LMFDB - Embedded newform 1764.2.e.e.1079.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1079,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1764.1079");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.e (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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1079.3
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1764.1079
Dual form			1764.2.e.e.1079.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -2.00000 q^{4} -2.00000i q^{5} -2.82843i q^{8} +O(q^{10})$	$q+1.41421i q^{2} -2.00000 q^{4} -2.00000i q^{5} -2.82843i q^{8} +2.82843 q^{10} -7.07107 q^{13} +4.00000 q^{16} +2.00000i q^{17} +4.00000i q^{20} +1.00000 q^{25} -10.0000i q^{26} +9.89949i q^{29} +5.65685i q^{32} -2.82843 q^{34} +12.0000 q^{37} -5.65685 q^{40} +8.00000i q^{41} +1.41421i q^{50} +14.1421 q^{52} +12.7279i q^{53} -14.0000 q^{58} +15.5563 q^{61} -8.00000 q^{64} +14.1421i q^{65} -4.00000i q^{68} +7.07107 q^{73} +16.9706i q^{74} -8.00000i q^{80} -11.3137 q^{82} +4.00000 q^{85} +16.0000i q^{89} -18.3848 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{4}+O(q^{10}) $ 4 * q - 8 * q^4	$ 4 q - 8 q^{4} + 16 q^{16} + 4 q^{25} + 48 q^{37} - 56 q^{58} - 32 q^{64} + 16 q^{85}+O(q^{100}) $ 4 * q - 8 * q^4 + 16 * q^16 + 4 * q^25 + 48 * q^37 - 56 * q^58 - 32 * q^64 + 16 * q^85

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	1.41421i	1.00000i
$2$	1.41421i	1.00000i
$3$	0	0
$3$	0	0
$4$	−2.00000	−1.00000
$5$	− 2.00000i	− 0.894427i	−0.894427	−	0.447214i	$-0.852416\pi$
$5$	− 2.00000i	− 0.894427i	0.894427	−	0.447214i	$-0.147584\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	− 2.82843i	− 1.00000i
$9$	0	0
$10$	2.82843	0.894427
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	0	0
$13$	−7.07107	−1.96116	−0.980581	−	0.196116i	$-0.937167\pi$
$13$	−7.07107	−1.96116	−0.980581	+	0.196116i	$0.937167\pi$
$14$	0	0
$15$	0	0
$16$	4.00000	1.00000
$17$	2.00000i	0.485071i	0.970143	+	0.242536i	$0.0779791\pi$
$17$	2.00000i	0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	4.00000i	0.894427i
$21$	0	0
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	− 10.0000i	− 1.96116i
$27$	0	0
$28$	0	0
$29$	9.89949i	1.83829i	0.393919	+	0.919145i	$0.371119\pi$
$29$	9.89949i	1.83829i	−0.393919	+	0.919145i	$0.628881\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	5.65685i	1.00000i
$33$	0	0
$34$	−2.82843	−0.485071
$35$	0	0
$36$	0	0
$37$	12.0000	1.97279	0.986394	−	0.164399i	$-0.0525685\pi$
$37$	12.0000	1.97279	0.986394	+	0.164399i	$0.0525685\pi$
$38$	0	0
$39$	0	0
$40$	−5.65685	−0.894427
$41$	8.00000i	1.24939i	0.780869	+	0.624695i	$0.214777\pi$
$41$	8.00000i	1.24939i	−0.780869	+	0.624695i	$0.785223\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	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
$49$	0	0
$50$	1.41421i	0.200000i
$51$	0	0
$52$	14.1421	1.96116
$53$	12.7279i	1.74831i	0.485643	+	0.874157i	$0.338586\pi$
$53$	12.7279i	1.74831i	−0.485643	+	0.874157i	$0.661414\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	−14.0000	−1.83829
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	0	0
$61$	15.5563	1.99179	0.995893	−	0.0905357i	$-0.0288579\pi$
$61$	15.5563	1.99179	0.995893	+	0.0905357i	$0.0288579\pi$
$62$	0	0
$63$	0	0
$64$	−8.00000	−1.00000
