Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(385,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.385");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.i (of order \(3\), 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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} + \cdots + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 385.6 | ||
Root | \(-1.15879 - 1.28733i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.385 |
Dual form | 1152.2.i.i.769.6 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.69425 | + | 0.359877i | 0.978177 | + | 0.207775i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.74260 | − | 3.01828i | −0.779317 | − | 1.34982i | −0.932336 | − | 0.361593i | \(-0.882233\pi\) |
0.153019 | − | 0.988223i | \(-0.451100\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.34988 | + | 2.33807i | −0.510208 | + | 0.883706i | 0.489722 | + | 0.871879i | \(0.337098\pi\) |
−0.999930 | + | 0.0118274i | \(0.996235\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.74098 | + | 1.21944i | 0.913659 | + | 0.406481i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.84274 | + | 4.92377i | −0.857119 | + | 1.48457i | 0.0175468 | + | 0.999846i | \(0.494414\pi\) |
−0.874665 | + | 0.484727i | \(0.838919\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.76055 | + | 3.04937i | 0.488289 | + | 0.845742i | 0.999909 | − | 0.0134701i | \(-0.00428779\pi\) |
−0.511620 | + | 0.859212i | \(0.670954\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.86620 | − | 5.74085i | −0.481851 | − | 1.48228i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.65970 | 1.85775 | 0.928875 | − | 0.370392i | \(-0.120777\pi\) | ||||
0.928875 | + | 0.370392i | \(0.120777\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.02060 | −0.463557 | −0.231778 | − | 0.972769i | \(-0.574454\pi\) | ||||
−0.231778 | + | 0.972769i | \(0.574454\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.12846 | + | 3.47548i | −0.682685 | + | 0.758412i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.0370909 | − | 0.0642434i | −0.00773399 | − | 0.0133957i | 0.862133 | − | 0.506683i | \(-0.169128\pi\) |
−0.869866 | + | 0.493287i | \(0.835795\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.57334 | + | 6.18921i | −0.714669 | + | 1.23784i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.20506 | + | 3.05246i | 0.809263 | + | 0.587446i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.46032 | − | 4.26140i | 0.456870 | − | 0.791321i | −0.541924 | − | 0.840428i | \(-0.682304\pi\) |
0.998794 | + | 0.0491062i | \(0.0156373\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.72257 | + | 6.44769i | 0.668594 | + | 1.15804i | 0.978297 | + | 0.207205i | \(0.0664368\pi\) |
−0.309704 | + | 0.950833i | \(0.600230\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.58827 | + | 7.31907i | −1.14687 | + | 1.27409i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.40925 | 1.59045 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.00631 | −0.823033 | −0.411516 | − | 0.911402i | \(-0.635001\pi\) | ||||
−0.411516 | + | 0.911402i | \(0.635001\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.88542 | + | 5.79997i | 0.301909 | + | 0.928739i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.482053 | + | 0.834941i | 0.0752841 | + | 0.130396i | 0.901210 | − | 0.433383i | \(-0.142680\pi\) |
−0.825926 | + | 0.563779i | \(0.809347\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.255495 | + | 0.442530i | −0.0389626 | + | 0.0674852i | −0.884849 | − | 0.465878i | \(-0.845739\pi\) |
0.845887 | + | 0.533363i | \(0.179072\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.09582 | − | 10.3980i | −0.163355 | − | 1.55005i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.83509 | + | 4.91053i | −0.413541 | + | 0.716274i | −0.995274 | − | 0.0971059i | \(-0.969041\pi\) |
0.581733 | + | 0.813380i | \(0.302375\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.144369 | − | 0.250055i | −0.0206242 | − | 0.0357221i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.9775 | + | 2.75655i | 1.81721 | + | 0.385994i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.4058 | 1.42935 | 0.714676 | − | 0.699455i | \(-0.246574\pi\) | ||||
0.714676 | + | 0.699455i | \(0.246574\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.8151 | 2.67187 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.42340 | − | 0.727166i | −0.453441 | − | 0.0963155i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.47636 | − | 7.75329i | −0.582773 | − | 1.00939i | −0.995149 | − | 0.0983788i | \(-0.968634\pi\) |
0.412376 | − | 0.911014i | \(-0.364699\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.46032 | + | 2.52935i | −0.186975 | + | 0.323849i | −0.944240 | − | 0.329258i | \(-0.893202\pi\) |
0.757266 | + | 0.653107i | \(0.226535\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.55114 | + | 4.76248i | −0.825366 | + | 0.600016i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.13589 | − | 10.6277i | 0.761064 | − | 1.31820i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.56829 | + | 2.71635i | 0.191597 | + | 0.331855i | 0.945780 | − | 0.324809i | \(-0.105300\pi\) |
−0.754183 | + | 0.656665i | \(0.771967\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.0397217 | − | 0.122193i | −0.00478193 | − | 0.0147103i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.19647 | 0.972742 | 0.486371 | − | 0.873752i | \(-0.338320\pi\) | ||||
0.486371 | + | 0.873752i | \(0.338320\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.21796 | 0.610716 | 0.305358 | − | 0.952238i | \(-0.401224\pi\) | ||||
0.305358 | + | 0.952238i | \(0.401224\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.28150 | + | 9.20012i | −0.956265 | + | 1.06234i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.67474 | − | 13.2930i | −0.874617 | − | 1.51488i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.716260 | + | 1.24060i | −0.0805855 | + | 0.139578i | −0.903502 | − | 0.428585i | \(-0.859012\pi\) |
0.822916 | + | 0.568163i | \(0.192346\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.02592 | + | 6.68493i | 0.669546 | + | 0.742770i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.74052 | − | 3.01467i | 0.191047 | − | 0.330903i | −0.754551 | − | 0.656242i | \(-0.772145\pi\) |
0.945597 | + | 0.325339i | \(0.105478\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.3478 | − | 23.1191i | −1.44778 | − | 2.50762i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.70198 | − | 6.33447i | 0.611316 | − | 0.679126i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.4058 | −1.31502 | −0.657509 | − | 0.753447i | \(-0.728390\pi\) | ||||
−0.657509 | + | 0.753447i | \(0.728390\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.50616 | −0.996516 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.98660 | + | 12.2637i | 0.413392 | + | 1.27168i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.52110 | + | 6.09873i | 0.361258 | + | 0.625717i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.50265 | + | 6.06677i | −0.355640 | + | 0.615987i | −0.987227 | − | 0.159318i | \(-0.949071\pi\) |
0.631587 | + | 0.775305i | \(0.282404\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.7962 | + | 10.0294i | −1.38657 | + | 1.00799i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.44237 | + | 7.69441i | −0.442032 | + | 0.765623i | −0.997840 | − | 0.0656882i | \(-0.979076\pi\) |
0.555808 | + | 0.831311i | \(0.312409\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.65012 | − | 4.59014i | −0.261124 | − | 0.452280i | 0.705417 | − | 0.708792i | \(-0.250760\pi\) |
−0.966541 | + | 0.256513i | \(0.917426\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 15.9416 | + | 3.38617i | 1.55574 | + | 0.330456i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.53993 | 0.728912 | 0.364456 | − | 0.931221i | \(-0.381255\pi\) | ||||
0.364456 | + | 0.931221i | \(0.381255\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.8840 | −1.32984 | −0.664922 | − | 0.746913i | \(-0.731535\pi\) | ||||
