Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(193,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.bs (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 357.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.357 |
Dual form | 1300.2.bs.b.193.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{5}{12}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | + | 1.86603i | 0.288675 | + | 1.07735i | 0.946112 | + | 0.323840i | \(0.104974\pi\) |
−0.657437 | + | 0.753510i | \(0.728359\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.86603 | − | 2.23205i | 1.46122 | − | 0.843636i | 0.462152 | − | 0.886801i | \(-0.347077\pi\) |
0.999068 | + | 0.0431647i | \(0.0137440\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.633975 | + | 0.366025i | −0.211325 | + | 0.122008i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.86603 | + | 0.767949i | −0.864139 | + | 0.231545i | −0.663552 | − | 0.748130i | \(-0.730952\pi\) |
−0.200587 | + | 0.979676i | \(0.564285\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | + | 3.00000i | 0.554700 | + | 0.832050i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.23205 | − | 0.866025i | −0.783887 | − | 0.210042i | −0.155390 | − | 0.987853i | \(-0.549663\pi\) |
−0.628498 | + | 0.777811i | \(0.716330\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.13397 | + | 4.23205i | −0.260152 | + | 0.970899i | 0.705000 | + | 0.709207i | \(0.250947\pi\) |
−0.965152 | + | 0.261692i | \(0.915720\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.09808 | + | 6.09808i | 1.33071 | + | 1.33071i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.96410 | − | 1.86603i | 1.45212 | − | 0.389093i | 0.555357 | − | 0.831612i | \(-0.312582\pi\) |
0.896759 | + | 0.442519i | \(0.145915\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.09808 | + | 3.09808i | 0.596225 | + | 0.596225i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50000 | − | 0.866025i | −0.278543 | − | 0.160817i | 0.354221 | − | 0.935162i | \(-0.384746\pi\) |
−0.632764 | + | 0.774345i | \(0.718080\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.19615 | − | 5.19615i | 0.933257 | − | 0.933257i | −0.0646514 | − | 0.997908i | \(-0.520594\pi\) |
0.997908 | + | 0.0646514i | \(0.0205935\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.86603 | − | 4.96410i | −0.498911 | − | 0.864139i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.33013 | + | 4.23205i | 1.20507 | + | 0.695745i | 0.961677 | − | 0.274184i | \(-0.0884078\pi\) |
0.243388 | + | 0.969929i | \(0.421741\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.59808 | + | 5.23205i | −0.736281 | + | 0.837799i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.669873 | + | 2.50000i | 0.104617 | + | 0.390434i | 0.998301 | − | 0.0582609i | \(-0.0185555\pi\) |
−0.893685 | + | 0.448695i | \(0.851889\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.964102 | + | 3.59808i | −0.147024 | + | 0.548701i | 0.852633 | + | 0.522511i | \(0.175004\pi\) |
−0.999657 | + | 0.0261910i | \(0.991662\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 2.92820i | − | 0.427122i | −0.976930 | − | 0.213561i | \(-0.931494\pi\) | ||
0.976930 | − | 0.213561i | \(-0.0685063\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.46410 | − | 11.1962i | 0.923443 | − | 1.59945i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 6.46410i | − | 0.905155i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.46410 | − | 4.46410i | 0.613192 | − | 0.613192i | −0.330585 | − | 0.943776i | \(-0.607246\pi\) |
0.943776 | + | 0.330585i | \(0.107246\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.46410 | −1.12110 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.33013 | − | 1.69615i | −0.824112 | − | 0.220820i | −0.177969 | − | 0.984036i | \(-0.556953\pi\) |
−0.646144 | + | 0.763216i | \(0.723619\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.50000 | + | 7.79423i | 0.576166 | + | 0.997949i | 0.995914 | + | 0.0903080i | \(0.0287851\pi\) |
−0.419748 | + | 0.907641i | \(0.637882\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.63397 | + | 2.83013i | −0.205861 | + | 0.356562i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.86603 | + | 13.6244i | −0.960988 | + | 1.66448i | −0.240960 | + | 0.970535i | \(0.577462\pi\) |
−0.720028 | + | 0.693945i | \(0.755871\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.96410 | + | 12.0622i | 0.838379 | + | 1.45212i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.59808 | − | 1.23205i | −0.545691 | − | 0.146218i | −0.0245667 | − | 0.999698i | \(-0.507821\pi\) |
−0.521125 | + | 0.853481i | \(0.674487\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.07180 | 0.125444 | 0.0627222 | − | 0.998031i | \(-0.480022\pi\) | ||||
0.0627222 | + | 0.998031i | \(0.480022\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.36603 | + | 9.36603i | −1.06736 | + | 1.06736i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.46410i | 0.839777i | 0.907576 | + | 0.419889i | \(0.137931\pi\) | ||||
−0.907576 | + | 0.419889i | \(0.862069\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.33013 | + | 9.23205i | −0.592236 | + | 1.02578i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 10.9282i | − | 1.19953i | −0.800178 | − | 0.599763i | \(-0.795261\pi\) | ||
0.800178 | − | 0.599763i | \(-0.204739\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.866025 | − | 3.23205i | 0.0928477 | − | 0.346512i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.794229 | + | 2.96410i | 0.0841881 | + | 0.314194i | 0.995159 | − | 0.0982760i | \(-0.0313328\pi\) |
−0.910971 | + | 0.412470i | \(0.864666\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.4282 | + | 7.13397i | 1.51249 | + | 0.747844i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.2942 | + | 7.09808i | 1.27485 | + | 0.736036i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.13397 | − | 3.69615i | −0.216672 | − | 0.375287i | 0.737116 | − | 0.675766i | \(-0.236187\pi\) |
−0.953789 | + | 0.300478i | \(0.902854\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.53590 | − | 1.53590i | 0.154364 | − | 0.154364i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.89230 | + | 3.40192i | 0.586306 | + | 0.338504i | 0.763636 | − | 0.645647i | \(-0.223412\pi\) |
−0.177329 | + | 0.984152i | \(0.556746\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.803848 | + | 0.803848i | 0.0792055 | + | 0.0792055i | 0.745600 | − | 0.666394i | \(-0.232163\pi\) |
−0.666394 | + | 0.745600i | \(0.732163\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.96410 | + | 1.33013i | −0.479898 | + | 0.128588i | −0.490655 | − | 0.871354i | \(-0.663242\pi\) |
0.0107572 | + | 0.999942i | \(0.496576\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.4641 | − | 10.4641i | −1.00228 | − | 1.00228i | −0.999997 | − | 0.00228176i | \(-0.999274\pi\) |
