Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,1,Mod(20,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(110))
chi = DirichletCharacter(H, H._module([55, 76]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.20");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.bb (of order \(110\), degree \(40\), 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: | \(0.422708065700\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Coefficient field: | \(\Q(\zeta_{55})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{40} - x^{39} + x^{35} - x^{34} + x^{30} - x^{28} + x^{25} - x^{23} + x^{20} - x^{17} + x^{15} - x^{12} + x^{10} - x^{6} + x^{5} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{55}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{55} - \cdots)\) |
Embedding invariants
Embedding label | 174.1 | ||
Root | \(0.993482 - 0.113991i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.174 |
Dual form | 847.1.bb.a.258.1 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{53}{55}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.38479 | − | 0.158890i | 1.38479 | − | 0.158890i | 0.610648 | − | 0.791902i | \(-0.290909\pi\) |
0.774142 | + | 0.633012i | \(0.218182\pi\) | |||||||
\(3\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(4\) | 0.918384 | − | 0.213561i | 0.918384 | − | 0.213561i | ||||
\(5\) | 0 | 0 | −0.564443 | − | 0.825472i | \(-0.690909\pi\) | ||||
0.564443 | + | 0.825472i | \(0.309091\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.696938 | − | 0.717132i | 0.696938 | − | 0.717132i | ||||
\(8\) | −0.0749775 | + | 0.0267519i | −0.0749775 | + | 0.0267519i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.736741 | + | 0.676175i | −0.736741 | + | 0.676175i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.516397 | − | 0.856349i | \(-0.672727\pi\) | ||||
0.516397 | + | 0.856349i | \(0.327273\pi\) | |||||||
\(14\) | 0.851167 | − | 1.10381i | 0.851167 | − | 1.10381i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.945724 | + | 0.464981i | −0.945724 | + | 0.464981i | ||||
\(17\) | 0 | 0 | −0.774142 | − | 0.633012i | \(-0.781818\pi\) | ||||
0.774142 | + | 0.633012i | \(0.218182\pi\) | |||||||
\(18\) | 0.276810 | − | 1.36611i | 0.276810 | − | 1.36611i | ||||
\(19\) | 0 | 0 | 0.998369 | − | 0.0570888i | \(-0.0181818\pi\) | ||||
−0.998369 | + | 0.0570888i | \(0.981818\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.912794 | + | 1.05342i | −0.912794 | + | 1.05342i | ||||
\(23\) | 0.132827 | + | 0.923835i | 0.132827 | + | 0.923835i | 0.941844 | + | 0.336049i | \(0.109091\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.362808 | + | 0.931864i | −0.362808 | + | 0.931864i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.486905 | − | 0.807441i | 0.486905 | − | 0.807441i | ||||
\(29\) | 0.409569 | + | 1.05197i | 0.409569 | + | 1.05197i | 0.974012 | + | 0.226497i | \(0.0727273\pi\) |
−0.564443 | + | 0.825472i | \(0.690909\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.921124 | − | 0.389270i | \(-0.127273\pi\) | ||||
−0.921124 | + | 0.389270i | \(0.872727\pi\) | |||||||
\(32\) | −1.16878 | + | 0.751128i | −1.16878 | + | 0.751128i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0806876 | − | 0.939429i | 0.0806876 | − | 0.939429i | ||||
\(37\) | −0.138463 | − | 1.61210i | −0.138463 | − | 1.61210i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.516397 | − | 0.856349i | \(-0.327273\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.870746 | − | 0.491733i | \(-0.836364\pi\) | ||||
0.870746 | + | 0.491733i | \(0.163636\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.72209 | − | 0.505653i | −1.72209 | − | 0.505653i | −0.736741 | − | 0.676175i | \(-0.763636\pi\) |
−0.985354 | + | 0.170522i | \(0.945455\pi\) | |||||||
\(44\) | −0.532207 | + | 0.778327i | −0.532207 | + | 0.778327i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.330726 | + | 1.25821i | 0.330726 | + | 1.25821i | ||||
\(47\) | 0 | 0 | −0.198590 | − | 0.980083i | \(-0.563636\pi\) | ||||
0.198590 | + | 0.980083i | \(0.436364\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.0285561 | − | 0.999592i | −0.0285561 | − | 0.999592i | ||||
\(50\) | −0.354349 | + | 1.34808i | −0.354349 | + | 1.34808i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.456270 | − | 0.224333i | −0.456270 | − | 0.224333i | 0.198590 | − | 0.980083i | \(-0.436364\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.0330700 | + | 0.0724132i | −0.0330700 | + | 0.0724132i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.734314 | + | 1.39168i | 0.734314 | + | 1.39168i | ||||
\(59\) | 0 | 0 | 0.870746 | − | 0.491733i | \(-0.163636\pi\) | ||||
−0.870746 | + | 0.491733i | \(0.836364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.993482 | − | 0.113991i | \(-0.963636\pi\) | ||||
0.993482 | + | 0.113991i | \(0.0363636\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.466667 | − | 0.884433i | −0.466667 | − | 0.884433i | ||||
\(64\) | −0.683335 | + | 0.558760i | −0.683335 | + | 0.558760i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.643180 | + | 1.40837i | 0.643180 | + | 1.40837i | 0.897398 | + | 0.441221i | \(0.145455\pi\) |
−0.254218 | + | 0.967147i | \(0.581818\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.262555 | + | 0.998864i | −0.262555 | + | 0.998864i | 0.696938 | + | 0.717132i | \(0.254545\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(72\) | 0.00227327 | + | 0.0795747i | 0.00227327 | + | 0.0795747i | ||||
\(73\) | 0 | 0 | 0.466667 | − | 0.884433i | \(-0.345455\pi\) | ||||
−0.466667 | + | 0.884433i | \(0.654545\pi\) | |||||||
