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 | 1349.11 | ||
Character | \(\chi\) | \(=\) | 3150.1349 |
Dual form | 3150.2.bp.h.899.11 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | \(-0.690507\pi\) |
0.433795 | + | 0.901011i | \(0.357174\pi\) | |||||||
\(12\) | 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 | \(-0.813044\pi\) |
0.0636974 | + | 0.997969i | \(0.479711\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.12125 | − | 1.80205i | −0.716064 | − | 0.413420i | 0.0972384 | − | 0.995261i | \(-0.468999\pi\) |
−0.813302 | + | 0.581841i | \(0.802332\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.496352i | 0.105823i | ||||||||
\(23\) | 3.21210 | − | 5.56351i | 0.669768 | − | 1.16007i | −0.308200 | − | 0.951321i | \(-0.599727\pi\) |
0.977969 | − | 0.208751i | \(-0.0669400\pi\) | |||||||
\(24\) | 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 | −0.969216 | − | 0.246211i | \(-0.920814\pi\) |
−0.271383 | + | 0.962472i | \(0.587481\pi\) | |||||||
\(32\) | 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 | 0.327973 | − | 0.944687i | \(-0.393634\pi\) |
−0.654136 | + | 0.756377i | \(0.726968\pi\) | |||||||
\(38\) | −3.12125 | + | 1.80205i | −0.506334 | + | 0.292332i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.22816 | 0.347980 | 0.173990 | − | 0.984747i | \(-0.444334\pi\) | ||||
0.173990 | + | 0.984747i | \(0.444334\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.22575i | − | 0.339424i | −0.985494 | − | 0.169712i | \(-0.945716\pi\) | ||
0.985494 | − | 0.169712i | \(-0.0542838\pi\) | |||||||
\(44\) | 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 | \(-0.491714\pi\) |
−0.852717 | + | 0.522373i | \(0.825047\pi\) | |||||||
\(48\) | 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 | −0.999239 | − | 0.0390085i | \(-0.987580\pi\) |
0.465837 | − | 0.884870i | \(-0.345753\pi\) | |||||||
\(54\) | 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 | \(-0.296729\pi\) |
−0.993395 | + | 0.114742i | \(0.963396\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.24271 | + | 1.87218i | 0.415187 | + | 0.239708i | 0.693016 | − | 0.720922i | \(-0.256282\pi\) |
−0.277829 | + | 0.960630i | \(0.589615\pi\) | |||||||
\(62\) | 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 | −0.000534152 | − | 1.00000i | \(-0.500170\pi\) |
0.865758 | + | 0.500463i | \(0.166837\pi\) | |||||||
\(68\) | 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 | −0.940405 | − | 0.340058i | \(-0.889553\pi\) |
0.175704 | − | 0.984443i | \(-0.443780\pi\) | |||||||
\(74\) | −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 | −1.00000 | 8.52501e-5i | \(-0.999973\pi\) | |
0.500074 | + | 0.865983i | \(0.333306\pi\) | |||||||
\(80\) | 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 | \(-0.808218\pi\) |
0.902741 | + | 0.430184i | \(0.141551\pi\) | |||||||
\(90\) | 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 | \(-0.214412\pi\) |
−0.931019 | + | 0.364972i | \(0.881079\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.18752 | − | 12.4491i | 0.708207 | − | 1.22665i | −0.257314 | − | 0.966328i | \(-0.582838\pi\) |
0.965522 | − | 0.260323i | \(-0.0838291\pi\) | |||||||
\(104\) | 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 | \(-0.866106\pi\) |
0.810050 | + | 0.586360i | \(0.199440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.95181 | + | 6.84474i | 0.378515 | + | 0.655607i | 0.990846 | − | 0.134994i | \(-0.0431015\pi\) |
