LMFDB - Embedded newform 211.5.b.a.210.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [211,5,Mod(210,211)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(211, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("211.210");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 211 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	211.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$21.8110622107$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.5697.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 15x - 17 $ x^3 - 15*x - 17
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			210.3
Root			$4.34849$ of defining polynomial
Character	$\chi$	$=$	211.210

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.0000 q^{4} +29.3774 q^{5} +81.0000 q^{9} +O(q^{10})$	$q+16.0000 q^{4} +29.3774 q^{5} +81.0000 q^{9} +240.017 q^{11} -310.979 q^{13} +256.000 q^{16} -285.490 q^{19} +470.038 q^{20} +238.032 q^{25} +1296.00 q^{36} -2733.95 q^{37} +298.192 q^{43} +3840.27 q^{44} +2379.57 q^{45} +2268.62 q^{47} +2401.00 q^{49} -4975.67 q^{52} +5407.00 q^{53} +7051.07 q^{55} +1687.00 q^{59} +4096.00 q^{64} -9135.76 q^{65} -8525.77 q^{71} -6433.00 q^{73} -4567.84 q^{76} +10617.4 q^{79} +7520.61 q^{80} +6561.00 q^{81} -11753.0 q^{83} -8386.95 q^{95} +19441.4 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 48 q^{4} + 243 q^{9}+O(q^{10}) $ 3 * q + 48 * q^4 + 243 * q^9	$ 3 q + 48 q^{4} + 243 q^{9} + 768 q^{16} + 1875 q^{25} + 3888 q^{36} + 7203 q^{49} + 16221 q^{53} + 12453 q^{55} + 5061 q^{59} + 12288 q^{64} - 5667 q^{65} - 19299 q^{73} + 19683 q^{81} - 35259 q^{83} - 52827 q^{95}+O(q^{100}) $ 3 * q + 48 * q^4 + 243 * q^9 + 768 * q^16 + 1875 * q^25 + 3888 * q^36 + 7203 * q^49 + 16221 * q^53 + 12453 * q^55 + 5061 * q^59 + 12288 * q^64 - 5667 * q^65 - 19299 * q^73 + 19683 * q^81 - 35259 * q^83 - 52827 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/211\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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			$\pi$
$3$	0	0	1.00000			$0$
$3$	0	0	−1.00000			$\pi$
$4$	16.0000	1.00000
$5$	29.3774	1.17510	0.587548	−	0.809189i	$-0.300093\pi$
$5$	29.3774	1.17510	0.587548	+	0.809189i	$0.300093\pi$
$6$	0	0
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	0	0
$9$	81.0000	1.00000
$10$	0	0
$11$	240.017	1.98361	0.991805	−	0.127761i	$-0.0407790\pi$
$11$	240.017	1.98361	0.991805	+	0.127761i	$0.0407790\pi$
$12$	0	0
$13$	−310.979	−1.84011	−0.920057	−	0.391784i	$-0.871858\pi$
$13$	−310.979	−1.84011	−0.920057	+	0.391784i	$0.871858\pi$
$14$	0	0
$15$	0	0
$16$	256.000	1.00000
$17$	0	0	1.00000			$0$
$17$	0	0	−1.00000			$\pi$
$18$	0	0
$19$	−285.490	−0.790831	−0.395415	−	0.918502i	$-0.629399\pi$
$19$	−285.490	−0.790831	−0.395415	+	0.918502i	$0.629399\pi$
$20$	470.038	1.17510
$21$	0	0
$22$	0	0
$23$	0	0	1.00000			$0$
$23$	0	0	−1.00000			$\pi$
$24$	0	0
$25$	238.032	0.380851
$26$	0	0
$27$	0	0
$28$	0	0
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0	0
$36$	1296.00	1.00000
$37$	−2733.95	−1.99704	−0.998522	−	0.0543574i	$-0.982689\pi$
$37$	−2733.95	−1.99704	−0.998522	+	0.0543574i	$0.982689\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	298.192	0.161272	0.0806361	−	0.996744i	$-0.474305\pi$
