Properties

Label 2646.2.f.n.883.3
Level $2646$
Weight $2$
Character 2646.883
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 883.3
Root \(0.500000 + 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 2646.883
Dual form 2646.2.f.n.1765.3

$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0.912908 0.408166i \(-0.133831\pi\)
−0.809936 + 0.586519i \(0.800498\pi\)
\(6\) 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 0.448374 + 0.893846i \(0.352003\pi\)
−0.998280 + 0.0586193i \(0.981330\pi\)
\(12\) 0 0
\(13\) −0.730252 1.26483i −0.202536 0.350802i 0.746809 0.665038i \(-0.231585\pi\)
−0.949345 + 0.314236i \(0.898252\pi\)
\(14\) 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 0.919027 0.394194i \(-0.128976\pi\)
−0.800896 + 0.598804i \(0.795643\pi\)
\(24\) 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 −0.0620772 0.998071i \(-0.519772\pi\)
0.895394 0.445275i \(-0.146894\pi\)
\(30\) 0 0
\(31\) −0.257295 0.445647i −0.0462115 0.0800406i 0.841994 0.539486i \(-0.181381\pi\)
−0.888206 + 0.459446i \(0.848048\pi\)
\(32\) 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 0.826728 0.562602i \(-0.190200\pi\)
−0.900592 + 0.434666i \(0.856866\pi\)
\(42\) 0 0
\(43\) 4.66372 8.07779i 0.711210 1.23185i −0.253193 0.967416i \(-0.581481\pi\)
0.964403 0.264436i \(-0.0851858\pi\)
\(44\) 3.64766 0.549906
\(45\) 0 0
\(46\) 1.13307 0.167063
\(47\) −1.16372 + 2.01561i −0.169745 + 0.294007i −0.938330 0.345740i \(-0.887628\pi\)
0.768585 + 0.639748i \(0.220961\pi\)
\(48\) 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 0.890343 + 0.455291i \(0.150465\pi\)
−0.0508779 + 0.998705i \(0.516202\pi\)
\(60\) 0 0
\(61\) 6.04163 10.4644i 0.773552 1.33983i −0.162053 0.986782i \(-0.551812\pi\)
0.935605 0.353049i \(-0.114855\pi\)
\(62\) −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 0.928148 0.372210i \(-0.121400\pi\)
−0.786418 + 0.617695i \(0.788067\pi\)
\(68\) −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 −0.690121 0.723694i \(-0.742443\pi\)
0.971798 + 0.235815i \(0.0757761\pi\)
\(80\) −0.460505 −0.0514860
\(81\) 0 0
\(82\) −0.945916 −0.104459
\(83\) 3.32383 5.75705i 0.364838 0.631918i −0.623912 0.781494i \(-0.714458\pi\)
0.988750 + 0.149577i \(0.0477911\pi\)
\(84\) 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 −0.428827 0.903386i \(-0.641073\pi\)
0.996769 0.0803178i \(-0.0255935\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −4.78794 −0.478794
\(101\) −6.87792 + 11.9129i −0.684378 + 1.18538i 0.289254 + 0.957253i \(0.406593\pi\)
−0.973632 + 0.228125i \(0.926740\pi\)
\(102\) 0 0
\(103\) 5.58113 + 9.66679i 0.549925 + 0.952498i 0.998279 + 0.0586417i \(0.0186769\pi\)
−0.448354 + 0.893856i \(0.647990\pi\)
\(104\) 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 0.687534 0.726152i \(-0.258693\pi\)
−0.972633 + 0.232346i \(0.925360\pi\)
\(114\) 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 −0.794131 0.607746i \(-0.792074\pi\)
−0.129258 0.991611i \(-0.541260\pi\)
\(132\) 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 −0.944661 0.328048i \(-0.893609\pi\)
