Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(104,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.104");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.z (of order \(6\), degree \(2\), 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: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.31116960000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} - 8x^{4} + 9x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 104.2 | ||
Root | \(-0.306808 - 1.70466i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.104 |
Dual form | 315.2.z.a.209.1 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | −1.32288 | + | 1.11803i | −0.763763 | + | 0.645497i | ||||
\(4\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(5\) | −1.93649 | − | 1.11803i | −0.866025 | − | 0.500000i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.32288 | + | 2.29129i | 0.500000 | + | 0.866025i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | − | 2.95804i | 0.166667 | − | 0.986013i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.311738 | + | 0.179982i | −0.0939925 | + | 0.0542666i | −0.546259 | − | 0.837616i | \(-0.683949\pi\) |
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | 0.613616 | + | 3.40932i | 0.177136 | + | 0.984186i | ||||
\(13\) | 3.56618 | − | 6.17680i | 0.989079 | − | 1.71314i | 0.366900 | − | 0.930261i | \(-0.380419\pi\) |
0.622179 | − | 0.782875i | \(-0.286247\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.81174 | − | 0.686044i | 0.984186 | − | 0.177136i | ||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | − | 5.75583i | − | 1.39599i | −0.716101 | − | 0.697997i | \(-0.754075\pi\) | ||
0.716101 | − | 0.697997i | \(-0.245925\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | −3.87298 | + | 2.23607i | −0.866025 | + | 0.500000i | ||||
\(21\) | −4.31174 | − | 1.55207i | −0.940898 | − | 0.338689i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | + | 4.33013i | 0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.64575 | + | 4.47214i | 0.509175 | + | 0.860663i | ||||
\(28\) | 5.29150 | 1.00000 | ||||||||
\(29\) | 5.12348 | − | 2.95804i | 0.951405 | − | 0.549294i | 0.0578882 | − | 0.998323i | \(-0.481563\pi\) |
0.893517 | + | 0.449029i | \(0.148230\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.211164 | − | 0.586627i | 0.0367590 | − | 0.102119i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 5.91608i | − | 1.00000i | ||||||
\(36\) | −4.62348 | − | 3.82407i | −0.770579 | − | 0.637344i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.18826 | + | 12.1582i | 0.350402 | + | 1.94688i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(44\) | 0.719927i | 0.108533i | ||||||||
\(45\) | −4.27543 | + | 5.16920i | −0.637344 | + | 0.770579i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.7942 | + | 6.23202i | −1.57449 | + | 0.909033i | −0.578884 | + | 0.815410i | \(0.696511\pi\) |
−0.995608 | + | 0.0936230i | \(0.970155\pi\) | |||||||
\(48\) | 6.51873 | + | 2.34651i | 0.940898 | + | 0.338689i | ||||
\(49\) | −3.50000 | + | 6.06218i | −0.500000 | + | 0.866025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.43521 | + | 7.61425i | 0.901110 | + | 1.06621i | ||||
\(52\) | −7.13235 | − | 12.3536i | −0.989079 | − | 1.71314i | ||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.804903 | 0.108533 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 2.62348 | − | 7.28817i | 0.338689 | − | 0.940898i | ||||
\(61\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.43916 | − | 2.76748i | 0.937246 | − | 0.348669i | ||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | −13.8117 | + | 7.97421i | −1.71314 | + | 0.989079i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | −9.96939 | − | 5.75583i | −1.20897 | − | 0.697997i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.3084i | 1.93545i | 0.252010 | + | 0.967725i | \(0.418908\pi\) | ||||
−0.252010 | + | 0.967725i | \(0.581092\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.32745 | 0.740572 | 0.370286 | − | 0.928918i | \(-0.379260\pi\) | ||||
0.370286 | + | 0.928918i | \(0.379260\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.14842 | − | 2.93313i | −0.940898 | − | 0.338689i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.824780 | − | 0.476187i | −0.0939925 | − | 0.0542666i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.93521 | − | 13.7442i | −0.892781 | − | 1.54634i | −0.836527 | − | 0.547926i | \(-0.815418\pi\) |
−0.0562544 | − | 0.998416i | \(-0.517916\pi\) | |||||||
\(80\) | 8.94427i | 1.00000i | ||||||||
\(81\) | −8.50000 | − | 2.95804i | −0.944444 | − | 0.328671i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.7789 | − | 9.10993i | 1.73196 | − | 0.999945i | 0.860729 | − | 0.509064i | \(-0.170008\pi\) |
0.871227 | − | 0.490881i | \(-0.163325\pi\) | |||||||
\(84\) | −7.00000 | + | 5.91608i | −0.763763 | + | 0.645497i | ||||
\(85\) | −6.43521 | + | 11.1461i | −0.697997 | + | 1.20897i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.47053 | + | 9.64134i | −0.372080 | + | 1.03366i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.8704 | 1.97816 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.53480 | + | 13.0507i | 0.765043 | + | 1.32509i | 0.940224 | + | 0.340557i | \(0.110616\pi\) |
