Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [312,2,Mod(41,312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(312, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 6, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("312.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 312 = 2^{3} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 312.bp (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: | \(2.49133254306\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 305.3 | ||
Character | \(\chi\) | \(=\) | 312.305 |
Dual form | 312.2.bp.a.89.3 |
$q$-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 \(\left(\mathbb{Z}/312\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(157\) | \(209\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.43567 | + | 0.968940i | −0.828886 | + | 0.559418i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.19967 | + | 2.19967i | 0.983725 | + | 0.983725i | 0.999870 | − | 0.0161451i | \(-0.00513938\pi\) |
−0.0161451 | + | 0.999870i | \(0.505139\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.17763 | − | 4.39498i | 0.445103 | − | 1.66115i | −0.270562 | − | 0.962703i | \(-0.587209\pi\) |
0.715665 | − | 0.698444i | \(-0.246124\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.12231 | − | 2.78216i | 0.374104 | − | 0.927387i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.917595 | + | 3.42451i | 0.276665 | + | 1.03253i | 0.954717 | + | 0.297515i | \(0.0961577\pi\) |
−0.678052 | + | 0.735014i | \(0.737176\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.225112 | + | 3.59852i | 0.0624348 | + | 0.998049i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.28937 | − | 1.02666i | −1.36571 | − | 0.265082i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.20507 | + | 3.81929i | 0.534808 | + | 0.926315i | 0.999173 | + | 0.0406707i | \(0.0129495\pi\) |
−0.464364 | + | 0.885644i | \(0.653717\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.06243 | + | 0.284677i | 0.243738 | + | 0.0653094i | 0.378620 | − | 0.925552i | \(-0.376399\pi\) |
−0.134882 | + | 0.990862i | \(0.543065\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.56778 | + | 7.45081i | 0.560335 | + | 1.62590i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.812870 | + | 1.40793i | −0.169495 | + | 0.293574i | −0.938242 | − | 0.345978i | \(-0.887547\pi\) |
0.768747 | + | 0.639553i | \(0.220880\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.67714i | 0.935428i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.08448 | + | 5.08172i | 0.208707 | + | 0.977978i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.61533 | − | 2.66466i | −0.857045 | − | 0.494815i | 0.00597654 | − | 0.999982i | \(-0.498098\pi\) |
−0.863022 | + | 0.505167i | \(0.831431\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.28177 | − | 3.28177i | 0.589423 | − | 0.589423i | −0.348052 | − | 0.937475i | \(-0.613157\pi\) |
0.937475 | + | 0.348052i | \(0.113157\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.63551 | − | 4.02738i | −0.806939 | − | 0.701077i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.2579 | − | 7.07712i | 2.07197 | − | 1.19625i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.75348 | − | 0.737792i | 0.452669 | − | 0.121292i | −0.0252790 | − | 0.999680i | \(-0.508047\pi\) |
0.477948 | + | 0.878388i | \(0.341381\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.80993 | − | 4.94817i | −0.610078 | − | 0.792342i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.76774 | − | 2.61726i | 1.52546 | − | 0.408747i | 0.603928 | − | 0.797039i | \(-0.293602\pi\) |
0.921536 | + | 0.388292i | \(0.126935\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.07183 | + | 3.50557i | −0.925946 | + | 0.534595i | −0.885527 | − | 0.464588i | \(-0.846203\pi\) |
−0.0404187 | + | 0.999183i | \(0.512869\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.58857 | − | 3.65113i | 1.28031 | − | 0.544278i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.14895 | + | 4.14895i | −0.605186 | + | 0.605186i | −0.941684 | − | 0.336498i | \(-0.890757\pi\) |
0.336498 | + | 0.941684i | \(0.390757\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11.8669 | − | 6.85134i | −1.69527 | − | 0.978762i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.86643 | − | 3.34667i | −0.961492 | − | 0.468628i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8.33491i | − | 1.14489i | −0.819944 | − | 0.572444i | \(-0.805995\pi\) | ||
0.819944 | − | 0.572444i | \(-0.194005\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.51440 | + | 9.55122i | −0.743561 | + | 1.28789i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.80113 | + | 0.620727i | −0.238566 | + | 0.0822173i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.97653 | − | 0.529610i | −0.257322 | − | 0.0689493i | 0.127852 | − | 0.991793i | \(-0.459192\pi\) |
−0.385174 | + | 0.922844i | \(0.625859\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.77501 | − | 8.27056i | −0.611378 | − | 1.05894i | −0.991008 | − | 0.133799i | \(-0.957282\pi\) |
0.379631 | − | 0.925138i | \(-0.376051\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.9059 | − | 8.20890i | −1.37401 | − | 1.03422i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.42039 | + | 8.41074i | −0.920387 | + | 1.04322i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.42966 | − | 5.33556i | −0.174661 | − | 0.651842i | −0.996609 | − | 0.0822804i | \(-0.973780\pi\) |
0.821949 | − | 0.569562i | \(-0.192887\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.197186 | − | 2.80895i | −0.0237385 | − | 0.338158i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.43147 | + | 5.34234i | −0.169885 | + | 0.634019i | 0.827482 | + | 0.561493i | \(0.189773\pi\) |
−0.997367 | + | 0.0725259i | \(0.976894\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.99445 | + | 2.99445i | 0.350473 | + | 0.350473i | 0.860286 | − | 0.509812i | \(-0.170285\pi\) |
−0.509812 | + | 0.860286i | \(0.670285\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.53187 | − | 6.71484i | −0.523295 | − | 0.775363i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.1312 | 1.83833 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.4490 | 1.73815 | 0.869077 | − | 0.494677i | \(-0.164714\pi\) | ||||
0.869077 | + | 0.494677i | \(0.164714\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.48084 | − | 6.24490i | −0.720093 | − | 0.693878i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.38106 | − | 6.38106i | −0.700413 | − | 0.700413i | 0.264086 | − | 0.964499i | \(-0.414930\pi\) |
−0.964499 | + | 0.264086i | \(0.914930\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.55077 | + | 13.2516i | −0.385135 | + | 1.43734i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.20800 | − | 0.646395i | 0.987201 | − | 0.0693008i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.98271 | − | 7.39957i | −0.210167 | − | 0.784353i | −0.987812 | − | 0.155650i | \(-0.950253\pi\) |
0.777646 | − | 0.628703i | \(-0.216414\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.0805 | + | 3.24837i | 1.68570 | + | 0.340521i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.53171 | + | 7.89138i | −0.158831 | + | 0.818298i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.71080 | + | 2.96319i | 0.175525 | + | 0.304017i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.75030 | − | 2.34464i | −0.888458 | − | 0.238062i | −0.214405 | − | 0.976745i | \(-0.568781\pi\) |
−0.674053 | + | 0.738683i | \(0.735448\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.5574 | + | 1.29047i | 1.06106 | + | 0.129697i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.52149 | − | 6.09939i | 0.350401 | − | 0.606912i | −0.635919 | − | 0.771756i | \(-0.719379\pi\) |
0.986320 | + | 0.164844i | \(0.0527120\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 7.10076i | − | 0.699658i | −0.936813 | − | 0.349829i | \(-0.886240\pi\) | ||
0.936813 | − | 0.349829i | \(-0.113760\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.7411 | + | 22.0376i | −1.04822 | + | 2.15065i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.7690 | − | 6.21749i | −1.04108 | − | 0.601068i | −0.120941 | − | 0.992660i | \(-0.538591\pi\) |
