LMFDB - Embedded newform 465.1.x.a.194.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [465,1,Mod(194,465)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(465, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("465.194");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	465.x (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.232065230874$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{5}$
Projective field:	Galois closure of 5.1.207792225.1

Embedding invariants

Embedding label			194.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	465.194
Dual form			465.1.x.a.314.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 1.53884i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-1.30902 - 0.951057i) q^{4} +1.00000 q^{5} -1.61803 q^{6} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 1.53884i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-1.30902 - 0.951057i) q^{4} +1.00000 q^{5} -1.61803 q^{6} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.500000 + 1.53884i) q^{10} +(0.500000 - 1.53884i) q^{12} +(0.309017 + 0.951057i) q^{15} +(-1.61803 + 1.17557i) q^{17} +(-0.500000 - 1.53884i) q^{18} +(0.190983 - 0.587785i) q^{19} +(-1.30902 - 0.951057i) q^{20} +(1.30902 - 0.951057i) q^{23} +(0.809017 + 0.587785i) q^{24} +1.00000 q^{25} +(-0.809017 - 0.587785i) q^{27} -1.61803 q^{30} +(0.309017 - 0.951057i) q^{31} +1.00000 q^{32} +(-1.00000 - 3.07768i) q^{34} +1.61803 q^{36} +(0.809017 + 0.587785i) q^{38} +(0.809017 - 0.587785i) q^{40} +(-0.809017 + 0.587785i) q^{45} +(0.809017 + 2.48990i) q^{46} +(-0.500000 - 1.53884i) q^{47} +(0.309017 + 0.951057i) q^{49} +(-0.500000 + 1.53884i) q^{50} +(-1.61803 - 1.17557i) q^{51} +(-0.500000 + 0.363271i) q^{53} +(1.30902 - 0.951057i) q^{54} +0.618034 q^{57} +(0.500000 - 1.53884i) q^{60} +0.618034 q^{61} +(1.30902 + 0.951057i) q^{62} +(-0.500000 + 1.53884i) q^{64} +3.23607 q^{68} +(1.30902 + 0.951057i) q^{69} +(-0.309017 + 0.951057i) q^{72} +(0.309017 + 0.951057i) q^{75} +(-0.809017 + 0.587785i) q^{76} +(-0.500000 + 0.363271i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-0.500000 + 1.53884i) q^{83} +(-1.61803 + 1.17557i) q^{85} +(-0.500000 - 1.53884i) q^{90} -2.61803 q^{92} +1.00000 q^{93} +2.61803 q^{94} +(0.190983 - 0.587785i) q^{95} +(0.309017 + 0.951057i) q^{96} -1.61803 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - q^{3} - 3 q^{4} + 4 q^{5} - 2 q^{6} + q^{8} - q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - q^3 - 3 * q^4 + 4 * q^5 - 2 * q^6 + q^8 - q^9	$ 4 q - 2 q^{2} - q^{3} - 3 q^{4} + 4 q^{5} - 2 q^{6} + q^{8} - q^{9} - 2 q^{10} + 2 q^{12} - q^{15} - 2 q^{17} - 2 q^{18} + 3 q^{19} - 3 q^{20} + 3 q^{23} + q^{24} + 4 q^{25} - q^{27} - 2 q^{30} - q^{31} + 4 q^{32} - 4 q^{34} + 2 q^{36} + q^{38} + q^{40} - q^{45} + q^{46} - 2 q^{47} - q^{49} - 2 q^{50} - 2 q^{51} - 2 q^{53} + 3 q^{54} - 2 q^{57} + 2 q^{60} - 2 q^{61} + 3 q^{62} - 2 q^{64} + 4 q^{68} + 3 q^{69} + q^{72} - q^{75} - q^{76} - 2 q^{79} - q^{81} - 2 q^{83} - 2 q^{85} - 2 q^{90} - 6 q^{92} + 4 q^{93} + 6 q^{94} + 3 q^{95} - q^{96} - 2 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - q^3 - 3 * q^4 + 4 * q^5 - 2 * q^6 + q^8 - q^9 - 2 * q^10 + 2 * q^12 - q^15 - 2 * q^17 - 2 * q^18 + 3 * q^19 - 3 * q^20 + 3 * q^23 + q^24 + 4 * q^25 - q^27 - 2 * q^30 - q^31 + 4 * q^32 - 4 * q^34 + 2 * q^36 + q^38 + q^40 - q^45 + q^46 - 2 * q^47 - q^49 - 2 * q^50 - 2 * q^51 - 2 * q^53 + 3 * q^54 - 2 * q^57 + 2 * q^60 - 2 * q^61 + 3 * q^62 - 2 * q^64 + 4 * q^68 + 3 * q^69 + q^72 - q^75 - q^76 - 2 * q^79 - q^81 - 2 * q^83 - 2 * q^85 - 2 * q^90 - 6 * q^92 + 4 * q^93 + 6 * q^94 + 3 * q^95 - q^96 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$2$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$3$	0.309017	+	0.951057i	0.309017	+	0.951057i
$3$	0.309017	+	0.951057i	0.309017	+	0.951057i
$4$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$5$	1.00000			1.00000
$5$	1.00000			1.00000
$6$	−1.61803			−1.61803
$7$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$7$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$8$	0.809017	−	0.587785i	0.809017	−	0.587785i
$9$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$10$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$11$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$11$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$12$	0.500000	−	1.53884i	0.500000	−	1.53884i
$13$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$13$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$14$		0			0
$15$	0.309017	+	0.951057i	0.309017	+	0.951057i
$16$		0			0
$17$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$17$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$18$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$19$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$19$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$20$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$21$		0			0
$22$		0			0
$23$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$23$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$24$	0.809017	+	0.587785i	0.809017	+	0.587785i
$25$	1.00000			1.00000
$26$		0			0
$27$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$28$		0			0
$29$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$29$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$30$	−1.61803			−1.61803
$31$	0.309017	−	0.951057i	0.309017	−	0.951057i
$31$	0.309017	−	0.951057i	0.309017	−	0.951057i
$32$	1.00000			1.00000
$33$		0			0
$34$	−1.00000	−	3.07768i	−1.00000	−	3.07768i
$35$		0			0
