LMFDB - Embedded newform 304.5.e.b.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,5,Mod(113,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("304.113");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	304.e (of order $2$, degree $1$, not 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:	$31.4244687775$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{57}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 14 $ x^2 - x - 14
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			113.2
Root			$-3.27492$ of defining polynomial
Character	$\chi$	$=$	304.113

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+18.4743 q^{5} +20.1238 q^{7} +81.0000 q^{9} +O(q^{10})$	$q+18.4743 q^{5} +20.1238 q^{7} +81.0000 q^{9} -59.8762 q^{11} +572.866 q^{17} -361.000 q^{19} +158.000 q^{23} -283.702 q^{25} +371.771 q^{35} +2726.10 q^{43} +1496.41 q^{45} +4284.04 q^{47} -1996.03 q^{49} -1106.17 q^{55} +4248.75 q^{61} +1630.02 q^{63} +8130.81 q^{73} -1204.94 q^{77} +6561.00 q^{81} +5678.00 q^{83} +10583.3 q^{85} -6669.21 q^{95} -4849.98 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 31 q^{5} - 73 q^{7} + 162 q^{9}+O(q^{10}) $ 2 * q - 31 * q^5 - 73 * q^7 + 162 * q^9	$ 2 q - 31 q^{5} - 73 q^{7} + 162 q^{9} - 233 q^{11} + 353 q^{17} - 722 q^{19} + 316 q^{23} + 1539 q^{25} + 4979 q^{35} + 3527 q^{43} - 2511 q^{45} + 1207 q^{47} + 4275 q^{49} + 7459 q^{55} - 3167 q^{61} - 5913 q^{63} + 10033 q^{73} + 14917 q^{77} + 13122 q^{81} + 11356 q^{83} + 21461 q^{85} + 11191 q^{95} - 18873 q^{99}+O(q^{100}) $ 2 * q - 31 * q^5 - 73 * q^7 + 162 * q^9 - 233 * q^11 + 353 * q^17 - 722 * q^19 + 316 * q^23 + 1539 * q^25 + 4979 * q^35 + 3527 * q^43 - 2511 * q^45 + 1207 * q^47 + 4275 * q^49 + 7459 * q^55 - 3167 * q^61 - 5913 * q^63 + 10033 * q^73 + 14917 * q^77 + 13122 * q^81 + 11356 * q^83 + 21461 * q^85 + 11191 * q^95 - 18873 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	0	0
$2$	0	0
$3$	0	0	1.00000			$0$
$3$	0	0	−1.00000			$\pi$
$4$	0	0
$5$	18.4743	0.738970	0.369485	−	0.929237i	$-0.379534\pi$
$5$	18.4743	0.738970	0.369485	+	0.929237i	$0.379534\pi$
$6$	0	0
$7$	20.1238	0.410689	0.205344	−	0.978690i	$-0.434169\pi$
$7$	20.1238	0.410689	0.205344	+	0.978690i	$0.434169\pi$
$8$	0	0
$9$	81.0000	1.00000
$10$	0	0
$11$	−59.8762	−0.494845	−0.247422	−	0.968908i	$-0.579584\pi$
$11$	−59.8762	−0.494845	−0.247422	+	0.968908i	$0.579584\pi$
$12$	0	0
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	572.866	1.98224	0.991118	−	0.132984i	$-0.0424559\pi$
$17$	572.866	1.98224	0.991118	+	0.132984i	$0.0424559\pi$
$18$	0	0
$19$	−361.000	−1.00000
$19$	−361.000	−1.00000
$20$	0	0
$21$	0	0
$22$	0	0
$23$	158.000	0.298677	0.149338	−	0.988786i	$-0.452286\pi$
$23$	158.000	0.298677	0.149338	+	0.988786i	$0.452286\pi$
$24$	0	0
$25$	−283.702	−0.453923
$26$	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
$35$	371.771	0.303487
$36$	0	0
$37$	0	0	1.00000			$0$
$37$	0	0	−1.00000			$\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	2726.10	1.47437	0.737183	−	0.675693i	$-0.236155\pi$
$43$	2726.10	1.47437	0.737183	+	0.675693i	$0.236155\pi$
$44$	0	0
$45$	1496.41	0.738970
$46$	0	0
$47$	4284.04	1.93936	0.969680	−	0.244380i	$-0.0785844\pi$
$47$	4284.04	1.93936	0.969680	+	0.244380i	$0.0785844\pi$
$48$	0	0
$49$	−1996.03	−0.831335
$50$	0	0
$51$	0	0
$52$	0	0
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	0	0
$55$	−1106.17	−0.365676
$56$	0	0
$57$	0	0
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	0	0
$61$	4248.75	1.14183	0.570915	−	0.821009i	$-0.306589\pi$
$61$	4248.75	1.14183	0.570915	+	0.821009i	$0.306589\pi$
$62$	0	0
