LMFDB - Embedded newform 171.2.g.a.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(106,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("171.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.g (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:	$1.36544187456$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	171.121
Dual form			171.2.g.a.106.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(-1.50000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(-1.50000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{10} +(-2.50000 - 4.33013i) q^{11} -1.73205i q^{12} +(-1.00000 - 1.73205i) q^{13} -1.00000 q^{14} +(-4.50000 - 2.59808i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.50000 + 4.33013i) q^{17} +3.00000 q^{18} +(-4.00000 - 1.73205i) q^{19} +(1.50000 + 2.59808i) q^{20} +1.73205i q^{21} -5.00000 q^{22} +(4.00000 + 6.92820i) q^{23} +(-4.50000 - 2.59808i) q^{24} +4.00000 q^{25} -2.00000 q^{26} -5.19615i q^{27} +(0.500000 - 0.866025i) q^{28} -1.00000 q^{29} +(-4.50000 + 2.59808i) q^{30} +(-1.50000 + 2.59808i) q^{31} +(2.50000 + 4.33013i) q^{32} +8.66025i q^{33} +5.00000 q^{34} +(-1.50000 - 2.59808i) q^{35} +(-1.50000 + 2.59808i) q^{36} -6.00000 q^{37} +(-3.50000 + 2.59808i) q^{38} +3.46410i q^{39} +9.00000 q^{40} -9.00000 q^{41} +(1.50000 + 0.866025i) q^{42} +(-4.00000 + 6.92820i) q^{43} +(2.50000 - 4.33013i) q^{44} +(4.50000 + 7.79423i) q^{45} +8.00000 q^{46} +3.00000 q^{47} +(-1.50000 + 0.866025i) q^{48} +(3.00000 - 5.19615i) q^{49} +(2.00000 - 3.46410i) q^{50} -8.66025i q^{51} +(1.00000 - 1.73205i) q^{52} +(0.500000 - 0.866025i) q^{53} +(-4.50000 - 2.59808i) q^{54} +(-7.50000 - 12.9904i) q^{55} +(-1.50000 - 2.59808i) q^{56} +(4.50000 + 6.06218i) q^{57} +(-0.500000 + 0.866025i) q^{58} +5.00000 q^{59} -5.19615i q^{60} -13.0000 q^{61} +(1.50000 + 2.59808i) q^{62} +(1.50000 - 2.59808i) q^{63} +7.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} +(7.50000 + 4.33013i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-2.50000 + 4.33013i) q^{68} -13.8564i q^{69} -3.00000 q^{70} +(-1.50000 - 2.59808i) q^{71} +(4.50000 + 7.79423i) q^{72} +(2.50000 + 4.33013i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(-6.00000 - 3.46410i) q^{75} +(-0.500000 - 4.33013i) q^{76} +(-2.50000 + 4.33013i) q^{77} +(3.00000 + 1.73205i) q^{78} +(-2.00000 + 3.46410i) q^{79} +(1.50000 - 2.59808i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-4.50000 + 7.79423i) q^{82} +(-4.50000 - 7.79423i) q^{83} +(-1.50000 + 0.866025i) q^{84} +(7.50000 + 12.9904i) q^{85} +(4.00000 + 6.92820i) q^{86} +(1.50000 + 0.866025i) q^{87} +(-7.50000 - 12.9904i) q^{88} +(4.50000 - 7.79423i) q^{89} +9.00000 q^{90} +(-1.00000 + 1.73205i) q^{91} +(-4.00000 + 6.92820i) q^{92} +(4.50000 - 2.59808i) q^{93} +(1.50000 - 2.59808i) q^{94} +(-12.0000 - 5.19615i) q^{95} -8.66025i q^{96} +(5.00000 - 8.66025i) q^{97} +(-3.00000 - 5.19615i) q^{98} +(7.50000 - 12.9904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 3 q^{3} + q^{4} + 6 q^{5} - 3 q^{6} - q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + q^2 - 3 * q^3 + q^4 + 6 * q^5 - 3 * q^6 - q^7 + 6 * q^8 + 3 * q^9	$ 2 q + q^{2} - 3 q^{3} + q^{4} + 6 q^{5} - 3 q^{6} - q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 5 q^{11} - 2 q^{13} - 2 q^{14} - 9 q^{15} + q^{16} + 5 q^{17} + 6 q^{18} - 8 q^{19} + 3 q^{20} - 10 q^{22} + 8 q^{23} - 9 q^{24} + 8 q^{25} - 4 q^{26} + q^{28} - 2 q^{29} - 9 q^{30} - 3 q^{31} + 5 q^{32} + 10 q^{34} - 3 q^{35} - 3 q^{36} - 12 q^{37} - 7 q^{38} + 18 q^{40} - 18 q^{41} + 3 q^{42} - 8 q^{43} + 5 q^{44} + 9 q^{45} + 16 q^{46} + 6 q^{47} - 3 q^{48} + 6 q^{49} + 4 q^{50} + 2 q^{52} + q^{53} - 9 q^{54} - 15 q^{55} - 3 q^{56} + 9 q^{57} - q^{58} + 10 q^{59} - 26 q^{61} + 3 q^{62} + 3 q^{63} + 14 q^{64} - 6 q^{65} + 15 q^{66} + 4 q^{67} - 5 q^{68} - 6 q^{70} - 3 q^{71} + 9 q^{72} + 5 q^{73} - 6 q^{74} - 12 q^{75} - q^{76} - 5 q^{77} + 6 q^{78} - 4 q^{79} + 3 q^{80} - 9 q^{81} - 9 q^{82} - 9 q^{83} - 3 q^{84} + 15 q^{85} + 8 q^{86} + 3 q^{87} - 15 q^{88} + 9 q^{89} + 18 q^{90} - 2 q^{91} - 8 q^{92} + 9 q^{93} + 3 q^{94} - 24 q^{95} + 10 q^{97} - 6 q^{98} + 15 q^{99}+O(q^{100}) $ 2 * q + q^2 - 3 * q^3 + q^4 + 6 * q^5 - 3 * q^6 - q^7 + 6 * q^8 + 3 * q^9 + 3 * q^10 - 5 * q^11 - 2 * q^13 - 2 * q^14 - 9 * q^15 + q^16 + 5 * q^17 + 6 * q^18 - 8 * q^19 + 3 * q^20 - 10 * q^22 + 8 * q^23 - 9 * q^24 + 8 * q^25 - 4 * q^26 + q^28 - 2 * q^29 - 9 * q^30 - 3 * q^31 + 5 * q^32 + 10 * q^34 - 3 * q^35 - 3 * q^36 - 12 * q^37 - 7 * q^38 + 18 * q^40 - 18 * q^41 + 3 * q^42 - 8 * q^43 + 5 * q^44 + 9 * q^45 + 16 * q^46 + 6 * q^47 - 3 * q^48 + 6 * q^49 + 4 * q^50 + 2 * q^52 + q^53 - 9 * q^54 - 15 * q^55 - 3 * q^56 + 9 * q^57 - q^58 + 10 * q^59 - 26 * q^61 + 3 * q^62 + 3 * q^63 + 14 * q^64 - 6 * q^65 + 15 * q^66 + 4 * q^67 - 5 * q^68 - 6 * q^70 - 3 * q^71 + 9 * q^72 + 5 * q^73 - 6 * q^74 - 12 * q^75 - q^76 - 5 * q^77 + 6 * q^78 - 4 * q^79 + 3 * q^80 - 9 * q^81 - 9 * q^82 - 9 * q^83 - 3 * q^84 + 15 * q^85 + 8 * q^86 + 3 * q^87 - 15 * q^88 + 9 * q^89 + 18 * q^90 - 2 * q^91 - 8 * q^92 + 9 * q^93 + 3 * q^94 - 24 * q^95 + 10 * q^97 - 6 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	−0.633316	−	0.773893i	$-0.718307\pi$
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	0.986869	+	0.161521i	$0.0516399\pi$
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	3.00000			1.34164			0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	−0.944911	+	0.327327i	$0.893852\pi$
$8$	3.00000			1.06066
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	1.50000	−	2.59808i	0.474342	−	0.821584i
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	−0.945979	−	0.324227i	$-0.894896\pi$
$11$	−2.50000	−	4.33013i	−0.753778	−	1.30558i	0.192201	−	0.981356i	$-0.438437\pi$
$12$		−	1.73205i		−	0.500000i
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−1.00000			−0.267261
$15$	−4.50000	−	2.59808i	−1.16190	−	0.670820i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	0.991838	+	0.127502i	$0.0406959\pi$
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	−0.385499	+	0.922708i	$0.625971\pi$
$18$	3.00000			0.707107
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$20$	1.50000	+	2.59808i	0.335410	+	0.580948i
$21$			1.73205i			0.377964i
$22$	−5.00000			−1.06600
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	0.894795	+	0.446476i	$0.147321\pi$
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	−0.0607377	+	0.998154i	$0.519345\pi$
$24$	−4.50000	−	2.59808i	−0.918559	−	0.530330i
$25$	4.00000			0.800000
$26$	−2.00000			−0.392232
$27$		−	5.19615i		−	1.00000i
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	−1.00000			−0.185695			−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000			−0.185695			−0.0928477	+	0.995680i	$0.529597\pi$
$30$	−4.50000	+	2.59808i	−0.821584	+	0.474342i
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	−0.968709	−	0.248199i	$-0.920161\pi$
$31$	−1.50000	+	2.59808i	−0.269408	+	0.466628i	0.699301	+	0.714827i	$0.253495\pi$
$32$	2.50000	+	4.33013i	0.441942	+	0.765466i
$33$			8.66025i			1.50756i
$34$	5.00000			0.857493
$35$	−1.50000	−	2.59808i	−0.253546	−	0.439155i
$36$	−1.50000	+	2.59808i	−0.250000	+	0.433013i
$37$	−6.00000			−0.986394			−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000			−0.986394			−0.493197	+	0.869918i	$0.664172\pi$
$38$	−3.50000	+	2.59808i	−0.567775	+	0.421464i
$39$			3.46410i			0.554700i
$40$	9.00000			1.42302
$41$	−9.00000			−1.40556			−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000			−1.40556			−0.702782	+	0.711405i	$0.748059\pi$
$42$	1.50000	+	0.866025i	0.231455	+	0.133631i
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$	2.50000	−	4.33013i	0.376889	−	0.652791i
$45$	4.50000	+	7.79423i	0.670820	+	1.16190i
$46$	8.00000			1.17954
$47$	3.00000			0.437595			0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000			0.437595			0.218797	+	0.975770i	$0.429787\pi$
$48$	−1.50000	+	0.866025i	−0.216506	+	0.125000i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$		−	8.66025i		−	1.21268i
$52$	1.00000	−	1.73205i	0.138675	−	0.240192i
$53$	0.500000	−	0.866025i	0.0686803	−	0.118958i	−0.829640	−	0.558298i	$-0.811454\pi$
$53$	0.500000	−	0.866025i	0.0686803	−	0.118958i	0.898321	+	0.439340i	$0.144788\pi$
$54$	−4.50000	−	2.59808i	−0.612372	−	0.353553i
$55$	−7.50000	−	12.9904i	−1.01130	−	1.75162i
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$	4.50000	+	6.06218i	0.596040	+	0.802955i
$58$	−0.500000	+	0.866025i	−0.0656532	+	0.113715i
$59$	5.00000			0.650945			0.325472	−	0.945552i	$-0.394477\pi$
$59$	5.00000			0.650945			0.325472	+	0.945552i	$0.394477\pi$
$60$		−	5.19615i		−	0.670820i
