LMFDB - Embedded newform 43.2.c.a.6.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,2,Mod(6,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("43.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	43.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.343356728692$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			6.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	43.6
Dual form			43.2.c.a.36.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.50000 - 2.59808i) q^{7} -3.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.50000 - 2.59808i) q^{7} -3.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.500000 - 0.866025i) q^{12} +(2.50000 + 4.33013i) q^{13} +(-1.50000 - 2.59808i) q^{14} +(0.500000 + 0.866025i) q^{15} -1.00000 q^{16} +(-1.50000 - 2.59808i) q^{17} +(1.00000 + 1.73205i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(-0.500000 + 0.866025i) q^{20} +3.00000 q^{21} +(3.50000 - 6.06218i) q^{23} +(1.50000 - 2.59808i) q^{24} +(2.00000 + 3.46410i) q^{25} +(2.50000 + 4.33013i) q^{26} -5.00000 q^{27} +(1.50000 + 2.59808i) q^{28} +(-1.50000 - 2.59808i) q^{29} +(0.500000 + 0.866025i) q^{30} +(-2.50000 + 4.33013i) q^{31} +5.00000 q^{32} +(-1.50000 - 2.59808i) q^{34} -3.00000 q^{35} +(-1.00000 - 1.73205i) q^{36} +(4.50000 - 7.79423i) q^{37} +(-0.500000 + 0.866025i) q^{38} -5.00000 q^{39} +(-1.50000 + 2.59808i) q^{40} -10.0000 q^{41} +3.00000 q^{42} +(-4.00000 + 5.19615i) q^{43} +2.00000 q^{45} +(3.50000 - 6.06218i) q^{46} -8.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(2.00000 + 3.46410i) q^{50} +3.00000 q^{51} +(-2.50000 - 4.33013i) q^{52} +(2.50000 - 4.33013i) q^{53} -5.00000 q^{54} +(4.50000 + 7.79423i) q^{56} +(-0.500000 - 0.866025i) q^{57} +(-1.50000 - 2.59808i) q^{58} +12.0000 q^{59} +(-0.500000 - 0.866025i) q^{60} +(6.50000 + 11.2583i) q^{61} +(-2.50000 + 4.33013i) q^{62} +(3.00000 - 5.19615i) q^{63} +7.00000 q^{64} +5.00000 q^{65} +(1.50000 - 2.59808i) q^{67} +(1.50000 + 2.59808i) q^{68} +(3.50000 + 6.06218i) q^{69} -3.00000 q^{70} +(0.500000 + 0.866025i) q^{71} +(-3.00000 - 5.19615i) q^{72} +(-5.50000 - 9.52628i) q^{73} +(4.50000 - 7.79423i) q^{74} -4.00000 q^{75} +(0.500000 - 0.866025i) q^{76} -5.00000 q^{78} +(2.50000 + 4.33013i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} -10.0000 q^{82} +(-4.50000 + 7.79423i) q^{83} -3.00000 q^{84} -3.00000 q^{85} +(-4.00000 + 5.19615i) q^{86} +3.00000 q^{87} +(0.500000 - 0.866025i) q^{89} +2.00000 q^{90} +(7.50000 - 12.9904i) q^{91} +(-3.50000 + 6.06218i) q^{92} +(-2.50000 - 4.33013i) q^{93} -8.00000 q^{94} +(0.500000 + 0.866025i) q^{95} +(-2.50000 + 4.33013i) q^{96} -2.00000 q^{97} +(-1.00000 + 1.73205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - q^{6} - 3 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - q^3 - 2 * q^4 + q^5 - q^6 - 3 * q^7 - 6 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - q^{6} - 3 q^{7} - 6 q^{8} + 2 q^{9} + q^{10} + q^{12} + 5 q^{13} - 3 q^{14} + q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - q^{19} - q^{20} + 6 q^{21} + 7 q^{23} + 3 q^{24} + 4 q^{25} + 5 q^{26} - 10 q^{27} + 3 q^{28} - 3 q^{29} + q^{30} - 5 q^{31} + 10 q^{32} - 3 q^{34} - 6 q^{35} - 2 q^{36} + 9 q^{37} - q^{38} - 10 q^{39} - 3 q^{40} - 20 q^{41} + 6 q^{42} - 8 q^{43} + 4 q^{45} + 7 q^{46} - 16 q^{47} + q^{48} - 2 q^{49} + 4 q^{50} + 6 q^{51} - 5 q^{52} + 5 q^{53} - 10 q^{54} + 9 q^{56} - q^{57} - 3 q^{58} + 24 q^{59} - q^{60} + 13 q^{61} - 5 q^{62} + 6 q^{63} + 14 q^{64} + 10 q^{65} + 3 q^{67} + 3 q^{68} + 7 q^{69} - 6 q^{70} + q^{71} - 6 q^{72} - 11 q^{73} + 9 q^{74} - 8 q^{75} + q^{76} - 10 q^{78} + 5 q^{79} - q^{80} - q^{81} - 20 q^{82} - 9 q^{83} - 6 q^{84} - 6 q^{85} - 8 q^{86} + 6 q^{87} + q^{89} + 4 q^{90} + 15 q^{91} - 7 q^{92} - 5 q^{93} - 16 q^{94} + q^{95} - 5 q^{96} - 4 q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - q^3 - 2 * q^4 + q^5 - q^6 - 3 * q^7 - 6 * q^8 + 2 * q^9 + q^10 + q^12 + 5 * q^13 - 3 * q^14 + q^15 - 2 * q^16 - 3 * q^17 + 2 * q^18 - q^19 - q^20 + 6 * q^21 + 7 * q^23 + 3 * q^24 + 4 * q^25 + 5 * q^26 - 10 * q^27 + 3 * q^28 - 3 * q^29 + q^30 - 5 * q^31 + 10 * q^32 - 3 * q^34 - 6 * q^35 - 2 * q^36 + 9 * q^37 - q^38 - 10 * q^39 - 3 * q^40 - 20 * q^41 + 6 * q^42 - 8 * q^43 + 4 * q^45 + 7 * q^46 - 16 * q^47 + q^48 - 2 * q^49 + 4 * q^50 + 6 * q^51 - 5 * q^52 + 5 * q^53 - 10 * q^54 + 9 * q^56 - q^57 - 3 * q^58 + 24 * q^59 - q^60 + 13 * q^61 - 5 * q^62 + 6 * q^63 + 14 * q^64 + 10 * q^65 + 3 * q^67 + 3 * q^68 + 7 * q^69 - 6 * q^70 + q^71 - 6 * q^72 - 11 * q^73 + 9 * q^74 - 8 * q^75 + q^76 - 10 * q^78 + 5 * q^79 - q^80 - q^81 - 20 * q^82 - 9 * q^83 - 6 * q^84 - 6 * q^85 - 8 * q^86 + 6 * q^87 + q^89 + 4 * q^90 + 15 * q^91 - 7 * q^92 - 5 * q^93 - 16 * q^94 + q^95 - 5 * q^96 - 4 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.00000			0.707107			0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000			0.707107			0.353553	+	0.935414i	$0.384973\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	0.684819	+	0.728714i	$0.259881\pi$
$4$	−1.00000			−0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	−0.996866	−	0.0791130i	$-0.974791\pi$
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	0.429919	−	0.902867i	$-0.358542\pi$
$8$	−3.00000			−1.06066
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	0.970725	+	0.240192i	$0.0772105\pi$
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	−0.277350	+	0.960769i	$0.589456\pi$
$14$	−1.50000	−	2.59808i	−0.400892	−	0.694365i
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	−1.00000			−0.250000
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	1.00000	+	1.73205i	0.235702	+	0.408248i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	3.00000			0.654654
$22$		0			0
$23$	3.50000	−	6.06218i	0.729800	−	1.26405i	−0.227167	−	0.973856i	$-0.572946\pi$
$23$	3.50000	−	6.06218i	0.729800	−	1.26405i	0.956967	−	0.290196i	$-0.0937204\pi$
$24$	1.50000	−	2.59808i	0.306186	−	0.530330i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	2.50000	+	4.33013i	0.490290	+	0.849208i
$27$	−5.00000			−0.962250
$28$	1.50000	+	2.59808i	0.283473	+	0.490990i
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	−0.998322	−	0.0579057i	$-0.981558\pi$
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	0.549309	+	0.835619i	$0.314891\pi$
$32$	5.00000			0.883883
$33$		0			0
$34$	−1.50000	−	2.59808i	−0.257248	−	0.445566i
$35$	−3.00000			−0.507093
$36$	−1.00000	−	1.73205i	−0.166667	−	0.288675i
$37$	4.50000	−	7.79423i	0.739795	−	1.28136i	−0.212792	−	0.977098i	$-0.568256\pi$
$37$	4.50000	−	7.79423i	0.739795	−	1.28136i	0.952587	−	0.304266i	$-0.0984111\pi$
$38$	−0.500000	+	0.866025i	−0.0811107	+	0.140488i
$39$	−5.00000			−0.800641
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$	−10.0000			−1.56174			−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000			−1.56174			−0.780869	+	0.624695i	$0.785223\pi$
$42$	3.00000			0.462910
$43$	−4.00000	+	5.19615i	−0.609994	+	0.792406i
$43$	−4.00000	+	5.19615i	−0.609994	+	0.792406i
$44$		0			0
$45$	2.00000			0.298142
$46$	3.50000	−	6.06218i	0.516047	−	0.893819i
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$	3.00000			0.420084
$52$	−2.50000	−	4.33013i	−0.346688	−	0.600481i
$53$	2.50000	−	4.33013i	0.343401	−	0.594789i	−0.641661	−	0.766989i	$-0.721754\pi$
$53$	2.50000	−	4.33013i	0.343401	−	0.594789i	0.985062	+	0.172200i	$0.0550875\pi$
$54$	−5.00000			−0.680414
$55$		0			0
$56$	4.50000	+	7.79423i	0.601338	+	1.04155i
$57$	−0.500000	−	0.866025i	−0.0662266	−	0.114708i
$58$	−1.50000	−	2.59808i	−0.196960	−	0.341144i
$59$	12.0000			1.56227			0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000			1.56227			0.781133	+	0.624364i	$0.214642\pi$
$60$	−0.500000	−	0.866025i	−0.0645497	−	0.111803i
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	0.896258	+	0.443533i	$0.146275\pi$
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	−2.50000	+	4.33013i	−0.317500	+	0.549927i
$63$	3.00000	−	5.19615i	0.377964	−	0.654654i
$64$	7.00000			0.875000
$65$	5.00000			0.620174
$66$		0			0
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	−0.759733	−	0.650236i	$-0.774670\pi$