−0.175180 | + | 0.984536i | \(0.556051\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.376525 | + | 1.01212i | 0.0378421 | + | 0.101722i | ||||
\(100\) | 10.0000 | 1.00000 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.32288 | + | 2.29129i | −0.130347 | + | 0.225767i | −0.923810 | − | 0.382851i | \(-0.874942\pi\) |
0.793463 | + | 0.608618i | \(0.208276\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.61438 | + | 7.82624i | 0.645497 | + | 0.763763i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 10.3917 | − | 0.110440i | 0.999944 | − | 0.0106271i | ||||
\(109\) | 9.87043 | 0.945415 | 0.472708 | − | 0.881219i | \(-0.343277\pi\) | ||||
0.472708 | + | 0.881219i | \(0.343277\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.29150 | − | 9.16515i | 0.500000 | − | 0.866025i | ||||
\(113\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 11.8322i | − | 1.09859i | ||||||
\(117\) | −16.4881 | − | 13.6373i | −1.52433 | − | 1.26077i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.1883 | − | 7.61425i | 1.20897 | − | 0.697997i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.43521 | + | 9.41407i | −0.494110 | + | 0.855824i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.1803i | − | 1.00000i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | −0.804903 | − | 0.952374i | −0.0700578 | − | 0.0828935i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.123475 | − | 11.6183i | −0.0106271 | − | 0.999944i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(140\) | −10.2470 | − | 5.91608i | −0.866025 | − | 0.500000i | ||||
\(141\) | 7.31174 | − | 20.3124i | 0.615759 | − | 1.71062i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.56739i | 0.214696i | ||||||||
\(144\) | −11.2470 | + | 4.18403i | −0.937246 | + | 0.348669i | ||||
\(145\) | −13.2288 | −1.09859 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.14766 | − | 11.9326i | −0.177136 | − | 0.984186i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.7470 | + | 8.51416i | 1.20812 | + | 0.697507i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.43521 | − | 5.94996i | −0.279554 | − | 0.484201i | 0.691720 | − | 0.722166i | \(-0.256853\pi\) |
−0.971274 | + | 0.237964i | \(0.923520\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.0260 | − | 2.87791i | −1.37647 | − | 0.232666i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 23.2470 | + | 8.36806i | 1.86125 | + | 0.669981i | ||||
\(157\) | −11.1010 | + | 19.2275i | −0.885954 | + | 1.53452i | −0.0413387 | + | 0.999145i | \(0.513162\pi\) |
−0.844616 | + | 0.535373i | \(0.820171\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.06479 | + | 0.899909i | −0.0828935 | + | 0.0700578i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.6036 | + | 9.58612i | 1.28483 | + | 0.741796i | 0.977727 | − | 0.209881i | \(-0.0673075\pi\) |
0.307102 | + | 0.951677i | \(0.400641\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.9352 | − | 32.7968i | −1.45655 | − | 2.52283i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.68246 | − | 5.59017i | 0.736144 | − | 0.425013i | −0.0845218 | − | 0.996422i | \(-0.526936\pi\) |
0.820666 | + | 0.571409i | \(0.193603\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.61438 | + | 11.4564i | −0.500000 | + | 0.866025i | ||||
\(176\) | 1.24695 | + | 0.719927i | 0.0939925 | + | 0.0542666i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 14.8685i | − | 1.11133i | −0.831408 | − | 0.555663i | \(-0.812464\pi\) | ||
0.831408 | − | 0.555663i | \(-0.187536\pi\) | |||||||
\(180\) | 4.67789 | + | 12.5745i | 0.348669 | + | 0.937246i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.03594 | + | 1.79431i | 0.0757558 | + | 0.131213i | ||||
\(188\) | 24.9281i | 1.81807i | ||||||||
\(189\) | −6.74695 | + | 11.9783i | −0.490768 | + | 0.871290i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.12348 | − | 2.95804i | 0.370722 | − | 0.214036i | −0.303052 | − | 0.952974i | \(-0.598006\pi\) |
0.673774 | + | 0.738938i | \(0.264672\pi\) | |||||||
\(192\) | 10.5830 | − | 8.94427i | 0.763763 | − | 0.645497i | ||||
\(193\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.35577 | − | 25.9909i | 0.669981 | − | 1.86125i | ||||
\(196\) | 7.00000 | + | 12.1244i | 0.500000 | + | 0.866025i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.5554 | + | 7.82624i | 0.951405 | + | 0.549294i | ||||
\(204\) | 19.6235 | − | 3.53187i | 1.37392 | − | 0.247280i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −28.5294 | −1.97816 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.93521 | + | 3.35189i | −0.133226 | + | 0.230753i | −0.924918 | − | 0.380166i | \(-0.875867\pi\) |
0.791693 | + | 0.610920i | \(0.209200\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −18.2333 | − | 21.5740i | −1.24933 | − | 1.47822i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.37043 | + | 7.07430i | −0.565621 | + | 0.478037i | ||||
\(220\) | 0.804903 | − | 1.39413i | 0.0542666 | − | 0.0939925i | ||||