$36$	1.61803			1.61803
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	0.809017	+	0.587785i	0.809017	+	0.587785i
$39$		0			0
$40$	0.809017	−	0.587785i	0.809017	−	0.587785i
$41$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$41$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$42$		0			0
$43$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$43$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$44$		0			0
$45$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$46$	0.809017	+	2.48990i	0.809017	+	2.48990i
$47$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$47$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.309017	+	0.951057i
$50$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$51$	−1.61803	−	1.17557i	−1.61803	−	1.17557i
$52$		0			0
$53$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$53$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$54$	1.30902	−	0.951057i	1.30902	−	0.951057i
$55$		0			0
$56$		0			0
$57$	0.618034			0.618034
$58$		0			0
$59$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$59$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$60$	0.500000	−	1.53884i	0.500000	−	1.53884i
$61$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$61$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$62$	1.30902	+	0.951057i	1.30902	+	0.951057i
$63$		0			0
$64$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$65$		0			0
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	3.23607			3.23607
$69$	1.30902	+	0.951057i	1.30902	+	0.951057i
$70$		0			0
$71$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$71$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$72$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$73$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$73$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$74$		0			0
$75$	0.309017	+	0.951057i	0.309017	+	0.951057i
$76$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$77$		0			0
$78$		0			0
$79$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$79$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.309017	−	0.951057i
$82$		0			0
$83$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$83$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$84$		0			0
$85$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$89$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$90$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$91$		0			0
$92$	−2.61803			−2.61803
$93$	1.00000			1.00000
$94$	2.61803			2.61803
$95$	0.190983	−	0.587785i	0.190983	−	0.587785i
$96$	0.309017	+	0.951057i	0.309017	+	0.951057i
$97$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$97$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$98$	−1.61803			−1.61803
$99$		0			0
$100$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$101$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$101$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$102$	2.61803	−	1.90211i	2.61803	−	1.90211i
$103$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$103$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$104$		0			0
$105$		0			0
$106$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$107$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$107$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$108$	0.500000	+	1.53884i	0.500000	+	1.53884i
$109$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$109$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$113$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$114$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$115$	1.30902	−	0.951057i	1.30902	−	0.951057i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$	0.809017	+	0.587785i	0.809017	+	0.587785i
$121$	0.309017	+	0.951057i	0.309017	+	0.951057i
$122$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$123$		0			0
$124$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$125$	1.00000			1.00000
$126$		0			0
$127$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$127$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$128$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$129$		0			0
$130$		0			0
$131$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$131$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$136$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$137$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$137$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$138$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$139$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$139$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$140$		0			0
$141$	1.30902	−	0.951057i	1.30902	−	0.951057i
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$148$		0			0
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	−1.61803			−1.61803
$151$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$151$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$152$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$153$	0.618034	−	1.90211i	0.618034	−	1.90211i
$154$		0			0
$155$	0.309017	−	0.951057i	0.309017	−	0.951057i
$156$		0			0
$157$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$157$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$158$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$159$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$160$	1.00000			1.00000
$161$		0			0
$162$	1.30902	+	0.951057i	1.30902	+	0.951057i
$163$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$163$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$164$		0			0