$43$	298.192	0.161272	0.0806361	+	0.996744i	$0.474305\pi$
$44$	3840.27	1.98361
$45$	2379.57	1.17510
$46$	0	0
$47$	2268.62	1.02699	0.513494	−	0.858093i	$-0.328351\pi$
$47$	2268.62	1.02699	0.513494	+	0.858093i	$0.328351\pi$
$48$	0	0
$49$	2401.00	1.00000
$50$	0	0
$51$	0	0
$52$	−4975.67	−1.84011
$53$	5407.00	1.92488	0.962442	−	0.271487i	$-0.0875153\pi$
$53$	5407.00	1.92488	0.962442	+	0.271487i	$0.0875153\pi$
$54$	0	0
$55$	7051.07	2.33093
$56$	0	0
$57$	0	0
$58$	0	0
$59$	1687.00	0.484631	0.242315	−	0.970198i	$-0.422093\pi$
$59$	1687.00	0.484631	0.242315	+	0.970198i	$0.422093\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	0	0
$64$	4096.00	1.00000
$65$	−9135.76	−2.16231
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	−8525.77	−1.69128	−0.845642	−	0.533750i	$-0.820782\pi$
$71$	−8525.77	−1.69128	−0.845642	+	0.533750i	$0.820782\pi$
$72$	0	0
$73$	−6433.00	−1.20717	−0.603584	−	0.797299i	$-0.706261\pi$
$73$	−6433.00	−1.20717	−0.603584	+	0.797299i	$0.706261\pi$
$74$	0	0
$75$	0	0
$76$	−4567.84	−0.790831
$77$	0	0
$78$	0	0
$79$	10617.4	1.70123	0.850617	−	0.525786i	$-0.176229\pi$
$79$	10617.4	1.70123	0.850617	+	0.525786i	$0.176229\pi$
$80$	7520.61	1.17510
$81$	6561.00	1.00000
$82$	0	0
$83$	−11753.0	−1.70605	−0.853027	−	0.521867i	$-0.825236\pi$
$83$	−11753.0	−1.70605	−0.853027	+	0.521867i	$0.825236\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	0	0
$94$	0	0
$95$	−8386.95	−0.929302
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	19441.4	1.98361
$100$	3808.51	0.380851
$101$	−7206.36	−0.706436	−0.353218	−	0.935541i	$-0.614913\pi$
$101$	−7206.36	−0.706436	−0.353218	+	0.935541i	$0.614913\pi$
$102$	0	0
$103$	−13260.3	−1.24991	−0.624954	−	0.780662i	$-0.714882\pi$
$103$	−13260.3	−1.24991	−0.624954	+	0.780662i	$0.714882\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−19903.8	−1.73848	−0.869239	−	0.494392i	$-0.835391\pi$
$107$	−19903.8	−1.73848	−0.869239	+	0.494392i	$0.835391\pi$
$108$	0	0
$109$	−23713.0	−1.99588	−0.997938	−	0.0641871i	$-0.979555\pi$
$109$	−23713.0	−1.99588	−0.997938	+	0.0641871i	$0.979555\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	19502.1	1.52730	0.763651	−	0.645630i	$-0.223405\pi$
$113$	19502.1	1.52730	0.763651	+	0.645630i	$0.223405\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−25189.3	−1.84011
$118$	0	0
$119$	0	0
$120$	0	0
$121$	42967.1	2.93471
$122$	0	0
$123$	0	0
$124$	0	0
$125$	−11368.1	−0.727560
$126$	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			$\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	6159.88	0.328194	0.164097	−	0.986444i	$-0.447529\pi$
$137$	6159.88	0.328194	0.164097	+	0.986444i	$0.447529\pi$
$138$	0	0
$139$	6892.81	0.356752	0.178376	−	0.983962i	$-0.442916\pi$
$139$	6892.81	0.356752	0.178376	+	0.983962i	$0.442916\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	−74640.3	−3.65007
$144$	20736.0	1.00000
$145$	0	0
$146$	0	0
$147$	0	0
$148$	−43743.2	−1.99704
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0	0
$151$	−19505.7	−0.855477	−0.427738	−	0.903903i	$-0.640690\pi$
$151$	−19505.7	−0.855477	−0.427738	+	0.903903i	$0.640690\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	0	0	1.00000			$0$
