Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,2,Mod(13,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.x (of order \(12\), degree \(4\), 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: | \(1.14984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 85.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.85 |
Dual form | 144.2.x.a.61.1 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.707107 | − | 0.707107i | ||||
\(3\) | 1.73205 | 1.00000 | ||||||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | −1.86603 | + | 0.500000i | −0.834512 | + | 0.223607i | −0.650681 | − | 0.759351i | \(-0.725517\pi\) |
−0.183831 | + | 0.982958i | \(0.558850\pi\) | |||||||
\(6\) | −1.73205 | − | 1.73205i | −0.707107 | − | 0.707107i | ||||
\(7\) | 3.86603 | − | 2.23205i | 1.46122 | − | 0.843636i | 0.462152 | − | 0.886801i | \(-0.347077\pi\) |
0.999068 | + | 0.0431647i | \(0.0137440\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | 2.36603 | + | 1.36603i | 0.748203 | + | 0.431975i | ||||
\(11\) | −0.500000 | + | 1.86603i | −0.150756 | + | 0.562628i | 0.848676 | + | 0.528913i | \(0.177400\pi\) |
−0.999432 | + | 0.0337145i | \(0.989266\pi\) | |||||||
\(12\) | 3.46410i | 1.00000i | ||||||||
\(13\) | −0.598076 | − | 2.23205i | −0.165876 | − | 0.619060i | −0.997927 | − | 0.0643593i | \(-0.979500\pi\) |
0.832050 | − | 0.554700i | \(-0.187167\pi\) | |||||||
\(14\) | −6.09808 | − | 1.63397i | −1.62978 | − | 0.436698i | ||||
\(15\) | −3.23205 | + | 0.866025i | −0.834512 | + | 0.223607i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | −3.00000 | − | 3.00000i | −0.707107 | − | 0.707107i | ||||
\(19\) | −3.00000 | + | 3.00000i | −0.688247 | + | 0.688247i | −0.961844 | − | 0.273597i | \(-0.911786\pi\) |
0.273597 | + | 0.961844i | \(0.411786\pi\) | |||||||
\(20\) | −1.00000 | − | 3.73205i | −0.223607 | − | 0.834512i | ||||
\(21\) | 6.69615 | − | 3.86603i | 1.46122 | − | 0.843636i | ||||
\(22\) | 2.36603 | − | 1.36603i | 0.504438 | − | 0.291238i | ||||
\(23\) | −5.59808 | − | 3.23205i | −1.16728 | − | 0.673929i | −0.214242 | − | 0.976781i | \(-0.568728\pi\) |
−0.953038 | + | 0.302851i | \(0.902061\pi\) | |||||||
\(24\) | 3.46410 | − | 3.46410i | 0.707107 | − | 0.707107i | ||||
\(25\) | −1.09808 | + | 0.633975i | −0.219615 | + | 0.126795i | ||||
\(26\) | −1.63397 | + | 2.83013i | −0.320449 | + | 0.555034i | ||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | 4.46410 | + | 7.73205i | 0.843636 | + | 1.46122i | ||||
\(29\) | −0.866025 | − | 0.232051i | −0.160817 | − | 0.0430908i | 0.177512 | − | 0.984119i | \(-0.443195\pi\) |
−0.338329 | + | 0.941028i | \(0.609862\pi\) | |||||||
\(30\) | 4.09808 | + | 2.36603i | 0.748203 | + | 0.431975i | ||||
\(31\) | −4.59808 | + | 7.96410i | −0.825839 | + | 1.43039i | 0.0754376 | + | 0.997151i | \(0.475965\pi\) |
−0.901277 | + | 0.433244i | \(0.857369\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.707107 | + | 0.707107i | ||||
\(33\) | −0.866025 | + | 3.23205i | −0.150756 | + | 0.562628i | ||||
\(34\) | −4.00000 | − | 4.00000i | −0.685994 | − | 0.685994i | ||||
\(35\) | −6.09808 | + | 6.09808i | −1.03076 | + | 1.03076i | ||||
\(36\) | 6.00000i | 1.00000i | ||||||||
\(37\) | −4.26795 | − | 4.26795i | −0.701647 | − | 0.701647i | 0.263117 | − | 0.964764i | \(-0.415249\pi\) |
−0.964764 | + | 0.263117i | \(0.915249\pi\) | |||||||
\(38\) | 6.00000 | 0.973329 | ||||||||
\(39\) | −1.03590 | − | 3.86603i | −0.165876 | − | 0.619060i | ||||
\(40\) | −2.73205 | + | 4.73205i | −0.431975 | + | 0.748203i | ||||
\(41\) | 0.696152 | + | 0.401924i | 0.108721 | + | 0.0627700i | 0.553374 | − | 0.832933i | \(-0.313340\pi\) |
−0.444654 | + | 0.895703i | \(0.646673\pi\) | |||||||
\(42\) | −10.5622 | − | 2.83013i | −1.62978 | − | 0.436698i | ||||
\(43\) | −1.69615 | + | 6.33013i | −0.258661 | + | 0.965335i | 0.707356 | + | 0.706857i | \(0.249888\pi\) |
−0.966017 | + | 0.258478i | \(0.916779\pi\) | |||||||
\(44\) | −3.73205 | − | 1.00000i | −0.562628 | − | 0.150756i | ||||
\(45\) | −5.59808 | + | 1.50000i | −0.834512 | + | 0.223607i | ||||
\(46\) | 2.36603 | + | 8.83013i | 0.348851 | + | 1.30193i | ||||
\(47\) | −0.598076 | − | 1.03590i | −0.0872384 | − | 0.151101i | 0.819104 | − | 0.573644i | \(-0.194471\pi\) |
−0.906343 | + | 0.422543i | \(0.861138\pi\) | |||||||
\(48\) | −6.92820 | −1.00000 | ||||||||
\(49\) | 6.46410 | − | 11.1962i | 0.923443 | − | 1.59945i | ||||
\(50\) | 1.73205 | + | 0.464102i | 0.244949 | + | 0.0656339i | ||||
\(51\) | 6.92820 | 0.970143 | ||||||||
\(52\) | 4.46410 | − | 1.19615i | 0.619060 | − | 0.165876i | ||||
\(53\) | 5.73205 | + | 5.73205i | 0.787358 | + | 0.787358i | 0.981060 | − | 0.193703i | \(-0.0620497\pi\) |
−0.193703 | + | 0.981060i | \(0.562050\pi\) | |||||||
\(54\) | −5.19615 | − | 5.19615i | −0.707107 | − | 0.707107i | ||||
\(55\) | − | 3.73205i | − | 0.503230i | ||||||
\(56\) | 3.26795 | − | 12.1962i | 0.436698 | − | 1.62978i | ||||
\(57\) | −5.19615 | + | 5.19615i | −0.688247 | + | 0.688247i | ||||
\(58\) | 0.633975 | + | 1.09808i | 0.0832449 | + | 0.144184i | ||||
\(59\) | −1.50000 | + | 0.401924i | −0.195283 | + | 0.0523260i | −0.355135 | − | 0.934815i | \(-0.615565\pi\) |
0.159852 | + | 0.987141i | \(0.448898\pi\) | |||||||
\(60\) | −1.73205 | − | 6.46410i | −0.223607 | − | 0.834512i | ||||
\(61\) | −2.13397 | − | 0.571797i | −0.273227 | − | 0.0732111i | 0.119604 | − | 0.992822i | \(-0.461838\pi\) |
−0.392831 | + | 0.919611i | \(0.628504\pi\) | |||||||
\(62\) | 12.5622 | − | 3.36603i | 1.59540 | − | 0.427486i | ||||
\(63\) | 11.5981 | − | 6.69615i | 1.46122 | − | 0.843636i | ||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 2.23205 | + | 3.86603i | 0.276852 | + | 0.479521i | ||||
\(66\) | 4.09808 | − | 2.36603i | 0.504438 | − | 0.291238i | ||||
\(67\) | −2.23205 | − | 8.33013i | −0.272688 | − | 1.01769i | −0.957375 | − | 0.288849i | \(-0.906727\pi\) |
0.684686 | − | 0.728838i | \(-0.259939\pi\) | |||||||
\(68\) | 8.00000i | 0.970143i | ||||||||
\(69\) | −9.69615 | − | 5.59808i | −1.16728 | − | 0.673929i | ||||
\(70\) | 12.1962 | 1.45772 | ||||||||
\(71\) | 2.92820i | 0.347514i | 0.984789 | + | 0.173757i | \(0.0555907\pi\) | ||||
−0.984789 | + | 0.173757i | \(0.944409\pi\) | |||||||
\(72\) | 6.00000 | − | 6.00000i | 0.707107 | − | 0.707107i | ||||
\(73\) | − | 7.46410i | − | 0.873607i | −0.899557 | − | 0.436804i | \(-0.856111\pi\) | ||
0.899557 | − | 0.436804i | \(-0.143889\pi\) | |||||||
\(74\) | 8.53590i | 0.992278i | ||||||||
\(75\) | −1.90192 | + | 1.09808i | −0.219615 | + | 0.126795i | ||||
\(76\) | −6.00000 | − | 6.00000i | −0.688247 | − | 0.688247i | ||||
\(77\) | 2.23205 | + | 8.33013i | 0.254366 | + | 0.949306i | ||||
\(78\) | −2.83013 | + | 4.90192i | −0.320449 | + | 0.555034i | ||||
\(79\) | −0.866025 | − | 1.50000i | −0.0974355 | − | 0.168763i | 0.813187 | − | 0.582003i | \(-0.197731\pi\) |
−0.910622 | + | 0.413239i | \(0.864397\pi\) | |||||||
\(80\) | 7.46410 | − | 2.00000i | 0.834512 | − | 0.223607i | ||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | −0.294229 | − | 1.09808i | −0.0324921 | − | 0.121262i | ||||
\(83\) | −14.1603 | − | 3.79423i | −1.55429 | − | 0.416471i | −0.623440 | − | 0.781872i | \(-0.714265\pi\) |
−0.930850 | + | 0.365401i | \(0.880932\pi\) | |||||||
\(84\) | 7.73205 | + | 13.3923i | 0.843636 | + | 1.46122i | ||||
\(85\) | −7.46410 | + | 2.00000i | −0.809595 | + | 0.216930i | ||||
\(86\) | 8.02628 | − | 4.63397i | 0.865496 | − | 0.499694i | ||||
\(87\) | −1.50000 | − | 0.401924i | −0.160817 | − | 0.0430908i | ||||
\(88\) | 2.73205 | + | 4.73205i | 0.291238 | + | 0.504438i | ||||
\(89\) | − | 15.8564i | − | 1.68078i | −0.541985 | − | 0.840388i | \(-0.682327\pi\) | ||
0.541985 | − | 0.840388i | \(-0.317673\pi\) | |||||||
\(90\) | 7.09808 | + | 4.09808i | 0.748203 | + | 0.431975i | ||||
\(91\) | −7.29423 | − | 7.29423i | −0.764643 | − | 0.764643i | ||||
\(92\) | 6.46410 | − | 11.1962i | 0.673929 | − | 1.16728i | ||||
\(93\) | −7.96410 | + | 13.7942i | −0.825839 | + | 1.43039i | ||||
\(94\) | −0.437822 | + | 1.63397i | −0.0451579 | + | 0.168532i | ||||
\(95\) | 4.09808 | − | 7.09808i | 0.420454 | − | 0.728247i | ||||
\(96\) | 6.92820 | + | 6.92820i | 0.707107 | + | 0.707107i | ||||
\(97\) | −0.500000 | − | 0.866025i | −0.0507673 | − | 0.0879316i | 0.839525 | − | 0.543321i | \(-0.182833\pi\) |
−0.890292 | + | 0.455389i | \(0.849500\pi\) | |||||||
\(98\) | −17.6603 | + | 4.73205i | −1.78396 | + | 0.478009i | ||||
\(99\) | −1.50000 | + | 5.59808i | −0.150756 | + | 0.562628i | ||||
\(100\) | −1.26795 | − | 2.19615i | −0.126795 | − | 0.219615i | ||||
\(101\) | −0.133975 | + | 0.500000i | −0.0133310 | + | 0.0497519i | −0.972271 | − | 0.233857i | \(-0.924865\pi\) |
0.958940 | + | 0.283609i | \(0.0915318\pi\) | |||||||
\(102\) | −6.92820 | − | 6.92820i | −0.685994 | − | 0.685994i | ||||
\(103\) | 13.7942 | + | 7.96410i | 1.35919 | + | 0.784726i | 0.989514 | − | 0.144436i | \(-0.0461369\pi\) |
0.369672 | + | 0.929162i | \(0.379470\pi\) | |||||||
\(104\) | −5.66025 | − | 3.26795i | −0.555034 | − | 0.320449i | ||||
\(105\) | −10.5622 | + | 10.5622i | −1.03076 | + | 1.03076i | ||||
\(106\) | − | 11.4641i | − | 1.11349i | ||||||
\(107\) | 9.39230 | + | 9.39230i | 0.907988 | + | 0.907988i | 0.996110 | − | 0.0881214i | \(-0.0280863\pi\) |
−0.0881214 | + | 0.996110i | \(0.528086\pi\) | |||||||
\(108\) | 10.3923i | 1.00000i | ||||||||
\(109\) | −1.73205 | + | 1.73205i | −0.165900 | + | 0.165900i | −0.785175 | − | 0.619274i | \(-0.787427\pi\) |
0.619274 | + | 0.785175i | \(0.287427\pi\) | |||||||
\(110\) | −3.73205 | + | 3.73205i | −0.355837 | + | 0.355837i | ||||
\(111\) | −7.39230 | − | 7.39230i | −0.701647 | − | 0.701647i | ||||
\(112\) | −15.4641 | + | 8.92820i | −1.46122 | + | 0.843636i | ||||
\(113\) | −6.23205 | + | 10.7942i | −0.586262 | + | 1.01544i | 0.408455 | + | 0.912779i | \(0.366068\pi\) |
−0.994717 | + | 0.102657i | \(0.967266\pi\) | |||||||
\(114\) | 10.3923 | 0.973329 | ||||||||
\(115\) | 12.0622 | + | 3.23205i | 1.12480 | + | 0.301390i | ||||
\(116\) | 0.464102 | − | 1.73205i | 0.0430908 | − | 0.160817i | ||||
\(117\) | −1.79423 | − | 6.69615i | −0.165876 | − | 0.619060i | ||||
\(118\) | 1.90192 | + | 1.09808i | 0.175086 | + | 0.101086i | ||||