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	0.942987	+	0.332830i	$0.108004\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	3.50000	+	6.06218i	0.421350	+	0.729800i
$70$	−3.00000			−0.358569
$71$	0.500000	+	0.866025i	0.0593391	+	0.102778i	0.894169	−	0.447730i	$-0.147767\pi$
$71$	0.500000	+	0.866025i	0.0593391	+	0.102778i	−0.834830	+	0.550508i	$0.814434\pi$
$72$	−3.00000	−	5.19615i	−0.353553	−	0.612372i
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	−0.984594	−	0.174855i	$-0.944054\pi$
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	0.340868	−	0.940111i	$-0.389279\pi$
$74$	4.50000	−	7.79423i	0.523114	−	0.906061i
$75$	−4.00000			−0.461880
$76$	0.500000	−	0.866025i	0.0573539	−	0.0993399i
$77$		0			0
$78$	−5.00000			−0.566139
$79$	2.50000	+	4.33013i	0.281272	+	0.487177i	0.971698	−	0.236225i	$-0.0759104\pi$
$79$	2.50000	+	4.33013i	0.281272	+	0.487177i	−0.690426	+	0.723403i	$0.742577\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−10.0000			−1.10432
$83$	−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	$0.331110\pi$
$84$	−3.00000			−0.327327
$85$	−3.00000			−0.325396
$86$	−4.00000	+	5.19615i	−0.431331	+	0.560316i
$87$	3.00000			0.321634
$88$		0			0
$89$	0.500000	−	0.866025i	0.0529999	−	0.0917985i	−0.838308	−	0.545197i	$-0.816455\pi$
$89$	0.500000	−	0.866025i	0.0529999	−	0.0917985i	0.891308	+	0.453398i	$0.149788\pi$
$90$	2.00000			0.210819
$91$	7.50000	−	12.9904i	0.786214	−	1.36176i
$92$	−3.50000	+	6.06218i	−0.364900	+	0.632026i
$93$	−2.50000	−	4.33013i	−0.259238	−	0.449013i
$94$	−8.00000			−0.825137
$95$	0.500000	+	0.866025i	0.0512989	+	0.0888523i
$96$	−2.50000	+	4.33013i	−0.255155	+	0.441942i
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$	−1.00000	+	1.73205i	−0.101015	+	0.174964i
$99$		0			0
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$	3.00000			0.297044
$103$	−3.50000	−	6.06218i	−0.344865	−	0.597324i	0.640464	−	0.767988i	$-0.278742\pi$
$103$	−3.50000	−	6.06218i	−0.344865	−	0.597324i	−0.985329	+	0.170664i	$0.945409\pi$
$104$	−7.50000	−	12.9904i	−0.735436	−	1.27381i
$105$	1.50000	−	2.59808i	0.146385	−	0.253546i
$106$	2.50000	−	4.33013i	0.242821	−	0.420579i
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$	5.00000			0.481125
$109$	−3.50000	+	6.06218i	−0.335239	+	0.580651i	−0.983531	−	0.180741i	$-0.942150\pi$
$109$	−3.50000	+	6.06218i	−0.335239	+	0.580651i	0.648292	+	0.761392i	$0.275484\pi$
$110$		0			0
$111$	4.50000	+	7.79423i	0.427121	+	0.739795i
$112$	1.50000	+	2.59808i	0.141737	+	0.245495i
$113$	−2.00000			−0.188144			−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000			−0.188144			−0.0940721	+	0.995565i	$0.529988\pi$
$114$	−0.500000	−	0.866025i	−0.0468293	−	0.0811107i
$115$	−3.50000	−	6.06218i	−0.326377	−	0.565301i
$116$	1.50000	+	2.59808i	0.139272	+	0.241225i
$117$	−5.00000	+	8.66025i	−0.462250	+	0.800641i
$118$	12.0000			1.10469
$119$	−4.50000	+	7.79423i	−0.412514	+	0.714496i
$120$	−1.50000	−	2.59808i	−0.136931	−	0.237171i
$121$	−11.0000			−1.00000
$122$	6.50000	+	11.2583i	0.588482	+	1.01928i
$123$	5.00000	−	8.66025i	0.450835	−	0.780869i
$124$	2.50000	−	4.33013i	0.224507	−	0.388857i
$125$	9.00000			0.804984
$126$	3.00000	−	5.19615i	0.267261	−	0.462910i
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$	−3.00000			−0.265165
$129$	−2.50000	−	6.06218i	−0.220113	−	0.533745i
$130$	5.00000			0.438529
$131$	−4.00000			−0.349482			−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000			−0.349482			−0.174741	+	0.984614i	$0.555909\pi$
$132$		0			0
$133$	3.00000			0.260133
$134$	1.50000	−	2.59808i	0.129580	−	0.224440i
$135$	−2.50000	+	4.33013i	−0.215166	+	0.372678i
$136$	4.50000	+	7.79423i	0.385872	+	0.668350i
$137$	−18.0000			−1.53784			−0.768922	−	0.639343i	$-0.779207\pi$
$137$	−18.0000			−1.53784			−0.768922	+	0.639343i	$0.779207\pi$
$138$	3.50000	+	6.06218i	0.297940	+	0.516047i
$139$	−6.50000	+	11.2583i	−0.551323	+	0.954919i	0.446857	+	0.894606i	$0.352543\pi$
$139$	−6.50000	+	11.2583i	−0.551323	+	0.954919i	−0.998179	+	0.0603135i	$0.980790\pi$
$140$	3.00000			0.253546
$141$	4.00000	−	6.92820i	0.336861	−	0.583460i
$142$	0.500000	+	0.866025i	0.0419591	+	0.0726752i
$143$		0			0
$144$	−1.00000	−	1.73205i	−0.0833333	−	0.144338i
$145$	−3.00000			−0.249136
$146$	−5.50000	−	9.52628i	−0.455183	−	0.788400i
$147$	−1.00000	−	1.73205i	−0.0824786	−	0.142857i
$148$	−4.50000	+	7.79423i	−0.369898	+	0.640682i
$149$	10.5000	−	18.1865i	0.860194	−	1.48990i	−0.0115483	−	0.999933i	$-0.503676\pi$
$149$	10.5000	−	18.1865i	0.860194	−	1.48990i	0.871742	−	0.489966i	$-0.162991\pi$
$150$	−4.00000			−0.326599
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$	1.50000	−	2.59808i	0.121666	−	0.210732i
$153$	3.00000	−	5.19615i	0.242536	−	0.420084i
$154$		0			0
$155$	2.50000	+	4.33013i	0.200805	+	0.347804i
$156$	5.00000			0.400320
$157$	0.500000	+	0.866025i	0.0399043	+	0.0691164i	0.885288	−	0.465044i	$-0.153961\pi$
$157$	0.500000	+	0.866025i	0.0399043	+	0.0691164i	−0.845383	+	0.534160i	$0.820628\pi$
$158$	2.50000	+	4.33013i	0.198889	+	0.344486i
$159$	2.50000	+	4.33013i	0.198263	+	0.343401i
$160$	2.50000	−	4.33013i	0.197642	−	0.342327i
$161$	−21.0000			−1.65503
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	0.500000	+	0.866025i	0.0391630	+	0.0678323i	0.884943	−	0.465700i	$-0.154198\pi$
$163$	0.500000	+	0.866025i	0.0391630	+	0.0678323i	−0.845780	+	0.533533i	$0.820864\pi$
$164$	10.0000			0.780869
$165$		0			0
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$	1.50000	−	2.59808i	0.116073	−	0.201045i	−0.802135	−	0.597143i	$-0.796303\pi$
$167$	1.50000	−	2.59808i	0.116073	−	0.201045i	0.918208	+	0.396098i	$0.129636\pi$
$168$	−9.00000			−0.694365
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$	−3.00000			−0.230089
$171$	−2.00000			−0.152944
$172$	4.00000	−	5.19615i	0.304997	−	0.396203i
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$	3.00000			0.227429
$175$	6.00000	−	10.3923i	0.453557	−	0.785584i
$176$		0			0
$177$	−6.00000	+	10.3923i	−0.450988	+	0.781133i
$178$	0.500000	−	0.866025i	0.0374766	−	0.0649113i
$179$	0.500000	+	0.866025i	0.0373718	+	0.0647298i	0.884106	−	0.467286i	$-0.154768\pi$
$179$	0.500000	+	0.866025i	0.0373718	+	0.0647298i	−0.846735	+	0.532016i	$0.821435\pi$
$180$	−2.00000			−0.149071
$181$	−3.50000	−	6.06218i	−0.260153	−	0.450598i	0.706129	−	0.708083i	$-0.250440\pi$
$181$	−3.50000	−	6.06218i	−0.260153	−	0.450598i	−0.966282	+	0.257485i	$0.917106\pi$
$182$	7.50000	−	12.9904i	0.555937	−	0.962911i
$183$	−13.0000			−0.960988
$184$	−10.5000	+	18.1865i	−0.774070	+	1.34073i
$185$	−4.50000	−	7.79423i	−0.330847	−	0.573043i
$186$	−2.50000	−	4.33013i	−0.183309	−	0.317500i
$187$		0			0
$188$	8.00000			0.583460
$189$	7.50000	+	12.9904i	0.545545	+	0.944911i
$190$	0.500000	+	0.866025i	0.0362738	+	0.0628281i
$191$	9.50000	−	16.4545i	0.687396	−	1.19060i	−0.285282	−	0.958444i	$-0.592087\pi$
$191$	9.50000	−	16.4545i	0.687396	−	1.19060i	0.972677	−	0.232161i	$-0.0745796\pi$
$192$	−3.50000	+	6.06218i	−0.252591	+	0.437500i
$193$	6.00000			0.431889			0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000			0.431889			0.215945	+	0.976406i	$0.430717\pi$
$194$	−2.00000			−0.143592
$195$	−2.50000	+	4.33013i	−0.179029	+	0.310087i
$196$	1.00000	−	1.73205i	0.0714286	−	0.123718i
$197$	−5.50000	−	9.52628i	−0.391859	−	0.678719i	0.600836	−	0.799372i	$-0.294834\pi$
$197$	−5.50000	−	9.52628i	−0.391859	−	0.678719i	−0.992695	+	0.120653i	$0.961501\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	−6.00000	−	10.3923i	−0.424264	−	0.734847i
$201$	1.50000	+	2.59808i	0.105802	+	0.183254i
$202$	4.50000	+	7.79423i	0.316619	+	0.548400i
$203$	−4.50000	+	7.79423i	−0.315838	+	0.547048i
$204$	−3.00000			−0.210042
$205$	−5.00000	+	8.66025i	−0.349215	+	0.604858i
$206$	−3.50000	−	6.06218i	−0.243857	−	0.422372i
$207$	14.0000			0.973067
$208$	−2.50000	−	4.33013i	−0.173344	−	0.300240i
$209$		0			0
$210$	1.50000	−	2.59808i	0.103510	−	0.179284i
$211$	8.00000			0.550743			0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000			0.550743			0.275371	+	0.961338i	$0.411199\pi$
$212$	−2.50000	+	4.33013i	−0.171701	+	0.297394i
$213$	−1.00000			−0.0685189