−0.920139 | + | 0.391592i | \(0.871924\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.09377 | − | 5.09377i | 0.487895 | − | 0.487895i | −0.419746 | − | 0.907641i | \(-0.637881\pi\) |
0.907641 | + | 0.419746i | \(0.137881\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.23822 | + | 3.72718i | −0.307358 | + | 0.353769i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.4784 | + | 6.04969i | −0.985722 | + | 0.569107i | −0.903993 | − | 0.427548i | \(-0.859378\pi\) |
−0.0817293 | + | 0.996655i | \(0.526044\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.88504 | + | 1.30894i | −0.455533 | + | 0.122060i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.2643 | + | 3.41236i | 0.948935 | + | 0.315473i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.3825 | − | 5.19352i | 1.77679 | − | 0.476089i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.35901 | + | 0.784625i | −0.123546 | + | 0.0713296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.4873 | + | 13.2219i | −1.03578 | + | 1.19218i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.710189 | − | 0.710189i | 0.0635212 | − | 0.0635212i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6158 | + | 6.70637i | 1.03073 | + | 0.595094i | 0.917195 | − | 0.398440i | \(-0.130448\pi\) |
0.113539 | + | 0.993534i | \(0.463781\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.32047 | − | 10.9161i | 0.468441 | − | 0.961109i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7616i | 0.940244i | 0.882601 | + | 0.470122i | \(0.155790\pi\) | ||||
−0.882601 | + | 0.470122i | \(0.844210\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.50230 | − | 4.33411i | 0.216977 | − | 0.375815i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.79265 | + | 13.5636i | −0.756750 | + | 1.16737i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.9042 | − | 5.06536i | −1.61509 | − | 0.432763i | −0.665539 | − | 0.746363i | \(-0.731798\pi\) |
−0.949555 | + | 0.313600i | \(0.898465\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.42992 | + | 2.47669i | 0.121284 | + | 0.210070i | 0.920274 | − | 0.391274i | \(-0.127966\pi\) |
−0.798990 | + | 0.601344i | \(0.794632\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.93645 | − | 9.97661i | 0.163078 | − | 0.840182i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.1166 | + | 4.07288i | −1.01324 | + | 0.340591i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.29083 | − | 16.0136i | −0.356334 | − | 1.32986i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 23.6755 | − | 1.66200i | 1.95272 | − | 0.137080i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.07006 | + | 18.9217i | −0.415356 | + | 1.55013i | 0.368766 | + | 0.929522i | \(0.379780\pi\) |
−0.784122 | + | 0.620607i | \(0.786886\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.8267 | − | 15.8267i | −1.28796 | − | 1.28796i | −0.936023 | − | 0.351940i | \(-0.885522\pi\) |
−0.351940 | − | 0.936023i | \(-0.614478\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.1007 | − | 1.84842i | 1.05913 | − | 0.149436i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.4376 | 1.15966 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.15713 | 0.0923494 | 0.0461747 | − | 0.998933i | \(-0.485297\pi\) | ||||
0.0461747 | + | 0.998933i | \(0.485297\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.07603 | + | 11.9662i | 0.640471 | + | 0.948982i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.23057 | + | 5.23057i | 0.412227 | + | 0.412227i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.58002 | + | 13.3608i | −0.280409 | + | 1.04650i | 0.671720 | + | 0.740805i | \(0.265556\pi\) |
−0.952129 | + | 0.305696i | \(0.901111\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.33769 | − | 19.0555i | −0.104139 | − | 1.48347i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.53415 | − | 9.45758i | −0.196098 | − | 0.731849i | −0.991980 | − | 0.126397i | \(-0.959659\pi\) |
0.795881 | − | 0.605453i | \(-0.207008\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8986 | + | 1.62014i | −0.992204 | + | 0.124626i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.98439 | − | 2.63635i | 0.151750 | − | 0.201607i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.36780 | + | 4.10115i | 0.180020 | + | 0.311804i | 0.941887 | − | 0.335929i | \(-0.109050\pi\) |
−0.761867 | + | 0.647734i | \(0.775717\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20.5559 | + | 5.50795i | 1.55388 | + | 0.416362i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.35081 | − | 1.15479i | 0.251862 | − | 0.0867995i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.29215 | − | 7.43422i | 0.320810 | − | 0.555660i | −0.659845 | − | 0.751402i | \(-0.729378\pi\) |
0.980655 | + | 0.195742i | \(0.0627115\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.64164i | 0.493670i | 0.969058 | + | 0.246835i | \(0.0793905\pi\) | ||||
−0.969058 | + | 0.246835i | \(0.920610\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.8690 | + | 7.24712i | 1.09915 | + | 0.535723i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.67966 | + | 4.43385i | 0.564620 | + | 0.325983i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.0559 | + | 11.0559i | −0.808484 | + | 0.808484i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 23.6112 | + | 1.21815i | 1.71746 | + | 0.0886073i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.75249 | − | 3.89855i | 0.488593 | − | 0.282089i | −0.235398 | − | 0.971899i | \(-0.575639\pi\) |
0.723991 | + | 0.689810i | \(0.242306\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.57872 | + | 0.690967i | −0.185621 | + | 0.0497369i | −0.350432 | − | 0.936588i | \(-0.613965\pi\) |
0.164811 | + | 0.986325i | \(0.447299\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.50375 | − | 19.2650i | 0.179298 | − | 1.37959i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.6823 | + | 5.00590i | −1.33106 | + | 0.356655i | −0.853109 | − | 0.521733i | \(-0.825286\pi\) |
−0.477947 | + | 0.878388i | \(0.658619\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.95427 | − | 4.01505i | 0.492975 | − | 0.284619i | −0.232833 | − | 0.972517i | \(-0.574800\pi\) |
0.725808 | + | 0.687898i | \(0.241466\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.22235 | + | 6.27486i | 0.509426 | + | 0.442594i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.1463 | + | 17.1463i | −1.20343 | + | 1.20343i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 27.2430 | + | 15.7287i | 1.90273 | + | 1.09854i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.00480 | + | 3.84167i | 0.208848 | + | 0.267015i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.89952i | 0.269735i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.69364 | − | 4.66552i | 0.185438 | − | 0.321187i | −0.758286 | − | 0.651922i | \(-0.773963\pi\) |
0.943724 | + | 0.330734i | \(0.107296\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.12127 | − | 9.05686i | −0.213866 | − | 0.620566i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21.0672 | − | 5.64493i | −1.43677 | − | 0.384981i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.5586 | − | 18.2880i | −0.716764 | − | 1.24147i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.20048 | − | 1.39761i | −0.486564 | − | 0.0944415i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.2474 | + | 8.79475i | −0.891117 | + | 0.591599i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.18490 | + | 8.15417i | 0.146312 | + | 0.546044i | 0.999693 | + | 0.0247569i | \(0.00788119\pi\) |
−0.853381 | + | 0.521287i | \(0.825452\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.0126 | + | 5.24920i | 0.867504 | + | 0.349947i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.237467 | + | 0.886239i | −0.0157612 | + | 0.0588217i | −0.973359 | − | 0.229288i | \(-0.926360\pi\) |
0.957597 | + | 0.288110i | \(0.0930268\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.28432 | − | 2.28432i | −0.150952 | − | 0.150952i | 0.627591 | − | 0.778543i | \(-0.284041\pi\) |
−0.778543 | + | 0.627591i | \(0.784041\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −23.1592 | + | 15.6302i | −1.52376 | + | 1.02839i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.30420 | −0.609538 | −0.304769 | − | 0.952426i | \(-0.598579\pi\) | ||||