−0.664922 | + | 0.746913i | \(0.731535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.48195 | − | 1.80166i | −0.805072 | − | 0.171006i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.36549 | + | 2.36510i | 0.128454 | + | 0.222489i | 0.923078 | − | 0.384613i | \(-0.125665\pi\) |
−0.794624 | + | 0.607102i | \(0.792332\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.129270 | + | 0.223902i | −0.0120545 | + | 0.0208789i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.10710 | + | 10.5051i | 0.102352 | + | 0.971200i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.3397 | + | 17.9089i | −0.947839 | + | 1.64171i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6624 | − | 18.4677i | −0.969305 | − | 1.67889i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.516244 | + | 1.58808i | 0.0465481 | + | 0.143192i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.48166 | 0.669180 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.89964 | −0.523509 | −0.261754 | − | 0.965135i | \(-0.584301\pi\) | ||||
−0.261754 | + | 0.965135i | \(0.584301\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.592129 | + | 0.657810i | −0.0521340 | + | 0.0579170i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.566027 | − | 0.980388i | −0.0494540 | − | 0.0856569i | 0.840239 | − | 0.542217i | \(-0.182415\pi\) |
−0.889693 | + | 0.456560i | \(0.849081\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.72757 | − | 4.72429i | 0.236510 | − | 0.409648i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.88542 | − | 18.0113i | 0.162271 | − | 1.55016i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.18182 | − | 5.51107i | 0.271841 | − | 0.470843i | −0.697492 | − | 0.716592i | \(-0.745701\pi\) |
0.969333 | + | 0.245750i | \(0.0790341\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.2001 | − | 19.3992i | −0.949983 | − | 1.64542i | −0.745453 | − | 0.666559i | \(-0.767767\pi\) |
−0.204531 | − | 0.978860i | \(-0.565567\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.57054 | + | 7.29938i | −0.553340 | + | 0.614719i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.0192 | −1.67409 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.1495 | −1.42418 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.154609 | − | 0.475611i | −0.0127519 | − | 0.0392277i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.939215 | − | 1.62677i | −0.0769435 | − | 0.133270i | 0.824986 | − | 0.565153i | \(-0.191183\pi\) |
−0.901930 | + | 0.431883i | \(0.857849\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.183779 | − | 0.318315i | 0.0149557 | − | 0.0259041i | −0.858451 | − | 0.512896i | \(-0.828573\pi\) |
0.873406 | + | 0.486992i | \(0.161906\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.9951 | + | 9.34057i | 1.69735 | + | 0.755141i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.9739 | − | 22.4715i | 1.04209 | − | 1.80496i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.15363 | + | 12.3905i | 0.570922 | + | 0.988866i | 0.996472 | + | 0.0839309i | \(0.0267475\pi\) |
−0.425550 | + | 0.904935i | \(0.639919\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 17.6301 | + | 3.74482i | 1.39816 | + | 0.296984i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.200274 | 0.0157838 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.02958 | 0.237295 | 0.118648 | − | 0.992936i | \(-0.462144\pi\) | ||||
0.118648 | + | 0.992936i | \(0.462144\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 33.5718 | + | 7.13099i | 2.61356 | + | 0.555147i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.629519 | − | 1.09036i | −0.0487137 | − | 0.0843745i | 0.840640 | − | 0.541594i | \(-0.182179\pi\) |
−0.889354 | + | 0.457219i | \(0.848846\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.300915 | − | 0.521200i | 0.0231473 | − | 0.0400923i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.53841 | − | 2.46400i | −0.423533 | − | 0.188427i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.14845 | − | 12.3815i | 0.543487 | − | 0.941347i | −0.455214 | − | 0.890382i | \(-0.650437\pi\) |
0.998700 | − | 0.0509644i | \(-0.0162295\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.64719 | − | 16.7094i | −0.729259 | − | 1.26311i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.79386 | − | 14.7470i | −0.360329 | − | 1.10845i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.7991 | 0.956647 | 0.478324 | − | 0.878184i | \(-0.341245\pi\) | ||||
0.478324 | + | 0.878184i | \(0.341245\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.4986 | −0.780355 | −0.390177 | − | 0.920740i | \(-0.627586\pi\) | ||||
−0.390177 | + | 0.920740i | \(0.627586\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.38440 | + | 3.75981i | −0.250182 | + | 0.277933i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.72403 | + | 15.1105i | 0.641403 | + | 1.11094i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.7746 | + | 37.7146i | −1.59231 | + | 2.75797i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.8132 | + | 5.71124i | −0.932022 | + | 0.415431i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.09526 | + | 7.09320i | −0.296323 | + | 0.513246i | −0.975292 | − | 0.220921i | \(-0.929094\pi\) |
0.678969 | + | 0.734167i | \(0.262427\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.46146 | − | 2.53132i | −0.105198 | − | 0.182208i | 0.808621 | − | 0.588330i | \(-0.200214\pi\) |
−0.913819 | + | 0.406122i | \(0.866881\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.2204 | − | 15.7978i | 1.01834 | − | 1.13130i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.44174 | −0.316461 | −0.158230 | − | 0.987402i | \(-0.550579\pi\) | ||||
−0.158230 | + | 0.987402i | \(0.550579\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.6898 | 1.04133 | 0.520665 | − | 0.853761i | \(-0.325684\pi\) | ||||
0.520665 | + | 0.853761i | \(0.325684\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.67952 | + | 5.16658i | 0.118464 | + | 0.364422i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.64228 | + | 11.5048i | 0.466197 | + | 0.807477i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.68006 | − | 2.90994i | 0.117340 | − | 0.203239i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.0233242 | − | 0.221320i | −0.00162115 | − | 0.0153828i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.74404 | − | 9.94896i | 0.397323 | − | 0.688184i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.04700 | − | 3.54551i | −0.140921 | − | 0.244083i | 0.786923 | − | 0.617052i | \(-0.211673\pi\) |
−0.927844 | + | 0.372969i | \(0.878340\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.8869 | + | 2.94972i | 0.951514 | + | 0.202111i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.78091 | 0.121457 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.1002 | −1.36449 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.84054 | + | 1.87782i | 0.597388 | + | 0.126892i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.4853 | + | 23.3572i | 0.907120 | + | 1.57118i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.24612 | − | 10.8186i | 0.418271 | − | 0.724467i | −0.577494 | − | 0.816395i | \(-0.695970\pi\) |
0.995766 | + | 0.0919276i | \(0.0293028\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −17.3419 | + | 12.6070i | −1.15612 | + | 0.840467i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.52721 | − | 7.84136i | 0.300482 | − | 0.520449i | −0.675764 | − | 0.737118i | \(-0.736186\pi\) |
0.976245 | + | 0.216669i | \(0.0695193\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.1073 | + | 22.7024i | 0.866152 | + | 1.50022i | 0.865899 | + | 0.500219i | \(0.166747\pi\) |
0.000252919 | 1.00000i | \(0.499919\pi\) | ||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.21908 | − | 25.2837i | −0.540776 | − | 1.66355i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.41840 | 0.0929224 | 0.0464612 | − | 0.998920i | \(-0.485206\pi\) | ||||
0.0464612 | + | 0.998920i | \(0.485206\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.7618 | 1.28912 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.65999 | + | 1.84412i | −0.107828 | + | 0.119788i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.18200 | − | 14.1716i | −0.529250 | − | 0.916688i | −0.999418 | − | 0.0341107i | \(-0.989140\pi\) |
