LMFDB - Embedded newform 72.2.n.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,2,Mod(13,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("72.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	72.n (of order $6$, 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:	$0.574922894553$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			13.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	72.13
Dual form			72.2.n.a.61.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 1.36603i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.73205 + 1.00000i) q^{5} +(2.36603 - 0.633975i) q^{6} +(-2.00000 - 3.46410i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.366025 - 1.36603i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.73205 + 1.00000i) q^{5} +(2.36603 - 0.633975i) q^{6} +(-2.00000 - 3.46410i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(2.00000 - 2.00000i) q^{10} +(-2.59808 + 1.50000i) q^{11} -3.46410i q^{12} +(-1.73205 - 1.00000i) q^{13} +(-5.46410 + 1.46410i) q^{14} +3.46410i q^{15} +(2.00000 + 3.46410i) q^{16} +5.00000 q^{17} +(3.00000 + 3.00000i) q^{18} +1.00000i q^{19} +(-2.00000 - 3.46410i) q^{20} +(3.46410 - 6.00000i) q^{21} +(1.09808 + 4.09808i) q^{22} +(-1.00000 + 1.73205i) q^{23} +(-4.73205 - 1.26795i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.00000 + 2.00000i) q^{26} -5.19615 q^{27} +8.00000i q^{28} +(4.73205 + 1.26795i) q^{30} +(2.00000 - 3.46410i) q^{31} +(5.46410 - 1.46410i) q^{32} +(-4.50000 - 2.59808i) q^{33} +(1.83013 - 6.83013i) q^{34} -8.00000i q^{35} +(5.19615 - 3.00000i) q^{36} +2.00000i q^{37} +(1.36603 + 0.366025i) q^{38} -3.46410i q^{39} +(-5.46410 + 1.46410i) q^{40} +(2.50000 - 4.33013i) q^{41} +(-6.92820 - 6.92820i) q^{42} +(9.52628 - 5.50000i) q^{43} +6.00000 q^{44} +(-5.19615 + 3.00000i) q^{45} +(2.00000 + 2.00000i) q^{46} +(3.00000 + 5.19615i) q^{47} +(-3.46410 + 6.00000i) q^{48} +(-4.50000 + 7.79423i) q^{49} +(-1.36603 + 0.366025i) q^{50} +(4.33013 + 7.50000i) q^{51} +(2.00000 + 3.46410i) q^{52} +(-1.90192 + 7.09808i) q^{54} -6.00000 q^{55} +(10.9282 + 2.92820i) q^{56} +(-1.50000 + 0.866025i) q^{57} +(0.866025 + 0.500000i) q^{59} +(3.46410 - 6.00000i) q^{60} +(-10.3923 + 6.00000i) q^{61} +(-4.00000 - 4.00000i) q^{62} +12.0000 q^{63} -8.00000i q^{64} +(-2.00000 - 3.46410i) q^{65} +(-5.19615 + 5.19615i) q^{66} +(-2.59808 - 1.50000i) q^{67} +(-8.66025 - 5.00000i) q^{68} -3.46410 q^{69} +(-10.9282 - 2.92820i) q^{70} -6.00000 q^{71} +(-2.19615 - 8.19615i) q^{72} +9.00000 q^{73} +(2.73205 + 0.732051i) q^{74} +(0.866025 - 1.50000i) q^{75} +(1.00000 - 1.73205i) q^{76} +(10.3923 + 6.00000i) q^{77} +(-4.73205 - 1.26795i) q^{78} +(7.00000 + 12.1244i) q^{79} +8.00000i q^{80} +(-4.50000 - 7.79423i) q^{81} +(-5.00000 - 5.00000i) q^{82} +(-3.46410 + 2.00000i) q^{83} +(-12.0000 + 6.92820i) q^{84} +(8.66025 + 5.00000i) q^{85} +(-4.02628 - 15.0263i) q^{86} +(2.19615 - 8.19615i) q^{88} -14.0000 q^{89} +(2.19615 + 8.19615i) q^{90} +8.00000i q^{91} +(3.46410 - 2.00000i) q^{92} +6.92820 q^{93} +(8.19615 - 2.19615i) q^{94} +(-1.00000 + 1.73205i) q^{95} +(6.92820 + 6.92820i) q^{96} +(-0.500000 - 0.866025i) q^{97} +(9.00000 + 9.00000i) q^{98} -9.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 6 q^{6} - 8 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 6 * q^6 - 8 * q^7 - 8 * q^8 - 6 * q^9	$ 4 q - 2 q^{2} + 6 q^{6} - 8 q^{7} - 8 q^{8} - 6 q^{9} + 8 q^{10} - 8 q^{14} + 8 q^{16} + 20 q^{17} + 12 q^{18} - 8 q^{20} - 6 q^{22} - 4 q^{23} - 12 q^{24} - 2 q^{25} - 8 q^{26} + 12 q^{30} + 8 q^{31} + 8 q^{32} - 18 q^{33} - 10 q^{34} + 2 q^{38} - 8 q^{40} + 10 q^{41} + 24 q^{44} + 8 q^{46} + 12 q^{47} - 18 q^{49} - 2 q^{50} + 8 q^{52} - 18 q^{54} - 24 q^{55} + 16 q^{56} - 6 q^{57} - 16 q^{62} + 48 q^{63} - 8 q^{65} - 16 q^{70} - 24 q^{71} + 12 q^{72} + 36 q^{73} + 4 q^{74} + 4 q^{76} - 12 q^{78} + 28 q^{79} - 18 q^{81} - 20 q^{82} - 48 q^{84} + 22 q^{86} - 12 q^{88} - 56 q^{89} - 12 q^{90} + 12 q^{94} - 4 q^{95} - 2 q^{97} + 36 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 6 * q^6 - 8 * q^7 - 8 * q^8 - 6 * q^9 + 8 * q^10 - 8 * q^14 + 8 * q^16 + 20 * q^17 + 12 * q^18 - 8 * q^20 - 6 * q^22 - 4 * q^23 - 12 * q^24 - 2 * q^25 - 8 * q^26 + 12 * q^30 + 8 * q^31 + 8 * q^32 - 18 * q^33 - 10 * q^34 + 2 * q^38 - 8 * q^40 + 10 * q^41 + 24 * q^44 + 8 * q^46 + 12 * q^47 - 18 * q^49 - 2 * q^50 + 8 * q^52 - 18 * q^54 - 24 * q^55 + 16 * q^56 - 6 * q^57 - 16 * q^62 + 48 * q^63 - 8 * q^65 - 16 * q^70 - 24 * q^71 + 12 * q^72 + 36 * q^73 + 4 * q^74 + 4 * q^76 - 12 * q^78 + 28 * q^79 - 18 * q^81 - 20 * q^82 - 48 * q^84 + 22 * q^86 - 12 * q^88 - 56 * q^89 - 12 * q^90 + 12 * q^94 - 4 * q^95 - 2 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$3$	0.866025	+	1.50000i	0.500000	+	0.866025i
$3$	0.866025	+	1.50000i	0.500000	+	0.866025i
$4$	−1.73205	−	1.00000i	−0.866025	−	0.500000i
$5$	1.73205	+	1.00000i	0.774597	+	0.447214i	0.834512	−	0.550990i	$-0.185750\pi$
$5$	1.73205	+	1.00000i	0.774597	+	0.447214i	−0.0599153	+	0.998203i	$0.519083\pi$
$6$	2.36603	−	0.633975i	0.965926	−	0.258819i
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	0.188982	−	0.981981i	$-0.439481\pi$
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$	2.00000	−	2.00000i	0.632456	−	0.632456i
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	−0.837616	−	0.546259i	$-0.816051\pi$
$11$	−2.59808	+	1.50000i	−0.783349	+	0.452267i	0.0542666	+	0.998526i	$0.482718\pi$
$12$		−	3.46410i		−	1.00000i
$13$	−1.73205	−	1.00000i	−0.480384	−	0.277350i	0.240192	−	0.970725i	$-0.422790\pi$
$13$	−1.73205	−	1.00000i	−0.480384	−	0.277350i	−0.720577	+	0.693375i	$0.756123\pi$
$14$	−5.46410	+	1.46410i	−1.46034	+	0.391298i
$15$			3.46410i			0.894427i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	5.00000			1.21268			0.606339	−	0.795206i	$-0.292637\pi$
$17$	5.00000			1.21268			0.606339	+	0.795206i	$0.292637\pi$
$18$	3.00000	+	3.00000i	0.707107	+	0.707107i
$19$			1.00000i			0.229416i	0.993399	+	0.114708i	$0.0365932\pi$
$19$			1.00000i			0.229416i	−0.993399	+	0.114708i	$0.963407\pi$
$20$	−2.00000	−	3.46410i	−0.447214	−	0.774597i
$21$	3.46410	−	6.00000i	0.755929	−	1.30931i
$22$	1.09808	+	4.09808i	0.234111	+	0.873713i
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	−0.951247	−	0.308431i	$-0.900196\pi$
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	0.742732	+	0.669588i	$0.233529\pi$
$24$	−4.73205	−	1.26795i	−0.965926	−	0.258819i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.00000	+	2.00000i	−0.392232	+	0.392232i
$27$	−5.19615			−1.00000
$28$			8.00000i			1.51186i
$29$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$29$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$30$	4.73205	+	1.26795i	0.863950	+	0.231495i
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	5.46410	−	1.46410i	0.965926	−	0.258819i
$33$	−4.50000	−	2.59808i	−0.783349	−	0.452267i
$34$	1.83013	−	6.83013i	0.313864	−	1.17136i
$35$		−	8.00000i		−	1.35225i
$36$	5.19615	−	3.00000i	0.866025	−	0.500000i
$37$			2.00000i			0.328798i	0.986394	+	0.164399i	$0.0525685\pi$
$37$			2.00000i			0.328798i	−0.986394	+	0.164399i	$0.947432\pi$
$38$	1.36603	+	0.366025i	0.221599	+	0.0593772i
$39$		−	3.46410i		−	0.554700i
$40$	−5.46410	+	1.46410i	−0.863950	+	0.231495i
$41$	2.50000	−	4.33013i	0.390434	−	0.676252i	−0.602072	−	0.798441i	$-0.705658\pi$
$41$	2.50000	−	4.33013i	0.390434	−	0.676252i	0.992507	+	0.122189i	$0.0389915\pi$
$42$	−6.92820	−	6.92820i	−1.06904	−	1.06904i
$43$	9.52628	−	5.50000i	1.45274	−	0.838742i	0.454108	−	0.890947i	$-0.349958\pi$
$43$	9.52628	−	5.50000i	1.45274	−	0.838742i	0.998636	+	0.0522047i	$0.0166248\pi$
$44$	6.00000			0.904534
$45$	−5.19615	+	3.00000i	−0.774597	+	0.447214i
$46$	2.00000	+	2.00000i	0.294884	+	0.294884i
$47$	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	$0.689164\pi$
$48$	−3.46410	+	6.00000i	−0.500000	+	0.866025i
$49$	−4.50000	+	7.79423i	−0.642857	+	1.11346i
$50$	−1.36603	+	0.366025i	−0.193185	+	0.0517638i
$51$	4.33013	+	7.50000i	0.606339	+	1.05021i
$52$	2.00000	+	3.46410i	0.277350	+	0.480384i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	−1.90192	+	7.09808i	−0.258819	+	0.965926i
$55$	−6.00000			−0.809040
$56$	10.9282	+	2.92820i	1.46034	+	0.391298i
$57$	−1.50000	+	0.866025i	−0.198680	+	0.114708i
$58$		0			0
$59$	0.866025	+	0.500000i	0.112747	+	0.0650945i	0.555313	−	0.831641i	$-0.312598\pi$
$59$	0.866025	+	0.500000i	0.112747	+	0.0650945i	−0.442566	+	0.896736i	$0.645932\pi$
$60$	3.46410	−	6.00000i	0.447214	−	0.774597i
$61$	−10.3923	+	6.00000i	−1.33060	+	0.768221i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−10.3923	+	6.00000i	−1.33060	+	0.768221i	−0.345207	+	0.938527i	$0.612191\pi$
$62$	−4.00000	−	4.00000i	−0.508001	−	0.508001i
$63$	12.0000			1.51186
$64$		−	8.00000i		−	1.00000i
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$	−5.19615	+	5.19615i	−0.639602	+	0.639602i
