Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(323,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.j (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.4 | ||
Character | \(\chi\) | \(=\) | 1512.323 |
Dual form | 1512.2.j.d.323.3 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.37397 | + | 0.334962i | −0.971545 | + | 0.236854i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.77560 | − | 0.920458i | 0.887800 | − | 0.460229i | ||||
\(5\) | 4.18263 | 1.87053 | 0.935264 | − | 0.353951i | \(-0.115162\pi\) | ||||
0.935264 | + | 0.353951i | \(0.115162\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | −2.13131 | + | 1.85944i | −0.753531 | + | 0.657412i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.74682 | + | 1.40102i | −1.81730 | + | 0.443042i | ||||
\(11\) | − | 1.86730i | − | 0.563011i | −0.959560 | − | 0.281506i | \(-0.909166\pi\) | ||
0.959560 | − | 0.281506i | \(-0.0908338\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.07604i | 0.853139i | 0.904455 | + | 0.426569i | \(0.140278\pi\) | ||||
−0.904455 | + | 0.426569i | \(0.859722\pi\) | |||||||
\(14\) | −0.334962 | − | 1.37397i | −0.0895224 | − | 0.367210i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.30551 | − | 3.26873i | 0.576379 | − | 0.817183i | ||||
\(17\) | 0.504885i | 0.122453i | 0.998124 | + | 0.0612263i | \(0.0195011\pi\) | ||||
−0.998124 | + | 0.0612263i | \(0.980499\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.05596 | 0.701085 | 0.350543 | − | 0.936547i | \(-0.385997\pi\) | ||||
0.350543 | + | 0.936547i | \(0.385997\pi\) | |||||||
\(20\) | 7.42668 | − | 3.84993i | 1.66066 | − | 0.860871i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.625474 | + | 2.56561i | 0.133352 | + | 0.546991i | ||||
\(23\) | −5.97229 | −1.24531 | −0.622654 | − | 0.782497i | \(-0.713946\pi\) | ||||
−0.622654 | + | 0.782497i | \(0.713946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.4944 | 2.49887 | ||||||||
\(26\) | −1.03036 | − | 4.22639i | −0.202069 | − | 0.828863i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.920458 | + | 1.77560i | 0.173950 | + | 0.335557i | ||||
\(29\) | 3.52884 | 0.655289 | 0.327644 | − | 0.944801i | \(-0.393745\pi\) | ||||
0.327644 | + | 0.944801i | \(0.393745\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.8980i | 1.95734i | 0.205435 | + | 0.978671i | \(0.434139\pi\) | ||||
−0.205435 | + | 0.978671i | \(0.565861\pi\) | |||||||
\(32\) | −2.07281 | + | 5.26341i | −0.366425 | + | 0.930448i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.169117 | − | 0.693698i | −0.0290034 | − | 0.118968i | ||||
\(35\) | 4.18263i | 0.706993i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.3660i | 1.86856i | 0.356542 | + | 0.934279i | \(0.383956\pi\) | ||||
−0.356542 | + | 0.934279i | \(0.616044\pi\) | |||||||
\(38\) | −4.19880 | + | 1.02363i | −0.681136 | + | 0.166055i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.91447 | + | 7.77736i | −1.40950 | + | 1.22971i | ||||
\(41\) | − | 7.26960i | − | 1.13532i | −0.823263 | − | 0.567660i | \(-0.807849\pi\) | ||
0.823263 | − | 0.567660i | \(-0.192151\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.02120 | 1.37572 | 0.687860 | − | 0.725844i | \(-0.258550\pi\) | ||||
0.687860 | + | 0.725844i | \(0.258550\pi\) | |||||||
\(44\) | −1.71877 | − | 3.31557i | −0.259114 | − | 0.499841i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.20576 | − | 2.00049i | 1.20987 | − | 0.294957i | ||||
\(47\) | 0.327367 | 0.0477513 | 0.0238757 | − | 0.999715i | \(-0.492399\pi\) | ||||
0.0238757 | + | 0.999715i | \(0.492399\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −17.1669 | + | 4.18514i | −2.42777 | + | 0.591869i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.83136 | + | 5.46181i | 0.392639 | + | 0.757417i | ||||
\(53\) | 8.32940 | 1.14413 | 0.572066 | − | 0.820208i | \(-0.306142\pi\) | ||||
0.572066 | + | 0.820208i | \(0.306142\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.81021i | − | 1.05313i | ||||||
\(56\) | −1.85944 | − | 2.13131i | −0.248479 | − | 0.284808i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.84853 | + | 1.18203i | −0.636643 | + | 0.155208i | ||||
\(59\) | − | 5.98008i | − | 0.778540i | −0.921124 | − | 0.389270i | \(-0.872727\pi\) | ||
0.921124 | − | 0.389270i | \(-0.127273\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 13.2783i | − | 1.70011i | −0.526691 | − | 0.850057i | \(-0.676568\pi\) | ||
0.526691 | − | 0.850057i | \(-0.323432\pi\) | |||||||
\(62\) | −3.65043 | − | 14.9736i | −0.463604 | − | 1.90165i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.08494 | − | 7.92609i | 0.135618 | − | 0.990761i | ||||
\(65\) | 12.8659i | 1.59582i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.21499 | −1.12579 | −0.562895 | − | 0.826528i | \(-0.690312\pi\) | ||||
−0.562895 | + | 0.826528i | \(0.690312\pi\) | |||||||
\(68\) | 0.464725 | + | 0.896474i | 0.0563562 | + | 0.108713i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.40102 | − | 5.74682i | −0.167454 | − | 0.686876i | ||||
\(71\) | −9.02460 | −1.07102 | −0.535512 | − | 0.844528i | \(-0.679881\pi\) | ||||
−0.535512 | + | 0.844528i | \(0.679881\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.416491 | 0.0487466 | 0.0243733 | − | 0.999703i | \(-0.492241\pi\) | ||||
0.0243733 | + | 0.999703i | \(0.492241\pi\) | |||||||
\(74\) | −3.80718 | − | 15.6166i | −0.442576 | − | 1.81539i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.42616 | − | 2.81288i | 0.622424 | − | 0.322660i | ||||
\(77\) | 1.86730 | 0.212798 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.00459i | − | 0.675569i | −0.941224 | − | 0.337784i | \(-0.890323\pi\) | ||
0.941224 | − | 0.337784i | \(-0.109677\pi\) | |||||||
\(80\) | 9.64311 | − | 13.6719i | 1.07813 | − | 1.52856i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.43504 | + | 9.98822i | 0.268905 | + | 1.10301i | ||||
\(83\) | 2.62368i | 0.287987i | 0.989579 | + | 0.143993i | \(0.0459944\pi\) | ||||
−0.989579 | + | 0.143993i | \(0.954006\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.11175i | 0.229051i | ||||||||
\(86\) | −12.3949 | + | 3.02176i | −1.33657 | + | 0.325845i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.47213 | + | 3.97978i | 0.370131 | + | 0.424246i | ||||
\(89\) | 5.69486i | 0.603654i | 0.953363 | + | 0.301827i | \(0.0975966\pi\) | ||||
−0.953363 | + | 0.301827i | \(0.902403\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.07604 | −0.322456 | ||||||||
\(92\) | −10.6044 | + | 5.49724i | −1.10559 | + | 0.573127i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.449793 | + | 0.109655i | −0.0463926 | + | 0.0113101i | ||||
\(95\) | 12.7819 | 1.31140 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.21289 | 0.630824 | 0.315412 | − | 0.948955i | \(-0.397857\pi\) | ||||
0.315412 | + | 0.948955i | \(0.397857\pi\) | |||||||
\(98\) | 1.37397 | − | 0.334962i | 0.138792 | − | 0.0338363i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 22.1850 | − | 11.5005i | 2.21850 | − | 1.15005i | ||||
\(101\) | −1.85216 | −0.184296 | −0.0921482 | − | 0.995745i | \(-0.529373\pi\) | ||||
−0.0921482 | + | 0.995745i | \(0.529373\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.74001i | − | 0.269982i | −0.990847 | − | 0.134991i | \(-0.956900\pi\) | ||
0.990847 | − | 0.134991i | \(-0.0431005\pi\) | |||||||
\(104\) | −5.71971 | − | 6.55598i | −0.560864 | − | 0.642867i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.4444 | + | 2.79004i | −1.11158 | + | 0.270992i | ||||
\(107\) | − | 4.22506i | − | 0.408452i | −0.978924 | − | 0.204226i | \(-0.934532\pi\) | ||
0.978924 | − | 0.204226i | \(-0.0654677\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.9420i | 1.33540i | 0.744432 | + | 0.667698i | \(0.232720\pi\) | ||||
−0.744432 | + | 0.667698i | \(0.767280\pi\) | |||||||
\(110\) | 2.61613 | + | 10.7310i | 0.249438 | + | 1.02316i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.26873 | + | 2.30551i | 0.308866 | + | 0.217851i | ||||
\(113\) | 7.49447i | 0.705020i | 0.935808 | + | 0.352510i | \(0.114672\pi\) | ||||
