Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [440,2,Mod(81,440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(440, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("440.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 440 = 2^{3} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 440.y (of order \(5\), degree \(4\), 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: | \(3.51341768894\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{12} - 2 x^{11} + 15 x^{10} - 22 x^{9} + 89 x^{8} - 118 x^{7} + 205 x^{6} - 68 x^{5} + 1061 x^{4} + \cdots + 400 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 361.3 | ||
Root | \(-1.51700 - 1.10216i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 440.361 |
Dual form | 440.2.y.b.401.3 |
$q$-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 \(\left(\mathbb{Z}/440\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(177\) | \(221\) | \(321\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 | 0 | ||||||||
\(3\) | 2.45455 | − | 1.78334i | 1.41714 | − | 1.02961i | 0.424900 | − | 0.905240i | \(-0.360309\pi\) |
0.992236 | − | 0.124369i | \(-0.0396907\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.309017 | − | 0.951057i | −0.138197 | − | 0.425325i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.700550 | − | 0.508979i | −0.264783 | − | 0.192376i | 0.447470 | − | 0.894299i | \(-0.352325\pi\) |
−0.712253 | + | 0.701923i | \(0.752325\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.91748 | − | 5.90141i | 0.639161 | − | 1.96714i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.21410 | − | 3.08642i | −0.366064 | − | 0.930590i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.37052 | + | 4.21802i | −0.380114 | + | 1.16987i | 0.559850 | + | 0.828594i | \(0.310859\pi\) |
−0.939963 | + | 0.341275i | \(0.889141\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.45455 | − | 1.78334i | −0.633762 | − | 0.460455i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.169969 | − | 0.523110i | −0.0412235 | − | 0.126873i | 0.928327 | − | 0.371765i | \(-0.121247\pi\) |
−0.969550 | + | 0.244892i | \(0.921247\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.209505 | − | 0.152214i | 0.0480637 | − | 0.0349203i | −0.563494 | − | 0.826120i | \(-0.690543\pi\) |
0.611558 | + | 0.791200i | \(0.290543\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.62722 | −0.573306 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.92701 | 1.65290 | 0.826448 | − | 0.563013i | \(-0.190358\pi\) | ||||
0.826448 | + | 0.563013i | \(0.190358\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.809017 | + | 0.587785i | −0.161803 | + | 0.117557i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.00497 | − | 9.24833i | −0.578306 | − | 1.77984i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.57410 | + | 5.50291i | 1.40648 | + | 1.02186i | 0.993823 | + | 0.110976i | \(0.0353975\pi\) |
0.412652 | + | 0.910889i | \(0.364602\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.64270 | + | 5.05570i | −0.295037 | + | 0.908031i | 0.688172 | + | 0.725548i | \(0.258413\pi\) |
−0.983209 | + | 0.182483i | \(0.941587\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.48418 | − | 5.41063i | −1.47691 | − | 0.941869i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.267586 | + | 0.823546i | −0.0452303 | + | 0.139205i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.16751 | − | 3.75441i | −0.849533 | − | 0.617222i | 0.0754844 | − | 0.997147i | \(-0.475950\pi\) |
−0.925017 | + | 0.379925i | \(0.875950\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.15814 | + | 12.7974i | 0.665836 | + | 2.04923i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.07258 | + | 5.13853i | −1.10455 | + | 0.802503i | −0.981797 | − | 0.189934i | \(-0.939173\pi\) |
−0.122754 | + | 0.992437i | \(0.539173\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.38622 | 0.973890 | 0.486945 | − | 0.873433i | \(-0.338111\pi\) | ||||
0.486945 | + | 0.873433i | \(0.338111\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.20511 | −0.925003 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.665989 | + | 0.483870i | −0.0971445 | + | 0.0705796i | −0.635297 | − | 0.772268i | \(-0.719122\pi\) |
0.538153 | + | 0.842847i | \(0.319122\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.93141 | − | 5.94426i | −0.275916 | − | 0.849181i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.35008 | − | 0.980890i | −0.189049 | − | 0.137352i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.741981 | − | 2.28358i | 0.101919 | − | 0.313674i | −0.887076 | − | 0.461623i | \(-0.847267\pi\) |
0.988995 | + | 0.147949i | \(0.0472672\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.56018 | + | 2.10843i | −0.345215 | + | 0.284301i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.242791 | − | 0.747235i | 0.0321585 | − | 0.0989737i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.9337 | + | 7.94382i | 1.42345 | + | 1.03420i | 0.991190 | + | 0.132449i | \(0.0422840\pi\) |
0.432261 | + | 0.901749i | \(0.357716\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.04186 | − | 6.28421i | −0.261434 | − | 0.804611i | −0.992494 | − | 0.122297i | \(-0.960974\pi\) |
0.731060 | − | 0.682313i | \(-0.239026\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.34699 | + | 3.15827i | −0.547669 | + | 0.397905i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.43509 | 0.550105 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.17725 | 0.876840 | 0.438420 | − | 0.898770i | \(-0.355538\pi\) | ||||
0.438420 | + | 0.898770i | \(0.355538\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 19.4573 | − | 14.1365i | 2.34238 | − | 1.70184i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.864970 | + | 2.66210i | 0.102653 | + | 0.315934i | 0.989172 | − | 0.146758i | \(-0.0468838\pi\) |
−0.886519 | + | 0.462691i | \(0.846884\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.33866 | + | 1.69913i | 0.273719 | + | 0.198868i | 0.716173 | − | 0.697923i | \(-0.245892\pi\) |
−0.442454 | + | 0.896791i | \(0.645892\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.937555 | + | 2.88550i | −0.108260 | + | 0.333189i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.720387 | + | 2.78014i | −0.0820958 | + | 0.316826i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.82769 | + | 5.62505i | −0.205631 | + | 0.632867i | 0.794056 | + | 0.607845i | \(0.207966\pi\) |
−0.999687 | + | 0.0250225i | \(0.992034\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.80862 | − | 6.39983i | −0.978735 | − | 0.711093i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.19347 | − | 6.75080i | −0.240764 | − | 0.740996i | −0.996304 | − | 0.0858936i | \(-0.972625\pi\) |
0.755540 | − | 0.655102i | \(-0.227375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.444984 | + | 0.323300i | −0.0482653 | + | 0.0350668i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 28.4046 | 3.04529 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.6470 | −1.76458 | −0.882291 | − | 0.470704i | \(-0.844000\pi\) | ||||
−0.882291 | + | 0.470704i | \(0.844000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.10700 | − | 2.25737i | 0.325702 | − | 0.236637i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.98393 | + | 15.3390i | 0.516809 | + | 1.59058i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.209505 | − | 0.152214i | −0.0214948 | − | 0.0156169i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.42082 | + | 7.45053i | −0.245797 | + | 0.756486i | 0.749707 | + | 0.661770i | \(0.230194\pi\) |
−0.995504 | + | 0.0947164i | \(0.969806\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −20.5422 | + | 1.24672i | −2.06457 | + | 0.125300i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.62378 | + | 17.3082i | −0.559587 | + | 1.72223i | 0.123923 | + | 0.992292i | \(0.460452\pi\) |
−0.683511 | + | 0.729941i | \(0.739548\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.54845 | − | 6.93735i | −0.940837 | − | 0.683558i | 0.00778529 | − | 0.999970i | \(-0.497522\pi\) |
