Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(361,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.h (of order \(3\), 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: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 882) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.361 |
Dual form | 2646.2.h.j.667.1 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.00000 | 0.447214 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | − | 1.73205i | 0.277350 | − | 0.480384i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) |
0.970725 | + | 0.240192i | \(0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.50000 | − | 6.06218i | −0.802955 | − | 1.39076i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.114708 | − | 0.993399i | \(-0.463407\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | − | 1.73205i | 0.213201 | − | 0.369274i | ||||
\(23\) | −3.00000 | −0.625543 | −0.312772 | − | 0.949828i | \(-0.601257\pi\) | ||||
−0.312772 | + | 0.949828i | \(0.601257\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | −1.00000 | − | 1.73205i | −0.196116 | − | 0.339683i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.00000 | − | 6.92820i | −0.742781 | − | 1.28654i | −0.951224 | − | 0.308500i | \(-0.900173\pi\) |
0.208443 | − | 0.978035i | \(-0.433160\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | + | 3.46410i | 0.359211 | + | 0.622171i | 0.987829 | − | 0.155543i | \(-0.0497126\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | + | 5.19615i | 0.493197 | + | 0.854242i | 0.999969 | − | 0.00783774i | \(-0.00249486\pi\) |
−0.506772 | + | 0.862080i | \(0.669162\pi\) | |||||||
\(38\) | −7.00000 | −1.13555 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 6.00000 | − | 10.3923i | 0.937043 | − | 1.62301i | 0.166092 | − | 0.986110i | \(-0.446885\pi\) |
0.770950 | − | 0.636895i | \(-0.219782\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | + | 6.92820i | 0.609994 | + | 1.05654i | 0.991241 | + | 0.132068i | \(0.0421616\pi\) |
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | −1.00000 | − | 1.73205i | −0.150756 | − | 0.261116i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.50000 | + | 2.59808i | −0.221163 | + | 0.383065i | ||||
\(47\) | 4.00000 | − | 6.92820i | 0.583460 | − | 1.01058i | −0.411606 | − | 0.911362i | \(-0.635032\pi\) |
0.995066 | − | 0.0992202i | \(-0.0316348\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.00000 | + | 3.46410i | −0.282843 | + | 0.489898i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.00000 | −0.277350 | ||||||||
\(53\) | 2.00000 | − | 3.46410i | 0.274721 | − | 0.475831i | −0.695344 | − | 0.718677i | \(-0.744748\pi\) |
0.970065 | + | 0.242846i | \(0.0780811\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.00000 | −1.05045 | ||||||||
\(59\) | −2.00000 | − | 3.46410i | −0.260378 | − | 0.450988i | 0.705965 | − | 0.708247i | \(-0.250514\pi\) |
−0.966342 | + | 0.257260i | \(0.917180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50000 | − | 11.2583i | 0.832240 | − | 1.44148i | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) |
0.896258 | − | 0.443533i | \(-0.146275\pi\) | |||||||
\(62\) | 4.00000 | 0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.00000 | − | 1.73205i | 0.124035 | − | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000 | + | 1.73205i | 0.122169 | + | 0.211604i | 0.920623 | − | 0.390453i | \(-0.127682\pi\) |
−0.798454 | + | 0.602056i | \(0.794348\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.00000 | 0.593391 | 0.296695 | − | 0.954972i | \(-0.404115\pi\) | ||||
0.296695 | + | 0.954972i | \(0.404115\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | + | 12.1244i | −0.819288 | + | 1.41905i | 0.0869195 | + | 0.996215i | \(0.472298\pi\) |
−0.906208 | + | 0.422833i | \(0.861036\pi\) | |||||||
\(74\) | 6.00000 | 0.697486 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.50000 | + | 6.06218i | −0.401478 | + | 0.695379i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.50000 | − | 9.52628i | 0.618798 | − | 1.07179i | −0.370907 | − | 0.928670i | \(-0.620953\pi\) |
0.989705 | − | 0.143120i | \(-0.0457135\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.00000 | − | 10.3923i | −0.662589 | − | 1.14764i | ||||
\(83\) | −6.00000 | − | 10.3923i | −0.658586 | − | 1.14070i | −0.980982 | − | 0.194099i | \(-0.937822\pi\) |
0.322396 | − | 0.946605i | \(-0.395512\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.00000 | 0.862662 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.00000 | −0.213201 | ||||||||
\(89\) | −7.00000 | − | 12.1244i | −0.741999 | − | 1.28518i | −0.951584 | − | 0.307389i | \(-0.900545\pi\) |
0.209585 | − | 0.977790i | \(-0.432789\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.50000 | + | 2.59808i | 0.156386 | + | 0.270868i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.00000 | − | 6.92820i | −0.412568 | − | 0.714590i | ||||
\(95\) | −3.50000 | − | 6.06218i | −0.359092 | − | 0.621966i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | − | 1.73205i | −0.101535 | − | 0.175863i | 0.810782 | − | 0.585348i | \(-0.199042\pi\) |
−0.912317 | + | 0.409484i | \(0.865709\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.00000 | + | 3.46410i | 0.200000 | + | 0.346410i | ||||
\(101\) | −11.0000 | −1.09454 | −0.547270 | − | 0.836956i | \(-0.684333\pi\) | ||||
−0.547270 | + | 0.836956i | \(0.684333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.00000 | −0.788263 | −0.394132 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(104\) | −1.00000 | + | 1.73205i | −0.0980581 | + | 0.169842i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.00000 | − | 3.46410i | −0.194257 | − | 0.336463i | ||||
\(107\) | 4.00000 | + | 6.92820i | 0.386695 | + | 0.669775i | 0.992003 | − | 0.126217i | \(-0.0402834\pi\) |
−0.605308 | + | 0.795991i | \(0.706950\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | + | 3.46410i | −0.191565 | + | 0.331801i | −0.945769 | − | 0.324840i | \(-0.894690\pi\) |
0.754204 | + | 0.656640i | \(0.228023\pi\) | |||||||
\(110\) | 1.00000 | − | 1.73205i | 0.0953463 | − | 0.165145i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.500000 | + | 0.866025i | −0.0470360 | + | 0.0814688i | −0.888585 | − | 0.458712i | \(-0.848311\pi\) |
0.841549 | + | 0.540181i | \(0.181644\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.00000 | −0.279751 | ||||||||
\(116\) | −4.00000 | + | 6.92820i | −0.371391 | + | 0.643268i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.00000 | −0.368230 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −6.50000 | − | 11.2583i | −0.588482 | − | 1.01928i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.00000 | − | 3.46410i | 0.179605 | − | 0.311086i | ||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.0000 | −1.68598 | −0.842989 | − | 0.537931i | \(-0.819206\pi\) | ||||
−0.842989 | + | 0.537931i | \(0.819206\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.00000 | − | 1.73205i | −0.0877058 | − | 0.151911i | ||||
\(131\) | 15.0000 | 1.31056 | 0.655278 | − | 0.755388i | \(-0.272551\pi\) | ||||
0.655278 | + | 0.755388i | \(0.272551\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.00000 | 0.172774 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | 0.170872 | 0.0854358 | − | 0.996344i | \(-0.472772\pi\) | ||||