$61$	−13.0000			−1.66448			−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−13.0000			−1.66448			−0.832240	+	0.554416i	$0.812942\pi$
$62$	1.50000	+	2.59808i	0.190500	+	0.329956i
$63$	1.50000	−	2.59808i	0.188982	−	0.327327i
$64$	7.00000			0.875000
$65$	−3.00000	−	5.19615i	−0.372104	−	0.644503i
$66$	7.50000	+	4.33013i	0.923186	+	0.533002i
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	−2.50000	+	4.33013i	−0.303170	+	0.525105i
$69$		−	13.8564i		−	1.66812i
$70$	−3.00000			−0.358569
$71$	−1.50000	−	2.59808i	−0.178017	−	0.308335i	0.763184	−	0.646181i	$-0.223635\pi$
$71$	−1.50000	−	2.59808i	−0.178017	−	0.308335i	−0.941201	+	0.337846i	$0.890302\pi$
$72$	4.50000	+	7.79423i	0.530330	+	0.918559i
$73$	2.50000	+	4.33013i	0.292603	+	0.506803i	0.974424	−	0.224716i	$-0.0721453\pi$
$73$	2.50000	+	4.33013i	0.292603	+	0.506803i	−0.681822	+	0.731519i	$0.738812\pi$
$74$	−3.00000	+	5.19615i	−0.348743	+	0.604040i
$75$	−6.00000	−	3.46410i	−0.692820	−	0.400000i
$76$	−0.500000	−	4.33013i	−0.0573539	−	0.496700i
$77$	−2.50000	+	4.33013i	−0.284901	+	0.493464i
$78$	3.00000	+	1.73205i	0.339683	+	0.196116i
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	0.731307	+	0.682048i	$0.238911\pi$
$80$	1.50000	−	2.59808i	0.167705	−	0.290474i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−4.50000	+	7.79423i	−0.496942	+	0.860729i
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	0.506036	−	0.862512i	$-0.331110\pi$
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	−0.999976	+	0.00698436i	$0.997777\pi$
$84$	−1.50000	+	0.866025i	−0.163663	+	0.0944911i
$85$	7.50000	+	12.9904i	0.813489	+	1.40900i
$86$	4.00000	+	6.92820i	0.431331	+	0.747087i
$87$	1.50000	+	0.866025i	0.160817	+	0.0928477i
$88$	−7.50000	−	12.9904i	−0.799503	−	1.38478i
$89$	4.50000	−	7.79423i	0.476999	−	0.826187i	−0.522654	−	0.852545i	$-0.675058\pi$
$89$	4.50000	−	7.79423i	0.476999	−	0.826187i	0.999653	+	0.0263586i	$0.00839118\pi$
$90$	9.00000			0.948683
$91$	−1.00000	+	1.73205i	−0.104828	+	0.181568i
$92$	−4.00000	+	6.92820i	−0.417029	+	0.722315i
$93$	4.50000	−	2.59808i	0.466628	−	0.269408i
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$	−12.0000	−	5.19615i	−1.23117	−	0.533114i
$96$		−	8.66025i		−	0.883883i
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	−0.492287	−	0.870433i	$-0.663839\pi$
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	0.999961	−	0.00888289i	$-0.00282755\pi$
$98$	−3.00000	−	5.19615i	−0.303046	−	0.524891i
$99$	7.50000	−	12.9904i	0.753778	−	1.30558i
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	7.00000			0.696526			0.348263	−	0.937397i	$-0.386772\pi$
$101$	7.00000			0.696526			0.348263	+	0.937397i	$0.386772\pi$
$102$	−7.50000	−	4.33013i	−0.742611	−	0.428746i
$103$	2.50000	−	4.33013i	0.246332	−	0.426660i	−0.716173	−	0.697923i	$-0.754108\pi$
$103$	2.50000	−	4.33013i	0.246332	−	0.426660i	0.962505	+	0.271263i	$0.0874412\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$			5.19615i			0.507093i
$106$	−0.500000	−	0.866025i	−0.0485643	−	0.0841158i
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$	4.50000	−	2.59808i	0.433013	−	0.250000i
$109$	2.50000	+	4.33013i	0.239457	+	0.414751i	0.960558	−	0.278078i	$-0.0896974\pi$
$109$	2.50000	+	4.33013i	0.239457	+	0.414751i	−0.721102	+	0.692829i	$0.756364\pi$
$110$	−15.0000			−1.43019
$111$	9.00000	+	5.19615i	0.854242	+	0.493197i
$112$	−1.00000			−0.0944911
$113$	8.50000	−	14.7224i	0.799613	−	1.38497i	−0.120256	−	0.992743i	$-0.538371\pi$
$113$	8.50000	−	14.7224i	0.799613	−	1.38497i	0.919868	−	0.392227i	$-0.128295\pi$
$114$	7.50000	−	0.866025i	0.702439	−	0.0811107i
$115$	12.0000	+	20.7846i	1.11901	+	1.93817i
$116$	−0.500000	−	0.866025i	−0.0464238	−	0.0804084i
$117$	3.00000	−	5.19615i	0.277350	−	0.480384i
$118$	2.50000	−	4.33013i	0.230144	−	0.398621i
$119$	2.50000	−	4.33013i	0.229175	−	0.396942i
$120$	−13.5000	−	7.79423i	−1.23238	−	0.711512i
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$	−6.50000	+	11.2583i	−0.588482	+	1.01928i
$123$	13.5000	+	7.79423i	1.21725	+	0.702782i
$124$	−3.00000			−0.269408
$125$	−3.00000			−0.268328
$126$	−1.50000	−	2.59808i	−0.133631	−	0.231455i
$127$	−6.50000	+	11.2583i	−0.576782	+	0.999015i	0.419064	+	0.907957i	$0.362358\pi$
$127$	−6.50000	+	11.2583i	−0.576782	+	0.999015i	−0.995846	+	0.0910585i	$0.970975\pi$
$128$	−1.50000	+	2.59808i	−0.132583	+	0.229640i
$129$	12.0000	−	6.92820i	1.05654	−	0.609994i
$130$	−6.00000			−0.526235
$131$	−7.00000			−0.611593			−0.305796	−	0.952097i	$-0.598923\pi$
$131$	−7.00000			−0.611593			−0.305796	+	0.952097i	$0.598923\pi$
$132$	−7.50000	+	4.33013i	−0.652791	+	0.376889i
$133$	0.500000	+	4.33013i	0.0433555	+	0.375470i
$134$	4.00000			0.345547
$135$		−	15.5885i		−	1.34164i
$136$	7.50000	+	12.9904i	0.643120	+	1.11392i
$137$	3.00000			0.256307			0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000			0.256307			0.128154	+	0.991754i	$0.459095\pi$
$138$	−12.0000	−	6.92820i	−1.02151	−	0.589768i
$139$	−10.0000	−	17.3205i	−0.848189	−	1.46911i	−0.882823	−	0.469706i	$-0.844360\pi$
$139$	−10.0000	−	17.3205i	−0.848189	−	1.46911i	0.0346338	−	0.999400i	$-0.488974\pi$
$140$	1.50000	−	2.59808i	0.126773	−	0.219578i
$141$	−4.50000	−	2.59808i	−0.378968	−	0.218797i
$142$	−3.00000			−0.251754
$143$	−5.00000	+	8.66025i	−0.418121	+	0.724207i
$144$	3.00000			0.250000
$145$	−3.00000			−0.249136
$146$	5.00000			0.413803
$147$	−9.00000	+	5.19615i	−0.742307	+	0.428571i
$148$	−3.00000	−	5.19615i	−0.246598	−	0.427121i
$149$	15.0000			1.22885			0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000			1.22885			0.614424	+	0.788976i	$0.289388\pi$
$150$	−6.00000	+	3.46410i	−0.489898	+	0.282843i
$151$	7.50000	+	12.9904i	0.610341	+	1.05714i	0.991183	+	0.132502i	$0.0423010\pi$
$151$	7.50000	+	12.9904i	0.610341	+	1.05714i	−0.380841	+	0.924640i	$0.624366\pi$
$152$	−12.0000	−	5.19615i	−0.973329	−	0.421464i
$153$	−7.50000	+	12.9904i	−0.606339	+	1.05021i
$154$	2.50000	+	4.33013i	0.201456	+	0.348932i
$155$	−4.50000	+	7.79423i	−0.361449	+	0.626048i
$156$	−3.00000	+	1.73205i	−0.240192	+	0.138675i
$157$	3.00000			0.239426			0.119713	−	0.992809i	$-0.461803\pi$
$157$	3.00000			0.239426			0.119713	+	0.992809i	$0.461803\pi$
$158$	2.00000	+	3.46410i	0.159111	+	0.275589i
$159$	−1.50000	+	0.866025i	−0.118958	+	0.0686803i
$160$	7.50000	+	12.9904i	0.592927	+	1.02698i
$161$	4.00000	−	6.92820i	0.315244	−	0.546019i
$162$	4.50000	+	7.79423i	0.353553	+	0.612372i
$163$	12.0000			0.939913			0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000			0.939913			0.469956	+	0.882690i	$0.344270\pi$
$164$	−4.50000	−	7.79423i	−0.351391	−	0.608627i
$165$			25.9808i			2.02260i
$166$	−9.00000			−0.698535
$167$	2.00000	+	3.46410i	0.154765	+	0.268060i	0.932973	−	0.359946i	$-0.117205\pi$
$167$	2.00000	+	3.46410i	0.154765	+	0.268060i	−0.778209	+	0.628006i	$0.783871\pi$
$168$			5.19615i			0.400892i
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	15.0000			1.15045
$171$	−1.50000	−	12.9904i	−0.114708	−	0.993399i
$172$	−8.00000			−0.609994
$173$	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	$0.0934200\pi$
$174$	1.50000	−	0.866025i	0.113715	−	0.0656532i
$175$	−2.00000	−	3.46410i	−0.151186	−	0.261861i
$176$	−5.00000			−0.376889
$177$	−7.50000	−	4.33013i	−0.563735	−	0.325472i
$178$	−4.50000	−	7.79423i	−0.337289	−	0.584202i
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	−4.50000	+	7.79423i	−0.335410	+	0.580948i
$181$	−3.50000	+	6.06218i	−0.260153	+	0.450598i	−0.966282	−	0.257485i	$-0.917106\pi$
$181$	−3.50000	+	6.06218i	−0.260153	+	0.450598i	0.706129	+	0.708083i	$0.250440\pi$
$182$	1.00000	+	1.73205i	0.0741249	+	0.128388i
$183$	19.5000	+	11.2583i	1.44148	+	0.832240i
$184$	12.0000	+	20.7846i	0.884652	+	1.53226i
$185$	−18.0000			−1.32339
$186$		−	5.19615i		−	0.381000i
$187$	12.5000	−	21.6506i	0.914091	−	1.58325i
$188$	1.50000	+	2.59808i	0.109399	+	0.189484i
$189$	−4.50000	+	2.59808i	−0.327327	+	0.188982i
$190$	−10.5000	+	7.79423i	−0.761750	+	0.565453i
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	0.915177	−	0.403051i	$-0.132050\pi$
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	−0.806641	+	0.591041i	$0.798717\pi$
$192$	−10.5000	−	6.06218i	−0.757772	−	0.437500i
$193$	−17.0000			−1.22369			−0.611843	−	0.790979i	$-0.709572\pi$
$193$	−17.0000			−1.22369			−0.611843	+	0.790979i	$0.709572\pi$
$194$	−5.00000	−	8.66025i	−0.358979	−	0.621770i
$195$			10.3923i			0.744208i
$196$	6.00000			0.428571
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$	−7.50000	−	12.9904i	−0.533002	−	0.923186i
$199$	1.50000	−	2.59808i	0.106332	−	0.184173i	−0.807950	−	0.589252i	$-0.799423\pi$
$199$	1.50000	−	2.59808i	0.106332	−	0.184173i	0.914282	+	0.405079i	$0.132756\pi$
