LMFDB - Embedded newform 1057.1.bq.a.846.1

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			846.1
Root			$0.929776 - 0.368125i$ of defining polynomial
Character	$\chi$	$=$	1057.846
Dual form			1057.1.bq.a.531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.541587 + 1.66683i) q^{2} +(-1.67600 + 1.21769i) q^{4} +(0.728969 + 0.684547i) q^{7} +(-1.51949 - 1.10397i) q^{8} +(-0.425779 + 0.904827i) q^{9} +O(q^{10})$	\(q+(0.541587 + 1.66683i) q^{2} +(-1.67600 + 1.21769i) q^{4} +(0.728969 + 0.684547i) q^{7} +(-1.51949 - 1.10397i) q^{8} +(-0.425779 + 0.904827i) q^{9} +(0.331159 - 0.521823i) q^{11} +(-0.746226 + 1.58581i) q^{14} +(0.377030 - 1.16038i) q^{16} +(-1.73879 - 0.219661i) q^{18} +(1.04914 + 0.269375i) q^{22} +(-0.500000 + 0.363271i) q^{23} +(-0.637424 - 0.770513i) q^{25} +(-2.05532 - 0.259647i) q^{28} +(0.121636 + 0.0312307i) q^{29} +0.260160 q^{32} +(-0.388189 - 2.03496i) q^{36} +(0.0388067 - 0.616814i) q^{37} +(0.781202 - 0.733597i) q^{43} +(0.0803940 + 1.27783i) q^{44} +(-0.876307 - 0.636674i) q^{46} +(0.0627905 + 0.998027i) q^{49} +(0.939097 - 1.47978i) q^{50} +(1.18532 - 0.469303i) q^{53} +(-0.351939 - 1.84493i) q^{56} +(0.0138199 + 0.219661i) q^{58} +(-0.929776 + 0.368125i) q^{63} +(-0.236131 - 0.726735i) q^{64} +(0.844844 + 1.79538i) q^{67} +(-0.620759 - 0.582932i) q^{71} +(1.64587 - 0.904827i) q^{72} +(1.04914 - 0.269375i) q^{74} +(0.598617 - 0.153699i) q^{77} +(1.53583 - 0.844328i) q^{79} +(-0.637424 - 0.770513i) q^{81} +(1.64587 + 0.904827i) q^{86} +(-1.07927 + 0.427315i) q^{88} +(0.395651 - 1.21769i) q^{92} +(-1.62954 + 0.645180i) q^{98} +(0.331159 + 0.521823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1057\mathbb{Z}\right)^\times$.

$n$	$605$	$610$
$\chi(n)$	$-1$	$e\left(\frac{18}{25}\right)$

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 $

$2$	0.541587	+	1.66683i	0.541587	+	1.66683i	0.728969	+	0.684547i	$0.240000\pi$
$2$	0.541587	+	1.66683i	0.541587	+	1.66683i	−0.187381	+	0.982287i	$0.560000\pi$
$3$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$3$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$4$	−1.67600	+	1.21769i	−1.67600	+	1.21769i
$5$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$5$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$6$		0			0
$7$	0.728969	+	0.684547i	0.728969	+	0.684547i
$7$	0.728969	+	0.684547i	0.728969	+	0.684547i
$8$	−1.51949	−	1.10397i	−1.51949	−	1.10397i
$9$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$10$		0			0
$11$	0.331159	−	0.521823i	0.331159	−	0.521823i	−0.637424	−	0.770513i	$-0.720000\pi$
$11$	0.331159	−	0.521823i	0.331159	−	0.521823i	0.968583	+	0.248690i	$0.0800000\pi$
$12$		0			0
$13$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$13$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$14$	−0.746226	+	1.58581i	−0.746226	+	1.58581i
$15$		0			0
$16$	0.377030	−	1.16038i	0.377030	−	1.16038i
$17$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$17$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$18$	−1.73879	−	0.219661i	−1.73879	−	0.219661i
$19$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$19$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$20$		0			0
$21$		0			0
$22$	1.04914	+	0.269375i	1.04914	+	0.269375i
$23$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$23$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$24$		0			0
$25$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$26$		0			0
$27$		0			0
$28$	−2.05532	−	0.259647i	−2.05532	−	0.259647i
$29$	0.121636	+	0.0312307i	0.121636	+	0.0312307i	0.309017	−	0.951057i	$-0.400000\pi$
$29$	0.121636	+	0.0312307i	0.121636	+	0.0312307i	−0.187381	+	0.982287i	$0.560000\pi$
$30$		0			0
$31$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$31$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$32$	0.260160			0.260160
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.388189	−	2.03496i	−0.388189	−	2.03496i
$37$	0.0388067	−	0.616814i	0.0388067	−	0.616814i	−0.929776	−	0.368125i	$-0.880000\pi$
$37$	0.0388067	−	0.616814i	0.0388067	−	0.616814i	0.968583	−	0.248690i	$-0.0800000\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$41$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$42$		0			0
$43$	0.781202	−	0.733597i	0.781202	−	0.733597i	−0.187381	−	0.982287i	$-0.560000\pi$
$43$	0.781202	−	0.733597i	0.781202	−	0.733597i	0.968583	+	0.248690i	$0.0800000\pi$
$44$	0.0803940	+	1.27783i	0.0803940	+	1.27783i
$45$		0			0
$46$	−0.876307	−	0.636674i	−0.876307	−	0.636674i
$47$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$47$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$48$		0			0
$49$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$50$	0.939097	−	1.47978i	0.939097	−	1.47978i
$51$		0			0
$52$		0			0
$53$	1.18532	−	0.469303i	1.18532	−	0.469303i	0.309017	−	0.951057i	$-0.400000\pi$
$53$	1.18532	−	0.469303i	1.18532	−	0.469303i	0.876307	+	0.481754i	$0.160000\pi$
$54$		0			0
$55$		0			0
$56$	−0.351939	−	1.84493i	−0.351939	−	1.84493i
$57$		0			0
$58$	0.0138199	+	0.219661i	0.0138199	+	0.219661i
$59$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$59$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$60$		0			0
$61$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$61$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$62$		0			0
$63$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$64$	−0.236131	−	0.726735i	−0.236131	−	0.726735i
$65$		0			0
$66$		0			0
$67$	0.844844	+	1.79538i	0.844844	+	1.79538i	0.535827	+	0.844328i	$0.320000\pi$
