Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(323,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.j (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.22 | ||
Character | \(\chi\) | \(=\) | 1512.323 |
Dual form | 1512.2.j.c.323.21 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.971008 | + | 1.02818i | 0.686606 | + | 0.727030i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.114288 | + | 1.99673i | −0.0571440 | + | 0.998366i | ||||
\(5\) | 2.21305 | 0.989704 | 0.494852 | − | 0.868977i | \(-0.335222\pi\) | ||||
0.494852 | + | 0.868977i | \(0.335222\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | −2.16396 | + | 1.82133i | −0.765077 | + | 0.643939i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.14889 | + | 2.27540i | 0.679537 | + | 0.719544i | ||||
\(11\) | 2.42373i | 0.730781i | 0.930854 | + | 0.365390i | \(0.119065\pi\) | ||||
−0.930854 | + | 0.365390i | \(0.880935\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.11593i | 0.309504i | 0.987953 | + | 0.154752i | \(0.0494579\pi\) | ||||
−0.987953 | + | 0.154752i | \(0.950542\pi\) | |||||||
\(14\) | −1.02818 | + | 0.971008i | −0.274791 | + | 0.259513i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.97388 | − | 0.456405i | −0.993469 | − | 0.114101i | ||||
\(17\) | 0.701326i | 0.170097i | 0.996377 | + | 0.0850483i | \(0.0271044\pi\) | ||||
−0.996377 | + | 0.0850483i | \(0.972896\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.938340 | 0.215270 | 0.107635 | − | 0.994190i | \(-0.465672\pi\) | ||||
0.107635 | + | 0.994190i | \(0.465672\pi\) | |||||||
\(20\) | −0.252925 | + | 4.41886i | −0.0565557 | + | 0.988087i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.49201 | + | 2.35346i | −0.531299 | + | 0.501759i | ||||
\(23\) | 4.30502 | 0.897658 | 0.448829 | − | 0.893618i | \(-0.351841\pi\) | ||||
0.448829 | + | 0.893618i | \(0.351841\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.102426 | −0.0204852 | ||||||||
\(26\) | −1.14737 | + | 1.08358i | −0.225019 | + | 0.212508i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.99673 | − | 0.114288i | −0.377347 | − | 0.0215984i | ||||
\(29\) | −4.26130 | −0.791303 | −0.395652 | − | 0.918401i | \(-0.629481\pi\) | ||||
−0.395652 | + | 0.918401i | \(0.629481\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.02221i | 1.26123i | 0.776098 | + | 0.630613i | \(0.217196\pi\) | ||||
−0.776098 | + | 0.630613i | \(0.782804\pi\) | |||||||
\(32\) | −3.38940 | − | 4.52901i | −0.599167 | − | 0.800624i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.721086 | + | 0.680993i | −0.123665 | + | 0.116789i | ||||
\(35\) | 2.21305i | 0.374073i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.12583i | − | 0.513883i | −0.966427 | − | 0.256941i | \(-0.917285\pi\) | ||
0.966427 | − | 0.256941i | \(-0.0827148\pi\) | |||||||
\(38\) | 0.911135 | + | 0.964777i | 0.147806 | + | 0.156508i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.78895 | + | 4.03070i | −0.757200 | + | 0.637309i | ||||
\(41\) | 0.157922i | 0.0246632i | 0.999924 | + | 0.0123316i | \(0.00392537\pi\) | ||||
−0.999924 | + | 0.0123316i | \(0.996075\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.08975 | 1.08118 | 0.540588 | − | 0.841287i | \(-0.318202\pi\) | ||||
0.540588 | + | 0.841287i | \(0.318202\pi\) | |||||||
\(44\) | −4.83953 | − | 0.277003i | −0.729587 | − | 0.0417597i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.18020 | + | 4.42631i | 0.616337 | + | 0.652624i | ||||
\(47\) | −0.867970 | −0.126607 | −0.0633033 | − | 0.997994i | \(-0.520164\pi\) | ||||
−0.0633033 | + | 0.997994i | \(0.520164\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −0.0994564 | − | 0.105312i | −0.0140653 | − | 0.0148933i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.22822 | − | 0.127538i | −0.308998 | − | 0.0176863i | ||||
\(53\) | −3.91444 | −0.537689 | −0.268845 | − | 0.963184i | \(-0.586642\pi\) | ||||
−0.268845 | + | 0.963184i | \(0.586642\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.36382i | 0.723257i | ||||||||
\(56\) | −1.82133 | − | 2.16396i | −0.243386 | − | 0.289172i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.13775 | − | 4.38136i | −0.543314 | − | 0.575301i | ||||
\(59\) | 7.28820i | 0.948843i | 0.880298 | + | 0.474421i | \(0.157343\pi\) | ||||
−0.880298 | + | 0.474421i | \(0.842657\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.57877i | − | 0.586251i | −0.956074 | − | 0.293126i | \(-0.905305\pi\) | ||
0.956074 | − | 0.293126i | \(-0.0946955\pi\) | |||||||
\(62\) | −7.22006 | + | 6.81862i | −0.916948 | + | 0.865965i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.36548 | − | 7.88260i | 0.170686 | − | 0.985326i | ||||
\(65\) | 2.46961i | 0.306318i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.1677 | 1.85303 | 0.926513 | − | 0.376264i | \(-0.122791\pi\) | ||||
0.926513 | + | 0.376264i | \(0.122791\pi\) | |||||||
\(68\) | −1.40036 | − | 0.0801531i | −0.169819 | − | 0.00971999i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.27540 | + | 2.14889i | −0.271962 | + | 0.256841i | ||||
\(71\) | −6.93451 | −0.822975 | −0.411487 | − | 0.911416i | \(-0.634991\pi\) | ||||
−0.411487 | + | 0.911416i | \(0.634991\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.02133 | 0.821785 | 0.410893 | − | 0.911684i | \(-0.365217\pi\) | ||||
0.410893 | + | 0.911684i | \(0.365217\pi\) | |||||||
\(74\) | 3.21390 | − | 3.03520i | 0.373608 | − | 0.352835i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.107241 | + | 1.87361i | −0.0123014 | + | 0.214918i | ||||
\(77\) | −2.42373 | −0.276209 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.65903i | − | 0.749200i | −0.927187 | − | 0.374600i | \(-0.877780\pi\) | ||
0.927187 | − | 0.374600i | \(-0.122220\pi\) | |||||||
\(80\) | −8.79437 | − | 1.01005i | −0.983241 | − | 0.112926i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.162371 | + | 0.153343i | −0.0179309 | + | 0.0169339i | ||||
\(83\) | 8.41084i | 0.923210i | 0.887086 | + | 0.461605i | \(0.152726\pi\) | ||||
−0.887086 | + | 0.461605i | \(0.847274\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.55207i | 0.168345i | ||||||||
\(86\) | 6.88420 | + | 7.28950i | 0.742342 | + | 0.786047i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.41441 | − | 5.24486i | −0.470578 | − | 0.559104i | ||||
\(89\) | − | 7.34335i | − | 0.778393i | −0.921155 | − | 0.389197i | \(-0.872753\pi\) | ||
0.921155 | − | 0.389197i | \(-0.127247\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.11593 | −0.116982 | ||||||||
\(92\) | −0.492011 | + | 8.59596i | −0.0512957 | + | 0.896191i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.842806 | − | 0.892426i | −0.0869288 | − | 0.0920467i | ||||
\(95\) | 2.07659 | 0.213054 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.99425 | 0.811693 | 0.405846 | − | 0.913941i | \(-0.366977\pi\) | ||||
0.405846 | + | 0.913941i | \(0.366977\pi\) | |||||||
\(98\) | −0.971008 | − | 1.02818i | −0.0980866 | − | 0.103861i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.0117061 | − | 0.204517i | 0.00117061 | − | 0.0204517i | ||||
\(101\) | −15.6519 | −1.55742 | −0.778709 | − | 0.627385i | \(-0.784125\pi\) | ||||
−0.778709 | + | 0.627385i | \(0.784125\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.90314i | 0.483121i | 0.970386 | + | 0.241560i | \(0.0776592\pi\) | ||||
−0.970386 | + | 0.241560i | \(0.922341\pi\) | |||||||
\(104\) | −2.03249 | − | 2.41484i | −0.199302 | − | 0.236795i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.80095 | − | 4.02473i | −0.369181 | − | 0.390916i | ||||
\(107\) | 15.1434i | 1.46397i | 0.681320 | + | 0.731986i | \(0.261406\pi\) | ||||
−0.681320 | + | 0.731986i | \(0.738594\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.72939i | 0.261428i | 0.991420 | + | 0.130714i | \(0.0417270\pi\) | ||||
−0.991420 | + | 0.130714i | \(0.958273\pi\) | |||||||
\(110\) | −5.51494 | + | 5.20831i | −0.525829 | + | 0.496593i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.456405 | − | 3.97388i | 0.0431262 | − | 0.375496i | ||||
\(113\) | − | 2.84331i | − | 0.267476i | −0.991017 | − | 0.133738i | \(-0.957302\pi\) | ||