0.0854358 | + | 0.996344i | \(0.472772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.50000 | − | 7.79423i | 0.381685 | − | 0.661098i | −0.609618 | − | 0.792695i | \(-0.708677\pi\) |
0.991303 | + | 0.131597i | \(0.0420106\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.50000 | − | 4.33013i | 0.209795 | − | 0.363376i | ||||
\(143\) | 2.00000 | − | 3.46410i | 0.167248 | − | 0.289683i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.00000 | − | 6.92820i | −0.332182 | − | 0.575356i | ||||
\(146\) | 7.00000 | + | 12.1244i | 0.579324 | + | 1.00342i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.00000 | − | 5.19615i | 0.246598 | − | 0.427121i | ||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.0000 | 1.54620 | 0.773099 | − | 0.634285i | \(-0.218706\pi\) | ||||
0.773099 | + | 0.634285i | \(0.218706\pi\) | |||||||
\(152\) | 3.50000 | + | 6.06218i | 0.283887 | + | 0.491708i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000 | + | 3.46410i | 0.160644 | + | 0.278243i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.50000 | + | 9.52628i | 0.438948 | + | 0.760280i | 0.997609 | − | 0.0691164i | \(-0.0220180\pi\) |
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | −5.50000 | − | 9.52628i | −0.437557 | − | 0.757870i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.00000 | + | 5.19615i | 0.234978 | + | 0.406994i | 0.959266 | − | 0.282503i | \(-0.0911648\pi\) |
−0.724288 | + | 0.689497i | \(0.757831\pi\) | |||||||
\(164\) | −12.0000 | −0.937043 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.0000 | −0.931381 | ||||||||
\(167\) | −1.00000 | + | 1.73205i | −0.0773823 | + | 0.134030i | −0.902120 | − | 0.431486i | \(-0.857990\pi\) |
0.824737 | + | 0.565516i | \(0.191323\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.00000 | − | 6.92820i | 0.304997 | − | 0.528271i | ||||
\(173\) | 11.0000 | − | 19.0526i | 0.836315 | − | 1.44854i | −0.0566411 | − | 0.998395i | \(-0.518039\pi\) |
0.892956 | − | 0.450145i | \(-0.148628\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | + | 1.73205i | −0.0753778 | + | 0.130558i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −14.0000 | −1.04934 | ||||||||
\(179\) | −12.0000 | + | 20.7846i | −0.896922 | + | 1.55351i | −0.0655145 | + | 0.997852i | \(0.520869\pi\) |
−0.831408 | + | 0.555663i | \(0.812464\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.00000 | −0.520306 | −0.260153 | − | 0.965567i | \(-0.583773\pi\) | ||||
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.00000 | 0.221163 | ||||||||
\(185\) | 3.00000 | + | 5.19615i | 0.220564 | + | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −8.00000 | −0.583460 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.00000 | −0.507833 | ||||||||
\(191\) | 1.50000 | − | 2.59808i | 0.108536 | − | 0.187990i | −0.806641 | − | 0.591041i | \(-0.798717\pi\) |
0.915177 | + | 0.403051i | \(0.132050\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.50000 | − | 4.33013i | −0.179954 | − | 0.311689i | 0.761911 | − | 0.647682i | \(-0.224262\pi\) |
−0.941865 | + | 0.335993i | \(0.890928\pi\) | |||||||
\(194\) | −2.00000 | −0.143592 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.00000 | + | 12.1244i | −0.496217 | + | 0.859473i | −0.999990 | − | 0.00436292i | \(-0.998611\pi\) |
0.503774 | + | 0.863836i | \(0.331945\pi\) | |||||||
\(200\) | 4.00000 | 0.282843 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.50000 | + | 9.52628i | −0.386979 | + | 0.670267i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | − | 10.3923i | 0.419058 | − | 0.725830i | ||||
\(206\) | −4.00000 | + | 6.92820i | −0.278693 | + | 0.482711i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00000 | + | 1.73205i | 0.0693375 | + | 0.120096i | ||||
\(209\) | −7.00000 | − | 12.1244i | −0.484200 | − | 0.838659i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.0000 | − | 19.0526i | 0.757271 | − | 1.31163i | −0.186966 | − | 0.982366i | \(-0.559865\pi\) |
0.944237 | − | 0.329266i | \(-0.106801\pi\) | |||||||
\(212\) | −4.00000 | −0.274721 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.00000 | 0.546869 | ||||||||
\(215\) | 4.00000 | + | 6.92820i | 0.272798 | + | 0.472500i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.00000 | + | 3.46410i | 0.135457 | + | 0.234619i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.00000 | − | 1.73205i | −0.0674200 | − | 0.116775i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | − | 1.73205i | −0.0669650 | − | 0.115987i | 0.830599 | − | 0.556871i | \(-0.187998\pi\) |
−0.897564 | + | 0.440884i | \(0.854665\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.500000 | + | 0.866025i | 0.0332595 | + | 0.0576072i | ||||
\(227\) | 17.0000 | 1.12833 | 0.564165 | − | 0.825662i | \(-0.309198\pi\) | ||||
0.564165 | + | 0.825662i | \(0.309198\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.0000 | 0.859064 | 0.429532 | − | 0.903052i | \(-0.358679\pi\) | ||||
0.429532 | + | 0.903052i | \(0.358679\pi\) | |||||||
\(230\) | −1.50000 | + | 2.59808i | −0.0989071 | + | 0.171312i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.00000 | + | 6.92820i | 0.262613 | + | 0.454859i | ||||
\(233\) | 0.500000 | + | 0.866025i | 0.0327561 | + | 0.0567352i | 0.881939 | − | 0.471364i | \(-0.156238\pi\) |
−0.849183 | + | 0.528099i | \(0.822905\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | − | 6.92820i | 0.260931 | − | 0.451946i | ||||
\(236\) | −2.00000 | + | 3.46410i | −0.130189 | + | 0.225494i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.50000 | + | 12.9904i | −0.485135 | + | 0.840278i | −0.999854 | − | 0.0170808i | \(-0.994563\pi\) |
0.514719 | + | 0.857359i | \(0.327896\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | −3.50000 | + | 6.06218i | −0.224989 | + | 0.389692i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.0000 | −0.832240 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.0000 | −0.890799 | ||||||||
\(248\) | −2.00000 | − | 3.46410i | −0.127000 | − | 0.219971i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.50000 | + | 7.79423i | −0.284605 | + | 0.492950i | ||||
\(251\) | 7.00000 | 0.441836 | 0.220918 | − | 0.975292i | \(-0.429095\pi\) | ||||
0.220918 | + | 0.975292i | \(0.429095\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | −0.377217 | ||||||||
\(254\) | −9.50000 | + | 16.4545i | −0.596083 | + | 1.03245i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 8.00000 | 0.499026 | 0.249513 | − | 0.968371i | \(-0.419729\pi\) | ||||
0.249513 | + | 0.968371i | \(0.419729\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.00000 | −0.124035 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.50000 | − | 12.9904i | 0.463352 | − | 0.802548i | ||||
\(263\) | −19.0000 | −1.17159 | −0.585795 | − | 0.810459i | \(-0.699218\pi\) | ||||
−0.585795 | + | 0.810459i | \(0.699218\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.00000 | − | 3.46410i | 0.122859 | − | 0.212798i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.00000 | − | 1.73205i | 0.0610847 | − | 0.105802i | ||||
\(269\) | −3.50000 | + | 6.06218i | −0.213399 | + | 0.369618i | −0.952776 | − | 0.303674i | \(-0.901787\pi\) |
