LMFDB - Embedded newform 2312.1.q.a.1221.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2312,1,Mod(653,2312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2312, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 8, 11]))

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

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

chi := DirichletCharacter("2312.653");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2312 = 2^{3} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2312.q (of order $16$, degree $8$, 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:	$1.15383830921$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{16})$
Coefficient field:	$\Q(\zeta_{32})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1 $ x^16 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Projective image:	$D_{4}$
Projective field:	Galois closure of 4.0.2312.1

Embedding invariants

Embedding label			1221.1
Root			$-0.195090 - 0.980785i$ of defining polynomial
Character	$\chi$	$=$	2312.1221
Dual form			2312.1.q.a.1405.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.923880 - 0.382683i) q^{2} +(-1.38704 - 0.275899i) q^{3} +(0.707107 - 0.707107i) q^{4} +(0.785695 + 1.17588i) q^{5} +(-1.38704 + 0.275899i) q^{6} +(0.382683 - 0.923880i) q^{8} +(0.923880 + 0.382683i) q^{9} +(1.17588 + 0.785695i) q^{10} +(-0.275899 - 1.38704i) q^{11} +(-1.17588 + 0.785695i) q^{12} +(-0.765367 - 1.84776i) q^{15} -1.00000i q^{16} +1.00000 q^{18} +(1.38704 + 0.275899i) q^{20} +(-0.785695 - 1.17588i) q^{22} +(-0.785695 + 1.17588i) q^{24} +(-0.382683 + 0.923880i) q^{25} +(1.17588 - 0.785695i) q^{29} +(-1.41421 - 1.41421i) q^{30} +(-0.382683 - 0.923880i) q^{32} +2.00000i q^{33} +(0.923880 - 0.382683i) q^{36} +(1.38704 + 0.275899i) q^{37} +(1.38704 - 0.275899i) q^{40} +(-1.17588 - 0.785695i) q^{44} +(0.275899 + 1.38704i) q^{45} +(1.41421 + 1.41421i) q^{47} +(-0.275899 + 1.38704i) q^{48} +(-0.382683 - 0.923880i) q^{49} +1.00000i q^{50} +(1.41421 - 1.41421i) q^{55} +(0.785695 - 1.17588i) q^{58} +(-1.84776 - 0.765367i) q^{60} +(-1.17588 - 0.785695i) q^{61} +(-0.707107 - 0.707107i) q^{64} +(0.765367 + 1.84776i) q^{66} +(0.707107 - 0.707107i) q^{72} +(1.38704 - 0.275899i) q^{74} +(0.785695 - 1.17588i) q^{75} +(1.17588 - 0.785695i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(-1.84776 + 0.765367i) q^{87} +(-1.38704 - 0.275899i) q^{88} +(-1.41421 + 1.41421i) q^{89} +(0.785695 + 1.17588i) q^{90} +(1.84776 + 0.765367i) q^{94} +(0.275899 + 1.38704i) q^{96} +(-0.707107 - 0.707107i) q^{98} +(0.275899 - 1.38704i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{18}+O(q^{100}) $ 16 * q + 16 * q^18

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2312\mathbb{Z}\right)^\times$.

$n$	$1157$	$1735$	$1737$
$\chi(n)$	$-1$	$1$	$e\left(\frac{9}{16}\right)$

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 $

$2$	0.923880	−	0.382683i	0.923880	−	0.382683i
$2$	0.923880	−	0.382683i	0.923880	−	0.382683i
$3$	−1.38704	−	0.275899i	−1.38704	−	0.275899i	−0.555570	−	0.831470i	$-0.687500\pi$
$3$	−1.38704	−	0.275899i	−1.38704	−	0.275899i	−0.831470	+	0.555570i	$0.812500\pi$
$4$	0.707107	−	0.707107i	0.707107	−	0.707107i
$5$	0.785695	+	1.17588i	0.785695	+	1.17588i	0.980785	+	0.195090i	$0.0625000\pi$
$5$	0.785695	+	1.17588i	0.785695	+	1.17588i	−0.195090	+	0.980785i	$0.562500\pi$
$6$	−1.38704	+	0.275899i	−1.38704	+	0.275899i
$7$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$7$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$8$	0.382683	−	0.923880i	0.382683	−	0.923880i
$9$	0.923880	+	0.382683i	0.923880	+	0.382683i
$10$	1.17588	+	0.785695i	1.17588	+	0.785695i
$11$	−0.275899	−	1.38704i	−0.275899	−	1.38704i	−0.831470	−	0.555570i	$-0.812500\pi$
$11$	−0.275899	−	1.38704i	−0.275899	−	1.38704i	0.555570	−	0.831470i	$-0.312500\pi$
$12$	−1.17588	+	0.785695i	−1.17588	+	0.785695i
$13$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$13$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$14$		0			0
$15$	−0.765367	−	1.84776i	−0.765367	−	1.84776i
$16$		−	1.00000i		−	1.00000i
$17$		0			0
$17$		0			0
$18$	1.00000			1.00000
$19$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$19$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$20$	1.38704	+	0.275899i	1.38704	+	0.275899i
$21$		0			0
$22$	−0.785695	−	1.17588i	−0.785695	−	1.17588i
$23$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$23$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$24$	−0.785695	+	1.17588i	−0.785695	+	1.17588i
$25$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.17588	−	0.785695i	1.17588	−	0.785695i	0.195090	−	0.980785i	$-0.437500\pi$
$29$	1.17588	−	0.785695i	1.17588	−	0.785695i	0.980785	+	0.195090i	$0.0625000\pi$
$30$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$31$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$31$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$32$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$33$			2.00000i			2.00000i
$34$		0			0
$35$		0			0
$36$	0.923880	−	0.382683i	0.923880	−	0.382683i
$37$	1.38704	+	0.275899i	1.38704	+	0.275899i	0.831470	−	0.555570i	$-0.187500\pi$
$37$	1.38704	+	0.275899i	1.38704	+	0.275899i	0.555570	+	0.831470i	$0.312500\pi$
$38$		0			0
$39$		0			0
$40$	1.38704	−	0.275899i	1.38704	−	0.275899i
$41$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$41$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$42$		0			0
$43$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$43$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$44$	−1.17588	−	0.785695i	−1.17588	−	0.785695i
$45$	0.275899	+	1.38704i	0.275899	+	1.38704i
$46$		0			0