−0.00228176 | − | 0.999997i | \(-0.500726\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.23205 | + | 15.7942i | −0.401688 | + | 1.49912i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.23205 | − | 1.13397i | −0.398118 | − | 0.106675i | 0.0542046 | − | 0.998530i | \(-0.482738\pi\) |
−0.452322 | + | 0.891854i | \(0.649404\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.36603 | − | 1.16987i | −0.218739 | − | 0.108155i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.4282 | + | 3.86603i | −1.32263 | + | 0.354398i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.90192 | + | 1.09808i | −0.172902 | + | 0.0998251i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.33013 | + | 2.50000i | −0.390434 | + | 0.225417i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.892305 | − | 3.33013i | −0.0791793 | − | 0.295501i | 0.914969 | − | 0.403524i | \(-0.132215\pi\) |
−0.994148 | + | 0.108023i | \(0.965548\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.19615 | −0.633586 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.8564 | −1.90960 | −0.954802 | − | 0.297244i | \(-0.903933\pi\) | ||||
−0.954802 | + | 0.297244i | \(0.903933\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.06218 | + | 18.8923i | 0.438946 | + | 1.63817i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.5981 | − | 10.1603i | 1.50351 | − | 0.868049i | 0.503513 | − | 0.863987i | \(-0.332040\pi\) |
0.999992 | − | 0.00406165i | \(-0.00129287\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.50000 | + | 2.59808i | −0.381685 | + | 0.220366i | −0.678551 | − | 0.734553i | \(-0.737392\pi\) |
0.296866 | + | 0.954919i | \(0.404058\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.46410 | − | 1.46410i | 0.460160 | − | 0.123300i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.03590 | − | 7.06218i | −0.671996 | − | 0.590569i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 24.1244 | + | 6.46410i | 1.98974 | + | 0.533150i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.33013 | − | 19.8923i | 0.436661 | − | 1.62964i | −0.300399 | − | 0.953814i | \(-0.597120\pi\) |
0.737060 | − | 0.675827i | \(-0.236214\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.73205 | − | 3.73205i | −0.303710 | − | 0.303710i | 0.538753 | − | 0.842463i | \(-0.318895\pi\) |
−0.842463 | + | 0.538753i | \(0.818895\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.36603 | − | 0.633975i | 0.191282 | − | 0.0512538i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.464102 | + | 0.464102i | 0.0370393 | + | 0.0370393i | 0.725384 | − | 0.688345i | \(-0.241662\pi\) |
−0.688345 | + | 0.725384i | \(0.741662\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.5622 | + | 6.09808i | 0.837635 | + | 0.483609i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.7583 | − | 22.7583i | 1.79361 | − | 1.79361i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.59808 | − | 6.23205i | −0.281823 | − | 0.488132i | 0.690011 | − | 0.723799i | \(-0.257606\pi\) |
−0.971834 | + | 0.235667i | \(0.924272\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.99038 | − | 5.76795i | −0.773079 | − | 0.446337i | 0.0608930 | − | 0.998144i | \(-0.480605\pi\) |
−0.833972 | + | 0.551807i | \(0.813939\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | + | 12.0000i | −0.384615 | + | 0.923077i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.830127 | − | 3.09808i | −0.0634814 | − | 0.236916i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.23205 | − | 23.2583i | 0.473814 | − | 1.76830i | −0.152057 | − | 0.988372i | \(-0.548590\pi\) |
0.625871 | − | 0.779926i | \(-0.284744\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 12.6603i | − | 0.951603i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.0358984 | − | 0.0621778i | 0.00268317 | − | 0.00464739i | −0.864681 | − | 0.502322i | \(-0.832479\pi\) |
0.867364 | + | 0.497675i | \(0.165813\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.07180i | − | 0.674301i | −0.941451 | − | 0.337151i | \(-0.890537\pi\) | ||
0.941451 | − | 0.337151i | \(-0.109463\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.2942 | + | 12.2942i | −0.908816 | + | 0.908816i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.92820 | 0.726022 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.8923 | + | 5.06218i | 1.37421 | + | 0.368219i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.50000 | + | 12.9904i | 0.542681 | + | 0.939951i | 0.998749 | + | 0.0500060i | \(0.0159241\pi\) |
−0.456068 | + | 0.889945i | \(0.650743\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.79423 | − | 4.83975i | 0.201133 | − | 0.348373i | −0.747761 | − | 0.663968i | \(-0.768871\pi\) |
0.948894 | + | 0.315596i | \(0.102204\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.86603 | + | 6.69615i | −0.275443 | + | 0.477081i | −0.970247 | − | 0.242118i | \(-0.922158\pi\) |
0.694804 | + | 0.719199i | \(0.255491\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.42820 | − | 7.66987i | −0.313907 | − | 0.543703i | 0.665298 | − | 0.746578i | \(-0.268305\pi\) |
−0.979205 | + | 0.202875i | \(0.934971\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −29.3564 | − | 7.86603i | −2.07064 | − | 0.554827i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.73205 | −0.542684 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.73205 | + | 3.73205i | −0.259395 | + | 0.259395i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 13.0000i | − | 0.899229i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.96410 | − | 6.86603i | 0.272900 | − | 0.472677i | −0.696703 | − | 0.717360i | \(-0.745351\pi\) |
0.969603 | + | 0.244683i | \(0.0786838\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 9.19615i | − | 0.630110i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.49038 | − | 31.6865i | 0.576365 | − | 2.15102i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.535898 | + | 2.00000i | 0.0362127 | + | 0.135147i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.86603 | − | 11.4282i | −0.260057 | − | 0.768744i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.33013 | − | 4.23205i | −0.490862 | − | 0.283399i | 0.234070 | − | 0.972220i | \(-0.424795\pi\) |
−0.724932 | + | 0.688821i | \(0.758129\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.59808 | + | 6.23205i | 0.238813 | + | 0.413636i | 0.960374 | − | 0.278715i | \(-0.0899085\pi\) |
−0.721561 | + | 0.692351i | \(0.756575\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.9282 | − | 13.9282i | 0.920402 | − | 0.920402i | −0.0766560 | − | 0.997058i | \(-0.524424\pi\) |
0.997058 | + | 0.0766560i | \(0.0244243\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −22.1603 | − | 12.7942i | −1.45804 | − | 0.841798i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.8564 | + | 14.8564i | 0.973276 | + | 0.973276i | 0.999652 | − | 0.0263765i | \(-0.00839688\pi\) |
