Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(899,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.899");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bp (of order \(6\), degree \(2\), not 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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 899.11 | ||
Character | \(\chi\) | \(=\) | 3150.899 |
Dual form | 3150.2.bp.g.1349.11 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.61577 | − | 0.397202i | 0.988667 | − | 0.150128i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.429853 | + | 0.248176i | 0.129606 | + | 0.0748278i | 0.563401 | − | 0.826184i | \(-0.309493\pi\) |
−0.433795 | + | 0.901011i | \(0.642826\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.74440 | −0.761160 | −0.380580 | − | 0.924748i | \(-0.624276\pi\) | ||||
−0.380580 | + | 0.924748i | \(0.624276\pi\) | |||||||
\(14\) | −1.65187 | − | 2.06672i | −0.441481 | − | 0.552354i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.16952 | + | 1.82992i | 0.768721 | + | 0.443821i | 0.832418 | − | 0.554148i | \(-0.186956\pi\) |
−0.0636974 | + | 0.997969i | \(0.520289\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.12125 | + | 1.80205i | −0.716064 | + | 0.413420i | −0.813302 | − | 0.581841i | \(-0.802332\pi\) |
0.0972384 | + | 0.995261i | \(0.468999\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 0.496352i | − | 0.105823i | ||||||
\(23\) | −3.21210 | − | 5.56351i | −0.669768 | − | 1.16007i | −0.977969 | − | 0.208751i | \(-0.933060\pi\) |
0.308200 | − | 0.951321i | \(-0.400273\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.37220 | + | 2.37672i | 0.269111 | + | 0.466114i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.963896 | + | 2.46392i | −0.182159 | + | 0.465637i | ||||
\(29\) | − | 8.87959i | − | 1.64890i | −0.565937 | − | 0.824449i | \(-0.691485\pi\) | ||
0.565937 | − | 0.824449i | \(-0.308515\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.90736 | − | 3.98797i | −1.24060 | − | 0.716260i | −0.271383 | − | 0.962472i | \(-0.587481\pi\) |
−0.969216 | + | 0.246211i | \(0.920814\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 3.65984i | − | 0.627658i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.98397 | + | 1.14545i | −0.326163 | + | 0.188311i | −0.654136 | − | 0.756377i | \(-0.726968\pi\) |
0.327973 | + | 0.944687i | \(0.393634\pi\) | |||||||
\(38\) | 3.12125 | + | 1.80205i | 0.506334 | + | 0.292332i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.22816 | −0.347980 | −0.173990 | − | 0.984747i | \(-0.555666\pi\) | ||||
−0.173990 | + | 0.984747i | \(0.555666\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.22575i | 0.339424i | 0.985494 | + | 0.169712i | \(0.0542838\pi\) | ||||
−0.985494 | + | 0.169712i | \(0.945716\pi\) | |||||||
\(44\) | −0.429853 | + | 0.248176i | −0.0648028 | + | 0.0374139i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.21210 | + | 5.56351i | −0.473598 | + | 0.820295i | ||||
\(47\) | 5.66749 | − | 3.27213i | 0.826688 | − | 0.477289i | −0.0260292 | − | 0.999661i | \(-0.508286\pi\) |
0.852717 | + | 0.522373i | \(0.174953\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.68446 | − | 2.07798i | 0.954923 | − | 0.296854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.37220 | − | 2.37672i | 0.190290 | − | 0.329592i | ||||
\(53\) | 3.88322 | − | 6.72594i | 0.533402 | − | 0.923879i | −0.465837 | − | 0.884870i | \(-0.654247\pi\) |
0.999239 | − | 0.0390085i | \(-0.0124199\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.61577 | − | 0.397202i | 0.349546 | − | 0.0530784i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.68995 | + | 4.43979i | −1.00974 | + | 0.582973i | ||||
\(59\) | 3.05194 | − | 5.28611i | 0.397328 | − | 0.688193i | −0.596067 | − | 0.802935i | \(-0.703271\pi\) |
0.993395 | + | 0.114742i | \(0.0366040\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.24271 | − | 1.87218i | 0.415187 | − | 0.239708i | −0.277829 | − | 0.960630i | \(-0.589615\pi\) |
0.693016 | + | 0.720922i | \(0.256282\pi\) | |||||||
\(62\) | 7.97593i | 1.01294i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.08216 | + | 4.08889i | 0.865224 | + | 0.499537i | 0.865758 | − | 0.500463i | \(-0.166837\pi\) |
−0.000534152 | 1.00000i | \(0.500170\pi\) | ||||||||
\(68\) | −3.16952 | + | 1.82992i | −0.384360 | + | 0.221911i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.3761i | − | 1.23141i | −0.787975 | − | 0.615707i | \(-0.788871\pi\) | ||
0.787975 | − | 0.615707i | \(-0.211129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.53361 | + | 11.3165i | −0.764701 | + | 1.32450i | 0.175704 | + | 0.984443i | \(0.443780\pi\) |
−0.940405 | + | 0.340058i | \(0.889553\pi\) | |||||||
\(74\) | 1.98397 | + | 1.14545i | 0.230632 | + | 0.133156i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.60411i | − | 0.413420i | ||||||
\(77\) | 1.22297 | + | 0.478431i | 0.139370 | + | 0.0545223i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.44344 | − | 7.69627i | −0.499926 | − | 0.865898i | 0.500074 | − | 0.865983i | \(-0.333306\pi\) |
−1.00000 | 8.52501e-5i | \(0.999973\pi\) | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.11408 | + | 1.92964i | 0.123030 | + | 0.213093i | ||||
\(83\) | − | 4.79091i | − | 0.525871i | −0.964813 | − | 0.262935i | \(-0.915309\pi\) | ||
0.964813 | − | 0.262935i | \(-0.0846906\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.92756 | − | 1.11288i | 0.207854 | − | 0.120005i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.429853 | + | 0.248176i | 0.0458225 | + | 0.0264556i | ||||
\(89\) | −0.743586 | − | 1.28793i | −0.0788199 | − | 0.136520i | 0.823921 | − | 0.566704i | \(-0.191782\pi\) |
−0.902741 | + | 0.430184i | \(0.858449\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.17871 | + | 1.09008i | −0.752534 | + | 0.114272i | ||||
\(92\) | 6.42419 | 0.669768 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.66749 | − | 3.27213i | −0.584557 | − | 0.337494i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.05174 | 0.919064 | 0.459532 | − | 0.888161i | \(-0.348017\pi\) | ||||
0.459532 | + | 0.888161i | \(0.348017\pi\) | |||||||
\(98\) | −5.14181 | − | 4.74992i | −0.519401 | − | 0.479815i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.50180 | − | 2.60119i | 0.149434 | − | 0.258828i | −0.781584 | − | 0.623800i | \(-0.785588\pi\) |
0.931019 | + | 0.364972i | \(0.118921\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.18752 | + | 12.4491i | 0.708207 | + | 1.22665i | 0.965522 | + | 0.260323i | \(0.0838291\pi\) |
−0.257314 | + | 0.966328i | \(0.582838\pi\) | |||||||
\(104\) | −2.74440 | −0.269111 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.76645 | −0.754344 | ||||||||
\(107\) | 1.06314 | + | 1.84141i | 0.102778 | + | 0.178016i | 0.912828 | − | 0.408344i | \(-0.133894\pi\) |
−0.810050 | + | 0.586360i | \(0.800560\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.95181 | − | 6.84474i | 0.378515 | − | 0.655607i | −0.612331 | − | 0.790601i | \(-0.709768\pi\) |
0.990846 | + | 0.134994i | \(0.0431015\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.65187 | − | 2.06672i | −0.156087 | − | 0.195287i | ||||
\(113\) | −12.2968 | −1.15678 | −0.578391 | − | 0.815760i | \(-0.696319\pi\) | ||||
−0.578391 | + | 0.815760i | \(0.696319\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.68995 | + | 4.43979i | 0.713994 | + | 0.412224i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.10388 | −0.561907 | ||||||||