0.991017 | − | 0.133738i | \(-0.0426980\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.52720 | 0.888416 | ||||||||
\(116\) | 0.487015 | − | 8.50867i | 0.0452182 | − | 0.790010i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.49355 | + | 7.07690i | −0.689837 | + | 0.651481i | ||||
\(119\) | −0.701326 | −0.0642905 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.12555 | 0.465959 | ||||||||
\(122\) | 4.70778 | − | 4.44602i | 0.426222 | − | 0.402524i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −14.0215 | − | 0.802554i | −1.25916 | − | 0.0720715i | ||||
\(125\) | −11.2919 | −1.00998 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.4243i | − | 0.925006i | −0.886618 | − | 0.462503i | \(-0.846951\pi\) | ||
0.886618 | − | 0.462503i | \(-0.153049\pi\) | |||||||
\(128\) | 9.43059 | − | 6.25011i | 0.833555 | − | 0.552437i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.53919 | + | 2.39801i | −0.222702 | + | 0.210320i | ||||
\(131\) | − | 21.3573i | − | 1.86600i | −0.359881 | − | 0.932998i | \(-0.617183\pi\) | ||
0.359881 | − | 0.932998i | \(-0.382817\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.938340i | 0.0813644i | ||||||||
\(134\) | 14.7279 | + | 15.5950i | 1.27230 | + | 1.34720i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.27735 | − | 1.51764i | −0.109532 | − | 0.130137i | ||||
\(137\) | − | 11.2577i | − | 0.961812i | −0.876772 | − | 0.480906i | \(-0.840308\pi\) | ||
0.876772 | − | 0.480906i | \(-0.159692\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.11586 | 0.688379 | 0.344189 | − | 0.938900i | \(-0.388154\pi\) | ||||
0.344189 | + | 0.938900i | \(0.388154\pi\) | |||||||
\(140\) | −4.41886 | − | 0.252925i | −0.373462 | − | 0.0213760i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.73346 | − | 7.12989i | −0.565059 | − | 0.598327i | ||||
\(143\) | −2.70472 | −0.226180 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.43045 | −0.783156 | ||||||||
\(146\) | 6.81777 | + | 7.21916i | 0.564243 | + | 0.597462i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.24144 | + | 0.357245i | 0.513043 | + | 0.0293653i | ||||
\(149\) | 4.90580 | 0.401899 | 0.200949 | − | 0.979602i | \(-0.435597\pi\) | ||||
0.200949 | + | 0.979602i | \(0.435597\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 18.9521i | − | 1.54230i | −0.636654 | − | 0.771150i | \(-0.719682\pi\) | ||
0.636654 | − | 0.771150i | \(-0.280318\pi\) | |||||||
\(152\) | −2.03053 | + | 1.70903i | −0.164698 | + | 0.138621i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.35346 | − | 2.49201i | −0.189647 | − | 0.200812i | ||||
\(155\) | 15.5405i | 1.24824i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.0907i | − | 0.805326i | −0.915348 | − | 0.402663i | \(-0.868085\pi\) | ||
0.915348 | − | 0.402663i | \(-0.131915\pi\) | |||||||
\(158\) | 6.84665 | − | 6.46597i | 0.544690 | − | 0.514405i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.50090 | − | 10.0229i | −0.592998 | − | 0.792381i | ||||
\(161\) | 4.30502i | 0.339283i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.9762 | −1.56466 | −0.782330 | − | 0.622864i | \(-0.785969\pi\) | ||||
−0.782330 | + | 0.622864i | \(0.785969\pi\) | |||||||
\(164\) | −0.315327 | − | 0.0180485i | −0.0246229 | − | 0.00140935i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.64782 | + | 8.16699i | −0.671201 | + | 0.633881i | ||||
\(167\) | 13.8623 | 1.07270 | 0.536348 | − | 0.843997i | \(-0.319803\pi\) | ||||
0.536348 | + | 0.843997i | \(0.319803\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.7547 | 0.904207 | ||||||||
\(170\) | −1.59580 | + | 1.50707i | −0.122392 | + | 0.115587i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.810273 | + | 14.1563i | −0.0617827 | + | 1.07941i | ||||
\(173\) | −21.4796 | −1.63306 | −0.816531 | − | 0.577301i | \(-0.804106\pi\) | ||||
−0.816531 | + | 0.577301i | \(0.804106\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 0.102426i | − | 0.00774268i | ||||||
\(176\) | 1.10620 | − | 9.63159i | 0.0833830 | − | 0.726008i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.55025 | − | 7.13045i | 0.565915 | − | 0.534450i | ||||
\(179\) | 3.94291i | 0.294707i | 0.989084 | + | 0.147354i | \(0.0470755\pi\) | ||||
−0.989084 | + | 0.147354i | \(0.952925\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.7849i | 0.875962i | 0.898984 | + | 0.437981i | \(0.144306\pi\) | ||||
−0.898984 | + | 0.437981i | \(0.855694\pi\) | |||||||
\(182\) | −1.08358 | − | 1.14737i | −0.0803203 | − | 0.0850491i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.31590 | + | 7.84087i | −0.686777 | + | 0.578037i | ||||
\(185\) | − | 6.91760i | − | 0.508592i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.69982 | −0.124303 | ||||||||
\(188\) | 0.0991986 | − | 1.73310i | 0.00723480 | − | 0.126400i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.01638 | + | 2.13510i | 0.146284 | + | 0.154896i | ||||
\(191\) | 16.6064 | 1.20160 | 0.600798 | − | 0.799401i | \(-0.294850\pi\) | ||||
0.600798 | + | 0.799401i | \(0.294850\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.90416 | 0.496972 | 0.248486 | − | 0.968635i | \(-0.420067\pi\) | ||||
0.248486 | + | 0.968635i | \(0.420067\pi\) | |||||||
\(194\) | 7.76247 | + | 8.21948i | 0.557313 | + | 0.590125i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.114288 | − | 1.99673i | 0.00816343 | − | 0.142624i | ||||
\(197\) | 8.98273 | 0.639993 | 0.319997 | − | 0.947419i | \(-0.396318\pi\) | ||||
0.319997 | + | 0.947419i | \(0.396318\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.4427i | 0.811153i | 0.914061 | + | 0.405577i | \(0.132929\pi\) | ||||
−0.914061 | + | 0.405577i | \(0.867071\pi\) | |||||||
\(200\) | 0.221646 | − | 0.186552i | 0.0156728 | − | 0.0131912i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.1981 | − | 16.0928i | −1.06933 | − | 1.13229i | ||||
\(203\) | − | 4.26130i | − | 0.299085i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.349488i | 0.0244093i | ||||||||
\(206\) | −5.04129 | + | 4.76099i | −0.351243 | + | 0.331714i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.509317 | − | 4.43458i | 0.0353148 | − | 0.307483i | ||||
\(209\) | 2.27428i | 0.157315i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.8035 | 1.63870 | 0.819351 | − | 0.573292i | \(-0.194334\pi\) | ||||
0.819351 | + | 0.573292i | \(0.194334\pi\) | |||||||
\(212\) | 0.447373 | − | 7.81608i | 0.0307257 | − | 0.536811i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −15.5701 | + | 14.7044i | −1.06435 | + | 1.00517i | ||||
\(215\) | 15.6899 | 1.07004 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.02221 | −0.476698 | ||||||||
\(218\) | −2.80629 | + | 2.65026i | −0.190066 | + | 0.179498i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −10.7101 | − | 0.613020i | −0.722075 | − | 0.0413298i | ||||
\(221\) | −0.782633 | −0.0526456 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4.42841i | − | 0.296549i | −0.988946 | − | 0.148274i | \(-0.952628\pi\) | ||
0.988946 | − | 0.148274i | \(-0.0473718\pi\) | |||||||
\(224\) | 4.52901 | − | 3.38940i | 0.302607 | − | 0.226464i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.92342 | − | 2.76087i | 0.194463 | − | 0.183651i | ||||
\(227\) | 6.46751i | 0.429264i | 0.976695 | + | 0.214632i | \(0.0688552\pi\) | ||||
−0.976695 | + | 0.214632i | \(0.931145\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 11.4715i | − | 0.758056i | −0.925385 | − | 0.379028i | \(-0.876258\pi\) | ||
0.925385 | − | 0.379028i | \(-0.123742\pi\) | |||||||
\(230\) | 9.25098 | + | 9.79563i | 0.609992 | + | 0.645905i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.22130 | − | 7.76125i | 0.605408 | − | 0.509551i | ||||
\(233\) | 19.8678i | 1.30158i | 0.759256 | + | 0.650792i | \(0.225563\pi\) | ||||
−0.759256 | + | 0.650792i | \(0.774437\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.92086 | −0.125303 | ||||||||
\(236\) | −14.5526 | − | 0.832953i | −0.947292 | − | 0.0542207i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.680993 | − | 0.721086i | −0.0441422 | − | 0.0467411i | ||||
