Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(899,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 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("3150.899");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bp (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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 899.1 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.899 |
Dual form | 3150.2.bp.a.1349.1 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.63896 | + | 0.189469i | −0.997433 | + | 0.0716124i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.55171 | − | 1.47323i | −0.769370 | − | 0.444196i | 0.0632797 | − | 0.997996i | \(-0.479844\pi\) |
−0.832650 | + | 0.553800i | \(0.813177\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.93185 | 1.09050 | 0.545250 | − | 0.838274i | \(-0.316435\pi\) | ||||
0.545250 | + | 0.838274i | \(0.316435\pi\) | |||||||
\(14\) | 1.48356 | + | 2.19067i | 0.396499 | + | 0.585481i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.346065 | + | 0.199801i | 0.0839331 | + | 0.0484588i | 0.541379 | − | 0.840779i | \(-0.317902\pi\) |
−0.457446 | + | 0.889237i | \(0.651236\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0305501 | + | 0.0176381i | −0.00700867 | + | 0.00404646i | −0.503500 | − | 0.863995i | \(-0.667955\pi\) |
0.496492 | + | 0.868042i | \(0.334621\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.94646i | 0.628188i | ||||||||
\(23\) | 1.86603 | + | 3.23205i | 0.389093 | + | 0.673929i | 0.992328 | − | 0.123635i | \(-0.0394551\pi\) |
−0.603235 | + | 0.797564i | \(0.706122\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.96593 | − | 3.40508i | −0.385550 | − | 0.667792i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.15539 | − | 2.38014i | 0.218349 | − | 0.449804i | ||||
\(29\) | − | 8.89898i | − | 1.65250i | −0.563304 | − | 0.826250i | \(-0.690470\pi\) | ||
0.563304 | − | 0.826250i | \(-0.309530\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.717439 | + | 0.414214i | 0.128856 | + | 0.0743950i | 0.563042 | − | 0.826428i | \(-0.309631\pi\) |
−0.434187 | + | 0.900823i | \(0.642964\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 0.399602i | − | 0.0685311i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.86919 | + | 3.96593i | −1.12929 | + | 0.651994i | −0.943756 | − | 0.330644i | \(-0.892734\pi\) |
−0.185532 | + | 0.982638i | \(0.559401\pi\) | |||||||
\(38\) | 0.0305501 | + | 0.0176381i | 0.00495588 | + | 0.00286128i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.31079 | −0.985580 | −0.492790 | − | 0.870148i | \(-0.664023\pi\) | ||||
−0.492790 | + | 0.870148i | \(0.664023\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.03528i | 0.462875i | 0.972850 | + | 0.231438i | \(0.0743429\pi\) | ||||
−0.972850 | + | 0.231438i | \(0.925657\pi\) | |||||||
\(44\) | 2.55171 | − | 1.47323i | 0.384685 | − | 0.222098i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.86603 | − | 3.23205i | 0.275130 | − | 0.476540i | ||||
\(47\) | −5.02520 | + | 2.90130i | −0.733001 | + | 0.423198i | −0.819519 | − | 0.573052i | \(-0.805759\pi\) |
0.0865180 | + | 0.996250i | \(0.472426\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.92820 | − | 1.00000i | 0.989743 | − | 0.142857i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.96593 | + | 3.40508i | −0.272625 | + | 0.472200i | ||||
\(53\) | 2.14929 | − | 3.72268i | 0.295228 | − | 0.511349i | −0.679810 | − | 0.733388i | \(-0.737938\pi\) |
0.975038 | + | 0.222039i | \(0.0712711\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.63896 | + | 0.189469i | −0.352646 | + | 0.0253188i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.70674 | + | 4.44949i | −1.01194 | + | 0.584247i | ||||
\(59\) | 2.78522 | − | 4.82415i | 0.362605 | − | 0.628050i | −0.625784 | − | 0.779997i | \(-0.715221\pi\) |
0.988389 | + | 0.151946i | \(0.0485540\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.97710 | + | 5.76028i | −1.27744 | + | 0.737528i | −0.976376 | − | 0.216077i | \(-0.930674\pi\) |
−0.301060 | + | 0.953605i | \(0.597340\pi\) | |||||||
\(62\) | − | 0.828427i | − | 0.105210i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.8420 | + | 6.25966i | 1.32457 | + | 0.764739i | 0.984453 | − | 0.175646i | \(-0.0562013\pi\) |
0.340113 | + | 0.940385i | \(0.389535\pi\) | |||||||
\(68\) | −0.346065 | + | 0.199801i | −0.0419666 | + | 0.0242294i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.93426i | 0.229554i | 0.993391 | + | 0.114777i | \(0.0366153\pi\) | ||||
−0.993391 | + | 0.114777i | \(0.963385\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.171573 | + | 0.297173i | −0.0200811 | + | 0.0347815i | −0.875891 | − | 0.482508i | \(-0.839726\pi\) |
0.855810 | + | 0.517290i | \(0.173059\pi\) | |||||||
\(74\) | 6.86919 | + | 3.96593i | 0.798527 | + | 0.461030i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 0.0352762i | − | 0.00404646i | ||||||
\(77\) | 7.01299 | + | 3.40433i | 0.799205 | + | 0.387959i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.15331 | + | 7.19375i | 0.467284 | + | 0.809360i | 0.999301 | − | 0.0373736i | \(-0.0118992\pi\) |
−0.532017 | + | 0.846734i | \(0.678566\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.15539 | + | 5.46530i | 0.348455 | + | 0.603542i | ||||
\(83\) | 10.3490i | 1.13595i | 0.823046 | + | 0.567974i | \(0.192273\pi\) | ||||
−0.823046 | + | 0.567974i | \(0.807727\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.62863 | − | 1.51764i | 0.283452 | − | 0.163651i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.55171 | − | 1.47323i | −0.272013 | − | 0.157047i | ||||
\(89\) | −3.08604 | − | 5.34519i | −0.327120 | − | 0.566589i | 0.654819 | − | 0.755786i | \(-0.272745\pi\) |
−0.981939 | + | 0.189197i | \(0.939411\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.3760 | + | 0.744963i | −1.08770 | + | 0.0780933i | ||||
\(92\) | −3.73205 | −0.389093 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.02520 | + | 2.90130i | 0.518310 | + | 0.299246i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.6344 | −1.58744 | −0.793718 | − | 0.608286i | \(-0.791857\pi\) | ||||
−0.793718 | + | 0.608286i | \(0.791857\pi\) | |||||||
\(98\) | −4.33013 | − | 5.50000i | −0.437409 | − | 0.555584i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.02458 | − | 15.6310i | 0.897979 | − | 1.55535i | 0.0679057 | − | 0.997692i | \(-0.478368\pi\) |
0.830074 | − | 0.557654i | \(-0.188298\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.26002 | + | 7.37857i | 0.419752 | + | 0.727032i | 0.995914 | − | 0.0903031i | \(-0.0287836\pi\) |
−0.576162 | + | 0.817336i | \(0.695450\pi\) | |||||||
\(104\) | 3.93185 | 0.385550 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.29858 | −0.417515 | ||||||||
\(107\) | 8.52761 | + | 14.7702i | 0.824395 | + | 1.42789i | 0.902381 | + | 0.430939i | \(0.141818\pi\) |
−0.0779862 | + | 0.996954i | \(0.524849\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.84909 | + | 10.1309i | −0.560241 | + | 0.970366i | 0.437234 | + | 0.899348i | \(0.355958\pi\) |
−0.997475 | + | 0.0710185i | \(0.977375\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.48356 | + | 2.19067i | 0.140184 | + | 0.206999i | ||||
\(113\) | 13.5546 | 1.27511 | 0.637554 | − | 0.770405i | \(-0.279946\pi\) | ||||
0.637554 | + | 0.770405i | \(0.279946\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.70674 | + | 4.44949i | 0.715553 | + | 0.413125i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.57045 | −0.512801 | ||||||||
\(119\) | −0.951108 | − | 0.461698i | −0.0871879 | − | 0.0423237i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.15918 | − | 2.00775i | −0.105380 | − | 0.182523i | ||||