\(119\) | 9.01756 | + | 3.52771i | 0.826638 | + | 0.323384i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.37682 | − | 9.31292i | −0.488802 | − | 0.846629i | ||||
\(122\) | −3.24271 | − | 1.87218i | −0.293581 | − | 0.169499i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.90736 | − | 3.98797i | 0.620299 | − | 0.358130i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 0.753445i | − | 0.0668574i | −0.999441 | − | 0.0334287i | \(-0.989357\pi\) | ||
0.999441 | − | 0.0334287i | \(-0.0106427\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.35624 | + | 11.0093i | 0.555347 | + | 0.961890i | 0.997876 | + | 0.0651355i | \(0.0207479\pi\) |
−0.442529 | + | 0.896754i | \(0.645919\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.44868 | + | 5.95352i | −0.645882 | + | 0.516236i | ||||
\(134\) | − | 8.17778i | − | 0.706452i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.16952 | + | 1.82992i | 0.271784 | + | 0.156914i | ||||
\(137\) | −2.15740 | + | 3.73673i | −0.184319 | + | 0.319250i | −0.943347 | − | 0.331808i | \(-0.892341\pi\) |
0.759028 | + | 0.651058i | \(0.225675\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 0.0681276i | − | 0.00577851i | −0.999996 | − | 0.00288926i | \(-0.999080\pi\) | ||
0.999996 | − | 0.00288926i | \(-0.000919680\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.98595 | + | 5.18804i | −0.754084 | + | 0.435371i | ||||
\(143\) | −1.17969 | − | 0.681094i | −0.0986507 | − | 0.0569560i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.0672 | 1.08145 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 2.29090i | − | 0.188311i | ||||||
\(149\) | 14.4611 | − | 8.34911i | 1.18470 | − | 0.683986i | 0.227602 | − | 0.973754i | \(-0.426912\pi\) |
0.957097 | + | 0.289768i | \(0.0935783\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.51016 | − | 11.2759i | 0.529789 | − | 0.917622i | −0.469607 | − | 0.882876i | \(-0.655604\pi\) |
0.999396 | − | 0.0347463i | \(-0.0110623\pi\) | |||||||
\(152\) | −3.12125 | + | 1.80205i | −0.253167 | + | 0.146166i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.197152 | − | 1.29834i | −0.0158870 | − | 0.104623i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.40408 | − | 12.8242i | 0.590910 | − | 1.02349i | −0.403200 | − | 0.915112i | \(-0.632102\pi\) |
0.994110 | − | 0.108374i | \(-0.0345645\pi\) | |||||||
\(158\) | −4.44344 | + | 7.69627i | −0.353501 | + | 0.612282i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.6119 | − | 13.2770i | −0.836337 | − | 1.04637i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.3189 | + | 7.68966i | −1.04322 | + | 0.602301i | −0.920742 | − | 0.390171i | \(-0.872416\pi\) |
−0.122473 | + | 0.992472i | \(0.539082\pi\) | |||||||
\(164\) | 1.11408 | − | 1.92964i | 0.0869950 | − | 0.150680i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.14905 | + | 2.39546i | −0.322029 | + | 0.185923i | ||||
\(167\) | − | 24.5161i | − | 1.89712i | −0.316603 | − | 0.948558i | \(-0.602542\pi\) | ||
0.316603 | − | 0.948558i | \(-0.397458\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.46825 | −0.420635 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.92756 | − | 1.11288i | −0.146975 | − | 0.0848561i | ||||
\(173\) | 10.8463 | − | 6.26213i | 0.824631 | − | 0.476101i | −0.0273795 | − | 0.999625i | \(-0.508716\pi\) |
0.852011 | + | 0.523524i | \(0.175383\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 0.496352i | − | 0.0374139i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.743586 | + | 1.28793i | −0.0557341 | + | 0.0965343i | ||||
\(179\) | −1.58961 | − | 0.917762i | −0.118813 | − | 0.0685968i | 0.439416 | − | 0.898284i | \(-0.355186\pi\) |
−0.558229 | + | 0.829687i | \(0.688519\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 23.6564i | − | 1.75837i | −0.476481 | − | 0.879185i | \(-0.658088\pi\) | ||
0.476481 | − | 0.879185i | \(-0.341912\pi\) | |||||||
\(182\) | 4.53340 | + | 5.67191i | 0.336038 | + | 0.420430i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.21210 | − | 5.56351i | −0.236799 | − | 0.410148i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.908284 | + | 1.57319i | 0.0664203 | + | 0.115043i | ||||
\(188\) | 6.54425i | 0.477289i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.02253 | + | 4.05446i | −0.508133 | + | 0.293371i | −0.732066 | − | 0.681234i | \(-0.761444\pi\) |
0.223933 | + | 0.974605i | \(0.428110\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.4356 | + | 6.02502i | 0.751174 | + | 0.433691i | 0.826118 | − | 0.563497i | \(-0.190544\pi\) |
−0.0749438 | + | 0.997188i | \(0.523878\pi\) | |||||||
\(194\) | −4.52587 | − | 7.83903i | −0.324938 | − | 0.562810i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.54265 | + | 6.82790i | −0.110189 | + | 0.487707i | ||||
\(197\) | 12.7463 | 0.908137 | 0.454068 | − | 0.890967i | \(-0.349972\pi\) | ||||
0.454068 | + | 0.890967i | \(0.349972\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.4954 | − | 9.52361i | −1.16933 | − | 0.675111i | −0.215805 | − | 0.976436i | \(-0.569238\pi\) |
−0.953521 | + | 0.301325i | \(0.902571\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.00359 | −0.211332 | ||||||||
\(203\) | −3.52699 | − | 23.2269i | −0.247546 | − | 1.63021i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.18752 | − | 12.4491i | 0.500778 | − | 0.867373i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.37220 | + | 2.37672i | 0.0951450 | + | 0.164796i | ||||
\(209\) | −1.78891 | −0.123741 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.92057 | −0.614117 | −0.307059 | − | 0.951691i | \(-0.599345\pi\) | ||||
−0.307059 | + | 0.951691i | \(0.599345\pi\) | |||||||
\(212\) | 3.88322 | + | 6.72594i | 0.266701 | + | 0.461939i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.06314 | − | 1.84141i | 0.0726748 | − | 0.125876i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.6521 | − | 7.68797i | −1.33407 | − | 0.521893i | ||||
\(218\) | −7.90363 | −0.535301 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.69843 | − | 5.02204i | −0.585120 | − | 0.337819i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.5443 | −1.57664 | −0.788320 | − | 0.615265i | \(-0.789049\pi\) | ||||
−0.788320 | + | 0.615265i | \(0.789049\pi\) | |||||||
\(224\) | −0.963896 | + | 2.46392i | −0.0644030 | + | 0.164628i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.14838 | + | 10.6493i | 0.408984 | + | 0.708382i | ||||
\(227\) | 8.07522 | + | 4.66223i | 0.535971 | + | 0.309443i | 0.743445 | − | 0.668797i | \(-0.233191\pi\) |
−0.207473 | + | 0.978241i | \(0.566524\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.1545 | + | 11.6362i | −1.33185 | + | 0.768944i | −0.985583 | − | 0.169193i | \(-0.945884\pi\) |
−0.346266 | + | 0.938136i | \(0.612551\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 8.87959i | − | 0.582973i | ||||||
\(233\) | −6.31017 | − | 10.9295i | −0.413393 | − | 0.716018i | 0.581865 | − | 0.813285i | \(-0.302323\pi\) |
−0.995258 | + | 0.0972676i | \(0.968990\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.05194 | + | 5.28611i | 0.198664 | + | 0.344097i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.45370 | − | 9.57329i | −0.0942292 | − | 0.620544i | ||||
\(239\) | 16.1198i | 1.04270i | 0.853342 | + | 0.521351i | \(0.174572\pi\) | ||||
−0.853342 | + | 0.521351i | \(0.825428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.3222 | − | 10.5783i | −1.18024 | − | 0.681411i | −0.224168 | − | 0.974550i | \(-0.571966\pi\) |
−0.956070 | + | 0.293140i | \(0.905300\pi\) | |||||||
