Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,2,Mod(325,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("648.325");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.17430605098\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 325.3 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.325 |
Dual form | 648.2.d.i.325.4 |
$q$-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 \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36603 | − | 0.366025i | 0.965926 | − | 0.258819i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.73205 | − | 1.00000i | 0.866025 | − | 0.500000i | ||||
\(5\) | 3.73205i | 1.66902i | 0.550990 | + | 0.834512i | \(0.314250\pi\) | ||||
−0.550990 | + | 0.834512i | \(0.685750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.732051 | −0.276689 | −0.138345 | − | 0.990384i | \(-0.544178\pi\) | ||||
−0.138345 | + | 0.990384i | \(0.544178\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.36603 | + | 5.09808i | 0.431975 | + | 1.61215i | ||||
\(11\) | 4.73205i | 1.42677i | 0.700774 | + | 0.713384i | \(0.252838\pi\) | ||||
−0.700774 | + | 0.713384i | \(0.747162\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.46410i | 0.683419i | 0.939806 | + | 0.341709i | \(0.111006\pi\) | ||||
−0.939806 | + | 0.341709i | \(0.888994\pi\) | |||||||
\(14\) | −1.00000 | + | 0.267949i | −0.267261 | + | 0.0716124i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | −3.73205 | −0.905155 | −0.452578 | − | 0.891725i | \(-0.649495\pi\) | ||||
−0.452578 | + | 0.891725i | \(0.649495\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.26795i | − | 0.749719i | −0.927082 | − | 0.374859i | \(-0.877691\pi\) | ||
0.927082 | − | 0.374859i | \(-0.122309\pi\) | |||||||
\(20\) | 3.73205 | + | 6.46410i | 0.834512 | + | 1.44542i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.73205 | + | 6.46410i | 0.369274 | + | 1.37815i | ||||
\(23\) | 8.73205 | 1.82076 | 0.910379 | − | 0.413775i | \(-0.135790\pi\) | ||||
0.910379 | + | 0.413775i | \(0.135790\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.92820 | −1.78564 | ||||||||
\(26\) | 0.901924 | + | 3.36603i | 0.176882 | + | 0.660132i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.26795 | + | 0.732051i | −0.239620 | + | 0.138345i | ||||
\(29\) | − | 5.19615i | − | 0.964901i | −0.875923 | − | 0.482451i | \(-0.839747\pi\) | ||
0.875923 | − | 0.482451i | \(-0.160253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 1.46410 | − | 5.46410i | 0.258819 | − | 0.965926i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.09808 | + | 1.36603i | −0.874313 | + | 0.234271i | ||||
\(35\) | − | 2.73205i | − | 0.461801i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000i | 0.821995i | 0.911636 | + | 0.410997i | \(0.134819\pi\) | ||||
−0.911636 | + | 0.410997i | \(0.865181\pi\) | |||||||
\(38\) | −1.19615 | − | 4.46410i | −0.194042 | − | 0.724173i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.46410 | + | 7.46410i | 1.18018 | + | 1.18018i | ||||
\(41\) | 4.53590 | 0.708388 | 0.354194 | − | 0.935172i | \(-0.384755\pi\) | ||||
0.354194 | + | 0.935172i | \(0.384755\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.66025i | − | 1.47317i | −0.676342 | − | 0.736587i | \(-0.736436\pi\) | ||
0.676342 | − | 0.736587i | \(-0.263564\pi\) | |||||||
\(44\) | 4.73205 | + | 8.19615i | 0.713384 | + | 1.23562i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.9282 | − | 3.19615i | 1.75872 | − | 0.471247i | ||||
\(47\) | 3.46410 | 0.505291 | 0.252646 | − | 0.967559i | \(-0.418699\pi\) | ||||
0.252646 | + | 0.967559i | \(0.418699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.46410 | −0.923443 | ||||||||
\(50\) | −12.1962 | + | 3.26795i | −1.72480 | + | 0.462158i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.46410 | + | 4.26795i | 0.341709 | + | 0.591858i | ||||
\(53\) | − | 0.928203i | − | 0.127499i | −0.997966 | − | 0.0637493i | \(-0.979694\pi\) | ||
0.997966 | − | 0.0637493i | \(-0.0203058\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17.6603 | −2.38131 | ||||||||
\(56\) | −1.46410 | + | 1.46410i | −0.195649 | + | 0.195649i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.90192 | − | 7.09808i | −0.249735 | − | 0.932023i | ||||
\(59\) | 8.39230i | 1.09259i | 0.837594 | + | 0.546293i | \(0.183961\pi\) | ||||
−0.837594 | + | 0.546293i | \(0.816039\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.00000i | − | 1.15233i | −0.817333 | − | 0.576166i | \(-0.804548\pi\) | ||
0.817333 | − | 0.576166i | \(-0.195452\pi\) | |||||||
\(62\) | 2.73205 | − | 0.732051i | 0.346971 | − | 0.0929705i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | −9.19615 | −1.14064 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.73205i | − | 0.578112i | −0.957312 | − | 0.289056i | \(-0.906659\pi\) | ||
0.957312 | − | 0.289056i | \(-0.0933414\pi\) | |||||||
\(68\) | −6.46410 | + | 3.73205i | −0.783887 | + | 0.452578i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.00000 | − | 3.73205i | −0.119523 | − | 0.446065i | ||||
\(71\) | 5.66025 | 0.671749 | 0.335874 | − | 0.941907i | \(-0.390968\pi\) | ||||
0.335874 | + | 0.941907i | \(0.390968\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.00000 | 1.05337 | 0.526685 | − | 0.850060i | \(-0.323435\pi\) | ||||
0.526685 | + | 0.850060i | \(0.323435\pi\) | |||||||
\(74\) | 1.83013 | + | 6.83013i | 0.212748 | + | 0.793986i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.26795 | − | 5.66025i | −0.374859 | − | 0.649276i | ||||
\(77\) | − | 3.46410i | − | 0.394771i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.26795 | 0.592691 | 0.296345 | − | 0.955081i | \(-0.404232\pi\) | ||||
0.296345 | + | 0.955081i | \(0.404232\pi\) | |||||||
\(80\) | 12.9282 | + | 7.46410i | 1.44542 | + | 0.834512i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.19615 | − | 1.66025i | 0.684251 | − | 0.183344i | ||||
\(83\) | − | 14.0000i | − | 1.53670i | −0.640030 | − | 0.768350i | \(-0.721078\pi\) | ||
0.640030 | − | 0.768350i | \(-0.278922\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 13.9282i | − | 1.51073i | ||||||
\(86\) | −3.53590 | − | 13.1962i | −0.381286 | − | 1.42298i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.46410 | + | 9.46410i | 1.00888 | + | 1.00888i | ||||
\(89\) | −11.7321 | −1.24359 | −0.621797 | − | 0.783178i | \(-0.713597\pi\) | ||||
−0.621797 | + | 0.783178i | \(0.713597\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.80385i | − | 0.189095i | ||||||
\(92\) | 15.1244 | − | 8.73205i | 1.57682 | − | 0.910379i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.73205 | − | 1.26795i | 0.488074 | − | 0.130779i | ||||
\(95\) | 12.1962 | 1.25130 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.00000 | −0.812277 | −0.406138 | − | 0.913812i | \(-0.633125\pi\) | ||||
−0.406138 | + | 0.913812i | \(0.633125\pi\) | |||||||
\(98\) | −8.83013 | + | 2.36603i | −0.891978 | + | 0.239005i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −15.4641 | + | 8.92820i | −1.54641 | + | 0.892820i | ||||
\(101\) | 8.00000i | 0.796030i | 0.917379 | + | 0.398015i | \(0.130301\pi\) | ||||
−0.917379 | + | 0.398015i | \(0.869699\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.46410 | −0.341328 | −0.170664 | − | 0.985329i | \(-0.554591\pi\) | ||||
−0.170664 | + | 0.985329i | \(0.554591\pi\) | |||||||
\(104\) | 4.92820 | + | 4.92820i | 0.483250 | + | 0.483250i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.339746 | − | 1.26795i | −0.0329990 | − | 0.123154i | ||||
\(107\) | 10.3923i | 1.00466i | 0.864675 | + | 0.502331i | \(0.167524\pi\) | ||||
−0.864675 | + | 0.502331i | \(0.832476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.8564i | − | 1.23142i | −0.787973 | − | 0.615710i | \(-0.788869\pi\) | ||
0.787973 | − | 0.615710i | \(-0.211131\pi\) | |||||||
\(110\) | −24.1244 | + | 6.46410i | −2.30017 | + | 0.616328i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.46410 | + | 2.53590i | −0.138345 | + | 0.239620i | ||||
\(113\) | −7.73205 | −0.727370 | −0.363685 | − | 0.931522i | \(-0.618482\pi\) | ||||
−0.363685 | + | 0.931522i | \(0.618482\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 32.5885i | 3.03889i | ||||||||
