LMFDB - Embedded newform 630.2.j.a.421.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(211,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.j (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:	$5.03057532734$
Analytic rank:	$1$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			421.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	630.421
Dual form			630.2.j.a.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +1.73205i q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +1.73205i q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} -3.00000 q^{9} +1.00000 q^{10} +(-1.50000 + 2.59808i) q^{11} +(1.50000 - 0.866025i) q^{12} +(-2.50000 - 4.33013i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(1.50000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} -3.00000 q^{17} +(1.50000 - 2.59808i) q^{18} +2.00000 q^{19} +(-0.500000 + 0.866025i) q^{20} +(-1.50000 - 0.866025i) q^{21} +(-1.50000 - 2.59808i) q^{22} +(-3.00000 - 5.19615i) q^{23} +1.73205i q^{24} +(-0.500000 + 0.866025i) q^{25} +5.00000 q^{26} -5.19615i q^{27} +1.00000 q^{28} +(-3.00000 + 5.19615i) q^{29} +1.73205i q^{30} +(-1.00000 - 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.50000 - 2.59808i) q^{33} +(1.50000 - 2.59808i) q^{34} +1.00000 q^{35} +(1.50000 + 2.59808i) q^{36} -10.0000 q^{37} +(-1.00000 + 1.73205i) q^{38} +(7.50000 - 4.33013i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(1.50000 - 0.866025i) q^{42} +(5.00000 - 8.66025i) q^{43} +3.00000 q^{44} +(1.50000 + 2.59808i) q^{45} +6.00000 q^{46} +(-1.50000 + 2.59808i) q^{47} +(-1.50000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} -5.19615i q^{51} +(-2.50000 + 4.33013i) q^{52} +(4.50000 + 2.59808i) q^{54} +3.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +3.46410i q^{57} +(-3.00000 - 5.19615i) q^{58} +(6.00000 + 10.3923i) q^{59} +(-1.50000 - 0.866025i) q^{60} +(5.00000 - 8.66025i) q^{61} +2.00000 q^{62} +(1.50000 - 2.59808i) q^{63} +1.00000 q^{64} +(-2.50000 + 4.33013i) q^{65} +(4.50000 - 2.59808i) q^{66} +(-1.00000 - 1.73205i) q^{67} +(1.50000 + 2.59808i) q^{68} +(9.00000 - 5.19615i) q^{69} +(-0.500000 + 0.866025i) q^{70} -9.00000 q^{71} -3.00000 q^{72} +11.0000 q^{73} +(5.00000 - 8.66025i) q^{74} +(-1.50000 - 0.866025i) q^{75} +(-1.00000 - 1.73205i) q^{76} +(-1.50000 - 2.59808i) q^{77} +8.66025i q^{78} +(0.500000 - 0.866025i) q^{79} +1.00000 q^{80} +9.00000 q^{81} +(-4.50000 + 7.79423i) q^{83} +1.73205i q^{84} +(1.50000 + 2.59808i) q^{85} +(5.00000 + 8.66025i) q^{86} +(-9.00000 - 5.19615i) q^{87} +(-1.50000 + 2.59808i) q^{88} -6.00000 q^{89} -3.00000 q^{90} +5.00000 q^{91} +(-3.00000 + 5.19615i) q^{92} +(3.00000 - 1.73205i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-1.00000 - 1.73205i) q^{95} +(1.50000 - 0.866025i) q^{96} +(-8.50000 + 14.7224i) q^{97} +1.00000 q^{98} +(4.50000 - 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - q^{5} - 3 q^{6} - q^{7} + 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q - q^2 - q^4 - q^5 - 3 * q^6 - q^7 + 2 * q^8 - 6 * q^9	$ 2 q - q^{2} - q^{4} - q^{5} - 3 q^{6} - q^{7} + 2 q^{8} - 6 q^{9} + 2 q^{10} - 3 q^{11} + 3 q^{12} - 5 q^{13} - q^{14} + 3 q^{15} - q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} - q^{20} - 3 q^{21} - 3 q^{22} - 6 q^{23} - q^{25} + 10 q^{26} + 2 q^{28} - 6 q^{29} - 2 q^{31} - q^{32} - 9 q^{33} + 3 q^{34} + 2 q^{35} + 3 q^{36} - 20 q^{37} - 2 q^{38} + 15 q^{39} - q^{40} + 3 q^{42} + 10 q^{43} + 6 q^{44} + 3 q^{45} + 12 q^{46} - 3 q^{47} - 3 q^{48} - q^{49} - q^{50} - 5 q^{52} + 9 q^{54} + 6 q^{55} - q^{56} - 6 q^{58} + 12 q^{59} - 3 q^{60} + 10 q^{61} + 4 q^{62} + 3 q^{63} + 2 q^{64} - 5 q^{65} + 9 q^{66} - 2 q^{67} + 3 q^{68} + 18 q^{69} - q^{70} - 18 q^{71} - 6 q^{72} + 22 q^{73} + 10 q^{74} - 3 q^{75} - 2 q^{76} - 3 q^{77} + q^{79} + 2 q^{80} + 18 q^{81} - 9 q^{83} + 3 q^{85} + 10 q^{86} - 18 q^{87} - 3 q^{88} - 12 q^{89} - 6 q^{90} + 10 q^{91} - 6 q^{92} + 6 q^{93} - 3 q^{94} - 2 q^{95} + 3 q^{96} - 17 q^{97} + 2 q^{98} + 9 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^4 - q^5 - 3 * q^6 - q^7 + 2 * q^8 - 6 * q^9 + 2 * q^10 - 3 * q^11 + 3 * q^12 - 5 * q^13 - q^14 + 3 * q^15 - q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 - q^20 - 3 * q^21 - 3 * q^22 - 6 * q^23 - q^25 + 10 * q^26 + 2 * q^28 - 6 * q^29 - 2 * q^31 - q^32 - 9 * q^33 + 3 * q^34 + 2 * q^35 + 3 * q^36 - 20 * q^37 - 2 * q^38 + 15 * q^39 - q^40 + 3 * q^42 + 10 * q^43 + 6 * q^44 + 3 * q^45 + 12 * q^46 - 3 * q^47 - 3 * q^48 - q^49 - q^50 - 5 * q^52 + 9 * q^54 + 6 * q^55 - q^56 - 6 * q^58 + 12 * q^59 - 3 * q^60 + 10 * q^61 + 4 * q^62 + 3 * q^63 + 2 * q^64 - 5 * q^65 + 9 * q^66 - 2 * q^67 + 3 * q^68 + 18 * q^69 - q^70 - 18 * q^71 - 6 * q^72 + 22 * q^73 + 10 * q^74 - 3 * q^75 - 2 * q^76 - 3 * q^77 + q^79 + 2 * q^80 + 18 * q^81 - 9 * q^83 + 3 * q^85 + 10 * q^86 - 18 * q^87 - 3 * q^88 - 12 * q^89 - 6 * q^90 + 10 * q^91 - 6 * q^92 + 6 * q^93 - 3 * q^94 - 2 * q^95 + 3 * q^96 - 17 * q^97 + 2 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$			1.73205i			1.00000i
$3$			1.73205i			1.00000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.50000	−	0.866025i	−0.612372	−	0.353553i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	1.00000			0.353553
$9$	−3.00000			−1.00000
$10$	1.00000			0.316228
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$	1.50000	−	0.866025i	0.433013	−	0.250000i
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	0.277350	−	0.960769i	$-0.410544\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$	1.50000	−	0.866025i	0.387298	−	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$	1.50000	−	2.59808i	0.353553	−	0.612372i
$19$	2.00000			0.458831			0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000			0.458831			0.229416	+	0.973329i	$0.426318\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	−1.50000	−	0.866025i	−0.327327	−	0.188982i
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$			1.73205i			0.353553i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	5.00000			0.980581
$27$		−	5.19615i		−	1.00000i
$28$	1.00000			0.188982
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$			1.73205i			0.316228i
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−4.50000	−	2.59808i	−0.783349	−	0.452267i
$34$	1.50000	−	2.59808i	0.257248	−	0.445566i
$35$	1.00000			0.169031
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	−10.0000			−1.64399			−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000			−1.64399			−0.821995	+	0.569495i	$0.807139\pi$
$38$	−1.00000	+	1.73205i	−0.162221	+	0.280976i
$39$	7.50000	−	4.33013i	1.20096	−	0.693375i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$	1.50000	−	0.866025i	0.231455	−	0.133631i
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	−0.179069	−	0.983836i	$-0.557309\pi$
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	0.941562	−	0.336840i	$-0.109358\pi$
$44$	3.00000			0.452267
$45$	1.50000	+	2.59808i	0.223607	+	0.387298i
$46$	6.00000			0.884652
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	−0.954441	−	0.298401i	$-0.903547\pi$
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	0.735643	+	0.677369i	$0.236880\pi$
$48$	−1.50000	−	0.866025i	−0.216506	−	0.125000i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$		−	5.19615i		−	0.727607i
$52$	−2.50000	+	4.33013i	−0.346688	+	0.600481i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$	3.00000			0.404520
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$			3.46410i			0.458831i
$58$	−3.00000	−	5.19615i	−0.393919	−	0.682288i
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	0.931282	+	0.364299i	$0.118692\pi$
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	−0.150148	+	0.988663i	$0.547975\pi$
$60$	−1.50000	−	0.866025i	−0.193649	−	0.111803i
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	−0.345207	−	0.938527i	$-0.612191\pi$
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	0.985391	−	0.170305i	$-0.0544754\pi$
$62$	2.00000			0.254000
$63$	1.50000	−	2.59808i	0.188982	−	0.327327i
$64$	1.00000			0.125000
$65$	−2.50000	+	4.33013i	−0.310087	+	0.537086i
