Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(97,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.r (of order \(6\), degree \(2\), 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: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 97.4 | ||
Root | \(-0.180407 + 0.673288i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.97 |
Dual form | 576.2.r.f.481.4 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.492881 | − | 1.66044i | 0.284565 | − | 0.958657i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.50000 | − | 0.866025i | 0.670820 | − | 0.387298i | −0.125567 | − | 0.992085i | \(-0.540075\pi\) |
0.796387 | + | 0.604787i | \(0.206742\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.17731 | − | 3.77121i | 0.822944 | − | 1.42538i | −0.0805357 | − | 0.996752i | \(-0.525663\pi\) |
0.903480 | − | 0.428630i | \(-0.141004\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.51414 | − | 1.63680i | −0.838046 | − | 0.545600i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.05328 | + | 2.91751i | 1.52362 | + | 0.879663i | 0.999609 | + | 0.0279511i | \(0.00889826\pi\) |
0.524011 | + | 0.851712i | \(0.324435\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.48133 | + | 2.00994i | −0.965546 | + | 0.557458i | −0.897876 | − | 0.440249i | \(-0.854890\pi\) |
−0.0676707 | + | 0.997708i | \(0.521557\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.698664 | − | 2.91751i | −0.180394 | − | 0.753298i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.70739 | 0.414103 | 0.207051 | − | 0.978330i | \(-0.433613\pi\) | ||||
0.207051 | + | 0.978330i | \(0.433613\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000i | 0.458831i | 0.973329 | + | 0.229416i | \(0.0736815\pi\) | ||||
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.18872 | − | 5.47405i | −1.13227 | − | 1.19453i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.32123 | − | 5.75253i | −0.692523 | − | 1.19949i | −0.971008 | − | 0.239045i | \(-0.923166\pi\) |
0.278485 | − | 0.960441i | \(-0.410168\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.95698 | + | 3.36783i | −0.761522 | + | 0.648139i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.06108 | − | 2.34467i | −0.754124 | − | 0.435394i | 0.0730578 | − | 0.997328i | \(-0.476724\pi\) |
−0.827182 | + | 0.561934i | \(0.810058\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.43071 | + | 4.21012i | 0.436569 | + | 0.756160i | 0.997422 | − | 0.0717553i | \(-0.0228601\pi\) |
−0.560853 | + | 0.827915i | \(0.689527\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.33502 | − | 6.95269i | 1.27686 | − | 1.21031i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 7.54241i | − | 1.27490i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.75194i | 0.945613i | 0.881166 | + | 0.472807i | \(0.156759\pi\) | ||||
−0.881166 | + | 0.472807i | \(0.843241\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.62152 | + | 6.77121i | 0.259651 | + | 1.08426i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.646305 | + | 1.11943i | 0.100936 | + | 0.174826i | 0.912071 | − | 0.410033i | \(-0.134483\pi\) |
−0.811135 | + | 0.584860i | \(0.801150\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.06782 | + | 1.77121i | 0.467838 | + | 0.270106i | 0.715334 | − | 0.698783i | \(-0.246274\pi\) |
−0.247496 | + | 0.968889i | \(0.579608\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.18872 | − | 0.277894i | −0.773488 | − | 0.0414260i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.30669 | − | 9.19145i | 0.774060 | − | 1.34071i | −0.161262 | − | 0.986912i | \(-0.551556\pi\) |
0.935322 | − | 0.353799i | \(-0.115110\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.98133 | − | 10.3600i | −0.854475 | − | 1.47999i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.841540 | − | 2.83502i | 0.117839 | − | 0.396982i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.506816i | 0.0696166i | 0.999394 | + | 0.0348083i | \(0.0110821\pi\) | ||||
−0.999394 | + | 0.0348083i | \(0.988918\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.1066 | 1.36277 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.32088 | + | 0.985762i | 0.439862 | + | 0.130567i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.62152 | + | 0.936184i | −0.211104 | + | 0.121881i | −0.601824 | − | 0.798629i | \(-0.705559\pi\) |
0.390721 | + | 0.920509i | \(0.372226\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.06108 | + | 0.612617i | 0.135858 | + | 0.0784376i | 0.566388 | − | 0.824138i | \(-0.308340\pi\) |
−0.430531 | + | 0.902576i | \(0.641674\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.6468 | + | 5.91751i | −1.46735 | + | 0.745536i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.48133 | + | 6.02983i | −0.431805 | + | 0.747909i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.36811 | − | 0.789879i | 0.167141 | − | 0.0964990i | −0.414096 | − | 0.910233i | \(-0.635902\pi\) |
0.581237 | + | 0.813734i | \(0.302569\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.1887 | + | 2.67939i | −1.34696 | + | 0.322561i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.88549 | −1.17319 | −0.586596 | − | 0.809880i | \(-0.699532\pi\) | ||||
−0.586596 | + | 0.809880i | \(0.699532\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.96265 | −0.931958 | −0.465979 | − | 0.884796i | \(-0.654298\pi\) | ||||
−0.465979 | + | 0.884796i | \(0.654298\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.38309 | + | 2.51414i | 0.275175 | + | 0.290308i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22.0051 | − | 12.7046i | 2.50771 | − | 1.44783i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.03339 | − | 1.78988i | 0.116265 | − | 0.201377i | −0.802020 | − | 0.597298i | \(-0.796241\pi\) |
0.918285 | + | 0.395921i | \(0.129574\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.64177 | + | 8.23028i | 0.404641 | + | 0.914476i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.33577 | − | 0.771205i | −0.146619 | − | 0.0846508i | 0.424896 | − | 0.905242i | \(-0.360311\pi\) |
−0.571515 | + | 0.820592i | \(0.693644\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.56108 | − | 1.47864i | 0.277789 | − | 0.160381i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.89482 | + | 5.58755i | −0.631991 | + | 0.599049i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.96265 | 0.420040 | 0.210020 | − | 0.977697i | \(-0.432647\pi\) | ||||
0.210020 | + | 0.977697i | \(0.432647\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.5051i | 1.83503i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.18872 | − | 1.96097i | 0.849130 | − | 0.203343i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.73205 | + | 3.00000i | 0.177705 | + | 0.307794i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.06108 | + | 5.30195i | −0.310806 | + | 0.538332i | −0.978537 | − | 0.206071i | \(-0.933932\pi\) |
0.667731 | + | 0.744403i | \(0.267266\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.92925 | − | 15.6062i | −0.796919 | − | 1.56848i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0051 | + | 5.77643i | 0.995541 | + | 0.574776i | 0.906926 | − | 0.421290i | \(-0.138423\pi\) |
0.0886151 | + | 0.996066i | \(0.471756\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.110533 | + | 0.191448i | 0.0108911 | + | 0.0188639i | 0.871420 | − | 0.490538i | \(-0.163200\pi\) |
−0.860528 | + | 0.509402i | \(0.829867\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.5237 | − | 3.71751i | −1.22219 | − | 0.362792i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 0.329957i | − | 0.0318982i | −0.999873 | − | 0.0159491i | \(-0.994923\pi\) | ||
0.999873 | − | 0.0159491i | \(-0.00507697\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.9253i | 1.71693i | 0.512873 | + | 0.858465i | \(0.328581\pi\) | ||||
−0.512873 | + | 0.858465i | \(0.671419\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.55077 | + | 2.83502i | 0.906519 | + | 0.269088i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.04241 | + | 15.6619i | 0.850638 | + | 1.47335i | 0.880633 | + | 0.473799i | \(0.157118\pi\) |
