LMFDB - Embedded newform 175.7.d.a.76.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,7,Mod(76,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("175.76");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$N$	$=$	$175 = 5^{2} \cdot 7$
Weight:	$k$	$=$	$7$
Character orbit:	$[\chi]$	$=$	175.d (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:	$40.2594646335$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			76.1
Character	$\chi$	$=$	175.76

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

f(q)

=

q-9.00000 q^{2} +17.0000 q^{4} +343.000 q^{7} +423.000 q^{8} +729.000 q^{9} +1962.00 q^{11} -3087.00 q^{14} -4895.00 q^{16} -6561.00 q^{18} -17658.0 q^{22} +22734.0 q^{23} +5831.00 q^{28} -21222.0 q^{29} +16983.0 q^{32} +12393.0 q^{36} -101194. q^{37} +126614. q^{43} +33354.0 q^{44} -204606. q^{46} +117649. q^{49} -50346.0 q^{53} +145089. q^{56} +190998. q^{58} +250047. q^{63} +160433. q^{64} +53926.0 q^{67} -242478. q^{71} +308367. q^{72} +910746. q^{74} +672966. q^{77} +929378. q^{79} +531441. q^{81} -1.13953e6 q^{86} +829926. q^{88} +386478. q^{92} -1.05884e6 q^{98} +1.43030e6 q^{99} +O(q^{100})

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$ .

$n$	$101$	$127$
$\chi(n)$	$-1$	$1$

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

)

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

$2$	−9.00000	−1.12500	−0.562500	−	0.826797i	$-0.690160\pi$
$2$	−9.00000	−1.12500	−0.562500	+	0.826797i	$0.690160\pi$
$3$	0	0	1.00000			$0$
$3$	0	0	−1.00000			$\pi$
$4$	17.0000	0.265625
$5$	0	0
$5$	0	0
$6$	0	0
$7$	343.000	1.00000
$7$	343.000	1.00000
$8$	423.000	0.826172
$9$	729.000	1.00000
$10$	0	0
$11$	1962.00	1.47408	0.737040	−	0.675849i	$-0.236223\pi$
$11$	1962.00	1.47408	0.737040	+	0.675849i	$0.236223\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	−3087.00	−1.12500
$15$	0	0
$16$	−4895.00	−1.19507
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	−6561.00	−1.12500
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	0	0
$22$	−17658.0	−1.65834
$23$	22734.0	1.86850	0.934248	−	0.356623i	$-0.116072\pi$
$23$	22734.0	1.86850	0.934248	+	0.356623i	$0.116072\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	0	0
$28$	5831.00	0.265625
$29$	−21222.0	−0.870146	−0.435073	−	0.900395i	$-0.643278\pi$
$29$	−21222.0	−0.870146	−0.435073	+	0.900395i	$0.643278\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	16983.0	0.518280
$33$	0	0
$34$	0	0
$35$	0	0
$36$	12393.0	0.265625
$37$	−101194.	−1.99779	−0.998894	−	0.0470096i	$-0.985031\pi$
$37$	−101194.	−1.99779	−0.998894	+	0.0470096i	$0.985031\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	126614.	1.59249	0.796244	−	0.604975i	$-0.206817\pi$
$43$	126614.	1.59249	0.796244	+	0.604975i	$0.206817\pi$
$44$	33354.0	0.391552
$45$	0	0
$46$	−204606.	−2.10206
$47$	0	0	1.00000			$0$
$47$	0	0	−1.00000			$\pi$
$48$	0	0
$49$	117649.	1.00000
$50$	0	0
$51$	0	0
$52$	0	0
$53$	−50346.0	−0.338172	−0.169086	−	0.985601i	$-0.554082\pi$
$53$	−50346.0	−0.338172	−0.169086	+	0.985601i	$0.554082\pi$
$54$	0	0
$55$	0	0
$56$	145089.	0.826172
$57$	0	0
$58$	190998.	0.978915
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	250047.	1.00000
$64$	160433.	0.612003
$65$	0	0
$66$	0	0
$67$	53926.0	0.179297	0.0896487	−	0.995973i	$-0.471426\pi$