$200$	12.0000			0.848528
$201$		−	6.92820i		−	0.488678i
$202$	3.50000	−	6.06218i	0.246259	−	0.426533i
$203$	0.500000	+	0.866025i	0.0350931	+	0.0607831i
$204$	7.50000	−	4.33013i	0.525105	−	0.303170i
$205$	−27.0000			−1.88576
$206$	−2.50000	−	4.33013i	−0.174183	−	0.301694i
$207$	−12.0000	+	20.7846i	−0.834058	+	1.44463i
$208$	−2.00000			−0.138675
$209$	2.50000	+	21.6506i	0.172929	+	1.49761i
$210$	4.50000	+	2.59808i	0.310530	+	0.179284i
$211$	−15.0000			−1.03264			−0.516321	−	0.856395i	$-0.672699\pi$
$211$	−15.0000			−1.03264			−0.516321	+	0.856395i	$0.672699\pi$
$212$	1.00000			0.0686803
$213$			5.19615i			0.356034i
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$	−12.0000	+	20.7846i	−0.818393	+	1.41750i
$216$		−	15.5885i		−	1.06066i
$217$	3.00000			0.203653
$218$	5.00000			0.338643
$219$		−	8.66025i		−	0.585206i
$220$	7.50000	−	12.9904i	0.505650	−	0.875811i
$221$	5.00000	−	8.66025i	0.336336	−	0.582552i
$222$	9.00000	−	5.19615i	0.604040	−	0.348743i
$223$	12.0000	−	20.7846i	0.803579	−	1.39184i	−0.113666	−	0.993519i	$-0.536260\pi$
$223$	12.0000	−	20.7846i	0.803579	−	1.39184i	0.917246	−	0.398321i	$-0.130407\pi$
$224$	2.50000	−	4.33013i	0.167038	−	0.289319i
$225$	6.00000	+	10.3923i	0.400000	+	0.692820i
$226$	−8.50000	−	14.7224i	−0.565412	−	0.979322i
$227$	−10.5000	−	18.1865i	−0.696909	−	1.20708i	−0.969533	−	0.244962i	$-0.921225\pi$
$227$	−10.5000	−	18.1865i	−0.696909	−	1.20708i	0.272623	−	0.962121i	$-0.412109\pi$
$228$	−3.00000	+	6.92820i	−0.198680	+	0.458831i
$229$	8.50000	−	14.7224i	0.561696	−	0.972886i	−0.435653	−	0.900115i	$-0.643482\pi$
$229$	8.50000	−	14.7224i	0.561696	−	0.972886i	0.997349	−	0.0727709i	$-0.0231842\pi$
$230$	24.0000			1.58251
$231$	7.50000	−	4.33013i	0.493464	−	0.284901i
$232$	−3.00000			−0.196960
$233$	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	$0.738079\pi$
$234$	−3.00000	−	5.19615i	−0.196116	−	0.339683i
$235$	9.00000			0.587095
$236$	2.50000	+	4.33013i	0.162736	+	0.281867i
$237$	6.00000	−	3.46410i	0.389742	−	0.225018i
$238$	−2.50000	−	4.33013i	−0.162051	−	0.280680i
$239$	−7.50000	+	12.9904i	−0.485135	+	0.840278i	−0.999854	−	0.0170808i	$-0.994563\pi$
$239$	−7.50000	+	12.9904i	−0.485135	+	0.840278i	0.514719	+	0.857359i	$0.327896\pi$
$240$	−4.50000	+	2.59808i	−0.290474	+	0.167705i
$241$	−1.00000			−0.0644157			−0.0322078	−	0.999481i	$-0.510254\pi$
$241$	−1.00000			−0.0644157			−0.0322078	+	0.999481i	$0.510254\pi$
$242$	7.00000	+	12.1244i	0.449977	+	0.779383i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	−6.50000	−	11.2583i	−0.416120	−	0.720741i
$245$	9.00000	−	15.5885i	0.574989	−	0.995910i
$246$	13.5000	−	7.79423i	0.860729	−	0.496942i
$247$	1.00000	+	8.66025i	0.0636285	+	0.551039i
$248$	−4.50000	+	7.79423i	−0.285750	+	0.494934i
$249$			15.5885i			0.987878i
$250$	−1.50000	+	2.59808i	−0.0948683	+	0.164317i
$251$	−2.50000	+	4.33013i	−0.157799	+	0.273315i	−0.934075	−	0.357078i	$-0.883773\pi$
$251$	−2.50000	+	4.33013i	−0.157799	+	0.273315i	0.776276	+	0.630393i	$0.217106\pi$
$252$	3.00000			0.188982
$253$	20.0000	−	34.6410i	1.25739	−	2.17786i
$254$	6.50000	+	11.2583i	0.407846	+	0.706410i
$255$		−	25.9808i		−	1.62698i
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	5.00000	+	8.66025i	0.311891	+	0.540212i	0.978772	−	0.204953i	$-0.0657041\pi$
$257$	5.00000	+	8.66025i	0.311891	+	0.540212i	−0.666880	+	0.745165i	$0.732371\pi$
$258$		−	13.8564i		−	0.862662i
$259$	3.00000	+	5.19615i	0.186411	+	0.322873i
$260$	3.00000	−	5.19615i	0.186052	−	0.322252i
$261$	−1.50000	−	2.59808i	−0.0928477	−	0.160817i
$262$	−3.50000	+	6.06218i	−0.216231	+	0.374523i
$263$	4.00000	−	6.92820i	0.246651	−	0.427211i	−0.715944	−	0.698158i	$-0.754003\pi$
$263$	4.00000	−	6.92820i	0.246651	−	0.427211i	0.962594	+	0.270947i	$0.0873367\pi$
$264$			25.9808i			1.59901i
$265$	1.50000	−	2.59808i	0.0921443	−	0.159599i
$266$	4.00000	+	1.73205i	0.245256	+	0.106199i
$267$	−13.5000	+	7.79423i	−0.826187	+	0.476999i
$268$	−2.00000	+	3.46410i	−0.122169	+	0.211604i
$269$	12.5000	+	21.6506i	0.762138	+	1.32006i	0.941746	+	0.336324i	$0.109184\pi$
$269$	12.5000	+	21.6506i	0.762138	+	1.32006i	−0.179608	+	0.983738i	$0.557483\pi$
$270$	−13.5000	−	7.79423i	−0.821584	−	0.474342i
$271$	−13.5000	−	23.3827i	−0.820067	−	1.42040i	−0.905632	−	0.424064i	$-0.860603\pi$
$271$	−13.5000	−	23.3827i	−0.820067	−	1.42040i	0.0855654	−	0.996333i	$-0.472730\pi$
$272$	5.00000			0.303170
$273$	3.00000	−	1.73205i	0.181568	−	0.104828i
$274$	1.50000	−	2.59808i	0.0906183	−	0.156956i
$275$	−10.0000	−	17.3205i	−0.603023	−	1.04447i
$276$	12.0000	−	6.92820i	0.722315	−	0.417029i
$277$	−3.50000	−	6.06218i	−0.210295	−	0.364241i	0.741512	−	0.670940i	$-0.234109\pi$
$277$	−3.50000	−	6.06218i	−0.210295	−	0.364241i	−0.951807	+	0.306699i	$0.900776\pi$
$278$	−20.0000			−1.19952
$279$	−9.00000			−0.538816
$280$	−4.50000	−	7.79423i	−0.268926	−	0.465794i
$281$	11.0000			0.656205			0.328102	−	0.944642i	$-0.393591\pi$
$281$	11.0000			0.656205			0.328102	+	0.944642i	$0.393591\pi$
$282$	−4.50000	+	2.59808i	−0.267971	+	0.154713i
$283$	29.0000			1.72387			0.861936	−	0.507018i	$-0.169252\pi$
$283$	29.0000			1.72387			0.861936	+	0.507018i	$0.169252\pi$
$284$	1.50000	−	2.59808i	0.0890086	−	0.154167i
$285$	13.5000	+	18.1865i	0.799671	+	1.07728i
$286$	5.00000	+	8.66025i	0.295656	+	0.512092i
$287$	4.50000	+	7.79423i	0.265627	+	0.460079i
$288$	−7.50000	+	12.9904i	−0.441942	+	0.765466i
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$	−1.50000	+	2.59808i	−0.0880830	+	0.152564i
$291$	−15.0000	+	8.66025i	−0.879316	+	0.507673i
$292$	−2.50000	+	4.33013i	−0.146301	+	0.253402i
$293$	2.50000	−	4.33013i	0.146052	−	0.252969i	−0.783713	−	0.621123i	$-0.786677\pi$
$293$	2.50000	−	4.33013i	0.146052	−	0.252969i	0.929765	+	0.368154i	$0.120010\pi$
$294$			10.3923i			0.606092i
$295$	15.0000			0.873334
$296$	−18.0000			−1.04623
$297$	−22.5000	+	12.9904i	−1.30558	+	0.753778i
$298$	7.50000	−	12.9904i	0.434463	−	0.752513i
$299$	8.00000	−	13.8564i	0.462652	−	0.801337i
$300$		−	6.92820i		−	0.400000i
$301$	8.00000			0.461112
$302$	15.0000			0.863153
$303$	−10.5000	−	6.06218i	−0.603209	−	0.348263i
$304$	−3.50000	+	2.59808i	−0.200739	+	0.149010i
$305$	−39.0000			−2.23313
$306$	7.50000	+	12.9904i	0.428746	+	0.742611i
$307$	16.5000	+	28.5788i	0.941705	+	1.63108i	0.762218	+	0.647320i	$0.224110\pi$
$307$	16.5000	+	28.5788i	0.941705	+	1.63108i	0.179486	+	0.983760i	$0.442556\pi$
$308$	−5.00000			−0.284901
$309$	−7.50000	+	4.33013i	−0.426660	+	0.246332i
$310$	4.50000	+	7.79423i	0.255583	+	0.442682i
$311$	10.5000	−	18.1865i	0.595400	−	1.03126i	−0.398090	−	0.917346i	$-0.630327\pi$
$311$	10.5000	−	18.1865i	0.595400	−	1.03126i	0.993490	−	0.113917i	$-0.0363399\pi$
$312$			10.3923i			0.588348i
$313$	−17.0000			−0.960897			−0.480448	−	0.877023i	$-0.659526\pi$
$313$	−17.0000			−0.960897			−0.480448	+	0.877023i	$0.659526\pi$
$314$	1.50000	−	2.59808i	0.0846499	−	0.146618i
$315$	4.50000	−	7.79423i	0.253546	−	0.439155i
$316$	−4.00000			−0.225018
$317$	−17.0000			−0.954815			−0.477408	−	0.878682i	$-0.658423\pi$
$317$	−17.0000			−0.954815			−0.477408	+	0.878682i	$0.658423\pi$
$318$			1.73205i			0.0971286i
$319$	2.50000	+	4.33013i	0.139973	+	0.242441i
$320$	21.0000			1.17394
$321$	−18.0000	−	10.3923i	−1.00466	−	0.580042i
$322$	−4.00000	−	6.92820i	−0.222911	−	0.386094i
$323$	−2.50000	−	21.6506i	−0.139104	−	1.20467i
$324$	−9.00000			−0.500000
$325$	−4.00000	−	6.92820i	−0.221880	−	0.384308i
$326$	6.00000	−	10.3923i	0.332309	−	0.575577i
$327$		−	8.66025i		−	0.478913i
$328$	−27.0000			−1.49083
$329$	−1.50000	−	2.59808i	−0.0826977	−	0.143237i
$330$	22.5000	+	12.9904i	1.23858	+	0.715097i
$331$	9.50000	+	16.4545i	0.522167	+	0.904420i	0.999667	+	0.0257885i	$0.00820965\pi$
$331$	9.50000	+	16.4545i	0.522167	+	0.904420i	−0.477500	+	0.878632i	$0.658457\pi$
$332$	4.50000	−	7.79423i	0.246970	−	0.427764i
$333$	−9.00000	−	15.5885i	−0.493197	−	0.854242i
$334$	4.00000			0.218870
$335$	6.00000	+	10.3923i	0.327815	+	0.567792i
$336$	1.50000	+	0.866025i	0.0818317	+	0.0472456i
$337$	−5.00000			−0.272367			−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000			−0.272367			−0.136184	+	0.990684i	$0.543484\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$	−25.5000	+	14.7224i	−1.38497	+	0.799613i
$340$	−7.50000	+	12.9904i	−0.406745	+	0.704502i
$341$	15.0000			0.812296
$342$	−12.0000	−	5.19615i	−0.648886	−	0.280976i
$343$	−13.0000			−0.701934
$344$	−12.0000	+	20.7846i	−0.646997	+	1.12063i
$345$		−	41.5692i		−	2.23801i
$346$	−3.00000	−	5.19615i	−0.161281	−	0.279347i
$347$	1.00000			0.0536828			0.0268414	−	0.999640i	$-0.491455\pi$
$347$	1.00000			0.0536828			0.0268414	+	0.999640i	$0.491455\pi$