$165$		0			0
$166$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$167$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$167$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$168$		0			0
$169$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$170$	−1.00000	−	3.07768i	−1.00000	−	3.07768i
$171$	0.190983	+	0.587785i	0.190983	+	0.587785i
$172$		0			0
$173$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$173$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$179$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$180$	1.61803			1.61803
$181$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$181$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$182$		0			0
$183$	0.190983	+	0.587785i	0.190983	+	0.587785i
$184$	0.500000	−	1.53884i	0.500000	−	1.53884i
$185$		0			0
$186$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$187$		0			0
$188$	−0.809017	+	2.48990i	−0.809017	+	2.48990i
$189$		0			0
$190$	0.809017	+	0.587785i	0.809017	+	0.587785i
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	−1.61803			−1.61803
$193$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$193$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$194$		0			0
$195$		0			0
$196$	0.500000	−	1.53884i	0.500000	−	1.53884i
$197$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$197$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$198$		0			0
$199$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$199$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$200$	0.809017	−	0.587785i	0.809017	−	0.587785i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	1.00000	+	3.07768i	1.00000	+	3.07768i
$205$		0			0
$206$		0			0
$207$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$211$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$212$	1.00000			1.00000
$213$		0			0
$214$	0.809017	+	2.48990i	0.809017	+	2.48990i
$215$		0			0
$216$	−1.00000			−1.00000
$217$		0			0
$218$	−1.00000			−1.00000
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$		0			0
$225$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$226$	2.61803	−	1.90211i	2.61803	−	1.90211i
$227$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$227$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$228$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$229$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$229$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$230$	0.809017	+	2.48990i	0.809017	+	2.48990i
$231$		0			0
$232$		0			0
$233$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$233$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$234$		0			0
$235$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$236$		0			0
$237$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$238$		0			0
$239$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$239$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$240$		0			0
$241$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$241$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$242$	−1.61803			−1.61803
$243$	1.00000			1.00000
$244$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$245$	0.309017	+	0.951057i	0.309017	+	0.951057i
$246$		0			0
$247$		0			0
$248$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$249$	−1.61803			−1.61803
$250$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$251$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$251$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−1.61803	−	1.17557i	−1.61803	−	1.17557i
$256$	0.809017	−	0.587785i	0.809017	−	0.587785i
$257$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$257$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$263$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$264$		0			0
$265$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$269$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$270$	1.30902	−	0.951057i	1.30902	−	0.951057i
$271$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$271$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$272$		0			0
$273$		0			0
$274$	2.61803			2.61803
$275$		0			0
$276$	−0.809017	−	2.48990i	−0.809017	−	2.48990i
$277$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$277$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$278$	2.61803			2.61803
$279$	0.309017	+	0.951057i	0.309017	+	0.951057i
$280$		0			0
$281$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$281$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$282$	0.809017	+	2.48990i	0.809017	+	2.48990i
$283$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$283$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$284$		0			0
$285$	0.618034			0.618034
$286$		0			0
$287$		0			0
$288$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$289$	0.927051	−	2.85317i	0.927051	−	2.85317i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$293$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$294$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$	0.500000	−	1.53884i	0.500000	−	1.53884i
$301$		0			0
$302$	0.809017	−	0.587785i	0.809017	−	0.587785i
$303$		0			0
$304$		0			0
$305$	0.618034			0.618034
$306$	2.61803	+	1.90211i	2.61803	+	1.90211i
$307$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$307$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$308$		0			0
$309$		0			0
$310$	1.30902	+	0.951057i	1.30902	+	0.951057i
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		0			0
$313$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$313$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$314$		0			0
$315$		0			0
$316$	1.00000			1.00000
