Properties

Label 252.2.bm.a.173.7
Level $252$
Weight $2$
Character 252.173
Analytic conductor $2.012$
Analytic rank $0$
Dimension $16$
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] = [252,2,Mod(173,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.173");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.bm (of order \(6\), degree \(2\), 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: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 173.7
Root \(-0.268067 + 1.71118i\) of defining polynomial
Character \(\chi\) \(=\) 252.173
Dual form 252.2.bm.a.185.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.42826 + 0.979841i) q^{3} -1.68574 q^{5} +(-0.0236360 + 2.64565i) q^{7} +(1.07983 + 2.79892i) q^{9} +O(q^{10})\) \(q+(1.42826 + 0.979841i) q^{3} -1.68574 q^{5} +(-0.0236360 + 2.64565i) q^{7} +(1.07983 + 2.79892i) q^{9} +3.90538i q^{11} +(5.24391 - 3.02757i) q^{13} +(-2.40766 - 1.65175i) q^{15} +(0.201244 + 0.348565i) q^{17} +(-0.145617 - 0.0840718i) q^{19} +(-2.62607 + 3.75550i) q^{21} -8.88395i q^{23} -2.15829 q^{25} +(-1.20023 + 5.05563i) q^{27} +(-6.15380 - 3.55290i) q^{29} +(5.44527 + 3.14383i) q^{31} +(-3.82665 + 5.57788i) q^{33} +(0.0398441 - 4.45986i) q^{35} +(3.13257 - 5.42578i) q^{37} +(10.4562 + 0.814049i) q^{39} +(-1.64707 - 2.85281i) q^{41} +(1.80474 - 3.12590i) q^{43} +(-1.82030 - 4.71825i) q^{45} +(4.38482 + 7.59474i) q^{47} +(-6.99888 - 0.125065i) q^{49} +(-0.0541101 + 0.695026i) q^{51} +(-4.94628 + 2.85574i) q^{53} -6.58345i q^{55} +(-0.125601 - 0.262757i) q^{57} +(2.25163 - 3.89994i) q^{59} +(4.43678 - 2.56157i) q^{61} +(-7.43049 + 2.79068i) q^{63} +(-8.83986 + 5.10369i) q^{65} +(2.95521 - 5.11857i) q^{67} +(8.70486 - 12.6886i) q^{69} -11.4308i q^{71} +(-6.05559 + 3.49620i) q^{73} +(-3.08259 - 2.11478i) q^{75} +(-10.3323 - 0.0923076i) q^{77} +(-0.603968 - 1.04610i) q^{79} +(-6.66796 + 6.04470i) q^{81} +(-0.181350 + 0.314108i) q^{83} +(-0.339244 - 0.587588i) q^{85} +(-5.30793 - 11.1042i) q^{87} +(1.38526 - 2.39934i) q^{89} +(7.88594 + 13.9451i) q^{91} +(4.69679 + 9.82569i) q^{93} +(0.245471 + 0.141723i) q^{95} +(0.508914 + 0.293821i) q^{97} +(-10.9309 + 4.21713i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - q^{7} + 3 q^{13} - 3 q^{15} - 9 q^{17} + 16 q^{25} - 9 q^{27} + 6 q^{29} + 6 q^{31} - 27 q^{33} + 15 q^{35} + q^{37} - 3 q^{39} + 6 q^{41} - 2 q^{43} - 15 q^{45} - 18 q^{47} + 13 q^{49} + 15 q^{51} + 15 q^{57} - 15 q^{59} + 3 q^{61} - 9 q^{63} - 39 q^{65} - 7 q^{67} - 21 q^{69} - 15 q^{75} - 45 q^{77} - q^{79} + 6 q^{85} - 3 q^{87} - 21 q^{89} + 9 q^{91} - 69 q^{93} + 6 q^{95} + 3 q^{97} - 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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



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 0
\(3\) 1.42826 + 0.979841i 0.824603 + 0.565711i
\(4\) 0 0
\(5\) −1.68574 −0.753885 −0.376942 0.926237i \(-0.623025\pi\)
−0.376942 + 0.926237i \(0.623025\pi\)
\(6\) 0 0
\(7\) −0.0236360 + 2.64565i −0.00893357 + 0.999960i
\(8\) 0 0
\(9\) 1.07983 + 2.79892i 0.359942 + 0.932975i
\(10\) 0 0
\(11\) 3.90538i 1.17752i 0.808309 + 0.588758i \(0.200383\pi\)
−0.808309 + 0.588758i \(0.799617\pi\)
\(12\) 0 0
\(13\) 5.24391 3.02757i 1.45440 0.839698i 0.455673 0.890147i \(-0.349399\pi\)
0.998727 + 0.0504496i \(0.0160654\pi\)
\(14\) 0 0
\(15\) −2.40766 1.65175i −0.621656 0.426481i
\(16\) 0 0
\(17\) 0.201244 + 0.348565i 0.0488088 + 0.0845393i 0.889398 0.457134i \(-0.151124\pi\)
−0.840589 + 0.541674i \(0.817791\pi\)
\(18\) 0 0
\(19\) −0.145617 0.0840718i −0.0334067 0.0192874i 0.483204 0.875508i \(-0.339473\pi\)
−0.516610 + 0.856221i \(0.672806\pi\)
\(20\) 0 0
\(21\) −2.62607 + 3.75550i −0.573055 + 0.819517i
\(22\) 0 0
\(23\) 8.88395i 1.85243i −0.376993 0.926216i \(-0.623042\pi\)
0.376993 0.926216i \(-0.376958\pi\)
\(24\) 0 0
\(25\) −2.15829 −0.431658
\(26\) 0 0
\(27\) −1.20023 + 5.05563i −0.230985 + 0.972957i
\(28\) 0 0
\(29\) −6.15380 3.55290i −1.14273 0.659757i −0.195627 0.980678i \(-0.562674\pi\)
−0.947106 + 0.320921i \(0.896007\pi\)
\(30\) 0 0
\(31\) 5.44527 + 3.14383i 0.978000 + 0.564649i 0.901666 0.432434i \(-0.142345\pi\)
0.0763342 + 0.997082i \(0.475678\pi\)
\(32\) 0 0
\(33\) −3.82665 + 5.57788i −0.666134 + 0.970984i
\(34\) 0 0
\(35\) 0.0398441 4.45986i 0.00673488 0.753855i
\(36\) 0 0
\(37\) 3.13257 5.42578i 0.514992 0.891992i −0.484857 0.874594i \(-0.661128\pi\)
0.999849 0.0173987i \(-0.00553846\pi\)
\(38\) 0 0
\(39\) 10.4562 + 0.814049i 1.67433 + 0.130352i
\(40\) 0 0
\(41\) −1.64707 2.85281i −0.257229 0.445534i 0.708269 0.705942i \(-0.249476\pi\)
−0.965499 + 0.260408i \(0.916143\pi\)
\(42\) 0 0
\(43\) 1.80474 3.12590i 0.275220 0.476695i −0.694971 0.719038i \(-0.744583\pi\)
0.970191 + 0.242343i \(0.0779161\pi\)
\(44\) 0 0
\(45\) −1.82030 4.71825i −0.271355 0.703355i
\(46\) 0 0
\(47\) 4.38482 + 7.59474i 0.639592 + 1.10781i 0.985522 + 0.169546i \(0.0542301\pi\)
−0.345930 + 0.938260i \(0.612437\pi\)
\(48\) 0 0
\(49\) −6.99888 0.125065i −0.999840 0.0178664i
\(50\) 0 0
\(51\) −0.0541101 + 0.695026i −0.00757693 + 0.0973231i
\(52\) 0 0
\(53\) −4.94628 + 2.85574i −0.679424 + 0.392266i −0.799638 0.600482i \(-0.794975\pi\)
0.120214 + 0.992748i \(0.461642\pi\)
\(54\) 0 0
\(55\) 6.58345i 0.887712i
\(56\) 0 0
\(57\) −0.125601 0.262757i −0.0166362 0.0348030i
\(58\) 0 0
\(59\) 2.25163 3.89994i 0.293138 0.507729i −0.681412 0.731900i \(-0.738634\pi\)
0.974550 + 0.224171i \(0.0719673\pi\)
\(60\) 0 0
\(61\) 4.43678 2.56157i 0.568071 0.327976i −0.188308 0.982110i \(-0.560300\pi\)
0.756379 + 0.654134i \(0.226967\pi\)
\(62\) 0 0
\(63\) −7.43049 + 2.79068i −0.936153 + 0.351593i
\(64\) 0 0
\(65\) −8.83986 + 5.10369i −1.09645 + 0.633035i
\(66\) 0 0
