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 | 1349.4 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.1349 |
Dual form | 3150.2.bp.d.899.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 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 | −0.832650 | − | 0.553800i | \(-0.813177\pi\) |
0.0632797 | + | 0.997996i | \(0.479844\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.93185 | −1.09050 | −0.545250 | − | 0.838274i | \(-0.683565\pi\) | ||||
−0.545250 | + | 0.838274i | \(0.683565\pi\) | |||||||
\(14\) | 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 | \(-0.682098\pi\) |
0.457446 | + | 0.889237i | \(0.348764\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0305501 | − | 0.0176381i | −0.00700867 | − | 0.00404646i | 0.496492 | − | 0.868042i | \(-0.334621\pi\) |
−0.503500 | + | 0.863995i | \(0.667955\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.94646i | 0.628188i | ||||||||
\(23\) | −1.86603 | + | 3.23205i | −0.389093 | + | 0.673929i | −0.992328 | − | 0.123635i | \(-0.960545\pi\) |
0.603235 | + | 0.797564i | \(0.293878\pi\) | |||||||
\(24\) | 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 | \(0.309530\pi\) | ||||
−0.563304 | + | 0.826250i | \(0.690470\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.717439 | − | 0.414214i | 0.128856 | − | 0.0743950i | −0.434187 | − | 0.900823i | \(-0.642964\pi\) |
0.563042 | + | 0.826428i | \(0.309631\pi\) | |||||||
\(32\) | 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 | \(-0.107266\pi\) |
0.185532 | + | 0.982638i | \(0.440599\pi\) | |||||||
\(38\) | −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 | \(-0.194241\pi\) |
−0.0865180 | + | 0.996250i | \(0.527574\pi\) | |||||||
\(48\) | 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 | \(-0.262062\pi\) |
−0.975038 | + | 0.222039i | \(0.928729\pi\) | |||||||
\(54\) | 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 | 0.988389 | − | 0.151946i | \(-0.0485540\pi\) |
−0.625784 | + | 0.779997i | \(0.715221\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.97710 | − | 5.76028i | −1.27744 | − | 0.737528i | −0.301060 | − | 0.953605i | \(-0.597340\pi\) |
−0.976376 | + | 0.216077i | \(0.930674\pi\) | |||||||
\(62\) | − | 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 | \(-0.943799\pi\) |
−0.340113 | + | 0.940385i | \(0.610465\pi\) | |||||||
\(68\) | 0.346065 | + | 0.199801i | 0.0419666 | + | 0.0242294i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.93426i | − | 0.229554i | −0.993391 | − | 0.114777i | \(-0.963385\pi\) | ||
0.993391 | − | 0.114777i | \(-0.0366153\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.171573 | + | 0.297173i | 0.0200811 | + | 0.0347815i | 0.875891 | − | 0.482508i | \(-0.160274\pi\) |
−0.855810 | + | 0.517290i | \(0.826941\pi\) | |||||||
\(74\) | 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 | −0.532017 | − | 0.846734i | \(-0.678566\pi\) |
0.999301 | + | 0.0373736i | \(0.0118992\pi\) | |||||||
\(80\) | 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 | −0.981939 | − | 0.189197i | \(-0.939411\pi\) |
0.654819 | + | 0.755786i | \(0.272745\pi\) | |||||||
\(90\) | 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 | \(-0.208143\pi\) | ||||
0.793718 | + | 0.608286i | \(0.208143\pi\) | |||||||
\(98\) | 4.33013 | − | 5.50000i | 0.437409 | − | 0.555584i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.02458 | + | 15.6310i | 0.897979 | + | 1.55535i | 0.830074 | + | 0.557654i | \(0.188298\pi\) |
0.0679057 | + | 0.997692i | \(0.478368\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.26002 | + | 7.37857i | −0.419752 | + | 0.727032i | −0.995914 | − | 0.0903031i | \(-0.971216\pi\) |
0.576162 | + | 0.817336i | \(0.304550\pi\) | |||||||