$317$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$317$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$318$	0.809017	−	0.587785i	0.809017	−	0.587785i
$319$		0			0
$320$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$321$	1.30902	+	0.951057i	1.30902	+	0.951057i
$322$		0			0
$323$	0.381966	+	1.17557i	0.381966	+	1.17557i
$324$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$325$		0			0
$326$		0			0
$327$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$331$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$332$	2.11803	−	1.53884i	2.11803	−	1.53884i
$333$		0			0
$334$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$335$		0			0
$336$		0			0
$337$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$337$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$338$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$339$	0.618034	−	1.90211i	0.618034	−	1.90211i
$340$	3.23607			3.23607
$341$		0			0
$342$	−1.00000			−1.00000
$343$		0			0
$344$		0			0
$345$	1.30902	+	0.951057i	1.30902	+	0.951057i
$346$	2.61803			2.61803
$347$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$347$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$348$		0			0
$349$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$349$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$353$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$359$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$360$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$361$	0.500000	+	0.363271i	0.500000	+	0.363271i
$362$	0.809017	−	2.48990i	0.809017	−	2.48990i
$363$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$364$		0			0
$365$		0			0
$366$	−1.00000			−1.00000
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$	0.309017	+	0.951057i	0.309017	+	0.951057i
$376$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$377$		0			0
$378$		0			0
$379$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$379$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$380$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$381$		0			0
$382$		0			0
$383$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$383$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$384$	0.500000	−	1.53884i	0.500000	−	1.53884i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$389$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$390$		0			0
$391$	−1.00000	+	3.07768i	−1.00000	+	3.07768i
$392$	0.809017	+	0.587785i	0.809017	+	0.587785i
$393$		0			0
$394$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$395$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$396$		0			0
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	−3.23607			−3.23607
$399$		0			0
$400$		0			0
$401$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$401$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	0.309017	−	0.951057i	0.309017	−	0.951057i
$406$		0			0
$407$		0			0
$408$	−2.00000			−2.00000
$409$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$409$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$410$		0			0
$411$	1.30902	−	0.951057i	1.30902	−	0.951057i
$412$		0			0
$413$		0			0
$414$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$415$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$416$		0			0
$417$	1.30902	−	0.951057i	1.30902	−	0.951057i
$418$		0			0
$419$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$419$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$420$		0			0
$421$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$421$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$422$	0.809017	−	2.48990i	0.809017	−	2.48990i
$423$	1.30902	+	0.951057i	1.30902	+	0.951057i
$424$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$425$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$426$		0			0
$427$		0			0
$428$	−2.61803			−2.61803
$429$		0			0
$430$		0			0
$431$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$431$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$432$		0			0
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$		0			0
$436$	0.309017	−	0.951057i	0.309017	−	0.951057i
$437$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$438$		0			0
$439$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$439$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$440$		0			0
$441$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$442$		0			0
$443$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$443$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$449$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$450$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$451$		0			0
$452$	1.00000	+	3.07768i	1.00000	+	3.07768i
$453$	0.190983	−	0.587785i	0.190983	−	0.587785i
$454$	2.61803	+	1.90211i	2.61803	+	1.90211i
$455$		0			0
$456$	0.500000	−	0.363271i	0.500000	−	0.363271i
$457$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$457$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$458$	0.809017	+	0.587785i	0.809017	+	0.587785i
$459$	2.00000			2.00000
$460$	−2.61803			−2.61803
$461$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$461$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$462$		0			0
$463$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$463$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$464$		0			0
$465$	1.00000			1.00000
$466$	−1.00000			−1.00000
$467$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$467$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$468$		0			0
$469$		0			0
$470$	2.61803			2.61803
$471$		0			0
$472$		0			0
$473$		0			0