−0.304769 | + | 0.952426i | \(0.598579\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.2527 | −1.19067 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −22.1798 | + | 14.9692i | −1.44073 | + | 0.972354i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.5336 | + | 18.5336i | 1.19884 | + | 1.19884i | 0.974515 | + | 0.224323i | \(0.0720171\pi\) |
0.224323 | + | 0.974515i | \(0.427983\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.15760 | + | 11.7843i | −0.203399 | + | 0.759094i | 0.786533 | + | 0.617548i | \(0.211874\pi\) |
−0.989932 | + | 0.141546i | \(0.954793\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.3553 | + | 2.68609i | 0.985042 | + | 0.172313i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.0325 | − | 41.1740i | −0.704842 | − | 2.63051i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.785250 | + | 3.88725i | −0.0499642 | + | 0.247340i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.3440 | + | 2.97825i | 0.972386 | + | 0.188739i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.56257 | − | 7.90260i | −0.287987 | − | 0.498808i | 0.685342 | − | 0.728221i | \(-0.259653\pi\) |
−0.973329 | + | 0.229413i | \(0.926319\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.56736 | − | 1.49177i | −0.350017 | − | 0.0937868i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.74231 | − | 22.4655i | −0.484842 | − | 1.40684i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.0791658 | − | 0.137119i | 0.00493823 | − | 0.00855326i | −0.863546 | − | 0.504271i | \(-0.831761\pi\) |
0.868484 | + | 0.495717i | \(0.165095\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 12.9703i | − | 0.805937i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.5934 | + | 9.85001i | −0.779509 | + | 0.609700i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.05457 | + | 1.76356i | 0.188353 | + | 0.108746i | 0.591211 | − | 0.806517i | \(-0.298650\pi\) |
−0.402858 | + | 0.915262i | \(0.631983\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.3341 | − | 18.3341i | 1.12625 | − | 1.12625i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.0163 | + | 8.70223i | 0.612985 | + | 0.532568i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.2959 | − | 9.40842i | 0.993576 | − | 0.573641i | 0.0872346 | − | 0.996188i | \(-0.472197\pi\) |
0.906341 | + | 0.422546i | \(0.138864\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.95323 | − | 0.523366i | 0.118650 | − | 0.0317922i | −0.199005 | − | 0.979998i | \(-0.563771\pi\) |
0.317656 | + | 0.948206i | \(0.397104\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −26.2338 | + | 10.9175i | −1.58774 | + | 0.660755i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.0169 | + | 4.29172i | −0.965856 | + | 0.258800i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.1882 | − | 8.76890i | 0.912569 | − | 0.526872i | 0.0313123 | − | 0.999510i | \(-0.490031\pi\) |
0.881257 | + | 0.472638i | \(0.156698\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.44724 | − | 12.8136i | −0.326118 | − | 0.767128i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.8319 | − | 13.8319i | 0.825142 | − | 0.825142i | −0.161698 | − | 0.986840i | \(-0.551697\pi\) |
0.986840 | + | 0.161698i | \(0.0516972\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.2851 | − | 8.82488i | −0.908607 | − | 0.524585i | −0.0286245 | − | 0.999590i | \(-0.509113\pi\) |
−0.879983 | + | 0.475006i | \(0.842446\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.32731 | − | 2.59651i | −0.315562 | − | 0.153804i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 46.0112i | − | 2.71595i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.22467 | + | 2.12120i | −0.0720396 | + | 0.124776i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.8344 | − | 5.11239i | 0.869607 | − | 0.299693i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.2454 | − | 3.28114i | −0.715383 | − | 0.191686i | −0.117272 | − | 0.993100i | \(-0.537415\pi\) |
−0.598111 | + | 0.801414i | \(0.704082\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.18275 | − | 5.51269i | −0.185307 | − | 0.320961i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −16.4073 | + | 8.37676i | −0.952048 | + | 0.486069i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.24945 | − | 2.60818i | −0.303584 | − | 0.150835i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.25655 | + | 30.8139i | 0.475900 | + | 1.77608i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.854244 | + | 12.1688i | 0.0490751 | + | 0.699082i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.68908 | − | 28.6960i | 0.440275 | − | 1.64313i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.09233 | − | 6.09233i | −0.347707 | − | 0.347707i | 0.511548 | − | 0.859255i | \(-0.329072\pi\) |
−0.859255 | + | 0.511548i | \(0.829072\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.88021 | + | 10.1944i | 0.391401 | + | 0.579937i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.87859 | −0.560164 | −0.280082 | − | 0.959976i | \(-0.590362\pi\) | ||||
−0.280082 | + | 0.959976i | \(0.590362\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.2222 | 0.973456 | 0.486728 | − | 0.873554i | \(-0.338190\pi\) | ||||
0.486728 | + | 0.873554i | \(0.338190\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.93248 | − | 42.0463i | −0.334257 | − | 2.36904i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.00884596 | + | 0.00884596i | 0.000496839 | + | 0.000496839i | 0.707355 | − | 0.706858i | \(-0.249888\pi\) |
−0.706858 | + | 0.707355i | \(0.749888\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.89016 | − | 18.2503i | 0.273796 | − | 1.02182i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.4852 | − | 1.50824i | 1.19918 | − | 0.0841819i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.25547 | + | 4.68546i | 0.0698560 | + | 0.260706i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.8308 | + | 1.05288i | −0.933603 | + | 0.0584032i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.37743 | + | 12.2486i | −0.131472 | + | 0.677346i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.3486 | + | 23.1205i | 0.735933 | + | 1.27467i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.360355 | + | 0.0965567i | 0.0198069 | + | 0.00530724i | 0.268709 | − | 0.963221i | \(-0.413403\pi\) |
−0.248902 | + | 0.968529i | \(0.580070\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.03760 | − | 8.48865i | 0.0568602 | − | 0.465175i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.59171 | − | 14.8813i | 0.469415 | − | 0.813051i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.3015i | 1.21484i | 0.794381 | + | 0.607420i | \(0.207796\pi\) | ||||
−0.794381 | + | 0.607420i | \(0.792204\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.18172 | − | 18.8383i | 0.498683 | − | 1.02316i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.2498 | + | 8.22711i | 0.771669 | + | 0.445523i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −21.5648 | + | 21.5648i | −1.16439 | + | 1.16439i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.74503 | − | 6.61253i | 0.309302 | − | 0.356006i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.801179 | − | 0.462561i | 0.0430095 | − | 0.0248316i | −0.478341 | − | 0.878174i | \(-0.658762\pi\) |
0.521351 | + | 0.853343i | \(0.325428\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.4270 | + | 4.40159i | −0.879315 | + | 0.235612i | −0.670112 | − | 0.742260i | \(-0.733754\pi\) |
−0.209204 | + | 0.977872i | \(0.567087\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.0425 | + | 5.04646i | −0.963040 | + | 0.269360i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.31686 | − | 0.352851i | 0.0700893 | − | 0.0187804i | −0.223604 | − | 0.974680i | \(-0.571782\pi\) |
0.293693 | + | 0.955900i | \(0.405116\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.9002 | + | 8.60262i | −0.790819 | + | 0.456580i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −22.7947 | + | 26.2367i | −1.20642 | + | 1.38859i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.2669 | + | 23.2669i | −1.22798 | + | 1.22798i | −0.263256 | + | 0.964726i | \(0.584796\pi\) |