$214$	12.0000			0.820303
$215$	2.50000	+	6.06218i	0.170499	+	0.413437i
$216$	15.0000			1.02062
$217$	15.0000			1.01827
$218$	−3.50000	+	6.06218i	−0.237050	+	0.410582i
$219$	11.0000			0.743311
$220$		0			0
$221$	7.50000	−	12.9904i	0.504505	−	0.873828i
$222$	4.50000	+	7.79423i	0.302020	+	0.523114i
$223$	20.0000			1.33930			0.669650	−	0.742677i	$-0.266444\pi$
$223$	20.0000			1.33930			0.669650	+	0.742677i	$0.266444\pi$
$224$	−7.50000	−	12.9904i	−0.501115	−	0.867956i
$225$	−4.00000	+	6.92820i	−0.266667	+	0.461880i
$226$	−2.00000			−0.133038
$227$	3.50000	−	6.06218i	0.232303	−	0.402361i	−0.726182	−	0.687502i	$-0.758707\pi$
$227$	3.50000	−	6.06218i	0.232303	−	0.402361i	0.958485	+	0.285141i	$0.0920405\pi$
$228$	0.500000	+	0.866025i	0.0331133	+	0.0573539i
$229$	4.50000	+	7.79423i	0.297368	+	0.515057i	0.975533	−	0.219853i	$-0.0705577\pi$
$229$	4.50000	+	7.79423i	0.297368	+	0.515057i	−0.678165	+	0.734910i	$0.737224\pi$
$230$	−3.50000	−	6.06218i	−0.230783	−	0.399728i
$231$		0			0
$232$	4.50000	+	7.79423i	0.295439	+	0.511716i
$233$	4.50000	+	7.79423i	0.294805	+	0.510617i	0.974939	−	0.222470i	$-0.0714120\pi$
$233$	4.50000	+	7.79423i	0.294805	+	0.510617i	−0.680135	+	0.733087i	$0.738079\pi$
$234$	−5.00000	+	8.66025i	−0.326860	+	0.566139i
$235$	−4.00000	+	6.92820i	−0.260931	+	0.451946i
$236$	−12.0000			−0.781133
$237$	−5.00000			−0.324785
$238$	−4.50000	+	7.79423i	−0.291692	+	0.505225i
$239$	−12.5000	+	21.6506i	−0.808558	+	1.40046i	0.105305	+	0.994440i	$0.466418\pi$
$239$	−12.5000	+	21.6506i	−0.808558	+	1.40046i	−0.913863	+	0.406023i	$0.866915\pi$
$240$	−0.500000	−	0.866025i	−0.0322749	−	0.0559017i
$241$	−7.50000	−	12.9904i	−0.483117	−	0.836784i	0.516695	−	0.856170i	$-0.327162\pi$
$241$	−7.50000	−	12.9904i	−0.483117	−	0.836784i	−0.999812	+	0.0193858i	$0.993829\pi$
$242$	−11.0000			−0.707107
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	−6.50000	−	11.2583i	−0.416120	−	0.720741i
$245$	1.00000	+	1.73205i	0.0638877	+	0.110657i
$246$	5.00000	−	8.66025i	0.318788	−	0.552158i
$247$	−5.00000			−0.318142
$248$	7.50000	−	12.9904i	0.476250	−	0.824890i
$249$	−4.50000	−	7.79423i	−0.285176	−	0.493939i
$250$	9.00000			0.569210
$251$	−3.50000	−	6.06218i	−0.220918	−	0.382641i	0.734169	−	0.678967i	$-0.237572\pi$
$251$	−3.50000	−	6.06218i	−0.220918	−	0.382641i	−0.955087	+	0.296326i	$0.904239\pi$
$252$	−3.00000	+	5.19615i	−0.188982	+	0.327327i
$253$		0			0
$254$	16.0000			1.00393
$255$	1.50000	−	2.59808i	0.0939336	−	0.162698i
$256$	−17.0000			−1.06250
$257$	6.00000			0.374270			0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000			0.374270			0.187135	+	0.982334i	$0.440080\pi$
$258$	−2.50000	−	6.06218i	−0.155643	−	0.377415i
$259$	−27.0000			−1.67770
$260$	−5.00000			−0.310087
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$	−4.00000			−0.247121
$263$	−10.5000	+	18.1865i	−0.647458	+	1.12143i	0.336270	+	0.941766i	$0.390834\pi$
$263$	−10.5000	+	18.1865i	−0.647458	+	1.12143i	−0.983728	+	0.179664i	$0.942499\pi$
$264$		0			0
$265$	−2.50000	−	4.33013i	−0.153574	−	0.265998i
$266$	3.00000			0.183942
$267$	0.500000	+	0.866025i	0.0305995	+	0.0529999i
$268$	−1.50000	+	2.59808i	−0.0916271	+	0.158703i
$269$	14.0000			0.853595			0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000			0.853595			0.426798	+	0.904347i	$0.359642\pi$
$270$	−2.50000	+	4.33013i	−0.152145	+	0.263523i
$271$	−11.5000	−	19.9186i	−0.698575	−	1.20997i	−0.968960	−	0.247216i	$-0.920484\pi$
$271$	−11.5000	−	19.9186i	−0.698575	−	1.20997i	0.270385	−	0.962752i	$-0.412849\pi$
$272$	1.50000	+	2.59808i	0.0909509	+	0.157532i
$273$	7.50000	+	12.9904i	0.453921	+	0.786214i
$274$	−18.0000			−1.08742
$275$		0			0
$276$	−3.50000	−	6.06218i	−0.210675	−	0.364900i
$277$	−3.50000	+	6.06218i	−0.210295	+	0.364241i	−0.951807	−	0.306699i	$-0.900776\pi$
$277$	−3.50000	+	6.06218i	−0.210295	+	0.364241i	0.741512	+	0.670940i	$0.234109\pi$
$278$	−6.50000	+	11.2583i	−0.389844	+	0.675230i
$279$	−10.0000			−0.598684
$280$	9.00000			0.537853
$281$	8.50000	−	14.7224i	0.507067	−	0.878267i	−0.492899	−	0.870087i	$-0.664063\pi$
$281$	8.50000	−	14.7224i	0.507067	−	0.878267i	0.999967	−	0.00818015i	$-0.00260385\pi$
$282$	4.00000	−	6.92820i	0.238197	−	0.412568i
$283$	−1.50000	−	2.59808i	−0.0891657	−	0.154440i	0.817993	−	0.575228i	$-0.195087\pi$
$283$	−1.50000	−	2.59808i	−0.0891657	−	0.154440i	−0.907159	+	0.420789i	$0.861753\pi$
$284$	−0.500000	−	0.866025i	−0.0296695	−	0.0513892i
$285$	−1.00000			−0.0592349
$286$		0			0
$287$	15.0000	+	25.9808i	0.885422	+	1.53360i
$288$	5.00000	+	8.66025i	0.294628	+	0.510310i
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	−3.00000			−0.176166
$291$	1.00000	−	1.73205i	0.0586210	−	0.101535i
$292$	5.50000	+	9.52628i	0.321863	+	0.557483i
$293$	−14.0000			−0.817889			−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000			−0.817889			−0.408944	+	0.912559i	$0.634103\pi$
$294$	−1.00000	−	1.73205i	−0.0583212	−	0.101015i
$295$	6.00000	−	10.3923i	0.349334	−	0.605063i
$296$	−13.5000	+	23.3827i	−0.784672	+	1.35909i
$297$		0			0
$298$	10.5000	−	18.1865i	0.608249	−	1.05352i
$299$	35.0000			2.02410
$300$	4.00000			0.230940
$301$	19.5000	+	2.59808i	1.12396	+	0.149751i
$302$	−8.00000			−0.460348
$303$	−9.00000			−0.517036
$304$	0.500000	−	0.866025i	0.0286770	−	0.0496700i
$305$	13.0000			0.744378
$306$	3.00000	−	5.19615i	0.171499	−	0.297044i
$307$	−2.50000	+	4.33013i	−0.142683	+	0.247133i	−0.928506	−	0.371318i	$-0.878906\pi$
$307$	−2.50000	+	4.33013i	−0.142683	+	0.247133i	0.785823	+	0.618451i	$0.212239\pi$
$308$		0			0
$309$	7.00000			0.398216
$310$	2.50000	+	4.33013i	0.141990	+	0.245935i
$311$	1.50000	−	2.59808i	0.0850572	−	0.147323i	−0.820358	−	0.571850i	$-0.806226\pi$
$311$	1.50000	−	2.59808i	0.0850572	−	0.147323i	0.905416	+	0.424526i	$0.139559\pi$
$312$	15.0000			0.849208
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	−0.519300	−	0.854592i	$-0.673807\pi$
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	0.999748	+	0.0224310i	$0.00714060\pi$
$314$	0.500000	+	0.866025i	0.0282166	+	0.0488726i
$315$	−3.00000	−	5.19615i	−0.169031	−	0.292770i
$316$	−2.50000	−	4.33013i	−0.140636	−	0.243589i
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$	2.50000	+	4.33013i	0.140193	+	0.242821i
$319$		0			0
$320$	3.50000	−	6.06218i	0.195656	−	0.338886i
$321$	−6.00000	+	10.3923i	−0.334887	+	0.580042i
$322$	−21.0000			−1.17028
$323$	3.00000			0.166924
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−10.0000	+	17.3205i	−0.554700	+	0.960769i
$326$	0.500000	+	0.866025i	0.0276924	+	0.0479647i
$327$	−3.50000	−	6.06218i	−0.193550	−	0.335239i
$328$	30.0000			1.65647
$329$	12.0000	+	20.7846i	0.661581	+	1.14589i
$330$		0			0
$331$	−9.50000	−	16.4545i	−0.522167	−	0.904420i	−0.999667	−	0.0257885i	$-0.991790\pi$
$331$	−9.50000	−	16.4545i	−0.522167	−	0.904420i	0.477500	−	0.878632i	$-0.341543\pi$
$332$	4.50000	−	7.79423i	0.246970	−	0.427764i
$333$	18.0000			0.986394
$334$	1.50000	−	2.59808i	0.0820763	−	0.142160i
$335$	−1.50000	−	2.59808i	−0.0819538	−	0.141948i
$336$	−3.00000			−0.163663
$337$	−1.50000	−	2.59808i	−0.0817102	−	0.141526i	0.822274	−	0.569091i	$-0.192705\pi$
$337$	−1.50000	−	2.59808i	−0.0817102	−	0.141526i	−0.903985	+	0.427565i	$0.859372\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$	1.00000	−	1.73205i	0.0543125	−	0.0940721i
$340$	3.00000			0.162698
$341$		0			0
$342$	−2.00000			−0.108148
$343$	−15.0000			−0.809924
$344$	12.0000	−	15.5885i	0.646997	−	0.840473i
$345$	7.00000			0.376867
$346$	−6.00000			−0.322562
$347$	−18.5000	+	32.0429i	−0.993132	+	1.72016i	−0.395242	+	0.918577i	$0.629339\pi$
$347$	−18.5000	+	32.0429i	−0.993132	+	1.72016i	−0.597890	+	0.801578i	$0.703994\pi$
$348$	−3.00000			−0.160817
$349$	0.500000	−	0.866025i	0.0267644	−	0.0463573i	−0.852333	−	0.523000i	$-0.824813\pi$
$349$	0.500000	−	0.866025i	0.0267644	−	0.0463573i	0.879097	+	0.476642i	$0.158146\pi$
$350$	6.00000	−	10.3923i	0.320713	−	0.555492i
$351$	−12.5000	−	21.6506i	−0.667201	−	1.15563i
$352$		0			0
$353$	12.5000	+	21.6506i	0.665308	+	1.15235i	0.979202	+	0.202889i	$0.0650330\pi$
$353$	12.5000	+	21.6506i	0.665308	+	1.15235i	−0.313894	+	0.949458i	$0.601634\pi$