−0.612331 | + | 0.790601i | \(0.709768\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.65187 | + | 2.06672i | −0.156087 | + | 0.195287i | ||||
\(113\) | 12.2968 | 1.15678 | 0.578391 | − | 0.815760i | \(-0.303681\pi\) | ||||
0.578391 | + | 0.815760i | \(0.303681\pi\) | |||||||
\(114\) | 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 | \(0.0106427\pi\) | ||||
−0.999441 | + | 0.0334287i | \(0.989357\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.35624 | + | 11.0093i | −0.555347 | + | 0.961890i | 0.442529 | + | 0.896754i | \(0.354081\pi\) |
−0.997876 | + | 0.0651355i | \(0.979252\pi\) | |||||||
\(132\) | 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 | \(-0.107659\pi\) |
−0.759028 | + | 0.651058i | \(0.774325\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.0681276i | 0.00577851i | 0.999996 | + | 0.00288926i | \(0.000919680\pi\) | ||||
−0.999996 | + | 0.00288926i | \(0.999080\pi\) | |||||||
\(140\) | 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 | \(-0.573088\pi\) |
−0.957097 | + | 0.289768i | \(0.906422\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.51016 | + | 11.2759i | 0.529789 | + | 0.917622i | 0.999396 | + | 0.0347463i | \(0.0110623\pi\) |
−0.469607 | + | 0.882876i | \(0.655604\pi\) | |||||||
\(152\) | 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 | 0.994110 | + | 0.108374i | \(0.0345645\pi\) |
−0.403200 | + | 0.915112i | \(0.632102\pi\) | |||||||
\(158\) | 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 | −0.122473 | − | 0.992472i | \(-0.539082\pi\) |
−0.920742 | + | 0.390171i | \(0.872416\pi\) | |||||||
\(164\) | −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 | \(-0.491284\pi\) |
−0.852011 | + | 0.523524i | \(0.824617\pi\) | |||||||
\(174\) | 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 | \(-0.644814\pi\) |
0.558229 | + | 0.829687i | \(0.311481\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.6564i | 1.75837i | 0.476481 | + | 0.879185i | \(0.341912\pi\) | ||||
−0.476481 | + | 0.879185i | \(0.658088\pi\) | |||||||
\(182\) | −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 | \(-0.238556\pi\) |
−0.223933 | + | 0.974605i | \(0.571890\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.4356 | − | 6.02502i | 0.751174 | − | 0.433691i | −0.0749438 | − | 0.997188i | \(-0.523878\pi\) |
0.826118 | + | 0.563497i | \(0.190544\pi\) | |||||||
\(194\) | 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 | \(-0.650028\pi\) | ||||
−0.454068 | + | 0.890967i | \(0.650028\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.4954 | + | 9.52361i | −1.16933 | + | 0.675111i | −0.953521 | − | 0.301325i | \(-0.902571\pi\) |
−0.215805 | + | 0.976436i | \(0.569238\pi\) | |||||||
\(200\) | 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 | \(-0.766809\pi\) |
0.207473 | + | 0.978241i | \(0.433476\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.1545 | − | 11.6362i | −1.33185 | − | 0.768944i | −0.346266 | − | 0.938136i | \(-0.612551\pi\) |
−0.985583 | + | 0.169193i | \(0.945884\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.87959i | 0.582973i | ||||||||
\(233\) | 6.31017 | − | 10.9295i | 0.413393 | − | 0.716018i | −0.581865 | − | 0.813285i | \(-0.697677\pi\) |
0.995258 | + | 0.0972676i | \(0.0310103\pi\) | |||||||
\(234\) | 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 | −0.956070 | − | 0.293140i | \(-0.905300\pi\) |
−0.224168 | + | 0.974550i | \(0.571966\pi\) | |||||||
\(242\) | 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 | \(-0.438713\pi\) | ||||
