LMFDB - Embedded newform 3240.2.f.c.649.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3240,2,Mod(649,3240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3240, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3240.649");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3240 = 2^{3} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3240.f (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:	$25.8715302549$
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			649.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	3240.649
Dual form			3240.2.f.c.649.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 2.00000i) q^{5} +2.00000i q^{7} +O(q^{10})$	$q+(-1.00000 + 2.00000i) q^{5} +2.00000i q^{7} +5.00000 q^{11} -4.00000i q^{13} -6.00000i q^{17} +7.00000 q^{19} -4.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} -5.00000 q^{29} -3.00000 q^{31} +(-4.00000 - 2.00000i) q^{35} -2.00000i q^{37} -7.00000 q^{41} -6.00000i q^{43} -6.00000i q^{47} +3.00000 q^{49} +10.0000i q^{53} +(-5.00000 + 10.0000i) q^{55} -15.0000 q^{59} +14.0000 q^{61} +(8.00000 + 4.00000i) q^{65} -4.00000i q^{67} +5.00000 q^{71} -14.0000i q^{73} +10.0000i q^{77} +8.00000 q^{79} -14.0000i q^{83} +(12.0000 + 6.00000i) q^{85} +3.00000 q^{89} +8.00000 q^{91} +(-7.00000 + 14.0000i) q^{95} -2.00000i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{5}+O(q^{10}) $ 2 * q - 2 * q^5	$ 2 q - 2 q^{5} + 10 q^{11} + 14 q^{19} - 6 q^{25} - 10 q^{29} - 6 q^{31} - 8 q^{35} - 14 q^{41} + 6 q^{49} - 10 q^{55} - 30 q^{59} + 28 q^{61} + 16 q^{65} + 10 q^{71} + 16 q^{79} + 24 q^{85} + 6 q^{89} + 16 q^{91} - 14 q^{95}+O(q^{100}) $ 2 * q - 2 * q^5 + 10 * q^11 + 14 * q^19 - 6 * q^25 - 10 * q^29 - 6 * q^31 - 8 * q^35 - 14 * q^41 + 6 * q^49 - 10 * q^55 - 30 * q^59 + 28 * q^61 + 16 * q^65 + 10 * q^71 + 16 * q^79 + 24 * q^85 + 6 * q^89 + 16 * q^91 - 14 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3240\mathbb{Z}\right)^\times$.

$n$	$1297$	$1621$	$2431$	$3161$
$\chi(n)$	$-1$	$1$	$1$	$1$

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
$11$	5.00000			1.50756			0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000			1.50756			0.753778	+	0.657129i	$0.228229\pi$
$12$		0			0
$13$		−	4.00000i		−	1.10940i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$		−	4.00000i		−	1.10940i	0.832050	−	0.554700i	$-0.187167\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	6.00000i		−	1.45521i	−0.685994	−	0.727607i	$-0.740633\pi$
$17$		−	6.00000i		−	1.45521i	0.685994	−	0.727607i	$-0.259367\pi$
$18$		0			0
$19$	7.00000			1.60591			0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000			1.60591			0.802955	+	0.596040i	$0.203260\pi$
$20$		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
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$		0			0
$31$	−3.00000			−0.538816			−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000			−0.538816			−0.269408	+	0.963026i	$0.586828\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.00000	−	2.00000i	−0.676123	−	0.338062i
$36$		0			0
$37$		−	2.00000i		−	0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$		−	2.00000i		−	0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−7.00000			−1.09322			−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000			−1.09322			−0.546608	+	0.837389i	$0.684081\pi$
$42$		0			0
$43$		−	6.00000i		−	0.914991i	−0.889212	−	0.457496i	$-0.848747\pi$
$43$		−	6.00000i		−	0.914991i	0.889212	−	0.457496i	$-0.151253\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	6.00000i		−	0.875190i	−0.899172	−	0.437595i	$-0.855830\pi$
$47$		−	6.00000i		−	0.875190i	0.899172	−	0.437595i	$-0.144170\pi$
$48$		0			0
$49$	3.00000			0.428571
$50$		0			0
$51$		0			0
$52$		0			0
$53$			10.0000i			1.37361i	0.726844	+	0.686803i	$0.240986\pi$
$53$			10.0000i			1.37361i	−0.726844	+	0.686803i	$0.759014\pi$
$54$		0			0
$55$	−5.00000	+	10.0000i	−0.674200	+	1.34840i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−15.0000			−1.95283			−0.976417	−	0.215894i	$-0.930733\pi$
