Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1584,2,Mod(17,1584)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1584, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 5, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1584.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1584.cd (of order \(10\), degree \(4\), 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: | \(12.6483036802\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 305.2 | ||
Root | \(0.0783900 + 1.17295i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1584.305 |
Dual form | 1584.2.cd.c.161.2 |
$q$-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 \(\left(\mathbb{Z}/1584\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(353\) | \(991\) | \(1189\) |
\(\chi(n)\) | \(e\left(\frac{3}{10}\right)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.71735 | + | 2.36373i | −0.768021 | + | 1.05709i | 0.228483 | + | 0.973548i | \(0.426624\pi\) |
−0.996504 | + | 0.0835427i | \(0.973376\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.58586 | − | 0.840196i | −0.977363 | − | 0.317564i | −0.223578 | − | 0.974686i | \(-0.571774\pi\) |
−0.753785 | + | 0.657122i | \(0.771774\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.71994 | + | 1.89788i | −0.820092 | + | 0.572232i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.67869 | − | 2.31052i | −0.465586 | − | 0.640824i | 0.510070 | − | 0.860133i | \(-0.329620\pi\) |
−0.975655 | + | 0.219309i | \(0.929620\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.60998 | + | 2.62280i | 0.875549 | + | 0.636124i | 0.932070 | − | 0.362278i | \(-0.118001\pi\) |
−0.0565211 | + | 0.998401i | \(0.518001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.81761 | − | 0.590579i | 0.416989 | − | 0.135488i | −0.0930053 | − | 0.995666i | \(-0.529647\pi\) |
0.509995 | + | 0.860178i | \(0.329647\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.816370i | − | 0.170225i | −0.996371 | − | 0.0851124i | \(-0.972875\pi\) | ||
0.996371 | − | 0.0851124i | \(-0.0271249\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.09283 | − | 3.36340i | −0.218567 | − | 0.672680i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.95006 | − | 9.07936i | 0.547813 | − | 1.68599i | −0.166394 | − | 0.986059i | \(-0.553212\pi\) |
0.714207 | − | 0.699935i | \(-0.246788\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.84281 | + | 3.51851i | −0.869795 | + | 0.631943i | −0.930532 | − | 0.366211i | \(-0.880655\pi\) |
0.0607369 | + | 0.998154i | \(0.480655\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.42681 | − | 4.66935i | 1.08633 | − | 0.789265i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.83750 | − | 5.65524i | 0.302083 | − | 0.929717i | −0.678666 | − | 0.734447i | \(-0.737442\pi\) |
0.980750 | − | 0.195270i | \(-0.0625583\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.60604 | + | 8.02058i | 0.406996 | + | 1.25260i | 0.919217 | + | 0.393751i | \(0.128823\pi\) |
−0.512221 | + | 0.858853i | \(0.671177\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.8763i | − | 1.81112i | −0.424214 | − | 0.905562i | \(-0.639450\pi\) | ||
0.424214 | − | 0.905562i | \(-0.360550\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.34041 | − | 2.38504i | 1.07071 | − | 0.347894i | 0.279945 | − | 0.960016i | \(-0.409684\pi\) |
0.790764 | + | 0.612122i | \(0.209684\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.317615 | + | 0.230761i | 0.0453735 | + | 0.0329658i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.14564 | − | 8.45874i | −0.844168 | − | 1.16190i | −0.985118 | − | 0.171881i | \(-0.945016\pi\) |
0.140950 | − | 0.990017i | \(-0.454984\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.185009 | − | 9.68851i | 0.0249466 | − | 1.30640i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.0887332 | − | 0.0288312i | −0.0115521 | − | 0.00375350i | 0.303235 | − | 0.952916i | \(-0.401933\pi\) |
−0.314787 | + | 0.949162i | \(0.601933\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.26024 | − | 1.73457i | 0.161357 | − | 0.222089i | −0.720681 | − | 0.693267i | \(-0.756171\pi\) |
0.882038 | + | 0.471177i | \(0.156171\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.34434 | 1.03499 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.40778 | 0.171988 | 0.0859941 | − | 0.996296i | \(-0.472593\pi\) | ||||
0.0859941 | + | 0.996296i | \(0.472593\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.12141 | − | 2.91987i | 0.251765 | − | 0.346525i | −0.664363 | − | 0.747410i | \(-0.731297\pi\) |
0.916128 | + | 0.400885i | \(0.131297\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.67338 | − | 0.543714i | −0.195854 | − | 0.0636369i | 0.209447 | − | 0.977820i | \(-0.432833\pi\) |
−0.405302 | + | 0.914183i | \(0.632833\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.62796 | − | 2.62237i | 0.983247 | − | 0.298846i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.19260 | + | 5.77063i | 0.471705 | + | 0.649246i | 0.976884 | − | 0.213768i | \(-0.0685737\pi\) |
−0.505180 | + | 0.863014i | \(0.668574\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.33808 | + | 4.60488i | 0.695695 | + | 0.505452i | 0.878527 | − | 0.477692i | \(-0.158527\pi\) |
−0.182833 | + | 0.983144i | \(0.558527\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.3992 | + | 4.02874i | −1.34488 | + | 0.436978i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.06830i | − | 0.219240i | −0.993974 | − | 0.109620i | \(-0.965037\pi\) | ||
0.993974 | − | 0.109620i | \(-0.0349633\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.39957 | + | 7.38512i | 0.251543 | + | 0.774171i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.72551 | + | 5.31057i | −0.177034 | + | 0.544853i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.35141 | + | 0.981858i | −0.137215 | + | 0.0996926i | −0.654275 | − | 0.756256i | \(-0.727026\pi\) |
0.517060 | + | 0.855949i | \(0.327026\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.31972 | − | 5.31809i | 0.728339 | − | 0.529170i | −0.160698 | − | 0.987004i | \(-0.551375\pi\) |
0.889038 | + | 0.457834i | \(0.151375\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.12132 | − | 15.7618i | 0.504618 | − | 1.55306i | −0.296793 | − | 0.954942i | \(-0.595917\pi\) |