\(239\) | 10.2210 | 0.661138 | 0.330569 | − | 0.943782i | \(-0.392759\pi\) | ||||
0.330569 | + | 0.943782i | \(0.392759\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.1808 | 1.81529 | 0.907643 | − | 0.419744i | \(-0.137880\pi\) | ||||
0.907643 | + | 0.419744i | \(0.137880\pi\) | |||||||
\(242\) | 4.97695 | + | 5.26997i | 0.319931 | + | 0.338766i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.14258 | + | 0.523298i | 0.585293 | + | 0.0335007i | ||||
\(245\) | −2.21305 | −0.141386 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.04712i | 0.0666269i | ||||||||
\(248\) | −12.7898 | − | 15.1958i | −0.812152 | − | 0.964935i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.9645 | − | 11.6101i | −0.693458 | − | 0.734284i | ||||
\(251\) | 4.62338i | 0.291825i | 0.989297 | + | 0.145913i | \(0.0466118\pi\) | ||||
−0.989297 | + | 0.145913i | \(0.953388\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.4342i | 0.655991i | ||||||||
\(254\) | 10.7180 | − | 10.1221i | 0.672507 | − | 0.635115i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.5834 | + | 3.62739i | 0.973962 | + | 0.226712i | ||||
\(257\) | − | 29.6682i | − | 1.85065i | −0.379174 | − | 0.925326i | \(-0.623792\pi\) | ||
0.379174 | − | 0.925326i | \(-0.376208\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.12583 | 0.194230 | ||||||||
\(260\) | −4.93115 | − | 0.282247i | −0.305817 | − | 0.0175042i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 21.9590 | − | 20.7381i | 1.35663 | − | 1.28120i | ||||
\(263\) | 15.8635 | 0.978185 | 0.489093 | − | 0.872232i | \(-0.337328\pi\) | ||||
0.489093 | + | 0.872232i | \(0.337328\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.66283 | −0.532153 | ||||||||
\(266\) | −0.964777 | + | 0.911135i | −0.0591543 | + | 0.0558653i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.73348 | + | 30.2858i | −0.105889 | + | 1.85000i | ||||
\(269\) | 3.13803 | 0.191329 | 0.0956644 | − | 0.995414i | \(-0.469502\pi\) | ||||
0.0956644 | + | 0.995414i | \(0.469502\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 22.7174i | − | 1.37998i | −0.723817 | − | 0.689992i | \(-0.757614\pi\) | ||
0.723817 | − | 0.689992i | \(-0.242386\pi\) | |||||||
\(272\) | 0.320089 | − | 2.78698i | 0.0194082 | − | 0.168986i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.5749 | − | 10.9313i | 0.699266 | − | 0.660386i | ||||
\(275\) | − | 0.248252i | − | 0.0149702i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 24.8267i | − | 1.49169i | −0.666119 | − | 0.745845i | \(-0.732046\pi\) | ||
0.666119 | − | 0.745845i | \(-0.267954\pi\) | |||||||
\(278\) | 7.88057 | + | 8.34453i | 0.472645 | + | 0.500472i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.03070 | − | 4.78895i | −0.240880 | − | 0.286195i | ||||
\(281\) | − | 30.2207i | − | 1.80282i | −0.432970 | − | 0.901408i | \(-0.642535\pi\) | ||
0.432970 | − | 0.901408i | \(-0.357465\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.9803 | −0.890488 | −0.445244 | − | 0.895409i | \(-0.646883\pi\) | ||||
−0.445244 | + | 0.895409i | \(0.646883\pi\) | |||||||
\(284\) | 0.792531 | − | 13.8464i | 0.0470280 | − | 0.821630i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.62630 | − | 2.78092i | −0.155296 | − | 0.164439i | ||||
\(287\) | −0.157922 | −0.00932182 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.5081 | 0.971067 | ||||||||
\(290\) | −9.15704 | − | 9.69616i | −0.537720 | − | 0.569378i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.802454 | + | 14.0197i | −0.0469601 | + | 0.820442i | ||||
\(293\) | 7.58993 | 0.443408 | 0.221704 | − | 0.975114i | \(-0.428838\pi\) | ||||
0.221704 | + | 0.975114i | \(0.428838\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.1291i | 0.939074i | ||||||||
\(296\) | 5.69318 | + | 6.76418i | 0.330909 | + | 0.393160i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.76357 | + | 5.04402i | 0.275946 | + | 0.292192i | ||||
\(299\) | 4.80411i | 0.277829i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.08975i | 0.408646i | ||||||||
\(302\) | 19.4861 | − | 18.4026i | 1.12130 | − | 1.05895i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.72885 | − | 0.428263i | −0.213864 | − | 0.0245626i | ||||
\(305\) | − | 10.1330i | − | 0.580216i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.1246 | −1.03443 | −0.517214 | − | 0.855856i | \(-0.673031\pi\) | ||||
−0.517214 | + | 0.855856i | \(0.673031\pi\) | |||||||
\(308\) | 0.277003 | − | 4.83953i | 0.0157837 | − | 0.275758i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.9783 | + | 15.0899i | −0.907508 | + | 0.857050i | ||||
\(311\) | −17.0291 | −0.965631 | −0.482816 | − | 0.875722i | \(-0.660386\pi\) | ||||
−0.482816 | + | 0.875722i | \(0.660386\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.44270 | 0.420686 | 0.210343 | − | 0.977628i | \(-0.432542\pi\) | ||||
0.210343 | + | 0.977628i | \(0.432542\pi\) | |||||||
\(314\) | 10.3750 | − | 9.79815i | 0.585496 | − | 0.552942i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.2963 | + | 0.761047i | 0.747975 | + | 0.0428123i | ||||
\(317\) | −2.40549 | −0.135106 | −0.0675528 | − | 0.997716i | \(-0.521519\pi\) | ||||
−0.0675528 | + | 0.997716i | \(0.521519\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 10.3282i | − | 0.578269i | ||||||
\(320\) | 3.02188 | − | 17.4446i | 0.168928 | − | 0.975181i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.42631 | + | 4.18020i | −0.246669 | + | 0.232954i | ||||
\(323\) | 0.658082i | 0.0366167i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 0.114301i | − | 0.00634025i | ||||||
\(326\) | −19.3971 | − | 20.5391i | −1.07431 | − | 1.13755i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.287628 | − | 0.341737i | −0.0158816 | − | 0.0188693i | ||||
\(329\) | − | 0.867970i | − | 0.0478528i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.3776 | 0.790265 | 0.395133 | − | 0.918624i | \(-0.370699\pi\) | ||||
0.395133 | + | 0.918624i | \(0.370699\pi\) | |||||||
\(332\) | −16.7942 | − | 0.961258i | −0.921701 | − | 0.0527559i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.4604 | + | 14.2529i | 0.736520 | + | 0.779882i | ||||
\(335\) | 33.5667 | 1.83395 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.4430 | 1.11360 | 0.556800 | − | 0.830646i | \(-0.312029\pi\) | ||||
0.556800 | + | 0.830646i | \(0.312029\pi\) | |||||||
\(338\) | 11.4139 | + | 12.0859i | 0.620834 | + | 0.657385i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.09906 | − | 0.177383i | −0.168070 | − | 0.00961992i | ||||
\(341\) | −17.0199 | −0.921679 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −15.3420 | + | 12.9128i | −0.827183 | + | 0.696211i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.8568 | − | 22.0848i | −1.12127 | − | 1.18728i | ||||
\(347\) | 6.62453i | 0.355623i | 0.984065 | + | 0.177812i | \(0.0569018\pi\) | ||||
−0.984065 | + | 0.177812i | \(0.943098\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.7876i | 1.80861i | 0.426889 | + | 0.904304i | \(0.359609\pi\) | ||||
−0.426889 | + | 0.904304i | \(0.640391\pi\) | |||||||
\(350\) | 0.105312 | − | 0.0994564i | 0.00562915 | − | 0.00531617i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.9771 | − | 8.21498i | 0.585081 | − | 0.437860i | ||||
\(353\) | − | 26.5976i | − | 1.41565i | −0.706390 | − | 0.707823i | \(-0.749677\pi\) | ||
0.706390 | − | 0.707823i | \(-0.250323\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.3464 | −0.814501 | ||||||||
\(356\) | 14.6627 | + | 0.839256i | 0.777122 | + | 0.0444805i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.05400 | + | 3.82860i | −0.214261 | + | 0.202348i | ||||
\(359\) | 29.7098 | 1.56802 | 0.784012 | − | 0.620746i | \(-0.213170\pi\) | ||||
0.784012 | + | 0.620746i | \(0.213170\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1195 | −0.953659 | ||||||||
\(362\) | −12.1169 | + | 11.4432i | −0.636850 | + | 0.601441i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.127538 | − | 2.22822i | 0.00668479 | − | 0.116790i | ||||
\(365\) | 15.5385 | 0.813324 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.6932i | 0.819176i | 0.912271 | + | 0.409588i | \(0.134328\pi\) | ||||