−0.0263765 | + | 0.999652i | \(0.508397\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.9282 | + | 3.73205i | −0.904734 | + | 0.242423i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.660254 | − | 0.660254i | −0.0427083 | − | 0.0427083i | 0.685430 | − | 0.728138i | \(-0.259614\pi\) |
−0.728138 | + | 0.685430i | \(0.759614\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.66987 | − | 9.96410i | 0.171982 | − | 0.641844i | −0.825064 | − | 0.565039i | \(-0.808861\pi\) |
0.997046 | − | 0.0768056i | \(-0.0244721\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.19615 | − | 1.92820i | −0.461633 | − | 0.123694i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.9641 | + | 5.06218i | −0.952143 | + | 0.322099i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.3923 | − | 5.46410i | 1.29231 | − | 0.346273i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.3564 | − | 7.13397i | 0.779929 | − | 0.450292i | −0.0564758 | − | 0.998404i | \(-0.517986\pi\) |
0.836405 | + | 0.548111i | \(0.184653\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.5263 | + | 10.6962i | −1.16474 | + | 0.672461i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.62436 | + | 9.79423i | 0.163703 | + | 0.610947i | 0.998202 | + | 0.0599382i | \(0.0190904\pi\) |
−0.834499 | + | 0.551009i | \(0.814243\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 37.7846 | 2.34782 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.26795 | 0.0784841 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.89230 | + | 25.7224i | 0.424998 | + | 1.58611i | 0.763928 | + | 0.645302i | \(0.223268\pi\) |
−0.338930 | + | 0.940812i | \(0.610065\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.13397 | + | 2.96410i | −0.314194 | + | 0.181400i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.8205 | + | 10.8660i | −1.14751 | + | 0.662513i | −0.948278 | − | 0.317440i | \(-0.897177\pi\) |
−0.199228 | + | 0.979953i | \(0.563844\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.33013 | + | 1.16025i | −0.263036 | + | 0.0704804i | −0.387927 | − | 0.921690i | \(-0.626809\pi\) |
0.124890 | + | 0.992171i | \(0.460142\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.09808 | + | 30.4904i | −0.369072 | + | 1.84536i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.23205 | + | 1.66987i | 0.374448 | + | 0.100333i | 0.441134 | − | 0.897441i | \(-0.354576\pi\) |
−0.0666868 | + | 0.997774i | \(0.521243\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.39230 | + | 5.19615i | −0.0833551 | + | 0.311086i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.53590 | − | 9.53590i | −0.568864 | − | 0.568864i | 0.362946 | − | 0.931810i | \(-0.381771\pi\) |
−0.931810 | + | 0.362946i | \(0.881771\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.03590 | + | 0.277568i | −0.0615778 | + | 0.0164997i | −0.289476 | − | 0.957185i | \(-0.593481\pi\) |
0.227899 | + | 0.973685i | \(0.426815\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.16987 | + | 8.16987i | 0.482252 | + | 0.482252i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.02628 | − | 2.90192i | −0.295663 | − | 0.170701i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.83013 | − | 5.83013i | 0.341768 | − | 0.341768i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.2583 | − | 21.2321i | −0.716139 | − | 1.24039i | −0.962518 | − | 0.271216i | \(-0.912574\pi\) |
0.246379 | − | 0.969174i | \(-0.420759\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.2583 | − | 6.50000i | −0.653275 | − | 0.377168i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 19.5263 | + | 17.1603i | 1.12923 | + | 0.992403i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.30385 | + | 16.0622i | 0.248070 | + | 0.925809i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.40192 | + | 12.6962i | −0.195435 | + | 0.729375i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.00000i | − | 0.228292i | −0.993464 | − | 0.114146i | \(-0.963587\pi\) | ||
0.993464 | − | 0.114146i | \(-0.0364132\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.09808 | + | 1.90192i | −0.0624674 | + | 0.108197i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 3.46410i | − | 0.196431i | −0.995165 | − | 0.0982156i | \(-0.968687\pi\) | ||
0.995165 | − | 0.0982156i | \(-0.0313135\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.4641 | − | 12.4641i | 0.704513 | − | 0.704513i | −0.260863 | − | 0.965376i | \(-0.584007\pi\) |
0.965376 | + | 0.260863i | \(0.0840071\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.07180 | 0.284860 | 0.142430 | − | 0.989805i | \(-0.454508\pi\) | ||||
0.142430 | + | 0.989805i | \(0.454508\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.96410 | + | 1.33013i | 0.277936 | + | 0.0744728i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.96410 | − | 8.59808i | −0.277069 | − | 0.479898i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.33013 | − | 12.6962i | 0.407859 | − | 0.706433i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.2942 | − | 24.7583i | 0.790473 | − | 1.36914i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.53590 | − | 11.3205i | −0.360336 | − | 0.624120i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.4545 | − | 7.62436i | −1.56400 | − | 0.419072i | −0.630073 | − | 0.776536i | \(-0.716975\pi\) |
−0.933927 | + | 0.357464i | \(0.883642\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.19615 | −0.339547 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.07180 | − | 2.07180i | 0.112858 | − | 0.112858i | −0.648423 | − | 0.761281i | \(-0.724571\pi\) |
0.761281 | + | 0.648423i | \(0.224571\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 8.46410i | − | 0.459707i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.9019 | + | 18.8827i | −0.590372 | + | 1.02255i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 26.4641i | − | 1.42893i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.42820 | + | 12.7942i | −0.184036 | + | 0.686830i | 0.810799 | + | 0.585324i | \(0.199033\pi\) |
−0.994835 | + | 0.101506i | \(0.967634\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.13397 | − | 22.8923i | −0.328344 | − | 1.22540i | −0.910907 | − | 0.412611i | \(-0.864617\pi\) |
0.582563 | − | 0.812786i | \(-0.302050\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.09808 | + | 15.4904i | −0.165363 | + | 0.826815i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.06218 | + | 1.76795i | 0.162983 | + | 0.0940984i | 0.579273 | − | 0.815134i | \(-0.303336\pi\) |
−0.416290 | + | 0.909232i | \(0.636670\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.4282 | − | 24.9904i | −0.763621 | − | 1.32263i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.80385 | − | 2.80385i | 0.147981 | − | 0.147981i | −0.629234 | − | 0.777216i | \(-0.716631\pi\) |