$67$	53926.0	0.179297	0.0896487	+	0.995973i	$0.471426\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	−242478.	−0.677481	−0.338741	−	0.940880i	$-0.610001\pi$
$71$	−242478.	−0.677481	−0.338741	+	0.940880i	$0.610001\pi$
$72$	308367.	0.826172
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	910746.	2.24751
$75$	0	0
$76$	0	0
$77$	672966.	1.47408
$78$	0	0
$79$	929378.	1.88500	0.942499	−	0.334208i	$-0.108469\pi$
$79$	929378.	1.88500	0.942499	+	0.334208i	$0.108469\pi$
$80$	0	0
$81$	531441.	1.00000
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	0	0
$86$	−1.13953e6	−1.79155
$87$	0	0
$88$	829926.	1.21784
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	0	0
$92$	386478.	0.496319
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	−1.05884e6	−1.12500
$99$	1.43030e6	1.47408
$100$	0	0
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	0	0
$105$	0	0
$106$	453114.	0.380443
$107$	−46314.0	−0.0378060	−0.0189030	−	0.999821i	$-0.506017\pi$
$107$	−46314.0	−0.0378060	−0.0189030	+	0.999821i	$0.506017\pi$
$108$	0	0
$109$	−2.58714e6	−1.99775	−0.998874	−	0.0474386i	$-0.984894\pi$
$109$	−2.58714e6	−1.99775	−0.998874	+	0.0474386i	$0.984894\pi$
$110$	0	0
$111$	0	0
$112$	−1.67898e6	−1.19507
$113$	2.43689e6	1.68889	0.844445	−	0.535642i	$-0.179931\pi$
$113$	2.43689e6	1.68889	0.844445	+	0.535642i	$0.179931\pi$
$114$	0	0
$115$	0	0
$116$	−360774.	−0.231133
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	2.07788e6	1.17291
$122$	0	0
$123$	0	0
$124$	0	0
$125$	0	0
$126$	−2.25042e6	−1.12500
$127$	96766.0	0.0472402	0.0236201	−	0.999721i	$-0.492481\pi$
$127$	96766.0	0.0472402	0.0236201	+	0.999721i	$0.492481\pi$
$128$	−2.53081e6	−1.20678
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0	0
$134$	−485334.	−0.201709
$135$	0	0
$136$	0	0
$137$	−4.52939e6	−1.76148	−0.880741	−	0.473598i	$-0.842955\pi$
$137$	−4.52939e6	−1.76148	−0.880741	+	0.473598i	$0.842955\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	0	0
$142$	2.18230e6	0.762166
$143$	0	0
$144$	−3.56846e6	−1.19507
$145$	0	0
$146$	0	0
$147$	0	0
$148$	−1.72030e6	−0.530663
$149$	−5.95330e6	−1.79970	−0.899848	−	0.436204i	$-0.856323\pi$
$149$	−5.95330e6	−1.79970	−0.899848	+	0.436204i	$0.856323\pi$
$150$	0	0
$151$	1.82840e6	0.531057	0.265528	−	0.964103i	$-0.414454\pi$
$151$	1.82840e6	0.531057	0.265528	+	0.964103i	$0.414454\pi$
$152$	0	0
$153$	0	0
$154$	−6.05669e6	−1.65834
$155$	0	0
$156$	0	0
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	−8.36440e6	−2.12062
$159$	0	0
$160$	0	0
$161$	7.79776e6	1.86850
$162$	−4.78297e6	−1.12500
$163$	5.49309e6	1.26839	0.634197	−	0.773171i	$-0.281331\pi$
$163$	5.49309e6	1.26839	0.634197	+	0.773171i	$0.281331\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	4.82681e6	1.00000
$170$	0	0
$171$	0	0
$172$	2.15244e6	0.423005
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0	0
$176$	−9.60399e6	−1.76163
$177$	0	0
$178$	0	0
$179$	−7.12762e6	−1.24276	−0.621378	−	0.783511i	$-0.713427\pi$
$179$	−7.12762e6	−1.24276	−0.621378	+	0.783511i	$0.713427\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	9.61648e6	1.54370
$185$	0	0
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	2.64544e6	0.379663	0.189831	−	0.981817i	$-0.439206\pi$
$191$	2.64544e6	0.379663	0.189831	+	0.981817i	$0.439206\pi$
$192$	0	0
$193$	−6.68999e6	−0.930579	−0.465290	−	0.885159i	$-0.654050\pi$
$193$	−6.68999e6	−0.930579	−0.465290	+	0.885159i	$0.654050\pi$
$194$	0	0
