LMFDB - Embedded newform 275.5.c.d.76.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,5,Mod(76,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("275.76");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	275.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:	$28.4267398481$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{11}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 11 $ x^2 - 11
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			76.1
Root			$3.31662$ of defining polynomial
Character	$\chi$	$=$	275.76

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.5831 q^{3} +16.0000 q^{4} +194.000 q^{9} +O(q^{10})$	$q-16.5831 q^{3} +16.0000 q^{4} +194.000 q^{9} -121.000 q^{11} -265.330 q^{12} +256.000 q^{16} -1044.74 q^{23} -1873.89 q^{27} +553.000 q^{31} +2006.56 q^{33} +3104.00 q^{36} +1741.23 q^{37} -1936.00 q^{44} +3979.95 q^{47} -4245.28 q^{48} +2401.00 q^{49} +5571.93 q^{53} -4487.00 q^{59} +4096.00 q^{64} +4527.19 q^{67} +17325.0 q^{69} +7607.00 q^{71} +15361.0 q^{81} -6433.00 q^{89} -16715.8 q^{92} -9170.47 q^{93} -16069.0 q^{97} -23474.0 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 32 q^{4} + 388 q^{9}+O(q^{10}) $ 2 * q + 32 * q^4 + 388 * q^9	$ 2 q + 32 q^{4} + 388 q^{9} - 242 q^{11} + 512 q^{16} + 1106 q^{31} + 6208 q^{36} - 3872 q^{44} + 4802 q^{49} - 8974 q^{59} + 8192 q^{64} + 34650 q^{69} + 15214 q^{71} + 30722 q^{81} - 12866 q^{89} - 46948 q^{99}+O(q^{100}) $ 2 * q + 32 * q^4 + 388 * q^9 - 242 * q^11 + 512 * q^16 + 1106 * q^31 + 6208 * q^36 - 3872 * q^44 + 4802 * q^49 - 8974 * q^59 + 8192 * q^64 + 34650 * q^69 + 15214 * q^71 + 30722 * q^81 - 12866 * q^89 - 46948 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$-1$	$1$

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			$\pi$
$3$	−16.5831	−1.84257	−0.921285	−	0.388889i	$-0.872859\pi$
$3$	−16.5831	−1.84257	−0.921285	+	0.388889i	$0.872859\pi$
$4$	16.0000	1.00000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	0	0
$9$	194.000	2.39506
$10$	0	0
$11$	−121.000	−1.00000
$11$	−121.000	−1.00000
$12$	−265.330	−1.84257
$13$	0	0	1.00000			$0$
$13$	0	0	−1.00000			$\pi$
$14$	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
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−1044.74	−1.97493	−0.987464	−	0.157845i	$-0.949545\pi$
$23$	−1044.74	−1.97493	−0.987464	+	0.157845i	$0.949545\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−1873.89	−2.57050
$28$	0	0
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	553.000	0.575442	0.287721	−	0.957714i	$-0.407102\pi$
$31$	553.000	0.575442	0.287721	+	0.957714i	$0.407102\pi$
$32$	0	0
$33$	2006.56	1.84257
$34$	0	0
$35$	0	0
$36$	3104.00	2.39506
$37$	1741.23	1.27190	0.635949	−	0.771731i	$-0.280609\pi$
$37$	1741.23	1.27190	0.635949	+	0.771731i	$0.280609\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	−1936.00	−1.00000
$45$	0	0
$46$	0	0
$47$	3979.95	1.80170	0.900849	−	0.434133i	$-0.142945\pi$
$47$	3979.95	1.80170	0.900849	+	0.434133i	$0.142945\pi$
$48$	−4245.28	−1.84257
$49$	2401.00	1.00000
$50$	0	0
$51$	0	0
$52$	0	0
$53$	5571.93	1.98360	0.991800	−	0.127803i	$-0.0407927\pi$
$53$	5571.93	1.98360	0.991800	+	0.127803i	$0.0407927\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	−4487.00	−1.28900	−0.644499	−	0.764605i	$-0.722934\pi$