$63$	1630.02	0.410689
$64$	0	0
$65$	0	0
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	0	0
$73$	8130.81	1.52577	0.762883	−	0.646537i	$-0.223783\pi$
$73$	8130.81	1.52577	0.762883	+	0.646537i	$0.223783\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−1204.94	−0.203227
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	6561.00	1.00000
$82$	0	0
$83$	5678.00	0.824213	0.412106	−	0.911136i	$-0.364793\pi$
$83$	5678.00	0.824213	0.412106	+	0.911136i	$0.364793\pi$
$84$	0	0
$85$	10583.3	1.46481
$86$	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
$95$	−6669.21	−0.738970
$96$	0	0
$97$	0	0	1.00000			$0$
$97$	0	0	−1.00000			$\pi$
$98$	0	0
$99$	−4849.98	−0.494845
$100$	0	0
$101$	−9998.00	−0.980100	−0.490050	−	0.871694i	$-0.663021\pi$
$101$	−9998.00	−0.980100	−0.490050	+	0.871694i	$0.663021\pi$
$102$	0	0
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	0	0
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	2918.93	0.220713
$116$	0	0
$117$	0	0
$118$	0	0
$119$	11528.2	0.814083
$120$	0	0
$121$	−11055.8	−0.755128
$122$	0	0
$123$	0	0
$124$	0	0
$125$	−16787.6	−1.07441
$126$	0	0
$127$	0	0	1.00000			$0$
$127$	0	0	−1.00000			$\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	33665.5	1.96175	0.980873	−	0.194651i	$-0.0623574\pi$
$131$	33665.5	1.96175	0.980873	+	0.194651i	$0.0623574\pi$
$132$	0	0
$133$	−7264.68	−0.410689
$134$	0	0
$135$	0	0
$136$	0	0
$137$	8396.39	0.447354	0.223677	−	0.974663i	$-0.428194\pi$
$137$	8396.39	0.447354	0.223677	+	0.974663i	$0.428194\pi$
$138$	0	0
$139$	−33381.1	−1.72771	−0.863856	−	0.503738i	$-0.831958\pi$
$139$	−33381.1	−1.72771	−0.863856	+	0.503738i	$0.831958\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	0	0
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−30212.3	−1.36085	−0.680427	−	0.732816i	$-0.738206\pi$
$149$	−30212.3	−1.36085	−0.680427	+	0.732816i	$0.738206\pi$
$150$	0	0
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	46402.2	1.98224
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−49198.0	−1.99594	−0.997972	−	0.0636620i	$-0.979722\pi$
$157$	−49198.0	−1.99594	−0.997972	+	0.0636620i	$0.979722\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	3179.55	0.122663
$162$	0	0
$163$	−9362.00	−0.352366	−0.176183	−	0.984357i	$-0.556375\pi$
$163$	−9362.00	−0.352366	−0.176183	+	0.984357i	$0.556375\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	0	0	1.00000			$0$
$167$	0	0	−1.00000			$\pi$
$168$	0	0
$169$	28561.0	1.00000
$170$	0	0
$171$	−29241.0	−1.00000
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	−5709.15	−0.186421
$176$	0	0
$177$	0	0
$178$	0	0
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	0	0	1.00000			$0$
$181$	0	0	−1.00000			$\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−34301.1	−0.980900
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−61997.2	−1.69944	−0.849719	−	0.527235i	$-0.823229\pi$
$191$	−61997.2	−1.69944	−0.849719	+	0.527235i	$0.823229\pi$
$192$	0	0
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−69518.0	−1.79129	−0.895643	−	0.444774i	$-0.853284\pi$
$197$	−69518.0	−1.79129	−0.895643	+	0.444774i	$0.853284\pi$
$198$	0	0
$199$	−78104.5	−1.97229	−0.986143	−	0.165900i	$-0.946947\pi$
$199$	−78104.5	−1.97229	−0.986143	+	0.165900i	$0.946947\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	12798.0	0.298677
$208$	0	0
$209$	21615.3	0.494845
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	50362.7	1.08951
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	0	0
$225$	−22979.9	−0.453923
$226$	0	0
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	59034.7	1.12574	0.562868	−	0.826547i	$-0.309698\pi$