\(74\) | −0.447888 | − | 2.21042i | −0.447888 | − | 2.21042i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0285561 | + | 0.999592i | −0.0285561 | + | 0.999592i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.0526073 | − | 1.84150i | 0.0526073 | − | 1.84150i | −0.362808 | − | 0.931864i | \(-0.618182\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.985354 | − | 0.170522i | \(-0.0545455\pi\) | ||||
−0.985354 | + | 0.170522i | \(0.945455\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.46508 | − | 0.426599i | −2.46508 | − | 0.426599i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.0371501 | − | 0.0704072i | 0.0371501 | − | 0.0704072i | ||||
\(89\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.319282 | + | 0.820068i | 0.319282 | + | 0.820068i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.564443 | − | 0.825472i | \(-0.309091\pi\) | ||||
−0.564443 | + | 0.825472i | \(0.690909\pi\) | |||||||
\(98\) | −0.198369 | − | 1.37969i | −0.198369 | − | 1.37969i | ||||
\(99\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(100\) | −0.134187 | + | 0.933291i | −0.134187 | + | 0.933291i | ||||
\(101\) | 0 | 0 | −0.736741 | − | 0.676175i | \(-0.763636\pi\) | ||||
0.736741 | + | 0.676175i | \(0.236364\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.198590 | − | 0.980083i | \(-0.436364\pi\) | ||||
−0.198590 | + | 0.980083i | \(0.563636\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.667482 | − | 0.238157i | −0.667482 | − | 0.238157i | ||||
\(107\) | −0.443096 | + | 0.574616i | −0.443096 | + | 0.574616i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.516397 | + | 0.856349i | \(0.327273\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.260098 | + | 0.300169i | −0.260098 | + | 0.300169i | −0.870746 | − | 0.491733i | \(-0.836364\pi\) |
0.610648 | + | 0.791902i | \(0.290909\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.325658 | + | 1.00227i | −0.325658 | + | 1.00227i | ||||
\(113\) | 1.87141 | − | 0.667718i | 1.87141 | − | 0.667718i | 0.897398 | − | 0.441221i | \(-0.145455\pi\) |
0.974012 | − | 0.226497i | \(-0.0727273\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.600801 | + | 0.878643i | 0.600801 | + | 0.878643i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.0855750 | − | 0.996332i | 0.0855750 | − | 0.996332i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.786763 | − | 1.15060i | −0.786763 | − | 1.15060i | ||||
\(127\) | −0.899779 | + | 0.825810i | −0.899779 | + | 0.825810i | −0.985354 | − | 0.170522i | \(-0.945455\pi\) |
0.0855750 | + | 0.996332i | \(0.472727\pi\) | |||||||
\(128\) | 0.110781 | − | 0.113991i | 0.110781 | − | 0.113991i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.11444 | + | 1.84810i | 1.11444 | + | 1.84810i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.74815 | − | 0.859509i | 1.74815 | − | 0.859509i | 0.774142 | − | 0.633012i | \(-0.218182\pi\) |
0.974012 | − | 0.226497i | \(-0.0727273\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.198590 | − | 0.980083i | \(-0.436364\pi\) | ||||
−0.198590 | + | 0.980083i | \(0.563636\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.204875 | + | 1.42493i | −0.204875 | + | 1.42493i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.149979 | + | 1.04312i | 0.149979 | + | 1.04312i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.471444 | − | 1.45096i | −0.471444 | − | 1.45096i | ||||
\(149\) | 0.429039 | − | 0.711480i | 0.429039 | − | 0.711480i | −0.564443 | − | 0.825472i | \(-0.690909\pi\) |
0.993482 | + | 0.113991i | \(0.0363636\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.83474 | + | 0.426649i | 1.83474 | + | 0.426649i | 0.993482 | − | 0.113991i | \(-0.0363636\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.119281 | + | 1.38876i | 0.119281 | + | 1.38876i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.0855750 | − | 0.996332i | \(-0.472727\pi\) | ||||
−0.0855750 | + | 0.996332i | \(0.527273\pi\) | |||||||
\(158\) | −0.219745 | − | 2.55844i | −0.219745 | − | 2.55844i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.755084 | + | 0.548600i | 0.755084 | + | 0.548600i | ||||
\(162\) | −1.21371 | − | 0.685414i | −1.21371 | − | 0.685414i | ||||
\(163\) | 0.0207207 | − | 0.725319i | 0.0207207 | − | 0.725319i | −0.921124 | − | 0.389270i | \(-0.872727\pi\) |
0.941844 | − | 0.336049i | \(-0.109091\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.254218 | − | 0.967147i | \(-0.581818\pi\) | ||||
0.254218 | + | 0.967147i | \(0.418182\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.466667 | + | 0.884433i | −0.466667 | + | 0.884433i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.68953 | − | 0.0966110i | −1.68953 | − | 0.0966110i | ||||
\(173\) | 0 | 0 | −0.696938 | − | 0.717132i | \(-0.745455\pi\) | ||||
0.696938 | + | 0.717132i | \(0.254545\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(176\) | 0.382345 | − | 0.982045i | 0.382345 | − | 0.982045i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.569939 | − | 1.08015i | −0.569939 | − | 1.08015i | −0.985354 | − | 0.170522i | \(-0.945455\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.993482 | − | 0.113991i | \(-0.963636\pi\) | ||||
0.993482 | + | 0.113991i | \(0.0363636\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.0346734 | − | 0.0657135i | −0.0346734 | − | 0.0657135i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.83924 | + | 0.105172i | 1.83924 | + | 0.105172i | 0.941844 | − | 0.336049i | \(-0.109091\pi\) |