$59$	−4487.00	−1.28900	−0.644499	+	0.764605i	$0.722934\pi$
$60$	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
$65$	0	0
$66$	0	0
$67$	4527.19	1.00851	0.504254	−	0.863555i	$-0.331768\pi$
$67$	4527.19	1.00851	0.504254	+	0.863555i	$0.331768\pi$
$68$	0	0
$69$	17325.0	3.63894
$70$	0	0
$71$	7607.00	1.50903	0.754513	−	0.656285i	$-0.227873\pi$
$71$	7607.00	1.50903	0.754513	+	0.656285i	$0.227873\pi$
$72$	0	0
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	15361.0	2.34126
$82$	0	0
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	0	0
$88$	0	0
$89$	−6433.00	−0.812145	−0.406072	−	0.913841i	$-0.633102\pi$
$89$	−6433.00	−0.812145	−0.406072	+	0.913841i	$0.633102\pi$
$90$	0	0
$91$	0	0
$92$	−16715.8	−1.97493
$93$	−9170.47	−1.06029
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−16069.0	−1.70784	−0.853919	−	0.520406i	$-0.825781\pi$
$97$	−16069.0	−1.70784	−0.853919	+	0.520406i	$0.825781\pi$
$98$	0	0
$99$	−23474.0	−2.39506
$100$	0	0
$101$	0	0	1.00000			$0$
$101$	0	0	−1.00000			$\pi$
$102$	0	0
$103$	15123.8	1.42556	0.712782	−	0.701386i	$-0.247435\pi$
$103$	15123.8	1.42556	0.712782	+	0.701386i	$0.247435\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	−29982.3	−2.57050
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	−28875.0	−2.34356
$112$	0	0
$113$	14974.6	1.17273	0.586364	−	0.810048i	$-0.300559\pi$
$113$	14974.6	1.17273	0.586364	+	0.810048i	$0.300559\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	0	0
$121$	14641.0	1.00000
$122$	0	0
$123$	0	0
$124$	8848.00	0.575442
$125$	0	0
$126$	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			$\pi$
$132$	32104.9	1.84257
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	18457.0	0.983378	0.491689	−	0.870771i	$-0.336380\pi$
$137$	18457.0	0.983378	0.491689	+	0.870771i	$0.336380\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	−66000.0	−3.31975
$142$	0	0
$143$	0	0
$144$	49664.0	2.39506
$145$	0	0
$146$	0	0
$147$	−39816.1	−1.84257
$148$	27859.6	1.27190
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	0	0
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	0	0
$156$	0	0
$157$	49202.1	1.99611	0.998055	−	0.0623352i	$-0.0198548\pi$
$157$	49202.1	1.99611	0.998055	+	0.0623352i	$0.0198548\pi$
$158$	0	0
$159$	−92400.0	−3.65492
$160$	0	0
$161$	0	0
$162$	0	0
$163$	−22287.7	−0.838862	−0.419431	−	0.907787i	$-0.637770\pi$
$163$	−22287.7	−0.838862	−0.419431	+	0.907787i	$0.637770\pi$
$164$	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
$171$	0	0
$172$	0	0
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	0	0
$176$	−30976.0	−1.00000
$177$	74408.5	2.37507
$178$	0	0
$179$	−57193.0	−1.78499	−0.892497	−	0.451053i	$-0.851048\pi$
$179$	−57193.0	−1.78499	−0.892497	+	0.451053i	$0.851048\pi$
$180$	0	0
$181$	−3647.00	−0.111321	−0.0556607	−	0.998450i	$-0.517727\pi$
$181$	−3647.00	−0.111321	−0.0556607	+	0.998450i	$0.517727\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	0	0
$188$	63679.2	1.80170
$189$	0	0
$190$	0	0
$191$	48313.0	1.32433	0.662167	−	0.749357i	$-0.269637\pi$
$191$	48313.0	1.32433	0.662167	+	0.749357i	$0.269637\pi$
$192$	−67924.5	−1.84257
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	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
