Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,3,Mod(19,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.n (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: | \(24.0327593166\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.19 |
Dual form | 882.3.n.d.325.2 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 1.22474i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | − | 1.73205i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.878680 | + | 0.507306i | 0.175736 | + | 0.101461i | 0.585288 | − | 0.810826i | \(-0.300982\pi\) |
−0.409552 | + | 0.912287i | \(0.634315\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.24264 | − | 0.717439i | 0.124264 | − | 0.0717439i | ||||
\(11\) | −5.12132 | − | 8.87039i | −0.465575 | − | 0.806399i | 0.533653 | − | 0.845704i | \(-0.320819\pi\) |
−0.999227 | + | 0.0393049i | \(0.987486\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 8.95743i | − | 0.689033i | −0.938780 | − | 0.344516i | \(-0.888043\pi\) | ||
0.938780 | − | 0.344516i | \(-0.111957\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | −26.3345 | + | 15.2042i | −1.54909 | + | 0.894367i | −0.550878 | + | 0.834586i | \(0.685707\pi\) |
−0.998211 | + | 0.0597816i | \(0.980960\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13.9706 | + | 8.06591i | 0.735293 | + | 0.424521i | 0.820355 | − | 0.571854i | \(-0.193776\pi\) |
−0.0850625 | + | 0.996376i | \(0.527109\pi\) | |||||||
\(20\) | − | 2.02922i | − | 0.101461i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −14.4853 | −0.658422 | ||||||||
\(23\) | −3.36396 | + | 5.82655i | −0.146259 | + | 0.253328i | −0.929842 | − | 0.367959i | \(-0.880057\pi\) |
0.783583 | + | 0.621287i | \(0.213390\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.9853 | − | 20.7591i | −0.479411 | − | 0.830365i | ||||
\(26\) | −10.9706 | − | 6.33386i | −0.421945 | − | 0.243610i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −30.0000 | −1.03448 | −0.517241 | − | 0.855840i | \(-0.673041\pi\) | ||||
−0.517241 | + | 0.855840i | \(0.673041\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 43.4558 | − | 25.0892i | 1.40180 | − | 0.809330i | 0.407224 | − | 0.913328i | \(-0.366497\pi\) |
0.994578 | + | 0.103998i | \(0.0331635\pi\) | |||||||
\(32\) | 2.82843 | + | 4.89898i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 43.0041i | 1.26483i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −15.4558 | + | 26.7703i | −0.417726 | + | 0.723522i | −0.995710 | − | 0.0925257i | \(-0.970506\pi\) |
0.577985 | + | 0.816048i | \(0.303839\pi\) | |||||||
\(38\) | 19.7574 | − | 11.4069i | 0.519931 | − | 0.300182i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.48528 | − | 1.43488i | −0.0621320 | − | 0.0358719i | ||||
\(41\) | 7.10228i | 0.173226i | 0.996242 | + | 0.0866132i | \(0.0276044\pi\) | ||||
−0.996242 | + | 0.0866132i | \(0.972396\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −74.4264 | −1.73085 | −0.865423 | − | 0.501041i | \(-0.832950\pi\) | ||||
−0.865423 | + | 0.501041i | \(0.832950\pi\) | |||||||
\(44\) | −10.2426 | + | 17.7408i | −0.232787 | + | 0.403199i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.75736 | + | 8.23999i | 0.103421 | + | 0.179130i | ||||
\(47\) | −50.4853 | − | 29.1477i | −1.07415 | − | 0.620164i | −0.144841 | − | 0.989455i | \(-0.546267\pi\) |
−0.929314 | + | 0.369291i | \(0.879600\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −33.8995 | −0.677990 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −15.5147 | + | 8.95743i | −0.298360 | + | 0.172258i | ||||
\(53\) | −35.4853 | − | 61.4623i | −0.669534 | − | 1.15967i | −0.978035 | − | 0.208442i | \(-0.933161\pi\) |
0.308501 | − | 0.951224i | \(-0.400173\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 10.3923i | − | 0.188951i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −21.2132 | + | 36.7423i | −0.365745 | + | 0.633489i | ||||
\(59\) | 0.426407 | − | 0.246186i | 0.00722724 | − | 0.00417265i | −0.496382 | − | 0.868104i | \(-0.665338\pi\) |
0.503609 | + | 0.863932i | \(0.332005\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.48528 | − | 1.43488i | −0.0407423 | − | 0.0235226i | 0.479490 | − | 0.877547i | \(-0.340821\pi\) |
−0.520233 | + | 0.854024i | \(0.674155\pi\) | |||||||
\(62\) | − | 70.9631i | − | 1.14457i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 4.54416 | − | 7.87071i | 0.0699101 | − | 0.121088i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.5147 | − | 23.4082i | −0.201712 | − | 0.349376i | 0.747368 | − | 0.664410i | \(-0.231317\pi\) |
−0.949080 | + | 0.315035i | \(0.897984\pi\) | |||||||
\(68\) | 52.6690 | + | 30.4085i | 0.774545 | + | 0.447184i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −50.6102 | −0.712819 | −0.356410 | − | 0.934330i | \(-0.615999\pi\) | ||||
−0.356410 | + | 0.934330i | \(0.615999\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −61.1543 | + | 35.3075i | −0.837731 | + | 0.483664i | −0.856492 | − | 0.516160i | \(-0.827361\pi\) |
0.0187616 | + | 0.999824i | \(0.494028\pi\) | |||||||
\(74\) | 21.8579 | + | 37.8589i | 0.295377 | + | 0.511607i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 32.2636i | − | 0.424521i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −66.9117 | + | 115.894i | −0.846983 | + | 1.46702i | 0.0369042 | + | 0.999319i | \(0.488250\pi\) |
−0.883888 | + | 0.467699i | \(0.845083\pi\) | |||||||
\(80\) | −3.51472 | + | 2.02922i | −0.0439340 | + | 0.0253653i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.69848 | + | 5.02207i | 0.106079 | + | 0.0612448i | ||||
\(83\) | 104.415i | 1.25802i | 0.777398 | + | 0.629009i | \(0.216539\pi\) | ||||
−0.777398 | + | 0.629009i | \(0.783461\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −30.8528 | −0.362974 | ||||||||
\(86\) | −52.6274 | + | 91.1534i | −0.611947 | + | 1.05992i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 14.4853 | + | 25.0892i | 0.164605 | + | 0.285105i | ||||
\(89\) | 125.548 | + | 72.4850i | 1.41065 | + | 0.814438i | 0.995449 | − | 0.0952921i | \(-0.0303785\pi\) |
0.415199 | + | 0.909730i | \(0.363712\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 13.4558 | 0.146259 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −71.3970 | + | 41.2211i | −0.759542 | + | 0.438522i | ||||
\(95\) | 8.18377 | + | 14.1747i | 0.0861449 | + | 0.149207i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 100.705i | − | 1.03820i | −0.854714 | − | 0.519099i | \(-0.826268\pi\) | ||
0.854714 | − | 0.519099i | \(-0.173732\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −23.9706 | + | 41.5182i | −0.239706 | + | 0.415182i | ||||
\(101\) | 120.276 | − | 69.4412i | 1.19085 | − | 0.687536i | 0.232349 | − | 0.972632i | \(-0.425359\pi\) |
0.958499 | + | 0.285096i | \(0.0920255\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −68.3087 | − | 39.4380i | −0.663191 | − | 0.382893i | 0.130301 | − | 0.991475i | \(-0.458406\pi\) |
−0.793492 | + | 0.608581i | \(0.791739\pi\) | |||||||
\(104\) | 25.3354i | 0.243610i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −100.368 | −0.946864 | ||||||||
\(107\) | −18.8787 | + | 32.6988i | −0.176436 | + | 0.305597i | −0.940657 | − | 0.339358i | \(-0.889790\pi\) |
0.764221 | + | 0.644954i | \(0.223124\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.9706 | − | 27.6618i | −0.146519 | − | 0.253778i | 0.783420 | − | 0.621493i | \(-0.213474\pi\) |
−0.929939 | + | 0.367715i | \(0.880140\pi\) | |||||||
\(110\) | −12.7279 | − | 7.34847i | −0.115708 | − | 0.0668043i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 106.971 | 0.946642 | 0.473321 | − | 0.880890i | \(-0.343055\pi\) | ||||
0.473321 | + | 0.880890i | \(0.343055\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.91169 | + | 3.41311i | −0.0514060 | + | 0.0296793i | ||||
\(116\) | 30.0000 | + | 51.9615i | 0.258621 | + | 0.447944i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 0.696320i | − | 0.00590101i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.04416 | − | 13.9329i | 0.0664806 | − | 0.115148i | ||||
