LMFDB - Embedded newform 1057.1.bq.a.1000.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1057,1,Mod(20,1057)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1057, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([25, 34]))

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

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

chi := DirichletCharacter("1057.20");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1057 = 7 \cdot 151 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1057.bq (of order $50$, degree $20$, 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:	$0.527511718353$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\Q(\zeta_{50})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{15} + x^{10} - x^{5} + 1 $ x^20 - x^15 + x^10 - x^5 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{25}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{25} - \cdots)$

Embedding invariants

Embedding label			1000.1
Root			$0.187381 - 0.982287i$ of defining polynomial
Character	$\chi$	$=$	1057.1000
Dual form			1057.1.bq.a.853.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56720 + 1.13864i) q^{2} +(0.850604 - 2.61789i) q^{4} +(-0.929776 + 0.368125i) q^{7} +(1.04914 + 3.22894i) q^{8} +(0.535827 - 0.844328i) q^{9} +O(q^{10})$	\(q+(-1.56720 + 1.13864i) q^{2} +(0.850604 - 2.61789i) q^{4} +(-0.929776 + 0.368125i) q^{7} +(1.04914 + 3.22894i) q^{8} +(0.535827 - 0.844328i) q^{9} +(-1.41789 - 0.779494i) q^{11} +(1.03799 - 1.63560i) q^{14} +(-3.09390 - 2.24785i) q^{16} +(0.121636 + 1.93334i) q^{18} +(3.10969 - 0.392845i) q^{22} +(-0.500000 + 1.53884i) q^{23} +(-0.425779 - 0.904827i) q^{25} +(0.172838 + 2.74718i) q^{28} +(-1.44644 + 0.182728i) q^{29} +4.01314 q^{32} +(-1.75458 - 2.12093i) q^{36} +(-1.17950 - 1.10762i) q^{37} +(-1.62954 - 0.645180i) q^{43} +(-3.24670 + 3.04885i) q^{44} +(-0.968583 - 2.98099i) q^{46} +(0.728969 - 0.684547i) q^{49} +(1.69755 + 0.933237i) q^{50} +(0.159566 - 0.836475i) q^{53} +(-2.16412 - 2.61597i) q^{56} +(2.05880 - 1.93334i) q^{58} +(-0.187381 + 0.982287i) q^{63} +(-3.19549 + 2.32166i) q^{64} +(0.0672897 + 0.106032i) q^{67} +(-0.996398 + 0.394502i) q^{71} +(3.28844 + 0.844328i) q^{72} +(3.10969 + 0.392845i) q^{74} +(1.60528 + 0.202793i) q^{77} +(1.87631 + 0.481754i) q^{79} +(-0.425779 - 0.904827i) q^{81} +(3.28844 - 0.844328i) q^{86} +(1.02936 - 5.39609i) q^{88} +(3.60322 + 2.61789i) q^{92} +(-0.362989 + 1.90285i) q^{98} +(-1.41789 + 0.779494i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{4}+O(q^{10}) $ 20 * q - 5 * q^4	$ 20 q - 5 q^{4} - 5 q^{14} - 5 q^{16} - 5 q^{18} - 10 q^{23} - 5 q^{29} - 10 q^{32} - 10 q^{44} - 5 q^{53} - 5 q^{56} - 5 q^{58} - 5 q^{64} - 5 q^{67} - 5 q^{71} + 20 q^{72} + 20 q^{79} + 20 q^{86} + 15 q^{88} + 15 q^{92}+O(q^{100}) $ 20 * q - 5 * q^4 - 5 * q^14 - 5 * q^16 - 5 * q^18 - 10 * q^23 - 5 * q^29 - 10 * q^32 - 10 * q^44 - 5 * q^53 - 5 * q^56 - 5 * q^58 - 5 * q^64 - 5 * q^67 - 5 * q^71 + 20 * q^72 + 20 * q^79 + 20 * q^86 + 15 * q^88 + 15 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1057\mathbb{Z}\right)^\times$.

$n$	$605$	$610$
$\chi(n)$	$-1$	$e\left(\frac{16}{25}\right)$

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 $

$2$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.637424	+	0.770513i	$0.720000\pi$
$2$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.929776	+	0.368125i	$0.880000\pi$
$3$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$3$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$4$	0.850604	−	2.61789i	0.850604	−	2.61789i
$5$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$5$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$6$		0			0
$7$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$7$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$8$	1.04914	+	3.22894i	1.04914	+	3.22894i
$9$	0.535827	−	0.844328i	0.535827	−	0.844328i
$10$		0			0
$11$	−1.41789	−	0.779494i	−1.41789	−	0.779494i	−0.425779	−	0.904827i	$-0.640000\pi$
$11$	−1.41789	−	0.779494i	−1.41789	−	0.779494i	−0.992115	+	0.125333i	$0.960000\pi$
$12$		0			0
$13$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$13$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$14$	1.03799	−	1.63560i	1.03799	−	1.63560i
$15$		0			0
$16$	−3.09390	−	2.24785i	−3.09390	−	2.24785i
$17$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$17$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$18$	0.121636	+	1.93334i	0.121636	+	1.93334i
$19$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$19$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$20$		0			0
$21$		0			0
$22$	3.10969	−	0.392845i	3.10969	−	0.392845i
$23$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$23$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$24$		0			0
$25$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$26$		0			0
$27$		0			0
$28$	0.172838	+	2.74718i	0.172838	+	2.74718i
$29$	−1.44644	+	0.182728i	−1.44644	+	0.182728i	−0.809017	−	0.587785i	$-0.800000\pi$
$29$	−1.44644	+	0.182728i	−1.44644	+	0.182728i	−0.637424	+	0.770513i	$0.720000\pi$
$30$		0			0
$31$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$31$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$32$	4.01314			4.01314
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−1.75458	−	2.12093i	−1.75458	−	2.12093i
$37$	−1.17950	−	1.10762i	−1.17950	−	1.10762i	−0.992115	−	0.125333i	$-0.960000\pi$
$37$	−1.17950	−	1.10762i	−1.17950	−	1.10762i	−0.187381	−	0.982287i	$-0.560000\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$41$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$42$		0			0
$43$	−1.62954	−	0.645180i	−1.62954	−	0.645180i	−0.637424	−	0.770513i	$-0.720000\pi$