0.897398 | + | 0.441221i | \(0.145455\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.0567398 | − | 1.98615i | −0.0567398 | − | 1.98615i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.0855750 | − | 0.996332i | \(-0.472727\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.239699 | − | 0.911911i | −0.239699 | − | 0.911911i | ||||
\(197\) | −1.86912 | + | 0.548822i | −1.86912 | + | 0.548822i | −0.870746 | + | 0.491733i | \(0.836364\pi\) |
−0.998369 | + | 0.0570888i | \(0.981818\pi\) | |||||||
\(198\) | 0.719794 | + | 1.19364i | 0.719794 | + | 1.19364i | ||||
\(199\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(200\) | 0.00227327 | − | 0.0795747i | 0.00227327 | − | 0.0795747i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.03984 | + | 0.439442i | 1.03984 | + | 0.439442i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.919665 | + | 0.159154i | 0.919665 | + | 0.159154i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.157650 | + | 0.0666236i | −0.157650 | + | 0.0666236i | −0.466667 | − | 0.884433i | \(-0.654545\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(212\) | −0.466940 | − | 0.108582i | −0.466940 | − | 0.108582i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.522293 | + | 0.866126i | −0.522293 | + | 0.866126i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.312487 | + | 0.456998i | −0.312487 | + | 0.456998i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.998369 | − | 0.0570888i | \(-0.0181818\pi\) | ||||
−0.998369 | + | 0.0570888i | \(0.981818\pi\) | |||||||
\(224\) | −0.275907 | + | 1.36166i | −0.275907 | + | 1.36166i | ||||
\(225\) | 0.774142 | + | 0.633012i | 0.774142 | + | 0.633012i | ||||
\(226\) | 2.48542 | − | 1.22200i | 2.48542 | − | 1.22200i | ||||
\(227\) | 0 | 0 | −0.941844 | − | 0.336049i | \(-0.890909\pi\) | ||||
0.941844 | + | 0.336049i | \(0.109091\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.516397 | − | 0.856349i | \(-0.672727\pi\) | ||||
0.516397 | + | 0.856349i | \(0.327273\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.0588506 | − | 0.0679173i | −0.0588506 | − | 0.0679173i | ||||
\(233\) | 0.519923 | − | 1.60016i | 0.519923 | − | 1.60016i | −0.254218 | − | 0.967147i | \(-0.581818\pi\) |
0.774142 | − | 0.633012i | \(-0.218182\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.25259 | + | 0.910058i | −1.25259 | + | 0.910058i | −0.998369 | − | 0.0570888i | \(-0.981818\pi\) |
−0.254218 | + | 0.967147i | \(0.581818\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | −0.0398036 | − | 1.39331i | −0.0398036 | − | 1.39331i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(252\) | −0.617460 | − | 0.712587i | −0.617460 | − | 0.712587i | ||||
\(253\) | −0.722533 | − | 0.590812i | −0.722533 | − | 0.590812i | ||||
\(254\) | −1.11479 | + | 1.28654i | −1.11479 | + | 1.28654i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.674316 | − | 0.874468i | 0.674316 | − | 0.874468i | ||||
\(257\) | 0 | 0 | −0.941844 | − | 0.336049i | \(-0.890909\pi\) | ||||
0.941844 | + | 0.336049i | \(0.109091\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.25259 | − | 1.02424i | −1.25259 | − | 1.02424i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.12705 | − | 0.0644468i | 1.12705 | − | 0.0644468i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.146982 | + | 1.02228i | −0.146982 | + | 1.02228i | 0.774142 | + | 0.633012i | \(0.218182\pi\) |
−0.921124 | + | 0.389270i | \(0.872727\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.891459 | + | 1.15606i | 0.891459 | + | 1.15606i | ||||
\(269\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.362808 | − | 0.931864i | \(-0.618182\pi\) | ||||
0.362808 | + | 0.931864i | \(0.381818\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.28426 | − | 1.46800i | 2.28426 | − | 1.46800i | ||||
\(275\) | −0.362808 | − | 0.931864i | −0.362808 | − | 0.931864i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.96749 | + | 0.340488i | 1.96749 | + | 0.340488i | 0.993482 | + | 0.113991i | \(0.0363636\pi\) |
0.974012 | + | 0.226497i | \(0.0727273\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.468333 | + | 0.197919i | 0.468333 | + | 0.197919i | 0.610648 | − | 0.791902i | \(-0.290909\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.870746 | − | 0.491733i | \(-0.836364\pi\) | ||||
0.870746 | + | 0.491733i | \(0.163636\pi\) | |||||||
\(284\) | −0.0278082 | + | 0.973413i | −0.0278082 | + | 0.973413i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.353193 | + | 1.34368i | 0.353193 | + | 1.34368i | ||||
\(289\) | 0.198590 | + | 0.980083i | 0.198590 | + | 0.980083i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.998369 | − | 0.0570888i | \(-0.981818\pi\) | ||||
0.998369 | + | 0.0570888i | \(0.0181818\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.0535084 | + | 0.117167i | 0.0535084 | + | 0.117167i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.481081 | − | 1.05342i | 0.481081 | − | 1.05342i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.56281 | + | 0.882561i | −1.56281 | + | 0.882561i | ||||
\(302\) | 2.60851 | + | 0.299299i | 2.60851 | + | 0.299299i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(308\) | 0.187249 | + | 0.924108i | 0.187249 | + | 0.924108i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.696938 | − | 0.717132i | \(-0.745455\pi\) | ||||
0.696938 | + | 0.717132i | \(0.254545\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.254218 | − | 0.967147i | \(-0.418182\pi\) | ||||
−0.254218 | + | 0.967147i | \(0.581818\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.344958 | − | 1.70244i | −0.344958 | − | 1.70244i | ||||
