LMFDB - Embedded newform 2008.1.w.a.243.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2008,1,Mod(51,2008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2008, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([25, 25, 18]))

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

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

chi := DirichletCharacter("2008.51");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2008 = 2^{3} \cdot 251 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2008.w (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:	$1.00212254537$
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:	$\Z[a_1, \ldots, a_{9}]$
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			243.1
Root			$0.992115 + 0.125333i$ of defining polynomial
Character	$\chi$	$=$	2008.243
Dual form			2008.1.w.a.1851.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(1.84489 + 0.730444i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.06320 - 1.67534i) q^{6} +(0.309017 - 0.951057i) q^{8} +(2.14110 + 2.01063i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(1.84489 + 0.730444i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.06320 - 1.67534i) q^{6} +(0.309017 - 0.951057i) q^{8} +(2.14110 + 2.01063i) q^{9} +(-0.0800484 + 1.27233i) q^{11} +(-0.124591 + 1.98031i) q^{12} +(-0.809017 + 0.587785i) q^{16} +(1.07165 - 1.68866i) q^{17} +(-0.550370 - 2.88514i) q^{18} +(-1.41789 - 0.779494i) q^{19} +(0.812619 - 0.982287i) q^{22} +(1.26480 - 1.52888i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(1.63660 + 3.47796i) q^{27} +1.00000 q^{32} +(-1.07705 + 2.28884i) q^{33} +(-1.85955 + 0.736249i) q^{34} +(-1.25058 + 2.65763i) q^{36} +(0.688925 + 1.46404i) q^{38} +(0.542804 + 0.656137i) q^{41} +(-1.06320 - 0.134314i) q^{43} +(-1.23480 + 0.317042i) q^{44} +(-1.92189 + 0.493458i) q^{48} +(-0.637424 + 0.770513i) q^{49} +(0.309017 + 0.951057i) q^{50} +(3.21055 - 2.33260i) q^{51} +(0.720253 - 3.77570i) q^{54} +(-2.04648 - 2.47377i) q^{57} +(0.0672897 + 0.106032i) q^{59} +(-0.809017 - 0.587785i) q^{64} +(2.21670 - 1.21864i) q^{66} +(-1.11716 - 1.35041i) q^{67} +(1.93717 + 0.497380i) q^{68} +(2.57386 - 1.41499i) q^{72} +(1.50441 - 0.595638i) q^{73} +(-1.06320 - 1.67534i) q^{75} +(0.303189 - 1.58937i) q^{76} +(0.294474 + 4.68053i) q^{81} +(-0.0534698 - 0.849878i) q^{82} +(-1.80113 - 0.462452i) q^{83} +(0.781202 + 0.733597i) q^{86} +(1.18532 + 0.469303i) q^{88} +(-0.200808 + 0.316423i) q^{89} +(1.84489 + 0.730444i) q^{96} +(-0.824805 - 0.211774i) q^{97} +(0.968583 - 0.248690i) q^{98} +(-2.72958 + 2.56325i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{2} - 5 q^{4} - 5 q^{8}+O(q^{10}) $ 20 * q - 5 * q^2 - 5 * q^4 - 5 * q^8	$ 20 q - 5 q^{2} - 5 q^{4} - 5 q^{8} - 5 q^{11} - 5 q^{16} + 20 q^{22} - 5 q^{25} - 5 q^{27} + 20 q^{32} - 5 q^{33} - 5 q^{44} - 5 q^{50} - 5 q^{54} - 5 q^{59} - 5 q^{64} - 5 q^{66} - 5 q^{81} - 5 q^{83} - 5 q^{88} - 5 q^{99}+O(q^{100}) $ 20 * q - 5 * q^2 - 5 * q^4 - 5 * q^8 - 5 * q^11 - 5 * q^16 + 20 * q^22 - 5 * q^25 - 5 * q^27 + 20 * q^32 - 5 * q^33 - 5 * q^44 - 5 * q^50 - 5 * q^54 - 5 * q^59 - 5 * q^64 - 5 * q^66 - 5 * q^81 - 5 * q^83 - 5 * q^88 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times$.

$n$	$257$	$503$	$1005$
$\chi(n)$	$e\left(\frac{8}{25}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$2$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$3$	1.84489	+	0.730444i	1.84489	+	0.730444i	0.968583	+	0.248690i	$0.0800000\pi$
$3$	1.84489	+	0.730444i	1.84489	+	0.730444i	0.876307	+	0.481754i	$0.160000\pi$
$4$	0.309017	+	0.951057i	0.309017	+	0.951057i
$5$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$5$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$6$	−1.06320	−	1.67534i	−1.06320	−	1.67534i
$7$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$7$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$8$	0.309017	−	0.951057i	0.309017	−	0.951057i
$9$	2.14110	+	2.01063i	2.14110	+	2.01063i
$10$		0			0
$11$	−0.0800484	+	1.27233i	−0.0800484	+	1.27233i	0.728969	+	0.684547i	$0.240000\pi$
$11$	−0.0800484	+	1.27233i	−0.0800484	+	1.27233i	−0.809017	+	0.587785i	$0.800000\pi$
$12$	−0.124591	+	1.98031i	−0.124591	+	1.98031i
$13$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$13$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$14$		0			0
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$17$	1.07165	−	1.68866i	1.07165	−	1.68866i	0.535827	−	0.844328i	$-0.320000\pi$
$17$	1.07165	−	1.68866i	1.07165	−	1.68866i	0.535827	−	0.844328i	$-0.320000\pi$
$18$	−0.550370	−	2.88514i	−0.550370	−	2.88514i
$19$	−1.41789	−	0.779494i	−1.41789	−	0.779494i	−0.425779	−	0.904827i	$-0.640000\pi$
$19$	−1.41789	−	0.779494i	−1.41789	−	0.779494i	−0.992115	+	0.125333i	$0.960000\pi$
$20$		0			0
$21$		0			0
$22$	0.812619	−	0.982287i	0.812619	−	0.982287i
$23$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$23$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$24$	1.26480	−	1.52888i	1.26480	−	1.52888i
$25$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$26$		0			0
$27$	1.63660	+	3.47796i	1.63660	+	3.47796i
$28$		0			0
$29$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$29$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$30$		0			0
$31$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$31$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$32$	1.00000			1.00000
$33$	−1.07705	+	2.28884i	−1.07705	+	2.28884i
$34$	−1.85955	+	0.736249i	−1.85955	+	0.736249i
$35$		0			0
$36$	−1.25058	+	2.65763i	−1.25058	+	2.65763i
$37$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$37$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$38$	0.688925	+	1.46404i	0.688925	+	1.46404i
$39$		0			0
$40$		0			0
$41$	0.542804	+	0.656137i	0.542804	+	0.656137i	0.968583	−	0.248690i	$-0.0800000\pi$
$41$	0.542804	+	0.656137i	0.542804	+	0.656137i	−0.425779	+	0.904827i	$0.640000\pi$
$42$		0			0
$43$	−1.06320	−	0.134314i	−1.06320	−	0.134314i	−0.425779	−	0.904827i	$-0.640000\pi$