$47$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$47$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$48$	−0.275899	+	1.38704i	−0.275899	+	1.38704i
$49$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$50$			1.00000i			1.00000i
$51$		0			0
$52$		0			0
$53$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$53$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$54$		0			0
$55$	1.41421	−	1.41421i	1.41421	−	1.41421i
$56$		0			0
$57$		0			0
$58$	0.785695	−	1.17588i	0.785695	−	1.17588i
$59$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$59$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$60$	−1.84776	−	0.765367i	−1.84776	−	0.765367i
$61$	−1.17588	−	0.785695i	−1.17588	−	0.785695i	−0.195090	−	0.980785i	$-0.562500\pi$
$61$	−1.17588	−	0.785695i	−1.17588	−	0.785695i	−0.980785	+	0.195090i	$0.937500\pi$
$62$		0			0
$63$		0			0
$64$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$65$		0			0
$66$	0.765367	+	1.84776i	0.765367	+	1.84776i
$67$		0			0			−	1.00000i	$-0.5\pi$
$67$		0			0				1.00000i	$0.5\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$71$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$72$	0.707107	−	0.707107i	0.707107	−	0.707107i
$73$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$73$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$74$	1.38704	−	0.275899i	1.38704	−	0.275899i
$75$	0.785695	−	1.17588i	0.785695	−	1.17588i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$79$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$80$	1.17588	−	0.785695i	1.17588	−	0.785695i
$81$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$82$		0			0
$83$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$83$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.84776	+	0.765367i	−1.84776	+	0.765367i
$88$	−1.38704	−	0.275899i	−1.38704	−	0.275899i
$89$	−1.41421	+	1.41421i	−1.41421	+	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$89$	−1.41421	+	1.41421i	−1.41421	+	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$90$	0.785695	+	1.17588i	0.785695	+	1.17588i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	1.84776	+	0.765367i	1.84776	+	0.765367i
$95$		0			0
$96$	0.275899	+	1.38704i	0.275899	+	1.38704i
$97$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$97$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$98$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$99$	0.275899	−	1.38704i	0.275899	−	1.38704i
$100$	0.382683	+	0.923880i	0.382683	+	0.923880i
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.785695	−	1.17588i	−0.785695	−	1.17588i	−0.980785	−	0.195090i	$-0.937500\pi$
$107$	−0.785695	−	1.17588i	−0.785695	−	1.17588i	0.195090	−	0.980785i	$-0.437500\pi$
$108$		0			0
$109$	−0.785695	+	1.17588i	−0.785695	+	1.17588i	0.195090	+	0.980785i	$0.437500\pi$
$109$	−0.785695	+	1.17588i	−0.785695	+	1.17588i	−0.980785	+	0.195090i	$0.937500\pi$
$110$	0.765367	−	1.84776i	0.765367	−	1.84776i
$111$	−1.84776	−	0.765367i	−1.84776	−	0.765367i
$112$		0			0
$113$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$113$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$114$		0			0
$115$		0			0
$116$	0.275899	−	1.38704i	0.275899	−	1.38704i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−2.00000			−2.00000
$121$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$122$	−1.38704	−	0.275899i	−1.38704	−	0.275899i
$123$		0			0
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$127$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$128$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$129$		0			0
$130$		0			0
$131$	−1.17588	+	0.785695i	−1.17588	+	0.785695i	−0.980785	−	0.195090i	$-0.937500\pi$
$131$	−1.17588	+	0.785695i	−1.17588	+	0.785695i	−0.195090	+	0.980785i	$0.562500\pi$
$132$	1.41421	+	1.41421i	1.41421	+	1.41421i
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$		0			0
$139$	1.38704	+	0.275899i	1.38704	+	0.275899i	0.831470	−	0.555570i	$-0.187500\pi$
$139$	1.38704	+	0.275899i	1.38704	+	0.275899i	0.555570	+	0.831470i	$0.312500\pi$
$140$		0			0
$141$	−1.57139	−	2.35175i	−1.57139	−	2.35175i
$142$		0			0
$143$		0			0
$144$	0.382683	−	0.923880i	0.382683	−	0.923880i
$145$	1.84776	+	0.765367i	1.84776	+	0.765367i
$146$		0			0
$147$	0.275899	+	1.38704i	0.275899	+	1.38704i
$148$	1.17588	−	0.785695i	1.17588	−	0.785695i
$149$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$149$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$150$	0.275899	−	1.38704i	0.275899	−	1.38704i
$151$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$151$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$157$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$158$		0			0
$159$		0			0
$160$	0.785695	−	1.17588i	0.785695	−	1.17588i
$161$		0			0
$162$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$163$	1.17588	+	0.785695i	1.17588	+	0.785695i	0.980785	−	0.195090i	$-0.0625000\pi$
$163$	1.17588	+	0.785695i	1.17588	+	0.785695i	0.195090	+	0.980785i	$0.437500\pi$
$164$		0			0
$165$	−2.35175	+	1.57139i	−2.35175	+	1.57139i
$166$		0			0
$167$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$167$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$168$		0			0
$169$			1.00000i			1.00000i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.38704	−	0.275899i	−1.38704	−	0.275899i	−0.555570	−	0.831470i	$-0.687500\pi$
$173$	−1.38704	−	0.275899i	−1.38704	−	0.275899i	−0.831470	+	0.555570i	$0.812500\pi$
$174$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$175$		0			0
$176$	−1.38704	+	0.275899i	−1.38704	+	0.275899i
$177$		0			0
$178$	−0.765367	+	1.84776i	−0.765367	+	1.84776i
$179$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$179$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$180$	1.17588	+	0.785695i	1.17588	+	0.785695i