\(116\) | −5.19615 | − | 9.00000i | −0.482451 | − | 0.835629i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.07180 | + | 11.4641i | 0.282782 | + | 1.05536i | ||||
\(119\) | 2.73205 | 0.250447 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.3923 | −1.03566 | ||||||||
\(122\) | −3.29423 | − | 12.2942i | −0.298245 | − | 1.11307i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.46410 | − | 2.00000i | 0.311086 | − | 0.179605i | ||||
\(125\) | − | 14.6603i | − | 1.31125i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.6603 | −1.21215 | −0.606076 | − | 0.795407i | \(-0.707257\pi\) | ||||
−0.606076 | + | 0.795407i | \(0.707257\pi\) | |||||||
\(128\) | −2.92820 | − | 10.9282i | −0.258819 | − | 0.965926i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.5622 | + | 3.36603i | −1.10178 | + | 0.295220i | ||||
\(131\) | 0.196152i | 0.0171379i | 0.999963 | + | 0.00856896i | \(0.00272762\pi\) | ||||
−0.999963 | + | 0.00856896i | \(0.997272\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.39230i | 0.207439i | ||||||||
\(134\) | −1.73205 | − | 6.46410i | −0.149626 | − | 0.558413i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.46410 | + | 7.46410i | −0.640041 | + | 0.640041i | ||||
\(137\) | −17.1962 | −1.46917 | −0.734583 | − | 0.678519i | \(-0.762622\pi\) | ||||
−0.734583 | + | 0.678519i | \(0.762622\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.4641i | 1.65092i | 0.564458 | + | 0.825462i | \(0.309085\pi\) | ||||
−0.564458 | + | 0.825462i | \(0.690915\pi\) | |||||||
\(140\) | −2.73205 | − | 4.73205i | −0.230900 | − | 0.399931i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.73205 | − | 2.07180i | 0.648859 | − | 0.173861i | ||||
\(143\) | −11.6603 | −0.975079 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.3923 | 1.61044 | ||||||||
\(146\) | 12.2942 | − | 3.29423i | 1.01748 | − | 0.272632i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.00000 | + | 8.66025i | 0.410997 | + | 0.711868i | ||||
\(149\) | − | 5.19615i | − | 0.425685i | −0.977086 | − | 0.212843i | \(-0.931728\pi\) | ||
0.977086 | − | 0.212843i | \(-0.0682722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.8564 | 1.12762 | 0.563809 | − | 0.825905i | \(-0.309335\pi\) | ||||
0.563809 | + | 0.825905i | \(0.309335\pi\) | |||||||
\(152\) | −6.53590 | − | 6.53590i | −0.530131 | − | 0.530131i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.26795 | − | 4.73205i | −0.102174 | − | 0.381320i | ||||
\(155\) | 7.46410i | 0.599531i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.46410i | 0.196657i | 0.995154 | + | 0.0983284i | \(0.0313495\pi\) | ||||
−0.995154 | + | 0.0983284i | \(0.968650\pi\) | |||||||
\(158\) | 7.19615 | − | 1.92820i | 0.572495 | − | 0.153400i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 20.3923 | + | 5.46410i | 1.61215 | + | 0.431975i | ||||
\(161\) | −6.39230 | −0.503784 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 6.53590i | − | 0.511931i | −0.966686 | − | 0.255966i | \(-0.917607\pi\) | ||
0.966686 | − | 0.255966i | \(-0.0823934\pi\) | |||||||
\(164\) | 7.85641 | − | 4.53590i | 0.613482 | − | 0.354194i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.12436 | − | 19.1244i | −0.397727 | − | 1.48434i | ||||
\(167\) | −14.7321 | −1.14000 | −0.570000 | − | 0.821645i | \(-0.693057\pi\) | ||||
−0.570000 | + | 0.821645i | \(0.693057\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.92820 | 0.532939 | ||||||||
\(170\) | −5.09808 | − | 19.0263i | −0.391005 | − | 1.45925i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.66025 | − | 16.7321i | −0.736587 | − | 1.27581i | ||||
\(173\) | 1.73205i | 0.131685i | 0.997830 | + | 0.0658427i | \(0.0209736\pi\) | ||||
−0.997830 | + | 0.0658427i | \(0.979026\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.53590 | 0.494067 | ||||||||
\(176\) | 16.3923 | + | 9.46410i | 1.23562 | + | 0.713384i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −16.0263 | + | 4.29423i | −1.20122 | + | 0.321866i | ||||
\(179\) | − | 14.0000i | − | 1.04641i | −0.852207 | − | 0.523205i | \(-0.824736\pi\) | ||
0.852207 | − | 0.523205i | \(-0.175264\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.53590i | 0.485810i | 0.970050 | + | 0.242905i | \(0.0781002\pi\) | ||||
−0.970050 | + | 0.242905i | \(0.921900\pi\) | |||||||
\(182\) | −0.660254 | − | 2.46410i | −0.0489413 | − | 0.182651i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 17.4641 | − | 17.4641i | 1.28747 | − | 1.28747i | ||||
\(185\) | −18.6603 | −1.37193 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 17.6603i | − | 1.29145i | ||||||
\(188\) | 6.00000 | − | 3.46410i | 0.437595 | − | 0.252646i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.6603 | − | 4.46410i | 1.20866 | − | 0.323860i | ||||
\(191\) | 16.5885 | 1.20030 | 0.600149 | − | 0.799888i | \(-0.295108\pi\) | ||||
0.600149 | + | 0.799888i | \(0.295108\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.8564 | 0.781461 | 0.390731 | − | 0.920505i | \(-0.372222\pi\) | ||||
0.390731 | + | 0.920505i | \(0.372222\pi\) | |||||||
\(194\) | −10.9282 | + | 2.92820i | −0.784599 | + | 0.210233i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.1962 | + | 6.46410i | −0.799725 | + | 0.461722i | ||||
\(197\) | 4.12436i | 0.293848i | 0.989148 | + | 0.146924i | \(0.0469373\pi\) | ||||
−0.989148 | + | 0.146924i | \(0.953063\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.39230 | 0.169586 | 0.0847930 | − | 0.996399i | \(-0.472977\pi\) | ||||
0.0847930 | + | 0.996399i | \(0.472977\pi\) | |||||||
\(200\) | −17.8564 | + | 17.8564i | −1.26264 | + | 1.26264i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.92820 | + | 10.9282i | 0.206028 | + | 0.768906i | ||||
\(203\) | 3.80385i | 0.266978i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.9282i | 1.18232i | ||||||||
\(206\) | −4.73205 | + | 1.26795i | −0.329698 | + | 0.0883422i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 8.53590 | + | 4.92820i | 0.591858 | + | 0.341709i | ||||
\(209\) | 15.4641 | 1.06967 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 26.0526i | − | 1.79353i | −0.442505 | − | 0.896766i | \(-0.645910\pi\) | ||
0.442505 | − | 0.896766i | \(-0.354090\pi\) | |||||||
\(212\) | −0.928203 | − | 1.60770i | −0.0637493 | − | 0.110417i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.80385 | + | 14.1962i | 0.260026 | + | 0.970429i | ||||
\(215\) | 36.0526 | 2.45876 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.46410 | −0.0993897 | ||||||||
\(218\) | −4.70577 | − | 17.5622i | −0.318715 | − | 1.18946i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −30.5885 | + | 17.6603i | −2.06227 | + | 1.19065i | ||||
\(221\) | − | 9.19615i | − | 0.618600i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.1244 | 1.54852 | 0.774261 | − | 0.632867i | \(-0.218122\pi\) | ||||
0.774261 | + | 0.632867i | \(0.218122\pi\) | |||||||
\(224\) | −1.07180 | + | 4.00000i | −0.0716124 | + | 0.267261i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.5622 | + | 2.83013i | −0.702586 | + | 0.188257i | ||||
\(227\) | 6.73205i | 0.446822i | 0.974724 | + | 0.223411i | \(0.0717192\pi\) | ||||
−0.974724 | + | 0.223411i | \(0.928281\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.3923i | 0.752825i | 0.926452 | + | 0.376412i | \(0.122842\pi\) | ||||
−0.926452 | + | 0.376412i | \(0.877158\pi\) | |||||||
\(230\) | 11.9282 | + | 44.5167i | 0.786522 | + | 2.93534i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.3923 | − | 10.3923i | −0.682288 | − | 0.682288i | ||||
\(233\) | 3.73205 | 0.244495 | 0.122247 | − | 0.992500i | \(-0.460990\pi\) | ||||
0.122247 | + | 0.992500i | \(0.460990\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.9282i | 0.843343i | ||||||||
\(236\) | 8.39230 | + | 14.5359i | 0.546293 | + | 0.946206i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.73205 | − | 1.00000i | 0.241913 | − | 0.0648204i | ||||
\(239\) | 7.85641 | 0.508189 | 0.254094 | − | 0.967179i | \(-0.418223\pi\) | ||||
0.254094 | + | 0.967179i | \(0.418223\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.46410 | −0.287558 | −0.143779 | − | 0.989610i | \(-0.545925\pi\) | ||||
−0.143779 | + | 0.989610i | \(0.545925\pi\) | |||||||