−0.935808 | + | 0.352510i | \(0.885328\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −24.9799 | −2.32938 | ||||||||
\(116\) | 6.26581 | − | 3.24815i | 0.581766 | − | 0.301583i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.00310 | + | 8.21646i | 0.184400 | + | 0.756387i | ||||
\(119\) | −0.504885 | −0.0462827 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.51320 | 0.683018 | ||||||||
\(122\) | 4.44773 | + | 18.2440i | 0.402679 | + | 1.65174i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.0312 | + | 19.3505i | 0.900825 | + | 1.73773i | ||||
\(125\) | 31.3462 | 2.80369 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 18.0939i | − | 1.60557i | −0.596267 | − | 0.802787i | \(-0.703350\pi\) | ||
0.596267 | − | 0.802787i | \(-0.296650\pi\) | |||||||
\(128\) | 1.16426 | + | 11.2536i | 0.102907 | + | 0.994691i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.30960 | − | 17.6774i | −0.377977 | − | 1.55041i | ||||
\(131\) | − | 9.32625i | − | 0.814839i | −0.913241 | − | 0.407419i | \(-0.866429\pi\) | ||
0.913241 | − | 0.407419i | \(-0.133571\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.05596i | 0.264985i | ||||||||
\(134\) | 12.6611 | − | 3.08667i | 1.09376 | − | 0.266648i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.938805 | − | 1.07607i | −0.0805019 | − | 0.0922718i | ||||
\(137\) | − | 6.53069i | − | 0.557955i | −0.960298 | − | 0.278977i | \(-0.910005\pi\) | ||
0.960298 | − | 0.278977i | \(-0.0899954\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.1589 | −0.861664 | −0.430832 | − | 0.902432i | \(-0.641780\pi\) | ||||
−0.430832 | + | 0.902432i | \(0.641780\pi\) | |||||||
\(140\) | 3.84993 | + | 7.42668i | 0.325379 | + | 0.627669i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.3996 | − | 3.02290i | 1.04055 | − | 0.253676i | ||||
\(143\) | 5.74387 | 0.480327 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.7598 | 1.22574 | ||||||||
\(146\) | −0.572247 | + | 0.139509i | −0.0473595 | + | 0.0115458i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.4619 | + | 20.1815i | 0.859965 | + | 1.65891i | ||||
\(149\) | 9.72516 | 0.796716 | 0.398358 | − | 0.917230i | \(-0.369580\pi\) | ||||
0.398358 | + | 0.917230i | \(0.369580\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.4664i | 1.01450i | 0.861800 | + | 0.507249i | \(0.169338\pi\) | ||||
−0.861800 | + | 0.507249i | \(0.830662\pi\) | |||||||
\(152\) | −6.51319 | + | 5.68238i | −0.528289 | + | 0.460902i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.56561 | + | 0.625474i | −0.206743 | + | 0.0504021i | ||||
\(155\) | 45.5823i | 3.66126i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.3627i | 0.906838i | 0.891297 | + | 0.453419i | \(0.149796\pi\) | ||||
−0.891297 | + | 0.453419i | \(0.850204\pi\) | |||||||
\(158\) | 2.01131 | + | 8.25014i | 0.160011 | + | 0.656346i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.66980 | + | 22.0149i | −0.685408 | + | 1.74043i | ||||
\(161\) | − | 5.97229i | − | 0.470682i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.59449 | −0.281542 | −0.140771 | − | 0.990042i | \(-0.544958\pi\) | ||||
−0.140771 | + | 0.990042i | \(0.544958\pi\) | |||||||
\(164\) | −6.69136 | − | 12.9079i | −0.522507 | − | 1.00794i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.878835 | − | 3.60487i | −0.0682108 | − | 0.279792i | ||||
\(167\) | 20.3801 | 1.57706 | 0.788531 | − | 0.614995i | \(-0.210842\pi\) | ||||
0.788531 | + | 0.614995i | \(0.210842\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.53800 | 0.272154 | ||||||||
\(170\) | −0.707355 | − | 2.90148i | −0.0542517 | − | 0.222533i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 16.0180 | − | 8.30363i | 1.22136 | − | 0.633146i | ||||
\(173\) | −4.49761 | −0.341947 | −0.170974 | − | 0.985276i | \(-0.554691\pi\) | ||||
−0.170974 | + | 0.985276i | \(0.554691\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.4944i | 0.944486i | ||||||||
\(176\) | −6.10369 | − | 4.30508i | −0.460083 | − | 0.324508i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.90756 | − | 7.82459i | −0.142978 | − | 0.586477i | ||||
\(179\) | 2.63430i | 0.196897i | 0.995142 | + | 0.0984485i | \(0.0313880\pi\) | ||||
−0.995142 | + | 0.0984485i | \(0.968612\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 10.3748i | − | 0.771151i | −0.922676 | − | 0.385576i | \(-0.874003\pi\) | ||
0.922676 | − | 0.385576i | \(-0.125997\pi\) | |||||||
\(182\) | 4.22639 | − | 1.03036i | 0.313281 | − | 0.0763751i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.7288 | − | 11.1051i | 0.938379 | − | 0.818681i | ||||
\(185\) | 47.5397i | 3.49519i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.942770 | 0.0689422 | ||||||||
\(188\) | 0.581272 | − | 0.301327i | 0.0423936 | − | 0.0219765i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −17.5620 | + | 4.28147i | −1.27408 | + | 0.310610i | ||||
\(191\) | 18.1707 | 1.31479 | 0.657395 | − | 0.753547i | \(-0.271659\pi\) | ||||
0.657395 | + | 0.753547i | \(0.271659\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.7704 | −1.20716 | −0.603578 | − | 0.797304i | \(-0.706259\pi\) | ||||
−0.603578 | + | 0.797304i | \(0.706259\pi\) | |||||||
\(194\) | −8.53634 | + | 2.08109i | −0.612874 | + | 0.149413i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.77560 | + | 0.920458i | −0.126829 | + | 0.0657470i | ||||
\(197\) | −19.2240 | −1.36965 | −0.684826 | − | 0.728706i | \(-0.740122\pi\) | ||||
−0.684826 | + | 0.728706i | \(0.740122\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.68931i | 0.119752i | 0.998206 | + | 0.0598761i | \(0.0190706\pi\) | ||||
−0.998206 | + | 0.0598761i | \(0.980929\pi\) | |||||||
\(200\) | −26.6294 | + | 23.2326i | −1.88298 | + | 1.64279i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.54481 | − | 0.620402i | 0.179052 | − | 0.0436514i | ||||
\(203\) | 3.52884i | 0.247676i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 30.4060i | − | 2.12365i | ||||||
\(206\) | 0.917801 | + | 3.76470i | 0.0639463 | + | 0.262299i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.0547 | + | 7.09184i | 0.697170 | + | 0.491731i | ||||
\(209\) | − | 5.70638i | − | 0.394719i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.1544 | −0.974427 | −0.487213 | − | 0.873283i | \(-0.661987\pi\) | ||||
−0.487213 | + | 0.873283i | \(0.661987\pi\) | |||||||
\(212\) | 14.7897 | − | 7.66687i | 1.01576 | − | 0.526563i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.41523 | + | 5.80511i | 0.0967434 | + | 0.396829i | ||||
\(215\) | 37.7323 | 2.57332 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.8980 | −0.739806 | ||||||||
\(218\) | −4.67003 | − | 19.1559i | −0.316294 | − | 1.29740i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.18897 | − | 13.8678i | −0.484680 | − | 0.934967i | ||||
\(221\) | −1.55304 | −0.104469 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.33032i | 0.0890851i | 0.999007 | + | 0.0445425i | \(0.0141830\pi\) | ||||
−0.999007 | + | 0.0445425i | \(0.985817\pi\) | |||||||
\(224\) | −5.26341 | − | 2.07281i | −0.351676 | − | 0.138496i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.51036 | − | 10.2972i | −0.166987 | − | 0.684959i | ||||
\(227\) | − | 6.34646i | − | 0.421229i | −0.977569 | − | 0.210615i | \(-0.932453\pi\) | ||
0.977569 | − | 0.210615i | \(-0.0675465\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 13.9920i | − | 0.924619i | −0.886719 | − | 0.462309i | \(-0.847021\pi\) | ||
0.886719 | − | 0.462309i | \(-0.152979\pi\) | |||||||
\(230\) | 34.3217 | − | 8.36732i | 2.26310 | − | 0.551724i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.52104 | + | 6.56168i | −0.493781 | + | 0.430795i | ||||
\(233\) | − | 14.0797i | − | 0.922392i | −0.887298 | − | 0.461196i | \(-0.847420\pi\) | ||
0.887298 | − | 0.461196i | \(-0.152580\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.36925 | 0.0893202 | ||||||||
\(236\) | −5.50441 | − | 10.6182i | −0.358307 | − | 0.691188i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.693698 | − | 0.169117i | 0.0449658 | − | 0.0109623i | ||||
