LMFDB - Embedded newform 3000.1.z.a.1349.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3000,1,Mod(149,3000)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3000.149"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3000, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 5, 1])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 3000 = 2^{3} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3000.z (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,2,0,-2,0,0,2,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.49719503790$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 600)
Projective image:	$D_{5}$
Projective field:	Galois closure of 5.1.225000000.2

Embedding invariants

Embedding label			1349.2
Root			$0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	3000.1349
Dual form			3000.1.z.a.149.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.951057 - 0.309017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.809017 - 0.587785i) q^{6} -1.61803i q^{7} +(0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-0.190983 - 0.587785i) q^{11} +(-0.951057 - 0.309017i) q^{12} +(-0.500000 - 1.53884i) q^{14} +(0.309017 - 0.951057i) q^{16} +1.00000i q^{18} +(-1.30902 + 0.951057i) q^{21} +(-0.363271 - 0.500000i) q^{22} -1.00000 q^{24} +(0.951057 - 0.309017i) q^{27} +(-0.951057 - 1.30902i) q^{28} +(-1.61803 + 1.17557i) q^{29} +(1.30902 + 0.951057i) q^{31} -1.00000i q^{32} +(-0.363271 + 0.500000i) q^{33} +(0.309017 + 0.951057i) q^{36} +(-0.951057 + 1.30902i) q^{42} +(-0.500000 - 0.363271i) q^{44} +(-0.951057 + 0.309017i) q^{48} -1.61803 q^{49} +(-0.363271 - 0.500000i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-1.30902 - 0.951057i) q^{56} +(-1.17557 + 1.61803i) q^{58} +(0.190983 - 0.587785i) q^{59} +(1.53884 + 0.500000i) q^{62} +(1.53884 + 0.500000i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-0.190983 + 0.587785i) q^{66} +(0.587785 + 0.809017i) q^{72} +(1.90211 - 0.618034i) q^{73} +(-0.951057 + 0.309017i) q^{77} +(0.500000 - 0.363271i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-0.951057 + 1.30902i) q^{83} +(-0.500000 + 1.53884i) q^{84} +(1.90211 + 0.618034i) q^{87} +(-0.587785 - 0.190983i) q^{88} -1.61803i q^{93} +(-0.809017 + 0.587785i) q^{96} +(0.951057 + 1.30902i) q^{97} +(-1.53884 + 0.500000i) q^{98} +0.618034 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 2 q^{6} + 2 q^{9} - 6 q^{11} - 4 q^{14} - 2 q^{16} - 6 q^{21} - 8 q^{24} - 4 q^{29} + 6 q^{31} - 2 q^{36} - 4 q^{44} - 4 q^{49} + 2 q^{54} - 6 q^{56} + 6 q^{59} + 2 q^{64} - 6 q^{66} + 4 q^{79}+ \cdots - 4 q^{99}+O(q^{100}) $ 8 * q + 2 * q^4 - 2 * q^6 + 2 * q^9 - 6 * q^11 - 4 * q^14 - 2 * q^16 - 6 * q^21 - 8 * q^24 - 4 * q^29 + 6 * q^31 - 2 * q^36 - 4 * q^44 - 4 * q^49 + 2 * q^54 - 6 * q^56 + 6 * q^59 + 2 * q^64 - 6 * q^66 + 4 * q^79 - 2 * q^81 - 4 * q^84 - 2 * q^96 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3000\mathbb{Z}\right)^\times$.