0.777216 | + | 0.629234i | \(0.216631\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.169873 | − | 0.0980762i | −0.00894068 | − | 0.00516191i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.00000 | − | 3.00000i | −0.157459 | − | 0.157459i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.96410 | + | 0.794229i | −0.154725 | + | 0.0414584i | −0.335350 | − | 0.942094i | \(-0.608855\pi\) |
0.180625 | + | 0.983552i | \(0.442188\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.33975 | − | 1.33975i | −0.0697444 | − | 0.0697444i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.29423 | − | 27.2224i | 0.378697 | − | 1.41332i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.6962 | − | 4.20577i | −0.812716 | − | 0.217767i | −0.171557 | − | 0.985174i | \(-0.554880\pi\) |
−0.641159 | + | 0.767408i | \(0.721546\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.401924 | − | 6.23205i | −0.0207001 | − | 0.320967i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.59808 | + | 0.696152i | −0.133454 | + | 0.0357589i | −0.324928 | − | 0.945739i | \(-0.605340\pi\) |
0.191474 | + | 0.981498i | \(0.438673\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.76795 | − | 3.33013i | 0.295501 | − | 0.170608i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.1147 | + | 16.2321i | −1.43660 | + | 0.829419i | −0.997611 | − | 0.0690756i | \(-0.977995\pi\) |
−0.438985 | + | 0.898495i | \(0.644662\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.705771 | − | 2.63397i | −0.0358764 | − | 0.133892i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −28.9282 | −1.46672 | −0.733359 | − | 0.679842i | \(-0.762049\pi\) | ||||
−0.733359 | + | 0.679842i | \(0.762049\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.1244 | −1.22002 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.9282 | − | 40.7846i | −0.551255 | − | 2.05731i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.13397 | − | 4.69615i | 0.408232 | − | 0.235693i | −0.281798 | − | 0.959474i | \(-0.590931\pi\) |
0.690030 | + | 0.723781i | \(0.257597\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −32.7224 | + | 18.8923i | −1.63817 | + | 0.945798i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.3301 | − | 3.03590i | 0.565800 | − | 0.151606i | 0.0354301 | − | 0.999372i | \(-0.488720\pi\) |
0.530369 | + | 0.847767i | \(0.322053\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.9808 | + | 5.19615i | 1.29419 | + | 0.258839i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.2583 | − | 6.50000i | −1.20244 | − | 0.322193i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.526279 | + | 1.96410i | −0.0260228 | + | 0.0971186i | −0.977716 | − | 0.209932i | \(-0.932676\pi\) |
0.951693 | + | 0.307051i | \(0.0993422\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 27.7583 | + | 27.7583i | 1.36922 | + | 1.36922i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −28.2583 | + | 7.57180i | −1.39050 | + | 0.372584i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.09808 | − | 7.09808i | −0.347594 | − | 0.347594i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.5000 | − | 18.1865i | −1.53888 | − | 0.888470i | −0.998905 | − | 0.0467865i | \(-0.985102\pi\) |
−0.539971 | − | 0.841684i | \(-0.681565\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.8564 | + | 20.8564i | −1.01648 | + | 1.01648i | −0.0166171 | + | 0.999862i | \(0.505290\pi\) |
−0.999862 | + | 0.0166171i | \(0.994710\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.07180 | + | 1.85641i | 0.0521125 | + | 0.0902616i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 34.7942 | + | 20.0885i | 1.68381 | + | 0.972149i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.16025 | − | 18.5263i | 0.442261 | − | 0.894457i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.741670 | − | 2.76795i | −0.0357250 | − | 0.133327i | 0.945760 | − | 0.324866i | \(-0.105319\pi\) |
−0.981485 | + | 0.191538i | \(0.938652\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.55256 | − | 20.7224i | 0.266839 | − | 0.995857i | −0.694276 | − | 0.719709i | \(-0.744275\pi\) |
0.961115 | − | 0.276148i | \(-0.0890580\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 31.5885i | 1.51108i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.96410 | − | 12.0622i | 0.332378 | − | 0.575696i | −0.650599 | − | 0.759421i | \(-0.725482\pi\) |
0.982978 | + | 0.183725i | \(0.0588156\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.46410i | 0.450672i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.5885 | + | 15.5885i | −0.740630 | + | 0.740630i | −0.972699 | − | 0.232069i | \(-0.925450\pi\) |
0.232069 | + | 0.972699i | \(0.425450\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 39.7846 | 1.88175 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.7942 | − | 5.57180i | −0.981340 | − | 0.262949i | −0.267731 | − | 0.963494i | \(-0.586274\pi\) |
−0.713609 | + | 0.700544i | \(0.752941\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.83975 | − | 6.65064i | −0.180807 | − | 0.313166i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.09808 | − | 8.83013i | 0.239529 | − | 0.414876i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.79423 | + | 15.2321i | −0.411377 | + | 0.712525i | −0.995041 | − | 0.0994701i | \(-0.968285\pi\) |
0.583664 | + | 0.811995i | \(0.301619\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.33013 | − | 12.6962i | −0.342141 | − | 0.592606i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.1865 | + | 9.96410i | 1.73195 | + | 0.464074i | 0.980631 | − | 0.195865i | \(-0.0627515\pi\) |
0.751319 | + | 0.659940i | \(0.229418\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 42.3923 | 1.97014 | 0.985069 | − | 0.172161i | \(-0.0550751\pi\) | ||||
0.985069 | + | 0.172161i | \(0.0550751\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.660254 | − | 0.660254i | 0.0305529 | − | 0.0305529i | −0.691665 | − | 0.722218i | \(-0.743123\pi\) |
0.722218 | + | 0.691665i | \(0.243123\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 70.2295i | 3.24290i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.633975 | + | 1.09808i | −0.0292120 | + | 0.0505967i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 11.0526i | − | 0.508197i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.19615 | + | 4.46410i | −0.0547681 | + | 0.204397i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.86603 | − | 18.1603i | −0.222334 | − | 0.829763i | −0.983455 | − | 0.181153i | \(-0.942017\pi\) |
0.761121 | − | 0.648610i | \(-0.224650\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.96410 | + | 30.4545i | 0.0895553 | + | 1.38860i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 53.8468 | + | 31.0885i | 2.45011 | + | 1.41457i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.7942 | − | 25.6244i | −0.670390 | − | 1.16115i | −0.977793 | − | 0.209571i | \(-0.932793\pi\) |