\(242\) | −5.37682 | + | 9.31292i | −0.345635 | + | 0.598657i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.74436i | 0.239708i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.56597 | − | 4.94556i | 0.545039 | − | 0.314679i | ||||
\(248\) | −6.90736 | − | 3.98797i | −0.438618 | − | 0.253236i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.06317 | −0.382704 | −0.191352 | − | 0.981522i | \(-0.561287\pi\) | ||||
−0.191352 | + | 0.981522i | \(0.561287\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.18866i | − | 0.200469i | ||||||
\(254\) | −0.652503 | + | 0.376723i | −0.0409416 | + | 0.0236377i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −9.51357 | + | 5.49266i | −0.593440 | + | 0.342623i | −0.766457 | − | 0.642296i | \(-0.777982\pi\) |
0.173016 | + | 0.984919i | \(0.444649\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.73464 | + | 3.78426i | −0.294196 | + | 0.235143i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.35624 | − | 11.0093i | 0.392690 | − | 0.680159i | ||||
\(263\) | −0.669365 | + | 1.15937i | −0.0412748 | + | 0.0714901i | −0.885925 | − | 0.463829i | \(-0.846475\pi\) |
0.844650 | + | 0.535319i | \(0.179809\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.88024 | + | 3.47399i | 0.544482 | + | 0.213004i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.08216 | + | 4.08889i | −0.432612 | + | 0.249769i | ||||
\(269\) | 0.311161 | − | 0.538946i | 0.0189718 | − | 0.0328601i | −0.856384 | − | 0.516340i | \(-0.827294\pi\) |
0.875355 | + | 0.483480i | \(0.160627\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.4634 | − | 10.6598i | 1.12157 | − | 0.647539i | 0.179769 | − | 0.983709i | \(-0.442465\pi\) |
0.941801 | + | 0.336170i | \(0.109132\pi\) | |||||||
\(272\) | − | 3.65984i | − | 0.221911i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.31480 | 0.260667 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.02805 | + | 0.593544i | 0.0617694 | + | 0.0356626i | 0.530567 | − | 0.847643i | \(-0.321979\pi\) |
−0.468797 | + | 0.883306i | \(0.655312\pi\) | |||||||
\(278\) | −0.0590003 | + | 0.0340638i | −0.00353860 | + | 0.00204301i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.97593i | − | 0.117874i | −0.998262 | − | 0.0589370i | \(-0.981229\pi\) | ||
0.998262 | − | 0.0589370i | \(-0.0187711\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.5654 | − | 23.4960i | 0.806382 | − | 1.39669i | −0.108972 | − | 0.994045i | \(-0.534756\pi\) |
0.915354 | − | 0.402650i | \(-0.131911\pi\) | |||||||
\(284\) | 8.98595 | + | 5.18804i | 0.533218 | + | 0.307853i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.36219i | 0.0805479i | ||||||||
\(287\) | −5.82835 | + | 0.885030i | −0.344036 | + | 0.0522417i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.80278 | − | 3.12250i | −0.106046 | − | 0.183677i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.53361 | − | 11.3165i | −0.382350 | − | 0.662250i | ||||
\(293\) | 10.3808i | 0.606456i | 0.952918 | + | 0.303228i | \(0.0980643\pi\) | ||||
−0.952918 | + | 0.303228i | \(0.901936\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.98397 | + | 1.14545i | −0.115316 | + | 0.0665778i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.4611 | − | 8.34911i | −0.837708 | − | 0.483651i | ||||
\(299\) | 8.81529 | + | 15.2685i | 0.509801 | + | 0.883002i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.884074 | + | 5.82205i | 0.0509572 | + | 0.335577i | ||||
\(302\) | −13.0203 | −0.749235 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.12125 | + | 1.80205i | 0.179016 | + | 0.103355i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.1364 | 0.806808 | 0.403404 | − | 0.915022i | \(-0.367827\pi\) | ||||
0.403404 | + | 0.915022i | \(0.367827\pi\) | |||||||
\(308\) | −1.02582 | + | 0.819908i | −0.0584515 | + | 0.0467186i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.32643 | − | 5.76155i | 0.188625 | − | 0.326708i | −0.756167 | − | 0.654378i | \(-0.772930\pi\) |
0.944792 | + | 0.327671i | \(0.106264\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.07282 | + | 10.5184i | 0.343256 | + | 0.594537i | 0.985035 | − | 0.172352i | \(-0.0551367\pi\) |
−0.641779 | + | 0.766890i | \(0.721803\pi\) | |||||||
\(314\) | −14.8082 | −0.835673 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.88688 | 0.499926 | ||||||||
\(317\) | −15.3605 | − | 26.6051i | −0.862730 | − | 1.49429i | −0.869283 | − | 0.494314i | \(-0.835419\pi\) |
0.00655283 | − | 0.999979i | \(-0.497914\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.20370 | − | 3.81692i | 0.123383 | − | 0.213706i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.19225 | + | 15.8287i | −0.345081 | + | 0.882099i | ||||
\(323\) | −13.1905 | −0.733937 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.3189 | + | 7.68966i | 0.737665 | + | 0.425891i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.22816 | −0.123030 | ||||||||
\(329\) | 13.5251 | − | 10.8103i | 0.745664 | − | 0.595989i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.5140 | + | 26.8710i | 0.852724 | + | 1.47696i | 0.878741 | + | 0.477300i | \(0.158384\pi\) |
−0.0260166 | + | 0.999662i | \(0.508282\pi\) | |||||||
\(332\) | 4.14905 | + | 2.39546i | 0.227709 | + | 0.131468i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −21.2316 | + | 12.2581i | −1.16174 | + | 0.670732i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.91470i | 0.376668i | 0.982105 | + | 0.188334i | \(0.0603087\pi\) | ||||
−0.982105 | + | 0.188334i | \(0.939691\pi\) | |||||||
\(338\) | 2.73413 | + | 4.73565i | 0.148717 | + | 0.257585i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.97943 | − | 3.42848i | −0.107192 | − | 0.185663i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.6596 | − | 8.09058i | 0.899534 | − | 0.436850i | ||||
\(344\) | 2.22575i | 0.120005i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.8463 | − | 6.26213i | −0.583103 | − | 0.336654i | ||||
\(347\) | 3.74704 | − | 6.49006i | 0.201152 | − | 0.348405i | −0.747748 | − | 0.663982i | \(-0.768865\pi\) |
0.948900 | + | 0.315578i | \(0.102198\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.4552i | 0.666714i | 0.942801 | + | 0.333357i | \(0.108181\pi\) | ||||
−0.942801 | + | 0.333357i | \(0.891819\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.429853 | + | 0.248176i | −0.0229113 | + | 0.0132278i | ||||
\(353\) | 16.4027 | + | 9.47011i | 0.873028 | + | 0.504043i | 0.868353 | − | 0.495946i | \(-0.165179\pi\) |
0.00467471 | + | 0.999989i | \(0.498512\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.48717 | 0.0788199 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.83552i | 0.0970105i | ||||||||
\(359\) | −23.0590 | + | 13.3131i | −1.21701 | + | 0.702639i | −0.964277 | − | 0.264898i | \(-0.914662\pi\) |
−0.252730 | + | 0.967537i | \(0.581329\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00520 | + | 5.20516i | −0.158168 | + | 0.273956i | ||||
\(362\) | −20.4871 | + | 11.8282i | −1.07678 | + | 0.621677i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.64532 | − | 6.76199i | 0.138652 | − | 0.354425i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.45606 | − | 9.45017i | 0.284804 | − | 0.493295i | −0.687758 | − | 0.725940i | \(-0.741405\pi\) |
0.972562 | + | 0.232646i | \(0.0747382\pi\) | |||||||
\(368\) | −3.21210 | + | 5.56351i | −0.167442 | + | 0.290018i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.48604 | − | 19.1359i | 0.388656 | − | 0.993487i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.4924 | + | 11.2539i | −1.00928 | + | 0.582707i | −0.910980 | − | 0.412450i | \(-0.864673\pi\) |
−0.0982976 | + | 0.995157i | \(0.531340\pi\) | |||||||