$354$	−6.00000	+	10.3923i	−0.318896	+	0.552345i
$355$	1.00000			0.0530745
$356$	−0.500000	+	0.866025i	−0.0264999	+	0.0458993i
$357$	−4.50000	−	7.79423i	−0.238165	−	0.412514i
$358$	0.500000	+	0.866025i	0.0264258	+	0.0457709i
$359$	−9.50000	−	16.4545i	−0.501391	−	0.868434i	−0.999999	−	0.00160673i	$-0.999489\pi$
$359$	−9.50000	−	16.4545i	−0.501391	−	0.868434i	0.498608	−	0.866828i	$-0.333845\pi$
$360$	−6.00000			−0.316228
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	−3.50000	−	6.06218i	−0.183956	−	0.318621i
$363$	5.50000	−	9.52628i	0.288675	−	0.500000i
$364$	−7.50000	+	12.9904i	−0.393107	+	0.680881i
$365$	−11.0000			−0.575766
$366$	−13.0000			−0.679521
$367$	−6.50000	+	11.2583i	−0.339297	+	0.587680i	−0.984301	−	0.176500i	$-0.943523\pi$
$367$	−6.50000	+	11.2583i	−0.339297	+	0.587680i	0.645003	+	0.764180i	$0.276856\pi$
$368$	−3.50000	+	6.06218i	−0.182450	+	0.316013i
$369$	−10.0000	−	17.3205i	−0.520579	−	0.901670i
$370$	−4.50000	−	7.79423i	−0.233944	−	0.405203i
$371$	−15.0000			−0.778761
$372$	2.50000	+	4.33013i	0.129619	+	0.224507i
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	0.687776	−	0.725923i	$-0.258587\pi$
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	−0.972556	+	0.232671i	$0.925254\pi$
$374$		0			0
$375$	−4.50000	+	7.79423i	−0.232379	+	0.402492i
$376$	24.0000			1.23771
$377$	7.50000	−	12.9904i	0.386270	−	0.669039i
$378$	7.50000	+	12.9904i	0.385758	+	0.668153i
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$	−0.500000	−	0.866025i	−0.0256495	−	0.0444262i
$381$	−8.00000	+	13.8564i	−0.409852	+	0.709885i
$382$	9.50000	−	16.4545i	0.486062	−	0.841885i
$383$	8.00000			0.408781			0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000			0.408781			0.204390	+	0.978889i	$0.434479\pi$
$384$	1.50000	−	2.59808i	0.0765466	−	0.132583i
$385$		0			0
$386$	6.00000			0.305392
$387$	−13.0000	−	1.73205i	−0.660827	−	0.0880451i
$388$	2.00000			0.101535
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$	−2.50000	+	4.33013i	−0.126592	+	0.219265i
$391$	−21.0000			−1.06202
$392$	3.00000	−	5.19615i	0.151523	−	0.262445i
$393$	2.00000	−	3.46410i	0.100887	−	0.174741i
$394$	−5.50000	−	9.52628i	−0.277086	−	0.479927i
$395$	5.00000			0.251577
$396$		0			0
$397$	10.5000	−	18.1865i	0.526980	−	0.912756i	−0.472526	−	0.881317i	$-0.656658\pi$
$397$	10.5000	−	18.1865i	0.526980	−	0.912756i	0.999506	−	0.0314391i	$-0.0100090\pi$
$398$	8.00000			0.401004
$399$	−1.50000	+	2.59808i	−0.0750939	+	0.130066i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	18.5000	+	32.0429i	0.923846	+	1.60015i	0.793407	+	0.608692i	$0.208305\pi$
$401$	18.5000	+	32.0429i	0.923846	+	1.60015i	0.130439	+	0.991456i	$0.458361\pi$
$402$	1.50000	+	2.59808i	0.0748132	+	0.129580i
$403$	−25.0000			−1.24534
$404$	−4.50000	−	7.79423i	−0.223883	−	0.387777i
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$	−4.50000	+	7.79423i	−0.223331	+	0.386821i
$407$		0			0
$408$	−9.00000			−0.445566
$409$	−18.0000			−0.890043			−0.445021	−	0.895520i	$-0.646804\pi$
$409$	−18.0000			−0.890043			−0.445021	+	0.895520i	$0.646804\pi$
$410$	−5.00000	+	8.66025i	−0.246932	+	0.427699i
$411$	9.00000	−	15.5885i	0.443937	−	0.768922i
$412$	3.50000	+	6.06218i	0.172433	+	0.298662i
$413$	−18.0000	−	31.1769i	−0.885722	−	1.53412i
$414$	14.0000			0.688062
$415$	4.50000	+	7.79423i	0.220896	+	0.382604i
$416$	12.5000	+	21.6506i	0.612863	+	1.06151i
$417$	−6.50000	−	11.2583i	−0.318306	−	0.551323i
$418$		0			0
$419$	−28.0000			−1.36789			−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000			−1.36789			−0.683945	+	0.729534i	$0.739737\pi$
$420$	−1.50000	+	2.59808i	−0.0731925	+	0.126773i
$421$	18.5000	+	32.0429i	0.901635	+	1.56168i	0.825372	+	0.564590i	$0.190966\pi$
$421$	18.5000	+	32.0429i	0.901635	+	1.56168i	0.0762630	+	0.997088i	$0.475701\pi$
$422$	8.00000			0.389434
$423$	−8.00000	−	13.8564i	−0.388973	−	0.673722i
$424$	−7.50000	+	12.9904i	−0.364232	+	0.630869i
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$	−1.00000			−0.0484502
$427$	19.5000	−	33.7750i	0.943671	−	1.63449i
$428$	−12.0000			−0.580042
$429$		0			0
$430$	2.50000	+	6.06218i	0.120561	+	0.292344i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	5.00000			0.240563
$433$	−13.5000	+	23.3827i	−0.648769	+	1.12370i	0.334649	+	0.942343i	$0.391382\pi$
$433$	−13.5000	+	23.3827i	−0.648769	+	1.12370i	−0.983417	+	0.181357i	$0.941951\pi$
$434$	15.0000			0.720023
$435$	1.50000	−	2.59808i	0.0719195	−	0.124568i
$436$	3.50000	−	6.06218i	0.167620	−	0.290326i
$437$	3.50000	+	6.06218i	0.167428	+	0.289993i
$438$	11.0000			0.525600
$439$	6.50000	+	11.2583i	0.310228	+	0.537331i	0.978412	−	0.206666i	$-0.0662612\pi$
$439$	6.50000	+	11.2583i	0.310228	+	0.537331i	−0.668184	+	0.743996i	$0.732928\pi$
$440$		0			0
$441$	−4.00000			−0.190476
$442$	7.50000	−	12.9904i	0.356739	−	0.617889i
$443$	18.5000	+	32.0429i	0.878962	+	1.52241i	0.852482	+	0.522757i	$0.175096\pi$
$443$	18.5000	+	32.0429i	0.878962	+	1.52241i	0.0264796	+	0.999649i	$0.491570\pi$
$444$	−4.50000	−	7.79423i	−0.213561	−	0.369898i
$445$	−0.500000	−	0.866025i	−0.0237023	−	0.0410535i
$446$	20.0000			0.947027
$447$	10.5000	+	18.1865i	0.496633	+	0.860194i
$448$	−10.5000	−	18.1865i	−0.496078	−	0.859233i
$449$	10.5000	−	18.1865i	0.495526	−	0.858276i	−0.504461	−	0.863434i	$-0.668309\pi$
$449$	10.5000	−	18.1865i	0.495526	−	0.858276i	0.999987	+	0.00515887i	$0.00164213\pi$
$450$	−4.00000	+	6.92820i	−0.188562	+	0.326599i
$451$		0			0
$452$	2.00000			0.0940721
$453$	4.00000	−	6.92820i	0.187936	−	0.325515i
$454$	3.50000	−	6.06218i	0.164263	−	0.284512i
$455$	−7.50000	−	12.9904i	−0.351605	−	0.608998i
$456$	1.50000	+	2.59808i	0.0702439	+	0.121666i
$457$	6.00000			0.280668			0.140334	−	0.990104i	$-0.455182\pi$
$457$	6.00000			0.280668			0.140334	+	0.990104i	$0.455182\pi$
$458$	4.50000	+	7.79423i	0.210271	+	0.364200i
$459$	7.50000	+	12.9904i	0.350070	+	0.606339i
$460$	3.50000	+	6.06218i	0.163188	+	0.282650i
$461$	−1.50000	+	2.59808i	−0.0698620	+	0.121004i	−0.898840	−	0.438276i	$-0.855589\pi$
$461$	−1.50000	+	2.59808i	−0.0698620	+	0.121004i	0.828978	+	0.559281i	$0.188923\pi$
$462$		0			0
$463$	11.5000	−	19.9186i	0.534450	−	0.925695i	−0.464739	−	0.885448i	$-0.653852\pi$
$463$	11.5000	−	19.9186i	0.534450	−	0.925695i	0.999190	−	0.0402476i	$-0.0128147\pi$
$464$	1.50000	+	2.59808i	0.0696358	+	0.120613i
$465$	−5.00000			−0.231869
$466$	4.50000	+	7.79423i	0.208458	+	0.361061i
$467$	−10.5000	+	18.1865i	−0.485882	+	0.841572i	−0.999868	−	0.0162260i	$-0.994835\pi$
$467$	−10.5000	+	18.1865i	−0.485882	+	0.841572i	0.513986	+	0.857798i	$0.328168\pi$
$468$	5.00000	−	8.66025i	0.231125	−	0.400320i
$469$	−9.00000			−0.415581
$470$	−4.00000	+	6.92820i	−0.184506	+	0.319574i
$471$	−1.00000			−0.0460776
$472$	−36.0000			−1.65703
$473$		0			0
$474$	−5.00000			−0.229658
$475$	−4.00000			−0.183533
$476$	4.50000	−	7.79423i	0.206257	−	0.357248i
$477$	10.0000			0.457869
$478$	−12.5000	+	21.6506i	−0.571737	+	0.990277i
$479$	7.50000	−	12.9904i	0.342684	−	0.593546i	−0.642246	−	0.766498i	$-0.721997\pi$
$479$	7.50000	−	12.9904i	0.342684	−	0.593546i	0.984930	+	0.172953i	$0.0553307\pi$
$480$	2.50000	+	4.33013i	0.114109	+	0.197642i
$481$	45.0000			2.05182
$482$	−7.50000	−	12.9904i	−0.341616	−	0.591696i
$483$	10.5000	−	18.1865i	0.477767	−	0.827516i
$484$	11.0000			0.500000
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$	−8.00000	−	13.8564i	−0.362887	−	0.628539i
$487$	4.50000	+	7.79423i	0.203914	+	0.353190i	0.949786	−	0.312899i	$-0.101300\pi$
$487$	4.50000	+	7.79423i	0.203914	+	0.353190i	−0.745872	+	0.666089i	$0.767967\pi$
$488$	−19.5000	−	33.7750i	−0.882724	−	1.52892i
$489$	−1.00000			−0.0452216
$490$	1.00000	+	1.73205i	0.0451754	+	0.0782461i
$491$	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	$0.768237\pi$
$492$	−5.00000	+	8.66025i	−0.225417	+	0.390434i
$493$	−4.50000	+	7.79423i	−0.202670	+	0.351034i
$494$	−5.00000			−0.224961
$495$		0			0
$496$	2.50000	−	4.33013i	0.112253	−	0.194428i
$497$	1.50000	−	2.59808i	0.0672842	−	0.116540i
$498$	−4.50000	−	7.79423i	−0.201650	−	0.349268i
$499$	8.50000	+	14.7224i	0.380512	+	0.659067i	0.991136	−	0.132855i	$-0.0424144\pi$
