Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(80,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.80");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.p (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{48})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 215.1 | ||
Root | \(-0.608761 + 0.793353i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.215 |
Dual form | 441.2.p.c.80.1 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.09077 | − | 1.20711i | −1.47840 | − | 0.853553i | −0.478696 | − | 0.877981i | \(-0.658890\pi\) |
−0.999702 | + | 0.0244272i | \(0.992224\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.91421 | + | 3.31552i | 0.957107 | + | 1.65776i | ||||
\(5\) | −1.68925 | + | 2.92586i | −0.755454 | + | 1.30848i | 0.189694 | + | 0.981843i | \(0.439250\pi\) |
−0.945148 | + | 0.326641i | \(0.894083\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 4.41421i | − | 1.56066i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.06365 | − | 4.07820i | 2.23372 | − | 1.28964i | ||||
\(11\) | 0.717439 | − | 0.414214i | 0.216316 | − | 0.124890i | −0.387927 | − | 0.921690i | \(-0.626809\pi\) |
0.604243 | + | 0.796800i | \(0.293476\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.37849i | 0.937025i | 0.883457 | + | 0.468513i | \(0.155210\pi\) | ||||
−0.883457 | + | 0.468513i | \(0.844790\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.50000 | + | 2.59808i | −0.375000 | + | 0.649519i | ||||
\(17\) | −0.699709 | − | 1.21193i | −0.169704 | − | 0.293936i | 0.768612 | − | 0.639716i | \(-0.220948\pi\) |
−0.938316 | + | 0.345779i | \(0.887615\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.85172 | − | 3.37849i | −1.34248 | − | 0.775079i | −0.355307 | − | 0.934750i | \(-0.615624\pi\) |
−0.987170 | + | 0.159670i | \(0.948957\pi\) | |||||||
\(20\) | −12.9343 | −2.89220 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.426401 | ||||||||
\(23\) | −1.73205 | − | 1.00000i | −0.361158 | − | 0.208514i | 0.308431 | − | 0.951247i | \(-0.400196\pi\) |
−0.669588 | + | 0.742732i | \(0.733529\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.20711 | − | 5.55487i | −0.641421 | − | 1.11097i | ||||
\(26\) | 4.07820 | − | 7.06365i | 0.799801 | − | 1.38530i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.82843i | − | 0.896616i | −0.893879 | − | 0.448308i | \(-0.852027\pi\) | ||
0.893879 | − | 0.448308i | \(-0.147973\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.85172 | + | 3.37849i | −1.05100 | + | 0.606795i | −0.922929 | − | 0.384970i | \(-0.874212\pi\) |
−0.128071 | + | 0.991765i | \(0.540879\pi\) | |||||||
\(32\) | −1.37333 | + | 0.792893i | −0.242773 | + | 0.140165i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.37849i | 0.579407i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.29289 | − | 2.23936i | 0.212550 | − | 0.368148i | −0.739962 | − | 0.672649i | \(-0.765156\pi\) |
0.952512 | + | 0.304501i | \(0.0984897\pi\) | |||||||
\(38\) | 8.15640 | + | 14.1273i | 1.32314 | + | 2.29175i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 12.9154 | + | 7.45669i | 2.04210 | + | 1.17901i | ||||
\(41\) | 8.15640 | 1.27382 | 0.636908 | − | 0.770940i | \(-0.280213\pi\) | ||||
0.636908 | + | 0.770940i | \(0.280213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.4853 | −1.90399 | −0.951994 | − | 0.306117i | \(-0.900970\pi\) | ||||
−0.951994 | + | 0.306117i | \(0.900970\pi\) | |||||||
\(44\) | 2.74666 | + | 1.58579i | 0.414075 | + | 0.239066i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.41421 | + | 4.18154i | 0.355956 | + | 0.616535i | ||||
\(47\) | −3.37849 | + | 5.85172i | −0.492804 | + | 0.853561i | −0.999966 | − | 0.00828959i | \(-0.997361\pi\) |
0.507162 | + | 0.861851i | \(0.330695\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 15.4853i | 2.18995i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −11.2014 | + | 6.46716i | −1.55336 | + | 0.896833i | ||||
\(53\) | −6.12372 | + | 3.53553i | −0.841158 | + | 0.485643i | −0.857658 | − | 0.514221i | \(-0.828081\pi\) |
0.0164995 | + | 0.999864i | \(0.494748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.79884i | 0.377395i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.82843 | + | 10.0951i | −0.765310 | + | 1.32556i | ||||
\(59\) | −3.37849 | − | 5.85172i | −0.439842 | − | 0.761829i | 0.557835 | − | 0.829952i | \(-0.311632\pi\) |
−0.997677 | + | 0.0681229i | \(0.978299\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.06365 | + | 4.07820i | 0.904408 | + | 0.522160i | 0.878628 | − | 0.477507i | \(-0.158460\pi\) |
0.0257803 | + | 0.999668i | \(0.491793\pi\) | |||||||
\(62\) | 16.3128 | 2.07173 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 9.82843 | 1.22855 | ||||||||
\(65\) | −9.88500 | − | 5.70711i | −1.22608 | − | 0.707879i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.24264 | − | 7.34847i | −0.518321 | − | 0.897758i | −0.999773 | − | 0.0212861i | \(-0.993224\pi\) |
0.481452 | − | 0.876472i | \(-0.340109\pi\) | |||||||
\(68\) | 2.67878 | − | 4.63979i | 0.324850 | − | 0.562657i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.82843i | 0.573029i | 0.958076 | + | 0.286514i | \(0.0924966\pi\) | ||||
−0.958076 | + | 0.286514i | \(0.907503\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.21193 | + | 0.699709i | −0.141846 | + | 0.0818947i | −0.569243 | − | 0.822169i | \(-0.692764\pi\) |
0.427398 | + | 0.904064i | \(0.359430\pi\) | |||||||
\(74\) | −5.40629 | + | 3.12132i | −0.628468 | + | 0.362846i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 25.8686i | − | 2.96734i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.82843 | − | 8.36308i | 0.543240 | − | 0.940920i | −0.455475 | − | 0.890249i | \(-0.650531\pi\) |
0.998715 | − | 0.0506715i | \(-0.0161361\pi\) | |||||||
\(80\) | −5.06774 | − | 8.77758i | −0.566590 | − | 0.981363i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −17.0532 | − | 9.84565i | −1.88321 | − | 1.08727i | ||||
\(83\) | −13.5140 | −1.48335 | −0.741676 | − | 0.670759i | \(-0.765969\pi\) | ||||
−0.741676 | + | 0.670759i | \(0.765969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.72792 | 0.512815 | ||||||||
\(86\) | 26.1039 | + | 15.0711i | 2.81485 | + | 1.62516i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.82843 | − | 3.16693i | −0.194911 | − | 0.337596i | ||||
\(89\) | −3.08866 | + | 5.34972i | −0.327398 | + | 0.567069i | −0.981995 | − | 0.188909i | \(-0.939505\pi\) |
0.654597 | + | 0.755978i | \(0.272838\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 7.65685i | − | 0.798282i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.1273 | − | 8.15640i | 1.45712 | − | 0.841269i | ||||
\(95\) | 19.7700 | − | 11.4142i | 2.02836 | − | 1.17107i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.39942i | 0.142089i | 0.997473 | + | 0.0710447i | \(0.0226333\pi\) | ||||
−0.997473 | + | 0.0710447i | \(0.977367\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 12.2782 | − | 21.2664i | 1.22782 | − | 2.12664i | ||||
\(101\) | −6.46716 | − | 11.2014i | −0.643506 | − | 1.11459i | −0.984644 | − | 0.174572i | \(-0.944146\pi\) |
0.341138 | − | 0.940013i | \(-0.389188\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.42386 | − | 1.39942i | −0.238830 | − | 0.137889i | 0.375809 | − | 0.926697i | \(-0.377365\pi\) |
−0.614639 | + | 0.788809i | \(0.710698\pi\) | |||||||
\(104\) | 14.9134 | 1.46238 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 17.0711 | 1.65809 | ||||||||
\(107\) | 8.06591 | + | 4.65685i | 0.779761 | + | 0.450195i | 0.836345 | − | 0.548203i | \(-0.184688\pi\) |
−0.0565847 | + | 0.998398i | \(0.518021\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.29289 | + | 2.23936i | 0.123837 | + | 0.214491i | 0.921278 | − | 0.388906i | \(-0.127147\pi\) |