\(122\) | 9.97710 | + | 5.76028i | 0.903284 | + | 0.521511i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.717439 | + | 0.414214i | −0.0644279 | + | 0.0371975i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.95983i | 0.795056i | 0.917590 | + | 0.397528i | \(0.130132\pi\) | ||||
−0.917590 | + | 0.397528i | \(0.869868\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.39047 | + | 11.0686i | 0.558338 | + | 0.967070i | 0.997635 | + | 0.0687282i | \(0.0218941\pi\) |
−0.439297 | + | 0.898342i | \(0.644773\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0772785 | − | 0.0523345i | 0.00670090 | − | 0.00453797i | ||||
\(134\) | − | 12.5193i | − | 1.08150i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.346065 | + | 0.199801i | 0.0296748 | + | 0.0171328i | ||||
\(137\) | −2.76028 | + | 4.78094i | −0.235827 | + | 0.408464i | −0.959513 | − | 0.281666i | \(-0.909113\pi\) |
0.723686 | + | 0.690129i | \(0.242446\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.8471i | 1.85305i | 0.376235 | + | 0.926524i | \(0.377218\pi\) | ||||
−0.376235 | + | 0.926524i | \(0.622782\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.67511 | − | 0.967128i | 0.140572 | − | 0.0811596i | ||||
\(143\) | −10.0330 | − | 5.79253i | −0.838998 | − | 0.484396i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.343146 | 0.0283989 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 7.93185i | − | 0.651994i | ||||||
\(149\) | −18.6179 | + | 10.7491i | −1.52524 | + | 0.880598i | −0.525688 | + | 0.850677i | \(0.676192\pi\) |
−0.999552 | + | 0.0299204i | \(0.990475\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.47531 | + | 2.55532i | −0.120059 | + | 0.207949i | −0.919791 | − | 0.392409i | \(-0.871642\pi\) |
0.799732 | + | 0.600358i | \(0.204975\pi\) | |||||||
\(152\) | −0.0305501 | + | 0.0176381i | −0.00247794 | + | 0.00143064i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.558263 | − | 7.77559i | −0.0449861 | − | 0.626575i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.2481 | + | 19.4823i | −0.897698 | + | 1.55486i | −0.0672682 | + | 0.997735i | \(0.521428\pi\) |
−0.830430 | + | 0.557123i | \(0.811905\pi\) | |||||||
\(158\) | 4.15331 | − | 7.19375i | 0.330420 | − | 0.572304i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.53674 | − | 8.17569i | −0.436356 | − | 0.644335i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.7515 | + | 11.4035i | −1.54705 | + | 0.893192i | −0.548690 | + | 0.836026i | \(0.684873\pi\) |
−0.998365 | + | 0.0571664i | \(0.981793\pi\) | |||||||
\(164\) | 3.15539 | − | 5.46530i | 0.246395 | − | 0.426769i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.96248 | − | 5.17449i | 0.695624 | − | 0.401618i | ||||
\(167\) | − | 8.84961i | − | 0.684803i | −0.939554 | − | 0.342402i | \(-0.888760\pi\) | ||
0.939554 | − | 0.342402i | \(-0.111240\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.45946 | 0.189189 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.62863 | − | 1.51764i | −0.200431 | − | 0.115719i | ||||
\(173\) | −6.70032 | + | 3.86843i | −0.509416 | + | 0.294111i | −0.732593 | − | 0.680667i | \(-0.761690\pi\) |
0.223178 | + | 0.974778i | \(0.428357\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.94646i | 0.222098i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.08604 | + | 5.34519i | −0.231309 | + | 0.400639i | ||||
\(179\) | −0.417291 | − | 0.240923i | −0.0311898 | − | 0.0180074i | 0.484324 | − | 0.874889i | \(-0.339066\pi\) |
−0.515514 | + | 0.856881i | \(0.672399\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.44876i | − | 0.182015i | −0.995850 | − | 0.0910075i | \(-0.970991\pi\) | ||
0.995850 | − | 0.0910075i | \(-0.0290087\pi\) | |||||||
\(182\) | 5.83315 | + | 8.61339i | 0.432382 | + | 0.638467i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.86603 | + | 3.23205i | 0.137565 | + | 0.238270i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.588706 | − | 1.01967i | −0.0430504 | − | 0.0745655i | ||||
\(188\) | − | 5.80260i | − | 0.423198i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.89241 | + | 2.24728i | −0.281645 | + | 0.162608i | −0.634168 | − | 0.773195i | \(-0.718657\pi\) |
0.352523 | + | 0.935803i | \(0.385324\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.8859 | − | 6.28497i | −0.783583 | − | 0.452402i | 0.0541158 | − | 0.998535i | \(-0.482766\pi\) |
−0.837698 | + | 0.546133i | \(0.816099\pi\) | |||||||
\(194\) | 7.81722 | + | 13.5398i | 0.561243 | + | 0.972102i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.59808 | + | 6.50000i | −0.185577 | + | 0.464286i | ||||
\(197\) | 13.3748 | 0.952916 | 0.476458 | − | 0.879197i | \(-0.341920\pi\) | ||||
0.476458 | + | 0.879197i | \(0.341920\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.5169 | + | 13.5775i | 1.66707 | + | 0.962483i | 0.969206 | + | 0.246253i | \(0.0791993\pi\) |
0.697864 | + | 0.716231i | \(0.254134\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −18.0492 | −1.26993 | ||||||||
\(203\) | 1.68608 | + | 23.4840i | 0.118339 | + | 1.64826i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.26002 | − | 7.37857i | 0.296810 | − | 0.514090i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.96593 | − | 3.40508i | −0.136312 | − | 0.236100i | ||||
\(209\) | 0.103940 | 0.00718968 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.4183 | 1.26797 | 0.633984 | − | 0.773346i | \(-0.281419\pi\) | ||||
0.633984 | + | 0.773346i | \(0.281419\pi\) | |||||||
\(212\) | 2.14929 | + | 3.72268i | 0.147614 | + | 0.255675i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.52761 | − | 14.7702i | 0.582935 | − | 1.00967i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.97177 | − | 0.957160i | −0.133853 | − | 0.0649763i | ||||
\(218\) | 11.6982 | 0.792301 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.36068 | + | 0.785587i | 0.0915290 | + | 0.0528443i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.8045 | 1.19228 | 0.596140 | − | 0.802881i | \(-0.296700\pi\) | ||||
0.596140 | + | 0.802881i | \(0.296700\pi\) | |||||||
\(224\) | 1.15539 | − | 2.38014i | 0.0771980 | − | 0.159030i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.77729 | − | 11.7386i | −0.450819 | − | 0.780841i | ||||
\(227\) | −1.48288 | − | 0.856140i | −0.0984220 | − | 0.0568240i | 0.449981 | − | 0.893038i | \(-0.351431\pi\) |
−0.548403 | + | 0.836214i | \(0.684764\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.26142 | + | 3.03768i | −0.347684 | + | 0.200736i | −0.663665 | − | 0.748030i | \(-0.731000\pi\) |
0.315981 | + | 0.948766i | \(0.397667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 8.89898i | − | 0.584247i | ||||||
\(233\) | −3.56288 | − | 6.17109i | −0.233412 | − | 0.404282i | 0.725398 | − | 0.688330i | \(-0.241656\pi\) |
−0.958810 | + | 0.284048i | \(0.908322\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.78522 | + | 4.82415i | 0.181303 | + | 0.314025i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.0757120 | + | 1.05453i | 0.00490768 | + | 0.0683552i | ||||
\(239\) | − | 18.7194i | − | 1.21085i | −0.795900 | − | 0.605427i | \(-0.793002\pi\) | ||
0.795900 | − | 0.605427i | \(-0.206998\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.68036 | + | 4.43426i | 0.494735 | + | 0.285636i | 0.726537 | − | 0.687128i | \(-0.241129\pi\) |
−0.231802 | + | 0.972763i | \(0.574462\pi\) | |||||||
\(242\) | −1.15918 | + | 2.00775i | −0.0745147 | + | 0.129063i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 11.5206i | − | 0.737528i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.120118 | + | 0.0693504i | −0.00764295 | + | 0.00441266i | ||||