−0.0299946 | + | 0.999550i | \(0.509549\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.96368 | − | 5.75253i | −0.929118 | − | 0.536426i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.0424 | + | 0.644960i | 1.11332 | + | 0.0596266i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.71751 | − | 6.43892i | 0.340784 | − | 0.590254i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.5237 | + | 19.9597i | 1.04761 | + | 1.81452i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.17731 | − | 0.521405i | 0.196321 | − | 0.0470135i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.57568 | 0.406026 | 0.203013 | − | 0.979176i | \(-0.434927\pi\) | ||||
0.203013 | + | 0.979176i | \(0.434927\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.45305 | − | 4.22094i | 0.392069 | − | 0.371633i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.7281 | − | 6.77121i | 1.02469 | − | 0.591603i | 0.109228 | − | 0.994017i | \(-0.465162\pi\) |
0.915458 | + | 0.402414i | \(0.131829\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.54241 | + | 4.35461i | 0.654010 | + | 0.377593i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.01885 | + | 8.47859i | −0.259821 | + | 0.729721i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.1887 | − | 19.3794i | 0.955917 | − | 1.65570i | 0.223660 | − | 0.974667i | \(-0.428200\pi\) |
0.732257 | − | 0.681029i | \(-0.238467\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.99602 | + | 5.77121i | −0.847851 | + | 0.489507i | −0.859925 | − | 0.510420i | \(-0.829490\pi\) |
0.0120739 | + | 0.999927i | \(0.496157\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.6463 | − | 13.3417i | −1.06501 | − | 1.12358i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.4561 | −1.96150 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.12217 | −0.674509 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −20.1502 | + | 4.82542i | −1.66196 | + | 0.397994i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.93892 | − | 1.11943i | 0.158842 | − | 0.0917076i | −0.418472 | − | 0.908230i | \(-0.637434\pi\) |
0.577314 | + | 0.816522i | \(0.304101\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.51738 | + | 14.7525i | −0.693134 | + | 1.20054i | 0.277671 | + | 0.960676i | \(0.410437\pi\) |
−0.970806 | + | 0.239868i | \(0.922896\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.29261 | − | 2.79466i | −0.347037 | − | 0.225935i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.29214 | + | 4.21012i | 0.585719 | + | 0.338165i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.0424108 | − | 0.0244859i | 0.00338475 | − | 0.00195419i | −0.498307 | − | 0.867001i | \(-0.666045\pi\) |
0.501691 | + | 0.865047i | \(0.332711\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.841540 | + | 0.249800i | 0.0667384 | + | 0.0198104i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −28.9253 | −2.27963 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 19.0848i | − | 1.49484i | −0.664353 | − | 0.747419i | \(-0.731293\pi\) | ||
0.664353 | − | 0.747419i | \(-0.268707\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.98133 | − | 16.7813i | 0.387796 | − | 1.30643i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.99602 | + | 17.3136i | 0.773515 | + | 1.33977i | 0.935625 | + | 0.352995i | \(0.114837\pi\) |
−0.162110 | + | 0.986773i | \(0.551830\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.57976 | − | 2.73622i | 0.121520 | − | 0.210478i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.27360 | − | 5.02827i | 0.250339 | − | 0.384522i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.5000 | − | 6.06218i | −0.798300 | − | 0.460899i | 0.0445762 | − | 0.999006i | \(-0.485806\pi\) |
−0.842876 | + | 0.538107i | \(0.819140\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.35461 | + | 7.54241i | 0.329178 | + | 0.570153i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.755264 | + | 3.15386i | 0.0567691 | + | 0.237059i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00000i | 0.448461i | 0.974536 | + | 0.224231i | \(0.0719869\pi\) | ||||
−0.974536 | + | 0.224231i | \(0.928013\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 5.75194i | − | 0.427538i | −0.976884 | − | 0.213769i | \(-0.931426\pi\) | ||
0.976884 | − | 0.213769i | \(-0.0685740\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.54020 | − | 1.45992i | 0.113855 | − | 0.107921i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.98133 | + | 8.62791i | 0.366234 | + | 0.634337i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.62791 | + | 4.98133i | 0.630935 | + | 0.364271i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.08522 | + | 22.2554i | 0.297156 | + | 1.61884i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.110533 | + | 0.191448i | −0.00799786 | + | 0.0138527i | −0.869997 | − | 0.493058i | \(-0.835879\pi\) |
0.861999 | + | 0.506910i | \(0.169212\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.02374 | − | 15.6296i | −0.649543 | − | 1.12504i | −0.983232 | − | 0.182358i | \(-0.941627\pi\) |
0.333689 | − | 0.942683i | \(-0.391706\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.29631 | + | 8.75253i | 0.594111 | + | 0.626782i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.82080i | − | 0.699703i | −0.936805 | − | 0.349852i | \(-0.886232\pi\) | ||
0.936805 | − | 0.349852i | \(-0.113768\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.604760 | −0.0428703 | −0.0214352 | − | 0.999770i | \(-0.506824\pi\) | ||||
−0.0214352 | + | 0.999770i | \(0.506824\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.637233 | − | 2.66098i | −0.0449469 | − | 0.187691i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.6844 | + | 10.2101i | −1.24120 | + | 0.716610i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.93892 | + | 1.11943i | 0.135420 | + | 0.0781846i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.06573 | + | 19.8988i | −0.0740734 | + | 1.38306i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.83502 | + | 10.1066i | −0.403617 | + | 0.699085i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.363941 | − | 0.210121i | 0.0250547 | − | 0.0144654i | −0.487420 | − | 0.873167i | \(-0.662062\pi\) |
0.512475 | + | 0.858702i | \(0.328729\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.87237 | + | 16.4143i | −0.333849 | + | 1.12469i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.13564 | 0.418447 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.1696 | 1.43709 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.92464 | + | 13.2215i | −0.265203 | + | 0.893428i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.94398 | + | 3.43176i | −0.399835 | + | 0.230845i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.3933 | − | 19.7339i | 0.762955 | − | 1.32148i | −0.178366 | − | 0.983964i | \(-0.557081\pi\) |
0.941321 | − | 0.337513i | \(-0.109586\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.34916 | − | 2.71781i | 0.356611 | − | 0.181188i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.2494 | − | 5.91751i | −0.680279 | − | 0.392759i | 0.119681 | − | 0.992812i | \(-0.461813\pi\) |
−0.799960 | + | 0.600053i | \(0.795146\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.5848 | + | 7.84320i | −0.897710 | + | 0.518293i | −0.876457 | − | 0.481481i | \(-0.840099\pi\) |
−0.0212537 | + | 0.999774i | \(0.506766\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.2494 | − | 42.8000i | −0.674363 | − | 2.81603i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.829557 | −0.0543461 | −0.0271731 | − | 0.999631i | \(-0.508651\pi\) | ||||
−0.0271731 | + | 0.999631i | \(0.508651\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 18.3829i | − | 1.19917i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.46265 | − | 2.59808i | −0.159967 | − | 0.168763i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.60698 | + | 6.24747i | 0.233316 | + | 0.404115i | 0.958782 | − | 0.284143i | \(-0.0917090\pi\) |
−0.725466 | + | 0.688258i | \(0.758376\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.4627 | − | 18.1218i | 0.673959 | − | 1.16733i | −0.302813 | − | 0.953050i | \(-0.597926\pi\) |
