Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(289,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.bw (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: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 560.289 |
Dual form | 560.2.bw.d.529.1 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.133975 | − | 2.23205i | 0.0599153 | − | 0.998203i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | − | 2.00000i | 0.654654 | − | 0.755929i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.50000 | + | 2.59808i | −0.500000 | + | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | + | 2.59808i | 0.452267 | + | 0.783349i | 0.998526 | − | 0.0542666i | \(-0.0172821\pi\) |
−0.546259 | + | 0.837616i | \(0.683949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.00000i | − | 1.38675i | −0.720577 | − | 0.693375i | \(-0.756123\pi\) | ||
0.720577 | − | 0.693375i | \(-0.243877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.73205 | − | 1.00000i | 0.420084 | − | 0.242536i | −0.275029 | − | 0.961436i | \(-0.588688\pi\) |
0.695113 | + | 0.718900i | \(0.255354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.50000 | − | 4.33013i | 0.573539 | − | 0.993399i | −0.422659 | − | 0.906289i | \(-0.638903\pi\) |
0.996199 | − | 0.0871106i | \(-0.0277634\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.06218 | − | 3.50000i | −1.26405 | − | 0.729800i | −0.290196 | − | 0.956967i | \(-0.593720\pi\) |
−0.973856 | + | 0.227167i | \(0.927054\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96410 | − | 0.598076i | −0.992820 | − | 0.119615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00000 | 0.742781 | 0.371391 | − | 0.928477i | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | − | 1.73205i | −0.179605 | − | 0.311086i | 0.762140 | − | 0.647412i | \(-0.224149\pi\) |
−0.941745 | + | 0.336327i | \(0.890815\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.23205 | − | 4.13397i | −0.715347 | − | 0.698769i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.866025 | + | 0.500000i | 0.142374 | + | 0.0821995i | 0.569495 | − | 0.821995i | \(-0.307139\pi\) |
−0.427121 | + | 0.904194i | \(0.640472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00000 | 0.468521 | 0.234261 | − | 0.972174i | \(-0.424733\pi\) | ||||
0.234261 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.00000i | − | 0.304997i | −0.988304 | − | 0.152499i | \(-0.951268\pi\) | ||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.59808 | + | 3.69615i | 0.834512 | + | 0.550990i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.06218 | + | 3.50000i | 0.884260 | + | 0.510527i | 0.872060 | − | 0.489398i | \(-0.162783\pi\) |
0.0121990 | + | 0.999926i | \(0.496117\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.79423 | − | 4.50000i | 1.07062 | − | 0.618123i | 0.142269 | − | 0.989828i | \(-0.454560\pi\) |
0.928351 | + | 0.371706i | \(0.121227\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00000 | − | 3.00000i | 0.809040 | − | 0.404520i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.00000 | + | 3.46410i | 0.260378 | + | 0.450988i | 0.966342 | − | 0.257260i | \(-0.0828195\pi\) |
−0.705965 | + | 0.708247i | \(0.749486\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | + | 5.19615i | −0.384111 | + | 0.665299i | −0.991645 | − | 0.128994i | \(-0.958825\pi\) |
0.607535 | + | 0.794293i | \(0.292159\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.59808 | + | 7.50000i | 0.327327 | + | 0.944911i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.1603 | − | 0.669873i | −1.38426 | − | 0.0830875i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.73205 | − | 1.00000i | 0.211604 | − | 0.122169i | −0.390453 | − | 0.920623i | \(-0.627682\pi\) |
0.602056 | + | 0.798454i | \(0.294348\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.8564 | + | 8.00000i | −1.62177 | + | 0.936329i | −0.635323 | + | 0.772246i | \(0.719133\pi\) |
−0.986447 | + | 0.164083i | \(0.947534\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.79423 | + | 1.50000i | 0.888235 | + | 0.170941i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.00000 | + | 12.1244i | −0.787562 | + | 1.36410i | 0.139895 | + | 0.990166i | \(0.455323\pi\) |
−0.927457 | + | 0.373930i | \(0.878010\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | − | 4.00000i | −0.216930 | − | 0.433861i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.00000 | − | 1.73205i | 0.106000 | − | 0.183597i | −0.808146 | − | 0.588982i | \(-0.799529\pi\) |
0.914146 | + | 0.405385i | \(0.132862\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0000 | − | 8.66025i | −1.04828 | − | 0.907841i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.33013 | − | 6.16025i | −0.957251 | − | 0.632029i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0000i | 1.21842i | 0.793011 | + | 0.609208i | \(0.208512\pi\) | ||||
−0.793011 | + | 0.609208i | \(0.791488\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.00000 | −0.904534 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.92820 | − | 4.00000i | −0.682656 | − | 0.394132i | 0.118199 | − | 0.992990i | \(-0.462288\pi\) |
−0.800855 | + | 0.598858i | \(0.795621\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.8564 | + | 8.00000i | 1.33955 | + | 0.773389i | 0.986740 | − | 0.162306i | \(-0.0518932\pi\) |
0.352809 | + | 0.935695i | \(0.385227\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | + | 1.73205i | 0.0957826 | + | 0.165900i | 0.909935 | − | 0.414751i | \(-0.136131\pi\) |
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0000i | 1.31701i | 0.752577 | + | 0.658505i | \(0.228811\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.62436 | + | 13.0622i | −0.804225 | + | 1.21805i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.9904 | + | 7.50000i | 1.20096 | + | 0.693375i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.00000 | − | 5.19615i | 0.0916698 | − | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.00000 | + | 11.0000i | −0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.00000i | 0.621150i | 0.950549 | + | 0.310575i | \(0.100522\pi\) | ||||
−0.950549 | + | 0.310575i | \(0.899478\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.500000 | + | 0.866025i | −0.0436852 | + | 0.0756650i | −0.887041 | − | 0.461690i | \(-0.847243\pi\) |