\(67\) 2.95521 5.11857i 0.361036 0.625332i −0.627096 0.778942i \(-0.715757\pi\)
0.988132 + 0.153610i \(0.0490899\pi\)
\(68\) 0 0
\(69\) 8.70486 12.6886i 1.04794 1.52752i
\(70\) 0 0
\(71\) 11.4308i 1.35658i −0.734792 0.678292i \(-0.762720\pi\)
0.734792 0.678292i \(-0.237280\pi\)
\(72\) 0 0
\(73\) −6.05559 + 3.49620i −0.708753 + 0.409199i −0.810599 0.585601i \(-0.800858\pi\)
0.101846 + 0.994800i \(0.467525\pi\)
\(74\) 0 0
\(75\) −3.08259 2.11478i −0.355947 0.244194i
\(76\) 0 0
\(77\) −10.3323 0.0923076i −1.17747 0.0105194i
\(78\) 0 0
\(79\) −0.603968 1.04610i −0.0679517 0.117696i 0.830048 0.557692i \(-0.188313\pi\)
−0.898000 + 0.439996i \(0.854980\pi\)
\(80\) 0 0
\(81\) −6.66796 + 6.04470i −0.740884 + 0.671633i
\(82\) 0 0
\(83\) −0.181350 + 0.314108i −0.0199058 + 0.0344779i −0.875807 0.482662i \(-0.839670\pi\)
0.855901 + 0.517140i \(0.173003\pi\)
\(84\) 0 0
\(85\) −0.339244 0.587588i −0.0367962 0.0637329i
\(86\) 0 0
\(87\) −5.30793 11.1042i −0.569069 1.19049i
\(88\) 0 0
\(89\) 1.38526 2.39934i 0.146837 0.254329i −0.783220 0.621745i \(-0.786424\pi\)
0.930057 + 0.367416i \(0.119757\pi\)
\(90\) 0 0
\(91\) 7.88594 + 13.9451i 0.826671 + 1.46184i
\(92\) 0 0
\(93\) 4.69679 + 9.82569i 0.487034 + 1.01888i
\(94\) 0 0
\(95\) 0.245471 + 0.141723i 0.0251848 + 0.0145405i
\(96\) 0 0
\(97\) 0.508914 + 0.293821i 0.0516723 + 0.0298330i 0.525614 0.850723i \(-0.323836\pi\)
−0.473941 + 0.880556i \(0.657169\pi\)
\(98\) 0 0
\(99\) −10.9309 + 4.21713i −1.09859 + 0.423837i
\(100\) 0 0
\(101\) 13.8466 1.37779 0.688893 0.724863i \(-0.258097\pi\)
0.688893 + 0.724863i \(0.258097\pi\)
\(102\) 0 0
\(103\) 12.0793i 1.19021i 0.803647 + 0.595106i \(0.202890\pi\)
−0.803647 + 0.595106i \(0.797110\pi\)
\(104\) 0 0
\(105\) 4.42686 6.33078i 0.432018 0.617821i
\(106\) 0 0
\(107\) 15.9299 + 9.19711i 1.54000 + 0.889118i 0.998838 + 0.0481978i \(0.0153478\pi\)
0.541159 + 0.840920i \(0.317986\pi\)
\(108\) 0 0
\(109\) −5.51036 9.54422i −0.527796 0.914170i −0.999475 0.0323997i \(-0.989685\pi\)
0.471679 0.881771i \(-0.343648\pi\)
\(110\) 0 0
\(111\) 9.79051 4.67997i 0.929274 0.444203i
\(112\) 0 0
\(113\) −7.36811 + 4.25398i −0.693133 + 0.400181i −0.804785 0.593567i \(-0.797719\pi\)
0.111652 + 0.993747i \(0.464386\pi\)
\(114\) 0 0
\(115\) 14.9760i 1.39652i
\(116\) 0 0
\(117\) 14.1365 + 11.4081i 1.30692 + 1.05468i
\(118\) 0 0
\(119\) −0.926935 + 0.524181i −0.0849720 + 0.0480516i
\(120\) 0 0
\(121\) −4.25200 −0.386545
\(122\) 0 0
\(123\) 0.442862 5.68841i 0.0399315 0.512906i
\(124\) 0 0
\(125\) 12.0670 1.07930
\(126\) 0 0
\(127\) −10.6312 −0.943365 −0.471682 0.881769i \(-0.656353\pi\)
−0.471682 + 0.881769i \(0.656353\pi\)
\(128\) 0 0
\(129\) 5.64050 2.69622i 0.496619 0.237389i
\(130\) 0 0
\(131\) 6.33480 0.553474 0.276737 0.960946i \(-0.410747\pi\)
0.276737 + 0.960946i \(0.410747\pi\)
\(132\) 0 0
\(133\) 0.225866 0.383263i 0.0195851 0.0332331i
\(134\) 0 0
\(135\) 2.02328 8.52247i 0.174136 0.733498i
\(136\) 0 0
\(137\) 16.6459i 1.42216i 0.703113 + 0.711078i \(0.251793\pi\)
−0.703113 + 0.711078i \(0.748207\pi\)
\(138\) 0 0
\(139\) −4.24007 + 2.44800i −0.359638 + 0.207637i −0.668922 0.743333i \(-0.733244\pi\)
0.309284 + 0.950970i \(0.399911\pi\)
\(140\) 0 0
\(141\) −1.17898 + 15.1437i −0.0992884 + 1.27533i
\(142\) 0 0
\(143\) 11.8238 + 20.4795i 0.988758 + 1.71258i
\(144\) 0 0
\(145\) 10.3737 + 5.98926i 0.861489 + 0.497381i
\(146\) 0 0
\(147\) −9.87365 7.03641i −0.814365 0.580354i
\(148\) 0 0
\(149\) 5.28696i 0.433125i 0.976269 + 0.216562i \(0.0694845\pi\)
−0.976269 + 0.216562i \(0.930516\pi\)
\(150\) 0 0
\(151\) −14.5833 −1.18677 −0.593385 0.804919i \(-0.702209\pi\)
−0.593385 + 0.804919i \(0.702209\pi\)
\(152\) 0 0
\(153\) −0.758298 + 0.939655i −0.0613047 + 0.0759666i
\(154\) 0 0
\(155\) −9.17930 5.29967i −0.737299 0.425680i
\(156\) 0 0
\(157\) −15.4160 8.90044i −1.23033 0.710332i −0.263232 0.964732i \(-0.584789\pi\)
−0.967099 + 0.254400i \(0.918122\pi\)
\(158\) 0 0
\(159\) −9.86272 0.767846i −0.782165 0.0608942i
\(160\) 0 0
\(161\) 23.5038 + 0.209981i 1.85236 + 0.0165488i
\(162\) 0 0
\(163\) 0.0482228 0.0835243i 0.00377710 0.00654213i −0.864131 0.503267i \(-0.832131\pi\)
0.867908 + 0.496725i \(0.165464\pi\)
\(164\) 0 0
\(165\) 6.45073 9.40284i 0.502188 0.732010i
\(166\) 0 0
\(167\) −2.47872 4.29327i −0.191809 0.332224i 0.754041 0.656828i \(-0.228102\pi\)
−0.945850 + 0.324604i \(0.894769\pi\)
\(168\) 0 0
\(169\) 11.8324 20.4943i 0.910185 1.57649i
\(170\) 0 0
\(171\) 0.0780701 0.498353i 0.00597017 0.0381100i
\(172\) 0 0
\(173\) −7.40033 12.8177i −0.562637 0.974515i −0.997265 0.0739055i \(-0.976454\pi\)
0.434629 0.900610i \(-0.356880\pi\)
\(174\) 0 0
\(175\) 0.0510133 5.71007i 0.00385625 0.431641i
\(176\) 0 0
\(177\) 7.03723 3.36387i 0.528950 0.252844i
\(178\) 0 0
\(179\) 0.592751 0.342225i 0.0443043 0.0255791i −0.477684 0.878532i \(-0.658524\pi\)
0.521989 + 0.852952i \(0.325190\pi\)
\(180\) 0 0
\(181\) 7.84745i 0.583297i 0.956526 + 0.291648i \(0.0942037\pi\)
−0.956526 + 0.291648i \(0.905796\pi\)
\(182\) 0 0
\(183\) 8.84678 + 0.688752i 0.653973 + 0.0509140i
\(184\) 0 0
\(185\) −5.28070 + 9.14644i −0.388245 + 0.672459i
\(186\) 0 0
\(187\) −1.36128 + 0.785934i −0.0995464 + 0.0574732i
\(188\) 0 0
\(189\) −13.3470 3.29489i −0.970855 0.239668i
\(190\) 0 0
\(191\) −16.9694 + 9.79729i −1.22786 + 0.708907i −0.966582 0.256356i \(-0.917478\pi\)
−0.261281 + 0.965263i \(0.584145\pi\)
\(192\) 0 0
\(193\) −9.18116 + 15.9022i −0.660875 + 1.14467i 0.319512 + 0.947582i \(0.396481\pi\)
−0.980386 + 0.197086i \(0.936852\pi\)
\(194\) 0 0
\(195\) −17.6264 1.37227i −1.26225 0.0982705i
\(196\) 0 0
\(197\) 5.92313i 0.422006i −0.977485 0.211003i \(-0.932327\pi\)
0.977485 0.211003i \(-0.0676730\pi\)
\(198\) 0 0