$67$	−2.59808	−	1.50000i	−0.317406	−	0.183254i	0.332830	−	0.942987i	$-0.391996\pi$
$67$	−2.59808	−	1.50000i	−0.317406	−	0.183254i	−0.650236	+	0.759733i	$0.725330\pi$
$68$	−8.66025	−	5.00000i	−1.05021	−	0.606339i
$69$	−3.46410			−0.417029
$70$	−10.9282	−	2.92820i	−1.30617	−	0.349987i
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	−2.19615	−	8.19615i	−0.258819	−	0.965926i
$73$	9.00000			1.05337			0.526685	−	0.850060i	$-0.323435\pi$
$73$	9.00000			1.05337			0.526685	+	0.850060i	$0.323435\pi$
$74$	2.73205	+	0.732051i	0.317594	+	0.0850992i
$75$	0.866025	−	1.50000i	0.100000	−	0.173205i
$76$	1.00000	−	1.73205i	0.114708	−	0.198680i
$77$	10.3923	+	6.00000i	1.18431	+	0.683763i
$78$	−4.73205	−	1.26795i	−0.535799	−	0.143567i
$79$	7.00000	+	12.1244i	0.787562	+	1.36410i	0.927457	+	0.373930i	$0.121990\pi$
$79$	7.00000	+	12.1244i	0.787562	+	1.36410i	−0.139895	+	0.990166i	$0.544677\pi$
$80$			8.00000i			0.894427i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−5.00000	−	5.00000i	−0.552158	−	0.552158i
$83$	−3.46410	+	2.00000i	−0.380235	+	0.219529i	−0.677920	−	0.735135i	$-0.737119\pi$
$83$	−3.46410	+	2.00000i	−0.380235	+	0.219529i	0.297686	+	0.954664i	$0.403785\pi$
$84$	−12.0000	+	6.92820i	−1.30931	+	0.755929i
$85$	8.66025	+	5.00000i	0.939336	+	0.542326i
$86$	−4.02628	−	15.0263i	−0.434165	−	1.62033i
$87$		0			0
$88$	2.19615	−	8.19615i	0.234111	−	0.873713i
$89$	−14.0000			−1.48400			−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000			−1.48400			−0.741999	+	0.670402i	$0.766122\pi$
$90$	2.19615	+	8.19615i	0.231495	+	0.863950i
$91$			8.00000i			0.838628i
$92$	3.46410	−	2.00000i	0.361158	−	0.208514i
$93$	6.92820			0.718421
$94$	8.19615	−	2.19615i	0.845369	−	0.226516i
$95$	−1.00000	+	1.73205i	−0.102598	+	0.177705i
$96$	6.92820	+	6.92820i	0.707107	+	0.707107i
$97$	−0.500000	−	0.866025i	−0.0507673	−	0.0879316i	0.839525	−	0.543321i	$-0.182833\pi$
$97$	−0.500000	−	0.866025i	−0.0507673	−	0.0879316i	−0.890292	+	0.455389i	$0.849500\pi$
$98$	9.00000	+	9.00000i	0.909137	+	0.909137i
$99$		−	9.00000i		−	0.904534i
$100$			2.00000i			0.200000i
$101$	−12.1244	+	7.00000i	−1.20642	+	0.696526i	−0.961975	−	0.273138i	$-0.911939\pi$
$101$	−12.1244	+	7.00000i	−1.20642	+	0.696526i	−0.244443	+	0.969664i	$0.578605\pi$
$102$	11.8301	−	3.16987i	1.17136	−	0.313864i
$103$	3.00000	−	5.19615i	0.295599	−	0.511992i	−0.679525	−	0.733652i	$-0.737814\pi$
$103$	3.00000	−	5.19615i	0.295599	−	0.511992i	0.975124	+	0.221660i	$0.0711475\pi$
$104$	5.46410	−	1.46410i	0.535799	−	0.143567i
$105$	12.0000	−	6.92820i	1.17108	−	0.676123i
$106$		0			0
$107$			3.00000i			0.290021i	0.989430	+	0.145010i	$0.0463216\pi$
$107$			3.00000i			0.290021i	−0.989430	+	0.145010i	$0.953678\pi$
$108$	9.00000	+	5.19615i	0.866025	+	0.500000i
$109$		−	20.0000i		−	1.91565i	−0.287348	−	0.957826i	$-0.592774\pi$
$109$		−	20.0000i		−	1.91565i	0.287348	−	0.957826i	$-0.407226\pi$
$110$	−2.19615	+	8.19615i	−0.209395	+	0.781472i
$111$	−3.00000	+	1.73205i	−0.284747	+	0.164399i
$112$	8.00000	−	13.8564i	0.755929	−	1.30931i
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	−0.971930	−	0.235269i	$-0.924403\pi$
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	0.689714	+	0.724082i	$0.257736\pi$
$114$	0.633975	+	2.36603i	0.0593772	+	0.221599i
$115$	−3.46410	+	2.00000i	−0.323029	+	0.186501i
$116$		0			0
$117$	5.19615	−	3.00000i	0.480384	−	0.277350i
$118$	1.00000	−	1.00000i	0.0920575	−	0.0920575i
$119$	−10.0000	−	17.3205i	−0.916698	−	1.58777i
$120$	−6.92820	−	6.92820i	−0.632456	−	0.632456i
$121$	−1.00000	+	1.73205i	−0.0909091	+	0.157459i
$122$	4.39230	+	16.3923i	0.397661	+	1.48409i
$123$	8.66025			0.780869
$124$	−6.92820	+	4.00000i	−0.622171	+	0.359211i
$125$		−	12.0000i		−	1.07331i
$126$	4.39230	−	16.3923i	0.391298	−	1.46034i
$127$	−2.00000			−0.177471			−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000			−0.177471			−0.0887357	+	0.996055i	$0.528283\pi$
$128$	−10.9282	−	2.92820i	−0.965926	−	0.258819i
$129$	16.5000	+	9.52628i	1.45274	+	0.838742i
$130$	−5.46410	+	1.46410i	−0.479233	+	0.128410i
$131$	3.46410	+	2.00000i	0.302660	+	0.174741i	0.643637	−	0.765331i	$-0.277425\pi$
$131$	3.46410	+	2.00000i	0.302660	+	0.174741i	−0.340977	+	0.940072i	$0.610758\pi$
$132$	5.19615	+	9.00000i	0.452267	+	0.783349i
$133$	3.46410	−	2.00000i	0.300376	−	0.173422i
$134$	−3.00000	+	3.00000i	−0.259161	+	0.259161i
$135$	−9.00000	−	5.19615i	−0.774597	−	0.447214i
$136$	−10.0000	+	10.0000i	−0.857493	+	0.857493i
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	0.991694	−	0.128618i	$-0.0410540\pi$
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	−0.607233	+	0.794524i	$0.707721\pi$
$138$	−1.26795	+	4.73205i	−0.107935	+	0.402819i
$139$	−11.2583	−	6.50000i	−0.954919	−	0.551323i	−0.0603135	−	0.998179i	$-0.519210\pi$
$139$	−11.2583	−	6.50000i	−0.954919	−	0.551323i	−0.894606	+	0.446857i	$0.852543\pi$
$140$	−8.00000	+	13.8564i	−0.676123	+	1.17108i
$141$	−5.19615	+	9.00000i	−0.437595	+	0.757937i
$142$	−2.19615	+	8.19615i	−0.184297	+	0.687806i
$143$	6.00000			0.501745
$144$	−12.0000			−1.00000
$145$		0			0
$146$	3.29423	−	12.2942i	0.272632	−	1.01748i
$147$	−15.5885			−1.28571
$148$	2.00000	−	3.46410i	0.164399	−	0.284747i
$149$	−15.5885	−	9.00000i	−1.27706	−	0.737309i	−0.300750	−	0.953703i	$-0.597237\pi$
$149$	−15.5885	−	9.00000i	−1.27706	−	0.737309i	−0.976306	+	0.216394i	$0.930570\pi$
$150$	−1.73205	−	1.73205i	−0.141421	−	0.141421i
$151$	3.00000	+	5.19615i	0.244137	+	0.422857i	0.961888	−	0.273442i	$-0.0881622\pi$
$151$	3.00000	+	5.19615i	0.244137	+	0.422857i	−0.717752	+	0.696299i	$0.754829\pi$
$152$	−2.00000	−	2.00000i	−0.162221	−	0.162221i
$153$	−7.50000	+	12.9904i	−0.606339	+	1.05021i
$154$	12.0000	−	12.0000i	0.966988	−	0.966988i
$155$	6.92820	−	4.00000i	0.556487	−	0.321288i
$156$	−3.46410	+	6.00000i	−0.277350	+	0.480384i
$157$	3.46410	+	2.00000i	0.276465	+	0.159617i	0.631822	−	0.775113i	$-0.282307\pi$
$157$	3.46410	+	2.00000i	0.276465	+	0.159617i	−0.355357	+	0.934731i	$0.615641\pi$
$158$	19.1244	−	5.12436i	1.52145	−	0.407672i
$159$		0			0
$160$	10.9282	+	2.92820i	0.863950	+	0.231495i
$161$	8.00000			0.630488
$162$	−12.2942	+	3.29423i	−0.965926	+	0.258819i
$163$		−	4.00000i		−	0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$		−	4.00000i		−	0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$	−8.66025	+	5.00000i	−0.676252	+	0.390434i
$165$	−5.19615	−	9.00000i	−0.404520	−	0.700649i
$166$	1.46410	+	5.46410i	0.113636	+	0.424097i
$167$	1.00000	−	1.73205i	0.0773823	−	0.134030i	−0.824737	−	0.565516i	$-0.808677\pi$
$167$	1.00000	−	1.73205i	0.0773823	−	0.134030i	0.902120	+	0.431486i	$0.142010\pi$
$168$	5.07180	+	18.9282i	0.391298	+	1.46034i
$169$	−4.50000	−	7.79423i	−0.346154	−	0.599556i
$170$	10.0000	−	10.0000i	0.766965	−	0.766965i
$171$	−2.59808	−	1.50000i	−0.198680	−	0.114708i
$172$	−22.0000			−1.67748
$173$	20.7846	−	12.0000i	1.58022	−	0.912343i	0.585399	−	0.810745i	$-0.300938\pi$
$173$	20.7846	−	12.0000i	1.58022	−	0.912343i	0.994826	−	0.101598i	$-0.0323955\pi$
$174$		0			0
$175$	−2.00000	+	3.46410i	−0.151186	+	0.261861i
$176$	−10.3923	−	6.00000i	−0.783349	−	0.452267i
$177$			1.73205i			0.130189i
$178$	−5.12436	+	19.1244i	−0.384087	+	1.43343i
$179$			20.0000i			1.49487i	0.664335	+	0.747435i	$0.268715\pi$
$179$			20.0000i			1.49487i	−0.664335	+	0.747435i	$0.731285\pi$
$180$	12.0000			0.894427
$181$			10.0000i			0.743294i	0.928374	+	0.371647i	$0.121207\pi$
$181$			10.0000i			0.743294i	−0.928374	+	0.371647i	$0.878793\pi$
$182$	10.9282	+	2.92820i	0.810052	+	0.217053i
$183$	−18.0000	−	10.3923i	−1.33060	−	0.768221i
$184$	−1.46410	−	5.46410i	−0.107935	−	0.402819i
$185$	−2.00000	+	3.46410i	−0.147043	+	0.254686i
$186$	2.53590	−	9.46410i	0.185941	−	0.693942i
$187$	−12.9904	+	7.50000i	−0.949951	+	0.548454i
$188$		−	12.0000i		−	0.875190i
$189$	10.3923	+	18.0000i	0.755929	+	1.30931i
$190$	2.00000	+	2.00000i	0.145095	+	0.145095i
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	0.995610	+	0.0935936i	$0.0298354\pi$
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	−0.416751	+	0.909021i	$0.636831\pi$
$192$	12.0000	−	6.92820i	0.866025	−	0.500000i
$193$	7.50000	−	12.9904i	0.539862	−	0.935068i	−0.459049	−	0.888411i	$-0.651810\pi$
$193$	7.50000	−	12.9904i	0.539862	−	0.935068i	0.998911	−	0.0466572i	$-0.0148568\pi$
$194$	−1.36603	+	0.366025i	−0.0980749	+	0.0262791i
$195$	3.46410	−	6.00000i	0.248069	−	0.429669i
$196$	15.5885	−	9.00000i	1.11346	−	0.642857i
$197$			8.00000i			0.569976i	0.958531	+	0.284988i	$0.0919897\pi$
$197$			8.00000i			0.569976i	−0.958531	+	0.284988i	$0.908010\pi$
$198$	−12.2942	−	3.29423i	−0.873713	−	0.234111i
$199$	−8.00000			−0.567105			−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000			−0.567105			−0.283552	+	0.958957i	$0.591513\pi$
$200$	2.73205	+	0.732051i	0.193185	+	0.0517638i
