LMFDB - Embedded newform 1400.1.bs.c.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,1,Mod(181,1400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1400, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 4, 5]))

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

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

chi := DirichletCharacter("1400.181");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1400.bs (of order $10$, 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:	$0.698691017686$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{10}$
Projective field:	Galois closure of 10.0.10504375000000000000.2

Embedding invariants

Embedding label			181.1
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	1400.181
Dual form			1400.1.bs.c.1021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-0.951057 + 0.690983i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(0.951057 + 0.690983i) q^{6} -1.00000 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.118034 - 0.363271i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.951057 + 0.690983i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(0.951057 + 0.690983i) q^{6} -1.00000 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.118034 - 0.363271i) q^{9} +(0.587785 + 0.809017i) q^{10} +(0.363271 - 1.11803i) q^{12} +(-0.363271 + 1.11803i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.690983 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} -0.381966 q^{18} +(0.587785 - 0.809017i) q^{20} +(0.951057 - 0.690983i) q^{21} +(-0.500000 - 1.53884i) q^{23} -1.17557 q^{24} +(0.809017 - 0.587785i) q^{25} +1.17557 q^{26} +(-0.224514 - 0.690983i) q^{27} +(0.809017 - 0.587785i) q^{28} +(-1.11803 - 0.363271i) q^{30} -1.00000 q^{32} +(0.951057 - 0.309017i) q^{35} +(0.118034 + 0.363271i) q^{36} +(-0.427051 - 1.31433i) q^{39} +(-0.951057 - 0.309017i) q^{40} +(-0.951057 - 0.690983i) q^{42} +0.381966i q^{45} +(-1.30902 + 0.951057i) q^{46} +(0.363271 + 1.11803i) q^{48} +1.00000 q^{49} +(-0.809017 - 0.587785i) q^{50} +(-0.363271 - 1.11803i) q^{52} +(-0.587785 + 0.427051i) q^{54} +(-0.809017 - 0.587785i) q^{56} +(0.587785 - 1.80902i) q^{59} +1.17557i q^{60} +(-0.587785 - 1.80902i) q^{61} +(-0.118034 + 0.363271i) q^{63} +(0.309017 + 0.951057i) q^{64} -1.17557i q^{65} +(1.53884 + 1.11803i) q^{69} +(-0.587785 - 0.809017i) q^{70} +(0.500000 - 0.363271i) q^{71} +(0.309017 - 0.224514i) q^{72} +(-0.363271 + 1.11803i) q^{75} +(-1.11803 + 0.812299i) q^{78} +(-1.30902 + 0.951057i) q^{79} +1.00000i q^{80} +(1.00000 + 0.726543i) q^{81} +(-1.53884 - 1.11803i) q^{83} +(-0.363271 + 1.11803i) q^{84} +(0.363271 - 0.118034i) q^{90} +(0.363271 - 1.11803i) q^{91} +(1.30902 + 0.951057i) q^{92} +(0.951057 - 0.690983i) q^{96} +(-0.309017 - 0.951057i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{4} - 8 q^{7} + 2 q^{8} - 8 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^4 - 8 * q^7 + 2 * q^8 - 8 * q^9	$ 8 q + 2 q^{2} - 2 q^{4} - 8 q^{7} + 2 q^{8} - 8 q^{9} - 2 q^{14} + 10 q^{15} - 2 q^{16} - 12 q^{18} - 4 q^{23} + 2 q^{25} + 2 q^{28} - 8 q^{32} - 8 q^{36} + 10 q^{39} - 6 q^{46} + 8 q^{49} - 2 q^{50} - 2 q^{56} + 8 q^{63} - 2 q^{64} + 4 q^{71} - 2 q^{72} - 6 q^{79} + 8 q^{81} + 6 q^{92} + 2 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^4 - 8 * q^7 + 2 * q^8 - 8 * q^9 - 2 * q^14 + 10 * q^15 - 2 * q^16 - 12 * q^18 - 4 * q^23 + 2 * q^25 + 2 * q^28 - 8 * q^32 - 8 * q^36 + 10 * q^39 - 6 * q^46 + 8 * q^49 - 2 * q^50 - 2 * q^56 + 8 * q^63 - 2 * q^64 + 4 * q^71 - 2 * q^72 - 6 * q^79 + 8 * q^81 + 6 * q^92 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times$.