0.801411 | − | 0.598114i | \(-0.204083\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.19803 | + | 6.76484i | 0.212492 | + | 0.653982i | 0.999322 | + | 0.0368130i | \(0.0117206\pi\) |
−0.786830 | + | 0.617169i | \(0.788279\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.62045i | − | 0.825690i | −0.910801 | − | 0.412845i | \(-0.864535\pi\) | ||
0.910801 | − | 0.412845i | \(-0.135465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.8495 | + | 3.52523i | −1.02064 | + | 0.331626i | −0.771083 | − | 0.636735i | \(-0.780285\pi\) |
−0.249556 | + | 0.968360i | \(0.580285\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.92967 | + | 1.40199i | 0.179943 | + | 0.130736i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.13123 | − | 9.81529i | −0.653719 | − | 0.899767i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.79611 | − | 10.3242i | 0.345101 | − | 0.938566i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.06670 | − | 1.32135i | −0.363737 | − | 0.118185i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.69463 | − | 2.33246i | 0.150374 | − | 0.206973i | −0.727184 | − | 0.686443i | \(-0.759171\pi\) |
0.877558 | + | 0.479470i | \(0.159171\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.10155 | 0.183613 | 0.0918067 | − | 0.995777i | \(-0.470736\pi\) | ||||
0.0918067 | + | 0.995777i | \(0.470736\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.19630 | −0.450576 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.98245 | + | 4.10498i | −0.254808 | + | 0.350712i | −0.917188 | − | 0.398455i | \(-0.869546\pi\) |
0.662380 | + | 0.749168i | \(0.269546\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.6282 | − | 5.40283i | −1.41039 | − | 0.458262i | −0.497852 | − | 0.867262i | \(-0.665878\pi\) |
−0.912535 | + | 0.409000i | \(0.865878\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.95103 | + | 3.09852i | 0.748523 | + | 0.259111i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.3948 | + | 22.5656i | 1.36152 | + | 1.87397i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.57623 | − | 3.32483i | −0.374900 | − | 0.272381i | 0.384340 | − | 0.923192i | \(-0.374429\pi\) |
−0.759240 | + | 0.650811i | \(0.774429\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.72640 | + | 2.83538i | −0.710145 | + | 0.230740i | −0.641745 | − | 0.766918i | \(-0.721789\pi\) |
−0.0683995 | + | 0.997658i | \(0.521789\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 17.4896i | − | 1.40480i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.943653 | − | 2.90426i | −0.0753117 | − | 0.231785i | 0.906313 | − | 0.422607i | \(-0.138885\pi\) |
−0.981625 | + | 0.190821i | \(0.938885\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.685911 | + | 2.11102i | −0.0540573 | + | 0.166371i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.39488 | − | 4.64615i | 0.500885 | − | 0.363914i | −0.308470 | − | 0.951234i | \(-0.599817\pi\) |
0.809355 | + | 0.587320i | \(0.199817\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.3065 | + | 9.66777i | −1.02969 | + | 0.748115i | −0.968247 | − | 0.249996i | \(-0.919571\pi\) |
−0.0614446 | + | 0.998110i | \(0.519571\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.49672 | − | 4.60642i | 0.115132 | − | 0.354340i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.79669 | + | 14.7627i | 0.364686 | + | 1.12239i | 0.950178 | + | 0.311709i | \(0.100901\pi\) |
−0.585492 | + | 0.810678i | \(0.699099\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.61547i | 0.726861i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.93538 | + | 1.60360i | −0.368888 | + | 0.119859i | −0.487594 | − | 0.873071i | \(-0.662125\pi\) |
0.118706 | + | 0.992929i | \(0.462125\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.29773 | − | 3.12248i | −0.319448 | − | 0.232092i | 0.416492 | − | 0.909139i | \(-0.363259\pi\) |
−0.735940 | + | 0.677047i | \(0.763259\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.2118 | + | 14.0554i | 0.750788 | + | 1.03337i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.7967 | − | 0.282553i | −1.08204 | − | 0.0206624i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.3662 | − | 3.36817i | −0.750069 | − | 0.243712i | −0.0910582 | − | 0.995846i | \(-0.529025\pi\) |
−0.659011 | + | 0.752133i | \(0.729025\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.03216 | − | 12.4317i | 0.650149 | − | 0.894853i | −0.348956 | − | 0.937139i | \(-0.613464\pi\) |
0.999106 | + | 0.0422855i | \(0.0134639\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.24149 | −0.515935 | −0.257967 | − | 0.966154i | \(-0.583053\pi\) | ||||
−0.257967 | + | 0.966154i | \(0.583053\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.3726 | 0.806181 | 0.403090 | − | 0.915160i | \(-0.367936\pi\) | ||||
0.403090 | + | 0.915160i | \(0.367936\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.2569 | + | 20.9993i | −1.07082 | + | 1.47386i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −23.4339 | − | 7.61415i | −1.63670 | − | 0.531795i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.82295 | + | 5.05595i | −0.264439 | + | 0.349727i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.17376 | + | 2.99193i | 0.149648 | + | 0.205973i | 0.877259 | − | 0.480017i | \(-0.159369\pi\) |
−0.727611 | + | 0.685990i | \(0.759369\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 28.0724 | + | 20.3958i | 1.91452 | + | 1.39098i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.4791 | − | 5.02946i | 1.05079 | − | 0.341422i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 12.7438i | − | 0.857243i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.0875209 | + | 0.269362i | 0.00586083 | + | 0.0180378i | 0.953944 | − | 0.299984i | \(-0.0969814\pi\) |
−0.948083 | + | 0.318022i | \(0.896981\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.64140 | − | 17.3625i | 0.374433 | − | 1.15239i | −0.569427 | − | 0.822042i | \(-0.692835\pi\) |
0.943860 | − | 0.330345i | \(-0.107165\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.3385 | + | 15.5033i | −1.41009 | + | 1.02449i | −0.416777 | + | 0.909009i | \(0.636840\pi\) |
