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: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
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.c.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 | ||||
\(5\) | 4.24264 | + | 2.44949i | 0.848528 | + | 0.489898i | 0.860154 | − | 0.510034i | \(-0.170367\pi\) |
−0.0116258 | + | 0.999932i | \(0.503701\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.00000 | − | 3.46410i | 0.600000 | − | 0.346410i | ||||
\(11\) | −8.48528 | − | 14.6969i | −0.771389 | − | 1.33609i | −0.936802 | − | 0.349861i | \(-0.886229\pi\) |
0.165412 | − | 0.986224i | \(-0.447104\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.73205i | − | 0.133235i | −0.997779 | − | 0.0666173i | \(-0.978779\pi\) | ||
0.997779 | − | 0.0666173i | \(-0.0212207\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | −4.24264 | + | 2.44949i | −0.249567 | + | 0.144088i | −0.619566 | − | 0.784945i | \(-0.712691\pi\) |
0.369999 | + | 0.929032i | \(0.379358\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −25.5000 | − | 14.7224i | −1.34211 | − | 0.774865i | −0.354989 | − | 0.934870i | \(-0.615515\pi\) |
−0.987116 | + | 0.160006i | \(0.948849\pi\) | |||||||
\(20\) | − | 9.79796i | − | 0.489898i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −24.0000 | −1.09091 | ||||||||
\(23\) | −4.24264 | + | 7.34847i | −0.184463 | + | 0.319499i | −0.943395 | − | 0.331670i | \(-0.892388\pi\) |
0.758933 | + | 0.651169i | \(0.225721\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(26\) | −2.12132 | − | 1.22474i | −0.0815892 | − | 0.0471056i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 33.9411 | 1.17038 | 0.585192 | − | 0.810895i | \(-0.301019\pi\) | ||||
0.585192 | + | 0.810895i | \(0.301019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.5000 | − | 6.06218i | 0.338710 | − | 0.195554i | −0.320992 | − | 0.947082i | \(-0.604016\pi\) |
0.659701 | + | 0.751528i | \(0.270683\pi\) | |||||||
\(32\) | 2.82843 | + | 4.89898i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.92820i | 0.203771i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 23.5000 | − | 40.7032i | 0.635135 | − | 1.10009i | −0.351351 | − | 0.936244i | \(-0.614278\pi\) |
0.986486 | − | 0.163843i | \(-0.0523889\pi\) | |||||||
\(38\) | −36.0624 | + | 20.8207i | −0.949012 | + | 0.547912i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −12.0000 | − | 6.92820i | −0.300000 | − | 0.173205i | ||||
\(41\) | − | 68.5857i | − | 1.67282i | −0.548103 | − | 0.836411i | \(-0.684650\pi\) | ||
0.548103 | − | 0.836411i | \(-0.315350\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 31.0000 | 0.720930 | 0.360465 | − | 0.932773i | \(-0.382618\pi\) | ||||
0.360465 | + | 0.932773i | \(0.382618\pi\) | |||||||
\(44\) | −16.9706 | + | 29.3939i | −0.385695 | + | 0.668043i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | + | 10.3923i | 0.130435 | + | 0.225920i | ||||
\(47\) | −72.1249 | − | 41.6413i | −1.53457 | − | 0.885986i | −0.999142 | − | 0.0414059i | \(-0.986816\pi\) |
−0.535430 | − | 0.844580i | \(-0.679850\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.41421 | −0.0282843 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.00000 | + | 1.73205i | −0.0576923 | + | 0.0333087i | ||||
\(53\) | −38.1838 | − | 66.1362i | −0.720448 | − | 1.24785i | −0.960820 | − | 0.277172i | \(-0.910603\pi\) |
0.240372 | − | 0.970681i | \(-0.422731\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 83.1384i | − | 1.51161i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 24.0000 | − | 41.5692i | 0.413793 | − | 0.716711i | ||||
\(59\) | −72.1249 | + | 41.6413i | −1.22246 | + | 0.705785i | −0.965441 | − | 0.260622i | \(-0.916072\pi\) |
−0.257015 | + | 0.966407i | \(0.582739\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 72.0000 | + | 41.5692i | 1.18033 | + | 0.681463i | 0.956090 | − | 0.293072i | \(-0.0946775\pi\) |
0.224237 | + | 0.974535i | \(0.428011\pi\) | |||||||
\(62\) | − | 17.1464i | − | 0.276555i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 4.24264 | − | 7.34847i | 0.0652714 | − | 0.113053i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.5000 | + | 26.8468i | 0.231343 | + | 0.400698i | 0.958204 | − | 0.286087i | \(-0.0923546\pi\) |
−0.726860 | + | 0.686785i | \(0.759021\pi\) | |||||||
\(68\) | 8.48528 | + | 4.89898i | 0.124784 | + | 0.0720438i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −59.3970 | −0.836577 | −0.418289 | − | 0.908314i | \(-0.637370\pi\) | ||||
−0.418289 | + | 0.908314i | \(0.637370\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 70.5000 | − | 40.7032i | 0.965753 | − | 0.557578i | 0.0678144 | − | 0.997698i | \(-0.478397\pi\) |
0.897939 | + | 0.440120i | \(0.145064\pi\) | |||||||
\(74\) | −33.2340 | − | 57.5630i | −0.449108 | − | 0.777878i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 58.8897i | 0.774865i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −20.5000 | + | 35.5070i | −0.259494 | + | 0.449456i | −0.966106 | − | 0.258144i | \(-0.916889\pi\) |
0.706613 | + | 0.707601i | \(0.250222\pi\) | |||||||
\(80\) | −16.9706 | + | 9.79796i | −0.212132 | + | 0.122474i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −84.0000 | − | 48.4974i | −1.02439 | − | 0.591432i | ||||
\(83\) | 4.89898i | 0.0590238i | 0.999564 | + | 0.0295119i | \(0.00939530\pi\) | ||||
−0.999564 | + | 0.0295119i | \(0.990605\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.0000 | −0.282353 | ||||||||
\(86\) | 21.9203 | − | 37.9671i | 0.254887 | − | 0.441478i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 24.0000 | + | 41.5692i | 0.272727 | + | 0.472377i | ||||
\(89\) | 50.9117 | + | 29.3939i | 0.572041 | + | 0.330268i | 0.757964 | − | 0.652296i | \(-0.226194\pi\) |
−0.185923 | + | 0.982564i | \(0.559527\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 16.9706 | 0.184463 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −102.000 | + | 58.8897i | −1.08511 | + | 0.626486i | ||||
\(95\) | −72.1249 | − | 124.924i | −0.759209 | − | 1.31499i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 41.5692i | 0.428549i | 0.976774 | + | 0.214274i | \(0.0687387\pi\) | ||||
−0.976774 | + | 0.214274i | \(0.931261\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | + | 1.73205i | −0.0100000 | + | 0.0173205i | ||||
\(101\) | −152.735 | + | 88.1816i | −1.51223 | + | 0.873085i | −0.512331 | + | 0.858788i | \(0.671218\pi\) |
−0.999898 | + | 0.0142971i | \(0.995449\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 25.5000 | + | 14.7224i | 0.247573 | + | 0.142936i | 0.618652 | − | 0.785665i | \(-0.287679\pi\) |
−0.371080 | + | 0.928601i | \(0.621012\pi\) | |||||||
\(104\) | 4.89898i | 0.0471056i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −108.000 | −1.01887 | ||||||||
\(107\) | −72.1249 | + | 124.924i | −0.674064 | + | 1.16751i | 0.302677 | + | 0.953093i | \(0.402120\pi\) |
−0.976741 | + | 0.214421i | \(0.931214\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −84.5000 | − | 146.358i | −0.775229 | − | 1.34274i | −0.934665 | − | 0.355528i | \(-0.884301\pi\) |
0.159436 | − | 0.987208i | \(-0.449032\pi\) | |||||||
\(110\) | −101.823 | − | 58.7878i | −0.925667 | − | 0.534434i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 59.3970 | 0.525637 | 0.262818 | − | 0.964845i | \(-0.415348\pi\) | ||||
0.262818 | + | 0.964845i | \(0.415348\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −36.0000 | + | 20.7846i | −0.313043 | + | 0.180736i | ||||
\(116\) | −33.9411 | − | 58.7878i | −0.292596 | − | 0.506791i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 117.779i | 0.998131i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −83.5000 | + | 144.626i | −0.690083 | + | 1.19526i | ||||
