Properties

Label 2646.2.l.b.1097.6
Level $2646$
Weight $2$
Character 2646.1097
Analytic conductor $21.128$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2646,2,Mod(521,2646)]
 
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([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2646.521");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.l (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: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1097.6
Root \(1.40917 + 1.00709i\) of defining polynomial
Character \(\chi\) \(=\) 2646.1097
Dual form 2646.2.l.b.521.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +(-1.17468 - 2.03460i) q^{5} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +(-1.17468 - 2.03460i) q^{5} -1.00000i q^{8} +(2.03460 - 1.17468i) q^{10} +(-4.91614 - 2.83834i) q^{11} +(1.48943 + 0.859925i) q^{13} +1.00000 q^{16} +(-0.884414 - 1.53185i) q^{17} +(-0.986680 - 0.569660i) q^{19} +(1.17468 + 2.03460i) q^{20} +(2.83834 - 4.91614i) q^{22} +(-3.18272 + 1.83755i) q^{23} +(-0.259741 + 0.449885i) q^{25} +(-0.859925 + 1.48943i) q^{26} +(-3.59886 + 2.07781i) q^{29} +8.37019i q^{31} +1.00000i q^{32} +(1.53185 - 0.884414i) q^{34} +(4.59886 - 7.96547i) q^{37} +(0.569660 - 0.986680i) q^{38} +(-2.03460 + 1.17468i) q^{40} +(-3.99709 + 6.92317i) q^{41} +(1.76053 + 3.04933i) q^{43} +(4.91614 + 2.83834i) q^{44} +(-1.83755 - 3.18272i) q^{46} +11.8099 q^{47} +(-0.449885 - 0.259741i) q^{50} +(-1.48943 - 0.859925i) q^{52} +13.3365i q^{55} +(-2.07781 - 3.59886i) q^{58} +2.22966 q^{59} +8.99970i q^{61} -8.37019 q^{62} -1.00000 q^{64} -4.04054i q^{65} +10.8712 q^{67} +(0.884414 + 1.53185i) q^{68} +4.52106i q^{71} +(-4.62660 + 2.67117i) q^{73} +(7.96547 + 4.59886i) q^{74} +(0.986680 + 0.569660i) q^{76} -13.0284 q^{79} +(-1.17468 - 2.03460i) q^{80} +(-6.92317 - 3.99709i) q^{82} +(6.27298 + 10.8651i) q^{83} +(-2.07781 + 3.59886i) q^{85} +(-3.04933 + 1.76053i) q^{86} +(-2.83834 + 4.91614i) q^{88} +(-0.580529 + 1.00551i) q^{89} +(3.18272 - 1.83755i) q^{92} +11.8099i q^{94} +2.67667i q^{95} +(-3.97536 + 2.29517i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{4} - 12 q^{11} + 16 q^{16} - 48 q^{23} - 8 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} + 12 q^{44} - 12 q^{46} - 60 q^{50} - 12 q^{58} - 16 q^{64} + 56 q^{67} + 36 q^{74} + 8 q^{79} - 12 q^{85} - 24 q^{86} + 48 q^{92}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) −1.17468 2.03460i −0.525332 0.909902i −0.999565 0.0295026i \(-0.990608\pi\)
0.474232 0.880400i \(-0.342726\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 2.03460 1.17468i 0.643398 0.371466i
\(11\) −4.91614 2.83834i −1.48227 0.855790i −0.482475 0.875910i \(-0.660262\pi\)
−0.999798 + 0.0201197i \(0.993595\pi\)
\(12\) 0 0
\(13\) 1.48943 + 0.859925i 0.413094 + 0.238500i 0.692118 0.721784i \(-0.256678\pi\)
−0.279024 + 0.960284i \(0.590011\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −0.884414 1.53185i −0.214502 0.371528i 0.738616 0.674126i \(-0.235480\pi\)
−0.953118 + 0.302598i \(0.902146\pi\)
\(18\) 0 0
\(19\) −0.986680 0.569660i −0.226360 0.130689i 0.382532 0.923942i \(-0.375052\pi\)
−0.608892 + 0.793253i \(0.708386\pi\)
\(20\) 1.17468 + 2.03460i 0.262666 + 0.454951i
\(21\) 0 0
\(22\) 2.83834 4.91614i 0.605135 1.04812i
\(23\) −3.18272 + 1.83755i −0.663644 + 0.383155i −0.793664 0.608356i \(-0.791829\pi\)
0.130020 + 0.991511i \(0.458496\pi\)
\(24\) 0 0
\(25\) −0.259741 + 0.449885i −0.0519482 + 0.0899769i
\(26\) −0.859925 + 1.48943i −0.168645 + 0.292102i
\(27\) 0 0
\(28\) 0 0
\(29\) −3.59886 + 2.07781i −0.668292 + 0.385839i −0.795429 0.606046i \(-0.792755\pi\)
0.127137 + 0.991885i \(0.459421\pi\)
\(30\) 0 0
\(31\) 8.37019i 1.50333i 0.659545 + 0.751665i \(0.270749\pi\)
−0.659545 + 0.751665i \(0.729251\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 1.53185 0.884414i 0.262710 0.151676i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.59886 7.96547i 0.756049 1.30951i −0.188803 0.982015i \(-0.560461\pi\)
0.944851 0.327500i \(-0.106206\pi\)
\(38\) 0.569660 0.986680i 0.0924111 0.160061i
\(39\) 0 0
\(40\) −2.03460 + 1.17468i −0.321699 + 0.185733i
\(41\) −3.99709 + 6.92317i −0.624241 + 1.08122i 0.364446 + 0.931225i \(0.381258\pi\)
−0.988687 + 0.149993i \(0.952075\pi\)
\(42\) 0 0
\(43\) 1.76053 + 3.04933i 0.268478 + 0.465018i 0.968469 0.249134i \(-0.0801459\pi\)
−0.699991 + 0.714152i \(0.746813\pi\)
\(44\) 4.91614 + 2.83834i 0.741136 + 0.427895i
\(45\) 0 0
\(46\) −1.83755 3.18272i −0.270931 0.469267i
\(47\) 11.8099 1.72265 0.861324 0.508055i \(-0.169635\pi\)
0.861324 + 0.508055i \(0.169635\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −0.449885 0.259741i −0.0636233 0.0367329i
\(51\) 0 0
\(52\) −1.48943 0.859925i −0.206547 0.119250i
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) 0 0
\(55\) 13.3365i 1.79830i
\(56\) 0 0
\(57\) 0 0
\(58\) −2.07781 3.59886i −0.272829 0.472554i
\(59\) 2.22966 0.290277 0.145139 0.989411i \(-0.453637\pi\)
0.145139 + 0.989411i \(0.453637\pi\)
\(60\) 0 0
\(61\) 8.99970i 1.15229i 0.817346 + 0.576146i \(0.195444\pi\)
−0.817346 + 0.576146i \(0.804556\pi\)
\(62\) −8.37019 −1.06301
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 4.04054i 0.501167i
\(66\) 0 0
\(67\) 10.8712 1.32813 0.664067 0.747673i \(-0.268829\pi\)
0.664067 + 0.747673i \(0.268829\pi\)
\(68\) 0.884414 + 1.53185i 0.107251 + 0.185764i
\(69\) 0 0
\(70\) 0 0
\(71\) 4.52106i 0.536551i 0.963342 + 0.268276i \(0.0864538\pi\)
−0.963342 + 0.268276i \(0.913546\pi\)
\(72\) 0 0
\(73\) −4.62660 + 2.67117i −0.541503 + 0.312637i −0.745688 0.666295i \(-0.767879\pi\)
0.204185 + 0.978932i \(0.434546\pi\)
\(74\) 7.96547 + 4.59886i 0.925967 + 0.534607i
\(75\) 0 0
\(76\) 0.986680 + 0.569660i 0.113180 + 0.0653445i
\(77\) 0 0