$59$	−15.0000			−1.95283			−0.976417	+	0.215894i	$0.930733\pi$
$60$		0			0
$61$	14.0000			1.79252			0.896258	−	0.443533i	$-0.146275\pi$
$61$	14.0000			1.79252			0.896258	+	0.443533i	$0.146275\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	8.00000	+	4.00000i	0.992278	+	0.496139i
$66$		0			0
$67$		−	4.00000i		−	0.488678i	−0.969690	−	0.244339i	$-0.921429\pi$
$67$		−	4.00000i		−	0.488678i	0.969690	−	0.244339i	$-0.0785709\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	5.00000			0.593391			0.296695	−	0.954972i	$-0.404115\pi$
$71$	5.00000			0.593391			0.296695	+	0.954972i	$0.404115\pi$
$72$		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
$77$			10.0000i			1.13961i
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	14.0000i		−	1.53670i	−0.640030	−	0.768350i	$-0.721078\pi$
$83$		−	14.0000i		−	1.53670i	0.640030	−	0.768350i	$-0.278922\pi$
$84$		0			0
$85$	12.0000	+	6.00000i	1.30158	+	0.650791i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.00000			0.317999			0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000			0.317999			0.159000	+	0.987279i	$0.449173\pi$
$90$		0			0
$91$	8.00000			0.838628
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−7.00000	+	14.0000i	−0.718185	+	1.43637i
$96$		0			0
$97$		−	2.00000i		−	0.203069i	−0.994832	−	0.101535i	$-0.967625\pi$
$97$		−	2.00000i		−	0.203069i	0.994832	−	0.101535i	$-0.0323753\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	15.0000			1.49256			0.746278	−	0.665635i	$-0.231839\pi$
$101$	15.0000			1.49256			0.746278	+	0.665635i	$0.231839\pi$
$102$		0			0
$103$		−	8.00000i		−	0.788263i	−0.919054	−	0.394132i	$-0.871045\pi$
$103$		−	8.00000i		−	0.788263i	0.919054	−	0.394132i	$-0.128955\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			8.00000i			0.773389i	0.922208	+	0.386695i	$0.126383\pi$
$107$			8.00000i			0.773389i	−0.922208	+	0.386695i	$0.873617\pi$
$108$		0			0
$109$	9.00000			0.862044			0.431022	−	0.902342i	$-0.358153\pi$
$109$	9.00000			0.862044			0.431022	+	0.902342i	$0.358153\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			2.00000i			0.188144i	0.995565	+	0.0940721i	$0.0299884\pi$
$113$			2.00000i			0.188144i	−0.995565	+	0.0940721i	$0.970012\pi$
$114$		0			0
$115$	8.00000	+	4.00000i	0.746004	+	0.373002i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	12.0000			1.10004
$120$		0			0
$121$	14.0000			1.27273
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		0			0
$127$			6.00000i			0.532414i	0.963916	+	0.266207i	$0.0857705\pi$
$127$			6.00000i			0.532414i	−0.963916	+	0.266207i	$0.914230\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.00000			0.262111			0.131056	−	0.991375i	$-0.458163\pi$
$131$	3.00000			0.262111			0.131056	+	0.991375i	$0.458163\pi$
$132$		0			0
$133$			14.0000i			1.21395i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			8.00000i			0.683486i	0.939793	+	0.341743i	$0.111017\pi$
$137$			8.00000i			0.683486i	−0.939793	+	0.341743i	$0.888983\pi$
$138$		0			0
$139$	5.00000			0.424094			0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000			0.424094			0.212047	+	0.977259i	$0.431987\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	20.0000i		−	1.67248i
$144$		0			0
$145$	5.00000	−	10.0000i	0.415227	−	0.830455i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.00000			−0.491539			−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000			−0.491539			−0.245770	+	0.969328i	$0.579041\pi$
$150$		0			0
$151$	−11.0000			−0.895167			−0.447584	−	0.894242i	$-0.647715\pi$
$151$	−11.0000			−0.895167			−0.447584	+	0.894242i	$0.647715\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.00000	−	6.00000i	0.240966	−	0.481932i
$156$		0			0
$157$			14.0000i			1.11732i	0.829396	+	0.558661i	$0.188685\pi$
$157$			14.0000i			1.11732i	−0.829396	+	0.558661i	$0.811315\pi$
$158$		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	$-0.815282\pi$