\(119\) | 15.4641 | − | 8.92820i | 1.41759 | − | 0.818447i | ||||
\(120\) | −4.73205 | + | 8.19615i | −0.431975 | + | 0.748203i | ||||
\(121\) | 6.29423 | + | 3.63397i | 0.572203 | + | 0.330361i | ||||
\(122\) | 1.56218 | + | 2.70577i | 0.141433 | + | 0.244969i | ||||
\(123\) | 1.20577 | + | 0.696152i | 0.108721 | + | 0.0627700i | ||||
\(124\) | −15.9282 | − | 9.19615i | −1.43039 | − | 0.825839i | ||||
\(125\) | 8.56218 | − | 8.56218i | 0.765824 | − | 0.765824i | ||||
\(126\) | −18.2942 | − | 4.90192i | −1.62978 | − | 0.436698i | ||||
\(127\) | 0.392305 | 0.0348114 | 0.0174057 | − | 0.999849i | \(-0.494459\pi\) | ||||
0.0174057 | + | 0.999849i | \(0.494459\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.707107 | + | 0.707107i | ||||
\(129\) | −2.93782 | + | 10.9641i | −0.258661 | + | 0.965335i | ||||
\(130\) | 1.63397 | − | 6.09808i | 0.143309 | − | 0.534837i | ||||
\(131\) | 1.30385 | + | 4.86603i | 0.113918 | + | 0.425147i | 0.999204 | − | 0.0399004i | \(-0.0127041\pi\) |
−0.885286 | + | 0.465047i | \(0.846037\pi\) | |||||||
\(132\) | −6.46410 | − | 1.73205i | −0.562628 | − | 0.150756i | ||||
\(133\) | −4.90192 | + | 18.2942i | −0.425051 | + | 1.58631i | ||||
\(134\) | −6.09808 | + | 10.5622i | −0.526794 | + | 0.912433i | ||||
\(135\) | −9.69615 | + | 2.59808i | −0.834512 | + | 0.223607i | ||||
\(136\) | 8.00000 | − | 8.00000i | 0.685994 | − | 0.685994i | ||||
\(137\) | −0.571797 | + | 0.330127i | −0.0488519 | + | 0.0282047i | −0.524227 | − | 0.851579i | \(-0.675646\pi\) |
0.475375 | + | 0.879783i | \(0.342312\pi\) | |||||||
\(138\) | 4.09808 | + | 15.2942i | 0.348851 | + | 1.30193i | ||||
\(139\) | 16.1603 | − | 4.33013i | 1.37069 | − | 0.367277i | 0.502962 | − | 0.864308i | \(-0.332243\pi\) |
0.867732 | + | 0.497032i | \(0.165577\pi\) | |||||||
\(140\) | −12.1962 | − | 12.1962i | −1.03076 | − | 1.03076i | ||||
\(141\) | −1.03590 | − | 1.79423i | −0.0872384 | − | 0.151101i | ||||
\(142\) | 2.92820 | − | 2.92820i | 0.245729 | − | 0.245729i | ||||
\(143\) | 4.46410 | 0.373307 | ||||||||
\(144\) | −12.0000 | −1.00000 | ||||||||
\(145\) | 1.73205 | 0.143839 | ||||||||
\(146\) | −7.46410 | + | 7.46410i | −0.617733 | + | 0.617733i | ||||
\(147\) | 11.1962 | − | 19.3923i | 0.923443 | − | 1.59945i | ||||
\(148\) | 8.53590 | − | 8.53590i | 0.701647 | − | 0.701647i | ||||
\(149\) | 16.0622 | − | 4.30385i | 1.31586 | − | 0.352585i | 0.468438 | − | 0.883497i | \(-0.344817\pi\) |
0.847427 | + | 0.530912i | \(0.178150\pi\) | |||||||
\(150\) | 3.00000 | + | 0.803848i | 0.244949 | + | 0.0656339i | ||||
\(151\) | −6.06218 | + | 3.50000i | −0.493333 | + | 0.284826i | −0.725956 | − | 0.687741i | \(-0.758602\pi\) |
0.232623 | + | 0.972567i | \(0.425269\pi\) | |||||||
\(152\) | 12.0000i | 0.973329i | ||||||||
\(153\) | 12.0000 | 0.970143 | ||||||||
\(154\) | 6.09808 | − | 10.5622i | 0.491397 | − | 0.851125i | ||||
\(155\) | 4.59808 | − | 17.1603i | 0.369326 | − | 1.37834i | ||||
\(156\) | 7.73205 | − | 2.07180i | 0.619060 | − | 0.165876i | ||||
\(157\) | −0.866025 | − | 3.23205i | −0.0691164 | − | 0.257946i | 0.922719 | − | 0.385474i | \(-0.125962\pi\) |
−0.991835 | + | 0.127529i | \(0.959296\pi\) | |||||||
\(158\) | −0.633975 | + | 2.36603i | −0.0504363 | + | 0.188231i | ||||
\(159\) | 9.92820 | + | 9.92820i | 0.787358 | + | 0.787358i | ||||
\(160\) | −9.46410 | − | 5.46410i | −0.748203 | − | 0.431975i | ||||
\(161\) | −28.8564 | −2.27420 | ||||||||
\(162\) | −9.00000 | − | 9.00000i | −0.707107 | − | 0.707107i | ||||
\(163\) | −1.92820 | + | 1.92820i | −0.151029 | + | 0.151029i | −0.778577 | − | 0.627549i | \(-0.784058\pi\) |
0.627549 | + | 0.778577i | \(0.284058\pi\) | |||||||
\(164\) | −0.803848 | + | 1.39230i | −0.0627700 | + | 0.108721i | ||||
\(165\) | − | 6.46410i | − | 0.503230i | ||||||
\(166\) | 10.3660 | + | 17.9545i | 0.804560 | + | 1.39354i | ||||
\(167\) | −14.2583 | − | 8.23205i | −1.10334 | − | 0.637015i | −0.166246 | − | 0.986084i | \(-0.553165\pi\) |
−0.937097 | + | 0.349069i | \(0.886498\pi\) | |||||||
\(168\) | 5.66025 | − | 21.1244i | 0.436698 | − | 1.62978i | ||||
\(169\) | 6.63397 | − | 3.83013i | 0.510306 | − | 0.294625i | ||||
\(170\) | 9.46410 | + | 5.46410i | 0.725863 | + | 0.419077i | ||||
\(171\) | −9.00000 | + | 9.00000i | −0.688247 | + | 0.688247i | ||||
\(172\) | −12.6603 | − | 3.39230i | −0.965335 | − | 0.258661i | ||||
\(173\) | 7.59808 | + | 2.03590i | 0.577671 | + | 0.154786i | 0.535812 | − | 0.844337i | \(-0.320005\pi\) |
0.0418586 | + | 0.999124i | \(0.486672\pi\) | |||||||
\(174\) | 1.09808 | + | 1.90192i | 0.0832449 | + | 0.144184i | ||||
\(175\) | −2.83013 | + | 4.90192i | −0.213937 | + | 0.370551i | ||||
\(176\) | 2.00000 | − | 7.46410i | 0.150756 | − | 0.562628i | ||||
\(177\) | −2.59808 | + | 0.696152i | −0.195283 | + | 0.0523260i | ||||
\(178\) | −15.8564 | + | 15.8564i | −1.18849 | + | 1.18849i | ||||
\(179\) | −5.92820 | + | 5.92820i | −0.443095 | + | 0.443095i | −0.893051 | − | 0.449956i | \(-0.851440\pi\) |
0.449956 | + | 0.893051i | \(0.351440\pi\) | |||||||
\(180\) | −3.00000 | − | 11.1962i | −0.223607 | − | 0.834512i | ||||
\(181\) | −7.73205 | − | 7.73205i | −0.574719 | − | 0.574719i | 0.358725 | − | 0.933443i | \(-0.383212\pi\) |
−0.933443 | + | 0.358725i | \(0.883212\pi\) | |||||||
\(182\) | 14.5885i | 1.08137i | ||||||||
\(183\) | −3.69615 | − | 0.990381i | −0.273227 | − | 0.0732111i | ||||
\(184\) | −17.6603 | + | 4.73205i | −1.30193 | + | 0.348851i | ||||
\(185\) | 10.0981 | + | 5.83013i | 0.742425 | + | 0.428639i | ||||
\(186\) | 21.7583 | − | 5.83013i | 1.59540 | − | 0.427486i | ||||
\(187\) | −2.00000 | + | 7.46410i | −0.146254 | + | 0.545829i | ||||
\(188\) | 2.07180 | − | 1.19615i | 0.151101 | − | 0.0872384i | ||||
\(189\) | 20.0885 | − | 11.5981i | 1.46122 | − | 0.843636i | ||||
\(190\) | −11.1962 | + | 3.00000i | −0.812254 | + | 0.217643i | ||||
\(191\) | 1.40192 | + | 2.42820i | 0.101440 | + | 0.175699i | 0.912278 | − | 0.409572i | \(-0.134322\pi\) |
−0.810838 | + | 0.585270i | \(0.800988\pi\) | |||||||
\(192\) | − | 13.8564i | − | 1.00000i | ||||||
\(193\) | 2.23205 | − | 3.86603i | 0.160667 | − | 0.278283i | −0.774441 | − | 0.632646i | \(-0.781969\pi\) |
0.935108 | + | 0.354363i | \(0.115302\pi\) | |||||||
\(194\) | −0.366025 | + | 1.36603i | −0.0262791 | + | 0.0980749i | ||||
\(195\) | 3.86603 | + | 6.69615i | 0.276852 | + | 0.479521i | ||||
\(196\) | 22.3923 | + | 12.9282i | 1.59945 | + | 0.923443i | ||||
\(197\) | 3.53590 | + | 3.53590i | 0.251922 | + | 0.251922i | 0.821758 | − | 0.569836i | \(-0.192993\pi\) |
−0.569836 | + | 0.821758i | \(0.692993\pi\) | |||||||
\(198\) | 7.09808 | − | 4.09808i | 0.504438 | − | 0.291238i | ||||
\(199\) | 21.8564i | 1.54936i | 0.632354 | + | 0.774680i | \(0.282089\pi\) | ||||
−0.632354 | + | 0.774680i | \(0.717911\pi\) | |||||||
\(200\) | −0.928203 | + | 3.46410i | −0.0656339 | + | 0.244949i | ||||
\(201\) | −3.86603 | − | 14.4282i | −0.272688 | − | 1.01769i | ||||
\(202\) | 0.633975 | − | 0.366025i | 0.0446063 | − | 0.0257535i | ||||
\(203\) | −3.86603 | + | 1.03590i | −0.271342 | + | 0.0727058i | ||||
\(204\) | 13.8564i | 0.970143i | ||||||||
\(205\) | −1.50000 | − | 0.401924i | −0.104765 | − | 0.0280716i | ||||
\(206\) | −5.83013 | − | 21.7583i | −0.406204 | − | 1.51597i | ||||
\(207\) | −16.7942 | − | 9.69615i | −1.16728 | − | 0.673929i | ||||
\(208\) | 2.39230 | + | 8.92820i | 0.165876 | + | 0.619060i | ||||
\(209\) | −4.09808 | − | 7.09808i | −0.283470 | − | 0.490984i | ||||
\(210\) | 21.1244 | 1.45772 | ||||||||
\(211\) | −4.96410 | − | 18.5263i | −0.341743 | − | 1.27540i | −0.896371 | − | 0.443304i | \(-0.853806\pi\) |
0.554629 | − | 0.832098i | \(-0.312860\pi\) | |||||||
\(212\) | −11.4641 | + | 11.4641i | −0.787358 | + | 0.787358i | ||||
\(213\) | 5.07180i | 0.347514i | ||||||||
\(214\) | − | 18.7846i | − | 1.28409i | ||||||
\(215\) | − | 12.6603i | − | 0.863422i | ||||||
\(216\) | 10.3923 | − | 10.3923i | 0.707107 | − | 0.707107i | ||||
\(217\) | 41.0526i | 2.78683i | ||||||||
\(218\) | 3.46410 | 0.234619 | ||||||||
\(219\) | − | 12.9282i | − | 0.873607i | ||||||
\(220\) | 7.46410 | 0.503230 | ||||||||
\(221\) | −2.39230 | − | 8.92820i | −0.160924 | − | 0.600576i | ||||
\(222\) | 14.7846i | 0.992278i | ||||||||
\(223\) | 7.79423 | + | 13.5000i | 0.521940 | + | 0.904027i | 0.999674 | + | 0.0255224i | \(0.00812491\pi\) |
−0.477734 | + | 0.878504i | \(0.658542\pi\) | |||||||
\(224\) | 24.3923 | + | 6.53590i | 1.62978 | + | 0.436698i | ||||
\(225\) | −3.29423 | + | 1.90192i | −0.219615 | + | 0.126795i | ||||
\(226\) | 17.0263 | − | 4.56218i | 1.13257 | − | 0.303472i | ||||
\(227\) | 19.6244 | + | 5.25833i | 1.30251 | + | 0.349008i | 0.842400 | − | 0.538852i | \(-0.181142\pi\) |
0.460114 | + | 0.887860i | \(0.347809\pi\) | |||||||
\(228\) | −10.3923 | − | 10.3923i | −0.688247 | − | 0.688247i | ||||
\(229\) | 16.5263 | − | 4.42820i | 1.09209 | − | 0.292624i | 0.332549 | − | 0.943086i | \(-0.392091\pi\) |
0.759539 | + | 0.650462i | \(0.225425\pi\) | |||||||
\(230\) | −8.83013 | − | 15.2942i | −0.582241 | − | 1.00847i | ||||
\(231\) | 3.86603 | + | 14.4282i | 0.254366 | + | 0.949306i | ||||
\(232\) | −2.19615 | + | 1.26795i | −0.144184 | + | 0.0832449i | ||||
\(233\) | − | 9.07180i | − | 0.594313i | −0.954829 | − | 0.297157i | \(-0.903962\pi\) | ||
0.954829 | − | 0.297157i | \(-0.0960383\pi\) | |||||||
\(234\) | −4.90192 | + | 8.49038i | −0.320449 | + | 0.555034i | ||||
\(235\) | 1.63397 | + | 1.63397i | 0.106589 | + | 0.106589i | ||||
\(236\) | −0.803848 | − | 3.00000i | −0.0523260 | − | 0.195283i | ||||
\(237\) | −1.50000 | − | 2.59808i | −0.0974355 | − | 0.168763i | ||||
\(238\) | −24.3923 | − | 6.53590i | −1.58112 | − | 0.423659i | ||||
\(239\) | −0.401924 | + | 0.696152i | −0.0259983 | + | 0.0450304i | −0.878732 | − | 0.477316i | \(-0.841610\pi\) |
0.852734 | + | 0.522346i | \(0.174943\pi\) | |||||||
\(240\) | 12.9282 | − | 3.46410i | 0.834512 | − | 0.223607i | ||||
\(241\) | −2.76795 | − | 4.79423i | −0.178299 | − | 0.308823i | 0.762999 | − | 0.646400i | \(-0.223726\pi\) |
−0.941298 | + | 0.337576i | \(0.890393\pi\) | |||||||
\(242\) | −2.66025 | − | 9.92820i | −0.171008 | − | 0.638209i | ||||
\(243\) | 15.5885 | 1.00000 | ||||||||