$201$		−	5.19615i		−	0.366508i
$202$	5.12436	+	19.1244i	0.360548	+	1.34558i
$203$		0			0
$204$		−	17.3205i		−	1.21268i
$205$	8.66025	−	5.00000i	0.604858	−	0.349215i
$206$	−6.00000	−	6.00000i	−0.418040	−	0.418040i
$207$	−3.00000	−	5.19615i	−0.208514	−	0.361158i
$208$		−	8.00000i		−	0.554700i
$209$	−1.50000	−	2.59808i	−0.103757	−	0.179713i
$210$	−5.07180	−	18.9282i	−0.349987	−	1.30617i
$211$	13.8564	+	8.00000i	0.953914	+	0.550743i	0.894295	−	0.447478i	$-0.147678\pi$
$211$	13.8564	+	8.00000i	0.953914	+	0.550743i	0.0596196	+	0.998221i	$0.481011\pi$
$212$		0			0
$213$	−5.19615	−	9.00000i	−0.356034	−	0.616670i
$214$	4.09808	+	1.09808i	0.280139	+	0.0750629i
$215$	22.0000			1.50039
$216$	10.3923	−	10.3923i	0.707107	−	0.707107i
$217$	−16.0000			−1.08615
$218$	−27.3205	−	7.32051i	−1.85038	−	0.495807i
$219$	7.79423	+	13.5000i	0.526685	+	0.912245i
$220$	10.3923	+	6.00000i	0.700649	+	0.404520i
$221$	−8.66025	−	5.00000i	−0.582552	−	0.336336i
$222$	1.26795	+	4.73205i	0.0850992	+	0.317594i
$223$	−1.00000	−	1.73205i	−0.0669650	−	0.115987i	0.830599	−	0.556871i	$-0.187998\pi$
$223$	−1.00000	−	1.73205i	−0.0669650	−	0.115987i	−0.897564	+	0.440884i	$0.854665\pi$
$224$	−16.0000	−	16.0000i	−1.06904	−	1.06904i
$225$	3.00000			0.200000
$226$	6.00000	+	6.00000i	0.399114	+	0.399114i
$227$	6.06218	−	3.50000i	0.402361	−	0.232303i	−0.285141	−	0.958485i	$-0.592041\pi$
$227$	6.06218	−	3.50000i	0.402361	−	0.232303i	0.687502	+	0.726182i	$0.258707\pi$
$228$	3.46410			0.229416
$229$	17.3205	+	10.0000i	1.14457	+	0.660819i	0.947559	−	0.319582i	$-0.103543\pi$
$229$	17.3205	+	10.0000i	1.14457	+	0.660819i	0.197013	+	0.980401i	$0.436876\pi$
$230$	1.46410	+	5.46410i	0.0965400	+	0.360292i
$231$			20.7846i			1.36753i
$232$		0			0
$233$	13.0000			0.851658			0.425829	−	0.904804i	$-0.359982\pi$
$233$	13.0000			0.851658			0.425829	+	0.904804i	$0.359982\pi$
$234$	−2.19615	−	8.19615i	−0.143567	−	0.535799i
$235$			12.0000i			0.782794i
$236$	−1.00000	−	1.73205i	−0.0650945	−	0.112747i
$237$	−12.1244	+	21.0000i	−0.787562	+	1.36410i
$238$	−27.3205	+	7.32051i	−1.77093	+	0.474518i
$239$	15.0000	−	25.9808i	0.970269	−	1.68056i	0.275533	−	0.961292i	$-0.411146\pi$
$239$	15.0000	−	25.9808i	0.970269	−	1.68056i	0.694737	−	0.719264i	$-0.255521\pi$
$240$	−12.0000	+	6.92820i	−0.774597	+	0.447214i
$241$	−8.50000	−	14.7224i	−0.547533	−	0.948355i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−8.50000	−	14.7224i	−0.547533	−	0.948355i	0.450910	−	0.892570i	$-0.351100\pi$
$242$	2.00000	+	2.00000i	0.128565	+	0.128565i
$243$	7.79423	−	13.5000i	0.500000	−	0.866025i
$244$	24.0000			1.53644
$245$	−15.5885	+	9.00000i	−0.995910	+	0.574989i
$246$	3.16987	−	11.8301i	0.202104	−	0.754261i
$247$	1.00000	−	1.73205i	0.0636285	−	0.110208i
$248$	2.92820	+	10.9282i	0.185941	+	0.693942i
$249$	−6.00000	−	3.46410i	−0.380235	−	0.219529i
$250$	−16.3923	−	4.39230i	−1.03674	−	0.277794i
$251$		−	15.0000i		−	0.946792i	−0.880850	−	0.473396i	$-0.843028\pi$
$251$		−	15.0000i		−	0.946792i	0.880850	−	0.473396i	$-0.156972\pi$
$252$	−20.7846	−	12.0000i	−1.30931	−	0.755929i
$253$		−	6.00000i		−	0.377217i
$254$	−0.732051	+	2.73205i	−0.0459330	+	0.171424i
$255$			17.3205i			1.08465i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	−0.999325	−	0.0367485i	$-0.988300\pi$
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	0.531487	+	0.847066i	$0.321633\pi$
$258$	19.0526	−	19.0526i	1.18616	−	1.18616i
$259$	6.92820	−	4.00000i	0.430498	−	0.248548i
$260$			8.00000i			0.496139i
$261$		0			0
$262$	4.00000	−	4.00000i	0.247121	−	0.247121i
$263$	4.00000	+	6.92820i	0.246651	+	0.427211i	0.962594	−	0.270947i	$-0.0873367\pi$
$263$	4.00000	+	6.92820i	0.246651	+	0.427211i	−0.715944	+	0.698158i	$0.754003\pi$
$264$	14.1962	−	3.80385i	0.873713	−	0.234111i
$265$		0			0
$266$	−1.46410	−	5.46410i	−0.0897698	−	0.335026i
$267$	−12.1244	−	21.0000i	−0.741999	−	1.28518i
$268$	3.00000	+	5.19615i	0.183254	+	0.317406i
$269$			12.0000i			0.731653i	0.930683	+	0.365826i	$0.119214\pi$
$269$			12.0000i			0.731653i	−0.930683	+	0.365826i	$0.880786\pi$
$270$	−10.3923	+	10.3923i	−0.632456	+	0.632456i
$271$	12.0000			0.728948			0.364474	−	0.931214i	$-0.381249\pi$
$271$	12.0000			0.728948			0.364474	+	0.931214i	$0.381249\pi$
$272$	10.0000	+	17.3205i	0.606339	+	1.05021i
$273$	−12.0000	+	6.92820i	−0.726273	+	0.419314i
$274$	12.2942	−	3.29423i	0.742722	−	0.199012i
$275$	2.59808	+	1.50000i	0.156670	+	0.0904534i
$276$	6.00000	+	3.46410i	0.361158	+	0.208514i
$277$	−1.73205	+	1.00000i	−0.104069	+	0.0600842i	−0.551131	−	0.834419i	$-0.685804\pi$
$277$	−1.73205	+	1.00000i	−0.104069	+	0.0600842i	0.447062	+	0.894503i	$0.352470\pi$
$278$	−13.0000	+	13.0000i	−0.779688	+	0.779688i
$279$	6.00000	+	10.3923i	0.359211	+	0.622171i
$280$	16.0000	+	16.0000i	0.956183	+	0.956183i
$281$	3.00000	+	5.19615i	0.178965	+	0.309976i	0.941526	−	0.336939i	$-0.109392\pi$
$281$	3.00000	+	5.19615i	0.178965	+	0.309976i	−0.762561	+	0.646916i	$0.776058\pi$
$282$	10.3923	+	10.3923i	0.618853	+	0.618853i
$283$	−17.3205	−	10.0000i	−1.02960	−	0.594438i	−0.112728	−	0.993626i	$-0.535959\pi$
$283$	−17.3205	−	10.0000i	−1.02960	−	0.594438i	−0.916869	+	0.399188i	$0.869292\pi$
$284$	10.3923	+	6.00000i	0.616670	+	0.356034i
$285$	−3.46410			−0.205196
$286$	2.19615	−	8.19615i	0.129861	−	0.484649i
$287$	−20.0000			−1.18056
$288$	−4.39230	+	16.3923i	−0.258819	+	0.965926i
$289$	8.00000			0.470588
$290$		0			0
$291$	0.866025	−	1.50000i	0.0507673	−	0.0879316i
$292$	−15.5885	−	9.00000i	−0.912245	−	0.526685i
$293$	−10.3923	−	6.00000i	−0.607125	−	0.350524i	0.164714	−	0.986341i	$-0.447330\pi$
$293$	−10.3923	−	6.00000i	−0.607125	−	0.350524i	−0.771839	+	0.635818i	$0.780663\pi$
$294$	−5.70577	+	21.2942i	−0.332767	+	1.24190i
$295$	1.00000	+	1.73205i	0.0582223	+	0.100844i
$296$	−4.00000	−	4.00000i	−0.232495	−	0.232495i
$297$	13.5000	−	7.79423i	0.783349	−	0.452267i
$298$	−18.0000	+	18.0000i	−1.04271	+	1.04271i
$299$	3.46410	−	2.00000i	0.200334	−	0.115663i
$300$	−3.00000	+	1.73205i	−0.173205	+	0.100000i
$301$	−38.1051	−	22.0000i	−2.19634	−	1.26806i
$302$	8.19615	−	2.19615i	0.471636	−	0.126374i
$303$	−21.0000	−	12.1244i	−1.20642	−	0.696526i
$304$	−3.46410	+	2.00000i	−0.198680	+	0.114708i
$305$	−24.0000			−1.37424
$306$	15.0000	+	15.0000i	0.857493	+	0.857493i
$307$		−	9.00000i		−	0.513657i	−0.966457	−	0.256829i	$-0.917322\pi$
$307$		−	9.00000i		−	0.513657i	0.966457	−	0.256829i	$-0.0826776\pi$
$308$	−12.0000	−	20.7846i	−0.683763	−	1.18431i
$309$	10.3923			0.591198
$310$	−2.92820	−	10.9282i	−0.166311	−	0.620680i
$311$	−10.0000	+	17.3205i	−0.567048	+	0.982156i	0.429808	+	0.902920i	$0.358581\pi$
$311$	−10.0000	+	17.3205i	−0.567048	+	0.982156i	−0.996856	+	0.0792356i	$0.974752\pi$
$312$	6.92820	+	6.92820i	0.392232	+	0.392232i
$313$	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	$0.824336\pi$
$314$	4.00000	−	4.00000i	0.225733	−	0.225733i
$315$	20.7846	+	12.0000i	1.17108	+	0.676123i
$316$		−	28.0000i		−	1.57512i
$317$	19.0526	−	11.0000i	1.07010	−	0.617822i	0.141890	−	0.989882i	$-0.454682\pi$
$317$	19.0526	−	11.0000i	1.07010	−	0.617822i	0.928208	+	0.372061i	$0.121349\pi$
$318$		0			0
$319$		0			0
$320$	8.00000	−	13.8564i	0.447214	−	0.774597i
$321$	−4.50000	+	2.59808i	−0.251166	+	0.145010i
$322$	2.92820	−	10.9282i	0.163182	−	0.609005i
$323$			5.00000i			0.278207i
$324$			18.0000i			1.00000i
$325$			2.00000i			0.110940i
$326$	−5.46410	−	1.46410i	−0.302629	−	0.0810891i
$327$	30.0000	−	17.3205i	1.65900	−	0.957826i
$328$	3.66025	+	13.6603i	0.202104	+	0.754261i
$329$	12.0000	−	20.7846i	0.661581	−	1.14589i
$330$	−14.1962	+	3.80385i	−0.781472	+	0.209395i
$331$	17.3205	−	10.0000i	0.952021	−	0.549650i	0.0583130	−	0.998298i	$-0.481428\pi$
$331$	17.3205	−	10.0000i	0.952021	−	0.549650i	0.893708	+	0.448649i	$0.148095\pi$
$332$	8.00000			0.439057
$333$	−5.19615	−	3.00000i	−0.284747	−	0.164399i
$334$	−2.00000	−	2.00000i	−0.109435	−	0.109435i
$335$	−3.00000	−	5.19615i	−0.163908	−	0.283896i
$336$	27.7128			1.51186
$337$	−3.50000	+	6.06218i	−0.190657	+	0.330228i	−0.945468	−	0.325714i	$-0.894395\pi$
$337$	−3.50000	+	6.06218i	−0.190657	+	0.330228i	0.754811	+	0.655942i	$0.227729\pi$
$338$	−12.2942	+	3.29423i	−0.668718	+	0.179182i
$339$	−10.3923			−0.564433
$340$	−10.0000	−	17.3205i	−0.542326	−	0.939336i
$341$			12.0000i			0.649836i
$342$	−3.00000	+	3.00000i	−0.162221	+	0.162221i
$343$	8.00000			0.431959
$344$	−8.05256	+	30.0526i	−0.434165	+	1.62033i
$345$	−6.00000	−	3.46410i	−0.323029	−	0.186501i
$346$	−8.78461	−	32.7846i	−0.472264	−	1.76251i
$347$	−11.2583	−	6.50000i	−0.604379	−	0.348938i	0.166383	−	0.986061i	$-0.446791\pi$
$347$	−11.2583	−	6.50000i	−0.604379	−	0.348938i	−0.770762	+	0.637123i	$0.780124\pi$
$348$		0			0
$349$	−13.8564	+	8.00000i	−0.741716	+	0.428230i	−0.822693	−	0.568486i	$-0.807529\pi$
$349$	−13.8564	+	8.00000i	−0.741716	+	0.428230i	0.0809766	+	0.996716i	$0.474196\pi$
