Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(1567,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.1567");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.b (of order \(2\), degree \(1\), 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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 4 x^{14} + 54 x^{12} - 112 x^{11} - 104 x^{10} + 1312 x^{9} - 3159 x^{8} + 2544 x^{7} + \cdots + 782 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1567.1 | ||
Root | \(0.271975 + 0.405613i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1567 |
Dual form | 1764.2.b.n.1567.4 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.05050 | − | 0.946809i | −0.742817 | − | 0.669495i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.207107 | + | 1.98925i | 0.103553 | + | 0.994624i | ||||
\(5\) | − | 1.60804i | − | 0.719136i | −0.933119 | − | 0.359568i | \(-0.882924\pi\) | ||
0.933119 | − | 0.359568i | \(-0.117076\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.66587 | − | 2.28580i | 0.588974 | − | 0.808152i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.52250 | + | 1.68925i | −0.481458 | + | 0.534187i | ||||
\(11\) | 2.67798i | 0.807441i | 0.914882 | + | 0.403721i | \(0.132283\pi\) | ||||
−0.914882 | + | 0.403721i | \(0.867717\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.37849i | 0.937025i | 0.883457 | + | 0.468513i | \(0.155210\pi\) | ||||
−0.883457 | + | 0.468513i | \(0.844790\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.91421 | + | 0.823973i | −0.978553 | + | 0.205993i | ||||
\(17\) | − | 1.60804i | − | 0.390007i | −0.980803 | − | 0.195003i | \(-0.937528\pi\) | ||
0.980803 | − | 0.195003i | \(-0.0624717\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.30629 | −0.987931 | −0.493966 | − | 0.869481i | \(-0.664453\pi\) | ||||
−0.493966 | + | 0.869481i | \(0.664453\pi\) | |||||||
\(20\) | 3.19879 | − | 0.333036i | 0.715270 | − | 0.0744690i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.53553 | − | 2.81322i | 0.540578 | − | 0.599781i | ||||
\(23\) | − | 6.46521i | − | 1.34809i | −0.738690 | − | 0.674045i | \(-0.764555\pi\) | ||
0.738690 | − | 0.674045i | \(-0.235445\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.41421 | 0.482843 | ||||||||
\(26\) | 3.19879 | − | 3.54911i | 0.627334 | − | 0.696038i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.71179 | −0.874958 | −0.437479 | − | 0.899229i | \(-0.644129\pi\) | ||||
−0.437479 | + | 0.899229i | \(0.644129\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.3963 | −1.86723 | −0.933616 | − | 0.358275i | \(-0.883365\pi\) | ||||
−0.933616 | + | 0.358275i | \(0.883365\pi\) | |||||||
\(32\) | 4.89203 | + | 2.84043i | 0.864797 | + | 0.502121i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.52250 | + | 1.68925i | −0.261107 | + | 0.289703i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.242641 | 0.0398899 | 0.0199449 | − | 0.999801i | \(-0.493651\pi\) | ||||
0.0199449 | + | 0.999801i | \(0.493651\pi\) | |||||||
\(38\) | 4.52377 | + | 4.07724i | 0.733852 | + | 0.661415i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.67565 | − | 2.67878i | −0.581171 | − | 0.423553i | ||||
\(41\) | − | 11.6464i | − | 1.81887i | −0.415848 | − | 0.909434i | \(-0.636515\pi\) | ||
0.415848 | − | 0.909434i | \(-0.363485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.95699i | − | 1.21343i | −0.794920 | − | 0.606715i | \(-0.792487\pi\) | ||
0.794920 | − | 0.606715i | \(-0.207513\pi\) | |||||||
\(44\) | −5.32716 | + | 0.554628i | −0.803100 | + | 0.0836133i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.12132 | + | 6.79172i | −0.902539 | + | 1.00138i | ||||
\(47\) | 9.04753 | 1.31972 | 0.659859 | − | 0.751389i | \(-0.270616\pi\) | ||||
0.659859 | + | 0.751389i | \(0.270616\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.53613 | − | 2.28580i | −0.358664 | − | 0.323261i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.72066 | + | 0.699709i | −0.931988 | + | 0.0970321i | ||||
\(53\) | 2.46148 | 0.338110 | 0.169055 | − | 0.985607i | \(-0.445928\pi\) | ||||
0.169055 | + | 0.985607i | \(0.445928\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.30629 | 0.580660 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.94975 | + | 4.46117i | 0.649934 | + | 0.585780i | ||||
\(59\) | −9.04753 | −1.17789 | −0.588944 | − | 0.808174i | \(-0.700456\pi\) | ||||
−0.588944 | + | 0.808174i | \(0.700456\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.37849i | − | 0.432572i | −0.976330 | − | 0.216286i | \(-0.930606\pi\) | ||
0.976330 | − | 0.216286i | \(-0.0693943\pi\) | |||||||
\(62\) | 10.9213 | + | 9.84332i | 1.38701 | + | 1.25010i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.44975 | − | 7.61569i | −0.306218 | − | 0.951961i | ||||
\(65\) | 5.43275 | 0.673849 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.2529i | 1.37476i | 0.726299 | + | 0.687379i | \(0.241239\pi\) | ||||
−0.726299 | + | 0.687379i | \(0.758761\pi\) | |||||||
\(68\) | 3.19879 | − | 0.333036i | 0.387910 | − | 0.0403865i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.03394i | 0.953453i | 0.879052 | + | 0.476726i | \(0.158177\pi\) | ||||
−0.879052 | + | 0.476726i | \(0.841823\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.17733i | − | 0.723002i | −0.932372 | − | 0.361501i | \(-0.882264\pi\) | ||
0.932372 | − | 0.361501i | \(-0.117736\pi\) | |||||||
\(74\) | −0.254894 | − | 0.229734i | −0.0296309 | − | 0.0267061i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.891862 | − | 8.56628i | −0.102304 | − | 0.982620i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.29589i | 0.370817i | 0.982662 | + | 0.185409i | \(0.0593608\pi\) | ||||
−0.982662 | + | 0.185409i | \(0.940639\pi\) | |||||||
\(80\) | 1.32498 | + | 6.29420i | 0.148137 | + | 0.703713i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −11.0270 | + | 12.2346i | −1.21772 | + | 1.35109i | ||||
\(83\) | −12.7951 | −1.40445 | −0.702225 | − | 0.711955i | \(-0.747810\pi\) | ||||
−0.702225 | + | 0.711955i | \(0.747810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.58579 | −0.280468 | ||||||||
\(86\) | −7.53375 | + | 8.35883i | −0.812385 | + | 0.901356i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.12132 | + | 4.46117i | 0.652535 | + | 0.475562i | ||||
\(89\) | − | 0.275896i | − | 0.0292449i | −0.999893 | − | 0.0146224i | \(-0.995345\pi\) | ||
0.999893 | − | 0.0146224i | \(-0.00465463\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 12.8609 | − | 1.33899i | 1.34084 | − | 0.139599i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.50445 | − | 8.56628i | −0.980309 | − | 0.883545i | ||||
\(95\) | 6.92468i | 0.710457i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.9343i | − | 1.31328i | −0.754204 | − | 0.656640i | \(-0.771977\pi\) | ||
0.754204 | − | 0.656640i | \(-0.228023\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | + | 4.80247i | 0.0500000 | + | 0.480247i | ||||
\(101\) | − | 16.1947i | − | 1.61143i | −0.592304 | − | 0.805714i | \(-0.701782\pi\) | ||
0.592304 | − | 0.805714i | \(-0.298218\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.3963 | −1.02438 | −0.512189 | − | 0.858873i | \(-0.671165\pi\) | ||||
−0.512189 | + | 0.858873i | \(0.671165\pi\) | |||||||
\(104\) | 7.72255 | + | 5.62813i | 0.757259 | + | 0.551884i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.58579 | − | 2.33055i | −0.251154 | − | 0.226363i | ||||
