LMFDB - Embedded newform 64.6.b.a.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,6,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, 6, names="a")

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

chi := DirichletCharacter("64.33");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 6 $
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:	$10.2645644680$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			33.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	64.33
Dual form			64.6.b.a.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{3} +239.000 q^{9} +474.000i q^{11} +1914.00 q^{17} +2882.00i q^{19} +3125.00 q^{25} +964.000i q^{27} -948.000 q^{33} -13926.0 q^{41} -22550.0i q^{43} -16807.0 q^{49} +3828.00i q^{51} -5764.00 q^{57} -48486.0i q^{59} +67186.0i q^{67} +50402.0 q^{73} +6250.00i q^{75} +56149.0 q^{81} +89298.0i q^{83} +7218.00 q^{89} +85450.0 q^{97} +113286. i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 478 q^{9} + 3828 q^{17} + 6250 q^{25} - 1896 q^{33} - 27852 q^{41} - 33614 q^{49} - 11528 q^{57} + 100804 q^{73} + 112298 q^{81} + 14436 q^{89} + 170900 q^{97}+O(q^{100}) $ 2 * q + 478 * q^9 + 3828 * q^17 + 6250 * q^25 - 1896 * q^33 - 27852 * q^41 - 33614 * q^49 - 11528 * q^57 + 100804 * q^73 + 112298 * q^81 + 14436 * q^89 + 170900 * q^97

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
$3$	2.00000i	0.128300i	0.997940	+	0.0641500i	$0.0204336\pi$
$3$	2.00000i	0.128300i	−0.997940	+	0.0641500i	$0.979566\pi$
$4$	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
$9$	239.000	0.983539
$10$	0	0
$11$	474.000i	1.18113i	0.806991	+	0.590564i	$0.201094\pi$
$11$	474.000i	1.18113i	−0.806991	+	0.590564i	$0.798906\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	1914.00	1.60627	0.803137	−	0.595794i	$-0.203163\pi$
$17$	1914.00	1.60627	0.803137	+	0.595794i	$0.203163\pi$
$18$	0	0
$19$	2882.00i	1.83151i	0.401734	+	0.915756i	$0.368408\pi$
$19$	2882.00i	1.83151i	−0.401734	+	0.915756i	$0.631592\pi$
$20$	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
$25$	3125.00	1.00000
$26$	0	0
$27$	964.000i	0.254488i
$28$	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
$33$	−948.000	−0.151539
$34$	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
$41$	−13926.0	−1.29380	−0.646899	−	0.762575i	$-0.723935\pi$
$41$	−13926.0	−1.29380	−0.646899	+	0.762575i	$0.723935\pi$
$42$	0	0
$43$	− 22550.0i	− 1.85984i	−0.367763	−	0.929920i	$-0.619876\pi$
$43$	− 22550.0i	− 1.85984i	0.367763	−	0.929920i	$-0.380124\pi$
$44$	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
$49$	−16807.0	−1.00000
$50$	0	0
$51$	3828.00i	0.206085i
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−5764.00	−0.234983
$58$	0	0
$59$	− 48486.0i	− 1.81337i	−0.421809	−	0.906685i	$-0.638605\pi$
$59$	− 48486.0i	− 1.81337i	0.421809	−	0.906685i	$-0.361395\pi$
$60$	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
$67$	67186.0i	1.82849i	0.405166	+	0.914243i	$0.367214\pi$
$67$	67186.0i	1.82849i	−0.405166	+	0.914243i	$0.632786\pi$
$68$	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
$73$	50402.0	1.10698	0.553491	−	0.832855i	$-0.313295\pi$
$73$	50402.0	1.10698	0.553491	+	0.832855i	$0.313295\pi$
$74$	0	0
$75$	6250.00i	0.128300i
$76$	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
$81$	56149.0	0.950888
$82$	0	0
$83$	89298.0i	1.42281i	0.702783	+	0.711404i	$0.251941\pi$
$83$	89298.0i	1.42281i	−0.702783	+	0.711404i	$0.748059\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	7218.00	0.0965922	0.0482961	−	0.998833i	$-0.484621\pi$
$89$	7218.00	0.0965922	0.0482961	+	0.998833i	$0.484621\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	85450.0	0.922110	0.461055	−	0.887372i	$-0.347471\pi$
$97$	85450.0	0.922110	0.461055	+	0.887372i	$0.347471\pi$
$98$	0	0
$99$	113286.i	1.16168i