0.843356 | + | 0.537355i | \(0.180577\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.33013 | − | 12.5000i | −0.375470 | − | 1.08389i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.92820 | − | 4.00000i | 0.591916 | − | 0.341743i | −0.173939 | − | 0.984757i | \(-0.555649\pi\) |
0.765855 | + | 0.643013i | \(0.222316\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.0000 | 1.35710 | 0.678551 | − | 0.734553i | \(-0.262608\pi\) | ||||
0.678551 | + | 0.734553i | \(0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.9904 | − | 7.50000i | 1.08631 | − | 0.627182i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.535898 | − | 8.92820i | 0.0445039 | − | 0.741447i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.00000 | + | 15.5885i | −0.737309 | + | 1.27706i | 0.216394 | + | 0.976306i | \(0.430570\pi\) |
−0.953703 | + | 0.300750i | \(0.902763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.00000 | − | 5.19615i | −0.244137 | − | 0.422857i | 0.717752 | − | 0.696299i | \(-0.245171\pi\) |
−0.961888 | + | 0.273442i | \(0.911838\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.00000i | 0.485071i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | + | 2.00000i | −0.321288 | + | 0.160644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.79423 | − | 4.50000i | 0.622047 | − | 0.359139i | −0.155618 | − | 0.987817i | \(-0.549737\pi\) |
0.777666 | + | 0.628678i | \(0.216404\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.5000 | + | 6.06218i | −1.37919 | + | 0.477767i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.3923 | − | 6.00000i | −0.813988 | − | 0.469956i | 0.0343508 | − | 0.999410i | \(-0.489064\pi\) |
−0.848339 | + | 0.529454i | \(0.822397\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.0000i | 1.16073i | 0.814355 | + | 0.580367i | \(0.197091\pi\) | ||||
−0.814355 | + | 0.580367i | \(0.802909\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.50000 | + | 12.9904i | 0.573539 | + | 0.993399i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.79423 | − | 4.50000i | −0.592584 | − | 0.342129i | 0.173534 | − | 0.984828i | \(-0.444481\pi\) |
−0.766119 | + | 0.642699i | \(0.777815\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.79423 | + | 8.89230i | −0.740374 | + | 0.672195i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.50000 | − | 11.2583i | −0.485833 | − | 0.841487i | 0.514035 | − | 0.857769i | \(-0.328150\pi\) |
−0.999867 | + | 0.0162823i | \(0.994817\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 26.0000 | 1.93256 | 0.966282 | − | 0.257485i | \(-0.0828937\pi\) | ||||
0.966282 | + | 0.257485i | \(0.0828937\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.23205 | − | 1.86603i | 0.0905822 | − | 0.137193i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.19615 | + | 3.00000i | 0.379980 | + | 0.219382i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.0000 | + | 17.3205i | −0.723575 | + | 1.25327i | 0.235983 | + | 0.971757i | \(0.424169\pi\) |
−0.959558 | + | 0.281511i | \(0.909164\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.66025 | + | 5.00000i | −0.623379 | + | 0.359908i | −0.778183 | − | 0.628037i | \(-0.783859\pi\) |
0.154805 | + | 0.987945i | \(0.450525\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.00000i | 0.356235i | 0.984009 | + | 0.178118i | \(0.0570008\pi\) | ||||
−0.984009 | + | 0.178118i | \(0.942999\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.00000 | − | 15.5885i | −0.637993 | − | 1.10504i | −0.985873 | − | 0.167497i | \(-0.946431\pi\) |
0.347879 | − | 0.937539i | \(-0.386902\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.92820 | − | 8.00000i | 0.486265 | − | 0.561490i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.401924 | − | 6.69615i | 0.0280716 | − | 0.467680i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.1865 | − | 10.5000i | 1.26405 | − | 0.729800i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.0000 | 1.03757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.00000 | 0.619586 | 0.309793 | − | 0.950804i | \(-0.399740\pi\) | ||||
0.309793 | + | 0.950804i | \(0.399740\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.46410 | − | 0.267949i | −0.304449 | − | 0.0182740i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.19615 | − | 1.00000i | −0.352738 | − | 0.0678844i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.00000 | − | 8.66025i | −0.336336 | − | 0.582552i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000i | 0.535720i | 0.963458 | + | 0.267860i | \(0.0863164\pi\) | ||||
−0.963458 | + | 0.267860i | \(0.913684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.00000 | − | 12.0000i | 0.600000 | − | 0.800000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.19615 | + | 3.00000i | −0.344881 | + | 0.199117i | −0.662428 | − | 0.749125i | \(-0.730474\pi\) |
0.317547 | + | 0.948242i | \(0.397141\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.00000 | − | 13.8564i | 0.528655 | − | 0.915657i | −0.470787 | − | 0.882247i | \(-0.656030\pi\) |
0.999442 | − | 0.0334101i | \(-0.0106368\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.92820 | + | 4.00000i | 0.453882 | + | 0.262049i | 0.709468 | − | 0.704737i | \(-0.248935\pi\) |
−0.255586 | + | 0.966786i | \(0.582269\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.62436 | − | 13.0622i | 0.562591 | − | 0.852083i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.0000 | 1.29369 | 0.646846 | − | 0.762620i | \(-0.276088\pi\) | ||||
0.646846 | + | 0.762620i | \(0.276088\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.50000 | + | 7.79423i | 0.289870 | + | 0.502070i | 0.973779 | − | 0.227498i | \(-0.0730544\pi\) |
−0.683908 | + | 0.729568i | \(0.739721\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.5981 | + | 1.30385i | −0.996525 | + | 0.0832998i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.6506 | − | 12.5000i | −1.37760 | − | 0.795356i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.00000 | −0.315597 | −0.157799 | − | 0.987471i | \(-0.550440\pi\) | ||||
−0.157799 | + | 0.987471i | \(0.550440\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 21.0000i | − | 1.32026i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.19615 | − | 3.00000i | −0.324127 | − | 0.187135i | 0.329104 | − | 0.944294i | \(-0.393253\pi\) |