$65$	14.1421i	1.75412i
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	− 4.00000i	− 0.485071i
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	7.07107	0.827606	0.413803	−	0.910366i	$-0.364200\pi$
$73$	7.07107	0.827606	0.413803	+	0.910366i	$0.364200\pi$
$74$	16.9706i	1.97279i
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	− 8.00000i	− 0.894427i
$81$	0	0
$82$	−11.3137	−1.24939
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	4.00000	0.433861
$86$	0	0
$87$	0	0
$88$	0	0
$89$	16.0000i	1.69600i	0.529999	+	0.847998i	$0.322192\pi$
$89$	16.0000i	1.69600i	−0.529999	+	0.847998i	$0.677808\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−18.3848	−1.86669	−0.933346	−	0.358979i	$-0.883125\pi$
$97$	−18.3848	−1.86669	−0.933346	+	0.358979i	$0.883125\pi$
$98$	0	0
$99$	0	0
$100$	−2.00000	−0.200000
$101$	− 20.0000i	− 1.99007i	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	− 20.0000i	− 1.99007i	0.0995037	−	0.995037i	$-0.468274\pi$
$102$	0	0
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	20.0000i	1.96116i
$105$	0	0
$106$	−18.0000	−1.74831
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	0	0
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	21.2132i	1.99557i	0.0665190	+	0.997785i	$0.478811\pi$
$113$	21.2132i	1.99557i	−0.0665190	+	0.997785i	$0.521189\pi$
$114$	0	0
$115$	0	0
$116$	− 19.7990i	− 1.83829i
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−11.0000	−1.00000
$122$	22.0000i	1.99179i
$123$	0	0
$124$	0	0
$125$	− 12.0000i	− 1.07331i
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	− 11.3137i	− 1.00000i
$129$	0	0
$130$	−20.0000	−1.75412
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	5.65685	0.485071
$137$	9.89949i	0.845771i	0.906183	+	0.422885i	$0.138983\pi$
$137$	9.89949i	0.845771i	−0.906183	+	0.422885i	$0.861017\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	19.7990	1.64422
$146$	10.0000i	0.827606i
$147$	0	0
$148$	−24.0000	−1.97279
$149$	− 4.24264i	− 0.347571i	−0.984784	−	0.173785i	$-0.944400\pi$
$149$	− 4.24264i	− 0.347571i	0.984784	−	0.173785i	$-0.0555999\pi$
$150$	0	0
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−24.0416	−1.91873	−0.959366	−	0.282166i	$-0.908947\pi$
$157$	−24.0416	−1.91873	−0.959366	+	0.282166i	$0.908947\pi$
$158$	0	0
$159$	0	0
$160$	11.3137	0.894427
$161$	0	0
$162$	0	0
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	− 16.0000i	− 1.24939i
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	37.0000	2.84615
$170$	5.65685i	0.433861i
$171$	0	0
$172$	0	0
$173$	− 4.00000i	− 0.304114i	−0.988372	−	0.152057i	$-0.951410\pi$
$173$	− 4.00000i	− 0.304114i	0.988372	−	0.152057i	$-0.0485898\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	−22.6274	−1.69600
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	−1.41421	−0.105118	−0.0525588	−	0.998618i	$-0.516738\pi$
$181$	−1.41421	−0.105118	−0.0525588	+	0.998618i	$0.516738\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	− 24.0000i	− 1.76452i
$186$	0	0
$187$	0	0
$188$	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
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	− 26.0000i	− 1.86669i
$195$	0	0
$196$	0	0
$197$	− 21.2132i	− 1.51138i	−0.654931	−	0.755689i	$-0.727302\pi$
$197$	− 21.2132i	− 1.51138i	0.654931	−	0.755689i	$-0.272698\pi$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	− 2.82843i	− 0.200000i