$229$	59034.7	1.12574	0.562868	+	0.826547i	$0.309698\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−66110.9	−1.21776	−0.608879	−	0.793263i	$-0.708380\pi$
$233$	−66110.9	−1.21776	−0.608879	+	0.793263i	$0.708380\pi$
$234$	0	0
$235$	79144.5	1.43313
$236$	0	0
$237$	0	0
$238$	0	0
$239$	105335.	1.84406	0.922032	−	0.387113i	$-0.126528\pi$
$239$	105335.	1.84406	0.922032	+	0.387113i	$0.126528\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	−36875.2	−0.614331
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	−74357.6	−1.18026	−0.590130	−	0.807308i	$-0.700924\pi$
$251$	−74357.6	−1.18026	−0.590130	+	0.807308i	$0.700924\pi$
$252$	0	0
$253$	−9460.45	−0.147799
$254$	0	0
$255$	0	0
$256$	0	0
$257$	0	0	1.00000			$0$
$257$	0	0	−1.00000			$\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	−104877.	−1.51625	−0.758124	−	0.652111i	$-0.773884\pi$
$263$	−104877.	−1.51625	−0.758124	+	0.652111i	$0.773884\pi$
$264$	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
$271$	126718.	1.72544	0.862720	−	0.505682i	$-0.168759\pi$
$271$	126718.	1.72544	0.862720	+	0.505682i	$0.168759\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	16987.0	0.224622
$276$	0	0
$277$	−133030.	−1.73376	−0.866880	−	0.498517i	$-0.833878\pi$
$277$	−133030.	−1.73376	−0.866880	+	0.498517i	$0.833878\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	0	0
$283$	136595.	1.70554	0.852771	−	0.522286i	$-0.174921\pi$
$283$	136595.	1.70554	0.852771	+	0.522286i	$0.174921\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	244655.	2.92926
$290$	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
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	54859.5	0.605506
$302$	0	0
$303$	0	0
$304$	0	0
$305$	78492.4	0.843778
$306$	0	0
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	5413.87	0.0559741	0.0279871	−	0.999608i	$-0.491090\pi$
$311$	5413.87	0.0559741	0.0279871	+	0.999608i	$0.491090\pi$
$312$	0	0
$313$	152162.	1.55316	0.776582	−	0.630016i	$-0.216952\pi$
$313$	152162.	1.55316	0.776582	+	0.630016i	$0.216952\pi$
$314$	0	0
$315$	30113.5	0.303487
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	−206805.	−1.98224
$324$	0	0
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	86211.1	0.796473
$330$	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
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	0	0
$342$	0	0
$343$	−88484.9	−0.752109
$344$	0	0
$345$	0	0
$346$	0	0
$347$	201682.	1.67497	0.837487	−	0.546457i	$-0.184024\pi$
$347$	201682.	1.67497	0.837487	+	0.546457i	$0.184024\pi$
$348$	0	0
$349$	−225949.	−1.85506	−0.927532	−	0.373745i	$-0.878074\pi$
$349$	−225949.	−1.85506	−0.927532	+	0.373745i	$0.878074\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	10882.0	0.0873292	0.0436646	−	0.999046i	$-0.486097\pi$
$353$	10882.0	0.0873292	0.0436646	+	0.999046i	$0.486097\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−241539.	−1.87412	−0.937061	−	0.349165i	$-0.886465\pi$
$359$	−241539.	−1.87412	−0.937061	+	0.349165i	$0.886465\pi$
$360$	0	0
$361$	130321.	1.00000
$362$	0	0
$363$	0	0
$364$	0	0
$365$	150211.	1.12750
$366$	0	0
$367$	266878.	1.98144	0.990719	−	0.135923i	$-0.0434001\pi$
$367$	266878.	1.98144	0.990719	+	0.135923i	$0.0434001\pi$
$368$	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			$\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	0	0	1.00000			$0$
$383$	0	0	−1.00000			$\pi$
$384$	0	0
$385$	−22260.3	−0.150179
$386$	0	0
$387$	220814.	1.47437
$388$	0	0
$389$	38543.1	0.254711	0.127355	−	0.991857i	$-0.459351\pi$
$389$	38543.1	0.254711	0.127355	+	0.991857i	$0.459351\pi$
$390$	0	0