\(122\) | 101.823 | − | 58.7878i | 0.834618 | − | 0.481867i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −21.0000 | − | 12.1244i | −0.169355 | − | 0.0977771i | ||||
\(125\) | − | 127.373i | − | 1.01899i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 209.000 | 1.64567 | 0.822835 | − | 0.568281i | \(-0.192391\pi\) | ||||
0.822835 | + | 0.568281i | \(0.192391\pi\) | |||||||
\(128\) | 5.65685 | − | 9.79796i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.00000 | − | 10.3923i | −0.0461538 | − | 0.0799408i | ||||
\(131\) | −50.9117 | − | 29.3939i | −0.388639 | − | 0.224381i | 0.292931 | − | 0.956133i | \(-0.405369\pi\) |
−0.681570 | + | 0.731753i | \(0.738703\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 43.8406 | 0.327169 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.0000 | − | 6.92820i | 0.0882353 | − | 0.0509427i | ||||
\(137\) | 76.3675 | + | 132.272i | 0.557427 | + | 0.965492i | 0.997710 | + | 0.0676333i | \(0.0215448\pi\) |
−0.440283 | + | 0.897859i | \(0.645122\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 195.722i | − | 1.40807i | −0.710165 | − | 0.704035i | \(-0.751380\pi\) | ||
0.710165 | − | 0.704035i | \(-0.248620\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −42.0000 | + | 72.7461i | −0.295775 | + | 0.512297i | ||||
\(143\) | −25.4558 | + | 14.6969i | −0.178013 | + | 0.102776i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 144.000 | + | 83.1384i | 0.993103 | + | 0.573369i | ||||
\(146\) | − | 115.126i | − | 0.788534i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −94.0000 | −0.635135 | ||||||||
\(149\) | 25.4558 | − | 44.0908i | 0.170845 | − | 0.295912i | −0.767871 | − | 0.640605i | \(-0.778684\pi\) |
0.938715 | + | 0.344693i | \(0.112017\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00000 | − | 8.66025i | −0.0331126 | − | 0.0573527i | 0.848994 | − | 0.528402i | \(-0.177209\pi\) |
−0.882107 | + | 0.471049i | \(0.843875\pi\) | |||||||
\(152\) | 72.1249 | + | 41.6413i | 0.474506 | + | 0.273956i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 59.3970 | 0.383206 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −36.0000 | + | 20.7846i | −0.229299 | + | 0.132386i | −0.610249 | − | 0.792210i | \(-0.708931\pi\) |
0.380949 | + | 0.924596i | \(0.375597\pi\) | |||||||
\(158\) | 28.9914 | + | 50.2145i | 0.183490 | + | 0.317814i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 27.7128i | 0.173205i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −43.0000 | + | 74.4782i | −0.263804 | + | 0.456921i | −0.967250 | − | 0.253828i | \(-0.918310\pi\) |
0.703446 | + | 0.710749i | \(0.251644\pi\) | |||||||
\(164\) | −118.794 | + | 68.5857i | −0.724353 | + | 0.418206i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | + | 3.46410i | 0.0361446 | + | 0.0208681i | ||||
\(167\) | − | 181.262i | − | 1.08540i | −0.839926 | − | 0.542701i | \(-0.817402\pi\) | ||
0.839926 | − | 0.542701i | \(-0.182598\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 166.000 | 0.982249 | ||||||||
\(170\) | −16.9706 | + | 29.3939i | −0.0998268 | + | 0.172905i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −31.0000 | − | 53.6936i | −0.180233 | − | 0.312172i | ||||
\(173\) | −38.1838 | − | 22.0454i | −0.220715 | − | 0.127430i | 0.385566 | − | 0.922680i | \(-0.374006\pi\) |
−0.606281 | + | 0.795250i | \(0.707340\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 67.8823 | 0.385695 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 72.0000 | − | 41.5692i | 0.404494 | − | 0.233535i | ||||
\(179\) | −4.24264 | − | 7.34847i | −0.0237019 | − | 0.0410529i | 0.853931 | − | 0.520386i | \(-0.174212\pi\) |
−0.877633 | + | 0.479333i | \(0.840879\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 43.3013i | 0.239234i | 0.992820 | + | 0.119617i | \(0.0381666\pi\) | ||||
−0.992820 | + | 0.119617i | \(0.961833\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.0000 | − | 20.7846i | 0.0652174 | − | 0.112960i | ||||
\(185\) | 199.404 | − | 115.126i | 1.07786 | − | 0.622303i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 72.0000 | + | 41.5692i | 0.385027 | + | 0.222295i | ||||
\(188\) | 166.565i | 0.885986i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −204.000 | −1.07368 | ||||||||
\(191\) | 38.1838 | − | 66.1362i | 0.199915 | − | 0.346263i | −0.748586 | − | 0.663038i | \(-0.769267\pi\) |
0.948501 | + | 0.316775i | \(0.102600\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 143.500 | + | 248.549i | 0.743523 | + | 1.28782i | 0.950882 | + | 0.309555i | \(0.100180\pi\) |
−0.207358 | + | 0.978265i | \(0.566487\pi\) | |||||||
\(194\) | 50.9117 | + | 29.3939i | 0.262431 | + | 0.151515i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −127.279 | −0.646087 | −0.323044 | − | 0.946384i | \(-0.604706\pi\) | ||||
−0.323044 | + | 0.946384i | \(0.604706\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −180.000 | + | 103.923i | −0.904523 | + | 0.522226i | −0.878665 | − | 0.477439i | \(-0.841565\pi\) |
−0.0258579 | + | 0.999666i | \(0.508232\pi\) | |||||||
\(200\) | 1.41421 | + | 2.44949i | 0.00707107 | + | 0.0122474i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 249.415i | 1.23473i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 168.000 | − | 290.985i | 0.819512 | − | 1.41944i | ||||
\(206\) | 36.0624 | − | 20.8207i | 0.175060 | − | 0.101071i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.00000 | + | 3.46410i | 0.0288462 | + | 0.0166543i | ||||
\(209\) | 499.696i | 2.39089i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 82.0000 | 0.388626 | 0.194313 | − | 0.980940i | \(-0.437752\pi\) | ||||
0.194313 | + | 0.980940i | \(0.437752\pi\) | |||||||
\(212\) | −76.3675 | + | 132.272i | −0.360224 | + | 0.623927i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 102.000 | + | 176.669i | 0.476636 | + | 0.825557i | ||||
\(215\) | 131.522 | + | 75.9342i | 0.611730 | + | 0.353182i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −239.002 | −1.09634 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −144.000 | + | 83.1384i | −0.654545 | + | 0.377902i | ||||
\(221\) | 4.24264 | + | 7.34847i | 0.0191975 | + | 0.0332510i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 41.5692i | − | 0.186409i | −0.995647 | − | 0.0932045i | \(-0.970289\pi\) | ||
0.995647 | − | 0.0932045i | \(-0.0297110\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 42.0000 | − | 72.7461i | 0.185841 | − | 0.321886i | ||||
\(227\) | 330.926 | − | 191.060i | 1.45782 | − | 0.841675i | 0.458920 | − | 0.888478i | \(-0.348237\pi\) |
0.998904 | + | 0.0468029i | \(0.0149033\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 70.5000 | + | 40.7032i | 0.307860 | + | 0.177743i | 0.645969 | − | 0.763364i | \(-0.276454\pi\) |
−0.338108 | + | 0.941107i | \(0.609787\pi\) | |||||||
\(230\) | 58.7878i | 0.255599i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −96.0000 | −0.413793 | ||||||||
\(233\) | 114.551 | − | 198.409i | 0.491636 | − | 0.851539i | −0.508317 | − | 0.861170i | \(-0.669732\pi\) |
0.999954 | + | 0.00963059i | \(0.00306556\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −204.000 | − | 353.338i | −0.868085 | − | 1.50357i | ||||
\(236\) | 144.250 | + | 83.2827i | 0.611228 | + | 0.352893i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 67.8823 | 0.284026 | 0.142013 | − | 0.989865i | \(-0.454642\pi\) | ||||
0.142013 | + | 0.989865i | \(0.454642\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 396.000 | − | 228.631i | 1.64315 | − | 0.948675i | 0.663451 | − | 0.748220i | \(-0.269091\pi\) |
0.979703 | − | 0.200455i | \(-0.0642421\pi\) | |||||||
\(242\) | 118.087 | + | 204.532i | 0.487962 | + | 0.845175i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 166.277i | − | 0.681463i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.5000 | + | 44.1673i | −0.103239 | + | 0.178815i | ||||