−0.797441 | + | 0.603397i | \(0.793813\pi\) | |||||||
\(110\) | 3.37849 | − | 5.85172i | 0.322127 | − | 0.557940i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.89949i | − | 0.554978i | −0.960729 | − | 0.277489i | \(-0.910498\pi\) | ||
0.960729 | − | 0.277489i | \(-0.0895022\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.85172 | − | 3.37849i | 0.545676 | − | 0.315046i | ||||
\(116\) | 16.0087 | − | 9.24264i | 1.48637 | − | 0.858158i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 16.3128i | 1.50172i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.15685 | + | 8.93193i | −0.468805 | + | 0.811994i | ||||
\(122\) | −9.84565 | − | 17.0532i | −0.891383 | − | 1.54392i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −22.4029 | − | 12.9343i | −2.01184 | − | 1.16154i | ||||
\(125\) | 4.77791 | 0.427349 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.485281 | −0.0430618 | −0.0215309 | − | 0.999768i | \(-0.506854\pi\) | ||||
−0.0215309 | + | 0.999768i | \(0.506854\pi\) | |||||||
\(128\) | −17.8023 | − | 10.2782i | −1.57352 | − | 0.908471i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 13.7782 | + | 23.8645i | 1.20843 | + | 2.09305i | ||||
\(131\) | 4.77791 | − | 8.27558i | 0.417448 | − | 0.723041i | −0.578234 | − | 0.815871i | \(-0.696258\pi\) |
0.995682 | + | 0.0928299i | \(0.0295913\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 20.4853i | 1.76966i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.34972 | + | 3.08866i | −0.458735 | + | 0.264851i | ||||
\(137\) | −0.717439 | + | 0.414214i | −0.0612949 | + | 0.0353887i | −0.530334 | − | 0.847789i | \(-0.677934\pi\) |
0.469039 | + | 0.883177i | \(0.344600\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.55582i | − | 0.810514i | −0.914203 | − | 0.405257i | \(-0.867182\pi\) | ||
0.914203 | − | 0.405257i | \(-0.132818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.82843 | − | 10.0951i | 0.489111 | − | 0.847165i | ||||
\(143\) | 1.39942 | + | 2.42386i | 0.117025 | + | 0.202694i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.1273 | + | 8.15640i | 1.17321 | + | 0.677352i | ||||
\(146\) | 3.37849 | 0.279606 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.89949 | 0.813733 | ||||||||
\(149\) | −3.67423 | − | 2.12132i | −0.301005 | − | 0.173785i | 0.341889 | − | 0.939740i | \(-0.388933\pi\) |
−0.642894 | + | 0.765955i | \(0.722267\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.24264 | + | 10.8126i | 0.508019 | + | 0.879915i | 0.999957 | + | 0.00928431i | \(0.00295533\pi\) |
−0.491938 | + | 0.870630i | \(0.663711\pi\) | |||||||
\(152\) | −14.9134 | + | 25.8307i | −1.20964 | + | 2.09515i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 22.8284i | − | 1.83362i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.35372 | + | 3.66832i | −0.507082 | + | 0.292764i | −0.731633 | − | 0.681698i | \(-0.761242\pi\) |
0.224551 | + | 0.974462i | \(0.427908\pi\) | |||||||
\(158\) | −20.1903 | + | 11.6569i | −1.60625 | + | 0.927370i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 5.35757i | − | 0.423553i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.41421 | + | 12.8418i | −0.580726 | + | 1.00585i | 0.414667 | + | 0.909973i | \(0.363898\pi\) |
−0.995393 | + | 0.0958740i | \(0.969435\pi\) | |||||||
\(164\) | 15.6131 | + | 27.0427i | 1.21918 | + | 2.11168i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 28.2546 | + | 16.3128i | 2.19298 | + | 1.26612i | ||||
\(167\) | 2.79884 | 0.216580 | 0.108290 | − | 0.994119i | \(-0.465462\pi\) | ||||
0.108290 | + | 0.994119i | \(0.465462\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.58579 | 0.121984 | ||||||||
\(170\) | −9.88500 | − | 5.70711i | −0.758145 | − | 0.437715i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −23.8995 | − | 41.3951i | −1.82232 | − | 3.15635i | ||||
\(173\) | −4.07820 | + | 7.06365i | −0.310060 | + | 0.537040i | −0.978375 | − | 0.206839i | \(-0.933682\pi\) |
0.668315 | + | 0.743878i | \(0.267016\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.48528i | 0.187335i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.9154 | − | 7.45669i | 0.968048 | − | 0.558903i | ||||
\(179\) | −8.23999 | + | 4.75736i | −0.615886 | + | 0.355582i | −0.775265 | − | 0.631636i | \(-0.782384\pi\) |
0.159380 | + | 0.987217i | \(0.449051\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 17.7122i | − | 1.31654i | −0.752782 | − | 0.658270i | \(-0.771289\pi\) | ||
0.752782 | − | 0.658270i | \(-0.228711\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.41421 | + | 7.64564i | −0.325420 | + | 0.563644i | ||||
\(185\) | 4.36803 | + | 7.56565i | 0.321144 | + | 0.556238i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.00400 | − | 0.579658i | −0.0734195 | − | 0.0423888i | ||||
\(188\) | −25.8686 | −1.88666 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −55.1127 | −3.99830 | ||||||||
\(191\) | 18.0379 | + | 10.4142i | 1.30518 | + | 0.753546i | 0.981288 | − | 0.192548i | \(-0.0616751\pi\) |
0.323892 | + | 0.946094i | \(0.395008\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.82843 | + | 15.2913i | 0.635484 | + | 1.10069i | 0.986412 | + | 0.164288i | \(0.0525328\pi\) |
−0.350928 | + | 0.936402i | \(0.614134\pi\) | |||||||
\(194\) | 1.68925 | − | 2.92586i | 0.121281 | − | 0.210065i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.2426i | 1.15724i | 0.815597 | + | 0.578620i | \(0.196409\pi\) | ||||
−0.815597 | + | 0.578620i | \(0.803591\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.5512 | + | 9.55582i | −1.17328 | + | 0.677394i | −0.954451 | − | 0.298369i | \(-0.903557\pi\) |
−0.218830 | + | 0.975763i | \(0.570224\pi\) | |||||||
\(200\) | −24.5204 | + | 14.1569i | −1.73385 | + | 1.00104i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 31.2262i | 2.19707i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.7782 | + | 23.8645i | −0.962309 | + | 1.66677i | ||||
\(206\) | 3.37849 | + | 5.85172i | 0.235391 | + | 0.407709i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.77758 | − | 5.06774i | −0.608616 | − | 0.351384i | ||||
\(209\) | −5.59767 | −0.387199 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.31371 | 0.503496 | 0.251748 | − | 0.967793i | \(-0.418995\pi\) | ||||
0.251748 | + | 0.967793i | \(0.418995\pi\) | |||||||
\(212\) | −23.4442 | − | 13.5355i | −1.61016 | − | 0.929624i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.2426 | − | 19.4728i | −0.768531 | − | 1.33113i | ||||
\(215\) | 21.0907 | − | 36.5302i | 1.43837 | − | 2.49134i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 6.24264i | − | 0.422805i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.27958 | + | 5.35757i | −0.625629 | + | 0.361207i | ||||
\(221\) | 4.09450 | − | 2.36396i | 0.275426 | − | 0.159017i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.0698i | 1.54487i | 0.635095 | + | 0.772434i | \(0.280961\pi\) | ||||
−0.635095 | + | 0.772434i | \(0.719039\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.12132 | + | 12.3345i | −0.473703 | + | 0.820478i | ||||
\(227\) | −1.39942 | − | 2.42386i | −0.0928826 | − | 0.160877i | 0.815840 | − | 0.578277i | \(-0.196275\pi\) |
−0.908723 | + | 0.417400i | \(0.862941\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.4915 | + | 6.05728i | 0.693299 | + | 0.400276i | 0.804847 | − | 0.593483i | \(-0.202248\pi\) |
−0.111548 | + | 0.993759i | \(0.535581\pi\) | |||||||
\(230\) | −16.3128 | −1.07563 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −21.3137 | −1.39931 | ||||||||
\(233\) | 9.37769 | + | 5.41421i | 0.614353 | + | 0.354697i | 0.774667 | − | 0.632369i | \(-0.217917\pi\) |
−0.160314 | + | 0.987066i | \(0.551251\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.4142 | − | 19.7700i | −0.744581 | − | 1.28965i | ||||