0.756428 + 0.654077i \(0.226943\pi\)
\(138\) 0 0
\(139\) 1.01245 + 1.75362i 0.0858751 + 0.148740i 0.905764 0.423783i \(-0.139298\pi\)
−0.819889 + 0.572523i \(0.805965\pi\)
\(140\) 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 0.615071 0.788471i \(-0.289127\pi\)
−0.990372 + 0.138432i \(0.955794\pi\)
\(150\) 0 0
\(151\) 0.0519482 0.0899768i 0.00422748 0.00732221i −0.863904 0.503657i \(-0.831988\pi\)
0.868131 + 0.496334i \(0.165321\pi\)
\(152\) 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 0.892157 + 0.451726i \(0.149192\pi\)
−0.0548721 + 0.998493i \(0.517475\pi\)
\(158\) −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 0.583745 0.811937i \(-0.301587\pi\)
−0.995031 + 0.0995698i \(0.968253\pi\)
\(168\) 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 −0.916461 0.400124i \(-0.868967\pi\)
0.804748 + 0.593617i \(0.202301\pi\)
\(174\) 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 −0.817468 0.575974i \(-0.804623\pi\)
0.907542 + 0.419962i \(0.137956\pi\)
\(192\) 0 0
\(193\) −2.24484 3.88818i −0.161587 0.279877i 0.773851 0.633368i \(-0.218328\pi\)
−0.935438 + 0.353491i \(0.884995\pi\)
\(194\) −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 0.844332 0.535820i \(-0.179998\pi\)
−0.886200 + 0.463303i \(0.846664\pi\)
\(212\) −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 −0.850709 0.525637i \(-0.823827\pi\)
0.880570 + 0.473917i \(0.157160\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −6.06128 −0.403190
\(227\) 7.32597 12.6889i 0.486242 0.842195i −0.513633 0.858010i \(-0.671701\pi\)
0.999875 + 0.0158147i \(0.00503418\pi\)
\(228\) 0 0
\(229\) −4.78794 8.29295i −0.316396 0.548013i 0.663338 0.748320i \(-0.269139\pi\)
−0.979733 + 0.200307i \(0.935806\pi\)
\(230\) 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 0.993938 + 0.109938i \(0.0350654\pi\)
−0.401760 + 0.915745i \(0.631601\pi\)
\(240\) 0 0
\(241\) 0.0466924 0.0808735i 0.00300772 0.00520952i −0.864518 0.502602i \(-0.832376\pi\)
0.867525 + 0.497393i \(0.165709\pi\)
\(242\) −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 0.981498 + 0.191471i \(0.0613257\pi\)
−0.324931 + 0.945738i \(0.605341\pi\)
\(258\) 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 −0.934598 0.355705i \(-0.884241\pi\)
0.775349 + 0.631533i \(0.217574\pi\)
\(264\) 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 −0.912339 0.409436i \(-0.865726\pi\)
0.810751 + 0.585391i \(0.199059\pi\)
\(278\) 2.02491 0.121446
\(279\) 0 0
\(280\) 0 0
\(281\) 10.1388 17.5609i 0.604831 1.04760i −0.387248 0.921976i \(-0.626574\pi\)
0.992078 0.125622i \(-0.0400925\pi\)
\(282\) 0 0
\(283\) 8.67471 + 15.0250i 0.515658 + 0.893145i 0.999835 + 0.0181754i \(0.00578571\pi\)
−0.484177 + 0.874970i \(0.660881\pi\)
\(284\) 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 0.685073 0.728474i \(-0.259770\pi\)
−0.973414 + 0.229054i \(0.926437\pi\)
\(294\) 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 0.560521 0.828140i \(-0.310601\pi\)
−0.997451 + 0.0713552i \(0.977268\pi\)
\(312\) 0 0