−0.653231 | + | 0.757159i | \(0.726587\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.50000 | − | 0.866025i | 0.155342 | − | 0.0538122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | + | 10.3923i | −0.371391 | + | 0.643268i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.00000 | − | 18.0000i | −0.552866 | − | 1.10573i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.00000 | − | 8.66025i | −0.304855 | − | 0.528025i | 0.672374 | − | 0.740212i | \(-0.265275\pi\) |
−0.977229 | + | 0.212187i | \(0.931941\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | − | 20.7846i | 0.728948 | − | 1.26258i | −0.228380 | − | 0.973572i | \(-0.573343\pi\) |
0.957328 | − | 0.289003i | \(-0.0933238\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.89230 | − | 13.7942i | −0.355319 | − | 0.831823i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.73205 | − | 1.00000i | 0.104069 | − | 0.0600842i | −0.447062 | − | 0.894503i | \(-0.647530\pi\) |
0.551131 | + | 0.834419i | \(0.314196\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.00000 | 0.536895 | 0.268447 | − | 0.963294i | \(-0.413489\pi\) | ||||
0.268447 | + | 0.963294i | \(0.413489\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.1244 | + | 7.00000i | −0.720718 | + | 0.416107i | −0.815017 | − | 0.579437i | \(-0.803272\pi\) |
0.0942988 | + | 0.995544i | \(0.469939\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.19615 | − | 6.00000i | 0.306719 | − | 0.354169i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.50000 | + | 11.2583i | −0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 9.00000i | − | 0.525786i | −0.964825 | − | 0.262893i | \(-0.915323\pi\) | ||
0.964825 | − | 0.262893i | \(-0.0846766\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | − | 4.00000i | 0.465778 | − | 0.232889i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.5000 | + | 30.3109i | −1.01205 | + | 1.75292i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00000 | − | 3.46410i | −0.230556 | − | 0.199667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.1962 | + | 7.39230i | 0.641090 | + | 0.423282i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 22.0000i | − | 1.25561i | −0.778372 | − | 0.627803i | \(-0.783954\pi\) | ||
0.778372 | − | 0.627803i | \(-0.216046\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.00000 | + | 5.19615i | 0.170114 | + | 0.294647i | 0.938460 | − | 0.345389i | \(-0.112253\pi\) |
−0.768345 | + | 0.640036i | \(0.778920\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.0526 | + | 11.0000i | 1.07691 | + | 0.621757i | 0.930062 | − | 0.367402i | \(-0.119753\pi\) |
0.146852 | + | 0.989158i | \(0.453086\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 17.0885 | − | 4.79423i | 0.962825 | − | 0.270124i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.73205 | − | 1.00000i | −0.0972817 | − | 0.0561656i | 0.450570 | − | 0.892741i | \(-0.351221\pi\) |
−0.547852 | + | 0.836576i | \(0.684554\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.00000 | + | 10.3923i | 0.335936 | + | 0.581857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 10.0000i | − | 0.556415i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.99038 | + | 24.8205i | −0.165876 | + | 1.37679i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.5000 | − | 6.06218i | 0.964806 | − | 0.334219i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.50000 | − | 4.33013i | 0.137412 | − | 0.238005i | −0.789104 | − | 0.614260i | \(-0.789455\pi\) |
0.926516 | + | 0.376254i | \(0.122788\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.59808 | + | 1.50000i | −0.142374 | + | 0.0821995i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.00000 | − | 4.00000i | −0.109272 | − | 0.218543i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 10.0000i | − | 0.544735i | −0.962193 | − | 0.272367i | \(-0.912193\pi\) | ||
0.962193 | − | 0.272367i | \(-0.0878066\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.00000 | − | 5.19615i | 0.162459 | − | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.3923 | + | 6.00000i | −0.557888 | + | 0.322097i | −0.752297 | − | 0.658824i | \(-0.771054\pi\) |
0.194409 | + | 0.980921i | \(0.437721\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.0000 | 0.642345 | 0.321173 | − | 0.947021i | \(-0.395923\pi\) | ||||
0.321173 | + | 0.947021i | \(0.395923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.7846 | − | 12.0000i | 1.10625 | − | 0.638696i | 0.168397 | − | 0.985719i | \(-0.446141\pi\) |
0.937856 | + | 0.347024i | \(0.112808\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.803848 | − | 13.3923i | 0.0426638 | − | 0.710790i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.00000 | + | 13.8564i | −0.422224 | + | 0.731313i | −0.996157 | − | 0.0875892i | \(-0.972084\pi\) |
0.573933 | + | 0.818902i | \(0.305417\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.0000 | + | 32.0000i | 0.837478 | + | 1.67496i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.2583 | − | 6.50000i | 0.587680 | − | 0.339297i | −0.176500 | − | 0.984301i | \(-0.556477\pi\) |
0.764180 | + | 0.645003i | \(0.223144\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.50000 | + | 7.79423i | −0.234261 | + | 0.405751i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.50000 | − | 23.3827i | 0.233628 | − | 1.21397i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.5167 | − | 13.0000i | −1.16587 | − | 0.673114i | −0.213165 | − | 0.977016i | \(-0.568377\pi\) |
−0.952703 | + | 0.303902i | \(0.901711\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 20.0000i | − | 1.03005i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.0000 | −1.48963 | −0.744815 | − | 0.667271i | \(-0.767462\pi\) | ||||
−0.744815 | + | 0.667271i | \(0.767462\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.1865 | + | 10.5000i | 0.929288 | + | 0.536525i | 0.886586 | − | 0.462563i | \(-0.153070\pi\) |
0.0427020 | + | 0.999088i | \(0.486403\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.39230 | − | 17.1962i | 0.223853 | − | 0.876397i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.19615 | + | 3.00000i | 0.264135 | + | 0.152499i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.00000 | − | 5.19615i | −0.152106 | − | 0.263455i | 0.779895 | − | 0.625910i | \(-0.215272\pi\) |