$474$	0.809017	−	0.587785i	0.809017	−	0.587785i
$475$	0.190983	−	0.587785i	0.190983	−	0.587785i
$476$		0			0
$477$	0.190983	−	0.587785i	0.190983	−	0.587785i
$478$		0			0
$479$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$479$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$480$	0.309017	+	0.951057i	0.309017	+	0.951057i
$481$		0			0
$482$	0.809017	−	0.587785i	0.809017	−	0.587785i
$483$		0			0
$484$	0.500000	−	1.53884i	0.500000	−	1.53884i
$485$		0			0
$486$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$487$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$487$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$488$	0.500000	−	0.363271i	0.500000	−	0.363271i
$489$		0			0
$490$	−1.61803			−1.61803
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.809017	−	2.48990i	0.809017	−	2.48990i
$499$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$499$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$500$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$501$	−1.61803			−1.61803
$502$		0			0
$503$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$503$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$508$		0			0
$509$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$509$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$510$	2.61803	−	1.90211i	2.61803	−	1.90211i
$511$		0			0
$512$		0			0
$513$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$514$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$515$		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		1.00000			$0$
$521$		0			0		−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			0
$525$		0			0
$526$	−1.00000			−1.00000
$527$	0.618034	+	1.90211i	0.618034	+	1.90211i
$528$		0			0
$529$	0.500000	−	1.53884i	0.500000	−	1.53884i
$530$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	1.30902	−	0.951057i	1.30902	−	0.951057i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$	0.500000	+	1.53884i	0.500000	+	1.53884i
$541$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$541$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$542$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$543$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$544$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$545$	0.190983	+	0.587785i	0.190983	+	0.587785i
$546$		0			0
$547$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$547$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$548$	−0.809017	+	2.48990i	−0.809017	+	2.48990i
$549$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$550$		0			0
$551$		0			0
$552$	1.61803			1.61803
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.809017	+	2.48990i	−0.809017	+	2.48990i
$557$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$557$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$558$	−1.61803			−1.61803
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$563$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$564$	−2.61803			−2.61803
$565$	−1.61803	−	1.17557i	−1.61803	−	1.17557i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$569$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$570$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$571$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$571$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.30902	−	0.951057i	1.30902	−	0.951057i
$576$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$577$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$577$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$578$	3.92705	+	2.85317i	3.92705	+	2.85317i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$587$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$587$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$588$	1.61803			1.61803
$589$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$590$		0			0
$591$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$592$		0			0
$593$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$593$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$598$		0			0
$599$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$599$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$600$	0.809017	+	0.587785i	0.809017	+	0.587785i
$601$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$601$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$602$		0			0
$603$		0			0
$604$	0.309017	+	0.951057i	0.309017	+	0.951057i
$605$	0.309017	+	0.951057i	0.309017	+	0.951057i
$606$		0			0
$607$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$607$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$608$	0.190983	−	0.587785i	0.190983	−	0.587785i
$609$		0			0
$610$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$611$		0			0
$612$	−2.61803	+	1.90211i	−2.61803	+	1.90211i
$613$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$613$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$617$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$618$		0			0
$619$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$619$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$620$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$621$	−1.61803			−1.61803
$622$		0			0
$623$		0			0
$624$		0			0
$625$	1.00000			1.00000
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$631$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$632$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$633$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$634$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$635$		0			0