0.307403 | − | 0.951579i | \(-0.400540\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.83013 | − | 9.83013i | 0.444534 | − | 0.444534i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.8923 | − | 8.59808i | −0.672080 | − | 0.388026i | 0.124784 | − | 0.992184i | \(-0.460176\pi\) |
−0.796864 | + | 0.604158i | \(0.793510\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.09808 | + | 4.09808i | 0.184568 | + | 0.184568i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.5263 | + | 5.50000i | −0.920729 | + | 0.246709i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.7321 | + | 23.7321i | 1.06239 | + | 1.06239i | 0.997919 | + | 0.0644731i | \(0.0205367\pi\) |
0.0644731 | + | 0.997919i | \(0.479463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.76795 | − | 21.5263i | 0.257693 | − | 0.961723i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.3564 | − | 6.52628i | −1.08600 | − | 0.290992i | −0.328947 | − | 0.944348i | \(-0.606694\pi\) |
−0.757051 | + | 0.653356i | \(0.773361\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −24.8923 | − | 3.33013i | −1.10551 | − | 0.147896i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.4545 | − | 6.82051i | 1.12825 | − | 0.302314i | 0.354032 | − | 0.935233i | \(-0.384810\pi\) |
0.774218 | + | 0.632919i | \(0.218144\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.14359 | − | 2.39230i | 0.183302 | − | 0.105829i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16.6244 | + | 9.59808i | −0.733983 | + | 0.423765i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.24871 | + | 8.39230i | 0.0988982 | + | 0.369093i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 46.5167 | 2.04185 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.8564 | 0.869925 | 0.434962 | − | 0.900449i | \(-0.356762\pi\) | ||||
0.434962 | + | 0.900449i | \(0.356762\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.03590 | − | 15.0622i | −0.176478 | − | 0.658623i | −0.996295 | − | 0.0859985i | \(-0.972592\pi\) |
0.819818 | − | 0.572625i | \(-0.194075\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.2942 | + | 12.2942i | −0.927591 | + | 0.535545i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.0981 | − | 14.4904i | 1.09122 | − | 0.630017i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.63397 | − | 1.24167i | 0.201097 | − | 0.0538839i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.16025 | + | 7.00962i | −0.266830 | + | 0.303620i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.133975 | + | 0.0358984i | 0.00578143 | + | 0.00154913i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.92820 | + | 37.0526i | −0.427638 | + | 1.59597i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.7846 | − | 19.7846i | −0.850607 | − | 0.850607i | 0.139601 | − | 0.990208i | \(-0.455418\pi\) |
−0.990208 | + | 0.139601i | \(0.955418\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.9282 | − | 4.53590i | 0.726459 | − | 0.194654i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.1244 | − | 24.1244i | −1.03148 | − | 1.03148i | −0.999488 | − | 0.0319949i | \(-0.989814\pi\) |
−0.0319949 | − | 0.999488i | \(-0.510186\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.70577 | − | 3.29423i | −0.243516 | − | 0.140594i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.36603 | − | 5.36603i | 0.228600 | − | 0.228600i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.6603 | + | 28.8564i | 0.708466 | + | 1.22710i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.66987 | − | 2.69615i | −0.197869 | − | 0.114240i | 0.397792 | − | 0.917476i | \(-0.369777\pi\) |
−0.595661 | + | 0.803236i | \(0.703110\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.7224 | + | 4.30385i | −0.538102 | + | 0.182033i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.96410 | + | 18.5263i | 0.209585 | + | 0.782180i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.10770 | − | 15.3301i | 0.173119 | − | 0.646088i | −0.823746 | − | 0.566959i | \(-0.808120\pi\) |
0.996864 | − | 0.0791284i | \(-0.0252137\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 47.5885i | 1.99853i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.8205 | + | 27.4019i | −0.663230 | + | 1.14875i | 0.316532 | + | 0.948582i | \(0.397482\pi\) |
−0.979762 | + | 0.200166i | \(0.935852\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.3923i | 1.77406i | 0.461709 | + | 0.887031i | \(0.347236\pi\) | ||||
−0.461709 | + | 0.887031i | \(0.652764\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.4904 | + | 20.4904i | −0.855998 | + | 0.855998i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.7846 | 0.865275 | 0.432637 | − | 0.901568i | \(-0.357583\pi\) | ||||
0.432637 | + | 0.901568i | \(0.357583\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.4282 | + | 2.79423i | 0.433381 | + | 0.116124i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.3923 | − | 42.2487i | −1.01196 | − | 1.75277i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.36603 | + | 16.2224i | −0.387901 | + | 0.671864i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.72243 | + | 9.91154i | −0.236190 | + | 0.409093i | −0.959618 | − | 0.281307i | \(-0.909232\pi\) |
0.723428 | + | 0.690400i | \(0.242565\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0981 | + | 27.8827i | 0.663310 | + | 1.14889i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.4282 | − | 3.86603i | −0.593497 | − | 0.159027i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.0718 | 0.701055 | 0.350527 | − | 0.936553i | \(-0.386002\pi\) | ||||
0.350527 | + | 0.936553i | \(0.386002\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.0981 | − | 12.0981i | 0.495141 | − | 0.495141i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 12.2487i | − | 0.500469i | −0.968185 | − | 0.250234i | \(-0.919492\pi\) | ||
0.968185 | − | 0.250234i | \(-0.0805077\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.42820 | + | 11.1340i | −0.262212 | + | 0.454164i | −0.966829 | − | 0.255423i | \(-0.917785\pi\) |
0.704618 | + | 0.709587i | \(0.251119\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 11.5167i | − | 0.468995i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.96410 | + | 37.1865i | −0.404430 | + | 1.50935i | 0.400673 | + | 0.916221i | \(0.368776\pi\) |
−0.805104 | + | 0.593134i | \(0.797890\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.86603 | − | 14.4282i | −0.156659 | − | 0.584660i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.78461 | − | 5.85641i | 0.355387 | − | 0.236925i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.1865 | − | 8.76795i | −0.613378 | − | 0.354134i | 0.160908 | − | 0.986969i | \(-0.448558\pi\) |
−0.774286 | + | 0.632835i | \(0.781891\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.79423 | + | 11.7679i | 0.273525 | + | 0.473760i | 0.969762 | − | 0.244053i | \(-0.0784769\pi\) |
−0.696237 | + | 0.717812i | \(0.745144\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.66025 | + | 2.66025i | −0.106925 | + | 0.106925i | −0.758545 | − | 0.651620i | \(-0.774089\pi\) |