\(248\) | −29.6985 | + | 17.1464i | −0.119752 | + | 0.0691388i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −156.000 | − | 90.0666i | −0.624000 | − | 0.360267i | ||||
\(251\) | 347.828i | 1.38577i | 0.721050 | + | 0.692884i | \(0.243660\pi\) | ||||
−0.721050 | + | 0.692884i | \(0.756340\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 144.000 | 0.569170 | ||||||||
\(254\) | 147.785 | − | 255.972i | 0.581832 | − | 1.00776i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 140.007 | + | 80.8332i | 0.544775 | + | 0.314526i | 0.747012 | − | 0.664811i | \(-0.231488\pi\) |
−0.202237 | + | 0.979337i | \(0.564821\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −16.9706 | −0.0652714 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −72.0000 | + | 41.5692i | −0.274809 | + | 0.158661i | ||||
\(263\) | 127.279 | + | 220.454i | 0.483951 | + | 0.838228i | 0.999830 | − | 0.0184332i | \(-0.00586781\pi\) |
−0.515879 | + | 0.856662i | \(0.672534\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 374.123i | − | 1.41178i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 31.0000 | − | 53.6936i | 0.115672 | − | 0.200349i | ||||
\(269\) | 16.9706 | − | 9.79796i | 0.0630876 | − | 0.0364236i | −0.468124 | − | 0.883663i | \(-0.655070\pi\) |
0.531212 | + | 0.847239i | \(0.321737\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −36.0000 | − | 20.7846i | −0.132841 | − | 0.0766960i | 0.432107 | − | 0.901823i | \(-0.357770\pi\) |
−0.564948 | + | 0.825127i | \(0.691104\pi\) | |||||||
\(272\) | − | 19.5959i | − | 0.0720438i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 216.000 | 0.788321 | ||||||||
\(275\) | −8.48528 | + | 14.6969i | −0.0308556 | + | 0.0534434i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 168.500 | + | 291.851i | 0.608303 | + | 1.05361i | 0.991520 | + | 0.129954i | \(0.0414829\pi\) |
−0.383217 | + | 0.923658i | \(0.625184\pi\) | |||||||
\(278\) | −239.709 | − | 138.396i | −0.862263 | − | 0.497828i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −246.073 | −0.875705 | −0.437853 | − | 0.899047i | \(-0.644261\pi\) | ||||
−0.437853 | + | 0.899047i | \(0.644261\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 169.500 | − | 97.8609i | 0.598940 | − | 0.345798i | −0.169685 | − | 0.985498i | \(-0.554275\pi\) |
0.768624 | + | 0.639700i | \(0.220942\pi\) | |||||||
\(284\) | 59.3970 | + | 102.879i | 0.209144 | + | 0.362248i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 41.5692i | 0.145347i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −132.500 | + | 229.497i | −0.458478 | + | 0.794106i | ||||
\(290\) | 203.647 | − | 117.576i | 0.702230 | − | 0.405433i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −141.000 | − | 81.4064i | −0.482877 | − | 0.278789i | ||||
\(293\) | − | 97.9796i | − | 0.334401i | −0.985923 | − | 0.167201i | \(-0.946527\pi\) | ||
0.985923 | − | 0.167201i | \(-0.0534728\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −408.000 | −1.38305 | ||||||||
\(296\) | −66.4680 | + | 115.126i | −0.224554 | + | 0.388939i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −36.0000 | − | 62.3538i | −0.120805 | − | 0.209241i | ||||
\(299\) | 12.7279 | + | 7.34847i | 0.0425683 | + | 0.0245768i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −14.1421 | −0.0468283 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 102.000 | − | 58.8897i | 0.335526 | − | 0.193716i | ||||
\(305\) | 203.647 | + | 352.727i | 0.667694 | + | 1.15648i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 71.0141i | − | 0.231316i | −0.993289 | − | 0.115658i | \(-0.963102\pi\) | ||
0.993289 | − | 0.115658i | \(-0.0368977\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 42.0000 | − | 72.7461i | 0.135484 | − | 0.234665i | ||||
\(311\) | 186.676 | − | 107.778i | 0.600245 | − | 0.346552i | −0.168893 | − | 0.985634i | \(-0.554019\pi\) |
0.769138 | + | 0.639083i | \(0.220686\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −253.500 | − | 146.358i | −0.809904 | − | 0.467598i | 0.0370184 | − | 0.999315i | \(-0.488214\pi\) |
−0.846923 | + | 0.531716i | \(0.821547\pi\) | |||||||
\(314\) | 58.7878i | 0.187222i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 82.0000 | 0.259494 | ||||||||
\(317\) | −118.794 | + | 205.757i | −0.374744 | + | 0.649076i | −0.990289 | − | 0.139026i | \(-0.955603\pi\) |
0.615544 | + | 0.788102i | \(0.288936\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −288.000 | − | 498.831i | −0.902821 | − | 1.56373i | ||||
\(320\) | 33.9411 | + | 19.5959i | 0.106066 | + | 0.0612372i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 144.250 | 0.446594 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.50000 | + | 0.866025i | −0.00461538 | + | 0.00266469i | ||||
\(326\) | 60.8112 | + | 105.328i | 0.186537 | + | 0.323092i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 193.990i | 0.591432i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 92.5000 | − | 160.215i | 0.279456 | − | 0.484032i | −0.691794 | − | 0.722095i | \(-0.743179\pi\) |
0.971250 | + | 0.238063i | \(0.0765125\pi\) | |||||||
\(332\) | 8.48528 | − | 4.89898i | 0.0255581 | − | 0.0147560i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −222.000 | − | 128.172i | −0.664671 | − | 0.383748i | ||||
\(335\) | 151.868i | 0.453338i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −359.000 | −1.06528 | −0.532641 | − | 0.846341i | \(-0.678800\pi\) | ||||
−0.532641 | + | 0.846341i | \(0.678800\pi\) | |||||||
\(338\) | 117.380 | − | 203.308i | 0.347277 | − | 0.601502i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 24.0000 | + | 41.5692i | 0.0705882 | + | 0.122262i | ||||
\(341\) | −178.191 | − | 102.879i | −0.522554 | − | 0.301697i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −87.6812 | −0.254887 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −54.0000 | + | 31.1769i | −0.156069 | + | 0.0901067i | ||||
\(347\) | 233.345 | + | 404.166i | 0.672465 | + | 1.16474i | 0.977203 | + | 0.212307i | \(0.0680976\pi\) |
−0.304738 | + | 0.952436i | \(0.598569\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 581.969i | 1.66753i | 0.552117 | + | 0.833767i | \(0.313820\pi\) | ||||
−0.552117 | + | 0.833767i | \(0.686180\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 48.0000 | − | 83.1384i | 0.136364 | − | 0.236189i | ||||
\(353\) | 250.316 | − | 144.520i | 0.709110 | − | 0.409405i | −0.101621 | − | 0.994823i | \(-0.532403\pi\) |
0.810731 | + | 0.585418i | \(0.199070\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −252.000 | − | 145.492i | −0.709859 | − | 0.409837i | ||||
\(356\) | − | 117.576i | − | 0.330268i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.0000 | −0.0335196 | ||||||||
\(359\) | 169.706 | − | 293.939i | 0.472718 | − | 0.818771i | −0.526795 | − | 0.849992i | \(-0.676606\pi\) |
0.999512 | + | 0.0312215i | \(0.00993973\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 253.000 | + | 438.209i | 0.700831 | + | 1.21387i | ||||
\(362\) | 53.0330 | + | 30.6186i | 0.146500 | + | 0.0845818i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 398.808 | 1.09263 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −133.500 | + | 77.0763i | −0.363760 | + | 0.210017i | −0.670729 | − | 0.741703i | \(-0.734019\pi\) |
0.306969 | + | 0.951720i | \(0.400685\pi\) | |||||||
\(368\) | −16.9706 | − | 29.3939i | −0.0461157 | − | 0.0798747i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 325.626i | − | 0.880069i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 144.500 | − | 250.281i | 0.387399 | − | 0.670996i | −0.604699 | − | 0.796454i | \(-0.706707\pi\) |
0.992099 | + | 0.125458i | \(0.0400401\pi\) | |||||||