$391$	90512.9	0.592048
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−297079.	−1.88491	−0.942456	−	0.334329i	$-0.891490\pi$
$397$	−297079.	−1.88491	−0.942456	+	0.334329i	$0.891490\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	0	0	1.00000			$0$
$401$	0	0	−1.00000			$\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	121210.	0.738970
$406$	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
$412$	0	0
$413$	0	0
$414$	0	0
$415$	104897.	0.609068
$416$	0	0
$417$	0	0
$418$	0	0
$419$	−229522.	−1.30736	−0.653682	−	0.756770i	$-0.726776\pi$
$419$	−229522.	−1.30736	−0.653682	+	0.756770i	$0.726776\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	347008.	1.93936
$424$	0	0
$425$	−162523.	−0.899783
$426$	0	0
$427$	85500.8	0.468937
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	0	0
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−57038.0	−0.298677
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	−161679.	−0.831335
$442$	0	0
$443$	−160753.	−0.819126	−0.409563	−	0.912282i	$-0.634319\pi$
$443$	−160753.	−0.819126	−0.409563	+	0.912282i	$0.634319\pi$
$444$	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
$452$	0	0
$453$	0	0
$454$	0	0
$455$	0	0
$456$	0	0
$457$	374513.	1.79322	0.896612	−	0.442817i	$-0.146021\pi$
$457$	374513.	1.79322	0.896612	+	0.442817i	$0.146021\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	−199550.	−0.938967	−0.469484	−	0.882941i	$-0.655560\pi$
$461$	−199550.	−0.938967	−0.469484	+	0.882941i	$0.655560\pi$
$462$	0	0
$463$	−279914.	−1.30576	−0.652879	−	0.757462i	$-0.726439\pi$
$463$	−279914.	−1.30576	−0.652879	+	0.757462i	$0.726439\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	51999.4	0.238432	0.119216	−	0.992868i	$-0.461962\pi$
$467$	51999.4	0.238432	0.119216	+	0.992868i	$0.461962\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	0	0
$473$	−163229.	−0.729583
$474$	0	0
$475$	102416.	0.453923
$476$	0	0
$477$	0	0
$478$	0	0
$479$	−428482.	−1.86750	−0.933752	−	0.357921i	$-0.883486\pi$
$479$	−428482.	−1.86750	−0.933752	+	0.357921i	$0.883486\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	0	0	1.00000			$0$
$487$	0	0	−1.00000			$\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−360562.	−1.49561	−0.747803	−	0.663921i	$-0.768891\pi$
$491$	−360562.	−1.49561	−0.747803	+	0.663921i	$0.768891\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	−89599.7	−0.365676
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−497221.	−1.99687	−0.998433	−	0.0559673i	$-0.982176\pi$
$499$	−497221.	−1.99687	−0.998433	+	0.0559673i	$0.982176\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	−358882.	−1.41846	−0.709228	−	0.704979i	$-0.750956\pi$
$503$	−358882.	−1.41846	−0.709228	+	0.704979i	$0.750956\pi$
$504$	0	0
$505$	−184706.	−0.724265
$506$	0	0
$507$	0	0
$508$	0	0
$509$	0	0	1.00000			$0$
$509$	0	0	−1.00000			$\pi$
$510$	0	0
$511$	163622.	0.626615
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−256512.	−0.959682
$518$	0	0
$519$	0	0
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	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
$529$	−254877.	−0.910792
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	119515.	0.411382
$540$	0	0
$541$	576412.	1.96942	0.984711	−	0.174196i	$-0.0557327\pi$
$541$	576412.	1.96942	0.984711	+	0.174196i	$0.0557327\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	344149.	1.14183
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−94987.4	−0.306165	−0.153083	−	0.988213i	$-0.548920\pi$
$557$	−94987.4	−0.306165	−0.153083	+	0.988213i	$0.548920\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	132032.	0.410689
