LMFDB - Embedded newform 371.1.n.a.342.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [371,1,Mod(13,371)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(371, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([13, 12]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("371.13");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 371 = 7 \cdot 53 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	371.n (of order $26$, degree $12$, 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:	$0.185153119687$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\Q(\zeta_{26})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{13}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{13} - \cdots)$

Embedding invariants

Embedding label			342.1
Root			$-0.120537 + 0.992709i$ of defining polynomial
Character	$\chi$	$=$	371.342
Dual form			371.1.n.a.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.627974 - 1.65583i) q^{2} +(-1.59892 + 1.41652i) q^{4} +(-0.354605 - 0.935016i) q^{7} +(1.78152 + 0.935016i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})$	\(q+(-0.627974 - 1.65583i) q^{2} +(-1.59892 + 1.41652i) q^{4} +(-0.354605 - 0.935016i) q^{7} +(1.78152 + 0.935016i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-1.10312 - 1.59814i) q^{11} +(-1.32555 + 1.17433i) q^{14} +(0.171996 - 1.41652i) q^{16} +(0.213460 + 1.75800i) q^{18} +(-1.95352 + 2.83016i) q^{22} +1.13613 q^{23} +(0.885456 + 0.464723i) q^{25} +(1.89145 + 0.992709i) q^{28} +(1.00599 - 1.45743i) q^{29} +(-0.500000 + 0.123239i) q^{32} +(1.89145 - 0.992709i) q^{36} +(-0.180446 + 1.48611i) q^{37} +(0.0290582 + 0.239316i) q^{43} +(4.02758 + 0.992709i) q^{44} +(-0.713460 - 1.88124i) q^{46} +(-0.748511 + 0.663123i) q^{49} +(0.213460 - 1.75800i) q^{50} +(-0.970942 + 0.239316i) q^{53} +(0.242518 - 1.99732i) q^{56} +(-3.04500 - 0.750525i) q^{58} +(0.120537 + 0.992709i) q^{63} +(-0.292533 - 0.423807i) q^{64} +(1.45352 - 1.28771i) q^{67} +(-0.0854858 - 0.704039i) q^{71} +(-1.50599 - 1.33419i) q^{72} +(2.57406 - 0.634448i) q^{74} +(-1.10312 + 1.59814i) q^{77} +(0.251489 - 0.663123i) q^{79} +(0.885456 + 0.464723i) q^{81} +(0.378019 - 0.198399i) q^{86} +(-0.470942 - 3.87855i) q^{88} +(-1.81658 + 1.60935i) q^{92} +(1.56806 + 0.822984i) q^{98} +(0.688601 + 1.81569i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 3 q^{4} - q^{7} + 9 q^{8} - q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 3 * q^4 - q^7 + 9 * q^8 - q^9	$ 12 q - 2 q^{2} - 3 q^{4} - q^{7} + 9 q^{8} - q^{9} - 2 q^{11} - 2 q^{14} - 5 q^{16} - 2 q^{18} - 4 q^{22} - 2 q^{23} - q^{25} - 3 q^{28} - 2 q^{29} - 6 q^{32} - 3 q^{36} - 2 q^{37} + 11 q^{43} + 7 q^{44} - 4 q^{46} - q^{49} - 2 q^{50} - q^{53} + 9 q^{56} - 4 q^{58} - q^{63} + 6 q^{64} - 2 q^{67} - 2 q^{71} - 4 q^{72} + 9 q^{74} - 2 q^{77} + 11 q^{79} - q^{81} - 4 q^{86} + 5 q^{88} - 6 q^{92} + 11 q^{98} - 2 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 3 * q^4 - q^7 + 9 * q^8 - q^9 - 2 * q^11 - 2 * q^14 - 5 * q^16 - 2 * q^18 - 4 * q^22 - 2 * q^23 - q^25 - 3 * q^28 - 2 * q^29 - 6 * q^32 - 3 * q^36 - 2 * q^37 + 11 * q^43 + 7 * q^44 - 4 * q^46 - q^49 - 2 * q^50 - q^53 + 9 * q^56 - 4 * q^58 - q^63 + 6 * q^64 - 2 * q^67 - 2 * q^71 - 4 * q^72 + 9 * q^74 - 2 * q^77 + 11 * q^79 - q^81 - 4 * q^86 + 5 * q^88 - 6 * q^92 + 11 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/371\mathbb{Z}\right)^\times$.

$n$	$213$	$267$
$\chi(n)$	$-1$	$e\left(\frac{5}{13}\right)$

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 $

$2$	−0.627974	−	1.65583i	−0.627974	−	1.65583i	−0.748511	−	0.663123i	$-0.769231\pi$
$2$	−0.627974	−	1.65583i	−0.627974	−	1.65583i	0.120537	−	0.992709i	$-0.461538\pi$
$3$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$3$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$4$	−1.59892	+	1.41652i	−1.59892	+	1.41652i
$5$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$5$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$6$		0			0
$7$	−0.354605	−	0.935016i	−0.354605	−	0.935016i
$7$	−0.354605	−	0.935016i	−0.354605	−	0.935016i
$8$	1.78152	+	0.935016i	1.78152	+	0.935016i
$9$	−0.970942	−	0.239316i	−0.970942	−	0.239316i
$10$		0			0
$11$	−1.10312	−	1.59814i	−1.10312	−	1.59814i	−0.748511	−	0.663123i	$-0.769231\pi$
$11$	−1.10312	−	1.59814i	−1.10312	−	1.59814i	−0.354605	−	0.935016i	$-0.615385\pi$
$12$		0			0
$13$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$13$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$14$	−1.32555	+	1.17433i	−1.32555	+	1.17433i
$15$		0			0
$16$	0.171996	−	1.41652i	0.171996	−	1.41652i
$17$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$17$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$18$	0.213460	+	1.75800i	0.213460	+	1.75800i
$19$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$19$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$20$		0			0
$21$		0			0
$22$	−1.95352	+	2.83016i	−1.95352	+	2.83016i
$23$	1.13613			1.13613			0.568065	−	0.822984i	$-0.307692\pi$
$23$	1.13613			1.13613			0.568065	+	0.822984i	$0.307692\pi$
$24$		0			0
$25$	0.885456	+	0.464723i	0.885456	+	0.464723i
$26$		0			0
$27$		0			0
$28$	1.89145	+	0.992709i	1.89145	+	0.992709i
$29$	1.00599	−	1.45743i	1.00599	−	1.45743i	0.120537	−	0.992709i	$-0.461538\pi$
$29$	1.00599	−	1.45743i	1.00599	−	1.45743i	0.885456	−	0.464723i	$-0.153846\pi$
$30$		0			0
$31$		0			0		0.568065	−	0.822984i	$-0.307692\pi$
$31$		0			0		−0.568065	+	0.822984i	$0.692308\pi$
$32$	−0.500000	+	0.123239i	−0.500000	+	0.123239i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	1.89145	−	0.992709i	1.89145	−	0.992709i
$37$	−0.180446	+	1.48611i	−0.180446	+	1.48611i	0.568065	+	0.822984i	$0.307692\pi$
$37$	−0.180446	+	1.48611i	−0.180446	+	1.48611i	−0.748511	+	0.663123i	$0.769231\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$41$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$42$		0			0