\(236\) | 12.9343 | − | 22.4029i | 0.841952 | − | 1.45830i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 0.343146i | − | 0.0221963i | −0.999938 | − | 0.0110981i | \(-0.996467\pi\) | ||
0.999938 | − | 0.0110981i | \(-0.00353272\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.77359 | − | 4.48808i | 0.500741 | − | 0.289103i | −0.228279 | − | 0.973596i | \(-0.573310\pi\) |
0.729019 | + | 0.684493i | \(0.239976\pi\) | |||||||
\(242\) | 21.5636 | − | 12.4497i | 1.38616 | − | 0.800300i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 31.2262i | 1.99905i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.4142 | − | 19.7700i | 0.726269 | − | 1.25793i | ||||
\(248\) | 14.9134 | + | 25.8307i | 0.947001 | + | 1.64025i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.98951 | − | 5.76745i | −0.631792 | − | 0.364765i | ||||
\(251\) | −25.8686 | −1.63281 | −0.816407 | − | 0.577477i | \(-0.804037\pi\) | ||||
−0.816407 | + | 0.577477i | \(0.804037\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.65685 | −0.104166 | ||||||||
\(254\) | 1.01461 | + | 0.585786i | 0.0636624 | + | 0.0367555i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.9853 | + | 25.9553i | 0.936580 | + | 1.62220i | ||||
\(257\) | −10.8352 | + | 18.7671i | −0.675880 | + | 1.17066i | 0.300330 | + | 0.953835i | \(0.402903\pi\) |
−0.976211 | + | 0.216824i | \(0.930430\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 43.6985i | − | 2.71006i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −19.9790 | + | 11.5349i | −1.23431 | + | 0.712628i | ||||
\(263\) | 20.9077 | − | 12.0711i | 1.28922 | − | 0.744334i | 0.310708 | − | 0.950505i | \(-0.399434\pi\) |
0.978516 | + | 0.206171i | \(0.0661004\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 23.8896i | − | 1.46752i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 16.2426 | − | 28.1331i | 0.992177 | − | 1.71850i | ||||
\(269\) | 15.6131 | + | 27.0427i | 0.951947 | + | 1.64882i | 0.741204 | + | 0.671280i | \(0.234255\pi\) |
0.210743 | + | 0.977541i | \(0.432412\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.85172 | + | 3.37849i | 0.355467 | + | 0.205229i | 0.667090 | − | 0.744977i | \(-0.267539\pi\) |
−0.311624 | + | 0.950206i | \(0.600873\pi\) | |||||||
\(272\) | 4.19825 | 0.254556 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.00000 | 0.120824 | ||||||||
\(275\) | −4.60181 | − | 2.65685i | −0.277499 | − | 0.160214i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.4853 | + | 18.1610i | 0.630000 | + | 1.09119i | 0.987551 | + | 0.157298i | \(0.0502783\pi\) |
−0.357552 | + | 0.933893i | \(0.616388\pi\) | |||||||
\(278\) | −11.5349 | + | 19.9790i | −0.691817 | + | 1.19826i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.8284i | 1.12321i | 0.827406 | + | 0.561605i | \(0.189816\pi\) | ||||
−0.827406 | + | 0.561605i | \(0.810184\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.8307 | − | 14.9134i | 1.53548 | − | 0.886509i | 0.536384 | − | 0.843974i | \(-0.319790\pi\) |
0.999095 | − | 0.0425346i | \(-0.0135433\pi\) | |||||||
\(284\) | −16.0087 | + | 9.24264i | −0.949943 | + | 0.548450i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 6.75699i | − | 0.399549i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.52082 | − | 13.0264i | 0.442401 | − | 0.766261i | ||||
\(290\) | −19.6913 | − | 34.1063i | −1.15631 | − | 2.00279i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.63979 | − | 2.67878i | −0.271523 | − | 0.156764i | ||||
\(293\) | 7.33664 | 0.428611 | 0.214306 | − | 0.976767i | \(-0.431251\pi\) | ||||
0.214306 | + | 0.976767i | \(0.431251\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22.8284 | 1.32912 | ||||||||
\(296\) | −9.88500 | − | 5.70711i | −0.574554 | − | 0.331719i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.12132 | + | 8.87039i | 0.296670 | + | 0.513848i | ||||
\(299\) | 3.37849 | − | 5.85172i | 0.195383 | − | 0.338414i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 30.1421i | − | 1.73448i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 17.5552 | − | 10.1355i | 1.00686 | − | 0.581310i | ||||
\(305\) | −23.8645 | + | 13.7782i | −1.36648 | + | 0.788936i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.3547i | 0.705117i | 0.935790 | + | 0.352559i | \(0.114688\pi\) | ||||
−0.935790 | + | 0.352559i | \(0.885312\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −27.5563 | + | 47.7290i | −1.56510 | + | 2.71082i | ||||
\(311\) | −5.35757 | − | 9.27958i | −0.303800 | − | 0.526197i | 0.673194 | − | 0.739466i | \(-0.264922\pi\) |
−0.976993 | + | 0.213270i | \(0.931589\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.2014 | − | 6.46716i | −0.633143 | − | 0.365545i | 0.148825 | − | 0.988864i | \(-0.452451\pi\) |
−0.781968 | + | 0.623318i | \(0.785784\pi\) | |||||||
\(314\) | 17.7122 | 0.999559 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 36.9706 | 2.07976 | ||||||||
\(317\) | −20.5745 | − | 11.8787i | −1.15558 | − | 0.667173i | −0.205338 | − | 0.978691i | \(-0.565829\pi\) |
−0.950240 | + | 0.311518i | \(0.899163\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.00000 | − | 3.46410i | −0.111979 | − | 0.193952i | ||||
\(320\) | −16.6026 | + | 28.7566i | −0.928116 | + | 1.60754i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.45584i | 0.526137i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.7671 | − | 10.8352i | 1.04101 | − | 0.601028i | ||||
\(326\) | 31.0028 | − | 17.8995i | 1.71709 | − | 0.991361i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 36.0041i | − | 1.98799i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.17157 | + | 8.95743i | −0.284255 | + | 0.492345i | −0.972428 | − | 0.233202i | \(-0.925080\pi\) |
0.688173 | + | 0.725547i | \(0.258413\pi\) | |||||||
\(332\) | −25.8686 | − | 44.8058i | −1.41973 | − | 2.45904i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.85172 | − | 3.37849i | −0.320192 | − | 0.184863i | ||||
\(335\) | 28.6675 | 1.56627 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.9289 | −0.704284 | −0.352142 | − | 0.935947i | \(-0.614547\pi\) | ||||
−0.352142 | + | 0.935947i | \(0.614547\pi\) | |||||||
\(338\) | −3.31552 | − | 1.91421i | −0.180340 | − | 0.104119i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.05025 | + | 15.6755i | 0.490819 | + | 0.850123i | ||||
\(341\) | −2.79884 | + | 4.84772i | −0.151565 | + | 0.262519i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 55.1127i | 2.97148i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.0532 | − | 9.84565i | 0.916784 | − | 0.529305i | ||||
\(347\) | −16.4290 | + | 9.48528i | −0.881954 | + | 0.509197i | −0.871302 | − | 0.490747i | \(-0.836724\pi\) |
−0.0106521 | + | 0.999943i | \(0.503391\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6.17733i | − | 0.330665i | −0.986238 | − | 0.165332i | \(-0.947130\pi\) | ||
0.986238 | − | 0.165332i | \(-0.0528697\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.656854 | + | 1.13770i | −0.0350104 | + | 0.0606399i | ||||
\(353\) | −11.8247 | − | 20.4810i | −0.629367 | − | 1.09009i | −0.987679 | − | 0.156493i | \(-0.949981\pi\) |
0.358312 | − | 0.933602i | \(-0.383352\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.1273 | − | 8.15640i | −0.749799 | − | 0.432897i | ||||
\(356\) | −23.6494 | −1.25342 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.9706 | 1.21403 | ||||||||
\(359\) | 0.891519 | + | 0.514719i | 0.0470526 | + | 0.0271658i | 0.523342 | − | 0.852123i | \(-0.324685\pi\) |
−0.476289 | + | 0.879289i | \(0.658018\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.3284 | + | 23.0855i | 0.701496 | + | 1.21503i | ||||
\(362\) | −21.3805 | + | 37.0322i | −1.12374 | + | 1.94637i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 4.72792i | − | 0.247471i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.42786 | − | 1.97908i | 0.178933 | − | 0.103307i | −0.407858 | − | 0.913045i | \(-0.633724\pi\) |