$100$	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
$107$	− 235686.i	− 1.99010i	−0.0993883	−	0.995049i	$-0.531689\pi$
$107$	− 235686.i	− 1.99010i	0.0993883	−	0.995049i	$-0.468311\pi$
$108$	0	0
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−256302.	−1.88823	−0.944117	−	0.329610i	$-0.893083\pi$
$113$	−256302.	−1.88823	−0.944117	+	0.329610i	$0.893083\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−63625.0	−0.395061
$122$	0	0
$123$	− 27852.0i	− 0.165994i
$124$	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
$129$	45100.0	0.238617
$130$	0	0
$131$	− 385902.i	− 1.96471i	−0.187022	−	0.982356i	$-0.559884\pi$
$131$	− 385902.i	− 1.96471i	0.187022	−	0.982356i	$-0.440116\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−422886.	−1.92496	−0.962480	−	0.271351i	$-0.912530\pi$
$137$	−422886.	−1.92496	−0.962480	+	0.271351i	$0.912530\pi$
$138$	0	0
$139$	121418.i	0.533023i	0.963832	+	0.266512i	$0.0858711\pi$
$139$	121418.i	0.533023i	−0.963832	+	0.266512i	$0.914129\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	− 33614.0i	− 0.128300i
$148$	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
$153$	457446.	1.57983
$154$	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
$163$	259202.i	0.764134i	0.924135	+	0.382067i	$0.124788\pi$
$163$	259202.i	0.764134i	−0.924135	+	0.382067i	$0.875212\pi$
$164$	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
$169$	371293.	1.00000
$170$	0	0
$171$	688798.i	1.80136i
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	96972.0	0.232655
$178$	0	0
$179$	− 446382.i	− 1.04130i	−0.853772	−	0.520648i	$-0.825690\pi$
$179$	− 446382.i	− 1.04130i	0.853772	−	0.520648i	$-0.174310\pi$
$180$	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
$187$	907236.i	1.89721i
$188$	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
$193$	1.02430e6	1.97940	0.989699	−	0.143165i	$-0.0457280\pi$
$193$	1.02430e6	1.97940	0.989699	+	0.143165i	$0.0457280\pi$
$194$	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
$201$	−134372.	−0.234595
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	−1.36607e6	−2.16325
$210$	0	0
$211$	− 759374.i	− 1.17422i	−0.809507	−	0.587110i	$-0.800266\pi$
$211$	− 759374.i	− 1.17422i	0.809507	−	0.587110i	$-0.199734\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	100804.i	0.142026i
$220$	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
$225$	746875.	0.983539
$226$	0	0
$227$	− 1.38435e6i	− 1.78312i	−0.452900	−	0.891561i	$-0.649610\pi$
$227$	− 1.38435e6i	− 1.78312i	0.452900	−	0.891561i	$-0.350390\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−988350.	−1.19267	−0.596336	−	0.802735i	$-0.703377\pi$
$233$	−988350.	−1.19267	−0.596336	+	0.802735i	$0.703377\pi$
$234$	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
$241$	−1.74717e6	−1.93773	−0.968866	−	0.247587i	$-0.920362\pi$
$241$	−1.74717e6	−1.93773	−0.968866	+	0.247587i	$0.920362\pi$
$242$	0	0
$243$	346550.i	0.376487i
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	−178596.	−0.182546
$250$	0	0
$251$	− 1.62673e6i	− 1.62978i	−0.579613	−	0.814892i	$-0.696796\pi$
$251$	− 1.62673e6i	− 1.62978i	0.579613	−	0.814892i	$-0.303204\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	0	0
$257$	487650.	0.460549	0.230274	−	0.973126i	$-0.426038\pi$
$257$	487650.	0.460549	0.230274	+	0.973126i	$0.426038\pi$
$258$	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
$267$	14436.0i	0.0123928i
$268$	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
$275$	1.48125e6i	1.18113i
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	802098.	0.605985	0.302992	−	0.952993i	$-0.402014\pi$
$281$	802098.	0.605985	0.302992	+	0.952993i	$0.402014\pi$
$282$	0	0
$283$	1.10350e6i	0.819041i	0.912301	+	0.409520i	$0.134304\pi$