−0.993310 | + | 0.115479i | \(0.963160\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.73916 | − | 6.34937i | 0.572521 | − | 0.415961i | −0.263499 | − | 0.964660i | \(-0.584877\pi\) |
0.836020 | + | 0.548699i | \(0.184877\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.96844 | + | 21.4467i | −0.454571 | + | 1.39903i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.29393 | − | 7.06000i | −0.148382 | − | 0.456673i | 0.849048 | − | 0.528315i | \(-0.177176\pi\) |
−0.997430 | + | 0.0716420i | \(0.977176\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 2.66873i | − | 0.171908i | −0.996299 | − | 0.0859539i | \(-0.972606\pi\) | ||
0.996299 | − | 0.0859539i | \(-0.0273938\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.09091 | + | 0.354458i | −0.0696957 | + | 0.0226455i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.41576 | − | 3.20824i | −0.280968 | − | 0.204135i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.2630 | − | 19.6313i | −0.900271 | − | 1.23912i | −0.970382 | − | 0.241577i | \(-0.922335\pi\) |
0.0701107 | − | 0.997539i | \(-0.477665\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.54937 | + | 2.22047i | 0.0974081 | + | 0.139600i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.9360 | − | 5.17791i | −0.994059 | − | 0.322989i | −0.233570 | − | 0.972340i | \(-0.575041\pi\) |
−0.760489 | + | 0.649351i | \(0.775041\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.50303 | + | 13.0798i | −0.590490 | + | 0.812739i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.9146 | −0.673021 | −0.336511 | − | 0.941680i | \(-0.609247\pi\) | ||||
−0.336511 | + | 0.941680i | \(0.609247\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 30.5484 | 1.87657 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.22041 | − | 12.6908i | 0.562178 | − | 0.773772i | −0.429423 | − | 0.903103i | \(-0.641283\pi\) |
0.991601 | + | 0.129331i | \(0.0412830\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.76289 | + | 0.897717i | 0.167834 | + | 0.0545324i | 0.391728 | − | 0.920081i | \(-0.371877\pi\) |
−0.223895 | + | 0.974613i | \(0.571877\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.35577 | + | 7.07416i | 0.564174 | + | 0.426588i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.4111 | + | 17.0824i | 0.745709 | + | 1.02638i | 0.998270 | + | 0.0587992i | \(0.0187272\pi\) |
−0.252561 | + | 0.967581i | \(0.581273\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.50015 | − | 1.81647i | −0.149147 | − | 0.108361i | 0.510709 | − | 0.859753i | \(-0.329383\pi\) |
−0.659856 | + | 0.751392i | \(0.729383\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.3272 | − | 6.92961i | 1.26777 | − | 0.411923i | 0.403512 | − | 0.914975i | \(-0.367789\pi\) |
0.864256 | + | 0.503052i | \(0.167789\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 22.9297i | − | 1.35350i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.899570 | + | 2.76859i | 0.0529159 | + | 0.162858i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.40930 | + | 19.7258i | −0.374435 | + | 1.15239i | 0.569423 | + | 0.822044i | \(0.307167\pi\) |
−0.943859 | + | 0.330349i | \(0.892833\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.220535 | − | 0.160228i | 0.0128400 | − | 0.00932883i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.88624 | + | 1.37043i | −0.109084 | + | 0.0792543i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.97845 | + | 30.7105i | −0.575148 | + | 1.77012i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.93578 | + | 5.95772i | 0.110843 | + | 0.341138i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.0077i | − | 0.856533i | −0.903652 | − | 0.428267i | \(-0.859124\pi\) | ||
0.903652 | − | 0.428267i | \(-0.140876\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.95824 | + | 0.636270i | −0.111042 | + | 0.0360796i | −0.364011 | − | 0.931395i | \(-0.618593\pi\) |
0.252969 | + | 0.967474i | \(0.418593\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.1223 | + | 14.6197i | 1.13738 | + | 0.826355i | 0.986752 | − | 0.162236i | \(-0.0518705\pi\) |
0.150628 | + | 0.988591i | \(0.451870\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.254351 | − | 0.350085i | −0.0142858 | − | 0.0196627i | 0.801814 | − | 0.597573i | \(-0.203868\pi\) |
−0.816100 | + | 0.577910i | \(0.803868\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.20754 | + | 30.2941i | 0.515523 | + | 1.69615i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.11053 | + | 2.63527i | 0.451282 | + | 0.146630i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.93668 | + | 8.17113i | −0.329308 | + | 0.453253i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.9852 | −1.15695 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.3090 | 0.951391 | 0.475696 | − | 0.879610i | \(-0.342196\pi\) | ||||
0.475696 | + | 0.879610i | \(0.342196\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.41766 | + | 3.32762i | −0.132091 | + | 0.181807i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.8381 | + | 7.74548i | 1.29855 | + | 0.421923i | 0.875076 | − | 0.483986i | \(-0.160812\pi\) |
0.423471 | + | 0.905910i | \(0.360812\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.49444 | − | 18.7612i | 0.351694 | − | 1.01598i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.5596 | + | 14.5341i | 0.570166 | + | 0.784766i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.8866 | − | 12.2688i | −0.906519 | − | 0.658625i | 0.0336127 | − | 0.999435i | \(-0.489299\pi\) |
−0.940132 | + | 0.340810i | \(0.889299\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.1385 | + | 5.56865i | −0.917405 | + | 0.298083i | −0.729402 | − | 0.684085i | \(-0.760202\pi\) |
−0.188003 | + | 0.982168i | \(0.560202\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 16.2953i | − | 0.867313i | −0.901078 | − | 0.433656i | \(-0.857223\pi\) | ||
0.901078 | − | 0.433656i | \(-0.142777\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.25858 | + | 10.0289i | 0.172947 | + | 0.532277i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.65875 | + | 23.5712i | −0.404213 | + | 1.24404i | 0.517337 | + | 0.855782i | \(0.326923\pi\) |