\(374\) | 0.908284 | − | 1.57319i | 0.0469663 | − | 0.0813480i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.66749 | − | 3.27213i | 0.292278 | − | 0.168747i | ||||
\(377\) | 24.3692i | 1.25508i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.25909 | 0.167408 | 0.0837040 | − | 0.996491i | \(-0.473325\pi\) | ||||
0.0837040 | + | 0.996491i | \(0.473325\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.02253 | + | 4.05446i | 0.359304 | + | 0.207444i | ||||
\(383\) | −15.0013 | + | 8.66098i | −0.766528 | + | 0.442555i | −0.831635 | − | 0.555323i | \(-0.812595\pi\) |
0.0651064 | + | 0.997878i | \(0.479261\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 12.0500i | − | 0.613331i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.52587 | + | 7.83903i | −0.229766 | + | 0.397967i | ||||
\(389\) | 27.4515 | + | 15.8491i | 1.39185 | + | 0.803582i | 0.993520 | − | 0.113662i | \(-0.0362580\pi\) |
0.398326 | + | 0.917244i | \(0.369591\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 23.5115i | − | 1.18903i | ||||||
\(392\) | 6.68446 | − | 2.07798i | 0.337616 | − | 0.104954i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.37315 | − | 11.0386i | −0.321075 | − | 0.556118i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.7561 | + | 29.0224i | 0.840964 | + | 1.45659i | 0.889081 | + | 0.457750i | \(0.151345\pi\) |
−0.0481170 | + | 0.998842i | \(0.515322\pi\) | |||||||
\(398\) | 19.0472i | 0.954751i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.0404 | + | 17.9212i | −1.55008 | + | 0.894940i | −0.551947 | + | 0.833879i | \(0.686115\pi\) |
−0.998134 | + | 0.0610611i | \(0.980552\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.9566 | + | 10.9446i | 0.944295 | + | 0.545189i | ||||
\(404\) | 1.50180 | + | 2.60119i | 0.0747171 | + | 0.129414i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.3516 | + | 14.6679i | −0.910775 | + | 0.727957i | ||||
\(407\) | −1.13709 | −0.0563635 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.3474 | + | 12.3249i | 1.05556 | + | 0.609429i | 0.924201 | − | 0.381905i | \(-0.124732\pi\) |
0.131361 | + | 0.991335i | \(0.458065\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.3750 | −0.708207 | ||||||||
\(413\) | 5.88350 | − | 15.0395i | 0.289508 | − | 0.740044i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.37220 | − | 2.37672i | 0.0672777 | − | 0.116528i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.894453 | + | 1.54924i | 0.0437491 | + | 0.0757757i | ||||
\(419\) | −10.6574 | −0.520646 | −0.260323 | − | 0.965522i | \(-0.583829\pi\) | ||||
−0.260323 | + | 0.965522i | \(0.583829\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.6815 | 1.10543 | 0.552714 | − | 0.833371i | \(-0.313592\pi\) | ||||
0.552714 | + | 0.833371i | \(0.313592\pi\) | |||||||
\(422\) | 4.46028 | + | 7.72544i | 0.217123 | + | 0.376068i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.88322 | − | 6.72594i | 0.188586 | − | 0.326641i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.73854 | − | 6.18520i | 0.374494 | − | 0.299323i | ||||
\(428\) | −2.12628 | −0.102778 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.0439 | − | 15.0364i | −1.25449 | − | 0.724279i | −0.282491 | − | 0.959270i | \(-0.591161\pi\) |
−0.971998 | + | 0.234991i | \(0.924494\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.9203 | 0.717025 | 0.358512 | − | 0.933525i | \(-0.383284\pi\) | ||||
0.358512 | + | 0.933525i | \(0.383284\pi\) | |||||||
\(434\) | 3.16806 | + | 20.8632i | 0.152072 | + | 1.00146i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.95181 | + | 6.84474i | 0.189258 | + | 0.327804i | ||||
\(437\) | 20.0515 | + | 11.5767i | 0.959194 | + | 0.553791i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.1126 | + | 6.41586i | −0.530375 | + | 0.306212i | −0.741169 | − | 0.671318i | \(-0.765728\pi\) |
0.210794 | + | 0.977530i | \(0.432395\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.0441i | 0.477748i | ||||||||
\(443\) | −10.2071 | − | 17.6792i | −0.484953 | − | 0.839963i | 0.514898 | − | 0.857252i | \(-0.327830\pi\) |
−0.999851 | + | 0.0172887i | \(0.994497\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.7721 | + | 20.3899i | 0.557426 | + | 0.965491i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.61577 | − | 0.397202i | 0.123583 | − | 0.0187660i | ||||
\(449\) | − | 20.8404i | − | 0.983519i | −0.870731 | − | 0.491760i | \(-0.836354\pi\) | ||
0.870731 | − | 0.491760i | \(-0.163646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.957782 | − | 0.552976i | −0.0451002 | − | 0.0260386i | ||||
\(452\) | 6.14838 | − | 10.6493i | 0.289196 | − | 0.500901i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 9.32446i | − | 0.437619i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.8811 | + | 8.01424i | −0.649329 | + | 0.374890i | −0.788199 | − | 0.615420i | \(-0.788986\pi\) |
0.138870 | + | 0.990311i | \(0.455653\pi\) | |||||||
\(458\) | 20.1545 | + | 11.6362i | 0.941760 | + | 0.543725i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.98400 | −0.0924039 | −0.0462020 | − | 0.998932i | \(-0.514712\pi\) | ||||
−0.0462020 | + | 0.998932i | \(0.514712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 36.3987i | − | 1.69159i | −0.533506 | − | 0.845796i | \(-0.679126\pi\) | ||
0.533506 | − | 0.845796i | \(-0.320874\pi\) | |||||||
\(464\) | −7.68995 | + | 4.43979i | −0.356997 | + | 0.206112i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.31017 | + | 10.9295i | −0.292313 | + | 0.506301i | ||||
\(467\) | −26.9113 | + | 15.5372i | −1.24530 | + | 0.718977i | −0.970169 | − | 0.242428i | \(-0.922056\pi\) |
−0.275136 | + | 0.961405i | \(0.588723\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.1494 | + | 7.88253i | 0.930413 | + | 0.363981i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.05194 | − | 5.28611i | 0.140477 | − | 0.243313i | ||||
\(473\) | −0.552378 | + | 0.956747i | −0.0253984 | + | 0.0439913i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.56386 | + | 6.04558i | −0.346689 | + | 0.277099i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13.9601 | − | 8.05990i | 0.638522 | − | 0.368651i | ||||
\(479\) | −18.2404 | + | 31.5933i | −0.833426 | + | 1.44354i | 0.0618788 | + | 0.998084i | \(0.480291\pi\) |
−0.895305 | + | 0.445453i | \(0.853043\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.44483 | − | 3.14357i | 0.248263 | − | 0.143335i | ||||
\(482\) | 21.1567i | 0.963660i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.7536 | 0.488802 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.2399 | − | 7.06672i | −0.554644 | − | 0.320224i | 0.196349 | − | 0.980534i | \(-0.437091\pi\) |
−0.750993 | + | 0.660310i | \(0.770425\pi\) | |||||||
\(488\) | 3.24271 | − | 1.87218i | 0.146791 | − | 0.0847496i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 32.5466i | − | 1.46881i | −0.678714 | − | 0.734403i | \(-0.737462\pi\) | ||
0.678714 | − | 0.734403i | \(-0.262538\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.2489 | − | 28.1440i | 0.731815 | − | 1.26754i | ||||
\(494\) | −8.56597 | − | 4.94556i | −0.385401 | − | 0.222511i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.97593i | 0.358130i | ||||||||
\(497\) | −4.12140 | − | 27.1414i | −0.184870 | − | 1.21746i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.87396 | + | 10.1740i | 0.262955 | + | 0.455451i | 0.967026 | − | 0.254679i | \(-0.0819697\pi\) |
−0.704071 | + | 0.710130i | \(0.748636\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.03158 | + | 5.25086i | 0.135306 | + | 0.234357i | ||||