−0.964726 | + | 0.263256i | \(0.915204\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.4068 | − | 8.89510i | −0.810883 | − | 0.468163i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.19084 | − | 2.44326i | 0.0625029 | − | 0.128238i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.1736i | 0.689539i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.66640 | − | 15.0106i | 0.452382 | − | 0.783549i | −0.546151 | − | 0.837687i | \(-0.683908\pi\) |
0.998533 | + | 0.0541374i | \(0.0172409\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.68081 | − | 30.1128i | 0.191615 | − | 1.56761i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −36.6318 | − | 9.81545i | −1.90183 | − | 0.509593i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.40911 | + | 2.44066i | 0.0729611 | + | 0.126372i | 0.900198 | − | 0.435481i | \(-0.143422\pi\) |
−0.827237 | + | 0.561854i | \(0.810088\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.331468 | + | 1.70773i | −0.0171169 | + | 0.0881867i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.54986 | − | 17.2082i | 0.440340 | − | 0.886267i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.23342 | − | 26.9955i | −0.371556 | − | 1.38667i | −0.858312 | − | 0.513128i | \(-0.828487\pi\) |
0.486756 | − | 0.873538i | \(-0.338180\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −23.1745 | + | 1.62684i | −1.18727 | + | 0.0833453i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.58764 | − | 5.92516i | 0.0811248 | − | 0.302762i | −0.913427 | − | 0.407002i | \(-0.866574\pi\) |
0.994552 | + | 0.104240i | \(0.0332410\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 35.4835 | + | 35.4835i | 1.80841 | + | 1.80841i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.93859 | + | 20.8272i | 0.149377 | + | 1.05870i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 34.3070 | 1.73943 | 0.869717 | − | 0.493550i | \(-0.164301\pi\) | ||||
0.869717 | + | 0.493550i | \(0.164301\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.16974 | −0.362589 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.4273 | − | 15.4501i | −0.525989 | − | 0.779355i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 33.9829 | + | 33.9829i | 1.70986 | + | 1.70986i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.44015 | − | 9.10677i | 0.122468 | − | 0.457056i | −0.877269 | − | 0.479999i | \(-0.840637\pi\) |
0.999737 | + | 0.0229433i | \(0.00730371\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.607009 | + | 8.64694i | 0.0303885 | + | 0.432888i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.09363 | + | 26.4738i | 0.354239 | + | 1.32204i | 0.881440 | + | 0.472297i | \(0.156575\pi\) |
−0.527201 | + | 0.849741i | \(0.676758\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.5483 | + | 11.0707i | 0.625073 | + | 0.551472i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.518985 | − | 27.9925i | −0.0257886 | − | 1.39096i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.05315 | + | 8.75232i | 0.250476 | + | 0.433836i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.8641 | + | 3.71487i | 0.685535 | + | 0.183689i | 0.584743 | − | 0.811219i | \(-0.301195\pi\) |
0.100793 | + | 0.994907i | \(0.467862\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 32.0483 | − | 11.0448i | 1.58082 | − | 0.544801i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.65525 | + | 8.06313i | −0.229070 | + | 0.396761i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 28.0725i | − | 1.37803i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.45265 | − | 2.17021i | −0.218047 | − | 0.106276i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.2181 | + | 15.7144i | 1.32969 | + | 0.767697i | 0.985252 | − | 0.171112i | \(-0.0547361\pi\) |
0.344438 | + | 0.938809i | \(0.388069\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.8765 | − | 15.8765i | 0.773773 | − | 0.773773i | −0.204991 | − | 0.978764i | \(-0.565717\pi\) |
0.978764 | + | 0.204991i | \(0.0657165\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.88663 | + | 16.1994i | 0.334839 | + | 0.787644i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.8634 | + | 10.3134i | −0.866501 | + | 0.500274i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −41.9722 | + | 11.2464i | −2.03118 | + | 0.544252i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.4491 | − | 17.5876i | 0.649328 | − | 0.849136i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.3582 | + | 3.31137i | −0.595274 | + | 0.159503i | −0.543862 | − | 0.839174i | \(-0.683039\pi\) |
−0.0514116 | + | 0.998678i | \(0.516372\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.1339 | − | 8.16020i | 0.679231 | − | 0.392154i | −0.120335 | − | 0.992733i | \(-0.538397\pi\) |
0.799565 | + | 0.600579i | \(0.205063\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 21.6765 | + | 18.8327i | 1.03931 | + | 0.902961i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.26442 | + | 1.26442i | −0.0604855 | + | 0.0604855i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.2300 | − | 11.6798i | −0.965525 | − | 0.557446i | −0.0676563 | − | 0.997709i | \(-0.521552\pi\) |
−0.897869 | + | 0.440262i | \(0.854885\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −32.3798 | + | 25.3262i | −1.54190 | + | 1.20601i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.6001i | 0.931228i | 0.884988 | + | 0.465614i | \(0.154166\pi\) | ||||
−0.884988 | + | 0.465614i | \(0.845834\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.9153 | − | 20.6380i | 0.564841 | − | 0.978333i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.0551 | − | 32.0780i | −0.522887 | − | 1.51724i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.4364 | − | 3.06438i | −0.539717 | − | 0.144617i | −0.0213456 | − | 0.999772i | \(-0.506795\pi\) |
−0.518372 | + | 0.855155i | \(0.673462\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.9256 | + | 31.0481i | 0.844086 | + | 1.46200i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 38.0572 | + | 7.38686i | 1.78808 | + | 0.347065i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 28.2266 | + | 42.5172i | 1.32328 | + | 1.99324i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.92124 | + | 33.2945i | 0.417318 | + | 1.55745i | 0.780147 | + | 0.625596i | \(0.215144\pi\) |
−0.362830 | + | 0.931856i | \(0.618189\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.0173 | + | 15.3475i | −0.794297 | + | 0.716359i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.84992 | + | 18.1002i | −0.225883 | + | 0.843008i | 0.756165 | + | 0.654381i | \(0.227071\pi\) |
−0.982049 | + | 0.188628i | \(0.939596\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.7806 | + | 16.7806i | 0.779860 | + | 0.779860i | 0.979807 | − | 0.199947i | \(-0.0640769\pi\) |
−0.199947 | + | 0.979807i | \(0.564077\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20.7277 | + | 13.9892i | −0.961225 | + | 0.648734i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.7628 | 1.42353 | 0.711767 | − | 0.702416i | \(-0.247895\pi\) | ||||
0.711767 | + | 0.702416i | \(0.247895\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.1333 | −1.16055 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.66127 | + | 1.12119i | −0.0765471 | + | 0.0516619i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17.5764 | − | 17.5764i | −0.808162 | − | 0.808162i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.33147 | + | 4.96913i | −0.0610922 | + | 0.227999i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.1891 | − | 9.35436i | −1.06175 | − | 0.428307i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.38660 | − | 16.3710i | −0.200429 | − | 0.748010i | −0.990794 | − | 0.135375i | \(-0.956776\pi\) |
0.790366 | − | 0.612635i | \(-0.209891\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.27480 | + | 9.74235i | 0.149318 | + | 0.444213i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.5775 | − | 2.44128i | −0.572296 | − | 0.111082i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.0904 | − | 24.4053i | −0.639811 | − | 1.10819i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.0620 | + | 7.25125i | 1.22630 | + | 0.328585i | 0.813137 | − | 0.582073i | \(-0.197758\pi\) |
