LMFDB - Embedded newform 21.2.e.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,2,Mod(4,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("21.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	21.e (of order $3$, degree $2$, 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:	$0.167685844245$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	21.4
Dual form			21.2.e.a.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.00000 + 1.73205i) q^{5} +2.00000 q^{6} +(-2.50000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.00000 + 1.73205i) q^{5} +2.00000 q^{6} +(-2.50000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-1.00000 - 1.73205i) q^{12} +1.00000 q^{13} +(1.00000 + 5.19615i) q^{14} -2.00000 q^{15} +(2.00000 + 3.46410i) q^{16} +(-1.00000 + 1.73205i) q^{18} +(-0.500000 - 0.866025i) q^{19} -4.00000 q^{20} +(2.00000 - 1.73205i) q^{21} -4.00000 q^{22} +(0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} +1.00000 q^{27} +(4.00000 - 3.46410i) q^{28} +4.00000 q^{29} +(2.00000 + 3.46410i) q^{30} +(-4.50000 + 7.79423i) q^{31} +(4.00000 - 6.92820i) q^{32} +(1.00000 + 1.73205i) q^{33} +(-1.00000 - 5.19615i) q^{35} +2.00000 q^{36} +(-1.50000 - 2.59808i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(-0.500000 + 0.866025i) q^{39} -10.0000 q^{41} +(-5.00000 - 1.73205i) q^{42} +5.00000 q^{43} +(2.00000 + 3.46410i) q^{44} +(1.00000 - 1.73205i) q^{45} +(3.00000 + 5.19615i) q^{47} -4.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -2.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(-1.00000 - 1.73205i) q^{54} +4.00000 q^{55} +1.00000 q^{57} +(-4.00000 - 6.92820i) q^{58} +(6.00000 - 10.3923i) q^{59} +(2.00000 - 3.46410i) q^{60} +(-5.00000 - 8.66025i) q^{61} +18.0000 q^{62} +(0.500000 + 2.59808i) q^{63} -8.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(2.00000 - 3.46410i) q^{66} +(2.50000 - 4.33013i) q^{67} +(-8.00000 + 6.92820i) q^{70} -6.00000 q^{71} +(1.50000 - 2.59808i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(0.500000 + 0.866025i) q^{75} +2.00000 q^{76} +(-4.00000 + 3.46410i) q^{77} +2.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(-4.00000 + 6.92820i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(10.0000 + 17.3205i) q^{82} +6.00000 q^{83} +(1.00000 + 5.19615i) q^{84} +(-5.00000 - 8.66025i) q^{86} +(-2.00000 + 3.46410i) q^{87} +(-8.00000 - 13.8564i) q^{89} -4.00000 q^{90} +(-2.50000 - 0.866025i) q^{91} +(-4.50000 - 7.79423i) q^{93} +(6.00000 - 10.3923i) q^{94} +(1.00000 - 1.73205i) q^{95} +(4.00000 + 6.92820i) q^{96} -6.00000 q^{97} +(2.00000 - 13.8564i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} - 5 q^{7} - q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 - 2 * q^4 + 2 * q^5 + 4 * q^6 - 5 * q^7 - q^9	$ 2 q - 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} - 5 q^{7} - q^{9} + 4 q^{10} + 2 q^{11} - 2 q^{12} + 2 q^{13} + 2 q^{14} - 4 q^{15} + 4 q^{16} - 2 q^{18} - q^{19} - 8 q^{20} + 4 q^{21} - 8 q^{22} + q^{25} - 2 q^{26} + 2 q^{27} + 8 q^{28} + 8 q^{29} + 4 q^{30} - 9 q^{31} + 8 q^{32} + 2 q^{33} - 2 q^{35} + 4 q^{36} - 3 q^{37} - 2 q^{38} - q^{39} - 20 q^{41} - 10 q^{42} + 10 q^{43} + 4 q^{44} + 2 q^{45} + 6 q^{47} - 8 q^{48} + 11 q^{49} - 4 q^{50} - 2 q^{52} - 12 q^{53} - 2 q^{54} + 8 q^{55} + 2 q^{57} - 8 q^{58} + 12 q^{59} + 4 q^{60} - 10 q^{61} + 36 q^{62} + q^{63} - 16 q^{64} + 2 q^{65} + 4 q^{66} + 5 q^{67} - 16 q^{70} - 12 q^{71} + 3 q^{73} - 6 q^{74} + q^{75} + 4 q^{76} - 8 q^{77} + 4 q^{78} + q^{79} - 8 q^{80} - q^{81} + 20 q^{82} + 12 q^{83} + 2 q^{84} - 10 q^{86} - 4 q^{87} - 16 q^{89} - 8 q^{90} - 5 q^{91} - 9 q^{93} + 12 q^{94} + 2 q^{95} + 8 q^{96} - 12 q^{97} + 4 q^{98} - 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - q^3 - 2 * q^4 + 2 * q^5 + 4 * q^6 - 5 * q^7 - q^9 + 4 * q^10 + 2 * q^11 - 2 * q^12 + 2 * q^13 + 2 * q^14 - 4 * q^15 + 4 * q^16 - 2 * q^18 - q^19 - 8 * q^20 + 4 * q^21 - 8 * q^22 + q^25 - 2 * q^26 + 2 * q^27 + 8 * q^28 + 8 * q^29 + 4 * q^30 - 9 * q^31 + 8 * q^32 + 2 * q^33 - 2 * q^35 + 4 * q^36 - 3 * q^37 - 2 * q^38 - q^39 - 20 * q^41 - 10 * q^42 + 10 * q^43 + 4 * q^44 + 2 * q^45 + 6 * q^47 - 8 * q^48 + 11 * q^49 - 4 * q^50 - 2 * q^52 - 12 * q^53 - 2 * q^54 + 8 * q^55 + 2 * q^57 - 8 * q^58 + 12 * q^59 + 4 * q^60 - 10 * q^61 + 36 * q^62 + q^63 - 16 * q^64 + 2 * q^65 + 4 * q^66 + 5 * q^67 - 16 * q^70 - 12 * q^71 + 3 * q^73 - 6 * q^74 + q^75 + 4 * q^76 - 8 * q^77 + 4 * q^78 + q^79 - 8 * q^80 - q^81 + 20 * q^82 + 12 * q^83 + 2 * q^84 - 10 * q^86 - 4 * q^87 - 16 * q^89 - 8 * q^90 - 5 * q^91 - 9 * q^93 + 12 * q^94 + 2 * q^95 + 8 * q^96 - 12 * q^97 + 4 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000	−	1.73205i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	−1.00000	−	1.73205i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	0.998203	−	0.0599153i	$-0.0190830\pi$
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	−0.550990	+	0.834512i	$0.685750\pi$
$6$	2.00000			0.816497
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	2.00000	−	3.46410i	0.632456	−	1.09545i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	−1.00000	−	1.73205i	−0.288675	−	0.500000i
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$	1.00000	+	5.19615i	0.267261	+	1.38873i
$15$	−2.00000			−0.516398
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	−1.00000	+	1.73205i	−0.235702	+	0.408248i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−4.00000			−0.894427
$21$	2.00000	−	1.73205i	0.436436	−	0.377964i
$22$	−4.00000			−0.852803
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$	1.00000			0.192450
$28$	4.00000	−	3.46410i	0.755929	−	0.654654i
$29$	4.00000			0.742781			0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000			0.742781			0.371391	+	0.928477i	$0.378881\pi$
$30$	2.00000	+	3.46410i	0.365148	+	0.632456i
$31$	−4.50000	+	7.79423i	−0.808224	+	1.39988i	0.105869	+	0.994380i	$0.466238\pi$
$31$	−4.50000	+	7.79423i	−0.808224	+	1.39988i	−0.914093	+	0.405505i	$0.867096\pi$
$32$	4.00000	−	6.92820i	0.707107	−	1.22474i
$33$	1.00000	+	1.73205i	0.174078	+	0.301511i
$34$		0			0
$35$	−1.00000	−	5.19615i	−0.169031	−	0.878310i
$36$	2.00000			0.333333
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$	−1.00000	+	1.73205i	−0.162221	+	0.280976i
$39$	−0.500000	+	0.866025i	−0.0800641	+	0.138675i
$40$		0			0
$41$	−10.0000			−1.56174			−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000			−1.56174			−0.780869	+	0.624695i	$0.785223\pi$
$42$	−5.00000	−	1.73205i	−0.771517	−	0.267261i
$43$	5.00000			0.762493			0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000			0.762493			0.381246	+	0.924473i	$0.375495\pi$
$44$	2.00000	+	3.46410i	0.301511	+	0.522233i
$45$	1.00000	−	1.73205i	0.149071	−	0.258199i
$46$		0			0
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$	−4.00000			−0.577350
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	−2.00000			−0.282843
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	0.0783936	+	0.996922i	$0.475021\pi$
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	−0.902557	+	0.430570i	$0.858312\pi$
$54$	−1.00000	−	1.73205i	−0.136083	−	0.235702i
$55$	4.00000			0.539360
$56$		0			0
$57$	1.00000			0.132453
$58$	−4.00000	−	6.92820i	−0.525226	−	0.909718i
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$	2.00000	−	3.46410i	0.258199	−	0.447214i
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$	18.0000			2.28600
$63$	0.500000	+	2.59808i	0.0629941	+	0.327327i
$64$	−8.00000			−1.00000
$65$	1.00000	+	1.73205i	0.124035	+	0.214834i
$66$	2.00000	−	3.46410i	0.246183	−	0.426401i
$67$	2.50000	−	4.33013i	0.305424	−	0.529009i	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	2.50000	−	4.33013i	0.305424	−	0.529009i	0.977356	+	0.211604i	$0.0678686\pi$
$68$		0			0
$69$		0			0
$70$	−8.00000	+	6.92820i	−0.956183	+	0.828079i
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	1.50000	−	2.59808i	0.175562	−	0.304082i	−0.764794	−	0.644275i	$-0.777159\pi$
$73$	1.50000	−	2.59808i	0.175562	−	0.304082i	0.940356	+	0.340193i	$0.110493\pi$
$74$	−3.00000	+	5.19615i	−0.348743	+	0.604040i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	2.00000			0.229416