\(107\) | − | 6.46521i | − | 0.625016i | −0.949915 | − | 0.312508i | \(-0.898831\pi\) | ||
0.949915 | − | 0.312508i | \(-0.101169\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.41421 | −0.710153 | −0.355076 | − | 0.934837i | \(-0.615545\pi\) | ||||
−0.355076 | + | 0.934837i | \(0.615545\pi\) | |||||||
\(110\) | −4.52377 | − | 4.07724i | −0.431324 | − | 0.388749i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.6060 | −1.18587 | −0.592937 | − | 0.805249i | \(-0.702032\pi\) | ||||
−0.592937 | + | 0.805249i | \(0.702032\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.3963 | −0.969461 | ||||||||
\(116\) | −0.975845 | − | 9.37293i | −0.0906049 | − | 0.870254i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.50445 | + | 8.56628i | 0.874955 | + | 0.788590i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.82843 | 0.348039 | ||||||||
\(122\) | −3.19879 | + | 3.54911i | −0.289604 | + | 0.321321i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.15315 | − | 20.6808i | −0.193358 | − | 1.85719i | ||||
\(125\) | − | 11.9223i | − | 1.06637i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.2529i | − | 0.998532i | −0.866449 | − | 0.499266i | \(-0.833603\pi\) | ||
0.866449 | − | 0.499266i | \(-0.166397\pi\) | |||||||
\(128\) | −4.63714 | + | 10.3197i | −0.409869 | + | 0.912144i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.70711 | − | 5.14377i | −0.500546 | − | 0.451138i | ||||
\(131\) | −12.7951 | −1.11792 | −0.558958 | − | 0.829196i | \(-0.688799\pi\) | ||||
−0.558958 | + | 0.829196i | \(0.688799\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 10.6543 | − | 11.8212i | 0.920394 | − | 1.02119i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.67565 | − | 2.67878i | −0.315184 | − | 0.229704i | ||||
\(137\) | −19.0583 | −1.62826 | −0.814132 | − | 0.580680i | \(-0.802787\pi\) | ||||
−0.814132 | + | 0.580680i | \(0.802787\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.09002 | −0.516549 | −0.258274 | − | 0.966072i | \(-0.583154\pi\) | ||||
−0.258274 | + | 0.966072i | \(0.583154\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.60660 | − | 8.43966i | 0.638332 | − | 0.708241i | ||||
\(143\) | −9.04753 | −0.756593 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.57675i | 0.629214i | ||||||||
\(146\) | −5.84875 | + | 6.48929i | −0.484046 | + | 0.537058i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.0502525 | + | 0.482672i | 0.00413073 | + | 0.0396754i | ||||
\(149\) | 23.7701 | 1.94733 | 0.973663 | − | 0.227993i | \(-0.0732165\pi\) | ||||
0.973663 | + | 0.227993i | \(0.0732165\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.95699i | 0.647531i | 0.946137 | + | 0.323765i | \(0.104949\pi\) | ||||
−0.946137 | + | 0.323765i | \(0.895051\pi\) | |||||||
\(152\) | −7.17373 | + | 9.84332i | −0.581866 | + | 0.798398i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.7177i | 1.34279i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.9552i | 0.874323i | 0.899383 | + | 0.437162i | \(0.144016\pi\) | ||||
−0.899383 | + | 0.437162i | \(0.855984\pi\) | |||||||
\(158\) | 3.12058 | − | 3.46234i | 0.248260 | − | 0.275449i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.56751 | − | 7.86657i | 0.361094 | − | 0.621907i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.2529i | 0.881394i | 0.897656 | + | 0.440697i | \(0.145269\pi\) | ||||
−0.897656 | + | 0.440697i | \(0.854731\pi\) | |||||||
\(164\) | 23.1677 | − | 2.41206i | 1.80909 | − | 0.188350i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.4413 | + | 12.1146i | 1.04325 | + | 0.940272i | ||||
\(167\) | −21.8427 | −1.69024 | −0.845119 | − | 0.534579i | \(-0.820470\pi\) | ||||
−0.845119 | + | 0.534579i | \(0.820470\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.58579 | 0.121984 | ||||||||
\(170\) | 2.71637 | + | 2.44824i | 0.208336 | + | 0.187772i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 15.8284 | − | 1.64795i | 1.20691 | − | 0.125655i | ||||
\(173\) | 11.2563i | 0.855798i | 0.903827 | + | 0.427899i | \(0.140746\pi\) | ||||
−0.903827 | + | 0.427899i | \(0.859254\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.20658 | − | 10.4822i | −0.166328 | − | 0.790124i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.261220 | + | 0.289829i | −0.0195793 | + | 0.0217236i | ||||
\(179\) | − | 12.4710i | − | 0.932123i | −0.884752 | − | 0.466062i | \(-0.845672\pi\) | ||
0.884752 | − | 0.466062i | \(-0.154328\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.9134i | 1.10850i | 0.832349 | + | 0.554252i | \(0.186996\pi\) | ||||
−0.832349 | + | 0.554252i | \(0.813004\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14.7782 | − | 10.7702i | −1.08946 | − | 0.793991i | ||||
\(185\) | − | 0.390175i | − | 0.0286863i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.30629 | 0.314907 | ||||||||
\(188\) | 1.87381 | + | 17.9978i | 0.136661 | + | 1.31262i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.55635 | − | 7.27439i | 0.475648 | − | 0.527740i | ||||
\(191\) | − | 10.2524i | − | 0.741841i | −0.928665 | − | 0.370921i | \(-0.879042\pi\) | ||
0.928665 | − | 0.370921i | \(-0.120958\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.65685 | −0.551152 | −0.275576 | − | 0.961279i | \(-0.588869\pi\) | ||||
−0.275576 | + | 0.961279i | \(0.588869\pi\) | |||||||
\(194\) | −12.2463 | + | 13.5875i | −0.879235 | + | 0.975527i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.1445 | −0.722769 | −0.361384 | − | 0.932417i | \(-0.617696\pi\) | ||||
−0.361384 | + | 0.932417i | \(0.617696\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.7026 | 1.04224 | 0.521120 | − | 0.853483i | \(-0.325514\pi\) | ||||
0.521120 | + | 0.853483i | \(0.325514\pi\) | |||||||
\(200\) | 4.02177 | − | 5.51841i | 0.284382 | − | 0.390210i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.3332 | + | 17.0125i | −1.07884 | + | 1.19700i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.7279 | −1.30801 | ||||||||
\(206\) | 10.9213 | + | 9.84332i | 0.760926 | + | 0.685816i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.78379 | − | 13.2241i | −0.193021 | − | 0.916929i | ||||
\(209\) | − | 11.5322i | − | 0.797696i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.9140i | 1.09556i | 0.836621 | + | 0.547782i | \(0.184528\pi\) | ||||
−0.836621 | + | 0.547782i | \(0.815472\pi\) | |||||||
\(212\) | 0.509789 | + | 4.89649i | 0.0350124 | + | 0.336292i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.12132 | + | 6.79172i | −0.418445 | + | 0.464272i | ||||
\(215\) | −12.7951 | −0.872622 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.78864 | + | 7.01984i | 0.527513 | + | 0.475444i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.891862 | + | 8.56628i | 0.0601294 | + | 0.577539i | ||||
\(221\) | 5.43275 | 0.365446 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.61259 | −0.576741 | −0.288371 | − | 0.957519i | \(-0.593114\pi\) | ||||
−0.288371 | + | 0.957519i | \(0.593114\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.2426 | + | 11.9355i | 0.880887 | + | 0.793937i | ||||
\(227\) | 3.74761 | 0.248738 | 0.124369 | − | 0.992236i | \(-0.460309\pi\) | ||||
0.124369 | + | 0.992236i | \(0.460309\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 4.19825i | − | 0.277428i | −0.990332 | − | 0.138714i | \(-0.955703\pi\) | ||
0.990332 | − | 0.138714i | \(-0.0442969\pi\) | |||||||