$67$	0.844844	+	1.79538i	0.844844	+	1.79538i	0.309017	+	0.951057i	$0.400000\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.620759	−	0.582932i	−0.620759	−	0.582932i	0.309017	−	0.951057i	$-0.400000\pi$
$71$	−0.620759	−	0.582932i	−0.620759	−	0.582932i	−0.929776	+	0.368125i	$0.880000\pi$
$72$	1.64587	−	0.904827i	1.64587	−	0.904827i
$73$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$73$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$74$	1.04914	−	0.269375i	1.04914	−	0.269375i
$75$		0			0
$76$		0			0
$77$	0.598617	−	0.153699i	0.598617	−	0.153699i
$78$		0			0
$79$	1.53583	−	0.844328i	1.53583	−	0.844328i	0.535827	−	0.844328i	$-0.320000\pi$
$79$	1.53583	−	0.844328i	1.53583	−	0.844328i	1.00000			$0$
$80$		0			0
$81$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$82$		0			0
$83$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$83$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$84$		0			0
$85$		0			0
$86$	1.64587	+	0.904827i	1.64587	+	0.904827i
$87$		0			0
$88$	−1.07927	+	0.427315i	−1.07927	+	0.427315i
$89$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$89$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$90$		0			0
$91$		0			0
$92$	0.395651	−	1.21769i	0.395651	−	1.21769i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$97$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$98$	−1.62954	+	0.645180i	−1.62954	+	0.645180i
$99$	0.331159	+	0.521823i	0.331159	+	0.521823i
$100$	2.00657	+	0.515199i	2.00657	+	0.515199i
$101$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$101$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$102$		0			0
$103$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$103$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$104$		0			0
$105$		0			0
$106$	1.42421	+	1.72157i	1.42421	+	1.72157i
$107$	0.0672897	+	1.06954i	0.0672897	+	1.06954i	0.876307	+	0.481754i	$0.160000\pi$
$107$	0.0672897	+	1.06954i	0.0672897	+	1.06954i	−0.809017	+	0.587785i	$0.800000\pi$
$108$		0			0
$109$	1.96858	−	0.248690i	1.96858	−	0.248690i	0.968583	−	0.248690i	$-0.0800000\pi$
$109$	1.96858	−	0.248690i	1.96858	−	0.248690i	1.00000			$0$
$110$		0			0
$111$		0			0
$112$	1.06918	−	0.587785i	1.06918	−	0.587785i
$113$	−1.17950	−	0.856954i	−1.17950	−	0.856954i	−0.187381	−	0.982287i	$-0.560000\pi$
$113$	−1.17950	−	0.856954i	−1.17950	−	0.856954i	−0.992115	+	0.125333i	$0.960000\pi$
$114$		0			0
$115$		0			0
$116$	−0.241891	+	0.0957714i	−0.241891	+	0.0957714i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.263146	+	0.559214i	0.263146	+	0.559214i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−1.11716	−	1.35041i	−1.11716	−	1.35041i
$127$	−0.0235315	+	0.374023i	−0.0235315	+	0.374023i	0.968583	+	0.248690i	$0.0800000\pi$
$127$	−0.0235315	+	0.374023i	−0.0235315	+	0.374023i	−0.992115	+	0.125333i	$0.960000\pi$
$128$	1.29394	−	0.940099i	1.29394	−	0.940099i
$129$		0			0
$130$		0			0
$131$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$131$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$132$		0			0
$133$		0			0
$134$	−2.53505	+	2.38057i	−2.53505	+	2.38057i
$135$		0			0
$136$		0			0
$137$	0.791759	−	1.68257i	0.791759	−	1.68257i	0.0627905	−	0.998027i	$-0.480000\pi$
$137$	0.791759	−	1.68257i	0.791759	−	1.68257i	0.728969	−	0.684547i	$-0.240000\pi$
$138$		0			0
$139$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$139$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$140$		0			0
$141$		0			0
$142$	0.635456	−	1.35041i	0.635456	−	1.35041i
$143$		0			0
$144$	0.889411	+	0.835213i	0.889411	+	0.835213i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	0.686047	+	1.08104i	0.686047	+	1.08104i
$149$	−0.263146	−	0.809880i	−0.263146	−	0.809880i	−0.992115	−	0.125333i	$-0.960000\pi$
$149$	−0.263146	−	0.809880i	−0.263146	−	0.809880i	0.728969	−	0.684547i	$-0.240000\pi$
$150$		0			0
$151$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$151$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$152$		0			0
$153$		0			0
$154$	0.580394	+	0.914555i	0.580394	+	0.914555i
$155$		0			0
$156$		0			0
$157$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$157$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$158$	2.23914	+	2.10269i	2.23914	+	2.10269i
$159$		0			0
$160$		0			0
$161$	−0.613161	−	0.0774602i	−0.613161	−	0.0774602i
$162$	0.939097	−	1.47978i	0.939097	−	1.47978i
$163$	1.18532	+	0.469303i	1.18532	+	0.469303i	0.876307	−	0.481754i	$-0.160000\pi$
$163$	1.18532	+	0.469303i	1.18532	+	0.469303i	0.309017	+	0.951057i	$0.400000\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$167$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$168$		0			0
$169$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$170$		0			0
$171$		0			0
$172$	−0.416004	+	2.18077i	−0.416004	+	2.18077i
$173$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$173$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$174$		0			0
$175$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$176$	−0.480656	−	0.581013i	−0.480656	−	0.581013i
$177$		0			0
$178$		0			0
$179$	−1.92189	−	0.242791i	−1.92189	−	0.242791i	−0.929776	−	0.368125i	$-0.880000\pi$
$179$	−1.92189	−	0.242791i	−1.92189	−	0.242791i	−0.992115	+	0.125333i	$0.960000\pi$
$180$		0			0
$181$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$181$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$182$		0			0
$183$		0			0
$184$	1.16079			1.16079
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.73879	+	0.955910i	−1.73879	+	0.955910i	−0.809017	+	0.587785i	$0.800000\pi$