$n$	$351$	$701$	$801$	$1177$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$2$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$3$	−0.951057	+	0.690983i	−0.951057	+	0.690983i	−0.951057	−	0.309017i	$-0.900000\pi$
$3$	−0.951057	+	0.690983i	−0.951057	+	0.690983i			1.00000i	$0.5\pi$
$4$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$5$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$5$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$6$	0.951057	+	0.690983i	0.951057	+	0.690983i
$7$	−1.00000			−1.00000
$7$	−1.00000			−1.00000
$8$	0.809017	+	0.587785i	0.809017	+	0.587785i
$9$	0.118034	−	0.363271i	0.118034	−	0.363271i
$10$	0.587785	+	0.809017i	0.587785	+	0.809017i
$11$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$11$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$12$	0.363271	−	1.11803i	0.363271	−	1.11803i
$13$	−0.363271	+	1.11803i	−0.363271	+	1.11803i	0.587785	+	0.809017i	$0.300000\pi$
$13$	−0.363271	+	1.11803i	−0.363271	+	1.11803i	−0.951057	+	0.309017i	$0.900000\pi$
$14$	0.309017	+	0.951057i	0.309017	+	0.951057i
$15$	0.690983	−	0.951057i	0.690983	−	0.951057i
$16$	0.309017	−	0.951057i	0.309017	−	0.951057i
$17$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$17$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$18$	−0.381966			−0.381966
$19$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$19$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$20$	0.587785	−	0.809017i	0.587785	−	0.809017i
$21$	0.951057	−	0.690983i	0.951057	−	0.690983i
$22$		0			0
$23$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$23$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$24$	−1.17557			−1.17557
$25$	0.809017	−	0.587785i	0.809017	−	0.587785i
$26$	1.17557			1.17557
$27$	−0.224514	−	0.690983i	−0.224514	−	0.690983i
$28$	0.809017	−	0.587785i	0.809017	−	0.587785i
$29$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$29$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$30$	−1.11803	−	0.363271i	−1.11803	−	0.363271i
$31$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$31$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$32$	−1.00000			−1.00000
$33$		0			0
$34$		0			0
$35$	0.951057	−	0.309017i	0.951057	−	0.309017i
$36$	0.118034	+	0.363271i	0.118034	+	0.363271i
$37$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$37$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$38$		0			0
$39$	−0.427051	−	1.31433i	−0.427051	−	1.31433i
$40$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$41$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$41$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$42$	−0.951057	−	0.690983i	−0.951057	−	0.690983i
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$		0			0
$45$			0.381966i			0.381966i
$46$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$47$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$47$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$48$	0.363271	+	1.11803i	0.363271	+	1.11803i
$49$	1.00000			1.00000
$50$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$51$		0			0
$52$	−0.363271	−	1.11803i	−0.363271	−	1.11803i
$53$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$53$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$54$	−0.587785	+	0.427051i	−0.587785	+	0.427051i
$55$		0			0
$56$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$57$		0			0
$58$		0			0
$59$	0.587785	−	1.80902i	0.587785	−	1.80902i		−	1.00000i	$-0.5\pi$
$59$	0.587785	−	1.80902i	0.587785	−	1.80902i	0.587785	−	0.809017i	$-0.300000\pi$
$60$			1.17557i			1.17557i
$61$	−0.587785	−	1.80902i	−0.587785	−	1.80902i	−0.587785	−	0.809017i	$-0.700000\pi$
$61$	−0.587785	−	1.80902i	−0.587785	−	1.80902i		−	1.00000i	$-0.5\pi$
$62$		0			0
$63$	−0.118034	+	0.363271i	−0.118034	+	0.363271i
$64$	0.309017	+	0.951057i	0.309017	+	0.951057i
$65$		−	1.17557i		−	1.17557i
$66$		0			0
$67$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$67$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$68$		0			0
$69$	1.53884	+	1.11803i	1.53884	+	1.11803i
$70$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$71$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$71$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$72$	0.309017	−	0.224514i	0.309017	−	0.224514i
$73$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$73$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$74$		0			0
$75$	−0.363271	+	1.11803i	−0.363271	+	1.11803i
$76$		0			0
$77$		0			0
$78$	−1.11803	+	0.812299i	−1.11803	+	0.812299i
$79$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$79$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$80$			1.00000i			1.00000i
$81$	1.00000	+	0.726543i	1.00000	+	0.726543i
$82$		0			0
$83$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.951057	−	0.309017i	$-0.900000\pi$
$83$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.587785	−	0.809017i	$-0.700000\pi$
$84$	−0.363271	+	1.11803i	−0.363271	+	1.11803i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$89$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$90$	0.363271	−	0.118034i	0.363271	−	0.118034i
$91$	0.363271	−	1.11803i	0.363271	−	1.11803i
$92$	1.30902	+	0.951057i	1.30902	+	0.951057i
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.951057	−	0.690983i	0.951057	−	0.690983i
$97$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$97$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$98$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$99$		0			0
$100$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$101$	1.17557			1.17557			0.587785	−	0.809017i	$-0.300000\pi$
$101$	1.17557			1.17557			0.587785	+	0.809017i	$0.300000\pi$
$102$		0			0
$103$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$103$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$104$	−0.951057	+	0.690983i	−0.951057	+	0.690983i
$105$	−0.690983	+	0.951057i	−0.690983	+	0.951057i
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$	0.587785	+	0.427051i	0.587785	+	0.427051i
$109$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$109$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$110$		0			0
$111$		0			0
$112$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$113$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$113$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$114$		0			0
