LMFDB - Embedded newform 3844.1.n.f.1807.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3844,1,Mod(235,3844)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3844, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 26]))

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

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

chi := DirichletCharacter("3844.235");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3844 = 2^{2} \cdot 31^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3844.n (of order $30$, degree $8$, not 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:	$1.91840590856$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{30})$
Coefficient field:	$\Q(\zeta_{60})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1 $ x^16 + x^14 - x^10 - x^8 - x^6 + x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 124)
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.15376.1

Embedding invariants

Embedding label			1807.2
Root			$0.743145 + 0.669131i$ of defining polynomial
Character	$\chi$	$=$	3844.1807
Dual form			3844.1.n.f.3727.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(0.207912 - 0.978148i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.406737 + 0.913545i) q^{7} +(0.587785 + 0.809017i) q^{8} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(0.207912 - 0.978148i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.406737 + 0.913545i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.207912 - 0.978148i) q^{10} +(-0.994522 - 0.104528i) q^{11} +(0.743145 - 0.669131i) q^{12} +(0.669131 - 0.743145i) q^{13} +(0.104528 + 0.994522i) q^{14} +(-0.951057 + 0.309017i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.104528 + 0.994522i) q^{17} +(0.743145 - 0.669131i) q^{19} +(0.104528 - 0.994522i) q^{20} +(0.978148 - 0.207912i) q^{21} +(-0.913545 - 0.406737i) q^{22} +(0.913545 - 0.406737i) q^{24} +(0.866025 - 0.500000i) q^{26} +(0.587785 - 0.809017i) q^{27} +(-0.207912 + 0.978148i) q^{28} -1.00000 q^{30} +1.00000i q^{32} +(-0.309017 + 0.951057i) q^{33} +(-0.207912 + 0.978148i) q^{34} +(0.587785 - 0.809017i) q^{35} +(0.500000 - 0.866025i) q^{37} +(0.913545 - 0.406737i) q^{38} +(-0.587785 - 0.809017i) q^{39} +(0.406737 - 0.913545i) q^{40} +(-0.978148 + 0.207912i) q^{41} +(0.994522 + 0.104528i) q^{42} +(-0.743145 + 0.669131i) q^{43} +(-0.743145 - 0.669131i) q^{44} +(0.994522 - 0.104528i) q^{48} +(0.994522 + 0.104528i) q^{51} +(0.978148 - 0.207912i) q^{52} +(0.913545 + 0.406737i) q^{53} +(0.809017 - 0.587785i) q^{54} +(0.406737 + 0.913545i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-0.500000 - 0.866025i) q^{57} +(0.207912 - 0.978148i) q^{59} +(-0.951057 - 0.309017i) q^{60} +(-0.309017 + 0.951057i) q^{64} +(-0.978148 - 0.207912i) q^{65} +(-0.587785 + 0.809017i) q^{66} +(-0.866025 + 0.500000i) q^{67} +(-0.500000 + 0.866025i) q^{68} +(0.809017 - 0.587785i) q^{70} +(-0.406737 + 0.913545i) q^{71} +(0.104528 - 0.994522i) q^{73} +(0.743145 - 0.669131i) q^{74} +(0.994522 - 0.104528i) q^{76} +(-0.309017 - 0.951057i) q^{77} +(-0.309017 - 0.951057i) q^{78} +(-0.994522 + 0.104528i) q^{79} +(0.669131 - 0.743145i) q^{80} +(-0.669131 - 0.743145i) q^{81} +(-0.994522 - 0.104528i) q^{82} +(0.207912 + 0.978148i) q^{83} +(0.913545 + 0.406737i) q^{84} +(0.809017 - 0.587785i) q^{85} +(-0.913545 + 0.406737i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(0.951057 + 0.309017i) q^{91} +(-0.951057 - 0.309017i) q^{95} +(0.978148 + 0.207912i) q^{96} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 8 q^{5} + 8 q^{6}+O(q^{10}) $ 16 * q + 4 * q^4 - 8 * q^5 + 8 * q^6	$ 16 q + 4 q^{4} - 8 q^{5} + 8 q^{6} + 2 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{17} - 2 q^{20} - 2 q^{21} - 2 q^{22} + 2 q^{24} - 16 q^{30} + 4 q^{33} + 8 q^{37} + 2 q^{38} + 2 q^{41} - 2 q^{52} + 2 q^{53} + 4 q^{54} - 8 q^{56} - 8 q^{57} + 4 q^{64} + 2 q^{65} - 8 q^{68} + 4 q^{70} - 2 q^{73} + 4 q^{77} + 4 q^{78} + 2 q^{80} - 2 q^{81} + 2 q^{84} + 4 q^{85} - 2 q^{86} - 8 q^{88} - 2 q^{96}+O(q^{100}) $ 16 * q + 4 * q^4 - 8 * q^5 + 8 * q^6 + 2 * q^13 - 2 * q^14 - 4 * q^16 - 2 * q^17 - 2 * q^20 - 2 * q^21 - 2 * q^22 + 2 * q^24 - 16 * q^30 + 4 * q^33 + 8 * q^37 + 2 * q^38 + 2 * q^41 - 2 * q^52 + 2 * q^53 + 4 * q^54 - 8 * q^56 - 8 * q^57 + 4 * q^64 + 2 * q^65 - 8 * q^68 + 4 * q^70 - 2 * q^73 + 4 * q^77 + 4 * q^78 + 2 * q^80 - 2 * q^81 + 2 * q^84 + 4 * q^85 - 2 * q^86 - 8 * q^88 - 2 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3844\mathbb{Z}\right)^\times$.

$n$	$1923$	$1925$
$\chi(n)$	$-1$	$e\left(\frac{1}{15}\right)$

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 $

$2$	0.951057	+	0.309017i	0.951057	+	0.309017i
$2$	0.951057	+	0.309017i	0.951057	+	0.309017i
$3$	0.207912	−	0.978148i	0.207912	−	0.978148i	−0.743145	−	0.669131i	$-0.766667\pi$
$3$	0.207912	−	0.978148i	0.207912	−	0.978148i	0.951057	−	0.309017i	$-0.100000\pi$
$4$	0.809017	+	0.587785i	0.809017	+	0.587785i
$5$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$5$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$6$	0.500000	−	0.866025i	0.500000	−	0.866025i
$7$	0.406737	+	0.913545i	0.406737	+	0.913545i	0.994522	+	0.104528i	$0.0333333\pi$
$7$	0.406737	+	0.913545i	0.406737	+	0.913545i	−0.587785	+	0.809017i	$0.700000\pi$
$8$	0.587785	+	0.809017i	0.587785	+	0.809017i
$9$		0			0
$10$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$11$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.406737	−	0.913545i	$-0.633333\pi$
$11$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.587785	+	0.809017i	$0.700000\pi$
$12$	0.743145	−	0.669131i	0.743145	−	0.669131i
$13$	0.669131	−	0.743145i	0.669131	−	0.743145i	−0.309017	−	0.951057i	$-0.600000\pi$
$13$	0.669131	−	0.743145i	0.669131	−	0.743145i	0.978148	+	0.207912i	$0.0666667\pi$
$14$	0.104528	+	0.994522i	0.104528	+	0.994522i
$15$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$16$	0.309017	+	0.951057i	0.309017	+	0.951057i
$17$	0.104528	+	0.994522i	0.104528	+	0.994522i	0.913545	+	0.406737i	$0.133333\pi$
$17$	0.104528	+	0.994522i	0.104528	+	0.994522i	−0.809017	+	0.587785i	$0.800000\pi$
$18$		0			0
$19$	0.743145	−	0.669131i	0.743145	−	0.669131i	−0.207912	−	0.978148i	$-0.566667\pi$
$19$	0.743145	−	0.669131i	0.743145	−	0.669131i	0.951057	+	0.309017i	$0.100000\pi$
$20$	0.104528	−	0.994522i	0.104528	−	0.994522i
$21$	0.978148	−	0.207912i	0.978148	−	0.207912i
$22$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$23$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$23$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$24$	0.913545	−	0.406737i	0.913545	−	0.406737i
$25$		0			0
$26$	0.866025	−	0.500000i	0.866025	−	0.500000i
$27$	0.587785	−	0.809017i	0.587785	−	0.809017i
$28$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$29$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$29$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$30$	−1.00000			−1.00000
$31$		0			0
$31$		0			0
$32$			1.00000i			1.00000i
$33$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$34$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$35$	0.587785	−	0.809017i	0.587785	−	0.809017i
$36$		0			0
$37$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$37$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$38$	0.913545	−	0.406737i	0.913545	−	0.406737i
$39$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$40$	0.406737	−	0.913545i	0.406737	−	0.913545i
$41$	−0.978148	+	0.207912i	−0.978148	+	0.207912i	−0.669131	−	0.743145i	$-0.733333\pi$
$41$	−0.978148	+	0.207912i	−0.978148	+	0.207912i	−0.309017	+	0.951057i	$0.600000\pi$
$42$	0.994522	+	0.104528i	0.994522	+	0.104528i
$43$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	−0.951057	−	0.309017i	$-0.900000\pi$
$43$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	0.207912	+	0.978148i	$0.433333\pi$
$44$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$45$		0			0
$46$		0			0
$47$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$47$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$48$	0.994522	−	0.104528i	0.994522	−	0.104528i
$49$		0			0
$50$		0			0
$51$	0.994522	+	0.104528i	0.994522	+	0.104528i
$52$	0.978148	−	0.207912i	0.978148	−	0.207912i
$53$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.809017	−	0.587785i	$-0.200000\pi$
$53$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.104528	+	0.994522i	$0.466667\pi$
$54$	0.809017	−	0.587785i	0.809017	−	0.587785i
$55$	0.406737	+	0.913545i	0.406737	+	0.913545i