\(221\) | −35.5526 | − | 20.5263i | −2.39153 | − | 1.38075i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.37108 | − | 7.57093i | −0.292709 | − | 0.506987i | 0.681740 | − | 0.731594i | \(-0.261223\pi\) |
−0.974449 | + | 0.224607i | \(0.927890\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.0587 | − | 5.23004i | 0.937246 | − | 0.348669i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.63426 | − | 3.83029i | 0.440331 | − | 0.254225i | −0.263407 | − | 0.964685i | \(-0.584846\pi\) |
0.703738 | + | 0.710460i | \(0.251513\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.62348 | − | 0.292196i | 0.106817 | − | 0.0192251i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.8704 | 1.81807 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 25.8638 | + | 9.31002i | 1.68003 | + | 0.604751i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.6174 | + | 14.7902i | 1.65705 | + | 0.956698i | 0.974066 | + | 0.226266i | \(0.0726518\pi\) |
0.682985 | + | 0.730433i | \(0.260682\pi\) | |||||||
\(240\) | −10.0000 | − | 11.8322i | −0.645497 | − | 0.763763i | ||||
\(241\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.5516 | − | 5.59017i | 0.933488 | − | 0.358610i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.5554 | − | 7.82624i | 0.866025 | − | 0.500000i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.6883 | + | 29.6926i | −0.677341 | + | 1.88169i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 2.64575 | − | 15.6525i | 0.166667 | − | 0.986013i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.94875 | − | 21.9397i | −0.247280 | − | 1.37392i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 25.7483 | + | 14.8658i | 1.60613 | + | 0.927301i | 0.990225 | + | 0.139482i | \(0.0445438\pi\) |
0.615907 | + | 0.787819i | \(0.288790\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 31.8968i | 1.97816i | ||||||||
\(261\) | −6.18826 | − | 16.6345i | −0.383044 | − | 1.02965i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | −19.9388 | + | 11.5117i | −1.20897 | + | 0.697997i | ||||
\(273\) | −24.9632 | + | 21.0978i | −1.51084 | + | 1.27690i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.55869 | − | 0.899909i | −0.0939925 | − | 0.0542666i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.3117 | + | 15.7684i | −1.62928 | + | 0.940666i | −0.644974 | + | 0.764204i | \(0.723132\pi\) |
−0.984307 | + | 0.176462i | \(0.943535\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.8622 | + | 24.0101i | −0.824025 | + | 1.42725i | 0.0786368 | + | 0.996903i | \(0.474943\pi\) |
−0.902662 | + | 0.430350i | \(0.858390\pi\) | |||||||
\(284\) | 28.2470 | + | 16.3084i | 1.67615 | + | 0.967725i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1296 | −0.948798 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24.5587 | − | 8.84024i | −1.43966 | − | 0.518224i | ||||
\(292\) | 6.32745 | − | 10.9595i | 0.370286 | − | 0.641354i | ||||
\(293\) | −21.3014 | − | 12.2984i | −1.24444 | − | 0.718479i | −0.274446 | − | 0.961602i | \(-0.588495\pi\) |
−0.969995 | + | 0.243124i | \(0.921828\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.62968 | − | 0.917946i | −0.0945638 | − | 0.0532646i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −13.2288 | + | 11.1803i | −0.763763 | + | 0.645497i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.0069 | −1.31307 | −0.656535 | − | 0.754295i | \(-0.727979\pi\) | ||||
−0.656535 | + | 0.754295i | \(0.727979\pi\) | |||||||
\(308\) | −1.64956 | + | 0.952374i | −0.0939925 | + | 0.0542666i | ||||
\(309\) | −0.811738 | − | 4.51011i | −0.0461781 | − | 0.256571i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.5516 | + | 25.2042i | 0.822507 | + | 1.42462i | 0.903810 | + | 0.427934i | \(0.140759\pi\) |
−0.0813030 | + | 0.996689i | \(0.525908\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.5000 | − | 2.95804i | −0.986013 | − | 0.166667i | ||||
\(316\) | −31.7409 | −1.78556 | ||||||||
\(317\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.06479 | + | 1.84427i | −0.0596166 | + | 0.103259i | ||||
\(320\) | 15.4919 | + | 8.94427i | 0.866025 | + | 0.500000i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −13.6235 | + | 11.7644i | −0.756860 | + | 0.653577i | ||||
\(325\) | 35.6618 | 1.97816 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.0573 | + | 11.0355i | −0.722073 | + | 0.610263i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −28.5587 | − | 16.4884i | −1.57449 | − | 0.909033i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.3704 | + | 30.0865i | 0.954765 | + | 1.65370i | 0.734905 | + | 0.678170i | \(0.237227\pi\) |
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | − | 36.4397i | − | 1.99989i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.24695 | + | 18.0404i | 0.177136 | + | 0.984186i | ||||
\(337\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.8704 | + | 22.2922i | 0.697997 | + | 1.20897i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5203 | −1.00000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(348\) | 13.2288 | + | 15.6525i | 0.709136 | + | 0.839061i | ||||
