Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1500,2,Mod(49,1500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1500, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1500.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1500.o (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.9775603032\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 5x^{14} + 6x^{12} - 20x^{10} - 79x^{8} - 80x^{6} + 96x^{4} + 320x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 649.3 | ||
Root | \(-0.462894 + 1.33631i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1500.649 |
Dual form | 1500.2.o.b.349.4 |
$q$-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 \(\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times\).
\(n\) | \(751\) | \(877\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.587785 | − | 0.809017i | 0.339358 | − | 0.467086i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.0883282i | − | 0.0333849i | −0.999861 | − | 0.0166925i | \(-0.994686\pi\) | ||
0.999861 | − | 0.0166925i | \(-0.00531362\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.309017 | − | 0.951057i | −0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.701409 | − | 2.15871i | 0.211483 | − | 0.650877i | −0.787902 | − | 0.615801i | \(-0.788833\pi\) |
0.999385 | − | 0.0350761i | \(-0.0111674\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.52199 | − | 0.819443i | 0.699473 | − | 0.227273i | 0.0623720 | − | 0.998053i | \(-0.480133\pi\) |
0.637101 | + | 0.770780i | \(0.280133\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.22749 | − | 1.68949i | −0.297710 | − | 0.409762i | 0.633790 | − | 0.773506i | \(-0.281499\pi\) |
−0.931499 | + | 0.363743i | \(0.881499\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.42464 | − | 1.03506i | 0.326835 | − | 0.237459i | −0.412252 | − | 0.911070i | \(-0.635258\pi\) |
0.739086 | + | 0.673611i | \(0.235258\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0714590 | − | 0.0519180i | −0.0155936 | − | 0.0113294i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.50810 | − | 1.46477i | −0.940005 | − | 0.305426i | −0.201357 | − | 0.979518i | \(-0.564535\pi\) |
−0.738647 | + | 0.674092i | \(0.764535\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.951057 | − | 0.309017i | −0.183031 | − | 0.0594703i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.99851 | + | 2.17855i | 0.556809 | + | 0.404546i | 0.830290 | − | 0.557332i | \(-0.188175\pi\) |
−0.273480 | + | 0.961878i | \(0.588175\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.32199 | − | 2.41356i | 0.596646 | − | 0.433489i | −0.248041 | − | 0.968750i | \(-0.579787\pi\) |
0.844687 | + | 0.535261i | \(0.179787\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.33416 | − | 1.83631i | −0.232247 | − | 0.319661i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.77065 | + | 2.19992i | −1.11309 | + | 0.361664i | −0.807126 | − | 0.590379i | \(-0.798978\pi\) |
−0.305963 | + | 0.952044i | \(0.598978\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.819443 | − | 2.52199i | 0.131216 | − | 0.403841i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.03623 | − | 6.26687i | −0.318006 | − | 0.978721i | −0.974499 | − | 0.224390i | \(-0.927961\pi\) |
0.656494 | − | 0.754332i | \(-0.272039\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.79469i | − | 0.273688i | −0.990593 | − | 0.136844i | \(-0.956304\pi\) | ||
0.990593 | − | 0.136844i | \(-0.0436959\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.94311 | − | 8.17999i | 0.866892 | − | 1.19317i | −0.112990 | − | 0.993596i | \(-0.536043\pi\) |
0.979882 | − | 0.199578i | \(-0.0639571\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.99220 | 0.998885 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.08833 | −0.292424 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.565120 | − | 0.777821i | 0.0776252 | − | 0.106842i | −0.768439 | − | 0.639923i | \(-0.778966\pi\) |
0.846064 | + | 0.533081i | \(0.178966\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.76095i | − | 0.233244i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.77436 | + | 8.53860i | 0.361191 | + | 1.11163i | 0.952332 | + | 0.305063i | \(0.0986774\pi\) |
−0.591142 | + | 0.806568i | \(0.701323\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.92521 | − | 9.00287i | 0.374535 | − | 1.15270i | −0.569257 | − | 0.822159i | \(-0.692769\pi\) |
0.943792 | − | 0.330540i | \(-0.107231\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0840051 | + | 0.0272949i | −0.0105836 | + | 0.00343883i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.17249 | − | 11.2485i | −0.998429 | − | 1.37422i | −0.926285 | − | 0.376825i | \(-0.877016\pi\) |
−0.0721440 | − | 0.997394i | \(-0.522984\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.83482 | + | 2.78616i | −0.461658 | + | 0.335414i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.97363 | − | 3.61355i | −0.590261 | − | 0.428850i | 0.252148 | − | 0.967689i | \(-0.418863\pi\) |
−0.842409 | + | 0.538839i | \(0.818863\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.00310 | + | 0.975766i | 0.351486 | + | 0.114205i | 0.479438 | − | 0.877576i | \(-0.340840\pi\) |
−0.127952 | + | 0.991780i | \(0.540840\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.190675 | − | 0.0619542i | −0.0217295 | − | 0.00706033i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.8021 | + | 7.84821i | 1.21534 | + | 0.882993i | 0.995704 | − | 0.0925903i | \(-0.0295147\pi\) |
0.219631 | + | 0.975583i | \(0.429515\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.29846 | − | 12.7982i | −1.02064 | − | 1.40479i | −0.911755 | − | 0.410734i | \(-0.865272\pi\) |
−0.108884 | − | 0.994054i | \(-0.534728\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.52496 | − | 1.14533i | 0.377915 | − | 0.122792i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.16767 | − | 9.74909i | 0.335772 | − | 1.03340i | −0.630568 | − | 0.776134i | \(-0.717178\pi\) |
0.966340 | − | 0.257267i | \(-0.0828220\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0723799 | − | 0.222762i | −0.00758747 | − | 0.0233518i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 4.10620i | − | 0.425793i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.52820 | + | 10.3617i | −0.764373 | + | 1.05207i | 0.232465 | + | 0.972605i | \(0.425321\pi\) |
−0.996838 | + | 0.0794643i | \(0.974679\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.26981 | −0.228124 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.72537 | −0.271185 | −0.135592 | − | 0.990765i | \(-0.543294\pi\) | ||||
−0.135592 | + | 0.990765i | \(0.543294\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.211589 | − | 0.291227i | 0.0208485 | − | 0.0286954i | −0.798466 | − | 0.602041i | \(-0.794355\pi\) |
0.819314 | + | 0.573345i | \(0.194355\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.0286533i | 0.00277002i | 0.999999 | + | 0.00138501i | \(0.000440863\pi\) | ||||