$201$	0	0
$202$	28.2843	1.99007
$203$	0	0
$204$	0	0
$205$	16.0000	1.11749
$206$	0	0
$207$	0	0
$208$	−28.2843	−1.96116
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	− 25.4558i	− 1.74831i
$213$	0	0
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	− 8.48528i	− 0.574696i
$219$	0	0
$220$	0	0
$221$	− 14.1421i	− 0.951303i
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	0	0
$225$	0	0
$226$	−30.0000	−1.99557
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	0	0
$229$	24.0416	1.58872	0.794358	−	0.607450i	$-0.207808\pi$
$229$	24.0416	1.58872	0.794358	+	0.607450i	$0.207808\pi$
$230$	0	0
$231$	0	0
$232$	28.0000	1.83829
$233$	7.07107i	0.463241i	0.972806	+	0.231621i	$0.0744028\pi$
$233$	7.07107i	0.463241i	−0.972806	+	0.231621i	$0.925597\pi$
$234$	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
$241$	−15.5563	−1.00207	−0.501036	−	0.865426i	$-0.667048\pi$
$241$	−15.5563	−1.00207	−0.501036	+	0.865426i	$0.667048\pi$
$242$	− 15.5563i	− 1.00000i
$243$	0	0
$244$	−31.1127	−1.99179
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	16.9706	1.07331
$251$	0	0		−	1.00000i	$-0.5\pi$
$251$	0	0			1.00000i	$0.5\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	16.0000	1.00000
$257$	32.0000i	1.99611i	0.0623783	+	0.998053i	$0.480131\pi$
$257$	32.0000i	1.99611i	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	0	0
$259$	0	0
$260$	− 28.2843i	− 1.75412i
$261$	0	0
$262$	0	0
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	25.4558	1.56374
$266$	0	0
$267$	0	0
$268$	0	0
$269$	26.0000i	1.58525i	0.609711	+	0.792624i	$0.291286\pi$
$269$	26.0000i	1.58525i	−0.609711	+	0.792624i	$0.708714\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	8.00000i	0.485071i
$273$	0	0
$274$	−14.0000	−0.845771
$275$	0	0
$276$	0	0
$277$	28.0000	1.68236	0.841178	−	0.540758i	$-0.181862\pi$
$277$	28.0000	1.68236	0.841178	+	0.540758i	$0.181862\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	15.5563i	0.928014i	0.885832	+	0.464007i	$0.153589\pi$
$281$	15.5563i	0.928014i	−0.885832	+	0.464007i	$0.846411\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	13.0000	0.764706
$290$	28.0000i	1.64422i
$291$	0	0
$292$	−14.1421	−0.827606
$293$	4.00000i	0.233682i	0.993151	+	0.116841i	$0.0372769\pi$
$293$	4.00000i	0.233682i	−0.993151	+	0.116841i	$0.962723\pi$
$294$	0	0
$295$	0	0
$296$	− 33.9411i	− 1.97279i
$297$	0	0
$298$	6.00000	0.347571
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	− 31.1127i	− 1.78151i
$306$	0	0
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	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
$313$	1.41421	0.0799361	0.0399680	−	0.999201i	$-0.487274\pi$
$313$	1.41421	0.0799361	0.0399680	+	0.999201i	$0.487274\pi$
$314$	− 34.0000i	− 1.91873i
$315$	0	0
$316$	0	0
$317$	− 4.24264i	− 0.238290i	−0.992877	−	0.119145i	$-0.961985\pi$
$317$	− 4.24264i	− 0.238290i	0.992877	−	0.119145i	$-0.0380154\pi$
$318$	0	0
$319$	0	0
$320$	16.0000i	0.894427i
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	−7.07107	−0.392232
$326$	0	0
$327$	0	0
$328$	22.6274	1.24939
$329$	0	0
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−18.0000	−0.980522	−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000	−0.980522	−0.490261	+	0.871576i	$0.663099\pi$