$n$	$751$	$1001$	$1501$	$2377$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{9}{10}\right)$

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
$3$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$3$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$4$	0.809017	−	0.587785i	0.809017	−	0.587785i
$5$		0			0
$5$		0			0
$6$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$7$		−	1.61803i		−	1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$7$		−	1.61803i		−	1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$8$	0.587785	−	0.809017i	0.587785	−	0.809017i
$9$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$10$		0			0
$11$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$11$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$12$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$13$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$13$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$14$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$15$		0			0
$16$	0.309017	−	0.951057i	0.309017	−	0.951057i
$17$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$17$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$18$			1.00000i			1.00000i
$19$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$19$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$20$		0			0
$21$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$22$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$23$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$23$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$24$	−1.00000			−1.00000
$25$		0			0
$26$		0			0
$27$	0.951057	−	0.309017i	0.951057	−	0.309017i
$28$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$29$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$29$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$30$		0			0
$31$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$31$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$32$		−	1.00000i		−	1.00000i
$33$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$34$		0			0
$35$		0			0
$36$	0.309017	+	0.951057i	0.309017	+	0.951057i
$37$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$37$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$41$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$42$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$45$		0			0
$46$		0			0
$47$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$47$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$48$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$49$	−1.61803			−1.61803
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$53$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$54$	0.809017	−	0.587785i	0.809017	−	0.587785i
$55$		0			0
$56$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$57$		0			0
$58$	−1.17557	+	1.61803i	−1.17557	+	1.61803i
$59$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$59$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$60$		0			0
$61$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$61$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$62$	1.53884	+	0.500000i	1.53884	+	0.500000i
$63$	1.53884	+	0.500000i	1.53884	+	0.500000i
$64$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$65$		0			0
$66$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$67$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$67$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$71$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$72$	0.587785	+	0.809017i	0.587785	+	0.809017i
$73$	1.90211	−	0.618034i	1.90211	−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$73$	1.90211	−	0.618034i	1.90211	−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$78$		0			0
$79$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$79$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$82$		0			0
$83$	−0.951057	+	1.30902i	−0.951057	+	1.30902i			1.00000i	$0.5\pi$
$83$	−0.951057	+	1.30902i	−0.951057	+	1.30902i	−0.951057	+	0.309017i	$0.900000\pi$
$84$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$85$		0			0
$86$		0			0
$87$	1.90211	+	0.618034i	1.90211	+	0.618034i
$88$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$89$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$89$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		−	1.61803i		−	1.61803i
$94$		0			0
$95$		0			0
$96$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$97$	0.951057	+	1.30902i	0.951057	+	1.30902i	0.951057	+	0.309017i	$0.100000\pi$
$97$	0.951057	+	1.30902i	0.951057	+	1.30902i			1.00000i	$0.5\pi$
$98$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$99$	0.618034			0.618034
$100$		0			0
$101$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$101$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$102$		0			0
$103$	−0.951057	−	1.30902i	−0.951057	−	1.30902i	−0.951057	−	0.309017i	$-0.900000\pi$
$103$	−0.951057	−	1.30902i	−0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$104$		0			0
$105$		0			0
$106$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$107$		−	0.618034i		−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$107$		−	0.618034i		−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$108$	0.587785	−	0.809017i	0.587785	−	0.809017i
$109$		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
$112$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$113$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$113$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$114$		0			0
$115$		0			0
$116$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$117$		0			0
$118$		−	0.618034i		−	0.618034i
$119$		0			0
$120$		0			0
$121$	0.500000	−	0.363271i	0.500000	−	0.363271i
$122$		0			0
$123$		0			0
$124$	1.61803			1.61803
$125$		0			0
$126$	1.61803			1.61803
$127$	−0.587785	+	0.190983i	−0.587785	+	0.190983i	−0.587785	−	0.809017i	$-0.700000\pi$
$127$	−0.587785	+	0.190983i	−0.587785	+	0.190983i			1.00000i	$0.5\pi$