\(242\) | −15.5622 | + | 4.16987i | −1.00037 | + | 0.268050i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.00000 | − | 15.5885i | −0.576166 | − | 0.997949i | ||||
\(245\) | − | 24.1244i | − | 1.54125i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.05256 | 0.512372 | ||||||||
\(248\) | 4.00000 | − | 4.00000i | 0.254000 | − | 0.254000i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.36603 | − | 20.0263i | −0.339377 | − | 1.26657i | ||||
\(251\) | 7.26795i | 0.458749i | 0.973338 | + | 0.229374i | \(0.0736680\pi\) | ||||
−0.973338 | + | 0.229374i | \(0.926332\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 41.3205i | 2.59780i | ||||||||
\(254\) | −18.6603 | + | 5.00000i | −1.17085 | + | 0.313728i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −3.33975 | −0.208328 | −0.104164 | − | 0.994560i | \(-0.533217\pi\) | ||||
−0.104164 | + | 0.994560i | \(0.533217\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.66025i | − | 0.227437i | ||||||
\(260\) | −15.9282 | + | 9.19615i | −0.987825 | + | 0.570321i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.0717968 | + | 0.267949i | 0.00443562 | + | 0.0165540i | ||||
\(263\) | −16.2487 | −1.00194 | −0.500969 | − | 0.865465i | \(-0.667023\pi\) | ||||
−0.500969 | + | 0.865465i | \(0.667023\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.46410 | 0.212798 | ||||||||
\(266\) | 0.875644 | + | 3.26795i | 0.0536892 | + | 0.200371i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.73205 | − | 8.19615i | −0.289056 | − | 0.500660i | ||||
\(269\) | 25.7321i | 1.56891i | 0.620185 | + | 0.784455i | \(0.287057\pi\) | ||||
−0.620185 | + | 0.784455i | \(0.712943\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.7321 | 0.651926 | 0.325963 | − | 0.945383i | \(-0.394312\pi\) | ||||
0.325963 | + | 0.945383i | \(0.394312\pi\) | |||||||
\(272\) | −7.46410 | + | 12.9282i | −0.452578 | + | 0.783887i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −23.4904 | + | 6.29423i | −1.41911 | + | 0.380248i | ||||
\(275\) | − | 42.2487i | − | 2.54769i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 9.85641i | − | 0.592214i | −0.955155 | − | 0.296107i | \(-0.904311\pi\) | ||
0.955155 | − | 0.296107i | \(-0.0956885\pi\) | |||||||
\(278\) | 7.12436 | + | 26.5885i | 0.427290 | + | 1.59467i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.46410 | − | 5.46410i | −0.326543 | − | 0.326543i | ||||
\(281\) | 13.7321 | 0.819185 | 0.409593 | − | 0.912268i | \(-0.365671\pi\) | ||||
0.409593 | + | 0.912268i | \(0.365671\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.39230i | 0.379983i | 0.981786 | + | 0.189992i | \(0.0608461\pi\) | ||||
−0.981786 | + | 0.189992i | \(0.939154\pi\) | |||||||
\(284\) | 9.80385 | − | 5.66025i | 0.581751 | − | 0.335874i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.9282 | + | 4.26795i | −0.941854 | + | 0.252369i | ||||
\(287\) | −3.32051 | −0.196003 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.07180 | −0.180694 | ||||||||
\(290\) | 26.4904 | − | 7.09808i | 1.55557 | − | 0.416813i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15.5885 | − | 9.00000i | 0.912245 | − | 0.526685i | ||||
\(293\) | 3.33975i | 0.195110i | 0.995230 | + | 0.0975550i | \(0.0311022\pi\) | ||||
−0.995230 | + | 0.0975550i | \(0.968898\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −31.3205 | −1.82355 | ||||||||
\(296\) | 10.0000 | + | 10.0000i | 0.581238 | + | 0.581238i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.90192 | − | 7.09808i | −0.110175 | − | 0.411181i | ||||
\(299\) | 21.5167i | 1.24434i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.07180i | 0.407612i | ||||||||
\(302\) | 18.9282 | − | 5.07180i | 1.08920 | − | 0.291849i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.3205 | − | 6.53590i | −0.649276 | − | 0.374859i | ||||
\(305\) | 33.5885 | 1.92327 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 14.7846i | − | 0.843802i | −0.906642 | − | 0.421901i | \(-0.861363\pi\) | ||
0.906642 | − | 0.421901i | \(-0.138637\pi\) | |||||||
\(308\) | −3.46410 | − | 6.00000i | −0.197386 | − | 0.341882i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.73205 | + | 10.1962i | 0.155170 | + | 0.579103i | ||||
\(311\) | −19.3205 | −1.09557 | −0.547783 | − | 0.836621i | \(-0.684528\pi\) | ||||
−0.547783 | + | 0.836621i | \(0.684528\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.46410 | 0.139279 | 0.0696396 | − | 0.997572i | \(-0.477815\pi\) | ||||
0.0696396 | + | 0.997572i | \(0.477815\pi\) | |||||||
\(314\) | 0.901924 | + | 3.36603i | 0.0508985 | + | 0.189956i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.12436 | − | 5.26795i | 0.513285 | − | 0.296345i | ||||
\(317\) | 1.19615i | 0.0671826i | 0.999436 | + | 0.0335913i | \(0.0106945\pi\) | ||||
−0.999436 | + | 0.0335913i | \(0.989306\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.5885 | 1.37669 | ||||||||
\(320\) | 29.8564 | 1.66902 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.73205 | + | 2.33975i | −0.486618 | + | 0.130389i | ||||
\(323\) | 12.1962i | 0.678612i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 22.0000i | − | 1.22034i | ||||||
\(326\) | −2.39230 | − | 8.92820i | −0.132498 | − | 0.494487i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.07180 | − | 9.07180i | 0.500906 | − | 0.500906i | ||||
\(329\) | −2.53590 | −0.139809 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 13.1244i | − | 0.721380i | −0.932686 | − | 0.360690i | \(-0.882541\pi\) | ||
0.932686 | − | 0.360690i | \(-0.117459\pi\) | |||||||
\(332\) | −14.0000 | − | 24.2487i | −0.768350 | − | 1.33082i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −20.1244 | + | 5.39230i | −1.10116 | + | 0.295054i | ||||
\(335\) | 17.6603 | 0.964883 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.00000 | 0.217894 | 0.108947 | − | 0.994048i | \(-0.465252\pi\) | ||||
0.108947 | + | 0.994048i | \(0.465252\pi\) | |||||||
\(338\) | 9.46410 | − | 2.53590i | 0.514779 | − | 0.137935i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −13.9282 | − | 24.1244i | −0.755363 | − | 1.30833i | ||||
\(341\) | 9.46410i | 0.512510i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.85641 | 0.532196 | ||||||||
\(344\) | −19.3205 | − | 19.3205i | −1.04169 | − | 1.04169i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.633975 | + | 2.36603i | 0.0340827 | + | 0.127198i | ||||
\(347\) | 6.73205i | 0.361395i | 0.983539 | + | 0.180698i | \(0.0578356\pi\) | ||||
−0.983539 | + | 0.180698i | \(0.942164\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 11.8564i | − | 0.634659i | −0.948315 | − | 0.317329i | \(-0.897214\pi\) | ||
0.948315 | − | 0.317329i | \(-0.102786\pi\) | |||||||
\(350\) | 8.92820 | − | 2.39230i | 0.477233 | − | 0.127874i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 25.8564 | + | 6.92820i | 1.37815 | + | 0.369274i | ||||
\(353\) | −6.92820 | −0.368751 | −0.184376 | − | 0.982856i | \(-0.559026\pi\) | ||||
−0.184376 | + | 0.982856i | \(0.559026\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.1244i | 1.12116i | ||||||||
\(356\) | −20.3205 | + | 11.7321i | −1.07698 | + | 0.621797i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.12436 | − | 19.1244i | −0.270831 | − | 1.01075i | ||||
\(359\) | 1.12436 | 0.0593412 | 0.0296706 | − | 0.999560i | \(-0.490554\pi\) | ||||
0.0296706 | + | 0.999560i | \(0.490554\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.32051 | 0.437921 | ||||||||
\(362\) | 2.39230 | + | 8.92820i | 0.125737 | + | 0.469256i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.80385 | − | 3.12436i | −0.0945473 | − | 0.163761i | ||||
\(365\) | 33.5885i | 1.75810i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.53590 | 0.132373 | 0.0661864 | − | 0.997807i | \(-0.478917\pi\) | ||||
0.0661864 | + | 0.997807i | \(0.478917\pi\) | |||||||
\(368\) | 17.4641 | − | 30.2487i | 0.910379 | − | 1.57682i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −25.4904 | + | 6.83013i | −1.32518 | + | 0.355081i | ||||
\(371\) | 0.679492i | 0.0352775i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.9282i | 1.18718i | 0.804769 | + | 0.593589i | \(0.202289\pi\) | ||||
−0.804769 | + | 0.593589i | \(0.797711\pi\) | |||||||