−0.912271 | + | 0.409588i | \(0.865672\pi\) | |||||||
\(368\) | −17.1076 | − | 1.96483i | −0.891795 | − | 0.102424i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.11251 | − | 6.71705i | 0.369762 | − | 0.349203i | ||||
\(371\) | − | 3.91444i | − | 0.203227i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0269i | 0.570951i | 0.958386 | + | 0.285475i | \(0.0921515\pi\) | ||||
−0.958386 | + | 0.285475i | \(0.907849\pi\) | |||||||
\(374\) | −1.65054 | − | 1.74771i | −0.0853474 | − | 0.0903722i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.87826 | − | 1.58086i | 0.0968637 | − | 0.0815268i | ||||
\(377\) | − | 4.75533i | − | 0.244912i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.84736 | −0.403092 | −0.201546 | − | 0.979479i | \(-0.564597\pi\) | ||||
−0.201546 | + | 0.979479i | \(0.564597\pi\) | |||||||
\(380\) | −0.237329 | + | 4.14639i | −0.0121747 | + | 0.212705i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.1249 | + | 17.0743i | 0.825023 | + | 0.873596i | ||||
\(383\) | −3.26238 | −0.166700 | −0.0833500 | − | 0.996520i | \(-0.526562\pi\) | ||||
−0.0833500 | + | 0.996520i | \(0.526562\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.36382 | −0.273365 | ||||||||
\(386\) | 6.70399 | + | 7.09868i | 0.341224 | + | 0.361313i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.913646 | + | 15.9624i | −0.0463833 | + | 0.810366i | ||||
\(389\) | −1.15697 | −0.0586609 | −0.0293304 | − | 0.999570i | \(-0.509338\pi\) | ||||
−0.0293304 | + | 0.999570i | \(0.509338\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.01922i | 0.152688i | ||||||||
\(392\) | 2.16396 | − | 1.82133i | 0.109297 | − | 0.0919913i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.72231 | + | 9.23582i | 0.439423 | + | 0.465294i | ||||
\(395\) | − | 14.7367i | − | 0.741486i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2.41295i | − | 0.121103i | −0.998165 | − | 0.0605513i | \(-0.980714\pi\) | ||
0.998165 | − | 0.0605513i | \(-0.0192859\pi\) | |||||||
\(398\) | −11.7651 | + | 11.1110i | −0.589732 | + | 0.556943i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.407028 | + | 0.0467477i | 0.0203514 | + | 0.00233739i | ||||
\(401\) | 7.48047i | 0.373557i | 0.982402 | + | 0.186778i | \(0.0598047\pi\) | ||||
−0.982402 | + | 0.186778i | \(0.940195\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.83631 | −0.390355 | ||||||||
\(404\) | 1.78882 | − | 31.2526i | 0.0889971 | − | 1.55487i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.38136 | − | 4.13775i | 0.217443 | − | 0.205353i | ||||
\(407\) | 7.57615 | 0.375536 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.49823 | −0.370764 | −0.185382 | − | 0.982667i | \(-0.559352\pi\) | ||||
−0.185382 | + | 0.982667i | \(0.559352\pi\) | |||||||
\(410\) | −0.359335 | + | 0.339355i | −0.0177463 | + | 0.0167596i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.79026 | − | 0.560370i | −0.482331 | − | 0.0276075i | ||||
\(413\) | −7.28820 | −0.358629 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.6136i | 0.913705i | ||||||||
\(416\) | 5.05408 | − | 3.78235i | 0.247797 | − | 0.185445i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.33836 | + | 2.20834i | −0.114373 | + | 0.108014i | ||||
\(419\) | − | 26.7682i | − | 1.30771i | −0.756619 | − | 0.653856i | \(-0.773150\pi\) | ||
0.756619 | − | 0.653856i | \(-0.226850\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.1616i | 1.37251i | 0.727359 | + | 0.686257i | \(0.240747\pi\) | ||||
−0.727359 | + | 0.686257i | \(0.759253\pi\) | |||||||
\(422\) | 23.1134 | + | 24.4742i | 1.12514 | + | 1.19139i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.47070 | − | 7.12950i | 0.411374 | − | 0.346239i | ||||
\(425\) | − | 0.0718340i | − | 0.00348446i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.57877 | 0.221582 | ||||||||
\(428\) | −30.2374 | − | 1.73071i | −1.46158 | − | 0.0836571i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.2350 | + | 16.1320i | 0.734699 | + | 0.777954i | ||||
\(431\) | −29.9359 | −1.44196 | −0.720980 | − | 0.692955i | \(-0.756308\pi\) | ||||
−0.720980 | + | 0.692955i | \(0.756308\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −39.1106 | −1.87954 | −0.939768 | − | 0.341814i | \(-0.888959\pi\) | ||||
−0.939768 | + | 0.341814i | \(0.888959\pi\) | |||||||
\(434\) | −6.81862 | − | 7.22006i | −0.327304 | − | 0.346574i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.44986 | − | 0.311937i | −0.261001 | − | 0.0149391i | ||||
\(437\) | 4.03957 | 0.193239 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.4351i | 1.50031i | 0.661260 | + | 0.750157i | \(0.270022\pi\) | ||||
−0.661260 | + | 0.750157i | \(0.729978\pi\) | |||||||
\(440\) | −9.76930 | − | 11.6071i | −0.465733 | − | 0.553347i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.759943 | − | 0.804684i | −0.0361468 | − | 0.0382749i | ||||
\(443\) | 24.2344i | 1.15141i | 0.817656 | + | 0.575707i | \(0.195273\pi\) | ||||
−0.817656 | + | 0.575707i | \(0.804727\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 16.2512i | − | 0.770379i | ||||||
\(446\) | 4.55318 | − | 4.30002i | 0.215600 | − | 0.203612i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.88260 | + | 1.36548i | 0.372418 | + | 0.0645131i | ||||
\(449\) | − | 22.6066i | − | 1.06687i | −0.845841 | − | 0.533435i | \(-0.820901\pi\) | ||
0.845841 | − | 0.533435i | \(-0.179099\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.382759 | −0.0180234 | ||||||||
\(452\) | 5.67732 | + | 0.324956i | 0.267039 | + | 0.0152846i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.64974 | + | 6.28001i | −0.312088 | + | 0.294735i | ||||
\(455\) | −2.46961 | −0.115777 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.35271 | −0.437502 | −0.218751 | − | 0.975781i | \(-0.570198\pi\) | ||||
−0.218751 | + | 0.975781i | \(0.570198\pi\) | |||||||
\(458\) | 11.7947 | − | 11.1389i | 0.551129 | − | 0.520486i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.08884 | + | 19.0233i | −0.0507676 | + | 0.886964i | ||||
\(461\) | −11.5898 | −0.539789 | −0.269895 | − | 0.962890i | \(-0.586989\pi\) | ||||
−0.269895 | + | 0.962890i | \(0.586989\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 17.8299i | − | 0.828625i | −0.910135 | − | 0.414312i | \(-0.864022\pi\) | ||
0.910135 | − | 0.414312i | \(-0.135978\pi\) | |||||||
\(464\) | 16.9339 | + | 1.94488i | 0.786135 | + | 0.0902887i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.4276 | + | 19.2918i | −0.946290 | + | 0.893676i | ||||
\(467\) | − | 3.50180i | − | 0.162044i | −0.996712 | − | 0.0810221i | \(-0.974182\pi\) | ||
0.996712 | − | 0.0810221i | \(-0.0258184\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.1677i | 0.700378i | ||||||||
\(470\) | −1.86517 | − | 1.97498i | −0.0860338 | − | 0.0910990i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −13.2742 | − | 15.7714i | −0.610997 | − | 0.725938i | ||||
\(473\) | 17.1836i | 0.790103i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.0961103 | −0.00440985 | ||||||||
\(476\) | 0.0801531 | − | 1.40036i | 0.00367381 | − | 0.0641854i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.92462 | + | 10.5089i | 0.453942 | + | 0.480667i | ||||
\(479\) | 18.2987 | 0.836087 | 0.418043 | − | 0.908427i | \(-0.362716\pi\) | ||||
0.418043 | + | 0.908427i | \(0.362716\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.48822 | 0.159049 | ||||||||
\(482\) | 27.3638 | + | 28.9748i | 1.24639 | + | 1.31977i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.585789 | + | 10.2344i | −0.0266268 | + | 0.465198i | ||||
\(485\) | 17.6916 | 0.803336 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 24.3559i | − | 1.10367i | −0.833953 | − | 0.551836i | \(-0.813928\pi\) | ||
0.833953 | − | 0.551836i | \(-0.186072\pi\) | |||||||
\(488\) | 8.33947 | + | 9.90830i | 0.377510 | + | 0.448527i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.14889 | − | 2.27540i | −0.0970767 | − | 0.102792i | ||||
\(491\) | 25.8479i | 1.16650i | 0.812292 | + | 0.583250i | \(0.198219\pi\) | ||||