\(239\) | −13.1737 | −0.852134 | −0.426067 | − | 0.904691i | \(-0.640101\pi\) | ||||
−0.426067 | + | 0.904691i | \(0.640101\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.46846 | 0.481086 | 0.240543 | − | 0.970639i | \(-0.422675\pi\) | ||||
0.240543 | + | 0.970639i | \(0.422675\pi\) | |||||||
\(242\) | −10.3229 | + | 2.51664i | −0.663583 | + | 0.161776i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.2221 | − | 23.5770i | −0.782442 | − | 1.50936i | ||||
\(245\) | −4.18263 | −0.267218 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.40024i | 0.598123i | ||||||||
\(248\) | −20.2642 | − | 23.2270i | −1.28678 | − | 1.47492i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −43.0688 | + | 10.4998i | −2.72391 | + | 0.664065i | ||||
\(251\) | 16.3203i | 1.03013i | 0.857151 | + | 0.515065i | \(0.172232\pi\) | ||||
−0.857151 | + | 0.515065i | \(0.827768\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.1520i | 0.701123i | ||||||||
\(254\) | 6.06077 | + | 24.8605i | 0.380287 | + | 1.55989i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.36921 | − | 15.0722i | −0.335576 | − | 0.942013i | ||||
\(257\) | − | 13.6939i | − | 0.854205i | −0.904203 | − | 0.427102i | \(-0.859534\pi\) | ||
0.904203 | − | 0.427102i | \(-0.140466\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.3660 | −0.706249 | ||||||||
\(260\) | 11.8425 | + | 22.8447i | 0.734443 | + | 1.41677i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.12394 | + | 12.8140i | 0.192998 | + | 0.791653i | ||||
\(263\) | −4.63480 | −0.285794 | −0.142897 | − | 0.989738i | \(-0.545642\pi\) | ||||
−0.142897 | + | 0.989738i | \(0.545642\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 34.8388 | 2.14013 | ||||||||
\(266\) | −1.02363 | − | 4.19880i | −0.0627629 | − | 0.257445i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −16.3621 | + | 8.48201i | −0.999477 | + | 0.518121i | ||||
\(269\) | −28.6544 | −1.74709 | −0.873545 | − | 0.486743i | \(-0.838185\pi\) | ||||
−0.873545 | + | 0.486743i | \(0.838185\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 8.27458i | − | 0.502645i | −0.967903 | − | 0.251322i | \(-0.919135\pi\) | ||
0.967903 | − | 0.251322i | \(-0.0808654\pi\) | |||||||
\(272\) | 1.65033 | + | 1.16402i | 0.100066 | + | 0.0705791i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.18754 | + | 8.97299i | 0.132154 | + | 0.542078i | ||||
\(275\) | − | 23.3307i | − | 1.40689i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.5278i | 0.752724i | 0.926473 | + | 0.376362i | \(0.122825\pi\) | ||||
−0.926473 | + | 0.376362i | \(0.877175\pi\) | |||||||
\(278\) | 13.9580 | − | 3.40284i | 0.837146 | − | 0.204089i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.77736 | − | 8.91447i | −0.464786 | − | 0.532741i | ||||
\(281\) | − | 8.63112i | − | 0.514889i | −0.966293 | − | 0.257445i | \(-0.917119\pi\) | ||
0.966293 | − | 0.257445i | \(-0.0828805\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.73498 | 0.519241 | 0.259620 | − | 0.965711i | \(-0.416403\pi\) | ||||
0.259620 | + | 0.965711i | \(0.416403\pi\) | |||||||
\(284\) | −16.0241 | + | 8.30677i | −0.950855 | + | 0.492916i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.89192 | + | 1.92398i | −0.466659 | + | 0.113767i | ||||
\(287\) | 7.26960 | 0.429111 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.7451 | 0.985005 | ||||||||
\(290\) | −20.2796 | + | 4.94398i | −1.19086 | + | 0.290321i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.739522 | − | 0.383362i | 0.0432772 | − | 0.0224346i | ||||
\(293\) | −30.3572 | −1.77348 | −0.886742 | − | 0.462265i | \(-0.847037\pi\) | ||||
−0.886742 | + | 0.462265i | \(0.847037\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 25.0124i | − | 1.45628i | ||||||
\(296\) | −21.1344 | − | 24.2244i | −1.22841 | − | 1.40802i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.3621 | + | 3.25756i | −0.774046 | + | 0.188706i | ||||
\(299\) | − | 18.3710i | − | 1.06242i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.02120i | 0.519973i | ||||||||
\(302\) | −4.17576 | − | 17.1284i | −0.240288 | − | 0.985630i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.04556 | − | 9.98911i | 0.404091 | − | 0.572915i | ||||
\(305\) | − | 55.5382i | − | 3.18011i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.1705 | −1.66485 | −0.832425 | − | 0.554138i | \(-0.813048\pi\) | ||||
−0.832425 | + | 0.554138i | \(0.813048\pi\) | |||||||
\(308\) | 3.31557 | − | 1.71877i | 0.188922 | − | 0.0979359i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.2684 | − | 62.6289i | −0.867185 | − | 3.55708i | ||||
\(311\) | 13.4778 | 0.764253 | 0.382127 | − | 0.924110i | \(-0.375192\pi\) | ||||
0.382127 | + | 0.924110i | \(0.375192\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.7291 | 1.17168 | 0.585838 | − | 0.810428i | \(-0.300765\pi\) | ||||
0.585838 | + | 0.810428i | \(0.300765\pi\) | |||||||
\(314\) | −3.80606 | − | 15.6120i | −0.214788 | − | 0.881034i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.52697 | − | 10.6617i | −0.310916 | − | 0.599770i | ||||
\(317\) | −0.453146 | −0.0254512 | −0.0127256 | − | 0.999919i | \(-0.504051\pi\) | ||||
−0.0127256 | + | 0.999919i | \(0.504051\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6.58939i | − | 0.368935i | ||||||
\(320\) | 4.53791 | − | 33.1519i | 0.253677 | − | 1.85325i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.00049 | + | 8.20576i | 0.111483 | + | 0.457289i | ||||
\(323\) | 1.54291i | 0.0858497i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 38.4331i | 2.13189i | ||||||||
\(326\) | 4.93873 | − | 1.20402i | 0.273531 | − | 0.0666844i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 13.5174 | + | 15.4937i | 0.746374 | + | 0.855499i | ||||
\(329\) | 0.327367i | 0.0180483i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.8798 | 1.36752 | 0.683759 | − | 0.729708i | \(-0.260344\pi\) | ||||
0.683759 | + | 0.729708i | \(0.260344\pi\) | |||||||
\(332\) | 2.41499 | + | 4.65861i | 0.132540 | + | 0.255675i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −28.0018 | + | 6.82658i | −1.53219 | + | 0.373534i | ||||
\(335\) | −38.5429 | −2.10582 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.8036 | 1.18772 | 0.593860 | − | 0.804568i | \(-0.297603\pi\) | ||||
0.593860 | + | 0.804568i | \(0.297603\pi\) | |||||||
\(338\) | −4.86112 | + | 1.18510i | −0.264410 | + | 0.0644608i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.94377 | + | 3.74962i | 0.105416 | + | 0.203352i | ||||
\(341\) | 20.3498 | 1.10201 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −19.2269 | + | 16.7744i | −1.03665 | + | 0.904415i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.17960 | − | 1.50653i | 0.332217 | − | 0.0809916i | ||||
\(347\) | 20.7794i | 1.11550i | 0.830010 | + | 0.557748i | \(0.188335\pi\) | ||||
−0.830010 | + | 0.557748i | \(0.811665\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 30.5928i | − | 1.63760i | −0.574081 | − | 0.818799i | \(-0.694640\pi\) | ||
0.574081 | − | 0.818799i | \(-0.305360\pi\) | |||||||
\(350\) | −4.18514 | − | 17.1669i | −0.223705 | − | 0.917611i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.82834 | + | 3.87055i | 0.523852 | + | 0.206301i | ||||
\(353\) | 19.5174i | 1.03881i | 0.854529 | + | 0.519403i | \(0.173846\pi\) | ||||
−0.854529 | + | 0.519403i | \(0.826154\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −37.7466 | −2.00338 | ||||||||
\(356\) | 5.24188 | + | 10.1118i | 0.277819 | + | 0.535924i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.882392 | − | 3.61946i | −0.0466358 | − | 0.191294i | ||||
\(359\) | 20.3969 | 1.07651 | 0.538254 | − | 0.842783i | \(-0.319084\pi\) | ||||
0.538254 | + | 0.842783i | \(0.319084\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.66111 | −0.508479 | ||||||||
\(362\) | 3.47516 | + | 14.2547i | 0.182650 | + | 0.749208i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.46181 | + | 2.83136i | −0.286277 | + | 0.148404i | ||||
\(365\) | 1.74203 | 0.0911818 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 25.6785i | − | 1.34041i | −0.742177 | − | 0.670203i | \(-0.766207\pi\) | ||