\(230\) | 10.9213 | + | 9.84332i | 0.720132 | + | 0.649049i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.84924 | + | 10.7702i | −0.515328 | + | 0.707099i | ||||
\(233\) | 3.69222 | 0.241885 | 0.120943 | − | 0.992660i | \(-0.461408\pi\) | ||||
0.120943 | + | 0.992660i | \(0.461408\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 14.5488i | − | 0.949058i | ||||||
\(236\) | −1.87381 | − | 17.9978i | −0.121974 | − | 1.17156i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.10926i | − | 0.0717518i | −0.999356 | − | 0.0358759i | \(-0.988578\pi\) | ||
0.999356 | − | 0.0358759i | \(-0.0114221\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 1.39942i | − | 0.0901444i | −0.998984 | − | 0.0450722i | \(-0.985648\pi\) | ||
0.998984 | − | 0.0450722i | \(-0.0143518\pi\) | |||||||
\(242\) | −4.02177 | − | 3.62479i | −0.258529 | − | 0.233010i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.72066 | − | 0.699709i | 0.430246 | − | 0.0447943i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 14.5488i | − | 0.925717i | ||||||
\(248\) | −17.3189 | + | 23.7639i | −1.09975 | + | 1.50901i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.2882 | + | 12.5244i | −0.713927 | + | 0.792115i | ||||
\(251\) | −21.8427 | −1.37870 | −0.689349 | − | 0.724430i | \(-0.742103\pi\) | ||||
−0.689349 | + | 0.724430i | \(0.742103\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.3137 | 1.08850 | ||||||||
\(254\) | −10.6543 | + | 11.8212i | −0.668512 | + | 0.741726i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.6421 | − | 6.45042i | 0.915133 | − | 0.403151i | ||||
\(257\) | 14.3107i | 0.892679i | 0.894864 | + | 0.446339i | \(0.147273\pi\) | ||||
−0.894864 | + | 0.446339i | \(0.852727\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.12516 | + | 10.8071i | 0.0697794 | + | 0.670226i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.4413 | + | 12.1146i | 0.830407 | + | 0.748440i | ||||
\(263\) | 2.67798i | 0.165131i | 0.996586 | + | 0.0825656i | \(0.0263114\pi\) | ||||
−0.996586 | + | 0.0825656i | \(0.973689\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.95815i | − | 0.243147i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −22.3848 | + | 2.33055i | −1.36737 | + | 0.142361i | ||||
\(269\) | − | 16.1947i | − | 0.987406i | −0.869631 | − | 0.493703i | \(-0.835643\pi\) | ||
0.869631 | − | 0.493703i | \(-0.164357\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.4863 | 1.00147 | 0.500737 | − | 0.865600i | \(-0.333063\pi\) | ||||
0.500737 | + | 0.865600i | \(0.333063\pi\) | |||||||
\(272\) | 1.32498 | + | 6.29420i | 0.0803388 | + | 0.381642i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.0208 | + | 18.0446i | 1.20950 | + | 1.09011i | ||||
\(275\) | 6.46521i | 0.389867i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.7990 | 1.42994 | 0.714971 | − | 0.699154i | \(-0.246440\pi\) | ||||
0.714971 | + | 0.699154i | \(0.246440\pi\) | |||||||
\(278\) | 6.39757 | + | 5.76608i | 0.383701 | + | 0.345827i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.19285 | 0.488744 | 0.244372 | − | 0.969681i | \(-0.421418\pi\) | ||||
0.244372 | + | 0.969681i | \(0.421418\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.3963 | 0.617996 | 0.308998 | − | 0.951063i | \(-0.400006\pi\) | ||||
0.308998 | + | 0.951063i | \(0.400006\pi\) | |||||||
\(284\) | −15.9815 | + | 1.66388i | −0.948327 | + | 0.0987333i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.50445 | + | 8.56628i | 0.562010 | + | 0.506535i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.4142 | 0.847895 | ||||||||
\(290\) | 7.17373 | − | 7.95938i | 0.421256 | − | 0.467391i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.2882 | − | 1.27937i | 0.719115 | − | 0.0748693i | ||||
\(293\) | 1.21786i | 0.0711483i | 0.999367 | + | 0.0355741i | \(0.0113260\pi\) | ||||
−0.999367 | + | 0.0355741i | \(0.988674\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.5488i | 0.847063i | ||||||||
\(296\) | 0.404208 | − | 0.554628i | 0.0234941 | − | 0.0322371i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −24.9706 | − | 22.5058i | −1.44651 | − | 1.30372i | ||||
\(299\) | 21.8427 | 1.26319 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.53375 | − | 8.35883i | 0.433518 | − | 0.480997i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.8557 | − | 3.54827i | 0.966743 | − | 0.203507i | ||||
\(305\) | −5.43275 | −0.311078 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.5763 | 1.28850 | 0.644250 | − | 0.764815i | \(-0.277170\pi\) | ||||
0.644250 | + | 0.764815i | \(0.277170\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15.8284 | − | 17.5619i | 0.898994 | − | 0.997451i | ||||
\(311\) | −21.8427 | −1.23858 | −0.619292 | − | 0.785161i | \(-0.712580\pi\) | ||||
−0.619292 | + | 0.785161i | \(0.712580\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6.17733i | − | 0.349163i | −0.984643 | − | 0.174582i | \(-0.944143\pi\) | ||
0.984643 | − | 0.174582i | \(-0.0558573\pi\) | |||||||
\(314\) | 10.3725 | − | 11.5085i | 0.585355 | − | 0.649462i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.55635 | + | 0.682602i | −0.368823 | + | 0.0383994i | ||||
\(317\) | 10.1445 | 0.569774 | 0.284887 | − | 0.958561i | \(-0.408044\pi\) | ||||
0.284887 | + | 0.958561i | \(0.408044\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 12.6181i | − | 0.706477i | ||||||
\(320\) | −12.2463 | + | 3.93929i | −0.684590 | + | 0.220213i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.92468i | 0.385300i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.15640i | 0.452436i | ||||||||
\(326\) | 10.6543 | − | 11.8212i | 0.590089 | − | 0.654714i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −26.6214 | − | 19.4015i | −1.46992 | − | 1.07127i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 22.5058i | − | 1.23703i | −0.785773 | − | 0.618514i | \(-0.787735\pi\) | ||
0.785773 | − | 0.618514i | \(-0.212265\pi\) | |||||||
\(332\) | −2.64996 | − | 25.4527i | −0.145436 | − | 1.39690i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 22.9458 | + | 20.6808i | 1.25554 | + | 1.13161i | ||||
\(335\) | 18.0951 | 0.988639 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.3848 | −1.87306 | −0.936529 | − | 0.350590i | \(-0.885981\pi\) | ||||
−0.936529 | + | 0.350590i | \(0.885981\pi\) | |||||||
\(338\) | −1.66587 | − | 1.50144i | −0.0906114 | − | 0.0816674i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.535534 | − | 5.14377i | −0.0290434 | − | 0.278960i | ||||
\(341\) | − | 27.8411i | − | 1.50768i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −18.1881 | − | 13.2553i | −0.980635 | − | 0.714679i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.6575 | − | 11.8247i | 0.572952 | − | 0.635701i | ||||
\(347\) | 14.0397i | 0.753690i | 0.926276 | + | 0.376845i | \(0.122991\pi\) | ||||
−0.926276 | + | 0.376845i | \(0.877009\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.15640i | 0.436602i | 0.975881 | + | 0.218301i | \(0.0700515\pi\) | ||||
−0.975881 | + | 0.218301i | \(0.929949\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.60660 | + | 13.1008i | −0.405433 | + | 0.698273i | ||||
\(353\) | − | 1.21786i | − | 0.0648203i | −0.999475 | − | 0.0324101i | \(-0.989682\pi\) | ||
0.999475 | − | 0.0324101i | \(-0.0103183\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.9189 | 0.685663 | ||||||||
\(356\) | 0.548825 | − | 0.0571399i | 0.0290877 | − | 0.00302841i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.8076 | + | 13.1008i | −0.624052 | + | 0.692397i | ||||