0.651620 | + | 0.758545i | \(0.274089\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 27.3564 | + | 15.7942i | 1.09777 | + | 0.633801i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.68653 | + | 9.68653i | 0.388083 | + | 0.388083i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 24.2583 | − | 6.50000i | 0.968784 | − | 0.259585i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.0263 | − | 20.0263i | −0.798500 | − | 0.798500i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.65064 | + | 6.16025i | −0.0657107 | + | 0.245236i | −0.990967 | − | 0.134107i | \(-0.957183\pi\) |
0.925256 | + | 0.379343i | \(0.123850\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.7942 | + | 3.96410i | 0.588018 | + | 0.157559i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 46.5167 | − | 3.00000i | 1.84306 | − | 0.118864i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.36603 | − | 0.901924i | 0.133158 | − | 0.0356796i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.3564 | − | 19.2583i | 1.31750 | − | 0.760658i | 0.334173 | − | 0.942512i | \(-0.391543\pi\) |
0.983326 | + | 0.181853i | \(0.0582096\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.6699 | − | 13.0885i | 0.894013 | − | 0.516158i | 0.0187597 | − | 0.999824i | \(-0.494028\pi\) |
0.875253 | + | 0.483666i | \(0.160695\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.50000 | − | 9.33013i | −0.0982851 | − | 0.366805i | 0.899212 | − | 0.437513i | \(-0.144141\pi\) |
−0.997497 | + | 0.0707082i | \(0.977474\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.4449 | 0.763278 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 63.3731 | 2.48379 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.9449 | + | 40.8468i | 0.428306 | + | 1.59846i | 0.756597 | + | 0.653882i | \(0.226861\pi\) |
−0.328291 | + | 0.944577i | \(0.606473\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.679492 | + | 0.392305i | −0.0265095 | + | 0.0153053i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.5718 | + | 12.4545i | −0.840318 | + | 0.485158i | −0.857372 | − | 0.514697i | \(-0.827904\pi\) |
0.0170544 | + | 0.999855i | \(0.494571\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.7942 | − | 3.96410i | 0.575429 | − | 0.154186i | 0.0406436 | − | 0.999174i | \(-0.487059\pi\) |
0.534785 | + | 0.844988i | \(0.320393\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 19.3923 | − | 12.9282i | 0.753135 | − | 0.502090i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.0622 | − | 3.23205i | −0.467049 | − | 0.125146i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.23205 | − | 15.7942i | 0.163621 | − | 0.610640i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.8827 | − | 18.8827i | −0.728958 | − | 0.728958i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.6244 | − | 3.91858i | 0.563727 | − | 0.151050i | 0.0343092 | − | 0.999411i | \(-0.489077\pi\) |
0.529418 | + | 0.848361i | \(0.322410\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −34.1769 | − | 34.1769i | −1.31353 | − | 1.31353i | −0.918798 | − | 0.394727i | \(-0.870839\pi\) |
−0.394727 | − | 0.918798i | \(-0.629161\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.5000 | − | 9.52628i | −0.633212 | − | 0.365585i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.83013 | + | 9.83013i | −0.376691 | + | 0.376691i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.33013 | + | 2.30385i | 0.0508959 | + | 0.0881543i | 0.890351 | − | 0.455275i | \(-0.150459\pi\) |
−0.839455 | + | 0.543429i | \(0.817126\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 32.9545 | + | 19.0263i | 1.25729 | + | 0.725898i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.3205 | + | 4.46410i | 0.850344 | + | 0.170069i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.65064 | + | 21.0885i | 0.214960 | + | 0.802243i | 0.986181 | + | 0.165674i | \(0.0529800\pi\) |
−0.771220 | + | 0.636568i | \(0.780353\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.50962 | − | 9.36603i | 0.0953325 | − | 0.355786i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 8.66025i | − | 0.328031i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.2942 | + | 35.1506i | −0.767598 | + | 1.32952i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.9282i | 1.31922i | 0.751608 | + | 0.659610i | \(0.229279\pi\) | ||||
−0.751608 | + | 0.659610i | \(0.770721\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26.2224 | + | 26.2224i | −0.988998 | + | 0.988998i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 30.3731 | 1.14230 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.7224 | − | 9.03590i | −1.26647 | − | 0.339350i | −0.437794 | − | 0.899075i | \(-0.644240\pi\) |
−0.828678 | + | 0.559725i | \(0.810907\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.73205 | − | 4.73205i | −0.102460 | − | 0.177466i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.4904 | − | 45.8827i | 0.992073 | − | 1.71832i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.901924 | − | 1.56218i | 0.0336830 | − | 0.0583406i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.0359 | − | 24.3109i | −0.523451 | − | 0.906643i | −0.999627 | − | 0.0272936i | \(-0.991311\pi\) |
0.476177 | − | 0.879350i | \(-0.342022\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.90192 | + | 1.31347i | 0.182557 | + | 0.0489160i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.9282 | 0.741138 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.41154 | − | 2.41154i | 0.0894392 | − | 0.0894392i | −0.660972 | − | 0.750411i | \(-0.729856\pi\) |
0.750411 | + | 0.660972i | \(0.229856\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.5885i | 0.651424i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.23205 | − | 10.7942i | 0.230501 | − | 0.399239i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 14.7846i | − | 0.546082i | −0.962002 | − | 0.273041i | \(-0.911971\pi\) | ||
0.962002 | − | 0.273041i | \(-0.0880295\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.0814 | − | 45.0885i | 0.445025 | − | 1.66085i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.91858 | + | 7.16025i | 0.0705763 | + | 0.263394i | 0.992194 | − | 0.124705i | \(-0.0397985\pi\) |
−0.921618 | + | 0.388099i | \(0.873132\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.9282 | − | 25.3923i | −0.621873 | − | 0.932810i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.6699 | + | 6.16025i | 0.391440 | + | 0.225998i | 0.682784 | − | 0.730621i | \(-0.260769\pi\) |
−0.291344 | + | 0.956618i | \(0.594102\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.00000 | + | 6.92820i | 0.146352 | + | 0.253490i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.2224 | + | 16.2224i | −0.592755 | + | 0.592755i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.3564 | + | 26.1865i | 1.65508 | + | 0.955560i | 0.974937 | + | 0.222479i | \(0.0714149\pi\) |