−0.948622 | + | 0.316412i | \(0.897522\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.811855 | + | 2.49863i | 0.0792289 | + | 0.243841i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.421469 | − | 0.306215i | 0.0407450 | − | 0.0296030i | −0.567226 | − | 0.823562i | \(-0.691984\pi\) |
0.607971 | + | 0.793959i | \(0.291984\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.22545 | −0.596290 | −0.298145 | − | 0.954521i | \(-0.596368\pi\) | ||||
−0.298145 | + | 0.954521i | \(0.596368\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19.3793 | −1.83940 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.98968 | − | 5.80484i | 0.751605 | − | 0.546073i | −0.144719 | − | 0.989473i | \(-0.546228\pi\) |
0.896324 | + | 0.443400i | \(0.146228\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.44958 | − | 7.53904i | −0.228425 | − | 0.703019i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 22.2643 | + | 16.1760i | 2.05834 | + | 1.49547i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.147181 | + | 0.452976i | −0.0134920 | + | 0.0415242i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.05194 | + | 7.49442i | −0.731995 | + | 0.681310i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.19628 | + | 25.2256i | −0.739034 | + | 2.27451i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.809017 | + | 0.587785i | 0.0723607 | + | 0.0525731i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.14934 | + | 3.53730i | 0.101987 | + | 0.313885i | 0.989012 | − | 0.147838i | \(-0.0472315\pi\) |
−0.887024 | + | 0.461723i | \(0.847231\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.6753 | − | 11.3888i | 1.38013 | − | 1.00273i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.4259 | 1.78462 | 0.892308 | − | 0.451426i | \(-0.149085\pi\) | ||||
0.892308 | + | 0.451426i | \(0.149085\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.224243 | −0.0194443 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.86710 | + | 5.71579i | −0.677092 | + | 0.491936i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.14751 | + | 12.7647i | 0.354346 | + | 1.09056i | 0.956388 | + | 0.292100i | \(0.0943540\pi\) |
−0.602042 | + | 0.798465i | \(0.705646\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.3955 | − | 8.27933i | −0.966555 | − | 0.702243i | −0.0118911 | − | 0.999929i | \(-0.503785\pi\) |
−0.954664 | + | 0.297686i | \(0.903785\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.771803 | + | 2.37537i | −0.0649975 | + | 0.200042i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.6825 | − | 0.891094i | 1.22781 | − | 0.0745170i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.89305 | − | 8.90389i | 0.240255 | − | 0.739428i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.3414 | − | 11.1462i | −1.26533 | − | 0.919319i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.553674 | + | 1.70403i | 0.0453588 | + | 0.139600i | 0.971171 | − | 0.238384i | \(-0.0766176\pi\) |
−0.925812 | + | 0.377984i | \(0.876618\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.4418 | + | 11.2191i | −1.25663 | + | 0.912996i | −0.998587 | − | 0.0531366i | \(-0.983078\pi\) |
−0.258045 | + | 0.966133i | \(0.583078\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.41300 | −0.275925 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.31588 | 0.426982 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.91828 | + | 5.75296i | −0.631947 | + | 0.459137i | −0.857074 | − | 0.515193i | \(-0.827720\pi\) |
0.225127 | + | 0.974329i | \(0.427720\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.25116 | − | 6.92837i | −0.178529 | − | 0.549455i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.55327 | − | 4.03469i | −0.437659 | − | 0.317978i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.122631 | − | 0.377420i | 0.00960522 | − | 0.0295618i | −0.946139 | − | 0.323761i | \(-0.895053\pi\) |
0.955744 | + | 0.294199i | \(0.0950528\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.52406 | + | 9.74091i | −0.196498 | + | 0.758329i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.29967 | − | 13.2330i | 0.332718 | − | 1.02400i | −0.635117 | − | 0.772416i | \(-0.719048\pi\) |
0.967835 | − | 0.251585i | \(-0.0809518\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.39618 | − | 3.92055i | −0.415091 | − | 0.301581i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.496556 | − | 1.52824i | −0.0379726 | − | 0.116868i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.31522 | + | 3.13519i | −0.328080 | + | 0.238364i | −0.739615 | − | 0.673030i | \(-0.764993\pi\) |
0.411535 | + | 0.911394i | \(0.364993\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.865927 | 0.0654580 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 41.0039 | 3.08204 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.17667 | + | 4.48761i | −0.461666 | + | 0.335420i | −0.794184 | − | 0.607677i | \(-0.792102\pi\) |
0.332519 | + | 0.943097i | \(0.392102\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.403121 | + | 1.24068i | 0.0299638 | + | 0.0922189i | 0.964920 | − | 0.262544i | \(-0.0845615\pi\) |
−0.934956 | + | 0.354763i | \(0.884562\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.2187 | − | 11.7836i | −1.19892 | − | 0.871068i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.97381 | + | 6.07477i | −0.145118 | + | 0.446626i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.40818 | + | 1.15970i | −0.102976 | + | 0.0848058i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.60208 | + | 8.00839i | −0.189274 | + | 0.582524i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.2928 | − | 14.7436i | −1.46834 | − | 1.06681i | −0.981091 | − | 0.193547i | \(-0.938001\pi\) |
−0.487248 | − | 0.873264i | \(-0.661999\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.16676 | − | 18.9793i | −0.443893 | − | 1.36616i | −0.883693 | − | 0.468067i | \(-0.844950\pi\) |
0.439799 | − | 0.898096i | \(-0.355050\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.8862 | − | 7.90926i | 0.779574 | − | 0.566394i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.31088 | −0.0933960 | −0.0466980 | − | 0.998909i | \(-0.514870\pi\) | ||||
−0.0466980 | + | 0.998909i | \(0.514870\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.99115 | −0.353813 | −0.176907 | − | 0.984228i | \(-0.556609\pi\) | ||||
−0.176907 | + | 0.984228i | \(0.556609\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.6169 | − | 12.7994i | 1.24260 | − | 0.902803i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.50517 | − | 7.71012i | −0.175829 | − | 0.541145i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.07258 | + | 5.13853i | 0.493970 | + | 0.358890i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.1999 | − | 46.7805i | 1.05647 | − | 3.25147i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.724156 | − | 0.461817i | −0.0500909 | − | 0.0319445i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.98113 | + | 6.09730i | −0.136387 | + | 0.419755i | −0.995803 | − | 0.0915210i | \(-0.970827\pi\) |
0.859416 | + | 0.511276i | \(0.170827\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.87054 | + | 4.99174i | 0.470762 | + | 0.342028i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.97345 | − | 6.07366i | −0.134588 | − | 0.414220i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.72404 | − | 2.70567i | 0.252804 | − | 0.183673i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.77047 | 0.592654 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.43944 | 0.164094 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.0126 | − | 8.72766i | 0.804423 | − | 0.584447i | −0.107786 | − | 0.994174i | \(-0.534376\pi\) |
0.912208 | + | 0.409727i | \(0.134376\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.91748 | + | 5.90141i | 0.127832 | + | 0.393427i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.9925 | + | 13.7989i | 1.26058 | + | 0.915865i | 0.998786 | − | 0.0492591i | \(-0.0156860\pi\) |
0.261794 | + | 0.965124i | \(0.415686\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.06694 | − | 18.6721i | 0.400914 | − | 1.23389i | −0.523344 | − | 0.852121i | \(-0.675316\pi\) |