$56$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$57$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$58$		0			0
$59$	0.207912	−	0.978148i	0.207912	−	0.978148i	−0.743145	−	0.669131i	$-0.766667\pi$
$59$	0.207912	−	0.978148i	0.207912	−	0.978148i	0.951057	−	0.309017i	$-0.100000\pi$
$60$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$61$		0			0			−	1.00000i	$-0.5\pi$
$61$		0			0				1.00000i	$0.5\pi$
$62$		0			0
$63$		0			0
$64$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$65$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$66$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$67$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$67$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$68$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$69$		0			0
$70$	0.809017	−	0.587785i	0.809017	−	0.587785i
$71$	−0.406737	+	0.913545i	−0.406737	+	0.913545i	0.587785	+	0.809017i	$0.300000\pi$
$71$	−0.406737	+	0.913545i	−0.406737	+	0.913545i	−0.994522	+	0.104528i	$0.966667\pi$
$72$		0			0
$73$	0.104528	−	0.994522i	0.104528	−	0.994522i	−0.809017	−	0.587785i	$-0.800000\pi$
$73$	0.104528	−	0.994522i	0.104528	−	0.994522i	0.913545	−	0.406737i	$-0.133333\pi$
$74$	0.743145	−	0.669131i	0.743145	−	0.669131i
$75$		0			0
$76$	0.994522	−	0.104528i	0.994522	−	0.104528i
$77$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$78$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$79$	−0.994522	+	0.104528i	−0.994522	+	0.104528i	−0.587785	−	0.809017i	$-0.700000\pi$
$79$	−0.994522	+	0.104528i	−0.994522	+	0.104528i	−0.406737	+	0.913545i	$0.633333\pi$
$80$	0.669131	−	0.743145i	0.669131	−	0.743145i
$81$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$82$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$83$	0.207912	+	0.978148i	0.207912	+	0.978148i	0.951057	+	0.309017i	$0.100000\pi$
$83$	0.207912	+	0.978148i	0.207912	+	0.978148i	−0.743145	+	0.669131i	$0.766667\pi$
$84$	0.913545	+	0.406737i	0.913545	+	0.406737i
$85$	0.809017	−	0.587785i	0.809017	−	0.587785i
$86$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$87$		0			0
$88$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$89$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$89$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$90$		0			0
$91$	0.951057	+	0.309017i	0.951057	+	0.309017i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$96$	0.978148	+	0.207912i	0.978148	+	0.207912i
$97$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$97$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$101$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$102$	0.913545	+	0.406737i	0.913545	+	0.406737i
$103$	0.207912	+	0.978148i	0.207912	+	0.978148i	0.951057	+	0.309017i	$0.100000\pi$
$103$	0.207912	+	0.978148i	0.207912	+	0.978148i	−0.743145	+	0.669131i	$0.766667\pi$
$104$	0.994522	+	0.104528i	0.994522	+	0.104528i
$105$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$106$	0.743145	+	0.669131i	0.743145	+	0.669131i
$107$	−0.994522	+	0.104528i	−0.994522	+	0.104528i	−0.587785	−	0.809017i	$-0.700000\pi$
$107$	−0.994522	+	0.104528i	−0.994522	+	0.104528i	−0.406737	+	0.913545i	$0.633333\pi$
$108$	0.951057	−	0.309017i	0.951057	−	0.309017i
$109$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$109$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$110$	0.104528	+	0.994522i	0.104528	+	0.994522i
$111$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$112$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$113$	0.104528	−	0.994522i	0.104528	−	0.994522i	−0.809017	−	0.587785i	$-0.800000\pi$
$113$	0.104528	−	0.994522i	0.104528	−	0.994522i	0.913545	−	0.406737i	$-0.133333\pi$
$114$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.500000	−	0.866025i	0.500000	−	0.866025i
$119$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$120$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$121$		0			0
$122$		0			0
$123$			1.00000i			1.00000i
$124$		0			0
$125$	−1.00000			−1.00000
$126$		0			0
$127$	0.207912	−	0.978148i	0.207912	−	0.978148i	−0.743145	−	0.669131i	$-0.766667\pi$
$127$	0.207912	−	0.978148i	0.207912	−	0.978148i	0.951057	−	0.309017i	$-0.100000\pi$
$128$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$129$	0.500000	+	0.866025i	0.500000	+	0.866025i
$130$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$131$	−0.406737	−	0.913545i	−0.406737	−	0.913545i	−0.994522	−	0.104528i	$-0.966667\pi$
$131$	−0.406737	−	0.913545i	−0.406737	−	0.913545i	0.587785	−	0.809017i	$-0.300000\pi$
$132$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$133$	0.913545	+	0.406737i	0.913545	+	0.406737i
$134$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$135$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$136$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$137$	−0.669131	+	0.743145i	−0.669131	+	0.743145i	−0.978148	−	0.207912i	$-0.933333\pi$
$137$	−0.669131	+	0.743145i	−0.669131	+	0.743145i	0.309017	+	0.951057i	$0.400000\pi$
$138$		0			0
$139$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$139$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$140$	0.951057	−	0.309017i	0.951057	−	0.309017i
$141$		0			0
$142$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$143$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$144$		0			0
$145$		0			0
$146$	0.406737	−	0.913545i	0.406737	−	0.913545i
$147$		0			0
$148$	0.913545	−	0.406737i	0.913545	−	0.406737i
$149$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$149$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$150$		0			0
$151$	−1.17557	+	1.61803i	−1.17557	+	1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$151$	−1.17557	+	1.61803i	−1.17557	+	1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$152$	0.978148	+	0.207912i	0.978148	+	0.207912i
$153$		0			0
$154$		−	1.00000i		−	1.00000i
$155$		0			0
$156$		−	1.00000i		−	1.00000i
$157$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$157$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$158$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$159$	0.587785	−	0.809017i	0.587785	−	0.809017i
$160$	0.866025	−	0.500000i	0.866025	−	0.500000i
$161$		0			0
$162$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$163$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$163$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$164$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$165$	0.978148	−	0.207912i	0.978148	−	0.207912i
$166$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$167$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	−0.951057	−	0.309017i	$-0.900000\pi$
$167$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	0.207912	+	0.978148i	$0.433333\pi$
$168$	0.743145	+	0.669131i	0.743145	+	0.669131i
$169$		0			0
$170$	0.951057	−	0.309017i	0.951057	−	0.309017i
$171$		0			0
$172$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$173$	0.669131	−	0.743145i	0.669131	−	0.743145i	−0.309017	−	0.951057i	$-0.600000\pi$
$173$	0.669131	−	0.743145i	0.669131	−	0.743145i	0.978148	+	0.207912i	$0.0666667\pi$
$174$		0			0
$175$		0			0
$176$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$177$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$178$		0			0
$179$	−0.406737	−	0.913545i	−0.406737	−	0.913545i	−0.994522	−	0.104528i	$-0.966667\pi$
$179$	−0.406737	−	0.913545i	−0.406737	−	0.913545i	0.587785	−	0.809017i	$-0.300000\pi$
$180$		0			0
$181$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$181$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$182$	0.809017	+	0.587785i	0.809017	+	0.587785i
$183$		0			0
$184$		0			0
$185$	−1.00000			−1.00000
$186$		0			0
$187$		−	1.00000i		−	1.00000i
$188$		0			0
$189$	0.978148	+	0.207912i	0.978148	+	0.207912i
$190$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$191$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$191$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$192$	0.866025	+	0.500000i	0.866025	+	0.500000i
$193$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.104528	−	0.994522i	$-0.466667\pi$
$193$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.809017	+	0.587785i	$0.200000\pi$
$194$		0			0
$195$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$196$		0			0
$197$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	0.809017	+	0.587785i	$0.200000\pi$
$197$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	−0.913545	+	0.406737i	$0.866667\pi$
$198$		0			0
$199$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	0.207912	−	0.978148i	$-0.433333\pi$
