LMFDB - Embedded newform 1620.2.d.a.649.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(649,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1620.649");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.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:	no
Analytic conductor:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			649.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1620.649
Dual form			1620.2.d.a.649.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 2.00000i) q^{5} +2.00000i q^{7} +O(q^{10})$	$q+(-1.00000 - 2.00000i) q^{5} +2.00000i q^{7} +1.00000 q^{11} -2.00000i q^{17} +3.00000 q^{19} -4.00000i q^{23} +(-3.00000 + 4.00000i) q^{25} +3.00000 q^{29} +1.00000 q^{31} +(4.00000 - 2.00000i) q^{35} -10.0000i q^{37} +1.00000 q^{41} +10.0000i q^{43} -10.0000i q^{47} +3.00000 q^{49} -6.00000i q^{53} +(-1.00000 - 2.00000i) q^{55} +13.0000 q^{59} -10.0000 q^{61} -8.00000i q^{67} +9.00000 q^{71} -14.0000i q^{73} +2.00000i q^{77} -10.0000i q^{83} +(-4.00000 + 2.00000i) q^{85} -13.0000 q^{89} +(-3.00000 - 6.00000i) q^{95} +10.0000i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{5}+O(q^{10}) $ 2 * q - 2 * q^5	$ 2 q - 2 q^{5} + 2 q^{11} + 6 q^{19} - 6 q^{25} + 6 q^{29} + 2 q^{31} + 8 q^{35} + 2 q^{41} + 6 q^{49} - 2 q^{55} + 26 q^{59} - 20 q^{61} + 18 q^{71} - 8 q^{85} - 26 q^{89} - 6 q^{95}+O(q^{100}) $ 2 * q - 2 * q^5 + 2 * q^11 + 6 * q^19 - 6 * q^25 + 6 * q^29 + 2 * q^31 + 8 * q^35 + 2 * q^41 + 6 * q^49 - 2 * q^55 + 26 * q^59 - 20 * q^61 + 18 * q^71 - 8 * q^85 - 26 * q^89 - 6 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$1$	$-1$	$1$

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
$3$		0			0
$4$		0			0
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$6$		0			0
$7$			2.00000i			0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$			2.00000i			0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.00000			0.301511			0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000			0.301511			0.150756	+	0.988571i	$0.451829\pi$
$12$		0			0
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	2.00000i		−	0.485071i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$		−	2.00000i		−	0.485071i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$		0			0
$19$	3.00000			0.688247			0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000			0.688247			0.344124	+	0.938924i	$0.388176\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$		0			0
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$		0			0
$31$	1.00000			0.179605			0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000			0.179605			0.0898027	+	0.995960i	$0.471376\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.00000	−	2.00000i	0.676123	−	0.338062i
$36$		0			0
$37$		−	10.0000i		−	1.64399i	−0.569495	−	0.821995i	$-0.692861\pi$
$37$		−	10.0000i		−	1.64399i	0.569495	−	0.821995i	$-0.307139\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.00000			0.156174			0.0780869	−	0.996947i	$-0.475119\pi$
$41$	1.00000			0.156174			0.0780869	+	0.996947i	$0.475119\pi$
$42$		0			0
$43$			10.0000i			1.52499i	0.646997	+	0.762493i	$0.276025\pi$
$43$			10.0000i			1.52499i	−0.646997	+	0.762493i	$0.723975\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	10.0000i		−	1.45865i	−0.684167	−	0.729325i	$-0.739834\pi$
$47$		−	10.0000i		−	1.45865i	0.684167	−	0.729325i	$-0.260166\pi$
$48$		0			0
$49$	3.00000			0.428571
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$		0			0
$55$	−1.00000	−	2.00000i	−0.134840	−	0.269680i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	13.0000			1.69246			0.846228	−	0.532821i	$-0.178868\pi$
$59$	13.0000			1.69246			0.846228	+	0.532821i	$0.178868\pi$
$60$		0			0