$181$	−0.275899	−	1.38704i	−0.275899	−	1.38704i	−0.831470	−	0.555570i	$-0.812500\pi$
$181$	−0.275899	−	1.38704i	−0.275899	−	1.38704i	0.555570	−	0.831470i	$-0.312500\pi$
$182$		0			0
$183$	1.41421	+	1.41421i	1.41421	+	1.41421i
$184$		0			0
$185$	0.765367	+	1.84776i	0.765367	+	1.84776i
$186$		0			0
$187$		0			0
$188$	2.00000			2.00000
$189$		0			0
$190$		0			0
$191$	−1.41421	+	1.41421i	−1.41421	+	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$191$	−1.41421	+	1.41421i	−1.41421	+	1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$192$	0.785695	+	1.17588i	0.785695	+	1.17588i
$193$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$193$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$194$		0			0
$195$		0			0
$196$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$197$	1.17588	+	0.785695i	1.17588	+	0.785695i	0.980785	−	0.195090i	$-0.0625000\pi$
$197$	1.17588	+	0.785695i	1.17588	+	0.785695i	0.195090	+	0.980785i	$0.437500\pi$
$198$	−0.275899	−	1.38704i	−0.275899	−	1.38704i
$199$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$199$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$200$	0.707107	+	0.707107i	0.707107	+	0.707107i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.785695	+	1.17588i	−0.785695	+	1.17588i	0.195090	+	0.980785i	$0.437500\pi$
$211$	−0.785695	+	1.17588i	−0.785695	+	1.17588i	−0.980785	+	0.195090i	$0.937500\pi$
$212$		0			0
$213$		0			0
$214$	−1.17588	−	0.785695i	−1.17588	−	0.785695i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.275899	+	1.38704i	−0.275899	+	1.38704i
$219$		0			0
$220$		−	2.00000i		−	2.00000i
$221$		0			0
$222$	−2.00000			−2.00000
$223$	1.84776	−	0.765367i	1.84776	−	0.765367i	0.923880	−	0.382683i	$-0.125000\pi$
$223$	1.84776	−	0.765367i	1.84776	−	0.765367i	0.923880	−	0.382683i	$-0.125000\pi$
$224$		0			0
$225$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$226$		0			0
$227$	−1.38704	+	0.275899i	−1.38704	+	0.275899i	−0.831470	−	0.555570i	$-0.812500\pi$
$227$	−1.38704	+	0.275899i	−1.38704	+	0.275899i	−0.555570	+	0.831470i	$0.687500\pi$
$228$		0			0
$229$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$229$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$230$		0			0
$231$		0			0
$232$	−0.275899	−	1.38704i	−0.275899	−	1.38704i
$233$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$233$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$234$		0			0
$235$	−0.551799	+	2.77408i	−0.551799	+	2.77408i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.00000			−2.00000			−1.00000			$\pi$
$239$	−2.00000			−2.00000			−1.00000			$\pi$
$240$	−1.84776	+	0.765367i	−1.84776	+	0.765367i
$241$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$241$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$242$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$243$	0.785695	+	1.17588i	0.785695	+	1.17588i
$244$	−1.38704	+	0.275899i	−1.38704	+	0.275899i
$245$	0.785695	−	1.17588i	0.785695	−	1.17588i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$251$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−1.00000			−1.00000
$257$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$257$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	1.38704	−	0.275899i	1.38704	−	0.275899i
$262$	−0.785695	+	1.17588i	−0.785695	+	1.17588i
$263$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$263$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$264$	1.84776	+	0.765367i	1.84776	+	0.765367i
$265$		0			0
$266$		0			0
$267$	2.35175	−	1.57139i	2.35175	−	1.57139i
$268$		0			0
$269$	−0.275899	+	1.38704i	−0.275899	+	1.38704i	0.555570	+	0.831470i	$0.312500\pi$
$269$	−0.275899	+	1.38704i	−0.275899	+	1.38704i	−0.831470	+	0.555570i	$0.812500\pi$
$270$		0			0
$271$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$271$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.38704	+	0.275899i	1.38704	+	0.275899i
$276$		0			0
$277$	0.785695	+	1.17588i	0.785695	+	1.17588i	0.980785	+	0.195090i	$0.0625000\pi$
$277$	0.785695	+	1.17588i	0.785695	+	1.17588i	−0.195090	+	0.980785i	$0.562500\pi$
$278$	1.38704	−	0.275899i	1.38704	−	0.275899i
$279$		0			0
$280$		0			0
$281$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$281$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$282$	−2.35175	−	1.57139i	−2.35175	−	1.57139i
$283$	0.275899	+	1.38704i	0.275899	+	1.38704i	0.831470	+	0.555570i	$0.187500\pi$
$283$	0.275899	+	1.38704i	0.275899	+	1.38704i	−0.555570	+	0.831470i	$0.687500\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		−	1.00000i		−	1.00000i
$289$		0			0
$290$	2.00000			2.00000
$291$		0			0
$292$		0			0
$293$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$293$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$294$	0.785695	+	1.17588i	0.785695	+	1.17588i
$295$		0			0
$296$	0.785695	−	1.17588i	0.785695	−	1.17588i
$297$		0			0
$298$		0			0
$299$		0			0
$300$	−0.275899	−	1.38704i	−0.275899	−	1.38704i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	2.00000i		−	2.00000i
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$311$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$312$		0			0
$313$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$313$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.275899	−	1.38704i	−0.275899	−	1.38704i	−0.831470	−	0.555570i	$-0.812500\pi$
$317$	−0.275899	−	1.38704i	−0.275899	−	1.38704i	0.555570	−	0.831470i	$-0.312500\pi$
$318$		0			0
$319$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$320$	0.275899	−	1.38704i	0.275899	−	1.38704i
$321$	0.765367	+	1.84776i	0.765367	+	1.84776i
$322$		0			0
$323$		0			0
$324$	−1.00000			−1.00000
$325$		0			0
$326$	1.38704	+	0.275899i	1.38704	+	0.275899i
$327$	1.41421	−	1.41421i	1.41421	−	1.41421i