$199$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	−0.951057	+	0.309017i	$0.900000\pi$
$200$		0			0
$201$	0.309017	+	0.951057i	0.309017	+	0.951057i
$202$		0			0
$203$		0			0
$204$	0.743145	+	0.669131i	0.743145	+	0.669131i
$205$	0.669131	+	0.743145i	0.669131	+	0.743145i
$206$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$207$		0			0
$208$	0.913545	+	0.406737i	0.913545	+	0.406737i
$209$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$210$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$211$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$211$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$212$	0.500000	+	0.866025i	0.500000	+	0.866025i
$213$	0.809017	+	0.587785i	0.809017	+	0.587785i
$214$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$215$	0.951057	+	0.309017i	0.951057	+	0.309017i
$216$	1.00000			1.00000
$217$		0			0
$218$		0			0
$219$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$220$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$221$	0.809017	+	0.587785i	0.809017	+	0.587785i
$222$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$223$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$223$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$224$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$225$		0			0
$226$	0.406737	−	0.913545i	0.406737	−	0.913545i
$227$	0.207912	+	0.978148i	0.207912	+	0.978148i	0.951057	+	0.309017i	$0.100000\pi$
$227$	0.207912	+	0.978148i	0.207912	+	0.978148i	−0.743145	+	0.669131i	$0.766667\pi$
$228$	0.104528	−	0.994522i	0.104528	−	0.994522i
$229$	0.669131	+	0.743145i	0.669131	+	0.743145i	0.978148	−	0.207912i	$-0.0666667\pi$
$229$	0.669131	+	0.743145i	0.669131	+	0.743145i	−0.309017	+	0.951057i	$0.600000\pi$
$230$		0			0
$231$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$232$		0			0
$233$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$233$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$234$		0			0
$235$		0			0
$236$	0.743145	−	0.669131i	0.743145	−	0.669131i
$237$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$238$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$239$	−0.406737	+	0.913545i	−0.406737	+	0.913545i	0.587785	+	0.809017i	$0.300000\pi$
$239$	−0.406737	+	0.913545i	−0.406737	+	0.913545i	−0.994522	+	0.104528i	$0.966667\pi$
$240$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$241$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.104528	−	0.994522i	$-0.466667\pi$
$241$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.809017	+	0.587785i	$0.200000\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$247$		−	1.00000i		−	1.00000i
$248$		0			0
$249$	1.00000			1.00000
$250$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$251$	−0.207912	+	0.978148i	−0.207912	+	0.978148i	0.743145	+	0.669131i	$0.233333\pi$
$251$	−0.207912	+	0.978148i	−0.207912	+	0.978148i	−0.951057	+	0.309017i	$0.900000\pi$
$252$		0			0
$253$		0			0
$254$	0.500000	−	0.866025i	0.500000	−	0.866025i
$255$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$256$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$257$	−0.913545	−	0.406737i	−0.913545	−	0.406737i	−0.104528	−	0.994522i	$-0.533333\pi$
$257$	−0.913545	−	0.406737i	−0.913545	−	0.406737i	−0.809017	+	0.587785i	$0.800000\pi$
$258$	0.207912	+	0.978148i	0.207912	+	0.978148i
$259$	0.994522	+	0.104528i	0.994522	+	0.104528i
$260$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$261$		0			0
$262$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$263$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$263$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$264$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$265$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$266$	0.743145	+	0.669131i	0.743145	+	0.669131i
$267$		0			0
$268$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$269$	−0.978148	+	0.207912i	−0.978148	+	0.207912i	−0.669131	−	0.743145i	$-0.733333\pi$
$269$	−0.978148	+	0.207912i	−0.978148	+	0.207912i	−0.309017	+	0.951057i	$0.600000\pi$
$270$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$271$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$271$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$272$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$273$	0.500000	−	0.866025i	0.500000	−	0.866025i
$274$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$275$		0			0
$276$		0			0
$277$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$277$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$278$		0			0
$279$		0			0
$280$	1.00000			1.00000
$281$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$281$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$282$		0			0
$283$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$283$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$284$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$285$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$286$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$287$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$288$		0			0
$289$		0			0
$290$		0			0
$291$		0			0
$292$	0.669131	−	0.743145i	0.669131	−	0.743145i
$293$	0.104528	+	0.994522i	0.104528	+	0.994522i	0.913545	+	0.406737i	$0.133333\pi$
$293$	0.104528	+	0.994522i	0.104528	+	0.994522i	−0.809017	+	0.587785i	$0.800000\pi$
$294$		0			0
$295$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$296$	0.994522	−	0.104528i	0.994522	−	0.104528i
$297$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$298$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$299$		0			0
$300$		0			0
$301$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$302$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$303$		0			0
$304$	0.866025	+	0.500000i	0.866025	+	0.500000i
$305$		0			0
$306$		0			0
$307$	0.207912	−	0.978148i	0.207912	−	0.978148i	−0.743145	−	0.669131i	$-0.766667\pi$
$307$	0.207912	−	0.978148i	0.207912	−	0.978148i	0.951057	−	0.309017i	$-0.100000\pi$
$308$	0.309017	−	0.951057i	0.309017	−	0.951057i
$309$	1.00000			1.00000
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$	0.309017	−	0.951057i	0.309017	−	0.951057i
$313$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.669131	−	0.743145i	$-0.266667\pi$
$313$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.309017	+	0.951057i	$0.400000\pi$
$314$		0			0
$315$		0			0
$316$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$317$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.809017	−	0.587785i	$-0.800000\pi$
$317$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.104528	+	0.994522i	$0.533333\pi$
$318$	0.809017	−	0.587785i	0.809017	−	0.587785i
$319$		0			0
$320$	0.978148	−	0.207912i	0.978148	−	0.207912i
$321$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$322$		0			0
$323$	0.743145	+	0.669131i	0.743145	+	0.669131i
$324$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$325$		0			0
$326$		0			0
$327$		0			0
$328$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$329$		0			0
$330$	0.994522	+	0.104528i	0.994522	+	0.104528i
$331$	0.207912	+	0.978148i	0.207912	+	0.978148i	0.951057	+	0.309017i	$0.100000\pi$
$331$	0.207912	+	0.978148i	0.207912	+	0.978148i	−0.743145	+	0.669131i	$0.766667\pi$
$332$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$333$		0			0
$334$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$335$	0.866025	+	0.500000i	0.866025	+	0.500000i
$336$	0.500000	+	0.866025i	0.500000	+	0.866025i
$337$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$337$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$338$		0			0
$339$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$340$	1.00000			1.00000
$341$		0			0
$342$		0			0
$343$	0.951057	+	0.309017i	0.951057	+	0.309017i
$344$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$345$		0			0
$346$	0.866025	−	0.500000i	0.866025	−	0.500000i
$347$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$347$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$348$		0			0
$349$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$349$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$350$		0			0
$351$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$352$	0.104528	−	0.994522i	0.104528	−	0.994522i
$353$	0.669131	+	0.743145i	0.669131	+	0.743145i	0.978148	−	0.207912i	$-0.0666667\pi$
$353$	0.669131	+	0.743145i	0.669131	+	0.743145i	−0.309017	+	0.951057i	$0.600000\pi$
$354$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$355$	0.994522	−	0.104528i	0.994522	−	0.104528i