$163$		−	14.0000i		−	1.09656i	0.836293	−	0.548282i	$-0.184718\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			6.00000i			0.464294i	0.972681	+	0.232147i	$0.0745750\pi$
$167$			6.00000i			0.464294i	−0.972681	+	0.232147i	$0.925425\pi$
$168$		0			0
$169$	−3.00000			−0.230769
$170$		0			0
$171$		0			0
$172$		0			0
$173$		−	12.0000i		−	0.912343i	−0.889892	−	0.456172i	$-0.849220\pi$
$173$		−	12.0000i		−	0.912343i	0.889892	−	0.456172i	$-0.150780\pi$
$174$		0			0
$175$	8.00000	−	6.00000i	0.604743	−	0.453557i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−11.0000			−0.822179			−0.411089	−	0.911595i	$-0.634852\pi$
$179$	−11.0000			−0.822179			−0.411089	+	0.911595i	$0.634852\pi$
$180$		0			0
$181$	−17.0000			−1.26360			−0.631800	−	0.775131i	$-0.717684\pi$
$181$	−17.0000			−1.26360			−0.631800	+	0.775131i	$0.717684\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.00000	+	2.00000i	0.294086	+	0.147043i
$186$		0			0
$187$		−	30.0000i		−	2.19382i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.00000			−0.217072			−0.108536	−	0.994092i	$-0.534616\pi$
$191$	−3.00000			−0.217072			−0.108536	+	0.994092i	$0.534616\pi$
$192$		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
$197$			12.0000i			0.854965i	0.904024	+	0.427482i	$0.140599\pi$
$197$			12.0000i			0.854965i	−0.904024	+	0.427482i	$0.859401\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		−	10.0000i		−	0.701862i
$204$		0			0
$205$	7.00000	−	14.0000i	0.488901	−	0.977802i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	35.0000			2.42100
$210$		0			0
$211$	13.0000			0.894957			0.447478	−	0.894295i	$-0.352322\pi$
$211$	13.0000			0.894957			0.447478	+	0.894295i	$0.352322\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	12.0000	+	6.00000i	0.818393	+	0.409197i
$216$		0			0
$217$		−	6.00000i		−	0.407307i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−24.0000			−1.61441
$222$		0			0
$223$			24.0000i			1.60716i	0.595198	+	0.803579i	$0.297074\pi$
$223$			24.0000i			1.60716i	−0.595198	+	0.803579i	$0.702926\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	2.00000i		−	0.132745i	−0.997795	−	0.0663723i	$-0.978857\pi$
$227$		−	2.00000i		−	0.132745i	0.997795	−	0.0663723i	$-0.0211425\pi$
$228$		0			0
$229$	−6.00000			−0.396491			−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000			−0.396491			−0.198246	+	0.980152i	$0.563524\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	6.00000i		−	0.393073i	−0.980497	−	0.196537i	$-0.937031\pi$
$233$		−	6.00000i		−	0.393073i	0.980497	−	0.196537i	$-0.0629694\pi$
$234$		0			0
$235$	12.0000	+	6.00000i	0.782794	+	0.391397i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−20.0000			−1.29369			−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000			−1.29369			−0.646846	+	0.762620i	$0.723912\pi$
$240$		0			0
$241$	17.0000			1.09507			0.547533	−	0.836784i	$-0.315567\pi$
$241$	17.0000			1.09507			0.547533	+	0.836784i	$0.315567\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.00000	+	6.00000i	−0.191663	+	0.383326i
$246$		0			0
$247$		−	28.0000i		−	1.78160i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−8.00000			−0.504956			−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000			−0.504956			−0.252478	+	0.967603i	$0.581245\pi$
$252$		0			0
$253$		−	20.0000i		−	1.25739i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			24.0000i			1.49708i	0.663090	+	0.748539i	$0.269245\pi$
$257$			24.0000i			1.49708i	−0.663090	+	0.748539i	$0.730755\pi$
$258$		0			0
$259$	4.00000			0.248548
$260$		0			0
$261$		0			0
$262$		0			0
$263$			12.0000i			0.739952i	0.929041	+	0.369976i	$0.120634\pi$
$263$			12.0000i			0.739952i	−0.929041	+	0.369976i	$0.879366\pi$
$264$		0			0
$265$	−20.0000	−	10.0000i	−1.22859	−	0.614295i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.00000			−0.182913			−0.0914566	−	0.995809i	$-0.529152\pi$
$269$	−3.00000			−0.182913			−0.0914566	+	0.995809i	$0.529152\pi$
$270$		0			0
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−15.0000	−	20.0000i	−0.904534	−	1.20605i