$61$	−10.0000			−1.28037			−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000			−1.28037			−0.640184	+	0.768221i	$0.721142\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		0			0
$66$		0			0
$67$		−	8.00000i		−	0.977356i	−0.872464	−	0.488678i	$-0.837479\pi$
$67$		−	8.00000i		−	0.977356i	0.872464	−	0.488678i	$-0.162521\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	9.00000			1.06810			0.534052	−	0.845452i	$-0.320669\pi$
$71$	9.00000			1.06810			0.534052	+	0.845452i	$0.320669\pi$
$72$		0			0
$73$		−	14.0000i		−	1.63858i	−0.573382	−	0.819288i	$-0.694369\pi$
$73$		−	14.0000i		−	1.63858i	0.573382	−	0.819288i	$-0.305631\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			2.00000i			0.227921i
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	10.0000i		−	1.09764i	−0.835940	−	0.548821i	$-0.815077\pi$
$83$		−	10.0000i		−	1.09764i	0.835940	−	0.548821i	$-0.184923\pi$
$84$		0			0
$85$	−4.00000	+	2.00000i	−0.433861	+	0.216930i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−13.0000			−1.37800			−0.688999	−	0.724763i	$-0.741949\pi$
$89$	−13.0000			−1.37800			−0.688999	+	0.724763i	$0.741949\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.00000	−	6.00000i	−0.307794	−	0.615587i
$96$		0			0
$97$			10.0000i			1.01535i	0.861550	+	0.507673i	$0.169494\pi$
$97$			10.0000i			1.01535i	−0.861550	+	0.507673i	$0.830506\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.00000			−0.0995037			−0.0497519	−	0.998762i	$-0.515843\pi$
$101$	−1.00000			−0.0995037			−0.0497519	+	0.998762i	$0.515843\pi$
$102$		0			0
$103$		−	4.00000i		−	0.394132i	−0.980390	−	0.197066i	$-0.936859\pi$
$103$		−	4.00000i		−	0.394132i	0.980390	−	0.197066i	$-0.0631413\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	12.0000i		−	1.16008i	−0.814587	−	0.580042i	$-0.803036\pi$
$107$		−	12.0000i		−	1.16008i	0.814587	−	0.580042i	$-0.196964\pi$
$108$		0			0
$109$	17.0000			1.62830			0.814152	−	0.580651i	$-0.197202\pi$
$109$	17.0000			1.62830			0.814152	+	0.580651i	$0.197202\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$		0			0
$115$	−8.00000	+	4.00000i	−0.746004	+	0.373002i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.00000			0.366679
$120$		0			0
$121$	−10.0000			−0.909091
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$		0			0
$127$			2.00000i			0.177471i	0.996055	+	0.0887357i	$0.0282826\pi$
$127$			2.00000i			0.177471i	−0.996055	+	0.0887357i	$0.971717\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−9.00000			−0.786334			−0.393167	−	0.919467i	$-0.628621\pi$
$131$	−9.00000			−0.786334			−0.393167	+	0.919467i	$0.628621\pi$
$132$		0			0
$133$			6.00000i			0.520266i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$		0			0
$139$	17.0000			1.44192			0.720961	−	0.692976i	$-0.243701\pi$
$139$	17.0000			1.44192			0.720961	+	0.692976i	$0.243701\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−3.00000	−	6.00000i	−0.249136	−	0.498273i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$		0			0
$151$	1.00000			0.0813788			0.0406894	−	0.999172i	$-0.487045\pi$
$151$	1.00000			0.0813788			0.0406894	+	0.999172i	$0.487045\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.00000	−	2.00000i	−0.0803219	−	0.160644i
$156$		0			0
$157$			10.0000i			0.798087i	0.916932	+	0.399043i	$0.130658\pi$
$157$			10.0000i			0.798087i	−0.916932	+	0.399043i	$0.869342\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	8.00000			0.630488
$162$		0			0
$163$			14.0000i			1.09656i	0.836293	+	0.548282i	$0.184718\pi$
$163$			14.0000i			1.09656i	−0.836293	+	0.548282i	$0.815282\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	18.0000i		−	1.39288i	−0.717614	−	0.696441i	$-0.754766\pi$
$167$		−	18.0000i		−	1.39288i	0.717614	−	0.696441i	$-0.245234\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$		0			0