$157$	0	0	−1.00000			$\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−39913.0	−1.50224	−0.751120	−	0.660166i	$-0.770486\pi$
$163$	−39913.0	−1.50224	−0.751120	+	0.660166i	$0.770486\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	68147.1	2.38602
$170$	0	0
$171$	−23124.7	−0.790831
$172$	4771.08	0.161272
$173$	59766.4	1.99694	0.998469	−	0.0553130i	$-0.0176157\pi$
$173$	59766.4	1.99694	0.998469	+	0.0553130i	$0.0176157\pi$
$174$	0	0
$175$	0	0
$176$	61444.3	1.98361
$177$	0	0
$178$	0	0
$179$	−43675.5	−1.36311	−0.681557	−	0.731765i	$-0.738697\pi$
$179$	−43675.5	−1.36311	−0.681557	+	0.731765i	$0.738697\pi$
$180$	38073.1	1.17510
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	−80316.4	−2.34672
$186$	0	0
$187$	0	0
$188$	36297.9	1.02699
$189$	0	0
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	0	0
$193$	65197.1	1.75030	0.875152	−	0.483848i	$-0.160761\pi$
$193$	65197.1	1.75030	0.875152	+	0.483848i	$0.160761\pi$
$194$	0	0
$195$	0	0
$196$	38416.0	1.00000
$197$	0	0	1.00000			$0$
$197$	0	0	−1.00000			$\pi$
$198$	0	0
$199$	−76016.3	−1.91955	−0.959777	−	0.280762i	$-0.909413\pi$
$199$	−76016.3	−1.91955	−0.959777	+	0.280762i	$0.909413\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	−79610.7	−1.84011
$209$	−68522.4	−1.56870
$210$	0	0
$211$	44521.0	1.00000
$211$	44521.0	1.00000
$212$	86512.0	1.92488
$213$	0	0
$214$	0	0
$215$	8760.11	0.189510
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	112817.	2.33093
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	0	0
$225$	19280.6	0.380851
$226$	0	0
$227$	49042.0	0.951736	0.475868	−	0.879517i	$-0.342134\pi$
$227$	49042.0	0.951736	0.475868	+	0.879517i	$0.342134\pi$
$228$	0	0
$229$	0	0	1.00000			$0$
$229$	0	0	−1.00000			$\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	66646.1	1.20681
$236$	26992.0	0.484631
$237$	0	0
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	−115355.	−1.98611	−0.993055	−	0.117653i	$-0.962463\pi$
$241$	−115355.	−1.98611	−0.993055	+	0.117653i	$0.962463\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	70535.1	1.17510
$246$	0	0
$247$	88781.5	1.45522
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	0	0
$256$	65536.0	1.00000
$257$	1318.04	0.0199555	0.00997773	−	0.999950i	$-0.496824\pi$
$257$	1318.04	0.0199555	0.00997773	+	0.999950i	$0.496824\pi$
$258$	0	0
$259$	0	0
$260$	−146172.	−2.16231
$261$	0	0
$262$	0	0
$263$	−39113.0	−0.565470	−0.282735	−	0.959198i	$-0.591242\pi$
$263$	−39113.0	−0.565470	−0.282735	+	0.959198i	$0.591242\pi$
$264$	0	0
$265$	158844.	2.26192
$266$	0	0
$267$	0	0
$268$	0	0
$269$	−136153.	−1.88158	−0.940790	−	0.338991i	$-0.889914\pi$
$269$	−136153.	−1.88158	−0.940790	+	0.338991i	$0.889914\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	57131.6	0.755459
$276$	0	0
$277$	−24092.4	−0.313993	−0.156997	−	0.987599i	$-0.550181\pi$
$277$	−24092.4	−0.313993	−0.156997	+	0.987599i	$0.550181\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	5100.79	0.0645989	0.0322994	−	0.999478i	$-0.489717\pi$
$281$	5100.79	0.0645989	0.0322994	+	0.999478i	$0.489717\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	−136412.	−1.69128
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	83521.0	1.00000
$290$	0	0
$291$	0	0
$292$	−102928.	−1.20717
