Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,6,Mod(193,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.193");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(53.8889634572\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.289 |
Dual form | 336.6.q.c.193.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.50000 | + | 7.79423i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.00000 | − | 5.19615i | 0.0536656 | − | 0.0929516i | −0.837945 | − | 0.545755i | \(-0.816243\pi\) |
0.891610 | + | 0.452804i | \(0.149576\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −59.5000 | − | 115.181i | −0.458957 | − | 0.888459i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −40.5000 | + | 70.1481i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −333.000 | − | 576.773i | −0.829779 | − | 1.43722i | −0.898211 | − | 0.439564i | \(-0.855133\pi\) |
0.0684322 | − | 0.997656i | \(-0.478200\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −559.000 | −0.917389 | −0.458694 | − | 0.888594i | \(-0.651683\pi\) | ||||
−0.458694 | + | 0.888594i | \(0.651683\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 54.0000 | 0.0619677 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 870.000 | + | 1506.88i | 0.730125 | + | 1.26461i | 0.956830 | + | 0.290649i | \(0.0938713\pi\) |
−0.226705 | + | 0.973963i | \(0.572795\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 578.500 | − | 1001.99i | 0.367637 | − | 0.636766i | −0.621558 | − | 0.783368i | \(-0.713500\pi\) |
0.989196 | + | 0.146602i | \(0.0468335\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 630.000 | − | 982.073i | 0.311740 | − | 0.485954i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1734.00 | + | 3003.38i | −0.683486 | + | 1.18383i | 0.290424 | + | 0.956898i | \(0.406204\pi\) |
−0.973910 | + | 0.226934i | \(0.927130\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1544.50 | + | 2675.15i | 0.494240 | + | 0.856049i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3372.00 | 0.744548 | 0.372274 | − | 0.928123i | \(-0.378578\pi\) | ||||
0.372274 | + | 0.928123i | \(0.378578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3146.50 | + | 5449.90i | 0.588063 | + | 1.01855i | 0.994486 | + | 0.104869i | \(0.0334424\pi\) |
−0.406423 | + | 0.913685i | \(0.633224\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2997.00 | − | 5190.96i | 0.479073 | − | 0.829779i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −777.000 | − | 36.3731i | −0.107214 | − | 0.00501891i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1565.50 | + | 2711.53i | −0.187996 | + | 0.325619i | −0.944582 | − | 0.328276i | \(-0.893533\pi\) |
0.756586 | + | 0.653894i | \(0.226866\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2515.50 | − | 4356.97i | −0.264827 | − | 0.458694i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4866.00 | −0.452077 | −0.226039 | − | 0.974118i | \(-0.572578\pi\) | ||||
−0.226039 | + | 0.974118i | \(0.572578\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11407.0 | 0.940806 | 0.470403 | − | 0.882452i | \(-0.344108\pi\) | ||||
0.470403 | + | 0.882452i | \(0.344108\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 243.000 | + | 420.888i | 0.0178885 | + | 0.0309839i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1155.00 | − | 2000.52i | 0.0762671 | − | 0.132099i | −0.825369 | − | 0.564593i | \(-0.809033\pi\) |
0.901637 | + | 0.432494i | \(0.142366\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9726.50 | + | 13706.6i | −0.578717 | + | 0.815528i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7830.00 | + | 13562.0i | −0.421538 | + | 0.730125i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14148.0 | + | 24505.1i | 0.691840 | + | 1.19830i | 0.971235 | + | 0.238125i | \(0.0765328\pi\) |
−0.279395 | + | 0.960176i | \(0.590134\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3996.00 | −0.178122 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10413.0 | 0.424511 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10272.0 | + | 17791.6i | 0.384171 | + | 0.665404i | 0.991654 | − | 0.128929i | \(-0.0411539\pi\) |
−0.607483 | + | 0.794333i | \(0.707821\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2315.00 | − | 4009.70i | 0.0796575 | − | 0.137971i | −0.823445 | − | 0.567397i | \(-0.807951\pi\) |
0.903102 | + | 0.429426i | \(0.141284\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10489.5 | + | 491.036i | 0.332969 | + | 0.0155870i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1677.00 | + | 2904.65i | −0.0492322 | + | 0.0852728i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9372.50 | − | 16233.6i | −0.255075 | − | 0.441803i | 0.709841 | − | 0.704362i | \(-0.248767\pi\) |
−0.964916 | + | 0.262559i | \(0.915434\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −31212.0 | −0.789221 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 38226.0 | 0.899939 | 0.449969 | − | 0.893044i | \(-0.351435\pi\) | ||||
0.449969 | + | 0.893044i | \(0.351435\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −35294.5 | − | 61131.9i | −0.775175 | − | 1.34264i | −0.934696 | − | 0.355448i | \(-0.884328\pi\) |
0.159521 | − | 0.987195i | \(-0.449005\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13900.5 | + | 24076.4i | −0.285350 | + | 0.494240i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −46620.0 | + | 72673.4i | −0.896077 | + | 1.39685i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −31146.5 | + | 53947.3i | −0.561489 | + | 0.972528i | 0.435877 | + | 0.900006i | \(0.356438\pi\) |
−0.997367 | + | 0.0725221i | \(0.976895\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3280.50 | − | 5681.99i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −79818.0 | −1.27176 | −0.635881 | − | 0.771787i | \(-0.719363\pi\) | ||||
−0.635881 | + | 0.771787i | \(0.719363\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10440.0 | 0.156730 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15174.0 | + | 26282.1i | 0.214932 | + | 0.372274i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9060.00 | − | 15692.4i | 0.121242 | − | 0.209997i | −0.799016 | − | 0.601310i | \(-0.794646\pi\) |
0.920258 | + | 0.391313i | \(0.127979\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 33260.5 | + | 64386.4i | 0.421042 | + | 0.815062i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −28318.5 | + | 49049.1i | −0.339518 | + | 0.588063i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3471.00 | − | 6011.95i | −0.0394590 | − | 0.0683449i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 124754. | 1.34625 | 0.673124 | − | 0.739530i | \(-0.264952\pi\) | ||||
0.673124 | + | 0.739530i | \(0.264952\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 53946.0 | 0.553186 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 46695.0 | + | 80878.1i | 0.455478 | + | 0.788910i | 0.998716 | − | 0.0506685i | \(-0.0161352\pi\) |
−0.543238 | + | 0.839579i | \(0.682802\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −83865.5 | + | 145259.i | −0.778915 | + | 1.34912i | 0.153652 | + | 0.988125i | \(0.450897\pi\) |
−0.932567 | + | 0.360996i | \(0.882437\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3213.00 | − | 6219.79i | −0.0284405 | − | 0.0550558i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 34590.0 | − | 59911.6i | 0.292073 | − | 0.505885i | −0.682227 | − | 0.731141i | \(-0.738988\pi\) |
0.974300 | + | 0.225256i | \(0.0723217\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 109779. | + | 190144.i | 0.885024 | + | 1.53291i | 0.845686 | + | 0.533680i | \(0.179191\pi\) |
0.0393377 | + | 0.999226i | \(0.487475\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −28179.0 | −0.217079 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −39354.0 | −0.289930 | −0.144965 | − | 0.989437i | \(-0.546307\pi\) | ||||