\(78\) 0 0
\(79\) −13.0284 −1.46581 −0.732907 0.680329i \(-0.761837\pi\)
−0.732907 + 0.680329i \(0.761837\pi\)
\(80\) −1.17468 2.03460i −0.131333 0.227476i
\(81\) 0 0
\(82\) −6.92317 3.99709i −0.764536 0.441405i
\(83\) 6.27298 + 10.8651i 0.688549 + 1.19260i 0.972307 + 0.233707i \(0.0750855\pi\)
−0.283758 + 0.958896i \(0.591581\pi\)
\(84\) 0 0
\(85\) −2.07781 + 3.59886i −0.225370 + 0.390352i
\(86\) −3.04933 + 1.76053i −0.328817 + 0.189843i
\(87\) 0 0
\(88\) −2.83834 + 4.91614i −0.302568 + 0.524062i
\(89\) −0.580529 + 1.00551i −0.0615360 + 0.106583i −0.895152 0.445761i \(-0.852933\pi\)
0.833616 + 0.552344i \(0.186267\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.18272 1.83755i 0.331822 0.191577i
\(93\) 0 0
\(94\) 11.8099i 1.21810i
\(95\) 2.67667i 0.274621i
\(96\) 0 0
\(97\) −3.97536 + 2.29517i −0.403636 + 0.233039i −0.688052 0.725662i \(-0.741534\pi\)
0.284416 + 0.958701i \(0.408200\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.259741 0.449885i 0.0259741 0.0449885i
\(101\) −3.31155 + 5.73577i −0.329511 + 0.570730i −0.982415 0.186711i \(-0.940217\pi\)
0.652904 + 0.757441i \(0.273551\pi\)
\(102\) 0 0
\(103\) 5.07471 2.92989i 0.500026 0.288690i −0.228698 0.973497i \(-0.573447\pi\)
0.728724 + 0.684807i \(0.240114\pi\)
\(104\) 0.859925 1.48943i 0.0843225 0.146051i
\(105\) 0 0
\(106\) 0 0
\(107\) 4.08386 + 2.35782i 0.394802 + 0.227939i 0.684239 0.729258i \(-0.260135\pi\)
−0.289437 + 0.957197i \(0.593468\pi\)
\(108\) 0 0
\(109\) −2.11835 3.66908i −0.202901 0.351435i 0.746561 0.665317i \(-0.231704\pi\)
−0.949462 + 0.313882i \(0.898370\pi\)
\(110\) −13.3365 −1.27159
\(111\) 0 0
\(112\) 0 0
\(113\) −5.91693 3.41614i −0.556618 0.321363i 0.195169 0.980770i \(-0.437474\pi\)
−0.751787 + 0.659406i \(0.770808\pi\)
\(114\) 0 0
\(115\) 7.47736 + 4.31705i 0.697267 + 0.402567i
\(116\) 3.59886 2.07781i 0.334146 0.192919i
\(117\) 0 0
\(118\) 2.22966i 0.205257i
\(119\) 0 0
\(120\) 0 0
\(121\) 10.6123 + 18.3810i 0.964754 + 1.67100i
\(122\) −8.99970 −0.814794
\(123\) 0 0
\(124\) 8.37019i 0.751665i
\(125\) −10.5263 −0.941504
\(126\) 0 0
\(127\) −6.67667 −0.592459 −0.296229 0.955117i \(-0.595729\pi\)
−0.296229 + 0.955117i \(0.595729\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 4.04054 0.354379
\(131\) −3.73653 6.47185i −0.326462 0.565448i 0.655345 0.755329i \(-0.272523\pi\)
−0.981807 + 0.189881i \(0.939190\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 10.8712i 0.939133i
\(135\) 0 0
\(136\) −1.53185 + 0.884414i −0.131355 + 0.0758379i
\(137\) 6.91772 + 3.99395i 0.591021 + 0.341226i 0.765501 0.643435i \(-0.222491\pi\)
−0.174480 + 0.984661i \(0.555825\pi\)
\(138\) 0 0
\(139\) 17.9792 + 10.3803i 1.52498 + 0.880446i 0.999562 + 0.0295993i \(0.00942312\pi\)
0.525415 + 0.850846i \(0.323910\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.52106 −0.379399
\(143\) −4.88151 8.45502i −0.408212 0.707044i
\(144\) 0 0
\(145\) 8.45502 + 4.88151i 0.702151 + 0.405387i
\(146\) −2.67117 4.62660i −0.221068 0.382900i
\(147\) 0 0
\(148\) −4.59886 + 7.96547i −0.378024 + 0.654757i
\(149\) −1.03726 + 0.598865i −0.0849760 + 0.0490609i −0.541886 0.840452i \(-0.682290\pi\)
0.456910 + 0.889513i \(0.348956\pi\)
\(150\) 0 0
\(151\) −7.61229 + 13.1849i −0.619480 + 1.07297i 0.370101 + 0.928991i \(0.379323\pi\)
−0.989581 + 0.143979i \(0.954010\pi\)
\(152\) −0.569660 + 0.986680i −0.0462055 + 0.0800303i
\(153\) 0 0
\(154\) 0 0
\(155\) 17.0300 9.83228i 1.36788 0.789748i
\(156\) 0 0
\(157\) 10.0269i 0.800237i −0.916463 0.400118i \(-0.868969\pi\)
0.916463 0.400118i \(-0.131031\pi\)
\(158\) 13.0284i 1.03649i
\(159\) 0 0
\(160\) 2.03460 1.17468i 0.160850 0.0928665i
\(161\) 0 0
\(162\) 0 0
\(163\) −6.00158 + 10.3950i −0.470080 + 0.814202i −0.999415 0.0342109i \(-0.989108\pi\)
0.529335 + 0.848413i \(0.322442\pi\)
\(164\) 3.99709 6.92317i 0.312121 0.540609i
\(165\) 0 0
\(166\) −10.8651 + 6.27298i −0.843297 + 0.486878i
\(167\) −8.57472 + 14.8518i −0.663532 + 1.14927i 0.316150 + 0.948709i \(0.397610\pi\)
−0.979681 + 0.200561i \(0.935723\pi\)
\(168\) 0 0
\(169\) −5.02106 8.69673i −0.386235 0.668979i
\(170\) −3.59886 2.07781i −0.276020 0.159360i
\(171\) 0 0
\(172\) −1.76053 3.04933i −0.134239 0.232509i
\(173\) 1.98748 0.151105 0.0755525 0.997142i \(-0.475928\pi\)
0.0755525 + 0.997142i \(0.475928\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −4.91614 2.83834i −0.370568 0.213948i
\(177\) 0 0
\(178\) −1.00551 0.580529i −0.0753659 0.0435125i
\(179\) −7.19773 + 4.15561i −0.537984 + 0.310605i −0.744261 0.667889i \(-0.767198\pi\)
0.206278 + 0.978493i \(0.433865\pi\)
\(180\) 0 0
\(181\) 15.4541i 1.14870i 0.818611 + 0.574348i \(0.194744\pi\)
−0.818611 + 0.574348i \(0.805256\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 1.83755 + 3.18272i 0.135466 + 0.234634i
\(185\) −21.6088 −1.58871
\(186\) 0 0
\(187\) 10.0411i 0.734275i
\(188\) −11.8099 −0.861324
\(189\) 0 0
\(190\) −2.67667 −0.194186
\(191\) 12.3381i 0.892752i −0.894845 0.446376i \(-0.852714\pi\)
0.894845 0.446376i \(-0.147286\pi\)
\(192\) 0 0
\(193\) 4.39388 0.316279 0.158139 0.987417i \(-0.449451\pi\)
0.158139 + 0.987417i \(0.449451\pi\)
\(194\) −2.29517 3.97536i −0.164784 0.285414i
\(195\) 0 0
\(196\) 0 0
\(197\) 10.8865i 0.775632i −0.921737 0.387816i \(-0.873230\pi\)
0.921737 0.387816i \(-0.126770\pi\)
\(198\) 0 0
\(199\) −23.8733 + 13.7832i −1.69233 + 0.977068i −0.739703 + 0.672933i \(0.765034\pi\)
−0.952629 + 0.304135i \(0.901633\pi\)
\(200\) 0.449885 + 0.259741i 0.0318116 + 0.0183665i
\(201\) 0 0
\(202\) −5.73577 3.31155i −0.403567 0.233000i
\(203\) 0 0
\(204\) 0 0
\(205\) 18.7812 1.31174
\(206\) 2.92989 + 5.07471i 0.204135 + 0.353572i
\(207\) 0 0
\(208\) 1.48943 + 0.859925i 0.103274 + 0.0596250i
\(209\) 3.23377 + 5.60106i 0.223685 + 0.387433i