$191$	−1.73879	+	0.955910i	−1.73879	+	0.955910i	−0.929776	+	0.368125i	$0.880000\pi$
$192$		0			0
$193$	1.26480	−	0.159781i	1.26480	−	0.159781i	0.535827	−	0.844328i	$-0.320000\pi$
$193$	1.26480	−	0.159781i	1.26480	−	0.159781i	0.728969	+	0.684547i	$0.240000\pi$
$194$		0			0
$195$		0			0
$196$	−1.32052	−	1.59624i	−1.32052	−	1.59624i
$197$	−1.41789	−	1.03016i	−1.41789	−	1.03016i	−0.992115	−	0.125333i	$-0.960000\pi$
$197$	−1.41789	−	1.03016i	−1.41789	−	1.03016i	−0.425779	−	0.904827i	$-0.640000\pi$
$198$	−0.690441	+	0.834600i	−0.690441	+	0.834600i
$199$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$199$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$200$	0.117933	+	1.87449i	0.117933	+	1.87449i
$201$		0			0
$202$		0			0
$203$	0.0672897	+	0.106032i	0.0672897	+	0.106032i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.115808	−	0.607087i	−0.115808	−	0.607087i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−1.44644	+	1.35830i	−1.44644	+	1.35830i	−0.637424	+	0.770513i	$0.720000\pi$
$211$	−1.44644	+	1.35830i	−1.44644	+	1.35830i	−0.809017	+	0.587785i	$0.800000\pi$
$212$	−1.41514	+	2.22991i	−1.41514	+	2.22991i
$213$		0			0
$214$	−1.74630	+	0.691409i	−1.74630	+	0.691409i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	1.48068	+	3.14661i	1.48068	+	3.14661i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$223$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$224$	0.189649	+	0.178092i	0.189649	+	0.178092i
$225$	0.968583	−	0.248690i	0.968583	−	0.248690i
$226$	0.789600	−	2.43014i	0.789600	−	2.43014i
$227$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$227$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$228$		0			0
$229$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$229$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$230$		0			0
$231$		0			0
$232$	−0.150346	−	0.181738i	−0.150346	−	0.181738i
$233$	−1.80113	−	0.713118i	−1.80113	−	0.713118i	−0.992115	−	0.125333i	$-0.960000\pi$
$233$	−1.80113	−	0.713118i	−1.80113	−	0.713118i	−0.809017	−	0.587785i	$-0.800000\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.35556	+	0.536702i	−1.35556	+	0.536702i	−0.929776	−	0.368125i	$-0.880000\pi$
$239$	−1.35556	+	0.536702i	−1.35556	+	0.536702i	−0.425779	+	0.904827i	$0.640000\pi$
$240$		0			0
$241$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$241$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$242$	−0.789600	+	0.741484i	−0.789600	+	0.741484i
$243$		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		−0.968583	−	0.248690i	$-0.920000\pi$
$251$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$252$	1.11005	−	1.74915i	1.11005	−	1.74915i
$253$	0.0239838	+	0.381212i	0.0239838	+	0.381212i
$254$	−0.636179	+	0.163343i	−0.636179	+	0.163343i
$255$		0			0
$256$	1.64957	+	1.19848i	1.64957	+	1.19848i
$257$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$257$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$258$		0			0
$259$	0.450527	−	0.423073i	0.450527	−	0.423073i
$260$		0			0
$261$	−0.0800484	+	0.0967619i	−0.0800484	+	0.0967619i
$262$		0			0
$263$	1.27760	−	0.702367i	1.27760	−	0.702367i	0.309017	−	0.951057i	$-0.400000\pi$
$263$	1.27760	−	0.702367i	1.27760	−	0.702367i	0.968583	+	0.248690i	$0.0800000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−3.60218	−	1.98031i	−3.60218	−	1.98031i
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$		0			0
$271$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$271$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$272$		0			0
$273$		0			0
$274$	3.23338	+	0.408471i	3.23338	+	0.408471i
$275$	−0.613161	+	0.0774602i	−0.613161	+	0.0774602i
$276$		0			0
$277$	0.238883	+	0.288760i	0.238883	+	0.288760i	0.876307	−	0.481754i	$-0.160000\pi$
$277$	0.238883	+	0.288760i	0.238883	+	0.288760i	−0.637424	+	0.770513i	$0.720000\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.303189	−	1.58937i	0.303189	−	1.58937i	−0.425779	−	0.904827i	$-0.640000\pi$
$281$	0.303189	−	1.58937i	0.303189	−	1.58937i	0.728969	−	0.684547i	$-0.240000\pi$
$282$		0			0
$283$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$283$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$284$	1.75022	+	0.221105i	1.75022	+	0.221105i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.110771	+	0.235400i	−0.110771	+	0.235400i
$289$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$293$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$294$		0			0
$295$		0			0
$296$	−0.739914	+	0.894403i	−0.739914	+	0.894403i
$297$		0			0
$298$	1.20742	−	0.877242i	1.20742	−	0.877242i
$299$		0			0
$300$		0			0
$301$	1.07165			1.07165
$302$	−0.328407	−	1.72157i	−0.328407	−	1.72157i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$307$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$308$	−0.816127	+	0.986528i	−0.816127	+	0.986528i
$309$		0			0
$310$		0			0
$311$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$311$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$312$		0			0
$313$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$313$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$314$		0			0
$315$		0			0
$316$	−1.54592	+	3.28525i	−1.54592	+	3.28525i
$317$	−0.124591	+	0.0157395i	−0.124591	+	0.0157395i	−0.187381	−	0.982287i	$-0.560000\pi$
$317$	−0.124591	+	0.0157395i	−0.124591	+	0.0157395i	0.0627905	+	0.998027i	$0.480000\pi$
$318$		0			0
$319$	0.0565777	−	0.0531300i	0.0565777	−	0.0531300i