$283$	1.10350e6i	0.819041i	−0.912301	+	0.409520i	$0.865696\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	2.24354e6	1.58012
$290$	0	0
$291$	170900.i	0.118307i
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−456936.	−0.300583
$298$	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
$307$	1.12611e6i	0.681925i	0.940077	+	0.340962i	$0.110753\pi$
$307$	1.12611e6i	0.681925i	−0.940077	+	0.340962i	$0.889247\pi$
$308$	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
$313$	3.43345e6	1.98093	0.990467	−	0.137752i	$-0.0439878\pi$
$313$	3.43345e6	1.98093	0.990467	+	0.137752i	$0.0439878\pi$
$314$	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
$321$	471372.	0.255330
$322$	0	0
$323$	5.51615e6i	2.94191i
$324$	0	0
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	− 2.96397e6i	− 1.48698i	−0.668748	−	0.743489i	$-0.733170\pi$
$331$	− 2.96397e6i	− 1.48698i	0.668748	−	0.743489i	$-0.266830\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−3.86401e6	−1.85338	−0.926689	−	0.375829i	$-0.877358\pi$
$337$	−3.86401e6	−1.85338	−0.926689	+	0.375829i	$0.877358\pi$
$338$	0	0
$339$	− 512604.i	− 0.242261i
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	− 3.24529e6i	− 1.44687i	−0.690393	−	0.723435i	$-0.742562\pi$
$347$	− 3.24529e6i	− 1.44687i	0.690393	−	0.723435i	$-0.257438\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	4.66365e6	1.99200	0.996000	−	0.0893570i	$-0.0284812\pi$
$353$	4.66365e6	1.99200	0.996000	+	0.0893570i	$0.0284812\pi$
$354$	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
$361$	−5.82982e6	−2.35444
$362$	0	0
$363$	− 127250.i	− 0.0506864i
$364$	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
$369$	−3.32831e6	−1.27250
$370$	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
$379$	− 2.54452e6i	− 0.909929i	−0.890510	−	0.454964i	$-0.849652\pi$
$379$	− 2.54452e6i	− 0.909929i	0.890510	−	0.454964i	$-0.150348\pi$
$380$	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
$387$	− 5.38945e6i	− 1.82922i
$388$	0	0
$389$	0	0	1.00000			$0$
$389$	0	0	−1.00000			$\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	771804.	0.252073
$394$	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
$401$	−4.39873e6	−1.36605	−0.683024	−	0.730396i	$-0.739336\pi$
$401$	−4.39873e6	−1.36605	−0.683024	+	0.730396i	$0.739336\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−1.77938e6	−0.525970	−0.262985	−	0.964800i	$-0.584707\pi$
$409$	−1.77938e6	−0.525970	−0.262985	+	0.964800i	$0.584707\pi$
$410$	0	0
$411$	− 845772.i	− 0.246973i
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−242836.	−0.0683869
$418$	0	0
$419$	5.47202e6i	1.52269i	0.648345	+	0.761347i	$0.275461\pi$
$419$	5.47202e6i	1.52269i	−0.648345	+	0.761347i	$0.724539\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	5.98125e6	1.60627
$426$	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
$433$	3.93980e6	1.00984	0.504922	−	0.863165i	$-0.331521\pi$
$433$	3.93980e6	1.00984	0.504922	+	0.863165i	$0.331521\pi$
$434$	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
$441$	−4.01687e6	−0.983539
$442$	0	0
$443$	7.79860e6i	1.88802i	0.329912	+	0.944012i	$0.392981\pi$
$443$	7.79860e6i	1.88802i	−0.329912	+	0.944012i	$0.607019\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	6.69988e6	1.56838	0.784190	−	0.620521i	$-0.213079\pi$
$449$	6.69988e6	1.56838	0.784190	+	0.620521i	$0.213079\pi$
$450$	0	0
$451$	− 6.60092e6i	− 1.52814i
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−1.12941e6	−0.252966	−0.126483	−	0.991969i	$-0.540369\pi$
$457$	−1.12941e6	−0.252966	−0.126483	+	0.991969i	$0.540369\pi$
$458$	0	0
$459$	1.84510e6i	0.408778i
$460$	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
$467$	6.03165e6i	1.27981i	0.768456	+	0.639903i	$0.221025\pi$
$467$	6.03165e6i	1.27981i	−0.768456	+	0.639903i	$0.778975\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	1.06887e7	2.19671