$77$	−4.00000	+	3.46410i	−0.455842	+	0.394771i
$78$	2.00000			0.226455
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$	−4.00000	+	6.92820i	−0.447214	+	0.774597i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	10.0000	+	17.3205i	1.10432	+	1.91273i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	1.00000	+	5.19615i	0.109109	+	0.566947i
$85$		0			0
$86$	−5.00000	−	8.66025i	−0.539164	−	0.933859i
$87$	−2.00000	+	3.46410i	−0.214423	+	0.371391i
$88$		0			0
$89$	−8.00000	−	13.8564i	−0.847998	−	1.46878i	−0.882992	−	0.469389i	$-0.844474\pi$
$89$	−8.00000	−	13.8564i	−0.847998	−	1.46878i	0.0349934	−	0.999388i	$-0.488859\pi$
$90$	−4.00000			−0.421637
$91$	−2.50000	−	0.866025i	−0.262071	−	0.0907841i
$92$		0			0
$93$	−4.50000	−	7.79423i	−0.466628	−	0.808224i
$94$	6.00000	−	10.3923i	0.618853	−	1.07188i
$95$	1.00000	−	1.73205i	0.102598	−	0.177705i
$96$	4.00000	+	6.92820i	0.408248	+	0.707107i
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$	2.00000	−	13.8564i	0.202031	−	1.39971i
$99$	−2.00000			−0.201008
$100$	1.00000	+	1.73205i	0.100000	+	0.173205i
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	−0.911479	−	0.411346i	$-0.865059\pi$
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	0.811976	+	0.583691i	$0.198392\pi$
$102$		0			0
$103$	3.50000	+	6.06218i	0.344865	+	0.597324i	0.985329	−	0.170664i	$-0.0545913\pi$
$103$	3.50000	+	6.06218i	0.344865	+	0.597324i	−0.640464	+	0.767988i	$0.721258\pi$
$104$		0			0
$105$	5.00000	+	1.73205i	0.487950	+	0.169031i
$106$	24.0000			2.33109
$107$	4.00000	+	6.92820i	0.386695	+	0.669775i	0.992003	−	0.126217i	$-0.0402834\pi$
$107$	4.00000	+	6.92820i	0.386695	+	0.669775i	−0.605308	+	0.795991i	$0.706950\pi$
$108$	−1.00000	+	1.73205i	−0.0962250	+	0.166667i
$109$	−4.50000	+	7.79423i	−0.431022	+	0.746552i	−0.996962	−	0.0778949i	$-0.975180\pi$
$109$	−4.50000	+	7.79423i	−0.431022	+	0.746552i	0.565940	+	0.824447i	$0.308513\pi$
$110$	−4.00000	−	6.92820i	−0.381385	−	0.660578i
$111$	3.00000			0.284747
$112$	−2.00000	−	10.3923i	−0.188982	−	0.981981i
$113$	10.0000			0.940721			0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000			0.940721			0.470360	+	0.882474i	$0.344124\pi$
$114$	−1.00000	−	1.73205i	−0.0936586	−	0.162221i
$115$		0			0
$116$	−4.00000	+	6.92820i	−0.371391	+	0.643268i
$117$	−0.500000	−	0.866025i	−0.0462250	−	0.0800641i
$118$	−24.0000			−2.20938
$119$		0			0
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−10.0000	+	17.3205i	−0.905357	+	1.56813i
$123$	5.00000	−	8.66025i	0.450835	−	0.780869i
$124$	−9.00000	−	15.5885i	−0.808224	−	1.39988i
$125$	12.0000			1.07331
$126$	4.00000	−	3.46410i	0.356348	−	0.308607i
$127$	−15.0000			−1.33103			−0.665517	−	0.746382i	$-0.731789\pi$
$127$	−15.0000			−1.33103			−0.665517	+	0.746382i	$0.731789\pi$
$128$		0			0
$129$	−2.50000	+	4.33013i	−0.220113	+	0.381246i
$130$	2.00000	−	3.46410i	0.175412	−	0.303822i
$131$	7.00000	+	12.1244i	0.611593	+	1.05931i	0.990972	+	0.134069i	$0.0428042\pi$
$131$	7.00000	+	12.1244i	0.611593	+	1.05931i	−0.379379	+	0.925241i	$0.623862\pi$
$132$	−4.00000			−0.348155
$133$	0.500000	+	2.59808i	0.0433555	+	0.225282i
$134$	−10.0000			−0.863868
$135$	1.00000	+	1.73205i	0.0860663	+	0.149071i
$136$		0			0
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$		0			0
$139$	−3.00000			−0.254457			−0.127228	−	0.991873i	$-0.540608\pi$
$139$	−3.00000			−0.254457			−0.127228	+	0.991873i	$0.540608\pi$
$140$	10.0000	+	3.46410i	0.845154	+	0.292770i
$141$	−6.00000			−0.505291
$142$	6.00000	+	10.3923i	0.503509	+	0.872103i
$143$	1.00000	−	1.73205i	0.0836242	−	0.144841i
$144$	2.00000	−	3.46410i	0.166667	−	0.288675i
$145$	4.00000	+	6.92820i	0.332182	+	0.575356i
$146$	−6.00000			−0.496564
$147$	−6.50000	+	2.59808i	−0.536111	+	0.214286i
$148$	6.00000			0.493197
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	0.999953	−	0.00974235i	$-0.00310113\pi$
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	−0.508413	+	0.861113i	$0.669768\pi$
$150$	1.00000	−	1.73205i	0.0816497	−	0.141421i
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$		0			0
$153$		0			0
$154$	10.0000	+	3.46410i	0.805823	+	0.279145i
$155$	−18.0000			−1.44579
$156$	−1.00000	−	1.73205i	−0.0800641	−	0.138675i
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	0.997609	−	0.0691164i	$-0.0220180\pi$
$158$	1.00000	−	1.73205i	0.0795557	−	0.137795i
$159$	−6.00000	−	10.3923i	−0.475831	−	0.824163i
$160$	16.0000			1.26491
$161$		0			0
$162$	2.00000			0.157135
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	0.777007	−	0.629492i	$-0.216737\pi$
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	−0.933659	+	0.358162i	$0.883403\pi$
$164$	10.0000	−	17.3205i	0.780869	−	1.35250i
$165$	−2.00000	+	3.46410i	−0.155700	+	0.269680i
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	−14.0000			−1.08335			−0.541676	−	0.840587i	$-0.682210\pi$
$167$	−14.0000			−1.08335			−0.541676	+	0.840587i	$0.682210\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		0			0
$171$	−0.500000	+	0.866025i	−0.0382360	+	0.0662266i
$172$	−5.00000	+	8.66025i	−0.381246	+	0.660338i
$173$	−4.00000	−	6.92820i	−0.304114	−	0.526742i	0.672949	−	0.739689i	$-0.265027\pi$
$173$	−4.00000	−	6.92820i	−0.304114	−	0.526742i	−0.977064	+	0.212947i	$0.931694\pi$
$174$	8.00000			0.606478
$175$	−2.00000	+	1.73205i	−0.151186	+	0.130931i
$176$	8.00000			0.603023
$177$	6.00000	+	10.3923i	0.450988	+	0.781133i
$178$	−16.0000	+	27.7128i	−1.19925	+	2.07716i
$179$	−1.00000	+	1.73205i	−0.0747435	+	0.129460i	−0.900975	−	0.433872i	$-0.857147\pi$
$179$	−1.00000	+	1.73205i	−0.0747435	+	0.129460i	0.826231	+	0.563331i	$0.190480\pi$
$180$	2.00000	+	3.46410i	0.149071	+	0.258199i
$181$	13.0000			0.966282			0.483141	−	0.875542i	$-0.339496\pi$
$181$	13.0000			0.966282			0.483141	+	0.875542i	$0.339496\pi$
$182$	1.00000	+	5.19615i	0.0741249	+	0.385164i
$183$	10.0000			0.739221
$184$		0			0
$185$	3.00000	−	5.19615i	0.220564	−	0.382029i
$186$	−9.00000	+	15.5885i	−0.659912	+	1.14300i
$187$		0			0
$188$	−12.0000			−0.875190
$189$	−2.50000	−	0.866025i	−0.181848	−	0.0629941i
$190$	−4.00000			−0.290191
$191$	−5.00000	−	8.66025i	−0.361787	−	0.626634i	0.626468	−	0.779447i	$-0.284500\pi$
$191$	−5.00000	−	8.66025i	−0.361787	−	0.626634i	−0.988255	+	0.152813i	$0.951167\pi$
$192$	4.00000	−	6.92820i	0.288675	−	0.500000i
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	−0.993215	−	0.116289i	$-0.962900\pi$
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	0.597317	+	0.802005i	$0.296234\pi$
$194$	6.00000	+	10.3923i	0.430775	+	0.746124i
$195$	−2.00000			−0.143223
$196$	−13.0000	+	5.19615i	−0.928571	+	0.371154i
$197$	16.0000			1.13995			0.569976	−	0.821661i	$-0.306952\pi$
$197$	16.0000			1.13995			0.569976	+	0.821661i	$0.306952\pi$
$198$	2.00000	+	3.46410i	0.142134	+	0.246183i
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$		0			0
$201$	2.50000	+	4.33013i	0.176336	+	0.305424i
$202$	4.00000			0.281439
$203$	−10.0000	−	3.46410i	−0.701862	−	0.243132i
$204$		0			0
$205$	−10.0000	−	17.3205i	−0.698430	−	1.20972i
$206$	7.00000	−	12.1244i	0.487713	−	0.844744i
$207$		0			0
$208$	2.00000	+	3.46410i	0.138675	+	0.240192i
$209$	−2.00000			−0.138343
$210$	−2.00000	−	10.3923i	−0.138013	−	0.717137i
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	−12.0000	−	20.7846i	−0.824163	−	1.42749i
$213$	3.00000	−	5.19615i	0.205557	−	0.356034i
$214$	8.00000	−	13.8564i	0.546869	−	0.947204i
$215$	5.00000	+	8.66025i	0.340997	+	0.590624i
$216$		0			0
$217$	18.0000	−	15.5885i	1.22192	−	1.05821i
$218$	18.0000			1.21911
$219$	1.50000	+	2.59808i	0.101361	+	0.175562i
$220$	−4.00000	+	6.92820i	−0.269680	+	0.467099i
$221$		0			0
$222$	−3.00000	−	5.19615i	−0.201347	−	0.348743i
$223$	16.0000			1.07144			0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000			1.07144			0.535720	+	0.844396i	$0.320040\pi$
$224$	−16.0000	+	13.8564i	−1.06904	+	0.925820i
$225$	−1.00000			−0.0666667
$226$	−10.0000	−	17.3205i	−0.665190	−	1.15214i
$227$	−9.00000	+	15.5885i	−0.597351	+	1.03464i	0.395860	+	0.918311i	$0.370447\pi$
$227$	−9.00000	+	15.5885i	−0.597351	+	1.03464i	−0.993210	+	0.116331i	$0.962887\pi$