$115$	0.951057	+	1.30902i	0.951057	+	1.30902i
$116$		0			0
$117$	0.363271	+	0.263932i	0.363271	+	0.263932i
$118$	−1.90211			−1.90211
$119$		0			0
$120$	1.11803	−	0.363271i	1.11803	−	0.363271i
$121$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$122$	−1.53884	+	1.11803i	−1.53884	+	1.11803i
$123$		0			0
$124$		0			0
$125$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$126$	0.381966			0.381966
$127$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$127$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$128$	0.809017	−	0.587785i	0.809017	−	0.587785i
$129$		0			0
$130$	−1.11803	+	0.363271i	−1.11803	+	0.363271i
$131$	1.53884	+	1.11803i	1.53884	+	1.11803i	0.951057	+	0.309017i	$0.100000\pi$
$131$	1.53884	+	1.11803i	1.53884	+	1.11803i	0.587785	+	0.809017i	$0.300000\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.427051	+	0.587785i	0.427051	+	0.587785i
$136$		0			0
$137$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$137$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$138$	0.587785	−	1.80902i	0.587785	−	1.80902i
$139$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$139$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$140$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$141$		0			0
$142$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$143$		0			0
$144$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$145$		0			0
$146$		0			0
$147$	−0.951057	+	0.690983i	−0.951057	+	0.690983i
$148$		0			0
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	1.17557			1.17557
$151$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$151$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	1.11803	+	0.812299i	1.11803	+	0.812299i
$157$	1.90211			1.90211			0.951057	−	0.309017i	$-0.100000\pi$
$157$	1.90211			1.90211			0.951057	+	0.309017i	$0.100000\pi$
$158$	1.30902	+	0.951057i	1.30902	+	0.951057i
$159$		0			0
$160$	0.951057	−	0.309017i	0.951057	−	0.309017i
$161$	0.500000	+	1.53884i	0.500000	+	1.53884i
$162$	0.381966	−	1.17557i	0.381966	−	1.17557i
$163$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$163$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$164$		0			0
$165$		0			0
$166$	−0.587785	+	1.80902i	−0.587785	+	1.80902i
$167$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$167$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$168$	1.17557			1.17557
$169$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.587785	−	1.80902i	−0.587785	−	1.80902i	−0.587785	−	0.809017i	$-0.700000\pi$
$173$	−0.587785	−	1.80902i	−0.587785	−	1.80902i		−	1.00000i	$-0.5\pi$
$174$		0			0
$175$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$176$		0			0
$177$	0.690983	+	2.12663i	0.690983	+	2.12663i
$178$		0			0
$179$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$179$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$180$	−0.224514	−	0.309017i	−0.224514	−	0.309017i
$181$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.951057	−	0.309017i	$-0.900000\pi$
$181$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.587785	−	0.809017i	$-0.700000\pi$
$182$	−1.17557			−1.17557
$183$	1.80902	+	1.31433i	1.80902	+	1.31433i
$184$	0.500000	−	1.53884i	0.500000	−	1.53884i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	0.224514	+	0.690983i	0.224514	+	0.690983i
$190$		0			0
$191$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$191$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$192$	−0.951057	−	0.690983i	−0.951057	−	0.690983i
$193$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$193$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$194$		0			0
$195$	0.812299	+	1.11803i	0.812299	+	1.11803i
$196$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$197$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$197$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	1.00000			1.00000
$201$		0			0
$202$	−0.363271	−	1.11803i	−0.363271	−	1.11803i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.618034			−0.618034
$208$	0.951057	+	0.690983i	0.951057	+	0.690983i
$209$		0			0
$210$	1.11803	+	0.363271i	1.11803	+	0.363271i
$211$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$211$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$212$		0			0
$213$	−0.224514	+	0.690983i	−0.224514	+	0.690983i
$214$		0			0
$215$		0			0
$216$	0.224514	−	0.690983i	0.224514	−	0.690983i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$223$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$224$	1.00000			1.00000
$225$	−0.118034	−	0.363271i	−0.118034	−	0.363271i
$226$	0.618034			0.618034
$227$	0.363271	+	1.11803i	0.363271	+	1.11803i	0.951057	+	0.309017i	$0.100000\pi$
$227$	0.363271	+	1.11803i	0.363271	+	1.11803i	−0.587785	+	0.809017i	$0.700000\pi$
$228$		0			0
$229$	−1.53884	+	1.11803i	−1.53884	+	1.11803i	−0.587785	+	0.809017i	$0.700000\pi$
$229$	−1.53884	+	1.11803i	−1.53884	+	1.11803i	−0.951057	+	0.309017i	$0.900000\pi$
$230$	0.951057	−	1.30902i	0.951057	−	1.30902i
$231$		0			0
$232$		0			0
$233$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$233$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$234$	0.138757	−	0.427051i	0.138757	−	0.427051i
$235$		0			0
$236$	0.587785	+	1.80902i	0.587785	+	1.80902i
$237$	0.587785	−	1.80902i	0.587785	−	1.80902i
$238$		0			0
$239$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$239$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$240$	−0.690983	−	0.951057i	−0.690983	−	0.951057i
$241$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$241$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$242$	0.809017	+	0.587785i	0.809017	+	0.587785i
$243$	−0.726543			−0.726543
$244$	1.53884	+	1.11803i	1.53884	+	1.11803i
$245$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	2.23607			2.23607
$250$	0.951057	+	0.309017i	0.951057	+	0.309017i
$251$	−1.90211			−1.90211			−0.951057	−	0.309017i	$-0.900000\pi$
$251$	−1.90211			−1.90211			−0.951057	+	0.309017i	$0.900000\pi$
$252$	−0.118034	−	0.363271i	−0.118034	−	0.363271i
$253$		0			0
$254$	1.61803	−	1.17557i	1.61803	−	1.17557i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$257$		0			0		1.00000			$0$
$257$		0			0		−1.00000			$\pi$