−0.999999 | + | 0.00138501i | \(0.999559\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.84714 | + | 17.9956i | 0.560054 | + | 1.72367i | 0.682207 | + | 0.731159i | \(0.261020\pi\) |
−0.122153 | + | 0.992511i | \(0.538980\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.19992 | + | 6.77065i | −0.208807 | + | 0.642642i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.65428 | − | 1.51227i | 0.437838 | − | 0.142262i | −0.0818000 | − | 0.996649i | \(-0.526067\pi\) |
0.519638 | + | 0.854387i | \(0.326067\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.55867 | − | 2.14533i | −0.144099 | − | 0.198336i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.149230 | + | 0.108422i | −0.0136799 | + | 0.00993901i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.73111 | + | 3.43736i | 0.430101 | + | 0.312487i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.26687 | − | 2.03623i | −0.565065 | − | 0.183601i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.10993 | − | 1.01048i | −0.275961 | − | 0.0896652i | 0.167767 | − | 0.985827i | \(-0.446344\pi\) |
−0.443728 | + | 0.896161i | \(0.646344\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.45193 | − | 1.05489i | −0.127836 | − | 0.0928781i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.90882 | + | 2.11338i | −0.254145 | + | 0.184647i | −0.707562 | − | 0.706651i | \(-0.750205\pi\) |
0.453417 | + | 0.891299i | \(0.350205\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0914251 | − | 0.125836i | −0.00792756 | − | 0.0109114i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.1867 | + | 5.25938i | −1.38292 | + | 0.449339i | −0.903629 | − | 0.428315i | \(-0.859107\pi\) |
−0.479294 | + | 0.877654i | \(0.659107\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.86699 | − | 18.0567i | 0.497632 | − | 1.53155i | −0.315184 | − | 0.949031i | \(-0.602066\pi\) |
0.812815 | − | 0.582522i | \(-0.197934\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.12448 | − | 9.61615i | −0.263128 | − | 0.809826i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 6.01901i | − | 0.503335i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.10991 | − | 5.65681i | 0.338980 | − | 0.466566i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.3441 | −1.66665 | −0.833327 | − | 0.552780i | \(-0.813567\pi\) | ||||
−0.833327 | + | 0.552780i | \(0.813567\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.2609 | 1.07915 | 0.539577 | − | 0.841936i | \(-0.318584\pi\) | ||||
0.539577 | + | 0.841936i | \(0.318584\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.22749 | + | 1.68949i | −0.0992366 | + | 0.136587i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.8066i | 1.02208i | 0.859558 | + | 0.511039i | \(0.170739\pi\) | ||||
−0.859558 | + | 0.511039i | \(0.829261\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.297101 | − | 0.914384i | −0.0235617 | − | 0.0725153i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.129381 | + | 0.398193i | −0.0101966 | + | 0.0313820i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.3273 | − | 4.65524i | 1.12220 | − | 0.364626i | 0.311596 | − | 0.950215i | \(-0.399137\pi\) |
0.810608 | + | 0.585589i | \(0.199137\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.02861 | + | 2.79215i | 0.156979 | + | 0.216063i | 0.880261 | − | 0.474490i | \(-0.157367\pi\) |
−0.723282 | + | 0.690553i | \(0.757367\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.82830 | + | 3.50796i | −0.371407 | + | 0.269843i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.42464 | − | 1.03506i | −0.108945 | − | 0.0791531i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.29639 | + | 0.746142i | 0.174591 | + | 0.0567281i | 0.395008 | − | 0.918678i | \(-0.370742\pi\) |
−0.220417 | + | 0.975406i | \(0.570742\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.53860 | + | 2.77436i | 0.641800 | + | 0.208533i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.29228 | − | 2.39198i | −0.246077 | − | 0.178785i | 0.457910 | − | 0.888999i | \(-0.348598\pi\) |
−0.703986 | + | 0.710214i | \(0.748598\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.7893 | − | 7.83888i | 0.801962 | − | 0.582660i | −0.109527 | − | 0.993984i | \(-0.534934\pi\) |
0.911489 | + | 0.411324i | \(0.134934\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.56408 | − | 7.65830i | −0.411309 | − | 0.566118i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.50810 | + | 1.46477i | −0.329665 | + | 0.107115i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.0272949 | + | 0.0840051i | −0.00198541 | + | 0.00611047i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.80358 | + | 24.0169i | 0.564647 | + | 1.73780i | 0.668998 | + | 0.743264i | \(0.266723\pi\) |
−0.104351 | + | 0.994541i | \(0.533277\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.6399i | 1.77362i | 0.462139 | + | 0.886808i | \(0.347082\pi\) | ||||
−0.462139 | + | 0.886808i | \(0.652918\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.9446 | − | 15.0640i | 0.779774 | − | 1.07327i | −0.215533 | − | 0.976496i | \(-0.569149\pi\) |
0.995307 | − | 0.0967697i | \(-0.0308510\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.85708 | −0.698750 | −0.349375 | − | 0.936983i | \(-0.613606\pi\) | ||||
−0.349375 | + | 0.936983i | \(0.613606\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.9039 | −0.980703 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.192427 | − | 0.264853i | 0.0135057 | − | 0.0185890i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.74010i | 0.329460i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.23515 | − | 3.80139i | −0.0854369 | − | 0.262948i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.44086 | + | 7.51219i | −0.168036 | + | 0.517161i | −0.999247 | − | 0.0387958i | \(-0.987648\pi\) |
0.831212 | + | 0.555956i | \(0.187648\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.84685 | + | 1.89976i | −0.400619 | + | 0.130169i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.213186 | − | 0.293425i | −0.0144720 | − | 0.0199190i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.55459 | − | 1.85602i | 0.172623 | − | 0.125418i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.48015 | − | 3.25502i | −0.301368 | − | 0.218956i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.73235 | + | 2.83731i | 0.584762 | + | 0.190001i | 0.586433 | − | 0.809998i | \(-0.300532\pi\) |
−0.00167090 | + | 0.999999i | \(0.500532\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.9994 | + | 3.57392i | 0.730056 | + | 0.237209i | 0.650377 | − | 0.759611i | \(-0.274611\pi\) |
0.0796781 | + | 0.996821i | \(0.474611\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.1820 | + | 14.6631i | 1.33366 | + | 0.968962i | 0.999652 | + | 0.0263923i | \(0.00840190\pi\) |
0.334010 | + | 0.942570i | \(0.391598\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.162198 | + | 0.117844i | −0.0106718 | + | 0.00775355i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.65295 | + | 10.5334i | 0.501361 | + | 0.690065i | 0.982433 | − | 0.186617i | \(-0.0597522\pi\) |
