Properties

Label 2646.2.f.n.1765.3
Level $2646$
Weight $2$
Character 2646.1765
Analytic conductor $21.128$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2646,2,Mod(883,2646)]
 
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([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2646.883");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.f (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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1765.3
Root \(0.500000 - 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 2646.1765
Dual form 2646.2.f.n.883.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.230252 - 0.398809i) q^{5} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.230252 - 0.398809i) q^{5} -1.00000 q^{8} +0.460505 q^{10} +(-1.82383 - 3.15897i) q^{11} +(-0.730252 + 1.26483i) q^{13} +(-0.500000 - 0.866025i) q^{16} +3.73385 q^{17} -4.05408 q^{19} +(0.230252 + 0.398809i) q^{20} +(1.82383 - 3.15897i) q^{22} +(0.566537 - 0.981271i) q^{23} +(2.39397 + 4.14647i) q^{25} -1.46050 q^{26} +(4.48755 + 7.77266i) q^{29} +(-0.257295 + 0.445647i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.86693 + 3.23361i) q^{34} +9.10817 q^{37} +(-2.02704 - 3.51094i) q^{38} +(-0.230252 + 0.398809i) q^{40} +(-0.472958 + 0.819187i) q^{41} +(4.66372 + 8.07779i) q^{43} +3.64766 q^{44} +1.13307 q^{46} +(-1.16372 - 2.01561i) q^{47} +(-2.39397 + 4.14647i) q^{50} +(-0.730252 - 1.26483i) q^{52} +12.4356 q^{53} -1.67977 q^{55} +(-4.48755 + 7.77266i) q^{58} +(6.44805 - 11.1684i) q^{59} +(6.04163 + 10.4644i) q^{61} -0.514589 q^{62} +1.00000 q^{64} +(0.336285 + 0.582462i) q^{65} +(1.16012 - 2.00938i) q^{67} +(-1.86693 + 3.23361i) q^{68} -1.67977 q^{71} -13.2412 q^{73} +(4.55408 + 7.88791i) q^{74} +(2.02704 - 3.51094i) q^{76} +(2.50360 + 4.33636i) q^{79} -0.460505 q^{80} -0.945916 q^{82} +(3.32383 + 5.75705i) q^{83} +(0.859728 - 1.48909i) q^{85} +(-4.66372 + 8.07779i) q^{86} +(1.82383 + 3.15897i) q^{88} +2.72665 q^{89} +(0.566537 + 0.981271i) q^{92} +(1.16372 - 2.01561i) q^{94} +(-0.933463 + 1.61680i) q^{95} +(5.59358 + 9.68836i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 3 q^{4} - 5 q^{5} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 3 q^{4} - 5 q^{5} - 6 q^{8} - 10 q^{10} + q^{11} + 2 q^{13} - 3 q^{16} + 8 q^{17} - 6 q^{19} - 5 q^{20} - q^{22} + 7 q^{23} - 2 q^{25} + 4 q^{26} + 5 q^{29} + 14 q^{31} + 3 q^{32} + 4 q^{34} + 18 q^{37} - 3 q^{38} + 5 q^{40} - 12 q^{41} + 18 q^{43} - 2 q^{44} + 14 q^{46} + 3 q^{47} + 2 q^{50} + 2 q^{52} + 18 q^{53} - 14 q^{55} - 5 q^{58} + 4 q^{59} - 4 q^{61} + 28 q^{62} + 6 q^{64} + 12 q^{65} + 5 q^{67} - 4 q^{68} - 14 q^{71} - 50 q^{73} + 9 q^{74} + 3 q^{76} + 7 q^{79} + 10 q^{80} - 24 q^{82} + 8 q^{83} + 14 q^{85} - 18 q^{86} - q^{88} + 18 q^{89} + 7 q^{92} - 3 q^{94} - 2 q^{95} + 28 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.230252 0.398809i 0.102972 0.178353i −0.809936 0.586519i \(-0.800498\pi\)
0.912908 + 0.408166i \(0.133831\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0.460505 0.145624
\(11\) −1.82383 3.15897i −0.549906 0.952465i −0.998280 0.0586193i \(-0.981330\pi\)
0.448374 0.893846i \(-0.352003\pi\)
\(12\) 0 0
\(13\) −0.730252 + 1.26483i −0.202536 + 0.350802i −0.949345 0.314236i \(-0.898252\pi\)
0.746809 + 0.665038i \(0.231585\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.73385 0.905592 0.452796 0.891614i \(-0.350427\pi\)
0.452796 + 0.891614i \(0.350427\pi\)
\(18\) 0 0
\(19\) −4.05408 −0.930071 −0.465035 0.885292i \(-0.653958\pi\)
−0.465035 + 0.885292i \(0.653958\pi\)
\(20\) 0.230252 + 0.398809i 0.0514860 + 0.0891764i
\(21\) 0 0
\(22\) 1.82383 3.15897i 0.388842 0.673495i
\(23\) 0.566537 0.981271i 0.118131 0.204609i −0.800896 0.598804i \(-0.795643\pi\)
0.919027 + 0.394194i \(0.128976\pi\)
\(24\) 0 0
\(25\) 2.39397 + 4.14647i 0.478794 + 0.829295i
\(26\) −1.46050 −0.286429
\(27\) 0 0
\(28\) 0 0
\(29\) 4.48755 + 7.77266i 0.833317 + 1.44335i 0.895394 + 0.445275i \(0.146894\pi\)
−0.0620772 + 0.998071i \(0.519772\pi\)
\(30\) 0 0
\(31\) −0.257295 + 0.445647i −0.0462115 + 0.0800406i −0.888206 0.459446i \(-0.848048\pi\)
0.841994 + 0.539486i \(0.181381\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 1.86693 + 3.23361i 0.320175 + 0.554560i
\(35\) 0 0
\(36\) 0 0
\(37\) 9.10817 1.49737 0.748687 0.662924i \(-0.230685\pi\)
0.748687 + 0.662924i \(0.230685\pi\)
\(38\) −2.02704 3.51094i −0.328830 0.569550i
\(39\) 0 0
\(40\) −0.230252 + 0.398809i −0.0364061 + 0.0630572i
\(41\) −0.472958 + 0.819187i −0.0738636 + 0.127936i −0.900592 0.434666i \(-0.856866\pi\)
0.826728 + 0.562602i \(0.190200\pi\)
\(42\) 0 0
\(43\) 4.66372 + 8.07779i 0.711210 + 1.23185i 0.964403 + 0.264436i \(0.0851858\pi\)
−0.253193 + 0.967416i \(0.581481\pi\)
\(44\) 3.64766 0.549906
\(45\) 0 0
\(46\) 1.13307 0.167063
\(47\) −1.16372 2.01561i −0.169745 0.294007i 0.768585 0.639748i \(-0.220961\pi\)
−0.938330 + 0.345740i \(0.887628\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.39397 + 4.14647i −0.338558 + 0.586400i
\(51\) 0 0
\(52\) −0.730252 1.26483i −0.101268 0.175401i
\(53\) 12.4356 1.70816 0.854080 0.520141i \(-0.174121\pi\)
0.854080 + 0.520141i \(0.174121\pi\)
\(54\) 0 0
\(55\) −1.67977 −0.226500
\(56\) 0 0
\(57\) 0 0
\(58\) −4.48755 + 7.77266i −0.589244 + 1.02060i
\(59\) 6.44805 11.1684i 0.839465 1.45400i −0.0508779 0.998705i \(-0.516202\pi\)
0.890343 0.455291i \(-0.150465\pi\)
\(60\) 0 0
\(61\) 6.04163 + 10.4644i 0.773552 + 1.33983i 0.935605 + 0.353049i \(0.114855\pi\)
−0.162053 + 0.986782i \(0.551812\pi\)
\(62\) −0.514589 −0.0653529
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.336285 + 0.582462i 0.0417110 + 0.0722456i
\(66\) 0 0
\(67\) 1.16012 2.00938i 0.141731 0.245485i −0.786418 0.617695i \(-0.788067\pi\)
0.928148 + 0.372210i \(0.121400\pi\)
\(68\) −1.86693 + 3.23361i −0.226398 + 0.392133i
\(69\) 0 0