\(244\) | 1.14359 | − | 4.26795i | 0.0732111 | − | 0.273227i | ||||
\(245\) | −6.46410 | + | 24.1244i | −0.412976 | + | 1.54125i | ||||
\(246\) | −0.509619 | − | 1.90192i | −0.0324921 | − | 0.121262i | ||||
\(247\) | 8.49038 | + | 4.90192i | 0.540230 | + | 0.311902i | ||||
\(248\) | 6.73205 | + | 25.1244i | 0.427486 | + | 1.59540i | ||||
\(249\) | −24.5263 | − | 6.57180i | −1.55429 | − | 0.416471i | ||||
\(250\) | −17.1244 | −1.08304 | ||||||||
\(251\) | −13.3923 | − | 13.3923i | −0.845315 | − | 0.845315i | 0.144229 | − | 0.989544i | \(-0.453930\pi\) |
−0.989544 | + | 0.144229i | \(0.953930\pi\) | |||||||
\(252\) | 13.3923 | + | 23.1962i | 0.843636 | + | 1.46122i | ||||
\(253\) | 8.83013 | − | 8.83013i | 0.555145 | − | 0.555145i | ||||
\(254\) | −0.392305 | − | 0.392305i | −0.0246154 | − | 0.0246154i | ||||
\(255\) | −12.9282 | + | 3.46410i | −0.809595 | + | 0.216930i | ||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 12.1603 | − | 21.0622i | 0.758536 | − | 1.31382i | −0.185061 | − | 0.982727i | \(-0.559248\pi\) |
0.943597 | − | 0.331096i | \(-0.107418\pi\) | |||||||
\(258\) | 13.9019 | − | 8.02628i | 0.865496 | − | 0.499694i | ||||
\(259\) | −26.0263 | − | 6.97372i | −1.61719 | − | 0.433326i | ||||
\(260\) | −7.73205 | + | 4.46410i | −0.479521 | + | 0.276852i | ||||
\(261\) | −2.59808 | − | 0.696152i | −0.160817 | − | 0.0430908i | ||||
\(262\) | 3.56218 | − | 6.16987i | 0.220072 | − | 0.381176i | ||||
\(263\) | −8.59808 | + | 4.96410i | −0.530180 | + | 0.306100i | −0.741090 | − | 0.671406i | \(-0.765691\pi\) |
0.210910 | + | 0.977506i | \(0.432357\pi\) | |||||||
\(264\) | 4.73205 | + | 8.19615i | 0.291238 | + | 0.504438i | ||||
\(265\) | −13.5622 | − | 7.83013i | −0.833118 | − | 0.481001i | ||||
\(266\) | 23.1962 | − | 13.3923i | 1.42225 | − | 0.821135i | ||||
\(267\) | − | 27.4641i | − | 1.68078i | ||||||
\(268\) | 16.6603 | − | 4.46410i | 1.01769 | − | 0.272688i | ||||
\(269\) | 4.26795 | − | 4.26795i | 0.260221 | − | 0.260221i | −0.564923 | − | 0.825144i | \(-0.691094\pi\) |
0.825144 | + | 0.564923i | \(0.191094\pi\) | |||||||
\(270\) | 12.2942 | + | 7.09808i | 0.748203 | + | 0.431975i | ||||
\(271\) | −1.07180 | −0.0651070 | −0.0325535 | − | 0.999470i | \(-0.510364\pi\) | ||||
−0.0325535 | + | 0.999470i | \(0.510364\pi\) | |||||||
\(272\) | −16.0000 | −0.970143 | ||||||||
\(273\) | −12.6340 | − | 12.6340i | −0.764643 | − | 0.764643i | ||||
\(274\) | 0.901924 | + | 0.241670i | 0.0544872 | + | 0.0145998i | ||||
\(275\) | −0.633975 | − | 2.36603i | −0.0382301 | − | 0.142677i | ||||
\(276\) | 11.1962 | − | 19.3923i | 0.673929 | − | 1.16728i | ||||
\(277\) | −1.79423 | + | 6.69615i | −0.107805 | + | 0.402333i | −0.998648 | − | 0.0519775i | \(-0.983448\pi\) |
0.890844 | + | 0.454310i | \(0.150114\pi\) | |||||||
\(278\) | −20.4904 | − | 11.8301i | −1.22893 | − | 0.709524i | ||||
\(279\) | −13.7942 | + | 23.8923i | −0.825839 | + | 1.43039i | ||||
\(280\) | 24.3923i | 1.45772i | ||||||||
\(281\) | −10.0359 | + | 5.79423i | −0.598692 | + | 0.345655i | −0.768527 | − | 0.639818i | \(-0.779010\pi\) |
0.169835 | + | 0.985472i | \(0.445676\pi\) | |||||||
\(282\) | −0.758330 | + | 2.83013i | −0.0451579 | + | 0.168532i | ||||
\(283\) | −13.1603 | + | 3.52628i | −0.782296 | + | 0.209616i | −0.627797 | − | 0.778377i | \(-0.716043\pi\) |
−0.154499 | + | 0.987993i | \(0.549376\pi\) | |||||||
\(284\) | −5.85641 | −0.347514 | ||||||||
\(285\) | 7.09808 | − | 12.2942i | 0.420454 | − | 0.728247i | ||||
\(286\) | −4.46410 | − | 4.46410i | −0.263968 | − | 0.263968i | ||||
\(287\) | 3.58846 | 0.211820 | ||||||||
\(288\) | 12.0000 | + | 12.0000i | 0.707107 | + | 0.707107i | ||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | −1.73205 | − | 1.73205i | −0.101710 | − | 0.101710i | ||||
\(291\) | −0.866025 | − | 1.50000i | −0.0507673 | − | 0.0879316i | ||||
\(292\) | 14.9282 | 0.873607 | ||||||||
\(293\) | 2.13397 | − | 0.571797i | 0.124668 | − | 0.0334047i | −0.195945 | − | 0.980615i | \(-0.562778\pi\) |
0.320614 | + | 0.947210i | \(0.396111\pi\) | |||||||
\(294\) | −30.5885 | + | 8.19615i | −1.78396 | + | 0.478009i | ||||
\(295\) | 2.59808 | − | 1.50000i | 0.151266 | − | 0.0873334i | ||||
\(296\) | −17.0718 | −0.992278 | ||||||||
\(297\) | −2.59808 | + | 9.69615i | −0.150756 | + | 0.562628i | ||||
\(298\) | −20.3660 | − | 11.7583i | −1.17977 | − | 0.681142i | ||||
\(299\) | −3.86603 | + | 14.4282i | −0.223578 | + | 0.834405i | ||||
\(300\) | −2.19615 | − | 3.80385i | −0.126795 | − | 0.219615i | ||||
\(301\) | 7.57180 | + | 28.2583i | 0.436431 | + | 1.62878i | ||||
\(302\) | 9.56218 | + | 2.56218i | 0.550242 | + | 0.147437i | ||||
\(303\) | −0.232051 | + | 0.866025i | −0.0133310 | + | 0.0497519i | ||||
\(304\) | 12.0000 | − | 12.0000i | 0.688247 | − | 0.688247i | ||||
\(305\) | 4.26795 | 0.244382 | ||||||||
\(306\) | −12.0000 | − | 12.0000i | −0.685994 | − | 0.685994i | ||||
\(307\) | 7.92820 | − | 7.92820i | 0.452486 | − | 0.452486i | −0.443693 | − | 0.896179i | \(-0.646332\pi\) |
0.896179 | + | 0.443693i | \(0.146332\pi\) | |||||||
\(308\) | −16.6603 | + | 4.46410i | −0.949306 | + | 0.254366i | ||||
\(309\) | 23.8923 | + | 13.7942i | 1.35919 | + | 0.784726i | ||||
\(310\) | −21.7583 | + | 12.5622i | −1.23579 | + | 0.713484i | ||||
\(311\) | 9.18653 | + | 5.30385i | 0.520921 | + | 0.300754i | 0.737311 | − | 0.675553i | \(-0.236095\pi\) |
−0.216391 | + | 0.976307i | \(0.569428\pi\) | |||||||
\(312\) | −9.80385 | − | 5.66025i | −0.555034 | − | 0.320449i | ||||
\(313\) | 25.1603 | − | 14.5263i | 1.42214 | − | 0.821074i | 0.425660 | − | 0.904883i | \(-0.360042\pi\) |
0.996482 | + | 0.0838094i | \(0.0267087\pi\) | |||||||
\(314\) | −2.36603 | + | 4.09808i | −0.133523 | + | 0.231268i | ||||
\(315\) | −18.2942 | + | 18.2942i | −1.03076 | + | 1.03076i | ||||
\(316\) | 3.00000 | − | 1.73205i | 0.168763 | − | 0.0974355i | ||||
\(317\) | −33.4545 | − | 8.96410i | −1.87899 | − | 0.503474i | −0.999627 | − | 0.0273246i | \(-0.991301\pi\) |
−0.879364 | − | 0.476150i | \(-0.842032\pi\) | |||||||
\(318\) | − | 19.8564i | − | 1.11349i | ||||||
\(319\) | 0.866025 | − | 1.50000i | 0.0484881 | − | 0.0839839i | ||||
\(320\) | 4.00000 | + | 14.9282i | 0.223607 | + | 0.834512i | ||||
\(321\) | 16.2679 | + | 16.2679i | 0.907988 | + | 0.907988i | ||||
\(322\) | 28.8564 | + | 28.8564i | 1.60810 | + | 1.60810i | ||||
\(323\) | −12.0000 | + | 12.0000i | −0.667698 | + | 0.667698i | ||||
\(324\) | 18.0000i | 1.00000i | ||||||||
\(325\) | 2.07180 | + | 2.07180i | 0.114923 | + | 0.114923i | ||||
\(326\) | 3.85641 | 0.213587 | ||||||||
\(327\) | −3.00000 | + | 3.00000i | −0.165900 | + | 0.165900i | ||||
\(328\) | 2.19615 | − | 0.588457i | 0.121262 | − | 0.0324921i | ||||
\(329\) | −4.62436 | − | 2.66987i | −0.254949 | − | 0.147195i | ||||
\(330\) | −6.46410 | + | 6.46410i | −0.355837 | + | 0.355837i | ||||
\(331\) | 1.35641 | − | 5.06218i | 0.0745548 | − | 0.278242i | −0.918577 | − | 0.395242i | \(-0.870661\pi\) |
0.993132 | + | 0.116999i | \(0.0373275\pi\) | |||||||
\(332\) | 7.58846 | − | 28.3205i | 0.416471 | − | 1.55429i | ||||
\(333\) | −12.8038 | − | 12.8038i | −0.701647 | − | 0.701647i | ||||
\(334\) | 6.02628 | + | 22.4904i | 0.329743 | + | 1.23062i | ||||
\(335\) | 8.33013 | + | 14.4282i | 0.455123 | + | 0.788297i | ||||
\(336\) | −26.7846 | + | 15.4641i | −1.46122 | + | 0.843636i | ||||
\(337\) | −9.69615 | + | 16.7942i | −0.528183 | + | 0.914840i | 0.471277 | + | 0.881985i | \(0.343793\pi\) |
−0.999460 | + | 0.0328547i | \(0.989540\pi\) | |||||||
\(338\) | −10.4641 | − | 2.80385i | −0.569172 | − | 0.152509i | ||||
\(339\) | −10.7942 | + | 18.6962i | −0.586262 | + | 1.01544i | ||||
\(340\) | −4.00000 | − | 14.9282i | −0.216930 | − | 0.809595i | ||||
\(341\) | −12.5622 | − | 12.5622i | −0.680280 | − | 0.680280i | ||||
\(342\) | 18.0000 | 0.973329 | ||||||||
\(343\) | − | 26.4641i | − | 1.42893i | ||||||
\(344\) | 9.26795 | + | 16.0526i | 0.499694 | + | 0.865496i | ||||
\(345\) | 20.8923 | + | 5.59808i | 1.12480 | + | 0.301390i | ||||
\(346\) | −5.56218 | − | 9.63397i | −0.299025 | − | 0.517926i | ||||
\(347\) | −1.76795 | + | 0.473721i | −0.0949085 | + | 0.0254307i | −0.305961 | − | 0.952044i | \(-0.598978\pi\) |
0.211052 | + | 0.977475i | \(0.432311\pi\) | |||||||
\(348\) | 0.803848 | − | 3.00000i | 0.0430908 | − | 0.160817i | ||||
\(349\) | −3.86603 | − | 1.03590i | −0.206944 | − | 0.0554504i | 0.153858 | − | 0.988093i | \(-0.450830\pi\) |
−0.360802 | + | 0.932643i | \(0.617497\pi\) | |||||||
\(350\) | 7.73205 | − | 2.07180i | 0.413296 | − | 0.110742i | ||||
\(351\) | −3.10770 | − | 11.5981i | −0.165876 | − | 0.619060i | ||||
\(352\) | −9.46410 | + | 5.46410i | −0.504438 | + | 0.291238i | ||||
\(353\) | −11.7679 | − | 20.3827i | −0.626345 | − | 1.08486i | −0.988279 | − | 0.152657i | \(-0.951217\pi\) |
0.361934 | − | 0.932204i | \(-0.382116\pi\) | |||||||
\(354\) | 3.29423 | + | 1.90192i | 0.175086 | + | 0.101086i | ||||
\(355\) | −1.46410 | − | 5.46410i | −0.0777064 | − | 0.290004i | ||||
\(356\) | 31.7128 | 1.68078 | ||||||||
\(357\) | 26.7846 | − | 15.4641i | 1.41759 | − | 0.818447i | ||||
\(358\) | 11.8564 | 0.626631 | ||||||||
\(359\) | 28.9282i | 1.52677i | 0.645942 | + | 0.763386i | \(0.276465\pi\) | ||||
−0.645942 | + | 0.763386i | \(0.723535\pi\) | |||||||
\(360\) | −8.19615 | + | 14.1962i | −0.431975 | + | 0.748203i | ||||
\(361\) | 1.00000i | 0.0526316i | ||||||||
\(362\) | 15.4641i | 0.812775i | ||||||||
\(363\) | 10.9019 | + | 6.29423i | 0.572203 | + | 0.330361i | ||||
\(364\) | 14.5885 | − | 14.5885i | 0.764643 | − | 0.764643i | ||||
\(365\) | 3.73205 | + | 13.9282i | 0.195344 | + | 0.729035i | ||||
\(366\) | 2.70577 | + | 4.68653i | 0.141433 | + | 0.244969i | ||||
\(367\) | −17.4545 | − | 30.2321i | −0.911117 | − | 1.57810i | −0.812490 | − | 0.582976i | \(-0.801888\pi\) |
−0.0986270 | − | 0.995124i | \(-0.531445\pi\) | |||||||
\(368\) | 22.3923 | + | 12.9282i | 1.16728 | + | 0.673929i | ||||
\(369\) | 2.08846 | + | 1.20577i | 0.108721 | + | 0.0627700i | ||||
\(370\) | −4.26795 | − | 15.9282i | −0.221880 | − | 0.828068i | ||||
\(371\) | 34.9545 | + | 9.36603i | 1.81475 | + | 0.486260i | ||||
\(372\) | −27.5885 | − | 15.9282i | −1.43039 | − | 0.825839i | ||||