\(359\) | 6.46521i | 0.341221i | 0.985339 | + | 0.170610i | \(0.0545740\pi\) | ||||
−0.985339 | + | 0.170610i | \(0.945426\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.455844 | −0.0239918 | ||||||||
\(362\) | 14.1201 | − | 15.6665i | 0.742137 | − | 0.823415i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.93338 | −0.519937 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.2701 | 0.953689 | 0.476844 | − | 0.878988i | \(-0.341780\pi\) | ||||
0.476844 | + | 0.878988i | \(0.341780\pi\) | |||||||
\(368\) | 5.32716 | + | 25.3062i | 0.277698 | + | 1.31918i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.369422 | + | 0.409880i | −0.0192053 | + | 0.0213086i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.82843 | 0.146450 | 0.0732252 | − | 0.997315i | \(-0.476671\pi\) | ||||
0.0732252 | + | 0.997315i | \(0.476671\pi\) | |||||||
\(374\) | −4.52377 | − | 4.07724i | −0.233918 | − | 0.210829i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.0720 | − | 20.6808i | 0.777280 | − | 1.06653i | ||||
\(377\) | − | 15.9188i | − | 0.819858i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | −13.7749 | + | 1.43415i | −0.706638 | + | 0.0735703i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.70711 | + | 10.7702i | −0.496659 | + | 0.551052i | ||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.04354 | + | 7.24958i | 0.409405 | + | 0.368994i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 25.7296 | − | 2.67878i | 1.30622 | − | 0.135995i | ||||
\(389\) | 0.211161 | 0.0107063 | 0.00535315 | − | 0.999986i | \(-0.498296\pi\) | ||||
0.00535315 | + | 0.999986i | \(0.498296\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.3963 | −0.525764 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.6569 | + | 9.60494i | 0.536885 | + | 0.483890i | ||||
\(395\) | 5.29992 | 0.266668 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.33664i | 0.368216i | 0.982906 | + | 0.184108i | \(0.0589395\pi\) | ||||
−0.982906 | + | 0.184108i | \(0.941060\pi\) | |||||||
\(398\) | −15.4451 | − | 13.9206i | −0.774193 | − | 0.697774i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.44975 | + | 1.98925i | −0.472487 | + | 0.0994624i | ||||
\(401\) | −29.9238 | −1.49432 | −0.747162 | − | 0.664642i | \(-0.768584\pi\) | ||||
−0.747162 | + | 0.664642i | \(0.768584\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 35.1239i | − | 1.74964i | ||||||
\(404\) | 32.2152 | − | 3.35402i | 1.60277 | − | 0.166869i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.649787i | 0.0322087i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 33.2053i | − | 1.64189i | −0.571004 | − | 0.820947i | \(-0.693446\pi\) | ||
0.571004 | − | 0.820947i | \(-0.306554\pi\) | |||||||
\(410\) | 19.6737 | + | 17.7318i | 0.971615 | + | 0.875709i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.15315 | − | 20.6808i | −0.106078 | − | 1.01887i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.5751i | 1.00999i | ||||||||
\(416\) | −9.59636 | + | 16.5277i | −0.470500 | + | 0.810337i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.9188 | + | 12.1146i | −0.534054 | + | 0.592542i | ||||
\(419\) | 34.6378 | 1.69217 | 0.846084 | − | 0.533049i | \(-0.178954\pi\) | ||||
0.846084 | + | 0.533049i | \(0.178954\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0000 | 0.779792 | 0.389896 | − | 0.920859i | \(-0.372511\pi\) | ||||
0.389896 | + | 0.920859i | \(0.372511\pi\) | |||||||
\(422\) | 15.0675 | − | 16.7177i | 0.733474 | − | 0.813803i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.10051 | − | 5.62644i | 0.199138 | − | 0.273244i | ||||
\(425\) | − | 3.88215i | − | 0.188312i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 12.8609 | − | 1.33899i | 0.621656 | − | 0.0647225i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13.4413 | + | 12.1146i | 0.648198 | + | 0.584216i | ||||
\(431\) | − | 2.67798i | − | 0.128994i | −0.997918 | − | 0.0644969i | \(-0.979456\pi\) | ||
0.997918 | − | 0.0644969i | \(-0.0205442\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 25.6285i | − | 1.23163i | −0.787891 | − | 0.615814i | \(-0.788827\pi\) | ||
0.787891 | − | 0.615814i | \(-0.211173\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.53553 | − | 14.7487i | −0.0735387 | − | 0.706335i | ||||
\(437\) | 27.8411i | 1.33182i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.7026 | 0.701717 | 0.350858 | − | 0.936429i | \(-0.385890\pi\) | ||||
0.350858 | + | 0.936429i | \(0.385890\pi\) | |||||||
\(440\) | 7.17373 | − | 9.84332i | 0.341994 | − | 0.469262i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.70711 | − | 5.14377i | −0.271459 | − | 0.244664i | ||||
\(443\) | − | 33.8948i | − | 1.61039i | −0.593010 | − | 0.805195i | \(-0.702061\pi\) | ||
0.593010 | − | 0.805195i | \(-0.297939\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.443651 | −0.0210311 | ||||||||
\(446\) | 9.04753 | + | 8.15447i | 0.428413 | + | 0.386125i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.70264 | −0.410703 | −0.205351 | − | 0.978688i | \(-0.565834\pi\) | ||||
−0.205351 | + | 0.978688i | \(0.565834\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.1889 | 1.46863 | ||||||||
\(452\) | −2.61079 | − | 25.0765i | −0.122801 | − | 1.17950i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.93687 | − | 3.54827i | −0.184767 | − | 0.166529i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.4853 | 1.51960 | 0.759799 | − | 0.650158i | \(-0.225297\pi\) | ||||
0.759799 | + | 0.650158i | \(0.225297\pi\) | |||||||
\(458\) | −3.97494 | + | 4.41027i | −0.185737 | + | 0.206078i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.15315 | − | 20.6808i | −0.100391 | − | 0.964249i | ||||
\(461\) | 29.4491i | 1.37158i | 0.727798 | + | 0.685792i | \(0.240544\pi\) | ||||
−0.727798 | + | 0.685792i | \(0.759456\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.4198i | 1.78552i | 0.450535 | + | 0.892759i | \(0.351233\pi\) | ||||
−0.450535 | + | 0.892759i | \(0.648767\pi\) | |||||||
\(464\) | 18.4430 | − | 3.88239i | 0.856193 | − | 0.180236i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.87868 | − | 3.49582i | −0.179676 | − | 0.161941i | ||||
\(467\) | 9.04753 | 0.418670 | 0.209335 | − | 0.977844i | \(-0.432870\pi\) | ||||
0.209335 | + | 0.977844i | \(0.432870\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −13.7749 | + | 15.2835i | −0.635389 | + | 0.704976i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15.0720 | + | 20.6808i | −0.693746 | + | 0.951913i | ||||
\(473\) | 21.3087 | 0.979773 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.3963 | −0.477015 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.05025 | + | 1.16527i | −0.0480374 | + | 0.0532984i | ||||
\(479\) | 34.6378 | 1.58264 | 0.791321 | − | 0.611401i | \(-0.209394\pi\) | ||||
0.791321 | + | 0.611401i | \(0.209394\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.819760i | 0.0373778i | ||||||||
\(482\) | −1.32498 | + | 1.47009i | −0.0603512 | + | 0.0669608i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.792893 | + | 7.61569i | 0.0360406 | + | 0.346168i | ||||
\(485\) | −20.7989 | −0.944428 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 14.5488i | − | 0.659268i | −0.944109 | − | 0.329634i | \(-0.893075\pi\) | ||
0.944109 | − | 0.329634i | \(-0.106925\pi\) | |||||||
\(488\) | −7.72255 | − | 5.62813i | −0.349584 | − | 0.254774i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 32.3261i | − | 1.45886i | −0.684058 | − | 0.729428i | \(-0.739787\pi\) | ||