−0.481071 | + | 0.876681i | \(0.659752\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.6987 | − | 4.12605i | 0.824867 | − | 0.268016i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.16071 | − | 25.1161i | 0.527872 | − | 1.62462i | −0.230693 | − | 0.973027i | \(-0.574099\pi\) |
0.758565 | − | 0.651597i | \(-0.225901\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.92700 | − | 5.93070i | −0.124129 | − | 0.382030i | 0.869612 | − | 0.493735i | \(-0.164369\pi\) |
−0.993741 | + | 0.111705i | \(0.964369\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.74475 | − | 3.77782i | 0.174644 | − | 0.240377i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.8195 | −1.00252 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.46802 | 0.471377 | 0.235689 | − | 0.971829i | \(-0.424265\pi\) | ||||
0.235689 | + | 0.971829i | \(0.424265\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.32405 | + | 8.70430i | −0.397589 | + | 0.547235i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.39880i | 0.523903i | 0.965081 | + | 0.261951i | \(0.0843660\pi\) | ||||
−0.965081 | + | 0.261951i | \(0.915634\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.194315 | + | 0.598039i | 0.0120741 | + | 0.0371604i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.14533 | − | 3.52496i | 0.0708941 | − | 0.218190i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.53415 | + | 3.09783i | −0.587901 | + | 0.191021i | −0.587837 | − | 0.808979i | \(-0.700020\pi\) |
−6.39037e−5 | 1.00000i | \(0.500020\pi\) | ||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.02527 | − | 8.29307i | −0.368740 | − | 0.507528i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.2542 | + | 10.3563i | −0.869094 | + | 0.631434i | −0.930344 | − | 0.366689i | \(-0.880491\pi\) |
0.0612496 | + | 0.998122i | \(0.480491\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.92718 | + | 2.85327i | 0.238559 | + | 0.173324i | 0.700641 | − | 0.713514i | \(-0.252897\pi\) |
−0.462082 | + | 0.886837i | \(0.652897\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.222762 | − | 0.0723799i | −0.0134822 | − | 0.00438063i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.5053 | + | 6.98748i | 1.29213 | + | 0.419837i | 0.872835 | − | 0.488015i | \(-0.162279\pi\) |
0.419291 | + | 0.907852i | \(0.362279\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.32199 | − | 2.41356i | −0.198882 | − | 0.144496i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.6671 | + | 17.1952i | −1.41186 | + | 1.02578i | −0.418815 | + | 0.908071i | \(0.637555\pi\) |
−0.993048 | + | 0.117708i | \(0.962445\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.1944 | + | 23.6661i | 1.02210 | + | 1.40680i | 0.910719 | + | 0.413026i | \(0.135528\pi\) |
0.111383 | + | 0.993778i | \(0.464472\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.553541 | + | 0.179857i | −0.0326745 | + | 0.0106166i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.90563 | − | 12.0203i | 0.229743 | − | 0.707076i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.95781 | + | 12.1809i | 0.232011 | + | 0.714056i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.4104i | 0.783447i | 0.920083 | + | 0.391723i | \(0.128121\pi\) | ||||
−0.920083 | + | 0.391723i | \(0.871879\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.33416 | + | 1.83631i | −0.0774157 | + | 0.106554i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.5697 | −0.726923 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.158522 | −0.00913704 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.60193 | + | 2.20487i | −0.0920287 | + | 0.126667i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.5444i | 0.773022i | 0.922285 | + | 0.386511i | \(0.126320\pi\) | ||||
−0.922285 | + | 0.386511i | \(0.873680\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.111239 | − | 0.342358i | −0.00632815 | − | 0.0194761i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.630031 | + | 1.93904i | −0.0357258 | + | 0.109953i | −0.967329 | − | 0.253524i | \(-0.918410\pi\) |
0.931603 | + | 0.363477i | \(0.118410\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.3840 | + | 5.64839i | −0.982599 | + | 0.319266i | −0.755892 | − | 0.654697i | \(-0.772796\pi\) |
−0.226708 | + | 0.973963i | \(0.572796\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.0491 | + | 15.2078i | 0.620579 | + | 0.854153i | 0.997395 | − | 0.0721348i | \(-0.0229812\pi\) |
−0.376816 | + | 0.926288i | \(0.622981\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.80604 | − | 4.94488i | 0.381065 | − | 0.276860i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.0231810 | + | 0.0168420i | 0.00129384 | + | 0.000940029i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.49746 | − | 1.13639i | −0.194604 | − | 0.0632306i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.9956 | + | 5.84714i | 0.995161 | + | 0.323348i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.722523 | − | 0.524944i | −0.0398340 | − | 0.0289411i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.73111 | − | 4.89044i | 0.369976 | − | 0.268803i | −0.387225 | − | 0.921985i | \(-0.626566\pi\) |
0.757201 | + | 0.653182i | \(0.226566\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.18449 | + | 5.75946i | 0.229309 | + | 0.315617i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.7331 | + | 5.43691i | −0.911509 | + | 0.296167i | −0.726979 | − | 0.686660i | \(-0.759076\pi\) |
−0.184530 | + | 0.982827i | \(0.559076\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.51227 | − | 4.65428i | 0.0821351 | − | 0.252786i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.88012 | − | 8.86411i | −0.155967 | − | 0.480019i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.23591i | − | 0.0667326i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.1151 | − | 24.9333i | 0.972469 | − | 1.33849i | 0.0316789 | − | 0.999498i | \(-0.489915\pi\) |
0.940790 | − | 0.338990i | \(-0.110085\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.0376 | −1.17964 | −0.589822 | − | 0.807533i | \(-0.700802\pi\) | ||||
−0.589822 | + | 0.807533i | \(0.700802\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.65177 | −0.141541 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.59496 | + | 4.94803i | −0.191340 | + | 0.263357i | −0.893899 | − | 0.448269i | \(-0.852041\pi\) |
0.702559 | + | 0.711626i | \(0.252041\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.184458i | 0.00976256i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.57676 | − | 14.0858i | −0.241552 | − | 0.743422i | −0.996184 | − | 0.0872735i | \(-0.972185\pi\) |
0.754632 | − | 0.656148i | \(-0.227815\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.91308 | + | 15.1209i | −0.258583 | + | 0.795836i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.56176 | − | 1.80712i | 0.291917 | − | 0.0948495i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.82431 | − | 10.7692i | −0.408426 | − | 0.562150i | 0.554408 | − | 0.832245i | \(-0.312945\pi\) |