−0.144965 | + | 0.989437i | \(0.546307\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10404.0 | + | 18020.3i | 0.0733594 | + | 0.127062i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 22639.5 | − | 39212.8i | 0.152898 | − | 0.264827i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 121800. | − | 189867.i | 0.788460 | − | 1.22909i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −141252. | + | 244657.i | −0.877067 | + | 1.51912i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −21897.0 | − | 37926.7i | −0.130503 | − | 0.226039i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 37284.0 | 0.213426 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −317093. | −1.74453 | −0.872263 | − | 0.489037i | \(-0.837348\pi\) | ||||
−0.872263 | + | 0.489037i | \(0.837348\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 51331.5 | + | 88908.8i | 0.271587 | + | 0.470403i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −77415.0 | + | 134087.i | −0.394137 | + | 0.682665i | −0.992991 | − | 0.118194i | \(-0.962290\pi\) |
0.598854 | + | 0.800858i | \(0.295623\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −149832. | − | 7013.94i | −0.734470 | − | 0.0343821i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2187.00 | + | 3788.00i | −0.0103280 | + | 0.0178885i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −33666.0 | − | 58311.2i | −0.153246 | − | 0.265430i | 0.779173 | − | 0.626809i | \(-0.215639\pi\) |
−0.932419 | + | 0.361379i | \(0.882306\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 365215. | 1.60329 | 0.801644 | − | 0.597802i | \(-0.203959\pi\) | ||||
0.801644 | + | 0.597802i | \(0.203959\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20790.0 | 0.0880657 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 186147. | + | 322416.i | 0.761230 | + | 1.31849i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10116.0 | − | 17521.4i | 0.0399566 | − | 0.0692069i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −150602. | − | 14130.9i | −0.574825 | − | 0.0539359i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 84030.0 | − | 145544.i | 0.310076 | − | 0.537068i | −0.668302 | − | 0.743890i | \(-0.732979\pi\) |
0.978379 | + | 0.206822i | \(0.0663120\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 76768.0 | + | 132966.i | 0.273992 | + | 0.474568i | 0.969880 | − | 0.243582i | \(-0.0783225\pi\) |
−0.695888 | + | 0.718150i | \(0.744989\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −140940. | −0.486750 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 37758.0 | 0.126235 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −101209. | − | 175299.i | −0.327695 | − | 0.567585i | 0.654359 | − | 0.756184i | \(-0.272939\pi\) |
−0.982054 | + | 0.188599i | \(0.939605\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −127332. | + | 220545.i | −0.399434 | + | 0.691840i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 449106. | + | 21023.6i | 1.36548 | + | 0.0639209i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −89882.0 | + | 155680.i | −0.264974 | + | 0.458949i | −0.967557 | − | 0.252653i | \(-0.918697\pi\) |
0.702583 | + | 0.711602i | \(0.252030\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −17982.0 | − | 31145.7i | −0.0514195 | − | 0.0890612i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −217302. | −0.602938 | −0.301469 | − | 0.953476i | \(-0.597477\pi\) | ||||
−0.301469 | + | 0.953476i | \(0.597477\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −58812.0 | −0.158398 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 46858.5 | + | 81161.3i | 0.122546 | + | 0.212255i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 36990.0 | − | 64068.6i | 0.0939656 | − | 0.162753i | −0.815211 | − | 0.579164i | \(-0.803379\pi\) |
0.909176 | + | 0.416411i | \(0.136712\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 216230. | − | 337069.i | 0.533729 | − | 0.832001i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −92448.0 | + | 160125.i | −0.221801 | + | 0.384171i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 394683. | + | 683611.i | 0.920695 | + | 1.59469i | 0.798342 | + | 0.602204i | \(0.205711\pi\) |
0.122353 | + | 0.992487i | \(0.460956\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −477739. | −1.08391 | −0.541956 | − | 0.840407i | \(-0.682316\pi\) | ||||
−0.541956 | + | 0.840407i | \(0.682316\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 41670.0 | 0.0919805 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9393.00 | + | 16269.2i | 0.0201779 | + | 0.0349491i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 579420. | − | 1.00358e6i | 1.21168 | − | 2.09870i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 43375.5 | + | 83967.2i | 0.0883263 | + | 0.170984i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 179487. | − | 310881.i | 0.356000 | − | 0.616609i | −0.631289 | − | 0.775548i | \(-0.717474\pi\) |
0.987289 | + | 0.158938i | \(0.0508071\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 90966.5 | + | 157559.i | 0.175788 | + | 0.304473i | 0.940434 | − | 0.339978i | \(-0.110419\pi\) |
−0.764646 | + | 0.644451i | \(0.777086\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −30186.0 | −0.0568485 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 717924. | 1.31799 | 0.658996 | − | 0.752146i | \(-0.270981\pi\) | ||||
0.658996 | + | 0.752146i | \(0.270981\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 101548. | + | 175886.i | 0.181777 | + | 0.314847i | 0.942486 | − | 0.334246i | \(-0.108482\pi\) |
−0.760709 | + | 0.649093i | \(0.775148\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 84352.5 | − | 146103.i | 0.147268 | − | 0.255075i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −200634. | − | 388392.i | −0.341715 | − | 0.661500i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14598.0 | + | 25284.5i | −0.0242610 | + | 0.0420213i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −140454. | − | 243273.i | −0.227829 | − | 0.394611i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −770562. | −1.22023 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.17098e6 | −1.81069 | −0.905343 | − | 0.424680i | \(-0.860387\pi\) | ||||
−0.905343 | + | 0.424680i | \(0.860387\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 172017. | + | 297942.i | 0.259790 | + | 0.449969i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 34221.0 | − | 59272.5i | 0.0504890 | − | 0.0874495i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 440510. | − | 686687.i | 0.635048 | − | 0.989942i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 317651. | − | 550187.i | 0.447548 | − | 0.775175i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −486330. | − | 842348.i | −0.669808 | − | 1.16014i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.24635e6 | −1.67833 | −0.839167 | − | 0.543873i | \(-0.816957\pi\) | ||||
−0.839167 | + | 0.543873i | \(0.816957\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −250209. | −0.329493 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −459471. | − | 795827.i | −0.591825 | − | 1.02507i | −0.993987 | − | 0.109503i | \(-0.965074\pi\) |
0.402161 | − | 0.915569i | \(-0.368259\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −601874. | + | 1.04248e6i | −0.758433 | + | 1.31364i | 0.185216 | + | 0.982698i | \(0.440701\pi\) |
−0.943649 | + | 0.330947i | \(0.892632\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −776223. | − | 36336.7i | −0.957098 | − | 0.0448039i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 459531. | − | 795931.i | 0.554530 | − | 0.960474i | −0.443410 | − | 0.896319i | \(-0.646231\pi\) |
0.997940 | − | 0.0641551i | \(-0.0204353\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6930.00 | − | 12003.1i | −0.00818585 | − | 0.0141783i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −560637. | −0.648352 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 625338. | 0.708142 | 0.354071 | − | 0.935219i | \(-0.384797\pi\) | ||||
0.354071 | + | 0.935219i | \(0.384797\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −626911. | − | 1.08584e6i | −0.695286 | − | 1.20427i | −0.970084 | − | 0.242768i | \(-0.921945\pi\) |