$350$	4.00000	+	4.00000i	0.213809	+	0.213809i
$351$	9.00000	+	5.19615i	0.480384	+	0.277350i
$352$	−12.0000	+	12.0000i	−0.639602	+	0.639602i
$353$	−7.50000	−	12.9904i	−0.399185	−	0.691408i	0.594441	−	0.804139i	$-0.297373\pi$
$353$	−7.50000	−	12.9904i	−0.399185	−	0.691408i	−0.993626	+	0.112731i	$0.964040\pi$
$354$	2.36603	+	0.633975i	0.125753	+	0.0336954i
$355$	−10.3923	−	6.00000i	−0.551566	−	0.318447i
$356$	24.2487	+	14.0000i	1.28518	+	0.741999i
$357$	17.3205	−	30.0000i	0.916698	−	1.58777i
$358$	27.3205	+	7.32051i	1.44393	+	0.386901i
$359$	−4.00000			−0.211112			−0.105556	−	0.994413i	$-0.533662\pi$
$359$	−4.00000			−0.211112			−0.105556	+	0.994413i	$0.533662\pi$
$360$	4.39230	−	16.3923i	0.231495	−	0.863950i
$361$	18.0000			0.947368
$362$	13.6603	+	3.66025i	0.717967	+	0.192379i
$363$	−3.46410			−0.181818
$364$	8.00000	−	13.8564i	0.419314	−	0.726273i
$365$	15.5885	+	9.00000i	0.815937	+	0.471082i
$366$	−20.7846	+	20.7846i	−1.08643	+	1.08643i
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	0.529607	−	0.848243i	$-0.322339\pi$
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	−0.999404	+	0.0345320i	$0.989006\pi$
$368$	−8.00000			−0.417029
$369$	7.50000	+	12.9904i	0.390434	+	0.676252i
$370$	4.00000	+	4.00000i	0.207950	+	0.207950i
$371$		0			0
$372$	−12.0000	−	6.92820i	−0.622171	−	0.359211i
$373$	22.5167	+	13.0000i	1.16587	+	0.673114i	0.952703	−	0.303902i	$-0.0982894\pi$
$373$	22.5167	+	13.0000i	1.16587	+	0.673114i	0.213165	+	0.977016i	$0.431623\pi$
$374$	5.49038	+	20.4904i	0.283901	+	1.05953i
$375$	18.0000	−	10.3923i	0.929516	−	0.536656i
$376$	−16.3923	−	4.39230i	−0.845369	−	0.226516i
$377$		0			0
$378$	28.3923	−	7.60770i	1.46034	−	0.391298i
$379$		−	5.00000i		−	0.256833i	−0.991720	−	0.128416i	$-0.959011\pi$
$379$		−	5.00000i		−	0.256833i	0.991720	−	0.128416i	$-0.0409894\pi$
$380$	3.46410	−	2.00000i	0.177705	−	0.102598i
$381$	−1.73205	−	3.00000i	−0.0887357	−	0.153695i
$382$	21.8564	−	5.85641i	1.11827	−	0.299640i
$383$	−9.00000	+	15.5885i	−0.459879	+	0.796533i	−0.998954	−	0.0457244i	$-0.985440\pi$
$383$	−9.00000	+	15.5885i	−0.459879	+	0.796533i	0.539076	+	0.842257i	$0.318774\pi$
$384$	−5.07180	−	18.9282i	−0.258819	−	0.965926i
$385$	12.0000	+	20.7846i	0.611577	+	1.05928i
$386$	−15.0000	−	15.0000i	−0.763480	−	0.763480i
$387$			33.0000i			1.67748i
$388$			2.00000i			0.101535i
$389$	6.92820	−	4.00000i	0.351274	−	0.202808i	−0.313972	−	0.949432i	$-0.601660\pi$
$389$	6.92820	−	4.00000i	0.351274	−	0.202808i	0.665246	+	0.746624i	$0.268327\pi$
$390$	−6.92820	−	6.92820i	−0.350823	−	0.350823i
$391$	−5.00000	+	8.66025i	−0.252861	+	0.437968i
$392$	−6.58846	−	24.5885i	−0.332767	−	1.24190i
$393$			6.92820i			0.349482i
$394$	10.9282	+	2.92820i	0.550555	+	0.147521i
$395$			28.0000i			1.40883i
$396$	−9.00000	+	15.5885i	−0.452267	+	0.783349i
$397$			22.0000i			1.10415i	0.833795	+	0.552074i	$0.186163\pi$
$397$			22.0000i			1.10415i	−0.833795	+	0.552074i	$0.813837\pi$
$398$	−2.92820	+	10.9282i	−0.146778	+	0.547781i
$399$	6.00000	+	3.46410i	0.300376	+	0.173422i
$400$	2.00000	−	3.46410i	0.100000	−	0.173205i
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	−0.615725	−	0.787961i	$-0.711137\pi$
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	0.990257	+	0.139253i	$0.0444700\pi$
$402$	−7.09808	−	1.90192i	−0.354020	−	0.0948593i
$403$	−6.92820	+	4.00000i	−0.345118	+	0.199254i
$404$	28.0000			1.39305
$405$		−	18.0000i		−	0.894427i
$406$		0			0
$407$	−3.00000	−	5.19615i	−0.148704	−	0.257564i
$408$	−23.6603	−	6.33975i	−1.17136	−	0.313864i
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	0.173064	+	0.984911i	$0.444633\pi$
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	−0.939490	+	0.342578i	$0.888700\pi$
$410$	−3.66025	−	13.6603i	−0.180767	−	0.674632i
$411$	−7.79423	+	13.5000i	−0.384461	+	0.665906i
$412$	−10.3923	+	6.00000i	−0.511992	+	0.295599i
$413$		−	4.00000i		−	0.196827i
$414$	−8.19615	+	2.19615i	−0.402819	+	0.107935i
$415$	−8.00000			−0.392705
$416$	−10.9282	−	2.92820i	−0.535799	−	0.143567i
$417$		−	22.5167i		−	1.10265i
$418$	−4.09808	+	1.09808i	−0.200443	+	0.0537087i
$419$	−31.1769	−	18.0000i	−1.52309	−	0.879358i	−0.999627	−	0.0273103i	$-0.991306\pi$
$419$	−31.1769	−	18.0000i	−1.52309	−	0.879358i	−0.523465	−	0.852047i	$-0.675361\pi$
$420$	−27.7128			−1.35225
$421$	19.0526	−	11.0000i	0.928565	−	0.536107i	0.0422075	−	0.999109i	$-0.486561\pi$
$421$	19.0526	−	11.0000i	0.928565	−	0.536107i	0.886357	+	0.463002i	$0.153228\pi$
$422$	16.0000	−	16.0000i	0.778868	−	0.778868i
$423$	−18.0000			−0.875190
$424$		0			0
$425$	−2.50000	−	4.33013i	−0.121268	−	0.210042i
$426$	−14.1962	+	3.80385i	−0.687806	+	0.184297i
$427$	41.5692	+	24.0000i	2.01168	+	1.16144i
$428$	3.00000	−	5.19615i	0.145010	−	0.251166i
$429$	5.19615	+	9.00000i	0.250873	+	0.434524i
$430$	8.05256	−	30.0526i	0.388329	−	1.44926i
$431$	−36.0000			−1.73406			−0.867029	−	0.498257i	$-0.833974\pi$
$431$	−36.0000			−1.73406			−0.867029	+	0.498257i	$0.833974\pi$
$432$	−10.3923	−	18.0000i	−0.500000	−	0.866025i
$433$	5.00000			0.240285			0.120142	−	0.992757i	$-0.461665\pi$
$433$	5.00000			0.240285			0.120142	+	0.992757i	$0.461665\pi$
$434$	−5.85641	+	21.8564i	−0.281117	+	1.04914i
$435$		0			0
$436$	−20.0000	+	34.6410i	−0.957826	+	1.65900i
$437$	−1.73205	−	1.00000i	−0.0828552	−	0.0478365i
$438$	21.2942	−	5.70577i	1.01748	−	0.272632i
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$	12.0000	−	12.0000i	0.572078	−	0.572078i
$441$	−13.5000	−	23.3827i	−0.642857	−	1.11346i
$442$	−10.0000	+	10.0000i	−0.475651	+	0.475651i
$443$	−7.79423	+	4.50000i	−0.370315	+	0.213801i	−0.673596	−	0.739100i	$-0.735251\pi$
$443$	−7.79423	+	4.50000i	−0.370315	+	0.213801i	0.303281	+	0.952901i	$0.401918\pi$
$444$	6.92820			0.328798
$445$	−24.2487	−	14.0000i	−1.14950	−	0.663664i
$446$	−2.73205	+	0.732051i	−0.129366	+	0.0346636i
$447$		−	31.1769i		−	1.47462i
$448$	−27.7128	+	16.0000i	−1.30931	+	0.755929i
$449$	21.0000			0.991051			0.495526	−	0.868593i	$-0.334975\pi$
$449$	21.0000			0.991051			0.495526	+	0.868593i	$0.334975\pi$
$450$	1.09808	−	4.09808i	0.0517638	−	0.193185i
$451$			15.0000i			0.706322i
$452$	10.3923	−	6.00000i	0.488813	−	0.282216i
$453$	−5.19615	+	9.00000i	−0.244137	+	0.422857i
$454$	−2.56218	−	9.56218i	−0.120249	−	0.448775i
$455$	−8.00000	+	13.8564i	−0.375046	+	0.649598i
$456$	1.26795	−	4.73205i	0.0593772	−	0.221599i
$457$	18.5000	+	32.0429i	0.865393	+	1.49891i	0.866656	+	0.498906i	$0.166265\pi$
$457$	18.5000	+	32.0429i	0.865393	+	1.49891i	−0.00126243	+	0.999999i	$0.500402\pi$
$458$	20.0000	−	20.0000i	0.934539	−	0.934539i
$459$	−25.9808			−1.21268
$460$	8.00000			0.373002
$461$	−5.19615	+	3.00000i	−0.242009	+	0.139724i	−0.616100	−	0.787668i	$-0.711288\pi$
$461$	−5.19615	+	3.00000i	−0.242009	+	0.139724i	0.374091	+	0.927392i	$0.377955\pi$
$462$	28.3923	+	7.60770i	1.32093	+	0.353942i
$463$	−5.00000	+	8.66025i	−0.232370	+	0.402476i	−0.958505	−	0.285076i	$-0.907981\pi$
$463$	−5.00000	+	8.66025i	−0.232370	+	0.402476i	0.726135	+	0.687552i	$0.241315\pi$
$464$		0			0
$465$	12.0000	+	6.92820i	0.556487	+	0.321288i
$466$	4.75833	−	17.7583i	0.220425	−	0.822639i
$467$		−	29.0000i		−	1.34196i	−0.741475	−	0.670980i	$-0.765874\pi$
$467$		−	29.0000i		−	1.34196i	0.741475	−	0.670980i	$-0.234126\pi$
$468$	−12.0000			−0.554700
$469$			12.0000i			0.554109i
$470$	16.3923	+	4.39230i	0.756121	+	0.202602i
$471$			6.92820i			0.319235i
$472$	−2.73205	+	0.732051i	−0.125753	+	0.0336954i
$473$	−16.5000	+	28.5788i	−0.758671	+	1.31406i
$474$	24.2487	+	24.2487i	1.11378	+	1.11378i
$475$	0.866025	−	0.500000i	0.0397360	−	0.0229416i
$476$			40.0000i			1.83340i
$477$		0			0
$478$	−30.0000	−	30.0000i	−1.37217	−	1.37217i
$479$	−8.00000	−	13.8564i	−0.365529	−	0.633115i	0.623332	−	0.781958i	$-0.285779\pi$
$479$	−8.00000	−	13.8564i	−0.365529	−	0.633115i	−0.988861	+	0.148842i	$0.952445\pi$
$480$	5.07180	+	18.9282i	0.231495	+	0.863950i
$481$	2.00000	−	3.46410i	0.0911922	−	0.157949i
$482$	−23.2224	+	6.22243i	−1.05775	+	0.283424i
$483$	6.92820	+	12.0000i	0.315244	+	0.546019i
$484$	3.46410	−	2.00000i	0.157459	−	0.0909091i
$485$		−	2.00000i		−	0.0908153i
$486$	−15.5885	−	15.5885i	−0.707107	−	0.707107i
$487$	20.0000			0.906287			0.453143	−	0.891438i	$-0.350303\pi$
$487$	20.0000			0.906287			0.453143	+	0.891438i	$0.350303\pi$
$488$	8.78461	−	32.7846i	0.397661	−	1.48409i
$489$	6.00000	−	3.46410i	0.271329	−	0.156652i
$490$	6.58846	+	24.5885i	0.297636	+	1.11079i
$491$	16.4545	+	9.50000i	0.742580	+	0.428729i	0.823007	−	0.568032i	$-0.192295\pi$
$491$	16.4545	+	9.50000i	0.742580	+	0.428729i	−0.0804264	+	0.996761i	$0.525628\pi$
$492$	−15.0000	−	8.66025i	−0.676252	−	0.390434i
$493$		0			0
$494$	−2.00000	−	2.00000i	−0.0899843	−	0.0899843i
$495$	9.00000	−	15.5885i	0.404520	−	0.700649i
$496$	16.0000			0.718421
$497$	12.0000	+	20.7846i	0.538274	+	0.932317i