0.739377 | + | 0.673291i | \(0.235120\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.00000 | + | 12.1244i | 0.425220 | + | 0.736502i | 0.996441 | − | 0.0842940i | \(-0.0268635\pi\) |
−0.571221 | + | 0.820796i | \(0.693530\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.00000 | − | 1.73205i | 0.0604122 | − | 0.104637i | ||||
\(275\) | −8.00000 | −0.482418 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00000 | −0.120168 | −0.0600842 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600842 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(278\) | −4.50000 | − | 7.79423i | −0.269892 | − | 0.467467i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.50000 | − | 12.9904i | −0.447412 | − | 0.774941i | 0.550804 | − | 0.834634i | \(-0.314321\pi\) |
−0.998217 | + | 0.0596933i | \(0.980988\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.5000 | + | 21.6506i | 0.743048 | + | 1.28700i | 0.951101 | + | 0.308879i | \(0.0999539\pi\) |
−0.208053 | + | 0.978117i | \(0.566713\pi\) | |||||||
\(284\) | −2.50000 | − | 4.33013i | −0.148348 | − | 0.256946i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.00000 | − | 3.46410i | −0.118262 | − | 0.204837i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | −8.00000 | −0.469776 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.0000 | 0.819288 | ||||||||
\(293\) | −4.50000 | + | 7.79423i | −0.262893 | + | 0.455344i | −0.967009 | − | 0.254741i | \(-0.918010\pi\) |
0.704117 | + | 0.710084i | \(0.251343\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.00000 | − | 3.46410i | −0.116445 | − | 0.201688i | ||||
\(296\) | −3.00000 | − | 5.19615i | −0.174371 | − | 0.302020i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.00000 | + | 8.66025i | −0.289642 | + | 0.501675i | ||||
\(299\) | −3.00000 | + | 5.19615i | −0.173494 | + | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.50000 | − | 16.4545i | 0.546664 | − | 0.946849i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.00000 | 0.401478 | ||||||||
\(305\) | 6.50000 | − | 11.2583i | 0.372189 | − | 0.644650i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.00000 | −0.399511 | −0.199756 | − | 0.979846i | \(-0.564015\pi\) | ||||
−0.199756 | + | 0.979846i | \(0.564015\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.00000 | 0.227185 | ||||||||
\(311\) | 5.00000 | + | 8.66025i | 0.283524 | + | 0.491078i | 0.972250 | − | 0.233944i | \(-0.0751631\pi\) |
−0.688726 | + | 0.725022i | \(0.741830\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.00000 | − | 5.19615i | 0.169570 | − | 0.293704i | −0.768699 | − | 0.639611i | \(-0.779095\pi\) |
0.938269 | + | 0.345907i | \(0.112429\pi\) | |||||||
\(314\) | 11.0000 | 0.620766 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.0000 | −0.618798 | ||||||||
\(317\) | 12.0000 | − | 20.7846i | 0.673987 | − | 1.16738i | −0.302777 | − | 0.953062i | \(-0.597914\pi\) |
0.976764 | − | 0.214318i | \(-0.0687530\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.00000 | − | 13.8564i | −0.447914 | − | 0.775810i | ||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | + | 6.92820i | −0.221880 | + | 0.384308i | ||||
\(326\) | 6.00000 | 0.332309 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.00000 | + | 10.3923i | −0.331295 | + | 0.573819i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | − | 3.46410i | 0.109930 | − | 0.190404i | −0.805812 | − | 0.592172i | \(-0.798271\pi\) |
0.915742 | + | 0.401768i | \(0.131604\pi\) | |||||||
\(332\) | −6.00000 | + | 10.3923i | −0.329293 | + | 0.570352i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.00000 | + | 1.73205i | 0.0547176 | + | 0.0947736i | ||||
\(335\) | 1.00000 | + | 1.73205i | 0.0546358 | + | 0.0946320i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0000 | − | 19.0526i | 0.599208 | − | 1.03786i | −0.393730 | − | 0.919226i | \(-0.628816\pi\) |
0.992938 | − | 0.118633i | \(-0.0378512\pi\) | |||||||
\(338\) | 9.00000 | 0.489535 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.00000 | + | 6.92820i | 0.216612 | + | 0.375183i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.00000 | − | 6.92820i | −0.215666 | − | 0.373544i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.0000 | − | 19.0526i | −0.591364 | − | 1.02427i | ||||
\(347\) | 6.00000 | + | 10.3923i | 0.322097 | + | 0.557888i | 0.980921 | − | 0.194409i | \(-0.0622790\pi\) |
−0.658824 | + | 0.752297i | \(0.728946\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.0000 | − | 25.9808i | −0.802932 | − | 1.39072i | −0.917679 | − | 0.397324i | \(-0.869939\pi\) |
0.114747 | − | 0.993395i | \(-0.463394\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | + | 1.73205i | 0.0533002 | + | 0.0923186i | ||||
\(353\) | 24.0000 | 1.27739 | 0.638696 | − | 0.769460i | \(-0.279474\pi\) | ||||
0.638696 | + | 0.769460i | \(0.279474\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.00000 | 0.265372 | ||||||||
\(356\) | −7.00000 | + | 12.1244i | −0.370999 | + | 0.642590i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0000 | + | 20.7846i | 0.634220 | + | 1.09850i | ||||
\(359\) | 14.5000 | + | 25.1147i | 0.765281 | + | 1.32551i | 0.940098 | + | 0.340904i | \(0.110733\pi\) |
−0.174817 | + | 0.984601i | \(0.555933\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | + | 25.9808i | −0.789474 | + | 1.36741i | ||||
\(362\) | −3.50000 | + | 6.06218i | −0.183956 | + | 0.318621i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.00000 | + | 12.1244i | −0.366397 | + | 0.634618i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.0000 | 1.67039 | 0.835193 | − | 0.549957i | \(-0.185356\pi\) | ||||
0.835193 | + | 0.549957i | \(0.185356\pi\) | |||||||
\(368\) | 1.50000 | − | 2.59808i | 0.0781929 | − | 0.135434i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.00000 | 0.311925 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.0000 | −1.65690 | −0.828449 | − | 0.560065i | \(-0.810776\pi\) | ||||
−0.828449 | + | 0.560065i | \(0.810776\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.00000 | + | 6.92820i | −0.206284 | + | 0.357295i | ||||
\(377\) | −16.0000 | −0.824042 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0000 | −0.616399 | −0.308199 | − | 0.951322i | \(-0.599726\pi\) | ||||
−0.308199 | + | 0.951322i | \(0.599726\pi\) | |||||||
\(380\) | −3.50000 | + | 6.06218i | −0.179546 | + | 0.310983i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.50000 | − | 2.59808i | −0.0767467 | − | 0.132929i | ||||
\(383\) | −6.00000 | −0.306586 | −0.153293 | − | 0.988181i | \(-0.548988\pi\) | ||||
−0.153293 | + | 0.988181i | \(0.548988\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.00000 | −0.254493 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.00000 | + | 1.73205i | −0.0507673 | + | 0.0879316i | ||||
\(389\) | 30.0000 | 1.52106 | 0.760530 | − | 0.649303i | \(-0.224939\pi\) | ||||
0.760530 | + | 0.649303i | \(0.224939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.00000 | − | 10.3923i | 0.302276 | − | 0.523557i | ||||
\(395\) | 5.50000 | − | 9.52628i | 0.276735 | − | 0.479319i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.00000 | + | 12.1244i | 0.351320 | + | 0.608504i | 0.986481 | − | 0.163876i | \(-0.0523996\pi\) |