\(374\) | −6.46410 | − | 24.1244i | −0.334251 | − | 1.24744i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.92820 | − | 6.92820i | 0.357295 | − | 0.357295i | ||||
\(377\) | 12.8038 | 0.659432 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0000i | 0.513665i | 0.966456 | + | 0.256833i | \(0.0826790\pi\) | ||||
−0.966456 | + | 0.256833i | \(0.917321\pi\) | |||||||
\(380\) | 21.1244 | − | 12.1962i | 1.08366 | − | 0.625649i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 22.6603 | − | 6.07180i | 1.15940 | − | 0.310660i | ||||
\(383\) | −20.1962 | −1.03198 | −0.515988 | − | 0.856596i | \(-0.672575\pi\) | ||||
−0.515988 | + | 0.856596i | \(0.672575\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.9282 | 0.658882 | ||||||||
\(386\) | 14.8301 | − | 3.97372i | 0.754834 | − | 0.202257i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.8564 | + | 8.00000i | −0.703452 | + | 0.406138i | ||||
\(389\) | 16.9282i | 0.858294i | 0.903235 | + | 0.429147i | \(0.141186\pi\) | ||||
−0.903235 | + | 0.429147i | \(0.858814\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −32.5885 | −1.64807 | ||||||||
\(392\) | −12.9282 | + | 12.9282i | −0.652973 | + | 0.652973i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.50962 | + | 5.63397i | 0.0760535 | + | 0.283836i | ||||
\(395\) | 19.6603i | 0.989215i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 32.4641i | − | 1.62933i | −0.579934 | − | 0.814663i | \(-0.696922\pi\) | ||
0.579934 | − | 0.814663i | \(-0.303078\pi\) | |||||||
\(398\) | 3.26795 | − | 0.875644i | 0.163807 | − | 0.0438921i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −17.8564 | + | 30.9282i | −0.892820 | + | 1.54641i | ||||
\(401\) | −9.58846 | −0.478825 | −0.239412 | − | 0.970918i | \(-0.576955\pi\) | ||||
−0.239412 | + | 0.970918i | \(0.576955\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.92820i | 0.245491i | ||||||||
\(404\) | 8.00000 | + | 13.8564i | 0.398015 | + | 0.689382i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.39230 | + | 5.19615i | 0.0690989 | + | 0.257881i | ||||
\(407\) | −23.6603 | −1.17280 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.7128 | 1.41976 | 0.709879 | − | 0.704324i | \(-0.248750\pi\) | ||||
0.709879 | + | 0.704324i | \(0.248750\pi\) | |||||||
\(410\) | 6.19615 | + | 23.1244i | 0.306006 | + | 1.14203i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.00000 | + | 3.46410i | −0.295599 | + | 0.170664i | ||||
\(413\) | − | 6.14359i | − | 0.302306i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 52.2487 | 2.56479 | ||||||||
\(416\) | 13.4641 | + | 3.60770i | 0.660132 | + | 0.176882i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 21.1244 | − | 5.66025i | 1.03323 | − | 0.276852i | ||||
\(419\) | 21.4641i | 1.04859i | 0.851537 | + | 0.524295i | \(0.175671\pi\) | ||||
−0.851537 | + | 0.524295i | \(0.824329\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0000i | 0.633581i | 0.948495 | + | 0.316791i | \(0.102605\pi\) | ||||
−0.948495 | + | 0.316791i | \(0.897395\pi\) | |||||||
\(422\) | −9.53590 | − | 35.5885i | −0.464200 | − | 1.73242i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.85641 | − | 1.85641i | −0.0901551 | − | 0.0901551i | ||||
\(425\) | 33.3205 | 1.61628 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.58846i | 0.318838i | ||||||||
\(428\) | 10.3923 | + | 18.0000i | 0.502331 | + | 0.870063i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 49.2487 | − | 13.1962i | 2.37498 | − | 0.636375i | ||||
\(431\) | −21.7128 | −1.04587 | −0.522935 | − | 0.852373i | \(-0.675163\pi\) | ||||
−0.522935 | + | 0.852373i | \(0.675163\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.7846 | −1.04690 | −0.523451 | − | 0.852056i | \(-0.675356\pi\) | ||||
−0.523451 | + | 0.852056i | \(0.675356\pi\) | |||||||
\(434\) | −2.00000 | + | 0.535898i | −0.0960031 | + | 0.0257239i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.8564 | − | 22.2679i | −0.615710 | − | 1.06644i | ||||
\(437\) | − | 28.5359i | − | 1.36506i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.0000 | −1.43182 | −0.715911 | − | 0.698192i | \(-0.753988\pi\) | ||||
−0.715911 | + | 0.698192i | \(0.753988\pi\) | |||||||
\(440\) | −35.3205 | + | 35.3205i | −1.68384 | + | 1.68384i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.36603 | − | 12.5622i | −0.160106 | − | 0.597522i | ||||
\(443\) | − | 29.3205i | − | 1.39306i | −0.717528 | − | 0.696530i | \(-0.754726\pi\) | ||
0.717528 | − | 0.696530i | \(-0.245274\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 43.7846i | − | 2.07559i | ||||||
\(446\) | 31.5885 | − | 8.46410i | 1.49576 | − | 0.400787i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.85641i | 0.276689i | ||||||||
\(449\) | −24.9282 | −1.17643 | −0.588217 | − | 0.808703i | \(-0.700170\pi\) | ||||
−0.588217 | + | 0.808703i | \(0.700170\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.4641i | 1.01071i | ||||||||
\(452\) | −13.3923 | + | 7.73205i | −0.629921 | + | 0.363685i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.46410 | + | 9.19615i | 0.115646 | + | 0.431597i | ||||
\(455\) | 6.73205 | 0.315603 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.32051 | −0.295661 | −0.147830 | − | 0.989013i | \(-0.547229\pi\) | ||||
−0.147830 | + | 0.989013i | \(0.547229\pi\) | |||||||
\(458\) | 4.16987 | + | 15.5622i | 0.194845 | + | 0.727173i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 32.5885 | + | 56.4449i | 1.51944 | + | 2.63176i | ||||
\(461\) | 41.3205i | 1.92449i | 0.272188 | + | 0.962244i | \(0.412253\pi\) | ||||
−0.272188 | + | 0.962244i | \(0.587747\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.4641 | 0.625730 | 0.312865 | − | 0.949798i | \(-0.398711\pi\) | ||||
0.312865 | + | 0.949798i | \(0.398711\pi\) | |||||||
\(464\) | −18.0000 | − | 10.3923i | −0.835629 | − | 0.482451i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.09808 | − | 1.36603i | 0.236164 | − | 0.0632799i | ||||
\(467\) | − | 24.7846i | − | 1.14689i | −0.819242 | − | 0.573447i | \(-0.805606\pi\) | ||
0.819242 | − | 0.573447i | \(-0.194394\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.46410i | 0.159957i | ||||||||
\(470\) | 4.73205 | + | 17.6603i | 0.218273 | + | 0.814607i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 16.7846 | + | 16.7846i | 0.772574 | + | 0.772574i | ||||
\(473\) | 45.7128 | 2.10188 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.1769i | 1.33873i | ||||||||
\(476\) | 4.73205 | − | 2.73205i | 0.216893 | − | 0.125223i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.7321 | − | 2.87564i | 0.490873 | − | 0.131529i | ||||
\(479\) | 1.66025 | 0.0758589 | 0.0379295 | − | 0.999280i | \(-0.487924\pi\) | ||||
0.0379295 | + | 0.999280i | \(0.487924\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.3205 | −0.561767 | ||||||||
\(482\) | −6.09808 | + | 1.63397i | −0.277760 | + | 0.0744255i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −19.7321 | + | 11.3923i | −0.896911 | + | 0.517832i | ||||
\(485\) | − | 29.8564i | − | 1.35571i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.7128 | −1.16516 | −0.582579 | − | 0.812774i | \(-0.697956\pi\) | ||||
−0.582579 | + | 0.812774i | \(0.697956\pi\) | |||||||
\(488\) | −18.0000 | − | 18.0000i | −0.814822 | − | 0.814822i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.83013 | − | 32.9545i | −0.398904 | − | 1.48873i | ||||
\(491\) | 13.8038i | 0.622959i | 0.950253 | + | 0.311479i | \(0.100825\pi\) | ||||
−0.950253 | + | 0.311479i | \(0.899175\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.3923i | 0.873385i | ||||||||
\(494\) | 11.0000 | − | 2.94744i | 0.494913 | − | 0.132612i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00000 | − | 6.92820i | 0.179605 | − | 0.311086i | ||||
\(497\) | −4.14359 | −0.185866 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 8.19615i | − | 0.366910i | −0.983028 | − | 0.183455i | \(-0.941272\pi\) | ||
0.983028 | − | 0.183455i | \(-0.0587282\pi\) | |||||||
\(500\) | −14.6603 | − | 25.3923i | −0.655626 | − | 1.13558i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.66025 | + | 9.92820i | 0.118733 | + | 0.443117i | ||||
\(503\) | −0.679492 | −0.0302970 | −0.0151485 | − | 0.999885i | \(-0.504822\pi\) | ||||