\(349\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 37.0587 | − | 0.393847i | 1.97805 | − | 0.0210220i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.1744 | + | 14.5344i | −1.33990 | + | 0.773590i | −0.986792 | − | 0.161993i | \(-0.948208\pi\) |
−0.353106 | + | 0.935583i | \(0.614874\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.2333 | − | 31.5811i | 0.967725 | − | 1.67615i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.93344 | + | 24.8176i | −0.472808 | + | 1.31349i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 11.8322i | − | 0.624477i | −0.950004 | − | 0.312239i | \(-0.898921\pi\) | ||
0.950004 | − | 0.312239i | \(-0.101079\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.33513 | − | 18.5304i | −0.175049 | − | 0.972593i | ||||
\(364\) | 18.8704 | − | 32.6845i | 0.989079 | − | 1.71314i | ||||
\(365\) | −12.2530 | − | 7.07430i | −0.641354 | − | 0.370286i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.89362 | − | 17.1363i | −0.516443 | − | 0.894505i | −0.999818 | − | 0.0190919i | \(-0.993923\pi\) |
0.483375 | − | 0.875413i | \(-0.339411\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.5000 | + | 14.7902i | 0.645497 | + | 0.763763i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 42.1956i | − | 2.17318i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.7409 | −1.16812 | −0.584060 | − | 0.811711i | \(-0.698537\pi\) | ||||
−0.584060 | + | 0.811711i | \(0.698537\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.3978 | − | 15.8181i | −1.39996 | − | 0.808269i | −0.405575 | − | 0.914062i | \(-0.632929\pi\) |
−0.994388 | + | 0.105793i | \(0.966262\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.06479 | + | 1.84427i | 0.0542666 | + | 0.0939925i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 30.1392 | 1.53009 | ||||||||
\(389\) | 26.6883 | − | 15.4085i | 1.35315 | − | 0.781241i | 0.364459 | − | 0.931219i | \(-0.381254\pi\) |
0.988689 | + | 0.149979i | \(0.0479205\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 35.4874i | 1.78556i | ||||||||
\(396\) | 2.12957 | + | 0.359964i | 0.107015 | + | 0.0180889i | ||||
\(397\) | 34.3948 | 1.72622 | 0.863112 | − | 0.505013i | \(-0.168512\pi\) | ||||
0.863112 | + | 0.505013i | \(0.168512\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.0000 | − | 17.3205i | 0.500000 | − | 0.866025i | ||||
\(401\) | 25.6174 | + | 14.7902i | 1.27927 | + | 0.738587i | 0.976714 | − | 0.214544i | \(-0.0688266\pi\) |
0.302556 | + | 0.953131i | \(0.402160\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.1530 | + | 15.2315i | 0.653577 | + | 0.756860i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.64575 | + | 4.58258i | 0.130347 | + | 0.225767i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −40.7409 | −1.99989 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(420\) | 20.1698 | − | 3.63020i | 0.984186 | − | 0.177136i | ||||
\(421\) | −16.9352 | − | 29.3326i | −0.825372 | − | 1.42959i | −0.901635 | − | 0.432498i | \(-0.857632\pi\) |
0.0762630 | − | 0.997088i | \(-0.475701\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.0375 | + | 35.0456i | 0.633903 | + | 1.70398i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.9235 | − | 14.3896i | 1.20897 | − | 0.697997i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.87043 | − | 3.39633i | −0.138585 | − | 0.163977i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 18.1082i | − | 0.872241i | −0.899888 | − | 0.436121i | \(-0.856352\pi\) | ||
0.899888 | − | 0.436121i | \(-0.143648\pi\) | |||||||
\(432\) | 10.2004 | − | 18.1094i | 0.490768 | − | 0.871290i | ||||
\(433\) | 10.5830 | 0.508587 | 0.254293 | − | 0.967127i | \(-0.418157\pi\) | ||||
0.254293 | + | 0.967127i | \(0.418157\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.5000 | − | 14.7902i | 0.839061 | − | 0.709136i | ||||
\(436\) | 9.87043 | − | 17.0961i | 0.472708 | − | 0.818754i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.1822 | + | 13.3842i | 0.770579 | + | 0.637344i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −29.0275 | + | 5.22442i | −1.37295 | + | 0.247107i | ||||
\(448\) | −10.5830 | − | 18.3303i | −0.500000 | − | 0.866025i | ||||
\(449\) | 41.4126i | 1.95438i | 0.212368 | + | 0.977190i | \(0.431882\pi\) | ||||
−0.212368 | + | 0.977190i | \(0.568118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.1966 | + | 4.03038i | 0.526063 | + | 0.189364i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −36.5424 | − | 21.0978i | −1.71314 | − | 0.989079i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.7409 | − | 15.2285i | 1.20148 | − | 0.710805i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(464\) | −20.4939 | − | 11.8322i | −0.951405 | − | 0.549294i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.3688i | 0.664908i | 0.943119 | + | 0.332454i | \(0.107877\pi\) | ||||
−0.943119 | + | 0.332454i | \(0.892123\pi\) | |||||||
\(468\) | −40.1086 | + | 14.9210i | −1.85402 | + | 0.689723i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.81174 | − | 37.8468i | −0.313868 | − | 1.74389i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 30.4570i | − | 1.39599i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.8704 | + | 18.8281i | 0.494110 | + | 0.855824i | ||||