\(199\) −13.6268 + 7.86741i −0.965975 + 0.557706i −0.898007 0.439982i \(-0.854985\pi\)
−0.0679681 + 0.997687i \(0.521652\pi\)
\(200\) 0 0
\(201\) 9.23617 4.41499i 0.651469 0.311409i
\(202\) 0 0
\(203\) 9.54517 16.1968i 0.669939 1.13679i
\(204\) 0 0
\(205\) 2.77653 + 4.80909i 0.193921 + 0.335881i
\(206\) 0 0
\(207\) 24.8655 9.59312i 1.72827 0.666768i
\(208\) 0 0
\(209\) 0.328332 0.568688i 0.0227112 0.0393370i
\(210\) 0 0
\(211\) 5.06619 + 8.77489i 0.348771 + 0.604088i 0.986031 0.166560i \(-0.0532659\pi\)
−0.637261 + 0.770648i \(0.719933\pi\)
\(212\) 0 0
\(213\) 11.2003 16.3261i 0.767435 1.11864i
\(214\) 0 0
\(215\) −3.04231 + 5.26944i −0.207484 + 0.359373i
\(216\) 0 0
\(217\) −8.44616 + 14.3320i −0.573363 + 0.972917i
\(218\) 0 0
\(219\) −12.0746 0.940052i −0.815928 0.0635228i
\(220\) 0 0
\(221\) 2.11061 + 1.21856i 0.141975 + 0.0819693i
\(222\) 0 0
\(223\) −13.3944 7.73325i −0.896955 0.517857i −0.0207437 0.999785i \(-0.506603\pi\)
−0.876211 + 0.481928i \(0.839937\pi\)
\(224\) 0 0
\(225\) −2.33058 6.04089i −0.155372 0.402726i
\(226\) 0 0
\(227\) 28.0719 1.86320 0.931600 0.363486i \(-0.118414\pi\)
0.931600 + 0.363486i \(0.118414\pi\)
\(228\) 0 0
\(229\) 17.0264i 1.12514i −0.826751 0.562568i \(-0.809814\pi\)
0.826751 0.562568i \(-0.190186\pi\)
\(230\) 0 0
\(231\) −14.6666 10.2558i −0.964995 0.674782i
\(232\) 0 0
\(233\) −16.0015 9.23847i −1.04829 0.605233i −0.126122 0.992015i \(-0.540253\pi\)
−0.922171 + 0.386782i \(0.873587\pi\)
\(234\) 0 0
\(235\) −7.39166 12.8027i −0.482179 0.835158i
\(236\) 0 0
\(237\) 0.162394 2.08590i 0.0105486 0.135493i
\(238\) 0 0
\(239\) −6.06656 + 3.50253i −0.392413 + 0.226560i −0.683205 0.730226i \(-0.739415\pi\)
0.290792 + 0.956786i \(0.406081\pi\)
\(240\) 0 0
\(241\) 6.21759i 0.400510i −0.979744 0.200255i \(-0.935823\pi\)
0.979744 0.200255i \(-0.0641771\pi\)
\(242\) 0 0
\(243\) −15.4464 + 2.09984i −0.990886 + 0.134705i
\(244\) 0 0
\(245\) 11.7983 + 0.210827i 0.753764 + 0.0134692i
\(246\) 0 0
\(247\) −1.01813 −0.0647823
\(248\) 0 0
\(249\) −0.566791 + 0.270932i −0.0359189 + 0.0171696i
\(250\) 0 0
\(251\) −9.81844 −0.619734 −0.309867 0.950780i \(-0.600285\pi\)
−0.309867 + 0.950780i \(0.600285\pi\)
\(252\) 0 0
\(253\) 34.6952 2.18127
\(254\) 0 0
\(255\) 0.0912155 1.17163i 0.00571213 0.0733704i
\(256\) 0 0
\(257\) −1.33581 −0.0833254 −0.0416627 0.999132i \(-0.513265\pi\)
−0.0416627 + 0.999132i \(0.513265\pi\)
\(258\) 0 0
\(259\) 14.2806 + 8.41593i 0.887356 + 0.522940i
\(260\) 0 0
\(261\) 3.29927 21.0605i 0.204219 1.30361i
\(262\) 0 0
\(263\) 20.3502i 1.25485i 0.778678 + 0.627424i \(0.215891\pi\)
−0.778678 + 0.627424i \(0.784109\pi\)
\(264\) 0 0
\(265\) 8.33814 4.81402i 0.512208 0.295723i
\(266\) 0 0
\(267\) 4.32947 2.06954i 0.264959 0.126654i
\(268\) 0 0
\(269\) −13.3614 23.1426i −0.814659 1.41103i −0.909572 0.415546i \(-0.863591\pi\)
0.0949131 0.995486i \(-0.469743\pi\)
\(270\) 0 0
\(271\) 3.76517 + 2.17382i 0.228718 + 0.132050i 0.609980 0.792417i \(-0.291177\pi\)
−0.381263 + 0.924467i \(0.624511\pi\)
\(272\) 0 0
\(273\) −2.40083 + 27.6441i −0.145305 + 1.67310i
\(274\) 0 0
\(275\) 8.42894i 0.508284i
\(276\) 0 0
\(277\) −4.39803 −0.264252 −0.132126 0.991233i \(-0.542180\pi\)
−0.132126 + 0.991233i \(0.542180\pi\)
\(278\) 0 0
\(279\) −2.91940 + 18.6357i −0.174780 + 1.11569i
\(280\) 0 0
\(281\) 4.62273 + 2.66893i 0.275769 + 0.159215i 0.631506 0.775371i \(-0.282437\pi\)
−0.355738 + 0.934586i \(0.615770\pi\)
\(282\) 0 0
\(283\) −15.5431 8.97381i −0.923941 0.533437i −0.0390505 0.999237i \(-0.512433\pi\)
−0.884890 + 0.465800i \(0.845767\pi\)
\(284\) 0 0
\(285\) 0.211730 + 0.442939i 0.0125418 + 0.0262375i
\(286\) 0 0
\(287\) 7.58645 4.29014i 0.447814 0.253239i
\(288\) 0 0
\(289\) 8.41900 14.5821i 0.495235 0.857773i
\(290\) 0 0
\(291\) 0.438960 + 0.918306i 0.0257323 + 0.0538320i
\(292\) 0 0
\(293\) 13.1126 + 22.7117i 0.766048 + 1.32683i 0.939691 + 0.342026i \(0.111113\pi\)
−0.173642 + 0.984809i \(0.555554\pi\)
\(294\) 0 0
\(295\) −3.79566 + 6.57428i −0.220992 + 0.382769i
\(296\) 0 0
\(297\) −19.7442 4.68737i −1.14567 0.271989i
\(298\) 0 0
\(299\) −26.8968 46.5867i −1.55548 2.69418i
\(300\) 0 0
\(301\) 8.22735 + 4.84858i 0.474217 + 0.279467i
\(302\) 0 0
\(303\) 19.7764 + 13.5674i 1.13613 + 0.779429i
\(304\) 0 0
\(305\) −7.47924 + 4.31814i −0.428260 + 0.247256i
\(306\) 0 0
\(307\) 7.19520i 0.410652i 0.978694 + 0.205326i \(0.0658254\pi\)
−0.978694 + 0.205326i \(0.934175\pi\)
\(308\) 0 0
\(309\) −11.8358 + 17.2524i −0.673317 + 0.981454i
\(310\) 0 0
\(311\) 1.08721 1.88311i 0.0616503 0.106781i −0.833553 0.552440i \(-0.813697\pi\)
0.895203 + 0.445658i \(0.147030\pi\)
\(312\) 0 0
\(313\) −10.2870 + 5.93922i −0.581457 + 0.335704i −0.761712 0.647916i \(-0.775641\pi\)
0.180255 + 0.983620i \(0.442308\pi\)
\(314\) 0 0
\(315\) 12.5258 4.70435i 0.705752 0.265060i
\(316\) 0 0
\(317\) 7.09969 4.09901i 0.398758 0.230223i −0.287190 0.957874i \(-0.592721\pi\)
0.685948 + 0.727651i \(0.259388\pi\)
\(318\) 0 0
\(319\) 13.8754 24.0329i 0.776875 1.34559i
\(320\) 0 0
\(321\) 13.7402 + 28.7445i 0.766903 + 1.60436i
\(322\) 0 0
\(323\) 0.0676757i 0.00376558i
\(324\) 0 0
\(325\) −11.3179 + 6.53438i −0.627803 + 0.362462i
\(326\) 0 0
\(327\) 1.48162 19.0308i 0.0819336 1.05241i
\(328\) 0 0
\(329\) −20.1966 + 11.4212i −1.11348 + 0.629670i
\(330\) 0 0
\(331\) −8.58540 14.8704i −0.471897 0.817349i 0.527586 0.849501i \(-0.323097\pi\)
−0.999483 + 0.0321526i \(0.989764\pi\)
\(332\) 0 0
\(333\) 18.5690 + 2.90895i 1.01757 + 0.159409i
\(334\) 0 0
\(335\) −4.98170 + 8.62856i −0.272179 + 0.471428i
\(336\) 0 0
\(337\) 3.95399 + 6.84850i 0.215387 + 0.373062i 0.953392 0.301733i \(-0.0975653\pi\)
−0.738005 + 0.674795i \(0.764232\pi\)
\(338\) 0 0
\(339\) −14.6918 1.14380i −0.797947 0.0621229i
\(340\) 0 0