\(104\) | 3.93185 | 0.385550 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.29858 | −0.417515 | ||||||||
\(107\) | −8.52761 | + | 14.7702i | −0.824395 | + | 1.42789i | 0.0779862 | + | 0.996954i | \(0.475151\pi\) |
−0.902381 | + | 0.430939i | \(0.858182\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.84909 | − | 10.1309i | −0.560241 | − | 0.970366i | −0.997475 | − | 0.0710185i | \(-0.977375\pi\) |
0.437234 | − | 0.899348i | \(-0.355958\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.48356 | + | 2.19067i | −0.140184 | + | 0.206999i | ||||
\(113\) | −13.5546 | −1.27511 | −0.637554 | − | 0.770405i | \(-0.720054\pi\) | ||||
−0.637554 | + | 0.770405i | \(0.720054\pi\) | |||||||
\(114\) | 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 | −0.439297 | − | 0.898342i | \(-0.644773\pi\) |
0.997635 | − | 0.0687282i | \(-0.0218941\pi\) | |||||||
\(132\) | 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 | \(-0.0908870\pi\) |
−0.723686 | + | 0.690129i | \(0.757554\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 21.8471i | − | 1.85305i | −0.376235 | − | 0.926524i | \(-0.622782\pi\) | ||
0.376235 | − | 0.926524i | \(-0.377218\pi\) | |||||||
\(140\) | 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 | −0.999552 | − | 0.0299204i | \(-0.990475\pi\) |
−0.525688 | − | 0.850677i | \(-0.676192\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.47531 | − | 2.55532i | −0.120059 | − | 0.207949i | 0.799732 | − | 0.600358i | \(-0.204975\pi\) |
−0.919791 | + | 0.392409i | \(0.871642\pi\) | |||||||
\(152\) | 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 | 0.830430 | + | 0.557123i | \(0.188095\pi\) |
0.0672682 | + | 0.997735i | \(0.478572\pi\) | |||||||
\(158\) | −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 | 0.998365 | + | 0.0571664i | \(0.0182066\pi\) |
0.548690 | + | 0.836026i | \(0.315127\pi\) | |||||||
\(164\) | 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 | \(-0.238310\pi\) |
−0.223178 | + | 0.974778i | \(0.571643\pi\) | |||||||
\(174\) | 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 | −0.515514 | − | 0.856881i | \(-0.672399\pi\) |
0.484324 | + | 0.874889i | \(0.339066\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.44876i | 0.182015i | 0.995850 | + | 0.0910075i | \(0.0290087\pi\) | ||||
−0.995850 | + | 0.0910075i | \(0.970991\pi\) | |||||||
\(182\) | −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 | 0.352523 | − | 0.935803i | \(-0.385324\pi\) |
−0.634168 | + | 0.773195i | \(0.718657\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.8859 | − | 6.28497i | 0.783583 | − | 0.452402i | −0.0541158 | − | 0.998535i | \(-0.517234\pi\) |
0.837698 | + | 0.546133i | \(0.183901\pi\) | |||||||
\(194\) | 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 | \(-0.658080\pi\) | ||||
−0.476458 | + | 0.879197i | \(0.658080\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.5169 | − | 13.5775i | 1.66707 | − | 0.962483i | 0.697864 | − | 0.716231i | \(-0.254134\pi\) |
0.969206 | − | 0.246253i | \(-0.0791993\pi\) | |||||||
\(200\) | 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 | \(-0.703300\pi\) | ||||
−0.596140 | + | 0.802881i | \(0.703300\pi\) | |||||||
\(224\) | 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 | \(-0.648569\pi\) |
0.548403 | + | 0.836214i | \(0.315236\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.26142 | − | 3.03768i | −0.347684 | − | 0.200736i | 0.315981 | − | 0.948766i | \(-0.397667\pi\) |
−0.663665 | + | 0.748030i | \(0.731000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 8.89898i | − | 0.584247i | ||||||
\(233\) | 3.56288 | − | 6.17109i | 0.233412 | − | 0.404282i | −0.725398 | − | 0.688330i | \(-0.758344\pi\) |