0.742177 | − | 0.670203i | \(-0.233793\pi\) | |||||||
\(368\) | −13.7692 | + | 19.5218i | −0.717769 | + | 1.01764i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −15.9240 | − | 65.3183i | −0.827850 | − | 3.39574i | ||||
\(371\) | 8.32940i | 0.432441i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 12.4313i | − | 0.643669i | −0.946796 | − | 0.321835i | \(-0.895700\pi\) | ||
0.946796 | − | 0.321835i | \(-0.104300\pi\) | |||||||
\(374\) | −1.29534 | + | 0.315792i | −0.0669804 | + | 0.0163292i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.697719 | + | 0.608720i | −0.0359821 | + | 0.0313923i | ||||
\(377\) | 10.8548i | 0.559053i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.90048 | −0.508553 | −0.254277 | − | 0.967132i | \(-0.581837\pi\) | ||||
−0.254277 | + | 0.967132i | \(0.581837\pi\) | |||||||
\(380\) | 22.6956 | − | 11.7652i | 1.16426 | − | 0.603544i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −24.9661 | + | 6.08652i | −1.27738 | + | 0.311413i | ||||
\(383\) | −23.6536 | −1.20864 | −0.604320 | − | 0.796741i | \(-0.706555\pi\) | ||||
−0.604320 | + | 0.796741i | \(0.706555\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.81021 | 0.398045 | ||||||||
\(386\) | 23.0420 | − | 5.61744i | 1.17281 | − | 0.285920i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.0316 | − | 5.71871i | 0.560045 | − | 0.290323i | ||||
\(389\) | 3.14513 | 0.159465 | 0.0797323 | − | 0.996816i | \(-0.474593\pi\) | ||||
0.0797323 | + | 0.996816i | \(0.474593\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.01532i | − | 0.152491i | ||||||
\(392\) | 2.13131 | − | 1.85944i | 0.107647 | − | 0.0939161i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 26.4132 | − | 6.43931i | 1.33068 | − | 0.324408i | ||||
\(395\) | − | 25.1150i | − | 1.26367i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.2176i | 0.613183i | 0.951841 | + | 0.306592i | \(0.0991886\pi\) | ||||
−0.951841 | + | 0.306592i | \(0.900811\pi\) | |||||||
\(398\) | −0.565856 | − | 2.32107i | −0.0283638 | − | 0.116345i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 28.8060 | − | 40.8408i | 1.44030 | − | 2.04204i | ||||
\(401\) | 35.0797i | 1.75180i | 0.482494 | + | 0.875899i | \(0.339731\pi\) | ||||
−0.482494 | + | 0.875899i | \(0.660269\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33.5227 | −1.66988 | ||||||||
\(404\) | −3.28869 | + | 1.70483i | −0.163618 | + | 0.0848186i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.18203 | − | 4.84853i | −0.0586631 | − | 0.240628i | ||||
\(407\) | 21.2237 | 1.05202 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.3489 | −1.35231 | −0.676157 | − | 0.736757i | \(-0.736356\pi\) | ||||
−0.676157 | + | 0.736757i | \(0.736356\pi\) | |||||||
\(410\) | 10.1849 | + | 41.7770i | 0.502995 | + | 2.06322i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.52207 | − | 4.86517i | −0.124253 | − | 0.239690i | ||||
\(413\) | 5.98008 | 0.294260 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.9739i | 0.538687i | ||||||||
\(416\) | −16.1904 | − | 6.37604i | −0.793801 | − | 0.312611i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.91142 | + | 7.84041i | 0.0934908 | + | 0.383487i | ||||
\(419\) | 14.6442i | 0.715417i | 0.933833 | + | 0.357709i | \(0.116442\pi\) | ||||
−0.933833 | + | 0.357709i | \(0.883558\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 20.2168i | − | 0.985305i | −0.870226 | − | 0.492653i | \(-0.836027\pi\) | ||
0.870226 | − | 0.492653i | \(-0.163973\pi\) | |||||||
\(422\) | 19.4477 | − | 4.74118i | 0.946700 | − | 0.230797i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.7525 | + | 15.4881i | −0.862139 | + | 0.752166i | ||||
\(425\) | 6.30822i | 0.305994i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.2783 | 0.642583 | ||||||||
\(428\) | −3.88899 | − | 7.50201i | −0.187981 | − | 0.362623i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −51.8431 | + | 12.6389i | −2.50010 | + | 0.609502i | ||||
\(431\) | −19.6656 | −0.947260 | −0.473630 | − | 0.880724i | \(-0.657057\pi\) | ||||
−0.473630 | + | 0.880724i | \(0.657057\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.9996 | 0.576666 | 0.288333 | − | 0.957530i | \(-0.406899\pi\) | ||||
0.288333 | + | 0.957530i | \(0.406899\pi\) | |||||||
\(434\) | 14.9736 | − | 3.65043i | 0.718755 | − | 0.175226i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.8330 | + | 24.7553i | 0.614588 | + | 1.18557i | ||||
\(437\) | −18.2511 | −0.873068 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 7.82113i | − | 0.373282i | −0.982428 | − | 0.186641i | \(-0.940240\pi\) | ||
0.982428 | − | 0.186641i | \(-0.0597601\pi\) | |||||||
\(440\) | 14.5226 | + | 16.6460i | 0.692340 | + | 0.793565i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.13384 | − | 0.520211i | 0.101496 | − | 0.0247439i | ||||
\(443\) | − | 29.9854i | − | 1.42465i | −0.701850 | − | 0.712325i | \(-0.747642\pi\) | ||
0.701850 | − | 0.712325i | \(-0.252358\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.8195i | 1.12915i | ||||||||
\(446\) | −0.445608 | − | 1.82783i | −0.0211002 | − | 0.0865502i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.92609 | + | 1.08494i | 0.374473 | + | 0.0512587i | ||||
\(449\) | − | 42.0892i | − | 1.98631i | −0.116797 | − | 0.993156i | \(-0.537263\pi\) | ||
0.116797 | − | 0.993156i | \(-0.462737\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.5745 | −0.639198 | ||||||||
\(452\) | 6.89834 | + | 13.3072i | 0.324471 | + | 0.625917i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.12582 | + | 8.71986i | 0.0997699 | + | 0.409243i | ||||
\(455\) | −12.8659 | −0.603163 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.1655 | −0.569079 | −0.284540 | − | 0.958664i | \(-0.591841\pi\) | ||||
−0.284540 | + | 0.958664i | \(0.591841\pi\) | |||||||
\(458\) | 4.68680 | + | 19.2247i | 0.219000 | + | 0.898309i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −44.3543 | + | 22.9929i | −2.06803 | + | 1.07205i | ||||
\(461\) | −29.0054 | −1.35091 | −0.675457 | − | 0.737399i | \(-0.736054\pi\) | ||||
−0.675457 | + | 0.737399i | \(0.736054\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 5.21317i | − | 0.242277i | −0.992636 | − | 0.121138i | \(-0.961346\pi\) | ||
0.992636 | − | 0.121138i | \(-0.0386545\pi\) | |||||||
\(464\) | 8.13579 | − | 11.5348i | 0.377695 | − | 0.535491i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.71617 | + | 19.3451i | 0.218472 | + | 0.896146i | ||||
\(467\) | 12.3061i | 0.569460i | 0.958608 | + | 0.284730i | \(0.0919039\pi\) | ||||
−0.958608 | + | 0.284730i | \(0.908096\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 9.21499i | − | 0.425509i | ||||||
\(470\) | −1.88132 | + | 0.458648i | −0.0867786 | + | 0.0211559i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.1196 | + | 12.7454i | 0.511822 | + | 0.586654i | ||||
\(473\) | − | 16.8452i | − | 0.774545i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 38.1823 | 1.75192 | ||||||||
\(476\) | −0.896474 | + | 0.464725i | −0.0410898 | + | 0.0213007i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.1003 | − | 4.41269i | 0.827887 | − | 0.201832i | ||||
\(479\) | −19.9609 | −0.912038 | −0.456019 | − | 0.889970i | \(-0.650725\pi\) | ||||
−0.456019 | + | 0.889970i | \(0.650725\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.9622 | −1.59414 | ||||||||
\(482\) | −10.2615 | + | 2.50165i | −0.467396 | + | 0.113947i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13.3404 | − | 6.91559i | 0.606384 | − | 0.314345i | ||||
\(485\) | 25.9862 | 1.17997 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.61420i | 0.254404i | 0.991877 | + | 0.127202i | \(0.0405996\pi\) | ||||
−0.991877 | + | 0.127202i | \(0.959400\pi\) | |||||||
\(488\) | 24.6903 | + | 28.3002i | 1.11768 | + | 1.28109i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.74682 | − | 1.40102i | 0.259615 | − | 0.0632918i | ||||
\(491\) | − | 9.07131i | − | 0.409382i | −0.978827 | − | 0.204691i | \(-0.934381\pi\) | ||