$43$	−1.06320	−	0.134314i	−1.06320	−	0.134314i	−0.637424	+	0.770513i	$0.720000\pi$
$44$	−1.23480	+	0.317042i	−1.23480	+	0.317042i
$45$		0			0
$46$		0			0
$47$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$47$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$48$	−1.92189	+	0.493458i	−1.92189	+	0.493458i
$49$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$50$	0.309017	+	0.951057i	0.309017	+	0.951057i
$51$	3.21055	−	2.33260i	3.21055	−	2.33260i
$52$		0			0
$53$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$53$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$54$	0.720253	−	3.77570i	0.720253	−	3.77570i
$55$		0			0
$56$		0			0
$57$	−2.04648	−	2.47377i	−2.04648	−	2.47377i
$58$		0			0
$59$	0.0672897	+	0.106032i	0.0672897	+	0.106032i	0.876307	−	0.481754i	$-0.160000\pi$
$59$	0.0672897	+	0.106032i	0.0672897	+	0.106032i	−0.809017	+	0.587785i	$0.800000\pi$
$60$		0			0
$61$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$61$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$62$		0			0
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$65$		0			0
$66$	2.21670	−	1.21864i	2.21670	−	1.21864i
$67$	−1.11716	−	1.35041i	−1.11716	−	1.35041i	−0.929776	−	0.368125i	$-0.880000\pi$
$67$	−1.11716	−	1.35041i	−1.11716	−	1.35041i	−0.187381	−	0.982287i	$-0.560000\pi$
$68$	1.93717	+	0.497380i	1.93717	+	0.497380i
$69$		0			0
$70$		0			0
$71$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$71$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$72$	2.57386	−	1.41499i	2.57386	−	1.41499i
$73$	1.50441	−	0.595638i	1.50441	−	0.595638i	0.535827	−	0.844328i	$-0.320000\pi$
$73$	1.50441	−	0.595638i	1.50441	−	0.595638i	0.968583	+	0.248690i	$0.0800000\pi$
$74$		0			0
$75$	−1.06320	−	1.67534i	−1.06320	−	1.67534i
$76$	0.303189	−	1.58937i	0.303189	−	1.58937i
$77$		0			0
$78$		0			0
$79$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$79$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$80$		0			0
$81$	0.294474	+	4.68053i	0.294474	+	4.68053i
$82$	−0.0534698	−	0.849878i	−0.0534698	−	0.849878i
$83$	−1.80113	−	0.462452i	−1.80113	−	0.462452i	−0.809017	−	0.587785i	$-0.800000\pi$
$83$	−1.80113	−	0.462452i	−1.80113	−	0.462452i	−0.992115	+	0.125333i	$0.960000\pi$
$84$		0			0
$85$		0			0
$86$	0.781202	+	0.733597i	0.781202	+	0.733597i
$87$		0			0
$88$	1.18532	+	0.469303i	1.18532	+	0.469303i
$89$	−0.200808	+	0.316423i	−0.200808	+	0.316423i	−0.929776	−	0.368125i	$-0.880000\pi$
$89$	−0.200808	+	0.316423i	−0.200808	+	0.316423i	0.728969	+	0.684547i	$0.240000\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	1.84489	+	0.730444i	1.84489	+	0.730444i
$97$	−0.824805	−	0.211774i	−0.824805	−	0.211774i	−0.187381	−	0.982287i	$-0.560000\pi$
$97$	−0.824805	−	0.211774i	−0.824805	−	0.211774i	−0.637424	+	0.770513i	$0.720000\pi$
$98$	0.968583	−	0.248690i	0.968583	−	0.248690i
$99$	−2.72958	+	2.56325i	−2.72958	+	2.56325i
$100$	0.309017	−	0.951057i	0.309017	−	0.951057i
$101$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$101$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$102$	−3.96846			−3.96846
$103$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$103$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.96858	+	0.248690i	1.96858	+	0.248690i	1.00000			$0$
$107$	1.96858	+	0.248690i	1.96858	+	0.248690i	0.968583	+	0.248690i	$0.0800000\pi$
$108$	−2.80200	+	2.63125i	−2.80200	+	2.63125i
$109$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$109$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.07165			1.07165			0.535827	−	0.844328i	$-0.320000\pi$
$113$	1.07165			1.07165			0.535827	+	0.844328i	$0.320000\pi$
$114$	0.201592	+	3.20422i	0.201592	+	3.20422i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.00788530	−	0.125333i	0.00788530	−	0.125333i
$119$		0			0
$120$		0			0
$121$	−0.620307	−	0.0783630i	−0.620307	−	0.0783630i
$122$		0			0
$123$	0.522142	+	1.60699i	0.522142	+	1.60699i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$127$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$128$	0.309017	+	0.951057i	0.309017	+	0.951057i
$129$	−1.86338	−	1.02440i	−1.86338	−	1.02440i
$130$		0			0
$131$	0.331159	+	0.521823i	0.331159	+	0.521823i	0.968583	−	0.248690i	$-0.0800000\pi$
$131$	0.331159	+	0.521823i	0.331159	+	0.521823i	−0.637424	+	0.770513i	$0.720000\pi$
$132$	−2.50964	−	0.317042i	−2.50964	−	0.317042i
$133$		0			0
$134$	0.110048	+	1.74915i	0.110048	+	1.74915i
$135$		0			0
$136$	−1.27485	−	1.54103i	−1.27485	−	1.54103i
$137$	−0.124591	−	1.98031i	−0.124591	−	1.98031i	−0.187381	−	0.982287i	$-0.560000\pi$
$137$	−0.124591	−	1.98031i	−0.124591	−	1.98031i	0.0627905	−	0.998027i	$-0.480000\pi$
$138$		0			0
$139$	−1.62954	−	0.895846i	−1.62954	−	0.895846i	−0.992115	−	0.125333i	$-0.960000\pi$
$139$	−1.62954	−	0.895846i	−1.62954	−	0.895846i	−0.637424	−	0.770513i	$-0.720000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−2.91401	−	0.368125i	−2.91401	−	0.368125i
$145$		0			0
$146$	−1.56720	−	0.402389i	−1.56720	−	0.402389i
$147$	−1.73879	+	0.955910i	−1.73879	+	0.955910i
$148$		0			0
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	−0.124591	+	1.98031i	−0.124591	+	1.98031i
$151$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$151$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$152$	−1.17950	+	1.10762i	−1.17950	+	1.10762i
$153$	5.68978	−	1.46089i	5.68978	−	1.46089i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$157$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	2.51291	−	3.95971i	2.51291	−	3.95971i
$163$	0.348445	+	0.137959i	0.348445	+	0.137959i	0.535827	−	0.844328i	$-0.320000\pi$
$163$	0.348445	+	0.137959i	0.348445	+	0.137959i	−0.187381	+	0.982287i	$0.560000\pi$
$164$	−0.456288	+	0.718995i	−0.456288	+	0.718995i
$165$		0			0
$166$	1.18532	+	1.43281i	1.18532	+	1.43281i
$167$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$167$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$168$		0			0
$169$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$170$		0			0
$171$	−1.46858	−	4.51983i	−1.46858	−	4.51983i