$228$	−1.00000	+	1.73205i	−0.0662266	+	0.114708i
$229$	9.50000	+	16.4545i	0.627778	+	1.08734i	0.987997	+	0.154475i	$0.0493686\pi$
$229$	9.50000	+	16.4545i	0.627778	+	1.08734i	−0.360219	+	0.932868i	$0.617298\pi$
$230$		0			0
$231$	−1.00000	−	5.19615i	−0.0657952	−	0.341882i
$232$		0			0
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	0.750867	−	0.660454i	$-0.229636\pi$
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	−0.947403	+	0.320043i	$0.896303\pi$
$234$	−1.00000	+	1.73205i	−0.0653720	+	0.113228i
$235$	−6.00000	+	10.3923i	−0.391397	+	0.677919i
$236$	12.0000	+	20.7846i	0.781133	+	1.35296i
$237$	−1.00000			−0.0649570
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$	−4.00000	−	6.92820i	−0.258199	−	0.447214i
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$	7.00000	−	12.1244i	0.449977	−	0.779383i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	20.0000			1.28037
$245$	−2.00000	+	13.8564i	−0.127775	+	0.885253i
$246$	−20.0000			−1.27515
$247$	−0.500000	−	0.866025i	−0.0318142	−	0.0551039i
$248$		0			0
$249$	−3.00000	+	5.19615i	−0.190117	+	0.329293i
$250$	−12.0000	−	20.7846i	−0.758947	−	1.31453i
$251$	−8.00000			−0.504956			−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000			−0.504956			−0.252478	+	0.967603i	$0.581245\pi$
$252$	−5.00000	−	1.73205i	−0.314970	−	0.109109i
$253$		0			0
$254$	15.0000	+	25.9808i	0.941184	+	1.63018i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−13.0000	−	22.5167i	−0.810918	−	1.40455i	−0.912222	−	0.409695i	$-0.865635\pi$
$257$	−13.0000	−	22.5167i	−0.810918	−	1.40455i	0.101305	−	0.994855i	$-0.467698\pi$
$258$	10.0000			0.622573
$259$	1.50000	+	7.79423i	0.0932055	+	0.484310i
$260$	−4.00000			−0.248069
$261$	−2.00000	−	3.46410i	−0.123797	−	0.214423i
$262$	14.0000	−	24.2487i	0.864923	−	1.49809i
$263$	−2.00000	+	3.46410i	−0.123325	+	0.213606i	−0.921077	−	0.389380i	$-0.872689\pi$
$263$	−2.00000	+	3.46410i	−0.123325	+	0.213606i	0.797752	+	0.602986i	$0.206023\pi$
$264$		0			0
$265$	−24.0000			−1.47431
$266$	4.00000	−	3.46410i	0.245256	−	0.212398i
$267$	16.0000			0.979184
$268$	5.00000	+	8.66025i	0.305424	+	0.529009i
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	−0.942871	−	0.333157i	$-0.891886\pi$
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	0.759958	+	0.649972i	$0.225219\pi$
$270$	2.00000	−	3.46410i	0.121716	−	0.210819i
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	0.513905	−	0.857847i	$-0.328199\pi$
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	−0.999870	+	0.0161307i	$0.994865\pi$
$272$		0			0
$273$	2.00000	−	1.73205i	0.121046	−	0.104828i
$274$	−24.0000			−1.44989
$275$	−1.00000	−	1.73205i	−0.0603023	−	0.104447i
$276$		0			0
$277$	−6.50000	+	11.2583i	−0.390547	+	0.676448i	−0.992522	−	0.122068i	$-0.961047\pi$
$277$	−6.50000	+	11.2583i	−0.390547	+	0.676448i	0.601975	+	0.798515i	$0.294381\pi$
$278$	3.00000	+	5.19615i	0.179928	+	0.311645i
$279$	9.00000			0.538816
$280$		0			0
$281$	−4.00000			−0.238620			−0.119310	−	0.992857i	$-0.538068\pi$
$281$	−4.00000			−0.238620			−0.119310	+	0.992857i	$0.538068\pi$
$282$	6.00000	+	10.3923i	0.357295	+	0.618853i
$283$	5.50000	−	9.52628i	0.326941	−	0.566279i	−0.654962	−	0.755662i	$-0.727315\pi$
$283$	5.50000	−	9.52628i	0.326941	−	0.566279i	0.981903	+	0.189383i	$0.0606488\pi$
$284$	6.00000	−	10.3923i	0.356034	−	0.616670i
$285$	1.00000	+	1.73205i	0.0592349	+	0.102598i
$286$	−4.00000			−0.236525
$287$	25.0000	+	8.66025i	1.47570	+	0.511199i
$288$	−8.00000			−0.471405
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	8.00000	−	13.8564i	0.469776	−	0.813676i
$291$	3.00000	−	5.19615i	0.175863	−	0.304604i
$292$	3.00000	+	5.19615i	0.175562	+	0.304082i
$293$	8.00000			0.467365			0.233682	−	0.972313i	$-0.424922\pi$
$293$	8.00000			0.467365			0.233682	+	0.972313i	$0.424922\pi$
$294$	11.0000	+	8.66025i	0.641533	+	0.505076i
$295$	24.0000			1.39733
$296$		0			0
$297$	1.00000	−	1.73205i	0.0580259	−	0.100504i
$298$	12.0000	−	20.7846i	0.695141	−	1.20402i
$299$		0			0
$300$	−2.00000			−0.115470
$301$	−12.5000	−	4.33013i	−0.720488	−	0.249584i
$302$	−32.0000			−1.84139
$303$	−1.00000	−	1.73205i	−0.0574485	−	0.0995037i
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$	10.0000	−	17.3205i	0.572598	−	0.991769i
$306$		0			0
$307$	−17.0000			−0.970241			−0.485121	−	0.874447i	$-0.661224\pi$
$307$	−17.0000			−0.970241			−0.485121	+	0.874447i	$0.661224\pi$
$308$	−2.00000	−	10.3923i	−0.113961	−	0.592157i
$309$	−7.00000			−0.398216
$310$	18.0000	+	31.1769i	1.02233	+	1.77073i
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	−0.768345	−	0.640036i	$-0.778920\pi$
$311$	3.00000	−	5.19615i	0.170114	−	0.294647i	0.938460	+	0.345389i	$0.112253\pi$
$312$		0			0
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	0.879810	−	0.475325i	$-0.157669\pi$
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	−0.851549	+	0.524276i	$0.824336\pi$
$314$	−28.0000			−1.58013
$315$	−4.00000	+	3.46410i	−0.225374	+	0.195180i
$316$	−2.00000			−0.112509
$317$	−12.0000	−	20.7846i	−0.673987	−	1.16738i	−0.976764	−	0.214318i	$-0.931247\pi$
$317$	−12.0000	−	20.7846i	−0.673987	−	1.16738i	0.302777	−	0.953062i	$-0.402086\pi$
$318$	−12.0000	+	20.7846i	−0.672927	+	1.16554i
$319$	4.00000	−	6.92820i	0.223957	−	0.387905i
$320$	−8.00000	−	13.8564i	−0.447214	−	0.774597i
$321$	−8.00000			−0.446516
$322$		0			0
$323$		0			0
$324$	−1.00000	−	1.73205i	−0.0555556	−	0.0962250i
$325$	0.500000	−	0.866025i	0.0277350	−	0.0480384i
$326$	−4.00000	+	6.92820i	−0.221540	+	0.383718i
$327$	−4.50000	−	7.79423i	−0.248851	−	0.431022i
$328$		0			0
$329$	−3.00000	−	15.5885i	−0.165395	−	0.859419i
$330$	8.00000			0.440386
$331$	12.5000	+	21.6506i	0.687062	+	1.19003i	0.972784	+	0.231714i	$0.0744333\pi$
$331$	12.5000	+	21.6506i	0.687062	+	1.19003i	−0.285722	+	0.958313i	$0.592233\pi$
$332$	−6.00000	+	10.3923i	−0.329293	+	0.570352i
$333$	−1.50000	+	2.59808i	−0.0821995	+	0.142374i
$334$	14.0000	+	24.2487i	0.766046	+	1.32683i
$335$	10.0000			0.546358
$336$	10.0000	+	3.46410i	0.545545	+	0.188982i
$337$	13.0000			0.708155			0.354078	−	0.935216i	$-0.384795\pi$
$337$	13.0000			0.708155			0.354078	+	0.935216i	$0.384795\pi$
$338$	12.0000	+	20.7846i	0.652714	+	1.13053i
$339$	−5.00000	+	8.66025i	−0.271563	+	0.470360i
$340$		0			0
$341$	9.00000	+	15.5885i	0.487377	+	0.844162i
$342$	2.00000			0.108148
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$		0			0
$346$	−8.00000	+	13.8564i	−0.430083	+	0.744925i
$347$	−16.0000	+	27.7128i	−0.858925	+	1.48770i	0.0140303	+	0.999902i	$0.495534\pi$
$347$	−16.0000	+	27.7128i	−0.858925	+	1.48770i	−0.872955	+	0.487800i	$0.837799\pi$
$348$	−4.00000	−	6.92820i	−0.214423	−	0.371391i
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$	5.00000	+	1.73205i	0.267261	+	0.0925820i
$351$	1.00000			0.0533761
$352$	−8.00000	−	13.8564i	−0.426401	−	0.738549i
$353$	−17.0000	+	29.4449i	−0.904819	+	1.56719i	−0.0836583	+	0.996495i	$0.526660\pi$
$353$	−17.0000	+	29.4449i	−0.904819	+	1.56719i	−0.821160	+	0.570697i	$0.806673\pi$
$354$	12.0000	−	20.7846i	0.637793	−	1.10469i
$355$	−6.00000	−	10.3923i	−0.318447	−	0.551566i
$356$	32.0000			1.69600
$357$		0			0
$358$	4.00000			0.211407
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	−0.999476	−	0.0323801i	$-0.989691\pi$
$359$	−10.0000	−	17.3205i	−0.527780	−	0.914141i	0.471696	−	0.881761i	$-0.343642\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	−13.0000	−	22.5167i	−0.683265	−	1.18345i
$363$	−7.00000			−0.367405
$364$	4.00000	−	3.46410i	0.209657	−	0.181568i
$365$	6.00000			0.314054
$366$	−10.0000	−	17.3205i	−0.522708	−	0.905357i
$367$	4.50000	−	7.79423i	0.234898	−	0.406855i	−0.724345	−	0.689438i	$-0.757858\pi$
$367$	4.50000	−	7.79423i	0.234898	−	0.406855i	0.959243	+	0.282582i	$0.0911910\pi$
$368$		0			0
$369$	5.00000	+	8.66025i	0.260290	+	0.450835i
$370$	−12.0000			−0.623850
$371$	24.0000	−	20.7846i	1.24602	−	1.07908i
$372$	18.0000			0.933257
$373$	−11.5000	−	19.9186i	−0.595447	−	1.03135i	−0.993484	−	0.113975i	$-0.963641\pi$
$373$	−11.5000	−	19.9186i	−0.595447	−	1.03135i	0.398036	−	0.917370i	$-0.369692\pi$
$374$		0			0