−0.921550 | + | 0.388259i | \(0.873077\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.4164 | + | 9.02103i | −0.653494 | + | 0.474791i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.15897 | − | 3.02167i | 0.217690 | − | 0.158161i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.76683 | + | 8.51544i | −0.144428 | + | 0.444502i | −0.996937 | − | 0.0782097i | \(-0.975080\pi\) |
0.852509 | + | 0.522712i | \(0.175080\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.78474 | + | 27.0367i | 0.456081 | + | 1.40367i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 16.9007i | − | 0.875088i | −0.899197 | − | 0.437544i | \(-0.855848\pi\) | ||
0.899197 | − | 0.437544i | \(-0.144152\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −25.9303 | + | 8.42527i | −1.33548 | + | 0.433923i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.9625 | + | 11.5975i | 0.819940 | + | 0.595722i | 0.916695 | − | 0.399587i | \(-0.130846\pi\) |
−0.0967550 | + | 0.995308i | \(0.530846\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.93889 | + | 4.04503i | 0.150170 | + | 0.206691i | 0.877474 | − | 0.479624i | \(-0.159227\pi\) |
−0.727304 | + | 0.686315i | \(0.759227\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.61865 | + | 24.8977i | −0.439247 | + | 1.26890i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.37115 | + | 3.04487i | 0.475136 | + | 0.154381i | 0.536789 | − | 0.843716i | \(-0.319637\pi\) |
−0.0616527 | + | 0.998098i | \(0.519637\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.14118 | − | 2.94708i | 0.108284 | − | 0.149040i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.8403 | −1.04859 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.0245 | −0.954812 | −0.477406 | − | 0.878683i | \(-0.658423\pi\) | ||||
−0.477406 | + | 0.878683i | \(0.658423\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0482 | + | 24.8413i | −0.901286 | + | 1.24051i | 0.0687699 | + | 0.997633i | \(0.478093\pi\) |
−0.970056 | + | 0.242881i | \(0.921907\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.2592 | + | 5.28293i | 0.809928 | + | 0.263162i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.73509 | + | 18.8693i | 0.284278 | + | 0.935315i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.97905 | − | 9.60583i | −0.345092 | − | 0.474978i | 0.600828 | − | 0.799378i | \(-0.294838\pi\) |
−0.945920 | + | 0.324400i | \(0.894838\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.205228 | + | 0.149107i | 0.0100986 | + | 0.00733706i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.7694 | + | 7.07330i | −1.06862 | + | 0.347215i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.0629i | 0.491606i | 0.969320 | + | 0.245803i | \(0.0790516\pi\) | ||||
−0.969320 | + | 0.245803i | \(0.920948\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.93337 | − | 5.95029i | −0.0942265 | − | 0.289999i | 0.892825 | − | 0.450404i | \(-0.148720\pi\) |
−0.987051 | + | 0.160405i | \(0.948720\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.87643 | − | 15.0081i | 0.236541 | − | 0.728000i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.71618 | + | 3.42651i | −0.228232 | + | 0.165820i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.8885 | − | 11.5436i | 0.765321 | − | 0.556038i | −0.135217 | − | 0.990816i | \(-0.543173\pi\) |
0.900538 | + | 0.434778i | \(0.143173\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.66882 | − | 29.7576i | 0.464654 | − | 1.43006i | −0.394764 | − | 0.918783i | \(-0.629174\pi\) |
0.859418 | − | 0.511274i | \(-0.170826\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.482131 | − | 1.48385i | −0.0230634 | − | 0.0709820i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 20.1935i | − | 0.963782i | −0.876231 | − | 0.481891i | \(-0.839950\pi\) | ||
0.876231 | − | 0.481891i | \(-0.160050\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.1752 | + | 7.53009i | −1.10109 | + | 0.357765i | −0.802521 | − | 0.596624i | \(-0.796509\pi\) |
−0.298567 | + | 0.954389i | \(0.596509\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.88890 | + | 3.55199i | 0.231756 | + | 0.168381i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.94082 | + | 2.67131i | 0.0915930 | + | 0.126067i | 0.852354 | − | 0.522965i | \(-0.175174\pi\) |
−0.760761 | + | 0.649032i | \(0.775174\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.3104 | − | 16.8695i | −1.05055 | − | 0.794354i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −21.5773 | − | 7.01089i | −1.01156 | − | 0.328675i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.17968 | + | 12.6347i | −0.429407 | + | 0.591028i | −0.967817 | − | 0.251655i | \(-0.919025\pi\) |
0.538410 | + | 0.842683i | \(0.319025\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.5685 | −1.70316 | −0.851582 | − | 0.524221i | \(-0.824356\pi\) | ||||
−0.851582 | + | 0.524221i | \(0.824356\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.45531 | −0.207056 | −0.103528 | − | 0.994627i | \(-0.533013\pi\) | ||||
−0.103528 | + | 0.994627i | \(0.533013\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.4676 | − | 33.6768i | 1.13223 | − | 1.55838i | 0.348458 | − | 0.937325i | \(-0.386706\pi\) |
0.783769 | − | 0.621052i | \(-0.213294\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.64033 | − | 1.18282i | −0.168095 | − | 0.0546173i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.5398 | + | 32.3029i | 1.03638 | + | 1.48529i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.97270 | − | 5.46796i | −0.182280 | − | 0.250887i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.84896 | − | 2.06989i | −0.130172 | − | 0.0945756i | 0.520794 | − | 0.853682i | \(-0.325636\pi\) |
−0.650966 | + | 0.759107i | \(0.725636\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.1512 | + | 5.24783i | −0.736430 | + | 0.239281i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 4.88056i | − | 0.221615i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.85775 | − | 30.3390i | −0.446697 | − | 1.37479i | −0.880611 | − | 0.473839i | \(-0.842868\pi\) |
0.433914 | − | 0.900954i | \(-0.357132\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.54595 | + | 23.2241i | −0.340544 | + | 1.04809i | 0.623382 | + | 0.781917i | \(0.285758\pi\) |