\(122\) | −3.51472 | + | 2.02922i | −0.0288092 | + | 0.0166330i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −86.9117 | − | 50.1785i | −0.700901 | − | 0.404665i | ||||
\(125\) | − | 49.6861i | − | 0.397489i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 22.0589 | 0.173692 | 0.0868460 | − | 0.996222i | \(-0.472321\pi\) | ||||
0.0868460 | + | 0.996222i | \(0.472321\pi\) | |||||||
\(128\) | 5.65685 | − | 9.79796i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.42641 | − | 11.1309i | −0.0494339 | − | 0.0856220i | ||||
\(131\) | −61.4558 | − | 35.4815i | −0.469129 | − | 0.270852i | 0.246746 | − | 0.969080i | \(-0.420639\pi\) |
−0.715875 | + | 0.698229i | \(0.753972\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −38.2254 | −0.285264 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 74.4853 | − | 43.0041i | 0.547686 | − | 0.316207i | ||||
\(137\) | −52.8823 | − | 91.5947i | −0.386002 | − | 0.668575i | 0.605906 | − | 0.795536i | \(-0.292811\pi\) |
−0.991908 | + | 0.126962i | \(0.959477\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 181.322i | 1.30447i | 0.758015 | + | 0.652237i | \(0.226169\pi\) | ||||
−0.758015 | + | 0.652237i | \(0.773831\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −35.7868 | + | 61.9845i | −0.252020 | + | 0.436511i | ||||
\(143\) | −79.4558 | + | 45.8739i | −0.555635 | + | 0.320796i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26.3604 | − | 15.2192i | −0.181796 | − | 0.104960i | ||||
\(146\) | 99.8646i | 0.684004i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 61.8234 | 0.417726 | ||||||||
\(149\) | 20.5736 | − | 35.6345i | 0.138078 | − | 0.239158i | −0.788691 | − | 0.614790i | \(-0.789241\pi\) |
0.926769 | + | 0.375632i | \(0.122574\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −40.1838 | − | 69.6003i | −0.266118 | − | 0.460929i | 0.701738 | − | 0.712435i | \(-0.252408\pi\) |
−0.967856 | + | 0.251506i | \(0.919074\pi\) | |||||||
\(152\) | −39.5147 | − | 22.8138i | −0.259965 | − | 0.150091i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 50.9117 | 0.328463 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −49.6325 | + | 28.6553i | −0.316130 | + | 0.182518i | −0.649666 | − | 0.760219i | \(-0.725091\pi\) |
0.333536 | + | 0.942737i | \(0.391758\pi\) | |||||||
\(158\) | 94.6274 | + | 163.899i | 0.598908 | + | 1.03734i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.73951i | 0.0358719i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 87.4558 | − | 151.478i | 0.536539 | − | 0.929313i | −0.462548 | − | 0.886594i | \(-0.653065\pi\) |
0.999087 | − | 0.0427185i | \(-0.0136019\pi\) | |||||||
\(164\) | 12.3015 | − | 7.10228i | 0.0750092 | − | 0.0433066i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 127.882 | + | 73.8329i | 0.770375 | + | 0.444776i | ||||
\(167\) | − | 196.163i | − | 1.17463i | −0.809359 | − | 0.587315i | \(-0.800185\pi\) | ||
0.809359 | − | 0.587315i | \(-0.199815\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 88.7645 | 0.525234 | ||||||||
\(170\) | −21.8162 | + | 37.7868i | −0.128331 | + | 0.222275i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 74.4264 | + | 128.910i | 0.432712 | + | 0.749479i | ||||
\(173\) | −33.3640 | − | 19.2627i | −0.192855 | − | 0.111345i | 0.400463 | − | 0.916313i | \(-0.368849\pi\) |
−0.593319 | + | 0.804968i | \(0.702183\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 40.9706 | 0.232787 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 177.551 | − | 102.509i | 0.997479 | − | 0.575895i | ||||
\(179\) | −95.5477 | − | 165.494i | −0.533786 | − | 0.924545i | −0.999221 | − | 0.0394627i | \(-0.987435\pi\) |
0.465435 | − | 0.885082i | \(-0.345898\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 120.793i | 0.667367i | 0.942685 | + | 0.333683i | \(0.108292\pi\) | ||||
−0.942685 | + | 0.333683i | \(0.891708\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.51472 | − | 16.4800i | 0.0517104 | − | 0.0895651i | ||||
\(185\) | −27.1615 | + | 15.6817i | −0.146819 | + | 0.0847659i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 269.735 | + | 155.732i | 1.44243 | + | 0.832789i | ||||
\(188\) | 116.591i | 0.620164i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 23.1472 | 0.121827 | ||||||||
\(191\) | 56.0330 | − | 97.0520i | 0.293367 | − | 0.508126i | −0.681237 | − | 0.732063i | \(-0.738558\pi\) |
0.974604 | + | 0.223937i | \(0.0718910\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.4558 | + | 19.8421i | 0.0593567 | + | 0.102809i | 0.894177 | − | 0.447714i | \(-0.147762\pi\) |
−0.834820 | + | 0.550523i | \(0.814428\pi\) | |||||||
\(194\) | −123.338 | − | 71.2093i | −0.635763 | − | 0.367058i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 116.059 | 0.589131 | 0.294566 | − | 0.955631i | \(-0.404825\pi\) | ||||
0.294566 | + | 0.955631i | \(0.404825\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 141.250 | − | 81.5506i | 0.709798 | − | 0.409802i | −0.101188 | − | 0.994867i | \(-0.532264\pi\) |
0.810986 | + | 0.585065i | \(0.198931\pi\) | |||||||
\(200\) | 33.8995 | + | 58.7156i | 0.169497 | + | 0.293578i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 196.409i | − | 0.972323i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.60303 | + | 6.24063i | −0.0175758 | + | 0.0304421i | ||||
\(206\) | −96.6030 | + | 55.7738i | −0.468947 | + | 0.270747i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 31.0294 | + | 17.9149i | 0.149180 | + | 0.0861291i | ||||
\(209\) | − | 165.232i | − | 0.790586i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 106.426 | 0.504391 | 0.252195 | − | 0.967676i | \(-0.418847\pi\) | ||||
0.252195 | + | 0.967676i | \(0.418847\pi\) | |||||||
\(212\) | −70.9706 | + | 122.925i | −0.334767 | + | 0.579833i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 26.6985 | + | 46.2431i | 0.124759 | + | 0.216089i | ||||
\(215\) | −65.3970 | − | 37.7570i | −0.304172 | − | 0.175614i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −45.1716 | −0.207209 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −18.0000 | + | 10.3923i | −0.0818182 | + | 0.0472377i | ||||
\(221\) | 136.191 | + | 235.890i | 0.616248 | + | 1.06737i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 57.0047i | − | 0.255627i | −0.991798 | − | 0.127813i | \(-0.959204\pi\) | ||
0.991798 | − | 0.127813i | \(-0.0407958\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 75.6396 | − | 131.012i | 0.334689 | − | 0.579698i | ||||
\(227\) | −248.912 | + | 143.709i | −1.09653 | + | 0.633080i | −0.935307 | − | 0.353838i | \(-0.884876\pi\) |
−0.161221 | + | 0.986918i | \(0.551543\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −120.728 | − | 69.7023i | −0.527196 | − | 0.304377i | 0.212678 | − | 0.977122i | \(-0.431782\pi\) |
−0.739874 | + | 0.672746i | \(0.765115\pi\) | |||||||
\(230\) | 9.65375i | 0.0419728i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 84.8528 | 0.365745 | ||||||||
\(233\) | 181.368 | − | 314.138i | 0.778401 | − | 1.34823i | −0.154461 | − | 0.987999i | \(-0.549364\pi\) |
0.932863 | − | 0.360232i | \(-0.117302\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −29.5736 | − | 51.2230i | −0.125845 | − | 0.217970i | ||||
\(236\) | −0.852814 | − | 0.492372i | −0.00361362 | − | 0.00208632i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.4781 | −0.0773144 | −0.0386572 | − | 0.999253i | \(-0.512308\pi\) | ||||
−0.0386572 | + | 0.999253i | \(0.512308\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −154.243 | + | 89.0520i | −0.640011 | + | 0.369510i | −0.784619 | − | 0.619979i | \(-0.787141\pi\) |
0.144608 | + | 0.989489i | \(0.453808\pi\) | |||||||
\(242\) | −11.3762 | − | 19.7041i | −0.0470089 | − | 0.0814218i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.73951i | 0.0235226i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 72.2498 | − | 125.140i | 0.292509 | − | 0.506641i | ||||