$293$	−31073.0	−0.361949	−0.180975	−	0.983488i	$-0.557925\pi$
$293$	−31073.0	−0.361949	−0.180975	+	0.983488i	$0.557925\pi$
$294$	0	0
$295$	49559.7	0.569488
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	−73085.4	−0.790831
$305$	0	0
$306$	0	0
$307$	184854.	1.96134	0.980669	−	0.195676i	$-0.0626902\pi$
$307$	184854.	1.96134	0.980669	+	0.195676i	$0.0626902\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−144158.	−1.49045	−0.745226	−	0.666812i	$-0.767658\pi$
$311$	−144158.	−1.49045	−0.745226	+	0.666812i	$0.767658\pi$
$312$	0	0
$313$	0	0	1.00000			$0$
$313$	0	0	−1.00000			$\pi$
$314$	0	0
$315$	0	0
$316$	169878.	1.70123
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	0	0
$320$	120330.	1.17510
$321$	0	0
$322$	0	0
$323$	0	0
$324$	104976.	1.00000
$325$	−74022.9	−0.700809
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−162059.	−1.47917	−0.739584	−	0.673064i	$-0.764978\pi$
$331$	−162059.	−1.47917	−0.739584	+	0.673064i	$0.764978\pi$
$332$	−188048.	−1.70605
$333$	−221450.	−1.99704
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−134108.	−1.18085	−0.590426	−	0.807092i	$-0.701040\pi$
$337$	−134108.	−1.18085	−0.590426	+	0.807092i	$0.701040\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	73840.0	0.613243	0.306622	−	0.951832i	$-0.400801\pi$
$347$	73840.0	0.613243	0.306622	+	0.951832i	$0.400801\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	−250465.	−1.98742
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−713.000	−0.00553224	−0.00276612	−	0.999996i	$-0.500880\pi$
$359$	−713.000	−0.00553224	−0.00276612	+	0.999996i	$0.500880\pi$
$360$	0	0
$361$	−48816.5	−0.374587
$362$	0	0
$363$	0	0
$364$	0	0
$365$	−188985.	−1.41854
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	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
$375$	0	0
$376$	0	0
$377$	0	0
$378$	0	0
$379$	0	0	1.00000			$0$
$379$	0	0	−1.00000			$\pi$
$380$	−134191.	−0.929302
$381$	0	0
$382$	0	0
$383$	245939.	1.67660	0.838302	−	0.545206i	$-0.183549\pi$
$383$	245939.	1.67660	0.838302	+	0.545206i	$0.183549\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	24153.6	0.161272
$388$	0	0
$389$	290770.	1.92155	0.960773	−	0.277336i	$-0.0894516\pi$
$389$	290770.	1.92155	0.960773	+	0.277336i	$0.0894516\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	311912.	1.99911
$396$	311062.	1.98361
$397$	0	0	1.00000			$0$
$397$	0	0	−1.00000			$\pi$
$398$	0	0
$399$	0	0
$400$	60936.1	0.380851
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	0	0
$404$	−115302.	−0.706436
$405$	192745.	1.17510
$406$	0	0
$407$	−656194.	−3.96135
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	−212164.	−1.24991
$413$	0	0
$414$	0	0
$415$	−345273.	−2.00478
$416$	0	0
$417$	0	0
$418$	0	0
$419$	335374.	1.91030	0.955149	−	0.296127i	$-0.0956950\pi$
$419$	335374.	1.91030	0.955149	+	0.296127i	$0.0956950\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	183758.	1.02699
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	−318461.	−1.73848
$429$	0	0
$430$	0	0
$431$	−261152.	−1.40585	−0.702923	−	0.711265i	$-0.748122\pi$
$431$	−261152.	−1.40585	−0.702923	+	0.711265i	$0.748122\pi$
$432$	0	0
$433$	54047.0	0.288268	0.144134	−	0.989558i	$-0.453960\pi$
$433$	54047.0	0.288268	0.144134	+	0.989558i	$0.453960\pi$
