LMFDB - Embedded newform 3808.1.cu.c.237.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3808,1,Mod(237,3808)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3808, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 4, 4]))

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

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

chi := DirichletCharacter("3808.237");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3808 = 2^{5} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3808.cu (of order $8$, degree $4$, 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:	$1.90043956811$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{40})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{40}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{40} + \cdots)$

Embedding invariants

Embedding label			237.1
Root			$0.987688 + 0.156434i$ of defining polynomial
Character	$\chi$	$=$	3808.237
Dual form			3808.1.cu.c.1189.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 - 0.156434i) q^{2} +(0.399903 - 0.965451i) q^{3} +(0.951057 + 0.309017i) q^{4} +(1.40505 - 0.581990i) q^{5} +(-0.546010 + 0.891007i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(-0.0650673 - 0.0650673i) q^{9} +O(q^{10})$	\(q+(-0.987688 - 0.156434i) q^{2} +(0.399903 - 0.965451i) q^{3} +(0.951057 + 0.309017i) q^{4} +(1.40505 - 0.581990i) q^{5} +(-0.546010 + 0.891007i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(-0.0650673 - 0.0650673i) q^{9} +(-1.47879 + 0.355026i) q^{10} +(0.678671 - 0.794622i) q^{12} +(0.809017 - 0.587785i) q^{14} -1.58924i q^{15} +(0.809017 + 0.587785i) q^{16} +1.00000i q^{17} +(0.0540874 + 0.0744449i) q^{18} +(1.51612 - 0.119322i) q^{20} +(0.399903 + 0.965451i) q^{21} +(-0.794622 + 0.678671i) q^{24} +(0.928339 - 0.928339i) q^{25} +(0.876612 - 0.363104i) q^{27} +(-0.891007 + 0.453990i) q^{28} +(-0.248613 + 1.56968i) q^{30} +0.618034 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.156434 - 0.987688i) q^{34} +(-0.581990 + 1.40505i) q^{35} +(-0.0417758 - 0.0819895i) q^{36} +(-1.51612 - 0.119322i) q^{40} +(1.14412 + 1.14412i) q^{41} +(-0.243950 - 1.01612i) q^{42} +(-0.744220 - 1.79671i) q^{43} +(-0.129291 - 0.0535541i) q^{45} +(0.891007 - 0.546010i) q^{48} -1.00000i q^{49} +(-1.06213 + 0.771685i) q^{50} +(0.965451 + 0.399903i) q^{51} +(-0.0600500 - 0.144974i) q^{53} +(-0.922621 + 0.221502i) q^{54} +(0.951057 - 0.309017i) q^{56} +(0.491103 - 1.51146i) q^{60} +(0.652583 - 1.57547i) q^{61} +(-0.610425 - 0.0966818i) q^{62} +0.0920190 q^{63} +(0.587785 + 0.809017i) q^{64} +(0.763007 - 1.84206i) q^{67} +(-0.309017 + 0.951057i) q^{68} +(0.794622 - 1.29671i) q^{70} +(0.0284354 + 0.0875153i) q^{72} +(1.39680 + 1.39680i) q^{73} +(-0.525020 - 1.26751i) q^{75} +(1.47879 + 0.355026i) q^{80} -1.08355i q^{81} +(-0.951057 - 1.30902i) q^{82} +(0.0819895 + 1.04178i) q^{84} +(0.581990 + 1.40505i) q^{85} +(0.453990 + 1.89101i) q^{86} +(0.119322 + 0.0731203i) q^{90} +(0.247154 - 0.596682i) q^{93} +(-0.965451 + 0.399903i) q^{96} -1.78201 q^{97} +(-0.156434 + 0.987688i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q - 16 * q^6 + 4 * q^9	$ 16 q - 16 q^{6} + 4 q^{9} + 4 q^{12} + 4 q^{14} + 4 q^{16} + 4 q^{20} + 4 q^{25} - 4 q^{27} + 16 q^{30} - 8 q^{31} - 4 q^{35} + 16 q^{36} - 4 q^{40} + 16 q^{45} - 4 q^{50} + 4 q^{51} - 4 q^{54} + 4 q^{61} + 16 q^{63} - 4 q^{67} + 4 q^{68} - 4 q^{72} + 4 q^{73} + 4 q^{75} - 4 q^{84} + 4 q^{85} - 4 q^{96}+O(q^{100}) $ 16 * q - 16 * q^6 + 4 * q^9 + 4 * q^12 + 4 * q^14 + 4 * q^16 + 4 * q^20 + 4 * q^25 - 4 * q^27 + 16 * q^30 - 8 * q^31 - 4 * q^35 + 16 * q^36 - 4 * q^40 + 16 * q^45 - 4 * q^50 + 4 * q^51 - 4 * q^54 + 4 * q^61 + 16 * q^63 - 4 * q^67 + 4 * q^68 - 4 * q^72 + 4 * q^73 + 4 * q^75 - 4 * q^84 + 4 * q^85 - 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3808\mathbb{Z}\right)^\times$.

$n$	$2143$	$2689$	$3265$	$3333$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−0.987688	−	0.156434i	−0.987688	−	0.156434i
$2$	−0.987688	−	0.156434i	−0.987688	−	0.156434i
$3$	0.399903	−	0.965451i	0.399903	−	0.965451i	−0.587785	−	0.809017i	$-0.700000\pi$
$3$	0.399903	−	0.965451i	0.399903	−	0.965451i	0.987688	−	0.156434i	$-0.0500000\pi$
$4$	0.951057	+	0.309017i	0.951057	+	0.309017i
$5$	1.40505	−	0.581990i	1.40505	−	0.581990i	0.453990	−	0.891007i	$-0.350000\pi$
$5$	1.40505	−	0.581990i	1.40505	−	0.581990i	0.951057	+	0.309017i	$0.100000\pi$
$6$	−0.546010	+	0.891007i	−0.546010	+	0.891007i
$7$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$7$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$8$	−0.891007	−	0.453990i	−0.891007	−	0.453990i
$9$	−0.0650673	−	0.0650673i	−0.0650673	−	0.0650673i
$10$	−1.47879	+	0.355026i	−1.47879	+	0.355026i
$11$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$11$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$12$	0.678671	−	0.794622i	0.678671	−	0.794622i
$13$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$13$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$14$	0.809017	−	0.587785i	0.809017	−	0.587785i
$15$		−	1.58924i		−	1.58924i
$16$	0.809017	+	0.587785i	0.809017	+	0.587785i
$17$			1.00000i			1.00000i
$17$			1.00000i			1.00000i
$18$	0.0540874	+	0.0744449i	0.0540874	+	0.0744449i
$19$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$19$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$20$	1.51612	−	0.119322i	1.51612	−	0.119322i
$21$	0.399903	+	0.965451i	0.399903	+	0.965451i
$22$		0			0
$23$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$23$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$24$	−0.794622	+	0.678671i	−0.794622	+	0.678671i
$25$	0.928339	−	0.928339i	0.928339	−	0.928339i
$26$		0			0
$27$	0.876612	−	0.363104i	0.876612	−	0.363104i
$28$	−0.891007	+	0.453990i	−0.891007	+	0.453990i
$29$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$29$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$30$	−0.248613	+	1.56968i	−0.248613	+	1.56968i
$31$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$31$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$32$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$33$		0			0
$34$	0.156434	−	0.987688i	0.156434	−	0.987688i
$35$	−0.581990	+	1.40505i	−0.581990	+	1.40505i
$36$	−0.0417758	−	0.0819895i	−0.0417758	−	0.0819895i
$37$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$37$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$38$		0			0
$39$		0			0
$40$	−1.51612	−	0.119322i	−1.51612	−	0.119322i
$41$	1.14412	+	1.14412i	1.14412	+	1.14412i	0.987688	+	0.156434i	$0.0500000\pi$