$568$	0	0
$569$	0	0	1.00000			$0$
$569$	0	0	−1.00000			$\pi$
$570$	0	0
$571$	442318.	1.35663	0.678317	−	0.734770i	$-0.262710\pi$
$571$	442318.	1.35663	0.678317	+	0.734770i	$0.262710\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	−44824.9	−0.135576
$576$	0	0
$577$	−179948.	−0.540500	−0.270250	−	0.962790i	$-0.587106\pi$
$577$	−179948.	−0.540500	−0.270250	+	0.962790i	$0.587106\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	114263.	0.338495
$582$	0	0
$583$	0	0
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−38758.7	−0.112485	−0.0562423	−	0.998417i	$-0.517912\pi$
$587$	−38758.7	−0.112485	−0.0562423	+	0.998417i	$0.517912\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	−702398.	−1.99744	−0.998720	−	0.0505740i	$-0.983895\pi$
$593$	−702398.	−1.99744	−0.998720	+	0.0505740i	$0.983895\pi$
$594$	0	0
$595$	212975.	0.601583
$596$	0	0
$597$	0	0
$598$	0	0
$599$	0	0	1.00000			$0$
$599$	0	0	−1.00000			$\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	−204248.	−0.558017
$606$	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
$613$	28243.5	0.0751620	0.0375810	−	0.999294i	$-0.488035\pi$
$613$	28243.5	0.0751620	0.0375810	+	0.999294i	$0.488035\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−761325.	−1.99986	−0.999930	−	0.0118526i	$-0.996227\pi$
$617$	−761325.	−1.99986	−0.999930	+	0.0118526i	$0.996227\pi$
$618$	0	0
$619$	328078.	0.856241	0.428120	−	0.903722i	$-0.359176\pi$
$619$	328078.	0.856241	0.428120	+	0.903722i	$0.359176\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−132825.	−0.340031
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	−506384.	−1.27181	−0.635903	−	0.771769i	$-0.719372\pi$
$631$	−506384.	−1.27181	−0.635903	+	0.771769i	$0.719372\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0	0
$638$	0	0
$639$	0	0
$640$	0	0
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	0	0
$643$	−410564.	−0.993023	−0.496511	−	0.868030i	$-0.665386\pi$
$643$	−410564.	−0.993023	−0.496511	+	0.868030i	$0.665386\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	795843.	1.90116	0.950580	−	0.310480i	$-0.100490\pi$
$647$	795843.	1.90116	0.950580	+	0.310480i	$0.100490\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	762372.	1.78789	0.893945	−	0.448178i	$-0.147927\pi$
$653$	762372.	1.78789	0.893945	+	0.448178i	$0.147927\pi$
$654$	0	0
$655$	621945.	1.44967
$656$	0	0
$657$	658595.	1.52577
$658$	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
$665$	−134209.	−0.303487
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	0	0
$671$	−254399.	−0.565029
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	155117.	0.330581
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	−278468.	−0.583202	−0.291601	−	0.956540i	$-0.594188\pi$
$691$	−278468.	−0.583202	−0.291601	+	0.956540i	$0.594188\pi$
$692$	0	0
$693$	−97599.7	−0.203227
$694$	0	0
$695$	−616692.	−1.27673
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	222802.	0.453402	0.226701	−	0.973964i	$-0.427206\pi$
$701$	222802.	0.453402	0.226701	+	0.973964i	$0.427206\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−201197.	−0.402516
$708$	0	0
$709$	731762.	1.45572	0.727859	−	0.685727i	$-0.240515\pi$
$709$	731762.	1.45572	0.727859	+	0.685727i	$0.240515\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	837359.	1.61977	0.809886	−	0.586588i	$-0.199529\pi$
$719$	837359.	1.61977	0.809886	+	0.586588i	$0.199529\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	0	0
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−631766.	−1.19533	−0.597664	−	0.801747i	$-0.703904\pi$
$727$	−631766.	−1.19533	−0.597664	+	0.801747i	$0.703904\pi$