$43$	−1.62954	−	0.645180i	−1.62954	−	0.645180i	−0.992115	+	0.125333i	$0.960000\pi$
$44$	−3.24670	+	3.04885i	−3.24670	+	3.04885i
$45$		0			0
$46$	−0.968583	−	2.98099i	−0.968583	−	2.98099i
$47$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$47$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$48$		0			0
$49$	0.728969	−	0.684547i	0.728969	−	0.684547i
$50$	1.69755	+	0.933237i	1.69755	+	0.933237i
$51$		0			0
$52$		0			0
$53$	0.159566	−	0.836475i	0.159566	−	0.836475i	−0.809017	−	0.587785i	$-0.800000\pi$
$53$	0.159566	−	0.836475i	0.159566	−	0.836475i	0.968583	−	0.248690i	$-0.0800000\pi$
$54$		0			0
$55$		0			0
$56$	−2.16412	−	2.61597i	−2.16412	−	2.61597i
$57$		0			0
$58$	2.05880	−	1.93334i	2.05880	−	1.93334i
$59$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$59$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$60$		0			0
$61$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$61$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$62$		0			0
$63$	−0.187381	+	0.982287i	−0.187381	+	0.982287i
$64$	−3.19549	+	2.32166i	−3.19549	+	2.32166i
$65$		0			0
$66$		0			0
$67$	0.0672897	+	0.106032i	0.0672897	+	0.106032i	0.876307	−	0.481754i	$-0.160000\pi$
$67$	0.0672897	+	0.106032i	0.0672897	+	0.106032i	−0.809017	+	0.587785i	$0.800000\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.996398	+	0.394502i	−0.996398	+	0.394502i	−0.809017	−	0.587785i	$-0.800000\pi$
$71$	−0.996398	+	0.394502i	−0.996398	+	0.394502i	−0.187381	+	0.982287i	$0.560000\pi$
$72$	3.28844	+	0.844328i	3.28844	+	0.844328i
$73$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$73$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$74$	3.10969	+	0.392845i	3.10969	+	0.392845i
$75$		0			0
$76$		0			0
$77$	1.60528	+	0.202793i	1.60528	+	0.202793i
$78$		0			0
$79$	1.87631	+	0.481754i	1.87631	+	0.481754i	1.00000			$0$
$79$	1.87631	+	0.481754i	1.87631	+	0.481754i	0.876307	+	0.481754i	$0.160000\pi$
$80$		0			0
$81$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$82$		0			0
$83$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$83$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$84$		0			0
$85$		0			0
$86$	3.28844	−	0.844328i	3.28844	−	0.844328i
$87$		0			0
$88$	1.02936	−	5.39609i	1.02936	−	5.39609i
$89$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$89$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$90$		0			0
$91$		0			0
$92$	3.60322	+	2.61789i	3.60322	+	2.61789i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$97$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$98$	−0.362989	+	1.90285i	−0.362989	+	1.90285i
$99$	−1.41789	+	0.779494i	−1.41789	+	0.779494i
$100$	−2.73091	+	0.344994i	−2.73091	+	0.344994i
$101$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$101$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$102$		0			0
$103$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$103$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$104$		0			0
$105$		0			0
$106$	0.702370	+	1.49261i	0.702370	+	1.49261i
$107$	1.27760	−	1.19975i	1.27760	−	1.19975i	0.309017	−	0.951057i	$-0.400000\pi$
$107$	1.27760	−	1.19975i	1.27760	−	1.19975i	0.968583	−	0.248690i	$-0.0800000\pi$
$108$		0			0
$109$	0.00788530	−	0.125333i	0.00788530	−	0.125333i	−0.992115	−	0.125333i	$-0.960000\pi$
$109$	0.00788530	−	0.125333i	0.00788530	−	0.125333i	1.00000			$0$
$110$		0			0
$111$		0			0
$112$	3.70412	+	0.951057i	3.70412	+	0.951057i
$113$	−0.574633	−	1.76854i	−0.574633	−	1.76854i	−0.637424	−	0.770513i	$-0.720000\pi$
$113$	−0.574633	−	1.76854i	−0.574633	−	1.76854i	0.0627905	−	0.998027i	$-0.480000\pi$
$114$		0			0
$115$		0			0
$116$	−0.751987	+	3.94205i	−0.751987	+	3.94205i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.866986	+	1.36615i	0.866986	+	1.36615i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−0.824805	−	1.75280i	−0.824805	−	1.75280i
$127$	−0.929324	−	0.872693i	−0.929324	−	0.872693i	0.0627905	−	0.998027i	$-0.480000\pi$
$127$	−0.929324	−	0.872693i	−0.929324	−	0.872693i	−0.992115	+	0.125333i	$0.960000\pi$
$128$	1.12432	−	3.46030i	1.12432	−	3.46030i
$129$		0			0
$130$		0			0
$131$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$131$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$132$		0			0
$133$		0			0
$134$	−0.226188	−	0.0895542i	−0.226188	−	0.0895542i
$135$		0			0
$136$		0			0
$137$	−0.200808	+	0.316423i	−0.200808	+	0.316423i	−0.929776	−	0.368125i	$-0.880000\pi$
$137$	−0.200808	+	0.316423i	−0.200808	+	0.316423i	0.728969	+	0.684547i	$0.240000\pi$
$138$		0			0
$139$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$139$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$140$		0			0
$141$		0			0
$142$	1.11236	−	1.75280i	1.11236	−	1.75280i
$143$		0			0
$144$	−3.55571	+	1.40781i	−3.55571	+	1.40781i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−3.90291	+	2.14565i	−3.90291	+	2.14565i
$149$	−0.866986	+	0.629902i	−0.866986	+	0.629902i	−0.929776	−	0.368125i	$-0.880000\pi$
$149$	−0.866986	+	0.629902i	−0.866986	+	0.629902i	0.0627905	+	0.998027i	$0.480000\pi$
$150$		0			0
$151$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$151$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$152$		0			0
$153$		0			0
$154$	−2.74670	+	1.51001i	−2.74670	+	1.51001i
$155$		0			0
$156$		0			0
$157$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$157$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$158$	−3.48909	+	1.38143i	−3.48909	+	1.38143i
$159$		0			0
$160$		0			0
$161$	−0.101597	−	1.61484i	−0.101597	−	1.61484i
$162$	1.69755	+	0.933237i	1.69755	+	0.933237i
$163$	0.159566	+	0.836475i	0.159566	+	0.836475i	0.968583	+	0.248690i	$0.0800000\pi$