0.978827 | − | 0.204691i | \(-0.0656190\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.78166i | 0.0802418i | ||||||||
\(494\) | −3.14873 | − | 12.9157i | −0.141668 | − | 0.581104i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 35.6227 | + | 25.1255i | 1.59951 | + | 1.12817i | ||||
\(497\) | − | 9.02460i | − | 0.404809i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.4346 | −1.63103 | −0.815517 | − | 0.578732i | \(-0.803548\pi\) | ||||
−0.815517 | + | 0.578732i | \(0.803548\pi\) | |||||||
\(500\) | 55.6583 | − | 28.8528i | 2.48911 | − | 1.29034i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.46669 | − | 22.4237i | −0.243990 | − | 1.00082i | ||||
\(503\) | −4.10995 | −0.183253 | −0.0916267 | − | 0.995793i | \(-0.529207\pi\) | ||||
−0.0916267 | + | 0.995793i | \(0.529207\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.74688 | −0.344732 | ||||||||
\(506\) | −3.73551 | − | 15.3226i | −0.166064 | − | 0.681172i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16.6547 | − | 32.1275i | −0.738931 | − | 1.42543i | ||||
\(509\) | −17.5175 | −0.776450 | −0.388225 | − | 0.921565i | \(-0.626912\pi\) | ||||
−0.388225 | + | 0.921565i | \(0.626912\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.416491i | 0.0184245i | ||||||||
\(512\) | 12.4258 | + | 18.9103i | 0.549147 | + | 0.835726i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.58696 | + | 18.8151i | 0.202322 | + | 0.829899i | ||||
\(515\) | − | 11.4605i | − | 0.505008i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.611291i | − | 0.0268845i | ||||||
\(518\) | 15.6166 | − | 3.80718i | 0.686153 | − | 0.167278i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −23.9234 | − | 27.4212i | −1.04911 | − | 1.20250i | ||||
\(521\) | 40.7567i | 1.78558i | 0.450472 | + | 0.892791i | \(0.351256\pi\) | ||||
−0.450472 | + | 0.892791i | \(0.648744\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.03412 | 0.307581 | 0.153790 | − | 0.988103i | \(-0.450852\pi\) | ||||
0.153790 | + | 0.988103i | \(0.450852\pi\) | |||||||
\(524\) | −8.58442 | − | 16.5597i | −0.375012 | − | 0.723414i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.36808 | − | 1.55248i | 0.277662 | − | 0.0676915i | ||||
\(527\) | −5.50225 | −0.239682 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.6683 | 0.550794 | ||||||||
\(530\) | −47.8675 | + | 11.6697i | −2.07923 | + | 0.506899i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.81288 | + | 5.42616i | 0.121954 | + | 0.235254i | ||||
\(533\) | 22.3615 | 0.968586 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 17.6718i | − | 0.764020i | ||||||
\(536\) | 19.6400 | − | 17.1347i | 0.848318 | − | 0.740108i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 39.3704 | − | 9.59815i | 1.69738 | − | 0.413806i | ||||
\(539\) | 1.86730i | 0.0804302i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 19.6764i | − | 0.845953i | −0.906141 | − | 0.422976i | \(-0.860985\pi\) | ||
0.906141 | − | 0.422976i | \(-0.139015\pi\) | |||||||
\(542\) | 2.77167 | + | 11.3690i | 0.119053 | + | 0.488342i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.65742 | − | 1.04653i | −0.113936 | − | 0.0448697i | ||||
\(545\) | 58.3140i | 2.49790i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.8078 | 0.761408 | 0.380704 | − | 0.924697i | \(-0.375682\pi\) | ||||
0.380704 | + | 0.924697i | \(0.375682\pi\) | |||||||
\(548\) | −6.01123 | − | 11.5959i | −0.256787 | − | 0.495352i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.81491 | + | 32.0557i | 0.333229 | + | 1.36686i | ||||
\(551\) | 10.7840 | 0.459413 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.00459 | 0.255341 | ||||||||
\(554\) | −4.19635 | − | 17.2129i | −0.178286 | − | 0.731306i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.0381 | + | 9.35081i | −0.764986 | + | 0.396563i | ||||
\(557\) | 5.99646 | 0.254078 | 0.127039 | − | 0.991898i | \(-0.459453\pi\) | ||||
0.127039 | + | 0.991898i | \(0.459453\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.7495i | 1.17368i | ||||||||
\(560\) | 13.6719 | + | 9.64311i | 0.577743 | + | 0.407496i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.89110 | + | 11.8589i | 0.121954 | + | 0.500238i | ||||
\(563\) | − | 20.4848i | − | 0.863333i | −0.902033 | − | 0.431667i | \(-0.857926\pi\) | ||
0.902033 | − | 0.431667i | \(-0.142074\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.3466i | 1.31876i | ||||||||
\(566\) | −12.0016 | + | 2.92589i | −0.504466 | + | 0.122984i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 19.2342 | − | 16.7807i | 0.807049 | − | 0.704104i | ||||
\(569\) | − | 38.1889i | − | 1.60096i | −0.599359 | − | 0.800480i | \(-0.704578\pi\) | ||
0.599359 | − | 0.800480i | \(-0.295422\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.3551 | 0.475198 | 0.237599 | − | 0.971363i | \(-0.423640\pi\) | ||||
0.237599 | + | 0.971363i | \(0.423640\pi\) | |||||||
\(572\) | 10.1988 | − | 5.28699i | 0.426434 | − | 0.221060i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.98822 | + | 2.43504i | −0.416900 | + | 0.101637i | ||||
\(575\) | −74.6200 | −3.11187 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.7869 | −0.865371 | −0.432685 | − | 0.901545i | \(-0.642434\pi\) | ||||
−0.432685 | + | 0.901545i | \(0.642434\pi\) | |||||||
\(578\) | −23.0073 | + | 5.60897i | −0.956977 | + | 0.233303i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 26.2075 | − | 13.5858i | 1.08821 | − | 0.564119i | ||||
\(581\) | −2.62368 | −0.108849 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 15.5535i | − | 0.644159i | ||||||
\(584\) | −0.887670 | + | 0.774441i | −0.0367321 | + | 0.0320466i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 41.7099 | − | 10.1685i | 1.72302 | − | 0.420057i | ||||
\(587\) | 24.3849i | 1.00647i | 0.864148 | + | 0.503237i | \(0.167858\pi\) | ||||
−0.864148 | + | 0.503237i | \(0.832142\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.3039i | 1.37226i | ||||||||
\(590\) | 8.37823 | + | 34.3664i | 0.344926 | + | 1.41484i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 37.1524 | + | 26.2045i | 1.52695 | + | 1.07700i | ||||
\(593\) | − | 32.5053i | − | 1.33483i | −0.744684 | − | 0.667417i | \(-0.767400\pi\) | ||
0.744684 | − | 0.667417i | \(-0.232600\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.11175 | −0.0865731 | ||||||||
\(596\) | 17.2680 | − | 8.95160i | 0.707325 | − | 0.366672i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.15359 | + | 25.2412i | 0.251639 | + | 1.03219i | ||||
\(599\) | 10.4800 | 0.428200 | 0.214100 | − | 0.976812i | \(-0.431318\pi\) | ||||
0.214100 | + | 0.976812i | \(0.431318\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.4946 | −0.917575 | −0.458787 | − | 0.888546i | \(-0.651716\pi\) | ||||
−0.458787 | + | 0.888546i | \(0.651716\pi\) | |||||||
\(602\) | −3.02176 | − | 12.3949i | −0.123158 | − | 0.505177i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.4748 | + | 22.1353i | 0.466901 | + | 0.900671i | ||||
\(605\) | 31.4249 | 1.27761 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.3672i | 1.31374i | 0.754002 | + | 0.656872i | \(0.228121\pi\) | ||||
−0.754002 | + | 0.656872i | \(0.771879\pi\) | |||||||
\(608\) | −6.33443 | + | 16.0848i | −0.256895 | + | 0.652323i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.6032 | + | 76.3080i | 0.753222 | + | 3.08962i | ||||
\(611\) | 1.00699i | 0.0407385i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 34.8714i | − | 1.40844i | −0.709981 | − | 0.704220i | \(-0.751297\pi\) | ||
0.709981 | − | 0.704220i | \(-0.248703\pi\) | |||||||
\(614\) | 40.0795 | − | 9.77102i | 1.61748 | − | 0.394326i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.97978 | + | 3.47213i | −0.160350 | + | 0.139896i | ||||
\(617\) | 2.47324i | 0.0995688i | 0.998760 | + | 0.0497844i | \(0.0158534\pi\) | ||||
−0.998760 | + | 0.0497844i | \(0.984147\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.2375 | −0.612447 | −0.306223 | − | 0.951960i | \(-0.599065\pi\) | ||||
−0.306223 | + | 0.951960i | \(0.599065\pi\) | |||||||