\(341\) −12.2779 + 21.2659i −0.664883 + 1.15161i
\(342\) 0 0
\(343\) 0.496303 18.5136i 0.0267979 0.999641i
\(344\) 0 0
\(345\) −14.6741 + 21.3896i −0.790027 + 1.15158i
\(346\) 0 0
\(347\) −0.443850 0.256257i −0.0238271 0.0137566i 0.488039 0.872822i \(-0.337712\pi\)
−0.511866 + 0.859065i \(0.671046\pi\)
\(348\) 0 0
\(349\) −5.74612 3.31752i −0.307583 0.177583i 0.338262 0.941052i \(-0.390161\pi\)
−0.645844 + 0.763469i \(0.723494\pi\)
\(350\) 0 0
\(351\) 9.01239 + 30.1451i 0.481046 + 1.60903i
\(352\) 0 0
\(353\) 18.0687 0.961702 0.480851 0.876802i \(-0.340328\pi\)
0.480851 + 0.876802i \(0.340328\pi\)
\(354\) 0 0
\(355\) 19.2693i 1.02271i
\(356\) 0 0
\(357\) −1.83751 0.159584i −0.0972515 0.00844607i
\(358\) 0 0
\(359\) −1.52677 0.881479i −0.0805796 0.0465227i 0.459169 0.888349i \(-0.348147\pi\)
−0.539748 + 0.841826i \(0.681481\pi\)
\(360\) 0 0
\(361\) −9.48586 16.4300i −0.499256 0.864737i
\(362\) 0 0
\(363\) −6.07294 4.16628i −0.318747 0.218673i
\(364\) 0 0
\(365\) 10.2081 5.89367i 0.534318 0.308489i
\(366\) 0 0
\(367\) 33.4417i 1.74564i 0.488038 + 0.872822i \(0.337713\pi\)
−0.488038 + 0.872822i \(0.662287\pi\)
\(368\) 0 0
\(369\) 6.20625 7.69056i 0.323085 0.400355i
\(370\) 0 0
\(371\) −7.43836 13.1536i −0.386180 0.682902i
\(372\) 0 0
\(373\) 25.5688 1.32390 0.661952 0.749546i \(-0.269728\pi\)
0.661952 + 0.749546i \(0.269728\pi\)
\(374\) 0 0
\(375\) 17.2347 + 11.8237i 0.889999 + 0.610575i
\(376\) 0 0
\(377\) −43.0267 −2.21599
\(378\) 0 0
\(379\) 25.7920 1.32485 0.662423 0.749130i \(-0.269528\pi\)
0.662423 + 0.749130i \(0.269528\pi\)
\(380\) 0 0
\(381\) −15.1840 10.4169i −0.777902 0.533672i
\(382\) 0 0
\(383\) 32.8316 1.67762 0.838808 0.544427i \(-0.183253\pi\)
0.838808 + 0.544427i \(0.183253\pi\)
\(384\) 0 0
\(385\) 17.4175 + 0.155606i 0.887676 + 0.00793044i
\(386\) 0 0
\(387\) 10.6979 + 1.67590i 0.543807 + 0.0851908i
\(388\) 0 0
\(389\) 20.1544i 1.02187i −0.859619 0.510935i \(-0.829299\pi\)
0.859619 0.510935i \(-0.170701\pi\)
\(390\) 0 0
\(391\) 3.09663 1.78784i 0.156603 0.0904150i
\(392\) 0 0
\(393\) 9.04771 + 6.20709i 0.456396 + 0.313106i
\(394\) 0 0
\(395\) 1.01813 + 1.76346i 0.0512278 + 0.0887291i
\(396\) 0 0
\(397\) −30.2125 17.4432i −1.51632 0.875449i −0.999816 0.0191652i \(-0.993899\pi\)
−0.516506 0.856284i \(-0.672768\pi\)
\(398\) 0 0
\(399\) 0.698131 0.326085i 0.0349503 0.0163246i
\(400\) 0 0
\(401\) 9.66245i 0.482520i −0.970461 0.241260i \(-0.922439\pi\)
0.970461 0.241260i \(-0.0775606\pi\)
\(402\) 0 0
\(403\) 38.0727 1.89654
\(404\) 0 0
\(405\) 11.2404 10.1898i 0.558541 0.506334i
\(406\) 0 0
\(407\) 21.1897 + 12.2339i 1.05034 + 0.606412i
\(408\) 0 0
\(409\) 32.1202 + 18.5446i 1.58824 + 0.916973i 0.993597 + 0.112986i \(0.0360416\pi\)
0.594647 + 0.803987i \(0.297292\pi\)
\(410\) 0 0
\(411\) −16.3103 + 23.7746i −0.804530 + 1.17271i
\(412\) 0 0
\(413\) 10.2646 + 6.04920i 0.505090 + 0.297662i
\(414\) 0 0
\(415\) 0.305709 0.529504i 0.0150067 0.0259923i
\(416\) 0 0
\(417\) −8.45455 0.658216i −0.414021 0.0322330i
\(418\) 0 0
\(419\) −1.84193 3.19031i −0.0899841 0.155857i 0.817520 0.575900i \(-0.195348\pi\)
−0.907504 + 0.420043i \(0.862015\pi\)
\(420\) 0 0
\(421\) −8.55139 + 14.8114i −0.416769 + 0.721866i −0.995612 0.0935732i \(-0.970171\pi\)
0.578843 + 0.815439i \(0.303504\pi\)
\(422\) 0 0
\(423\) −16.5223 + 20.4738i −0.803339 + 0.995469i
\(424\) 0 0
\(425\) −0.434342 0.752303i −0.0210687 0.0364921i
\(426\) 0 0
\(427\) 6.67215 + 11.7987i 0.322888 + 0.570978i
\(428\) 0 0
\(429\) −3.17917 + 40.8354i −0.153492 + 1.97155i
\(430\) 0 0
\(431\) −27.3242 + 15.7756i −1.31616 + 0.759885i −0.983108 0.183024i \(-0.941411\pi\)
−0.333051 + 0.942909i \(0.608078\pi\)
\(432\) 0 0
\(433\) 10.0692i 0.483893i 0.970290 + 0.241947i \(0.0777859\pi\)
−0.970290 + 0.241947i \(0.922214\pi\)
\(434\) 0 0
\(435\) 8.94777 + 18.7188i 0.429013 + 0.897496i
\(436\) 0 0
\(437\) −0.746890 + 1.29365i −0.0357286 + 0.0618837i
\(438\) 0 0
\(439\) 24.1966 13.9699i 1.15484 0.666748i 0.204779 0.978808i \(-0.434352\pi\)
0.950062 + 0.312060i \(0.101019\pi\)
\(440\) 0 0
\(441\) −7.20752 19.7244i −0.343215 0.939257i
\(442\) 0 0
\(443\) −30.1930 + 17.4319i −1.43451 + 0.828215i −0.997460 0.0712223i \(-0.977310\pi\)
−0.437050 + 0.899437i \(0.643977\pi\)
\(444\) 0 0
\(445\) −2.33518 + 4.04466i −0.110698 + 0.191735i
\(446\) 0 0
\(447\) −5.18038 + 7.55113i −0.245023 + 0.357156i
\(448\) 0 0
\(449\) 23.2411i 1.09682i −0.836211 0.548408i \(-0.815234\pi\)
0.836211 0.548408i \(-0.184766\pi\)
\(450\) 0 0
\(451\) 11.1413 6.43244i 0.524624 0.302892i
\(452\) 0 0
\(453\) −20.8286 14.2893i −0.978614 0.671369i
\(454\) 0 0
\(455\) −13.2936 23.5078i −0.623215 1.10206i
\(456\) 0 0
\(457\) 3.10938 + 5.38560i 0.145451 + 0.251928i 0.929541 0.368719i \(-0.120203\pi\)
−0.784090 + 0.620647i \(0.786870\pi\)
\(458\) 0 0
\(459\) −2.00375 + 0.599056i −0.0935272 + 0.0279616i
\(460\) 0 0
\(461\) 2.17165 3.76140i 0.101144 0.175186i −0.811012 0.585029i \(-0.801083\pi\)
0.912156 + 0.409843i \(0.134416\pi\)
\(462\) 0 0
\(463\) 3.57451 + 6.19124i 0.166122 + 0.287731i 0.937053 0.349187i \(-0.113542\pi\)
−0.770931 + 0.636918i \(0.780209\pi\)
\(464\) 0 0
\(465\) −7.91755 16.5635i −0.367168 0.768115i
\(466\) 0 0
\(467\) −0.944451 + 1.63584i −0.0437040 + 0.0756975i −0.887050 0.461673i \(-0.847249\pi\)
0.843346 + 0.537371i \(0.180583\pi\)
\(468\) 0 0
\(469\) 13.4721 + 7.93941i 0.622082 + 0.366608i
\(470\) 0 0
\(471\) −13.2970 27.8173i −0.612693 1.28175i
\(472\) 0 0
\(473\) 12.2078 + 7.04818i 0.561316 + 0.324076i
\(474\) 0 0
\(475\) 0.314283 + 0.181451i 0.0144203 + 0.00832555i
\(476\) 0 0
\(477\) −13.3341 10.7606i −0.610527 0.492693i
\(478\) 0 0
\(479\) −10.4498 −0.477465 −0.238732 0.971085i \(-0.576732\pi\)