\(374\) | 101.823 | − | 58.7878i | 0.272255 | − | 0.157187i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 204.000 | + | 117.779i | 0.542553 | + | 0.313243i | ||||
\(377\) | − | 58.7878i | − | 0.155936i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.00000 | 0.0184697 | 0.00923483 | − | 0.999957i | \(-0.497060\pi\) | ||||
0.00923483 | + | 0.999957i | \(0.497060\pi\) | |||||||
\(380\) | −144.250 | + | 249.848i | −0.379605 | + | 0.657495i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −54.0000 | − | 93.5307i | −0.141361 | − | 0.244845i | ||||
\(383\) | 428.507 | + | 247.398i | 1.11882 | + | 0.645949i | 0.941099 | − | 0.338132i | \(-0.109795\pi\) |
0.177718 | + | 0.984081i | \(0.443129\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 405.879 | 1.05150 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 72.0000 | − | 41.5692i | 0.185567 | − | 0.107137i | ||||
\(389\) | −114.551 | − | 198.409i | −0.294476 | − | 0.510048i | 0.680387 | − | 0.732853i | \(-0.261812\pi\) |
−0.974863 | + | 0.222805i | \(0.928479\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 41.5692i | − | 0.106315i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −90.0000 | + | 155.885i | −0.228426 | + | 0.395646i | ||||
\(395\) | −173.948 | + | 100.429i | −0.440375 | + | 0.254251i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −70.5000 | − | 40.7032i | −0.177582 | − | 0.102527i | 0.408574 | − | 0.912725i | \(-0.366026\pi\) |
−0.586156 | + | 0.810198i | \(0.699359\pi\) | |||||||
\(398\) | 293.939i | 0.738540i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.00000 | 0.0100000 | ||||||||
\(401\) | −46.6690 | + | 80.8332i | −0.116382 | + | 0.201579i | −0.918331 | − | 0.395813i | \(-0.870463\pi\) |
0.801950 | + | 0.597392i | \(0.203796\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.5000 | − | 18.1865i | −0.0260546 | − | 0.0451279i | ||||
\(404\) | 305.470 | + | 176.363i | 0.756114 | + | 0.436543i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −797.616 | −1.95975 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 361.500 | − | 208.712i | 0.883863 | − | 0.510299i | 0.0119329 | − | 0.999929i | \(-0.496202\pi\) |
0.871930 | + | 0.489630i | \(0.162868\pi\) | |||||||
\(410\) | −237.588 | − | 411.514i | −0.579483 | − | 1.00369i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 58.8897i | − | 0.142936i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | + | 20.7846i | −0.0289157 | + | 0.0500834i | ||||
\(416\) | 8.48528 | − | 4.89898i | 0.0203973 | − | 0.0117764i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 612.000 | + | 353.338i | 1.46411 | + | 0.845307i | ||||
\(419\) | − | 19.5959i | − | 0.0467683i | −0.999727 | − | 0.0233842i | \(-0.992556\pi\) | ||
0.999727 | − | 0.0233842i | \(-0.00744408\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 407.000 | 0.966746 | 0.483373 | − | 0.875415i | \(-0.339412\pi\) | ||||
0.483373 | + | 0.875415i | \(0.339412\pi\) | |||||||
\(422\) | 57.9828 | − | 100.429i | 0.137400 | − | 0.237984i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 108.000 | + | 187.061i | 0.254717 | + | 0.441183i | ||||
\(425\) | 4.24264 | + | 2.44949i | 0.00998268 | + | 0.00576351i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 288.500 | 0.674064 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 186.000 | − | 107.387i | 0.432558 | − | 0.249738i | ||||
\(431\) | −80.6102 | − | 139.621i | −0.187031 | − | 0.323946i | 0.757228 | − | 0.653150i | \(-0.226553\pi\) |
−0.944259 | + | 0.329204i | \(0.893220\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 168.009i | − | 0.388011i | −0.981000 | − | 0.194006i | \(-0.937852\pi\) | ||
0.981000 | − | 0.194006i | \(-0.0621480\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −169.000 | + | 292.717i | −0.387615 | + | 0.671368i | ||||
\(437\) | 216.375 | − | 124.924i | 0.495137 | − | 0.285867i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 468.000 | + | 270.200i | 1.06606 | + | 0.615490i | 0.927102 | − | 0.374809i | \(-0.122292\pi\) |
0.138957 | + | 0.990298i | \(0.455625\pi\) | |||||||
\(440\) | 235.151i | 0.534434i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.0000 | 0.0271493 | ||||||||
\(443\) | 63.6396 | − | 110.227i | 0.143656 | − | 0.248819i | −0.785215 | − | 0.619224i | \(-0.787447\pi\) |
0.928871 | + | 0.370404i | \(0.120781\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 144.000 | + | 249.415i | 0.323596 | + | 0.560484i | ||||
\(446\) | −50.9117 | − | 29.3939i | −0.114152 | − | 0.0659056i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −110.309 | −0.245676 | −0.122838 | − | 0.992427i | \(-0.539200\pi\) | ||||
−0.122838 | + | 0.992427i | \(0.539200\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1008.00 | + | 581.969i | −2.23503 | + | 1.29040i | ||||
\(452\) | −59.3970 | − | 102.879i | −0.131409 | − | 0.227607i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 540.400i | − | 1.19031i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5000 | + | 21.6506i | −0.0273523 | + | 0.0473756i | −0.879378 | − | 0.476125i | \(-0.842041\pi\) |
0.852025 | + | 0.523501i | \(0.175374\pi\) | |||||||
\(458\) | 99.7021 | − | 57.5630i | 0.217690 | − | 0.125683i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 72.0000 | + | 41.5692i | 0.156522 | + | 0.0903679i | ||||
\(461\) | 78.3837i | 0.170030i | 0.996380 | + | 0.0850148i | \(0.0270938\pi\) | ||||
−0.996380 | + | 0.0850148i | \(0.972906\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 521.000 | 1.12527 | 0.562635 | − | 0.826705i | \(-0.309788\pi\) | ||||
0.562635 | + | 0.826705i | \(0.309788\pi\) | |||||||
\(464\) | −67.8823 | + | 117.576i | −0.146298 | + | 0.253395i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −162.000 | − | 280.592i | −0.347639 | − | 0.602129i | ||||
\(467\) | −190.919 | − | 110.227i | −0.408820 | − | 0.236032i | 0.281463 | − | 0.959572i | \(-0.409180\pi\) |
−0.690283 | + | 0.723540i | \(0.742514\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −576.999 | −1.22766 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 204.000 | − | 117.779i | 0.432203 | − | 0.249533i | ||||
\(473\) | −263.044 | − | 455.605i | −0.556118 | − | 0.963224i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.4449i | 0.0619892i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 48.0000 | − | 83.1384i | 0.100418 | − | 0.173930i | ||||
\(479\) | −759.433 | + | 438.459i | −1.58545 | + | 0.915363i | −0.591412 | + | 0.806370i | \(0.701429\pi\) |
−0.994043 | + | 0.108993i | \(0.965237\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −70.5000 | − | 40.7032i | −0.146570 | − | 0.0846220i | ||||
\(482\) | − | 646.665i | − | 1.34163i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 334.000 | 0.690083 | ||||||||
\(485\) | −101.823 | + | 176.363i | −0.209945 | + | 0.363636i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −63.5000 | − | 109.985i | −0.130390 | − | 0.225842i | 0.793437 | − | 0.608653i | \(-0.208290\pi\) |
−0.923827 | + | 0.382810i | \(0.874956\pi\) | |||||||
\(488\) | −203.647 | − | 117.576i | −0.417309 | − | 0.240933i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 627.911 | 1.27884 | 0.639420 | − | 0.768857i | \(-0.279174\pi\) | ||||
0.639420 | + | 0.768857i | \(0.279174\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −144.000 | + | 83.1384i | −0.292089 | + | 0.168638i | ||||
\(494\) | 36.0624 | + | 62.4620i | 0.0730009 | + | 0.126441i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 48.4974i | 0.0977771i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 116.500 | − | 201.784i | 0.233467 | − | 0.404377i | −0.725359 | − | 0.688371i | \(-0.758326\pi\) |
0.958826 | + | 0.283994i | \(0.0916596\pi\) | |||||||
\(500\) | −220.617 | + | 127.373i | −0.441235 | + | 0.254747i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 426.000 | + | 245.951i | 0.848606 | + | 0.489943i | ||||