$66$	4.50000	−	2.59808i	0.553912	−	0.319801i
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	9.00000	−	5.19615i	1.08347	−	0.625543i
$70$	−0.500000	+	0.866025i	−0.0597614	+	0.103510i
$71$	−9.00000			−1.06810			−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000			−1.06810			−0.534052	+	0.845452i	$0.679331\pi$
$72$	−3.00000			−0.353553
$73$	11.0000			1.28745			0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000			1.28745			0.643726	+	0.765256i	$0.277388\pi$
$74$	5.00000	−	8.66025i	0.581238	−	1.00673i
$75$	−1.50000	−	0.866025i	−0.173205	−	0.100000i
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$	−1.50000	−	2.59808i	−0.170941	−	0.296078i
$78$			8.66025i			0.980581i
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$	1.00000			0.111803
$81$	9.00000			1.00000
$82$		0			0
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	−0.999976	−	0.00698436i	$-0.997777\pi$
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	0.506036	+	0.862512i	$0.331110\pi$
$84$			1.73205i			0.188982i
$85$	1.50000	+	2.59808i	0.162698	+	0.281801i
$86$	5.00000	+	8.66025i	0.539164	+	0.933859i
$87$	−9.00000	−	5.19615i	−0.964901	−	0.557086i
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$	−3.00000			−0.316228
$91$	5.00000			0.524142
$92$	−3.00000	+	5.19615i	−0.312772	+	0.541736i
$93$	3.00000	−	1.73205i	0.311086	−	0.179605i
$94$	−1.50000	−	2.59808i	−0.154713	−	0.267971i
$95$	−1.00000	−	1.73205i	−0.102598	−	0.177705i
$96$	1.50000	−	0.866025i	0.153093	−	0.0883883i
$97$	−8.50000	+	14.7224i	−0.863044	+	1.49484i	0.00593185	+	0.999982i	$0.498112\pi$
$97$	−8.50000	+	14.7224i	−0.863044	+	1.49484i	−0.868976	+	0.494854i	$0.835222\pi$
$98$	1.00000			0.101015
$99$	4.50000	−	7.79423i	0.452267	−	0.783349i
$100$	1.00000			0.100000
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.0623905	+	0.998052i	$0.519872\pi$
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.833143	+	0.553058i	$0.813461\pi$
$102$	4.50000	+	2.59808i	0.445566	+	0.257248i
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$	−2.50000	−	4.33013i	−0.245145	−	0.424604i
$105$			1.73205i			0.169031i
$106$		0			0
$107$	−6.00000			−0.580042			−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000			−0.580042			−0.290021	+	0.957020i	$0.593662\pi$
$108$	−4.50000	+	2.59808i	−0.433013	+	0.250000i
$109$	−13.0000			−1.24517			−0.622587	−	0.782551i	$-0.713918\pi$
$109$	−13.0000			−1.24517			−0.622587	+	0.782551i	$0.713918\pi$
$110$	−1.50000	+	2.59808i	−0.143019	+	0.247717i
$111$		−	17.3205i		−	1.64399i
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	0.689714	−	0.724082i	$-0.257736\pi$
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	−0.971930	+	0.235269i	$0.924403\pi$
$114$	−3.00000	−	1.73205i	−0.280976	−	0.162221i
$115$	−3.00000	+	5.19615i	−0.279751	+	0.484544i
$116$	6.00000			0.557086
$117$	7.50000	+	12.9904i	0.693375	+	1.20096i
$118$	−12.0000			−1.10469
$119$	1.50000	−	2.59808i	0.137505	−	0.238165i
$120$	1.50000	−	0.866025i	0.136931	−	0.0790569i
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	5.00000	+	8.66025i	0.452679	+	0.784063i
$123$		0			0
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$	1.00000			0.0894427
$126$	1.50000	+	2.59808i	0.133631	+	0.231455i
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	15.0000	+	8.66025i	1.32068	+	0.762493i
$130$	−2.50000	−	4.33013i	−0.219265	−	0.379777i
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	0.999602	+	0.0281993i	$0.00897729\pi$
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	−0.475380	+	0.879781i	$0.657689\pi$
$132$			5.19615i			0.452267i
$133$	−1.00000	+	1.73205i	−0.0867110	+	0.150188i
$134$	2.00000			0.172774
$135$	−4.50000	+	2.59808i	−0.387298	+	0.223607i
$136$	−3.00000			−0.257248
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	−0.965250	−	0.261329i	$-0.915839\pi$
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	0.708942	+	0.705266i	$0.249173\pi$
$138$			10.3923i			0.884652i
$139$	−1.00000	−	1.73205i	−0.0848189	−	0.146911i	0.820495	−	0.571654i	$-0.193698\pi$
$139$	−1.00000	−	1.73205i	−0.0848189	−	0.146911i	−0.905314	+	0.424743i	$0.860365\pi$
$140$	−0.500000	−	0.866025i	−0.0422577	−	0.0731925i
$141$	−4.50000	−	2.59808i	−0.378968	−	0.218797i
$142$	4.50000	−	7.79423i	0.377632	−	0.654077i
$143$	15.0000			1.25436
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	6.00000			0.498273
$146$	−5.50000	+	9.52628i	−0.455183	+	0.788400i
$147$	1.50000	−	0.866025i	0.123718	−	0.0714286i
$148$	5.00000	+	8.66025i	0.410997	+	0.711868i
$149$	−10.5000	−	18.1865i	−0.860194	−	1.48990i	−0.871742	−	0.489966i	$-0.837009\pi$
$149$	−10.5000	−	18.1865i	−0.860194	−	1.48990i	0.0115483	−	0.999933i	$-0.496324\pi$
$150$	1.50000	−	0.866025i	0.122474	−	0.0707107i
$151$	−8.50000	+	14.7224i	−0.691720	+	1.19809i	0.279554	+	0.960130i	$0.409814\pi$
$151$	−8.50000	+	14.7224i	−0.691720	+	1.19809i	−0.971274	+	0.237964i	$0.923520\pi$
$152$	2.00000			0.162221
$153$	9.00000			0.727607
$154$	3.00000			0.241747
$155$	−1.00000	+	1.73205i	−0.0803219	+	0.139122i
$156$	−7.50000	−	4.33013i	−0.600481	−	0.346688i
$157$	3.50000	+	6.06218i	0.279330	+	0.483814i	0.971219	−	0.238190i	$-0.0765542\pi$
$157$	3.50000	+	6.06218i	0.279330	+	0.483814i	−0.691888	+	0.722005i	$0.743221\pi$
$158$	0.500000	+	0.866025i	0.0397779	+	0.0688973i
$159$		0			0
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	6.00000			0.472866
$162$	−4.50000	+	7.79423i	−0.353553	+	0.612372i
$163$	2.00000			0.156652			0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000			0.156652			0.0783260	+	0.996928i	$0.475042\pi$
$164$		0			0
$165$			5.19615i			0.404520i
$166$	−4.50000	−	7.79423i	−0.349268	−	0.604949i
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	0.918208	−	0.396098i	$-0.129636\pi$
$167$	1.50000	+	2.59808i	0.116073	+	0.201045i	−0.802135	+	0.597143i	$0.796303\pi$
$168$	−1.50000	−	0.866025i	−0.115728	−	0.0668153i
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$	−3.00000			−0.230089
$171$	−6.00000			−0.458831
$172$	−10.0000			−0.762493
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$	9.00000	−	5.19615i	0.682288	−	0.393919i
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	−1.50000	−	2.59808i	−0.113067	−	0.195837i
$177$	−18.0000	+	10.3923i	−1.35296	+	0.781133i
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	15.0000			1.12115			0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000			1.12115			0.560576	+	0.828103i	$0.310580\pi$
$180$	1.50000	−	2.59808i	0.111803	−	0.193649i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	−2.50000	+	4.33013i	−0.185312	+	0.320970i
$183$	15.0000	+	8.66025i	1.10883	+	0.640184i
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$	5.00000	+	8.66025i	0.367607	+	0.636715i
$186$			3.46410i			0.254000i
$187$	4.50000	−	7.79423i	0.329073	−	0.569970i
$188$	3.00000			0.218797
$189$	4.50000	+	2.59808i	0.327327	+	0.188982i
$190$	2.00000			0.145095
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$			1.73205i			0.125000i
$193$	11.0000	+	19.0526i	0.791797	+	1.37143i	0.924853	+	0.380325i	$0.124188\pi$
$193$	11.0000	+	19.0526i	0.791797	+	1.37143i	−0.133056	+	0.991109i	$0.542479\pi$
$194$	−8.50000	−	14.7224i	−0.610264	−	1.05701i
$195$	−7.50000	−	4.33013i	−0.537086	−	0.310087i
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$	4.50000	+	7.79423i	0.319801	+	0.553912i
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	3.00000	−	1.73205i	0.211604	−	0.122169i
$202$	−9.00000	−	15.5885i	−0.633238	−	1.09680i
$203$	−3.00000	−	5.19615i	−0.210559	−	0.364698i
$204$	−4.50000	+	2.59808i	−0.315063	+	0.181902i
$205$		0			0
$206$	8.00000			0.557386
$207$	9.00000	+	15.5885i	0.625543	+	1.08347i
$208$	5.00000			0.346688
$209$	−3.00000	+	5.19615i	−0.207514	+	0.359425i
$210$	−1.50000	−	0.866025i	−0.103510	−	0.0597614i
$211$	3.50000	+	6.06218i	0.240950	+	0.417338i	0.960985	−	0.276600i	$-0.0892077\pi$
$211$	3.50000	+	6.06218i	0.240950	+	0.417338i	−0.720035	+	0.693938i	$0.755874\pi$
$212$		0			0
$213$		−	15.5885i		−	1.06810i
$214$	3.00000	−	5.19615i	0.205076	−	0.355202i
$215$	−10.0000			−0.681994
$216$		−	5.19615i		−	0.353553i