0.976772 | − | 0.214281i | \(-0.0687408\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.4609 | − | 1.99040i | 0.991815 | − | 0.127684i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.9440 | − | 10.3600i | −1.14640 | − | 0.661874i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.01989 | − | 6.96265i | −0.255779 | − | 0.443023i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.93892 | + | 1.83785i | −0.122874 | + | 0.116469i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 20.2553i | − | 1.27850i | −0.768999 | − | 0.639250i | \(-0.779245\pi\) | ||
0.768999 | − | 0.639250i | \(-0.220755\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 38.7588i | − | 2.43675i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.19289 | − | 4.98133i | −0.0747018 | − | 0.311943i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.37237 | + | 5.84111i | 0.210363 | + | 0.364359i | 0.951828 | − | 0.306632i | \(-0.0992022\pi\) |
−0.741465 | + | 0.670991i | \(0.765869\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.6917 | + | 12.5237i | 1.34786 | + | 0.778187i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.37237 | + | 12.5420i | 0.394440 | + | 0.776330i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.2067 | − | 22.8747i | 0.814361 | − | 1.41051i | −0.0954250 | − | 0.995437i | \(-0.530421\pi\) |
0.909786 | − | 0.415078i | \(-0.136246\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.438916 | + | 0.760225i | 0.0269624 | + | 0.0467002i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.95312 | − | 6.57976i | 0.119529 | − | 0.402675i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.1704i | 1.41272i | 0.707851 | + | 0.706362i | \(0.249665\pi\) | ||||
−0.707851 | + | 0.706362i | \(0.750335\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.7626 | −1.07900 | −0.539502 | − | 0.841984i | \(-0.681387\pi\) | ||||
−0.539502 | + | 0.841984i | \(0.681387\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 29.0661 | + | 8.62791i | 1.75916 | + | 0.522185i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.1066 | + | 5.83502i | −0.609448 | + | 0.351865i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.04241 | − | 5.22064i | −0.543306 | − | 0.313678i | 0.203112 | − | 0.979156i | \(-0.434894\pi\) |
−0.746418 | + | 0.665478i | \(0.768228\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.779979 | − | 14.5634i | 0.0466961 | − | 0.871889i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.4440 | − | 23.2857i | 0.802001 | − | 1.38911i | −0.116297 | − | 0.993215i | \(-0.537102\pi\) |
0.918297 | − | 0.395891i | \(-0.129564\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.1317 | − | 9.31362i | 0.958927 | − | 0.553637i | 0.0630847 | − | 0.998008i | \(-0.479906\pi\) |
0.895843 | + | 0.444371i | \(0.146573\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.83502 | − | 1.39733i | 0.345637 | − | 0.0827706i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.62882 | 0.332259 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0848 | −0.828519 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.29484 | + | 7.69598i | 0.427631 | + | 0.451147i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.00506 | + | 0.580274i | −0.0587165 | + | 0.0339000i | −0.529071 | − | 0.848578i | \(-0.677459\pi\) |
0.470354 | + | 0.882478i | \(0.344126\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.62152 | + | 2.80855i | −0.0944084 | + | 0.163520i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −29.8214 | + | 5.47405i | −1.73041 | + | 0.317636i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 23.1245 | + | 13.3510i | 1.33733 | + | 0.772106i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.3592 | − | 7.71291i | 0.770009 | − | 0.444565i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.5227 | − | 13.7657i | 0.834309 | − | 0.790821i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.12217 | 0.121515 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.0848i | 1.08923i | 0.838687 | + | 0.544614i | \(0.183324\pi\) | ||||
−0.838687 | + | 0.544614i | \(0.816676\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.372368 | − | 0.0891719i | 0.0211833 | − | 0.00507281i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.56009 | + | 9.63036i | 0.315284 | + | 0.546088i | 0.979498 | − | 0.201455i | \(-0.0645669\pi\) |
−0.664214 | + | 0.747543i | \(0.731234\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.4627 | + | 23.3180i | −0.760954 | + | 1.31801i | 0.181405 | + | 0.983408i | \(0.441935\pi\) |
−0.942359 | + | 0.334603i | \(0.891398\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.3454 | + | 18.9627i | −0.695586 | + | 1.06842i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.4440 | − | 11.2260i | −1.09208 | − | 0.630514i | −0.157953 | − | 0.987447i | \(-0.550489\pi\) |
−0.934130 | + | 0.356932i | \(0.883823\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.6812 | − | 23.6965i | −0.765999 | − | 1.32675i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.547875 | − | 0.162630i | −0.0305794 | − | 0.00907710i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.41478i | 0.190003i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 8.03978i | − | 0.445967i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 29.7639 | + | 8.83502i | 1.64595 | + | 0.488578i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −23.1086 | − | 40.0252i | −1.27402 | − | 2.20666i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.5634 | − | 11.2949i | −1.07530 | − | 0.620826i | −0.145677 | − | 0.989332i | \(-0.546536\pi\) |
−0.929625 | + | 0.368506i | \(0.879869\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.41478 | − | 14.4612i | 0.515927 | − | 0.792467i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.36811 | − | 2.36964i | 0.0747478 | − | 0.129467i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.04241 | + | 12.1978i | 0.383625 | + | 0.664457i | 0.991577 | − | 0.129516i | \(-0.0413423\pi\) |
−0.607953 | + | 0.793973i | \(0.708009\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 30.4625 | − | 7.29494i | 1.65450 | − | 0.396207i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.3665i | 1.53613i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −21.6104 | −1.16685 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −14.4627 | + | 13.7088i | −0.778643 | + | 0.738057i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.05745 | + | 3.49727i | −0.325181 | + | 0.187743i | −0.653699 | − | 0.756754i | \(-0.726784\pi\) |
0.328519 | + | 0.944497i | \(0.393451\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.16458 | − | 4.71382i | −0.437040 | − | 0.252325i | 0.265301 | − | 0.964166i | \(-0.414529\pi\) |
−0.702341 | + | 0.711840i | \(0.747862\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.00639 | − | 19.6778i | 0.373974 | − | 1.05033i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.81128 | − | 6.60134i | 0.202854 | − | 0.351354i | −0.746593 | − | 0.665281i | \(-0.768312\pi\) |
0.949447 | + | 0.313928i | \(0.101645\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.8282 | + | 8.56108i | −0.787001 | + | 0.454375i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.85916 | − | 9.34633i | −0.468876 | − | 0.494660i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.8344 | −0.571820 | −0.285910 | − | 0.958257i | \(-0.592296\pi\) | ||||
−0.285910 | + | 0.958257i | \(0.592296\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 38.8218 | − | 9.29675i | 2.03761 | − | 0.487953i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.9440 | + | 6.89586i | −0.625176 | + | 0.360946i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.4747 | + | 19.8747i | −0.598973 | + | 1.03745i | 0.394000 | + | 0.919110i | \(0.371091\pi\) |
−0.992973 | + | 0.118341i | \(0.962243\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.207389 | − | 3.87228i | 0.0107963 | − | 0.201583i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.91131 | + | 1.10349i | 0.0992302 | + | 0.0572906i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.0984305 | + | 0.0568289i | −0.00509654 | + | 0.00294249i | −0.502546 | − | 0.864550i | \(-0.667603\pi\) |