0.586791 | + | 0.809738i | \(0.300391\pi\) | |||||||
\(368\) | 5.19615 | − | 3.00000i | 0.270868 | − | 0.156386i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 21.0907i | − | 1.09645i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.3137 | − | 19.5959i | 0.585802 | − | 1.01464i | −0.408973 | − | 0.912546i | \(-0.634113\pi\) |
0.994775 | − | 0.102092i | \(-0.0325536\pi\) | |||||||
\(374\) | 1.39942 | + | 2.42386i | 0.0723622 | + | 0.125335i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 25.8307 | + | 14.9134i | 1.33212 | + | 0.769099i | ||||
\(377\) | 16.3128 | 0.840152 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 75.6880 | + | 43.6985i | 3.88271 | + | 2.24168i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −25.1421 | − | 43.5475i | −1.28638 | − | 2.22808i | ||||
\(383\) | 13.5140 | − | 23.4069i | 0.690532 | − | 1.19604i | −0.281132 | − | 0.959669i | \(-0.590710\pi\) |
0.971664 | − | 0.236367i | \(-0.0759567\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 42.6274i | − | 2.16968i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.63979 | + | 2.67878i | −0.235550 | + | 0.135995i | ||||
\(389\) | −11.9503 | + | 6.89949i | −0.605903 | + | 0.349818i | −0.771360 | − | 0.636399i | \(-0.780423\pi\) |
0.165457 | + | 0.986217i | \(0.447090\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.79884i | 0.141543i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 19.6066 | − | 33.9596i | 0.987766 | − | 1.71086i | ||||
\(395\) | 16.3128 | + | 28.2546i | 0.820786 | + | 1.42164i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.6148 | − | 13.6340i | −1.18519 | − | 0.684272i | −0.227983 | − | 0.973665i | \(-0.573213\pi\) |
−0.957210 | + | 0.289393i | \(0.906547\pi\) | |||||||
\(398\) | 46.1396 | 2.31277 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.2426 | 0.962132 | ||||||||
\(401\) | −9.37769 | − | 5.41421i | −0.468300 | − | 0.270373i | 0.247228 | − | 0.968957i | \(-0.420480\pi\) |
−0.715528 | + | 0.698584i | \(0.753814\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.4142 | − | 19.7700i | −0.568582 | − | 0.984814i | ||||
\(404\) | 24.7590 | − | 42.8839i | 1.23181 | − | 2.13355i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.14214i | − | 0.106182i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.3392 | + | 8.85611i | −0.758476 | + | 0.437907i | −0.828748 | − | 0.559621i | \(-0.810947\pi\) |
0.0702721 | + | 0.997528i | \(0.477613\pi\) | |||||||
\(410\) | 57.6140 | − | 33.2635i | 2.84535 | − | 1.64276i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 10.7151i | − | 0.527897i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.8284 | − | 39.5400i | 1.12060 | − | 1.94094i | ||||
\(416\) | −2.67878 | − | 4.63979i | −0.131338 | − | 0.227484i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 11.7034 | + | 6.75699i | 0.572434 | + | 0.330495i | ||||
\(419\) | −35.4244 | −1.73060 | −0.865299 | − | 0.501256i | \(-0.832871\pi\) | ||||
−0.865299 | + | 0.501256i | \(0.832871\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.3137 | −1.13624 | −0.568120 | − | 0.822946i | \(-0.692329\pi\) | ||||
−0.568120 | + | 0.822946i | \(0.692329\pi\) | |||||||
\(422\) | −15.2913 | − | 8.82843i | −0.744368 | − | 0.429761i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 15.6066 | + | 27.0314i | 0.757924 | + | 1.31276i | ||||
\(425\) | −4.48808 | + | 7.77359i | −0.217704 | + | 0.377074i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 35.6569i | 1.72354i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −88.1917 | + | 50.9175i | −4.25298 | + | 2.45546i | ||||
\(431\) | −13.3852 | + | 7.72792i | −0.644740 | + | 0.372241i | −0.786438 | − | 0.617669i | \(-0.788077\pi\) |
0.141698 | + | 0.989910i | \(0.454744\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.15640i | 0.391972i | 0.980607 | + | 0.195986i | \(0.0627907\pi\) | ||||
−0.980607 | + | 0.195986i | \(0.937209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.94975 | + | 8.57321i | −0.237050 | + | 0.410582i | ||||
\(437\) | 6.75699 | + | 11.7034i | 0.323230 | + | 0.559852i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.8268 | − | 14.3337i | −1.18492 | − | 0.684112i | −0.227769 | − | 0.973715i | \(-0.573143\pi\) |
−0.957147 | + | 0.289603i | \(0.906477\pi\) | |||||||
\(440\) | 12.3547 | 0.588985 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.4142 | −0.542919 | ||||||||
\(443\) | 21.5020 | + | 12.4142i | 1.02159 | + | 0.589817i | 0.914565 | − | 0.404439i | \(-0.132533\pi\) |
0.107028 | + | 0.994256i | \(0.465867\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.4350 | − | 18.0740i | −0.494668 | − | 0.856790i | ||||
\(446\) | 27.8477 | − | 48.2336i | 1.31863 | − | 2.28393i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.2426i | 1.14408i | 0.820225 | + | 0.572040i | \(0.193848\pi\) | ||||
−0.820225 | + | 0.572040i | \(0.806152\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.85172 | − | 3.37849i | 0.275547 | − | 0.159087i | ||||
\(452\) | 19.5599 | − | 11.2929i | 0.920019 | − | 0.531173i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.75699i | 0.317121i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.3137 | + | 24.7921i | −0.669567 | + | 1.15972i | 0.308458 | + | 0.951238i | \(0.400187\pi\) |
−0.978025 | + | 0.208486i | \(0.933146\pi\) | |||||||
\(458\) | −14.6236 | − | 25.3287i | −0.683314 | − | 1.18353i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 22.4029 | + | 12.9343i | 1.04454 | + | 0.603065i | ||||
\(461\) | 21.6704 | 1.00929 | 0.504645 | − | 0.863327i | \(-0.331623\pi\) | ||||
0.504645 | + | 0.863327i | \(0.331623\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.51472 | 0.163343 | 0.0816714 | − | 0.996659i | \(-0.473974\pi\) | ||||
0.0816714 | + | 0.996659i | \(0.473974\pi\) | |||||||
\(464\) | 12.5446 | + | 7.24264i | 0.582369 | + | 0.336231i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.0711 | − | 22.6398i | −0.605506 | − | 1.04877i | ||||
\(467\) | 1.39942 | − | 2.42386i | 0.0647573 | − | 0.112163i | −0.831829 | − | 0.555032i | \(-0.812706\pi\) |
0.896586 | + | 0.442869i | \(0.146039\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 55.1127i | 2.54216i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −25.8307 | + | 14.9134i | −1.18896 | + | 0.686444i | ||||
\(473\) | −8.95743 | + | 5.17157i | −0.411863 | + | 0.237789i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 43.3407i | 1.98861i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.414214 | + | 0.717439i | −0.0189457 | + | 0.0328149i | ||||
\(479\) | 4.19825 | + | 7.27159i | 0.191823 | + | 0.332247i | 0.945854 | − | 0.324591i | \(-0.105227\pi\) |
−0.754031 | + | 0.656838i | \(0.771893\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.56565 | + | 4.36803i | 0.344964 | + | 0.199165i | ||||
\(482\) | −21.6704 | −0.987059 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −39.4853 | −1.79479 | ||||||||
\(485\) | −4.09450 | − | 2.36396i | −0.185922 | − | 0.107342i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.72792 | − | 8.18900i | −0.214243 | − | 0.371079i | 0.738795 | − | 0.673930i | \(-0.235395\pi\) |
−0.953038 | + | 0.302851i | \(0.902062\pi\) | |||||||
\(488\) | 18.0021 | − | 31.1805i | 0.814915 | − | 1.41147i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.68629i | − | 0.121231i | −0.998161 | − | 0.0606153i | \(-0.980694\pi\) | ||
0.998161 | − | 0.0606153i | \(-0.0193063\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.85172 | + | 3.37849i | −0.263548 | + | 0.152160i | ||||