$276$		0			0
$277$		−	18.0000i		−	1.08152i	−0.841178	−	0.540758i	$-0.818138\pi$
$277$		−	18.0000i		−	1.08152i	0.841178	−	0.540758i	$-0.181862\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$		−	24.0000i		−	1.42665i	−0.700832	−	0.713326i	$-0.747188\pi$
$283$		−	24.0000i		−	1.42665i	0.700832	−	0.713326i	$-0.252812\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	14.0000i		−	0.826394i
$288$		0			0
$289$	−19.0000			−1.11765
$290$		0			0
$291$		0			0
$292$		0			0
$293$			14.0000i			0.817889i	0.912559	+	0.408944i	$0.134103\pi$
$293$			14.0000i			0.817889i	−0.912559	+	0.408944i	$0.865897\pi$
$294$		0			0
$295$	15.0000	−	30.0000i	0.873334	−	1.74667i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−16.0000			−0.925304
$300$		0			0
$301$	12.0000			0.691669
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−14.0000	+	28.0000i	−0.801638	+	1.60328i
$306$		0			0
$307$			34.0000i			1.94048i	0.242140	+	0.970241i	$0.422151\pi$
$307$			34.0000i			1.94048i	−0.242140	+	0.970241i	$0.577849\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.00000			−0.510343			−0.255172	−	0.966896i	$-0.582132\pi$
$311$	−9.00000			−0.510343			−0.255172	+	0.966896i	$0.582132\pi$
$312$		0			0
$313$			28.0000i			1.58265i	0.611393	+	0.791327i	$0.290609\pi$
$313$			28.0000i			1.58265i	−0.611393	+	0.791327i	$0.709391\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			6.00000i			0.336994i	0.985702	+	0.168497i	$0.0538913\pi$
$317$			6.00000i			0.336994i	−0.985702	+	0.168497i	$0.946109\pi$
$318$		0			0
$319$	−25.0000			−1.39973
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	42.0000i		−	2.33694i
$324$		0			0
$325$	−16.0000	+	12.0000i	−0.887520	+	0.665640i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	12.0000			0.661581
$330$		0			0
$331$	−11.0000			−0.604615			−0.302307	−	0.953211i	$-0.597757\pi$
$331$	−11.0000			−0.604615			−0.302307	+	0.953211i	$0.597757\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	8.00000	+	4.00000i	0.437087	+	0.218543i
$336$		0			0
$337$			8.00000i			0.435788i	0.975972	+	0.217894i	$0.0699187\pi$
$337$			8.00000i			0.435788i	−0.975972	+	0.217894i	$0.930081\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−15.0000			−0.812296
$342$		0			0
$343$			20.0000i			1.07990i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	26.0000i		−	1.39575i	−0.716218	−	0.697877i	$-0.754128\pi$
$347$		−	26.0000i		−	1.39575i	0.716218	−	0.697877i	$-0.245872\pi$
$348$		0			0
$349$	7.00000			0.374701			0.187351	−	0.982293i	$-0.440010\pi$
$349$	7.00000			0.374701			0.187351	+	0.982293i	$0.440010\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	30.0000i		−	1.59674i	−0.602168	−	0.798369i	$-0.705696\pi$
$353$		−	30.0000i		−	1.59674i	0.602168	−	0.798369i	$-0.294304\pi$
$354$		0			0
$355$	−5.00000	+	10.0000i	−0.265372	+	0.530745i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	11.0000			0.580558			0.290279	−	0.956942i	$-0.406252\pi$
$359$	11.0000			0.580558			0.290279	+	0.956942i	$0.406252\pi$
$360$		0			0
$361$	30.0000			1.57895
$362$		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	$0.260850\pi$
$367$			28.0000i			1.46159i	−0.682598	+	0.730794i	$0.739150\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−20.0000			−1.03835
$372$		0			0
$373$			26.0000i			1.34623i	0.739538	+	0.673114i	$0.235044\pi$
$373$			26.0000i			1.34623i	−0.739538	+	0.673114i	$0.764956\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			20.0000i			1.03005i
$378$		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
$383$		0			0		1.00000			$0$
$383$		0			0		−1.00000			$\pi$
$384$		0			0
$385$	−20.0000	−	10.0000i	−1.01929	−	0.509647i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−18.0000			−0.912636			−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000			−0.912636			−0.456318	+	0.889817i	$0.650832\pi$
$390$		0			0
$391$	−24.0000			−1.21373
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−8.00000	+	16.0000i	−0.402524	+	0.805047i