$474$	0	0
$475$	9.00625e6i	1.83151i
$476$	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
$489$	−518404.	−0.0980384
$490$	0	0
$491$	− 567798.i	− 0.106289i	−0.998587	−	0.0531447i	$-0.983076\pi$
$491$	− 567798.i	− 0.106289i	0.998587	−	0.0531447i	$-0.0169245\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	− 1.11216e7i	− 1.99948i	−0.0228636	−	0.999739i	$-0.507278\pi$
$499$	− 1.11216e7i	− 1.99948i	0.0228636	−	0.999739i	$-0.492722\pi$
$500$	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
$507$	742586.i	0.128300i
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−2.77825e6	−0.466098
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−7.58833e6	−1.22476	−0.612381	−	0.790563i	$-0.709788\pi$
$521$	−7.58833e6	−1.22476	−0.612381	+	0.790563i	$0.709788\pi$
$522$	0	0
$523$	1.22846e7i	1.96384i	0.189287	+	0.981922i	$0.439382\pi$
$523$	1.22846e7i	1.96384i	−0.189287	+	0.981922i	$0.560618\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−6.43634e6	−1.00000
$530$	0	0
$531$	− 1.15882e7i	− 1.78352i
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	892764.	0.133598
$538$	0	0
$539$	− 7.96652e6i	− 1.18113i
$540$	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
$547$	− 8.56709e6i	− 1.22424i	−0.790767	−	0.612118i	$-0.790318\pi$
$547$	− 8.56709e6i	− 1.22424i	0.790767	−	0.612118i	$-0.209682\pi$
$548$	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
$561$	−1.81447e6	−0.243413
$562$	0	0
$563$	4.15965e6i	0.553077i	0.961003	+	0.276539i	$0.0891874\pi$
$563$	4.15965e6i	0.553077i	−0.961003	+	0.276539i	$0.910813\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−1.20993e7	−1.56668	−0.783340	−	0.621594i	$-0.786486\pi$
$569$	−1.20993e7	−1.56668	−0.783340	+	0.621594i	$0.786486\pi$
$570$	0	0
$571$	− 1.06181e7i	− 1.36288i	−0.731875	−	0.681438i	$-0.761355\pi$
$571$	− 1.06181e7i	− 1.36288i	0.731875	−	0.681438i	$-0.238645\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−1.13587e7	−1.42033	−0.710164	−	0.704036i	$-0.751379\pi$
$577$	−1.13587e7	−1.42033	−0.710164	+	0.704036i	$0.751379\pi$
$578$	0	0
$579$	2.04860e6i	0.253957i
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	− 9.71089e6i	− 1.16322i	−0.813466	−	0.581612i	$-0.802422\pi$
$587$	− 9.71089e6i	− 1.16322i	0.813466	−	0.581612i	$-0.197578\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	1.62461e7	1.89720	0.948598	−	0.316483i	$-0.102502\pi$
$593$	1.62461e7	1.89720	0.948598	+	0.316483i	$0.102502\pi$
$594$	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
$601$	3.45547e6	0.390231	0.195115	−	0.980780i	$-0.437492\pi$
$601$	3.45547e6	0.390231	0.195115	+	0.980780i	$0.437492\pi$
$602$	0	0
$603$	1.60575e7i	1.79839i
$604$	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
$617$	1.89165e6	0.200045	0.100023	−	0.994985i	$-0.468109\pi$
$617$	1.89165e6	0.200045	0.100023	+	0.994985i	$0.468109\pi$
$618$	0	0
$619$	7.29459e6i	0.765198i	0.923914	+	0.382599i	$0.124971\pi$
$619$	7.29459e6i	0.765198i	−0.923914	+	0.382599i	$0.875029\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	9.76562e6	1.00000
$626$	0	0
$627$	− 2.73214e6i	− 0.277545i
$628$	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
$633$	1.51875e6	0.150653
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	−2.04758e7	−1.96832	−0.984160	−	0.177282i	$-0.943270\pi$
$641$	−2.04758e7	−1.96832	−0.984160	+	0.177282i	$0.943270\pi$
$642$	0	0
$643$	1.39872e7i	1.33415i	0.744990	+	0.667075i	$0.232454\pi$
$643$	1.39872e7i	1.33415i	−0.744990	+	0.667075i	$0.767546\pi$
$644$	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
$649$	2.29824e7	2.14182
$650$	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
$657$	1.20461e7	1.08876
$658$	0	0
$659$	2.17584e7i	1.95170i	0.218435	+	0.975852i	$0.429905\pi$
$659$	2.17584e7i	1.95170i	−0.218435	+	0.975852i	$0.570095\pi$