−0.635161 | + | 0.772380i | \(0.719066\pi\) | |||||||
\(398\) | 7.00000 | + | 12.1244i | 0.350878 | + | 0.607739i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.00000 | − | 3.46410i | 0.100000 | − | 0.173205i | ||||
\(401\) | −3.00000 | −0.149813 | −0.0749064 | − | 0.997191i | \(-0.523866\pi\) | ||||
−0.0749064 | + | 0.997191i | \(0.523866\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.00000 | 0.398508 | ||||||||
\(404\) | 5.50000 | + | 9.52628i | 0.273635 | + | 0.473950i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.00000 | + | 10.3923i | 0.297409 | + | 0.515127i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.0000 | − | 20.7846i | −0.593362 | − | 1.02773i | −0.993776 | − | 0.111398i | \(-0.964467\pi\) |
0.400414 | − | 0.916334i | \(-0.368866\pi\) | |||||||
\(410\) | −6.00000 | − | 10.3923i | −0.296319 | − | 0.513239i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.00000 | + | 6.92820i | 0.197066 | + | 0.341328i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.00000 | − | 10.3923i | −0.294528 | − | 0.510138i | ||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −14.0000 | −0.684762 | ||||||||
\(419\) | 2.50000 | − | 4.33013i | 0.122133 | − | 0.211541i | −0.798476 | − | 0.602027i | \(-0.794360\pi\) |
0.920609 | + | 0.390487i | \(0.127693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0000 | + | 31.1769i | 0.877266 | + | 1.51947i | 0.854329 | + | 0.519733i | \(0.173969\pi\) |
0.0229375 | + | 0.999737i | \(0.492698\pi\) | |||||||
\(422\) | −11.0000 | − | 19.0526i | −0.535472 | − | 0.927464i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.00000 | + | 3.46410i | −0.0971286 | + | 0.168232i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.00000 | − | 6.92820i | 0.193347 | − | 0.334887i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.00000 | 0.385794 | ||||||||
\(431\) | 16.0000 | − | 27.7128i | 0.770693 | − | 1.33488i | −0.166491 | − | 0.986043i | \(-0.553244\pi\) |
0.937184 | − | 0.348836i | \(-0.113423\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.0000 | 1.34559 | 0.672797 | − | 0.739827i | \(-0.265093\pi\) | ||||
0.672797 | + | 0.739827i | \(0.265093\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.00000 | 0.191565 | ||||||||
\(437\) | 10.5000 | + | 18.1865i | 0.502283 | + | 0.869980i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.0000 | + | 31.1769i | −0.859093 | + | 1.48799i | 0.0137020 | + | 0.999906i | \(0.495638\pi\) |
−0.872795 | + | 0.488087i | \(0.837695\pi\) | |||||||
\(440\) | −2.00000 | −0.0953463 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0000 | − | 20.7846i | 0.570137 | − | 0.987507i | −0.426414 | − | 0.904528i | \(-0.640223\pi\) |
0.996551 | − | 0.0829786i | \(-0.0264433\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.00000 | − | 12.1244i | −0.331832 | − | 0.574750i | ||||
\(446\) | −2.00000 | −0.0947027 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.00000 | −0.424736 | −0.212368 | − | 0.977190i | \(-0.568118\pi\) | ||||
−0.212368 | + | 0.977190i | \(0.568118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | − | 20.7846i | 0.565058 | − | 0.978709i | ||||
\(452\) | 1.00000 | 0.0470360 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.50000 | − | 14.7224i | 0.398925 | − | 0.690958i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.50000 | + | 14.7224i | −0.397613 | + | 0.688686i | −0.993431 | − | 0.114433i | \(-0.963495\pi\) |
0.595818 | + | 0.803120i | \(0.296828\pi\) | |||||||
\(458\) | 6.50000 | − | 11.2583i | 0.303725 | − | 0.526067i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.50000 | + | 2.59808i | 0.0699379 | + | 0.121136i | ||||
\(461\) | 4.50000 | + | 7.79423i | 0.209586 | + | 0.363013i | 0.951584 | − | 0.307388i | \(-0.0994551\pi\) |
−0.741998 | + | 0.670402i | \(0.766122\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.500000 | − | 0.866025i | 0.0232370 | − | 0.0402476i | −0.854173 | − | 0.519989i | \(-0.825936\pi\) |
0.877410 | + | 0.479741i | \(0.159269\pi\) | |||||||
\(464\) | 8.00000 | 0.371391 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.00000 | 0.0463241 | ||||||||
\(467\) | 14.0000 | + | 24.2487i | 0.647843 | + | 1.12210i | 0.983637 | + | 0.180161i | \(0.0576619\pi\) |
−0.335794 | + | 0.941935i | \(0.609005\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.00000 | − | 6.92820i | −0.184506 | − | 0.319574i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.00000 | + | 3.46410i | 0.0920575 | + | 0.159448i | ||||
\(473\) | 8.00000 | + | 13.8564i | 0.367840 | + | 0.637118i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.0000 | + | 24.2487i | 0.642364 | + | 1.11261i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.50000 | + | 12.9904i | 0.343042 | + | 0.594166i | ||||
\(479\) | 24.0000 | 1.09659 | 0.548294 | − | 0.836286i | \(-0.315277\pi\) | ||||
0.548294 | + | 0.836286i | \(0.315277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0000 | 0.547153 | ||||||||
\(482\) | −5.00000 | + | 8.66025i | −0.227744 | + | 0.394464i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.50000 | + | 6.06218i | 0.159091 | + | 0.275554i | ||||
\(485\) | −1.00000 | − | 1.73205i | −0.0454077 | − | 0.0786484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.5000 | + | 21.6506i | −0.566429 | + | 0.981084i | 0.430486 | + | 0.902597i | \(0.358342\pi\) |
−0.996915 | + | 0.0784867i | \(0.974991\pi\) | |||||||
\(488\) | −6.50000 | + | 11.2583i | −0.294241 | + | 0.509641i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.00000 | − | 5.19615i | 0.135388 | − | 0.234499i | −0.790358 | − | 0.612646i | \(-0.790105\pi\) |
0.925746 | + | 0.378147i | \(0.123439\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −7.00000 | + | 12.1244i | −0.314945 | + | 0.545501i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.0000 | 1.07439 | 0.537194 | − | 0.843459i | \(-0.319484\pi\) | ||||
0.537194 | + | 0.843459i | \(0.319484\pi\) | |||||||
\(500\) | 4.50000 | + | 7.79423i | 0.201246 | + | 0.348569i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.50000 | − | 6.06218i | 0.156213 | − | 0.270568i | ||||
\(503\) | 14.0000 | 0.624229 | 0.312115 | − | 0.950044i | \(-0.398963\pi\) | ||||
0.312115 | + | 0.950044i | \(0.398963\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.0000 | −0.489494 | ||||||||
\(506\) | −3.00000 | + | 5.19615i | −0.133366 | + | 0.230997i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.50000 | + | 16.4545i | 0.421494 | + | 0.730050i | ||||
\(509\) | −34.0000 | −1.50702 | −0.753512 | − | 0.657434i | \(-0.771642\pi\) | ||||
−0.753512 | + | 0.657434i | \(0.771642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.00000 | − | 6.92820i | 0.176432 | − | 0.305590i | ||||
\(515\) | −8.00000 | −0.352522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.00000 | − | 13.8564i | 0.351840 | − | 0.609404i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.00000 | + | 1.73205i | −0.0438529 | + | 0.0759555i | ||||
\(521\) | −7.00000 | + | 12.1244i | −0.306676 | + | 0.531178i | −0.977633 | − | 0.210318i | \(-0.932550\pi\) |
0.670957 | + | 0.741496i | \(0.265883\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.5000 | + | 30.3109i | 0.765222 | + | 1.32540i | 0.940129 | + | 0.340818i | \(0.110704\pi\) |