$199$	79198.0	1.99990	0.999949	−	0.0100501i	$-0.00319911\pi$
$199$	79198.0	1.99990	0.999949	+	0.0100501i	$0.00319911\pi$
$200$	0	0
$201$	−75075.0	−1.85825
$202$	0	0
$203$	0	0
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−202679.	−4.73007
$208$	0	0
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	89150.9	1.98360
$213$	−126148.	−2.78048
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	13283.1	0.267109	0.133555	−	0.991041i	$-0.457361\pi$
$223$	13283.1	0.267109	0.133555	+	0.991041i	$0.457361\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	0	0	1.00000			$0$
$227$	0	0	−1.00000			$\pi$
$228$	0	0
$229$	−82607.0	−1.57524	−0.787618	−	0.616163i	$-0.788686\pi$
$229$	−82607.0	−1.57524	−0.787618	+	0.616163i	$0.788686\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	0	0
$236$	−71792.0	−1.28900
$237$	0	0
$238$	0	0
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	−102948.	−1.74343
$244$	0	0
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	−74473.0	−1.18209	−0.591046	−	0.806638i	$-0.701285\pi$
$251$	−74473.0	−1.18209	−0.591046	+	0.806638i	$0.701285\pi$
$252$	0	0
$253$	126413.	1.97493
$254$	0	0
$255$	0	0
$256$	65536.0	1.00000
$257$	−90742.9	−1.37387	−0.686936	−	0.726718i	$-0.741045\pi$
$257$	−90742.9	−1.37387	−0.686936	+	0.726718i	$0.741045\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	0	0
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	106679.	1.49643
$268$	72435.1	1.00851
$269$	13678.0	0.189024	0.0945122	−	0.995524i	$-0.469871\pi$
$269$	13678.0	0.189024	0.0945122	+	0.995524i	$0.469871\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	0	0
$276$	277200.	3.63894
$277$	0	0	1.00000			$0$
$277$	0	0	−1.00000			$\pi$
$278$	0	0
$279$	107282.	1.37822
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	121712.	1.50903
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	83521.0	1.00000
$290$	0	0
$291$	266475.	3.14681
$292$	0	0
$293$	0	0	1.00000			$0$
$293$	0	0	−1.00000			$\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	226741.	2.57050
$298$	0	0
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0	0
$309$	−250800.	−2.62670
$310$	0	0
$311$	35042.0	0.362300	0.181150	−	0.983455i	$-0.442018\pi$
$311$	35042.0	0.362300	0.181150	+	0.983455i	$0.442018\pi$
$312$	0	0
$313$	−150293.	−1.53409	−0.767043	−	0.641596i	$-0.778273\pi$
$313$	−150293.	−1.53409	−0.767043	+	0.641596i	$0.778273\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	59550.0	0.592602	0.296301	−	0.955095i	$-0.404247\pi$
$317$	59550.0	0.592602	0.296301	+	0.955095i	$0.404247\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	245776.	2.34126
$325$	0	0
$326$	0	0
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−97847.0	−0.893082	−0.446541	−	0.894763i	$-0.647344\pi$
$331$	−97847.0	−0.893082	−0.446541	+	0.894763i	$0.647344\pi$
$332$	0	0
$333$	337798.	3.04627
$334$	0	0
$335$	0	0
$336$	0	0
$337$	0	0	1.00000			$0$
$337$	0	0	−1.00000			$\pi$
$338$	0	0
$339$	−248325.	−2.16083
$340$	0	0
$341$	−66913.0	−0.575442
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	205216.	1.64688	0.823440	−	0.567403i	$-0.192052\pi$
$353$	205216.	1.64688	0.823440	+	0.567403i	$0.192052\pi$
$354$	0	0
$355$	0	0