\(248\) | −122.912 | + | 70.9631i | −0.495612 | + | 0.286142i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −60.8528 | − | 35.1334i | −0.243411 | − | 0.140534i | ||||
\(251\) | − | 50.6709i | − | 0.201876i | −0.994893 | − | 0.100938i | \(-0.967816\pi\) | ||
0.994893 | − | 0.100938i | \(-0.0321844\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 68.9117 | 0.272378 | ||||||||
\(254\) | 15.5980 | − | 27.0165i | 0.0614094 | − | 0.106364i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 162.452 | + | 93.7919i | 0.632110 | + | 0.364949i | 0.781569 | − | 0.623819i | \(-0.214420\pi\) |
−0.149459 | + | 0.988768i | \(0.547753\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −18.1766 | −0.0699101 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −86.9117 | + | 50.1785i | −0.331724 | + | 0.191521i | ||||
\(263\) | −201.489 | − | 348.989i | −0.766117 | − | 1.32695i | −0.939654 | − | 0.342127i | \(-0.888853\pi\) |
0.173537 | − | 0.984827i | \(-0.444481\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 72.0076i | − | 0.271727i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −27.0294 | + | 46.8164i | −0.100856 | + | 0.174688i | ||||
\(269\) | 416.158 | − | 240.269i | 1.54706 | − | 0.893193i | 0.548691 | − | 0.836025i | \(-0.315126\pi\) |
0.998365 | − | 0.0571675i | \(-0.0182069\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.3087 | + | 18.6534i | 0.119220 | + | 0.0688318i | 0.558424 | − | 0.829556i | \(-0.311406\pi\) |
−0.439204 | + | 0.898387i | \(0.644739\pi\) | |||||||
\(272\) | − | 121.634i | − | 0.447184i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −149.574 | −0.545889 | ||||||||
\(275\) | −122.761 | + | 212.628i | −0.446403 | + | 0.773193i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 41.3381 | + | 71.5997i | 0.149235 | + | 0.258483i | 0.930945 | − | 0.365160i | \(-0.118986\pi\) |
−0.781710 | + | 0.623642i | \(0.785652\pi\) | |||||||
\(278\) | 222.073 | + | 128.214i | 0.798824 | + | 0.461201i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 150.853 | 0.536843 | 0.268421 | − | 0.963302i | \(-0.413498\pi\) | ||||
0.268421 | + | 0.963302i | \(0.413498\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 246.088 | − | 142.079i | 0.869570 | − | 0.502046i | 0.00236468 | − | 0.999997i | \(-0.499247\pi\) |
0.867205 | + | 0.497951i | \(0.165914\pi\) | |||||||
\(284\) | 50.6102 | + | 87.6594i | 0.178205 | + | 0.308660i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 129.751i | 0.453674i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 317.838 | − | 550.512i | 1.09979 | − | 1.90488i | ||||
\(290\) | −37.2792 | + | 21.5232i | −0.128549 | + | 0.0742178i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 122.309 | + | 70.6149i | 0.418865 | + | 0.241832i | ||||
\(293\) | 537.237i | 1.83357i | 0.399379 | + | 0.916786i | \(0.369226\pi\) | ||||
−0.399379 | + | 0.916786i | \(0.630774\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.499567 | 0.00169345 | ||||||||
\(296\) | 43.7157 | − | 75.7179i | 0.147688 | − | 0.255804i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −29.0955 | − | 50.3948i | −0.0976358 | − | 0.169110i | ||||
\(299\) | 52.1909 | + | 30.1324i | 0.174552 | + | 0.100777i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −113.657 | −0.376347 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −55.8823 | + | 32.2636i | −0.183823 | + | 0.106130i | ||||
\(305\) | −1.45584 | − | 2.52160i | −0.00477326 | − | 0.00826753i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 34.7430i | − | 0.113169i | −0.998398 | − | 0.0565847i | \(-0.981979\pi\) | ||
0.998398 | − | 0.0565847i | \(-0.0180211\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 36.0000 | − | 62.3538i | 0.116129 | − | 0.201141i | ||||
\(311\) | 77.2203 | − | 44.5832i | 0.248297 | − | 0.143354i | −0.370687 | − | 0.928758i | \(-0.620878\pi\) |
0.618984 | + | 0.785403i | \(0.287544\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −450.073 | − | 259.850i | −1.43793 | − | 0.830191i | −0.440227 | − | 0.897886i | \(-0.645102\pi\) |
−0.997706 | + | 0.0676951i | \(0.978435\pi\) | |||||||
\(314\) | 81.0495i | 0.258119i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 267.647 | 0.846983 | ||||||||
\(317\) | 271.014 | − | 469.411i | 0.854935 | − | 1.48079i | −0.0217710 | − | 0.999763i | \(-0.506930\pi\) |
0.876706 | − | 0.481027i | \(-0.159736\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 153.640 | + | 266.112i | 0.481629 | + | 0.834206i | ||||
\(320\) | 7.02944 | + | 4.05845i | 0.0219670 | + | 0.0126826i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −490.544 | −1.51871 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −185.948 | + | 107.357i | −0.572149 | + | 0.330330i | ||||
\(326\) | −123.681 | − | 214.222i | −0.379390 | − | 0.657123i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 20.0883i | − | 0.0612448i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −89.8162 | + | 155.566i | −0.271348 | + | 0.469989i | −0.969207 | − | 0.246246i | \(-0.920803\pi\) |
0.697859 | + | 0.716235i | \(0.254136\pi\) | |||||||
\(332\) | 180.853 | − | 104.415i | 0.544737 | − | 0.314504i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −240.250 | − | 138.708i | −0.719311 | − | 0.415294i | ||||
\(335\) | − | 27.4244i | − | 0.0818638i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 291.823 | 0.865945 | 0.432972 | − | 0.901407i | \(-0.357465\pi\) | ||||
0.432972 | + | 0.901407i | \(0.357465\pi\) | |||||||
\(338\) | 62.7660 | − | 108.714i | 0.185698 | − | 0.321639i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 30.8528 | + | 53.4386i | 0.0907436 | + | 0.157172i | ||||
\(341\) | −445.103 | − | 256.980i | −1.30529 | − | 0.753607i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 210.510 | 0.611947 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −47.1838 | + | 27.2416i | −0.136369 | + | 0.0787328i | ||||
\(347\) | 226.040 | + | 391.513i | 0.651413 | + | 1.12828i | 0.982780 | + | 0.184778i | \(0.0591566\pi\) |
−0.331368 | + | 0.943502i | \(0.607510\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 235.067i | 0.673543i | 0.941586 | + | 0.336772i | \(0.109335\pi\) | ||||
−0.941586 | + | 0.336772i | \(0.890665\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 28.9706 | − | 50.1785i | 0.0823027 | − | 0.142553i | ||||
\(353\) | 21.8635 | − | 12.6229i | 0.0619363 | − | 0.0357590i | −0.468712 | − | 0.883351i | \(-0.655282\pi\) |
0.530648 | + | 0.847592i | \(0.321948\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −44.4701 | − | 25.6748i | −0.125268 | − | 0.0723235i | ||||
\(356\) | − | 289.940i | − | 0.814438i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −270.250 | −0.754888 | ||||||||
\(359\) | −53.1213 | + | 92.0088i | −0.147970 | + | 0.256292i | −0.930477 | − | 0.366350i | \(-0.880607\pi\) |
0.782507 | + | 0.622642i | \(0.213941\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −50.3823 | − | 87.2646i | −0.139563 | − | 0.241730i | ||||
\(362\) | 147.941 | + | 85.4138i | 0.408677 | + | 0.235950i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −71.6468 | −0.196292 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −248.044 | + | 143.208i | −0.675868 | + | 0.390213i | −0.798297 | − | 0.602265i | \(-0.794265\pi\) |
0.122428 | + | 0.992477i | \(0.460932\pi\) | |||||||
\(368\) | −13.4558 | − | 23.3062i | −0.0365648 | − | 0.0633321i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 44.3545i | 0.119877i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 211.735 | − | 366.736i | 0.567654 | − | 0.983206i | −0.429143 | − | 0.903237i | \(-0.641184\pi\) |
0.996797 | − | 0.0799696i | \(-0.0254823\pi\) | |||||||
\(374\) | 381.463 | − | 220.238i | 1.01995 | − | 0.588871i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 142.794 | + | 82.4421i | 0.379771 | + | 0.219261i | ||||