$338$	52.3259i	2.84615i
$339$	0	0
$340$	−8.00000	−0.433861
$341$	0	0
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	5.65685	0.304114
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	0	0
$349$	−32.5269	−1.74113	−0.870563	−	0.492057i	$-0.836245\pi$
$349$	−32.5269	−1.74113	−0.870563	+	0.492057i	$0.836245\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	34.0000i	1.80964i	0.425797	+	0.904819i	$0.359994\pi$
$353$	34.0000i	1.80964i	−0.425797	+	0.904819i	$0.640006\pi$
$354$	0	0
$355$	0	0
$356$	− 32.0000i	− 1.69600i
$357$	0	0
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	19.0000	1.00000
$362$	− 2.00000i	− 0.105118i
$363$	0	0
$364$	0	0
$365$	− 14.1421i	− 0.740233i
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	0	0
$369$	0	0
$370$	33.9411	1.76452
$371$	0	0
$372$	0	0
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	− 70.0000i	− 3.60518i
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	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
$386$	− 19.7990i	− 1.00774i
$387$	0	0
$388$	36.7696	1.86669
$389$	9.89949i	0.501924i	0.967997	+	0.250962i	$0.0807470\pi$
$389$	9.89949i	0.501924i	−0.967997	+	0.250962i	$0.919253\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	30.0000	1.51138
$395$	0	0
$396$	0	0
$397$	−35.3553	−1.77443	−0.887217	−	0.461353i	$-0.847364\pi$
$397$	−35.3553	−1.77443	−0.887217	+	0.461353i	$0.847364\pi$
$398$	0	0
$399$	0	0
$400$	4.00000	0.200000
$401$	− 26.8701i	− 1.34183i	−0.741536	−	0.670913i	$-0.765902\pi$
$401$	− 26.8701i	− 1.34183i	0.741536	−	0.670913i	$-0.234098\pi$
$402$	0	0
$403$	0	0
$404$	40.0000i	1.99007i
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	32.5269	1.60835	0.804176	−	0.594391i	$-0.202607\pi$
$409$	32.5269	1.60835	0.804176	+	0.594391i	$0.202607\pi$
$410$	22.6274i	1.11749i
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	0	0
$416$	− 40.0000i	− 1.96116i
$417$	0	0
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	28.0000	1.36464	0.682318	−	0.731055i	$-0.260972\pi$
$421$	28.0000	1.36464	0.682318	+	0.731055i	$0.260972\pi$
$422$	0	0
$423$	0	0
$424$	36.0000	1.74831
$425$	2.00000i	0.0970143i
$426$	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
$433$	41.0122	1.97092	0.985460	−	0.169907i	$-0.0543467\pi$
$433$	41.0122	1.97092	0.985460	+	0.169907i	$0.0543467\pi$
$434$	0	0
$435$	0	0
$436$	12.0000	0.574696
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	0	0
$442$	20.0000	0.951303
$443$	0	0		−	1.00000i	$-0.5\pi$
$443$	0	0			1.00000i	$0.5\pi$
$444$	0	0
$445$	32.0000	1.51695
$446$	0	0
$447$	0	0
$448$	0	0
$449$	38.1838i	1.80200i	0.433816	+	0.901002i	$0.357167\pi$
$449$	38.1838i	1.80200i	−0.433816	+	0.901002i	$0.642833\pi$
$450$	0	0
$451$	0	0
$452$	− 42.4264i	− 1.99557i
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	8.00000	0.374224	0.187112	−	0.982339i	$-0.440087\pi$
$457$	8.00000	0.374224	0.187112	+	0.982339i	$0.440087\pi$
$458$	34.0000i	1.58872i
$459$	0	0
$460$	0	0
$461$	20.0000i	0.931493i	0.884918	+	0.465746i	$0.154214\pi$
$461$	20.0000i	0.931493i	−0.884918	+	0.465746i	$0.845786\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	39.5980i	1.83829i
$465$	0	0
$466$	−10.0000	−0.463241
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	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