0.470168 | − | 0.882577i | \(-0.344193\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.17500 | + | 8.96336i | −0.333351 | + | 0.577381i | −0.983167 | − | 0.182711i | \(-0.941513\pi\) |
0.649816 | + | 0.760092i | \(0.274846\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.80366 | + | 13.4945i | 0.500605 | + | 0.865676i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.503157 | + | 0.871493i | −0.0321455 | + | 0.0556776i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.55737 | − | 6.16154i | −0.226350 | − | 0.392049i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.03379 | − | 4.48124i | 0.255631 | − | 0.283987i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.9624 | −1.70185 | −0.850927 | − | 0.525283i | \(-0.823959\pi\) | ||||
−0.850927 | + | 0.525283i | \(0.823959\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.421759 | 0.0265158 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14.2946 | − | 43.9732i | −0.895160 | − | 2.75371i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.8380 | − | 25.7001i | −0.925568 | − | 1.60313i | −0.790646 | − | 0.612274i | \(-0.790255\pi\) |
−0.134922 | − | 0.990856i | \(-0.543078\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.75794 | − | 11.7051i | 0.419918 | − | 0.727319i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.9402 | − | 8.68017i | 0.739080 | − | 0.537289i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.46961 | + | 2.54544i | −0.0906200 | + | 0.156959i | −0.907772 | − | 0.419464i | \(-0.862218\pi\) |
0.817152 | + | 0.576422i | \(0.195552\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.1333 | − | 31.4078i | −1.11392 | − | 1.92936i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.0186 | − | 4.46458i | −1.28632 | − | 0.273228i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.4251 | 0.818541 | 0.409270 | − | 0.912413i | \(-0.365783\pi\) | ||||
0.409270 | + | 0.912413i | \(0.365783\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.3320 | 1.90329 | 0.951643 | − | 0.307207i | \(-0.0993944\pi\) | ||||
0.951643 | + | 0.307207i | \(0.0993944\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.1058 | − | 3.42104i | −0.974769 | − | 0.207051i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20.3162 | − | 35.1887i | −1.22511 | − | 2.12196i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.78089 | − | 8.28075i | 0.287256 | − | 0.497542i | −0.685898 | − | 0.727698i | \(-0.740590\pi\) |
0.973154 | + | 0.230156i | \(0.0739236\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.34090 | + | 22.2124i | 0.140146 | + | 1.32982i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.39152 | − | 5.87429i | 0.202321 | − | 0.350431i | −0.746955 | − | 0.664875i | \(-0.768485\pi\) |
0.949276 | + | 0.314444i | \(0.101818\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.61895 | − | 16.6605i | −0.571787 | − | 0.990364i | −0.996383 | − | 0.0849812i | \(-0.972917\pi\) |
0.424595 | − | 0.905383i | \(-0.360416\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.77084 | + | 11.5999i | 0.223366 | + | 0.687122i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.60286 | −0.153642 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.6710 | 2.45124 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.11766 | + | 9.01811i | −0.475866 | + | 0.528651i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.63884 | + | 9.76676i | 0.329425 | + | 0.570580i | 0.982398 | − | 0.186801i | \(-0.0598119\pi\) |
−0.652973 | + | 0.757381i | \(0.726479\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.6011 | + | 27.0218i | −0.908329 | + | 1.57327i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −26.9835 | + | 12.0274i | −1.56574 | + | 0.697900i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.130601 | − | 0.226207i | 0.00755285 | − | 0.0130819i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.689776 | − | 1.19473i | −0.0397580 | − | 0.0688629i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.2955 | + | 11.4376i | −0.591463 | + | 0.657071i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.1790 | 0.582850 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.2819 | −1.27169 | −0.635846 | − | 0.771816i | \(-0.719349\pi\) | ||||
−0.635846 | + | 0.771816i | \(0.719349\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.83808 | − | 8.73056i | −0.161453 | − | 0.496664i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.0604 | − | 20.8893i | −0.683884 | − | 1.18452i | −0.973786 | − | 0.227466i | \(-0.926956\pi\) |
0.289902 | − | 0.957056i | \(-0.406377\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.5297 | − | 25.1661i | 0.821265 | − | 1.42247i | −0.0834762 | − | 0.996510i | \(-0.526602\pi\) |
0.904741 | − | 0.425962i | \(-0.140064\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 25.7905 | + | 11.4741i | 1.45313 | + | 0.646490i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.2862 | − | 28.2085i | 0.914724 | − | 1.58435i | 0.107418 | − | 0.994214i | \(-0.465742\pi\) |
0.807305 | − | 0.590134i | \(-0.200925\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.9881 | + | 24.2281i | 0.783183 | + | 1.35651i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.7745 | + | 2.71344i | 0.713005 | + | 0.151450i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.4772 | −0.861173 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −25.1642 | −1.39586 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23.5230 | − | 4.99652i | −1.30082 | − | 0.276308i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.65409 | − | 13.2573i | −0.421984 | − | 0.730897i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.05963 | − | 13.9597i | 0.442997 | − | 0.767293i | −0.554913 | − | 0.831908i | \(-0.687249\pi\) |
0.997910 | + | 0.0646148i | \(0.0205819\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.7222 | − | 6.10492i | −0.751972 | − | 0.334547i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.46581 | − | 9.46706i | 0.298629 | − | 0.517241i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.6119 | + | 21.8445i | 0.687015 | + | 1.18995i | 0.972799 | + | 0.231651i | \(0.0744128\pi\) |
−0.285783 | + | 0.958294i | \(0.592254\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.46234 | + | 4.49847i | 0.0794233 | + | 0.244324i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −42.3292 | −2.29226 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.1188 | −0.978325 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.299592 | + | 0.332824i | −0.0161295 | + | 0.0179187i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.16774 | + | 3.75464i | 0.116371 | + | 0.201560i | 0.918327 | − | 0.395823i | \(-0.129541\pi\) |
−0.801956 | + | 0.597383i | \(0.796207\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.77744 | + | 16.9350i | −0.523374 | + | 0.906511i | 0.476255 | + | 0.879307i | \(0.341994\pi\) |
−0.999630 | + | 0.0272042i | \(0.991340\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.90484 | + | 18.1968i | −0.101673 | + | 0.971271i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.13835 | − | 15.8281i | 0.486385 | − | 0.842444i | −0.513492 | − | 0.858094i | \(-0.671648\pi\) |
0.999878 | + | 0.0156502i | \(0.00498183\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.2832 | − | 24.7392i | −0.758074 | − | 1.31302i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −23.9631 | + | 26.6212i | −1.26826 | + | 1.40894i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.41976 | 0.180488 | 0.0902440 | − | 0.995920i | \(-0.471235\pi\) | ||||
0.0902440 | + | 0.995920i | \(0.471235\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.9172 | −0.785115 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.4186 | − | 35.1261i | −0.599321 | − | 1.84364i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.09285 | − | 15.7493i | −0.475941 | − | 0.824355i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.46341 | + | 9.46291i | −0.285188 | + | 0.493960i | −0.972655 | − | 0.232256i | \(-0.925389\pi\) |