$320$		0			0
$321$		0			0
$322$	−0.202967	−	1.06399i	−0.202967	−	1.06399i
$323$		0			0
$324$	2.00657	+	0.515199i	2.00657	+	0.515199i
$325$		0			0
$326$	−0.140294	+	2.22991i	−0.140294	+	2.22991i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.824805	−	0.211774i	−0.824805	−	0.211774i	−0.187381	−	0.982287i	$-0.560000\pi$
$331$	−0.824805	−	0.211774i	−0.824805	−	0.211774i	−0.637424	+	0.770513i	$0.720000\pi$
$332$		0			0
$333$	0.541587	+	0.297740i	0.541587	+	0.297740i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.72897	−	0.684547i	1.72897	−	0.684547i	0.728969	−	0.684547i	$-0.240000\pi$
$337$	1.72897	−	0.684547i	1.72897	−	0.684547i	1.00000			$0$
$338$	−0.328407	−	1.72157i	−0.328407	−	1.72157i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$344$	−1.99690	+	0.252267i	−1.99690	+	0.252267i
$345$		0			0
$346$		0			0
$347$	1.26480	+	1.52888i	1.26480	+	1.52888i	0.728969	+	0.684547i	$0.240000\pi$
$347$	1.26480	+	1.52888i	1.26480	+	1.52888i	0.535827	+	0.844328i	$0.320000\pi$
$348$		0			0
$349$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$349$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$350$	1.69755	−	0.435857i	1.69755	−	0.435857i
$351$		0			0
$352$	0.0861545	−	0.135758i	0.0861545	−	0.135758i
$353$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$353$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−0.636179	−	3.33497i	−0.636179	−	3.33497i
$359$	0.791759	+	0.313480i	0.791759	+	0.313480i	0.728969	−	0.684547i	$-0.240000\pi$
$359$	0.791759	+	0.313480i	0.791759	+	0.313480i	0.0627905	+	0.998027i	$0.480000\pi$
$360$		0			0
$361$	0.309017	−	0.951057i	0.309017	−	0.951057i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$367$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$368$	0.233017	+	0.717154i	0.233017	+	0.717154i
$369$		0			0
$370$		0			0
$371$	1.18532	+	0.469303i	1.18532	+	0.469303i
$372$		0			0
$373$	−1.35556	−	1.27295i	−1.35556	−	1.27295i	−0.929776	−	0.368125i	$-0.880000\pi$
$373$	−1.35556	−	1.27295i	−1.35556	−	1.27295i	−0.425779	−	0.904827i	$-0.640000\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.362989	+	0.0931997i	−0.362989	+	0.0931997i	−0.425779	−	0.904827i	$-0.640000\pi$
$379$	−0.362989	+	0.0931997i	−0.362989	+	0.0931997i	0.0627905	+	0.998027i	$0.480000\pi$
$380$		0			0
$381$		0			0
$382$	−2.53505	−	2.38057i	−2.53505	−	2.38057i
$383$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$383$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$384$		0			0
$385$		0			0
$386$	0.951325	+	2.02167i	0.951325	+	2.02167i
$387$	0.331159	+	1.01920i	0.331159	+	1.01920i
$388$		0			0
$389$	−0.574633	−	1.76854i	−0.574633	−	1.76854i	−0.637424	−	0.770513i	$-0.720000\pi$
$389$	−0.574633	−	1.76854i	−0.574633	−	1.76854i	0.0627905	−	0.998027i	$-0.480000\pi$
$390$		0			0
$391$		0			0
$392$	1.00639	−	1.58581i	1.00639	−	1.58581i
$393$		0			0
$394$	0.949193	−	2.92132i	0.949193	−	2.92132i
$395$		0			0
$396$	−1.19044	−	0.471329i	−1.19044	−	0.471329i
$397$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$397$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$398$		0			0
$399$		0			0
$400$	−1.13442	+	0.449147i	−1.13442	+	0.449147i
$401$	1.07165	+	1.68866i	1.07165	+	1.68866i	0.535827	+	0.844328i	$0.320000\pi$
$401$	1.07165	+	1.68866i	1.07165	+	1.68866i	0.535827	+	0.844328i	$0.320000\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−0.140294	+	0.169586i	−0.140294	+	0.169586i
$407$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$408$		0			0
$409$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$409$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.949193	−	0.521823i	0.949193	−	0.521823i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$419$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$420$		0			0
$421$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$421$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$422$	−3.04743	−	1.67534i	−3.04743	−	1.67534i
$423$		0			0
$424$	−2.31919	−	0.595466i	−2.31919	−	0.595466i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−1.41514	−	1.71061i	−1.41514	−	1.71061i
$429$		0			0
$430$		0			0
$431$	−1.80113	−	0.462452i	−1.80113	−	0.462452i	−0.809017	−	0.587785i	$-0.800000\pi$
$431$	−1.80113	−	0.462452i	−1.80113	−	0.462452i	−0.992115	+	0.125333i	$0.960000\pi$
$432$		0			0
$433$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$433$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$434$		0			0
$435$		0			0
$436$	−2.99652	+	2.81392i	−2.99652	+	2.81392i
$437$		0			0
$438$		0			0
$439$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$439$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$440$		0			0
$441$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$442$		0			0
$443$	1.60528	+	0.202793i	1.60528	+	0.202793i	0.876307	−	0.481754i	$-0.160000\pi$
$443$	1.60528	+	0.202793i	1.60528	+	0.202793i	0.728969	+	0.684547i	$0.240000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.325353	−	0.691409i	0.325353	−	0.691409i
$449$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.637424	+	0.770513i	$0.720000\pi$
$449$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.929776	+	0.368125i	$0.880000\pi$
$450$	0.939097	+	1.47978i	0.939097	+	1.47978i
$451$		0			0
$452$	3.02034			3.02034
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.41789	+	1.03016i	−1.41789	+	1.03016i	−0.425779	+	0.904827i	$0.640000\pi$
$457$	−1.41789	+	1.03016i	−1.41789	+	1.03016i	−0.992115	+	0.125333i	$0.960000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$461$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$462$		0			0