\(248\) | 0.717439 | + | 0.414214i | 0.0455574 | + | 0.0263026i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.1738 | −1.39960 | −0.699798 | − | 0.714341i | \(-0.746727\pi\) | ||||
−0.699798 | + | 0.714341i | \(0.746727\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 10.9964i | − | 0.691335i | ||||||
\(254\) | 7.75944 | − | 4.47992i | 0.486871 | − | 0.281095i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −14.5780 | + | 8.41662i | −0.909351 | + | 0.525014i | −0.880222 | − | 0.474561i | \(-0.842607\pi\) |
−0.0291289 | + | 0.999576i | \(0.509273\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.3761 | − | 11.7674i | 1.07970 | − | 0.731191i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.39047 | − | 11.0686i | 0.394805 | − | 0.683822i | ||||
\(263\) | −11.0599 | + | 19.1562i | −0.681980 | + | 1.18122i | 0.292396 | + | 0.956297i | \(0.405548\pi\) |
−0.974376 | + | 0.224926i | \(0.927786\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.0839622 | − | 0.0407579i | −0.00514805 | − | 0.00249903i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.8420 | + | 6.25966i | −0.662283 | + | 0.382369i | ||||
\(269\) | 1.45049 | − | 2.51231i | 0.0884377 | − | 0.153179i | −0.818413 | − | 0.574630i | \(-0.805146\pi\) |
0.906851 | + | 0.421452i | \(0.138479\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1244 | − | 8.73205i | 0.918739 | − | 0.530434i | 0.0355066 | − | 0.999369i | \(-0.488696\pi\) |
0.883233 | + | 0.468935i | \(0.155362\pi\) | |||||||
\(272\) | − | 0.399602i | − | 0.0242294i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.52056 | 0.333509 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.96336 | − | 2.28825i | −0.238135 | − | 0.137488i | 0.376184 | − | 0.926545i | \(-0.377236\pi\) |
−0.614319 | + | 0.789057i | \(0.710569\pi\) | |||||||
\(278\) | 18.9202 | − | 10.9236i | 1.13476 | − | 0.655152i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.55948i | 0.570271i | 0.958487 | + | 0.285135i | \(0.0920386\pi\) | ||||
−0.958487 | + | 0.285135i | \(0.907961\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.46311 | − | 9.46238i | 0.324748 | − | 0.562480i | −0.656713 | − | 0.754140i | \(-0.728054\pi\) |
0.981461 | + | 0.191660i | \(0.0613872\pi\) | |||||||
\(284\) | −1.67511 | − | 0.967128i | −0.0993998 | − | 0.0573885i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.5851i | 0.685039i | ||||||||
\(287\) | 16.6539 | − | 1.19570i | 0.983049 | − | 0.0705798i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.42016 | − | 14.5841i | −0.495303 | − | 0.857891i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.171573 | − | 0.297173i | −0.0100405 | − | 0.0173907i | ||||
\(293\) | 16.2280i | 0.948052i | 0.880511 | + | 0.474026i | \(0.157200\pi\) | ||||
−0.880511 | + | 0.474026i | \(0.842800\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.86919 | + | 3.96593i | −0.399263 | + | 0.230515i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 18.6179 | + | 10.7491i | 1.07851 | + | 0.622677i | ||||
\(299\) | 7.33694 | + | 12.7079i | 0.424306 | + | 0.734919i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.575090 | − | 8.00997i | −0.0331476 | − | 0.461687i | ||||
\(302\) | 2.95063 | 0.169790 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.0305501 | + | 0.0176381i | 0.00175217 | + | 0.00101161i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.3782 | −0.706462 | −0.353231 | − | 0.935536i | \(-0.614917\pi\) | ||||
−0.353231 | + | 0.935536i | \(0.614917\pi\) | |||||||
\(308\) | −6.45473 | + | 4.37127i | −0.367792 | + | 0.249076i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.4312 | + | 19.7995i | −0.648206 | + | 1.12272i | 0.335346 | + | 0.942095i | \(0.391147\pi\) |
−0.983551 | + | 0.180630i | \(0.942186\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.4013 | + | 30.1399i | 0.983578 | + | 1.70361i | 0.648091 | + | 0.761563i | \(0.275568\pi\) |
0.335487 | + | 0.942045i | \(0.391099\pi\) | |||||||
\(314\) | 22.4962 | 1.26954 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.30663 | −0.467284 | ||||||||
\(317\) | −3.39355 | − | 5.87780i | −0.190601 | − | 0.330130i | 0.754849 | − | 0.655899i | \(-0.227710\pi\) |
−0.945449 | + | 0.325769i | \(0.894377\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.1103 | + | 22.7076i | −0.734034 | + | 1.27138i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.31199 | + | 8.88280i | −0.240298 | + | 0.495019i | ||||
\(323\) | −0.0140964 | −0.000784346 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 19.7515 | + | 11.4035i | 1.09393 | + | 0.631582i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.31079 | −0.348455 | ||||||||
\(329\) | 12.7116 | − | 8.60853i | 0.700813 | − | 0.474604i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.56985 | − | 9.64726i | −0.306147 | − | 0.530261i | 0.671369 | − | 0.741123i | \(-0.265706\pi\) |
−0.977516 | + | 0.210862i | \(0.932373\pi\) | |||||||
\(332\) | −8.96248 | − | 5.17449i | −0.491880 | − | 0.283987i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.66398 | + | 4.42480i | −0.419355 | + | 0.242114i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.59111i | 0.0866733i | 0.999061 | + | 0.0433366i | \(0.0137988\pi\) | ||||
−0.999061 | + | 0.0433366i | \(0.986201\pi\) | |||||||
\(338\) | −1.22973 | − | 2.12995i | −0.0668884 | − | 0.115854i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.22047 | − | 2.11391i | −0.0660919 | − | 0.114475i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0938 | + | 3.95164i | −0.976972 | + | 0.213368i | ||||
\(344\) | 3.03528i | 0.163651i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.70032 | + | 3.86843i | 0.360211 | + | 0.207968i | ||||
\(347\) | 7.72840 | − | 13.3860i | 0.414882 | − | 0.718597i | −0.580534 | − | 0.814236i | \(-0.697156\pi\) |
0.995416 | + | 0.0956388i | \(0.0304894\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.585057i | 0.0313174i | 0.999877 | + | 0.0156587i | \(0.00498452\pi\) | ||||
−0.999877 | + | 0.0156587i | \(0.995015\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.55171 | − | 1.47323i | 0.136007 | − | 0.0785235i | ||||
\(353\) | −3.18330 | − | 1.83788i | −0.169430 | − | 0.0978204i | 0.412887 | − | 0.910782i | \(-0.364520\pi\) |
−0.582317 | + | 0.812962i | \(0.697854\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.17209 | 0.327120 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.481846i | 0.0254664i | ||||||||
\(359\) | −17.4069 | + | 10.0499i | −0.918702 | + | 0.530413i | −0.883221 | − | 0.468958i | \(-0.844630\pi\) |
−0.0354812 | + | 0.999370i | \(0.511296\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.49938 | + | 16.4534i | −0.499967 | + | 0.865969i | ||||
\(362\) | −2.12069 | + | 1.22438i | −0.111461 | + | 0.0643520i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.54284 | − | 9.35835i | 0.238110 | − | 0.490511i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.96885 | − | 17.2665i | 0.520369 | − | 0.901306i | −0.479350 | − | 0.877624i | \(-0.659128\pi\) |
0.999720 | − | 0.0236826i | \(-0.00753911\pi\) | |||||||
\(368\) | 1.86603 | − | 3.23205i | 0.0972733 | − | 0.168482i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.96656 | + | 10.2312i | −0.257851 | + | 0.531179i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.2856 | − | 16.9081i | 1.51635 | − | 0.875467i | 0.516537 | − | 0.856265i | \(-0.327221\pi\) |
0.999816 | − | 0.0192016i | \(-0.00611243\pi\) | |||||||
\(374\) | −0.588706 | + | 1.01967i | −0.0304413 | + | 0.0527258i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.02520 | + | 2.90130i | −0.259155 | + | 0.149623i | ||||