\(313\) 4.24844 7.35851i 0.240136 0.415928i −0.720617 0.693334i \(-0.756141\pi\)
0.960753 + 0.277406i \(0.0894746\pi\)
\(314\) 20.9823 1.18410
\(315\) 0 0
\(316\) −5.00720 −0.281677
\(317\) −7.05262 + 12.2155i −0.396115 + 0.686091i −0.993243 0.116055i \(-0.962975\pi\)
0.597128 + 0.802146i \(0.296308\pi\)
\(318\) 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 0.187417 + 0.982280i \(0.439988\pi\)
−0.944388 + 0.328832i \(0.893345\pi\)
\(332\) −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 0.885690 0.464276i \(-0.153686\pi\)
−0.844920 + 0.534892i \(0.820352\pi\)
\(338\) −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 0.509066 0.860728i \(-0.329991\pi\)
−0.999945 + 0.0105001i \(0.996658\pi\)
\(348\) 0 0
\(349\) 3.90136 6.75735i 0.208835 0.361713i −0.742513 0.669832i \(-0.766366\pi\)
0.951348 + 0.308119i \(0.0996995\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −3.64766 −0.194421
\(353\) −13.4626 + 23.3180i −0.716544 + 1.24109i 0.245817 + 0.969316i \(0.420944\pi\)
−0.962361 + 0.271774i \(0.912390\pi\)
\(354\) 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 −0.176731 0.984259i \(-0.556552\pi\)
0.940759 0.339076i \(-0.110114\pi\)
\(368\) −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 0.536708 0.843768i \(-0.319668\pi\)
−0.999079 + 0.0429184i \(0.986334\pi\)
\(374\) 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 0.988170 0.153365i \(-0.0490109\pi\)
−0.626903 + 0.779098i \(0.715678\pi\)
\(384\) 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 0.408330 + 0.912834i \(0.366111\pi\)
−0.994703 + 0.102793i \(0.967222\pi\)
\(390\) 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 0.881409 + 0.472353i \(0.156595\pi\)
−0.0316345 + 0.999500i \(0.510071\pi\)
\(402\) 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 0.819658 0.572854i \(-0.194164\pi\)
−0.905935 + 0.423418i \(0.860830\pi\)
\(410\) −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 0.965647 + 0.259858i \(0.0836759\pi\)
−0.257779 + 0.966204i \(0.582991\pi\)
\(420\) 0 0
\(421\) −1.06128 + 1.83819i −0.0517237 + 0.0895881i −0.890728 0.454537i \(-0.849805\pi\)
0.839004 + 0.544125i \(0.183138\pi\)
\(422\) −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 −0.802135 0.597143i \(-0.796303\pi\)
0.918208 + 0.396098i \(0.129636\pi\)
\(440\) 1.67977 0.0800797
\(441\) 0 0
\(442\) −5.45331 −0.259387
\(443\) −5.76975 + 9.99350i −0.274129 + 0.474805i −0.969915 0.243444i \(-0.921723\pi\)
0.695786 + 0.718249i \(0.255056\pi\)
\(444\) 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 −0.818994 0.573803i \(-0.805468\pi\)
0.906425 + 0.422368i \(0.138801\pi\)
\(458\) −9.57587 −0.447451
\(459\) 0 0
\(460\) 0.521786 0.0243284
\(461\) −7.90496 + 13.6918i −0.368171 + 0.637690i −0.989280 0.146034i \(-0.953349\pi\)
0.621109 + 0.783724i \(0.286682\pi\)
\(462\) 0 0
\(463\) 19.1965 + 33.2493i 0.892137 + 1.54523i 0.837309 + 0.546730i \(0.184128\pi\)
0.0548278 + 0.998496i \(0.482539\pi\)
\(464\) 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 −0.532901 0.846178i \(-0.678898\pi\)
0.999262 + 0.0384168i \(0.0122314\pi\)
