LMFDB - Embedded newform 35.5.c.b.34.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(34,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("35.34");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.c (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:	yes
Analytic conductor:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			34.1
Character	$\chi$	$=$	35.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+17.0000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -49.0000 q^{7} +208.000 q^{9} +O(q^{10})$

$q+17.0000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -49.0000 q^{7} +208.000 q^{9} -73.0000 q^{11} +272.000 q^{12} -23.0000 q^{13} -425.000 q^{15} +256.000 q^{16} -263.000 q^{17} -400.000 q^{20} -833.000 q^{21} +625.000 q^{25} +2159.00 q^{27} -784.000 q^{28} -1153.00 q^{29} -1241.00 q^{33} +1225.00 q^{35} +3328.00 q^{36} -391.000 q^{39} -1168.00 q^{44} -5200.00 q^{45} +3457.00 q^{47} +4352.00 q^{48} +2401.00 q^{49} -4471.00 q^{51} -368.000 q^{52} +1825.00 q^{55} -6800.00 q^{60} -10192.0 q^{63} +4096.00 q^{64} +575.000 q^{65} -4208.00 q^{68} -10078.0 q^{71} +9502.00 q^{73} +10625.0 q^{75} +3577.00 q^{77} +12167.0 q^{79} -6400.00 q^{80} +19855.0 q^{81} +6382.00 q^{83} -13328.0 q^{84} +6575.00 q^{85} -19601.0 q^{87} +1127.00 q^{91} -3383.00 q^{97} -15184.0 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$-1$	$-1$

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	1.00000			$0$
$2$	0	0	−1.00000			$\pi$
$3$	17.0000	1.88889	0.944444	−	0.328671i	$-0.106601\pi$
$3$	17.0000	1.88889	0.944444	+	0.328671i	$0.106601\pi$
$4$	16.0000	1.00000
$5$	−25.0000	−1.00000
$5$	−25.0000	−1.00000
$6$	0	0
$7$	−49.0000	−1.00000
$7$	−49.0000	−1.00000
$8$	0	0
$9$	208.000	2.56790
$10$	0	0
$11$	−73.0000	−0.603306	−0.301653	−	0.953418i	$-0.597538\pi$
$11$	−73.0000	−0.603306	−0.301653	+	0.953418i	$0.597538\pi$
$12$	272.000	1.88889
$13$	−23.0000	−0.136095	−0.0680473	−	0.997682i	$-0.521677\pi$
$13$	−23.0000	−0.136095	−0.0680473	+	0.997682i	$0.521677\pi$
$14$	0	0
$15$	−425.000	−1.88889
$16$	256.000	1.00000
$17$	−263.000	−0.910035	−0.455017	−	0.890483i	$-0.650367\pi$
$17$	−263.000	−0.910035	−0.455017	+	0.890483i	$0.650367\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	−400.000	−1.00000
$21$	−833.000	−1.88889
$22$	0	0
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	0	0
$25$	625.000	1.00000
$26$	0	0
$27$	2159.00	2.96159
$28$	−784.000	−1.00000
$29$	−1153.00	−1.37099	−0.685493	−	0.728079i	$-0.740413\pi$
$29$	−1153.00	−1.37099	−0.685493	+	0.728079i	$0.740413\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0	0
$33$	−1241.00	−1.13958
$34$	0	0
$35$	1225.00	1.00000
$36$	3328.00	2.56790
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	−391.000	−0.257068
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	−1168.00	−0.603306
$45$	−5200.00	−2.56790
$46$	0	0
$47$	3457.00	1.56496	0.782481	−	0.622675i	$-0.213954\pi$
$47$	3457.00	1.56496	0.782481	+	0.622675i	$0.213954\pi$
$48$	4352.00	1.88889
$49$	2401.00	1.00000
$50$	0	0
$51$	−4471.00	−1.71895
$52$	−368.000	−0.136095
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0	0
$55$	1825.00	0.603306
$56$	0	0
$57$	0	0
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	−6800.00	−1.88889
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	−10192.0	−2.56790
$64$	4096.00	1.00000
$65$	575.000	0.136095