0.497450 | + | 0.867493i | \(0.334270\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.1318 | + | 5.97586i | 1.03960 | + | 0.308592i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.8506 | 0.970856 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 16.2070i | − | 0.832497i | −0.909251 | − | 0.416249i | \(-0.863345\pi\) | ||
0.909251 | − | 0.416249i | \(-0.136655\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.25526 | − | 7.59765i | 0.115541 | − | 0.389239i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.03874 | + | 12.1914i | 0.359663 | + | 0.622954i | 0.987904 | − | 0.155064i | \(-0.0495585\pi\) |
−0.628242 | + | 0.778018i | \(0.716225\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 22.0051 | − | 38.1139i | 1.12148 | − | 1.94246i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.81380 | − | 9.47446i | −0.244699 | − | 0.481614i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.0051 | − | 14.4367i | −1.26781 | − | 0.731969i | −0.293234 | − | 0.956041i | \(-0.594732\pi\) |
−0.974573 | + | 0.224072i | \(0.928065\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.67063 | − | 9.82181i | −0.286776 | − | 0.496710i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.46265 | − | 22.8112i | −0.275554 | − | 1.15067i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 3.57976i | − | 0.180117i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.85934i | 0.143506i | 0.997422 | + | 0.0717531i | \(0.0228594\pi\) | ||||
−0.997422 | + | 0.0717531i | \(0.977141\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.9481 | − | 10.3774i | 0.548090 | − | 0.519521i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.7739 | − | 18.6610i | −0.538025 | − | 0.931886i | −0.999010 | − | 0.0444786i | \(-0.985837\pi\) |
0.460986 | − | 0.887408i | \(-0.347496\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.9242 | − | 9.77121i | −0.843056 | − | 0.486738i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.5903 | + | 9.19156i | 0.625616 | + | 0.456732i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.7813 | + | 29.0661i | −0.831821 | + | 1.44076i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.4627 | + | 18.1218i | 0.517345 | + | 0.896068i | 0.999797 | + | 0.0201454i | \(0.00641290\pi\) |
−0.482452 | + | 0.875922i | \(0.660254\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −26.6637 | − | 28.1300i | −1.31522 | − | 1.38755i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.15344i | 0.401204i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.67153 | −0.131140 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.65591 | + | 19.4423i | 0.228001 | + | 0.952095i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.9678 | + | 6.33229i | −0.535814 | + | 0.309353i | −0.743381 | − | 0.668868i | \(-0.766779\pi\) |
0.207567 | + | 0.978221i | \(0.433446\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.1086 | − | 13.3417i | −1.12624 | − | 0.650236i | −0.183255 | − | 0.983065i | \(-0.558663\pi\) |
−0.942987 | + | 0.332829i | \(0.891997\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −28.3863 | + | 14.4226i | −1.38019 | + | 0.701250i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.70739 | + | 2.95729i | −0.0828205 | + | 0.143449i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.62061 | − | 2.66771i | 0.223607 | − | 0.129100i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.5611 | + | 38.9476i | −0.558174 | + | 1.88041i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.6772 | 1.14049 | 0.570246 | − | 0.821474i | \(-0.306848\pi\) | ||||
0.570246 | + | 0.821474i | \(0.306848\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.96265 | 0.382661 | 0.191330 | − | 0.981526i | \(-0.438720\pi\) | ||||
0.191330 | + | 0.981526i | \(0.438720\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.00326 | + | 13.4864i | −0.191942 | + | 0.646623i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.5051 | − | 6.64245i | 0.550362 | − | 0.317752i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.33903 | − | 9.24747i | 0.254818 | − | 0.441358i | −0.710028 | − | 0.704173i | \(-0.751318\pi\) |
0.964846 | + | 0.262816i | \(0.0846511\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.91932 | + | 35.8366i | −0.0913960 | + | 1.70650i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.1566 | − | 6.44125i | −0.530065 | − | 0.306033i | 0.210978 | − | 0.977491i | \(-0.432335\pi\) |
−0.741043 | + | 0.671458i | \(0.765668\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.94398 | − | 3.43176i | 0.281772 | − | 0.162681i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.903100 | − | 3.77121i | −0.0427152 | − | 0.178372i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.547875 | −0.0258558 | −0.0129279 | − | 0.999916i | \(-0.504115\pi\) | ||||
−0.0129279 | + | 0.999916i | \(0.504115\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.54241i | 0.355158i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.2977 | + | 21.4139i | 0.953668 | + | 1.00611i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.1598 | + | 26.2576i | 0.710704 | + | 1.23098i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.90157 | + | 17.1500i | −0.463176 | + | 0.802244i | −0.999117 | − | 0.0420111i | \(-0.986624\pi\) |
0.535941 | + | 0.844255i | \(0.319957\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.75611 | + | 5.75020i | −0.315348 | + | 0.268396i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.1833 | + | 7.03400i | 0.567431 | + | 0.327606i | 0.756122 | − | 0.654430i | \(-0.227091\pi\) |
−0.188692 | + | 0.982036i | \(0.560425\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.22954 | + | 10.7899i | 0.289511 | + | 0.501448i | 0.973693 | − | 0.227863i | \(-0.0731739\pi\) |
−0.684182 | + | 0.729311i | \(0.739841\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.5848 | − | 10.0331i | 0.490859 | − | 0.465274i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.3401i | 1.35770i | 0.734278 | + | 0.678849i | \(0.237521\pi\) | ||||
−0.734278 | + | 0.678849i | \(0.762479\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 6.87923i | − | 0.317653i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.0197539 | − | 0.0824893i | −0.000910213 | − | 0.00380091i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.3350 | + | 17.9008i | 0.475205 | + | 0.823079i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.46410 | − | 2.00000i | −0.158944 | − | 0.0917663i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.829557 | − | 1.27421i | 0.0379828 | − | 0.0583419i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.96368 | + | 17.2576i | −0.455252 | + | 0.788520i | −0.998703 | − | 0.0509214i | \(-0.983784\pi\) |
0.543451 | + | 0.839441i | \(0.317118\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.5611 | − | 20.0244i | −0.527140 | − | 0.913033i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.2567 | + | 48.0288i | −0.648704 | + | 2.18539i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.6039i | 0.481499i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.46828 | 0.338420 | 0.169210 | − | 0.985580i | \(-0.445878\pi\) | ||||
0.169210 | + | 0.985580i | \(0.445878\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −31.6892 | − | 9.40654i | −1.43304 | − | 0.425379i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.2186 | + | 17.4467i | −1.36375 | + | 0.787359i | −0.990120 | − | 0.140220i | \(-0.955219\pi\) |
−0.373626 | + | 0.927580i | \(0.621886\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.93385 | − | 4.00326i | −0.312285 | − | 0.180298i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −25.4093 | − | 16.5424i | −1.14206 | − | 0.743526i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21.5237 | + | 37.2802i | −0.965472 | + | 1.67225i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.4480 | − | 18.7339i | 1.45257 | − | 0.838643i | 0.453945 | − | 0.891030i | \(-0.350016\pi\) |
0.998627 | + | 0.0523870i | \(0.0166830\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 33.6751 | − | 8.06427i | 1.50449 | − | 0.360285i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.8991 | −0.485968 | −0.242984 | − | 0.970030i | \(-0.578126\pi\) | ||||
