LMFDB - Embedded newform 975.1.cj.a.341.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,1,Mod(146,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 18, 10]))

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

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

chi := DirichletCharacter("975.146");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	975.cj (of order $30$, degree $8$, 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:	$0.486588387317$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{30})$
Coefficient field:	$\Q(\zeta_{60})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1 $ x^16 + x^14 - x^10 - x^8 - x^6 + x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$A_{5}$
Projective field:	Galois closure of 5.1.594140625.2

Embedding invariants

Embedding label			341.1
Root			$0.994522 - 0.104528i$ of defining polynomial
Character	$\chi$	$=$	975.341
Dual form			975.1.cj.a.386.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.614648 - 0.0646021i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(-0.604528 - 0.128496i) q^{4} +(0.587785 - 0.809017i) q^{5} +(0.413545 + 0.459289i) q^{6} +(-0.500000 + 0.866025i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.614648 - 0.0646021i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(-0.604528 - 0.128496i) q^{4} +(0.587785 - 0.809017i) q^{5} +(0.413545 + 0.459289i) q^{6} +(-0.500000 + 0.866025i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +(-0.413545 + 0.459289i) q^{10} +(0.614648 + 0.0646021i) q^{11} +(0.363271 + 0.500000i) q^{12} +(0.809017 - 0.587785i) q^{13} +(0.363271 - 0.500000i) q^{14} +(-0.978148 + 0.207912i) q^{15} +(0.743145 - 0.669131i) q^{17} -0.618034i q^{18} +(0.669131 + 0.743145i) q^{19} +(-0.459289 + 0.413545i) q^{20} +(0.951057 - 0.309017i) q^{21} +(-0.373619 - 0.0794152i) q^{22} +(-0.994522 - 0.104528i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.309017 - 0.951057i) q^{25} +(-0.535233 + 0.309017i) q^{26} +(0.587785 - 0.809017i) q^{27} +(0.413545 - 0.459289i) q^{28} +(0.614648 - 0.0646021i) q^{30} +(-0.866025 - 0.500000i) q^{32} +(-0.413545 - 0.459289i) q^{33} +(-0.500000 + 0.363271i) q^{34} +(0.406737 + 0.913545i) q^{35} +(0.0646021 - 0.614648i) q^{36} +(-0.913545 - 0.406737i) q^{37} +(-0.363271 - 0.500000i) q^{38} +(-0.994522 - 0.104528i) q^{39} +(0.809017 - 0.587785i) q^{40} +(0.406737 - 0.913545i) q^{41} +(-0.604528 + 0.128496i) q^{42} +(0.809017 - 1.40126i) q^{43} +(-0.363271 - 0.118034i) q^{44} +(0.866025 + 0.500000i) q^{45} +(0.604528 + 0.128496i) q^{46} +(-1.53884 + 0.500000i) q^{47} +(0.128496 + 0.604528i) q^{50} -1.00000 q^{51} +(-0.564602 + 0.251377i) q^{52} +(-0.587785 + 0.190983i) q^{53} +(-0.413545 + 0.459289i) q^{54} +(0.413545 - 0.459289i) q^{55} +(-0.743145 + 0.669131i) q^{56} -1.00000i q^{57} +(0.994522 - 0.104528i) q^{59} +0.618034 q^{60} +(0.913545 - 0.406737i) q^{61} +(-0.913545 - 0.406737i) q^{63} +(0.500000 + 0.363271i) q^{64} -1.00000i q^{65} +(0.224514 + 0.309017i) q^{66} +(1.58268 - 0.336408i) q^{67} +(-0.535233 + 0.309017i) q^{68} +(0.669131 + 0.743145i) q^{69} +(-0.190983 - 0.587785i) q^{70} +(-0.207912 + 0.978148i) q^{72} +(0.809017 + 0.587785i) q^{73} +(0.535233 + 0.309017i) q^{74} +(-0.406737 + 0.913545i) q^{75} +(-0.309017 - 0.535233i) q^{76} +(-0.363271 + 0.500000i) q^{77} +(0.604528 + 0.128496i) q^{78} +(-0.978148 + 0.207912i) q^{81} +(-0.309017 + 0.535233i) q^{82} +(0.951057 + 0.309017i) q^{83} +(-0.614648 + 0.0646021i) q^{84} +(-0.104528 - 0.994522i) q^{85} +(-0.587785 + 0.809017i) q^{86} +(0.564602 + 0.251377i) q^{88} +(0.994522 + 0.104528i) q^{89} +(-0.500000 - 0.363271i) q^{90} +(0.104528 + 0.994522i) q^{91} +(0.587785 + 0.190983i) q^{92} +(0.978148 - 0.207912i) q^{94} +(0.994522 - 0.104528i) q^{95} +(0.309017 + 0.951057i) q^{96} +(-1.58268 - 0.336408i) q^{97} +0.618034i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} - 6 q^{6} - 8 q^{7} - 2 q^{9}+O(q^{10}) $ 16 * q - 6 * q^4 - 6 * q^6 - 8 * q^7 - 2 * q^9	$ 16 q - 6 q^{4} - 6 q^{6} - 8 q^{7} - 2 q^{9} + 6 q^{10} + 4 q^{13} + 2 q^{15} + 2 q^{19} + 8 q^{22} - 8 q^{24} + 4 q^{25} - 6 q^{28} + 6 q^{33} - 8 q^{34} - 4 q^{36} - 2 q^{37} + 4 q^{40} - 6 q^{42} + 4 q^{43} + 6 q^{46} - 16 q^{51} - 4 q^{52} + 6 q^{54} - 6 q^{55} - 8 q^{60} + 2 q^{61} - 2 q^{63} + 8 q^{64} + 4 q^{67} + 2 q^{69} - 12 q^{70} + 4 q^{73} + 4 q^{76} + 6 q^{78} + 2 q^{81} + 4 q^{82} + 2 q^{85} + 4 q^{88} - 8 q^{90} - 2 q^{91} - 2 q^{94} - 4 q^{96} - 4 q^{97}+O(q^{100}) $ 16 * q - 6 * q^4 - 6 * q^6 - 8 * q^7 - 2 * q^9 + 6 * q^10 + 4 * q^13 + 2 * q^15 + 2 * q^19 + 8 * q^22 - 8 * q^24 + 4 * q^25 - 6 * q^28 + 6 * q^33 - 8 * q^34 - 4 * q^36 - 2 * q^37 + 4 * q^40 - 6 * q^42 + 4 * q^43 + 6 * q^46 - 16 * q^51 - 4 * q^52 + 6 * q^54 - 6 * q^55 - 8 * q^60 + 2 * q^61 - 2 * q^63 + 8 * q^64 + 4 * q^67 + 2 * q^69 - 12 * q^70 + 4 * q^73 + 4 * q^76 + 6 * q^78 + 2 * q^81 + 4 * q^82 + 2 * q^85 + 4 * q^88 - 8 * q^90 - 2 * q^91 - 2 * q^94 - 4 * q^96 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i	−0.207912	−	0.978148i	$-0.566667\pi$
$2$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i	−0.406737	+	0.913545i	$0.633333\pi$
$3$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$3$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$4$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$5$	0.587785	−	0.809017i	0.587785	−	0.809017i
$5$	0.587785	−	0.809017i	0.587785	−	0.809017i
$6$	0.413545	+	0.459289i	0.413545	+	0.459289i
$7$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$7$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$8$	0.951057	+	0.309017i	0.951057	+	0.309017i
$9$	0.104528	+	0.994522i	0.104528	+	0.994522i
$10$	−0.413545	+	0.459289i	−0.413545	+	0.459289i
$11$	0.614648	+	0.0646021i	0.614648	+	0.0646021i	0.406737	−	0.913545i	$-0.366667\pi$
$11$	0.614648	+	0.0646021i	0.614648	+	0.0646021i	0.207912	+	0.978148i	$0.433333\pi$
$12$	0.363271	+	0.500000i	0.363271	+	0.500000i
$13$	0.809017	−	0.587785i	0.809017	−	0.587785i
$13$	0.809017	−	0.587785i	0.809017	−	0.587785i
$14$	0.363271	−	0.500000i	0.363271	−	0.500000i
$15$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$16$		0			0
$17$	0.743145	−	0.669131i	0.743145	−	0.669131i	−0.207912	−	0.978148i	$-0.566667\pi$
$17$	0.743145	−	0.669131i	0.743145	−	0.669131i	0.951057	+	0.309017i	$0.100000\pi$
$18$		−	0.618034i		−	0.618034i
$19$	0.669131	+	0.743145i	0.669131	+	0.743145i	0.978148	−	0.207912i	$-0.0666667\pi$
$19$	0.669131	+	0.743145i	0.669131	+	0.743145i	−0.309017	+	0.951057i	$0.600000\pi$
$20$	−0.459289	+	0.413545i	−0.459289	+	0.413545i
$21$	0.951057	−	0.309017i	0.951057	−	0.309017i
$22$	−0.373619	−	0.0794152i	−0.373619	−	0.0794152i
$23$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.406737	−	0.913545i	$-0.633333\pi$
$23$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.587785	+	0.809017i	$0.700000\pi$
$24$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$25$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$26$	−0.535233	+	0.309017i	−0.535233	+	0.309017i
$27$	0.587785	−	0.809017i	0.587785	−	0.809017i
$28$	0.413545	−	0.459289i	0.413545	−	0.459289i
$29$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$29$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$30$	0.614648	−	0.0646021i	0.614648	−	0.0646021i
$31$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$31$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$32$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$33$	−0.413545	−	0.459289i	−0.413545	−	0.459289i
$34$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$35$	0.406737	+	0.913545i	0.406737	+	0.913545i
$36$	0.0646021	−	0.614648i	0.0646021	−	0.614648i
$37$	−0.913545	−	0.406737i	−0.913545	−	0.406737i	−0.104528	−	0.994522i	$-0.533333\pi$
$37$	−0.913545	−	0.406737i	−0.913545	−	0.406737i	−0.809017	+	0.587785i	$0.800000\pi$
$38$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$39$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$40$	0.809017	−	0.587785i	0.809017	−	0.587785i
$41$	0.406737	−	0.913545i	0.406737	−	0.913545i	−0.587785	−	0.809017i	$-0.700000\pi$
$41$	0.406737	−	0.913545i	0.406737	−	0.913545i	0.994522	−	0.104528i	$-0.0333333\pi$
$42$	−0.604528	+	0.128496i	−0.604528	+	0.128496i
$43$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$43$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$44$	−0.363271	−	0.118034i	−0.363271	−	0.118034i
$45$	0.866025	+	0.500000i	0.866025	+	0.500000i
$46$	0.604528	+	0.128496i	0.604528	+	0.128496i
$47$	−1.53884	+	0.500000i	−1.53884	+	0.500000i	−0.951057	−	0.309017i	$-0.900000\pi$