\(503\) | − | 538.888i | − | 1.07135i | −0.844425 | − | 0.535674i | \(-0.820058\pi\) | ||
0.844425 | − | 0.535674i | \(-0.179942\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −864.000 | −1.71089 | ||||||||
\(506\) | 101.823 | − | 176.363i | 0.201232 | − | 0.348544i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −209.000 | − | 361.999i | −0.411417 | − | 0.712596i | ||||
\(509\) | 275.772 | + | 159.217i | 0.541791 | + | 0.312803i | 0.745805 | − | 0.666165i | \(-0.232065\pi\) |
−0.204013 | + | 0.978968i | \(0.565399\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 198.000 | − | 114.315i | 0.385214 | − | 0.222403i | ||||
\(515\) | 72.1249 | + | 124.924i | 0.140048 | + | 0.242571i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1413.35i | 2.73376i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.0000 | + | 20.7846i | −0.0230769 | + | 0.0399704i | ||||
\(521\) | −492.146 | + | 284.141i | −0.944619 | + | 0.545376i | −0.891405 | − | 0.453207i | \(-0.850280\pi\) |
−0.0532135 | + | 0.998583i | \(0.516946\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −457.500 | − | 264.138i | −0.874761 | − | 0.505043i | −0.00583355 | − | 0.999983i | \(-0.501857\pi\) |
−0.868927 | + | 0.494939i | \(0.835190\pi\) | |||||||
\(524\) | 117.576i | 0.224381i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 360.000 | 0.684411 | ||||||||
\(527\) | −29.6985 | + | 51.4393i | −0.0563539 | + | 0.0976078i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 228.500 | + | 395.774i | 0.431947 | + | 0.748154i | ||||
\(530\) | −458.205 | − | 264.545i | −0.864538 | − | 0.499141i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −118.794 | −0.222878 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −612.000 | + | 353.338i | −1.14393 | + | 0.660446i | ||||
\(536\) | −43.8406 | − | 75.9342i | −0.0817922 | − | 0.141668i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 27.7128i | − | 0.0515108i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −167.500 | + | 290.119i | −0.309612 | + | 0.536263i | −0.978277 | − | 0.207300i | \(-0.933532\pi\) |
0.668666 | + | 0.743563i | \(0.266866\pi\) | |||||||
\(542\) | −50.9117 | + | 29.3939i | −0.0939330 | + | 0.0542322i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −24.0000 | − | 13.8564i | −0.0441176 | − | 0.0254713i | ||||
\(545\) | − | 827.928i | − | 1.51913i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −658.000 | −1.20293 | −0.601463 | − | 0.798901i | \(-0.705415\pi\) | ||||
−0.601463 | + | 0.798901i | \(0.705415\pi\) | |||||||
\(548\) | 152.735 | − | 264.545i | 0.278714 | − | 0.482746i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.0000 | + | 20.7846i | 0.0218182 | + | 0.0377902i | ||||
\(551\) | −865.499 | − | 499.696i | −1.57078 | − | 0.906889i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 476.590 | 0.860271 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −339.000 | + | 195.722i | −0.609712 | + | 0.352018i | ||||
\(557\) | −135.765 | − | 235.151i | −0.243742 | − | 0.422174i | 0.718035 | − | 0.696007i | \(-0.245042\pi\) |
−0.961777 | + | 0.273833i | \(0.911708\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 53.6936i | − | 0.0960529i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −174.000 | + | 301.377i | −0.309609 | + | 0.536258i | ||||
\(563\) | −12.7279 | + | 7.34847i | −0.0226073 | + | 0.0130523i | −0.511261 | − | 0.859425i | \(-0.670821\pi\) |
0.488654 | + | 0.872478i | \(0.337488\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 252.000 | + | 145.492i | 0.446018 | + | 0.257508i | ||||
\(566\) | − | 276.792i | − | 0.489032i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 168.000 | 0.295775 | ||||||||
\(569\) | −424.264 | + | 734.847i | −0.745631 | + | 1.29147i | 0.204268 | + | 0.978915i | \(0.434519\pi\) |
−0.949899 | + | 0.312556i | \(0.898815\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −224.500 | − | 388.845i | −0.393170 | − | 0.680990i | 0.599696 | − | 0.800228i | \(-0.295288\pi\) |
−0.992866 | + | 0.119238i | \(0.961955\pi\) | |||||||
\(572\) | 50.9117 | + | 29.3939i | 0.0890064 | + | 0.0513879i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.48528 | 0.0147570 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 253.500 | − | 146.358i | 0.439341 | − | 0.253654i | −0.263977 | − | 0.964529i | \(-0.585034\pi\) |
0.703318 | + | 0.710875i | \(0.251701\pi\) | |||||||
\(578\) | 187.383 | + | 324.557i | 0.324193 | + | 0.561518i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 332.554i | − | 0.573369i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −648.000 | + | 1122.37i | −1.11149 | + | 1.92516i | ||||
\(584\) | −199.404 | + | 115.126i | −0.341445 | + | 0.197134i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −120.000 | − | 69.2820i | −0.204778 | − | 0.118229i | ||||
\(587\) | 529.090i | 0.901345i | 0.892689 | + | 0.450673i | \(0.148816\pi\) | ||||
−0.892689 | + | 0.450673i | \(0.851184\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −357.000 | −0.606112 | ||||||||
\(590\) | −288.500 | + | 499.696i | −0.488982 | + | 0.846942i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 94.0000 | + | 162.813i | 0.158784 | + | 0.275022i | ||||
\(593\) | −907.925 | − | 524.191i | −1.53107 | − | 0.883964i | −0.999313 | − | 0.0370681i | \(-0.988198\pi\) |
−0.531758 | − | 0.846896i | \(-0.678469\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −101.823 | −0.170845 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 18.0000 | − | 10.3923i | 0.0301003 | − | 0.0173784i | ||||
\(599\) | −322.441 | − | 558.484i | −0.538298 | − | 0.932360i | −0.998996 | − | 0.0448028i | \(-0.985734\pi\) |
0.460698 | − | 0.887557i | \(-0.347599\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 458.993i | 0.763716i | 0.924221 | + | 0.381858i | \(0.124716\pi\) | ||||
−0.924221 | + | 0.381858i | \(0.875284\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.0000 | + | 17.3205i | −0.0165563 | + | 0.0286763i | ||||
\(605\) | −708.521 | + | 409.065i | −1.17111 | + | 0.676140i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −910.500 | − | 525.677i | −1.50000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(608\) | − | 166.565i | − | 0.273956i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 576.000 | 0.944262 | ||||||||
\(611\) | −72.1249 | + | 124.924i | −0.118044 | + | 0.204458i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −145.000 | − | 251.147i | −0.236542 | − | 0.409702i | 0.723178 | − | 0.690662i | \(-0.242681\pi\) |
−0.959720 | + | 0.280960i | \(0.909347\pi\) | |||||||
\(614\) | −86.9741 | − | 50.2145i | −0.141652 | − | 0.0817826i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 729.734 | 1.18271 | 0.591357 | − | 0.806410i | \(-0.298593\pi\) | ||||
0.591357 | + | 0.806410i | \(0.298593\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 709.500 | − | 409.630i | 1.14620 | − | 0.661761i | 0.198244 | − | 0.980153i | \(-0.436476\pi\) |
0.947959 | + | 0.318392i | \(0.103143\pi\) | |||||||
\(620\) | −59.3970 | − | 102.879i | −0.0958016 | − | 0.165933i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 304.841i | − | 0.490098i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 299.500 | − | 518.749i | 0.479200 | − | 0.829999i | ||||
\(626\) | −358.503 | + | 206.982i | −0.572689 | + | 0.330642i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 72.0000 | + | 41.5692i | 0.114650 | + | 0.0661930i | ||||
\(629\) | 230.252i | 0.366060i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −58.0000 | −0.0919176 | −0.0459588 | − | 0.998943i | \(-0.514634\pi\) | ||||
−0.0459588 | + | 0.998943i | \(0.514634\pi\) | |||||||