−0.963926 | + | 0.266170i | \(0.914242\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 34.4630 | − | 25.0389i | 1.55214 | − | 1.12769i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.93893 | + | 5.76797i | −0.356110 | + | 0.258729i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.19057 | − | 22.1303i | 0.321894 | − | 0.990689i | −0.650929 | − | 0.759139i | \(-0.725620\pi\) |
0.972823 | − | 0.231550i | \(-0.0743797\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.2856 | − | 34.7334i | −0.503199 | − | 1.54869i | −0.803778 | − | 0.594930i | \(-0.797180\pi\) |
0.300579 | − | 0.953757i | \(-0.402820\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.4348i | 1.17633i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.6347 | + | 7.67938i | −1.04759 | + | 0.340383i | −0.781722 | − | 0.623627i | \(-0.785659\pi\) |
−0.265868 | + | 0.964009i | \(0.585659\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.87030 | + | 2.81193i | 0.171212 | + | 0.124393i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.4615 | + | 39.1739i | 1.25416 | + | 1.72621i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.4389 | + | 20.4184i | −0.679003 | + | 0.897999i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.26334 | + | 3.00984i | 0.405834 | + | 0.131864i | 0.504819 | − | 0.863225i | \(-0.331559\pi\) |
−0.0989844 | + | 0.995089i | \(0.531559\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.5526 | + | 26.9118i | −0.854975 | + | 1.17677i | 0.127769 | + | 0.991804i | \(0.459218\pi\) |
−0.982744 | + | 0.184968i | \(0.940782\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.7108 | −1.16354 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.3335 | 0.971023 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.1570 | − | 19.4854i | 0.613207 | − | 0.844007i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.7650 | − | 6.42205i | −0.854517 | − | 0.277649i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.30185 | − | 0.0248597i | −0.0560746 | − | 0.00107078i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.85075 | − | 9.42925i | −0.294537 | − | 0.405395i | 0.635944 | − | 0.771735i | \(-0.280611\pi\) |
−0.930481 | + | 0.366340i | \(0.880611\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.3764 | + | 14.8043i | 0.872829 | + | 0.634147i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.773004 | + | 0.251164i | −0.0330513 | + | 0.0107390i | −0.325496 | − | 0.945543i | \(-0.605531\pi\) |
0.292445 | + | 0.956282i | \(0.405531\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 18.2450i | − | 0.777264i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.99302 | − | 18.4446i | −0.254849 | − | 0.784345i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.14843 | − | 6.61219i | 0.0910320 | − | 0.280168i | −0.895167 | − | 0.445730i | \(-0.852944\pi\) |
0.986199 | + | 0.165563i | \(0.0529440\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.4405 | + | 19.9367i | −1.16061 | + | 0.843233i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.2654 | − | 16.9033i | 0.980519 | − | 0.712388i | 0.0226941 | − | 0.999742i | \(-0.492776\pi\) |
0.957824 | + | 0.287354i | \(0.0927756\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.2998 | − | 31.6994i | 0.433314 | − | 1.33360i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.22890 | − | 9.93752i | −0.135362 | − | 0.416602i | 0.860284 | − | 0.509815i | \(-0.170286\pi\) |
−0.995646 | + | 0.0932129i | \(0.970286\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.2530i | 0.889409i | 0.895677 | + | 0.444704i | \(0.146691\pi\) | ||||
−0.895677 | + | 0.444704i | \(0.853309\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.74578 | + | 0.892157i | −0.114507 | + | 0.0372055i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.6856 | − | 9.21665i | −0.528110 | − | 0.383694i | 0.291541 | − | 0.956558i | \(-0.405832\pi\) |
−0.819650 | + | 0.572864i | \(0.805832\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.5204 | − | 17.2328i | −0.519432 | − | 0.714937i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.7694 | + | 11.3436i | 1.35717 | + | 0.469803i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.1691 | + | 6.22843i | 0.791195 | + | 0.257075i | 0.676613 | − | 0.736339i | \(-0.263447\pi\) |
0.114582 | + | 0.993414i | \(0.463447\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.72441 | + | 9.25536i | −0.277075 | + | 0.381360i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.5694 | 1.66599 | 0.832993 | − | 0.553284i | \(-0.186626\pi\) | ||||
0.832993 | + | 0.553284i | \(0.186626\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 35.4475 | 1.45320 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.42889 | − | 8.84861i | 0.262678 | − | 0.361545i | −0.657223 | − | 0.753696i | \(-0.728269\pi\) |
0.919901 | + | 0.392151i | \(0.128269\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.5556 | + | 5.05433i | 0.634527 | + | 0.206170i | 0.608580 | − | 0.793493i | \(-0.291740\pi\) |
0.0259478 | + | 0.999663i | \(0.491740\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.8844 | + | 26.7032i | 0.727104 | + | 1.08564i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.0272 | + | 19.3068i | 0.569348 | + | 0.783641i | 0.992477 | − | 0.122429i | \(-0.0390683\pi\) |
−0.423129 | + | 0.906069i | \(0.639068\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.8330 | − | 12.9564i | −0.721445 | − | 0.524161i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.0461533 | − | 0.0149961i | 0.00186411 | − | 0.000605687i | −0.308085 | − | 0.951359i | \(-0.599688\pi\) |
0.309949 | + | 0.950753i | \(0.399688\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 8.24561i | − | 0.331956i | −0.986129 | − | 0.165978i | \(-0.946922\pi\) | ||
0.986129 | − | 0.165978i | \(-0.0530780\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.537464 | + | 1.65414i | 0.0216025 | + | 0.0664857i | 0.961277 | − | 0.275585i | \(-0.0888717\pi\) |
−0.939674 | + | 0.342071i | \(0.888872\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.73778 | + | 5.34834i | −0.0696227 | + | 0.214277i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.4126 | − | 17.7368i | 0.976506 | − | 0.709473i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.4659 | − | 15.5959i | 0.855903 | − | 0.621850i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.14182 | − | 25.0580i | 0.324121 | − | 0.997541i | −0.647715 | − | 0.761883i | \(-0.724275\pi\) |