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	−4208.00	−0.910035
$69$	0	0
$70$	0	0
$71$	−10078.0	−1.99921	−0.999603	−	0.0281662i	$-0.991033\pi$
$71$	−10078.0	−1.99921	−0.999603	+	0.0281662i	$0.991033\pi$
$72$	0	0
$73$	9502.00	1.78307	0.891537	−	0.452948i	$-0.149628\pi$
$73$	9502.00	1.78307	0.891537	+	0.452948i	$0.149628\pi$
$74$	0	0
$75$	10625.0	1.88889
$76$	0	0
$77$	3577.00	0.603306
$78$	0	0
$79$	12167.0	1.94953	0.974764	−	0.223239i	$-0.0716632\pi$
$79$	12167.0	1.94953	0.974764	+	0.223239i	$0.0716632\pi$
$80$	−6400.00	−1.00000
$81$	19855.0	3.02622
$82$	0	0
$83$	6382.00	0.926404	0.463202	−	0.886253i	$-0.346700\pi$
$83$	6382.00	0.926404	0.463202	+	0.886253i	$0.346700\pi$
$84$	−13328.0	−1.88889
$85$	6575.00	0.910035
$86$	0	0
$87$	−19601.0	−2.58964
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	1127.00	0.136095
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−3383.00	−0.359549	−0.179775	−	0.983708i	$-0.557537\pi$
$97$	−3383.00	−0.359549	−0.179775	+	0.983708i	$0.557537\pi$
$98$	0	0
$99$	−15184.0	−1.54923
$100$	10000.0	1.00000
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	−18383.0	−1.73277	−0.866387	−	0.499373i	$-0.833564\pi$
$103$	−18383.0	−1.73277	−0.866387	+	0.499373i	$0.833564\pi$
$104$	0	0
$105$	20825.0	1.88889
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	34544.0	2.96159
$109$	−14353.0	−1.20806	−0.604032	−	0.796960i	$-0.706440\pi$
$109$	−14353.0	−1.20806	−0.604032	+	0.796960i	$0.706440\pi$
$110$	0	0
$111$	0	0
$112$	−12544.0	−1.00000
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	0	0
$116$	−18448.0	−1.37099
$117$	−4784.00	−0.349478
$118$	0	0
$119$	12887.0	0.910035
$120$	0	0
$121$	−9312.00	−0.636022
$122$	0	0
$123$	0	0
$124$	0	0
$125$	−15625.0	−1.00000
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	−19856.0	−1.13958
$133$	0	0
$134$	0	0
$135$	−53975.0	−2.96159
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	19600.0	1.00000
$141$	58769.0	2.95604
$142$	0	0
$143$	1679.00	0.0821067
$144$	53248.0	2.56790
$145$	28825.0	1.37099
$146$	0	0
$147$	40817.0	1.88889
$148$	0	0
$149$	24242.0	1.09193	0.545966	−	0.837807i	$-0.316163\pi$
$149$	24242.0	1.09193	0.545966	+	0.837807i	$0.316163\pi$
$150$	0	0
$151$	−45433.0	−1.99259	−0.996294	−	0.0860129i	$-0.972587\pi$
$151$	−45433.0	−1.99259	−0.996294	+	0.0860129i	$0.972587\pi$
$152$	0	0
$153$	−54704.0	−2.33688
$154$	0	0
$155$	0	0
$156$	−6256.00	−0.257068
$157$	31342.0	1.27153	0.635766	−	0.771882i	$-0.280684\pi$
$157$	31342.0	1.27153	0.635766	+	0.771882i	$0.280684\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0	0
$165$	31025.0	1.13958
$166$	0	0
$167$	−17663.0	−0.633332	−0.316666	−	0.948537i	$-0.602563\pi$
$167$	−17663.0	−0.633332	−0.316666	+	0.948537i	$0.602563\pi$
$168$	0	0
$169$	−28032.0	−0.981478
$170$	0	0
$171$	0	0
$172$	0	0
$173$	11017.0	0.368105	0.184052	−	0.982916i	$-0.441078\pi$
$173$	11017.0	0.368105	0.184052	+	0.982916i	$0.441078\pi$
$174$	0	0
$175$	−30625.0	−1.00000
$176$	−18688.0	−0.603306
$177$	0	0
$178$	0	0
$179$	−16558.0	−0.516775	−0.258388	−	0.966041i	$-0.583191\pi$
$179$	−16558.0	−0.516775	−0.258388	+	0.966041i	$0.583191\pi$
$180$	−83200.0	−2.56790
$181$	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
$187$	19199.0	0.549029
$188$	55312.0	1.56496
$189$	−105791.	−2.96159
$190$	0	0
$191$	47447.0	1.30059	0.650297	−	0.759680i	$-0.274644\pi$