$356$	−102928.	−0.812145
$357$	0	0
$358$	0	0
$359$	0	0	1.00000			$0$
$359$	0	0	−1.00000			$\pi$
$360$	0	0
$361$	130321.	1.00000
$362$	0	0
$363$	−242794.	−1.84257
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−233772.	−1.73565	−0.867823	−	0.496874i	$-0.834481\pi$
$367$	−233772.	−1.73565	−0.867823	+	0.496874i	$0.834481\pi$
$368$	−267453.	−1.97493
$369$	0	0
$370$	0	0
$371$	0	0
$372$	−146727.	−1.06029
$373$	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
$379$	269593.	1.87685	0.938426	−	0.345479i	$-0.112284\pi$
$379$	269593.	1.87685	0.938426	+	0.345479i	$0.112284\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	−97658.0	−0.665749	−0.332874	−	0.942971i	$-0.608019\pi$
$383$	−97658.0	−0.665749	−0.332874	+	0.942971i	$0.608019\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	0	0
$388$	−257105.	−1.70784
$389$	−3167.00	−0.0209290	−0.0104645	−	0.999945i	$-0.503331\pi$
$389$	−3167.00	−0.0209290	−0.0104645	+	0.999945i	$0.503331\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	0	0
$396$	−375584.	−2.39506
$397$	−62883.2	−0.398982	−0.199491	−	0.979900i	$-0.563929\pi$
$397$	−62883.2	−0.398982	−0.199491	+	0.979900i	$0.563929\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	311998.	1.94027	0.970137	−	0.242558i	$-0.0779863\pi$
$401$	311998.	1.94027	0.970137	+	0.242558i	$0.0779863\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−210689.	−1.27190
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	−306075.	−1.81194
$412$	241981.	1.42556
$413$	0	0
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	0	0
$419$	−282478.	−1.60900	−0.804501	−	0.593951i	$-0.797567\pi$
$419$	−282478.	−1.60900	−0.804501	+	0.593951i	$0.797567\pi$
$420$	0	0
$421$	−196082.	−1.10630	−0.553151	−	0.833081i	$-0.686575\pi$
$421$	−196082.	−1.10630	−0.553151	+	0.833081i	$0.686575\pi$
$422$	0	0
$423$	772110.	4.31518
$424$	0	0
$425$	0	0
$426$	0	0
$427$	0	0
$428$	0	0
$429$	0	0
$430$	0	0
$431$	0	0	1.00000			$0$
$431$	0	0	−1.00000			$\pi$
$432$	−479717.	−2.57050
$433$	−21641.0	−0.115425	−0.0577127	−	0.998333i	$-0.518381\pi$
$433$	−21641.0	−0.115425	−0.0577127	+	0.998333i	$0.518381\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0	0
$438$	0	0
$439$	0	0	1.00000			$0$
$439$	0	0	−1.00000			$\pi$
$440$	0	0
$441$	465794.	2.39506
$442$	0	0
$443$	−340932.	−1.73724	−0.868622	−	0.495475i	$-0.834994\pi$
$443$	−340932.	−1.73724	−0.868622	+	0.495475i	$0.834994\pi$
$444$	−462000.	−2.34356
$445$	0	0
$446$	0	0
$447$	0	0
$448$	0	0
$449$	−15073.0	−0.0747665	−0.0373832	−	0.999301i	$-0.511902\pi$
$449$	−15073.0	−0.0747665	−0.0373832	+	0.999301i	$0.511902\pi$
$450$	0	0
$451$	0	0
$452$	239593.	1.17273
$453$	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
$463$	−32386.8	−0.151080	−0.0755399	−	0.997143i	$-0.524068\pi$
$463$	−32386.8	−0.151080	−0.0755399	+	0.997143i	$0.524068\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−119647.	−0.548617	−0.274308	−	0.961642i	$-0.588449\pi$
$467$	−119647.	−0.548617	−0.274308	+	0.961642i	$0.588449\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	−815925.	−3.67797
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	1.08095e6	4.75084
$478$	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
$484$	234256.	1.00000
$485$	0	0
$486$	0	0