$481$	−84.8528	−3.86896
$482$	− 22.0000i	− 1.00207i
$483$	0	0
$484$	22.0000	1.00000
$485$	36.7696i	1.66962i
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	− 44.0000i	− 1.99179i
$489$	0	0
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	0	0
$493$	−19.7990	−0.891702
$494$	0	0
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	24.0000i	1.07331i
$501$	0	0
$502$	0	0
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	−40.0000	−1.77998
$506$	0	0
$507$	0	0
$508$	0	0
$509$	− 10.0000i	− 0.443242i	−0.975133	−	0.221621i	$-0.928865\pi$
$509$	− 10.0000i	− 0.443242i	0.975133	−	0.221621i	$-0.0711348\pi$
$510$	0	0
$511$	0	0
$512$	22.6274i	1.00000i
$513$	0	0
$514$	−45.2548	−1.99611
$515$	0	0
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	40.0000	1.75412
$521$	22.0000i	0.963837i	0.876216	+	0.481919i	$0.160060\pi$
$521$	22.0000i	0.963837i	−0.876216	+	0.481919i	$0.839940\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−23.0000	−1.00000
$530$	36.0000i	1.56374i
$531$	0	0
$532$	0	0
$533$	− 56.5685i	− 2.45026i
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	−36.7696	−1.58525
$539$	0	0
$540$	0	0
$541$	20.0000	0.859867	0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000	0.859867	0.429934	+	0.902861i	$0.358537\pi$
$542$	0	0
$543$	0	0
$544$	−11.3137	−0.485071
$545$	12.0000i	0.514024i
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	− 19.7990i	− 0.845771i
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	39.5980i	1.68236i
$555$	0	0
$556$	0	0
$557$	− 46.6690i	− 1.97743i	−0.149805	−	0.988716i	$-0.547865\pi$
$557$	− 46.6690i	− 1.97743i	0.149805	−	0.988716i	$-0.452135\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	−22.0000	−0.928014
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	0	0
$565$	42.4264	1.78489
$566$	0	0
$567$	0	0
$568$	0	0
$569$	9.89949i	0.415008i	0.978234	+	0.207504i	$0.0665341\pi$
$569$	9.89949i	0.415008i	−0.978234	+	0.207504i	$0.933466\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	32.5269	1.35411	0.677057	−	0.735931i	$-0.263255\pi$
$577$	32.5269	1.35411	0.677057	+	0.735931i	$0.263255\pi$
$578$	18.3848i	0.764706i
$579$	0	0
$580$	−39.5980	−1.64422
$581$	0	0
$582$	0	0
$583$	0	0
$584$	− 20.0000i	− 0.827606i
$585$	0	0
$586$	−5.65685	−0.233682
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	48.0000	1.97279
$593$	− 46.0000i	− 1.88899i	−0.328521	−	0.944497i	$-0.606550\pi$
$593$	− 46.0000i	− 1.88899i	0.328521	−	0.944497i	$-0.393450\pi$
$594$	0	0
$595$	0	0
$596$	8.48528i	0.347571i
$597$	0	0
$598$	0	0
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	26.8701	1.09605	0.548026	−	0.836461i	$-0.315379\pi$
$601$	26.8701	1.09605	0.548026	+	0.836461i	$0.315379\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	22.0000i	0.894427i
$606$	0	0
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	0	0
$609$	0	0
$610$	44.0000	1.78151
$611$	0	0
$612$	0	0
$613$	−36.0000	−1.45403	−0.727013	−	0.686624i	$-0.759092\pi$
$613$	−36.0000	−1.45403	−0.727013	+	0.686624i	$0.759092\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	− 49.4975i	− 1.99269i	−0.0854011	−	0.996347i	$-0.527217\pi$
$617$	− 49.4975i	− 1.99269i	0.0854011	−	0.996347i	$-0.472783\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−19.0000	−0.760000
$626$	2.00000i	0.0799361i
$627$	0	0