$41$	1.14412	+	1.14412i	1.14412	+	1.14412i	0.156434	+	0.987688i	$0.450000\pi$
$42$	−0.243950	−	1.01612i	−0.243950	−	1.01612i
$43$	−0.744220	−	1.79671i	−0.744220	−	1.79671i	−0.587785	−	0.809017i	$-0.700000\pi$
$43$	−0.744220	−	1.79671i	−0.744220	−	1.79671i	−0.156434	−	0.987688i	$-0.550000\pi$
$44$		0			0
$45$	−0.129291	−	0.0535541i	−0.129291	−	0.0535541i
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	0.891007	−	0.546010i	0.891007	−	0.546010i
$49$		−	1.00000i		−	1.00000i
$50$	−1.06213	+	0.771685i	−1.06213	+	0.771685i
$51$	0.965451	+	0.399903i	0.965451	+	0.399903i
$52$		0			0
$53$	−0.0600500	−	0.144974i	−0.0600500	−	0.144974i	0.891007	−	0.453990i	$-0.150000\pi$
$53$	−0.0600500	−	0.144974i	−0.0600500	−	0.144974i	−0.951057	+	0.309017i	$0.900000\pi$
$54$	−0.922621	+	0.221502i	−0.922621	+	0.221502i
$55$		0			0
$56$	0.951057	−	0.309017i	0.951057	−	0.309017i
$57$		0			0
$58$		0			0
$59$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$59$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$60$	0.491103	−	1.51146i	0.491103	−	1.51146i
$61$	0.652583	−	1.57547i	0.652583	−	1.57547i	−0.156434	−	0.987688i	$-0.550000\pi$
$61$	0.652583	−	1.57547i	0.652583	−	1.57547i	0.809017	−	0.587785i	$-0.200000\pi$
$62$	−0.610425	−	0.0966818i	−0.610425	−	0.0966818i
$63$	0.0920190			0.0920190
$64$	0.587785	+	0.809017i	0.587785	+	0.809017i
$65$		0			0
$66$		0			0
$67$	0.763007	−	1.84206i	0.763007	−	1.84206i	0.309017	−	0.951057i	$-0.400000\pi$
$67$	0.763007	−	1.84206i	0.763007	−	1.84206i	0.453990	−	0.891007i	$-0.350000\pi$
$68$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$69$		0			0
$70$	0.794622	−	1.29671i	0.794622	−	1.29671i
$71$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$71$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$72$	0.0284354	+	0.0875153i	0.0284354	+	0.0875153i
$73$	1.39680	+	1.39680i	1.39680	+	1.39680i	0.809017	+	0.587785i	$0.200000\pi$
$73$	1.39680	+	1.39680i	1.39680	+	1.39680i	0.587785	+	0.809017i	$0.300000\pi$
$74$		0			0
$75$	−0.525020	−	1.26751i	−0.525020	−	1.26751i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	1.47879	+	0.355026i	1.47879	+	0.355026i
$81$		−	1.08355i		−	1.08355i
$82$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$83$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$83$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$84$	0.0819895	+	1.04178i	0.0819895	+	1.04178i
$85$	0.581990	+	1.40505i	0.581990	+	1.40505i
$86$	0.453990	+	1.89101i	0.453990	+	1.89101i
$87$		0			0
$88$		0			0
$89$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$89$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$90$	0.119322	+	0.0731203i	0.119322	+	0.0731203i
$91$		0			0
$92$		0			0
$93$	0.247154	−	0.596682i	0.247154	−	0.596682i
$94$		0			0
$95$		0			0
$96$	−0.965451	+	0.399903i	−0.965451	+	0.399903i
$97$	−1.78201			−1.78201			−0.891007	−	0.453990i	$-0.850000\pi$
$97$	−1.78201			−1.78201			−0.891007	+	0.453990i	$0.850000\pi$
$98$	−0.156434	+	0.987688i	−0.156434	+	0.987688i
$99$		0			0
$100$	1.16977	−	0.596030i	1.16977	−	0.596030i
$101$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$101$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$102$	−0.891007	−	0.546010i	−0.891007	−	0.546010i
$103$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$103$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$104$		0			0
$105$	1.12377	+	1.12377i	1.12377	+	1.12377i
$106$	0.0366318	+	0.152583i	0.0366318	+	0.152583i
$107$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$107$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$108$	0.945913	−	0.0744449i	0.945913	−	0.0744449i
$109$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$109$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$110$		0			0
$111$		0			0
$112$	−0.987688	+	0.156434i	−0.987688	+	0.156434i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$120$	−0.721502	+	1.41603i	−0.721502	+	1.41603i
$121$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$122$	−0.891007	+	1.45399i	−0.891007	+	1.45399i
$123$	1.56213	−	0.647057i	1.56213	−	0.647057i
$124$	0.587785	+	0.190983i	0.587785	+	0.190983i
$125$	0.182086	−	0.439596i	0.182086	−	0.439596i
$126$	−0.0908861	−	0.0143949i	−0.0908861	−	0.0143949i
$127$	−0.907981			−0.907981			−0.453990	−	0.891007i	$-0.650000\pi$
$127$	−0.907981			−0.907981			−0.453990	+	0.891007i	$0.650000\pi$
$128$	−0.453990	−	0.891007i	−0.453990	−	0.891007i
$129$	−2.03225			−2.03225
$130$		0			0
$131$	−0.292893	+	0.707107i	−0.292893	+	0.707107i	0.707107	+	0.707107i	$0.250000\pi$
$131$	−0.292893	+	0.707107i	−0.292893	+	0.707107i	−1.00000			$\pi$
$132$		0			0
$133$		0			0
$134$	−1.04178	+	1.70002i	−1.04178	+	1.70002i
$135$	1.02036	−	1.02036i	1.02036	−	1.02036i
$136$	0.453990	−	0.891007i	0.453990	−	0.891007i
$137$	1.14412	+	1.14412i	1.14412	+	1.14412i	0.987688	+	0.156434i	$0.0500000\pi$
$137$	1.14412	+	1.14412i	1.14412	+	1.14412i	0.156434	+	0.987688i	$0.450000\pi$
$138$		0			0
$139$	0.497066	+	1.20002i	0.497066	+	1.20002i	0.951057	+	0.309017i	$0.100000\pi$
$139$	0.497066	+	1.20002i	0.497066	+	1.20002i	−0.453990	+	0.891007i	$0.650000\pi$
$140$	−0.987688	+	1.15643i	−0.987688	+	1.15643i
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.0143949	−	0.0908861i	−0.0143949	−	0.0908861i
$145$		0			0
$146$	−1.16110	−	1.59811i	−1.16110	−	1.59811i
$147$	−0.965451	−	0.399903i	−0.965451	−	0.399903i
$148$		0			0
$149$	−0.178671	−	0.431351i	−0.178671	−	0.431351i	0.809017	−	0.587785i	$-0.200000\pi$
$149$	−0.178671	−	0.431351i	−0.178671	−	0.431351i	−0.987688	+	0.156434i	$0.950000\pi$
$150$	0.320274	+	1.33404i	0.320274	+	1.33404i
$151$	0.831254	+	0.831254i	0.831254	+	0.831254i	0.987688	−	0.156434i	$-0.0500000\pi$
$151$	0.831254	+	0.831254i	0.831254	+	0.831254i	−0.156434	+	0.987688i	$0.550000\pi$
$152$		0			0
$153$	0.0650673	−	0.0650673i	0.0650673	−	0.0650673i
$154$		0			0
$155$	0.868367	−	0.359689i	0.868367	−	0.359689i
$156$		0			0
$157$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$157$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$158$		0			0
$159$	−0.163979			−0.163979
$160$	−1.40505	−	0.581990i	−1.40505	−	0.581990i
$161$		0			0
$162$	−0.169505	+	1.07021i	−0.169505	+	1.07021i
$163$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$163$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$164$	0.734572	+	1.44168i	0.734572	+	1.44168i
$165$		0			0
$166$		0			0
$167$	−1.39680	+	1.39680i	−1.39680	+	1.39680i	−0.587785	+	0.809017i	$0.700000\pi$
$167$	−1.39680	+	1.39680i	−1.39680	+	1.39680i	−0.809017	+	0.587785i	$0.800000\pi$