$128$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$129$		0			0
$130$		0			0
$131$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$131$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$132$			0.618034i			0.618034i
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$137$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$138$		0			0
$139$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$139$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.809017	+	0.587785i	0.809017	+	0.587785i
$145$		0			0
$146$	1.61803	−	1.17557i	1.61803	−	1.17557i
$147$	0.951057	+	1.30902i	0.951057	+	1.30902i
$148$		0			0
$149$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$149$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$150$		0			0
$151$	−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
$154$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$155$		0			0
$156$		0			0
$157$		0			0			−	1.00000i	$-0.5\pi$
$157$		0			0				1.00000i	$0.5\pi$
$158$	0.363271	−	0.500000i	0.363271	−	0.500000i
$159$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$160$		0			0
$161$		0			0
$162$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$163$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$163$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$164$		0			0
$165$		0			0
$166$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$167$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$167$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$168$			1.61803i			1.61803i
$169$	0.809017	+	0.587785i	0.809017	+	0.587785i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$173$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$174$	2.00000			2.00000
$175$		0			0
$176$	−0.618034			−0.618034
$177$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$178$		0			0
$179$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$179$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$180$		0			0
$181$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$181$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$187$		0			0
$188$		0			0
$189$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$190$		0			0
$191$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$191$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$192$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$193$			1.61803i			1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$193$			1.61803i			1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$194$	1.30902	+	0.951057i	1.30902	+	0.951057i
$195$		0			0
$196$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$197$	−0.951057	−	1.30902i	−0.951057	−	1.30902i	−0.951057	−	0.309017i	$-0.900000\pi$
$197$	−0.951057	−	1.30902i	−0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$198$	0.587785	−	0.190983i	0.587785	−	0.190983i
$199$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$199$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$200$		0			0
$201$		0			0
$202$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$203$	1.90211	+	2.61803i	1.90211	+	2.61803i
$204$		0			0
$205$		0			0
$206$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$211$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$212$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$213$		0			0
$214$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$215$		0			0
$216$	0.309017	−	0.951057i	0.309017	−	0.951057i
$217$	1.53884	−	2.11803i	1.53884	−	2.11803i
$218$		0			0
$219$	−1.61803	−	1.17557i	−1.61803	−	1.17557i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.587785	−	0.190983i	0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$223$	0.587785	−	0.190983i	0.587785	−	0.190983i	0.587785	+	0.809017i	$0.300000\pi$
$224$	−1.61803			−1.61803
$225$		0			0
$226$		0			0
$227$	0.587785	−	0.190983i	0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$227$	0.587785	−	0.190983i	0.587785	−	0.190983i	0.587785	+	0.809017i	$0.300000\pi$
$228$		0			0
$229$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$229$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$230$		0			0
$231$	0.809017	+	0.587785i	0.809017	+	0.587785i
$232$			2.00000i			2.00000i
$233$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$233$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$234$		0			0
$235$		0			0
$236$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$237$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$238$		0			0
$239$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$239$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$240$		0			0
$241$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$241$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$242$	0.363271	−	0.500000i	0.363271	−	0.500000i
$243$			1.00000i			1.00000i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$	1.53884	−	0.500000i	1.53884	−	0.500000i
$249$	1.61803			1.61803
$250$		0			0
$251$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$251$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$252$	1.53884	−	0.500000i	1.53884	−	0.500000i
$253$		0			0
$254$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$257$		0			0			−	1.00000i	$-0.5\pi$
$257$		0			0				1.00000i	$0.5\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$262$	1.90211	+	0.618034i	1.90211	+	0.618034i
$263$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$263$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$264$	0.190983	+	0.587785i	0.190983	+	0.587785i
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$269$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$270$		0			0
$271$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$271$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$277$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$278$		0			0
$279$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$280$		0			0