$191$	47447.0	1.30059	0.650297	+	0.759680i	$0.274644\pi$
$192$	69632.0	1.88889
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	9775.00	0.257068
$196$	38416.0	1.00000
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	56497.0	1.37099
$204$	−71536.0	−1.71895
$205$	0	0
$206$	0	0
$207$	0	0
$208$	−5888.00	−0.136095
$209$	0	0
$210$	0	0
$211$	−77593.0	−1.74284	−0.871420	−	0.490537i	$-0.836801\pi$
$211$	−77593.0	−1.74284	−0.871420	+	0.490537i	$0.836801\pi$
$212$	0	0
$213$	−171326.	−3.77628
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	161534.	3.36803
$220$	29200.0	0.603306
$221$	6049.00	0.123851
$222$	0	0
$223$	−61343.0	−1.23355	−0.616773	−	0.787141i	$-0.711560\pi$
$223$	−61343.0	−1.23355	−0.616773	+	0.787141i	$0.711560\pi$
$224$	0	0
$225$	130000.	2.56790
$226$	0	0
$227$	−49823.0	−0.966892	−0.483446	−	0.875374i	$-0.660615\pi$
$227$	−49823.0	−0.966892	−0.483446	+	0.875374i	$0.660615\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	60809.0	1.13958
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	−86425.0	−1.56496
$236$	0	0
$237$	206839.	3.68244
$238$	0	0
$239$	43367.0	0.759213	0.379606	−	0.925148i	$-0.376059\pi$
$239$	43367.0	0.759213	0.379606	+	0.925148i	$0.376059\pi$
$240$	−108800.	−1.88889
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	162656.	2.75459
$244$	0	0
$245$	−60025.0	−1.00000
$246$	0	0
$247$	0	0
$248$	0	0
$249$	108494.	1.74988
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	−163072.	−2.56790
$253$	0	0
$254$	0	0
$255$	111775.	1.71895
$256$	65536.0	1.00000
$257$	−111938.	−1.69477	−0.847386	−	0.530977i	$-0.821825\pi$
$257$	−111938.	−1.69477	−0.847386	+	0.530977i	$0.821825\pi$
$258$	0	0
$259$	0	0
$260$	9200.00	0.136095
$261$	−239824.	−3.52056
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	−67328.0	−0.910035
$273$	19159.0	0.257068
$274$	0	0
$275$	−45625.0	−0.603306
$276$	0	0
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	119807.	1.51729	0.758647	−	0.651502i	$-0.225861\pi$
$281$	119807.	1.51729	0.758647	+	0.651502i	$0.225861\pi$
$282$	0	0
$283$	−152303.	−1.90167	−0.950836	−	0.309695i	$-0.899773\pi$
$283$	−152303.	−1.90167	−0.950836	+	0.309695i	$0.899773\pi$
$284$	−161248.	−1.99921
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−14352.0	−0.171837
$290$	0	0
$291$	−57511.0	−0.679149
$292$	152032.	1.78307
$293$	171337.	1.99579	0.997897	−	0.0648123i	$-0.0206449\pi$
$293$	171337.	1.99579	0.997897	+	0.0648123i	$0.0206449\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−157607.	−1.78675
$298$	0	0
$299$	0	0
$300$	170000.	1.88889
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−135263.	−1.43517	−0.717583	−	0.696473i	$-0.754752\pi$
$307$	−135263.	−1.43517	−0.717583	+	0.696473i	$0.754752\pi$
$308$	57232.0	0.603306
$309$	−312511.	−3.27302
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	147097.	1.50146	0.750732	−	0.660606i	$-0.229701\pi$
$313$	147097.	1.50146	0.750732	+	0.660606i	$0.229701\pi$
$314$	0	0
$315$	254800.	2.56790
$316$	194672.	1.94953
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	84169.0	0.827124
$320$	−102400.	−1.00000
$321$	0	0
$322$	0	0
$323$	0	0
$324$	317680.	3.02622
$325$	−14375.0	−0.136095
$326$	0	0
$327$	−244001.	−2.28190
$328$	0	0
$329$	−169393.	−1.56496
$330$	0	0
$331$	138482.	1.26397	0.631986	−	0.774980i	$-0.282240\pi$
$331$	138482.	1.26397	0.631986	+	0.774980i	$0.282240\pi$