−0.962834 | + | 0.270095i | \(0.912945\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.33092 | + | 3.87314i | −0.277517 | + | 0.201628i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.0687035 | − | 0.0499160i | −0.00356691 | − | 0.00259151i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.1897 | + | 5.26035i | 0.838271 | + | 0.272371i | 0.696525 | − | 0.717532i | \(-0.254728\pi\) |
0.141746 | + | 0.989903i | \(0.454728\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.34739 | + | 3.03715i | 0.481415 | + | 0.156421i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.29328 | − | 1.66617i | −0.117798 | − | 0.0855852i | 0.527326 | − | 0.849663i | \(-0.323194\pi\) |
−0.645124 | + | 0.764078i | \(0.723194\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.64546 | + | 1.92204i | −0.135531 | + | 0.0984691i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.90634 | + | 8.12938i | 0.301800 | + | 0.415392i | 0.932802 | − | 0.360389i | \(-0.117356\pi\) |
−0.631002 | + | 0.775781i | \(0.717356\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.70685 | + | 0.554590i | −0.0867642 | + | 0.0281914i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.58687 | + | 7.96156i | −0.131159 | + | 0.403667i | −0.994973 | − | 0.100144i | \(-0.968070\pi\) |
0.863813 | + | 0.503812i | \(0.168070\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.05892 | + | 9.41440i | 0.154696 | + | 0.476107i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.59550i | 0.181369i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.92797 | + | 6.78277i | −0.247328 | + | 0.340418i | −0.914573 | − | 0.404420i | \(-0.867473\pi\) |
0.667245 | + | 0.744838i | \(0.267473\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.155542 | −0.00778682 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.14450 | 0.107091 | 0.0535455 | − | 0.998565i | \(-0.482948\pi\) | ||||
0.0535455 | + | 0.998565i | \(0.482948\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.40022 | − | 8.80915i | 0.318818 | − | 0.438815i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.1589i | 0.800969i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.10861 | + | 3.41195i | 0.0548173 | + | 0.168710i | 0.974717 | − | 0.223444i | \(-0.0717300\pi\) |
−0.919900 | + | 0.392154i | \(0.871730\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.25938 | + | 16.1867i | −0.259426 | + | 0.798431i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.754199 | − | 0.245054i | 0.0371117 | − | 0.0120583i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.1597 | − | 15.3600i | −0.546492 | − | 0.752181i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.44874 | + | 5.41183i | −0.363895 | + | 0.264385i | −0.754675 | − | 0.656099i | \(-0.772205\pi\) |
0.390780 | + | 0.920484i | \(0.372205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.0957 | + | 24.0454i | 1.61299 | + | 1.17190i | 0.852890 | + | 0.522090i | \(0.174848\pi\) |
0.760095 | + | 0.649812i | \(0.225152\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.61615 | − | 3.12448i | −0.467553 | − | 0.151917i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.795207 | − | 0.258378i | −0.0384828 | − | 0.0125038i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.86948 | − | 3.53789i | −0.235101 | − | 0.170811i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.83058 | + | 1.32999i | −0.0881758 | + | 0.0640634i | −0.631000 | − | 0.775783i | \(-0.717355\pi\) |
0.542824 | + | 0.839847i | \(0.317355\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.68923 | − | 3.70141i | −0.129236 | − | 0.177878i | 0.739495 | − | 0.673162i | \(-0.235064\pi\) |
−0.868731 | + | 0.495283i | \(0.835064\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.93855 | + | 2.57939i | −0.379753 | + | 0.123389i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.541703 | − | 1.66719i | 0.0258541 | − | 0.0795706i | −0.937297 | − | 0.348532i | \(-0.886680\pi\) |
0.963151 | + | 0.268961i | \(0.0866803\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.16071 | − | 6.64998i | −0.102891 | − | 0.316666i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 20.8364i | − | 0.989967i | −0.868902 | − | 0.494983i | \(-0.835174\pi\) | ||
0.868902 | − | 0.494983i | \(-0.164826\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.9580 | + | 16.4587i | −0.565592 | + | 0.778471i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.1952 | −1.18904 | −0.594518 | − | 0.804082i | \(-0.702657\pi\) | ||||
−0.594518 | + | 0.804082i | \(0.702657\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.9566 | −0.704280 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.79454 | − | 10.7283i | 0.366220 | − | 0.504058i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 39.5166i | 1.84851i | 0.381775 | + | 0.924255i | \(0.375313\pi\) | ||||
−0.381775 | + | 0.924255i | \(0.624687\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.645329 | + | 1.98612i | 0.0301214 | + | 0.0927041i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.50731 | − | 13.8721i | 0.209927 | − | 0.646087i | −0.789548 | − | 0.613688i | \(-0.789685\pi\) |
0.999475 | − | 0.0323993i | \(-0.0103148\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.38989 | − | 3.05096i | 0.436385 | − | 0.141790i | −0.0825821 | − | 0.996584i | \(-0.526317\pi\) |
0.518967 | + | 0.854794i | \(0.326317\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.4268 | + | 17.1041i | 0.575045 | + | 0.791481i | 0.993141 | − | 0.116921i | \(-0.0373025\pi\) |
−0.418096 | + | 0.908403i | \(0.637303\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.993557 | + | 0.721861i | −0.0458782 | + | 0.0333324i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.3608 | + | 7.52753i | 0.477399 | + | 0.346850i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.87422 | − | 1.25881i | −0.178137 | − | 0.0578802i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.914384 | − | 0.297101i | −0.0418667 | − | 0.0136033i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.5317 | + | 24.3622i | 1.53210 | + | 1.11314i | 0.955055 | + | 0.296429i | \(0.0957957\pi\) |
0.577049 | + | 0.816710i | \(0.304204\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.2728 | + | 11.0963i | −0.696379 | + | 0.505949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.246097 | + | 0.338723i | 0.0111978 | + | 0.0154124i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.84198 | − | 1.24834i | 0.174097 | − | 0.0565675i | −0.220671 | − | 0.975348i | \(-0.570825\pi\) |
0.394768 | + | 0.918781i | \(0.370825\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.65524 | − | 14.3273i | 0.210517 | − | 0.647905i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.95383 | + | 27.5570i | 0.404081 | + | 1.24363i | 0.921661 | + | 0.387997i | \(0.126833\pi\) |
