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.67423 | + | 16.7563i | 0.450574 | + | 0.780417i | 0.998422 | − | 0.0561610i | \(-0.0178860\pi\) |
−0.547848 | + | 0.836578i | \(0.684553\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.09601 | + | 4.67423i | 0.376254 | + | 0.217230i | 0.676187 | − | 0.736730i | \(-0.263631\pi\) |
−0.299933 | + | 0.953960i | \(0.596964\pi\) | |||||||
\(464\) | −1.22474 | + | 2.12132i | −0.0568574 | + | 0.0984798i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.84847 | + | 4.93369i | 0.131953 | + | 0.228549i | ||||
\(467\) | − | 4.34847i | − | 0.201223i | −0.994926 | − | 0.100612i | \(-0.967920\pi\) | ||
0.994926 | − | 0.100612i | \(-0.0320799\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 63.8434 | 2.94801 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.476756 | − | 0.275255i | −0.0219445 | − | 0.0126696i | ||||
\(473\) | −31.6055 | − | 18.2474i | −1.45322 | − | 0.839019i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 21.7980 | 0.999108 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.55051i | 0.436830i | ||||||||
\(479\) | 12.1237 | + | 20.9989i | 0.553947 | + | 0.959465i | 0.997985 | + | 0.0634563i | \(0.0202124\pi\) |
−0.444038 | + | 0.896008i | \(0.646454\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.44949 | + | 12.9029i | −0.339667 | + | 0.588321i | ||||
\(482\) | 19.7436 | + | 11.3990i | 0.899297 | + | 0.519209i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.50000 | + | 11.2583i | 0.295455 | + | 0.511742i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 19.5505i | − | 0.885918i | −0.896542 | − | 0.442959i | \(-0.853929\pi\) | ||
0.896542 | − | 0.442959i | \(-0.146071\pi\) | |||||||
\(488\) | −6.92820 | + | 4.00000i | −0.313625 | + | 0.181071i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.37628 | + | 2.38378i | −0.0621105 | + | 0.107578i | −0.895409 | − | 0.445245i | \(-0.853116\pi\) |
0.833298 | + | 0.552824i | \(0.186450\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.3923 | − | 6.00000i | 0.468046 | − | 0.270226i | ||||
\(494\) | −11.3485 | −0.510592 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.449490 | −0.0201827 | ||||||||
\(497\) | 5.19615 | − | 3.00000i | 0.233079 | − | 0.134568i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.17423 | − | 5.49794i | 0.142098 | − | 0.246121i | −0.786188 | − | 0.617987i | \(-0.787948\pi\) |
0.928287 | + | 0.371866i | \(0.121282\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.71940 | − | 2.72474i | 0.210637 | − | 0.121611i | ||||
\(503\) | 26.4495i | 1.17932i | 0.807650 | + | 0.589662i | \(0.200739\pi\) | ||||
−0.807650 | + | 0.589662i | \(0.799261\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.00000 | − | 10.3923i | −0.266733 | − | 0.461994i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.82806 | − | 5.67423i | −0.436050 | − | 0.251753i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.22474 | + | 3.85337i | 0.0984169 | + | 0.170463i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.79796 | 0.299845 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.67123 | + | 2.69694i | 0.205441 | + | 0.118611i | ||||
\(518\) | 12.9029 | + | 7.44949i | 0.566921 | + | 0.327312i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.3939 | −1.28777 | −0.643885 | − | 0.765123i | \(-0.722678\pi\) | ||||
−0.643885 | + | 0.765123i | \(0.722678\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.65153i | 0.247124i | 0.992337 | + | 0.123562i | \(0.0394318\pi\) | ||||
−0.992337 | + | 0.123562i | \(0.960568\pi\) | |||||||
\(524\) | −7.89898 | − | 13.6814i | −0.345069 | − | 0.597676i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.77526 | − | 13.4671i | 0.339017 | − | 0.587195i | ||||
\(527\) | 1.90702 | + | 1.10102i | 0.0830712 | + | 0.0479612i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.50000 | − | 14.7224i | −0.369565 | − | 0.640106i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11.3485i | 0.492019i | ||||||||
