LMFDB - Embedded newform 171.2.g.b.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.b.106.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 - 0.866025i) q^{6} +(-1.50000 - 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 - 0.866025i) q^{6} +(-1.50000 - 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-1.50000 - 2.59808i) q^{11} +1.73205i q^{12} +(3.00000 + 5.19615i) q^{13} -3.00000 q^{14} +(-1.50000 - 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +3.00000 q^{18} +(-4.00000 + 1.73205i) q^{19} +(-0.500000 - 0.866025i) q^{20} -5.19615i q^{21} -3.00000 q^{22} +(-4.00000 - 6.92820i) q^{23} +(4.50000 + 2.59808i) q^{24} -4.00000 q^{25} +6.00000 q^{26} +5.19615i q^{27} +(1.50000 - 2.59808i) q^{28} -5.00000 q^{29} +(-1.50000 + 0.866025i) q^{30} +(3.50000 - 6.06218i) q^{31} +(2.50000 + 4.33013i) q^{32} -5.19615i q^{33} -3.00000 q^{34} +(1.50000 + 2.59808i) q^{35} +(-1.50000 + 2.59808i) q^{36} +2.00000 q^{37} +(-0.500000 + 4.33013i) q^{38} +10.3923i q^{39} -3.00000 q^{40} -1.00000 q^{41} +(-4.50000 - 2.59808i) q^{42} +(-4.00000 + 6.92820i) q^{43} +(1.50000 - 2.59808i) q^{44} +(-1.50000 - 2.59808i) q^{45} -8.00000 q^{46} +9.00000 q^{47} +(1.50000 - 0.866025i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(-2.00000 + 3.46410i) q^{50} -5.19615i q^{51} +(-3.00000 + 5.19615i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(4.50000 + 2.59808i) q^{54} +(1.50000 + 2.59808i) q^{55} +(-4.50000 - 7.79423i) q^{56} +(-7.50000 - 0.866025i) q^{57} +(-2.50000 + 4.33013i) q^{58} +3.00000 q^{59} -1.73205i q^{60} +7.00000 q^{61} +(-3.50000 - 6.06218i) q^{62} +(4.50000 - 7.79423i) q^{63} +7.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} +(-4.50000 - 2.59808i) q^{66} +(2.00000 + 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} -13.8564i q^{69} +3.00000 q^{70} +(7.50000 + 12.9904i) q^{71} +(4.50000 + 7.79423i) q^{72} +(2.50000 + 4.33013i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-6.00000 - 3.46410i) q^{75} +(-3.50000 - 2.59808i) q^{76} +(-4.50000 + 7.79423i) q^{77} +(9.00000 + 5.19615i) q^{78} +(6.00000 - 10.3923i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-0.500000 + 0.866025i) q^{82} +(0.500000 + 0.866025i) q^{83} +(4.50000 - 2.59808i) q^{84} +(1.50000 + 2.59808i) q^{85} +(4.00000 + 6.92820i) q^{86} +(-7.50000 - 4.33013i) q^{87} +(-4.50000 - 7.79423i) q^{88} +(0.500000 - 0.866025i) q^{89} -3.00000 q^{90} +(9.00000 - 15.5885i) q^{91} +(4.00000 - 6.92820i) q^{92} +(10.5000 - 6.06218i) q^{93} +(4.50000 - 7.79423i) q^{94} +(4.00000 - 1.73205i) q^{95} +8.66025i q^{96} +(1.00000 - 1.73205i) q^{97} +(1.00000 + 1.73205i) q^{98} +(4.50000 - 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} + q^{4} - 2 q^{5} + 3 q^{6} - 3 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + q^2 + 3 * q^3 + q^4 - 2 * q^5 + 3 * q^6 - 