\(373\) | −1.59808 | + | 0.428203i | −0.0827452 | + | 0.0221715i | −0.299954 | − | 0.953954i | \(-0.596971\pi\) |
0.217209 | + | 0.976125i | \(0.430305\pi\) | |||||||
\(374\) | 9.46410 | − | 5.46410i | 0.489377 | − | 0.282542i | ||||
\(375\) | 14.8301 | − | 14.8301i | 0.765824 | − | 0.765824i | ||||
\(376\) | −3.26795 | − | 0.875644i | −0.168532 | − | 0.0451579i | ||||
\(377\) | 2.07180i | 0.106703i | ||||||||
\(378\) | −31.6865 | − | 8.49038i | −1.62978 | − | 0.436698i | ||||
\(379\) | −15.5885 | − | 15.5885i | −0.800725 | − | 0.800725i | 0.182484 | − | 0.983209i | \(-0.441586\pi\) |
−0.983209 | + | 0.182484i | \(0.941586\pi\) | |||||||
\(380\) | 14.1962 | + | 8.19615i | 0.728247 | + | 0.420454i | ||||
\(381\) | 0.679492 | 0.0348114 | ||||||||
\(382\) | 1.02628 | − | 3.83013i | 0.0525090 | − | 0.195966i | ||||
\(383\) | 3.66987 | − | 6.35641i | 0.187522 | − | 0.324797i | −0.756902 | − | 0.653529i | \(-0.773288\pi\) |
0.944423 | + | 0.328732i | \(0.106621\pi\) | |||||||
\(384\) | −13.8564 | + | 13.8564i | −0.707107 | + | 0.707107i | ||||
\(385\) | −8.33013 | − | 14.4282i | −0.424543 | − | 0.735329i | ||||
\(386\) | −6.09808 | + | 1.63397i | −0.310384 | + | 0.0831671i | ||||
\(387\) | −5.08846 | + | 18.9904i | −0.258661 | + | 0.965335i | ||||
\(388\) | 1.73205 | − | 1.00000i | 0.0879316 | − | 0.0507673i | ||||
\(389\) | 2.40192 | − | 8.96410i | 0.121782 | − | 0.454498i | −0.877922 | − | 0.478803i | \(-0.841071\pi\) |
0.999705 | + | 0.0243053i | \(0.00773738\pi\) | |||||||
\(390\) | 2.83013 | − | 10.5622i | 0.143309 | − | 0.534837i | ||||
\(391\) | −22.3923 | − | 12.9282i | −1.13243 | − | 0.653807i | ||||
\(392\) | −9.46410 | − | 35.3205i | −0.478009 | − | 1.78396i | ||||
\(393\) | 2.25833 | + | 8.42820i | 0.113918 | + | 0.425147i | ||||
\(394\) | − | 7.07180i | − | 0.356272i | ||||||
\(395\) | 2.36603 | + | 2.36603i | 0.119048 | + | 0.119048i | ||||
\(396\) | −11.1962 | − | 3.00000i | −0.562628 | − | 0.150756i | ||||
\(397\) | 17.0526 | − | 17.0526i | 0.855843 | − | 0.855843i | −0.135002 | − | 0.990845i | \(-0.543104\pi\) |
0.990845 | + | 0.135002i | \(0.0431041\pi\) | |||||||
\(398\) | 21.8564 | − | 21.8564i | 1.09556 | − | 1.09556i | ||||
\(399\) | −8.49038 | + | 31.6865i | −0.425051 | + | 1.58631i | ||||
\(400\) | 4.39230 | − | 2.53590i | 0.219615 | − | 0.126795i | ||||
\(401\) | −16.1603 | + | 27.9904i | −0.807005 | + | 1.39777i | 0.107925 | + | 0.994159i | \(0.465579\pi\) |
−0.914929 | + | 0.403614i | \(0.867754\pi\) | |||||||
\(402\) | −10.5622 | + | 18.2942i | −0.526794 | + | 0.912433i | ||||
\(403\) | 20.5263 | + | 5.50000i | 1.02249 | + | 0.273975i | ||||
\(404\) | −1.00000 | − | 0.267949i | −0.0497519 | − | 0.0133310i | ||||
\(405\) | −16.7942 | + | 4.50000i | −0.834512 | + | 0.223607i | ||||
\(406\) | 4.90192 | + | 2.83013i | 0.243278 | + | 0.140457i | ||||
\(407\) | 10.0981 | − | 5.83013i | 0.500543 | − | 0.288989i | ||||
\(408\) | 13.8564 | − | 13.8564i | 0.685994 | − | 0.685994i | ||||
\(409\) | −19.6244 | − | 11.3301i | −0.970362 | − | 0.560239i | −0.0710154 | − | 0.997475i | \(-0.522624\pi\) |
−0.899347 | + | 0.437236i | \(0.855957\pi\) | |||||||
\(410\) | 1.09808 | + | 1.90192i | 0.0542301 | + | 0.0939293i | ||||
\(411\) | −0.990381 | + | 0.571797i | −0.0488519 | + | 0.0282047i | ||||
\(412\) | −15.9282 | + | 27.5885i | −0.784726 | + | 1.35919i | ||||
\(413\) | −4.90192 | + | 4.90192i | −0.241208 | + | 0.241208i | ||||
\(414\) | 7.09808 | + | 26.4904i | 0.348851 | + | 1.30193i | ||||
\(415\) | 28.3205 | 1.39020 | ||||||||
\(416\) | 6.53590 | − | 11.3205i | 0.320449 | − | 0.555034i | ||||
\(417\) | 27.9904 | − | 7.50000i | 1.37069 | − | 0.367277i | ||||
\(418\) | −3.00000 | + | 11.1962i | −0.146735 | + | 0.547622i | ||||
\(419\) | −4.96410 | − | 18.5263i | −0.242512 | − | 0.905068i | −0.974618 | − | 0.223876i | \(-0.928129\pi\) |
0.732105 | − | 0.681191i | \(-0.238538\pi\) | |||||||
\(420\) | −21.1244 | − | 21.1244i | −1.03076 | − | 1.03076i | ||||
\(421\) | −4.79423 | + | 17.8923i | −0.233656 | + | 0.872018i | 0.745094 | + | 0.666960i | \(0.232405\pi\) |
−0.978750 | + | 0.205058i | \(0.934262\pi\) | |||||||
\(422\) | −13.5622 | + | 23.4904i | −0.660196 | + | 1.14349i | ||||
\(423\) | −1.79423 | − | 3.10770i | −0.0872384 | − | 0.151101i | ||||
\(424\) | 22.9282 | 1.11349 | ||||||||
\(425\) | −4.39230 | + | 2.53590i | −0.213058 | + | 0.123009i | ||||
\(426\) | 5.07180 | − | 5.07180i | 0.245729 | − | 0.245729i | ||||
\(427\) | −9.52628 | + | 2.55256i | −0.461009 | + | 0.123527i | ||||
\(428\) | −18.7846 | + | 18.7846i | −0.907988 | + | 0.907988i | ||||
\(429\) | 7.73205 | 0.373307 | ||||||||
\(430\) | −12.6603 | + | 12.6603i | −0.610532 | + | 0.610532i | ||||
\(431\) | −3.32051 | −0.159943 | −0.0799716 | − | 0.996797i | \(-0.525483\pi\) | ||||
−0.0799716 | + | 0.996797i | \(0.525483\pi\) | |||||||
\(432\) | −20.7846 | −1.00000 | ||||||||
\(433\) | 3.60770 | 0.173375 | 0.0866874 | − | 0.996236i | \(-0.472372\pi\) | ||||
0.0866874 | + | 0.996236i | \(0.472372\pi\) | |||||||
\(434\) | 41.0526 | − | 41.0526i | 1.97059 | − | 1.97059i | ||||
\(435\) | 3.00000 | 0.143839 | ||||||||
\(436\) | −3.46410 | − | 3.46410i | −0.165900 | − | 0.165900i | ||||
\(437\) | 26.4904 | − | 7.09808i | 1.26721 | − | 0.339547i | ||||
\(438\) | −12.9282 | + | 12.9282i | −0.617733 | + | 0.617733i | ||||
\(439\) | 5.93782 | − | 3.42820i | 0.283397 | − | 0.163619i | −0.351563 | − | 0.936164i | \(-0.614350\pi\) |
0.634960 | + | 0.772545i | \(0.281016\pi\) | |||||||
\(440\) | −7.46410 | − | 7.46410i | −0.355837 | − | 0.355837i | ||||
\(441\) | 19.3923 | − | 33.5885i | 0.923443 | − | 1.59945i | ||||
\(442\) | −6.53590 | + | 11.3205i | −0.310881 | + | 0.538462i | ||||
\(443\) | −1.16025 | + | 4.33013i | −0.0551253 | + | 0.205731i | −0.987996 | − | 0.154482i | \(-0.950629\pi\) |
0.932870 | + | 0.360213i | \(0.117296\pi\) | |||||||
\(444\) | 14.7846 | − | 14.7846i | 0.701647 | − | 0.701647i | ||||
\(445\) | 7.92820 | + | 29.5885i | 0.375833 | + | 1.40263i | ||||
\(446\) | 5.70577 | − | 21.2942i | 0.270176 | − | 1.00831i | ||||
\(447\) | 27.8205 | − | 7.45448i | 1.31586 | − | 0.352585i | ||||
\(448\) | −17.8564 | − | 30.9282i | −0.843636 | − | 1.46122i | ||||
\(449\) | 35.3205 | 1.66688 | 0.833439 | − | 0.552612i | \(-0.186369\pi\) | ||||
0.833439 | + | 0.552612i | \(0.186369\pi\) | |||||||
\(450\) | 5.19615 | + | 1.39230i | 0.244949 | + | 0.0656339i | ||||
\(451\) | −1.09808 | + | 1.09808i | −0.0517064 | + | 0.0517064i | ||||
\(452\) | −21.5885 | − | 12.4641i | −1.01544 | − | 0.586262i | ||||
\(453\) | −10.5000 | + | 6.06218i | −0.493333 | + | 0.284826i | ||||
\(454\) | −14.3660 | − | 24.8827i | −0.674231 | − | 1.16780i | ||||
\(455\) | 17.2583 | + | 9.96410i | 0.809083 | + | 0.467124i | ||||
\(456\) | 20.7846i | 0.973329i | ||||||||
\(457\) | 25.9641 | − | 14.9904i | 1.21455 | − | 0.701220i | 0.250802 | − | 0.968038i | \(-0.419306\pi\) |
0.963747 | + | 0.266818i | \(0.0859722\pi\) | |||||||
\(458\) | −20.9545 | − | 12.0981i | −0.979139 | − | 0.565306i | ||||
\(459\) | 20.7846 | 0.970143 | ||||||||
\(460\) | −6.46410 | + | 24.1244i | −0.301390 | + | 1.12480i | ||||
\(461\) | 4.59808 | + | 1.23205i | 0.214154 | + | 0.0573823i | 0.364301 | − | 0.931281i | \(-0.381308\pi\) |
−0.150147 | + | 0.988664i | \(0.547975\pi\) | |||||||
\(462\) | 10.5622 | − | 18.2942i | 0.491397 | − | 0.851125i | ||||
\(463\) | −5.33013 | + | 9.23205i | −0.247712 | + | 0.429050i | −0.962891 | − | 0.269892i | \(-0.913012\pi\) |
0.715179 | + | 0.698942i | \(0.246345\pi\) | |||||||
\(464\) | 3.46410 | + | 0.928203i | 0.160817 | + | 0.0430908i | ||||
\(465\) | 7.96410 | − | 29.7224i | 0.369326 | − | 1.37834i | ||||
\(466\) | −9.07180 | + | 9.07180i | −0.420243 | + | 0.420243i | ||||
\(467\) | 21.7846 | − | 21.7846i | 1.00807 | − | 1.00807i | 0.00810436 | − | 0.999967i | \(-0.497420\pi\) |
0.999967 | − | 0.00810436i | \(-0.00257972\pi\) | |||||||
\(468\) | 13.3923 | − | 3.58846i | 0.619060 | − | 0.165876i | ||||
\(469\) | −27.2224 | − | 27.2224i | −1.25702 | − | 1.25702i | ||||
\(470\) | − | 3.26795i | − | 0.150739i | ||||||
\(471\) | −1.50000 | − | 5.59808i | −0.0691164 | − | 0.257946i | ||||
\(472\) | −2.19615 | + | 3.80385i | −0.101086 | + | 0.175086i | ||||
\(473\) | −10.9641 | − | 6.33013i | −0.504130 | − | 0.291060i | ||||
\(474\) | −1.09808 | + | 4.09808i | −0.0504363 | + | 0.188231i | ||||
\(475\) | 1.39230 | − | 5.19615i | 0.0638833 | − | 0.238416i | ||||
\(476\) | 17.8564 | + | 30.9282i | 0.818447 | + | 1.41759i | ||||
\(477\) | 17.1962 | + | 17.1962i | 0.787358 | + | 0.787358i | ||||
\(478\) | 1.09808 | − | 0.294229i | 0.0502248 | − | 0.0134577i | ||||
\(479\) | 9.33013 | + | 16.1603i | 0.426304 | + | 0.738381i | 0.996541 | − | 0.0830995i | \(-0.0264819\pi\) |
−0.570237 | + | 0.821480i | \(0.693149\pi\) | |||||||
\(480\) | −16.3923 | − | 9.46410i | −0.748203 | − | 0.431975i | ||||
\(481\) | −6.97372 | + | 12.0788i | −0.317974 | + | 0.550748i | ||||
\(482\) | −2.02628 | + | 7.56218i | −0.0922945 | + | 0.344448i | ||||
\(483\) | −49.9808 | −2.27420 | ||||||||
\(484\) | −7.26795 | + | 12.5885i | −0.330361 | + | 0.572203i | ||||
\(485\) | 1.36603 | + | 1.36603i | 0.0620280 | + | 0.0620280i | ||||
\(486\) | −15.5885 | − | 15.5885i | −0.707107 | − | 0.707107i | ||||
\(487\) | 6.78461i | 0.307440i | 0.988114 | + | 0.153720i | \(0.0491254\pi\) | ||||
−0.988114 | + | 0.153720i | \(0.950875\pi\) | |||||||
\(488\) | −5.41154 | + | 3.12436i | −0.244969 | + | 0.141433i | ||||
\(489\) | −3.33975 | + | 3.33975i | −0.151029 | + | 0.151029i | ||||
\(490\) | 30.5885 | − | 17.6603i | 1.38185 | − | 0.797809i | ||||
\(491\) | 0.500000 | − | 0.133975i | 0.0225647 | − | 0.00604619i | −0.247519 | − | 0.968883i | \(-0.579615\pi\) |
0.270084 | + | 0.962837i | \(0.412949\pi\) | |||||||
\(492\) | −1.39230 | + | 2.41154i | −0.0627700 | + | 0.108721i | ||||
\(493\) | −3.46410 | − | 0.928203i | −0.156015 | − | 0.0418042i | ||||
\(494\) | −3.58846 | − | 13.3923i | −0.161452 | − | 0.602548i | ||||
\(495\) | − | 11.1962i | − | 0.503230i | ||||||
\(496\) | 18.3923 | − | 31.8564i | 0.825839 | − | 1.43039i | ||||
\(497\) | 6.53590 | + | 11.3205i | 0.293175 | + | 0.507794i | ||||
\(498\) | 17.9545 | + | 31.0981i | 0.804560 | + | 1.39354i | ||||