\(533\) | 34.6803 | − | 20.0227i | 1.50217 | − | 0.867280i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.17423 | − | 12.4261i | 0.309880 | − | 0.536727i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.27098 | − | 4.77526i | 0.356587 | − | 0.205876i | ||||
\(539\) | 62.6969 | 2.70055 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.2020 | −0.782567 | −0.391283 | − | 0.920270i | \(-0.627969\pi\) | ||||
−0.391283 | + | 0.920270i | \(0.627969\pi\) | |||||||
\(542\) | 0.564242 | − | 0.325765i | 0.0242363 | − | 0.0139928i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.44949 | − | 4.24264i | 0.105021 | − | 0.181902i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.2825 | − | 15.1742i | 1.12376 | − | 0.648803i | 0.181402 | − | 0.983409i | \(-0.441936\pi\) |
0.942358 | + | 0.334606i | \(0.108603\pi\) | |||||||
\(548\) | 3.00000i | 0.128154i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.12372 | + | 5.41045i | 0.133075 | + | 0.230493i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −48.9260 | − | 28.2474i | −2.08055 | − | 1.20120i | ||||
\(554\) | −3.22474 | + | 5.58542i | −0.137006 | + | 0.237302i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | + | 3.46410i | 0.0848189 | + | 0.146911i | ||||
\(557\) | 17.3939i | 0.737002i | 0.929627 | + | 0.368501i | \(0.120129\pi\) | ||||
−0.929627 | + | 0.368501i | \(0.879871\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −33.1464 | −1.40194 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 25.0273 | + | 14.4495i | 1.05571 | + | 0.609515i | ||||
\(563\) | −25.9326 | − | 14.9722i | −1.09293 | − | 0.631003i | −0.158574 | − | 0.987347i | \(-0.550690\pi\) |
−0.934355 | + | 0.356344i | \(0.884023\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.2474 | 0.472766 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 1.34847i | − | 0.0565805i | ||||||
\(569\) | −7.10102 | − | 12.2993i | −0.297690 | − | 0.515615i | 0.677917 | − | 0.735139i | \(-0.262883\pi\) |
−0.975607 | + | 0.219524i | \(0.929550\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.9722 | − | 24.2005i | 0.584718 | − | 1.01276i | −0.410192 | − | 0.911999i | \(-0.634538\pi\) |
0.994911 | − | 0.100762i | \(-0.0321282\pi\) | |||||||
\(572\) | 18.8776 | + | 10.8990i | 0.789312 | + | 0.455709i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −20.0227 | − | 34.6803i | −0.835732 | − | 1.44753i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 18.3939i | − | 0.765747i | −0.923801 | − | 0.382874i | \(-0.874934\pi\) | ||
0.923801 | − | 0.382874i | \(-0.125066\pi\) | |||||||
\(578\) | −6.06218 | + | 3.50000i | −0.252153 | + | 0.145581i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.22474 | + | 2.12132i | −0.0508110 | + | 0.0880072i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.8481 | − | 20.6969i | 1.48468 | − | 0.857180i | ||||
\(584\) | 1.00000 | 0.0413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.0454 | 1.15855 | ||||||||
\(587\) | −2.33562 | + | 1.34847i | −0.0964012 | + | 0.0556573i | −0.547426 | − | 0.836854i | \(-0.684392\pi\) |
0.451024 | + | 0.892512i | \(0.351059\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.573214 | + | 0.992836i | −0.0236189 | + | 0.0409091i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.89986 | − | 1.67423i | 0.119183 | − | 0.0688106i | ||||
\(593\) | 1.89898i | 0.0779817i | 0.999240 | + | 0.0389909i | \(0.0124143\pi\) | ||||
−0.999240 | + | 0.0389909i | \(0.987586\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.00000 | − | 5.19615i | −0.122885 | − | 0.212843i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.43879 | − | 5.44949i | −0.385981 | − | 0.222846i | ||||
\(599\) | 18.6742 | − | 32.3447i | 0.763009 | − | 1.32157i | −0.178285 | − | 0.983979i | \(-0.557055\pi\) |
0.941293 | − | 0.337591i | \(-0.109612\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.2474 | − | 28.1414i | −0.662747 | − | 1.14791i | −0.979891 | − | 0.199534i | \(-0.936057\pi\) |
0.317144 | − | 0.948378i | \(-0.397276\pi\) | |||||||
\(602\) | 33.1464i | 1.35095i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −20.0000 | −0.813788 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.82806 | + | 5.67423i | 0.398909 | + | 0.230310i | 0.686013 | − | 0.727589i | \(-0.259359\pi\) |