$217$	2.00000			0.135769
$218$	6.50000	−	11.2583i	0.440236	−	0.762510i
$219$			19.0526i			1.28745i
$220$	−1.50000	−	2.59808i	−0.101130	−	0.175162i
$221$	7.50000	+	12.9904i	0.504505	+	0.873828i
$222$	15.0000	+	8.66025i	1.00673	+	0.581238i
$223$	3.50000	−	6.06218i	0.234377	−	0.405953i	−0.724714	−	0.689050i	$-0.758028\pi$
$223$	3.50000	−	6.06218i	0.234377	−	0.405953i	0.959092	+	0.283096i	$0.0913615\pi$
$224$	1.00000			0.0668153
$225$	1.50000	−	2.59808i	0.100000	−	0.173205i
$226$	6.00000			0.399114
$227$	10.5000	−	18.1865i	0.696909	−	1.20708i	−0.272623	−	0.962121i	$-0.587891\pi$
$227$	10.5000	−	18.1865i	0.696909	−	1.20708i	0.969533	−	0.244962i	$-0.0787754\pi$
$228$	3.00000	−	1.73205i	0.198680	−	0.114708i
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	0.958187	+	0.286143i	$0.0923732\pi$
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	−0.231287	+	0.972886i	$0.574293\pi$
$230$	−3.00000	−	5.19615i	−0.197814	−	0.342624i
$231$	4.50000	−	2.59808i	0.296078	−	0.170941i
$232$	−3.00000	+	5.19615i	−0.196960	+	0.341144i
$233$	−24.0000			−1.57229			−0.786146	−	0.618041i	$-0.787927\pi$
$233$	−24.0000			−1.57229			−0.786146	+	0.618041i	$0.787927\pi$
$234$	−15.0000			−0.980581
$235$	3.00000			0.195698
$236$	6.00000	−	10.3923i	0.390567	−	0.676481i
$237$	1.50000	+	0.866025i	0.0974355	+	0.0562544i
$238$	1.50000	+	2.59808i	0.0972306	+	0.168408i
$239$	−12.0000	−	20.7846i	−0.776215	−	1.34444i	−0.934109	−	0.356988i	$-0.883804\pi$
$239$	−12.0000	−	20.7846i	−0.776215	−	1.34444i	0.157893	−	0.987456i	$-0.449530\pi$
$240$			1.73205i			0.111803i
$241$	14.0000	−	24.2487i	0.901819	−	1.56200i	0.0766885	−	0.997055i	$-0.475565\pi$
$241$	14.0000	−	24.2487i	0.901819	−	1.56200i	0.825131	−	0.564942i	$-0.191101\pi$
$242$	−2.00000			−0.128565
$243$			15.5885i			1.00000i
$244$	−10.0000			−0.640184
$245$	−0.500000	+	0.866025i	−0.0319438	+	0.0553283i
$246$		0			0
$247$	−5.00000	−	8.66025i	−0.318142	−	0.551039i
$248$	−1.00000	−	1.73205i	−0.0635001	−	0.109985i
$249$	−13.5000	−	7.79423i	−0.855528	−	0.493939i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	6.00000			0.378717			0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000			0.378717			0.189358	+	0.981908i	$0.439359\pi$
$252$	−3.00000			−0.188982
$253$	18.0000			1.13165
$254$	8.00000	−	13.8564i	0.501965	−	0.869428i
$255$	−4.50000	+	2.59808i	−0.281801	+	0.162698i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.5000	−	18.1865i	−0.654972	−	1.13444i	−0.981901	−	0.189396i	$-0.939347\pi$
$257$	−10.5000	−	18.1865i	−0.654972	−	1.13444i	0.326929	−	0.945049i	$-0.393986\pi$
$258$	−15.0000	+	8.66025i	−0.933859	+	0.539164i
$259$	5.00000	−	8.66025i	0.310685	−	0.538122i
$260$	5.00000			0.310087
$261$	9.00000	−	15.5885i	0.557086	−	0.964901i
$262$	−12.0000			−0.741362
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$	−4.50000	−	2.59808i	−0.276956	−	0.159901i
$265$		0			0
$266$	−1.00000	−	1.73205i	−0.0613139	−	0.106199i
$267$		−	10.3923i		−	0.635999i
$268$	−1.00000	+	1.73205i	−0.0610847	+	0.105802i
$269$	30.0000			1.82913			0.914566	−	0.404436i	$-0.132532\pi$
$269$	30.0000			1.82913			0.914566	+	0.404436i	$0.132532\pi$
$270$		−	5.19615i		−	0.316228i
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$	1.50000	−	2.59808i	0.0909509	−	0.157532i
$273$			8.66025i			0.524142i
$274$	−3.00000	−	5.19615i	−0.181237	−	0.313911i
$275$	−1.50000	−	2.59808i	−0.0904534	−	0.156670i
$276$	−9.00000	−	5.19615i	−0.541736	−	0.312772i
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	0.150210	+	0.988654i	$0.452005\pi$
$277$	−13.0000	+	22.5167i	−0.781094	+	1.35290i	−0.931305	+	0.364241i	$0.881328\pi$
$278$	2.00000			0.119952
$279$	3.00000	+	5.19615i	0.179605	+	0.311086i
$280$	1.00000			0.0597614
$281$	−7.50000	+	12.9904i	−0.447412	+	0.774941i	−0.998217	−	0.0596933i	$-0.980988\pi$
$281$	−7.50000	+	12.9904i	−0.447412	+	0.774941i	0.550804	+	0.834634i	$0.314321\pi$
$282$	4.50000	−	2.59808i	0.267971	−	0.154713i
$283$	−11.5000	−	19.9186i	−0.683604	−	1.18404i	−0.973873	−	0.227092i	$-0.927078\pi$
$283$	−11.5000	−	19.9186i	−0.683604	−	1.18404i	0.290269	−	0.956945i	$-0.406255\pi$
$284$	4.50000	+	7.79423i	0.267026	+	0.462502i
$285$	3.00000	−	1.73205i	0.177705	−	0.102598i
$286$	−7.50000	+	12.9904i	−0.443484	+	0.768137i
$287$		0			0
$288$	1.50000	+	2.59808i	0.0883883	+	0.153093i
$289$	−8.00000			−0.470588
$290$	−3.00000	+	5.19615i	−0.176166	+	0.305129i
$291$	−25.5000	−	14.7224i	−1.49484	−	0.863044i
$292$	−5.50000	−	9.52628i	−0.321863	−	0.557483i
$293$	−3.00000	−	5.19615i	−0.175262	−	0.303562i	0.764990	−	0.644042i	$-0.222744\pi$
$293$	−3.00000	−	5.19615i	−0.175262	−	0.303562i	−0.940252	+	0.340480i	$0.889411\pi$
$294$			1.73205i			0.101015i
$295$	6.00000	−	10.3923i	0.349334	−	0.605063i
$296$	−10.0000			−0.581238
$297$	13.5000	+	7.79423i	0.783349	+	0.452267i
$298$	21.0000			1.21650
$299$	−15.0000	+	25.9808i	−0.867472	+	1.50251i
$300$			1.73205i			0.100000i
$301$	5.00000	+	8.66025i	0.288195	+	0.499169i
$302$	−8.50000	−	14.7224i	−0.489120	−	0.847181i
$303$	−27.0000	−	15.5885i	−1.55111	−	0.895533i
$304$	−1.00000	+	1.73205i	−0.0573539	+	0.0993399i
$305$	−10.0000			−0.572598
$306$	−4.50000	+	7.79423i	−0.257248	+	0.445566i
$307$	5.00000			0.285365			0.142683	−	0.989769i	$-0.454427\pi$
$307$	5.00000			0.285365			0.142683	+	0.989769i	$0.454427\pi$
$308$	−1.50000	+	2.59808i	−0.0854704	+	0.148039i
$309$	12.0000	−	6.92820i	0.682656	−	0.394132i
$310$	−1.00000	−	1.73205i	−0.0567962	−	0.0983739i
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$	7.50000	−	4.33013i	0.424604	−	0.245145i
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	−0.993186	−	0.116543i	$-0.962819\pi$
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	0.597522	+	0.801852i	$0.296152\pi$
$314$	−7.00000			−0.395033
$315$	−3.00000			−0.169031
$316$	−1.00000			−0.0562544
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	−0.769395	−	0.638774i	$-0.779442\pi$
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	0.937892	+	0.346929i	$0.112775\pi$
$318$		0			0
$319$	−9.00000	−	15.5885i	−0.503903	−	0.872786i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		−	10.3923i		−	0.580042i
$322$	−3.00000	+	5.19615i	−0.167183	+	0.289570i
$323$	−6.00000			−0.333849
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	5.00000			0.277350
$326$	−1.00000	+	1.73205i	−0.0553849	+	0.0959294i
$327$		−	22.5167i		−	1.24517i
$328$		0			0
$329$	−1.50000	−	2.59808i	−0.0826977	−	0.143237i
$330$	−4.50000	−	2.59808i	−0.247717	−	0.143019i
$331$	15.5000	−	26.8468i	0.851957	−	1.47563i	−0.0274825	−	0.999622i	$-0.508749\pi$
$331$	15.5000	−	26.8468i	0.851957	−	1.47563i	0.879440	−	0.476011i	$-0.157918\pi$
$332$	9.00000			0.493939
$333$	30.0000			1.64399
$334$	−3.00000			−0.164153
$335$	−1.00000	+	1.73205i	−0.0546358	+	0.0946320i
$336$	1.50000	−	0.866025i	0.0818317	−	0.0472456i
$337$	17.0000	+	29.4449i	0.926049	+	1.60396i	0.789865	+	0.613280i	$0.210150\pi$
$337$	17.0000	+	29.4449i	0.926049	+	1.60396i	0.136184	+	0.990684i	$0.456516\pi$
$338$	−6.00000	−	10.3923i	−0.326357	−	0.565267i
$339$	9.00000	−	5.19615i	0.488813	−	0.282216i
$340$	1.50000	−	2.59808i	0.0813489	−	0.140900i
$341$	6.00000			0.324918
$342$	3.00000	−	5.19615i	0.162221	−	0.280976i
$343$	1.00000			0.0539949
$344$	5.00000	−	8.66025i	0.269582	−	0.466930i
$345$	−9.00000	−	5.19615i	−0.484544	−	0.279751i
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$			10.3923i			0.557086i
$349$	−4.00000	+	6.92820i	−0.214115	+	0.370858i	−0.952998	−	0.302975i	$-0.902020\pi$
$349$	−4.00000	+	6.92820i	−0.214115	+	0.370858i	0.738883	+	0.673833i	$0.235353\pi$
$350$	1.00000			0.0534522
$351$	−22.5000	+	12.9904i	−1.20096	+	0.693375i
$352$	3.00000			0.159901
$353$	15.0000	−	25.9808i	0.798369	−	1.38282i	−0.122308	−	0.992492i	$-0.539030\pi$
$353$	15.0000	−	25.9808i	0.798369	−	1.38282i	0.920677	−	0.390324i	$-0.127637\pi$
$354$		−	20.7846i		−	1.10469i
$355$	4.50000	+	7.79423i	0.238835	+	0.413675i
$356$	3.00000	+	5.19615i	0.159000	+	0.275396i
$357$	4.50000	+	2.59808i	0.238165	+	0.137505i
$358$	−7.50000	+	12.9904i	−0.396387	+	0.686563i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$	1.50000	+	2.59808i	0.0790569	+	0.136931i