\(485\) | − | 33.6967i | − | 1.53009i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.9413 | + | 6.89432i | 0.538904 | + | 0.311136i | 0.744635 | − | 0.667472i | \(-0.232624\pi\) |
−0.205731 | + | 0.978609i | \(0.565957\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.0260 | − | 29.4899i | −0.766811 | − | 1.32816i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.402452 | − | 2.38094i | 0.0180889 | − | 0.107015i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −37.3672 | + | 21.5740i | −1.67615 | + | 0.967725i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.56479 | − | 4.44234i | 0.114816 | − | 0.198867i | −0.802890 | − | 0.596127i | \(-0.796706\pi\) |
0.917706 | + | 0.397260i | \(0.130039\pi\) | |||||||
\(500\) | −19.3649 | − | 11.1803i | −0.866025 | − | 0.500000i | ||||
\(501\) | −32.6822 | + | 5.88220i | −1.46013 | + | 0.262797i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.0132i | 1.69492i | 0.530857 | + | 0.847461i | \(0.321870\pi\) | ||||
−0.530857 | + | 0.847461i | \(0.678130\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 61.7168 | + | 22.2158i | 2.74094 | + | 0.986639i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.37043 | + | 14.4980i | 0.370286 | + | 0.641354i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.12348 | − | 2.95804i | 0.225767 | − | 0.130347i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.24330 | − | 3.88551i | 0.0986602 | − | 0.170884i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.55869 | + | 18.2204i | −0.287894 | + | 0.799788i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.71764 | −0.206288 | −0.103144 | − | 0.994666i | \(-0.532890\pi\) | ||||
−0.103144 | + | 0.994666i | \(0.532890\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.05869 | − | 22.5505i | −0.177136 | − | 0.984186i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −2.45446 | + | 0.441759i | −0.106817 | + | 0.0192251i | ||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.6235 | + | 19.6692i | 0.717358 | + | 0.848789i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 2.51975i | − | 0.108533i | ||||||
\(540\) | −20.2470 | − | 11.4044i | −0.871290 | − | 0.490768i | ||||
\(541\) | 36.8704 | 1.58518 | 0.792592 | − | 0.609753i | \(-0.208731\pi\) | ||||
0.792592 | + | 0.609753i | \(0.208731\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.1140 | − | 11.0355i | −0.818754 | − | 0.472708i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.9946 | − | 36.3637i | 0.892781 | − | 1.54634i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −20.4939 | + | 11.8322i | −0.866025 | + | 0.500000i | ||||
\(561\) | −3.37652 | − | 1.21543i | −0.142557 | − | 0.0513153i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.45904 | + | 4.30648i | 0.314361 | + | 0.181496i | 0.648876 | − | 0.760894i | \(-0.275239\pi\) |
−0.334515 | + | 0.942390i | \(0.608573\pi\) | |||||||
\(564\) | −27.8704 | − | 32.9767i | −1.17356 | − | 1.38857i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.46672 | − | 23.3891i | −0.187585 | − | 0.982248i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.9939 | − | 9.23408i | 0.670499 | − | 0.387113i | −0.125767 | − | 0.992060i | \(-0.540139\pi\) |
0.796266 | + | 0.604947i | \(0.206806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.3704 | − | 40.4788i | 0.978022 | − | 1.69398i | 0.308443 | − | 0.951243i | \(-0.400192\pi\) |
0.669579 | − | 0.742741i | \(-0.266474\pi\) | |||||||
\(572\) | 4.44685 | + | 2.56739i | 0.185932 | + | 0.107348i | ||||
\(573\) | −3.47053 | + | 9.64134i | −0.144984 | + | 0.402773i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.00000 | + | 23.6643i | −0.166667 | + | 0.986013i | ||||
\(577\) | 11.8500 | 0.493322 | 0.246661 | − | 0.969102i | \(-0.420667\pi\) | ||||
0.246661 | + | 0.969102i | \(0.420667\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −13.2288 | + | 22.9129i | −0.549294 | + | 0.951405i | ||||
\(581\) | 41.7470 | + | 24.1026i | 1.73196 | + | 0.999945i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16.6822 | + | 44.8428i | 0.689723 | + | 1.85402i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.74597 | + | 4.47214i | −0.319710 | + | 0.184585i | −0.651263 | − | 0.758852i | \(-0.725761\pi\) |
0.331553 | + | 0.943437i | \(0.392427\pi\) | |||||||
\(588\) | −22.8156 | − | 8.21278i | −0.940898 | − | 0.338689i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 42.4853i | − | 1.74466i | −0.488916 | − | 0.872331i | \(-0.662608\pi\) | ||
0.488916 | − | 0.872331i | \(-0.337392\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −34.0519 | −1.39599 | ||||||||
\(596\) | 29.4939 | − | 17.0283i | 1.20812 | − | 0.697507i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.0587 | − | 24.2826i | −1.71847 | − | 0.992160i | −0.921723 | − | 0.387849i | \(-0.873218\pi\) |
−0.796748 | − | 0.604311i | \(-0.793448\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13.7409 | −0.559107 | ||||||||