−0.287104 | + | 0.957899i | \(0.592693\pi\) | |||||||
\(608\) | 2.20881 | + | 1.27526i | 0.0895789 | + | 0.0517184i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.89898 | 0.198191 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.0454i | 1.29430i | 0.762362 | + | 0.647151i | \(0.224040\pi\) | ||||
−0.762362 | + | 0.647151i | \(0.775960\pi\) | |||||||
\(614\) | −3.34847 | − | 5.79972i | −0.135133 | − | 0.234058i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.8990 | − | 18.8776i | 0.439132 | − | 0.760600i | ||||
\(617\) | −12.4655 | − | 7.19694i | −0.501841 | − | 0.289738i | 0.227633 | − | 0.973747i | \(-0.426901\pi\) |
−0.729473 | + | 0.684009i | \(0.760235\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.8712 | + | 36.1499i | 0.838883 | + | 1.45299i | 0.890829 | + | 0.454339i | \(0.150124\pi\) |
−0.0519458 | + | 0.998650i | \(0.516542\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.8990i | 0.437009i | ||||||||
\(623\) | −34.6803 | + | 20.0227i | −1.38944 | + | 0.802193i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.94949 | + | 3.37662i | −0.0779173 | + | 0.134957i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.174973 | − | 0.101021i | 0.00698217 | − | 0.00403116i | ||||
\(629\) | −16.4041 | −0.654074 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.7980 | −1.02700 | −0.513500 | − | 0.858089i | \(-0.671651\pi\) | ||||
−0.513500 | + | 0.858089i | \(0.671651\pi\) | |||||||
\(632\) | −10.9959 | + | 6.34847i | −0.437392 | + | 0.252529i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.57321 | − | 14.8492i | 0.340486 | − | 0.589739i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 49.3153 | − | 28.4722i | 1.95394 | − | 1.12811i | ||||
\(638\) | − | 12.0000i | − | 0.475085i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.1969 | + | 38.4462i | 0.876726 | + | 1.51853i | 0.854912 | + | 0.518773i | \(0.173611\pi\) |
0.0218141 | + | 0.999762i | \(0.493056\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.0146 | − | 16.1742i | −1.10479 | − | 0.637850i | −0.167313 | − | 0.985904i | \(-0.553509\pi\) |
−0.937474 | + | 0.348054i | \(0.886843\pi\) | |||||||
\(644\) | −5.44949 | + | 9.43879i | −0.214740 | + | 0.371941i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.24745 | − | 10.8209i | −0.245803 | − | 0.425743i | ||||
\(647\) | 0.247449i | 0.00972821i | 0.999988 | + | 0.00486411i | \(0.00154830\pi\) | ||||
−0.999988 | + | 0.00486411i | \(0.998452\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.69694 | 0.105864 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.20881 | − | 1.27526i | −0.0865035 | − | 0.0499428i | ||||
\(653\) | 5.41045 | + | 3.12372i | 0.211727 | + | 0.122241i | 0.602114 | − | 0.798410i | \(-0.294325\pi\) |
−0.390387 | + | 0.920651i | \(0.627659\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.00000 | −0.351391 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 4.89898i | − | 0.190982i | ||||||
\(659\) | −22.0732 | − | 38.2319i | −0.859850 | − | 1.48930i | −0.872071 | − | 0.489379i | \(-0.837223\pi\) |
0.0122208 | − | 0.999925i | \(-0.496110\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.6969 | − | 44.5084i | 0.999495 | − | 1.73118i | 0.472230 | − | 0.881475i | \(-0.343449\pi\) |
0.527265 | − | 0.849701i | \(-0.323218\pi\) | |||||||
\(662\) | 7.22999 | + | 4.17423i | 0.281001 | + | 0.162236i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.275255 | + | 0.476756i | 0.0106820 | + | 0.0185017i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.00000i | 0.232321i | ||||||||
\(668\) | −16.9706 | + | 9.79796i | −0.656611 | + | 0.379094i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.5959 | − | 33.9411i | 0.756492 | − | 1.31028i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.79972 | − | 3.34847i | 0.223563 | − | 0.129074i | −0.384036 | − | 0.923318i | \(-0.625466\pi\) |
0.607599 | + | 0.794244i | \(0.292133\pi\) | |||||||