$43$	0.0290582	+	0.239316i	0.0290582	+	0.239316i	1.00000			$0$
$43$	0.0290582	+	0.239316i	0.0290582	+	0.239316i	−0.970942	+	0.239316i	$0.923077\pi$
$44$	4.02758	+	0.992709i	4.02758	+	0.992709i
$45$		0			0
$46$	−0.713460	−	1.88124i	−0.713460	−	1.88124i
$47$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$47$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$48$		0			0
$49$	−0.748511	+	0.663123i	−0.748511	+	0.663123i
$50$	0.213460	−	1.75800i	0.213460	−	1.75800i
$51$		0			0
$52$		0			0
$53$	−0.970942	+	0.239316i	−0.970942	+	0.239316i
$53$	−0.970942	+	0.239316i	−0.970942	+	0.239316i
$54$		0			0
$55$		0			0
$56$	0.242518	−	1.99732i	0.242518	−	1.99732i
$57$		0			0
$58$	−3.04500	−	0.750525i	−3.04500	−	0.750525i
$59$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$59$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$60$		0			0
$61$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$61$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$62$		0			0
$63$	0.120537	+	0.992709i	0.120537	+	0.992709i
$64$	−0.292533	−	0.423807i	−0.292533	−	0.423807i
$65$		0			0
$66$		0			0
$67$	1.45352	−	1.28771i	1.45352	−	1.28771i	0.568065	−	0.822984i	$-0.307692\pi$
$67$	1.45352	−	1.28771i	1.45352	−	1.28771i	0.885456	−	0.464723i	$-0.153846\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.0854858	−	0.704039i	−0.0854858	−	0.704039i	−0.970942	−	0.239316i	$-0.923077\pi$
$71$	−0.0854858	−	0.704039i	−0.0854858	−	0.704039i	0.885456	−	0.464723i	$-0.153846\pi$
$72$	−1.50599	−	1.33419i	−1.50599	−	1.33419i
$73$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$73$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$74$	2.57406	−	0.634448i	2.57406	−	0.634448i
$75$		0			0
$76$		0			0
$77$	−1.10312	+	1.59814i	−1.10312	+	1.59814i
$78$		0			0
$79$	0.251489	−	0.663123i	0.251489	−	0.663123i	−0.748511	−	0.663123i	$-0.769231\pi$
$79$	0.251489	−	0.663123i	0.251489	−	0.663123i	1.00000			$0$
$80$		0			0
$81$	0.885456	+	0.464723i	0.885456	+	0.464723i
$82$		0			0
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$		0			0
$86$	0.378019	−	0.198399i	0.378019	−	0.198399i
$87$		0			0
$88$	−0.470942	−	3.87855i	−0.470942	−	3.87855i
$89$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$89$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$90$		0			0
$91$		0			0
$92$	−1.81658	+	1.60935i	−1.81658	+	1.60935i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$97$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$98$	1.56806	+	0.822984i	1.56806	+	0.822984i
$99$	0.688601	+	1.81569i	0.688601	+	1.81569i
$100$	−2.07406	+	0.511209i	−2.07406	+	0.511209i
$101$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$101$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$102$		0			0
$103$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$103$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$104$		0			0
$105$		0			0
$106$	1.00599	+	1.45743i	1.00599	+	1.45743i
$107$	0.241073			0.241073			0.120537	−	0.992709i	$-0.461538\pi$
$107$	0.241073			0.241073			0.120537	+	0.992709i	$0.461538\pi$
$108$		0			0
$109$	0.241073	−	1.98542i	0.241073	−	1.98542i	0.120537	−	0.992709i	$-0.461538\pi$
$109$	0.241073	−	1.98542i	0.241073	−	1.98542i	0.120537	−	0.992709i	$-0.461538\pi$
$110$		0			0
$111$		0			0
$112$	−1.38546	+	0.341484i	−1.38546	+	0.341484i
$113$	0.530851	+	1.39974i	0.530851	+	1.39974i	0.885456	+	0.464723i	$0.153846\pi$
$113$	0.530851	+	1.39974i	0.530851	+	1.39974i	−0.354605	+	0.935016i	$0.615385\pi$
$114$		0			0
$115$		0			0
$116$	0.455978	+	3.75532i	0.455978	+	3.75532i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.982579	+	2.59085i	−0.982579	+	2.59085i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	1.56806	−	0.822984i	1.56806	−	0.822984i
$127$	−1.10312	+	0.271894i	−1.10312	+	0.271894i	−0.748511	−	0.663123i	$-0.769231\pi$
$127$	−1.10312	+	0.271894i	−1.10312	+	0.271894i	−0.354605	+	0.935016i	$0.615385\pi$
$128$	−0.810583	+	1.17433i	−0.810583	+	1.17433i
$129$		0			0
$130$		0			0
$131$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$131$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$132$		0			0
$133$		0			0
$134$	−3.04500	−	1.59814i	−3.04500	−	1.59814i
$135$		0			0
$136$		0			0
$137$	0.136945	−	0.198399i	0.136945	−	0.198399i	−0.748511	−	0.663123i	$-0.769231\pi$
$137$	0.136945	−	0.198399i	0.136945	−	0.198399i	0.885456	+	0.464723i	$0.153846\pi$
$138$		0			0
$139$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$139$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$140$		0			0
$141$		0			0
$142$	−1.11209	+	0.583668i	−1.11209	+	0.583668i
$143$		0			0
$144$	−0.505993	+	1.33419i	−0.505993	+	1.33419i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−1.81658	−	2.63176i	−1.81658	−	2.63176i
$149$	−0.0854858	−	0.704039i	−0.0854858	−	0.704039i	−0.970942	−	0.239316i	$-0.923077\pi$
$149$	−0.0854858	−	0.704039i	−0.0854858	−	0.704039i	0.885456	−	0.464723i	$-0.153846\pi$
$150$		0			0
$151$	0.213460	+	0.112032i	0.213460	+	0.112032i	0.568065	−	0.822984i	$-0.307692\pi$
$151$	0.213460	+	0.112032i	0.213460	+	0.112032i	−0.354605	+	0.935016i	$0.615385\pi$
$152$		0			0
$153$		0			0
$154$	3.33898	+	0.822984i	3.33898	+	0.822984i
$155$		0			0
$156$		0			0
$157$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$157$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$158$	−1.25595			−1.25595
$159$		0			0
$160$		0			0
$161$	−0.402877	−	1.06230i	−0.402877	−	1.06230i
$162$	0.213460	−	1.75800i	0.213460	−	1.75800i
$163$	0.530851	−	0.470293i	0.530851	−	0.470293i	−0.354605	−	0.935016i	$-0.615385\pi$
$163$	0.530851	−	0.470293i	0.530851	−	0.470293i	0.885456	+	0.464723i	$0.153846\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$167$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$168$		0			0
$169$	0.120537	+	0.992709i	0.120537	+	0.992709i