−0.812292 | + | 0.583250i | \(0.801781\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2.98856i | − | 0.134598i | ||||||
\(494\) | −1.07663 | + | 1.01677i | −0.0484398 | + | 0.0457465i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.20497 | − | 27.9054i | 0.143907 | − | 1.25299i | ||||
\(497\) | − | 6.93451i | − | 0.311055i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.5430 | −0.606270 | −0.303135 | − | 0.952948i | \(-0.598033\pi\) | ||||
−0.303135 | + | 0.952948i | \(0.598033\pi\) | |||||||
\(500\) | 1.29053 | − | 22.5469i | 0.0577142 | − | 1.00833i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.75365 | + | 4.48934i | −0.212166 | + | 0.200369i | ||||
\(503\) | −17.6930 | −0.788890 | −0.394445 | − | 0.918920i | \(-0.629063\pi\) | ||||
−0.394445 | + | 0.918920i | \(0.629063\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.6383 | −1.54138 | ||||||||
\(506\) | −10.7282 | + | 10.1317i | −0.476925 | + | 0.450408i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.8145 | + | 1.19137i | 0.923494 | + | 0.0528585i | ||||
\(509\) | −12.0147 | −0.532544 | −0.266272 | − | 0.963898i | \(-0.585792\pi\) | ||||
−0.266272 | + | 0.963898i | \(0.585792\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.02133i | 0.310606i | ||||||||
\(512\) | 11.4020 | + | 19.5447i | 0.503902 | + | 0.863761i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 30.5041 | − | 28.8080i | 1.34548 | − | 1.27067i | ||||
\(515\) | 10.8509i | 0.478147i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.10372i | − | 0.0925216i | ||||||
\(518\) | 3.03520 | + | 3.21390i | 0.133359 | + | 0.141211i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.49799 | − | 5.34415i | −0.197250 | − | 0.234357i | ||||
\(521\) | − | 17.5217i | − | 0.767638i | −0.923408 | − | 0.383819i | \(-0.874609\pi\) | ||
0.923408 | − | 0.383819i | \(-0.125391\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.61428 | −0.245495 | −0.122748 | − | 0.992438i | \(-0.539171\pi\) | ||||
−0.122748 | + | 0.992438i | \(0.539171\pi\) | |||||||
\(524\) | 42.6448 | + | 2.44088i | 1.86295 | + | 0.106630i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.4036 | + | 16.3105i | 0.671628 | + | 0.711170i | ||||
\(527\) | −4.92486 | −0.214530 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.46684 | −0.194210 | ||||||||
\(530\) | −8.41168 | − | 8.90691i | −0.365380 | − | 0.386891i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.87361 | − | 0.107241i | −0.0812314 | − | 0.00464948i | ||||
\(533\) | −0.176230 | −0.00763337 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.5131i | 1.44890i | ||||||||
\(536\) | −32.8223 | + | 27.6254i | −1.41771 | + | 1.19323i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.04705 | + | 3.22644i | 0.131368 | + | 0.139102i | ||||
\(539\) | − | 2.42373i | − | 0.104397i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 34.1532i | − | 1.46836i | −0.678954 | − | 0.734181i | \(-0.737567\pi\) | ||
0.678954 | − | 0.734181i | \(-0.262433\pi\) | |||||||
\(542\) | 23.3575 | − | 22.0588i | 1.00329 | − | 0.947505i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.17631 | − | 2.37707i | 0.136183 | − | 0.101916i | ||||
\(545\) | 6.04027i | 0.258737i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.6399 | 0.925255 | 0.462627 | − | 0.886553i | \(-0.346907\pi\) | ||||
0.462627 | + | 0.886553i | \(0.346907\pi\) | |||||||
\(548\) | 22.4787 | + | 1.28662i | 0.960240 | + | 0.0549618i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.255247 | − | 0.241055i | 0.0108838 | − | 0.0102786i | ||||
\(551\) | −3.99855 | −0.170344 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.65903 | 0.283171 | ||||||||
\(554\) | 25.5262 | − | 24.1069i | 1.08450 | − | 1.02420i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.927546 | + | 16.2052i | −0.0393367 | + | 0.687254i | ||||
\(557\) | −25.9554 | −1.09976 | −0.549882 | − | 0.835242i | \(-0.685327\pi\) | ||||
−0.549882 | + | 0.835242i | \(0.685327\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.91168i | 0.334629i | ||||||||
\(560\) | 1.01005 | − | 8.79437i | 0.0426822 | − | 0.371630i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 31.0722 | − | 29.3445i | 1.31070 | − | 1.23782i | ||||
\(563\) | 13.9262i | 0.586921i | 0.955971 | + | 0.293460i | \(0.0948069\pi\) | ||||
−0.955971 | + | 0.293460i | \(0.905193\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 6.29237i | − | 0.264722i | ||||||
\(566\) | −14.5460 | − | 15.4024i | −0.611415 | − | 0.647411i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.0060 | − | 12.6301i | 0.629639 | − | 0.529945i | ||||
\(569\) | − | 18.6130i | − | 0.780296i | −0.920752 | − | 0.390148i | \(-0.872424\pi\) | ||
0.920752 | − | 0.390148i | \(-0.127576\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.69112 | 0.196317 | 0.0981586 | − | 0.995171i | \(-0.468705\pi\) | ||||
0.0981586 | + | 0.995171i | \(0.468705\pi\) | |||||||
\(572\) | 0.309117 | − | 5.40059i | 0.0129248 | − | 0.225810i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.153343 | − | 0.162371i | −0.00640042 | − | 0.00677724i | ||||
\(575\) | −0.440945 | −0.0183887 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.27967 | −0.386318 | −0.193159 | − | 0.981167i | \(-0.561873\pi\) | ||||
−0.193159 | + | 0.981167i | \(0.561873\pi\) | |||||||
\(578\) | 16.0295 | + | 16.9733i | 0.666741 | + | 0.705995i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.07779 | − | 18.8301i | 0.0447527 | − | 0.781877i | ||||
\(581\) | −8.41084 | −0.348940 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 9.48752i | − | 0.392933i | ||||||
\(584\) | −15.1939 | + | 12.7882i | −0.628729 | + | 0.529179i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.36988 | + | 7.80377i | 0.304447 | + | 0.322371i | ||||
\(587\) | 34.3528i | 1.41789i | 0.705264 | + | 0.708945i | \(0.250829\pi\) | ||||
−0.705264 | + | 0.708945i | \(0.749171\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.58922i | 0.271504i | ||||||||
\(590\) | −16.5836 | + | 15.6615i | −0.682734 | + | 0.644774i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.42664 | + | 12.4217i | −0.0586347 | + | 0.510527i | ||||
\(593\) | 44.4288i | 1.82447i | 0.409666 | + | 0.912236i | \(0.365645\pi\) | ||||
−0.409666 | + | 0.912236i | \(0.634355\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.55207 | −0.0636285 | ||||||||
\(596\) | −0.560674 | + | 9.79557i | −0.0229661 | + | 0.401242i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.93947 | + | 4.66483i | −0.201990 | + | 0.190759i | ||||
\(599\) | −13.8604 | −0.566322 | −0.283161 | − | 0.959072i | \(-0.591383\pi\) | ||||
−0.283161 | + | 0.959072i | \(0.591383\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.51128 | −0.265601 | −0.132800 | − | 0.991143i | \(-0.542397\pi\) | ||||
−0.132800 | + | 0.991143i | \(0.542397\pi\) | |||||||
\(602\) | −7.28950 | + | 6.88420i | −0.297098 | + | 0.280579i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 37.8422 | + | 2.16600i | 1.53978 | + | 0.0881331i | ||||
\(605\) | 11.3431 | 0.461162 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 43.5994i | − | 1.76964i | −0.465929 | − | 0.884822i | \(-0.654280\pi\) | ||
0.465929 | − | 0.884822i | \(-0.345720\pi\) | |||||||
\(608\) | −3.18041 | − | 4.24975i | −0.128983 | − | 0.172350i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.4185 | − | 9.83925i | 0.421834 | − | 0.398380i | ||||
\(611\) | − | 0.968597i | − | 0.0391852i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 22.4072i | − | 0.905017i | −0.891760 | − | 0.452508i | \(-0.850529\pi\) | ||
0.891760 | − | 0.452508i | \(-0.149471\pi\) | |||||||
\(614\) | −17.5992 | − | 18.6353i | −0.710245 | − | 0.752060i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.24486 | − | 4.41441i | 0.211321 | − | 0.177862i | ||||
\(617\) | 30.5128i | 1.22840i | 0.789151 | + | 0.614199i | \(0.210521\pi\) | ||||
−0.789151 | + | 0.614199i | \(0.789479\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.5504 | −0.544637 | −0.272319 | − | 0.962207i | \(-0.587790\pi\) | ||||
−0.272319 | + | 0.962207i | \(0.587790\pi\) | |||||||