$375$	−6.00000	+	10.3923i	−0.309839	+	0.536656i
$376$		0			0
$377$	4.00000			0.206010
$378$	1.00000	+	5.19615i	0.0514344	+	0.267261i
$379$	3.00000			0.154100			0.0770498	−	0.997027i	$-0.475450\pi$
$379$	3.00000			0.154100			0.0770498	+	0.997027i	$0.475450\pi$
$380$	2.00000	+	3.46410i	0.102598	+	0.177705i
$381$	7.50000	−	12.9904i	0.384237	−	0.665517i
$382$	−10.0000	+	17.3205i	−0.511645	+	0.886194i
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	0.977613	−	0.210411i	$-0.0674801\pi$
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	−0.671027	+	0.741433i	$0.734147\pi$
$384$		0			0
$385$	−10.0000	−	3.46410i	−0.509647	−	0.176547i
$386$	22.0000			1.11977
$387$	−2.50000	−	4.33013i	−0.127082	−	0.220113i
$388$	6.00000	−	10.3923i	0.304604	−	0.527589i
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	−0.779895	−	0.625910i	$-0.784728\pi$
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	0.932002	+	0.362454i	$0.118061\pi$
$390$	2.00000	+	3.46410i	0.101274	+	0.175412i
$391$		0			0
$392$		0			0
$393$	−14.0000			−0.706207
$394$	−16.0000	−	27.7128i	−0.806068	−	1.39615i
$395$	−1.00000	+	1.73205i	−0.0503155	+	0.0871489i
$396$	2.00000	−	3.46410i	0.100504	−	0.174078i
$397$	4.50000	+	7.79423i	0.225849	+	0.391181i	0.956574	−	0.291491i	$-0.0941512\pi$
$397$	4.50000	+	7.79423i	0.225849	+	0.391181i	−0.730725	+	0.682672i	$0.760818\pi$
$398$		0			0
$399$	−2.50000	−	0.866025i	−0.125157	−	0.0433555i
$400$	4.00000			0.200000
$401$	18.0000	+	31.1769i	0.898877	+	1.55690i	0.828932	+	0.559350i	$0.188949\pi$
$401$	18.0000	+	31.1769i	0.898877	+	1.55690i	0.0699455	+	0.997551i	$0.477717\pi$
$402$	5.00000	−	8.66025i	0.249377	−	0.431934i
$403$	−4.50000	+	7.79423i	−0.224161	+	0.388258i
$404$	−2.00000	−	3.46410i	−0.0995037	−	0.172345i
$405$	−2.00000			−0.0993808
$406$	4.00000	+	20.7846i	0.198517	+	1.03152i
$407$	−6.00000			−0.297409
$408$		0			0
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	−0.921192	−	0.389109i	$-0.872783\pi$
$409$	−2.50000	+	4.33013i	−0.123617	+	0.214111i	0.797574	+	0.603220i	$0.206116\pi$
$410$	−20.0000	+	34.6410i	−0.987730	+	1.71080i
$411$	6.00000	+	10.3923i	0.295958	+	0.512615i
$412$	−14.0000			−0.689730
$413$	−24.0000	+	20.7846i	−1.18096	+	1.02274i
$414$		0			0
$415$	6.00000	+	10.3923i	0.294528	+	0.510138i
$416$	4.00000	−	6.92820i	0.196116	−	0.339683i
$417$	1.50000	−	2.59808i	0.0734553	−	0.127228i
$418$	2.00000	+	3.46410i	0.0978232	+	0.169435i
$419$	30.0000			1.46560			0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000			1.46560			0.732798	+	0.680446i	$0.238214\pi$
$420$	−8.00000	+	6.92820i	−0.390360	+	0.338062i
$421$	−7.00000			−0.341159			−0.170580	−	0.985344i	$-0.554564\pi$
$421$	−7.00000			−0.341159			−0.170580	+	0.985344i	$0.554564\pi$
$422$	−4.00000	−	6.92820i	−0.194717	−	0.337260i
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$		0			0
$425$		0			0
$426$	−12.0000			−0.581402
$427$	5.00000	+	25.9808i	0.241967	+	1.25730i
$428$	−16.0000			−0.773389
$429$	1.00000	+	1.73205i	0.0482805	+	0.0836242i
$430$	10.0000	−	17.3205i	0.482243	−	0.835269i
$431$	9.00000	−	15.5885i	0.433515	−	0.750870i	−0.563658	−	0.826008i	$-0.690607\pi$
$431$	9.00000	−	15.5885i	0.433515	−	0.750870i	0.997173	+	0.0751385i	$0.0239399\pi$
$432$	2.00000	+	3.46410i	0.0962250	+	0.166667i
$433$	31.0000			1.48976			0.744882	−	0.667196i	$-0.232506\pi$
$433$	31.0000			1.48976			0.744882	+	0.667196i	$0.232506\pi$
$434$	−45.0000	−	15.5885i	−2.16007	−	0.748270i
$435$	−8.00000			−0.383571
$436$	−9.00000	−	15.5885i	−0.431022	−	0.746552i
$437$		0			0
$438$	3.00000	−	5.19615i	0.143346	−	0.248282i
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$		0			0
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	0.687557	−	0.726130i	$-0.258683\pi$
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	−0.972626	+	0.232377i	$0.925350\pi$
$444$	−3.00000	+	5.19615i	−0.142374	+	0.246598i
$445$	16.0000	−	27.7128i	0.758473	−	1.31371i
$446$	−16.0000	−	27.7128i	−0.757622	−	1.31224i
$447$	−12.0000			−0.567581
$448$	20.0000	+	6.92820i	0.944911	+	0.327327i
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$	1.00000	+	1.73205i	0.0471405	+	0.0816497i
$451$	−10.0000	+	17.3205i	−0.470882	+	0.815591i
$452$	−10.0000	+	17.3205i	−0.470360	+	0.814688i
$453$	8.00000	+	13.8564i	0.375873	+	0.651031i
$454$	36.0000			1.68956
$455$	−1.00000	−	5.19615i	−0.0468807	−	0.243599i
$456$		0			0
$457$	5.50000	+	9.52628i	0.257279	+	0.445621i	0.965512	−	0.260358i	$-0.0838407\pi$
$457$	5.50000	+	9.52628i	0.257279	+	0.445621i	−0.708233	+	0.705979i	$0.750507\pi$
$458$	19.0000	−	32.9090i	0.887812	−	1.53773i
$459$		0			0
$460$		0			0
$461$	20.0000			0.931493			0.465746	−	0.884918i	$-0.345786\pi$
$461$	20.0000			0.931493			0.465746	+	0.884918i	$0.345786\pi$
$462$	−8.00000	+	6.92820i	−0.372194	+	0.322329i
$463$	−17.0000			−0.790057			−0.395029	−	0.918669i	$-0.629265\pi$
$463$	−17.0000			−0.790057			−0.395029	+	0.918669i	$0.629265\pi$
$464$	8.00000	+	13.8564i	0.371391	+	0.643268i
$465$	9.00000	−	15.5885i	0.417365	−	0.722897i
$466$	−6.00000	+	10.3923i	−0.277945	+	0.481414i
$467$	−3.00000	−	5.19615i	−0.138823	−	0.240449i	0.788228	−	0.615383i	$-0.210999\pi$
$467$	−3.00000	−	5.19615i	−0.138823	−	0.240449i	−0.927052	+	0.374934i	$0.877665\pi$
$468$	2.00000			0.0924500
$469$	−10.0000	+	8.66025i	−0.461757	+	0.399893i
$470$	24.0000			1.10704
$471$	7.00000	+	12.1244i	0.322543	+	0.558661i
$472$		0			0
$473$	5.00000	−	8.66025i	0.229900	−	0.398199i
$474$	1.00000	+	1.73205i	0.0459315	+	0.0795557i
$475$	−1.00000			−0.0458831
$476$		0			0
$477$	12.0000			0.549442
$478$	−6.00000	−	10.3923i	−0.274434	−	0.475333i
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	−0.345827	−	0.938298i	$-0.612402\pi$
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	0.985504	−	0.169654i	$-0.0542649\pi$
$480$	−8.00000	+	13.8564i	−0.365148	+	0.632456i
$481$	−1.50000	−	2.59808i	−0.0683941	−	0.118462i
$482$	28.0000			1.27537
$483$		0			0
$484$	−14.0000			−0.636364
$485$	−6.00000	−	10.3923i	−0.272446	−	0.471890i
$486$	−1.00000	+	1.73205i	−0.0453609	+	0.0785674i
$487$	−15.5000	+	26.8468i	−0.702372	+	1.21654i	0.265260	+	0.964177i	$0.414542\pi$
$487$	−15.5000	+	26.8468i	−0.702372	+	1.21654i	−0.967632	+	0.252367i	$0.918791\pi$
$488$		0			0
$489$	4.00000			0.180886
$490$	26.0000	−	10.3923i	1.17456	−	0.469476i
$491$	−28.0000			−1.26362			−0.631811	−	0.775122i	$-0.717688\pi$
$491$	−28.0000			−1.26362			−0.631811	+	0.775122i	$0.717688\pi$
$492$	10.0000	+	17.3205i	0.450835	+	0.780869i
$493$		0			0
$494$	−1.00000	+	1.73205i	−0.0449921	+	0.0779287i
$495$	−2.00000	−	3.46410i	−0.0898933	−	0.155700i
$496$	−36.0000			−1.61645
$497$	15.0000	+	5.19615i	0.672842	+	0.233079i
$498$	12.0000			0.537733
$499$	−18.5000	−	32.0429i	−0.828174	−	1.43444i	−0.899469	−	0.436984i	$-0.856047\pi$
$499$	−18.5000	−	32.0429i	−0.828174	−	1.43444i	0.0712957	−	0.997455i	$-0.477287\pi$
$500$	−12.0000	+	20.7846i	−0.536656	+	0.929516i
$501$	7.00000	−	12.1244i	0.312737	−	0.541676i
$502$	8.00000	+	13.8564i	0.357057	+	0.618442i
$503$	−42.0000			−1.87269			−0.936344	−	0.351085i	$-0.885813\pi$
$503$	−42.0000			−1.87269			−0.936344	+	0.351085i	$0.885813\pi$
$504$		0			0
$505$	−4.00000			−0.177998
$506$		0			0
$507$	6.00000	−	10.3923i	0.266469	−	0.461538i
$508$	15.0000	−	25.9808i	0.665517	−	1.15271i
$509$	−1.00000	−	1.73205i	−0.0443242	−	0.0767718i	0.843012	−	0.537895i	$-0.180780\pi$
$509$	−1.00000	−	1.73205i	−0.0443242	−	0.0767718i	−0.887336	+	0.461123i	$0.847447\pi$
$510$		0			0
$511$	−6.00000	+	5.19615i	−0.265424	+	0.229864i
$512$	32.0000			1.41421
$513$	−0.500000	−	0.866025i	−0.0220755	−	0.0382360i
$514$	−26.0000	+	45.0333i	−1.14681	+	1.98633i
$515$	−7.00000	+	12.1244i	−0.308457	+	0.534263i
$516$	−5.00000	−	8.66025i	−0.220113	−	0.381246i
$517$	12.0000			0.527759
$518$	12.0000	−	10.3923i	0.527250	−	0.456612i
$519$	8.00000			0.351161
$520$		0			0
$521$	−6.00000	+	10.3923i	−0.262865	+	0.455295i	−0.967002	−	0.254769i	$-0.918001\pi$
$521$	−6.00000	+	10.3923i	−0.262865	+	0.455295i	0.704137	+	0.710064i	$0.251334\pi$
$522$	−4.00000	+	6.92820i	−0.175075	+	0.303239i
$523$	−15.5000	−	26.8468i	−0.677768	−	1.17393i	−0.975652	−	0.219326i	$-0.929614\pi$