0.971836 | − | 0.235659i | \(-0.0757248\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.60303 | + | 8.01130i | 0.103298 | + | 0.317919i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.12123i | − | 0.0444249i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.27017 | + | 2.68714i | −0.326652 | + | 0.106136i | −0.467752 | − | 0.883860i | \(-0.654936\pi\) |
0.141100 | + | 0.989995i | \(0.454936\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.4877 | − | 12.7055i | −0.689646 | − | 0.501057i | 0.186897 | − | 0.982379i | \(-0.440157\pi\) |
−0.876544 | + | 0.481322i | \(0.840157\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.2616 | + | 23.7586i | 0.678625 | + | 0.934048i | 0.999916 | − | 0.0129330i | \(-0.00411681\pi\) |
−0.321291 | + | 0.946980i | \(0.604117\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.296067 | − | 0.0899860i | 0.0116216 | − | 0.00353226i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.5339 | − | 7.32170i | −0.881818 | − | 0.286520i | −0.167106 | − | 0.985939i | \(-0.553442\pi\) |
−0.714712 | + | 0.699419i | \(0.753442\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.60909 | + | 4.96749i | −0.141019 | + | 0.194096i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.5941 | −1.34759 | −0.673797 | − | 0.738916i | \(-0.735338\pi\) | ||||
−0.673797 | + | 0.738916i | \(0.735338\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.4913 | 1.38045 | 0.690225 | − | 0.723595i | \(-0.257512\pi\) | ||||
0.690225 | + | 0.723595i | \(0.257512\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.92385 | − | 12.2826i | 0.346052 | − | 0.476300i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.41211 | − | 2.40834i | −0.286998 | − | 0.0932513i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.135765 | + | 7.10971i | −0.00524115 | + | 0.274467i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.2854 | − | 16.9095i | −0.473569 | − | 0.651812i | 0.503684 | − | 0.863888i | \(-0.331978\pi\) |
−0.977253 | + | 0.212076i | \(0.931978\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.6090 | + | 14.2468i | 0.753634 | + | 0.547547i | 0.896951 | − | 0.442130i | \(-0.145777\pi\) |
−0.143317 | + | 0.989677i | \(0.545777\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.31951 | − | 1.40350i | 0.165768 | − | 0.0538612i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 17.6311i | − | 0.674636i | −0.941391 | − | 0.337318i | \(-0.890480\pi\) | ||
0.941391 | − | 0.337318i | \(-0.109520\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.58116 | − | 14.0994i | −0.175037 | − | 0.538709i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.22748 | + | 28.3993i | −0.351539 | + | 1.08193i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.5718 | − | 17.1259i | 0.896713 | − | 0.651500i | −0.0409063 | − | 0.999163i | \(-0.513024\pi\) |
0.937620 | + | 0.347663i | \(0.113024\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 41.3272 | − | 30.0260i | 1.56763 | − | 1.13895i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.6286 | + | 35.7893i | −0.440466 | + | 1.35562i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.54301 | − | 13.9820i | −0.171587 | − | 0.528091i | 0.827874 | − | 0.560914i | \(-0.189550\pi\) |
−0.999461 | + | 0.0328229i | \(0.989550\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 11.3642i | − | 0.428611i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23.3960 | + | 7.60182i | −0.879897 | + | 0.285896i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.72312 | − | 6.33772i | −0.327604 | − | 0.238018i | 0.411810 | − | 0.911270i | \(-0.364897\pi\) |
−0.739413 | + | 0.673252i | \(0.764897\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.87241 | + | 3.95353i | 0.107572 | + | 0.148061i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.6961 | + | 15.8366i | −0.848785 | + | 0.592254i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.1960 | − | 9.81128i | −1.12612 | − | 0.365899i | −0.314020 | − | 0.949416i | \(-0.601676\pi\) |
−0.812101 | + | 0.583517i | \(0.801676\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.4860 | + | 36.4549i | −0.986390 | + | 1.35765i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −33.7614 | −1.25387 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.6418 | −0.876828 | −0.438414 | − | 0.898773i | \(-0.644460\pi\) | ||||
−0.438414 | + | 0.898773i | \(0.644460\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.1493 | − | 42.8733i | 1.15210 | − | 1.58573i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.6206 | + | 5.07543i | 0.576959 | + | 0.187465i | 0.582938 | − | 0.812517i | \(-0.301903\pi\) |
−0.00597872 | + | 0.999982i | \(0.501903\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.82908 | + | 2.67181i | −0.141046 | + | 0.0984172i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.4813 | − | 28.1901i | −0.753417 | − | 1.03699i | −0.997733 | − | 0.0672942i | \(-0.978563\pi\) |
0.244316 | − | 0.969696i | \(-0.421437\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 42.7101 | + | 31.0307i | 1.56688 | + | 1.13841i | 0.930068 | + | 0.367387i | \(0.119748\pi\) |
0.636813 | + | 0.771019i | \(0.280252\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.7180 | − | 5.10708i | 0.575862 | − | 0.187109i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 19.3397i | − | 0.706657i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.8766 | − | 48.8631i | −0.579345 | − | 1.78304i | −0.620883 | − | 0.783903i | \(-0.713226\pi\) |
0.0415382 | − | 0.999137i | \(-0.486774\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.28421 | − | 25.4962i | 0.301493 | − | 0.927900i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.71877 | − | 4.15493i | 0.207852 | − | 0.151013i | −0.478989 | − | 0.877821i | \(-0.658997\pi\) |
0.686841 | + | 0.726807i | \(0.258997\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.5688 | − | 17.1238i | 0.854370 | − | 0.620736i | −0.0719775 | − | 0.997406i | \(-0.522931\pi\) |
0.926347 | + | 0.376670i | \(0.122931\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.24287 | + | 22.2913i | −0.262210 | + | 0.806998i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.0823407 | + | 0.253419i | 0.00297315 | + | 0.00915042i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 44.2408i | − | 1.59536i | −0.603079 | − | 0.797682i | \(-0.706060\pi\) | ||