$396$		0			0
$397$		−	24.0000i		−	1.20453i	−0.798298	−	0.602263i	$-0.794266\pi$
$397$		−	24.0000i		−	1.20453i	0.798298	−	0.602263i	$-0.205734\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.00000			−0.0998752			−0.0499376	−	0.998752i	$-0.515902\pi$
$401$	−2.00000			−0.0998752			−0.0499376	+	0.998752i	$0.515902\pi$
$402$		0			0
$403$			12.0000i			0.597763i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	10.0000i		−	0.495682i
$408$		0			0
$409$	34.0000			1.68119			0.840596	−	0.541663i	$-0.182205\pi$
$409$	34.0000			1.68119			0.840596	+	0.541663i	$0.182205\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		−	30.0000i		−	1.47620i
$414$		0			0
$415$	28.0000	+	14.0000i	1.37447	+	0.687233i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	36.0000			1.75872			0.879358	−	0.476162i	$-0.157972\pi$
$419$	36.0000			1.75872			0.879358	+	0.476162i	$0.157972\pi$
$420$		0			0
$421$	−35.0000			−1.70580			−0.852898	−	0.522078i	$-0.825157\pi$
$421$	−35.0000			−1.70580			−0.852898	+	0.522078i	$0.825157\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−24.0000	+	18.0000i	−1.16417	+	0.873128i
$426$		0			0
$427$			28.0000i			1.35501i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−5.00000			−0.240842			−0.120421	−	0.992723i	$-0.538424\pi$
$431$	−5.00000			−0.240842			−0.120421	+	0.992723i	$0.538424\pi$
$432$		0			0
$433$		−	12.0000i		−	0.576683i	−0.957528	−	0.288342i	$-0.906896\pi$
$433$		−	12.0000i		−	0.576683i	0.957528	−	0.288342i	$-0.0931039\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	28.0000i		−	1.33942i
$438$		0			0
$439$	−9.00000			−0.429547			−0.214773	−	0.976664i	$-0.568901\pi$
$439$	−9.00000			−0.429547			−0.214773	+	0.976664i	$0.568901\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	30.0000i		−	1.42534i	−0.701498	−	0.712672i	$-0.747485\pi$
$443$		−	30.0000i		−	1.42534i	0.701498	−	0.712672i	$-0.252515\pi$
$444$		0			0
$445$	−3.00000	+	6.00000i	−0.142214	+	0.284427i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	21.0000			0.991051			0.495526	−	0.868593i	$-0.334975\pi$
$449$	21.0000			0.991051			0.495526	+	0.868593i	$0.334975\pi$
$450$		0			0
$451$	−35.0000			−1.64809
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−8.00000	+	16.0000i	−0.375046	+	0.750092i
$456$		0			0
$457$			18.0000i			0.842004i	0.907060	+	0.421002i	$0.138322\pi$
$457$			18.0000i			0.842004i	−0.907060	+	0.421002i	$0.861678\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	39.0000			1.81641			0.908206	−	0.418524i	$-0.137453\pi$
$461$	39.0000			1.81641			0.908206	+	0.418524i	$0.137453\pi$
$462$		0			0
$463$		−	16.0000i		−	0.743583i	−0.928316	−	0.371792i	$-0.878744\pi$
$463$		−	16.0000i		−	0.743583i	0.928316	−	0.371792i	$-0.121256\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	6.00000i		−	0.277647i	−0.990317	−	0.138823i	$-0.955668\pi$
$467$		−	6.00000i		−	0.277647i	0.990317	−	0.138823i	$-0.0443321\pi$
$468$		0			0
$469$	8.00000			0.369406
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	30.0000i		−	1.37940i
$474$		0			0
$475$	−21.0000	−	28.0000i	−0.963546	−	1.28473i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5.00000			−0.228456			−0.114228	−	0.993455i	$-0.536439\pi$
$479$	−5.00000			−0.228456			−0.114228	+	0.993455i	$0.536439\pi$
$480$		0			0
$481$	−8.00000			−0.364769
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.00000	+	2.00000i	0.181631	+	0.0908153i
$486$		0			0
$487$		−	4.00000i		−	0.181257i	−0.995885	−	0.0906287i	$-0.971112\pi$
$487$		−	4.00000i		−	0.181257i	0.995885	−	0.0906287i	$-0.0288876\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	23.0000			1.03798			0.518988	−	0.854782i	$-0.326309\pi$
$491$	23.0000			1.03798			0.518988	+	0.854782i	$0.326309\pi$
$492$		0			0
$493$			30.0000i			1.35113i
$494$		0			0
$495$		0			0
$496$		0			0
$497$			10.0000i			0.448561i
$498$		0			0
$499$	31.0000			1.38775			0.693875	−	0.720095i	$-0.255902\pi$