$258$		0			0
$259$		0			0
$260$	0.690983	+	0.951057i	0.690983	+	0.951057i
$261$		0			0
$262$	0.587785	−	1.80902i	0.587785	−	1.80902i
$263$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$263$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.951057	−	0.309017i	$-0.900000\pi$
$269$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.587785	−	0.809017i	$-0.700000\pi$
$270$	0.427051	−	0.587785i	0.427051	−	0.587785i
$271$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$271$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$272$		0			0
$273$	0.427051	+	1.31433i	0.427051	+	1.31433i
$274$	−2.00000			−2.00000
$275$		0			0
$276$	−1.90211			−1.90211
$277$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$277$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$278$		0			0
$279$		0			0
$280$	0.951057	+	0.309017i	0.951057	+	0.309017i
$281$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$281$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$282$		0			0
$283$	−0.951057	−	0.690983i	−0.951057	−	0.690983i		−	1.00000i	$-0.5\pi$
$283$	−0.951057	−	0.690983i	−0.951057	−	0.690983i	−0.951057	+	0.309017i	$0.900000\pi$
$284$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.118034	+	0.363271i	−0.118034	+	0.363271i
$289$	0.309017	+	0.951057i	0.309017	+	0.951057i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0			−	1.00000i	$-0.5\pi$
$293$		0			0				1.00000i	$0.5\pi$
$294$	0.951057	+	0.690983i	0.951057	+	0.690983i
$295$			1.90211i			1.90211i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.90211			1.90211
$300$	−0.363271	−	1.11803i	−0.363271	−	1.11803i
$301$		0			0
$302$	0.500000	+	1.53884i	0.500000	+	1.53884i
$303$	−1.11803	+	0.812299i	−1.11803	+	0.812299i
$304$		0			0
$305$	1.11803	+	1.53884i	1.11803	+	1.53884i
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$311$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$312$	0.427051	−	1.31433i	0.427051	−	1.31433i
$313$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$313$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$314$	−0.587785	−	1.80902i	−0.587785	−	1.80902i
$315$		−	0.381966i		−	0.381966i
$316$	0.500000	−	1.53884i	0.500000	−	1.53884i
$317$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$317$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$318$		0			0
$319$		0			0
$320$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$321$		0			0
$322$	1.30902	−	0.951057i	1.30902	−	0.951057i
$323$		0			0
$324$	−1.23607			−1.23607
$325$	0.363271	+	1.11803i	0.363271	+	1.11803i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$331$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$332$	1.90211			1.90211
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−0.363271	−	1.11803i	−0.363271	−	1.11803i
$337$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$337$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$338$	−0.118034	+	0.363271i	−0.118034	+	0.363271i
$339$	−0.224514	−	0.690983i	−0.224514	−	0.690983i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−1.00000			−1.00000
$344$		0			0
$345$	−1.80902	−	0.587785i	−1.80902	−	0.587785i
$346$	−1.53884	+	1.11803i	−1.53884	+	1.11803i
$347$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$347$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$348$		0			0
$349$	1.17557			1.17557			0.587785	−	0.809017i	$-0.300000\pi$
$349$	1.17557			1.17557			0.587785	+	0.809017i	$0.300000\pi$
$350$	0.809017	+	0.587785i	0.809017	+	0.587785i
$351$	0.854102			0.854102
$352$		0			0
$353$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$353$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$354$	1.80902	−	1.31433i	1.80902	−	1.31433i
$355$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$359$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$360$	−0.224514	+	0.309017i	−0.224514	+	0.309017i
$361$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$362$	−0.587785	+	1.80902i	−0.587785	+	1.80902i
$363$	0.363271	−	1.11803i	0.363271	−	1.11803i
$364$	0.363271	+	1.11803i	0.363271	+	1.11803i
$365$		0			0
$366$	0.690983	−	2.12663i	0.690983	−	2.12663i
$367$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$367$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$368$	−1.61803			−1.61803
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$373$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$374$		0			0
$375$		−	1.17557i		−	1.17557i
$376$		0			0
$377$		0			0
$378$	0.587785	−	0.427051i	0.587785	−	0.427051i
$379$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$379$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$380$		0			0
$381$	−1.90211	−	1.38197i	−1.90211	−	1.38197i
$382$	−1.61803			−1.61803
$383$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$383$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$384$	−0.363271	+	1.11803i	−0.363271	+	1.11803i
$385$		0			0
$386$	0.190983	+	0.587785i	0.190983	+	0.587785i
$387$		0			0
$388$		0			0
$389$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$389$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$390$	0.812299	−	1.11803i	0.812299	−	1.11803i
$391$		0			0
$392$	0.809017	+	0.587785i	0.809017	+	0.587785i
$393$	−2.23607			−2.23607
$394$		0			0
$395$	0.951057	−	1.30902i	0.951057	−	1.30902i
$396$		0			0
$397$	0.951057	−	0.690983i	0.951057	−	0.690983i		−	1.00000i	$-0.5\pi$
$397$	0.951057	−	0.690983i	0.951057	−	0.690983i	0.951057	+	0.309017i	$0.100000\pi$
$398$		0			0
$399$		0			0
$400$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$401$	−2.00000			−2.00000			−1.00000			$\pi$
$401$	−2.00000			−2.00000			−1.00000			$\pi$
$402$		0			0
$403$		0			0
$404$	−0.951057	+	0.690983i	−0.951057	+	0.690983i
$405$	−1.17557	−	0.381966i	−1.17557	−	0.381966i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$409$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$410$		0			0
$411$	0.726543	+	2.23607i	0.726543	+	2.23607i
$412$		0			0
$413$	−0.587785	+	1.80902i	−0.587785	+	1.80902i
$414$	0.190983	+	0.587785i	0.190983	+	0.587785i
$415$	1.80902	+	0.587785i	1.80902	+	0.587785i
$416$	0.363271	−	1.11803i	0.363271	−	1.11803i
$417$		0			0
$418$		0			0
$419$	0.951057	+	0.690983i	0.951057	+	0.690983i	0.951057	−	0.309017i	$-0.100000\pi$