0.603079 | − | 0.797682i | \(-0.293940\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.0786 | − | 12.3725i | 1.36959 | − | 0.445007i | 0.470358 | − | 0.882476i | \(-0.344125\pi\) |
0.899234 | + | 0.437468i | \(0.144125\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.1266 | + | 12.4432i | 0.615204 | + | 0.446972i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.47357 | + | 13.0393i | 0.339426 | + | 0.467180i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.228538 | + | 11.9680i | −0.00817775 | + | 0.428250i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.48547 | + | 2.75709i | 0.302859 | + | 0.0984049i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.6720 | − | 22.9470i | 0.594292 | − | 0.817973i | −0.400878 | − | 0.916131i | \(-0.631295\pi\) |
0.995171 | + | 0.0981579i | \(0.0312950\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.0173 | 1.10285 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.12332 | −0.217446 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.78371 | − | 12.0897i | 0.311135 | − | 0.428241i | −0.624600 | − | 0.780945i | \(-0.714738\pi\) |
0.935735 | + | 0.352704i | \(0.114738\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.7542 | + | 10.6425i | 1.15876 | + | 0.376504i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.58339 | − | 1.69700i | 0.197034 | − | 0.0598860i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.81192 | − | 5.24666i | −0.134352 | − | 0.184920i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.0892 | + | 17.5019i | 0.846933 | + | 0.615333i | 0.924299 | − | 0.381670i | \(-0.124651\pi\) |
−0.0773660 | + | 0.997003i | \(0.524651\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.9856 | + | 13.6420i | −1.47432 | + | 0.479034i | −0.932409 | − | 0.361405i | \(-0.882297\pi\) |
−0.541906 | + | 0.840439i | \(0.682297\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.0948i | 0.808975i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.01391 | − | 21.5866i | −0.245386 | − | 0.755220i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.23760 | + | 3.80893i | −0.0431924 | + | 0.132933i | −0.970327 | − | 0.241795i | \(-0.922264\pi\) |
0.927135 | + | 0.374728i | \(0.122264\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.1262 | − | 24.7941i | 1.18956 | − | 0.864268i | 0.196345 | − | 0.980535i | \(-0.437093\pi\) |
0.993218 | + | 0.116266i | \(0.0370926\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.5183 | − | 15.6340i | 0.748266 | − | 0.543647i | −0.147023 | − | 0.989133i | \(-0.546969\pi\) |
0.895289 | + | 0.445486i | \(0.146969\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.77976 | − | 11.6329i | 0.131276 | − | 0.404027i | −0.863716 | − | 0.503979i | \(-0.831869\pi\) |
0.994992 | + | 0.0999518i | \(0.0318689\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.541343 | + | 1.66608i | 0.0187564 | + | 0.0577264i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 48.0560i | − | 1.66305i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.17434 | − | 2.98092i | 0.316733 | − | 0.102913i | −0.146336 | − | 0.989235i | \(-0.546748\pi\) |
0.463069 | + | 0.886322i | \(0.346748\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −50.2704 | − | 36.5236i | −1.73346 | − | 1.25943i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.31793 | + | 11.4486i | 0.286146 | + | 0.393846i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.4906 | + | 23.5075i | −0.635344 | + | 0.807727i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.61677 | − | 1.50008i | −0.158261 | − | 0.0514221i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.89976 | + | 9.49670i | −0.236243 | + | 0.325161i | −0.910634 | − | 0.413214i | \(-0.864406\pi\) |
0.674391 | + | 0.738374i | \(0.264406\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.7738 | −1.66608 | −0.833041 | − | 0.553212i | \(-0.813402\pi\) | ||||
−0.833041 | + | 0.553212i | \(0.813402\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.0880 | 1.06071 | 0.530355 | − | 0.847776i | \(-0.322059\pi\) | ||||
0.530355 | + | 0.847776i | \(0.322059\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.6459 | + | 42.1805i | −1.04320 | + | 1.43584i | −0.148641 | + | 0.988891i | \(0.547490\pi\) |
−0.894559 | + | 0.446950i | \(0.852510\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43.1325 | − | 14.0146i | −1.46655 | − | 0.476511i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.3556 | − | 7.73868i | −0.758361 | − | 0.262517i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.36324 | − | 3.25272i | −0.0800753 | − | 0.110214i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.40572 | + | 6.83366i | 0.317971 | + | 0.231020i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.1564 | − | 5.24952i | 0.545561 | − | 0.177264i | −0.0232530 | − | 0.999730i | \(-0.507402\pi\) |
0.568814 | + | 0.822466i | \(0.307402\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 50.3115i | − | 1.69504i | −0.530765 | − | 0.847519i | \(-0.678095\pi\) | ||
0.530765 | − | 0.847519i | \(-0.321905\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.44037 | − | 13.6660i | −0.149430 | − | 0.459899i | 0.848124 | − | 0.529798i | \(-0.177732\pi\) |
−0.997554 | + | 0.0698990i | \(0.977732\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.7625 | + | 39.2790i | −0.428523 | + | 1.31886i | 0.471057 | + | 0.882103i | \(0.343873\pi\) |
−0.899580 | + | 0.436756i | \(0.856127\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.34181 | + | 4.60760i | −0.212698 | + | 0.154534i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.9335 | − | 8.67018i | 0.399339 | − | 0.290136i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.68529 | − | 14.4198i | 0.156612 | − | 0.482002i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.6592 | + | 54.3495i | 0.588968 | + | 1.81266i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 46.6547i | − | 1.55429i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.7614 | − | 4.79627i | 0.490685 | − | 0.159433i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.1288 | − | 15.3510i | −0.701571 | − | 0.509721i | 0.178872 | − | 0.983872i | \(-0.442755\pi\) |