\(210\) 0 0
\(211\) 5.15561 8.92978i 0.354927 0.614751i −0.632179 0.774823i \(-0.717839\pi\)
0.987105 + 0.160071i \(0.0511724\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −2.35782 + 4.08386i −0.161177 + 0.279167i
\(215\) 4.13611 7.16396i 0.282081 0.488578i
\(216\) 0 0
\(217\) 0 0
\(218\) 3.66908 2.11835i 0.248502 0.143473i
\(219\) 0 0
\(220\) 13.3365i 0.899149i
\(221\) 3.04212i 0.204635i
\(222\) 0 0
\(223\) −6.24329 + 3.60456i −0.418081 + 0.241379i −0.694256 0.719728i \(-0.744267\pi\)
0.276175 + 0.961107i \(0.410933\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 3.41614 5.91693i 0.227238 0.393588i
\(227\) −6.37800 + 11.0470i −0.423323 + 0.733217i −0.996262 0.0863812i \(-0.972470\pi\)
0.572939 + 0.819598i \(0.305803\pi\)
\(228\) 0 0
\(229\) −3.89208 + 2.24709i −0.257196 + 0.148492i −0.623055 0.782178i \(-0.714109\pi\)
0.365859 + 0.930670i \(0.380775\pi\)
\(230\) −4.31705 + 7.47736i −0.284658 + 0.493042i
\(231\) 0 0
\(232\) 2.07781 + 3.59886i 0.136415 + 0.236277i
\(233\) 1.86545 + 1.07702i 0.122210 + 0.0705577i 0.559859 0.828588i \(-0.310855\pi\)
−0.437649 + 0.899146i \(0.644189\pi\)
\(234\) 0 0
\(235\) −13.8728 24.0284i −0.904963 1.56744i
\(236\) −2.22966 −0.145139
\(237\) 0 0
\(238\) 0 0
\(239\) 8.78317 + 5.07096i 0.568136 + 0.328013i 0.756404 0.654104i \(-0.226954\pi\)
−0.188269 + 0.982118i \(0.560288\pi\)
\(240\) 0 0
\(241\) −9.13490 5.27404i −0.588431 0.339731i 0.176046 0.984382i \(-0.443669\pi\)
−0.764477 + 0.644651i \(0.777003\pi\)
\(242\) −18.3810 + 10.6123i −1.18158 + 0.682184i
\(243\) 0 0
\(244\) 8.99970i 0.576146i
\(245\) 0 0
\(246\) 0 0
\(247\) −0.979729 1.69694i −0.0623387 0.107974i
\(248\) 8.37019 0.531507
\(249\) 0 0
\(250\) 10.5263i 0.665744i
\(251\) 29.3005 1.84943 0.924714 0.380662i \(-0.124304\pi\)
0.924714 + 0.380662i \(0.124304\pi\)
\(252\) 0 0
\(253\) 20.8623 1.31160
\(254\) 6.67667i 0.418932i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 3.81430 + 6.60656i 0.237930 + 0.412106i 0.960120 0.279588i \(-0.0901979\pi\)
−0.722190 + 0.691694i \(0.756865\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 4.04054i 0.250584i
\(261\) 0 0
\(262\) 6.47185 3.73653i 0.399832 0.230843i
\(263\) −10.5531 6.09281i −0.650729 0.375699i 0.138006 0.990431i \(-0.455931\pi\)
−0.788736 + 0.614733i \(0.789264\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −10.8712 −0.664067
\(269\) 1.38717 + 2.40264i 0.0845771 + 0.146492i 0.905211 0.424963i \(-0.139713\pi\)
−0.820634 + 0.571454i \(0.806379\pi\)
\(270\) 0 0
\(271\) −2.77815 1.60396i −0.168760 0.0974338i 0.413241 0.910622i \(-0.364397\pi\)
−0.582001 + 0.813188i \(0.697730\pi\)
\(272\) −0.884414 1.53185i −0.0536255 0.0928821i
\(273\) 0 0
\(274\) −3.99395 + 6.91772i −0.241283 + 0.417915i
\(275\) 2.55385 1.47446i 0.154003 0.0889135i
\(276\) 0 0
\(277\) −5.04054 + 8.73047i −0.302857 + 0.524563i −0.976782 0.214236i \(-0.931274\pi\)
0.673925 + 0.738800i \(0.264607\pi\)
\(278\) −10.3803 + 17.9792i −0.622569 + 1.07832i
\(279\) 0 0
\(280\) 0 0
\(281\) −4.21999 + 2.43641i −0.251743 + 0.145344i −0.620562 0.784157i \(-0.713096\pi\)
0.368819 + 0.929501i \(0.379762\pi\)
\(282\) 0 0
\(283\) 2.81781i 0.167502i 0.996487 + 0.0837508i \(0.0266900\pi\)
−0.996487 + 0.0837508i \(0.973310\pi\)
\(284\) 4.52106i 0.268276i
\(285\) 0 0
\(286\) 8.45502 4.88151i 0.499956 0.288650i
\(287\) 0 0
\(288\) 0 0
\(289\) 6.93562 12.0129i 0.407978 0.706638i
\(290\) −4.88151 + 8.45502i −0.286652 + 0.496496i
\(291\) 0 0
\(292\) 4.62660 2.67117i 0.270751 0.156318i
\(293\) 4.05694 7.02683i 0.237009 0.410512i −0.722846 0.691010i \(-0.757166\pi\)
0.959855 + 0.280498i \(0.0904995\pi\)
\(294\) 0 0
\(295\) −2.61914 4.53648i −0.152492 0.264124i
\(296\) −7.96547 4.59886i −0.462983 0.267304i
\(297\) 0 0
\(298\) −0.598865 1.03726i −0.0346913 0.0600871i
\(299\) −6.32061 −0.365530
\(300\) 0 0
\(301\) 0 0
\(302\) −13.1849 7.61229i −0.758705 0.438038i
\(303\) 0 0
\(304\) −0.986680 0.569660i −0.0565900 0.0326722i
\(305\) 18.3108 10.5718i 1.04847 0.605337i
\(306\) 0 0
\(307\) 10.8996i 0.622074i −0.950398 0.311037i \(-0.899324\pi\)
0.950398 0.311037i \(-0.100676\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 9.83228 + 17.0300i 0.558436 + 0.967240i
\(311\) 8.23637 0.467042 0.233521 0.972352i \(-0.424975\pi\)
0.233521 + 0.972352i \(0.424975\pi\)
\(312\) 0 0
\(313\) 33.8023i 1.91062i −0.295611 0.955308i \(-0.595523\pi\)
0.295611 0.955308i \(-0.404477\pi\)
\(314\) 10.0269 0.565853
\(315\) 0 0
\(316\) 13.0284 0.732907
\(317\) 6.73090i 0.378045i −0.981973 0.189022i \(-0.939468\pi\)
0.981973 0.189022i \(-0.0605319\pi\)
\(318\) 0 0
\(319\) 23.5900 1.32079
\(320\) 1.17468 + 2.03460i 0.0656665 + 0.113738i
\(321\) 0 0
\(322\) 0 0
\(323\) 2.01526i 0.112132i
\(324\) 0 0
\(325\) −0.773734 + 0.446715i −0.0429190 + 0.0247793i
\(326\) −10.3950 6.00158i −0.575728 0.332397i
\(327\) 0 0
\(328\) 6.92317 + 3.99709i 0.382268 + 0.220703i
\(329\) 0 0
\(330\) 0 0
\(331\) −32.0569 −1.76200 −0.881002 0.473112i \(-0.843131\pi\)
−0.881002 + 0.473112i \(0.843131\pi\)
\(332\) −6.27298 10.8651i −0.344275 0.596301i
\(333\) 0 0
\(334\) −14.8518 8.57472i −0.812657 0.469188i
\(335\) −12.7702 22.1187i −0.697712 1.20847i
\(336\) 0 0
\(337\) −12.1123 + 20.9791i −0.659799 + 1.14280i 0.320869 + 0.947124i \(0.396025\pi\)
−0.980668 + 0.195681i \(0.937308\pi\)
\(338\) 8.69673 5.02106i 0.473040 0.273110i
\(339\) 0 0
\(340\) 2.07781 3.59886i 0.112685 0.195176i
\(341\) 23.7574 41.1490i 1.28654 2.22834i
\(342\) 0 0
\(343\) 0 0
\(344\) 3.04933 1.76053i 0.164409 0.0949214i
\(345\) 0 0
\(346\) 1.98748i 0.106847i
\(347\) 22.7999i 1.22396i 0.790873 + 0.611981i \(0.209627\pi\)
−0.790873 + 0.611981i \(0.790373\pi\)
\(348\) 0 0
\(349\) −2.46389 + 1.42253i −0.131889 + 0.0761461i −0.564493 0.825438i \(-0.690928\pi\)