−0.174908 | + | 0.984585i | \(0.555963\pi\) | |||||||
\(524\) | −7.50000 | − | 12.9904i | −0.327639 | − | 0.567487i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.50000 | + | 16.4545i | −0.414220 | + | 0.717450i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.0000 | −0.608696 | ||||||||
\(530\) | −2.00000 | − | 3.46410i | −0.0868744 | − | 0.150471i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.0000 | − | 20.7846i | −0.519778 | − | 0.900281i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.00000 | + | 6.92820i | 0.172935 | + | 0.299532i | ||||
\(536\) | −1.00000 | − | 1.73205i | −0.0431934 | − | 0.0748132i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.50000 | + | 6.06218i | 0.150896 | + | 0.261359i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.0000 | + | 17.3205i | 0.429934 | + | 0.744667i | 0.996867 | − | 0.0790969i | \(-0.0252036\pi\) |
−0.566933 | + | 0.823764i | \(0.691870\pi\) | |||||||
\(542\) | 14.0000 | 0.601351 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.00000 | + | 3.46410i | −0.0856706 | + | 0.148386i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.00000 | + | 6.92820i | 0.171028 | + | 0.296229i | 0.938779 | − | 0.344519i | \(-0.111958\pi\) |
−0.767752 | + | 0.640747i | \(0.778625\pi\) | |||||||
\(548\) | −1.00000 | − | 1.73205i | −0.0427179 | − | 0.0739895i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.00000 | + | 6.92820i | −0.170561 | + | 0.295420i | ||||
\(551\) | −28.0000 | + | 48.4974i | −1.19284 | + | 2.06606i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.00000 | + | 1.73205i | −0.0424859 | + | 0.0735878i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.00000 | −0.381685 | ||||||||
\(557\) | 9.00000 | − | 15.5885i | 0.381342 | − | 0.660504i | −0.609912 | − | 0.792469i | \(-0.708795\pi\) |
0.991254 | + | 0.131965i | \(0.0421286\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.0000 | −0.632737 | ||||||||
\(563\) | −5.50000 | − | 9.52628i | −0.231797 | − | 0.401485i | 0.726540 | − | 0.687124i | \(-0.241127\pi\) |
−0.958337 | + | 0.285640i | \(0.907794\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.500000 | + | 0.866025i | −0.0210352 | + | 0.0364340i | ||||
\(566\) | 25.0000 | 1.05083 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.00000 | −0.209795 | ||||||||
\(569\) | −9.00000 | + | 15.5885i | −0.377300 | + | 0.653502i | −0.990668 | − | 0.136295i | \(-0.956481\pi\) |
0.613369 | + | 0.789797i | \(0.289814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.00000 | − | 10.3923i | −0.251092 | − | 0.434904i | 0.712735 | − | 0.701434i | \(-0.247456\pi\) |
−0.963827 | + | 0.266529i | \(0.914123\pi\) | |||||||
\(572\) | −4.00000 | −0.167248 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0000 | − | 24.2487i | 0.582828 | − | 1.00949i | −0.412315 | − | 0.911041i | \(-0.635280\pi\) |
0.995142 | − | 0.0984456i | \(-0.0313871\pi\) | |||||||
\(578\) | 17.0000 | 0.707107 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.00000 | + | 6.92820i | −0.166091 | + | 0.287678i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.00000 | − | 6.92820i | 0.165663 | − | 0.286937i | ||||
\(584\) | 7.00000 | − | 12.1244i | 0.289662 | − | 0.501709i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.50000 | + | 7.79423i | 0.185893 | + | 0.321977i | ||||
\(587\) | 11.5000 | + | 19.9186i | 0.474656 | + | 0.822128i | 0.999579 | − | 0.0290218i | \(-0.00923921\pi\) |
−0.524923 | + | 0.851150i | \(0.675906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.0000 | − | 24.2487i | 0.576860 | − | 0.999151i | ||||
\(590\) | −4.00000 | −0.164677 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.00000 | −0.246598 | ||||||||
\(593\) | −21.0000 | − | 36.3731i | −0.862367 | − | 1.49366i | −0.869638 | − | 0.493689i | \(-0.835648\pi\) |
0.00727173 | − | 0.999974i | \(-0.497685\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.00000 | + | 8.66025i | 0.204808 | + | 0.354738i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.00000 | + | 5.19615i | 0.122679 | + | 0.212486i | ||||
\(599\) | 6.00000 | + | 10.3923i | 0.245153 | + | 0.424618i | 0.962175 | − | 0.272433i | \(-0.0878284\pi\) |
−0.717021 | + | 0.697051i | \(0.754495\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.0000 | + | 22.5167i | 0.530281 | + | 0.918474i | 0.999376 | + | 0.0353259i | \(0.0112469\pi\) |
−0.469095 | + | 0.883148i | \(0.655420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.50000 | − | 16.4545i | −0.386550 | − | 0.669523i | ||||
\(605\) | −7.00000 | −0.284590 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.00000 | 0.243532 | 0.121766 | − | 0.992559i | \(-0.461144\pi\) | ||||
0.121766 | + | 0.992559i | \(0.461144\pi\) | |||||||
\(608\) | 3.50000 | − | 6.06218i | 0.141944 | − | 0.245854i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.50000 | − | 11.2583i | −0.263177 | − | 0.455836i | ||||
\(611\) | −8.00000 | − | 13.8564i | −0.323645 | − | 0.560570i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.00000 | − | 8.66025i | 0.201948 | − | 0.349784i | −0.747208 | − | 0.664590i | \(-0.768606\pi\) |
0.949156 | + | 0.314806i | \(0.101939\pi\) | |||||||
\(614\) | −3.50000 | + | 6.06218i | −0.141249 | + | 0.244650i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.0000 | + | 19.0526i | −0.442843 | + | 0.767027i | −0.997899 | − | 0.0647859i | \(-0.979364\pi\) |
0.555056 | + | 0.831813i | \(0.312697\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.0000 | 0.442127 | 0.221064 | − | 0.975259i | \(-0.429047\pi\) | ||||
0.221064 | + | 0.975259i | \(0.429047\pi\) | |||||||
\(620\) | 2.00000 | − | 3.46410i | 0.0803219 | − | 0.139122i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.0000 | 0.400963 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | −3.00000 | − | 5.19615i | −0.119904 | − | 0.207680i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.50000 | − | 9.52628i | 0.219474 | − | 0.380140i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.00000 | 0.358284 | 0.179142 | − | 0.983823i | \(-0.442668\pi\) | ||||
0.179142 | + | 0.983823i | \(0.442668\pi\) | |||||||
\(632\) | −5.50000 | + | 9.52628i | −0.218778 | + | 0.378935i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.0000 | − | 20.7846i | −0.476581 | − | 0.825462i | ||||
\(635\) | −19.0000 | −0.753992 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −16.0000 | −0.633446 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | −47.0000 | −1.85639 | −0.928194 | − | 0.372096i | \(-0.878639\pi\) | ||||
−0.928194 | + | 0.372096i | \(0.878639\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.00000 | + | 10.3923i | −0.236617 | + | 0.409832i | −0.959741 | − | 0.280885i | \(-0.909372\pi\) |
0.723124 | + | 0.690718i | \(0.242705\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.0000 | − | 36.3731i | 0.825595 | − | 1.42997i | −0.0758684 | − | 0.997118i | \(-0.524173\pi\) |
0.901464 | − | 0.432855i | \(-0.142494\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.00000 | − | 6.92820i | −0.157014 | − | 0.271956i | ||||
\(650\) | 4.00000 | + | 6.92820i | 0.156893 | + | 0.271746i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.00000 | − | 5.19615i | 0.117489 | − | 0.203497i | ||||