0.684058 | − | 0.729428i | \(-0.260213\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.57675i | 0.341239i | ||||||||
\(494\) | −13.7749 | + | 15.2835i | −0.619762 | + | 0.687638i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 40.6934 | − | 8.56628i | 1.82719 | − | 0.384637i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 19.2099i | − | 0.859952i | −0.902840 | − | 0.429976i | \(-0.858522\pi\) | ||
0.902840 | − | 0.429976i | \(-0.141478\pi\) | |||||||
\(500\) | 23.7165 | − | 2.46920i | 1.06063 | − | 0.110426i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 22.9458 | + | 20.6808i | 1.02412 | + | 0.923031i | ||||
\(503\) | −5.29992 | −0.236312 | −0.118156 | − | 0.992995i | \(-0.537698\pi\) | ||||
−0.118156 | + | 0.992995i | \(0.537698\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.0416 | −1.15884 | ||||||||
\(506\) | −18.1881 | − | 16.3928i | −0.808559 | − | 0.728747i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 22.3848 | − | 2.33055i | 0.993164 | − | 0.103401i | ||||
\(509\) | − | 1.21786i | − | 0.0539808i | −0.999636 | − | 0.0269904i | \(-0.991408\pi\) | ||
0.999636 | − | 0.0269904i | \(-0.00859236\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −21.4889 | − | 7.08713i | −0.949684 | − | 0.313210i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.5495 | − | 15.0334i | 0.597644 | − | 0.663097i | ||||
\(515\) | 16.7177i | 0.736668i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.2291i | 1.06559i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.05025 | − | 12.4182i | 0.396880 | − | 0.544572i | ||||
\(521\) | 15.6429i | 0.685327i | 0.939458 | + | 0.342663i | \(0.111329\pi\) | ||||
−0.939458 | + | 0.342663i | \(0.888671\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.7026 | −0.642900 | −0.321450 | − | 0.946927i | \(-0.604170\pi\) | ||||
−0.321450 | + | 0.946927i | \(0.604170\pi\) | |||||||
\(524\) | −2.64996 | − | 25.4527i | −0.115764 | − | 1.11191i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.53553 | − | 2.81322i | 0.110555 | − | 0.122662i | ||||
\(527\) | 16.7177i | 0.728233i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.7990 | −0.817347 | ||||||||
\(530\) | −3.74761 | + | 4.15804i | −0.162786 | + | 0.180614i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 39.3474 | 1.70433 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.3963 | −0.449472 | ||||||||
\(536\) | 25.7218 | + | 18.7459i | 1.11101 | + | 0.809698i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15.3332 | + | 17.0125i | −0.661063 | + | 0.733462i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.1127 | −1.42363 | −0.711813 | − | 0.702369i | \(-0.752126\pi\) | ||||
−0.711813 | + | 0.702369i | \(0.752126\pi\) | |||||||
\(542\) | −17.3189 | − | 15.6094i | −0.743911 | − | 0.670481i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.56751 | − | 7.86657i | 0.195831 | − | 0.337277i | ||||
\(545\) | 11.9223i | 0.510697i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 3.29589i | − | 0.140922i | −0.997515 | − | 0.0704611i | \(-0.977553\pi\) | ||
0.997515 | − | 0.0704611i | \(-0.0224471\pi\) | |||||||
\(548\) | −3.94711 | − | 37.9118i | −0.168612 | − | 1.61951i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.12132 | − | 6.79172i | 0.261014 | − | 0.289600i | ||||
\(551\) | 20.2904 | 0.864399 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −25.0009 | − | 22.5331i | −1.06219 | − | 0.957339i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.26128 | − | 12.1146i | −0.0534904 | − | 0.513772i | ||||
\(557\) | 31.4532 | 1.33271 | 0.666357 | − | 0.745633i | \(-0.267853\pi\) | ||||
0.666357 | + | 0.745633i | \(0.267853\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.8826 | 1.13701 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.60660 | − | 7.75706i | −0.363048 | − | 0.327212i | ||||
\(563\) | −3.74761 | −0.157943 | −0.0789715 | − | 0.996877i | \(-0.525164\pi\) | ||||
−0.0789715 | + | 0.996877i | \(0.525164\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.2710i | 0.852806i | ||||||||
\(566\) | −10.9213 | − | 9.84332i | −0.459058 | − | 0.413745i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18.3640 | + | 13.3835i | 0.770535 | + | 0.561559i | ||||
\(569\) | 12.0962 | 0.507100 | 0.253550 | − | 0.967322i | \(-0.418402\pi\) | ||||
0.253550 | + | 0.967322i | \(0.418402\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.4628i | 1.27483i | 0.770522 | + | 0.637413i | \(0.219996\pi\) | ||||
−0.770522 | + | 0.637413i | \(0.780004\pi\) | |||||||
\(572\) | −1.87381 | − | 17.9978i | −0.0783477 | − | 0.752525i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 15.6084i | − | 0.650916i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.8715i | 0.785632i | 0.919617 | + | 0.392816i | \(0.128499\pi\) | ||||
−0.919617 | + | 0.392816i | \(0.871501\pi\) | |||||||
\(578\) | −15.1422 | − | 13.6475i | −0.629831 | − | 0.567661i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −15.0720 | + | 1.56920i | −0.625832 | + | 0.0651573i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.59179i | 0.273004i | ||||||||
\(584\) | −14.1201 | − | 10.2906i | −0.584295 | − | 0.425829i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.15308 | − | 1.27937i | 0.0476334 | − | 0.0528501i | ||||
\(587\) | 34.6378 | 1.42966 | 0.714828 | − | 0.699300i | \(-0.246505\pi\) | ||||
0.714828 | + | 0.699300i | \(0.246505\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.7696 | 1.84470 | ||||||||
\(590\) | 13.7749 | − | 15.2835i | 0.567104 | − | 0.629212i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.949747 | + | 0.199929i | −0.0390344 | + | 0.00821705i | ||||
\(593\) | − | 18.4688i | − | 0.758421i | −0.925310 | − | 0.379211i | \(-0.876196\pi\) | ||
0.925310 | − | 0.379211i | \(-0.123804\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.92296 | + | 47.2847i | 0.201652 | + | 1.93686i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −22.9458 | − | 20.6808i | −0.938322 | − | 0.845702i | ||||
\(599\) | − | 16.5273i | − | 0.675289i | −0.941274 | − | 0.337644i | \(-0.890370\pi\) | ||
0.941274 | − | 0.337644i | \(-0.109630\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 16.8925i | − | 0.689058i | −0.938776 | − | 0.344529i | \(-0.888039\pi\) | ||
0.938776 | − | 0.344529i | \(-0.111961\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.8284 | + | 1.64795i | −0.644050 | + | 0.0670540i | ||||
\(605\) | − | 6.15626i | − | 0.250287i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.52257 | 0.102388 | 0.0511939 | − | 0.998689i | \(-0.483697\pi\) | ||||
0.0511939 | + | 0.998689i | \(0.483697\pi\) | |||||||
\(608\) | −21.0665 | − | 12.2317i | −0.854360 | − | 0.496061i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.70711 | + | 5.14377i | 0.231074 | + | 0.208265i | ||||
\(611\) | 30.5670i | 1.23661i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.0416 | 0.890253 | 0.445127 | − | 0.895468i | \(-0.353159\pi\) | ||||
0.445127 | + | 0.895468i | \(0.353159\pi\) | |||||||
\(614\) | −23.7165 | − | 21.3755i | −0.957119 | − | 0.862644i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.5969 | 0.668165 | 0.334082 | − | 0.942544i | \(-0.391574\pi\) | ||||
0.334082 | + | 0.942544i | \(0.391574\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.09002 | −0.244778 | −0.122389 | − | 0.992482i | \(-0.539056\pi\) | ||||