0.687467 | + | 0.726216i | \(0.258723\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.303134 | + | 2.87639i | 0.0157805 | + | 0.149739i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.0467 | + | 24.3296i | −0.729267 | + | 1.26313i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.4603 | + | 18.1178i | 0.541615 | + | 0.938104i | 0.998812 | + | 0.0487387i | \(0.0155202\pi\) |
−0.457197 | + | 0.889366i | \(0.651147\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.6758 | + | 2.69247i | 0.654576 | + | 0.139039i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.3261 | 0.892338 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.0219 | 0.925725 | 0.462862 | − | 0.886430i | \(-0.346822\pi\) | ||||
0.462862 | + | 0.886430i | \(0.346822\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.99548 | − | 2.12314i | −0.512084 | − | 0.108772i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.4732 | + | 21.6042i | 0.637350 | + | 1.10392i | 0.986012 | + | 0.166674i | \(0.0533028\pi\) |
−0.348662 | + | 0.937249i | \(0.613364\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26.7481 | + | 46.3290i | −1.36321 | + | 2.36115i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.23995 | + | 0.901403i | −0.0630300 | + | 0.0458209i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.96347 | + | 12.0611i | −0.353062 | + | 0.611522i | −0.986784 | − | 0.162039i | \(-0.948193\pi\) |
0.633722 | + | 0.773561i | \(0.281526\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.284105 | − | 0.492085i | −0.0143678 | − | 0.0248858i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.606174 | − | 1.86472i | −0.0305774 | − | 0.0940629i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.99263 | 0.251206 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.54840 | −0.328655 | −0.164327 | − | 0.986406i | \(-0.552545\pi\) | ||||
−0.164327 | + | 0.986406i | \(0.552545\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.32135 | − | 7.02255i | 0.316464 | − | 0.351567i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.1738 | − | 21.0857i | −0.607933 | − | 1.05297i | −0.991581 | − | 0.129491i | \(-0.958666\pi\) |
0.383648 | − | 0.923480i | \(-0.374668\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.1076 | + | 22.7030i | −0.652934 | + | 1.13092i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.67622 | − | 29.8371i | 0.480815 | − | 1.48262i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.2317 | − | 24.6499i | 0.705437 | − | 1.22185i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.08792 | + | 14.0087i | 0.399922 | + | 0.692685i | 0.993716 | − | 0.111932i | \(-0.0357040\pi\) |
−0.593794 | + | 0.804617i | \(0.702371\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.37411 | − | 8.19208i | 0.363738 | − | 0.404086i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.1703 | 1.18934 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.1322 | −0.595544 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.9945 | − | 36.8978i | −0.587374 | − | 1.80689i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.2436 | + | 29.8668i | 0.842405 | + | 1.45909i | 0.887856 | + | 0.460121i | \(0.152194\pi\) |
−0.0454518 | + | 0.998967i | \(0.514473\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.6909 | − | 27.1774i | 0.764728 | − | 1.32455i | −0.175662 | − | 0.984451i | \(-0.556207\pi\) |
0.940390 | − | 0.340097i | \(-0.110460\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.7590 | + | 10.0024i | −0.668987 | + | 0.486333i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −27.3708 | + | 47.4075i | −1.32768 | + | 2.29960i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.94252 | − | 6.82864i | −0.190792 | − | 0.330461i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −33.9175 | − | 7.20443i | −1.63755 | − | 0.347833i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.1491 | 0.585200 | 0.292600 | − | 0.956235i | \(-0.405480\pi\) | ||||
0.292600 | + | 0.956235i | \(0.405480\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.40374 | 0.115517 | 0.0577583 | − | 0.998331i | \(-0.481605\pi\) | ||||
0.0577583 | + | 0.998331i | \(0.481605\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −29.0555 | − | 6.17169i | −1.39310 | − | 0.295910i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0749458 | + | 0.129810i | 0.00358514 | + | 0.00620965i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.6941 | − | 32.3792i | 0.892222 | − | 1.54537i | 0.0550162 | − | 0.998485i | \(-0.482479\pi\) |
0.837206 | − | 0.546888i | \(-0.184188\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.0907850 | − | 0.861444i | −0.00432310 | − | 0.0410212i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.22340 | − | 7.31515i | 0.200660 | − | 0.347553i | −0.748081 | − | 0.663607i | \(-0.769025\pi\) |
0.948741 | + | 0.316054i | \(0.102358\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.6185 | + | 37.4443i | 1.02481 | + | 1.77503i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.00583 | − | 3.09415i | −0.0475741 | − | 0.146348i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.6531 | 0.880295 | 0.440147 | − | 0.897926i | \(-0.354926\pi\) | ||||
0.440147 | + | 0.897926i | \(0.354926\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.48141 | −0.258109 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.425922 | − | 0.473167i | 0.0200116 | − | 0.0222313i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.5655 | + | 28.6922i | 0.776601 | + | 1.34511i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.91748 | + | 15.4455i | −0.417142 | + | 0.722511i | −0.995651 | − | 0.0931650i | \(-0.970302\pi\) |
0.578509 | + | 0.815676i | \(0.303635\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 32.2095 | + | 23.3809i | 1.50341 | + | 1.09133i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.0563 | − | 17.4181i | 0.468370 | − | 0.811240i | −0.530977 | − | 0.847386i | \(-0.678175\pi\) |
0.999347 | + | 0.0361463i | \(0.0115082\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.10747 | − | 7.11435i | −0.190890 | − | 0.330632i | 0.754655 | − | 0.656122i | \(-0.227804\pi\) |
−0.945546 | + | 0.325490i | \(0.894471\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 30.0681 | − | 33.4034i | 1.39438 | − | 1.54905i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.3274 | 0.894364 | 0.447182 | − | 0.894443i | \(-0.352428\pi\) | ||||
0.447182 | + | 0.894443i | \(0.352428\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.46802 | −0.391017 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.66102 | + | 23.5670i | 0.353001 | + | 1.08591i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.45261 | − | 2.51600i | −0.0667911 | − | 0.115686i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.22029 | − | 12.5059i | 0.331290 | − | 0.573811i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 28.5222 | + | 12.6893i | 1.30594 | + | 0.581005i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.1597 | − | 36.6498i | 0.966814 | − | 1.67457i | 0.262152 | − | 0.965027i | \(-0.415568\pi\) |
0.704661 | − | 0.709544i | \(-0.251099\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.81387 | − | 15.2661i | −0.401878 | − | 0.696073i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.339314 | + | 0.0720738i | 0.0154393 | + | 0.00327947i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24.4149 | 1.10863 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.36060 | −0.0616547 | −0.0308273 | − | 0.999525i | \(-0.509814\pi\) | ||||
−0.0308273 | + | 0.999525i | \(0.509814\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.13287 | + | 1.09028i | 0.232116 | + | 0.0493040i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.6328 | + | 27.0768i | 0.705497 | + | 1.22196i | 0.966512 | + | 0.256622i | \(0.0826096\pi\) |
−0.261015 | + | 0.965335i | \(0.584057\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.8453 | − | 32.6410i | 0.848750 | − | 1.47008i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 54.3127 | + | 24.1634i | 2.44118 | + | 1.08606i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.0643 | + | 19.1639i | −0.496301 | + | 0.859618i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.37981 | + | 12.7822i | 0.330366 | + | 0.572210i | 0.982584 | − | 0.185821i | \(-0.0594946\pi\) |