0.924259 | − | 0.381766i | \(-0.124684\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.18969 | + | 8.10869i | 0.209866 | + | 0.533512i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.48770 | − | 19.9671i | 0.425024 | − | 1.30809i | −0.477948 | − | 0.878388i | \(-0.658619\pi\) |
0.902972 | − | 0.429700i | \(-0.141381\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.665989 | + | 0.483870i | 0.0434444 | + | 0.0315642i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.54519 | + | 17.0664i | 0.360199 | + | 1.10858i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.2527 | − | 11.0817i | 0.986614 | − | 0.716817i | 0.0274367 | − | 0.999624i | \(-0.491266\pi\) |
0.959177 | + | 0.282807i | \(0.0912655\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.8318 | −0.890987 | −0.445494 | − | 0.895285i | \(-0.646972\pi\) | ||||
−0.445494 | + | 0.895285i | \(0.646972\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.86143 | −0.247711 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.05649 | + | 3.67376i | −0.323048 | + | 0.234708i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.354913 | + | 1.09231i | 0.0225826 | + | 0.0695020i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.4229 | − | 12.6585i | −1.10413 | − | 0.802199i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.71929 | − | 14.5245i | 0.297879 | − | 0.916777i | −0.684360 | − | 0.729144i | \(-0.739919\pi\) |
0.982239 | − | 0.187633i | \(-0.0600815\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.62416 | − | 24.4661i | −0.605066 | − | 1.53817i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.515684 | + | 1.58711i | −0.0322934 | + | 0.0993889i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.2900 | − | 16.9212i | −1.45279 | − | 1.05551i | −0.985170 | − | 0.171584i | \(-0.945112\pi\) |
−0.467620 | − | 0.883930i | \(-0.654888\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.70918 | + | 5.26031i | 0.106203 | + | 0.326860i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 46.9981 | − | 34.1461i | 2.90911 | − | 2.11359i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.23218 | −0.569281 | −0.284640 | − | 0.958634i | \(-0.591874\pi\) | ||||
−0.284640 | + | 0.958634i | \(0.591874\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.40110 | −0.147498 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −40.8610 | + | 29.6873i | −2.50065 | + | 1.81683i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.29165 | + | 25.5191i | 0.505551 | + | 1.55593i | 0.799842 | + | 0.600210i | \(0.204916\pi\) |
−0.294291 | + | 0.955716i | \(0.595084\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.0614 | − | 13.8489i | −1.15790 | − | 0.841261i | −0.168386 | − | 0.985721i | \(-0.553856\pi\) |
−0.989511 | + | 0.144460i | \(0.953856\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.60065 | − | 11.0817i | 0.217921 | − | 0.670693i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.79638 | + | 1.78334i | 0.168628 | + | 0.107539i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.08782 | − | 9.50334i | 0.185529 | − | 0.571001i | −0.814428 | − | 0.580265i | \(-0.802949\pi\) |
0.999957 | + | 0.00926435i | \(0.00294898\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 26.6859 | + | 19.3884i | 1.59764 | + | 1.16076i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.26401 | + | 3.89022i | 0.0754044 | + | 0.232071i | 0.981654 | − | 0.190673i | \(-0.0610670\pi\) |
−0.906249 | + | 0.422744i | \(0.861067\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.86118 | + | 2.80531i | −0.229523 | + | 0.166758i | −0.696603 | − | 0.717457i | \(-0.745306\pi\) |
0.467080 | + | 0.884215i | \(0.345306\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.785690 | −0.0465402 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.57010 | 0.446849 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5085 | − | 9.81452i | 0.794620 | − | 0.577325i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.34476 | + | 22.6048i | 0.430557 | + | 1.32512i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.116508 | − | 0.0846481i | −0.00680648 | − | 0.00494520i | 0.584377 | − | 0.811482i | \(-0.301339\pi\) |
−0.591183 | + | 0.806537i | \(0.701339\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.17631 | − | 12.8534i | 0.243154 | − | 0.748352i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −24.8959 | + | 20.5029i | −1.44461 | + | 1.18970i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.8641 | + | 33.4363i | −0.628288 | + | 1.93367i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.47387 | − | 3.25046i | −0.257869 | − | 0.187353i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.0625 | + | 52.5130i | 0.980216 | + | 3.01679i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.34567 | + | 3.88385i | −0.306092 | + | 0.222389i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.7576 | −1.47006 | −0.735031 | − | 0.678034i | \(-0.762832\pi\) | ||||
−0.735031 | + | 0.678034i | \(0.762832\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −35.8088 | −2.03709 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.2610 | + | 9.63467i | −0.751961 | + | 0.546332i | −0.896434 | − | 0.443177i | \(-0.853851\pi\) |
0.144473 | + | 0.989509i | \(0.453851\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.19629 | + | 25.2256i | 0.463282 | + | 1.42583i | 0.861131 | + | 0.508384i | \(0.169757\pi\) |
−0.397849 | + | 0.917451i | \(0.630243\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.34699 | + | 3.15827i | 0.244925 | + | 0.177948i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.16546 | − | 15.8977i | 0.290121 | − | 0.892902i | −0.694695 | − | 0.719304i | \(-0.744461\pi\) |
0.984817 | − | 0.173598i | \(-0.0555392\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.78858 | − | 30.0579i | 0.436077 | − | 1.68292i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.488433 | − | 1.50324i | 0.0272617 | − | 0.0839028i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.115234 | − | 0.0837225i | −0.00641180 | − | 0.00465845i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.37052 | − | 4.21802i | −0.0760227 | − | 0.233974i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.2807 | + | 11.1021i | −0.845025 | + | 0.613946i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.712839 | 0.0393001 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.39584 | 0.241617 | 0.120809 | − | 0.992676i | \(-0.461451\pi\) | ||||
0.120809 | + | 0.992676i | \(0.461451\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −32.0649 | + | 23.2965i | −1.75715 | + | 1.27664i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.21789 | − | 6.82597i | −0.121176 | − | 0.372942i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.1965 | − | 7.40817i | −0.555437 | − | 0.403549i | 0.274349 | − | 0.961630i | \(-0.411538\pi\) |
−0.829786 | + | 0.558082i | \(0.811538\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.25909 | − | 28.4966i | 0.502885 | − | 1.54772i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.5984 | − | 1.06806i | 0.953006 | − | 0.0578387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.54556 | + | 10.9121i | −0.191442 | + | 0.589199i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −19.4573 | − | 14.1365i | −1.04754 | − | 0.761085i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.41108 | − | 22.8089i | −0.397847 | − | 1.22445i | −0.926722 | − | 0.375748i | \(-0.877386\pi\) |
0.528874 | − | 0.848700i | \(-0.322614\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.0848 | + | 13.8659i | −1.02159 | + | 0.742227i | −0.966608 | − | 0.256261i | \(-0.917509\pi\) |
−0.0549798 | + | 0.998487i | \(0.517509\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 43.1281 | 2.30201 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.46751 | 0.344231 | 0.172115 | − | 0.985077i | \(-0.444940\pi\) | ||||
0.172115 | + | 0.985077i | \(0.444940\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.26452 | − | 1.64527i | 0.120188 | − | 0.0873219i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.446545 | + | 1.37432i | 0.0236337 | + | 0.0727370i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.56591 | − | 6.95004i | −0.504869 | − | 0.366809i | 0.306005 | − | 0.952030i | \(-0.401008\pi\) |