\(480\) 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 0.861317 0.508069i \(-0.169640\pi\)
−0.870659 + 0.491888i \(0.836307\pi\)
\(492\) 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 0.876180 0.481983i \(-0.160083\pi\)
−0.855500 + 0.517803i \(0.826750\pi\)
\(500\) −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 0.975307 + 0.220855i \(0.0708846\pi\)
−0.296388 + 0.955068i \(0.595782\pi\)
\(510\) 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 0.492860 + 0.870108i \(0.335951\pi\)
−0.999966 + 0.00822465i \(0.997382\pi\)
\(548\) 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 0.714127 0.700016i \(-0.246824\pi\)
−0.963295 + 0.268445i \(0.913490\pi\)
\(564\) 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 −0.677925 0.735131i \(-0.737120\pi\)
0.975605 + 0.219534i \(0.0704538\pi\)
\(570\) 0 0
\(571\) −5.97869 10.3554i −0.250200 0.433360i 0.713380 0.700777i \(-0.247163\pi\)
−0.963581 + 0.267417i \(0.913830\pi\)
\(572\) −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 −0.0359730 0.999353i \(-0.511453\pi\)
0.883451 0.468523i \(-0.155214\pi\)
\(588\) 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 0.992399 0.123060i \(-0.0392709\pi\)
−0.602773 + 0.797913i \(0.705938\pi\)
\(600\) 0 0
\(601\) −4.27188 + 7.39912i −0.174254 + 0.301816i −0.939903 0.341442i \(-0.889085\pi\)
0.765649 + 0.643259i \(0.222418\pi\)
\(602\) 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 0.936785 + 0.349905i \(0.113786\pi\)
−0.165366 + 0.986232i \(0.552881\pi\)
\(608\) −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 0.994685 0.102964i \(-0.0328327\pi\)
−0.586512 + 0.809941i \(0.699499\pi\)
\(618\) 0 0
\(619\) 1.03064 1.78512i 0.0414249 0.0717501i −0.844570 0.535446i \(-0.820144\pi\)
0.885994 + 0.463696i \(0.153477\pi\)
\(620\) −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 −0.564001 0.825774i \(-0.690739\pi\)
0.997142 + 0.0755526i \(0.0240721\pi\)
\(642\) 0 0
\(643\) 14.1819 + 24.5638i 0.559280 + 0.968701i 0.997557 + 0.0698609i \(0.0222555\pi\)
−0.438277 + 0.898840i \(0.644411\pi\)
\(644\) 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 0.833035 0.553221i \(-0.186601\pi\)
−0.895621 + 0.444819i \(0.853268\pi\)
\(654\) 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 −0.950648 0.310271i \(-0.899580\pi\)
0.744027 + 0.668150i \(0.232914\pi\)
\(660\) 0 0
\(661\) 5.06507 + 8.77297i 0.197009 + 0.341229i 0.947557 0.319586i \(-0.103544\pi\)
−0.750549 + 0.660815i \(0.770211\pi\)
\(662\) 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 −0.833365 0.552724i \(-0.813589\pi\)
0.895355 + 0.445353i \(0.146922\pi\)
\(674\) 1.49688 0.0576577
\(675\) 0 0
\(676\) −10.8669 −0.417959
\(677\) 14.6819 25.4298i 0.564271 0.977347i −0.432846 0.901468i \(-0.642491\pi\)
0.997117 0.0758786i \(-0.0241762\pi\)
\(678\) 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 −0.974338 0.225092i \(-0.927732\pi\)
0.682104 + 0.731255i \(0.261065\pi\)
\(692\) 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 −0.855261 0.518197i \(-0.826603\pi\)
0.876403 + 0.481579i \(0.159937\pi\)