−0.652218 | + | 0.758032i | \(0.726161\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.674169 | − | 2.07389i | −0.0301196 | − | 0.0926547i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −44.6336 | −1.99011 | −0.995056 | − | 0.0993124i | \(-0.968336\pi\) | ||||
−0.995056 | + | 0.0993124i | \(0.968336\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30.9652 | 1.37793 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.697393 | − | 0.774751i | 0.0309723 | − | 0.0344079i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.854549 | − | 1.48012i | −0.0378772 | − | 0.0656053i | 0.846465 | − | 0.532444i | \(-0.178726\pi\) |
−0.884343 | + | 0.466839i | \(0.845393\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.04364 | + | 12.1999i | −0.311592 | + | 0.539694i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.49673 | − | 6.16779i | −0.375140 | − | 0.272315i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.23621 | + | 15.9976i | −0.406996 | + | 0.704938i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.1189 | − | 27.9187i | −0.708907 | − | 1.22786i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.5671 | − | 18.4048i | 0.727214 | − | 0.807880i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.6018 | −0.464475 | −0.232237 | − | 0.972659i | \(-0.574605\pi\) | ||||
−0.232237 | + | 0.972659i | \(0.574605\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.1565 | 1.18747 | 0.593736 | − | 0.804660i | \(-0.297652\pi\) | ||||
0.593736 | + | 0.804660i | \(0.297652\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −10.3314 | − | 31.7818i | −0.450901 | − | 1.38707i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.5138 | + | 49.3874i | 1.24208 | + | 2.15135i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4972 | − | 19.9138i | 0.499880 | − | 0.865818i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.81491 | − | 26.7103i | −0.122157 | − | 1.15913i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.69736 | + | 2.93991i | −0.0735208 | + | 0.127342i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.1391 | − | 22.7576i | −0.568053 | − | 0.983897i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.6848 | + | 4.60609i | 0.935770 | + | 0.198767i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.64162 | 0.0707094 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.1225 | 1.51003 | 0.755017 | − | 0.655705i | \(-0.227629\pi\) | ||||
0.755017 | + | 0.655705i | \(0.227629\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.7873 | − | 3.77820i | −0.763325 | − | 0.162138i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.1943 | + | 41.9057i | 1.03637 | + | 1.79504i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.0029 | + | 22.5218i | −0.555966 | + | 0.962961i | 0.441862 | + | 0.897083i | \(0.354318\pi\) |
−0.997828 | + | 0.0658781i | \(0.979015\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.08709 | + | 5.15210i | −0.302470 | + | 0.219886i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.97131 | + | 8.61057i | −0.211785 | + | 0.366822i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.93373 | − | 3.34932i | −0.0822307 | − | 0.142428i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.34279 | + | 28.7405i | 0.396580 | + | 1.21997i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.8670 | −1.22314 | −0.611568 | − | 0.791192i | \(-0.709461\pi\) | ||||
−0.611568 | + | 0.791192i | \(0.709461\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.79925 | −0.0761000 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −50.4642 | + | 56.0619i | −2.13060 | + | 2.36694i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.876491 | − | 1.51813i | −0.0369397 | − | 0.0639815i | 0.846964 | − | 0.531649i | \(-0.178428\pi\) |
−0.883904 | + | 0.467668i | \(0.845094\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.75901 | − | 8.24285i | 0.200213 | − | 0.346779i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.7641 | + | 5.06511i | −0.997998 | + | 0.212715i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.3974 | + | 23.2049i | −0.561647 | + | 0.972801i | 0.435706 | + | 0.900089i | \(0.356499\pi\) |
−0.997353 | + | 0.0727120i | \(0.976835\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.6759 | + | 21.9553i | 0.530471 | + | 0.918803i | 0.999368 | + | 0.0355497i | \(0.0113182\pi\) |
−0.468897 | + | 0.883253i | \(0.655348\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.49108 | + | 10.5439i | −0.396496 | + | 0.440477i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.530154 | 0.0221090 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.8507 | 1.40922 | 0.704612 | − | 0.709593i | \(-0.251121\pi\) | ||||
0.704612 | + | 0.709593i | \(0.251121\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.56511 | − | 4.81463i | −0.0650438 | − | 0.200089i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.69900 | + | 8.13890i | 0.194947 | + | 0.337659i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −29.5811 | + | 51.2360i | −1.22513 | + | 2.12198i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 29.7782 | − | 21.6479i | 1.23118 | − | 0.895028i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.2279 | − | 19.4474i | 0.463427 | − | 0.802679i | −0.535702 | − | 0.844407i | \(-0.679953\pi\) |
0.999129 | + | 0.0417284i | \(0.0132864\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.52182 | − | 13.0282i | −0.309931 | − | 0.536817i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.52543 | − | 1.59848i | −0.309555 | − | 0.0657526i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.35530 | −0.384176 | −0.192088 | − | 0.981378i | \(-0.561526\pi\) | ||||
−0.192088 | + | 0.981378i | \(0.561526\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 72.0721 | 2.95467 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.8882 | + | 5.28651i | 1.01860 | + | 0.216362i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.2259 | − | 21.1759i | −0.499538 | − | 0.865226i | 0.500462 | − | 0.865759i | \(-0.333164\pi\) |
−1.00000 | 0.000533153i | \(0.999830\pi\) | ||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.64643 | + | 11.5120i | −0.271114 | + | 0.469583i | −0.969147 | − | 0.246482i | \(-0.920725\pi\) |
0.698034 | + | 0.716065i | \(0.254059\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.986201 | + | 9.35790i | 0.0401612 | + | 0.381083i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −37.1605 | + | 64.3639i | −1.51079 | + | 2.61677i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.1403 | − | 31.4198i | −0.736290 | − | 1.27529i | −0.954155 | − | 0.299313i | \(-0.903242\pi\) |
0.217864 | − | 0.975979i | \(-0.430091\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.11340 | + | 21.8824i | 0.288250 | + | 0.886719i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.9653 | −0.807710 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.73390 | −0.271980 | −0.135990 | − | 0.990710i | \(-0.543421\pi\) | ||||
−0.135990 | + | 0.990710i | \(0.543421\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.89366 | − | 4.32556i | 0.157007 | − | 0.174424i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.553446 | + | 0.958597i | 0.0222809 | + | 0.0385917i | 0.876951 | − | 0.480580i | \(-0.159574\pi\) |
−0.854670 | + | 0.519172i | \(0.826241\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.60418 | + | 13.1708i | −0.305638 | + | 0.529380i | −0.977403 | − | 0.211384i | \(-0.932203\pi\) |
0.671765 | + | 0.740764i | \(0.265536\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.0401307 | − | 0.383365i | 0.00161039 | − | 0.0153839i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.7464 | − | 29.0057i | 0.670932 | − | 1.16209i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.82915 | + | 8.36432i | 0.193166 | + | 0.334573i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.3122 | − | 14.7889i | 0.531640 | − | 0.590612i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −38.3469 | −1.52899 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.2163 | 1.16308 | 0.581541 | − | 0.813517i | \(-0.302450\pi\) | ||||