0.680141 | + | 0.733081i | \(0.261918\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.4904 | + | 19.4904i | 0.710269 | + | 0.710269i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.1603 | − | 5.93782i | 0.805428 | − | 0.215814i | 0.167462 | − | 0.985878i | \(-0.446443\pi\) |
0.637966 | + | 0.770065i | \(0.279776\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −29.2224 | − | 29.2224i | −1.06071 | − | 1.06071i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.33013 | + | 34.8205i | −0.338217 | + | 1.26224i | 0.562123 | + | 0.827054i | \(0.309985\pi\) |
−0.900339 | + | 0.435188i | \(0.856682\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −63.8109 | − | 17.0981i | −2.31011 | − | 0.618992i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.57180 | − | 22.3827i | −0.273402 | − | 0.808192i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.5263 | − | 6.57180i | 0.884440 | − | 0.236985i | 0.212118 | − | 0.977244i | \(-0.431964\pi\) |
0.672322 | + | 0.740259i | \(0.265297\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.9641 | + | 9.79423i | −0.610947 | + | 0.352731i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 47.0429 | − | 27.1603i | 1.69202 | − | 0.976886i | 0.739129 | − | 0.673564i | \(-0.235237\pi\) |
0.952888 | − | 0.303323i | \(-0.0980960\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.8923 | + | 70.5070i | 0.677758 | + | 2.52943i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.3397 | −0.406289 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.1244 | 0.505409 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.96410 | − | 7.33013i | −0.0701913 | − | 0.261957i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.54552 | − | 2.62436i | 0.162030 | − | 0.0935482i | −0.416792 | − | 0.909002i | \(-0.636846\pi\) |
0.578822 | + | 0.815454i | \(0.303512\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −44.5526 | + | 25.7224i | −1.58611 | + | 0.915743i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.8923 | + | 5.06218i | −0.671733 | + | 0.179990i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.3827 | + | 29.0885i | −0.510744 | + | 1.03296i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.6244 | + | 4.99038i | 0.659709 | + | 0.176768i | 0.573114 | − | 0.819475i | \(-0.305735\pi\) |
0.0865940 | + | 0.996244i | \(0.472402\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.53590 | + | 9.46410i | −0.0897136 | + | 0.334816i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.58846 | − | 1.58846i | −0.0561254 | − | 0.0561254i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.07180 | + | 0.823085i | −0.108401 | + | 0.0290461i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.6865 | − | 29.6865i | −1.04502 | − | 1.04502i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.2846 | + | 18.0622i | 1.09991 | + | 0.635032i | 0.936197 | − | 0.351476i | \(-0.114320\pi\) |
0.163711 | + | 0.986508i | \(0.447653\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.0526 | − | 15.0526i | 0.528567 | − | 0.528567i | −0.391578 | − | 0.920145i | \(-0.628071\pi\) |
0.920145 | + | 0.391578i | \(0.128071\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.33013 | − | 7.50000i | −0.151864 | − | 0.263036i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.1340 | − | 8.16025i | −0.494485 | − | 0.285491i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11.7583 | + | 0.758330i | −0.410869 | + | 0.0264982i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.45448 | + | 20.3564i | 0.190363 | + | 0.710443i | 0.993419 | + | 0.114540i | \(0.0365393\pi\) |
−0.803056 | + | 0.595904i | \(0.796794\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.10770 | + | 11.5981i | −0.108327 | + | 0.404284i | −0.998701 | − | 0.0509463i | \(-0.983776\pi\) |
0.890374 | + | 0.455230i | \(0.150443\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1.85641i | − | 0.0645536i | −0.999479 | − | 0.0322768i | \(-0.989724\pi\) | ||
0.999479 | − | 0.0322768i | \(-0.0102758\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.42820 | + | 16.3301i | −0.327455 | + | 0.567169i | −0.982006 | − | 0.188849i | \(-0.939524\pi\) |
0.654551 | + | 0.756018i | \(0.272858\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.4641i | 0.432375i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −30.5885 | + | 30.5885i | −1.05983 | + | 1.05983i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 32.1962 | 1.11286 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.79423 | − | 2.08846i | −0.269087 | − | 0.0721016i | 0.121753 | − | 0.992560i | \(-0.461149\pi\) |
−0.390839 | + | 0.920459i | \(0.627815\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | − | 22.5167i | −0.448276 | − | 0.776437i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.0263 | − | 22.5622i | 0.448649 | − | 0.777083i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.90192 | + | 8.49038i | −0.168432 | + | 0.291733i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.03590 | − | 1.79423i | −0.0355519 | − | 0.0615778i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 58.9449 | + | 15.7942i | 2.02060 | + | 0.541419i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.1436 | 0.895140 | 0.447570 | − | 0.894249i | \(-0.352290\pi\) | ||||
0.447570 | + | 0.894249i | \(0.352290\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.2487 | + | 29.2487i | −0.999117 | + | 0.999117i | −1.00000 | 0.000882665i | \(-0.999719\pi\) | |
0.000882665 | 1.00000i | \(0.499719\pi\) | ||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.3923i | 0.627537i | 0.949499 | + | 0.313769i | \(0.101592\pi\) | ||||
−0.949499 | + | 0.313769i | \(0.898408\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.1603 | + | 19.3301i | −0.380340 | + | 0.658769i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 29.8564i | − | 1.01632i | −0.861262 | − | 0.508162i | \(-0.830325\pi\) | ||
0.861262 | − | 0.508162i | \(-0.169675\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.90192 | − | 10.8301i | 0.0985545 | − | 0.367810i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.73205 | − | 21.3923i | −0.194447 | − | 0.725684i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −56.6051 | + | 3.65064i | −1.91799 | + | 0.123697i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.70577 | + | 1.56218i | 0.0915765 | + | 0.0528717i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.20577 | − | 5.55256i | −0.108251 | − | 0.187497i | 0.806811 | − | 0.590810i | \(-0.201192\pi\) |
−0.915062 | + | 0.403313i | \(0.867858\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 33.4904 | − | 33.4904i | 1.12960 | − | 1.12960i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.96410 | − | 1.13397i | −0.0661723 | − | 0.0382046i | 0.466549 | − | 0.884495i | \(-0.345497\pi\) |
