LMFDB - Embedded newform 64.10.b.a.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,10,Mod(33,64)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("64.33");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	64.b (of order $2$, degree $1$, 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:	$32.9622935145$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			33.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	64.33
Dual form			64.10.b.a.33.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-190.000i q^{3} -16417.0 q^{9} +O(q^{10})$	$q-190.000i q^{3} -16417.0 q^{9} +66042.0i q^{11} -597510. q^{17} +990146. i q^{19} +1.95312e6 q^{25} -620540. i q^{27} +1.25480e7 q^{33} +3.43064e7 q^{41} +4.47821e7i q^{43} -4.03536e7 q^{49} +1.13527e8i q^{51} +1.88128e8 q^{57} +8.42438e7i q^{59} -6.28172e7i q^{67} +4.22325e8 q^{73} -3.71094e8i q^{75} -4.41038e8 q^{81} +1.44638e8i q^{83} -1.08985e9 q^{89} -1.73825e9 q^{97} -1.08421e9i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32834 q^{9}+O(q^{10}) $ 2 * q - 32834 * q^9	$ 2 q - 32834 q^{9} - 1195020 q^{17} + 3906250 q^{25} + 25095960 q^{33} + 68612724 q^{41} - 80707214 q^{49} + 376255480 q^{57} + 844649860 q^{73} - 882076822 q^{81} - 2179698012 q^{89} - 3476509420 q^{97}+O(q^{100}) $ 2 * q - 32834 * q^9 - 1195020 * q^17 + 3906250 * q^25 + 25095960 * q^33 + 68612724 * q^41 - 80707214 * q^49 + 376255480 * q^57 + 844649860 * q^73 - 882076822 * q^81 - 2179698012 * q^89 - 3476509420 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$-1$	$1$

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 $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0	0
$2$	0	0
$3$	− 190.000i	− 1.35428i	−0.735855	−	0.677139i	$-0.763219\pi$
$3$	− 190.000i	− 1.35428i	0.735855	−	0.677139i	$-0.236781\pi$
$4$	0	0
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	0	0
$9$	−16417.0	−0.834070
$10$	0	0
$11$	66042.0i	1.36004i	0.733191	+	0.680022i	$0.238030\pi$
$11$	66042.0i	1.36004i	−0.733191	+	0.680022i	$0.761970\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−597510.	−1.73510	−0.867551	−	0.497348i	$-0.834307\pi$
$17$	−597510.	−1.73510	−0.867551	+	0.497348i	$0.834307\pi$
$18$	0	0
$19$	990146.i	1.74304i	0.490358	+	0.871521i	$0.336866\pi$
$19$	990146.i	1.74304i	−0.490358	+	0.871521i	$0.663134\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	1.95312e6	1.00000
$26$	0	0
$27$	− 620540.i	− 0.224715i
$28$	0	0
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	0	0
$33$	1.25480e7	1.84188
$34$	0	0
$35$	0	0
$36$	0	0
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	3.43064e7	1.89604	0.948020	−	0.318212i	$-0.103082\pi$
$41$	3.43064e7	1.89604	0.948020	+	0.318212i	$0.103082\pi$
$42$	0	0
$43$	4.47821e7i	1.99754i	0.0495450	+	0.998772i	$0.484223\pi$
$43$	4.47821e7i	1.99754i	−0.0495450	+	0.998772i	$0.515777\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	−4.03536e7	−1.00000
$50$	0	0
$51$	1.13527e8i	2.34981i
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	1.88128e8	2.36057
$58$	0	0
$59$	8.42438e7i	0.905116i	0.891735	+	0.452558i	$0.149488\pi$
$59$	8.42438e7i	0.905116i	−0.891735	+	0.452558i	$0.850512\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	0	0
$66$	0	0
$67$	− 6.28172e7i	− 0.380840i	−0.981703	−	0.190420i	$-0.939015\pi$