$728$	0	0
$729$	531441.	1.00000
$730$	0	0
$731$	1.56169e6	2.92254
$732$	0	0
$733$	538322.	1.00192	0.500961	−	0.865470i	$-0.332980\pi$
$733$	538322.	1.00192	0.500961	+	0.865470i	$0.332980\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	0	0
$738$	0	0
$739$	−1.04695e6	−1.91707	−0.958536	−	0.284970i	$-0.908016\pi$
$739$	−1.04695e6	−1.91707	−0.958536	+	0.284970i	$0.908016\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	−558150.	−1.00563
$746$	0	0
$747$	459918.	0.824213
$748$	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
$754$	0	0
$755$	0	0
$756$	0	0
$757$	1.14504e6	1.99815	0.999076	−	0.0429669i	$-0.0136810\pi$
$757$	1.14504e6	1.99815	0.999076	+	0.0429669i	$0.0136810\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−238330.	−0.411537	−0.205769	−	0.978601i	$-0.565969\pi$
$761$	−238330.	−0.411537	−0.205769	+	0.978601i	$0.565969\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	857246.	1.46481
$766$	0	0
$767$	0	0
$768$	0	0
$769$	1.04962e6	1.77493	0.887465	−	0.460875i	$-0.152464\pi$
$769$	1.04962e6	1.77493	0.887465	+	0.460875i	$0.152464\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	0	0	1.00000			$0$
$773$	0	0	−1.00000			$\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	0	0
$785$	−908896.	−1.47494
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	0	0
$799$	2.45418e6	3.84427
$800$	0	0
$801$	0	0
$802$	0	0
$803$	−486842.	−0.755018
$804$	0	0
$805$	58739.9	0.0906445
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−223470.	−0.341446	−0.170723	−	0.985319i	$-0.554610\pi$
$809$	−223470.	−0.341446	−0.170723	+	0.985319i	$0.554610\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	−172956.	−0.260388
$816$	0	0
$817$	−984124.	−1.47437
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−1.17432e6	−1.74220	−0.871101	−	0.491104i	$-0.836594\pi$
$821$	−1.17432e6	−1.74220	−0.871101	+	0.491104i	$0.836594\pi$
$822$	0	0
$823$	−143923.	−0.212486	−0.106243	−	0.994340i	$-0.533882\pi$
$823$	−143923.	−0.212486	−0.106243	+	0.994340i	$0.533882\pi$
$824$	0	0
$825$	0	0
$826$	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
$832$	0	0
$833$	−1.14346e6	−1.64790
$834$	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
$841$	707281.	1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	527643.	0.738970
$846$	0	0
$847$	−222485.	−0.310123
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0	0
$852$	0	0
$853$	−394318.	−0.541937	−0.270968	−	0.962588i	$-0.587344\pi$
$853$	−394318.	−0.541937	−0.270968	+	0.962588i	$0.587344\pi$
$854$	0	0
$855$	−540206.	−0.738970
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	1.47565e6	1.99985	0.999927	−	0.0120966i	$-0.00385055\pi$
$859$	1.47565e6	1.99985	0.999927	+	0.0120966i	$0.00385055\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	0	0	1.00000			$0$
$863$	0	0	−1.00000			$\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	0	0
$875$	−337829.	−0.441247
$876$	0	0
$877$	0	0	1.00000			$0$
$877$	0	0	−1.00000			$\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	1.41242e6	1.81975	0.909877	−	0.414879i	$-0.136176\pi$
$881$	1.41242e6	1.81975	0.909877	+	0.414879i	$0.136176\pi$
$882$	0	0
$883$	694207.	0.890365	0.445182	−	0.895440i	$-0.353139\pi$
$883$	694207.	0.890365	0.445182	+	0.895440i	$0.353139\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	0	0	1.00000			$0$
$887$	0	0	−1.00000			$\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−392848.	−0.494845
$892$	0	0
$893$	−1.54654e6	−1.93936
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	−809838.	−0.980100
$910$	0	0
$911$	0	0	1.00000			$0$
$911$	0	0	−1.00000			$\pi$