$332$	102112.	0.926404
$333$	0	0
$334$	0	0
$335$	0	0
$336$	−213248.	−1.88889
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0	0
$339$	0	0
$340$	105200.	0.910035
$341$	0	0
$342$	0	0
$343$	−117649.	−1.00000
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	−313616.	−2.58964
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	−49657.0	−0.403057
$352$	0	0
$353$	229897.	1.84495	0.922473	−	0.386060i	$-0.126164\pi$
$353$	229897.	1.84495	0.922473	+	0.386060i	$0.126164\pi$
$354$	0	0
$355$	251950.	1.99921
$356$	0	0
$357$	219079.	1.71895
$358$	0	0
$359$	76322.0	0.592190	0.296095	−	0.955159i	$-0.404316\pi$
$359$	76322.0	0.592190	0.296095	+	0.955159i	$0.404316\pi$
$360$	0	0
$361$	130321.	1.00000
$362$	0	0
$363$	−158304.	−1.20138
$364$	18032.0	0.136095
$365$	−237550.	−1.78307
$366$	0	0
$367$	116497.	0.864933	0.432467	−	0.901650i	$-0.357643\pi$
$367$	116497.	0.864933	0.432467	+	0.901650i	$0.357643\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0	0	1.00000			$0$
$373$	0	0	−1.00000			$\pi$
$374$	0	0
$375$	−265625.	−1.88889
$376$	0	0
$377$	26519.0	0.186584
$378$	0	0
$379$	−35278.0	−0.245598	−0.122799	−	0.992432i	$-0.539187\pi$
$379$	−35278.0	−0.245598	−0.122799	+	0.992432i	$0.539187\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	29182.0	0.198938	0.0994689	−	0.995041i	$-0.468286\pi$
$383$	29182.0	0.198938	0.0994689	+	0.995041i	$0.468286\pi$
$384$	0	0
$385$	−89425.0	−0.603306
$386$	0	0
$387$	0	0
$388$	−54128.0	−0.359549
$389$	249407.	1.64820	0.824099	−	0.566446i	$-0.191682\pi$
$389$	249407.	1.64820	0.824099	+	0.566446i	$0.191682\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	−304175.	−1.94953
$396$	−242944.	−1.54923
$397$	163897.	1.03990	0.519948	−	0.854198i	$-0.325951\pi$
$397$	163897.	1.03990	0.519948	+	0.854198i	$0.325951\pi$
$398$	0	0
$399$	0	0
$400$	160000.	1.00000
$401$	−316273.	−1.96686	−0.983430	−	0.181289i	$-0.941973\pi$
$401$	−316273.	−1.96686	−0.983430	+	0.181289i	$0.941973\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	−496375.	−3.02622
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	−294128.	−1.73277
$413$	0	0
$414$	0	0
$415$	−159550.	−0.926404
$416$	0	0
$417$	0	0
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	333200.	1.88889
$421$	−76753.0	−0.433043	−0.216522	−	0.976278i	$-0.569471\pi$
$421$	−76753.0	−0.433043	−0.216522	+	0.976278i	$0.569471\pi$
$422$	0	0
$423$	719056.	4.01867
$424$	0	0
$425$	−164375.	−0.910035
$426$	0	0
$427$	0	0
$428$	0	0
$429$	28543.0	0.155090
$430$	0	0
$431$	356087.	1.91691	0.958455	−	0.285245i	$-0.0920749\pi$
$431$	356087.	1.91691	0.958455	+	0.285245i	$0.0920749\pi$
$432$	552704.	2.96159
$433$	−193538.	−1.03226	−0.516132	−	0.856509i	$-0.672628\pi$
$433$	−193538.	−1.03226	−0.516132	+	0.856509i	$0.672628\pi$
$434$	0	0
$435$	490025.	2.58964
$436$	−229648.	−1.20806
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	499408.	2.56790
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	412114.	2.06254
$448$	−200704.	−1.00000
$449$	264287.	1.31094	0.655470	−	0.755221i	$-0.272470\pi$
$449$	264287.	1.31094	0.655470	+	0.755221i	$0.272470\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	−772361.	−3.76378
$454$	0	0
$455$	−28175.0	−0.136095
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	−567817.	−2.69515
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	−295168.	−1.37099