$67$	− 6.28172e7i	− 0.380840i	0.981703	−	0.190420i	$-0.0609849\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	4.22325e8	1.74058	0.870290	−	0.492540i	$-0.163932\pi$
$73$	4.22325e8	1.74058	0.870290	+	0.492540i	$0.163932\pi$
$74$	0	0
$75$	− 3.71094e8i	− 1.35428i
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	−4.41038e8	−1.13840
$82$	0	0
$83$	1.44638e8i	0.334526i	0.985912	+	0.167263i	$0.0534929\pi$
$83$	1.44638e8i	0.334526i	−0.985912	+	0.167263i	$0.946507\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	−1.08985e9	−1.84124	−0.920622	−	0.390455i	$-0.872318\pi$
$89$	−1.08985e9	−1.84124	−0.920622	+	0.390455i	$0.872318\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−1.73825e9	−1.99361	−0.996806	−	0.0798619i	$-0.974552\pi$
$97$	−1.73825e9	−1.99361	−0.996806	+	0.0798619i	$0.974552\pi$
$98$	0	0
$99$	− 1.08421e9i	− 1.13437i
$100$	0	0
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	− 1.28426e9i	− 0.947165i	−0.880749	−	0.473583i	$-0.842961\pi$
$107$	− 1.28426e9i	− 0.947165i	0.880749	−	0.473583i	$-0.157039\pi$
$108$	0	0
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	1.14906e9	0.662966	0.331483	−	0.943461i	$-0.392451\pi$
$113$	1.14906e9	0.662966	0.331483	+	0.943461i	$0.392451\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−2.00360e9	−0.849721
$122$	0	0
$123$	− 6.51821e9i	− 2.56776i
$124$	0	0
$125$	0	0
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	0	0
$129$	8.50860e9	2.70523
$130$	0	0
$131$	6.46052e9i	1.91667i	0.285651	+	0.958334i	$0.407790\pi$
$131$	6.46052e9i	1.91667i	−0.285651	+	0.958334i	$0.592210\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−5.96601e9	−1.44691	−0.723455	−	0.690372i	$-0.757447\pi$
$137$	−5.96601e9	−1.44691	−0.723455	+	0.690372i	$0.757447\pi$
$138$	0	0
$139$	8.67328e9i	1.97068i	0.170592	+	0.985342i	$0.445432\pi$
$139$	8.67328e9i	1.97068i	−0.170592	+	0.985342i	$0.554568\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	7.66719e9i	1.35428i
$148$	0	0
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	0	0
$153$	9.80932e9	1.44720
$154$	0	0
$155$	0	0
$156$	0	0
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	1.16898e10i	1.29707i	0.761186	+	0.648534i	$0.224618\pi$
$163$	1.16898e10i	1.29707i	−0.761186	+	0.648534i	$0.775382\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	1.06045e10	1.00000
$170$	0	0
$171$	− 1.62552e10i	− 1.45382i
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	1.60063e10	1.22578
$178$	0	0
$179$	9.60977e9i	0.699640i	0.936817	+	0.349820i	$0.113757\pi$
$179$	9.60977e9i	0.699640i	−0.936817	+	0.349820i	$0.886243\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	− 3.94608e10i	− 2.35982i
$188$	0	0
$189$	0	0
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	−3.59461e10	−1.86485	−0.932424	−	0.361366i	$-0.882310\pi$
$193$	−3.59461e10	−1.86485	−0.932424	+	0.361366i	$0.882310\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	−1.19353e10	−0.515763
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	−6.53912e10	−2.37062
$210$	0	0
$211$	5.65801e10i	1.96514i	0.185906	+	0.982568i	$0.440478\pi$
$211$	5.65801e10i	1.96514i	−0.185906	+	0.982568i	$0.559522\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	− 8.02417e10i	− 2.35723i
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	0	0
$225$	−3.20645e10	−0.834070
$226$	0	0
$227$	− 5.30439e10i	− 1.32593i	−0.748653	−	0.662963i	$-0.769299\pi$