$171$		0			0
$172$		0			0
$173$			16.0000i			1.21646i	0.793762	+	0.608229i	$0.208120\pi$
$173$			16.0000i			1.21646i	−0.793762	+	0.608229i	$0.791880\pi$
$174$		0			0
$175$	−8.00000	−	6.00000i	−0.604743	−	0.453557i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−23.0000			−1.71910			−0.859550	−	0.511051i	$-0.829256\pi$
$179$	−23.0000			−1.71910			−0.859550	+	0.511051i	$0.829256\pi$
$180$		0			0
$181$	−1.00000			−0.0743294			−0.0371647	−	0.999309i	$-0.511833\pi$
$181$	−1.00000			−0.0743294			−0.0371647	+	0.999309i	$0.511833\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−20.0000	+	10.0000i	−1.47043	+	0.735215i
$186$		0			0
$187$		−	2.00000i		−	0.146254i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.00000			0.651217			0.325609	−	0.945505i	$-0.394431\pi$
$191$	9.00000			0.651217			0.325609	+	0.945505i	$0.394431\pi$
$192$		0			0
$193$			10.0000i			0.719816i	0.932988	+	0.359908i	$0.117192\pi$
$193$			10.0000i			0.719816i	−0.932988	+	0.359908i	$0.882808\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			20.0000i			1.42494i	0.701702	+	0.712470i	$0.252424\pi$
$197$			20.0000i			1.42494i	−0.701702	+	0.712470i	$0.747576\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$			6.00000i			0.421117i
$204$		0			0
$205$	−1.00000	−	2.00000i	−0.0698430	−	0.139686i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.00000			0.207514
$210$		0			0
$211$	9.00000			0.619586			0.309793	−	0.950804i	$-0.399740\pi$
$211$	9.00000			0.619586			0.309793	+	0.950804i	$0.399740\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	20.0000	−	10.0000i	1.36399	−	0.681994i
$216$		0			0
$217$			2.00000i			0.135769i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		−	20.0000i		−	1.33930i	−0.742677	−	0.669650i	$-0.766444\pi$
$223$		−	20.0000i		−	1.33930i	0.742677	−	0.669650i	$-0.233556\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			22.0000i			1.46019i	0.683345	+	0.730096i	$0.260525\pi$
$227$			22.0000i			1.46019i	−0.683345	+	0.730096i	$0.739475\pi$
$228$		0			0
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			10.0000i			0.655122i	0.944830	+	0.327561i	$0.106227\pi$
$233$			10.0000i			0.655122i	−0.944830	+	0.327561i	$0.893773\pi$
$234$		0			0
$235$	−20.0000	+	10.0000i	−1.30466	+	0.652328i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	20.0000			1.29369			0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000			1.29369			0.646846	+	0.762620i	$0.276088\pi$
$240$		0			0
$241$	1.00000			0.0644157			0.0322078	−	0.999481i	$-0.489746\pi$
$241$	1.00000			0.0644157			0.0322078	+	0.999481i	$0.489746\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.00000	−	6.00000i	−0.191663	−	0.383326i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		−	4.00000i		−	0.251478i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			12.0000i			0.748539i	0.927320	+	0.374270i	$0.122107\pi$
$257$			12.0000i			0.748539i	−0.927320	+	0.374270i	$0.877893\pi$
$258$		0			0
$259$	20.0000			1.24274
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	16.0000i		−	0.986602i	−0.869859	−	0.493301i	$-0.835790\pi$
$263$		−	16.0000i		−	0.986602i	0.869859	−	0.493301i	$-0.164210\pi$
$264$		0			0
$265$	−12.0000	+	6.00000i	−0.737154	+	0.368577i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−27.0000			−1.64622			−0.823110	−	0.567883i	$-0.807763\pi$
$269$	−27.0000			−1.64622			−0.823110	+	0.567883i	$0.807763\pi$
$270$		0			0
$271$	−20.0000			−1.21491			−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000			−1.21491			−0.607457	+	0.794353i	$0.707810\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.00000	+	4.00000i	−0.180907	+	0.241209i
$276$		0			0
$277$		−	10.0000i		−	0.600842i	−0.953807	−	0.300421i	$-0.902873\pi$