$465$	0	0
$466$	0	0
$467$	−322463.	−1.47858	−0.739292	−	0.673385i	$-0.764840\pi$
$467$	−322463.	−1.47858	−0.739292	+	0.673385i	$0.764840\pi$
$468$	−76544.0	−0.349478
$469$	0	0
$470$	0	0
$471$	532814.	2.40178
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	206192.	0.910035
$477$	0	0
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	−148992.	−0.636022
$485$	84575.0	0.359549
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−470713.	−1.95251	−0.976255	−	0.216625i	$-0.930495\pi$
$491$	−470713.	−1.95251	−0.976255	+	0.216625i	$0.930495\pi$
$492$	0	0
$493$	303239.	1.24765
$494$	0	0
$495$	379600.	1.54923
$496$	0	0
$497$	493822.	1.99921
$498$	0	0
$499$	−31513.0	−0.126558	−0.0632789	−	0.997996i	$-0.520156\pi$
$499$	−31513.0	−0.126558	−0.0632789	+	0.997996i	$0.520156\pi$
$500$	−250000.	−1.00000
$501$	−300271.	−1.19629
$502$	0	0
$503$	313297.	1.23828	0.619142	−	0.785279i	$-0.287481\pi$
$503$	313297.	1.23828	0.619142	+	0.785279i	$0.287481\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−476544.	−1.85390
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	−465598.	−1.78307
$512$	0	0
$513$	0	0
$514$	0	0
$515$	459575.	1.73277
$516$	0	0
$517$	−252361.	−0.944150
$518$	0	0
$519$	187289.	0.695309
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	440782.	1.61146	0.805732	−	0.592281i	$-0.201772\pi$
$523$	440782.	1.61146	0.805732	+	0.592281i	$0.201772\pi$
$524$	0	0
$525$	−520625.	−1.88889
$526$	0	0
$527$	0	0
$528$	−317696.	−1.13958
$529$	279841.	1.00000
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−281486.	−0.976131
$538$	0	0
$539$	−175273.	−0.603306
$540$	−863600.	−2.96159
$541$	2927.00	0.0100006	0.00500032	−	0.999987i	$-0.498408\pi$
$541$	2927.00	0.0100006	0.00500032	+	0.999987i	$0.498408\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	358825.	1.20806
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−596183.	−1.94953
$554$	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
$560$	313600.	1.00000
$561$	326383.	1.03706
$562$	0	0
$563$	−129938.	−0.409939	−0.204970	−	0.978768i	$-0.565710\pi$
$563$	−129938.	−0.409939	−0.204970	+	0.978768i	$0.565710\pi$
$564$	940304.	2.95604
$565$	0	0
$566$	0	0
$567$	−972895.	−3.02622
$568$	0	0
$569$	566882.	1.75093	0.875464	−	0.483284i	$-0.160556\pi$
$569$	566882.	1.75093	0.875464	+	0.483284i	$0.160556\pi$
$570$	0	0
$571$	−638158.	−1.95729	−0.978647	−	0.205549i	$-0.934102\pi$
$571$	−638158.	−1.95729	−0.978647	+	0.205549i	$0.934102\pi$
$572$	26864.0	0.0821067
$573$	806599.	2.45668
$574$	0	0
$575$	0	0
$576$	851968.	2.56790
$577$	665017.	1.99747	0.998737	−	0.0502441i	$-0.0159999\pi$
$577$	665017.	1.99747	0.998737	+	0.0502441i	$0.0159999\pi$
$578$	0	0
$579$	0	0
$580$	461200.	1.37099
$581$	−312718.	−0.926404
$582$	0	0
$583$	0	0
$584$	0	0
$585$	119600.	0.349478
$586$	0	0
$587$	−507698.	−1.47343	−0.736715	−	0.676204i	$-0.763624\pi$
$587$	−507698.	−1.47343	−0.736715	+	0.676204i	$0.763624\pi$
$588$	653072.	1.88889
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	320137.	0.910388	0.455194	−	0.890392i	$-0.349570\pi$
$593$	320137.	0.910388	0.455194	+	0.890392i	$0.349570\pi$
$594$	0	0
$595$	−322175.	−0.910035
$596$	387872.	1.09193
$597$	0	0
$598$	0	0
$599$	−613273.	−1.70923	−0.854614	−	0.519263i	$-0.826206\pi$
$599$	−613273.	−1.70923	−0.854614	+	0.519263i	$0.826206\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	0	0