\(620\) | 41.9566 | + | 80.9360i | 1.68502 | + | 3.25047i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.5181 | + | 4.51454i | −0.742507 | + | 0.181017i | ||||
\(623\) | −5.69486 | −0.228160 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 68.6375 | 2.74550 | ||||||||
\(626\) | −28.4812 | + | 6.94346i | −1.13834 | + | 0.277516i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.4588 | + | 20.1755i | 0.417353 | + | 0.805091i | ||||
\(629\) | −5.73852 | −0.228810 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 23.2064i | − | 0.923832i | −0.886924 | − | 0.461916i | \(-0.847162\pi\) | ||
0.886924 | − | 0.461916i | \(-0.152838\pi\) | |||||||
\(632\) | 11.1652 | + | 12.7976i | 0.444127 | + | 0.509062i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.622610 | − | 0.151787i | 0.0247270 | − | 0.00602823i | ||||
\(635\) | − | 75.6800i | − | 3.00327i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 3.07604i | − | 0.121877i | ||||||
\(638\) | 2.20720 | + | 9.05364i | 0.0873838 | + | 0.358437i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.86967 | + | 47.0698i | 0.192491 | + | 1.86060i | ||||
\(641\) | − | 29.5988i | − | 1.16908i | −0.811364 | − | 0.584541i | \(-0.801275\pi\) | ||
0.811364 | − | 0.584541i | \(-0.198725\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.8060 | 1.13600 | 0.567999 | − | 0.823029i | \(-0.307718\pi\) | ||||
0.567999 | + | 0.823029i | \(0.307718\pi\) | |||||||
\(644\) | −5.49724 | − | 10.6044i | −0.216622 | − | 0.417872i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.516816 | − | 2.11991i | −0.0203339 | − | 0.0834069i | ||||
\(647\) | −27.3622 | −1.07572 | −0.537860 | − | 0.843034i | \(-0.680767\pi\) | ||||
−0.537860 | + | 0.843034i | \(0.680767\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.1666 | −0.438327 | ||||||||
\(650\) | −12.8737 | − | 52.8061i | −0.504946 | − | 2.07123i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.38238 | + | 3.30858i | −0.249953 | + | 0.129574i | ||||
\(653\) | −39.9292 | −1.56255 | −0.781275 | − | 0.624187i | \(-0.785430\pi\) | ||||
−0.781275 | + | 0.624187i | \(0.785430\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 39.0082i | − | 1.52418i | ||||||
\(656\) | −23.7624 | − | 16.7602i | −0.927764 | − | 0.654374i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.109655 | − | 0.449793i | −0.00427482 | − | 0.0175347i | ||||
\(659\) | 14.9809i | 0.583572i | 0.956484 | + | 0.291786i | \(0.0942495\pi\) | ||||
−0.956484 | + | 0.291786i | \(0.905751\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.0963i | 1.28730i | 0.765322 | + | 0.643648i | \(0.222580\pi\) | ||||
−0.765322 | + | 0.643648i | \(0.777420\pi\) | |||||||
\(662\) | −34.1842 | + | 8.33380i | −1.32861 | + | 0.323902i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.87859 | − | 5.59187i | −0.189326 | − | 0.217007i | ||||
\(665\) | 12.7819i | 0.495662i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.0753 | −0.816037 | ||||||||
\(668\) | 36.1870 | − | 18.7591i | 1.40012 | − | 0.725810i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 52.9568 | − | 12.9104i | 2.04590 | − | 0.498773i | ||||
\(671\) | −24.7945 | −0.957183 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.1189 | −0.467150 | −0.233575 | − | 0.972339i | \(-0.575043\pi\) | ||||
−0.233575 | + | 0.972339i | \(0.575043\pi\) | |||||||
\(674\) | −29.9576 | + | 7.30340i | −1.15392 | + | 0.281316i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.28208 | − | 3.25658i | 0.241618 | − | 0.125253i | ||||
\(677\) | 27.7231 | 1.06549 | 0.532743 | − | 0.846277i | \(-0.321161\pi\) | ||||
0.532743 | + | 0.846277i | \(0.321161\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.21289i | 0.238429i | ||||||||
\(680\) | −3.92667 | − | 4.50078i | −0.150581 | − | 0.172597i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −27.9601 | + | 6.81643i | −1.07065 | + | 0.261014i | ||||
\(683\) | − | 9.79813i | − | 0.374915i | −0.982273 | − | 0.187457i | \(-0.939975\pi\) | ||
0.982273 | − | 0.187457i | \(-0.0600247\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 27.3155i | − | 1.04367i | ||||||
\(686\) | 0.334962 | + | 1.37397i | 0.0127889 | + | 0.0524585i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20.7985 | − | 29.4879i | 0.792935 | − | 1.12421i | ||||
\(689\) | 25.6215i | 0.976103i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.4765 | −1.42567 | −0.712837 | − | 0.701330i | \(-0.752590\pi\) | ||||
−0.712837 | + | 0.701330i | \(0.752590\pi\) | |||||||
\(692\) | −7.98597 | + | 4.13987i | −0.303581 | + | 0.157374i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.96032 | − | 28.5503i | −0.264210 | − | 1.08376i | ||||
\(695\) | −42.4908 | −1.61177 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.67031 | 0.139023 | ||||||||
\(698\) | 10.2475 | + | 42.0337i | 0.387872 | + | 1.59100i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 11.5005 | + | 22.1850i | 0.434680 | + | 0.838515i | ||||
\(701\) | −22.6525 | −0.855575 | −0.427787 | − | 0.903879i | \(-0.640707\pi\) | ||||
−0.427787 | + | 0.903879i | \(0.640707\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 34.7340i | 1.31002i | ||||||||
\(704\) | −14.8004 | − | 2.02591i | −0.557810 | − | 0.0763543i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.53759 | − | 26.8164i | −0.246045 | − | 1.00925i | ||||
\(707\) | − | 1.85216i | − | 0.0696575i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.58535i | − | 0.0595393i | −0.999557 | − | 0.0297696i | \(-0.990523\pi\) | ||
0.999557 | − | 0.0297696i | \(-0.00947737\pi\) | |||||||
\(710\) | 51.8627 | − | 12.6437i | 1.94637 | − | 0.474509i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.5893 | − | 12.1375i | −0.396850 | − | 0.454872i | ||||
\(713\) | − | 65.0861i | − | 2.43749i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0245 | 0.898465 | ||||||||
\(716\) | 2.42476 | + | 4.67747i | 0.0906177 | + | 0.174805i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −28.0248 | + | 6.83220i | −1.04588 | + | 0.254975i | ||||
\(719\) | −17.7228 | −0.660948 | −0.330474 | − | 0.943815i | \(-0.607209\pi\) | ||||
−0.330474 | + | 0.943815i | \(0.607209\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.74001 | 0.102043 | ||||||||
\(722\) | 13.2741 | − | 3.23611i | 0.494011 | − | 0.120435i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.54955 | − | 18.4215i | −0.354906 | − | 0.684628i | ||||
\(725\) | 44.0906 | 1.63749 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.31812i | 0.123062i | 0.998105 | + | 0.0615312i | \(0.0195984\pi\) | ||||
−0.998105 | + | 0.0615312i | \(0.980402\pi\) | |||||||
\(728\) | 6.55598 | − | 5.71971i | 0.242981 | − | 0.211987i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.39350 | + | 0.583513i | −0.0885873 | + | 0.0215968i | ||||
\(731\) | 4.55467i | 0.168460i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 18.8547i | − | 0.696414i | −0.937418 | − | 0.348207i | \(-0.886791\pi\) | ||
0.937418 | − | 0.348207i | \(-0.113209\pi\) | |||||||
\(734\) | 8.60133 | + | 35.2816i | 0.317481 | + | 1.30227i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.3794 | − | 31.4346i | 0.456312 | − | 1.15869i | ||||
\(737\) | 17.2071i | 0.633832i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.3560 | −1.22702 | −0.613510 | − | 0.789687i | \(-0.710243\pi\) | ||||
−0.613510 | + | 0.789687i | \(0.710243\pi\) | |||||||
\(740\) | 43.7583 | + | 84.4116i | 1.60859 | + | 3.10303i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.79004 | − | 11.4444i | −0.102425 | − | 0.420136i | ||||
\(743\) | 27.0826 | 0.993565 | 0.496783 | − | 0.867875i | \(-0.334515\pi\) | ||||
0.496783 | + | 0.867875i | \(0.334515\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40.6767 | 1.49028 | ||||||||
\(746\) | 4.16402 | + | 17.0803i | 0.152456 | + | 0.625354i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.67398 | − | 0.867780i | 0.0612069 | − | 0.0317292i | ||||
\(749\) | 4.22506 | 0.154380 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 44.3284i | − | 1.61757i | −0.588107 | − | 0.808783i | \(-0.700126\pi\) | ||