\(317\) | −0.157116 | − | 0.597730i | −0.157116 | − | 0.597730i | −0.998369 | − | 0.0570888i | \(-0.981818\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.01306 | − | 0.498089i | −1.01306 | − | 0.498089i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.13280 | + | 0.639721i | 1.13280 | + | 0.639721i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.868516 | − | 0.367038i | −0.868516 | − | 0.367038i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.0865520 | − | 1.00771i | −0.0865520 | − | 1.00771i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.46504 | + | 0.941522i | −1.46504 | + | 0.941522i | −0.466667 | + | 0.884433i | \(0.654545\pi\) |
−0.998369 | + | 0.0570888i | \(0.981818\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.57598 | − | 0.366479i | −1.57598 | − | 0.366479i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.06344 | − | 1.37909i | −1.06344 | − | 1.37909i | −0.921124 | − | 0.389270i | \(-0.872727\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(338\) | −0.505709 | + | 1.29890i | −0.505709 | + | 1.29890i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.736741 | − | 0.676175i | −0.736741 | − | 0.676175i | ||||
\(344\) | 0.142646 | − | 0.00815677i | 0.142646 | − | 0.00815677i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.76851 | + | 0.869518i | −1.76851 | + | 0.869518i | −0.809017 | + | 0.587785i | \(0.800000\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.610648 | − | 0.791902i | \(-0.290909\pi\) | ||||
−0.610648 | + | 0.791902i | \(0.709091\pi\) | |||||||
\(350\) | 0.719794 | + | 1.19364i | 0.719794 | + | 1.19364i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.353193 | − | 1.34368i | 0.353193 | − | 1.34368i | ||||
\(353\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.960871 | − | 1.40523i | −0.960871 | − | 1.40523i | ||||
\(359\) | −1.69623 | + | 0.394442i | −1.69623 | + | 0.394442i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.736741 | + | 0.676175i | \(0.763636\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.993482 | − | 0.113991i | 0.993482 | − | 0.113991i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.974012 | − | 0.226497i | \(-0.0727273\pi\) | ||||
−0.974012 | + | 0.226497i | \(0.927273\pi\) | |||||||
\(368\) | −0.555184 | − | 0.811930i | −0.555184 | − | 0.811930i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.478868 | + | 0.170860i | −0.478868 | + | 0.170860i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.186393 | + | 0.215109i | 0.186393 | + | 0.215109i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.69042 | − | 0.831123i | 1.69042 | − | 0.831123i | 0.696938 | − | 0.717132i | \(-0.254545\pi\) |
0.993482 | − | 0.113991i | \(-0.0363636\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.56367 | − | 0.146596i | 2.56367 | − | 0.146596i | ||||
\(383\) | 0 | 0 | −0.736741 | − | 0.676175i | \(-0.763636\pi\) | ||||
0.736741 | + | 0.676175i | \(0.236364\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.394152 | − | 2.74139i | −0.394152 | − | 2.74139i | ||||
\(387\) | −1.01306 | + | 1.48155i | −1.01306 | + | 1.48155i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.15027 | + | 1.49170i | 1.15027 | + | 1.49170i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.0288821 | + | 0.0741830i | 0.0288821 | + | 0.0741830i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.50113 | + | 1.05699i | −2.50113 | + | 1.05699i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.575772 | + | 0.746675i | 0.575772 | + | 0.746675i | ||||
\(397\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.0901832 | − | 1.04998i | −0.0901832 | − | 1.04998i | ||||
\(401\) | −0.168643 | + | 0.0291849i | −0.168643 | + | 0.0291849i | −0.254218 | − | 0.967147i | \(-0.581818\pi\) |
0.0855750 | + | 0.996332i | \(0.472727\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.50979 | + | 0.443314i | 1.50979 | + | 0.443314i | ||||
\(407\) | 1.19207 | + | 1.09407i | 1.19207 | + | 1.09407i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.254218 | − | 0.967147i | \(-0.581818\pi\) | ||||
0.254218 | + | 0.967147i | \(0.418182\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.29883 | + | 0.0742698i | 1.29883 | + | 0.0742698i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.812697 | + | 1.54023i | 0.812697 | + | 1.54023i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.0285561 | + | 0.999592i | \(0.509091\pi\) | |||||||
\(422\) | −0.207727 | + | 0.117309i | −0.207727 | + | 0.117309i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.0402114 | + | 0.00461382i | 0.0402114 | + | 0.00461382i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.284216 | + | 0.622347i | −0.284216 | + | 0.622347i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.79187 | − | 0.881003i | −1.79187 | − | 0.881003i | −0.921124 | − | 0.389270i | \(-0.872727\pi\) |
−0.870746 | − | 0.491733i | \(-0.836364\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.998369 | − | 0.0570888i | \(-0.981818\pi\) | ||||
0.998369 | + | 0.0570888i | \(0.0181818\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.174766 | + | 0.331218i | −0.174766 | + | 0.331218i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.71599 | + | 0.969062i | 1.71599 | + | 0.969062i | 0.941844 | + | 0.336049i | \(0.109091\pi\) |
0.774142 | + | 0.633012i | \(0.218182\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.0755371 | + | 0.879462i | −0.0755371 | + | 0.879462i | ||||
\(449\) | −0.391364 | − | 0.0677282i | −0.391364 | − | 0.0677282i | −0.0285561 | − | 0.999592i | \(-0.509091\pi\) |
−0.362808 | + | 0.931864i | \(0.618182\pi\) | |||||||