$463$	−1.73879	−	0.219661i	−1.73879	−	0.219661i	−0.809017	−	0.587785i	$-0.800000\pi$
$463$	−1.73879	−	0.219661i	−1.73879	−	0.219661i	−0.929776	+	0.368125i	$0.880000\pi$
$464$	0.0820998	−	0.129369i	0.0820998	−	0.129369i
$465$		0			0
$466$	0.213180	−	3.38840i	0.213180	−	3.38840i
$467$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$467$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$468$		0			0
$469$	−0.613161	+	1.88711i	−0.613161	+	1.88711i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.124106	−	0.650587i	−0.124106	−	0.650587i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.0800484	+	1.27233i	−0.0800484	+	1.27233i
$478$	−1.62875	−	1.96882i	−1.62875	−	1.96882i
$479$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$479$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−1.12198	−	0.616814i	−1.12198	−	0.616814i
$485$		0			0
$486$		0			0
$487$	0.110048	+	0.0604991i	0.110048	+	0.0604991i	0.535827	−	0.844328i	$-0.320000\pi$
$487$	0.110048	+	0.0604991i	0.110048	+	0.0604991i	−0.425779	+	0.904827i	$0.640000\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.50441	+	1.09302i	1.50441	+	1.09302i	0.968583	+	0.248690i	$0.0800000\pi$
$491$	1.50441	+	1.09302i	1.50441	+	1.09302i	0.535827	+	0.844328i	$0.320000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.0534698	−	0.849878i	−0.0534698	−	0.849878i
$498$		0			0
$499$	1.03137	+	0.749337i	1.03137	+	0.749337i	0.968583	−	0.248690i	$-0.0800000\pi$
$499$	1.03137	+	0.749337i	1.03137	+	0.749337i	0.0627905	+	0.998027i	$0.480000\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$503$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$504$	1.81919	+	0.467088i	1.81919	+	0.467088i
$505$		0			0
$506$	−0.622428	+	0.246437i	−0.622428	+	0.246437i
$507$		0			0
$508$	−0.416004	−	0.655518i	−0.416004	−	0.655518i
$509$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$509$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$510$		0			0
$511$		0			0
$512$	−0.610048	+	1.87753i	−0.610048	+	1.87753i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	0.949193	+	0.521823i	0.949193	+	0.521823i
$519$		0			0
$520$		0			0
$521$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$521$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$522$	−0.204639	−	0.0810224i	−0.204639	−	0.0810224i
$523$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$523$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$524$		0			0
$525$		0			0
$526$	1.86266	+	1.74915i	1.86266	+	1.74915i
$527$		0			0
$528$		0			0
$529$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	0.698327	−	3.66076i	0.698327	−	3.66076i
$537$		0			0
$538$		0			0
$539$	0.541587	+	0.297740i	0.541587	+	0.297740i
$540$		0			0
$541$	−1.35556	+	0.536702i	−1.35556	+	0.536702i	−0.929776	−	0.368125i	$-0.880000\pi$
$541$	−1.35556	+	0.536702i	−1.35556	+	0.536702i	−0.425779	+	0.904827i	$0.640000\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.62954	−	0.645180i	−1.62954	−	0.645180i	−0.637424	−	0.770513i	$-0.720000\pi$
$547$	−1.62954	−	0.645180i	−1.62954	−	0.645180i	−0.992115	+	0.125333i	$0.960000\pi$
$548$	0.721858	+	3.78411i	0.721858	+	3.78411i
$549$		0			0
$550$	−0.461193	−	0.980086i	−0.461193	−	0.980086i
$551$		0			0
$552$		0			0
$553$	1.69755	+	0.435857i	1.69755	+	0.435857i
$554$	−0.351939	+	0.554566i	−0.351939	+	0.554566i
$555$		0			0
$556$		0			0
$557$	0.812619	−	0.982287i	0.812619	−	0.982287i	−0.187381	−	0.982287i	$-0.560000\pi$
$557$	0.812619	−	0.982287i	0.812619	−	0.982287i	1.00000			$0$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	2.81343	−	0.355418i	2.81343	−	0.355418i
$563$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$563$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$568$	0.299696	+	1.57106i	0.299696	+	1.57106i
$569$	−1.80113	+	0.713118i	−1.80113	+	0.713118i	−0.809017	+	0.587785i	$0.800000\pi$
$569$	−1.80113	+	0.713118i	−1.80113	+	0.713118i	−0.992115	+	0.125333i	$0.960000\pi$
$570$		0			0
$571$	−0.374763			−0.374763			−0.187381	−	0.982287i	$-0.560000\pi$
$571$	−0.374763			−0.374763			−0.187381	+	0.982287i	$0.560000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.598617	+	0.153699i	0.598617	+	0.153699i
$576$	0.758109	+	0.0957714i	0.758109	+	0.0957714i
$577$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$577$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$578$	1.69755	−	0.435857i	1.69755	−	0.435857i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.147638	−	0.773944i	0.147638	−	0.773944i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$587$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.701107	−	0.277588i	−0.701107	−	0.277588i
$593$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$593$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$594$		0			0
$595$		0			0
$596$	1.42721	+	1.03693i	1.42721	+	1.03693i
$597$		0			0
$598$		0			0
$599$	−0.0534698	+	0.113629i	−0.0534698	+	0.113629i	−0.929776	−	0.368125i	$-0.880000\pi$
$599$	−0.0534698	+	0.113629i	−0.0534698	+	0.113629i	0.876307	+	0.481754i	$0.160000\pi$
$600$		0			0
$601$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$601$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$602$	0.580394	+	1.78627i	0.580394	+	1.78627i
$603$	−1.98423			−1.98423
$604$	1.81540	−	0.998027i	1.81540	−	0.998027i
$605$		0			0
$606$		0			0