−0.0151485 | + | 0.999885i | \(0.504822\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.8564 | −1.32859 | ||||||||
\(506\) | 15.1244 | + | 56.4449i | 0.672360 | + | 2.50928i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −23.6603 | + | 13.6603i | −1.04975 | + | 0.606076i | ||||
\(509\) | − | 29.3205i | − | 1.29961i | −0.760102 | − | 0.649804i | \(-0.774851\pi\) | ||
0.760102 | − | 0.649804i | \(-0.225149\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.58846 | −0.291456 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.56218 | + | 1.22243i | −0.201229 | + | 0.0539192i | ||||
\(515\) | − | 12.9282i | − | 0.569685i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.3923i | 0.720933i | ||||||||
\(518\) | −1.33975 | − | 5.00000i | −0.0588651 | − | 0.219687i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −18.3923 | + | 18.3923i | −0.806556 | + | 0.806556i | ||||
\(521\) | 26.7846 | 1.17346 | 0.586728 | − | 0.809784i | \(-0.300416\pi\) | ||||
0.586728 | + | 0.809784i | \(0.300416\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.2679i | 0.580167i | 0.957001 | + | 0.290083i | \(0.0936831\pi\) | ||||
−0.957001 | + | 0.290083i | \(0.906317\pi\) | |||||||
\(524\) | 0.196152 | + | 0.339746i | 0.00856896 | + | 0.0148419i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.1962 | + | 5.94744i | −0.967798 | + | 0.259321i | ||||
\(527\) | −7.46410 | −0.325141 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 53.2487 | 2.31516 | ||||||||
\(530\) | 4.73205 | − | 1.26795i | 0.205547 | − | 0.0550762i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.39230 | + | 4.14359i | 0.103720 | + | 0.179648i | ||||
\(533\) | 11.1769i | 0.484126i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −38.7846 | −1.67680 | ||||||||
\(536\) | −9.46410 | − | 9.46410i | −0.408787 | − | 0.408787i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.41858 | + | 35.1506i | 0.406064 | + | 1.51545i | ||||
\(539\) | − | 30.5885i | − | 1.31754i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.1769i | 1.03945i | 0.854335 | + | 0.519723i | \(0.173965\pi\) | ||||
−0.854335 | + | 0.519723i | \(0.826035\pi\) | |||||||
\(542\) | 14.6603 | − | 3.92820i | 0.629712 | − | 0.168731i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.46410 | + | 20.3923i | −0.234271 | + | 0.874313i | ||||
\(545\) | 47.9808 | 2.05527 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 26.0000i | − | 1.11168i | −0.831289 | − | 0.555840i | \(-0.812397\pi\) | ||
0.831289 | − | 0.555840i | \(-0.187603\pi\) | |||||||
\(548\) | −29.7846 | + | 17.1962i | −1.27234 | + | 0.734583i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −15.4641 | − | 57.7128i | −0.659392 | − | 2.46088i | ||||
\(551\) | −16.9808 | −0.723405 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.85641 | −0.163991 | ||||||||
\(554\) | −3.60770 | − | 13.4641i | −0.153276 | − | 0.572035i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.4641 | + | 33.7128i | 0.825462 | + | 1.42974i | ||||
\(557\) | 13.0526i | 0.553055i | 0.961006 | + | 0.276527i | \(0.0891836\pi\) | ||||
−0.961006 | + | 0.276527i | \(0.910816\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.8038 | 1.00680 | ||||||||
\(560\) | −9.46410 | − | 5.46410i | −0.399931 | − | 0.230900i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.7583 | − | 5.02628i | 0.791272 | − | 0.212021i | ||||
\(563\) | 24.2487i | 1.02196i | 0.859592 | + | 0.510981i | \(0.170718\pi\) | ||||
−0.859592 | + | 0.510981i | \(0.829282\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 28.8564i | − | 1.21400i | ||||||
\(566\) | 2.33975 | + | 8.73205i | 0.0983469 | + | 0.367035i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.3205 | − | 11.3205i | 0.474998 | − | 0.474998i | ||||
\(569\) | −33.5885 | −1.40810 | −0.704051 | − | 0.710150i | \(-0.748627\pi\) | ||||
−0.704051 | + | 0.710150i | \(0.748627\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 26.2487i | − | 1.09847i | −0.835667 | − | 0.549237i | \(-0.814918\pi\) | ||
0.835667 | − | 0.549237i | \(-0.185082\pi\) | |||||||
\(572\) | −20.1962 | + | 11.6603i | −0.844444 | + | 0.487540i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.53590 | + | 1.21539i | −0.189325 | + | 0.0507294i | ||||
\(575\) | −77.9615 | −3.25122 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.2487 | −1.88373 | −0.941864 | − | 0.335994i | \(-0.890928\pi\) | ||||
−0.941864 | + | 0.335994i | \(0.890928\pi\) | |||||||
\(578\) | −4.19615 | + | 1.12436i | −0.174537 | + | 0.0467670i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 33.5885 | − | 19.3923i | 1.39468 | − | 0.805222i | ||||
\(581\) | 10.2487i | 0.425188i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.39230 | 0.181911 | ||||||||
\(584\) | 18.0000 | − | 18.0000i | 0.744845 | − | 0.744845i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.22243 | + | 4.56218i | 0.0504982 | + | 0.188462i | ||||
\(587\) | − | 42.3013i | − | 1.74596i | −0.487756 | − | 0.872980i | \(-0.662184\pi\) | ||
0.487756 | − | 0.872980i | \(-0.337816\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 6.53590i | − | 0.269307i | ||||||
\(590\) | −42.7846 | + | 11.4641i | −1.76141 | + | 0.471970i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 17.3205 | + | 10.0000i | 0.711868 | + | 0.410997i | ||||
\(593\) | −14.4115 | −0.591811 | −0.295906 | − | 0.955217i | \(-0.595621\pi\) | ||||
−0.295906 | + | 0.955217i | \(0.595621\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.1962i | 0.418001i | ||||||||
\(596\) | −5.19615 | − | 9.00000i | −0.212843 | − | 0.368654i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.87564 | + | 29.3923i | 0.322059 | + | 1.20194i | ||||
\(599\) | −8.24871 | −0.337033 | −0.168517 | − | 0.985699i | \(-0.553898\pi\) | ||||
−0.168517 | + | 0.985699i | \(0.553898\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.2487 | 0.703590 | 0.351795 | − | 0.936077i | \(-0.385571\pi\) | ||||
0.351795 | + | 0.936077i | \(0.385571\pi\) | |||||||
\(602\) | 2.58846 | + | 9.66025i | 0.105498 | + | 0.393723i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 24.0000 | − | 13.8564i | 0.976546 | − | 0.563809i | ||||
\(605\) | − | 42.5167i | − | 1.72855i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.9090 | −1.05161 | −0.525806 | − | 0.850604i | \(-0.676236\pi\) | ||||
−0.525806 | + | 0.850604i | \(0.676236\pi\) | |||||||
\(608\) | −17.8564 | − | 4.78461i | −0.724173 | − | 0.194042i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 45.8827 | − | 12.2942i | 1.85774 | − | 0.497779i | ||||
\(611\) | 8.53590i | 0.345325i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 24.3923i | − | 0.985196i | −0.870257 | − | 0.492598i | \(-0.836047\pi\) | ||
0.870257 | − | 0.492598i | \(-0.163953\pi\) | |||||||
\(614\) | −5.41154 | − | 20.1962i | −0.218392 | − | 0.815050i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.92820 | − | 6.92820i | −0.279145 | − | 0.279145i | ||||
\(617\) | −26.1244 | −1.05173 | −0.525863 | − | 0.850569i | \(-0.676258\pi\) | ||||
−0.525863 | + | 0.850569i | \(0.676258\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.24871i | 0.251157i | 0.992084 | + | 0.125578i | \(0.0400787\pi\) | ||||
−0.992084 | + | 0.125578i | \(0.959921\pi\) | |||||||
\(620\) | 7.46410 | + | 12.9282i | 0.299766 | + | 0.519209i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −26.3923 | + | 7.07180i | −1.05824 | + | 0.283553i | ||||
\(623\) | 8.58846 | 0.344089 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.0718 | 0.402872 | ||||||||
\(626\) | 3.36603 | − | 0.901924i | 0.134533 | − | 0.0360481i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.46410 | + | 4.26795i | 0.0983284 | + | 0.170310i | ||||
\(629\) | − | 18.6603i | − | 0.744033i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.784610 | 0.0312348 | 0.0156174 | − | 0.999878i | \(-0.495029\pi\) | ||||
0.0156174 | + | 0.999878i | \(0.495029\pi\) | |||||||
\(632\) | 10.5359 | − | 10.5359i | 0.419096 | − | 0.419096i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.437822 | + | 1.63397i | 0.0173881 | + | 0.0648934i | ||||
\(635\) | − | 50.9808i | − | 2.02311i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 15.9282i | − | 0.631098i | ||||||