$434$	0	0
$435$	0	0
$436$	−379408.	−1.99588
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	194481.	1.00000
$442$	0	0
$443$	3244.16	0.0165308	0.00826541	−	0.999966i	$-0.497369\pi$
$443$	3244.16	0.0165308	0.00826541	+	0.999966i	$0.497369\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	0	0	1.00000			$0$
$449$	0	0	−1.00000			$\pi$
$450$	0	0
$451$	0	0
$452$	312034.	1.52730
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−428078.	−1.96286	−0.981430	−	0.191823i	$-0.938560\pi$
$467$	−428078.	−1.96286	−0.981430	+	0.191823i	$0.938560\pi$
$468$	−403029.	−1.84011
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	71571.1	0.319901
$474$	0	0
$475$	−67955.6	−0.301188
$476$	0	0
$477$	437967.	1.92488
$478$	0	0
$479$	0	0	1.00000			$0$
$479$	0	0	−1.00000			$\pi$
$480$	0	0
$481$	850203.	3.67479
$482$	0	0
$483$	0	0
$484$	687473.	2.93471
$485$	0	0
$486$	0	0
$487$	381287.	1.60766	0.803830	−	0.594859i	$-0.202792\pi$
$487$	381287.	1.60766	0.803830	+	0.594859i	$0.202792\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−448206.	−1.85915	−0.929576	−	0.368632i	$-0.879826\pi$
$491$	−448206.	−1.85915	−0.929576	+	0.368632i	$0.879826\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	571137.	2.33093
$496$	0	0
$497$	0	0
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	−181890.	−0.727560
$501$	0	0
$502$	0	0
$503$	−263373.	−1.04096	−0.520482	−	0.853872i	$-0.674248\pi$
$503$	−263373.	−1.04096	−0.520482	+	0.853872i	$0.674248\pi$
$504$	0	0
$505$	−211704.	−0.830131
$506$	0	0
$507$	0	0
$508$	0	0
$509$	344445.	1.32949	0.664743	−	0.747072i	$-0.268541\pi$
$509$	344445.	1.32949	0.664743	+	0.747072i	$0.268541\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	−389552.	−1.46876
$516$	0	0
$517$	544506.	2.03714
$518$	0	0
$519$	0	0
$520$	0	0
$521$	147364.	0.542895	0.271447	−	0.962453i	$-0.412498\pi$
$521$	147364.	0.542895	0.271447	+	0.962453i	$0.412498\pi$
$522$	0	0
$523$	476982.	1.74381	0.871903	−	0.489678i	$-0.162886\pi$
$523$	476982.	1.74381	0.871903	+	0.489678i	$0.162886\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	0	0
$528$	0	0
$529$	279841.	1.00000
$530$	0	0
$531$	136647.	0.484631
$532$	0	0
$533$	0	0
$534$	0	0
$535$	−584723.	−2.04288
$536$	0	0
$537$	0	0
$538$	0	0
$539$	576280.	1.98361
$540$	0	0
$541$	39546.7	0.135119	0.0675594	−	0.997715i	$-0.478479\pi$
$541$	39546.7	0.135119	0.0675594	+	0.997715i	$0.478479\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	−696626.	−2.34535
$546$	0	0
$547$	49607.0	0.165794	0.0828969	−	0.996558i	$-0.473583\pi$
$547$	49607.0	0.165794	0.0828969	+	0.996558i	$0.473583\pi$
$548$	98558.1	0.328194
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	110285.	0.356752
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	−92731.6	−0.296759
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	572921.	1.79473
$566$	0	0
$567$	0	0
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	−1.19424e6	−3.65007
$573$	0	0
$574$	0	0
$575$	0	0
$576$	331776.	1.00000
$577$	0	0	1.00000			$0$
$577$	0	0	−1.00000			$\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	1.29777e6	3.81822
$584$	0	0
$585$	−739997.	−2.16231
$586$	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
$592$	−699892.	−1.99704