0.958810 | + | 0.284048i | \(0.0916775\pi\) | |||||||
\(234\) | 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 | \(0.206998\pi\) | ||||
−0.795900 | + | 0.605427i | \(0.793002\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.68036 | − | 4.43426i | 0.494735 | − | 0.285636i | −0.231802 | − | 0.972763i | \(-0.574462\pi\) |
0.726537 | + | 0.687128i | \(0.241129\pi\) | |||||||
\(242\) | 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 | \(-0.157393\pi\) |
0.0291289 | + | 0.999576i | \(0.490727\pi\) | |||||||
\(258\) | 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 | 0.974376 | + | 0.224926i | \(0.0722142\pi\) |
−0.292396 | + | 0.956297i | \(0.594452\pi\) | |||||||
\(264\) | 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 | 0.906851 | − | 0.421452i | \(-0.138479\pi\) |
−0.818413 | + | 0.574630i | \(0.805146\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1244 | + | 8.73205i | 0.918739 | + | 0.530434i | 0.883233 | − | 0.468935i | \(-0.155362\pi\) |
0.0355066 | + | 0.999369i | \(0.488696\pi\) | |||||||
\(272\) | − | 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 | \(-0.622764\pi\) |
0.614319 | + | 0.789057i | \(0.289431\pi\) | |||||||
\(278\) | −18.9202 | − | 10.9236i | −1.13476 | − | 0.655152i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 9.55948i | − | 0.570271i | −0.958487 | − | 0.285135i | \(-0.907961\pi\) | ||
0.958487 | − | 0.285135i | \(-0.0920386\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.46311 | − | 9.46238i | −0.324748 | − | 0.562480i | 0.656713 | − | 0.754140i | \(-0.271946\pi\) |
−0.981461 | + | 0.191660i | \(0.938613\pi\) | |||||||
\(284\) | −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 | \(-0.385083\pi\) | ||||
0.353231 | + | 0.935536i | \(0.385083\pi\) | |||||||
\(308\) | 6.45473 | + | 4.37127i | 0.367792 | + | 0.249076i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.4312 | − | 19.7995i | −0.648206 | − | 1.12272i | −0.983551 | − | 0.180630i | \(-0.942186\pi\) |
0.335346 | − | 0.942095i | \(-0.391147\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.4013 | + | 30.1399i | −0.983578 | + | 1.70361i | −0.335487 | + | 0.942045i | \(0.608901\pi\) |
−0.648091 | + | 0.761563i | \(0.724432\pi\) | |||||||
\(314\) | 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 | \(-0.772290\pi\) |
0.945449 | + | 0.325769i | \(0.105623\pi\) | |||||||
\(318\) | 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 | −0.977516 | − | 0.210862i | \(-0.932373\pi\) |
0.671369 | + | 0.741123i | \(0.265706\pi\) | |||||||
\(332\) | 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 | \(-0.302844\pi\) |
−0.995416 | + | 0.0956388i | \(0.969511\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 0.585057i | − | 0.0313174i | −0.999877 | − | 0.0156587i | \(-0.995015\pi\) | ||
0.999877 | − | 0.0156587i | \(-0.00498452\pi\) | |||||||
\(350\) | 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 | \(-0.635480\pi\) |
0.582317 | + | 0.812962i | \(0.302146\pi\) | |||||||
\(354\) | 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 | −0.0354812 | − | 0.999370i | \(-0.511296\pi\) |
−0.883221 | + | 0.468958i | \(0.844630\pi\) | |||||||
\(360\) | 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 | −0.999720 | − | 0.0236826i | \(-0.992461\pi\) |
0.479350 | − | 0.877624i | \(-0.340872\pi\) | |||||||
\(368\) | −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 | −0.999816 | − | 0.0192016i | \(-0.993888\pi\) |
−0.516537 | − | 0.856265i | \(-0.672779\pi\) | |||||||
\(374\) | −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 | \(-0.501983\pi\) |
−0.869124 | + | 0.494594i | \(0.835317\pi\) | |||||||