$163$	0.159566	+	0.836475i	0.159566	+	0.836475i	−0.809017	+	0.587785i	$0.800000\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$167$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$168$		0			0
$169$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$170$		0			0
$171$		0			0
$172$	−3.07510	+	3.71716i	−3.07510	+	3.71716i
$173$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$173$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$174$		0			0
$175$	0.728969	+	0.684547i	0.728969	+	0.684547i
$176$	2.63463	+	5.59888i	2.63463	+	5.59888i
$177$		0			0
$178$		0			0
$179$	−0.124591	−	1.98031i	−0.124591	−	1.98031i	−0.187381	−	0.982287i	$-0.560000\pi$
$179$	−0.124591	−	1.98031i	−0.124591	−	1.98031i	0.0627905	−	0.998027i	$-0.480000\pi$
$180$		0			0
$181$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$181$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$182$		0			0
$183$		0			0
$184$	−5.49339			−5.49339
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.121636	+	0.0312307i	0.121636	+	0.0312307i	0.309017	−	0.951057i	$-0.400000\pi$
$191$	0.121636	+	0.0312307i	0.121636	+	0.0312307i	−0.187381	+	0.982287i	$0.560000\pi$
$192$		0			0
$193$	−0.0534698	+	0.849878i	−0.0534698	+	0.849878i	0.876307	+	0.481754i	$0.160000\pi$
$193$	−0.0534698	+	0.849878i	−0.0534698	+	0.849878i	−0.929776	+	0.368125i	$0.880000\pi$
$194$		0			0
$195$		0			0
$196$	−1.17201	−	2.49064i	−1.17201	−	2.49064i
$197$	0.598617	+	1.84235i	0.598617	+	1.84235i	0.535827	+	0.844328i	$0.320000\pi$
$197$	0.598617	+	1.84235i	0.598617	+	1.84235i	0.0627905	+	0.998027i	$0.480000\pi$
$198$	1.33456	−	2.83609i	1.33456	−	2.83609i
$199$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$199$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$200$	2.47492	−	2.32411i	2.47492	−	2.32411i
$201$		0			0
$202$		0			0
$203$	1.27760	−	0.702367i	1.27760	−	0.702367i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.03137	+	1.24672i	1.03137	+	1.24672i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.116762	−	0.0462295i	−0.116762	−	0.0462295i	0.309017	−	0.951057i	$-0.400000\pi$
$211$	−0.116762	−	0.0462295i	−0.116762	−	0.0462295i	−0.425779	+	0.904827i	$0.640000\pi$
$212$	−2.05407	−	1.12924i	−2.05407	−	1.12924i
$213$		0			0
$214$	−0.636179	+	3.33497i	−0.636179	+	3.33497i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.130351	+	0.205401i	0.130351	+	0.205401i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$223$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$224$	−3.73132	+	1.47733i	−3.73132	+	1.47733i
$225$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$226$	2.91429	+	2.11736i	2.91429	+	2.11736i
$227$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$227$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$228$		0			0
$229$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$229$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$230$		0			0
$231$		0			0
$232$	−2.10754	−	4.47876i	−2.10754	−	4.47876i
$233$	0.371808	+	1.94908i	0.371808	+	1.94908i	0.309017	+	0.951057i	$0.400000\pi$
$233$	0.371808	+	1.94908i	0.371808	+	1.94908i	0.0627905	+	0.998027i	$0.480000\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.348445	−	1.82662i	0.348445	−	1.82662i	−0.187381	−	0.982287i	$-0.560000\pi$
$239$	0.348445	−	1.82662i	0.348445	−	1.82662i	0.535827	−	0.844328i	$-0.320000\pi$
$240$		0			0
$241$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$241$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$242$	−2.91429	−	1.15385i	−2.91429	−	1.15385i
$243$		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		0.992115	−	0.125333i	$-0.0400000\pi$
$251$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$252$	2.41213	+	1.32608i	2.41213	+	1.32608i
$253$	1.90846	−	1.79217i	1.90846	−	1.79217i
$254$	2.45012	+	0.309522i	2.45012	+	0.309522i
$255$		0			0
$256$	0.957424	+	2.94665i	0.957424	+	2.94665i
$257$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$257$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$258$		0			0
$259$	1.50441	+	0.595638i	1.50441	+	0.595638i
$260$		0			0
$261$	−0.620759	+	1.31918i	−0.620759	+	1.31918i
$262$		0			0
$263$	−1.80113	−	0.462452i	−1.80113	−	0.462452i	−0.809017	−	0.587785i	$-0.800000\pi$
$263$	−1.80113	−	0.462452i	−1.80113	−	0.462452i	−0.992115	+	0.125333i	$0.960000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	0.334816	−	0.0859661i	0.334816	−	0.0859661i
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$		0			0
$271$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$271$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$272$		0			0
$273$		0			0
$274$	−0.0455845	−	0.724545i	−0.0455845	−	0.724545i
$275$	−0.101597	+	1.61484i	−0.101597	+	1.61484i
$276$		0			0
$277$	0.542804	+	1.15352i	0.542804	+	1.15352i	0.968583	+	0.248690i	$0.0800000\pi$
$277$	0.542804	+	1.15352i	0.542804	+	1.15352i	−0.425779	+	0.904827i	$0.640000\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.393950	+	0.476203i	−0.393950	+	0.476203i	−0.929776	−	0.368125i	$-0.880000\pi$
$281$	−0.393950	+	0.476203i	−0.393950	+	0.476203i	0.535827	+	0.844328i	$0.320000\pi$
$282$		0			0
$283$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$283$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$284$	0.185222	+	2.94403i	0.185222	+	2.94403i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	2.15035	−	3.38840i	2.15035	−	3.38840i
$289$	0.728969	+	0.684547i	0.728969	+	0.684547i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$293$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$294$		0			0
$295$		0			0
$296$	2.33897	−	4.97057i	2.33897	−	4.97057i
$297$		0			0
$298$	0.641510	−	1.97437i	0.641510	−	1.97437i
$299$		0			0
$300$		0			0
$301$	1.75261			1.75261