0.432604 + 0.901584i \(0.357595\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 2.83834 4.91614i 0.151284 0.262031i
\(353\) 3.57212 6.18709i 0.190125 0.329306i −0.755167 0.655533i \(-0.772444\pi\)
0.945291 + 0.326227i \(0.105777\pi\)
\(354\) 0 0
\(355\) 9.19856 5.31079i 0.488209 0.281868i
\(356\) 0.580529 1.00551i 0.0307680 0.0532917i
\(357\) 0 0
\(358\) −4.15561 7.19773i −0.219631 0.380412i
\(359\) 10.0491 + 5.80186i 0.530372 + 0.306210i 0.741168 0.671320i \(-0.234272\pi\)
−0.210796 + 0.977530i \(0.567606\pi\)
\(360\) 0 0
\(361\) −8.85097 15.3303i −0.465841 0.806860i
\(362\) −15.4541 −0.812250
\(363\) 0 0
\(364\) 0 0
\(365\) 10.8695 + 6.27554i 0.568938 + 0.328477i
\(366\) 0 0
\(367\) −6.78525 3.91747i −0.354187 0.204490i 0.312341 0.949970i \(-0.398887\pi\)
−0.666528 + 0.745480i \(0.732220\pi\)
\(368\) −3.18272 + 1.83755i −0.165911 + 0.0957887i
\(369\) 0 0
\(370\) 21.6088i 1.12339i
\(371\) 0 0
\(372\) 0 0
\(373\) −12.8339 22.2289i −0.664512 1.15097i −0.979417 0.201845i \(-0.935306\pi\)
0.314905 0.949123i \(-0.398027\pi\)
\(374\) −10.0411 −0.519211
\(375\) 0 0
\(376\) 11.8099i 0.609048i
\(377\) −7.14702 −0.368091
\(378\) 0 0
\(379\) −15.1045 −0.775868 −0.387934 0.921687i \(-0.626811\pi\)
−0.387934 + 0.921687i \(0.626811\pi\)
\(380\) 2.67667i 0.137310i
\(381\) 0 0
\(382\) 12.3381 0.631271
\(383\) −0.763322 1.32211i −0.0390040 0.0675568i 0.845864 0.533398i \(-0.179085\pi\)
−0.884868 + 0.465841i \(0.845752\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 4.39388i 0.223643i
\(387\) 0 0
\(388\) 3.97536 2.29517i 0.201818 0.116520i
\(389\) 12.8948 + 7.44483i 0.653794 + 0.377468i 0.789908 0.613225i \(-0.210128\pi\)
−0.136115 + 0.990693i \(0.543462\pi\)
\(390\) 0 0
\(391\) 5.62969 + 3.25030i 0.284706 + 0.164375i
\(392\) 0 0
\(393\) 0 0
\(394\) 10.8865 0.548454
\(395\) 15.3042 + 26.5077i 0.770039 + 1.33375i
\(396\) 0 0
\(397\) 24.9302 + 14.3935i 1.25121 + 0.722388i 0.971350 0.237653i \(-0.0763780\pi\)
0.279862 + 0.960040i \(0.409711\pi\)
\(398\) −13.7832 23.8733i −0.690892 1.19666i
\(399\) 0 0
\(400\) −0.259741 + 0.449885i −0.0129871 + 0.0224942i
\(401\) −33.0592 + 19.0868i −1.65090 + 0.953147i −0.674196 + 0.738552i \(0.735510\pi\)
−0.976703 + 0.214595i \(0.931157\pi\)
\(402\) 0 0
\(403\) −7.19773 + 12.4668i −0.358544 + 0.621017i
\(404\) 3.31155 5.73577i 0.164756 0.285365i
\(405\) 0 0
\(406\) 0 0
\(407\) −45.2173 + 26.1062i −2.24134 + 1.29404i
\(408\) 0 0
\(409\) 6.96694i 0.344493i −0.985054 0.172247i \(-0.944897\pi\)
0.985054 0.172247i \(-0.0551026\pi\)
\(410\) 18.7812i 0.927538i
\(411\) 0 0
\(412\) −5.07471 + 2.92989i −0.250013 + 0.144345i
\(413\) 0 0
\(414\) 0 0
\(415\) 14.7375 25.5261i 0.723435 1.25303i
\(416\) −0.859925 + 1.48943i −0.0421613 + 0.0730255i
\(417\) 0 0
\(418\) −5.60106 + 3.23377i −0.273957 + 0.158169i
\(419\) 17.4232 30.1778i 0.851177 1.47428i −0.0289690 0.999580i \(-0.509222\pi\)
0.880146 0.474702i \(-0.157444\pi\)
\(420\) 0 0
\(421\) 2.84597 + 4.92936i 0.138704 + 0.240242i 0.927006 0.375046i \(-0.122373\pi\)
−0.788302 + 0.615288i \(0.789040\pi\)
\(422\) 8.92978 + 5.15561i 0.434695 + 0.250971i
\(423\) 0 0
\(424\) 0 0
\(425\) 0.918875 0.0445720
\(426\) 0 0
\(427\) 0 0
\(428\) −4.08386 2.35782i −0.197401 0.113969i
\(429\) 0 0
\(430\) 7.16396 + 4.13611i 0.345477 + 0.199461i
\(431\) 26.2350 15.1468i 1.26370 0.729595i 0.289908 0.957055i \(-0.406375\pi\)
0.973787 + 0.227460i \(0.0730420\pi\)
\(432\) 0 0
\(433\) 23.6094i 1.13459i −0.823513 0.567297i \(-0.807989\pi\)
0.823513 0.567297i \(-0.192011\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2.11835 + 3.66908i 0.101450 + 0.175717i
\(437\) 4.18711 0.200297
\(438\) 0 0
\(439\) 25.0202i 1.19415i 0.802185 + 0.597075i \(0.203671\pi\)
−0.802185 + 0.597075i \(0.796329\pi\)
\(440\) 13.3365 0.635794
\(441\) 0 0
\(442\) 3.04212 0.144699
\(443\) 23.0300i 1.09419i 0.837071 + 0.547094i \(0.184266\pi\)
−0.837071 + 0.547094i \(0.815734\pi\)
\(444\) 0 0
\(445\) 2.72774 0.129307
\(446\) −3.60456 6.24329i −0.170681 0.295628i
\(447\) 0 0
\(448\) 0 0
\(449\) 15.9028i 0.750501i −0.926923 0.375251i \(-0.877557\pi\)
0.926923 0.375251i \(-0.122443\pi\)
\(450\) 0 0
\(451\) 39.3006 22.6902i 1.85059 1.06844i
\(452\) 5.91693 + 3.41614i 0.278309 + 0.160682i
\(453\) 0 0
\(454\) −11.0470 6.37800i −0.518462 0.299334i
\(455\) 0 0
\(456\) 0 0
\(457\) −5.66614 −0.265051 −0.132525 0.991180i \(-0.542309\pi\)
−0.132525 + 0.991180i \(0.542309\pi\)
\(458\) −2.24709 3.89208i −0.105000 0.181865i
\(459\) 0 0
\(460\) −7.47736 4.31705i −0.348634 0.201284i
\(461\) 15.7292 + 27.2438i 0.732582 + 1.26887i 0.955776 + 0.294095i \(0.0950183\pi\)
−0.223194 + 0.974774i \(0.571648\pi\)
\(462\) 0 0
\(463\) 4.55148 7.88340i 0.211525 0.366373i −0.740667 0.671873i \(-0.765490\pi\)
0.952192 + 0.305500i \(0.0988236\pi\)
\(464\) −3.59886 + 2.07781i −0.167073 + 0.0964597i
\(465\) 0 0
\(466\) −1.07702 + 1.86545i −0.0498918 + 0.0864152i
\(467\) −15.1516 + 26.2433i −0.701132 + 1.21440i 0.266938 + 0.963714i \(0.413988\pi\)
−0.968069 + 0.250682i \(0.919345\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 24.0284 13.8728i 1.10835 0.639906i
\(471\) 0 0
\(472\) 2.22966i 0.102628i
\(473\) 19.9879i 0.919044i
\(474\) 0 0
\(475\) 0.512563 0.295928i 0.0235180 0.0135781i
\(476\) 0 0
\(477\) 0 0
\(478\) −5.07096 + 8.78317i −0.231940 + 0.401733i
\(479\) 2.33143 4.03816i 0.106526 0.184508i −0.807835 0.589409i \(-0.799361\pi\)
0.914361 + 0.404901i \(0.132694\pi\)
\(480\) 0 0
\(481\) 13.6994 7.90935i 0.624639 0.360636i
\(482\) 5.27404 9.13490i 0.240226 0.416083i
\(483\) 0 0
\(484\) −10.6123 18.3810i −0.482377 0.835501i
\(485\) 9.33953 + 5.39218i 0.424086 + 0.244846i
\(486\) 0 0
\(487\) 9.74105 + 16.8720i 0.441409 + 0.764543i 0.997794 0.0663816i \(-0.0211455\pi\)