\(494\) | −47.7290 | + | 27.5563i | −2.14743 | + | 1.23982i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 20.2710i | − | 0.910193i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.07107 | − | 1.85514i | 0.0479476 | − | 0.0830476i | −0.841056 | − | 0.540949i | \(-0.818065\pi\) |
0.889003 | + | 0.457901i | \(0.151399\pi\) | |||||||
\(500\) | 9.14594 | + | 15.8412i | 0.409019 | + | 0.708442i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 54.0854 | + | 31.2262i | 2.41395 | + | 1.39369i | ||||
\(503\) | 32.6256 | 1.45470 | 0.727352 | − | 0.686264i | \(-0.240751\pi\) | ||||
0.727352 | + | 0.686264i | \(0.240751\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 43.6985 | 1.94456 | ||||||||
\(506\) | 3.46410 | + | 2.00000i | 0.153998 | + | 0.0889108i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.928932 | − | 1.60896i | −0.0412147 | − | 0.0713860i | ||||
\(509\) | −18.4119 | + | 31.8904i | −0.816095 | + | 1.41352i | 0.0924447 | + | 0.995718i | \(0.470532\pi\) |
−0.908539 | + | 0.417799i | \(0.862801\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 31.2426i | − | 1.38074i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 45.3078 | − | 26.1585i | 1.99844 | − | 1.15380i | ||||
\(515\) | 8.18900 | − | 4.72792i | 0.360851 | − | 0.208337i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.59767i | 0.246185i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −25.1924 | + | 43.6345i | −1.10476 | + | 1.91350i | ||||
\(521\) | 21.3805 | + | 37.0322i | 0.936699 | + | 1.62241i | 0.771576 | + | 0.636137i | \(0.219469\pi\) |
0.165122 | + | 0.986273i | \(0.447198\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.1313 | − | 8.73606i | −0.661646 | − | 0.382001i | 0.131258 | − | 0.991348i | \(-0.458098\pi\) |
−0.792904 | + | 0.609347i | \(0.791432\pi\) | |||||||
\(524\) | 36.5838 | 1.59817 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −58.2843 | −2.54131 | ||||||||
\(527\) | 8.18900 | + | 4.72792i | 0.356718 | + | 0.205952i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.50000 | − | 16.4545i | −0.413043 | − | 0.715412i | ||||
\(530\) | −28.8372 | + | 49.9476i | −1.25261 | + | 2.16958i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.5563i | 1.19360i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27.2506 | + | 15.7331i | −1.17815 | + | 0.680203i | ||||
\(536\) | −32.4377 | + | 18.7279i | −1.40110 | + | 0.808923i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 75.3867i | − | 3.25015i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.48528 | + | 16.4290i | −0.407804 | + | 0.706337i | −0.994643 | − | 0.103366i | \(-0.967039\pi\) |
0.586839 | + | 0.809703i | \(0.300372\pi\) | |||||||
\(542\) | −8.15640 | − | 14.1273i | −0.350348 | − | 0.606820i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.92186 | + | 1.10959i | 0.0823992 | + | 0.0475732i | ||||
\(545\) | −8.73606 | −0.374212 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.6274 | −1.13851 | −0.569253 | − | 0.822162i | \(-0.692768\pi\) | ||||
−0.569253 | + | 0.822162i | \(0.692768\pi\) | |||||||
\(548\) | −2.74666 | − | 1.58579i | −0.117332 | − | 0.0677414i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.41421 | + | 11.1097i | 0.273503 | + | 0.473721i | ||||
\(551\) | −16.3128 | + | 28.2546i | −0.694949 | + | 1.20369i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 50.6274i | − | 2.15095i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 31.6825 | − | 18.2919i | 1.34364 | − | 0.775749i | ||||
\(557\) | −9.16756 | + | 5.29289i | −0.388442 | + | 0.224267i | −0.681485 | − | 0.731832i | \(-0.738665\pi\) |
0.293043 | + | 0.956099i | \(0.405332\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 42.1814i | − | 1.78408i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22.7279 | − | 39.3659i | 0.958720 | − | 1.66055i | ||||
\(563\) | −1.39942 | − | 2.42386i | −0.0589784 | − | 0.102154i | 0.835029 | − | 0.550206i | \(-0.185451\pi\) |
−0.894007 | + | 0.448053i | \(0.852118\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.2611 | + | 9.96570i | 0.726180 | + | 0.419260i | ||||
\(566\) | −72.0082 | −3.02673 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 21.3137 | 0.894303 | ||||||||
\(569\) | −21.7482 | − | 12.5563i | −0.911733 | − | 0.526390i | −0.0307450 | − | 0.999527i | \(-0.509788\pi\) |
−0.880988 | + | 0.473138i | \(0.843121\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.65685 | + | 9.79796i | 0.236732 | + | 0.410032i | 0.959775 | − | 0.280772i | \(-0.0905903\pi\) |
−0.723043 | + | 0.690803i | \(0.757257\pi\) | |||||||
\(572\) | −5.35757 | + | 9.27958i | −0.224011 | + | 0.387999i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.8284i | 0.534982i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.9114 | − | 6.87704i | 0.495877 | − | 0.286295i | −0.231132 | − | 0.972922i | \(-0.574243\pi\) |
0.727009 | + | 0.686628i | \(0.240910\pi\) | |||||||
\(578\) | −31.4486 | + | 18.1569i | −1.30809 | + | 0.755226i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 62.4524i | 2.59319i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.92893 | + | 5.07306i | −0.121304 | + | 0.210105i | ||||
\(584\) | 3.08866 | + | 5.34972i | 0.127810 | + | 0.221373i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.3392 | − | 8.85611i | −0.633658 | − | 0.365843i | ||||
\(587\) | −20.2710 | −0.836672 | −0.418336 | − | 0.908292i | \(-0.637387\pi\) | ||||
−0.418336 | + | 0.908292i | \(0.637387\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 45.6569 | 1.88126 | ||||||||
\(590\) | −47.7290 | − | 27.5563i | −1.96497 | − | 1.13448i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.87868 | + | 6.71807i | 0.159413 | + | 0.276111i | ||||
\(593\) | 10.2555 | − | 17.7631i | 0.421144 | − | 0.729443i | −0.574908 | − | 0.818218i | \(-0.694962\pi\) |
0.996052 | + | 0.0887754i | \(0.0282953\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 16.2426i | − | 0.665324i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −14.1273 | + | 8.15640i | −0.577708 | + | 0.333540i | ||||
\(599\) | 5.61642 | − | 3.24264i | 0.229481 | − | 0.132491i | −0.380852 | − | 0.924636i | \(-0.624369\pi\) |
0.610332 | + | 0.792145i | \(0.291036\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.6076i | 1.12614i | 0.826410 | + | 0.563069i | \(0.190379\pi\) | ||||
−0.826410 | + | 0.563069i | \(0.809621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −23.8995 | + | 41.3951i | −0.972457 | + | 1.68434i | ||||
\(605\) | −17.4224 | − | 30.1765i | −0.708321 | − | 1.22685i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.9790 | − | 11.5349i | −0.810924 | − | 0.468187i | 0.0363529 | − | 0.999339i | \(-0.488426\pi\) |
−0.847277 | + | 0.531152i | \(0.821759\pi\) | |||||||
\(608\) | 10.7151 | 0.434556 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 66.5269 | 2.69360 | ||||||||
\(611\) | −19.7700 | − | 11.4142i | −0.799809 | − | 0.461770i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.43503 | + | 9.41375i | 0.219519 | + | 0.380218i | 0.954661 | − | 0.297695i | \(-0.0962180\pi\) |
−0.735142 | + | 0.677913i | \(0.762885\pi\) | |||||||
\(614\) | 14.9134 | − | 25.8307i | 0.601855 | − | 1.04244i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 30.4853i | − | 1.22729i | −0.789582 | − | 0.613646i | \(-0.789702\pi\) | ||
0.789582 | − | 0.613646i | \(-0.210298\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.3989 | − | 12.3547i | 0.860094 | − | 0.496576i | −0.00394972 | − | 0.999992i | \(-0.501257\pi\) |
0.864044 | + | 0.503417i | \(0.167924\pi\) | |||||||
\(620\) | 75.6880 | − | 43.6985i | 3.03970 | − | 1.75497i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 25.8686i | 1.03724i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.96447 | − | 13.7949i | 0.318579 | − | 0.551794i | ||||
\(626\) | 15.6131 | + | 27.0427i | 0.624025 | + | 1.08084i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −24.3248 | − | 14.0439i | −0.970663 | − | 0.560413i | ||||