$302$	−1.23480	−	1.49261i	−1.23480	−	1.49261i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$307$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$308$	1.89635	−	4.02994i	1.89635	−	4.02994i
$309$		0			0
$310$		0			0
$311$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$311$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$312$		0			0
$313$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$313$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$314$		0			0
$315$		0			0
$316$	2.85717	−	4.50218i	2.85717	−	4.50218i
$317$	0.0915446	−	1.45506i	0.0915446	−	1.45506i	−0.637424	−	0.770513i	$-0.720000\pi$
$317$	0.0915446	−	1.45506i	0.0915446	−	1.45506i	0.728969	−	0.684547i	$-0.240000\pi$
$318$		0			0
$319$	2.19334	+	0.868403i	2.19334	+	0.868403i
$320$		0			0
$321$		0			0
$322$	1.99794	+	2.41510i	1.99794	+	2.41510i
$323$		0			0
$324$	−2.73091	+	0.344994i	−2.73091	+	0.344994i
$325$		0			0
$326$	−1.20251	−	1.12924i	−1.20251	−	1.12924i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.06320	+	0.134314i	−1.06320	+	0.134314i	−0.637424	−	0.770513i	$-0.720000\pi$
$331$	−1.06320	+	0.134314i	−1.06320	+	0.134314i	−0.425779	+	0.904827i	$0.640000\pi$
$332$		0			0
$333$	−1.56720	+	0.402389i	−1.56720	+	0.402389i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.0702235	−	0.368125i	0.0702235	−	0.368125i	−0.929776	−	0.368125i	$-0.880000\pi$
$337$	0.0702235	−	0.368125i	0.0702235	−	0.368125i	1.00000			$0$
$338$	−1.23480	−	1.49261i	−1.23480	−	1.49261i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$344$	0.373623	−	5.93856i	0.373623	−	5.93856i
$345$		0			0
$346$		0			0
$347$	−0.0534698	−	0.113629i	−0.0534698	−	0.113629i	0.876307	−	0.481754i	$-0.160000\pi$
$347$	−0.0534698	−	0.113629i	−0.0534698	−	0.113629i	−0.929776	+	0.368125i	$0.880000\pi$
$348$		0			0
$349$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$349$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$350$	−1.92189	−	0.242791i	−1.92189	−	0.242791i
$351$		0			0
$352$	−5.69020	−	3.12822i	−5.69020	−	3.12822i
$353$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$353$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	2.45012	+	2.96169i	2.45012	+	2.96169i
$359$	−0.200808	−	1.05267i	−0.200808	−	1.05267i	−0.929776	−	0.368125i	$-0.880000\pi$
$359$	−0.200808	−	1.05267i	−0.200808	−	1.05267i	0.728969	−	0.684547i	$-0.240000\pi$
$360$		0			0
$361$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$367$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$368$	5.00603	−	3.63709i	5.00603	−	3.63709i
$369$		0			0
$370$		0			0
$371$	0.159566	+	0.836475i	0.159566	+	0.836475i
$372$		0			0
$373$	0.348445	−	0.137959i	0.348445	−	0.137959i	−0.187381	−	0.982287i	$-0.560000\pi$
$373$	0.348445	−	0.137959i	0.348445	−	0.137959i	0.535827	+	0.844328i	$0.320000\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.26480	+	0.159781i	1.26480	+	0.159781i	0.728969	−	0.684547i	$-0.240000\pi$
$379$	1.26480	+	0.159781i	1.26480	+	0.159781i	0.535827	+	0.844328i	$0.320000\pi$
$380$		0			0
$381$		0			0
$382$	−0.226188	+	0.0895542i	−0.226188	+	0.0895542i
$383$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$383$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$384$		0			0
$385$		0			0
$386$	−0.883906	−	1.39281i	−0.883906	−	1.39281i
$387$	−1.41789	+	1.03016i	−1.41789	+	1.03016i
$388$		0			0
$389$	0.303189	−	0.220280i	0.303189	−	0.220280i	−0.425779	−	0.904827i	$-0.640000\pi$
$389$	0.303189	−	0.220280i	0.303189	−	0.220280i	0.728969	+	0.684547i	$0.240000\pi$
$390$		0			0
$391$		0			0
$392$	2.97515	+	1.63560i	2.97515	+	1.63560i
$393$		0			0
$394$	−3.03593	−	2.20573i	−3.03593	−	2.20573i
$395$		0			0
$396$	0.834563	+	4.37493i	0.834563	+	4.37493i
$397$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$397$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$398$		0			0
$399$		0			0
$400$	−0.716596	+	3.75653i	−0.716596	+	3.75653i
$401$	1.75261	−	0.963507i	1.75261	−	0.963507i	0.876307	−	0.481754i	$-0.160000\pi$
$401$	1.75261	−	0.963507i	1.75261	−	0.963507i	0.876307	−	0.481754i	$-0.160000\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−1.20251	+	2.55547i	−1.20251	+	2.55547i
$407$	0.809017	+	2.48990i	0.809017	+	2.48990i
$408$		0			0
$409$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$409$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−3.03593	−	0.779494i	−3.03593	−	0.779494i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$419$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$420$		0			0
$421$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$421$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$422$	0.235629	−	0.0604991i	0.235629	−	0.0604991i
$423$		0			0
$424$	2.86833	−	0.362355i	2.86833	−	0.362355i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−2.05407	−	4.36513i	−2.05407	−	4.36513i
$429$		0			0
$430$		0			0
$431$	0.371808	−	0.0469702i	0.371808	−	0.0469702i	0.0627905	−	0.998027i	$-0.480000\pi$
$431$	0.371808	−	0.0469702i	0.371808	−	0.0469702i	0.309017	+	0.951057i	$0.400000\pi$
$432$		0			0
$433$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$433$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$434$		0			0
$435$		0			0
$436$	−0.321401	−	0.127252i	−0.321401	−	0.127252i
$437$		0			0
$438$		0			0
$439$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$439$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$440$		0			0
$441$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$442$		0			0
$443$	0.0388067	+	0.616814i	0.0388067	+	0.616814i	0.968583	+	0.248690i	$0.0800000\pi$
$443$	0.0388067	+	0.616814i	0.0388067	+	0.616814i	−0.929776	+	0.368125i	$0.880000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	2.11643	−	3.33497i	2.11643	−	3.33497i