$593$	−522280.	−1.48523	−0.742615	−	0.669718i	$-0.766415\pi$
$593$	−522280.	−1.48523	−0.742615	+	0.669718i	$0.766415\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	0	0
$601$	600131.	1.66149	0.830744	−	0.556655i	$-0.187915\pi$
$601$	600131.	1.66149	0.830744	+	0.556655i	$0.187915\pi$
$602$	0	0
$603$	0	0
$604$	−312092.	−0.855477
$605$	1.26226e6	3.44856
$606$	0	0
$607$	−267673.	−0.726486	−0.363243	−	0.931694i	$-0.618331\pi$
$607$	−267673.	−0.726486	−0.363243	+	0.931694i	$0.618331\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−705493.	−1.88978
$612$	0	0
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	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
$624$	0	0
$625$	−482736.	−1.23580
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	−390553.	−0.980892	−0.490446	−	0.871472i	$-0.663166\pi$
$631$	−390553.	−0.980892	−0.490446	+	0.871472i	$0.663166\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−746661.	−1.84011
$638$	0	0
$639$	−690587.	−1.69128
$640$	0	0
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	0	0
$643$	0	0	1.00000			$0$
$643$	0	0	−1.00000			$\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	509307.	1.21667	0.608333	−	0.793682i	$-0.291839\pi$
$647$	509307.	1.21667	0.608333	+	0.793682i	$0.291839\pi$
$648$	0	0
$649$	404908.	0.961319
$650$	0	0
$651$	0	0
$652$	−638608.	−1.50224
$653$	346207.	0.811913	0.405956	−	0.913892i	$-0.366938\pi$
$653$	346207.	0.811913	0.405956	+	0.913892i	$0.366938\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−521073.	−1.20717
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	0	0
$676$	1.09035e6	2.38602
$677$	375182.	0.818588	0.409294	−	0.912403i	$-0.365775\pi$
$677$	375182.	0.818588	0.409294	+	0.912403i	$0.365775\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	−369995.	−0.790831
$685$	180961.	0.385660
$686$	0	0
$687$	0	0
$688$	76337.2	0.161272
$689$	−1.68147e6	−3.54201
$690$	0	0
$691$	−950588.	−1.99084	−0.995420	−	0.0956016i	$-0.969523\pi$
$691$	−950588.	−1.99084	−0.995420	+	0.0956016i	$0.969523\pi$
$692$	956262.	1.99694
$693$	0	0
$694$	0	0
$695$	202493.	0.419218
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	0	0	1.00000			$0$
$701$	0	0	−1.00000			$\pi$
$702$	0	0
$703$	780516.	1.57932
$704$	983109.	1.98361
$705$	0	0
$706$	0	0
$707$	0	0
$708$	0	0
$709$	−251098.	−0.499517	−0.249759	−	0.968308i	$-0.580351\pi$
$709$	−251098.	−0.499517	−0.249759	+	0.968308i	$0.580351\pi$
$710$	0	0
$711$	860010.	1.70123
$712$	0	0
$713$	0	0
$714$	0	0
$715$	−2.19274e6	−4.28918
$716$	−698809.	−1.36311
$717$	0	0
$718$	0	0
$719$	0	0	1.00000			$0$
$719$	0	0	−1.00000			$\pi$
$720$	609170.	1.17510
$721$	0	0
$722$	0	0
$723$	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
$729$	531441.	1.00000
$730$	0	0
$731$	0	0
$732$	0	0
$733$	1.05405e6	1.96179	0.980896	−	0.194531i	$-0.0623184\pi$
$733$	1.05405e6	1.96179	0.980896	+	0.194531i	$0.0623184\pi$
$734$	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			$\pi$
$740$	−1.28506e6	−2.34672
$741$	0	0
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−951993.	−1.70605
$748$	0	0
$749$	0	0
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	580766.	1.02699
$753$	0	0
$754$	0	0
$755$	−573028.	−1.00527
$756$	0	0