$195$	0	0
$196$	2.00003e6	0.265625
$197$	1.04066e7	1.36117	0.680585	−	0.732670i	$-0.261726\pi$
$197$	1.04066e7	1.36117	0.680585	+	0.732670i	$0.261726\pi$
$198$	−1.28727e7	−1.65834
$199$	0	0	1.00000			$0$
$199$	0	0	−1.00000			$\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	−7.27915e6	−0.870146
$204$	0	0
$205$	0	0
$206$	0	0
$207$	1.65731e7	1.86850
$208$	0	0
$209$	0	0
$210$	0	0
$211$	1.56456e7	1.66550	0.832748	−	0.553652i	$-0.186766\pi$
$211$	1.56456e7	1.66550	0.832748	+	0.553652i	$0.186766\pi$
$212$	−855882.	−0.0898269
$213$	0	0
$214$	416826.	0.0425318
$215$	0	0
$216$	0	0
$217$	0	0
$218$	2.32843e7	2.24747
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	5.82517e6	0.518280
$225$	0	0
$226$	−2.19320e7	−1.90000
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	−8.97691e6	−0.718890
$233$	2.92577e6	0.231299	0.115649	−	0.993290i	$-0.463105\pi$
$233$	2.92577e6	0.231299	0.115649	+	0.993290i	$0.463105\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	0	0
$238$	0	0
$239$	2.71015e7	1.98518	0.992591	−	0.121505i	$-0.0387721\pi$
$239$	2.71015e7	1.98518	0.992591	+	0.121505i	$0.0387721\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	−1.87009e7	−1.31952
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	4.25080e6	0.265625
$253$	4.46041e7	2.75431
$254$	−870894.	−0.0531452
$255$	0	0
$256$	1.25096e7	0.745628
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	−3.47095e7	−1.99779
$260$	0	0
$261$	−1.54708e7	−0.870146
$262$	0	0
$263$	−2.01675e7	−1.10863	−0.554313	−	0.832308i	$-0.687019\pi$
$263$	−2.01675e7	−1.10863	−0.554313	+	0.832308i	$0.687019\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	916742.	0.0476259
$269$	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			$\pi$
$272$	0	0
$273$	0	0
$274$	4.07645e7	1.98167
$275$	0	0
$276$	0	0
$277$	−1.09282e7	−0.514175	−0.257087	−	0.966388i	$-0.582763\pi$
$277$	−1.09282e7	−0.514175	−0.257087	+	0.966388i	$0.582763\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−2.55231e7	−1.15031	−0.575155	−	0.818045i	$-0.695058\pi$
$281$	−2.55231e7	−1.15031	−0.575155	+	0.818045i	$0.695058\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	−4.12213e6	−0.179956
$285$	0	0
$286$	0	0
$287$	0	0
$288$	1.23806e7	0.518280
$289$	2.41376e7	1.00000
$290$	0	0
$291$	0	0
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	0	0
$296$	−4.28051e7	−1.65052
$297$	0	0
$298$	5.35797e7	2.02466
$299$	0	0
$300$	0	0
$301$	4.34286e7	1.59249
$302$	−1.64556e7	−0.597439
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	1.14404e7	0.391552
$309$	0	0
$310$	0	0
$311$	0	0	1.00000			$0$
$311$	0	0	−1.00000			$\pi$
$312$	0	0
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0	0
$315$	0	0
$316$	1.57994e7	0.500703
$317$	1.51291e7	0.474937	0.237469	−	0.971395i	$-0.423682\pi$
$317$	1.51291e7	0.474937	0.237469	+	0.971395i	$0.423682\pi$
$318$	0	0
$319$	−4.16376e7	−1.28267
$320$	0	0
$321$	0	0
$322$	−7.01799e7	−2.10206
$323$	0	0
$324$	9.03450e6	0.265625
$325$	0	0
$326$	−4.94378e7	−1.42694
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	4.64551e7	1.28100	0.640500	−	0.767958i	$-0.278727\pi$
$331$	4.64551e7	1.28100	0.640500	+	0.767958i	$0.278727\pi$
$332$	0	0
$333$	−7.37704e7	−1.99779
$334$	0	0
$335$	0	0
$336$	0	0
$337$	6.54566e7	1.71027	0.855133	−	0.518408i	$-0.173475\pi$
$337$	6.54566e7	1.71027	0.855133	+	0.518408i	$0.173475\pi$