\(384\) | 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 | −0.381787 | − | 0.924250i | \(-0.624691\pi\) |
0.609531 | + | 0.792762i | \(0.291358\pi\) | |||||||
\(390\) | 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 | \(-0.879546\pi\) |
0.784578 | + | 0.620030i | \(0.212880\pi\) | |||||||
\(398\) | − | 27.1550i | − | 1.36116i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.4361 | + | 8.91202i | 0.770841 | + | 0.445045i | 0.833175 | − | 0.553010i | \(-0.186521\pi\) |
−0.0623335 | + | 0.998055i | \(0.519854\pi\) | |||||||
\(402\) | 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 | 0.416681 | − | 0.909053i | \(-0.363193\pi\) |
0.995603 | + | 0.0936705i | \(0.0298600\pi\) | |||||||
\(410\) | 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 | −0.824150 | − | 0.566372i | \(-0.808347\pi\) |
0.0784178 | + | 0.996921i | \(0.475013\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.56388 | −0.267383 | −0.133691 | − | 0.991023i | \(-0.542683\pi\) | ||||
−0.133691 | + | 0.991023i | \(0.542683\pi\) | |||||||
\(434\) | 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 | 0.254874 | − | 0.966974i | \(-0.417966\pi\) |
−0.709987 | + | 0.704214i | \(0.751299\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 1.57117i | − | 0.0747332i | ||||||
\(443\) | −8.49233 | + | 14.7091i | −0.403483 | + | 0.698853i | −0.994144 | − | 0.108067i | \(-0.965534\pi\) |
0.590661 | + | 0.806920i | \(0.298867\pi\) | |||||||
\(444\) | 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 | \(0.0960065\pi\) | ||||
−0.954858 | + | 0.297061i | \(0.903994\pi\) | |||||||
\(450\) | 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 | \(-0.317183\pi\) |
−0.455436 | + | 0.890269i | \(0.650517\pi\) | |||||||
\(458\) | −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 | \(-0.364365\pi\) |
−0.581920 | + | 0.813246i | \(0.697698\pi\) | |||||||
\(468\) | 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 | 0.647456 | − | 0.762103i | \(-0.275833\pi\) |
−0.983728 | + | 0.179662i | \(0.942500\pi\) | |||||||
\(480\) | 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 | \(-0.680212\pi\) |
0.462706 | + | 0.886512i | \(0.346878\pi\) | |||||||
\(488\) | 9.97710 | + | 5.76028i | 0.451642 | + | 0.260756i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 10.4281i | − | 0.470613i | −0.971921 | − | 0.235307i | \(-0.924391\pi\) | ||
0.971921 | − | 0.235307i | \(-0.0756095\pi\) | |||||||
\(492\) | 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 | 0.0400890 | + | 0.999196i | \(0.487236\pi\) |
−0.885374 | + | 0.464880i | \(0.846097\pi\) | |||||||
\(500\) | 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 | −0.610520 | − | 0.792001i | \(-0.709040\pi\) |
0.991153 | + | 0.132726i | \(0.0423729\pi\) | |||||||
\(510\) | 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 | 0.812125 | − | 0.583483i | \(-0.198311\pi\) |
−0.911374 | + | 0.411580i | \(0.864977\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.2368 | + | 22.9267i | −0.578803 | + | 1.00252i | 0.416814 | + | 0.908992i | \(0.363147\pi\) |
−0.995617 | + | 0.0935241i | \(0.970187\pi\) | |||||||
\(524\) | −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 | −0.926008 | − | 0.377504i | \(-0.876782\pi\) |
0.789932 | + | 0.613194i | \(0.210116\pi\) | |||||||
\(542\) | 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 | \(-0.103931\pi\) |
−0.751351 | + | 0.659902i | \(0.770598\pi\) | |||||||
\(558\) | 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 | \(-0.475851\pi\) |
0.901431 | + | 0.432923i | \(0.142518\pi\) | |||||||
\(564\) | 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 | −0.971443 | − | 0.237274i | \(-0.923746\pi\) |