−0.880444 | + | 0.474151i | \(0.842755\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.6929 | − | 36.7397i | −0.884377 | − | 1.21724i | −0.975189 | − | 0.221372i | \(-0.928946\pi\) |
0.0908128 | − | 0.995868i | \(-0.471054\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.9787 | − | 0.496082i | −0.859769 | − | 0.0164179i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.43431 | − | 1.76572i | −0.179457 | − | 0.0583091i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.3737 | − | 22.5365i | 0.540119 | − | 0.743410i | −0.448511 | − | 0.893777i | \(-0.648046\pi\) |
0.988630 | + | 0.150367i | \(0.0480456\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.3076 | −0.339280 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.0289 | −0.691427 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.2450 | − | 40.2523i | 0.959497 | − | 1.32063i | 0.0123191 | − | 0.999924i | \(-0.496079\pi\) |
0.947178 | − | 0.320710i | \(-0.103921\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.713584 | + | 0.231857i | 0.0233868 | + | 0.00759882i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26.0789 | − | 34.4901i | 0.852872 | − | 1.12795i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.9943 | + | 16.5087i | 0.391837 | + | 0.539317i | 0.958672 | − | 0.284514i | \(-0.0918323\pi\) |
−0.566835 | + | 0.823831i | \(0.691832\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.1929 | + | 10.3117i | 0.462675 | + | 0.336153i | 0.794580 | − | 0.607160i | \(-0.207691\pi\) |
−0.331904 | + | 0.943313i | \(0.607691\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.54776 | − | 2.12750i | 0.213224 | − | 0.0692808i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 47.0672i | − | 1.52948i | −0.644340 | − | 0.764739i | \(-0.722868\pi\) | ||
0.644340 | − | 0.764739i | \(-0.277132\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.55283 | + | 4.77911i | 0.0504069 | + | 0.155136i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.9545 | + | 49.1029i | −0.516817 | + | 1.59060i | 0.263136 | + | 0.964759i | \(0.415243\pi\) |
−0.779952 | + | 0.625839i | \(0.784757\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.7637 | − | 18.7185i | 0.833695 | − | 0.605715i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.1612 | − | 8.10907i | 0.360413 | − | 0.261855i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.49341 | − | 4.59623i | 0.0481744 | − | 0.148266i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.8738 | + | 42.6991i | 0.446613 | + | 1.37453i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.6964i | 1.08360i | 0.840506 | + | 0.541802i | \(0.182258\pi\) | ||||
−0.840506 | + | 0.541802i | \(0.817742\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53.1467 | + | 17.2684i | −1.70556 | + | 0.554170i | −0.989584 | − | 0.143955i | \(-0.954018\pi\) |
−0.715976 | + | 0.698125i | \(0.754018\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38.4588 | + | 27.9419i | 1.23293 | + | 0.895777i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.1432 | + | 16.7137i | 0.388496 | + | 0.534719i | 0.957810 | − | 0.287401i | \(-0.0927912\pi\) |
−0.569314 | + | 0.822120i | \(0.692791\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.92539 | + | 5.62565i | 0.125456 | + | 0.179797i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47.6740 | + | 15.4902i | 1.52056 | + | 0.494061i | 0.945936 | − | 0.324354i | \(-0.105147\pi\) |
0.574628 | + | 0.818415i | \(0.305147\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.4362 | − | 17.1169i | 0.396249 | − | 0.545390i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.69548 | −0.308298 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.3068 | −1.43922 | −0.719609 | − | 0.694379i | \(-0.755679\pi\) | ||||
−0.719609 | + | 0.694379i | \(0.755679\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.5307 | + | 26.8817i | −0.619164 | + | 0.852206i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.77676 | + | 3.17666i | 0.309633 | + | 0.100606i | 0.459712 | − | 0.888068i | \(-0.347953\pi\) |
−0.150079 | + | 0.988674i | \(0.547953\pi\) | |||||||
\(998\) | 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 | 1584.2.cd.c.305.2 | 16 | ||
3.2 | odd | 2 | inner | 1584.2.cd.c.305.3 | 16 | ||
4.3 | odd | 2 | 99.2.j.a.8.2 | ✓ | 16 | ||
11.7 | odd | 10 | inner | 1584.2.cd.c.161.3 | 16 | ||
12.11 | even | 2 | 99.2.j.a.8.3 | yes | 16 | ||
33.29 | even | 10 | inner | 1584.2.cd.c.161.2 | 16 | ||
36.7 | odd | 6 | 891.2.u.c.701.3 | 32 | |||
36.11 | even | 6 | 891.2.u.c.701.2 | 32 | |||
36.23 | even | 6 | 891.2.u.c.107.3 | 32 | |||
36.31 | odd | 6 | 891.2.u.c.107.2 | 32 | |||
44.7 | even | 10 | 99.2.j.a.62.3 | yes | 16 | ||
44.31 | odd | 10 | 1089.2.d.g.1088.9 | 16 | |||
44.35 | even | 10 | 1089.2.d.g.1088.7 | 16 | |||
132.35 | odd | 10 | 1089.2.d.g.1088.10 | 16 | |||
132.95 | odd | 10 | 99.2.j.a.62.2 | yes | 16 | ||
132.119 | even | 10 | 1089.2.d.g.1088.8 | 16 | |||
396.7 | even | 30 | 891.2.u.c.458.3 | 32 | |||
396.95 | odd | 30 | 891.2.u.c.755.3 | 32 | |||
396.139 | even | 30 | 891.2.u.c.755.2 | 32 | |||
396.227 | odd | 30 | 891.2.u.c.458.2 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.j.a.8.2 | ✓ | 16 | 4.3 | odd | 2 | ||
99.2.j.a.8.3 | yes | 16 | 12.11 | even | 2 | ||
99.2.j.a.62.2 | yes | 16 | 132.95 | odd | 10 | ||
99.2.j.a.62.3 | yes | 16 | 44.7 | even | 10 | ||
891.2.u.c.107.2 | 32 | 36.31 | odd | 6 | |||
891.2.u.c.107.3 | 32 | 36.23 | even | 6 | |||
891.2.u.c.458.2 | 32 | 396.227 | odd | 30 | |||
891.2.u.c.458.3 | 32 | 396.7 | even | 30 | |||
891.2.u.c.701.2 | 32 | 36.11 | even | 6 | |||
891.2.u.c.701.3 | 32 | 36.7 | odd | 6 | |||
891.2.u.c.755.2 | 32 | 396.139 | even | 30 | |||
891.2.u.c.755.3 | 32 | 396.95 | odd | 30 | |||
1089.2.d.g.1088.7 | 16 | 44.35 | even | 10 | |||
1089.2.d.g.1088.8 | 16 | 132.119 | even | 10 | |||
1089.2.d.g.1088.9 | 16 | 44.31 | odd | 10 | |||
1089.2.d.g.1088.10 | 16 | 132.35 | odd | 10 | |||
1584.2.cd.c.161.2 | 16 | 33.29 | even | 10 | inner | ||
1584.2.cd.c.161.3 | 16 | 11.7 | odd | 10 | inner | ||
1584.2.cd.c.305.2 | 16 | 1.1 | even | 1 | trivial | ||
1584.2.cd.c.305.3 | 16 | 3.2 | odd | 2 | inner |