$168$	0.0819895	−	1.04178i	0.0819895	−	1.04178i
$169$	0.707107	+	0.707107i	0.707107	+	0.707107i
$170$	−0.355026	−	1.47879i	−0.355026	−	1.47879i
$171$		0			0
$172$	−0.152583	−	1.93874i	−0.152583	−	1.93874i
$173$	−1.79671	−	0.744220i	−1.79671	−	0.744220i	−0.987688	−	0.156434i	$-0.950000\pi$
$173$	−1.79671	−	0.744220i	−1.79671	−	0.744220i	−0.809017	−	0.587785i	$-0.800000\pi$
$174$		0			0
$175$			1.31287i			1.31287i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.431351	−	0.178671i	−0.431351	−	0.178671i	0.156434	−	0.987688i	$-0.450000\pi$
$179$	−0.431351	−	0.178671i	−0.431351	−	0.178671i	−0.587785	+	0.809017i	$0.700000\pi$
$180$	−0.106414	−	0.0908861i	−0.106414	−	0.0908861i
$181$	−0.292893	−	0.707107i	−0.292893	−	0.707107i	0.707107	−	0.707107i	$-0.250000\pi$
$181$	−0.292893	−	0.707107i	−0.292893	−	0.707107i	−1.00000			$\pi$
$182$		0			0
$183$	−1.26007	−	1.26007i	−1.26007	−	1.26007i
$184$		0			0
$185$		0			0
$186$	−0.337452	+	0.550672i	−0.337452	+	0.550672i
$187$		0			0
$188$		0			0
$189$	−0.363104	+	0.876612i	−0.363104	+	0.876612i
$190$		0			0
$191$	−1.78201			−1.78201			−0.891007	−	0.453990i	$-0.850000\pi$
$191$	−1.78201			−1.78201			−0.891007	+	0.453990i	$0.850000\pi$
$192$	1.01612	−	0.243950i	1.01612	−	0.243950i
$193$		0			0		1.00000			$0$
$193$		0			0		−1.00000			$\pi$
$194$	1.76007	+	0.278768i	1.76007	+	0.278768i
$195$		0			0
$196$	0.309017	−	0.951057i	0.309017	−	0.951057i
$197$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$197$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$198$		0			0
$199$	−0.831254	+	0.831254i	−0.831254	+	0.831254i	−0.987688	−	0.156434i	$-0.950000\pi$
$199$	−0.831254	+	0.831254i	−0.831254	+	0.831254i	0.156434	+	0.987688i	$0.450000\pi$
$200$	−1.24861	+	0.405699i	−1.24861	+	0.405699i
$201$	−1.47329	−	1.47329i	−1.47329	−	1.47329i
$202$		0			0
$203$		0			0
$204$	0.794622	+	0.678671i	0.794622	+	0.678671i
$205$	2.27341	+	0.941679i	2.27341	+	0.941679i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$	−0.934134	−	1.28573i	−0.934134	−	1.28573i
$211$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$211$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$212$	−0.0123117	−	0.156434i	−0.0123117	−	0.156434i
$213$		0			0
$214$		0			0
$215$	−2.09133	−	2.09133i	−2.09133	−	2.09133i
$216$	−0.945913	−	0.0744449i	−0.945913	−	0.0744449i
$217$	−0.437016	+	0.437016i	−0.437016	+	0.437016i
$218$		0			0
$219$	1.90713	−	0.789959i	1.90713	−	0.789959i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$	1.00000			1.00000
$225$	−0.120809			−0.120809
$226$		0			0
$227$	−0.497066	+	1.20002i	−0.497066	+	1.20002i	0.453990	+	0.891007i	$0.350000\pi$
$227$	−0.497066	+	1.20002i	−0.497066	+	1.20002i	−0.951057	+	0.309017i	$0.900000\pi$
$228$		0			0
$229$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$229$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$233$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	0.587785	+	0.809017i	0.587785	+	0.809017i
$239$		−	1.17557i		−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$239$		−	1.17557i		−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$240$	0.934134	−	1.28573i	0.934134	−	1.28573i
$241$		−	0.618034i		−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$241$		−	0.618034i		−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$242$	0.809017	−	0.587785i	0.809017	−	0.587785i
$243$	−0.169505	−	0.0702112i	−0.169505	−	0.0702112i
$244$	1.10749	−	1.29671i	1.10749	−	1.29671i
$245$	−0.581990	−	1.40505i	−0.581990	−	1.40505i
$246$	−1.64412	+	0.394719i	−1.64412	+	0.394719i
$247$		0			0
$248$	−0.550672	−	0.280582i	−0.550672	−	0.280582i
$249$		0			0
$250$	−0.248613	+	0.405699i	−0.248613	+	0.405699i
$251$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$251$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$252$	0.0875153	+	0.0284354i	0.0875153	+	0.0284354i
$253$		0			0
$254$	0.896802	+	0.142040i	0.896802	+	0.142040i
$255$	1.58924			1.58924
$256$	0.309017	+	0.951057i	0.309017	+	0.951057i
$257$		0			0		1.00000			$0$
$257$		0			0		−1.00000			$\pi$
$258$	2.00723	+	0.317914i	2.00723	+	0.317914i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.399903	−	0.652583i	0.399903	−	0.652583i
$263$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$263$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$264$		0			0
$265$	−0.168746	−	0.168746i	−0.168746	−	0.168746i
$266$		0			0
$267$		0			0
$268$	1.29489	−	1.51612i	1.29489	−	1.51612i
$269$	−0.707107	−	0.292893i	−0.707107	−	0.292893i		−	1.00000i	$-0.5\pi$
$269$	−0.707107	−	0.292893i	−0.707107	−	0.292893i	−0.707107	+	0.707107i	$0.750000\pi$
$270$	−1.16741	+	0.848176i	−1.16741	+	0.848176i
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$273$		0			0
$274$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$275$		0			0
$276$		0			0
$277$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$277$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$278$	−0.303221	−	1.26301i	−0.303221	−	1.26301i
$279$	−0.0402138	−	0.0402138i	−0.0402138	−	0.0402138i
$280$	1.15643	−	0.987688i	1.15643	−	0.987688i
$281$	1.34500	−	1.34500i	1.34500	−	1.34500i	0.453990	−	0.891007i	$-0.350000\pi$
$281$	1.34500	−	1.34500i	1.34500	−	1.34500i	0.891007	−	0.453990i	$-0.150000\pi$
$282$		0			0
$283$	0.144974	−	0.0600500i	0.144974	−	0.0600500i	−0.309017	−	0.951057i	$-0.600000\pi$
$283$	0.144974	−	0.0600500i	0.144974	−	0.0600500i	0.453990	+	0.891007i	$0.350000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.61803			−1.61803
$288$			0.0920190i			0.0920190i
$289$	−1.00000			−1.00000
$290$		0			0
$291$	−0.712633	+	1.72045i	−0.712633	+	1.72045i
$292$	0.896802	+	1.76007i	0.896802	+	1.76007i
$293$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$293$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$294$	0.891007	+	0.546010i	0.891007	+	0.546010i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	0.108993	+	0.453990i	0.108993	+	0.453990i
$299$		0			0
$300$	−0.107642	−	1.36772i	−0.107642	−	1.36772i
$301$	1.79671	+	0.744220i	1.79671	+	0.744220i
$302$	−0.690983	−	0.951057i	−0.690983	−	0.951057i
$303$		0			0
$304$		0			0
$305$		−	2.59341i		−	2.59341i
$306$	−0.0744449	+	0.0540874i	−0.0744449	+	0.0540874i
$307$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$307$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$308$		0			0
$309$		0			0
$310$	−0.913944	+	0.219418i	−0.913944	+	0.219418i
$311$	1.34500	+	1.34500i	1.34500	+	1.34500i	0.891007	+	0.453990i	$0.150000\pi$
$311$	1.34500	+	1.34500i	1.34500	+	1.34500i	0.453990	+	0.891007i	$0.350000\pi$