\(653\) | 32.0000 | 1.25226 | 0.626128 | − | 0.779720i | \(-0.284639\pi\) | ||||
0.626128 | + | 0.779720i | \(0.284639\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.0000 | 0.586098 | ||||||||
\(656\) | 6.00000 | + | 10.3923i | 0.234261 | + | 0.405751i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.0000 | + | 17.3205i | 0.389545 | + | 0.674711i | 0.992388 | − | 0.123148i | \(-0.0392990\pi\) |
−0.602844 | + | 0.797859i | \(0.705966\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.5000 | − | 26.8468i | −0.602880 | − | 1.04422i | −0.992383 | − | 0.123194i | \(-0.960686\pi\) |
0.389503 | − | 0.921025i | \(-0.372647\pi\) | |||||||
\(662\) | −2.00000 | − | 3.46410i | −0.0777322 | − | 0.134636i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | + | 10.3923i | 0.232845 | + | 0.403300i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0000 | + | 20.7846i | 0.464642 | + | 0.804783i | ||||
\(668\) | 2.00000 | 0.0773823 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.00000 | 0.0772667 | ||||||||
\(671\) | 13.0000 | − | 22.5167i | 0.501859 | − | 0.869246i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.500000 | + | 0.866025i | 0.0192736 | + | 0.0333828i | 0.875501 | − | 0.483216i | \(-0.160531\pi\) |
−0.856228 | + | 0.516599i | \(0.827198\pi\) | |||||||
\(674\) | −11.0000 | − | 19.0526i | −0.423704 | − | 0.733877i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.50000 | − | 7.79423i | 0.173077 | − | 0.299778i | ||||
\(677\) | −3.00000 | + | 5.19615i | −0.115299 | + | 0.199704i | −0.917899 | − | 0.396813i | \(-0.870116\pi\) |
0.802600 | + | 0.596518i | \(0.203449\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.00000 | 0.306336 | ||||||||
\(683\) | −5.00000 | + | 8.66025i | −0.191320 | + | 0.331375i | −0.945688 | − | 0.325076i | \(-0.894610\pi\) |
0.754368 | + | 0.656452i | \(0.227943\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.00000 | 0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.00000 | −0.304997 | ||||||||
\(689\) | −4.00000 | − | 6.92820i | −0.152388 | − | 0.263944i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.5000 | + | 25.1147i | −0.551606 | + | 0.955410i | 0.446553 | + | 0.894757i | \(0.352651\pi\) |
−0.998159 | + | 0.0606524i | \(0.980682\pi\) | |||||||
\(692\) | −22.0000 | −0.836315 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | 4.50000 | − | 7.79423i | 0.170695 | − | 0.295652i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −30.0000 | −1.13552 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.00000 | −0.0755390 | −0.0377695 | − | 0.999286i | \(-0.512025\pi\) | ||||
−0.0377695 | + | 0.999286i | \(0.512025\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.0000 | − | 36.3731i | 0.792030 | − | 1.37184i | ||||
\(704\) | 2.00000 | 0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.0000 | − | 20.7846i | 0.451626 | − | 0.782239i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.0000 | − | 27.7128i | 0.600893 | − | 1.04078i | −0.391794 | − | 0.920053i | \(-0.628145\pi\) |
0.992686 | − | 0.120723i | \(-0.0385214\pi\) | |||||||
\(710\) | 2.50000 | − | 4.33013i | 0.0938233 | − | 0.162507i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.00000 | + | 12.1244i | 0.262336 | + | 0.454379i | ||||
\(713\) | −6.00000 | − | 10.3923i | −0.224702 | − | 0.389195i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.00000 | − | 3.46410i | 0.0747958 | − | 0.129550i | ||||
\(716\) | 24.0000 | 0.896922 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 29.0000 | 1.08227 | ||||||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 15.0000 | + | 25.9808i | 0.558242 | + | 0.966904i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.50000 | + | 6.06218i | 0.130076 | + | 0.225299i | ||||
\(725\) | 16.0000 | + | 27.7128i | 0.594225 | + | 1.02923i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.0000 | + | 22.5167i | 0.482143 | + | 0.835097i | 0.999790 | − | 0.0204978i | \(-0.00652512\pi\) |
−0.517647 | + | 0.855595i | \(0.673192\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.00000 | + | 12.1244i | 0.259082 | + | 0.448743i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.00000 | −0.0369358 | −0.0184679 | − | 0.999829i | \(-0.505879\pi\) | ||||
−0.0184679 | + | 0.999829i | \(0.505879\pi\) | |||||||
\(734\) | 16.0000 | − | 27.7128i | 0.590571 | − | 1.02290i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.50000 | − | 2.59808i | −0.0552907 | − | 0.0957664i | ||||
\(737\) | 2.00000 | + | 3.46410i | 0.0736709 | + | 0.127602i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.0000 | − | 32.9090i | 0.698926 | − | 1.21058i | −0.269913 | − | 0.962885i | \(-0.586995\pi\) |
0.968839 | − | 0.247691i | \(-0.0796718\pi\) | |||||||
\(740\) | 3.00000 | − | 5.19615i | 0.110282 | − | 0.191014i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.0000 | − | 41.5692i | 0.880475 | − | 1.52503i | 0.0296605 | − | 0.999560i | \(-0.490557\pi\) |
0.850814 | − | 0.525467i | \(-0.176109\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.0000 | −0.366372 | ||||||||
\(746\) | −16.0000 | + | 27.7128i | −0.585802 | + | 1.01464i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.0000 | −1.42313 | −0.711565 | − | 0.702620i | \(-0.752013\pi\) | ||||
−0.711565 | + | 0.702620i | \(0.752013\pi\) | |||||||
\(752\) | 4.00000 | + | 6.92820i | 0.145865 | + | 0.252646i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.00000 | + | 13.8564i | −0.291343 | + | 0.504621i | ||||
\(755\) | 19.0000 | 0.691481 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.0000 | −0.944986 | −0.472493 | − | 0.881334i | \(-0.656646\pi\) | ||||
−0.472493 | + | 0.881334i | \(0.656646\pi\) | |||||||
\(758\) | −6.00000 | + | 10.3923i | −0.217930 | + | 0.377466i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.50000 | + | 6.06218i | 0.126958 | + | 0.219898i | ||||
\(761\) | −20.0000 | −0.724999 | −0.362500 | − | 0.931984i | \(-0.618077\pi\) | ||||
−0.362500 | + | 0.931984i | \(0.618077\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3.00000 | −0.108536 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.00000 | + | 5.19615i | −0.108394 | + | 0.187745i | ||||
\(767\) | −8.00000 | −0.288863 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.00000 | − | 1.73205i | 0.0360609 | − | 0.0624593i | −0.847432 | − | 0.530904i | \(-0.821852\pi\) |
0.883493 | + | 0.468445i | \(0.155186\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.50000 | + | 4.33013i | −0.0899770 | + | 0.155845i | ||||
\(773\) | −10.5000 | + | 18.1865i | −0.377659 | + | 0.654124i | −0.990721 | − | 0.135910i | \(-0.956604\pi\) |
0.613062 | + | 0.790034i | \(0.289937\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.00000 | − | 13.8564i | −0.287368 | − | 0.497737i | ||||
\(776\) | 1.00000 | + | 1.73205i | 0.0358979 | + | 0.0621770i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.0000 | − | 25.9808i | 0.537776 | − | 0.931455i | ||||
\(779\) | −84.0000 | −3.00961 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0000 | 0.357828 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.50000 | + | 9.52628i | 0.196303 | + | 0.340007i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.00000 | + | 3.46410i | 0.0712923 | + | 0.123482i | 0.899468 | − | 0.436987i | \(-0.143954\pi\) |