\(377\) | − | 34.9895i | − | 1.80205i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.7614 | −1.37464 | −0.687321 | − | 0.726353i | \(-0.741214\pi\) | ||||
−0.687321 | + | 0.726353i | \(0.741214\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.89241 | + | 2.24728i | 0.199153 | + | 0.114981i | ||||
\(383\) | 17.1310 | − | 9.89060i | 0.875355 | − | 0.505386i | 0.00623078 | − | 0.999981i | \(-0.498017\pi\) |
0.869124 | + | 0.494594i | \(0.164683\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.5699i | 0.639793i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.81722 | − | 13.5398i | 0.396859 | − | 0.687380i | ||||
\(389\) | 4.49181 | + | 2.59335i | 0.227744 | + | 0.131488i | 0.609531 | − | 0.792762i | \(-0.291358\pi\) |
−0.381787 | + | 0.924250i | \(0.624691\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.49133i | 0.0754200i | ||||||||
\(392\) | 6.92820 | − | 1.00000i | 0.349927 | − | 0.0505076i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.68740 | − | 11.5829i | −0.336907 | − | 0.583539i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.88259 | + | 4.99280i | 0.144673 | + | 0.250581i | 0.929251 | − | 0.369449i | \(-0.120454\pi\) |
−0.784578 | + | 0.620030i | \(0.787120\pi\) | |||||||
\(398\) | − | 27.1550i | − | 1.36116i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.4361 | − | 8.91202i | 0.770841 | − | 0.445045i | −0.0623335 | − | 0.998055i | \(-0.519854\pi\) |
0.833175 | + | 0.553010i | \(0.186521\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.82086 | + | 1.62863i | 0.140517 | + | 0.0811277i | ||||
\(404\) | 9.02458 | + | 15.6310i | 0.448990 | + | 0.777673i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 19.4947 | − | 13.2022i | 0.967507 | − | 0.655214i | ||||
\(407\) | 23.3709 | 1.15845 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.5617 | + | 16.4901i | 1.41228 | + | 0.815382i | 0.995603 | − | 0.0936705i | \(-0.0298600\pi\) |
0.416681 | + | 0.909053i | \(0.363193\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.52004 | −0.419752 | ||||||||
\(413\) | −6.43606 | + | 13.2584i | −0.316698 | + | 0.652405i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.96593 | + | 3.40508i | −0.0963874 | + | 0.166948i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.0519700 | − | 0.0900147i | −0.00254194 | − | 0.00440276i | ||||
\(419\) | −15.2287 | −0.743969 | −0.371985 | − | 0.928239i | \(-0.621323\pi\) | ||||
−0.371985 | + | 0.928239i | \(0.621323\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.9939 | 0.828234 | 0.414117 | − | 0.910224i | \(-0.364090\pi\) | ||||
0.414117 | + | 0.910224i | \(0.364090\pi\) | |||||||
\(422\) | −9.20915 | − | 15.9507i | −0.448294 | − | 0.776468i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.14929 | − | 3.72268i | 0.104379 | − | 0.180789i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.2377 | − | 17.0915i | 1.22134 | − | 0.827115i | ||||
\(428\) | −17.0552 | −0.824395 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.4818 | − | 8.93842i | −0.745732 | − | 0.430549i | 0.0784178 | − | 0.996921i | \(-0.475013\pi\) |
−0.824150 | + | 0.566372i | \(0.808347\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.56388 | 0.267383 | 0.133691 | − | 0.991023i | \(-0.457317\pi\) | ||||
0.133691 | + | 0.991023i | \(0.457317\pi\) | |||||||
\(434\) | 0.156961 | + | 2.18618i | 0.00753437 | + | 0.104940i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.84909 | − | 10.1309i | −0.280121 | − | 0.485183i | ||||
\(437\) | −0.114014 | − | 0.0658262i | −0.00545405 | − | 0.00314890i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.53568 | + | 5.50543i | −0.455113 | + | 0.262760i | −0.709987 | − | 0.704214i | \(-0.751299\pi\) |
0.254874 | + | 0.966974i | \(0.417966\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 1.57117i | − | 0.0747332i | ||||||
\(443\) | 8.49233 | + | 14.7091i | 0.403483 | + | 0.698853i | 0.994144 | − | 0.108067i | \(-0.0344662\pi\) |
−0.590661 | + | 0.806920i | \(0.701133\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.90226 | − | 15.4192i | −0.421534 | − | 0.730119i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.63896 | + | 0.189469i | −0.124679 | + | 0.00895155i | ||||
\(449\) | − | 12.5892i | − | 0.594122i | −0.954858 | − | 0.297061i | \(-0.903994\pi\) | ||
0.954858 | − | 0.297061i | \(-0.0960065\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.1033 | + | 9.29725i | 0.758276 | + | 0.437791i | ||||
\(452\) | −6.77729 | + | 11.7386i | −0.318777 | + | 0.552138i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.71228i | 0.0803612i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.87783 | + | 1.08417i | −0.0878414 | + | 0.0507153i | −0.543277 | − | 0.839553i | \(-0.682817\pi\) |
0.455436 | + | 0.890269i | \(0.349483\pi\) | |||||||
\(458\) | 5.26142 | + | 3.03768i | 0.245850 | + | 0.141941i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.3032 | 1.59766 | 0.798829 | − | 0.601558i | \(-0.205453\pi\) | ||||
0.798829 | + | 0.601558i | \(0.205453\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 28.2133i | − | 1.31118i | −0.755115 | − | 0.655592i | \(-0.772419\pi\) | ||
0.755115 | − | 0.655592i | \(-0.227581\pi\) | |||||||
\(464\) | −7.70674 | + | 4.44949i | −0.357777 | + | 0.206562i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.56288 | + | 6.17109i | −0.165047 | + | 0.285870i | ||||
\(467\) | 3.64324 | − | 2.10342i | 0.168589 | − | 0.0973349i | −0.413331 | − | 0.910581i | \(-0.635635\pi\) |
0.581920 | + | 0.813246i | \(0.302302\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −29.7977 | − | 14.4647i | −1.37593 | − | 0.667920i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.78522 | − | 4.82415i | 0.128200 | − | 0.222049i | ||||
\(473\) | 4.47167 | − | 7.74515i | 0.205607 | − | 0.356122i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.875396 | − | 0.592835i | 0.0401237 | − | 0.0271725i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −16.2114 | + | 9.35968i | −0.741494 | + | 0.428102i | ||||
\(479\) | −7.35968 | + | 12.7473i | −0.336272 | + | 0.582441i | −0.983728 | − | 0.179662i | \(-0.942500\pi\) |
0.647456 | + | 0.762103i | \(0.275833\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.0086 | + | 15.5934i | −1.23149 | + | 0.710999i | ||||
\(482\) | − | 8.86851i | − | 0.403950i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.31835 | 0.105380 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.62602 | + | 0.938784i | 0.0736821 | + | 0.0425404i | 0.536388 | − | 0.843971i | \(-0.319788\pi\) |
−0.462706 | + | 0.886512i | \(0.653122\pi\) | |||||||
\(488\) | −9.97710 | + | 5.76028i | −0.451642 | + | 0.260756i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.4281i | 0.470613i | 0.971921 | + | 0.235307i | \(0.0756095\pi\) | ||||
−0.971921 | + | 0.235307i | \(0.924391\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.77802 | − | 3.07963i | 0.0800782 | − | 0.138699i | ||||
\(494\) | 0.120118 | + | 0.0693504i | 0.00540438 | + | 0.00312022i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 0.828427i | − | 0.0371975i | ||||||
\(497\) | −0.366481 | − | 5.10442i | −0.0164389 | − | 0.228965i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.8822 | − | 32.7050i | −0.845285 | − | 1.46408i | −0.885374 | − | 0.464880i | \(-0.846097\pi\) |
0.0400890 | − | 0.999196i | \(-0.487236\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.0869 | + | 19.2030i | 0.494832 | + | 0.857074i | ||||
\(503\) | − | 35.8895i | − | 1.60023i | −0.599845 | − | 0.800116i | \(-0.704771\pi\) | ||