$312$		0			0
$313$	1.34500	−	1.34500i	1.34500	−	1.34500i	0.453990	−	0.891007i	$-0.350000\pi$
$313$	1.34500	−	1.34500i	1.34500	−	1.34500i	0.891007	−	0.453990i	$-0.150000\pi$
$314$		0			0
$315$	0.129291	−	0.0535541i	0.129291	−	0.0535541i
$316$		0			0
$317$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$317$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$318$	0.161960	+	0.0256520i	0.161960	+	0.0256520i
$319$		0			0
$320$	1.29671	+	0.794622i	1.29671	+	0.794622i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.334836	−	1.03052i	0.334836	−	1.03052i
$325$		0			0
$326$		0			0
$327$		0			0
$328$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$329$		0			0
$330$		0			0
$331$	−0.497066	−	1.20002i	−0.497066	−	1.20002i	−0.951057	−	0.309017i	$-0.900000\pi$
$331$	−0.497066	−	1.20002i	−0.497066	−	1.20002i	0.453990	−	0.891007i	$-0.350000\pi$
$332$		0			0
$333$		0			0
$334$	1.59811	−	1.16110i	1.59811	−	1.16110i
$335$		−	3.03225i		−	3.03225i
$336$	−0.243950	+	1.01612i	−0.243950	+	1.01612i
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$339$		0			0
$340$	0.119322	+	1.51612i	0.119322	+	1.51612i
$341$		0			0
$342$		0			0
$343$	0.707107	+	0.707107i	0.707107	+	0.707107i
$344$	−0.152583	+	1.93874i	−0.152583	+	1.93874i
$345$		0			0
$346$	1.65816	+	1.01612i	1.65816	+	1.01612i
$347$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$347$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$348$		0			0
$349$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$349$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$350$	0.205378	−	1.29671i	0.205378	−	1.29671i
$351$		0			0
$352$		0			0
$353$		0			0		1.00000			$0$
$353$		0			0		−1.00000			$\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.965451	+	0.399903i	−0.965451	+	0.399903i
$358$	0.398090	+	0.243950i	0.398090	+	0.243950i
$359$	0.642040	−	0.642040i	0.642040	−	0.642040i	−0.309017	−	0.951057i	$-0.600000\pi$
$359$	0.642040	−	0.642040i	0.642040	−	0.642040i	0.951057	+	0.309017i	$0.100000\pi$
$360$	0.0908861	+	0.106414i	0.0908861	+	0.106414i
$361$	0.707107	+	0.707107i	0.707107	+	0.707107i
$362$	0.178671	+	0.744220i	0.178671	+	0.744220i
$363$	0.399903	+	0.965451i	0.399903	+	0.965451i
$364$		0			0
$365$	2.77550	+	1.14965i	2.77550	+	1.14965i
$366$	1.04744	+	1.44168i	1.04744	+	1.44168i
$367$			1.61803i			1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$367$			1.61803i			1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$368$		0			0
$369$		−	0.148890i		−	0.148890i
$370$		0			0
$371$	0.144974	+	0.0600500i	0.144974	+	0.0600500i
$372$	0.419442	−	0.491103i	0.419442	−	0.491103i
$373$	−0.744220	−	1.79671i	−0.744220	−	1.79671i	−0.587785	−	0.809017i	$-0.700000\pi$
$373$	−0.744220	−	1.79671i	−0.744220	−	1.79671i	−0.156434	−	0.987688i	$-0.550000\pi$
$374$		0			0
$375$	−0.351591	−	0.351591i	−0.351591	−	0.351591i
$376$		0			0
$377$		0			0
$378$	0.495766	−	0.809017i	0.495766	−	0.809017i
$379$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$379$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$380$		0			0
$381$	−0.363104	+	0.876612i	−0.363104	+	0.876612i
$382$	1.76007	+	0.278768i	1.76007	+	0.278768i
$383$		0			0		1.00000			$0$
$383$		0			0		−1.00000			$\pi$
$384$	−1.04178	+	0.0819895i	−1.04178	+	0.0819895i
$385$		0			0
$386$		0			0
$387$	−0.0684824	+	0.165331i	−0.0684824	+	0.165331i
$388$	−1.69480	−	0.550672i	−1.69480	−	0.550672i
$389$	−1.40505	+	0.581990i	−1.40505	+	0.581990i	−0.951057	−	0.309017i	$-0.900000\pi$
$389$	−1.40505	+	0.581990i	−1.40505	+	0.581990i	−0.453990	+	0.891007i	$0.650000\pi$
$390$		0			0
$391$		0			0
$392$	−0.453990	+	0.891007i	−0.453990	+	0.891007i
$393$	0.565548	+	0.565548i	0.565548	+	0.565548i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−0.144974	−	0.0600500i	−0.144974	−	0.0600500i	0.309017	−	0.951057i	$-0.400000\pi$
$397$	−0.144974	−	0.0600500i	−0.144974	−	0.0600500i	−0.453990	+	0.891007i	$0.650000\pi$
$398$	0.951057	−	0.690983i	0.951057	−	0.690983i
$399$		0			0
$400$	1.29671	−	0.205378i	1.29671	−	0.205378i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$	1.22468	+	1.68563i	1.22468	+	1.68563i
$403$		0			0
$404$		0			0
$405$	−0.630616	−	1.52244i	−0.630616	−	1.52244i
$406$		0			0
$407$		0			0
$408$	−0.678671	−	0.794622i	−0.678671	−	0.794622i
$409$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$409$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$410$	−2.09811	−	1.28573i	−2.09811	−	1.28573i
$411$	1.56213	−	0.647057i	1.56213	−	0.647057i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.35734			1.35734
$418$		0			0
$419$	−0.581990	+	1.40505i	−0.581990	+	1.40505i	0.309017	+	0.951057i	$0.400000\pi$
$419$	−0.581990	+	1.40505i	−0.581990	+	1.40505i	−0.891007	+	0.453990i	$0.850000\pi$
$420$	0.721502	+	1.41603i	0.721502	+	1.41603i
$421$	−1.57547	+	0.652583i	−1.57547	+	0.652583i	−0.987688	−	0.156434i	$-0.950000\pi$
$421$	−1.57547	+	0.652583i	−1.57547	+	0.652583i	−0.587785	+	0.809017i	$0.700000\pi$
$422$		0			0
$423$		0			0
$424$	−0.0123117	+	0.156434i	−0.0123117	+	0.156434i
$425$	0.928339	+	0.928339i	0.928339	+	0.928339i
$426$		0			0
$427$	0.652583	+	1.57547i	0.652583	+	1.57547i
$428$		0			0
$429$		0			0
$430$	1.73842	+	2.39274i	1.73842	+	2.39274i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	0.922621	+	0.221502i	0.922621	+	0.221502i
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$	0.500000	−	0.363271i	0.500000	−	0.363271i
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−2.00723	+	0.481893i	−2.00723	+	0.481893i
$439$	−1.39680	−	1.39680i	−1.39680	−	1.39680i	−0.809017	−	0.587785i	$-0.800000\pi$
$439$	−1.39680	−	1.39680i	−1.39680	−	1.39680i	−0.587785	−	0.809017i	$-0.700000\pi$
$440$		0			0
$441$	−0.0650673	+	0.0650673i	−0.0650673	+	0.0650673i
$442$		0			0
$443$	−1.70711	+	0.707107i	−1.70711	+	0.707107i	−0.707107	+	0.707107i	$0.750000\pi$
$443$	−1.70711	+	0.707107i	−1.70711	+	0.707107i	−1.00000			$\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−0.487899			−0.487899
$448$	−0.987688	−	0.156434i	−0.987688	−	0.156434i
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	0.119322	+	0.0188987i	0.119322	+	0.0188987i
$451$		0			0
$452$		0			0
$453$	1.13496	−	0.470114i	1.13496	−	0.470114i
$454$	0.678671	−	1.10749i	0.678671	−	1.10749i
$455$		0			0
$456$		0			0
$457$	−1.34500	−	1.34500i	−1.34500	−	1.34500i	−0.891007	−	0.453990i	$-0.850000\pi$
$457$	−1.34500	−	1.34500i	−1.34500	−	1.34500i	−0.453990	−	0.891007i	$-0.650000\pi$
$458$		0			0
$459$	0.363104	+	0.876612i	0.363104	+	0.876612i
$460$		0			0