−0.691207 | − | 0.722657i | \(-0.742921\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.390149 | − | 0.675759i | −0.0163272 | − | 0.0282796i | 0.857746 | − | 0.514073i | \(-0.171864\pi\) |
−0.874074 | + | 0.485794i | \(0.838531\pi\) | |||||||
\(572\) | −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 | \(-0.241914\pi\) |
−0.959040 | + | 0.283270i | \(0.908581\pi\) | |||||||
\(578\) | 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 | \(-0.461491\pi\) |
−0.799354 | + | 0.600860i | \(0.794825\pi\) | |||||||
\(594\) | 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 | −0.910271 | − | 0.414013i | \(-0.864127\pi\) |
−0.0965902 | + | 0.995324i | \(0.530794\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.2553i | 1.19335i | 0.802484 | + | 0.596673i | \(0.203511\pi\) | ||||
−0.802484 | + | 0.596673i | \(0.796489\pi\) | |||||||
\(602\) | 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 | −0.475356 | − | 0.879794i | \(-0.657681\pi\) |
0.999602 | − | 0.0282267i | \(-0.00898603\pi\) | |||||||
\(608\) | − | 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 | \(-0.773058\pi\) |
0.188230 | + | 0.982125i | \(0.439725\pi\) | |||||||
\(614\) | 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 | \(-0.278557\pi\) | ||||
0.640911 | + | 0.767615i | \(0.278557\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.01055 | + | 4.62490i | −0.321971 | + | 0.185890i | −0.652271 | − | 0.757986i | \(-0.726184\pi\) |
0.330300 | + | 0.943876i | \(0.392850\pi\) | |||||||
\(620\) | 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 | −0.264093 | − | 0.964497i | \(-0.585072\pi\) |
0.703233 | + | 0.710960i | \(0.251739\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.96224 | −0.353436 | −0.176718 | − | 0.984262i | \(-0.556548\pi\) | ||||
−0.176718 | + | 0.984262i | \(0.556548\pi\) | |||||||
\(644\) | 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 | 0.546191 | − | 0.837660i | \(-0.316077\pi\) |
0.998531 | − | 0.0541854i | \(-0.0172562\pi\) | |||||||
\(648\) | 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 | 0.343268 | + | 0.939237i | \(0.388466\pi\) |
−0.985038 | + | 0.172340i | \(0.944867\pi\) | |||||||
\(654\) | 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 | \(-0.881266\pi\) | ||
0.931233 | − | 0.364425i | \(-0.118734\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.41761 | − | 4.28256i | 0.288512 | − | 0.166572i | −0.348759 | − | 0.937213i | \(-0.613397\pi\) |
0.637270 | + | 0.770640i | \(0.280063\pi\) | |||||||
\(662\) | 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 | \(-0.0404037\pi\) |
0.386346 | + | 0.922354i | \(0.373737\pi\) | |||||||
\(678\) | 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 | −0.897700 | − | 0.440608i | \(-0.854763\pi\) |
0.0672723 | − | 0.997735i | \(-0.478570\pi\) | |||||||
\(684\) | 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 | 0.143464 | − | 0.989656i | \(-0.454176\pi\) |
−0.785335 | + | 0.619071i | \(0.787509\pi\) | |||||||
\(692\) | − | 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 | \(0.347937\pi\) | ||||
−0.459755 | + | 0.888046i | \(0.652063\pi\) | |||||||
\(702\) | 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 | −0.0952213 | + | 0.995456i | \(0.530356\pi\) |
−0.814480 | + | 0.580192i | \(0.802977\pi\) | |||||||
\(710\) | 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 | −0.166625 | − | 0.986020i | \(-0.553287\pi\) |
0.937231 | − | 0.348709i | \(-0.113380\pi\) | |||||||
\(720\) | 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 | \(-0.399214\pi\) | ||||
0.311363 | + | 0.950291i | \(0.399214\pi\) | |||||||
\(728\) | 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 | 0.429494 | + | 0.903070i | \(0.358692\pi\) |