\(605\) | 21.0505 | − | 12.1535i | 0.855824 | − | 0.494110i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.4889 | − | 38.9519i | 0.912796 | − | 1.58101i | 0.102699 | − | 0.994712i | \(-0.467252\pi\) |
0.810097 | − | 0.586296i | \(-0.199414\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −26.6822 | + | 4.80230i | −1.08122 | + | 0.194599i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 88.8979i | 3.59642i | ||||||||
\(612\) | −22.0107 | + | 26.6119i | −0.889729 | + | 1.07572i | ||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 37.7409 | − | 31.8968i | 1.51084 | − | 1.27690i | ||||
\(625\) | −12.5000 | + | 21.6506i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.2020 | + | 38.4549i | 0.885954 | + | 1.53452i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.12957 | −0.323633 | −0.161817 | − | 0.986821i | \(-0.551735\pi\) | ||||
−0.161817 | + | 0.986821i | \(0.551735\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.18748 | − | 6.59776i | −0.0471980 | − | 0.262238i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.9632 | + | 43.2376i | 0.989079 | + | 1.71314i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 48.2409 | + | 8.15419i | 1.90838 | + | 0.322575i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.9878 | + | 23.6643i | −1.61892 | + | 0.934684i | −0.631721 | + | 0.775196i | \(0.717651\pi\) |
−0.987200 | + | 0.159489i | \(0.949015\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.4721 | − | 26.7984i | 0.610158 | − | 1.05683i | −0.381055 | − | 0.924552i | \(-0.624439\pi\) |
0.991213 | − | 0.132273i | \(-0.0422275\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.8885i | 0.703271i | 0.936137 | + | 0.351636i | \(0.114374\pi\) | ||||
−0.936137 | + | 0.351636i | \(0.885626\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.16372 | − | 18.7168i | 0.123429 | − | 0.730214i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.8117 | + | 23.5627i | −1.58980 | + | 0.917871i | −0.596461 | + | 0.802642i | \(0.703427\pi\) |
−0.993339 | + | 0.115229i | \(0.963240\pi\) | |||||||
\(660\) | 0.493902 | + | 2.74417i | 0.0192251 | + | 0.106817i | ||||
\(661\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 69.9808 | − | 12.5953i | 2.71783 | − | 0.489160i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 33.2073 | − | 19.1722i | 1.28483 | − | 0.741796i | ||||
\(669\) | 14.2470 | + | 5.12838i | 0.550819 | + | 0.198275i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.7505 | + | 22.6368i | −0.490768 | + | 0.871290i | ||||
\(676\) | −75.7409 | −2.91311 | ||||||||
\(677\) | −28.2226 | + | 16.2943i | −1.08468 | + | 0.626242i | −0.932156 | − | 0.362058i | \(-0.882074\pi\) |
−0.152527 | + | 0.988299i | \(0.548741\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.9352 | + | 34.5288i | −0.765043 | + | 1.32509i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.49390 | + | 12.4843i | −0.172207 | + | 0.478400i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(692\) | − | 22.3607i | − | 0.850026i | ||||||
\(693\) | −1.82097 | + | 2.20164i | −0.0691730 | + | 0.0836334i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 13.2288 | + | 22.9129i | 0.500000 | + | 0.866025i | ||||
\(701\) | − | 49.2851i | − | 1.86147i | −0.365690 | − | 0.930737i | \(-0.619167\pi\) | ||
0.365690 | − | 0.930737i | \(-0.380833\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 2.49390 | − | 1.43985i | 0.0939925 | − | 0.0542666i | ||||
\(705\) | −36.8691 | + | 31.1601i | −1.38857 | + | 1.17356i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.500000 | + | 0.866025i | 0.0187779 | + | 0.0325243i | 0.875262 | − | 0.483650i | \(-0.160689\pi\) |
−0.856484 | + | 0.516174i | \(0.827356\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −44.6235 | + | 16.6006i | −1.67351 | + | 0.622570i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.87043 | − | 4.97172i | 0.107348 | − | 0.185932i | ||||
\(716\) | −25.7530 | − | 14.8685i | −0.962437 | − | 0.555663i | ||||
\(717\) | −50.4245 | + | 9.07550i | −1.88314 | + | 0.338931i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 26.4575 | + | 4.47214i | 0.986013 | + | 0.166667i | ||||
\(721\) | −7.00000 | −0.260694 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.6174 | + | 14.7902i | 0.951405 | + | 0.549294i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.5608 | − | 42.5405i | −0.910909 | − | 1.57774i | −0.812783 | − | 0.582566i | \(-0.802049\pi\) |
−0.0981255 | − | 0.995174i | \(-0.531285\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | + | 23.6643i | −0.481481 | + | 0.876456i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.1346 | + | 43.5345i | −0.928369 | + | 1.60798i | −0.142318 | + | 0.989821i | \(0.545455\pi\) |
−0.786051 | + | 0.618161i | \(0.787878\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.18216 | + | 25.5086i | −0.338689 | + | 0.940898i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.0000 | 0.404642 | 0.202321 | − | 0.979319i | \(-0.435152\pi\) | ||||
0.202321 | + | 0.979319i | \(0.435152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.0382 | − | 32.9752i | −0.697507 | − | 1.20812i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.0581 | − | 51.2295i | −0.697300 | − | 1.87439i | ||||