3 * q^7 + 6 * q^8 + 3 * q^9	$ 2 q + q^{2} + 3 q^{3} + q^{4} - 2 q^{5} + 3 q^{6} - 3 q^{7} + 6 q^{8} + 3 q^{9} - q^{10} - 3 q^{11} + 6 q^{13} - 6 q^{14} - 3 q^{15} + q^{16} - 3 q^{17} + 6 q^{18} - 8 q^{19} - q^{20} - 6 q^{22} - 8 q^{23} + 9 q^{24} - 8 q^{25} + 12 q^{26} + 3 q^{28} - 10 q^{29} - 3 q^{30} + 7 q^{31} + 5 q^{32} - 6 q^{34} + 3 q^{35} - 3 q^{36} + 4 q^{37} - q^{38} - 6 q^{40} - 2 q^{41} - 9 q^{42} - 8 q^{43} + 3 q^{44} - 3 q^{45} - 16 q^{46} + 18 q^{47} + 3 q^{48} - 2 q^{49} - 4 q^{50} - 6 q^{52} - 3 q^{53} + 9 q^{54} + 3 q^{55} - 9 q^{56} - 15 q^{57} - 5 q^{58} + 6 q^{59} + 14 q^{61} - 7 q^{62} + 9 q^{63} + 14 q^{64} - 6 q^{65} - 9 q^{66} + 4 q^{67} + 3 q^{68} + 6 q^{70} + 15 q^{71} + 9 q^{72} + 5 q^{73} + 2 q^{74} - 12 q^{75} - 7 q^{76} - 9 q^{77} + 18 q^{78} + 12 q^{79} - q^{80} - 9 q^{81} - q^{82} + q^{83} + 9 q^{84} + 3 q^{85} + 8 q^{86} - 15 q^{87} - 9 q^{88} + q^{89} - 6 q^{90} + 18 q^{91} + 8 q^{92} + 21 q^{93} + 9 q^{94} + 8 q^{95} + 2 q^{97} + 2 q^{98} + 9 q^{99}+O(q^{100}) $ 2 * q + q^2 + 3 * q^3 + q^4 - 2 * q^5 + 3 * q^6 - 3 * q^7 + 6 * q^8 + 3 * q^9 - q^10 - 3 * q^11 + 6 * q^13 - 6 * q^14 - 3 * q^15 + q^16 - 3 * q^17 + 6 * q^18 - 8 * q^19 - q^20 - 6 * q^22 - 8 * q^23 + 9 * q^24 - 8 * q^25 + 12 * q^26 + 3 * q^28 - 10 * q^29 - 3 * q^30 + 7 * q^31 + 5 * q^32 - 6 * q^34 + 3 * q^35 - 3 * q^36 + 4 * q^37 - q^38 - 6 * q^40 - 2 * q^41 - 9 * q^42 - 8 * q^43 + 3 * q^44 - 3 * q^45 - 16 * q^46 + 18 * q^47 + 3 * q^48 - 2 * q^49 - 4 * q^50 - 6 * q^52 - 3 * q^53 + 9 * q^54 + 3 * q^55 - 9 * q^56 - 15 * q^57 - 5 * q^58 + 6 * q^59 + 14 * q^61 - 7 * q^62 + 9 * q^63 + 14 * q^64 - 6 * q^65 - 9 * q^66 + 4 * q^67 + 3 * q^68 + 6 * q^70 + 15 * q^71 + 9 * q^72 + 5 * q^73 + 2 * q^74 - 12 * q^75 - 7 * q^76 - 9 * q^77 + 18 * q^78 + 12 * q^79 - q^80 - 9 * q^81 - q^82 + q^83 + 9 * q^84 + 3 * q^85 + 8 * q^86 - 15 * q^87 - 9 * q^88 + q^89 - 6 * q^90 + 18 * q^91 + 8 * q^92 + 21 * q^93 + 9 * q^94 + 8 * q^95 + 2 * q^97 + 2 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−1.00000			−0.447214			−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000			−0.447214			−0.223607	+	0.974679i	$0.571783\pi$
$6$	1.50000	−	0.866025i	0.612372	−	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
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$			1.73205i			0.500000i
$13$	3.00000	+	5.19615i	0.832050	+	1.44115i	0.896410	+	0.443227i	$0.146166\pi$
$13$	3.00000	+	5.19615i	0.832050	+	1.44115i	−0.0643593	+	0.997927i	$0.520500\pi$
$14$	−3.00000			−0.801784
$15$	−1.50000	−	0.866025i	−0.387298	−	0.223607i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−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	$0.951855\pi$
$18$	3.00000			0.707107
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$		−	5.19615i		−	1.13389i
$22$	−3.00000			−0.639602