$227$	− 5.30439e10i	− 1.32593i	0.748653	−	0.662963i	$-0.230701\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	9.57028e9	0.212727	0.106364	−	0.994327i	$-0.466079\pi$
$233$	9.57028e9	0.212727	0.106364	+	0.994327i	$0.466079\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	0	0
$241$	4.94901e10	0.945022	0.472511	−	0.881325i	$-0.343348\pi$
$241$	4.94901e10	0.945022	0.472511	+	0.881325i	$0.343348\pi$
$242$	0	0
$243$	7.15832e10i	1.31699i
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	2.74812e10	0.453041
$250$	0	0
$251$	− 1.24468e11i	− 1.97936i	−0.143286	−	0.989681i	$-0.545767\pi$
$251$	− 1.24468e11i	− 1.97936i	0.143286	−	0.989681i	$-0.454233\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	0	0
$257$	1.39114e11	1.98918	0.994588	−	0.103900i	$-0.0331322\pi$
$257$	1.39114e11	1.98918	0.994588	+	0.103900i	$0.0331322\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	2.07071e11i	2.49356i
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	1.28988e11i	1.36004i
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−1.93462e11	−1.85105	−0.925523	−	0.378691i	$-0.876374\pi$
$281$	−1.93462e11	−1.85105	−0.925523	+	0.378691i	$0.876374\pi$
$282$	0	0
$283$	− 2.82227e10i	− 0.261553i	−0.991412	−	0.130777i	$-0.958253\pi$
$283$	− 2.82227e10i	− 0.261553i	0.991412	−	0.130777i	$-0.0417471\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	2.38430e11	2.01058
$290$	0	0
$291$	3.30268e11i	2.69991i
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	4.09817e10	0.305623
$298$	0	0
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	− 1.83476e11i	− 1.17885i	−0.807825	−	0.589423i	$-0.799355\pi$
$307$	− 1.83476e11i	− 1.17885i	0.807825	−	0.589423i	$-0.200645\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	1.81231e11	1.06729	0.533645	−	0.845709i	$-0.320822\pi$
$313$	1.81231e11	1.06729	0.533645	+	0.845709i	$0.320822\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	−2.44009e11	−1.28273
$322$	0	0
$323$	− 5.91622e11i	− 3.02436i
$324$	0	0
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	3.36797e11i	1.54221i	0.636711	+	0.771103i	$0.280295\pi$
$331$	3.36797e11i	1.54221i	−0.636711	+	0.771103i	$0.719705\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	1.75370e11	0.740663	0.370331	−	0.928900i	$-0.379244\pi$
$337$	1.75370e11	0.740663	0.370331	+	0.928900i	$0.379244\pi$
$338$	0	0
$339$	− 2.18322e11i	− 0.897840i
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	− 5.36579e11i	− 1.98678i	−0.114767	−	0.993392i	$-0.536612\pi$
$347$	− 5.36579e11i	− 1.98678i	0.114767	−	0.993392i	$-0.463388\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	−5.20922e11	−1.78561	−0.892805	−	0.450443i	$-0.851266\pi$
$353$	−5.20922e11	−1.78561	−0.892805	+	0.450443i	$0.851266\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	−6.57701e11	−2.03820
$362$	0	0
$363$	3.80684e11i	1.15076i
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	0	0
$369$	−5.63208e11	−1.58143
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	3.17598e11i	0.790682i	0.918535	+	0.395341i	$0.129374\pi$
$379$	3.17598e11i	0.790682i	−0.918535	+	0.395341i	$0.870626\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	− 7.35188e11i	− 1.66609i
$388$	0	0
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	1.22750e12	2.59570
$394$	0	0
$395$	0	0
$396$	0	0
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−1.01120e12	−1.95293	−0.976465	−	0.215677i	$-0.930804\pi$