0.581541 | + | 0.813517i | \(0.302450\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.19219 | − | 6.74365i | −0.0871316 | − | 0.268036i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.2807 | + | 17.8068i | 0.407979 | + | 0.706641i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.508339 | − | 0.880468i | 0.0201411 | − | 0.0348854i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22.4663 | + | 9.99513i | 0.888755 | + | 0.395401i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.4412 | + | 23.2809i | −0.530897 | + | 0.919540i | 0.468453 | + | 0.883488i | \(0.344811\pi\) |
−0.999350 | + | 0.0360519i | \(0.988522\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.36207 | + | 11.0194i | 0.250896 | + | 0.434564i | 0.963773 | − | 0.266725i | \(-0.0859416\pi\) |
−0.712877 | + | 0.701289i | \(0.752608\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.01730 | + | 0.640907i | 0.118806 | + | 0.0252357i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 47.3838 | 1.86285 | 0.931425 | − | 0.363933i | \(-0.118566\pi\) | ||||
0.931425 | + | 0.363933i | \(0.118566\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 50.9006 | 1.99802 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −34.0547 | − | 7.23358i | −1.33471 | − | 0.283506i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.13506 | − | 7.16213i | −0.161817 | − | 0.280276i | 0.773703 | − | 0.633548i | \(-0.218402\pi\) |
−0.935521 | + | 0.353272i | \(0.885069\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.97272 | + | 3.41686i | −0.0770807 | + | 0.133508i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.3023 | + | 6.36301i | 0.557987 | + | 0.248245i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.00770 | + | 1.74539i | −0.0392544 | + | 0.0679906i | −0.884985 | − | 0.465619i | \(-0.845832\pi\) |
0.845731 | + | 0.533610i | \(0.179165\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.70432 | − | 2.95196i | −0.0662902 | − | 0.114818i | 0.830975 | − | 0.556309i | \(-0.187783\pi\) |
−0.897266 | + | 0.441491i | \(0.854450\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 14.4418 | + | 44.4261i | 0.560872 | + | 1.72537i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.0123 | −0.737266 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.365022 | −0.0141337 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.4759 | − | 16.0816i | 0.559669 | − | 0.621750i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.30261 | − | 14.3805i | −0.320519 | − | 0.555155i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.56791 | − | 13.1080i | 0.291722 | − | 0.505277i | −0.682495 | − | 0.730890i | \(-0.739105\pi\) |
0.974217 | + | 0.225613i | \(0.0724386\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −33.9184 | + | 15.1185i | −1.30552 | + | 0.581912i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.31110 | + | 16.1273i | −0.357855 | + | 0.619822i | −0.987602 | − | 0.156978i | \(-0.949825\pi\) |
0.629748 | + | 0.776800i | \(0.283158\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.45634 | − | 16.3789i | −0.362901 | − | 0.628563i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.4922 | − | 11.6560i | 0.402060 | − | 0.446659i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.4656 | −1.47185 | −0.735923 | − | 0.677066i | \(-0.763251\pi\) | ||||
−0.735923 | + | 0.677066i | \(0.763251\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.1786 | −0.847401 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.0369 | + | 43.1806i | 0.535542 | + | 1.64744i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.3200 | + | 31.7312i | 0.697938 | + | 1.20886i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.2999 | + | 19.5720i | −0.429869 | + | 0.744555i | −0.996861 | − | 0.0791683i | \(-0.974774\pi\) |
0.566992 | + | 0.823723i | \(0.308107\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.82618 | − | 45.7948i | −0.183331 | − | 1.73960i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −39.0348 | + | 67.6103i | −1.48068 | + | 2.56460i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.69238 | + | 6.39540i | 0.139859 | + | 0.242243i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.40312 | + | 0.510449i | 0.0908945 | + | 0.0193069i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.8883 | −1.43102 | −0.715510 | − | 0.698602i | \(-0.753806\pi\) | ||||
−0.715510 | + | 0.698602i | \(0.753806\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.1157 | 0.381523 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 33.4814 | + | 7.11181i | 1.26098 | + | 0.267846i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.9934 | − | 20.7731i | −0.451057 | − | 0.781253i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.75701 | − | 13.4355i | 0.291321 | − | 0.504582i | −0.682802 | − | 0.730604i | \(-0.739239\pi\) |
0.974122 | + | 0.226022i | \(0.0725720\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.47609 | + | 2.52701i | −0.130364 | + | 0.0947704i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.276147 | − | 0.478301i | 0.0103418 | − | 0.0179125i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 34.8855 | + | 60.4235i | 1.30464 | + | 2.25971i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.76233 | − | 26.9548i | −0.327235 | − | 1.00665i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.8701 | −1.11397 | −0.556983 | − | 0.830524i | \(-0.688041\pi\) | ||||
−0.556983 | + | 0.830524i | \(0.688041\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.3094 | 0.532910 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.9935 | + | 13.3238i | −0.446041 | + | 0.495518i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.5831 | + | 30.4549i | 0.653021 | + | 1.13107i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.80759 | − | 4.86288i | 0.104128 | − | 0.180354i | −0.809254 | − | 0.587459i | \(-0.800128\pi\) |
0.913381 | + | 0.407105i | \(0.133462\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.36500 | + | 25.6715i | 0.309815 | + | 0.950797i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.95701 | + | 3.38965i | −0.0723828 | + | 0.125371i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.02803 | + | 10.4409i | 0.222650 | + | 0.385642i | 0.955612 | − | 0.294628i | \(-0.0951958\pi\) |
−0.732962 | + | 0.680270i | \(0.761863\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.16610 | + | 1.29545i | −0.0430124 | + | 0.0477835i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.8329 | −0.656885 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.8187 | 1.61190 | 0.805948 | − | 0.591986i | \(-0.201656\pi\) | ||||
0.805948 | + | 0.591986i | \(0.201656\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.80968 | − | 11.7194i | −0.139952 | − | 0.430523i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.0004 | − | 25.9814i | −0.550310 | − | 0.953164i | −0.998252 | − | 0.0591018i | \(-0.981176\pi\) |
0.447942 | − | 0.894062i | \(-0.352157\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.27336 | + | 5.66963i | −0.119927 | + | 0.207719i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.44694 | − | 6.14067i | 0.309058 | − | 0.224676i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.1780 | + | 17.6288i | −0.371897 | + | 0.644144i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.69583 | − | 8.13342i | −0.171353 | − | 0.296793i | 0.767540 | − | 0.641001i | \(-0.221481\pi\) |
−0.938893 | + | 0.344208i | \(0.888147\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −45.6812 | − | 9.70316i | −1.66471 | − | 0.353603i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.28102 | −0.0466210 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.7285 | 0.789737 | 0.394868 | − | 0.918738i | \(-0.370790\pi\) | ||||
0.394868 | + | 0.918738i | \(0.370790\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.714567 | + | 0.151781i | 0.0259371 | + | 0.00550932i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.78398 | − | 11.7502i | −0.245919 | − | 0.425944i | 0.716471 | − | 0.697617i | \(-0.245756\pi\) |