$461$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$461$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$462$		0			0
$463$		−	1.61803i		−	1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$463$		−	1.61803i		−	1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$464$		0			0
$465$		−	0.982207i		−	0.982207i
$466$		0			0
$467$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$467$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$468$		0			0
$469$	0.763007	+	1.84206i	0.763007	+	1.84206i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$	−0.453990	−	0.891007i	−0.453990	−	0.891007i
$477$	−0.00552574	+	0.0133403i	−0.00552574	+	0.0133403i
$478$	−0.183900	+	1.16110i	−0.183900	+	1.16110i
$479$	0.312869			0.312869			0.156434	−	0.987688i	$-0.450000\pi$
$479$	0.312869			0.312869			0.156434	+	0.987688i	$0.450000\pi$
$480$	−1.12377	+	1.12377i	−1.12377	+	1.12377i
$481$		0			0
$482$	−0.0966818	+	0.610425i	−0.0966818	+	0.610425i
$483$		0			0
$484$	−0.891007	+	0.453990i	−0.891007	+	0.453990i
$485$	−2.50381	+	1.03711i	−2.50381	+	1.03711i
$486$	0.156434	+	0.0958632i	0.156434	+	0.0958632i
$487$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$487$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$488$	−1.29671	+	1.10749i	−1.29671	+	1.10749i
$489$		0			0
$490$	0.355026	+	1.47879i	0.355026	+	1.47879i
$491$	0.0600500	+	0.144974i	0.0600500	+	0.144974i	0.951057	−	0.309017i	$-0.100000\pi$
$491$	0.0600500	+	0.144974i	0.0600500	+	0.144974i	−0.891007	+	0.453990i	$0.850000\pi$
$492$	1.68563	−	0.132662i	1.68563	−	0.132662i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.500000	+	0.363271i	0.500000	+	0.363271i
$497$		0			0
$498$		0			0
$499$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$499$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$500$	0.309017	−	0.361812i	0.309017	−	0.361812i
$501$	0.789959	+	1.90713i	0.789959	+	1.90713i
$502$		0			0
$503$	−0.642040	−	0.642040i	−0.642040	−	0.642040i	0.309017	−	0.951057i	$-0.400000\pi$
$503$	−0.642040	−	0.642040i	−0.642040	−	0.642040i	−0.951057	+	0.309017i	$0.900000\pi$
$504$	−0.0819895	−	0.0417758i	−0.0819895	−	0.0417758i
$505$		0			0
$506$		0			0
$507$	0.965451	−	0.399903i	0.965451	−	0.399903i
$508$	−0.863541	−	0.280582i	−0.863541	−	0.280582i
$509$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$509$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$510$	−1.56968	−	0.248613i	−1.56968	−	0.248613i
$511$	−1.97538			−1.97538
$512$	−0.156434	−	0.987688i	−0.156434	−	0.987688i
$513$		0			0
$514$		0			0
$515$		0			0
$516$	−1.93278	−	0.627999i	−1.93278	−	0.627999i
$517$		0			0
$518$		0			0
$519$	−1.43702	+	1.43702i	−1.43702	+	1.43702i
$520$		0			0
$521$	−1.39680	−	1.39680i	−1.39680	−	1.39680i	−0.809017	−	0.587785i	$-0.800000\pi$
$521$	−1.39680	−	1.39680i	−1.39680	−	1.39680i	−0.587785	−	0.809017i	$-0.700000\pi$
$522$		0			0
$523$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$523$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$524$	−0.497066	+	0.581990i	−0.497066	+	0.581990i
$525$	1.26751	+	0.525020i	1.26751	+	0.525020i
$526$	1.14412	−	0.831254i	1.14412	−	0.831254i
$527$			0.618034i			0.618034i
$528$		0			0
$529$			1.00000i			1.00000i
$530$	0.140271	+	0.193066i	0.140271	+	0.193066i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−1.51612	+	1.29489i	−1.51612	+	1.29489i
$537$	−0.344997	+	0.344997i	−0.344997	+	0.344997i
$538$	0.652583	+	0.399903i	0.652583	+	0.399903i
$539$		0			0
$540$	1.28573	−	0.655110i	1.28573	−	0.655110i
$541$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$541$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$542$		0			0
$543$	−0.799806			−0.799806
$544$	0.707107	−	0.707107i	0.707107	−	0.707107i
$545$		0			0
$546$		0			0
$547$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$547$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$548$	0.734572	+	1.44168i	0.734572	+	1.44168i
$549$	−0.144974	+	0.0600500i	−0.144974	+	0.0600500i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.101910	+	1.29489i	0.101910	+	1.29489i
$557$	−1.70711	−	0.707107i	−1.70711	−	0.707107i	−0.707107	−	0.707107i	$-0.750000\pi$
$557$	−1.70711	−	0.707107i	−1.70711	−	0.707107i	−1.00000			$\pi$
$558$	0.0334279	+	0.0460095i	0.0334279	+	0.0460095i
$559$		0			0
$560$	−1.29671	+	0.794622i	−1.29671	+	0.794622i
$561$		0			0
$562$	−1.53884	+	1.11803i	−1.53884	+	1.11803i
$563$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$563$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$564$		0			0
$565$		0			0
$566$	−0.152583	+	0.0366318i	−0.152583	+	0.0366318i
$567$	0.766187	+	0.766187i	0.766187	+	0.766187i
$568$		0			0
$569$	−0.831254	+	0.831254i	−0.831254	+	0.831254i	−0.987688	−	0.156434i	$-0.950000\pi$
$569$	−0.831254	+	0.831254i	−0.831254	+	0.831254i	0.156434	+	0.987688i	$0.450000\pi$
$570$		0			0
$571$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$571$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$572$		0			0
$573$	−0.712633	+	1.72045i	−0.712633	+	1.72045i
$574$	1.59811	+	0.253116i	1.59811	+	0.253116i
$575$		0			0
$576$	0.0143949	−	0.0908861i	0.0143949	−	0.0908861i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	0.987688	+	0.156434i	0.987688	+	0.156434i
$579$		0			0
$580$		0			0
$581$		0			0
$582$	0.972996	−	1.58779i	0.972996	−	1.58779i
$583$		0			0
$584$	−0.610425	−	1.87869i	−0.610425	−	1.87869i
$585$		0			0
$586$		0			0
$587$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$587$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$588$	−0.794622	−	0.678671i	−0.794622	−	0.678671i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$	−1.40505	−	0.581990i	−1.40505	−	0.581990i
$596$	−0.0366318	−	0.465451i	−0.0366318	−	0.465451i
$597$	0.470114	+	1.13496i	0.470114	+	1.13496i
$598$		0			0
$599$	1.39680	+	1.39680i	1.39680	+	1.39680i	0.809017	+	0.587785i	$0.200000\pi$
$599$	1.39680	+	1.39680i	1.39680	+	1.39680i	0.587785	+	0.809017i	$0.300000\pi$
$600$	−0.107642	+	1.36772i	−0.107642	+	1.36772i
$601$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$601$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$602$	−1.65816	−	1.01612i	−1.65816	−	1.01612i
$603$	−0.169505	+	0.0702112i	−0.169505	+	0.0702112i
$604$	0.533698	+	1.04744i	0.533698	+	1.04744i
$605$	−0.581990	+	1.40505i	−0.581990	+	1.40505i
$606$		0			0
$607$	1.78201			1.78201			0.891007	−	0.453990i	$-0.150000\pi$
$607$	1.78201			1.78201			0.891007	+	0.453990i	$0.150000\pi$
$608$		0			0
$609$		0			0
$610$	−0.405699	+	2.56148i	−0.405699	+	2.56148i
$611$		0			0