$498$	−6.92820	+	6.92820i	−0.310460	+	0.310460i
$499$	12.9904	+	7.50000i	0.581529	+	0.335746i	0.761741	−	0.647882i	$-0.224345\pi$
$499$	12.9904	+	7.50000i	0.581529	+	0.335746i	−0.180212	+	0.983628i	$0.557678\pi$
$500$	−12.0000	+	20.7846i	−0.536656	+	0.929516i
$501$	3.46410			0.154765
$502$	−20.4904	−	5.49038i	−0.914530	−	0.245048i
$503$	36.0000			1.60516			0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000			1.60516			0.802580	+	0.596544i	$0.203460\pi$
$504$	−24.0000	+	24.0000i	−1.06904	+	1.06904i
$505$	−28.0000			−1.24598
$506$	−8.19615	−	2.19615i	−0.364363	−	0.0976309i
$507$	7.79423	−	13.5000i	0.346154	−	0.599556i
$508$	3.46410	+	2.00000i	0.153695	+	0.0887357i
$509$	31.1769	+	18.0000i	1.38189	+	0.797836i	0.992384	−	0.123187i	$-0.0393114\pi$
$509$	31.1769	+	18.0000i	1.38189	+	0.797836i	0.389509	+	0.921023i	$0.372645\pi$
$510$	23.6603	+	6.33975i	1.04769	+	0.280729i
$511$	−18.0000	−	31.1769i	−0.796273	−	1.37919i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$		−	5.19615i		−	0.229416i
$514$	15.0000	+	15.0000i	0.661622	+	0.661622i
$515$	10.3923	−	6.00000i	0.457940	−	0.264392i
$516$	−19.0526	−	33.0000i	−0.838742	−	1.45274i
$517$	−15.5885	−	9.00000i	−0.685580	−	0.395820i
$518$	−2.92820	−	10.9282i	−0.128658	−	0.480158i
$519$	36.0000	+	20.7846i	1.58022	+	0.912343i
$520$	10.9282	+	2.92820i	0.479233	+	0.128410i
$521$	15.0000			0.657162			0.328581	−	0.944476i	$-0.393430\pi$
$521$	15.0000			0.657162			0.328581	+	0.944476i	$0.393430\pi$
$522$		0			0
$523$		−	36.0000i		−	1.57417i	−0.616844	−	0.787085i	$-0.711589\pi$
$523$		−	36.0000i		−	1.57417i	0.616844	−	0.787085i	$-0.288411\pi$
$524$	−4.00000	−	6.92820i	−0.174741	−	0.302660i
$525$	−6.92820			−0.302372
$526$	10.9282	−	2.92820i	0.476492	−	0.127676i
$527$	10.0000	−	17.3205i	0.435607	−	0.754493i
$528$		−	20.7846i		−	0.904534i
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$		0			0
$531$	−2.59808	+	1.50000i	−0.112747	+	0.0650945i
$532$	−8.00000			−0.346844
$533$	−8.66025	+	5.00000i	−0.375117	+	0.216574i
$534$	−33.1244	+	8.87564i	−1.43343	+	0.384087i
$535$	−3.00000	+	5.19615i	−0.129701	+	0.224649i
$536$	8.19615	−	2.19615i	0.354020	−	0.0948593i
$537$	−30.0000	+	17.3205i	−1.29460	+	0.747435i
$538$	16.3923	+	4.39230i	0.706722	+	0.189366i
$539$		−	27.0000i		−	1.16297i
$540$	10.3923	+	18.0000i	0.447214	+	0.774597i
$541$		−	22.0000i		−	0.945854i	−0.881102	−	0.472927i	$-0.843197\pi$
$541$		−	22.0000i		−	0.945854i	0.881102	−	0.472927i	$-0.156803\pi$
$542$	4.39230	−	16.3923i	0.188666	−	0.704110i
$543$	−15.0000	+	8.66025i	−0.643712	+	0.371647i
$544$	27.3205	−	7.32051i	1.17136	−	0.313864i
$545$	20.0000	−	34.6410i	0.856706	−	1.48386i
$546$	5.07180	+	18.9282i	0.217053	+	0.810052i
$547$	−30.3109	+	17.5000i	−1.29600	+	0.748246i	−0.979711	−	0.200417i	$-0.935770\pi$
$547$	−30.3109	+	17.5000i	−1.29600	+	0.748246i	−0.316289	+	0.948663i	$0.602437\pi$
$548$		−	18.0000i		−	0.768922i
$549$		−	36.0000i		−	1.53644i
$550$	3.00000	−	3.00000i	0.127920	−	0.127920i
$551$		0			0
$552$	6.92820	−	6.92820i	0.294884	−	0.294884i
$553$	28.0000	−	48.4974i	1.19068	−	2.06232i
$554$	0.732051	+	2.73205i	0.0311019	+	0.116074i
$555$	−6.92820			−0.294086
$556$	13.0000	+	22.5167i	0.551323	+	0.954919i
$557$		−	24.0000i		−	1.01691i	−0.861088	−	0.508456i	$-0.830216\pi$
$557$		−	24.0000i		−	1.01691i	0.861088	−	0.508456i	$-0.169784\pi$
$558$	16.3923	−	4.39230i	0.693942	−	0.185941i
$559$	−22.0000			−0.930501
$560$	27.7128	−	16.0000i	1.17108	−	0.676123i
$561$	−22.5000	−	12.9904i	−0.949951	−	0.548454i
$562$	8.19615	−	2.19615i	0.345734	−	0.0926391i
$563$	7.79423	+	4.50000i	0.328488	+	0.189652i	0.655169	−	0.755482i	$-0.272597\pi$
$563$	7.79423	+	4.50000i	0.328488	+	0.189652i	−0.326682	+	0.945134i	$0.605931\pi$
$564$	18.0000	−	10.3923i	0.757937	−	0.437595i
$565$	−10.3923	+	6.00000i	−0.437208	+	0.252422i
$566$	−20.0000	+	20.0000i	−0.840663	+	0.840663i
$567$	−18.0000	+	31.1769i	−0.755929	+	1.30931i
$568$	12.0000	−	12.0000i	0.503509	−	0.503509i
$569$	−19.5000	−	33.7750i	−0.817483	−	1.41592i	−0.907532	−	0.419984i	$-0.862036\pi$
$569$	−19.5000	−	33.7750i	−0.817483	−	1.41592i	0.0900490	−	0.995937i	$-0.471298\pi$
$570$	−1.26795	+	4.73205i	−0.0531085	+	0.198204i
$571$	4.33013	+	2.50000i	0.181210	+	0.104622i	0.587861	−	0.808962i	$-0.299970\pi$
$571$	4.33013	+	2.50000i	0.181210	+	0.104622i	−0.406651	+	0.913584i	$0.633303\pi$
$572$	−10.3923	−	6.00000i	−0.434524	−	0.250873i
$573$	−13.8564	+	24.0000i	−0.578860	+	1.00261i
$574$	−7.32051	+	27.3205i	−0.305552	+	1.14034i
$575$	2.00000			0.0834058
$576$	20.7846	+	12.0000i	0.866025	+	0.500000i
$577$	−33.0000			−1.37381			−0.686904	−	0.726748i	$-0.741031\pi$
$577$	−33.0000			−1.37381			−0.686904	+	0.726748i	$0.741031\pi$
$578$	2.92820	−	10.9282i	0.121797	−	0.454553i
$579$	25.9808			1.07972
$580$		0			0
$581$	13.8564	+	8.00000i	0.574861	+	0.331896i
$582$	−1.73205	−	1.73205i	−0.0717958	−	0.0717958i
$583$		0			0
$584$	−18.0000	+	18.0000i	−0.744845	+	0.744845i
$585$	12.0000			0.496139
$586$	−12.0000	+	12.0000i	−0.495715	+	0.495715i
$587$	−32.0429	+	18.5000i	−1.32255	+	0.763577i	−0.984135	−	0.177419i	$-0.943225\pi$
$587$	−32.0429	+	18.5000i	−1.32255	+	0.763577i	−0.338418	+	0.940996i	$0.609892\pi$
$588$	27.0000	+	15.5885i	1.11346	+	0.642857i
$589$	3.46410	+	2.00000i	0.142736	+	0.0824086i
$590$	2.73205	−	0.732051i	0.112477	−	0.0301381i
$591$	−12.0000	+	6.92820i	−0.493614	+	0.284988i
$592$	−6.92820	+	4.00000i	−0.284747	+	0.164399i
$593$	−30.0000			−1.23195			−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000			−1.23195			−0.615976	+	0.787765i	$0.711238\pi$
$594$	−5.70577	−	21.2942i	−0.234111	−	0.873713i
$595$		−	40.0000i		−	1.63984i
$596$	18.0000	+	31.1769i	0.737309	+	1.27706i
$597$	−6.92820	−	12.0000i	−0.283552	−	0.491127i
$598$	−1.46410	−	5.46410i	−0.0598716	−	0.223444i
$599$	−19.0000	+	32.9090i	−0.776319	+	1.34462i	0.157731	+	0.987482i	$0.449582\pi$
$599$	−19.0000	+	32.9090i	−0.776319	+	1.34462i	−0.934050	+	0.357142i	$0.883751\pi$
$600$	1.26795	+	4.73205i	0.0517638	+	0.193185i
$601$	−2.50000	−	4.33013i	−0.101977	−	0.176630i	0.810522	−	0.585708i	$-0.199184\pi$
$601$	−2.50000	−	4.33013i	−0.101977	−	0.176630i	−0.912499	+	0.409079i	$0.865850\pi$
$602$	−44.0000	+	44.0000i	−1.79331	+	1.79331i
$603$	7.79423	−	4.50000i	0.317406	−	0.183254i
$604$		−	12.0000i		−	0.488273i
$605$	−3.46410	+	2.00000i	−0.140836	+	0.0813116i
$606$	−24.2487	+	24.2487i	−0.985037	+	0.985037i
$607$	10.0000	−	17.3205i	0.405887	−	0.703018i	−0.588537	−	0.808470i	$-0.700296\pi$
$607$	10.0000	−	17.3205i	0.405887	−	0.703018i	0.994424	+	0.105453i	$0.0336291\pi$
$608$	1.46410	+	5.46410i	0.0593772	+	0.221599i
$609$		0			0
$610$	−8.78461	+	32.7846i	−0.355678	+	1.32741i
$611$		−	12.0000i		−	0.485468i
$612$	25.9808	−	15.0000i	1.05021	−	0.606339i
$613$			34.0000i			1.37325i	0.727013	+	0.686624i	$0.240908\pi$
$613$			34.0000i			1.37325i	−0.727013	+	0.686624i	$0.759092\pi$
$614$	−12.2942	−	3.29423i	−0.496155	−	0.132944i
$615$	15.0000	+	8.66025i	0.604858	+	0.349215i
$616$	−32.7846	+	8.78461i	−1.32093	+	0.353942i
$617$	−2.50000	+	4.33013i	−0.100646	+	0.174324i	−0.911951	−	0.410299i	$-0.865424\pi$
$617$	−2.50000	+	4.33013i	−0.100646	+	0.174324i	0.811305	+	0.584623i	$0.198758\pi$
$618$	3.80385	−	14.1962i	0.153013	−	0.571053i
$619$	2.59808	−	1.50000i	0.104425	−	0.0602901i	−0.446878	−	0.894595i	$-0.647464\pi$
$619$	2.59808	−	1.50000i	0.104425	−	0.0602901i	0.551303	+	0.834305i	$0.314131\pi$
$620$	−16.0000			−0.642575
$621$	5.19615	−	9.00000i	0.208514	−	0.361158i
$622$	20.0000	+	20.0000i	0.801927	+	0.801927i
$623$	28.0000	+	48.4974i	1.12180	+	1.94301i
$624$	12.0000	−	6.92820i	0.480384	−	0.277350i
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	1.36603	−	0.366025i	0.0545974	−	0.0146293i
$627$	2.59808	−	4.50000i	0.103757	−	0.179713i
$628$	−4.00000	−	6.92820i	−0.159617	−	0.276465i
$629$			10.0000i			0.398726i
$630$	24.0000	−	24.0000i	0.956183	−	0.956183i
$631$	34.0000			1.35352			0.676759	−	0.736204i	$-0.263384\pi$
$631$	34.0000			1.35352			0.676759	+	0.736204i	$0.263384\pi$
$632$	−38.2487	−	10.2487i	−1.52145	−	0.407672i
$633$			27.7128i			1.10149i
$634$	−8.05256	−	30.0526i	−0.319808	−	1.19354i
$635$	−3.46410	−	2.00000i	−0.137469	−	0.0793676i
$636$		0			0
$637$	15.5885	−	9.00000i	0.617637	−	0.356593i
$638$		0			0
$639$	9.00000	−	15.5885i	0.356034	−	0.616670i
$640$	−16.0000	−	16.0000i	−0.632456	−	0.632456i
$641$	15.5000	+	26.8468i	0.612213	+	1.06038i	0.990867	+	0.134846i	$0.0430539\pi$
$641$	15.5000	+	26.8468i	0.612213	+	1.06038i	−0.378653	+	0.925539i	$0.623613\pi$
$642$	1.90192	+	7.09808i	0.0750629	+	0.280139i
$643$	−4.33013	−	2.50000i	−0.170764	−	0.0985904i	0.412182	−	0.911101i	$-0.364767\pi$
$643$	−4.33013	−	2.50000i	−0.170764	−	0.0985904i	−0.582946	+	0.812511i	$0.698100\pi$
$644$	−13.8564	−	8.00000i	−0.546019	−	0.315244i
$645$	19.0526	+	33.0000i	0.750194	+	1.29937i