$170$		0			0
$171$		0			0
$172$	−0.385456	−	0.341484i	−0.385456	−	0.341484i
$173$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$173$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$174$		0			0
$175$	0.120537	−	0.992709i	0.120537	−	0.992709i
$176$	−2.45352	+	1.28771i	−2.45352	+	1.28771i
$177$		0			0
$178$		0			0
$179$	−1.32555	+	0.695701i	−1.32555	+	0.695701i	−0.970942	−	0.239316i	$-0.923077\pi$
$179$	−1.32555	+	0.695701i	−1.32555	+	0.695701i	−0.354605	+	0.935016i	$0.615385\pi$
$180$		0			0
$181$		0			0		0.568065	−	0.822984i	$-0.307692\pi$
$181$		0			0		−0.568065	+	0.822984i	$0.692308\pi$
$182$		0			0
$183$		0			0
$184$	2.02404	+	1.06230i	2.02404	+	1.06230i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.94188	+	0.478631i	−1.94188	+	0.478631i	−0.970942	+	0.239316i	$0.923077\pi$
$191$	−1.94188	+	0.478631i	−1.94188	+	0.478631i	−0.970942	+	0.239316i	$0.923077\pi$
$192$		0			0
$193$	1.12054	+	0.992709i	1.12054	+	0.992709i	1.00000			$0$
$193$	1.12054	+	0.992709i	1.12054	+	0.992709i	0.120537	+	0.992709i	$0.461538\pi$
$194$		0			0
$195$		0			0
$196$	0.257482	−	2.12055i	0.257482	−	2.12055i
$197$	−0.402877	+	1.06230i	−0.402877	+	1.06230i	0.568065	+	0.822984i	$0.307692\pi$
$197$	−0.402877	+	1.06230i	−0.402877	+	1.06230i	−0.970942	+	0.239316i	$0.923077\pi$
$198$	2.57406	−	2.28042i	2.57406	−	2.28042i
$199$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$199$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$200$	1.14294	+	1.65583i	1.14294	+	1.65583i
$201$		0			0
$202$		0			0
$203$	−1.71945	−	0.423807i	−1.71945	−	0.423807i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.10312	−	0.271894i	−1.10312	−	0.271894i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	1.13613			1.13613			0.568065	−	0.822984i	$-0.307692\pi$
$211$	1.13613			1.13613			0.568065	+	0.822984i	$0.307692\pi$
$212$	1.21346	−	1.75800i	1.21346	−	1.75800i
$213$		0			0
$214$	−0.151388	−	0.399177i	−0.151388	−	0.399177i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−3.43891	+	0.847614i	−3.43891	+	0.847614i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$223$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$224$	0.292533	+	0.423807i	0.292533	+	0.423807i
$225$	−0.748511	−	0.663123i	−0.748511	−	0.663123i
$226$	1.98437	−	1.75800i	1.98437	−	1.75800i
$227$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$227$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$228$		0			0
$229$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$229$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$230$		0			0
$231$		0			0
$232$	3.15492	−	1.65583i	3.15492	−	1.65583i
$233$	1.88546	−	0.464723i	1.88546	−	0.464723i	0.885456	−	0.464723i	$-0.153846\pi$
$233$	1.88546	−	0.464723i	1.88546	−	0.464723i	1.00000			$0$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.530851	−	1.39974i	0.530851	−	1.39974i	−0.354605	−	0.935016i	$-0.615385\pi$
$239$	0.530851	−	1.39974i	0.530851	−	1.39974i	0.885456	−	0.464723i	$-0.153846\pi$
$240$		0			0
$241$		0			0		0.568065	−	0.822984i	$-0.307692\pi$
$241$		0			0		−0.568065	+	0.822984i	$0.692308\pi$
$242$	4.90704			4.90704
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$251$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$252$	−1.59892	−	1.41652i	−1.59892	−	1.41652i
$253$	−1.25328	−	1.81569i	−1.25328	−	1.81569i
$254$	1.14294	+	1.65583i	1.14294	+	1.65583i
$255$		0			0
$256$	1.95352	+	0.481500i	1.95352	+	0.481500i
$257$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$257$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$258$		0			0
$259$	1.45352	−	0.358261i	1.45352	−	0.358261i
$260$		0			0
$261$	−1.32555	+	1.17433i	−1.32555	+	1.17433i
$262$		0			0
$263$	0.688601	+	1.81569i	0.688601	+	1.81569i	0.568065	+	0.822984i	$0.307692\pi$
$263$	0.688601	+	1.81569i	0.688601	+	1.81569i	0.120537	+	0.992709i	$0.461538\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.500000	+	4.11787i	−0.500000	+	4.11787i
$269$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$269$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$270$		0			0
$271$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$271$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$272$		0			0
$273$		0			0
$274$	−0.414514	−	0.102169i	−0.414514	−	0.102169i
$275$	−0.234068	−	1.92773i	−0.234068	−	1.92773i
$276$		0			0
$277$	−0.402877	−	0.583668i	−0.402877	−	0.583668i	0.568065	−	0.822984i	$-0.307692\pi$
$277$	−0.402877	−	0.583668i	−0.402877	−	0.583668i	−0.970942	+	0.239316i	$0.923077\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.0290582	−	0.239316i	0.0290582	−	0.239316i	−0.970942	−	0.239316i	$-0.923077\pi$
$281$	0.0290582	−	0.239316i	0.0290582	−	0.239316i	1.00000			$0$
$282$		0			0
$283$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$283$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$284$	1.13397	+	1.00461i	1.13397	+	1.00461i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.514964			0.514964
$289$	0.568065	−	0.822984i	0.568065	−	0.822984i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$293$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$294$		0			0
$295$		0			0
$296$	−1.71100	+	2.47882i	−1.71100	+	2.47882i
$297$		0			0
$298$	−1.11209	+	0.583668i	−1.11209	+	0.583668i
$299$		0			0
$300$		0			0
$301$	0.213460	−	0.112032i	0.213460	−	0.112032i
$302$	0.0514595	−	0.423807i	0.0514595	−	0.423807i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$307$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$308$	−0.500000	−	4.11787i	−0.500000	−	4.11787i
$309$		0			0
$310$		0			0
$311$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$311$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$312$		0			0
$313$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$313$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$314$		0			0