0.413161 | + | 0.910658i | \(0.364425\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.80610 | − | 22.6506i | −0.353004 | − | 1.02430i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.45173 | − | 11.1747i | 0.291162 | − | 0.504308i | −0.682922 | − | 0.730491i | \(-0.739291\pi\) |
0.974085 | + | 0.226183i | \(0.0726247\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 23.5031i | − | 1.05852i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 20.3842 | + | 26.0614i | 0.916200 | + | 1.17137i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 21.7937 | + | 12.5826i | 0.977582 | + | 0.564407i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.22600 | + | 2.22600i | −0.0996495 | + | 0.0996495i | −0.755174 | − | 0.655524i | \(-0.772448\pi\) |
0.655524 | + | 0.755174i | \(0.272448\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.8020 | + | 11.1225i | 0.571953 | + | 0.496919i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.89079 | − | 2.24635i | 0.173482 | − | 0.100160i | −0.410745 | − | 0.911750i | \(-0.634731\pi\) |
0.584226 | + | 0.811591i | \(0.301398\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.1628 | − | 5.67056i | 0.941733 | − | 0.252336i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.9484 | − | 14.8240i | 0.752706 | − | 0.658357i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.9448 | − | 6.14805i | 1.01701 | − | 0.272508i | 0.288456 | − | 0.957493i | \(-0.406858\pi\) |
0.728556 | + | 0.684986i | \(0.240192\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.6869 | − | 9.63418i | 0.738185 | − | 0.426191i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.294472 | + | 5.70769i | −0.0130012 | + | 0.252001i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.6194 | − | 15.6194i | 0.688271 | − | 0.688271i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.0152 | − | 10.4011i | −0.792306 | − | 0.457438i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.37314 | − | 3.59365i | −0.323645 | − | 0.157744i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 9.05417i | − | 0.396670i | −0.980134 | − | 0.198335i | \(-0.936447\pi\) | ||
0.980134 | − | 0.198335i | \(-0.0635534\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.6521 | + | 25.3781i | −0.640691 | + | 1.10971i | 0.344588 | + | 0.938754i | \(0.388019\pi\) |
−0.985279 | + | 0.170955i | \(0.945315\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −34.8485 | + | 12.0099i | −1.52091 | + | 0.524153i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.7706 | + | 5.29751i | 0.861219 | + | 0.230763i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.1785 | + | 17.6297i | 0.442543 | + | 0.766507i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.69174 | + | 4.90464i | −0.160208 | + | 0.212843i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.6171 | + | 34.5602i | 0.503191 | + | 1.49697i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.0119 | − | 37.3648i | −0.432851 | − | 1.61542i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.04119 | + | 14.8319i | 0.0449308 | + | 0.640045i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.5735 | − | 46.9249i | 0.541579 | − | 2.02120i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.7524 | − | 29.7524i | −1.27916 | − | 1.27916i | −0.941141 | − | 0.338015i | \(-0.890244\pi\) |
−0.338015 | − | 0.941141i | \(-0.609756\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.43535 | − | 9.53523i | −0.276167 | − | 0.409196i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22.4093 | 0.959909 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.72797 | −0.415938 | −0.207969 | − | 0.978135i | \(-0.566685\pi\) | ||||
−0.207969 | + | 0.978135i | \(0.566685\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −28.3691 | + | 4.00271i | −1.21076 | + | 0.170831i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.14489 | − | 4.14489i | −0.176578 | − | 0.176578i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.1933 | − | 67.8983i | 0.773657 | − | 2.88733i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.3216 | + | 1.07557i | −0.650366 | + | 0.0456553i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.30023 | + | 8.58457i | 0.0974638 | + | 0.363740i | 0.997381 | − | 0.0723199i | \(-0.0230402\pi\) |
−0.899918 | + | 0.436060i | \(0.856374\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.9817 | − | 21.0604i | −0.591363 | − | 0.890762i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.16013 | − | 26.5850i | 0.217861 | − | 1.12242i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.952635 | − | 1.65001i | −0.0401488 | − | 0.0695398i | 0.845253 | − | 0.534367i | \(-0.179450\pi\) |
−0.885402 | + | 0.464827i | \(0.846117\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −36.3564 | − | 9.74166i | −1.52952 | − | 0.409835i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −35.0782 | + | 21.1290i | −1.47315 | + | 0.887333i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.02931 | − | 8.71103i | 0.210840 | − | 0.365185i | −0.741138 | − | 0.671353i | \(-0.765713\pi\) |
0.951978 | + | 0.306168i | \(0.0990468\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.2231i | 0.846309i | 0.906057 | + | 0.423155i | \(0.139077\pi\) | ||||
−0.906057 | + | 0.423155i | \(0.860923\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.91690 | + | 12.1398i | −0.247182 | + | 0.507147i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.58509 | − | 3.80191i | −0.274617 | − | 0.158550i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.71564 | + | 7.71564i | −0.321206 | + | 0.321206i | −0.849230 | − | 0.528024i | \(-0.822933\pi\) |
0.528024 | + | 0.849230i | \(0.322933\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.03270 | − | 3.49063i | 0.126035 | − | 0.145066i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −35.5592 | + | 20.5301i | −1.47524 | + | 0.851733i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.5430 | − | 7.64807i | 1.18213 | − | 0.316751i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.0720 | + | 30.0842i | 0.623152 | + | 1.24383i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.87678 | − | 0.502881i | 0.0774630 | − | 0.0207561i | −0.219879 | − | 0.975527i | \(-0.570566\pi\) |
0.297342 | + | 0.954771i | \(0.403900\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.42089 | − | 2.55240i | 0.182159 | − | 0.105170i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.9712 | − | 25.2888i | 0.903774 | − | 1.04024i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.1037 | + | 23.1037i | −0.948756 | + | 0.948756i | −0.998750 | − | 0.0499940i | \(-0.984080\pi\) |
0.0499940 | + | 0.998750i | \(0.484080\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 54.0592 | + | 31.2111i | 2.21621 | + | 1.27953i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.09371 | + | 12.5026i | −0.249399 | + | 0.511696i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 8.98472i | − | 0.367106i | −0.983010 | − | 0.183553i | \(-0.941240\pi\) | ||
0.983010 | − | 0.183553i | \(-0.0587598\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.6602 | + | 28.8563i | −0.679583 | + | 1.17707i | 0.295523 | + | 0.955336i | \(0.404506\pi\) |
−0.975107 | + | 0.221737i | \(0.928827\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.4489 | − | 2.01062i | −0.669851 | − | 0.0818786i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.71530 | − | 1.26346i | −0.191704 | − | 0.0513670i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.1672 | + | 38.3948i | 0.899740 | + | 1.55840i | 0.827826 | + | 0.560984i | \(0.189577\pi\) |
0.0719135 | + | 0.997411i | \(0.477089\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.00273 | − | 41.2302i | 0.324287 | − | 1.67073i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.8640 | − | 13.9961i | −0.641790 | − | 0.566221i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.5021 | + | 42.9265i | 0.464566 | + | 1.73379i | 0.658323 | + | 0.752736i | \(0.271266\pi\) |
−0.193756 | + | 0.981050i | \(0.562067\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −54.3522 | + | 3.81549i | −2.19169 | + | 0.153855i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.01395 | + | 7.51616i | −0.0810785 | + | 0.302589i | −0.994543 | − | 0.104330i | \(-0.966730\pi\) |