0.599845 | − | 0.800116i | \(-0.295229\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.52312 | + | 5.49818i | −0.423354 | + | 0.244424i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.75944 | − | 4.47992i | −0.344270 | − | 0.198764i | ||||
\(509\) | 8.58746 | + | 14.8739i | 0.380633 | + | 0.659275i | 0.991153 | − | 0.132726i | \(-0.0423729\pi\) |
−0.610520 | + | 0.792001i | \(0.709040\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.396469 | − | 0.816735i | 0.0175387 | − | 0.0361302i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.5780 | + | 8.41662i | 0.643008 | + | 0.371241i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.0972 | 0.751932 | ||||||||
\(518\) | −18.8789 | − | 9.16442i | −0.829492 | − | 0.402661i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.26539 | + | 3.92377i | −0.0992484 | + | 0.171903i | −0.911374 | − | 0.411580i | \(-0.864977\pi\) |
0.812125 | + | 0.583483i | \(0.198311\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.2368 | + | 22.9267i | 0.578803 | + | 1.00252i | 0.995617 | + | 0.0935241i | \(0.0298132\pi\) |
−0.416814 | + | 0.908992i | \(0.636853\pi\) | |||||||
\(524\) | −12.7809 | −0.558338 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.1197 | 0.964465 | ||||||||
\(527\) | 0.165520 | + | 0.286690i | 0.00721018 | + | 0.0124884i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.53590 | − | 7.85641i | 0.197213 | − | 0.341583i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.00668373 | + | 0.0930924i | 0.000289777 | + | 0.00403607i | ||||
\(533\) | −24.8131 | −1.07477 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 10.8420 | + | 6.25966i | 0.468305 | + | 0.270376i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.90097 | −0.125070 | ||||||||
\(539\) | −19.1520 | − | 7.65514i | −0.824936 | − | 0.329730i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.16504 | − | 5.48201i | −0.136076 | − | 0.235690i | 0.789932 | − | 0.613194i | \(-0.210116\pi\) |
−0.926008 | + | 0.377504i | \(0.876782\pi\) | |||||||
\(542\) | −15.1244 | − | 8.73205i | −0.649647 | − | 0.375074i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.346065 | + | 0.199801i | −0.0148374 | + | 0.00856639i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 38.5271i | − | 1.64730i | −0.567097 | − | 0.823651i | \(-0.691934\pi\) | ||
0.567097 | − | 0.823651i | \(-0.308066\pi\) | |||||||
\(548\) | −2.76028 | − | 4.78094i | −0.117913 | − | 0.204232i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.156961 | + | 0.271864i | 0.00668676 | + | 0.0115818i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.3234 | − | 18.1971i | −0.524045 | − | 0.773819i | ||||
\(554\) | 4.57650i | 0.194437i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.9202 | − | 10.9236i | −0.802393 | − | 0.463262i | ||||
\(557\) | −4.62144 | + | 8.00456i | −0.195817 | + | 0.339164i | −0.947168 | − | 0.320738i | \(-0.896069\pi\) |
0.751351 | + | 0.659902i | \(0.229402\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.9343i | 0.504765i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.27875 | − | 4.77974i | 0.349218 | − | 0.201621i | ||||
\(563\) | −23.1872 | − | 13.3871i | −0.977225 | − | 0.564201i | −0.0757935 | − | 0.997124i | \(-0.524149\pi\) |
−0.901431 | + | 0.432923i | \(0.857482\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.9262 | −0.459263 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.93426i | 0.0811596i | ||||||||
\(569\) | −39.6604 | + | 22.8979i | −1.66265 | + | 0.959931i | −0.691207 | + | 0.722657i | \(0.742921\pi\) |
−0.971443 | + | 0.237274i | \(0.923746\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.390149 | + | 0.675759i | −0.0163272 | + | 0.0282796i | −0.874074 | − | 0.485794i | \(-0.838531\pi\) |
0.857746 | + | 0.514073i | \(0.171864\pi\) | |||||||
\(572\) | 10.0330 | − | 5.79253i | 0.419499 | − | 0.242198i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.36246 | − | 13.8249i | −0.390781 | − | 0.577039i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.62571 | − | 9.74401i | 0.234201 | − | 0.405648i | −0.724839 | − | 0.688918i | \(-0.758086\pi\) |
0.959040 | + | 0.283270i | \(0.0914192\pi\) | |||||||
\(578\) | −8.42016 | + | 14.5841i | −0.350232 | + | 0.606620i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.96081 | − | 27.3105i | −0.0813480 | − | 1.13303i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.9687 | + | 6.33281i | −0.454279 | + | 0.262278i | ||||
\(584\) | −0.171573 | + | 0.297173i | −0.00709974 | + | 0.0122971i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.0539 | − | 8.11401i | 0.580561 | − | 0.335187i | ||||
\(587\) | 40.1593i | 1.65755i | 0.559582 | + | 0.828775i | \(0.310962\pi\) | ||||
−0.559582 | + | 0.828775i | \(0.689038\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0292237 | −0.00120414 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.86919 | + | 3.96593i | 0.282322 | + | 0.162999i | ||||
\(593\) | 16.5267 | − | 9.54170i | 0.678671 | − | 0.391831i | −0.120683 | − | 0.992691i | \(-0.538509\pi\) |
0.799354 | + | 0.600860i | \(0.205175\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 21.4981i | − | 0.880598i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.33694 | − | 12.7079i | 0.300030 | − | 0.519666i | ||||
\(599\) | −24.6424 | − | 14.2273i | −1.00686 | − | 0.581312i | −0.0965902 | − | 0.995324i | \(-0.530794\pi\) |
−0.910271 | + | 0.414013i | \(0.864127\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 29.2553i | − | 1.19335i | −0.802484 | − | 0.596673i | \(-0.796489\pi\) | ||
0.802484 | − | 0.596673i | \(-0.203511\pi\) | |||||||
\(602\) | −6.64929 | + | 4.50303i | −0.271005 | + | 0.183530i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.47531 | − | 2.55532i | −0.0600297 | − | 0.103974i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.9160 | − | 22.3712i | −0.524246 | − | 0.908020i | −0.999602 | − | 0.0282267i | \(-0.991014\pi\) |
0.475356 | − | 0.879794i | \(-0.342319\pi\) | |||||||
\(608\) | − | 0.0352762i | − | 0.00143064i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.7583 | + | 11.4075i | −0.799337 | + | 0.461498i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.0680 | + | 8.12216i | 0.568201 | + | 0.328051i | 0.756430 | − | 0.654074i | \(-0.226942\pi\) |
−0.188230 | + | 0.982125i | \(0.560275\pi\) | |||||||
\(614\) | 6.18910 | + | 10.7198i | 0.249772 | + | 0.432618i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.01299 | + | 3.40433i | 0.282562 | + | 0.137164i | ||||
\(617\) | −31.8398 | −1.28182 | −0.640911 | − | 0.767615i | \(-0.721443\pi\) | ||||
−0.640911 | + | 0.767615i | \(0.721443\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.01055 | − | 4.62490i | −0.321971 | − | 0.185890i | 0.330300 | − | 0.943876i | \(-0.392850\pi\) |
−0.652271 | + | 0.757986i | \(0.726184\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 22.8625 | 0.916701 | ||||||||
\(623\) | 9.15669 | + | 13.5210i | 0.366855 | + | 0.541708i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.4013 | − | 30.1399i | 0.695495 | − | 1.20463i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.2481 | − | 19.4823i | −0.448849 | − | 0.777429i | ||||
\(629\) | −3.16958 | −0.126379 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.3096 | −0.410421 | −0.205210 | − | 0.978718i | \(-0.565788\pi\) | ||||
−0.205210 | + | 0.978718i | \(0.565788\pi\) | |||||||
\(632\) | 4.15331 | + | 7.19375i | 0.165210 | + | 0.286152i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.39355 | + | 5.87780i | −0.134775 | + | 0.233437i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.2407 | − | 3.93185i | 1.07931 | − | 0.155786i | ||||