$172$	−0.200808	−	1.05267i	−0.200808	−	1.05267i
$173$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$173$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$174$		0			0
$175$		0			0
$176$	−0.683098	−	1.07639i	−0.683098	−	1.07639i
$177$	0.0466920	+	0.244768i	0.0466920	+	0.244768i
$178$	0.348445	−	0.137959i	0.348445	−	0.137959i
$179$	1.27760	−	0.702367i	1.27760	−	0.702367i	0.309017	−	0.951057i	$-0.400000\pi$
$179$	1.27760	−	0.702367i	1.27760	−	0.702367i	0.968583	+	0.248690i	$0.0800000\pi$
$180$		0			0
$181$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$181$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.06275	+	1.49867i	2.06275	+	1.49867i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$191$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$192$	−1.06320	−	1.67534i	−1.06320	−	1.67534i
$193$	0.0915446	−	0.0859661i	0.0915446	−	0.0859661i	−0.637424	−	0.770513i	$-0.720000\pi$
$193$	0.0915446	−	0.0859661i	0.0915446	−	0.0859661i	0.728969	+	0.684547i	$0.240000\pi$
$194$	0.542804	+	0.656137i	0.542804	+	0.656137i
$195$		0			0
$196$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$197$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$197$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$198$	3.71491	−	0.469303i	3.71491	−	0.469303i
$199$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$199$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$200$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$201$	−1.07463	−	3.30738i	−1.07463	−	3.30738i
$202$		0			0
$203$		0			0
$204$	3.21055	+	2.33260i	3.21055	+	2.33260i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.10528	−	1.74164i	1.10528	−	1.74164i
$210$		0			0
$211$	0.303189	+	0.220280i	0.303189	+	0.220280i	0.728969	−	0.684547i	$-0.240000\pi$
$211$	0.303189	+	0.220280i	0.303189	+	0.220280i	−0.425779	+	0.904827i	$0.640000\pi$
$212$		0			0
$213$		0			0
$214$	−1.44644	−	1.35830i	−1.44644	−	1.35830i
$215$		0			0
$216$	3.81347	−	0.481754i	3.81347	−	0.481754i
$217$		0			0
$218$		0			0
$219$	3.21055			3.21055
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$223$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$224$		0			0
$225$	−0.550370	−	2.88514i	−0.550370	−	2.88514i
$226$	−0.866986	−	0.629902i	−0.866986	−	0.629902i
$227$	−0.393950	+	0.476203i	−0.393950	+	0.476203i	−0.929776	−	0.368125i	$-0.880000\pi$
$227$	−0.393950	+	0.476203i	−0.393950	+	0.476203i	0.535827	+	0.844328i	$0.320000\pi$
$228$	1.72030	−	2.71076i	1.72030	−	2.71076i
$229$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$229$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.200808	−	1.05267i	−0.200808	−	1.05267i	−0.929776	−	0.368125i	$-0.880000\pi$
$233$	−0.200808	−	1.05267i	−0.200808	−	1.05267i	0.728969	−	0.684547i	$-0.240000\pi$
$234$		0			0
$235$		0			0
$236$	−0.0800484	+	0.0967619i	−0.0800484	+	0.0967619i
$237$		0			0
$238$		0			0
$239$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$239$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$240$		0			0
$241$	−1.17950	+	0.856954i	−1.17950	+	0.856954i	−0.992115	−	0.125333i	$-0.960000\pi$
$241$	−1.17950	+	0.856954i	−1.17950	+	0.856954i	−0.187381	+	0.982287i	$0.560000\pi$
$242$	0.455778	+	0.428004i	0.455778	+	0.428004i
$243$	−1.68779	+	5.19450i	−1.68779	+	5.19450i
$244$		0			0
$245$		0			0
$246$	0.522142	−	1.60699i	0.522142	−	1.60699i
$247$		0			0
$248$		0			0
$249$	−2.98509	−	2.16880i	−2.98509	−	2.16880i
$250$		0			0
$251$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$251$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.309017	−	0.951057i	0.309017	−	0.951057i
$257$	0.0672897	+	0.106032i	0.0672897	+	0.106032i	0.876307	−	0.481754i	$-0.160000\pi$
$257$	0.0672897	+	0.106032i	0.0672897	+	0.106032i	−0.809017	+	0.587785i	$0.800000\pi$
$258$	0.905380	+	1.92403i	0.905380	+	1.92403i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.0388067	−	0.616814i	0.0388067	−	0.616814i
$263$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$263$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$264$	1.84399	+	1.73162i	1.84399	+	1.73162i
$265$		0			0
$266$		0			0
$267$	−0.601597	+	0.437086i	−0.601597	+	0.437086i
$268$	0.939097	−	1.47978i	0.939097	−	1.47978i
$269$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$269$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	0.125581	+	1.99605i	0.125581	+	1.99605i
$273$		0			0
$274$	−1.06320	+	1.67534i	−1.06320	+	1.67534i
$275$	0.812619	−	0.982287i	0.812619	−	0.982287i
$276$		0			0
$277$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$277$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$278$	0.791759	+	1.68257i	0.791759	+	1.68257i
$279$		0			0
$280$		0			0
$281$	−0.824805	+	0.211774i	−0.824805	+	0.211774i	−0.637424	−	0.770513i	$-0.720000\pi$
$281$	−0.824805	+	0.211774i	−0.824805	+	0.211774i	−0.187381	+	0.982287i	$0.560000\pi$
$282$		0			0
$283$	1.45794			1.45794			0.728969	−	0.684547i	$-0.240000\pi$
$283$	1.45794			1.45794			0.728969	+	0.684547i	$0.240000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	2.14110	+	2.01063i	2.14110	+	2.01063i
$289$	−1.27734	−	2.71448i	−1.27734	−	2.71448i
$290$		0			0
$291$	−1.36699	−	0.993173i	−1.36699	−	0.993173i
$292$	1.03137	+	1.24672i	1.03137	+	1.24672i
$293$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$293$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$294$	1.96858	+	0.248690i	1.96858	+	0.248690i
$295$		0			0
$296$		0			0
$297$	−4.55613	+	1.80390i	−4.55613	+	1.80390i
$298$		0			0
$299$		0			0
$300$	1.26480	−	1.52888i	1.26480	−	1.52888i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	1.60528	−	0.202793i	1.60528	−	0.202793i
$305$		0			0
$306$	−5.46182	−	2.16249i	−5.46182	−	2.16249i
$307$	−1.44644	+	0.182728i	−1.44644	+	0.182728i	−0.809017	−	0.587785i	$-0.800000\pi$
$307$	−1.44644	+	0.182728i	−1.44644	+	0.182728i	−0.637424	+	0.770513i	$0.720000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$311$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$312$		0			0