$449$	−0.613161	+	1.88711i	−0.613161	+	1.88711i	−0.187381	+	0.982287i	$0.560000\pi$
$449$	−0.613161	+	1.88711i	−0.613161	+	1.88711i	−0.425779	+	0.904827i	$0.640000\pi$
$450$	1.69755	−	0.933237i	1.69755	−	0.933237i
$451$		0			0
$452$	−5.11863			−5.11863
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.598617	−	1.84235i	0.598617	−	1.84235i	0.0627905	−	0.998027i	$-0.480000\pi$
$457$	0.598617	−	1.84235i	0.598617	−	1.84235i	0.535827	−	0.844328i	$-0.320000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$461$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$462$		0			0
$463$	0.121636	+	1.93334i	0.121636	+	1.93334i	0.309017	+	0.951057i	$0.400000\pi$
$463$	0.121636	+	1.93334i	0.121636	+	1.93334i	−0.187381	+	0.982287i	$0.560000\pi$
$464$	4.88588	+	2.68604i	4.88588	+	2.68604i
$465$		0			0
$466$	−2.80200	−	2.63125i	−2.80200	−	2.63125i
$467$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$467$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$468$		0			0
$469$	−0.101597	−	0.0738147i	−0.101597	−	0.0738147i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.80760	+	2.18501i	1.80760	+	2.18501i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.620759	−	0.582932i	−0.620759	−	0.582932i
$478$	1.53377	+	3.25943i	1.53377	+	3.25943i
$479$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$479$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	4.31390	−	1.10762i	4.31390	−	1.10762i
$485$		0			0
$486$		0			0
$487$	1.41213	−	0.362574i	1.41213	−	0.362574i	0.535827	−	0.844328i	$-0.320000\pi$
$487$	1.41213	−	0.362574i	1.41213	−	0.362574i	0.876307	+	0.481754i	$0.160000\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	0.876307	−	0.481754i	$-0.160000\pi$
$491$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	−0.992115	+	0.125333i	$0.960000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.781202	−	0.733597i	0.781202	−	0.733597i
$498$		0			0
$499$	−0.263146	−	0.809880i	−0.263146	−	0.809880i	−0.992115	−	0.125333i	$-0.960000\pi$
$499$	−0.263146	−	0.809880i	−0.263146	−	0.809880i	0.728969	−	0.684547i	$-0.240000\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$503$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$504$	−3.36833	+	0.425519i	−3.36833	+	0.425519i
$505$		0			0
$506$	−0.950317	+	4.98174i	−0.950317	+	4.98174i
$507$		0			0
$508$	−3.07510	+	1.69055i	−3.07510	+	1.69055i
$509$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$509$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$510$		0			0
$511$		0			0
$512$	−1.91213	−	1.38925i	−1.91213	−	1.38925i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−3.03593	+	0.779494i	−3.03593	+	0.779494i
$519$		0			0
$520$		0			0
$521$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$521$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$522$	−0.529215	−	2.77424i	−0.529215	−	2.77424i
$523$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$523$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$524$		0			0
$525$		0			0
$526$	3.34930	−	1.32608i	3.34930	−	1.32608i
$527$		0			0
$528$		0			0
$529$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−0.271772	+	0.328517i	−0.271772	+	0.328517i
$537$		0			0
$538$		0			0
$539$	−1.56720	+	0.402389i	−1.56720	+	0.402389i
$540$		0			0
$541$	0.348445	−	1.82662i	0.348445	−	1.82662i	−0.187381	−	0.982287i	$-0.560000\pi$
$541$	0.348445	−	1.82662i	0.348445	−	1.82662i	0.535827	−	0.844328i	$-0.320000\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.362989	−	1.90285i	−0.362989	−	1.90285i	−0.425779	−	0.904827i	$-0.640000\pi$
$547$	−0.362989	−	1.90285i	−0.362989	−	1.90285i	0.0627905	−	0.998027i	$-0.480000\pi$
$548$	0.657552	+	0.794843i	0.657552	+	0.794843i
$549$		0			0
$550$	−1.67950	−	2.64646i	−1.67950	−	2.64646i
$551$		0			0
$552$		0			0
$553$	−1.92189	+	0.242791i	−1.92189	+	0.242791i
$554$	−2.16412	−	1.18974i	−2.16412	−	1.18974i
$555$		0			0
$556$		0			0
$557$	0.362576	−	0.770513i	0.362576	−	0.770513i	−0.637424	−	0.770513i	$-0.720000\pi$
$557$	0.362576	−	0.770513i	0.362576	−	0.770513i	1.00000			$0$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.0751750	−	1.19487i	0.0751750	−	1.19487i
$563$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$563$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.728969	+	0.684547i	0.728969	+	0.684547i
$568$	−2.31919	−	2.80342i	−2.31919	−	2.80342i
$569$	0.371808	−	1.94908i	0.371808	−	1.94908i	0.0627905	−	0.998027i	$-0.480000\pi$
$569$	0.371808	−	1.94908i	0.371808	−	1.94908i	0.309017	−	0.951057i	$-0.400000\pi$
$570$		0			0
$571$	−1.27485			−1.27485			−0.637424	−	0.770513i	$-0.720000\pi$
$571$	−1.27485			−1.27485			−0.637424	+	0.770513i	$0.720000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.60528	−	0.202793i	1.60528	−	0.202793i
$576$	0.248013	+	3.94205i	0.248013	+	3.94205i
$577$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$577$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$578$	−1.92189	−	0.242791i	−1.92189	−	0.242791i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.878275	+	1.06165i	−0.878275	+	1.06165i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$587$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.15948	+	6.07819i	1.15948	+	6.07819i
$593$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$593$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$594$		0			0
$595$		0			0
$596$	0.911553	+	2.80547i	0.911553	+	2.80547i
$597$		0			0
$598$		0			0
$599$	0.781202	−	1.23098i	0.781202	−	1.23098i	−0.187381	−	0.982287i	$-0.560000\pi$
$599$	0.781202	−	1.23098i	0.781202	−	1.23098i	0.968583	−	0.248690i	$-0.0800000\pi$
$600$		0			0