$338$	−4.34413e7	−1.12500
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	4.03536e7	1.00000
$344$	5.35577e7	1.31567
$345$	0	0
$346$	0	0
$347$	6.67538e7	1.59767	0.798836	−	0.601548i	$-0.205449\pi$
$347$	6.67538e7	1.59767	0.798836	+	0.601548i	$0.205449\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	0	0
$352$	3.33206e7	0.763986
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	6.41486e7	1.39810
$359$	−2.68617e7	−0.580565	−0.290282	−	0.956941i	$-0.593749\pi$
$359$	−2.68617e7	−0.580565	−0.290282	+	0.956941i	$0.593749\pi$
$360$	0	0
$361$	4.70459e7	1.00000
$362$	0	0
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	−1.11283e8	−2.23298
$369$	0	0
$370$	0	0
$371$	−1.72687e7	−0.338172
$372$	0	0
$373$	−9.13707e7	−1.76068	−0.880340	−	0.474344i	$-0.842685\pi$
$373$	−9.13707e7	−1.76068	−0.880340	+	0.474344i	$0.842685\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	3.31112e7	0.608215	0.304107	−	0.952638i	$-0.401642\pi$
$379$	3.31112e7	0.608215	0.304107	+	0.952638i	$0.401642\pi$
$380$	0	0
$381$	0	0
$382$	−2.38090e7	−0.427121
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	0	0
$385$	0	0
$386$	6.02099e7	1.04690
$387$	9.23016e7	1.59249
$388$	0	0
$389$	−6.93106e6	−0.117747	−0.0588737	−	0.998265i	$-0.518751\pi$
$389$	−6.93106e6	−0.117747	−0.0588737	+	0.998265i	$0.518751\pi$
$390$	0	0
$391$	0	0
$392$	4.97655e7	0.826172
$393$	0	0
$394$	−9.36598e7	−1.53132
$395$	0	0
$396$	2.43151e7	0.391552
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−1.26409e8	−1.96040	−0.980199	−	0.198016i	$-0.936550\pi$
$401$	−1.26409e8	−1.96040	−0.980199	+	0.198016i	$0.936550\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	6.55123e7	0.978915
$407$	−1.98543e8	−2.94490
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	−1.49158e8	−2.10206
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	8.36917e7	1.12160	0.560798	−	0.827953i	$-0.310495\pi$
$421$	8.36917e7	1.12160	0.560798	+	0.827953i	$0.310495\pi$
$422$	−1.40810e8	−1.87368
$423$	0	0
$424$	−2.12964e7	−0.279388
$425$	0	0
$426$	0	0
$427$	0	0
$428$	−787338.	−0.0100422
$429$	0	0
$430$	0	0
$431$	−8.60283e7	−1.07451	−0.537254	−	0.843421i	$-0.680538\pi$
$431$	−8.60283e7	−1.07451	−0.537254	+	0.843421i	$0.680538\pi$
$432$	0	0
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	−4.39814e7	−0.530652
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	8.57661e7	1.00000
$442$	0	0
$443$	−1.71340e8	−1.97082	−0.985410	−	0.170196i	$-0.945560\pi$
$443$	−1.71340e8	−1.97082	−0.985410	+	0.170196i	$0.945560\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	5.50285e7	0.612003
$449$	−1.73823e8	−1.92030	−0.960149	−	0.279490i	$-0.909835\pi$
$449$	−1.73823e8	−1.92030	−0.960149	+	0.279490i	$0.909835\pi$
$450$	0	0
$451$	0	0
$452$	4.14272e7	0.448611
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	1.26728e8	1.32777	0.663886	−	0.747834i	$-0.268906\pi$
$457$	1.26728e8	1.32777	0.663886	+	0.747834i	$0.268906\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	1.27272e8	1.28230	0.641151	−	0.767415i	$-0.278457\pi$
$463$	1.27272e8	1.28230	0.641151	+	0.767415i	$0.278457\pi$
$464$	1.03882e8	1.03988
$465$	0	0
$466$	−2.63320e7	−0.260211
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	0	0
$469$	1.84966e7	0.179297
$470$	0	0
$471$	0	0
$472$	0	0
$473$	2.48417e8	2.34746
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−3.67022e7	−0.338172