$47$	−1.53884	+	0.500000i	−1.53884	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$48$		0			0
$49$		0			0
$50$	0.128496	+	0.604528i	0.128496	+	0.604528i
$51$	−1.00000			−1.00000
$52$	−0.564602	+	0.251377i	−0.564602	+	0.251377i
$53$	−0.587785	+	0.190983i	−0.587785	+	0.190983i	−0.587785	−	0.809017i	$-0.700000\pi$
$53$	−0.587785	+	0.190983i	−0.587785	+	0.190983i			1.00000i	$0.5\pi$
$54$	−0.413545	+	0.459289i	−0.413545	+	0.459289i
$55$	0.413545	−	0.459289i	0.413545	−	0.459289i
$56$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$57$		−	1.00000i		−	1.00000i
$58$		0			0
$59$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.406737	−	0.913545i	$-0.366667\pi$
$59$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.587785	+	0.809017i	$0.300000\pi$
$60$	0.618034			0.618034
$61$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.104528	−	0.994522i	$-0.466667\pi$
$61$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.809017	+	0.587785i	$0.200000\pi$
$62$		0			0
$63$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$64$	0.500000	+	0.363271i	0.500000	+	0.363271i
$65$		−	1.00000i		−	1.00000i
$66$	0.224514	+	0.309017i	0.224514	+	0.309017i
$67$	1.58268	−	0.336408i	1.58268	−	0.336408i	0.669131	−	0.743145i	$-0.266667\pi$
$67$	1.58268	−	0.336408i	1.58268	−	0.336408i	0.913545	+	0.406737i	$0.133333\pi$
$68$	−0.535233	+	0.309017i	−0.535233	+	0.309017i
$69$	0.669131	+	0.743145i	0.669131	+	0.743145i
$70$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$71$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$71$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$72$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$73$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$73$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$74$	0.535233	+	0.309017i	0.535233	+	0.309017i
$75$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$76$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$77$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$78$	0.604528	+	0.128496i	0.604528	+	0.128496i
$79$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$79$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$80$		0			0
$81$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$82$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$83$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.743145	−	0.669131i	$-0.233333\pi$
$83$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.207912	+	0.978148i	$0.433333\pi$
$84$	−0.614648	+	0.0646021i	−0.614648	+	0.0646021i
$85$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$86$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$87$		0			0
$88$	0.564602	+	0.251377i	0.564602	+	0.251377i
$89$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.587785	−	0.809017i	$-0.300000\pi$
$89$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.406737	+	0.913545i	$0.366667\pi$
$90$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$91$	0.104528	+	0.994522i	0.104528	+	0.994522i
$92$	0.587785	+	0.190983i	0.587785	+	0.190983i
$93$		0			0
$94$	0.978148	−	0.207912i	0.978148	−	0.207912i
$95$	0.994522	−	0.104528i	0.994522	−	0.104528i
$96$	0.309017	+	0.951057i	0.309017	+	0.951057i
$97$	−1.58268	−	0.336408i	−1.58268	−	0.336408i	−0.669131	−	0.743145i	$-0.733333\pi$
$97$	−1.58268	−	0.336408i	−1.58268	−	0.336408i	−0.913545	+	0.406737i	$0.866667\pi$
$98$		0			0
$99$			0.618034i			0.618034i
$100$	0.0646021	+	0.614648i	0.0646021	+	0.614648i
$101$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$101$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$102$	0.614648	+	0.0646021i	0.614648	+	0.0646021i
$103$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$103$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$104$	0.951057	−	0.309017i	0.951057	−	0.309017i
$105$	0.309017	−	0.951057i	0.309017	−	0.951057i
$106$	0.373619	−	0.0794152i	0.373619	−	0.0794152i
$107$	−0.535233	+	0.309017i	−0.535233	+	0.309017i	−0.743145	−	0.669131i	$-0.766667\pi$
$107$	−0.535233	+	0.309017i	−0.535233	+	0.309017i	0.207912	+	0.978148i	$0.433333\pi$
$108$	−0.459289	+	0.413545i	−0.459289	+	0.413545i
$109$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$109$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$110$	−0.283856	+	0.255585i	−0.283856	+	0.255585i
$111$	0.406737	+	0.913545i	0.406737	+	0.913545i
$112$		0			0
$113$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$113$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$114$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i
$115$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$116$		0			0
$117$	0.669131	+	0.743145i	0.669131	+	0.743145i
$118$	−0.618034			−0.618034
$119$	0.207912	+	0.978148i	0.207912	+	0.978148i
$120$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$121$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$122$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$123$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$124$		0			0
$125$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$126$	0.535233	+	0.309017i	0.535233	+	0.309017i
$127$	0.104528	−	0.994522i	0.104528	−	0.994522i	−0.809017	−	0.587785i	$-0.800000\pi$
$127$	0.104528	−	0.994522i	0.104528	−	0.994522i	0.913545	−	0.406737i	$-0.133333\pi$
$128$	0.459289	+	0.413545i	0.459289	+	0.413545i
$129$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$130$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i
$131$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$131$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$132$	0.190983	+	0.330792i	0.190983	+	0.330792i
$133$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$134$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$135$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$136$	0.913545	−	0.406737i	0.913545	−	0.406737i
$137$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.406737	−	0.913545i	$-0.366667\pi$
$137$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.587785	+	0.809017i	$0.300000\pi$
$138$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$139$	−1.47815	+	0.658114i	−1.47815	+	0.658114i	−0.978148	−	0.207912i	$-0.933333\pi$
$139$	−1.47815	+	0.658114i	−1.47815	+	0.658114i	−0.500000	+	0.866025i	$0.666667\pi$
$140$	−0.128496	−	0.604528i	−0.128496	−	0.604528i
$141$	1.47815	+	0.658114i	1.47815	+	0.658114i
$142$		0			0
$143$	0.535233	−	0.309017i	0.535233	−	0.309017i
$144$		0			0
$145$		0			0
$146$	−0.459289	−	0.413545i	−0.459289	−	0.413545i
$147$		0			0
$148$	0.500000	+	0.363271i	0.500000	+	0.363271i
$149$	−1.40126	−	0.809017i	−1.40126	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$149$	−1.40126	−	0.809017i	−1.40126	−	0.809017i	−0.994522	+	0.104528i	$0.966667\pi$
$150$	0.309017	−	0.535233i	0.309017	−	0.535233i
$151$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$151$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$152$	0.406737	+	0.913545i	0.406737	+	0.913545i
$153$	0.743145	+	0.669131i	0.743145	+	0.669131i
$154$	0.255585	−	0.283856i	0.255585	−	0.283856i
$155$		0			0
$156$	0.587785	+	0.190983i	0.587785	+	0.190983i
$157$		0			0			−	1.00000i	$-0.5\pi$
$157$		0			0				1.00000i	$0.5\pi$
$158$		0			0
$159$	0.564602	+	0.251377i	0.564602	+	0.251377i
$160$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$161$	0.587785	−	0.809017i	0.587785	−	0.809017i
$162$	0.614648	−	0.0646021i	0.614648	−	0.0646021i
$163$	0.104528	+	0.994522i	0.104528	+	0.994522i	0.913545	+	0.406737i	$0.133333\pi$
$163$	0.104528	+	0.994522i	0.104528	+	0.994522i	−0.809017	+	0.587785i	$0.800000\pi$
$164$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$165$	−0.614648	+	0.0646021i	−0.614648	+	0.0646021i
$166$	−0.564602	−	0.251377i	−0.564602	−	0.251377i
$167$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$167$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$168$	1.00000			1.00000
$169$	0.309017	−	0.951057i	0.309017	−	0.951057i
$170$			0.618034i			0.618034i
$171$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$172$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$173$	0.658114	+	1.47815i	0.658114	+	1.47815i	0.866025	+	0.500000i	$0.166667\pi$
$173$	0.658114	+	1.47815i	0.658114	+	1.47815i	−0.207912	+	0.978148i	$0.566667\pi$
$174$		0			0
$175$	0.978148	+	0.207912i	0.978148	+	0.207912i
$176$		0			0
$177$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$178$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$179$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$179$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$180$	−0.459289	−	0.413545i	−0.459289	−	0.413545i