\(638\) | 33.5885 | − | 9.00000i | 1.32978 | − | 0.356313i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 40.7846 | − | 10.9282i | 1.61215 | − | 0.431975i | ||||
\(641\) | 23.0526 | 0.910521 | 0.455261 | − | 0.890358i | \(-0.349546\pi\) | ||||
0.455261 | + | 0.890358i | \(0.349546\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.39230i | 0.252088i | 0.992025 | + | 0.126044i | \(0.0402280\pi\) | ||||
−0.992025 | + | 0.126044i | \(0.959772\pi\) | |||||||
\(644\) | −11.0718 | + | 6.39230i | −0.436290 | + | 0.251892i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.46410 | + | 16.6603i | 0.175638 | + | 0.655489i | ||||
\(647\) | 49.7654 | 1.95648 | 0.978239 | − | 0.207480i | \(-0.0665261\pi\) | ||||
0.978239 | + | 0.207480i | \(0.0665261\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39.7128 | −1.55886 | ||||||||
\(650\) | −8.05256 | − | 30.0526i | −0.315847 | − | 1.17876i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.53590 | − | 11.3205i | −0.255966 | − | 0.443345i | ||||
\(653\) | 35.5692i | 1.39193i | 0.718075 | + | 0.695966i | \(0.245023\pi\) | ||||
−0.718075 | + | 0.695966i | \(0.754977\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.732051 | −0.0286036 | ||||||||
\(656\) | 9.07180 | − | 15.7128i | 0.354194 | − | 0.613482i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.46410 | + | 0.928203i | −0.135045 | + | 0.0361851i | ||||
\(659\) | 10.0526i | 0.391592i | 0.980645 | + | 0.195796i | \(0.0627291\pi\) | ||||
−0.980645 | + | 0.195796i | \(0.937271\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 32.1769i | − | 1.25154i | −0.780009 | − | 0.625768i | \(-0.784785\pi\) | ||
0.780009 | − | 0.625768i | \(-0.215215\pi\) | |||||||
\(662\) | −4.80385 | − | 17.9282i | −0.186707 | − | 0.696799i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −28.0000 | − | 28.0000i | −1.08661 | − | 1.08661i | ||||
\(665\) | −8.92820 | −0.346221 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 45.3731i | − | 1.75685i | ||||||
\(668\) | −25.5167 | + | 14.7321i | −0.987269 | + | 0.570000i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 24.1244 | − | 6.46410i | 0.932005 | − | 0.249730i | ||||
\(671\) | 42.5885 | 1.64411 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.2487 | −1.43583 | −0.717916 | − | 0.696130i | \(-0.754904\pi\) | ||||
−0.717916 | + | 0.696130i | \(0.754904\pi\) | |||||||
\(674\) | 5.46410 | − | 1.46410i | 0.210469 | − | 0.0563951i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.0000 | − | 6.92820i | 0.461538 | − | 0.266469i | ||||
\(677\) | − | 29.3205i | − | 1.12688i | −0.826157 | − | 0.563439i | \(-0.809478\pi\) | ||
0.826157 | − | 0.563439i | \(-0.190522\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.85641 | 0.224748 | ||||||||
\(680\) | −27.8564 | − | 27.8564i | −1.06824 | − | 1.06824i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.46410 | + | 12.9282i | 0.132647 | + | 0.495046i | ||||
\(683\) | − | 34.1051i | − | 1.30500i | −0.757790 | − | 0.652498i | \(-0.773721\pi\) | ||
0.757790 | − | 0.652498i | \(-0.226279\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 64.1769i | − | 2.45207i | ||||||
\(686\) | 13.4641 | − | 3.60770i | 0.514062 | − | 0.137742i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −33.4641 | − | 19.3205i | −1.27581 | − | 0.736587i | ||||
\(689\) | 2.28719 | 0.0871349 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 12.7321i | − | 0.484350i | −0.970233 | − | 0.242175i | \(-0.922139\pi\) | ||
0.970233 | − | 0.242175i | \(-0.0778608\pi\) | |||||||
\(692\) | 1.73205 | + | 3.00000i | 0.0658427 | + | 0.114043i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.46410 | + | 9.19615i | 0.0935360 | + | 0.349081i | ||||
\(695\) | −72.6410 | −2.75543 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.9282 | −0.641201 | ||||||||
\(698\) | −4.33975 | − | 16.1962i | −0.164262 | − | 0.613033i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 11.3205 | − | 6.53590i | 0.427875 | − | 0.247034i | ||||
\(701\) | − | 10.1244i | − | 0.382392i | −0.981552 | − | 0.191196i | \(-0.938763\pi\) | ||
0.981552 | − | 0.191196i | \(-0.0612365\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.3397 | 0.616265 | ||||||||
\(704\) | 37.8564 | 1.42677 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.46410 | + | 2.53590i | −0.356186 | + | 0.0954398i | ||||
\(707\) | − | 5.85641i | − | 0.220253i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 47.3923i | 1.77986i | 0.456102 | + | 0.889928i | \(0.349245\pi\) | ||||
−0.456102 | + | 0.889928i | \(0.650755\pi\) | |||||||
\(710\) | 7.73205 | + | 28.8564i | 0.290179 | + | 1.08296i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −23.4641 | + | 23.4641i | −0.879354 | + | 0.879354i | ||||
\(713\) | 17.4641 | 0.654036 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 43.5167i | − | 1.62743i | ||||||
\(716\) | −14.0000 | − | 24.2487i | −0.523205 | − | 0.906217i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.53590 | − | 0.411543i | 0.0573192 | − | 0.0153586i | ||||
\(719\) | −48.0526 | −1.79206 | −0.896029 | − | 0.443995i | \(-0.853561\pi\) | ||||
−0.896029 | + | 0.443995i | \(0.853561\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.53590 | 0.0944418 | ||||||||
\(722\) | 11.3660 | − | 3.04552i | 0.423000 | − | 0.113342i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.53590 | + | 11.3205i | 0.242905 | + | 0.420723i | ||||
\(725\) | 46.3923i | 1.72297i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −49.5167 | −1.83647 | −0.918236 | − | 0.396034i | \(-0.870386\pi\) | ||||
−0.918236 | + | 0.396034i | \(0.870386\pi\) | |||||||
\(728\) | −3.60770 | − | 3.60770i | −0.133710 | − | 0.133710i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.2942 | + | 45.8827i | 0.455030 | + | 1.69819i | ||||
\(731\) | 36.0526i | 1.33345i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.4641i | 1.08828i | 0.838994 | + | 0.544141i | \(0.183144\pi\) | ||||
−0.838994 | + | 0.544141i | \(0.816856\pi\) | |||||||
\(734\) | 3.46410 | − | 0.928203i | 0.127862 | − | 0.0342606i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.7846 | − | 47.7128i | 0.471247 | − | 1.75872i | ||||
\(737\) | 22.3923 | 0.824831 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.60770i | 0.353425i | 0.984263 | + | 0.176712i | \(0.0565462\pi\) | ||||
−0.984263 | + | 0.176712i | \(0.943454\pi\) | |||||||
\(740\) | −32.3205 | + | 18.6603i | −1.18813 | + | 0.685965i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.248711 | + | 0.928203i | 0.00913048 | + | 0.0340754i | ||||
\(743\) | −30.7846 | −1.12938 | −0.564689 | − | 0.825304i | \(-0.691004\pi\) | ||||
−0.564689 | + | 0.825304i | \(0.691004\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.3923 | 0.710479 | ||||||||
\(746\) | 8.39230 | + | 31.3205i | 0.307264 | + | 1.14673i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −17.6603 | − | 30.5885i | −0.645723 | − | 1.11842i | ||||
\(749\) | − | 7.60770i | − | 0.277979i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.5167 | −0.639192 | −0.319596 | − | 0.947554i | \(-0.603547\pi\) | ||||
−0.319596 | + | 0.947554i | \(0.603547\pi\) | |||||||
\(752\) | 6.92820 | − | 12.0000i | 0.252646 | − | 0.437595i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 17.4904 | − | 4.68653i | 0.636962 | − | 0.170673i | ||||
\(755\) | 51.7128i | 1.88202i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.2487i | 0.663261i | 0.943409 | + | 0.331630i | \(0.107599\pi\) | ||||
−0.943409 | + | 0.331630i | \(0.892401\pi\) | |||||||
\(758\) | 3.66025 | + | 13.6603i | 0.132946 | + | 0.496163i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 24.3923 | − | 24.3923i | 0.884802 | − | 0.884802i | ||||
\(761\) | 35.9808 | 1.30430 | 0.652151 | − | 0.758089i | \(-0.273867\pi\) | ||||
0.652151 | + | 0.758089i | \(0.273867\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.41154i | 0.340721i | ||||||||
\(764\) | 28.7321 | − | 16.5885i | 1.03949 | − | 0.600149i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.5885 | + | 7.39230i | −0.996811 | + | 0.267095i | ||||
\(767\) | −20.6795 | −0.746693 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.3923 | −1.42052 | −0.710261 | − | 0.703938i | \(-0.751423\pi\) | ||||