$277$		−	10.0000i		−	0.600842i	0.953807	−	0.300421i	$-0.0971271\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−30.0000			−1.78965			−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000			−1.78965			−0.894825	+	0.446417i	$0.852700\pi$
$282$		0			0
$283$		−	16.0000i		−	0.951101i	−0.879688	−	0.475551i	$-0.842249\pi$
$283$		−	16.0000i		−	0.951101i	0.879688	−	0.475551i	$-0.157751\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			2.00000i			0.118056i
$288$		0			0
$289$	13.0000			0.764706
$290$		0			0
$291$		0			0
$292$		0			0
$293$			30.0000i			1.75262i	0.481749	+	0.876309i	$0.340002\pi$
$293$			30.0000i			1.75262i	−0.481749	+	0.876309i	$0.659998\pi$
$294$		0			0
$295$	−13.0000	−	26.0000i	−0.756889	−	1.51378i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−20.0000			−1.15278
$302$		0			0
$303$		0			0
$304$		0			0
$305$	10.0000	+	20.0000i	0.572598	+	1.14520i
$306$		0			0
$307$			30.0000i			1.71219i	0.516818	+	0.856095i	$0.327116\pi$
$307$			30.0000i			1.71219i	−0.516818	+	0.856095i	$0.672884\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−21.0000			−1.19080			−0.595400	−	0.803429i	$-0.703007\pi$
$311$	−21.0000			−1.19080			−0.595400	+	0.803429i	$0.703007\pi$
$312$		0			0
$313$		−	20.0000i		−	1.13047i	−0.824931	−	0.565233i	$-0.808786\pi$
$313$		−	20.0000i		−	1.13047i	0.824931	−	0.565233i	$-0.191214\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			10.0000i			0.561656i	0.959758	+	0.280828i	$0.0906090\pi$
$317$			10.0000i			0.561656i	−0.959758	+	0.280828i	$0.909391\pi$
$318$		0			0
$319$	3.00000			0.167968
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	6.00000i		−	0.333849i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	20.0000			1.10264
$330$		0			0
$331$	1.00000			0.0549650			0.0274825	−	0.999622i	$-0.491251\pi$
$331$	1.00000			0.0549650			0.0274825	+	0.999622i	$0.491251\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−16.0000	+	8.00000i	−0.874173	+	0.437087i
$336$		0			0
$337$			20.0000i			1.08947i	0.838608	+	0.544735i	$0.183370\pi$
$337$			20.0000i			1.08947i	−0.838608	+	0.544735i	$0.816630\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.00000			0.0541530
$342$		0			0
$343$			20.0000i			1.07990i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			18.0000i			0.966291i	0.875540	+	0.483145i	$0.160506\pi$
$347$			18.0000i			0.966291i	−0.875540	+	0.483145i	$0.839494\pi$
$348$		0			0
$349$	23.0000			1.23116			0.615581	−	0.788074i	$-0.288921\pi$
$349$	23.0000			1.23116			0.615581	+	0.788074i	$0.288921\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			10.0000i			0.532246i	0.963939	+	0.266123i	$0.0857428\pi$
$353$			10.0000i			0.532246i	−0.963939	+	0.266123i	$0.914257\pi$
$354$		0			0
$355$	−9.00000	−	18.0000i	−0.477670	−	0.955341i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−33.0000			−1.74167			−0.870837	−	0.491572i	$-0.836422\pi$
$359$	−33.0000			−1.74167			−0.870837	+	0.491572i	$0.836422\pi$
$360$		0			0
$361$	−10.0000			−0.526316
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−28.0000	+	14.0000i	−1.46559	+	0.732793i
$366$		0			0
$367$		−	28.0000i		−	1.46159i	−0.682598	−	0.730794i	$-0.739150\pi$
$367$		−	28.0000i		−	1.46159i	0.682598	−	0.730794i	$-0.260850\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	12.0000			0.623009
$372$		0			0
$373$			6.00000i			0.310668i	0.987862	+	0.155334i	$0.0496454\pi$
$373$			6.00000i			0.310668i	−0.987862	+	0.155334i	$0.950355\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	4.00000			0.205466			0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000			0.205466			0.102733	+	0.994709i	$0.467241\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		−	20.0000i		−	1.02195i	−0.859595	−	0.510976i	$-0.829284\pi$