$601$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$601$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$602$	−2.74670	+	1.99559i	−2.74670	+	1.99559i
$603$	0.125581			0.125581
$604$	2.66613	+	0.684547i	2.66613	+	0.684547i
$605$		0			0
$606$		0			0
$607$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$607$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.200808	+	0.316423i	−0.200808	+	0.316423i	−0.929776	−	0.368125i	$-0.880000\pi$
$613$	−0.200808	+	0.316423i	−0.200808	+	0.316423i	0.728969	+	0.684547i	$0.240000\pi$
$614$		0			0
$615$		0			0
$616$	1.02936	+	5.39609i	1.02936	+	5.39609i
$617$	−1.17950	−	1.10762i	−1.17950	−	1.10762i	−0.992115	−	0.125333i	$-0.960000\pi$
$617$	−1.17950	−	1.10762i	−1.17950	−	1.10762i	−0.187381	−	0.982287i	$-0.560000\pi$
$618$		0			0
$619$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$619$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.0388067	−	0.616814i	0.0388067	−	0.616814i	−0.929776	−	0.368125i	$-0.880000\pi$
$631$	0.0388067	−	0.616814i	0.0388067	−	0.616814i	0.968583	−	0.248690i	$-0.0800000\pi$
$632$	0.412966	+	6.56390i	0.412966	+	6.56390i
$633$		0			0
$634$	1.51332	+	2.38461i	1.51332	+	2.38461i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−4.42619	+	1.13645i	−4.42619	+	1.13645i
$639$	−0.200808	+	1.05267i	−0.200808	+	1.05267i
$640$		0			0
$641$	0.0915446	+	0.0859661i	0.0915446	+	0.0859661i	0.728969	−	0.684547i	$-0.240000\pi$
$641$	0.0915446	+	0.0859661i	0.0915446	+	0.0859661i	−0.637424	+	0.770513i	$0.720000\pi$
$642$		0			0
$643$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$643$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$644$	−4.31390	−	1.10762i	−4.31390	−	1.10762i
$645$		0			0
$646$		0			0
$647$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$647$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$648$	2.47492	−	2.32411i	2.47492	−	2.32411i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	2.32553	+	0.293783i	2.32553	+	0.293783i
$653$	1.06279	−	0.998027i	1.06279	−	0.998027i	0.0627905	−	0.998027i	$-0.480000\pi$
$653$	1.06279	−	0.998027i	1.06279	−	0.998027i	1.00000			$0$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.73879	+	0.955910i	−1.73879	+	0.955910i	−0.809017	+	0.587785i	$0.800000\pi$
$659$	−1.73879	+	0.955910i	−1.73879	+	0.955910i	−0.929776	+	0.368125i	$0.880000\pi$
$660$		0			0
$661$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$661$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$662$	1.51332	−	1.42110i	1.51332	−	1.42110i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	1.99794	−	2.41510i	1.99794	−	2.41510i
$667$	0.442031	−	2.31721i	0.442031	−	2.31721i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.238883	+	1.25227i	0.238883	+	1.25227i	0.876307	+	0.481754i	$0.160000\pi$
$673$	0.238883	+	1.25227i	0.238883	+	1.25227i	−0.637424	+	0.770513i	$0.720000\pi$
$674$	0.309106	+	0.656884i	0.309106	+	0.656884i
$675$		0			0
$676$	2.66613	+	0.684547i	2.66613	+	0.684547i
$677$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$677$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.23480	−	0.317042i	−1.23480	−	0.317042i	−0.425779	−	0.904827i	$-0.640000\pi$
$683$	−1.23480	−	0.317042i	−1.23480	−	0.317042i	−0.809017	+	0.587785i	$0.800000\pi$
$684$		0			0
$685$		0			0
$686$	−0.362989	−	1.90285i	−0.362989	−	1.90285i
$687$		0			0
$688$	3.59136	+	5.65908i	3.59136	+	5.65908i
$689$		0			0
$690$		0			0
$691$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$691$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$692$		0			0
$693$	1.03137	−	1.24672i	1.03137	−	1.24672i
$694$	0.213180	+	0.117197i	0.213180	+	0.117197i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	2.41213	−	1.32608i	2.41213	−	1.32608i
$701$	0.574221	+	0.904827i	0.574221	+	0.904827i	1.00000			$0$
$701$	0.574221	+	0.904827i	0.574221	+	0.904827i	−0.425779	+	0.904827i	$0.640000\pi$
$702$		0			0
$703$		0			0
$704$	6.34059	−	0.801003i	6.34059	−	0.801003i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	0.876307	−	0.481754i	$-0.160000\pi$
$709$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	−0.992115	+	0.125333i	$0.960000\pi$
$710$		0			0
$711$	1.41213	−	1.32608i	1.41213	−	1.32608i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−5.29022	−	1.35830i	−5.29022	−	1.35830i
$717$		0			0
$718$	1.51332	+	1.42110i	1.51332	+	1.42110i
$719$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$719$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$720$		0			0
$721$		0			0
$722$	1.93717			1.93717
$723$		0			0
$724$		0			0
$725$	0.781202	+	1.23098i	0.781202	+	1.23098i
$726$		0			0
$727$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$727$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$728$		0			0
$729$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$733$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$734$		0			0
$735$		0			0
$736$	−2.00657	+	6.17558i	−2.00657	+	6.17558i
$737$	−0.0127587	−	0.202793i	−0.0127587	−	0.202793i
$738$		0			0
$739$	−1.17950	−	0.856954i	−1.17950	−	0.856954i	−0.187381	−	0.982287i	$-0.560000\pi$
$739$	−1.17950	−	0.856954i	−1.17950	−	0.856954i	−0.992115	+	0.125333i	$0.960000\pi$
$740$		0			0
$741$		0			0
$742$	−1.20251	−	1.12924i	−1.20251	−	1.12924i
$743$	−0.328407	−	1.72157i	−0.328407	−	1.72157i	−0.637424	−	0.770513i	$-0.720000\pi$
$743$	−0.328407	−	1.72157i	−0.328407	−	1.72157i	0.309017	−	0.951057i	$-0.400000\pi$
$744$		0			0
$745$		0			0
$746$	−0.388998	+	0.612963i	−0.388998	+	0.612963i
$747$		0			0
$748$		0			0
$749$	−0.746226	+	1.58581i	−0.746226	+	1.58581i
$750$		0			0
$751$	−0.613161	+	1.88711i	−0.613161	+	1.88711i	−0.187381	+	0.982287i	$0.560000\pi$