$628$	48.0833	1.91873
$629$	24.0000i	0.956943i
$630$	0	0
$631$	0	0	1.00000			$0$
$631$	0	0	−1.00000			$\pi$
$632$	0	0
$633$	0	0
$634$	6.00000	0.238290
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	−22.6274	−0.894427
$641$	41.0122i	1.61988i	0.586510	+	0.809942i	$0.300502\pi$
$641$	41.0122i	1.61988i	−0.586510	+	0.809942i	$0.699498\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	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
$649$	0	0
$650$	− 10.0000i	− 0.392232i
$651$	0	0
$652$	0	0
$653$	− 49.4975i	− 1.93699i	−0.249041	−	0.968493i	$-0.580115\pi$
$653$	− 49.4975i	− 1.93699i	0.249041	−	0.968493i	$-0.419885\pi$
$654$	0	0
$655$	0	0
$656$	32.0000i	1.24939i
$657$	0	0
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	43.8406	1.70520	0.852601	−	0.522562i	$-0.175024\pi$
$661$	43.8406	1.70520	0.852601	+	0.522562i	$0.175024\pi$
$662$	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
$673$	−24.0000	−0.925132	−0.462566	−	0.886585i	$-0.653071\pi$
$673$	−24.0000	−0.925132	−0.462566	+	0.886585i	$0.653071\pi$
$674$	− 25.4558i	− 0.980522i
$675$	0	0
$676$	−74.0000	−2.84615
$677$	− 52.0000i	− 1.99852i	−0.0384331	−	0.999261i	$-0.512237\pi$
$677$	− 52.0000i	− 1.99852i	0.0384331	−	0.999261i	$-0.487763\pi$
$678$	0	0
$679$	0	0
$680$	− 11.3137i	− 0.433861i
$681$	0	0
$682$	0	0
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	0	0
$685$	19.7990	0.756481
$686$	0	0
$687$	0	0
$688$	0	0
$689$	− 90.0000i	− 3.42873i
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	8.00000i	0.304114i
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−16.0000	−0.606043
$698$	− 46.0000i	− 1.74113i
$699$	0	0
$700$	0	0
$701$	− 43.8406i	− 1.65584i	−0.560848	−	0.827919i	$-0.689525\pi$
$701$	− 43.8406i	− 1.65584i	0.560848	−	0.827919i	$-0.310475\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	−48.0833	−1.80964
$707$	0	0
$708$	0	0
$709$	−30.0000	−1.12667	−0.563337	−	0.826227i	$-0.690483\pi$
$709$	−30.0000	−1.12667	−0.563337	+	0.826227i	$0.690483\pi$
$710$	0	0
$711$	0	0
$712$	45.2548	1.69600
$713$	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
$722$	26.8701i	1.00000i
$723$	0	0
$724$	2.82843	0.105118
$725$	9.89949i	0.367658i
$726$	0	0
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	0	0
$730$	20.0000	0.740233
$731$	0	0
$732$	0	0
$733$	−35.3553	−1.30588	−0.652940	−	0.757410i	$-0.726464\pi$
$733$	−35.3553	−1.30588	−0.652940	+	0.757410i	$0.726464\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	48.0000i	1.76452i
$741$	0	0
$742$	0	0
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	0	0
$745$	−8.48528	−0.310877
$746$	− 19.7990i	− 0.724893i
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	0	0
$753$	0	0
$754$	98.9949	3.60518
$755$	0	0
$756$	0	0
$757$	−18.0000	−0.654221	−0.327111	−	0.944986i	$-0.606075\pi$
$757$	−18.0000	−0.654221	−0.327111	+	0.944986i	$0.606075\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	40.0000i	1.45000i	0.688749	+	0.724999i	$0.258160\pi$
$761$	40.0000i	1.45000i	−0.688749	+	0.724999i	$0.741840\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	−18.3848	−0.662972	−0.331486	−	0.943460i	$-0.607550\pi$
$769$	−18.3848	−0.662972	−0.331486	+	0.943460i	$0.607550\pi$
$770$	0	0
$771$	0	0
$772$	28.0000	1.00774
$773$	44.0000i	1.58257i	0.611448	+	0.791285i	$0.290588\pi$