$383$		−	20.0000i		−	1.02195i	0.859595	−	0.510976i	$-0.170716\pi$
$384$		0			0
$385$	4.00000	−	2.00000i	0.203859	−	0.101929i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−10.0000			−0.507020			−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000			−0.507020			−0.253510	+	0.967333i	$0.581585\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$			8.00000i			0.401508i	0.979642	+	0.200754i	$0.0643393\pi$
$397$			8.00000i			0.401508i	−0.979642	+	0.200754i	$0.935661\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−10.0000			−0.499376			−0.249688	−	0.968326i	$-0.580328\pi$
$401$	−10.0000			−0.499376			−0.249688	+	0.968326i	$0.580328\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	10.0000i		−	0.495682i
$408$		0			0
$409$	10.0000			0.494468			0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000			0.494468			0.247234	+	0.968956i	$0.420478\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			26.0000i			1.27938i
$414$		0			0
$415$	−20.0000	+	10.0000i	−0.981761	+	0.490881i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	20.0000			0.977064			0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000			0.977064			0.488532	+	0.872546i	$0.337533\pi$
$420$		0			0
$421$	−11.0000			−0.536107			−0.268054	−	0.963404i	$-0.586380\pi$
$421$	−11.0000			−0.536107			−0.268054	+	0.963404i	$0.586380\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	8.00000	+	6.00000i	0.388057	+	0.291043i
$426$		0			0
$427$		−	20.0000i		−	0.967868i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	31.0000			1.49322			0.746609	−	0.665263i	$-0.231681\pi$
$431$	31.0000			1.49322			0.746609	+	0.665263i	$0.231681\pi$
$432$		0			0
$433$			4.00000i			0.192228i	0.995370	+	0.0961139i	$0.0306413\pi$
$433$			4.00000i			0.192228i	−0.995370	+	0.0961139i	$0.969359\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	12.0000i		−	0.574038i
$438$		0			0
$439$	27.0000			1.28864			0.644320	−	0.764756i	$-0.277141\pi$
$439$	27.0000			1.28864			0.644320	+	0.764756i	$0.277141\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			30.0000i			1.42534i	0.701498	+	0.712672i	$0.252515\pi$
$443$			30.0000i			1.42534i	−0.701498	+	0.712672i	$0.747485\pi$
$444$		0			0
$445$	13.0000	+	26.0000i	0.616259	+	1.23252i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−27.0000			−1.27421			−0.637104	−	0.770778i	$-0.719868\pi$
$449$	−27.0000			−1.27421			−0.637104	+	0.770778i	$0.719868\pi$
$450$		0			0
$451$	1.00000			0.0470882
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	10.0000i		−	0.467780i	−0.972263	−	0.233890i	$-0.924854\pi$
$457$		−	10.0000i		−	0.467780i	0.972263	−	0.233890i	$-0.0751456\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−9.00000			−0.419172			−0.209586	−	0.977790i	$-0.567212\pi$
$461$	−9.00000			−0.419172			−0.209586	+	0.977790i	$0.567212\pi$
$462$		0			0
$463$			24.0000i			1.11537i	0.830051	+	0.557687i	$0.188311\pi$
$463$			24.0000i			1.11537i	−0.830051	+	0.557687i	$0.811689\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			18.0000i			0.832941i	0.909149	+	0.416470i	$0.136733\pi$
$467$			18.0000i			0.832941i	−0.909149	+	0.416470i	$0.863267\pi$
$468$		0			0
$469$	16.0000			0.738811
$470$		0			0
$471$		0			0
$472$		0			0
$473$			10.0000i			0.459800i
$474$		0			0
$475$	−9.00000	+	12.0000i	−0.412948	+	0.550598i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	23.0000			1.05090			0.525448	−	0.850825i	$-0.323898\pi$
$479$	23.0000			1.05090			0.525448	+	0.850825i	$0.323898\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$	20.0000	−	10.0000i	0.908153	−	0.454077i
$486$		0			0
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−21.0000			−0.947717			−0.473858	−	0.880601i	$-0.657139\pi$
$491$	−21.0000			−0.947717			−0.473858	+	0.880601i	$0.657139\pi$