\(710\) −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 −0.447553 0.894257i \(-0.647705\pi\)
0.998226 0.0595359i \(-0.0189621\pi\)
\(728\) 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 0.987135 0.159891i \(-0.0511143\pi\)
−0.632037 + 0.774938i \(0.717781\pi\)
\(734\) −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 0.997368 0.0725076i \(-0.0231002\pi\)
−0.561477 + 0.827492i \(0.689767\pi\)
\(744\) 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 0.727006 0.686631i \(-0.240911\pi\)
−0.958143 + 0.286291i \(0.907578\pi\)
\(752\) −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 −0.999416 0.0341724i \(-0.989120\pi\)
0.470114 0.882606i \(-0.344213\pi\)
\(762\) 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 0.544730 0.838611i \(-0.316632\pi\)
−0.998624 + 0.0524443i \(0.983299\pi\)
\(770\) 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 0.701448 0.712721i \(-0.252537\pi\)
−0.967958 + 0.251111i \(0.919204\pi\)
\(788\) 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 0.773825 0.633400i \(-0.218341\pi\)
−0.935453 + 0.353452i \(0.885008\pi\)
\(798\) 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 −0.613352 0.789810i \(-0.710179\pi\)
0.990671 + 0.136273i \(0.0435125\pi\)
\(822\) 0 0
\(823\) 0.753501 + 1.30510i 0.0262654 + 0.0454930i 0.878859 0.477081i \(-0.158305\pi\)
−0.852594 + 0.522574i \(0.824972\pi\)
\(824\) −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 −0.883825 0.467818i \(-0.845040\pi\)
0.847055 + 0.531506i \(0.178374\pi\)
\(840\) 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 −0.799835 0.600220i \(-0.795080\pi\)
0.919723 + 0.392568i \(0.128413\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 7.78074 0.265940
\(857\) −5.46410 + 9.46410i −0.186650 + 0.323288i −0.944131 0.329569i \(-0.893096\pi\)
0.757481 + 0.652857i \(0.226430\pi\)
\(858\) 0 0
\(859\) −6.95379 12.0443i −0.237260 0.410947i 0.722667 0.691196i \(-0.242916\pi\)
−0.959927 + 0.280250i \(0.909583\pi\)
\(860\) −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 0.940130 0.340817i \(-0.110704\pi\)
−0.765221 + 0.643767i \(0.777370\pi\)
\(878\) −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 0.999182 0.0404309i \(-0.0128731\pi\)
−0.534605 + 0.845102i \(0.679540\pi\)
\(888\) 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 −0.840664 0.541557i \(-0.817835\pi\)
0.889334 + 0.457258i \(0.151168\pi\)
\(908\) −14.6519 −0.486242
\(909\) 0 0
\(910\) 0 0
\(911\) −15.3171 + 26.5300i −0.507479 + 0.878979i 0.492484 + 0.870322i \(0.336089\pi\)
−0.999963 + 0.00865719i \(0.997244\pi\)
\(912\) 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 −0.974568 0.224091i \(-0.928059\pi\)
0.681353 + 0.731955i \(0.261392\pi\)
\(930\) 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 0.967659 0.252261i \(-0.0811741\pi\)
−0.702294 + 0.711887i \(0.747841\pi\)
\(942\) 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 −0.999180 0.0404846i \(-0.987110\pi\)
0.534651 + 0.845073i \(0.320443\pi\)
\(948\) 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 0.780543 0.625102i \(-0.214943\pi\)