−0.238732 + 0.971085i \(0.576732\pi\)
\(480\) 0 0
\(481\) 37.9364i 1.72975i
\(482\) 0 0
\(483\) 33.3637 + 23.3299i 1.51810 + 1.06155i
\(484\) 0 0
\(485\) −0.857895 0.495306i −0.0389550 0.0224907i
\(486\) 0 0
\(487\) −11.8298 20.4898i −0.536060 0.928483i −0.999111 0.0421513i \(-0.986579\pi\)
0.463052 0.886331i \(-0.346754\pi\)
\(488\) 0 0
\(489\) 0.150715 0.0720434i 0.00681557 0.00325792i
\(490\) 0 0
\(491\) −11.6767 + 6.74152i −0.526960 + 0.304241i −0.739778 0.672851i \(-0.765069\pi\)
0.212817 + 0.977092i \(0.431736\pi\)
\(492\) 0 0
\(493\) 2.86000i 0.128808i
\(494\) 0 0
\(495\) 18.4266 7.10897i 0.828213 0.319524i
\(496\) 0 0
\(497\) 30.2418 + 0.270178i 1.35653 + 0.0121191i
\(498\) 0 0
\(499\) −12.0807 −0.540807 −0.270403 0.962747i \(-0.587157\pi\)
−0.270403 + 0.962747i \(0.587157\pi\)
\(500\) 0 0
\(501\) 0.666475 8.56064i 0.0297759 0.382461i
\(502\) 0 0
\(503\) −20.5283 −0.915310 −0.457655 0.889130i \(-0.651310\pi\)
−0.457655 + 0.889130i \(0.651310\pi\)
\(504\) 0 0
\(505\) −23.3417 −1.03869
\(506\) 0 0
\(507\) 36.9809 17.6773i 1.64238 0.785074i
\(508\) 0 0
\(509\) 8.18085 0.362610 0.181305 0.983427i \(-0.441968\pi\)
0.181305 + 0.983427i \(0.441968\pi\)
\(510\) 0 0
\(511\) −9.10656 16.1036i −0.402851 0.712380i
\(512\) 0 0
\(513\) 0.599810 0.635279i 0.0264823 0.0280482i
\(514\) 0 0
\(515\) 20.3626i 0.897283i
\(516\) 0 0
\(517\) −29.6603 + 17.1244i −1.30446 + 0.753131i
\(518\) 0 0
\(519\) 1.98979 25.5582i 0.0873421 1.12188i
\(520\) 0 0
\(521\) −13.8746 24.0314i −0.607856 1.05284i −0.991593 0.129395i \(-0.958697\pi\)
0.383738 0.923442i \(-0.374637\pi\)
\(522\) 0 0
\(523\) 19.8843 + 11.4802i 0.869478 + 0.501993i 0.867175 0.498004i \(-0.165934\pi\)
0.00230311 + 0.999997i \(0.499267\pi\)
\(524\) 0 0
\(525\) 5.66782 8.10545i 0.247364 0.353751i
\(526\) 0 0
\(527\) 2.53071i 0.110239i
\(528\) 0 0
\(529\) −55.9246 −2.43151
\(530\) 0 0
\(531\) 13.3470 + 2.09089i 0.579211 + 0.0907370i
\(532\) 0 0
\(533\) −17.2742 9.97325i −0.748228 0.431990i
\(534\) 0 0
\(535\) −26.8536 15.5039i −1.16098 0.670292i
\(536\) 0 0
\(537\) 1.18193 + 0.0920169i 0.0510039 + 0.00397082i
\(538\) 0 0
\(539\) 0.488426 27.3333i 0.0210380 1.17733i
\(540\) 0 0
\(541\) −2.60405 + 4.51035i −0.111957 + 0.193915i −0.916559 0.399899i \(-0.869045\pi\)
0.804602 + 0.593814i \(0.202379\pi\)
\(542\) 0 0
\(543\) −7.68925 + 11.2082i −0.329977 + 0.480988i
\(544\) 0 0
\(545\) 9.28902 + 16.0890i 0.397898 + 0.689179i
\(546\) 0 0
\(547\) 10.6224 18.3985i 0.454181 0.786664i −0.544460 0.838787i \(-0.683265\pi\)
0.998641 + 0.0521229i \(0.0165988\pi\)
\(548\) 0 0
\(549\) 11.9606 + 9.65215i 0.510466 + 0.411944i
\(550\) 0 0
\(551\) 0.597397 + 1.03472i 0.0254500 + 0.0440807i
\(552\) 0 0
\(553\) 2.78189 1.57316i 0.118298 0.0668976i
\(554\) 0 0
\(555\) −16.5042 + 7.88920i −0.700566 + 0.334878i
\(556\) 0 0
\(557\) −11.0945 + 6.40543i −0.470090 + 0.271407i −0.716277 0.697816i \(-0.754156\pi\)
0.246187 + 0.969222i \(0.420822\pi\)
\(558\) 0 0
\(559\) 21.8559i 0.924406i
\(560\) 0 0
\(561\) −2.71434 0.211321i −0.114600 0.00892197i
\(562\) 0 0
\(563\) −18.7396 + 32.4580i −0.789781 + 1.36794i 0.136319 + 0.990665i \(0.456473\pi\)
−0.926101 + 0.377277i \(0.876861\pi\)
\(564\) 0 0
\(565\) 12.4207 7.17109i 0.522542 0.301690i
\(566\) 0 0
\(567\) −15.8345 17.7839i −0.664988 0.746854i
\(568\) 0 0
\(569\) 5.94906 3.43469i 0.249397 0.143990i −0.370091 0.928996i \(-0.620673\pi\)
0.619488 + 0.785006i \(0.287340\pi\)
\(570\) 0 0
\(571\) −0.0847909 + 0.146862i −0.00354839 + 0.00614599i −0.867794 0.496924i \(-0.834463\pi\)
0.864246 + 0.503070i \(0.167796\pi\)
\(572\) 0 0
\(573\) −33.8364 2.63428i −1.41354 0.110049i
\(574\) 0 0
\(575\) 19.1741i 0.799617i
\(576\) 0 0
\(577\) −5.41193 + 3.12458i −0.225302 + 0.130078i −0.608403 0.793628i \(-0.708189\pi\)
0.383101 + 0.923706i \(0.374856\pi\)
\(578\) 0 0
\(579\) −28.6947 + 13.7164i −1.19251 + 0.570033i
\(580\) 0 0
\(581\) −0.826733 0.487213i −0.0342987 0.0202130i
\(582\) 0 0
\(583\) −11.1527 19.3171i −0.461900 0.800033i
\(584\) 0 0
\(585\) −23.8304 19.2310i −0.985264 0.795104i
\(586\) 0 0
\(587\) 10.7881 18.6855i 0.445273 0.771235i −0.552799 0.833315i \(-0.686440\pi\)
0.998071 + 0.0620801i \(0.0197734\pi\)
\(588\) 0 0
\(589\) −0.528615 0.915588i −0.0217812 0.0377261i
\(590\) 0 0
\(591\) 5.80373 8.45975i 0.238733 0.347987i
\(592\) 0 0
\(593\) 4.13036 7.15399i 0.169613 0.293779i −0.768671 0.639645i \(-0.779081\pi\)
0.938284 + 0.345866i \(0.112415\pi\)
\(594\) 0 0
\(595\) 1.56257 0.883632i 0.0640591 0.0362254i
\(596\) 0 0
\(597\) −27.1713 2.11538i −1.11205 0.0865766i
\(598\) 0 0
\(599\) 30.7618 + 17.7603i 1.25689 + 0.725667i 0.972469 0.233033i \(-0.0748649\pi\)
0.284422 + 0.958699i \(0.408198\pi\)
\(600\) 0 0
\(601\) 35.8981 + 20.7258i 1.46432 + 0.845423i 0.999206 0.0398308i \(-0.0126819\pi\)
0.465109 + 0.885254i \(0.346015\pi\)
\(602\) 0 0
\(603\) 17.5176 + 2.74424i 0.713371 + 0.111754i
\(604\) 0 0
\(605\) 7.16776 0.291411
\(606\) 0 0
\(607\) 2.41990i 0.0982206i −0.998793 0.0491103i \(-0.984361\pi\)
0.998793 0.0491103i \(-0.0156386\pi\)
\(608\) 0 0
\(609\) 29.5032 13.7804i 1.19553 0.558411i
\(610\) 0 0
\(611\) 45.9873 + 26.5508i 1.86045 + 1.07413i
\(612\) 0 0
\(613\) 21.3228 + 36.9321i 0.861219 + 1.49168i 0.870753 + 0.491720i \(0.163632\pi\)
−0.00953416 + 0.999955i \(0.503035\pi\)
\(614\) 0 0
\(615\) −0.746549 + 9.58916i −0.0301038 + 0.386672i
\(616\) 0 0
\(617\) 13.2535 7.65193i 0.533567 0.308055i −0.208901 0.977937i \(-0.566989\pi\)
0.742468 + 0.669882i \(0.233655\pi\)
\(618\) 0 0
\(619\) 27.6178i 1.11005i −0.831833 0.555026i \(-0.812708\pi\)
0.831833 0.555026i \(-0.187292\pi\)
\(620\) 0 0
\(621\) 44.9140 + 10.6628i 1.80234 + 0.427884i
\(622\) 0 0
\(623\) 6.31506 + 3.72162i 0.253008 + 0.149103i