$328$		0			0
$329$		0			0
$330$	−1.57139	+	2.35175i	−1.57139	+	2.35175i
$331$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$331$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$332$		0			0
$333$	1.17588	+	0.785695i	1.17588	+	0.785695i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$337$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$338$	0.382683	+	0.923880i	0.382683	+	0.923880i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−1.38704	+	0.275899i	−1.38704	+	0.275899i
$347$	−0.785695	+	1.17588i	−0.785695	+	1.17588i	0.195090	+	0.980785i	$0.437500\pi$
$347$	−0.785695	+	1.17588i	−0.785695	+	1.17588i	−0.980785	+	0.195090i	$0.937500\pi$
$348$	−0.765367	+	1.84776i	−0.765367	+	1.84776i
$349$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$349$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$350$		0			0
$351$		0			0
$352$	−1.17588	+	0.785695i	−1.17588	+	0.785695i
$353$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$353$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$354$		0			0
$355$		0			0
$356$			2.00000i			2.00000i
$357$		0			0
$358$		0			0
$359$	−1.84776	+	0.765367i	−1.84776	+	0.765367i	−0.923880	+	0.382683i	$0.875000\pi$
$359$	−1.84776	+	0.765367i	−1.84776	+	0.765367i	−0.923880	+	0.382683i	$0.875000\pi$
$360$	1.38704	+	0.275899i	1.38704	+	0.275899i
$361$	0.707107	−	0.707107i	0.707107	−	0.707107i
$362$	−0.785695	−	1.17588i	−0.785695	−	1.17588i
$363$	1.38704	−	0.275899i	1.38704	−	0.275899i
$364$		0			0
$365$		0			0
$366$	1.84776	+	0.765367i	1.84776	+	0.765367i
$367$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$367$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$368$		0			0
$369$		0			0
$370$	1.41421	+	1.41421i	1.41421	+	1.41421i
$371$		0			0
$372$		0			0
$373$		0			0			−	1.00000i	$-0.5\pi$
$373$		0			0				1.00000i	$0.5\pi$
$374$		0			0
$375$		0			0
$376$	1.84776	−	0.765367i	1.84776	−	0.765367i
$377$		0			0
$378$		0			0
$379$	0.785695	+	1.17588i	0.785695	+	1.17588i	0.980785	+	0.195090i	$0.0625000\pi$
$379$	0.785695	+	1.17588i	0.785695	+	1.17588i	−0.195090	+	0.980785i	$0.562500\pi$
$380$		0			0
$381$		0			0
$382$	−0.765367	+	1.84776i	−0.765367	+	1.84776i
$383$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$383$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$384$	1.17588	+	0.785695i	1.17588	+	0.785695i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$389$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$390$		0			0
$391$		0			0
$392$	−1.00000			−1.00000
$393$	1.84776	−	0.765367i	1.84776	−	0.765367i
$394$	1.38704	+	0.275899i	1.38704	+	0.275899i
$395$		0			0
$396$	−0.785695	−	1.17588i	−0.785695	−	1.17588i
$397$	−1.38704	+	0.275899i	−1.38704	+	0.275899i	−0.831470	−	0.555570i	$-0.812500\pi$
$397$	−1.38704	+	0.275899i	−1.38704	+	0.275899i	−0.555570	+	0.831470i	$0.687500\pi$
$398$		0			0
$399$		0			0
$400$	0.923880	+	0.382683i	0.923880	+	0.382683i
$401$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$401$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	0.275899	−	1.38704i	0.275899	−	1.38704i
$406$		0			0
$407$		−	2.00000i		−	2.00000i
$408$		0			0
$409$		0			0			−	1.00000i	$-0.5\pi$
$409$		0			0				1.00000i	$0.5\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.84776	−	0.765367i	−1.84776	−	0.765367i
$418$		0			0
$419$	0.275899	+	1.38704i	0.275899	+	1.38704i	0.831470	+	0.555570i	$0.187500\pi$
$419$	0.275899	+	1.38704i	0.275899	+	1.38704i	−0.555570	+	0.831470i	$0.687500\pi$
$420$		0			0
$421$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$421$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$422$	−0.275899	+	1.38704i	−0.275899	+	1.38704i
$423$	0.765367	+	1.84776i	0.765367	+	1.84776i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−1.38704	−	0.275899i	−1.38704	−	0.275899i
$429$		0			0
$430$		0			0
$431$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$431$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$432$		0			0
$433$	−0.765367	+	1.84776i	−0.765367	+	1.84776i	−0.382683	+	0.923880i	$0.625000\pi$
$433$	−0.765367	+	1.84776i	−0.765367	+	1.84776i	−0.382683	+	0.923880i	$0.625000\pi$
$434$		0			0
$435$	−2.35175	−	1.57139i	−2.35175	−	1.57139i
$436$	0.275899	+	1.38704i	0.275899	+	1.38704i
$437$		0			0
$438$		0			0
$439$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$439$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$440$	−0.765367	−	1.84776i	−0.765367	−	1.84776i
$441$		−	1.00000i		−	1.00000i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$	−1.84776	+	0.765367i	−1.84776	+	0.765367i
$445$	−2.77408	−	0.551799i	−2.77408	−	0.551799i
$446$	1.41421	−	1.41421i	1.41421	−	1.41421i
$447$		0			0
$448$		0			0
$449$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$449$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$450$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−1.17588	+	0.785695i	−1.17588	+	0.785695i
$455$		0			0
$456$		0			0
$457$	−0.765367	−	1.84776i	−0.765367	−	1.84776i	−0.382683	−	0.923880i	$-0.625000\pi$
$457$	−0.765367	−	1.84776i	−0.765367	−	1.84776i	−0.382683	−	0.923880i	$-0.625000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$461$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$462$		0			0
$463$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$463$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$464$	−0.785695	−	1.17588i	−0.785695	−	1.17588i
$465$		0			0
$466$		0			0
$467$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$467$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$468$		0			0
$469$		0			0
$470$	0.551799	+	2.77408i	0.551799	+	2.77408i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−1.84776	+	0.765367i	−1.84776	+	0.765367i