−0.810874 | + | 0.585221i | \(0.801008\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.85060 | + | 18.0063i | −0.307926 | + | 0.947700i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.39884 | + | 32.7547i | −0.335852 | + | 1.71918i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.893287 | − | 2.74925i | 0.0467568 | − | 0.143903i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.78533 | − | 4.92983i | −0.354191 | − | 0.257335i | 0.396434 | − | 0.918063i | \(-0.370248\pi\) |
−0.750625 | + | 0.660728i | \(0.770248\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.7630 | + | 51.5912i | 0.872647 | + | 2.68573i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.68209 | + | 1.22211i | −0.0873298 | + | 0.0634488i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.6263 | 1.79288 | 0.896441 | − | 0.443163i | \(-0.146144\pi\) | ||||
0.896441 | + | 0.443163i | \(0.146144\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.03399 | 0.156675 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −33.5918 | + | 24.4059i | −1.73007 | + | 1.25697i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.96669 | + | 15.2859i | 0.255122 | + | 0.785185i | 0.993806 | + | 0.111132i | \(0.0354478\pi\) |
−0.738684 | + | 0.674052i | \(0.764552\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.12931 | + | 6.63283i | 0.467709 | + | 0.339810i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.60059 | − | 8.00380i | 0.132884 | − | 0.408975i | −0.862371 | − | 0.506277i | \(-0.831021\pi\) |
0.995255 | + | 0.0973020i | \(0.0310213\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.86668 | − | 0.173981i | 0.146100 | − | 0.00886690i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.2455 | − | 37.6877i | 0.622473 | − | 1.91577i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.0410 | − | 10.9279i | −0.762608 | − | 0.554067i | 0.137101 | − | 0.990557i | \(-0.456222\pi\) |
−0.899709 | + | 0.436490i | \(0.856222\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.34735 | − | 4.14670i | −0.0681382 | − | 0.209708i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 50.1364 | − | 36.4262i | 2.52904 | − | 1.83746i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.91452 | 0.297592 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.9897 | −0.601743 | −0.300872 | − | 0.953665i | \(-0.597278\pi\) | ||||
−0.300872 | + | 0.953665i | \(0.597278\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.550415 | + | 0.399900i | −0.0275552 | + | 0.0200200i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.80924 | + | 17.8790i | 0.290099 | + | 0.892834i | 0.984824 | + | 0.173558i | \(0.0555264\pi\) |
−0.694724 | + | 0.719276i | \(0.744474\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.0737 | − | 13.8579i | −0.950129 | − | 0.690309i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.36459 | + | 10.3551i | −0.167188 | + | 0.514551i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.31383 | + | 20.5073i | −0.263397 | + | 1.01651i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.93699 | + | 9.03912i | −0.145225 | + | 0.446956i | −0.997040 | − | 0.0768869i | \(-0.975502\pi\) |
0.851815 | + | 0.523842i | \(0.175502\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 32.9441 | + | 23.9353i | 1.62501 | + | 1.18064i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.61638 | − | 11.1301i | −0.177951 | − | 0.547676i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.74257 | + | 4.17222i | −0.281892 | + | 0.204806i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −42.7357 | −2.09278 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.9152 | 1.60801 | 0.804007 | − | 0.594620i | \(-0.202698\pi\) | ||||
0.804007 | + | 0.594620i | \(0.202698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.837812 | − | 0.608706i | 0.0408325 | − | 0.0296665i | −0.567182 | − | 0.823593i | \(-0.691966\pi\) |
0.608014 | + | 0.793926i | \(0.291966\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.57849 | + | 4.85809i | 0.0767487 | + | 0.236208i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.444984 | + | 0.323300i | 0.0215849 | + | 0.0156824i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.76811 | + | 5.44167i | −0.0855646 | + | 0.263341i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 34.4499 | − | 28.3711i | 1.66326 | − | 1.36977i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.96068 | − | 24.5005i | 0.383452 | − | 1.18015i | −0.554144 | − | 0.832421i | \(-0.686954\pi\) |
0.937597 | − | 0.347725i | \(-0.113046\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.9188 | + | 10.8391i | 0.716951 | + | 0.520896i | 0.885409 | − | 0.464813i | \(-0.153879\pi\) |
−0.168457 | + | 0.985709i | \(0.553879\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.77749 | − | 27.0143i | −0.420848 | − | 1.29524i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.66075 | − | 1.20660i | 0.0794444 | − | 0.0577197i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.44724 | −0.212255 | −0.106128 | − | 0.994353i | \(-0.533845\pi\) | ||||
−0.106128 | + | 0.994353i | \(0.533845\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −38.7830 | −1.84681 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.2851 | − | 14.7380i | 0.963775 | − | 0.700224i | 0.00975065 | − | 0.999952i | \(-0.496896\pi\) |
0.954024 | + | 0.299729i | \(0.0968962\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.14422 | + | 15.8323i | 0.243859 | + | 0.750522i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.39789 | + | 3.19525i | 0.208013 | + | 0.151130i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.77075 | + | 17.7605i | −0.272338 | + | 0.838172i | 0.717573 | + | 0.696483i | \(0.245253\pi\) |
−0.989911 | + | 0.141688i | \(0.954747\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.4464 | + | 15.5903i | 1.15114 | + | 0.734116i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.8952 | + | 55.0757i | −0.840788 | + | 2.58768i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.10700 | − | 2.25737i | −0.145659 | − | 0.105827i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.49832 | − | 13.8444i | −0.210422 | − | 0.647614i | −0.999447 | − | 0.0332521i | \(-0.989414\pi\) |
0.789025 | − | 0.614362i | \(-0.210586\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.32715 | + | 3.14386i | −0.201974 | + | 0.146743i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.6525 | 0.961884 | 0.480942 | − | 0.876752i | \(-0.340295\pi\) | ||||
0.480942 | + | 0.876752i | \(0.340295\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.8605 | −1.01594 | −0.507971 | − | 0.861374i | \(-0.669604\pi\) | ||||
−0.507971 | + | 0.861374i | \(0.669604\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.0481 | − | 9.48000i | 0.605091 | − | 0.439624i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.27254 | + | 19.3049i | 0.290258 | + | 0.893324i | 0.984773 | + | 0.173845i | \(0.0556192\pi\) |
−0.694515 | + | 0.719479i | \(0.744381\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.02802 | − | 3.65307i | −0.232172 | − | 0.168683i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.17635 | + | 28.2419i | −0.422824 | + | 1.30132i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.75349 | − | 19.7105i | −0.356506 | − | 0.906292i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.0800238 | + | 0.246288i | −0.00367174 | + | 0.0113005i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.0536 | − | 8.75746i | −0.551897 | − | 0.400977i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.05665 | − | 9.40740i | −0.139662 | − | 0.429835i | 0.856624 | − | 0.515941i | \(-0.172558\pi\) |
−0.996286 | + | 0.0861060i | \(0.972558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.9184 | − | 16.6512i | 1.04499 | − | 0.759228i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.8260 | −0.947615 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.83395 | 0.355721 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.80458 | + | 3.49073i | −0.217716 | + | 0.158180i | −0.691298 | − | 0.722570i | \(-0.742961\pi\) |