$487$	374364.	1.57847	0.789235	−	0.614092i	$-0.210477\pi$
$487$	374364.	1.57847	0.789235	+	0.614092i	$0.210477\pi$
$488$	0	0
$489$	369600.	1.54566
$490$	0	0
$491$	0	0	1.00000			$0$
$491$	0	0	−1.00000			$\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	0	0
$496$	141568.	0.575442
$497$	0	0
$498$	0	0
$499$	135598.	0.544568	0.272284	−	0.962217i	$-0.412221\pi$
$499$	135598.	0.544568	0.272284	+	0.962217i	$0.412221\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	0	0	1.00000			$0$
$503$	0	0	−1.00000			$\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−473631.	−1.84257
$508$	0	0
$509$	−495887.	−1.91402	−0.957012	−	0.290050i	$-0.906328\pi$
$509$	−495887.	−1.91402	−0.957012	+	0.290050i	$0.906328\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−481574.	−1.80170
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−124607.	−0.459057	−0.229529	−	0.973302i	$-0.573718\pi$
$521$	−124607.	−0.459057	−0.229529	+	0.973302i	$0.573718\pi$
$522$	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
$528$	513679.	1.84257
$529$	811634.	2.90034
$530$	0	0
$531$	−870478.	−3.08723
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	948439.	3.28898
$538$	0	0
$539$	−290521.	−1.00000
$540$	0	0
$541$	0	0	1.00000			$0$
$541$	0	0	−1.00000			$\pi$
$542$	0	0
$543$	60478.7	0.205117
$544$	0	0
$545$	0	0
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	295312.	0.983378
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	0	0
$554$	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
$560$	0	0
$561$	0	0
$562$	0	0
$563$	0	0	1.00000			$0$
$563$	0	0	−1.00000			$\pi$
$564$	−1.05600e6	−3.31975
$565$	0	0
$566$	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			$\pi$
$572$	0	0
$573$	−801180.	−2.44018
$574$	0	0
$575$	0	0
$576$	794624.	2.39506
$577$	−493365.	−1.48189	−0.740946	−	0.671565i	$-0.765622\pi$
$577$	−493365.	−1.48189	−0.740946	+	0.671565i	$0.765622\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	−674203.	−1.98360
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−359787.	−1.04417	−0.522083	−	0.852894i	$-0.674845\pi$
$587$	−359787.	−1.04417	−0.522083	+	0.852894i	$0.674845\pi$
$588$	−637057.	−1.84257
$589$	0	0
$590$	0	0
$591$	0	0
$592$	445754.	1.27190
$593$	0	0	1.00000			$0$
$593$	0	0	−1.00000			$\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−1.31335e6	−3.68495
$598$	0	0
$599$	−707998.	−1.97323	−0.986617	−	0.163058i	$-0.947864\pi$
$599$	−707998.	−1.97323	−0.986617	+	0.163058i	$0.947864\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	878275.	2.41544
$604$	0	0
$605$	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
$613$	0	0	1.00000			$0$
$613$	0	0	−1.00000			$\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−590625.	−1.55146	−0.775731	−	0.631064i	$-0.782619\pi$
$617$	−590625.	−1.55146	−0.775731	+	0.631064i	$0.782619\pi$
$618$	0	0
$619$	763847.	1.99354	0.996770	−	0.0803056i	$-0.0255896\pi$
$619$	763847.	1.99354	0.996770	+	0.0803056i	$0.0255896\pi$
$620$	0	0
$621$	1.95772e6	5.07655
$622$	0	0
$623$	0	0
$624$	0	0
$625$	0	0
$626$	0	0
$627$	0	0
$628$	787234.	1.99611
$629$	0	0
$630$	0	0
$631$	675047.	1.69541	0.847706	−	0.530466i	$-0.177983\pi$
$631$	675047.	1.69541	0.847706	+	0.530466i	$0.177983\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	−1.47840e6	−3.65492