$315$		0			0
$316$	0.537214	+	1.41652i	0.537214	+	1.41652i
$317$	−0.709210			−0.709210			−0.354605	−	0.935016i	$-0.615385\pi$
$317$	−0.709210			−0.709210			−0.354605	+	0.935016i	$0.615385\pi$
$318$		0			0
$319$	−3.43891			−3.43891
$320$		0			0
$321$		0			0
$322$	−1.50599	+	1.33419i	−1.50599	+	1.33419i
$323$		0			0
$324$	−2.07406	+	0.511209i	−2.07406	+	0.511209i
$325$		0			0
$326$	−1.11209	−	0.583668i	−1.11209	−	0.583668i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.530851	+	0.470293i	0.530851	+	0.470293i	0.885456	−	0.464723i	$-0.153846\pi$
$331$	0.530851	+	0.470293i	0.530851	+	0.470293i	−0.354605	+	0.935016i	$0.615385\pi$
$332$		0			0
$333$	0.530851	−	1.39974i	0.530851	−	1.39974i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.45352	+	1.28771i	1.45352	+	1.28771i	0.885456	+	0.464723i	$0.153846\pi$
$337$	1.45352	+	1.28771i	1.45352	+	1.28771i	0.568065	+	0.822984i	$0.307692\pi$
$338$	1.56806	−	0.822984i	1.56806	−	0.822984i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.885456	+	0.464723i	0.885456	+	0.464723i
$344$	−0.171996	+	0.453517i	−0.171996	+	0.453517i
$345$		0			0
$346$		0			0
$347$	−1.10312	+	1.59814i	−1.10312	+	1.59814i	−0.354605	+	0.935016i	$0.615385\pi$
$347$	−1.10312	+	1.59814i	−1.10312	+	1.59814i	−0.748511	+	0.663123i	$0.769231\pi$
$348$		0			0
$349$		0			0		0.568065	−	0.822984i	$-0.307692\pi$
$349$		0			0		−0.568065	+	0.822984i	$0.692308\pi$
$350$	−1.71945	+	0.423807i	−1.71945	+	0.423807i
$351$		0			0
$352$	0.748511	+	0.663123i	0.748511	+	0.663123i
$353$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$353$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	1.98437	+	1.75800i	1.98437	+	1.75800i
$359$	1.00599	+	1.45743i	1.00599	+	1.45743i	0.885456	+	0.464723i	$0.153846\pi$
$359$	1.00599	+	1.45743i	1.00599	+	1.45743i	0.120537	+	0.992709i	$0.461538\pi$
$360$		0			0
$361$	0.120537	+	0.992709i	0.120537	+	0.992709i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$367$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$368$	0.195410	−	1.60935i	0.195410	−	1.60935i
$369$		0			0
$370$		0			0
$371$	0.568065	+	0.822984i	0.568065	+	0.822984i
$372$		0			0
$373$	−0.627974	−	1.65583i	−0.627974	−	1.65583i	−0.748511	−	0.663123i	$-0.769231\pi$
$373$	−0.627974	−	1.65583i	−0.627974	−	1.65583i	0.120537	−	0.992709i	$-0.461538\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.71945	−	0.902438i	−1.71945	−	0.902438i	−0.970942	−	0.239316i	$-0.923077\pi$
$379$	−1.71945	−	0.902438i	−1.71945	−	0.902438i	−0.748511	−	0.663123i	$-0.769231\pi$
$380$		0			0
$381$		0			0
$382$	2.01199	+	2.91486i	2.01199	+	2.91486i
$383$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$383$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$384$		0			0
$385$		0			0
$386$	0.940091	−	2.47882i	0.940091	−	2.47882i
$387$	0.0290582	−	0.239316i	0.0290582	−	0.239316i
$388$		0			0
$389$	−0.234068	−	1.92773i	−0.234068	−	1.92773i	−0.354605	−	0.935016i	$-0.615385\pi$
$389$	−0.234068	−	1.92773i	−0.234068	−	1.92773i	0.120537	−	0.992709i	$-0.461538\pi$
$390$		0			0
$391$		0			0
$392$	−1.95352	+	0.481500i	−1.95352	+	0.481500i
$393$		0			0
$394$	2.01199			2.01199
$395$		0			0
$396$	−3.67297	−	1.92773i	−3.67297	−	1.92773i
$397$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$397$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$398$		0			0
$399$		0			0
$400$	0.810583	−	1.17433i	0.810583	−	1.17433i
$401$	−1.49702			−1.49702			−0.748511	−	0.663123i	$-0.769231\pi$
$401$	−1.49702			−1.49702			−0.748511	+	0.663123i	$0.769231\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	0.378019	+	3.11326i	0.378019	+	3.11326i
$407$	2.57406	−	1.35097i	2.57406	−	1.35097i
$408$		0			0
$409$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$409$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.242518	+	1.99732i	0.242518	+	1.99732i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$419$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$420$		0			0
$421$	−0.180446	+	1.48611i	−0.180446	+	1.48611i	0.568065	+	0.822984i	$0.307692\pi$
$421$	−0.180446	+	1.48611i	−0.180446	+	1.48611i	−0.748511	+	0.663123i	$0.769231\pi$
$422$	−0.713460	−	1.88124i	−0.713460	−	1.88124i
$423$		0			0
$424$	−1.95352	−	0.481500i	−1.95352	−	0.481500i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.385456	+	0.341484i	−0.385456	+	0.341484i
$429$		0			0
$430$		0			0
$431$	0.251489	+	0.663123i	0.251489	+	0.663123i	1.00000			$0$
$431$	0.251489	+	0.663123i	0.251489	+	0.663123i	−0.748511	+	0.663123i	$0.769231\pi$
$432$		0			0
$433$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$433$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$434$		0			0
$435$		0			0
$436$	2.42692	+	3.51600i	2.42692	+	3.51600i
$437$		0			0
$438$		0			0
$439$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$439$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$440$		0			0
$441$	0.885456	−	0.464723i	0.885456	−	0.464723i
$442$		0			0
$443$	1.12054	+	0.992709i	1.12054	+	0.992709i	1.00000			$0$
$443$	1.12054	+	0.992709i	1.12054	+	0.992709i	0.120537	+	0.992709i	$0.461538\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.292533	+	0.423807i	−0.292533	+	0.423807i
$449$	1.00599	+	0.527986i	1.00599	+	0.527986i	0.885456	−	0.464723i	$-0.153846\pi$
$449$	1.00599	+	0.527986i	1.00599	+	0.527986i	0.120537	+	0.992709i	$0.461538\pi$
$450$	−0.627974	+	1.65583i	−0.627974	+	1.65583i
$451$		0			0
$452$	−2.83154	−	1.48611i	−2.83154	−	1.48611i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.56806	−	0.822984i	1.56806	−	0.822984i	0.568065	−	0.822984i	$-0.307692\pi$
$457$	1.56806	−	0.822984i	1.56806	−	0.822984i	1.00000			$0$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$461$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$462$		0			0
$463$	1.12054	−	0.992709i	1.12054	−	0.992709i	0.120537	−	0.992709i	$-0.461538\pi$