$523$	−15.5000	−	26.8468i	−0.677768	−	1.17393i	0.297884	−	0.954602i	$-0.403719\pi$
$524$	−28.0000			−1.22319
$525$	−0.500000	−	2.59808i	−0.0218218	−	0.113389i
$526$	8.00000			0.348817
$527$		0			0
$528$	−4.00000	+	6.92820i	−0.174078	+	0.301511i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	24.0000	+	41.5692i	1.04249	+	1.80565i
$531$	−12.0000			−0.520756
$532$	−5.00000	−	1.73205i	−0.216777	−	0.0750939i
$533$	−10.0000			−0.433148
$534$	−16.0000	−	27.7128i	−0.692388	−	1.19925i
$535$	−8.00000	+	13.8564i	−0.345870	+	0.599065i
$536$		0			0
$537$	−1.00000	−	1.73205i	−0.0431532	−	0.0747435i
$538$	12.0000			0.517357
$539$	13.0000	−	5.19615i	0.559950	−	0.223814i
$540$	−4.00000			−0.172133
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	0.994715	−	0.102677i	$-0.0327407\pi$
$541$	9.50000	+	16.4545i	0.408437	+	0.707433i	−0.586278	+	0.810110i	$0.699407\pi$
$542$	−16.0000	+	27.7128i	−0.687259	+	1.19037i
$543$	−6.50000	+	11.2583i	−0.278942	+	0.483141i
$544$		0			0
$545$	−18.0000			−0.771035
$546$	−5.00000	−	1.73205i	−0.213980	−	0.0741249i
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	12.0000	+	20.7846i	0.512615	+	0.887875i
$549$	−5.00000	+	8.66025i	−0.213395	+	0.369611i
$550$	−2.00000	+	3.46410i	−0.0852803	+	0.147710i
$551$	−2.00000	−	3.46410i	−0.0852029	−	0.147576i
$552$		0			0
$553$	−0.500000	−	2.59808i	−0.0212622	−	0.110481i
$554$	26.0000			1.10463
$555$	3.00000	+	5.19615i	0.127343	+	0.220564i
$556$	3.00000	−	5.19615i	0.127228	−	0.220366i
$557$	1.00000	−	1.73205i	0.0423714	−	0.0733893i	−0.844062	−	0.536246i	$-0.819842\pi$
$557$	1.00000	−	1.73205i	0.0423714	−	0.0733893i	0.886433	+	0.462856i	$0.153175\pi$
$558$	−9.00000	−	15.5885i	−0.381000	−	0.659912i
$559$	5.00000			0.211477
$560$	16.0000	−	13.8564i	0.676123	−	0.585540i
$561$		0			0
$562$	4.00000	+	6.92820i	0.168730	+	0.292249i
$563$	13.0000	−	22.5167i	0.547885	−	0.948964i	−0.450535	−	0.892759i	$-0.648767\pi$
$563$	13.0000	−	22.5167i	0.547885	−	0.948964i	0.998419	−	0.0562051i	$-0.0179001\pi$
$564$	6.00000	−	10.3923i	0.252646	−	0.437595i
$565$	10.0000	+	17.3205i	0.420703	+	0.728679i
$566$	−22.0000			−0.924729
$567$	2.00000	−	1.73205i	0.0839921	−	0.0727393i
$568$		0			0
$569$	13.0000	+	22.5167i	0.544988	+	0.943948i	0.998608	+	0.0527519i	$0.0167993\pi$
$569$	13.0000	+	22.5167i	0.544988	+	0.943948i	−0.453619	+	0.891196i	$0.649867\pi$
$570$	2.00000	−	3.46410i	0.0837708	−	0.145095i
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	−0.595862	−	0.803087i	$-0.703189\pi$
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	0.993425	+	0.114488i	$0.0365228\pi$
$572$	2.00000	+	3.46410i	0.0836242	+	0.144841i
$573$	10.0000			0.417756
$574$	−10.0000	−	51.9615i	−0.417392	−	2.16883i
$575$		0			0
$576$	4.00000	+	6.92820i	0.166667	+	0.288675i
$577$	8.50000	−	14.7224i	0.353860	−	0.612903i	−0.633062	−	0.774101i	$-0.718202\pi$
$577$	8.50000	−	14.7224i	0.353860	−	0.612903i	0.986922	+	0.161198i	$0.0515357\pi$
$578$	17.0000	−	29.4449i	0.707107	−	1.22474i
$579$	−5.50000	−	9.52628i	−0.228572	−	0.395899i
$580$	−16.0000			−0.664364
$581$	−15.0000	−	5.19615i	−0.622305	−	0.215573i
$582$	−12.0000			−0.497416
$583$	12.0000	+	20.7846i	0.496989	+	0.860811i
$584$		0			0
$585$	1.00000	−	1.73205i	0.0413449	−	0.0716115i
$586$	−8.00000	−	13.8564i	−0.330477	−	0.572403i
$587$	16.0000			0.660391			0.330195	−	0.943913i	$-0.392885\pi$
$587$	16.0000			0.660391			0.330195	+	0.943913i	$0.392885\pi$
$588$	2.00000	−	13.8564i	0.0824786	−	0.571429i
$589$	9.00000			0.370839
$590$	−24.0000	−	41.5692i	−0.988064	−	1.71138i
$591$	−8.00000	+	13.8564i	−0.329076	+	0.569976i
$592$	6.00000	−	10.3923i	0.246598	−	0.427121i
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	0.921026	−	0.389501i	$-0.127353\pi$
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	−0.797831	+	0.602881i	$0.794019\pi$
$594$	−4.00000			−0.164122
$595$		0			0
$596$	−24.0000			−0.983078
$597$		0			0
$598$		0			0
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	−0.962175	−	0.272433i	$-0.912172\pi$
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	0.717021	+	0.697051i	$0.245505\pi$
$600$		0			0
$601$	−9.00000			−0.367118			−0.183559	−	0.983009i	$-0.558762\pi$
$601$	−9.00000			−0.367118			−0.183559	+	0.983009i	$0.558762\pi$
$602$	5.00000	+	25.9808i	0.203785	+	1.05890i
$603$	−5.00000			−0.203616
$604$	16.0000	+	27.7128i	0.651031	+	1.12762i
$605$	−7.00000	+	12.1244i	−0.284590	+	0.492925i
$606$	−2.00000	+	3.46410i	−0.0812444	+	0.140720i
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	0.532509	−	0.846424i	$-0.321249\pi$
$607$	−11.5000	−	19.9186i	−0.466771	−	0.808470i	−0.999279	+	0.0379540i	$0.987916\pi$
$608$	−8.00000			−0.324443
$609$	8.00000	−	6.92820i	0.324176	−	0.280745i
$610$	−40.0000			−1.61955
$611$	3.00000	+	5.19615i	0.121367	+	0.210214i
$612$		0			0
$613$	−17.0000	+	29.4449i	−0.686624	+	1.18927i	0.286300	+	0.958140i	$0.407575\pi$
$613$	−17.0000	+	29.4449i	−0.686624	+	1.18927i	−0.972924	+	0.231127i	$0.925759\pi$
$614$	17.0000	+	29.4449i	0.686064	+	1.18830i
$615$	20.0000			0.806478
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$	7.00000	+	12.1244i	0.281581	+	0.487713i
$619$	14.5000	−	25.1147i	0.582804	−	1.00945i	−0.412341	−	0.911030i	$-0.635289\pi$
$619$	14.5000	−	25.1147i	0.582804	−	1.00945i	0.995145	−	0.0984169i	$-0.0313779\pi$
$620$	18.0000	−	31.1769i	0.722897	−	1.25210i
$621$		0			0
$622$	−12.0000			−0.481156
$623$	8.00000	+	41.5692i	0.320513	+	1.66544i
$624$	−4.00000			−0.160128
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	1.00000	−	1.73205i	0.0399680	−	0.0692267i
$627$	1.00000	−	1.73205i	0.0399362	−	0.0691714i
$628$	14.0000	+	24.2487i	0.558661	+	0.967629i
$629$		0			0
$630$	10.0000	+	3.46410i	0.398410	+	0.138013i
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$		0			0
$633$	−2.00000	+	3.46410i	−0.0794929	+	0.137686i
$634$	−24.0000	+	41.5692i	−0.953162	+	1.65092i
$635$	−15.0000	−	25.9808i	−0.595257	−	1.03102i
$636$	24.0000			0.951662
$637$	5.50000	+	4.33013i	0.217918	+	0.171566i
$638$	−16.0000			−0.633446
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$		0			0
$641$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$641$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$642$	8.00000	+	13.8564i	0.315735	+	0.546869i
$643$	−19.0000			−0.749287			−0.374643	−	0.927169i	$-0.622235\pi$
$643$	−19.0000			−0.749287			−0.374643	+	0.927169i	$0.622235\pi$
$644$		0			0
$645$	−10.0000			−0.393750
$646$		0			0
$647$	−1.00000	+	1.73205i	−0.0393141	+	0.0680939i	−0.885013	−	0.465566i	$-0.845851\pi$
$647$	−1.00000	+	1.73205i	−0.0393141	+	0.0680939i	0.845699	+	0.533660i	$0.179184\pi$
$648$		0			0
$649$	−12.0000	−	20.7846i	−0.471041	−	0.815867i
$650$	−2.00000			−0.0784465
$651$	4.50000	+	23.3827i	0.176369	+	0.916440i
$652$	8.00000			0.313304
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	0.634437	−	0.772975i	$-0.281232\pi$
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	−0.986634	+	0.162951i	$0.947899\pi$
$654$	−9.00000	+	15.5885i	−0.351928	+	0.609557i
$655$	−14.0000	+	24.2487i	−0.547025	+	0.947476i
$656$	−20.0000	−	34.6410i	−0.780869	−	1.35250i
$657$	−3.00000			−0.117041
$658$	−24.0000	+	20.7846i	−0.935617	+	0.810268i
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$	−4.00000	−	6.92820i	−0.155700	−	0.269680i
$661$	20.5000	−	35.5070i	0.797358	−	1.38106i	−0.123974	−	0.992286i	$-0.539564\pi$
$661$	20.5000	−	35.5070i	0.797358	−	1.38106i	0.921331	−	0.388778i	$-0.127103\pi$
$662$	25.0000	−	43.3013i	0.971653	−	1.68295i
$663$		0			0
$664$		0			0
$665$	−4.00000	+	3.46410i	−0.155113	+	0.134332i
$666$	6.00000			0.232495
$667$		0			0
$668$	14.0000	−	24.2487i	0.541676	−	0.938211i
$669$	−8.00000	+	13.8564i	−0.309298	+	0.535720i
$670$	−10.0000	−	17.3205i	−0.386334	−	0.669150i
$671$	−20.0000			−0.772091
$672$	−4.00000	−	20.7846i	−0.154303	−	0.801784i
$673$	−41.0000			−1.58043			−0.790217	−	0.612827i	$-0.790032\pi$
$673$	−41.0000			−1.58043			−0.790217	+	0.612827i	$0.790032\pi$
$674$	−13.0000	−	22.5167i	−0.500741	−	0.867309i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	12.0000	−	20.7846i	0.461538	−	0.799408i