0.473582 | + | 0.880750i | \(0.342961\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.372062 | − | 1.14509i | −0.0168252 | − | 0.0517828i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.1143 | − | 16.0670i | −0.998005 | − | 0.725093i | −0.0363455 | − | 0.999339i | \(-0.511572\pi\) |
−0.961660 | + | 0.274246i | \(0.911572\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.59127 | − | 4.89741i | 0.0716670 | − | 0.220568i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.53360 | + | 19.1516i | 0.338610 | + | 0.860798i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.749001 | − | 2.30519i | 0.0335973 | − | 0.103402i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.84395 | + | 7.15205i | 0.440676 | + | 0.320170i | 0.785903 | − | 0.618349i | \(-0.212198\pi\) |
−0.345228 | + | 0.938519i | \(0.612198\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.0452 | − | 40.1488i | −0.582814 | − | 1.79372i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.67903 | − | 5.57914i | 0.342391 | − | 0.248762i | −0.403279 | − | 0.915077i | \(-0.632130\pi\) |
0.745670 | + | 0.666315i | \(0.232130\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.1989 | 0.809842 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.2369 | −0.898750 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.774792 | − | 0.562919i | 0.0343421 | − | 0.0249510i | −0.570482 | − | 0.821310i | \(-0.693244\pi\) |
0.604824 | + | 0.796359i | \(0.293244\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.773521 | − | 2.38065i | −0.0342186 | − | 0.105314i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.03728 | − | 1.48017i | −0.0899483 | − | 0.0653512i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.64718 | + | 11.2249i | −0.160714 | + | 0.494627i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.30200 | + | 1.46806i | 0.101242 | + | 0.0645651i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.00083 | + | 15.3910i | −0.219512 | + | 0.675589i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.7577 | + | 10.7221i | 0.646547 | + | 0.469744i | 0.862093 | − | 0.506750i | \(-0.169153\pi\) |
−0.215546 | + | 0.976494i | \(0.569153\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.75364 | + | 26.9409i | 0.382770 | + | 1.17804i | 0.938085 | + | 0.346405i | \(0.112598\pi\) |
−0.555315 | + | 0.831640i | \(0.687402\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.12546 | − | 1.54424i | 0.0927628 | − | 0.0673961i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.92390 | 0.127367 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 39.8375 | 1.73207 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 67.8450 | − | 49.2923i | 2.94422 | − | 2.13910i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.9813 | − | 36.8747i | −0.518969 | − | 1.59722i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.421469 | − | 0.306215i | −0.0182217 | − | 0.0132388i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.15803 | + | 22.0301i | −0.308892 | + | 0.950671i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.0016 | + | 13.1780i | −0.689236 | + | 0.567618i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.81343 | + | 30.2026i | −0.421912 | + | 1.29851i | 0.484008 | + | 0.875064i | \(0.339181\pi\) |
−0.905920 | + | 0.423448i | \(0.860819\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.20203 | + | 2.32641i | 0.137412 | + | 0.0998358i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.92377 | + | 5.92076i | 0.0824053 | + | 0.253617i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.89975 | + | 2.10679i | −0.123984 | + | 0.0900798i | −0.648049 | − | 0.761598i | \(-0.724415\pi\) |
0.524065 | + | 0.851678i | \(0.324415\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −41.0009 | −1.74988 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.42443 | 0.103284 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.14342 | − | 3.01037i | 0.176196 | − | 0.128014i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.98853 | + | 18.4308i | 0.254199 | + | 0.782344i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.4746 | + | 9.78990i | 0.570939 | + | 0.414811i | 0.835446 | − | 0.549572i | \(-0.185209\pi\) |
−0.264507 | + | 0.964384i | \(0.585209\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.75244 | + | 26.9372i | −0.370189 | + | 1.13932i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.38831 | + | 5.35780i | −0.0586144 | + | 0.226207i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.3291 | − | 37.9450i | 0.519609 | − | 1.59919i | −0.255127 | − | 0.966907i | \(-0.582117\pi\) |
0.774736 | − | 0.632285i | \(-0.217883\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.98968 | − | 5.80484i | −0.336128 | − | 0.244211i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.91349 | + | 8.96681i | 0.122355 | + | 0.376570i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −36.7814 | + | 26.7233i | −1.54196 | + | 1.12030i | −0.592866 | + | 0.805301i | \(0.702004\pi\) |
−0.949093 | + | 0.314997i | \(0.897996\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.8877 | −0.664880 | −0.332440 | − | 0.943124i | \(-0.607872\pi\) | ||||
−0.332440 | + | 0.943124i | \(0.607872\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −76.1027 | −3.17923 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.41309 | + | 4.65938i | −0.267444 | + | 0.194310i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.06088 | − | 12.4981i | −0.169057 | − | 0.520302i | 0.830256 | − | 0.557383i | \(-0.188194\pi\) |
−0.999312 | + | 0.0370801i | \(0.988194\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −48.9832 | − | 35.5884i | −2.03567 | − | 1.47900i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.89938 | + | 5.84570i | −0.0787997 | + | 0.242520i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.94892 | + | 0.482427i | −0.329211 | + | 0.0199801i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.50422 | − | 26.1733i | 0.351606 | − | 1.08213i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.1061 | − | 8.79560i | −0.499672 | − | 0.363033i | 0.309220 | − | 0.950991i | \(-0.399932\pi\) |
−0.808892 | + | 0.587958i | \(0.799932\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.425397 | + | 1.30924i | 0.0175282 | + | 0.0539461i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.21761 | + | 2.33773i | −0.132355 | + | 0.0961615i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.7967 | −0.566564 | −0.283282 | − | 0.959037i | \(-0.591423\pi\) | ||||
−0.283282 | + | 0.959037i | \(0.591423\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.476287 | 0.0195259 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.2510 | + | 8.90090i | −0.501401 | + | 0.364289i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.69984 | + | 29.8530i | 0.396325 | + | 1.21976i | 0.927925 | + | 0.372767i | \(0.121591\pi\) |
−0.531600 | + | 0.846995i | \(0.678409\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.06813 | + | 1.50259i | 0.0843608 | + | 0.0612917i | 0.629166 | − | 0.777271i | \(-0.283396\pi\) |
−0.544805 | + | 0.838563i | \(0.683396\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.7623 | − | 42.3559i | 0.560442 | − | 1.72486i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.61580 | + | 5.34195i | 0.390938 | + | 0.217181i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.6898 | + | 35.9774i | −0.474473 | + | 1.46028i | 0.372194 | + | 0.928155i | \(0.378605\pi\) |
−0.846667 | + | 0.532123i | \(0.821395\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −19.8988 | − | 14.4573i | −0.806340 | − | 0.585841i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.12822 | − | 3.47231i | −0.0456430 | − | 0.140475i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.43309 | + | 6.85354i | −0.380999 | + | 0.276812i | −0.761757 | − | 0.647863i | \(-0.775663\pi\) |
0.380758 | + | 0.924675i | \(0.375663\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 26.5237 | 1.06954 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.5910 | 1.55361 | 0.776807 | − | 0.629739i | \(-0.216838\pi\) | ||||