$463$	1.12054	−	0.992709i	1.12054	−	0.992709i	1.00000			$0$
$464$	−1.89145	−	1.67568i	−1.89145	−	1.67568i
$465$		0			0
$466$	−1.95352	−	2.83016i	−1.95352	−	2.83016i
$467$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$467$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$468$		0			0
$469$	−1.71945	−	0.902438i	−1.71945	−	0.902438i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.350405	−	0.310432i	0.350405	−	0.310432i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.00000			1.00000
$478$	−2.65109			−2.65109
$479$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$479$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−2.09892	−	5.53439i	−2.09892	−	5.53439i
$485$		0			0
$486$		0			0
$487$	−0.0854858	−	0.704039i	−0.0854858	−	0.704039i	−0.970942	−	0.239316i	$-0.923077\pi$
$487$	−0.0854858	−	0.704039i	−0.0854858	−	0.704039i	0.885456	−	0.464723i	$-0.153846\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.49702	+	1.32625i	−1.49702	+	1.32625i	−0.748511	+	0.663123i	$0.769231\pi$
$491$	−1.49702	+	1.32625i	−1.49702	+	1.32625i	−0.748511	+	0.663123i	$0.769231\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.627974	+	0.329586i	−0.627974	+	0.329586i
$498$		0			0
$499$	1.00599	−	1.45743i	1.00599	−	1.45743i	0.120537	−	0.992709i	$-0.461538\pi$
$499$	1.00599	−	1.45743i	1.00599	−	1.45743i	0.885456	−	0.464723i	$-0.153846\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$503$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$504$	−0.713460	+	1.88124i	−0.713460	+	1.88124i
$505$		0			0
$506$	−2.21945	+	3.21543i	−2.21945	+	3.21543i
$507$		0			0
$508$	1.37865	−	1.99732i	1.37865	−	1.99732i
$509$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$509$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$510$		0			0
$511$		0			0
$512$	−0.257482	−	2.12055i	−0.257482	−	2.12055i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−1.50599	−	2.18181i	−1.50599	−	2.18181i
$519$		0			0
$520$		0			0
$521$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$521$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$522$	2.77690	+	1.45743i	2.77690	+	1.45743i
$523$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$523$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$524$		0			0
$525$		0			0
$526$	2.57406	−	2.28042i	2.57406	−	2.28042i
$527$		0			0
$528$		0			0
$529$	0.290790			0.290790
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	3.79351	−	0.935016i	3.79351	−	0.935016i
$537$		0			0
$538$		0			0
$539$	1.88546	+	0.464723i	1.88546	+	0.464723i
$540$		0			0
$541$	0.136945	+	0.198399i	0.136945	+	0.198399i	0.885456	−	0.464723i	$-0.153846\pi$
$541$	0.136945	+	0.198399i	0.136945	+	0.198399i	−0.748511	+	0.663123i	$0.769231\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.32555	+	0.695701i	−1.32555	+	0.695701i	−0.970942	−	0.239316i	$-0.923077\pi$
$547$	−1.32555	+	0.695701i	−1.32555	+	0.695701i	−0.354605	+	0.935016i	$0.615385\pi$
$548$	0.0620720	+	0.511209i	0.0620720	+	0.511209i
$549$		0			0
$550$	−3.04500	+	1.59814i	−3.04500	+	1.59814i
$551$		0			0
$552$		0			0
$553$	−0.709210			−0.709210
$554$	−0.713460	+	1.03363i	−0.713460	+	1.03363i
$555$		0			0
$556$		0			0
$557$	−0.402877	+	1.06230i	−0.402877	+	1.06230i	0.568065	+	0.822984i	$0.307692\pi$
$557$	−0.402877	+	1.06230i	−0.402877	+	1.06230i	−0.970942	+	0.239316i	$0.923077\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.414514	+	0.102169i	−0.414514	+	0.102169i
$563$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$563$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.120537	−	0.992709i	0.120537	−	0.992709i
$568$	0.505993	−	1.33419i	0.505993	−	1.33419i
$569$	0.530851	−	0.470293i	0.530851	−	0.470293i	−0.354605	−	0.935016i	$-0.615385\pi$
$569$	0.530851	−	0.470293i	0.530851	−	0.470293i	0.885456	+	0.464723i	$0.153846\pi$
$570$		0			0
$571$	0.136945	+	0.198399i	0.136945	+	0.198399i	0.885456	−	0.464723i	$-0.153846\pi$
$571$	0.136945	+	0.198399i	0.136945	+	0.198399i	−0.748511	+	0.663123i	$0.769231\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.00599	+	0.527986i	1.00599	+	0.527986i
$576$	0.182609	+	0.481500i	0.182609	+	0.481500i
$577$		0			0		0.970942	−	0.239316i	$-0.0769231\pi$
$577$		0			0		−0.970942	+	0.239316i	$0.923077\pi$
$578$	−1.71945	−	0.423807i	−1.71945	−	0.423807i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.45352	+	1.28771i	1.45352	+	1.28771i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$587$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	2.07406	+	0.511209i	2.07406	+	0.511209i
$593$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$593$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$594$		0			0
$595$		0			0
$596$	1.13397	+	1.00461i	1.13397	+	1.00461i
$597$		0			0
$598$		0			0
$599$	−0.180446	+	1.48611i	−0.180446	+	1.48611i	0.568065	+	0.822984i	$0.307692\pi$
$599$	−0.180446	+	1.48611i	−0.180446	+	1.48611i	−0.748511	+	0.663123i	$0.769231\pi$
$600$		0			0
$601$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$601$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$602$	−0.319554	−	0.283100i	−0.319554	−	0.283100i
$603$	−1.71945	+	0.902438i	−1.71945	+	0.902438i
$604$	−0.500000	+	0.123239i	−0.500000	+	0.123239i
$605$		0			0
$606$		0			0
$607$		0			0		0.568065	−	0.822984i	$-0.307692\pi$
$607$		0			0		−0.568065	+	0.822984i	$0.692308\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.241073			0.241073			0.120537	−	0.992709i	$-0.461538\pi$
$613$	0.241073			0.241073			0.120537	+	0.992709i	$0.461538\pi$
$614$		0			0
$615$		0			0
$616$	−3.45951	+	1.81569i	−3.45951	+	1.81569i
$617$	−0.180446	−	0.159861i	−0.180446	−	0.159861i	0.568065	−	0.822984i	$-0.307692\pi$
$617$	−0.180446	−	0.159861i	−0.180446	−	0.159861i	−0.748511	+	0.663123i	$0.769231\pi$
$618$		0			0