−0.962390 | + | 0.271673i | \(0.912423\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.7417 | − | 32.4617i | 0.678497 | − | 1.17519i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.39365 | − | 79.6459i | −0.303473 | − | 2.87961i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.7617 | − | 27.3001i | 0.569124 | − | 0.985751i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.3949 | − | 37.0571i | −0.771520 | − | 1.33631i | −0.936730 | − | 0.350054i | \(-0.886163\pi\) |
0.165209 | − | 0.986259i | \(-0.447170\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.8904 | − | 48.8823i | −0.572278 | − | 1.76045i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.4288 | 0.447034 | 0.223517 | − | 0.974700i | \(-0.428246\pi\) | ||||
0.223517 | + | 0.974700i | \(0.428246\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −53.2081 | −1.91129 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.6620 | − | 17.3993i | 0.561873 | − | 0.624198i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.974036 | − | 1.68708i | −0.0348984 | − | 0.0604459i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.3004 | + | 40.3576i | −0.833756 | + | 1.44411i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 23.3535 | − | 10.4094i | 0.834586 | − | 0.372001i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24.9319 | − | 43.1833i | 0.889858 | − | 1.54128i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.5079 | − | 37.2527i | −0.766673 | − | 1.32792i | −0.939357 | − | 0.342940i | \(-0.888577\pi\) |
0.172684 | − | 0.984977i | \(-0.444756\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.40593 | + | 3.78374i | −0.121254 | + | 0.134705i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.37300 | −0.262154 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.2839 | −0.365191 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −19.4194 | − | 59.7384i | −0.688736 | − | 2.11870i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.6697 | − | 23.6766i | −0.484205 | − | 0.838668i | 0.515630 | − | 0.856811i | \(-0.327558\pi\) |
−0.999835 | + | 0.0181431i | \(0.994225\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.7160 | + | 37.6132i | −0.768256 | + | 1.33066i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −34.0041 | − | 15.1282i | −1.20148 | − | 0.534530i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.8333 | + | 25.6921i | −0.523456 | + | 0.906653i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.348998 | − | 0.604482i | −0.0123006 | − | 0.0213052i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.7454 | + | 4.83137i | 0.800677 | + | 0.170072i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.2692 | 0.642311 | 0.321156 | − | 0.947026i | \(-0.395929\pi\) | ||||
0.321156 | + | 0.947026i | \(0.395929\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.6619 | −1.18203 | −0.591015 | − | 0.806660i | \(-0.701273\pi\) | ||||
−0.591015 | + | 0.806660i | \(0.701273\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 53.0843 | + | 11.2757i | 1.86175 | + | 0.395455i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.27936 | − | 9.14412i | −0.184928 | − | 0.320305i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.516252 | − | 0.894175i | 0.0180614 | − | 0.0312832i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −26.0562 | − | 11.5922i | −0.910476 | − | 0.405065i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.5703 | − | 37.3609i | 0.752810 | − | 1.30391i | −0.193645 | − | 0.981072i | \(-0.562031\pi\) |
0.946456 | − | 0.322834i | \(-0.104636\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.45533 | + | 14.6451i | 0.294734 | + | 0.510494i | 0.974923 | − | 0.222542i | \(-0.0714356\pi\) |
−0.680189 | + | 0.733037i | \(0.738102\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −21.7571 | − | 66.9298i | −0.757487 | − | 2.33020i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.2376 | 0.425542 | 0.212771 | − | 0.977102i | \(-0.431751\pi\) | ||||
0.212771 | + | 0.977102i | \(0.431751\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.4794 | −0.398696 | −0.199348 | − | 0.979929i | \(-0.563882\pi\) | ||||
−0.199348 | + | 0.979929i | \(0.563882\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.0801 | − | 12.3091i | 0.384364 | − | 0.426999i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.10582 | − | 1.91534i | −0.0383146 | − | 0.0663627i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.19401 | + | 3.80013i | −0.0759267 | + | 0.131509i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.02766 | + | 38.4759i | −0.139216 | + | 1.32992i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.5224 | − | 39.0100i | 0.777560 | − | 1.34677i | −0.155784 | − | 0.987791i | \(-0.549790\pi\) |
0.933344 | − | 0.358983i | \(-0.116876\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.39367 | + | 4.14596i | 0.0825403 | + | 0.142964i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.86012 | − | 8.73200i | 0.270717 | − | 0.300746i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.09750 | −0.0721563 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 57.5717 | 1.97819 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.3012 | − | 31.6887i | −0.353536 | − | 1.08755i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.185689 | + | 0.321622i | 0.00636533 | + | 0.0110251i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.84105 | − | 11.8490i | 0.234233 | − | 0.405703i | −0.724817 | − | 0.688942i | \(-0.758075\pi\) |
0.959049 | + | 0.283239i | \(0.0914088\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.21421 | + | 21.0103i | 0.0757243 | + | 0.718536i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.9348 | + | 25.8679i | −0.510164 | + | 0.883631i | 0.489766 | + | 0.871854i | \(0.337082\pi\) |
−0.999931 | + | 0.0117768i | \(0.996251\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.77095 | + | 6.53148i | 0.128663 | + | 0.222851i | 0.923159 | − | 0.384418i | \(-0.125598\pi\) |
−0.794496 | + | 0.607270i | \(0.792265\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.40990 | − | 0.936709i | −0.150289 | − | 0.0319230i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.0591 | 0.580698 | 0.290349 | − | 0.956921i | \(-0.406229\pi\) | ||||
0.290349 | + | 0.956921i | \(0.406229\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −49.8277 | −1.69419 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 70.6012 | + | 14.9964i | 2.39774 | + | 0.509306i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.07228 | − | 7.05340i | −0.138143 | − | 0.239270i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.52210 | + | 9.56456i | −0.187109 | + | 0.324083i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.9988 | + | 12.3576i | −0.575321 | + | 0.418241i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.0994 | + | 17.4926i | −0.341421 | + | 0.591358i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.74247 | + | 13.4103i | 0.261445 | + | 0.452835i | 0.966626 | − | 0.256192i | \(-0.0824678\pi\) |
−0.705181 | + | 0.709027i | \(0.749134\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.03879 | + | 18.5766i | 0.203683 | + | 0.626575i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.5541 | −0.894631 | −0.447316 | − | 0.894376i | \(-0.647620\pi\) | ||||
−0.447316 | + | 0.894376i | \(0.647620\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.2262 | −1.08450 | −0.542250 | − | 0.840217i | \(-0.682427\pi\) | ||||
−0.542250 | + | 0.840217i | \(0.682427\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −36.1567 | + | 40.1673i | −1.21539 | + | 1.35021i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.4763 | − | 32.0018i | −0.620373 | − | 1.07452i | −0.989416 | − | 0.145105i | \(-0.953648\pi\) |