$356$		0			0
$357$	0.309017	+	0.951057i	0.309017	+	0.951057i
$358$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$359$	0.743145	+	0.669131i	0.743145	+	0.669131i	0.951057	−	0.309017i	$-0.100000\pi$
$359$	0.743145	+	0.669131i	0.743145	+	0.669131i	−0.207912	+	0.978148i	$0.566667\pi$
$360$		0			0
$361$		0			0
$362$	0.207912	+	0.978148i	0.207912	+	0.978148i
$363$		0			0
$364$	0.587785	+	0.809017i	0.587785	+	0.809017i
$365$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$366$		0			0
$367$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$367$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$368$		0			0
$369$		0			0
$370$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$371$			1.00000i			1.00000i
$372$		0			0
$373$	−2.00000			−2.00000			−1.00000			$\pi$
$373$	−2.00000			−2.00000			−1.00000			$\pi$
$374$	0.309017	−	0.951057i	0.309017	−	0.951057i
$375$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$376$		0			0
$377$		0			0
$378$	0.866025	+	0.500000i	0.866025	+	0.500000i
$379$	0.406737	+	0.913545i	0.406737	+	0.913545i	0.994522	+	0.104528i	$0.0333333\pi$
$379$	0.406737	+	0.913545i	0.406737	+	0.913545i	−0.587785	+	0.809017i	$0.700000\pi$
$380$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$381$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$382$	0.978148	−	0.207912i	0.978148	−	0.207912i
$383$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.406737	−	0.913545i	$-0.633333\pi$
$383$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.587785	+	0.809017i	$0.700000\pi$
$384$	0.669131	+	0.743145i	0.669131	+	0.743145i
$385$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$386$	0.994522	−	0.104528i	0.994522	−	0.104528i
$387$		0			0
$388$		0			0
$389$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	−0.913545	−	0.406737i	$-0.866667\pi$
$389$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	0.809017	−	0.587785i	$-0.200000\pi$
$390$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$391$		0			0
$392$		0			0
$393$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$394$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$395$	0.587785	+	0.809017i	0.587785	+	0.809017i
$396$		0			0
$397$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$397$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$398$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$399$	0.587785	−	0.809017i	0.587785	−	0.809017i
$400$		0			0
$401$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$401$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$402$			1.00000i			1.00000i
$403$		0			0
$404$		0			0
$405$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$406$		0			0
$407$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$408$	0.500000	+	0.866025i	0.500000	+	0.866025i
$409$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$409$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$410$	0.406737	+	0.913545i	0.406737	+	0.913545i
$411$	0.587785	+	0.809017i	0.587785	+	0.809017i
$412$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$413$	0.978148	−	0.207912i	0.978148	−	0.207912i
$414$		0			0
$415$	0.743145	−	0.669131i	0.743145	−	0.669131i
$416$	0.743145	+	0.669131i	0.743145	+	0.669131i
$417$		0			0
$418$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$419$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$419$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$420$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$421$	−0.669131	+	0.743145i	−0.669131	+	0.743145i	−0.978148	−	0.207912i	$-0.933333\pi$
$421$	−0.669131	+	0.743145i	−0.669131	+	0.743145i	0.309017	+	0.951057i	$0.400000\pi$
$422$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$423$		0			0
$424$	0.207912	+	0.978148i	0.207912	+	0.978148i
$425$		0			0
$426$	0.587785	+	0.809017i	0.587785	+	0.809017i
$427$		0			0
$428$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$429$	0.500000	+	0.866025i	0.500000	+	0.866025i
$430$	0.809017	+	0.587785i	0.809017	+	0.587785i
$431$	−0.207912	+	0.978148i	−0.207912	+	0.978148i	0.743145	+	0.669131i	$0.233333\pi$
$431$	−0.207912	+	0.978148i	−0.207912	+	0.978148i	−0.951057	+	0.309017i	$0.900000\pi$
$432$	0.951057	+	0.309017i	0.951057	+	0.309017i
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$439$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$439$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$440$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$441$		0			0
$442$	0.587785	+	0.809017i	0.587785	+	0.809017i
$443$	0.406737	−	0.913545i	0.406737	−	0.913545i	−0.587785	−	0.809017i	$-0.700000\pi$
$443$	0.406737	−	0.913545i	0.406737	−	0.913545i	0.994522	−	0.104528i	$-0.0333333\pi$
$444$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$445$		0			0
$446$	0.669131	+	0.743145i	0.669131	+	0.743145i
$447$	0.743145	+	0.669131i	0.743145	+	0.669131i
$448$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$449$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$449$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$450$		0			0
$451$	0.994522	−	0.104528i	0.994522	−	0.104528i
$452$	0.669131	−	0.743145i	0.669131	−	0.743145i
$453$	1.33826	+	1.48629i	1.33826	+	1.48629i
$454$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$455$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$456$	0.406737	−	0.913545i	0.406737	−	0.913545i
$457$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$457$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$458$	0.406737	+	0.913545i	0.406737	+	0.913545i
$459$	0.866025	+	0.500000i	0.866025	+	0.500000i
$460$		0			0
$461$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$461$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$462$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$463$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$463$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$467$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$468$		0			0
$469$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$470$		0			0
$471$		0			0
$472$	0.913545	−	0.406737i	0.913545	−	0.406737i
$473$	0.809017	−	0.587785i	0.809017	−	0.587785i
$474$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$475$		0			0
$476$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$477$		0			0
$478$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$479$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.406737	−	0.913545i	$-0.366667\pi$
$479$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.587785	+	0.809017i	$0.300000\pi$
$480$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$481$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$482$	0.994522	−	0.104528i	0.994522	−	0.104528i
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$	0.406737	−	0.913545i	0.406737	−	0.913545i	−0.587785	−	0.809017i	$-0.700000\pi$
$487$	0.406737	−	0.913545i	0.406737	−	0.913545i	0.994522	−	0.104528i	$-0.0333333\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$491$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$492$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$493$		0			0
$494$	0.309017	−	0.951057i	0.309017	−	0.951057i
$495$		0			0
$496$		0			0
$497$	−1.00000			−1.00000
$498$	0.951057	+	0.309017i	0.951057	+	0.309017i
$499$	0.207912	−	0.978148i	0.207912	−	0.978148i	−0.743145	−	0.669131i	$-0.766667\pi$
$499$	0.207912	−	0.978148i	0.207912	−	0.978148i	0.951057	−	0.309017i	$-0.100000\pi$
$500$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$501$	0.500000	+	0.866025i	0.500000	+	0.866025i
$502$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$503$	0.406737	+	0.913545i	0.406737	+	0.913545i	0.994522	+	0.104528i	$0.0333333\pi$
$503$	0.406737	+	0.913545i	0.406737	+	0.913545i	−0.587785	+	0.809017i	$0.700000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$	0.743145	−	0.669131i	0.743145	−	0.669131i
$509$	0.669131	−	0.743145i	0.669131	−	0.743145i	−0.309017	−	0.951057i	$-0.600000\pi$
$509$	0.669131	−	0.743145i	0.669131	−	0.743145i	0.978148	+	0.207912i	$0.0666667\pi$
$510$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$511$	0.951057	−	0.309017i	0.951057	−	0.309017i
$512$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$513$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$514$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$515$	0.743145	−	0.669131i	0.743145	−	0.669131i
$516$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$517$		0			0
$518$	0.913545	+	0.406737i	0.913545	+	0.406737i