−0.932002 | + | 0.362454i | \(0.881939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.0000 | −0.708010 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 26.1244 | + | 17.2487i | 1.31446 | + | 0.867877i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.1244 | − | 7.00000i | −0.608504 | − | 0.351320i | 0.163876 | − | 0.986481i | \(-0.447600\pi\) |
−0.772380 | + | 0.635161i | \(0.780934\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.50000 | − | 12.9904i | 0.374532 | − | 0.648709i | −0.615725 | − | 0.787961i | \(-0.711137\pi\) |
0.990257 | + | 0.139253i | \(0.0444700\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.66025 | + | 5.00000i | −0.431398 | + | 0.249068i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.0000 | + | 9.00000i | −0.894427 | + | 0.447214i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.00000i | 0.148704i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.00000 | − | 12.1244i | −0.346128 | − | 0.599511i | 0.639430 | − | 0.768849i | \(-0.279170\pi\) |
−0.985558 | + | 0.169338i | \(0.945837\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.3923 | + | 2.00000i | 0.511372 | + | 0.0984136i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.3923 | + | 0.803848i | 0.657402 | + | 0.0394593i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 35.0000 | 1.70986 | 0.854931 | − | 0.518742i | \(-0.173599\pi\) | ||||
0.854931 | + | 0.518742i | \(0.173599\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0000 | −0.974740 | −0.487370 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487370 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −18.1865 | + | 10.5000i | −0.884260 | + | 0.510527i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.19615 | + | 3.92820i | −0.446079 | + | 0.190546i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.19615 | + | 15.0000i | 0.251459 | + | 0.725901i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.00000 | + | 1.73205i | 0.0481683 | + | 0.0834300i | 0.889104 | − | 0.457705i | \(-0.151328\pi\) |
−0.840936 | + | 0.541135i | \(0.817995\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.0000i | 1.34559i | 0.739827 | + | 0.672797i | \(0.234907\pi\) | ||||
−0.739827 | + | 0.672797i | \(0.765093\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −30.3109 | + | 17.5000i | −1.44997 | + | 0.837139i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0000 | − | 24.2487i | 0.668184 | − | 1.15733i | −0.310228 | − | 0.950662i | \(-0.600405\pi\) |
0.978412 | − | 0.206666i | \(-0.0662612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.5000 | + | 7.79423i | 0.928571 | + | 0.371154i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.9808 | + | 15.0000i | 1.23438 | + | 0.712672i | 0.967941 | − | 0.251179i | \(-0.0808184\pi\) |
0.266443 | + | 0.963851i | \(0.414152\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.73205 | − | 2.46410i | −0.176916 | − | 0.116810i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.00000 | −0.235965 | −0.117982 | − | 0.993016i | \(-0.537643\pi\) | ||||
−0.117982 | + | 0.993016i | \(0.537643\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.50000 | + | 7.79423i | 0.211897 | + | 0.367016i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.6699 | + | 21.1603i | −0.969019 | + | 0.992008i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.66025 | − | 5.00000i | −0.405110 | − | 0.233890i | 0.283577 | − | 0.958950i | \(-0.408479\pi\) |
−0.688686 | + | 0.725059i | \(0.741812\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.0000 | −1.49039 | −0.745194 | − | 0.666847i | \(-0.767643\pi\) | ||||
−0.745194 | + | 0.666847i | \(0.767643\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.0000i | 0.790057i | 0.918669 | + | 0.395029i | \(0.129265\pi\) | ||||
−0.918669 | + | 0.395029i | \(0.870735\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.4449 | − | 17.0000i | −1.36255 | − | 0.786666i | −0.372584 | − | 0.927999i | \(-0.621528\pi\) |
−0.989962 | + | 0.141332i | \(0.954861\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.00000 | − | 5.19615i | 0.0461757 | − | 0.239936i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.19615 | − | 3.00000i | 0.238919 | − | 0.137940i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.0000 | + | 20.0000i | −0.688247 | + | 0.917663i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 27.0000i | 1.23625i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.0000 | − | 31.1769i | −0.822441 | − | 1.42451i | −0.903859 | − | 0.427830i | \(-0.859278\pi\) |
0.0814184 | − | 0.996680i | \(-0.474055\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.50000 | − | 4.33013i | 0.113990 | − | 0.197437i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.7846 | + | 1.60770i | 1.21623 | + | 0.0730017i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.7128 | + | 16.0000i | −1.25579 | + | 0.725029i | −0.972253 | − | 0.233933i | \(-0.924840\pi\) |
−0.283535 | + | 0.958962i | \(0.591507\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.0000 | −1.08310 | −0.541552 | − | 0.840667i | \(-0.682163\pi\) | ||||
−0.541552 | + | 0.840667i | \(0.682163\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.92820 | − | 4.00000i | 0.312031 | − | 0.180151i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.20577 | + | 20.0885i | −0.0541954 | + | 0.902909i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.3923 | − | 12.0000i | 0.466159 | − | 0.538274i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.00000 | + | 3.46410i | −0.0895323 | + | 0.155074i | −0.907314 | − | 0.420455i | \(-0.861871\pi\) |
0.817781 | + | 0.575529i | \(0.195204\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 40.0000i | − | 1.78351i | −0.452517 | − | 0.891756i | \(-0.649474\pi\) | ||
0.452517 | − | 0.891756i | \(-0.350526\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.0000 | + | 29.4449i | −0.753512 | + | 1.30512i | 0.192599 | + | 0.981278i | \(0.438308\pi\) |
−0.946111 | + | 0.323843i | \(0.895025\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.00000 | + | 41.5692i | −0.353899 | + | 1.83891i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.85641 | + | 14.9282i | −0.434325 | + | 0.657815i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.0000i | 0.923579i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.5000 | + | 23.3827i | 0.591446 | + | 1.02441i | 0.994038 | + | 0.109035i | \(0.0347759\pi\) |