\(638\) | 26.2205 | 1.03808 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.1181 | + | 6.41906i | 0.439140 | + | 0.253538i | 0.703233 | − | 0.710960i | \(-0.251739\pi\) |
−0.264093 | + | 0.964497i | \(0.585072\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.96224 | 0.353436 | 0.176718 | − | 0.984262i | \(-0.443452\pi\) | ||||
0.176718 | + | 0.984262i | \(0.443452\pi\) | |||||||
\(644\) | 9.84873 | − | 0.707107i | 0.388094 | − | 0.0278639i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.00704821 | + | 0.0122079i | 0.000277308 | + | 0.000480312i | ||||
\(647\) | −39.2919 | − | 22.6852i | −1.54472 | − | 0.891846i | −0.998531 | − | 0.0541854i | \(-0.982744\pi\) |
−0.546191 | − | 0.837660i | \(-0.683923\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.2142 | + | 8.20656i | −0.557955 | + | 0.322136i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 22.8070i | − | 0.893192i | ||||||
\(653\) | 16.3997 | + | 28.4051i | 0.641769 | + | 1.11158i | 0.985038 | + | 0.172340i | \(0.0551326\pi\) |
−0.343268 | + | 0.939237i | \(0.611534\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.15539 | + | 5.46530i | 0.123197 | + | 0.213384i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13.8110 | − | 6.70430i | −0.538409 | − | 0.261361i | ||||
\(659\) | 18.7103i | 0.728850i | 0.931233 | + | 0.364425i | \(0.118734\pi\) | ||||
−0.931233 | + | 0.364425i | \(0.881266\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.41761 | + | 4.28256i | 0.288512 | + | 0.166572i | 0.637270 | − | 0.770640i | \(-0.280063\pi\) |
−0.348759 | + | 0.937213i | \(0.613397\pi\) | |||||||
\(662\) | −5.56985 | + | 9.64726i | −0.216478 | + | 0.374951i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.3490i | 0.401618i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.7620 | − | 16.6057i | 1.11367 | − | 0.642976i | ||||
\(668\) | 7.66398 | + | 4.42480i | 0.296528 | + | 0.171201i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33.9449 | 1.31043 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.179617i | 0.00692372i | 0.999994 | + | 0.00346186i | \(0.00110195\pi\) | ||||
−0.999994 | + | 0.00346186i | \(0.998898\pi\) | |||||||
\(674\) | 1.37794 | − | 0.795555i | 0.0530763 | − | 0.0306436i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.22973 | + | 2.12995i | −0.0472973 | + | 0.0819213i | ||||
\(677\) | −35.8623 | + | 20.7051i | −1.37830 | + | 0.795763i | −0.991955 | − | 0.126591i | \(-0.959596\pi\) |
−0.386346 | + | 0.922354i | \(0.626263\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.2586 | − | 2.96224i | 1.58336 | − | 0.113680i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.22047 | + | 2.11391i | −0.0467340 | + | 0.0809457i | ||||
\(683\) | 21.7026 | − | 37.5900i | 0.830427 | − | 1.43834i | −0.0672723 | − | 0.997735i | \(-0.521430\pi\) |
0.897700 | − | 0.440608i | \(-0.145237\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12.4691 | + | 13.6938i | 0.476073 | + | 0.522834i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.62863 | − | 1.51764i | 0.100215 | − | 0.0578594i | ||||
\(689\) | 8.45069 | − | 14.6370i | 0.321946 | − | 0.557626i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.8728 | + | 9.74150i | −0.641871 | + | 0.370584i | −0.785335 | − | 0.619071i | \(-0.787509\pi\) |
0.143464 | + | 0.989656i | \(0.454176\pi\) | |||||||
\(692\) | − | 7.73686i | − | 0.294111i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15.4568 | −0.586732 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.18394 | − | 1.26090i | −0.0827228 | − | 0.0477600i | ||||
\(698\) | 0.506675 | − | 0.292529i | 0.0191779 | − | 0.0110724i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 47.0245i | − | 1.77609i | −0.459755 | − | 0.888046i | \(-0.652063\pi\) | ||
0.459755 | − | 0.888046i | \(-0.347937\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.139903 | − | 0.242319i | 0.00527653 | − | 0.00913922i | ||||
\(704\) | −2.55171 | − | 1.47323i | −0.0961713 | − | 0.0555245i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.67576i | 0.138339i | ||||||||
\(707\) | −20.8539 | + | 42.9595i | −0.784292 | + | 1.61566i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.2227 | − | 41.9549i | −0.909701 | − | 1.57565i | −0.814480 | − | 0.580192i | \(-0.802977\pi\) |
−0.0952213 | − | 0.995456i | \(-0.530356\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.08604 | − | 5.34519i | −0.115654 | − | 0.200319i | ||||
\(713\) | 3.09173i | 0.115786i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.417291 | − | 0.240923i | 0.0155949 | − | 0.00900372i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.4069 | + | 10.0499i | 0.649620 | + | 0.375058i | ||||
\(719\) | 20.6632 | + | 35.7897i | 0.770606 | + | 1.33473i | 0.937231 | + | 0.348709i | \(0.113380\pi\) |
−0.166625 | + | 0.986020i | \(0.553287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.6400 | − | 18.6646i | −0.470739 | − | 0.695106i | ||||
\(722\) | 18.9988 | 0.707060 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.12069 | + | 1.22438i | 0.0788148 | + | 0.0455037i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.7905 | −0.622726 | −0.311363 | − | 0.950291i | \(-0.600786\pi\) | ||||
−0.311363 | + | 0.950291i | \(0.600786\pi\) | |||||||
\(728\) | −10.3760 | + | 0.744963i | −0.384560 | + | 0.0276102i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.606451 | + | 1.05040i | −0.0224304 | + | 0.0388506i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.3600 | + | 26.6043i | 0.567335 | + | 0.982652i | 0.996828 | + | 0.0795826i | \(0.0253587\pi\) |
−0.429494 | + | 0.903070i | \(0.641308\pi\) | |||||||
\(734\) | −19.9377 | −0.735914 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.73205 | −0.137565 | ||||||||
\(737\) | −18.4438 | − | 31.9457i | −0.679388 | − | 1.17673i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.3876 | − | 26.6521i | 0.566041 | − | 0.980412i | −0.430911 | − | 0.902395i | \(-0.641808\pi\) |
0.996952 | − | 0.0780176i | \(-0.0248590\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.3438 | − | 0.814447i | 0.416443 | − | 0.0298993i | ||||
\(743\) | −33.3616 | −1.22392 | −0.611960 | − | 0.790889i | \(-0.709619\pi\) | ||||
−0.611960 | + | 0.790889i | \(0.709619\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −29.2856 | − | 16.9081i | −1.07222 | − | 0.619048i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.17741 | 0.0430504 | ||||||||
\(749\) | −25.3025 | − | 37.3624i | −0.924533 | − | 1.36519i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.9452 | + | 27.6179i | 0.581849 | + | 1.00779i | 0.995260 | + | 0.0972480i | \(0.0310040\pi\) |
−0.413411 | + | 0.910545i | \(0.635663\pi\) | |||||||
\(752\) | 5.02520 | + | 2.90130i | 0.183250 | + | 0.105800i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −30.3018 | + | 17.4947i | −1.10353 | + | 0.637121i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 10.9065i | − | 0.396404i | −0.980161 | − | 0.198202i | \(-0.936490\pi\) | ||
0.980161 | − | 0.198202i | \(-0.0635102\pi\) | |||||||
\(758\) | 13.3807 | + | 23.1761i | 0.486010 | + | 0.841793i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.2097 | + | 21.1479i | 0.442602 | + | 0.766610i | 0.997882 | − | 0.0650543i | \(-0.0207220\pi\) |
−0.555280 | + | 0.831664i | \(0.687389\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.5160 | − | 27.8433i | 0.489313 | − | 1.00800i | ||||
\(764\) | − | 4.49457i | − | 0.162608i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.1310 | − | 9.89060i | −0.618969 | − | 0.357362i | ||||