$361$	−15.0000			−0.789474
$362$	5.00000	−	8.66025i	0.262794	−	0.455173i
$363$	−3.00000	+	1.73205i	−0.157459	+	0.0909091i
$364$	−2.50000	−	4.33013i	−0.131036	−	0.226960i
$365$	−5.50000	−	9.52628i	−0.287883	−	0.498628i
$366$	−15.0000	+	8.66025i	−0.784063	+	0.452679i
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	−0.997960	−	0.0638362i	$-0.979666\pi$
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	0.554264	+	0.832341i	$0.313000\pi$
$368$	6.00000			0.312772
$369$		0			0
$370$	−10.0000			−0.519875
$371$		0			0
$372$	−3.00000	−	1.73205i	−0.155543	−	0.0898027i
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$	4.50000	+	7.79423i	0.232689	+	0.403030i
$375$			1.73205i			0.0894427i
$376$	−1.50000	+	2.59808i	−0.0773566	+	0.133986i
$377$	30.0000			1.54508
$378$	−4.50000	+	2.59808i	−0.231455	+	0.133631i
$379$	5.00000			0.256833			0.128416	−	0.991720i	$-0.459011\pi$
$379$	5.00000			0.256833			0.128416	+	0.991720i	$0.459011\pi$
$380$	−1.00000	+	1.73205i	−0.0512989	+	0.0888523i
$381$		−	27.7128i		−	1.41977i
$382$		0			0
$383$	−4.50000	−	7.79423i	−0.229939	−	0.398266i	0.727851	−	0.685736i	$-0.240519\pi$
$383$	−4.50000	−	7.79423i	−0.229939	−	0.398266i	−0.957790	+	0.287469i	$0.907186\pi$
$384$	−1.50000	−	0.866025i	−0.0765466	−	0.0441942i
$385$	−1.50000	+	2.59808i	−0.0764471	+	0.132410i
$386$	−22.0000			−1.11977
$387$	−15.0000	+	25.9808i	−0.762493	+	1.32068i
$388$	17.0000			0.863044
$389$	10.5000	−	18.1865i	0.532371	−	0.922094i	−0.466915	−	0.884302i	$-0.654634\pi$
$389$	10.5000	−	18.1865i	0.532371	−	0.922094i	0.999286	−	0.0377914i	$-0.0120322\pi$
$390$	7.50000	−	4.33013i	0.379777	−	0.219265i
$391$	9.00000	+	15.5885i	0.455150	+	0.788342i
$392$	−0.500000	−	0.866025i	−0.0252538	−	0.0437409i
$393$	−18.0000	+	10.3923i	−0.907980	+	0.524222i
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$	−1.00000			−0.0503155
$396$	−9.00000			−0.452267
$397$	26.0000			1.30490			0.652451	−	0.757831i	$-0.273741\pi$
$397$	26.0000			1.30490			0.652451	+	0.757831i	$0.273741\pi$
$398$	−4.00000	+	6.92820i	−0.200502	+	0.347279i
$399$	−3.00000	−	1.73205i	−0.150188	−	0.0867110i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$			3.46410i			0.172774i
$403$	−5.00000	+	8.66025i	−0.249068	+	0.431398i
$404$	18.0000			0.895533
$405$	−4.50000	−	7.79423i	−0.223607	−	0.387298i
$406$	6.00000			0.297775
$407$	15.0000	−	25.9808i	0.743522	−	1.28782i
$408$		−	5.19615i		−	0.257248i
$409$	−4.00000	−	6.92820i	−0.197787	−	0.342578i	0.750023	−	0.661411i	$-0.230042\pi$
$409$	−4.00000	−	6.92820i	−0.197787	−	0.342578i	−0.947811	+	0.318834i	$0.896709\pi$
$410$		0			0
$411$	−9.00000	−	5.19615i	−0.443937	−	0.256307i
$412$	−4.00000	+	6.92820i	−0.197066	+	0.341328i
$413$	−12.0000			−0.590481
$414$	−18.0000			−0.884652
$415$	9.00000			0.441793
$416$	−2.50000	+	4.33013i	−0.122573	+	0.212302i
$417$	3.00000	−	1.73205i	0.146911	−	0.0848189i
$418$	−3.00000	−	5.19615i	−0.146735	−	0.254152i
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$	1.50000	−	0.866025i	0.0731925	−	0.0422577i
$421$	12.5000	−	21.6506i	0.609213	−	1.05519i	−0.382158	−	0.924097i	$-0.624819\pi$
$421$	12.5000	−	21.6506i	0.609213	−	1.05519i	0.991370	−	0.131090i	$-0.0418478\pi$
$422$	−7.00000			−0.340755
$423$	4.50000	−	7.79423i	0.218797	−	0.378968i
$424$		0			0
$425$	1.50000	−	2.59808i	0.0727607	−	0.126025i
$426$	13.5000	+	7.79423i	0.654077	+	0.377632i
$427$	5.00000	+	8.66025i	0.241967	+	0.419099i
$428$	3.00000	+	5.19615i	0.145010	+	0.251166i
$429$			25.9808i			1.25436i
$430$	5.00000	−	8.66025i	0.241121	−	0.417635i
$431$	−21.0000			−1.01153			−0.505767	−	0.862670i	$-0.668791\pi$
$431$	−21.0000			−1.01153			−0.505767	+	0.862670i	$0.668791\pi$
$432$	4.50000	+	2.59808i	0.216506	+	0.125000i
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$	−1.00000	+	1.73205i	−0.0480015	+	0.0831411i
$435$			10.3923i			0.498273i
$436$	6.50000	+	11.2583i	0.311294	+	0.539176i
$437$	−6.00000	−	10.3923i	−0.287019	−	0.497131i
$438$	−16.5000	−	9.52628i	−0.788400	−	0.455183i
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	0.978412	−	0.206666i	$-0.0662612\pi$
$440$	3.00000			0.143019
$441$	1.50000	+	2.59808i	0.0714286	+	0.123718i
$442$	−15.0000			−0.713477
$443$	3.00000	−	5.19615i	0.142534	−	0.246877i	−0.785916	−	0.618333i	$-0.787808\pi$
$443$	3.00000	−	5.19615i	0.142534	−	0.246877i	0.928450	+	0.371457i	$0.121142\pi$
$444$	−15.0000	+	8.66025i	−0.711868	+	0.410997i
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$	3.50000	+	6.06218i	0.165730	+	0.287052i
$447$	31.5000	−	18.1865i	1.48990	−	0.860194i
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$	1.50000	+	2.59808i	0.0707107	+	0.122474i
$451$		0			0
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$	−25.5000	−	14.7224i	−1.19809	−	0.691720i
$454$	10.5000	+	18.1865i	0.492789	+	0.853536i
$455$	−2.50000	−	4.33013i	−0.117202	−	0.202999i
$456$			3.46410i			0.162221i
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	0.958950	+	0.283577i	$0.0915211\pi$
$458$	−22.0000			−1.02799
$459$			15.5885i			0.727607i
$460$	6.00000			0.279751
$461$	−3.00000	+	5.19615i	−0.139724	+	0.242009i	−0.927392	−	0.374091i	$-0.877955\pi$
$461$	−3.00000	+	5.19615i	−0.139724	+	0.242009i	0.787668	+	0.616100i	$0.211288\pi$
$462$			5.19615i			0.241747i
$463$	−10.0000	−	17.3205i	−0.464739	−	0.804952i	0.534450	−	0.845200i	$-0.320519\pi$
$463$	−10.0000	−	17.3205i	−0.464739	−	0.804952i	−0.999190	+	0.0402476i	$0.987185\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$	−3.00000	−	1.73205i	−0.139122	−	0.0803219i
$466$	12.0000	−	20.7846i	0.555889	−	0.962828i
$467$	27.0000			1.24941			0.624705	−	0.780860i	$-0.285219\pi$
$467$	27.0000			1.24941			0.624705	+	0.780860i	$0.285219\pi$
$468$	7.50000	−	12.9904i	0.346688	−	0.600481i
$469$	2.00000			0.0923514
$470$	−1.50000	+	2.59808i	−0.0691898	+	0.119840i
$471$	−10.5000	+	6.06218i	−0.483814	+	0.279330i
$472$	6.00000	+	10.3923i	0.276172	+	0.478345i
$473$	15.0000	+	25.9808i	0.689701	+	1.19460i
$474$	−1.50000	+	0.866025i	−0.0688973	+	0.0397779i
$475$	−1.00000	+	1.73205i	−0.0458831	+	0.0794719i
$476$	−3.00000			−0.137505
$477$		0			0
$478$	24.0000			1.09773
$479$	−21.0000	+	36.3731i	−0.959514	+	1.66193i	−0.235833	+	0.971794i	$0.575782\pi$
$479$	−21.0000	+	36.3731i	−0.959514	+	1.66193i	−0.723681	+	0.690134i	$0.757551\pi$
$480$	−1.50000	−	0.866025i	−0.0684653	−	0.0395285i
$481$	25.0000	+	43.3013i	1.13990	+	1.97437i
$482$	14.0000	+	24.2487i	0.637683	+	1.10450i
$483$			10.3923i			0.472866i
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	17.0000			0.771930
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	−22.0000			−0.996915			−0.498458	−	0.866914i	$-0.666100\pi$
$487$	−22.0000			−0.996915			−0.498458	+	0.866914i	$0.666100\pi$
$488$	5.00000	−	8.66025i	0.226339	−	0.392031i
$489$			3.46410i			0.156652i
$490$	−0.500000	−	0.866025i	−0.0225877	−	0.0391230i
$491$	4.50000	+	7.79423i	0.203082	+	0.351749i	0.949520	−	0.313707i	$-0.101571\pi$
$491$	4.50000	+	7.79423i	0.203082	+	0.351749i	−0.746438	+	0.665455i	$0.768237\pi$
$492$		0			0
$493$	9.00000	−	15.5885i	0.405340	−	0.702069i
$494$	10.0000			0.449921
$495$	−9.00000			−0.404520
$496$	2.00000			0.0898027
$497$	4.50000	−	7.79423i	0.201853	−	0.349619i
$498$	13.5000	−	7.79423i	0.604949	−	0.349268i
$499$	21.5000	+	37.2391i	0.962472	+	1.66705i	0.716258	+	0.697835i	$0.245853\pi$
$499$	21.5000	+	37.2391i	0.962472	+	1.66705i	0.246214	+	0.969216i	$0.420813\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	−4.50000	+	2.59808i	−0.201045	+	0.116073i
$502$	−3.00000	+	5.19615i	−0.133897	+	0.231916i
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$	1.50000	−	2.59808i	0.0668153	−	0.115728i
$505$	18.0000			0.800989
$506$	−9.00000	+	15.5885i	−0.400099	+	0.692991i
$507$	−18.0000	−	10.3923i	−0.799408	−	0.461538i
$508$	8.00000	+	13.8564i	0.354943	+	0.614779i
$509$	15.0000	+	25.9808i	0.664863	+	1.15158i	0.979322	+	0.202306i	$0.0648436\pi$
$509$	15.0000	+	25.9808i	0.664863	+	1.15158i	−0.314459	+	0.949271i	$0.601823\pi$
$510$		−	5.19615i		−	0.230089i
$511$	−5.50000	+	9.52628i	−0.243306	+	0.421418i