$612$	0.0819895	−	0.0417758i	0.0819895	−	0.0417758i
$613$	0.144974	−	0.0600500i	0.144974	−	0.0600500i	−0.309017	−	0.951057i	$-0.600000\pi$
$613$	0.144974	−	0.0600500i	0.144974	−	0.0600500i	0.453990	+	0.891007i	$0.350000\pi$
$614$		0			0
$615$	1.81829	−	1.81829i	1.81829	−	1.81829i
$616$		0			0
$617$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$617$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$618$		0			0
$619$	0.292893	+	0.707107i	0.292893	+	0.707107i	1.00000			$0$
$619$	0.292893	+	0.707107i	0.292893	+	0.707107i	−0.707107	+	0.707107i	$0.750000\pi$
$620$	0.937016	−	0.0737448i	0.937016	−	0.0737448i
$621$		0			0
$622$	−1.11803	−	1.53884i	−1.11803	−	1.53884i
$623$		0			0
$624$		0			0
$625$			0.589244i			0.589244i
$626$	−1.53884	+	1.11803i	−1.53884	+	1.11803i
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.136077	+	0.0326692i	−0.136077	+	0.0326692i
$631$	0.437016	+	0.437016i	0.437016	+	0.437016i	0.891007	−	0.453990i	$-0.150000\pi$
$631$	0.437016	+	0.437016i	0.437016	+	0.437016i	−0.453990	+	0.891007i	$0.650000\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.27576	+	0.528435i	−1.27576	+	0.528435i
$636$	−0.155953	−	0.0506723i	−0.155953	−	0.0506723i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−1.15643	−	0.987688i	−1.15643	−	0.987688i
$641$		0			0		1.00000			$0$
$641$		0			0		−1.00000			$\pi$
$642$		0			0
$643$	0.744220	−	1.79671i	0.744220	−	1.79671i	0.156434	−	0.987688i	$-0.450000\pi$
$643$	0.744220	−	1.79671i	0.744220	−	1.79671i	0.587785	−	0.809017i	$-0.300000\pi$
$644$		0			0
$645$	−2.85540	+	1.18275i	−2.85540	+	1.18275i
$646$		0			0
$647$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$647$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$648$	−0.491922	+	0.965451i	−0.491922	+	0.965451i
$649$		0			0
$650$		0			0
$651$	0.247154	+	0.596682i	0.247154	+	0.596682i
$652$		0			0
$653$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$653$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$654$		0			0
$655$			1.16398i			1.16398i
$656$	0.253116	+	1.59811i	0.253116	+	1.59811i
$657$		−	0.181772i		−	0.181772i
$658$		0			0
$659$	1.84206	+	0.763007i	1.84206	+	0.763007i	0.951057	+	0.309017i	$0.100000\pi$
$659$	1.84206	+	0.763007i	1.84206	+	0.763007i	0.891007	+	0.453990i	$0.150000\pi$
$660$		0			0
$661$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$661$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$662$	0.303221	+	1.26301i	0.303221	+	1.26301i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−1.76007	+	0.896802i	−1.76007	+	0.896802i
$669$		0			0
$670$	−0.474348	+	2.99492i	−0.474348	+	2.99492i
$671$		0			0
$672$	0.399903	−	0.965451i	0.399903	−	0.965451i
$673$		0			0		1.00000			$0$
$673$		0			0		−1.00000			$\pi$
$674$		0			0
$675$	0.476708	−	1.15088i	0.476708	−	1.15088i
$676$	0.453990	+	0.891007i	0.453990	+	0.891007i
$677$	−1.70711	+	0.707107i	−1.70711	+	0.707107i	−0.707107	+	0.707107i	$0.750000\pi$
$677$	−1.70711	+	0.707107i	−1.70711	+	0.707107i	−1.00000			$\pi$
$678$		0			0
$679$	1.26007	−	1.26007i	1.26007	−	1.26007i
$680$	0.119322	−	1.51612i	0.119322	−	1.51612i
$681$	0.959786	+	0.959786i	0.959786	+	0.959786i
$682$		0			0
$683$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$683$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$684$		0			0
$685$	2.27341	+	0.941679i	2.27341	+	0.941679i
$686$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$687$		0			0
$688$	0.453990	−	1.89101i	0.453990	−	1.89101i
$689$		0			0
$690$		0			0
$691$	−0.431351	−	0.178671i	−0.431351	−	0.178671i	0.156434	−	0.987688i	$-0.450000\pi$
$691$	−0.431351	−	0.178671i	−0.431351	−	0.178671i	−0.587785	+	0.809017i	$0.700000\pi$
$692$	−1.47879	−	1.26301i	−1.47879	−	1.26301i
$693$		0			0
$694$		0			0
$695$	1.39680	+	1.39680i	1.39680	+	1.39680i
$696$		0			0
$697$	−1.14412	+	1.14412i	−1.14412	+	1.14412i
$698$		0			0
$699$		0			0
$700$	−0.405699	+	1.24861i	−0.405699	+	1.24861i
$701$	−0.707107	+	1.70711i	−0.707107	+	1.70711i			1.00000i	$0.5\pi$
$701$	−0.707107	+	1.70711i	−0.707107	+	1.70711i	−0.707107	+	0.707107i	$0.750000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$709$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$	1.01612	−	0.243950i	1.01612	−	0.243950i
$715$		0			0
$716$	−0.355026	−	0.303221i	−0.355026	−	0.303221i
$717$	−1.13496	−	0.470114i	−1.13496	−	0.470114i
$718$	−0.734572	+	0.533698i	−0.734572	+	0.533698i
$719$		−	0.312869i		−	0.312869i	−0.987688	−	0.156434i	$-0.950000\pi$
$719$		−	0.312869i		−	0.312869i	0.987688	−	0.156434i	$-0.0500000\pi$
$720$	−0.0731203	−	0.119322i	−0.0731203	−	0.119322i
$721$		0			0
$722$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$723$	−0.596682	−	0.247154i	−0.596682	−	0.247154i
$724$	−0.0600500	−	0.763007i	−0.0600500	−	0.763007i
$725$		0			0
$726$	−0.243950	−	1.01612i	−0.243950	−	1.01612i
$727$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$727$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$728$		0			0
$729$	0.630616	−	0.630616i	0.630616	−	0.630616i
$730$	−2.56148	−	1.56968i	−2.56148	−	1.56968i
$731$	1.79671	−	0.744220i	1.79671	−	0.744220i
$732$	−0.809017	−	1.58779i	−0.809017	−	1.58779i
$733$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$733$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$734$	0.253116	−	1.59811i	0.253116	−	1.59811i
$735$	−1.58924			−1.58924
$736$		0			0
$737$		0			0
$738$	−0.0232915	+	0.147057i	−0.0232915	+	0.147057i
$739$	0.399903	−	0.965451i	0.399903	−	0.965451i	−0.587785	−	0.809017i	$-0.700000\pi$
$739$	0.399903	−	0.965451i	0.399903	−	0.965451i	0.987688	−	0.156434i	$-0.0500000\pi$
$740$		0			0
$741$		0			0
$742$	−0.133795	−	0.0819895i	−0.133795	−	0.0819895i
$743$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$743$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$744$	−0.491103	+	0.419442i	−0.491103	+	0.419442i
$745$	−0.502083	−	0.502083i	−0.502083	−	0.502083i
$746$	0.453990	+	1.89101i	0.453990	+	1.89101i
$747$		0			0
$748$		0			0
$749$		0			0
$750$	0.292262	+	0.402264i	0.292262	+	0.402264i
$751$		0			0			−	1.00000i	$-0.5\pi$
$751$		0			0				1.00000i	$0.5\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.65173	+	0.684170i	1.65173	+	0.684170i
$756$	−0.616221	+	0.721502i	−0.616221	+	0.721502i
$757$	0.652583	+	1.57547i	0.652583	+	1.57547i	0.809017	+	0.587785i	$0.200000\pi$
$757$	0.652583	+	1.57547i	0.652583	+	1.57547i	−0.156434	+	0.987688i	$0.550000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$761$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$762$	0.495766	−	0.809017i	0.495766	−	0.809017i
$763$		0			0