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	−0.894795	−	0.446476i	$-0.852679\pi$
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	0.0607377	−	0.998154i	$-0.480655\pi$
$24$	4.50000	+	2.59808i	0.918559	+	0.530330i
$25$	−4.00000			−0.800000
$26$	6.00000			1.17670
$27$			5.19615i			1.00000i
$28$	1.50000	−	2.59808i	0.283473	−	0.490990i
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$	−1.50000	+	0.866025i	−0.273861	+	0.158114i
$31$	3.50000	−	6.06218i	0.628619	−	1.08880i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	3.50000	−	6.06218i	0.628619	−	1.08880i	0.987829	−	0.155543i	$-0.0497126\pi$
$32$	2.50000	+	4.33013i	0.441942	+	0.765466i
$33$		−	5.19615i		−	0.904534i
$34$	−3.00000			−0.514496
$35$	1.50000	+	2.59808i	0.253546	+	0.439155i
$36$	−1.50000	+	2.59808i	−0.250000	+	0.433013i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	−0.500000	+	4.33013i	−0.0811107	+	0.702439i
$39$			10.3923i			1.66410i
$40$	−3.00000			−0.474342
$41$	−1.00000			−0.156174			−0.0780869	−	0.996947i	$-0.524881\pi$
$41$	−1.00000			−0.156174			−0.0780869	+	0.996947i	$0.524881\pi$
$42$	−4.50000	−	2.59808i	−0.694365	−	0.400892i
$43$	−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	$0.957838\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$	−1.50000	−	2.59808i	−0.223607	−	0.387298i
$46$	−8.00000			−1.17954
$47$	9.00000			1.31278			0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000			1.31278			0.656392	+	0.754420i	$0.272082\pi$
$48$	1.50000	−	0.866025i	0.216506	−	0.125000i
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$		−	5.19615i		−	0.727607i
$52$	−3.00000	+	5.19615i	−0.416025	+	0.720577i
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$	1.50000	+	2.59808i	0.202260	+	0.350325i
$56$	−4.50000	−	7.79423i	−0.601338	−	1.04155i
$57$	−7.50000	−	0.866025i	−0.993399	−	0.114708i
$58$	−2.50000	+	4.33013i	−0.328266	+	0.568574i
$59$	3.00000			0.390567			0.195283	−	0.980747i	$-0.437437\pi$
$59$	3.00000			0.390567			0.195283	+	0.980747i	$0.437437\pi$
$60$		−	1.73205i		−	0.223607i
$61$	7.00000			0.896258			0.448129	−	0.893969i	$-0.352090\pi$
$61$	7.00000			0.896258			0.448129	+	0.893969i	$0.352090\pi$
$62$	−3.50000	−	6.06218i	−0.444500	−	0.769897i
$63$	4.50000	−	7.79423i	0.566947	−	0.981981i
$64$	7.00000			0.875000
$65$	−3.00000	−	5.19615i	−0.372104	−	0.644503i
$66$	−4.50000	−	2.59808i	−0.553912	−	0.319801i
$67$	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	$0.754762\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		−	13.8564i		−	1.66812i
$70$	3.00000			0.358569
$71$	7.50000	+	12.9904i	0.890086	+	1.54167i	0.839771	+	0.542941i	$0.182689\pi$
$71$	7.50000	+	12.9904i	0.890086	+	1.54167i	0.0503155	+	0.998733i	$0.483977\pi$
$72$	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	$0.738812\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	−6.00000	−	3.46410i	−0.692820	−	0.400000i