$619$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$619$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.568065	+	0.822984i	0.568065	+	0.822984i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.234068	−	0.0576926i	−0.234068	−	0.0576926i	0.120537	−	0.992709i	$-0.461538\pi$
$631$	−0.234068	−	0.0576926i	−0.234068	−	0.0576926i	−0.354605	+	0.935016i	$0.615385\pi$
$632$	1.06806	−	0.946223i	1.06806	−	0.946223i
$633$		0			0
$634$	0.445365	+	1.17433i	0.445365	+	1.17433i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	2.15954	+	5.69425i	2.15954	+	5.69425i
$639$	−0.0854858	+	0.704039i	−0.0854858	+	0.704039i
$640$		0			0
$641$	0.688601	+	0.169725i	0.688601	+	0.169725i	0.568065	−	0.822984i	$-0.307692\pi$
$641$	0.688601	+	0.169725i	0.688601	+	0.169725i	0.120537	+	0.992709i	$0.461538\pi$
$642$		0			0
$643$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$643$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$644$	2.14893	+	1.12785i	2.14893	+	1.12785i
$645$		0			0
$646$		0			0
$647$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$647$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$648$	1.14294	+	1.65583i	1.14294	+	1.65583i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.182609	+	1.50392i	−0.182609	+	1.50392i
$653$	1.56806	−	0.822984i	1.56806	−	0.822984i	0.568065	−	0.822984i	$-0.307692\pi$
$653$	1.56806	−	0.822984i	1.56806	−	0.822984i	1.00000			$0$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.13613			1.13613			0.568065	−	0.822984i	$-0.307692\pi$
$659$	1.13613			1.13613			0.568065	+	0.822984i	$0.307692\pi$
$660$		0			0
$661$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$661$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$662$	0.445365	−	1.17433i	0.445365	−	1.17433i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−2.65109			−2.65109
$667$	1.14294	−	1.65583i	1.14294	−	1.65583i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.0854858	+	0.704039i	−0.0854858	+	0.704039i	0.885456	+	0.464723i	$0.153846\pi$
$673$	−0.0854858	+	0.704039i	−0.0854858	+	0.704039i	−0.970942	+	0.239316i	$0.923077\pi$
$674$	1.21945	−	3.21543i	1.21945	−	3.21543i
$675$		0			0
$676$	−1.59892	−	1.41652i	−1.59892	−	1.41652i
$677$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$677$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.71945	+	0.423807i	−1.71945	+	0.423807i	−0.970942	−	0.239316i	$-0.923077\pi$
$683$	−1.71945	+	0.423807i	−1.71945	+	0.423807i	−0.748511	+	0.663123i	$0.769231\pi$
$684$		0			0
$685$		0			0
$686$	0.213460	−	1.75800i	0.213460	−	1.75800i
$687$		0			0
$688$	0.343992			0.343992
$689$		0			0
$690$		0			0
$691$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$691$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$692$		0			0
$693$	1.45352	−	1.28771i	1.45352	−	1.28771i
$694$	3.33898	+	0.822984i	3.33898	+	0.822984i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	1.21346	+	1.75800i	1.21346	+	1.75800i
$701$	−1.10312	−	1.59814i	−1.10312	−	1.59814i	−0.748511	−	0.663123i	$-0.769231\pi$
$701$	−1.10312	−	1.59814i	−1.10312	−	1.59814i	−0.354605	−	0.935016i	$-0.615385\pi$
$702$		0			0
$703$		0			0
$704$	−0.354605	+	0.935016i	−0.354605	+	0.935016i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.213460	−	0.112032i	0.213460	−	0.112032i	−0.354605	−	0.935016i	$-0.615385\pi$
$709$	0.213460	−	0.112032i	0.213460	−	0.112032i	0.568065	+	0.822984i	$0.307692\pi$
$710$		0			0
$711$	−0.402877	+	0.583668i	−0.402877	+	0.583668i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.13397	−	2.99002i	1.13397	−	2.99002i
$717$		0			0
$718$	1.78152	−	2.58098i	1.78152	−	2.58098i
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$	1.56806	−	0.822984i	1.56806	−	0.822984i
$723$		0			0
$724$		0			0
$725$	1.56806	−	0.822984i	1.56806	−	0.822984i
$726$		0			0
$727$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$727$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$728$		0			0
$729$	−0.748511	−	0.663123i	−0.748511	−	0.663123i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$733$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$734$		0			0
$735$		0			0
$736$	−0.568065	+	0.140015i	−0.568065	+	0.140015i
$737$	−3.66134	−	0.902438i	−3.66134	−	0.902438i
$738$		0			0
$739$	−0.180446	+	1.48611i	−0.180446	+	1.48611i	0.568065	+	0.822984i	$0.307692\pi$
$739$	−0.180446	+	1.48611i	−0.180446	+	1.48611i	−0.748511	+	0.663123i	$0.769231\pi$
$740$		0			0
$741$		0			0
$742$	1.00599	−	1.45743i	1.00599	−	1.45743i
$743$	−0.709210			−0.709210			−0.354605	−	0.935016i	$-0.615385\pi$
$743$	−0.709210			−0.709210			−0.354605	+	0.935016i	$0.615385\pi$
$744$		0			0
$745$		0			0
$746$	−2.34743	+	2.07964i	−2.34743	+	2.07964i
$747$		0			0
$748$		0			0
$749$	−0.0854858	−	0.225408i	−0.0854858	−	0.225408i
$750$		0			0
$751$	−1.71945	−	0.423807i	−1.71945	−	0.423807i	−0.748511	−	0.663123i	$-0.769231\pi$
$751$	−1.71945	−	0.423807i	−1.71945	−	0.423807i	−0.970942	+	0.239316i	$0.923077\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.530851	−	1.39974i	0.530851	−	1.39974i	−0.354605	−	0.935016i	$-0.615385\pi$
$757$	0.530851	−	1.39974i	0.530851	−	1.39974i	0.885456	−	0.464723i	$-0.153846\pi$
$758$	−0.414514	+	3.41383i	−0.414514	+	3.41383i
$759$		0			0
$760$		0			0
$761$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$761$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$762$		0			0
$763$	−1.94188	+	0.478631i	−1.94188	+	0.478631i
$764$	2.42692	−	3.51600i	2.42692	−	3.51600i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.354605	−	0.935016i	$-0.384615\pi$
$769$		0			0		−0.354605	+	0.935016i	$0.615385\pi$
$770$		0			0
$771$		0			0
$772$	−3.19783			−3.19783
$773$		0			0		0.568065	−	0.822984i	$-0.307692\pi$
$773$		0			0		−0.568065	+	0.822984i	$0.692308\pi$
$774$	−0.414514	+	0.102169i	−0.414514	+	0.102169i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−3.04500	+	1.59814i	−3.04500	+	1.59814i