$512$	1.00000			0.0441942
$513$		−	10.3923i		−	0.458831i
$514$	21.0000			0.926270
$515$	−4.00000	+	6.92820i	−0.176261	+	0.305293i
$516$		−	17.3205i		−	0.762493i
$517$	−4.50000	−	7.79423i	−0.197910	−	0.342790i
$518$	5.00000	+	8.66025i	0.219687	+	0.380510i
$519$	9.00000	+	5.19615i	0.395056	+	0.228086i
$520$	−2.50000	+	4.33013i	−0.109632	+	0.189889i
$521$	−6.00000			−0.262865			−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000			−0.262865			−0.131432	+	0.991325i	$0.541958\pi$
$522$	9.00000	+	15.5885i	0.393919	+	0.682288i
$523$	11.0000			0.480996			0.240498	−	0.970650i	$-0.422689\pi$
$523$	11.0000			0.480996			0.240498	+	0.970650i	$0.422689\pi$
$524$	6.00000	−	10.3923i	0.262111	−	0.453990i
$525$	1.50000	−	0.866025i	0.0654654	−	0.0377964i
$526$		0			0
$527$	3.00000	+	5.19615i	0.130682	+	0.226348i
$528$	4.50000	−	2.59808i	0.195837	−	0.113067i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$	−18.0000	−	31.1769i	−0.781133	−	1.35296i
$532$	2.00000			0.0867110
$533$		0			0
$534$	9.00000	+	5.19615i	0.389468	+	0.224860i
$535$	3.00000	+	5.19615i	0.129701	+	0.224649i
$536$	−1.00000	−	1.73205i	−0.0431934	−	0.0748132i
$537$			25.9808i			1.12115i
$538$	−15.0000	+	25.9808i	−0.646696	+	1.12011i
$539$	3.00000			0.129219
$540$	4.50000	+	2.59808i	0.193649	+	0.111803i
$541$	−7.00000			−0.300954			−0.150477	−	0.988614i	$-0.548081\pi$
$541$	−7.00000			−0.300954			−0.150477	+	0.988614i	$0.548081\pi$
$542$	−4.00000	+	6.92820i	−0.171815	+	0.297592i
$543$		−	17.3205i		−	0.743294i
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$	6.50000	+	11.2583i	0.278429	+	0.482254i
$546$	−7.50000	−	4.33013i	−0.320970	−	0.185312i
$547$	11.0000	−	19.0526i	0.470326	−	0.814629i	−0.529098	−	0.848561i	$-0.677470\pi$
$547$	11.0000	−	19.0526i	0.470326	−	0.814629i	0.999424	+	0.0339321i	$0.0108030\pi$
$548$	6.00000			0.256307
$549$	−15.0000	+	25.9808i	−0.640184	+	1.10883i
$550$	3.00000			0.127920
$551$	−6.00000	+	10.3923i	−0.255609	+	0.442727i
$552$	9.00000	−	5.19615i	0.383065	−	0.221163i
$553$	0.500000	+	0.866025i	0.0212622	+	0.0368271i
$554$	−13.0000	−	22.5167i	−0.552317	−	0.956641i
$555$	−15.0000	+	8.66025i	−0.636715	+	0.367607i
$556$	−1.00000	+	1.73205i	−0.0424094	+	0.0734553i
$557$	−6.00000			−0.254228			−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000			−0.254228			−0.127114	+	0.991888i	$0.540571\pi$
$558$	−6.00000			−0.254000
$559$	−50.0000			−2.11477
$560$	−0.500000	+	0.866025i	−0.0211289	+	0.0365963i
$561$	13.5000	+	7.79423i	0.569970	+	0.329073i
$562$	−7.50000	−	12.9904i	−0.316368	−	0.547966i
$563$	−4.50000	−	7.79423i	−0.189652	−	0.328488i	0.755482	−	0.655169i	$-0.227403\pi$
$563$	−4.50000	−	7.79423i	−0.189652	−	0.328488i	−0.945134	+	0.326682i	$0.894069\pi$
$564$			5.19615i			0.218797i
$565$	−3.00000	+	5.19615i	−0.126211	+	0.218604i
$566$	23.0000			0.966762
$567$	−4.50000	+	7.79423i	−0.188982	+	0.327327i
$568$	−9.00000			−0.377632
$569$	−16.5000	+	28.5788i	−0.691716	+	1.19809i	0.279559	+	0.960128i	$0.409812\pi$
$569$	−16.5000	+	28.5788i	−0.691716	+	1.19809i	−0.971275	+	0.237959i	$0.923522\pi$
$570$			3.46410i			0.145095i
$571$	−2.50000	−	4.33013i	−0.104622	−	0.181210i	0.808962	−	0.587861i	$-0.200030\pi$
$571$	−2.50000	−	4.33013i	−0.104622	−	0.181210i	−0.913584	+	0.406651i	$0.866697\pi$
$572$	−7.50000	−	12.9904i	−0.313591	−	0.543155i
$573$		0			0
$574$		0			0
$575$	6.00000			0.250217
$576$	−3.00000			−0.125000
$577$	−25.0000			−1.04076			−0.520382	−	0.853934i	$-0.674210\pi$
$577$	−25.0000			−1.04076			−0.520382	+	0.853934i	$0.674210\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	−33.0000	+	19.0526i	−1.37143	+	0.791797i
$580$	−3.00000	−	5.19615i	−0.124568	−	0.215758i
$581$	−4.50000	−	7.79423i	−0.186691	−	0.323359i
$582$	25.5000	−	14.7224i	1.05701	−	0.610264i
$583$		0			0
$584$	11.0000			0.455183
$585$	7.50000	−	12.9904i	0.310087	−	0.537086i
$586$	6.00000			0.247858
$587$	−6.00000	+	10.3923i	−0.247647	+	0.428936i	−0.962872	−	0.269957i	$-0.912990\pi$
$587$	−6.00000	+	10.3923i	−0.247647	+	0.428936i	0.715226	+	0.698893i	$0.246324\pi$
$588$	−1.50000	−	0.866025i	−0.0618590	−	0.0357143i
$589$	−2.00000	−	3.46410i	−0.0824086	−	0.142736i
$590$	6.00000	+	10.3923i	0.247016	+	0.427844i
$591$			10.3923i			0.427482i
$592$	5.00000	−	8.66025i	0.205499	−	0.355934i
$593$	−42.0000			−1.72473			−0.862367	−	0.506284i	$-0.831019\pi$
$593$	−42.0000			−1.72473			−0.862367	+	0.506284i	$0.831019\pi$
$594$	−13.5000	+	7.79423i	−0.553912	+	0.319801i
$595$	−3.00000			−0.122988
$596$	−10.5000	+	18.1865i	−0.430097	+	0.744949i
$597$			13.8564i			0.567105i
$598$	−15.0000	−	25.9808i	−0.613396	−	1.06243i
$599$	−1.50000	−	2.59808i	−0.0612883	−	0.106155i	0.833753	−	0.552137i	$-0.186188\pi$
$599$	−1.50000	−	2.59808i	−0.0612883	−	0.106155i	−0.895042	+	0.445983i	$0.852854\pi$
$600$	−1.50000	−	0.866025i	−0.0612372	−	0.0353553i
$601$	8.00000	−	13.8564i	0.326327	−	0.565215i	−0.655453	−	0.755236i	$-0.727522\pi$
$601$	8.00000	−	13.8564i	0.326327	−	0.565215i	0.981780	+	0.190021i	$0.0608557\pi$
$602$	−10.0000			−0.407570
$603$	3.00000	+	5.19615i	0.122169	+	0.211604i
$604$	17.0000			0.691720
$605$	1.00000	−	1.73205i	0.0406558	−	0.0704179i
$606$	27.0000	−	15.5885i	1.09680	−	0.633238i
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	0.773358	−	0.633970i	$-0.218576\pi$
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	−0.935713	+	0.352763i	$0.885242\pi$
$608$	−1.00000	−	1.73205i	−0.0405554	−	0.0702439i
$609$	9.00000	−	5.19615i	0.364698	−	0.210559i
$610$	5.00000	−	8.66025i	0.202444	−	0.350643i
$611$	15.0000			0.606835
$612$	−4.50000	−	7.79423i	−0.181902	−	0.315063i
$613$	−10.0000			−0.403896			−0.201948	−	0.979396i	$-0.564727\pi$
$613$	−10.0000			−0.403896			−0.201948	+	0.979396i	$0.564727\pi$
$614$	−2.50000	+	4.33013i	−0.100892	+	0.174750i
$615$		0			0
$616$	−1.50000	−	2.59808i	−0.0604367	−	0.104679i
$617$	−12.0000	−	20.7846i	−0.483102	−	0.836757i	0.516710	−	0.856161i	$-0.327157\pi$
$617$	−12.0000	−	20.7846i	−0.483102	−	0.836757i	−0.999812	+	0.0194037i	$0.993823\pi$
$618$			13.8564i			0.557386i
$619$	−13.0000	+	22.5167i	−0.522514	+	0.905021i	0.477143	+	0.878826i	$0.341672\pi$
$619$	−13.0000	+	22.5167i	−0.522514	+	0.905021i	−0.999657	+	0.0261952i	$0.991661\pi$
$620$	2.00000			0.0803219
$621$	−27.0000	+	15.5885i	−1.08347	+	0.625543i
$622$		0			0
$623$	3.00000	−	5.19615i	0.120192	−	0.208179i
$624$			8.66025i			0.346688i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−7.00000	−	12.1244i	−0.279776	−	0.484587i
$627$	−9.00000	−	5.19615i	−0.359425	−	0.207514i
$628$	3.50000	−	6.06218i	0.139665	−	0.241907i
$629$	30.0000			1.19618
$630$	1.50000	−	2.59808i	0.0597614	−	0.103510i
$631$	29.0000			1.15447			0.577236	−	0.816577i	$-0.304131\pi$
$631$	29.0000			1.15447			0.577236	+	0.816577i	$0.304131\pi$
$632$	0.500000	−	0.866025i	0.0198889	−	0.0344486i
$633$	−10.5000	+	6.06218i	−0.417338	+	0.240950i
$634$	3.00000	+	5.19615i	0.119145	+	0.206366i
$635$	8.00000	+	13.8564i	0.317470	+	0.549875i
$636$		0			0
$637$	−2.50000	+	4.33013i	−0.0990536	+	0.171566i
$638$	18.0000			0.712627
$639$	27.0000			1.06810
$640$	1.00000			0.0395285
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	−0.631721	−	0.775196i	$-0.717651\pi$
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	0.987200	+	0.159489i	$0.0509845\pi$
$642$	9.00000	+	5.19615i	0.355202	+	0.205076i
$643$	15.5000	+	26.8468i	0.611260	+	1.05873i	0.991028	+	0.133652i	$0.0426705\pi$
$643$	15.5000	+	26.8468i	0.611260	+	1.05873i	−0.379768	+	0.925082i	$0.623996\pi$
$644$	−3.00000	−	5.19615i	−0.118217	−	0.204757i
$645$		−	17.3205i		−	0.681994i
$646$	3.00000	−	5.19615i	0.118033	−	0.204440i
$647$	12.0000			0.471769			0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000			0.471769			0.235884	+	0.971781i	$0.424201\pi$
$648$	9.00000			0.353553
$649$	−36.0000			−1.41312
$650$	−2.50000	+	4.33013i	−0.0980581	+	0.169842i
$651$			3.46410i			0.135769i
$652$	−1.00000	−	1.73205i	−0.0391630	−	0.0678323i
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	0.529799	−	0.848123i	$-0.322267\pi$
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	−0.999396	+	0.0347583i	$0.988934\pi$