$607$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$607$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.791759	−	1.68257i	0.791759	−	1.68257i	0.0627905	−	0.998027i	$-0.480000\pi$
$613$	0.791759	−	1.68257i	0.791759	−	1.68257i	0.728969	−	0.684547i	$-0.240000\pi$
$614$		0			0
$615$		0			0
$616$	−1.07927	−	0.427315i	−1.07927	−	0.427315i
$617$	0.0388067	−	0.616814i	0.0388067	−	0.616814i	−0.929776	−	0.368125i	$-0.880000\pi$
$617$	0.0388067	−	0.616814i	0.0388067	−	0.616814i	0.968583	−	0.248690i	$-0.0800000\pi$
$618$		0			0
$619$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$619$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.187381	+	0.982287i	−0.187381	+	0.982287i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	1.60528	−	0.202793i	1.60528	−	0.202793i	0.728969	−	0.684547i	$-0.240000\pi$
$631$	1.60528	−	0.202793i	1.60528	−	0.202793i	0.876307	+	0.481754i	$0.160000\pi$
$632$	−3.26579	−	0.412565i	−3.26579	−	0.412565i
$633$		0			0
$634$	−0.0937119	−	0.199148i	−0.0937119	−	0.199148i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	0.119201	+	0.0655311i	0.119201	+	0.0655311i
$639$	0.791759	−	0.313480i	0.791759	−	0.313480i
$640$		0			0
$641$	−0.124591	+	1.98031i	−0.124591	+	1.98031i	0.0627905	+	0.998027i	$0.480000\pi$
$641$	−0.124591	+	1.98031i	−0.124591	+	1.98031i	−0.187381	+	0.982287i	$0.560000\pi$
$642$		0			0
$643$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$643$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$644$	1.12198	−	0.616814i	1.12198	−	0.616814i
$645$		0			0
$646$		0			0
$647$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$647$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$648$	0.117933	+	1.87449i	0.117933	+	1.87449i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−2.55807	+	0.656801i	−2.55807	+	0.656801i
$653$	0.00788530	+	0.125333i	0.00788530	+	0.125333i	1.00000			$0$
$653$	0.00788530	+	0.125333i	0.00788530	+	0.125333i	−0.992115	+	0.125333i	$0.960000\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.03799	+	1.63560i	1.03799	+	1.63560i	0.728969	+	0.684547i	$0.240000\pi$
$659$	1.03799	+	1.63560i	1.03799	+	1.63560i	0.309017	+	0.951057i	$0.400000\pi$
$660$		0			0
$661$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$661$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$662$	−0.0937119	−	1.48951i	−0.0937119	−	1.48951i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.202967	+	1.06399i	−0.202967	+	1.06399i
$667$	−0.0721631	+	0.0285714i	−0.0721631	+	0.0285714i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.348445	+	0.137959i	0.348445	+	0.137959i	0.535827	−	0.844328i	$-0.320000\pi$
$673$	0.348445	+	0.137959i	0.348445	+	0.137959i	−0.187381	+	0.982287i	$0.560000\pi$
$674$	2.07741	+	2.51116i	2.07741	+	2.51116i
$675$		0			0
$676$	1.81540	−	0.998027i	1.81540	−	0.998027i
$677$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$677$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.328407	+	0.180543i	−0.328407	+	0.180543i	−0.637424	−	0.770513i	$-0.720000\pi$
$683$	−0.328407	+	0.180543i	−0.328407	+	0.180543i	0.309017	+	0.951057i	$0.400000\pi$
$684$		0			0
$685$		0			0
$686$	−1.62954	−	0.645180i	−1.62954	−	0.645180i
$687$		0			0
$688$	−0.556715	−	1.18308i	−0.556715	−	1.18308i
$689$		0			0
$690$		0			0
$691$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$691$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$692$		0			0
$693$	−0.115808	+	0.607087i	−0.115808	+	0.607087i
$694$	−1.86338	+	2.93622i	−1.86338	+	2.93622i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	1.11005	+	1.74915i	1.11005	+	1.74915i
$701$	0.362576	+	0.770513i	0.362576	+	0.770513i	1.00000			$0$
$701$	0.362576	+	0.770513i	0.362576	+	0.770513i	−0.637424	+	0.770513i	$0.720000\pi$
$702$		0			0
$703$		0			0
$704$	−0.457424	−	0.117447i	−0.457424	−	0.117447i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.50441	+	1.09302i	1.50441	+	1.09302i	0.968583	+	0.248690i	$0.0800000\pi$
$709$	1.50441	+	1.09302i	1.50441	+	1.09302i	0.535827	+	0.844328i	$0.320000\pi$
$710$		0			0
$711$	0.110048	+	1.74915i	0.110048	+	1.74915i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	3.51674	−	1.93334i	3.51674	−	1.93334i
$717$		0			0
$718$	−0.0937119	+	1.48951i	−0.0937119	+	1.48951i
$719$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$719$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$720$		0			0
$721$		0			0
$722$	1.75261			1.75261
$723$		0			0
$724$		0			0
$725$	−0.0534698	−	0.113629i	−0.0534698	−	0.113629i
$726$		0			0
$727$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$727$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$728$		0			0
$729$	0.968583	−	0.248690i	0.968583	−	0.248690i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$733$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$734$		0			0
$735$		0			0
$736$	−0.130080	+	0.0945088i	−0.130080	+	0.0945088i
$737$	1.21665	+	0.153699i	1.21665	+	0.153699i
$738$		0			0
$739$	0.0388067	−	0.119435i	0.0388067	−	0.119435i	−0.929776	−	0.368125i	$-0.880000\pi$
$739$	0.0388067	−	0.119435i	0.0388067	−	0.119435i	0.968583	+	0.248690i	$0.0800000\pi$
$740$		0			0
$741$		0			0
$742$	−0.140294	+	2.22991i	−0.140294	+	2.22991i
$743$	−0.996398	−	0.394502i	−0.996398	−	0.394502i	−0.187381	−	0.982287i	$-0.560000\pi$
$743$	−0.996398	−	0.394502i	−0.996398	−	0.394502i	−0.809017	+	0.587785i	$0.800000\pi$
$744$		0			0
$745$		0			0
$746$	1.38765	−	2.94890i	1.38765	−	2.94890i
$747$		0			0
$748$		0			0
$749$	−0.683098	+	0.825723i	−0.683098	+	0.825723i
$750$		0			0