$479$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$479$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$480$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$485$		0			0
$486$	1.17588	+	0.785695i	1.17588	+	0.785695i
$487$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$487$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$488$	−1.17588	+	0.785695i	−1.17588	+	0.785695i
$489$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$490$	0.275899	−	1.38704i	0.275899	−	1.38704i
$491$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$491$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	1.84776	−	0.765367i	1.84776	−	0.765367i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.38704	−	0.275899i	1.38704	−	0.275899i	0.555570	−	0.831470i	$-0.312500\pi$
$499$	1.38704	−	0.275899i	1.38704	−	0.275899i	0.831470	+	0.555570i	$0.187500\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$503$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.275899	−	1.38704i	0.275899	−	1.38704i
$508$		0			0
$509$		0			0			−	1.00000i	$-0.5\pi$
$509$		0			0				1.00000i	$0.5\pi$
$510$		0			0
$511$		0			0
$512$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$	1.57139	−	2.35175i	1.57139	−	2.35175i
$518$		0			0
$519$	1.84776	+	0.765367i	1.84776	+	0.765367i
$520$		0			0
$521$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$521$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$522$	1.17588	−	0.785695i	1.17588	−	0.785695i
$523$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$523$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$524$	−0.275899	+	1.38704i	−0.275899	+	1.38704i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	2.00000			2.00000
$529$	0.923880	−	0.382683i	0.923880	−	0.382683i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	1.57139	−	2.35175i	1.57139	−	2.35175i
$535$	0.765367	−	1.84776i	0.765367	−	1.84776i
$536$		0			0
$537$		0			0
$538$	0.275899	+	1.38704i	0.275899	+	1.38704i
$539$	−1.17588	+	0.785695i	−1.17588	+	0.785695i
$540$		0			0
$541$	0.275899	−	1.38704i	0.275899	−	1.38704i	−0.555570	−	0.831470i	$-0.687500\pi$
$541$	0.275899	−	1.38704i	0.275899	−	1.38704i	0.831470	−	0.555570i	$-0.187500\pi$
$542$	−0.765367	−	1.84776i	−0.765367	−	1.84776i
$543$			2.00000i			2.00000i
$544$		0			0
$545$	−2.00000			−2.00000
$546$		0			0
$547$	−1.38704	−	0.275899i	−1.38704	−	0.275899i	−0.555570	−	0.831470i	$-0.687500\pi$
$547$	−1.38704	−	0.275899i	−1.38704	−	0.275899i	−0.831470	+	0.555570i	$0.812500\pi$
$548$		0			0
$549$	−0.785695	−	1.17588i	−0.785695	−	1.17588i
$550$	1.38704	−	0.275899i	1.38704	−	0.275899i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	1.17588	+	0.785695i	1.17588	+	0.785695i
$555$	−0.551799	−	2.77408i	−0.551799	−	2.77408i
$556$	1.17588	−	0.785695i	1.17588	−	0.785695i
$557$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$557$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$563$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$564$	−2.77408	−	0.551799i	−2.77408	−	0.551799i
$565$		0			0
$566$	0.785695	+	1.17588i	0.785695	+	1.17588i
$567$		0			0
$568$		0			0
$569$	0.765367	−	1.84776i	0.765367	−	1.84776i	0.382683	−	0.923880i	$-0.375000\pi$
$569$	0.765367	−	1.84776i	0.765367	−	1.84776i	0.382683	−	0.923880i	$-0.375000\pi$
$570$		0			0
$571$	−1.17588	−	0.785695i	−1.17588	−	0.785695i	−0.195090	−	0.980785i	$-0.562500\pi$
$571$	−1.17588	−	0.785695i	−1.17588	−	0.785695i	−0.980785	+	0.195090i	$0.937500\pi$
$572$		0			0
$573$	2.35175	−	1.57139i	2.35175	−	1.57139i
$574$		0			0
$575$		0			0
$576$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$		0			0
$579$		0			0
$580$	1.84776	−	0.765367i	1.84776	−	0.765367i
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$587$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$588$	1.17588	+	0.785695i	1.17588	+	0.785695i
$589$		0			0
$590$		0			0
$591$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$592$	0.275899	−	1.38704i	0.275899	−	1.38704i
$593$	0.765367	+	1.84776i	0.765367	+	1.84776i	0.382683	+	0.923880i	$0.375000\pi$
$593$	0.765367	+	1.84776i	0.765367	+	1.84776i	0.382683	+	0.923880i	$0.375000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$599$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$600$	−0.785695	−	1.17588i	−0.785695	−	1.17588i
$601$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$601$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.17588	−	0.785695i	−1.17588	−	0.785695i
$606$		0			0
$607$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$607$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$608$		0			0
$609$		0			0
$610$	−0.765367	−	1.84776i	−0.765367	−	1.84776i
$611$		0			0
$612$		0			0
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$617$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$618$		0			0
$619$	0.785695	−	1.17588i	0.785695	−	1.17588i	−0.195090	−	0.980785i	$-0.562500\pi$
$619$	0.785695	−	1.17588i	0.785695	−	1.17588i	0.980785	−	0.195090i	$-0.0625000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.707107	+	0.707107i	0.707107	+	0.707107i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	1.84776	−	0.765367i	1.84776	−	0.765367i	0.923880	−	0.382683i	$-0.125000\pi$
$631$	1.84776	−	0.765367i	1.84776	−	0.765367i	0.923880	−	0.382683i	$-0.125000\pi$
$632$		0			0
$633$	1.41421	−	1.41421i	1.41421	−	1.41421i
$634$	−0.785695	−	1.17588i	−0.785695	−	1.17588i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−1.84776	−	0.765367i	−1.84776	−	0.765367i
$639$		0			0
$640$	−0.275899	−	1.38704i	−0.275899	−	1.38704i
$641$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$641$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$642$	1.41421	+	1.41421i	1.41421	+	1.41421i