$604$	−726928.	−1.99259
$605$	232800.	0.636022
$606$	0	0
$607$	82417.0	0.223686	0.111843	−	0.993726i	$-0.464325\pi$
$607$	82417.0	0.223686	0.111843	+	0.993726i	$0.464325\pi$
$608$	0	0
$609$	960449.	2.58964
$610$	0	0
$611$	−79511.0	−0.212983
$612$	−875264.	−2.33688
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	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
$624$	−100096.	−0.257068
$625$	390625.	1.00000
$626$	0	0
$627$	0	0
$628$	501472.	1.27153
$629$	0	0
$630$	0	0
$631$	100487.	0.252378	0.126189	−	0.992006i	$-0.459725\pi$
$631$	100487.	0.252378	0.126189	+	0.992006i	$0.459725\pi$
$632$	0	0
$633$	−1.31908e6	−3.29203
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−55223.0	−0.136095
$638$	0	0
$639$	−2.09622e6	−5.13376
$640$	0	0
$641$	96002.0	0.233649	0.116825	−	0.993153i	$-0.462728\pi$
$641$	96002.0	0.233649	0.116825	+	0.993153i	$0.462728\pi$
$642$	0	0
$643$	−713183.	−1.72496	−0.862480	−	0.506091i	$-0.831090\pi$
$643$	−713183.	−1.72496	−0.862480	+	0.506091i	$0.831090\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−111458.	−0.266258	−0.133129	−	0.991099i	$-0.542502\pi$
$647$	−111458.	−0.266258	−0.133129	+	0.991099i	$0.542502\pi$
$648$	0	0
$649$	0	0
$650$	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
$657$	1.97642e6	4.57876
$658$	0	0
$659$	777527.	1.79038	0.895189	−	0.445687i	$-0.147041\pi$
$659$	777527.	1.79038	0.895189	+	0.445687i	$0.147041\pi$
$660$	496400.	1.13958
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	102833.	0.233941
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	−282608.	−0.633332
$669$	−1.04283e6	−2.33003
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	1.34938e6	2.96159
$676$	−448512.	−0.981478
$677$	−750023.	−1.63643	−0.818215	−	0.574913i	$-0.805036\pi$
$677$	−750023.	−1.63643	−0.818215	+	0.574913i	$0.805036\pi$
$678$	0	0
$679$	165767.	0.359549
$680$	0	0
$681$	−846991.	−1.82635
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	176272.	0.368105
$693$	744016.	1.54923
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	−490000.	−1.00000
$701$	−884833.	−1.80063	−0.900317	−	0.435235i	$-0.856665\pi$
$701$	−884833.	−1.80063	−0.900317	+	0.435235i	$0.856665\pi$
$702$	0	0
$703$	0	0
$704$	−299008.	−0.603306
$705$	−1.46922e6	−2.95604
$706$	0	0
$707$	0	0
$708$	0	0
$709$	1.00253e6	1.99436	0.997180	−	0.0750454i	$-0.0239102\pi$
$709$	1.00253e6	1.99436	0.997180	+	0.0750454i	$0.0239102\pi$
$710$	0	0
$711$	2.53074e6	5.00619
$712$	0	0
$713$	0	0
$714$	0	0
$715$	−41975.0	−0.0821067
$716$	−264928.	−0.516775
$717$	737239.	1.43407
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	−1.33120e6	−2.56790
$721$	900767.	1.73277
$722$	0	0
$723$	0	0
$724$	0	0
$725$	−720625.	−1.37099
$726$	0	0
$727$	−976418.	−1.84743	−0.923713	−	0.383086i	$-0.874861\pi$
$727$	−976418.	−1.84743	−0.923713	+	0.383086i	$0.874861\pi$
$728$	0	0
$729$	1.15690e6	2.17691
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−51143.0	−0.0951871	−0.0475936	−	0.998867i	$-0.515155\pi$
$733$	−51143.0	−0.0951871	−0.0475936	+	0.998867i	$0.515155\pi$
$734$	0	0
$735$	−1.02042e6	−1.88889
$736$	0	0
$737$	0	0
$738$	0	0
$739$	749207.	1.37187	0.685935	−	0.727663i	$-0.259393\pi$
$739$	749207.	1.37187	0.685935	+	0.727663i	$0.259393\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	−606050.	−1.09193
$746$	0	0
$747$	1.32746e6	2.37892