$646$	6.83013	+	1.83013i	0.268728	+	0.0720054i
$647$	24.0000			0.943537			0.471769	−	0.881722i	$-0.343616\pi$
$647$	24.0000			0.943537			0.471769	+	0.881722i	$0.343616\pi$
$648$	24.5885	+	6.58846i	0.965926	+	0.258819i
$649$	−3.00000			−0.117760
$650$	2.73205	+	0.732051i	0.107160	+	0.0287134i
$651$	−13.8564	−	24.0000i	−0.543075	−	0.940634i
$652$	−4.00000	+	6.92820i	−0.156652	+	0.271329i
$653$	−31.1769	−	18.0000i	−1.22005	−	0.704394i	−0.255119	−	0.966910i	$-0.582115\pi$
$653$	−31.1769	−	18.0000i	−1.22005	−	0.704394i	−0.964928	+	0.262515i	$0.915448\pi$
$654$	−12.6795	−	47.3205i	−0.495807	−	1.85038i
$655$	4.00000	+	6.92820i	0.156293	+	0.270707i
$656$	20.0000			0.780869
$657$	−13.5000	+	23.3827i	−0.526685	+	0.912245i
$658$	−24.0000	−	24.0000i	−0.935617	−	0.935617i
$659$	−10.3923	+	6.00000i	−0.404827	+	0.233727i	−0.688565	−	0.725175i	$-0.741759\pi$
$659$	−10.3923	+	6.00000i	−0.404827	+	0.233727i	0.283738	+	0.958902i	$0.408425\pi$
$660$			20.7846i			0.809040i
$661$	−12.1244	−	7.00000i	−0.471583	−	0.272268i	0.245319	−	0.969442i	$-0.421107\pi$
$661$	−12.1244	−	7.00000i	−0.471583	−	0.272268i	−0.716902	+	0.697174i	$0.754441\pi$
$662$	−7.32051	−	27.3205i	−0.284520	−	1.06184i
$663$		−	17.3205i		−	0.672673i
$664$	2.92820	−	10.9282i	0.113636	−	0.424097i
$665$	8.00000			0.310227
$666$	−6.00000	+	6.00000i	−0.232495	+	0.232495i
$667$		0			0
$668$	−3.46410	+	2.00000i	−0.134030	+	0.0773823i
$669$	1.73205	−	3.00000i	0.0669650	−	0.115987i
$670$	−8.19615	+	2.19615i	−0.316645	+	0.0848448i
$671$	18.0000	−	31.1769i	0.694882	−	1.20357i
$672$	10.1436	−	37.8564i	0.391298	−	1.46034i
$673$	−13.0000	−	22.5167i	−0.501113	−	0.867953i	−0.999999	−	0.00128586i	$-0.999591\pi$
$673$	−13.0000	−	22.5167i	−0.501113	−	0.867953i	0.498886	−	0.866668i	$-0.333743\pi$
$674$	7.00000	+	7.00000i	0.269630	+	0.269630i
$675$	2.59808	+	4.50000i	0.100000	+	0.173205i
$676$			18.0000i			0.692308i
$677$	−41.5692	+	24.0000i	−1.59763	+	0.922395i	−0.605693	+	0.795698i	$0.707104\pi$
$677$	−41.5692	+	24.0000i	−1.59763	+	0.922395i	−0.991941	+	0.126697i	$0.959562\pi$
$678$	−3.80385	+	14.1962i	−0.146086	+	0.545200i
$679$	−2.00000	+	3.46410i	−0.0767530	+	0.132940i
$680$	−27.3205	+	7.32051i	−1.04769	+	0.280729i
$681$	10.5000	+	6.06218i	0.402361	+	0.232303i
$682$	16.3923	+	4.39230i	0.627694	+	0.168190i
$683$			35.0000i			1.33924i	0.742705	+	0.669619i	$0.233543\pi$
$683$			35.0000i			1.33924i	−0.742705	+	0.669619i	$0.766457\pi$
$684$	3.00000	+	5.19615i	0.114708	+	0.198680i
$685$			18.0000i			0.687745i
$686$	2.92820	−	10.9282i	0.111799	−	0.417241i
$687$			34.6410i			1.32164i
$688$	38.1051	+	22.0000i	1.45274	+	0.838742i
$689$		0			0
$690$	−6.92820	+	6.92820i	−0.263752	+	0.263752i
$691$	24.2487	−	14.0000i	0.922464	−	0.532585i	0.0380440	−	0.999276i	$-0.487887\pi$
$691$	24.2487	−	14.0000i	0.922464	−	0.532585i	0.884420	+	0.466691i	$0.154554\pi$
$692$	−48.0000			−1.82469
$693$	−31.1769	+	18.0000i	−1.18431	+	0.683763i
$694$	−13.0000	+	13.0000i	−0.493473	+	0.493473i
$695$	−13.0000	−	22.5167i	−0.493118	−	0.854106i
$696$		0			0
$697$	12.5000	−	21.6506i	0.473471	−	0.820076i
$698$	5.85641	+	21.8564i	0.221668	+	0.827277i
$699$	11.2583	+	19.5000i	0.425829	+	0.737558i
$700$	6.92820	−	4.00000i	0.261861	−	0.151186i
$701$			10.0000i			0.377695i	0.982006	+	0.188847i	$0.0604752\pi$
$701$			10.0000i			0.377695i	−0.982006	+	0.188847i	$0.939525\pi$
$702$	10.3923	−	10.3923i	0.392232	−	0.392232i
$703$	−2.00000			−0.0754314
$704$	12.0000	+	20.7846i	0.452267	+	0.783349i
$705$	−18.0000	+	10.3923i	−0.677919	+	0.391397i
$706$	−20.4904	+	5.49038i	−0.771166	+	0.206633i
$707$	48.4974	+	28.0000i	1.82393	+	1.05305i
$708$	1.73205	−	3.00000i	0.0650945	−	0.112747i
$709$	−6.92820	+	4.00000i	−0.260194	+	0.150223i	−0.624423	−	0.781086i	$-0.714666\pi$
$709$	−6.92820	+	4.00000i	−0.260194	+	0.150223i	0.364229	+	0.931309i	$0.381333\pi$
$710$	−12.0000	+	12.0000i	−0.450352	+	0.450352i
$711$	−42.0000			−1.57512
$712$	28.0000	−	28.0000i	1.04934	−	1.04934i
$713$	4.00000	+	6.92820i	0.149801	+	0.259463i
$714$	−34.6410	−	34.6410i	−1.29641	−	1.29641i
$715$	10.3923	+	6.00000i	0.388650	+	0.224387i
$716$	20.0000	−	34.6410i	0.747435	−	1.29460i
$717$	51.9615			1.94054
$718$	−1.46410	+	5.46410i	−0.0546398	+	0.203918i
$719$	−34.0000			−1.26799			−0.633993	−	0.773339i	$-0.718585\pi$
$719$	−34.0000			−1.26799			−0.633993	+	0.773339i	$0.718585\pi$
$720$	−20.7846	−	12.0000i	−0.774597	−	0.447214i
$721$	−24.0000			−0.893807
$722$	6.58846	−	24.5885i	0.245197	−	0.915088i
$723$	14.7224	−	25.5000i	0.547533	−	0.948355i
$724$	10.0000	−	17.3205i	0.371647	−	0.643712i
$725$		0			0
$726$	−1.26795	+	4.73205i	−0.0470580	+	0.175623i
$727$	−3.00000	−	5.19615i	−0.111264	−	0.192715i	0.805016	−	0.593253i	$-0.202157\pi$
$727$	−3.00000	−	5.19615i	−0.111264	−	0.192715i	−0.916280	+	0.400538i	$0.868823\pi$
$728$	−16.0000	−	16.0000i	−0.592999	−	0.592999i
$729$	27.0000			1.00000
$730$	18.0000	−	18.0000i	0.666210	−	0.666210i
$731$	47.6314	−	27.5000i	1.76171	−	1.01712i
$732$	20.7846	+	36.0000i	0.768221	+	1.33060i
$733$	24.2487	+	14.0000i	0.895647	+	0.517102i	0.875785	−	0.482701i	$-0.160344\pi$
$733$	24.2487	+	14.0000i	0.895647	+	0.517102i	0.0198613	+	0.999803i	$0.493678\pi$
$734$	−24.5885	+	6.58846i	−0.907577	+	0.243184i
$735$	−27.0000	−	15.5885i	−0.995910	−	0.574989i
$736$	−2.92820	+	10.9282i	−0.107935	+	0.402819i
$737$	9.00000			0.331519
$738$	20.4904	−	5.49038i	0.754261	−	0.202104i
$739$			41.0000i			1.50821i	0.656754	+	0.754105i	$0.271929\pi$
$739$			41.0000i			1.50821i	−0.656754	+	0.754105i	$0.728071\pi$
$740$	6.92820	−	4.00000i	0.254686	−	0.147043i
$741$	3.46410			0.127257
$742$		0			0
$743$	22.0000	−	38.1051i	0.807102	−	1.39794i	−0.107761	−	0.994177i	$-0.534368\pi$
$743$	22.0000	−	38.1051i	0.807102	−	1.39794i	0.914863	−	0.403764i	$-0.132298\pi$
$744$	−13.8564	+	13.8564i	−0.508001	+	0.508001i
$745$	−18.0000	−	31.1769i	−0.659469	−	1.14223i
$746$	26.0000	−	26.0000i	0.951928	−	0.951928i
$747$		−	12.0000i		−	0.439057i
$748$	30.0000			1.09691
$749$	10.3923	−	6.00000i	0.379727	−	0.219235i
$750$	−7.60770	−	28.3923i	−0.277794	−	1.03674i
$751$	−1.00000	+	1.73205i	−0.0364905	+	0.0632034i	−0.883694	−	0.468065i	$-0.844951\pi$
$751$	−1.00000	+	1.73205i	−0.0364905	+	0.0632034i	0.847203	+	0.531269i	$0.178285\pi$
$752$	−12.0000	+	20.7846i	−0.437595	+	0.757937i
$753$	22.5000	−	12.9904i	0.819946	−	0.473396i
$754$		0			0
$755$			12.0000i			0.436725i
$756$		−	41.5692i		−	1.51186i
$757$		−	36.0000i		−	1.30844i	−0.756303	−	0.654221i	$-0.772997\pi$
$757$		−	36.0000i		−	1.30844i	0.756303	−	0.654221i	$-0.227003\pi$
$758$	−6.83013	−	1.83013i	−0.248081	−	0.0664732i
$759$	9.00000	−	5.19615i	0.326679	−	0.188608i
$760$	−1.46410	−	5.46410i	−0.0531085	−	0.198204i
$761$	−7.00000	+	12.1244i	−0.253750	+	0.439508i	−0.964555	−	0.263881i	$-0.914997\pi$
$761$	−7.00000	+	12.1244i	−0.253750	+	0.439508i	0.710805	+	0.703389i	$0.248331\pi$
$762$	−4.73205	+	1.26795i	−0.171424	+	0.0459330i
$763$	−69.2820	+	40.0000i	−2.50818	+	1.44810i
$764$		−	32.0000i		−	1.15772i
$765$	−25.9808	+	15.0000i	−0.939336	+	0.542326i
$766$	18.0000	+	18.0000i	0.650366	+	0.650366i
$767$	−1.00000	−	1.73205i	−0.0361079	−	0.0625407i
$768$	−27.7128			−1.00000
$769$	−17.0000	+	29.4449i	−0.613036	+	1.06181i	0.377690	+	0.925932i	$0.376718\pi$
$769$	−17.0000	+	29.4449i	−0.613036	+	1.06181i	−0.990726	+	0.135877i	$0.956615\pi$
$770$	32.7846	−	8.78461i	1.18148	−	0.316575i
$771$	−25.9808			−0.935674
$772$	−25.9808	+	15.0000i	−0.935068	+	0.539862i
$773$		−	38.0000i		−	1.36677i	−0.730061	−	0.683383i	$-0.760508\pi$
$773$		−	38.0000i		−	1.36677i	0.730061	−	0.683383i	$-0.239492\pi$
$774$	45.0788	+	12.0788i	1.62033	+	0.434165i
$775$	−4.00000			−0.143684
$776$	2.73205	+	0.732051i	0.0980749	+	0.0262791i
$777$	12.0000	+	6.92820i	0.430498	+	0.248548i
$778$	−2.92820	−	10.9282i	−0.104981	−	0.391795i
$779$	4.33013	+	2.50000i	0.155143	+	0.0895718i
$780$	−12.0000	+	6.92820i	−0.429669	+	0.248069i
$781$	15.5885	−	9.00000i	0.557799	−	0.322045i
$782$	10.0000	+	10.0000i	0.357599	+	0.357599i
$783$		0			0
$784$	−36.0000			−1.28571
$785$	4.00000	+	6.92820i	0.142766	+	0.247278i
$786$	9.46410	+	2.53590i	0.337573	+	0.0904525i
$787$	−10.3923	−	6.00000i	−0.370446	−	0.213877i	0.303207	−	0.952925i	$-0.401942\pi$
$787$	−10.3923	−	6.00000i	−0.370446	−	0.213877i	−0.673653	+	0.739048i	$0.735276\pi$
$788$	8.00000	−	13.8564i	0.284988	−	0.493614i
$789$	−6.92820	+	12.0000i	−0.246651	+	0.427211i
$790$	38.2487	+	10.2487i	1.36083	+	0.364633i
$791$	24.0000			0.853342
$792$	18.0000	+	18.0000i	0.639602	+	0.639602i
$793$	24.0000			0.852265
$794$	30.0526	+	8.05256i	1.06653	+	0.285775i
$795$		0			0
$796$	13.8564	+	8.00000i	0.491127	+	0.283552i
$797$	19.0526	+	11.0000i	0.674876	+	0.389640i	0.797922	−	0.602761i	$-0.205933\pi$
$797$	19.0526	+	11.0000i	0.674876	+	0.389640i	−0.123045	+	0.992401i	$0.539266\pi$
$798$	6.92820	−	6.92820i	0.245256	−	0.245256i