\(377\) | 268.723i | 0.712793i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 101.103 | 0.266761 | 0.133381 | − | 0.991065i | \(-0.457417\pi\) | ||||
0.133381 | + | 0.991065i | \(0.457417\pi\) | |||||||
\(380\) | 16.3675 | − | 28.3494i | 0.0430725 | − | 0.0746037i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −79.2426 | − | 137.252i | −0.207441 | − | 0.359299i | ||||
\(383\) | 190.867 | + | 110.197i | 0.498348 | + | 0.287721i | 0.728031 | − | 0.685544i | \(-0.240436\pi\) |
−0.229683 | + | 0.973265i | \(0.573769\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 32.4020 | 0.0839431 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −174.426 | + | 100.705i | −0.449553 | + | 0.259549i | ||||
\(389\) | −191.735 | − | 332.095i | −0.492892 | − | 0.853714i | 0.507074 | − | 0.861902i | \(-0.330727\pi\) |
−0.999966 | + | 0.00818803i | \(0.997394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 204.586i | − | 0.523238i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 82.0660 | − | 142.143i | 0.208289 | − | 0.360768i | ||||
\(395\) | −117.588 | + | 67.8894i | −0.297691 | + | 0.171872i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 420.177 | + | 242.589i | 1.05838 | + | 0.611056i | 0.924984 | − | 0.380007i | \(-0.124078\pi\) |
0.133396 | + | 0.991063i | \(0.457412\pi\) | |||||||
\(398\) | − | 230.660i | − | 0.579548i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 95.8823 | 0.239706 | ||||||||
\(401\) | −126.588 | + | 219.257i | −0.315680 | + | 0.546775i | −0.979582 | − | 0.201045i | \(-0.935566\pi\) |
0.663901 | + | 0.747820i | \(0.268899\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −224.735 | − | 389.253i | −0.557655 | − | 0.965887i | ||||
\(404\) | −240.551 | − | 138.882i | −0.595424 | − | 0.343768i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 316.617 | 0.777930 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.66905 | − | 2.69568i | 0.0114158 | − | 0.00659089i | −0.494281 | − | 0.869302i | \(-0.664569\pi\) |
0.505697 | + | 0.862711i | \(0.331235\pi\) | |||||||
\(410\) | 5.09545 | + | 8.82559i | 0.0124279 | + | 0.0215258i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 157.752i | 0.382893i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −52.9706 | + | 91.7477i | −0.127640 | + | 0.221079i | ||||
\(416\) | 43.8823 | − | 25.3354i | 0.105486 | − | 0.0609025i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −202.368 | − | 116.837i | −0.484133 | − | 0.279514i | ||||
\(419\) | − | 294.431i | − | 0.702700i | −0.936244 | − | 0.351350i | \(-0.885723\pi\) | ||
0.936244 | − | 0.351350i | \(-0.114277\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −290.441 | −0.689883 | −0.344941 | − | 0.938624i | \(-0.612101\pi\) | ||||
−0.344941 | + | 0.938624i | \(0.612101\pi\) | |||||||
\(422\) | 75.2548 | − | 130.345i | 0.178329 | − | 0.308875i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 100.368 | + | 173.842i | 0.236716 | + | 0.410004i | ||||
\(425\) | 631.253 | + | 364.454i | 1.48530 | + | 0.857540i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 75.5147 | 0.176436 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −92.4853 | + | 53.3964i | −0.215082 | + | 0.124178i | ||||
\(431\) | 25.3568 | + | 43.9193i | 0.0588325 | + | 0.101901i | 0.893942 | − | 0.448183i | \(-0.147929\pi\) |
−0.835109 | + | 0.550084i | \(0.814596\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 724.761i | − | 1.67381i | −0.547347 | − | 0.836906i | \(-0.684362\pi\) | ||
0.547347 | − | 0.836906i | \(-0.315638\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −31.9411 | + | 55.3237i | −0.0732595 | + | 0.126889i | ||||
\(437\) | −93.9929 | + | 54.2668i | −0.215087 | + | 0.124180i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 321.926 | + | 185.864i | 0.733317 | + | 0.423381i | 0.819634 | − | 0.572887i | \(-0.194177\pi\) |
−0.0863177 | + | 0.996268i | \(0.527510\pi\) | |||||||
\(440\) | 29.3939i | 0.0668043i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 385.206 | 0.871507 | ||||||||
\(443\) | −114.629 | + | 198.543i | −0.258756 | + | 0.448178i | −0.965909 | − | 0.258882i | \(-0.916646\pi\) |
0.707153 | + | 0.707061i | \(0.249979\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 73.5442 | + | 127.382i | 0.165268 | + | 0.286252i | ||||
\(446\) | −69.8162 | − | 40.3084i | −0.156539 | − | 0.0903776i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 600.323 | 1.33702 | 0.668511 | − | 0.743702i | \(-0.266932\pi\) | ||||
0.668511 | + | 0.743702i | \(0.266932\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 63.0000 | − | 36.3731i | 0.139690 | − | 0.0806498i | ||||
\(452\) | −106.971 | − | 185.278i | −0.236661 | − | 0.409908i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 406.471i | 0.895311i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −241.912 | + | 419.003i | −0.529347 | + | 0.916856i | 0.470067 | + | 0.882631i | \(0.344230\pi\) |
−0.999414 | + | 0.0342255i | \(0.989104\pi\) | |||||||
\(458\) | −170.735 | + | 98.5739i | −0.372784 | + | 0.215227i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11.8234 | + | 6.82623i | 0.0257030 | + | 0.0148396i | ||||
\(461\) | − | 274.661i | − | 0.595794i | −0.954598 | − | 0.297897i | \(-0.903715\pi\) | ||
0.954598 | − | 0.297897i | \(-0.0962852\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −153.470 | −0.331469 | −0.165734 | − | 0.986170i | \(-0.552999\pi\) | ||||
−0.165734 | + | 0.986170i | \(0.552999\pi\) | |||||||
\(464\) | 60.0000 | − | 103.923i | 0.129310 | − | 0.223972i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −256.492 | − | 444.258i | −0.550413 | − | 0.953343i | ||||
\(467\) | −53.4701 | − | 30.8710i | −0.114497 | − | 0.0661049i | 0.441658 | − | 0.897184i | \(-0.354391\pi\) |
−0.556155 | + | 0.831079i | \(0.687724\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −83.6468 | −0.177972 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.20606 | + | 0.696320i | −0.00255521 | + | 0.00147525i | ||||
\(473\) | 381.161 | + | 660.191i | 0.805838 | + | 1.39575i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 386.689i | − | 0.814082i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.0660 | + | 22.6310i | −0.0273348 | + | 0.0473452i | ||||
\(479\) | −481.955 | + | 278.257i | −1.00617 | + | 0.580912i | −0.910068 | − | 0.414459i | \(-0.863971\pi\) |
−0.0961020 | + | 0.995371i | \(0.530637\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 239.793 | + | 138.445i | 0.498530 | + | 0.287827i | ||||
\(482\) | 251.877i | 0.522567i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −32.1766 | −0.0664806 | ||||||||
\(485\) | 51.0883 | − | 88.4876i | 0.105337 | − | 0.182449i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 162.610 | + | 281.649i | 0.333902 | + | 0.578335i | 0.983273 | − | 0.182136i | \(-0.0583013\pi\) |
−0.649371 | + | 0.760471i | \(0.724968\pi\) | |||||||
\(488\) | 7.02944 | + | 4.05845i | 0.0144046 | + | 0.00831649i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −643.477 | −1.31054 | −0.655272 | − | 0.755393i | \(-0.727446\pi\) | ||||
−0.655272 | + | 0.755393i | \(0.727446\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 790.036 | − | 456.127i | 1.60251 | − | 0.925208i | ||||
\(494\) | −102.177 | − | 176.975i | −0.206835 | − | 0.358249i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 200.714i | 0.404665i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −377.713 | + | 654.218i | −0.756939 | + | 1.31106i | 0.187465 | + | 0.982271i | \(0.439973\pi\) |
−0.944404 | + | 0.328786i | \(0.893360\pi\) | |||||||
\(500\) | −86.0589 | + | 49.6861i | −0.172118 | + | 0.0993722i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −62.0589 | − | 35.8297i | −0.123623 | − | 0.0713739i | ||||
\(503\) | 509.409i | 1.01274i | 0.862316 | + | 0.506371i | \(0.169013\pi\) | ||||
−0.862316 | + | 0.506371i | \(0.830987\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 140.912 | 0.279033 | ||||||||