−0.122389 | + | 0.992482i | \(0.539056\pi\) | |||||||
\(620\) | −33.2556 | + | 3.46234i | −1.33558 | + | 0.139051i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 22.9458 | + | 20.6808i | 0.920041 | + | 0.829226i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.10051 | −0.284020 | ||||||||
\(626\) | −5.84875 | + | 6.48929i | −0.233763 | + | 0.259364i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.7927 | + | 2.26890i | −0.869623 | + | 0.0905391i | ||||
\(629\) | − | 0.390175i | − | 0.0155573i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 45.0115i | − | 1.79188i | −0.444174 | − | 0.895941i | \(-0.646503\pi\) | ||
0.444174 | − | 0.895941i | \(-0.353497\pi\) | |||||||
\(632\) | 7.53375 | + | 5.49053i | 0.299676 | + | 0.218402i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.6569 | − | 9.60494i | −0.423238 | − | 0.381461i | ||||
\(635\) | −18.0951 | −0.718081 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11.9469 | + | 13.2553i | −0.472983 | + | 0.524783i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 16.5945 | + | 7.45669i | 0.655956 | + | 0.294752i | ||||
\(641\) | −28.9043 | −1.14165 | −0.570825 | − | 0.821072i | \(-0.693376\pi\) | ||||
−0.570825 | + | 0.821072i | \(0.693376\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −45.8915 | −1.80979 | −0.904893 | − | 0.425640i | \(-0.860049\pi\) | ||||
−0.904893 | + | 0.425640i | \(0.860049\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.55635 | − | 7.27439i | 0.257956 | − | 0.286207i | ||||
\(647\) | 27.1426 | 1.06709 | 0.533543 | − | 0.845773i | \(-0.320860\pi\) | ||||
0.533543 | + | 0.845773i | \(0.320860\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 24.2291i | − | 0.951076i | ||||||
\(650\) | 7.72255 | − | 8.56831i | 0.302903 | − | 0.336077i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −22.3848 | + | 2.33055i | −0.876655 | + | 0.0912713i | ||||
\(653\) | −37.3083 | −1.45999 | −0.729993 | − | 0.683455i | \(-0.760477\pi\) | ||||
−0.729993 | + | 0.683455i | \(0.760477\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.5751i | 0.803935i | ||||||||
\(656\) | 9.59636 | + | 45.5867i | 0.374675 | + | 1.77986i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 31.6763i | − | 1.23393i | −0.786990 | − | 0.616966i | \(-0.788361\pi\) | ||
0.786990 | − | 0.616966i | \(-0.211639\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.5809i | 1.69510i | 0.530717 | + | 0.847549i | \(0.321923\pi\) | ||||
−0.530717 | + | 0.847549i | \(0.678077\pi\) | |||||||
\(662\) | −21.3087 | + | 23.6423i | −0.828184 | + | 0.918886i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21.3151 | + | 29.2471i | −0.827185 | + | 1.13501i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.4628i | 1.17952i | ||||||||
\(668\) | −4.52377 | − | 43.4505i | −0.175030 | − | 1.68115i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −19.0089 | − | 17.1326i | −0.734378 | − | 0.661889i | ||||
\(671\) | 9.04753 | 0.349276 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.1005 | −0.620629 | −0.310314 | − | 0.950634i | \(-0.600434\pi\) | ||||
−0.310314 | + | 0.950634i | \(0.600434\pi\) | |||||||
\(674\) | 36.1213 | + | 32.5558i | 1.39134 | + | 1.25400i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.328427 | + | 3.15452i | 0.0126318 | + | 0.121328i | ||||
\(677\) | 31.8849i | 1.22543i | 0.790302 | + | 0.612717i | \(0.209924\pi\) | ||||
−0.790302 | + | 0.612717i | \(0.790076\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.30759 | + | 5.91059i | −0.165188 | + | 0.226661i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −26.3602 | + | 29.2471i | −1.00938 | + | 1.11993i | ||||
\(683\) | − | 16.5273i | − | 0.632401i | −0.948692 | − | 0.316201i | \(-0.897593\pi\) | ||
0.948692 | − | 0.316201i | \(-0.102407\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.6465i | 1.17094i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.55635 | + | 31.1454i | 0.249958 | + | 1.18741i | ||||
\(689\) | 8.31609i | 0.316818i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.1800 | 0.463350 | 0.231675 | − | 0.972793i | \(-0.425579\pi\) | ||||
0.231675 | + | 0.972793i | \(0.425579\pi\) | |||||||
\(692\) | −22.3915 | + | 2.33125i | −0.851197 | + | 0.0886208i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.2929 | − | 14.7487i | 0.504591 | − | 0.559853i | ||||
\(695\) | 9.79298i | 0.371469i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.7279 | −0.709371 | ||||||||
\(698\) | 7.72255 | − | 8.56831i | 0.292303 | − | 0.324315i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.0583 | 0.719824 | 0.359912 | − | 0.932986i | \(-0.382807\pi\) | ||||
0.359912 | + | 0.932986i | \(0.382807\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.04488 | −0.0394085 | ||||||||
\(704\) | 20.3947 | − | 6.56037i | 0.768653 | − | 0.247253i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.15308 | + | 1.27937i | −0.0433968 | + | 0.0481496i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.4142 | −1.17979 | −0.589893 | − | 0.807482i | \(-0.700830\pi\) | ||||
−0.589893 | + | 0.807482i | \(0.700830\pi\) | |||||||
\(710\) | −13.5713 | − | 12.2317i | −0.509322 | − | 0.459048i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.630642 | − | 0.459607i | −0.0236343 | − | 0.0172245i | ||||
\(713\) | 67.2144i | 2.51720i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.5488i | 0.544093i | ||||||||
\(716\) | 24.8078 | − | 2.58282i | 0.927112 | − | 0.0965245i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.12132 | − | 6.79172i | 0.228446 | − | 0.253465i | ||||
\(719\) | −43.6854 | −1.62919 | −0.814594 | − | 0.580031i | \(-0.803040\pi\) | ||||
−0.814594 | + | 0.580031i | \(0.803040\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.478865 | + | 0.431597i | 0.0178215 | + | 0.0160624i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −29.6664 | + | 3.08866i | −1.10254 | + | 0.114789i | ||||
\(725\) | −11.3753 | −0.422467 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.78372 | −0.0661547 | −0.0330773 | − | 0.999453i | \(-0.510531\pi\) | ||||
−0.0330773 | + | 0.999453i | \(0.510531\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.4350 | + | 9.40501i | 0.386218 | + | 0.348095i | ||||
\(731\) | −12.7951 | −0.473246 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 23.3099i | − | 0.860971i | −0.902598 | − | 0.430485i | \(-0.858342\pi\) | ||
0.902598 | − | 0.430485i | \(-0.141658\pi\) | |||||||
\(734\) | −19.1927 | − | 17.2982i | −0.708416 | − | 0.638490i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 18.3640 | − | 31.6280i | 0.676905 | − | 1.16582i | ||||
\(737\) | −30.1350 | −1.11004 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.8280i | 1.17081i | 0.810741 | + | 0.585405i | \(0.199065\pi\) | ||||
−0.810741 | + | 0.585405i | \(0.800935\pi\) | |||||||
\(740\) | 0.776156 | − | 0.0808080i | 0.0285321 | − | 0.00297056i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.8269i | 0.654006i | 0.945023 | + | 0.327003i | \(0.106039\pi\) | ||||
−0.945023 | + | 0.327003i | \(0.893961\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 38.2233i | − | 1.40039i | ||||||
\(746\) | −2.97127 | − | 2.67798i | −0.108786 | − | 0.0980478i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.891862 | + | 8.56628i | 0.0326097 | + | 0.313214i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 36.4891i | − | 1.33150i | −0.746173 | − | 0.665752i | \(-0.768111\pi\) | ||