$677$	−6.00000	−	10.3923i	−0.230599	−	0.399409i	0.727386	−	0.686229i	$-0.240735\pi$
$677$	−6.00000	−	10.3923i	−0.230599	−	0.399409i	−0.957984	+	0.286820i	$0.907402\pi$
$678$	20.0000			0.768095
$679$	15.0000	+	5.19615i	0.575647	+	0.199410i
$680$		0			0
$681$	−9.00000	−	15.5885i	−0.344881	−	0.597351i
$682$	18.0000	−	31.1769i	0.689256	−	1.19383i
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	−0.728101	−	0.685470i	$-0.759597\pi$
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	0.957685	+	0.287819i	$0.0929302\pi$
$684$	−1.00000	−	1.73205i	−0.0382360	−	0.0662266i
$685$	24.0000			0.916993
$686$	−17.0000	+	32.9090i	−0.649063	+	1.25647i
$687$	−19.0000			−0.724895
$688$	10.0000	+	17.3205i	0.381246	+	0.660338i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	18.5000	+	32.0429i	0.703773	+	1.21897i	0.967132	+	0.254273i	$0.0818362\pi$
$691$	18.5000	+	32.0429i	0.703773	+	1.21897i	−0.263359	+	0.964698i	$0.584830\pi$
$692$	16.0000			0.608229
$693$	5.00000	+	1.73205i	0.189934	+	0.0657952i
$694$	64.0000			2.42941
$695$	−3.00000	−	5.19615i	−0.113796	−	0.197101i
$696$		0			0
$697$		0			0
$698$	14.0000	+	24.2487i	0.529908	+	0.917827i
$699$	6.00000			0.226941
$700$	−1.00000	−	5.19615i	−0.0377964	−	0.196396i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	−1.00000	−	1.73205i	−0.0377426	−	0.0653720i
$703$	−1.50000	+	2.59808i	−0.0565736	+	0.0979883i
$704$	−8.00000	+	13.8564i	−0.301511	+	0.522233i
$705$	−6.00000	−	10.3923i	−0.225973	−	0.391397i
$706$	68.0000			2.55921
$707$	4.00000	−	3.46410i	0.150435	−	0.130281i
$708$	−24.0000			−0.901975
$709$	−15.0000	−	25.9808i	−0.563337	−	0.975728i	−0.997202	−	0.0747503i	$-0.976184\pi$
$709$	−15.0000	−	25.9808i	−0.563337	−	0.975728i	0.433865	−	0.900978i	$-0.357149\pi$
$710$	−12.0000	+	20.7846i	−0.450352	+	0.780033i
$711$	0.500000	−	0.866025i	0.0187515	−	0.0324785i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	4.00000			0.149592
$716$	−2.00000	−	3.46410i	−0.0747435	−	0.129460i
$717$	−3.00000	+	5.19615i	−0.112037	+	0.194054i
$718$	−20.0000	+	34.6410i	−0.746393	+	1.29279i
$719$	9.00000	+	15.5885i	0.335643	+	0.581351i	0.983608	−	0.180319i	$-0.0577130\pi$
$719$	9.00000	+	15.5885i	0.335643	+	0.581351i	−0.647965	+	0.761670i	$0.724380\pi$
$720$	8.00000			0.298142
$721$	−3.50000	−	18.1865i	−0.130347	−	0.677302i
$722$	−36.0000			−1.33978
$723$	−7.00000	−	12.1244i	−0.260333	−	0.450910i
$724$	−13.0000	+	22.5167i	−0.483141	+	0.836825i
$725$	2.00000	−	3.46410i	0.0742781	−	0.128654i
$726$	7.00000	+	12.1244i	0.259794	+	0.449977i
$727$	−13.0000			−0.482143			−0.241072	−	0.970507i	$-0.577499\pi$
$727$	−13.0000			−0.482143			−0.241072	+	0.970507i	$0.577499\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−6.00000	−	10.3923i	−0.222070	−	0.384636i
$731$		0			0
$732$	−10.0000	+	17.3205i	−0.369611	+	0.640184i
$733$	7.50000	+	12.9904i	0.277019	+	0.479811i	0.970642	−	0.240527i	$-0.0773202\pi$
$733$	7.50000	+	12.9904i	0.277019	+	0.479811i	−0.693624	+	0.720338i	$0.743987\pi$
$734$	−18.0000			−0.664392
$735$	−11.0000	−	8.66025i	−0.405741	−	0.319438i
$736$		0			0
$737$	−5.00000	−	8.66025i	−0.184177	−	0.319005i
$738$	10.0000	−	17.3205i	0.368105	−	0.637577i
$739$	7.50000	−	12.9904i	0.275892	−	0.477859i	−0.694468	−	0.719524i	$-0.744360\pi$
$739$	7.50000	−	12.9904i	0.275892	−	0.477859i	0.970360	+	0.241665i	$0.0776935\pi$
$740$	6.00000	+	10.3923i	0.220564	+	0.382029i
$741$	1.00000			0.0367359
$742$	−60.0000	−	20.7846i	−2.20267	−	0.763027i
$743$	42.0000			1.54083			0.770415	−	0.637542i	$-0.220049\pi$
$743$	42.0000			1.54083			0.770415	+	0.637542i	$0.220049\pi$
$744$		0			0
$745$	−12.0000	+	20.7846i	−0.439646	+	0.761489i
$746$	−23.0000	+	39.8372i	−0.842090	+	1.45854i
$747$	−3.00000	−	5.19615i	−0.109764	−	0.190117i
$748$		0			0
$749$	−4.00000	−	20.7846i	−0.146157	−	0.759453i
$750$	24.0000			0.876356
$751$	−6.50000	−	11.2583i	−0.237188	−	0.410822i	0.722718	−	0.691143i	$-0.242893\pi$
$751$	−6.50000	−	11.2583i	−0.237188	−	0.410822i	−0.959906	+	0.280321i	$0.909559\pi$
$752$	−12.0000	+	20.7846i	−0.437595	+	0.757937i
$753$	4.00000	−	6.92820i	0.145768	−	0.252478i
$754$	−4.00000	−	6.92820i	−0.145671	−	0.252310i
$755$	32.0000			1.16460
$756$	4.00000	−	3.46410i	0.145479	−	0.125988i
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	−3.00000	−	5.19615i	−0.108965	−	0.188733i
$759$		0			0
$760$		0			0
$761$	24.0000	+	41.5692i	0.869999	+	1.50688i	0.861996	+	0.506915i	$0.169214\pi$
$761$	24.0000	+	41.5692i	0.869999	+	1.50688i	0.00800331	+	0.999968i	$0.497452\pi$
$762$	−30.0000			−1.08679
$763$	18.0000	−	15.5885i	0.651644	−	0.564340i
$764$	20.0000			0.723575
$765$		0			0
$766$	12.0000	−	20.7846i	0.433578	−	0.750978i
$767$	6.00000	−	10.3923i	0.216647	−	0.375244i
$768$	−8.00000	−	13.8564i	−0.288675	−	0.500000i
$769$	−49.0000			−1.76699			−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−49.0000			−1.76699			−0.883493	+	0.468445i	$0.844814\pi$
$770$	4.00000	+	20.7846i	0.144150	+	0.749025i
$771$	26.0000			0.936367
$772$	−11.0000	−	19.0526i	−0.395899	−	0.685717i
$773$	17.0000	−	29.4449i	0.611448	−	1.05906i	−0.379549	−	0.925172i	$-0.623921\pi$
$773$	17.0000	−	29.4449i	0.611448	−	1.05906i	0.990997	−	0.133887i	$-0.0427458\pi$
$774$	−5.00000	+	8.66025i	−0.179721	+	0.311286i
$775$	4.50000	+	7.79423i	0.161645	+	0.279977i
$776$		0			0
$777$	−7.50000	−	2.59808i	−0.269061	−	0.0932055i
$778$	−12.0000			−0.430221
$779$	5.00000	+	8.66025i	0.179144	+	0.310286i
$780$	2.00000	−	3.46410i	0.0716115	−	0.124035i
$781$	−6.00000	+	10.3923i	−0.214697	+	0.371866i
$782$		0			0
$783$	4.00000			0.142948
$784$	−4.00000	+	27.7128i	−0.142857	+	0.989743i
$785$	28.0000			0.999363
$786$	14.0000	+	24.2487i	0.499363	+	0.864923i
$787$	−20.0000	+	34.6410i	−0.712923	+	1.23482i	0.250832	+	0.968031i	$0.419296\pi$
$787$	−20.0000	+	34.6410i	−0.712923	+	1.23482i	−0.963755	+	0.266788i	$0.914038\pi$
$788$	−16.0000	+	27.7128i	−0.569976	+	0.987228i
$789$	−2.00000	−	3.46410i	−0.0712019	−	0.123325i
$790$	4.00000			0.142314
$791$	−25.0000	−	8.66025i	−0.888898	−	0.307923i
$792$		0			0
$793$	−5.00000	−	8.66025i	−0.177555	−	0.307535i
$794$	9.00000	−	15.5885i	0.319398	−	0.553214i
$795$	12.0000	−	20.7846i	0.425596	−	0.737154i
$796$		0			0
$797$	−8.00000			−0.283375			−0.141687	−	0.989911i	$-0.545253\pi$
$797$	−8.00000			−0.283375			−0.141687	+	0.989911i	$0.545253\pi$
$798$	1.00000	+	5.19615i	0.0353996	+	0.183942i
$799$		0			0
$800$	−4.00000	−	6.92820i	−0.141421	−	0.244949i
$801$	−8.00000	+	13.8564i	−0.282666	+	0.489592i
$802$	36.0000	−	62.3538i	1.27120	−	2.20179i
$803$	−3.00000	−	5.19615i	−0.105868	−	0.183368i
$804$	−10.0000			−0.352673
$805$		0			0
$806$	18.0000			0.634023
$807$	−3.00000	−	5.19615i	−0.105605	−	0.182913i
$808$		0			0
$809$	−15.0000	+	25.9808i	−0.527372	+	0.913435i	0.472119	+	0.881535i	$0.343489\pi$
$809$	−15.0000	+	25.9808i	−0.527372	+	0.913435i	−0.999491	+	0.0319002i	$0.989844\pi$
$810$	2.00000	+	3.46410i	0.0702728	+	0.121716i
$811$	32.0000			1.12367			0.561836	−	0.827249i	$-0.310095\pi$
$811$	32.0000			1.12367			0.561836	+	0.827249i	$0.310095\pi$
$812$	16.0000	−	13.8564i	0.561490	−	0.486265i
$813$	16.0000			0.561144
$814$	6.00000	+	10.3923i	0.210300	+	0.364250i
$815$	4.00000	−	6.92820i	0.140114	−	0.242684i
$816$		0			0
$817$	−2.50000	−	4.33013i	−0.0874639	−	0.151492i
$818$	10.0000			0.349642
$819$	0.500000	+	2.59808i	0.0174714	+	0.0907841i
$820$	40.0000			1.39686
$821$	−1.00000	−	1.73205i	−0.0349002	−	0.0604490i	0.848048	−	0.529920i	$-0.177778\pi$
$821$	−1.00000	−	1.73205i	−0.0349002	−	0.0604490i	−0.882948	+	0.469471i	$0.844445\pi$
$822$	12.0000	−	20.7846i	0.418548	−	0.724947i
$823$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$823$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$824$		0			0
$825$	2.00000			0.0696311
$826$	60.0000	+	20.7846i	2.08767	+	0.723189i
$827$	−30.0000			−1.04320			−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000			−1.04320			−0.521601	+	0.853189i	$0.674665\pi$
$828$		0			0
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	0.252113	+	0.967698i	$0.418875\pi$
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	−0.964107	+	0.265513i	$0.914459\pi$