\(767\) | 10.9511 | − | 18.9678i | 0.395421 | − | 0.684889i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.9416i | 0.827294i | 0.910437 | + | 0.413647i | \(0.135745\pi\) | ||||
−0.910437 | + | 0.413647i | \(0.864255\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10.8859 | − | 6.28497i | 0.391791 | − | 0.226201i | ||||
\(773\) | −39.2894 | − | 22.6837i | −1.41314 | − | 0.815877i | −0.417458 | − | 0.908696i | \(-0.637079\pi\) |
−0.995683 | + | 0.0928193i | \(0.970412\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −15.6344 | −0.561243 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 5.18670i | − | 0.185952i | ||||||
\(779\) | 0.192795 | − | 0.111310i | 0.00690760 | − | 0.00398810i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.84961 | − | 4.93566i | 0.101967 | − | 0.176612i | ||||
\(782\) | 1.29153 | − | 0.745667i | 0.0461851 | − | 0.0266650i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.33013 | − | 5.50000i | −0.154647 | − | 0.196429i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.67335 | + | 2.89834i | −0.0596487 | + | 0.103314i | −0.894308 | − | 0.447452i | \(-0.852331\pi\) |
0.834659 | + | 0.550767i | \(0.185665\pi\) | |||||||
\(788\) | −6.68740 | + | 11.5829i | −0.238229 | + | 0.412625i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.7700 | + | 2.56817i | −1.27183 | + | 0.0913136i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.2285 | + | 22.6486i | −1.39304 | + | 0.804274i | ||||
\(794\) | 2.88259 | − | 4.99280i | 0.102299 | − | 0.177188i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −23.5169 | + | 13.5775i | −0.833535 | + | 0.481242i | ||||
\(797\) | − | 36.5402i | − | 1.29432i | −0.762354 | − | 0.647160i | \(-0.775956\pi\) | ||
0.762354 | − | 0.647160i | \(-0.224044\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.31873 | −0.0820308 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15.4361 | − | 8.91202i | −0.545067 | − | 0.314695i | ||||
\(803\) | 0.875609 | − | 0.505533i | 0.0308996 | − | 0.0178399i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 3.25725i | − | 0.114732i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.02458 | − | 15.6310i | 0.317484 | − | 0.549898i | ||||
\(809\) | 41.5179 | + | 23.9704i | 1.45969 | + | 0.842753i | 0.998996 | − | 0.0448048i | \(-0.0142666\pi\) |
0.460696 | + | 0.887558i | \(0.347600\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.6994i | 1.74518i | 0.488452 | + | 0.872591i | \(0.337562\pi\) | ||||
−0.488452 | + | 0.872591i | \(0.662438\pi\) | |||||||
\(812\) | −21.1808 | − | 10.2818i | −0.743301 | − | 0.360822i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11.6855 | − | 20.2398i | −0.409575 | − | 0.709405i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.0535365 | − | 0.0927279i | −0.00187300 | − | 0.00324414i | ||||
\(818\) | − | 32.9802i | − | 1.15312i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.6520 | − | 11.3461i | 0.685858 | − | 0.395980i | −0.116200 | − | 0.993226i | \(-0.537071\pi\) |
0.802059 | + | 0.597245i | \(0.203738\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.76628 | − | 1.59711i | −0.0964266 | − | 0.0556719i | 0.451011 | − | 0.892518i | \(-0.351063\pi\) |
−0.547438 | + | 0.836846i | \(0.684397\pi\) | |||||||
\(824\) | 4.26002 | + | 7.37857i | 0.148405 | + | 0.257045i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.7002 | − | 1.05543i | 0.511484 | − | 0.0367229i | ||||
\(827\) | 29.7259 | 1.03367 | 0.516836 | − | 0.856084i | \(-0.327110\pi\) | ||||
0.516836 | + | 0.856084i | \(0.327110\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.8588 | − | 15.5069i | −0.932845 | − | 0.538578i | −0.0451348 | − | 0.998981i | \(-0.514372\pi\) |
−0.887710 | + | 0.460403i | \(0.847705\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.93185 | 0.136312 | ||||||||
\(833\) | 2.59741 | + | 1.03820i | 0.0899950 | + | 0.0359713i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.0519700 | + | 0.0900147i | −0.00179742 | + | 0.00311322i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 7.61434 | + | 13.1884i | 0.263033 | + | 0.455586i | ||||
\(839\) | −35.8462 | −1.23755 | −0.618773 | − | 0.785570i | \(-0.712370\pi\) | ||||
−0.618773 | + | 0.785570i | \(0.712370\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −50.1918 | −1.73075 | ||||||||
\(842\) | −8.49697 | − | 14.7172i | −0.292825 | − | 0.507188i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.20915 | + | 15.9507i | −0.316992 | + | 0.549046i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.43942 | + | 5.07875i | 0.118180 | + | 0.174508i | ||||
\(848\) | −4.29858 | −0.147614 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.6361 | − | 14.8010i | −0.878796 | − | 0.507373i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.8818 | −0.783456 | −0.391728 | − | 0.920081i | \(-0.628123\pi\) | ||||
−0.391728 | + | 0.920081i | \(0.628123\pi\) | |||||||
\(854\) | −27.4205 | − | 13.3108i | −0.938311 | − | 0.455486i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.52761 | + | 14.7702i | 0.291468 | + | 0.504837i | ||||
\(857\) | −29.2012 | − | 16.8593i | −0.997494 | − | 0.575904i | −0.0899883 | − | 0.995943i | \(-0.528683\pi\) |
−0.907506 | + | 0.420039i | \(0.862016\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.3926 | + | 9.46427i | −0.559308 | + | 0.322917i | −0.752868 | − | 0.658172i | \(-0.771330\pi\) |
0.193560 | + | 0.981088i | \(0.437997\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.8768i | 0.608888i | ||||||||
\(863\) | 2.62854 | + | 4.55277i | 0.0894767 | + | 0.154978i | 0.907290 | − | 0.420505i | \(-0.138147\pi\) |
−0.817813 | + | 0.575484i | \(0.804814\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.78194 | − | 4.81846i | −0.0945341 | − | 0.163738i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.81481 | − | 1.22902i | 0.0615987 | − | 0.0417158i | ||||
\(869\) | − | 24.4752i | − | 0.830263i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42.6293 | + | 24.6120i | 1.44444 | + | 0.833947i | ||||
\(872\) | −5.84909 | + | 10.1309i | −0.198075 | + | 0.343076i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.131652i | 0.00445321i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.2170 | + | 20.3326i | −1.18919 | + | 0.686582i | −0.958124 | − | 0.286355i | \(-0.907556\pi\) |
−0.231071 | + | 0.972937i | \(0.574223\pi\) | |||||||
\(878\) | 9.53568 | + | 5.50543i | 0.321814 | + | 0.185799i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.01828 | 0.0343067 | 0.0171533 | − | 0.999853i | \(-0.494540\pi\) | ||||
0.0171533 | + | 0.999853i | \(0.494540\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 11.0436i | − | 0.371647i | −0.982583 | − | 0.185823i | \(-0.940505\pi\) | ||
0.982583 | − | 0.185823i | \(-0.0594952\pi\) | |||||||
\(884\) | −1.36068 | + | 0.785587i | −0.0457645 | + | 0.0264222i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.49233 | − | 14.7091i | 0.285305 | − | 0.494163i | ||||
\(887\) | −20.8698 | + | 12.0492i | −0.700738 | + | 0.404571i | −0.807622 | − | 0.589700i | \(-0.799246\pi\) |
0.106884 | + | 0.994271i | \(0.465913\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.69761 | − | 23.6446i | −0.0569359 | − | 0.793015i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.90226 | + | 15.4192i | −0.298070 | + | 0.516272i | ||||
\(893\) | 0.102347 | − | 0.177270i | 0.00342491 | − | 0.00593211i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.48356 | + | 2.19067i | 0.0495624 | + | 0.0731852i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.9026 | + | 6.29461i | −0.363824 | + | 0.210054i | ||||
\(899\) | 3.68608 | − | 6.38447i | 0.122938 | − | 0.212934i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.48759 | − | 0.858860i | 0.0495588 | − | 0.0286128i | ||||