0.274799 | − | 0.961502i | \(-0.411389\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 29524.5 | − | 51137.9i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 42042.0 | + | 91660.1i | 0.0447474 | + | 0.0975585i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −323382. | + | 560113.i | −0.337266 | + | 0.584162i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −359181. | − | 622120.i | −0.367126 | − | 0.635881i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.51333e6 | 1.51618 | 0.758089 | − | 0.652152i | \(-0.226133\pi\) | ||||
0.758089 | + | 0.652152i | \(0.226133\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.30969e6 | 2.26857 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 46980.0 | + | 81371.7i | 0.0452442 | + | 0.0783652i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 777465. | − | 1.34661e6i | 0.734257 | − | 1.27177i | −0.220792 | − | 0.975321i | \(-0.570864\pi\) |
0.955049 | − | 0.296449i | \(-0.0958026\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 405464. | + | 18980.7i | 0.375581 | + | 0.0175818i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −136566. | + | 236539.i | −0.124091 | + | 0.214932i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −557658. | − | 965892.i | −0.497140 | − | 0.861071i | 0.502855 | − | 0.864371i | \(-0.332283\pi\) |
−0.999995 | + | 0.00329949i | \(0.998950\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 169776. | 0.148512 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 163080. | 0.139998 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17835.0 | − | 30891.1i | −0.0150277 | − | 0.0260287i | 0.858414 | − | 0.512958i | \(-0.171450\pi\) |
−0.873441 | + | 0.486929i | \(0.838117\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −146384. | + | 253545.i | −0.121079 | + | 0.209716i | −0.920194 | − | 0.391464i | \(-0.871969\pi\) |
0.799114 | + | 0.601179i | \(0.205302\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −352170. | + | 548979.i | −0.285987 | + | 0.445809i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.02864e6 | − | 1.78165e6i | 0.820220 | − | 1.42066i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −431607. | − | 747564.i | −0.337978 | − | 0.585395i | 0.646074 | − | 0.763275i | \(-0.276410\pi\) |
−0.984052 | + | 0.177879i | \(0.943076\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −509733. | −0.392042 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.47110e6 | 1.11142 | 0.555709 | − | 0.831377i | \(-0.312447\pi\) | ||||
0.555709 | + | 0.831377i | \(0.312447\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 344420. | + | 596554.i | 0.255637 | + | 0.442775i | 0.965068 | − | 0.261999i | \(-0.0843816\pi\) |
−0.709432 | + | 0.704774i | \(0.751048\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 31239.0 | − | 54107.5i | 0.0227816 | − | 0.0394590i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 289527. | + | 560473.i | 0.207484 | + | 0.401652i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −803872. | + | 1.39235e6i | −0.566164 | + | 0.980624i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 561393. | + | 972361.i | 0.388628 | + | 0.673124i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 722832. | 0.491890 | 0.245945 | − | 0.969284i | \(-0.420902\pi\) | ||||
0.245945 | + | 0.969284i | \(0.420902\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 123264. | 0.0824672 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 242757. | + | 420467.i | 0.159691 | + | 0.276593i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 969306. | − | 1.67889e6i | 0.627022 | − | 1.08603i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −678716. | − | 1.31387e6i | −0.431790 | − | 0.835868i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −420255. | + | 727903.i | −0.262970 | + | 0.455478i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13890.0 | − | 24058.2i | −0.00854973 | − | 0.0148086i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20125.0 | 0.0121868 | 0.00609340 | − | 0.999981i | \(-0.498060\pi\) | ||||
0.00609340 | + | 0.999981i | \(0.498060\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.50958e6 | −0.899414 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −871779. | − | 1.50997e6i | −0.511099 | − | 0.885250i | −0.999917 | − | 0.0128643i | \(-0.995905\pi\) |
0.488818 | − | 0.872386i | \(-0.337428\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −904272. | + | 1.56624e6i | −0.521721 | + | 0.903647i | 0.477960 | + | 0.878382i | \(0.341376\pi\) |
−0.999681 | + | 0.0252651i | \(0.991957\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 34020.0 | − | 53031.9i | 0.0193178 | − | 0.0301135i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −511776. | + | 886422.i | −0.286043 | + | 0.495442i | −0.972862 | − | 0.231388i | \(-0.925673\pi\) |
0.686818 | + | 0.726829i | \(0.259007\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.12288e6 | − | 1.94488e6i | −0.617810 | − | 1.07008i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 622620. | 0.337257 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.01318e6 | 1.07368 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −863376. | − | 1.49541e6i | −0.453410 | − | 0.785330i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −988016. | + | 1.71129e6i | −0.510969 | + | 0.885024i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −299145. | − | 14003.6i | −0.152367 | − | 0.00713265i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −503766. | + | 872549.i | −0.252731 | + | 0.437744i | −0.964277 | − | 0.264896i | \(-0.914662\pi\) |
0.711545 | + | 0.702640i | \(0.247996\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −126806. | − | 219634.i | −0.0626654 | − | 0.108540i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −112470. | −0.0547551 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.56571e6 | −0.750993 | −0.375496 | − | 0.926824i | \(-0.622528\pi\) | ||||
−0.375496 | + | 0.926824i | \(0.622528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −177093. | − | 306734.i | −0.0836955 | − | 0.144965i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.09557e6 | − | 3.62963e6i | 0.975924 | − | 1.69035i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.15747e6 | + | 304770.i | 0.990169 | + | 0.139874i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −93636.0 | + | 162182.i | −0.0423541 | + | 0.0733594i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 378642. | + | 655827.i | 0.168813 | + | 0.292392i | 0.938003 | − | 0.346628i | \(-0.112673\pi\) |
−0.769190 | + | 0.639020i | \(0.779340\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −455638. | −0.200243 | −0.100121 | − | 0.994975i | \(-0.531923\pi\) | ||||
−0.100121 | + | 0.994975i | \(0.531923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 407511. | 0.176552 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.81569e6 | + | 3.14487e6i | 0.775543 | + | 1.34328i | 0.934489 | + | 0.355992i | \(0.115857\pi\) |
−0.158946 | + | 0.987287i | \(0.550810\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 114678. | − | 198628.i | 0.0482958 | − | 0.0836508i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.02797e6 | + | 94933.7i | 0.842153 | + | 0.0394230i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.01242e6 | + | 3.48561e6i | −0.824104 | + | 1.42739i | 0.0784980 | + | 0.996914i | \(0.474988\pi\) |
−0.902602 | + | 0.430476i | \(0.858346\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 568725. | + | 985061.i | 0.229686 | + | 0.397828i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.54254e6 | −1.01275 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −423534. | −0.166401 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.28894e6 | + | 2.23251e6i | 0.499536 | + | 0.865222i | 1.00000 | 0.000535822i | \(-0.000170558\pi\) | |
−0.500464 | + | 0.865757i | \(0.666837\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 197073. | − | 341340.i | 0.0753462 | − | 0.130503i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.98072e6 | − | 3.08764e6i | 0.747116 | − | 1.16464i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.26566e6 | − | 2.19220e6i | 0.471028 | − | 0.815844i | −0.528423 | − | 0.848981i | \(-0.677216\pi\) |