$751$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.637424	+	0.770513i	$0.720000\pi$
$751$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.929776	+	0.368125i	$0.880000\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.450527	+	1.38658i	0.450527	+	1.38658i	0.876307	+	0.481754i	$0.160000\pi$
$757$	0.450527	+	1.38658i	0.450527	+	1.38658i	−0.425779	+	0.904827i	$0.640000\pi$
$758$	−0.351939	−	0.554566i	−0.351939	−	0.554566i
$759$		0			0
$760$		0			0
$761$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$761$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$762$		0			0
$763$	1.60528	+	1.16630i	1.60528	+	1.16630i
$764$	1.75022	−	3.71941i	1.75022	−	3.71941i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$769$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$770$		0			0
$771$		0			0
$772$	−1.92524	+	1.80792i	−1.92524	+	1.80792i
$773$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$773$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$774$	−1.51949	+	1.10397i	−1.51949	+	1.10397i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	2.63665	−	1.91564i	2.63665	−	1.91564i
$779$		0			0
$780$		0			0
$781$	−0.509758	+	0.130884i	−0.509758	+	0.130884i
$782$		0			0
$783$		0			0
$784$	1.18176	+	0.303425i	1.18176	+	0.303425i
$785$		0			0
$786$		0			0
$787$		0			0		1.00000			$0$
$787$		0			0		−1.00000			$\pi$
$788$	3.63081			3.63081
$789$		0			0
$790$		0			0
$791$	−0.273190	−	1.43211i	−0.273190	−	1.43211i
$792$	0.0728865	−	1.15850i	0.0728865	−	1.15850i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$797$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$798$		0			0
$799$		0			0
$800$	−0.165832	−	0.200457i	−0.165832	−	0.200457i
$801$		0			0
$802$	−2.23432	+	2.70082i	−2.23432	+	2.70082i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.0534698	−	0.113629i	−0.0534698	−	0.113629i	0.876307	−	0.481754i	$-0.160000\pi$
$809$	−0.0534698	−	0.113629i	−0.0534698	−	0.113629i	−0.929776	+	0.368125i	$0.880000\pi$
$810$		0			0
$811$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$811$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$812$	−0.241891	−	0.0957714i	−0.241891	−	0.0957714i
$813$		0			0
$814$	0.206868	−	0.636674i	0.206868	−	0.636674i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.0388067	+	0.119435i	0.0388067	+	0.119435i	0.968583	−	0.248690i	$-0.0800000\pi$
$821$	0.0388067	+	0.119435i	0.0388067	+	0.119435i	−0.929776	+	0.368125i	$0.880000\pi$
$822$		0			0
$823$	0.159566	−	0.836475i	0.159566	−	0.836475i	−0.809017	−	0.587785i	$-0.800000\pi$
$823$	0.159566	−	0.836475i	0.159566	−	0.836475i	0.968583	−	0.248690i	$-0.0800000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.11716	+	0.614163i	−1.11716	+	0.614163i	−0.929776	−	0.368125i	$-0.880000\pi$
$827$	−1.11716	+	0.614163i	−1.11716	+	0.614163i	−0.187381	+	0.982287i	$0.560000\pi$
$828$	0.933337	+	0.876461i	0.933337	+	0.876461i
$829$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$829$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$830$		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		−0.425779	−	0.904827i	$-0.640000\pi$
$839$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$840$		0			0
$841$	−0.862487	−	0.474156i	−0.862487	−	0.474156i
$842$	−0.876307	−	2.69699i	−0.876307	−	2.69699i
$843$		0			0
$844$	0.770256	−	4.03783i	0.770256	−	4.03783i
$845$		0			0
$846$		0			0
$847$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$848$	−0.0976666	−	1.55237i	−0.0976666	−	1.55237i
$849$		0			0
$850$		0			0
$851$	0.204668	+	0.322505i	0.204668	+	0.322505i
$852$		0			0
$853$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$853$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$854$		0			0
$855$		0			0
$856$	1.07850	−	1.69944i	1.07850	−	1.69944i
$857$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$857$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$858$		0			0
$859$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$859$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$860$		0			0
$861$		0			0
$862$	−0.204639	−	3.25265i	−0.204639	−	3.25265i
$863$	1.27760	−	1.19975i	1.27760	−	1.19975i	0.309017	−	0.951057i	$-0.400000\pi$
$863$	1.27760	−	1.19975i	1.27760	−	1.19975i	0.968583	−	0.248690i	$-0.0800000\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.0680131	−	1.08104i	0.0680131	−	1.08104i
$870$		0			0
$871$		0			0
$872$	−3.26579	−	1.79538i	−3.26579	−	1.79538i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.824805	−	0.211774i	−0.824805	−	0.211774i	−0.187381	−	0.982287i	$-0.560000\pi$
$877$	−0.824805	−	0.211774i	−0.824805	−	0.211774i	−0.637424	+	0.770513i	$0.720000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$881$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$882$	0.110048	−	1.74915i	0.110048	−	1.74915i
$883$	−1.17950	+	0.856954i	−1.17950	+	0.856954i	−0.992115	−	0.125333i	$-0.960000\pi$
$883$	−1.17950	+	0.856954i	−1.17950	+	0.856954i	−0.187381	+	0.982287i	$0.560000\pi$
$884$		0			0
$885$		0			0
$886$	0.531374	+	2.78556i	0.531374	+	2.78556i
$887$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$887$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$888$		0			0
$889$	−0.273190	+	0.256543i	−0.273190	+	0.256543i
$890$		0			0
$891$	−0.613161	+	0.0774602i	−0.613161	+	0.0774602i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	1.58678	+	0.200457i	1.58678	+	0.200457i
$897$		0			0
$898$	−2.74670	−	1.99559i	−2.74670	−	1.99559i
$899$		0			0
$900$	−1.32052	+	1.59624i	−1.32052	+	1.59624i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.846178	+	2.60427i	0.846178	+	2.60427i