$499$	8.50000	+	14.7224i	0.380512	+	0.659067i	−0.610623	+	0.791921i	$0.709081\pi$
$500$	−9.00000			−0.402492
$501$	1.50000	+	2.59808i	0.0670151	+	0.116073i
$502$	−3.50000	−	6.06218i	−0.156213	−	0.270568i
$503$	4.50000	+	7.79423i	0.200645	+	0.347527i	0.948736	−	0.316068i	$-0.102363\pi$
$503$	4.50000	+	7.79423i	0.200645	+	0.347527i	−0.748091	+	0.663596i	$0.769030\pi$
$504$	−9.00000	+	15.5885i	−0.400892	+	0.694365i
$505$	9.00000			0.400495
$506$		0			0
$507$	−6.00000	−	10.3923i	−0.266469	−	0.461538i
$508$	−16.0000			−0.709885
$509$	−13.5000	−	23.3827i	−0.598377	−	1.03642i	−0.993061	−	0.117602i	$-0.962479\pi$
$509$	−13.5000	−	23.3827i	−0.598377	−	1.03642i	0.394684	−	0.918817i	$-0.370854\pi$
$510$	1.50000	−	2.59808i	0.0664211	−	0.115045i
$511$	−16.5000	+	28.5788i	−0.729917	+	1.26425i
$512$	−11.0000			−0.486136
$513$	2.50000	−	4.33013i	0.110378	−	0.191180i
$514$	6.00000			0.264649
$515$	−7.00000			−0.308457
$516$	2.50000	+	6.06218i	0.110056	+	0.266872i
$517$		0			0
$518$	−27.0000			−1.18631
$519$	3.00000	−	5.19615i	0.131685	−	0.228086i
$520$	−15.0000			−0.657794
$521$	−17.5000	+	30.3109i	−0.766689	+	1.32794i	0.172660	+	0.984981i	$0.444764\pi$
$521$	−17.5000	+	30.3109i	−0.766689	+	1.32794i	−0.939349	+	0.342963i	$0.888570\pi$
$522$	3.00000	−	5.19615i	0.131306	−	0.227429i
$523$	10.5000	+	18.1865i	0.459133	+	0.795242i	0.998915	−	0.0465630i	$-0.0148268\pi$
$523$	10.5000	+	18.1865i	0.459133	+	0.795242i	−0.539782	+	0.841805i	$0.681493\pi$
$524$	4.00000			0.174741
$525$	6.00000	+	10.3923i	0.261861	+	0.453557i
$526$	−10.5000	+	18.1865i	−0.457822	+	0.792971i
$527$	15.0000			0.653410
$528$		0			0
$529$	−13.0000	−	22.5167i	−0.565217	−	0.978985i
$530$	−2.50000	−	4.33013i	−0.108593	−	0.188089i
$531$	12.0000	+	20.7846i	0.520756	+	0.901975i
$532$	−3.00000			−0.130066
$533$	−25.0000	−	43.3013i	−1.08287	−	1.87559i
$534$	0.500000	+	0.866025i	0.0216371	+	0.0374766i
$535$	6.00000	−	10.3923i	0.259403	−	0.449299i
$536$	−4.50000	+	7.79423i	−0.194370	+	0.336659i
$537$	−1.00000			−0.0431532
$538$	14.0000			0.603583
$539$		0			0
$540$	2.50000	−	4.33013i	0.107583	−	0.186339i
$541$	−15.5000	−	26.8468i	−0.666397	−	1.15423i	−0.978905	−	0.204318i	$-0.934502\pi$
$541$	−15.5000	−	26.8468i	−0.666397	−	1.15423i	0.312507	−	0.949915i	$-0.398831\pi$
$542$	−11.5000	−	19.9186i	−0.493967	−	0.855576i
$543$	7.00000			0.300399
$544$	−7.50000	−	12.9904i	−0.321560	−	0.556958i
$545$	3.50000	+	6.06218i	0.149924	+	0.259675i
$546$	7.50000	+	12.9904i	0.320970	+	0.555937i
$547$	−0.500000	+	0.866025i	−0.0213785	+	0.0370286i	−0.876517	−	0.481371i	$-0.840139\pi$
$547$	−0.500000	+	0.866025i	−0.0213785	+	0.0370286i	0.855138	+	0.518400i	$0.173472\pi$
$548$	18.0000			0.768922
$549$	−13.0000	+	22.5167i	−0.554826	+	0.960988i
$550$		0			0
$551$	3.00000			0.127804
$552$	−10.5000	−	18.1865i	−0.446910	−	0.774070i
$553$	7.50000	−	12.9904i	0.318932	−	0.552407i
$554$	−3.50000	+	6.06218i	−0.148701	+	0.257557i
$555$	9.00000			0.382029
$556$	6.50000	−	11.2583i	0.275661	−	0.477460i
$557$	−6.00000			−0.254228			−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000			−0.254228			−0.127114	+	0.991888i	$0.540571\pi$
$558$	−10.0000			−0.423334
$559$	−32.5000	−	4.33013i	−1.37460	−	0.183145i
$560$	3.00000			0.126773
$561$		0			0
$562$	8.50000	−	14.7224i	0.358551	−	0.621028i
$563$	4.00000			0.168580			0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000			0.168580			0.0842900	+	0.996441i	$0.473138\pi$
$564$	−4.00000	+	6.92820i	−0.168430	+	0.291730i
$565$	−1.00000	+	1.73205i	−0.0420703	+	0.0728679i
$566$	−1.50000	−	2.59808i	−0.0630497	−	0.109205i
$567$	3.00000			0.125988
$568$	−1.50000	−	2.59808i	−0.0629386	−	0.109013i
$569$	8.50000	−	14.7224i	0.356339	−	0.617196i	−0.631008	−	0.775777i	$-0.717358\pi$
$569$	8.50000	−	14.7224i	0.356339	−	0.617196i	0.987346	+	0.158580i	$0.0506917\pi$
$570$	−1.00000			−0.0418854
$571$	−6.50000	+	11.2583i	−0.272017	+	0.471146i	−0.969378	−	0.245573i	$-0.921024\pi$
$571$	−6.50000	+	11.2583i	−0.272017	+	0.471146i	0.697362	+	0.716720i	$0.254357\pi$
$572$		0			0
$573$	9.50000	+	16.4545i	0.396868	+	0.687396i
$574$	15.0000	+	25.9808i	0.626088	+	1.08442i
$575$	28.0000			1.16768
$576$	7.00000	+	12.1244i	0.291667	+	0.505181i
$577$	2.50000	+	4.33013i	0.104076	+	0.180266i	0.913360	−	0.407152i	$-0.133478\pi$
$577$	2.50000	+	4.33013i	0.104076	+	0.180266i	−0.809284	+	0.587417i	$0.800145\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	−3.00000	+	5.19615i	−0.124676	+	0.215945i
$580$	3.00000			0.124568
$581$	27.0000			1.12015
$582$	1.00000	−	1.73205i	0.0414513	−	0.0717958i
$583$		0			0
$584$	16.5000	+	28.5788i	0.682775	+	1.18260i
$585$	5.00000	+	8.66025i	0.206725	+	0.358057i
$586$	−14.0000			−0.578335
$587$	6.50000	+	11.2583i	0.268284	+	0.464681i	0.968419	−	0.249329i	$-0.0802102\pi$
$587$	6.50000	+	11.2583i	0.268284	+	0.464681i	−0.700135	+	0.714010i	$0.746877\pi$
$588$	1.00000	+	1.73205i	0.0412393	+	0.0714286i
$589$	−2.50000	−	4.33013i	−0.103011	−	0.178420i
$590$	6.00000	−	10.3923i	0.247016	−	0.427844i
$591$	11.0000			0.452480
$592$	−4.50000	+	7.79423i	−0.184949	+	0.320341i
$593$	0.500000	+	0.866025i	0.0205325	+	0.0355634i	0.876109	−	0.482113i	$-0.160130\pi$
$593$	0.500000	+	0.866025i	0.0205325	+	0.0355634i	−0.855577	+	0.517676i	$0.826797\pi$
$594$		0			0
$595$	4.50000	+	7.79423i	0.184482	+	0.319532i
$596$	−10.5000	+	18.1865i	−0.430097	+	0.744949i
$597$	−4.00000	+	6.92820i	−0.163709	+	0.283552i
$598$	35.0000			1.43126
$599$	15.5000	−	26.8468i	0.633313	−	1.09693i	−0.353557	−	0.935413i	$-0.615028\pi$
$599$	15.5000	−	26.8468i	0.633313	−	1.09693i	0.986870	−	0.161517i	$-0.0516387\pi$
$600$	12.0000			0.489898
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$	19.5000	+	2.59808i	0.794761	+	0.105890i
$603$	6.00000			0.244339
$604$	8.00000			0.325515
$605$	−5.50000	+	9.52628i	−0.223607	+	0.387298i
$606$	−9.00000			−0.365600
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.0134214	−	0.999910i	$-0.495728\pi$
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.859237	−	0.511578i	$-0.170939\pi$
$608$	−2.50000	+	4.33013i	−0.101388	+	0.175610i
$609$	−4.50000	−	7.79423i	−0.182349	−	0.315838i
$610$	13.0000			0.526355
$611$	−20.0000	−	34.6410i	−0.809113	−	1.40143i
$612$	−3.00000	+	5.19615i	−0.121268	+	0.210042i
$613$	−30.0000			−1.21169			−0.605844	−	0.795583i	$-0.707165\pi$
$613$	−30.0000			−1.21169			−0.605844	+	0.795583i	$0.707165\pi$
$614$	−2.50000	+	4.33013i	−0.100892	+	0.174750i
$615$	−5.00000	−	8.66025i	−0.201619	−	0.349215i
$616$		0			0
$617$	−1.50000	−	2.59808i	−0.0603877	−	0.104595i	0.834251	−	0.551385i	$-0.185900\pi$
$617$	−1.50000	−	2.59808i	−0.0603877	−	0.104595i	−0.894639	+	0.446790i	$0.852567\pi$
$618$	7.00000			0.281581
$619$	10.5000	+	18.1865i	0.422031	+	0.730978i	0.996138	−	0.0878015i	$-0.0279841\pi$
$619$	10.5000	+	18.1865i	0.422031	+	0.730978i	−0.574107	+	0.818780i	$0.694651\pi$
$620$	−2.50000	−	4.33013i	−0.100402	−	0.173902i
$621$	−17.5000	+	30.3109i	−0.702251	+	1.21633i
$622$	1.50000	−	2.59808i	0.0601445	−	0.104173i
$623$	−3.00000			−0.120192
$624$	5.00000			0.200160
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	8.50000	−	14.7224i	0.339728	−	0.588427i
$627$		0			0
$628$	−0.500000	−	0.866025i	−0.0199522	−	0.0345582i
$629$	−27.0000			−1.07656
$630$	−3.00000	−	5.19615i	−0.119523	−	0.207020i
$631$	4.50000	+	7.79423i	0.179142	+	0.310283i	0.941587	−	0.336770i	$-0.109334\pi$
$631$	4.50000	+	7.79423i	0.179142	+	0.310283i	−0.762445	+	0.647053i	$0.776001\pi$
$632$	−7.50000	−	12.9904i	−0.298334	−	0.516730i
$633$	−4.00000	+	6.92820i	−0.158986	+	0.275371i
$634$	−18.0000			−0.714871
$635$	8.00000	−	13.8564i	0.317470	−	0.549875i
$636$	−2.50000	−	4.33013i	−0.0991314	−	0.171701i
$637$	−10.0000			−0.396214
$638$		0			0
$639$	−1.00000	+	1.73205i	−0.0395594	+	0.0685189i
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	−18.0000			−0.710957			−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000			−0.710957			−0.355479	+	0.934684i	$0.615682\pi$
$642$	−6.00000	+	10.3923i	−0.236801	+	0.410152i
$643$	12.0000			0.473234			0.236617	−	0.971603i	$-0.423961\pi$
$643$	12.0000			0.473234			0.236617	+	0.971603i	$0.423961\pi$
$644$	21.0000			0.827516