−0.402592 | + | 0.915379i | \(0.631891\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.8564 | + | 8.00000i | 0.605898 | + | 0.349816i | 0.771358 | − | 0.636401i | \(-0.219578\pi\) |
−0.165460 | + | 0.986216i | \(0.552911\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.46410 | − | 2.00000i | −0.150899 | − | 0.0871214i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | + | 22.5167i | 0.565217 | + | 0.978985i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.0000 | −0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 15.0000i | − | 0.649722i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.7128 | − | 29.8564i | 0.852259 | − | 1.29081i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.5000 | − | 12.9904i | 0.710705 | − | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | − | 13.8564i | 0.343947 | − | 0.595733i | −0.641215 | − | 0.767361i | \(-0.721569\pi\) |
0.985162 | + | 0.171628i | \(0.0549027\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.00000 | − | 2.00000i | 0.171341 | − | 0.0856706i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 26.0000i | − | 1.11168i | −0.831289 | − | 0.555840i | \(-0.812397\pi\) | ||
0.831289 | − | 0.555840i | \(-0.187603\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.00000 | − | 15.5885i | −0.384111 | − | 0.665299i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.0000 | − | 17.3205i | 0.426014 | − | 0.737878i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.1244 | + | 35.0000i | 0.515580 | + | 1.48835i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.9186 | + | 11.5000i | −0.843978 | + | 0.487271i | −0.858614 | − | 0.512622i | \(-0.828674\pi\) |
0.0146368 | + | 0.999893i | \(0.495341\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.0000 | −0.422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.73205 | + | 1.00000i | −0.0729972 | + | 0.0421450i | −0.536054 | − | 0.844183i | \(-0.680086\pi\) |
0.463057 | + | 0.886328i | \(0.346752\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.2487 | + | 1.87564i | 1.31464 | + | 0.0789090i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.3827 | − | 4.50000i | −0.981981 | − | 0.188982i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.50000 | + | 12.9904i | −0.314416 | + | 0.544585i | −0.979313 | − | 0.202350i | \(-0.935142\pi\) |
0.664897 | + | 0.746935i | \(0.268475\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.0000 | + | 27.7128i | 0.669579 | + | 1.15975i | 0.978022 | + | 0.208502i | \(0.0668588\pi\) |
−0.308443 | + | 0.951243i | \(0.599808\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.0000 | + | 21.0000i | 1.16768 | + | 0.875761i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.46410 | − | 2.00000i | 0.144212 | − | 0.0832611i | −0.426158 | − | 0.904649i | \(-0.640133\pi\) |
0.570370 | + | 0.821388i | \(0.306800\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | + | 10.3923i | 0.497844 | + | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.3827 | + | 13.5000i | 0.968412 | + | 0.559113i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.4808 | − | 27.9904i | 0.764085 | − | 1.15726i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.0000i | 1.40333i | 0.712507 | + | 0.701665i | \(0.247560\pi\) | ||||
−0.712507 | + | 0.701665i | \(0.752440\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.0000 | −0.412043 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.19615 | + | 3.00000i | 0.213380 | + | 0.123195i | 0.602881 | − | 0.797831i | \(-0.294019\pi\) |
−0.389501 | + | 0.921026i | \(0.627353\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.4641 | − | 2.92820i | −0.469982 | − | 0.120045i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.00000 | + | 10.3923i | 0.245153 | + | 0.424618i | 0.962175 | − | 0.272433i | \(-0.0878284\pi\) |
−0.717021 | + | 0.697051i | \(0.754495\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.00000i | 0.244339i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.73205 | − | 2.46410i | −0.151729 | − | 0.100180i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.2583 | + | 6.50000i | 0.456962 | + | 0.263827i | 0.710766 | − | 0.703429i | \(-0.248349\pi\) |
−0.253804 | + | 0.967256i | \(0.581682\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.5000 | − | 30.3109i | 0.707974 | − | 1.22625i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.9904 | + | 7.50000i | −0.524677 | + | 0.302922i | −0.738846 | − | 0.673874i | \(-0.764629\pi\) |
0.214169 | + | 0.976797i | \(0.431296\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 14.0000i | − | 0.563619i | −0.959470 | − | 0.281809i | \(-0.909065\pi\) | ||
0.959470 | − | 0.281809i | \(-0.0909346\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.50000 | − | 16.4545i | −0.381837 | − | 0.661361i | 0.609488 | − | 0.792796i | \(-0.291375\pi\) |
−0.991325 | + | 0.131434i | \(0.958042\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.73205 | − | 5.00000i | −0.0693932 | − | 0.200321i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.2846 | + | 5.93782i | 0.971384 | + | 0.237513i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.00000 | 0.0797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.0000 | 0.716569 | 0.358284 | − | 0.933613i | \(-0.383362\pi\) | ||||
0.358284 | + | 0.933613i | \(0.383362\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.6244 | + | 0.937822i | 0.620034 | + | 0.0372163i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −34.6410 | + | 5.00000i | −1.37253 | + | 0.198107i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.00000 | + | 15.5885i | −0.356034 | + | 0.616670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.50000 | + | 4.33013i | 0.0987441 | + | 0.171030i | 0.911165 | − | 0.412042i | \(-0.135184\pi\) |
−0.812421 | + | 0.583071i | \(0.801851\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.0000i | 0.552106i | 0.961142 | + | 0.276053i | \(0.0890266\pi\) | ||||
−0.961142 | + | 0.276053i | \(0.910973\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.3827 | + | 13.5000i | −0.919268 | + | 0.530740i | −0.883402 | − | 0.468617i | \(-0.844753\pi\) |
−0.0358667 | + | 0.999357i | \(0.511419\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.00000 | + | 10.3923i | −0.235521 | + | 0.407934i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.59808 | − | 1.50000i | −0.101671 | − | 0.0586995i | 0.448303 | − | 0.893882i | \(-0.352029\pi\) |