\(620\) | −31.0302 | − | 1.77609i | −1.24620 | − | 0.0713294i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −16.5354 | − | 17.5089i | −0.663008 | − | 0.702042i | ||||
\(623\) | 7.34335 | 0.294205 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.4774 | −0.979095 | ||||||||
\(626\) | 7.22692 | + | 7.65240i | 0.288846 | + | 0.305851i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.1484 | + | 1.15325i | 0.804010 | + | 0.0460195i | ||||
\(629\) | 2.19222 | 0.0874097 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.5393i | 1.05651i | 0.849085 | + | 0.528257i | \(0.177154\pi\) | ||||
−0.849085 | + | 0.528257i | \(0.822846\pi\) | |||||||
\(632\) | 12.1283 | + | 14.4099i | 0.482439 | + | 0.573195i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.33575 | − | 2.47326i | −0.0927644 | − | 0.0982258i | ||||
\(635\) | − | 23.0694i | − | 0.915482i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.11593i | − | 0.0442149i | ||||||
\(638\) | 10.6192 | − | 10.0288i | 0.420419 | − | 0.397043i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 20.8703 | − | 13.8318i | 0.824973 | − | 0.546749i | ||||
\(641\) | − | 10.3318i | − | 0.408083i | −0.978962 | − | 0.204041i | \(-0.934592\pi\) | ||
0.978962 | − | 0.204041i | \(-0.0654077\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.5130 | 0.532901 | 0.266450 | − | 0.963849i | \(-0.414149\pi\) | ||||
0.266450 | + | 0.963849i | \(0.414149\pi\) | |||||||
\(644\) | −8.59596 | − | 0.492011i | −0.338728 | − | 0.0193880i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.676624 | + | 0.639003i | −0.0266214 | + | 0.0251412i | ||||
\(647\) | −8.31247 | −0.326797 | −0.163399 | − | 0.986560i | \(-0.552246\pi\) | ||||
−0.163399 | + | 0.986560i | \(0.552246\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.6646 | −0.693396 | ||||||||
\(650\) | 0.117521 | − | 0.110987i | 0.00460955 | − | 0.00435326i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.28304 | − | 39.8872i | 0.0894109 | − | 1.56210i | ||||
\(653\) | 2.56899 | 0.100533 | 0.0502663 | − | 0.998736i | \(-0.483993\pi\) | ||||
0.0502663 | + | 0.998736i | \(0.483993\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 47.2647i | − | 1.84678i | ||||||
\(656\) | 0.0720762 | − | 0.627561i | 0.00281410 | − | 0.0245021i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.892426 | − | 0.842806i | 0.0347904 | − | 0.0328560i | ||||
\(659\) | 12.7747i | 0.497632i | 0.968551 | + | 0.248816i | \(0.0800414\pi\) | ||||
−0.968551 | + | 0.248816i | \(0.919959\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.8624i | 1.00593i | 0.864307 | + | 0.502965i | \(0.167758\pi\) | ||||
−0.864307 | + | 0.502965i | \(0.832242\pi\) | |||||||
\(662\) | 13.9608 | + | 14.7827i | 0.542601 | + | 0.574546i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.3190 | − | 18.2008i | −0.594491 | − | 0.706326i | ||||
\(665\) | 2.07659i | 0.0805267i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.3450 | −0.710320 | ||||||||
\(668\) | −1.58429 | + | 27.6793i | −0.0612981 | + | 1.07094i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 32.5936 | + | 34.5125i | 1.25920 | + | 1.33333i | ||||
\(671\) | 11.0977 | 0.428421 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.9446 | −1.30847 | −0.654235 | − | 0.756292i | \(-0.727009\pi\) | ||||
−0.654235 | + | 0.756292i | \(0.727009\pi\) | |||||||
\(674\) | 19.8503 | + | 21.0190i | 0.764605 | + | 0.809621i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.34342 | + | 23.4710i | −0.0516700 | + | 0.902730i | ||||
\(677\) | −34.1280 | −1.31165 | −0.655823 | − | 0.754915i | \(-0.727678\pi\) | ||||
−0.655823 | + | 0.754915i | \(0.727678\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.99425i | 0.306791i | ||||||||
\(680\) | −2.82683 | − | 3.35862i | −0.108404 | − | 0.128797i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16.5265 | − | 17.4994i | −0.632831 | − | 0.670088i | ||||
\(683\) | − | 6.80951i | − | 0.260559i | −0.991477 | − | 0.130279i | \(-0.958413\pi\) | ||
0.991477 | − | 0.130279i | \(-0.0415874\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 24.9139i | − | 0.951910i | ||||||
\(686\) | 1.02818 | − | 0.971008i | 0.0392559 | − | 0.0370732i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −28.1738 | − | 3.23579i | −1.07412 | − | 0.123363i | ||||
\(689\) | − | 4.36825i | − | 0.166417i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.06521 | −0.192690 | −0.0963448 | − | 0.995348i | \(-0.530715\pi\) | ||||
−0.0963448 | + | 0.995348i | \(0.530715\pi\) | |||||||
\(692\) | 2.45486 | − | 42.8890i | 0.0933197 | − | 1.63039i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.81117 | + | 6.43247i | −0.258549 | + | 0.244173i | ||||
\(695\) | 17.9608 | 0.681291 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.110755 | −0.00419513 | ||||||||
\(698\) | −34.7396 | + | 32.8080i | −1.31491 | + | 1.24180i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.204517 | + | 0.0117061i | 0.00773002 | + | 0.000442447i | ||||
\(701\) | 44.7933 | 1.69182 | 0.845910 | − | 0.533326i | \(-0.179058\pi\) | ||||
0.845910 | + | 0.533326i | \(0.179058\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 2.93309i | − | 0.110624i | ||||||
\(704\) | 19.1053 | + | 3.30956i | 0.720057 | + | 0.124734i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27.3470 | − | 25.8265i | 1.02922 | − | 0.971992i | ||||
\(707\) | − | 15.6519i | − | 0.588649i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 40.5597i | − | 1.52325i | −0.648018 | − | 0.761625i | \(-0.724402\pi\) | ||
0.648018 | − | 0.761625i | \(-0.275598\pi\) | |||||||
\(710\) | −14.9015 | − | 15.7788i | −0.559242 | − | 0.592167i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13.3747 | + | 15.8907i | 0.501238 | + | 0.595531i | ||||
\(713\) | 30.2307i | 1.13215i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.98566 | −0.223851 | ||||||||
\(716\) | −7.87294 | − | 0.450627i | −0.294225 | − | 0.0168407i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.8484 | + | 30.5469i | 1.07661 | + | 1.14000i | ||||
\(719\) | −13.2926 | −0.495729 | −0.247864 | − | 0.968795i | \(-0.579729\pi\) | ||||
−0.247864 | + | 0.968795i | \(0.579729\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.90314 | −0.182603 | ||||||||
\(722\) | −17.5942 | − | 18.6300i | −0.654788 | − | 0.693338i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −23.5312 | − | 1.34687i | −0.874530 | − | 0.0500559i | ||||
\(725\) | 0.436468 | 0.0162100 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.6102i | 1.06109i | 0.847656 | + | 0.530546i | \(0.178013\pi\) | ||||
−0.847656 | + | 0.530546i | \(0.821987\pi\) | |||||||
\(728\) | 2.41484 | − | 2.03249i | 0.0894999 | − | 0.0753290i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 15.0880 | + | 15.9763i | 0.558433 | + | 0.591311i | ||||
\(731\) | 4.97222i | 0.183904i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 33.9007i | − | 1.25215i | −0.779763 | − | 0.626075i | \(-0.784660\pi\) | ||
0.779763 | − | 0.626075i | \(-0.215340\pi\) | |||||||
\(734\) | −16.1353 | + | 15.2382i | −0.595565 | + | 0.562452i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.5914 | − | 19.4975i | −0.537847 | − | 0.718686i | ||||
\(737\) | 36.7623i | 1.35416i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.1200 | −0.409055 | −0.204528 | − | 0.978861i | \(-0.565566\pi\) | ||||
−0.204528 | + | 0.978861i | \(0.565566\pi\) | |||||||
\(740\) | 13.8126 | + | 0.790599i | 0.507761 | + | 0.0290630i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.02473 | − | 3.80095i | 0.147752 | − | 0.139537i | ||||
\(743\) | −45.7857 | −1.67971 | −0.839857 | − | 0.542808i | \(-0.817361\pi\) | ||||
−0.839857 | + | 0.542808i | \(0.817361\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.8568 | 0.397761 | ||||||||
\(746\) | −11.3376 | + | 10.7072i | −0.415098 | + | 0.392018i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.194269 | − | 3.39409i | 0.00710319 | − | 0.124100i | ||||
\(749\) | −15.1434 | −0.553329 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 13.8013i | − | 0.503616i | −0.967777 | − | 0.251808i | \(-0.918975\pi\) | ||
0.967777 | − | 0.251808i | \(-0.0810252\pi\) | |||||||