$645$	−6.50000	−	0.866025i	−0.255937	−	0.0340997i
$646$	3.00000			0.118033
$647$	−12.0000			−0.471769			−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000			−0.471769			−0.235884	+	0.971781i	$0.575799\pi$
$648$	1.50000	−	2.59808i	0.0589256	−	0.102062i
$649$		0			0
$650$	−10.0000	+	17.3205i	−0.392232	+	0.679366i
$651$	−7.50000	+	12.9904i	−0.293948	+	0.509133i
$652$	−0.500000	−	0.866025i	−0.0195815	−	0.0339162i
$653$	−50.0000			−1.95665			−0.978326	−	0.207072i	$-0.933606\pi$
$653$	−50.0000			−1.95665			−0.978326	+	0.207072i	$0.933606\pi$
$654$	−3.50000	−	6.06218i	−0.136861	−	0.237050i
$655$	−2.00000	+	3.46410i	−0.0781465	+	0.135354i
$656$	10.0000			0.390434
$657$	11.0000	−	19.0526i	0.429151	−	0.743311i
$658$	12.0000	+	20.7846i	0.467809	+	0.810268i
$659$	−11.5000	−	19.9186i	−0.447976	−	0.775918i	0.550278	−	0.834982i	$-0.314522\pi$
$659$	−11.5000	−	19.9186i	−0.447976	−	0.775918i	−0.998254	+	0.0590638i	$0.981188\pi$
$660$		0			0
$661$	−14.0000			−0.544537			−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000			−0.544537			−0.272268	+	0.962221i	$0.587774\pi$
$662$	−9.50000	−	16.4545i	−0.369228	−	0.639522i
$663$	7.50000	+	12.9904i	0.291276	+	0.504505i
$664$	13.5000	−	23.3827i	0.523902	−	0.907424i
$665$	1.50000	−	2.59808i	0.0581675	−	0.100749i
$666$	18.0000			0.697486
$667$	−21.0000			−0.813123
$668$	−1.50000	+	2.59808i	−0.0580367	+	0.100523i
$669$	−10.0000	+	17.3205i	−0.386622	+	0.669650i
$670$	−1.50000	−	2.59808i	−0.0579501	−	0.100372i
$671$		0			0
$672$	15.0000			0.578638
$673$	−23.5000	−	40.7032i	−0.905858	−	1.56899i	−0.819761	−	0.572706i	$-0.805894\pi$
$673$	−23.5000	−	40.7032i	−0.905858	−	1.56899i	−0.0860977	−	0.996287i	$-0.527440\pi$
$674$	−1.50000	−	2.59808i	−0.0577778	−	0.100074i
$675$	−10.0000	−	17.3205i	−0.384900	−	0.666667i
$676$	6.00000	−	10.3923i	0.230769	−	0.399704i
$677$	−14.0000			−0.538064			−0.269032	−	0.963131i	$-0.586704\pi$
$677$	−14.0000			−0.538064			−0.269032	+	0.963131i	$0.586704\pi$
$678$	1.00000	−	1.73205i	0.0384048	−	0.0665190i
$679$	3.00000	+	5.19615i	0.115129	+	0.199410i
$680$	9.00000			0.345134
$681$	3.50000	+	6.06218i	0.134120	+	0.232303i
$682$		0			0
$683$	−4.50000	+	7.79423i	−0.172188	+	0.298238i	−0.939184	−	0.343413i	$-0.888417\pi$
$683$	−4.50000	+	7.79423i	−0.172188	+	0.298238i	0.766997	+	0.641651i	$0.221750\pi$
$684$	2.00000			0.0764719
$685$	−9.00000	+	15.5885i	−0.343872	+	0.595604i
$686$	−15.0000			−0.572703
$687$	−9.00000			−0.343371
$688$	4.00000	−	5.19615i	0.152499	−	0.198101i
$689$	25.0000			0.952424
$690$	7.00000			0.266485
$691$	−2.50000	+	4.33013i	−0.0951045	+	0.164726i	−0.909652	−	0.415371i	$-0.863652\pi$
$691$	−2.50000	+	4.33013i	−0.0951045	+	0.164726i	0.814548	+	0.580097i	$0.196985\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−18.5000	+	32.0429i	−0.702250	+	1.21633i
$695$	6.50000	+	11.2583i	0.246559	+	0.427053i
$696$	−9.00000			−0.341144
$697$	15.0000	+	25.9808i	0.568166	+	0.984092i
$698$	0.500000	−	0.866025i	0.0189253	−	0.0327795i
$699$	−9.00000			−0.340411
$700$	−6.00000	+	10.3923i	−0.226779	+	0.392792i
$701$	−3.50000	−	6.06218i	−0.132193	−	0.228965i	0.792329	−	0.610095i	$-0.208869\pi$
$701$	−3.50000	−	6.06218i	−0.132193	−	0.228965i	−0.924522	+	0.381129i	$0.875535\pi$
$702$	−12.5000	−	21.6506i	−0.471782	−	0.817151i
$703$	4.50000	+	7.79423i	0.169721	+	0.293965i
$704$		0			0
$705$	−4.00000	−	6.92820i	−0.150649	−	0.260931i
$706$	12.5000	+	21.6506i	0.470444	+	0.814832i
$707$	13.5000	−	23.3827i	0.507720	−	0.879396i
$708$	6.00000	−	10.3923i	0.225494	−	0.390567i
$709$	26.0000			0.976450			0.488225	−	0.872718i	$-0.337644\pi$
$709$	26.0000			0.976450			0.488225	+	0.872718i	$0.337644\pi$
$710$	1.00000			0.0375293
$711$	−5.00000	+	8.66025i	−0.187515	+	0.324785i
$712$	−1.50000	+	2.59808i	−0.0562149	+	0.0973670i
$713$	17.5000	+	30.3109i	0.655380	+	1.13515i
$714$	−4.50000	−	7.79423i	−0.168408	−	0.291692i
$715$		0			0
$716$	−0.500000	−	0.866025i	−0.0186859	−	0.0323649i
$717$	−12.5000	−	21.6506i	−0.466821	−	0.808558i
$718$	−9.50000	−	16.4545i	−0.354537	−	0.614076i
$719$	15.5000	−	26.8468i	0.578052	−	1.00122i	−0.417650	−	0.908608i	$-0.637146\pi$
$719$	15.5000	−	26.8468i	0.578052	−	1.00122i	0.995703	−	0.0926083i	$-0.0295204\pi$
$720$	−2.00000			−0.0745356
$721$	−10.5000	+	18.1865i	−0.391040	+	0.677302i
$722$	9.00000	+	15.5885i	0.334945	+	0.580142i
$723$	15.0000			0.557856
$724$	3.50000	+	6.06218i	0.130076	+	0.225299i
$725$	6.00000	−	10.3923i	0.222834	−	0.385961i
$726$	5.50000	−	9.52628i	0.204124	−	0.353553i
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$	−22.5000	+	38.9711i	−0.833905	+	1.44437i
$729$	13.0000			0.481481
$730$	−11.0000			−0.407128
$731$	19.5000	+	2.59808i	0.721234	+	0.0960933i
$732$	13.0000			0.480494
$733$	26.0000			0.960332			0.480166	−	0.877178i	$-0.340576\pi$
$733$	26.0000			0.960332			0.480166	+	0.877178i	$0.340576\pi$
$734$	−6.50000	+	11.2583i	−0.239919	+	0.415553i
$735$	−2.00000			−0.0737711
$736$	17.5000	−	30.3109i	0.645059	−	1.11727i
$737$		0			0
$738$	−10.0000	−	17.3205i	−0.368105	−	0.637577i
$739$	−4.00000			−0.147142			−0.0735712	−	0.997290i	$-0.523440\pi$
$739$	−4.00000			−0.147142			−0.0735712	+	0.997290i	$0.523440\pi$
$740$	4.50000	+	7.79423i	0.165423	+	0.286522i
$741$	2.50000	−	4.33013i	0.0918398	−	0.159071i
$742$	−15.0000			−0.550667
$743$	−10.5000	+	18.1865i	−0.385208	+	0.667199i	−0.991798	−	0.127815i	$-0.959204\pi$
$743$	−10.5000	+	18.1865i	−0.385208	+	0.667199i	0.606590	+	0.795015i	$0.292537\pi$
$744$	7.50000	+	12.9904i	0.274963	+	0.476250i
$745$	−10.5000	−	18.1865i	−0.384690	−	0.666303i
$746$	−5.50000	−	9.52628i	−0.201369	−	0.348782i
$747$	−18.0000			−0.658586
$748$		0			0
$749$	−18.0000	−	31.1769i	−0.657706	−	1.13918i
$750$	−4.50000	+	7.79423i	−0.164317	+	0.284605i
$751$	13.5000	−	23.3827i	0.492622	−	0.853246i	−0.507342	−	0.861745i	$-0.669372\pi$
$751$	13.5000	−	23.3827i	0.492622	−	0.853246i	0.999964	+	0.00849853i	$0.00270520\pi$
$752$	8.00000			0.291730
$753$	7.00000			0.255094
$754$	7.50000	−	12.9904i	0.273134	−	0.473082i
$755$	−4.00000	+	6.92820i	−0.145575	+	0.252143i
$756$	−7.50000	−	12.9904i	−0.272772	−	0.472456i
$757$	2.50000	+	4.33013i	0.0908640	+	0.157381i	0.907875	−	0.419241i	$-0.137704\pi$
$757$	2.50000	+	4.33013i	0.0908640	+	0.157381i	−0.817011	+	0.576622i	$0.804370\pi$
$758$	20.0000			0.726433
$759$		0			0
$760$	−1.50000	−	2.59808i	−0.0544107	−	0.0942421i
$761$	18.5000	+	32.0429i	0.670624	+	1.16156i	0.977727	+	0.209879i	$0.0673071\pi$
$761$	18.5000	+	32.0429i	0.670624	+	1.16156i	−0.307103	+	0.951676i	$0.599360\pi$
$762$	−8.00000	+	13.8564i	−0.289809	+	0.501965i
$763$	21.0000			0.760251
$764$	−9.50000	+	16.4545i	−0.343698	+	0.595302i
$765$	−3.00000	−	5.19615i	−0.108465	−	0.187867i
$766$	8.00000			0.289052
$767$	30.0000	+	51.9615i	1.08324	+	1.87622i
$768$	8.50000	−	14.7224i	0.306717	−	0.531250i
$769$	16.5000	−	28.5788i	0.595005	−	1.03058i	−0.398541	−	0.917151i	$-0.630483\pi$
$769$	16.5000	−	28.5788i	0.595005	−	1.03058i	0.993546	−	0.113429i	$-0.0361834\pi$
$770$		0			0
$771$	−3.00000	+	5.19615i	−0.108042	+	0.187135i
$772$	−6.00000			−0.215945
$773$	26.0000			0.935155			0.467578	−	0.883952i	$-0.345127\pi$
$773$	26.0000			0.935155			0.467578	+	0.883952i	$0.345127\pi$
$774$	−13.0000	−	1.73205i	−0.467275	−	0.0622573i
$775$	−20.0000			−0.718421
$776$	6.00000			0.215387
$777$	13.5000	−	23.3827i	0.484310	−	0.838849i
$778$	−6.00000			−0.215110
$779$	5.00000	−	8.66025i	0.179144	−	0.310286i
$780$	2.50000	−	4.33013i	0.0895144	−	0.155043i
$781$		0			0
$782$	−21.0000			−0.750958
$783$	7.50000	+	12.9904i	0.268028	+	0.464238i
$784$	1.00000	−	1.73205i	0.0357143	−	0.0618590i
$785$	1.00000			0.0356915
$786$	2.00000	−	3.46410i	0.0713376	−	0.123560i
$787$	2.50000	+	4.33013i	0.0891154	+	0.154352i	0.907137	−	0.420834i	$-0.138263\pi$
$787$	2.50000	+	4.33013i	0.0891154	+	0.154352i	−0.818022	+	0.575187i	$0.804929\pi$
$788$	5.50000	+	9.52628i	0.195929	+	0.339360i
$789$	−10.5000	−	18.1865i	−0.373810	−	0.647458i
$790$	5.00000			0.177892
$791$	3.00000	+	5.19615i	0.106668	+	0.184754i
$792$		0			0
$793$	−32.5000	+	56.2917i	−1.15411	+	1.99898i
$794$	10.5000	−	18.1865i	0.372631	−	0.645416i
$795$	5.00000			0.177332