\(450\) | 1.17260 | + | 0.753586i | 1.17260 | + | 0.753586i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.57607 | − | 1.01288i | 1.57607 | − | 1.01288i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.209698 | − | 1.45848i | 0.209698 | − | 1.45848i | −0.564443 | − | 0.825472i | \(-0.690909\pi\) |
0.774142 | − | 0.633012i | \(-0.218182\pi\) | |||||||
\(464\) | −0.876484 | − | 0.804430i | −0.876484 | − | 0.804430i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.465735 | − | 2.29849i | 0.465735 | − | 2.29849i | ||||
\(467\) | 0 | 0 | −0.774142 | − | 0.633012i | \(-0.781818\pi\) | ||||
0.774142 | + | 0.633012i | \(0.218182\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.45824 | + | 0.520300i | 1.45824 | + | 0.520300i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.61065 | − | 0.791902i | 1.61065 | − | 0.791902i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.354349 | + | 0.364616i | −0.354349 | + | 0.364616i | ||||
\(478\) | −1.58997 | + | 1.45926i | −1.58997 | + | 1.45926i | ||||
\(479\) | 0 | 0 | −0.564443 | − | 0.825472i | \(-0.690909\pi\) | ||||
0.564443 | + | 0.825472i | \(0.309091\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.134187 | − | 0.933291i | −0.134187 | − | 0.933291i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.45202 | + | 1.05496i | −1.45202 | + | 1.05496i | −0.466667 | + | 0.884433i | \(0.654545\pi\) |
−0.985354 | + | 0.170522i | \(0.945455\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.198369 | + | 0.204117i | −0.198369 | + | 0.204117i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.610648 | + | 0.791902i | \(0.290909\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.533333 | + | 0.884433i | 0.533333 | + | 0.884433i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.582092 | + | 0.207690i | 0.582092 | + | 0.207690i | 0.610648 | − | 0.791902i | \(-0.290909\pi\) |
−0.0285561 | + | 0.999592i | \(0.509091\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.998369 | − | 0.0570888i | \(-0.0181818\pi\) | ||||
−0.998369 | + | 0.0570888i | \(0.981818\pi\) | |||||||
\(504\) | 0.0586499 | + | 0.0538283i | 0.0586499 | + | 0.0538283i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.09443 | − | 0.703348i | −1.09443 | − | 0.703348i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.649982 | + | 0.950568i | −0.649982 | + | 0.950568i | ||||
\(509\) | 0 | 0 | 0.362808 | − | 0.931864i | \(-0.381818\pi\) | ||||
−0.362808 | + | 0.931864i | \(0.618182\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.712758 | − | 1.18198i | 0.712758 | − | 1.18198i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.89731 | − | 1.21933i | −1.89731 | − | 1.21933i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.0855750 | − | 0.996332i | \(-0.527273\pi\) | ||||
0.0855750 | + | 0.996332i | \(0.472727\pi\) | |||||||
\(522\) | 1.55048 | − | 0.268321i | 1.55048 | − | 0.268321i | ||||
\(523\) | 0 | 0 | −0.921124 | − | 0.389270i | \(-0.872727\pi\) | ||||
0.921124 | + | 0.389270i | \(0.127273\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.0411089 | + | 1.43900i | −0.0411089 | + | 1.43900i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.123666 | − | 0.0363115i | 0.123666 | − | 0.0363115i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.0859006 | − | 0.0883896i | −0.0859006 | − | 0.0883896i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.696938 | + | 0.717132i | 0.696938 | + | 0.717132i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.132494 | − | 0.108340i | 0.132494 | − | 0.108340i | −0.564443 | − | 0.825472i | \(-0.690909\pi\) |
0.696938 | + | 0.717132i | \(0.254545\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.785171 | − | 1.48806i | −0.785171 | − | 1.48806i | −0.870746 | − | 0.491733i | \(-0.836364\pi\) |
0.0855750 | − | 0.996332i | \(-0.472727\pi\) | |||||||
\(548\) | 1.42192 | − | 1.16270i | 1.42192 | − | 1.16270i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.650476 | − | 1.23279i | −0.650476 | − | 1.23279i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.28393 | − | 1.32113i | −1.28393 | − | 1.32113i | ||||
\(554\) | 2.77866 | + | 0.158890i | 2.77866 | + | 0.158890i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.288416 | + | 0.546610i | −0.288416 | + | 0.546610i | −0.985354 | − | 0.170522i | \(-0.945455\pi\) |
0.696938 | + | 0.717132i | \(0.254545\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.679990 | + | 0.199663i | 0.679990 | + | 0.199663i | ||||
\(563\) | 0 | 0 | 0.0285561 | − | 0.999592i | \(-0.490909\pi\) | ||||
−0.0285561 | + | 0.999592i | \(0.509091\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.985354 | + | 0.170522i | −0.985354 | + | 0.170522i | ||||
\(568\) | −0.00703579 | − | 0.0819163i | −0.00703579 | − | 0.0819163i | ||||
\(569\) | −0.164217 | + | 1.91195i | −0.164217 | + | 1.91195i | 0.198590 | + | 0.980083i | \(0.436364\pi\) |
−0.362808 | + | 0.931864i | \(0.618182\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.63878 | + | 1.05318i | 1.63878 | + | 1.05318i | 0.941844 | + | 0.336049i | \(0.109091\pi\) |
0.696938 | + | 0.717132i | \(0.254545\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.909079 | − | 0.211397i | −0.909079 | − | 0.211397i | ||||
\(576\) | 0.320250 | + | 0.822557i | 0.320250 | + | 0.822557i | ||||
\(577\) | 0 | 0 | 0.516397 | − | 0.856349i | \(-0.327273\pi\) | ||||
−0.516397 | + | 0.856349i | \(0.672727\pi\) | |||||||
\(578\) | 0.430731 | + | 1.32565i | 0.430731 | + | 1.32565i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.487841 | − | 0.143243i | 0.487841 | − | 0.143243i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.198590 | − | 0.980083i | \(-0.436364\pi\) | ||||