$478$	−2.43914e8	−2.23333
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	3.53240e7	0.311554
$485$	0	0
$486$	0	0
$487$	−2.20135e8	−1.90591	−0.952955	−	0.303113i	$-0.901974\pi$
$487$	−2.20135e8	−1.90591	−0.952955	+	0.303113i	$0.901974\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	1.78277e8	1.50609	0.753044	−	0.657970i	$-0.228585\pi$
$491$	1.78277e8	1.50609	0.753044	+	0.657970i	$0.228585\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−8.31700e7	−0.677481
$498$	0	0
$499$	−1.96143e8	−1.57860	−0.789300	−	0.614008i	$-0.789556\pi$
$499$	−1.96143e8	−1.57860	−0.789300	+	0.614008i	$0.789556\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	1.05770e8	0.826172
$505$	0	0
$506$	−4.01437e8	−3.09860
$507$	0	0
$508$	1.64502e6	0.0125482
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	0	0
$512$	4.93857e7	0.367952
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	0	0
$518$	3.12386e8	2.24751
$519$	0	0
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	1.39238e8	0.978915
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	0	0
$526$	1.81508e8	1.24720
$527$	0	0
$528$	0	0
$529$	3.68799e8	2.49128
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	2.28107e7	0.148130
$537$	0	0
$538$	0	0
$539$	2.30827e8	1.47408
$540$	0	0
$541$	−6.45700e7	−0.407792	−0.203896	−	0.978993i	$-0.565360\pi$
$541$	−6.45700e7	−0.407792	−0.203896	+	0.978993i	$0.565360\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	1.58854e8	0.970592	0.485296	−	0.874350i	$-0.338712\pi$
$547$	1.58854e8	0.970592	0.485296	+	0.874350i	$0.338712\pi$
$548$	−7.69997e7	−0.467894
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	3.18777e8	1.88500
$554$	9.83541e7	0.578447
$555$	0	0
$556$	0	0
$557$	−7.34035e7	−0.424767	−0.212384	−	0.977186i	$-0.568123\pi$
$557$	−7.34035e7	−0.424767	−0.212384	+	0.977186i	$0.568123\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	2.29708e8	1.29410
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	1.82284e8	1.00000
$568$	−1.02568e8	−0.559716
$569$	3.55493e8	1.92972	0.964859	−	0.262767i	$-0.0846349\pi$
$569$	3.55493e8	1.92972	0.964859	+	0.262767i	$0.0846349\pi$
$570$	0	0
$571$	−3.26262e8	−1.75250	−0.876250	−	0.481857i	$-0.839963\pi$
$571$	−3.26262e8	−1.75250	−0.876250	+	0.481857i	$0.839963\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	1.16956e8	0.612003
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	−2.17238e8	−1.12500
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−9.87789e7	−0.498492
$584$	0	0
$585$	0	0
$586$	0	0
$587$	0	0	1.00000			$0$
$587$	0	0	−1.00000			$\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	4.95345e8	2.38749
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	0	0
$596$	−1.01206e8	−0.478044
$597$	0	0
$598$	0	0
$599$	1.82026e8	0.846941	0.423471	−	0.905910i	$-0.360812\pi$
$599$	1.82026e8	0.846941	0.423471	+	0.905910i	$0.360812\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	−3.90857e8	−1.79155
$603$	3.93121e7	0.179297
$604$	3.10828e7	0.141062
$605$	0	0
$606$	0	0
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	2.35393e8	1.02191	0.510954	−	0.859608i	$-0.329292\pi$
$613$	2.35393e8	1.02191	0.510954	+	0.859608i	$0.329292\pi$
$614$	0	0
$615$	0	0
$616$	2.84665e8	1.21784
$617$	−4.63532e8	−1.97344	−0.986721	−	0.162423i	$-0.948069\pi$
$617$	−4.63532e8	−1.97344	−0.986721	+	0.162423i	$0.948069\pi$