$348$			1.73205i			0.0928477i
$349$	−7.50000	−	12.9904i	−0.401466	−	0.695359i	0.592437	−	0.805617i	$-0.298166\pi$
$349$	−7.50000	−	12.9904i	−0.401466	−	0.695359i	−0.993903	+	0.110257i	$0.964832\pi$
$350$	−4.00000			−0.213809
$351$	−9.00000	+	5.19615i	−0.480384	+	0.277350i
$352$	12.5000	−	21.6506i	0.666252	−	1.15398i
$353$	18.5000	+	32.0429i	0.984656	+	1.70547i	0.643457	+	0.765482i	$0.277500\pi$
$353$	18.5000	+	32.0429i	0.984656	+	1.70547i	0.341199	+	0.939991i	$0.389167\pi$
$354$	−7.50000	+	4.33013i	−0.398621	+	0.230144i
$355$	−4.50000	−	7.79423i	−0.238835	−	0.413675i
$356$	9.00000			0.476999
$357$	−7.50000	+	4.33013i	−0.396942	+	0.229175i
$358$	−6.00000	+	10.3923i	−0.317110	+	0.549250i
$359$	6.50000	+	11.2583i	0.343057	+	0.594192i	0.984999	−	0.172561i	$-0.0552043\pi$
$359$	6.50000	+	11.2583i	0.343057	+	0.594192i	−0.641942	+	0.766753i	$0.721871\pi$
$360$	13.5000	+	23.3827i	0.711512	+	1.23238i
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$	3.50000	+	6.06218i	0.183956	+	0.318621i
$363$	21.0000	−	12.1244i	1.10221	−	0.636364i
$364$	−2.00000			−0.104828
$365$	7.50000	+	12.9904i	0.392568	+	0.679948i
$366$	19.5000	−	11.2583i	1.01928	−	0.588482i
$367$	−5.00000			−0.260998			−0.130499	−	0.991448i	$-0.541658\pi$
$367$	−5.00000			−0.260998			−0.130499	+	0.991448i	$0.541658\pi$
$368$	8.00000			0.417029
$369$	−13.5000	−	23.3827i	−0.702782	−	1.21725i
$370$	−9.00000	+	15.5885i	−0.467888	+	0.810405i
$371$	−1.00000			−0.0519174
$372$	4.50000	+	2.59808i	0.233314	+	0.134704i
$373$	2.50000	−	4.33013i	0.129445	−	0.224205i	−0.794017	−	0.607896i	$-0.792014\pi$
$373$	2.50000	−	4.33013i	0.129445	−	0.224205i	0.923462	+	0.383691i	$0.125347\pi$
$374$	−12.5000	−	21.6506i	−0.646360	−	1.11953i
$375$	4.50000	+	2.59808i	0.232379	+	0.134164i
$376$	9.00000			0.464140
$377$	1.00000	+	1.73205i	0.0515026	+	0.0892052i
$378$			5.19615i			0.267261i
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	−1.50000	−	12.9904i	−0.0769484	−	0.666392i
$381$	19.5000	−	11.2583i	0.999015	−	0.576782i
$382$	3.00000			0.153493
$383$	−23.0000			−1.17525			−0.587623	−	0.809135i	$-0.699936\pi$
$383$	−23.0000			−1.17525			−0.587623	+	0.809135i	$0.699936\pi$
$384$	4.50000	−	2.59808i	0.229640	−	0.132583i
$385$	−7.50000	+	12.9904i	−0.382235	+	0.662051i
$386$	−8.50000	+	14.7224i	−0.432639	+	0.749352i
$387$	−24.0000			−1.21999
$388$	10.0000			0.507673
$389$	3.00000			0.152106			0.0760530	−	0.997104i	$-0.475768\pi$
$389$	3.00000			0.152106			0.0760530	+	0.997104i	$0.475768\pi$
$390$	9.00000	+	5.19615i	0.455733	+	0.263117i
$391$	−20.0000	+	34.6410i	−1.01144	+	1.75187i
$392$	9.00000	−	15.5885i	0.454569	−	0.787336i
$393$	10.5000	+	6.06218i	0.529655	+	0.305796i
$394$	1.00000	−	1.73205i	0.0503793	−	0.0872595i
$395$	−6.00000	+	10.3923i	−0.301893	+	0.522894i
$396$	15.0000			0.753778
$397$	−3.50000	−	6.06218i	−0.175660	−	0.304252i	0.764730	−	0.644351i	$-0.222873\pi$
$397$	−3.50000	−	6.06218i	−0.175660	−	0.304252i	−0.940389	+	0.340099i	$0.889539\pi$
$398$	−1.50000	−	2.59808i	−0.0751882	−	0.130230i
$399$	3.00000	−	6.92820i	0.150188	−	0.346844i
$400$	2.00000	−	3.46410i	0.100000	−	0.173205i
$401$	−33.0000			−1.64794			−0.823971	−	0.566632i	$-0.808246\pi$
$401$	−33.0000			−1.64794			−0.823971	+	0.566632i	$0.808246\pi$
$402$	−6.00000	−	3.46410i	−0.299253	−	0.172774i
$403$	6.00000			0.298881
$404$	3.50000	+	6.06218i	0.174132	+	0.301605i
$405$	−13.5000	+	23.3827i	−0.670820	+	1.16190i
$406$	1.00000			0.0496292
$407$	15.0000	+	25.9808i	0.743522	+	1.28782i
$408$		−	25.9808i		−	1.28624i
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	0.715523	−	0.698589i	$-0.246188\pi$
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	−0.962757	+	0.270367i	$0.912855\pi$
$410$	−13.5000	+	23.3827i	−0.666717	+	1.15479i
$411$	−4.50000	−	2.59808i	−0.221969	−	0.128154i
$412$	5.00000			0.246332
$413$	−2.50000	−	4.33013i	−0.123017	−	0.213072i
$414$	12.0000	+	20.7846i	0.589768	+	1.02151i
$415$	−13.5000	−	23.3827i	−0.662689	−	1.14781i
$416$	5.00000	−	8.66025i	0.245145	−	0.424604i
$417$			34.6410i			1.69638i
$418$	20.0000	+	8.66025i	0.978232	+	0.423587i
$419$	0.500000	−	0.866025i	0.0244266	−	0.0423081i	−0.853554	−	0.521005i	$-0.825557\pi$
$419$	0.500000	−	0.866025i	0.0244266	−	0.0423081i	0.877980	+	0.478697i	$0.158891\pi$
$420$	−4.50000	+	2.59808i	−0.219578	+	0.126773i
$421$	−13.0000	+	22.5167i	−0.633581	+	1.09739i	0.353233	+	0.935536i	$0.385082\pi$
$421$	−13.0000	+	22.5167i	−0.633581	+	1.09739i	−0.986814	+	0.161859i	$0.948251\pi$
$422$	−7.50000	+	12.9904i	−0.365094	+	0.632362i
$423$	4.50000	+	7.79423i	0.218797	+	0.378968i
$424$	1.50000	−	2.59808i	0.0728464	−	0.126174i
$425$	10.0000	+	17.3205i	0.485071	+	0.840168i
$426$	4.50000	+	2.59808i	0.218026	+	0.125877i
$427$	6.50000	+	11.2583i	0.314557	+	0.544829i
$428$	6.00000	+	10.3923i	0.290021	+	0.502331i
$429$	15.0000	−	8.66025i	0.724207	−	0.418121i
$430$	12.0000	+	20.7846i	0.578691	+	1.00232i
$431$	−0.500000	+	0.866025i	−0.0240842	+	0.0417150i	−0.877816	−	0.478997i	$-0.841000\pi$
$431$	−0.500000	+	0.866025i	−0.0240842	+	0.0417150i	0.853732	+	0.520712i	$0.174334\pi$
$432$	−4.50000	−	2.59808i	−0.216506	−	0.125000i
$433$	−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	$0.941951\pi$
$434$	1.50000	−	2.59808i	0.0720023	−	0.124712i
$435$	4.50000	+	2.59808i	0.215758	+	0.124568i
$436$	−2.50000	+	4.33013i	−0.119728	+	0.207375i
$437$	−4.00000	−	34.6410i	−0.191346	−	1.65710i
$438$	−7.50000	−	4.33013i	−0.358364	−	0.206901i
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	−0.609503	−	0.792784i	$-0.708631\pi$
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	0.991322	+	0.131453i	$0.0419644\pi$
$440$	−22.5000	−	38.9711i	−1.07265	−	1.85788i
$441$	18.0000			0.857143
$442$	−5.00000	−	8.66025i	−0.237826	−	0.411926i
$443$	−25.0000			−1.18779			−0.593893	−	0.804544i	$-0.702410\pi$
$443$	−25.0000			−1.18779			−0.593893	+	0.804544i	$0.702410\pi$
$444$			10.3923i			0.493197i
$445$	13.5000	−	23.3827i	0.639961	−	1.10845i
$446$	−12.0000	−	20.7846i	−0.568216	−	0.984180i
$447$	−22.5000	−	12.9904i	−1.06421	−	0.614424i
$448$	−3.50000	−	6.06218i	−0.165359	−	0.286411i
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$	12.0000			0.565685
$451$	22.5000	+	38.9711i	1.05948	+	1.83508i
$452$	17.0000			0.799613
$453$		−	25.9808i		−	1.22068i
$454$	−21.0000			−0.985579
$455$	−3.00000	+	5.19615i	−0.140642	+	0.243599i
$456$	13.5000	+	18.1865i	0.632195	+	0.851662i
$457$	−9.50000	−	16.4545i	−0.444391	−	0.769708i	0.553618	−	0.832771i	$-0.313247\pi$
$457$	−9.50000	−	16.4545i	−0.444391	−	0.769708i	−0.998010	+	0.0630623i	$0.979913\pi$
$458$	−8.50000	−	14.7224i	−0.397179	−	0.687934i
$459$	22.5000	−	12.9904i	1.05021	−	0.606339i
$460$	−12.0000	+	20.7846i	−0.559503	+	0.969087i
$461$	15.0000	−	25.9808i	0.698620	−	1.21004i	−0.270326	−	0.962769i	$-0.587131\pi$
$461$	15.0000	−	25.9808i	0.698620	−	1.21004i	0.968945	−	0.247276i	$-0.0795353\pi$
$462$		−	8.66025i		−	0.402911i
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	−0.854173	−	0.519989i	$-0.825936\pi$
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	0.877410	+	0.479741i	$0.159269\pi$
$464$	−0.500000	+	0.866025i	−0.0232119	+	0.0402042i
$465$	13.5000	−	7.79423i	0.626048	−	0.361449i
$466$	9.00000			0.416917
$467$	8.00000			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$	6.00000			0.277350
$469$	2.00000	−	3.46410i	0.0923514	−	0.159957i
$470$	4.50000	−	7.79423i	0.207570	−	0.359521i
$471$	−4.50000	−	2.59808i	−0.207349	−	0.119713i
$472$	15.0000			0.690431
$473$	40.0000			1.83920
$474$		−	6.92820i		−	0.318223i
$475$	−16.0000	−	6.92820i	−0.734130	−	0.317888i
$476$	5.00000			0.229175
$477$	3.00000			0.137361
$478$	7.50000	+	12.9904i	0.343042	+	0.594166i
$479$	−5.00000			−0.228456			−0.114228	−	0.993455i	$-0.536439\pi$
$479$	−5.00000			−0.228456			−0.114228	+	0.993455i	$0.536439\pi$
$480$		−	25.9808i		−	1.18585i
$481$	6.00000	+	10.3923i	0.273576	+	0.473848i
$482$	−0.500000	+	0.866025i	−0.0227744	+	0.0394464i
$483$	−12.0000	+	6.92820i	−0.546019	+	0.315244i
$484$	−14.0000			−0.636364
$485$	15.0000	−	25.9808i	0.681115	−	1.17973i
$486$		−	15.5885i		−	0.707107i
$487$	32.0000			1.45006			0.725029	−	0.688718i	$-0.241826\pi$
$487$	32.0000			1.45006			0.725029	+	0.688718i	$0.241826\pi$
$488$	−39.0000			−1.76545
$489$	−18.0000	−	10.3923i	−0.813988	−	0.469956i
$490$	−9.00000	−	15.5885i	−0.406579	−	0.704215i
$491$	−27.0000			−1.21849			−0.609246	−	0.792981i	$-0.708528\pi$
$491$	−27.0000			−1.21849			−0.609246	+	0.792981i	$0.708528\pi$
$492$			15.5885i			0.702782i
$493$	−2.50000	−	4.33013i	−0.112594	−	0.195019i
$494$	8.00000	+	3.46410i	0.359937	+	0.155857i
$495$	22.5000	−	38.9711i	1.01130	−	1.75162i
$496$	1.50000	+	2.59808i	0.0673520	+	0.116657i