−0.996828 | + | 0.0795826i | \(0.974641\pi\) | |||||||
\(734\) | −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 | 0.996952 | + | 0.0780176i | \(0.0248590\pi\) |
−0.430911 | + | 0.902395i | \(0.641808\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.3438 | − | 0.814447i | −0.416443 | − | 0.0298993i | ||||
\(743\) | 33.3616 | 1.22392 | 0.611960 | − | 0.790889i | \(-0.290381\pi\) | ||||
0.611960 | + | 0.790889i | \(0.290381\pi\) | |||||||
\(744\) | 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 | −0.413411 | − | 0.910545i | \(-0.635663\pi\) |
0.995260 | − | 0.0972480i | \(-0.0310040\pi\) | |||||||
\(752\) | −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 | −0.555280 | − | 0.831664i | \(-0.687389\pi\) |
0.997882 | + | 0.0650543i | \(0.0207220\pi\) | |||||||
\(762\) | 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 | \(-0.864255\pi\) | ||
0.910437 | − | 0.413647i | \(-0.135745\pi\) | |||||||
\(770\) | 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 | \(-0.362921\pi\) |
0.995683 | + | 0.0928193i | \(0.0295879\pi\) | |||||||
\(774\) | 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 | \(-0.147669\pi\) |
−0.834659 | + | 0.550767i | \(0.814335\pi\) | |||||||
\(788\) | 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 | 0.460696 | − | 0.887558i | \(-0.347600\pi\) |
0.998996 | + | 0.0448048i | \(0.0142666\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 49.6994i | − | 1.74518i | −0.488452 | − | 0.872591i | \(-0.662438\pi\) | ||
0.488452 | − | 0.872591i | \(-0.337562\pi\) | |||||||
\(812\) | 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 | 0.802059 | − | 0.597245i | \(-0.203738\pi\) |
−0.116200 | + | 0.993226i | \(0.537071\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.76628 | − | 1.59711i | 0.0964266 | − | 0.0556719i | −0.451011 | − | 0.892518i | \(-0.648937\pi\) |
0.547438 | + | 0.836846i | \(0.315603\pi\) | |||||||
\(824\) | 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 | \(-0.672890\pi\) | ||||
−0.516836 | + | 0.856084i | \(0.672890\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.8588 | + | 15.5069i | −0.932845 | + | 0.538578i | −0.887710 | − | 0.460403i | \(-0.847705\pi\) |
−0.0451348 | + | 0.998981i | \(0.514372\pi\) | |||||||
\(830\) | 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 | \(-0.371877\pi\) | ||||
0.391728 | + | 0.920081i | \(0.371877\pi\) | |||||||
\(854\) | −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 | \(-0.471317\pi\) |
0.907506 | + | 0.420039i | \(0.137984\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.3926 | − | 9.46427i | −0.559308 | − | 0.322917i | 0.193560 | − | 0.981088i | \(-0.437997\pi\) |
−0.752868 | + | 0.658172i | \(0.771330\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.8768i | 0.608888i | ||||||||
\(863\) | −2.62854 | + | 4.55277i | −0.0894767 | + | 0.154978i | −0.907290 | − | 0.420505i | \(-0.861853\pi\) |
0.817813 | + | 0.575484i | \(0.195186\pi\) | |||||||
\(864\) | 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 | \(-0.0924437\pi\) |
0.231071 | + | 0.972937i | \(0.425777\pi\) | |||||||
\(878\) | −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 | \(-0.200754\pi\) |
−0.106884 | + | 0.994271i | \(0.534087\pi\) | |||||||
\(888\) | 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 | \(-0.753372\pi\) |
0.248572 | + | 0.968613i | \(0.420039\pi\) | |||||||
\(908\) | −1.48288 | − | 0.856140i | −0.0492110 | − | 0.0284120i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.4586i | 0.710955i | 0.934685 | + | 0.355477i | \(0.115682\pi\) | ||||
−0.934685 | + | 0.355477i | \(0.884318\pi\) | |||||||
\(912\) | 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 | −0.289360 | + | 0.957220i | \(0.593442\pi\) |