$519$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$520$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$521$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$521$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$522$		0			0
$523$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$523$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$524$	0.207912	−	0.978148i	0.207912	−	0.978148i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1.00000			−1.00000
$529$	0.309017	−	0.951057i	0.309017	−	0.951057i
$530$	0.207912	−	0.978148i	0.207912	−	0.978148i
$531$		0			0
$532$	0.500000	+	0.866025i	0.500000	+	0.866025i
$533$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$534$		0			0
$535$	0.587785	+	0.809017i	0.587785	+	0.809017i
$536$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$537$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$538$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$539$		0			0
$540$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$541$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	−0.913545	−	0.406737i	$-0.866667\pi$
$541$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	0.809017	−	0.587785i	$-0.200000\pi$
$542$		0			0
$543$	0.951057	−	0.309017i	0.951057	−	0.309017i
$544$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$545$		0			0
$546$	0.743145	−	0.669131i	0.743145	−	0.669131i
$547$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.406737	−	0.913545i	$-0.633333\pi$
$547$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.587785	+	0.809017i	$0.700000\pi$
$548$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$554$		0			0
$555$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$556$		0			0
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$		0			0
$559$			1.00000i			1.00000i
$560$	0.951057	+	0.309017i	0.951057	+	0.309017i
$561$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$562$	1.17557	−	1.61803i	1.17557	−	1.61803i
$563$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$563$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$564$		0			0
$565$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$566$		0			0
$567$	0.406737	−	0.913545i	0.406737	−	0.913545i
$568$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$569$	0.104528	−	0.994522i	0.104528	−	0.994522i	−0.809017	−	0.587785i	$-0.800000\pi$
$569$	0.104528	−	0.994522i	0.104528	−	0.994522i	0.913545	−	0.406737i	$-0.133333\pi$
$570$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$571$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	0.207912	−	0.978148i	$-0.433333\pi$
$571$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	−0.951057	+	0.309017i	$0.900000\pi$
$572$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$573$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$574$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$575$		0			0
$576$		0			0
$577$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	0.309017	−	0.951057i	$-0.400000\pi$
$577$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	−0.978148	+	0.207912i	$0.933333\pi$
$578$		0			0
$579$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$580$		0			0
$581$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$582$		0			0
$583$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$584$	0.866025	−	0.500000i	0.866025	−	0.500000i
$585$		0			0
$586$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$587$	−1.90211	−	0.618034i	−1.90211	−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$587$	−1.90211	−	0.618034i	−1.90211	−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$588$		0			0
$589$		0			0
$590$	−1.00000			−1.00000
$591$	0.951057	+	0.309017i	0.951057	+	0.309017i
$592$	0.978148	+	0.207912i	0.978148	+	0.207912i
$593$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$593$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$594$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$595$	0.866025	+	0.500000i	0.866025	+	0.500000i
$596$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$597$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$598$		0			0
$599$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	−0.951057	−	0.309017i	$-0.900000\pi$
$599$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	0.743145	−	0.669131i	$-0.233333\pi$
$600$		0			0
$601$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	0.309017	−	0.951057i	$-0.400000\pi$
$601$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	−0.978148	+	0.207912i	$0.933333\pi$
$602$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$603$		0			0
$604$	−1.90211	+	0.618034i	−1.90211	+	0.618034i
$605$		0			0
$606$		0			0
$607$	0.743145	+	0.669131i	0.743145	+	0.669131i	0.951057	−	0.309017i	$-0.100000\pi$
$607$	0.743145	+	0.669131i	0.743145	+	0.669131i	−0.207912	+	0.978148i	$0.566667\pi$
$608$	0.669131	+	0.743145i	0.669131	+	0.743145i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.809017	−	0.587785i	$-0.800000\pi$
$613$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.104528	+	0.994522i	$0.533333\pi$
$614$	0.500000	−	0.866025i	0.500000	−	0.866025i
$615$	0.866025	−	0.500000i	0.866025	−	0.500000i
$616$	0.587785	−	0.809017i	0.587785	−	0.809017i
$617$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.669131	−	0.743145i	$-0.266667\pi$
$617$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.309017	+	0.951057i	$0.400000\pi$
$618$	0.951057	+	0.309017i	0.951057	+	0.309017i
$619$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$619$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	0.587785	−	0.809017i	0.587785	−	0.809017i
$625$	0.500000	+	0.866025i	0.500000	+	0.866025i
$626$	0.866025	+	0.500000i	0.866025	+	0.500000i
$627$	0.406737	+	0.913545i	0.406737	+	0.913545i
$628$		0			0
$629$	0.913545	+	0.406737i	0.913545	+	0.406737i
$630$		0			0
$631$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.587785	−	0.809017i	$-0.300000\pi$
$631$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.406737	+	0.913545i	$0.366667\pi$
$632$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$633$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$634$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$635$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$636$	0.951057	−	0.309017i	0.951057	−	0.309017i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.994522	+	0.104528i	0.994522	+	0.104528i
$641$	−0.978148	+	0.207912i	−0.978148	+	0.207912i	−0.669131	−	0.743145i	$-0.733333\pi$
$641$	−0.978148	+	0.207912i	−0.978148	+	0.207912i	−0.309017	+	0.951057i	$0.600000\pi$
$642$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$643$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$643$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$644$		0			0
$645$	0.500000	−	0.866025i	0.500000	−	0.866025i
$646$	0.500000	+	0.866025i	0.500000	+	0.866025i
$647$	1.17557	−	1.61803i	1.17557	−	1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$647$	1.17557	−	1.61803i	1.17557	−	1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$648$	0.207912	−	0.978148i	0.207912	−	0.978148i
$649$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$653$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$654$		0			0
$655$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$656$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$657$		0			0
$658$		0			0
$659$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$659$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$660$	0.913545	+	0.406737i	0.913545	+	0.406737i
$661$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.309017	−	0.951057i	$-0.400000\pi$
$661$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.669131	+	0.743145i	$0.266667\pi$
$662$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$663$	0.743145	−	0.669131i	0.743145	−	0.669131i
$664$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$665$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$666$		0			0
$667$		0			0
$668$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$669$	0.669131	−	0.743145i	0.669131	−	0.743145i
$670$	0.669131	+	0.743145i	0.669131	+	0.743145i
$671$		0			0
$672$	0.207912	+	0.978148i	0.207912	+	0.978148i
$673$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.809017	−	0.587785i	$-0.200000\pi$
$673$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.104528	+	0.994522i	$0.466667\pi$
$674$	−1.17557	−	1.61803i	−1.17557	−	1.61803i
$675$		0			0
$676$		0			0