$830$	12.0000	−	20.7846i	0.416526	−	0.721444i
$831$	−6.50000	−	11.2583i	−0.225483	−	0.390547i
$832$	−8.00000			−0.277350
$833$		0			0
$834$	−6.00000			−0.207763
$835$	−14.0000	−	24.2487i	−0.484490	−	0.839161i
$836$	2.00000	−	3.46410i	0.0691714	−	0.119808i
$837$	−4.50000	+	7.79423i	−0.155543	+	0.269408i
$838$	−30.0000	−	51.9615i	−1.03633	−	1.79498i
$839$	−44.0000			−1.51905			−0.759524	−	0.650479i	$-0.774568\pi$
$839$	−44.0000			−1.51905			−0.759524	+	0.650479i	$0.774568\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	7.00000	+	12.1244i	0.241236	+	0.417833i
$843$	2.00000	−	3.46410i	0.0688837	−	0.119310i
$844$	−4.00000	+	6.92820i	−0.137686	+	0.238479i
$845$	−12.0000	−	20.7846i	−0.412813	−	0.715012i
$846$	−12.0000			−0.412568
$847$	−3.50000	−	18.1865i	−0.120261	−	0.624897i
$848$	−48.0000			−1.64833
$849$	5.50000	+	9.52628i	0.188760	+	0.326941i
$850$		0			0
$851$		0			0
$852$	6.00000	+	10.3923i	0.205557	+	0.356034i
$853$	35.0000			1.19838			0.599189	−	0.800608i	$-0.295490\pi$
$853$	35.0000			1.19838			0.599189	+	0.800608i	$0.295490\pi$
$854$	40.0000	−	34.6410i	1.36877	−	1.18539i
$855$	−2.00000			−0.0683986
$856$		0			0
$857$	16.0000	−	27.7128i	0.546550	−	0.946652i	−0.451958	−	0.892039i	$-0.649274\pi$
$857$	16.0000	−	27.7128i	0.546550	−	0.946652i	0.998508	−	0.0546125i	$-0.0173923\pi$
$858$	2.00000	−	3.46410i	0.0682789	−	0.118262i
$859$	20.0000	+	34.6410i	0.682391	+	1.18194i	0.974249	+	0.225475i	$0.0723932\pi$
$859$	20.0000	+	34.6410i	0.682391	+	1.18194i	−0.291858	+	0.956462i	$0.594273\pi$
$860$	−20.0000			−0.681994
$861$	−20.0000	+	17.3205i	−0.681598	+	0.590281i
$862$	−36.0000			−1.22616
$863$	27.0000	+	46.7654i	0.919091	+	1.59191i	0.800799	+	0.598933i	$0.204408\pi$
$863$	27.0000	+	46.7654i	0.919091	+	1.59191i	0.118291	+	0.992979i	$0.462258\pi$
$864$	4.00000	−	6.92820i	0.136083	−	0.235702i
$865$	8.00000	−	13.8564i	0.272008	−	0.471132i
$866$	−31.0000	−	53.6936i	−1.05342	−	1.82458i
$867$	−17.0000			−0.577350
$868$	9.00000	+	46.7654i	0.305480	+	1.58732i
$869$	2.00000			0.0678454
$870$	8.00000	+	13.8564i	0.271225	+	0.469776i
$871$	2.50000	−	4.33013i	0.0847093	−	0.146721i
$872$		0			0
$873$	3.00000	+	5.19615i	0.101535	+	0.175863i
$874$		0			0
$875$	−30.0000	−	10.3923i	−1.01419	−	0.351324i
$876$	−6.00000			−0.202721
$877$	19.0000	+	32.9090i	0.641584	+	1.11126i	0.985079	+	0.172102i	$0.0550559\pi$
$877$	19.0000	+	32.9090i	0.641584	+	1.11126i	−0.343495	+	0.939155i	$0.611611\pi$
$878$		0			0
$879$	−4.00000	+	6.92820i	−0.134917	+	0.233682i
$880$	8.00000	+	13.8564i	0.269680	+	0.467099i
$881$	24.0000			0.808581			0.404290	−	0.914631i	$-0.367519\pi$
$881$	24.0000			0.808581			0.404290	+	0.914631i	$0.367519\pi$
$882$	−13.0000	+	5.19615i	−0.437733	+	0.174964i
$883$	−13.0000			−0.437485			−0.218742	−	0.975783i	$-0.570195\pi$
$883$	−13.0000			−0.437485			−0.218742	+	0.975783i	$0.570195\pi$
$884$		0			0
$885$	−12.0000	+	20.7846i	−0.403376	+	0.698667i
$886$	−12.0000	+	20.7846i	−0.403148	+	0.698273i
$887$	17.0000	+	29.4449i	0.570804	+	0.988662i	0.996484	+	0.0837878i	$0.0267018\pi$
$887$	17.0000	+	29.4449i	0.570804	+	0.988662i	−0.425679	+	0.904874i	$0.639965\pi$
$888$		0			0
$889$	37.5000	+	12.9904i	1.25771	+	0.435683i
$890$	−64.0000			−2.14528
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$	−16.0000	+	27.7128i	−0.535720	+	0.927894i
$893$	3.00000	−	5.19615i	0.100391	−	0.173883i
$894$	12.0000	+	20.7846i	0.401340	+	0.695141i
$895$	−4.00000			−0.133705
$896$		0			0
$897$		0			0
$898$	18.0000	+	31.1769i	0.600668	+	1.04039i
$899$	−18.0000	+	31.1769i	−0.600334	+	1.03981i
$900$	1.00000	−	1.73205i	0.0333333	−	0.0577350i
$901$		0			0
$902$	40.0000			1.33185
$903$	10.0000	−	8.66025i	0.332779	−	0.288195i
$904$		0			0
$905$	13.0000	+	22.5167i	0.432135	+	0.748479i
$906$	16.0000	−	27.7128i	0.531564	−	0.920697i
$907$	18.5000	−	32.0429i	0.614282	−	1.06397i	−0.376228	−	0.926527i	$-0.622779\pi$
$907$	18.5000	−	32.0429i	0.614282	−	1.06397i	0.990510	−	0.137441i	$-0.0438878\pi$
$908$	−18.0000	−	31.1769i	−0.597351	−	1.03464i
$909$	2.00000			0.0663358
$910$	−8.00000	+	6.92820i	−0.265197	+	0.229668i
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$	2.00000	+	3.46410i	0.0662266	+	0.114708i
$913$	6.00000	−	10.3923i	0.198571	−	0.343935i
$914$	11.0000	−	19.0526i	0.363848	−	0.630203i
$915$	10.0000	+	17.3205i	0.330590	+	0.572598i
$916$	−38.0000			−1.25556
$917$	−7.00000	−	36.3731i	−0.231160	−	1.20114i
$918$		0			0
$919$	−11.5000	−	19.9186i	−0.379350	−	0.657053i	0.611618	−	0.791153i	$-0.290519\pi$
$919$	−11.5000	−	19.9186i	−0.379350	−	0.657053i	−0.990968	+	0.134100i	$0.957186\pi$
$920$		0			0
$921$	8.50000	−	14.7224i	0.280085	−	0.485121i
$922$	−20.0000	−	34.6410i	−0.658665	−	1.14084i
$923$	−6.00000			−0.197492
$924$	10.0000	+	3.46410i	0.328976	+	0.113961i
$925$	−3.00000			−0.0986394
$926$	17.0000	+	29.4449i	0.558655	+	0.967618i
$927$	3.50000	−	6.06218i	0.114955	−	0.199108i
$928$	16.0000	−	27.7128i	0.525226	−	0.909718i
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	0.728046	−	0.685529i	$-0.240429\pi$
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	−0.957708	+	0.287742i	$0.907096\pi$
$930$	−36.0000			−1.18049
$931$	1.00000	−	6.92820i	0.0327737	−	0.227063i
$932$	12.0000			0.393073
$933$	3.00000	+	5.19615i	0.0982156	+	0.170114i
$934$	−6.00000	+	10.3923i	−0.196326	+	0.340047i
$935$		0			0
$936$		0			0
$937$	15.0000			0.490029			0.245014	−	0.969519i	$-0.421207\pi$
$937$	15.0000			0.490029			0.245014	+	0.969519i	$0.421207\pi$
$938$	25.0000	+	8.66025i	0.816279	+	0.282767i
$939$	−1.00000			−0.0326338
$940$	−12.0000	−	20.7846i	−0.391397	−	0.677919i
$941$	2.00000	−	3.46410i	0.0651981	−	0.112926i	−0.831584	−	0.555399i	$-0.812565\pi$
$941$	2.00000	−	3.46410i	0.0651981	−	0.112926i	0.896782	+	0.442473i	$0.145899\pi$
$942$	14.0000	−	24.2487i	0.456145	−	0.790066i
$943$		0			0
$944$	48.0000			1.56227
$945$	−1.00000	−	5.19615i	−0.0325300	−	0.169031i
$946$	−20.0000			−0.650256
$947$	5.00000	+	8.66025i	0.162478	+	0.281420i	0.935757	−	0.352646i	$-0.114718\pi$
$947$	5.00000	+	8.66025i	0.162478	+	0.281420i	−0.773279	+	0.634066i	$0.781385\pi$
$948$	1.00000	−	1.73205i	0.0324785	−	0.0562544i
$949$	1.50000	−	2.59808i	0.0486921	−	0.0843371i
$950$	1.00000	+	1.73205i	0.0324443	+	0.0561951i
$951$	24.0000			0.778253
$952$		0			0
$953$	44.0000			1.42530			0.712650	−	0.701520i	$-0.247495\pi$
$953$	44.0000			1.42530			0.712650	+	0.701520i	$0.247495\pi$
$954$	−12.0000	−	20.7846i	−0.388514	−	0.672927i
$955$	10.0000	−	17.3205i	0.323592	−	0.560478i
$956$	−6.00000	+	10.3923i	−0.194054	+	0.336111i
$957$	4.00000	+	6.92820i	0.129302	+	0.223957i
$958$	−56.0000			−1.80928
$959$	−24.0000	+	20.7846i	−0.775000	+	0.671170i
$960$	16.0000			0.516398
$961$	−25.0000	−	43.3013i	−0.806452	−	1.39682i
$962$	−3.00000	+	5.19615i	−0.0967239	+	0.167531i
$963$	4.00000	−	6.92820i	0.128898	−	0.223258i
$964$	−14.0000	−	24.2487i	−0.450910	−	0.780998i
$965$	−22.0000			−0.708205
$966$		0			0
$967$	19.0000			0.610999			0.305499	−	0.952192i	$-0.401177\pi$
$967$	19.0000			0.610999			0.305499	+	0.952192i	$0.401177\pi$
$968$		0			0
$969$		0			0
$970$	−12.0000	+	20.7846i	−0.385297	+	0.667354i
$971$	−18.0000	−	31.1769i	−0.577647	−	1.00051i	−0.995748	−	0.0921142i	$-0.970638\pi$
$971$	−18.0000	−	31.1769i	−0.577647	−	1.00051i	0.418101	−	0.908401i	$-0.362696\pi$
$972$	2.00000			0.0641500
$973$	7.50000	+	2.59808i	0.240439	+	0.0832905i
$974$	62.0000			1.98661
$975$	0.500000	+	0.866025i	0.0160128	+	0.0277350i
$976$	20.0000	−	34.6410i	0.640184	−	1.10883i
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	−0.685381	−	0.728184i	$-0.740364\pi$
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	0.973317	+	0.229465i	$0.0736978\pi$
$978$	−4.00000	−	6.92820i	−0.127906	−	0.221540i
$979$	−32.0000			−1.02272
$980$	−22.0000	−	17.3205i	−0.702764	−	0.553283i
$981$	9.00000			0.287348
$982$	28.0000	+	48.4974i	0.893516	+	1.54761i
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	0.422027	+	0.906583i	$0.361319\pi$
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	−0.996138	+	0.0878058i	$0.972015\pi$
$984$		0			0
$985$	16.0000	+	27.7128i	0.509802	+	0.883004i