−0.517580 | + | 0.855635i | \(0.673167\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 7.74010i | − | 0.348597i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.319178 | + | 0.439311i | −0.0143171 | + | 0.0197058i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.6824 | −1.06017 | −0.530086 | − | 0.847944i | \(-0.677840\pi\) | ||||
−0.530086 | + | 0.847944i | \(0.677840\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.45128 | 0.154192 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.84233 | + | 10.7940i | −0.349672 | + | 0.481282i | −0.947235 | − | 0.320540i | \(-0.896136\pi\) |
0.597563 | + | 0.801822i | \(0.296136\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.96810i | 0.265053i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.20479 | + | 9.86333i | 0.142050 | + | 0.437184i | 0.996620 | − | 0.0821518i | \(-0.0261792\pi\) |
−0.854570 | + | 0.519336i | \(0.826179\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.0861877 | − | 0.265258i | 0.00381272 | − | 0.0117343i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.67476 | + | 0.544164i | −0.0739427 | + | 0.0240254i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.4897 | − | 18.5670i | −0.593277 | − | 0.816575i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.95343 | − | 1.41925i | 0.0857458 | − | 0.0622980i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.9450 | − | 17.3970i | −1.04905 | − | 0.762178i | −0.0770169 | − | 0.997030i | \(-0.524540\pi\) |
−0.972031 | + | 0.234852i | \(0.924540\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.03505 | − | 0.661227i | −0.0889864 | − | 0.0289134i | 0.264185 | − | 0.964472i | \(-0.414897\pi\) |
−0.353172 | + | 0.935558i | \(0.614897\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.15540 | − | 2.64985i | −0.355255 | − | 0.115429i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.429950 | − | 0.312377i | −0.0186935 | − | 0.0135816i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.26336 | − | 5.27714i | 0.315203 | − | 0.229008i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.2707 | − | 14.1364i | −0.444873 | − | 0.612315i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.87031 | + | 1.25754i | −0.167016 | + | 0.0542668i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.90439 | − | 15.0942i | 0.211247 | − | 0.650151i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.66128 | − | 8.19057i | −0.114417 | − | 0.352140i | 0.877408 | − | 0.479745i | \(-0.159271\pi\) |
−0.991825 | + | 0.127605i | \(0.959271\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 13.3363i | − | 0.572316i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.7004 | − | 18.8570i | 0.585787 | − | 0.806267i | −0.408528 | − | 0.912746i | \(-0.633958\pi\) |
0.994315 | + | 0.106479i | \(0.0339577\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.46618 | −0.404007 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.52673 | 0.278048 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.693218 | − | 0.954133i | 0.0294786 | − | 0.0405739i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 37.2790i | − | 1.57956i | −0.613389 | − | 0.789781i | \(-0.710194\pi\) | ||
0.613389 | − | 0.789781i | \(-0.289806\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.47065 | − | 4.52618i | −0.0622017 | − | 0.191437i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.46477 | + | 4.50810i | −0.0618427 | + | 0.190332i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.2225 | + | 3.32150i | −0.430828 | + | 0.139985i | −0.516400 | − | 0.856347i | \(-0.672728\pi\) |
0.0855718 | + | 0.996332i | \(0.472728\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.0519180 | + | 0.0714590i | 0.00218035 | + | 0.00300100i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.10555 | − | 4.43594i | 0.255958 | − | 0.185964i | −0.452405 | − | 0.891812i | \(-0.649434\pi\) |
0.708363 | + | 0.705848i | \(0.249434\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.9648 | − | 17.4115i | −1.00290 | − | 0.728647i | −0.0401891 | − | 0.999192i | \(-0.512796\pi\) |
−0.962707 | + | 0.270545i | \(0.912796\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.0169 | + | 7.80358i | 1.00332 | + | 0.325999i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.8124 | + | 4.81283i | 0.616647 | + | 0.200361i | 0.600651 | − | 0.799511i | \(-0.294908\pi\) |
0.0159961 | + | 0.999872i | \(0.494908\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.9341 | + | 14.4829i | 0.828431 | + | 0.601891i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.13044 | + | 0.821316i | −0.0468987 | + | 0.0340739i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.28271 | − | 1.76550i | −0.0531246 | − | 0.0731197i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.1780 | + | 12.0799i | −1.53450 | + | 0.498590i | −0.949853 | − | 0.312697i | \(-0.898768\pi\) |
−0.584649 | + | 0.811287i | \(0.698768\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.23445 | − | 6.87692i | 0.0920688 | − | 0.283358i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.75394 | − | 17.7088i | −0.236685 | − | 0.728443i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.6722i | 0.766775i | 0.923588 | + | 0.383387i | \(0.125243\pi\) | ||||
−0.923588 | + | 0.383387i | \(0.874757\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.79385 | + | 7.97455i | −0.237126 | + | 0.326376i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.0186 | 0.572783 | 0.286392 | − | 0.958113i | \(-0.407544\pi\) | ||||
0.286392 | + | 0.958113i | \(0.407544\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.89791 | −0.403744 | −0.201872 | − | 0.979412i | \(-0.564703\pi\) | ||||
−0.201872 | + | 0.979412i | \(0.564703\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.17249 | + | 11.2485i | −0.332810 | + | 0.458073i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 22.2953i | − | 0.904939i | −0.891780 | − | 0.452469i | \(-0.850543\pi\) | ||
0.891780 | − | 0.452469i | \(-0.149457\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.101165 | − | 0.311353i | −0.00409940 | − | 0.0126167i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.28540 | − | 25.4998i | 0.335192 | − | 1.03161i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.6247 | + | 5.07676i | −0.631075 | + | 0.205049i | −0.607051 | − | 0.794663i | \(-0.707648\pi\) |
−0.0240235 | + | 0.999711i | \(0.507648\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.22486 | + | 3.06226i | 0.0895696 | + | 0.123282i | 0.851450 | − | 0.524436i | \(-0.175724\pi\) |
−0.761880 | + | 0.647718i | \(0.775724\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.341478 | + | 0.248098i | −0.0137252 | + | 0.00997192i | −0.594627 | − | 0.804002i | \(-0.702700\pi\) |