\(629\) | −3.61859 | −0.144283 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.1716 | −0.842827 | −0.421414 | − | 0.906869i | \(-0.638466\pi\) | ||||
−0.421414 | + | 0.906869i | \(0.638466\pi\) | |||||||
\(632\) | −36.9164 | − | 21.3137i | −1.46846 | − | 0.847814i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 28.6777 | + | 49.6712i | 1.13894 | + | 1.97269i | ||||
\(635\) | 0.819760 | − | 1.41987i | 0.0325312 | − | 0.0563456i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.65685i | 0.382319i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 60.1450 | − | 34.7247i | 2.37744 | − | 1.37262i | ||||
\(641\) | 6.50794 | − | 3.75736i | 0.257048 | − | 0.148407i | −0.365939 | − | 0.930639i | \(-0.619252\pi\) |
0.622987 | + | 0.782232i | \(0.285919\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.75699i | 0.266469i | 0.991085 | + | 0.133235i | \(0.0425364\pi\) | ||||
−0.991085 | + | 0.133235i | \(0.957464\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.4142 | − | 19.7700i | 0.449086 | − | 0.777840i | ||||
\(647\) | −12.9343 | − | 22.4029i | −0.508500 | − | 0.880748i | −0.999952 | − | 0.00984331i | \(-0.996867\pi\) |
0.491451 | − | 0.870905i | \(-0.336467\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.84772 | − | 2.79884i | −0.190290 | − | 0.109864i | ||||
\(650\) | −52.3169 | −2.05204 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −56.7696 | −2.22327 | ||||||||
\(653\) | 33.3292 | + | 19.2426i | 1.30427 | + | 0.753023i | 0.981134 | − | 0.193329i | \(-0.0619283\pi\) |
0.323140 | + | 0.946351i | \(0.395262\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.1421 | + | 27.9590i | 0.630725 | + | 1.09245i | ||||
\(656\) | −12.2346 | + | 21.1910i | −0.477681 | + | 0.827368i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 47.4558i | − | 1.84862i | −0.381646 | − | 0.924309i | \(-0.624643\pi\) | ||
0.381646 | − | 0.924309i | \(-0.375357\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.35372 | − | 3.66832i | 0.247131 | − | 0.142681i | −0.371319 | − | 0.928505i | \(-0.621094\pi\) |
0.618450 | + | 0.785824i | \(0.287761\pi\) | |||||||
\(662\) | 21.6251 | − | 12.4853i | 0.840485 | − | 0.485254i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 59.6536i | 2.31501i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.82843 | + | 8.36308i | −0.186957 | + | 0.323820i | ||||
\(668\) | 5.35757 | + | 9.27958i | 0.207291 | + | 0.359038i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −59.9371 | − | 34.6047i | −2.31557 | − | 1.33690i | ||||
\(671\) | 6.75699 | 0.260851 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.8995 | −1.46092 | −0.730459 | − | 0.682956i | \(-0.760694\pi\) | ||||
−0.730459 | + | 0.682956i | \(0.760694\pi\) | |||||||
\(674\) | 27.0314 | + | 15.6066i | 1.04121 | + | 0.601144i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.03553 | + | 5.25770i | 0.116751 | + | 0.202219i | ||||
\(677\) | 16.4329 | − | 28.4625i | 0.631566 | − | 1.09390i | −0.355666 | − | 0.934613i | \(-0.615746\pi\) |
0.987232 | − | 0.159291i | \(-0.0509209\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 20.8701i | − | 0.800330i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11.7034 | − | 6.75699i | 0.448148 | − | 0.258738i | ||||
\(683\) | 33.5754 | − | 19.3848i | 1.28473 | − | 0.741738i | 0.307019 | − | 0.951703i | \(-0.400669\pi\) |
0.977709 | + | 0.209966i | \(0.0673352\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 2.79884i | − | 0.106938i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 18.7279 | − | 32.4377i | 0.713995 | − | 1.23668i | ||||
\(689\) | −11.9448 | − | 20.6890i | −0.455060 | − | 0.788187i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.27558 | + | 4.77791i | 0.314818 | + | 0.181760i | 0.649080 | − | 0.760720i | \(-0.275154\pi\) |
−0.334262 | + | 0.942480i | \(0.608487\pi\) | |||||||
\(692\) | −31.2262 | −1.18704 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 45.7990 | 1.73851 | ||||||||
\(695\) | 27.9590 | + | 16.1421i | 1.06055 | + | 0.612306i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.70711 | − | 9.88500i | −0.216172 | − | 0.374421i | ||||
\(698\) | −7.45669 | + | 12.9154i | −0.282240 | + | 0.488854i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 40.7696i | − | 1.53984i | −0.638138 | − | 0.769922i | \(-0.720295\pi\) | ||
0.638138 | − | 0.769922i | \(-0.279705\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.1313 | + | 8.73606i | −0.570688 | + | 0.329487i | ||||
\(704\) | 7.05130 | − | 4.07107i | 0.265756 | − | 0.153434i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 57.0948i | 2.14879i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.3640 | − | 28.3432i | 0.614561 | − | 1.06445i | −0.375900 | − | 0.926660i | \(-0.622666\pi\) |
0.990461 | − | 0.137791i | \(-0.0440003\pi\) | |||||||
\(710\) | 19.6913 | + | 34.1063i | 0.739001 | + | 1.27999i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 23.6148 | + | 13.6340i | 0.885003 | + | 0.510957i | ||||
\(713\) | 13.5140 | 0.506102 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.45584 | −0.353629 | ||||||||
\(716\) | −31.5462 | − | 18.2132i | −1.17894 | − | 0.680659i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.24264 | − | 2.15232i | −0.0463749 | − | 0.0803237i | ||||
\(719\) | 6.75699 | − | 11.7034i | 0.251993 | − | 0.436465i | −0.712081 | − | 0.702097i | \(-0.752247\pi\) |
0.964074 | + | 0.265632i | \(0.0855807\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 64.3553i | − | 2.39506i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 58.7251 | − | 33.9050i | 2.18250 | − | 1.26007i | ||||
\(725\) | −26.8213 | + | 15.4853i | −0.996118 | + | 0.575109i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 43.3407i | − | 1.60742i | −0.595022 | − | 0.803710i | \(-0.702857\pi\) | ||
0.595022 | − | 0.803710i | \(-0.297143\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.70711 | + | 9.88500i | −0.211229 | + | 0.365860i | ||||
\(731\) | 8.73606 | + | 15.1313i | 0.323115 | + | 0.559651i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.1870 | + | 11.6549i | 0.745622 | + | 0.430485i | 0.824110 | − | 0.566430i | \(-0.191676\pi\) |
−0.0784876 | + | 0.996915i | \(0.525009\pi\) | |||||||
\(734\) | −9.55582 | −0.352712 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.17157 | 0.116906 | ||||||||
\(737\) | −6.08767 | − | 3.51472i | −0.224242 | − | 0.129466i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.41421 | + | 16.3059i | 0.346307 | + | 0.599822i | 0.985590 | − | 0.169149i | \(-0.0541021\pi\) |
−0.639283 | + | 0.768972i | \(0.720769\pi\) | |||||||
\(740\) | −16.7227 | + | 28.9645i | −0.614738 | + | 1.06476i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 52.4264i | 1.92334i | 0.274212 | + | 0.961669i | \(0.411583\pi\) | ||||
−0.274212 | + | 0.961669i | \(0.588417\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.4134 | − | 7.16687i | 0.454791 | − | 0.262574i | ||||
\(746\) | −47.3087 | + | 27.3137i | −1.73210 | + | 1.00003i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 4.43835i | − | 0.162282i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.3431 | + | 17.9149i | −0.377427 | + | 0.653722i | −0.990687 | − | 0.136159i | \(-0.956524\pi\) |
0.613260 | + | 0.789881i | \(0.289858\pi\) | |||||||
\(752\) | −10.1355 | − | 17.5552i | −0.369603 | − | 0.640171i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −34.1063 | − | 19.6913i | −1.24208 | − | 0.717115i | ||||
\(755\) | −42.1814 | −1.53514 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.87006 | 0.249696 | 0.124848 | − | 0.992176i | \(-0.460156\pi\) | ||||
0.124848 | + | 0.992176i | \(0.460156\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −50.3848 | − | 87.2690i | −1.82765 | − | 3.16558i | ||||