$637$	0	0
$638$	0	0
$639$	1.47576e6	3.61421
$640$	0	0
$641$	269713.	0.656426	0.328213	−	0.944604i	$-0.393554\pi$
$641$	269713.	0.656426	0.328213	+	0.944604i	$0.393554\pi$
$642$	0	0
$643$	−483415.	−1.16922	−0.584612	−	0.811313i	$-0.698753\pi$
$643$	−483415.	−1.16922	−0.584612	+	0.811313i	$0.698753\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	657736.	1.57124	0.785621	−	0.618707i	$-0.212343\pi$
$647$	657736.	1.57124	0.785621	+	0.618707i	$0.212343\pi$
$648$	0	0
$649$	542927.	1.28900
$650$	0	0
$651$	0	0
$652$	−356603.	−0.838862
$653$	219046.	0.513700	0.256850	−	0.966451i	$-0.417315\pi$
$653$	219046.	0.513700	0.256850	+	0.966451i	$0.417315\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	0	0
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	455567.	1.04268	0.521338	−	0.853350i	$-0.325433\pi$
$661$	455567.	1.04268	0.521338	+	0.853350i	$0.325433\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	−220275.	−0.492168
$670$	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
$676$	456976.	1.00000
$677$	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
$683$	−880365.	−1.88721	−0.943607	−	0.331067i	$-0.892591\pi$
$683$	−880365.	−1.88721	−0.943607	+	0.331067i	$0.892591\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	1.36988e6	2.90248
$688$	0	0
$689$	0	0
$690$	0	0
$691$	239687.	0.501982	0.250991	−	0.967989i	$-0.419243\pi$
$691$	239687.	0.501982	0.250991	+	0.967989i	$0.419243\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	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
$703$	0	0
$704$	−495616.	−1.00000
$705$	0	0
$706$	0	0
$707$	0	0
$708$	1.19054e6	2.37507
$709$	111887.	0.222581	0.111290	−	0.993788i	$-0.464502\pi$
$709$	111887.	0.222581	0.111290	+	0.993788i	$0.464502\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	−577739.	−1.13646
$714$	0	0
$715$	0	0
$716$	−915088.	−1.78499
$717$	0	0
$718$	0	0
$719$	318647.	0.616385	0.308192	−	0.951324i	$-0.400276\pi$
$719$	318647.	0.616385	0.308192	+	0.951324i	$0.400276\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	0	0
$724$	−58352.0	−0.111321
$725$	0	0
$726$	0	0
$727$	714550.	1.35196	0.675980	−	0.736920i	$-0.263720\pi$
$727$	714550.	1.35196	0.675980	+	0.736920i	$0.263720\pi$
$728$	0	0
$729$	462959.	0.871139
$730$	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
$736$	0	0
$737$	−547790.	−1.00851
$738$	0	0
$739$	0	0	1.00000			$0$
$739$	0	0	−1.00000			$\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	0	0	1.00000			$0$
$743$	0	0	−1.00000			$\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−181273.	−0.321405	−0.160703	−	0.987003i	$-0.551376\pi$
$751$	−181273.	−0.321405	−0.160703	+	0.987003i	$0.551376\pi$
$752$	1.01887e6	1.80170
$753$	1.23499e6	2.17809
$754$	0	0
$755$	0	0
$756$	0	0
$757$	105867.	0.184743	0.0923714	−	0.995725i	$-0.470555\pi$
$757$	105867.	0.184743	0.0923714	+	0.995725i	$0.470555\pi$
$758$	0	0
$759$	−2.09632e6	−3.63894
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	0	0
$764$	773008.	1.32433
$765$	0	0
$766$	0	0
$767$	0	0
$768$	−1.08679e6	−1.84257
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	1.50480e6	2.53145
$772$	0	0
$773$	981456.	1.64252	0.821262	−	0.570551i	$-0.193270\pi$