$492$		0			0
$493$		−	6.00000i		−	0.270226i
$494$		0			0
$495$		0			0
$496$		0			0
$497$			18.0000i			0.807410i
$498$		0			0
$499$	27.0000			1.20869			0.604343	−	0.796724i	$-0.293436\pi$
$499$	27.0000			1.20869			0.604343	+	0.796724i	$0.293436\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$	1.00000	+	2.00000i	0.0444994	+	0.0889988i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−6.00000			−0.265945			−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000			−0.265945			−0.132973	+	0.991120i	$0.542452\pi$
$510$		0			0
$511$	28.0000			1.23865
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−8.00000	+	4.00000i	−0.352522	+	0.176261i
$516$		0			0
$517$		−	10.0000i		−	0.439799i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$		0			0
$523$			20.0000i			0.874539i	0.899331	+	0.437269i	$0.144054\pi$
$523$			20.0000i			0.874539i	−0.899331	+	0.437269i	$0.855946\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	2.00000i		−	0.0871214i
$528$		0			0
$529$	7.00000			0.304348
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−24.0000	+	12.0000i	−1.03761	+	0.518805i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.00000			0.129219
$540$		0			0
$541$	−29.0000			−1.24681			−0.623404	−	0.781900i	$-0.714251\pi$
$541$	−29.0000			−1.24681			−0.623404	+	0.781900i	$0.714251\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−17.0000	−	34.0000i	−0.728200	−	1.45640i
$546$		0			0
$547$			20.0000i			0.855138i	0.903983	+	0.427569i	$0.140630\pi$
$547$			20.0000i			0.855138i	−0.903983	+	0.427569i	$0.859370\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	9.00000			0.383413
$552$		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
$563$			10.0000i			0.421450i	0.977545	+	0.210725i	$0.0675824\pi$
$563$			10.0000i			0.421450i	−0.977545	+	0.210725i	$0.932418\pi$
$564$		0			0
$565$	−12.0000	+	6.00000i	−0.504844	+	0.252422i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	17.0000			0.712677			0.356339	−	0.934357i	$-0.384025\pi$
$569$	17.0000			0.712677			0.356339	+	0.934357i	$0.384025\pi$
$570$		0			0
$571$	19.0000			0.795125			0.397563	−	0.917575i	$-0.369856\pi$
$571$	19.0000			0.795125			0.397563	+	0.917575i	$0.369856\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	16.0000	+	12.0000i	0.667246	+	0.500435i
$576$		0			0
$577$		−	22.0000i		−	0.915872i	−0.888985	−	0.457936i	$-0.848589\pi$
$577$		−	22.0000i		−	0.915872i	0.888985	−	0.457936i	$-0.151411\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	20.0000			0.829740
$582$		0			0
$583$		−	6.00000i		−	0.248495i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	30.0000i		−	1.23823i	−0.785299	−	0.619116i	$-0.787491\pi$
$587$		−	30.0000i		−	1.23823i	0.785299	−	0.619116i	$-0.212509\pi$
$588$		0			0
$589$	3.00000			0.123613
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	24.0000i		−	0.985562i	−0.870153	−	0.492781i	$-0.835980\pi$
$593$		−	24.0000i		−	0.985562i	0.870153	−	0.492781i	$-0.164020\pi$
$594$		0			0
$595$	−4.00000	−	8.00000i	−0.163984	−	0.327968i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	33.0000			1.34834			0.674172	−	0.738575i	$-0.264501\pi$
$599$	33.0000			1.34834			0.674172	+	0.738575i	$0.264501\pi$
$600$		0			0
$601$	−31.0000			−1.26452			−0.632258	−	0.774758i	$-0.717872\pi$
$601$	−31.0000			−1.26452			−0.632258	+	0.774758i	$0.717872\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	10.0000	+	20.0000i	0.406558	+	0.813116i
$606$		0			0
$607$			10.0000i			0.405887i	0.979190	+	0.202944i	$0.0650509\pi$
$607$			10.0000i			0.405887i	−0.979190	+	0.202944i	$0.934949\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		−	20.0000i		−	0.807792i	−0.914805	−	0.403896i	$-0.867656\pi$