$912$	0	0
$913$	−339977.	−0.407857
$914$	0	0
$915$	0	0
$916$	0	0
$917$	677477.	0.805667
$918$	0	0
$919$	−1.41552e6	−1.67604	−0.838022	−	0.545636i	$-0.816288\pi$
$919$	−1.41552e6	−1.67604	−0.838022	+	0.545636i	$0.816288\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	0	0
$928$	0	0
$929$	−1.31392e6	−1.52243	−0.761214	−	0.648501i	$-0.775396\pi$
$929$	−1.31392e6	−1.52243	−0.761214	+	0.648501i	$0.775396\pi$
$930$	0	0
$931$	720568.	0.831335
$932$	0	0
$933$	0	0
$934$	0	0
$935$	−633687.	−0.724856
$936$	0	0
$937$	1.35678e6	1.54536	0.772682	−	0.634794i	$-0.218915\pi$
$937$	1.35678e6	1.54536	0.772682	+	0.634794i	$0.218915\pi$
$938$	0	0
$939$	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
$946$	0	0
$947$	−1.55528e6	−1.73424	−0.867120	−	0.498099i	$-0.834031\pi$
$947$	−1.55528e6	−1.73424	−0.867120	+	0.498099i	$0.834031\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	−1.14535e6	−1.25583
$956$	0	0
$957$	0	0
$958$	0	0
$959$	168967.	0.183723
$960$	0	0
$961$	923521.	1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−1.33392e6	−1.42652	−0.713259	−	0.700900i	$-0.752782\pi$
$967$	−1.33392e6	−1.42652	−0.713259	+	0.700900i	$0.752782\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	0	0
$973$	−671754.	−0.709553
$974$	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
$980$	0	0
$981$	0	0
$982$	0	0
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	0	0
$985$	−1.28429e6	−1.32371
$986$	0	0
$987$	0	0
$988$	0	0
$989$	430724.	0.440359
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	−1.44292e6	−1.45746
$996$	0	0
$997$	−486609.	−0.489542	−0.244771	−	0.969581i	$-0.578713\pi$
$997$	−486609.	−0.489542	−0.244771	+	0.969581i	$0.578713\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.e.b.113.2		2
4.3	odd	2		76.5.c.a.37.2	✓	2
12.11	even	2		684.5.h.b.37.1		2
19.18	odd	2	CM	304.5.e.b.113.2		2
76.75	even	2		76.5.c.a.37.2	✓	2
228.227	odd	2		684.5.h.b.37.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.c.a.37.2	✓	2	4.3	odd	2
76.5.c.a.37.2	✓	2	76.75	even	2
304.5.e.b.113.2		2	1.1	even	1	trivial
304.5.e.b.113.2		2	19.18	odd	2	CM
684.5.h.b.37.1		2	12.11	even	2
684.5.h.b.37.1		2	228.227	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	304.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+18.4743 q^{5} +20.1238 q^{7} +81.0000 q^{9} +O(q^{10})\)	\(q+18.4743 q^{5} +20.1238 q^{7} +81.0000 q^{9} -59.8762 q^{11} +572.866 q^{17} -361.000 q^{19} +158.000 q^{23} -283.702 q^{25} +371.771 q^{35} +2726.10 q^{43} +1496.41 q^{45} +4284.04 q^{47} -1996.03 q^{49} -1106.17 q^{55} +4248.75 q^{61} +1630.02 q^{63} +8130.81 q^{73} -1204.94 q^{77} +6561.00 q^{81} +5678.00 q^{83} +10583.3 q^{85} -6669.21 q^{95} -4849.98 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 31 q^{5} - 73 q^{7} + 162 q^{9}+O(q^{10}) \) 2 * q - 31 * q^5 - 73 * q^7 + 162 * q^9	\( 2 q - 31 q^{5} - 73 q^{7} + 162 q^{9} - 233 q^{11} + 353 q^{17} - 722 q^{19} + 316 q^{23} + 1539 q^{25} + 4979 q^{35} + 3527 q^{43} - 2511 q^{45} + 1207 q^{47} + 4275 q^{49} + 7459 q^{55} - 3167 q^{61} - 5913 q^{63} + 10033 q^{73} + 14917 q^{77} + 13122 q^{81} + 11356 q^{83} + 21461 q^{85} + 11191 q^{95} - 18873 q^{99}+O(q^{100}) \) 2 * q - 31 * q^5 - 73 * q^7 + 162 * q^9 - 233 * q^11 + 353 * q^17 - 722 * q^19 + 316 * q^23 + 1539 * q^25 + 4979 * q^35 + 3527 * q^43 - 2511 * q^45 + 1207 * q^47 + 4275 * q^49 + 7459 * q^55 - 3167 * q^61 - 5913 * q^63 + 10033 * q^73 + 14917 * q^77 + 13122 * q^81 + 11356 * q^83 + 21461 * q^85 + 11191 * q^95 - 18873 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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