\(70\) 0 0
\(71\) −1.67977 −0.199352 −0.0996758 0.995020i \(-0.531781\pi\)
−0.0996758 + 0.995020i \(0.531781\pi\)
\(72\) 0 0
\(73\) −13.2412 −1.54977 −0.774885 0.632102i \(-0.782192\pi\)
−0.774885 + 0.632102i \(0.782192\pi\)
\(74\) 4.55408 + 7.88791i 0.529402 + 0.916950i
\(75\) 0 0
\(76\) 2.02704 3.51094i 0.232518 0.402732i
\(77\) 0 0
\(78\) 0 0
\(79\) 2.50360 + 4.33636i 0.281677 + 0.487879i 0.971798 0.235815i \(-0.0757761\pi\)
−0.690121 + 0.723694i \(0.742443\pi\)
\(80\) −0.460505 −0.0514860
\(81\) 0 0
\(82\) −0.945916 −0.104459
\(83\) 3.32383 + 5.75705i 0.364838 + 0.631918i 0.988750 0.149577i \(-0.0477911\pi\)
−0.623912 + 0.781494i \(0.714458\pi\)
\(84\) 0 0
\(85\) 0.859728 1.48909i 0.0932506 0.161515i
\(86\) −4.66372 + 8.07779i −0.502901 + 0.871051i
\(87\) 0 0
\(88\) 1.82383 + 3.15897i 0.194421 + 0.336747i
\(89\) 2.72665 0.289025 0.144512 0.989503i \(-0.453839\pi\)
0.144512 + 0.989503i \(0.453839\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.566537 + 0.981271i 0.0590656 + 0.102305i
\(93\) 0 0
\(94\) 1.16372 2.01561i 0.120028 0.207895i
\(95\) −0.933463 + 1.61680i −0.0957713 + 0.165881i
\(96\) 0 0
\(97\) 5.59358 + 9.68836i 0.567942 + 0.983704i 0.996769 + 0.0803178i \(0.0255935\pi\)
−0.428827 + 0.903386i \(0.641073\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −4.78794 −0.478794
\(101\) −6.87792 11.9129i −0.684378 1.18538i −0.973632 0.228125i \(-0.926740\pi\)
0.289254 0.957253i \(-0.406593\pi\)
\(102\) 0 0
\(103\) 5.58113 9.66679i 0.549925 0.952498i −0.448354 0.893856i \(-0.647990\pi\)
0.998279 0.0586417i \(-0.0186769\pi\)
\(104\) 0.730252 1.26483i 0.0716071 0.124027i
\(105\) 0 0
\(106\) 6.21780 + 10.7695i 0.603926 + 1.04603i
\(107\) −7.78074 −0.752192 −0.376096 0.926581i \(-0.622734\pi\)
−0.376096 + 0.926581i \(0.622734\pi\)
\(108\) 0 0
\(109\) 7.51459 0.719767 0.359884 0.932997i \(-0.382816\pi\)
0.359884 + 0.932997i \(0.382816\pi\)
\(110\) −0.839883 1.45472i −0.0800797 0.138702i
\(111\) 0 0
\(112\) 0 0
\(113\) −3.03064 + 5.24922i −0.285099 + 0.493805i −0.972633 0.232346i \(-0.925360\pi\)
0.687534 + 0.726152i \(0.258693\pi\)
\(114\) 0 0
\(115\) −0.260893 0.451880i −0.0243284 0.0421380i
\(116\) −8.97509 −0.833317
\(117\) 0 0
\(118\) 12.8961 1.18718
\(119\) 0 0
\(120\) 0 0
\(121\) −1.15272 + 1.99658i −0.104793 + 0.181507i
\(122\) −6.04163 + 10.4644i −0.546984 + 0.947403i
\(123\) 0 0
\(124\) −0.257295 0.445647i −0.0231057 0.0400203i
\(125\) 4.50739 0.403153
\(126\) 0 0
\(127\) 8.80992 0.781754 0.390877 0.920443i \(-0.372172\pi\)
0.390877 + 0.920443i \(0.372172\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −0.336285 + 0.582462i −0.0294941 + 0.0510853i
\(131\) −10.5687 + 18.3055i −0.923389 + 1.59936i −0.129258 + 0.991611i \(0.541260\pi\)
−0.794131 + 0.607746i \(0.792074\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 2.32023 0.200438
\(135\) 0 0
\(136\) −3.73385 −0.320175
\(137\) −2.20321 3.81607i −0.188233 0.326029i 0.756428 0.654077i \(-0.226943\pi\)
−0.944661 + 0.328048i \(0.893609\pi\)
\(138\) 0 0
\(139\) 1.01245 1.75362i 0.0858751 0.148740i −0.819889 0.572523i \(-0.805965\pi\)
0.905764 + 0.423783i \(0.139298\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.839883 1.45472i −0.0704815 0.122077i
\(143\) 5.32743 0.445502
\(144\) 0 0
\(145\) 4.13307 0.343233
\(146\) −6.62062 11.4673i −0.547927 0.949037i
\(147\) 0 0
\(148\) −4.55408 + 7.88791i −0.374343 + 0.648382i
\(149\) −4.58113 + 7.93474i −0.375300 + 0.650040i −0.990372 0.138432i \(-0.955794\pi\)
0.615071 + 0.788471i \(0.289127\pi\)
\(150\) 0 0
\(151\) 0.0519482 + 0.0899768i 0.00422748 + 0.00732221i 0.868131 0.496334i \(-0.165321\pi\)
−0.863904 + 0.503657i \(0.831988\pi\)
\(152\) 4.05408 0.328830
\(153\) 0 0
\(154\) 0 0
\(155\) 0.118485 + 0.205223i 0.00951698 + 0.0164839i
\(156\) 0 0
\(157\) 10.4911 18.1712i 0.837285 1.45022i −0.0548721 0.998493i \(-0.517475\pi\)
0.892157 0.451726i \(-0.149192\pi\)
\(158\) −2.50360 + 4.33636i −0.199176 + 0.344982i
\(159\) 0 0
\(160\) −0.230252 0.398809i −0.0182031 0.0315286i
\(161\) 0 0
\(162\) 0 0
\(163\) 23.0364 1.80435 0.902174 0.431372i \(-0.141970\pi\)
0.902174 + 0.431372i \(0.141970\pi\)
\(164\) −0.472958 0.819187i −0.0369318 0.0639678i
\(165\) 0 0
\(166\) −3.32383 + 5.75705i −0.257979 + 0.446833i
\(167\) −5.31498 + 9.20581i −0.411285 + 0.712367i −0.995031 0.0995698i \(-0.968253\pi\)
0.583745 + 0.811937i \(0.301587\pi\)
\(168\) 0 0
\(169\) 5.43346 + 9.41103i 0.417959 + 0.723926i
\(170\) 1.71946 0.131876
\(171\) 0 0
\(172\) −9.32743 −0.711210
\(173\) −1.46936 2.54500i −0.111713 0.193493i 0.804748 0.593617i \(-0.202301\pi\)
−0.916461 + 0.400124i \(0.868967\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.82383 + 3.15897i −0.137476 + 0.238116i
\(177\) 0 0
\(178\) 1.36333 + 2.36135i 0.102186 + 0.176991i
\(179\) −9.16225 −0.684819 −0.342409 0.939551i \(-0.611243\pi\)
−0.342409 + 0.939551i \(0.611243\pi\)
\(180\) 0 0
\(181\) −22.4284 −1.66709 −0.833545 0.552452i \(-0.813692\pi\)
−0.833545 + 0.552452i \(0.813692\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.566537 + 0.981271i −0.0417657 + 0.0723403i
\(185\) 2.09718 3.63242i 0.154188 0.267061i
\(186\) 0 0
\(187\) −6.80992 11.7951i −0.497990 0.862545i
\(188\) 2.32743 0.169745
\(189\) 0 0
\(190\) −1.86693 −0.135441
\(191\) 1.24484 + 2.15613i 0.0900736 + 0.156012i 0.907542 0.419962i \(-0.137956\pi\)
−0.817468 + 0.575974i \(0.804623\pi\)
\(192\) 0 0
\(193\) −2.24484 + 3.88818i −0.161587 + 0.279877i −0.935438 0.353491i \(-0.884995\pi\)
0.773851 + 0.633368i \(0.218328\pi\)
\(194\) −5.59358 + 9.68836i −0.401596 + 0.695584i
\(195\) 0 0
\(196\) 0 0
\(197\) −12.7339 −0.907249 −0.453625 0.891193i \(-0.649869\pi\)
−0.453625 + 0.891193i \(0.649869\pi\)
\(198\) 0 0
\(199\) −2.94592 −0.208830 −0.104415 0.994534i \(-0.533297\pi\)
−0.104415 + 0.994534i \(0.533297\pi\)
\(200\) −2.39397 4.14647i −0.169279 0.293200i