$796$	−8.00000			−0.283552
$797$	10.5000	−	18.1865i	0.371929	−	0.644200i	−0.617933	−	0.786231i	$-0.712030\pi$
$797$	10.5000	−	18.1865i	0.371929	−	0.644200i	0.989862	+	0.142031i	$0.0453631\pi$
$798$	−1.50000	+	2.59808i	−0.0530994	+	0.0919709i
$799$	12.0000	+	20.7846i	0.424529	+	0.735307i
$800$	10.0000	+	17.3205i	0.353553	+	0.612372i
$801$	2.00000			0.0706665
$802$	18.5000	+	32.0429i	0.653258	+	1.13148i
$803$		0			0
$804$	−1.50000	−	2.59808i	−0.0529009	−	0.0916271i
$805$	−10.5000	+	18.1865i	−0.370076	+	0.640991i
$806$	−25.0000			−0.880587
$807$	−7.00000	+	12.1244i	−0.246412	+	0.426798i
$808$	−13.5000	−	23.3827i	−0.474928	−	0.822600i
$809$	−34.0000			−1.19538			−0.597688	−	0.801729i	$-0.703914\pi$
$809$	−34.0000			−1.19538			−0.597688	+	0.801729i	$0.703914\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	23.5000	−	40.7032i	0.825197	−	1.42928i	−0.0765723	−	0.997064i	$-0.524398\pi$
$811$	23.5000	−	40.7032i	0.825197	−	1.42928i	0.901769	−	0.432218i	$-0.142269\pi$
$812$	4.50000	−	7.79423i	0.157919	−	0.273524i
$813$	23.0000			0.806645
$814$		0			0
$815$	1.00000			0.0350285
$816$	−3.00000			−0.105021
$817$	−2.50000	−	6.06218i	−0.0874639	−	0.212089i
$818$	−18.0000			−0.629355
$819$	30.0000			1.04828
$820$	5.00000	−	8.66025i	0.174608	−	0.302429i
$821$	10.0000			0.349002			0.174501	−	0.984657i	$-0.444169\pi$
$821$	10.0000			0.349002			0.174501	+	0.984657i	$0.444169\pi$
$822$	9.00000	−	15.5885i	0.313911	−	0.543710i
$823$	15.5000	−	26.8468i	0.540296	−	0.935820i	−0.458591	−	0.888648i	$-0.651646\pi$
$823$	15.5000	−	26.8468i	0.540296	−	0.935820i	0.998887	−	0.0471726i	$-0.0150211\pi$
$824$	10.5000	+	18.1865i	0.365785	+	0.633558i
$825$		0			0
$826$	−18.0000	−	31.1769i	−0.626300	−	1.08478i
$827$	−16.5000	+	28.5788i	−0.573761	+	0.993784i	0.422414	+	0.906403i	$0.361183\pi$
$827$	−16.5000	+	28.5788i	−0.573761	+	0.993784i	−0.996175	+	0.0873805i	$0.972150\pi$
$828$	−14.0000			−0.486534
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	−0.945589	−	0.325362i	$-0.894514\pi$
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	0.754567	+	0.656223i	$0.227847\pi$
$830$	4.50000	+	7.79423i	0.156197	+	0.270542i
$831$	−3.50000	−	6.06218i	−0.121414	−	0.210295i
$832$	17.5000	+	30.3109i	0.606703	+	1.05084i
$833$	6.00000			0.207888
$834$	−6.50000	−	11.2583i	−0.225077	−	0.389844i
$835$	−1.50000	−	2.59808i	−0.0519096	−	0.0899101i
$836$		0			0
$837$	12.5000	−	21.6506i	0.432063	−	0.748355i
$838$	−28.0000			−0.967244
$839$	−52.0000			−1.79524			−0.897620	−	0.440771i	$-0.854705\pi$
$839$	−52.0000			−1.79524			−0.897620	+	0.440771i	$0.854705\pi$
$840$	−4.50000	+	7.79423i	−0.155265	+	0.268926i
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	18.5000	+	32.0429i	0.637552	+	1.10427i
$843$	8.50000	+	14.7224i	0.292756	+	0.507067i
$844$	−8.00000			−0.275371
$845$	6.00000	+	10.3923i	0.206406	+	0.357506i
$846$	−8.00000	−	13.8564i	−0.275046	−	0.476393i
$847$	16.5000	+	28.5788i	0.566947	+	0.981981i
$848$	−2.50000	+	4.33013i	−0.0858504	+	0.148697i
$849$	3.00000			0.102960
$850$	6.00000	−	10.3923i	0.205798	−	0.356453i
$851$	−31.5000	−	54.5596i	−1.07981	−	1.87028i
$852$	1.00000			0.0342594
$853$	2.50000	+	4.33013i	0.0855984	+	0.148261i	0.905646	−	0.424034i	$-0.139386\pi$
$853$	2.50000	+	4.33013i	0.0855984	+	0.148261i	−0.820048	+	0.572295i	$0.806053\pi$
$854$	19.5000	−	33.7750i	0.667276	−	1.15576i
$855$	−1.00000	+	1.73205i	−0.0341993	+	0.0592349i
$856$	−36.0000			−1.23045
$857$	−17.5000	+	30.3109i	−0.597789	+	1.03540i	0.395358	+	0.918527i	$0.370620\pi$
$857$	−17.5000	+	30.3109i	−0.597789	+	1.03540i	−0.993147	+	0.116873i	$0.962713\pi$
$858$		0			0
$859$	4.00000			0.136478			0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000			0.136478			0.0682391	+	0.997669i	$0.478262\pi$
$860$	−2.50000	−	6.06218i	−0.0852493	−	0.206719i
$861$	−30.0000			−1.02240
$862$		0			0
$863$	13.5000	−	23.3827i	0.459545	−	0.795956i	−0.539392	−	0.842055i	$-0.681346\pi$
$863$	13.5000	−	23.3827i	0.459545	−	0.795956i	0.998937	+	0.0460992i	$0.0146790\pi$
$864$	−25.0000			−0.850517
$865$	−3.00000	+	5.19615i	−0.102003	+	0.176674i
$866$	−13.5000	+	23.3827i	−0.458749	+	0.794576i
$867$	4.00000	+	6.92820i	0.135847	+	0.235294i
$868$	−15.0000			−0.509133
$869$		0			0
$870$	1.50000	−	2.59808i	0.0508548	−	0.0880830i
$871$	15.0000			0.508256
$872$	10.5000	−	18.1865i	0.355575	−	0.615874i
$873$	−2.00000	−	3.46410i	−0.0676897	−	0.117242i
$874$	3.50000	+	6.06218i	0.118389	+	0.205056i
$875$	−13.5000	−	23.3827i	−0.456383	−	0.790479i
$876$	−11.0000			−0.371656
$877$	−11.5000	−	19.9186i	−0.388327	−	0.672603i	0.603897	−	0.797062i	$-0.293614\pi$
$877$	−11.5000	−	19.9186i	−0.388327	−	0.672603i	−0.992225	+	0.124459i	$0.960280\pi$
$878$	6.50000	+	11.2583i	0.219364	+	0.379950i
$879$	7.00000	−	12.1244i	0.236104	−	0.408944i
$880$		0			0
$881$	46.0000			1.54978			0.774890	−	0.632096i	$-0.217805\pi$
$881$	46.0000			1.54978			0.774890	+	0.632096i	$0.217805\pi$
$882$	−4.00000			−0.134687
$883$	−6.50000	+	11.2583i	−0.218742	+	0.378873i	−0.954424	−	0.298455i	$-0.903529\pi$
$883$	−6.50000	+	11.2583i	−0.218742	+	0.378873i	0.735681	+	0.677328i	$0.236862\pi$
$884$	−7.50000	+	12.9904i	−0.252252	+	0.436914i
$885$	6.00000	+	10.3923i	0.201688	+	0.349334i
$886$	18.5000	+	32.0429i	0.621520	+	1.07650i
$887$	−16.0000			−0.537227			−0.268614	−	0.963248i	$-0.586566\pi$
$887$	−16.0000			−0.537227			−0.268614	+	0.963248i	$0.586566\pi$
$888$	−13.5000	−	23.3827i	−0.453030	−	0.784672i
$889$	−24.0000	−	41.5692i	−0.804934	−	1.39419i
$890$	−0.500000	−	0.866025i	−0.0167600	−	0.0290292i
$891$		0			0
$892$	−20.0000			−0.669650
$893$	4.00000	−	6.92820i	0.133855	−	0.231843i
$894$	10.5000	+	18.1865i	0.351173	+	0.608249i
$895$	1.00000			0.0334263
$896$	4.50000	+	7.79423i	0.150334	+	0.260387i
$897$	−17.5000	+	30.3109i	−0.584308	+	1.01205i
$898$	10.5000	−	18.1865i	0.350390	−	0.606892i
$899$	15.0000			0.500278
$900$	4.00000	−	6.92820i	0.133333	−	0.230940i
$901$	−15.0000			−0.499722
$902$		0			0
$903$	−12.0000	+	15.5885i	−0.399335	+	0.518751i
$904$	6.00000			0.199557
$905$	−7.00000			−0.232688
$906$	4.00000	−	6.92820i	0.132891	−	0.230174i
$907$	20.0000			0.664089			0.332045	−	0.943264i	$-0.392262\pi$
$907$	20.0000			0.664089			0.332045	+	0.943264i	$0.392262\pi$
$908$	−3.50000	+	6.06218i	−0.116152	+	0.201180i
$909$	−9.00000	+	15.5885i	−0.298511	+	0.517036i
$910$	−7.50000	−	12.9904i	−0.248623	−	0.430627i
$911$	−52.0000			−1.72284			−0.861418	−	0.507896i	$-0.830423\pi$
$911$	−52.0000			−1.72284			−0.861418	+	0.507896i	$0.830423\pi$
$912$	0.500000	+	0.866025i	0.0165567	+	0.0286770i
$913$		0			0
$914$	6.00000			0.198462
$915$	−6.50000	+	11.2583i	−0.214883	+	0.372189i
$916$	−4.50000	−	7.79423i	−0.148684	−	0.257529i
$917$	6.00000	+	10.3923i	0.198137	+	0.343184i
$918$	7.50000	+	12.9904i	0.247537	+	0.428746i
$919$	20.0000			0.659739			0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000			0.659739			0.329870	+	0.944027i	$0.392995\pi$
$920$	10.5000	+	18.1865i	0.346175	+	0.599592i
$921$	−2.50000	−	4.33013i	−0.0823778	−	0.142683i
$922$	−1.50000	+	2.59808i	−0.0493999	+	0.0855631i
$923$	−2.50000	+	4.33013i	−0.0822885	+	0.142528i
$924$		0			0
$925$	36.0000			1.18367
$926$	11.5000	−	19.9186i	0.377913	−	0.654565i
$927$	7.00000	−	12.1244i	0.229910	−	0.398216i
$928$	−7.50000	−	12.9904i	−0.246200	−	0.426430i
$929$	28.5000	+	49.3634i	0.935055	+	1.61956i	0.774536	+	0.632529i	$0.217983\pi$
$929$	28.5000	+	49.3634i	0.935055	+	1.61956i	0.160518	+	0.987033i	$0.448683\pi$
$930$	−5.00000			−0.163956
$931$	−1.00000	−	1.73205i	−0.0327737	−	0.0567657i
$932$	−4.50000	−	7.79423i	−0.147402	−	0.255308i
$933$	1.50000	+	2.59808i	0.0491078	+	0.0850572i
$934$	−10.5000	+	18.1865i	−0.343570	+	0.595082i
$935$		0			0
$936$	15.0000	−	25.9808i	0.490290	−	0.849208i
$937$	−17.5000	−	30.3109i	−0.571700	−	0.990214i	−0.996392	−	0.0848755i	$-0.972951\pi$
$937$	−17.5000	−	30.3109i	−0.571700	−	0.990214i	0.424691	−	0.905338i	$-0.360383\pi$
$938$	−9.00000			−0.293860
$939$	8.50000	+	14.7224i	0.277387	+	0.480448i
$940$	4.00000	−	6.92820i	0.130466	−	0.225973i
$941$	4.50000	−	7.79423i	0.146696	−	0.254085i	−0.783309	−	0.621633i	$-0.786469\pi$