\(506\) | 48.7279 | − | 84.3992i | 0.0963002 | − | 0.166797i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −22.0589 | − | 38.2071i | −0.0434230 | − | 0.0752108i | ||||
\(509\) | −666.349 | − | 384.717i | −1.30913 | − | 0.755828i | −0.327182 | − | 0.944961i | \(-0.606099\pi\) |
−0.981951 | + | 0.189133i | \(0.939432\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 229.742 | − | 132.642i | 0.446969 | − | 0.258058i | ||||
\(515\) | −40.0143 | − | 69.3068i | −0.0776976 | − | 0.134576i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 597.099i | 1.15493i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.8528 | + | 22.2617i | −0.0247169 | + | 0.0428110i | ||||
\(521\) | −463.503 | + | 267.604i | −0.889641 | + | 0.513635i | −0.873825 | − | 0.486240i | \(-0.838368\pi\) |
−0.0158162 | + | 0.999875i | \(0.505035\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −726.999 | − | 419.733i | −1.39006 | − | 0.802549i | −0.396735 | − | 0.917933i | \(-0.629857\pi\) |
−0.993321 | + | 0.115384i | \(0.963190\pi\) | |||||||
\(524\) | 141.926i | 0.270852i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −569.897 | −1.08345 | ||||||||
\(527\) | −762.926 | + | 1321.43i | −1.44768 | + | 2.50745i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 241.868 | + | 418.927i | 0.457217 | + | 0.791922i | ||||
\(530\) | −88.1909 | − | 50.9170i | −0.166398 | − | 0.0960699i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 63.6182 | 0.119359 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −33.1766 | + | 19.1545i | −0.0620124 | + | 0.0358029i | ||||
\(536\) | 38.2254 | + | 66.2083i | 0.0713160 | + | 0.123523i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 679.583i | − | 1.26317i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −142.926 | + | 247.555i | −0.264188 | + | 0.457588i | −0.967351 | − | 0.253442i | \(-0.918437\pi\) |
0.703162 | + | 0.711029i | \(0.251771\pi\) | |||||||
\(542\) | 45.6913 | − | 26.3799i | 0.0843014 | − | 0.0486714i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −148.971 | − | 86.0082i | −0.273843 | − | 0.158103i | ||||
\(545\) | − | 32.4078i | − | 0.0594639i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −741.470 | −1.35552 | −0.677761 | − | 0.735283i | \(-0.737049\pi\) | ||||
−0.677761 | + | 0.735283i | \(0.737049\pi\) | |||||||
\(548\) | −105.765 | + | 183.189i | −0.193001 | + | 0.334287i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 173.610 | + | 300.702i | 0.315655 | + | 0.546730i | ||||
\(551\) | −419.117 | − | 241.977i | −0.760648 | − | 0.439160i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 116.922 | 0.211050 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 314.059 | − | 181.322i | 0.564854 | − | 0.326119i | ||||
\(557\) | 417.426 | + | 723.004i | 0.749419 | + | 1.29803i | 0.948101 | + | 0.317968i | \(0.103000\pi\) |
−0.198682 | + | 0.980064i | \(0.563666\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 666.669i | 1.19261i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 106.669 | − | 184.756i | 0.189803 | − | 0.328748i | ||||
\(563\) | 361.809 | − | 208.891i | 0.642645 | − | 0.371031i | −0.142988 | − | 0.989724i | \(-0.545671\pi\) |
0.785633 | + | 0.618693i | \(0.212338\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 93.9929 | + | 54.2668i | 0.166359 | + | 0.0960474i | ||||
\(566\) | − | 401.861i | − | 0.710001i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 143.147 | 0.252020 | ||||||||
\(569\) | 336.515 | − | 582.861i | 0.591414 | − | 1.02436i | −0.402628 | − | 0.915364i | \(-0.631903\pi\) |
0.994042 | − | 0.108996i | \(-0.0347635\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 132.544 | + | 229.573i | 0.232126 | + | 0.402055i | 0.958434 | − | 0.285315i | \(-0.0920984\pi\) |
−0.726307 | + | 0.687370i | \(0.758765\pi\) | |||||||
\(572\) | 158.912 | + | 91.7477i | 0.277818 | + | 0.160398i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 161.272 | 0.280473 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 405.941 | − | 234.370i | 0.703537 | − | 0.406188i | −0.105126 | − | 0.994459i | \(-0.533525\pi\) |
0.808664 | + | 0.588271i | \(0.200191\pi\) | |||||||
\(578\) | −449.491 | − | 778.541i | −0.777666 | − | 1.34696i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 60.8767i | 0.104960i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −363.463 | + | 629.536i | −0.623436 | + | 1.07982i | ||||
\(584\) | 172.971 | − | 99.8646i | 0.296182 | − | 0.171001i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 657.978 | + | 379.884i | 1.12283 | + | 0.648266i | ||||
\(587\) | 120.530i | 0.205332i | 0.994716 | + | 0.102666i | \(0.0327372\pi\) | ||||
−0.994716 | + | 0.102666i | \(0.967263\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 809.470 | 1.37431 | ||||||||
\(590\) | 0.353247 | − | 0.611842i | 0.000598724 | − | 0.00103702i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −61.8234 | − | 107.081i | −0.104431 | − | 0.180880i | ||||
\(593\) | 486.245 | + | 280.734i | 0.819975 | + | 0.473413i | 0.850408 | − | 0.526124i | \(-0.176355\pi\) |
−0.0304327 | + | 0.999537i | \(0.509689\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −82.2944 | −0.138078 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 73.8091 | − | 42.6137i | 0.123427 | − | 0.0712604i | ||||
\(599\) | 470.054 | + | 814.158i | 0.784732 | + | 1.35920i | 0.929159 | + | 0.369680i | \(0.120533\pi\) |
−0.144427 | + | 0.989515i | \(0.546134\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 563.527i | 0.937649i | 0.883291 | + | 0.468824i | \(0.155322\pi\) | ||||
−0.883291 | + | 0.468824i | \(0.844678\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −80.3675 | + | 139.201i | −0.133059 | + | 0.230465i | ||||
\(605\) | 14.1365 | − | 8.16170i | 0.0233661 | − | 0.0134904i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 265.514 | + | 153.294i | 0.437420 | + | 0.252544i | 0.702503 | − | 0.711681i | \(-0.252066\pi\) |
−0.265083 | + | 0.964226i | \(0.585399\pi\) | |||||||
\(608\) | 91.2553i | 0.150091i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.11775 | −0.00675041 | ||||||||
\(611\) | −261.088 | + | 452.218i | −0.427313 | + | 0.740128i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −137.794 | − | 238.666i | −0.224786 | − | 0.389341i | 0.731469 | − | 0.681875i | \(-0.238835\pi\) |
−0.956255 | + | 0.292533i | \(0.905502\pi\) | |||||||
\(614\) | −42.5513 | − | 24.5670i | −0.0693018 | − | 0.0400114i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −461.294 | −0.747639 | −0.373820 | − | 0.927501i | \(-0.621952\pi\) | ||||
−0.373820 | + | 0.927501i | \(0.621952\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −324.676 | + | 187.452i | −0.524517 | + | 0.302830i | −0.738781 | − | 0.673946i | \(-0.764598\pi\) |
0.214264 | + | 0.976776i | \(0.431265\pi\) | |||||||
\(620\) | −50.9117 | − | 88.1816i | −0.0821156 | − | 0.142228i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 126.100i | − | 0.202734i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −274.426 | + | 475.320i | −0.439082 | + | 0.760512i | ||||
\(626\) | −636.500 | + | 367.483i | −1.01677 | + | 0.587034i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 99.2649 | + | 57.3106i | 0.158065 | + | 0.0912590i | ||||
\(629\) | − | 939.978i | − | 1.49440i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1127.32 | −1.78656 | −0.893282 | − | 0.449496i | \(-0.851603\pi\) | ||||
−0.893282 | + | 0.449496i | \(0.851603\pi\) | |||||||
\(632\) | 189.255 | − | 327.799i | 0.299454 | − | 0.518669i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −383.272 | − | 663.847i | −0.604530 | − | 1.04708i | ||||
\(635\) | 19.3827 | + | 11.1906i | 0.0305239 | + | 0.0176230i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 434.558 | 0.681126 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.94113 | − | 5.73951i | 0.0155330 | − | 0.00896799i | ||||