−0.242984 | + | 0.970030i | \(0.578126\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.0101 | 0.890439 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.76470 | − | 3.97173i | −0.167196 | − | 0.176391i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.06108 | + | 2.34467i | −0.180004 | + | 0.103926i | −0.587295 | − | 0.809373i | \(-0.699807\pi\) |
0.407290 | + | 0.913299i | \(0.366474\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.3371 | + | 30.0288i | −0.766950 | + | 1.32840i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.73566 | − | 7.91396i | −0.297387 | − | 0.349410i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.331598 | + | 0.191448i | 0.0146119 | + | 0.00843621i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 53.6323 | − | 30.9646i | 2.35875 | − | 1.36182i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.2411 | + | 14.4467i | −0.669012 | + | 0.634140i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.4249 | −1.15770 | −0.578848 | − | 0.815435i | \(-0.696498\pi\) | ||||
−0.578848 | + | 0.815435i | \(0.696498\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 13.8880i | − | 0.607278i | −0.952787 | − | 0.303639i | \(-0.901798\pi\) | ||
0.952787 | − | 0.303639i | \(-0.0982017\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.6700 | − | 3.51307i | 0.640253 | − | 0.153323i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.15018 | + | 7.18832i | 0.180785 | + | 0.313128i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.5611 | + | 18.2923i | −0.459178 | + | 0.795319i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.60907 | + | 0.300407i | 0.243413 | + | 0.0130366i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.50000 | − | 2.59808i | −0.194917 | − | 0.112535i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.285751 | − | 0.494936i | −0.0123541 | − | 0.0213979i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.96265 | + | 2.95729i | 0.429920 | + | 0.127616i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 69.8023i | − | 3.00660i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.0161i | 1.07553i | 0.843096 | + | 0.537763i | \(0.180731\pi\) | ||||
−0.843096 | + | 0.537763i | \(0.819269\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.55077 | − | 2.83502i | −0.409863 | − | 0.121662i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.5237 | + | 26.8879i | 0.664964 | + | 1.15175i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.4236 | + | 7.17277i | 0.531195 | + | 0.306686i | 0.741503 | − | 0.670950i | \(-0.234113\pi\) |
−0.210308 | + | 0.977635i | \(0.567447\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.66498 | − | 3.27699i | −0.0710596 | − | 0.139858i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.68934 | − | 8.12217i | 0.199772 | − | 0.346016i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.50000 | − | 7.79423i | −0.191359 | − | 0.331444i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16.7813 | − | 4.01867i | 0.712329 | − | 0.170583i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 32.9912i | − | 1.39788i | −0.715179 | − | 0.698941i | \(-0.753655\pi\) | ||
0.715179 | − | 0.698941i | \(-0.246345\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.2401 | −0.602292 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.5237 | − | 11.8709i | 0.528753 | − | 0.501192i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.6459 | − | 12.4973i | 0.912266 | − | 0.526697i | 0.0311065 | − | 0.999516i | \(-0.490097\pi\) |
0.881160 | + | 0.472819i | \(0.156764\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.1272 | + | 15.6619i | 1.14125 | + | 0.658902i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 38.9673 | + | 4.18598i | 1.63647 | + | 0.175795i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.79261 | − | 4.83694i | 0.117072 | − | 0.202775i | −0.801534 | − | 0.597949i | \(-0.795982\pi\) |
0.918606 | + | 0.395174i | \(0.129316\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.83221 | − | 2.78988i | 0.202222 | − | 0.116753i | −0.395470 | − | 0.918479i | \(-0.629418\pi\) |
0.597691 | + | 0.801726i | \(0.296085\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.263409 | + | 0.277894i | 0.0110041 | + | 0.0116092i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.2849 | 0.554019 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.04748 | −0.376651 | −0.188326 | − | 0.982107i | \(-0.560306\pi\) | ||||
−0.188326 | + | 0.982107i | \(0.560306\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −30.3996 | + | 7.27988i | −1.26337 | + | 0.302541i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.81675 | + | 3.35830i | −0.241319 | + | 0.139326i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.47864 | + | 2.56108i | −0.0612391 | + | 0.106069i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.6222 | − | 9.46159i | 0.769932 | − | 0.391189i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.24617 | − | 3.60623i | −0.257807 | − | 0.148845i | 0.365527 | − | 0.930801i | \(-0.380889\pi\) |
−0.623334 | + | 0.781956i | \(0.714222\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.42024 | + | 4.86143i | −0.346950 | + | 0.200312i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.3069 | − | 4.84049i | −0.670775 | − | 0.199111i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.0475 | −1.02858 | −0.514288 | − | 0.857617i | \(-0.671944\pi\) | ||||
−0.514288 | + | 0.857617i | \(0.671944\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 12.8778i | − | 0.527940i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.298075 | + | 1.00417i | −0.0121994 | + | 0.0410979i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.1026 | − | 34.8187i | −0.821369 | − | 1.42265i | −0.904663 | − | 0.426128i | \(-0.859877\pi\) |
0.0832941 | − | 0.996525i | \(-0.473456\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.48133 | − | 9.49394i | 0.223588 | − | 0.387266i | −0.732307 | − | 0.680975i | \(-0.761556\pi\) |
0.955895 | + | 0.293709i | \(0.0948897\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.73249 | − | 0.253460i | −0.192722 | − | 0.0103217i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 34.5712 | + | 19.9597i | 1.40552 | + | 0.811477i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.2370 | + | 24.6592i | 0.577861 | + | 1.00088i | 0.995724 | + | 0.0923747i | \(0.0294458\pi\) |
−0.417863 | + | 0.908510i | \(0.637221\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.23699 | + | 34.3964i | 0.333780 | + | 1.39381i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 42.6646i | 1.72602i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.3632i | 0.580125i | 0.957008 | + | 0.290063i | \(0.0936761\pi\) | ||||
−0.957008 | + | 0.290063i | \(0.906324\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.81441 | − | 2.66771i | 0.113488 | − | 0.107572i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.316348 | + | 0.547931i | 0.0127357 | + | 0.0220589i | 0.872323 | − | 0.488930i | \(-0.162613\pi\) |
−0.859587 | + | 0.510989i | \(0.829279\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.9516 | − | 16.7152i | −1.16366 | − | 0.671840i | −0.211482 | − | 0.977382i | \(-0.567829\pi\) |
−0.952179 | + | 0.305542i | \(0.901162\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 32.5156 | + | 11.5773i | 1.30481 | + | 0.464583i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.62791 | − | 14.9440i | 0.345670 | − | 0.598718i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.9054 | + | 14.6700i | 0.555327 | + | 0.585865i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.82080i | 0.391581i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.59765 | 0.302458 | 0.151229 | − | 0.988499i | \(-0.451677\pi\) | ||||
0.151229 | + | 0.988499i | \(0.451677\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.169515 | − | 0.707868i | −0.00673761 | − | 0.0281352i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.86352 | − | 3.96265i | 0.272370 | − | 0.157253i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 41.6459 | + | 24.0443i | 1.65007 | + | 0.952669i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.8535 | + | 16.1806i | 0.983188 | + | 0.640094i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.8774 | − | 20.5723i | 0.469130 | − | 0.812558i | −0.530247 | − | 0.847843i | \(-0.677901\pi\) |