$799$	15.0000	+	25.9808i	0.530662	+	0.919133i
$800$	−4.00000	−	4.00000i	−0.141421	−	0.141421i
$801$	21.0000	−	36.3731i	0.741999	−	1.28518i
$802$	−15.0000	−	15.0000i	−0.529668	−	0.529668i
$803$	−23.3827	+	13.5000i	−0.825157	+	0.476405i
$804$	−5.19615	+	9.00000i	−0.183254	+	0.317406i
$805$	13.8564	+	8.00000i	0.488374	+	0.281963i
$806$	2.92820	+	10.9282i	0.103142	+	0.384930i
$807$	−18.0000	+	10.3923i	−0.633630	+	0.365826i
$808$	10.2487	−	38.2487i	0.360548	−	1.34558i
$809$	−9.00000			−0.316423			−0.158212	−	0.987405i	$-0.550573\pi$
$809$	−9.00000			−0.316423			−0.158212	+	0.987405i	$0.550573\pi$
$810$	−24.5885	−	6.58846i	−0.863950	−	0.231495i
$811$		−	7.00000i		−	0.245803i	−0.992419	−	0.122902i	$-0.960780\pi$
$811$		−	7.00000i		−	0.245803i	0.992419	−	0.122902i	$-0.0392200\pi$
$812$		0			0
$813$	10.3923	+	18.0000i	0.364474	+	0.631288i
$814$	−8.19615	+	2.19615i	−0.287275	+	0.0769751i
$815$	4.00000	−	6.92820i	0.140114	−	0.242684i
$816$	−17.3205	+	30.0000i	−0.606339	+	1.05021i
$817$	5.50000	+	9.52628i	0.192421	+	0.333282i
$818$	31.0000	+	31.0000i	1.08389	+	1.08389i
$819$	−20.7846	−	12.0000i	−0.726273	−	0.419314i
$820$	−20.0000			−0.698430
$821$	24.2487	−	14.0000i	0.846286	−	0.488603i	−0.0131101	−	0.999914i	$-0.504173\pi$
$821$	24.2487	−	14.0000i	0.846286	−	0.488603i	0.859396	+	0.511311i	$0.170840\pi$
$822$	15.5885	+	15.5885i	0.543710	+	0.543710i
$823$	−13.0000	+	22.5167i	−0.453152	+	0.784881i	−0.998580	−	0.0532760i	$-0.983034\pi$
$823$	−13.0000	+	22.5167i	−0.453152	+	0.784881i	0.545428	+	0.838157i	$0.316367\pi$
$824$	4.39230	+	16.3923i	0.153013	+	0.571053i
$825$			5.19615i			0.180907i
$826$	−5.46410	−	1.46410i	−0.190120	−	0.0509426i
$827$		−	48.0000i		−	1.66912i	−0.550914	−	0.834562i	$-0.685721\pi$
$827$		−	48.0000i		−	1.66912i	0.550914	−	0.834562i	$-0.314279\pi$
$828$			12.0000i			0.417029i
$829$		−	32.0000i		−	1.11141i	−0.831381	−	0.555703i	$-0.812449\pi$
$829$		−	32.0000i		−	1.11141i	0.831381	−	0.555703i	$-0.187551\pi$
$830$	−2.92820	+	10.9282i	−0.101639	+	0.379323i
$831$	−3.00000	−	1.73205i	−0.104069	−	0.0600842i
$832$	−8.00000	+	13.8564i	−0.277350	+	0.480384i
$833$	−22.5000	+	38.9711i	−0.779579	+	1.35027i
$834$	−30.7583	−	8.24167i	−1.06507	−	0.285386i
$835$	3.46410	−	2.00000i	0.119880	−	0.0692129i
$836$			6.00000i			0.207514i
$837$	−10.3923	+	18.0000i	−0.359211	+	0.622171i
$838$	−36.0000	+	36.0000i	−1.24360	+	1.24360i
$839$	−2.00000	−	3.46410i	−0.0690477	−	0.119594i	0.829435	−	0.558604i	$-0.188663\pi$
$839$	−2.00000	−	3.46410i	−0.0690477	−	0.119594i	−0.898482	+	0.439010i	$0.855329\pi$
$840$	−10.1436	+	37.8564i	−0.349987	+	1.30617i
$841$	−14.5000	+	25.1147i	−0.500000	+	0.866025i
$842$	−8.05256	−	30.0526i	−0.277510	−	1.03568i
$843$	−5.19615	+	9.00000i	−0.178965	+	0.309976i
$844$	−16.0000	−	27.7128i	−0.550743	−	0.953914i
$845$		−	18.0000i		−	0.619219i
$846$	−6.58846	+	24.5885i	−0.226516	+	0.845369i
$847$	8.00000			0.274883
$848$		0			0
$849$		−	34.6410i		−	1.18888i
$850$	−6.83013	+	1.83013i	−0.234271	+	0.0627728i
$851$	−3.46410	−	2.00000i	−0.118748	−	0.0685591i
$852$			20.7846i			0.712069i
$853$	36.3731	−	21.0000i	1.24539	−	0.719026i	0.275204	−	0.961386i	$-0.411255\pi$
$853$	36.3731	−	21.0000i	1.24539	−	0.719026i	0.970186	+	0.242360i	$0.0779214\pi$
$854$	48.0000	−	48.0000i	1.64253	−	1.64253i
$855$	−3.00000	−	5.19615i	−0.102598	−	0.177705i
$856$	−6.00000	−	6.00000i	−0.205076	−	0.205076i
$857$	−3.00000	−	5.19615i	−0.102478	−	0.177497i	0.810227	−	0.586116i	$-0.199344\pi$
$857$	−3.00000	−	5.19615i	−0.102478	−	0.177497i	−0.912705	+	0.408619i	$0.866010\pi$
$858$	14.1962	−	3.80385i	0.484649	−	0.129861i
$859$	−30.3109	−	17.5000i	−1.03419	−	0.597092i	−0.116011	−	0.993248i	$-0.537011\pi$
$859$	−30.3109	−	17.5000i	−1.03419	−	0.597092i	−0.918183	+	0.396156i	$0.870344\pi$
$860$	−38.1051	−	22.0000i	−1.29937	−	0.750194i
$861$	−17.3205	−	30.0000i	−0.590281	−	1.02240i
$862$	−13.1769	+	49.1769i	−0.448807	+	1.67497i
$863$	6.00000			0.204242			0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000			0.204242			0.102121	+	0.994772i	$0.467437\pi$
$864$	−28.3923	+	7.60770i	−0.965926	+	0.258819i
$865$	48.0000			1.63205
$866$	1.83013	−	6.83013i	0.0621902	−	0.232097i
$867$	6.92820	+	12.0000i	0.235294	+	0.407541i
$868$	27.7128	+	16.0000i	0.940634	+	0.543075i
$869$	−36.3731	−	21.0000i	−1.23387	−	0.712376i
$870$		0			0
$871$	3.00000	+	5.19615i	0.101651	+	0.176065i
$872$	40.0000	+	40.0000i	1.35457	+	1.35457i
$873$	3.00000			0.101535
$874$	−2.00000	+	2.00000i	−0.0676510	+	0.0676510i
$875$	−41.5692	+	24.0000i	−1.40530	+	0.811348i
$876$		−	31.1769i		−	1.05337i
$877$	6.92820	+	4.00000i	0.233949	+	0.135070i	0.612392	−	0.790554i	$-0.290207\pi$
$877$	6.92820	+	4.00000i	0.233949	+	0.135070i	−0.378444	+	0.925624i	$0.623541\pi$
$878$		0			0
$879$		−	20.7846i		−	0.701047i
$880$	−12.0000	−	20.7846i	−0.404520	−	0.700649i
$881$	−2.00000			−0.0673817			−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$	−36.8827	+	9.88269i	−1.24190	+	0.332767i
$883$			23.0000i			0.774012i	0.922077	+	0.387006i	$0.126491\pi$
$883$			23.0000i			0.774012i	−0.922077	+	0.387006i	$0.873509\pi$
$884$	10.0000	+	17.3205i	0.336336	+	0.582552i
$885$	−1.73205	+	3.00000i	−0.0582223	+	0.100844i
$886$	3.29423	+	12.2942i	0.110672	+	0.413033i
$887$	−15.0000	+	25.9808i	−0.503651	+	0.872349i	0.496340	+	0.868128i	$0.334677\pi$
$887$	−15.0000	+	25.9808i	−0.503651	+	0.872349i	−0.999991	+	0.00422062i	$0.998657\pi$
$888$	2.53590	−	9.46410i	0.0850992	−	0.317594i
$889$	4.00000	+	6.92820i	0.134156	+	0.232364i
$890$	−28.0000	+	28.0000i	−0.938562	+	0.938562i
$891$	23.3827	+	13.5000i	0.783349	+	0.452267i
$892$			4.00000i			0.133930i
$893$	−5.19615	+	3.00000i	−0.173883	+	0.100391i
$894$	−42.5885	−	11.4115i	−1.42437	−	0.381659i
$895$	−20.0000	+	34.6410i	−0.668526	+	1.15792i
$896$	11.7128	+	43.7128i	0.391298	+	1.46034i
$897$	6.00000	+	3.46410i	0.200334	+	0.115663i
$898$	7.68653	−	28.6865i	0.256503	−	0.957282i
$899$		0			0
$900$	−5.19615	−	3.00000i	−0.173205	−	0.100000i
$901$		0			0
$902$	20.4904	+	5.49038i	0.682255	+	0.182810i
$903$		−	76.2102i		−	2.53612i
$904$	−4.39230	−	16.3923i	−0.146086	−	0.545200i
$905$	−10.0000	+	17.3205i	−0.332411	+	0.575753i
$906$	10.3923	+	10.3923i	0.345261	+	0.345261i
$907$	21.6506	−	12.5000i	0.718898	−	0.415056i	−0.0954492	−	0.995434i	$-0.530429\pi$
$907$	21.6506	−	12.5000i	0.718898	−	0.415056i	0.814347	+	0.580379i	$0.197095\pi$
$908$	−14.0000			−0.464606
$909$		−	42.0000i		−	1.39305i
$910$	16.0000	+	16.0000i	0.530395	+	0.530395i
$911$	−6.00000	−	10.3923i	−0.198789	−	0.344312i	0.749347	−	0.662177i	$-0.230367\pi$
$911$	−6.00000	−	10.3923i	−0.198789	−	0.344312i	−0.948136	+	0.317865i	$0.897034\pi$
$912$	−6.00000	−	3.46410i	−0.198680	−	0.114708i
$913$	6.00000	−	10.3923i	0.198571	−	0.343935i
$914$	50.5429	−	13.5429i	1.67181	−	0.447961i
$915$	−20.7846	−	36.0000i	−0.687118	−	1.19012i
$916$	−20.0000	−	34.6410i	−0.660819	−	1.14457i
$917$		−	16.0000i		−	0.528367i
$918$	−9.50962	+	35.4904i	−0.313864	+	1.17136i
$919$	−42.0000			−1.38545			−0.692726	−	0.721201i	$-0.743591\pi$
$919$	−42.0000			−1.38545			−0.692726	+	0.721201i	$0.743591\pi$
$920$	2.92820	−	10.9282i	0.0965400	−	0.360292i
$921$	13.5000	−	7.79423i	0.444840	−	0.256829i
$922$	2.19615	+	8.19615i	0.0723264	+	0.269926i
$923$	10.3923	+	6.00000i	0.342067	+	0.197492i
$924$	20.7846	−	36.0000i	0.683763	−	1.18431i
$925$	1.73205	−	1.00000i	0.0569495	−	0.0328798i
$926$	10.0000	+	10.0000i	0.328620	+	0.328620i
$927$	9.00000	+	15.5885i	0.295599	+	0.511992i
$928$		0			0
$929$	−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	$0.907096\pi$
$930$	13.8564	−	13.8564i	0.454369	−	0.454369i
$931$	−7.79423	−	4.50000i	−0.255446	−	0.147482i
$932$	−22.5167	−	13.0000i	−0.737558	−	0.425829i
$933$	−34.6410			−1.13410
$934$	−39.6147	−	10.6147i	−1.29623	−	0.347325i
$935$	−30.0000			−0.981105
$936$	−4.39230	+	16.3923i	−0.143567	+	0.535799i
$937$	2.00000			0.0653372			0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000			0.0653372			0.0326686	+	0.999466i	$0.489599\pi$
$938$	16.3923	+	4.39230i	0.535228	+	0.143414i
$939$	−0.866025	+	1.50000i	−0.0282617	+	0.0489506i
$940$	12.0000	−	20.7846i	0.391397	−	0.677919i
$941$	−20.7846	−	12.0000i	−0.677559	−	0.391189i	0.121376	−	0.992607i	$-0.461269\pi$
$941$	−20.7846	−	12.0000i	−0.677559	−	0.391189i	−0.798935	+	0.601418i	$0.794603\pi$
$942$	9.46410	+	2.53590i	0.308357	+	0.0826240i
$943$	5.00000	+	8.66025i	0.162822	+	0.282017i
$944$			4.00000i			0.130189i
$945$			41.5692i			1.35225i
$946$	33.0000	+	33.0000i	1.07292	+	1.07292i
$947$	−2.59808	+	1.50000i	−0.0844261	+	0.0487435i	−0.541619	−	0.840624i	$-0.682188\pi$
$947$	−2.59808	+	1.50000i	−0.0844261	+	0.0487435i	0.457193	+	0.889368i	$0.348855\pi$
$948$	42.0000	−	24.2487i	1.36410	−	0.787562i
$949$	−15.5885	−	9.00000i	−0.506023	−	0.292152i
$950$	−0.366025	−	1.36603i	−0.0118754	−	0.0443197i