$773$	981456.	1.64252	0.821262	+	0.570551i	$0.193270\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	−920447.	−1.50903
$782$	0	0
$783$	0	0
$784$	614656.	1.00000
$785$	0	0
$786$	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
$796$	1.26717e6	1.99990
$797$	268099.	0.422065	0.211032	−	0.977479i	$-0.432317\pi$
$797$	268099.	0.422065	0.211032	+	0.977479i	$0.432317\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	−1.24800e6	−1.94514
$802$	0	0
$803$	0	0
$804$	−1.20120e6	−1.85825
$805$	0	0
$806$	0	0
$807$	−226824.	−0.348291
$808$	0	0
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	0	0
$820$	0	0
$821$	0	0	1.00000			$0$
$821$	0	0	−1.00000			$\pi$
$822$	0	0
$823$	1.10429e6	1.63036	0.815178	−	0.579211i	$-0.196639\pi$
$823$	1.10429e6	1.63036	0.815178	+	0.579211i	$0.196639\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	−3.24286e6	−4.73007
$829$	−706993.	−1.02874	−0.514371	−	0.857568i	$-0.671974\pi$
$829$	−706993.	−1.02874	−0.514371	+	0.857568i	$0.671974\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0	0
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−1.03626e6	−1.47917
$838$	0	0
$839$	1.28743e6	1.82895	0.914473	−	0.404648i	$-0.132606\pi$
$839$	1.28743e6	1.82895	0.914473	+	0.404648i	$0.132606\pi$
$840$	0	0
$841$	707281.	1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	0	0
$846$	0	0
$847$	0	0
$848$	1.42641e6	1.98360
$849$	0	0
$850$	0	0
$851$	−1.81912e6	−2.51191
$852$	−2.01837e6	−2.78048
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	−902713.	−1.22339	−0.611693	−	0.791095i	$-0.709511\pi$
$859$	−902713.	−1.22339	−0.611693	+	0.791095i	$0.709511\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	718779.	0.965103	0.482552	−	0.875868i	$-0.339710\pi$
$863$	718779.	0.965103	0.482552	+	0.875868i	$0.339710\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−1.38504e6	−1.84257
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	−3.11740e6	−4.09038
$874$	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
$880$	0	0
$881$	658847.	0.848854	0.424427	−	0.905462i	$-0.360476\pi$
$881$	658847.	0.848854	0.424427	+	0.905462i	$0.360476\pi$
$882$	0	0
$883$	1.52671e6	1.95810	0.979050	−	0.203621i	$-0.0652710\pi$
$883$	1.52671e6	1.95810	0.979050	+	0.203621i	$0.0652710\pi$
$884$	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
$891$	−1.85868e6	−2.34126
$892$	212529.	0.267109
$893$	0	0
$894$	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
$907$	−835789.	−1.01597	−0.507987	−	0.861365i	$-0.669610\pi$
$907$	−835789.	−1.01597	−0.507987	+	0.861365i	$0.669610\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	−1.50144e6	−1.80914	−0.904569	−	0.426327i	$-0.859807\pi$
$911$	−1.50144e6	−1.80914	−0.904569	+	0.426327i	$0.859807\pi$
$912$	0	0
$913$	0	0
$914$	0	0
$915$	0	0
$916$	−1.32171e6	−1.57524
$917$	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
$923$	0	0
$924$	0	0
$925$	0	0
$926$	0	0
$927$	2.93402e6	3.41431
$928$	0	0
$929$	808318.	0.936593	0.468296	−	0.883571i	$-0.344868\pi$
$929$	808318.	0.936593	0.468296	+	0.883571i	$0.344868\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	−581106.	−0.667563
$934$	0	0
$935$	0	0
$936$	0	0
$937$	0	0	1.00000			$0$
$937$	0	0	−1.00000			$\pi$
$938$	0	0