0.999451 | + | 0.0331372i | \(0.0105498\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 167778. | + | 290600.i | 0.0616108 | + | 0.106713i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.88495e6 | −0.683040 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.06677e6 | 1.09669 | 0.548344 | − | 0.836253i | \(-0.315258\pi\) | ||||
0.548344 | + | 0.836253i | \(0.315258\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.42692e6 | − | 2.47150e6i | −0.503601 | − | 0.872263i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.96260e6 | + | 3.39932e6i | −0.683652 | + | 1.18412i | 0.290207 | + | 0.956964i | \(0.406276\pi\) |
−0.973859 | + | 0.227155i | \(0.927057\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 237762. | + | 460265.i | 0.0817505 | + | 0.158254i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −461984. | + | 800179.i | −0.156801 | + | 0.271587i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.01334e6 | + | 3.48722e6i | 0.674597 | + | 1.16844i | 0.976587 | + | 0.215125i | \(0.0690158\pi\) |
−0.301990 | + | 0.953311i | \(0.597651\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.03432e6 | −1.99612 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.39347e6 | −0.455110 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 186879. | + | 323684.i | 0.0602654 | + | 0.104383i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.28720e6 | + | 3.96155e6i | −0.728329 | + | 1.26150i | 0.229260 | + | 0.973365i | \(0.426370\pi\) |
−0.957589 | + | 0.288138i | \(0.906964\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −619574. | − | 1.19938e6i | −0.194832 | − | 0.377160i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.13472e6 | − | 1.96539e6i | 0.352393 | − | 0.610363i | −0.634275 | − | 0.773108i | \(-0.718701\pi\) |
0.986668 | + | 0.162744i | \(0.0520346\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.75889e6 | − | 3.04649e6i | −0.539482 | − | 0.934410i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −39366.0 | −0.0119257 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.08525e6 | 0.623981 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.02298e6 | + | 3.50391e6i | 0.597976 | + | 1.03572i | 0.993120 | + | 0.117105i | \(0.0373615\pi\) |
−0.395144 | + | 0.918619i | \(0.629305\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 302994. | − | 524801.i | 0.0884768 | − | 0.153246i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.43808e6 | − | 2.24174e6i | 0.414866 | − | 0.646712i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −239454. | + | 414746.i | −0.0682499 | + | 0.118212i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.64347e6 | + | 2.84657e6i | 0.462829 | + | 0.801644i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.91281e6 | 1.08881 | 0.544407 | − | 0.838821i | \(-0.316755\pi\) | ||||
0.544407 | + | 0.838821i | \(0.316755\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.78086e6 | −0.764671 | −0.382335 | − | 0.924024i | \(-0.624880\pi\) | ||||
−0.382335 | + | 0.924024i | \(0.624880\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 93555.0 | + | 162042.i | 0.0254224 | + | 0.0440328i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.68743e6 | + | 4.65477e6i | −0.721714 | + | 1.25004i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −599585. | − | 28067.9i | −0.159141 | − | 0.00744972i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.67532e6 | + | 2.90174e6i | −0.439496 | + | 0.761230i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.19104e6 | − | 3.79498e6i | −0.568141 | − | 0.984049i | −0.996750 | − | 0.0805589i | \(-0.974329\pi\) |
0.428609 | − | 0.903490i | \(-0.359004\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.24946e6 | 0.320261 | 0.160130 | − | 0.987096i | \(-0.448809\pi\) | ||||
0.160130 | + | 0.987096i | \(0.448809\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 182088. | 0.0461379 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.00624e6 | + | 3.47491e6i | 0.502550 | + | 0.870441i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.37210e6 | + | 5.84066e6i | −0.835102 | + | 1.44644i | 0.0588449 | + | 0.998267i | \(0.481258\pi\) |
−0.893947 | + | 0.448172i | \(0.852075\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −567567. | − | 1.23741e6i | −0.138970 | − | 0.302983i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 239448. | − | 414736.i | 0.0579698 | − | 0.100407i | −0.835584 | − | 0.549362i | \(-0.814871\pi\) |
0.893554 | + | 0.448956i | \(0.148204\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −54360.0 | − | 94154.3i | −0.0130131 | − | 0.0225393i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.51254e6 | 0.358045 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 724506. | 0.169600 | 0.0848001 | − | 0.996398i | \(-0.472975\pi\) | ||||
0.0848001 | + | 0.996398i | \(0.472975\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.62038e6 | + | 2.80658e6i | 0.375124 | + | 0.649734i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −690912. | + | 1.19669e6i | −0.158189 | + | 0.273992i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 434343. | + | 20332.5i | 0.0983568 | + | 0.00460430i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.16978e6 | − | 2.02612e6i | 0.262008 | − | 0.453811i | −0.704768 | − | 0.709438i | \(-0.748949\pi\) |
0.966775 | + | 0.255627i | \(0.0822820\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −634230. | − | 1.09852e6i | −0.140513 | − | 0.243375i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.98247e6 | 0.653617 | 0.326809 | − | 0.945091i | \(-0.394027\pi\) | ||||
0.326809 | + | 0.945091i | \(0.394027\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.28423e6 | −0.928795 | −0.464398 | − | 0.885627i | \(-0.653729\pi\) | ||||
−0.464398 | + | 0.885627i | \(0.653729\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 169911. | + | 294294.i | 0.0364409 | + | 0.0631175i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.87018e6 | + | 4.97129e6i | −0.608998 | + | 1.05482i | 0.382407 | + | 0.923994i | \(0.375095\pi\) |
−0.991406 | + | 0.130822i | \(0.958238\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.31215e6 | + | 2.04544e6i | −0.275455 | + | 0.429393i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 910881. | − | 1.57769e6i | 0.189195 | − | 0.327695i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.79853e6 | − | 6.57925e6i | −0.780662 | − | 1.35215i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.57397e6 | 0.726804 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.29198e6 | −0.461226 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.32526e6 | + | 2.29541e6i | 0.263913 | + | 0.457111i | 0.967278 | − | 0.253718i | \(-0.0816534\pi\) |
−0.703365 | + | 0.710829i | \(0.748320\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 875114. | − | 1.51574e6i | 0.172465 | − | 0.298719i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.85711e6 | + | 3.59504e6i | 0.362219 | + | 0.701191i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 374262. | − | 648241.i | 0.0722473 | − | 0.125136i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.40277e6 | + | 2.42967e6i | 0.268018 | + | 0.464221i | 0.968350 | − | 0.249597i | \(-0.0802980\pi\) |
−0.700332 | + | 0.713817i | \(0.746965\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.61788e6 | −0.305966 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.68450e6 | 0.876919 | 0.438460 | − | 0.898751i | \(-0.355524\pi\) | ||||
0.438460 | + | 0.898751i | \(0.355524\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.93364e6 | + | 5.08121e6i | 0.543613 | + | 0.941565i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 161838. | − | 280312.i | 0.0296871 | − | 0.0514195i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.27445e6 | − | 4.40292e6i | −0.413033 | − | 0.799558i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 737876. | − | 1.27804e6i | 0.132658 | − | 0.229770i | −0.792043 | − | 0.610466i | \(-0.790982\pi\) |