$636$	0.309017	+	0.951057i	0.309017	+	0.951057i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$641$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$641$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$642$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$643$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$643$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$644$		0			0
$645$		0			0
$646$	−2.00000			−2.00000
$647$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$647$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$648$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$653$	0.618034	−	1.90211i	0.618034	−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$654$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$655$		0			0
$656$		0			0
$657$		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			0
$661$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$661$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$662$	0.809017	+	0.587785i	0.809017	+	0.587785i
$663$		0			0
$664$	0.500000	+	1.53884i	0.500000	+	1.53884i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	2.11803	−	1.53884i	2.11803	−	1.53884i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$673$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$674$		0			0
$675$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$676$	1.61803			1.61803
$677$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$677$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$678$	2.61803	+	1.90211i	2.61803	+	1.90211i
$679$		0			0
$680$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$681$	2.00000			2.00000
$682$		0			0
$683$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$683$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$684$	0.309017	−	0.951057i	0.309017	−	0.951057i
$685$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$686$		0			0
$687$	0.618034			0.618034
$688$		0			0
$689$		0			0
$690$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$691$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$691$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$692$	−0.809017	+	2.48990i	−0.809017	+	2.48990i
$693$		0			0
$694$	0.809017	−	2.48990i	0.809017	−	2.48990i
$695$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$696$		0			0
$697$		0			0
$698$	0.809017	+	2.48990i	0.809017	+	2.48990i
$699$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$700$		0			0
$701$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$701$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	1.30902	−	0.951057i	1.30902	−	0.951057i
$706$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$707$		0			0
$708$		0			0
$709$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$709$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$710$		0			0
$711$	0.190983	−	0.587785i	0.190983	−	0.587785i
$712$		0			0
$713$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$		0			0
$721$		0			0
$722$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$723$	0.190983	−	0.587785i	0.190983	−	0.587785i
$724$	2.11803	+	1.53884i	2.11803	+	1.53884i
$725$		0			0
$726$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$727$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$727$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.309017	+	0.951057i
$730$		0			0
$731$		0			0
$732$	0.309017	−	0.951057i	0.309017	−	0.951057i
$733$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$733$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$734$		0			0
$735$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$736$	1.30902	−	0.951057i	1.30902	−	0.951057i
$737$		0			0
$738$		0			0
$739$	2.00000			2.00000			1.00000			$0$
$739$	2.00000			2.00000			1.00000			$0$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$743$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$744$	0.809017	−	0.587785i	0.809017	−	0.587785i
$745$		0			0
$746$		0			0
$747$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$748$		0			0
$749$		0			0
$750$	−1.61803			−1.61803
$751$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$751$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$756$		0			0
$757$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$757$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$758$	0.809017	−	0.587785i	0.809017	−	0.587785i
$759$		0			0
$760$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$761$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$761$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.618034	−	1.90211i	0.618034	−	1.90211i
$766$	0.809017	−	0.587785i	0.809017	−	0.587785i
$767$		0			0
$768$	0.809017	+	0.587785i	0.809017	+	0.587785i
$769$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$769$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$770$		0			0
$771$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$772$		0			0
$773$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$773$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$774$		0			0
$775$	0.309017	−	0.951057i	0.309017	−	0.951057i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−4.23607	−	3.07768i	−4.23607	−	3.07768i
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$787$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$788$	−0.809017	−	2.48990i	−0.809017	−	2.48990i
$789$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$790$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$796$	1.00000	−	3.07768i	1.00000	−	3.07768i
$797$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$797$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$798$		0			0