\(201\) 0 0
\(202\) 6.87792 11.9129i 0.483928 0.838189i
\(203\) 0 0
\(204\) 0 0
\(205\) 0.217799 + 0.377240i 0.0152118 + 0.0263476i
\(206\) 11.1623 0.777711
\(207\) 0 0
\(208\) 1.46050 0.101268
\(209\) 7.39397 + 12.8067i 0.511451 + 0.885860i
\(210\) 0 0
\(211\) −0.608168 + 1.05338i −0.0418680 + 0.0725176i −0.886200 0.463303i \(-0.846664\pi\)
0.844332 + 0.535820i \(0.179998\pi\)
\(212\) −6.21780 + 10.7695i −0.427040 + 0.739655i
\(213\) 0 0
\(214\) −3.89037 6.73832i −0.265940 0.460622i
\(215\) 4.29533 0.292939
\(216\) 0 0
\(217\) 0 0
\(218\) 3.75729 + 6.50783i 0.254476 + 0.440766i
\(219\) 0 0
\(220\) 0.839883 1.45472i 0.0566249 0.0980773i
\(221\) −2.72665 + 4.72270i −0.183415 + 0.317683i
\(222\) 0 0
\(223\) 0.445916 + 0.772349i 0.0298607 + 0.0517203i 0.880570 0.473917i \(-0.157160\pi\)
−0.850709 + 0.525637i \(0.823827\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −6.06128 −0.403190
\(227\) 7.32597 + 12.6889i 0.486242 + 0.842195i 0.999875 0.0158147i \(-0.00503418\pi\)
−0.513633 + 0.858010i \(0.671701\pi\)
\(228\) 0 0
\(229\) −4.78794 + 8.29295i −0.316396 + 0.548013i −0.979733 0.200307i \(-0.935806\pi\)
0.663338 + 0.748320i \(0.269139\pi\)
\(230\) 0.260893 0.451880i 0.0172028 0.0297961i
\(231\) 0 0
\(232\) −4.48755 7.77266i −0.294622 0.510300i
\(233\) 14.4284 0.945236 0.472618 0.881267i \(-0.343309\pi\)
0.472618 + 0.881267i \(0.343309\pi\)
\(234\) 0 0
\(235\) −1.07179 −0.0699161
\(236\) 6.44805 + 11.1684i 0.419732 + 0.726998i
\(237\) 0 0
\(238\) 0 0
\(239\) 9.15486 15.8567i 0.592179 1.02568i −0.401760 0.915745i \(-0.631601\pi\)
0.993938 0.109938i \(-0.0350654\pi\)
\(240\) 0 0
\(241\) 0.0466924 + 0.0808735i 0.00300772 + 0.00520952i 0.867525 0.497393i \(-0.165709\pi\)
−0.864518 + 0.502602i \(0.832376\pi\)
\(242\) −2.30545 −0.148200
\(243\) 0 0
\(244\) −12.0833 −0.773552
\(245\) 0 0
\(246\) 0 0
\(247\) 2.96050 5.12774i 0.188372 0.326271i
\(248\) 0.257295 0.445647i 0.0163382 0.0282986i
\(249\) 0 0
\(250\) 2.25370 + 3.90352i 0.142536 + 0.246880i
\(251\) −18.2733 −1.15340 −0.576702 0.816955i \(-0.695661\pi\)
−0.576702 + 0.816955i \(0.695661\pi\)
\(252\) 0 0
\(253\) −4.13307 −0.259844
\(254\) 4.40496 + 7.62961i 0.276392 + 0.478724i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 10.5256 18.2308i 0.656568 1.13721i −0.324931 0.945738i \(-0.605341\pi\)
0.981498 0.191471i \(-0.0613257\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.672570 −0.0417110
\(261\) 0 0
\(262\) −21.1373 −1.30587
\(263\) −2.58259 4.47318i −0.159249 0.275828i 0.775349 0.631533i \(-0.217574\pi\)
−0.934598 + 0.355705i \(0.884241\pi\)
\(264\) 0 0
\(265\) 2.86333 4.95943i 0.175893 0.304655i
\(266\) 0 0
\(267\) 0 0
\(268\) 1.16012 + 2.00938i 0.0708654 + 0.122742i
\(269\) −16.8568 −1.02778 −0.513889 0.857857i \(-0.671796\pi\)
−0.513889 + 0.857857i \(0.671796\pi\)
\(270\) 0 0
\(271\) 25.1124 1.52547 0.762736 0.646710i \(-0.223856\pi\)
0.762736 + 0.646710i \(0.223856\pi\)
\(272\) −1.86693 3.23361i −0.113199 0.196066i
\(273\) 0 0
\(274\) 2.20321 3.81607i 0.133101 0.230537i
\(275\) 8.73239 15.1249i 0.526583 0.912068i
\(276\) 0 0
\(277\) −1.69076 2.92848i −0.101588 0.175955i 0.810751 0.585391i \(-0.199059\pi\)
−0.912339 + 0.409436i \(0.865726\pi\)
\(278\) 2.02491 0.121446
\(279\) 0 0
\(280\) 0 0
\(281\) 10.1388 + 17.5609i 0.604831 + 1.04760i 0.992078 + 0.125622i \(0.0400925\pi\)
−0.387248 + 0.921976i \(0.626574\pi\)
\(282\) 0 0
\(283\) 8.67471 15.0250i 0.515658 0.893145i −0.484177 0.874970i \(-0.660881\pi\)
0.999835 0.0181754i \(-0.00578571\pi\)
\(284\) 0.839883 1.45472i 0.0498379 0.0863218i
\(285\) 0 0
\(286\) 2.66372 + 4.61369i 0.157509 + 0.272813i
\(287\) 0 0
\(288\) 0 0
\(289\) −3.05836 −0.179903
\(290\) 2.06654 + 3.57935i 0.121351 + 0.210187i
\(291\) 0 0
\(292\) 6.62062 11.4673i 0.387443 0.671070i
\(293\) −4.93560 + 8.54871i −0.288341 + 0.499421i −0.973414 0.229054i \(-0.926437\pi\)
0.685073 + 0.728474i \(0.259770\pi\)
\(294\) 0 0
\(295\) −2.96936 5.14308i −0.172883 0.299442i
\(296\) −9.10817 −0.529402
\(297\) 0 0
\(298\) −9.16225 −0.530755
\(299\) 0.827430 + 1.43315i 0.0478515 + 0.0828813i
\(300\) 0 0
\(301\) 0 0
\(302\) −0.0519482 + 0.0899768i −0.00298928 + 0.00517759i
\(303\) 0 0
\(304\) 2.02704 + 3.51094i 0.116259 + 0.201366i
\(305\) 5.56440 0.318617
\(306\) 0 0
\(307\) −7.78794 −0.444481 −0.222240 0.974992i \(-0.571337\pi\)
−0.222240 + 0.974992i \(0.571337\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.118485 + 0.205223i −0.00672952 + 0.0116559i
\(311\) −7.70535 + 13.3461i −0.436930 + 0.756785i −0.997451 0.0713552i \(-0.977268\pi\)
0.560521 + 0.828140i \(0.310601\pi\)
\(312\) 0 0
\(313\) 4.24844 + 7.35851i 0.240136 + 0.415928i 0.960753 0.277406i \(-0.0894746\pi\)
−0.720617 + 0.693334i \(0.756141\pi\)
\(314\) 20.9823 1.18410
\(315\) 0 0
\(316\) −5.00720 −0.281677
\(317\) −7.05262 12.2155i −0.396115 0.686091i 0.597128 0.802146i \(-0.296308\pi\)
−0.993243 + 0.116055i \(0.962975\pi\)
\(318\) 0 0
\(319\) 16.3691 28.3520i 0.916491 1.58741i
\(320\) 0.230252 0.398809i 0.0128715 0.0222941i
\(321\) 0 0
\(322\) 0 0
\(323\) −15.1373 −0.842264
\(324\) 0 0
\(325\) −6.99280 −0.387891
\(326\) 11.5182 + 19.9501i 0.637933 + 1.10493i
\(327\) 0 0
\(328\) 0.472958 0.819187i 0.0261147 0.0452320i
\(329\) 0 0
\(330\) 0 0
\(331\) −13.7719 23.8536i −0.756971 1.31111i −0.944388 0.328832i \(-0.893345\pi\)
0.187417 0.982280i \(-0.439988\pi\)
\(332\) −6.64766 −0.364838
\(333\) 0 0
\(334\) −10.6300 −0.581645
\(335\) −0.534239 0.925330i −0.0291886 0.0505562i
\(336\) 0 0
\(337\) 0.748440 1.29634i 0.0407701 0.0706159i −0.844920 0.534892i \(-0.820352\pi\)
0.885690 + 0.464276i \(0.153686\pi\)
\(338\) −5.43346 + 9.41103i −0.295541 + 0.511893i
\(339\) 0 0
\(340\) 0.859728 + 1.48909i 0.0466253 + 0.0807574i
\(341\) 1.87705 0.101648
\(342\) 0 0
\(343\) 0 0
\(344\) −4.66372 8.07779i −0.251451 0.435525i