$773$	44.0000i	1.58257i	−0.611448	+	0.791285i	$0.709412\pi$
$774$	0	0
$775$	0	0
$776$	52.0000i	1.86669i
$777$	0	0
$778$	−14.0000	−0.501924
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	48.0833i	1.71617i
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	42.4264i	1.51138i
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−110.000	−3.90621
$794$	− 50.0000i	− 1.77443i
$795$	0	0
$796$	0	0
$797$	52.0000i	1.84193i	0.389640	+	0.920967i	$0.372599\pi$
$797$	52.0000i	1.84193i	−0.389640	+	0.920967i	$0.627401\pi$
$798$	0	0
$799$	0	0
$800$	5.65685i	0.200000i
$801$	0	0
$802$	38.0000	1.34183
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	−56.5685	−1.99007
$809$	46.6690i	1.64080i	0.571793	+	0.820398i	$0.306248\pi$
$809$	46.6690i	1.64080i	−0.571793	+	0.820398i	$0.693752\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	46.0000i	1.60835i
$819$	0	0
$820$	−32.0000	−1.11749
$821$	− 55.1543i	− 1.92490i	−0.271460	−	0.962450i	$-0.587507\pi$
$821$	− 55.1543i	− 1.92490i	0.271460	−	0.962450i	$-0.412493\pi$
$822$	0	0
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0		−	1.00000i	$-0.5\pi$
$827$	0	0			1.00000i	$0.5\pi$
$828$	0	0
$829$	−24.0416	−0.835000	−0.417500	−	0.908677i	$-0.637094\pi$
$829$	−24.0416	−0.835000	−0.417500	+	0.908677i	$0.637094\pi$
$830$	0	0
$831$	0	0
$832$	56.5685	1.96116
$833$	0	0
$834$	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
$841$	−69.0000	−2.37931
$842$	39.5980i	1.36464i
$843$	0	0
$844$	0	0
$845$	− 74.0000i	− 2.54568i
$846$	0	0
$847$	0	0
$848$	50.9117i	1.74831i
$849$	0	0
$850$	−2.82843	−0.0970143
$851$	0	0
$852$	0	0
$853$	−7.07107	−0.242109	−0.121054	−	0.992646i	$-0.538628\pi$
$853$	−7.07107	−0.242109	−0.121054	+	0.992646i	$0.538628\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	− 8.00000i	− 0.273275i	−0.990621	−	0.136637i	$-0.956370\pi$
$857$	− 8.00000i	− 0.273275i	0.990621	−	0.136637i	$-0.0436295\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	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
$865$	−8.00000	−0.272008
$866$	58.0000i	1.97092i
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	16.9706i	0.574696i
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−12.0000	−0.405211	−0.202606	−	0.979260i	$-0.564941\pi$
$877$	−12.0000	−0.405211	−0.202606	+	0.979260i	$0.564941\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	50.0000i	1.68454i	0.539054	+	0.842271i	$0.318782\pi$
$881$	50.0000i	1.68454i	−0.539054	+	0.842271i	$0.681218\pi$
$882$	0	0
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	28.2843i	0.951303i
$885$	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
$890$	45.2548i	1.51695i
$891$	0	0
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	−54.0000	−1.80200
$899$	0	0
$900$	0	0
$901$	−25.4558	−0.848057
$902$	0	0
$903$	0	0
$904$	60.0000	1.99557
$905$	2.82843i	0.0940201i
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	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
$913$	0	0
$914$	11.3137i	0.374224i
$915$	0	0
$916$	−48.0833	−1.58872
$917$	0	0
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	−28.2843	−0.931493
$923$	0	0
$924$	0	0
$925$	12.0000	0.394558
$926$	0	0
$927$	0	0
$928$	−56.0000	−1.83829
$929$	40.0000i	1.31236i	0.754606	+	0.656179i	$0.227828\pi$
$929$	40.0000i	1.31236i	−0.754606	+	0.656179i	$0.772172\pi$