\(632\) | 57.9828 | − | 100.429i | 0.0917449 | − | 0.158907i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 168.000 | + | 290.985i | 0.264984 | + | 0.458966i | ||||
\(635\) | 886.712 | + | 511.943i | 1.39640 | + | 0.806210i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −814.587 | −1.27678 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 48.0000 | − | 27.7128i | 0.0750000 | − | 0.0433013i | ||||
\(641\) | −479.418 | − | 830.377i | −0.747923 | − | 1.29544i | −0.948817 | − | 0.315827i | \(-0.897718\pi\) |
0.200894 | − | 0.979613i | \(-0.435615\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 760.370i | − | 1.18254i | −0.806475 | − | 0.591268i | \(-0.798628\pi\) | ||
0.806475 | − | 0.591268i | \(-0.201372\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 102.000 | − | 176.669i | 0.157895 | − | 0.273482i | ||||
\(647\) | 305.470 | − | 176.363i | 0.472133 | − | 0.272586i | −0.244999 | − | 0.969523i | \(-0.578788\pi\) |
0.717132 | + | 0.696937i | \(0.245454\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1224.00 | + | 706.677i | 1.88598 | + | 1.08887i | ||||
\(650\) | 2.44949i | 0.00376845i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 172.000 | 0.263804 | ||||||||
\(653\) | 220.617 | − | 382.120i | 0.337852 | − | 0.585177i | −0.646177 | − | 0.763188i | \(-0.723633\pi\) |
0.984028 | + | 0.178011i | \(0.0569664\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −144.000 | − | 249.415i | −0.219847 | − | 0.380787i | ||||
\(656\) | 237.588 | + | 137.171i | 0.362177 | + | 0.209103i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 161.220 | 0.244644 | 0.122322 | − | 0.992490i | \(-0.460966\pi\) | ||||
0.122322 | + | 0.992490i | \(0.460966\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 721.500 | − | 416.558i | 1.09153 | − | 0.630194i | 0.157545 | − | 0.987512i | \(-0.449642\pi\) |
0.933983 | + | 0.357318i | \(0.116309\pi\) | |||||||
\(662\) | −130.815 | − | 226.578i | −0.197605 | − | 0.342263i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 13.8564i | − | 0.0208681i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −144.000 | + | 249.415i | −0.215892 | + | 0.373936i | ||||
\(668\) | −313.955 | + | 181.262i | −0.469993 | + | 0.271351i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 186.000 | + | 107.387i | 0.277612 | + | 0.160279i | ||||
\(671\) | − | 1410.91i | − | 2.10269i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −263.000 | −0.390788 | −0.195394 | − | 0.980725i | \(-0.562598\pi\) | ||||
−0.195394 | + | 0.980725i | \(0.562598\pi\) | |||||||
\(674\) | −253.851 | + | 439.683i | −0.376634 | + | 0.652349i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −166.000 | − | 287.520i | −0.245562 | − | 0.425326i | ||||
\(677\) | −432.749 | − | 249.848i | −0.639216 | − | 0.369052i | 0.145096 | − | 0.989418i | \(-0.453651\pi\) |
−0.784313 | + | 0.620366i | \(0.786984\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 67.8823 | 0.0998268 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −252.000 | + | 145.492i | −0.369501 | + | 0.213332i | ||||
\(683\) | −479.418 | − | 830.377i | −0.701930 | − | 1.21578i | −0.967788 | − | 0.251767i | \(-0.918988\pi\) |
0.265858 | − | 0.964012i | \(-0.414345\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 748.246i | 1.09233i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −62.0000 | + | 107.387i | −0.0901163 | + | 0.156086i | ||||
\(689\) | −114.551 | + | 66.1362i | −0.166257 | + | 0.0959887i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1069.50 | − | 617.476i | −1.54776 | − | 0.893598i | −0.998313 | − | 0.0580674i | \(-0.981506\pi\) |
−0.549444 | − | 0.835530i | \(-0.685161\pi\) | |||||||
\(692\) | 88.1816i | 0.127430i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 660.000 | 0.951009 | ||||||||
\(695\) | 479.418 | − | 830.377i | 0.689811 | − | 1.19479i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 168.000 | + | 290.985i | 0.241033 | + | 0.417481i | ||||
\(698\) | 712.764 | + | 411.514i | 1.02115 | + | 0.589562i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −975.807 | −1.39202 | −0.696011 | − | 0.718031i | \(-0.745044\pi\) | ||||
−0.696011 | + | 0.718031i | \(0.745044\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1198.50 | + | 691.954i | −1.70484 | + | 0.984288i | ||||
\(704\) | −67.8823 | − | 117.576i | −0.0964237 | − | 0.167011i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 408.764i | − | 0.578986i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 553.000 | − | 957.824i | 0.779972 | − | 1.35095i | −0.151986 | − | 0.988383i | \(-0.548567\pi\) |
0.931957 | − | 0.362568i | \(-0.118100\pi\) | |||||||
\(710\) | −356.382 | + | 205.757i | −0.501946 | + | 0.289799i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −144.000 | − | 83.1384i | −0.202247 | − | 0.116767i | ||||
\(713\) | 102.879i | 0.144290i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −144.000 | −0.201399 | ||||||||
\(716\) | −8.48528 | + | 14.6969i | −0.0118510 | + | 0.0205265i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −240.000 | − | 415.692i | −0.334262 | − | 0.578958i | ||||
\(719\) | 593.970 | + | 342.929i | 0.826105 | + | 0.476952i | 0.852517 | − | 0.522699i | \(-0.175075\pi\) |
−0.0264120 | + | 0.999651i | \(0.508408\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 715.592 | 0.991125 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 75.0000 | − | 43.3013i | 0.103591 | − | 0.0598084i | ||||
\(725\) | −16.9706 | − | 29.3939i | −0.0234077 | − | 0.0405433i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 427.817i | − | 0.588468i | −0.955733 | − | 0.294234i | \(-0.904935\pi\) | ||
0.955733 | − | 0.294234i | \(-0.0950646\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 282.000 | − | 488.438i | 0.386301 | − | 0.669094i | ||||
\(731\) | −131.522 | + | 75.9342i | −0.179920 | + | 0.103877i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.5000 | − | 19.9186i | −0.0470668 | − | 0.0271741i | 0.476282 | − | 0.879293i | \(-0.341984\pi\) |
−0.523349 | + | 0.852119i | \(0.675318\pi\) | |||||||
\(734\) | 218.005i | 0.297009i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −48.0000 | −0.0652174 | ||||||||
\(737\) | 263.044 | − | 455.605i | 0.356911 | − | 0.618189i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 243.500 | + | 421.754i | 0.329499 | + | 0.570710i | 0.982413 | − | 0.186723i | \(-0.0597867\pi\) |
−0.652913 | + | 0.757433i | \(0.726453\pi\) | |||||||
\(740\) | −398.808 | − | 230.252i | −0.538930 | − | 0.311151i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 509.117 | 0.685218 | 0.342609 | − | 0.939478i | \(-0.388689\pi\) | ||||
0.342609 | + | 0.939478i | \(0.388689\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 216.000 | − | 124.708i | 0.289933 | − | 0.167393i | ||||
\(746\) | −204.354 | − | 353.951i | −0.273933 | − | 0.474466i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 166.277i | − | 0.222295i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 272.500 | − | 471.984i | 0.362850 | − | 0.628474i | −0.625579 | − | 0.780161i | \(-0.715137\pi\) |
0.988429 | + | 0.151687i | \(0.0484706\pi\) | |||||||
\(752\) | 288.500 | − | 166.565i | 0.383643 | − | 0.221496i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −72.0000 | − | 41.5692i | −0.0954907 | − | 0.0551316i | ||||
\(755\) | − | 48.9898i | − | 0.0648871i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −770.000 | −1.01717 | −0.508587 | − | 0.861011i | \(-0.669832\pi\) | ||||
−0.508587 | + | 0.861011i | \(0.669832\pi\) | |||||||
\(758\) | 4.94975 | − | 8.57321i | 0.00653001 | − | 0.0113103i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 204.000 | + | 353.338i | 0.268421 | + | 0.464919i | ||||
\(761\) | 148.492 | + | 85.7321i | 0.195128 | + | 0.112657i | 0.594381 | − | 0.804184i | \(-0.297397\pi\) |