$618$	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
$625$	0	0
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	1.83542e8	0.730544	0.365272	−	0.930901i	$-0.380976\pi$
$631$	1.83542e8	0.730544	0.365272	+	0.930901i	$0.380976\pi$
$632$	3.93127e8	1.55733
$633$	0	0
$634$	−1.36162e8	−0.534304
$635$	0	0
$636$	0	0
$637$	0	0
$638$	3.74738e8	1.44300
$639$	−1.76766e8	−0.677481
$640$	0	0
$641$	−4.47931e8	−1.70073	−0.850367	−	0.526189i	$-0.823620\pi$
$641$	−4.47931e8	−1.70073	−0.850367	+	0.526189i	$0.823620\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	1.32562e8	0.496319
$645$	0	0
$646$	0	0
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	2.24800e8	0.826172
$649$	0	0
$650$	0	0
$651$	0	0
$652$	9.33826e7	0.336917
$653$	−1.74812e8	−0.627816	−0.313908	−	0.949453i	$-0.601638\pi$
$653$	−1.74812e8	−0.627816	−0.313908	+	0.949453i	$0.601638\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	−5.69128e8	−1.98863	−0.994314	−	0.106485i	$-0.966040\pi$
$659$	−5.69128e8	−1.98863	−0.994314	+	0.106485i	$0.966040\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	−4.18096e8	−1.44113
$663$	0	0
$664$	0	0
$665$	0	0
$666$	6.63934e8	2.24751
$667$	−4.82461e8	−1.62587
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−5.17302e8	−1.69707	−0.848534	−	0.529141i	$-0.822514\pi$
$673$	−5.17302e8	−1.69707	−0.848534	+	0.529141i	$0.822514\pi$
$674$	−5.89109e8	−1.92405
$675$	0	0
$676$	8.20558e7	0.265625
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	−5.22860e8	−1.64105	−0.820527	−	0.571607i	$-0.806320\pi$
$683$	−5.22860e8	−1.64105	−0.820527	+	0.571607i	$0.806320\pi$
$684$	0	0
$685$	0	0
$686$	−3.63182e8	−1.12500
$687$	0	0
$688$	−6.19776e8	−1.90313
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	4.90592e8	1.47408
$694$	−6.00785e8	−1.79738
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−6.71321e8	−1.94884	−0.974420	−	0.224735i	$-0.927848\pi$
$701$	−6.71321e8	−1.94884	−0.974420	+	0.224735i	$0.927848\pi$
$702$	0	0
$703$	0	0
$704$	3.14770e8	0.902142
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−5.55400e8	−1.55836	−0.779178	−	0.626802i	$-0.784363\pi$
$709$	−5.55400e8	−1.55836	−0.779178	+	0.626802i	$0.784363\pi$
$710$	0	0
$711$	6.77517e8	1.88500
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	−1.21170e8	−0.330107
$717$	0	0
$718$	2.41756e8	0.653136
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	0	0
$721$	0	0
$722$	−4.23413e8	−1.12500
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	0	0	1.00000			$0$
$727$	0	0	−1.00000			$\pi$
$728$	0	0
$729$	3.87420e8	1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	0	0
$736$	3.86092e8	0.968405
$737$	1.05803e8	0.264299
$738$	0	0
$739$	−1.65862e8	−0.410973	−0.205486	−	0.978660i	$-0.565878\pi$
$739$	−1.65862e8	−0.410973	−0.205486	+	0.978660i	$0.565878\pi$
$740$	0	0
$741$	0	0
$742$	1.55418e8	0.380443
$743$	1.87319e8	0.456684	0.228342	−	0.973581i	$-0.426670\pi$
$743$	1.87319e8	0.456684	0.228342	+	0.973581i	$0.426670\pi$
$744$	0	0
$745$	0	0
$746$	8.22336e8	1.98076
$747$	0	0
$748$	0	0
$749$	−1.58857e7	−0.0378060
$750$	0	0
$751$	−8.41137e8	−1.98585	−0.992926	−	0.118736i	$-0.962116\pi$
$751$	−8.41137e8	−1.98585	−0.992926	+	0.118736i	$0.962116\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−3.45533e8	−0.796529	−0.398264	−	0.917271i	$-0.630387\pi$