0.776807 | + | 0.629739i | \(0.216838\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.60453 | − | 4.79847i | 0.265458 | − | 0.192867i | −0.447092 | − | 0.894488i | \(-0.647540\pi\) |
0.712550 | + | 0.701621i | \(0.247540\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −23.8204 | − | 73.3117i | −0.955880 | − | 2.94190i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.6621 | + | 8.47300i | 0.467231 | + | 0.339463i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.309017 | − | 0.951057i | 0.0123607 | − | 0.0380423i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.60105 | + | 0.157860i | −0.103876 | + | 0.00630432i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.08566 | + | 3.34131i | −0.0432880 | + | 0.133227i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.5830 | + | 7.68900i | 0.421303 | + | 0.306094i | 0.778162 | − | 0.628064i | \(-0.216152\pi\) |
−0.356859 | + | 0.934158i | \(0.616152\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.01074 | + | 18.4992i | 0.238906 | + | 0.735276i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.00901 | − | 2.18617i | 0.119409 | − | 0.0867556i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.7201 | 1.09831 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.3687 | 0.687096 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.8414 | + | 20.9545i | −1.13917 | + | 0.827654i | −0.987003 | − | 0.160702i | \(-0.948624\pi\) |
−0.152164 | + | 0.988355i | \(0.548624\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.36588 | − | 7.28142i | −0.0933011 | − | 0.287151i | 0.893506 | − | 0.449051i | \(-0.148238\pi\) |
−0.986807 | + | 0.161900i | \(0.948238\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.6753 | − | 11.3888i | −0.617215 | − | 0.448433i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.83754 | − | 8.73304i | 0.111555 | − | 0.343331i | −0.879658 | − | 0.475607i | \(-0.842228\pi\) |
0.991213 | + | 0.132276i | \(0.0422285\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.2433 | − | 43.3906i | 0.441340 | − | 1.70323i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.31572 | − | 13.2824i | 0.169146 | − | 0.520579i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.73503 | + | 3.44020i | 0.185296 | + | 0.134626i | 0.676566 | − | 0.736382i | \(-0.263467\pi\) |
−0.491270 | + | 0.871007i | \(0.663467\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.31194 | − | 19.4262i | −0.246628 | − | 0.759043i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.5116 | − | 10.5433i | 0.566152 | − | 0.411333i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.6530 | −0.882434 | −0.441217 | − | 0.897400i | \(-0.645453\pi\) | ||||
−0.441217 | + | 0.897400i | \(0.645453\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.68482 | 0.0655320 | 0.0327660 | − | 0.999463i | \(-0.489568\pi\) | ||||
0.0327660 | + | 0.999463i | \(0.489568\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.98772 | − | 4.35034i | 0.232544 | − | 0.168953i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.0692948 | + | 0.213267i | 0.00268714 | + | 0.00827015i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 60.0400 | + | 43.6216i | 2.32476 | + | 1.68904i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.9212 | − | 42.8450i | 0.538224 | − | 1.65648i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.9167 | + | 13.9317i | −0.653061 | + | 0.537826i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.93100 | + | 9.02070i | −0.112982 | + | 0.347722i | −0.991521 | − | 0.129948i | \(-0.958519\pi\) |
0.878539 | + | 0.477671i | \(0.158519\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.86710 | + | 5.71579i | 0.302805 | + | 0.220001i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.27300 | − | 3.91790i | −0.0489255 | − | 0.150577i | 0.923609 | − | 0.383336i | \(-0.125225\pi\) |
−0.972535 | + | 0.232759i | \(0.925225\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.48807 | − | 3.98732i | 0.210613 | − | 0.153019i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 71.2262 | 2.72940 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.0594 | 1.11193 | 0.555963 | − | 0.831207i | \(-0.312349\pi\) | ||||
0.555963 | + | 0.831207i | \(0.312349\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.8583 | − | 7.88904i | 0.414875 | − | 0.301425i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.4070 | − | 56.6510i | −0.702272 | − | 2.16137i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.61530 | + | 6.25938i | 0.328217 | + | 0.238464i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.01448 | − | 18.5107i | 0.228802 | − | 0.704179i | −0.769082 | − | 0.639150i | \(-0.779286\pi\) |
0.997883 | − | 0.0650287i | \(-0.0207139\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.0254 | + | 9.58217i | 0.570768 | + | 0.363997i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.35270 | + | 13.3962i | −0.165107 | + | 0.508148i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.89013 | + | 2.82635i | 0.147349 | + | 0.107056i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.6836 | − | 60.5800i | −0.744504 | − | 2.29135i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.2452 | − | 8.89666i | 0.462495 | − | 0.336022i | −0.332014 | − | 0.943274i | \(-0.607728\pi\) |
0.794509 | + | 0.607252i | \(0.207728\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.65409 | −0.0623853 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.49761 | 0.0940653 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.7493 | − | 9.26288i | 0.479486 | − | 0.348367i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.35512 | − | 25.7144i | −0.313783 | − | 0.965725i | −0.976252 | − | 0.216636i | \(-0.930492\pi\) |
0.662469 | − | 0.749089i | \(-0.269508\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.6911 | + | 21.5719i | 1.11350 | + | 0.809009i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.0217 | + | 40.0766i | −0.487666 | + | 1.50088i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.38463 | − | 13.6885i | −0.201374 | − | 0.511923i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.6760 | − | 54.4013i | 0.660124 | − | 2.03165i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.03354 | − | 2.20400i | −0.113132 | − | 0.0821953i | 0.529781 | − | 0.848135i | \(-0.322274\pi\) |
−0.642913 | + | 0.765939i | \(0.722274\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.15820 | + | 9.71993i | 0.117617 | + | 0.361989i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −33.9510 | + | 24.6668i | −1.26265 | + | 0.917369i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.36210 | −0.347700 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.5685 | 1.69004 | 0.845022 | − | 0.534732i | \(-0.179587\pi\) | ||||
0.845022 | + | 0.534732i | \(0.179587\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16.9478 | − | 12.3133i | 0.627695 | − | 0.456047i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.08546 | − | 3.34070i | −0.0401472 | − | 0.123560i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.0787 | + | 21.8535i | 1.11098 | + | 0.807176i | 0.982818 | − | 0.184577i | \(-0.0590915\pi\) |
0.128164 | + | 0.991753i | \(0.459091\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.85988 | + | 18.0349i | −0.216145 | + | 0.665226i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.71387 | − | 22.1520i | −0.320980 | − | 0.815979i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.19398 | + | 3.67469i | −0.0439213 | + | 0.135176i | −0.970613 | − | 0.240648i | \(-0.922640\pi\) |
0.926691 | + | 0.375824i | \(0.122640\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.81911 | + | 2.04820i | 0.103562 | + | 0.0752425i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.39028 | − | 7.35652i | −0.0876908 | − | 0.269885i | 0.897589 | − | 0.440833i | \(-0.145317\pi\) |
−0.985280 | + | 0.170948i | \(0.945317\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.44954 | − | 1.05315i | 0.0531070 | − | 0.0385845i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −44.0451 | −1.61153 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.451118 | −0.0164835 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.9688 | − | 11.6020i | 0.582711 | − | 0.423364i | −0.256989 | − | 0.966414i | \(-0.582731\pi\) |