$941$	4.50000	−	7.79423i	0.146696	−	0.254085i	0.930004	+	0.367549i	$0.119803\pi$
$942$	−1.00000			−0.0325818
$943$	−35.0000	+	60.6218i	−1.13976	+	1.97412i
$944$	−12.0000			−0.390567
$945$	15.0000			0.487950
$946$		0			0
$947$	−12.0000			−0.389948			−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000			−0.389948			−0.194974	+	0.980808i	$0.562462\pi$
$948$	5.00000			0.162392
$949$	27.5000	−	47.6314i	0.892688	−	1.54618i
$950$	−4.00000			−0.129777
$951$	9.00000	−	15.5885i	0.291845	−	0.505490i
$952$	13.5000	−	23.3827i	0.437538	−	0.757837i
$953$	20.5000	+	35.5070i	0.664060	+	1.15019i	0.979539	+	0.201253i	$0.0645015\pi$
$953$	20.5000	+	35.5070i	0.664060	+	1.15019i	−0.315479	+	0.948933i	$0.602165\pi$
$954$	10.0000			0.323762
$955$	−9.50000	−	16.4545i	−0.307413	−	0.532455i
$956$	12.5000	−	21.6506i	0.404279	−	0.700232i
$957$		0			0
$958$	7.50000	−	12.9904i	0.242314	−	0.419700i
$959$	27.0000	+	46.7654i	0.871875	+	1.51013i
$960$	3.50000	+	6.06218i	0.112962	+	0.195656i
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$	45.0000			1.45086
$963$	12.0000	+	20.7846i	0.386695	+	0.669775i
$964$	7.50000	+	12.9904i	0.241559	+	0.418392i
$965$	3.00000	−	5.19615i	0.0965734	−	0.167270i
$966$	10.5000	−	18.1865i	0.337832	−	0.585142i
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$	33.0000			1.06066
$969$	−1.50000	+	2.59808i	−0.0481869	+	0.0834622i
$970$	−1.00000	+	1.73205i	−0.0321081	+	0.0556128i
$971$	−17.5000	−	30.3109i	−0.561602	−	0.972723i	−0.997357	−	0.0726575i	$-0.976852\pi$
$971$	−17.5000	−	30.3109i	−0.561602	−	0.972723i	0.435755	−	0.900065i	$-0.356481\pi$
$972$	8.00000	+	13.8564i	0.256600	+	0.444444i
$973$	39.0000			1.25028
$974$	4.50000	+	7.79423i	0.144189	+	0.249743i
$975$	−10.0000	−	17.3205i	−0.320256	−	0.554700i
$976$	−6.50000	−	11.2583i	−0.208060	−	0.360370i
$977$	20.5000	−	35.5070i	0.655853	−	1.13597i	−0.325826	−	0.945430i	$-0.605642\pi$
$977$	20.5000	−	35.5070i	0.655853	−	1.13597i	0.981679	−	0.190541i	$-0.0610243\pi$
$978$	−1.00000			−0.0319765
$979$		0			0
$980$	−1.00000	−	1.73205i	−0.0319438	−	0.0553283i
$981$	−14.0000			−0.446986
$982$	4.50000	+	7.79423i	0.143601	+	0.248724i
$983$	25.5000	−	44.1673i	0.813324	−	1.40872i	−0.0972017	−	0.995265i	$-0.530989\pi$
$983$	25.5000	−	44.1673i	0.813324	−	1.40872i	0.910525	−	0.413453i	$-0.135677\pi$
$984$	−15.0000	+	25.9808i	−0.478183	+	0.828236i
$985$	−11.0000			−0.350489
$986$	−4.50000	+	7.79423i	−0.143309	+	0.248219i
$987$	−24.0000			−0.763928
$988$	5.00000			0.159071
$989$	17.5000	+	42.4352i	0.556468	+	1.34936i
$990$		0			0
$991$	8.00000			0.254128			0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000			0.254128			0.127064	+	0.991894i	$0.459445\pi$
$992$	−12.5000	+	21.6506i	−0.396875	+	0.687408i
$993$	19.0000			0.602947
$994$	1.50000	−	2.59808i	0.0475771	−	0.0824060i
$995$	4.00000	−	6.92820i	0.126809	−	0.219639i
$996$	4.50000	+	7.79423i	0.142588	+	0.246970i
$997$	−14.0000			−0.443384			−0.221692	−	0.975117i	$-0.571158\pi$
$997$	−14.0000			−0.443384			−0.221692	+	0.975117i	$0.571158\pi$
$998$	8.50000	+	14.7224i	0.269063	+	0.466030i
$999$	−22.5000	+	38.9711i	−0.711868	+	1.23299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.c.a.6.1	✓	2
3.2	odd	2		387.2.h.a.307.1		2
4.3	odd	2		688.2.i.d.49.1		2
43.6	even	3		1849.2.a.c.1.1		1
43.36	even	3	inner	43.2.c.a.36.1	yes	2
43.37	odd	6		1849.2.a.a.1.1		1
129.122	odd	6		387.2.h.a.208.1		2
172.79	odd	6		688.2.i.d.337.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.c.a.6.1	✓	2	1.1	even	1	trivial
43.2.c.a.36.1	yes	2	43.36	even	3	inner
387.2.h.a.208.1		2	129.122	odd	6
387.2.h.a.307.1		2	3.2	odd	2
688.2.i.d.49.1		2	4.3	odd	2
688.2.i.d.337.1		2	172.79	odd	6
1849.2.a.a.1.1		1	43.37	odd	6
1849.2.a.c.1.1		1	43.6	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.50000 - 2.59808i) q^{7} -3.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.50000 - 2.59808i) q^{7} -3.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.500000 - 0.866025i) q^{12} +(2.50000 + 4.33013i) q^{13} +(-1.50000 - 2.59808i) q^{14} +(0.500000 + 0.866025i) q^{15} -1.00000 q^{16} +(-1.50000 - 2.59808i) q^{17} +(1.00000 + 1.73205i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(-0.500000 + 0.866025i) q^{20} +3.00000 q^{21} +(3.50000 - 6.06218i) q^{23} +(1.50000 - 2.59808i) q^{24} +(2.00000 + 3.46410i) q^{25} +(2.50000 + 4.33013i) q^{26} -5.00000 q^{27} +(1.50000 + 2.59808i) q^{28} +(-1.50000 - 2.59808i) q^{29} +(0.500000 + 0.866025i) q^{30} +(-2.50000 + 4.33013i) q^{31} +5.00000 q^{32} +(-1.50000 - 2.59808i) q^{34} -3.00000 q^{35} +(-1.00000 - 1.73205i) q^{36} +(4.50000 - 7.79423i) q^{37} +(-0.500000 + 0.866025i) q^{38} -5.00000 q^{39} +(-1.50000 + 2.59808i) q^{40} -10.0000 q^{41} +3.00000 q^{42} +(-4.00000 + 5.19615i) q^{43} +2.00000 q^{45} +(3.50000 - 6.06218i) q^{46} -8.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(2.00000 + 3.46410i) q^{50} +3.00000 q^{51} +(-2.50000 - 4.33013i) q^{52} +(2.50000 - 4.33013i) q^{53} -5.00000 q^{54} +(4.50000 + 7.79423i) q^{56} +(-0.500000 - 0.866025i) q^{57} +(-1.50000 - 2.59808i) q^{58} +12.0000 q^{59} +(-0.500000 - 0.866025i) q^{60} +(6.50000 + 11.2583i) q^{61} +(-2.50000 + 4.33013i) q^{62} +(3.00000 - 5.19615i) q^{63} +7.00000 q^{64} +5.00000 q^{65} +(1.50000 - 2.59808i) q^{67} +(1.50000 + 2.59808i) q^{68} +(3.50000 + 6.06218i) q^{69} -3.00000 q^{70} +(0.500000 + 0.866025i) q^{71} +(-3.00000 - 5.19615i) q^{72} +(-5.50000 - 9.52628i) q^{73} +(4.50000 - 7.79423i) q^{74} -4.00000 q^{75} +(0.500000 - 0.866025i) q^{76} -5.00000 q^{78} +(2.50000 + 4.33013i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} -10.0000 q^{82} +(-4.50000 + 7.79423i) q^{83} -3.00000 q^{84} -3.00000 q^{85} +(-4.00000 + 5.19615i) q^{86} +3.00000 q^{87} +(0.500000 - 0.866025i) q^{89} +2.00000 q^{90} +(7.50000 - 12.9904i) q^{91} +(-3.50000 + 6.06218i) q^{92} +(-2.50000 - 4.33013i) q^{93} -8.00000 q^{94} +(0.500000 + 0.866025i) q^{95} +(-2.50000 + 4.33013i) q^{96} -2.00000 q^{97} +(-1.00000 + 1.73205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - q^{6} - 3 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - q^3 - 2 * q^4 + q^5 - q^6 - 3 * q^7 - 6 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - q^{6} - 3 q^{7} - 6 q^{8} + 2 q^{9} + q^{10} + q^{12} + 5 q^{13} - 3 q^{14} + q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - q^{19} - q^{20} + 6 q^{21} + 7 q^{23} + 3 q^{24} + 4 q^{25} + 5 q^{26} - 10 q^{27} + 3 q^{28} - 3 q^{29} + q^{30} - 5 q^{31} + 10 q^{32} - 3 q^{34} - 6 q^{35} - 2 q^{36} + 9 q^{37} - q^{38} - 10 q^{39} - 3 q^{40} - 20 q^{41} + 6 q^{42} - 8 q^{43} + 4 q^{45} + 7 q^{46} - 16 q^{47} + q^{48} - 2 q^{49} + 4 q^{50} + 6 q^{51} - 5 q^{52} + 5 q^{53} - 10 q^{54} + 9 q^{56} - q^{57} - 3 q^{58} + 24 q^{59} - q^{60} + 13 q^{61} - 5 q^{62} + 6 q^{63} + 14 q^{64} + 10 q^{65} + 3 q^{67} + 3 q^{68} + 7 q^{69} - 6 q^{70} + q^{71} - 6 q^{72} - 11 q^{73} + 9 q^{74} - 8 q^{75} + q^{76} - 10 q^{78} + 5 q^{79} - q^{80} - q^{81} - 20 q^{82} - 9 q^{83} - 6 q^{84} - 6 q^{85} - 8 q^{86} + 6 q^{87} + q^{89} + 4 q^{90} + 15 q^{91} - 7 q^{92} - 5 q^{93} - 16 q^{94} + q^{95} - 5 q^{96} - 4 q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 - 2 * q^4 + q^5 - q^6 - 3 * q^7 - 6 * q^8 + 2 * q^9 + q^10 + q^12 + 5 * q^13 - 3 * q^14 + q^15 - 2 * q^16 - 3 * q^17 + 2 * q^18 - q^19 - q^20 + 6 * q^21 + 7 * q^23 + 3 * q^24 + 4 * q^25 + 5 * q^26 - 10 * q^27 + 3 * q^28 - 3 * q^29 + q^30 - 5 * q^31 + 10 * q^32 - 3 * q^34 - 6 * q^35 - 2 * q^36 + 9 * q^37 - q^38 - 10 * q^39 - 3 * q^40 - 20 * q^41 + 6 * q^42 - 8 * q^43 + 4 * q^45 + 7 * q^46 - 16 * q^47 + q^48 - 2 * q^49 + 4 * q^50 + 6 * q^51 - 5 * q^52 + 5 * q^53 - 10 * q^54 + 9 * q^56 - q^57 - 3 * q^58 + 24 * q^59 - q^60 + 13 * q^61 - 5 * q^62 + 6 * q^63 + 14 * q^64 + 10 * q^65 + 3 * q^67 + 3 * q^68 + 7 * q^69 - 6 * q^70 + q^71 - 6 * q^72 - 11 * q^73 + 9 * q^74 - 8 * q^75 + q^76 - 10 * q^78 + 5 * q^79 - q^80 - q^81 - 20 * q^82 - 9 * q^83 - 6 * q^84 - 6 * q^85 - 8 * q^86 + 6 * q^87 + q^89 + 4 * q^90 + 15 * q^91 - 7 * q^92 - 5 * q^93 - 16 * q^94 + q^95 - 5 * q^96 - 4 * q^97 - 2 * q^98

Introduction

L-functions

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