$497$	−1.50000	+	2.59808i	−0.0672842	+	0.116540i
$498$	13.5000	+	7.79423i	0.604949	+	0.349268i
$499$	29.0000			1.29822			0.649109	−	0.760695i	$-0.275142\pi$
$499$	29.0000			1.29822			0.649109	+	0.760695i	$0.275142\pi$
$500$	−1.50000	−	2.59808i	−0.0670820	−	0.116190i
$501$		−	6.92820i		−	0.309529i
$502$	2.50000	+	4.33013i	0.111580	+	0.193263i
$503$	−14.5000	+	25.1147i	−0.646523	+	1.11981i	0.337424	+	0.941353i	$0.390444\pi$
$503$	−14.5000	+	25.1147i	−0.646523	+	1.11981i	−0.983948	+	0.178458i	$0.942889\pi$
$504$	4.50000	−	7.79423i	0.200446	−	0.347183i
$505$	21.0000			0.934488
$506$	−20.0000	−	34.6410i	−0.889108	−	1.53998i
$507$	−13.5000	+	7.79423i	−0.599556	+	0.346154i
$508$	−13.0000			−0.576782
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	0.594675	−	0.803966i	$-0.297281\pi$
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	−0.993593	+	0.113020i	$0.963948\pi$
$510$	−22.5000	−	12.9904i	−0.996317	−	0.575224i
$511$	2.50000	−	4.33013i	0.110593	−	0.191554i
$512$	11.0000			0.486136
$513$	−9.00000	+	20.7846i	−0.397360	+	0.917663i
$514$	10.0000			0.441081
$515$	7.50000	−	12.9904i	0.330489	−	0.572425i
$516$	12.0000	+	6.92820i	0.528271	+	0.304997i
$517$	−7.50000	−	12.9904i	−0.329850	−	0.571316i
$518$	6.00000			0.263625
$519$	−9.00000	+	5.19615i	−0.395056	+	0.228086i
$520$	−9.00000	−	15.5885i	−0.394676	−	0.683599i
$521$	−42.0000			−1.84005			−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000			−1.84005			−0.920027	+	0.391856i	$0.871833\pi$
$522$	−3.00000			−0.131306
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	0.352677	+	0.935745i	$0.385272\pi$
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	−0.986718	+	0.162446i	$0.948062\pi$
$524$	−3.50000	−	6.06218i	−0.152898	−	0.264827i
$525$			6.92820i			0.302372i
$526$	−4.00000	−	6.92820i	−0.174408	−	0.302084i
$527$	−15.0000			−0.653410
$528$	7.50000	+	4.33013i	0.326396	+	0.188445i
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$	−1.50000	−	2.59808i	−0.0651558	−	0.112853i
$531$	7.50000	+	12.9904i	0.325472	+	0.563735i
$532$	−3.50000	+	2.59808i	−0.151744	+	0.112641i
$533$	9.00000	+	15.5885i	0.389833	+	0.675211i
$534$			15.5885i			0.674579i
$535$	36.0000			1.55642
$536$	6.00000	+	10.3923i	0.259161	+	0.448879i
$537$	18.0000	+	10.3923i	0.776757	+	0.448461i
$538$	25.0000			1.07783
$539$	−30.0000			−1.29219
$540$	13.5000	−	7.79423i	0.580948	−	0.335410i
$541$	−1.50000	+	2.59808i	−0.0644900	+	0.111700i	−0.896468	−	0.443109i	$-0.853875\pi$
$541$	−1.50000	+	2.59808i	−0.0644900	+	0.111700i	0.831978	+	0.554809i	$0.187209\pi$
$542$	−27.0000			−1.15975
$543$	10.5000	−	6.06218i	0.450598	−	0.260153i
$544$	−12.5000	+	21.6506i	−0.535933	+	0.928263i
$545$	7.50000	+	12.9904i	0.321265	+	0.556447i
$546$		−	3.46410i		−	0.148250i
$547$	−5.00000			−0.213785			−0.106892	−	0.994271i	$-0.534090\pi$
$547$	−5.00000			−0.213785			−0.106892	+	0.994271i	$0.534090\pi$
$548$	1.50000	+	2.59808i	0.0640768	+	0.110984i
$549$	−19.5000	−	33.7750i	−0.832240	−	1.44148i
$550$	−20.0000			−0.852803
$551$	4.00000	+	1.73205i	0.170406	+	0.0737878i
$552$		−	41.5692i		−	1.76930i
$553$	4.00000			0.170097
$554$	−7.00000			−0.297402
$555$	27.0000	+	15.5885i	1.14609	+	0.661693i
$556$	10.0000	−	17.3205i	0.424094	−	0.734553i
$557$	6.50000	−	11.2583i	0.275414	−	0.477031i	−0.694826	−	0.719178i	$-0.744518\pi$
$557$	6.50000	−	11.2583i	0.275414	−	0.477031i	0.970239	+	0.242147i	$0.0778518\pi$
$558$	−4.50000	+	7.79423i	−0.190500	+	0.329956i
$559$	16.0000			0.676728
$560$	−3.00000			−0.126773
$561$	−37.5000	+	21.6506i	−1.58325	+	0.914091i
$562$	5.50000	−	9.52628i	0.232003	−	0.401842i
$563$	−13.5000	+	23.3827i	−0.568957	+	0.985463i	0.427712	+	0.903915i	$0.359320\pi$
$563$	−13.5000	+	23.3827i	−0.568957	+	0.985463i	−0.996669	+	0.0815478i	$0.974014\pi$
$564$		−	5.19615i		−	0.218797i
$565$	25.5000	−	44.1673i	1.07279	−	1.85813i
$566$	14.5000	−	25.1147i	0.609480	−	1.05565i
$567$	9.00000			0.377964
$568$	−4.50000	−	7.79423i	−0.188816	−	0.327039i
$569$	4.50000	+	7.79423i	0.188650	+	0.326751i	0.944800	−	0.327647i	$-0.106256\pi$
$569$	4.50000	+	7.79423i	0.188650	+	0.326751i	−0.756151	+	0.654398i	$0.772922\pi$
$570$	22.5000	−	2.59808i	0.942421	−	0.108821i
$571$	10.5000	−	18.1865i	0.439411	−	0.761083i	−0.558233	−	0.829684i	$-0.688520\pi$
$571$	10.5000	−	18.1865i	0.439411	−	0.761083i	0.997644	+	0.0686016i	$0.0218537\pi$
$572$	−10.0000			−0.418121
$573$		−	5.19615i		−	0.217072i
$574$	9.00000			0.375653
$575$	16.0000	+	27.7128i	0.667246	+	1.15570i
$576$	10.5000	+	18.1865i	0.437500	+	0.757772i
$577$	−42.0000			−1.74848			−0.874241	−	0.485491i	$-0.838641\pi$
$577$	−42.0000			−1.74848			−0.874241	+	0.485491i	$0.838641\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$	25.5000	+	14.7224i	1.05974	+	0.611843i
$580$	−1.50000	−	2.59808i	−0.0622841	−	0.107879i
$581$	−4.50000	+	7.79423i	−0.186691	+	0.323359i
$582$			17.3205i			0.717958i
$583$	−5.00000			−0.207079
$584$	7.50000	+	12.9904i	0.310352	+	0.537546i
$585$	9.00000	−	15.5885i	0.372104	−	0.644503i
$586$	−2.50000	−	4.33013i	−0.103274	−	0.178876i
$587$	2.00000	−	3.46410i	0.0825488	−	0.142979i	−0.821795	−	0.569783i	$-0.807027\pi$
$587$	2.00000	−	3.46410i	0.0825488	−	0.142979i	0.904344	+	0.426804i	$0.140361\pi$
$588$	−9.00000	−	5.19615i	−0.371154	−	0.214286i
$589$	10.5000	−	7.79423i	0.432645	−	0.321156i
$590$	7.50000	−	12.9904i	0.308770	−	0.534806i
$591$	−3.00000	−	1.73205i	−0.123404	−	0.0712470i
$592$	−3.00000	+	5.19615i	−0.123299	+	0.213561i
$593$	4.50000	−	7.79423i	0.184793	−	0.320071i	−0.758714	−	0.651424i	$-0.774172\pi$
$593$	4.50000	−	7.79423i	0.184793	−	0.320071i	0.943507	+	0.331353i	$0.107505\pi$
$594$			25.9808i			1.06600i
$595$	7.50000	−	12.9904i	0.307470	−	0.532554i
$596$	7.50000	+	12.9904i	0.307212	+	0.532107i
$597$	−4.50000	+	2.59808i	−0.184173	+	0.106332i
$598$	−8.00000	−	13.8564i	−0.327144	−	0.566631i
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	0.962175	−	0.272433i	$-0.0878284\pi$
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	−0.717021	+	0.697051i	$0.754495\pi$
$600$	−18.0000	−	10.3923i	−0.734847	−	0.424264i
$601$	−1.50000	−	2.59808i	−0.0611863	−	0.105978i	0.833810	−	0.552052i	$-0.186155\pi$
$601$	−1.50000	−	2.59808i	−0.0611863	−	0.105978i	−0.894996	+	0.446074i	$0.852822\pi$
$602$	4.00000	−	6.92820i	0.163028	−	0.282372i
$603$	−6.00000	+	10.3923i	−0.244339	+	0.423207i
$604$	−7.50000	+	12.9904i	−0.305171	+	0.528571i
$605$	−21.0000	+	36.3731i	−0.853771	+	1.47878i
$606$	−10.5000	+	6.06218i	−0.426533	+	0.246259i
$607$	−11.5000	+	19.9186i	−0.466771	+	0.808470i	−0.999279	−	0.0379540i	$-0.987916\pi$
$607$	−11.5000	+	19.9186i	−0.466771	+	0.808470i	0.532509	+	0.846424i	$0.321249\pi$
$608$	−2.50000	−	21.6506i	−0.101388	−	0.878049i
$609$		−	1.73205i		−	0.0701862i
$610$	−19.5000	+	33.7750i	−0.789532	+	1.36751i
$611$	−3.00000	−	5.19615i	−0.121367	−	0.210214i
$612$	−15.0000			−0.606339
$613$	4.50000	+	7.79423i	0.181753	+	0.314806i	0.942478	−	0.334269i	$-0.108489\pi$
$613$	4.50000	+	7.79423i	0.181753	+	0.314806i	−0.760724	+	0.649075i	$0.775156\pi$
$614$	33.0000			1.33177
$615$	40.5000	+	23.3827i	1.63312	+	0.942881i
$616$	−7.50000	+	12.9904i	−0.302184	+	0.523397i
$617$	−15.0000	−	25.9808i	−0.603877	−	1.04595i	−0.992228	−	0.124434i	$-0.960288\pi$
$617$	−15.0000	−	25.9808i	−0.603877	−	1.04595i	0.388351	−	0.921512i	$-0.373045\pi$
$618$			8.66025i			0.348367i
$619$	5.50000	+	9.52628i	0.221064	+	0.382893i	0.955131	−	0.296183i	$-0.0957138\pi$
$619$	5.50000	+	9.52628i	0.221064	+	0.382893i	−0.734068	+	0.679076i	$0.762380\pi$
$620$	−9.00000			−0.361449
$621$	36.0000	−	20.7846i	1.44463	−	0.834058i
$622$	−10.5000	−	18.1865i	−0.421012	−	0.729214i
$623$	−9.00000			−0.360577
$624$	3.00000	+	1.73205i	0.120096	+	0.0693375i
$625$	−29.0000			−1.16000
$626$	−8.50000	+	14.7224i	−0.339728	+	0.588427i
$627$	15.0000	−	34.6410i	0.599042	−	1.38343i
$628$	1.50000	+	2.59808i	0.0598565	+	0.103675i
$629$	−15.0000	−	25.9808i	−0.598089	−	1.03592i
$630$	−4.50000	−	7.79423i	−0.179284	−	0.310530i
$631$	19.5000	−	33.7750i	0.776283	−	1.34456i	−0.157788	−	0.987473i	$-0.550436\pi$
$631$	19.5000	−	33.7750i	0.776283	−	1.34456i	0.934071	−	0.357088i	$-0.116230\pi$
$632$	−6.00000	+	10.3923i	−0.238667	+	0.413384i
$633$	22.5000	+	12.9904i	0.894295	+	0.516321i
$634$	−8.50000	+	14.7224i	−0.337578	+	0.584702i
$635$	−19.5000	+	33.7750i	−0.773834	+	1.34032i
$636$	−1.50000	−	0.866025i	−0.0594789	−	0.0343401i
$637$	−12.0000			−0.475457
$638$	5.00000			0.197952
$639$	4.50000	−	7.79423i	0.178017	−	0.308335i
$640$	−4.50000	+	7.79423i	−0.177878	+	0.308094i
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$	−18.0000	+	10.3923i	−0.710403	+	0.410152i