$181$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$181$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$182$		−	0.618034i		−	0.618034i
$183$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$184$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$185$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$186$		0			0
$187$	0.500000	−	0.363271i	0.500000	−	0.363271i
$188$	0.994522	−	0.104528i	0.994522	−	0.104528i
$189$	0.406737	+	0.913545i	0.406737	+	0.913545i
$190$	−0.618034			−0.618034
$191$	0.614648	−	0.0646021i	0.614648	−	0.0646021i	0.207912	−	0.978148i	$-0.433333\pi$
$191$	0.614648	−	0.0646021i	0.614648	−	0.0646021i	0.406737	+	0.913545i	$0.366667\pi$
$192$	−0.128496	−	0.604528i	−0.128496	−	0.604528i
$193$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$193$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$194$	0.951057	+	0.309017i	0.951057	+	0.309017i
$195$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$196$		0			0
$197$	1.20243	+	1.08268i	1.20243	+	1.08268i	0.994522	+	0.104528i	$0.0333333\pi$
$197$	1.20243	+	1.08268i	1.20243	+	1.08268i	0.207912	+	0.978148i	$0.433333\pi$
$198$	0.0399263	−	0.379874i	0.0399263	−	0.379874i
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$		−	1.00000i		−	1.00000i
$201$	−1.40126	−	0.809017i	−1.40126	−	0.809017i
$202$		0			0
$203$		0			0
$204$	0.604528	+	0.128496i	0.604528	+	0.128496i
$205$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$206$	−0.0794152	−	0.373619i	−0.0794152	−	0.373619i
$207$		−	1.00000i		−	1.00000i
$208$		0			0
$209$	0.363271	+	0.500000i	0.363271	+	0.500000i
$210$	−0.251377	+	0.564602i	−0.251377	+	0.564602i
$211$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$211$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$212$	0.379874	−	0.0399263i	0.379874	−	0.0399263i
$213$		0			0
$214$	0.348943	−	0.155360i	0.348943	−	0.155360i
$215$	−0.658114	−	1.47815i	−0.658114	−	1.47815i
$216$	0.809017	−	0.587785i	0.809017	−	0.587785i
$217$		0			0
$218$		0			0
$219$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$220$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$221$	0.207912	−	0.978148i	0.207912	−	0.978148i
$222$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$223$	0.169131	−	1.60917i	0.169131	−	1.60917i	−0.500000	−	0.866025i	$-0.666667\pi$
$223$	0.169131	−	1.60917i	0.169131	−	1.60917i	0.669131	−	0.743145i	$-0.266667\pi$
$224$	0.866025	−	0.500000i	0.866025	−	0.500000i
$225$	0.913545	−	0.406737i	0.913545	−	0.406737i
$226$		0			0
$227$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$227$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$228$	−0.128496	+	0.604528i	−0.128496	+	0.604528i
$229$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$229$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$230$	0.459289	−	0.413545i	0.459289	−	0.413545i
$231$	0.604528	−	0.128496i	0.604528	−	0.128496i
$232$		0			0
$233$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$233$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$234$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$235$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$236$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i
$237$		0			0
$238$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i
$239$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$239$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$240$		0			0
$241$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$241$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$242$	0.363271	+	0.118034i	0.363271	+	0.118034i
$243$	0.866025	+	0.500000i	0.866025	+	0.500000i
$244$	−0.604528	+	0.128496i	−0.604528	+	0.128496i
$245$		0			0
$246$	0.587785	−	0.190983i	0.587785	−	0.190983i
$247$	0.978148	+	0.207912i	0.978148	+	0.207912i
$248$		0			0
$249$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$250$	0.564602	+	0.251377i	0.564602	+	0.251377i
$251$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$251$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$252$	0.500000	+	0.363271i	0.500000	+	0.363271i
$253$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$254$	−0.128496	+	0.604528i	−0.128496	+	0.604528i
$255$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$256$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$257$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$257$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$258$	0.978148	−	0.207912i	0.978148	−	0.207912i
$259$	0.809017	−	0.587785i	0.809017	−	0.587785i
$260$	−0.128496	+	0.604528i	−0.128496	+	0.604528i
$261$		0			0
$262$	0.913545	+	0.406737i	0.913545	+	0.406737i
$263$	−0.658114	+	1.47815i	−0.658114	+	1.47815i	0.207912	+	0.978148i	$0.433333\pi$
$263$	−0.658114	+	1.47815i	−0.658114	+	1.47815i	−0.866025	+	0.500000i	$0.833333\pi$
$264$	−0.251377	−	0.564602i	−0.251377	−	0.564602i
$265$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$266$	0.614648	−	0.0646021i	0.614648	−	0.0646021i
$267$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$268$	−1.00000			−1.00000
$269$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	−0.951057	−	0.309017i	$-0.900000\pi$
$269$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	0.207912	+	0.978148i	$0.433333\pi$
$270$	0.128496	+	0.604528i	0.128496	+	0.604528i
$271$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$271$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$272$		0			0
$273$	0.587785	−	0.809017i	0.587785	−	0.809017i
$274$	−0.618034			−0.618034
$275$	−0.128496	−	0.604528i	−0.128496	−	0.604528i
$276$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$277$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.104528	−	0.994522i	$-0.466667\pi$
$277$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.809017	+	0.587785i	$0.200000\pi$
$278$	0.951057	−	0.309017i	0.951057	−	0.309017i
$279$		0			0
$280$	0.104528	+	0.994522i	0.104528	+	0.994522i
$281$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.743145	−	0.669131i	$-0.233333\pi$
$281$	0.951057	+	0.309017i	0.951057	+	0.309017i	0.207912	+	0.978148i	$0.433333\pi$
$282$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$283$	−0.604528	+	0.128496i	−0.604528	+	0.128496i	−0.500000	−	0.866025i	$-0.666667\pi$
$283$	−0.604528	+	0.128496i	−0.604528	+	0.128496i	−0.104528	+	0.994522i	$0.533333\pi$
$284$		0			0
$285$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$286$	−0.348943	+	0.155360i	−0.348943	+	0.155360i
$287$	0.587785	+	0.809017i	0.587785	+	0.809017i
$288$	0.406737	−	0.913545i	0.406737	−	0.913545i
$289$		0			0
$290$		0			0
$291$	0.951057	+	1.30902i	0.951057	+	1.30902i
$292$	−0.413545	−	0.459289i	−0.413545	−	0.459289i
$293$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$293$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$294$		0			0
$295$	0.500000	−	0.866025i	0.500000	−	0.866025i
$296$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$297$	0.413545	−	0.459289i	0.413545	−	0.459289i
$298$	0.809017	+	0.587785i	0.809017	+	0.587785i
$299$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$300$	0.363271	−	0.500000i	0.363271	−	0.500000i
$301$	0.809017	+	1.40126i	0.809017	+	1.40126i
$302$	−0.379874	−	0.0399263i	−0.379874	−	0.0399263i
$303$		0			0
$304$		0			0
$305$	0.207912	−	0.978148i	0.207912	−	0.978148i
$306$	−0.413545	−	0.459289i	−0.413545	−	0.459289i
$307$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$307$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$308$	0.283856	−	0.255585i	0.283856	−	0.255585i
$309$	0.251377	−	0.564602i	0.251377	−	0.564602i
$310$		0			0
$311$	−0.951057	+	1.30902i	−0.951057	+	1.30902i			1.00000i	$0.5\pi$
$311$	−0.951057	+	1.30902i	−0.951057	+	1.30902i	−0.951057	+	0.309017i	$0.900000\pi$
$312$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$313$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$313$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$314$		0			0
$315$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$316$		0			0
$317$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$317$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$318$	−0.330792	−	0.190983i	−0.330792	−	0.190983i
$319$		0			0
$320$	0.587785	−	0.190983i	0.587785	−	0.190983i
$321$	0.604528	+	0.128496i	0.604528	+	0.128496i
$322$	−0.413545	+	0.459289i	−0.413545	+	0.459289i
$323$	0.994522	+	0.104528i	0.994522	+	0.104528i
$324$	0.618034			0.618034
$325$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$326$		−	0.618034i		−	0.618034i
$327$		0			0