\(345\) 0 0
\(346\) 1.46936 2.54500i 0.0789932 0.136820i
\(347\) −9.14406 + 15.8380i −0.490879 + 0.850228i −0.999945 0.0105001i \(-0.996658\pi\)
0.509066 + 0.860728i \(0.329991\pi\)
\(348\) 0 0
\(349\) 3.90136 + 6.75735i 0.208835 + 0.361713i 0.951348 0.308119i \(-0.0996995\pi\)
−0.742513 + 0.669832i \(0.766366\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −3.64766 −0.194421
\(353\) −13.4626 23.3180i −0.716544 1.24109i −0.962361 0.271774i \(-0.912390\pi\)
0.245817 0.969316i \(-0.420944\pi\)
\(354\) 0 0
\(355\) −0.386770 + 0.669906i −0.0205276 + 0.0355549i
\(356\) −1.36333 + 2.36135i −0.0722562 + 0.125151i
\(357\) 0 0
\(358\) −4.58113 7.93474i −0.242120 0.419364i
\(359\) −6.26322 −0.330560 −0.165280 0.986247i \(-0.552853\pi\)
−0.165280 + 0.986247i \(0.552853\pi\)
\(360\) 0 0
\(361\) −2.56440 −0.134968
\(362\) −11.2142 19.4236i −0.589405 1.02088i
\(363\) 0 0
\(364\) 0 0
\(365\) −3.04883 + 5.28073i −0.159583 + 0.276406i
\(366\) 0 0
\(367\) 14.6367 + 25.3515i 0.764028 + 1.32334i 0.940759 + 0.339076i \(0.110114\pi\)
−0.176731 + 0.984259i \(0.556552\pi\)
\(368\) −1.13307 −0.0590656
\(369\) 0 0
\(370\) 4.19436 0.218054
\(371\) 0 0
\(372\) 0 0
\(373\) −8.92986 + 15.4670i −0.462371 + 0.800850i −0.999079 0.0429184i \(-0.986334\pi\)
0.536708 + 0.843768i \(0.319668\pi\)
\(374\) 6.80992 11.7951i 0.352132 0.609911i
\(375\) 0 0
\(376\) 1.16372 + 2.01561i 0.0600140 + 0.103947i
\(377\) −13.1082 −0.675105
\(378\) 0 0
\(379\) −22.4255 −1.15192 −0.575960 0.817478i \(-0.695371\pi\)
−0.575960 + 0.817478i \(0.695371\pi\)
\(380\) −0.933463 1.61680i −0.0478856 0.0829403i
\(381\) 0 0
\(382\) −1.24484 + 2.15613i −0.0636916 + 0.110317i
\(383\) 7.07014 12.2458i 0.361267 0.625733i −0.626903 0.779098i \(-0.715678\pi\)
0.988170 + 0.153365i \(0.0490109\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −4.48968 −0.228519
\(387\) 0 0
\(388\) −11.1872 −0.567942
\(389\) −11.5651 20.0313i −0.586373 1.01563i −0.994703 0.102793i \(-0.967222\pi\)
0.408330 0.912834i \(-0.366111\pi\)
\(390\) 0 0
\(391\) 2.11537 3.66392i 0.106979 0.185292i
\(392\) 0 0
\(393\) 0 0
\(394\) −6.36693 11.0278i −0.320761 0.555574i
\(395\) 2.30584 0.116019
\(396\) 0 0
\(397\) −10.2661 −0.515243 −0.257622 0.966246i \(-0.582939\pi\)
−0.257622 + 0.966246i \(0.582939\pi\)
\(398\) −1.47296 2.55124i −0.0738327 0.127882i
\(399\) 0 0
\(400\) 2.39397 4.14647i 0.119698 0.207324i
\(401\) 17.0167 29.4738i 0.849775 1.47185i −0.0316345 0.999500i \(-0.510071\pi\)
0.881409 0.472353i \(-0.156595\pi\)
\(402\) 0 0
\(403\) −0.375780 0.650870i −0.0187189 0.0324221i
\(404\) 13.7558 0.684378
\(405\) 0 0
\(406\) 0 0
\(407\) −16.6118 28.7724i −0.823415 1.42620i
\(408\) 0 0
\(409\) −1.74484 + 3.02215i −0.0862769 + 0.149436i −0.905935 0.423418i \(-0.860830\pi\)
0.819658 + 0.572854i \(0.194164\pi\)
\(410\) −0.217799 + 0.377240i −0.0107563 + 0.0186305i
\(411\) 0 0
\(412\) 5.58113 + 9.66679i 0.274962 + 0.476249i
\(413\) 0 0
\(414\) 0 0
\(415\) 3.06128 0.150272
\(416\) 0.730252 + 1.26483i 0.0358036 + 0.0620136i
\(417\) 0 0
\(418\) −7.39397 + 12.8067i −0.361651 + 0.626398i
\(419\) 14.4897 25.0969i 0.707867 1.22606i −0.257779 0.966204i \(-0.582991\pi\)
0.965647 0.259858i \(-0.0836759\pi\)
\(420\) 0 0
\(421\) −1.06128 1.83819i −0.0517237 0.0895881i 0.839004 0.544125i \(-0.183138\pi\)
−0.890728 + 0.454537i \(0.849805\pi\)
\(422\) −1.21634 −0.0592104
\(423\) 0 0
\(424\) −12.4356 −0.603926
\(425\) 8.93872 + 15.4823i 0.433592 + 0.751003i
\(426\) 0 0
\(427\) 0 0
\(428\) 3.89037 6.73832i 0.188048 0.325709i
\(429\) 0 0
\(430\) 2.14766 + 3.71986i 0.103570 + 0.179388i
\(431\) 21.8712 1.05350 0.526749 0.850021i \(-0.323411\pi\)
0.526749 + 0.850021i \(0.323411\pi\)
\(432\) 0 0
\(433\) 13.0512 0.627199 0.313599 0.949555i \(-0.398465\pi\)
0.313599 + 0.949555i \(0.398465\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −3.75729 + 6.50783i −0.179942 + 0.311668i
\(437\) −2.29679 + 3.97816i −0.109870 + 0.190301i
\(438\) 0 0
\(439\) 2.43200 + 4.21235i 0.116073 + 0.201044i 0.918208 0.396098i \(-0.129636\pi\)
−0.802135 + 0.597143i \(0.796303\pi\)
\(440\) 1.67977 0.0800797
\(441\) 0 0
\(442\) −5.45331 −0.259387
\(443\) −5.76975 9.99350i −0.274129 0.474805i 0.695786 0.718249i \(-0.255056\pi\)
−0.969915 + 0.243444i \(0.921723\pi\)
\(444\) 0 0
\(445\) 0.627819 1.08741i 0.0297615 0.0515484i
\(446\) −0.445916 + 0.772349i −0.0211147 + 0.0365718i
\(447\) 0 0
\(448\) 0 0
\(449\) 26.4251 1.24708 0.623538 0.781793i \(-0.285694\pi\)
0.623538 + 0.781793i \(0.285694\pi\)
\(450\) 0 0
\(451\) 3.45038 0.162472
\(452\) −3.03064 5.24922i −0.142549 0.246903i
\(453\) 0 0
\(454\) −7.32597 + 12.6889i −0.343825 + 0.595522i
\(455\) 0 0
\(456\) 0 0
\(457\) 1.86906 + 3.23731i 0.0874310 + 0.151435i 0.906425 0.422368i \(-0.138801\pi\)
−0.818994 + 0.573803i \(0.805468\pi\)
\(458\) −9.57587 −0.447451
\(459\) 0 0
\(460\) 0.521786 0.0243284
\(461\) −7.90496 13.6918i −0.368171 0.637690i 0.621109 0.783724i \(-0.286682\pi\)
−0.989280 + 0.146034i \(0.953349\pi\)
\(462\) 0 0
\(463\) 19.1965 33.2493i 0.892137 1.54523i 0.0548278 0.998496i \(-0.482539\pi\)
0.837309 0.546730i \(-0.184128\pi\)
\(464\) 4.48755 7.77266i 0.208329 0.360837i
\(465\) 0 0
\(466\) 7.21420 + 12.4954i 0.334191 + 0.578836i
\(467\) −6.31304 −0.292132 −0.146066 0.989275i \(-0.546661\pi\)
−0.146066 + 0.989275i \(0.546661\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −0.535897 0.928200i −0.0247191 0.0428147i
\(471\) 0 0
\(472\) −6.44805 + 11.1684i −0.296796 + 0.514065i
\(473\) 17.0117 29.4651i 0.782197 1.35481i
\(474\) 0 0
\(475\) −9.70535 16.8102i −0.445312 0.771303i
\(476\) 0 0
\(477\) 0 0
\(478\) 18.3097 0.837467
\(479\) 10.2068 + 17.6787i 0.466361 + 0.807761i 0.999262 0.0384168i \(-0.0122314\pi\)
−0.532901 + 0.846178i \(0.678898\pi\)
\(480\) 0 0
\(481\) −6.65126 + 11.5203i −0.303271 + 0.525282i