$951$	33.0000	+	19.0526i	1.07010	+	0.617822i
$952$	54.6410	+	14.6410i	1.77093	+	0.474518i
$953$	−21.0000			−0.680257			−0.340128	−	0.940379i	$-0.610471\pi$
$953$	−21.0000			−0.680257			−0.340128	+	0.940379i	$0.610471\pi$
$954$		0			0
$955$			32.0000i			1.03550i
$956$	−51.9615	+	30.0000i	−1.68056	+	0.970269i
$957$		0			0
$958$	−21.8564	+	5.85641i	−0.706148	+	0.189212i
$959$	18.0000	−	31.1769i	0.581250	−	1.00676i
$960$	27.7128			0.894427
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	−4.00000	−	4.00000i	−0.128965	−	0.128965i
$963$	−7.79423	−	4.50000i	−0.251166	−	0.145010i
$964$			34.0000i			1.09507i
$965$	25.9808	−	15.0000i	0.836350	−	0.482867i
$966$	18.9282	−	5.07180i	0.609005	−	0.163182i
$967$	2.00000	−	3.46410i	0.0643157	−	0.111398i	−0.832075	−	0.554664i	$-0.812847\pi$
$967$	2.00000	−	3.46410i	0.0643157	−	0.111398i	0.896390	+	0.443266i	$0.146180\pi$
$968$	−1.46410	−	5.46410i	−0.0470580	−	0.175623i
$969$	−7.50000	+	4.33013i	−0.240935	+	0.139104i
$970$	−2.73205	−	0.732051i	−0.0877209	−	0.0235047i
$971$			12.0000i			0.385098i	0.981287	+	0.192549i	$0.0616755\pi$
$971$			12.0000i			0.385098i	−0.981287	+	0.192549i	$0.938325\pi$
$972$	−27.0000	+	15.5885i	−0.866025	+	0.500000i
$973$			52.0000i			1.66704i
$974$	7.32051	−	27.3205i	0.234564	−	0.875406i
$975$	−3.00000	+	1.73205i	−0.0960769	+	0.0554700i
$976$	−41.5692	−	24.0000i	−1.33060	−	0.768221i
$977$	15.5000	−	26.8468i	0.495889	−	0.858905i	−0.504100	−	0.863645i	$-0.668176\pi$
$977$	15.5000	−	26.8468i	0.495889	−	0.858905i	0.999989	+	0.00474056i	$0.00150897\pi$
$978$	−2.53590	−	9.46410i	−0.0810891	−	0.302629i
$979$	36.3731	−	21.0000i	1.16249	−	0.671163i
$980$	36.0000			1.14998
$981$	51.9615	+	30.0000i	1.65900	+	0.957826i
$982$	19.0000	−	19.0000i	0.606314	−	0.606314i
$983$	−23.0000	−	39.8372i	−0.733586	−	1.27061i	−0.955341	−	0.295506i	$-0.904512\pi$
$983$	−23.0000	−	39.8372i	−0.733586	−	1.27061i	0.221755	−	0.975102i	$-0.428822\pi$
$984$	−17.3205	+	17.3205i	−0.552158	+	0.552158i
$985$	−8.00000	+	13.8564i	−0.254901	+	0.441502i
$986$		0			0
$987$	41.5692			1.32316
$988$	−3.46410	+	2.00000i	−0.110208	+	0.0636285i
$989$			22.0000i			0.699559i
$990$	−18.0000	−	18.0000i	−0.572078	−	0.572078i
$991$	56.0000			1.77890			0.889449	−	0.457034i	$-0.151088\pi$
$991$	56.0000			1.77890			0.889449	+	0.457034i	$0.151088\pi$
$992$	5.85641	−	21.8564i	0.185941	−	0.693942i
$993$	30.0000	+	17.3205i	0.952021	+	0.549650i
$994$	32.7846	−	8.78461i	1.03986	−	0.278631i
$995$	−13.8564	−	8.00000i	−0.439278	−	0.253617i
$996$	6.92820	+	12.0000i	0.219529	+	0.380235i
$997$	−10.3923	+	6.00000i	−0.329128	+	0.190022i	−0.655454	−	0.755235i	$-0.727523\pi$
$997$	−10.3923	+	6.00000i	−0.329128	+	0.190022i	0.326326	+	0.945257i	$0.394189\pi$
$998$	15.0000	−	15.0000i	0.474817	−	0.474817i
$999$		−	10.3923i		−	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.2.n.a.13.2	yes	4
3.2	odd	2		216.2.n.a.37.1		4
4.3	odd	2		288.2.r.a.49.1		4
8.3	odd	2		288.2.r.a.49.2		4
8.5	even	2	inner	72.2.n.a.13.1	✓	4
9.2	odd	6		216.2.n.a.181.2		4
9.4	even	3		648.2.d.d.325.2		2
9.5	odd	6		648.2.d.a.325.1		2
9.7	even	3	inner	72.2.n.a.61.1	yes	4
12.11	even	2		864.2.r.a.145.1		4
24.5	odd	2		216.2.n.a.37.2		4
24.11	even	2		864.2.r.a.145.2		4
36.7	odd	6		288.2.r.a.241.2		4
36.11	even	6		864.2.r.a.721.2		4
36.23	even	6		2592.2.d.a.1297.2		2
36.31	odd	6		2592.2.d.b.1297.1		2
72.5	odd	6		648.2.d.a.325.2		2
72.11	even	6		864.2.r.a.721.1		4
72.13	even	6		648.2.d.d.325.1		2
72.29	odd	6		216.2.n.a.181.1		4
72.43	odd	6		288.2.r.a.241.1		4
72.59	even	6		2592.2.d.a.1297.1		2
72.61	even	6	inner	72.2.n.a.61.2	yes	4
72.67	odd	6		2592.2.d.b.1297.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.n.a.13.1	✓	4	8.5	even	2	inner
72.2.n.a.13.2	yes	4	1.1	even	1	trivial
72.2.n.a.61.1	yes	4	9.7	even	3	inner
72.2.n.a.61.2	yes	4	72.61	even	6	inner
216.2.n.a.37.1		4	3.2	odd	2
216.2.n.a.37.2		4	24.5	odd	2
216.2.n.a.181.1		4	72.29	odd	6
216.2.n.a.181.2		4	9.2	odd	6
288.2.r.a.49.1		4	4.3	odd	2
288.2.r.a.49.2		4	8.3	odd	2
288.2.r.a.241.1		4	72.43	odd	6
288.2.r.a.241.2		4	36.7	odd	6
648.2.d.a.325.1		2	9.5	odd	6
648.2.d.a.325.2		2	72.5	odd	6
648.2.d.d.325.1		2	72.13	even	6
648.2.d.d.325.2		2	9.4	even	3
864.2.r.a.145.1		4	12.11	even	2
864.2.r.a.145.2		4	24.11	even	2
864.2.r.a.721.1		4	72.11	even	6
864.2.r.a.721.2		4	36.11	even	6
2592.2.d.a.1297.1		2	72.59	even	6
2592.2.d.a.1297.2		2	36.23	even	6
2592.2.d.b.1297.1		2	36.31	odd	6
2592.2.d.b.1297.2		2	72.67	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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	72.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.73205 + 1.00000i) q^{5} +(2.36603 - 0.633975i) q^{6} +(-2.00000 - 3.46410i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.366025 - 1.36603i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.73205 + 1.00000i) q^{5} +(2.36603 - 0.633975i) q^{6} +(-2.00000 - 3.46410i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(2.00000 - 2.00000i) q^{10} +(-2.59808 + 1.50000i) q^{11} -3.46410i q^{12} +(-1.73205 - 1.00000i) q^{13} +(-5.46410 + 1.46410i) q^{14} +3.46410i q^{15} +(2.00000 + 3.46410i) q^{16} +5.00000 q^{17} +(3.00000 + 3.00000i) q^{18} +1.00000i q^{19} +(-2.00000 - 3.46410i) q^{20} +(3.46410 - 6.00000i) q^{21} +(1.09808 + 4.09808i) q^{22} +(-1.00000 + 1.73205i) q^{23} +(-4.73205 - 1.26795i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.00000 + 2.00000i) q^{26} -5.19615 q^{27} +8.00000i q^{28} +(4.73205 + 1.26795i) q^{30} +(2.00000 - 3.46410i) q^{31} +(5.46410 - 1.46410i) q^{32} +(-4.50000 - 2.59808i) q^{33} +(1.83013 - 6.83013i) q^{34} -8.00000i q^{35} +(5.19615 - 3.00000i) q^{36} +2.00000i q^{37} +(1.36603 + 0.366025i) q^{38} -3.46410i q^{39} +(-5.46410 + 1.46410i) q^{40} +(2.50000 - 4.33013i) q^{41} +(-6.92820 - 6.92820i) q^{42} +(9.52628 - 5.50000i) q^{43} +6.00000 q^{44} +(-5.19615 + 3.00000i) q^{45} +(2.00000 + 2.00000i) q^{46} +(3.00000 + 5.19615i) q^{47} +(-3.46410 + 6.00000i) q^{48} +(-4.50000 + 7.79423i) q^{49} +(-1.36603 + 0.366025i) q^{50} +(4.33013 + 7.50000i) q^{51} +(2.00000 + 3.46410i) q^{52} +(-1.90192 + 7.09808i) q^{54} -6.00000 q^{55} +(10.9282 + 2.92820i) q^{56} +(-1.50000 + 0.866025i) q^{57} +(0.866025 + 0.500000i) q^{59} +(3.46410 - 6.00000i) q^{60} +(-10.3923 + 6.00000i) q^{61} +(-4.00000 - 4.00000i) q^{62} +12.0000 q^{63} -8.00000i q^{64} +(-2.00000 - 3.46410i) q^{65} +(-5.19615 + 5.19615i) q^{66} +(-2.59808 - 1.50000i) q^{67} +(-8.66025 - 5.00000i) q^{68} -3.46410 q^{69} +(-10.9282 - 2.92820i) q^{70} -6.00000 q^{71} +(-2.19615 - 8.19615i) q^{72} +9.00000 q^{73} +(2.73205 + 0.732051i) q^{74} +(0.866025 - 1.50000i) q^{75} +(1.00000 - 1.73205i) q^{76} +(10.3923 + 6.00000i) q^{77} +(-4.73205 - 1.26795i) q^{78} +(7.00000 + 12.1244i) q^{79} +8.00000i q^{80} +(-4.50000 - 7.79423i) q^{81} +(-5.00000 - 5.00000i) q^{82} +(-3.46410 + 2.00000i) q^{83} +(-12.0000 + 6.92820i) q^{84} +(8.66025 + 5.00000i) q^{85} +(-4.02628 - 15.0263i) q^{86} +(2.19615 - 8.19615i) q^{88} -14.0000 q^{89} +(2.19615 + 8.19615i) q^{90} +8.00000i q^{91} +(3.46410 - 2.00000i) q^{92} +6.92820 q^{93} +(8.19615 - 2.19615i) q^{94} +(-1.00000 + 1.73205i) q^{95} +(6.92820 + 6.92820i) q^{96} +(-0.500000 - 0.866025i) q^{97} +(9.00000 + 9.00000i) q^{98} -9.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{6} - 8 q^{7} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 6 * q^6 - 8 * q^7 - 8 * q^8 - 6 * q^9	\( 4 q - 2 q^{2} + 6 q^{6} - 8 q^{7} - 8 q^{8} - 6 q^{9} + 8 q^{10} - 8 q^{14} + 8 q^{16} + 20 q^{17} + 12 q^{18} - 8 q^{20} - 6 q^{22} - 4 q^{23} - 12 q^{24} - 2 q^{25} - 8 q^{26} + 12 q^{30} + 8 q^{31} + 8 q^{32} - 18 q^{33} - 10 q^{34} + 2 q^{38} - 8 q^{40} + 10 q^{41} + 24 q^{44} + 8 q^{46} + 12 q^{47} - 18 q^{49} - 2 q^{50} + 8 q^{52} - 18 q^{54} - 24 q^{55} + 16 q^{56} - 6 q^{57} - 16 q^{62} + 48 q^{63} - 8 q^{65} - 16 q^{70} - 24 q^{71} + 12 q^{72} + 36 q^{73} + 4 q^{74} + 4 q^{76} - 12 q^{78} + 28 q^{79} - 18 q^{81} - 20 q^{82} - 48 q^{84} + 22 q^{86} - 12 q^{88} - 56 q^{89} - 12 q^{90} + 12 q^{94} - 4 q^{95} - 2 q^{97} + 36 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^6 - 8 * q^7 - 8 * q^8 - 6 * q^9 + 8 * q^10 - 8 * q^14 + 8 * q^16 + 20 * q^17 + 12 * q^18 - 8 * q^20 - 6 * q^22 - 4 * q^23 - 12 * q^24 - 2 * q^25 - 8 * q^26 + 12 * q^30 + 8 * q^31 + 8 * q^32 - 18 * q^33 - 10 * q^34 + 2 * q^38 - 8 * q^40 + 10 * q^41 + 24 * q^44 + 8 * q^46 + 12 * q^47 - 18 * q^49 - 2 * q^50 + 8 * q^52 - 18 * q^54 - 24 * q^55 + 16 * q^56 - 6 * q^57 - 16 * q^62 + 48 * q^63 - 8 * q^65 - 16 * q^70 - 24 * q^71 + 12 * q^72 + 36 * q^73 + 4 * q^74 + 4 * q^76 - 12 * q^78 + 28 * q^79 - 18 * q^81 - 20 * q^82 - 48 * q^84 + 22 * q^86 - 12 * q^88 - 56 * q^89 - 12 * q^90 + 12 * q^94 - 4 * q^95 - 2 * q^97 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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