\(674\) | 11.1010 | 0.427595 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.79796 | 0.261460 | ||||||||
\(677\) | −32.7733 | + | 18.9217i | −1.25958 | + | 0.727219i | −0.972993 | − | 0.230835i | \(-0.925854\pi\) |
−0.286588 | + | 0.958054i | \(0.592521\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.0227 | + | 41.6085i | −0.921907 | + | 1.59679i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.90702 | − | 1.10102i | 0.0730237 | − | 0.0421603i | ||||
\(683\) | − | 11.9444i | − | 0.457039i | −0.973539 | − | 0.228520i | \(-0.926611\pi\) | ||
0.973539 | − | 0.228520i | \(-0.0733885\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12.8990 | − | 22.3417i | −0.492485 | − | 0.853010i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.45145 | + | 3.72474i | 0.245959 | + | 0.142005i | ||||
\(689\) | 18.7980 | − | 32.5590i | 0.716145 | − | 1.24040i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.52270 | + | 4.36945i | 0.0959682 | + | 0.166222i | 0.910012 | − | 0.414581i | \(-0.136072\pi\) |
−0.814044 | + | 0.580803i | \(0.802739\pi\) | |||||||
\(692\) | 9.79796i | 0.372463i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.1838 | + | 22.0454i | 1.44631 | + | 0.835029i | ||||
\(698\) | 12.1244 | + | 7.00000i | 0.458914 | + | 0.264954i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.2020 | −0.536404 | −0.268202 | − | 0.963363i | \(-0.586429\pi\) | ||||
−0.268202 | + | 0.963363i | \(0.586429\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 8.54031i | − | 0.322104i | ||||||
\(704\) | −2.44949 | − | 4.24264i | −0.0923186 | − | 0.159901i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.50000 | + | 7.79423i | −0.169360 | + | 0.293340i | ||||
\(707\) | 13.6814 | + | 7.89898i | 0.514543 | + | 0.297072i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.224745 | − | 0.389270i | −0.00844047 | − | 0.0146193i | 0.861774 | − | 0.507292i | \(-0.169353\pi\) |
−0.870215 | + | 0.492673i | \(0.836020\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.00000i | 0.337289i | ||||||||
\(713\) | −0.953512 | + | 0.550510i | −0.0357093 | + | 0.0206168i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.62372 | + | 13.2047i | −0.284912 | + | 0.493482i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −29.2699 | + | 16.8990i | −1.09234 | + | 0.630664i | ||||
\(719\) | 52.0454 | 1.94097 | 0.970483 | − | 0.241169i | \(-0.0775309\pi\) | ||||
0.970483 | + | 0.241169i | \(0.0775309\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −56.4949 | −2.10398 | ||||||||
\(722\) | −10.8209 | + | 6.24745i | −0.402712 | + | 0.232506i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.898979 | + | 1.55708i | −0.0334103 | + | 0.0578684i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.8564 | + | 8.00000i | −0.513906 | + | 0.296704i | −0.734438 | − | 0.678676i | \(-0.762554\pi\) |
0.220532 | + | 0.975380i | \(0.429221\pi\) | |||||||
\(728\) | − | 19.7980i | − | 0.733761i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.2474 | − | 31.6055i | −0.674906 | − | 1.16897i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.5167 | + | 13.0000i | 0.831672 | + | 0.480166i | 0.854425 | − | 0.519575i | \(-0.173910\pi\) |
−0.0227529 | + | 0.999741i | \(0.507243\pi\) | |||||||
\(734\) | 8.34847 | − | 14.4600i | 0.308148 | − | 0.533727i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.22474 | + | 2.12132i | 0.0451447 | + | 0.0781929i | ||||
\(737\) | 70.2929i | 2.58927i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.0454 | 1.50988 | 0.754940 | − | 0.655794i | \(-0.227666\pi\) | ||||
0.754940 | + | 0.655794i | \(0.227666\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −32.5590 | − | 18.7980i | −1.19528 | − | 0.690095i | ||||
\(743\) | −30.0091 | − | 17.3258i | −1.10093 | − | 0.635621i | −0.164463 | − | 0.986383i | \(-0.552589\pi\) |
−0.936464 | + | 0.350763i | \(0.885922\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 15.5959 | 0.571007 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 24.0000i | 0.877527i | ||||||||