\(482\) −0.0466924 + 0.0808735i −0.00212678 + 0.00368369i
\(483\) 0 0
\(484\) −1.15272 1.99658i −0.0523966 0.0907535i
\(485\) 5.15174 0.233929
\(486\) 0 0
\(487\) −12.3638 −0.560258 −0.280129 0.959962i \(-0.590377\pi\)
−0.280129 + 0.959962i \(0.590377\pi\)
\(488\) −6.04163 10.4644i −0.273492 0.473702i
\(489\) 0 0
\(490\) 0 0
\(491\) −0.207004 + 0.358541i −0.00934194 + 0.0161807i −0.870659 0.491888i \(-0.836307\pi\)
0.861317 + 0.508069i \(0.169640\pi\)
\(492\) 0 0
\(493\) 16.7558 + 29.0220i 0.754645 + 1.30708i
\(494\) 5.92101 0.266399
\(495\) 0 0
\(496\) 0.514589 0.0231057
\(497\) 0 0
\(498\) 0 0
\(499\) 0.461967 0.800151i 0.0206805 0.0358197i −0.855500 0.517803i \(-0.826750\pi\)
0.876180 + 0.481983i \(0.160083\pi\)
\(500\) −2.25370 + 3.90352i −0.100788 + 0.174571i
\(501\) 0 0
\(502\) −9.13667 15.8252i −0.407790 0.706312i
\(503\) −23.8142 −1.06182 −0.530911 0.847428i \(-0.678150\pi\)
−0.530911 + 0.847428i \(0.678150\pi\)
\(504\) 0 0
\(505\) −6.33463 −0.281887
\(506\) −2.06654 3.57935i −0.0918688 0.159121i
\(507\) 0 0
\(508\) −4.40496 + 7.62961i −0.195438 + 0.338509i
\(509\) 15.3171 26.5300i 0.678919 1.17592i −0.296388 0.955068i \(-0.595782\pi\)
0.975307 0.220855i \(-0.0708846\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 21.0512 0.928527
\(515\) −2.57014 4.45161i −0.113254 0.196161i
\(516\) 0 0
\(517\) −4.24484 + 7.35228i −0.186688 + 0.323353i
\(518\) 0 0
\(519\) 0 0
\(520\) −0.336285 0.582462i −0.0147471 0.0255427i
\(521\) 26.9037 1.17867 0.589336 0.807888i \(-0.299389\pi\)
0.589336 + 0.807888i \(0.299389\pi\)
\(522\) 0 0
\(523\) −15.7060 −0.686776 −0.343388 0.939194i \(-0.611575\pi\)
−0.343388 + 0.939194i \(0.611575\pi\)
\(524\) −10.5687 18.3055i −0.461695 0.799679i
\(525\) 0 0
\(526\) 2.58259 4.47318i 0.112606 0.195040i
\(527\) −0.960699 + 1.66398i −0.0418487 + 0.0724841i
\(528\) 0 0
\(529\) 10.8581 + 18.8067i 0.472090 + 0.817684i
\(530\) 5.72665 0.248750
\(531\) 0 0
\(532\) 0 0
\(533\) −0.690757 1.19643i −0.0299200 0.0518230i
\(534\) 0 0
\(535\) −1.79153 + 3.10303i −0.0774548 + 0.134156i
\(536\) −1.16012 + 2.00938i −0.0501094 + 0.0867920i
\(537\) 0 0
\(538\) −8.42840 14.5984i −0.363374 0.629383i
\(539\) 0 0
\(540\) 0 0
\(541\) 4.11868 0.177076 0.0885379 0.996073i \(-0.471781\pi\)
0.0885379 + 0.996073i \(0.471781\pi\)
\(542\) 12.5562 + 21.7480i 0.539336 + 0.934157i
\(543\) 0 0
\(544\) 1.86693 3.23361i 0.0800438 0.138640i
\(545\) 1.73025 2.99689i 0.0741159 0.128372i
\(546\) 0 0
\(547\) −11.8602 20.5425i −0.507106 0.878333i −0.999966 0.00822465i \(-0.997382\pi\)
0.492860 0.870108i \(-0.335951\pi\)
\(548\) 4.40642 0.188233
\(549\) 0 0
\(550\) 17.4648 0.744701
\(551\) −18.1929 31.5110i −0.775043 1.34241i
\(552\) 0 0
\(553\) 0 0
\(554\) 1.69076 2.92848i 0.0718334 0.124419i
\(555\) 0 0
\(556\) 1.01245 + 1.75362i 0.0429376 + 0.0743701i
\(557\) −42.0626 −1.78225 −0.891125 0.453757i \(-0.850083\pi\)
−0.891125 + 0.453757i \(0.850083\pi\)
\(558\) 0 0
\(559\) −13.6228 −0.576181
\(560\) 0 0
\(561\) 0 0
\(562\) −10.1388 + 17.5609i −0.427680 + 0.740763i
\(563\) −5.91216 + 10.2402i −0.249168 + 0.431571i −0.963295 0.268445i \(-0.913490\pi\)
0.714127 + 0.700016i \(0.246824\pi\)
\(564\) 0 0
\(565\) 1.39562 + 2.41729i 0.0587144 + 0.101696i
\(566\) 17.3494 0.729250
\(567\) 0 0
\(568\) 1.67977 0.0704815
\(569\) 7.10078 + 12.2989i 0.297680 + 0.515597i 0.975605 0.219534i \(-0.0704538\pi\)
−0.677925 + 0.735131i \(0.737120\pi\)
\(570\) 0 0
\(571\) −5.97869 + 10.3554i −0.250200 + 0.433360i −0.963581 0.267417i \(-0.913830\pi\)
0.713380 + 0.700777i \(0.247163\pi\)
\(572\) −2.66372 + 4.61369i −0.111376 + 0.192908i
\(573\) 0 0
\(574\) 0 0
\(575\) 5.42509 0.226242
\(576\) 0 0
\(577\) 42.6270 1.77459 0.887293 0.461206i \(-0.152583\pi\)
0.887293 + 0.461206i \(0.152583\pi\)
\(578\) −1.52918 2.64861i −0.0636054 0.110168i
\(579\) 0 0
\(580\) −2.06654 + 3.57935i −0.0858083 + 0.148624i
\(581\) 0 0
\(582\) 0 0
\(583\) −22.6804 39.2837i −0.939328 1.62696i
\(584\) 13.2412 0.547927
\(585\) 0 0
\(586\) −9.87120 −0.407775
\(587\) 20.5328 + 35.5638i 0.847478 + 1.46788i 0.883451 + 0.468523i \(0.155214\pi\)
−0.0359730 + 0.999353i \(0.511453\pi\)
\(588\) 0 0
\(589\) 1.04309 1.80669i 0.0429799 0.0744434i
\(590\) 2.96936 5.14308i 0.122247 0.211737i
\(591\) 0 0
\(592\) −4.55408 7.88791i −0.187172 0.324191i
\(593\) −32.2016 −1.32236 −0.661180 0.750228i \(-0.729944\pi\)
−0.661180 + 0.750228i \(0.729944\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −4.58113 7.93474i −0.187650 0.325020i
\(597\) 0 0
\(598\) −0.827430 + 1.43315i −0.0338361 + 0.0586059i
\(599\) 9.53590 16.5167i 0.389626 0.674852i −0.602773 0.797913i \(-0.705938\pi\)
0.992399 + 0.123060i \(0.0392709\pi\)
\(600\) 0 0
\(601\) −4.27188 7.39912i −0.174254 0.301816i 0.765649 0.643259i \(-0.222418\pi\)
−0.939903 + 0.341442i \(0.889085\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −0.103896 −0.00422748
\(605\) 0.530835 + 0.919434i 0.0215815 + 0.0373803i
\(606\) 0 0
\(607\) 19.0057 32.9189i 0.771419 1.33614i −0.165366 0.986232i \(-0.552881\pi\)
0.936785 0.349905i \(-0.113786\pi\)
\(608\) −2.02704 + 3.51094i −0.0822074 + 0.142387i
\(609\) 0 0
\(610\) 2.78220 + 4.81891i 0.112648 + 0.195112i
\(611\) 3.39922 0.137518
\(612\) 0 0
\(613\) −22.6591 −0.915194 −0.457597 0.889160i \(-0.651290\pi\)
−0.457597 + 0.889160i \(0.651290\pi\)
\(614\) −3.89397 6.74455i −0.157148 0.272188i
\(615\) 0 0
\(616\) 0 0
\(617\) 10.1388 17.5609i 0.408173 0.706977i −0.586512 0.809941i \(-0.699499\pi\)
0.994685 + 0.102964i \(0.0328327\pi\)
\(618\) 0 0
\(619\) 1.03064 + 1.78512i 0.0414249 + 0.0717501i 0.885994 0.463696i \(-0.153477\pi\)
−0.844570 + 0.535446i \(0.820144\pi\)
\(620\) −0.236971 −0.00951698
\(621\) 0 0
\(622\) −15.4107 −0.617912
\(623\) 0 0
\(624\) 0 0
\(625\) −10.9320 + 18.9348i −0.437280 + 0.757391i
\(626\) −4.24844 + 7.35851i −0.169802 + 0.294105i
\(627\) 0 0