$764$	−1.69480	−	0.550672i	−1.69480	−	0.550672i
$765$	0.0535541	−	0.129291i	0.0535541	−	0.129291i
$766$		0			0
$767$		0			0
$768$	1.04178	+	0.0819895i	1.04178	+	0.0819895i
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$773$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$774$	0.0935027	−	0.152583i	0.0935027	−	0.152583i
$775$	0.573745	−	0.573745i	0.573745	−	0.573745i
$776$	1.58779	+	0.809017i	1.58779	+	0.809017i
$777$		0			0
$778$	1.47879	−	0.355026i	1.47879	−	0.355026i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.587785	−	0.809017i	0.587785	−	0.809017i
$785$		0			0
$786$	−0.470114	−	0.647057i	−0.470114	−	0.647057i
$787$	1.70711	+	0.707107i	1.70711	+	0.707107i	1.00000			$0$
$787$	1.70711	+	0.707107i	1.70711	+	0.707107i	0.707107	+	0.707107i	$0.250000\pi$
$788$		0			0
$789$	0.565548	+	1.36535i	0.565548	+	1.36535i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	0.133795	+	0.0819895i	0.133795	+	0.0819895i
$795$	−0.230398	+	0.0954341i	−0.230398	+	0.0954341i
$796$	−1.04744	+	0.533698i	−1.04744	+	0.533698i
$797$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$797$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$798$		0			0
$799$		0			0
$800$	−1.31287			−1.31287
$801$		0			0
$802$		0			0
$803$		0			0
$804$	−0.945913	−	1.85646i	−0.945913	−	1.85646i
$805$		0			0
$806$		0			0
$807$	−0.565548	+	0.565548i	−0.565548	+	0.565548i
$808$		0			0
$809$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$809$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$810$	0.384689	+	1.60235i	0.384689	+	1.60235i
$811$	0.178671	+	0.431351i	0.178671	+	0.431351i	0.987688	−	0.156434i	$-0.0500000\pi$
$811$	0.178671	+	0.431351i	0.178671	+	0.431351i	−0.809017	+	0.587785i	$0.800000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.546010	+	0.891007i	0.546010	+	0.891007i
$817$		0			0
$818$		0			0
$819$		0			0
$820$	1.87115	+	1.59811i	1.87115	+	1.59811i
$821$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$821$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$822$	−1.64412	+	0.394719i	−1.64412	+	0.394719i
$823$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$823$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$827$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$828$		0			0
$829$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$829$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.00000			1.00000
$834$	−1.34063	−	0.212335i	−1.34063	−	0.212335i
$835$	−1.14965	+	2.77550i	−1.14965	+	2.77550i
$836$		0			0
$837$	0.541776	−	0.224411i	0.541776	−	0.224411i
$838$	0.794622	−	1.29671i	0.794622	−	1.29671i
$839$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$839$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$840$	−0.491103	−	1.51146i	−0.491103	−	1.51146i
$841$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$842$	1.65816	−	0.398090i	1.65816	−	0.398090i
$843$	−0.760661	−	1.83640i	−0.760661	−	1.83640i
$844$		0			0
$845$	1.40505	+	0.581990i	1.40505	+	0.581990i
$846$		0			0
$847$		−	1.00000i		−	1.00000i
$848$	0.0366318	−	0.152583i	0.0366318	−	0.152583i
$849$		−	0.163979i		−	0.163979i
$850$	−0.771685	−	1.06213i	−0.771685	−	1.06213i
$851$		0			0
$852$		0			0
$853$	0.707107	+	1.70711i	0.707107	+	1.70711i	0.707107	+	0.707107i	$0.250000\pi$
$853$	0.707107	+	1.70711i	0.707107	+	1.70711i			1.00000i	$0.5\pi$
$854$	−0.398090	−	1.65816i	−0.398090	−	1.65816i
$855$		0			0
$856$		0			0
$857$	0.437016	−	0.437016i	0.437016	−	0.437016i	−0.453990	−	0.891007i	$-0.650000\pi$
$857$	0.437016	−	0.437016i	0.437016	−	0.437016i	0.891007	+	0.453990i	$0.150000\pi$
$858$		0			0
$859$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$859$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$860$	−1.34271	−	2.63523i	−1.34271	−	2.63523i
$861$	−0.647057	+	1.56213i	−0.647057	+	1.56213i
$862$		0			0
$863$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$863$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$864$	−0.876612	−	0.363104i	−0.876612	−	0.363104i
$865$	−2.95758			−2.95758
$866$		0			0
$867$	−0.399903	+	0.965451i	−0.399903	+	0.965451i
$868$	−0.550672	+	0.280582i	−0.550672	+	0.280582i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.115951	+	0.115951i	0.115951	+	0.115951i
$874$		0			0
$875$	0.182086	+	0.439596i	0.182086	+	0.439596i
$876$	2.05790	−	0.161960i	2.05790	−	0.161960i
$877$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$877$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$878$	1.16110	+	1.59811i	1.16110	+	1.59811i
$879$		0			0
$880$		0			0
$881$		−	0.907981i		−	0.907981i	−0.891007	−	0.453990i	$-0.850000\pi$
$881$		−	0.907981i		−	0.907981i	0.891007	−	0.453990i	$-0.150000\pi$
$882$	0.0744449	−	0.0540874i	0.0744449	−	0.0540874i
$883$	−1.40505	−	0.581990i	−1.40505	−	0.581990i	−0.453990	−	0.891007i	$-0.650000\pi$
$883$	−1.40505	−	0.581990i	−1.40505	−	0.581990i	−0.951057	+	0.309017i	$0.900000\pi$
$884$		0			0
$885$		0			0
$886$	1.79671	−	0.431351i	1.79671	−	0.431351i
$887$	−1.34500	−	1.34500i	−1.34500	−	1.34500i	−0.891007	−	0.453990i	$-0.850000\pi$
$887$	−1.34500	−	1.34500i	−1.34500	−	1.34500i	−0.453990	−	0.891007i	$-0.650000\pi$
$888$		0			0
$889$	0.642040	−	0.642040i	0.642040	−	0.642040i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$	0.481893	+	0.0763243i	0.481893	+	0.0763243i
$895$	−0.710053			−0.710053
$896$	0.951057	+	0.309017i	0.951057	+	0.309017i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.114896	−	0.0373320i	−0.114896	−	0.0373320i
$901$	0.144974	−	0.0600500i	0.144974	−	0.0600500i
$902$		0			0
$903$	1.43702	−	1.43702i	1.43702	−	1.43702i
$904$		0			0
$905$	−0.823057	−	0.823057i	−0.823057	−	0.823057i
$906$	−1.19453	+	0.286780i	−1.19453	+	0.286780i
$907$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$907$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$908$	−0.843566	+	0.987688i	−0.843566	+	0.987688i
$909$		0			0
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$		0			0
$914$	1.11803	+	1.53884i	1.11803	+	1.53884i
$915$	−2.50381	−	1.03711i	−2.50381	−	1.03711i
$916$		0			0
$917$	−0.292893	−	0.707107i	−0.292893	−	0.707107i
$918$	−0.221502	−	0.922621i	−0.221502	−	0.922621i
$919$	−1.14412	−	1.14412i	−1.14412	−	1.14412i	−0.987688	−	0.156434i	$-0.950000\pi$
$919$	−1.14412	−	1.14412i	−1.14412	−	1.14412i	−0.156434	−	0.987688i	$-0.550000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$	−0.253116	+	1.59811i	−0.253116	+	1.59811i
$927$		0			0
$928$		0			0
$929$	1.90211			1.90211			0.951057	−	0.309017i	$-0.100000\pi$
$929$	1.90211			1.90211			0.951057	+	0.309017i	$0.100000\pi$