0.746173 | − | 0.665752i | \(-0.231889\pi\) | |||||||
\(752\) | −35.4140 | + | 7.45493i | −1.29141 | + | 0.271853i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15.0720 | + | 16.7227i | −0.548891 | + | 0.609004i | ||||
\(755\) | 12.7951 | 0.465663 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.8995 | 0.432494 | 0.216247 | − | 0.976339i | \(-0.430618\pi\) | ||||
0.216247 | + | 0.976339i | \(0.430618\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 15.8284 | + | 11.5356i | 0.574157 | + | 0.418441i | ||||
\(761\) | − | 8.26875i | − | 0.299742i | −0.988706 | − | 0.149871i | \(-0.952114\pi\) | ||
0.988706 | − | 0.149871i | \(-0.0478858\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 20.3947 | − | 2.12335i | 0.737853 | − | 0.0768202i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 30.5670i | − | 1.10371i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 43.5809i | − | 1.57157i | −0.618502 | − | 0.785783i | \(-0.712260\pi\) | ||
0.618502 | − | 0.785783i | \(-0.287740\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.58579 | − | 15.2314i | −0.0570737 | − | 0.548189i | ||||
\(773\) | 41.7617i | 1.50206i | 0.660267 | + | 0.751031i | \(0.270443\pi\) | ||||
−0.660267 | + | 0.751031i | \(0.729557\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25.0989 | −0.901580 | ||||||||
\(776\) | −29.5652 | − | 21.5469i | −1.06133 | − | 0.773489i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.221825 | − | 0.199929i | −0.00795283 | − | 0.00716782i | ||||
\(779\) | 50.1530i | 1.79692i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.5147 | −0.769857 | ||||||||
\(782\) | 10.9213 | + | 9.84332i | 0.390546 | + | 0.351996i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.6164 | 0.628758 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.1078 | −1.57227 | −0.786137 | − | 0.618053i | \(-0.787922\pi\) | ||||
−0.786137 | + | 0.618053i | \(0.787922\pi\) | |||||||
\(788\) | −2.10100 | − | 20.1800i | −0.0748451 | − | 0.718883i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.56758 | − | 5.01801i | −0.198085 | − | 0.178533i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.4142 | 0.405331 | ||||||||
\(794\) | 6.94640 | − | 7.70715i | 0.246518 | − | 0.273517i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.04501 | + | 29.2471i | 0.107927 | + | 1.03664i | ||||
\(797\) | 28.5072i | 1.00978i | 0.863185 | + | 0.504888i | \(0.168466\pi\) | ||||
−0.863185 | + | 0.504888i | \(0.831534\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 14.5488i | − | 0.514699i | ||||||
\(800\) | 11.8104 | + | 6.85739i | 0.417561 | + | 0.242446i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 31.4350 | + | 28.3321i | 1.11001 | + | 1.00044i | ||||
\(803\) | 16.5428 | 0.583781 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −33.2556 | + | 36.8977i | −1.17138 | + | 1.29966i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −37.0177 | − | 26.9782i | −1.30228 | − | 0.949090i | ||||
\(809\) | 29.1154 | 1.02364 | 0.511822 | − | 0.859092i | \(-0.328971\pi\) | ||||
0.511822 | + | 0.859092i | \(0.328971\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.1978 | 1.76268 | 0.881342 | − | 0.472479i | \(-0.156641\pi\) | ||||
0.881342 | + | 0.472479i | \(0.156641\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.615224 | − | 0.682602i | 0.0215636 | − | 0.0239252i | ||||
\(815\) | 18.0951 | 0.633843 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.2651i | 1.19879i | ||||||||
\(818\) | −31.4390 | + | 34.8822i | −1.09924 | + | 1.21963i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.87868 | − | 37.2545i | −0.135449 | − | 1.30098i | ||||
\(821\) | 19.9905 | 0.697672 | 0.348836 | − | 0.937184i | \(-0.386577\pi\) | ||||
0.348836 | + | 0.937184i | \(0.386577\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.36520i | − | 0.0475880i | −0.999717 | − | 0.0237940i | \(-0.992425\pi\) | ||
0.999717 | − | 0.0237940i | \(-0.00757458\pi\) | |||||||
\(824\) | −17.3189 | + | 23.7639i | −0.603333 | + | 0.827854i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.5331i | 0.783552i | 0.920061 | + | 0.391776i | \(0.128139\pi\) | ||||
−0.920061 | + | 0.391776i | \(0.871861\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 0.579658i | − | 0.0201323i | −0.999949 | − | 0.0100662i | \(-0.996796\pi\) | ||
0.999949 | − | 0.0100662i | \(-0.00320422\pi\) | |||||||
\(830\) | 19.4807 | − | 21.6142i | 0.676184 | − | 0.750238i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 25.7296 | − | 8.27645i | 0.892012 | − | 0.286934i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.1239i | 1.21551i | ||||||||
\(836\) | 22.9403 | − | 2.38839i | 0.793408 | − | 0.0826042i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −36.3871 | − | 32.7954i | −1.25697 | − | 1.13290i | ||||
\(839\) | 39.9377 | 1.37880 | 0.689402 | − | 0.724379i | \(-0.257873\pi\) | ||||
0.689402 | + | 0.724379i | \(0.257873\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.79899 | −0.234448 | ||||||||
\(842\) | −16.8080 | − | 15.1489i | −0.579243 | − | 0.522067i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −31.6569 | + | 3.29589i | −1.08967 | + | 0.113449i | ||||
\(845\) | − | 2.55000i | − | 0.0877228i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.63475 | + | 2.02819i | −0.330859 | + | 0.0696484i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.67565 | + | 4.07820i | −0.126074 | + | 0.139881i | ||||
\(851\) | − | 1.56872i | − | 0.0537752i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.1425i | 1.34021i | 0.742265 | + | 0.670107i | \(0.233752\pi\) | ||||
−0.742265 | + | 0.670107i | \(0.766248\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.7782 | − | 10.7702i | −0.505108 | − | 0.368118i | ||||
\(857\) | 31.8849i | 1.08917i | 0.838707 | + | 0.544583i | \(0.183312\pi\) | ||||
−0.838707 | + | 0.544583i | \(0.816688\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.9189 | −0.440786 | −0.220393 | − | 0.975411i | \(-0.570734\pi\) | ||||
−0.220393 | + | 0.975411i | \(0.570734\pi\) | |||||||
\(860\) | −2.64996 | − | 25.4527i | −0.0903629 | − | 0.867930i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.53553 | + | 2.81322i | −0.0863606 | + | 0.0958187i | ||||
\(863\) | 50.6125i | 1.72287i | 0.507870 | + | 0.861434i | \(0.330433\pi\) | ||||
−0.507870 | + | 0.861434i | \(0.669567\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.1005 | 0.615436 | ||||||||
\(866\) | −24.2653 | + | 26.9228i | −0.824569 | + | 0.914874i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.82633 | −0.299413 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38.0178 | −1.28818 | ||||||||
\(872\) | −12.3511 | + | 16.9474i | −0.418262 | + | 0.573911i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 26.3602 | − | 29.2471i | 0.891647 | − | 0.989299i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.75736 | −0.0593418 | −0.0296709 | − | 0.999560i | \(-0.509446\pi\) | ||||
−0.0296709 | + | 0.999560i | \(0.509446\pi\) | |||||||
\(878\) | −15.4451 | − | 13.9206i | −0.521247 | − | 0.469796i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −16.8557 | + | 3.54827i | −0.568207 | + | 0.119612i | ||||
\(881\) | 33.9974i | 1.14540i | 0.819765 | + | 0.572700i | \(0.194104\pi\) | ||||
−0.819765 | + | 0.572700i | \(0.805896\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 44.4461i | − | 1.49573i | −0.663852 | − | 0.747864i | \(-0.731079\pi\) | ||