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−524622.	−0.891776
$768$	0	0
$769$	89010.4	0.150518	0.0752590	−	0.997164i	$-0.476022\pi$
$769$	89010.4	0.150518	0.0752590	+	0.997164i	$0.476022\pi$
$770$	0	0
$771$	0	0
$772$	1.04315e6	1.75030
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	−2.04633e6	−3.35485
$782$	0	0
$783$	0	0
$784$	614656.	1.00000
$785$	0	0
$786$	0	0
$787$	−705838.	−1.13961	−0.569804	−	0.821781i	$-0.692981\pi$
$787$	−705838.	−1.13961	−0.569804	+	0.821781i	$0.692981\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	−1.21626e6	−1.91955
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	0	0
$803$	−1.54403e6	−2.39455
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	670687.	1.02476	0.512381	−	0.858758i	$-0.328764\pi$
$809$	670687.	1.02476	0.512381	+	0.858758i	$0.328764\pi$
$810$	0	0
$811$	1.31512e6	1.99951	0.999753	−	0.0222218i	$-0.00707400\pi$
$811$	1.31512e6	1.99951	0.999753	+	0.0222218i	$0.00707400\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	−1.17254e6	−1.76528
$816$	0	0
$817$	−85130.9	−0.127539
$818$	0	0
$819$	0	0
$820$	0	0
$821$	941886.	1.39737	0.698686	−	0.715429i	$-0.253768\pi$
$821$	941886.	1.39737	0.698686	+	0.715429i	$0.253768\pi$
$822$	0	0
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	1.23759e6	1.80953	0.904767	−	0.425907i	$-0.140045\pi$
$827$	1.23759e6	1.80953	0.904767	+	0.425907i	$0.140045\pi$
$828$	0	0
$829$	−1.24165e6	−1.80671	−0.903357	−	0.428890i	$-0.858905\pi$
$829$	−1.24165e6	−1.80671	−0.903357	+	0.428890i	$0.858905\pi$
$830$	0	0
$831$	0	0
$832$	−1.27377e6	−1.84011
$833$	0	0
$834$	0	0
$835$	0	0
$836$	−1.09636e6	−1.56870
$837$	0	0
$838$	0	0
$839$	0	0	1.00000			$0$
$839$	0	0	−1.00000			$\pi$
$840$	0	0
$841$	707281.	1.00000
$842$	0	0
$843$	0	0
$844$	712336.	1.00000
$845$	2.00199e6	2.80380
$846$	0	0
$847$	0	0
$848$	1.38419e6	1.92488
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	1.33368e6	1.83297	0.916483	−	0.400075i	$-0.131016\pi$
$853$	1.33368e6	1.83297	0.916483	+	0.400075i	$0.131016\pi$
$854$	0	0
$855$	−679343.	−0.929302
$856$	0	0
$857$	1.09576e6	1.49195	0.745976	−	0.665973i	$-0.231983\pi$
$857$	1.09576e6	1.49195	0.745976	+	0.665973i	$0.231983\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	140162.	0.189510
$861$	0	0
$862$	0	0
$863$	341858.	0.459012	0.229506	−	0.973307i	$-0.426289\pi$
$863$	341858.	0.459012	0.229506	+	0.973307i	$0.426289\pi$
$864$	0	0
$865$	1.75578e6	2.34659
$866$	0	0
$867$	0	0
$868$	0	0
$869$	2.54836e6	3.37459
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0	0
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	1.80507e6	2.33093
$881$	−106364.	−0.137038	−0.0685191	−	0.997650i	$-0.521827\pi$
$881$	−106364.	−0.137038	−0.0685191	+	0.997650i	$0.521827\pi$
$882$	0	0
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−708638.	−0.900694	−0.450347	−	0.892854i	$-0.648700\pi$
$887$	−708638.	−0.900694	−0.450347	+	0.892854i	$0.648700\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	1.57475e6	1.98361
$892$	0	0
$893$	−647667.	−0.812174
$894$	0	0
$895$	−1.28307e6	−1.60179
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	308489.	0.380851
$901$	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			$\pi$
$908$	784672.	0.951736