\(628\) 10.4911 + 18.1712i 0.418642 + 0.725110i
\(629\) 34.0085 1.35601
\(630\) 0 0
\(631\) 1.63715 0.0651740 0.0325870 0.999469i \(-0.489625\pi\)
0.0325870 + 0.999469i \(0.489625\pi\)
\(632\) −2.50360 4.33636i −0.0995878 0.172491i
\(633\) 0 0
\(634\) 7.05262 12.2155i 0.280095 0.485139i
\(635\) 2.02850 3.51347i 0.0804988 0.139428i
\(636\) 0 0
\(637\) 0 0
\(638\) 32.7381 1.29611
\(639\) 0 0
\(640\) 0.460505 0.0182031
\(641\) 10.9662 + 18.9941i 0.433140 + 0.750221i 0.997142 0.0755526i \(-0.0240721\pi\)
−0.564001 + 0.825774i \(0.690739\pi\)
\(642\) 0 0
\(643\) 14.1819 24.5638i 0.559280 0.968701i −0.438277 0.898840i \(-0.644411\pi\)
0.997557 0.0698609i \(-0.0222555\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −7.56867 13.1093i −0.297785 0.515780i
\(647\) −34.7807 −1.36737 −0.683686 0.729776i \(-0.739624\pi\)
−0.683686 + 0.729776i \(0.739624\pi\)
\(648\) 0 0
\(649\) −47.0406 −1.84651
\(650\) −3.49640 6.05594i −0.137140 0.237534i
\(651\) 0 0
\(652\) −11.5182 + 19.9501i −0.451087 + 0.781306i
\(653\) −1.59931 + 2.77009i −0.0625860 + 0.108402i −0.895621 0.444819i \(-0.853268\pi\)
0.833035 + 0.553221i \(0.186601\pi\)
\(654\) 0 0
\(655\) 4.86693 + 8.42976i 0.190167 + 0.329378i
\(656\) 0.945916 0.0369318
\(657\) 0 0
\(658\) 0 0
\(659\) −5.30418 9.18711i −0.206622 0.357879i 0.744027 0.668150i \(-0.232914\pi\)
−0.950648 + 0.310271i \(0.899580\pi\)
\(660\) 0 0
\(661\) 5.06507 8.77297i 0.197009 0.341229i −0.750549 0.660815i \(-0.770211\pi\)
0.947557 + 0.319586i \(0.103544\pi\)
\(662\) 13.7719 23.8536i 0.535259 0.927097i
\(663\) 0 0
\(664\) −3.32383 5.75705i −0.128990 0.223417i
\(665\) 0 0
\(666\) 0 0
\(667\) 10.1694 0.393763
\(668\) −5.31498 9.20581i −0.205643 0.356184i
\(669\) 0 0
\(670\) 0.534239 0.925330i 0.0206395 0.0357486i
\(671\) 22.0378 38.1707i 0.850761 1.47356i
\(672\) 0 0
\(673\) 1.60817 + 2.78543i 0.0619903 + 0.107370i 0.895355 0.445353i \(-0.146922\pi\)
−0.833365 + 0.552724i \(0.813589\pi\)
\(674\) 1.49688 0.0576577
\(675\) 0 0
\(676\) −10.8669 −0.417959
\(677\) 14.6819 + 25.4298i 0.564271 + 0.977347i 0.997117 + 0.0758786i \(0.0241762\pi\)
−0.432846 + 0.901468i \(0.642491\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −0.859728 + 1.48909i −0.0329691 + 0.0571041i
\(681\) 0 0
\(682\) 0.938524 + 1.62557i 0.0359379 + 0.0622463i
\(683\) 25.2556 0.966380 0.483190 0.875515i \(-0.339478\pi\)
0.483190 + 0.875515i \(0.339478\pi\)
\(684\) 0 0
\(685\) −2.02918 −0.0775309
\(686\) 0 0
\(687\) 0 0
\(688\) 4.66372 8.07779i 0.177802 0.307963i
\(689\) −9.08113 + 15.7290i −0.345963 + 0.599226i
\(690\) 0 0
\(691\) −7.68190 13.3054i −0.292233 0.506163i 0.682104 0.731255i \(-0.261065\pi\)
−0.974338 + 0.225092i \(0.927732\pi\)
\(692\) 2.93872 0.111713
\(693\) 0 0
\(694\) −18.2881 −0.694208
\(695\) −0.466240 0.807551i −0.0176855 0.0306321i
\(696\) 0 0
\(697\) −1.76595 + 3.05872i −0.0668903 + 0.115857i
\(698\) −3.90136 + 6.75735i −0.147669 + 0.255770i
\(699\) 0 0
\(700\) 0 0
\(701\) 13.3700 0.504980 0.252490 0.967600i \(-0.418751\pi\)
0.252490 + 0.967600i \(0.418751\pi\)
\(702\) 0 0
\(703\) −36.9253 −1.39266
\(704\) −1.82383 3.15897i −0.0687382 0.119058i
\(705\) 0 0
\(706\) 13.4626 23.3180i 0.506673 0.877584i
\(707\) 0 0
\(708\) 0 0
\(709\) 0.562939 + 0.975038i 0.0211416 + 0.0366183i 0.876403 0.481579i \(-0.159937\pi\)
−0.855261 + 0.518197i \(0.826603\pi\)
\(710\) −0.773541 −0.0290305
\(711\) 0 0
\(712\) −2.72665 −0.102186
\(713\) 0.291534 + 0.504951i 0.0109180 + 0.0189106i
\(714\) 0 0
\(715\) 1.22665 2.12463i 0.0458743 0.0794565i
\(716\) 4.58113 7.93474i 0.171205 0.296535i
\(717\) 0 0
\(718\) −3.13161 5.42411i −0.116871 0.202426i
\(719\) −18.2733 −0.681481 −0.340740 0.940157i \(-0.610678\pi\)
−0.340740 + 0.940157i \(0.610678\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.28220 2.22084i −0.0477186 0.0826510i
\(723\) 0 0
\(724\) 11.2142 19.4236i 0.416772 0.721871i
\(725\) −21.4861 + 37.2150i −0.797973 + 1.38213i
\(726\) 0 0
\(727\) 14.8478 + 25.7171i 0.550673 + 0.953793i 0.998226 + 0.0595359i \(0.0189621\pi\)
−0.447553 + 0.894257i \(0.647705\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −6.09766 −0.225684
\(731\) 17.4136 + 30.1613i 0.644066 + 1.11555i
\(732\) 0 0
\(733\) 9.61390 16.6518i 0.355098 0.615047i −0.632037 0.774938i \(-0.717781\pi\)
0.987135 + 0.159891i \(0.0511143\pi\)
\(734\) −14.6367 + 25.3515i −0.540249 + 0.935740i
\(735\) 0 0
\(736\) −0.566537 0.981271i −0.0208828 0.0361701i
\(737\) −8.46343 −0.311754
\(738\) 0 0
\(739\) 30.2671 1.11339 0.556697 0.830716i \(-0.312069\pi\)
0.556697 + 0.830716i \(0.312069\pi\)
\(740\) 2.09718 + 3.63242i 0.0770938 + 0.133530i
\(741\) 0 0
\(742\) 0 0
\(743\) 11.8815 20.5794i 0.435890 0.754984i −0.561477 0.827492i \(-0.689767\pi\)
0.997368 + 0.0725076i \(0.0231002\pi\)
\(744\) 0 0
\(745\) 2.10963 + 3.65399i 0.0772909 + 0.133872i
\(746\) −17.8597 −0.653891
\(747\) 0 0
\(748\) 13.6198 0.497990
\(749\) 0 0
\(750\) 0 0
\(751\) −6.33415 + 10.9711i −0.231136 + 0.400340i −0.958143 0.286291i \(-0.907578\pi\)
0.727006 + 0.686631i \(0.240911\pi\)
\(752\) −1.16372 + 2.01561i −0.0424363 + 0.0735019i
\(753\) 0 0
\(754\) −6.55408 11.3520i −0.238686 0.413416i
\(755\) 0.0478448 0.00174125
\(756\) 0 0
\(757\) −29.0799 −1.05693 −0.528464 0.848955i \(-0.677232\pi\)
−0.528464 + 0.848955i \(0.677232\pi\)
\(758\) −11.2127 19.4210i −0.407265 0.705404i
\(759\) 0 0
\(760\) 0.933463 1.61680i 0.0338603 0.0586477i
\(761\) −14.6015 + 25.2905i −0.529302 + 0.916778i 0.470114 + 0.882606i \(0.344213\pi\)
−0.999416 + 0.0341724i \(0.989120\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −2.48968 −0.0900736
\(765\) 0 0
\(766\) 14.1403 0.510909
\(767\) 9.41741 + 16.3114i 0.340043 + 0.588972i
\(768\) 0 0
\(769\) −12.5869 + 21.8011i −0.453894 + 0.786167i −0.998624 0.0524443i \(-0.983299\pi\)
0.544730 + 0.838611i \(0.316632\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −2.24484 3.88818i −0.0807936 0.139939i