$677$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$677$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$678$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$679$		0			0
$680$	0.951057	+	0.309017i	0.951057	+	0.309017i
$681$	1.00000			1.00000
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$		0			0
$685$	0.978148	+	0.207912i	0.978148	+	0.207912i
$686$	0.809017	+	0.587785i	0.809017	+	0.587785i
$687$	0.866025	−	0.500000i	0.866025	−	0.500000i
$688$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$689$	0.913545	−	0.406737i	0.913545	−	0.406737i
$690$		0			0
$691$	0.406737	−	0.913545i	0.406737	−	0.913545i	−0.587785	−	0.809017i	$-0.700000\pi$
$691$	0.406737	−	0.913545i	0.406737	−	0.913545i	0.994522	−	0.104528i	$-0.0333333\pi$
$692$	0.978148	−	0.207912i	0.978148	−	0.207912i
$693$		0			0
$694$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$695$		0			0
$696$		0			0
$697$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	0.309017	−	0.951057i	$-0.400000\pi$
$701$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	−0.978148	+	0.207912i	$0.933333\pi$
$702$	0.104528	−	0.994522i	0.104528	−	0.994522i
$703$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$704$	0.406737	−	0.913545i	0.406737	−	0.913545i
$705$		0			0
$706$	0.406737	+	0.913545i	0.406737	+	0.913545i
$707$		0			0
$708$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$709$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$709$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$710$	0.978148	+	0.207912i	0.978148	+	0.207912i
$711$		0			0
$712$		0			0
$713$		0			0
$714$			1.00000i			1.00000i
$715$	0.951057	+	0.309017i	0.951057	+	0.309017i
$716$	0.207912	−	0.978148i	0.207912	−	0.978148i
$717$	0.809017	+	0.587785i	0.809017	+	0.587785i
$718$	0.500000	+	0.866025i	0.500000	+	0.866025i
$719$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$719$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$720$		0			0
$721$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$722$		0			0
$723$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$724$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$725$		0			0
$726$		0			0
$727$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.406737	−	0.913545i	$-0.366667\pi$
$727$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.587785	+	0.809017i	$0.300000\pi$
$728$	0.309017	+	0.951057i	0.309017	+	0.951057i
$729$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$730$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$731$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$732$		0			0
$733$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	0.809017	+	0.587785i	$0.200000\pi$
$733$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	−0.913545	+	0.406737i	$0.866667\pi$
$734$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$735$		0			0
$736$		0			0
$737$	0.913545	−	0.406737i	0.913545	−	0.406737i
$738$		0			0
$739$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$739$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$740$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$741$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$742$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$743$		0			0		1.00000			$0$
$743$		0			0		−1.00000			$\pi$
$744$		0			0
$745$	1.00000			1.00000
$746$	−1.90211	−	0.618034i	−1.90211	−	0.618034i
$747$		0			0
$748$	0.587785	−	0.809017i	0.587785	−	0.809017i
$749$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$750$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$751$	−0.406737	−	0.913545i	−0.406737	−	0.913545i	−0.994522	−	0.104528i	$-0.966667\pi$
$751$	−0.406737	−	0.913545i	−0.406737	−	0.913545i	0.587785	−	0.809017i	$-0.300000\pi$
$752$		0			0
$753$	0.913545	+	0.406737i	0.913545	+	0.406737i
$754$		0			0
$755$	1.98904	+	0.209057i	1.98904	+	0.209057i
$756$	0.669131	+	0.743145i	0.669131	+	0.743145i
$757$	−0.669131	+	0.743145i	−0.669131	+	0.743145i	−0.978148	−	0.207912i	$-0.933333\pi$
$757$	−0.669131	+	0.743145i	−0.669131	+	0.743145i	0.309017	+	0.951057i	$0.400000\pi$
$758$	0.104528	+	0.994522i	0.104528	+	0.994522i
$759$		0			0
$760$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$761$	0.104528	+	0.994522i	0.104528	+	0.994522i	0.913545	+	0.406737i	$0.133333\pi$
$761$	0.104528	+	0.994522i	0.104528	+	0.994522i	−0.809017	+	0.587785i	$0.800000\pi$
$762$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$763$		0			0
$764$	0.994522	+	0.104528i	0.994522	+	0.104528i
$765$		0			0
$766$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$767$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$768$	0.406737	+	0.913545i	0.406737	+	0.913545i
$769$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$769$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$770$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$771$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$772$	0.978148	+	0.207912i	0.978148	+	0.207912i
$773$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$773$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.309017	−	0.951057i	0.309017	−	0.951057i
$778$	0.207912	−	0.978148i	0.207912	−	0.978148i
$779$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$780$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$781$	0.500000	−	0.866025i	0.500000	−	0.866025i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$787$	0.743145	−	0.669131i	0.743145	−	0.669131i	−0.207912	−	0.978148i	$-0.566667\pi$
$787$	0.743145	−	0.669131i	0.743145	−	0.669131i	0.951057	+	0.309017i	$0.100000\pi$
$788$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$789$		0			0
$790$	0.309017	+	0.951057i	0.309017	+	0.951057i
$791$	0.951057	−	0.309017i	0.951057	−	0.309017i
$792$		0			0
$793$		0			0
$794$	0.743145	−	0.669131i	0.743145	−	0.669131i
$795$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$796$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$797$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.809017	−	0.587785i	$-0.200000\pi$
$797$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.104528	+	0.994522i	$0.466667\pi$
$798$	0.809017	−	0.587785i	0.809017	−	0.587785i
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$804$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$805$		0			0
$806$		0			0
$807$			1.00000i			1.00000i
$808$		0			0
$809$	−0.978148	−	0.207912i	−0.978148	−	0.207912i	−0.309017	−	0.951057i	$-0.600000\pi$
$809$	−0.978148	−	0.207912i	−0.978148	−	0.207912i	−0.669131	+	0.743145i	$0.733333\pi$
$810$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$811$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$811$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$812$		0			0
$813$		0			0
$814$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$815$		0			0
$816$	0.207912	+	0.978148i	0.207912	+	0.978148i
$817$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$818$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$819$		0			0
$820$	0.104528	+	0.994522i	0.104528	+	0.994522i
$821$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$821$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$822$	0.309017	+	0.951057i	0.309017	+	0.951057i
$823$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.406737	−	0.913545i	$-0.366667\pi$
$823$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.587785	+	0.809017i	$0.300000\pi$
$824$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$825$		0			0
$826$	0.994522	+	0.104528i	0.994522	+	0.104528i
$827$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	−0.951057	−	0.309017i	$-0.900000\pi$
$827$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	0.743145	−	0.669131i	$-0.233333\pi$
$828$		0			0
$829$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$829$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$830$	0.913545	−	0.406737i	0.913545	−	0.406737i
$831$		0			0
$832$	0.500000	+	0.866025i	0.500000	+	0.866025i
$833$		0			0
$834$		0			0
$835$	0.951057	+	0.309017i	0.951057	+	0.309017i
$836$	−1.00000			−1.00000
$837$		0			0
$838$		0			0
$839$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$839$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$840$	0.207912	−	0.978148i	0.207912	−	0.978148i
$841$	0.809017	+	0.587785i	0.809017	+	0.587785i
$842$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$843$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$844$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$845$		0			0
$846$		0			0
$847$		0			0
$848$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$849$		0			0
$850$		0			0
$851$		0			0