$748$	307184.	0.549029
$749$	0	0
$750$	0	0
$751$	648887.	1.15051	0.575253	−	0.817975i	$-0.304903\pi$
$751$	648887.	1.15051	0.575253	+	0.817975i	$0.304903\pi$
$752$	884992.	1.56496
$753$	0	0
$754$	0	0
$755$	1.13582e6	1.99259
$756$	−1.69266e6	−2.96159
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	703297.	1.20806
$764$	759152.	1.30059
$765$	1.36760e6	2.33688
$766$	0	0
$767$	0	0
$768$	1.11411e6	1.88889
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	−1.90295e6	−3.20124
$772$	0	0
$773$	−1.17962e6	−1.97417	−0.987084	−	0.160202i	$-0.948786\pi$
$773$	−1.17962e6	−1.97417	−0.987084	+	0.160202i	$0.948786\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	156400.	0.257068
$781$	735694.	1.20613
$782$	0	0
$783$	−2.48933e6	−4.06030
$784$	614656.	1.00000
$785$	−783550.	−1.27153
$786$	0	0
$787$	1.03714e6	1.67451	0.837253	−	0.546816i	$-0.184160\pi$
$787$	1.03714e6	1.67451	0.837253	+	0.546816i	$0.184160\pi$
$788$	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
$797$	−1.07354e6	−1.69006	−0.845031	−	0.534717i	$-0.820418\pi$
$797$	−1.07354e6	−1.69006	−0.845031	+	0.534717i	$0.820418\pi$
$798$	0	0
$799$	−909191.	−1.42417
$800$	0	0
$801$	0	0
$802$	0	0
$803$	−693646.	−1.07574
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−1.29955e6	−1.98562	−0.992812	−	0.119685i	$-0.961811\pi$
$809$	−1.29955e6	−1.98562	−0.992812	+	0.119685i	$0.961811\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	903952.	1.37099
$813$	0	0
$814$	0	0
$815$	0	0
$816$	−1.14458e6	−1.71895
$817$	0	0
$818$	0	0
$819$	234416.	0.349478
$820$	0	0
$821$	1.23437e6	1.83129	0.915647	−	0.401984i	$-0.131679\pi$
$821$	1.23437e6	1.83129	0.915647	+	0.401984i	$0.131679\pi$
$822$	0	0
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	−775625.	−1.13958
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	−94208.0	−0.136095
$833$	−631463.	−0.910035
$834$	0	0
$835$	441575.	0.633332
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	622128.	0.879605
$842$	0	0
$843$	2.03672e6	2.86600
$844$	−1.24149e6	−1.74284
$845$	700800.	0.981478
$846$	0	0
$847$	456288.	0.636022
$848$	0	0
$849$	−2.58915e6	−3.59205
$850$	0	0
$851$	0	0
$852$	−2.74122e6	−3.77628
$853$	1.44782e6	1.98984	0.994918	−	0.100692i	$-0.0321058\pi$
$853$	1.44782e6	1.98984	0.994918	+	0.100692i	$0.0321058\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	970462.	1.32135	0.660674	−	0.750673i	$-0.270271\pi$
$857$	970462.	1.32135	0.660674	+	0.750673i	$0.270271\pi$
$858$	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	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	−275425.	−0.368105
$866$	0	0
$867$	−243984.	−0.324581
$868$	0	0
$869$	−888191.	−1.17616
$870$	0	0
$871$	0	0
$872$	0	0
$873$	−703664.	−0.923287
$874$	0	0
$875$	765625.	1.00000
$876$	2.58454e6	3.36803
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	2.91273e6	3.76983
$880$	467200.	0.603306
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	0	0
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	96784.0	0.123851
$885$	0	0
$886$	0	0
$887$	1.32950e6	1.68983	0.844913	−	0.534904i	$-0.179652\pi$
$887$	1.32950e6	1.68983	0.844913	+	0.534904i	$0.179652\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−1.44942e6	−1.82573
$892$	−981488.	−1.23355
$893$	0	0
$894$	0	0
$895$	413950.	0.516775
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	2.08000e6	2.56790