0.913464 | + | 0.406919i | \(0.133397\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.82416 | − | 3.82416i | −0.153706 | − | 0.153706i | 0.626065 | − | 0.779771i | \(-0.284664\pi\) |
−0.779771 | + | 0.626065i | \(0.784664\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.03626 | − | 2.60391i | −0.322484 | − | 0.104491i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −34.8559 | −1.39647 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 26.5101 | 1.06040 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.77840 | − | 5.59843i | −0.150895 | − | 0.223580i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.88946 | + | 8.88946i | 0.354446 | + | 0.354446i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.24796 | + | 15.8536i | −0.169109 | + | 0.631122i | 0.828372 | + | 0.560179i | \(0.189268\pi\) |
−0.997480 | + | 0.0709434i | \(0.977399\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.653424 | + | 9.30812i | 0.0259713 | + | 0.369965i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.7991 | + | 40.3028i | 0.428549 | + | 1.59937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.9833 | − | 44.2454i | 0.871009 | − | 1.75307i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.2567 | + | 9.97835i | 0.524426 | + | 0.394738i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.3557 | − | 42.1853i | −0.961993 | − | 1.66622i | −0.717487 | − | 0.696572i | \(-0.754708\pi\) |
−0.244506 | − | 0.969648i | \(-0.578626\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.3066 | − | 4.36934i | −0.643069 | − | 0.172310i | −0.0774759 | − | 0.996994i | \(-0.524686\pi\) |
−0.565593 | + | 0.824684i | \(0.691353\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 35.7152 | − | 12.3086i | 1.40628 | − | 0.484649i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.9410 | − | 18.9504i | 0.430137 | − | 0.745018i | −0.566748 | − | 0.823891i | \(-0.691799\pi\) |
0.996885 | + | 0.0788727i | \(0.0251321\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 7.25461i | − | 0.284769i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32.8787 | + | 16.0250i | 1.28862 | + | 0.628068i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.2265 | + | 11.1004i | 0.752392 | + | 0.434393i | 0.826557 | − | 0.562852i | \(-0.190296\pi\) |
−0.0741658 | + | 0.997246i | \(0.523629\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.6720 | + | 23.6720i | −0.924941 | + | 0.924941i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.6917 | − | 4.97033i | 0.456138 | − | 0.193911i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.6857 | + | 21.7578i | −1.46803 | + | 0.847565i | −0.999359 | − | 0.0358100i | \(-0.988599\pi\) |
−0.468667 | + | 0.883375i | \(0.655266\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.55235 | + | 1.48775i | −0.215961 | + | 0.0578667i | −0.365177 | − | 0.930938i | \(-0.618992\pi\) |
0.149216 | + | 0.988805i | \(0.452325\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.4974 | − | 25.4623i | 0.407683 | − | 0.988875i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.0379 | − | 4.02939i | 0.583144 | − | 0.156253i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.50332 | − | 4.33205i | 0.290530 | − | 0.167738i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.0377 | − | 9.58968i | −0.426743 | − | 0.370759i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.9411 | − | 23.9411i | 0.924236 | − | 0.924236i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.1318 | − | 11.0458i | −0.737478 | − | 0.425783i | 0.0836738 | − | 0.996493i | \(-0.473335\pi\) |
−0.821152 | + | 0.570710i | \(0.806668\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.7679 | + | 5.07224i | −0.914828 | + | 0.195231i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 29.1088i | − | 1.11874i | −0.828917 | − | 0.559371i | \(-0.811043\pi\) | ||
0.828917 | − | 0.559371i | \(-0.188957\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.6093 | + | 35.6963i | −0.790911 | + | 1.36990i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.517787 | − | 1.50244i | −0.0198416 | − | 0.0575736i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.8514 | + | 5.31917i | 0.759593 | + | 0.203532i | 0.617769 | − | 0.786360i | \(-0.288037\pi\) |
0.141824 | + | 0.989892i | \(0.454703\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30.4409 | − | 52.7252i | −1.16309 | − | 2.01453i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.49290 | + | 1.06617i | 0.209567 | + | 0.0406768i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.9933 | − | 1.87629i | 1.14265 | − | 0.0714808i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.53183 | − | 28.1092i | −0.286524 | − | 1.06932i | −0.947718 | − | 0.319109i | \(-0.896617\pi\) |
0.661194 | − | 0.750215i | \(-0.270050\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.1043 | − | 44.8797i | 0.687724 | − | 1.70484i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.30256 | + | 8.59325i | −0.0873409 | + | 0.325961i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.5346 | + | 31.5346i | 1.19446 | + | 1.19446i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.3578 | − | 9.01521i | 0.505238 | − | 0.340986i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −47.9676 | −1.81171 | −0.905855 | − | 0.423588i | \(-0.860770\pi\) | ||||
−0.905855 | + | 0.423588i | \(0.860770\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.13541 | 0.118254 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 26.2048 | − | 17.6857i | 0.986932 | − | 0.666083i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −22.6597 | − | 22.6597i | −0.852206 | − | 0.852206i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.0177 | + | 48.5829i | −0.488891 | + | 1.82457i | 0.0729667 | + | 0.997334i | \(0.476753\pi\) |
−0.561858 | + | 0.827234i | \(0.689913\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.3386 | − | 42.9817i | 0.650250 | − | 1.61194i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.95285 | + | 7.28815i | 0.0731350 | + | 0.272943i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −35.6116 | − | 17.6936i | −1.33180 | − | 0.661702i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −44.5661 | − | 8.65023i | −1.66435 | − | 0.323049i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.43706 | + | 7.68521i | 0.165474 | + | 0.286610i | 0.936824 | − | 0.349802i | \(-0.113751\pi\) |
−0.771349 | + | 0.636412i | \(0.780418\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.2077 | − | 8.36208i | −1.16224 | − | 0.311420i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.88501 | − | 19.9779i | −0.256056 | − | 0.742987i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.4630 | − | 21.5865i | 0.462864 | − | 0.801704i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 11.4138i | − | 0.423315i | −0.977344 | − | 0.211658i | \(-0.932114\pi\) | ||
0.977344 | − | 0.211658i | \(-0.0678861\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.6478 | + | 11.0220i | −0.912882 | + | 0.408223i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.7776 | − | 15.4601i | −0.990407 | − | 0.571812i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.4825 | + | 14.4825i | −0.534923 | + | 0.534923i | −0.922033 | − | 0.387110i | \(-0.873473\pi\) |
0.387110 | + | 0.922033i | \(0.373473\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 55.7342 | + | 48.4225i | 2.05579 | + | 1.78609i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.9598 | − | 9.79176i | 0.624723 | − | 0.360684i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.8764 | − | 9.61305i | 1.31973 | − | 0.353622i | 0.470856 | − | 0.882210i | \(-0.343945\pi\) |
0.848879 | + | 0.528588i | \(0.177278\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.63915 | − | 6.34168i | −0.0969517 | − | 0.232967i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.1935 | − | 3.26724i | 0.447337 | − | 0.119864i | −0.0281161 | − | 0.999605i | \(-0.508951\pi\) |
0.475453 | + | 0.879741i | \(0.342284\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −52.7741 | + | 30.4692i | −1.93350 | + | 1.11630i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −24.9147 | + | 10.5916i | −0.911581 | + | 0.387527i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −40.0077 | + | 40.0077i | −1.46185 | + | 1.46185i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.30561 | − | 1.33114i | −0.0841328 | − | 0.0485741i | 0.457343 | − | 0.889290i | \(-0.348801\pi\) |