0.191352 | + | 0.981522i | \(0.438713\pi\) | |||||||
\(252\) | 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 | \(-0.222018\pi\) |
−0.173016 | + | 0.984919i | \(0.555351\pi\) | |||||||
\(258\) | 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 | \(-0.153525\pi\) |
−0.844650 | + | 0.535319i | \(0.820191\pi\) | |||||||
\(264\) | 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 | \(-0.172706\pi\) |
−0.875355 | + | 0.483480i | \(0.839373\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.4634 | + | 10.6598i | 1.12157 | + | 0.647539i | 0.941801 | − | 0.336170i | \(-0.109132\pi\) |
0.179769 | + | 0.983709i | \(0.442465\pi\) | |||||||
\(272\) | − | 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 | −0.468797 | − | 0.883306i | \(-0.655312\pi\) |
0.530567 | + | 0.847643i | \(0.321979\pi\) | |||||||
\(278\) | 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 | 0.915354 | + | 0.402650i | \(0.131911\pi\) |
−0.108972 | + | 0.994045i | \(0.534756\pi\) | |||||||
\(284\) | −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 | \(-0.227070\pi\) |
−0.944792 | + | 0.327671i | \(0.893736\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.07282 | − | 10.5184i | 0.343256 | − | 0.594537i | −0.641779 | − | 0.766890i | \(-0.721803\pi\) |
0.985035 | + | 0.172352i | \(0.0551367\pi\) | |||||||
\(314\) | 14.8082 | 0.835673 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.88688 | 0.499926 | ||||||||
\(317\) | 15.3605 | − | 26.6051i | 0.862730 | − | 1.49429i | −0.00655283 | − | 0.999979i | \(-0.502086\pi\) |
0.869283 | − | 0.494314i | \(-0.164581\pi\) | |||||||
\(318\) | 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 | −0.0260166 | − | 0.999662i | \(-0.508282\pi\) |
0.878741 | − | 0.477300i | \(-0.158384\pi\) | |||||||
\(332\) | −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 | \(-0.939691\pi\) | ||
0.982105 | − | 0.188334i | \(-0.0603087\pi\) | |||||||
\(338\) | −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 | \(-0.231135\pi\) |
−0.948900 | + | 0.315578i | \(0.897802\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 12.4552i | − | 0.666714i | −0.942801 | − | 0.333357i | \(-0.891819\pi\) | ||
0.942801 | − | 0.333357i | \(-0.108181\pi\) | |||||||
\(350\) | 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 | \(-0.834821\pi\) |
−0.00467471 | + | 0.999989i | \(0.501488\pi\) | |||||||
\(354\) | 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 | \(-0.0853381\pi\) |
0.252730 | + | 0.967537i | \(0.418671\pi\) | |||||||
\(360\) | 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 | 0.972562 | − | 0.232646i | \(-0.0747382\pi\) |
−0.687758 | + | 0.725940i | \(0.741405\pi\) | |||||||
\(368\) | 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 | −0.0982976 | − | 0.995157i | \(-0.531340\pi\) |
−0.910980 | + | 0.412450i | \(0.864673\pi\) | |||||||
\(374\) | −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 | \(-0.187405\pi\) |
−0.0651064 | + | 0.997878i | \(0.520739\pi\) | |||||||
\(384\) | 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 | \(-0.963742\pi\) |
−0.398326 | + | 0.917244i | \(0.630409\pi\) | |||||||
\(390\) | 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 | −0.0481170 | − | 0.998842i | \(-0.515322\pi\) |
0.889081 | − | 0.457750i | \(-0.151345\pi\) | |||||||
\(398\) | 19.0472i | 0.954751i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.0404 | + | 17.9212i | 1.55008 | + | 0.894940i | 0.998134 | + | 0.0610611i | \(0.0194485\pi\) |
0.551947 | + | 0.833879i | \(0.313885\pi\) | |||||||