$313$	0.238883	−	0.288760i	0.238883	−	0.288760i	−0.637424	−	0.770513i	$-0.720000\pi$
$313$	0.238883	−	0.288760i	0.238883	−	0.288760i	0.876307	+	0.481754i	$0.160000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$317$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	3.45017	+	1.89674i	3.45017	+	1.89674i
$322$		0			0
$323$	−2.83579	+	1.55899i	−2.83579	+	1.55899i
$324$	−4.36045	+	1.72642i	−4.36045	+	1.72642i
$325$		0			0
$326$	−0.200808	−	0.316423i	−0.200808	−	0.316423i
$327$		0			0
$328$	0.791759	−	0.313480i	0.791759	−	0.313480i
$329$		0			0
$330$		0			0
$331$	0.0388067	+	0.119435i	0.0388067	+	0.119435i	0.968583	−	0.248690i	$-0.0800000\pi$
$331$	0.0388067	+	0.119435i	0.0388067	+	0.119435i	−0.929776	+	0.368125i	$0.880000\pi$
$332$	−0.116762	−	1.85588i	−0.116762	−	1.85588i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.929324	−	0.872693i	−0.929324	−	0.872693i	0.0627905	−	0.998027i	$-0.480000\pi$
$337$	−0.929324	−	0.872693i	−0.929324	−	0.872693i	−0.992115	+	0.125333i	$0.960000\pi$
$338$	0.535827	−	0.844328i	0.535827	−	0.844328i
$339$	1.97708	+	0.782782i	1.97708	+	0.782782i
$340$		0			0
$341$		0			0
$342$	−1.46858	+	4.51983i	−1.46858	+	4.51983i
$343$		0			0
$344$	−0.456288	+	0.969661i	−0.456288	+	0.969661i
$345$		0			0
$346$		0			0
$347$	−0.116762	−	0.0462295i	−0.116762	−	0.0462295i	0.309017	−	0.951057i	$-0.400000\pi$
$347$	−0.116762	−	0.0462295i	−0.116762	−	0.0462295i	−0.425779	+	0.904827i	$0.640000\pi$
$348$		0			0
$349$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$349$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$350$		0			0
$351$		0			0
$352$	−0.0800484	+	1.27233i	−0.0800484	+	1.27233i
$353$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$353$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$354$	0.106096	−	0.225466i	0.106096	−	0.225466i
$355$		0			0
$356$	−0.362989	−	0.0931997i	−0.362989	−	0.0931997i
$357$		0			0
$358$	−1.44644	−	0.182728i	−1.44644	−	0.182728i
$359$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$359$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$360$		0			0
$361$	0.866986	+	1.36615i	0.866986	+	1.36615i
$362$		0			0
$363$	−1.08716	−	0.597671i	−1.08716	−	0.597671i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$367$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$368$		0			0
$369$	−0.157050	+	2.49623i	−0.157050	+	2.49623i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$373$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$374$	−0.787899	−	2.42490i	−0.787899	−	2.42490i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.541587	+	1.66683i	0.541587	+	1.66683i	0.728969	+	0.684547i	$0.240000\pi$
$379$	0.541587	+	1.66683i	0.541587	+	1.66683i	−0.187381	+	0.982287i	$0.560000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$383$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$384$	−0.124591	+	1.98031i	−0.124591	+	1.98031i
$385$		0			0
$386$	−0.124591	+	0.0157395i	−0.124591	+	0.0157395i
$387$	−2.00637	−	2.42529i	−2.00637	−	2.42529i
$388$	−0.0534698	−	0.849878i	−0.0534698	−	0.849878i
$389$		0			0		1.00000			$0$
$389$		0			0		−1.00000			$\pi$
$390$		0			0
$391$		0			0
$392$	0.535827	+	0.844328i	0.535827	+	0.844328i
$393$	0.229790	+	1.20460i	0.229790	+	1.20460i
$394$		0			0
$395$		0			0
$396$	−3.28128	−	1.80390i	−3.28128	−	1.80390i
$397$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$397$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$398$		0			0
$399$		0			0
$400$	1.00000			1.00000
$401$	0.121636	−	1.93334i	0.121636	−	1.93334i	−0.187381	−	0.982287i	$-0.560000\pi$
$401$	0.121636	−	1.93334i	0.121636	−	1.93334i	0.309017	−	0.951057i	$-0.400000\pi$
$402$	−1.07463	+	3.30738i	−1.07463	+	3.30738i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−1.22632	−	3.77423i	−1.22632	−	3.77423i
$409$	0.791759	−	1.68257i	0.791759	−	1.68257i	0.0627905	−	0.998027i	$-0.480000\pi$
$409$	0.791759	−	1.68257i	0.791759	−	1.68257i	0.728969	−	0.684547i	$-0.240000\pi$
$410$		0			0
$411$	1.21665	−	3.74447i	1.21665	−	3.74447i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−2.35195	−	2.84302i	−2.35195	−	2.84302i
$418$	−1.91789	+	0.759348i	−1.91789	+	0.759348i
$419$	−1.80113	−	0.462452i	−1.80113	−	0.462452i	−0.809017	−	0.587785i	$-0.800000\pi$
$419$	−1.80113	−	0.462452i	−1.80113	−	0.462452i	−0.992115	+	0.125333i	$0.960000\pi$
$420$		0			0
$421$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$421$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$422$	−0.115808	−	0.356420i	−0.115808	−	0.356420i
$423$		0			0
$424$		0			0
$425$	−1.85955	+	0.736249i	−1.85955	+	0.736249i
$426$		0			0
$427$		0			0
$428$	0.371808	+	1.94908i	0.371808	+	1.94908i
$429$		0			0
$430$		0			0
$431$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$431$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$432$	−3.36833	−	1.85176i	−3.36833	−	1.85176i
$433$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$433$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−2.59739	−	1.88711i	−2.59739	−	1.88711i
$439$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$439$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$440$		0			0
$441$	−2.91401	+	0.368125i	−2.91401	+	0.368125i
$442$		0			0
$443$	1.07165	+	1.68866i	1.07165	+	1.68866i	0.535827	+	0.844328i	$0.320000\pi$
$443$	1.07165	+	1.68866i	1.07165	+	1.68866i	0.535827	+	0.844328i	$0.320000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.84489	−	0.233064i	1.84489	−	0.233064i	0.876307	−	0.481754i	$-0.160000\pi$
$449$	1.84489	−	0.233064i	1.84489	−	0.233064i	0.968583	+	0.248690i	$0.0800000\pi$
$450$	−1.25058	+	2.65763i	−1.25058	+	2.65763i
$451$	−0.878275	+	0.638104i	−0.878275	+	0.638104i
$452$	0.331159	+	1.01920i	0.331159	+	1.01920i
$453$		0			0
$454$	0.598617	−	0.153699i	0.598617	−	0.153699i
$455$		0			0
$456$	−2.98509	+	1.18188i	−2.98509	+	1.18188i
$457$	−1.41789	+	0.779494i	−1.41789	+	0.779494i	−0.992115	−	0.125333i	$-0.960000\pi$
$457$	−1.41789	+	0.779494i	−1.41789	+	0.779494i	−0.425779	+	0.904827i	$0.640000\pi$