$643$	−7.00000			−0.276053			−0.138027	−	0.990429i	$-0.544076\pi$
$643$	−7.00000			−0.276053			−0.138027	+	0.990429i	$0.544076\pi$
$644$	8.00000			0.315244
$645$	36.0000	−	20.7846i	1.41750	−	0.818393i
$646$	−20.0000	−	8.66025i	−0.786889	−	0.340733i
$647$	48.0000			1.88707			0.943537	−	0.331266i	$-0.107476\pi$
$647$	48.0000			1.88707			0.943537	+	0.331266i	$0.107476\pi$
$648$	−13.5000	+	23.3827i	−0.530330	+	0.918559i
$649$	−12.5000	−	21.6506i	−0.490668	−	0.849862i
$650$	−8.00000			−0.313786
$651$	−4.50000	−	2.59808i	−0.176369	−	0.101827i
$652$	6.00000	+	10.3923i	0.234978	+	0.406994i
$653$	4.50000	−	7.79423i	0.176099	−	0.305012i	−0.764442	−	0.644692i	$-0.776986\pi$
$653$	4.50000	−	7.79423i	0.176099	−	0.305012i	0.940541	+	0.339680i	$0.110319\pi$
$654$	−7.50000	−	4.33013i	−0.293273	−	0.169321i
$655$	−21.0000			−0.820538
$656$	−4.50000	+	7.79423i	−0.175695	+	0.304314i
$657$	−7.50000	+	12.9904i	−0.292603	+	0.506803i
$658$	−3.00000			−0.116952
$659$	23.0000			0.895953			0.447976	−	0.894045i	$-0.352145\pi$
$659$	23.0000			0.895953			0.447976	+	0.894045i	$0.352145\pi$
$660$	−22.5000	+	12.9904i	−0.875811	+	0.505650i
$661$	15.0000	+	25.9808i	0.583432	+	1.01053i	0.995069	+	0.0991864i	$0.0316240\pi$
$661$	15.0000	+	25.9808i	0.583432	+	1.01053i	−0.411636	+	0.911348i	$0.635043\pi$
$662$	19.0000			0.738456
$663$	−15.0000	+	8.66025i	−0.582552	+	0.336336i
$664$	−13.5000	−	23.3827i	−0.523902	−	0.907424i
$665$	1.50000	+	12.9904i	0.0581675	+	0.503745i
$666$	−18.0000			−0.697486
$667$	−4.00000	−	6.92820i	−0.154881	−	0.268261i
$668$	−2.00000	+	3.46410i	−0.0773823	+	0.134030i
$669$	−36.0000	+	20.7846i	−1.39184	+	0.803579i
$670$	12.0000			0.463600
$671$	32.5000	+	56.2917i	1.25465	+	2.17312i
$672$	−7.50000	+	4.33013i	−0.289319	+	0.167038i
$673$	4.50000	+	7.79423i	0.173462	+	0.300445i	0.939628	−	0.342198i	$-0.111171\pi$
$673$	4.50000	+	7.79423i	0.173462	+	0.300445i	−0.766166	+	0.642643i	$0.777838\pi$
$674$	−2.50000	+	4.33013i	−0.0962964	+	0.166790i
$675$		−	20.7846i		−	0.800000i
$676$	9.00000			0.346154
$677$	18.5000	+	32.0429i	0.711013	+	1.23151i	0.964477	+	0.264166i	$0.0850965\pi$
$677$	18.5000	+	32.0429i	0.711013	+	1.23151i	−0.253465	+	0.967345i	$0.581570\pi$
$678$			29.4449i			1.13082i
$679$	−10.0000			−0.383765
$680$	22.5000	+	38.9711i	0.862836	+	1.49448i
$681$			36.3731i			1.39382i
$682$	7.50000	−	12.9904i	0.287190	−	0.497427i
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$	10.5000	−	7.79423i	0.401478	−	0.298020i
$685$	9.00000			0.343872
$686$	−6.50000	+	11.2583i	−0.248171	+	0.429845i
$687$	−25.5000	+	14.7224i	−0.972886	+	0.561696i
$688$	4.00000	+	6.92820i	0.152499	+	0.264135i
$689$	−2.00000			−0.0761939
$690$	−36.0000	−	20.7846i	−1.37050	−	0.791257i
$691$	9.50000	+	16.4545i	0.361397	+	0.625958i	0.988191	−	0.153227i	$-0.0489666\pi$
$691$	9.50000	+	16.4545i	0.361397	+	0.625958i	−0.626794	+	0.779185i	$0.715633\pi$
$692$	6.00000			0.228086
$693$	−15.0000			−0.569803
$694$	0.500000	−	0.866025i	0.0189797	−	0.0328739i
$695$	−30.0000	−	51.9615i	−1.13796	−	1.97101i
$696$	4.50000	+	2.59808i	0.170572	+	0.0984798i
$697$	−22.5000	−	38.9711i	−0.852248	−	1.47614i
$698$	−15.0000			−0.567758
$699$		−	15.5885i		−	0.589610i
$700$	2.00000	−	3.46410i	0.0755929	−	0.130931i
$701$	−9.50000	−	16.4545i	−0.358810	−	0.621477i	0.628952	−	0.777444i	$-0.283484\pi$
$701$	−9.50000	−	16.4545i	−0.358810	−	0.621477i	−0.987762	+	0.155967i	$0.950151\pi$
$702$			10.3923i			0.392232i
$703$	24.0000	+	10.3923i	0.905177	+	0.391953i
$704$	−17.5000	−	30.3109i	−0.659556	−	1.14238i
$705$	−13.5000	−	7.79423i	−0.508439	−	0.293548i
$706$	37.0000			1.39251
$707$	−3.50000	−	6.06218i	−0.131631	−	0.227992i
$708$		−	8.66025i		−	0.325472i
$709$	39.0000			1.46468			0.732338	−	0.680941i	$-0.238429\pi$
$709$	39.0000			1.46468			0.732338	+	0.680941i	$0.238429\pi$
$710$	−9.00000			−0.337764
$711$	−12.0000			−0.450035
$712$	13.5000	−	23.3827i	0.505934	−	0.876303i
$713$	−24.0000			−0.898807
$714$			8.66025i			0.324102i
$715$	−15.0000	+	25.9808i	−0.560968	+	0.971625i
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$	22.5000	−	12.9904i	0.840278	−	0.485135i
$718$	13.0000			0.485156
$719$	−1.50000	−	2.59808i	−0.0559406	−	0.0968919i	0.836699	−	0.547663i	$-0.184482\pi$
$719$	−1.50000	−	2.59808i	−0.0559406	−	0.0968919i	−0.892640	+	0.450771i	$0.851149\pi$
$720$	9.00000			0.335410
$721$	−5.00000			−0.186210
$722$	18.5000	−	4.33013i	0.688499	−	0.161151i
$723$	1.50000	+	0.866025i	0.0557856	+	0.0322078i
$724$	−7.00000			−0.260153
$725$	−4.00000			−0.148556
$726$		−	24.2487i		−	0.899954i
$727$	4.00000	−	6.92820i	0.148352	−	0.256953i	−0.782267	−	0.622944i	$-0.785937\pi$
$727$	4.00000	−	6.92820i	0.148352	−	0.256953i	0.930618	+	0.365991i	$0.119270\pi$
$728$	−3.00000	+	5.19615i	−0.111187	+	0.192582i
$729$	−27.0000			−1.00000
$730$	15.0000			0.555175
$731$	−40.0000			−1.47945
$732$			22.5167i			0.832240i
$733$	−9.50000	+	16.4545i	−0.350891	+	0.607760i	−0.986406	−	0.164328i	$-0.947454\pi$
$733$	−9.50000	+	16.4545i	−0.350891	+	0.607760i	0.635515	+	0.772088i	$0.280788\pi$
$734$	−2.50000	+	4.33013i	−0.0922767	+	0.159828i
$735$	−27.0000	+	15.5885i	−0.995910	+	0.574989i
$736$	−20.0000	+	34.6410i	−0.737210	+	1.27688i
$737$	10.0000	−	17.3205i	0.368355	−	0.638009i
$738$	−27.0000			−0.993884
$739$	−9.50000	−	16.4545i	−0.349463	−	0.605288i	0.636691	−	0.771119i	$-0.280303\pi$
$739$	−9.50000	−	16.4545i	−0.349463	−	0.605288i	−0.986154	+	0.165831i	$0.946969\pi$
$740$	−9.00000	−	15.5885i	−0.330847	−	0.573043i
$741$	6.00000	−	13.8564i	0.220416	−	0.509028i
$742$	−0.500000	+	0.866025i	−0.0183556	+	0.0317928i
$743$	41.0000			1.50414			0.752072	−	0.659081i	$-0.229055\pi$
$743$	41.0000			1.50414			0.752072	+	0.659081i	$0.229055\pi$
$744$	13.5000	−	7.79423i	0.494934	−	0.285750i
$745$	45.0000			1.64867
$746$	−2.50000	−	4.33013i	−0.0915315	−	0.158537i
$747$	13.5000	−	23.3827i	0.493939	−	0.855528i
$748$	25.0000			0.914091
$749$	−6.00000	−	10.3923i	−0.219235	−	0.379727i
$750$	4.50000	−	2.59808i	0.164317	−	0.0948683i
$751$	−12.0000	−	20.7846i	−0.437886	−	0.758441i	0.559640	−	0.828736i	$-0.310939\pi$
$751$	−12.0000	−	20.7846i	−0.437886	−	0.758441i	−0.997526	+	0.0702946i	$0.977606\pi$
$752$	1.50000	−	2.59808i	0.0546994	−	0.0947421i
$753$	7.50000	−	4.33013i	0.273315	−	0.157799i
$754$	2.00000			0.0728357
$755$	22.5000	+	38.9711i	0.818859	+	1.41831i
$756$	−4.50000	−	2.59808i	−0.163663	−	0.0944911i
$757$	−15.5000	−	26.8468i	−0.563357	−	0.975763i	−0.997200	−	0.0747748i	$-0.976176\pi$
$757$	−15.5000	−	26.8468i	−0.563357	−	0.975763i	0.433843	−	0.900988i	$-0.357157\pi$
$758$	−10.0000	+	17.3205i	−0.363216	+	0.629109i
$759$	−60.0000	+	34.6410i	−2.17786	+	1.25739i
$760$	−36.0000	−	15.5885i	−1.30586	−	0.565453i
$761$	4.50000	−	7.79423i	0.163125	−	0.282541i	−0.772863	−	0.634573i	$-0.781176\pi$
$761$	4.50000	−	7.79423i	0.163125	−	0.282541i	0.935988	+	0.352032i	$0.114509\pi$
$762$		−	22.5167i		−	0.815693i
$763$	2.50000	−	4.33013i	0.0905061	−	0.156761i
$764$	−1.50000	+	2.59808i	−0.0542681	+	0.0939951i
$765$	−22.5000	+	38.9711i	−0.813489	+	1.40900i
$766$	−11.5000	+	19.9186i	−0.415512	+	0.719688i
$767$	−5.00000	−	8.66025i	−0.180540	−	0.312704i
$768$		−	29.4449i		−	1.06250i
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	0.711767	−	0.702416i	$-0.247895\pi$
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	−0.964193	+	0.265200i	$0.914562\pi$
$770$	7.50000	+	12.9904i	0.270281	+	0.468141i
$771$		−	17.3205i		−	0.623783i
$772$	−8.50000	−	14.7224i	−0.305922	−	0.529872i
$773$	8.50000	−	14.7224i	0.305724	−	0.529529i	−0.671698	−	0.740825i	$-0.734435\pi$
$773$	8.50000	−	14.7224i	0.305724	−	0.529529i	0.977422	+	0.211296i	$0.0677683\pi$
$774$	−12.0000	+	20.7846i	−0.431331	+	0.747087i
$775$	−6.00000	+	10.3923i	−0.215526	+	0.373303i
$776$	15.0000	−	25.9808i	0.538469	−	0.932655i
$777$		−	10.3923i		−	0.372822i
$778$	1.50000	−	2.59808i	0.0537776	−	0.0931455i
$779$	36.0000	+	15.5885i	1.28983	+	0.558514i
$780$	−9.00000	+	5.19615i	−0.322252	+	0.186052i
$781$	−7.50000	+	12.9904i	−0.268371	+	0.464832i
$782$	20.0000	+	34.6410i	0.715199	+	1.23876i
$783$			5.19615i			0.185695i
$784$	−3.00000	−	5.19615i	−0.107143	−	0.185577i
$785$	9.00000			0.321224
$786$	10.5000	−	6.06218i	0.374523	−	0.216231i
$787$	−3.50000	+	6.06218i	−0.124762	+	0.216093i	−0.921640	−	0.388047i	$-0.873150\pi$
$787$	−3.50000	+	6.06218i	−0.124762	+	0.216093i	0.796878	+	0.604140i	$0.206483\pi$
$788$	1.00000	+	1.73205i	0.0356235	+	0.0617018i
$789$	−12.0000	+	6.92820i	−0.427211	+	0.246651i
$790$	6.00000	+	10.3923i	0.213470	+	0.369742i
$791$	−17.0000			−0.604450
$792$	22.5000	−	38.9711i	0.799503	−	1.38478i
$793$	13.0000	+	22.5167i	0.461644	+	0.799590i
$794$	−7.00000			−0.248421