$939$	2.49232e6	2.82666
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	0	0
$943$	0	0
$944$	−1.14867e6	−1.28900
$945$	0	0
$946$	0	0
$947$	1.79312e6	1.99944	0.999720	−	0.0236433i	$-0.00752659\pi$
$947$	1.79312e6	1.99944	0.999720	+	0.0236433i	$0.00752659\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	−987525.	−1.09191
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−617712.	−0.668866
$962$	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
$971$	1.87879e6	1.99269	0.996347	−	0.0854008i	$-0.0272171\pi$
$971$	1.87879e6	1.99269	0.996347	+	0.0854008i	$0.0272171\pi$
$972$	−1.64717e6	−1.74343
$973$	0	0
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−1.86486e6	−1.95369	−0.976846	−	0.213945i	$-0.931369\pi$
$977$	−1.86486e6	−1.95369	−0.976846	+	0.213945i	$0.931369\pi$
$978$	0	0
$979$	778393.	0.812145
$980$	0	0
$981$	0	0
$982$	0	0
$983$	1.18150e6	1.22272	0.611358	−	0.791354i	$-0.290623\pi$
$983$	1.18150e6	1.22272	0.611358	+	0.791354i	$0.290623\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	0	0
$989$	0	0
$990$	0	0
$991$	−538562.	−0.548389	−0.274194	−	0.961674i	$-0.588411\pi$
$991$	−538562.	−0.548389	−0.274194	+	0.961674i	$0.588411\pi$
$992$	0	0
$993$	1.62261e6	1.64557
$994$	0	0
$995$	0	0
$996$	0	0
$997$	0	0	1.00000			$0$
$997$	0	0	−1.00000			$\pi$
$998$	0	0
$999$	−3.26288e6	−3.26941

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.5.c.d.76.1		2
5.2	odd	4		55.5.d.c.54.2	yes	2
5.3	odd	4		55.5.d.c.54.1	✓	2
5.4	even	2	inner	275.5.c.d.76.2		2
11.10	odd	2	CM	275.5.c.d.76.1		2
55.32	even	4		55.5.d.c.54.2	yes	2
55.43	even	4		55.5.d.c.54.1	✓	2
55.54	odd	2	inner	275.5.c.d.76.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.5.d.c.54.1	✓	2	5.3	odd	4
55.5.d.c.54.1	✓	2	55.43	even	4
55.5.d.c.54.2	yes	2	5.2	odd	4
55.5.d.c.54.2	yes	2	55.32	even	4
275.5.c.d.76.1		2	1.1	even	1	trivial
275.5.c.d.76.1		2	11.10	odd	2	CM
275.5.c.d.76.2		2	5.4	even	2	inner
275.5.c.d.76.2		2	55.54	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	275.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-16.5831 q^{3} +16.0000 q^{4} +194.000 q^{9} +O(q^{10})\)	\(q-16.5831 q^{3} +16.0000 q^{4} +194.000 q^{9} -121.000 q^{11} -265.330 q^{12} +256.000 q^{16} -1044.74 q^{23} -1873.89 q^{27} +553.000 q^{31} +2006.56 q^{33} +3104.00 q^{36} +1741.23 q^{37} -1936.00 q^{44} +3979.95 q^{47} -4245.28 q^{48} +2401.00 q^{49} +5571.93 q^{53} -4487.00 q^{59} +4096.00 q^{64} +4527.19 q^{67} +17325.0 q^{69} +7607.00 q^{71} +15361.0 q^{81} -6433.00 q^{89} -16715.8 q^{92} -9170.47 q^{93} -16069.0 q^{97} -23474.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 32 q^{4} + 388 q^{9}+O(q^{10}) \) 2 * q + 32 * q^4 + 388 * q^9	\( 2 q + 32 q^{4} + 388 q^{9} - 242 q^{11} + 512 q^{16} + 1106 q^{31} + 6208 q^{36} - 3872 q^{44} + 4802 q^{49} - 8974 q^{59} + 8192 q^{64} + 34650 q^{69} + 15214 q^{71} + 30722 q^{81} - 12866 q^{89} - 46948 q^{99}+O(q^{100}) \) 2 * q + 32 * q^4 + 388 * q^9 - 242 * q^11 + 512 * q^16 + 1106 * q^31 + 6208 * q^36 - 3872 * q^44 + 4802 * q^49 - 8974 * q^59 + 8192 * q^64 + 34650 * q^69 + 15214 * q^71 + 30722 * q^81 - 12866 * q^89 - 46948 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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