−0.198590 | + | 0.980083i | \(0.563636\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.880543 | + | 1.46022i | 0.880543 | + | 1.46022i | ||||
\(593\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.242078 | − | 0.745038i | 0.242078 | − | 0.745038i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.292620 | + | 0.268564i | −0.292620 | + | 0.268564i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.516397 | + | 0.856349i | \(0.327273\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.974012 | − | 0.226497i | \(-0.0727273\pi\) | ||||
−0.974012 | + | 0.226497i | \(0.927273\pi\) | |||||||
\(602\) | −2.02394 | + | 1.47048i | −2.02394 | + | 1.47048i | ||||
\(603\) | 1.53819 | − | 0.176491i | 1.53819 | − | 0.176491i | ||||
\(604\) | 1.77611 | 1.77611 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.993482 | − | 0.113991i | \(-0.0363636\pi\) | ||||
−0.993482 | + | 0.113991i | \(0.963636\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.85610 | + | 0.662255i | −1.85610 | + | 0.662255i | −0.870746 | + | 0.491733i | \(0.836364\pi\) |
−0.985354 | + | 0.170522i | \(0.945455\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.0246000 | − | 0.0757109i | −0.0246000 | − | 0.0757109i | ||||
\(617\) | 0.964926 | − | 1.11358i | 0.964926 | − | 1.11358i | −0.0285561 | − | 0.999592i | \(-0.509091\pi\) |
0.993482 | − | 0.113991i | \(-0.0363636\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.610648 | − | 0.791902i | \(-0.290909\pi\) | ||||
−0.610648 | + | 0.791902i | \(0.709091\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.736741 | − | 0.676175i | −0.736741 | − | 0.676175i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.104512 | + | 0.135534i | 0.104512 | + | 0.135534i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.736741 | + | 0.676175i | \(0.763636\pi\) | |||||||
\(632\) | 0.0453192 | + | 0.139478i | 0.0453192 | + | 0.139478i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.312545 | − | 0.802766i | −0.312545 | − | 0.802766i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.48202 | − | 0.528783i | −1.48202 | − | 0.528783i | ||||
\(639\) | 0.868842 | + | 0.558371i | 0.868842 | + | 0.558371i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.168643 | + | 1.96348i | −0.168643 | + | 1.96348i | 0.0855750 | + | 0.996332i | \(0.472727\pi\) |
−0.254218 | + | 0.967147i | \(0.581818\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.985354 | − | 0.170522i | \(-0.0545455\pi\) | ||||
−0.985354 | + | 0.170522i | \(0.945455\pi\) | |||||||
\(644\) | 0.810616 | + | 0.342569i | 0.810616 | + | 0.342569i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.0285561 | − | 0.999592i | \(-0.490909\pi\) | ||||
−0.0285561 | + | 0.999592i | \(0.509091\pi\) | |||||||
\(648\) | 0.0763825 | + | 0.0224279i | 0.0763825 | + | 0.0224279i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.135870 | − | 0.670547i | −0.135870 | − | 0.670547i | ||||
\(653\) | −0.569939 | + | 1.08015i | −0.569939 | + | 1.08015i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.985354 | + | 0.170522i | \(0.945455\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.797176 | − | 1.74557i | −0.797176 | − | 1.74557i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(662\) | −1.87917 | + | 1.53659i | −1.87917 | + | 1.53659i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.24064 | − | 0.257089i | −2.24064 | − | 0.257089i | ||||
\(667\) | −0.917443 | + | 0.518104i | −0.917443 | + | 0.518104i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.76851 | − | 0.869518i | −1.76851 | − | 0.869518i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.809017 | − | 0.587785i | \(-0.800000\pi\) | |||||||
\(674\) | −1.69176 | − | 1.74078i | −1.69176 | − | 1.74078i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.239699 | + | 0.911911i | −0.239699 | + | 0.911911i | ||||
\(677\) | 0 | 0 | −0.0285561 | − | 0.999592i | \(-0.509091\pi\) | ||||
0.0285561 | + | 0.999592i | \(0.490909\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.164217 | − | 0.0482185i | −0.164217 | − | 0.0482185i | 0.198590 | − | 0.980083i | \(-0.436364\pi\) |
−0.362808 | + | 0.931864i | \(0.618182\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.12767 | − | 0.819299i | −1.12767 | − | 0.819299i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.86374 | − | 0.322534i | 1.86374 | − | 0.322534i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.985354 | − | 0.170522i | \(-0.945455\pi\) | ||||
0.985354 | + | 0.170522i | \(0.0545455\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.941844 | + | 0.336049i | 0.941844 | + | 0.336049i | ||||
\(694\) | −2.31086 | + | 1.48510i | −2.31086 | + | 1.48510i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.575772 | + | 0.746675i | 0.575772 | + | 0.746675i | ||||
\(701\) | −0.683417 | + | 1.75534i | −0.683417 | + | 1.75534i | −0.0285561 | + | 0.999592i | \(0.509091\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.125621 | − | 0.873716i | 0.125621 | − | 0.873716i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.52561 | − | 1.24748i | −1.52561 | − | 1.24748i | −0.870746 | − | 0.491733i | \(-0.836364\pi\) |
−0.654861 | − | 0.755750i | \(-0.727273\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.73511 | − | 0.619086i | −1.73511 | − | 0.619086i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.754102 | − | 0.870280i | −0.754102 | − | 0.870280i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.28625 | + | 0.815734i | −2.28625 | + | 0.815734i | ||||
\(719\) | 0 | 0 | 0.696938 | − | 0.717132i | \(-0.254545\pi\) | ||||