−0.710261 | + | 0.703938i | \(0.751423\pi\) | |||||||
\(770\) | 17.6603 | − | 4.73205i | 0.636431 | − | 0.170531i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18.8038 | − | 10.8564i | 0.676765 | − | 0.390731i | ||||
\(773\) | 40.6603i | 1.46245i | 0.682138 | + | 0.731224i | \(0.261051\pi\) | ||||
−0.682138 | + | 0.731224i | \(0.738949\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.8564 | −0.641421 | ||||||||
\(776\) | −16.0000 | + | 16.0000i | −0.574367 | + | 0.574367i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.19615 | + | 23.1244i | 0.222143 | + | 0.829048i | ||||
\(779\) | − | 14.8231i | − | 0.531092i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.7846i | 0.958429i | ||||||||
\(782\) | −44.5167 | + | 11.9282i | −1.59191 | + | 0.426552i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12.9282 | + | 22.3923i | −0.461722 | + | 0.799725i | ||||
\(785\) | −9.19615 | −0.328225 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.4449i | 0.514904i | 0.966291 | + | 0.257452i | \(0.0828829\pi\) | ||||
−0.966291 | + | 0.257452i | \(0.917117\pi\) | |||||||
\(788\) | 4.12436 | + | 7.14359i | 0.146924 | + | 0.254480i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.19615 | + | 26.8564i | 0.256028 | + | 0.955508i | ||||
\(791\) | 5.66025 | 0.201255 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.1769 | 0.787525 | ||||||||
\(794\) | −11.8827 | − | 44.3468i | −0.421701 | − | 1.57381i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.14359 | − | 2.39230i | 0.146866 | − | 0.0847930i | ||||
\(797\) | − | 12.2679i | − | 0.434553i | −0.976110 | − | 0.217277i | \(-0.930283\pi\) | ||
0.976110 | − | 0.217277i | \(-0.0697173\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.9282 | −0.457367 | ||||||||
\(800\) | −13.0718 | + | 48.7846i | −0.462158 | + | 1.72480i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −13.0981 | + | 3.50962i | −0.462509 | + | 0.123929i | ||||
\(803\) | 42.5885i | 1.50291i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 23.8564i | − | 0.840828i | ||||||
\(806\) | 1.80385 | + | 6.73205i | 0.0635378 | + | 0.237126i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.0000 | + | 16.0000i | 0.562878 | + | 0.562878i | ||||
\(809\) | −49.0526 | −1.72460 | −0.862298 | − | 0.506401i | \(-0.830976\pi\) | ||||
−0.862298 | + | 0.506401i | \(0.830976\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 48.7846i | − | 1.71306i | −0.516098 | − | 0.856530i | \(-0.672616\pi\) | ||
0.516098 | − | 0.856530i | \(-0.327384\pi\) | |||||||
\(812\) | 3.80385 | + | 6.58846i | 0.133489 | + | 0.231210i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −32.3205 | + | 8.66025i | −1.13283 | + | 0.303542i | ||||
\(815\) | 24.3923 | 0.854425 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.5692 | −1.10447 | ||||||||
\(818\) | 39.2224 | − | 10.5096i | 1.37138 | − | 0.367460i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16.9282 | + | 29.3205i | 0.591158 | + | 1.02392i | ||||
\(821\) | − | 1.58846i | − | 0.0554375i | −0.999616 | − | 0.0277188i | \(-0.991176\pi\) | ||
0.999616 | − | 0.0277188i | \(-0.00882429\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.6077 | −0.613766 | −0.306883 | − | 0.951747i | \(-0.599286\pi\) | ||||
−0.306883 | + | 0.951747i | \(0.599286\pi\) | |||||||
\(824\) | −6.92820 | + | 6.92820i | −0.241355 | + | 0.241355i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.24871 | − | 8.39230i | −0.0782427 | − | 0.292006i | ||||
\(827\) | − | 12.3397i | − | 0.429095i | −0.976714 | − | 0.214548i | \(-0.931172\pi\) | ||
0.976714 | − | 0.214548i | \(-0.0688277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 53.1769i | 1.84691i | 0.383706 | + | 0.923455i | \(0.374648\pi\) | ||||
−0.383706 | + | 0.923455i | \(0.625352\pi\) | |||||||
\(830\) | 71.3731 | − | 19.1244i | 2.47740 | − | 0.663816i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 19.7128 | 0.683419 | ||||||||
\(833\) | 24.1244 | 0.835859 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 54.9808i | − | 1.90269i | ||||||
\(836\) | 26.7846 | − | 15.4641i | 0.926365 | − | 0.534837i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.85641 | + | 29.3205i | 0.271395 | + | 1.01286i | ||||
\(839\) | 41.8038 | 1.44323 | 0.721615 | − | 0.692295i | \(-0.243400\pi\) | ||||
0.721615 | + | 0.692295i | \(0.243400\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.00000 | 0.0689655 | ||||||||
\(842\) | 4.75833 | + | 17.7583i | 0.163983 | + | 0.611992i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −26.0526 | − | 45.1244i | −0.896766 | − | 1.55324i | ||||
\(845\) | 25.8564i | 0.889487i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.33975 | 0.286557 | ||||||||
\(848\) | −3.21539 | − | 1.85641i | −0.110417 | − | 0.0637493i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 45.5167 | − | 12.1962i | 1.56121 | − | 0.418325i | ||||
\(851\) | 43.6603i | 1.49665i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 5.07180i | − | 0.173655i | −0.996223 | − | 0.0868275i | \(-0.972327\pi\) | ||
0.996223 | − | 0.0868275i | \(-0.0276729\pi\) | |||||||
\(854\) | 2.41154 | + | 9.00000i | 0.0825213 | + | 0.307974i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.7846 | + | 20.7846i | 0.710403 | + | 0.710403i | ||||
\(857\) | 0.124356 | 0.00424791 | 0.00212395 | − | 0.999998i | \(-0.499324\pi\) | ||||
0.00212395 | + | 0.999998i | \(0.499324\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.00000i | 0.0682391i | 0.999418 | + | 0.0341196i | \(0.0108627\pi\) | ||||
−0.999418 | + | 0.0341196i | \(0.989137\pi\) | |||||||
\(860\) | 62.4449 | − | 36.0526i | 2.12935 | − | 1.22938i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −29.6603 | + | 7.94744i | −1.01023 | + | 0.270691i | ||||
\(863\) | −25.5167 | −0.868597 | −0.434299 | − | 0.900769i | \(-0.643004\pi\) | ||||
−0.434299 | + | 0.900769i | \(0.643004\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.46410 | −0.219786 | ||||||||
\(866\) | −29.7583 | + | 7.97372i | −1.01123 | + | 0.270958i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.53590 | + | 1.46410i | −0.0860740 | + | 0.0496948i | ||||
\(869\) | 24.9282i | 0.845631i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.6603 | 0.395093 | ||||||||
\(872\) | −25.7128 | − | 25.7128i | −0.870746 | − | 0.870746i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.4449 | − | 38.9808i | −0.353303 | − | 1.31854i | ||||
\(875\) | 10.7321i | 0.362810i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 57.1051i | 1.92830i | 0.265353 | + | 0.964151i | \(0.414512\pi\) | ||||
−0.265353 | + | 0.964151i | \(0.585488\pi\) | |||||||
\(878\) | −40.9808 | + | 10.9808i | −1.38303 | + | 0.370583i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −35.3205 | + | 61.1769i | −1.19065 | + | 2.06227i | ||||
\(881\) | 27.8564 | 0.938506 | 0.469253 | − | 0.883064i | \(-0.344523\pi\) | ||||
0.469253 | + | 0.883064i | \(0.344523\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.32051i | 0.0444386i | 0.999753 | + | 0.0222193i | \(0.00707321\pi\) | ||||
−0.999753 | + | 0.0222193i | \(0.992927\pi\) | |||||||
\(884\) | −9.19615 | − | 15.9282i | −0.309300 | − | 0.535723i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.7321 | − | 40.0526i | −0.360550 | − | 1.34559i | ||||
\(887\) | 2.19615 | 0.0737396 | 0.0368698 | − | 0.999320i | \(-0.488261\pi\) | ||||
0.0368698 | + | 0.999320i | \(0.488261\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.0000 | 0.335389 | ||||||||
\(890\) | −16.0263 | − | 59.8109i | −0.537202 | − | 2.00487i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 40.0526 | − | 23.1244i | 1.34106 | − | 0.774261i | ||||
\(893\) | − | 11.3205i | − | 0.378826i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 52.2487 | 1.74648 | ||||||||
\(896\) | 2.14359 | + | 8.00000i | 0.0716124 | + | 0.267261i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −34.0526 | + | 9.12436i | −1.13635 | + | 0.304484i | ||||
\(899\) | − | 10.3923i | − | 0.346603i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.46410i | 0.115406i | ||||||||