−0.931626 + 0.363419i \(0.881609\pi\)
\(968\) 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 0.778992 0.627034i \(-0.215731\pi\)
−0.932523 + 0.361110i \(0.882398\pi\)
\(978\) 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 −0.201964 0.979393i \(-0.564732\pi\)
0.949161 0.314790i \(-0.101934\pi\)
\(984\) 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 −0.0873064 + 0.996182i \(0.527826\pi\)
−0.819065 + 0.573700i \(0.805507\pi\)
\(998\) 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.883.3 6
3.2 odd 2 882.2.f.m.295.2 6
7.2 even 3 2646.2.e.o.2125.3 6
7.3 odd 6 378.2.h.d.289.3 6
7.4 even 3 2646.2.h.p.667.1 6
7.5 odd 6 378.2.e.c.235.1 6
7.6 odd 2 2646.2.f.o.883.1 6
9.2 odd 6 7938.2.a.by.1.3 3
9.4 even 3 inner 2646.2.f.n.1765.3 6
9.5 odd 6 882.2.f.m.589.2 6
9.7 even 3 7938.2.a.bx.1.1 3
21.2 odd 6 882.2.e.p.655.2 6
21.5 even 6 126.2.e.d.25.2 6
21.11 odd 6 882.2.h.o.79.1 6
21.17 even 6 126.2.h.c.79.3 yes 6
21.20 even 2 882.2.f.l.295.2 6
28.3 even 6 3024.2.t.g.289.3 6
28.19 even 6 3024.2.q.h.2881.1 6
63.4 even 3 2646.2.e.o.1549.3 6
63.5 even 6 126.2.h.c.67.3 yes 6
63.13 odd 6 2646.2.f.o.1765.1 6
63.20 even 6 7938.2.a.cb.1.1 3
63.23 odd 6 882.2.h.o.67.1 6
63.31 odd 6 378.2.e.c.37.1 6
63.32 odd 6 882.2.e.p.373.2 6
63.34 odd 6 7938.2.a.bu.1.3 3
63.38 even 6 1134.2.g.k.163.3 6
63.40 odd 6 378.2.h.d.361.3 6
63.41 even 6 882.2.f.l.589.2 6
63.47 even 6 1134.2.g.k.487.3 6
63.52 odd 6 1134.2.g.n.163.1 6
63.58 even 3 2646.2.h.p.361.1 6
63.59 even 6 126.2.e.d.121.2 yes 6
63.61 odd 6 1134.2.g.n.487.1 6
84.47 odd 6 1008.2.q.h.529.2 6
84.59 odd 6 1008.2.t.g.961.1 6
252.31 even 6 3024.2.q.h.2305.1 6
252.59 odd 6 1008.2.q.h.625.2 6
252.103 even 6 3024.2.t.g.1873.3 6
252.131 odd 6 1008.2.t.g.193.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.e.d.25.2 6 21.5 even 6
126.2.e.d.121.2 yes 6 63.59 even 6
126.2.h.c.67.3 yes 6 63.5 even 6
126.2.h.c.79.3 yes 6 21.17 even 6
378.2.e.c.37.1 6 63.31 odd 6
378.2.e.c.235.1 6 7.5 odd 6
378.2.h.d.289.3 6 7.3 odd 6
378.2.h.d.361.3 6 63.40 odd 6
882.2.e.p.373.2 6 63.32 odd 6
882.2.e.p.655.2 6 21.2 odd 6
882.2.f.l.295.2 6 21.20 even 2
882.2.f.l.589.2 6 63.41 even 6
882.2.f.m.295.2 6 3.2 odd 2
882.2.f.m.589.2 6 9.5 odd 6
882.2.h.o.67.1 6 63.23 odd 6
882.2.h.o.79.1 6 21.11 odd 6
1008.2.q.h.529.2 6 84.47 odd 6
1008.2.q.h.625.2 6 252.59 odd 6
1008.2.t.g.193.1 6 252.131 odd 6
1008.2.t.g.961.1 6 84.59 odd 6
1134.2.g.k.163.3 6 63.38 even 6
1134.2.g.k.487.3 6 63.47 even 6
1134.2.g.n.163.1 6 63.52 odd 6
1134.2.g.n.487.1 6 63.61 odd 6
2646.2.e.o.1549.3 6 63.4 even 3
2646.2.e.o.2125.3 6 7.2 even 3
2646.2.f.n.883.3 6 1.1 even 1 trivial
2646.2.f.n.1765.3 6 9.4 even 3 inner
2646.2.f.o.883.1 6 7.6 odd 2
2646.2.f.o.1765.1 6 63.13 odd 6
2646.2.h.p.361.1 6 63.58 even 3
2646.2.h.p.667.1 6 7.4 even 3
3024.2.q.h.2305.1 6 252.31 even 6
3024.2.q.h.2881.1 6 28.19 even 6
3024.2.t.g.289.3 6 28.3 even 6
3024.2.t.g.1873.3 6 252.103 even 6
7938.2.a.bu.1.3 3 63.34 odd 6
7938.2.a.bx.1.1 3 9.7 even 3
7938.2.a.by.1.3 3 9.2 odd 6
7938.2.a.cb.1.1 3 63.20 even 6