$499$	31.0000			1.38775			0.693875	+	0.720095i	$0.255902\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			28.0000i			1.24846i	0.781241	+	0.624229i	$0.214587\pi$
$503$			28.0000i			1.24846i	−0.781241	+	0.624229i	$0.785413\pi$
$504$		0			0
$505$	−15.0000	+	30.0000i	−0.667491	+	1.33498i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	2.00000			0.0886484			0.0443242	−	0.999017i	$-0.485887\pi$
$509$	2.00000			0.0886484			0.0443242	+	0.999017i	$0.485887\pi$
$510$		0			0
$511$	28.0000			1.23865
$512$		0			0
$513$		0			0
$514$		0			0
$515$	16.0000	+	8.00000i	0.705044	+	0.352522i
$516$		0			0
$517$		−	30.0000i		−	1.31940i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	22.0000			0.963837			0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000			0.963837			0.481919	+	0.876216i	$0.339940\pi$
$522$		0			0
$523$		−	40.0000i		−	1.74908i	−0.484955	−	0.874539i	$-0.661164\pi$
$523$		−	40.0000i		−	1.74908i	0.484955	−	0.874539i	$-0.338836\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			18.0000i			0.784092i
$528$		0			0
$529$	7.00000			0.304348
$530$		0			0
$531$		0			0
$532$		0			0
$533$			28.0000i			1.21281i
$534$		0			0
$535$	−16.0000	−	8.00000i	−0.691740	−	0.345870i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	15.0000			0.646096
$540$		0			0
$541$	−5.00000			−0.214967			−0.107483	−	0.994207i	$-0.534279\pi$
$541$	−5.00000			−0.214967			−0.107483	+	0.994207i	$0.534279\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−9.00000	+	18.0000i	−0.385518	+	0.771035i
$546$		0			0
$547$		−	40.0000i		−	1.71028i	−0.518400	−	0.855138i	$-0.673472\pi$
$547$		−	40.0000i		−	1.71028i	0.518400	−	0.855138i	$-0.326528\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−35.0000			−1.49105
$552$		0			0
$553$			16.0000i			0.680389i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			24.0000i			1.01691i	0.861088	+	0.508456i	$0.169784\pi$
$557$			24.0000i			1.01691i	−0.861088	+	0.508456i	$0.830216\pi$
$558$		0			0
$559$	−24.0000			−1.01509
$560$		0			0
$561$		0			0
$562$		0			0
$563$		−	30.0000i		−	1.26435i	−0.774826	−	0.632175i	$-0.782163\pi$
$563$		−	30.0000i		−	1.26435i	0.774826	−	0.632175i	$-0.217837\pi$
$564$		0			0
$565$	−4.00000	−	2.00000i	−0.168281	−	0.0841406i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−39.0000			−1.63497			−0.817483	−	0.575953i	$-0.804631\pi$
$569$	−39.0000			−1.63497			−0.817483	+	0.575953i	$0.804631\pi$
$570$		0			0
$571$	−41.0000			−1.71580			−0.857898	−	0.513820i	$-0.828230\pi$
$571$	−41.0000			−1.71580			−0.857898	+	0.513820i	$0.828230\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−16.0000	+	12.0000i	−0.667246	+	0.500435i
$576$		0			0
$577$			14.0000i			0.582828i	0.956597	+	0.291414i	$0.0941257\pi$
$577$			14.0000i			0.582828i	−0.956597	+	0.291414i	$0.905874\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	28.0000			1.16164
$582$		0			0
$583$			50.0000i			2.07079i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			2.00000i			0.0825488i	0.999148	+	0.0412744i	$0.0131418\pi$
$587$			2.00000i			0.0825488i	−0.999148	+	0.0412744i	$0.986858\pi$
$588$		0			0
$589$	−21.0000			−0.865290
$590$		0			0
$591$		0			0
$592$		0			0
$593$			4.00000i			0.164260i	0.996622	+	0.0821302i	$0.0261723\pi$
$593$			4.00000i			0.164260i	−0.996622	+	0.0821302i	$0.973828\pi$
$594$		0			0
$595$	−12.0000	+	24.0000i	−0.491952	+	0.983904i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	29.0000			1.18491			0.592454	−	0.805604i	$-0.298159\pi$
$599$	29.0000			1.18491			0.592454	+	0.805604i	$0.298159\pi$
$600$		0			0
$601$	9.00000			0.367118			0.183559	−	0.983009i	$-0.441238\pi$
$601$	9.00000			0.367118			0.183559	+	0.983009i	$0.441238\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−14.0000	+	28.0000i	−0.569181	+	1.13836i
$606$		0			0
$607$		−	2.00000i		−	0.0811775i	−0.999176	−	0.0405887i	$-0.987077\pi$
$607$		−	2.00000i		−	0.0811775i	0.999176	−	0.0405887i	$-0.0129233\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−24.0000			−0.970936
$612$		0			0