\(641\) | −442.176 | − | 765.871i | −0.689822 | − | 1.19481i | −0.971895 | − | 0.235414i | \(-0.924356\pi\) |
0.282074 | − | 0.959393i | \(-0.408978\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 300.765i | − | 0.467753i | −0.972266 | − | 0.233876i | \(-0.924859\pi\) | ||
0.972266 | − | 0.233876i | \(-0.0751411\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −346.867 | + | 600.791i | −0.536946 | + | 0.930018i | ||||
\(647\) | 814.587 | − | 470.302i | 1.25902 | − | 0.726896i | 0.286137 | − | 0.958189i | \(-0.407629\pi\) |
0.972884 | + | 0.231292i | \(0.0742953\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.36753 | − | 2.52160i | −0.00672963 | − | 0.00388536i | ||||
\(650\) | 303.652i | 0.467157i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −349.823 | −0.536539 | ||||||||
\(653\) | −227.985 | + | 394.881i | −0.349135 | + | 0.604719i | −0.986096 | − | 0.166177i | \(-0.946858\pi\) |
0.636961 | + | 0.770896i | \(0.280191\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −36.0000 | − | 62.3538i | −0.0549618 | − | 0.0951967i | ||||
\(656\) | −24.6030 | − | 14.2046i | −0.0375046 | − | 0.0216533i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −403.684 | −0.612571 | −0.306285 | − | 0.951940i | \(-0.599086\pi\) | ||||
−0.306285 | + | 0.951940i | \(0.599086\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −998.881 | + | 576.704i | −1.51117 | + | 0.872473i | −0.511252 | + | 0.859431i | \(0.670818\pi\) |
−0.999915 | + | 0.0130418i | \(0.995849\pi\) | |||||||
\(662\) | 127.019 | + | 220.004i | 0.191872 | + | 0.332332i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 295.331i | − | 0.444776i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 100.919 | − | 174.797i | 0.151303 | − | 0.262064i | ||||
\(668\) | −339.765 | + | 196.163i | −0.508629 | + | 0.293657i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −33.5879 | − | 19.3920i | −0.0501312 | − | 0.0289432i | ||||
\(671\) | 29.3939i | 0.0438061i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −607.440 | −0.902585 | −0.451293 | − | 0.892376i | \(-0.649037\pi\) | ||||
−0.451293 | + | 0.892376i | \(0.649037\pi\) | |||||||
\(674\) | 206.350 | − | 357.409i | 0.306158 | − | 0.530281i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −88.7645 | − | 153.745i | −0.131308 | − | 0.227433i | ||||
\(677\) | −985.180 | − | 568.794i | −1.45521 | − | 0.840168i | −0.456444 | − | 0.889752i | \(-0.650877\pi\) |
−0.998770 | + | 0.0495834i | \(0.984211\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 87.2649 | 0.128331 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −629.470 | + | 363.425i | −0.922977 | + | 0.532881i | ||||
\(683\) | −409.055 | − | 708.505i | −0.598910 | − | 1.03734i | −0.992982 | − | 0.118263i | \(-0.962268\pi\) |
0.394073 | − | 0.919079i | \(-0.371066\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 107.310i | − | 0.156657i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 148.853 | − | 257.821i | 0.216356 | − | 0.374739i | ||||
\(689\) | −550.544 | + | 317.857i | −0.799048 | + | 0.461331i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −176.912 | − | 102.140i | −0.256023 | − | 0.147815i | 0.366496 | − | 0.930420i | \(-0.380557\pi\) |
−0.622519 | + | 0.782605i | \(0.713891\pi\) | |||||||
\(692\) | 77.0508i | 0.111345i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 639.338 | 0.921236 | ||||||||
\(695\) | −91.9857 | + | 159.324i | −0.132354 | + | 0.229243i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −107.985 | − | 187.035i | −0.154928 | − | 0.268343i | ||||
\(698\) | 287.897 | + | 166.217i | 0.412459 | + | 0.238133i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 318.853 | 0.454854 | 0.227427 | − | 0.973795i | \(-0.426969\pi\) | ||||
0.227427 | + | 0.973795i | \(0.426969\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −431.854 | + | 249.331i | −0.614301 | + | 0.354667i | ||||
\(704\) | −40.9706 | − | 70.9631i | −0.0581968 | − | 0.100800i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 35.7030i | − | 0.0505708i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 108.823 | − | 188.488i | 0.153489 | − | 0.265850i | −0.779019 | − | 0.627000i | \(-0.784283\pi\) |
0.932508 | + | 0.361150i | \(0.117616\pi\) | |||||||
\(710\) | −62.8903 | + | 36.3097i | −0.0885778 | + | 0.0511404i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −355.103 | − | 205.019i | −0.498740 | − | 0.287947i | ||||
\(713\) | 337.597i | 0.473488i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −93.0883 | −0.130193 | ||||||||
\(716\) | −191.095 | + | 330.987i | −0.266893 | + | 0.462272i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 75.1249 | + | 130.120i | 0.104631 | + | 0.181226i | ||||
\(719\) | 1045.60 | + | 603.679i | 1.45425 | + | 0.839609i | 0.998718 | − | 0.0506134i | \(-0.0161176\pi\) |
0.455527 | + | 0.890222i | \(0.349451\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −142.503 | −0.197372 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 209.220 | − | 120.793i | 0.288978 | − | 0.166842i | ||||
\(725\) | 359.558 | + | 622.773i | 0.495943 | + | 0.858998i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 123.231i | 0.169506i | 0.996402 | + | 0.0847528i | \(0.0270100\pi\) | ||||
−0.996402 | + | 0.0847528i | \(0.972990\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −50.6619 | + | 87.7490i | −0.0693999 | + | 0.120204i | ||||
\(731\) | 1959.98 | − | 1131.60i | 2.68124 | − | 1.54801i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 325.434 | + | 187.890i | 0.443976 | + | 0.256330i | 0.705283 | − | 0.708926i | \(-0.250820\pi\) |
−0.261307 | + | 0.965256i | \(0.584153\pi\) | |||||||
\(734\) | 405.054i | 0.551844i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −38.0589 | −0.0517104 | ||||||||
\(737\) | −138.426 | + | 239.762i | −0.187824 | + | 0.325321i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −361.265 | − | 625.729i | −0.488856 | − | 0.846724i | 0.511061 | − | 0.859544i | \(-0.329252\pi\) |
−0.999918 | + | 0.0128200i | \(0.995919\pi\) | |||||||
\(740\) | 54.3229 | + | 31.3634i | 0.0734094 | + | 0.0423829i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1268.48 | −1.70724 | −0.853618 | − | 0.520899i | \(-0.825597\pi\) | ||||
−0.853618 | + | 0.520899i | \(0.825597\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 36.1552 | − | 20.8742i | 0.0485305 | − | 0.0280191i | ||||
\(746\) | −299.439 | − | 518.643i | −0.401392 | − | 0.695232i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 622.926i | − | 0.832789i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −219.581 | + | 380.325i | −0.292384 | + | 0.506425i | −0.974373 | − | 0.224938i | \(-0.927782\pi\) |
0.681989 | + | 0.731363i | \(0.261115\pi\) | |||||||
\(752\) | 201.941 | − | 116.591i | 0.268539 | − | 0.155041i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 329.117 | + | 190.016i | 0.436495 | + | 0.252010i | ||||
\(755\) | − | 81.5419i | − | 0.108002i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −668.530 | −0.883131 | −0.441565 | − | 0.897229i | \(-0.645577\pi\) | ||||
−0.441565 | + | 0.897229i | \(0.645577\pi\) | |||||||
\(758\) | 71.4903 | − | 123.825i | 0.0943144 | − | 0.163357i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −23.1472 | − | 40.0921i | −0.0304568 | − | 0.0527528i | ||||
\(761\) | 762.202 | + | 440.058i | 1.00158 | + | 0.578263i | 0.908715 | − | 0.417416i | \(-0.137064\pi\) |
0.0928647 | + | 0.995679i | \(0.470398\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −224.132 | −0.293367 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 269.927 | − | 155.842i | 0.352385 | − | 0.203450i | ||||
\(767\) | −2.20519 | − | 3.81951i | −0.00287509 | − | 0.00497980i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1163.41i | − | 1.51289i | −0.654059 | − | 0.756444i | \(-0.726935\pi\) | ||
0.654059 | − | 0.756444i | \(-0.273065\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22.9117 | − | 39.6842i | 0.0296784 | − | 0.0514044i | ||||