−0.549973 | + | 0.835182i | \(0.685362\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.86603 | + | 1.23205i | 0.0729116 | + | 0.0481402i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 48.0000i | − | 1.87266i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.00000 | − | 13.8564i | −0.311164 | − | 0.538952i | 0.667451 | − | 0.744654i | \(-0.267385\pi\) |
−0.978615 | + | 0.205702i | \(0.934052\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −28.4808 | + | 7.99038i | −1.10444 | + | 0.309854i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.2487 | − | 14.0000i | −0.938914 | − | 0.542082i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.0000 | −0.694882 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.0000i | 1.23351i | 0.787155 | + | 0.616755i | \(0.211553\pi\) | ||||
−0.787155 | + | 0.616755i | \(0.788447\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.7224 | − | 8.50000i | −0.565829 | − | 0.326682i | 0.189653 | − | 0.981851i | \(-0.439264\pi\) |
−0.755482 | + | 0.655170i | \(0.772597\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.0000 | + | 20.7846i | 0.921035 | + | 0.797640i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.1051 | − | 22.0000i | 1.45805 | − | 0.841807i | 0.459136 | − | 0.888366i | \(-0.348159\pi\) |
0.998916 | + | 0.0465592i | \(0.0148256\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.00000 | − | 16.0000i | −0.305664 | − | 0.611329i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.5000 | − | 38.9711i | −0.857182 | − | 1.48468i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.0000 | + | 38.1051i | −0.836919 | + | 1.44959i | 0.0555386 | + | 0.998457i | \(0.482312\pi\) |
−0.892458 | + | 0.451130i | \(0.851021\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −15.5885 | + | 18.0000i | −0.592157 | + | 0.683763i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.14359 | − | 35.7128i | 0.0813111 | − | 1.35466i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.19615 | − | 3.00000i | 0.196818 | − | 0.113633i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.0000 | 0.982006 | 0.491003 | − | 0.871158i | \(-0.336630\pi\) | ||||
0.491003 | + | 0.871158i | \(0.336630\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.33013 | − | 2.50000i | 0.163314 | − | 0.0942893i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.00000 | − | 10.3923i | 0.225335 | − | 0.390291i | −0.731085 | − | 0.682286i | \(-0.760986\pi\) |
0.956420 | + | 0.291995i | \(0.0943191\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21.0000 | − | 36.3731i | −0.787562 | − | 1.36410i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.0000i | 0.524304i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.0000 | − | 30.0000i | −0.560968 | − | 1.12194i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.0000 | + | 22.5167i | −0.484818 | + | 0.839730i | −0.999848 | − | 0.0174426i | \(-0.994448\pi\) |
0.515030 | + | 0.857172i | \(0.327781\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.0000 | + | 6.92820i | −0.744839 | + | 0.258020i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −19.8564 | − | 2.39230i | −0.737448 | − | 0.0888480i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 29.0000i | − | 1.07555i | −0.843088 | − | 0.537775i | \(-0.819265\pi\) | ||
0.843088 | − | 0.537775i | \(-0.180735\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.00000 | − | 3.46410i | −0.0739727 | − | 0.128124i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.5070 | − | 20.5000i | −1.31148 | − | 0.757185i | −0.329141 | − | 0.944281i | \(-0.606759\pi\) |
−0.982342 | + | 0.187096i | \(0.940092\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.19615 | + | 3.00000i | 0.191403 | + | 0.110506i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.5000 | + | 25.1147i | 0.533391 | + | 0.923861i | 0.999239 | + | 0.0389959i | \(0.0124159\pi\) |
−0.465848 | + | 0.884865i | \(0.654251\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.0000i | 0.770415i | 0.922830 | + | 0.385208i | \(0.125870\pi\) | ||||
−0.922830 | + | 0.385208i | \(0.874130\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33.5885 | + | 22.1769i | 1.23059 | + | 0.812499i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.5885 | − | 9.00000i | −0.570352 | − | 0.329293i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 40.0000 | − | 13.8564i | 1.46157 | − | 0.506302i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.0000 | − | 24.2487i | 0.510867 | − | 0.884848i | −0.489053 | − | 0.872254i | \(-0.662658\pi\) |
0.999921 | − | 0.0125942i | \(-0.00400897\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.0000 | + | 6.00000i | −0.436725 | + | 0.218362i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 42.0000i | − | 1.52652i | −0.646094 | − | 0.763258i | \(-0.723599\pi\) | ||
0.646094 | − | 0.763258i | \(-0.276401\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.500000 | + | 0.866025i | −0.0181250 | + | 0.0313934i | −0.874946 | − | 0.484221i | \(-0.839103\pi\) |
0.856821 | + | 0.515615i | \(0.172436\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.19615 | + | 1.00000i | 0.188113 | + | 0.0362024i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.3923 | + | 0.803848i | 0.484200 | + | 0.0290632i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.3205 | − | 10.0000i | 0.625407 | − | 0.361079i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.0000 | 1.04577 | 0.522883 | − | 0.852404i | \(-0.324856\pi\) | ||||
0.522883 | + | 0.852404i | \(0.324856\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.9711 | − | 22.5000i | 1.40169 | − | 0.809269i | 0.407128 | − | 0.913371i | \(-0.366530\pi\) |
0.994567 | + | 0.104102i | \(0.0331970\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.92820 | + | 9.19615i | 0.141105 | + | 0.330336i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.50000 | − | 12.9904i | 0.268715 | − | 0.465429i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.00000 | + | 15.5885i | 0.322045 | + | 0.557799i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.00000 | − | 18.0000i | −0.321224 | − | 0.642448i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.5885 | − | 9.00000i | 0.555668 | − | 0.320815i | −0.195737 | − | 0.980656i | \(-0.562710\pi\) |