\(402\) | 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 | 0.131361 | − | 0.991335i | \(-0.458065\pi\) |
0.924201 | + | 0.381905i | \(0.124732\pi\) | |||||||
\(410\) | 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 | \(-0.416171\pi\) | ||||
0.260323 | + | 0.965522i | \(0.416171\pi\) | |||||||
\(420\) | 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 | \(-0.408839\pi\) |
0.971998 | + | 0.234991i | \(0.0755061\pi\) | |||||||
\(432\) | 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 | 0.210794 | − | 0.977530i | \(-0.432395\pi\) |
−0.741169 | + | 0.671318i | \(0.765728\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 10.0441i | − | 0.477748i | ||||||
\(443\) | 10.2071 | − | 17.6792i | 0.484953 | − | 0.839963i | −0.514898 | − | 0.857252i | \(-0.672170\pi\) |
0.999851 | + | 0.0172887i | \(0.00550344\pi\) | |||||||
\(444\) | 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 | 0.138870 | − | 0.990311i | \(-0.455653\pi\) |
−0.788199 | + | 0.615420i | \(0.788986\pi\) | |||||||
\(458\) | −20.1545 | + | 11.6362i | −0.941760 | + | 0.543725i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.98400 | 0.0924039 | 0.0462020 | − | 0.998932i | \(-0.485288\pi\) | ||||
0.0462020 | + | 0.998932i | \(0.485288\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.3987i | 1.69159i | 0.533506 | + | 0.845796i | \(0.320874\pi\) | ||||
−0.533506 | + | 0.845796i | \(0.679126\pi\) | |||||||
\(464\) | 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 | \(-0.0779439\pi\) |
0.275136 | + | 0.961405i | \(0.411277\pi\) | |||||||
\(468\) | 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 | 0.895305 | + | 0.445453i | \(0.146957\pi\) |
−0.0618788 | + | 0.998084i | \(0.519709\pi\) | |||||||
\(480\) | 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 | −0.750993 | − | 0.660310i | \(-0.770425\pi\) |
0.196349 | + | 0.980534i | \(0.437091\pi\) | |||||||
\(488\) | −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 | −0.704071 | − | 0.710130i | \(-0.748636\pi\) |
0.967026 | + | 0.254679i | \(0.0819697\pi\) | |||||||
\(500\) | 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 | \(-0.916771\pi\) |
0.706876 | + | 0.707338i | \(0.250104\pi\) | |||||||
\(510\) | 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 | 0.982795 | + | 0.184702i | \(0.0591319\pi\) |
−0.331441 | + | 0.943476i | \(0.607535\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.82915 | − | 4.90024i | 0.123710 | − | 0.214272i | −0.797518 | − | 0.603295i | \(-0.793854\pi\) |
0.921228 | + | 0.389023i | \(0.127187\pi\) | |||||||
\(524\) | 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 | −0.183041 | − | 0.983105i | \(-0.558594\pi\) |
0.942915 | − | 0.333035i | \(-0.108073\pi\) | |||||||
\(542\) | 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 | \(0.151872\pi\) | ||||
−0.888321 | + | 0.459223i | \(0.848128\pi\) | |||||||
\(548\) | 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 | 0.886635 | + | 0.462469i | \(0.153036\pi\) |
−0.0428076 | + | 0.999083i | \(0.513630\pi\) | |||||||
\(558\) | 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 | \(-0.736592\pi\) |
0.299266 | + | 0.954170i | \(0.403258\pi\) | |||||||
\(564\) | 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 | \(-0.533920\pi\) |
−0.914293 | + | 0.405053i | \(0.867253\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.7146 | + | 23.7544i | 0.573938 | + | 0.994090i | 0.996156 | + | 0.0875958i | \(0.0279184\pi\) |