−0.532721 | + | 0.846291i | \(0.678831\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.1962 | − | 11.1962i | −0.376781 | − | 0.376781i | 0.493159 | − | 0.869939i | \(-0.335842\pi\) |
−0.869939 | + | 0.493159i | \(0.835842\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.96410 | + | 1.86603i | −0.233832 | + | 0.0626550i | −0.373832 | − | 0.927496i | \(-0.621956\pi\) |
0.140000 | + | 0.990151i | \(0.455290\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.8827 | − | 10.8827i | −0.364994 | − | 0.364994i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.18653 | − | 30.5526i | 0.274259 | − | 1.02355i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.3923 | + | 3.32051i | 0.414693 | + | 0.111117i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.2583 | + | 45.0167i | −0.743184 | + | 1.50306i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.2942 | + | 3.29423i | −0.410035 | + | 0.109869i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.2942 | + | 10.5622i | −0.609469 | + | 0.351877i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −27.8205 | + | 16.0622i | −0.925809 | + | 0.534516i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.6436 | − | 54.6506i | −0.486233 | − | 1.81464i | −0.574445 | − | 0.818543i | \(-0.694782\pi\) |
0.0882129 | − | 0.996102i | \(-0.471884\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.98076 | −0.165201 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −57.5692 | −1.90735 | −0.953677 | − | 0.300834i | \(-0.902735\pi\) | ||||
−0.953677 | + | 0.300834i | \(0.902735\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.39230 | + | 31.3205i | 0.277745 | + | 1.03656i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −84.4974 | + | 48.7846i | −2.79035 | + | 1.61101i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.1410 | − | 20.8660i | 1.19218 | − | 0.688307i | 0.233381 | − | 0.972385i | \(-0.425021\pi\) |
0.958801 | + | 0.284079i | \(0.0916877\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.46410 | − | 2.00000i | 0.245951 | − | 0.0659022i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.50000 | − | 16.2583i | −0.181035 | − | 0.535149i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.803848 | − | 0.215390i | −0.0264018 | − | 0.00707435i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.99038 | + | 14.8923i | −0.130920 | + | 0.488601i | −0.999981 | − | 0.00610389i | \(-0.998057\pi\) |
0.869061 | + | 0.494705i | \(0.164724\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40.0526 | + | 40.0526i | 1.31267 | + | 1.31267i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.46410 | − | 1.73205i | 0.211625 | − | 0.0567048i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.8564 | + | 24.8564i | 0.812023 | + | 0.812023i | 0.984937 | − | 0.172914i | \(-0.0553181\pi\) |
−0.172914 | + | 0.984937i | \(0.555318\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.4904 | + | 17.0263i | 0.962382 | + | 0.555632i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.8564 | + | 20.8564i | −0.679899 | + | 0.679899i | −0.959977 | − | 0.280078i | \(-0.909640\pi\) |
0.280078 | + | 0.959977i | \(0.409640\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.33013 | + | 16.1603i | 0.303831 | + | 0.526250i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.4545 | − | 21.6244i | −1.21711 | − | 0.702697i | −0.252809 | − | 0.967516i | \(-0.581354\pi\) |
−0.964298 | + | 0.264819i | \(0.914688\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.14359 | + | 3.21539i | 0.0695840 | + | 0.104376i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.53590 | + | 9.46410i | 0.0822321 | + | 0.306895i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.6244 | + | 43.3827i | −0.376550 | + | 1.40530i | 0.474517 | + | 0.880246i | \(0.342623\pi\) |
−0.851067 | + | 0.525057i | \(0.824044\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.92820i | 0.320933i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.3564 | − | 78.5596i | 1.46463 | − | 2.53682i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 23.0000i | − | 0.741935i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.66025 | − | 2.66025i | 0.0857255 | − | 0.0857255i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.6077 | −1.20938 | −0.604691 | − | 0.796460i | \(-0.706703\pi\) | ||||
−0.604691 | + | 0.796460i | \(0.706703\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 27.3564 | + | 7.33013i | 0.878814 | + | 0.235478i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.89230 | − | 5.00962i | −0.0928185 | − | 0.160766i | 0.815878 | − | 0.578225i | \(-0.196254\pi\) |
−0.908696 | + | 0.417458i | \(0.862921\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.5981 | + | 20.0885i | −0.371817 | + | 0.644006i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.79423 | + | 11.7679i | −0.217367 | + | 0.376490i | −0.954002 | − | 0.299800i | \(-0.903080\pi\) |
0.736635 | + | 0.676290i | \(0.236413\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.55256 | − | 7.88526i | −0.145500 | − | 0.252014i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.4641 | + | 2.80385i | 0.334093 | + | 0.0895200i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.3923 | −0.714204 | −0.357102 | − | 0.934065i | \(-0.616235\pi\) | ||||
−0.357102 | + | 0.934065i | \(0.616235\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17.8564 | − | 17.8564i | 0.568376 | − | 0.568376i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.8564i | 0.853984i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.8205 | − | 23.9378i | 0.439023 | − | 0.760410i | −0.558591 | − | 0.829443i | \(-0.688658\pi\) |
0.997614 | + | 0.0690329i | \(0.0219914\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 56.9090i | − | 1.80595i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.76795 | + | 17.7942i | −0.151002 | + | 0.563549i | 0.848412 | + | 0.529336i | \(0.177559\pi\) |
−0.999415 | + | 0.0342126i | \(0.989108\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.59808 | + | 35.8205i | 0.303670 | + | 1.13331i |
(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 | 1300.2.bs.b.357.1 | 4 | ||
5.2 | odd | 4 | 260.2.bf.b.253.1 | yes | 4 | ||
5.3 | odd | 4 | 1300.2.bn.a.1293.1 | 4 | |||
5.4 | even | 2 | 260.2.bk.a.97.1 | yes | 4 | ||
13.11 | odd | 12 | 1300.2.bn.a.557.1 | 4 | |||
65.24 | odd | 12 | 260.2.bf.b.37.1 | ✓ | 4 | ||
65.37 | even | 12 | 260.2.bk.a.193.1 | yes | 4 | ||
65.63 | even | 12 | inner | 1300.2.bs.b.193.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.bf.b.37.1 | ✓ | 4 | 65.24 | odd | 12 | ||
260.2.bf.b.253.1 | yes | 4 | 5.2 | odd | 4 | ||
260.2.bk.a.97.1 | yes | 4 | 5.4 | even | 2 | ||
260.2.bk.a.193.1 | yes | 4 | 65.37 | even | 12 | ||
1300.2.bn.a.557.1 | 4 | 13.11 | odd | 12 | |||
1300.2.bn.a.1293.1 | 4 | 5.3 | odd | 4 | |||
1300.2.bs.b.193.1 | 4 | 65.63 | even | 12 | inner | ||
1300.2.bs.b.357.1 | 4 | 1.1 | even | 1 | trivial |