$643$	0.275899	−	1.38704i	0.275899	−	1.38704i	−0.555570	−	0.831470i	$-0.687500\pi$
$643$	0.275899	−	1.38704i	0.275899	−	1.38704i	0.831470	−	0.555570i	$-0.187500\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	2.00000			2.00000			1.00000			$0$
$647$	2.00000			2.00000			1.00000			$0$
$648$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	1.38704	−	0.275899i	1.38704	−	0.275899i
$653$	−0.785695	+	1.17588i	−0.785695	+	1.17588i	0.195090	+	0.980785i	$0.437500\pi$
$653$	−0.785695	+	1.17588i	−0.785695	+	1.17588i	−0.980785	+	0.195090i	$0.937500\pi$
$654$	0.765367	−	1.84776i	0.765367	−	1.84776i
$655$	−1.84776	−	0.765367i	−1.84776	−	0.765367i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$659$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$660$	−0.551799	+	2.77408i	−0.551799	+	2.77408i
$661$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$661$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	1.38704	+	0.275899i	1.38704	+	0.275899i
$667$		0			0
$668$		0			0
$669$	−2.77408	+	0.551799i	−2.77408	+	0.551799i
$670$		0			0
$671$	−0.765367	+	1.84776i	−0.765367	+	1.84776i
$672$		0			0
$673$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$673$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$674$		0			0
$675$		0			0
$676$	0.707107	+	0.707107i	0.707107	+	0.707107i
$677$	0.275899	−	1.38704i	0.275899	−	1.38704i	−0.555570	−	0.831470i	$-0.687500\pi$
$677$	0.275899	−	1.38704i	0.275899	−	1.38704i	0.831470	−	0.555570i	$-0.187500\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	2.00000			2.00000
$682$		0			0
$683$	1.38704	+	0.275899i	1.38704	+	0.275899i	0.831470	−	0.555570i	$-0.187500\pi$
$683$	1.38704	+	0.275899i	1.38704	+	0.275899i	0.555570	+	0.831470i	$0.312500\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.275899	−	1.38704i	−0.275899	−	1.38704i	−0.831470	−	0.555570i	$-0.812500\pi$
$691$	−0.275899	−	1.38704i	−0.275899	−	1.38704i	0.555570	−	0.831470i	$-0.312500\pi$
$692$	−1.17588	+	0.785695i	−1.17588	+	0.785695i
$693$		0			0
$694$	−0.275899	+	1.38704i	−0.275899	+	1.38704i
$695$	0.765367	+	1.84776i	0.765367	+	1.84776i
$696$			2.00000i			2.00000i
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$701$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$702$		0			0
$703$		0			0
$704$	−0.785695	+	1.17588i	−0.785695	+	1.17588i
$705$	1.53073	−	3.69552i	1.53073	−	3.69552i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.17588	−	0.785695i	1.17588	−	0.785695i	0.195090	−	0.980785i	$-0.437500\pi$
$709$	1.17588	−	0.785695i	1.17588	−	0.785695i	0.980785	+	0.195090i	$0.0625000\pi$
$710$		0			0
$711$		0			0
$712$	0.765367	+	1.84776i	0.765367	+	1.84776i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	2.77408	+	0.551799i	2.77408	+	0.551799i
$718$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$719$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$719$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$720$	1.38704	−	0.275899i	1.38704	−	0.275899i
$721$		0			0
$722$	0.382683	−	0.923880i	0.382683	−	0.923880i
$723$		0			0
$724$	−1.17588	−	0.785695i	−1.17588	−	0.785695i
$725$	0.275899	+	1.38704i	0.275899	+	1.38704i
$726$	1.17588	−	0.785695i	1.17588	−	0.785695i
$727$	−1.41421	−	1.41421i	−1.41421	−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$727$	−1.41421	−	1.41421i	−1.41421	−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$728$		0			0
$729$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$730$		0			0
$731$		0			0
$732$	2.00000			2.00000
$733$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$733$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$734$		0			0
$735$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$739$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$740$	1.84776	+	0.765367i	1.84776	+	0.765367i
$741$		0			0
$742$		0			0
$743$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$743$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$751$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$752$	1.41421	−	1.41421i	1.41421	−	1.41421i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$757$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$758$	1.17588	+	0.785695i	1.17588	+	0.785695i
$759$		0			0
$760$		0			0
$761$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$761$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$762$		0			0
$763$		0			0
$764$			2.00000i			2.00000i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.38704	+	0.275899i	1.38704	+	0.275899i
$769$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$769$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$773$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$785$		0			0
$786$	1.41421	−	1.41421i	1.41421	−	1.41421i
$787$	−0.785695	−	1.17588i	−0.785695	−	1.17588i	−0.980785	−	0.195090i	$-0.937500\pi$
$787$	−0.785695	−	1.17588i	−0.785695	−	1.17588i	0.195090	−	0.980785i	$-0.437500\pi$
$788$	1.38704	−	0.275899i	1.38704	−	0.275899i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−1.17588	−	0.785695i	−1.17588	−	0.785695i
$793$		0			0
$794$	−1.17588	+	0.785695i	−1.17588	+	0.785695i
$795$		0			0
$796$		0			0
$797$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$797$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$798$		0			0
$799$		0			0
$800$	1.00000			1.00000
$801$	−1.84776	+	0.765367i	−1.84776	+	0.765367i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.765367	−	1.84776i	0.765367	−	1.84776i
$808$		0			0
$809$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$809$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$810$	−0.275899	−	1.38704i	−0.275899	−	1.38704i
$811$	−1.17588	+	0.785695i	−1.17588	+	0.785695i	−0.980785	−	0.195090i	$-0.937500\pi$
$811$	−1.17588	+	0.785695i	−1.17588	+	0.785695i	−0.195090	+	0.980785i	$0.562500\pi$