\(499\) | −2.50000 | − | 9.33013i | −0.111915 | − | 0.417674i | 0.887122 | − | 0.461534i | \(-0.152701\pi\) |
−0.999038 | + | 0.0438606i | \(0.986034\pi\) | |||||||
\(500\) | 17.1244 | + | 17.1244i | 0.765824 | + | 0.765824i | ||||
\(501\) | −24.6962 | − | 14.2583i | −1.10334 | − | 0.637015i | ||||
\(502\) | 26.7846i | 1.19546i | ||||||||
\(503\) | − | 13.8564i | − | 0.617827i | −0.951090 | − | 0.308913i | \(-0.900035\pi\) | ||
0.951090 | − | 0.308913i | \(-0.0999653\pi\) | |||||||
\(504\) | 9.80385 | − | 36.5885i | 0.436698 | − | 1.62978i | ||||
\(505\) | − | 1.00000i | − | 0.0444994i | ||||||
\(506\) | −17.6603 | −0.785094 | ||||||||
\(507\) | 11.4904 | − | 6.63397i | 0.510306 | − | 0.294625i | ||||
\(508\) | 0.784610i | 0.0348114i | ||||||||
\(509\) | 1.25833 | + | 4.69615i | 0.0557745 | + | 0.208153i | 0.988190 | − | 0.153236i | \(-0.0489693\pi\) |
−0.932415 | + | 0.361389i | \(0.882303\pi\) | |||||||
\(510\) | 16.3923 | + | 9.46410i | 0.725863 | + | 0.419077i | ||||
\(511\) | −16.6603 | − | 28.8564i | −0.737006 | − | 1.27653i | ||||
\(512\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(513\) | −15.5885 | + | 15.5885i | −0.688247 | + | 0.688247i | ||||
\(514\) | −33.2224 | + | 8.90192i | −1.46538 | + | 0.392647i | ||||
\(515\) | −29.7224 | − | 7.96410i | −1.30973 | − | 0.350940i | ||||
\(516\) | −21.9282 | − | 5.87564i | −0.965335 | − | 0.258661i | ||||
\(517\) | 2.23205 | − | 0.598076i | 0.0981655 | − | 0.0263034i | ||||
\(518\) | 19.0526 | + | 33.0000i | 0.837121 | + | 1.44994i | ||||
\(519\) | 13.1603 | + | 3.52628i | 0.577671 | + | 0.154786i | ||||
\(520\) | 12.1962 | + | 3.26795i | 0.534837 | + | 0.143309i | ||||
\(521\) | 41.8564i | 1.83376i | 0.399160 | + | 0.916881i | \(0.369302\pi\) | ||||
−0.399160 | + | 0.916881i | \(0.630698\pi\) | |||||||
\(522\) | 1.90192 | + | 3.29423i | 0.0832449 | + | 0.144184i | ||||
\(523\) | 22.1244 | + | 22.1244i | 0.967431 | + | 0.967431i | 0.999486 | − | 0.0320556i | \(-0.0102054\pi\) |
−0.0320556 | + | 0.999486i | \(0.510205\pi\) | |||||||
\(524\) | −9.73205 | + | 2.60770i | −0.425147 | + | 0.113918i | ||||
\(525\) | −4.90192 | + | 8.49038i | −0.213937 | + | 0.370551i | ||||
\(526\) | 13.5622 | + | 3.63397i | 0.591339 | + | 0.158449i | ||||
\(527\) | −18.3923 | + | 31.8564i | −0.801181 | + | 1.38769i | ||||
\(528\) | 3.46410 | − | 12.9282i | 0.150756 | − | 0.562628i | ||||
\(529\) | 9.39230 | + | 16.2679i | 0.408361 | + | 0.707302i | ||||
\(530\) | 5.73205 | + | 21.3923i | 0.248984 | + | 0.929222i | ||||
\(531\) | −4.50000 | + | 1.20577i | −0.195283 | + | 0.0523260i | ||||
\(532\) | −36.5885 | − | 9.80385i | −1.58631 | − | 0.425051i | ||||
\(533\) | 0.480762 | − | 1.79423i | 0.0208241 | − | 0.0777167i | ||||
\(534\) | −27.4641 | + | 27.4641i | −1.18849 | + | 1.18849i | ||||
\(535\) | −22.2224 | − | 12.8301i | −0.960760 | − | 0.554695i | ||||
\(536\) | −21.1244 | − | 12.1962i | −0.912433 | − | 0.526794i | ||||
\(537\) | −10.2679 | + | 10.2679i | −0.443095 | + | 0.443095i | ||||
\(538\) | −8.53590 | −0.368009 | ||||||||
\(539\) | 17.6603 | + | 17.6603i | 0.760681 | + | 0.760681i | ||||
\(540\) | −5.19615 | − | 19.3923i | −0.223607 | − | 0.834512i | ||||
\(541\) | −15.0000 | + | 15.0000i | −0.644900 | + | 0.644900i | −0.951756 | − | 0.306856i | \(-0.900723\pi\) |
0.306856 | + | 0.951756i | \(0.400723\pi\) | |||||||
\(542\) | 1.07180 | + | 1.07180i | 0.0460376 | + | 0.0460376i | ||||
\(543\) | −13.3923 | − | 13.3923i | −0.574719 | − | 0.574719i | ||||
\(544\) | 16.0000 | + | 16.0000i | 0.685994 | + | 0.685994i | ||||
\(545\) | 2.36603 | − | 4.09808i | 0.101349 | − | 0.175542i | ||||
\(546\) | 25.2679i | 1.08137i | ||||||||
\(547\) | 21.4282 | + | 5.74167i | 0.916204 | + | 0.245496i | 0.685962 | − | 0.727637i | \(-0.259382\pi\) |
0.230242 | + | 0.973133i | \(0.426048\pi\) | |||||||
\(548\) | −0.660254 | − | 1.14359i | −0.0282047 | − | 0.0488519i | ||||
\(549\) | −6.40192 | − | 1.71539i | −0.273227 | − | 0.0732111i | ||||
\(550\) | −1.73205 | + | 3.00000i | −0.0738549 | + | 0.127920i | ||||
\(551\) | 3.29423 | − | 1.90192i | 0.140339 | − | 0.0810247i | ||||
\(552\) | −30.5885 | + | 8.19615i | −1.30193 | + | 0.348851i | ||||
\(553\) | −6.69615 | − | 3.86603i | −0.284749 | − | 0.164400i | ||||
\(554\) | 8.49038 | − | 4.90192i | 0.360722 | − | 0.208263i | ||||
\(555\) | 17.4904 | + | 10.0981i | 0.742425 | + | 0.428639i | ||||
\(556\) | 8.66025 | + | 32.3205i | 0.367277 | + | 1.37069i | ||||
\(557\) | −23.9808 | + | 23.9808i | −1.01610 | + | 1.01610i | −0.0162292 | + | 0.999868i | \(0.505166\pi\) |
−0.999868 | + | 0.0162292i | \(0.994834\pi\) | |||||||
\(558\) | 37.6865 | − | 10.0981i | 1.59540 | − | 0.427486i | ||||
\(559\) | 15.1436 | 0.640506 | ||||||||
\(560\) | 24.3923 | − | 24.3923i | 1.03076 | − | 1.03076i | ||||
\(561\) | −3.46410 | + | 12.9282i | −0.146254 | + | 0.545829i | ||||
\(562\) | 15.8301 | + | 4.24167i | 0.667754 | + | 0.178924i | ||||
\(563\) | −1.64359 | − | 6.13397i | −0.0692692 | − | 0.258516i | 0.922604 | − | 0.385749i | \(-0.126057\pi\) |
−0.991873 | + | 0.127233i | \(0.959390\pi\) | |||||||
\(564\) | 3.58846 | − | 2.07180i | 0.151101 | − | 0.0872384i | ||||
\(565\) | 6.23205 | − | 23.2583i | 0.262184 | − | 0.978485i | ||||
\(566\) | 16.6865 | + | 9.63397i | 0.701387 | + | 0.404946i | ||||
\(567\) | 34.7942 | − | 20.0885i | 1.46122 | − | 0.843636i | ||||
\(568\) | 5.85641 | + | 5.85641i | 0.245729 | + | 0.245729i | ||||
\(569\) | −27.4808 | + | 15.8660i | −1.15205 | + | 0.665138i | −0.949387 | − | 0.314109i | \(-0.898294\pi\) |
−0.202667 | + | 0.979248i | \(0.564961\pi\) | |||||||
\(570\) | −19.3923 | + | 5.19615i | −0.812254 | + | 0.217643i | ||||
\(571\) | 39.5526 | − | 10.5981i | 1.65522 | − | 0.443516i | 0.694155 | − | 0.719826i | \(-0.255778\pi\) |
0.961068 | + | 0.276310i | \(0.0891117\pi\) | |||||||
\(572\) | 8.92820i | 0.373307i | ||||||||
\(573\) | 2.42820 | + | 4.20577i | 0.101440 | + | 0.175699i | ||||
\(574\) | −3.58846 | − | 3.58846i | −0.149779 | − | 0.149779i | ||||
\(575\) | 8.19615 | 0.341803 | ||||||||
\(576\) | − | 24.0000i | − | 1.00000i | ||||||
\(577\) | −25.1769 | −1.04813 | −0.524064 | − | 0.851679i | \(-0.675585\pi\) | ||||
−0.524064 | + | 0.851679i | \(0.675585\pi\) | |||||||
\(578\) | 1.00000 | + | 1.00000i | 0.0415945 | + | 0.0415945i | ||||
\(579\) | 3.86603 | − | 6.69615i | 0.160667 | − | 0.278283i | ||||
\(580\) | 3.46410i | 0.143839i | ||||||||
\(581\) | −63.2128 | + | 16.9378i | −2.62251 | + | 0.702699i | ||||
\(582\) | −0.633975 | + | 2.36603i | −0.0262791 | + | 0.0980749i | ||||
\(583\) | −13.5622 | + | 7.83013i | −0.561688 | + | 0.324291i | ||||
\(584\) | −14.9282 | − | 14.9282i | −0.617733 | − | 0.617733i | ||||
\(585\) | 6.69615 | + | 11.5981i | 0.276852 | + | 0.479521i | ||||
\(586\) | −2.70577 | − | 1.56218i | −0.111774 | − | 0.0645330i | ||||
\(587\) | 3.96410 | − | 14.7942i | 0.163616 | − | 0.610623i | −0.834597 | − | 0.550861i | \(-0.814299\pi\) |
0.998213 | − | 0.0597617i | \(-0.0190341\pi\) | |||||||
\(588\) | 38.7846 | + | 22.3923i | 1.59945 | + | 0.923443i | ||||
\(589\) | −10.0981 | − | 37.6865i | −0.416084 | − | 1.55285i | ||||
\(590\) | −4.09808 | − | 1.09808i | −0.168715 | − | 0.0452071i | ||||
\(591\) | 6.12436 | + | 6.12436i | 0.251922 | + | 0.251922i | ||||
\(592\) | 17.0718 | + | 17.0718i | 0.701647 | + | 0.701647i | ||||
\(593\) | −5.46410 | −0.224384 | −0.112192 | − | 0.993687i | \(-0.535787\pi\) | ||||
−0.112192 | + | 0.993687i | \(0.535787\pi\) | |||||||
\(594\) | 12.2942 | − | 7.09808i | 0.504438 | − | 0.291238i | ||||
\(595\) | −24.3923 | + | 24.3923i | −0.999987 | + | 0.999987i | ||||
\(596\) | 8.60770 | + | 32.1244i | 0.352585 | + | 1.31586i | ||||
\(597\) | 37.8564i | 1.54936i | ||||||||
\(598\) | 18.2942 | − | 10.5622i | 0.748107 | − | 0.431920i | ||||
\(599\) | −30.3109 | − | 17.5000i | −1.23847 | − | 0.715031i | −0.269688 | − | 0.962948i | \(-0.586921\pi\) |
−0.968781 | + | 0.247917i | \(0.920254\pi\) | |||||||
\(600\) | −1.60770 | + | 6.00000i | −0.0656339 | + | 0.244949i | ||||
\(601\) | −26.7679 | + | 15.4545i | −1.09189 | + | 0.630401i | −0.934078 | − | 0.357068i | \(-0.883776\pi\) |
−0.157809 | + | 0.987470i | \(0.550443\pi\) | |||||||
\(602\) | 20.6865 | − | 35.8301i | 0.843120 | − | 1.46033i | ||||
\(603\) | −6.69615 | − | 24.9904i | −0.272688 | − | 1.01769i | ||||
\(604\) | −7.00000 | − | 12.1244i | −0.284826 | − | 0.493333i | ||||
\(605\) | −13.5622 | − | 3.63397i | −0.551381 | − | 0.147742i | ||||
\(606\) | 1.09808 | − | 0.633975i | 0.0446063 | − | 0.0257535i | ||||
\(607\) | 0.598076 | − | 1.03590i | 0.0242752 | − | 0.0420458i | −0.853633 | − | 0.520876i | \(-0.825606\pi\) |
0.877908 | + | 0.478830i | \(0.158939\pi\) | |||||||
\(608\) | −24.0000 | −0.973329 | ||||||||
\(609\) | −6.69615 | + | 1.79423i | −0.271342 | + | 0.0727058i | ||||
\(610\) | −4.26795 | − | 4.26795i | −0.172804 | − | 0.172804i | ||||
\(611\) | −1.95448 | + | 1.95448i | −0.0790699 | + | 0.0790699i | ||||
\(612\) | 24.0000i | 0.970143i | ||||||||
\(613\) | 23.5885 | + | 23.5885i | 0.952729 | + | 0.952729i | 0.998932 | − | 0.0462032i | \(-0.0147122\pi\) |
−0.0462032 | + | 0.998932i | \(0.514712\pi\) | |||||||
\(614\) | −15.8564 | −0.639912 | ||||||||
\(615\) | −2.59808 | − | 0.696152i | −0.104765 | − | 0.0280716i | ||||
\(616\) | 21.1244 | + | 12.1962i | 0.851125 | + | 0.491397i | ||||
\(617\) | 23.0885 | + | 13.3301i | 0.929506 | + | 0.536651i | 0.886655 | − | 0.462431i | \(-0.153023\pi\) |
0.0428509 | + | 0.999081i | \(0.486356\pi\) | |||||||
\(618\) | −10.0981 | − | 37.6865i | −0.406204 | − | 1.51597i | ||||
\(619\) | −1.91154 | + | 7.13397i | −0.0768314 | + | 0.286739i | −0.993642 | − | 0.112583i | \(-0.964088\pi\) |
0.916811 | + | 0.399322i | \(0.130754\pi\) | |||||||
\(620\) | 34.3205 | + | 9.19615i | 1.37834 | + | 0.369326i | ||||
\(621\) | −29.0885 | − | 16.7942i | −1.16728 | − | 0.673929i | ||||
\(622\) | −3.88269 | − | 14.4904i | −0.155682 | − | 0.581011i | ||||
\(623\) | −35.3923 | − | 61.3013i | −1.41796 | − | 2.45598i | ||||
\(624\) | 4.14359 | + | 15.4641i | 0.165876 | + | 0.619060i | ||||
\(625\) | −8.52628 | + | 14.7679i | −0.341051 | + | 0.590718i | ||||
\(626\) | −39.6865 | − | 10.6340i | −1.58619 | − | 0.425019i | ||||