$328$	0.669131	−	0.743145i	0.669131	−	0.743145i
$329$	0.336408	−	1.58268i	0.336408	−	1.58268i
$330$	0.381966			0.381966
$331$	−0.413545	−	0.459289i	−0.413545	−	0.459289i	0.500000	−	0.866025i	$-0.333333\pi$
$331$	−0.413545	−	0.459289i	−0.413545	−	0.459289i	−0.913545	+	0.406737i	$0.866667\pi$
$332$	−0.535233	−	0.309017i	−0.535233	−	0.309017i
$333$	0.309017	−	0.951057i	0.309017	−	0.951057i
$334$		0			0
$335$	0.658114	−	1.47815i	0.658114	−	1.47815i
$336$		0			0
$337$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$337$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$338$	−0.251377	+	0.564602i	−0.251377	+	0.564602i
$339$		0			0
$340$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i
$341$		0			0
$342$	0.459289	−	0.413545i	0.459289	−	0.413545i
$343$	−1.00000			−1.00000
$344$	1.20243	−	1.08268i	1.20243	−	1.08268i
$345$	0.994522	−	0.104528i	0.994522	−	0.104528i
$346$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$347$	−0.336408	+	1.58268i	−0.336408	+	1.58268i	0.406737	+	0.913545i	$0.366667\pi$
$347$	−0.336408	+	1.58268i	−0.336408	+	1.58268i	−0.743145	+	0.669131i	$0.766667\pi$
$348$		0			0
$349$	0.309017	+	0.535233i	0.309017	+	0.535233i	0.978148	−	0.207912i	$-0.0666667\pi$
$349$	0.309017	+	0.535233i	0.309017	+	0.535233i	−0.669131	+	0.743145i	$0.733333\pi$
$350$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$351$		−	1.00000i		−	1.00000i
$352$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$353$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	0.207912	−	0.978148i	$-0.433333\pi$
$353$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	−0.951057	+	0.309017i	$0.900000\pi$
$354$	0.459289	+	0.413545i	0.459289	+	0.413545i
$355$		0			0
$356$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$357$	0.500000	−	0.866025i	0.500000	−	0.866025i
$358$		0			0
$359$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$359$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$360$	0.669131	+	0.743145i	0.669131	+	0.743145i
$361$		0			0
$362$	0.251377	−	0.564602i	0.251377	−	0.564602i
$363$	0.363271	+	0.500000i	0.363271	+	0.500000i
$364$	0.0646021	−	0.614648i	0.0646021	−	0.614648i
$365$	0.951057	−	0.309017i	0.951057	−	0.309017i
$366$	0.564602	+	0.251377i	0.564602	+	0.251377i
$367$	−0.604528	+	0.128496i	−0.604528	+	0.128496i	−0.500000	−	0.866025i	$-0.666667\pi$
$367$	−0.604528	+	0.128496i	−0.604528	+	0.128496i	−0.104528	+	0.994522i	$0.533333\pi$
$368$		0			0
$369$	0.951057	+	0.309017i	0.951057	+	0.309017i
$370$	0.564602	−	0.251377i	0.564602	−	0.251377i
$371$	0.128496	−	0.604528i	0.128496	−	0.604528i
$372$		0			0
$373$	−1.47815	+	0.658114i	−1.47815	+	0.658114i	−0.978148	−	0.207912i	$-0.933333\pi$
$373$	−1.47815	+	0.658114i	−1.47815	+	0.658114i	−0.500000	+	0.866025i	$0.666667\pi$
$374$	−0.330792	+	0.190983i	−0.330792	+	0.190983i
$375$	0.500000	+	0.866025i	0.500000	+	0.866025i
$376$	−1.61803			−1.61803
$377$		0			0
$378$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$379$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$379$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$380$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i
$381$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$382$	−0.381966			−0.381966
$383$	−0.459289	+	0.413545i	−0.459289	+	0.413545i	−0.866025	−	0.500000i	$-0.833333\pi$
$383$	−0.459289	+	0.413545i	−0.459289	+	0.413545i	0.406737	+	0.913545i	$0.366667\pi$
$384$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i
$385$	0.190983	+	0.587785i	0.190983	+	0.587785i
$386$		0			0
$387$	1.47815	+	0.658114i	1.47815	+	0.658114i
$388$	0.913545	+	0.406737i	0.913545	+	0.406737i
$389$	0.363271	−	0.500000i	0.363271	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$389$	0.363271	−	0.500000i	0.363271	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$390$	0.459289	−	0.413545i	0.459289	−	0.413545i
$391$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$392$		0			0
$393$	0.809017	+	1.40126i	0.809017	+	1.40126i
$394$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$395$		0			0
$396$	0.0794152	−	0.373619i	0.0794152	−	0.373619i
$397$	1.58268	+	0.336408i	1.58268	+	0.336408i	0.913545	−	0.406737i	$-0.133333\pi$
$397$	1.58268	+	0.336408i	1.58268	+	0.336408i	0.669131	+	0.743145i	$0.266667\pi$
$398$		0			0
$399$	0.866025	+	0.500000i	0.866025	+	0.500000i
$400$		0			0
$401$	0.535233	−	0.309017i	0.535233	−	0.309017i	−0.207912	−	0.978148i	$-0.566667\pi$
$401$	0.535233	−	0.309017i	0.535233	−	0.309017i	0.743145	+	0.669131i	$0.233333\pi$
$402$	0.809017	+	0.587785i	0.809017	+	0.587785i
$403$		0			0
$404$		0			0
$405$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$406$		0			0
$407$	−0.535233	−	0.309017i	−0.535233	−	0.309017i
$408$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$409$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$409$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$410$	0.251377	+	0.564602i	0.251377	+	0.564602i
$411$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$412$	−0.0399263	−	0.379874i	−0.0399263	−	0.379874i
$413$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$414$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i
$415$	0.809017	−	0.587785i	0.809017	−	0.587785i
$416$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$417$	1.53884	+	0.500000i	1.53884	+	0.500000i
$418$	−0.190983	−	0.330792i	−0.190983	−	0.330792i
$419$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	−0.951057	−	0.309017i	$-0.900000\pi$
$419$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	0.743145	−	0.669131i	$-0.233333\pi$
$420$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$421$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$421$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$422$		0			0
$423$	−0.658114	−	1.47815i	−0.658114	−	1.47815i
$424$	−0.618034			−0.618034
$425$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$426$		0			0
$427$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$428$	0.363271	−	0.118034i	0.363271	−	0.118034i
$429$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$430$	0.309017	+	0.951057i	0.309017	+	0.951057i
$431$	0.128496	+	0.604528i	0.128496	+	0.604528i	0.994522	+	0.104528i	$0.0333333\pi$
$431$	0.128496	+	0.604528i	0.128496	+	0.604528i	−0.866025	+	0.500000i	$0.833333\pi$
$432$		0			0
$433$	1.08268	+	1.20243i	1.08268	+	1.20243i	0.978148	+	0.207912i	$0.0666667\pi$
$433$	1.08268	+	1.20243i	1.08268	+	1.20243i	0.104528	+	0.994522i	$0.466667\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$438$	0.0646021	+	0.614648i	0.0646021	+	0.614648i
$439$	0.104528	−	0.994522i	0.104528	−	0.994522i	−0.809017	−	0.587785i	$-0.800000\pi$
$439$	0.104528	−	0.994522i	0.104528	−	0.994522i	0.913545	−	0.406737i	$-0.133333\pi$
$440$	0.535233	−	0.309017i	0.535233	−	0.309017i
$441$		0			0
$442$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$443$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$443$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$444$	−0.128496	−	0.604528i	−0.128496	−	0.604528i
$445$	0.669131	−	0.743145i	0.669131	−	0.743145i
$446$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$447$	0.500000	+	1.53884i	0.500000	+	1.53884i
$448$	−0.564602	+	0.251377i	−0.564602	+	0.251377i
$449$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$449$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$450$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$451$	0.309017	−	0.535233i	0.309017	−	0.535233i
$452$		0			0
$453$	−0.459289	−	0.413545i	−0.459289	−	0.413545i
$454$		0			0
$455$	0.866025	+	0.500000i	0.866025	+	0.500000i
$456$	0.309017	−	0.951057i	0.309017	−	0.951057i
$457$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$457$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$458$	−0.128496	−	0.604528i	−0.128496	−	0.604528i
$459$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$460$	0.500000	−	0.363271i	0.500000	−	0.363271i
$461$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$461$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$462$	−0.379874	+	0.0399263i	−0.379874	+	0.0399263i
$463$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$463$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$467$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$468$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$469$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$470$	0.406737	−	0.913545i	0.406737	−	0.913545i
$471$		0			0
$472$	0.978148	+	0.207912i	0.978148	+	0.207912i
$473$	0.587785	−	0.809017i	0.587785	−	0.809017i
$474$		0			0