−0.422218 | + | 0.906494i | \(0.638748\pi\) | |||||||
\(572\) | −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 | 0.697825 | − | 0.716268i | \(-0.254151\pi\) |
−0.969219 | + | 0.246200i | \(0.920818\pi\) | |||||||
\(578\) | 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 | \(-0.442568\pi\) |
−0.762242 | + | 0.647292i | \(0.775901\pi\) | |||||||
\(594\) | 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 | \(-0.455810\pi\) |
0.926884 | + | 0.375347i | \(0.122476\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.75569i | 0.0716162i | 0.999359 | + | 0.0358081i | \(0.0114005\pi\) | ||||
−0.999359 | + | 0.0358081i | \(0.988599\pi\) | |||||||
\(602\) | −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 | −0.622292 | − | 0.782785i | \(-0.713798\pi\) |
0.989058 | + | 0.147528i | \(0.0471315\pi\) | |||||||
\(608\) | − | 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 | −0.258132 | − | 0.966110i | \(-0.583107\pi\) |
0.707610 | + | 0.706604i | \(0.249774\pi\) | |||||||
\(614\) | 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 | \(-0.770956\pi\) | ||||
−0.752094 | + | 0.659055i | \(0.770956\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.7213 | + | 13.6955i | −0.953439 | + | 0.550468i | −0.894147 | − | 0.447773i | \(-0.852217\pi\) |
−0.0592911 | + | 0.998241i | \(0.518884\pi\) | |||||||
\(620\) | 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 | \(-0.891574\pi\) |
−0.181951 | + | 0.983308i | \(0.558241\pi\) | |||||||
\(642\) | 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 | \(-0.633482\pi\) |
0.587408 | + | 0.809291i | \(0.300148\pi\) | |||||||
\(648\) | 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 | −0.320956 | + | 0.947094i | \(0.604004\pi\) |
−0.659729 | + | 0.751503i | \(0.729329\pi\) | |||||||
\(654\) | 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 | −0.982618 | − | 0.185638i | \(-0.940565\pi\) |
−0.330542 | + | 0.943791i | \(0.607231\pi\) | |||||||
\(662\) | −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 | \(0.316318\pi\) | ||||
−0.545556 | + | 0.838074i | \(0.683682\pi\) | |||||||
\(674\) | −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 | \(-0.628818\pi\) |
−0.992939 | + | 0.118626i | \(0.962151\pi\) | |||||||
\(678\) | 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 | −0.809630 | − | 0.586940i | \(-0.800332\pi\) |
−0.103490 | − | 0.994631i | \(-0.533001\pi\) | |||||||
\(684\) | 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 | 0.977183 | − | 0.212399i | \(-0.0681277\pi\) |
0.304648 | + | 0.952465i | \(0.401461\pi\) | |||||||
\(692\) | 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 | −0.668331 | − | 0.743864i | \(-0.732991\pi\) |
0.978371 | + | 0.206860i | \(0.0663244\pi\) | |||||||
\(710\) | 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 | −0.0476171 | − | 0.998866i | \(-0.515163\pi\) |
0.888852 | − | 0.458195i | \(-0.151504\pi\) | |||||||
\(720\) | 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 | −0.00632839 | − | 0.999980i | \(-0.502014\pi\) |
0.869172 | − | 0.494509i | \(-0.164652\pi\) | |||||||
\(734\) | 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 | 0.769084 | − | 0.639147i | \(-0.220713\pi\) |
−0.938060 | + | 0.346473i | \(0.887379\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −20.3152 | − | 3.08485i | −0.745795 | − | 0.113248i | ||||
\(743\) | −28.5353 | −1.04686 | −0.523430 | − | 0.852069i | \(-0.675348\pi\) | ||||
−0.523430 | + | 0.852069i | \(0.675348\pi\) | |||||||