0.751405 | + | 0.659841i | \(0.229376\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.0000 | + | 24.2487i | 0.995565 | + | 0.862185i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.9808 | + | 15.0000i | 0.922604 | + | 0.532666i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.00000i | 0.0708436i | 0.999372 | + | 0.0354218i | \(0.0112775\pi\) | ||||
−0.999372 | + | 0.0354218i | \(0.988723\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.0000 | 0.495284 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.00000 | + | 5.19615i | 0.106000 | + | 0.183597i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −41.5692 | − | 24.0000i | −1.46695 | − | 0.846942i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.1865 | + | 39.8731i | 0.394273 | + | 1.40534i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.50000 | − | 4.33013i | −0.0878953 | − | 0.152239i | 0.818726 | − | 0.574184i | \(-0.194681\pi\) |
−0.906621 | + | 0.421945i | \(0.861347\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.0000 | 1.15879 | 0.579393 | − | 0.815048i | \(-0.303290\pi\) | ||||
0.579393 | + | 0.815048i | \(0.303290\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.7846 | + | 22.3923i | −0.517882 | + | 0.784368i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.66025 | − | 5.00000i | −0.302984 | − | 0.174928i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 37.5000 | − | 12.9904i | 1.31036 | − | 0.453921i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.00000 | − | 15.5885i | 0.314102 | − | 0.544041i | −0.665144 | − | 0.746715i | \(-0.731630\pi\) |
0.979246 | + | 0.202674i | \(0.0649632\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.7846 | − | 12.0000i | 0.724506 | − | 0.418294i | −0.0919029 | − | 0.995768i | \(-0.529295\pi\) |
0.816409 | + | 0.577474i | \(0.195962\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 22.0000i | − | 0.765015i | −0.923952 | − | 0.382507i | \(-0.875061\pi\) | ||
0.923952 | − | 0.382507i | \(-0.124939\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.0000 | − | 22.5167i | −0.451509 | − | 0.782036i | 0.546971 | − | 0.837151i | \(-0.315781\pi\) |
−0.998480 | + | 0.0551154i | \(0.982447\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.66025 | − | 11.0000i | −0.300060 | − | 0.381127i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.4808 | + | 2.00962i | 1.15865 | + | 0.0695457i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.0000 | −1.17381 | −0.586905 | − | 0.809656i | \(-0.699654\pi\) | ||||
−0.586905 | + | 0.809656i | \(0.699654\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.60770 | + | 26.7846i | −0.0553064 | + | 0.921419i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.73205 | − | 5.00000i | −0.0595140 | − | 0.171802i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.50000 | − | 6.06218i | −0.119978 | − | 0.207809i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 43.0000i | − | 1.47229i | −0.676823 | − | 0.736146i | \(-0.736644\pi\) | ||
0.676823 | − | 0.736146i | \(-0.263356\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 30.0000 | − | 15.0000i | 1.02598 | − | 0.512989i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.92820 | + | 4.00000i | −0.236663 | + | 0.136637i | −0.613642 | − | 0.789584i | \(-0.710296\pi\) |
0.376979 | + | 0.926222i | \(0.376963\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.00000 | − | 10.3923i | 0.204717 | − | 0.354581i | −0.745325 | − | 0.666701i | \(-0.767706\pi\) |
0.950043 | + | 0.312120i | \(0.101039\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.52628 | − | 5.50000i | −0.324278 | − | 0.187222i | 0.329020 | − | 0.944323i | \(-0.393282\pi\) |
−0.653298 | + | 0.757101i | \(0.726615\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.0885 | + | 16.7942i | −0.377019 | + | 0.571021i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −42.0000 | −1.42475 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.00000 | − | 8.66025i | −0.169419 | − | 0.293442i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −31.1769 | − | 18.0000i | −1.05518 | − | 0.609208i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.5359 | + | 23.0526i | 0.626628 | + | 0.779319i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.8468 | + | 15.5000i | 0.906552 | + | 0.523398i | 0.879320 | − | 0.476231i | \(-0.157998\pi\) |
0.0272316 | + | 0.999629i | \(0.491331\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.0000 | −0.505363 | −0.252681 | − | 0.967550i | \(-0.581312\pi\) | ||||
−0.252681 | + | 0.967550i | \(0.581312\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 16.0000i | − | 0.538443i | −0.963078 | − | 0.269221i | \(-0.913234\pi\) | ||
0.963078 | − | 0.269221i | \(-0.0867663\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.1769 | − | 18.0000i | −1.04682 | − | 0.604381i | −0.125061 | − | 0.992149i | \(-0.539913\pi\) |
−0.921757 | + | 0.387768i | \(0.873246\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.0000 | + | 12.1244i | 0.469545 | + | 0.406638i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.5000 | − | 23.3827i | 0.452267 | − | 0.783349i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.3109 | − | 17.5000i | 1.01432 | − | 0.585615i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.0000 | + | 13.0000i | −0.869084 | + | 0.434542i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.00000 | − | 6.92820i | −0.133407 | − | 0.231069i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.00000 | − | 15.5885i | 0.299833 | − | 0.519327i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.48334 | − | 58.0333i | 0.115790 | − | 1.92909i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.6410 | + | 20.0000i | −1.15024 | + | 0.664089i | −0.948945 | − | 0.315442i | \(-0.897847\pi\) |
−0.201291 | + | 0.979531i | \(0.564514\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.00000 | −0.0662630 | −0.0331315 | − | 0.999451i | \(-0.510548\pi\) | ||||
−0.0331315 | + | 0.999451i | \(0.510548\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.5885 | + | 9.00000i | −0.515903 | + | 0.297857i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.866025 | + | 2.50000i | 0.0285987 | + | 0.0825573i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.0000 | + | 17.3205i | −0.329870 | + | 0.571351i | −0.982486 | − | 0.186338i | \(-0.940338\pi\) |