0.580902 | + | 0.813974i | \(0.302700\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.83482 | + | 2.78616i | 0.153886 | + | 0.111805i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.861119 | − | 0.279795i | −0.0345000 | − | 0.0112097i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.80139 | − | 1.23515i | −0.151813 | − | 0.0493270i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.0276 | + | 8.73860i | 0.479574 | + | 0.348431i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.2527 | − | 20.5268i | 1.12472 | − | 0.817159i | 0.139805 | − | 0.990179i | \(-0.455353\pi\) |
0.984918 | + | 0.173020i | \(0.0553525\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.64279 | + | 6.39025i | 0.184534 | + | 0.253990i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.6342 | − | 5.72971i | 0.698693 | − | 0.227019i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.89976 | + | 5.84685i | −0.0751532 | + | 0.231298i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.12876 | + | 3.47396i | 0.0445833 | + | 0.137213i | 0.970870 | − | 0.239605i | \(-0.0770180\pi\) |
−0.926287 | + | 0.376819i | \(0.877018\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 34.3967i | − | 1.35647i | −0.734844 | − | 0.678236i | \(-0.762745\pi\) | ||
0.734844 | − | 0.678236i | \(-0.237255\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.4817 | − | 25.4378i | 0.726589 | − | 1.00006i | −0.272690 | − | 0.962102i | \(-0.587913\pi\) |
0.999279 | − | 0.0379623i | \(-0.0120867\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.3783 | 0.799920 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.362693 | −0.0142151 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.5020 | − | 28.2185i | 0.802304 | − | 1.10428i | −0.190161 | − | 0.981753i | \(-0.560901\pi\) |
0.992466 | − | 0.122524i | \(-0.0390989\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 3.15765i | − | 0.123192i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.3549 | + | 41.1021i | 0.520232 | + | 1.60111i | 0.773555 | + | 0.633729i | \(0.218477\pi\) |
−0.253323 | + | 0.967382i | \(0.581523\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.10111 | + | 9.54425i | −0.120619 | + | 0.371228i | −0.993078 | − | 0.117461i | \(-0.962525\pi\) |
0.872458 | + | 0.488689i | \(0.162525\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.26673 | + | 1.71127i | −0.204543 | + | 0.0664600i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.3265 | − | 14.2132i | −0.399845 | − | 0.550339i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.42818 | − | 5.39689i | 0.287190 | − | 0.208656i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.3829 | − | 12.6294i | −0.671058 | − | 0.487552i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.4237 | − | 9.23541i | −1.09565 | − | 0.355999i | −0.295224 | − | 0.955428i | \(-0.595394\pi\) |
−0.800428 | + | 0.599429i | \(0.795394\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.5205 | − | 6.99242i | −0.827098 | − | 0.268740i | −0.135276 | − | 0.990808i | \(-0.543192\pi\) |
−0.691823 | + | 0.722068i | \(0.743192\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.915228 | + | 0.664952i | 0.0351232 | + | 0.0255185i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.35664 | − | 6.79800i | 0.358547 | − | 0.260500i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.0830 | + | 20.7599i | 0.577134 | + | 0.794357i | 0.993378 | − | 0.114896i | \(-0.0366535\pi\) |
−0.416243 | + | 0.909253i | \(0.636654\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.7253 | − | 7.70882i | 0.905177 | − | 0.294110i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.787845 | − | 2.42474i | 0.0300145 | − | 0.0923751i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.5879 | − | 32.5862i | −0.402782 | − | 1.23964i | −0.922733 | − | 0.385440i | \(-0.874050\pi\) |
0.519950 | − | 0.854196i | \(-0.325950\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.200488i | 0.00761590i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.08839 | + | 11.1327i | −0.306370 | + | 0.421682i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.0200 | 0.492461 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.0813 | 1.58939 | 0.794695 | − | 0.607009i | \(-0.207631\pi\) | ||||
0.794695 | + | 0.607009i | \(0.207631\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.36869 | + | 10.1421i | −0.277916 | + | 0.382518i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.240727i | 0.00905347i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.41915 | + | 19.7561i | 0.241076 | + | 0.741956i | 0.996257 | + | 0.0864398i | \(0.0275490\pi\) |
−0.755181 | + | 0.655516i | \(0.772451\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.12605 | − | 12.6987i | 0.154739 | − | 0.476237i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.5112 | + | 6.01464i | −0.693249 | + | 0.225250i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.5226 | − | 21.3650i | −0.579702 | − | 0.797891i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.8627 | − | 15.1577i | 0.778049 | − | 0.565285i | −0.126344 | − | 0.991986i | \(-0.540324\pi\) |
0.904393 | + | 0.426701i | \(0.140324\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0257235 | − | 0.0186892i | −0.000957995 | − | 0.000696024i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.93070 | − | 1.92700i | −0.220565 | − | 0.0716659i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.81476 | − | 2.86409i | −0.326921 | − | 0.106223i | 0.140958 | − | 0.990016i | \(-0.454982\pi\) |
−0.467879 | + | 0.883792i | \(0.654982\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.809017 | + | 0.587785i | 0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.03212 | + | 2.20296i | −0.112147 | + | 0.0814795i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.3663 | − | 17.0208i | −0.456760 | − | 0.628676i | 0.517073 | − | 0.855941i | \(-0.327022\pi\) |
−0.973833 | + | 0.227265i | \(0.927022\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −30.0145 | + | 9.75230i | −1.10560 | + | 0.359230i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.73729 | − | 8.42450i | 0.100693 | − | 0.309900i | −0.888003 | − | 0.459838i | \(-0.847907\pi\) |
0.988695 | + | 0.149938i | \(0.0479074\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.44300 | − | 4.44110i | −0.0530099 | − | 0.163148i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13.9773i | − | 0.512778i | −0.966574 | − | 0.256389i | \(-0.917467\pi\) | ||
0.966574 | − | 0.256389i | \(-0.0825328\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.29846 | + | 12.7982i | −0.340213 | + | 0.468263i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.00253090 | 9.24769e−5 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.8762 | −1.19967 | −0.599834 | − | 0.800124i | \(-0.704767\pi\) | ||||
−0.599834 | + | 0.800124i | \(0.704767\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.38959 | − | 6.04175i | 0.159966 | − | 0.220174i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 31.4556i | − | 1.14327i | −0.820507 | − | 0.571636i | \(-0.806309\pi\) | ||