$401$	−1.01120e12	−1.95293	−0.976465	+	0.215677i	$0.930804\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	1.01244e12	1.78901	0.894506	−	0.447056i	$-0.147527\pi$
$409$	1.01244e12	1.78901	0.894506	+	0.447056i	$0.147527\pi$
$410$	0	0
$411$	1.13354e12i	1.95952i
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	1.64792e12	2.66885
$418$	0	0
$419$	− 1.03045e12i	− 1.63329i	−0.577138	−	0.816646i	$-0.695831\pi$
$419$	− 1.03045e12i	− 1.63329i	0.577138	−	0.816646i	$-0.304169\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	−1.16701e12	−1.73510
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	1.17467e12	1.60590	0.802951	−	0.596045i	$-0.203262\pi$
$433$	1.17467e12	1.60590	0.802951	+	0.596045i	$0.203262\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	6.62485e11	0.834070
$442$	0	0
$443$	1.33331e12i	1.64480i	0.568908	+	0.822401i	$0.307366\pi$
$443$	1.33331e12i	1.64480i	−0.568908	+	0.822401i	$0.692634\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	6.16206e11	0.715513	0.357757	−	0.933815i	$-0.383542\pi$
$449$	6.16206e11	0.715513	0.357757	+	0.933815i	$0.383542\pi$
$450$	0	0
$451$	2.26566e12i	2.57870i
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−7.26286e11	−0.778906	−0.389453	−	0.921046i	$-0.627336\pi$
$457$	−7.26286e11	−0.778906	−0.389453	+	0.921046i	$0.627336\pi$
$458$	0	0
$459$	3.70779e11i	0.389904i
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	0	0		−	1.00000i	$-0.5\pi$
$463$	0	0			1.00000i	$0.5\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	− 1.19702e12i	− 1.16459i	−0.812977	−	0.582296i	$-0.802154\pi$
$467$	− 1.19702e12i	− 1.16459i	0.812977	−	0.582296i	$-0.197846\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	−2.95750e12	−2.71675
$474$	0	0
$475$	1.93388e12i	1.74304i
$476$	0	0
$477$	0	0
$478$	0	0
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	0	0		−	1.00000i	$-0.5\pi$
$487$	0	0			1.00000i	$0.5\pi$
$488$	0	0
$489$	2.22106e12	1.75659
$490$	0	0
$491$	− 2.51449e12i	− 1.95247i	−0.216720	−	0.976234i	$-0.569536\pi$
$491$	− 2.51449e12i	− 1.95247i	0.216720	−	0.976234i	$-0.430464\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	− 7.46860e11i	− 0.539245i	−0.962966	−	0.269623i	$-0.913101\pi$
$499$	− 7.46860e11i	− 0.539245i	0.962966	−	0.269623i	$-0.0868990\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	− 2.01485e12i	− 1.35428i
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	6.14425e11	0.391689
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−3.11801e12	−1.85399	−0.926996	−	0.375070i	$-0.877619\pi$
$521$	−3.11801e12	−1.85399	−0.926996	+	0.375070i	$0.877619\pi$
$522$	0	0
$523$	− 1.93137e12i	− 1.12878i	−0.825509	−	0.564389i	$-0.809112\pi$
$523$	− 1.93137e12i	− 1.12878i	0.825509	−	0.564389i	$-0.190888\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−1.80115e12	−1.00000
$530$	0	0
$531$	− 1.38303e12i	− 0.754930i
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	1.82586e12	0.947507
$538$	0	0
$539$	− 2.66503e12i	− 1.36004i
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	2.96711e11i	0.141707i	0.997487	+	0.0708535i	$0.0225723\pi$
$547$	2.96711e11i	0.141707i	−0.997487	+	0.0708535i	$0.977428\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	−7.49754e12	−3.19585
$562$	0	0
$563$	5.89578e11i	0.247317i	0.992325	+	0.123658i	$0.0394627\pi$