\(503\) | 24.5250i | 1.09352i | 0.837291 | + | 0.546758i | \(0.184138\pi\) | ||||
−0.837291 | + | 0.546758i | \(0.815862\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.76146 | + | 1.59433i | −0.122762 | + | 0.0708766i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.652503 | + | 0.376723i | 0.0289501 | + | 0.0167144i | ||||
\(509\) | 5.84634 | + | 10.1262i | 0.259135 | + | 0.448834i | 0.966010 | − | 0.258503i | \(-0.0832293\pi\) |
−0.706876 | + | 0.707338i | \(0.749896\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.5954 | + | 32.1966i | −0.557189 | + | 1.42429i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.51357 | + | 5.49266i | 0.419626 | + | 0.242271i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.24825 | 0.142858 | ||||||||
\(518\) | 5.64459 | + | 2.20819i | 0.248009 | + | 0.0970221i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.8674 | + | 25.7511i | −0.651354 | + | 1.12818i | 0.331441 | + | 0.943476i | \(0.392465\pi\) |
−0.982795 | + | 0.184702i | \(0.940868\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.82915 | + | 4.90024i | 0.123710 | + | 0.214272i | 0.921228 | − | 0.389023i | \(-0.127187\pi\) |
−0.797518 | + | 0.603295i | \(0.793854\pi\) | |||||||
\(524\) | −12.7125 | −0.555347 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.33873 | 0.0583714 | ||||||||
\(527\) | −14.5953 | − | 25.2799i | −0.635783 | − | 1.10121i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.13513 | + | 15.8225i | −0.397179 | + | 0.687935i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.43156 | − | 9.42751i | −0.0620660 | − | 0.408734i | ||||
\(533\) | 6.11497 | 0.264869 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.08216 | + | 4.08889i | 0.305903 | + | 0.176613i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.622322 | −0.0268302 | ||||||||
\(539\) | 3.38904 | + | 0.765697i | 0.145976 | + | 0.0329809i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.6742 | + | 30.6126i | 0.759874 | + | 1.31614i | 0.942915 | + | 0.333035i | \(0.108073\pi\) |
−0.183041 | + | 0.983105i | \(0.558594\pi\) | |||||||
\(542\) | −18.4634 | − | 10.6598i | −0.793070 | − | 0.457879i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.16952 | + | 1.82992i | −0.135892 | + | 0.0784572i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 21.4806i | − | 0.918445i | −0.888321 | − | 0.459223i | \(-0.848128\pi\) | ||
0.888321 | − | 0.459223i | \(-0.151872\pi\) | |||||||
\(548\) | −2.15740 | − | 3.73673i | −0.0921595 | − | 0.159625i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.0015 | + | 27.7154i | 0.681687 | + | 1.18072i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.6800 | − | 18.3667i | −0.624256 | − | 0.781031i | ||||
\(554\) | − | 1.18709i | − | 0.0504345i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.0590003 | + | 0.0340638i | 0.00250217 | + | 0.00144463i | ||||
\(557\) | −19.9150 | + | 34.4939i | −0.843828 | + | 1.46155i | 0.0428076 | + | 0.999083i | \(0.486370\pi\) |
−0.886635 | + | 0.462469i | \(0.846964\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.10836i | − | 0.258356i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.71120 | + | 0.987964i | −0.0721828 | + | 0.0416747i | ||||
\(563\) | 8.95567 | + | 5.17056i | 0.377437 | + | 0.217913i | 0.676702 | − | 0.736257i | \(-0.263408\pi\) |
−0.299266 | + | 0.954170i | \(0.596742\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −27.1309 | −1.14040 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 10.3761i | − | 0.435371i | ||||||
\(569\) | 24.3464 | − | 14.0564i | 1.02065 | − | 0.589275i | 0.106361 | − | 0.994328i | \(-0.466080\pi\) |
0.914293 | + | 0.405053i | \(0.132747\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.7146 | − | 23.7544i | 0.573938 | − | 0.994090i | −0.422218 | − | 0.906494i | \(-0.638748\pi\) |
0.996156 | − | 0.0875958i | \(-0.0279184\pi\) | |||||||
\(572\) | 1.17969 | − | 0.681094i | 0.0493253 | − | 0.0284780i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.68063 | + | 4.60498i | 0.153627 | + | 0.192208i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.51910 | + | 11.2914i | −0.271394 | + | 0.470068i | −0.969219 | − | 0.246200i | \(-0.920818\pi\) |
0.697825 | + | 0.716268i | \(0.254151\pi\) | |||||||
\(578\) | −1.80278 | + | 3.12250i | −0.0749857 | + | 0.129879i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.90296 | − | 12.5319i | −0.0789481 | − | 0.519911i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.33843 | − | 1.92744i | 0.138264 | − | 0.0798266i | ||||
\(584\) | −6.53361 | + | 11.3165i | −0.270363 | + | 0.468282i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.99008 | − | 5.19042i | 0.371377 | − | 0.214414i | ||||
\(587\) | − | 35.0223i | − | 1.44553i | −0.691096 | − | 0.722763i | \(-0.742872\pi\) | ||
0.691096 | − | 0.722763i | \(-0.257128\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.7461 | 1.18446 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.98397 | + | 1.14545i | 0.0815409 | + | 0.0470776i | ||||
\(593\) | 14.1919 | − | 8.19370i | 0.582792 | − | 0.336475i | −0.179450 | − | 0.983767i | \(-0.557432\pi\) |
0.762242 | + | 0.647292i | \(0.224099\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.6982i | 0.683986i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.81529 | − | 15.2685i | 0.360484 | − | 0.624376i | ||||
\(599\) | −26.0718 | − | 15.0526i | −1.06527 | − | 0.615032i | −0.138382 | − | 0.990379i | \(-0.544190\pi\) |
−0.926884 | + | 0.375347i | \(0.877524\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.75569i | − | 0.0716162i | −0.999359 | − | 0.0358081i | \(-0.988599\pi\) | ||
0.999359 | − | 0.0358081i | \(-0.0114005\pi\) | |||||||
\(602\) | 4.60001 | − | 3.67666i | 0.187482 | − | 0.149849i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.51016 | + | 11.2759i | 0.264895 | + | 0.458811i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.03616 | + | 15.6511i | 0.366766 | + | 0.635258i | 0.989058 | − | 0.147528i | \(-0.0471315\pi\) |
−0.622292 | + | 0.782785i | \(0.713798\pi\) | |||||||
\(608\) | − | 3.60411i | − | 0.146166i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.5539 | + | 8.98003i | −0.629242 | + | 0.363293i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.1285 | + | 6.42507i | 0.449478 | + | 0.259506i | 0.707610 | − | 0.706604i | \(-0.249774\pi\) |
−0.258132 | + | 0.966110i | \(0.583107\pi\) | |||||||
\(614\) | −7.06821 | − | 12.2425i | −0.285250 | − | 0.494067i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.22297 | + | 0.478431i | 0.0492749 | + | 0.0192765i | ||||
\(617\) | 37.3633 | 1.50419 | 0.752094 | − | 0.659055i | \(-0.229044\pi\) | ||||
0.752094 | + | 0.659055i | \(0.229044\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.7213 | − | 13.6955i | −0.953439 | − | 0.550468i | −0.0592911 | − | 0.998241i | \(-0.518884\pi\) |
−0.894147 | + | 0.447773i | \(0.852217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.65287 | −0.266756 | ||||||||
\(623\) | −2.45661 | − | 3.07356i | −0.0984222 | − | 0.123140i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.07282 | − | 10.5184i | 0.242719 | − | 0.420401i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.40408 | + | 12.8242i | 0.295455 | + | 0.511743i | ||||
\(629\) | −8.38432 | −0.334305 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.09420 | −0.162987 | −0.0814937 | − | 0.996674i | \(-0.525969\pi\) | ||||
−0.0814937 | + | 0.996674i | \(0.525969\pi\) | |||||||