\(761\) | 0.289829 | − | 0.501998i | 0.0105063 | − | 0.0181974i | −0.860724 | − | 0.509071i | \(-0.829989\pi\) |
0.871231 | + | 0.490874i | \(0.163322\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 79.7401i | 2.88490i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −56.5092 | + | 32.6256i | −2.04176 | + | 1.17881i | ||||
\(767\) | 19.7700 | − | 11.4142i | 0.713853 | − | 0.412143i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 45.8995i | − | 1.65518i | −0.561335 | − | 0.827589i | \(-0.689712\pi\) | ||
0.561335 | − | 0.827589i | \(-0.310288\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −33.7990 | + | 58.5416i | −1.21645 | + | 2.10696i | ||||
\(773\) | −9.43577 | − | 16.3432i | −0.339381 | − | 0.587825i | 0.644935 | − | 0.764237i | \(-0.276884\pi\) |
−0.984316 | + | 0.176412i | \(0.943551\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37.5342 | + | 21.6704i | 1.34827 | + | 0.778423i | ||||
\(776\) | 6.17733 | 0.221753 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 33.3137 | 1.19435 | ||||||||
\(779\) | −47.7290 | − | 27.5563i | −1.71007 | − | 0.987309i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00000 | + | 3.46410i | 0.0715656 | + | 0.123955i | ||||
\(782\) | 3.37849 | − | 5.85172i | 0.120815 | − | 0.209257i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 24.7868i | − | 0.884679i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.7034 | + | 6.75699i | −0.417183 | + | 0.240861i | −0.693871 | − | 0.720099i | \(-0.744096\pi\) |
0.276689 | + | 0.960960i | \(0.410763\pi\) | |||||||
\(788\) | −53.8527 | + | 31.0919i | −1.91842 | + | 1.10760i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 78.7652i | − | 2.80234i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.7782 | + | 23.8645i | −0.489277 | + | 0.847453i | ||||
\(794\) | 32.9154 | + | 57.0112i | 1.16813 | + | 2.02325i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −63.3649 | − | 36.5838i | −2.24591 | − | 1.29668i | ||||
\(797\) | −1.73897 | −0.0615976 | −0.0307988 | − | 0.999526i | \(-0.509805\pi\) | ||||
−0.0307988 | + | 0.999526i | \(0.509805\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.45584 | 0.334524 | ||||||||
\(800\) | 8.80884 | + | 5.08579i | 0.311440 | + | 0.179810i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 13.0711 | + | 22.6398i | 0.461555 | + | 0.799437i | ||||
\(803\) | −0.579658 | + | 1.00400i | −0.0204557 | + | 0.0354303i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 55.1127i | 1.94126i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −49.4456 | + | 28.5474i | −1.73949 | + | 1.00429i | ||||
\(809\) | 27.7489 | − | 16.0208i | 0.975598 | − | 0.563262i | 0.0746599 | − | 0.997209i | \(-0.476213\pi\) |
0.900938 | + | 0.433947i | \(0.142880\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.55582i | 0.335550i | 0.985825 | + | 0.167775i | \(0.0536583\pi\) | ||||
−0.985825 | + | 0.167775i | \(0.946342\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.58579 | + | 4.47871i | −0.0906318 | + | 0.156979i | ||||
\(815\) | −25.0489 | − | 43.3859i | −0.877424 | − | 1.51974i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 73.0604 | + | 42.1814i | 2.55606 | + | 1.47574i | ||||
\(818\) | 42.7611 | 1.49511 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −105.497 | −3.68413 | ||||||||
\(821\) | −27.9229 | − | 16.1213i | −0.974518 | − | 0.562638i | −0.0739071 | − | 0.997265i | \(-0.523547\pi\) |
−0.900610 | + | 0.434627i | \(0.856880\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.9706 | − | 22.4657i | −0.452125 | − | 0.783104i | 0.546392 | − | 0.837529i | \(-0.316001\pi\) |
−0.998518 | + | 0.0544251i | \(0.982667\pi\) | |||||||
\(824\) | −6.17733 | + | 10.6994i | −0.215197 | + | 0.372733i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.3431i | 0.985588i | 0.870146 | + | 0.492794i | \(0.164024\pi\) | ||||
−0.870146 | + | 0.492794i | \(0.835976\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.1765 | + | 17.4224i | −1.04807 | + | 0.605105i | −0.922109 | − | 0.386930i | \(-0.873535\pi\) |
−0.125963 | + | 0.992035i | \(0.540202\pi\) | |||||||
\(830\) | −95.4580 | + | 55.1127i | −3.31340 | + | 1.91299i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 33.2053i | 1.15119i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.72792 | + | 8.18900i | −0.163616 | + | 0.283392i | ||||
\(836\) | −10.7151 | − | 18.5592i | −0.370591 | − | 0.641882i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 74.0644 | + | 42.7611i | 2.55851 | + | 1.47716i | ||||
\(839\) | −20.2710 | −0.699831 | −0.349916 | − | 0.936781i | \(-0.613790\pi\) | ||||
−0.349916 | + | 0.936781i | \(0.613790\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.68629 | 0.196079 | ||||||||
\(842\) | 48.7436 | + | 28.1421i | 1.67982 | + | 0.969842i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.0000 | + | 24.2487i | 0.481900 | + | 0.834675i | ||||
\(845\) | −2.67878 | + | 4.63979i | −0.0921530 | + | 0.159614i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 21.2132i | − | 0.728464i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 18.7671 | − | 10.8352i | 0.643706 | − | 0.371644i | ||||
\(851\) | −4.47871 | + | 2.58579i | −0.153528 | + | 0.0886396i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.8029i | 1.32859i | 0.747472 | + | 0.664294i | \(0.231268\pi\) | ||||
−0.747472 | + | 0.664294i | \(0.768732\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.5563 | − | 35.6046i | 0.702602 | − | 1.21694i | ||||
\(857\) | 9.84565 | + | 17.0532i | 0.336321 | + | 0.582525i | 0.983738 | − | 0.179611i | \(-0.0574840\pi\) |
−0.647417 | + | 0.762136i | \(0.724151\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.8307 | + | 14.9134i | 0.881334 | + | 0.508838i | 0.871098 | − | 0.491109i | \(-0.163408\pi\) |
0.0102358 | + | 0.999948i | \(0.496742\pi\) | |||||||
\(860\) | 161.489 | 5.50671 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 37.3137 | 1.27091 | ||||||||
\(863\) | 28.8505 | + | 16.6569i | 0.982083 | + | 0.567006i | 0.902898 | − | 0.429854i | \(-0.141435\pi\) |
0.0791847 | + | 0.996860i | \(0.474768\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.7782 | − | 23.8645i | −0.468472 | − | 0.811417i | ||||
\(866\) | 9.84565 | − | 17.0532i | 0.334569 | − | 0.579490i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 8.00000i | − | 0.271381i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.8268 | − | 14.3337i | 0.841222 | − | 0.485680i | ||||
\(872\) | 9.88500 | − | 5.70711i | 0.334748 | − | 0.193267i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 32.6256i | − | 1.10358i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.2635 | + | 28.1691i | −0.549178 | + | 0.951204i | 0.449153 | + | 0.893455i | \(0.351726\pi\) |
−0.998331 | + | 0.0577493i | \(0.981608\pi\) | |||||||
\(878\) | 34.6047 | + | 59.9371i | 1.16785 | + | 2.02278i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7.27159 | − | 4.19825i | −0.245125 | − | 0.141523i | ||||
\(881\) | 20.5111 | 0.691035 | 0.345518 | − | 0.938412i | \(-0.387703\pi\) | ||||
0.345518 | + | 0.938412i | \(0.387703\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.4558 | −1.26049 | −0.630245 | − | 0.776397i | \(-0.717045\pi\) | ||||
−0.630245 | + | 0.776397i | \(0.717045\pi\) | |||||||
\(884\) | 15.6755 | + | 9.05025i | 0.527224 | + | 0.304393i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29.9706 | − | 51.9105i | −1.00688 | − | 1.74397i | ||||
\(887\) | −8.97616 | + | 15.5472i | −0.301390 | + | 0.522023i | −0.976451 | − | 0.215739i | \(-0.930784\pi\) |
0.675061 | + | 0.737762i | \(0.264117\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 50.3848i | 1.68890i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −76.4882 | + | 44.1605i | −2.56102 | + | 1.47860i | ||||