0.924700 | + | 0.380696i | \(0.124316\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −977859. | − | 1.69370e6i | −0.174053 | − | 0.301469i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −63606.0 | −0.0112093 | −0.00560465 | − | 0.999984i | \(-0.501784\pi\) | ||||
−0.00560465 | + | 0.999984i | \(0.501784\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 560340. | 0.0977740 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −264654. | − | 458394.i | −0.0457255 | − | 0.0791989i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.10578e6 | + | 5.37937e6i | −0.531345 | + | 0.920317i | 0.467986 | + | 0.883736i | \(0.344980\pi\) |
−0.999331 | + | 0.0365806i | \(0.988353\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.94123e6 | + | 7.70262e6i | −0.837111 | + | 1.30493i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −421726. | + | 730452.i | −0.0707518 | + | 0.122546i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 503193. | + | 871556.i | 0.0836020 | + | 0.144803i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.53846e6 | −0.253139 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 665820. | 0.108502 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −706026. | − | 1.22287e6i | −0.113953 | − | 0.197373i | 0.803408 | − | 0.595429i | \(-0.203018\pi\) |
−0.917361 | + | 0.398057i | \(0.869685\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.61467e6 | − | 4.52875e6i | 0.417987 | − | 0.723976i | −0.577749 | − | 0.816214i | \(-0.696069\pi\) |
0.995737 | + | 0.0922386i | \(0.0294023\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.60023e6 | + | 168535.i | 0.570075 | + | 0.0266865i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.47491e6 | + | 9.48282e6i | −0.858718 | + | 1.48734i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.79534e6 | − | 4.84167e6i | −0.434306 | − | 0.752240i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.66406e6 | −0.256114 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.72009e6 | 0.414730 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −207540. | − | 359470.i | −0.0313485 | − | 0.0542973i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.55215e6 | + | 6.15250e6i | −0.531564 | + | 0.920695i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.11445e7 | + | 1.04569e6i | 1.65230 | + | 0.155035i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.20686e6 | + | 3.82240e6i | −0.324177 | + | 0.561491i | −0.981345 | − | 0.192253i | \(-0.938421\pi\) |
0.657169 | + | 0.753744i | \(0.271754\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.14983e6 | − | 3.72361e6i | −0.312899 | − | 0.541956i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.31735e6 | 0.189981 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.19038e7 | 1.70105 | 0.850523 | − | 0.525938i | \(-0.176286\pi\) | ||||
0.850523 | + | 0.525938i | \(0.176286\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 187515. | + | 324786.i | 0.0265525 | + | 0.0459903i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.95070e6 | − | 3.37871e6i | 0.273723 | − | 0.474103i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.06694e6 | + | 377631.i | 1.12175 | + | 0.0525116i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −84537.0 | + | 146422.i | −0.0116497 | + | 0.0201779i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.45665e6 | − | 1.11832e7i | −0.881798 | − | 1.52732i | −0.849340 | − | 0.527847i | \(-0.823000\pi\) |
−0.0324587 | − | 0.999473i | \(-0.510334\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.37651e6 | −0.863085 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.04296e7 | 1.39913 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.68492e6 | − | 9.84657e6i | −0.755881 | − | 1.30922i | −0.944935 | − | 0.327257i | \(-0.893876\pi\) |
0.189055 | − | 0.981967i | \(-0.439458\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −118062. | + | 204489.i | −0.0155593 | + | 0.0269494i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −459270. | + | 715931.i | −0.0599944 | + | 0.0935220i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.84898e6 | − | 4.93457e6i | 0.368900 | − | 0.638953i | −0.620494 | − | 0.784211i | \(-0.713068\pi\) |
0.989394 | + | 0.145258i | \(0.0464013\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.52110e6 | − | 6.09873e6i | −0.451948 | − | 0.782797i | 0.546559 | − | 0.837421i | \(-0.315937\pi\) |
−0.998507 | + | 0.0546236i | \(0.982604\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.23077e6 | 0.411073 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.07127e7 | −1.35122 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.29098e6 | + | 2.23605e6i | 0.161429 | + | 0.279603i | 0.935381 | − | 0.353641i | \(-0.115056\pi\) |
−0.773952 | + | 0.633244i | \(0.781723\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −818698. | + | 1.41803e6i | −0.101491 | + | 0.175788i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.74917e6 | + | 9.19355e6i | 0.583684 | + | 1.12991i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.42257e6 | − | 1.63204e7i | 1.14815 | − | 1.98865i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −135837. | − | 235277.i | −0.0164107 | − | 0.0284243i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.69459e6 | −0.562345 | −0.281172 | − | 0.959657i | \(-0.590723\pi\) | ||||
−0.281172 | + | 0.959657i | \(0.590723\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.28100e6 | 0.864774 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.23066e6 | + | 5.59566e6i | 0.380472 | + | 0.658996i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.71175e6 | + | 1.16251e7i | −0.783789 | + | 1.35756i | 0.145931 | + | 0.989295i | \(0.453382\pi\) |
−0.929720 | + | 0.368268i | \(0.879951\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −621180. | − | 1.20249e6i | −0.0719325 | − | 0.139248i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −913932. | + | 1.58298e6i | −0.104949 | + | 0.181777i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.52301e6 | + | 4.36997e6i | 0.287310 | + | 0.497636i | 0.973167 | − | 0.230101i | \(-0.0739056\pi\) |
−0.685856 | + | 0.727737i | \(0.740572\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.06391e7 | −1.20148 | −0.600742 | − | 0.799443i | \(-0.705128\pi\) | ||||
−0.600742 | + | 0.799443i | \(0.705128\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.51834e6 | 0.170050 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 847515. | + | 1.46794e6i | 0.0941367 | + | 0.163050i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 708041. | − | 1.22636e6i | 0.0779986 | − | 0.135098i | −0.824388 | − | 0.566026i | \(-0.808480\pi\) |
0.902386 | + | 0.430928i | \(0.141814\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.12436e6 | − | 3.31155e6i | 0.232105 | − | 0.361816i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −645645. | + | 1.11829e6i | −0.0699666 | + | 0.121186i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.73152e6 | − | 8.19523e6i | −0.508568 | − | 0.880866i | −0.999951 | − | 0.00992215i | \(-0.996842\pi\) |
0.491383 | − | 0.870944i | \(-0.336492\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −262764. | −0.0280142 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.29388e7 | 1.36830 | 0.684148 | − | 0.729343i | \(-0.260174\pi\) | ||||
0.684148 | + | 0.729343i | \(0.260174\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.90188e6 | − | 3.29415e6i | −0.199506 | − | 0.345555i | 0.748862 | − | 0.662726i | \(-0.230600\pi\) |
−0.948368 | + | 0.317171i | \(0.897267\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.26409e6 | − | 2.18946e6i | 0.131537 | − | 0.227829i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.34654e6 | − | 109847.i | −0.242219 | − | 0.0113388i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.71471e6 | + | 8.16612e6i | −0.482786 | + | 0.836210i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.46753e6 | − | 6.00594e6i | −0.352250 | − | 0.610115i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.44794e6 | −0.549042 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.17498e6 | 0.917343 | 0.458671 | − | 0.888606i | \(-0.348326\pi\) | ||||