$930$	−0.153651	+	0.970114i	−0.153651	+	0.970114i
$931$		0			0
$932$		0			0
$933$	1.83640	−	0.760661i	1.83640	−	0.760661i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$937$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$938$	−0.465451	−	1.93874i	−0.465451	−	1.93874i
$939$	−0.760661	−	1.83640i	−0.760661	−	1.83640i
$940$		0			0
$941$	0.431351	+	0.178671i	0.431351	+	0.178671i	0.587785	−	0.809017i	$-0.300000\pi$
$941$	0.431351	+	0.178671i	0.431351	+	0.178671i	−0.156434	+	0.987688i	$0.550000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$			1.44300i			1.44300i
$946$		0			0
$947$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$947$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$	0.309017	+	0.951057i	0.309017	+	0.951057i
$953$	1.26007	−	1.26007i	1.26007	−	1.26007i	0.309017	−	0.951057i	$-0.400000\pi$
$953$	1.26007	−	1.26007i	1.26007	−	1.26007i	0.951057	−	0.309017i	$-0.100000\pi$
$954$	0.00754459	−	0.0123117i	0.00754459	−	0.0123117i
$955$	−2.50381	+	1.03711i	−2.50381	+	1.03711i
$956$	0.363271	−	1.11803i	0.363271	−	1.11803i
$957$		0			0
$958$	−0.309017	−	0.0489435i	−0.309017	−	0.0489435i
$959$	−1.61803			−1.61803
$960$	1.28573	−	0.934134i	1.28573	−	0.934134i
$961$	−0.618034			−0.618034
$962$		0			0
$963$		0			0
$964$	0.190983	−	0.587785i	0.190983	−	0.587785i
$965$		0			0
$966$		0			0
$967$	−1.39680	+	1.39680i	−1.39680	+	1.39680i	−0.587785	+	0.809017i	$0.700000\pi$
$967$	−1.39680	+	1.39680i	−1.39680	+	1.39680i	−0.809017	+	0.587785i	$0.800000\pi$
$968$	0.951057	−	0.309017i	0.951057	−	0.309017i
$969$		0			0
$970$	2.63523	−	0.632662i	2.63523	−	0.632662i
$971$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$971$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$972$	−0.139512	−	0.119155i	−0.139512	−	0.119155i
$973$	−1.20002	−	0.497066i	−1.20002	−	0.497066i
$974$		0			0
$975$		0			0
$976$	1.45399	−	0.891007i	1.45399	−	0.891007i
$977$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$977$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$978$		0			0
$979$		0			0
$980$	−0.119322	−	1.51612i	−0.119322	−	1.51612i
$981$		0			0
$982$	−0.0366318	−	0.152583i	−0.0366318	−	0.152583i
$983$	0.437016	+	0.437016i	0.437016	+	0.437016i	0.891007	−	0.453990i	$-0.150000\pi$
$983$	0.437016	+	0.437016i	0.437016	+	0.437016i	−0.453990	+	0.891007i	$0.650000\pi$
$984$	−1.68563	−	0.132662i	−1.68563	−	0.132662i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$	−0.437016	−	0.437016i	−0.437016	−	0.437016i
$993$	−1.35734			−1.35734
$994$		0			0
$995$	−0.684170	+	1.65173i	−0.684170	+	1.65173i
$996$		0			0
$997$	−1.79671	+	0.744220i	−1.79671	+	0.744220i	−0.809017	+	0.587785i	$0.800000\pi$
$997$	−1.79671	+	0.744220i	−1.79671	+	0.744220i	−0.987688	+	0.156434i	$0.950000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3808.1.cu.c.237.1	✓	16
7.6	odd	2		3808.1.cu.d.237.1	yes	16
17.16	even	2		3808.1.cu.d.237.1	yes	16
32.5	even	8	inner	3808.1.cu.c.1189.1	yes	16
119.118	odd	2	CM	3808.1.cu.c.237.1	✓	16
224.69	odd	8		3808.1.cu.d.1189.1	yes	16
544.101	even	8		3808.1.cu.d.1189.1	yes	16
3808.1189	odd	8	inner	3808.1.cu.c.1189.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3808.1.cu.c.237.1	✓	16	1.1	even	1	trivial
3808.1.cu.c.237.1	✓	16	119.118	odd	2	CM
3808.1.cu.c.1189.1	yes	16	32.5	even	8	inner
3808.1.cu.c.1189.1	yes	16	3808.1189	odd	8	inner
3808.1.cu.d.237.1	yes	16	7.6	odd	2
3808.1.cu.d.237.1	yes	16	17.16	even	2
3808.1.cu.d.1189.1	yes	16	224.69	odd	8
3808.1.cu.d.1189.1	yes	16	544.101	even	8

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:	\( N \)	\(=\)	\( 3808 = 2^{5} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3808.cu (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 - 0.156434i) q^{2} +(0.399903 - 0.965451i) q^{3} +(0.951057 + 0.309017i) q^{4} +(1.40505 - 0.581990i) q^{5} +(-0.546010 + 0.891007i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(-0.0650673 - 0.0650673i) q^{9} +O(q^{10})\)	\(q+(-0.987688 - 0.156434i) q^{2} +(0.399903 - 0.965451i) q^{3} +(0.951057 + 0.309017i) q^{4} +(1.40505 - 0.581990i) q^{5} +(-0.546010 + 0.891007i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(-0.0650673 - 0.0650673i) q^{9} +(-1.47879 + 0.355026i) q^{10} +(0.678671 - 0.794622i) q^{12} +(0.809017 - 0.587785i) q^{14} -1.58924i q^{15} +(0.809017 + 0.587785i) q^{16} +1.00000i q^{17} +(0.0540874 + 0.0744449i) q^{18} +(1.51612 - 0.119322i) q^{20} +(0.399903 + 0.965451i) q^{21} +(-0.794622 + 0.678671i) q^{24} +(0.928339 - 0.928339i) q^{25} +(0.876612 - 0.363104i) q^{27} +(-0.891007 + 0.453990i) q^{28} +(-0.248613 + 1.56968i) q^{30} +0.618034 q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.156434 - 0.987688i) q^{34} +(-0.581990 + 1.40505i) q^{35} +(-0.0417758 - 0.0819895i) q^{36} +(-1.51612 - 0.119322i) q^{40} +(1.14412 + 1.14412i) q^{41} +(-0.243950 - 1.01612i) q^{42} +(-0.744220 - 1.79671i) q^{43} +(-0.129291 - 0.0535541i) q^{45} +(0.891007 - 0.546010i) q^{48} -1.00000i q^{49} +(-1.06213 + 0.771685i) q^{50} +(0.965451 + 0.399903i) q^{51} +(-0.0600500 - 0.144974i) q^{53} +(-0.922621 + 0.221502i) q^{54} +(0.951057 - 0.309017i) q^{56} +(0.491103 - 1.51146i) q^{60} +(0.652583 - 1.57547i) q^{61} +(-0.610425 - 0.0966818i) q^{62} +0.0920190 q^{63} +(0.587785 + 0.809017i) q^{64} +(0.763007 - 1.84206i) q^{67} +(-0.309017 + 0.951057i) q^{68} +(0.794622 - 1.29671i) q^{70} +(0.0284354 + 0.0875153i) q^{72} +(1.39680 + 1.39680i) q^{73} +(-0.525020 - 1.26751i) q^{75} +(1.47879 + 0.355026i) q^{80} -1.08355i q^{81} +(-0.951057 - 1.30902i) q^{82} +(0.0819895 + 1.04178i) q^{84} +(0.581990 + 1.40505i) q^{85} +(0.453990 + 1.89101i) q^{86} +(0.119322 + 0.0731203i) q^{90} +(0.247154 - 0.596682i) q^{93} +(-0.965451 + 0.399903i) q^{96} -1.78201 q^{97} +(-0.156434 + 0.987688i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q - 16 * q^6 + 4 * q^9	\( 16 q - 16 q^{6} + 4 q^{9} + 4 q^{12} + 4 q^{14} + 4 q^{16} + 4 q^{20} + 4 q^{25} - 4 q^{27} + 16 q^{30} - 8 q^{31} - 4 q^{35} + 16 q^{36} - 4 q^{40} + 16 q^{45} - 4 q^{50} + 4 q^{51} - 4 q^{54} + 4 q^{61} + 16 q^{63} - 4 q^{67} + 4 q^{68} - 4 q^{72} + 4 q^{73} + 4 q^{75} - 4 q^{84} + 4 q^{85} - 4 q^{96}+O(q^{100}) \) 16 * q - 16 * q^6 + 4 * q^9 + 4 * q^12 + 4 * q^14 + 4 * q^16 + 4 * q^20 + 4 * q^25 - 4 * q^27 + 16 * q^30 - 8 * q^31 - 4 * q^35 + 16 * q^36 - 4 * q^40 + 16 * q^45 - 4 * q^50 + 4 * q^51 - 4 * q^54 + 4 * q^61 + 16 * q^63 - 4 * q^67 + 4 * q^68 - 4 * q^72 + 4 * q^73 + 4 * q^75 - 4 * q^84 + 4 * q^85 - 4 * q^96

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