−0.399253 | + | 0.916841i | \(0.630730\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −152.735 | −0.199915 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 606.000 | − | 349.874i | 0.791123 | − | 0.456755i | ||||
\(767\) | 72.1249 | + | 124.924i | 0.0940351 | + | 0.162874i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 704.945i | 0.916703i | 0.888771 | + | 0.458352i | \(0.151560\pi\) | ||||
−0.888771 | + | 0.458352i | \(0.848440\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 287.000 | − | 497.099i | 0.371762 | − | 0.643910i | ||||
\(773\) | 797.616 | − | 460.504i | 1.03185 | − | 0.595736i | 0.114333 | − | 0.993443i | \(-0.463527\pi\) |
0.917513 | + | 0.397706i | \(0.130194\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.5000 | − | 6.06218i | −0.0135484 | − | 0.00782216i | ||||
\(776\) | − | 117.576i | − | 0.151515i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −324.000 | −0.416452 | ||||||||
\(779\) | −1009.75 | + | 1748.94i | −1.29621 | + | 2.24510i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 504.000 | + | 872.954i | 0.645327 | + | 1.11774i | ||||
\(782\) | −50.9117 | − | 29.3939i | −0.0651045 | − | 0.0375881i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −203.647 | −0.259423 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −396.000 | + | 228.631i | −0.503177 | + | 0.290509i | −0.730024 | − | 0.683421i | \(-0.760491\pi\) |
0.226848 | + | 0.973930i | \(0.427158\pi\) | |||||||
\(788\) | 127.279 | + | 220.454i | 0.161522 | + | 0.279764i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 284.056i | 0.359565i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 72.0000 | − | 124.708i | 0.0907945 | − | 0.157261i | ||||
\(794\) | −99.7021 | + | 57.5630i | −0.125569 | + | 0.0724975i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 360.000 | + | 207.846i | 0.452261 | + | 0.261113i | ||||
\(797\) | 14.6969i | 0.0184403i | 0.999957 | + | 0.00922016i | \(0.00293491\pi\) | ||||
−0.999957 | + | 0.00922016i | \(0.997065\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 408.000 | 0.510638 | ||||||||
\(800\) | 2.82843 | − | 4.89898i | 0.00353553 | − | 0.00612372i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 66.0000 | + | 114.315i | 0.0822943 | + | 0.142538i | ||||
\(803\) | −1196.42 | − | 690.756i | −1.48994 | − | 0.860219i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −29.6985 | −0.0368468 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 432.000 | − | 249.415i | 0.534653 | − | 0.308682i | ||||
\(809\) | 470.933 | + | 815.680i | 0.582118 | + | 1.00826i | 0.995228 | + | 0.0975763i | \(0.0311090\pi\) |
−0.413110 | + | 0.910681i | \(0.635558\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 498.831i | − | 0.615081i | −0.951535 | − | 0.307540i | \(-0.900494\pi\) | ||
0.951535 | − | 0.307540i | \(-0.0995059\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −564.000 | + | 976.877i | −0.692875 | + | 1.20009i | ||||
\(815\) | −364.867 | + | 210.656i | −0.447690 | + | 0.258474i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −790.500 | − | 456.395i | −0.967564 | − | 0.558623i | ||||
\(818\) | − | 590.327i | − | 0.721671i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −672.000 | −0.819512 | ||||||||
\(821\) | 301.227 | − | 521.741i | 0.366903 | − | 0.635495i | −0.622176 | − | 0.782877i | \(-0.713751\pi\) |
0.989080 | + | 0.147382i | \(0.0470847\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.0000 | − | 32.9090i | −0.0230863 | − | 0.0399866i | 0.854251 | − | 0.519860i | \(-0.174016\pi\) |
−0.877338 | + | 0.479873i | \(0.840683\pi\) | |||||||
\(824\) | −72.1249 | − | 41.6413i | −0.0875302 | − | 0.0505356i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 687.308 | 0.831086 | 0.415543 | − | 0.909574i | \(-0.363592\pi\) | ||||
0.415543 | + | 0.909574i | \(0.363592\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 721.500 | − | 416.558i | 0.870326 | − | 0.502483i | 0.00286924 | − | 0.999996i | \(-0.499087\pi\) |
0.867456 | + | 0.497513i | \(0.165753\pi\) | |||||||
\(830\) | 16.9706 | + | 29.3939i | 0.0204465 | + | 0.0354143i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 13.8564i | − | 0.0166543i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 444.000 | − | 769.031i | 0.531737 | − | 0.920995i | ||||
\(836\) | 865.499 | − | 499.696i | 1.03529 | − | 0.597722i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24.0000 | − | 13.8564i | −0.0286396 | − | 0.0165351i | ||||
\(839\) | 244.949i | 0.291953i | 0.989288 | + | 0.145977i | \(0.0466325\pi\) | ||||
−0.989288 | + | 0.145977i | \(0.953368\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 311.000 | 0.369798 | ||||||||
\(842\) | 287.792 | − | 498.471i | 0.341796 | − | 0.592009i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −82.0000 | − | 142.028i | −0.0971564 | − | 0.168280i | ||||
\(845\) | 704.278 | + | 406.615i | 0.833466 | + | 0.481202i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 305.470 | 0.360224 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.00000 | − | 3.46410i | 0.00705882 | − | 0.00407541i | ||||
\(851\) | 199.404 | + | 345.378i | 0.234317 | + | 0.405850i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1245.34i | − | 1.45996i | −0.683469 | − | 0.729979i | \(-0.739530\pi\) | ||
0.683469 | − | 0.729979i | \(-0.260470\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 204.000 | − | 353.338i | 0.238318 | − | 0.412778i | ||||
\(857\) | −1060.66 | + | 612.372i | −1.23764 | + | 0.714554i | −0.968612 | − | 0.248578i | \(-0.920037\pi\) |
−0.269031 | + | 0.963131i | \(0.586703\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −216.000 | − | 124.708i | −0.251455 | − | 0.145178i | 0.368975 | − | 0.929439i | \(-0.379709\pi\) |
−0.620430 | + | 0.784262i | \(0.713042\pi\) | |||||||
\(860\) | − | 303.737i | − | 0.353182i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −228.000 | −0.264501 | ||||||||
\(863\) | −330.926 | + | 573.181i | −0.383460 | + | 0.664172i | −0.991554 | − | 0.129693i | \(-0.958601\pi\) |
0.608094 | + | 0.793865i | \(0.291934\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −108.000 | − | 187.061i | −0.124855 | − | 0.216256i | ||||
\(866\) | −205.768 | − | 118.800i | −0.237607 | − | 0.137183i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 695.793 | 0.800682 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.5000 | − | 26.8468i | 0.0533869 | − | 0.0308229i | ||||
\(872\) | 239.002 | + | 413.964i | 0.274085 | + | 0.474729i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 353.338i | − | 0.404277i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 287.000 | − | 497.099i | 0.327252 | − | 0.566817i | −0.654714 | − | 0.755877i | \(-0.727211\pi\) |
0.981966 | + | 0.189060i | \(0.0605441\pi\) | |||||||
\(878\) | 661.852 | − | 382.120i | 0.753818 | − | 0.435217i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 288.000 | + | 166.277i | 0.327273 | + | 0.188951i | ||||
\(881\) | 161.666i | 0.183503i | 0.995782 | + | 0.0917516i | \(0.0292466\pi\) | ||||
−0.995782 | + | 0.0917516i | \(0.970753\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1735.00 | 1.96489 | 0.982446 | − | 0.186546i | \(-0.0597294\pi\) | ||||
0.982446 | + | 0.186546i | \(0.0597294\pi\) | |||||||
\(884\) | 8.48528 | − | 14.6969i | 0.00959873 | − | 0.0166255i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −90.0000 | − | 155.885i | −0.101580 | − | 0.175942i | ||||
\(887\) | 169.706 | + | 97.9796i | 0.191325 | + | 0.110462i | 0.592603 | − | 0.805495i | \(-0.298100\pi\) |
−0.401277 | + | 0.915957i | \(0.631434\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 407.294 | 0.457633 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −72.0000 | + | 41.5692i | −0.0807175 | + | 0.0466023i | ||||