$76$	−3.50000	−	2.59808i	−0.401478	−	0.298020i
$77$	−4.50000	+	7.79423i	−0.512823	+	0.888235i
$78$	9.00000	+	5.19615i	1.01905	+	0.588348i
$79$	6.00000	−	10.3923i	0.675053	−	1.16923i	−0.301401	−	0.953498i	$-0.597454\pi$
$79$	6.00000	−	10.3923i	0.675053	−	1.16923i	0.976453	−	0.215728i	$-0.0692125\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−0.500000	+	0.866025i	−0.0552158	+	0.0956365i
$83$	0.500000	+	0.866025i	0.0548821	+	0.0950586i	0.892161	−	0.451717i	$-0.149188\pi$
$83$	0.500000	+	0.866025i	0.0548821	+	0.0950586i	−0.837279	+	0.546776i	$0.815855\pi$
$84$	4.50000	−	2.59808i	0.490990	−	0.283473i
$85$	1.50000	+	2.59808i	0.162698	+	0.281801i
$86$	4.00000	+	6.92820i	0.431331	+	0.747087i
$87$	−7.50000	−	4.33013i	−0.804084	−	0.464238i
$88$	−4.50000	−	7.79423i	−0.479702	−	0.830868i
$89$	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	$0.149788\pi$
$90$	−3.00000			−0.316228
$91$	9.00000	−	15.5885i	0.943456	−	1.63411i
$92$	4.00000	−	6.92820i	0.417029	−	0.722315i
$93$	10.5000	−	6.06218i	1.08880	−	0.628619i
$94$	4.50000	−	7.79423i	0.464140	−	0.803913i
$95$	4.00000	−	1.73205i	0.410391	−	0.177705i
$96$			8.66025i			0.883883i
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	−0.810782	−	0.585348i	$-0.800958\pi$
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	0.912317	+	0.409484i	$0.134291\pi$
$98$	1.00000	+	1.73205i	0.101015	+	0.174964i
$99$	4.50000	−	7.79423i	0.452267	−	0.783349i
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−5.00000			−0.497519			−0.248759	−	0.968565i	$-0.580023\pi$
$101$	−5.00000			−0.497519			−0.248759	+	0.968565i	$0.580023\pi$
$102$	−4.50000	−	2.59808i	−0.445566	−	0.257248i
$103$	3.50000	−	6.06218i	0.344865	−	0.597324i	−0.640464	−	0.767988i	$-0.721258\pi$
$103$	3.50000	−	6.06218i	0.344865	−	0.597324i	0.985329	+	0.170664i	$0.0545913\pi$
$104$	9.00000	+	15.5885i	0.882523	+	1.52857i
$105$			5.19615i			0.507093i
$106$	1.50000	+	2.59808i	0.145693	+	0.252347i
$107$	−4.00000			−0.386695			−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000			−0.386695			−0.193347	+	0.981130i	$0.561934\pi$
$108$	−4.50000	+	2.59808i	−0.433013	+	0.250000i
$109$	0.500000	+	0.866025i	0.0478913	+	0.0829502i	0.888977	−	0.457951i	$-0.151417\pi$
$109$	0.500000	+	0.866025i	0.0478913	+	0.0829502i	−0.841086	+	0.540901i	$0.818083\pi$
$110$	3.00000			0.286039
$111$	3.00000	+	1.73205i	0.284747	+	0.164399i
$112$	−3.00000			−0.283473
$113$	−7.50000	+	12.9904i	−0.705541	+	1.22203i	0.260955	+	0.965351i	$0.415962\pi$
$113$	−7.50000	+	12.9904i	−0.705541	+	1.22203i	−0.966496	+	0.256681i	$0.917371\pi$
$114$	−4.50000	+	6.06218i	−0.421464	+	0.567775i
$115$	4.00000	+	6.92820i	0.373002	+	0.646058i
$116$	−2.50000	−	4.33013i	−0.232119	−	0.402042i
$117$	−9.00000	+	15.5885i	−0.832050	+	1.44115i
$118$	1.50000	−	2.59808i	0.138086	−	0.239172i