$475$	0.500000	−	0.866025i	0.500000	−	0.866025i
$476$		−	0.618034i		−	0.618034i
$477$	−0.251377	−	0.564602i	−0.251377	−	0.564602i
$478$		0			0
$479$	0.459289	+	0.413545i	0.459289	+	0.413545i	0.866025	−	0.500000i	$-0.166667\pi$
$479$	0.459289	+	0.413545i	0.459289	+	0.413545i	−0.406737	+	0.913545i	$0.633333\pi$
$480$	0.951057	+	0.309017i	0.951057	+	0.309017i
$481$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$482$		0			0
$483$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$484$	0.348943	+	0.155360i	0.348943	+	0.155360i
$485$	−1.20243	+	1.08268i	−1.20243	+	1.08268i
$486$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$487$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$487$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$488$	0.994522	−	0.104528i	0.994522	−	0.104528i
$489$	0.587785	−	0.809017i	0.587785	−	0.809017i
$490$		0			0
$491$	−0.658114	+	1.47815i	−0.658114	+	1.47815i	0.207912	+	0.978148i	$0.433333\pi$
$491$	−0.658114	+	1.47815i	−0.658114	+	1.47815i	−0.866025	+	0.500000i	$0.833333\pi$
$492$	0.604528	−	0.128496i	0.604528	−	0.128496i
$493$		0			0
$494$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$495$	0.500000	+	0.363271i	0.500000	+	0.363271i
$496$		0			0
$497$		0			0
$498$	0.251377	+	0.564602i	0.251377	+	0.564602i
$499$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$499$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$500$	0.535233	+	0.309017i	0.535233	+	0.309017i
$501$		0			0
$502$	0.500000	+	0.363271i	0.500000	+	0.363271i
$503$	0.128496	−	0.604528i	0.128496	−	0.604528i	−0.866025	−	0.500000i	$-0.833333\pi$
$503$	0.128496	−	0.604528i	0.128496	−	0.604528i	0.994522	−	0.104528i	$-0.0333333\pi$
$504$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$505$		0			0
$506$	0.363271	+	0.118034i	0.363271	+	0.118034i
$507$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$508$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$509$	0.406737	−	0.913545i	0.406737	−	0.913545i	−0.587785	−	0.809017i	$-0.700000\pi$
$509$	0.406737	−	0.913545i	0.406737	−	0.913545i	0.994522	−	0.104528i	$-0.0333333\pi$
$510$	0.413545	−	0.459289i	0.413545	−	0.459289i
$511$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$512$		0			0
$513$	0.994522	−	0.104528i	0.994522	−	0.104528i
$514$		0			0
$515$	0.587785	+	0.190983i	0.587785	+	0.190983i
$516$	0.994522	−	0.104528i	0.994522	−	0.104528i
$517$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$518$	−0.535233	+	0.309017i	−0.535233	+	0.309017i
$519$	0.500000	−	1.53884i	0.500000	−	1.53884i
$520$	0.309017	−	0.951057i	0.309017	−	0.951057i
$521$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.743145	−	0.669131i	$-0.766667\pi$
$521$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.207912	+	0.978148i	$0.566667\pi$
$522$		0			0
$523$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	0.809017	+	0.587785i	$0.200000\pi$
$523$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	−0.913545	+	0.406737i	$0.866667\pi$
$524$	0.866025	+	0.500000i	0.866025	+	0.500000i
$525$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$526$	0.500000	−	0.866025i	0.500000	−	0.866025i
$527$		0			0
$528$		0			0
$529$		0			0
$530$	0.155360	−	0.348943i	0.155360	−	0.348943i
$531$	0.207912	+	0.978148i	0.207912	+	0.978148i
$532$	0.618034			0.618034
$533$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$534$	0.363271	+	0.500000i	0.363271	+	0.500000i
$535$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i
$536$	1.60917	+	0.169131i	1.60917	+	0.169131i
$537$		0			0
$538$	0.500000	−	0.363271i	0.500000	−	0.363271i
$539$		0			0
$540$	0.0646021	+	0.614648i	0.0646021	+	0.614648i
$541$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	−0.913545	−	0.406737i	$-0.866667\pi$
$541$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	0.104528	+	0.994522i	$0.466667\pi$
$542$		0			0
$543$	0.866025	−	0.500000i	0.866025	−	0.500000i
$544$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$545$		0			0
$546$	−0.413545	+	0.459289i	−0.413545	+	0.459289i
$547$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$547$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$548$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i
$549$	0.500000	+	0.866025i	0.500000	+	0.866025i
$550$	0.0399263	+	0.379874i	0.0399263	+	0.379874i
$551$		0			0
$552$	0.406737	+	0.913545i	0.406737	+	0.913545i
$553$		0			0
$554$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$555$	0.978148	+	0.207912i	0.978148	+	0.207912i
$556$	0.978148	−	0.207912i	0.978148	−	0.207912i
$557$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$557$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$558$		0			0
$559$	−0.169131	−	1.60917i	−0.169131	−	1.60917i
$560$		0			0
$561$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i
$562$	−0.564602	−	0.251377i	−0.564602	−	0.251377i
$563$	−0.994522	+	0.104528i	−0.994522	+	0.104528i	−0.587785	−	0.809017i	$-0.700000\pi$
$563$	−0.994522	+	0.104528i	−0.994522	+	0.104528i	−0.406737	+	0.913545i	$0.633333\pi$
$564$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$565$		0			0
$566$	0.379874	−	0.0399263i	0.379874	−	0.0399263i
$567$	0.309017	−	0.951057i	0.309017	−	0.951057i
$568$		0			0
$569$	0.207912	+	0.978148i	0.207912	+	0.978148i	0.951057	+	0.309017i	$0.100000\pi$
$569$	0.207912	+	0.978148i	0.207912	+	0.978148i	−0.743145	+	0.669131i	$0.766667\pi$
$570$	0.459289	+	0.413545i	0.459289	+	0.413545i
$571$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$571$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$572$	−0.363271	+	0.118034i	−0.363271	+	0.118034i
$573$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$574$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$575$	0.207912	+	0.978148i	0.207912	+	0.978148i
$576$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$577$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	0.104528	−	0.994522i	$-0.466667\pi$
$577$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$582$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$583$	−0.373619	+	0.0794152i	−0.373619	+	0.0794152i
$584$	0.587785	+	0.809017i	0.587785	+	0.809017i
$585$	0.994522	−	0.104528i	0.994522	−	0.104528i
$586$		0			0
$587$	−0.658114	+	1.47815i	−0.658114	+	1.47815i	0.207912	+	0.978148i	$0.433333\pi$
$587$	−0.658114	+	1.47815i	−0.658114	+	1.47815i	−0.866025	+	0.500000i	$0.833333\pi$
$588$		0			0
$589$		0			0
$590$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$591$	−0.169131	−	1.60917i	−0.169131	−	1.60917i
$592$		0			0
$593$			1.61803i			1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$593$			1.61803i			1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$594$	−0.283856	+	0.255585i	−0.283856	+	0.255585i
$595$	0.913545	+	0.406737i	0.913545	+	0.406737i
$596$	0.743145	+	0.669131i	0.743145	+	0.669131i
$597$		0			0
$598$	0.564602	−	0.251377i	0.564602	−	0.251377i
$599$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$599$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$600$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$601$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$601$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$602$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$603$	0.500000	+	1.53884i	0.500000	+	1.53884i
$604$	−0.373619	−	0.0794152i	−0.373619	−	0.0794152i
$605$	−0.459289	+	0.413545i	−0.459289	+	0.413545i
$606$		0			0
$607$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$607$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$608$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$609$		0			0
$610$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$611$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$612$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$613$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$613$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$614$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i
$615$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$616$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$617$	−0.459289	+	0.413545i	−0.459289	+	0.413545i	−0.866025	−	0.500000i	$-0.833333\pi$
$617$	−0.459289	+	0.413545i	−0.459289	+	0.413545i	0.406737	+	0.913545i	$0.366667\pi$
$618$	−0.190983	+	0.330792i	−0.190983	+	0.330792i
$619$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$619$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$620$		0			0
$621$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$622$	0.669131	−	0.743145i	0.669131	−	0.743145i