$419$	0.951057	+	0.690983i	0.951057	+	0.690983i			1.00000i	$0.5\pi$
$420$		−	1.17557i		−	1.17557i
$421$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$421$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	0.726543			0.726543
$427$	0.587785	+	1.80902i	0.587785	+	1.80902i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$431$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$432$	−0.726543			−0.726543
$433$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$433$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$439$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$440$		0			0
$441$	0.118034	−	0.363271i	0.118034	−	0.363271i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$449$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$449$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$450$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$451$		0			0
$452$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$453$	1.53884	−	1.11803i	1.53884	−	1.11803i
$454$	0.951057	−	0.690983i	0.951057	−	0.690983i
$455$			1.17557i			1.17557i
$456$		0			0
$457$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$457$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$458$	1.53884	+	1.11803i	1.53884	+	1.11803i
$459$		0			0
$460$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$461$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$461$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$462$		0			0
$463$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$463$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$464$		0			0
$465$		0			0
$466$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$467$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$467$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$468$	−0.449028			−0.449028
$469$		0			0
$470$		0			0
$471$	−1.80902	+	1.31433i	−1.80902	+	1.31433i
$472$	1.53884	−	1.11803i	1.53884	−	1.11803i
$473$		0			0
$474$	−1.90211			−1.90211
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$479$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$479$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$480$	−0.690983	+	0.951057i	−0.690983	+	0.951057i
$481$		0			0
$482$		0			0
$483$	−1.53884	−	1.11803i	−1.53884	−	1.11803i
$484$	0.309017	−	0.951057i	0.309017	−	0.951057i
$485$		0			0
$486$	0.224514	+	0.690983i	0.224514	+	0.690983i
$487$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$487$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$488$	0.587785	−	1.80902i	0.587785	−	1.80902i
$489$		0			0
$490$	0.587785	+	0.809017i	0.587785	+	0.809017i
$491$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$491$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$498$	−0.690983	−	2.12663i	−0.690983	−	2.12663i
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$		−	1.00000i		−	1.00000i
$501$		0			0
$502$	0.587785	+	1.80902i	0.587785	+	1.80902i
$503$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$503$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$504$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$505$	−1.11803	+	0.363271i	−1.11803	+	0.363271i
$506$		0			0
$507$	0.449028			0.449028
$508$	−1.61803	−	1.17557i	−1.61803	−	1.17557i
$509$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$509$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$510$		0			0
$511$		0			0
$512$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	1.80902	+	1.31433i	1.80902	+	1.31433i
$520$	0.690983	−	0.951057i	0.690983	−	0.951057i
$521$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$521$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$522$		0			0
$523$	−0.363271	−	1.11803i	−0.363271	−	1.11803i	−0.951057	−	0.309017i	$-0.900000\pi$
$523$	−0.363271	−	1.11803i	−0.363271	−	1.11803i	0.587785	−	0.809017i	$-0.300000\pi$
$524$	−1.90211			−1.90211
$525$	0.363271	−	1.11803i	0.363271	−	1.11803i
$526$	−1.61803			−1.61803
$527$		0			0
$528$		0			0
$529$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$530$		0			0
$531$	−0.587785	−	0.427051i	−0.587785	−	0.427051i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−0.587785	+	1.80902i	−0.587785	+	1.80902i
$539$		0			0
$540$	−0.690983	−	0.224514i	−0.690983	−	0.224514i
$541$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$541$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$542$		0			0
$543$	2.23607			2.23607
$544$		0			0
$545$		0			0
$546$	1.11803	−	0.812299i	1.11803	−	0.812299i
$547$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$547$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$548$	0.618034	+	1.90211i	0.618034	+	1.90211i
$549$	−0.726543			−0.726543
$550$		0			0
$551$		0			0
$552$	0.587785	+	1.80902i	0.587785	+	1.80902i
$553$	1.30902	−	0.951057i	1.30902	−	0.951057i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		1.00000			$0$
$557$		0			0		−1.00000			$\pi$
$558$		0			0
$559$		0			0
$560$		−	1.00000i		−	1.00000i
$561$		0			0
$562$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$563$	−0.363271	+	1.11803i	−0.363271	+	1.11803i	0.587785	+	0.809017i	$0.300000\pi$
$563$	−0.363271	+	1.11803i	−0.363271	+	1.11803i	−0.951057	+	0.309017i	$0.900000\pi$
$564$		0			0
$565$		−	0.618034i		−	0.618034i
$566$	−0.363271	+	1.11803i	−0.363271	+	1.11803i
$567$	−1.00000	−	0.726543i	−1.00000	−	0.726543i
$568$	0.618034			0.618034
$569$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$569$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$570$		0			0
$571$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$571$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$572$		0			0
$573$	0.587785	+	1.80902i	0.587785	+	1.80902i
$574$		0			0
$575$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$576$	0.381966			0.381966
$577$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$577$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$578$	0.809017	−	0.587785i	0.809017	−	0.587785i
$579$	0.587785	−	0.427051i	0.587785	−	0.427051i
$580$		0			0
$581$	1.53884	+	1.11803i	1.53884	+	1.11803i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−0.427051	−	0.138757i	−0.427051	−	0.138757i
$586$		0			0
$587$	−0.587785	+	1.80902i	−0.587785	+	1.80902i			1.00000i	$0.5\pi$
$587$	−0.587785	+	1.80902i	−0.587785	+	1.80902i	−0.587785	+	0.809017i	$0.700000\pi$