\(752\) | 3.44921 | + | 0.396146i | 0.125780 | + | 0.0144460i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.88931 | − | 4.61746i | 0.178058 | − | 0.168158i | ||||
\(755\) | − | 41.9418i | − | 1.52642i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 5.94985i | − | 0.216251i | −0.994137 | − | 0.108126i | \(-0.965515\pi\) | ||
0.994137 | − | 0.108126i | \(-0.0344848\pi\) | |||||||
\(758\) | −7.61985 | − | 8.06846i | −0.276765 | − | 0.293060i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.49366 | + | 3.78216i | −0.163002 | + | 0.137193i | ||||
\(761\) | 38.1237i | 1.38198i | 0.722864 | + | 0.690991i | \(0.242825\pi\) | ||||
−0.722864 | + | 0.690991i | \(0.757175\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.72939 | −0.0988106 | ||||||||
\(764\) | −1.89791 | + | 33.1585i | −0.0686640 | + | 1.19963i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.16780 | − | 3.35430i | −0.114457 | − | 0.121196i | ||||
\(767\) | −8.13314 | −0.293671 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.5207 | 0.559689 | 0.279845 | − | 0.960045i | \(-0.409717\pi\) | ||||
0.279845 | + | 0.960045i | \(0.409717\pi\) | |||||||
\(770\) | −5.20831 | − | 5.51494i | −0.187694 | − | 0.198745i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.789062 | + | 13.7858i | −0.0283990 | + | 0.496160i | ||||
\(773\) | −39.6525 | −1.42620 | −0.713101 | − | 0.701061i | \(-0.752710\pi\) | ||||
−0.713101 | + | 0.701061i | \(0.752710\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 0.719256i | − | 0.0258365i | ||||||
\(776\) | −17.2993 | + | 14.5602i | −0.621007 | + | 0.522680i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.12343 | − | 1.18957i | −0.0402769 | − | 0.0426482i | ||||
\(779\) | 0.148184i | 0.00530925i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 16.8073i | − | 0.601414i | ||||||
\(782\) | −3.10429 | + | 2.93169i | −0.111009 | + | 0.104837i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.97388 | + | 0.456405i | 0.141924 | + | 0.0163002i | ||||
\(785\) | − | 22.3312i | − | 0.797035i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −50.2403 | −1.79087 | −0.895436 | − | 0.445189i | \(-0.853136\pi\) | ||||
−0.895436 | + | 0.445189i | \(0.853136\pi\) | |||||||
\(788\) | −1.02662 | + | 17.9361i | −0.0365718 | + | 0.638948i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 15.1520 | − | 14.3095i | 0.539082 | − | 0.509109i | ||||
\(791\) | 2.84331 | 0.101096 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.10960 | 0.181447 | ||||||||
\(794\) | 2.48094 | − | 2.34299i | 0.0880451 | − | 0.0831498i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.8481 | − | 1.30777i | −0.809828 | − | 0.0463525i | ||||
\(797\) | −1.78519 | −0.0632345 | −0.0316173 | − | 0.999500i | \(-0.510066\pi\) | ||||
−0.0316173 | + | 0.999500i | \(0.510066\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 0.608730i | − | 0.0215353i | ||||||
\(800\) | 0.347163 | + | 0.463889i | 0.0122741 | + | 0.0164009i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.69123 | + | 7.26359i | −0.271587 | + | 0.256486i | ||||
\(803\) | 17.0178i | 0.600545i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.52720i | 0.335790i | ||||||||
\(806\) | −7.60912 | − | 8.05710i | −0.268020 | − | 0.283799i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 33.8701 | − | 28.5073i | 1.19154 | − | 1.00288i | ||||
\(809\) | − | 31.9043i | − | 1.12169i | −0.827919 | − | 0.560847i | \(-0.810476\pi\) | ||
0.827919 | − | 0.560847i | \(-0.189524\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.5528 | −0.440789 | −0.220394 | − | 0.975411i | \(-0.570734\pi\) | ||||
−0.220394 | + | 0.975411i | \(0.570734\pi\) | |||||||
\(812\) | 8.50867 | + | 0.487015i | 0.298596 | + | 0.0170909i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.35650 | + | 7.78961i | 0.257845 | + | 0.273026i | ||||
\(815\) | −44.2084 | −1.54855 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.65259 | 0.232745 | ||||||||
\(818\) | −7.28084 | − | 7.70950i | −0.254569 | − | 0.269556i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.697834 | − | 0.0399423i | −0.0243694 | − | 0.00139484i | ||||
\(821\) | −42.1349 | −1.47052 | −0.735260 | − | 0.677786i | \(-0.762940\pi\) | ||||
−0.735260 | + | 0.677786i | \(0.762940\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.50592i | − | 0.0524931i | −0.999656 | − | 0.0262465i | \(-0.991645\pi\) | ||
0.999656 | − | 0.0262465i | \(-0.00835549\pi\) | |||||||
\(824\) | −8.93026 | − | 10.6102i | −0.311100 | − | 0.369625i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.07690 | − | 7.49355i | −0.246237 | − | 0.260734i | ||||
\(827\) | 40.6098i | 1.41214i | 0.708141 | + | 0.706071i | \(0.249534\pi\) | ||||
−0.708141 | + | 0.706071i | \(0.750466\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.4547i | 1.23139i | 0.787984 | + | 0.615696i | \(0.211125\pi\) | ||||
−0.787984 | + | 0.615696i | \(0.788875\pi\) | |||||||
\(830\) | −19.1380 | + | 18.0739i | −0.664290 | + | 0.627355i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.79646 | + | 1.52379i | 0.304962 | + | 0.0528279i | ||||
\(833\) | − | 0.701326i | − | 0.0242995i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.6779 | 1.06165 | ||||||||
\(836\) | −4.54112 | − | 0.259923i | −0.157058 | − | 0.00898961i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 27.5224 | − | 25.9921i | 0.950745 | − | 0.897883i | ||||
\(839\) | 31.8372 | 1.09914 | 0.549571 | − | 0.835447i | \(-0.314791\pi\) | ||||
0.549571 | + | 0.835447i | \(0.314791\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.8413 | −0.373839 | ||||||||
\(842\) | −28.9551 | + | 27.3452i | −0.997858 | + | 0.942377i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.72046 | + | 47.5293i | −0.0936420 | + | 1.63602i | ||||
\(845\) | 26.0137 | 0.894898 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.12555i | 0.176116i | ||||||||
\(848\) | 15.5555 | + | 1.78657i | 0.534178 | + | 0.0613510i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.0738579 | − | 0.0697514i | 0.00253331 | − | 0.00239245i | ||||
\(851\) | − | 13.4567i | − | 0.461291i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.0499i | 1.02889i | 0.857523 | + | 0.514445i | \(0.172002\pi\) | ||||
−0.857523 | + | 0.514445i | \(0.827998\pi\) | |||||||
\(854\) | 4.44602 | + | 4.70778i | 0.152140 | + | 0.161097i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −27.5813 | − | 32.7699i | −0.942708 | − | 1.12005i | ||||
\(857\) | − | 26.7594i | − | 0.914085i | −0.889445 | − | 0.457043i | \(-0.848909\pi\) | ||
0.889445 | − | 0.457043i | \(-0.151091\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.98544 | −0.135981 | −0.0679907 | − | 0.997686i | \(-0.521659\pi\) | ||||
−0.0679907 | + | 0.997686i | \(0.521659\pi\) | |||||||
\(860\) | −1.79317 | + | 31.3286i | −0.0611466 | + | 1.06830i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −29.0680 | − | 30.7793i | −0.990059 | − | 1.04835i | ||||
\(863\) | 33.1318 | 1.12782 | 0.563910 | − | 0.825836i | \(-0.309296\pi\) | ||||
0.563910 | + | 0.825836i | \(0.309296\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −47.5353 | −1.61625 | ||||||||
\(866\) | −37.9767 | − | 40.2125i | −1.29050 | − | 1.36648i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.802554 | − | 14.0215i | 0.0272404 | − | 0.475920i | ||||
\(869\) | 16.1397 | 0.547501 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.9261i | 0.573519i | ||||||||
\(872\) | −4.97113 | − | 5.90631i | −0.168344 | − | 0.200013i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.92245 | + | 4.15338i | 0.132679 | + | 0.140490i | ||||
\(875\) | − | 11.2919i | − | 0.381736i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.35210i | 0.146960i | 0.997297 | + | 0.0734800i | \(0.0234105\pi\) | ||||
−0.997297 | + | 0.0734800i | \(0.976589\pi\) | |||||||
\(878\) | −32.3208 | + | 30.5237i | −1.09077 | + | 1.03013i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.44807 | − | 21.3151i | 0.0825245 | − | 0.718534i | ||||
\(881\) | 37.2945i | 1.25648i | 0.778018 | + | 0.628242i | \(0.216225\pi\) | ||||