$281$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$281$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$282$		0			0
$283$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$283$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.951057	+	0.309017i	0.951057	+	0.309017i
$289$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$290$		0			0
$291$	0.500000	−	1.53884i	0.500000	−	1.53884i
$292$	1.17557	−	1.61803i	1.17557	−	1.61803i
$293$			0.618034i			0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$293$			0.618034i			0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$294$	1.30902	+	0.951057i	1.30902	+	0.951057i
$295$		0			0
$296$		0			0
$297$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$298$	0.587785	−	0.190983i	0.587785	−	0.190983i
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$303$	0.363271	+	0.500000i	0.363271	+	0.500000i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$309$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$310$		0			0
$311$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$311$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$312$		0			0
$313$	−0.587785	−	0.190983i	−0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$313$	−0.587785	−	0.190983i	−0.587785	−	0.190983i	−0.587785	+	0.809017i	$0.700000\pi$
$314$		0			0
$315$		0			0
$316$	0.190983	−	0.587785i	0.190983	−	0.587785i
$317$	−0.363271	+	0.500000i	−0.363271	+	0.500000i	−0.951057	−	0.309017i	$-0.900000\pi$
$317$	−0.363271	+	0.500000i	−0.363271	+	0.500000i	0.587785	+	0.809017i	$0.300000\pi$
$318$			0.618034i			0.618034i
$319$	1.00000	+	0.726543i	1.00000	+	0.726543i
$320$		0			0
$321$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$322$		0			0
$323$		0			0
$324$	−1.00000			−1.00000
$325$		0			0
$326$		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	$0.200000\pi$
$332$			1.61803i			1.61803i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	0.500000	+	1.53884i	0.500000	+	1.53884i
$337$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$337$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$338$	0.951057	+	0.309017i	0.951057	+	0.309017i
$339$		0			0
$340$		0			0
$341$	0.309017	−	0.951057i	0.309017	−	0.951057i
$342$		0			0
$343$			1.00000i			1.00000i
$344$		0			0
$345$		0			0
$346$	1.30902	−	0.951057i	1.30902	−	0.951057i
$347$	0.363271	+	0.500000i	0.363271	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$347$	0.363271	+	0.500000i	0.363271	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$348$	1.90211	−	0.618034i	1.90211	−	0.618034i
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$		0			0
$351$		0			0
$352$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$353$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$353$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$354$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.951057	−	1.30902i	0.951057	−	1.30902i
$359$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$359$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$360$		0			0
$361$	0.309017	+	0.951057i	0.309017	+	0.951057i
$362$		0			0
$363$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−0.951057	+	1.30902i	−0.951057	+	1.30902i			1.00000i	$0.5\pi$
$367$	−0.951057	+	1.30902i	−0.951057	+	1.30902i	−0.951057	+	0.309017i	$0.900000\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$372$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$373$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$373$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$379$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$379$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$380$		0			0
$381$	0.500000	+	0.363271i	0.500000	+	0.363271i
$382$		0			0
$383$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$383$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$384$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$385$		0			0
$386$	0.500000	+	1.53884i	0.500000	+	1.53884i
$387$		0			0
$388$	1.53884	+	0.500000i	1.53884	+	0.500000i
$389$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$389$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$390$		0			0
$391$		0			0
$392$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$393$		−	2.00000i		−	2.00000i
$394$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$395$		0			0
$396$	0.500000	−	0.363271i	0.500000	−	0.363271i
$397$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$397$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$398$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$399$		0			0
$400$		0			0
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$		0			0
$403$		0			0
$404$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$405$		0			0
$406$	2.61803	+	1.90211i	2.61803	+	1.90211i
$407$		0			0
$408$		0			0
$409$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$409$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$410$		0			0
$411$		0			0
$412$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$413$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$419$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$420$		0			0
$421$		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
$424$	−0.618034			−0.618034
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$429$		0			0
$430$		0			0
$431$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$431$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$432$		−	1.00000i		−	1.00000i
$433$	−0.363271	+	0.500000i	−0.363271	+	0.500000i	−0.951057	−	0.309017i	$-0.900000\pi$
$433$	−0.363271	+	0.500000i	−0.363271	+	0.500000i	0.587785	+	0.809017i	$0.300000\pi$
$434$	0.809017	−	2.48990i	0.809017	−	2.48990i
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−1.90211	−	0.618034i	−1.90211	−	0.618034i
$439$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$439$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$440$		0			0
$441$	0.500000	−	1.53884i	0.500000	−	1.53884i
$442$		0			0
$443$		−	1.61803i		−	1.61803i	−0.587785	−	0.809017i	$-0.700000\pi$