\(749\) | 33.9217 | + | 58.7541i | 1.23947 | + | 2.14683i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.0227 | − | 43.3406i | 0.913091 | − | 1.58152i | 0.103420 | − | 0.994638i | \(-0.467022\pi\) |
0.809672 | − | 0.586883i | \(-0.199645\pi\) | |||||||
\(752\) | −0.953512 | − | 0.550510i | −0.0347710 | − | 0.0200750i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.44949 | − | 9.43879i | −0.198459 | − | 0.343741i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.04541i | 0.219724i | 0.993947 | + | 0.109862i | \(0.0350409\pi\) | ||||
−0.993947 | + | 0.109862i | \(0.964959\pi\) | |||||||
\(758\) | −0.778539 | + | 0.449490i | −0.0282778 | + | 0.0163262i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.05051 | − | 3.55159i | 0.0743309 | − | 0.128745i | −0.826464 | − | 0.562989i | \(-0.809651\pi\) |
0.900795 | + | 0.434244i | \(0.142985\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −40.2658 | + | 23.2474i | −1.45772 | + | 0.841614i | ||||
\(764\) | −10.8990 | −0.394311 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.4495 | −0.955659 | ||||||||
\(767\) | 2.12132 | − | 1.22474i | 0.0765964 | − | 0.0442230i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.0959 | − | 43.4674i | 0.904982 | − | 1.56747i | 0.0840405 | − | 0.996462i | \(-0.473217\pi\) |
0.820941 | − | 0.571012i | \(-0.193449\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.3205 | − | 10.0000i | 0.623379 | − | 0.359908i | ||||
\(773\) | − | 49.5959i | − | 1.78384i | −0.452192 | − | 0.891921i | \(-0.649358\pi\) | ||
0.452192 | − | 0.891921i | \(-0.350642\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.39898 | + | 9.35131i | 0.193812 | + | 0.335692i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.7744 | + | 6.79796i | 0.422133 | + | 0.243719i | ||||
\(779\) | −11.4773 | + | 19.8793i | −0.411217 | + | 0.712248i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.30306 | + | 5.72107i | 0.118193 | + | 0.204716i | ||||
\(782\) | − | 12.0000i | − | 0.429119i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12.7980 | −0.457070 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.59259 | − | 2.65153i | −0.163708 | − | 0.0945169i | 0.415908 | − | 0.909407i | \(-0.363464\pi\) |
−0.579616 | + | 0.814890i | \(0.696797\pi\) | |||||||
\(788\) | −20.9989 | − | 12.1237i | −0.748055 | − | 0.431890i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 61.8434 | 2.19890 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 35.5959i | − | 1.26405i | ||||||
\(794\) | 10.7980 | + | 18.7026i | 0.383205 | + | 0.663731i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.89898 | + | 5.02118i | −0.102752 | + | 0.177971i | ||||
\(797\) | −4.98186 | − | 2.87628i | −0.176466 | − | 0.101883i | 0.409165 | − | 0.912460i | \(-0.365820\pi\) |
−0.585631 | + | 0.810577i | \(0.699153\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.69694 | + | 4.67123i | 0.0954108 | + | 0.165256i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 9.30306i | − | 0.328503i | ||||||
\(803\) | −4.24264 | + | 2.44949i | −0.149720 | + | 0.0864406i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.00000 | − | 1.73205i | 0.0352235 | − | 0.0610089i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.07483 | − | 1.77526i | 0.108172 | − | 0.0624533i | ||||
\(809\) | −35.6969 | −1.25504 | −0.627519 | − | 0.778601i | \(-0.715929\pi\) | ||||
−0.627519 | + | 0.778601i | \(0.715929\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.4495 | −1.17457 | −0.587285 | − | 0.809380i | \(-0.699803\pi\) | ||||
−0.587285 | + | 0.809380i | \(0.699803\pi\) | |||||||
\(812\) | −9.43879 | + | 5.44949i | −0.331237 | + | 0.191240i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.20204 | + | 14.2064i | −0.287481 | + | 0.497932i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.4545 | − | 9.50000i | 0.575669 | − | 0.332363i | ||||
\(818\) | − | 9.89898i | − | 0.346110i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.5959 | − | 44.3334i | −0.893304 | − | 1.54725i | −0.835890 | − | 0.548897i | \(-0.815048\pi\) |