$909$	−583715.	−0.706436
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	−2.82092e6	−3.38414
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	2.65134e6	3.11216
$924$	0	0
$925$	−650767.	−0.760575
$926$	0	0
$927$	−1.07408e6	−1.24991
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	−685461.	−0.790831
$932$	0	0
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−1.75531e6	−1.99929	−0.999644	−	0.0266785i	$-0.991507\pi$
$937$	−1.75531e6	−1.99929	−0.999644	+	0.0266785i	$0.991507\pi$
$938$	0	0
$939$	0	0
$940$	1.06634e6	1.20681
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	431872.	0.484631
$945$	0	0
$946$	0	0
$947$	−1.07553e6	−1.19928	−0.599641	−	0.800269i	$-0.704690\pi$
$947$	−1.07553e6	−1.19928	−0.599641	+	0.800269i	$0.704690\pi$
$948$	0	0
$949$	2.00053e6	2.22133
$950$	0	0
$951$	0	0
$952$	0	0
$953$	1.71136e6	1.88432	0.942159	−	0.335165i	$-0.108792\pi$
$953$	1.71136e6	1.88432	0.942159	+	0.335165i	$0.108792\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	923521.	1.00000
$962$	0	0
$963$	−1.61221e6	−1.73848
$964$	−1.84568e6	−1.98611
$965$	1.91532e6	2.05678
$966$	0	0
$967$	−396775.	−0.424318	−0.212159	−	0.977235i	$-0.568049\pi$
$967$	−396775.	−0.424318	−0.212159	+	0.977235i	$0.568049\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	1.12856e6	1.17510
$981$	−1.92075e6	−1.99588
$982$	0	0
$983$	1.14745e6	1.18748	0.593739	−	0.804658i	$-0.297651\pi$
$983$	1.14745e6	1.18748	0.593739	+	0.804658i	$0.297651\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	1.42050e6	1.45522
$989$	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
$995$	−2.23316e6	−2.25566
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	211.5.b.a.210.3	✓	3
211.210	odd	2	CM	211.5.b.a.210.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
211.5.b.a.210.3	✓	3	1.1	even	1	trivial
211.5.b.a.210.3	✓	3	211.210	odd	2	CM

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:	\( N \)	\(=\)	\( 211 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	211.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+16.0000 q^{4} +29.3774 q^{5} +81.0000 q^{9} +O(q^{10})\)	\(q+16.0000 q^{4} +29.3774 q^{5} +81.0000 q^{9} +240.017 q^{11} -310.979 q^{13} +256.000 q^{16} -285.490 q^{19} +470.038 q^{20} +238.032 q^{25} +1296.00 q^{36} -2733.95 q^{37} +298.192 q^{43} +3840.27 q^{44} +2379.57 q^{45} +2268.62 q^{47} +2401.00 q^{49} -4975.67 q^{52} +5407.00 q^{53} +7051.07 q^{55} +1687.00 q^{59} +4096.00 q^{64} -9135.76 q^{65} -8525.77 q^{71} -6433.00 q^{73} -4567.84 q^{76} +10617.4 q^{79} +7520.61 q^{80} +6561.00 q^{81} -11753.0 q^{83} -8386.95 q^{95} +19441.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 48 q^{4} + 243 q^{9}+O(q^{10}) \) 3 * q + 48 * q^4 + 243 * q^9	\( 3 q + 48 q^{4} + 243 q^{9} + 768 q^{16} + 1875 q^{25} + 3888 q^{36} + 7203 q^{49} + 16221 q^{53} + 12453 q^{55} + 5061 q^{59} + 12288 q^{64} - 5667 q^{65} - 19299 q^{73} + 19683 q^{81} - 35259 q^{83} - 52827 q^{95}+O(q^{100}) \) 3 * q + 48 * q^4 + 243 * q^9 + 768 * q^16 + 1875 * q^25 + 3888 * q^36 + 7203 * q^49 + 16221 * q^53 + 12453 * q^55 + 5061 * q^59 + 12288 * q^64 - 5667 * q^65 - 19299 * q^73 + 19683 * q^81 - 35259 * q^83 - 52827 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more