$757$	−3.45533e8	−0.796529	−0.398264	+	0.917271i	$0.630387\pi$
$758$	−2.98001e8	−0.684242
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	−8.87390e8	−1.99775
$764$	4.49725e7	0.100848
$765$	0	0
$766$	0	0
$767$	0	0
$768$	0	0
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	0	0
$772$	−1.13730e8	−0.247185
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	−8.30714e8	−1.79155
$775$	0	0
$776$	0	0
$777$	0	0
$778$	6.23796e7	0.132466
$779$	0	0
$780$	0	0
$781$	−4.75742e8	−0.998661
$782$	0	0
$783$	0	0
$784$	−5.75892e8	−1.19507
$785$	0	0
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	1.76913e8	0.361561
$789$	0	0
$790$	0	0
$791$	8.35855e8	1.68889
$792$	6.05016e8	1.21784
$793$	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
$801$	0	0
$802$	1.13768e9	2.20545
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	3.36371e8	0.635292	0.317646	−	0.948209i	$-0.397108\pi$
$809$	3.36371e8	0.635292	0.317646	+	0.948209i	$0.397108\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	−1.23745e8	−0.231133
$813$	0	0
$814$	1.78688e9	3.31301
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	7.88782e8	1.42537	0.712685	−	0.701484i	$-0.247479\pi$
$821$	7.88782e8	1.42537	0.712685	+	0.701484i	$0.247479\pi$
$822$	0	0
$823$	−1.02325e9	−1.83563	−0.917813	−	0.397014i	$-0.870046\pi$
$823$	−1.02325e9	−1.83563	−0.917813	+	0.397014i	$0.870046\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	5.56178e8	0.983326	0.491663	−	0.870786i	$-0.336389\pi$
$827$	5.56178e8	0.983326	0.491663	+	0.870786i	$0.336389\pi$
$828$	2.81742e8	0.496319
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	−1.44450e8	−0.242845
$842$	−7.53225e8	−1.26179
$843$	0	0
$844$	2.65975e8	0.442398
$845$	0	0
$846$	0	0
$847$	7.12714e8	1.17291
$848$	2.46444e8	0.404138
$849$	0	0
$850$	0	0
$851$	−2.30054e9	−3.73286
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	−1.95908e7	−0.0312343
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	7.74255e8	1.20882
$863$	8.77431e8	1.36515	0.682576	−	0.730815i	$-0.260860\pi$
$863$	8.77431e8	1.36515	0.682576	+	0.730815i	$0.260860\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0	0
$868$	0	0
$869$	1.82344e9	2.77864
$870$	0	0
$871$	0	0
$872$	−1.09436e9	−1.65048
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	1.30615e9	1.93640	0.968198	−	0.250185i	$-0.0804915\pi$
$877$	1.30615e9	1.93640	0.968198	+	0.250185i	$0.0804915\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	−7.71895e8	−1.12500
$883$	4.73327e8	0.687510	0.343755	−	0.939059i	$-0.388301\pi$
$883$	4.73327e8	0.687510	0.343755	+	0.939059i	$0.388301\pi$
$884$	0	0
$885$	0	0
$886$	1.54206e9	2.21717
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	3.31907e7	0.0472402
$890$	0	0
$891$	1.04269e9	1.47408
$892$	0	0
$893$	0	0
$894$	0	0
$895$	0	0
$896$	−8.68067e8	−1.20678
$897$	0	0
$898$	1.56441e9	2.16033
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	1.03081e9	1.39531
$905$	0	0
$906$	0	0
$907$	−1.28922e9	−1.72785	−0.863925	−	0.503621i	$-0.832001\pi$
$907$	−1.28922e9	−1.72785	−0.863925	+	0.503621i	$0.832001\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	5.85794e7	0.0774800	0.0387400	−	0.999249i	$-0.487666\pi$
$911$	5.85794e7	0.0774800	0.0387400	+	0.999249i	$0.487666\pi$
$912$	0	0
$913$	0	0
$914$	−1.14055e9	−1.49374
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−1.07950e9	−1.39084	−0.695419	−	0.718604i	$-0.744781\pi$