−0.696938 | + | 0.717132i | \(0.745455\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.35765 | − | 0.315708i | 1.35765 | − | 0.315708i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.12889 | −1.12889 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.696938 | − | 0.717132i | \(-0.254545\pi\) | ||||
−0.696938 | + | 0.717132i | \(0.745455\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.849163 | − | 0.979987i | −0.849163 | − | 0.979987i | ||||
\(737\) | −1.42616 | − | 0.602700i | −1.42616 | − | 0.602700i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.319151 | + | 0.529253i | 0.319151 | + | 0.529253i | 0.974012 | − | 0.226497i | \(-0.0727273\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.635984 | + | 0.312692i | −0.635984 | + | 0.312692i | ||||
\(743\) | 0.478446 | + | 0.391223i | 0.478446 | + | 0.391223i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.362808 | + | 0.931864i | \(0.618182\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.292293 | + | 0.268264i | 0.292293 | + | 0.268264i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.103266 | + | 0.718230i | 0.103266 | + | 0.718230i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.706758 | + | 1.81529i | −0.706758 | + | 1.81529i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.564443 | + | 0.825472i | \(0.690909\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.35726 | − | 0.573583i | 1.35726 | − | 0.573583i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.941844 | + | 0.336049i | \(0.109091\pi\) | |||||||
\(758\) | 2.20882 | − | 1.41952i | 2.20882 | − | 1.41952i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.985354 | − | 0.170522i | \(-0.945455\pi\) | ||||
0.985354 | + | 0.170522i | \(0.0545455\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.0339888 | + | 0.395724i | 0.0339888 | + | 0.395724i | ||||
\(764\) | 1.71159 | − | 0.296203i | 1.71159 | − | 0.296203i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.476274 | − | 1.81193i | −0.476274 | − | 1.81193i | ||||
\(773\) | 0 | 0 | −0.198590 | − | 0.980083i | \(-0.563636\pi\) | ||||
0.198590 | + | 0.980083i | \(0.436364\pi\) | |||||||
\(774\) | −1.16747 | + | 2.21261i | −1.16747 | + | 2.21261i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.82990 | + | 1.88292i | 1.82990 | + | 1.88292i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.481972 | − | 0.913438i | −0.481972 | − | 0.913438i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.491798 | + | 0.932060i | 0.491798 | + | 0.932060i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.993482 | − | 0.113991i | \(-0.963636\pi\) | ||||
0.993482 | + | 0.113991i | \(0.0363636\pi\) | |||||||
\(788\) | −1.59936 | + | 0.903199i | −1.59936 | + | 0.903199i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.825414 | − | 1.80741i | 0.825414 | − | 1.80741i | ||||
\(792\) | −0.0554812 | − | 0.0570888i | −0.0554812 | − | 0.0570888i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.254218 | − | 0.967147i | \(-0.418182\pi\) | ||||
−0.254218 | + | 0.967147i | \(0.581818\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.275907 | − | 1.36166i | −0.275907 | − | 1.36166i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.228898 | + | 0.0672106i | −0.228898 | + | 0.0672106i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.20341 | + | 0.208258i | −1.20341 | + | 0.208258i | −0.736741 | − | 0.676175i | \(-0.763636\pi\) |
−0.466667 | + | 0.884433i | \(0.654545\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.0855750 | − | 0.996332i | \(-0.472727\pi\) | ||||
−0.0855750 | + | 0.996332i | \(0.527273\pi\) | |||||||
\(812\) | 1.04882 | + | 0.181506i | 1.04882 | + | 0.181506i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.82461 | + | 1.32565i | 1.82461 | + | 1.32565i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.799779 | − | 1.03717i | −0.799779 | − | 1.03717i | −0.998369 | − | 0.0570888i | \(-0.981818\pi\) |
0.198590 | − | 0.980083i | \(-0.436364\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.348845 | + | 0.510170i | −0.348845 | + | 0.510170i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.610648 | + | 0.791902i | \(0.290909\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.612107 | − | 0.561786i | −0.612107 | − | 0.561786i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.921124 | + | 0.389270i | \(0.872727\pi\) | |||||||
\(828\) | 0.878595 | − | 0.0502399i | 0.878595 | − | 0.0502399i | ||||
\(829\) | 0 | 0 | 0.198590 | − | 0.980083i | \(-0.436364\pi\) | ||||
−0.198590 | + | 0.980083i | \(0.563636\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.941844 | − | 0.336049i | \(-0.109091\pi\) | ||||
−0.941844 | + | 0.336049i | \(0.890909\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.202150 | + | 0.185532i | −0.202150 | + | 0.185532i | ||||
\(842\) | 1.37014 | + | 2.00377i | 1.37014 | + | 2.00377i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.130555 | + | 0.0948540i | −0.130555 | + | 0.0948540i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(848\) | 0.535816 | 0.535816 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.47092 | − | 0.342048i | 1.47092 | − | 0.342048i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.736741 | − | 0.676175i | \(-0.236364\pi\) | ||||
−0.736741 | + | 0.676175i | \(0.763636\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.0178501 | − | 0.0549370i | 0.0178501 | − | 0.0549370i | ||||
\(857\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.62134 | − | 0.935294i | −2.62134 | − | 0.935294i | ||||