0.820507 | − | 0.571636i | \(-0.193691\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.32475 | + | 10.2325i | 0.120681 | + | 0.371417i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.7053 | − | 36.0252i | 0.424317 | − | 1.30591i | −0.479330 | − | 0.877635i | \(-0.659120\pi\) |
0.903647 | − | 0.428279i | \(-0.140880\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.58952 | − | 0.516467i | 0.0575446 | − | 0.0186974i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.9938 | + | 19.2608i | 0.505286 | + | 0.695467i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.4835 | − | 8.34323i | 0.414105 | − | 0.300865i | −0.361157 | − | 0.932505i | \(-0.617618\pi\) |
0.775261 | + | 0.631640i | \(0.217618\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.79477 | + | 4.93669i | 0.244708 | + | 0.177791i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.5978 | + | 11.2415i | 1.24440 | + | 0.404329i | 0.855910 | − | 0.517126i | \(-0.172998\pi\) |
0.388487 | + | 0.921454i | \(0.372998\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.598039 | + | 0.194315i | 0.0214545 | + | 0.00697100i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.38750 | − | 6.82041i | −0.336342 | − | 0.244367i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.2892 | + | 8.20206i | −0.403958 | + | 0.293493i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.17855 | − | 2.99851i | −0.0778548 | − | 0.107158i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.7612 | − | 10.6448i | 1.16781 | − | 0.379445i | 0.339985 | − | 0.940431i | \(-0.389578\pi\) |
0.827825 | + | 0.560986i | \(0.189578\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.09783 | + | 9.53415i | −0.110286 | + | 0.339425i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.133576 | − | 0.411104i | −0.00474941 | − | 0.0146172i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 25.1021i | − | 0.891403i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.6903 | − | 29.8541i | 0.768310 | − | 1.05749i | −0.228167 | − | 0.973622i | \(-0.573273\pi\) |
0.996477 | − | 0.0838661i | \(-0.0267268\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.1151 | −0.747000 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.2508 | −0.362194 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.21280 | − | 5.79842i | 0.148667 | − | 0.204622i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.6192i | 0.620224i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.1567 | − | 34.3367i | −0.392248 | − | 1.20721i | −0.931084 | − | 0.364804i | \(-0.881136\pi\) |
0.538837 | − | 0.842410i | \(-0.318864\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.03780 | − | 12.4271i | 0.141786 | − | 0.436374i | −0.854797 | − | 0.518962i | \(-0.826319\pi\) |
0.996584 | + | 0.0825883i | \(0.0263186\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.61668 | − | 1.50005i | 0.161914 | − | 0.0526091i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.85762 | − | 2.55679i | −0.0649897 | − | 0.0894507i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.189493 | + | 0.137675i | −0.00662142 | + | 0.00481074i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.9421 | + | 15.2153i | 0.730885 | + | 0.531019i | 0.889843 | − | 0.456266i | \(-0.150813\pi\) |
−0.158958 | + | 0.987285i | \(0.550813\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.2583 | − | 12.1060i | −1.29874 | − | 0.421987i | −0.423599 | − | 0.905850i | \(-0.639233\pi\) |
−0.875144 | + | 0.483863i | \(0.839233\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43.2012 | − | 14.0369i | −1.50225 | − | 0.488112i | −0.561580 | − | 0.827423i | \(-0.689806\pi\) |
−0.940674 | + | 0.339311i | \(0.889806\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.0692 | + | 9.49531i | 0.453911 | + | 0.329786i | 0.791138 | − | 0.611638i | \(-0.209489\pi\) |
−0.337227 | + | 0.941423i | \(0.609489\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.2935 | − | 13.2910i | 0.634593 | − | 0.461059i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.58284 | − | 11.8133i | −0.297378 | − | 0.409306i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.90523 | + | 1.26889i | −0.134984 | + | 0.0438591i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.23891 | + | 9.96835i | −0.111820 | + | 0.344146i | −0.991270 | − | 0.131844i | \(-0.957910\pi\) |
0.879451 | + | 0.475990i | \(0.157910\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.71649 | − | 14.5159i | −0.162638 | − | 0.500547i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 29.2542i | 1.00757i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.303615 | − | 0.417891i | 0.0104323 | − | 0.0143589i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.2529 | 1.00396 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33.7452 | 1.15677 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.4658 | − | 30.9215i | 0.769214 | − | 1.05873i | −0.227177 | − | 0.973854i | \(-0.572950\pi\) |
0.996391 | − | 0.0848793i | \(-0.0270505\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.3637i | 0.866408i | 0.901296 | + | 0.433204i | \(0.142617\pi\) | ||||
−0.901296 | + | 0.433204i | \(0.857383\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.0541 | − | 34.0209i | −0.377159 | − | 1.16078i | −0.942010 | − | 0.335584i | \(-0.891066\pi\) |
0.564851 | − | 0.825193i | \(-0.308934\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.179857 | + | 0.553541i | −0.00612949 | + | 0.0188646i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42.1228 | − | 13.6865i | 1.43388 | − | 0.465894i | 0.513893 | − | 0.857854i | \(-0.328203\pi\) |
0.919982 | + | 0.391960i | \(0.128203\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.42895 | − | 10.2251i | −0.252300 | − | 0.347262i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.5188 | − | 17.8139i | 0.831742 | − | 0.604296i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.8284 | − | 21.6716i | −1.01070 | − | 0.734314i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.1809 | + | 3.95781i | 0.412260 | + | 0.133952i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.32715 | + | 3.03057i | 0.314955 | + | 0.102335i | 0.462229 | − | 0.886761i | \(-0.347050\pi\) |
−0.147274 | + | 0.989096i | \(0.547050\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.8493 | + | 7.88246i | 0.365937 | + | 0.265869i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.794690 | − | 0.577376i | 0.0267738 | − | 0.0194523i | −0.574318 | − | 0.818632i | \(-0.694733\pi\) |
0.601092 | + | 0.799180i | \(0.294733\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.48223 | − | 13.0512i | −0.319103 | − | 0.439207i | 0.619090 | − | 0.785320i | \(-0.287501\pi\) |
−0.938193 | + | 0.346113i | \(0.887501\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −47.9395 | + | 15.5765i | −1.60965 | + | 0.523008i | −0.969469 | − | 0.245215i | \(-0.921141\pi\) |