\(632\) | −4.44344 | − | 7.69627i | −0.176751 | − | 0.306141i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.3605 | + | 26.6051i | −0.610043 | + | 1.05662i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.3449 | + | 5.70280i | −0.726850 | + | 0.225953i | ||||
\(638\) | −4.40740 | −0.174491 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.4700 | + | 16.4371i | 1.12450 | + | 0.649228i | 0.942545 | − | 0.334080i | \(-0.108426\pi\) |
0.181951 | + | 0.983308i | \(0.441759\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 48.1790 | 1.89999 | 0.949996 | − | 0.312261i | \(-0.101086\pi\) | ||||
0.949996 | + | 0.312261i | \(0.101086\pi\) | |||||||
\(644\) | 16.8042 | − | 2.55170i | 0.662178 | − | 0.100551i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.59524 | + | 11.4233i | 0.259486 | + | 0.449443i | ||||
\(647\) | −4.58478 | − | 2.64703i | −0.180246 | − | 0.104065i | 0.407162 | − | 0.913356i | \(-0.366518\pi\) |
−0.587408 | + | 0.809291i | \(0.699852\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.62377 | − | 1.51483i | 0.102992 | − | 0.0594625i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 15.3793i | − | 0.602301i | ||||||
\(653\) | 25.0603 | + | 43.4057i | 0.980686 | + | 1.69860i | 0.659729 | + | 0.751503i | \(0.270671\pi\) |
0.320956 | + | 0.947094i | \(0.395996\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.11408 | + | 1.92964i | 0.0434975 | + | 0.0753399i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16.1245 | − | 6.30798i | −0.628599 | − | 0.245911i | ||||
\(659\) | − | 2.20149i | − | 0.0857579i | −0.999080 | − | 0.0428790i | \(-0.986347\pi\) | ||
0.999080 | − | 0.0428790i | \(-0.0136530\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.7612 | − | 19.4921i | −1.31316 | − | 0.758153i | −0.330542 | − | 0.943791i | \(-0.607231\pi\) |
−0.982618 | + | 0.185638i | \(0.940565\pi\) | |||||||
\(662\) | 15.5140 | − | 26.8710i | 0.602967 | − | 1.04437i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 4.79091i | − | 0.185923i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −49.4017 | + | 28.5221i | −1.91284 | + | 1.10438i | ||||
\(668\) | 21.2316 | + | 12.2581i | 0.821475 | + | 0.474279i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.85852 | 0.0717473 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 43.4830i | − | 1.67615i | −0.545556 | − | 0.838074i | \(-0.683682\pi\) | ||
0.545556 | − | 0.838074i | \(-0.316318\pi\) | |||||||
\(674\) | 5.98830 | − | 3.45735i | 0.230661 | − | 0.133172i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.73413 | − | 4.73565i | 0.105159 | − | 0.182140i | ||||
\(677\) | 36.0802 | − | 20.8309i | 1.38668 | − | 0.800597i | 0.393736 | − | 0.919223i | \(-0.371182\pi\) |
0.992939 | + | 0.118626i | \(0.0378489\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.6772 | − | 3.59537i | 0.908648 | − | 0.137978i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.97943 | + | 3.42848i | −0.0757965 | + | 0.131283i | ||||
\(683\) | 23.8637 | − | 41.3332i | 0.913120 | − | 1.58157i | 0.103490 | − | 0.994631i | \(-0.466999\pi\) |
0.809630 | − | 0.586940i | \(-0.199668\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.3365 | − | 10.3824i | −0.585548 | − | 0.396400i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.92756 | − | 1.11288i | 0.0734875 | − | 0.0424280i | ||||
\(689\) | −10.6571 | + | 18.4587i | −0.406004 | + | 0.703220i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.6953 | − | 19.4540i | 1.28183 | − | 0.740066i | 0.304648 | − | 0.952465i | \(-0.401461\pi\) |
0.977183 | + | 0.212399i | \(0.0681277\pi\) | |||||||
\(692\) | 12.5243i | 0.476101i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.49408 | −0.284471 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.06219 | − | 4.07736i | −0.267500 | − | 0.154441i | ||||
\(698\) | 10.7866 | − | 6.22762i | 0.408277 | − | 0.235719i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.73610i | 0.329958i | 0.986297 | + | 0.164979i | \(0.0527556\pi\) | ||||
−0.986297 | + | 0.164979i | \(0.947244\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.12832 | − | 7.15046i | 0.155703 | − | 0.269685i | ||||
\(704\) | 0.429853 | + | 0.248176i | 0.0162007 | + | 0.00935348i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 18.9402i | − | 0.712824i | ||||||
\(707\) | 2.89515 | − | 7.40061i | 0.108883 | − | 0.278329i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.25544 | + | 14.2988i | 0.310039 | + | 0.537004i | 0.978371 | − | 0.206860i | \(-0.0663244\pi\) |
−0.668331 | + | 0.743864i | \(0.732991\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.743586 | − | 1.28793i | −0.0278671 | − | 0.0482671i | ||||
\(713\) | 51.2389i | 1.91891i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.58961 | − | 0.917762i | 0.0594066 | − | 0.0342984i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 23.0590 | + | 13.3131i | 0.860554 | + | 0.496841i | ||||
\(719\) | −22.5570 | − | 39.0699i | −0.841234 | − | 1.45706i | −0.888852 | − | 0.458195i | \(-0.848496\pi\) |
0.0476171 | − | 0.998866i | \(-0.484837\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.7457 | + | 29.7092i | 0.884336 | + | 1.10643i | ||||
\(722\) | 6.01040 | 0.223684 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 20.4871 | + | 11.8282i | 0.761396 | + | 0.439592i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.9760 | 1.18593 | 0.592963 | − | 0.805230i | \(-0.297958\pi\) | ||||
0.592963 | + | 0.805230i | \(0.297958\pi\) | |||||||
\(728\) | −7.17871 | + | 1.09008i | −0.266061 | + | 0.0404012i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.07295 | + | 7.05456i | −0.150644 | + | 0.260922i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.3606 | + | 40.4618i | 0.862844 | + | 1.49449i | 0.869172 | + | 0.494509i | \(0.164652\pi\) |
−0.00632839 | + | 0.999980i | \(0.502014\pi\) | |||||||
\(734\) | −10.9121 | −0.402773 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.42419 | 0.236799 | ||||||||
\(737\) | 2.02953 | + | 3.51524i | 0.0747586 | + | 0.129486i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.59353 | + | 7.95623i | −0.168976 | + | 0.292675i | −0.938060 | − | 0.346473i | \(-0.887379\pi\) |
0.769084 | + | 0.639147i | \(0.220713\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −20.3152 | + | 3.08485i | −0.745795 | + | 0.113248i | ||||
\(743\) | 28.5353 | 1.04686 | 0.523430 | − | 0.852069i | \(-0.324652\pi\) | ||||
0.523430 | + | 0.852069i | \(0.324652\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 19.4924 | + | 11.2539i | 0.713667 | + | 0.412036i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.81657 | −0.0664203 | ||||||||
\(749\) | 3.51234 | + | 4.39442i | 0.128338 | + | 0.160569i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.4749 | + | 37.1956i | 0.783629 | + | 1.35729i | 0.929814 | + | 0.368029i | \(0.119967\pi\) |
−0.146185 | + | 0.989257i | \(0.546700\pi\) | |||||||
\(752\) | −5.66749 | − | 3.27213i | −0.206672 | − | 0.119322i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 21.1043 | − | 12.1846i | 0.768574 | − | 0.443736i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.4415i | 0.706612i | 0.935508 | + | 0.353306i | \(0.114943\pi\) | ||||
−0.935508 | + | 0.353306i | \(0.885057\pi\) | |||||||
\(758\) | −1.62954 | − | 2.82245i | −0.0591877 | − | 0.102516i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.9154 | + | 43.1547i | 0.903182 | + | 1.56436i | 0.823339 | + | 0.567550i | \(0.192109\pi\) |
0.0798434 | + | 0.996807i | \(0.474558\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.61827 | − | 19.4739i | 0.275800 | − | 0.705003i | ||||