\(902\) | − | 18.5945i | − | 0.619129i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.5546 | 0.450819 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.0338 | + | 8.10243i | 0.465985 | + | 0.269037i | 0.714558 | − | 0.699577i | \(-0.246628\pi\) |
−0.248572 | + | 0.968613i | \(0.579961\pi\) | |||||||
\(908\) | 1.48288 | − | 0.856140i | 0.0492110 | − | 0.0284120i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 21.4586i | − | 0.710955i | −0.934685 | − | 0.355477i | \(-0.884318\pi\) | ||
0.934685 | − | 0.355477i | \(-0.115682\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.2465 | − | 26.4076i | 0.504584 | − | 0.873965i | ||||
\(914\) | 1.87783 | + | 1.08417i | 0.0621133 | + | 0.0358611i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 6.07536i | − | 0.200736i | ||||||
\(917\) | −18.9613 | − | 27.9988i | −0.626159 | − | 0.924603i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.5164 | − | 51.1240i | −0.973657 | − | 1.68642i | −0.684297 | − | 0.729203i | \(-0.739891\pi\) |
−0.289360 | − | 0.957220i | \(-0.593442\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.1516 | − | 29.7074i | −0.564857 | − | 0.978362i | ||||
\(923\) | 7.60521i | 0.250328i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −24.4335 | + | 14.1067i | −0.802933 | + | 0.463574i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.70674 | + | 4.44949i | 0.252986 | + | 0.146062i | ||||
\(929\) | 12.3197 | + | 21.3383i | 0.404195 | + | 0.700087i | 0.994227 | − | 0.107293i | \(-0.0342183\pi\) |
−0.590032 | + | 0.807380i | \(0.700885\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.194019 | + | 0.152750i | −0.00635872 | + | 0.00500619i | ||||
\(932\) | 7.12576 | 0.233412 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.64324 | − | 2.10342i | −0.119210 | − | 0.0688262i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.5496 | 1.71672 | 0.858360 | − | 0.513048i | \(-0.171484\pi\) | ||||
0.858360 | + | 0.513048i | \(0.171484\pi\) | |||||||
\(938\) | 2.37202 | + | 33.0379i | 0.0774491 | + | 1.07873i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.752551 | − | 1.30346i | 0.0245325 | − | 0.0424915i | −0.853499 | − | 0.521095i | \(-0.825524\pi\) |
0.878031 | + | 0.478604i | \(0.158857\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.7761 | − | 20.3968i | −0.383482 | − | 0.664211i | ||||
\(944\) | −5.57045 | −0.181303 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.94333 | −0.290773 | ||||||||
\(947\) | −5.68191 | − | 9.84136i | −0.184637 | − | 0.319801i | 0.758817 | − | 0.651304i | \(-0.225778\pi\) |
−0.943454 | + | 0.331503i | \(0.892444\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.674599 | + | 1.16844i | −0.0218984 | + | 0.0379292i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.951108 | − | 0.461698i | −0.0308256 | − | 0.0149637i | ||||
\(953\) | 21.9184 | 0.710006 | 0.355003 | − | 0.934865i | \(-0.384480\pi\) | ||||
0.355003 | + | 0.934865i | \(0.384480\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 16.2114 | + | 9.35968i | 0.524316 | + | 0.302714i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.7194 | 0.475561 | ||||||||
\(959\) | 6.37842 | − | 13.1397i | 0.205970 | − | 0.424303i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.1569 | − | 26.2524i | −0.488931 | − | 0.846853i | ||||
\(962\) | 27.0086 | + | 15.5934i | 0.870793 | + | 0.502752i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.68036 | + | 4.43426i | −0.247368 | + | 0.142818i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.6634i | 0.696649i | 0.937374 | + | 0.348324i | \(0.113249\pi\) | ||||
−0.937374 | + | 0.348324i | \(0.886751\pi\) | |||||||
\(968\) | −1.15918 | − | 2.00775i | −0.0372573 | − | 0.0645316i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.0858379 | + | 0.148676i | 0.00275467 | + | 0.00477123i | 0.867399 | − | 0.497612i | \(-0.165790\pi\) |
−0.864645 | + | 0.502384i | \(0.832456\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.13934 | − | 57.6536i | −0.132701 | − | 1.84829i | ||||
\(974\) | − | 1.87757i | − | 0.0601612i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.97710 | + | 5.76028i | 0.319359 | + | 0.184382i | ||||
\(977\) | 5.61642 | − | 9.72792i | 0.179685 | − | 0.311224i | −0.762088 | − | 0.647474i | \(-0.775825\pi\) |
0.941773 | + | 0.336250i | \(0.109159\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.1858i | 0.581222i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.03100 | − | 5.21405i | 0.288191 | − | 0.166387i | ||||
\(983\) | −23.2026 | − | 13.3960i | −0.740048 | − | 0.427267i | 0.0820385 | − | 0.996629i | \(-0.473857\pi\) |
−0.822087 | + | 0.569362i | \(0.807190\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.55605 | −0.113248 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 0.138701i | − | 0.00441266i | ||||||
\(989\) | −9.81017 | + | 5.66390i | −0.311945 | + | 0.180102i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.99635 | + | 12.1180i | −0.222246 | + | 0.384942i | −0.955490 | − | 0.295024i | \(-0.904672\pi\) |
0.733243 | + | 0.679966i | \(0.238006\pi\) | |||||||
\(992\) | −0.717439 | + | 0.414214i | −0.0227787 | + | 0.0131513i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.23732 | + | 2.86959i | −0.134400 | + | 0.0910179i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.7740 | + | 34.2497i | −0.626250 | + | 1.08470i | 0.362047 | + | 0.932160i | \(0.382078\pi\) |
−0.988298 | + | 0.152538i | \(0.951255\pi\) | |||||||
\(998\) | −18.8822 | + | 32.7050i | −0.597707 | + | 1.03526i | ||||
\(999\) | 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 | 3150.2.bp.a.899.1 | 8 | ||
3.2 | odd | 2 | 3150.2.bp.f.899.1 | 8 | |||
5.2 | odd | 4 | 3150.2.bf.b.1151.3 | 8 | |||
5.3 | odd | 4 | 630.2.be.a.521.2 | yes | 8 | ||
5.4 | even | 2 | 3150.2.bp.d.899.4 | 8 | |||
7.5 | odd | 6 | 3150.2.bp.c.1349.4 | 8 | |||
15.2 | even | 4 | 3150.2.bf.c.1151.1 | 8 | |||
15.8 | even | 4 | 630.2.be.b.521.4 | yes | 8 | ||
15.14 | odd | 2 | 3150.2.bp.c.899.4 | 8 | |||
21.5 | even | 6 | 3150.2.bp.d.1349.4 | 8 | |||
35.3 | even | 12 | 4410.2.b.b.881.3 | 8 | |||
35.12 | even | 12 | 3150.2.bf.c.1601.1 | 8 | |||
35.18 | odd | 12 | 4410.2.b.e.881.3 | 8 | |||
35.19 | odd | 6 | 3150.2.bp.f.1349.1 | 8 | |||
35.33 | even | 12 | 630.2.be.b.341.4 | yes | 8 | ||
105.38 | odd | 12 | 4410.2.b.e.881.6 | 8 | |||
105.47 | odd | 12 | 3150.2.bf.b.1601.3 | 8 | |||
105.53 | even | 12 | 4410.2.b.b.881.6 | 8 | |||
105.68 | odd | 12 | 630.2.be.a.341.2 | ✓ | 8 | ||
105.89 | even | 6 | inner | 3150.2.bp.a.1349.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.be.a.341.2 | ✓ | 8 | 105.68 | odd | 12 | ||
630.2.be.a.521.2 | yes | 8 | 5.3 | odd | 4 | ||
630.2.be.b.341.4 | yes | 8 | 35.33 | even | 12 | ||
630.2.be.b.521.4 | yes | 8 | 15.8 | even | 4 | ||
3150.2.bf.b.1151.3 | 8 | 5.2 | odd | 4 | |||
3150.2.bf.b.1601.3 | 8 | 105.47 | odd | 12 | |||
3150.2.bf.c.1151.1 | 8 | 15.2 | even | 4 | |||
3150.2.bf.c.1601.1 | 8 | 35.12 | even | 12 | |||
3150.2.bp.a.899.1 | 8 | 1.1 | even | 1 | trivial | ||
3150.2.bp.a.1349.1 | 8 | 105.89 | even | 6 | inner | ||
3150.2.bp.c.899.4 | 8 | 15.14 | odd | 2 | |||
3150.2.bp.c.1349.4 | 8 | 7.5 | odd | 6 | |||
3150.2.bp.d.899.4 | 8 | 5.4 | even | 2 | |||
3150.2.bp.d.1349.4 | 8 | 21.5 | even | 6 | |||
3150.2.bp.f.899.1 | 8 | 3.2 | odd | 2 | |||
3150.2.bp.f.1349.1 | 8 | 35.19 | odd | 6 | |||
4410.2.b.b.881.3 | 8 | 35.3 | even | 12 | |||
4410.2.b.b.881.6 | 8 | 105.53 | even | 12 | |||
4410.2.b.e.881.3 | 8 | 35.18 | odd | 12 | |||
4410.2.b.e.881.6 | 8 | 105.38 | odd | 12 |