\(773\) | −464.511 | + | 268.186i | −0.600920 | + | 0.346941i | −0.769403 | − | 0.638763i | \(-0.779446\pi\) |
0.168483 | + | 0.985704i | \(0.446113\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1041.66 | − | 601.403i | −1.34408 | − | 0.776004i | ||||
\(776\) | 284.837i | 0.367058i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −542.309 | −0.697055 | ||||||||
\(779\) | −57.2864 | + | 99.2229i | −0.0735383 | + | 0.127372i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 259.191 | + | 448.932i | 0.331871 | + | 0.574817i | ||||
\(782\) | −250.566 | − | 144.664i | −0.320416 | − | 0.184992i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −58.1481 | −0.0740740 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −72.6762 | + | 41.9596i | −0.0923459 | + | 0.0533159i | −0.545462 | − | 0.838136i | \(-0.683646\pi\) |
0.453116 | + | 0.891452i | \(0.350312\pi\) | |||||||
\(788\) | −116.059 | − | 201.020i | −0.147283 | − | 0.255101i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 192.020i | 0.243064i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.8528 | + | 22.2617i | −0.0162078 | + | 0.0280728i | ||||
\(794\) | 594.219 | − | 343.073i | 0.748387 | − | 0.432082i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −282.500 | − | 163.101i | −0.354899 | − | 0.204901i | ||||
\(797\) | − | 1005.57i | − | 1.26169i | −0.775908 | − | 0.630846i | \(-0.782708\pi\) | ||
0.775908 | − | 0.630846i | \(-0.217292\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1772.67 | 2.21862 | ||||||||
\(800\) | 67.7990 | − | 117.431i | 0.0847487 | − | 0.146789i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 179.022 | + | 310.076i | 0.223220 | + | 0.386628i | ||||
\(803\) | 626.382 | + | 361.642i | 0.780052 | + | 0.450363i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −635.647 | −0.788644 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −340.191 | + | 196.409i | −0.421028 | + | 0.243081i | ||||
\(809\) | −141.426 | − | 244.958i | −0.174816 | − | 0.302791i | 0.765281 | − | 0.643696i | \(-0.222600\pi\) |
−0.940098 | + | 0.340905i | \(0.889266\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 923.997i | 1.13933i | 0.821877 | + | 0.569665i | \(0.192927\pi\) | ||||
−0.821877 | + | 0.569665i | \(0.807073\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 223.882 | − | 387.775i | 0.275040 | − | 0.476383i | ||||
\(815\) | 153.691 | − | 88.7337i | 0.188578 | − | 0.108876i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1039.78 | − | 600.317i | −1.27268 | − | 0.734782i | ||||
\(818\) | − | 7.62452i | − | 0.00932093i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14.4121 | 0.0175758 | ||||||||
\(821\) | 636.161 | − | 1101.86i | 0.774862 | − | 1.34210i | −0.160010 | − | 0.987115i | \(-0.551153\pi\) |
0.934872 | − | 0.354985i | \(-0.115514\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −190.926 | − | 330.693i | −0.231988 | − | 0.401815i | 0.726405 | − | 0.687267i | \(-0.241190\pi\) |
−0.958393 | + | 0.285452i | \(0.907856\pi\) | |||||||
\(824\) | 193.206 | + | 111.548i | 0.234473 | + | 0.135373i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −653.022 | −0.789628 | −0.394814 | − | 0.918761i | \(-0.629191\pi\) | ||||
−0.394814 | + | 0.918761i | \(0.629191\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −186.698 | + | 107.790i | −0.225208 | + | 0.130024i | −0.608360 | − | 0.793662i | \(-0.708172\pi\) |
0.383151 | + | 0.923686i | \(0.374839\pi\) | |||||||
\(830\) | 74.9117 | + | 129.751i | 0.0902550 | + | 0.156326i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 71.6594i | − | 0.0861291i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 99.5147 | − | 172.365i | 0.119179 | − | 0.206425i | ||||
\(836\) | −286.191 | + | 165.232i | −0.342334 | + | 0.197646i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −360.603 | − | 208.194i | −0.430314 | − | 0.248442i | ||||
\(839\) | 632.267i | 0.753596i | 0.926295 | + | 0.376798i | \(0.122975\pi\) | ||||
−0.926295 | + | 0.376798i | \(0.877025\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.0000 | 0.0701546 | ||||||||
\(842\) | −205.373 | + | 355.716i | −0.243910 | + | 0.422465i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −106.426 | − | 184.336i | −0.126098 | − | 0.218408i | ||||
\(845\) | 77.9956 | + | 45.0308i | 0.0923024 | + | 0.0532908i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 283.882 | 0.334767 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 892.727 | − | 515.416i | 1.05027 | − | 0.606372i | ||||
\(851\) | −103.986 | − | 180.109i | −0.122192 | − | 0.211643i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 919.650i | 1.07814i | 0.842262 | + | 0.539068i | \(0.181224\pi\) | ||||
−0.842262 | + | 0.539068i | \(0.818776\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 53.3970 | − | 92.4863i | 0.0623796 | − | 0.108045i | ||||
\(857\) | −456.525 | + | 263.575i | −0.532702 | + | 0.307556i | −0.742116 | − | 0.670272i | \(-0.766178\pi\) |
0.209414 | + | 0.977827i | \(0.432844\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 207.676 | + | 119.902i | 0.241765 | + | 0.139583i | 0.615988 | − | 0.787756i | \(-0.288757\pi\) |
−0.374223 | + | 0.927339i | \(0.622090\pi\) | |||||||
\(860\) | 151.028i | 0.175614i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 71.7199 | 0.0832018 | ||||||||
\(863\) | 181.253 | − | 313.940i | 0.210027 | − | 0.363778i | −0.741696 | − | 0.670737i | \(-0.765978\pi\) |
0.951723 | + | 0.306959i | \(0.0993115\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.5442 | − | 33.8515i | −0.0225944 | − | 0.0391346i | ||||
\(866\) | −887.647 | − | 512.483i | −1.02500 | − | 0.591782i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1370.70 | 1.57734 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −209.677 | + | 121.057i | −0.240731 | + | 0.138986i | ||||
\(872\) | 45.1716 | + | 78.2395i | 0.0518023 | + | 0.0897242i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 153.490i | 0.175617i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 430.823 | − | 746.208i | 0.491247 | − | 0.850864i | −0.508702 | − | 0.860942i | \(-0.669875\pi\) |
0.999949 | + | 0.0100781i | \(0.00320801\pi\) | |||||||
\(878\) | 455.272 | − | 262.851i | 0.518533 | − | 0.299375i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 36.0000 | + | 20.7846i | 0.0409091 | + | 0.0236189i | ||||
\(881\) | 334.553i | 0.379742i | 0.981809 | + | 0.189871i | \(0.0608071\pi\) | ||||
−0.981809 | + | 0.189871i | \(0.939193\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1488.01 | −1.68518 | −0.842590 | − | 0.538555i | \(-0.818970\pi\) | ||||
−0.842590 | + | 0.538555i | \(0.818970\pi\) | |||||||
\(884\) | 272.382 | − | 471.779i | 0.308124 | − | 0.533687i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 162.110 | + | 280.782i | 0.182968 | + | 0.316910i | ||||
\(887\) | −694.118 | − | 400.749i | −0.782545 | − | 0.451803i | 0.0547862 | − | 0.998498i | \(-0.482552\pi\) |
−0.837332 | + | 0.546695i | \(0.815886\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 208.014 | 0.233724 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −98.7351 | + | 57.0047i | −0.110690 | + | 0.0639066i | ||||
\(893\) | −470.205 | − | 814.419i | −0.526546 | − | 0.912004i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 193.888i | − | 0.216634i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 424.492 | − | 735.242i | 0.472709 | − | 0.818756i | ||||
\(899\) | −1303.68 | + | 752.677i | −1.45014 | + | 0.837238i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1868.98 | + | 1079.05i | 2.07434 | + | 1.19762i | ||||
\(902\) | − | 102.879i | − | 0.114056i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −302.558 | −0.334689 | ||||||||
\(905\) | −61.2792 | + | 106.139i | −0.0677118 | + | 0.117280i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 403.640 | + | 699.124i | 0.445027 | + | 0.770810i | 0.998054 | − | 0.0623537i | \(-0.0198607\pi\) |