$751$	−0.613161	+	1.88711i	−0.613161	+	1.88711i	−0.425779	+	0.904827i	$0.640000\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.50441	−	1.09302i	1.50441	−	1.09302i	0.535827	−	0.844328i	$-0.320000\pi$
$757$	1.50441	−	1.09302i	1.50441	−	1.09302i	0.968583	−	0.248690i	$-0.0800000\pi$
$758$	−2.16412	+	1.18974i	−2.16412	+	1.18974i
$759$		0			0
$760$		0			0
$761$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$761$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$762$		0			0
$763$	0.0388067	+	0.119435i	0.0388067	+	0.119435i
$764$	0.185222	−	0.291864i	0.185222	−	0.291864i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$769$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$770$		0			0
$771$		0			0
$772$	2.17941	+	0.862888i	2.17941	+	0.862888i
$773$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$773$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$774$	1.04914	−	3.22894i	1.04914	−	3.22894i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.224339	+	0.690446i	−0.224339	+	0.690446i
$779$		0			0
$780$		0			0
$781$	1.72030	+	0.217324i	1.72030	+	0.217324i
$782$		0			0
$783$		0			0
$784$	−3.79411	+	0.479308i	−3.79411	+	0.479308i
$785$		0			0
$786$		0			0
$787$		0			0		1.00000			$0$
$787$		0			0		−1.00000			$\pi$
$788$	5.33227			5.33227
$789$		0			0
$790$		0			0
$791$	1.18532	+	1.43281i	1.18532	+	1.43281i
$792$	−4.00451	−	3.76049i	−4.00451	−	3.76049i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$797$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$798$		0			0
$799$		0			0
$800$	−1.70871	−	3.63120i	−1.70871	−	3.63120i
$801$		0			0
$802$	−1.64961	+	3.50560i	−1.64961	+	3.50560i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.781202	+	1.23098i	0.781202	+	1.23098i	0.968583	+	0.248690i	$0.0800000\pi$
$809$	0.781202	+	1.23098i	0.781202	+	1.23098i	−0.187381	+	0.982287i	$0.560000\pi$
$810$		0			0
$811$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$811$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$812$	−0.751987	−	3.94205i	−0.751987	−	3.94205i
$813$		0			0
$814$	−4.10298	−	2.98099i	−4.10298	−	2.98099i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.17950	+	0.856954i	−1.17950	+	0.856954i	−0.992115	−	0.125333i	$-0.960000\pi$
$821$	−1.17950	+	0.856954i	−1.17950	+	0.856954i	−0.187381	+	0.982287i	$0.560000\pi$
$822$		0			0
$823$	−0.683098	+	0.825723i	−0.683098	+	0.825723i	−0.992115	−	0.125333i	$-0.960000\pi$
$823$	−0.683098	+	0.825723i	−0.683098	+	0.825723i	0.309017	+	0.951057i	$0.400000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.824805	−	0.211774i	−0.824805	−	0.211774i	−0.187381	−	0.982287i	$-0.560000\pi$
$827$	−0.824805	−	0.211774i	−0.824805	−	0.211774i	−0.637424	+	0.770513i	$0.720000\pi$
$828$	4.14106	−	1.63956i	4.14106	−	1.63956i
$829$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$829$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$830$		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		−0.535827	−	0.844328i	$-0.680000\pi$
$839$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$840$		0			0
$841$	1.09022	−	0.279921i	1.09022	−	0.279921i
$842$	−0.968583	+	0.703717i	−0.968583	+	0.703717i
$843$		0			0
$844$	−0.220342	+	0.266348i	−0.220342	+	0.266348i
$845$		0			0
$846$		0			0
$847$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$848$	−2.37395	+	2.22929i	−2.37395	+	2.22929i
$849$		0			0
$850$		0			0
$851$	2.29420	−	1.26125i	2.29420	−	1.26125i
$852$		0			0
$853$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$853$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$854$		0			0
$855$		0			0
$856$	5.21429	+	2.86658i	5.21429	+	2.86658i
$857$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$857$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$858$		0			0
$859$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$859$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$860$		0			0
$861$		0			0
$862$	−0.529215	+	0.496966i	−0.529215	+	0.496966i
$863$	−1.80113	−	0.713118i	−1.80113	−	0.713118i	−0.992115	−	0.125333i	$-0.960000\pi$
$863$	−1.80113	−	0.713118i	−1.80113	−	0.713118i	−0.809017	−	0.587785i	$-0.800000\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.28488	−	2.14565i	−2.28488	−	2.14565i
$870$		0			0
$871$		0			0
$872$	0.412966	−	0.106032i	0.412966	−	0.106032i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.06320	+	0.134314i	−1.06320	+	0.134314i	−0.637424	−	0.770513i	$-0.720000\pi$
$877$	−1.06320	+	0.134314i	−1.06320	+	0.134314i	−0.425779	+	0.904827i	$0.640000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$881$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$882$	1.41213	+	1.32608i	1.41213	+	1.32608i
$883$	−0.574633	+	1.76854i	−0.574633	+	1.76854i	0.0627905	+	0.998027i	$0.480000\pi$
$883$	−0.574633	+	1.76854i	−0.574633	+	1.76854i	−0.637424	+	0.770513i	$0.720000\pi$
$884$		0			0
$885$		0			0
$886$	−0.763146	−	0.922485i	−0.763146	−	0.922485i
$887$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$887$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$888$		0			0
$889$	1.18532	+	0.469303i	1.18532	+	0.469303i
$890$		0			0
$891$	−0.101597	+	1.61484i	−0.101597	+	1.61484i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.228455	+	3.63120i	0.228455	+	3.63120i
$897$		0			0
$898$	−1.18779	−	3.65565i	−1.18779	−	3.65565i
$899$		0			0
$900$	−1.17201	+	2.49064i	−1.17201	+	2.49064i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	5.10763	−	3.71091i	5.10763	−	3.71091i
$905$		0			0
$906$		0			0
$907$	−1.98423			−1.98423			−0.992115	−	0.125333i	$-0.960000\pi$
$907$	−1.98423			−1.98423			−0.992115	+	0.125333i	$0.960000\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.456288	+	0.718995i	−0.456288	+	0.718995i	−0.992115	−	0.125333i	$-0.960000\pi$