0.458671 | + | 0.888606i | \(0.348326\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.26941e6 | − | 9.12689e6i | −0.522700 | − | 0.905343i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −951279. | + | 1.64766e6i | −0.0936211 | + | 0.162156i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.43711e6 | − | 7.66198e6i | 0.530909 | − | 0.748157i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.54815e6 | + | 2.68148e6i | −0.149990 | + | 0.259790i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.12269e6 | − | 8.87275e6i | −0.492439 | − | 0.852930i | 0.507523 | − | 0.861638i | \(-0.330561\pi\) |
−0.999962 | + | 0.00870851i | \(0.997228\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.72346e6 | 0.545922 | 0.272961 | − | 0.962025i | \(-0.411997\pi\) | ||||
0.272961 | + | 0.962025i | \(0.411997\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 615978. | 0.0582996 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.99397e6 | − | 8.64981e6i | −0.469013 | − | 0.812355i | 0.530359 | − | 0.847773i | \(-0.322057\pi\) |
−0.999373 | + | 0.0354179i | \(0.988724\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.84115e6 | − | 1.18492e7i | 0.637555 | − | 1.10428i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.33449e6 | + | 343344.i | 0.678293 | + | 0.0317524i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 599439. | − | 1.03826e6i | 0.0550126 | − | 0.0952846i | −0.837208 | − | 0.546885i | \(-0.815813\pi\) |
0.892220 | + | 0.451601i | \(0.149147\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 464490. | + | 804520.i | 0.0423032 | + | 0.0732713i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.71771e6 | 0.516783 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.18065e7 | −1.05903 | −0.529516 | − | 0.848300i | \(-0.677626\pi\) | ||||
−0.529516 | + | 0.848300i | \(0.677626\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.36020e6 | − | 4.08798e6i | −0.210109 | − | 0.363919i | 0.741640 | − | 0.670799i | \(-0.234049\pi\) |
−0.951748 | + | 0.306879i | \(0.900715\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.37697e6 | − | 7.58113e6i | 0.386714 | − | 0.669808i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −485940. | + | 757505.i | −0.0426117 | + | 0.0664250i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.84705e6 | + | 1.01274e7i | −0.508888 | + | 0.881420i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.60858e6 | − | 9.71435e6i | −0.484493 | − | 0.839167i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.08358e6 | −0.264392 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.70826e6 | −0.741129 | −0.370564 | − | 0.928807i | \(-0.620836\pi\) | ||||
−0.370564 | + | 0.928807i | \(0.620836\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.12594e6 | − | 1.95019e6i | −0.0951165 | − | 0.164747i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.55553e6 | + | 4.42630e6i | −0.214293 | + | 0.371167i | −0.953054 | − | 0.302801i | \(-0.902078\pi\) |
0.738760 | + | 0.673968i | \(0.235412\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.42286e6 | − | 1.43693e7i | −0.617870 | − | 1.19609i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.13524e6 | − | 7.16244e6i | 0.341690 | − | 0.591825i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.85989e6 | − | 1.53458e7i | −0.726736 | − | 1.25874i | −0.958256 | − | 0.285913i | \(-0.907703\pi\) |
0.231520 | − | 0.972830i | \(-0.425630\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −403992. | −0.0328962 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.08337e7 | −0.875763 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.90873e6 | − | 1.36983e7i | −0.634686 | − | 1.09931i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.12997e7 | + | 1.95716e7i | −0.900265 | + | 1.55931i | −0.0731160 | + | 0.997323i | \(0.523294\pi\) |
−0.827149 | + | 0.561982i | \(0.810039\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.20979e6 | − | 6.21357e6i | −0.253889 | − | 0.491483i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.09564e6 | − | 1.89771e6i | 0.0860415 | − | 0.149028i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.23342e6 | − | 7.33250e6i | −0.330073 | − | 0.571702i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.27156e6 | 0.640316 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −818148. | −0.0628835 | −0.0314418 | − | 0.999506i | \(-0.510010\pi\) | ||||
−0.0314418 | + | 0.999506i | \(0.510010\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.81128e6 | + | 3.13724e6i | 0.138229 | + | 0.239419i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 62370.0 | − | 108028.i | 0.00472610 | − | 0.00818585i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.53730e6 | − | 1.01906e7i | 0.491869 | − | 0.766749i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.54591e6 | − | 4.40965e6i | 0.190208 | − | 0.329449i | −0.755111 | − | 0.655597i | \(-0.772417\pi\) |
0.945319 | + | 0.326147i | \(0.105751\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.52287e6 | − | 4.36973e6i | −0.187163 | − | 0.324176i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.18241e7 | −1.60773 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.23376e6 | 0.163408 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.81402e6 | + | 4.87403e6i | 0.204423 | + | 0.354071i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −240429. | + | 416435.i | −0.0173446 | + | 0.0300418i | −0.874567 | − | 0.484904i | \(-0.838855\pi\) |
0.857223 | + | 0.514946i | \(0.172188\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.17212e7 | + | 1.01682e6i | 1.55613 | + | 0.0728457i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.64220e6 | − | 9.77258e6i | 0.401423 | − | 0.695286i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.20805e6 | + | 9.02061e6i | 0.367985 | + | 0.637369i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.40783e7 | 0.987905 | 0.493952 | − | 0.869489i | \(-0.335552\pi\) | ||||
0.493952 | + | 0.869489i | \(0.335552\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.92409e6 | + | 1.71890e7i | 0.686906 | + | 1.18976i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.01966e6 | + | 1.76610e6i | −0.0700964 | + | 0.121411i | −0.898943 | − | 0.438065i | \(-0.855664\pi\) |
0.828847 | + | 0.559475i | \(0.188997\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −525231. | + | 740156.i | −0.0358618 | + | 0.0505364i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.24209e6 | + | 1.08116e7i | −0.423312 | + | 0.733199i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.24785e6 | − | 1.42857e7i | −0.555558 | − | 0.962255i | −0.997860 | − | 0.0653888i | \(-0.979171\pi\) |
0.442302 | − | 0.896866i | \(-0.354162\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.82087e6 | −0.389441 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.38121e7 | 1.58243 | 0.791217 | − | 0.611536i | \(-0.209448\pi\) | ||||
0.791217 | + | 0.611536i | \(0.209448\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −504180. | − | 873265.i | −0.0332809 | − | 0.0576442i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.23263e6 | − | 5.59908e6i | 0.211960 | − | 0.367126i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.95881e6 | − | 419381.i | −0.583507 | − | 0.0273152i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 962480. | − | 1.66707e6i | 0.0622719 | − | 0.107858i | −0.833209 | − | 0.552959i | \(-0.813499\pi\) |
0.895481 | + | 0.445101i | \(0.146832\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.80999e6 | + | 1.17953e7i | 0.437683 | + | 0.758089i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 921216. | 0.0588158 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.98092e6 | 0.569615 | 0.284807 | − | 0.958585i | \(-0.408070\pi\) | ||||