−0.553027 | + | 0.833163i | \(0.686527\pi\) | |||||||
\(908\) | 497.823 | + | 287.418i | 0.548264 | + | 0.316540i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 442.742 | 0.485996 | 0.242998 | − | 0.970027i | \(-0.421869\pi\) | ||||
0.242998 | + | 0.970027i | \(0.421869\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 926.205 | − | 534.745i | 1.01446 | − | 0.585701i | ||||
\(914\) | 342.115 | + | 592.560i | 0.374305 | + | 0.648315i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 278.809i | 0.304377i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 59.2275 | − | 102.585i | 0.0644478 | − | 0.111627i | −0.832001 | − | 0.554774i | \(-0.812805\pi\) |
0.896449 | + | 0.443147i | \(0.146138\pi\) | |||||||
\(920\) | 16.7208 | − | 9.65375i | 0.0181748 | − | 0.0104932i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −336.390 | − | 194.215i | −0.364848 | − | 0.210645i | ||||
\(923\) | 453.337i | 0.491156i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 740.971 | 0.801049 | ||||||||
\(926\) | −108.520 | + | 187.962i | −0.117192 | + | 0.202982i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −84.8528 | − | 146.969i | −0.0914362 | − | 0.158372i | ||||
\(929\) | −544.988 | − | 314.649i | −0.586639 | − | 0.338696i | 0.177128 | − | 0.984188i | \(-0.443319\pi\) |
−0.763767 | + | 0.645492i | \(0.776653\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −725.470 | −0.778401 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −75.6182 | + | 43.6582i | −0.0809617 | + | 0.0467432i | ||||
\(935\) | 158.007 | + | 273.676i | 0.168992 | + | 0.292702i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 210.631i | − | 0.224793i | −0.993663 | − | 0.112397i | \(-0.964147\pi\) | ||
0.993663 | − | 0.112397i | \(-0.0358527\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −59.1472 | + | 102.446i | −0.0629225 | + | 0.108985i | ||||
\(941\) | 154.518 | − | 89.2112i | 0.164206 | − | 0.0948047i | −0.415645 | − | 0.909527i | \(-0.636444\pi\) |
0.579851 | + | 0.814722i | \(0.303111\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −41.3818 | − | 23.8918i | −0.0438832 | − | 0.0253360i | ||||
\(944\) | 1.96949i | 0.00208632i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1078.09 | 1.13963 | ||||||||
\(947\) | 211.731 | − | 366.730i | 0.223581 | − | 0.387254i | −0.732312 | − | 0.680970i | \(-0.761559\pi\) |
0.955893 | + | 0.293716i | \(0.0948918\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 316.264 | + | 547.785i | 0.333260 | + | 0.577224i | ||||
\(950\) | −473.595 | − | 273.430i | −0.498521 | − | 0.287821i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 546.706 | 0.573669 | 0.286834 | − | 0.957980i | \(-0.407397\pi\) | ||||
0.286834 | + | 0.957980i | \(0.407397\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 98.4701 | − | 56.8518i | 0.103110 | − | 0.0595306i | ||||
\(956\) | 18.4781 | + | 32.0051i | 0.0193286 | + | 0.0334781i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 787.030i | 0.821534i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 778.440 | − | 1348.30i | 0.810031 | − | 1.40302i | ||||
\(962\) | 339.119 | − | 195.790i | 0.352514 | − | 0.203524i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 308.485 | + | 178.104i | 0.320005 | + | 0.184755i | ||||
\(965\) | 23.2465i | 0.0240896i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1262.32 | 1.30540 | 0.652701 | − | 0.757616i | \(-0.273636\pi\) | ||||
0.652701 | + | 0.757616i | \(0.273636\pi\) | |||||||
\(968\) | −22.7523 | + | 39.4082i | −0.0235045 | + | 0.0407109i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −72.2498 | − | 125.140i | −0.0744843 | − | 0.129011i | ||||
\(971\) | −936.116 | − | 540.467i | −0.964074 | − | 0.556608i | −0.0666496 | − | 0.997776i | \(-0.521231\pi\) |
−0.897425 | + | 0.441168i | \(0.854564\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 459.931 | 0.472208 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.94113 | − | 5.73951i | 0.0101856 | − | 0.00588065i | ||||
\(977\) | 900.131 | + | 1559.07i | 0.921322 | + | 1.59578i | 0.797373 | + | 0.603487i | \(0.206223\pi\) |
0.123949 | + | 0.992289i | \(0.460444\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1484.88i | − | 1.51673i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −455.007 | + | 788.095i | −0.463347 | + | 0.802541i | ||||
\(983\) | −863.263 | + | 498.405i | −0.878192 | + | 0.507025i | −0.870062 | − | 0.492942i | \(-0.835921\pi\) |
−0.00813046 | + | 0.999967i | \(0.502588\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 101.979 | + | 58.8774i | 0.103532 | + | 0.0597740i | ||||
\(986\) | − | 1290.12i | − | 1.30844i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −288.999 | −0.292509 | ||||||||
\(989\) | 250.368 | − | 433.649i | 0.253152 | − | 0.438472i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −394.360 | − | 683.052i | −0.397942 | − | 0.689256i | 0.595530 | − | 0.803333i | \(-0.296942\pi\) |
−0.993472 | + | 0.114078i | \(0.963609\pi\) | |||||||
\(992\) | 245.823 | + | 141.926i | 0.247806 | + | 0.143071i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 165.484 | 0.166316 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1682.42 | − | 971.348i | 1.68749 | − | 0.974271i | 0.731054 | − | 0.682320i | \(-0.239029\pi\) |
0.956433 | − | 0.291952i | \(-0.0943046\pi\) | |||||||
\(998\) | 534.167 | + | 925.204i | 0.535237 | + | 0.927058i | ||||
\(999\) | 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 | 882.3.n.d.19.2 | 4 | ||
3.2 | odd | 2 | 294.3.g.c.19.1 | 4 | |||
7.2 | even | 3 | 126.3.c.b.55.1 | 4 | |||
7.3 | odd | 6 | inner | 882.3.n.d.325.2 | 4 | ||
7.4 | even | 3 | 882.3.n.a.325.2 | 4 | |||
7.5 | odd | 6 | 126.3.c.b.55.2 | 4 | |||
7.6 | odd | 2 | 882.3.n.a.19.2 | 4 | |||
21.2 | odd | 6 | 42.3.c.a.13.4 | yes | 4 | ||
21.5 | even | 6 | 42.3.c.a.13.3 | ✓ | 4 | ||
21.11 | odd | 6 | 294.3.g.b.31.1 | 4 | |||
21.17 | even | 6 | 294.3.g.c.31.1 | 4 | |||
21.20 | even | 2 | 294.3.g.b.19.1 | 4 | |||
28.19 | even | 6 | 1008.3.f.g.433.3 | 4 | |||
28.23 | odd | 6 | 1008.3.f.g.433.2 | 4 | |||
84.23 | even | 6 | 336.3.f.c.97.1 | 4 | |||
84.47 | odd | 6 | 336.3.f.c.97.4 | 4 | |||
105.2 | even | 12 | 1050.3.h.a.349.8 | 8 | |||
105.23 | even | 12 | 1050.3.h.a.349.1 | 8 | |||
105.44 | odd | 6 | 1050.3.f.a.601.1 | 4 | |||
105.47 | odd | 12 | 1050.3.h.a.349.5 | 8 | |||
105.68 | odd | 12 | 1050.3.h.a.349.4 | 8 | |||
105.89 | even | 6 | 1050.3.f.a.601.2 | 4 | |||
168.5 | even | 6 | 1344.3.f.f.769.3 | 4 | |||
168.107 | even | 6 | 1344.3.f.e.769.4 | 4 | |||
168.131 | odd | 6 | 1344.3.f.e.769.1 | 4 | |||
168.149 | odd | 6 | 1344.3.f.f.769.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.3.c.a.13.3 | ✓ | 4 | 21.5 | even | 6 | ||
42.3.c.a.13.4 | yes | 4 | 21.2 | odd | 6 | ||
126.3.c.b.55.1 | 4 | 7.2 | even | 3 | |||
126.3.c.b.55.2 | 4 | 7.5 | odd | 6 | |||
294.3.g.b.19.1 | 4 | 21.20 | even | 2 | |||
294.3.g.b.31.1 | 4 | 21.11 | odd | 6 | |||
294.3.g.c.19.1 | 4 | 3.2 | odd | 2 | |||
294.3.g.c.31.1 | 4 | 21.17 | even | 6 | |||
336.3.f.c.97.1 | 4 | 84.23 | even | 6 | |||
336.3.f.c.97.4 | 4 | 84.47 | odd | 6 | |||
882.3.n.a.19.2 | 4 | 7.6 | odd | 2 | |||
882.3.n.a.325.2 | 4 | 7.4 | even | 3 | |||
882.3.n.d.19.2 | 4 | 1.1 | even | 1 | trivial | ||
882.3.n.d.325.2 | 4 | 7.3 | odd | 6 | inner | ||
1008.3.f.g.433.2 | 4 | 28.23 | odd | 6 | |||
1008.3.f.g.433.3 | 4 | 28.19 | even | 6 | |||
1050.3.f.a.601.1 | 4 | 105.44 | odd | 6 | |||
1050.3.f.a.601.2 | 4 | 105.89 | even | 6 | |||
1050.3.h.a.349.1 | 8 | 105.23 | even | 12 | |||
1050.3.h.a.349.4 | 8 | 105.68 | odd | 12 | |||
1050.3.h.a.349.5 | 8 | 105.47 | odd | 12 | |||
1050.3.h.a.349.8 | 8 | 105.2 | even | 12 | |||
1344.3.f.e.769.1 | 4 | 168.131 | odd | 6 | |||
1344.3.f.e.769.4 | 4 | 168.107 | even | 6 | |||
1344.3.f.f.769.2 | 4 | 168.149 | odd | 6 | |||
1344.3.f.f.769.3 | 4 | 168.5 | even | 6 |