\(893\) | 39.5400 | − | 22.8284i | 1.32316 | − | 0.763924i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 32.1454i | − | 1.07450i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29.2635 | − | 50.6858i | 0.976534 | − | 1.69141i | ||||
\(899\) | 16.3128 | + | 28.2546i | 0.544063 | + | 0.942344i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.56965 | + | 4.94769i | 0.285496 | + | 0.164831i | ||||
\(902\) | −16.3128 | −0.543157 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −26.0416 | −0.866132 | ||||||||
\(905\) | 51.8235 | + | 29.9203i | 1.72267 | + | 0.994585i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.3848 | + | 38.7716i | 0.743274 | + | 1.28739i | 0.950997 | + | 0.309201i | \(0.100062\pi\) |
−0.207722 | + | 0.978188i | \(0.566605\pi\) | |||||||
\(908\) | 5.35757 | − | 9.27958i | 0.177797 | − | 0.307954i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.5147i | 0.845340i | 0.906284 | + | 0.422670i | \(0.138907\pi\) | ||||
−0.906284 | + | 0.422670i | \(0.861093\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.69545 | + | 5.59767i | −0.320873 | + | 0.185256i | ||||
\(914\) | 59.8534 | − | 34.5563i | 1.97977 | − | 1.14302i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 46.3797i | 1.53243i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.72792 | + | 8.18900i | −0.155960 | + | 0.270130i | −0.933408 | − | 0.358817i | \(-0.883180\pi\) |
0.777448 | + | 0.628947i | \(0.216514\pi\) | |||||||
\(920\) | −14.9134 | − | 25.8307i | −0.491680 | − | 0.851615i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −45.3078 | − | 26.1585i | −1.49213 | − | 0.861483i | ||||
\(923\) | −16.3128 | −0.536943 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.5858 | −0.545337 | ||||||||
\(926\) | −7.34847 | − | 4.24264i | −0.241486 | − | 0.139422i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.82843 | + | 6.63103i | 0.125674 | + | 0.217674i | ||||
\(929\) | 9.84565 | − | 17.0532i | 0.323025 | − | 0.559496i | −0.658085 | − | 0.752943i | \(-0.728633\pi\) |
0.981111 | + | 0.193447i | \(0.0619668\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 41.4558i | 1.35793i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.85172 | + | 3.37849i | −0.191474 | + | 0.110548i | ||||
\(935\) | 3.39200 | − | 1.95837i | 0.110930 | − | 0.0640455i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.73897i | 0.0568098i | 0.999596 | + | 0.0284049i | \(0.00904277\pi\) | ||||
−0.999596 | + | 0.0284049i | \(0.990957\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 43.6985 | − | 75.6880i | 1.42529 | − | 2.46867i | ||||
\(941\) | −7.45669 | − | 12.9154i | −0.243081 | − | 0.421029i | 0.718509 | − | 0.695518i | \(-0.244825\pi\) |
−0.961590 | + | 0.274488i | \(0.911492\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.1273 | − | 8.15640i | −0.460048 | − | 0.265609i | ||||
\(944\) | 20.2710 | 0.659763 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.9706 | 0.811863 | ||||||||
\(947\) | −19.8931 | − | 11.4853i | −0.646439 | − | 0.373221i | 0.140652 | − | 0.990059i | \(-0.455080\pi\) |
−0.787090 | + | 0.616838i | \(0.788414\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.36396 | − | 4.09450i | −0.0767374 | − | 0.132913i | ||||
\(950\) | 52.3169 | − | 90.6155i | 1.69738 | − | 2.93996i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 26.3848i | − | 0.854687i | −0.904089 | − | 0.427343i | \(-0.859450\pi\) | ||
0.904089 | − | 0.427343i | \(-0.140550\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −60.9411 | + | 35.1843i | −1.97201 | + | 1.13854i | ||||
\(956\) | 1.13770 | − | 0.656854i | 0.0367960 | − | 0.0212442i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 20.2710i | − | 0.654925i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.32843 | − | 12.6932i | 0.236401 | − | 0.409458i | ||||
\(962\) | −10.5454 | − | 18.2651i | −0.339996 | − | 0.588890i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 29.7606 | + | 17.1823i | 0.958525 | + | 0.553404i | ||||
\(965\) | −59.6536 | −1.92032 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.1127 | 1.38641 | 0.693205 | − | 0.720740i | \(-0.256198\pi\) | ||||
0.693205 | + | 0.720740i | \(0.256198\pi\) | |||||||
\(968\) | 39.4275 | + | 22.7635i | 1.26725 | + | 0.731645i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.70711 | + | 9.88500i | 0.183244 | + | 0.317388i | ||||
\(971\) | −16.3128 | + | 28.2546i | −0.523503 | + | 0.906734i | 0.476123 | + | 0.879379i | \(0.342042\pi\) |
−0.999626 | + | 0.0273548i | \(0.991292\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 22.8284i | 0.731470i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −21.1910 | + | 12.2346i | −0.678306 | + | 0.391620i | ||||
\(977\) | 33.9236 | − | 19.5858i | 1.08531 | − | 0.626605i | 0.152987 | − | 0.988228i | \(-0.451111\pi\) |
0.932324 | + | 0.361623i | \(0.117777\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.11747i | 0.163555i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.24264 | + | 5.61642i | −0.103477 | + | 0.179227i | ||||
\(983\) | −8.73606 | − | 15.1313i | −0.278637 | − | 0.482614i | 0.692409 | − | 0.721505i | \(-0.256549\pi\) |
−0.971046 | + | 0.238891i | \(0.923216\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −47.5237 | − | 27.4378i | −1.51423 | − | 0.874242i | ||||
\(986\) | 16.3128 | 0.519506 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 87.3970 | 2.78047 | ||||||||
\(989\) | 21.6251 | + | 12.4853i | 0.687639 | + | 0.397009i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.6985 | − | 51.4393i | −0.943403 | − | 1.63402i | −0.758917 | − | 0.651188i | \(-0.774271\pi\) |
−0.184487 | − | 0.982835i | \(-0.559062\pi\) | |||||||
\(992\) | 5.35757 | − | 9.27958i | 0.170103 | − | 0.294627i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 64.5685i | − | 2.04696i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.1974 | − | 5.88750i | 0.322956 | − | 0.186459i | −0.329753 | − | 0.944067i | \(-0.606966\pi\) |
0.652710 | + | 0.757608i | \(0.273632\pi\) | |||||||
\(998\) | −4.47871 | + | 2.58579i | −0.141771 | + | 0.0818516i | ||||
\(999\) | 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 | 441.2.p.c.215.1 | 16 | ||
3.2 | odd | 2 | inner | 441.2.p.c.215.8 | 16 | ||
7.2 | even | 3 | 441.2.c.b.440.8 | yes | 8 | ||
7.3 | odd | 6 | inner | 441.2.p.c.80.8 | 16 | ||
7.4 | even | 3 | inner | 441.2.p.c.80.7 | 16 | ||
7.5 | odd | 6 | 441.2.c.b.440.7 | yes | 8 | ||
7.6 | odd | 2 | inner | 441.2.p.c.215.2 | 16 | ||
21.2 | odd | 6 | 441.2.c.b.440.1 | ✓ | 8 | ||
21.5 | even | 6 | 441.2.c.b.440.2 | yes | 8 | ||
21.11 | odd | 6 | inner | 441.2.p.c.80.2 | 16 | ||
21.17 | even | 6 | inner | 441.2.p.c.80.1 | 16 | ||
21.20 | even | 2 | inner | 441.2.p.c.215.7 | 16 | ||
28.19 | even | 6 | 7056.2.k.g.881.1 | 8 | |||
28.23 | odd | 6 | 7056.2.k.g.881.7 | 8 | |||
84.23 | even | 6 | 7056.2.k.g.881.2 | 8 | |||
84.47 | odd | 6 | 7056.2.k.g.881.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.c.b.440.1 | ✓ | 8 | 21.2 | odd | 6 | ||
441.2.c.b.440.2 | yes | 8 | 21.5 | even | 6 | ||
441.2.c.b.440.7 | yes | 8 | 7.5 | odd | 6 | ||
441.2.c.b.440.8 | yes | 8 | 7.2 | even | 3 | ||
441.2.p.c.80.1 | 16 | 21.17 | even | 6 | inner | ||
441.2.p.c.80.2 | 16 | 21.11 | odd | 6 | inner | ||
441.2.p.c.80.7 | 16 | 7.4 | even | 3 | inner | ||
441.2.p.c.80.8 | 16 | 7.3 | odd | 6 | inner | ||
441.2.p.c.215.1 | 16 | 1.1 | even | 1 | trivial | ||
441.2.p.c.215.2 | 16 | 7.6 | odd | 2 | inner | ||
441.2.p.c.215.7 | 16 | 21.20 | even | 2 | inner | ||
441.2.p.c.215.8 | 16 | 3.2 | odd | 2 | inner | ||
7056.2.k.g.881.1 | 8 | 28.19 | even | 6 | |||
7056.2.k.g.881.2 | 8 | 84.23 | even | 6 | |||
7056.2.k.g.881.7 | 8 | 28.23 | odd | 6 | |||
7056.2.k.g.881.8 | 8 | 84.47 | odd | 6 |