0.284807 | + | 0.958585i | \(0.408070\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.03936e7 | + | 1.80022e7i | 0.654879 | + | 1.13428i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.29955e6 | + | 1.26432e7i | −0.456914 | + | 0.791398i | −0.998796 | − | 0.0490566i | \(-0.984379\pi\) |
0.541882 | + | 0.840454i | \(0.317712\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.53691e7 | − | 2.39581e7i | 0.955736 | − | 1.48984i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −422820. | + | 732346.i | −0.0261217 | + | 0.0452442i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.74205e6 | − | 9.94552e6i | −0.352434 | − | 0.610434i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.78381e7 | 1.69755 | 0.848776 | − | 0.528753i | \(-0.177340\pi\) | ||||
0.848776 | + | 0.528753i | \(0.177340\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.39944e7 | 0.847847 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.41429e7 | + | 2.44962e7i | 0.851312 | + | 1.47451i | 0.880025 | + | 0.474927i | \(0.157526\pi\) |
−0.0287135 | + | 0.999588i | \(0.509141\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.71954e6 | + | 1.68347e7i | −0.581288 | + | 1.00682i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.67665e6 | + | 3.24570e6i | 0.0996300 | + | 0.192866i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.81498e6 | + | 4.87569e6i | −0.166200 | + | 0.287867i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.27293e7 | − | 2.20477e7i | −0.746750 | − | 1.29341i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.45819e6 | −0.143288 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.21451e6 | −0.0703439 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4936.00 | + | 8549.40i | 0.000284078 | + | 0.000492038i | 0.866167 | − | 0.499754i | \(-0.166576\pi\) |
−0.865883 | + | 0.500246i | \(0.833243\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.01892e6 | − | 8.69303e6i | 0.287024 | − | 0.497140i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.34156e6 | + | 4.53285e6i | 0.133065 | + | 0.257591i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.29409e6 | + | 2.24142e6i | −0.0730769 | + | 0.126573i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 763992. | + | 1.32327e6i | 0.0428717 | + | 0.0742560i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.08919e7 | −0.607377 | −0.303688 | − | 0.952771i | \(-0.598218\pi\) | ||||
−0.303688 | + | 0.952771i | \(0.598218\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.01940e6 | 0.222738 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 733860. | + | 1.27108e6i | 0.0404140 | + | 0.0699991i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.35061e7 | + | 4.07138e7i | −1.28645 | + | 2.22819i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.45656e6 | − | 2.27055e6i | 0.0792207 | − | 0.123493i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 160515. | − | 278020.i | 0.00867624 | − | 0.0150277i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.61765e6 | + | 4.53390e6i | 0.140618 | + | 0.243557i | 0.927729 | − | 0.373254i | \(-0.121758\pi\) |
−0.787112 | + | 0.616810i | \(0.788425\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.26147e7 | −0.673482 | −0.336741 | − | 0.941597i | \(-0.609325\pi\) | ||||
−0.336741 | + | 0.941597i | \(0.609325\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.63491e6 | −0.139810 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 539292. | + | 934081.i | 0.0284400 | + | 0.0492596i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.59895e6 | − | 1.14297e7i | 0.345875 | − | 0.599074i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.86363e6 | − | 274489.i | −0.305462 | − | 0.0142993i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.67119e6 | − | 1.32869e7i | 0.397196 | − | 0.687964i | −0.596183 | − | 0.802849i | \(-0.703317\pi\) |
0.993379 | + | 0.114885i | \(0.0366500\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.47975e6 | − | 1.29553e7i | −0.384935 | − | 0.666727i | 0.606825 | − | 0.794835i | \(-0.292443\pi\) |
−0.991760 | + | 0.128108i | \(0.959110\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.85155e7 | 0.947109 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.80498e7 | −1.42615 | −0.713076 | − | 0.701087i | \(-0.752699\pi\) | ||||
−0.713076 | + | 0.701087i | \(0.752699\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.36555e6 | − | 1.27575e7i | −0.372236 | − | 0.644732i | 0.617673 | − | 0.786435i | \(-0.288076\pi\) |
−0.989909 | + | 0.141703i | \(0.954742\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.88446e6 | − | 6.72808e6i | 0.195132 | − | 0.337978i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.91163e7 | − | 2.73198e6i | −1.45386 | − | 0.136416i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −651906. | + | 1.12913e6i | −0.0323570 | + | 0.0560440i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.29380e6 | − | 3.97298e6i | −0.113173 | − | 0.196021i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.36347e7 | −1.15916 | −0.579581 | − | 0.814914i | \(-0.696784\pi\) | ||||
−0.579581 | + | 0.814914i | \(0.696784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.14076e6 | −0.445649 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.61997e6 | + | 1.14661e7i | 0.320839 | + | 0.555709i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −176436. | + | 305596.i | −0.00850052 | + | 0.0147233i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.65844e7 | + | 1.71260e6i | 1.75221 | + | 0.0820250i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.09978e6 | + | 5.36898e6i | −0.147592 | + | 0.255637i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.42915e6 | − | 9.40357e6i | −0.256985 | − | 0.445112i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.43965e7 | 0.677459 | 0.338730 | − | 0.940884i | \(-0.390003\pi\) | ||||
0.338730 | + | 0.940884i | \(0.390003\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 562302. | 0.0263060 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.23549e6 | − | 1.08002e7i | −0.290014 | − | 0.502318i | 0.683799 | − | 0.729670i | \(-0.260327\pi\) |
−0.973813 | + | 0.227352i | \(0.926993\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.25294e6 | + | 1.08304e7i | −0.289136 | + | 0.500798i | −0.973604 | − | 0.228245i | \(-0.926701\pi\) |
0.684468 | + | 0.729043i | \(0.260035\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.06558e6 | + | 4.77877e6i | −0.140930 | + | 0.219689i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.40145e7 | − | 2.42738e7i | 0.640545 | − | 1.10946i | −0.344767 | − | 0.938688i | \(-0.612042\pi\) |
0.985311 | − | 0.170767i | \(-0.0546247\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −221940. | − | 384411.i | −0.0100855 | − | 0.0174685i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.44697e7 | −0.653750 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.14871e7 | 1.86365 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.23923e6 | + | 9.07461e6i | 0.234003 | + | 0.405305i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.05254e6 | + | 8.75125e6i | −0.224375 | + | 0.388628i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.21840e6 | − | 4.29442e6i | −0.0979534 | − | 0.189620i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.15586e7 | + | 2.00202e7i | −0.507467 | + | 0.878959i | 0.492496 | + | 0.870315i | \(0.336085\pi\) |
−0.999963 | + | 0.00864370i | \(0.997249\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.25274e6 | + | 5.63392e6i | 0.141997 | + | 0.245945i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.59891e6 | −0.416660 | −0.208330 | − | 0.978059i | \(-0.566803\pi\) | ||||
−0.208330 | + | 0.978059i | \(0.566803\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −443183. | −0.0191285 | −0.00956426 | − | 0.999954i | \(-0.503044\pi\) | ||||
−0.00956426 | + | 0.999954i | \(0.503044\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 554688. | + | 960748.i | 0.0238062 | + | 0.0412336i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.20048e7 | + | 2.07930e7i | −0.512327 | + | 0.887376i | 0.487571 | + | 0.873083i | \(0.337883\pi\) |