$660$	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
$673$	1.93814e7	1.64949	0.824743	−	0.565508i	$-0.191320\pi$
$673$	1.93814e7	1.64949	0.824743	+	0.565508i	$0.191320\pi$
$674$	0	0
$675$	3.01250e6i	0.254488i
$676$	0	0
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	2.76870e6	0.228775
$682$	0	0
$683$	− 2.43566e7i	− 1.99786i	−0.0462568	−	0.998930i	$-0.514729\pi$
$683$	− 2.43566e7i	− 1.99786i	0.0462568	−	0.998930i	$-0.485271\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	2.05123e7i	1.63425i	0.576460	+	0.817125i	$0.304434\pi$
$691$	2.05123e7i	1.63425i	−0.576460	+	0.817125i	$0.695566\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−2.66544e7	−2.07820
$698$	0	0
$699$	− 1.97670e6i	− 0.153020i
$700$	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
$723$	− 3.49435e6i	− 0.248611i
$724$	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
$729$	1.29511e7	0.902585
$730$	0	0
$731$	− 4.31607e7i	− 2.98741i
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−3.18462e7	−2.15968
$738$	0	0
$739$	− 6.95229e6i	− 0.468292i	−0.972201	−	0.234146i	$-0.924771\pi$
$739$	− 6.95229e6i	− 0.468292i	0.972201	−	0.234146i	$-0.0752293\pi$
$740$	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
$747$	2.13422e7i	1.39939i
$748$	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
$753$	3.25345e6	0.209101
$754$	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
$761$	−1.63772e7	−1.02513	−0.512563	−	0.858650i	$-0.671304\pi$
$761$	−1.63772e7	−1.02513	−0.512563	+	0.858650i	$0.671304\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−2.92618e7	−1.78437	−0.892185	−	0.451670i	$-0.850828\pi$
$769$	−2.92618e7	−1.78437	−0.892185	+	0.451670i	$0.850828\pi$
$770$	0	0
$771$	975300.i	0.0590884i
$772$	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
$779$	− 4.01347e7i	− 2.36961i
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	0	0
$786$	0	0
$787$	− 2.45328e7i	− 1.41192i	−0.708253	−	0.705959i	$-0.750516\pi$
$787$	− 2.45328e7i	− 1.41192i	0.708253	−	0.705959i	$-0.249484\pi$
$788$	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
$801$	1.72510e6	0.0950022
$802$	0	0
$803$	2.38905e7i	1.30749i
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−1.87685e7	−1.00823	−0.504113	−	0.863638i	$-0.668181\pi$
$809$	−1.87685e7	−1.00823	−0.504113	+	0.863638i	$0.668181\pi$
$810$	0	0
$811$	1.83038e7i	0.977213i	0.872504	+	0.488606i	$0.162495\pi$
$811$	1.83038e7i	0.977213i	−0.872504	+	0.488606i	$0.837505\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	6.49891e7	3.40632
$818$	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
$825$	−2.96250e6	−0.151539
$826$	0	0
$827$	7.28779e6i	0.370537i	0.982688	+	0.185269i	$0.0593155\pi$
$827$	7.28779e6i	0.370537i	−0.982688	+	0.185269i	$0.940684\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	−3.21686e7	−1.60627
$834$	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
$841$	2.05111e7	1.00000
$842$	0	0
$843$	1.60420e6i	0.0777479i
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	0	0
$849$	−2.20700e6	−0.105083
$850$	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
$857$	1.72670e7	0.803090	0.401545	−	0.915839i	$-0.368473\pi$
$857$	1.72670e7	0.803090	0.401545	+	0.915839i	$0.368473\pi$
$858$	0	0
$859$	3.23362e7i	1.49522i	0.664136	+	0.747612i	$0.268800\pi$
$859$	3.23362e7i	1.49522i	−0.664136	+	0.747612i	$0.731200\pi$
$860$	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
$867$	4.48708e6i	0.202729i
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	2.04226e7	0.906931
$874$	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
$881$	4.60541e7	1.99907	0.999536	−	0.0304540i	$-0.00969531\pi$
$881$	4.60541e7	1.99907	0.999536	+	0.0304540i	$0.00969531\pi$
$882$	0	0
$883$	7.76160e6i	0.335004i	0.985872	+	0.167502i	$0.0535700\pi$