−0.556385 + 0.830924i \(0.687812\pi\)
\(488\) 8.99970 0.407397
\(489\) 0 0
\(490\) 0 0
\(491\) 17.7437 + 10.2443i 0.800762 + 0.462320i 0.843737 0.536756i \(-0.180351\pi\)
−0.0429758 + 0.999076i \(0.513684\pi\)
\(492\) 0 0
\(493\) 6.36577 + 3.67528i 0.286700 + 0.165526i
\(494\) 1.69694 0.979729i 0.0763490 0.0440801i
\(495\) 0 0
\(496\) 8.37019i 0.375832i
\(497\) 0 0
\(498\) 0 0
\(499\) 5.12598 + 8.87845i 0.229470 + 0.397454i 0.957651 0.287931i \(-0.0929673\pi\)
−0.728181 + 0.685385i \(0.759634\pi\)
\(500\) 10.5263 0.470752
\(501\) 0 0
\(502\) 29.3005i 1.30774i
\(503\) 14.5521 0.648845 0.324422 0.945912i \(-0.394830\pi\)
0.324422 + 0.945912i \(0.394830\pi\)
\(504\) 0 0
\(505\) 15.5600 0.692412
\(506\) 20.8623i 0.927442i
\(507\) 0 0
\(508\) 6.67667 0.296229
\(509\) 16.6617 + 28.8589i 0.738517 + 1.27915i 0.953163 + 0.302457i \(0.0978068\pi\)
−0.214646 + 0.976692i \(0.568860\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −6.60656 + 3.81430i −0.291403 + 0.168242i
\(515\) −11.9223 6.88335i −0.525360 0.303317i
\(516\) 0 0
\(517\) −58.0591 33.5204i −2.55343 1.47423i
\(518\) 0 0
\(519\) 0 0
\(520\) −4.04054 −0.177189
\(521\) −3.26963 5.66316i −0.143245 0.248108i 0.785472 0.618897i \(-0.212420\pi\)
−0.928717 + 0.370790i \(0.879087\pi\)
\(522\) 0 0
\(523\) −0.681439 0.393429i −0.0297972 0.0172034i 0.485027 0.874499i \(-0.338810\pi\)
−0.514825 + 0.857296i \(0.672143\pi\)
\(524\) 3.73653 + 6.47185i 0.163231 + 0.282724i
\(525\) 0 0
\(526\) 6.09281 10.5531i 0.265659 0.460135i
\(527\) 12.8219 7.40271i 0.558530 0.322467i
\(528\) 0 0
\(529\) −4.74685 + 8.22178i −0.206385 + 0.357469i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −11.9068 + 6.87440i −0.515741 + 0.297763i
\(534\) 0 0
\(535\) 11.0787i 0.478975i
\(536\) 10.8712i 0.469566i
\(537\) 0 0
\(538\) −2.40264 + 1.38717i −0.103585 + 0.0598050i
\(539\) 0 0
\(540\) 0 0
\(541\) −2.80227 + 4.85367i −0.120479 + 0.208676i −0.919957 0.392020i \(-0.871776\pi\)
0.799478 + 0.600696i \(0.205110\pi\)
\(542\) 1.60396 2.77815i 0.0688961 0.119332i
\(543\) 0 0
\(544\) 1.53185 0.884414i 0.0656775 0.0379189i
\(545\) −4.97675 + 8.61999i −0.213181 + 0.369240i
\(546\) 0 0
\(547\) −6.91456 11.9764i −0.295645 0.512073i 0.679489 0.733685i \(-0.262201\pi\)
−0.975135 + 0.221612i \(0.928868\pi\)
\(548\) −6.91772 3.99395i −0.295510 0.170613i
\(549\) 0 0
\(550\) 1.47446 + 2.55385i 0.0628714 + 0.108896i
\(551\) 4.73457 0.201700
\(552\) 0 0
\(553\) 0 0
\(554\) −8.73047 5.04054i −0.370922 0.214152i
\(555\) 0 0
\(556\) −17.9792 10.3803i −0.762488 0.440223i
\(557\) −24.0957 + 13.9117i −1.02097 + 0.589456i −0.914384 0.404848i \(-0.867325\pi\)
−0.106584 + 0.994304i \(0.533991\pi\)
\(558\) 0 0
\(559\) 6.05569i 0.256128i
\(560\) 0 0
\(561\) 0 0
\(562\) −2.43641 4.21999i −0.102774 0.178009i
\(563\) 24.5300 1.03382 0.516909 0.856040i \(-0.327083\pi\)
0.516909 + 0.856040i \(0.327083\pi\)
\(564\) 0 0
\(565\) 16.0515i 0.675291i
\(566\) −2.81781 −0.118441
\(567\) 0 0
\(568\) 4.52106 0.189699
\(569\) 27.1079i 1.13642i 0.822882 + 0.568212i \(0.192365\pi\)
−0.822882 + 0.568212i \(0.807635\pi\)
\(570\) 0 0
\(571\) −29.8354 −1.24857 −0.624287 0.781195i \(-0.714610\pi\)
−0.624287 + 0.781195i \(0.714610\pi\)
\(572\) 4.88151 + 8.45502i 0.204106 + 0.353522i
\(573\) 0 0
\(574\) 0 0
\(575\) 1.90915i 0.0796169i
\(576\) 0 0
\(577\) 24.3930 14.0833i 1.01549 0.586296i 0.102699 0.994712i \(-0.467252\pi\)
0.912796 + 0.408416i \(0.133919\pi\)
\(578\) 12.0129 + 6.93562i 0.499669 + 0.288484i
\(579\) 0 0
\(580\) −8.45502 4.88151i −0.351076 0.202694i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 2.67117 + 4.62660i 0.110534 + 0.191450i
\(585\) 0 0
\(586\) 7.02683 + 4.05694i 0.290276 + 0.167591i
\(587\) −4.95928 8.58973i −0.204692 0.354536i 0.745343 0.666681i \(-0.232286\pi\)
−0.950034 + 0.312145i \(0.898952\pi\)
\(588\) 0 0
\(589\) 4.76816 8.25870i 0.196469 0.340294i
\(590\) 4.53648 2.61914i 0.186764 0.107828i
\(591\) 0 0
\(592\) 4.59886 7.96547i 0.189012 0.327379i
\(593\) −2.34936 + 4.06921i −0.0964766 + 0.167102i −0.910224 0.414116i \(-0.864091\pi\)
0.813747 + 0.581219i \(0.197424\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.03726 0.598865i 0.0424880 0.0245305i
\(597\) 0 0
\(598\) 6.32061i 0.258469i
\(599\) 14.7004i 0.600641i 0.953838 + 0.300320i \(0.0970936\pi\)
−0.953838 + 0.300320i \(0.902906\pi\)
\(600\) 0 0
\(601\) 16.2923 9.40634i 0.664575 0.383693i −0.129443 0.991587i \(-0.541319\pi\)
0.794018 + 0.607894i \(0.207986\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 7.61229 13.1849i 0.309740 0.536485i
\(605\) 24.9321 43.1836i 1.01363 1.75566i
\(606\) 0 0
\(607\) −10.9051 + 6.29608i −0.442625 + 0.255550i −0.704711 0.709495i \(-0.748923\pi\)
0.262085 + 0.965045i \(0.415590\pi\)
\(608\) 0.569660 0.986680i 0.0231028 0.0400152i
\(609\) 0 0
\(610\) 10.5718 + 18.3108i 0.428038 + 0.741383i
\(611\) 17.5900 + 10.1556i 0.711617 + 0.410852i
\(612\) 0 0
\(613\) 4.91009 + 8.50452i 0.198317 + 0.343494i 0.947983 0.318322i \(-0.103119\pi\)
−0.749666 + 0.661816i \(0.769786\pi\)
\(614\) 10.8996 0.439873
\(615\) 0 0
\(616\) 0 0
\(617\) 3.25158 + 1.87730i 0.130904 + 0.0755772i 0.564022 0.825760i \(-0.309253\pi\)
−0.433118 + 0.901337i \(0.642587\pi\)
\(618\) 0 0
\(619\) −9.56902 5.52468i −0.384611 0.222055i 0.295211 0.955432i \(-0.404610\pi\)
−0.679823 + 0.733376i \(0.737943\pi\)
\(620\) −17.0300 + 9.83228i −0.683942 + 0.394874i
\(621\) 0 0
\(622\) 8.23637i 0.330248i
\(623\) 0 0
\(624\) 0 0
\(625\) 13.6638 + 23.6664i 0.546551 + 0.946654i
\(626\) 33.8023 1.35101
\(627\) 0 0
\(628\) 10.0269i 0.400118i
\(629\) −16.2692 −0.648696
\(630\) 0 0
\(631\) 19.4921 0.775969 0.387984 0.921666i \(-0.373171\pi\)
0.387984 + 0.921666i \(0.373171\pi\)
\(632\) 13.0284i 0.518243i