\(744\) | 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 | −0.146185 | − | 0.989257i | \(-0.546700\pi\) |
0.929814 | − | 0.368029i | \(-0.119967\pi\) | |||||||
\(752\) | 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 | \(-0.885057\pi\) | ||
0.935508 | − | 0.353306i | \(-0.114943\pi\) | |||||||
\(758\) | 1.62954 | − | 2.82245i | 0.0591877 | − | 0.102516i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.9154 | + | 43.1547i | −0.903182 | + | 1.56436i | −0.0798434 | + | 0.996807i | \(0.525442\pi\) |
−0.823339 | + | 0.567550i | \(0.807891\pi\) | |||||||
\(762\) | 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 | \(-0.821462\pi\) | ||
0.846779 | − | 0.531944i | \(-0.178538\pi\) | |||||||
\(770\) | 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 | \(-0.817205\pi\) |
0.0506458 | + | 0.998717i | \(0.483872\pi\) | |||||||
\(774\) | 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 | 0.920271 | − | 0.391282i | \(-0.127968\pi\) |
−0.798996 | + | 0.601337i | \(0.794635\pi\) | |||||||
\(788\) | 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 | \(-0.512559\pi\) |
0.845629 | + | 0.533772i | \(0.179226\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 25.4799i | − | 0.894720i | −0.894354 | − | 0.447360i | \(-0.852364\pi\) | ||
0.894354 | − | 0.447360i | \(-0.147636\pi\) | |||||||
\(812\) | −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 | \(-0.102362\pi\) |
0.200649 | + | 0.979663i | \(0.435695\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.09676 | − | 1.78791i | 0.107946 | − | 0.0623228i | −0.445055 | − | 0.895503i | \(-0.646816\pi\) |
0.553001 | + | 0.833181i | \(0.313483\pi\) | |||||||
\(824\) | −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 | \(-0.415642\pi\) | ||||
0.261927 | + | 0.965088i | \(0.415642\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.5046 | − | 15.8798i | 0.955273 | − | 0.551527i | 0.0605582 | − | 0.998165i | \(-0.480712\pi\) |
0.894715 | + | 0.446637i | \(0.147379\pi\) | |||||||
\(830\) | 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 | \(-0.415888\pi\) | ||||
0.261181 | + | 0.965290i | \(0.415888\pi\) | |||||||
\(840\) | 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 | \(-0.846418\pi\) |
−0.0410947 | + | 0.999155i | \(0.513085\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.7872 | + | 7.38268i | 0.436293 | + | 0.251894i | 0.702024 | − | 0.712153i | \(-0.252280\pi\) |
−0.265731 | + | 0.964047i | \(0.585613\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 30.0728i | − | 1.02429i | ||||||
\(863\) | 7.21398 | − | 12.4950i | 0.245567 | − | 0.425334i | −0.716724 | − | 0.697357i | \(-0.754359\pi\) |
0.962291 | + | 0.272023i | \(0.0876926\pi\) | |||||||
\(864\) | 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 | 0.337533 | − | 0.941314i | \(-0.390408\pi\) |
−0.646435 | + | 0.762969i | \(0.723741\pi\) | |||||||
\(878\) | −11.1126 | + | 6.41586i | −0.375032 | + | 0.216525i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.4300 | −0.452469 | −0.226234 | − | 0.974073i | \(-0.572642\pi\) | ||||
−0.226234 | + | 0.974073i | \(0.572642\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 4.06019i | − | 0.136636i | −0.997664 | − | 0.0683181i | \(-0.978237\pi\) | ||
0.997664 | − | 0.0683181i | \(-0.0217633\pi\) | |||||||
\(884\) | −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 | \(-0.146201\pi\) |
0.0642519 | + | 0.997934i | \(0.479534\pi\) | |||||||
\(888\) | 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 | −0.838535 | − | 0.544848i | \(-0.816587\pi\) |