−0.541476 | + | 0.840716i | \(0.682134\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.2075 | + | 6.92469i | 0.517750 | + | 0.252350i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 69.6274i | − | 2.53400i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.12709 | + | 7.14833i | −0.150002 | + | 0.259810i | −0.931228 | − | 0.364438i | \(-0.881261\pi\) |
0.781226 | + | 0.624248i | \(0.214595\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.43834 | − | 3.25275i | 0.342590 | − | 0.118067i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.6088 | − | 4.71825i | −0.638317 | − | 0.171037i | −0.0748761 | − | 0.997193i | \(-0.523856\pi\) |
−0.563441 | + | 0.826156i | \(0.690523\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.3884 | − | 28.3856i | −0.593302 | − | 1.02763i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 32.8831 | + | 24.7513i | 1.18889 | + | 0.894884i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.46087 | − | 7.23180i | 0.0527489 | − | 0.261125i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.20203 | + | 4.48602i | 0.0433462 | + | 0.161770i | 0.984206 | − | 0.177025i | \(-0.0566473\pi\) |
−0.940860 | + | 0.338795i | \(0.889981\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.0192041 | + | 0.273565i | 0.000691618 | + | 0.00985221i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.06155 | − | 15.1579i | 0.146084 | − | 0.545193i | −0.853621 | − | 0.520895i | \(-0.825598\pi\) |
0.999705 | − | 0.0242978i | \(-0.00773498\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.3493 | + | 15.3493i | 0.551362 | + | 0.551362i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.5675 | + | 18.6211i | 0.450855 | + | 0.668030i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.1226 | 0.398508 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.6084 | −0.701644 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.53586 | − | 26.3436i | 0.305047 | − | 0.941443i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.54532 | + | 2.54532i | 0.0908464 | + | 0.0908464i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.6603 | − | 47.2487i | 0.451290 | − | 1.68424i | −0.247483 | − | 0.968892i | \(-0.579604\pi\) |
0.698773 | − | 0.715343i | \(-0.253730\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.09415 | + | 0.427805i | −0.216957 | + | 0.0152303i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.2486 | + | 53.1765i | 0.506622 | + | 1.89074i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.6869 | − | 19.0448i | 1.01870 | − | 0.676299i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.55712 | + | 44.0864i | −0.303490 | + | 1.56358i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.4830 | − | 38.9417i | −0.796388 | − | 1.37938i | −0.921954 | − | 0.387299i | \(-0.873408\pi\) |
0.125566 | − | 0.992085i | \(-0.459925\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.9948 | − | 6.69733i | −0.884251 | − | 0.236934i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.8120 | − | 2.78840i | −0.806022 | − | 0.0985234i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.50682 | + | 13.0022i | −0.264910 | + | 0.458838i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 23.0111i | 0.811035i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.2793 | + | 29.2971i | −0.502656 | + | 1.03131i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.6360 | − | 13.6462i | −0.830996 | − | 0.479776i | 0.0231976 | − | 0.999731i | \(-0.492615\pi\) |
−0.854194 | + | 0.519955i | \(0.825949\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.2312 | + | 11.2312i | −0.394382 | + | 0.394382i | −0.876246 | − | 0.481864i | \(-0.839960\pi\) |
0.481864 | + | 0.876246i | \(0.339960\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.29709 | + | 2.64394i | −0.0805624 | + | 0.0927272i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −37.2644 | + | 21.5146i | −1.30531 | + | 0.753623i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.44885 | + | 1.99591i | −0.260602 | + | 0.0698281i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27.0848 | − | 41.0929i | 0.946420 | − | 1.43590i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.0916 | − | 4.84764i | 0.631402 | − | 0.169184i | 0.0710962 | − | 0.997469i | \(-0.477350\pi\) |
0.560306 | + | 0.828286i | \(0.310684\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.110358 | − | 0.0637153i | 0.00384684 | − | 0.00222098i | −0.498075 | − | 0.867134i | \(-0.665960\pi\) |
0.501922 | + | 0.864913i | \(0.332626\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.8366 | − | 21.6809i | 0.655807 | − | 0.754833i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.2443 | + | 26.2443i | −0.912603 | + | 0.912603i | −0.996476 | − | 0.0838739i | \(-0.973271\pi\) |
0.0838739 | + | 0.996476i | \(0.473271\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 48.2799 | + | 27.8744i | 1.67683 | + | 0.968119i | 0.963661 | + | 0.267128i | \(0.0860747\pi\) |
0.713170 | + | 0.700991i | \(0.247259\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.3087 | + | 27.3057i | −0.461674 | + | 0.947224i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 60.4307i | − | 2.09380i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.2293 | − | 26.3779i | 0.527031 | − | 0.912845i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.2360 | + | 13.1180i | 0.699459 | + | 0.453426i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.9950 | + | 3.21404i | 0.414112 | + | 0.110961i | 0.459859 | − | 0.887992i | \(-0.347900\pi\) |
−0.0457468 | + | 0.998953i | \(0.514567\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.299157 | − | 0.518156i | −0.0103158 | − | 0.0178674i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.45580 | + | 33.2603i | −0.222349 | + | 1.14555i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −31.9366 | − | 24.8091i | −1.09865 | − | 0.853458i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.84800 | + | 6.89682i | 0.0634980 | + | 0.236978i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.4952 | − | 2.14074i | 1.04659 | − | 0.0734702i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.19946 | + | 4.47644i | −0.0411169 | + | 0.153450i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.60751 | − | 3.60751i | −0.123519 | − | 0.123519i | 0.642645 | − | 0.766164i | \(-0.277837\pi\) |
−0.766164 | + | 0.642645i | \(0.777837\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.1641 | − | 1.43410i | 0.347606 | − | 0.0490451i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.9079 | 1.43155 | 0.715773 | − | 0.698333i | \(-0.246075\pi\) | ||||
0.715773 | + | 0.698333i | \(0.246075\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.5846 | 0.941174 | 0.470587 | − | 0.882354i | \(-0.344042\pi\) | ||||
0.470587 | + | 0.882354i | \(0.344042\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 44.5821 | + | 66.0570i | 1.51935 | + | 2.25122i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.5622 | + | 19.5622i | 0.665905 | + | 0.665905i | 0.956765 | − | 0.290861i | \(-0.0939416\pi\) |
−0.290861 | + | 0.956765i | \(0.593942\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.81280 | + | 14.2296i | −0.129639 | + | 0.483820i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.297082 | − | 4.23198i | −0.0100894 | − | 0.143725i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.1760 | + | 52.9054i | 0.480887 | + | 1.79469i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.8783 | − | 6.34575i | 0.639665 | − | 0.215017i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.3437 | + | 21.7133i | −0.553151 | + | 0.734885i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.28492 | − | 3.95761i | −0.0772446 | − | 0.133792i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.29152 | + | 2.48965i | 0.313752 | + | 0.0840697i | 0.412259 | − | 0.911067i | \(-0.364740\pi\) |
−0.0985066 | + | 0.995136i | \(0.531407\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.7596 | − | 7.15440i | 0.700203 | − | 0.241312i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.63029 | + | 4.55580i | −0.0886168 | + | 0.153489i | −0.906927 | − | 0.421288i | \(-0.861578\pi\) |