$654$	19.5000	+	11.2583i	0.762510	+	0.440236i
$655$	6.00000	−	10.3923i	0.234439	−	0.406061i
$656$		0			0
$657$	−33.0000			−1.28745
$658$	3.00000			0.116952
$659$	13.5000	−	23.3827i	0.525885	−	0.910860i	−0.473660	−	0.880708i	$-0.657067\pi$
$659$	13.5000	−	23.3827i	0.525885	−	0.910860i	0.999545	−	0.0301523i	$-0.00959924\pi$
$660$	4.50000	−	2.59808i	0.175162	−	0.101130i
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	0.697174	−	0.716902i	$-0.254441\pi$
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	−0.969442	+	0.245319i	$0.921107\pi$
$662$	15.5000	+	26.8468i	0.602425	+	1.04343i
$663$	−22.5000	+	12.9904i	−0.873828	+	0.504505i
$664$	−4.50000	+	7.79423i	−0.174634	+	0.302475i
$665$	2.00000			0.0775567
$666$	−15.0000	+	25.9808i	−0.581238	+	1.00673i
$667$	36.0000			1.39393
$668$	1.50000	−	2.59808i	0.0580367	−	0.100523i
$669$	10.5000	+	6.06218i	0.405953	+	0.234377i
$670$	−1.00000	−	1.73205i	−0.0386334	−	0.0669150i
$671$	15.0000	+	25.9808i	0.579069	+	1.00298i
$672$			1.73205i			0.0668153i
$673$	−16.0000	+	27.7128i	−0.616755	+	1.06825i	0.373319	+	0.927703i	$0.378220\pi$
$673$	−16.0000	+	27.7128i	−0.616755	+	1.06825i	−0.990074	+	0.140548i	$0.955114\pi$
$674$	−34.0000			−1.30963
$675$	4.50000	+	2.59808i	0.173205	+	0.100000i
$676$	12.0000			0.461538
$677$	13.5000	−	23.3827i	0.518847	−	0.898670i	−0.480913	−	0.876768i	$-0.659695\pi$
$677$	13.5000	−	23.3827i	0.518847	−	0.898670i	0.999760	−	0.0219013i	$-0.00697196\pi$
$678$			10.3923i			0.399114i
$679$	−8.50000	−	14.7224i	−0.326200	−	0.564995i
$680$	1.50000	+	2.59808i	0.0575224	+	0.0996317i
$681$	31.5000	+	18.1865i	1.20708	+	0.696909i
$682$	−3.00000	+	5.19615i	−0.114876	+	0.198971i
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$	3.00000	+	5.19615i	0.114708	+	0.198680i
$685$	6.00000			0.229248
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	−33.0000	+	19.0526i	−1.25903	+	0.726900i
$688$	5.00000	+	8.66025i	0.190623	+	0.330169i
$689$		0			0
$690$	9.00000	−	5.19615i	0.342624	−	0.197814i
$691$	5.00000	−	8.66025i	0.190209	−	0.329452i	−0.755110	−	0.655598i	$-0.772417\pi$
$691$	5.00000	−	8.66025i	0.190209	−	0.329452i	0.945319	+	0.326146i	$0.105750\pi$
$692$	−6.00000			−0.228086
$693$	4.50000	+	7.79423i	0.170941	+	0.296078i
$694$	12.0000			0.455514
$695$	−1.00000	+	1.73205i	−0.0379322	+	0.0657004i
$696$	−9.00000	−	5.19615i	−0.341144	−	0.196960i
$697$		0			0
$698$	−4.00000	−	6.92820i	−0.151402	−	0.262236i
$699$		−	41.5692i		−	1.57229i
$700$	−0.500000	+	0.866025i	−0.0188982	+	0.0327327i
$701$	−39.0000			−1.47301			−0.736505	−	0.676432i	$-0.763525\pi$
$701$	−39.0000			−1.47301			−0.736505	+	0.676432i	$0.763525\pi$
$702$		−	25.9808i		−	0.980581i
$703$	−20.0000			−0.754314
$704$	−1.50000	+	2.59808i	−0.0565334	+	0.0979187i
$705$			5.19615i			0.195698i
$706$	15.0000	+	25.9808i	0.564532	+	0.977799i
$707$	−9.00000	−	15.5885i	−0.338480	−	0.586264i
$708$	18.0000	+	10.3923i	0.676481	+	0.390567i
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	−0.756730	−	0.653727i	$-0.773204\pi$
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	0.944509	+	0.328484i	$0.106538\pi$
$710$	−9.00000			−0.337764
$711$	−1.50000	+	2.59808i	−0.0562544	+	0.0974355i
$712$	−6.00000			−0.224860
$713$	−6.00000	+	10.3923i	−0.224702	+	0.389195i
$714$	−4.50000	+	2.59808i	−0.168408	+	0.0972306i
$715$	−7.50000	−	12.9904i	−0.280484	−	0.485813i
$716$	−7.50000	−	12.9904i	−0.280288	−	0.485473i
$717$	36.0000	−	20.7846i	1.34444	−	0.776215i
$718$	−12.0000	+	20.7846i	−0.447836	+	0.775675i
$719$	−6.00000			−0.223762			−0.111881	−	0.993722i	$-0.535688\pi$
$719$	−6.00000			−0.223762			−0.111881	+	0.993722i	$0.535688\pi$
$720$	−3.00000			−0.111803
$721$	8.00000			0.297936
$722$	7.50000	−	12.9904i	0.279121	−	0.483452i
$723$	42.0000	+	24.2487i	1.56200	+	0.901819i
$724$	5.00000	+	8.66025i	0.185824	+	0.321856i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$		−	3.46410i		−	0.128565i
$727$	15.5000	−	26.8468i	0.574863	−	0.995692i	−0.421193	−	0.906971i	$-0.638389\pi$
$727$	15.5000	−	26.8468i	0.574863	−	0.995692i	0.996056	−	0.0887213i	$-0.0282781\pi$
$728$	5.00000			0.185312
$729$	−27.0000			−1.00000
$730$	11.0000			0.407128
$731$	−15.0000	+	25.9808i	−0.554795	+	0.960933i
$732$		−	17.3205i		−	0.640184i
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	0.707303	−	0.706910i	$-0.249912\pi$
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	−0.965854	+	0.259087i	$0.916578\pi$
$734$	−8.50000	−	14.7224i	−0.313741	−	0.543415i
$735$	−1.50000	−	0.866025i	−0.0553283	−	0.0319438i
$736$	−3.00000	+	5.19615i	−0.110581	+	0.191533i
$737$	6.00000			0.221013
$738$		0			0
$739$	20.0000			0.735712			0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000			0.735712			0.367856	+	0.929883i	$0.380092\pi$
$740$	5.00000	−	8.66025i	0.183804	−	0.318357i
$741$	15.0000	−	8.66025i	0.551039	−	0.318142i
$742$		0			0
$743$	18.0000	+	31.1769i	0.660356	+	1.14377i	0.980522	+	0.196409i	$0.0629279\pi$
$743$	18.0000	+	31.1769i	0.660356	+	1.14377i	−0.320166	+	0.947361i	$0.603739\pi$
$744$	3.00000	−	1.73205i	0.109985	−	0.0635001i
$745$	−10.5000	+	18.1865i	−0.384690	+	0.666303i
$746$	−4.00000			−0.146450
$747$	13.5000	−	23.3827i	0.493939	−	0.855528i
$748$	−9.00000			−0.329073
$749$	3.00000	−	5.19615i	0.109618	−	0.189863i
$750$	−1.50000	−	0.866025i	−0.0547723	−	0.0316228i
$751$	14.0000	+	24.2487i	0.510867	+	0.884848i	0.999921	+	0.0125942i	$0.00400897\pi$
$751$	14.0000	+	24.2487i	0.510867	+	0.884848i	−0.489053	+	0.872254i	$0.662658\pi$
$752$	−1.50000	−	2.59808i	−0.0546994	−	0.0947421i
$753$			10.3923i			0.378717i
$754$	−15.0000	+	25.9808i	−0.546268	+	0.946164i
$755$	17.0000			0.618693
$756$		−	5.19615i		−	0.188982i
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−2.50000	+	4.33013i	−0.0908041	+	0.157277i
$759$			31.1769i			1.13165i
$760$	−1.00000	−	1.73205i	−0.0362738	−	0.0628281i
$761$	9.00000	+	15.5885i	0.326250	+	0.565081i	0.981764	−	0.190101i	$-0.0608816\pi$
$761$	9.00000	+	15.5885i	0.326250	+	0.565081i	−0.655515	+	0.755182i	$0.727548\pi$
$762$	24.0000	+	13.8564i	0.869428	+	0.501965i
$763$	6.50000	−	11.2583i	0.235316	−	0.407579i
$764$		0			0
$765$	−4.50000	−	7.79423i	−0.162698	−	0.281801i
$766$	9.00000			0.325183
$767$	30.0000	−	51.9615i	1.08324	−	1.87622i
$768$	1.50000	−	0.866025i	0.0541266	−	0.0312500i
$769$	−13.0000	−	22.5167i	−0.468792	−	0.811972i	0.530572	−	0.847640i	$-0.321977\pi$
$769$	−13.0000	−	22.5167i	−0.468792	−	0.811972i	−0.999364	+	0.0356685i	$0.988644\pi$
$770$	−1.50000	−	2.59808i	−0.0540562	−	0.0936282i
$771$	31.5000	−	18.1865i	1.13444	−	0.654972i
$772$	11.0000	−	19.0526i	0.395899	−	0.685717i
$773$	33.0000			1.18693			0.593464	−	0.804861i	$-0.297760\pi$
$773$	33.0000			1.18693			0.593464	+	0.804861i	$0.297760\pi$
$774$	−15.0000	−	25.9808i	−0.539164	−	0.933859i
$775$	2.00000			0.0718421
$776$	−8.50000	+	14.7224i	−0.305132	+	0.528505i
$777$	15.0000	+	8.66025i	0.538122	+	0.310685i
$778$	10.5000	+	18.1865i	0.376443	+	0.652019i
$779$		0			0
$780$			8.66025i			0.310087i
$781$	13.5000	−	23.3827i	0.483068	−	0.836698i
$782$	−18.0000			−0.643679
$783$	27.0000	+	15.5885i	0.964901	+	0.557086i
$784$	1.00000			0.0357143
$785$	3.50000	−	6.06218i	0.124920	−	0.216368i
$786$		−	20.7846i		−	0.741362i
$787$	−11.5000	−	19.9186i	−0.409931	−	0.710021i	0.584951	−	0.811069i	$-0.301114\pi$
$787$	−11.5000	−	19.9186i	−0.409931	−	0.710021i	−0.994882	+	0.101048i	$0.967780\pi$
$788$	−3.00000	−	5.19615i	−0.106871	−	0.185105i
$789$		0			0
$790$	0.500000	−	0.866025i	0.0177892	−	0.0308118i
$791$	6.00000			0.213335
$792$	4.50000	−	7.79423i	0.159901	−	0.276956i
$793$	−50.0000			−1.77555
$794$	−13.0000	+	22.5167i	−0.461353	+	0.799086i
$795$		0			0
$796$	−4.00000	−	6.92820i	−0.141776	−	0.245564i
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	0.521493	−	0.853256i	$-0.325375\pi$
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	−0.999687	+	0.0249984i	$0.992042\pi$
$798$	3.00000	−	1.73205i	0.106199	−	0.0613139i
$799$	4.50000	−	7.79423i	0.159199	−	0.275740i
$800$	1.00000			0.0353553
$801$	18.0000			0.635999
$802$	18.0000			0.635602
$803$	−16.5000	+	28.5788i	−0.582272	+	1.00853i