$812$		0			0
$813$	−0.551799	+	2.77408i	−0.551799	+	2.77408i
$814$	−0.765367	−	1.84776i	−0.765367	−	1.84776i
$815$			2.00000i			2.00000i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.785695	+	1.17588i	0.785695	+	1.17588i	0.980785	+	0.195090i	$0.0625000\pi$
$821$	0.785695	+	1.17588i	0.785695	+	1.17588i	−0.195090	+	0.980785i	$0.562500\pi$
$822$		0			0
$823$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$823$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$824$		0			0
$825$	−1.84776	−	0.765367i	−1.84776	−	0.765367i
$826$		0			0
$827$	0.275899	+	1.38704i	0.275899	+	1.38704i	0.831470	+	0.555570i	$0.187500\pi$
$827$	0.275899	+	1.38704i	0.275899	+	1.38704i	−0.555570	+	0.831470i	$0.687500\pi$
$828$		0			0
$829$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$829$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$830$		0			0
$831$	−0.765367	−	1.84776i	−0.765367	−	1.84776i
$832$		0			0
$833$		0			0
$834$	−2.00000			−2.00000
$835$		0			0
$836$		0			0
$837$		0			0
$838$	0.785695	+	1.17588i	0.785695	+	1.17588i
$839$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$839$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$840$		0			0
$841$	0.382683	−	0.923880i	0.382683	−	0.923880i
$842$		0			0
$843$		0			0
$844$	0.275899	+	1.38704i	0.275899	+	1.38704i
$845$	−1.17588	+	0.785695i	−1.17588	+	0.785695i
$846$	1.41421	+	1.41421i	1.41421	+	1.41421i
$847$		0			0
$848$		0			0
$849$		−	2.00000i		−	2.00000i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	1.38704	+	0.275899i	1.38704	+	0.275899i	0.831470	−	0.555570i	$-0.187500\pi$
$853$	1.38704	+	0.275899i	1.38704	+	0.275899i	0.555570	+	0.831470i	$0.312500\pi$
$854$		0			0
$855$		0			0
$856$	−1.38704	+	0.275899i	−1.38704	+	0.275899i
$857$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$857$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$858$		0			0
$859$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$859$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$863$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$864$		0			0
$865$	−0.765367	−	1.84776i	−0.765367	−	1.84776i
$866$			2.00000i			2.00000i
$867$		0			0
$868$		0			0
$869$		0			0
$870$	−2.77408	−	0.551799i	−2.77408	−	0.551799i
$871$		0			0
$872$	0.785695	+	1.17588i	0.785695	+	1.17588i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.17588	+	0.785695i	1.17588	+	0.785695i	0.980785	−	0.195090i	$-0.0625000\pi$
$877$	1.17588	+	0.785695i	1.17588	+	0.785695i	0.195090	+	0.980785i	$0.437500\pi$
$878$		0			0
$879$		0			0
$880$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$881$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$881$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$882$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$887$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$888$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$889$		0			0
$890$	−2.77408	+	0.551799i	−2.77408	+	0.551799i
$891$	−0.785695	+	1.17588i	−0.785695	+	1.17588i
$892$	0.765367	−	1.84776i	0.765367	−	1.84776i
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$			1.00000i			1.00000i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.41421	−	1.41421i	1.41421	−	1.41421i
$906$		0			0
$907$	−1.38704	+	0.275899i	−1.38704	+	0.275899i	−0.831470	−	0.555570i	$-0.812500\pi$
$907$	−1.38704	+	0.275899i	−1.38704	+	0.275899i	−0.555570	+	0.831470i	$0.687500\pi$
$908$	−0.785695	+	1.17588i	−0.785695	+	1.17588i
$909$		0			0
$910$		0			0
$911$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$911$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$912$		0			0
$913$		0			0
$914$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$915$	−0.551799	+	2.77408i	−0.551799	+	2.77408i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	2.00000			2.00000			1.00000			$0$
$919$	2.00000			2.00000			1.00000			$0$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.785695	+	1.17588i	−0.785695	+	1.17588i
$926$		0			0
$927$		0			0
$928$	−1.17588	−	0.785695i	−1.17588	−	0.785695i
$929$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$929$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$937$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$938$		0			0
$939$		0			0
$940$	1.57139	+	2.35175i	1.57139	+	2.35175i
$941$	1.38704	−	0.275899i	1.38704	−	0.275899i	0.555570	−	0.831470i	$-0.312500\pi$
$941$	1.38704	−	0.275899i	1.38704	−	0.275899i	0.831470	+	0.555570i	$0.187500\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.17588	−	0.785695i	1.17588	−	0.785695i	0.195090	−	0.980785i	$-0.437500\pi$
$947$	1.17588	−	0.785695i	1.17588	−	0.785695i	0.980785	+	0.195090i	$0.0625000\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$			2.00000i			2.00000i
$952$		0			0
$953$	−2.00000			−2.00000			−1.00000			$\pi$
$953$	−2.00000			−2.00000			−1.00000			$\pi$
$954$		0			0
$955$	−2.77408	−	0.551799i	−2.77408	−	0.551799i
$956$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$957$	1.57139	+	2.35175i	1.57139	+	2.35175i
$958$		0			0
$959$		0			0
$960$	−0.765367	+	1.84776i	−0.765367	+	1.84776i
$961$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$962$		0			0
$963$	−0.275899	−	1.38704i	−0.275899	−	1.38704i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.765367	+	1.84776i	0.765367	+	1.84776i	0.382683	+	0.923880i	$0.375000\pi$
$967$	0.765367	+	1.84776i	0.765367	+	1.84776i	0.382683	+	0.923880i	$0.375000\pi$
$968$			1.00000i			1.00000i
$969$		0			0
$970$		0			0
$971$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$971$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$972$	1.38704	+	0.275899i	1.38704	+	0.275899i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.785695	+	1.17588i	−0.785695	+	1.17588i