−0.778018 | + | 0.628242i | \(0.783775\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.7359 | −1.50548 | −0.752742 | − | 0.658315i | \(-0.771269\pi\) | ||||
−0.752742 | + | 0.658315i | \(0.771269\pi\) | |||||||
\(884\) | 0.0894455 | − | 1.56271i | 0.00300838 | − | 0.0525596i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.9173 | + | 23.5318i | −0.837112 | + | 0.790568i | ||||
\(887\) | −3.69357 | −0.124018 | −0.0620090 | − | 0.998076i | \(-0.519751\pi\) | ||||
−0.0620090 | + | 0.998076i | \(0.519751\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.4243 | 0.349619 | ||||||||
\(890\) | 16.7090 | − | 15.7800i | 0.560089 | − | 0.528947i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.84236 | + | 0.506114i | 0.296064 | + | 0.0169460i | ||||
\(893\) | −0.814451 | −0.0272546 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.72584i | 0.291673i | ||||||||
\(896\) | 6.25011 | + | 9.43059i | 0.208802 | + | 0.315054i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 23.2435 | − | 21.9511i | 0.775645 | − | 0.732519i | ||||
\(899\) | − | 29.9237i | − | 0.998012i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2.74530i | − | 0.0914591i | ||||||
\(902\) | −0.371662 | − | 0.393543i | −0.0123750 | − | 0.0131035i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.17861 | + | 6.15282i | 0.172238 | + | 0.204640i | ||||
\(905\) | 26.0804i | 0.866943i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.61629 | −0.319304 | −0.159652 | − | 0.987173i | \(-0.551037\pi\) | ||||
−0.159652 | + | 0.987173i | \(0.551037\pi\) | |||||||
\(908\) | −12.9139 | − | 0.739159i | −0.428563 | − | 0.0245299i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.39801 | − | 2.53919i | −0.0794933 | − | 0.0841735i | ||||
\(911\) | −53.1598 | −1.76126 | −0.880632 | − | 0.473802i | \(-0.842881\pi\) | ||||
−0.880632 | + | 0.473802i | \(0.842881\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.3856 | −0.674664 | ||||||||
\(914\) | −9.08156 | − | 9.61623i | −0.300391 | − | 0.318077i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 22.9054 | + | 1.31105i | 0.756817 | + | 0.0433183i | ||||
\(917\) | 21.3573 | 0.705280 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.3183i | 1.09907i | 0.835471 | + | 0.549534i | \(0.185195\pi\) | ||||
−0.835471 | + | 0.549534i | \(0.814805\pi\) | |||||||
\(920\) | −20.6165 | + | 17.3522i | −0.679707 | + | 0.572085i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11.2538 | − | 11.9163i | −0.370623 | − | 0.392443i | ||||
\(923\) | − | 7.73845i | − | 0.254714i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.320166i | 0.0105270i | ||||||||
\(926\) | 18.3322 | − | 17.3129i | 0.602435 | − | 0.568939i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 14.4433 | + | 19.2995i | 0.474123 | + | 0.633536i | ||||
\(929\) | 13.5434i | 0.444343i | 0.975008 | + | 0.222172i | \(0.0713146\pi\) | ||||
−0.975008 | + | 0.222172i | \(0.928685\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.938340 | −0.0307528 | ||||||||
\(932\) | −39.6707 | − | 2.27065i | −1.29946 | − | 0.0743777i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.60047 | − | 3.40028i | 0.117811 | − | 0.111261i | ||||
\(935\) | −3.76178 | −0.123024 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.3432 | 1.38329 | 0.691647 | − | 0.722236i | \(-0.256886\pi\) | ||||
0.691647 | + | 0.722236i | \(0.256886\pi\) | |||||||
\(938\) | −15.5950 | + | 14.7279i | −0.509195 | + | 0.480884i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.219531 | − | 3.83544i | 0.00716031 | − | 0.125098i | ||||
\(941\) | 60.9773 | 1.98780 | 0.993902 | − | 0.110267i | \(-0.0351707\pi\) | ||||
0.993902 | + | 0.110267i | \(0.0351707\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.679855i | 0.0221391i | ||||||||
\(944\) | 3.32637 | − | 28.9624i | 0.108264 | − | 0.942646i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.6677 | + | 16.6854i | −0.574428 | + | 0.542489i | ||||
\(947\) | − | 39.4879i | − | 1.28318i | −0.767047 | − | 0.641591i | \(-0.778275\pi\) | ||
0.767047 | − | 0.641591i | \(-0.221725\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.83534i | 0.254346i | ||||||||
\(950\) | −0.0933239 | − | 0.0988183i | −0.00302783 | − | 0.00320609i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.51764 | − | 1.27735i | 0.0491871 | − | 0.0413991i | ||||
\(953\) | − | 25.8210i | − | 0.836425i | −0.908349 | − | 0.418213i | \(-0.862657\pi\) | ||
0.908349 | − | 0.418213i | \(-0.137343\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36.7507 | 1.18922 | ||||||||
\(956\) | −1.16813 | + | 20.4085i | −0.0377801 | + | 0.660058i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.7681 | + | 18.8142i | 0.574062 | + | 0.607860i | ||||
\(959\) | 11.2577 | 0.363531 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.3114 | −0.590690 | ||||||||
\(962\) | 3.38708 | + | 3.58650i | 0.109204 | + | 0.115633i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.22073 | + | 56.2695i | −0.103733 | + | 1.81232i | ||||
\(965\) | 15.2792 | 0.491856 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.92813i | 0.158478i | 0.996856 | + | 0.0792390i | \(0.0252490\pi\) | ||||
−0.996856 | + | 0.0792390i | \(0.974751\pi\) | |||||||
\(968\) | −11.0915 | + | 9.33534i | −0.356495 | + | 0.300049i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 17.1787 | + | 18.1901i | 0.551575 | + | 0.584049i | ||||
\(971\) | − | 20.9043i | − | 0.670850i | −0.942067 | − | 0.335425i | \(-0.891120\pi\) | ||
0.942067 | − | 0.335425i | \(-0.108880\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.11586i | 0.260183i | ||||||||
\(974\) | 25.0421 | − | 23.6498i | 0.802402 | − | 0.757787i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.08977 | + | 18.1955i | −0.0668920 | + | 0.582423i | ||||
\(977\) | 16.6995i | 0.534266i | 0.963660 | + | 0.267133i | \(0.0860763\pi\) | ||||
−0.963660 | + | 0.267133i | \(0.913924\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.7983 | 0.568835 | ||||||||
\(980\) | 0.252925 | − | 4.41886i | 0.00807938 | − | 0.141155i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −26.5762 | + | 25.0985i | −0.848081 | + | 0.800927i | ||||
\(983\) | −27.7932 | −0.886465 | −0.443232 | − | 0.896407i | \(-0.646168\pi\) | ||||
−0.443232 | + | 0.896407i | \(0.646168\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.8792 | 0.633404 | ||||||||
\(986\) | 3.07276 | − | 2.90191i | 0.0978567 | − | 0.0924158i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.09083 | − | 0.119674i | −0.0665181 | − | 0.00380733i | ||||
\(989\) | 30.5215 | 0.970526 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 38.3482i | − | 1.21817i | −0.793104 | − | 0.609086i | \(-0.791536\pi\) | ||
0.793104 | − | 0.609086i | \(-0.208464\pi\) | |||||||
\(992\) | 31.8037 | − | 23.8011i | 1.00977 | − | 0.755685i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.12989 | − | 6.73346i | 0.226146 | − | 0.213572i | ||||
\(995\) | 25.3233i | 0.802802i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 27.7418i | − | 0.878590i | −0.898343 | − | 0.439295i | \(-0.855228\pi\) | ||
0.898343 | − | 0.439295i | \(-0.144772\pi\) | |||||||
\(998\) | −13.1504 | − | 13.9246i | −0.416269 | − | 0.440776i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1512.2.j.c.323.22 | yes | 32 | |
3.2 | odd | 2 | inner | 1512.2.j.c.323.11 | ✓ | 32 | |
4.3 | odd | 2 | 6048.2.j.c.5615.27 | 32 | |||
8.3 | odd | 2 | inner | 1512.2.j.c.323.12 | yes | 32 | |
8.5 | even | 2 | 6048.2.j.c.5615.5 | 32 | |||
12.11 | even | 2 | 6048.2.j.c.5615.6 | 32 | |||
24.5 | odd | 2 | 6048.2.j.c.5615.28 | 32 | |||
24.11 | even | 2 | inner | 1512.2.j.c.323.21 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.c.323.11 | ✓ | 32 | 3.2 | odd | 2 | inner | |
1512.2.j.c.323.12 | yes | 32 | 8.3 | odd | 2 | inner | |
1512.2.j.c.323.21 | yes | 32 | 24.11 | even | 2 | inner | |
1512.2.j.c.323.22 | yes | 32 | 1.1 | even | 1 | trivial | |
6048.2.j.c.5615.5 | 32 | 8.5 | even | 2 | |||
6048.2.j.c.5615.6 | 32 | 12.11 | even | 2 | |||
6048.2.j.c.5615.27 | 32 | 4.3 | odd | 2 | |||
6048.2.j.c.5615.28 | 32 | 24.5 | odd | 2 |