0.0525853 | + | 0.998616i | \(0.483254\pi\) | |||||||
\(908\) | 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 | −0.0418743 | + | 0.999123i | \(0.513333\pi\) |
−0.844329 | + | 0.535826i | \(0.820000\pi\) | |||||||
\(920\) | 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 | \(-0.782920\pi\) |
0.934045 | + | 0.357154i | \(0.116253\pi\) | |||||||
\(930\) | 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 | −0.926202 | − | 0.377028i | \(-0.876946\pi\) |
0.136586 | − | 0.990628i | \(-0.456387\pi\) | |||||||
\(942\) | 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 | −0.372614 | − | 0.927986i | \(-0.621539\pi\) |
0.989967 | − | 0.141300i | \(-0.0451281\pi\) | |||||||
\(948\) | 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 | \(-0.420612\pi\) | ||||
0.246826 | + | 0.969060i | \(0.420612\pi\) | |||||||
\(954\) | 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 | \(-0.852805\pi\) | ||
0.894972 | − | 0.446122i | \(-0.147195\pi\) | |||||||
\(968\) | 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 | \(-0.940273\pi\) |
0.652771 | + | 0.757556i | \(0.273607\pi\) | |||||||
\(972\) | 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 | \(-0.127729\pi\) |
−0.798544 | + | 0.601937i | \(0.794396\pi\) | |||||||
\(978\) | 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 | \(-0.789872\pi\) |
0.136113 | + | 0.990693i | \(0.456539\pi\) | |||||||
\(984\) | 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 | 0.570970 | − | 0.820971i | \(-0.306567\pi\) |
−0.996467 | + | 0.0839887i | \(0.973234\pi\) | |||||||
\(992\) | −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 | −0.978297 | − | 0.207209i | \(-0.933562\pi\) |
0.309700 | − | 0.950834i | \(-0.399771\pi\) | |||||||
\(998\) | −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.h.1349.11 | 24 | ||
3.2 | odd | 2 | 3150.2.bp.g.1349.11 | 24 | |||
5.2 | odd | 4 | 3150.2.bf.d.1601.9 | yes | 24 | ||
5.3 | odd | 4 | 3150.2.bf.e.1601.4 | yes | 24 | ||
5.4 | even | 2 | 3150.2.bp.g.1349.2 | 24 | |||
7.3 | odd | 6 | inner | 3150.2.bp.h.899.2 | 24 | ||
15.2 | even | 4 | 3150.2.bf.d.1601.4 | yes | 24 | ||
15.8 | even | 4 | 3150.2.bf.e.1601.9 | yes | 24 | ||
15.14 | odd | 2 | inner | 3150.2.bp.h.1349.2 | 24 | ||
21.17 | even | 6 | 3150.2.bp.g.899.2 | 24 | |||
35.3 | even | 12 | 3150.2.bf.e.1151.9 | yes | 24 | ||
35.17 | even | 12 | 3150.2.bf.d.1151.4 | ✓ | 24 | ||
35.24 | odd | 6 | 3150.2.bp.g.899.11 | 24 | |||
105.17 | odd | 12 | 3150.2.bf.d.1151.9 | yes | 24 | ||
105.38 | odd | 12 | 3150.2.bf.e.1151.4 | yes | 24 | ||
105.59 | even | 6 | inner | 3150.2.bp.h.899.11 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.bf.d.1151.4 | ✓ | 24 | 35.17 | even | 12 | ||
3150.2.bf.d.1151.9 | yes | 24 | 105.17 | odd | 12 | ||
3150.2.bf.d.1601.4 | yes | 24 | 15.2 | even | 4 | ||
3150.2.bf.d.1601.9 | yes | 24 | 5.2 | odd | 4 | ||
3150.2.bf.e.1151.4 | yes | 24 | 105.38 | odd | 12 | ||
3150.2.bf.e.1151.9 | yes | 24 | 35.3 | even | 12 | ||
3150.2.bf.e.1601.4 | yes | 24 | 5.3 | odd | 4 | ||
3150.2.bf.e.1601.9 | yes | 24 | 15.8 | even | 4 | ||
3150.2.bp.g.899.2 | 24 | 21.17 | even | 6 | |||
3150.2.bp.g.899.11 | 24 | 35.24 | odd | 6 | |||
3150.2.bp.g.1349.2 | 24 | 5.4 | even | 2 | |||
3150.2.bp.g.1349.11 | 24 | 3.2 | odd | 2 | |||
3150.2.bp.h.899.2 | 24 | 7.3 | odd | 6 | inner | ||
3150.2.bp.h.899.11 | 24 | 105.59 | even | 6 | inner | ||
3150.2.bp.h.1349.2 | 24 | 15.14 | odd | 2 | inner | ||
3150.2.bp.h.1349.11 | 24 | 1.1 | even | 1 | trivial |