$779$		0			0
$780$		0			0
$781$	−1.03085	+	0.913254i	−1.03085	+	0.913254i
$782$		0			0
$783$		0			0
$784$	0.810583	+	1.17433i	0.810583	+	1.17433i
$785$		0			0
$786$		0			0
$787$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$787$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$788$	−0.860598	−	2.26921i	−0.860598	−	2.26921i
$789$		0			0
$790$		0			0
$791$	1.12054	−	0.992709i	1.12054	−	0.992709i
$792$	−0.470942	+	3.87855i	−0.470942	+	3.87855i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.354605	−	0.935016i	$-0.615385\pi$
$797$		0			0		0.354605	+	0.935016i	$0.384615\pi$
$798$		0			0
$799$		0			0
$800$	−0.500000	−	0.123239i	−0.500000	−	0.123239i
$801$		0			0
$802$	0.940091	+	2.47882i	0.940091	+	2.47882i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.12054	−	0.992709i	1.12054	−	0.992709i	0.120537	−	0.992709i	$-0.461538\pi$
$809$	1.12054	−	0.992709i	1.12054	−	0.992709i	1.00000			$0$
$810$		0			0
$811$		0			0		0.120537	−	0.992709i	$-0.461538\pi$
$811$		0			0		−0.120537	+	0.992709i	$0.538462\pi$
$812$	3.34959	−	1.75800i	3.34959	−	1.75800i
$813$		0			0
$814$	−3.85342	−	3.41383i	−3.85342	−	3.41383i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.688601	−	1.81569i	0.688601	−	1.81569i	0.120537	−	0.992709i	$-0.461538\pi$
$821$	0.688601	−	1.81569i	0.688601	−	1.81569i	0.568065	−	0.822984i	$-0.307692\pi$
$822$		0			0
$823$	0.213460	+	0.112032i	0.213460	+	0.112032i	0.568065	−	0.822984i	$-0.307692\pi$
$823$	0.213460	+	0.112032i	0.213460	+	0.112032i	−0.354605	+	0.935016i	$0.615385\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.234068	+	0.0576926i	−0.234068	+	0.0576926i	−0.354605	−	0.935016i	$-0.615385\pi$
$827$	−0.234068	+	0.0576926i	−0.234068	+	0.0576926i	0.120537	+	0.992709i	$0.461538\pi$
$828$	2.14893	−	1.12785i	2.14893	−	1.12785i
$829$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$829$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$839$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$840$		0			0
$841$	−0.757482	−	1.99732i	−0.757482	−	1.99732i
$842$	2.57406	−	0.634448i	2.57406	−	0.634448i
$843$		0			0
$844$	−1.81658	+	1.60935i	−1.81658	+	1.60935i
$845$		0			0
$846$		0			0
$847$	2.77091			2.77091
$848$	0.171996	+	1.41652i	0.171996	+	1.41652i
$849$		0			0
$850$		0			0
$851$	−0.205010	+	1.68841i	−0.205010	+	1.68841i
$852$		0			0
$853$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$853$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$854$		0			0
$855$		0			0
$856$	0.429478	+	0.225408i	0.429478	+	0.225408i
$857$		0			0		−0.970942	−	0.239316i	$-0.923077\pi$
$857$		0			0		0.970942	+	0.239316i	$0.0769231\pi$
$858$		0			0
$859$		0			0		−0.568065	−	0.822984i	$-0.692308\pi$
$859$		0			0		0.568065	+	0.822984i	$0.307692\pi$
$860$		0			0
$861$		0			0
$862$	0.940091	−	0.832848i	0.940091	−	0.832848i
$863$	−0.0854858	+	0.225408i	−0.0854858	+	0.225408i	−0.970942	−	0.239316i	$-0.923077\pi$
$863$	−0.0854858	+	0.225408i	−0.0854858	+	0.225408i	0.885456	+	0.464723i	$0.153846\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.33718	+	0.329586i	−1.33718	+	0.329586i
$870$		0			0
$871$		0			0
$872$	2.28588	−	3.31166i	2.28588	−	3.31166i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.850405	+	1.23202i	−0.850405	+	1.23202i	0.120537	+	0.992709i	$0.461538\pi$
$877$	−0.850405	+	1.23202i	−0.850405	+	1.23202i	−0.970942	+	0.239316i	$0.923077\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$881$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$882$	−1.32555	−	1.17433i	−1.32555	−	1.17433i
$883$	0.136945	+	1.12785i	0.136945	+	1.12785i	0.885456	+	0.464723i	$0.153846\pi$
$883$	0.136945	+	1.12785i	0.136945	+	1.12785i	−0.748511	+	0.663123i	$0.769231\pi$
$884$		0			0
$885$		0			0
$886$	0.940091	−	2.47882i	0.940091	−	2.47882i
$887$		0			0		0.748511	−	0.663123i	$-0.230769\pi$
$887$		0			0		−0.748511	+	0.663123i	$0.769231\pi$
$888$		0			0
$889$	0.645395	+	0.935016i	0.645395	+	0.935016i
$890$		0			0
$891$	−0.234068	−	1.92773i	−0.234068	−	1.92773i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	1.38546	+	0.341484i	1.38546	+	0.341484i
$897$		0			0
$898$	0.242518	−	1.99732i	0.242518	−	1.99732i
$899$		0			0
$900$	2.13613			2.13613
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−0.363055	+	2.99002i	−0.363055	+	2.99002i
$905$		0			0
$906$		0			0
$907$	1.88546	−	0.464723i	1.88546	−	0.464723i	0.885456	−	0.464723i	$-0.153846\pi$
$907$	1.88546	−	0.464723i	1.88546	−	0.464723i	1.00000			$0$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.136945	+	1.12785i	0.136945	+	1.12785i	0.885456	+	0.464723i	$0.153846\pi$
$911$	0.136945	+	1.12785i	0.136945	+	1.12785i	−0.748511	+	0.663123i	$0.769231\pi$
$912$		0			0
$913$		0			0
$914$	−2.34743	−	2.07964i	−2.34743	−	2.07964i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.180446	−	1.48611i	−0.180446	−	1.48611i	−0.748511	−	0.663123i	$-0.769231\pi$
$919$	−0.180446	−	1.48611i	−0.180446	−	1.48611i	0.568065	−	0.822984i	$-0.307692\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.850405	+	1.23202i	−0.850405	+	1.23202i
$926$	−2.34743	−	1.23202i	−2.34743	−	1.23202i
$927$		0			0
$928$	−0.323384	+	0.852693i	−0.323384	+	0.852693i
$929$		0			0		−0.885456	−	0.464723i	$-0.846154\pi$
$929$		0			0		0.885456	+	0.464723i	$0.153846\pi$
$930$		0			0
$931$		0			0
$932$	−2.35640	+	3.41383i	−2.35640	+	3.41383i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$937$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$938$	−0.414514	+	3.41383i	−0.414514	+	3.41383i
$939$		0			0
$940$		0			0
$941$		0			0		−0.748511	−	0.663123i	$-0.769231\pi$
$941$		0			0		0.748511	+	0.663123i	$0.230769\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−0.734068	−	0.385269i	−0.734068	−	0.385269i
$947$	0.530851	+	1.39974i	0.530851	+	1.39974i	0.885456	+	0.464723i	$0.153846\pi$