0.663852 | − | 0.747864i | \(-0.268921\pi\) | |||||||
\(884\) | 1.12516 | + | 10.8071i | 0.0378432 | + | 0.363481i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32.0919 | + | 35.6065i | −1.07815 | + | 1.19622i | ||||
\(887\) | −9.04753 | −0.303786 | −0.151893 | − | 0.988397i | \(-0.548537\pi\) | ||||
−0.151893 | + | 0.988397i | \(0.548537\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.466056 | + | 0.420052i | 0.0156222 | + | 0.0140802i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.78372 | − | 17.1326i | −0.0597235 | − | 0.573641i | ||||
\(893\) | −38.9613 | −1.30379 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.0538 | −0.670324 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.14214 | + | 8.23973i | 0.305077 | + | 0.274963i | ||||
\(899\) | 48.9853 | 1.63375 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 3.95815i | − | 0.131865i | ||||||
\(902\) | −32.7640 | − | 29.5299i | −1.09092 | − | 0.983240i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −21.0000 | + | 28.8148i | −0.698450 | + | 0.958366i | ||||
\(905\) | 23.9813 | 0.797165 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.1406i | 0.701961i | 0.936383 | + | 0.350980i | \(0.114152\pi\) | ||||
−0.936383 | + | 0.350980i | \(0.885848\pi\) | |||||||
\(908\) | 0.776156 | + | 7.45493i | 0.0257576 | + | 0.247400i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 29.4578i | − | 0.975980i | −0.872849 | − | 0.487990i | \(-0.837730\pi\) | ||
0.872849 | − | 0.487990i | \(-0.162270\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 34.2651i | − | 1.13401i | ||||||
\(914\) | −34.1258 | − | 30.7573i | −1.12878 | − | 1.01736i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.35136 | − | 0.869487i | 0.275937 | − | 0.0287286i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.5488i | 0.479920i | 0.970783 | + | 0.239960i | \(0.0771343\pi\) | ||||
−0.970783 | + | 0.239960i | \(0.922866\pi\) | |||||||
\(920\) | −17.3189 | + | 23.7639i | −0.570988 | + | 0.783472i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 27.8827 | − | 30.9364i | 0.918268 | − | 1.01883i | ||||
\(923\) | −27.1426 | −0.893410 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.585786 | 0.0192605 | ||||||||
\(926\) | 36.3762 | − | 40.3600i | 1.19539 | − | 1.32631i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −23.0503 | − | 13.3835i | −0.756662 | − | 0.439335i | ||||
\(929\) | 50.0777i | 1.64300i | 0.570210 | + | 0.821499i | \(0.306862\pi\) | ||||
−0.570210 | + | 0.821499i | \(0.693138\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.764683 | + | 7.34473i | 0.0250480 | + | 0.240585i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.50445 | − | 8.56628i | −0.310995 | − | 0.280297i | ||||
\(935\) | − | 6.92468i | − | 0.226461i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 49.5181i | − | 1.61769i | −0.588025 | − | 0.808843i | \(-0.700094\pi\) | ||
0.588025 | − | 0.808843i | \(-0.299906\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 28.9411 | − | 3.01315i | 0.943955 | − | 0.0982781i | ||||
\(941\) | − | 14.0822i | − | 0.459066i | −0.973301 | − | 0.229533i | \(-0.926280\pi\) | ||
0.973301 | − | 0.229533i | \(-0.0737198\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −75.2967 | −2.45200 | ||||||||
\(944\) | 35.4140 | − | 7.45493i | 1.15263 | − | 0.242637i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.3848 | − | 20.1752i | −0.727792 | − | 0.655953i | ||||
\(947\) | − | 20.3146i | − | 0.660135i | −0.943957 | − | 0.330068i | \(-0.892928\pi\) | ||
0.943957 | − | 0.330068i | \(-0.107072\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.8701 | 0.677471 | ||||||||
\(950\) | 10.9213 | + | 9.84332i | 0.354335 | + | 0.319359i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.1546 | 1.00920 | 0.504598 | − | 0.863355i | \(-0.331641\pi\) | ||||
0.504598 | + | 0.863355i | \(0.331641\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.4863 | −0.533485 | ||||||||
\(956\) | 2.20658 | − | 0.229734i | 0.0713660 | − | 0.00743014i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −36.3871 | − | 32.7954i | −1.17561 | − | 1.05957i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 77.0833 | 2.48656 | ||||||||
\(962\) | 0.776156 | − | 0.861159i | 0.0250243 | − | 0.0277649i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.78379 | − | 0.289829i | 0.0896598 | − | 0.00933476i | ||||
\(965\) | 12.3125i | 0.396354i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 15.9140i | − | 0.511759i | −0.966709 | − | 0.255880i | \(-0.917635\pi\) | ||
0.966709 | − | 0.255880i | \(-0.0823651\pi\) | |||||||
\(968\) | 6.37767 | − | 8.75101i | 0.204986 | − | 0.281268i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 21.8492 | + | 19.6925i | 0.701537 | + | 0.632290i | ||||
\(971\) | −48.9853 | −1.57201 | −0.786006 | − | 0.618219i | \(-0.787855\pi\) | ||||
−0.786006 | + | 0.618219i | \(0.787855\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −13.7749 | + | 15.2835i | −0.441377 | + | 0.489715i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.78379 | + | 13.2241i | 0.0891069 | + | 0.423294i | ||||
\(977\) | 42.8285 | 1.37020 | 0.685102 | − | 0.728447i | \(-0.259758\pi\) | ||||
0.685102 | + | 0.728447i | \(0.259758\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.738843 | 0.0236135 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −30.6066 | + | 33.9586i | −0.976696 | + | 1.08366i | ||||
\(983\) | −18.0951 | −0.577143 | −0.288572 | − | 0.957458i | \(-0.593180\pi\) | ||||
−0.288572 | + | 0.957458i | \(0.593180\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.3128i | 0.519769i | ||||||||
\(986\) | 7.17373 | − | 7.95938i | 0.228458 | − | 0.253478i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 28.9411 | − | 3.01315i | 0.920740 | − | 0.0958611i | ||||
\(989\) | −51.4436 | −1.63581 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.29589i | 0.104698i | 0.998629 | + | 0.0523488i | \(0.0166707\pi\) | ||||
−0.998629 | + | 0.0523488i | \(0.983329\pi\) | |||||||
\(992\) | −50.8591 | − | 29.5299i | −1.61478 | − | 0.937577i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 23.6423i | − | 0.749513i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.0669i | 0.952228i | 0.879384 | + | 0.476114i | \(0.157955\pi\) | ||||
−0.879384 | + | 0.476114i | \(0.842045\pi\) | |||||||
\(998\) | −18.1881 | + | 20.1800i | −0.575734 | + | 0.638787i | ||||
\(999\) | 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 | 1764.2.b.n.1567.1 | ✓ | 16 | |
3.2 | odd | 2 | inner | 1764.2.b.n.1567.16 | yes | 16 | |
4.3 | odd | 2 | inner | 1764.2.b.n.1567.3 | yes | 16 | |
7.6 | odd | 2 | inner | 1764.2.b.n.1567.2 | yes | 16 | |
12.11 | even | 2 | inner | 1764.2.b.n.1567.14 | yes | 16 | |
21.20 | even | 2 | inner | 1764.2.b.n.1567.15 | yes | 16 | |
28.27 | even | 2 | inner | 1764.2.b.n.1567.4 | yes | 16 | |
84.83 | odd | 2 | inner | 1764.2.b.n.1567.13 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.2.b.n.1567.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1764.2.b.n.1567.2 | yes | 16 | 7.6 | odd | 2 | inner | |
1764.2.b.n.1567.3 | yes | 16 | 4.3 | odd | 2 | inner | |
1764.2.b.n.1567.4 | yes | 16 | 28.27 | even | 2 | inner | |
1764.2.b.n.1567.13 | yes | 16 | 84.83 | odd | 2 | inner | |
1764.2.b.n.1567.14 | yes | 16 | 12.11 | even | 2 | inner | |
1764.2.b.n.1567.15 | yes | 16 | 21.20 | even | 2 | inner | |
1764.2.b.n.1567.16 | yes | 16 | 3.2 | odd | 2 | inner |