−0.0574136 | − | 0.998350i | \(-0.518285\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.2952 | − | 13.4495i | −0.812020 | − | 0.468820i | 0.0356371 | − | 0.999365i | \(-0.488654\pi\) |
−0.847657 | + | 0.530545i | \(0.821987\pi\) | |||||||
\(824\) | −6.34847 | + | 10.9959i | −0.221159 | + | 0.383059i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.22474 | − | 2.12132i | −0.0426143 | − | 0.0738102i | ||||
\(827\) | − | 17.9444i | − | 0.623987i | −0.950084 | − | 0.311994i | \(-0.899003\pi\) | ||
0.950084 | − | 0.311994i | \(-0.100997\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.7423 | −0.928800 | −0.464400 | − | 0.885626i | \(-0.653730\pi\) | ||||
−0.464400 | + | 0.885626i | \(0.653730\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.85337 | − | 2.22474i | −0.133592 | − | 0.0771292i | ||||
\(833\) | 54.2971 | + | 31.3485i | 1.88128 | + | 1.08616i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.4949 | −0.432145 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.14643i | 0.281414i | ||||||||
\(839\) | −11.3258 | − | 19.6168i | −0.391009 | − | 0.677247i | 0.601574 | − | 0.798817i | \(-0.294540\pi\) |
−0.992583 | + | 0.121570i | \(0.961207\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.5000 | − | 19.9186i | 0.396552 | − | 0.686848i | ||||
\(842\) | −15.6278 | − | 9.02270i | −0.538569 | − | 0.310943i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.724745 | + | 1.25529i | 0.0249467 | + | 0.0432090i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 57.8434i | 1.98752i | ||||||||
\(848\) | −7.31747 | + | 4.22474i | −0.251283 | + | 0.145078i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.10102 | − | 7.10318i | 0.140581 | − | 0.243494i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.8372 | − | 23.0000i | 1.36400 | − | 0.787505i | 0.373845 | − | 0.927491i | \(-0.378039\pi\) |
0.990153 | + | 0.139986i | \(0.0447058\pi\) | |||||||
\(854\) | −35.5959 | −1.21807 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.2474 | 0.521147 | ||||||||
\(857\) | 34.7285 | − | 20.0505i | 1.18630 | − | 0.684912i | 0.228839 | − | 0.973464i | \(-0.426507\pi\) |
0.957464 | + | 0.288552i | \(0.0931738\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.82577 | + | 4.89437i | −0.0964139 | + | 0.166994i | −0.910198 | − | 0.414174i | \(-0.864071\pi\) |
0.813784 | + | 0.581168i | \(0.197404\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.22450 | + | 5.32577i | −0.314188 | + | 0.181396i | ||||
\(863\) | 19.8434i | 0.675476i | 0.941240 | + | 0.337738i | \(0.109662\pi\) | ||||
−0.941240 | + | 0.337738i | \(0.890338\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.7980 | + | 25.6308i | 0.502855 | + | 0.870971i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.73205 | − | 1.00000i | −0.0587896 | − | 0.0339422i | ||||
\(869\) | 31.1010 | − | 53.8685i | 1.05503 | − | 1.82737i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.9217 | + | 55.2900i | 1.08162 | + | 1.87343i | ||||
\(872\) | 10.4495i | 0.353864i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.24745 | 0.211323 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.5673 | + | 6.10102i | 0.356832 | + | 0.206017i | 0.667690 | − | 0.744439i | \(-0.267283\pi\) |
−0.310858 | + | 0.950456i | \(0.600617\pi\) | |||||||
\(878\) | −9.82806 | − | 5.67423i | −0.331681 | − | 0.191496i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.30306 | −0.313428 | −0.156714 | − | 0.987644i | \(-0.550090\pi\) | ||||
−0.156714 | + | 0.987644i | \(0.550090\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 28.2020i | − | 0.949074i | −0.880235 | − | 0.474537i | \(-0.842615\pi\) | ||
0.880235 | − | 0.474537i | \(-0.157385\pi\) | |||||||
\(884\) | 10.8990 | + | 18.8776i | 0.366572 | + | 0.634922i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.8990 | − | 24.0737i | 0.466945 | − | 0.808773i | ||||
\(887\) | 47.1940 | + | 27.2474i | 1.58462 | + | 0.914880i | 0.994172 | + | 0.107803i | \(0.0343815\pi\) |
0.590446 | + | 0.807077i | \(0.298952\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.2474 | − | 43.7299i | −0.846772 | − | 1.46665i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 1.79796i | − | 0.0602001i | ||||||