0.839700 | + | 0.543050i | \(0.182731\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.3183 | − | 44.0671i | −0.521787 | − | 1.60590i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.4418 | + | 11.2191i | 0.561983 | + | 0.408304i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.27026 | − | 10.0648i | 0.118859 | − | 0.365812i | −0.873873 | − | 0.486154i | \(-0.838399\pi\) |
0.992732 | + | 0.120343i | \(0.0383993\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −67.2542 | − | 42.8901i | −2.44117 | − | 1.55681i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.6578 | − | 48.1899i | 0.567596 | − | 1.74688i | −0.0925129 | − | 0.995711i | \(-0.529490\pi\) |
0.660109 | − | 0.751170i | \(-0.270510\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.36124 | + | 3.16863i | 0.157888 | + | 0.114712i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.05468 | + | 3.24596i | 0.0381319 | + | 0.117358i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −48.4921 | + | 35.2316i | −1.75095 | + | 1.27214i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.2588 | −0.586306 | −0.293153 | − | 0.956066i | \(-0.594705\pi\) | ||||
−0.293153 | + | 0.956066i | \(0.594705\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −87.3426 | −3.14557 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.3405 | + | 9.69243i | −0.479824 | + | 0.348612i | −0.801257 | − | 0.598320i | \(-0.795835\pi\) |
0.321434 | + | 0.946932i | \(0.395835\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.64270 | − | 5.05570i | −0.0590074 | − | 0.181606i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.5762 | + | 9.86366i | 0.487042 | + | 0.353857i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.699582 | + | 2.15309i | −0.0250651 | + | 0.0771426i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.16621 | − | 5.90171i | 0.256427 | − | 0.211180i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 28.1328 | − | 86.5839i | 1.00538 | − | 3.09426i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.91828 | + | 5.75296i | 0.282615 | + | 0.205332i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.94742 | + | 24.4597i | 0.283295 | + | 0.871892i | 0.986905 | + | 0.161306i | \(0.0515705\pi\) |
−0.703610 | + | 0.710587i | \(0.748430\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.6609 | + | 16.4641i | −0.806748 | + | 0.586137i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.55171 | −0.304064 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.3054 | 1.04066 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.89362 | + | 4.28197i | −0.209025 | + | 0.151866i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.72973 | + | 5.32356i | 0.0612701 | + | 0.188570i | 0.977006 | − | 0.213210i | \(-0.0683917\pi\) |
−0.915736 | + | 0.401780i | \(0.868392\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.366315 | + | 0.266143i | 0.0129593 | + | 0.00941547i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −31.9204 | + | 98.2410i | −1.12785 | + | 3.47117i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.40488 | − | 9.28098i | 0.0848663 | − | 0.327519i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.12116 | + | 6.52826i | −0.0747611 | + | 0.230091i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 65.8614 | + | 47.8511i | 2.31843 | + | 1.68444i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.08110 | + | 18.7157i | 0.213800 | + | 0.658009i | 0.999237 | + | 0.0390667i | \(0.0124385\pi\) |
−0.785437 | + | 0.618942i | \(0.787562\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.99885 | − | 4.35842i | 0.210648 | − | 0.153045i | −0.477459 | − | 0.878654i | \(-0.658442\pi\) |
0.688107 | + | 0.725609i | \(0.258442\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −71.4844 | −2.50707 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.396843 | −0.0139008 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.33795 | − | 0.972074i | 0.0468088 | − | 0.0340086i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.36404 | − | 22.6642i | −0.257320 | − | 0.791950i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.29404 | + | 3.11981i | 0.149863 | + | 0.108882i | 0.660190 | − | 0.751098i | \(-0.270476\pi\) |
−0.510327 | + | 0.859980i | \(0.670476\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.00458 | + | 15.4025i | −0.174449 | + | 0.536898i | −0.999608 | − | 0.0280024i | \(-0.991085\pi\) |
0.825159 | + | 0.564900i | \(0.191085\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.0441 | − | 0.609587i | 0.349692 | − | 0.0212231i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.08205 | + | 9.48557i | −0.107173 | + | 0.329846i | −0.990234 | − | 0.139412i | \(-0.955479\pi\) |
0.883061 | + | 0.469258i | \(0.155479\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.4275 | + | 15.5680i | 0.744209 | + | 0.540700i | 0.894027 | − | 0.448014i | \(-0.147869\pi\) |
−0.149817 | + | 0.988714i | \(0.547869\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.36843 | − | 28.8331i | −0.324987 | − | 1.00021i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.78123 | + | 2.02068i | −0.0963638 | + | 0.0700124i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.9140 | −0.481514 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 51.6931 | 1.78677 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.4642 | + | 14.1416i | −0.671980 | + | 0.488222i | −0.870687 | − | 0.491837i | \(-0.836326\pi\) |
0.198707 | + | 0.980059i | \(0.436326\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.1235 | + | 55.7785i | 0.624950 | + | 1.92340i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.0401 | + | 7.29458i | 0.345801 | + | 0.251239i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.06116 | + | 6.34359i | −0.0709059 | + | 0.218226i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.45529 | − | 1.15194i | 0.324888 | − | 0.0395812i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.47465 | + | 13.7716i | −0.153570 | + | 0.472639i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −40.9629 | − | 29.7613i | −1.40419 | − | 1.02020i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.96743 | + | 21.4436i | 0.238560 | + | 0.734213i | 0.996629 | + | 0.0820386i | \(0.0261431\pi\) |
−0.758069 | + | 0.652175i | \(0.773857\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.30000 | + | 0.944506i | −0.0444591 | + | 0.0323014i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.0453 | 0.343143 | 0.171571 | − | 0.985172i | \(-0.445116\pi\) | ||||
0.171571 | + | 0.985172i | \(0.445116\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.7921 | 0.538819 | 0.269409 | − | 0.963026i | \(-0.413172\pi\) | ||||
0.269409 | + | 0.963026i | \(0.413172\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.5812 | − | 13.5000i | 0.633245 | − | 0.460080i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.99653 | − | 21.5331i | −0.238165 | − | 0.732995i | −0.996686 | − | 0.0813469i | \(-0.974078\pi\) |
0.758521 | − | 0.651648i | \(-0.225922\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.31522 | + | 3.13519i | 0.146722 | + | 0.106600i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.6548 | − | 48.1805i | 0.531665 | − | 1.63630i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.5802 | − | 1.18834i | 0.664214 | − | 0.0403117i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.83655 | + | 30.2738i | −0.333299 | + | 1.02579i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 39.3267 | + | 28.5725i | 1.33101 | + | 0.967034i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.267586 | − | 0.823546i | −0.00904607 | − | 0.0278409i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.2215 | + | 13.9652i | −0.649064 | + | 0.471573i | −0.862952 | − | 0.505285i | \(-0.831387\pi\) |
0.213888 | + | 0.976858i | \(0.431387\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.436931 | −0.0147373 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.6772 | −0.730323 | −0.365161 | − | 0.930944i | \(-0.618986\pi\) | ||||