$919$	−1.07950e9	−1.39084	−0.695419	+	0.718604i	$0.744781\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	−1.14545e9	−1.44259
$927$	0	0
$928$	−3.60413e8	−0.450979
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	4.97382e7	0.0614387
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	−1.66470e8	−0.201709
$939$	0	0
$940$	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
$946$	−2.23575e9	−2.64089
$947$	−6.84836e8	−0.806374	−0.403187	−	0.915118i	$-0.632098\pi$
$947$	−6.84836e8	−0.806374	−0.403187	+	0.915118i	$0.632098\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	8.73142e8	1.00880	0.504401	−	0.863469i	$-0.331713\pi$
$953$	8.73142e8	1.00880	0.504401	+	0.863469i	$0.331713\pi$
$954$	3.30320e8	0.380443
$955$	0	0
$956$	4.60726e8	0.527314
$957$	0	0
$958$	0	0
$959$	−1.55358e9	−1.76148
$960$	0	0
$961$	8.87504e8	1.00000
$962$	0	0
$963$	−3.37629e7	−0.0378060
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−8.99699e8	−0.994988	−0.497494	−	0.867467i	$-0.665746\pi$
$967$	−8.99699e8	−0.994988	−0.497494	+	0.867467i	$0.665746\pi$
$968$	8.78945e8	0.969026
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	0	0
$973$	0	0
$974$	1.98121e9	2.14415
$975$	0	0
$976$	0	0
$977$	4.59650e8	0.492882	0.246441	−	0.969158i	$-0.420739\pi$
$977$	4.59650e8	0.492882	0.246441	+	0.969158i	$0.420739\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−1.88603e9	−1.99775
$982$	−1.60449e9	−1.69435
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	2.87844e9	2.97556
$990$	0	0
$991$	1.36299e9	1.40046	0.700230	−	0.713918i	$-0.253081\pi$
$991$	1.36299e9	1.40046	0.700230	+	0.713918i	$0.253081\pi$
$992$	0	0
$993$	0	0
$994$	7.48530e8	0.762166
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	1.76529e9	1.77592
$999$	0	0

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.7.d.a.76.1		1
5.2	odd	4		175.7.c.a.174.1		2
5.3	odd	4		175.7.c.a.174.2		2
5.4	even	2		7.7.b.a.6.1	✓	1
7.6	odd	2	CM	175.7.d.a.76.1		1
15.14	odd	2		63.7.d.a.55.1		1
20.19	odd	2		112.7.c.a.97.1		1
35.4	even	6		49.7.d.a.19.1		2
35.9	even	6		49.7.d.a.31.1		2
35.13	even	4		175.7.c.a.174.2		2
35.19	odd	6		49.7.d.a.31.1		2
35.24	odd	6		49.7.d.a.19.1		2
35.27	even	4		175.7.c.a.174.1		2
35.34	odd	2		7.7.b.a.6.1	✓	1
40.19	odd	2		448.7.c.b.321.1		1
40.29	even	2		448.7.c.a.321.1		1
105.104	even	2		63.7.d.a.55.1		1
140.139	even	2		112.7.c.a.97.1		1
280.69	odd	2		448.7.c.a.321.1		1
280.139	even	2		448.7.c.b.321.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.7.b.a.6.1	✓	1	5.4	even	2
7.7.b.a.6.1	✓	1	35.34	odd	2
49.7.d.a.19.1		2	35.4	even	6
49.7.d.a.19.1		2	35.24	odd	6
49.7.d.a.31.1		2	35.9	even	6
49.7.d.a.31.1		2	35.19	odd	6
63.7.d.a.55.1		1	15.14	odd	2
63.7.d.a.55.1		1	105.104	even	2
112.7.c.a.97.1		1	20.19	odd	2
112.7.c.a.97.1		1	140.139	even	2
175.7.c.a.174.1		2	5.2	odd	4
175.7.c.a.174.1		2	35.27	even	4
175.7.c.a.174.2		2	5.3	odd	4
175.7.c.a.174.2		2	35.13	even	4
175.7.d.a.76.1		1	1.1	even	1	trivial
175.7.d.a.76.1		1	7.6	odd	2	CM
448.7.c.a.321.1		1	40.29	even	2
448.7.c.a.321.1		1	280.69	odd	2
448.7.c.b.321.1		1	40.19	odd	2
448.7.c.b.321.1		1	280.139	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	175.7.d.a.76.1

Level	$175$
Weight	$7$
Character	175.76
Self dual	yes
Analytic conductor	$40.259$
Analytic rank	$0$
Dimension	$1$
CM discriminant	-7
Inner twists	$2$