\(893\) | −2.43194 | + | 1.40408i | −0.0813818 | + | 0.0469858i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.22474 | + | 3.85337i | −0.0743235 | + | 0.128732i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.17633 | − | 5.29796i | 0.306218 | − | 0.176795i | ||||
\(899\) | −1.10102 | −0.0367211 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.3939 | 1.37903 | ||||||||
\(902\) | 38.1838 | − | 22.0454i | 1.27138 | − | 0.734032i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.94949 | − | 12.0369i | 0.231137 | − | 0.400340i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.7508 | − | 10.8258i | 0.622609 | − | 0.359464i | −0.155275 | − | 0.987871i | \(-0.549626\pi\) |
0.777884 | + | 0.628408i | \(0.216293\pi\) | |||||||
\(908\) | 28.3485i | 0.940777i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.67423 | + | 6.36396i | 0.121733 | + | 0.210847i | 0.920451 | − | 0.390858i | \(-0.127822\pi\) |
−0.798718 | + | 0.601705i | \(0.794488\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.33562 | − | 1.34847i | −0.0772976 | − | 0.0446278i | ||||
\(914\) | −7.84847 | + | 13.5939i | −0.259604 | + | 0.449648i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.5732 | + | 18.3133i | 0.349349 | + | 0.605090i | ||||
\(917\) | − | 70.2929i | − | 2.32127i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.3485 | 0.374351 | 0.187176 | − | 0.982326i | \(-0.440067\pi\) | ||||
0.187176 | + | 0.982326i | \(0.440067\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 16.7563 | + | 9.67423i | 0.551838 | + | 0.318604i | ||||
\(923\) | 5.19615 | + | 3.00000i | 0.171033 | + | 0.0987462i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.34847 | 0.307210 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.44949i | 0.0804084i | ||||||||
\(929\) | −13.5959 | − | 23.5488i | −0.446068 | − | 0.772612i | 0.552058 | − | 0.833806i | \(-0.313843\pi\) |
−0.998126 | + | 0.0611938i | \(0.980509\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.3207 | + | 28.2682i | −0.534888 | + | 0.926453i | ||||
\(932\) | 4.93369 | + | 2.84847i | 0.161609 | + | 0.0933047i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.17423 | − | 3.76588i | −0.0711431 | − | 0.123224i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.7980i | 0.875451i | 0.899109 | + | 0.437726i | \(0.144216\pi\) | ||||
−0.899109 | + | 0.437726i | \(0.855784\pi\) | |||||||
\(938\) | 55.2900 | − | 31.9217i | 1.80528 | − | 1.04228i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.8207 | + | 25.6701i | −0.483140 | + | 0.836823i | −0.999813 | − | 0.0193603i | \(-0.993837\pi\) |
0.516673 | + | 0.856183i | \(0.327170\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.0919 | + | 11.0227i | −0.621717 | + | 0.358949i | ||||
\(944\) | −0.550510 | −0.0179176 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −36.4949 | −1.18655 | ||||||||
\(947\) | 7.05501 | − | 4.07321i | 0.229257 | − | 0.132362i | −0.380972 | − | 0.924587i | \(-0.624411\pi\) |
0.610229 | + | 0.792225i | \(0.291077\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.22474 | + | 3.85337i | −0.0722183 | + | 0.125086i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 18.8776 | − | 10.8990i | 0.611826 | − | 0.353238i | ||||
\(953\) | 21.7980i | 0.706105i | 0.935603 | + | 0.353053i | \(0.114856\pi\) | ||||
−0.935603 | + | 0.353053i | \(0.885144\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.77526 | + | 8.27098i | 0.154443 | + | 0.267503i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20.9989 | + | 12.1237i | 0.678444 | + | 0.391700i | ||||
\(959\) | −6.67423 | + | 11.5601i | −0.215522 | + | 0.373296i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3990 | + | 26.6718i | 0.496741 | + | 0.860381i | ||||
\(962\) | 14.8990i | 0.480362i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22.7980 | 0.734273 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.7128 | − | 16.0000i | −0.891184 | − | 0.514525i | −0.0168544 | − | 0.999858i | \(-0.505365\pi\) |
−0.874330 | + | 0.485333i | \(0.838699\pi\) | |||||||