$804$	−3.00000	−	1.73205i	−0.105802	−	0.0610847i
$805$	−3.00000	−	5.19615i	−0.105736	−	0.183140i
$806$	−5.00000	−	8.66025i	−0.176117	−	0.305044i
$807$			51.9615i			1.82913i
$808$	−9.00000	+	15.5885i	−0.316619	+	0.548400i
$809$	−39.0000			−1.37117			−0.685583	−	0.727994i	$-0.740453\pi$
$809$	−39.0000			−1.37117			−0.685583	+	0.727994i	$0.740453\pi$
$810$	9.00000			0.316228
$811$	−40.0000			−1.40459			−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000			−1.40459			−0.702295	+	0.711886i	$0.747841\pi$
$812$	−3.00000	+	5.19615i	−0.105279	+	0.182349i
$813$			13.8564i			0.485965i
$814$	15.0000	+	25.9808i	0.525750	+	0.910625i
$815$	−1.00000	−	1.73205i	−0.0350285	−	0.0606711i
$816$	4.50000	+	2.59808i	0.157532	+	0.0909509i
$817$	10.0000	−	17.3205i	0.349856	−	0.605968i
$818$	8.00000			0.279713
$819$	−15.0000			−0.524142
$820$		0			0
$821$	22.5000	−	38.9711i	0.785255	−	1.36010i	−0.143591	−	0.989637i	$-0.545865\pi$
$821$	22.5000	−	38.9711i	0.785255	−	1.36010i	0.928846	−	0.370465i	$-0.120802\pi$
$822$	9.00000	−	5.19615i	0.313911	−	0.181237i
$823$	−28.0000	−	48.4974i	−0.976019	−	1.69051i	−0.676532	−	0.736413i	$-0.736518\pi$
$823$	−28.0000	−	48.4974i	−0.976019	−	1.69051i	−0.299487	−	0.954100i	$-0.596815\pi$
$824$	−4.00000	−	6.92820i	−0.139347	−	0.241355i
$825$	4.50000	−	2.59808i	0.156670	−	0.0904534i
$826$	6.00000	−	10.3923i	0.208767	−	0.361595i
$827$	54.0000			1.87776			0.938882	−	0.344239i	$-0.111863\pi$
$827$	54.0000			1.87776			0.938882	+	0.344239i	$0.111863\pi$
$828$	9.00000	−	15.5885i	0.312772	−	0.541736i
$829$	−28.0000			−0.972480			−0.486240	−	0.873825i	$-0.661632\pi$
$829$	−28.0000			−0.972480			−0.486240	+	0.873825i	$0.661632\pi$
$830$	−4.50000	+	7.79423i	−0.156197	+	0.270542i
$831$	−39.0000	−	22.5167i	−1.35290	−	0.781094i
$832$	−2.50000	−	4.33013i	−0.0866719	−	0.150120i
$833$	1.50000	+	2.59808i	0.0519719	+	0.0900180i
$834$			3.46410i			0.119952i
$835$	1.50000	−	2.59808i	0.0519096	−	0.0899101i
$836$	6.00000			0.207514
$837$	−9.00000	+	5.19615i	−0.311086	+	0.179605i
$838$		0			0
$839$	−18.0000	+	31.1769i	−0.621429	+	1.07635i	0.367791	+	0.929909i	$0.380114\pi$
$839$	−18.0000	+	31.1769i	−0.621429	+	1.07635i	−0.989220	+	0.146438i	$0.953219\pi$
$840$			1.73205i			0.0597614i
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	12.5000	+	21.6506i	0.430778	+	0.746130i
$843$	−22.5000	−	12.9904i	−0.774941	−	0.447412i
$844$	3.50000	−	6.06218i	0.120475	−	0.208669i
$845$	12.0000			0.412813
$846$	4.50000	+	7.79423i	0.154713	+	0.267971i
$847$	−2.00000			−0.0687208
$848$		0			0
$849$	34.5000	−	19.9186i	1.18404	−	0.683604i
$850$	1.50000	+	2.59808i	0.0514496	+	0.0891133i
$851$	30.0000	+	51.9615i	1.02839	+	1.78122i
$852$	−13.5000	+	7.79423i	−0.462502	+	0.267026i
$853$	−13.0000	+	22.5167i	−0.445112	+	0.770956i	−0.998060	−	0.0622597i	$-0.980169\pi$
$853$	−13.0000	+	22.5167i	−0.445112	+	0.770956i	0.552948	+	0.833215i	$0.313503\pi$
$854$	−10.0000			−0.342193
$855$	3.00000	+	5.19615i	0.102598	+	0.177705i
$856$	−6.00000			−0.205076
$857$	−1.50000	+	2.59808i	−0.0512390	+	0.0887486i	−0.890507	−	0.454969i	$-0.849650\pi$
$857$	−1.50000	+	2.59808i	−0.0512390	+	0.0887486i	0.839268	+	0.543718i	$0.182984\pi$
$858$	−22.5000	−	12.9904i	−0.768137	−	0.443484i
$859$	−7.00000	−	12.1244i	−0.238837	−	0.413678i	0.721544	−	0.692369i	$-0.243433\pi$
$859$	−7.00000	−	12.1244i	−0.238837	−	0.413678i	−0.960381	+	0.278691i	$0.910099\pi$
$860$	5.00000	+	8.66025i	0.170499	+	0.295312i
$861$		0			0
$862$	10.5000	−	18.1865i	0.357631	−	0.619436i
$863$	−6.00000			−0.204242			−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000			−0.204242			−0.102121	+	0.994772i	$0.532563\pi$
$864$	−4.50000	+	2.59808i	−0.153093	+	0.0883883i
$865$	−6.00000			−0.204006
$866$	17.0000	−	29.4449i	0.577684	−	1.00058i
$867$		−	13.8564i		−	0.470588i
$868$	−1.00000	−	1.73205i	−0.0339422	−	0.0587896i
$869$	1.50000	+	2.59808i	0.0508840	+	0.0881337i
$870$	−9.00000	−	5.19615i	−0.305129	−	0.176166i
$871$	−5.00000	+	8.66025i	−0.169419	+	0.293442i
$872$	−13.0000			−0.440236
$873$	25.5000	−	44.1673i	0.863044	−	1.49484i
$874$	12.0000			0.405906
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$	16.5000	−	9.52628i	0.557483	−	0.321863i
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	0.989788	−	0.142548i	$-0.0455296\pi$
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	−0.618344	+	0.785907i	$0.712196\pi$
$878$	14.0000	+	24.2487i	0.472477	+	0.818354i
$879$	9.00000	−	5.19615i	0.303562	−	0.175262i
$880$	−1.50000	+	2.59808i	−0.0505650	+	0.0875811i
$881$	−12.0000			−0.404290			−0.202145	−	0.979356i	$-0.564791\pi$
$881$	−12.0000			−0.404290			−0.202145	+	0.979356i	$0.564791\pi$
$882$	−3.00000			−0.101015
$883$	38.0000			1.27880			0.639401	−	0.768874i	$-0.279182\pi$
$883$	38.0000			1.27880			0.639401	+	0.768874i	$0.279182\pi$
$884$	7.50000	−	12.9904i	0.252252	−	0.436914i
$885$	18.0000	+	10.3923i	0.605063	+	0.349334i
$886$	3.00000	+	5.19615i	0.100787	+	0.174568i
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	−0.915722	−	0.401813i	$-0.868380\pi$
$887$	−24.0000	−	41.5692i	−0.805841	−	1.39576i	0.109881	−	0.993945i	$-0.464953\pi$
$888$		−	17.3205i		−	0.581238i
$889$	8.00000	−	13.8564i	0.268311	−	0.464729i
$890$	−6.00000			−0.201120
$891$	−13.5000	+	23.3827i	−0.452267	+	0.783349i
$892$	−7.00000			−0.234377
$893$	−3.00000	+	5.19615i	−0.100391	+	0.173883i
$894$			36.3731i			1.21650i
$895$	−7.50000	−	12.9904i	−0.250697	−	0.434221i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$	−45.0000	−	25.9808i	−1.50251	−	0.867472i
$898$	15.0000	−	25.9808i	0.500556	−	0.866989i
$899$	12.0000			0.400222
$900$	−3.00000			−0.100000
$901$		0			0
$902$		0			0
$903$	−15.0000	+	8.66025i	−0.499169	+	0.288195i
$904$	−3.00000	−	5.19615i	−0.0997785	−	0.172821i
$905$	5.00000	+	8.66025i	0.166206	+	0.287877i
$906$	25.5000	−	14.7224i	0.847181	−	0.489120i
$907$	−13.0000	+	22.5167i	−0.431658	+	0.747653i	−0.997016	−	0.0771920i	$-0.975405\pi$
$907$	−13.0000	+	22.5167i	−0.431658	+	0.747653i	0.565358	+	0.824845i	$0.308738\pi$
$908$	−21.0000			−0.696909
$909$	27.0000	−	46.7654i	0.895533	−	1.55111i
$910$	5.00000			0.165748
$911$	7.50000	−	12.9904i	0.248486	−	0.430391i	−0.714620	−	0.699513i	$-0.753400\pi$
$911$	7.50000	−	12.9904i	0.248486	−	0.430391i	0.963106	+	0.269122i	$0.0867336\pi$
$912$	−3.00000	−	1.73205i	−0.0993399	−	0.0573539i
$913$	−13.5000	−	23.3827i	−0.446785	−	0.773854i
$914$	5.00000	+	8.66025i	0.165385	+	0.286456i
$915$		−	17.3205i		−	0.572598i
$916$	11.0000	−	19.0526i	0.363450	−	0.629514i
$917$	−12.0000			−0.396275
$918$	−13.5000	−	7.79423i	−0.445566	−	0.257248i
$919$	−40.0000			−1.31948			−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000			−1.31948			−0.659739	+	0.751495i	$0.729333\pi$
$920$	−3.00000	+	5.19615i	−0.0989071	+	0.171312i
$921$			8.66025i			0.285365i
$922$	−3.00000	−	5.19615i	−0.0987997	−	0.171126i
$923$	22.5000	+	38.9711i	0.740597	+	1.28275i
$924$	−4.50000	−	2.59808i	−0.148039	−	0.0854704i
$925$	5.00000	−	8.66025i	0.164399	−	0.284747i
$926$	20.0000			0.657241
$927$	12.0000	+	20.7846i	0.394132	+	0.682656i
$928$	6.00000			0.196960
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	−0.911034	−	0.412332i	$-0.864714\pi$
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	0.812607	+	0.582812i	$0.198048\pi$
$930$	3.00000	−	1.73205i	0.0983739	−	0.0567962i
$931$	−1.00000	−	1.73205i	−0.0327737	−	0.0567657i
$932$	12.0000	+	20.7846i	0.393073	+	0.680823i
$933$		0			0
$934$	−13.5000	+	23.3827i	−0.441733	+	0.765105i
$935$	−9.00000			−0.294331
$936$	7.50000	+	12.9904i	0.245145	+	0.424604i
$937$	−43.0000			−1.40475			−0.702374	−	0.711808i	$-0.747877\pi$
$937$	−43.0000			−1.40475			−0.702374	+	0.711808i	$0.747877\pi$
$938$	−1.00000	+	1.73205i	−0.0326512	+	0.0565535i
$939$	−21.0000	−	12.1244i	−0.685309	−	0.395663i
$940$	−1.50000	−	2.59808i	−0.0489246	−	0.0847399i
$941$	−30.0000	−	51.9615i	−0.977972	−	1.69390i	−0.669757	−	0.742581i	$-0.733602\pi$
$941$	−30.0000	−	51.9615i	−0.977972	−	1.69390i	−0.308215	−	0.951317i	$-0.599732\pi$
$942$		−	12.1244i		−	0.395033i
$943$		0			0
$944$	−12.0000			−0.390567
$945$		−	5.19615i		−	0.169031i