$443$		−	1.61803i		−	1.61803i	0.587785	−	0.809017i	$-0.300000\pi$
$444$		0			0
$445$		0			0
$446$	0.500000	−	0.363271i	0.500000	−	0.363271i
$447$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$448$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	0.951057	+	1.30902i	0.951057	+	1.30902i
$454$	0.500000	−	0.363271i	0.500000	−	0.363271i
$455$		0			0
$456$		0			0
$457$			0.618034i			0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$457$			0.618034i			0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$461$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$462$	0.951057	+	0.309017i	0.951057	+	0.309017i
$463$	−1.90211	−	0.618034i	−1.90211	−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$463$	−1.90211	−	0.618034i	−1.90211	−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$464$	0.618034	+	1.90211i	0.618034	+	1.90211i
$465$		0			0
$466$		0			0
$467$	−0.363271	+	0.500000i	−0.363271	+	0.500000i	−0.951057	−	0.309017i	$-0.900000\pi$
$467$	−0.363271	+	0.500000i	−0.363271	+	0.500000i	0.587785	+	0.809017i	$0.300000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$473$		0			0
$474$	−0.618034			−0.618034
$475$		0			0
$476$		0			0
$477$	0.587785	−	0.190983i	0.587785	−	0.190983i
$478$		0			0
$479$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$479$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$480$		0			0
$481$		0			0
$482$			1.61803i			1.61803i
$483$		0			0
$484$	0.190983	−	0.587785i	0.190983	−	0.587785i
$485$		0			0
$486$	0.309017	+	0.951057i	0.309017	+	0.951057i
$487$	0.587785	+	0.190983i	0.587785	+	0.190983i	0.587785	−	0.809017i	$-0.300000\pi$
$487$	0.587785	+	0.190983i	0.587785	+	0.190983i			1.00000i	$0.5\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$491$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	1.30902	−	0.951057i	1.30902	−	0.951057i
$497$		0			0
$498$	1.53884	−	0.500000i	1.53884	−	0.500000i
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$		0			0
$501$		0			0
$502$	1.53884	−	0.500000i	1.53884	−	0.500000i
$503$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$503$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$504$	1.30902	−	0.951057i	1.30902	−	0.951057i
$505$		0			0
$506$		0			0
$507$		−	1.00000i		−	1.00000i
$508$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$509$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$509$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$510$		0			0
$511$	−1.00000	−	3.07768i	−1.00000	−	3.07768i
$512$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$520$		0			0
$521$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$521$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$522$	−1.17557	−	1.61803i	−1.17557	−	1.61803i
$523$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$523$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$524$	2.00000			2.00000
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.363271	+	0.500000i	0.363271	+	0.500000i
$529$	0.809017	−	0.587785i	0.809017	−	0.587785i
$530$		0			0
$531$	0.500000	+	0.363271i	0.500000	+	0.363271i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$538$	1.53884	+	0.500000i	1.53884	+	0.500000i
$539$	0.309017	+	0.951057i	0.309017	+	0.951057i
$540$		0			0
$541$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$541$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$542$	0.951057	−	1.30902i	0.951057	−	1.30902i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$547$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			1.61803i			1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$557$			1.61803i			1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$558$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$563$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$568$		0			0
$569$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$569$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$570$		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			0
$574$		0			0
$575$		0			0
$576$	1.00000			1.00000
$577$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$577$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$578$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$579$	1.30902	−	0.951057i	1.30902	−	0.951057i
$580$		0			0
$581$	2.11803	+	1.53884i	2.11803	+	1.53884i
$582$		−	1.61803i		−	1.61803i
$583$	−0.224514	+	0.309017i	−0.224514	+	0.309017i
$584$	0.618034	−	1.90211i	0.618034	−	1.90211i
$585$		0			0
$586$	0.190983	+	0.587785i	0.190983	+	0.587785i
$587$	−0.587785	−	0.190983i	−0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$587$	−0.587785	−	0.190983i	−0.587785	−	0.190983i	−0.587785	+	0.809017i	$0.700000\pi$
$588$	1.53884	+	0.500000i	1.53884	+	0.500000i
$589$		0			0
$590$		0			0
$591$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$592$		0			0
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$595$		0			0
$596$	0.500000	−	0.363271i	0.500000	−	0.363271i
$597$	0.363271	+	0.500000i	0.363271	+	0.500000i
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$		0			0
$601$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$601$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$602$		0			0
$603$		0			0
$604$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$605$		0			0
$606$	0.500000	+	0.363271i	0.500000	+	0.363271i
$607$			0.618034i			0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$607$			0.618034i			0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$608$		0			0
$609$	1.00000	−	3.07768i	1.00000	−	3.07768i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$613$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$614$		0			0
$615$		0			0
$616$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$617$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$617$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$618$			1.61803i			1.61803i