$613$		−	20.0000i		−	0.807792i	0.914805	−	0.403896i	$-0.132344\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			40.0000i			1.61034i	0.593045	+	0.805170i	$0.297926\pi$
$617$			40.0000i			1.61034i	−0.593045	+	0.805170i	$0.702074\pi$
$618$		0			0
$619$	−20.0000			−0.803868			−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000			−0.803868			−0.401934	+	0.915669i	$0.631662\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		−	26.0000i		−	1.04167i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−20.0000			−0.797452
$630$		0			0
$631$	41.0000			1.63218			0.816092	−	0.577922i	$-0.196136\pi$
$631$	41.0000			1.63218			0.816092	+	0.577922i	$0.196136\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	4.00000	−	2.00000i	0.158735	−	0.0793676i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−11.0000			−0.434474			−0.217237	−	0.976119i	$-0.569704\pi$
$641$	−11.0000			−0.434474			−0.217237	+	0.976119i	$0.569704\pi$
$642$		0			0
$643$		−	30.0000i		−	1.18308i	−0.806274	−	0.591542i	$-0.798519\pi$
$643$		−	30.0000i		−	1.18308i	0.806274	−	0.591542i	$-0.201481\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	48.0000i		−	1.88707i	−0.331266	−	0.943537i	$-0.607476\pi$
$647$		−	48.0000i		−	1.88707i	0.331266	−	0.943537i	$-0.392524\pi$
$648$		0			0
$649$	13.0000			0.510295
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	40.0000i		−	1.56532i	−0.622449	−	0.782660i	$-0.713862\pi$
$653$		−	40.0000i		−	1.56532i	0.622449	−	0.782660i	$-0.286138\pi$
$654$		0			0
$655$	9.00000	+	18.0000i	0.351659	+	0.703318i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−44.0000			−1.71400			−0.856998	−	0.515319i	$-0.827673\pi$
$659$	−44.0000			−1.71400			−0.856998	+	0.515319i	$0.827673\pi$
$660$		0			0
$661$	−31.0000			−1.20576			−0.602880	−	0.797832i	$-0.705980\pi$
$661$	−31.0000			−1.20576			−0.602880	+	0.797832i	$0.705980\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	12.0000	−	6.00000i	0.465340	−	0.232670i
$666$		0			0
$667$		−	12.0000i		−	0.464642i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−10.0000			−0.386046
$672$		0			0
$673$			36.0000i			1.38770i	0.720121	+	0.693849i	$0.244086\pi$
$673$			36.0000i			1.38770i	−0.720121	+	0.693849i	$0.755914\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	32.0000i		−	1.22986i	−0.788582	−	0.614930i	$-0.789184\pi$
$677$		−	32.0000i		−	1.22986i	0.788582	−	0.614930i	$-0.210816\pi$
$678$		0			0
$679$	−20.0000			−0.767530
$680$		0			0
$681$		0			0
$682$		0			0
$683$			20.0000i			0.765279i	0.923898	+	0.382639i	$0.124985\pi$
$683$			20.0000i			0.765279i	−0.923898	+	0.382639i	$0.875015\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−20.0000			−0.760836			−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000			−0.760836			−0.380418	+	0.924815i	$0.624220\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−17.0000	−	34.0000i	−0.644847	−	1.28969i
$696$		0			0
$697$		−	2.00000i		−	0.0757554i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.00000			0.0377695			0.0188847	−	0.999822i	$-0.493988\pi$
$701$	1.00000			0.0377695			0.0188847	+	0.999822i	$0.493988\pi$
$702$		0			0
$703$		−	30.0000i		−	1.13147i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	2.00000i		−	0.0752177i
$708$		0			0
$709$	−6.00000			−0.225335			−0.112667	−	0.993633i	$-0.535939\pi$
$709$	−6.00000			−0.225335			−0.112667	+	0.993633i	$0.535939\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	4.00000i		−	0.149801i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−7.00000			−0.261056			−0.130528	−	0.991445i	$-0.541667\pi$
$719$	−7.00000			−0.261056			−0.130528	+	0.991445i	$0.541667\pi$
$720$		0			0
$721$	8.00000			0.297936
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−9.00000	+	12.0000i	−0.334252	+	0.445669i