−0.684297 | + | 0.729203i | \(0.739891\pi\) | |||||||
\(920\) | 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 | −0.590032 | − | 0.807380i | \(-0.700885\pi\) |
0.994227 | + | 0.107293i | \(0.0342183\pi\) | |||||||
\(930\) | 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 | \(-0.828516\pi\) | ||||
−0.858360 | + | 0.513048i | \(0.828516\pi\) | |||||||
\(938\) | −2.37202 | + | 33.0379i | −0.0774491 | + | 1.07873i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.752551 | + | 1.30346i | 0.0245325 | + | 0.0424915i | 0.878031 | − | 0.478604i | \(-0.158857\pi\) |
−0.853499 | + | 0.521095i | \(0.825524\pi\) | |||||||
\(942\) | 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 | \(-0.774222\pi\) |
0.943454 | + | 0.331503i | \(0.107556\pi\) | |||||||
\(948\) | 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 | \(-0.615520\pi\) | ||||
−0.355003 | + | 0.934865i | \(0.615520\pi\) | |||||||
\(954\) | 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 | −0.864645 | − | 0.502384i | \(-0.832456\pi\) |
0.867399 | + | 0.497612i | \(0.165790\pi\) | |||||||
\(972\) | 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 | \(-0.224175\pi\) |
−0.941773 | + | 0.336250i | \(0.890841\pi\) | |||||||
\(978\) | 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 | \(-0.526143\pi\) |
0.822087 | + | 0.569362i | \(0.192810\pi\) | |||||||
\(984\) | 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 | 0.733243 | − | 0.679966i | \(-0.238006\pi\) |
−0.955490 | + | 0.295024i | \(0.904672\pi\) | |||||||
\(992\) | 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 | 0.988298 | + | 0.152538i | \(0.0487445\pi\) |
−0.362047 | + | 0.932160i | \(0.617922\pi\) | |||||||
\(998\) | 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.d.1349.4 | 8 | ||
3.2 | odd | 2 | 3150.2.bp.c.1349.4 | 8 | |||
5.2 | odd | 4 | 3150.2.bf.b.1601.3 | 8 | |||
5.3 | odd | 4 | 630.2.be.a.341.2 | ✓ | 8 | ||
5.4 | even | 2 | 3150.2.bp.a.1349.1 | 8 | |||
7.3 | odd | 6 | 3150.2.bp.f.899.1 | 8 | |||
15.2 | even | 4 | 3150.2.bf.c.1601.1 | 8 | |||
15.8 | even | 4 | 630.2.be.b.341.4 | yes | 8 | ||
15.14 | odd | 2 | 3150.2.bp.f.1349.1 | 8 | |||
21.17 | even | 6 | 3150.2.bp.a.899.1 | 8 | |||
35.3 | even | 12 | 630.2.be.b.521.4 | yes | 8 | ||
35.17 | even | 12 | 3150.2.bf.c.1151.1 | 8 | |||
35.23 | odd | 12 | 4410.2.b.e.881.6 | 8 | |||
35.24 | odd | 6 | 3150.2.bp.c.899.4 | 8 | |||
35.33 | even | 12 | 4410.2.b.b.881.6 | 8 | |||
105.17 | odd | 12 | 3150.2.bf.b.1151.3 | 8 | |||
105.23 | even | 12 | 4410.2.b.b.881.3 | 8 | |||
105.38 | odd | 12 | 630.2.be.a.521.2 | yes | 8 | ||
105.59 | even | 6 | inner | 3150.2.bp.d.899.4 | 8 | ||
105.68 | odd | 12 | 4410.2.b.e.881.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.be.a.341.2 | ✓ | 8 | 5.3 | odd | 4 | ||
630.2.be.a.521.2 | yes | 8 | 105.38 | odd | 12 | ||
630.2.be.b.341.4 | yes | 8 | 15.8 | even | 4 | ||
630.2.be.b.521.4 | yes | 8 | 35.3 | even | 12 | ||
3150.2.bf.b.1151.3 | 8 | 105.17 | odd | 12 | |||
3150.2.bf.b.1601.3 | 8 | 5.2 | odd | 4 | |||
3150.2.bf.c.1151.1 | 8 | 35.17 | even | 12 | |||
3150.2.bf.c.1601.1 | 8 | 15.2 | even | 4 | |||
3150.2.bp.a.899.1 | 8 | 21.17 | even | 6 | |||
3150.2.bp.a.1349.1 | 8 | 5.4 | even | 2 | |||
3150.2.bp.c.899.4 | 8 | 35.24 | odd | 6 | |||
3150.2.bp.c.1349.4 | 8 | 3.2 | odd | 2 | |||
3150.2.bp.d.899.4 | 8 | 105.59 | even | 6 | inner | ||
3150.2.bp.d.1349.4 | 8 | 1.1 | even | 1 | trivial | ||
3150.2.bp.f.899.1 | 8 | 7.3 | odd | 6 | |||
3150.2.bp.f.1349.1 | 8 | 15.14 | odd | 2 | |||
4410.2.b.b.881.3 | 8 | 105.23 | even | 12 | |||
4410.2.b.b.881.6 | 8 | 35.33 | even | 12 | |||
4410.2.b.e.881.3 | 8 | 105.68 | odd | 12 | |||
4410.2.b.e.881.6 | 8 | 35.23 | odd | 12 |