$619$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$619$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$		0			0
$626$	−0.618034			−0.618034
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$631$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$632$		−	0.618034i		−	0.618034i
$633$		0			0
$634$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$635$		0			0
$636$	0.190983	+	0.587785i	0.190983	+	0.587785i
$637$		0			0
$638$	1.17557	+	0.381966i	1.17557	+	0.381966i
$639$		0			0
$640$		0			0
$641$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$641$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$642$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$643$		0			0			−	1.00000i	$-0.5\pi$
$643$		0			0				1.00000i	$0.5\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$647$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$648$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$649$	−0.381966			−0.381966
$650$		0			0
$651$	−2.61803			−2.61803
$652$		0			0
$653$	0.951057	+	1.30902i	0.951057	+	1.30902i	0.951057	+	0.309017i	$0.100000\pi$
$653$	0.951057	+	1.30902i	0.951057	+	1.30902i			1.00000i	$0.5\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			2.00000i			2.00000i
$658$		0			0
$659$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$659$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$660$		0			0
$661$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$661$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$662$		0			0
$663$		0			0
$664$	0.500000	+	1.53884i	0.500000	+	1.53884i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$670$		0			0
$671$		0			0
$672$	0.951057	+	1.30902i	0.951057	+	1.30902i
$673$	−1.53884	+	0.500000i	−1.53884	+	0.500000i	−0.951057	−	0.309017i	$-0.900000\pi$
$673$	−1.53884	+	0.500000i	−1.53884	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$674$	−1.61803			−1.61803
$675$		0			0
$676$	1.00000			1.00000
$677$	−1.53884	+	0.500000i	−1.53884	+	0.500000i	−0.951057	−	0.309017i	$-0.900000\pi$
$677$	−1.53884	+	0.500000i	−1.53884	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$678$		0			0
$679$	2.11803	−	1.53884i	2.11803	−	1.53884i
$680$		0			0
$681$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$682$		−	1.00000i		−	1.00000i
$683$	0.363271	−	0.500000i	0.363271	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$683$	0.363271	−	0.500000i	0.363271	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$684$		0			0
$685$		0			0
$686$	0.309017	+	0.951057i	0.309017	+	0.951057i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$691$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$692$	0.951057	−	1.30902i	0.951057	−	1.30902i
$693$		−	1.00000i		−	1.00000i
$694$	0.500000	+	0.363271i	0.500000	+	0.363271i
$695$		0			0
$696$	1.61803	−	1.17557i	1.61803	−	1.17557i
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−2.00000			−2.00000			−1.00000			$\pi$
$701$	−2.00000			−2.00000			−1.00000			$\pi$
$702$		0			0
$703$		0			0
$704$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$705$		0			0
$706$		0			0
$707$			1.00000i			1.00000i
$708$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$709$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$709$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$710$		0			0
$711$	0.190983	+	0.587785i	0.190983	+	0.587785i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.500000	−	1.53884i	0.500000	−	1.53884i
$717$		0			0
$718$		0			0
$719$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$719$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$720$		0			0
$721$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$722$	0.587785	+	0.809017i	0.587785	+	0.809017i
$723$	1.53884	−	0.500000i	1.53884	−	0.500000i
$724$		0			0
$725$		0			0
$726$	−0.618034			−0.618034
$727$	−1.90211	+	0.618034i	−1.90211	+	0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$727$	−1.90211	+	0.618034i	−1.90211	+	0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$728$		0			0
$729$	0.809017	−	0.587785i	0.809017	−	0.587785i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$733$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$734$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$735$		0			0
$736$		0			0
$737$		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
$742$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$743$		0			0			−	1.00000i	$-0.5\pi$
$743$		0			0				1.00000i	$0.5\pi$
$744$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$745$		0			0
$746$		0			0
$747$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$748$		0			0
$749$	−1.00000			−1.00000
$750$		0			0
$751$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$751$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$752$		0			0
$753$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$754$		0			0
$755$		0			0
$756$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$757$		0			0			−	1.00000i	$-0.5\pi$
$757$		0			0				1.00000i	$0.5\pi$
$758$		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	$0.400000\pi$
$762$	0.587785	+	0.190983i	0.587785	+	0.190983i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$			1.00000i			1.00000i
$769$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$769$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$770$		0			0
$771$		0			0
$772$	0.951057	+	1.30902i	0.951057	+	1.30902i
$773$	−0.587785	+	0.190983i	−0.587785	+	0.190983i	−0.587785	−	0.809017i	$-0.700000\pi$
$773$	−0.587785	+	0.190983i	−0.587785	+	0.190983i			1.00000i	$0.5\pi$
$774$		0			0
$775$		0			0
$776$	1.61803			1.61803
$777$		0			0
$778$	0.363271	+	0.500000i	0.363271	+	0.500000i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−1.17557	+	1.61803i	−1.17557	+	1.61803i
$784$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$785$		0			0