$563$	5.89578e11i	0.247317i	−0.992325	+	0.123658i	$0.960537\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−1.30935e12	−0.523660	−0.261830	−	0.965114i	$-0.584326\pi$
$569$	−1.30935e12	−0.523660	−0.261830	+	0.965114i	$0.584326\pi$
$570$	0	0
$571$	4.66528e12i	1.83660i	0.395883	+	0.918301i	$0.370438\pi$
$571$	4.66528e12i	1.83660i	−0.395883	+	0.918301i	$0.629562\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	3.79461e12	1.42520	0.712600	−	0.701571i	$-0.247518\pi$
$577$	3.79461e12	1.42520	0.712600	+	0.701571i	$0.247518\pi$
$578$	0	0
$579$	6.82975e12i	2.52552i
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	− 5.17152e12i	− 1.79782i	−0.438132	−	0.898911i	$-0.644360\pi$
$587$	− 5.17152e12i	− 1.79782i	0.438132	−	0.898911i	$-0.355640\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	−1.58011e12	−0.524736	−0.262368	−	0.964968i	$-0.584503\pi$
$593$	−1.58011e12	−0.524736	−0.262368	+	0.964968i	$0.584503\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	6.39189e12	1.99845	0.999227	−	0.0393057i	$-0.0125146\pi$
$601$	6.39189e12	1.99845	0.999227	+	0.0393057i	$0.0125146\pi$
$602$	0	0
$603$	1.03127e12i	0.317647i
$604$	0	0
$605$	0	0
$606$	0	0
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	3.11849e12	0.866285	0.433142	−	0.901325i	$-0.357405\pi$
$617$	3.11849e12	0.866285	0.433142	+	0.901325i	$0.357405\pi$
$618$	0	0
$619$	− 7.10317e12i	− 1.94466i	−0.233605	−	0.972332i	$-0.575052\pi$
$619$	− 7.10317e12i	− 1.94466i	0.233605	−	0.972332i	$-0.424948\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	3.81470e12	1.00000
$626$	0	0
$627$	1.24243e13i	3.21047i
$628$	0	0
$629$	0	0
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	0	0
$633$	1.07502e13	2.66134
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	4.97864e12	1.16480	0.582398	−	0.812904i	$-0.302115\pi$
$641$	4.97864e12	1.16480	0.582398	+	0.812904i	$0.302115\pi$
$642$	0	0
$643$	5.01320e11i	0.115655i	0.998327	+	0.0578277i	$0.0184174\pi$
$643$	5.01320e11i	0.115655i	−0.998327	+	0.0578277i	$0.981583\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	0	0
$649$	−5.56363e12	−1.23100
$650$	0	0
$651$	0	0
$652$	0	0
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−6.93331e12	−1.45177
$658$	0	0
$659$	− 7.95235e11i	− 0.164252i	−0.996622	−	0.0821260i	$-0.973829\pi$
$659$	− 7.95235e11i	− 0.164252i	0.996622	−	0.0821260i	$-0.0261710\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	1.04817e13	1.96954	0.984770	−	0.173861i	$-0.0556244\pi$
$673$	1.04817e13	1.96954	0.984770	+	0.173861i	$0.0556244\pi$
$674$	0	0
$675$	− 1.21199e12i	− 0.224715i
$676$	0	0
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−1.00783e13	−1.79567
$682$	0	0
$683$	9.72628e12i	1.71023i	0.518441	+	0.855114i	$0.326513\pi$
$683$	9.72628e12i	1.71023i	−0.518441	+	0.855114i	$0.673487\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	1.95012e12i	0.325395i	0.986676	+	0.162697i	$0.0520194\pi$
$691$	1.95012e12i	0.325395i	−0.986676	+	0.162697i	$0.947981\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−2.04984e13	−3.28982
$698$	0	0
$699$	− 1.81835e12i	− 0.288092i
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	− 9.40312e12i	− 1.27982i
$724$	0	0
$725$	0	0
$726$	0	0
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	4.91985e12	0.645176
$730$	0	0
$731$	− 2.67577e13i	− 3.46594i
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	4.14858e12	0.517959
$738$	0	0