\(627\) | −7.09808 | − | 12.2942i | −0.283470 | − | 0.490984i | ||||
\(628\) | 6.46410 | − | 1.73205i | 0.257946 | − | 0.0691164i | ||||
\(629\) | −17.0718 | − | 17.0718i | −0.680697 | − | 0.680697i | ||||
\(630\) | 36.5885 | 1.45772 | ||||||||
\(631\) | − | 16.2487i | − | 0.646851i | −0.946254 | − | 0.323425i | \(-0.895165\pi\) | ||
0.946254 | − | 0.323425i | \(-0.104835\pi\) | |||||||
\(632\) | −4.73205 | − | 1.26795i | −0.188231 | − | 0.0504363i | ||||
\(633\) | −8.59808 | − | 32.0885i | −0.341743 | − | 1.27540i | ||||
\(634\) | 24.4904 | + | 42.4186i | 0.972637 | + | 1.68466i | ||||
\(635\) | −0.732051 | + | 0.196152i | −0.0290506 | + | 0.00778407i | ||||
\(636\) | −19.8564 | + | 19.8564i | −0.787358 | + | 0.787358i | ||||
\(637\) | −28.8564 | − | 7.73205i | −1.14333 | − | 0.306355i | ||||
\(638\) | −2.36603 | + | 0.633975i | −0.0936718 | + | 0.0250993i | ||||
\(639\) | 8.78461i | 0.347514i | ||||||||
\(640\) | 10.9282 | − | 18.9282i | 0.431975 | − | 0.748203i | ||||
\(641\) | 9.23205 | + | 15.9904i | 0.364644 | + | 0.631582i | 0.988719 | − | 0.149782i | \(-0.0478573\pi\) |
−0.624075 | + | 0.781365i | \(0.714524\pi\) | |||||||
\(642\) | − | 32.5359i | − | 1.28409i | ||||||
\(643\) | 7.96410 | + | 29.7224i | 0.314074 | + | 1.17214i | 0.924849 | + | 0.380334i | \(0.124191\pi\) |
−0.610776 | + | 0.791804i | \(0.709142\pi\) | |||||||
\(644\) | − | 57.7128i | − | 2.27420i | ||||||
\(645\) | − | 21.9282i | − | 0.863422i | ||||||
\(646\) | 24.0000 | 0.944267 | ||||||||
\(647\) | − | 25.6077i | − | 1.00674i | −0.864070 | − | 0.503371i | \(-0.832093\pi\) | ||
0.864070 | − | 0.503371i | \(-0.167907\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.707107 | − | 0.707107i | ||||
\(649\) | − | 3.00000i | − | 0.117760i | ||||||
\(650\) | − | 4.14359i | − | 0.162525i | ||||||
\(651\) | 71.1051i | 2.78683i | ||||||||
\(652\) | −3.85641 | − | 3.85641i | −0.151029 | − | 0.151029i | ||||
\(653\) | −12.6699 | − | 47.2846i | −0.495810 | − | 1.85039i | −0.525443 | − | 0.850829i | \(-0.676100\pi\) |
0.0296324 | − | 0.999561i | \(-0.490566\pi\) | |||||||
\(654\) | 6.00000 | 0.234619 | ||||||||
\(655\) | −4.86603 | − | 8.42820i | −0.190131 | − | 0.329317i | ||||
\(656\) | −2.78461 | − | 1.60770i | −0.108721 | − | 0.0627700i | ||||
\(657\) | − | 22.3923i | − | 0.873607i | ||||||
\(658\) | 1.95448 | + | 7.29423i | 0.0761937 | + | 0.284359i | ||||
\(659\) | 1.23205 | + | 0.330127i | 0.0479939 | + | 0.0128599i | 0.282736 | − | 0.959198i | \(-0.408758\pi\) |
−0.234742 | + | 0.972058i | \(0.575425\pi\) | |||||||
\(660\) | 12.9282 | 0.503230 | ||||||||
\(661\) | 19.7942 | − | 5.30385i | 0.769906 | − | 0.206296i | 0.147576 | − | 0.989051i | \(-0.452853\pi\) |
0.622330 | + | 0.782755i | \(0.286186\pi\) | |||||||
\(662\) | −6.41858 | + | 3.70577i | −0.249465 | + | 0.144029i | ||||
\(663\) | −4.14359 | − | 15.4641i | −0.160924 | − | 0.600576i | ||||
\(664\) | −35.9090 | + | 20.7321i | −1.39354 | + | 0.804560i | ||||
\(665\) | − | 36.5885i | − | 1.41884i | ||||||
\(666\) | 25.6077i | 0.992278i | ||||||||
\(667\) | 4.09808 | + | 4.09808i | 0.158678 | + | 0.158678i | ||||
\(668\) | 16.4641 | − | 28.5167i | 0.637015 | − | 1.10334i | ||||
\(669\) | 13.5000 | + | 23.3827i | 0.521940 | + | 0.904027i | ||||
\(670\) | 6.09808 | − | 22.7583i | 0.235589 | − | 0.879231i | ||||
\(671\) | 2.13397 | − | 3.69615i | 0.0823812 | − | 0.142688i | ||||
\(672\) | 42.2487 | + | 11.3205i | 1.62978 | + | 0.436698i | ||||
\(673\) | 21.1603 | + | 36.6506i | 0.815668 | + | 1.41278i | 0.908847 | + | 0.417129i | \(0.136964\pi\) |
−0.0931795 | + | 0.995649i | \(0.529703\pi\) | |||||||
\(674\) | 26.4904 | − | 7.09808i | 1.02037 | − | 0.273408i | ||||
\(675\) | −5.70577 | + | 3.29423i | −0.219615 | + | 0.126795i | ||||
\(676\) | 7.66025 | + | 13.2679i | 0.294625 | + | 0.510306i | ||||
\(677\) | 2.34936 | − | 8.76795i | 0.0902934 | − | 0.336980i | −0.905970 | − | 0.423341i | \(-0.860857\pi\) |
0.996264 | + | 0.0863612i | \(0.0275239\pi\) | |||||||
\(678\) | 29.4904 | − | 7.90192i | 1.13257 | − | 0.303472i | ||||
\(679\) | −3.86603 | − | 2.23205i | −0.148364 | − | 0.0856582i | ||||
\(680\) | −10.9282 | + | 18.9282i | −0.419077 | + | 0.725863i | ||||
\(681\) | 33.9904 | + | 9.10770i | 1.30251 | + | 0.349008i | ||||
\(682\) | 25.1244i | 0.962061i | ||||||||
\(683\) | 15.3923 | + | 15.3923i | 0.588970 | + | 0.588970i | 0.937353 | − | 0.348382i | \(-0.113269\pi\) |
−0.348382 | + | 0.937353i | \(0.613269\pi\) | |||||||
\(684\) | −18.0000 | − | 18.0000i | −0.688247 | − | 0.688247i | ||||
\(685\) | 0.901924 | − | 0.901924i | 0.0344607 | − | 0.0344607i | ||||
\(686\) | −26.4641 | + | 26.4641i | −1.01040 | + | 1.01040i | ||||
\(687\) | 28.6244 | − | 7.66987i | 1.09209 | − | 0.292624i | ||||
\(688\) | 6.78461 | − | 25.3205i | 0.258661 | − | 0.965335i | ||||
\(689\) | 9.36603 | − | 16.2224i | 0.356817 | − | 0.618025i | ||||
\(690\) | −15.2942 | − | 26.4904i | −0.582241 | − | 1.00847i | ||||
\(691\) | −1.96410 | − | 0.526279i | −0.0747179 | − | 0.0200206i | 0.221266 | − | 0.975213i | \(-0.428981\pi\) |
−0.295984 | + | 0.955193i | \(0.595648\pi\) | |||||||
\(692\) | −4.07180 | + | 15.1962i | −0.154786 | + | 0.577671i | ||||
\(693\) | 6.69615 | + | 24.9904i | 0.254366 | + | 0.949306i | ||||
\(694\) | 2.24167 | + | 1.29423i | 0.0850926 | + | 0.0491282i | ||||
\(695\) | −27.9904 | + | 16.1603i | −1.06174 | + | 0.612993i | ||||
\(696\) | −3.80385 | + | 2.19615i | −0.144184 | + | 0.0832449i | ||||
\(697\) | 2.78461 | + | 1.60770i | 0.105475 | + | 0.0608958i | ||||
\(698\) | 2.83013 | + | 4.90192i | 0.107122 | + | 0.185541i | ||||
\(699\) | − | 15.7128i | − | 0.594313i | ||||||
\(700\) | −9.80385 | − | 5.66025i | −0.370551 | − | 0.213937i | ||||
\(701\) | 17.0526 | − | 17.0526i | 0.644066 | − | 0.644066i | −0.307486 | − | 0.951553i | \(-0.599488\pi\) |
0.951553 | + | 0.307486i | \(0.0994878\pi\) | |||||||
\(702\) | −8.49038 | + | 14.7058i | −0.320449 | + | 0.555034i | ||||
\(703\) | 25.6077 | 0.965813 | ||||||||
\(704\) | 14.9282 | + | 4.00000i | 0.562628 | + | 0.150756i | ||||
\(705\) | 2.83013 | + | 2.83013i | 0.106589 | + | 0.106589i | ||||
\(706\) | −8.61474 | + | 32.1506i | −0.324220 | + | 1.21001i | ||||
\(707\) | 0.598076 | + | 2.23205i | 0.0224930 | + | 0.0839449i | ||||
\(708\) | −1.39230 | − | 5.19615i | −0.0523260 | − | 0.195283i | ||||
\(709\) | 10.1147 | − | 37.7487i | 0.379867 | − | 1.41768i | −0.466235 | − | 0.884661i | \(-0.654390\pi\) |
0.846102 | − | 0.533022i | \(-0.178944\pi\) | |||||||
\(710\) | −4.00000 | + | 6.92820i | −0.150117 | + | 0.260011i | ||||
\(711\) | −2.59808 | − | 4.50000i | −0.0974355 | − | 0.168763i | ||||
\(712\) | −31.7128 | − | 31.7128i | −1.18849 | − | 1.18849i | ||||
\(713\) | 51.4808 | − | 29.7224i | 1.92797 | − | 1.11311i | ||||
\(714\) | −42.2487 | − | 11.3205i | −1.58112 | − | 0.423659i | ||||
\(715\) | −8.33013 | + | 2.23205i | −0.311529 | + | 0.0834740i | ||||
\(716\) | −11.8564 | − | 11.8564i | −0.443095 | − | 0.443095i | ||||
\(717\) | −0.696152 | + | 1.20577i | −0.0259983 | + | 0.0450304i | ||||
\(718\) | 28.9282 | − | 28.9282i | 1.07959 | − | 1.07959i | ||||
\(719\) | −11.3205 | −0.422184 | −0.211092 | − | 0.977466i | \(-0.567702\pi\) | ||||
−0.211092 | + | 0.977466i | \(0.567702\pi\) | |||||||
\(720\) | 22.3923 | − | 6.00000i | 0.834512 | − | 0.223607i | ||||
\(721\) | 71.1051 | 2.64809 | ||||||||
\(722\) | 1.00000 | − | 1.00000i | 0.0372161 | − | 0.0372161i | ||||
\(723\) | −4.79423 | − | 8.30385i | −0.178299 | − | 0.308823i | ||||
\(724\) | 15.4641 | − | 15.4641i | 0.574719 | − | 0.574719i | ||||
\(725\) | 1.09808 | − | 0.294229i | 0.0407815 | − | 0.0109274i | ||||
\(726\) | −4.60770 | − | 17.1962i | −0.171008 | − | 0.638209i | ||||
\(727\) | 3.06218 | − | 1.76795i | 0.113570 | − | 0.0655696i | −0.442139 | − | 0.896947i | \(-0.645780\pi\) |
0.555709 | + | 0.831377i | \(0.312447\pi\) | |||||||
\(728\) | −29.1769 | −1.08137 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 10.1962 | − | 17.6603i | 0.377377 | − | 0.653635i | ||||
\(731\) | −6.78461 | + | 25.3205i | −0.250938 | + | 0.936513i | ||||
\(732\) | 1.98076 | − | 7.39230i | 0.0732111 | − | 0.273227i | ||||
\(733\) | 8.47372 | + | 31.6244i | 0.312984 | + | 1.16807i | 0.925852 | + | 0.377887i | \(0.123349\pi\) |
−0.612868 | + | 0.790185i | \(0.709984\pi\) | |||||||
\(734\) | −12.7776 | + | 47.6865i | −0.471629 | + | 1.76014i | ||||
\(735\) | −11.1962 | + | 41.7846i | −0.412976 | + | 1.54125i | ||||
\(736\) | −9.46410 | − | 35.3205i | −0.348851 | − | 1.30193i | ||||
\(737\) | 16.6603 | 0.613688 | ||||||||
\(738\) | −0.882686 | − | 3.29423i | −0.0324921 | − | 0.121262i | ||||
\(739\) | −26.2679 | + | 26.2679i | −0.966282 | + | 0.966282i | −0.999450 | − | 0.0331677i | \(-0.989440\pi\) |
0.0331677 | + | 0.999450i | \(0.489440\pi\) | |||||||
\(740\) | −11.6603 | + | 20.1962i | −0.428639 | + | 0.742425i | ||||
\(741\) | 14.7058 | + | 8.49038i | 0.540230 | + | 0.311902i | ||||
\(742\) | −25.5885 | − | 44.3205i | −0.939382 | − | 1.62706i | ||||
\(743\) | 25.1147 | + | 14.5000i | 0.921370 | + | 0.531953i | 0.884072 | − | 0.467351i | \(-0.154791\pi\) |
0.0372984 | + | 0.999304i | \(0.488125\pi\) | |||||||
\(744\) | 11.6603 | + | 43.5167i | 0.427486 | + | 1.59540i | ||||
\(745\) | −27.8205 | + | 16.0622i | −1.01926 | + | 0.588473i | ||||
\(746\) | 2.02628 | + | 1.16987i | 0.0741874 | + | 0.0428321i | ||||
\(747\) | −42.4808 | − | 11.3827i | −1.55429 | − | 0.416471i | ||||
\(748\) | −14.9282 | − | 4.00000i | −0.545829 | − | 0.146254i | ||||
\(749\) | 57.2750 | + | 15.3468i | 2.09278 | + | 0.560759i | ||||
\(750\) | −29.6603 | −1.08304 | ||||||||
\(751\) | −24.7224 | + | 42.8205i | −0.902134 | + | 1.56254i | −0.0774160 | + | 0.996999i | \(0.524667\pi\) |
−0.824718 | + | 0.565544i | \(0.808666\pi\) | |||||||
\(752\) | 2.39230 | + | 4.14359i | 0.0872384 | + | 0.151101i | ||||
\(753\) | −23.1962 | − | 23.1962i | −0.845315 | − | 0.845315i | ||||
\(754\) | 2.07180 | − | 2.07180i | 0.0754504 | − | 0.0754504i | ||||
\(755\) | 9.56218 | − | 9.56218i | 0.348003 | − | 0.348003i | ||||
\(756\) | 23.1962 | + | 40.1769i | 0.843636 | + | 1.46122i | ||||
\(757\) | 1.53590 | + | 1.53590i | 0.0558232 | + | 0.0558232i | 0.734467 | − | 0.678644i | \(-0.237432\pi\) |