0.999377 | + | 0.0352856i | \(0.0112341\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.4236 | + | 7.17277i | −0.489939 | + | 0.282867i | −0.724549 | − | 0.689223i | \(-0.757952\pi\) |
0.234610 | + | 0.972090i | \(0.424619\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.02414 | − | 10.1879i | 0.119075 | − | 0.401147i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.5781 | −1.12352 | −0.561761 | − | 0.827299i | \(-0.689876\pi\) | ||||
−0.561761 | + | 0.827299i | \(0.689876\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.9253 | −0.428856 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.4341 | − | 35.1510i | 0.408945 | − | 1.37768i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.7443 | + | 8.51265i | −0.576990 | + | 0.333126i | −0.759936 | − | 0.649997i | \(-0.774770\pi\) |
0.182946 | + | 0.983123i | \(0.441437\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.7281 | − | 20.3136i | 0.458254 | − | 0.793719i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.0192 | + | 13.0333i | 0.781023 | + | 0.508476i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.8209 | − | 6.24747i | −0.421524 | − | 0.243367i | 0.274205 | − | 0.961671i | \(-0.411585\pi\) |
−0.695729 | + | 0.718304i | \(0.744919\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.1272 | + | 17.3940i | −1.17181 | + | 0.676547i | −0.954107 | − | 0.299467i | \(-0.903191\pi\) |
−0.217707 | + | 0.976014i | \(0.569858\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.76856 | + | 11.5611i | 0.107522 | + | 0.448995i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.0848 | 0.584964 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.1487i | 1.20608i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.1514 | − | 28.6444i | −1.04973 | − | 1.10746i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.57463 | + | 6.19145i | 0.137997 | + | 0.239018i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.0237 | + | 22.5578i | −0.502028 | + | 0.869538i | 0.497969 | + | 0.867195i | \(0.334079\pi\) |
−0.999997 | + | 0.00234354i | \(0.999254\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.87627 | − | 10.2215i | −0.0722178 | − | 0.393427i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.8829 | + | 16.6755i | 1.11006 | + | 0.640893i | 0.938845 | − | 0.344340i | \(-0.111897\pi\) |
0.171215 | + | 0.985234i | \(0.445231\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.3298 | + | 23.0880i | 0.511552 | + | 0.886034i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.8774 | + | 14.1020i | −0.570104 | + | 0.540388i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.4249i | 1.01112i | 0.862791 | + | 0.505560i | \(0.168714\pi\) | ||||
−0.862791 | + | 0.505560i | \(0.831286\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 38.7588i | − | 1.48090i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.32748 | + | 26.4226i | 0.241409 | + | 1.00808i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.01867 | − | 1.76439i | −0.0388084 | − | 0.0672181i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.6521 | − | 10.1914i | −0.671518 | − | 0.387701i | 0.125134 | − | 0.992140i | \(-0.460064\pi\) |
−0.796651 | + | 0.604439i | \(0.793397\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −76.1187 | − | 4.07672i | −2.89151 | − | 0.154862i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.99602 | + | 17.3136i | −0.379171 | + | 0.656743i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.10349 | + | 1.91131i | 0.0417978 | + | 0.0723960i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.408873 | + | 1.37743i | −0.0154650 | + | 0.0520993i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 49.8696i | − | 1.88355i | −0.336247 | − | 0.941774i | \(-0.609158\pi\) | ||
0.336247 | − | 0.941774i | \(-0.390842\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.5039 | −0.433877 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −30.5237 | − | 9.06058i | −1.14959 | − | 0.341241i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 43.5682 | − | 25.1541i | 1.63855 | − | 0.946017i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.57469 | − | 4.95060i | −0.322029 | − | 0.185924i | 0.330267 | − | 0.943887i | \(-0.392861\pi\) |
−0.652297 | + | 0.757964i | \(0.726194\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.52775 | + | 2.80855i | −0.207307 | + | 0.105329i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.1459 | − | 27.9655i | 0.604669 | − | 1.04732i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −35.1842 | + | 20.3136i | −1.31582 | + | 0.759686i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.1514 | − | 2.90992i | 0.453801 | − | 0.108673i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.5562 | −0.953084 | −0.476542 | − | 0.879152i | \(-0.658110\pi\) | ||||
−0.476542 | + | 0.879152i | \(0.658110\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.962653 | 0.0358511 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.9334 | − | 26.3045i | −0.927285 | − | 0.978277i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.12217 | − | 4.68934i | 0.301650 | − | 0.174158i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.0702 | − | 34.7627i | 0.744364 | − | 1.28928i | −0.206128 | − | 0.978525i | \(-0.566086\pi\) |
0.950491 | − | 0.310751i | \(-0.100580\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.31542 | − | 26.6529i | 0.159830 | − | 0.987144i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.23796 | + | 3.02414i | 0.193733 | + | 0.111852i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.9965 | + | 23.6694i | −1.51424 | + | 0.874247i | −0.514380 | + | 0.857562i | \(0.671978\pi\) |
−0.999861 | + | 0.0166852i | \(0.994689\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −26.0464 | + | 24.6887i | −0.960735 | + | 0.910657i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.21792 | 0.339546 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.9627i | 1.39648i | 0.715864 | + | 0.698239i | \(0.246033\pi\) | ||||
−0.715864 | + | 0.698239i | \(0.753967\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.5424 | + | 3.24304i | −0.497493 | + | 0.119136i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.25980 | − | 12.5743i | −0.266336 | − | 0.461308i | 0.701577 | − | 0.712594i | \(-0.252480\pi\) |
−0.967913 | + | 0.251286i | \(0.919146\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.93892 | − | 3.35830i | 0.0710364 | − | 0.123039i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.09599 | + | 4.12530i | 0.0766883 | + | 0.150937i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.24434 | − | 0.718418i | −0.0454671 | − | 0.0262504i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.3216 | − | 31.7339i | −0.668563 | − | 1.15798i | −0.978306 | − | 0.207165i | \(-0.933576\pi\) |
0.309743 | − | 0.950820i | \(-0.399757\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −33.6327 | − | 9.98343i | −1.22564 | − | 0.363816i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29.5051i | 1.07380i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.02727i | 0.0736822i | 0.999321 | + | 0.0368411i | \(0.0117295\pi\) | ||||
−0.999321 | + | 0.0368411i | \(0.988270\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −64.3568 | − | 19.1035i | −2.33600 | − | 0.693413i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.60349 | + | 14.9017i | 0.311876 | + | 0.540186i | 0.978769 | − | 0.204968i | \(-0.0657092\pi\) |
−0.666892 | + | 0.745154i | \(0.732376\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 67.5999 | + | 39.0288i | 2.44728 | + | 1.41294i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.85916 | − | 0.474473i | −0.320304 | − | 0.0171546i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.76336 | − | 6.51832i | 0.135887 | − | 0.235363i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.4253 | − | 23.2533i | −0.484129 | − | 0.838536i | 0.515705 | − | 0.856766i | \(-0.327530\pi\) |