$739$	− 3.26770e12i	− 0.403034i	−0.979485	−	0.201517i	$-0.935413\pi$
$739$	− 3.26770e12i	− 0.403034i	0.979485	−	0.201517i	$-0.0645872\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	− 2.37452e12i	− 0.279018i
$748$	0	0
$749$	0	0
$750$	0	0
$751$	0	0		−	1.00000i	$-0.5\pi$
$751$	0	0			1.00000i	$0.5\pi$
$752$	0	0
$753$	−2.36489e13	−2.68061
$754$	0	0
$755$	0	0
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	5.25460e12	0.567948	0.283974	−	0.958832i	$-0.408347\pi$
$761$	5.25460e12	0.567948	0.283974	+	0.958832i	$0.408347\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	9.79474e12	1.01001	0.505004	−	0.863117i	$-0.331491\pi$
$769$	9.79474e12	1.01001	0.505004	+	0.863117i	$0.331491\pi$
$770$	0	0
$771$	− 2.64317e13i	− 2.69390i
$772$	0	0
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	3.39683e13i	3.30488i
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	0	0
$786$	0	0
$787$	− 9.82749e12i	− 0.913180i	−0.889677	−	0.456590i	$-0.849071\pi$
$787$	− 9.82749e12i	− 0.913180i	0.889677	−	0.456590i	$-0.150929\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	1.78921e13	1.53573
$802$	0	0
$803$	2.78912e13i	2.36727i
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−1.98350e13	−1.62804	−0.814019	−	0.580838i	$-0.802725\pi$
$809$	−1.98350e13	−1.62804	−0.814019	+	0.580838i	$0.802725\pi$
$810$	0	0
$811$	− 7.05897e12i	− 0.572991i	−0.958082	−	0.286495i	$-0.907510\pi$
$811$	− 7.05897e12i	− 0.572991i	0.958082	−	0.286495i	$-0.0924903\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−4.43408e13	−3.48180
$818$	0	0
$819$	0	0
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	0	0
$823$	0	0		−	1.00000i	$-0.5\pi$
$823$	0	0			1.00000i	$0.5\pi$
$824$	0	0
$825$	2.45078e13	1.84188
$826$	0	0
$827$	2.68972e13i	1.99955i	0.0212605	+	0.999774i	$0.493232\pi$
$827$	2.68972e13i	1.99955i	−0.0212605	+	0.999774i	$0.506768\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	2.41117e13	1.73510
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	1.45071e13	1.00000
$842$	0	0
$843$	3.67578e13i	2.50683i
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−5.36232e12	−0.354216
$850$	0	0
$851$	0	0
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	2.87124e13	1.81826	0.909130	−	0.416514i	$-0.136748\pi$
$857$	2.87124e13	1.81826	0.909130	+	0.416514i	$0.136748\pi$
$858$	0	0
$859$	8.30931e12i	0.520709i	0.965513	+	0.260355i	$0.0838395\pi$
$859$	8.30931e12i	0.520709i	−0.965513	+	0.260355i	$0.916160\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	− 4.53018e13i	− 2.72288i
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	2.85369e13	1.66281
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	1.28982e13	0.721338	0.360669	−	0.932694i	$-0.382548\pi$
$881$	1.28982e13	0.721338	0.360669	+	0.932694i	$0.382548\pi$
$882$	0	0
$883$	1.07779e13i	0.596639i	0.954466	+	0.298319i	$0.0964260\pi$
$883$	1.07779e13i	0.596639i	−0.954466	+	0.298319i	$0.903574\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	0	0		−	1.00000i	$-0.5\pi$
$887$	0	0			1.00000i	$0.5\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	− 2.91271e13i	− 1.54827i
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	4.06639e13i	1.99515i	0.0695888	+	0.997576i	$0.477831\pi$
$907$	4.06639e13i	1.99515i	−0.0695888	+	0.997576i	$0.522169\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	0	0
$913$	−9.55216e12	−0.454970