\(633\) 0 0
\(634\) 6.73090 0.267318
\(635\) 7.84294 + 13.5844i 0.311238 + 0.539080i
\(636\) 0 0
\(637\) 0 0
\(638\) 23.5900i 0.933938i
\(639\) 0 0
\(640\) −2.03460 + 1.17468i −0.0804248 + 0.0464333i
\(641\) −22.6669 13.0868i −0.895290 0.516896i −0.0196208 0.999807i \(-0.506246\pi\)
−0.875669 + 0.482912i \(0.839579\pi\)
\(642\) 0 0
\(643\) 9.50955 + 5.49034i 0.375020 + 0.216518i 0.675649 0.737223i \(-0.263863\pi\)
−0.300629 + 0.953741i \(0.597197\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −2.01526 −0.0792894
\(647\) 16.0063 + 27.7237i 0.629273 + 1.08993i 0.987698 + 0.156374i \(0.0499805\pi\)
−0.358425 + 0.933558i \(0.616686\pi\)
\(648\) 0 0
\(649\) −10.9613 6.32852i −0.430270 0.248416i
\(650\) −0.446715 0.773734i −0.0175216 0.0303483i
\(651\) 0 0
\(652\) 6.00158 10.3950i 0.235040 0.407101i
\(653\) 19.3686 11.1825i 0.757952 0.437604i −0.0706080 0.997504i \(-0.522494\pi\)
0.828560 + 0.559900i \(0.189161\pi\)
\(654\) 0 0
\(655\) −8.77843 + 15.2047i −0.343002 + 0.594097i
\(656\) −3.99709 + 6.92317i −0.156060 + 0.270304i
\(657\) 0 0
\(658\) 0 0
\(659\) 19.2546 11.1166i 0.750053 0.433043i −0.0756603 0.997134i \(-0.524106\pi\)
0.825713 + 0.564091i \(0.190773\pi\)
\(660\) 0 0
\(661\) 10.5499i 0.410343i 0.978726 + 0.205171i \(0.0657751\pi\)
−0.978726 + 0.205171i \(0.934225\pi\)
\(662\) 32.0569i 1.24593i
\(663\) 0 0
\(664\) 10.8651 6.27298i 0.421649 0.243439i
\(665\) 0 0
\(666\) 0 0
\(667\) 7.63613 13.2262i 0.295672 0.512119i
\(668\) 8.57472 14.8518i 0.331766 0.574635i
\(669\) 0 0
\(670\) 22.1187 12.7702i 0.854519 0.493357i
\(671\) 25.5442 44.2438i 0.986121 1.70801i
\(672\) 0 0
\(673\) 9.93562 + 17.2090i 0.382990 + 0.663358i 0.991488 0.130197i \(-0.0415610\pi\)
−0.608498 + 0.793555i \(0.708228\pi\)
\(674\) −20.9791 12.1123i −0.808085 0.466548i
\(675\) 0 0
\(676\) 5.02106 + 8.69673i 0.193118 + 0.334490i
\(677\) −15.9290 −0.612201 −0.306100 0.951999i \(-0.599024\pi\)
−0.306100 + 0.951999i \(0.599024\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 3.59886 + 2.07781i 0.138010 + 0.0796802i
\(681\) 0 0
\(682\) 41.1490 + 23.7574i 1.57568 + 0.909718i
\(683\) 16.4777 9.51343i 0.630503 0.364021i −0.150444 0.988619i \(-0.548070\pi\)
0.780947 + 0.624597i \(0.214737\pi\)
\(684\) 0 0
\(685\) 18.7664i 0.717028i
\(686\) 0 0
\(687\) 0 0
\(688\) 1.76053 + 3.04933i 0.0671196 + 0.116254i
\(689\) 0 0
\(690\) 0 0
\(691\) 0.161055i 0.00612681i 0.999995 + 0.00306340i \(0.000975113\pi\)
−0.999995 + 0.00306340i \(0.999025\pi\)
\(692\) −1.98748 −0.0755525
\(693\) 0 0
\(694\) −22.7999 −0.865471
\(695\) 48.7741i 1.85011i
\(696\) 0 0
\(697\) 14.1403 0.535604
\(698\) −1.42253 2.46389i −0.0538434 0.0932595i
\(699\) 0 0
\(700\) 0 0
\(701\) 9.98234i 0.377028i −0.982071 0.188514i \(-0.939633\pi\)
0.982071 0.188514i \(-0.0603670\pi\)
\(702\) 0 0
\(703\) −9.07522 + 5.23958i −0.342278 + 0.197614i
\(704\) 4.91614 + 2.83834i 0.185284 + 0.106974i
\(705\) 0 0
\(706\) 6.18709 + 3.57212i 0.232854 + 0.134438i
\(707\) 0 0
\(708\) 0 0
\(709\) −24.3923 −0.916072 −0.458036 0.888934i \(-0.651447\pi\)
−0.458036 + 0.888934i \(0.651447\pi\)
\(710\) 5.31079 + 9.19856i 0.199311 + 0.345216i
\(711\) 0 0
\(712\) 1.00551 + 0.580529i 0.0376829 + 0.0217563i
\(713\) −15.3806 26.6400i −0.576008 0.997676i
\(714\) 0 0
\(715\) −11.4684 + 19.8639i −0.428894 + 0.742867i
\(716\) 7.19773 4.15561i 0.268992 0.155302i
\(717\) 0 0
\(718\) −5.80186 + 10.0491i −0.216523 + 0.375030i
\(719\) −8.13460 + 14.0895i −0.303370 + 0.525451i −0.976897 0.213711i \(-0.931445\pi\)
0.673527 + 0.739162i \(0.264778\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 15.3303 8.85097i 0.570536 0.329399i
\(723\) 0 0
\(724\) 15.4541i 0.574348i
\(725\) 2.15877i 0.0801745i
\(726\) 0 0
\(727\) 20.6626 11.9296i 0.766335 0.442444i −0.0652306 0.997870i \(-0.520778\pi\)
0.831566 + 0.555427i \(0.187445\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −6.27554 + 10.8695i −0.232268 + 0.402300i
\(731\) 3.11408 5.39374i 0.115178 0.199495i
\(732\) 0 0
\(733\) −10.6259 + 6.13486i −0.392476 + 0.226596i −0.683233 0.730201i \(-0.739426\pi\)
0.290756 + 0.956797i \(0.406093\pi\)
\(734\) 3.91747 6.78525i 0.144596 0.250448i
\(735\) 0 0
\(736\) −1.83755 3.18272i −0.0677329 0.117317i
\(737\) −53.4446 30.8562i −1.96866 1.13660i
\(738\) 0 0
\(739\) −20.9446 36.2771i −0.770459 1.33447i −0.937312 0.348492i \(-0.886694\pi\)
0.166853 0.985982i \(-0.446639\pi\)
\(740\) 21.6088 0.794354
\(741\) 0 0
\(742\) 0 0
\(743\) −43.9160 25.3549i −1.61112 0.930182i −0.989111 0.147173i \(-0.952982\pi\)
−0.622011 0.783008i \(-0.713684\pi\)
\(744\) 0 0
\(745\) 2.43690 + 1.40695i 0.0892813 + 0.0515466i
\(746\) 22.2289 12.8339i 0.813858 0.469881i
\(747\) 0 0
\(748\) 10.0411i 0.367137i
\(749\) 0 0
\(750\) 0 0
\(751\) 16.3683 + 28.3508i 0.597289 + 1.03454i 0.993219 + 0.116255i \(0.0370890\pi\)
−0.395930 + 0.918281i \(0.629578\pi\)
\(752\) 11.8099 0.430662
\(753\) 0 0
\(754\) 7.14702i 0.260279i
\(755\) 35.7680 1.30173
\(756\) 0 0
\(757\) −17.9255 −0.651512 −0.325756 0.945454i \(-0.605619\pi\)
−0.325756 + 0.945454i \(0.605619\pi\)
\(758\) 15.1045i 0.548622i
\(759\) 0 0
\(760\) 2.67667 0.0970930
\(761\) −21.8509 37.8469i −0.792096 1.37195i −0.924667 0.380777i \(-0.875657\pi\)
0.132571 0.991174i \(-0.457677\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 12.3381i 0.446376i
\(765\) 0 0
\(766\) 1.32211 0.763322i 0.0477699 0.0275800i
\(767\) 3.32093 + 1.91734i 0.119912 + 0.0692311i
\(768\) 0 0
\(769\) −37.0864 21.4118i −1.33737 0.772131i −0.350953 0.936393i \(-0.614142\pi\)
−0.986417 + 0.164262i \(0.947476\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4.39388 −0.158139
\(773\) −10.8025 18.7105i −0.388540 0.672971i 0.603714 0.797201i \(-0.293687\pi\)
−0.992253 + 0.124231i \(0.960354\pi\)