\(902\) | 7.85641 | + | 29.3205i | 0.261590 | + | 0.976266i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.4641 | + | 15.4641i | −0.514328 | + | 0.514328i | ||||
\(905\) | −24.3923 | −0.810828 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.3923i | 1.07557i | 0.843082 | + | 0.537784i | \(0.180739\pi\) | ||||
−0.843082 | + | 0.537784i | \(0.819261\pi\) | |||||||
\(908\) | 6.73205 | + | 11.6603i | 0.223411 | + | 0.386959i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 9.19615 | − | 2.46410i | 0.304849 | − | 0.0816842i | ||||
\(911\) | 16.7321 | 0.554358 | 0.277179 | − | 0.960818i | \(-0.410601\pi\) | ||||
0.277179 | + | 0.960818i | \(0.410601\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 66.2487 | 2.19251 | ||||||||
\(914\) | −8.63397 | + | 2.31347i | −0.285586 | + | 0.0765227i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.3923 | + | 19.7321i | 0.376412 | + | 0.651965i | ||||
\(917\) | − | 0.143594i | − | 0.00474188i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.9808 | 0.560144 | 0.280072 | − | 0.959979i | \(-0.409642\pi\) | ||||
0.280072 | + | 0.959979i | \(0.409642\pi\) | |||||||
\(920\) | 65.1769 | + | 65.1769i | 2.14882 | + | 2.14882i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.1244 | + | 56.4449i | 0.498094 | + | 1.85891i | ||||
\(923\) | 13.9474i | 0.459086i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 44.6410i | − | 1.46779i | ||||||
\(926\) | 18.3923 | − | 4.92820i | 0.604409 | − | 0.161951i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −28.3923 | − | 7.60770i | −0.932023 | − | 0.249735i | ||||
\(929\) | −0.516660 | −0.0169511 | −0.00847554 | − | 0.999964i | \(-0.502698\pi\) | ||||
−0.00847554 | + | 0.999964i | \(0.502698\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.1244i | 0.692323i | ||||||||
\(932\) | 6.46410 | − | 3.73205i | 0.211739 | − | 0.122247i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.07180 | − | 33.8564i | −0.296838 | − | 1.10782i | ||||
\(935\) | 65.9090 | 2.15545 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.24871 | −0.236805 | −0.118403 | − | 0.992966i | \(-0.537777\pi\) | ||||
−0.118403 | + | 0.992966i | \(0.537777\pi\) | |||||||
\(938\) | 1.26795 | + | 4.73205i | 0.0414000 | + | 0.154507i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.9282 | + | 22.3923i | 0.421671 | + | 0.730356i | ||||
\(941\) | − | 18.3731i | − | 0.598945i | −0.954105 | − | 0.299472i | \(-0.903189\pi\) | ||
0.954105 | − | 0.299472i | \(-0.0968107\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.6077 | 1.28980 | ||||||||
\(944\) | 29.0718 | + | 16.7846i | 0.946206 | + | 0.546293i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 62.4449 | − | 16.7321i | 2.03026 | − | 0.544006i | ||||
\(947\) | − | 20.1962i | − | 0.656287i | −0.944628 | − | 0.328143i | \(-0.893577\pi\) | ||
0.944628 | − | 0.328143i | \(-0.106423\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.1769i | 0.719893i | ||||||||
\(950\) | 10.6795 | + | 39.8564i | 0.346488 | + | 1.29311i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.46410 | − | 5.46410i | 0.177093 | − | 0.177093i | ||||
\(953\) | 26.6603 | 0.863610 | 0.431805 | − | 0.901967i | \(-0.357877\pi\) | ||||
0.431805 | + | 0.901967i | \(0.357877\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 61.9090i | 2.00333i | ||||||||
\(956\) | 13.6077 | − | 7.85641i | 0.440104 | − | 0.254094i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.26795 | − | 0.607695i | 0.0732741 | − | 0.0196337i | ||||
\(959\) | 12.5885 | 0.406502 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −16.8301 | + | 4.50962i | −0.542625 | + | 0.145396i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.73205 | + | 4.46410i | −0.249033 | + | 0.143779i | ||||
\(965\) | 40.5167i | 1.30428i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.1962 | 0.327886 | 0.163943 | − | 0.986470i | \(-0.447579\pi\) | ||||
0.163943 | + | 0.986470i | \(0.447579\pi\) | |||||||
\(968\) | −22.7846 | + | 22.7846i | −0.732325 | + | 0.732325i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.9282 | − | 40.7846i | −0.350883 | − | 1.30951i | ||||
\(971\) | − | 51.1244i | − | 1.64066i | −0.571891 | − | 0.820329i | \(-0.693790\pi\) | ||
0.571891 | − | 0.820329i | \(-0.306210\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 14.2487i | − | 0.456793i | ||||||
\(974\) | −35.1244 | + | 9.41154i | −1.12546 | + | 0.301565i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.1769 | − | 18.0000i | −0.997949 | − | 0.576166i | ||||
\(977\) | −22.7846 | −0.728944 | −0.364472 | − | 0.931214i | \(-0.618751\pi\) | ||||
−0.364472 | + | 0.931214i | \(0.618751\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 55.5167i | − | 1.77432i | ||||||
\(980\) | −24.1244 | − | 41.7846i | −0.770624 | − | 1.33476i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.05256 | + | 18.8564i | 0.161234 | + | 0.601732i | ||||
\(983\) | −1.46410 | −0.0466976 | −0.0233488 | − | 0.999727i | \(-0.507433\pi\) | ||||
−0.0233488 | + | 0.999727i | \(0.507433\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.3923 | −0.490440 | ||||||||
\(986\) | 7.09808 | + | 26.4904i | 0.226049 | + | 0.843626i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.9474 | − | 8.05256i | 0.443727 | − | 0.256186i | ||||
\(989\) | − | 84.3538i | − | 2.68230i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.58846 | 0.0822251 | 0.0411125 | − | 0.999155i | \(-0.486910\pi\) | ||||
0.0411125 | + | 0.999155i | \(0.486910\pi\) | |||||||
\(992\) | 2.92820 | − | 10.9282i | 0.0929705 | − | 0.346971i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.66025 | + | 1.51666i | −0.179532 | + | 0.0481055i | ||||
\(995\) | 8.92820i | 0.283043i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 27.9282i | − | 0.884495i | −0.896893 | − | 0.442248i | \(-0.854181\pi\) | ||
0.896893 | − | 0.442248i | \(-0.145819\pi\) | |||||||
\(998\) | −3.00000 | − | 11.1962i | −0.0949633 | − | 0.354408i | ||||
\(999\) | 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 | 648.2.d.i.325.3 | yes | 4 | |
3.2 | odd | 2 | 648.2.d.e.325.2 | yes | 4 | ||
4.3 | odd | 2 | 2592.2.d.g.1297.4 | 4 | |||
8.3 | odd | 2 | 2592.2.d.g.1297.1 | 4 | |||
8.5 | even | 2 | inner | 648.2.d.i.325.4 | yes | 4 | |
9.2 | odd | 6 | 648.2.n.m.109.2 | 4 | |||
9.4 | even | 3 | 648.2.n.l.541.1 | 4 | |||
9.5 | odd | 6 | 648.2.n.b.541.2 | 4 | |||
9.7 | even | 3 | 648.2.n.a.109.1 | 4 | |||
12.11 | even | 2 | 2592.2.d.h.1297.1 | 4 | |||
24.5 | odd | 2 | 648.2.d.e.325.1 | ✓ | 4 | ||
24.11 | even | 2 | 2592.2.d.h.1297.4 | 4 | |||
36.7 | odd | 6 | 2592.2.r.a.433.1 | 4 | |||
36.11 | even | 6 | 2592.2.r.j.433.2 | 4 | |||
36.23 | even | 6 | 2592.2.r.b.2161.1 | 4 | |||
36.31 | odd | 6 | 2592.2.r.k.2161.2 | 4 | |||
72.5 | odd | 6 | 648.2.n.m.541.1 | 4 | |||
72.11 | even | 6 | 2592.2.r.b.433.1 | 4 | |||
72.13 | even | 6 | 648.2.n.a.541.2 | 4 | |||
72.29 | odd | 6 | 648.2.n.b.109.2 | 4 | |||
72.43 | odd | 6 | 2592.2.r.k.433.2 | 4 | |||
72.59 | even | 6 | 2592.2.r.j.2161.2 | 4 | |||
72.61 | even | 6 | 648.2.n.l.109.1 | 4 | |||
72.67 | odd | 6 | 2592.2.r.a.2161.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
648.2.d.e.325.1 | ✓ | 4 | 24.5 | odd | 2 | ||
648.2.d.e.325.2 | yes | 4 | 3.2 | odd | 2 | ||
648.2.d.i.325.3 | yes | 4 | 1.1 | even | 1 | trivial | |
648.2.d.i.325.4 | yes | 4 | 8.5 | even | 2 | inner | |
648.2.n.a.109.1 | 4 | 9.7 | even | 3 | |||
648.2.n.a.541.2 | 4 | 72.13 | even | 6 | |||
648.2.n.b.109.2 | 4 | 72.29 | odd | 6 | |||
648.2.n.b.541.2 | 4 | 9.5 | odd | 6 | |||
648.2.n.l.109.1 | 4 | 72.61 | even | 6 | |||
648.2.n.l.541.1 | 4 | 9.4 | even | 3 | |||
648.2.n.m.109.2 | 4 | 9.2 | odd | 6 | |||
648.2.n.m.541.1 | 4 | 72.5 | odd | 6 | |||
2592.2.d.g.1297.1 | 4 | 8.3 | odd | 2 | |||
2592.2.d.g.1297.4 | 4 | 4.3 | odd | 2 | |||
2592.2.d.h.1297.1 | 4 | 12.11 | even | 2 | |||
2592.2.d.h.1297.4 | 4 | 24.11 | even | 2 | |||
2592.2.r.a.433.1 | 4 | 36.7 | odd | 6 | |||
2592.2.r.a.2161.1 | 4 | 72.67 | odd | 6 | |||
2592.2.r.b.433.1 | 4 | 72.11 | even | 6 | |||
2592.2.r.b.2161.1 | 4 | 36.23 | even | 6 | |||
2592.2.r.j.433.2 | 4 | 36.11 | even | 6 | |||
2592.2.r.j.2161.2 | 4 | 72.59 | even | 6 | |||
2592.2.r.k.433.2 | 4 | 72.43 | odd | 6 | |||
2592.2.r.k.2161.2 | 4 | 36.31 | odd | 6 |