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	0	0
$921$	−3.48605e13	−1.59649
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	1.64173e13	0.723153	0.361576	−	0.932343i	$-0.382239\pi$
$929$	1.64173e13	0.723153	0.361576	+	0.932343i	$0.382239\pi$
$930$	0	0
$931$	− 3.99560e13i	− 1.74304i
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−3.92957e13	−1.66539	−0.832697	−	0.553729i	$-0.813204\pi$
$937$	−3.92957e13	−1.66539	−0.832697	+	0.553729i	$0.813204\pi$
$938$	0	0
$939$	− 3.44338e13i	− 1.44541i
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	4.90820e13i	1.98311i	0.129680	+	0.991556i	$0.458605\pi$
$947$	4.90820e13i	1.98311i	−0.129680	+	0.991556i	$0.541395\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	2.21437e13	0.869625	0.434813	−	0.900521i	$-0.356815\pi$
$953$	2.21437e13	0.869625	0.434813	+	0.900521i	$0.356815\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−2.64396e13	−1.00000
$962$	0	0
$963$	2.10837e13i	0.790002i
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0	0		−	1.00000i	$-0.5\pi$
$967$	0	0			1.00000i	$0.5\pi$
$968$	0	0
$969$	−1.12408e14	−4.09582
$970$	0	0
$971$	4.44928e11i	0.0160621i	0.999968	+	0.00803107i	$0.00255640\pi$
$971$	4.44928e11i	0.0160621i	−0.999968	+	0.00803107i	$0.997444\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−4.33557e13	−1.52237	−0.761185	−	0.648535i	$-0.775382\pi$
$977$	−4.33557e13	−1.52237	−0.761185	+	0.648535i	$0.775382\pi$
$978$	0	0
$979$	− 7.19758e13i	− 2.50417i
$980$	0	0
$981$	0	0
$982$	0	0
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	0	0
$993$	6.39914e13	2.08858
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.10.b.a.33.1	✓	2
4.3	odd	2	inner	64.10.b.a.33.2	yes	2
8.3	odd	2	CM	64.10.b.a.33.1	✓	2
8.5	even	2	inner	64.10.b.a.33.2	yes	2
16.3	odd	4		256.10.a.a.1.1		1
16.5	even	4		256.10.a.a.1.1		1
16.11	odd	4		256.10.a.d.1.1		1
16.13	even	4		256.10.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.10.b.a.33.1	✓	2	1.1	even	1	trivial
64.10.b.a.33.1	✓	2	8.3	odd	2	CM
64.10.b.a.33.2	yes	2	4.3	odd	2	inner
64.10.b.a.33.2	yes	2	8.5	even	2	inner
256.10.a.a.1.1		1	16.3	odd	4
256.10.a.a.1.1		1	16.5	even	4
256.10.a.d.1.1		1	16.11	odd	4
256.10.a.d.1.1		1	16.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	64.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-190.000i q^{3} -16417.0 q^{9} +O(q^{10})\)	\(q-190.000i q^{3} -16417.0 q^{9} +66042.0i q^{11} -597510. q^{17} +990146. i q^{19} +1.95312e6 q^{25} -620540. i q^{27} +1.25480e7 q^{33} +3.43064e7 q^{41} +4.47821e7i q^{43} -4.03536e7 q^{49} +1.13527e8i q^{51} +1.88128e8 q^{57} +8.42438e7i q^{59} -6.28172e7i q^{67} +4.22325e8 q^{73} -3.71094e8i q^{75} -4.41038e8 q^{81} +1.44638e8i q^{83} -1.08985e9 q^{89} -1.73825e9 q^{97} -1.08421e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32834 q^{9}+O(q^{10}) \) 2 * q - 32834 * q^9	\( 2 q - 32834 q^{9} - 1195020 q^{17} + 3906250 q^{25} + 25095960 q^{33} + 68612724 q^{41} - 80707214 q^{49} + 376255480 q^{57} + 844649860 q^{73} - 882076822 q^{81} - 2179698012 q^{89} - 3476509420 q^{97}+O(q^{100}) \) 2 * q - 32834 * q^9 - 1195020 * q^17 + 3906250 * q^25 + 25095960 * q^33 + 68612724 * q^41 - 80707214 * q^49 + 376255480 * q^57 + 844649860 * q^73 - 882076822 * q^81 - 2179698012 * q^89 - 3476509420 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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