$588$	0.363271	−	1.11803i	0.363271	−	1.11803i
$589$		0			0
$590$	1.80902	−	0.587785i	1.80902	−	0.587785i
$591$		0			0
$592$		0			0
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−0.587785	−	1.80902i	−0.587785	−	1.80902i
$599$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$599$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$600$	−0.951057	+	0.690983i	−0.951057	+	0.690983i
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$	1.30902	−	0.951057i	1.30902	−	0.951057i
$605$	0.587785	−	0.809017i	0.587785	−	0.809017i
$606$	1.11803	+	0.812299i	1.11803	+	0.812299i
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		0			0
$609$		0			0
$610$	1.11803	−	1.53884i	1.11803	−	1.53884i
$611$		0			0
$612$		0			0
$613$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$613$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$617$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$618$		0			0
$619$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.951057	−	0.309017i	$-0.900000\pi$
$619$	−1.53884	−	1.11803i	−1.53884	−	1.11803i	−0.587785	−	0.809017i	$-0.700000\pi$
$620$		0			0
$621$	−0.951057	+	0.690983i	−0.951057	+	0.690983i
$622$		0			0
$623$		0			0
$624$	−1.38197			−1.38197
$625$	0.309017	−	0.951057i	0.309017	−	0.951057i
$626$		0			0
$627$		0			0
$628$	−1.53884	+	1.11803i	−1.53884	+	1.11803i
$629$		0			0
$630$	−0.363271	+	0.118034i	−0.363271	+	0.118034i
$631$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$631$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$632$	−1.61803			−1.61803
$633$		0			0
$634$		0			0
$635$	−1.17557	−	1.61803i	−1.17557	−	1.61803i
$636$		0			0
$637$	−0.363271	+	1.11803i	−0.363271	+	1.11803i
$638$		0			0
$639$	−0.0729490	−	0.224514i	−0.0729490	−	0.224514i
$640$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$641$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$641$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$642$		0			0
$643$	1.90211			1.90211			0.951057	−	0.309017i	$-0.100000\pi$
$643$	1.90211			1.90211			0.951057	+	0.309017i	$0.100000\pi$
$644$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$645$		0			0
$646$		0			0
$647$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$647$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$648$	0.381966	+	1.17557i	0.381966	+	1.17557i
$649$		0			0
$650$	0.951057	−	0.690983i	0.951057	−	0.690983i
$651$		0			0
$652$		0			0
$653$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$653$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$654$		0			0
$655$	−1.80902	−	0.587785i	−1.80902	−	0.587785i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$659$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$660$		0			0
$661$	−0.587785	−	1.80902i	−0.587785	−	1.80902i	−0.587785	−	0.809017i	$-0.700000\pi$
$661$	−0.587785	−	1.80902i	−0.587785	−	1.80902i		−	1.00000i	$-0.5\pi$
$662$		0			0
$663$		0			0
$664$	−0.587785	−	1.80902i	−0.587785	−	1.80902i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.951057	+	0.690983i	−0.951057	+	0.690983i
$673$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$673$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$674$	−1.61803			−1.61803
$675$	−0.587785	−	0.427051i	−0.587785	−	0.427051i
$676$	0.381966			0.381966
$677$	0.587785	+	1.80902i	0.587785	+	1.80902i	0.587785	+	0.809017i	$0.300000\pi$
$677$	0.587785	+	1.80902i	0.587785	+	1.80902i			1.00000i	$0.5\pi$
$678$	−0.587785	+	0.427051i	−0.587785	+	0.427051i
$679$		0			0
$680$		0			0
$681$	−1.11803	−	0.812299i	−1.11803	−	0.812299i
$682$		0			0
$683$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$683$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$684$		0			0
$685$			2.00000i			2.00000i
$686$	0.309017	+	0.951057i	0.309017	+	0.951057i
$687$	0.690983	−	2.12663i	0.690983	−	2.12663i
$688$		0			0
$689$		0			0
$690$			1.90211i			1.90211i
$691$	0.363271	−	1.11803i	0.363271	−	1.11803i	−0.587785	−	0.809017i	$-0.700000\pi$
$691$	0.363271	−	1.11803i	0.363271	−	1.11803i	0.951057	−	0.309017i	$-0.100000\pi$
$692$	1.53884	+	1.11803i	1.53884	+	1.11803i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−0.363271	−	1.11803i	−0.363271	−	1.11803i
$699$	0.726543			0.726543
$700$	0.309017	−	0.951057i	0.309017	−	0.951057i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	−0.263932	−	0.812299i	−0.263932	−	0.812299i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.17557			−1.17557
$708$	−1.80902	−	1.31433i	−1.80902	−	1.31433i
$709$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$709$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$710$	0.587785	+	0.190983i	0.587785	+	0.190983i
$711$	0.190983	+	0.587785i	0.190983	+	0.587785i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.53884	+	1.11803i	1.53884	+	1.11803i
$718$	1.61803			1.61803
$719$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$719$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$720$	0.363271	+	0.118034i	0.363271	+	0.118034i
$721$		0			0
$722$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$723$		0			0
$724$	1.90211			1.90211
$725$		0			0
$726$	−1.17557			−1.17557
$727$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$727$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$728$	0.951057	−	0.690983i	0.951057	−	0.690983i
$729$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$730$		0			0
$731$		0			0
$732$	−2.23607			−2.23607
$733$	1.53884	+	1.11803i	1.53884	+	1.11803i	0.951057	+	0.309017i	$0.100000\pi$
$733$	1.53884	+	1.11803i	1.53884	+	1.11803i	0.587785	+	0.809017i	$0.300000\pi$
$734$		0			0
$735$	0.690983	−	0.951057i	0.690983	−	0.951057i
$736$	0.500000	+	1.53884i	0.500000	+	1.53884i
$737$		0			0
$738$		0			0
$739$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$739$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$743$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.587785	+	0.427051i	−0.587785	+	0.427051i
$748$		0			0
$749$		0			0
$750$	−1.11803	+	0.363271i	−1.11803	+	0.363271i
$751$	2.00000			2.00000			1.00000			$0$
$751$	2.00000			2.00000			1.00000			$0$
$752$		0			0
$753$	1.80902	−	1.31433i	1.80902	−	1.31433i
$754$		0			0
$755$	1.53884	−	0.500000i	1.53884	−	0.500000i