$852$	0.309017	+	0.951057i	0.309017	+	0.951057i
$853$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$853$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$854$		0			0
$855$		0			0
$856$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$857$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	0.809017	+	0.587785i	$0.200000\pi$
$857$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	−0.913545	+	0.406737i	$0.866667\pi$
$858$	0.207912	+	0.978148i	0.207912	+	0.978148i
$859$	0.406737	−	0.913545i	0.406737	−	0.913545i	−0.587785	−	0.809017i	$-0.700000\pi$
$859$	0.406737	−	0.913545i	0.406737	−	0.913545i	0.994522	−	0.104528i	$-0.0333333\pi$
$860$	0.587785	+	0.809017i	0.587785	+	0.809017i
$861$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$862$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$863$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$863$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$864$	0.809017	+	0.587785i	0.809017	+	0.587785i
$865$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.00000			1.00000
$870$		0			0
$871$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$876$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$877$	−0.913545	−	0.406737i	−0.913545	−	0.406737i	−0.104528	−	0.994522i	$-0.533333\pi$
$877$	−0.913545	−	0.406737i	−0.913545	−	0.406737i	−0.809017	+	0.587785i	$0.800000\pi$
$878$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$879$	0.994522	+	0.104528i	0.994522	+	0.104528i
$880$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$881$	0.669131	−	0.743145i	0.669131	−	0.743145i	−0.309017	−	0.951057i	$-0.600000\pi$
$881$	0.669131	−	0.743145i	0.669131	−	0.743145i	0.978148	+	0.207912i	$0.0666667\pi$
$882$		0			0
$883$	1.90211	−	0.618034i	1.90211	−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$883$	1.90211	−	0.618034i	1.90211	−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$884$	0.309017	+	0.951057i	0.309017	+	0.951057i
$885$	0.104528	+	0.994522i	0.104528	+	0.994522i
$886$	0.669131	−	0.743145i	0.669131	−	0.743145i
$887$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	−0.951057	−	0.309017i	$-0.900000\pi$
$887$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	0.207912	+	0.978148i	$0.433333\pi$
$888$	0.104528	−	0.994522i	0.104528	−	0.994522i
$889$	0.978148	−	0.207912i	0.978148	−	0.207912i
$890$		0			0
$891$	0.587785	+	0.809017i	0.587785	+	0.809017i
$892$	0.406737	+	0.913545i	0.406737	+	0.913545i
$893$		0			0
$894$	0.500000	+	0.866025i	0.500000	+	0.866025i
$895$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$896$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$897$		0			0
$898$			2.00000i			2.00000i
$899$		0			0
$900$		0			0
$901$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$902$	0.978148	+	0.207912i	0.978148	+	0.207912i
$903$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$904$	0.866025	−	0.500000i	0.866025	−	0.500000i
$905$	0.500000	−	0.866025i	0.500000	−	0.866025i
$906$	0.813473	+	1.82709i	0.813473	+	1.82709i
$907$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$907$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$908$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$909$		0			0
$910$	0.104528	−	0.994522i	0.104528	−	0.994522i
$911$	0.743145	−	0.669131i	0.743145	−	0.669131i	−0.207912	−	0.978148i	$-0.566667\pi$
$911$	0.743145	−	0.669131i	0.743145	−	0.669131i	0.951057	+	0.309017i	$0.100000\pi$
$912$	0.669131	−	0.743145i	0.669131	−	0.743145i
$913$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$914$		0			0
$915$		0			0
$916$	0.104528	+	0.994522i	0.104528	+	0.994522i
$917$	0.669131	−	0.743145i	0.669131	−	0.743145i
$918$	0.669131	+	0.743145i	0.669131	+	0.743145i
$919$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.587785	−	0.809017i	$-0.300000\pi$
$919$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.406737	+	0.913545i	$0.366667\pi$
$920$		0			0
$921$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$922$		0			0
$923$	0.406737	+	0.913545i	0.406737	+	0.913545i
$924$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0			−	1.00000i	$-0.5\pi$
$929$		0			0				1.00000i	$0.5\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$936$		0			0
$937$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.809017	−	0.587785i	$-0.800000\pi$
$937$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.104528	+	0.994522i	$0.533333\pi$
$938$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$939$	0.406737	−	0.913545i	0.406737	−	0.913545i
$940$		0			0
$941$	0.104528	−	0.994522i	0.104528	−	0.994522i	−0.809017	−	0.587785i	$-0.800000\pi$
$941$	0.104528	−	0.994522i	0.104528	−	0.994522i	0.913545	−	0.406737i	$-0.133333\pi$
$942$		0			0
$943$		0			0
$944$	0.994522	−	0.104528i	0.994522	−	0.104528i
$945$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$946$	0.951057	−	0.309017i	0.951057	−	0.309017i
$947$	−0.994522	+	0.104528i	−0.994522	+	0.104528i	−0.587785	−	0.809017i	$-0.700000\pi$
$947$	−0.994522	+	0.104528i	−0.994522	+	0.104528i	−0.406737	+	0.913545i	$0.633333\pi$
$948$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$949$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$950$		0			0
$951$	0.207912	+	0.978148i	0.207912	+	0.978148i
$952$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$953$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$953$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$954$		0			0
$955$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$956$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$957$		0			0
$958$	0.978148	+	0.207912i	0.978148	+	0.207912i
$959$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$960$		−	1.00000i		−	1.00000i
$961$		0			0
$962$		−	1.00000i		−	1.00000i
$963$		0			0
$964$	0.978148	+	0.207912i	0.978148	+	0.207912i
$965$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$966$		0			0
$967$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$967$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$968$		0			0
$969$	0.809017	−	0.587785i	0.809017	−	0.587785i
$970$		0			0
$971$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	−0.951057	−	0.309017i	$-0.900000\pi$
$971$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	0.743145	−	0.669131i	$-0.233333\pi$
$972$		0			0
$973$		0			0
$974$	0.669131	−	0.743145i	0.669131	−	0.743145i
$975$		0			0
$976$		0			0
$977$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$977$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	0.978148	−	0.207912i	0.978148	−	0.207912i
$983$	0.406737	−	0.913545i	0.406737	−	0.913545i	−0.587785	−	0.809017i	$-0.700000\pi$
$983$	0.406737	−	0.913545i	0.406737	−	0.913545i	0.994522	−	0.104528i	$-0.0333333\pi$
$984$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$985$	0.913545	−	0.406737i	0.913545	−	0.406737i
$986$		0			0
$987$		0			0
$988$	0.587785	−	0.809017i	0.587785	−	0.809017i
$989$		0			0
$990$		0			0
$991$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$991$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$992$		0			0
$993$	1.00000			1.00000
$994$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$995$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$996$	0.809017	+	0.587785i	0.809017	+	0.587785i
$997$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$997$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$998$	0.500000	−	0.866025i	0.500000	−	0.866025i
$999$	−0.406737	−	0.913545i	−0.406737	−	0.913545i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3844.1.n.f.1807.2		16
4.3	odd	2	inner	3844.1.n.f.1807.1		16
31.2	even	5		3844.1.i.d.439.2		4
31.3	odd	30		3844.1.n.e.3615.2		16
31.4	even	5	inner	3844.1.n.f.547.1		16
31.5	even	3		3844.1.l.c.3511.2		8
31.6	odd	6		3844.1.n.e.3331.2		16
31.7	even	15	inner	3844.1.n.f.3727.1		16
31.8	even	5	inner	3844.1.n.f.235.1		16
31.9	even	15		3844.1.l.c.3271.1		8
31.10	even	15		3844.1.b.c.1923.2		2
31.11	odd	30		3844.1.l.d.531.1		8
31.12	odd	30		124.1.i.a.87.2	yes	4
31.13	odd	30		3844.1.l.d.1335.2		8
31.14	even	15	inner	3844.1.n.f.1299.1		16
31.15	odd	10		3844.1.n.e.3699.2		16
31.16	even	5	inner	3844.1.n.f.3699.2		16
31.17	odd	30		3844.1.n.e.1299.1		16
31.18	even	15		3844.1.l.c.1335.2		8
31.19	even	15		3844.1.i.d.2443.2		4
31.20	even	15		3844.1.l.c.531.1		8
31.21	odd	30		3844.1.b.d.1923.2		2
31.22	odd	30		3844.1.l.d.3271.1		8
31.23	odd	10		3844.1.n.e.235.1		16
31.24	odd	30		3844.1.n.e.3727.1		16
31.25	even	3	inner	3844.1.n.f.3331.2		16
31.26	odd	6		3844.1.l.d.3511.2		8
31.27	odd	10		3844.1.n.e.547.1		16