$786$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$787$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$787$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$788$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.363271	−	0.500000i	0.363271	−	0.500000i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$797$	0.363271	+	0.500000i	0.363271	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$797$	0.363271	+	0.500000i	0.363271	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.726543	−	1.00000i	−0.726543	−	1.00000i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	1.61803i		−	1.61803i
$808$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$809$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$809$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$810$		0			0
$811$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$811$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$812$	3.07768	+	1.00000i	3.07768	+	1.00000i
$813$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$			0.618034i			0.618034i
$819$		0			0
$820$		0			0
$821$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$821$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$822$		0			0
$823$	0.587785	−	0.190983i	0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$823$	0.587785	−	0.190983i	0.587785	−	0.190983i	0.587785	+	0.809017i	$0.300000\pi$
$824$	−1.61803			−1.61803
$825$		0			0
$826$	−1.00000			−1.00000
$827$	−1.53884	+	0.500000i	−1.53884	+	0.500000i	−0.951057	−	0.309017i	$-0.900000\pi$
$827$	−1.53884	+	0.500000i	−1.53884	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$828$		0			0
$829$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$829$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.53884	+	0.500000i	1.53884	+	0.500000i
$838$	1.53884	+	0.500000i	1.53884	+	0.500000i
$839$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$839$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$840$		0			0
$841$	0.927051	−	2.85317i	0.927051	−	2.85317i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$848$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$853$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$854$		0			0
$855$		0			0
$856$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$859$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$863$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$864$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$865$		0			0
$866$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$867$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$868$		−	2.61803i		−	2.61803i
$869$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$874$		0			0
$875$		0			0
$876$	−2.00000			−2.00000
$877$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$877$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$878$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$879$	0.500000	−	0.363271i	0.500000	−	0.363271i
$880$		0			0
$881$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$881$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$882$		−	1.61803i		−	1.61803i
$883$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$883$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$884$		0			0
$885$		0			0
$886$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$887$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$887$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$888$		0			0
$889$	0.309017	+	0.951057i	0.309017	+	0.951057i
$890$		0			0
$891$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$892$	0.363271	−	0.500000i	0.363271	−	0.500000i
$893$		0			0
$894$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$895$		0			0
$896$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$897$		0			0
$898$		0			0
$899$	−3.23607			−3.23607
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	1.30902	+	0.951057i	1.30902	+	0.951057i
$907$		0			0			−	1.00000i	$-0.5\pi$
$907$		0			0				1.00000i	$0.5\pi$
$908$	0.363271	−	0.500000i	0.363271	−	0.500000i
$909$	0.190983	−	0.587785i	0.190983	−	0.587785i
$910$		0			0
$911$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$911$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$912$		0			0
$913$	0.951057	+	0.309017i	0.951057	+	0.309017i
$914$	0.190983	+	0.587785i	0.190983	+	0.587785i
$915$		0			0
$916$		0			0
$917$	1.90211	−	2.61803i	1.90211	−	2.61803i
$918$		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	$0.200000\pi$
$920$		0			0
$921$		0			0
$922$	0.951057	+	1.30902i	0.951057	+	1.30902i
$923$		0			0
$924$	1.00000			1.00000
$925$		0			0
$926$	−2.00000			−2.00000
$927$	1.53884	−	0.500000i	1.53884	−	0.500000i
$928$	1.17557	+	1.61803i	1.17557	+	1.61803i
$929$		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			0
$933$		0			0
$934$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$935$		0			0
$936$		0			0
$937$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$937$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$938$		0			0
$939$	0.190983	+	0.587785i	0.190983	+	0.587785i
$940$		0			0
$941$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$941$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$942$		0			0
$943$		0			0
$944$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$945$		0			0
$946$		0			0
$947$	−0.951057	−	1.30902i	−0.951057	−	1.30902i	−0.951057	−	0.309017i	$-0.900000\pi$
$947$	−0.951057	−	1.30902i	−0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$948$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$949$		0			0
$950$		0			0
$951$	0.618034			0.618034
$952$		0			0
$953$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$953$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$954$	0.500000	−	0.363271i	0.500000	−	0.363271i
$955$		0			0
$956$		0			0
$957$		−	1.23607i		−	1.23607i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.500000	+	1.53884i	0.500000	+	1.53884i
$962$		0			0
$963$	0.587785	+	0.190983i	0.587785	+	0.190983i
$964$	0.500000	+	1.53884i	0.500000	+	1.53884i
$965$		0			0
$966$		0			0
$967$	−0.951057	+	1.30902i	−0.951057	+	1.30902i			1.00000i	$0.5\pi$