$930$	0	0
$931$	0	0
$932$	− 14.1421i	− 0.463241i
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−7.07107	−0.231002	−0.115501	−	0.993307i	$-0.536847\pi$
$937$	−7.07107	−0.231002	−0.115501	+	0.993307i	$0.536847\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	− 58.0000i	− 1.89075i	−0.325991	−	0.945373i	$-0.605698\pi$
$941$	− 58.0000i	− 1.89075i	0.325991	−	0.945373i	$-0.394302\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	0	0
$946$	0	0
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	0	0
$949$	−50.0000	−1.62307
$950$	0	0
$951$	0	0
$952$	0	0
$953$	21.2132i	0.687163i	0.939123	+	0.343582i	$0.111640\pi$
$953$	21.2132i	0.687163i	−0.939123	+	0.343582i	$0.888360\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	31.0000	1.00000
$962$	− 120.000i	− 3.86896i
$963$	0	0
$964$	31.1127	1.00207
$965$	28.0000i	0.901352i
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	31.1127i	1.00000i
$969$	0	0
$970$	−52.0000	−1.66962
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	62.2254	1.99179
$977$	− 49.4975i	− 1.58356i	−0.610803	−	0.791782i	$-0.709153\pi$
$977$	− 49.4975i	− 1.58356i	0.610803	−	0.791782i	$-0.290847\pi$
$978$	0	0
$979$	0	0
$980$	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
$985$	−42.4264	−1.35182
$986$	− 28.0000i	− 0.891702i
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	35.3553	1.11971	0.559857	−	0.828589i	$-0.310856\pi$
$997$	35.3553	1.11971	0.559857	+	0.828589i	$0.310856\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.e.e.1079.3	yes	4
3.2	odd	2	inner	1764.2.e.e.1079.2	yes	4
4.3	odd	2	CM	1764.2.e.e.1079.3	yes	4
7.6	odd	2	inner	1764.2.e.e.1079.4	yes	4
12.11	even	2	inner	1764.2.e.e.1079.2	yes	4
21.20	even	2	inner	1764.2.e.e.1079.1	✓	4
28.27	even	2	inner	1764.2.e.e.1079.4	yes	4
84.83	odd	2	inner	1764.2.e.e.1079.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1764.2.e.e.1079.1	✓	4	21.20	even	2	inner
1764.2.e.e.1079.1	✓	4	84.83	odd	2	inner
1764.2.e.e.1079.2	yes	4	3.2	odd	2	inner
1764.2.e.e.1079.2	yes	4	12.11	even	2	inner
1764.2.e.e.1079.3	yes	4	1.1	even	1	trivial
1764.2.e.e.1079.3	yes	4	4.3	odd	2	CM
1764.2.e.e.1079.4	yes	4	7.6	odd	2	inner
1764.2.e.e.1079.4	yes	4	28.27	even	2	inner

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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -2.00000 q^{4} -2.00000i q^{5} -2.82843i q^{8} +O(q^{10})\)	\(q+1.41421i q^{2} -2.00000 q^{4} -2.00000i q^{5} -2.82843i q^{8} +2.82843 q^{10} -7.07107 q^{13} +4.00000 q^{16} +2.00000i q^{17} +4.00000i q^{20} +1.00000 q^{25} -10.0000i q^{26} +9.89949i q^{29} +5.65685i q^{32} -2.82843 q^{34} +12.0000 q^{37} -5.65685 q^{40} +8.00000i q^{41} +1.41421i q^{50} +14.1421 q^{52} +12.7279i q^{53} -14.0000 q^{58} +15.5563 q^{61} -8.00000 q^{64} +14.1421i q^{65} -4.00000i q^{68} +7.07107 q^{73} +16.9706i q^{74} -8.00000i q^{80} -11.3137 q^{82} +4.00000 q^{85} +16.0000i q^{89} -18.3848 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{4}+O(q^{10}) \) 4 * q - 8 * q^4	\( 4 q - 8 q^{4} + 16 q^{16} + 4 q^{25} + 48 q^{37} - 56 q^{58} - 32 q^{64} + 16 q^{85}+O(q^{100}) \) 4 * q - 8 * q^4 + 16 * q^16 + 4 * q^25 + 48 * q^37 - 56 * q^58 - 32 * q^64 + 16 * q^85

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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