−0.365161 | + | 0.930944i | \(0.618986\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.8621 | − | 23.8757i | 1.10590 | − | 0.803482i | 0.123885 | − | 0.992297i | \(-0.460465\pi\) |
0.982013 | + | 0.188815i | \(0.0604645\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.6709 | − | 38.9970i | −0.425928 | − | 1.31087i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.6287 | − | 20.0734i | −0.927680 | − | 0.673999i | 0.0177436 | − | 0.999843i | \(-0.494352\pi\) |
−0.945424 | + | 0.325843i | \(0.894352\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.995244 | − | 3.06305i | 0.0333794 | − | 0.102731i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.05805 | + | 34.9571i | −0.303456 | + | 1.17111i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.0658762 | + | 0.202746i | −0.00220446 | + | 0.00678464i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.17667 | + | 4.48761i | 0.206463 | + | 0.150004i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32.9617 | + | 101.446i | 1.10056 | + | 3.38717i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −40.2630 | + | 29.2528i | −1.34285 | + | 0.975635i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.32068 | −0.0439982 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.7780 | −0.558337 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.05538 | − | 0.766782i | 0.0350822 | − | 0.0254887i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.57041 | + | 10.9886i | 0.118554 | + | 0.364870i | 0.992672 | − | 0.120843i | \(-0.0385598\pi\) |
−0.874118 | + | 0.485714i | \(0.838560\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 91.3594 | + | 66.3765i | 3.03020 | + | 2.20157i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.45162 | + | 13.7007i | −0.147489 | + | 0.453924i | −0.997323 | − | 0.0731269i | \(-0.976702\pi\) |
0.849834 | + | 0.527051i | \(0.176702\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.1727 | + | 14.9661i | −0.601428 | + | 0.495305i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.19500 | + | 19.0662i | −0.204800 | + | 0.630310i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.3093 | − | 10.3963i | −0.472536 | − | 0.343318i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.1775 | − | 46.7116i | −0.500660 | − | 1.54087i | −0.807946 | − | 0.589256i | \(-0.799421\pi\) |
0.307286 | − | 0.951617i | \(-0.400579\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −63.2232 | + | 45.9344i | −2.08328 | + | 1.51359i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.4143 | −0.408621 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.38739 | 0.210016 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −59.2492 | + | 43.0470i | −1.94600 | + | 1.41385i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.41296 | + | 22.8147i | 0.243211 | + | 0.748527i | 0.995925 | + | 0.0901799i | \(0.0287442\pi\) |
−0.752714 | + | 0.658347i | \(0.771256\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.30944 | − | 0.951365i | −0.0429152 | − | 0.0311797i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.3679 | + | 47.2976i | −0.503123 | + | 1.54845i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.53809 | + | 0.980890i | 0.0503010 | + | 0.0320785i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.04879 | − | 12.4609i | 0.132268 | − | 0.407079i | −0.862887 | − | 0.505397i | \(-0.831346\pi\) |
0.995155 | + | 0.0983175i | \(0.0313461\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 65.1039 | + | 47.3008i | 2.12459 | + | 1.54360i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.3355 | − | 34.8872i | −0.369528 | − | 1.13729i | −0.947097 | − | 0.320948i | \(-0.895998\pi\) |
0.577569 | − | 0.816342i | \(-0.304002\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −56.0644 | + | 40.7332i | −1.82571 | + | 1.32645i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.42052 | 0.273919 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.6112 | 0.669774 | 0.334887 | − | 0.942258i | \(-0.391302\pi\) | ||||
0.334887 | + | 0.942258i | \(0.391302\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.3722 | + | 7.53581i | −0.336694 | + | 0.244623i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.6720 | − | 48.2334i | −0.508199 | − | 1.56407i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.3964 | − | 10.4596i | −0.466344 | − | 0.338819i | 0.329671 | − | 0.944096i | \(-0.393062\pi\) |
−0.796015 | + | 0.605277i | \(0.793062\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.75118 | + | 23.8557i | −0.250822 | + | 0.771951i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −34.4859 | − | 87.6683i | −1.11477 | − | 2.83391i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.59144 | − | 11.0533i | 0.115974 | − | 0.356931i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.21787 | + | 1.61138i | 0.0715443 | + | 0.0519800i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.998941 | − | 3.07443i | −0.0321904 | − | 0.0990720i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.1448 | + | 11.7299i | −0.519719 | + | 0.377598i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.828077 | −0.0266292 | −0.0133146 | − | 0.999911i | \(-0.504238\pi\) | ||||
−0.0133146 | + | 0.999911i | \(0.504238\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.432154 | −0.0138828 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.100751 | − | 0.0732001i | 0.00323326 | − | 0.00234910i | −0.586167 | − | 0.810190i | \(-0.699364\pi\) |
0.589401 | + | 0.807841i | \(0.299364\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.76912 | + | 11.6002i | 0.120832 | + | 0.371884i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.8862 | − | 7.90926i | −0.348636 | − | 0.253299i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.63347 | + | 20.4157i | −0.212223 | + | 0.653157i | 0.787116 | + | 0.616805i | \(0.211573\pi\) |
−0.999339 | + | 0.0363512i | \(0.988427\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.2111 | + | 51.3797i | 0.645950 | + | 1.64210i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.9372 | + | 36.7390i | −0.381126 | + | 1.17298i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.6917 | − | 18.6661i | −0.819436 | − | 0.595355i | 0.0971146 | − | 0.995273i | \(-0.469039\pi\) |
−0.916551 | + | 0.399918i | \(0.869039\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.405083 | + | 1.24672i | 0.0129070 | + | 0.0397237i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.74970 | − | 1.27123i | 0.0556935 | − | 0.0404637i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 50.6237 | 1.60974 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.7101 | 1.48379 | 0.741897 | − | 0.670514i | \(-0.233926\pi\) | ||||
0.741897 | + | 0.670514i | \(0.233926\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.7898 | − | 7.83927i | 0.342405 | − | 0.248772i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.54235 | + | 4.74686i | 0.0488958 | + | 0.150486i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.7896 | − | 30.3619i | −1.32349 | − | 0.961572i | −0.999882 | − | 0.0153805i | \(-0.995104\pi\) |
−0.323608 | − | 0.946191i | \(-0.604896\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −19.1939 | + | 59.0727i | −0.607268 | + | 1.86898i |
(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 | 440.2.y.b.361.3 | ✓ | 12 | |
4.3 | odd | 2 | 880.2.bo.j.801.1 | 12 | |||
11.4 | even | 5 | 4840.2.a.bf.1.1 | 6 | |||
11.5 | even | 5 | inner | 440.2.y.b.401.3 | yes | 12 | |
11.7 | odd | 10 | 4840.2.a.be.1.1 | 6 | |||
44.7 | even | 10 | 9680.2.a.cy.1.6 | 6 | |||
44.15 | odd | 10 | 9680.2.a.cx.1.6 | 6 | |||
44.27 | odd | 10 | 880.2.bo.j.401.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
440.2.y.b.361.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
440.2.y.b.401.3 | yes | 12 | 11.5 | even | 5 | inner | |
880.2.bo.j.401.1 | 12 | 44.27 | odd | 10 | |||
880.2.bo.j.801.1 | 12 | 4.3 | odd | 2 | |||
4840.2.a.be.1.1 | 6 | 11.7 | odd | 10 | |||
4840.2.a.bf.1.1 | 6 | 11.4 | even | 5 | |||
9680.2.a.cx.1.6 | 6 | 44.15 | odd | 10 | |||
9680.2.a.cy.1.6 | 6 | 44.7 | even | 10 |