−0.640183 | + | 0.768222i | \(0.721141\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.0892535 | + | 0.274694i | −0.00299347 | + | 0.00921294i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.701409 | + | 2.15871i | 0.0234981 | + | 0.0723196i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 17.8050i | − | 0.595822i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.38827 | + | 10.1691i | −0.246687 | + | 0.339536i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.2191 | 0.507584 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.00780 | −0.0668896 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.0931767 | + | 0.128247i | −0.00310073 | + | 0.00426779i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 26.1281i | − | 0.867570i | −0.901016 | − | 0.433785i | \(-0.857178\pi\) | ||
0.901016 | − | 0.433785i | \(-0.142822\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.842186 | + | 2.59198i | 0.0279336 | + | 0.0859706i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.71659 | + | 29.9046i | −0.321925 | + | 0.990783i | 0.650885 | + | 0.759177i | \(0.274398\pi\) |
−0.972810 | + | 0.231607i | \(0.925602\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34.1498 | + | 11.0959i | −1.13019 | + | 0.367222i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.186671 | + | 0.256931i | 0.00616443 | + | 0.00848461i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.7376 | + | 28.8711i | −1.31082 | + | 0.952368i | −0.310824 | + | 0.950467i | \(0.600605\pi\) |
−0.999998 | + | 0.00190086i | \(0.999395\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.9577 | + | 7.96122i | 0.361068 | + | 0.262331i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.5045 | − | 5.03772i | −0.510337 | − | 0.165819i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.342358 | − | 0.111239i | −0.0112445 | − | 0.00365356i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.9520 | + | 9.41016i | 0.424941 | + | 0.308737i | 0.779623 | − | 0.626249i | \(-0.215411\pi\) |
−0.354682 | + | 0.934987i | \(0.615411\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.96137 | − | 7.23736i | 0.326471 | − | 0.237195i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.19839 | + | 1.64944i | 0.0392335 | + | 0.0540003i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.7856 | − | 9.35301i | 0.940385 | − | 0.305550i | 0.201583 | − | 0.979472i | \(-0.435392\pi\) |
0.738803 | + | 0.673922i | \(0.235392\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.64839 | + | 17.3840i | −0.184328 | + | 0.567304i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.80436 | − | 11.7086i | −0.124019 | − | 0.381690i | 0.869702 | − | 0.493577i | \(-0.164311\pi\) |
−0.993721 | + | 0.111886i | \(0.964311\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 31.2343i | 1.01713i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.8549 | + | 32.8335i | −0.775181 | + | 1.06695i | 0.220616 | + | 0.975361i | \(0.429193\pi\) |
−0.995797 | + | 0.0915849i | \(0.970807\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.37336 | 0.271811 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.7978 | 0.609562 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.72082 | − | 6.49765i | 0.152922 | − | 0.210479i | −0.725682 | − | 0.688031i | \(-0.758475\pi\) |
0.878604 | + | 0.477551i | \(0.158475\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 8.41272i | − | 0.271945i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.464551 | + | 1.42974i | 0.0150011 | + | 0.0461688i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.36923 | + | 13.4471i | −0.140943 | + | 0.433778i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.0272509 | − | 0.00885436i | 0.000878149 | − | 0.000285328i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.8530 | − | 21.8198i | −0.509798 | − | 0.701677i | 0.474087 | − | 0.880478i | \(-0.342778\pi\) |
−0.983885 | + | 0.178801i | \(0.942778\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.97512 | + | 2.16155i | −0.0955745 | + | 0.0694389i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.0715 | − | 17.4889i | −0.772490 | − | 0.561247i | 0.130226 | − | 0.991484i | \(-0.458430\pi\) |
−0.902716 | + | 0.430238i | \(0.858430\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.59492 | − | 0.518220i | −0.0511307 | − | 0.0166134i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.35239 | − | 0.439419i | −0.0432669 | − | 0.0140583i | 0.287304 | − | 0.957840i | \(-0.407241\pi\) |
−0.330570 | + | 0.943781i | \(0.607241\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.8237 | − | 13.6762i | −0.601607 | − | 0.437093i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.3080 | − | 11.1219i | 0.488747 | − | 0.355096i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.19298 | + | 1.64200i | 0.0380502 | + | 0.0523716i | 0.827618 | − | 0.561291i | \(-0.189695\pi\) |
−0.789568 | + | 0.613663i | \(0.789695\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.849377 | + | 0.275979i | −0.0270360 | + | 0.00878452i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.62881 | + | 8.09065i | −0.0835913 | + | 0.257268i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.25185 | + | 19.2412i | 0.198597 | + | 0.611217i | 0.999916 | + | 0.0129803i | \(0.00413187\pi\) |
−0.801319 | + | 0.598237i | \(0.795868\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 8.32012i | − | 0.264031i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.7566 | + | 14.8051i | −0.340663 | + | 0.468883i | −0.944635 | − | 0.328123i | \(-0.893584\pi\) |
0.603972 | + | 0.797006i | \(0.293584\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.11909 | 0.225238 |
(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 | 1500.2.o.b.649.3 | 16 | ||
5.2 | odd | 4 | 1500.2.m.a.601.2 | 8 | |||
5.3 | odd | 4 | 300.2.m.b.121.2 | ✓ | 8 | ||
5.4 | even | 2 | inner | 1500.2.o.b.649.2 | 16 | ||
15.8 | even | 4 | 900.2.n.b.721.1 | 8 | |||
25.6 | even | 5 | inner | 1500.2.o.b.349.1 | 16 | ||
25.8 | odd | 20 | 300.2.m.b.181.2 | yes | 8 | ||
25.9 | even | 10 | 7500.2.d.c.1249.3 | 8 | |||
25.12 | odd | 20 | 7500.2.a.f.1.3 | 4 | |||
25.13 | odd | 20 | 7500.2.a.e.1.2 | 4 | |||
25.16 | even | 5 | 7500.2.d.c.1249.6 | 8 | |||
25.17 | odd | 20 | 1500.2.m.a.901.2 | 8 | |||
25.19 | even | 10 | inner | 1500.2.o.b.349.4 | 16 | ||
75.8 | even | 20 | 900.2.n.b.181.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.m.b.121.2 | ✓ | 8 | 5.3 | odd | 4 | ||
300.2.m.b.181.2 | yes | 8 | 25.8 | odd | 20 | ||
900.2.n.b.181.1 | 8 | 75.8 | even | 20 | |||
900.2.n.b.721.1 | 8 | 15.8 | even | 4 | |||
1500.2.m.a.601.2 | 8 | 5.2 | odd | 4 | |||
1500.2.m.a.901.2 | 8 | 25.17 | odd | 20 | |||
1500.2.o.b.349.1 | 16 | 25.6 | even | 5 | inner | ||
1500.2.o.b.349.4 | 16 | 25.19 | even | 10 | inner | ||
1500.2.o.b.649.2 | 16 | 5.4 | even | 2 | inner | ||
1500.2.o.b.649.3 | 16 | 1.1 | even | 1 | trivial | ||
7500.2.a.e.1.2 | 4 | 25.13 | odd | 20 | |||
7500.2.a.f.1.3 | 4 | 25.12 | odd | 20 | |||
7500.2.d.c.1249.3 | 8 | 25.9 | even | 10 | |||
7500.2.d.c.1249.6 | 8 | 25.16 | even | 5 |