$756$	−0.587785	−	0.427051i	−0.587785	−	0.427051i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$761$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$762$	−0.726543	+	2.23607i	−0.726543	+	2.23607i
$763$		0			0
$764$	0.500000	+	1.53884i	0.500000	+	1.53884i
$765$		0			0
$766$		0			0
$767$	1.80902	+	1.31433i	1.80902	+	1.31433i
$768$	1.17557			1.17557
$769$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$769$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$770$		0			0
$771$		0			0
$772$	0.500000	−	0.363271i	0.500000	−	0.363271i
$773$	0.363271	+	1.11803i	0.363271	+	1.11803i	0.951057	+	0.309017i	$0.100000\pi$
$773$	0.363271	+	1.11803i	0.363271	+	1.11803i	−0.587785	+	0.809017i	$0.700000\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−1.31433	−	0.427051i	−1.31433	−	0.427051i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.309017	−	0.951057i	0.309017	−	0.951057i
$785$	−1.80902	+	0.587785i	−1.80902	+	0.587785i
$786$	0.690983	+	2.12663i	0.690983	+	2.12663i
$787$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$787$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$788$		0			0
$789$	0.587785	+	1.80902i	0.587785	+	1.80902i
$790$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$791$	0.190983	−	0.587785i	0.190983	−	0.587785i
$792$		0			0
$793$	2.23607			2.23607
$794$	−0.951057	−	0.690983i	−0.951057	−	0.690983i
$795$		0			0
$796$		0			0
$797$	1.53884	−	1.11803i	1.53884	−	1.11803i	0.587785	−	0.809017i	$-0.300000\pi$
$797$	1.53884	−	1.11803i	1.53884	−	1.11803i	0.951057	−	0.309017i	$-0.100000\pi$
$798$		0			0
$799$		0			0
$800$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$801$		0			0
$802$	0.618034	+	1.90211i	0.618034	+	1.90211i
$803$		0			0
$804$		0			0
$805$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$806$		0			0
$807$	2.23607			2.23607
$808$	0.951057	+	0.690983i	0.951057	+	0.690983i
$809$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$809$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$810$			1.23607i			1.23607i
$811$	−0.363271	−	1.11803i	−0.363271	−	1.11803i	−0.951057	−	0.309017i	$-0.900000\pi$
$811$	−0.363271	−	1.11803i	−0.363271	−	1.11803i	0.587785	−	0.809017i	$-0.300000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−0.363271	−	0.263932i	−0.363271	−	0.263932i
$820$		0			0
$821$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$821$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$822$	1.90211	−	1.38197i	1.90211	−	1.38197i
$823$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$823$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$824$		0			0
$825$		0			0
$826$	1.90211			1.90211
$827$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$827$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$828$	0.500000	−	0.363271i	0.500000	−	0.363271i
$829$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$829$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$830$		−	1.90211i		−	1.90211i
$831$		0			0
$832$	−1.17557			−1.17557
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	0.363271	−	1.11803i	0.363271	−	1.11803i
$839$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$839$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$840$	−1.11803	+	0.363271i	−1.11803	+	0.363271i
$841$	0.309017	−	0.951057i	0.309017	−	0.951057i
$842$		0			0
$843$	0.726543			0.726543
$844$		0			0
$845$	0.363271	+	0.118034i	0.363271	+	0.118034i
$846$		0			0
$847$	0.809017	−	0.587785i	0.809017	−	0.587785i
$848$		0			0
$849$	1.38197			1.38197
$850$		0			0
$851$		0			0
$852$	−0.224514	−	0.690983i	−0.224514	−	0.690983i
$853$	1.53884	−	1.11803i	1.53884	−	1.11803i	0.587785	−	0.809017i	$-0.300000\pi$
$853$	1.53884	−	1.11803i	1.53884	−	1.11803i	0.951057	−	0.309017i	$-0.100000\pi$
$854$	1.53884	−	1.11803i	1.53884	−	1.11803i
$855$		0			0
$856$		0			0
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$		0			0
$859$	0.587785	−	1.80902i	0.587785	−	1.80902i		−	1.00000i	$-0.5\pi$
$859$	0.587785	−	1.80902i	0.587785	−	1.80902i	0.587785	−	0.809017i	$-0.300000\pi$
$860$		0			0
$861$		0			0
$862$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$863$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$863$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$864$	0.224514	+	0.690983i	0.224514	+	0.690983i
$865$	1.11803	+	1.53884i	1.11803	+	1.53884i
$866$		0			0
$867$	−0.951057	−	0.690983i	−0.951057	−	0.690983i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.587785	−	0.809017i	0.587785	−	0.809017i
$876$		0			0
$877$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$877$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$881$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$882$	−0.381966			−0.381966
$883$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$883$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$884$		0			0
$885$	−1.31433	−	1.80902i	−1.31433	−	1.80902i
$886$		0			0
$887$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$887$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$888$		0			0
$889$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$897$	−1.80902	+	1.31433i	−1.80902	+	1.31433i
$898$	0.500000	+	1.53884i	0.500000	+	1.53884i
$899$		0			0
$900$	0.309017	+	0.224514i	0.309017	+	0.224514i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$905$	1.80902	+	0.587785i	1.80902	+	0.587785i
$906$	−1.53884	−	1.11803i	−1.53884	−	1.11803i
$907$		0			0		1.00000			$0$
$907$		0			0		−1.00000			$\pi$
$908$	−0.951057	−	0.690983i	−0.951057	−	0.690983i
$909$	0.138757	−	0.427051i	0.138757	−	0.427051i
$910$	1.11803	−	0.363271i	1.11803	−	0.363271i
$911$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$911$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$912$		0			0
$913$		0			0
$914$	0.190983	+	0.587785i	0.190983	+	0.587785i
$915$	−2.12663	−	0.690983i	−2.12663	−	0.690983i
$916$	0.587785	−	1.80902i	0.587785	−	1.80902i
$917$	−1.53884	−	1.11803i	−1.53884	−	1.11803i
$918$		0			0
$919$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$919$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$920$			1.61803i			1.61803i
$921$		0			0
$922$		0			0
$923$	0.224514	+	0.690983i	0.224514	+	0.690983i
$924$		0			0
$925$		0			0
$926$	0.618034			0.618034
$927$		0			0
$928$		0			0