$623$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$626$	0.330792	−	0.190983i	0.330792	−	0.190983i
$627$	0.0646021	−	0.614648i	0.0646021	−	0.614648i
$628$		0			0
$629$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$630$	0.564602	−	0.251377i	0.564602	−	0.251377i
$631$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$631$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$636$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.604528	−	0.128496i	0.604528	−	0.128496i
$641$	1.60917	−	0.169131i	1.60917	−	0.169131i	0.743145	−	0.669131i	$-0.233333\pi$
$641$	1.60917	−	0.169131i	1.60917	−	0.169131i	0.866025	+	0.500000i	$0.166667\pi$
$642$	−0.363271	−	0.118034i	−0.363271	−	0.118034i
$643$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	0.104528	+	0.994522i	$0.466667\pi$
$643$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	−0.913545	+	0.406737i	$0.866667\pi$
$644$	−0.459289	+	0.413545i	−0.459289	+	0.413545i
$645$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$646$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$647$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$647$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$648$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$649$	0.618034			0.618034
$650$	0.459289	+	0.413545i	0.459289	+	0.413545i
$651$		0			0
$652$	0.0646021	−	0.614648i	0.0646021	−	0.614648i
$653$	0.459289	+	0.413545i	0.459289	+	0.413545i	0.866025	−	0.500000i	$-0.166667\pi$
$653$	0.459289	+	0.413545i	0.459289	+	0.413545i	−0.406737	+	0.913545i	$0.633333\pi$
$654$		0			0
$655$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$656$		0			0
$657$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$658$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$659$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$659$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$660$	0.379874	+	0.0399263i	0.379874	+	0.0399263i
$661$	−0.169131	+	1.60917i	−0.169131	+	1.60917i	0.500000	+	0.866025i	$0.333333\pi$
$661$	−0.169131	+	1.60917i	−0.169131	+	1.60917i	−0.669131	+	0.743145i	$0.733333\pi$
$662$	0.224514	+	0.309017i	0.224514	+	0.309017i
$663$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$664$	0.809017	+	0.587785i	0.809017	+	0.587785i
$665$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$666$	−0.251377	+	0.564602i	−0.251377	+	0.564602i
$667$		0			0
$668$		0			0
$669$	−1.20243	+	1.08268i	−1.20243	+	1.08268i
$670$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$671$	0.587785	−	0.190983i	0.587785	−	0.190983i
$672$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$673$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i	0.913545	+	0.406737i	$0.133333\pi$
$673$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i	−0.978148	+	0.207912i	$0.933333\pi$
$674$	0.866025	−	0.500000i	0.866025	−	0.500000i
$675$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$676$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$677$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	−0.994522	−	0.104528i	$-0.966667\pi$
$677$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	0.406737	+	0.913545i	$0.366667\pi$
$678$		0			0
$679$	1.08268	−	1.20243i	1.08268	−	1.20243i
$680$	0.207912	−	0.978148i	0.207912	−	0.978148i
$681$		0			0
$682$		0			0
$683$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	−0.951057	−	0.309017i	$-0.900000\pi$
$683$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	0.207912	+	0.978148i	$0.433333\pi$
$684$	0.500000	−	0.363271i	0.500000	−	0.363271i
$685$	0.500000	−	0.866025i	0.500000	−	0.866025i
$686$	0.614648	+	0.0646021i	0.614648	+	0.0646021i
$687$	0.406737	−	0.913545i	0.406737	−	0.913545i
$688$		0			0
$689$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$690$	−0.618034			−0.618034
$691$	0.564602	+	0.251377i	0.564602	+	0.251377i	0.669131	−	0.743145i	$-0.266667\pi$
$691$	0.564602	+	0.251377i	0.564602	+	0.251377i	−0.104528	+	0.994522i	$0.533333\pi$
$692$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$693$	−0.535233	−	0.309017i	−0.535233	−	0.309017i
$694$	0.309017	−	0.951057i	0.309017	−	0.951057i
$695$	−0.336408	+	1.58268i	−0.336408	+	1.58268i
$696$		0			0
$697$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$698$	−0.155360	−	0.348943i	−0.155360	−	0.348943i
$699$		0			0
$700$	−0.564602	−	0.251377i	−0.564602	−	0.251377i
$701$		−	0.618034i		−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$701$		−	0.618034i		−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$702$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i
$703$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$704$	0.283856	+	0.255585i	0.283856	+	0.255585i
$705$	1.40126	−	0.809017i	1.40126	−	0.809017i
$706$	0.413545	+	0.459289i	0.413545	+	0.459289i
$707$		0			0
$708$	0.413545	+	0.459289i	0.413545	+	0.459289i
$709$	0.104528	+	0.994522i	0.104528	+	0.994522i	0.913545	+	0.406737i	$0.133333\pi$
$709$	0.104528	+	0.994522i	0.104528	+	0.994522i	−0.809017	+	0.587785i	$0.800000\pi$
$710$		0			0
$711$		0			0
$712$	0.913545	+	0.406737i	0.913545	+	0.406737i
$713$		0			0
$714$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$715$	0.0646021	−	0.614648i	0.0646021	−	0.614648i
$716$		0			0
$717$		0			0
$718$	0.190983	+	0.330792i	0.190983	+	0.330792i
$719$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$719$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$720$		0			0
$721$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$722$		0			0
$723$		0			0
$724$	0.309017	−	0.535233i	0.309017	−	0.535233i
$725$		0			0
$726$	−0.190983	−	0.330792i	−0.190983	−	0.330792i
$727$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$727$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$728$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$729$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$730$	−0.604528	+	0.128496i	−0.604528	+	0.128496i
$731$	−0.336408	−	1.58268i	−0.336408	−	1.58268i
$732$	0.535233	+	0.309017i	0.535233	+	0.309017i
$733$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$733$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$734$	0.379874	−	0.0399263i	0.379874	−	0.0399263i
$735$		0			0
$736$	0.809017	+	0.587785i	0.809017	+	0.587785i
$737$	0.994522	−	0.104528i	0.994522	−	0.104528i
$738$	−0.564602	−	0.251377i	−0.564602	−	0.251377i
$739$	0.0646021	−	0.614648i	0.0646021	−	0.614648i	−0.913545	−	0.406737i	$-0.866667\pi$
$739$	0.0646021	−	0.614648i	0.0646021	−	0.614648i	0.978148	−	0.207912i	$-0.0666667\pi$
$740$	0.587785	−	0.190983i	0.587785	−	0.190983i
$741$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$742$	−0.118034	+	0.363271i	−0.118034	+	0.363271i
$743$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$743$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$744$		0			0
$745$	−1.47815	+	0.658114i	−1.47815	+	0.658114i
$746$	0.951057	−	0.309017i	0.951057	−	0.309017i
$747$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$748$	−0.348943	+	0.155360i	−0.348943	+	0.155360i
$749$		−	0.618034i		−	0.618034i
$750$	−0.251377	−	0.564602i	−0.251377	−	0.564602i
$751$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$751$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$752$		0			0
$753$	0.309017	+	0.951057i	0.309017	+	0.951057i
$754$		0			0
$755$	0.363271	−	0.500000i	0.363271	−	0.500000i
$756$	−0.128496	−	0.604528i	−0.128496	−	0.604528i
$757$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$757$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$758$		0			0
$759$	0.363271	+	0.500000i	0.363271	+	0.500000i
$760$	0.978148	+	0.207912i	0.978148	+	0.207912i
$761$	0.406737	+	0.913545i	0.406737	+	0.913545i	0.994522	+	0.104528i	$0.0333333\pi$
$761$	0.406737	+	0.913545i	0.406737	+	0.913545i	−0.587785	+	0.809017i	$0.700000\pi$
$762$	0.500000	−	0.363271i	0.500000	−	0.363271i
$763$		0			0
$764$	−0.379874	−	0.0399263i	−0.379874	−	0.0399263i
$765$	0.978148	−	0.207912i	0.978148	−	0.207912i
$766$	0.309017	−	0.224514i	0.309017	−	0.224514i
$767$	0.743145	−	0.669131i	0.743145	−	0.669131i
$768$			1.00000i			1.00000i
$769$	−1.58268	+	0.336408i	−1.58268	+	0.336408i	−0.913545	−	0.406737i	$-0.866667\pi$
$769$	−1.58268	+	0.336408i	−1.58268	+	0.336408i	−0.669131	+	0.743145i	$0.733333\pi$
$770$	−0.0794152	−	0.373619i	−0.0794152	−	0.373619i
$771$		0			0
$772$		0			0
$773$	0.658114	+	1.47815i	0.658114	+	1.47815i	0.866025	+	0.500000i	$0.166667\pi$
$773$	0.658114	+	1.47815i	0.658114	+	1.47815i	−0.207912	+	0.978148i	$0.566667\pi$
$774$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$775$		0			0
$776$	−1.40126	−	0.809017i	−1.40126	−	0.809017i