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	20.0000			0.739727
$732$		0			0
$733$		−	4.00000i		−	0.147743i	−0.997268	−	0.0738717i	$-0.976464\pi$
$733$		−	4.00000i		−	0.147743i	0.997268	−	0.0738717i	$-0.0235355\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	8.00000i		−	0.294684i
$738$		0			0
$739$	17.0000			0.625355			0.312678	−	0.949859i	$-0.398774\pi$
$739$	17.0000			0.625355			0.312678	+	0.949859i	$0.398774\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	6.00000i		−	0.220119i	−0.993925	−	0.110059i	$-0.964896\pi$
$743$		−	6.00000i		−	0.220119i	0.993925	−	0.110059i	$-0.0351041\pi$
$744$		0			0
$745$	−10.0000	−	20.0000i	−0.366372	−	0.732743i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	24.0000			0.876941
$750$		0			0
$751$	20.0000			0.729810			0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000			0.729810			0.364905	+	0.931045i	$0.381101\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−1.00000	−	2.00000i	−0.0363937	−	0.0727875i
$756$		0			0
$757$		−	40.0000i		−	1.45382i	−0.686730	−	0.726912i	$-0.740955\pi$
$757$		−	40.0000i		−	1.45382i	0.686730	−	0.726912i	$-0.259045\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	51.0000			1.84875			0.924374	−	0.381487i	$-0.124588\pi$
$761$	51.0000			1.84875			0.924374	+	0.381487i	$0.124588\pi$
$762$		0			0
$763$			34.0000i			1.23088i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	27.0000			0.973645			0.486822	−	0.873501i	$-0.338156\pi$
$769$	27.0000			0.973645			0.486822	+	0.873501i	$0.338156\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	30.0000i		−	1.07903i	−0.841978	−	0.539513i	$-0.818609\pi$
$773$		−	30.0000i		−	1.07903i	0.841978	−	0.539513i	$-0.181391\pi$
$774$		0			0
$775$	−3.00000	+	4.00000i	−0.107763	+	0.143684i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.00000			0.107486
$780$		0			0
$781$	9.00000			0.322045
$782$		0			0
$783$		0			0
$784$		0			0
$785$	20.0000	−	10.0000i	0.713831	−	0.356915i
$786$		0			0
$787$		−	22.0000i		−	0.784215i	−0.919919	−	0.392108i	$-0.871746\pi$
$787$		−	22.0000i		−	0.784215i	0.919919	−	0.392108i	$-0.128254\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	12.0000			0.426671
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	20.0000i		−	0.708436i	−0.935163	−	0.354218i	$-0.884747\pi$
$797$		−	20.0000i		−	0.708436i	0.935163	−	0.354218i	$-0.115253\pi$
$798$		0			0
$799$	−20.0000			−0.707549
$800$		0			0
$801$		0			0
$802$		0			0
$803$		−	14.0000i		−	0.494049i

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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 2.00000i) q^{5} +2.00000i q^{7} +O(q^{10})\)	\(q+(-1.00000 - 2.00000i) q^{5} +2.00000i q^{7} +1.00000 q^{11} -2.00000i q^{17} +3.00000 q^{19} -4.00000i q^{23} +(-3.00000 + 4.00000i) q^{25} +3.00000 q^{29} +1.00000 q^{31} +(4.00000 - 2.00000i) q^{35} -10.0000i q^{37} +1.00000 q^{41} +10.0000i q^{43} -10.0000i q^{47} +3.00000 q^{49} -6.00000i q^{53} +(-1.00000 - 2.00000i) q^{55} +13.0000 q^{59} -10.0000 q^{61} -8.00000i q^{67} +9.00000 q^{71} -14.0000i q^{73} +2.00000i q^{77} -10.0000i q^{83} +(-4.00000 + 2.00000i) q^{85} -13.0000 q^{89} +(-3.00000 - 6.00000i) q^{95} +10.0000i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{5}+O(q^{10}) \) 2 * q - 2 * q^5	\( 2 q - 2 q^{5} + 2 q^{11} + 6 q^{19} - 6 q^{25} + 6 q^{29} + 2 q^{31} + 8 q^{35} + 2 q^{41} + 6 q^{49} - 2 q^{55} + 26 q^{59} - 20 q^{61} + 18 q^{71} - 8 q^{85} - 26 q^{89} - 6 q^{95}+O(q^{100}) \) 2 * q - 2 * q^5 + 2 * q^11 + 6 * q^19 - 6 * q^25 + 6 * q^29 + 2 * q^31 + 8 * q^35 + 2 * q^41 + 6 * q^49 - 2 * q^55 + 26 * q^59 - 20 * q^61 + 18 * q^71 - 8 * q^85 - 26 * q^89 - 6 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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