$458$		0			0
$459$	7.62695	+	0.963507i	7.62695	+	0.963507i
$460$		0			0
$461$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$461$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$462$		0			0
$463$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$463$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$464$		0			0
$465$		0			0
$466$	−0.456288	+	0.969661i	−0.456288	+	0.969661i
$467$	−1.92189	+	0.242791i	−1.92189	+	0.242791i	−0.992115	−	0.125333i	$-0.960000\pi$
$467$	−1.92189	+	0.242791i	−1.92189	+	0.242791i	−0.929776	+	0.368125i	$0.880000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.121636	−	0.0312307i	0.121636	−	0.0312307i
$473$	0.255999	−	1.34200i	0.255999	−	1.34200i
$474$		0			0
$475$	0.688925	+	1.46404i	0.688925	+	1.46404i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$479$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$480$		0			0
$481$		0			0
$482$	1.45794			1.45794
$483$		0			0
$484$	−0.117158	−	0.614163i	−0.117158	−	0.614163i
$485$		0			0
$486$	4.41870	−	3.21038i	4.41870	−	3.21038i
$487$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$487$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$488$		0			0
$489$	0.542072	+	0.509040i	0.542072	+	0.509040i
$490$		0			0
$491$	−0.0534698	+	0.849878i	−0.0534698	+	0.849878i	0.876307	+	0.481754i	$0.160000\pi$
$491$	−0.0534698	+	0.849878i	−0.0534698	+	0.849878i	−0.929776	+	0.368125i	$0.880000\pi$
$492$	−1.36699	+	0.993173i	−1.36699	+	0.993173i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	1.14020	+	3.50919i	1.14020	+	3.50919i
$499$	−1.62954	−	0.645180i	−1.62954	−	0.645180i	−0.637424	−	0.770513i	$-0.720000\pi$
$499$	−1.62954	−	0.645180i	−1.62954	−	0.645180i	−0.992115	+	0.125333i	$0.960000\pi$
$500$		0			0
$501$		0			0
$502$	0.876307	−	0.481754i	0.876307	−	0.481754i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.613161	+	1.88711i	−0.613161	+	1.88711i
$508$		0			0
$509$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$509$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$510$		0			0
$511$		0			0
$512$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$513$	0.390518	−	6.20710i	0.390518	−	6.20710i
$514$	0.00788530	−	0.125333i	0.00788530	−	0.125333i
$515$		0			0
$516$	0.398449	−	2.08874i	0.398449	−	2.08874i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.27760	+	0.702367i	1.27760	+	0.702367i	0.968583	−	0.248690i	$-0.0800000\pi$
$521$	1.27760	+	0.702367i	1.27760	+	0.702367i	0.309017	+	0.951057i	$0.400000\pi$
$522$		0			0
$523$	0.121636	+	1.93334i	0.121636	+	1.93334i	0.309017	+	0.951057i	$0.400000\pi$
$523$	0.121636	+	1.93334i	0.121636	+	1.93334i	−0.187381	+	0.982287i	$0.560000\pi$
$524$	−0.393950	+	0.476203i	−0.393950	+	0.476203i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.473998	−	2.48478i	−0.473998	−	2.48478i
$529$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$530$		0			0
$531$	−0.0691160	+	0.362319i	−0.0691160	+	0.362319i
$532$		0			0
$533$		0			0
$534$	0.743615			0.743615
$535$		0			0
$536$	−1.62954	+	0.645180i	−1.62954	+	0.645180i
$537$	2.87007	−	0.362574i	2.87007	−	0.362574i
$538$		0			0
$539$	−0.929324	−	0.872693i	−0.929324	−	0.872693i
$540$		0			0
$541$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$541$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$542$		0			0
$543$		0			0
$544$	1.07165	−	1.68866i	1.07165	−	1.68866i
$545$		0			0
$546$		0			0
$547$	1.53583	−	0.844328i	1.53583	−	0.844328i	0.535827	−	0.844328i	$-0.320000\pi$
$547$	1.53583	−	0.844328i	1.53583	−	0.844328i	1.00000			$0$
$548$	1.84489	−	0.730444i	1.84489	−	0.730444i
$549$		0			0
$550$	−1.23480	+	0.317042i	−1.23480	+	0.317042i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.348445	−	1.82662i	0.348445	−	1.82662i
$557$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$557$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	2.71085	+	4.27161i	2.71085	+	4.27161i
$562$	0.791759	+	0.313480i	0.791759	+	0.313480i
$563$	−0.613161	+	0.0774602i	−0.613161	+	0.0774602i	−0.425779	−	0.904827i	$-0.640000\pi$
$563$	−0.613161	+	0.0774602i	−0.613161	+	0.0774602i	−0.187381	+	0.982287i	$0.560000\pi$
$564$		0			0
$565$		0			0
$566$	−1.17950	−	0.856954i	−1.17950	−	0.856954i
$567$		0			0
$568$		0			0
$569$	−0.0800484	−	0.0967619i	−0.0800484	−	0.0967619i	0.728969	−	0.684547i	$-0.240000\pi$
$569$	−0.0800484	−	0.0967619i	−0.0800484	−	0.0967619i	−0.809017	+	0.587785i	$0.800000\pi$
$570$		0			0
$571$	1.03137	−	0.749337i	1.03137	−	0.749337i	0.0627905	−	0.998027i	$-0.480000\pi$
$571$	1.03137	−	0.749337i	1.03137	−	0.749337i	0.968583	+	0.248690i	$0.0800000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.550370	−	2.88514i	−0.550370	−	2.88514i
$577$	0.939097	+	1.47978i	0.939097	+	1.47978i	0.876307	+	0.481754i	$0.160000\pi$
$577$	0.939097	+	1.47978i	0.939097	+	1.47978i	0.0627905	+	0.998027i	$0.480000\pi$
$578$	−0.562144	+	2.94686i	−0.562144	+	2.94686i
$579$	0.231683	−	0.0917299i	0.231683	−	0.0917299i
$580$		0			0
$581$		0			0
$582$	0.522142	+	1.60699i	0.522142	+	1.60699i
$583$		0			0
$584$	−0.101597	−	1.61484i	−0.101597	−	1.61484i
$585$		0			0
$586$		0			0
$587$	0.238883	+	0.288760i	0.238883	+	0.288760i	0.876307	−	0.481754i	$-0.160000\pi$
$587$	0.238883	+	0.288760i	0.238883	+	0.288760i	−0.637424	+	0.770513i	$0.720000\pi$
$588$	−1.44644	−	1.35830i	−1.44644	−	1.35830i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.613161	+	1.88711i	−0.613161	+	1.88711i	−0.187381	+	0.982287i	$0.560000\pi$
$593$	−0.613161	+	1.88711i	−0.613161	+	1.88711i	−0.425779	+	0.904827i	$0.640000\pi$
$594$	4.74629	+	1.21864i	4.74629	+	1.21864i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$599$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$600$	−1.92189	+	0.493458i	−1.92189	+	0.493458i
$601$	−1.17950	+	1.10762i	−1.17950	+	1.10762i	−0.187381	+	0.982287i	$0.560000\pi$
$601$	−1.17950	+	1.10762i	−1.17950	+	1.10762i	−0.992115	+	0.125333i	$0.960000\pi$
$602$		0			0