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	−797168.	−0.966892
$909$	0	0
$910$	0	0
$911$	1.15584e6	1.39271	0.696357	−	0.717696i	$-0.254803\pi$
$911$	1.15584e6	1.39271	0.696357	+	0.717696i	$0.254803\pi$
$912$	0	0
$913$	−465886.	−0.558905
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−695113.	−0.823047	−0.411523	−	0.911399i	$-0.635003\pi$
$919$	−695113.	−0.823047	−0.411523	+	0.911399i	$0.635003\pi$
$920$	0	0
$921$	−2.29947e6	−2.71087
$922$	0	0
$923$	231794.	0.272081
$924$	972944.	1.13958
$925$	0	0
$926$	0	0
$927$	−3.82366e6	−4.44959
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	−479975.	−0.549029
$936$	0	0
$937$	−1.58930e6	−1.81020	−0.905102	−	0.425195i	$-0.860206\pi$
$937$	−1.58930e6	−1.81020	−0.905102	+	0.425195i	$0.860206\pi$
$938$	0	0
$939$	2.50065e6	2.83610
$940$	−1.38280e6	−1.56496
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	2.64478e6	2.96159
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	3.30942e6	3.68244
$949$	−218546.	−0.242667
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	−1.18618e6	−1.30059
$956$	693872.	0.759213
$957$	1.43087e6	1.56235
$958$	0	0
$959$	0	0
$960$	−1.74080e6	−1.88889
$961$	923521.	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	2.60250e6	2.75459
$973$	0	0
$974$	0	0
$975$	−244375.	−0.257068
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	−960400.	−1.00000
$981$	−2.98542e6	−3.10219
$982$	0	0
$983$	675937.	0.699518	0.349759	−	0.936840i	$-0.386263\pi$
$983$	675937.	0.699518	0.349759	+	0.936840i	$0.386263\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	−2.87968e6	−2.95604
$988$	0	0
$989$	0	0
$990$	0	0
$991$	−1.44288e6	−1.46920	−0.734602	−	0.678498i	$-0.762631\pi$
$991$	−1.44288e6	−1.46920	−0.734602	+	0.678498i	$0.762631\pi$
$992$	0	0
$993$	2.35419e6	2.38750
$994$	0	0
$995$	0	0
$996$	1.73590e6	1.74988
$997$	−737783.	−0.742230	−0.371115	−	0.928587i	$-0.621024\pi$
$997$	−737783.	−0.742230	−0.371115	+	0.928587i	$0.621024\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.c.b.34.1	yes	1
3.2	odd	2		315.5.e.b.244.1		1
4.3	odd	2		560.5.p.a.209.1		1
5.2	odd	4		175.5.d.c.76.1		2
5.3	odd	4		175.5.d.c.76.2		2
5.4	even	2		35.5.c.a.34.1	✓	1
7.6	odd	2		35.5.c.a.34.1	✓	1
15.14	odd	2		315.5.e.a.244.1		1
20.19	odd	2		560.5.p.b.209.1		1
21.20	even	2		315.5.e.a.244.1		1
28.27	even	2		560.5.p.b.209.1		1
35.13	even	4		175.5.d.c.76.1		2
35.27	even	4		175.5.d.c.76.2		2
35.34	odd	2	CM	35.5.c.b.34.1	yes	1
105.104	even	2		315.5.e.b.244.1		1
140.139	even	2		560.5.p.a.209.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.c.a.34.1	✓	1	5.4	even	2
35.5.c.a.34.1	✓	1	7.6	odd	2
35.5.c.b.34.1	yes	1	1.1	even	1	trivial
35.5.c.b.34.1	yes	1	35.34	odd	2	CM
175.5.d.c.76.1		2	5.2	odd	4
175.5.d.c.76.1		2	35.13	even	4
175.5.d.c.76.2		2	5.3	odd	4
175.5.d.c.76.2		2	35.27	even	4
315.5.e.a.244.1		1	15.14	odd	2
315.5.e.a.244.1		1	21.20	even	2
315.5.e.b.244.1		1	3.2	odd	2
315.5.e.b.244.1		1	105.104	even	2
560.5.p.a.209.1		1	4.3	odd	2
560.5.p.a.209.1		1	140.139	even	2
560.5.p.b.209.1		1	20.19	odd	2
560.5.p.b.209.1		1	28.27	even	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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.c (of order \(2\), degree \(1\), minimal)

\(n\)	\(22\)	\(31\)
\(\chi(n)\)	\(-1\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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