31.28	even	15	inner	3844.1.n.f.3615.2		16
31.29	odd	10		124.1.i.a.67.2	yes	4
31.30	odd	2		3844.1.n.e.1807.2		16
93.29	even	10		1116.1.x.a.811.1		4
93.74	even	30		1116.1.x.a.955.1		4
124.3	even	30		3844.1.n.e.3615.1		16
124.7	odd	30	inner	3844.1.n.f.3727.2		16
124.11	even	30		3844.1.l.d.531.2		8
124.15	even	10		3844.1.n.e.3699.1		16
124.19	odd	30		3844.1.i.d.2443.1		4
124.23	even	10		3844.1.n.e.235.2		16
124.27	even	10		3844.1.n.e.547.2		16
124.35	odd	10	inner	3844.1.n.f.547.2		16
124.39	odd	10	inner	3844.1.n.f.235.2		16
124.43	even	30		124.1.i.a.87.1	yes	4
124.47	odd	10	inner	3844.1.n.f.3699.1		16
124.51	odd	30		3844.1.l.c.531.2		8
124.55	even	30		3844.1.n.e.3727.2		16
124.59	odd	30	inner	3844.1.n.f.3615.1		16
124.67	odd	6		3844.1.l.c.3511.1		8
124.71	odd	30		3844.1.l.c.3271.2		8
124.75	even	30		3844.1.l.d.1335.1		8
124.79	even	30		3844.1.n.e.1299.2		16
124.83	even	30		3844.1.b.d.1923.1		2
124.87	odd	6	inner	3844.1.n.f.3331.1		16
124.91	even	10		124.1.i.a.67.1	✓	4
124.95	odd	10		3844.1.i.d.439.1		4
124.99	even	6		3844.1.n.e.3331.1		16
124.103	odd	30		3844.1.b.c.1923.1		2
124.107	odd	30	inner	3844.1.n.f.1299.2		16
124.111	odd	30		3844.1.l.c.1335.1		8
124.115	even	30		3844.1.l.d.3271.2		8
124.119	even	6		3844.1.l.d.3511.1		8
124.123	even	2		3844.1.n.e.1807.1		16
155.12	even	60		3100.1.t.a.1699.2		4
155.29	odd	10		3100.1.z.a.2051.1		4
155.43	even	60		3100.1.t.b.1699.2		4
155.74	odd	30		3100.1.z.a.1451.1		4
155.122	even	20		3100.1.t.a.2299.1		4
155.153	even	20		3100.1.t.b.2299.1		4
248.29	odd	10		1984.1.s.a.191.1		4
248.43	even	30		1984.1.s.a.831.1		4
248.91	even	10		1984.1.s.a.191.2		4
248.229	odd	30		1984.1.s.a.831.2		4
372.167	odd	30		1116.1.x.a.955.2		4
372.215	odd	10		1116.1.x.a.811.2		4
620.43	odd	60		3100.1.t.a.1699.1		4
620.167	odd	60		3100.1.t.b.1699.1		4
620.339	even	10		3100.1.z.a.2051.2		4
620.463	odd	20		3100.1.t.a.2299.2		4
620.539	even	30		3100.1.z.a.1451.2		4
620.587	odd	20		3100.1.t.b.2299.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.1.i.a.67.1	✓	4	124.91	even	10
124.1.i.a.67.2	yes	4	31.29	odd	10
124.1.i.a.87.1	yes	4	124.43	even	30
124.1.i.a.87.2	yes	4	31.12	odd	30
1116.1.x.a.811.1		4	93.29	even	10
1116.1.x.a.811.2		4	372.215	odd	10
1116.1.x.a.955.1		4	93.74	even	30
1116.1.x.a.955.2		4	372.167	odd	30
1984.1.s.a.191.1		4	248.29	odd	10
1984.1.s.a.191.2		4	248.91	even	10
1984.1.s.a.831.1		4	248.43	even	30
1984.1.s.a.831.2		4	248.229	odd	30
3100.1.t.a.1699.1		4	620.43	odd	60
3100.1.t.a.1699.2		4	155.12	even	60
3100.1.t.a.2299.1		4	155.122	even	20
3100.1.t.a.2299.2		4	620.463	odd	20
3100.1.t.b.1699.1		4	620.167	odd	60
3100.1.t.b.1699.2		4	155.43	even	60
3100.1.t.b.2299.1		4	155.153	even	20
3100.1.t.b.2299.2		4	620.587	odd	20
3100.1.z.a.1451.1		4	155.74	odd	30
3100.1.z.a.1451.2		4	620.539	even	30
3100.1.z.a.2051.1		4	155.29	odd	10
3100.1.z.a.2051.2		4	620.339	even	10
3844.1.b.c.1923.1		2	124.103	odd	30
3844.1.b.c.1923.2		2	31.10	even	15
3844.1.b.d.1923.1		2	124.83	even	30
3844.1.b.d.1923.2		2	31.21	odd	30
3844.1.i.d.439.1		4	124.95	odd	10
3844.1.i.d.439.2		4	31.2	even	5
3844.1.i.d.2443.1		4	124.19	odd	30
3844.1.i.d.2443.2		4	31.19	even	15
3844.1.l.c.531.1		8	31.20	even	15
3844.1.l.c.531.2		8	124.51	odd	30
3844.1.l.c.1335.1		8	124.111	odd	30
3844.1.l.c.1335.2		8	31.18	even	15
3844.1.l.c.3271.1		8	31.9	even	15
3844.1.l.c.3271.2		8	124.71	odd	30
3844.1.l.c.3511.1		8	124.67	odd	6
3844.1.l.c.3511.2		8	31.5	even	3
3844.1.l.d.531.1		8	31.11	odd	30
3844.1.l.d.531.2		8	124.11	even	30
3844.1.l.d.1335.1		8	124.75	even	30
3844.1.l.d.1335.2		8	31.13	odd	30
3844.1.l.d.3271.1		8	31.22	odd	30
3844.1.l.d.3271.2		8	124.115	even	30
3844.1.l.d.3511.1		8	124.119	even	6
3844.1.l.d.3511.2		8	31.26	odd	6
3844.1.n.e.235.1		16	31.23	odd	10
3844.1.n.e.235.2		16	124.23	even	10
3844.1.n.e.547.1		16	31.27	odd	10
3844.1.n.e.547.2		16	124.27	even	10
3844.1.n.e.1299.1		16	31.17	odd	30
3844.1.n.e.1299.2		16	124.79	even	30
3844.1.n.e.1807.1		16	124.123	even	2
3844.1.n.e.1807.2		16	31.30	odd	2
3844.1.n.e.3331.1		16	124.99	even	6
3844.1.n.e.3331.2		16	31.6	odd	6
3844.1.n.e.3615.1		16	124.3	even	30
3844.1.n.e.3615.2		16	31.3	odd	30
3844.1.n.e.3699.1		16	124.15	even	10
3844.1.n.e.3699.2		16	31.15	odd	10
3844.1.n.e.3727.1		16	31.24	odd	30
3844.1.n.e.3727.2		16	124.55	even	30
3844.1.n.f.235.1		16	31.8	even	5	inner
3844.1.n.f.235.2		16	124.39	odd	10	inner
3844.1.n.f.547.1		16	31.4	even	5	inner
3844.1.n.f.547.2		16	124.35	odd	10	inner
3844.1.n.f.1299.1		16	31.14	even	15	inner
3844.1.n.f.1299.2		16	124.107	odd	30	inner
3844.1.n.f.1807.1		16	4.3	odd	2	inner
3844.1.n.f.1807.2		16	1.1	even	1	trivial
3844.1.n.f.3331.1		16	124.87	odd	6	inner
3844.1.n.f.3331.2		16	31.25	even	3	inner
3844.1.n.f.3615.1		16	124.59	odd	30	inner
3844.1.n.f.3615.2		16	31.28	even	15	inner
3844.1.n.f.3699.1		16	124.47	odd	10	inner
3844.1.n.f.3699.2		16	31.16	even	5	inner
3844.1.n.f.3727.1		16	31.7	even	15	inner
3844.1.n.f.3727.2		16	124.7	odd	30	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:	\( N \)	\(=\)	\( 3844 = 2^{2} \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3844.n (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.207912 - 0.978148i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.406737 + 0.913545i) q^{7} +(0.587785 + 0.809017i) q^{8} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.207912 - 0.978148i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(0.406737 + 0.913545i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-0.207912 - 0.978148i) q^{10} +(-0.994522 - 0.104528i) q^{11} +(0.743145 - 0.669131i) q^{12} +(0.669131 - 0.743145i) q^{13} +(0.104528 + 0.994522i) q^{14} +(-0.951057 + 0.309017i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.104528 + 0.994522i) q^{17} +(0.743145 - 0.669131i) q^{19} +(0.104528 - 0.994522i) q^{20} +(0.978148 - 0.207912i) q^{21} +(-0.913545 - 0.406737i) q^{22} +(0.913545 - 0.406737i) q^{24} +(0.866025 - 0.500000i) q^{26} +(0.587785 - 0.809017i) q^{27} +(-0.207912 + 0.978148i) q^{28} -1.00000 q^{30} +1.00000i q^{32} +(-0.309017 + 0.951057i) q^{33} +(-0.207912 + 0.978148i) q^{34} +(0.587785 - 0.809017i) q^{35} +(0.500000 - 0.866025i) q^{37} +(0.913545 - 0.406737i) q^{38} +(-0.587785 - 0.809017i) q^{39} +(0.406737 - 0.913545i) q^{40} +(-0.978148 + 0.207912i) q^{41} +(0.994522 + 0.104528i) q^{42} +(-0.743145 + 0.669131i) q^{43} +(-0.743145 - 0.669131i) q^{44} +(0.994522 - 0.104528i) q^{48} +(0.994522 + 0.104528i) q^{51} +(0.978148 - 0.207912i) q^{52} +(0.913545 + 0.406737i) q^{53} +(0.809017 - 0.587785i) q^{54} +(0.406737 + 0.913545i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-0.500000 - 0.866025i) q^{57} +(0.207912 - 0.978148i) q^{59} +(-0.951057 - 0.309017i) q^{60} +(-0.309017 + 0.951057i) q^{64} +(-0.978148 - 0.207912i) q^{65} +(-0.587785 + 0.809017i) q^{66} +(-0.866025 + 0.500000i) q^{67} +(-0.500000 + 0.866025i) q^{68} +(0.809017 - 0.587785i) q^{70} +(-0.406737 + 0.913545i) q^{71} +(0.104528 - 0.994522i) q^{73} +(0.743145 - 0.669131i) q^{74} +(0.994522 - 0.104528i) q^{76} +(-0.309017 - 0.951057i) q^{77} +(-0.309017 - 0.951057i) q^{78} +(-0.994522 + 0.104528i) q^{79} +(0.669131 - 0.743145i) q^{80} +(-0.669131 - 0.743145i) q^{81} +(-0.994522 - 0.104528i) q^{82} +(0.207912 + 0.978148i) q^{83} +(0.913545 + 0.406737i) q^{84} +(0.809017 - 0.587785i) q^{85} +(-0.913545 + 0.406737i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(0.951057 + 0.309017i) q^{91} +(-0.951057 - 0.309017i) q^{95} +(0.978148 + 0.207912i) q^{96} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 8 q^{5} + 8 q^{6}+O(q^{10}) \) 16 * q + 4 * q^4 - 8 * q^5 + 8 * q^6	\( 16 q + 4 q^{4} - 8 q^{5} + 8 q^{6} + 2 q^{13} - 2 q^{14} - 4 q^{16} - 2 q^{17} - 2 q^{20} - 2 q^{21} - 2 q^{22} + 2 q^{24} - 16 q^{30} + 4 q^{33} + 8 q^{37} + 2 q^{38} + 2 q^{41} - 2 q^{52} + 2 q^{53} + 4 q^{54} - 8 q^{56} - 8 q^{57} + 4 q^{64} + 2 q^{65} - 8 q^{68} + 4 q^{70} - 2 q^{73} + 4 q^{77} + 4 q^{78} + 2 q^{80} - 2 q^{81} + 2 q^{84} + 4 q^{85} - 2 q^{86} - 8 q^{88} - 2 q^{96}+O(q^{100}) \) 16 * q + 4 * q^4 - 8 * q^5 + 8 * q^6 + 2 * q^13 - 2 * q^14 - 4 * q^16 - 2 * q^17 - 2 * q^20 - 2 * q^21 - 2 * q^22 + 2 * q^24 - 16 * q^30 + 4 * q^33 + 8 * q^37 + 2 * q^38 + 2 * q^41 - 2 * q^52 + 2 * q^53 + 4 * q^54 - 8 * q^56 - 8 * q^57 + 4 * q^64 + 2 * q^65 - 8 * q^68 + 4 * q^70 - 2 * q^73 + 4 * q^77 + 4 * q^78 + 2 * q^80 - 2 * q^81 + 2 * q^84 + 4 * q^85 - 2 * q^86 - 8 * q^88 - 2 * q^96

Introduction

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