$905$		0			0
$906$		0			0
$907$	1.93717			1.93717			0.968583	−	0.248690i	$-0.0800000\pi$
$907$	1.93717			1.93717			0.968583	+	0.248690i	$0.0800000\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.542804	−	1.15352i	0.542804	−	1.15352i	−0.425779	−	0.904827i	$-0.640000\pi$
$911$	0.542804	−	1.15352i	0.542804	−	1.15352i	0.968583	−	0.248690i	$-0.0800000\pi$
$912$		0			0
$913$		0			0
$914$	−2.48502	−	1.80547i	−2.48502	−	1.80547i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.125581	−	1.99605i	0.125581	−	1.99605i	0.0627905	−	0.998027i	$-0.480000\pi$
$919$	0.125581	−	1.99605i	0.125581	−	1.99605i	0.0627905	−	0.998027i	$-0.480000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$926$	−0.575570	−	3.01725i	−0.575570	−	3.01725i
$927$		0			0
$928$	0.0316448	+	0.00812500i	0.0316448	+	0.00812500i
$929$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$929$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$930$		0			0
$931$		0			0
$932$	3.88706	−	0.998027i	3.88706	−	0.998027i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$937$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$938$	−3.47759			−3.47759
$939$		0			0
$940$		0			0
$941$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$941$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	1.01721	−	0.559214i	1.01721	−	0.559214i
$947$	0.238883	−	0.288760i	0.238883	−	0.288760i	−0.637424	−	0.770513i	$-0.720000\pi$
$947$	0.238883	−	0.288760i	0.238883	−	0.288760i	0.876307	+	0.481754i	$0.160000\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.18532	−	1.43281i	1.18532	−	1.43281i	0.309017	−	0.951057i	$-0.400000\pi$
$953$	1.18532	−	1.43281i	1.18532	−	1.43281i	0.876307	−	0.481754i	$-0.160000\pi$
$954$	−2.16412	+	0.555652i	−2.16412	+	0.555652i
$955$		0			0
$956$	1.61838	−	2.55016i	1.61838	−	2.55016i
$957$		0			0
$958$		0			0
$959$	1.72897	−	0.684547i	1.72897	−	0.684547i
$960$		0			0
$961$	0.535827	+	0.844328i	0.535827	+	0.844328i
$962$		0			0
$963$	−0.996398	−	0.394502i	−0.996398	−	0.394502i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.03799	−	1.63560i	1.03799	−	1.63560i	0.309017	−	0.951057i	$-0.400000\pi$
$967$	1.03799	−	1.63560i	1.03799	−	1.63560i	0.728969	−	0.684547i	$-0.240000\pi$
$968$	0.217510	−	1.14023i	0.217510	−	1.14023i
$969$		0			0
$970$		0			0
$971$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$971$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$972$		0			0
$973$		0			0
$974$	−0.0412417	+	0.216197i	−0.0412417	+	0.216197i
$975$		0			0
$976$		0			0
$977$	1.06279	+	0.998027i	1.06279	+	0.998027i	1.00000			$0$
$977$	1.06279	+	0.998027i	1.06279	+	0.998027i	0.0627905	+	0.998027i	$0.480000\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−0.613161	+	1.88711i	−0.613161	+	1.88711i
$982$	−1.00711	+	3.09957i	−1.00711	+	3.09957i
$983$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$983$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.124106	+	0.650587i	−0.124106	+	0.650587i
$990$		0			0
$991$	0.598617	+	1.84235i	0.598617	+	1.84235i	0.535827	+	0.844328i	$0.320000\pi$
$991$	0.598617	+	1.84235i	0.598617	+	1.84235i	0.0627905	+	0.998027i	$0.480000\pi$
$992$		0			0
$993$		0			0
$994$	1.38765	−	0.549409i	1.38765	−	0.549409i
$995$		0			0
$996$		0			0
$997$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$997$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$998$	−0.690441	+	2.12496i	−0.690441	+	2.12496i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1057.1.bq.a.846.1	yes	20
7.6	odd	2	CM	1057.1.bq.a.846.1	yes	20
151.78	even	25	inner	1057.1.bq.a.531.1	✓	20
1057.531	odd	50	inner	1057.1.bq.a.531.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1057.1.bq.a.531.1	✓	20	151.78	even	25	inner
1057.1.bq.a.531.1	✓	20	1057.531	odd	50	inner
1057.1.bq.a.846.1	yes	20	1.1	even	1	trivial
1057.1.bq.a.846.1	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)

\(f(q)\)	\(=\)	\(q+(0.541587 + 1.66683i) q^{2} +(-1.67600 + 1.21769i) q^{4} +(0.728969 + 0.684547i) q^{7} +(-1.51949 - 1.10397i) q^{8} +(-0.425779 + 0.904827i) q^{9} +O(q^{10})\)	\(q+(0.541587 + 1.66683i) q^{2} +(-1.67600 + 1.21769i) q^{4} +(0.728969 + 0.684547i) q^{7} +(-1.51949 - 1.10397i) q^{8} +(-0.425779 + 0.904827i) q^{9} +(0.331159 - 0.521823i) q^{11} +(-0.746226 + 1.58581i) q^{14} +(0.377030 - 1.16038i) q^{16} +(-1.73879 - 0.219661i) q^{18} +(1.04914 + 0.269375i) q^{22} +(-0.500000 + 0.363271i) q^{23} +(-0.637424 - 0.770513i) q^{25} +(-2.05532 - 0.259647i) q^{28} +(0.121636 + 0.0312307i) q^{29} +0.260160 q^{32} +(-0.388189 - 2.03496i) q^{36} +(0.0388067 - 0.616814i) q^{37} +(0.781202 - 0.733597i) q^{43} +(0.0803940 + 1.27783i) q^{44} +(-0.876307 - 0.636674i) q^{46} +(0.0627905 + 0.998027i) q^{49} +(0.939097 - 1.47978i) q^{50} +(1.18532 - 0.469303i) q^{53} +(-0.351939 - 1.84493i) q^{56} +(0.0138199 + 0.219661i) q^{58} +(-0.929776 + 0.368125i) q^{63} +(-0.236131 - 0.726735i) q^{64} +(0.844844 + 1.79538i) q^{67} +(-0.620759 - 0.582932i) q^{71} +(1.64587 - 0.904827i) q^{72} +(1.04914 - 0.269375i) q^{74} +(0.598617 - 0.153699i) q^{77} +(1.53583 - 0.844328i) q^{79} +(-0.637424 - 0.770513i) q^{81} +(1.64587 + 0.904827i) q^{86} +(-1.07927 + 0.427315i) q^{88} +(0.395651 - 1.21769i) q^{92} +(-1.62954 + 0.645180i) q^{98} +(0.331159 + 0.521823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{4}+O(q^{10}) \) 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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