$929$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$929$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$930$		0			0
$931$		0			0
$932$	0.618034			0.618034
$933$		0			0
$934$		0			0
$935$		0			0
$936$	0.138757	+	0.427051i	0.138757	+	0.427051i
$937$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$937$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.587785	+	1.80902i	−0.587785	+	1.80902i			1.00000i	$0.5\pi$
$941$	−0.587785	+	1.80902i	−0.587785	+	1.80902i	−0.587785	+	0.809017i	$0.700000\pi$
$942$	1.80902	+	1.31433i	1.80902	+	1.31433i
$943$		0			0
$944$	−1.53884	−	1.11803i	−1.53884	−	1.11803i
$945$	−0.427051	−	0.587785i	−0.427051	−	0.587785i
$946$		0			0
$947$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$947$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$948$	0.587785	+	1.80902i	0.587785	+	1.80902i
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$953$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$954$		0			0
$955$			1.61803i			1.61803i
$956$	1.30902	+	0.951057i	1.30902	+	0.951057i
$957$		0			0
$958$		0			0
$959$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$960$	1.11803	+	0.363271i	1.11803	+	0.363271i
$961$	0.309017	+	0.951057i	0.309017	+	0.951057i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.587785	−	0.190983i	0.587785	−	0.190983i
$966$	−0.587785	+	1.80902i	−0.587785	+	1.80902i
$967$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$967$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$968$	−1.00000			−1.00000
$969$		0			0
$970$		0			0
$971$	−0.951057	+	0.690983i	−0.951057	+	0.690983i	−0.951057	−	0.309017i	$-0.900000\pi$
$971$	−0.951057	+	0.690983i	−0.951057	+	0.690983i			1.00000i	$0.5\pi$
$972$	0.587785	−	0.427051i	0.587785	−	0.427051i
$973$		0			0
$974$	−0.618034			−0.618034
$975$	−1.11803	−	0.812299i	−1.11803	−	0.812299i
$976$	−1.90211			−1.90211
$977$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$977$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$978$		0			0
$979$		0			0
$980$	0.587785	−	0.809017i	0.587785	−	0.809017i
$981$		0			0
$982$		0			0
$983$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$983$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$991$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$992$		0			0
$993$		0			0
$994$	0.500000	+	0.363271i	0.500000	+	0.363271i
$995$		0			0
$996$	−1.80902	+	1.31433i	−1.80902	+	1.31433i
$997$	−0.951057	+	0.690983i	−0.951057	+	0.690983i	−0.951057	−	0.309017i	$-0.900000\pi$
$997$	−0.951057	+	0.690983i	−0.951057	+	0.690983i			1.00000i	$0.5\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.1.bs.c.181.1	✓	8
7.6	odd	2	inner	1400.1.bs.c.181.2	yes	8
8.5	even	2	inner	1400.1.bs.c.181.2	yes	8
25.21	even	5	inner	1400.1.bs.c.1021.1	yes	8
56.13	odd	2	CM	1400.1.bs.c.181.1	✓	8
175.146	odd	10	inner	1400.1.bs.c.1021.2	yes	8
200.21	even	10	inner	1400.1.bs.c.1021.2	yes	8
1400.1021	odd	10	inner	1400.1.bs.c.1021.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1400.1.bs.c.181.1	✓	8	1.1	even	1	trivial
1400.1.bs.c.181.1	✓	8	56.13	odd	2	CM
1400.1.bs.c.181.2	yes	8	7.6	odd	2	inner
1400.1.bs.c.181.2	yes	8	8.5	even	2	inner
1400.1.bs.c.1021.1	yes	8	25.21	even	5	inner
1400.1.bs.c.1021.1	yes	8	1400.1021	odd	10	inner
1400.1.bs.c.1021.2	yes	8	175.146	odd	10	inner
1400.1.bs.c.1021.2	yes	8	200.21	even	10	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:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1400.bs (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.951057 + 0.690983i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(0.951057 + 0.690983i) q^{6} -1.00000 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.118034 - 0.363271i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.951057 + 0.690983i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(0.951057 + 0.690983i) q^{6} -1.00000 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.118034 - 0.363271i) q^{9} +(0.587785 + 0.809017i) q^{10} +(0.363271 - 1.11803i) q^{12} +(-0.363271 + 1.11803i) q^{13} +(0.309017 + 0.951057i) q^{14} +(0.690983 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} -0.381966 q^{18} +(0.587785 - 0.809017i) q^{20} +(0.951057 - 0.690983i) q^{21} +(-0.500000 - 1.53884i) q^{23} -1.17557 q^{24} +(0.809017 - 0.587785i) q^{25} +1.17557 q^{26} +(-0.224514 - 0.690983i) q^{27} +(0.809017 - 0.587785i) q^{28} +(-1.11803 - 0.363271i) q^{30} -1.00000 q^{32} +(0.951057 - 0.309017i) q^{35} +(0.118034 + 0.363271i) q^{36} +(-0.427051 - 1.31433i) q^{39} +(-0.951057 - 0.309017i) q^{40} +(-0.951057 - 0.690983i) q^{42} +0.381966i q^{45} +(-1.30902 + 0.951057i) q^{46} +(0.363271 + 1.11803i) q^{48} +1.00000 q^{49} +(-0.809017 - 0.587785i) q^{50} +(-0.363271 - 1.11803i) q^{52} +(-0.587785 + 0.427051i) q^{54} +(-0.809017 - 0.587785i) q^{56} +(0.587785 - 1.80902i) q^{59} +1.17557i q^{60} +(-0.587785 - 1.80902i) q^{61} +(-0.118034 + 0.363271i) q^{63} +(0.309017 + 0.951057i) q^{64} -1.17557i q^{65} +(1.53884 + 1.11803i) q^{69} +(-0.587785 - 0.809017i) q^{70} +(0.500000 - 0.363271i) q^{71} +(0.309017 - 0.224514i) q^{72} +(-0.363271 + 1.11803i) q^{75} +(-1.11803 + 0.812299i) q^{78} +(-1.30902 + 0.951057i) q^{79} +1.00000i q^{80} +(1.00000 + 0.726543i) q^{81} +(-1.53884 - 1.11803i) q^{83} +(-0.363271 + 1.11803i) q^{84} +(0.363271 - 0.118034i) q^{90} +(0.363271 - 1.11803i) q^{91} +(1.30902 + 0.951057i) q^{92} +(0.951057 - 0.690983i) q^{96} +(-0.309017 - 0.951057i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{4} - 8 q^{7} + 2 q^{8} - 8 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^4 - 8 * q^7 + 2 * q^8 - 8 * q^9	\( 8 q + 2 q^{2} - 2 q^{4} - 8 q^{7} + 2 q^{8} - 8 q^{9} - 2 q^{14} + 10 q^{15} - 2 q^{16} - 12 q^{18} - 4 q^{23} + 2 q^{25} + 2 q^{28} - 8 q^{32} - 8 q^{36} + 10 q^{39} - 6 q^{46} + 8 q^{49} - 2 q^{50} - 2 q^{56} + 8 q^{63} - 2 q^{64} + 4 q^{71} - 2 q^{72} - 6 q^{79} + 8 q^{81} + 6 q^{92} + 2 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^4 - 8 * q^7 + 2 * q^8 - 8 * q^9 - 2 * q^14 + 10 * q^15 - 2 * q^16 - 12 * q^18 - 4 * q^23 + 2 * q^25 + 2 * q^28 - 8 * q^32 - 8 * q^36 + 10 * q^39 - 6 * q^46 + 8 * q^49 - 2 * q^50 - 2 * q^56 + 8 * q^63 - 2 * q^64 + 4 * q^71 - 2 * q^72 - 6 * q^79 + 8 * q^81 + 6 * q^92 + 2 * q^98

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