\(624\) 0 0
\(625\) −9.55034 −0.382014
\(626\) 0 0
\(627\) 1.02617 0.490519i 0.0409811 0.0195894i
\(628\) 0 0
\(629\) 2.52164 0.100545
\(630\) 0 0
\(631\) 8.28775 0.329930 0.164965 0.986299i \(-0.447249\pi\)
0.164965 + 0.986299i \(0.447249\pi\)
\(632\) 0 0
\(633\) −1.36219 + 17.4968i −0.0541421 + 0.695437i
\(634\) 0 0
\(635\) 17.9214 0.711188
\(636\) 0 0
\(637\) −37.0802 + 20.5338i −1.46917 + 0.813579i
\(638\) 0 0
\(639\) 31.9939 12.3432i 1.26566 0.488291i
\(640\) 0 0
\(641\) 9.91088i 0.391456i −0.980658 0.195728i \(-0.937293\pi\)
0.980658 0.195728i \(-0.0627070\pi\)
\(642\) 0 0
\(643\) 6.83668 3.94716i 0.269612 0.155661i −0.359099 0.933299i \(-0.616916\pi\)
0.628711 + 0.777639i \(0.283583\pi\)
\(644\) 0 0
\(645\) −9.50841 + 4.54512i −0.374393 + 0.178964i
\(646\) 0 0
\(647\) 2.15966 + 3.74063i 0.0849049 + 0.147060i 0.905351 0.424665i \(-0.139608\pi\)
−0.820446 + 0.571724i \(0.806275\pi\)
\(648\) 0 0
\(649\) 15.2308 + 8.79348i 0.597859 + 0.345174i
\(650\) 0 0
\(651\) −26.1063 + 12.1938i −1.02319 + 0.477912i
\(652\) 0 0
\(653\) 43.3997i 1.69836i −0.528102 0.849181i \(-0.677096\pi\)
0.528102 0.849181i \(-0.322904\pi\)
\(654\) 0 0
\(655\) −10.6788 −0.417256
\(656\) 0 0
\(657\) −16.3246 13.1739i −0.636882 0.513961i
\(658\) 0 0
\(659\) −9.34894 5.39761i −0.364183 0.210261i 0.306731 0.951796i \(-0.400765\pi\)
−0.670914 + 0.741535i \(0.734098\pi\)
\(660\) 0 0
\(661\) 3.39495 + 1.96008i 0.132048 + 0.0762381i 0.564569 0.825386i \(-0.309042\pi\)
−0.432521 + 0.901624i \(0.642376\pi\)
\(662\) 0 0
\(663\) 1.82049 + 3.80848i 0.0707021 + 0.147909i
\(664\) 0 0
\(665\) −0.380751 + 0.646081i −0.0147649 + 0.0250539i
\(666\) 0 0
\(667\) −31.5638 + 54.6701i −1.22216 + 2.11683i
\(668\) 0 0
\(669\) −11.5532 24.1694i −0.446674 0.934444i
\(670\) 0 0
\(671\) 10.0039 + 17.3273i 0.386197 + 0.668913i
\(672\) 0 0
\(673\) −12.3404 + 21.3742i −0.475687 + 0.823915i −0.999612 0.0278497i \(-0.991134\pi\)
0.523925 + 0.851765i \(0.324467\pi\)
\(674\) 0 0
\(675\) 2.59045 10.9115i 0.0997065 0.419985i
\(676\) 0 0
\(677\) 7.36327 + 12.7536i 0.282994 + 0.490159i 0.972121 0.234481i \(-0.0753392\pi\)
−0.689127 + 0.724641i \(0.742006\pi\)
\(678\) 0 0
\(679\) −0.789376 + 1.33946i −0.0302935 + 0.0514038i
\(680\) 0 0
\(681\) 40.0939 + 27.5060i 1.53640 + 1.05403i
\(682\) 0 0
\(683\) −1.60128 + 0.924499i −0.0612712 + 0.0353750i −0.530323 0.847796i \(-0.677929\pi\)
0.469051 + 0.883171i \(0.344596\pi\)
\(684\) 0 0
\(685\) 28.0606i 1.07214i
\(686\) 0 0
\(687\) 16.6831 24.3180i 0.636502 0.927790i
\(688\) 0 0
\(689\) −17.2919 + 29.9505i −0.658769 + 1.14102i
\(690\) 0 0
\(691\) −33.7613 + 19.4921i −1.28434 + 0.741514i −0.977639 0.210292i \(-0.932559\pi\)
−0.306701 + 0.951806i \(0.599225\pi\)
\(692\) 0 0
\(693\) −10.8987 29.0189i −0.414006 1.10234i
\(694\) 0 0
\(695\) 7.14764 4.12669i 0.271126 0.156534i
\(696\) 0 0
\(697\) 0.662926 1.14822i 0.0251101 0.0434920i
\(698\) 0 0
\(699\) −13.8020 28.8738i −0.522040 1.09211i
\(700\) 0 0
\(701\) 25.4389i 0.960813i 0.877046 + 0.480406i \(0.159511\pi\)
−0.877046 + 0.480406i \(0.840489\pi\)
\(702\) 0 0
\(703\) −0.912310 + 0.526722i −0.0344084 + 0.0198657i
\(704\) 0 0
\(705\) 1.98746 25.5282i 0.0748520 0.961448i
\(706\) 0 0
\(707\) −0.327278 + 36.6331i −0.0123086 + 1.37773i
\(708\) 0 0
\(709\) 7.14517 + 12.3758i 0.268342 + 0.464783i 0.968434 0.249270i \(-0.0801908\pi\)
−0.700092 + 0.714053i \(0.746857\pi\)
\(710\) 0 0
\(711\) 2.27578 2.82007i 0.0853486 0.105761i
\(712\) 0 0
\(713\) 27.9296 48.3756i 1.04597 1.81168i
\(714\) 0 0
\(715\) −19.9319 34.5230i −0.745410 1.29109i
\(716\) 0 0
\(717\) −12.0965 0.941755i −0.451753 0.0351705i
\(718\) 0 0
\(719\) −16.7344 + 28.9848i −0.624088 + 1.08095i 0.364629 + 0.931153i \(0.381196\pi\)
−0.988716 + 0.149799i \(0.952137\pi\)
\(720\) 0 0
\(721\) −31.9577 0.285507i −1.19017 0.0106329i
\(722\) 0 0
\(723\) 6.09225 8.88030i 0.226573 0.330262i
\(724\) 0 0
\(725\) 13.2817 + 7.66819i 0.493269 + 0.284789i
\(726\) 0 0
\(727\) 12.1354 + 7.00636i 0.450076 + 0.259851i 0.707862 0.706350i \(-0.249660\pi\)
−0.257786 + 0.966202i \(0.582993\pi\)
\(728\) 0 0
\(729\) −24.1189 12.1359i −0.893292 0.449477i
\(730\) 0 0
\(731\) 1.45277 0.0537326
\(732\) 0 0
\(733\) 27.3077i 1.00863i 0.863519 + 0.504316i \(0.168255\pi\)
−0.863519 + 0.504316i \(0.831745\pi\)
\(734\) 0 0
\(735\) 16.6444 + 11.8615i 0.613937 + 0.437520i
\(736\) 0 0
\(737\) 19.9899 + 11.5412i 0.736339 + 0.425126i
\(738\) 0 0
\(739\) 26.3157 + 45.5801i 0.968039 + 1.67669i 0.701220 + 0.712945i \(0.252639\pi\)
0.266819 + 0.963747i \(0.414027\pi\)
\(740\) 0 0
\(741\) −1.45416 0.997609i −0.0534197 0.0366481i
\(742\) 0 0
\(743\) −30.9523 + 17.8703i −1.13553 + 0.655599i −0.945320 0.326144i \(-0.894250\pi\)
−0.190211 + 0.981743i \(0.560917\pi\)
\(744\) 0 0
\(745\) 8.91243i 0.326526i
\(746\) 0 0
\(747\) −1.07499 0.168404i −0.0393319 0.00616159i
\(748\) 0 0
\(749\) −24.7088 + 41.9274i −0.902840 + 1.53199i
\(750\) 0 0
\(751\) −33.1282 −1.20887 −0.604433 0.796656i \(-0.706600\pi\)
−0.604433 + 0.796656i \(0.706600\pi\)
\(752\) 0 0
\(753\) −14.0232 9.62051i −0.511035 0.350591i
\(754\) 0 0
\(755\) 24.5836 0.894687
\(756\) 0 0
\(757\) −13.6903 −0.497584 −0.248792 0.968557i \(-0.580034\pi\)
−0.248792 + 0.968557i \(0.580034\pi\)
\(758\) 0 0
\(759\) 49.5536 + 33.9958i 1.79868 + 1.23397i
\(760\) 0 0
\(761\) −13.0347 −0.472509 −0.236255 0.971691i \(-0.575920\pi\)
−0.236255 + 0.971691i \(0.575920\pi\)
\(762\) 0 0
\(763\) 25.3809 14.3529i 0.918849 0.519609i
\(764\) 0 0
\(765\) 1.27829 1.58401i 0.0462167 0.0572701i
\(766\) 0 0
\(767\) 27.2679i 0.984588i
\(768\) 0 0
\(769\) −18.4866 + 10.6732i −0.666642 + 0.384886i −0.794803 0.606867i \(-0.792426\pi\)
0.128161 + 0.991753i \(0.459093\pi\)
\(770\) 0 0