0.588107 | − | 0.808783i | \(-0.299874\pi\) | |||||||
\(752\) | 0.754748 | − | 1.07007i | 0.0275228 | − | 0.0390216i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.63596 | − | 14.9142i | −0.132414 | − | 0.543145i | ||||
\(755\) | 52.1421i | 1.89765i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.3093i | 0.447391i | 0.974659 | + | 0.223695i | \(0.0718121\pi\) | ||||
−0.974659 | + | 0.223695i | \(0.928188\pi\) | |||||||
\(758\) | 13.6030 | − | 3.31629i | 0.494083 | − | 0.120453i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −27.2422 | + | 23.7673i | −0.988180 | + | 0.862130i | ||||
\(761\) | 1.85054i | 0.0670820i | 0.999437 | + | 0.0335410i | \(0.0106784\pi\) | ||||
−0.999437 | + | 0.0335410i | \(0.989322\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.9420 | −0.504733 | ||||||||
\(764\) | 32.2640 | − | 16.7254i | 1.16727 | − | 0.605104i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.4993 | − | 7.92305i | 1.17425 | − | 0.286272i | ||||
\(767\) | 18.3949 | 0.664203 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.2463 | −1.12677 | −0.563386 | − | 0.826194i | \(-0.690502\pi\) | ||||
−0.563386 | + | 0.826194i | \(0.690502\pi\) | |||||||
\(770\) | −10.7310 | + | 2.61613i | −0.386719 | + | 0.0942786i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −29.7775 | + | 15.4364i | −1.07171 | + | 0.555569i | ||||
\(773\) | −44.4521 | −1.59883 | −0.799415 | − | 0.600779i | \(-0.794857\pi\) | ||||
−0.799415 | + | 0.600779i | \(0.794857\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 136.164i | 4.89115i | ||||||||
\(776\) | −13.2416 | + | 11.5525i | −0.475345 | + | 0.414711i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.32133 | + | 1.05350i | −0.154927 | + | 0.0377698i | ||||
\(779\) | − | 22.2156i | − | 0.795956i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.8516i | 0.602998i | ||||||||
\(782\) | 1.01002 | + | 4.14297i | 0.0361182 | + | 0.148152i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.30551 | + | 3.26873i | −0.0823398 | + | 0.116740i | ||||
\(785\) | 47.5257i | 1.69627i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.0995 | 1.00164 | 0.500820 | − | 0.865551i | \(-0.333032\pi\) | ||||
0.500820 | + | 0.865551i | \(0.333032\pi\) | |||||||
\(788\) | −34.1341 | + | 17.6949i | −1.21598 | + | 0.630354i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.41256 | + | 34.5073i | 0.299306 | + | 1.22771i | ||||
\(791\) | −7.49447 | −0.266473 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.8446 | 1.45043 | ||||||||
\(794\) | −4.09243 | − | 16.7866i | −0.145235 | − | 0.595735i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.55494 | + | 2.99955i | 0.0551135 | + | 0.106316i | ||||
\(797\) | 42.9492 | 1.52134 | 0.760670 | − | 0.649139i | \(-0.224871\pi\) | ||||
0.760670 | + | 0.649139i | \(0.224871\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.165282i | 0.00584727i | ||||||||
\(800\) | −25.8985 | + | 65.7630i | −0.915649 | + | 2.32507i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.7504 | − | 48.1986i | −0.414921 | − | 1.70195i | ||||
\(803\) | − | 0.777712i | − | 0.0274449i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 24.9799i | − | 0.880425i | ||||||
\(806\) | 46.0593 | − | 11.2288i | 1.62237 | − | 0.395519i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.94751 | − | 3.44398i | 0.138873 | − | 0.121159i | ||||
\(809\) | 8.54301i | 0.300356i | 0.988659 | + | 0.150178i | \(0.0479847\pi\) | ||||
−0.988659 | + | 0.150178i | \(0.952015\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.6880 | 1.21806 | 0.609030 | − | 0.793147i | \(-0.291559\pi\) | ||||
0.609030 | + | 0.793147i | \(0.291559\pi\) | |||||||
\(812\) | 3.24815 | + | 6.26581i | 0.113988 | + | 0.219887i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −29.1608 | + | 7.10914i | −1.02208 | + | 0.249175i | ||||
\(815\) | −15.0344 | −0.526632 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.5684 | 0.964497 | ||||||||
\(818\) | 37.5766 | − | 9.16084i | 1.31383 | − | 0.320301i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −27.9875 | − | 53.9889i | −0.977364 | − | 1.88538i | ||||
\(821\) | −8.46951 | −0.295588 | −0.147794 | − | 0.989018i | \(-0.547217\pi\) | ||||
−0.147794 | + | 0.989018i | \(0.547217\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.5109i | 1.55155i | 0.631008 | + | 0.775777i | \(0.282642\pi\) | ||||
−0.631008 | + | 0.775777i | \(0.717358\pi\) | |||||||
\(824\) | 5.09490 | + | 5.83981i | 0.177489 | + | 0.203439i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.21646 | + | 2.00310i | −0.285887 | + | 0.0696968i | ||||
\(827\) | 36.3895i | 1.26539i | 0.774403 | + | 0.632693i | \(0.218051\pi\) | ||||
−0.774403 | + | 0.632693i | \(0.781949\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 39.2607i | − | 1.36358i | −0.731548 | − | 0.681790i | \(-0.761202\pi\) | ||
0.731548 | − | 0.681790i | \(-0.238798\pi\) | |||||||
\(830\) | −3.67584 | − | 15.0778i | −0.127590 | − | 0.523359i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24.3809 | + | 3.33732i | 0.845257 | + | 0.115701i | ||||
\(833\) | − | 0.504885i | − | 0.0174932i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 85.2425 | 2.94994 | ||||||||
\(836\) | −5.25249 | − | 10.1323i | −0.181661 | − | 0.350431i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.90527 | − | 20.1208i | −0.169450 | − | 0.695060i | ||||
\(839\) | −15.1101 | −0.521659 | −0.260830 | − | 0.965385i | \(-0.583996\pi\) | ||||
−0.260830 | + | 0.965385i | \(0.583996\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.5473 | −0.570596 | ||||||||
\(842\) | 6.77186 | + | 27.7773i | 0.233374 | + | 0.957268i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −25.1325 | + | 13.0285i | −0.865096 | + | 0.448459i | ||||
\(845\) | 14.7981 | 0.509072 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.51320i | 0.258157i | ||||||||
\(848\) | 19.2036 | − | 27.2266i | 0.659453 | − | 0.934965i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.11302 | − | 8.66732i | −0.0724759 | − | 0.297287i | ||||
\(851\) | − | 67.8810i | − | 2.32693i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 23.4153i | − | 0.801724i | −0.916138 | − | 0.400862i | \(-0.868711\pi\) | ||
0.916138 | − | 0.400862i | \(-0.131289\pi\) | |||||||
\(854\) | −18.2440 | + | 4.44773i | −0.624298 | + | 0.152198i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.85625 | + | 9.00489i | 0.268521 | + | 0.307781i | ||||
\(857\) | 20.7800i | 0.709833i | 0.934898 | + | 0.354916i | \(0.115491\pi\) | ||||
−0.934898 | + | 0.354916i | \(0.884509\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.0088 | 0.409735 | 0.204868 | − | 0.978790i | \(-0.434324\pi\) | ||||
0.204868 | + | 0.978790i | \(0.434324\pi\) | |||||||
\(860\) | 66.9975 | − | 34.7310i | 2.28460 | − | 1.18432i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27.0200 | − | 6.58725i | 0.920306 | − | 0.224363i | ||||
\(863\) | −11.5254 | −0.392328 | −0.196164 | − | 0.980571i | \(-0.562849\pi\) | ||||
−0.196164 | + | 0.980571i | \(0.562849\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.8118 | −0.639622 | ||||||||
\(866\) | −16.4872 | + | 4.01943i | −0.560257 | + | 0.136586i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −19.3505 | + | 10.0312i | −0.656800 | + | 0.340480i | ||||
\(869\) | −11.2123 | −0.380353 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 28.3456i | − | 0.960455i | ||||||
\(872\) | −25.9243 | − | 29.7146i | −0.877906 | − | 1.00626i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 25.0765 | − | 6.11342i | 0.848225 | − | 0.206790i | ||||
\(875\) | 31.3462i | 1.05969i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 7.25986i | − | 0.245148i | −0.992459 | − | 0.122574i | \(-0.960885\pi\) | ||
0.992459 | − | 0.122574i | \(-0.0391149\pi\) | |||||||
\(878\) | 2.61978 | + | 10.7460i | 0.0884134 | + | 0.362660i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −25.5295 | − | 18.0065i | −0.860598 | − | 0.607000i | ||||
\(881\) | 10.7411i | 0.361876i | 0.983495 | + | 0.180938i | \(0.0579133\pi\) | ||||