$613$		−	28.0000i		−	1.13091i	−0.824779	−	0.565455i	$-0.808701\pi$
$613$		−	28.0000i		−	1.13091i	0.824779	−	0.565455i	$-0.191299\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			4.00000i			0.161034i	0.996753	+	0.0805170i	$0.0256571\pi$
$617$			4.00000i			0.161034i	−0.996753	+	0.0805170i	$0.974343\pi$
$618$		0			0
$619$	−4.00000			−0.160774			−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000			−0.160774			−0.0803868	+	0.996764i	$0.525616\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$			6.00000i			0.240385i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−43.0000			−1.71180			−0.855901	−	0.517139i	$-0.826997\pi$
$631$	−43.0000			−1.71180			−0.855901	+	0.517139i	$0.826997\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−12.0000	−	6.00000i	−0.476205	−	0.238103i
$636$		0			0
$637$		−	12.0000i		−	0.475457i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.00000			−0.118493			−0.0592464	−	0.998243i	$-0.518870\pi$
$641$	−3.00000			−0.118493			−0.0592464	+	0.998243i	$0.518870\pi$
$642$		0			0
$643$			18.0000i			0.709851i	0.934895	+	0.354925i	$0.115494\pi$
$643$			18.0000i			0.709851i	−0.934895	+	0.354925i	$0.884506\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			8.00000i			0.314512i	0.987558	+	0.157256i	$0.0502649\pi$
$647$			8.00000i			0.314512i	−0.987558	+	0.157256i	$0.949735\pi$
$648$		0			0
$649$	−75.0000			−2.94401
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	36.0000i		−	1.40879i	−0.709809	−	0.704394i	$-0.751219\pi$
$653$		−	36.0000i		−	1.40879i	0.709809	−	0.704394i	$-0.248781\pi$
$654$		0			0
$655$	−3.00000	+	6.00000i	−0.117220	+	0.234439i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$	17.0000			0.661223			0.330612	−	0.943767i	$-0.392745\pi$
$661$	17.0000			0.661223			0.330612	+	0.943767i	$0.392745\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−28.0000	−	14.0000i	−1.08579	−	0.542897i
$666$		0			0
$667$			20.0000i			0.774403i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	70.0000			2.70232
$672$		0			0
$673$		−	8.00000i		−	0.308377i	−0.988041	−	0.154189i	$-0.950724\pi$
$673$		−	8.00000i		−	0.308377i	0.988041	−	0.154189i	$-0.0492764\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			36.0000i			1.38359i	0.722093	+	0.691796i	$0.243180\pi$
$677$			36.0000i			1.38359i	−0.722093	+	0.691796i	$0.756820\pi$
$678$		0			0
$679$	4.00000			0.153506
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	4.00000i		−	0.153056i	−0.997067	−	0.0765279i	$-0.975617\pi$
$683$		−	4.00000i		−	0.153056i	0.997067	−	0.0765279i	$-0.0243834\pi$
$684$		0			0
$685$	−16.0000	−	8.00000i	−0.611329	−	0.305664i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	40.0000			1.52388
$690$		0			0
$691$	−36.0000			−1.36950			−0.684752	−	0.728776i	$-0.740090\pi$
$691$	−36.0000			−1.36950			−0.684752	+	0.728776i	$0.740090\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−5.00000	+	10.0000i	−0.189661	+	0.379322i
$696$		0			0
$697$			42.0000i			1.59086i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	25.0000			0.944237			0.472118	−	0.881535i	$-0.343489\pi$
$701$	25.0000			0.944237			0.472118	+	0.881535i	$0.343489\pi$
$702$		0			0
$703$		−	14.0000i		−	0.528020i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			30.0000i			1.12827i
$708$		0			0
$709$	−22.0000			−0.826227			−0.413114	−	0.910679i	$-0.635559\pi$
$709$	−22.0000			−0.826227			−0.413114	+	0.910679i	$0.635559\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			12.0000i			0.449404i
$714$		0			0
$715$	40.0000	+	20.0000i	1.49592	+	0.747958i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−19.0000			−0.708580			−0.354290	−	0.935136i	$-0.615277\pi$
$719$	−19.0000			−0.708580			−0.354290	+	0.935136i	$0.615277\pi$
$720$		0			0
$721$	16.0000			0.595871
$722$		0			0
$723$		0			0
$724$		0			0
$725$	15.0000	+	20.0000i	0.557086	+	0.742781i
$726$		0			0
$727$			12.0000i			0.445055i	0.974926	+	0.222528i	$0.0714308\pi$