\(748\) | 4.14378 | 0.151512 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.50000 | − | 11.2583i | 0.237188 | − | 0.410822i | −0.722718 | − | 0.691143i | \(-0.757107\pi\) |
0.959906 | + | 0.280321i | \(0.0904408\pi\) | |||||||
\(752\) | 43.1767 | + | 24.9281i | 1.57449 | + | 0.909033i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.3627i | 0.559107i | ||||||||
\(756\) | 14.0000 | + | 23.6643i | 0.509175 | + | 0.860663i | ||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.0573 | + | 22.6160i | 0.472708 | + | 0.818754i | ||||
\(764\) | − | 11.8322i | − | 0.428073i | ||||||
\(765\) | 29.7530 | + | 24.6087i | 1.07572 | + | 0.889729i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −4.90893 | − | 27.2746i | −0.177136 | − | 0.984186i | ||||
\(769\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −50.6822 | + | 9.12187i | −1.82527 | + | 0.328516i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 46.9990i | − | 1.69044i | −0.534421 | − | 0.845218i | \(-0.679470\pi\) | ||
0.534421 | − | 0.845218i | \(-0.320530\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −35.6618 | − | 42.1956i | −1.27690 | − | 1.51084i | ||||
\(781\) | −2.93521 | − | 5.08394i | −0.105030 | − | 0.181918i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 26.7842 | + | 15.0866i | 0.957189 | + | 0.539153i | ||||
\(784\) | 28.0000 | 1.00000 | ||||||||
\(785\) | 42.9939 | − | 24.8225i | 1.53452 | − | 0.885954i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.7681 | + | 44.6317i | −0.918535 | + | 1.59095i | −0.116892 | + | 0.993145i | \(0.537293\pi\) |
−0.801642 | + | 0.597804i | \(0.796040\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.2532 | − | 10.5385i | −0.646562 | − | 0.373293i | 0.140576 | − | 0.990070i | \(-0.455105\pi\) |
−0.787138 | + | 0.616777i | \(0.788438\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.8704 | + | 62.1294i | 1.26900 | + | 2.19798i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.97250 | + | 1.13883i | −0.0696081 | + | 0.0401883i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.0687i | 0.459471i | 0.973253 | + | 0.229736i | \(0.0737862\pi\) | ||||
−0.973253 | + | 0.229736i | \(0.926214\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 27.1109 | − | 15.6525i | 0.951405 | − | 0.549294i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 13.5061 | − | 37.5207i | 0.472808 | − | 1.31349i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.43521 | − | 55.8195i | 0.329693 | − | 1.95049i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.1883 | − | 23.2027i | 1.40258 | − | 0.809780i | 0.407923 | − | 0.913016i | \(-0.366253\pi\) |
0.994657 | + | 0.103236i | \(0.0329198\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.06808 | − | 0.552199i | 0.106817 | − | 0.0192251i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −28.5294 | + | 49.4144i | −0.989079 | + | 1.71314i | ||||
\(833\) | 34.8929 | + | 20.1454i | 1.20897 | + | 0.697997i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.4352 | − | 37.1269i | −0.741796 | − | 1.28483i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.00000 | − | 5.19615i | 0.103448 | − | 0.179178i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.5004 | − | 51.3951i | 0.637187 | − | 1.77014i | ||||
\(844\) | 3.87043 | + | 6.70377i | 0.133226 | + | 0.230753i | ||||
\(845\) | 84.6808i | 2.91311i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.7604 | −0.988221 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.50610 | − | 47.2609i | −0.291929 | − | 1.62199i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −55.6005 | + | 10.0071i | −1.90484 | + | 0.342837i | ||||
\(853\) | −21.1660 | − | 36.6606i | −0.724710 | − | 1.25524i | −0.959093 | − | 0.283091i | \(-0.908640\pi\) |
0.234383 | − | 0.972144i | \(-0.424693\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.51035 | + | 1.44935i | −0.0857520 | + | 0.0495090i | −0.542263 | − | 0.840209i | \(-0.682432\pi\) |
0.456511 | + | 0.889718i | \(0.349099\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25.0000 | −0.850026 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.3374 | − | 18.0334i | 0.724657 | − | 0.612447i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.94741 | + | 2.85639i | 0.167829 | + | 0.0968963i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 42.3718 | − | 15.7629i | 1.43407 | − | 0.533494i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 25.6174 | − | 14.7902i | 0.866025 | − | 0.500000i | ||||
\(876\) | 3.88262 | + | 21.5723i | 0.131182 | + | 0.728861i | ||||
\(877\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 41.9291 | − | 7.54648i | 1.41423 | − | 0.254536i | ||||
\(880\) | −1.60981 | − | 2.78827i | −0.0542666 | − | 0.0939925i | ||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | −71.1052 | + | 41.0526i | −2.39153 | + | 1.38075i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.9839 | + | 17.8885i | 1.04034 | + | 0.600639i | 0.919929 | − | 0.392086i | \(-0.128246\pi\) |
0.120408 | + | 0.992725i | \(0.461580\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.18216 | − | 0.607713i | 0.106606 | − | 0.0203592i | ||||