0.818310 | + | 0.574777i | \(0.194911\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.8287i | 1.27304i | 0.771262 | + | 0.636518i | \(0.219626\pi\) | ||||
−0.771262 | + | 0.636518i | \(0.780374\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.91086 | + | 4.83052i | 0.333150 | + | 0.162376i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.84110 | − | 3.37236i | −0.196125 | − | 0.113233i | 0.398722 | − | 0.917072i | \(-0.369454\pi\) |
−0.594847 | + | 0.803839i | \(0.702787\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 43.1535 | − | 43.1535i | 1.44732 | − | 1.44732i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.4389 | − | 27.9240i | 0.517224 | − | 0.935488i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.58907 | + | 3.22685i | −0.187031 | + | 0.107982i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.7942 | − | 6.91154i | 0.862205 | − | 0.231027i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.0637 | − | 1.34191i | 0.336016 | − | 0.0448050i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23.8912 | + | 6.40164i | −0.796817 | + | 0.213507i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.8335 | − | 18.3791i | 1.06053 | − | 0.612296i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −41.7105 | − | 36.2385i | −1.38804 | − | 1.20594i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.6095 | + | 14.6095i | −0.485635 | + | 0.485635i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.8555 | − | 8.57683i | −0.493269 | − | 0.284789i | 0.232661 | − | 0.972558i | \(-0.425257\pi\) |
−0.725930 | + | 0.687769i | \(0.758590\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.0173 | − | 16.6428i | −0.431756 | − | 0.552005i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.770931i | 0.0255421i | 0.999918 | + | 0.0127710i | \(0.00406526\pi\) | ||||
−0.999918 | + | 0.0127710i | \(0.995935\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.9968 | − | 27.7072i | 0.529416 | − | 0.916976i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.7657 | + | 48.6483i | 0.554258 | + | 1.60826i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 47.2970 | + | 12.6732i | 1.56188 | + | 0.418505i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.3203 | + | 24.8035i | 0.472384 | + | 0.818192i | 0.999501 | − | 0.0316003i | \(-0.0100604\pi\) |
−0.527117 | + | 0.849793i | \(0.676727\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.6497 | + | 2.84349i | 0.482723 | + | 0.0936961i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −19.5467 | − | 3.94856i | −0.643388 | − | 0.129969i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.45076 | + | 12.8784i | 0.113460 | + | 0.423439i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.7554 | − | 7.96926i | −0.648854 | − | 0.261745i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.882669 | − | 3.29417i | 0.0289594 | − | 0.108078i | −0.949933 | − | 0.312453i | \(-0.898849\pi\) |
0.978893 | + | 0.204375i | \(0.0655161\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.6573 | − | 10.6573i | −0.349278 | − | 0.349278i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.1824 | − | 9.57176i | 0.464312 | − | 0.313365i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −48.6386 | −1.59065 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.0973 | −0.787225 | −0.393613 | − | 0.919276i | \(-0.628775\pi\) | ||||
−0.393613 | + | 0.919276i | \(0.628775\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.7254 | + | 16.6873i | −0.806884 | + | 0.544568i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.8741 | + | 23.8741i | 0.778274 | + | 0.778274i | 0.979537 | − | 0.201263i | \(-0.0645045\pi\) |
−0.201263 | + | 0.979537i | \(0.564505\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.25498 | + | 15.8798i | −0.138561 | + | 0.517117i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 49.2574 | + | 54.6165i | 1.60234 | + | 1.77667i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.42796 | − | 12.7933i | −0.111394 | − | 0.415727i | 0.887598 | − | 0.460618i | \(-0.152372\pi\) |
−0.998992 | + | 0.0448919i | \(0.985706\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.1015 | + | 11.4497i | −0.327908 | + | 0.371671i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.0212711 | − | 0.00412870i | −0.000689763 | − | 0.000133882i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.9590 | + | 31.1060i | 0.581751 | + | 1.00762i | 0.995272 | + | 0.0971272i | \(0.0309654\pi\) |
−0.413521 | + | 0.910494i | \(0.635701\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.4288 | + | 6.27773i | 0.758139 | + | 0.203143i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.6628 | + | 30.9398i | 0.344679 | + | 1.00014i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −44.5243 | + | 77.1184i | −1.43777 | + | 2.49028i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.46001i | 0.305162i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −29.3842 | + | 22.9832i | −0.946894 | + | 0.740622i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.19226 | − | 4.15245i | −0.231527 | − | 0.133672i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.3505 | − | 32.3505i | 1.04032 | − | 1.04032i | 0.0411686 | − | 0.999152i | \(-0.486892\pi\) |
0.999152 | − | 0.0411686i | \(-0.0131081\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.34237 | − | 5.51032i | −0.203746 | − | 0.177017i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.1052 | + | 8.14364i | −0.452657 | + | 0.261342i | −0.708952 | − | 0.705257i | \(-0.750832\pi\) |
0.256294 | + | 0.966599i | \(0.417498\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.5689 | − | 3.36783i | 0.402941 | − | 0.107968i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23.1433 | − | 17.8196i | 0.741178 | − | 0.570684i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.6294 | + | 10.3507i | −1.23587 | + | 0.331149i | −0.816861 | − | 0.576835i | \(-0.804288\pi\) |
−0.419005 | + | 0.907984i | \(0.637621\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.5206 | − | 13.5796i | 0.751721 | − | 0.434006i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.45490 | − | 19.8885i | −0.269944 | − | 0.634991i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.22554 | − | 7.22554i | 0.230459 | − | 0.230459i | −0.582425 | − | 0.812884i | \(-0.697896\pi\) |
0.812884 | + | 0.582425i | \(0.197896\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −52.1063 | − | 30.0836i | −1.66024 | − | 0.958542i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −41.5666 | − | 20.2594i | −1.32308 | − | 0.644864i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 11.3983i | − | 0.362445i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.7017 | − | 23.7321i | 0.435250 | − | 0.753875i | −0.562066 | − | 0.827092i | \(-0.689993\pi\) |
0.997316 | + | 0.0732176i | \(0.0233268\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.610909 | + | 0.210538i | −0.0193866 | + | 0.00668122i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.1289 | + | 6.46532i | 0.764938 | + | 0.204965i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.8049 | + | 32.5710i | 0.595556 | + | 1.03153i | 0.993468 | + | 0.114110i | \(0.0364016\pi\) |
−0.397912 | + | 0.917424i | \(0.630265\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.73534 | + | 13.1923i | 0.213097 | + | 0.417386i |
(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 | 312.2.bp.a.305.3 | yes | 56 | |
3.2 | odd | 2 | inner | 312.2.bp.a.305.7 | yes | 56 | |
4.3 | odd | 2 | 624.2.cn.f.305.12 | 56 | |||
12.11 | even | 2 | 624.2.cn.f.305.8 | 56 | |||
13.11 | odd | 12 | inner | 312.2.bp.a.89.7 | yes | 56 | |
39.11 | even | 12 | inner | 312.2.bp.a.89.3 | ✓ | 56 | |
52.11 | even | 12 | 624.2.cn.f.401.8 | 56 | |||
156.11 | odd | 12 | 624.2.cn.f.401.12 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.2.bp.a.89.3 | ✓ | 56 | 39.11 | even | 12 | inner | |
312.2.bp.a.89.7 | yes | 56 | 13.11 | odd | 12 | inner | |
312.2.bp.a.305.3 | yes | 56 | 1.1 | even | 1 | trivial | |
312.2.bp.a.305.7 | yes | 56 | 3.2 | odd | 2 | inner | |
624.2.cn.f.305.8 | 56 | 12.11 | even | 2 | |||
624.2.cn.f.305.12 | 56 | 4.3 | odd | 2 | |||
624.2.cn.f.401.8 | 56 | 52.11 | even | 12 | |||
624.2.cn.f.401.12 | 56 | 156.11 | odd | 12 |