$799$	2.61803	+	1.90211i	2.61803	+	1.90211i
$800$	1.00000			1.00000
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$809$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$810$	1.30902	+	0.951057i	1.30902	+	0.951057i
$811$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$811$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$812$		0			0
$813$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	0.809017	−	2.48990i	0.809017	−	2.48990i
$819$		0			0
$820$		0			0
$821$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$821$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$822$	0.809017	+	2.48990i	0.809017	+	2.48990i
$823$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$823$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$827$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$828$	2.11803	−	1.53884i	2.11803	−	1.53884i
$829$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$829$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$830$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$831$		0			0
$832$		0			0
$833$	−1.61803	−	1.17557i	−1.61803	−	1.17557i
$834$	0.809017	+	2.48990i	0.809017	+	2.48990i
$835$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$836$		0			0
$837$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$838$		0			0
$839$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$839$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$840$		0			0
$841$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$842$	−3.23607			−3.23607
$843$		0			0
$844$	2.11803	+	1.53884i	2.11803	+	1.53884i
$845$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$846$	−2.11803	+	1.53884i	−2.11803	+	1.53884i
$847$		0			0
$848$		0			0
$849$		0			0
$850$	−1.00000	−	3.07768i	−1.00000	−	3.07768i
$851$		0			0
$852$		0			0
$853$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$853$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$854$		0			0
$855$	0.190983	+	0.587785i	0.190983	+	0.587785i
$856$	0.500000	−	1.53884i	0.500000	−	1.53884i
$857$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$857$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$858$		0			0
$859$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$859$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.00000			2.00000			1.00000			$0$
$863$	2.00000			2.00000			1.00000			$0$
$864$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$865$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$866$		0			0
$867$	3.00000			3.00000
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.500000	+	0.363271i	0.500000	+	0.363271i
$873$		0			0
$874$	1.61803			1.61803
$875$		0			0
$876$		0			0
$877$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$877$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$878$	0.809017	−	2.48990i	0.809017	−	2.48990i
$879$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$880$		0			0
$881$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$881$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$882$	1.30902	−	0.951057i	1.30902	−	0.951057i
$883$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$883$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$884$		0			0
$885$		0			0
$886$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$887$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$887$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.00000			−1.00000
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	1.61803			1.61803
$901$	0.381966	−	1.17557i	0.381966	−	1.17557i
$902$		0			0
$903$		0			0
$904$	−2.00000			−2.00000
$905$	−1.61803			−1.61803
$906$	0.809017	+	0.587785i	0.809017	+	0.587785i
$907$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$907$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$908$	−2.61803	+	1.90211i	−2.61803	+	1.90211i
$909$		0			0
$910$		0			0
$911$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$911$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	0.190983	+	0.587785i	0.190983	+	0.587785i
$916$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$917$		0			0
$918$	−1.00000	+	3.07768i	−1.00000	+	3.07768i
$919$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$919$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$920$	0.500000	−	1.53884i	0.500000	−	1.53884i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		1.00000			$0$
$929$		0			0		−1.00000			$\pi$
$930$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$931$	0.618034			0.618034
$932$	0.309017	−	0.951057i	0.309017	−	0.951057i
$933$		0			0
$934$	0.809017	+	0.587785i	0.809017	+	0.587785i
$935$		0			0
$936$		0			0
$937$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$937$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$938$		0			0
$939$		0			0
$940$	−0.809017	+	2.48990i	−0.809017	+	2.48990i
$941$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$941$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$947$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$948$	0.309017	+	0.951057i	0.309017	+	0.951057i
$949$		0			0
$950$	0.809017	+	0.587785i	0.809017	+	0.587785i
$951$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$952$		0			0
$953$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$953$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$954$	0.809017	+	0.587785i	0.809017	+	0.587785i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−1.61803			−1.61803
$961$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$962$		0			0
$963$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$964$	0.309017	+	0.951057i	0.309017	+	0.951057i