$883$	7.76160e6i	0.335004i	−0.985872	+	0.167502i	$0.946430\pi$
$884$	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
$891$	2.66146e7i	1.12312i
$892$	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
$907$	3.66974e7i	1.48121i	0.671939	+	0.740607i	$0.265462\pi$
$907$	3.66974e7i	1.48121i	−0.671939	+	0.740607i	$0.734538\pi$
$908$	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
$913$	−4.23273e7	−1.68052
$914$	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
$921$	−2.25223e6	−0.0874910
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	3.92342e7	1.49151	0.745754	−	0.666222i	$-0.232090\pi$
$929$	3.92342e7	1.49151	0.745754	+	0.666222i	$0.232090\pi$
$930$	0	0
$931$	− 4.84378e7i	− 1.83151i
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	1.05509e7	0.392592	0.196296	−	0.980545i	$-0.437109\pi$
$937$	1.05509e7	0.392592	0.196296	+	0.980545i	$0.437109\pi$
$938$	0	0
$939$	6.86690e6i	0.254154i
$940$	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
$947$	− 3.09764e7i	− 1.12242i	−0.827674	−	0.561210i	$-0.810336\pi$
$947$	− 3.09764e7i	− 1.12242i	0.827674	−	0.561210i	$-0.189664\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−3.16142e7	−1.12759	−0.563793	−	0.825916i	$-0.690659\pi$
$953$	−3.16142e7	−1.12759	−0.563793	+	0.825916i	$0.690659\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−2.86292e7	−1.00000
$962$	0	0
$963$	− 5.63290e7i	− 1.95734i
$964$	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
$969$	−1.10323e7	−0.377447
$970$	0	0
$971$	5.07556e7i	1.72757i	0.503859	+	0.863786i	$0.331913\pi$
$971$	5.07556e7i	1.72757i	−0.503859	+	0.863786i	$0.668087\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−2.75885e7	−0.924680	−0.462340	−	0.886703i	$-0.652990\pi$
$977$	−2.75885e7	−0.924680	−0.462340	+	0.886703i	$0.652990\pi$
$978$	0	0
$979$	3.42133e6i	0.114088i
$980$	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
$993$	5.92795e6	0.190779
$994$	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	64.6.b.a.33.2	yes	2
3.2	odd	2		576.6.d.a.289.1		2
4.3	odd	2	inner	64.6.b.a.33.1	✓	2
8.3	odd	2	CM	64.6.b.a.33.2	yes	2
8.5	even	2	inner	64.6.b.a.33.1	✓	2
12.11	even	2		576.6.d.a.289.2		2
16.3	odd	4		256.6.a.d.1.1		1
16.5	even	4		256.6.a.d.1.1		1
16.11	odd	4		256.6.a.a.1.1		1
16.13	even	4		256.6.a.a.1.1		1
24.5	odd	2		576.6.d.a.289.2		2
24.11	even	2		576.6.d.a.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.6.b.a.33.1	✓	2	4.3	odd	2	inner
64.6.b.a.33.1	✓	2	8.5	even	2	inner
64.6.b.a.33.2	yes	2	1.1	even	1	trivial
64.6.b.a.33.2	yes	2	8.3	odd	2	CM
256.6.a.a.1.1		1	16.11	odd	4
256.6.a.a.1.1		1	16.13	even	4
256.6.a.d.1.1		1	16.3	odd	4
256.6.a.d.1.1		1	16.5	even	4
576.6.d.a.289.1		2	3.2	odd	2
576.6.d.a.289.1		2	24.11	even	2
576.6.d.a.289.2		2	12.11	even	2
576.6.d.a.289.2		2	24.5	odd	2

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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	64.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{3} +239.000 q^{9} +474.000i q^{11} +1914.00 q^{17} +2882.00i q^{19} +3125.00 q^{25} +964.000i q^{27} -948.000 q^{33} -13926.0 q^{41} -22550.0i q^{43} -16807.0 q^{49} +3828.00i q^{51} -5764.00 q^{57} -48486.0i q^{59} +67186.0i q^{67} +50402.0 q^{73} +6250.00i q^{75} +56149.0 q^{81} +89298.0i q^{83} +7218.00 q^{89} +85450.0 q^{97} +113286. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 478 q^{9} + 3828 q^{17} + 6250 q^{25} - 1896 q^{33} - 27852 q^{41} - 33614 q^{49} - 11528 q^{57} + 100804 q^{73} + 112298 q^{81} + 14436 q^{89} + 170900 q^{97}+O(q^{100}) \) 2 * q + 478 * q^9 + 3828 * q^17 + 6250 * q^25 - 1896 * q^33 - 27852 * q^41 - 33614 * q^49 - 11528 * q^57 + 100804 * q^73 + 112298 * q^81 + 14436 * q^89 + 170900 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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