$603$	0.323228	−	5.13756i	0.323228	−	5.13756i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$607$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$608$	−1.41789	−	0.779494i	−1.41789	−	0.779494i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	3.14762	+	4.95986i	3.14762	+	4.95986i
$613$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$613$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$614$	1.27760	+	0.702367i	1.27760	+	0.702367i
$615$		0			0
$616$		0			0
$617$	−0.0800484	−	0.0967619i	−0.0800484	−	0.0967619i	0.728969	−	0.684547i	$-0.240000\pi$
$617$	−0.0800484	−	0.0967619i	−0.0800484	−	0.0967619i	−0.809017	+	0.587785i	$0.800000\pi$
$618$		0			0
$619$	0.0672897	+	1.06954i	0.0672897	+	1.06954i	0.876307	+	0.481754i	$0.160000\pi$
$619$	0.0672897	+	1.06954i	0.0672897	+	1.06954i	−0.809017	+	0.587785i	$0.800000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.309017	+	0.951057i	0.309017	+	0.951057i
$626$	−0.362989	+	0.0931997i	−0.362989	+	0.0931997i
$627$	3.31128	−	2.40578i	3.31128	−	2.40578i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$631$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$632$		0			0
$633$	0.398449	+	0.627855i	0.398449	+	0.627855i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.541587	+	0.297740i	0.541587	+	0.297740i	0.728969	−	0.684547i	$-0.240000\pi$
$641$	0.541587	+	0.297740i	0.541587	+	0.297740i	−0.187381	+	0.982287i	$0.560000\pi$
$642$	−1.67636	−	3.56245i	−1.67636	−	3.56245i
$643$	1.03799	+	1.63560i	1.03799	+	1.63560i	0.728969	+	0.684547i	$0.240000\pi$
$643$	1.03799	+	1.63560i	1.03799	+	1.63560i	0.309017	+	0.951057i	$0.400000\pi$
$644$		0			0
$645$		0			0
$646$	3.21055	+	0.405587i	3.21055	+	0.405587i
$647$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$647$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$648$	4.54244	+	1.16630i	4.54244	+	1.16630i
$649$	−0.140294	+	0.0771272i	−0.140294	+	0.0771272i
$650$		0			0
$651$		0			0
$652$	−0.0235315	+	0.374023i	−0.0235315	+	0.374023i
$653$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$653$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$654$		0			0
$655$		0			0
$656$	−0.824805	−	0.211774i	−0.824805	−	0.211774i
$657$	4.41870	+	1.74949i	4.41870	+	1.74949i
$658$		0			0
$659$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$659$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$660$		0			0
$661$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$661$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$662$	0.0388067	−	0.119435i	0.0388067	−	0.119435i
$663$		0			0
$664$	−0.996398	+	1.57007i	−0.996398	+	1.57007i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	0.876307	−	0.481754i	$-0.160000\pi$
$673$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	−0.992115	+	0.125333i	$0.960000\pi$
$674$	0.238883	+	1.25227i	0.238883	+	1.25227i
$675$	0.720253	−	3.77570i	0.720253	−	3.77570i
$676$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$677$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$677$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$678$	−1.13939	−	1.79538i	−1.13939	−	1.79538i
$679$		0			0
$680$		0			0
$681$	−1.07463	+	0.590785i	−1.07463	+	0.590785i
$682$		0			0
$683$	−1.11716	−	0.614163i	−1.11716	−	0.614163i	−0.187381	−	0.982287i	$-0.560000\pi$
$683$	−1.11716	−	0.614163i	−1.11716	−	0.614163i	−0.929776	+	0.368125i	$0.880000\pi$
$684$	3.84480	−	2.79341i	3.84480	−	2.79341i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.939097	−	0.516273i	0.939097	−	0.516273i
$689$		0			0
$690$		0			0
$691$	0.542804	−	0.656137i	0.542804	−	0.656137i	−0.425779	−	0.904827i	$-0.640000\pi$
$691$	0.542804	−	0.656137i	0.542804	−	0.656137i	0.968583	+	0.248690i	$0.0800000\pi$
$692$		0			0
$693$		0			0
$694$	0.0672897	+	0.106032i	0.0672897	+	0.106032i
$695$		0			0
$696$		0			0
$697$	1.68969	−	0.213457i	1.68969	−	0.213457i
$698$		0			0
$699$	0.398449	−	2.08874i	0.398449	−	2.08874i
$700$		0			0
$701$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$701$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$702$		0			0
$703$		0			0
$704$	0.812619	−	0.982287i	0.812619	−	0.982287i
$705$		0			0
$706$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$707$		0			0
$708$	−0.218359	+	0.120044i	−0.218359	+	0.120044i
$709$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$709$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$710$		0			0
$711$		0			0
$712$	0.238883	+	0.288760i	0.238883	+	0.288760i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.06279	+	0.998027i	1.06279	+	0.998027i
$717$		0			0
$718$		0			0
$719$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$719$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$720$		0			0
$721$		0			0
$722$	0.101597	−	1.61484i	0.101597	−	1.61484i
$723$	−2.80200	+	0.719430i	−2.80200	+	0.719430i
$724$		0			0
$725$		0			0
$726$	0.528228	+	1.12254i	0.528228	+	1.12254i
$727$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$727$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$728$		0			0
$729$	−3.91870	+	4.73690i	−3.91870	+	4.73690i
$730$		0			0
$731$	−1.36620	+	1.65145i	−1.36620	+	1.65145i
$732$		0			0
$733$		0			0		1.00000			$0$
$733$		0			0		−1.00000			$\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.80760	−	1.31330i	1.80760	−	1.31330i
$738$	1.59431	−	1.92718i	1.59431	−	1.92718i
$739$	0.238883	−	1.25227i	0.238883	−	1.25227i	−0.637424	−	0.770513i	$-0.720000\pi$
$739$	0.238883	−	1.25227i	0.238883	−	1.25227i	0.876307	−	0.481754i	$-0.160000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$743$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−2.92659	−	4.61156i	−2.92659	−	4.61156i
$748$	−0.787899	+	2.42490i	−0.787899	+	2.42490i
$749$		0			0
$750$		0			0
$751$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$751$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$752$		0			0
$753$	−1.44644	+	1.35830i	−1.44644	+	1.35830i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$757$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$758$	0.541587	−	1.66683i	0.541587	−	1.66683i
$759$		0			0
$760$		0			0