$965$		0			0
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	0.809017	+	0.587785i	0.809017	+	0.587785i
$969$	−1.00000	+	0.726543i	−1.00000	+	0.726543i
$970$		0			0
$971$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$971$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$972$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$977$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$978$		0			0
$979$		0			0
$980$	0.500000	−	1.53884i	0.500000	−	1.53884i
$981$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$982$		0			0
$983$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$983$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$984$		0			0
$985$	1.30902	+	0.951057i	1.30902	+	0.951057i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$991$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$992$	0.309017	−	0.951057i	0.309017	−	0.951057i
$993$	0.618034			0.618034
$994$		0			0
$995$	0.618034	+	1.90211i	0.618034	+	1.90211i
$996$	2.11803	+	1.53884i	2.11803	+	1.53884i
$997$		0			0		1.00000			$0$
$997$		0			0		−1.00000			$\pi$
$998$	−1.00000			−1.00000
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.1.x.a.194.1	✓	4
3.2	odd	2		465.1.x.b.194.1	yes	4
5.2	odd	4		2325.1.ca.b.101.1		8
5.3	odd	4		2325.1.ca.b.101.2		8
5.4	even	2		465.1.x.b.194.1	yes	4
15.2	even	4		2325.1.ca.b.101.2		8
15.8	even	4		2325.1.ca.b.101.1		8
15.14	odd	2	CM	465.1.x.a.194.1	✓	4
31.4	even	5	inner	465.1.x.a.314.1	yes	4
93.35	odd	10		465.1.x.b.314.1	yes	4
155.4	even	10		465.1.x.b.314.1	yes	4
155.97	odd	20		2325.1.ca.b.1151.2		8
155.128	odd	20		2325.1.ca.b.1151.1		8
465.128	even	20		2325.1.ca.b.1151.2		8
465.314	odd	10	inner	465.1.x.a.314.1	yes	4
465.407	even	20		2325.1.ca.b.1151.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.1.x.a.194.1	✓	4	1.1	even	1	trivial
465.1.x.a.194.1	✓	4	15.14	odd	2	CM
465.1.x.a.314.1	yes	4	31.4	even	5	inner
465.1.x.a.314.1	yes	4	465.314	odd	10	inner
465.1.x.b.194.1	yes	4	3.2	odd	2
465.1.x.b.194.1	yes	4	5.4	even	2
465.1.x.b.314.1	yes	4	93.35	odd	10
465.1.x.b.314.1	yes	4	155.4	even	10
2325.1.ca.b.101.1		8	5.2	odd	4
2325.1.ca.b.101.1		8	15.8	even	4
2325.1.ca.b.101.2		8	5.3	odd	4
2325.1.ca.b.101.2		8	15.2	even	4
2325.1.ca.b.1151.1		8	155.128	odd	20
2325.1.ca.b.1151.1		8	465.407	even	20
2325.1.ca.b.1151.2		8	155.97	odd	20
2325.1.ca.b.1151.2		8	465.128	even	20

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:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	465.x (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 1.53884i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-1.30902 - 0.951057i) q^{4} +1.00000 q^{5} -1.61803 q^{6} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 1.53884i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-1.30902 - 0.951057i) q^{4} +1.00000 q^{5} -1.61803 q^{6} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.500000 + 1.53884i) q^{10} +(0.500000 - 1.53884i) q^{12} +(0.309017 + 0.951057i) q^{15} +(-1.61803 + 1.17557i) q^{17} +(-0.500000 - 1.53884i) q^{18} +(0.190983 - 0.587785i) q^{19} +(-1.30902 - 0.951057i) q^{20} +(1.30902 - 0.951057i) q^{23} +(0.809017 + 0.587785i) q^{24} +1.00000 q^{25} +(-0.809017 - 0.587785i) q^{27} -1.61803 q^{30} +(0.309017 - 0.951057i) q^{31} +1.00000 q^{32} +(-1.00000 - 3.07768i) q^{34} +1.61803 q^{36} +(0.809017 + 0.587785i) q^{38} +(0.809017 - 0.587785i) q^{40} +(-0.809017 + 0.587785i) q^{45} +(0.809017 + 2.48990i) q^{46} +(-0.500000 - 1.53884i) q^{47} +(0.309017 + 0.951057i) q^{49} +(-0.500000 + 1.53884i) q^{50} +(-1.61803 - 1.17557i) q^{51} +(-0.500000 + 0.363271i) q^{53} +(1.30902 - 0.951057i) q^{54} +0.618034 q^{57} +(0.500000 - 1.53884i) q^{60} +0.618034 q^{61} +(1.30902 + 0.951057i) q^{62} +(-0.500000 + 1.53884i) q^{64} +3.23607 q^{68} +(1.30902 + 0.951057i) q^{69} +(-0.309017 + 0.951057i) q^{72} +(0.309017 + 0.951057i) q^{75} +(-0.809017 + 0.587785i) q^{76} +(-0.500000 + 0.363271i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-0.500000 + 1.53884i) q^{83} +(-1.61803 + 1.17557i) q^{85} +(-0.500000 - 1.53884i) q^{90} -2.61803 q^{92} +1.00000 q^{93} +2.61803 q^{94} +(0.190983 - 0.587785i) q^{95} +(0.309017 + 0.951057i) q^{96} -1.61803 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - q^{3} - 3 q^{4} + 4 q^{5} - 2 q^{6} + q^{8} - q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - q^3 - 3 * q^4 + 4 * q^5 - 2 * q^6 + q^8 - q^9	\( 4 q - 2 q^{2} - q^{3} - 3 q^{4} + 4 q^{5} - 2 q^{6} + q^{8} - q^{9} - 2 q^{10} + 2 q^{12} - q^{15} - 2 q^{17} - 2 q^{18} + 3 q^{19} - 3 q^{20} + 3 q^{23} + q^{24} + 4 q^{25} - q^{27} - 2 q^{30} - q^{31} + 4 q^{32} - 4 q^{34} + 2 q^{36} + q^{38} + q^{40} - q^{45} + q^{46} - 2 q^{47} - q^{49} - 2 q^{50} - 2 q^{51} - 2 q^{53} + 3 q^{54} - 2 q^{57} + 2 q^{60} - 2 q^{61} + 3 q^{62} - 2 q^{64} + 4 q^{68} + 3 q^{69} + q^{72} - q^{75} - q^{76} - 2 q^{79} - q^{81} - 2 q^{83} - 2 q^{85} - 2 q^{90} - 6 q^{92} + 4 q^{93} + 6 q^{94} + 3 q^{95} - q^{96} - 2 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - q^3 - 3 * q^4 + 4 * q^5 - 2 * q^6 + q^8 - q^9 - 2 * q^10 + 2 * q^12 - q^15 - 2 * q^17 - 2 * q^18 + 3 * q^19 - 3 * q^20 + 3 * q^23 + q^24 + 4 * q^25 - q^27 - 2 * q^30 - q^31 + 4 * q^32 - 4 * q^34 + 2 * q^36 + q^38 + q^40 - q^45 + q^46 - 2 * q^47 - q^49 - 2 * q^50 - 2 * q^51 - 2 * q^53 + 3 * q^54 - 2 * q^57 + 2 * q^60 - 2 * q^61 + 3 * q^62 - 2 * q^64 + 4 * q^68 + 3 * q^69 + q^72 - q^75 - q^76 - 2 * q^79 - q^81 - 2 * q^83 - 2 * q^85 - 2 * q^90 - 6 * q^92 + 4 * q^93 + 6 * q^94 + 3 * q^95 - q^96 - 2 * q^98

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