$795$	−4.50000	+	2.59808i	−0.159599	+	0.0921443i
$796$	3.00000			0.106332
$797$	−5.50000	+	9.52628i	−0.194820	+	0.337438i	−0.946841	−	0.321700i	$-0.895746\pi$
$797$	−5.50000	+	9.52628i	−0.194820	+	0.337438i	0.752022	+	0.659139i	$0.229079\pi$
$798$	−4.50000	−	6.06218i	−0.159298	−	0.214599i
$799$	7.50000	+	12.9904i	0.265331	+	0.459567i
$800$	10.0000	+	17.3205i	0.353553	+	0.612372i
$801$	27.0000			0.953998
$802$	−16.5000	+	28.5788i	−0.582635	+	1.00915i
$803$	12.5000	−	21.6506i	0.441115	−	0.764034i
$804$	6.00000	−	3.46410i	0.211604	−	0.122169i
$805$	12.0000	−	20.7846i	0.422944	−	0.732561i
$806$	3.00000	−	5.19615i	0.105670	−	0.183027i
$807$		−	43.3013i		−	1.52428i
$808$	21.0000			0.738777
$809$	−2.00000			−0.0703163			−0.0351581	−	0.999382i	$-0.511193\pi$
$809$	−2.00000			−0.0703163			−0.0351581	+	0.999382i	$0.511193\pi$
$810$	13.5000	+	23.3827i	0.474342	+	0.821584i
$811$	−12.5000	+	21.6506i	−0.438934	+	0.760257i	−0.997608	−	0.0691313i	$-0.977977\pi$
$811$	−12.5000	+	21.6506i	−0.438934	+	0.760257i	0.558673	+	0.829388i	$0.311311\pi$
$812$	−0.500000	+	0.866025i	−0.0175466	+	0.0303915i
$813$			46.7654i			1.64013i
$814$	30.0000			1.05150
$815$	36.0000			1.26102
$816$	−7.50000	−	4.33013i	−0.262553	−	0.151585i
$817$	28.0000	−	20.7846i	0.979596	−	0.727161i
$818$	−10.0000			−0.349642
$819$	−6.00000			−0.209657
$820$	−13.5000	−	23.3827i	−0.471440	−	0.816559i
$821$	15.0000			0.523504			0.261752	−	0.965135i	$-0.415700\pi$
$821$	15.0000			0.523504			0.261752	+	0.965135i	$0.415700\pi$
$822$	−4.50000	+	2.59808i	−0.156956	+	0.0906183i
$823$	−20.0000	−	34.6410i	−0.697156	−	1.20751i	−0.969448	−	0.245295i	$-0.921115\pi$
$823$	−20.0000	−	34.6410i	−0.697156	−	1.20751i	0.272292	−	0.962215i	$-0.412218\pi$
$824$	7.50000	−	12.9904i	0.261275	−	0.452541i
$825$			34.6410i			1.20605i
$826$	−5.00000			−0.173972
$827$	−4.50000	+	7.79423i	−0.156480	+	0.271032i	−0.933597	−	0.358325i	$-0.883348\pi$
$827$	−4.50000	+	7.79423i	−0.156480	+	0.271032i	0.777117	+	0.629356i	$0.216681\pi$
$828$	−24.0000			−0.834058
$829$	−38.0000			−1.31979			−0.659897	−	0.751356i	$-0.729400\pi$
$829$	−38.0000			−1.31979			−0.659897	+	0.751356i	$0.729400\pi$
$830$	−27.0000			−0.937184
$831$			12.1244i			0.420589i
$832$	−7.00000	−	12.1244i	−0.242681	−	0.420336i
$833$	30.0000			1.03944
$834$	30.0000	+	17.3205i	1.03882	+	0.599760i
$835$	6.00000	+	10.3923i	0.207639	+	0.359641i
$836$	−17.5000	+	12.9904i	−0.605250	+	0.449282i
$837$	13.5000	+	7.79423i	0.466628	+	0.269408i
$838$	−0.500000	−	0.866025i	−0.0172722	−	0.0299164i
$839$	12.0000	−	20.7846i	0.414286	−	0.717564i	−0.581067	−	0.813856i	$-0.697365\pi$
$839$	12.0000	−	20.7846i	0.414286	−	0.717564i	0.995353	+	0.0962912i	$0.0306980\pi$
$840$			15.5885i			0.537853i
$841$	−28.0000			−0.965517
$842$	13.0000	+	22.5167i	0.448010	+	0.775975i
$843$	−16.5000	−	9.52628i	−0.568290	−	0.328102i
$844$	−7.50000	−	12.9904i	−0.258161	−	0.447147i
$845$	13.5000	−	23.3827i	0.464414	−	0.804389i
$846$	9.00000			0.309426
$847$	14.0000			0.481046
$848$	−0.500000	−	0.866025i	−0.0171701	−	0.0297394i
$849$	−43.5000	−	25.1147i	−1.49292	−	0.861936i
$850$	20.0000			0.685994
$851$	−24.0000	−	41.5692i	−0.822709	−	1.42497i
$852$	−4.50000	+	2.59808i	−0.154167	+	0.0890086i
$853$	19.0000	−	32.9090i	0.650548	−	1.12678i	−0.332443	−	0.943123i	$-0.607873\pi$
$853$	19.0000	−	32.9090i	0.650548	−	1.12678i	0.982990	−	0.183658i	$-0.0587939\pi$
$854$	13.0000			0.444851
$855$	−4.50000	−	38.9711i	−0.153897	−	1.33278i
$856$	36.0000			1.23045
$857$	−7.00000	+	12.1244i	−0.239115	+	0.414160i	−0.960461	−	0.278416i	$-0.910191\pi$
$857$	−7.00000	+	12.1244i	−0.239115	+	0.414160i	0.721345	+	0.692576i	$0.243524\pi$
$858$		−	17.3205i		−	0.591312i
$859$	6.00000	+	10.3923i	0.204717	+	0.354581i	0.950043	−	0.312120i	$-0.101039\pi$
$859$	6.00000	+	10.3923i	0.204717	+	0.354581i	−0.745325	+	0.666701i	$0.767706\pi$
$860$	−24.0000			−0.818393
$861$		−	15.5885i		−	0.531253i
$862$	0.500000	+	0.866025i	0.0170301	+	0.0294969i
$863$	−16.0000			−0.544646			−0.272323	−	0.962206i	$-0.587792\pi$
$863$	−16.0000			−0.544646			−0.272323	+	0.962206i	$0.587792\pi$
$864$	22.5000	−	12.9904i	0.765466	−	0.441942i
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$	13.5000	+	23.3827i	0.458749	+	0.794576i
$867$	12.0000	−	6.92820i	0.407541	−	0.235294i
$868$	1.50000	+	2.59808i	0.0509133	+	0.0881845i
$869$	20.0000			0.678454
$870$	4.50000	−	2.59808i	0.152564	−	0.0880830i
$871$	4.00000	−	6.92820i	0.135535	−	0.234753i
$872$	7.50000	+	12.9904i	0.253982	+	0.439910i
$873$	30.0000			1.01535
$874$	−32.0000	−	13.8564i	−1.08242	−	0.468700i
$875$	1.50000	+	2.59808i	0.0507093	+	0.0878310i
$876$	7.50000	−	4.33013i	0.253402	−	0.146301i
$877$	39.0000			1.31694			0.658468	−	0.752609i	$-0.271205\pi$
$877$	39.0000			1.31694			0.658468	+	0.752609i	$0.271205\pi$
$878$	−8.00000	−	13.8564i	−0.269987	−	0.467631i
$879$	−7.50000	+	4.33013i	−0.252969	+	0.146052i
$880$	−15.0000			−0.505650
$881$	−2.00000			−0.0673817			−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$	9.00000	−	15.5885i	0.303046	−	0.524891i
$883$	−14.5000	+	25.1147i	−0.487964	+	0.845178i	−0.999904	−	0.0138428i	$-0.995594\pi$
$883$	−14.5000	+	25.1147i	−0.487964	+	0.845178i	0.511940	+	0.859021i	$0.328927\pi$
$884$	10.0000			0.336336
$885$	−22.5000	−	12.9904i	−0.756329	−	0.436667i
$886$	−12.5000	+	21.6506i	−0.419946	+	0.727367i
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	0.994077	−	0.108678i	$-0.0346618\pi$
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	−0.591156	+	0.806557i	$0.701328\pi$
$888$	27.0000	+	15.5885i	0.906061	+	0.523114i
$889$	13.0000			0.436006
$890$	−13.5000	−	23.3827i	−0.452521	−	0.783789i
$891$	45.0000			1.50756
$892$	24.0000			0.803579
$893$	−12.0000	−	5.19615i	−0.401565	−	0.173883i
$894$	−22.5000	+	12.9904i	−0.752513	+	0.434463i
$895$	−36.0000			−1.20335
$896$	3.00000			0.100223
$897$	−24.0000	+	13.8564i	−0.801337	+	0.462652i
$898$	15.0000	−	25.9808i	0.500556	−	0.866989i
$899$	1.50000	−	2.59808i	0.0500278	−	0.0866507i
$900$	−6.00000	+	10.3923i	−0.200000	+	0.346410i
$901$	5.00000			0.166574
$902$	45.0000			1.49834
$903$	−12.0000	−	6.92820i	−0.399335	−	0.230556i
$904$	25.5000	−	44.1673i	0.848117	−	1.46898i
$905$	−10.5000	+	18.1865i	−0.349032	+	0.604541i
$906$	−22.5000	−	12.9904i	−0.747512	−	0.431577i
$907$	−8.00000	+	13.8564i	−0.265636	+	0.460094i	−0.967730	−	0.251990i	$-0.918915\pi$
$907$	−8.00000	+	13.8564i	−0.265636	+	0.460094i	0.702094	+	0.712084i	$0.252248\pi$
$908$	10.5000	−	18.1865i	0.348455	−	0.603541i
$909$	10.5000	+	18.1865i	0.348263	+	0.603209i
$910$	3.00000	+	5.19615i	0.0994490	+	0.172251i
$911$	−22.5000	−	38.9711i	−0.745458	−	1.29117i	−0.949980	−	0.312310i	$-0.898897\pi$
$911$	−22.5000	−	38.9711i	−0.745458	−	1.29117i	0.204522	−	0.978862i	$-0.434436\pi$
$912$	7.50000	−	0.866025i	0.248350	−	0.0286770i
$913$	−22.5000	+	38.9711i	−0.744641	+	1.28976i
$914$	−19.0000			−0.628464
$915$	58.5000	+	33.7750i	1.93395	+	1.11657i
$916$	17.0000			0.561696
$917$	3.50000	+	6.06218i	0.115580	+	0.200191i
$918$		−	25.9808i		−	0.857493i
$919$	20.0000			0.659739			0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000			0.659739			0.329870	+	0.944027i	$0.392995\pi$
$920$	36.0000	+	62.3538i	1.18688	+	2.05574i
$921$		−	57.1577i		−	1.88341i
$922$	−15.0000	−	25.9808i	−0.493999	−	0.855631i
$923$	−3.00000	+	5.19615i	−0.0987462	+	0.171033i
$924$	7.50000	+	4.33013i	0.246732	+	0.142451i
$925$	−24.0000			−0.789115
$926$	−0.500000	−	0.866025i	−0.0164310	−	0.0284594i
$927$	15.0000			0.492665
$928$	−2.50000	−	4.33013i	−0.0820665	−	0.142143i
$929$	−25.0000	+	43.3013i	−0.820223	+	1.42067i	0.0852924	+	0.996356i	$0.472818\pi$
$929$	−25.0000	+	43.3013i	−0.820223	+	1.42067i	−0.905516	+	0.424313i	$0.860516\pi$
$930$		−	15.5885i		−	0.511166i
$931$	−21.0000	+	15.5885i	−0.688247	+	0.510891i
$932$	−4.50000	+	7.79423i	−0.147402	+	0.255308i
$933$	−31.5000	+	18.1865i	−1.03126	+	0.595400i
$934$	4.00000	−	6.92820i	0.130884	−	0.226698i
$935$	37.5000	−	64.9519i	1.22638	−	2.12415i
$936$	9.00000	−	15.5885i	0.294174	−	0.509525i
$937$	4.50000	−	7.79423i	0.147009	−	0.254626i	−0.783112	−	0.621881i	$-0.786369\pi$
$937$	4.50000	−	7.79423i	0.147009	−	0.254626i	0.930121	+	0.367254i	$0.119702\pi$
$938$	−2.00000	−	3.46410i	−0.0653023	−	0.113107i
$939$	25.5000	+	14.7224i	0.832161	+	0.480448i
$940$	4.50000	+	7.79423i	0.146774	+	0.254220i
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	0.681218	−	0.732081i	$-0.261451\pi$
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	−0.974609	+	0.223912i	$0.928117\pi$
$942$	−4.50000	+	2.59808i	−0.146618	+	0.0846499i
$943$	−36.0000	−	62.3538i	−1.17232	−	2.03052i
$944$	2.50000	−	4.33013i	0.0813681	−	0.140934i