\(764\) | − | 8.10892i | − | 0.293371i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.0013 | + | 8.66098i | 0.542017 | + | 0.312934i | ||||
\(767\) | −8.37575 | + | 14.5072i | −0.302431 | + | 0.523825i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.5025i | 1.06389i | 0.846779 | + | 0.531944i | \(0.178538\pi\) | ||||
−0.846779 | + | 0.531944i | \(0.821462\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.4356 | + | 6.02502i | −0.375587 | + | 0.216845i | ||||
\(773\) | 21.9349 | + | 12.6641i | 0.788945 | + | 0.455498i | 0.839591 | − | 0.543219i | \(-0.182795\pi\) |
−0.0506458 | + | 0.998717i | \(0.516128\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.05174 | 0.324938 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 31.6982i | − | 1.13644i | ||||||
\(779\) | 6.95465 | − | 4.01527i | 0.249176 | − | 0.143862i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.57509 | − | 4.46019i | 0.0921440 | − | 0.159598i | ||||
\(782\) | −20.3616 | + | 11.7558i | −0.728129 | + | 0.420385i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.14181 | − | 4.74992i | −0.183636 | − | 0.169640i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.40220 | − | 5.89278i | 0.121275 | − | 0.210055i | −0.798996 | − | 0.601337i | \(-0.794635\pi\) |
0.920271 | + | 0.391282i | \(0.127968\pi\) | |||||||
\(788\) | −6.37315 | + | 11.0386i | −0.227034 | + | 0.393235i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.1655 | + | 4.88430i | −1.14367 | + | 0.173666i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.89931 | + | 5.13802i | −0.316024 | + | 0.182456i | ||||
\(794\) | 16.7561 | − | 29.0224i | 0.594651 | − | 1.02997i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.4954 | − | 9.52361i | 0.584663 | − | 0.337556i | ||||
\(797\) | − | 31.6373i | − | 1.12065i | −0.828272 | − | 0.560326i | \(-0.810676\pi\) | ||
0.828272 | − | 0.560326i | \(-0.189324\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.9509 | 0.847323 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 31.0404 | + | 17.9212i | 1.09607 | + | 0.632818i | ||||
\(803\) | −5.61698 | + | 3.24297i | −0.198219 | + | 0.114442i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 21.8892i | − | 0.771013i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.50180 | − | 2.60119i | 0.0528330 | − | 0.0915094i | ||||
\(809\) | −22.9302 | − | 13.2388i | −0.806183 | − | 0.465450i | 0.0394457 | − | 0.999222i | \(-0.487441\pi\) |
−0.845629 | + | 0.533772i | \(0.820774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.4799i | 0.894720i | 0.894354 | + | 0.447360i | \(0.147636\pi\) | ||||
−0.894354 | + | 0.447360i | \(0.852364\pi\) | |||||||
\(812\) | 21.8786 | + | 8.55899i | 0.767788 | + | 0.300362i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.568545 | + | 0.984749i | 0.0199275 | + | 0.0345154i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.01093 | − | 6.94713i | −0.140325 | − | 0.243049i | ||||
\(818\) | − | 24.6499i | − | 0.861863i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.9335 | + | 19.0141i | −1.14939 | + | 0.663598i | −0.948738 | − | 0.316065i | \(-0.897638\pi\) |
−0.200649 | + | 0.979663i | \(0.564305\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.09676 | + | 1.78791i | 0.107946 | + | 0.0623228i | 0.553001 | − | 0.833181i | \(-0.313483\pi\) |
−0.445055 | + | 0.895503i | \(0.646816\pi\) | |||||||
\(824\) | 7.18752 | + | 12.4491i | 0.250389 | + | 0.433687i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.9663 | + | 2.42447i | −0.555539 | + | 0.0843582i | ||||
\(827\) | −15.0648 | −0.523855 | −0.261927 | − | 0.965088i | \(-0.584358\pi\) | ||||
−0.261927 | + | 0.965088i | \(0.584358\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.5046 | + | 15.8798i | 0.955273 | + | 0.551527i | 0.894715 | − | 0.446637i | \(-0.147379\pi\) |
0.0605582 | + | 0.998165i | \(0.480712\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.74440 | −0.0951450 | ||||||||
\(833\) | 24.9890 | + | 5.64586i | 0.865819 | + | 0.195617i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.894453 | − | 1.54924i | 0.0309353 | − | 0.0535815i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.32868 | + | 9.22954i | 0.184076 | + | 0.318829i | ||||
\(839\) | −15.1305 | −0.522362 | −0.261181 | − | 0.965290i | \(-0.584112\pi\) | ||||
−0.261181 | + | 0.965290i | \(0.584112\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −49.8470 | −1.71886 | ||||||||
\(842\) | −11.3407 | − | 19.6427i | −0.390828 | − | 0.676933i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.46028 | − | 7.72544i | 0.153529 | − | 0.265920i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.7636 | − | 22.2247i | −0.610365 | − | 0.763651i | ||||
\(848\) | −7.76645 | −0.266701 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.7454 | + | 7.35858i | 0.436908 | + | 0.252249i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.1586 | −0.416302 | −0.208151 | − | 0.978097i | \(-0.566745\pi\) | ||||
−0.208151 | + | 0.978097i | \(0.566745\pi\) | |||||||
\(854\) | −9.22581 | − | 3.60917i | −0.315701 | − | 0.123503i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.06314 | + | 1.84141i | 0.0363374 | + | 0.0629382i | ||||
\(857\) | 27.1356 | + | 15.6668i | 0.926936 | + | 0.535167i | 0.885841 | − | 0.463989i | \(-0.153582\pi\) |
0.0410947 | + | 0.999155i | \(0.486915\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.7872 | − | 7.38268i | 0.436293 | − | 0.251894i | −0.265731 | − | 0.964047i | \(-0.585613\pi\) |
0.702024 | + | 0.712153i | \(0.252280\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.0728i | 1.02429i | ||||||||
\(863\) | −7.21398 | − | 12.4950i | −0.245567 | − | 0.425334i | 0.716724 | − | 0.697357i | \(-0.245641\pi\) |
−0.962291 | + | 0.272023i | \(0.912307\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.46016 | − | 12.9214i | −0.253507 | − | 0.439086i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.4840 | − | 13.1752i | 0.559504 | − | 0.447196i | ||||
\(869\) | − | 4.41102i | − | 0.149634i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.4363 | − | 11.2216i | −0.658574 | − | 0.380228i | ||||
\(872\) | 3.95181 | − | 6.84474i | 0.133825 | − | 0.231792i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 23.1535i | − | 0.783179i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.14788 | + | 5.28153i | −0.308902 | + | 0.178345i | −0.646435 | − | 0.762969i | \(-0.723741\pi\) |
0.337533 | + | 0.941314i | \(0.390408\pi\) | |||||||
\(878\) | 11.1126 | + | 6.41586i | 0.375032 | + | 0.216525i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.4300 | 0.452469 | 0.226234 | − | 0.974073i | \(-0.427358\pi\) | ||||
0.226234 | + | 0.974073i | \(0.427358\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.06019i | 0.136636i | 0.997664 | + | 0.0683181i | \(0.0217633\pi\) | ||||
−0.997664 | + | 0.0683181i | \(0.978237\pi\) | |||||||
\(884\) | 8.69843 | − | 5.02204i | 0.292560 | − | 0.168909i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.2071 | + | 17.6792i | −0.342913 | + | 0.593943i | ||||
\(887\) | −28.6095 | + | 16.5177i | −0.960614 | + | 0.554611i | −0.896362 | − | 0.443323i | \(-0.853799\pi\) |
−0.0642519 | + | 0.997934i | \(0.520466\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.299270 | − | 1.97084i | −0.0100372 | − | 0.0660997i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.7721 | − | 20.3899i | 0.394160 | − | 0.682705i | ||||
\(893\) | −11.7931 | + | 20.4262i | −0.394641 | + | 0.683538i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.65187 | − | 2.06672i | −0.0551851 | − | 0.0690442i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.0483 | + | 10.4202i | −0.602280 | + | 0.347727i | ||||