$947$	0.530851	+	1.39974i	0.530851	+	1.39974i	−0.354605	+	0.935016i	$0.615385\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.241073			0.241073			0.120537	−	0.992709i	$-0.461538\pi$
$953$	0.241073			0.241073			0.120537	+	0.992709i	$0.461538\pi$
$954$	−0.627974	−	1.65583i	−0.627974	−	1.65583i
$955$		0			0
$956$	1.13397	+	2.99002i	1.13397	+	2.99002i
$957$		0			0
$958$		0			0
$959$	−0.234068	−	0.0576926i	−0.234068	−	0.0576926i
$960$		0			0
$961$	−0.354605	−	0.935016i	−0.354605	−	0.935016i
$962$		0			0
$963$	−0.234068	−	0.0576926i	−0.234068	−	0.0576926i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1.32555	−	1.17433i	−1.32555	−	1.17433i	−0.970942	−	0.239316i	$-0.923077\pi$
$967$	−1.32555	−	1.17433i	−1.32555	−	1.17433i	−0.354605	−	0.935016i	$-0.615385\pi$
$968$	−4.17297	+	3.69693i	−4.17297	+	3.69693i
$969$		0			0
$970$		0			0
$971$		0			0		0.885456	−	0.464723i	$-0.153846\pi$
$971$		0			0		−0.885456	+	0.464723i	$0.846154\pi$
$972$		0			0
$973$		0			0
$974$	−1.11209	+	0.583668i	−1.11209	+	0.583668i
$975$		0			0
$976$		0			0
$977$	−1.94188			−1.94188			−0.970942	−	0.239316i	$-0.923077\pi$
$977$	−1.94188			−1.94188			−0.970942	+	0.239316i	$0.923077\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−0.709210	+	1.87003i	−0.709210	+	1.87003i
$982$	3.13613	+	1.64597i	3.13613	+	1.64597i
$983$		0			0		0.568065	−	0.822984i	$-0.307692\pi$
$983$		0			0		−0.568065	+	0.822984i	$0.692308\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.0330139	+	0.271894i	0.0330139	+	0.271894i
$990$		0			0
$991$	−0.234068	+	1.92773i	−0.234068	+	1.92773i	0.120537	+	0.992709i	$0.461538\pi$
$991$	−0.234068	+	1.92773i	−0.234068	+	1.92773i	−0.354605	+	0.935016i	$0.615385\pi$
$992$		0			0
$993$		0			0
$994$	0.940091	+	0.832848i	0.940091	+	0.832848i
$995$		0			0
$996$		0			0
$997$		0			0		−0.120537	−	0.992709i	$-0.538462\pi$
$997$		0			0		0.120537	+	0.992709i	$0.461538\pi$
$998$	−3.04500	−	0.750525i	−3.04500	−	0.750525i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	371.1.n.a.342.1	yes	12
3.2	odd	2		3339.1.ck.a.2197.1		12
7.2	even	3		2597.1.bf.a.766.1		24
7.3	odd	6		2597.1.bf.a.607.1		24
7.4	even	3		2597.1.bf.a.607.1		24
7.5	odd	6		2597.1.bf.a.766.1		24
7.6	odd	2	CM	371.1.n.a.342.1	yes	12
21.20	even	2		3339.1.ck.a.2197.1		12
53.42	even	13	inner	371.1.n.a.307.1	✓	12
159.95	odd	26		3339.1.ck.a.307.1		12
371.95	even	39		2597.1.bf.a.1685.1		24
371.201	odd	78		2597.1.bf.a.1844.1		24
371.254	even	39		2597.1.bf.a.1844.1		24
371.307	odd	26	inner	371.1.n.a.307.1	✓	12
371.360	odd	78		2597.1.bf.a.1685.1		24
1113.1049	even	26		3339.1.ck.a.307.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
371.1.n.a.307.1	✓	12	53.42	even	13	inner
371.1.n.a.307.1	✓	12	371.307	odd	26	inner
371.1.n.a.342.1	yes	12	1.1	even	1	trivial
371.1.n.a.342.1	yes	12	7.6	odd	2	CM
2597.1.bf.a.607.1		24	7.3	odd	6
2597.1.bf.a.607.1		24	7.4	even	3
2597.1.bf.a.766.1		24	7.2	even	3
2597.1.bf.a.766.1		24	7.5	odd	6
2597.1.bf.a.1685.1		24	371.95	even	39
2597.1.bf.a.1685.1		24	371.360	odd	78
2597.1.bf.a.1844.1		24	371.201	odd	78
2597.1.bf.a.1844.1		24	371.254	even	39
3339.1.ck.a.307.1		12	159.95	odd	26
3339.1.ck.a.307.1		12	1113.1049	even	26
3339.1.ck.a.2197.1		12	3.2	odd	2
3339.1.ck.a.2197.1		12	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 371 = 7 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	371.n (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.627974 - 1.65583i) q^{2} +(-1.59892 + 1.41652i) q^{4} +(-0.354605 - 0.935016i) q^{7} +(1.78152 + 0.935016i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})\)	\(q+(-0.627974 - 1.65583i) q^{2} +(-1.59892 + 1.41652i) q^{4} +(-0.354605 - 0.935016i) q^{7} +(1.78152 + 0.935016i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-1.10312 - 1.59814i) q^{11} +(-1.32555 + 1.17433i) q^{14} +(0.171996 - 1.41652i) q^{16} +(0.213460 + 1.75800i) q^{18} +(-1.95352 + 2.83016i) q^{22} +1.13613 q^{23} +(0.885456 + 0.464723i) q^{25} +(1.89145 + 0.992709i) q^{28} +(1.00599 - 1.45743i) q^{29} +(-0.500000 + 0.123239i) q^{32} +(1.89145 - 0.992709i) q^{36} +(-0.180446 + 1.48611i) q^{37} +(0.0290582 + 0.239316i) q^{43} +(4.02758 + 0.992709i) q^{44} +(-0.713460 - 1.88124i) q^{46} +(-0.748511 + 0.663123i) q^{49} +(0.213460 - 1.75800i) q^{50} +(-0.970942 + 0.239316i) q^{53} +(0.242518 - 1.99732i) q^{56} +(-3.04500 - 0.750525i) q^{58} +(0.120537 + 0.992709i) q^{63} +(-0.292533 - 0.423807i) q^{64} +(1.45352 - 1.28771i) q^{67} +(-0.0854858 - 0.704039i) q^{71} +(-1.50599 - 1.33419i) q^{72} +(2.57406 - 0.634448i) q^{74} +(-1.10312 + 1.59814i) q^{77} +(0.251489 - 0.663123i) q^{79} +(0.885456 + 0.464723i) q^{81} +(0.378019 - 0.198399i) q^{86} +(-0.470942 - 3.87855i) q^{88} +(-1.81658 + 1.60935i) q^{92} +(1.56806 + 0.822984i) q^{98} +(0.688601 + 1.81569i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 3 q^{4} - q^{7} + 9 q^{8} - q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 3 * q^4 - q^7 + 9 * q^8 - q^9	\( 12 q - 2 q^{2} - 3 q^{4} - q^{7} + 9 q^{8} - q^{9} - 2 q^{11} - 2 q^{14} - 5 q^{16} - 2 q^{18} - 4 q^{22} - 2 q^{23} - q^{25} - 3 q^{28} - 2 q^{29} - 6 q^{32} - 3 q^{36} - 2 q^{37} + 11 q^{43} + 7 q^{44} - 4 q^{46} - q^{49} - 2 q^{50} - q^{53} + 9 q^{56} - 4 q^{58} - q^{63} + 6 q^{64} - 2 q^{67} - 2 q^{71} - 4 q^{72} + 9 q^{74} - 2 q^{77} + 11 q^{79} - q^{81} - 4 q^{86} + 5 q^{88} - 6 q^{92} + 11 q^{98} - 2 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 3 * q^4 - q^7 + 9 * q^8 - q^9 - 2 * q^11 - 2 * q^14 - 5 * q^16 - 2 * q^18 - 4 * q^22 - 2 * q^23 - q^25 - 3 * q^28 - 2 * q^29 - 6 * q^32 - 3 * q^36 - 2 * q^37 + 11 * q^43 + 7 * q^44 - 4 * q^46 - q^49 - 2 * q^50 - q^53 + 9 * q^56 - 4 * q^58 - q^63 + 6 * q^64 - 2 * q^67 - 2 * q^71 - 4 * q^72 + 9 * q^74 - 2 * q^77 + 11 * q^79 - q^81 - 4 * q^86 + 5 * q^88 - 6 * q^92 + 11 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more