\(773\) 1.50408 0.0540979 0.0270490 0.999634i \(-0.491389\pi\)
0.0270490 + 0.999634i \(0.491389\pi\)
\(774\) 0 0
\(775\) −2.46382 −0.0885030
\(776\) −5.59358 9.68836i −0.200798 0.347792i
\(777\) 0 0
\(778\) 11.5651 20.0313i 0.414628 0.718157i
\(779\) 1.91741 3.32105i 0.0686984 0.118989i
\(780\) 0 0
\(781\) 3.06361 + 5.30633i 0.109625 + 0.189875i
\(782\) 4.23073 0.151291
\(783\) 0 0
\(784\) 0 0
\(785\) −4.83122 8.36792i −0.172434 0.298664i
\(786\) 0 0
\(787\) −7.47656 + 12.9498i −0.266510 + 0.461610i −0.967958 0.251111i \(-0.919204\pi\)
0.701448 + 0.712721i \(0.252537\pi\)
\(788\) 6.36693 11.0278i 0.226812 0.392850i
\(789\) 0 0
\(790\) 1.15292 + 1.99691i 0.0410190 + 0.0710470i
\(791\) 0 0
\(792\) 0 0
\(793\) −17.6477 −0.626687
\(794\) −5.13307 8.89075i −0.182166 0.315521i
\(795\) 0 0
\(796\) 1.47296 2.55124i 0.0522076 0.0904262i
\(797\) −4.56294 + 7.90324i −0.161628 + 0.279947i −0.935453 0.353452i \(-0.885008\pi\)
0.773825 + 0.633400i \(0.218341\pi\)
\(798\) 0 0
\(799\) −4.34514 7.52600i −0.153720 0.266251i
\(800\) 4.78794 0.169279
\(801\) 0 0
\(802\) 34.0335 1.20176
\(803\) 24.1498 + 41.8287i 0.852228 + 1.47610i
\(804\) 0 0
\(805\) 0 0
\(806\) 0.375780 0.650870i 0.0132363 0.0229259i
\(807\) 0 0
\(808\) 6.87792 + 11.9129i 0.241964 + 0.419094i
\(809\) 35.5510 1.24991 0.624953 0.780663i \(-0.285118\pi\)
0.624953 + 0.780663i \(0.285118\pi\)
\(810\) 0 0
\(811\) 13.5070 0.474295 0.237148 0.971474i \(-0.423788\pi\)
0.237148 + 0.971474i \(0.423788\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 16.6118 28.7724i 0.582242 1.00847i
\(815\) 5.30418 9.18711i 0.185797 0.321810i
\(816\) 0 0
\(817\) −18.9071 32.7480i −0.661475 1.14571i
\(818\) −3.48968 −0.122014
\(819\) 0 0
\(820\) −0.435599 −0.0152118
\(821\) 10.8114 + 18.7259i 0.377320 + 0.653537i 0.990671 0.136273i \(-0.0435125\pi\)
−0.613352 + 0.789810i \(0.710179\pi\)
\(822\) 0 0
\(823\) 0.753501 1.30510i 0.0262654 0.0454930i −0.852594 0.522574i \(-0.824972\pi\)
0.878859 + 0.477081i \(0.158305\pi\)
\(824\) −5.58113 + 9.66679i −0.194428 + 0.336759i
\(825\) 0 0
\(826\) 0 0
\(827\) −23.3786 −0.812953 −0.406477 0.913661i \(-0.633243\pi\)
−0.406477 + 0.913661i \(0.633243\pi\)
\(828\) 0 0
\(829\) −22.0191 −0.764753 −0.382377 0.924007i \(-0.624894\pi\)
−0.382377 + 0.924007i \(0.624894\pi\)
\(830\) 1.53064 + 2.65115i 0.0531293 + 0.0920227i
\(831\) 0 0
\(832\) −0.730252 + 1.26483i −0.0253169 + 0.0438502i
\(833\) 0 0
\(834\) 0 0
\(835\) 2.44757 + 4.23932i 0.0847018 + 0.146708i
\(836\) −14.7879 −0.511451
\(837\) 0 0
\(838\) 28.9794 1.00108
\(839\) −1.06507 1.84476i −0.0367705 0.0636883i 0.847055 0.531506i \(-0.178374\pi\)
−0.883825 + 0.467818i \(0.845040\pi\)
\(840\) 0 0
\(841\) −25.7762 + 44.6456i −0.888833 + 1.53950i
\(842\) 1.06128 1.83819i 0.0365742 0.0633483i
\(843\) 0 0
\(844\) −0.608168 1.05338i −0.0209340 0.0362588i
\(845\) 5.00427 0.172152
\(846\) 0 0
\(847\) 0 0
\(848\) −6.21780 10.7695i −0.213520 0.369828i
\(849\) 0 0
\(850\) −8.93872 + 15.4823i −0.306596 + 0.531039i
\(851\) 5.16012 8.93758i 0.176887 0.306376i
\(852\) 0 0
\(853\) 3.50146 + 6.06471i 0.119888 + 0.207652i 0.919723 0.392568i \(-0.128413\pi\)
−0.799835 + 0.600220i \(0.795080\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 7.78074 0.265940
\(857\) −5.46410 9.46410i −0.186650 0.323288i 0.757481 0.652857i \(-0.226430\pi\)
−0.944131 + 0.329569i \(0.893096\pi\)
\(858\) 0 0
\(859\) −6.95379 + 12.0443i −0.237260 + 0.410947i −0.959927 0.280250i \(-0.909583\pi\)
0.722667 + 0.691196i \(0.242916\pi\)
\(860\) −2.14766 + 3.71986i −0.0732347 + 0.126846i
\(861\) 0 0
\(862\) 10.9356 + 18.9410i 0.372468 + 0.645133i
\(863\) −36.8463 −1.25426 −0.627131 0.778914i \(-0.715771\pi\)
−0.627131 + 0.778914i \(0.715771\pi\)
\(864\) 0 0
\(865\) −1.35329 −0.0460134
\(866\) 6.52558 + 11.3026i 0.221748 + 0.384079i
\(867\) 0 0
\(868\) 0 0
\(869\) 9.13229 15.8176i 0.309792 0.536575i
\(870\) 0 0
\(871\) 1.69436 + 2.93471i 0.0574111 + 0.0994389i
\(872\) −7.51459 −0.254476
\(873\) 0 0
\(874\) −4.59358 −0.155380
\(875\) 0 0
\(876\) 0 0
\(877\) 5.17977 8.97162i 0.174908 0.302950i −0.765221 0.643767i \(-0.777370\pi\)
0.940130 + 0.340817i \(0.110704\pi\)
\(878\) −2.43200 + 4.21235i −0.0820760 + 0.142160i
\(879\) 0 0
\(880\) 0.839883 + 1.45472i 0.0283125 + 0.0490386i
\(881\) 9.34806 0.314944 0.157472 0.987523i \(-0.449666\pi\)
0.157472 + 0.987523i \(0.449666\pi\)
\(882\) 0 0
\(883\) 2.29494 0.0772308 0.0386154 0.999254i \(-0.487705\pi\)
0.0386154 + 0.999254i \(0.487705\pi\)
\(884\) −2.72665 4.72270i −0.0917073 0.158842i
\(885\) 0 0
\(886\) 5.76975 9.99350i 0.193838 0.335738i
\(887\) 13.8363 23.9651i 0.464577 0.804671i −0.534605 0.845102i \(-0.679540\pi\)
0.999182 + 0.0404309i \(0.0128731\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 1.25564 0.0420891
\(891\) 0 0
\(892\) −0.891832 −0.0298607
\(893\) 4.71780 + 8.17147i 0.157875 + 0.273448i
\(894\) 0 0
\(895\) −2.10963 + 3.65399i −0.0705172 + 0.122139i
\(896\) 0 0
\(897\) 0 0
\(898\) 13.2125 + 22.8848i 0.440908 + 0.763676i
\(899\) −4.61849 −0.154035
\(900\) 0 0
\(901\) 46.4327 1.54690
\(902\) 1.72519 + 2.98812i 0.0574426 + 0.0994935i
\(903\) 0 0
\(904\) 3.03064 5.24922i 0.100798 0.174587i
\(905\) −5.16419 + 8.94465i −0.171664 + 0.297330i
\(906\) 0 0
\(907\) 1.46576 + 2.53877i 0.0486698 + 0.0842985i 0.889334 0.457258i \(-0.151168\pi\)
−0.840664 + 0.541557i \(0.817835\pi\)
\(908\) −14.6519 −0.486242
\(909\) 0 0
\(910\) 0 0
\(911\) −15.3171 26.5300i −0.507479 0.878979i −0.999963 0.00865719i \(-0.997244\pi\)
0.492484 0.870322i \(-0.336089\pi\)
\(912\) 0 0
\(913\) 12.1242 20.9998i 0.401253 0.694991i
\(914\) −1.86906 + 3.23731i −0.0618231 + 0.107081i
\(915\) 0 0
\(916\) −4.78794 8.29295i −0.158198 0.274007i
\(917\) 0 0
\(918\) 0 0
\(919\) −26.3714 −0.869912 −0.434956 0.900452i \(-0.643236\pi\)