\(899\) | −35.4115 | + | 61.3345i | −1.18104 | + | 2.04562i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.6159 | − | 14.2120i | 0.820074 | − | 0.473470i | ||||
\(902\) | 1.10595i | 0.0368241i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.2968 | −0.408984 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.6700 | − | 13.6659i | −0.785949 | − | 0.453768i | 0.0525853 | − | 0.998616i | \(-0.483254\pi\) |
−0.838535 | + | 0.544848i | \(0.816587\pi\) | |||||||
\(908\) | −8.07522 | + | 4.66223i | −0.267986 | + | 0.154722i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.06838i | 0.0353972i | 0.999843 | + | 0.0176986i | \(0.00563393\pi\) | ||||
−0.999843 | + | 0.0176986i | \(0.994366\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.18899 | − | 2.05939i | 0.0393498 | − | 0.0681558i | ||||
\(914\) | 13.8811 | + | 8.01424i | 0.459145 | + | 0.265087i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 23.2725i | − | 0.768944i | ||||||
\(917\) | 20.9994 | + | 26.2731i | 0.693460 | + | 0.867615i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.8653 | − | 46.5320i | −0.886203 | − | 1.53495i | −0.844329 | − | 0.535826i | \(-0.820000\pi\) |
−0.0418743 | − | 0.999123i | \(-0.513333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.991998 | + | 1.71819i | 0.0326697 | + | 0.0565856i | ||||
\(923\) | 28.4761i | 0.937303i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −31.5222 | + | 18.1994i | −1.03588 | + | 0.598068i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.68995 | + | 4.43979i | 0.252435 | + | 0.145743i | ||||
\(929\) | −4.80716 | − | 8.32625i | −0.157718 | − | 0.273175i | 0.776327 | − | 0.630330i | \(-0.217080\pi\) |
−0.934045 | + | 0.357154i | \(0.883747\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.1192 | + | 18.5316i | −0.561061 | + | 0.607350i | ||||
\(932\) | 12.6203 | 0.413393 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 26.9113 | + | 15.5372i | 0.880563 | + | 0.508394i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.8030 | 0.418256 | 0.209128 | − | 0.977888i | \(-0.432937\pi\) | ||||
0.209128 | + | 0.977888i | \(0.432937\pi\) | |||||||
\(938\) | −3.24823 | − | 21.3912i | −0.106059 | − | 0.698446i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.2221 | − | 41.9538i | 0.789616 | − | 1.36766i | −0.136586 | − | 0.990628i | \(-0.543613\pi\) |
0.926202 | − | 0.377028i | \(-0.123054\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.15707 | + | 12.3964i | 0.233066 | + | 0.403682i | ||||
\(944\) | −6.10388 | −0.198664 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.10476 | 0.0359187 | ||||||||
\(947\) | −18.9980 | − | 32.9055i | −0.617353 | − | 1.06929i | −0.989967 | − | 0.141300i | \(-0.954872\pi\) |
0.372614 | − | 0.927986i | \(-0.378461\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.9308 | − | 31.0571i | 0.582060 | − | 1.00816i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.01756 | + | 3.52771i | 0.292261 | + | 0.114334i | ||||
\(953\) | −15.2394 | −0.493652 | −0.246826 | − | 0.969060i | \(-0.579388\pi\) | ||||
−0.246826 | + | 0.969060i | \(0.579388\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −13.9601 | − | 8.05990i | −0.451503 | − | 0.260676i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 36.4809 | 1.17864 | ||||||||
\(959\) | −4.15902 | + | 10.6313i | −0.134302 | + | 0.343303i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.3078 | + | 28.2459i | 0.526057 | + | 0.911157i | ||||
\(962\) | −5.44483 | − | 3.14357i | −0.175548 | − | 0.101353i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 18.3222 | − | 10.5783i | 0.590119 | − | 0.340705i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.7458i | 0.892244i | 0.894972 | + | 0.446122i | \(0.147195\pi\) | ||||
−0.894972 | + | 0.446122i | \(0.852805\pi\) | |||||||
\(968\) | −5.37682 | − | 9.31292i | −0.172817 | − | 0.299329i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.2730 | + | 17.7934i | 0.329677 | + | 0.571018i | 0.982448 | − | 0.186538i | \(-0.0597268\pi\) |
−0.652771 | + | 0.757556i | \(0.726393\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.0270604 | − | 0.178206i | −0.000867518 | − | 0.00571302i | ||||
\(974\) | 14.1334i | 0.452865i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.24271 | − | 1.87218i | −0.103797 | − | 0.0599270i | ||||
\(977\) | −3.81400 | + | 6.60604i | −0.122021 | + | 0.211346i | −0.920564 | − | 0.390591i | \(-0.872271\pi\) |
0.798544 | + | 0.601937i | \(0.205604\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 0.738160i | − | 0.0235917i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −28.1861 | + | 16.2733i | −0.899456 | + | 0.519301i | ||||
\(983\) | 20.4984 | + | 11.8347i | 0.653797 | + | 0.377470i | 0.789909 | − | 0.613224i | \(-0.210128\pi\) |
−0.136113 | + | 0.990693i | \(0.543461\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −32.4979 | −1.03494 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.89113i | 0.314679i | ||||||||
\(989\) | 12.3830 | − | 7.14933i | 0.393757 | − | 0.227336i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.3947 | + | 23.2003i | −0.425497 | + | 0.736982i | −0.996467 | − | 0.0839887i | \(-0.973234\pi\) |
0.570970 | + | 0.820971i | \(0.306567\pi\) | |||||||
\(992\) | 6.90736 | − | 3.98797i | 0.219309 | − | 0.126618i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −21.4444 | + | 17.1399i | −0.680176 | + | 0.543646i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.1111 | + | 36.5656i | −0.668596 | + | 1.15804i | 0.309700 | + | 0.950834i | \(0.399771\pi\) |
−0.978297 | + | 0.207209i | \(0.933562\pi\) | |||||||
\(998\) | 5.87396 | − | 10.1740i | 0.185937 | − | 0.322053i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3150.2.bp.g.899.11 | 24 | ||
3.2 | odd | 2 | 3150.2.bp.h.899.11 | 24 | |||
5.2 | odd | 4 | 3150.2.bf.e.1151.9 | yes | 24 | ||
5.3 | odd | 4 | 3150.2.bf.d.1151.4 | ✓ | 24 | ||
5.4 | even | 2 | 3150.2.bp.h.899.2 | 24 | |||
7.5 | odd | 6 | inner | 3150.2.bp.g.1349.2 | 24 | ||
15.2 | even | 4 | 3150.2.bf.e.1151.4 | yes | 24 | ||
15.8 | even | 4 | 3150.2.bf.d.1151.9 | yes | 24 | ||
15.14 | odd | 2 | inner | 3150.2.bp.g.899.2 | 24 | ||
21.5 | even | 6 | 3150.2.bp.h.1349.2 | 24 | |||
35.12 | even | 12 | 3150.2.bf.e.1601.4 | yes | 24 | ||
35.19 | odd | 6 | 3150.2.bp.h.1349.11 | 24 | |||
35.33 | even | 12 | 3150.2.bf.d.1601.9 | yes | 24 | ||
105.47 | odd | 12 | 3150.2.bf.e.1601.9 | yes | 24 | ||
105.68 | odd | 12 | 3150.2.bf.d.1601.4 | yes | 24 | ||
105.89 | even | 6 | inner | 3150.2.bp.g.1349.11 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.bf.d.1151.4 | ✓ | 24 | 5.3 | odd | 4 | ||
3150.2.bf.d.1151.9 | yes | 24 | 15.8 | even | 4 | ||
3150.2.bf.d.1601.4 | yes | 24 | 105.68 | odd | 12 | ||
3150.2.bf.d.1601.9 | yes | 24 | 35.33 | even | 12 | ||
3150.2.bf.e.1151.4 | yes | 24 | 15.2 | even | 4 | ||
3150.2.bf.e.1151.9 | yes | 24 | 5.2 | odd | 4 | ||
3150.2.bf.e.1601.4 | yes | 24 | 35.12 | even | 12 | ||
3150.2.bf.e.1601.9 | yes | 24 | 105.47 | odd | 12 | ||
3150.2.bp.g.899.2 | 24 | 15.14 | odd | 2 | inner | ||
3150.2.bp.g.899.11 | 24 | 1.1 | even | 1 | trivial | ||
3150.2.bp.g.1349.2 | 24 | 7.5 | odd | 6 | inner | ||
3150.2.bp.g.1349.11 | 24 | 105.89 | even | 6 | inner | ||
3150.2.bp.h.899.2 | 24 | 5.4 | even | 2 | |||
3150.2.bp.h.899.11 | 24 | 3.2 | odd | 2 | |||
3150.2.bp.h.1349.2 | 24 | 21.5 | even | 6 | |||
3150.2.bp.h.1349.11 | 24 | 35.19 | odd | 6 |