\(774\) 0 0
\(775\) −3.76562 2.17408i −0.135265 0.0780953i
\(776\) 2.29517 + 3.97536i 0.0823919 + 0.142707i
\(777\) 0 0
\(778\) −7.44483 + 12.8948i −0.266910 + 0.462302i
\(779\) 7.88771 4.55397i 0.282606 0.163163i
\(780\) 0 0
\(781\) 12.8323 22.2262i 0.459175 0.795315i
\(782\) −3.25030 + 5.62969i −0.116231 + 0.201317i
\(783\) 0 0
\(784\) 0 0
\(785\) −20.4008 + 11.7784i −0.728137 + 0.420390i
\(786\) 0 0
\(787\) 51.3042i 1.82880i 0.404817 + 0.914398i \(0.367335\pi\)
−0.404817 + 0.914398i \(0.632665\pi\)
\(788\) 10.8865i 0.387816i
\(789\) 0 0
\(790\) −26.5077 + 15.3042i −0.943102 + 0.544500i
\(791\) 0 0
\(792\) 0 0
\(793\) −7.73906 + 13.4044i −0.274822 + 0.476006i
\(794\) −14.3935 + 24.9302i −0.510805 + 0.884740i
\(795\) 0 0
\(796\) 23.8733 13.7832i 0.846166 0.488534i
\(797\) 0.899094 1.55728i 0.0318476 0.0551616i −0.849662 0.527327i \(-0.823194\pi\)
0.881510 + 0.472166i \(0.156528\pi\)
\(798\) 0 0
\(799\) −10.4448 18.0910i −0.369512 0.640013i
\(800\) −0.449885 0.259741i −0.0159058 0.00918323i
\(801\) 0 0
\(802\) −19.0868 33.0592i −0.673977 1.16736i
\(803\) 30.3267 1.07021
\(804\) 0 0
\(805\) 0 0
\(806\) −12.4668 7.19773i −0.439125 0.253529i
\(807\) 0 0
\(808\) 5.73577 + 3.31155i 0.201784 + 0.116500i
\(809\) −35.2371 + 20.3441i −1.23887 + 0.715262i −0.968863 0.247597i \(-0.920359\pi\)
−0.270006 + 0.962859i \(0.587026\pi\)
\(810\) 0 0
\(811\) 0.378710i 0.0132983i 0.999978 + 0.00664916i \(0.00211651\pi\)
−0.999978 + 0.00664916i \(0.997883\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −26.1062 45.2173i −0.915023 1.58487i
\(815\) 28.1997 0.987793
\(816\) 0 0
\(817\) 4.01161i 0.140349i
\(818\) 6.96694 0.243593
\(819\) 0 0
\(820\) −18.7812 −0.655868
\(821\) 13.2754i 0.463315i −0.972797 0.231658i \(-0.925585\pi\)
0.972797 0.231658i \(-0.0744149\pi\)
\(822\) 0 0
\(823\) 27.7422 0.967034 0.483517 0.875335i \(-0.339359\pi\)
0.483517 + 0.875335i \(0.339359\pi\)
\(824\) −2.92989 5.07471i −0.102067 0.176786i
\(825\) 0 0
\(826\) 0 0
\(827\) 27.7183i 0.963859i −0.876210 0.481929i \(-0.839936\pi\)
0.876210 0.481929i \(-0.160064\pi\)
\(828\) 0 0
\(829\) 37.0105 21.3680i 1.28543 0.742143i 0.307593 0.951518i \(-0.400476\pi\)
0.977835 + 0.209375i \(0.0671431\pi\)
\(830\) 25.5261 + 14.7375i 0.886023 + 0.511545i
\(831\) 0 0
\(832\) −1.48943 0.859925i −0.0516368 0.0298125i
\(833\) 0 0
\(834\) 0 0
\(835\) 40.2902 1.39430
\(836\) −3.23377 5.60106i −0.111842 0.193717i
\(837\) 0 0
\(838\) 30.1778 + 17.4232i 1.04248 + 0.601873i
\(839\) 1.92438 + 3.33313i 0.0664370 + 0.115072i 0.897331 0.441359i \(-0.145504\pi\)
−0.830894 + 0.556431i \(0.812170\pi\)
\(840\) 0 0
\(841\) −5.86545 + 10.1593i −0.202257 + 0.350319i
\(842\) −4.92936 + 2.84597i −0.169877 + 0.0980785i
\(843\) 0 0
\(844\) −5.15561 + 8.92978i −0.177463 + 0.307376i
\(845\) −11.7963 + 20.4317i −0.405804 + 0.702873i
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0.918875i 0.0315171i
\(851\) 33.8025i 1.15874i
\(852\) 0 0
\(853\) −26.3470 + 15.2114i −0.902103 + 0.520830i −0.877882 0.478877i \(-0.841044\pi\)
−0.0242213 + 0.999707i \(0.507711\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 2.35782 4.08386i 0.0805885 0.139583i
\(857\) −19.4657 + 33.7156i −0.664937 + 1.15170i 0.314366 + 0.949302i \(0.398208\pi\)
−0.979303 + 0.202402i \(0.935125\pi\)
\(858\) 0 0
\(859\) −11.5922 + 6.69275i −0.395520 + 0.228354i −0.684549 0.728967i \(-0.740001\pi\)
0.289029 + 0.957320i \(0.406668\pi\)
\(860\) −4.13611 + 7.16396i −0.141040 + 0.244289i
\(861\) 0 0
\(862\) 15.1468 + 26.2350i 0.515901 + 0.893567i
\(863\) −18.8118 10.8610i −0.640360 0.369712i 0.144393 0.989520i \(-0.453877\pi\)
−0.784753 + 0.619809i \(0.787210\pi\)
\(864\) 0 0
\(865\) −2.33465 4.04373i −0.0793804 0.137491i
\(866\) 23.6094 0.802279
\(867\) 0 0
\(868\) 0 0
\(869\) 64.0496 + 36.9791i 2.17273 + 1.25443i
\(870\) 0 0
\(871\) 16.1920 + 9.34845i 0.548645 + 0.316760i
\(872\) −3.66908 + 2.11835i −0.124251 + 0.0717363i
\(873\) 0 0
\(874\) 4.18711i 0.141631i
\(875\) 0 0
\(876\) 0 0
\(877\) −0.196152 0.339746i −0.00662360 0.0114724i 0.862695 0.505725i \(-0.168775\pi\)
−0.869318 + 0.494253i \(0.835442\pi\)
\(878\) −25.0202 −0.844392
\(879\) 0 0
\(880\) 13.3365i 0.449574i
\(881\) −43.3363 −1.46004 −0.730018 0.683427i \(-0.760489\pi\)
−0.730018 + 0.683427i \(0.760489\pi\)
\(882\) 0 0
\(883\) 2.17403 0.0731618 0.0365809 0.999331i \(-0.488353\pi\)
0.0365809 + 0.999331i \(0.488353\pi\)
\(884\) 3.04212i 0.102318i
\(885\) 0 0
\(886\) −23.0300 −0.773708
\(887\) 5.72215 + 9.91105i 0.192131 + 0.332781i 0.945956 0.324294i \(-0.105127\pi\)
−0.753825 + 0.657075i \(0.771793\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 2.72774i 0.0914341i
\(891\) 0 0
\(892\) 6.24329 3.60456i 0.209041 0.120690i
\(893\) −11.6526 6.72762i −0.389939 0.225131i
\(894\) 0 0
\(895\) 16.9100 + 9.76302i 0.565240 + 0.326342i
\(896\) 0 0
\(897\) 0 0
\(898\) 15.9028 0.530684
\(899\) −17.3916 30.1232i −0.580043 1.00466i
\(900\) 0 0
\(901\) 0 0
\(902\) 22.6902 + 39.3006i 0.755501 + 1.30857i
\(903\) 0 0
\(904\) −3.41614 + 5.91693i −0.113619 + 0.196794i
\(905\) 31.4430 18.1536i 1.04520 0.603447i
\(906\) 0 0
\(907\) 26.9446 46.6694i 0.894680 1.54963i 0.0604797 0.998169i \(-0.480737\pi\)
0.834200 0.551462i \(-0.185930\pi\)
\(908\) 6.37800 11.0470i 0.211661 0.366608i
\(909\) 0 0
\(910\) 0 0
\(911\) 7.00460 4.04411i 0.232073 0.133987i −0.379455 0.925210i \(-0.623889\pi\)
0.611528 + 0.791223i \(0.290555\pi\)
\(912\) 0 0
\(913\) 71.2193i 2.35702i
\(914\) 5.66614i 0.187419i
\(915\) 0 0
\(916\) 3.89208 2.24709i 0.128598 0.0742460i
\(917\) 0 0
\(918\) 0 0
\(919\) −12.8375 + 22.2353i −0.423472 + 0.733474i −0.996276 0.0862175i \(-0.972522\pi\)
0.572805 + 0.819692i \(0.305855\pi\)
\(920\) 4.31705 7.47736i 0.142329 0.246521i