$946$	−30.0000			−0.975384
$947$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$947$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$948$		−	1.73205i		−	0.0562544i
$949$	−27.5000	−	47.6314i	−0.892688	−	1.54618i
$950$	−1.00000	−	1.73205i	−0.0324443	−	0.0561951i
$951$	9.00000	+	5.19615i	0.291845	+	0.168497i
$952$	1.50000	−	2.59808i	0.0486153	−	0.0842041i
$953$	18.0000			0.583077			0.291539	−	0.956559i	$-0.405833\pi$
$953$	18.0000			0.583077			0.291539	+	0.956559i	$0.405833\pi$
$954$		0			0
$955$		0			0
$956$	−12.0000	+	20.7846i	−0.388108	+	0.672222i
$957$	27.0000	−	15.5885i	0.872786	−	0.503903i
$958$	−21.0000	−	36.3731i	−0.678479	−	1.17516i
$959$	−3.00000	−	5.19615i	−0.0968751	−	0.167793i
$960$	1.50000	−	0.866025i	0.0484123	−	0.0279508i
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−50.0000			−1.61206
$963$	18.0000			0.580042
$964$	−28.0000			−0.901819
$965$	11.0000	−	19.0526i	0.354103	−	0.613324i
$966$	−9.00000	−	5.19615i	−0.289570	−	0.167183i
$967$	23.0000	+	39.8372i	0.739630	+	1.28108i	0.952662	+	0.304032i	$0.0983329\pi$
$967$	23.0000	+	39.8372i	0.739630	+	1.28108i	−0.213032	+	0.977045i	$0.568334\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$		−	10.3923i		−	0.333849i
$970$	−8.50000	+	14.7224i	−0.272919	+	0.472709i
$971$	−30.0000			−0.962746			−0.481373	−	0.876516i	$-0.659862\pi$
$971$	−30.0000			−0.962746			−0.481373	+	0.876516i	$0.659862\pi$
$972$	13.5000	−	7.79423i	0.433013	−	0.250000i
$973$	2.00000			0.0641171
$974$	11.0000	−	19.0526i	0.352463	−	0.610483i
$975$			8.66025i			0.277350i
$976$	5.00000	+	8.66025i	0.160046	+	0.277208i
$977$	12.0000	+	20.7846i	0.383914	+	0.664959i	0.991618	−	0.129205i	$-0.0412426\pi$
$977$	12.0000	+	20.7846i	0.383914	+	0.664959i	−0.607704	+	0.794164i	$0.707909\pi$
$978$	−3.00000	−	1.73205i	−0.0959294	−	0.0553849i
$979$	9.00000	−	15.5885i	0.287641	−	0.498209i
$980$	1.00000			0.0319438
$981$	39.0000			1.24517
$982$	−9.00000			−0.287202
$983$	7.50000	−	12.9904i	0.239213	−	0.414329i	−0.721276	−	0.692648i	$-0.756444\pi$
$983$	7.50000	−	12.9904i	0.239213	−	0.414329i	0.960489	+	0.278319i	$0.0897773\pi$
$984$		0			0
$985$	−3.00000	−	5.19615i	−0.0955879	−	0.165563i
$986$	9.00000	+	15.5885i	0.286618	+	0.496438i
$987$	4.50000	−	2.59808i	0.143237	−	0.0826977i
$988$	−5.00000	+	8.66025i	−0.159071	+	0.275519i
$989$	−60.0000			−1.90789
$990$	4.50000	−	7.79423i	0.143019	−	0.247717i
$991$	−43.0000			−1.36594			−0.682970	−	0.730446i	$-0.739312\pi$
$991$	−43.0000			−1.36594			−0.682970	+	0.730446i	$0.739312\pi$
$992$	−1.00000	+	1.73205i	−0.0317500	+	0.0549927i
$993$	46.5000	+	26.8468i	1.47563	+	0.851957i
$994$	4.50000	+	7.79423i	0.142731	+	0.247218i
$995$	−4.00000	−	6.92820i	−0.126809	−	0.219639i
$996$			15.5885i			0.493939i
$997$	−13.0000	+	22.5167i	−0.411714	+	0.713110i	−0.995077	−	0.0991016i	$-0.968403\pi$
$997$	−13.0000	+	22.5167i	−0.411714	+	0.713110i	0.583363	+	0.812211i	$0.301736\pi$
$998$	−43.0000			−1.36114
$999$			51.9615i			1.64399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.j.a.421.1	yes	2
3.2	odd	2		1890.2.j.e.1261.1		2
9.2	odd	6		5670.2.a.d.1.1		1
9.4	even	3	inner	630.2.j.a.211.1	✓	2
9.5	odd	6		1890.2.j.e.631.1		2
9.7	even	3		5670.2.a.r.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.a.211.1	✓	2	9.4	even	3	inner
630.2.j.a.421.1	yes	2	1.1	even	1	trivial
1890.2.j.e.631.1		2	9.5	odd	6
1890.2.j.e.1261.1		2	3.2	odd	2
5670.2.a.d.1.1		1	9.2	odd	6
5670.2.a.r.1.1		1	9.7	even	3

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +1.73205i q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +1.73205i q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} -3.00000 q^{9} +1.00000 q^{10} +(-1.50000 + 2.59808i) q^{11} +(1.50000 - 0.866025i) q^{12} +(-2.50000 - 4.33013i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(1.50000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} -3.00000 q^{17} +(1.50000 - 2.59808i) q^{18} +2.00000 q^{19} +(-0.500000 + 0.866025i) q^{20} +(-1.50000 - 0.866025i) q^{21} +(-1.50000 - 2.59808i) q^{22} +(-3.00000 - 5.19615i) q^{23} +1.73205i q^{24} +(-0.500000 + 0.866025i) q^{25} +5.00000 q^{26} -5.19615i q^{27} +1.00000 q^{28} +(-3.00000 + 5.19615i) q^{29} +1.73205i q^{30} +(-1.00000 - 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.50000 - 2.59808i) q^{33} +(1.50000 - 2.59808i) q^{34} +1.00000 q^{35} +(1.50000 + 2.59808i) q^{36} -10.0000 q^{37} +(-1.00000 + 1.73205i) q^{38} +(7.50000 - 4.33013i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(1.50000 - 0.866025i) q^{42} +(5.00000 - 8.66025i) q^{43} +3.00000 q^{44} +(1.50000 + 2.59808i) q^{45} +6.00000 q^{46} +(-1.50000 + 2.59808i) q^{47} +(-1.50000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} -5.19615i q^{51} +(-2.50000 + 4.33013i) q^{52} +(4.50000 + 2.59808i) q^{54} +3.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +3.46410i q^{57} +(-3.00000 - 5.19615i) q^{58} +(6.00000 + 10.3923i) q^{59} +(-1.50000 - 0.866025i) q^{60} +(5.00000 - 8.66025i) q^{61} +2.00000 q^{62} +(1.50000 - 2.59808i) q^{63} +1.00000 q^{64} +(-2.50000 + 4.33013i) q^{65} +(4.50000 - 2.59808i) q^{66} +(-1.00000 - 1.73205i) q^{67} +(1.50000 + 2.59808i) q^{68} +(9.00000 - 5.19615i) q^{69} +(-0.500000 + 0.866025i) q^{70} -9.00000 q^{71} -3.00000 q^{72} +11.0000 q^{73} +(5.00000 - 8.66025i) q^{74} +(-1.50000 - 0.866025i) q^{75} +(-1.00000 - 1.73205i) q^{76} +(-1.50000 - 2.59808i) q^{77} +8.66025i q^{78} +(0.500000 - 0.866025i) q^{79} +1.00000 q^{80} +9.00000 q^{81} +(-4.50000 + 7.79423i) q^{83} +1.73205i q^{84} +(1.50000 + 2.59808i) q^{85} +(5.00000 + 8.66025i) q^{86} +(-9.00000 - 5.19615i) q^{87} +(-1.50000 + 2.59808i) q^{88} -6.00000 q^{89} -3.00000 q^{90} +5.00000 q^{91} +(-3.00000 + 5.19615i) q^{92} +(3.00000 - 1.73205i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-1.00000 - 1.73205i) q^{95} +(1.50000 - 0.866025i) q^{96} +(-8.50000 + 14.7224i) q^{97} +1.00000 q^{98} +(4.50000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - q^{5} - 3 q^{6} - q^{7} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q - q^2 - q^4 - q^5 - 3 * q^6 - q^7 + 2 * q^8 - 6 * q^9	\( 2 q - q^{2} - q^{4} - q^{5} - 3 q^{6} - q^{7} + 2 q^{8} - 6 q^{9} + 2 q^{10} - 3 q^{11} + 3 q^{12} - 5 q^{13} - q^{14} + 3 q^{15} - q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} - q^{20} - 3 q^{21} - 3 q^{22} - 6 q^{23} - q^{25} + 10 q^{26} + 2 q^{28} - 6 q^{29} - 2 q^{31} - q^{32} - 9 q^{33} + 3 q^{34} + 2 q^{35} + 3 q^{36} - 20 q^{37} - 2 q^{38} + 15 q^{39} - q^{40} + 3 q^{42} + 10 q^{43} + 6 q^{44} + 3 q^{45} + 12 q^{46} - 3 q^{47} - 3 q^{48} - q^{49} - q^{50} - 5 q^{52} + 9 q^{54} + 6 q^{55} - q^{56} - 6 q^{58} + 12 q^{59} - 3 q^{60} + 10 q^{61} + 4 q^{62} + 3 q^{63} + 2 q^{64} - 5 q^{65} + 9 q^{66} - 2 q^{67} + 3 q^{68} + 18 q^{69} - q^{70} - 18 q^{71} - 6 q^{72} + 22 q^{73} + 10 q^{74} - 3 q^{75} - 2 q^{76} - 3 q^{77} + q^{79} + 2 q^{80} + 18 q^{81} - 9 q^{83} + 3 q^{85} + 10 q^{86} - 18 q^{87} - 3 q^{88} - 12 q^{89} - 6 q^{90} + 10 q^{91} - 6 q^{92} + 6 q^{93} - 3 q^{94} - 2 q^{95} + 3 q^{96} - 17 q^{97} + 2 q^{98} + 9 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^4 - q^5 - 3 * q^6 - q^7 + 2 * q^8 - 6 * q^9 + 2 * q^10 - 3 * q^11 + 3 * q^12 - 5 * q^13 - q^14 + 3 * q^15 - q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 - q^20 - 3 * q^21 - 3 * q^22 - 6 * q^23 - q^25 + 10 * q^26 + 2 * q^28 - 6 * q^29 - 2 * q^31 - q^32 - 9 * q^33 + 3 * q^34 + 2 * q^35 + 3 * q^36 - 20 * q^37 - 2 * q^38 + 15 * q^39 - q^40 + 3 * q^42 + 10 * q^43 + 6 * q^44 + 3 * q^45 + 12 * q^46 - 3 * q^47 - 3 * q^48 - q^49 - q^50 - 5 * q^52 + 9 * q^54 + 6 * q^55 - q^56 - 6 * q^58 + 12 * q^59 - 3 * q^60 + 10 * q^61 + 4 * q^62 + 3 * q^63 + 2 * q^64 - 5 * q^65 + 9 * q^66 - 2 * q^67 + 3 * q^68 + 18 * q^69 - q^70 - 18 * q^71 - 6 * q^72 + 22 * q^73 + 10 * q^74 - 3 * q^75 - 2 * q^76 - 3 * q^77 + q^79 + 2 * q^80 + 18 * q^81 - 9 * q^83 + 3 * q^85 + 10 * q^86 - 18 * q^87 - 3 * q^88 - 12 * q^89 - 6 * q^90 + 10 * q^91 - 6 * q^92 + 6 * q^93 - 3 * q^94 - 2 * q^95 + 3 * q^96 - 17 * q^97 + 2 * q^98 + 9 * q^99

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