$977$	−0.765367	+	1.84776i	−0.765367	+	1.84776i	−0.382683	+	0.923880i	$0.625000\pi$
$977$	−0.765367	+	1.84776i	−0.765367	+	1.84776i	−0.382683	+	0.923880i	$0.625000\pi$
$978$	−1.84776	−	0.765367i	−1.84776	−	0.765367i
$979$	2.35175	+	1.57139i	2.35175	+	1.57139i
$980$	−0.275899	−	1.38704i	−0.275899	−	1.38704i
$981$	−1.17588	+	0.785695i	−1.17588	+	0.785695i
$982$		0			0
$983$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$983$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$984$		0			0
$985$			2.00000i			2.00000i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	1.41421	−	1.41421i	1.41421	−	1.41421i
$991$		0			0		−0.555570	−	0.831470i	$-0.687500\pi$
$991$		0			0		0.555570	+	0.831470i	$0.312500\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.275899	+	1.38704i	0.275899	+	1.38704i	0.831470	+	0.555570i	$0.187500\pi$
$997$	0.275899	+	1.38704i	0.275899	+	1.38704i	−0.555570	+	0.831470i	$0.687500\pi$
$998$	1.17588	−	0.785695i	1.17588	−	0.785695i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2312.1.q.a.1221.1	yes	16
8.5	even	2	inner	2312.1.q.a.1221.2	yes	16
17.2	even	8	inner	2312.1.q.a.2181.1	yes	16
17.3	odd	16	inner	2312.1.q.a.653.1	✓	16
17.4	even	4	inner	2312.1.q.a.1669.1	yes	16
17.5	odd	16	inner	2312.1.q.a.2237.2	yes	16
17.6	odd	16	inner	2312.1.q.a.1405.1	yes	16
17.7	odd	16	inner	2312.1.q.a.1485.2	yes	16
17.8	even	8	inner	2312.1.q.a.709.2	yes	16
17.9	even	8	inner	2312.1.q.a.709.1	yes	16
17.10	odd	16	inner	2312.1.q.a.1485.1	yes	16
17.11	odd	16	inner	2312.1.q.a.1405.2	yes	16
17.12	odd	16	inner	2312.1.q.a.2237.1	yes	16
17.13	even	4	inner	2312.1.q.a.1669.2	yes	16
17.14	odd	16	inner	2312.1.q.a.653.2	yes	16
17.15	even	8	inner	2312.1.q.a.2181.2	yes	16
17.16	even	2	inner	2312.1.q.a.1221.2	yes	16
136.5	odd	16	inner	2312.1.q.a.2237.1	yes	16
136.13	even	4	inner	2312.1.q.a.1669.1	yes	16
136.21	even	4	inner	2312.1.q.a.1669.2	yes	16
136.29	odd	16	inner	2312.1.q.a.2237.2	yes	16
136.37	odd	16	inner	2312.1.q.a.653.2	yes	16
136.45	odd	16	inner	2312.1.q.a.1405.1	yes	16
136.53	even	8	inner	2312.1.q.a.2181.2	yes	16
136.61	odd	16	inner	2312.1.q.a.1485.2	yes	16
136.77	even	8	inner	2312.1.q.a.709.2	yes	16
136.93	even	8	inner	2312.1.q.a.709.1	yes	16
136.101	even	2	RM	2312.1.q.a.1221.1	yes	16
136.109	odd	16	inner	2312.1.q.a.1485.1	yes	16
136.117	even	8	inner	2312.1.q.a.2181.1	yes	16
136.125	odd	16	inner	2312.1.q.a.1405.2	yes	16
136.133	odd	16	inner	2312.1.q.a.653.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2312.1.q.a.653.1	✓	16	17.3	odd	16	inner
2312.1.q.a.653.1	✓	16	136.133	odd	16	inner
2312.1.q.a.653.2	yes	16	17.14	odd	16	inner
2312.1.q.a.653.2	yes	16	136.37	odd	16	inner
2312.1.q.a.709.1	yes	16	17.9	even	8	inner
2312.1.q.a.709.1	yes	16	136.93	even	8	inner
2312.1.q.a.709.2	yes	16	17.8	even	8	inner
2312.1.q.a.709.2	yes	16	136.77	even	8	inner
2312.1.q.a.1221.1	yes	16	1.1	even	1	trivial
2312.1.q.a.1221.1	yes	16	136.101	even	2	RM
2312.1.q.a.1221.2	yes	16	8.5	even	2	inner
2312.1.q.a.1221.2	yes	16	17.16	even	2	inner
2312.1.q.a.1405.1	yes	16	17.6	odd	16	inner
2312.1.q.a.1405.1	yes	16	136.45	odd	16	inner
2312.1.q.a.1405.2	yes	16	17.11	odd	16	inner
2312.1.q.a.1405.2	yes	16	136.125	odd	16	inner
2312.1.q.a.1485.1	yes	16	17.10	odd	16	inner
2312.1.q.a.1485.1	yes	16	136.109	odd	16	inner
2312.1.q.a.1485.2	yes	16	17.7	odd	16	inner
2312.1.q.a.1485.2	yes	16	136.61	odd	16	inner
2312.1.q.a.1669.1	yes	16	17.4	even	4	inner
2312.1.q.a.1669.1	yes	16	136.13	even	4	inner
2312.1.q.a.1669.2	yes	16	17.13	even	4	inner
2312.1.q.a.1669.2	yes	16	136.21	even	4	inner
2312.1.q.a.2181.1	yes	16	17.2	even	8	inner
2312.1.q.a.2181.1	yes	16	136.117	even	8	inner
2312.1.q.a.2181.2	yes	16	17.15	even	8	inner
2312.1.q.a.2181.2	yes	16	136.53	even	8	inner
2312.1.q.a.2237.1	yes	16	17.12	odd	16	inner
2312.1.q.a.2237.1	yes	16	136.5	odd	16	inner
2312.1.q.a.2237.2	yes	16	17.5	odd	16	inner
2312.1.q.a.2237.2	yes	16	136.29	odd	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2312 = 2^{3} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2312.q (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.923880 - 0.382683i) q^{2} +(-1.38704 - 0.275899i) q^{3} +(0.707107 - 0.707107i) q^{4} +(0.785695 + 1.17588i) q^{5} +(-1.38704 + 0.275899i) q^{6} +(0.382683 - 0.923880i) q^{8} +(0.923880 + 0.382683i) q^{9} +(1.17588 + 0.785695i) q^{10} +(-0.275899 - 1.38704i) q^{11} +(-1.17588 + 0.785695i) q^{12} +(-0.765367 - 1.84776i) q^{15} -1.00000i q^{16} +1.00000 q^{18} +(1.38704 + 0.275899i) q^{20} +(-0.785695 - 1.17588i) q^{22} +(-0.785695 + 1.17588i) q^{24} +(-0.382683 + 0.923880i) q^{25} +(1.17588 - 0.785695i) q^{29} +(-1.41421 - 1.41421i) q^{30} +(-0.382683 - 0.923880i) q^{32} +2.00000i q^{33} +(0.923880 - 0.382683i) q^{36} +(1.38704 + 0.275899i) q^{37} +(1.38704 - 0.275899i) q^{40} +(-1.17588 - 0.785695i) q^{44} +(0.275899 + 1.38704i) q^{45} +(1.41421 + 1.41421i) q^{47} +(-0.275899 + 1.38704i) q^{48} +(-0.382683 - 0.923880i) q^{49} +1.00000i q^{50} +(1.41421 - 1.41421i) q^{55} +(0.785695 - 1.17588i) q^{58} +(-1.84776 - 0.765367i) q^{60} +(-1.17588 - 0.785695i) q^{61} +(-0.707107 - 0.707107i) q^{64} +(0.765367 + 1.84776i) q^{66} +(0.707107 - 0.707107i) q^{72} +(1.38704 - 0.275899i) q^{74} +(0.785695 - 1.17588i) q^{75} +(1.17588 - 0.785695i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(-1.84776 + 0.765367i) q^{87} +(-1.38704 - 0.275899i) q^{88} +(-1.41421 + 1.41421i) q^{89} +(0.785695 + 1.17588i) q^{90} +(1.84776 + 0.765367i) q^{94} +(0.275899 + 1.38704i) q^{96} +(-0.707107 - 0.707107i) q^{98} +(0.275899 - 1.38704i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{18}+O(q^{100}) \) 16 * q + 16 * q^18

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more