\(921\) 0 0
\(922\) −27.2438 + 15.7292i −0.897226 + 0.518014i
\(923\) −3.88777 + 6.73382i −0.127968 + 0.221646i
\(924\) 0 0
\(925\) 2.38903 + 4.13792i 0.0785507 + 0.136054i
\(926\) 7.88340 + 4.55148i 0.259064 + 0.149571i
\(927\) 0 0
\(928\) −2.07781 3.59886i −0.0682073 0.118139i
\(929\) 10.8524 0.356055 0.178027 0.984026i \(-0.443028\pi\)
0.178027 + 0.984026i \(0.443028\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −1.86545 1.07702i −0.0611048 0.0352789i
\(933\) 0 0
\(934\) −26.2433 15.1516i −0.858708 0.495775i
\(935\) 20.4296 11.7950i 0.668118 0.385738i
\(936\) 0 0
\(937\) 0.458120i 0.0149661i 0.999972 + 0.00748306i \(0.00238195\pi\)
−0.999972 + 0.00748306i \(0.997618\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 13.8728 + 24.0284i 0.452482 + 0.783721i
\(941\) −7.37780 −0.240510 −0.120255 0.992743i \(-0.538371\pi\)
−0.120255 + 0.992743i \(0.538371\pi\)
\(942\) 0 0
\(943\) 29.3794i 0.956725i
\(944\) 2.22966 0.0725693
\(945\) 0 0
\(946\) 19.9879 0.649862
\(947\) 11.9910i 0.389657i 0.980837 + 0.194828i \(0.0624150\pi\)
−0.980837 + 0.194828i \(0.937585\pi\)
\(948\) 0 0
\(949\) −9.18802 −0.298256
\(950\) 0.295928 + 0.512563i 0.00960118 + 0.0166297i
\(951\) 0 0
\(952\) 0 0
\(953\) 58.6883i 1.90110i −0.310572 0.950550i \(-0.600521\pi\)
0.310572 0.950550i \(-0.399479\pi\)
\(954\) 0 0
\(955\) −25.1031 + 14.4933i −0.812317 + 0.468992i
\(956\) −8.78317 5.07096i −0.284068 0.164007i
\(957\) 0 0
\(958\) 4.03816 + 2.33143i 0.130467 + 0.0753251i
\(959\) 0 0
\(960\) 0 0
\(961\) −39.0600 −1.26000
\(962\) 7.90935 + 13.6994i 0.255008 + 0.441686i
\(963\) 0 0
\(964\) 9.13490 + 5.27404i 0.294215 + 0.169865i
\(965\) −5.16140 8.93981i −0.166151 0.287783i
\(966\) 0 0
\(967\) −3.37560 + 5.84671i −0.108552 + 0.188018i −0.915184 0.403037i \(-0.867955\pi\)
0.806632 + 0.591054i \(0.201288\pi\)
\(968\) 18.3810 10.6123i 0.590789 0.341092i
\(969\) 0 0
\(970\) −5.39218 + 9.33953i −0.173133 + 0.299874i
\(971\) −3.20362 + 5.54883i −0.102809 + 0.178070i −0.912841 0.408315i \(-0.866116\pi\)
0.810032 + 0.586386i \(0.199450\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −16.8720 + 9.74105i −0.540613 + 0.312123i
\(975\) 0 0
\(976\) 8.99970i 0.288073i
\(977\) 13.5987i 0.435062i 0.976053 + 0.217531i \(0.0698004\pi\)
−0.976053 + 0.217531i \(0.930200\pi\)
\(978\) 0 0
\(979\) 5.70793 3.29547i 0.182426 0.105324i
\(980\) 0 0
\(981\) 0 0
\(982\) −10.2443 + 17.7437i −0.326910 + 0.566224i
\(983\) −11.3849 + 19.7192i −0.363122 + 0.628946i −0.988473 0.151398i \(-0.951623\pi\)
0.625351 + 0.780344i \(0.284956\pi\)
\(984\) 0 0
\(985\) −22.1497 + 12.7882i −0.705749 + 0.407464i
\(986\) −3.67528 + 6.36577i −0.117045 + 0.202728i
\(987\) 0 0
\(988\) 0.979729 + 1.69694i 0.0311693 + 0.0539869i
\(989\) −11.2066 6.47011i −0.356348 0.205738i
\(990\) 0 0
\(991\) 13.4953 + 23.3745i 0.428691 + 0.742515i 0.996757 0.0804680i \(-0.0256415\pi\)
−0.568066 + 0.822983i \(0.692308\pi\)
\(992\) −8.37019 −0.265754
\(993\) 0 0
\(994\) 0 0
\(995\) 56.0869 + 32.3818i 1.77807 + 1.02657i
\(996\) 0 0
\(997\) 16.7263 + 9.65694i 0.529728 + 0.305838i 0.740906 0.671609i \(-0.234397\pi\)
−0.211178 + 0.977448i \(0.567730\pi\)
\(998\) −8.87845 + 5.12598i −0.281043 + 0.162260i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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.l.b.1097.6 16
3.2 odd 2 882.2.l.a.509.3 16
7.2 even 3 378.2.m.a.125.6 16
7.3 odd 6 2646.2.t.a.2285.2 16
7.4 even 3 2646.2.t.a.2285.3 16
7.5 odd 6 378.2.m.a.125.7 16
7.6 odd 2 inner 2646.2.l.b.1097.7 16
9.2 odd 6 2646.2.t.a.1979.2 16
9.7 even 3 882.2.t.b.803.8 16
21.2 odd 6 126.2.m.a.41.3 yes 16
21.5 even 6 126.2.m.a.41.2 16
21.11 odd 6 882.2.t.b.815.5 16
21.17 even 6 882.2.t.b.815.8 16
21.20 even 2 882.2.l.a.509.2 16
28.19 even 6 3024.2.cc.b.881.7 16
28.23 odd 6 3024.2.cc.b.881.2 16
63.2 odd 6 378.2.m.a.251.7 16
63.5 even 6 1134.2.d.a.1133.7 16
63.11 odd 6 inner 2646.2.l.b.521.3 16
63.16 even 3 126.2.m.a.83.2 yes 16
63.20 even 6 2646.2.t.a.1979.3 16
63.23 odd 6 1134.2.d.a.1133.2 16
63.25 even 3 882.2.l.a.227.6 16
63.34 odd 6 882.2.t.b.803.5 16
63.38 even 6 inner 2646.2.l.b.521.2 16
63.40 odd 6 1134.2.d.a.1133.10 16
63.47 even 6 378.2.m.a.251.6 16
63.52 odd 6 882.2.l.a.227.7 16
63.58 even 3 1134.2.d.a.1133.15 16
63.61 odd 6 126.2.m.a.83.3 yes 16
84.23 even 6 1008.2.cc.b.545.3 16
84.47 odd 6 1008.2.cc.b.545.6 16
252.47 odd 6 3024.2.cc.b.2897.2 16
252.79 odd 6 1008.2.cc.b.209.6 16
252.187 even 6 1008.2.cc.b.209.3 16
252.191 even 6 3024.2.cc.b.2897.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.m.a.41.2 16 21.5 even 6
126.2.m.a.41.3 yes 16 21.2 odd 6
126.2.m.a.83.2 yes 16 63.16 even 3
126.2.m.a.83.3 yes 16 63.61 odd 6
378.2.m.a.125.6 16 7.2 even 3
378.2.m.a.125.7 16 7.5 odd 6
378.2.m.a.251.6 16 63.47 even 6
378.2.m.a.251.7 16 63.2 odd 6
882.2.l.a.227.6 16 63.25 even 3
882.2.l.a.227.7 16 63.52 odd 6
882.2.l.a.509.2 16 21.20 even 2
882.2.l.a.509.3 16 3.2 odd 2
882.2.t.b.803.5 16 63.34 odd 6
882.2.t.b.803.8 16 9.7 even 3
882.2.t.b.815.5 16 21.11 odd 6
882.2.t.b.815.8 16 21.17 even 6
1008.2.cc.b.209.3 16 252.187 even 6
1008.2.cc.b.209.6 16 252.79 odd 6
1008.2.cc.b.545.3 16 84.23 even 6
1008.2.cc.b.545.6 16 84.47 odd 6
1134.2.d.a.1133.2 16 63.23 odd 6
1134.2.d.a.1133.7 16 63.5 even 6
1134.2.d.a.1133.10 16 63.40 odd 6
1134.2.d.a.1133.15 16 63.58 even 3
2646.2.l.b.521.2 16 63.38 even 6 inner
2646.2.l.b.521.3 16 63.11 odd 6 inner
2646.2.l.b.1097.6 16 1.1 even 1 trivial
2646.2.l.b.1097.7 16 7.6 odd 2 inner
2646.2.t.a.1979.2 16 9.2 odd 6
2646.2.t.a.1979.3 16 63.20 even 6
2646.2.t.a.2285.2 16 7.3 odd 6
2646.2.t.a.2285.3 16 7.4 even 3
3024.2.cc.b.881.2 16 28.23 odd 6
3024.2.cc.b.881.7 16 28.19 even 6
3024.2.cc.b.2897.2 16 252.47 odd 6
3024.2.cc.b.2897.7 16 252.191 even 6