$727$			12.0000i			0.445055i	−0.974926	+	0.222528i	$0.928569\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−36.0000			−1.33151
$732$		0			0
$733$		−	48.0000i		−	1.77292i	−0.462805	−	0.886460i	$-0.653157\pi$
$733$		−	48.0000i		−	1.77292i	0.462805	−	0.886460i	$-0.346843\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	20.0000i		−	0.736709i
$738$		0			0
$739$	21.0000			0.772497			0.386249	−	0.922395i	$-0.373771\pi$
$739$	21.0000			0.772497			0.386249	+	0.922395i	$0.373771\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	54.0000i		−	1.98107i	−0.137268	−	0.990534i	$-0.543832\pi$
$743$		−	54.0000i		−	1.98107i	0.137268	−	0.990534i	$-0.456168\pi$
$744$		0			0
$745$	6.00000	−	12.0000i	0.219823	−	0.439646i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−16.0000			−0.584627
$750$		0			0
$751$	−52.0000			−1.89751			−0.948753	−	0.316017i	$-0.897654\pi$
$751$	−52.0000			−1.89751			−0.948753	+	0.316017i	$0.897654\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	11.0000	−	22.0000i	0.400331	−	0.800662i
$756$		0			0
$757$			40.0000i			1.45382i	0.686730	+	0.726912i	$0.259045\pi$
$757$			40.0000i			1.45382i	−0.686730	+	0.726912i	$0.740955\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−5.00000			−0.181250			−0.0906249	−	0.995885i	$-0.528886\pi$
$761$	−5.00000			−0.181250			−0.0906249	+	0.995885i	$0.528886\pi$
$762$		0			0
$763$			18.0000i			0.651644i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			60.0000i			2.16647i
$768$		0			0
$769$	−13.0000			−0.468792			−0.234396	−	0.972141i	$-0.575311\pi$
$769$	−13.0000			−0.468792			−0.234396	+	0.972141i	$0.575311\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	22.0000i		−	0.791285i	−0.918405	−	0.395643i	$-0.870522\pi$
$773$		−	22.0000i		−	0.791285i	0.918405	−	0.395643i	$-0.129478\pi$
$774$		0			0
$775$	9.00000	+	12.0000i	0.323290	+	0.431053i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−49.0000			−1.75561
$780$		0			0
$781$	25.0000			0.894570
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−28.0000	−	14.0000i	−0.999363	−	0.499681i
$786$		0			0
$787$			46.0000i			1.63972i	0.572562	+	0.819861i	$0.305950\pi$
$787$			46.0000i			1.63972i	−0.572562	+	0.819861i	$0.694050\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−4.00000			−0.142224
$792$		0			0
$793$		−	56.0000i		−	1.98862i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		1.00000			$0$
$797$		0			0		−1.00000			$\pi$
$798$		0			0
$799$	−36.0000			−1.27359

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:	\( N \)	\(=\)	\( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3240.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 2.00000i) q^{5} +2.00000i q^{7} +O(q^{10})\)	\(q+(-1.00000 + 2.00000i) q^{5} +2.00000i q^{7} +5.00000 q^{11} -4.00000i q^{13} -6.00000i q^{17} +7.00000 q^{19} -4.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} -5.00000 q^{29} -3.00000 q^{31} +(-4.00000 - 2.00000i) q^{35} -2.00000i q^{37} -7.00000 q^{41} -6.00000i q^{43} -6.00000i q^{47} +3.00000 q^{49} +10.0000i q^{53} +(-5.00000 + 10.0000i) q^{55} -15.0000 q^{59} +14.0000 q^{61} +(8.00000 + 4.00000i) q^{65} -4.00000i q^{67} +5.00000 q^{71} -14.0000i q^{73} +10.0000i q^{77} +8.00000 q^{79} -14.0000i q^{83} +(12.0000 + 6.00000i) q^{85} +3.00000 q^{89} +8.00000 q^{91} +(-7.00000 + 14.0000i) q^{95} -2.00000i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{5}+O(q^{10}) \) 2 * q - 2 * q^5	\( 2 q - 2 q^{5} + 10 q^{11} + 14 q^{19} - 6 q^{25} - 10 q^{29} - 6 q^{31} - 8 q^{35} - 14 q^{41} + 6 q^{49} - 10 q^{55} - 30 q^{59} + 28 q^{61} + 16 q^{65} + 10 q^{71} + 16 q^{79} + 24 q^{85} + 6 q^{89} + 16 q^{91} - 14 q^{95}+O(q^{100}) \) 2 * q - 2 * q^5 + 10 * q^11 + 14 * q^19 - 6 * q^25 - 10 * q^29 - 6 * q^31 - 8 * q^35 - 14 * q^41 + 6 * q^49 - 10 * q^55 - 30 * q^59 + 28 * q^61 + 16 * q^65 + 10 * q^71 + 16 * q^79 + 24 * q^85 + 6 * q^89 + 16 * q^91 - 14 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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