−0.828176 | + | 0.560469i | \(0.810621\pi\) | |||||||
\(788\) | −6.00000 | − | 10.3923i | −0.213741 | − | 0.370211i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.50000 | − | 9.52628i | −0.195681 | − | 0.338930i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.0000 | − | 22.5167i | −0.461644 | − | 0.799590i | ||||
\(794\) | 14.0000 | 0.496841 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.0000 | 0.496217 | ||||||||
\(797\) | −25.5000 | + | 44.1673i | −0.903256 | + | 1.56449i | −0.0800155 | + | 0.996794i | \(0.525497\pi\) |
−0.823241 | + | 0.567692i | \(0.807836\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −2.00000 | − | 3.46410i | −0.0707107 | − | 0.122474i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.50000 | + | 2.59808i | −0.0529668 | + | 0.0917413i | ||||
\(803\) | −14.0000 | + | 24.2487i | −0.494049 | + | 0.855718i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.00000 | − | 6.92820i | 0.140894 | − | 0.244036i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.0000 | 0.386979 | ||||||||
\(809\) | 9.00000 | − | 15.5885i | 0.316423 | − | 0.548061i | −0.663316 | − | 0.748340i | \(-0.730851\pi\) |
0.979739 | + | 0.200279i | \(0.0641847\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.0000 | 0.983213 | 0.491606 | − | 0.870817i | \(-0.336410\pi\) | ||||
0.491606 | + | 0.870817i | \(0.336410\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.0000 | 0.420600 | ||||||||
\(815\) | 3.00000 | + | 5.19615i | 0.105085 | + | 0.182013i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.0000 | − | 48.4974i | 0.979596 | − | 1.69671i | ||||
\(818\) | −24.0000 | −0.839140 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.0000 | −0.419058 | ||||||||
\(821\) | −16.0000 | + | 27.7128i | −0.558404 | + | 0.967184i | 0.439226 | + | 0.898377i | \(0.355253\pi\) |
−0.997630 | + | 0.0688073i | \(0.978081\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.0000 | + | 38.1051i | 0.766872 | + | 1.32826i | 0.939251 | + | 0.343230i | \(0.111521\pi\) |
−0.172379 | + | 0.985031i | \(0.555146\pi\) | |||||||
\(824\) | 8.00000 | 0.278693 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.0000 | −1.04320 | −0.521601 | − | 0.853189i | \(-0.674665\pi\) | ||||
−0.521601 | + | 0.853189i | \(0.674665\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.00000 | + | 12.1244i | −0.243120 | + | 0.421096i | −0.961601 | − | 0.274450i | \(-0.911504\pi\) |
0.718481 | + | 0.695546i | \(0.244838\pi\) | |||||||
\(830\) | −12.0000 | −0.416526 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.00000 | − | 1.73205i | 0.0346688 | − | 0.0600481i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.00000 | + | 1.73205i | −0.0346064 | + | 0.0599401i | ||||
\(836\) | −7.00000 | + | 12.1244i | −0.242100 | + | 0.419330i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.50000 | − | 4.33013i | −0.0863611 | − | 0.149582i | ||||
\(839\) | 15.0000 | + | 25.9808i | 0.517858 | + | 0.896956i | 0.999785 | + | 0.0207443i | \(0.00660359\pi\) |
−0.481927 | + | 0.876211i | \(0.660063\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.5000 | + | 30.3109i | −0.603448 | + | 1.04520i | ||||
\(842\) | 36.0000 | 1.24064 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −22.0000 | −0.757271 | ||||||||
\(845\) | 4.50000 | + | 7.79423i | 0.154805 | + | 0.268130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.00000 | + | 3.46410i | 0.0686803 | + | 0.118958i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.00000 | − | 15.5885i | −0.308516 | − | 0.534365i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.5000 | − | 32.0429i | −0.633428 | − | 1.09713i | −0.986846 | − | 0.161664i | \(-0.948314\pi\) |
0.353418 | − | 0.935466i | \(-0.385019\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.00000 | − | 6.92820i | −0.136717 | − | 0.236801i | ||||
\(857\) | −18.0000 | −0.614868 | −0.307434 | − | 0.951569i | \(-0.599470\pi\) | ||||
−0.307434 | + | 0.951569i | \(0.599470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.0000 | −1.22830 | −0.614152 | − | 0.789188i | \(-0.710502\pi\) | ||||
−0.614152 | + | 0.789188i | \(0.710502\pi\) | |||||||
\(860\) | 4.00000 | − | 6.92820i | 0.136399 | − | 0.236250i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.0000 | − | 27.7128i | −0.544962 | − | 0.943902i | ||||
\(863\) | 28.5000 | + | 49.3634i | 0.970151 | + | 1.68035i | 0.695087 | + | 0.718925i | \(0.255366\pi\) |
0.275064 | + | 0.961426i | \(0.411301\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.0000 | − | 19.0526i | 0.374011 | − | 0.647806i | ||||
\(866\) | 14.0000 | − | 24.2487i | 0.475739 | − | 0.824005i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.0000 | − | 19.0526i | 0.373149 | − | 0.646314i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.00000 | 0.135535 | ||||||||
\(872\) | 2.00000 | − | 3.46410i | 0.0677285 | − | 0.117309i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 21.0000 | 0.710336 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.0000 | 0.810422 | 0.405211 | − | 0.914223i | \(-0.367198\pi\) | ||||
0.405211 | + | 0.914223i | \(0.367198\pi\) | |||||||
\(878\) | 18.0000 | + | 31.1769i | 0.607471 | + | 1.05217i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.00000 | + | 1.73205i | −0.0337100 | + | 0.0583874i | ||||
\(881\) | 28.0000 | 0.943344 | 0.471672 | − | 0.881774i | \(-0.343651\pi\) | ||||
0.471672 | + | 0.881774i | \(0.343651\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.0000 | −0.874970 | −0.437485 | − | 0.899226i | \(-0.644131\pi\) | ||||
−0.437485 | + | 0.899226i | \(0.644131\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.0000 | − | 20.7846i | −0.403148 | − | 0.698273i | ||||
\(887\) | 36.0000 | 1.20876 | 0.604381 | − | 0.796696i | \(-0.293421\pi\) | ||||
0.604381 | + | 0.796696i | \(0.293421\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −14.0000 | −0.469281 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.00000 | + | 1.73205i | −0.0334825 | + | 0.0579934i | ||||
\(893\) | −56.0000 | −1.87397 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0000 | + | 20.7846i | −0.401116 | + | 0.694753i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.50000 | + | 7.79423i | −0.150167 | + | 0.260097i | ||||
\(899\) | 16.0000 | − | 27.7128i | 0.533630 | − | 0.924274i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −12.0000 | − | 20.7846i | −0.399556 | − | 0.692052i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.500000 | − | 0.866025i | 0.0166298 | − | 0.0288036i | ||||
\(905\) | −7.00000 | −0.232688 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.00000 | −0.0664089 | −0.0332045 | − | 0.999449i | \(-0.510571\pi\) | ||||
−0.0332045 | + | 0.999449i | \(0.510571\pi\) | |||||||
\(908\) | −8.50000 | − | 14.7224i | −0.282082 | − | 0.488581i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.500000 | − | 0.866025i | −0.0165657 | − | 0.0286927i | 0.857624 | − | 0.514278i | \(-0.171940\pi\) |
−0.874189 | + | 0.485585i | \(0.838607\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.0000 | − | 20.7846i | −0.397142 | − | 0.687870i | ||||