\(968\) | 11.2583 | + | 6.50000i | 0.361856 | + | 0.208918i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.8434 | −0.733079 | −0.366539 | − | 0.930403i | \(-0.619457\pi\) | ||||
−0.366539 | + | 0.930403i | \(0.619457\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.7980i | 0.570576i | ||||||||
\(974\) | −9.77526 | − | 16.9312i | −0.313219 | − | 0.542512i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.00000 | + | 6.92820i | −0.128037 | + | 0.221766i | ||||
\(977\) | −7.79423 | − | 4.50000i | −0.249359 | − | 0.143968i | 0.370111 | − | 0.928987i | \(-0.379319\pi\) |
−0.619471 | + | 0.785020i | \(0.712653\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.0454 | − | 38.1838i | −0.704574 | − | 1.22036i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.75255i | 0.0878374i | ||||||||
\(983\) | −19.8311 | + | 11.4495i | −0.632514 | + | 0.365182i | −0.781725 | − | 0.623623i | \(-0.785660\pi\) |
0.149211 | + | 0.988805i | \(0.452327\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.00000 | − | 10.3923i | 0.191079 | − | 0.330958i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.82806 | + | 5.67423i | −0.312672 | + | 0.180521i | ||||
\(989\) | 18.2474 | 0.580235 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | −0.508257 | −0.254128 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | −0.389270 | + | 0.224745i | −0.0123593 | + | 0.00713566i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.00000 | − | 5.19615i | 0.0951542 | − | 0.164812i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.2162 | − | 18.0227i | 0.988628 | − | 0.570785i | 0.0837642 | − | 0.996486i | \(-0.473306\pi\) |
0.904864 | + | 0.425701i | \(0.139972\pi\) | |||||||
\(998\) | − | 6.34847i | − | 0.200957i | ||||||
\(999\) | 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 | 1350.2.j.g.199.4 | 8 | ||
3.2 | odd | 2 | 450.2.j.f.49.2 | 8 | |||
5.2 | odd | 4 | 1350.2.e.n.901.2 | 4 | |||
5.3 | odd | 4 | 1350.2.e.k.901.1 | 4 | |||
5.4 | even | 2 | inner | 1350.2.j.g.199.1 | 8 | ||
9.2 | odd | 6 | 450.2.j.f.349.3 | 8 | |||
9.4 | even | 3 | 4050.2.c.w.649.4 | 4 | |||
9.5 | odd | 6 | 4050.2.c.y.649.2 | 4 | |||
9.7 | even | 3 | inner | 1350.2.j.g.1099.1 | 8 | ||
15.2 | even | 4 | 450.2.e.l.301.1 | yes | 4 | ||
15.8 | even | 4 | 450.2.e.m.301.2 | yes | 4 | ||
15.14 | odd | 2 | 450.2.j.f.49.3 | 8 | |||
45.2 | even | 12 | 450.2.e.l.151.2 | ✓ | 4 | ||
45.4 | even | 6 | 4050.2.c.w.649.1 | 4 | |||
45.7 | odd | 12 | 1350.2.e.n.451.2 | 4 | |||
45.13 | odd | 12 | 4050.2.a.by.1.2 | 2 | |||
45.14 | odd | 6 | 4050.2.c.y.649.3 | 4 | |||
45.22 | odd | 12 | 4050.2.a.bl.1.1 | 2 | |||
45.23 | even | 12 | 4050.2.a.br.1.2 | 2 | |||
45.29 | odd | 6 | 450.2.j.f.349.2 | 8 | |||
45.32 | even | 12 | 4050.2.a.bu.1.1 | 2 | |||
45.34 | even | 6 | inner | 1350.2.j.g.1099.4 | 8 | ||
45.38 | even | 12 | 450.2.e.m.151.1 | yes | 4 | ||
45.43 | odd | 12 | 1350.2.e.k.451.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.e.l.151.2 | ✓ | 4 | 45.2 | even | 12 | ||
450.2.e.l.301.1 | yes | 4 | 15.2 | even | 4 | ||
450.2.e.m.151.1 | yes | 4 | 45.38 | even | 12 | ||
450.2.e.m.301.2 | yes | 4 | 15.8 | even | 4 | ||
450.2.j.f.49.2 | 8 | 3.2 | odd | 2 | |||
450.2.j.f.49.3 | 8 | 15.14 | odd | 2 | |||
450.2.j.f.349.2 | 8 | 45.29 | odd | 6 | |||
450.2.j.f.349.3 | 8 | 9.2 | odd | 6 | |||
1350.2.e.k.451.1 | 4 | 45.43 | odd | 12 | |||
1350.2.e.k.901.1 | 4 | 5.3 | odd | 4 | |||
1350.2.e.n.451.2 | 4 | 45.7 | odd | 12 | |||
1350.2.e.n.901.2 | 4 | 5.2 | odd | 4 | |||
1350.2.j.g.199.1 | 8 | 5.4 | even | 2 | inner | ||
1350.2.j.g.199.4 | 8 | 1.1 | even | 1 | trivial | ||
1350.2.j.g.1099.1 | 8 | 9.7 | even | 3 | inner | ||
1350.2.j.g.1099.4 | 8 | 45.34 | even | 6 | inner | ||
4050.2.a.bl.1.1 | 2 | 45.22 | odd | 12 | |||
4050.2.a.br.1.2 | 2 | 45.23 | even | 12 | |||
4050.2.a.bu.1.1 | 2 | 45.32 | even | 12 | |||
4050.2.a.by.1.2 | 2 | 45.13 | odd | 12 | |||
4050.2.c.w.649.1 | 4 | 45.4 | even | 6 | |||
4050.2.c.w.649.4 | 4 | 9.4 | even | 3 | |||
4050.2.c.y.649.2 | 4 | 9.5 | odd | 6 | |||
4050.2.c.y.649.3 | 4 | 45.14 | odd | 6 |