$761$	−0.574633	+	1.76854i	−0.574633	+	1.76854i	0.0627905	+	0.998027i	$0.480000\pi$
$761$	−0.574633	+	1.76854i	−0.574633	+	1.76854i	−0.637424	+	0.770513i	$0.720000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.26480	−	1.52888i	1.26480	−	1.52888i
$769$	1.03137	−	0.749337i	1.03137	−	0.749337i	0.0627905	−	0.998027i	$-0.480000\pi$
$769$	1.03137	−	0.749337i	1.03137	−	0.749337i	0.968583	+	0.248690i	$0.0800000\pi$
$770$		0			0
$771$	0.0466920	+	0.244768i	0.0466920	+	0.244768i
$772$	0.110048	+	0.0604991i	0.110048	+	0.0604991i
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$	0.197641	+	3.14141i	0.197641	+	3.14141i
$775$		0			0
$776$	−0.456288	+	0.718995i	−0.456288	+	0.718995i
$777$		0			0
$778$		0			0
$779$	−0.258183	−	1.35345i	−0.258183	−	1.35345i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$785$		0			0
$786$	0.522142	−	1.10961i	0.522142	−	1.10961i
$787$	−0.996398	+	0.394502i	−0.996398	+	0.394502i	−0.809017	−	0.587785i	$-0.800000\pi$
$787$	−0.996398	+	0.394502i	−0.996398	+	0.394502i	−0.187381	+	0.982287i	$0.560000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	1.59431	+	3.38807i	1.59431	+	3.38807i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$797$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$798$		0			0
$799$		0			0
$800$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$801$	−1.06616	+	0.273743i	−1.06616	+	0.273743i
$802$	−1.23480	+	1.49261i	−1.23480	+	1.49261i
$803$	0.637424	+	1.96179i	0.637424	+	1.96179i
$804$	2.81343	−	2.04407i	2.81343	−	2.04407i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.26480	−	0.159781i	1.26480	−	0.159781i	0.535827	−	0.844328i	$-0.320000\pi$
$809$	1.26480	−	0.159781i	1.26480	−	0.159781i	0.728969	+	0.684547i	$0.240000\pi$
$810$		0			0
$811$	−0.273190	+	0.256543i	−0.273190	+	0.256543i	−0.809017	−	0.587785i	$-0.800000\pi$
$811$	−0.273190	+	0.256543i	−0.273190	+	0.256543i	0.535827	+	0.844328i	$0.320000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.22632	+	3.77423i	−1.22632	+	3.77423i
$817$	1.40281	+	1.01920i	1.40281	+	1.01920i
$818$	−1.62954	+	0.895846i	−1.62954	+	0.895846i
$819$		0			0
$820$		0			0
$821$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$821$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$822$	−3.18523	+	2.31421i	−3.18523	+	2.31421i
$823$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$823$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$824$		0			0
$825$	2.21670	−	1.21864i	2.21670	−	1.21864i
$826$		0			0
$827$	−0.362989	−	1.90285i	−0.362989	−	1.90285i	−0.425779	−	0.904827i	$-0.640000\pi$
$827$	−0.362989	−	1.90285i	−0.362989	−	1.90285i	0.0627905	−	0.998027i	$-0.480000\pi$
$828$		0			0
$829$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$829$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.618034	+	1.90211i	0.618034	+	1.90211i
$834$	0.231683	+	3.68250i	0.231683	+	3.68250i
$835$		0			0
$836$	1.99794	+	0.512984i	1.99794	+	0.512984i
$837$		0			0
$838$	1.18532	+	1.43281i	1.18532	+	1.43281i
$839$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$839$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$840$		0			0
$841$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$842$		0			0
$843$	−1.67636	−	0.211774i	−1.67636	−	0.211774i
$844$	−0.115808	+	0.356420i	−0.115808	+	0.356420i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	2.68973	+	1.06494i	2.68973	+	1.06494i
$850$	1.93717	+	0.497380i	1.93717	+	0.497380i
$851$		0			0
$852$		0			0
$853$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$853$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$854$		0			0
$855$		0			0
$856$	0.844844	−	1.79538i	0.844844	−	1.79538i
$857$	−0.328407	+	0.180543i	−0.328407	+	0.180543i	−0.637424	−	0.770513i	$-0.720000\pi$
$857$	−0.328407	+	0.180543i	−0.328407	+	0.180543i	0.309017	+	0.951057i	$0.400000\pi$
$858$		0			0
$859$	−0.328407	−	0.180543i	−0.328407	−	0.180543i	0.309017	−	0.951057i	$-0.400000\pi$
$859$	−0.328407	−	0.180543i	−0.328407	−	0.180543i	−0.637424	+	0.770513i	$0.720000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$863$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$864$	1.63660	+	3.47796i	1.63660	+	3.47796i
$865$		0			0
$866$	0.618034			0.618034
$867$	−0.373772	−	5.94094i	−0.373772	−	5.94094i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−1.34019	−	2.11181i	−1.34019	−	2.11181i
$874$		0			0
$875$		0			0
$876$	0.992115	+	3.05342i	0.992115	+	3.05342i
$877$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$877$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.393950	−	1.21245i	−0.393950	−	1.21245i	−0.929776	−	0.368125i	$-0.880000\pi$
$881$	−0.393950	−	1.21245i	−0.393950	−	1.21245i	0.535827	−	0.844328i	$-0.320000\pi$
$882$	2.57386	+	1.41499i	2.57386	+	1.41499i
$883$	1.60528	+	0.202793i	1.60528	+	0.202793i	0.876307	−	0.481754i	$-0.160000\pi$
$883$	1.60528	+	0.202793i	1.60528	+	0.202793i	0.728969	+	0.684547i	$0.240000\pi$
$884$		0			0
$885$		0			0
$886$	0.125581	−	1.99605i	0.125581	−	1.99605i
$887$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$887$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−5.97876			−5.97876
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−1.62954	−	0.895846i	−1.62954	−	0.895846i
$899$		0			0
$900$	2.57386	−	1.41499i	2.57386	−	1.41499i
$901$		0			0
$902$	1.08561			1.08561
$903$		0			0
$904$	0.331159	−	1.01920i	0.331159	−	1.01920i
$905$		0			0
$906$		0			0
$907$	1.87631	+	0.481754i	1.87631	+	0.481754i	1.00000			$0$
$907$	1.87631	+	0.481754i	1.87631	+	0.481754i	0.876307	+	0.481754i	$0.160000\pi$
$908$	−0.574633	−	0.227513i	−0.574633	−	0.227513i
$909$		0			0
$910$		0			0
$911$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$911$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$912$	3.10969	+	0.798431i	3.10969	+	0.798431i
$913$	0.732570	−	2.25462i	0.732570	−	2.25462i
$914$	1.60528	+	0.202793i	1.60528	+	0.202793i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−5.60399	−	5.26250i	−5.60399	−	5.26250i