−0.999834 | + | 0.0182304i | \(0.994197\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.3610 | − | 2.72065i | 0.409157 | − | 0.0979818i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.41305i | 0.158726i | 0.996846 | + | 0.0793632i | \(0.0252887\pi\) | ||||
−0.996846 | + | 0.0793632i | \(0.974711\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.72286 | −0.349255 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 31.4864 | − | 29.8452i | 1.12957 | − | 1.07069i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.23887 | + | 1.29261i | −0.0802157 | + | 0.0463126i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −49.9541 | − | 28.8410i | −1.78750 | − | 1.03201i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 23.9661 | − | 4.39924i | 0.856478 | − | 0.157216i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.0424108 | − | 0.0734576i | 0.00151371 | − | 0.00262182i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.7765 | + | 17.1914i | −1.06142 | + | 0.612809i | −0.925824 | − | 0.377956i | \(-0.876627\pi\) |
−0.135593 | + | 0.990765i | \(0.543294\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −31.4728 | − | 33.2035i | −1.12046 | − | 1.18208i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 78.7524 | 2.80011 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.92531 | −0.174903 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.47864 | − | 0.354094i | 0.0524420 | − | 0.0125584i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.8269 | − | 11.4471i | 0.702304 | − | 0.405475i | −0.105901 | − | 0.994377i | \(-0.533773\pi\) |
0.808205 | + | 0.588901i | \(0.200439\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.06058 | − | 15.6934i | 0.320540 | − | 0.555192i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.96265 | − | 6.48607i | −0.352013 | − | 0.229174i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −40.2375 | − | 23.2311i | −1.41995 | − | 0.819809i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −43.3880 | + | 25.0501i | −1.52922 | + | 0.882898i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 38.4731 | + | 11.4202i | 1.35432 | + | 0.402012i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34.7922 | 1.22323 | 0.611614 | − | 0.791156i | \(-0.290520\pi\) | ||||
0.611614 | + | 0.791156i | \(0.290520\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 11.6810i | − | 0.410174i | −0.978744 | − | 0.205087i | \(-0.934252\pi\) | ||
0.978744 | − | 0.205087i | \(-0.0657478\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.75486 | + | 29.4938i | −0.307047 | + | 1.03439i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.5279 | − | 28.6272i | −0.578948 | − | 1.00277i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.54241 | + | 6.13564i | −0.123933 | + | 0.214659i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 28.6523 | − | 44.0101i | 1.00119 | − | 1.53784i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.9389 | + | 8.04764i | 0.486472 | + | 0.280864i | 0.723109 | − | 0.690733i | \(-0.242712\pi\) |
−0.236638 | + | 0.971598i | \(0.576046\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.40163 | + | 11.0880i | 0.223147 | + | 0.386502i | 0.955762 | − | 0.294142i | \(-0.0950337\pi\) |
−0.732615 | + | 0.680643i | \(0.761700\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.70739 | + | 19.6573i | 0.163890 | + | 0.684380i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 25.9253i | − | 0.901511i | −0.892647 | − | 0.450756i | \(-0.851155\pi\) | ||
0.892647 | − | 0.450756i | \(-0.148845\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 49.0708i | 1.70430i | 0.523299 | + | 0.852149i | \(0.324701\pi\) | ||||
−0.523299 | + | 0.852149i | \(0.675299\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.1254 | + | 12.4412i | −0.455315 | + | 0.431582i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.2125 | − | 17.6885i | −0.353841 | − | 0.612870i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.9881 | + | 17.3136i | 1.03778 | + | 0.599162i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.7973 | − | 8.47314i | −0.822554 | − | 0.292875i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.1275 | − | 26.2016i | 0.522259 | − | 0.904579i | −0.477406 | − | 0.878683i | \(-0.658423\pi\) |
0.999665 | − | 0.0258959i | \(-0.00824385\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50506 | − | 6.07095i | −0.120864 | − | 0.209343i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32.0382 | − | 33.8000i | −1.10345 | − | 1.16413i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 5.47244i | − | 0.188258i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 100.363 | 3.44851 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.51374 | − | 31.3762i | −0.257871 | − | 1.07683i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33.0882 | − | 19.1035i | 1.13425 | − | 0.654859i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.9389 | + | 14.9758i | 0.888132 | + | 0.512763i | 0.873331 | − | 0.487127i | \(-0.161955\pi\) |
0.0148007 | + | 0.999890i | \(0.495289\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.555788 | − | 10.3774i | 0.0190076 | − | 0.354901i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.9016 | + | 20.6141i | −0.406550 | + | 0.704165i | −0.994501 | − | 0.104732i | \(-0.966602\pi\) |
0.587951 | + | 0.808897i | \(0.299935\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.5000 | − | 16.4545i | 0.972406 | − | 0.561419i | 0.0724371 | − | 0.997373i | \(-0.476922\pi\) |
0.899969 | + | 0.435954i | \(0.143589\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.77434 | − | 9.34633i | 0.0945492 | − | 0.318522i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.3906 | −1.23875 | −0.619375 | − | 0.785095i | \(-0.712614\pi\) | ||||
−0.619375 | + | 0.785095i | \(0.712614\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.0000 | −0.714021 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.94214 | + | 23.3870i | −0.235767 | + | 0.794265i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.4440 | − | 6.02983i | 0.354288 | − | 0.204548i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.17523 | + | 5.49965i | −0.107588 | + | 0.186349i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.3742 | − | 8.31945i | 0.554183 | − | 0.281571i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 45.7234 | + | 26.3984i | 1.54573 | + | 0.892430i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.3529 | − | 24.4525i | 1.43016 | − | 0.825701i | 0.433024 | − | 0.901383i | \(-0.357447\pi\) |
0.997132 | + | 0.0756818i | \(0.0241133\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.468135 | + | 1.95486i | 0.0157898 | + | 0.0659357i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.9627 | 1.34638 | 0.673188 | − | 0.739471i | \(-0.264924\pi\) | ||||
0.673188 | + | 0.739471i | \(0.264924\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 10.0000i | − | 0.336527i | −0.985742 | − | 0.168263i | \(-0.946184\pi\) | ||
0.985742 | − | 0.168263i | \(-0.0538159\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.86422 | + | 4.07672i | 0.129894 | + | 0.137037i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.5949 | − | 39.1354i | −0.758661 | − | 1.31404i | −0.943534 | − | 0.331277i | \(-0.892521\pi\) |
0.184873 | − | 0.982762i | \(-0.440813\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.96265 | − | 17.2558i | 0.334137 | − | 0.578742i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.60907 | + | 52.2148i | −0.187911 | + | 1.74926i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.3829 | + | 10.6134i | 0.615160 | + | 0.355163i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.19615 | + | 9.00000i | 0.173688 | + | 0.300837i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 33.5661 | − | 31.8165i | 1.12074 | − | 1.06232i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 22.7969i | − | 0.760318i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.865333i | 0.0288284i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.22237 | − | 25.9837i | −0.207068 | − | 0.864682i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.98133 | − | 8.62791i | −0.165585 | − | 0.286801i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.9726 | − | 20.1914i | −1.16125 | − | 0.670446i | −0.209644 | − | 0.977778i | \(-0.567231\pi\) |