$986$		0			0
$987$	15.0000	+	5.19615i	0.477455	+	0.165395i
$988$	2.00000			0.0636285
$989$		0			0
$990$	−4.00000	+	6.92820i	−0.127128	+	0.220193i
$991$	−8.50000	+	14.7224i	−0.270011	+	0.467673i	−0.968864	−	0.247592i	$-0.920361\pi$
$991$	−8.50000	+	14.7224i	−0.270011	+	0.467673i	0.698853	+	0.715265i	$0.253694\pi$
$992$	36.0000	+	62.3538i	1.14300	+	1.97974i
$993$	−25.0000			−0.793351
$994$	−6.00000	−	31.1769i	−0.190308	−	0.988872i
$995$		0			0
$996$	−6.00000	−	10.3923i	−0.190117	−	0.329293i
$997$	−9.50000	+	16.4545i	−0.300868	+	0.521119i	−0.976333	−	0.216274i	$-0.930610\pi$
$997$	−9.50000	+	16.4545i	−0.300868	+	0.521119i	0.675465	+	0.737392i	$0.263943\pi$
$998$	−37.0000	+	64.0859i	−1.17121	+	2.02860i
$999$	−1.50000	−	2.59808i	−0.0474579	−	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.2.e.a.4.1	✓	2
3.2	odd	2		63.2.e.b.46.1		2
4.3	odd	2		336.2.q.f.193.1		2
5.2	odd	4		525.2.r.e.424.2		4
5.3	odd	4		525.2.r.e.424.1		4
5.4	even	2		525.2.i.e.151.1		2
7.2	even	3	inner	21.2.e.a.16.1	yes	2
7.3	odd	6		147.2.a.b.1.1		1
7.4	even	3		147.2.a.c.1.1		1
7.5	odd	6		147.2.e.a.79.1		2
7.6	odd	2		147.2.e.a.67.1		2
8.3	odd	2		1344.2.q.c.193.1		2
8.5	even	2		1344.2.q.m.193.1		2
9.2	odd	6		567.2.g.f.109.1		2
9.4	even	3		567.2.h.f.298.1		2
9.5	odd	6		567.2.h.a.298.1		2
9.7	even	3		567.2.g.a.109.1		2
12.11	even	2		1008.2.s.d.865.1		2
21.2	odd	6		63.2.e.b.37.1		2
21.5	even	6		441.2.e.e.226.1		2
21.11	odd	6		441.2.a.b.1.1		1
21.17	even	6		441.2.a.a.1.1		1
21.20	even	2		441.2.e.e.361.1		2
28.3	even	6		2352.2.a.w.1.1		1
28.11	odd	6		2352.2.a.d.1.1		1
28.19	even	6		2352.2.q.c.961.1		2
28.23	odd	6		336.2.q.f.289.1		2
28.27	even	2		2352.2.q.c.1537.1		2
35.2	odd	12		525.2.r.e.499.1		4
35.4	even	6		3675.2.a.a.1.1		1
35.9	even	6		525.2.i.e.226.1		2
35.23	odd	12		525.2.r.e.499.2		4
35.24	odd	6		3675.2.a.c.1.1		1
56.3	even	6		9408.2.a.k.1.1		1
56.11	odd	6		9408.2.a.cv.1.1		1
56.37	even	6		1344.2.q.m.961.1		2
56.45	odd	6		9408.2.a.bz.1.1		1
56.51	odd	6		1344.2.q.c.961.1		2
56.53	even	6		9408.2.a.bg.1.1		1
63.2	odd	6		567.2.h.a.352.1		2
63.16	even	3		567.2.h.f.352.1		2
63.23	odd	6		567.2.g.f.541.1		2
63.58	even	3		567.2.g.a.541.1		2
84.11	even	6		7056.2.a.bp.1.1		1
84.23	even	6		1008.2.s.d.289.1		2
84.59	odd	6		7056.2.a.m.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.2.e.a.4.1	✓	2	1.1	even	1	trivial
21.2.e.a.16.1	yes	2	7.2	even	3	inner
63.2.e.b.37.1		2	21.2	odd	6
63.2.e.b.46.1		2	3.2	odd	2
147.2.a.b.1.1		1	7.3	odd	6
147.2.a.c.1.1		1	7.4	even	3
147.2.e.a.67.1		2	7.6	odd	2
147.2.e.a.79.1		2	7.5	odd	6
336.2.q.f.193.1		2	4.3	odd	2
336.2.q.f.289.1		2	28.23	odd	6
441.2.a.a.1.1		1	21.17	even	6
441.2.a.b.1.1		1	21.11	odd	6
441.2.e.e.226.1		2	21.5	even	6
441.2.e.e.361.1		2	21.20	even	2
525.2.i.e.151.1		2	5.4	even	2
525.2.i.e.226.1		2	35.9	even	6
525.2.r.e.424.1		4	5.3	odd	4
525.2.r.e.424.2		4	5.2	odd	4
525.2.r.e.499.1		4	35.2	odd	12
525.2.r.e.499.2		4	35.23	odd	12
567.2.g.a.109.1		2	9.7	even	3
567.2.g.a.541.1		2	63.58	even	3
567.2.g.f.109.1		2	9.2	odd	6
567.2.g.f.541.1		2	63.23	odd	6
567.2.h.a.298.1		2	9.5	odd	6
567.2.h.a.352.1		2	63.2	odd	6
567.2.h.f.298.1		2	9.4	even	3
567.2.h.f.352.1		2	63.16	even	3
1008.2.s.d.289.1		2	84.23	even	6
1008.2.s.d.865.1		2	12.11	even	2
1344.2.q.c.193.1		2	8.3	odd	2
1344.2.q.c.961.1		2	56.51	odd	6
1344.2.q.m.193.1		2	8.5	even	2
1344.2.q.m.961.1		2	56.37	even	6
2352.2.a.d.1.1		1	28.11	odd	6
2352.2.a.w.1.1		1	28.3	even	6
2352.2.q.c.961.1		2	28.19	even	6
2352.2.q.c.1537.1		2	28.27	even	2
3675.2.a.a.1.1		1	35.4	even	6
3675.2.a.c.1.1		1	35.24	odd	6
7056.2.a.m.1.1		1	84.59	odd	6
7056.2.a.bp.1.1		1	84.11	even	6
9408.2.a.k.1.1		1	56.3	even	6
9408.2.a.bg.1.1		1	56.53	even	6
9408.2.a.bz.1.1		1	56.45	odd	6
9408.2.a.cv.1.1		1	56.11	odd	6

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	21.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.00000 + 1.73205i) q^{5} +2.00000 q^{6} +(-2.50000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.00000 + 1.73205i) q^{5} +2.00000 q^{6} +(-2.50000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-1.00000 - 1.73205i) q^{12} +1.00000 q^{13} +(1.00000 + 5.19615i) q^{14} -2.00000 q^{15} +(2.00000 + 3.46410i) q^{16} +(-1.00000 + 1.73205i) q^{18} +(-0.500000 - 0.866025i) q^{19} -4.00000 q^{20} +(2.00000 - 1.73205i) q^{21} -4.00000 q^{22} +(0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} +1.00000 q^{27} +(4.00000 - 3.46410i) q^{28} +4.00000 q^{29} +(2.00000 + 3.46410i) q^{30} +(-4.50000 + 7.79423i) q^{31} +(4.00000 - 6.92820i) q^{32} +(1.00000 + 1.73205i) q^{33} +(-1.00000 - 5.19615i) q^{35} +2.00000 q^{36} +(-1.50000 - 2.59808i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(-0.500000 + 0.866025i) q^{39} -10.0000 q^{41} +(-5.00000 - 1.73205i) q^{42} +5.00000 q^{43} +(2.00000 + 3.46410i) q^{44} +(1.00000 - 1.73205i) q^{45} +(3.00000 + 5.19615i) q^{47} -4.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -2.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(-1.00000 - 1.73205i) q^{54} +4.00000 q^{55} +1.00000 q^{57} +(-4.00000 - 6.92820i) q^{58} +(6.00000 - 10.3923i) q^{59} +(2.00000 - 3.46410i) q^{60} +(-5.00000 - 8.66025i) q^{61} +18.0000 q^{62} +(0.500000 + 2.59808i) q^{63} -8.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(2.00000 - 3.46410i) q^{66} +(2.50000 - 4.33013i) q^{67} +(-8.00000 + 6.92820i) q^{70} -6.00000 q^{71} +(1.50000 - 2.59808i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(0.500000 + 0.866025i) q^{75} +2.00000 q^{76} +(-4.00000 + 3.46410i) q^{77} +2.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(-4.00000 + 6.92820i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(10.0000 + 17.3205i) q^{82} +6.00000 q^{83} +(1.00000 + 5.19615i) q^{84} +(-5.00000 - 8.66025i) q^{86} +(-2.00000 + 3.46410i) q^{87} +(-8.00000 - 13.8564i) q^{89} -4.00000 q^{90} +(-2.50000 - 0.866025i) q^{91} +(-4.50000 - 7.79423i) q^{93} +(6.00000 - 10.3923i) q^{94} +(1.00000 - 1.73205i) q^{95} +(4.00000 + 6.92820i) q^{96} -6.00000 q^{97} +(2.00000 - 13.8564i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} - 5 q^{7} - q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 - 2 * q^4 + 2 * q^5 + 4 * q^6 - 5 * q^7 - q^9	\( 2 q - 2 q^{2} - q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{6} - 5 q^{7} - q^{9} + 4 q^{10} + 2 q^{11} - 2 q^{12} + 2 q^{13} + 2 q^{14} - 4 q^{15} + 4 q^{16} - 2 q^{18} - q^{19} - 8 q^{20} + 4 q^{21} - 8 q^{22} + q^{25} - 2 q^{26} + 2 q^{27} + 8 q^{28} + 8 q^{29} + 4 q^{30} - 9 q^{31} + 8 q^{32} + 2 q^{33} - 2 q^{35} + 4 q^{36} - 3 q^{37} - 2 q^{38} - q^{39} - 20 q^{41} - 10 q^{42} + 10 q^{43} + 4 q^{44} + 2 q^{45} + 6 q^{47} - 8 q^{48} + 11 q^{49} - 4 q^{50} - 2 q^{52} - 12 q^{53} - 2 q^{54} + 8 q^{55} + 2 q^{57} - 8 q^{58} + 12 q^{59} + 4 q^{60} - 10 q^{61} + 36 q^{62} + q^{63} - 16 q^{64} + 2 q^{65} + 4 q^{66} + 5 q^{67} - 16 q^{70} - 12 q^{71} + 3 q^{73} - 6 q^{74} + q^{75} + 4 q^{76} - 8 q^{77} + 4 q^{78} + q^{79} - 8 q^{80} - q^{81} + 20 q^{82} + 12 q^{83} + 2 q^{84} - 10 q^{86} - 4 q^{87} - 16 q^{89} - 8 q^{90} - 5 q^{91} - 9 q^{93} + 12 q^{94} + 2 q^{95} + 8 q^{96} - 12 q^{97} + 4 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 - 2 * q^4 + 2 * q^5 + 4 * q^6 - 5 * q^7 - q^9 + 4 * q^10 + 2 * q^11 - 2 * q^12 + 2 * q^13 + 2 * q^14 - 4 * q^15 + 4 * q^16 - 2 * q^18 - q^19 - 8 * q^20 + 4 * q^21 - 8 * q^22 + q^25 - 2 * q^26 + 2 * q^27 + 8 * q^28 + 8 * q^29 + 4 * q^30 - 9 * q^31 + 8 * q^32 + 2 * q^33 - 2 * q^35 + 4 * q^36 - 3 * q^37 - 2 * q^38 - q^39 - 20 * q^41 - 10 * q^42 + 10 * q^43 + 4 * q^44 + 2 * q^45 + 6 * q^47 - 8 * q^48 + 11 * q^49 - 4 * q^50 - 2 * q^52 - 12 * q^53 - 2 * q^54 + 8 * q^55 + 2 * q^57 - 8 * q^58 + 12 * q^59 + 4 * q^60 - 10 * q^61 + 36 * q^62 + q^63 - 16 * q^64 + 2 * q^65 + 4 * q^66 + 5 * q^67 - 16 * q^70 - 12 * q^71 + 3 * q^73 - 6 * q^74 + q^75 + 4 * q^76 - 8 * q^77 + 4 * q^78 + q^79 - 8 * q^80 - q^81 + 20 * q^82 + 12 * q^83 + 2 * q^84 - 10 * q^86 - 4 * q^87 - 16 * q^89 - 8 * q^90 - 5 * q^91 - 9 * q^93 + 12 * q^94 + 2 * q^95 + 8 * q^96 - 12 * q^97 + 4 * q^98 - 4 * q^99

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