−0.678644 | + | 0.734467i | \(0.737432\pi\) | |||||||
\(758\) | 31.1769i | 1.13240i | ||||||||
\(759\) | 15.2942 | − | 15.2942i | 0.555145 | − | 0.555145i | ||||
\(760\) | −6.00000 | − | 22.3923i | −0.217643 | − | 0.812254i | ||||
\(761\) | −16.2846 | − | 9.40192i | −0.590317 | − | 0.340819i | 0.174906 | − | 0.984585i | \(-0.444038\pi\) |
−0.765223 | + | 0.643766i | \(0.777371\pi\) | |||||||
\(762\) | −0.679492 | − | 0.679492i | −0.0246154 | − | 0.0246154i | ||||
\(763\) | −2.83013 | + | 10.5622i | −0.102457 | + | 0.382377i | ||||
\(764\) | −4.85641 | + | 2.80385i | −0.175699 | + | 0.101440i | ||||
\(765\) | −22.3923 | + | 6.00000i | −0.809595 | + | 0.216930i | ||||
\(766\) | −10.0263 | + | 2.68653i | −0.362264 | + | 0.0970684i | ||||
\(767\) | 1.79423 | + | 3.10770i | 0.0647858 | + | 0.112212i | ||||
\(768\) | 27.7128 | 1.00000 | ||||||||
\(769\) | −3.50000 | + | 6.06218i | −0.126213 | + | 0.218608i | −0.922207 | − | 0.386698i | \(-0.873616\pi\) |
0.795993 | + | 0.605305i | \(0.206949\pi\) | |||||||
\(770\) | −6.09808 | + | 22.7583i | −0.219759 | + | 0.820153i | ||||
\(771\) | 21.0622 | − | 36.4808i | 0.758536 | − | 1.31382i | ||||
\(772\) | 7.73205 | + | 4.46410i | 0.278283 | + | 0.160667i | ||||
\(773\) | −23.5885 | − | 23.5885i | −0.848418 | − | 0.848418i | 0.141518 | − | 0.989936i | \(-0.454802\pi\) |
−0.989936 | + | 0.141518i | \(0.954802\pi\) | |||||||
\(774\) | 24.0788 | − | 13.9019i | 0.865496 | − | 0.499694i | ||||
\(775\) | − | 11.6603i | − | 0.418849i | ||||||
\(776\) | −2.73205 | − | 0.732051i | −0.0980749 | − | 0.0262791i | ||||
\(777\) | −45.0788 | − | 12.0788i | −1.61719 | − | 0.433326i | ||||
\(778\) | −11.3660 | + | 6.56218i | −0.407492 | + | 0.235265i | ||||
\(779\) | −3.29423 | + | 0.882686i | −0.118028 | + | 0.0316255i | ||||
\(780\) | −13.3923 | + | 7.73205i | −0.479521 | + | 0.276852i | ||||
\(781\) | −5.46410 | − | 1.46410i | −0.195521 | − | 0.0523897i | ||||
\(782\) | 9.46410 | + | 35.3205i | 0.338436 | + | 1.26306i | ||||
\(783\) | −4.50000 | − | 1.20577i | −0.160817 | − | 0.0430908i | ||||
\(784\) | −25.8564 | + | 44.7846i | −0.923443 | + | 1.59945i | ||||
\(785\) | 3.23205 | + | 5.59808i | 0.115357 | + | 0.199804i | ||||
\(786\) | 6.16987 | − | 10.6865i | 0.220072 | − | 0.381176i | ||||
\(787\) | 0.820508 | + | 3.06218i | 0.0292480 | + | 0.109155i | 0.979007 | − | 0.203828i | \(-0.0653384\pi\) |
−0.949759 | + | 0.312983i | \(0.898672\pi\) | |||||||
\(788\) | −7.07180 | + | 7.07180i | −0.251922 | + | 0.251922i | ||||
\(789\) | −14.8923 | + | 8.59808i | −0.530180 | + | 0.306100i | ||||
\(790\) | − | 4.73205i | − | 0.168359i | ||||||
\(791\) | 55.6410i | 1.97837i | ||||||||
\(792\) | 8.19615 | + | 14.1962i | 0.291238 | + | 0.504438i | ||||
\(793\) | 5.10512i | 0.181288i | ||||||||
\(794\) | −34.1051 | −1.21035 | ||||||||
\(795\) | −23.4904 | − | 13.5622i | −0.833118 | − | 0.481001i | ||||
\(796\) | −43.7128 | −1.54936 | ||||||||
\(797\) | 11.0622 | + | 41.2846i | 0.391842 | + | 1.46238i | 0.827092 | + | 0.562066i | \(0.189993\pi\) |
−0.435250 | + | 0.900310i | \(0.643340\pi\) | |||||||
\(798\) | 40.1769 | − | 23.1962i | 1.42225 | − | 0.821135i | ||||
\(799\) | −2.39230 | − | 4.14359i | −0.0846337 | − | 0.146590i | ||||
\(800\) | −6.92820 | − | 1.85641i | −0.244949 | − | 0.0656339i | ||||
\(801\) | − | 47.5692i | − | 1.68078i | ||||||
\(802\) | 44.1506 | − | 11.8301i | 1.55901 | − | 0.417736i | ||||
\(803\) | 13.9282 | + | 3.73205i | 0.491516 | + | 0.131701i | ||||
\(804\) | 28.8564 | − | 7.73205i | 1.01769 | − | 0.272688i | ||||
\(805\) | 53.8468 | − | 14.4282i | 1.89785 | − | 0.508527i | ||||
\(806\) | −15.0263 | − | 26.0263i | −0.529278 | − | 0.916737i | ||||
\(807\) | 7.39230 | − | 7.39230i | 0.260221 | − | 0.260221i | ||||
\(808\) | 0.732051 | + | 1.26795i | 0.0257535 | + | 0.0446063i | ||||
\(809\) | 36.6410i | 1.28823i | 0.764929 | + | 0.644115i | \(0.222774\pi\) | ||||
−0.764929 | + | 0.644115i | \(0.777226\pi\) | |||||||
\(810\) | 21.2942 | + | 12.2942i | 0.748203 | + | 0.431975i | ||||
\(811\) | −18.4641 | − | 18.4641i | −0.648362 | − | 0.648362i | 0.304235 | − | 0.952597i | \(-0.401599\pi\) |
−0.952597 | + | 0.304235i | \(0.901599\pi\) | |||||||
\(812\) | −2.07180 | − | 7.73205i | −0.0727058 | − | 0.271342i | ||||
\(813\) | −1.85641 | −0.0651070 | ||||||||
\(814\) | −15.9282 | − | 4.26795i | −0.558283 | − | 0.149592i | ||||
\(815\) | 2.63397 | − | 4.56218i | 0.0922641 | − | 0.159806i | ||||
\(816\) | −27.7128 | −0.970143 | ||||||||
\(817\) | −13.9019 | − | 24.0788i | −0.486367 | − | 0.842412i | ||||
\(818\) | 8.29423 | + | 30.9545i | 0.290001 | + | 1.08230i | ||||
\(819\) | −21.8827 | − | 21.8827i | −0.764643 | − | 0.764643i | ||||
\(820\) | 0.803848 | − | 3.00000i | 0.0280716 | − | 0.104765i | ||||
\(821\) | 10.7224 | − | 40.0167i | 0.374215 | − | 1.39659i | −0.480272 | − | 0.877119i | \(-0.659462\pi\) |
0.854488 | − | 0.519472i | \(-0.173871\pi\) | |||||||
\(822\) | 1.56218 | + | 0.418584i | 0.0544872 | + | 0.0145998i | ||||
\(823\) | 36.6506 | + | 21.1603i | 1.27756 | + | 0.737600i | 0.976399 | − | 0.215973i | \(-0.0692923\pi\) |
0.301162 | + | 0.953573i | \(0.402626\pi\) | |||||||
\(824\) | 43.5167 | − | 11.6603i | 1.51597 | − | 0.406204i | ||||
\(825\) | −1.09808 | − | 4.09808i | −0.0382301 | − | 0.142677i | ||||
\(826\) | 9.80385 | 0.341119 | ||||||||
\(827\) | −31.3923 | − | 31.3923i | −1.09162 | − | 1.09162i | −0.995356 | − | 0.0962613i | \(-0.969312\pi\) |
−0.0962613 | − | 0.995356i | \(-0.530688\pi\) | |||||||
\(828\) | 19.3923 | − | 33.5885i | 0.673929 | − | 1.16728i | ||||
\(829\) | −14.2679 | + | 14.2679i | −0.495546 | + | 0.495546i | −0.910048 | − | 0.414502i | \(-0.863956\pi\) |
0.414502 | + | 0.910048i | \(0.363956\pi\) | |||||||
\(830\) | −28.3205 | − | 28.3205i | −0.983019 | − | 0.983019i | ||||
\(831\) | −3.10770 | + | 11.5981i | −0.107805 | + | 0.402333i | ||||
\(832\) | −17.8564 | + | 4.78461i | −0.619060 | + | 0.165876i | ||||
\(833\) | 25.8564 | − | 44.7846i | 0.895871 | − | 1.55169i | ||||
\(834\) | −35.4904 | − | 20.4904i | −1.22893 | − | 0.709524i | ||||
\(835\) | 30.7224 | + | 8.23205i | 1.06319 | + | 0.284882i | ||||
\(836\) | 14.1962 | − | 8.19615i | 0.490984 | − | 0.283470i | ||||
\(837\) | −23.8923 | + | 41.3827i | −0.825839 | + | 1.43039i | ||||
\(838\) | −13.5622 | + | 23.4904i | −0.468498 | + | 0.811462i | ||||
\(839\) | 6.74167 | − | 3.89230i | 0.232748 | − | 0.134377i | −0.379091 | − | 0.925359i | \(-0.623763\pi\) |
0.611839 | + | 0.790982i | \(0.290430\pi\) | |||||||
\(840\) | 42.2487i | 1.45772i | ||||||||
\(841\) | −24.4186 | − | 14.0981i | −0.842020 | − | 0.486141i | ||||
\(842\) | 22.6865 | − | 13.0981i | 0.781830 | − | 0.451390i | ||||
\(843\) | −17.3827 | + | 10.0359i | −0.598692 | + | 0.345655i | ||||
\(844\) | 37.0526 | − | 9.92820i | 1.27540 | − | 0.341743i | ||||
\(845\) | −10.4641 | + | 10.4641i | −0.359976 | + | 0.359976i | ||||
\(846\) | −1.31347 | + | 4.90192i | −0.0451579 | + | 0.168532i | ||||
\(847\) | 32.4449 | 1.11482 | ||||||||
\(848\) | −22.9282 | − | 22.9282i | −0.787358 | − | 0.787358i | ||||
\(849\) | −22.7942 | + | 6.10770i | −0.782296 | + | 0.209616i | ||||
\(850\) | 6.92820 | + | 1.85641i | 0.237635 | + | 0.0636742i | ||||
\(851\) | 10.0981 | + | 37.6865i | 0.346158 | + | 1.29188i | ||||
\(852\) | −10.1436 | −0.347514 | ||||||||
\(853\) | −2.06218 | + | 7.69615i | −0.0706076 | + | 0.263511i | −0.992201 | − | 0.124644i | \(-0.960221\pi\) |
0.921594 | + | 0.388156i | \(0.126888\pi\) | |||||||
\(854\) | 12.0788 | + | 6.97372i | 0.413329 | + | 0.238636i | ||||
\(855\) | 12.2942 | − | 21.2942i | 0.420454 | − | 0.728247i | ||||
\(856\) | 37.5692 | 1.28409 | ||||||||
\(857\) | 14.6436 | − | 8.45448i | 0.500216 | − | 0.288800i | −0.228587 | − | 0.973523i | \(-0.573411\pi\) |
0.728803 | + | 0.684724i | \(0.240077\pi\) | |||||||
\(858\) | −7.73205 | − | 7.73205i | −0.263968 | − | 0.263968i | ||||
\(859\) | −4.50000 | + | 1.20577i | −0.153538 | + | 0.0411404i | −0.334769 | − | 0.942300i | \(-0.608658\pi\) |
0.181231 | + | 0.983440i | \(0.441992\pi\) | |||||||
\(860\) | 25.3205 | 0.863422 | ||||||||
\(861\) | 6.21539 | 0.211820 | ||||||||
\(862\) | 3.32051 | + | 3.32051i | 0.113097 | + | 0.113097i | ||||
\(863\) | −26.5359 | −0.903292 | −0.451646 | − | 0.892197i | \(-0.649163\pi\) | ||||
−0.451646 | + | 0.892197i | \(0.649163\pi\) | |||||||
\(864\) | 20.7846 | + | 20.7846i | 0.707107 | + | 0.707107i | ||||
\(865\) | −15.1962 | −0.516685 | ||||||||
\(866\) | −3.60770 | − | 3.60770i | −0.122594 | − | 0.122594i | ||||
\(867\) | −1.73205 | −0.0588235 | ||||||||
\(868\) | −82.1051 | −2.78683 | ||||||||
\(869\) | 3.23205 | − | 0.866025i | 0.109640 | − | 0.0293779i | ||||
\(870\) | −3.00000 | − | 3.00000i | −0.101710 | − | 0.101710i | ||||
\(871\) | −17.2583 | + | 9.96410i | −0.584776 | + | 0.337621i | ||||
\(872\) | 6.92820i | 0.234619i | ||||||||
\(873\) | −1.50000 | − | 2.59808i | −0.0507673 | − | 0.0879316i | ||||
\(874\) | −33.5885 | − | 19.3923i | −1.13615 | − | 0.655954i | ||||
\(875\) | 13.9904 | − | 52.2128i | 0.472961 | − | 1.76512i | ||||
\(876\) | 25.8564 | 0.873607 | ||||||||
\(877\) | −13.3827 | − | 49.9449i | −0.451901 | − | 1.68652i | −0.697042 | − | 0.717031i | \(-0.745501\pi\) |
0.245140 | − | 0.969488i | \(-0.421166\pi\) | |||||||
\(878\) | −9.36603 | − | 2.50962i | −0.316088 | − | 0.0846955i | ||||
\(879\) | 3.69615 | − | 0.990381i | 0.124668 | − | 0.0334047i | ||||
\(880\) | 14.9282i | 0.503230i | ||||||||
\(881\) | 31.3205 | 1.05521 | 0.527607 | − | 0.849488i | \(-0.323089\pi\) | ||||
0.527607 | + | 0.849488i | \(0.323089\pi\) | |||||||
\(882\) | −52.9808 | + | 14.1962i | −1.78396 | + | 0.478009i | ||||
\(883\) | −3.00000 | + | 3.00000i | −0.100958 | + | 0.100958i | −0.755782 | − | 0.654824i | \(-0.772743\pi\) |
0.654824 | + | 0.755782i | \(0.272743\pi\) | |||||||
\(884\) | 17.8564 | − | 4.78461i | 0.600576 | − | 0.160924i | ||||
\(885\) | 4.50000 | − | 2.59808i | 0.151266 | − | 0.0873334i | ||||
\(886\) | 5.49038 | − | 3.16987i | 0.184453 | − | 0.106494i | ||||
\(887\) | 8.93782 | + | 5.16025i | 0.300103 | + | 0.173264i | 0.642489 | − | 0.766295i | \(-0.277902\pi\) |
−0.342386 | + | 0.939559i | \(0.611235\pi\) | |||||||