$911$	−0.456288	+	0.718995i	−0.456288	+	0.718995i	0.535827	+	0.844328i	$0.320000\pi$
$912$		0			0
$913$		0			0
$914$	1.15962	+	3.56895i	1.15962	+	3.56895i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	1.45794	+	1.36909i	1.45794	+	1.36909i	0.728969	+	0.684547i	$0.240000\pi$
$919$	1.45794	+	1.36909i	1.45794	+	1.36909i	0.728969	+	0.684547i	$0.240000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$926$	−2.39201	−	2.89144i	−2.39201	−	2.89144i
$927$		0			0
$928$	−5.80477	+	0.733313i	−5.80477	+	0.733313i
$929$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$929$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$930$		0			0
$931$		0			0
$932$	5.41875	+	0.684547i	5.41875	+	0.684547i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$937$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$938$	0.243271			0.243271
$939$		0			0
$940$		0			0
$941$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$941$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−5.32081	−	1.36615i	−5.32081	−	1.36615i
$947$	0.542804	−	1.15352i	0.542804	−	1.15352i	−0.425779	−	0.904827i	$-0.640000\pi$
$947$	0.542804	−	1.15352i	0.542804	−	1.15352i	0.968583	−	0.248690i	$-0.0800000\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.159566	−	0.339095i	0.159566	−	0.339095i	−0.809017	−	0.587785i	$-0.800000\pi$
$953$	0.159566	−	0.339095i	0.159566	−	0.339095i	0.968583	+	0.248690i	$0.0800000\pi$
$954$	1.63660	+	0.206751i	1.63660	+	0.206751i
$955$		0			0
$956$	−4.48549	−	2.46592i	−4.48549	−	2.46592i
$957$		0			0
$958$		0			0
$959$	0.0702235	−	0.368125i	0.0702235	−	0.368125i
$960$		0			0
$961$	0.876307	−	0.481754i	0.876307	−	0.481754i
$962$		0			0
$963$	−0.328407	−	1.72157i	−0.328407	−	1.72157i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1.73879	−	0.955910i	−1.73879	−	0.955910i	−0.929776	−	0.368125i	$-0.880000\pi$
$967$	−1.73879	−	0.955910i	−1.73879	−	0.955910i	−0.809017	−	0.587785i	$-0.800000\pi$
$968$	−3.50162	+	4.23273i	−3.50162	+	4.23273i
$969$		0			0
$970$		0			0
$971$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$971$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$972$		0			0
$973$		0			0
$974$	−1.80026	+	2.17614i	−1.80026	+	2.17614i
$975$		0			0
$976$		0			0
$977$	1.72897	−	0.684547i	1.72897	−	0.684547i	0.728969	−	0.684547i	$-0.240000\pi$
$977$	1.72897	−	0.684547i	1.72897	−	0.684547i	1.00000			$0$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−0.101597	−	0.0738147i	−0.101597	−	0.0738147i
$982$	0.587328	+	0.426719i	0.587328	+	0.426719i
$983$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$983$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.80760	−	2.18501i	1.80760	−	2.18501i
$990$		0			0
$991$	1.60528	−	1.16630i	1.60528	−	1.16630i	0.728969	−	0.684547i	$-0.240000\pi$
$991$	1.60528	−	1.16630i	1.60528	−	1.16630i	0.876307	−	0.481754i	$-0.160000\pi$
$992$		0			0
$993$		0			0
$994$	−0.388998	+	2.03920i	−0.388998	+	2.03920i
$995$		0			0
$996$		0			0
$997$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$997$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$998$	1.33456	+	0.969617i	1.33456	+	0.969617i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1057.1.bq.a.1000.1	yes	20
7.6	odd	2	CM	1057.1.bq.a.1000.1	yes	20
151.98	even	25	inner	1057.1.bq.a.853.1	✓	20
1057.853	odd	50	inner	1057.1.bq.a.853.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1057.1.bq.a.853.1	✓	20	151.98	even	25	inner
1057.1.bq.a.853.1	✓	20	1057.853	odd	50	inner
1057.1.bq.a.1000.1	yes	20	1.1	even	1	trivial
1057.1.bq.a.1000.1	yes	20	7.6	odd	2	CM

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:	\( N \)	\(=\)	\( 1057 = 7 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1057.bq (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.56720 + 1.13864i) q^{2} +(0.850604 - 2.61789i) q^{4} +(-0.929776 + 0.368125i) q^{7} +(1.04914 + 3.22894i) q^{8} +(0.535827 - 0.844328i) q^{9} +O(q^{10})\)	\(q+(-1.56720 + 1.13864i) q^{2} +(0.850604 - 2.61789i) q^{4} +(-0.929776 + 0.368125i) q^{7} +(1.04914 + 3.22894i) q^{8} +(0.535827 - 0.844328i) q^{9} +(-1.41789 - 0.779494i) q^{11} +(1.03799 - 1.63560i) q^{14} +(-3.09390 - 2.24785i) q^{16} +(0.121636 + 1.93334i) q^{18} +(3.10969 - 0.392845i) q^{22} +(-0.500000 + 1.53884i) q^{23} +(-0.425779 - 0.904827i) q^{25} +(0.172838 + 2.74718i) q^{28} +(-1.44644 + 0.182728i) q^{29} +4.01314 q^{32} +(-1.75458 - 2.12093i) q^{36} +(-1.17950 - 1.10762i) q^{37} +(-1.62954 - 0.645180i) q^{43} +(-3.24670 + 3.04885i) q^{44} +(-0.968583 - 2.98099i) q^{46} +(0.728969 - 0.684547i) q^{49} +(1.69755 + 0.933237i) q^{50} +(0.159566 - 0.836475i) q^{53} +(-2.16412 - 2.61597i) q^{56} +(2.05880 - 1.93334i) q^{58} +(-0.187381 + 0.982287i) q^{63} +(-3.19549 + 2.32166i) q^{64} +(0.0672897 + 0.106032i) q^{67} +(-0.996398 + 0.394502i) q^{71} +(3.28844 + 0.844328i) q^{72} +(3.10969 + 0.392845i) q^{74} +(1.60528 + 0.202793i) q^{77} +(1.87631 + 0.481754i) q^{79} +(-0.425779 - 0.904827i) q^{81} +(3.28844 - 0.844328i) q^{86} +(1.02936 - 5.39609i) q^{88} +(3.60322 + 2.61789i) q^{92} +(-0.362989 + 1.90285i) q^{98} +(-1.41789 + 0.779494i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{4}+O(q^{10}) \) 20 * q - 5 * q^4	\( 20 q - 5 q^{4} - 5 q^{14} - 5 q^{16} - 5 q^{18} - 10 q^{23} - 5 q^{29} - 10 q^{32} - 10 q^{44} - 5 q^{53} - 5 q^{56} - 5 q^{58} - 5 q^{64} - 5 q^{67} - 5 q^{71} + 20 q^{72} + 20 q^{79} + 20 q^{86} + 15 q^{88} + 15 q^{92}+O(q^{100}) \) 20 * q - 5 * q^4 - 5 * q^14 - 5 * q^16 - 5 * q^18 - 10 * q^23 - 5 * q^29 - 10 * q^32 - 10 * q^44 - 5 * q^53 - 5 * q^56 - 5 * q^58 - 5 * q^64 - 5 * q^67 - 5 * q^71 + 20 * q^72 + 20 * q^79 + 20 * q^86 + 15 * q^88 + 15 * q^92

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