\(771\) −1.90788 1.30888i −0.0687104 0.0471381i
\(772\) 0 0
\(773\) −5.73940 9.94093i −0.206432 0.357550i 0.744156 0.668006i \(-0.232852\pi\)
−0.950588 + 0.310455i \(0.899518\pi\)
\(774\) 0 0
\(775\) −11.7525 6.78529i −0.422161 0.243735i
\(776\) 0 0
\(777\) 12.1501 + 26.0128i 0.435884 + 0.933206i
\(778\) 0 0
\(779\) 0.553889i 0.0198451i
\(780\) 0 0
\(781\) 44.6416 1.59740
\(782\) 0 0
\(783\) 25.3482 26.8471i 0.905870 0.959436i
\(784\) 0 0
\(785\) 25.9873 + 15.0038i 0.927528 + 0.535509i
\(786\) 0 0
\(787\) 35.6808 + 20.6003i 1.27188 + 0.734322i 0.975342 0.220698i \(-0.0708337\pi\)
0.296541 + 0.955020i \(0.404167\pi\)
\(788\) 0 0
\(789\) −19.9400 + 29.0653i −0.709881 + 1.03475i
\(790\) 0 0
\(791\) −11.0804 19.5939i −0.393972 0.696681i
\(792\) 0 0
\(793\) 15.5107 26.8653i 0.550801 0.954016i
\(794\) 0 0
\(795\) 16.6260 + 1.29439i 0.589662 + 0.0459072i
\(796\) 0 0
\(797\) 25.0066 + 43.3127i 0.885779 + 1.53421i 0.844819 + 0.535053i \(0.179708\pi\)
0.0409600 + 0.999161i \(0.486958\pi\)
\(798\) 0 0
\(799\) −1.76484 + 3.05679i −0.0624355 + 0.108141i
\(800\) 0 0
\(801\) 8.21141 + 1.28637i 0.290136 + 0.0454516i
\(802\) 0 0
\(803\) −13.6540 23.6494i −0.481838 0.834568i
\(804\) 0 0
\(805\) −39.6212 0.353973i −1.39646 0.0124759i
\(806\) 0 0
\(807\) 3.59259 46.1456i 0.126465 1.62440i
\(808\) 0 0
\(809\) 43.8995 25.3454i 1.54343 0.891097i 0.544807 0.838562i \(-0.316603\pi\)
0.998619 0.0525356i \(-0.0167303\pi\)
\(810\) 0 0
\(811\) 8.96566i 0.314827i 0.987533 + 0.157413i \(0.0503155\pi\)
−0.987533 + 0.157413i \(0.949684\pi\)
\(812\) 0 0
\(813\) 3.24762 + 6.79403i 0.113899 + 0.238277i
\(814\) 0 0
\(815\) −0.0812910 + 0.140800i −0.00284750 + 0.00493201i
\(816\) 0 0
\(817\) −0.525599 + 0.303455i −0.0183884 + 0.0106165i
\(818\) 0 0
\(819\) −30.5158 + 37.1304i −1.06631 + 1.29744i
\(820\) 0 0
\(821\) −28.2190 + 16.2922i −0.984849 + 0.568603i −0.903731 0.428102i \(-0.859183\pi\)
−0.0811184 + 0.996704i \(0.525849\pi\)
\(822\) 0 0
\(823\) 10.0877 17.4724i 0.351636 0.609051i −0.634901 0.772594i \(-0.718959\pi\)
0.986536 + 0.163543i \(0.0522923\pi\)
\(824\) 0 0
\(825\) 8.25902 12.0387i 0.287542 0.419133i
\(826\) 0 0
\(827\) 0.253288i 0.00880770i 0.999990 + 0.00440385i \(0.00140179\pi\)
−0.999990 + 0.00440385i \(0.998598\pi\)
\(828\) 0 0
\(829\) −6.10909 + 3.52708i −0.212177 + 0.122501i −0.602323 0.798253i \(-0.705758\pi\)
0.390146 + 0.920753i \(0.372425\pi\)
\(830\) 0 0
\(831\) −6.28151 4.30937i −0.217903 0.149490i
\(832\) 0 0
\(833\) −1.36489 2.46473i −0.0472906 0.0853979i
\(834\) 0 0
\(835\) 4.17848 + 7.23733i 0.144602 + 0.250458i
\(836\) 0 0
\(837\) −22.4297 + 23.7560i −0.775282 + 0.821127i
\(838\) 0 0
\(839\) −17.0936 + 29.6069i −0.590136 + 1.02215i 0.404078 + 0.914725i \(0.367592\pi\)
−0.994214 + 0.107420i \(0.965741\pi\)
\(840\) 0 0
\(841\) 10.7462 + 18.6130i 0.370558 + 0.641826i
\(842\) 0 0
\(843\) 3.98731 + 8.34145i 0.137330 + 0.287295i
\(844\) 0 0
\(845\) −19.9463 + 34.5480i −0.686174 + 1.18849i
\(846\) 0 0
\(847\) 0.100500 11.2493i 0.00345323 0.386530i
\(848\) 0 0
\(849\) −13.4066 28.0466i −0.460113 0.962558i
\(850\) 0 0
\(851\) −48.2024 27.8296i −1.65236 0.953988i
\(852\) 0 0
\(853\) −21.7586 12.5623i −0.745000 0.430126i 0.0788844 0.996884i \(-0.474864\pi\)
−0.823884 + 0.566758i \(0.808198\pi\)
\(854\) 0 0
\(855\) −0.131606 + 0.840092i −0.00450082 + 0.0287305i
\(856\) 0 0
\(857\) 42.1907 1.44121 0.720604 0.693347i \(-0.243865\pi\)
0.720604 + 0.693347i \(0.243865\pi\)
\(858\) 0 0
\(859\) 4.71278i 0.160798i 0.996763 + 0.0803990i \(0.0256195\pi\)
−0.996763 + 0.0803990i \(0.974381\pi\)
\(860\) 0 0
\(861\) 15.0390 + 1.30611i 0.512529 + 0.0445120i
\(862\) 0 0
\(863\) 30.8409 + 17.8060i 1.04984 + 0.606123i 0.922603 0.385750i \(-0.126057\pi\)
0.127232 + 0.991873i \(0.459391\pi\)
\(864\) 0 0
\(865\) 12.4750 + 21.6074i 0.424163 + 0.734672i
\(866\) 0 0
\(867\) 26.3127 12.5777i 0.893625 0.427162i
\(868\) 0 0
\(869\) 4.08543 2.35873i 0.138589 0.0800143i
\(870\) 0 0
\(871\) 35.7884i 1.21264i
\(872\) 0 0
\(873\) −0.272846 + 1.74169i −0.00923444 + 0.0589471i
\(874\) 0 0
\(875\) −0.285216 + 31.9250i −0.00964205 + 1.07926i
\(876\) 0 0
\(877\) 40.9064 1.38131 0.690655 0.723184i \(-0.257322\pi\)
0.690655 + 0.723184i \(0.257322\pi\)
\(878\) 0 0
\(879\) −3.52570 + 45.2865i −0.118919 + 1.52747i
\(880\) 0 0
\(881\) 37.4443 1.26153 0.630765 0.775974i \(-0.282741\pi\)
0.630765 + 0.775974i \(0.282741\pi\)
\(882\) 0 0
\(883\) −49.8357 −1.67711 −0.838553 0.544821i \(-0.816598\pi\)
−0.838553 + 0.544821i \(0.816598\pi\)
\(884\) 0 0
\(885\) −11.8629 + 5.67060i −0.398768 + 0.190615i
\(886\) 0 0
\(887\) 28.8965 0.970248 0.485124 0.874445i \(-0.338774\pi\)
0.485124 + 0.874445i \(0.338774\pi\)
\(888\) 0 0
\(889\) 0.251279 28.1263i 0.00842761 0.943327i
\(890\) 0 0
\(891\) −23.6068 26.0409i −0.790859 0.872403i
\(892\) 0 0
\(893\) 1.47456i 0.0493443i
\(894\) 0 0
\(895\) −0.999223 + 0.576902i −0.0334003 + 0.0192837i
\(896\) 0 0
\(897\) 7.23198 92.8922i 0.241469 3.10158i
\(898\) 0 0
\(899\) −22.3394 38.6930i −0.745062 1.29048i
\(900\) 0 0
\(901\) −1.99082 1.14940i −0.0663238 0.0382920i
\(902\) 0 0
\(903\) 6.99993 + 14.9865i 0.232943 + 0.498719i
\(904\) 0 0
\(905\) 13.2287i 0.439738i
\(906\) 0 0
\(907\) −14.8700 −0.493749 −0.246874 0.969048i \(-0.579403\pi\)
−0.246874 + 0.969048i \(0.579403\pi\)
\(908\) 0 0
\(909\) 14.9519 + 38.7555i 0.495923 + 1.28544i
\(910\) 0 0
\(911\) 7.81616 + 4.51266i 0.258961 + 0.149511i 0.623861 0.781536i \(-0.285563\pi\)
−0.364899 + 0.931047i \(0.618897\pi\)
\(912\) 0 0
\(913\) −1.22671 0.708243i −0.0405982 0.0234394i
\(914\) 0 0
\(915\) −14.9134 1.16106i −0.493020 0.0383833i
\(916\) 0 0
\(917\) −0.149729 + 16.7596i −0.00494450 + 0.553452i
\(918\) 0 0