\(888\) | −29.5692 | −0.992278 | ||||||||
\(889\) | 1.51666 | − | 0.875644i | 0.0508672 | − | 0.0293682i | ||||
\(890\) | 21.6603 | − | 37.5167i | 0.726053 | − | 1.25756i | ||||
\(891\) | −4.50000 | + | 16.7942i | −0.150756 | + | 0.562628i | ||||
\(892\) | −27.0000 | + | 15.5885i | −0.904027 | + | 0.521940i | ||||
\(893\) | 4.90192 | + | 1.31347i | 0.164037 | + | 0.0439535i | ||||
\(894\) | −35.2750 | − | 20.3660i | −1.17977 | − | 0.681142i | ||||
\(895\) | 8.09808 | − | 14.0263i | 0.270689 | − | 0.468847i | ||||
\(896\) | −13.0718 | + | 48.7846i | −0.436698 | + | 1.62978i | ||||
\(897\) | −6.69615 | + | 24.9904i | −0.223578 | + | 0.834405i | ||||
\(898\) | −35.3205 | − | 35.3205i | −1.17866 | − | 1.17866i | ||||
\(899\) | 5.83013 | − | 5.83013i | 0.194446 | − | 0.194446i | ||||
\(900\) | −3.80385 | − | 6.58846i | −0.126795 | − | 0.219615i | ||||
\(901\) | 22.9282 | + | 22.9282i | 0.763849 | + | 0.763849i | ||||
\(902\) | 2.19615 | 0.0731239 | ||||||||
\(903\) | 13.1147 | + | 48.9449i | 0.436431 | + | 1.62878i | ||||
\(904\) | 9.12436 | + | 34.0526i | 0.303472 | + | 1.13257i | ||||
\(905\) | 18.2942 | + | 10.5622i | 0.608121 | + | 0.351099i | ||||
\(906\) | 16.5622 | + | 4.43782i | 0.550242 | + | 0.147437i | ||||
\(907\) | −2.42820 | + | 9.06218i | −0.0806272 | + | 0.300905i | −0.994450 | − | 0.105208i | \(-0.966449\pi\) |
0.913823 | + | 0.406112i | \(0.133116\pi\) | |||||||
\(908\) | −10.5167 | + | 39.2487i | −0.349008 | + | 1.30251i | ||||
\(909\) | −0.401924 | + | 1.50000i | −0.0133310 | + | 0.0497519i | ||||
\(910\) | −7.29423 | − | 27.2224i | −0.241801 | − | 0.902415i | ||||
\(911\) | −4.13397 | − | 7.16025i | −0.136965 | − | 0.237230i | 0.789382 | − | 0.613903i | \(-0.210401\pi\) |
−0.926346 | + | 0.376673i | \(0.877068\pi\) | |||||||
\(912\) | 20.7846 | − | 20.7846i | 0.688247 | − | 0.688247i | ||||
\(913\) | 14.1603 | − | 24.5263i | 0.468636 | − | 0.811701i | ||||
\(914\) | −40.9545 | − | 10.9737i | −1.35465 | − | 0.362978i | ||||
\(915\) | 7.39230 | 0.244382 | ||||||||
\(916\) | 8.85641 | + | 33.0526i | 0.292624 | + | 1.09209i | ||||
\(917\) | 15.9019 | + | 15.9019i | 0.525128 | + | 0.525128i | ||||
\(918\) | −20.7846 | − | 20.7846i | −0.685994 | − | 0.685994i | ||||
\(919\) | 36.5359i | 1.20521i | 0.798040 | + | 0.602604i | \(0.205870\pi\) | ||||
−0.798040 | + | 0.602604i | \(0.794130\pi\) | |||||||
\(920\) | 30.5885 | − | 17.6603i | 1.00847 | − | 0.582241i | ||||
\(921\) | 13.7321 | − | 13.7321i | 0.452486 | − | 0.452486i | ||||
\(922\) | −3.36603 | − | 5.83013i | −0.110854 | − | 0.192005i | ||||
\(923\) | 6.53590 | − | 1.75129i | 0.215132 | − | 0.0576444i | ||||
\(924\) | −28.8564 | + | 7.73205i | −0.949306 | + | 0.254366i | ||||
\(925\) | 7.39230 | + | 1.98076i | 0.243057 | + | 0.0651271i | ||||
\(926\) | 14.5622 | − | 3.90192i | 0.478543 | − | 0.128225i | ||||
\(927\) | 41.3827 | + | 23.8923i | 1.35919 | + | 0.784726i | ||||
\(928\) | −2.53590 | − | 4.39230i | −0.0832449 | − | 0.144184i | ||||
\(929\) | 9.35641 | + | 16.2058i | 0.306974 | + | 0.531694i | 0.977699 | − | 0.210012i | \(-0.0673503\pi\) |
−0.670725 | + | 0.741706i | \(0.734017\pi\) | |||||||
\(930\) | −37.6865 | + | 21.7583i | −1.23579 | + | 0.713484i | ||||
\(931\) | 14.1962 | + | 52.9808i | 0.465260 | + | 1.73637i | ||||
\(932\) | 18.1436 | 0.594313 | ||||||||
\(933\) | 15.9115 | + | 9.18653i | 0.520921 | + | 0.300754i | ||||
\(934\) | −43.5692 | −1.42563 | ||||||||
\(935\) | − | 14.9282i | − | 0.488204i | ||||||
\(936\) | −16.9808 | − | 9.80385i | −0.555034 | − | 0.320449i | ||||
\(937\) | − | 19.0718i | − | 0.623048i | −0.950238 | − | 0.311524i | \(-0.899160\pi\) | ||
0.950238 | − | 0.311524i | \(-0.100840\pi\) | |||||||
\(938\) | 54.4449i | 1.77769i | ||||||||
\(939\) | 43.5788 | − | 25.1603i | 1.42214 | − | 0.821074i | ||||
\(940\) | −3.26795 | + | 3.26795i | −0.106589 | + | 0.106589i | ||||
\(941\) | 9.13397 | + | 34.0885i | 0.297759 | + | 1.11125i | 0.939001 | + | 0.343913i | \(0.111753\pi\) |
−0.641242 | + | 0.767338i | \(0.721581\pi\) | |||||||
\(942\) | −4.09808 | + | 7.09808i | −0.133523 | + | 0.231268i | ||||
\(943\) | −2.59808 | − | 4.50000i | −0.0846050 | − | 0.146540i | ||||
\(944\) | 6.00000 | − | 1.60770i | 0.195283 | − | 0.0523260i | ||||
\(945\) | −31.6865 | + | 31.6865i | −1.03076 | + | 1.03076i | ||||
\(946\) | 4.63397 | + | 17.2942i | 0.150664 | + | 0.562284i | ||||
\(947\) | −41.0167 | − | 10.9904i | −1.33286 | − | 0.357139i | −0.479081 | − | 0.877771i | \(-0.659030\pi\) |
−0.853782 | + | 0.520631i | \(0.825697\pi\) | |||||||
\(948\) | 5.19615 | − | 3.00000i | 0.168763 | − | 0.0974355i | ||||
\(949\) | −16.6603 | + | 4.46410i | −0.540815 | + | 0.144911i | ||||
\(950\) | −6.58846 | + | 3.80385i | −0.213758 | + | 0.123413i | ||||
\(951\) | −57.9449 | − | 15.5263i | −1.87899 | − | 0.503474i | ||||
\(952\) | 13.0718 | − | 48.7846i | 0.423659 | − | 1.58112i | ||||
\(953\) | 32.5359i | 1.05394i | 0.849884 | + | 0.526971i | \(0.176672\pi\) | ||||
−0.849884 | + | 0.526971i | \(0.823328\pi\) | |||||||
\(954\) | − | 34.3923i | − | 1.11349i | ||||||
\(955\) | −3.83013 | − | 3.83013i | −0.123940 | − | 0.123940i | ||||
\(956\) | −1.39230 | − | 0.803848i | −0.0450304 | − | 0.0259983i | ||||
\(957\) | 1.50000 | − | 2.59808i | 0.0484881 | − | 0.0839839i | ||||
\(958\) | 6.83013 | − | 25.4904i | 0.220671 | − | 0.823557i | ||||
\(959\) | −1.47372 | + | 2.55256i | −0.0475889 | + | 0.0824264i | ||||
\(960\) | 6.92820 | + | 25.8564i | 0.223607 | + | 0.834512i | ||||
\(961\) | −26.7846 | − | 46.3923i | −0.864020 | − | 1.49653i | ||||
\(962\) | 19.0526 | − | 5.10512i | 0.614279 | − | 0.164596i | ||||
\(963\) | 28.1769 | + | 28.1769i | 0.907988 | + | 0.907988i | ||||
\(964\) | 9.58846 | − | 5.53590i | 0.308823 | − | 0.178299i | ||||
\(965\) | −2.23205 | + | 8.33013i | −0.0718523 | + | 0.268156i | ||||
\(966\) | 49.9808 | + | 49.9808i | 1.60810 | + | 1.60810i | ||||
\(967\) | −27.0622 | − | 15.6244i | −0.870261 | − | 0.502445i | −0.00282602 | − | 0.999996i | \(-0.500900\pi\) |
−0.867435 | + | 0.497551i | \(0.834233\pi\) | |||||||
\(968\) | 19.8564 | − | 5.32051i | 0.638209 | − | 0.171008i | ||||
\(969\) | −20.7846 | + | 20.7846i | −0.667698 | + | 0.667698i | ||||
\(970\) | − | 2.73205i | − | 0.0877209i | ||||||
\(971\) | −23.9808 | − | 23.9808i | −0.769579 | − | 0.769579i | 0.208453 | − | 0.978032i | \(-0.433157\pi\) |
−0.978032 | + | 0.208453i | \(0.933157\pi\) | |||||||
\(972\) | 31.1769i | 1.00000i | ||||||||
\(973\) | 52.8109 | − | 52.8109i | 1.69304 | − | 1.69304i | ||||
\(974\) | 6.78461 | − | 6.78461i | 0.217393 | − | 0.217393i | ||||
\(975\) | 3.58846 | + | 3.58846i | 0.114923 | + | 0.114923i | ||||
\(976\) | 8.53590 | + | 2.28719i | 0.273227 | + | 0.0732111i | ||||
\(977\) | −24.2846 | + | 42.0622i | −0.776933 | + | 1.34569i | 0.156768 | + | 0.987635i | \(0.449893\pi\) |
−0.933701 | + | 0.358053i | \(0.883441\pi\) | |||||||
\(978\) | 6.67949 | 0.213587 | ||||||||
\(979\) | 29.5885 | + | 7.92820i | 0.945651 | + | 0.253386i | ||||
\(980\) | −48.2487 | − | 12.9282i | −1.54125 | − | 0.412976i | ||||
\(981\) | −5.19615 | + | 5.19615i | −0.165900 | + | 0.165900i | ||||
\(982\) | −0.633975 | − | 0.366025i | −0.0202309 | − | 0.0116803i | ||||
\(983\) | −1.08142 | + | 0.624356i | −0.0344918 | + | 0.0199139i | −0.517147 | − | 0.855897i | \(-0.673006\pi\) |
0.482655 | + | 0.875811i | \(0.339673\pi\) | |||||||
\(984\) | 3.80385 | − | 1.01924i | 0.121262 | − | 0.0324921i | ||||
\(985\) | −8.36603 | − | 4.83013i | −0.266564 | − | 0.153901i | ||||
\(986\) | 2.53590 | + | 4.39230i | 0.0807595 | + | 0.139879i | ||||
\(987\) | −8.00962 | − | 4.62436i | −0.254949 | − | 0.147195i | ||||
\(988\) | −9.80385 | + | 16.9808i | −0.311902 | + | 0.540230i | ||||
\(989\) | 29.9545 | − | 29.9545i | 0.952497 | − | 0.952497i | ||||
\(990\) | −11.1962 | + | 11.1962i | −0.355837 | + | 0.355837i | ||||
\(991\) | −44.3923 | −1.41017 | −0.705084 | − | 0.709124i | \(-0.749091\pi\) | ||||
−0.705084 | + | 0.709124i | \(0.749091\pi\) | |||||||
\(992\) | −50.2487 | + | 13.4641i | −1.59540 | + | 0.427486i | ||||
\(993\) | 2.34936 | − | 8.76795i | 0.0745548 | − | 0.278242i | ||||
\(994\) | 4.78461 | − | 17.8564i | 0.151759 | − | 0.566371i | ||||
\(995\) | −10.9282 | − | 40.7846i | −0.346447 | − | 1.29296i | ||||
\(996\) | 13.1436 | − | 49.0526i | 0.416471 | − | 1.55429i | ||||
\(997\) | −1.06218 | + | 3.96410i | −0.0336395 | + | 0.125544i | −0.980704 | − | 0.195500i | \(-0.937367\pi\) |
0.947064 | + | 0.321044i | \(0.104034\pi\) | |||||||
\(998\) | −6.83013 | + | 11.8301i | −0.216204 | + | 0.374476i | ||||
\(999\) | −22.1769 | − | 22.1769i | −0.701647 | − | 0.701647i |
(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 | 144.2.x.a.85.1 | yes | 4 | |
3.2 | odd | 2 | 432.2.y.d.37.1 | 4 | |||
4.3 | odd | 2 | 576.2.bb.a.49.1 | 4 | |||
9.2 | odd | 6 | 432.2.y.a.181.1 | 4 | |||
9.7 | even | 3 | 144.2.x.d.133.1 | yes | 4 | ||
12.11 | even | 2 | 1728.2.bc.c.1009.1 | 4 | |||
16.3 | odd | 4 | 576.2.bb.b.337.1 | 4 | |||
16.13 | even | 4 | 144.2.x.d.13.1 | yes | 4 | ||
36.7 | odd | 6 | 576.2.bb.b.241.1 | 4 | |||
36.11 | even | 6 | 1728.2.bc.b.1585.1 | 4 | |||
48.29 | odd | 4 | 432.2.y.a.253.1 | 4 | |||
48.35 | even | 4 | 1728.2.bc.b.145.1 | 4 | |||
144.29 | odd | 12 | 432.2.y.d.397.1 | 4 | |||
144.61 | even | 12 | inner | 144.2.x.a.61.1 | ✓ | 4 | |
144.83 | even | 12 | 1728.2.bc.c.721.1 | 4 | |||
144.115 | odd | 12 | 576.2.bb.a.529.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.a.61.1 | ✓ | 4 | 144.61 | even | 12 | inner | |
144.2.x.a.85.1 | yes | 4 | 1.1 | even | 1 | trivial | |
144.2.x.d.13.1 | yes | 4 | 16.13 | even | 4 | ||
144.2.x.d.133.1 | yes | 4 | 9.7 | even | 3 | ||
432.2.y.a.181.1 | 4 | 9.2 | odd | 6 | |||
432.2.y.a.253.1 | 4 | 48.29 | odd | 4 | |||
432.2.y.d.37.1 | 4 | 3.2 | odd | 2 | |||
432.2.y.d.397.1 | 4 | 144.29 | odd | 12 | |||
576.2.bb.a.49.1 | 4 | 4.3 | odd | 2 | |||
576.2.bb.a.529.1 | 4 | 144.115 | odd | 12 | |||
576.2.bb.b.241.1 | 4 | 36.7 | odd | 6 | |||
576.2.bb.b.337.1 | 4 | 16.3 | odd | 4 | |||
1728.2.bc.b.145.1 | 4 | 48.35 | even | 4 | |||
1728.2.bc.b.1585.1 | 4 | 36.11 | even | 6 | |||
1728.2.bc.c.721.1 | 4 | 144.83 | even | 12 | |||
1728.2.bc.c.1009.1 | 4 | 12.11 | even | 2 |