0.369044 | − | 0.929412i | \(-0.379685\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.96383 | − | 13.7938i | 0.267098 | − | 0.462628i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −50.0452 | + | 10.6667i | −1.67658 | + | 0.357348i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.72858 | − | 9.92220i | 0.191700 | − | 0.332034i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.3037 | − | 38.6312i | −0.745531 | − | 1.29130i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.302678 | − | 0.336252i | 0.0101061 | − | 0.0112271i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 36.6349 | 1.22184 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 79.7057 | 2.65538 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.738700 | − | 2.27240i | −0.0245824 | − | 0.0756208i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.2949 | + | 31.6877i | 0.608144 | + | 1.05334i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.591871 | + | 1.02515i | −0.0196528 | + | 0.0340396i | −0.875685 | − | 0.482884i | \(-0.839589\pi\) |
0.856032 | + | 0.516923i | \(0.172923\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −21.5593 | + | 15.6730i | −0.715078 | + | 0.519840i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.7752 | + | 46.3760i | −0.887103 | + | 1.53651i | −0.0438179 | + | 0.999040i | \(0.513952\pi\) |
−0.843285 | + | 0.537467i | \(0.819381\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.89569 | + | 17.1398i | 0.327500 | + | 0.567246i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17.2458 | + | 3.66320i | 0.570130 | + | 0.121102i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.05628 | 0.100927 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.67908 | −0.0553878 | −0.0276939 | − | 0.999616i | \(-0.508816\pi\) | ||||
−0.0276939 | + | 0.999616i | \(0.508816\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −37.7511 | − | 8.01872i | −1.24394 | − | 0.264226i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.4303 | + | 24.9940i | 0.474980 | + | 0.822689i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.8893 | − | 30.9851i | 0.588196 | − | 1.01879i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.66650 | − | 15.8131i | −0.0547350 | − | 0.519371i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.2756 | + | 24.7261i | −0.468368 | + | 0.811237i | −0.999346 | − | 0.0361482i | \(-0.988491\pi\) |
0.530978 | + | 0.847385i | \(0.321825\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.291712 | + | 0.505260i | 0.00956047 | + | 0.0165592i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.9158 | − | 39.7320i | −0.422846 | − | 1.30077i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 151.778 | 4.96366 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.8620 | 1.10622 | 0.553111 | − | 0.833108i | \(-0.313441\pi\) | ||||
0.553111 | + | 0.833108i | \(0.313441\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.6736 | − | 37.4088i | 1.09890 | − | 1.22079i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.28984 | + | 14.3584i | 0.270241 | + | 0.468071i | 0.968923 | − | 0.247361i | \(-0.0795633\pi\) |
−0.698682 | + | 0.715432i | \(0.746230\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.0357596 | − | 0.0619374i | 0.00116449 | − | 0.00201696i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 39.5664 | + | 28.7213i | 1.28710 | + | 0.934306i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.8930 | + | 48.3121i | −0.906401 | + | 1.56993i | −0.0873743 | + | 0.996176i | \(0.527848\pi\) |
−0.819026 | + | 0.573756i | \(0.805486\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.18649 | + | 15.9115i | 0.298206 | + | 0.516508i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 37.7445 | − | 41.9313i | 1.22395 | − | 1.35972i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.5366 | −1.44268 | −0.721341 | − | 0.692580i | \(-0.756474\pi\) | ||||
−0.721341 | + | 0.692580i | \(0.756474\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.5457 | 0.923717 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.9802 | + | 46.0825i | 0.484242 | + | 1.48963i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.59017 | + | 14.8786i | 0.277391 | + | 0.480455i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.2151 | + | 21.1572i | −0.394035 | + | 0.682489i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.6668 | + | 9.19451i | 0.665977 | + | 0.296289i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.09348 | + | 8.82216i | −0.163965 | + | 0.283996i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.0863 | + | 24.3982i | 0.452986 | + | 0.784595i | 0.998570 | − | 0.0534616i | \(-0.0170255\pi\) |
−0.545584 | + | 0.838056i | \(0.683692\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −26.2222 | − | 5.56988i | −0.842380 | − | 0.178930i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.8598 | −0.990338 | −0.495169 | − | 0.868797i | \(-0.664894\pi\) | ||||
−0.495169 | + | 0.868797i | \(0.664894\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 60.4755 | 1.93876 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −42.6345 | − | 9.05602i | −1.36540 | − | 0.290025i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.6967 | − | 25.4555i | −0.470190 | − | 0.814393i | 0.529229 | − | 0.848479i | \(-0.322481\pi\) |
−0.999419 | + | 0.0340864i | \(0.989148\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.2666 | − | 61.0836i | 1.12713 | − | 1.95224i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −38.0557 | − | 16.9307i | −1.21502 | − | 0.540557i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.08964 | − | 12.2796i | 0.226124 | − | 0.391659i | −0.730532 | − | 0.682879i | \(-0.760728\pi\) |
0.956656 | + | 0.291220i | \(0.0940610\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.74020 | + | 13.4064i | 0.246623 | + | 0.427164i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.19697 | − | 25.2157i | −0.260912 | − | 0.802624i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.0379061 | 0.00120535 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.0022 | −1.46131 | −0.730654 | − | 0.682748i | \(-0.760785\pi\) | ||||
−0.730654 | + | 0.682748i | \(0.760785\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.6788 | − | 20.7507i | 0.592754 | − | 0.658505i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.5985 | − | 44.3378i | −0.811526 | − | 1.40560i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.1749 | + | 52.2645i | −0.955650 | + | 1.65523i | −0.222777 | + | 0.974869i | \(0.571512\pi\) |
−0.732873 | + | 0.680365i | \(0.761821\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.0518 | − | 15.2816i | −0.666050 | − | 0.483487i |
(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 | 1152.2.i.i.385.6 | ✓ | 12 | |
3.2 | odd | 2 | 3456.2.i.k.1153.6 | 12 | |||
4.3 | odd | 2 | 1152.2.i.k.385.1 | yes | 12 | ||
8.3 | odd | 2 | 1152.2.i.j.385.6 | yes | 12 | ||
8.5 | even | 2 | 1152.2.i.l.385.1 | yes | 12 | ||
9.4 | even | 3 | inner | 1152.2.i.i.769.6 | yes | 12 | |
9.5 | odd | 6 | 3456.2.i.k.2305.6 | 12 | |||
12.11 | even | 2 | 3456.2.i.l.1153.6 | 12 | |||
24.5 | odd | 2 | 3456.2.i.i.1153.1 | 12 | |||
24.11 | even | 2 | 3456.2.i.j.1153.1 | 12 | |||
36.23 | even | 6 | 3456.2.i.l.2305.6 | 12 | |||
36.31 | odd | 6 | 1152.2.i.k.769.1 | yes | 12 | ||
72.5 | odd | 6 | 3456.2.i.i.2305.1 | 12 | |||
72.13 | even | 6 | 1152.2.i.l.769.1 | yes | 12 | ||
72.59 | even | 6 | 3456.2.i.j.2305.1 | 12 | |||
72.67 | odd | 6 | 1152.2.i.j.769.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.i.i.385.6 | ✓ | 12 | 1.1 | even | 1 | trivial | |
1152.2.i.i.769.6 | yes | 12 | 9.4 | even | 3 | inner | |
1152.2.i.j.385.6 | yes | 12 | 8.3 | odd | 2 | ||
1152.2.i.j.769.6 | yes | 12 | 72.67 | odd | 6 | ||
1152.2.i.k.385.1 | yes | 12 | 4.3 | odd | 2 | ||
1152.2.i.k.769.1 | yes | 12 | 36.31 | odd | 6 | ||
1152.2.i.l.385.1 | yes | 12 | 8.5 | even | 2 | ||
1152.2.i.l.769.1 | yes | 12 | 72.13 | even | 6 | ||
3456.2.i.i.1153.1 | 12 | 24.5 | odd | 2 | |||
3456.2.i.i.2305.1 | 12 | 72.5 | odd | 6 | |||
3456.2.i.j.1153.1 | 12 | 24.11 | even | 2 | |||
3456.2.i.j.2305.1 | 12 | 72.59 | even | 6 | |||
3456.2.i.k.1153.6 | 12 | 3.2 | odd | 2 | |||
3456.2.i.k.2305.6 | 12 | 9.5 | odd | 6 | |||
3456.2.i.l.1153.6 | 12 | 12.11 | even | 2 | |||
3456.2.i.l.2305.6 | 12 | 36.23 | even | 6 |