\(914\) | 8.50000 | + | 14.7224i | 0.281155 | + | 0.486975i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.50000 | − | 11.2583i | −0.214766 | − | 0.371986i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.50000 | − | 12.9904i | −0.247402 | − | 0.428513i | 0.715402 | − | 0.698713i | \(-0.246244\pi\) |
−0.962804 | + | 0.270200i | \(0.912910\pi\) | |||||||
\(920\) | 3.00000 | 0.0989071 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.00000 | 0.296399 | ||||||||
\(923\) | 5.00000 | − | 8.66025i | 0.164577 | − | 0.285056i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.0000 | − | 20.7846i | −0.394558 | − | 0.683394i | ||||
\(926\) | −0.500000 | − | 0.866025i | −0.0164310 | − | 0.0284594i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.00000 | − | 6.92820i | 0.131306 | − | 0.227429i | ||||
\(929\) | −3.00000 | + | 5.19615i | −0.0984268 | + | 0.170480i | −0.911034 | − | 0.412332i | \(-0.864714\pi\) |
0.812607 | + | 0.582812i | \(0.198048\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.500000 | − | 0.866025i | 0.0163780 | − | 0.0283676i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28.0000 | 0.916188 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.00000 | −0.260931 | ||||||||
\(941\) | 1.50000 | + | 2.59808i | 0.0488986 | + | 0.0846949i | 0.889439 | − | 0.457054i | \(-0.151096\pi\) |
−0.840540 | + | 0.541749i | \(0.817762\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.0000 | + | 31.1769i | −0.586161 | + | 1.01526i | ||||
\(944\) | 4.00000 | 0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.0000 | 0.520205 | ||||||||
\(947\) | 5.00000 | − | 8.66025i | 0.162478 | − | 0.281420i | −0.773279 | − | 0.634066i | \(-0.781385\pi\) |
0.935757 | + | 0.352646i | \(0.114718\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.0000 | + | 24.2487i | 0.454459 | + | 0.787146i | ||||
\(950\) | 28.0000 | 0.908440 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.0000 | 1.74923 | 0.874616 | − | 0.484817i | \(-0.161114\pi\) | ||||
0.874616 | + | 0.484817i | \(0.161114\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.50000 | − | 2.59808i | 0.0485389 | − | 0.0840718i | ||||
\(956\) | 15.0000 | 0.485135 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.0000 | − | 20.7846i | 0.387702 | − | 0.671520i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | 6.00000 | − | 10.3923i | 0.193448 | − | 0.335061i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.00000 | + | 8.66025i | 0.161039 | + | 0.278928i | ||||
\(965\) | −2.50000 | − | 4.33013i | −0.0804778 | − | 0.139392i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.50000 | + | 11.2583i | −0.209026 | + | 0.362043i | −0.951408 | − | 0.307933i | \(-0.900363\pi\) |
0.742382 | + | 0.669977i | \(0.233696\pi\) | |||||||
\(968\) | 7.00000 | 0.224989 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.00000 | −0.0642161 | ||||||||
\(971\) | 17.5000 | + | 30.3109i | 0.561602 | + | 0.972723i | 0.997357 | + | 0.0726575i | \(0.0231480\pi\) |
−0.435755 | + | 0.900065i | \(0.643519\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 12.5000 | + | 21.6506i | 0.400526 | + | 0.693731i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.50000 | + | 11.2583i | 0.208060 | + | 0.360370i | ||||
\(977\) | −1.00000 | − | 1.73205i | −0.0319928 | − | 0.0554132i | 0.849586 | − | 0.527451i | \(-0.176852\pi\) |
−0.881579 | + | 0.472037i | \(0.843519\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.0000 | − | 24.2487i | −0.447442 | − | 0.774992i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.00000 | − | 5.19615i | −0.0957338 | − | 0.165816i | ||||
\(983\) | −32.0000 | −1.02064 | −0.510321 | − | 0.859984i | \(-0.670473\pi\) | ||||
−0.510321 | + | 0.859984i | \(0.670473\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.0000 | 0.382352 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.00000 | + | 12.1244i | 0.222700 | + | 0.385727i | ||||
\(989\) | −12.0000 | − | 20.7846i | −0.381578 | − | 0.660912i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | + | 27.7128i | −0.508257 | + | 0.880327i | 0.491698 | + | 0.870766i | \(0.336377\pi\) |
−0.999954 | + | 0.00956046i | \(0.996957\pi\) | |||||||
\(992\) | −2.00000 | + | 3.46410i | −0.0635001 | + | 0.109985i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.00000 | + | 12.1244i | −0.221915 | + | 0.384368i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.0000 | −0.538395 | −0.269198 | − | 0.963085i | \(-0.586759\pi\) | ||||
−0.269198 | + | 0.963085i | \(0.586759\pi\) | |||||||
\(998\) | 12.0000 | − | 20.7846i | 0.379853 | − | 0.657925i | ||||
\(999\) | 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 | 2646.2.h.j.361.1 | 2 | ||
3.2 | odd | 2 | 882.2.h.a.67.1 | 2 | |||
7.2 | even | 3 | 2646.2.e.a.1549.1 | 2 | |||
7.3 | odd | 6 | 2646.2.f.h.1765.1 | 2 | |||
7.4 | even | 3 | 2646.2.f.f.1765.1 | 2 | |||
7.5 | odd | 6 | 2646.2.e.d.1549.1 | 2 | |||
7.6 | odd | 2 | 2646.2.h.g.361.1 | 2 | |||
9.2 | odd | 6 | 882.2.e.j.655.1 | 2 | |||
9.7 | even | 3 | 2646.2.e.a.2125.1 | 2 | |||
21.2 | odd | 6 | 882.2.e.j.373.1 | 2 | |||
21.5 | even | 6 | 882.2.e.f.373.1 | 2 | |||
21.11 | odd | 6 | 882.2.f.c.589.1 | yes | 2 | ||
21.17 | even | 6 | 882.2.f.b.589.1 | yes | 2 | ||
21.20 | even | 2 | 882.2.h.d.67.1 | 2 | |||
63.2 | odd | 6 | 882.2.h.a.79.1 | 2 | |||
63.4 | even | 3 | 7938.2.a.k.1.1 | 1 | |||
63.11 | odd | 6 | 882.2.f.c.295.1 | yes | 2 | ||
63.16 | even | 3 | inner | 2646.2.h.j.667.1 | 2 | ||
63.20 | even | 6 | 882.2.e.f.655.1 | 2 | |||
63.25 | even | 3 | 2646.2.f.f.883.1 | 2 | |||
63.31 | odd | 6 | 7938.2.a.f.1.1 | 1 | |||
63.32 | odd | 6 | 7938.2.a.v.1.1 | 1 | |||
63.34 | odd | 6 | 2646.2.e.d.2125.1 | 2 | |||
63.38 | even | 6 | 882.2.f.b.295.1 | ✓ | 2 | ||
63.47 | even | 6 | 882.2.h.d.79.1 | 2 | |||
63.52 | odd | 6 | 2646.2.f.h.883.1 | 2 | |||
63.59 | even | 6 | 7938.2.a.ba.1.1 | 1 | |||
63.61 | odd | 6 | 2646.2.h.g.667.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.2.e.f.373.1 | 2 | 21.5 | even | 6 | |||
882.2.e.f.655.1 | 2 | 63.20 | even | 6 | |||
882.2.e.j.373.1 | 2 | 21.2 | odd | 6 | |||
882.2.e.j.655.1 | 2 | 9.2 | odd | 6 | |||
882.2.f.b.295.1 | ✓ | 2 | 63.38 | even | 6 | ||
882.2.f.b.589.1 | yes | 2 | 21.17 | even | 6 | ||
882.2.f.c.295.1 | yes | 2 | 63.11 | odd | 6 | ||
882.2.f.c.589.1 | yes | 2 | 21.11 | odd | 6 | ||
882.2.h.a.67.1 | 2 | 3.2 | odd | 2 | |||
882.2.h.a.79.1 | 2 | 63.2 | odd | 6 | |||
882.2.h.d.67.1 | 2 | 21.20 | even | 2 | |||
882.2.h.d.79.1 | 2 | 63.47 | even | 6 | |||
2646.2.e.a.1549.1 | 2 | 7.2 | even | 3 | |||
2646.2.e.a.2125.1 | 2 | 9.7 | even | 3 | |||
2646.2.e.d.1549.1 | 2 | 7.5 | odd | 6 | |||
2646.2.e.d.2125.1 | 2 | 63.34 | odd | 6 | |||
2646.2.f.f.883.1 | 2 | 63.25 | even | 3 | |||
2646.2.f.f.1765.1 | 2 | 7.4 | even | 3 | |||
2646.2.f.h.883.1 | 2 | 63.52 | odd | 6 | |||
2646.2.f.h.1765.1 | 2 | 7.3 | odd | 6 | |||
2646.2.h.g.361.1 | 2 | 7.6 | odd | 2 | |||
2646.2.h.g.667.1 | 2 | 63.61 | odd | 6 | |||
2646.2.h.j.361.1 | 2 | 1.1 | even | 1 | trivial | ||
2646.2.h.j.667.1 | 2 | 63.16 | even | 3 | inner | ||
7938.2.a.f.1.1 | 1 | 63.31 | odd | 6 | |||
7938.2.a.k.1.1 | 1 | 63.4 | even | 3 | |||
7938.2.a.v.1.1 | 1 | 63.32 | odd | 6 | |||
7938.2.a.ba.1.1 | 1 | 63.59 | even | 6 |