−0.983495 | + | 0.180938i | \(0.942087\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.09009 | 0.305906 | 0.152953 | − | 0.988233i | \(-0.451122\pi\) | ||||
0.152953 | + | 0.988233i | \(0.451122\pi\) | |||||||
\(884\) | −2.75759 | + | 1.42951i | −0.0927477 | + | 0.0480797i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.0440 | + | 41.1991i | 0.337434 | + | 1.38411i | ||||
\(887\) | 29.0988 | 0.977041 | 0.488521 | − | 0.872552i | \(-0.337537\pi\) | ||||
0.488521 | + | 0.872552i | \(0.337537\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0939 | 0.606850 | ||||||||
\(890\) | −7.97863 | − | 32.7273i | −0.267444 | − | 1.09702i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.22451 | + | 2.36212i | 0.0409995 | + | 0.0790898i | ||||
\(893\) | 1.00042 | 0.0334778 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.0183i | 0.368301i | ||||||||
\(896\) | −11.2536 | + | 1.16426i | −0.375958 | + | 0.0388952i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.0983 | + | 57.8294i | 0.470466 | + | 1.92979i | ||||
\(899\) | 38.4574i | 1.28262i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.20539i | 0.140102i | ||||||||
\(902\) | 18.6510 | − | 4.54694i | 0.621010 | − | 0.151397i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.9355 | − | 15.9730i | −0.463489 | − | 0.531254i | ||||
\(905\) | − | 43.3938i | − | 1.44246i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.9962 | 0.996008 | 0.498004 | − | 0.867175i | \(-0.334067\pi\) | ||||
0.498004 | + | 0.867175i | \(0.334067\pi\) | |||||||
\(908\) | −5.84165 | − | 11.2688i | −0.193862 | − | 0.373967i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 17.6774 | − | 4.30960i | 0.586000 | − | 0.142862i | ||||
\(911\) | 43.3253 | 1.43543 | 0.717716 | − | 0.696336i | \(-0.245188\pi\) | ||||
0.717716 | + | 0.696336i | \(0.245188\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.89919 | 0.162140 | ||||||||
\(914\) | 16.7151 | − | 4.07499i | 0.552886 | − | 0.134789i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.8791 | − | 24.8442i | −0.425536 | − | 0.820877i | ||||
\(917\) | 9.32625 | 0.307980 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 44.6079i | − | 1.47148i | −0.677264 | − | 0.735740i | \(-0.736835\pi\) | ||
0.677264 | − | 0.735740i | \(-0.263165\pi\) | |||||||
\(920\) | 53.2398 | − | 46.4486i | 1.75526 | − | 1.53137i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 39.8526 | − | 9.71570i | 1.31247 | − | 0.319970i | ||||
\(923\) | − | 27.7600i | − | 0.913732i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 142.011i | 4.66929i | ||||||||
\(926\) | 1.74622 | + | 7.16275i | 0.0573842 | + | 0.235383i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.31462 | + | 18.5737i | −0.240114 | + | 0.609712i | ||||
\(929\) | − | 7.73251i | − | 0.253695i | −0.991922 | − | 0.126848i | \(-0.959514\pi\) | ||
0.991922 | − | 0.126848i | \(-0.0404860\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.05596 | −0.100155 | ||||||||
\(932\) | −12.9598 | − | 24.9999i | −0.424512 | − | 0.818900i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.12209 | − | 16.9083i | −0.134879 | − | 0.553256i | ||||
\(935\) | 3.94326 | 0.128958 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.6210 | 0.837002 | 0.418501 | − | 0.908216i | \(-0.362556\pi\) | ||||
0.418501 | + | 0.908216i | \(0.362556\pi\) | |||||||
\(938\) | 3.08667 | + | 12.6611i | 0.100783 | + | 0.413401i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.43125 | − | 1.26034i | 0.0792985 | − | 0.0411077i | ||||
\(941\) | 30.8529 | 1.00578 | 0.502888 | − | 0.864352i | \(-0.332271\pi\) | ||||
0.502888 | + | 0.864352i | \(0.332271\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.4161i | 1.41382i | ||||||||
\(944\) | −19.5473 | − | 13.7872i | −0.636209 | − | 0.448734i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.64252 | + | 23.1449i | 0.183454 | + | 0.752506i | ||||
\(947\) | 39.5682i | 1.28579i | 0.765953 | + | 0.642897i | \(0.222268\pi\) | ||||
−0.765953 | + | 0.642897i | \(0.777732\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.28114i | 0.0415876i | ||||||||
\(950\) | −52.4614 | + | 12.7896i | −1.70207 | + | 0.414951i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.07607 | − | 0.938805i | 0.0348755 | − | 0.0304268i | ||||
\(953\) | 4.36408i | 0.141366i | 0.997499 | + | 0.0706832i | \(0.0225179\pi\) | ||||
−0.997499 | + | 0.0706832i | \(0.977482\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 76.0015 | 2.45935 | ||||||||
\(956\) | −23.3912 | + | 12.1258i | −0.756525 | + | 0.392177i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.4258 | − | 6.68616i | 0.886086 | − | 0.216020i | ||||
\(959\) | 6.53069 | 0.210887 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −87.7668 | −2.83119 | ||||||||
\(962\) | 48.0371 | − | 11.7110i | 1.54878 | − | 0.377579i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.2610 | − | 6.87440i | 0.427108 | − | 0.221410i | ||||
\(965\) | −70.1442 | −2.25802 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 51.1938i | − | 1.64628i | −0.567837 | − | 0.823141i | \(-0.692220\pi\) | ||
0.567837 | − | 0.823141i | \(-0.307780\pi\) | |||||||
\(968\) | −16.0129 | + | 13.9704i | −0.514676 | + | 0.449025i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −35.7044 | + | 8.70440i | −1.14640 | + | 0.279482i | ||||
\(971\) | 47.6773i | 1.53004i | 0.644008 | + | 0.765019i | \(0.277270\pi\) | ||||
−0.644008 | + | 0.765019i | \(0.722730\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 10.1589i | − | 0.325678i | ||||||
\(974\) | −1.88055 | − | 7.71376i | −0.0602566 | − | 0.247165i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −43.4032 | − | 30.6133i | −1.38930 | − | 0.979909i | ||||
\(977\) | − | 10.1656i | − | 0.325225i | −0.986690 | − | 0.162613i | \(-0.948008\pi\) | ||
0.986690 | − | 0.162613i | \(-0.0519921\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.6340 | 0.339864 | ||||||||
\(980\) | −7.42668 | + | 3.84993i | −0.237236 | + | 0.122982i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.03855 | + | 12.4637i | 0.0969639 | + | 0.397734i | ||||
\(983\) | 7.35716 | 0.234657 | 0.117328 | − | 0.993093i | \(-0.462567\pi\) | ||||
0.117328 | + | 0.993093i | \(0.462567\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −80.4068 | −2.56197 | ||||||||
\(986\) | −0.596788 | − | 2.44795i | −0.0190056 | − | 0.0779586i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.65253 | + | 16.6911i | 0.275274 | + | 0.531014i | ||||
\(989\) | −53.8772 | −1.71320 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 18.5907i | − | 0.590552i | −0.955412 | − | 0.295276i | \(-0.904588\pi\) | ||
0.955412 | − | 0.295276i | \(-0.0954116\pi\) | |||||||
\(992\) | −57.3607 | − | 22.5895i | −1.82120 | − | 0.717218i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.02290 | + | 12.3996i | 0.0958806 | + | 0.393290i | ||||
\(995\) | 7.06577i | 0.224000i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.19288i | 0.132790i | 0.997793 | + | 0.0663950i | \(0.0211497\pi\) | ||||
−0.997793 | + | 0.0663950i | \(0.978850\pi\) | |||||||
\(998\) | 50.0601 | − | 12.2042i | 1.58462 | − | 0.386317i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1512.2.j.d.323.4 | yes | 48 | |
3.2 | odd | 2 | inner | 1512.2.j.d.323.45 | yes | 48 | |
4.3 | odd | 2 | 6048.2.j.d.5615.47 | 48 | |||
8.3 | odd | 2 | inner | 1512.2.j.d.323.46 | yes | 48 | |
8.5 | even | 2 | 6048.2.j.d.5615.1 | 48 | |||
12.11 | even | 2 | 6048.2.j.d.5615.2 | 48 | |||
24.5 | odd | 2 | 6048.2.j.d.5615.48 | 48 | |||
24.11 | even | 2 | inner | 1512.2.j.d.323.3 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.d.323.3 | ✓ | 48 | 24.11 | even | 2 | inner | |
1512.2.j.d.323.4 | yes | 48 | 1.1 | even | 1 | trivial | |
1512.2.j.d.323.45 | yes | 48 | 3.2 | odd | 2 | inner | |
1512.2.j.d.323.46 | yes | 48 | 8.3 | odd | 2 | inner | |
6048.2.j.d.5615.1 | 48 | 8.5 | even | 2 | |||
6048.2.j.d.5615.2 | 48 | 12.11 | even | 2 | |||
6048.2.j.d.5615.47 | 48 | 4.3 | odd | 2 | |||
6048.2.j.d.5615.48 | 48 | 24.5 | odd | 2 |