$919$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$919$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$920$		0			0
$921$	−2.80200	−	0.719430i	−2.80200	−	0.719430i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.781202	+	1.23098i	0.781202	+	1.23098i	0.968583	+	0.248690i	$0.0800000\pi$
$929$	0.781202	+	1.23098i	0.781202	+	1.23098i	−0.187381	+	0.982287i	$0.560000\pi$
$930$		0			0
$931$	1.50441	−	0.595638i	1.50441	−	0.595638i
$932$	0.939097	−	0.516273i	0.939097	−	0.516273i
$933$		0			0
$934$	1.69755	+	0.933237i	1.69755	+	0.933237i
$935$		0			0
$936$		0			0
$937$	0.812619	+	0.982287i	0.812619	+	0.982287i	1.00000			$0$
$937$	0.812619	+	0.982287i	0.812619	+	0.982287i	−0.187381	+	0.982287i	$0.560000\pi$
$938$		0			0
$939$	0.651635	−	0.358239i	0.651635	−	0.358239i
$940$		0			0
$941$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$941$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$942$		0			0
$943$		0			0
$944$	−0.116762	−	0.0462295i	−0.116762	−	0.0462295i
$945$		0			0
$946$	−0.995914	+	0.935225i	−0.995914	+	0.935225i
$947$	1.03137	+	1.24672i	1.03137	+	1.24672i	0.968583	+	0.248690i	$0.0800000\pi$
$947$	1.03137	+	1.24672i	1.03137	+	1.24672i	0.0627905	+	0.998027i	$0.480000\pi$
$948$		0			0
$949$		0			0
$950$	0.303189	−	1.58937i	0.303189	−	1.58937i
$951$		0			0
$952$		0			0
$953$	−0.866986	+	0.629902i	−0.866986	+	0.629902i	−0.929776	−	0.368125i	$-0.880000\pi$
$953$	−0.866986	+	0.629902i	−0.866986	+	0.629902i	0.0627905	+	0.998027i	$0.480000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$962$		0			0
$963$	3.71491	+	4.49056i	3.71491	+	4.49056i
$964$	−1.17950	−	0.856954i	−1.17950	−	0.856954i
$965$		0			0
$966$		0			0
$967$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$967$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$968$	−0.266213	+	0.565732i	−0.266213	+	0.565732i
$969$	−6.37047	+	0.804777i	−6.37047	+	0.804777i
$970$		0			0
$971$	0.688925	−	1.46404i	0.688925	−	1.46404i	−0.187381	−	0.982287i	$-0.560000\pi$
$971$	0.688925	−	1.46404i	0.688925	−	1.46404i	0.876307	−	0.481754i	$-0.160000\pi$
$972$	−5.46182			−5.46182
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.791759	+	1.68257i	0.791759	+	1.68257i	0.728969	+	0.684547i	$0.240000\pi$
$977$	0.791759	+	1.68257i	0.791759	+	1.68257i	0.0627905	+	0.998027i	$0.480000\pi$
$978$	−0.139340	−	0.730444i	−0.139340	−	0.730444i
$979$	−0.386520	−	0.280823i	−0.386520	−	0.280823i
$980$		0			0
$981$		0			0
$982$	0.542804	−	0.656137i	0.542804	−	0.656137i
$983$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$983$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$984$	1.68969			1.68969
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$991$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$992$		0			0
$993$	−0.0156462	+	0.248690i	−0.0156462	+	0.248690i
$994$		0			0
$995$		0			0
$996$	1.14020	−	3.50919i	1.14020	−	3.50919i
$997$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$997$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$998$	0.939097	+	1.47978i	0.939097	+	1.47978i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2008.1.w.a.243.1	✓	20
8.3	odd	2	CM	2008.1.w.a.243.1	✓	20
251.94	even	25	inner	2008.1.w.a.1851.1	yes	20
2008.1851	odd	50	inner	2008.1.w.a.1851.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2008.1.w.a.243.1	✓	20	1.1	even	1	trivial
2008.1.w.a.243.1	✓	20	8.3	odd	2	CM
2008.1.w.a.1851.1	yes	20	251.94	even	25	inner
2008.1.w.a.1851.1	yes	20	2008.1851	odd	50	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2008 = 2^{3} \cdot 251 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2008.w (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(1.84489 + 0.730444i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.06320 - 1.67534i) q^{6} +(0.309017 - 0.951057i) q^{8} +(2.14110 + 2.01063i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(1.84489 + 0.730444i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.06320 - 1.67534i) q^{6} +(0.309017 - 0.951057i) q^{8} +(2.14110 + 2.01063i) q^{9} +(-0.0800484 + 1.27233i) q^{11} +(-0.124591 + 1.98031i) q^{12} +(-0.809017 + 0.587785i) q^{16} +(1.07165 - 1.68866i) q^{17} +(-0.550370 - 2.88514i) q^{18} +(-1.41789 - 0.779494i) q^{19} +(0.812619 - 0.982287i) q^{22} +(1.26480 - 1.52888i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(1.63660 + 3.47796i) q^{27} +1.00000 q^{32} +(-1.07705 + 2.28884i) q^{33} +(-1.85955 + 0.736249i) q^{34} +(-1.25058 + 2.65763i) q^{36} +(0.688925 + 1.46404i) q^{38} +(0.542804 + 0.656137i) q^{41} +(-1.06320 - 0.134314i) q^{43} +(-1.23480 + 0.317042i) q^{44} +(-1.92189 + 0.493458i) q^{48} +(-0.637424 + 0.770513i) q^{49} +(0.309017 + 0.951057i) q^{50} +(3.21055 - 2.33260i) q^{51} +(0.720253 - 3.77570i) q^{54} +(-2.04648 - 2.47377i) q^{57} +(0.0672897 + 0.106032i) q^{59} +(-0.809017 - 0.587785i) q^{64} +(2.21670 - 1.21864i) q^{66} +(-1.11716 - 1.35041i) q^{67} +(1.93717 + 0.497380i) q^{68} +(2.57386 - 1.41499i) q^{72} +(1.50441 - 0.595638i) q^{73} +(-1.06320 - 1.67534i) q^{75} +(0.303189 - 1.58937i) q^{76} +(0.294474 + 4.68053i) q^{81} +(-0.0534698 - 0.849878i) q^{82} +(-1.80113 - 0.462452i) q^{83} +(0.781202 + 0.733597i) q^{86} +(1.18532 + 0.469303i) q^{88} +(-0.200808 + 0.316423i) q^{89} +(1.84489 + 0.730444i) q^{96} +(-0.824805 - 0.211774i) q^{97} +(0.968583 - 0.248690i) q^{98} +(-2.72958 + 2.56325i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{2} - 5 q^{4} - 5 q^{8}+O(q^{10}) \) 20 * q - 5 * q^2 - 5 * q^4 - 5 * q^8	\( 20 q - 5 q^{2} - 5 q^{4} - 5 q^{8} - 5 q^{11} - 5 q^{16} + 20 q^{22} - 5 q^{25} - 5 q^{27} + 20 q^{32} - 5 q^{33} - 5 q^{44} - 5 q^{50} - 5 q^{54} - 5 q^{59} - 5 q^{64} - 5 q^{66} - 5 q^{81} - 5 q^{83} - 5 q^{88} - 5 q^{99}+O(q^{100}) \) 20 * q - 5 * q^2 - 5 * q^4 - 5 * q^8 - 5 * q^11 - 5 * q^16 + 20 * q^22 - 5 * q^25 - 5 * q^27 + 20 * q^32 - 5 * q^33 - 5 * q^44 - 5 * q^50 - 5 * q^54 - 5 * q^59 - 5 * q^64 - 5 * q^66 - 5 * q^81 - 5 * q^83 - 5 * q^88 - 5 * q^99

Introduction

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