−0.951602 | + | 0.307332i | \(0.900564\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.6992 | − | 30.8990i | −0.520711 | − | 1.02486i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.26071 | − | 7.37976i | 0.141164 | − | 0.244503i | −0.786771 | − | 0.617244i | \(-0.788249\pi\) |
0.927935 | + | 0.372742i | \(0.121582\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.50000 | − | 7.79423i | −0.148928 | − | 0.257951i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.04598 | − | 3.52374i | 0.0345789 | − | 0.116491i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 58.9720i | − | 1.94743i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.00834 | −0.0662490 | −0.0331245 | − | 0.999451i | \(-0.510546\pi\) | ||||
−0.0331245 | + | 0.999451i | \(0.510546\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.6892 | + | 9.40654i | 1.04420 | + | 0.309956i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 34.4146 | − | 19.8693i | 1.13277 | − | 0.654006i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.96265 | − | 5.75194i | −0.327570 | − | 0.189123i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.0354682 | − | 0.662247i | 0.00116493 | − | 0.0217510i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.9864 | + | 25.9572i | −0.491688 | + | 0.851628i | −0.999954 | − | 0.00957195i | \(-0.996953\pi\) |
0.508267 | + | 0.861200i | \(0.330286\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.7199 | − | 11.9627i | 0.679068 | − | 0.392060i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.7311 | − | 4.48559i | 0.613230 | − | 0.146852i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.2558 | 0.564326 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.0475 | −1.47164 | −0.735818 | − | 0.677179i | \(-0.763202\pi\) | ||||
−0.735818 | + | 0.677179i | \(0.763202\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.0827 | + | 33.8470i | 1.04698 | + | 1.10455i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.3880 | + | 26.7821i | −1.51220 | + | 0.873072i | −0.512306 | + | 0.858803i | \(0.671209\pi\) |
−0.999898 | + | 0.0142686i | \(0.995458\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.29305 | − | 7.43578i | 0.139801 | − | 0.242142i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 25.4016 | + | 29.8452i | 0.826313 | + | 0.970864i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.6417 | − | 11.9175i | −0.670766 | − | 0.387267i | 0.125601 | − | 0.992081i | \(-0.459914\pi\) |
−0.796367 | + | 0.604814i | \(0.793248\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.7206 | − | 16.0045i | 0.899849 | − | 0.519528i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28.2237 | + | 26.7525i | −0.915215 | + | 0.867510i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.4732 | −1.05191 | −0.525955 | − | 0.850513i | \(-0.676292\pi\) | ||||
−0.525955 | + | 0.850513i | \(0.676292\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.382896i | 0.0123902i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −46.0899 | + | 11.0373i | −1.48987 | + | 0.356784i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −48.7225 | − | 84.3899i | −1.57333 | − | 2.72509i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.68325 | − | 6.37958i | 0.118815 | − | 0.205793i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.540074 | + | 0.829557i | −0.0174036 | + | 0.0267321i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −27.0712 | − | 15.6296i | −0.871453 | − | 0.503134i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.83221 | − | 8.36964i | −0.155393 | − | 0.269149i | 0.777809 | − | 0.628501i | \(-0.216331\pi\) |
−0.933202 | + | 0.359352i | \(0.882998\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.67004 | + | 1.68308i | 0.182148 | + | 0.0540683i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.8133i | 1.59858i | 0.600943 | + | 0.799292i | \(0.294792\pi\) | ||||
−0.600943 | + | 0.799292i | \(0.705208\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 50.2627i | 1.61135i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.3496 | − | 3.96265i | −0.427529 | − | 0.126906i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.59029 | + | 6.21856i | 0.114863 | + | 0.198949i | 0.917725 | − | 0.397216i | \(-0.130024\pi\) |
−0.802862 | + | 0.596165i | \(0.796690\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0244 | + | 11.5611i | 0.639982 | + | 0.369494i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.3401 | − | 45.0666i | 0.936757 | − | 1.43887i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.38174 | − | 4.12530i | 0.0759658 | − | 0.131577i | −0.825540 | − | 0.564344i | \(-0.809129\pi\) |
0.901506 | + | 0.432767i | \(0.142463\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.50506 | − | 14.7312i | −0.270994 | − | 0.469375i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −77.8493 | + | 18.6428i | −2.47797 | + | 0.593406i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 23.5303i | − | 0.748220i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.5781 | 0.907815 | 0.453907 | − | 0.891049i | \(-0.350030\pi\) | ||||
0.453907 | + | 0.891049i | \(0.350030\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −28.3970 | + | 26.9169i | −0.901153 | + | 0.854181i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.907140 | + | 0.523738i | −0.0287583 | + | 0.0166036i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.2494 | + | 18.6192i | 1.02135 | + | 0.589676i | 0.914494 | − | 0.404599i | \(-0.132589\pi\) |
0.106854 | + | 0.994275i | \(0.465922\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −19.3716 | − | 22.7603i | −0.612889 | − | 0.720105i |
(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 | 576.2.r.f.97.4 | yes | 12 | |
3.2 | odd | 2 | 1728.2.r.e.289.6 | 12 | |||
4.3 | odd | 2 | inner | 576.2.r.f.97.3 | yes | 12 | |
8.3 | odd | 2 | 576.2.r.e.97.4 | yes | 12 | ||
8.5 | even | 2 | 576.2.r.e.97.3 | ✓ | 12 | ||
9.2 | odd | 6 | 5184.2.d.r.2593.1 | 12 | |||
9.4 | even | 3 | 576.2.r.e.481.3 | yes | 12 | ||
9.5 | odd | 6 | 1728.2.r.f.1441.6 | 12 | |||
9.7 | even | 3 | 5184.2.d.q.2593.7 | 12 | |||
12.11 | even | 2 | 1728.2.r.e.289.1 | 12 | |||
24.5 | odd | 2 | 1728.2.r.f.289.6 | 12 | |||
24.11 | even | 2 | 1728.2.r.f.289.1 | 12 | |||
36.7 | odd | 6 | 5184.2.d.q.2593.12 | 12 | |||
36.11 | even | 6 | 5184.2.d.r.2593.6 | 12 | |||
36.23 | even | 6 | 1728.2.r.f.1441.1 | 12 | |||
36.31 | odd | 6 | 576.2.r.e.481.4 | yes | 12 | ||
72.5 | odd | 6 | 1728.2.r.e.1441.6 | 12 | |||
72.11 | even | 6 | 5184.2.d.r.2593.12 | 12 | |||
72.13 | even | 6 | inner | 576.2.r.f.481.4 | yes | 12 | |
72.29 | odd | 6 | 5184.2.d.r.2593.7 | 12 | |||
72.43 | odd | 6 | 5184.2.d.q.2593.6 | 12 | |||
72.59 | even | 6 | 1728.2.r.e.1441.1 | 12 | |||
72.61 | even | 6 | 5184.2.d.q.2593.1 | 12 | |||
72.67 | odd | 6 | inner | 576.2.r.f.481.3 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.2.r.e.97.3 | ✓ | 12 | 8.5 | even | 2 | ||
576.2.r.e.97.4 | yes | 12 | 8.3 | odd | 2 | ||
576.2.r.e.481.3 | yes | 12 | 9.4 | even | 3 | ||
576.2.r.e.481.4 | yes | 12 | 36.31 | odd | 6 | ||
576.2.r.f.97.3 | yes | 12 | 4.3 | odd | 2 | inner | |
576.2.r.f.97.4 | yes | 12 | 1.1 | even | 1 | trivial | |
576.2.r.f.481.3 | yes | 12 | 72.67 | odd | 6 | inner | |
576.2.r.f.481.4 | yes | 12 | 72.13 | even | 6 | inner | |
1728.2.r.e.289.1 | 12 | 12.11 | even | 2 | |||
1728.2.r.e.289.6 | 12 | 3.2 | odd | 2 | |||
1728.2.r.e.1441.1 | 12 | 72.59 | even | 6 | |||
1728.2.r.e.1441.6 | 12 | 72.5 | odd | 6 | |||
1728.2.r.f.289.1 | 12 | 24.11 | even | 2 | |||
1728.2.r.f.289.6 | 12 | 24.5 | odd | 2 | |||
1728.2.r.f.1441.1 | 12 | 36.23 | even | 6 | |||
1728.2.r.f.1441.6 | 12 | 9.5 | odd | 6 | |||
5184.2.d.q.2593.1 | 12 | 72.61 | even | 6 | |||
5184.2.d.q.2593.6 | 12 | 72.43 | odd | 6 | |||
5184.2.d.q.2593.7 | 12 | 9.7 | even | 3 | |||
5184.2.d.q.2593.12 | 12 | 36.7 | odd | 6 | |||
5184.2.d.r.2593.1 | 12 | 9.2 | odd | 6 | |||
5184.2.d.r.2593.6 | 12 | 36.11 | even | 6 | |||
5184.2.d.r.2593.7 | 12 | 72.29 | odd | 6 | |||
5184.2.d.r.2593.12 | 12 | 72.11 | even | 6 |