−0.434956 + 0.900452i \(0.643236\pi\)
\(920\) 0.260893 + 0.451880i 0.00860139 + 0.0148980i
\(921\) 0 0
\(922\) 7.90496 13.6918i 0.260336 0.450915i
\(923\) 1.22665 2.12463i 0.0403758 0.0699329i
\(924\) 0 0
\(925\) 21.8047 + 37.7668i 0.716933 + 1.24176i
\(926\) 38.3930 1.26167
\(927\) 0 0
\(928\) 8.97509 0.294622
\(929\) −8.93706 15.4794i −0.293215 0.507864i 0.681353 0.731955i \(-0.261392\pi\)
−0.974568 + 0.224091i \(0.928059\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −7.21420 + 12.4954i −0.236309 + 0.409299i
\(933\) 0 0
\(934\) −3.15652 5.46725i −0.103284 0.178894i
\(935\) −6.27200 −0.205116
\(936\) 0 0
\(937\) −15.9134 −0.519869 −0.259934 0.965626i \(-0.583701\pi\)
−0.259934 + 0.965626i \(0.583701\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0.535897 0.928200i 0.0174790 0.0302745i
\(941\) 8.14027 14.0994i 0.265365 0.459626i −0.702294 0.711887i \(-0.747841\pi\)
0.967659 + 0.252261i \(0.0811741\pi\)
\(942\) 0 0
\(943\) 0.535897 + 0.928200i 0.0174512 + 0.0302264i
\(944\) −12.8961 −0.419732
\(945\) 0 0
\(946\) 34.0233 1.10619
\(947\) −14.2951 24.7599i −0.464529 0.804589i 0.534651 0.845073i \(-0.320443\pi\)
−0.999180 + 0.0404846i \(0.987110\pi\)
\(948\) 0 0
\(949\) 9.66945 16.7480i 0.313884 0.543662i
\(950\) 9.70535 16.8102i 0.314883 0.545393i
\(951\) 0 0
\(952\) 0 0
\(953\) 29.3537 0.950859 0.475430 0.879754i \(-0.342293\pi\)
0.475430 + 0.879754i \(0.342293\pi\)
\(954\) 0 0
\(955\) 1.14651 0.0371002
\(956\) 9.15486 + 15.8567i 0.296089 + 0.512842i
\(957\) 0 0
\(958\) −10.2068 + 17.6787i −0.329767 + 0.571173i
\(959\) 0 0
\(960\) 0 0
\(961\) 15.3676 + 26.6175i 0.495729 + 0.858628i
\(962\) −13.3025 −0.428891
\(963\) 0 0
\(964\) −0.0933847 −0.00300772
\(965\) 1.03376 + 1.79053i 0.0332779 + 0.0576391i
\(966\) 0 0
\(967\) −4.69815 + 8.13743i −0.151082 + 0.261682i −0.931626 0.363419i \(-0.881609\pi\)
0.780543 + 0.625102i \(0.214943\pi\)
\(968\) 1.15272 1.99658i 0.0370500 0.0641724i
\(969\) 0 0
\(970\) 2.57587 + 4.46154i 0.0827062 + 0.143251i
\(971\) −15.5467 −0.498917 −0.249459 0.968385i \(-0.580253\pi\)
−0.249459 + 0.968385i \(0.580253\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −6.18190 10.7074i −0.198081 0.343086i
\(975\) 0 0
\(976\) 6.04163 10.4644i 0.193388 0.334958i
\(977\) −4.79893 + 8.31198i −0.153531 + 0.265924i −0.932523 0.361110i \(-0.882398\pi\)
0.778992 + 0.627034i \(0.215731\pi\)
\(978\) 0 0
\(979\) −4.97296 8.61342i −0.158936 0.275286i
\(980\) 0 0
\(981\) 0 0
\(982\) −0.414007 −0.0132115
\(983\) 23.4267 + 40.5763i 0.747197 + 1.29418i 0.949161 + 0.314790i \(0.101934\pi\)
−0.201964 + 0.979393i \(0.564732\pi\)
\(984\) 0 0
\(985\) −2.93200 + 5.07837i −0.0934213 + 0.161810i
\(986\) −16.7558 + 29.0220i −0.533614 + 0.924247i
\(987\) 0 0
\(988\) 2.96050 + 5.12774i 0.0941862 + 0.163135i
\(989\) 10.5687 0.336064
\(990\) 0 0
\(991\) −21.6519 −0.687796 −0.343898 0.939007i \(-0.611748\pi\)
−0.343898 + 0.939007i \(0.611748\pi\)
\(992\) 0.257295 + 0.445647i 0.00816911 + 0.0141493i
\(993\) 0 0
\(994\) 0 0
\(995\) −0.678304 + 1.17486i −0.0215037 + 0.0372455i
\(996\) 0 0
\(997\) −28.6190 49.5695i −0.906372 1.56988i −0.819065 0.573700i \(-0.805507\pi\)
−0.0873064 0.996182i \(-0.527826\pi\)
\(998\) 0.923935 0.0292466
\(999\) 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.f.n.1765.3 6
3.2 odd 2 882.2.f.m.589.2 6
7.2 even 3 2646.2.h.p.361.1 6
7.3 odd 6 378.2.e.c.37.1 6
7.4 even 3 2646.2.e.o.1549.3 6
7.5 odd 6 378.2.h.d.361.3 6
7.6 odd 2 2646.2.f.o.1765.1 6
9.2 odd 6 882.2.f.m.295.2 6
9.4 even 3 7938.2.a.bx.1.1 3
9.5 odd 6 7938.2.a.by.1.3 3
9.7 even 3 inner 2646.2.f.n.883.3 6
21.2 odd 6 882.2.h.o.67.1 6
21.5 even 6 126.2.h.c.67.3 yes 6
21.11 odd 6 882.2.e.p.373.2 6
21.17 even 6 126.2.e.d.121.2 yes 6
21.20 even 2 882.2.f.l.589.2 6
28.3 even 6 3024.2.q.h.2305.1 6
28.19 even 6 3024.2.t.g.1873.3 6
63.2 odd 6 882.2.e.p.655.2 6
63.5 even 6 1134.2.g.k.487.3 6
63.11 odd 6 882.2.h.o.79.1 6
63.13 odd 6 7938.2.a.bu.1.3 3
63.16 even 3 2646.2.e.o.2125.3 6
63.20 even 6 882.2.f.l.295.2 6
63.25 even 3 2646.2.h.p.667.1 6
63.31 odd 6 1134.2.g.n.163.1 6
63.34 odd 6 2646.2.f.o.883.1 6
63.38 even 6 126.2.h.c.79.3 yes 6
63.40 odd 6 1134.2.g.n.487.1 6
63.41 even 6 7938.2.a.cb.1.1 3
63.47 even 6 126.2.e.d.25.2 6
63.52 odd 6 378.2.h.d.289.3 6
63.59 even 6 1134.2.g.k.163.3 6
63.61 odd 6 378.2.e.c.235.1 6
84.47 odd 6 1008.2.t.g.193.1 6
84.59 odd 6 1008.2.q.h.625.2 6
252.47 odd 6 1008.2.q.h.529.2 6
252.115 even 6 3024.2.t.g.289.3 6
252.187 even 6 3024.2.q.h.2881.1 6
252.227 odd 6 1008.2.t.g.961.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.e.d.25.2 6 63.47 even 6
126.2.e.d.121.2 yes 6 21.17 even 6
126.2.h.c.67.3 yes 6 21.5 even 6
126.2.h.c.79.3 yes 6 63.38 even 6
378.2.e.c.37.1 6 7.3 odd 6
378.2.e.c.235.1 6 63.61 odd 6
378.2.h.d.289.3 6 63.52 odd 6
378.2.h.d.361.3 6 7.5 odd 6
882.2.e.p.373.2 6 21.11 odd 6
882.2.e.p.655.2 6 63.2 odd 6
882.2.f.l.295.2 6 63.20 even 6
882.2.f.l.589.2 6 21.20 even 2
882.2.f.m.295.2 6 9.2 odd 6
882.2.f.m.589.2 6 3.2 odd 2
882.2.h.o.67.1 6 21.2 odd 6
882.2.h.o.79.1 6 63.11 odd 6
1008.2.q.h.529.2 6 252.47 odd 6
1008.2.q.h.625.2 6 84.59 odd 6
1008.2.t.g.193.1 6 84.47 odd 6
1008.2.t.g.961.1 6 252.227 odd 6
1134.2.g.k.163.3 6 63.59 even 6
1134.2.g.k.487.3 6 63.5 even 6
1134.2.g.n.163.1 6 63.31 odd 6
1134.2.g.n.487.1 6 63.40 odd 6
2646.2.e.o.1549.3 6 7.4 even 3
2646.2.e.o.2125.3 6 63.16 even 3
2646.2.f.n.883.3 6 9.7 even 3 inner
2646.2.f.n.1765.3 6 1.1 even 1 trivial
2646.2.f.o.883.1 6 63.34 odd 6
2646.2.f.o.1765.1 6 7.6 odd 2
2646.2.h.p.361.1 6 7.2 even 3
2646.2.h.p.667.1 6 63.25 even 3
3024.2.q.h.2305.1 6 28.3 even 6
3024.2.q.h.2881.1 6 252.187 even 6
3024.2.t.g.289.3 6 252.115 even 6
3024.2.t.g.1873.3 6 28.19 even 6
7938.2.a.bu.1.3 3 63.13 odd 6
7938.2.a.bx.1.1 3 9.4 even 3
7938.2.a.by.1.3 3 9.5 odd 6
7938.2.a.cb.1.1 3 63.41 even 6