$777$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$778$	−0.255585	+	0.283856i	−0.255585	+	0.283856i
$779$	0.951057	−	0.309017i	0.951057	−	0.309017i
$780$	0.500000	−	0.363271i	0.500000	−	0.363271i
$781$		0			0
$782$	0.535233	−	0.309017i	0.535233	−	0.309017i
$783$		0			0
$784$		0			0
$785$		0			0
$786$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$787$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	−0.913545	−	0.406737i	$-0.866667\pi$
$787$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	0.809017	−	0.587785i	$-0.200000\pi$
$788$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$789$	1.47815	−	0.658114i	1.47815	−	0.658114i
$790$		0			0
$791$		0			0
$792$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$793$	0.500000	−	0.866025i	0.500000	−	0.866025i
$794$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$795$	0.535233	−	0.309017i	0.535233	−	0.309017i
$796$		0			0
$797$	−0.128496	+	0.604528i	−0.128496	+	0.604528i	0.866025	+	0.500000i	$0.166667\pi$
$797$	−0.128496	+	0.604528i	−0.128496	+	0.604528i	−0.994522	+	0.104528i	$0.966667\pi$
$798$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$799$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$800$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$801$			1.00000i			1.00000i
$802$	−0.348943	+	0.155360i	−0.348943	+	0.155360i
$803$	0.459289	+	0.413545i	0.459289	+	0.413545i
$804$	0.743145	+	0.669131i	0.743145	+	0.669131i
$805$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$806$		0			0
$807$	1.00000			1.00000
$808$		0			0
$809$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$809$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$810$	0.309017	−	0.535233i	0.309017	−	0.535233i
$811$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	0.104528	−	0.994522i	$-0.466667\pi$
$811$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$812$		0			0
$813$		0			0
$814$	0.309017	+	0.224514i	0.309017	+	0.224514i
$815$	0.866025	+	0.500000i	0.866025	+	0.500000i
$816$		0			0
$817$	1.58268	−	0.336408i	1.58268	−	0.336408i
$818$		0			0
$819$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$820$	0.190983	+	0.587785i	0.190983	+	0.587785i
$821$	0.459289	+	0.413545i	0.459289	+	0.413545i	0.866025	−	0.500000i	$-0.166667\pi$
$821$	0.459289	+	0.413545i	0.459289	+	0.413545i	−0.406737	+	0.913545i	$0.633333\pi$
$822$	0.459289	+	0.413545i	0.459289	+	0.413545i
$823$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.809017	−	0.587785i	$-0.800000\pi$
$823$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.104528	+	0.994522i	$0.533333\pi$
$824$			0.618034i			0.618034i
$825$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$826$	0.309017	−	0.535233i	0.309017	−	0.535233i
$827$	0.363271	−	0.500000i	0.363271	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$827$	0.363271	−	0.500000i	0.363271	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$828$	−0.128496	+	0.604528i	−0.128496	+	0.604528i
$829$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$829$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$830$	−0.535233	+	0.309017i	−0.535233	+	0.309017i
$831$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$832$	0.618034			0.618034
$833$		0			0
$834$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$835$		0			0
$836$	−0.155360	−	0.348943i	−0.155360	−	0.348943i
$837$		0			0
$838$	0.0646021	+	0.614648i	0.0646021	+	0.614648i
$839$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$839$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$840$	0.587785	−	0.809017i	0.587785	−	0.809017i
$841$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$842$	0.128496	+	0.604528i	0.128496	+	0.604528i
$843$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$844$		0			0
$845$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$846$	0.309017	+	0.951057i	0.309017	+	0.951057i
$847$	0.413545	−	0.459289i	0.413545	−	0.459289i
$848$		0			0
$849$	0.535233	+	0.309017i	0.535233	+	0.309017i
$850$	0.500000	+	0.363271i	0.500000	+	0.363271i
$851$	0.866025	+	0.500000i	0.866025	+	0.500000i
$852$		0			0
$853$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$853$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$854$	0.128496	−	0.604528i	0.128496	−	0.604528i
$855$	0.207912	+	0.978148i	0.207912	+	0.978148i
$856$	−0.604528	+	0.128496i	−0.604528	+	0.128496i
$857$		−	0.618034i		−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$857$		−	0.618034i		−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$858$	0.363271	+	0.118034i	0.363271	+	0.118034i
$859$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$859$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$860$	0.207912	+	0.978148i	0.207912	+	0.978148i
$861$	0.104528	−	0.994522i	0.104528	−	0.994522i
$862$	−0.0399263	−	0.379874i	−0.0399263	−	0.379874i
$863$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$863$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$864$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$865$	1.58268	+	0.336408i	1.58268	+	0.336408i
$866$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	1.08268	−	1.20243i	1.08268	−	1.20243i
$872$		0			0
$873$	0.169131	−	1.60917i	0.169131	−	1.60917i
$874$	0.309017	+	0.535233i	0.309017	+	0.535233i
$875$	0.743145	−	0.669131i	0.743145	−	0.669131i
$876$			0.618034i			0.618034i
$877$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.104528	−	0.994522i	$-0.466667\pi$
$877$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.809017	+	0.587785i	$0.200000\pi$
$878$	−0.128496	+	0.604528i	−0.128496	+	0.604528i
$879$		0			0
$880$		0			0
$881$	0.207912	+	0.978148i	0.207912	+	0.978148i	0.951057	+	0.309017i	$0.100000\pi$
$881$	0.207912	+	0.978148i	0.207912	+	0.978148i	−0.743145	+	0.669131i	$0.766667\pi$
$882$		0			0
$883$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$883$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$884$	−0.251377	+	0.564602i	−0.251377	+	0.564602i
$885$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$886$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i
$887$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$887$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$888$	0.104528	+	0.994522i	0.104528	+	0.994522i
$889$	0.809017	+	0.587785i	0.809017	+	0.587785i
$890$	−0.459289	+	0.413545i	−0.459289	+	0.413545i
$891$	−0.614648	+	0.0646021i	−0.614648	+	0.0646021i
$892$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$893$	−1.40126	−	0.809017i	−1.40126	−	0.809017i
$894$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$895$		0			0
$896$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$897$	0.978148	+	0.207912i	0.978148	+	0.207912i
$898$		0			0
$899$		0			0
$900$	−0.604528	+	0.128496i	−0.604528	+	0.128496i
$901$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$902$	−0.224514	+	0.309017i	−0.224514	+	0.309017i
$903$	0.336408	−	1.58268i	0.336408	−	1.58268i
$904$		0			0
$905$	0.587785	+	0.809017i	0.587785	+	0.809017i
$906$	0.255585	+	0.283856i	0.255585	+	0.283856i
$907$	0.309017	+	0.535233i	0.309017	+	0.535233i	0.978148	−	0.207912i	$-0.0666667\pi$
$907$	0.309017	+	0.535233i	0.309017	+	0.535233i	−0.669131	+	0.743145i	$0.733333\pi$
$908$		0			0
$909$		0			0
$910$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$911$	0.587785	−	0.809017i	0.587785	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$911$	0.587785	−	0.809017i	0.587785	−	0.809017i	0.994522	+	0.104528i	$0.0333333\pi$
$912$		0			0
$913$	0.564602	+	0.251377i	0.564602	+	0.251377i
$914$	0.155360	+	0.348943i	0.155360	+	0.348943i
$915$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$916$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i
$917$	1.20243	−	1.08268i	1.20243	−	1.08268i
$918$			0.618034i			0.618034i
$919$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$919$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$920$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$921$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$922$		0			0
$923$		0			0
$924$	−0.381966			−0.381966
$925$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$926$		0			0
$927$	−0.564602	+	0.251377i	−0.564602	+	0.251377i
$928$		0			0
$929$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$929$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	1.58268	−	0.336408i	1.58268	−	0.336408i
$934$		0			0
$935$		−	0.618034i		−	0.618034i
$936$	0.406737	+	0.913545i	0.406737	+	0.913545i
$937$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$937$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$938$	0.406737	−	0.913545i	0.406737	−	0.913545i