0.652616 | + | 0.757689i | \(0.273671\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 30.0000i | − | 0.987462i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | − | 3.00000i | −0.131519 | − | 0.0986394i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.7846 | − | 12.0000i | 0.682656 | − | 0.394132i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.5000 | − | 18.1865i | 0.344494 | − | 0.596681i | −0.640768 | − | 0.767735i | \(-0.721384\pi\) |
0.985262 | + | 0.171054i | \(0.0547172\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.5000 | − | 12.9904i | −1.06514 | − | 0.425743i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.39230 | − | 11.1962i | 0.241754 | − | 0.366153i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0000i | 0.849383i | 0.905338 | + | 0.424691i | \(0.139617\pi\) | ||||
−0.905338 | + | 0.424691i | \(0.860383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.0000 | + | 24.2487i | 0.456387 | + | 0.790485i | 0.998767 | − | 0.0496480i | \(-0.0158099\pi\) |
−0.542380 | + | 0.840133i | \(0.682477\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.1865 | − | 10.5000i | −0.592235 | − | 0.341927i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.3923 | + | 6.00000i | 0.337705 | + | 0.194974i | 0.659256 | − | 0.751918i | \(-0.270871\pi\) |
−0.321552 | + | 0.946892i | \(0.604204\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.0000 | + | 69.2820i | 1.29845 | + | 2.24899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 24.0000i | − | 0.777436i | −0.921357 | − | 0.388718i | \(-0.872918\pi\) | ||
0.921357 | − | 0.388718i | \(-0.127082\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37.3205 | + | 24.6410i | 1.20766 | + | 0.797365i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.00000 | − | 20.7846i | 0.129167 | − | 0.671170i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −41.5692 | + | 24.0000i | −1.33955 | + | 0.773389i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.0000 | + | 20.0000i | 0.321911 | + | 0.643823i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.0000i | 1.02905i | 0.857475 | + | 0.514525i | \(0.172032\pi\) | ||||
−0.857475 | + | 0.514525i | \(0.827968\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.5000 | + | 28.5788i | −0.529510 | + | 0.917139i | 0.469897 | + | 0.882721i | \(0.344291\pi\) |
−0.999408 | + | 0.0344175i | \(0.989042\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 27.7128 | − | 32.0000i | 0.888432 | − | 1.02587i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46.7654 | + | 27.0000i | −1.49616 | + | 0.863807i | −0.999990 | − | 0.00442082i | \(-0.998593\pi\) |
−0.496167 | + | 0.868227i | \(0.665259\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.00000 | 0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.00000 | −0.191565 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.1147 | − | 14.5000i | 0.801036 | − | 0.462478i | −0.0427975 | − | 0.999084i | \(-0.513627\pi\) |
0.843833 | + | 0.536606i | \(0.180294\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.1603 | + | 0.669873i | 0.355595 | + | 0.0213439i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.00000 | + | 12.1244i | −0.222587 | + | 0.385532i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.00000 | − | 6.92820i | −0.127064 | − | 0.220082i | 0.795474 | − | 0.605988i | \(-0.207222\pi\) |
−0.922538 | + | 0.385906i | \(0.873889\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −36.0000 | + | 18.0000i | −1.14128 | + | 0.570638i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.9090 | − | 19.0000i | 1.04224 | − | 0.601736i | 0.121771 | − | 0.992558i | \(-0.461143\pi\) |
0.920466 | + | 0.390822i | \(0.127809\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 560.2.bw.d.289.1 | 4 | ||
4.3 | odd | 2 | 70.2.i.b.9.2 | yes | 4 | ||
5.4 | even | 2 | inner | 560.2.bw.d.289.2 | 4 | ||
7.4 | even | 3 | inner | 560.2.bw.d.529.2 | 4 | ||
12.11 | even | 2 | 630.2.u.a.289.1 | 4 | |||
20.3 | even | 4 | 350.2.e.j.51.1 | 2 | |||
20.7 | even | 4 | 350.2.e.c.51.1 | 2 | |||
20.19 | odd | 2 | 70.2.i.b.9.1 | ✓ | 4 | ||
28.3 | even | 6 | 490.2.i.a.459.1 | 4 | |||
28.11 | odd | 6 | 70.2.i.b.39.1 | yes | 4 | ||
28.19 | even | 6 | 490.2.c.d.99.1 | 2 | |||
28.23 | odd | 6 | 490.2.c.a.99.1 | 2 | |||
28.27 | even | 2 | 490.2.i.a.79.2 | 4 | |||
35.4 | even | 6 | inner | 560.2.bw.d.529.1 | 4 | ||
60.59 | even | 2 | 630.2.u.a.289.2 | 4 | |||
84.11 | even | 6 | 630.2.u.a.109.2 | 4 | |||
140.19 | even | 6 | 490.2.c.d.99.2 | 2 | |||
140.23 | even | 12 | 2450.2.a.k.1.1 | 1 | |||
140.39 | odd | 6 | 70.2.i.b.39.2 | yes | 4 | ||
140.47 | odd | 12 | 2450.2.a.bb.1.1 | 1 | |||
140.59 | even | 6 | 490.2.i.a.459.2 | 4 | |||
140.67 | even | 12 | 350.2.e.c.151.1 | 2 | |||
140.79 | odd | 6 | 490.2.c.a.99.2 | 2 | |||
140.103 | odd | 12 | 2450.2.a.j.1.1 | 1 | |||
140.107 | even | 12 | 2450.2.a.ba.1.1 | 1 | |||
140.123 | even | 12 | 350.2.e.j.151.1 | 2 | |||
140.139 | even | 2 | 490.2.i.a.79.1 | 4 | |||
420.179 | even | 6 | 630.2.u.a.109.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.i.b.9.1 | ✓ | 4 | 20.19 | odd | 2 | ||
70.2.i.b.9.2 | yes | 4 | 4.3 | odd | 2 | ||
70.2.i.b.39.1 | yes | 4 | 28.11 | odd | 6 | ||
70.2.i.b.39.2 | yes | 4 | 140.39 | odd | 6 | ||
350.2.e.c.51.1 | 2 | 20.7 | even | 4 | |||
350.2.e.c.151.1 | 2 | 140.67 | even | 12 | |||
350.2.e.j.51.1 | 2 | 20.3 | even | 4 | |||
350.2.e.j.151.1 | 2 | 140.123 | even | 12 | |||
490.2.c.a.99.1 | 2 | 28.23 | odd | 6 | |||
490.2.c.a.99.2 | 2 | 140.79 | odd | 6 | |||
490.2.c.d.99.1 | 2 | 28.19 | even | 6 | |||
490.2.c.d.99.2 | 2 | 140.19 | even | 6 | |||
490.2.i.a.79.1 | 4 | 140.139 | even | 2 | |||
490.2.i.a.79.2 | 4 | 28.27 | even | 2 | |||
490.2.i.a.459.1 | 4 | 28.3 | even | 6 | |||
490.2.i.a.459.2 | 4 | 140.59 | even | 6 | |||
560.2.bw.d.289.1 | 4 | 1.1 | even | 1 | trivial | ||
560.2.bw.d.289.2 | 4 | 5.4 | even | 2 | inner | ||
560.2.bw.d.529.1 | 4 | 35.4 | even | 6 | inner | ||
560.2.bw.d.529.2 | 4 | 7.4 | even | 3 | inner | ||
630.2.u.a.109.1 | 4 | 420.179 | even | 6 | |||
630.2.u.a.109.2 | 4 | 84.11 | even | 6 | |||
630.2.u.a.289.1 | 4 | 12.11 | even | 2 | |||
630.2.u.a.289.2 | 4 | 60.59 | even | 2 | |||
2450.2.a.j.1.1 | 1 | 140.103 | odd | 12 | |||
2450.2.a.k.1.1 | 1 | 140.23 | even | 12 | |||
2450.2.a.ba.1.1 | 1 | 140.107 | even | 12 | |||
2450.2.a.bb.1.1 | 1 | 140.47 | odd | 12 |