\(893\) | 1226.12 | + | 2123.71i | 1.37304 | + | 2.37817i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 41.5692i | − | 0.0464461i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −78.0000 | + | 135.100i | −0.0868597 | + | 0.150445i | ||||
\(899\) | 356.382 | − | 205.757i | 0.396420 | − | 0.228873i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 324.000 | + | 187.061i | 0.359600 | + | 0.207615i | ||||
\(902\) | 1646.06i | 1.82490i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −168.000 | −0.185841 | ||||||||
\(905\) | −106.066 | + | 183.712i | −0.117200 | + | 0.202996i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −375.500 | − | 650.385i | −0.414002 | − | 0.717073i | 0.581321 | − | 0.813674i | \(-0.302536\pi\) |
−0.995323 | + | 0.0966015i | \(0.969203\pi\) | |||||||
\(908\) | −661.852 | − | 382.120i | −0.728912 | − | 0.420837i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1247.34 | −1.36919 | −0.684597 | − | 0.728921i | \(-0.740022\pi\) | ||||
−0.684597 | + | 0.728921i | \(0.740022\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 72.0000 | − | 41.5692i | 0.0788609 | − | 0.0455304i | ||||
\(914\) | 17.6777 | + | 30.6186i | 0.0193410 | + | 0.0334996i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 162.813i | − | 0.177743i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −507.500 | + | 879.016i | −0.552231 | + | 0.956492i | 0.445883 | + | 0.895091i | \(0.352890\pi\) |
−0.998113 | + | 0.0614001i | \(0.980443\pi\) | |||||||
\(920\) | 101.823 | − | 58.7878i | 0.110678 | − | 0.0638997i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 96.0000 | + | 55.4256i | 0.104121 | + | 0.0601146i | ||||
\(923\) | 102.879i | 0.111461i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −47.0000 | −0.0508108 | ||||||||
\(926\) | 368.403 | − | 638.092i | 0.397843 | − | 0.689084i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 96.0000 | + | 166.277i | 0.103448 | + | 0.179178i | ||||
\(929\) | 946.109 | + | 546.236i | 1.01842 | + | 0.587983i | 0.913645 | − | 0.406513i | \(-0.133256\pi\) |
0.104772 | + | 0.994496i | \(0.466589\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −458.205 | −0.491636 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −270.000 | + | 155.885i | −0.289079 | + | 0.166900i | ||||
\(935\) | 203.647 | + | 352.727i | 0.217804 | + | 0.377248i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1747.64i | 1.86514i | 0.360985 | + | 0.932572i | \(0.382441\pi\) | ||||
−0.360985 | + | 0.932572i | \(0.617559\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −408.000 | + | 706.677i | −0.434043 | + | 0.751784i | ||||
\(941\) | 1073.39 | − | 619.721i | 1.14069 | − | 0.658577i | 0.194088 | − | 0.980984i | \(-0.437825\pi\) |
0.946601 | + | 0.322407i | \(0.104492\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 504.000 | + | 290.985i | 0.534464 | + | 0.308573i | ||||
\(944\) | − | 333.131i | − | 0.352893i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −744.000 | −0.786469 | ||||||||
\(947\) | 602.455 | − | 1043.48i | 0.636172 | − | 1.10188i | −0.350093 | − | 0.936715i | \(-0.613850\pi\) |
0.986266 | − | 0.165168i | \(-0.0528165\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −70.5000 | − | 122.110i | −0.0742887 | − | 0.128672i | ||||
\(950\) | 36.0624 | + | 20.8207i | 0.0379605 | + | 0.0219165i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1026.72 | −1.07735 | −0.538677 | − | 0.842512i | \(-0.681076\pi\) | ||||
−0.538677 | + | 0.842512i | \(0.681076\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 324.000 | − | 187.061i | 0.339267 | − | 0.195876i | ||||
\(956\) | −67.8823 | − | 117.576i | −0.0710065 | − | 0.122987i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1240.15i | 1.29452i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −407.000 | + | 704.945i | −0.423517 | + | 0.733553i | ||||
\(962\) | −99.7021 | + | 57.5630i | −0.103640 | + | 0.0598368i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −792.000 | − | 457.261i | −0.821577 | − | 0.474338i | ||||
\(965\) | 1406.01i | 1.45700i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −895.000 | −0.925543 | −0.462771 | − | 0.886478i | \(-0.653145\pi\) | ||||
−0.462771 | + | 0.886478i | \(0.653145\pi\) | |||||||
\(968\) | 236.174 | − | 409.065i | 0.243981 | − | 0.422588i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 144.000 | + | 249.415i | 0.148454 | + | 0.257129i | ||||
\(971\) | −182.434 | − | 105.328i | −0.187882 | − | 0.108474i | 0.403109 | − | 0.915152i | \(-0.367930\pi\) |
−0.590991 | + | 0.806678i | \(0.701263\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −179.605 | −0.184400 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −288.000 | + | 166.277i | −0.295082 | + | 0.170366i | ||||
\(977\) | −627.911 | − | 1087.57i | −0.642693 | − | 1.11318i | −0.984829 | − | 0.173526i | \(-0.944484\pi\) |
0.342136 | − | 0.939650i | \(-0.388849\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 997.661i | − | 1.01906i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 444.000 | − | 769.031i | 0.452138 | − | 0.783127i | ||||
\(983\) | 1022.48 | − | 590.327i | 1.04016 | − | 0.600536i | 0.120281 | − | 0.992740i | \(-0.461621\pi\) |
0.919878 | + | 0.392204i | \(0.128287\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −540.000 | − | 311.769i | −0.548223 | − | 0.316517i | ||||
\(986\) | 235.151i | 0.238490i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 102.000 | 0.103239 | ||||||||
\(989\) | −131.522 | + | 227.803i | −0.132985 | + | 0.230336i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −327.500 | − | 567.247i | −0.330474 | − | 0.572398i | 0.652131 | − | 0.758107i | \(-0.273875\pi\) |
−0.982605 | + | 0.185708i | \(0.940542\pi\) | |||||||
\(992\) | 59.3970 | + | 34.2929i | 0.0598760 | + | 0.0345694i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1018.23 | −1.02335 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −397.500 | + | 229.497i | −0.398696 | + | 0.230187i | −0.685921 | − | 0.727676i | \(-0.740601\pi\) |
0.287225 | + | 0.957863i | \(0.407267\pi\) | |||||||
\(998\) | −164.756 | − | 285.366i | −0.165086 | − | 0.285937i | ||||
\(999\) | 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.c.19.2 | 4 | ||
3.2 | odd | 2 | inner | 882.3.n.c.19.1 | 4 | ||
7.2 | even | 3 | 882.3.c.c.685.1 | 4 | |||
7.3 | odd | 6 | inner | 882.3.n.c.325.2 | 4 | ||
7.4 | even | 3 | 126.3.n.b.73.2 | yes | 4 | ||
7.5 | odd | 6 | 882.3.c.c.685.2 | 4 | |||
7.6 | odd | 2 | 126.3.n.b.19.2 | yes | 4 | ||
21.2 | odd | 6 | 882.3.c.c.685.4 | 4 | |||
21.5 | even | 6 | 882.3.c.c.685.3 | 4 | |||
21.11 | odd | 6 | 126.3.n.b.73.1 | yes | 4 | ||
21.17 | even | 6 | inner | 882.3.n.c.325.1 | 4 | ||
21.20 | even | 2 | 126.3.n.b.19.1 | ✓ | 4 | ||
28.11 | odd | 6 | 1008.3.cg.i.577.1 | 4 | |||
28.27 | even | 2 | 1008.3.cg.i.145.1 | 4 | |||
84.11 | even | 6 | 1008.3.cg.i.577.2 | 4 | |||
84.83 | odd | 2 | 1008.3.cg.i.145.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.n.b.19.1 | ✓ | 4 | 21.20 | even | 2 | ||
126.3.n.b.19.2 | yes | 4 | 7.6 | odd | 2 | ||
126.3.n.b.73.1 | yes | 4 | 21.11 | odd | 6 | ||
126.3.n.b.73.2 | yes | 4 | 7.4 | even | 3 | ||
882.3.c.c.685.1 | 4 | 7.2 | even | 3 | |||
882.3.c.c.685.2 | 4 | 7.5 | odd | 6 | |||
882.3.c.c.685.3 | 4 | 21.5 | even | 6 | |||
882.3.c.c.685.4 | 4 | 21.2 | odd | 6 | |||
882.3.n.c.19.1 | 4 | 3.2 | odd | 2 | inner | ||
882.3.n.c.19.2 | 4 | 1.1 | even | 1 | trivial | ||
882.3.n.c.325.1 | 4 | 21.17 | even | 6 | inner | ||
882.3.n.c.325.2 | 4 | 7.3 | odd | 6 | inner | ||
1008.3.cg.i.145.1 | 4 | 28.27 | even | 2 | |||
1008.3.cg.i.145.2 | 4 | 84.83 | odd | 2 | |||
1008.3.cg.i.577.1 | 4 | 28.11 | odd | 6 | |||
1008.3.cg.i.577.2 | 4 | 84.11 | even | 6 |