$945$	−13.5000	+	7.79423i	−0.439155	+	0.253546i
$946$	20.0000	−	34.6410i	0.650256	−	1.12628i
$947$	−14.0000	+	24.2487i	−0.454939	+	0.787977i	−0.998685	−	0.0512727i	$-0.983672\pi$
$947$	−14.0000	+	24.2487i	−0.454939	+	0.787977i	0.543746	+	0.839250i	$0.317006\pi$
$948$	6.00000	+	3.46410i	0.194871	+	0.112509i
$949$	5.00000	−	8.66025i	0.162307	−	0.281124i
$950$	−14.0000	+	10.3923i	−0.454220	+	0.337171i
$951$	25.5000	+	14.7224i	0.826894	+	0.477408i
$952$	7.50000	−	12.9904i	0.243076	−	0.421021i
$953$	−11.5000	−	19.9186i	−0.372522	−	0.645226i	0.617431	−	0.786625i	$-0.288173\pi$
$953$	−11.5000	−	19.9186i	−0.372522	−	0.645226i	−0.989953	+	0.141399i	$0.954840\pi$
$954$	1.50000	−	2.59808i	0.0485643	−	0.0841158i
$955$	4.50000	+	7.79423i	0.145617	+	0.252215i
$956$	−15.0000			−0.485135
$957$		−	8.66025i		−	0.279946i
$958$	−2.50000	+	4.33013i	−0.0807713	+	0.139900i
$959$	−1.50000	−	2.59808i	−0.0484375	−	0.0838963i
$960$	−31.5000	−	18.1865i	−1.01666	−	0.586968i
$961$	11.0000	+	19.0526i	0.354839	+	0.614599i
$962$	12.0000			0.386896
$963$	18.0000	+	31.1769i	0.580042	+	1.00466i
$964$	−0.500000	−	0.866025i	−0.0161039	−	0.0278928i
$965$	−51.0000			−1.64175
$966$			13.8564i			0.445823i
$967$	37.0000			1.18984			0.594920	−	0.803785i	$-0.297184\pi$
$967$	37.0000			1.18984			0.594920	+	0.803785i	$0.297184\pi$
$968$	−21.0000	+	36.3731i	−0.674966	+	1.16907i
$969$	−15.0000	+	34.6410i	−0.481869	+	1.11283i
$970$	−15.0000	−	25.9808i	−0.481621	−	0.834192i
$971$	10.5000	+	18.1865i	0.336961	+	0.583634i	0.983860	−	0.178942i	$-0.0572676\pi$
$971$	10.5000	+	18.1865i	0.336961	+	0.583634i	−0.646899	+	0.762576i	$0.723934\pi$
$972$	13.5000	+	7.79423i	0.433013	+	0.250000i
$973$	−10.0000	+	17.3205i	−0.320585	+	0.555270i
$974$	16.0000	−	27.7128i	0.512673	−	0.887976i
$975$			13.8564i			0.443760i
$976$	−6.50000	+	11.2583i	−0.208060	+	0.360370i
$977$	10.5000	−	18.1865i	0.335925	−	0.581839i	−0.647737	−	0.761864i	$-0.724285\pi$
$977$	10.5000	−	18.1865i	0.335925	−	0.581839i	0.983662	+	0.180025i	$0.0576179\pi$
$978$	−18.0000	+	10.3923i	−0.575577	+	0.332309i
$979$	−45.0000			−1.43821
$980$	18.0000			0.574989
$981$	−7.50000	+	12.9904i	−0.239457	+	0.414751i
$982$	−13.5000	+	23.3827i	−0.430802	+	0.746171i
$983$	−4.00000	+	6.92820i	−0.127580	+	0.220975i	−0.922739	−	0.385426i	$-0.874054\pi$
$983$	−4.00000	+	6.92820i	−0.127580	+	0.220975i	0.795158	+	0.606402i	$0.207388\pi$
$984$	40.5000	+	23.3827i	1.29109	+	0.745413i
$985$	6.00000			0.191176
$986$	−5.00000			−0.159232
$987$			5.19615i			0.165395i
$988$	−7.00000	+	5.19615i	−0.222700	+	0.165312i
$989$	−64.0000			−2.03508
$990$	−22.5000	−	38.9711i	−0.715097	−	1.23858i
$991$	−11.5000	−	19.9186i	−0.365310	−	0.632735i	0.623516	−	0.781810i	$-0.285704\pi$
$991$	−11.5000	−	19.9186i	−0.365310	−	0.632735i	−0.988826	+	0.149076i	$0.952370\pi$
$992$	−15.0000			−0.476250
$993$		−	32.9090i		−	1.04433i
$994$	1.50000	+	2.59808i	0.0475771	+	0.0824060i
$995$	4.50000	−	7.79423i	0.142660	−	0.247094i
$996$	−13.5000	+	7.79423i	−0.427764	+	0.246970i
$997$	−5.00000			−0.158352			−0.0791758	−	0.996861i	$-0.525229\pi$
$997$	−5.00000			−0.158352			−0.0791758	+	0.996861i	$0.525229\pi$
$998$	14.5000	−	25.1147i	0.458989	−	0.794993i
$999$			31.1769i			0.986394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.g.a.121.1	yes	2
3.2	odd	2		513.2.g.a.64.1		2
9.2	odd	6		513.2.h.b.235.1		2
9.7	even	3		171.2.h.a.7.1	yes	2
19.11	even	3		171.2.h.a.49.1	yes	2
57.11	odd	6		513.2.h.b.334.1		2
171.11	odd	6		513.2.g.a.505.1		2
171.106	even	3	inner	171.2.g.a.106.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.a.106.1	✓	2	171.106	even	3	inner
171.2.g.a.121.1	yes	2	1.1	even	1	trivial
171.2.h.a.7.1	yes	2	9.7	even	3
171.2.h.a.49.1	yes	2	19.11	even	3
513.2.g.a.64.1		2	3.2	odd	2
513.2.g.a.505.1		2	171.11	odd	6
513.2.h.b.235.1		2	9.2	odd	6
513.2.h.b.334.1		2	57.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(-1.50000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +(-1.50000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{10} +(-2.50000 - 4.33013i) q^{11} -1.73205i q^{12} +(-1.00000 - 1.73205i) q^{13} -1.00000 q^{14} +(-4.50000 - 2.59808i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.50000 + 4.33013i) q^{17} +3.00000 q^{18} +(-4.00000 - 1.73205i) q^{19} +(1.50000 + 2.59808i) q^{20} +1.73205i q^{21} -5.00000 q^{22} +(4.00000 + 6.92820i) q^{23} +(-4.50000 - 2.59808i) q^{24} +4.00000 q^{25} -2.00000 q^{26} -5.19615i q^{27} +(0.500000 - 0.866025i) q^{28} -1.00000 q^{29} +(-4.50000 + 2.59808i) q^{30} +(-1.50000 + 2.59808i) q^{31} +(2.50000 + 4.33013i) q^{32} +8.66025i q^{33} +5.00000 q^{34} +(-1.50000 - 2.59808i) q^{35} +(-1.50000 + 2.59808i) q^{36} -6.00000 q^{37} +(-3.50000 + 2.59808i) q^{38} +3.46410i q^{39} +9.00000 q^{40} -9.00000 q^{41} +(1.50000 + 0.866025i) q^{42} +(-4.00000 + 6.92820i) q^{43} +(2.50000 - 4.33013i) q^{44} +(4.50000 + 7.79423i) q^{45} +8.00000 q^{46} +3.00000 q^{47} +(-1.50000 + 0.866025i) q^{48} +(3.00000 - 5.19615i) q^{49} +(2.00000 - 3.46410i) q^{50} -8.66025i q^{51} +(1.00000 - 1.73205i) q^{52} +(0.500000 - 0.866025i) q^{53} +(-4.50000 - 2.59808i) q^{54} +(-7.50000 - 12.9904i) q^{55} +(-1.50000 - 2.59808i) q^{56} +(4.50000 + 6.06218i) q^{57} +(-0.500000 + 0.866025i) q^{58} +5.00000 q^{59} -5.19615i q^{60} -13.0000 q^{61} +(1.50000 + 2.59808i) q^{62} +(1.50000 - 2.59808i) q^{63} +7.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} +(7.50000 + 4.33013i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-2.50000 + 4.33013i) q^{68} -13.8564i q^{69} -3.00000 q^{70} +(-1.50000 - 2.59808i) q^{71} +(4.50000 + 7.79423i) q^{72} +(2.50000 + 4.33013i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(-6.00000 - 3.46410i) q^{75} +(-0.500000 - 4.33013i) q^{76} +(-2.50000 + 4.33013i) q^{77} +(3.00000 + 1.73205i) q^{78} +(-2.00000 + 3.46410i) q^{79} +(1.50000 - 2.59808i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-4.50000 + 7.79423i) q^{82} +(-4.50000 - 7.79423i) q^{83} +(-1.50000 + 0.866025i) q^{84} +(7.50000 + 12.9904i) q^{85} +(4.00000 + 6.92820i) q^{86} +(1.50000 + 0.866025i) q^{87} +(-7.50000 - 12.9904i) q^{88} +(4.50000 - 7.79423i) q^{89} +9.00000 q^{90} +(-1.00000 + 1.73205i) q^{91} +(-4.00000 + 6.92820i) q^{92} +(4.50000 - 2.59808i) q^{93} +(1.50000 - 2.59808i) q^{94} +(-12.0000 - 5.19615i) q^{95} -8.66025i q^{96} +(5.00000 - 8.66025i) q^{97} +(-3.00000 - 5.19615i) q^{98} +(7.50000 - 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 3 q^{3} + q^{4} + 6 q^{5} - 3 q^{6} - q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + q^2 - 3 * q^3 + q^4 + 6 * q^5 - 3 * q^6 - q^7 + 6 * q^8 + 3 * q^9	\( 2 q + q^{2} - 3 q^{3} + q^{4} + 6 q^{5} - 3 q^{6} - q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 5 q^{11} - 2 q^{13} - 2 q^{14} - 9 q^{15} + q^{16} + 5 q^{17} + 6 q^{18} - 8 q^{19} + 3 q^{20} - 10 q^{22} + 8 q^{23} - 9 q^{24} + 8 q^{25} - 4 q^{26} + q^{28} - 2 q^{29} - 9 q^{30} - 3 q^{31} + 5 q^{32} + 10 q^{34} - 3 q^{35} - 3 q^{36} - 12 q^{37} - 7 q^{38} + 18 q^{40} - 18 q^{41} + 3 q^{42} - 8 q^{43} + 5 q^{44} + 9 q^{45} + 16 q^{46} + 6 q^{47} - 3 q^{48} + 6 q^{49} + 4 q^{50} + 2 q^{52} + q^{53} - 9 q^{54} - 15 q^{55} - 3 q^{56} + 9 q^{57} - q^{58} + 10 q^{59} - 26 q^{61} + 3 q^{62} + 3 q^{63} + 14 q^{64} - 6 q^{65} + 15 q^{66} + 4 q^{67} - 5 q^{68} - 6 q^{70} - 3 q^{71} + 9 q^{72} + 5 q^{73} - 6 q^{74} - 12 q^{75} - q^{76} - 5 q^{77} + 6 q^{78} - 4 q^{79} + 3 q^{80} - 9 q^{81} - 9 q^{82} - 9 q^{83} - 3 q^{84} + 15 q^{85} + 8 q^{86} + 3 q^{87} - 15 q^{88} + 9 q^{89} + 18 q^{90} - 2 q^{91} - 8 q^{92} + 9 q^{93} + 3 q^{94} - 24 q^{95} + 10 q^{97} - 6 q^{98} + 15 q^{99}+O(q^{100}) \) 2 * q + q^2 - 3 * q^3 + q^4 + 6 * q^5 - 3 * q^6 - q^7 + 6 * q^8 + 3 * q^9 + 3 * q^10 - 5 * q^11 - 2 * q^13 - 2 * q^14 - 9 * q^15 + q^16 + 5 * q^17 + 6 * q^18 - 8 * q^19 + 3 * q^20 - 10 * q^22 + 8 * q^23 - 9 * q^24 + 8 * q^25 - 4 * q^26 + q^28 - 2 * q^29 - 9 * q^30 - 3 * q^31 + 5 * q^32 + 10 * q^34 - 3 * q^35 - 3 * q^36 - 12 * q^37 - 7 * q^38 + 18 * q^40 - 18 * q^41 + 3 * q^42 - 8 * q^43 + 5 * q^44 + 9 * q^45 + 16 * q^46 + 6 * q^47 - 3 * q^48 + 6 * q^49 + 4 * q^50 + 2 * q^52 + q^53 - 9 * q^54 - 15 * q^55 - 3 * q^56 + 9 * q^57 - q^58 + 10 * q^59 - 26 * q^61 + 3 * q^62 + 3 * q^63 + 14 * q^64 - 6 * q^65 + 15 * q^66 + 4 * q^67 - 5 * q^68 - 6 * q^70 - 3 * q^71 + 9 * q^72 + 5 * q^73 - 6 * q^74 - 12 * q^75 - q^76 - 5 * q^77 + 6 * q^78 - 4 * q^79 + 3 * q^80 - 9 * q^81 - 9 * q^82 - 9 * q^83 - 3 * q^84 + 15 * q^85 + 8 * q^86 + 3 * q^87 - 15 * q^88 + 9 * q^89 + 18 * q^90 - 2 * q^91 - 8 * q^92 + 9 * q^93 + 3 * q^94 - 24 * q^95 + 10 * q^97 - 6 * q^98 + 15 * q^99

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