$939$	0.614648	+	0.0646021i	0.614648	+	0.0646021i
$940$	0.500000	−	0.866025i	0.500000	−	0.866025i
$941$	0.587785	+	0.809017i	0.587785	+	0.809017i	0.994522	−	0.104528i	$-0.0333333\pi$
$941$	0.587785	+	0.809017i	0.587785	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$942$		0			0
$943$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$944$		0			0
$945$	0.978148	+	0.207912i	0.978148	+	0.207912i
$946$	−0.413545	+	0.459289i	−0.413545	+	0.459289i
$947$	−1.20243	−	1.08268i	−1.20243	−	1.08268i	−0.994522	−	0.104528i	$-0.966667\pi$
$947$	−1.20243	−	1.08268i	−1.20243	−	1.08268i	−0.207912	−	0.978148i	$-0.566667\pi$
$948$		0			0
$949$	1.00000			1.00000
$950$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$951$		0			0
$952$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$953$	0.336408	−	1.58268i	0.336408	−	1.58268i	−0.406737	−	0.913545i	$-0.633333\pi$
$953$	0.336408	−	1.58268i	0.336408	−	1.58268i	0.743145	−	0.669131i	$-0.233333\pi$
$954$	0.118034	+	0.363271i	0.118034	+	0.363271i
$955$	0.309017	−	0.535233i	0.309017	−	0.535233i
$956$		0			0
$957$		0			0
$958$	−0.255585	−	0.283856i	−0.255585	−	0.283856i
$959$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$960$	−0.564602	−	0.251377i	−0.564602	−	0.251377i
$961$	0.809017	+	0.587785i	0.809017	+	0.587785i
$962$	0.614648	−	0.0646021i	0.614648	−	0.0646021i
$963$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$964$		0			0
$965$		0			0
$966$	0.614648	−	0.0646021i	0.614648	−	0.0646021i
$967$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$967$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$968$	−0.535233	−	0.309017i	−0.535233	−	0.309017i
$969$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$970$	0.809017	−	0.587785i	0.809017	−	0.587785i
$971$	0.207912	−	0.978148i	0.207912	−	0.978148i	−0.743145	−	0.669131i	$-0.766667\pi$
$971$	0.207912	−	0.978148i	0.207912	−	0.978148i	0.951057	−	0.309017i	$-0.100000\pi$
$972$	−0.459289	−	0.413545i	−0.459289	−	0.413545i
$973$	0.169131	−	1.60917i	0.169131	−	1.60917i
$974$		0			0
$975$	0.207912	+	0.978148i	0.207912	+	0.978148i
$976$		0			0
$977$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.587785	−	0.809017i	$-0.300000\pi$
$977$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.406737	+	0.913545i	$0.366667\pi$
$978$	−0.413545	+	0.459289i	−0.413545	+	0.459289i
$979$	0.604528	+	0.128496i	0.604528	+	0.128496i
$980$		0			0
$981$		0			0
$982$	0.500000	−	0.866025i	0.500000	−	0.866025i
$983$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$983$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.587785	+	0.809017i	$0.300000\pi$
$984$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$985$	1.58268	−	0.336408i	1.58268	−	0.336408i
$986$		0			0
$987$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$988$	−0.564602	−	0.251377i	−0.564602	−	0.251377i
$989$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$990$	−0.283856	−	0.255585i	−0.283856	−	0.255585i
$991$	−1.47815	−	0.658114i	−1.47815	−	0.658114i	−0.500000	−	0.866025i	$-0.666667\pi$
$991$	−1.47815	−	0.658114i	−1.47815	−	0.658114i	−0.978148	+	0.207912i	$0.933333\pi$
$992$		0			0
$993$			0.618034i			0.618034i
$994$		0			0
$995$		0			0
$996$	0.190983	+	0.587785i	0.190983	+	0.587785i
$997$	−0.604528	−	0.128496i	−0.604528	−	0.128496i	−0.104528	−	0.994522i	$-0.533333\pi$
$997$	−0.604528	−	0.128496i	−0.604528	−	0.128496i	−0.500000	+	0.866025i	$0.666667\pi$
$998$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i
$999$	−0.866025	+	0.500000i	−0.866025	+	0.500000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.1.cj.a.341.1	yes	16
3.2	odd	2	inner	975.1.cj.a.341.2	yes	16
13.9	even	3	inner	975.1.cj.a.191.2	yes	16
25.11	even	5	inner	975.1.cj.a.536.1	yes	16
39.35	odd	6	inner	975.1.cj.a.191.1	✓	16
75.11	odd	10	inner	975.1.cj.a.536.2	yes	16
325.61	even	15	inner	975.1.cj.a.386.2	yes	16
975.386	odd	30	inner	975.1.cj.a.386.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.1.cj.a.191.1	✓	16	39.35	odd	6	inner
975.1.cj.a.191.2	yes	16	13.9	even	3	inner
975.1.cj.a.341.1	yes	16	1.1	even	1	trivial
975.1.cj.a.341.2	yes	16	3.2	odd	2	inner
975.1.cj.a.386.1	yes	16	975.386	odd	30	inner
975.1.cj.a.386.2	yes	16	325.61	even	15	inner
975.1.cj.a.536.1	yes	16	25.11	even	5	inner
975.1.cj.a.536.2	yes	16	75.11	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	975.cj (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.614648 - 0.0646021i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(-0.604528 - 0.128496i) q^{4} +(0.587785 - 0.809017i) q^{5} +(0.413545 + 0.459289i) q^{6} +(-0.500000 + 0.866025i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.614648 - 0.0646021i) q^{2} +(-0.743145 - 0.669131i) q^{3} +(-0.604528 - 0.128496i) q^{4} +(0.587785 - 0.809017i) q^{5} +(0.413545 + 0.459289i) q^{6} +(-0.500000 + 0.866025i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.104528 + 0.994522i) q^{9} +(-0.413545 + 0.459289i) q^{10} +(0.614648 + 0.0646021i) q^{11} +(0.363271 + 0.500000i) q^{12} +(0.809017 - 0.587785i) q^{13} +(0.363271 - 0.500000i) q^{14} +(-0.978148 + 0.207912i) q^{15} +(0.743145 - 0.669131i) q^{17} -0.618034i q^{18} +(0.669131 + 0.743145i) q^{19} +(-0.459289 + 0.413545i) q^{20} +(0.951057 - 0.309017i) q^{21} +(-0.373619 - 0.0794152i) q^{22} +(-0.994522 - 0.104528i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.309017 - 0.951057i) q^{25} +(-0.535233 + 0.309017i) q^{26} +(0.587785 - 0.809017i) q^{27} +(0.413545 - 0.459289i) q^{28} +(0.614648 - 0.0646021i) q^{30} +(-0.866025 - 0.500000i) q^{32} +(-0.413545 - 0.459289i) q^{33} +(-0.500000 + 0.363271i) q^{34} +(0.406737 + 0.913545i) q^{35} +(0.0646021 - 0.614648i) q^{36} +(-0.913545 - 0.406737i) q^{37} +(-0.363271 - 0.500000i) q^{38} +(-0.994522 - 0.104528i) q^{39} +(0.809017 - 0.587785i) q^{40} +(0.406737 - 0.913545i) q^{41} +(-0.604528 + 0.128496i) q^{42} +(0.809017 - 1.40126i) q^{43} +(-0.363271 - 0.118034i) q^{44} +(0.866025 + 0.500000i) q^{45} +(0.604528 + 0.128496i) q^{46} +(-1.53884 + 0.500000i) q^{47} +(0.128496 + 0.604528i) q^{50} -1.00000 q^{51} +(-0.564602 + 0.251377i) q^{52} +(-0.587785 + 0.190983i) q^{53} +(-0.413545 + 0.459289i) q^{54} +(0.413545 - 0.459289i) q^{55} +(-0.743145 + 0.669131i) q^{56} -1.00000i q^{57} +(0.994522 - 0.104528i) q^{59} +0.618034 q^{60} +(0.913545 - 0.406737i) q^{61} +(-0.913545 - 0.406737i) q^{63} +(0.500000 + 0.363271i) q^{64} -1.00000i q^{65} +(0.224514 + 0.309017i) q^{66} +(1.58268 - 0.336408i) q^{67} +(-0.535233 + 0.309017i) q^{68} +(0.669131 + 0.743145i) q^{69} +(-0.190983 - 0.587785i) q^{70} +(-0.207912 + 0.978148i) q^{72} +(0.809017 + 0.587785i) q^{73} +(0.535233 + 0.309017i) q^{74} +(-0.406737 + 0.913545i) q^{75} +(-0.309017 - 0.535233i) q^{76} +(-0.363271 + 0.500000i) q^{77} +(0.604528 + 0.128496i) q^{78} +(-0.978148 + 0.207912i) q^{81} +(-0.309017 + 0.535233i) q^{82} +(0.951057 + 0.309017i) q^{83} +(-0.614648 + 0.0646021i) q^{84} +(-0.104528 - 0.994522i) q^{85} +(-0.587785 + 0.809017i) q^{86} +(0.564602 + 0.251377i) q^{88} +(0.994522 + 0.104528i) q^{89} +(-0.500000 - 0.363271i) q^{90} +(0.104528 + 0.994522i) q^{91} +(0.587785 + 0.190983i) q^{92} +(0.978148 - 0.207912i) q^{94} +(0.994522 - 0.104528i) q^{95} +(0.309017 + 0.951057i) q^{96} +(-1.58268 - 0.336408i) q^{97} +0.618034i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} - 6 q^{6} - 8 q^{7} - 2 q^{9}+O(q^{10}) \) 16 * q - 6 * q^4 - 6 * q^6 - 8 * q^7 - 2 * q^9	\( 16 q - 6 q^{4} - 6 q^{6} - 8 q^{7} - 2 q^{9} + 6 q^{10} + 4 q^{13} + 2 q^{15} + 2 q^{19} + 8 q^{22} - 8 q^{24} + 4 q^{25} - 6 q^{28} + 6 q^{33} - 8 q^{34} - 4 q^{36} - 2 q^{37} + 4 q^{40} - 6 q^{42} + 4 q^{43} + 6 q^{46} - 16 q^{51} - 4 q^{52} + 6 q^{54} - 6 q^{55} - 8 q^{60} + 2 q^{61} - 2 q^{63} + 8 q^{64} + 4 q^{67} + 2 q^{69} - 12 q^{70} + 4 q^{73} + 4 q^{76} + 6 q^{78} + 2 q^{81} + 4 q^{82} + 2 q^{85} + 4 q^{88} - 8 q^{90} - 2 q^{91} - 2 q^{94} - 4 q^{96} - 4 q^{97}+O(q^{100}) \) 16 * q - 6 * q^4 - 6 * q^6 - 8 * q^7 - 2 * q^9 + 6 * q^10 + 4 * q^13 + 2 * q^15 + 2 * q^19 + 8 * q^22 - 8 * q^24 + 4 * q^25 - 6 * q^28 + 6 * q^33 - 8 * q^34 - 4 * q^36 - 2 * q^37 + 4 * q^40 - 6 * q^42 + 4 * q^43 + 6 * q^46 - 16 * q^51 - 4 * q^52 + 6 * q^54 - 6 * q^55 - 8 * q^60 + 2 * q^61 - 2 * q^63 + 8 * q^64 + 4 * q^67 + 2 * q^69 - 12 * q^70 + 4 * q^73 + 4 * q^76 + 6 * q^78 + 2 * q^81 + 4 * q^82 + 2 * q^85 + 4 * q^88 - 8 * q^90 - 2 * q^91 - 2 * q^94 - 4 * q^96 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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