\(863\) | −1.17534 | + | 0.577877i | −1.17534 | + | 0.577877i | −0.921124 | − | 0.389270i | \(-0.872727\pi\) |
−0.254218 | + | 0.967147i | \(0.581818\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.20642 | + | 1.39228i | 1.20642 | + | 1.39228i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.0114714 | − | 0.0294641i | 0.0114714 | − | 0.0294641i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.00595 | + | 0.233925i | 1.00595 | + | 0.233925i | 0.696938 | − | 0.717132i | \(-0.254545\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(882\) | −1.37346 | − | 0.237687i | −1.37346 | − | 0.237687i | ||||
\(883\) | 0.143981 | − | 1.67634i | 0.143981 | − | 1.67634i | −0.466667 | − | 0.884433i | \(-0.654545\pi\) |
0.610648 | − | 0.791902i | \(-0.290909\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.53025 | + | 1.06929i | 2.53025 | + | 1.06929i | ||||
\(887\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.0348754 | + | 1.22080i | −0.0348754 | + | 1.22080i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.993482 | − | 0.113991i | 0.993482 | − | 0.113991i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.00453912 | − | 0.158890i | −0.00453912 | − | 0.158890i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.552718 | − | 0.0316055i | −0.552718 | − | 0.0316055i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.846146 | + | 0.416022i | 0.846146 | + | 0.416022i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.122451 | + | 0.100128i | −0.122451 | + | 0.100128i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.97401 | + | 0.226497i | 1.97401 | + | 0.226497i | 1.00000 | \(0\) | ||
0.974012 | + | 0.226497i | \(0.0727273\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.643180 | − | 0.525926i | 0.643180 | − | 0.525926i | −0.254218 | − | 0.967147i | \(-0.581818\pi\) |
0.897398 | + | 0.441221i | \(0.145455\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −0.936901 | − | 2.05153i | −0.936901 | − | 2.05153i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.00163090 | + | 0.0570888i | 0.00163090 | + | 0.0570888i | 1.00000 | \(0\) | ||
−0.998369 | + | 0.0570888i | \(0.981818\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.55249 | + | 0.455853i | 1.55249 | + | 0.455853i | ||||
\(926\) | 0.0586499 | − | 2.05301i | 0.0586499 | − | 2.05301i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.26886 | − | 0.921879i | −1.26886 | − | 0.921879i | ||||
\(929\) | 0 | 0 | −0.921124 | − | 0.389270i | \(-0.872727\pi\) | ||||
0.921124 | + | 0.389270i | \(0.127273\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.135758 | − | 1.58060i | 0.135758 | − | 1.58060i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.921124 | − | 0.389270i | \(-0.127273\pi\) | ||||
−0.921124 | + | 0.389270i | \(0.872727\pi\) | |||||||
\(938\) | 2.10203 | + | 0.488806i | 2.10203 | + | 0.488806i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.10458 | − | 1.35253i | 2.10458 | − | 1.35253i | ||||
\(947\) | 0.273100 | − | 1.89945i | 0.273100 | − | 1.89945i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.161197 | + | 0.0575149i | 0.161197 | + | 0.0575149i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.254218 | + | 0.967147i | \(0.581818\pi\) | |||||||
\(954\) | −0.432764 | + | 0.561219i | −0.432764 | + | 0.561219i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.956003 | + | 1.10329i | −0.956003 | + | 1.10329i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.601972 | − | 1.85268i | 0.601972 | − | 1.85268i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.696938 | − | 0.717132i | 0.696938 | − | 0.717132i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.409569 | + | 0.598975i | 0.409569 | + | 0.598975i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.397181 | 0.397181 | 0.198590 | − | 0.980083i | \(-0.436364\pi\) | ||||
0.198590 | + | 0.980083i | \(0.436364\pi\) | |||||||
\(968\) | 0.0202376 | + | 0.0769918i | 0.0202376 | + | 0.0769918i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.84312 | + | 1.69160i | −1.84312 | + | 1.69160i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.538151 | + | 1.65626i | −0.538151 | + | 1.65626i | 0.198590 | + | 0.980083i | \(0.436364\pi\) |
−0.736741 | + | 0.676175i | \(0.763636\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.205103 | + | 0.340126i | 0.205103 | + | 0.340126i | ||||
\(982\) | −0.242267 | + | 0.314178i | −0.242267 | + | 0.314178i | ||||
\(983\) | 0 | 0 | −0.941844 | − | 0.336049i | \(-0.890909\pi\) | ||||
0.941844 | + | 0.336049i | \(0.109091\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.238398 | − | 1.65810i | 0.238398 | − | 1.65810i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.273100 | + | 1.89945i | 0.273100 | + | 1.89945i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.879081 | + | 1.14001i | 0.879081 | + | 1.14001i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.362808 | − | 0.931864i | \(-0.618182\pi\) | ||||
0.362808 | + | 0.931864i | \(0.381818\pi\) | |||||||
\(998\) | 0.839074 | + | 0.195118i | 0.839074 | + | 0.195118i | ||||
\(999\) | 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 | 847.1.bb.a.174.1 | ✓ | 40 | |
7.6 | odd | 2 | CM | 847.1.bb.a.174.1 | ✓ | 40 | |
121.16 | even | 55 | inner | 847.1.bb.a.258.1 | yes | 40 | |
847.258 | odd | 110 | inner | 847.1.bb.a.258.1 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.1.bb.a.174.1 | ✓ | 40 | 1.1 | even | 1 | trivial | |
847.1.bb.a.174.1 | ✓ | 40 | 7.6 | odd | 2 | CM | |
847.1.bb.a.258.1 | yes | 40 | 121.16 | even | 55 | inner | |
847.1.bb.a.258.1 | yes | 40 | 847.258 | odd | 110 | inner |