\(919\) 13.2083 22.8774i 0.435702 0.754657i −0.561651 0.827374i \(-0.689834\pi\)
0.997353 + 0.0727170i \(0.0231670\pi\)
\(920\) 0 0
\(921\) −7.05015 + 10.2766i −0.232310 + 0.338625i
\(922\) 0 0
\(923\) −34.6075 59.9420i −1.13912 1.97302i
\(924\) 0 0
\(925\) −6.76100 + 11.7104i −0.222300 + 0.385036i
\(926\) 0 0
\(927\) −33.8092 + 13.0436i −1.11044 + 0.428407i
\(928\) 0 0
\(929\) 11.1259 + 19.2706i 0.365029 + 0.632249i 0.988781 0.149373i \(-0.0477257\pi\)
−0.623752 + 0.781623i \(0.714392\pi\)
\(930\) 0 0
\(931\) 1.00864 + 0.606620i 0.0330568 + 0.0198812i
\(932\) 0 0
\(933\) 3.39797 1.62427i 0.111244 0.0531761i
\(934\) 0 0
\(935\) 2.29476 1.32488i 0.0750465 0.0433281i
\(936\) 0 0
\(937\) 14.6822i 0.479647i −0.970817 0.239823i \(-0.922910\pi\)
0.970817 0.239823i \(-0.0770896\pi\)
\(938\) 0 0
\(939\) −20.5120 1.59693i −0.669383 0.0521137i
\(940\) 0 0
\(941\) 23.0396 39.9058i 0.751070 1.30089i −0.196235 0.980557i \(-0.562871\pi\)
0.947305 0.320334i \(-0.103795\pi\)
\(942\) 0 0
\(943\) −25.3442 + 14.6325i −0.825322 + 0.476500i
\(944\) 0 0
\(945\) 22.4996 + 5.55432i 0.731913 + 0.180682i
\(946\) 0 0
\(947\) 6.96116 4.01903i 0.226207 0.130601i −0.382614 0.923908i \(-0.624976\pi\)
0.608821 + 0.793308i \(0.291643\pi\)
\(948\) 0 0
\(949\) −21.1700 + 36.6675i −0.687206 + 1.19028i
\(950\) 0 0
\(951\) 14.1565 + 1.10213i 0.459057 + 0.0357392i
\(952\) 0 0
\(953\) 54.9348i 1.77951i −0.456437 0.889756i \(-0.650875\pi\)
0.456437 0.889756i \(-0.349125\pi\)
\(954\) 0 0
\(955\) 28.6060 16.5157i 0.925667 0.534434i
\(956\) 0 0
\(957\) 43.3661 20.7295i 1.40183 0.670089i
\(958\) 0 0
\(959\) −44.0392 0.393443i −1.42210 0.0127049i
\(960\) 0 0
\(961\) 4.26733 + 7.39124i 0.137656 + 0.238427i
\(962\) 0 0
\(963\) −8.54055 + 54.5177i −0.275215 + 1.75681i
\(964\) 0 0
\(965\) 15.4770 26.8070i 0.498223 0.862948i
\(966\) 0 0
\(967\) −26.5917 46.0582i −0.855132 1.48113i −0.876522 0.481361i \(-0.840143\pi\)
0.0213900 0.999771i \(-0.493191\pi\)
\(968\) 0 0
\(969\) 0.0663114 0.0966582i 0.00213023 0.00310511i
\(970\) 0 0
\(971\) 7.61403 13.1879i 0.244346 0.423219i −0.717602 0.696454i \(-0.754760\pi\)
0.961947 + 0.273234i \(0.0880935\pi\)
\(972\) 0 0
\(973\) −6.37634 11.2756i −0.204416 0.361479i
\(974\) 0 0
\(975\) −22.5675 1.75695i −0.722737 0.0562676i
\(976\) 0 0
\(977\) 1.49418 + 0.862667i 0.0478031 + 0.0275992i 0.523711 0.851896i \(-0.324547\pi\)
−0.475908 + 0.879495i \(0.657880\pi\)
\(978\) 0 0
\(979\) 9.37033 + 5.40997i 0.299477 + 0.172903i
\(980\) 0 0
\(981\) 20.7633 25.7292i 0.662922 0.821469i
\(982\) 0 0
\(983\) −60.2383 −1.92130 −0.960651 0.277758i \(-0.910409\pi\)
−0.960651 + 0.277758i \(0.910409\pi\)
\(984\) 0 0
\(985\) 9.98485i 0.318144i
\(986\) 0 0
\(987\) −40.0369 3.47711i −1.27439 0.110678i
\(988\) 0 0
\(989\) −27.7703 16.0332i −0.883044 0.509826i
\(990\) 0 0
\(991\) −2.87312 4.97639i −0.0912676 0.158080i 0.816777 0.576953i \(-0.195759\pi\)
−0.908045 + 0.418873i \(0.862425\pi\)
\(992\) 0 0
\(993\) 2.30843 29.6510i 0.0732558 0.940946i
\(994\) 0 0
\(995\) 22.9711 13.2624i 0.728234 0.420446i
\(996\) 0 0
\(997\) 0.0259240i 0.000821020i −1.00000 0.000410510i \(-0.999869\pi\)
1.00000 0.000410510i \(-0.000130669\pi\)
\(998\) 0 0
\(999\) 23.6709 + 22.3494i 0.748915 + 0.707102i
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 252.2.bm.a.173.7 yes 16
3.2 odd 2 756.2.bm.a.89.6 16
4.3 odd 2 1008.2.df.d.929.2 16
7.2 even 3 1764.2.x.b.1469.1 16
7.3 odd 6 252.2.w.a.101.4 yes 16
7.4 even 3 1764.2.w.b.1109.5 16
7.5 odd 6 1764.2.x.a.1469.8 16
7.6 odd 2 1764.2.bm.a.1685.2 16
9.2 odd 6 2268.2.t.b.2105.3 16
9.4 even 3 756.2.w.a.341.6 16
9.5 odd 6 252.2.w.a.5.4 16
9.7 even 3 2268.2.t.a.2105.6 16
12.11 even 2 3024.2.df.d.1601.6 16
21.2 odd 6 5292.2.x.b.4409.3 16
21.5 even 6 5292.2.x.a.4409.6 16
21.11 odd 6 5292.2.w.b.521.3 16
21.17 even 6 756.2.w.a.521.6 16
21.20 even 2 5292.2.bm.a.4625.3 16
28.3 even 6 1008.2.ca.d.353.5 16
36.23 even 6 1008.2.ca.d.257.5 16
36.31 odd 6 3024.2.ca.d.2609.6 16
63.4 even 3 5292.2.bm.a.2285.3 16
63.5 even 6 1764.2.x.b.293.1 16
63.13 odd 6 5292.2.w.b.1097.3 16
63.23 odd 6 1764.2.x.a.293.8 16
63.31 odd 6 756.2.bm.a.17.6 16
63.32 odd 6 1764.2.bm.a.1697.2 16
63.38 even 6 2268.2.t.a.1781.6 16
63.40 odd 6 5292.2.x.b.881.3 16
63.41 even 6 1764.2.w.b.509.5 16
63.52 odd 6 2268.2.t.b.1781.3 16
63.58 even 3 5292.2.x.a.881.6 16
63.59 even 6 inner 252.2.bm.a.185.7 yes 16
84.59 odd 6 3024.2.ca.d.2033.6 16
252.31 even 6 3024.2.df.d.17.6 16
252.59 odd 6 1008.2.df.d.689.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.w.a.5.4 16 9.5 odd 6
252.2.w.a.101.4 yes 16 7.3 odd 6
252.2.bm.a.173.7 yes 16 1.1 even 1 trivial
252.2.bm.a.185.7 yes 16 63.59 even 6 inner
756.2.w.a.341.6 16 9.4 even 3
756.2.w.a.521.6 16 21.17 even 6
756.2.bm.a.17.6 16 63.31 odd 6
756.2.bm.a.89.6 16 3.2 odd 2
1008.2.ca.d.257.5 16 36.23 even 6
1008.2.ca.d.353.5 16 28.3 even 6
1008.2.df.d.689.2 16 252.59 odd 6
1008.2.df.d.929.2 16 4.3 odd 2
1764.2.w.b.509.5 16 63.41 even 6
1764.2.w.b.1109.5 16 7.4 even 3
1764.2.x.a.293.8 16 63.23 odd 6
1764.2.x.a.1469.8 16 7.5 odd 6
1764.2.x.b.293.1 16 63.5 even 6
1764.2.x.b.1469.1 16 7.2 even 3
1764.2.bm.a.1685.2 16 7.6 odd 2
1764.2.bm.a.1697.2 16 63.32 odd 6
2268.2.t.a.1781.6 16 63.38 even 6
2268.2.t.a.2105.6 16 9.7 even 3
2268.2.t.b.1781.3 16 63.52 odd 6
2268.2.t.b.2105.3 16 9.2 odd 6
3024.2.ca.d.2033.6 16 84.59 odd 6
3024.2.ca.d.2609.6 16 36.31 odd 6
3024.2.df.d.17.6 16 252.31 even 6
3024.2.df.d.1601.6 16 12.11 even 2
5292.2.w.b.521.3 16 21.11 odd 6
5292.2.w.b.1097.3 16 63.13 odd 6
5292.2.x.a.881.6 16 63.58 even 3
5292.2.x.a.4409.6 16 21.5 even 6
5292.2.x.b.881.3 16 63.40 odd 6
5292.2.x.b.4409.3 16 21.2 odd 6
5292.2.bm.a.2285.3 16 63.4 even 3
5292.2.bm.a.4625.3 16 21.20 even 2