−0.999898 | + | 0.0142927i | \(0.995450\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.88670e7 | + | 3.65232e7i | 0.800662 | + | 1.54994i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.18481e6 | + | 3.78421e6i | −0.0921977 | + | 0.159691i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.33634e6 | − | 2.31460e6i | −0.0560772 | − | 0.0971286i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.73620e6 | 0.197639 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.74475e7 | 0.724023 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.06100e7 | + | 1.83771e7i | 0.437841 | + | 0.758362i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.46175e7 | + | 4.26388e7i | −1.01026 | + | 1.74982i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.18641e6 | − | 1.12025e7i | 0.293287 | − | 0.457189i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.43322e6 | + | 2.48240e6i | −0.0581689 | + | 0.100751i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.79269e6 | + | 1.52294e7i | 0.354898 | + | 0.614701i | 0.987100 | − | 0.160102i | \(-0.0511823\pi\) |
−0.632203 | + | 0.774803i | \(0.717849\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.56459e6 | −0.303652 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.95599e7 | 1.18007 | 0.590033 | − | 0.807379i | \(-0.299115\pi\) | ||||
0.590033 | + | 0.807379i | \(0.299115\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.65794e7 | + | 4.60369e7i | 1.05528 | + | 1.82780i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 125010. | − | 216524.i | 0.00493619 | − | 0.00854973i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.00505e7 | + | 938607.i | 0.787411 | + | 0.0368604i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.95741e6 | + | 3.39033e6i | −0.0764528 | + | 0.132420i | −0.901717 | − | 0.432327i | \(-0.857693\pi\) |
0.825264 | + | 0.564747i | \(0.191026\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 90562.5 | + | 156859.i | 0.00351803 | + | 0.00609340i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.13683e7 | −0.825594 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.67166e6 | −0.371661 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.79311e6 | − | 1.17660e7i | −0.259638 | − | 0.449707i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.61004e6 | − | 2.78868e6i | 0.0612066 | − | 0.106013i | −0.833798 | − | 0.552069i | \(-0.813838\pi\) |
0.895005 | + | 0.446056i | \(0.147172\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.10710e6 | + | 1.76751e7i | 0.306543 | + | 0.668326i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.84601e6 | − | 1.35897e7i | 0.295083 | − | 0.511099i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.47652e6 | − | 6.02151e6i | −0.130052 | − | 0.225256i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.16504e7 | −1.92187 | −0.960936 | − | 0.276772i | \(-0.910735\pi\) | ||||
−0.960936 | + | 0.276772i | \(0.910735\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.62769e7 | −0.602431 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.64349e6 | + | 6.31071e6i | 0.134135 | + | 0.232329i | 0.925267 | − | 0.379317i | \(-0.123841\pi\) |
−0.791131 | + | 0.611646i | \(0.790508\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.43764e6 | − | 1.46144e7i | 0.308988 | − | 0.535183i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 566433. | + | 26516.0i | 0.0206333 | + | 0.000965891i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.56224e7 | + | 2.70588e7i | −0.566073 | + | 0.980467i | 0.430876 | + | 0.902411i | \(0.358205\pi\) |
−0.996949 | + | 0.0780561i | \(0.975129\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.97296e7 | + | 3.41727e7i | 0.711137 | + | 1.23173i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.21197e6 | −0.330294 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.68273e7 | −0.956853 | −0.478426 | − | 0.878128i | \(-0.658793\pi\) | ||||
−0.478426 | + | 0.878128i | \(0.658793\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.07692e6 | − | 1.86528e6i | −0.0382099 | − | 0.0661815i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.01059e7 | − | 1.75039e7i | 0.356693 | − | 0.617810i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.71324e6 | + | 7.34721e6i | −0.165490 | + | 0.257974i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.48635e6 | + | 9.50264e6i | −0.191635 | + | 0.331922i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.80179e6 | + | 4.85284e6i | 0.0973576 | + | 0.168628i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.09160e6 | 0.0377350 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.00257e7 | 0.344784 | 0.172392 | − | 0.985028i | \(-0.444850\pi\) | ||||
0.172392 | + | 0.985028i | \(0.444850\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.05931e6 | + | 1.56912e7i | 0.309946 | + | 0.536842i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57900.0 | − | 100286.i | 0.00197075 | − | 0.00341343i | −0.865038 | − | 0.501706i | \(-0.832706\pi\) |
0.867009 | + | 0.498292i | \(0.166039\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.17303e7 | − | 4.20660e7i | −0.735840 | − | 1.42446i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.77038e6 | − | 1.34587e7i | 0.261777 | − | 0.453410i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.36905e6 | − | 7.56741e6i | −0.146437 | − | 0.253636i | 0.783471 | − | 0.621428i | \(-0.213447\pi\) |
−0.929908 | + | 0.367792i | \(0.880114\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.20679e7 | −0.402416 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.77843e7 | −0.590016 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.19206e7 | + | 2.06471e7i | 0.393473 | + | 0.681516i | 0.992905 | − | 0.118910i | \(-0.0379400\pi\) |
−0.599432 | + | 0.800426i | \(0.704607\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.15377e6 | − | 3.73044e6i | 0.0707309 | − | 0.122510i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.23700e6 | − | 2.39462e6i | −0.0404183 | − | 0.0782427i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.97797e7 | + | 3.42595e7i | −0.643028 | + | 1.11376i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.66860e7 | − | 2.89009e7i | −0.539718 | − | 0.934819i | −0.998919 | − | 0.0464869i | \(-0.985197\pi\) |
0.459201 | − | 0.888333i | \(-0.348136\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.06780e6 | −0.291829 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.21858e6 | 0.0390207 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.72343e7 | − | 4.71712e7i | −0.867718 | − | 1.50293i | −0.864322 | − | 0.502938i | \(-0.832252\pi\) |
−0.00339592 | − | 0.999994i | \(-0.501081\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.14125e6 | − | 1.97670e6i | 0.0361799 | − | 0.0626654i |
(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 | 336.6.q.c.289.1 | 2 | ||
4.3 | odd | 2 | 42.6.e.a.37.1 | yes | 2 | ||
7.4 | even | 3 | inner | 336.6.q.c.193.1 | 2 | ||
12.11 | even | 2 | 126.6.g.c.37.1 | 2 | |||
28.3 | even | 6 | 294.6.e.e.67.1 | 2 | |||
28.11 | odd | 6 | 42.6.e.a.25.1 | ✓ | 2 | ||
28.19 | even | 6 | 294.6.a.j.1.1 | 1 | |||
28.23 | odd | 6 | 294.6.a.l.1.1 | 1 | |||
28.27 | even | 2 | 294.6.e.e.79.1 | 2 | |||
84.11 | even | 6 | 126.6.g.c.109.1 | 2 | |||
84.23 | even | 6 | 882.6.a.f.1.1 | 1 | |||
84.47 | odd | 6 | 882.6.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.6.e.a.25.1 | ✓ | 2 | 28.11 | odd | 6 | ||
42.6.e.a.37.1 | yes | 2 | 4.3 | odd | 2 | ||
126.6.g.c.37.1 | 2 | 12.11 | even | 2 | |||
126.6.g.c.109.1 | 2 | 84.11 | even | 6 | |||
294.6.a.j.1.1 | 1 | 28.19 | even | 6 | |||
294.6.a.l.1.1 | 1 | 28.23 | odd | 6 | |||
294.6.e.e.67.1 | 2 | 28.3 | even | 6 | |||
294.6.e.e.79.1 | 2 | 28.27 | even | 2 | |||
336.6.q.c.193.1 | 2 | 7.4 | even | 3 | inner | ||
336.6.q.c.289.1 | 2 | 1.1 | even | 1 | trivial | ||
882.6.a.e.1.1 | 1 | 84.47 | odd | 6 | |||
882.6.a.f.1.1 | 1 | 84.23 | even | 6 |