$967$	−0.951057	+	1.30902i	−0.951057	+	1.30902i	−0.951057	+	0.309017i	$0.900000\pi$
$968$		−	0.618034i		−	0.618034i
$969$		0			0
$970$		0			0
$971$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$971$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$972$	0.587785	+	0.809017i	0.587785	+	0.809017i
$973$		0			0
$974$	0.618034			0.618034
$975$		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
$982$		−	1.61803i		−	1.61803i
$983$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$983$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$991$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$992$	0.951057	−	1.30902i	0.951057	−	1.30902i
$993$		0			0
$994$		0			0
$995$		0			0
$996$	1.30902	−	0.951057i	1.30902	−	0.951057i
$997$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$997$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3000.1.z.a.1349.2		8
3.2	odd	2		3000.1.z.b.1349.1		8
5.2	odd	4		3000.1.bj.a.1901.1		4
5.3	odd	4		600.1.bj.b.581.1	yes	4
5.4	even	2	inner	3000.1.z.a.1349.1		8
8.5	even	2		3000.1.z.b.1349.1		8
15.2	even	4		3000.1.bj.b.1901.1		4
15.8	even	4		600.1.bj.a.581.1	yes	4
15.14	odd	2		3000.1.z.b.1349.2		8
20.3	even	4		2400.1.cp.a.881.1		4
24.5	odd	2	CM	3000.1.z.a.1349.2		8
25.3	odd	20		600.1.bj.b.221.1	yes	4
25.4	even	10	inner	3000.1.z.a.149.2		8
25.21	even	5	inner	3000.1.z.a.149.1		8
25.22	odd	20		3000.1.bj.a.101.1		4
40.3	even	4		2400.1.cp.b.881.1		4
40.13	odd	4		600.1.bj.a.581.1	yes	4
40.29	even	2		3000.1.z.b.1349.2		8
40.37	odd	4		3000.1.bj.b.1901.1		4
60.23	odd	4		2400.1.cp.b.881.1		4
75.29	odd	10		3000.1.z.b.149.1		8
75.47	even	20		3000.1.bj.b.101.1		4
75.53	even	20		600.1.bj.a.221.1	✓	4
75.71	odd	10		3000.1.z.b.149.2		8
100.3	even	20		2400.1.cp.a.2321.1		4
120.29	odd	2	inner	3000.1.z.a.1349.1		8
120.53	even	4		600.1.bj.b.581.1	yes	4
120.77	even	4		3000.1.bj.a.1901.1		4
120.83	odd	4		2400.1.cp.a.881.1		4
200.3	even	20		2400.1.cp.b.2321.1		4
200.21	even	10		3000.1.z.b.149.2		8
200.29	even	10		3000.1.z.b.149.1		8
200.53	odd	20		600.1.bj.a.221.1	✓	4
200.197	odd	20		3000.1.bj.b.101.1		4
300.203	odd	20		2400.1.cp.b.2321.1		4
600.29	odd	10	inner	3000.1.z.a.149.2		8
600.53	even	20		600.1.bj.b.221.1	yes	4
600.197	even	20		3000.1.bj.a.101.1		4
600.203	odd	20		2400.1.cp.a.2321.1		4
600.221	odd	10	inner	3000.1.z.a.149.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.1.bj.a.221.1	✓	4	75.53	even	20
600.1.bj.a.221.1	✓	4	200.53	odd	20
600.1.bj.a.581.1	yes	4	15.8	even	4
600.1.bj.a.581.1	yes	4	40.13	odd	4
600.1.bj.b.221.1	yes	4	25.3	odd	20
600.1.bj.b.221.1	yes	4	600.53	even	20
600.1.bj.b.581.1	yes	4	5.3	odd	4
600.1.bj.b.581.1	yes	4	120.53	even	4
2400.1.cp.a.881.1		4	20.3	even	4
2400.1.cp.a.881.1		4	120.83	odd	4
2400.1.cp.a.2321.1		4	100.3	even	20
2400.1.cp.a.2321.1		4	600.203	odd	20
2400.1.cp.b.881.1		4	40.3	even	4
2400.1.cp.b.881.1		4	60.23	odd	4
2400.1.cp.b.2321.1		4	200.3	even	20
2400.1.cp.b.2321.1		4	300.203	odd	20
3000.1.z.a.149.1		8	25.21	even	5	inner
3000.1.z.a.149.1		8	600.221	odd	10	inner
3000.1.z.a.149.2		8	25.4	even	10	inner
3000.1.z.a.149.2		8	600.29	odd	10	inner
3000.1.z.a.1349.1		8	5.4	even	2	inner
3000.1.z.a.1349.1		8	120.29	odd	2	inner
3000.1.z.a.1349.2		8	1.1	even	1	trivial
3000.1.z.a.1349.2		8	24.5	odd	2	CM
3000.1.z.b.149.1		8	75.29	odd	10
3000.1.z.b.149.1		8	200.29	even	10
3000.1.z.b.149.2		8	75.71	odd	10
3000.1.z.b.149.2		8	200.21	even	10
3000.1.z.b.1349.1		8	3.2	odd	2
3000.1.z.b.1349.1		8	8.5	even	2
3000.1.z.b.1349.2		8	15.14	odd	2
3000.1.z.b.1349.2		8	40.29	even	2
3000.1.bj.a.101.1		4	25.22	odd	20
3000.1.bj.a.101.1		4	600.197	even	20
3000.1.bj.a.1901.1		4	5.2	odd	4
3000.1.bj.a.1901.1		4	120.77	even	4
3000.1.bj.b.101.1		4	75.47	even	20
3000.1.bj.b.101.1		4	200.197	odd	20
3000.1.bj.b.1901.1		4	15.2	even	4
3000.1.bj.b.1901.1		4	40.37	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3000 = 2^{3} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3000.z (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.809017 - 0.587785i) q^{6} -1.61803i q^{7} +(0.587785 - 0.809017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(-0.190983 - 0.587785i) q^{11} +(-0.951057 - 0.309017i) q^{12} +(-0.500000 - 1.53884i) q^{14} +(0.309017 - 0.951057i) q^{16} +1.00000i q^{18} +(-1.30902 + 0.951057i) q^{21} +(-0.363271 - 0.500000i) q^{22} -1.00000 q^{24} +(0.951057 - 0.309017i) q^{27} +(-0.951057 - 1.30902i) q^{28} +(-1.61803 + 1.17557i) q^{29} +(1.30902 + 0.951057i) q^{31} -1.00000i q^{32} +(-0.363271 + 0.500000i) q^{33} +(0.309017 + 0.951057i) q^{36} +(-0.951057 + 1.30902i) q^{42} +(-0.500000 - 0.363271i) q^{44} +(-0.951057 + 0.309017i) q^{48} -1.61803 q^{49} +(-0.363271 - 0.500000i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-1.30902 - 0.951057i) q^{56} +(-1.17557 + 1.61803i) q^{58} +(0.190983 - 0.587785i) q^{59} +(1.53884 + 0.500000i) q^{62} +(1.53884 + 0.500000i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-0.190983 + 0.587785i) q^{66} +(0.587785 + 0.809017i) q^{72} +(1.90211 - 0.618034i) q^{73} +(-0.951057 + 0.309017i) q^{77} +(0.500000 - 0.363271i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-0.951057 + 1.30902i) q^{83} +(-0.500000 + 1.53884i) q^{84} +(1.90211 + 0.618034i) q^{87} +(-0.587785 - 0.190983i) q^{88} -1.61803i q^{93} +(-0.809017 + 0.587785i) q^{96} +(0.951057 + 1.30902i) q^{97} +(-1.53884 + 0.500000i) q^{98} +0.618034 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 2 q^{6} + 2 q^{9} - 6 q^{11} - 4 q^{14} - 2 q^{16} - 6 q^{21} - 8 q^{24} - 4 q^{29} + 6 q^{31} - 2 q^{36} - 4 q^{44} - 4 q^{49} + 2 q^{54} - 6 q^{56} + 6 q^{59} + 2 q^{64} - 6 q^{66} + 4 q^{79}+ \cdots - 4 q^{99}+O(q^{100}) \) 8 * q + 2 * q^4 - 2 * q^6 + 2 * q^9 - 6 * q^11 - 4 * q^14 - 2 * q^16 - 6 * q^21 - 8 * q^24 - 4 * q^29 + 6 * q^31 - 2 * q^36 - 4 * q^44 - 4 * q^49 + 2 * q^54 - 6 * q^56 + 6 * q^59 + 2 * q^64 - 6 * q^66 + 4 * q^79 - 2 * q^81 - 4 * q^84 - 2 * q^96 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more