\(892\) | −17.4843 | −0.585418 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.6235 | + | 28.7928i | −0.555663 | + | 0.962437i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 5.00000 | − | 29.5804i | 0.166667 | − | 0.986013i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(908\) | − | 15.3212i | − | 0.508450i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.6174 | + | 9.59405i | −0.550558 | + | 0.317865i | −0.749347 | − | 0.662177i | \(-0.769633\pi\) |
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.27924 | + | 5.67982i | −0.108527 | + | 0.187975i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.0000 | 0.956622 | 0.478311 | − | 0.878191i | \(-0.341249\pi\) | ||||
0.478311 | + | 0.878191i | \(0.341249\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.4352 | − | 25.7224i | 1.00287 | − | 0.847584i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 100.734 | + | 58.1586i | 3.31569 | + | 1.91431i | ||||
\(924\) | 1.11738 | − | 3.10414i | 0.0367590 | − | 0.102119i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.11628 | + | 5.05876i | 0.200885 | + | 0.166152i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 4.63289i | − | 0.151512i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.6167 | 0.804191 | 0.402096 | − | 0.915598i | \(-0.368282\pi\) | ||||
0.402096 | + | 0.915598i | \(0.368282\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −47.4291 | − | 17.0728i | −1.54779 | − | 0.557148i | ||||
\(940\) | 27.8704 | − | 48.2730i | 0.909033 | − | 1.57449i | ||||
\(941\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 26.4575 | − | 15.6525i | 0.860663 | − | 0.509175i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(948\) | 41.9892 | − | 35.4874i | 1.36375 | − | 1.15258i | ||||
\(949\) | 22.5648 | − | 39.0834i | 0.732484 | − | 1.26870i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.2288 | −0.428073 | ||||||||
\(956\) | 51.2348 | − | 29.5804i | 1.65705 | − | 0.956698i | ||||
\(957\) | −0.653370 | − | 3.63020i | −0.0211205 | − | 0.117348i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −30.4939 | + | 5.48835i | −0.984186 | + | 0.177136i | ||||
\(961\) | −15.5000 | − | 26.8468i | −0.500000 | − | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 4.86917 | − | 30.7943i | 0.156179 | − | 0.987729i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −47.1761 | + | 39.8711i | −1.51084 | + | 1.27690i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 31.3050i | − | 1.00000i | ||||||
\(981\) | 4.93521 | − | 29.1971i | 0.157569 | − | 0.932192i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.0834 | + | 16.7913i | −0.927616 | + | 0.535559i | −0.886057 | − | 0.463577i | \(-0.846566\pi\) |
−0.0415592 | + | 0.999136i | \(0.513233\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 56.2141 | − | 10.1175i | 1.78932 | − | 0.322044i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.74085 | −0.150598 | −0.0752991 | − | 0.997161i | \(-0.523991\pi\) | ||||
−0.0752991 | + | 0.997161i | \(0.523991\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −56.6166 | − | 20.3799i | −1.79667 | − | 0.646737i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 40.7409 | + | 48.2052i | 1.29092 | + | 1.52744i | ||||
\(997\) | −9.26013 | − | 16.0390i | −0.293271 | − | 0.507961i | 0.681310 | − | 0.731995i | \(-0.261411\pi\) |
−0.974581 | + | 0.224034i | \(0.928077\pi\) | |||||||
\(998\) | 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 | 315.2.z.a.104.2 | ✓ | 8 | |
3.2 | odd | 2 | 945.2.z.a.314.4 | 8 | |||
5.4 | even | 2 | inner | 315.2.z.a.104.3 | yes | 8 | |
7.6 | odd | 2 | inner | 315.2.z.a.104.3 | yes | 8 | |
9.2 | odd | 6 | inner | 315.2.z.a.209.1 | yes | 8 | |
9.7 | even | 3 | 945.2.z.a.629.4 | 8 | |||
15.14 | odd | 2 | 945.2.z.a.314.1 | 8 | |||
21.20 | even | 2 | 945.2.z.a.314.1 | 8 | |||
35.34 | odd | 2 | CM | 315.2.z.a.104.2 | ✓ | 8 | |
45.29 | odd | 6 | inner | 315.2.z.a.209.4 | yes | 8 | |
45.34 | even | 6 | 945.2.z.a.629.1 | 8 | |||
63.20 | even | 6 | inner | 315.2.z.a.209.4 | yes | 8 | |
63.34 | odd | 6 | 945.2.z.a.629.1 | 8 | |||
105.104 | even | 2 | 945.2.z.a.314.4 | 8 | |||
315.34 | odd | 6 | 945.2.z.a.629.4 | 8 | |||
315.209 | even | 6 | inner | 315.2.z.a.209.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.z.a.104.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
315.2.z.a.104.2 | ✓ | 8 | 35.34 | odd | 2 | CM | |
315.2.z.a.104.3 | yes | 8 | 5.4 | even | 2 | inner | |
315.2.z.a.104.3 | yes | 8 | 7.6 | odd | 2 | inner | |
315.2.z.a.209.1 | yes | 8 | 9.2 | odd | 6 | inner | |
315.2.z.a.209.1 | yes | 8 | 315.209 | even | 6 | inner | |
315.2.z.a.209.4 | yes | 8 | 45.29 | odd | 6 | inner | |
315.2.z.a.209.4 | yes | 8 | 63.20 | even | 6 | inner | |
945.2.z.a.314.1 | 8 | 15.14 | odd | 2 | |||
945.2.z.a.314.1 | 8 | 21.20 | even | 2 | |||
945.2.z.a.314.4 | 8 | 3.2 | odd | 2 | |||
945.2.z.a.314.4 | 8 | 105.104 | even | 2 | |||
945.2.z.a.629.1 | 8 | 45.34 | even | 6 | |||
945.2.z.a.629.1 | 8 | 63.34 | odd | 6 | |||
945.2.z.a.629.4 | 8 | 9.7 | even | 3 | |||
945.2.z.a.629.4 | 8 | 315.34 | odd | 6 |