$119$	−4.50000	+	7.79423i	−0.412514	+	0.714496i
$120$	−4.50000	−	2.59808i	−0.410792	−	0.237171i
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	3.50000	−	6.06218i	0.316875	−	0.548844i
$123$	−1.50000	−	0.866025i	−0.135250	−	0.0780869i
$124$	7.00000			0.628619
$125$	9.00000			0.804984
$126$	−4.50000	−	7.79423i	−0.400892	−	0.694365i
$127$	−3.50000	+	6.06218i	−0.310575	+	0.537931i	−0.978487	−	0.206309i	$-0.933855\pi$
$127$	−3.50000	+	6.06218i	−0.310575	+	0.537931i	0.667912	+	0.744240i	$0.267188\pi$
$128$	−1.50000	+	2.59808i	−0.132583	+	0.229640i
$129$	−12.0000	+	6.92820i	−1.05654	+	0.609994i
$130$	−6.00000			−0.526235
$131$	−17.0000			−1.48530			−0.742648	−	0.669681i	$-0.766431\pi$
$131$	−17.0000			−1.48530			−0.742648	+	0.669681i	$0.766431\pi$
$132$	4.50000	−	2.59808i	0.391675	−	0.226134i
$133$	10.5000	+	7.79423i	0.910465	+	0.675845i
$134$	4.00000			0.345547
$135$		−	5.19615i		−	0.447214i
$136$	−4.50000	−	7.79423i	−0.385872	−	0.668350i
$137$	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
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	0.768655	−	0.639664i	$-0.220926\pi$
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	−0.938293	+	0.345843i	$0.887593\pi$
$140$	−1.50000	+	2.59808i	−0.126773	+	0.219578i
$141$	13.5000	+	7.79423i	1.13691	+	0.656392i
$142$	15.0000			1.25877
$143$	9.00000	−	15.5885i	0.752618	−	1.30357i
$144$	3.00000			0.250000
$145$	5.00000			0.415227
$146$	5.00000			0.413803
$147$	−3.00000	+	1.73205i	−0.247436	+	0.142857i
$148$	1.00000	+	1.73205i	0.0821995	+	0.142374i
$149$	3.00000			0.245770			0.122885	−	0.992421i	$-0.460785\pi$
$149$	3.00000			0.245770			0.122885	+	0.992421i	$0.460785\pi$
$150$	−6.00000	+	3.46410i	−0.489898	+	0.282843i
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	−0.935857	−	0.352381i	$-0.885372\pi$
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	0.162758	−	0.986666i	$-0.447961\pi$
$152$	−12.0000	+	5.19615i	−0.973329	+	0.421464i
$153$	4.50000	−	7.79423i	0.363803	−	0.630126i
$154$	4.50000	+	7.79423i	0.362620	+	0.628077i
$155$	−3.50000	+	6.06218i	−0.281127	+	0.486926i
$156$	−9.00000	+	5.19615i	−0.720577	+	0.416025i
$157$	7.00000			0.558661			0.279330	−	0.960195i	$-0.409888\pi$
$157$	7.00000			0.558661			0.279330	+	0.960195i	$0.409888\pi$
$158$	−6.00000	−	10.3923i	−0.477334	−	0.826767i
$159$	−4.50000	+	2.59808i	−0.356873	+	0.206041i
$160$	−2.50000	−	4.33013i	−0.197642	−	0.342327i
$161$	−12.0000	+	20.7846i	−0.945732	+	1.63806i
$162$	4.50000	+	7.79423i	0.353553	+	0.612372i
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	−0.500000	−	0.866025i	−0.0390434	−	0.0676252i
$165$			5.19615i			0.404520i
$166$	1.00000			0.0776151
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	0.534875	−	0.844931i	$-0.320359\pi$
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	−0.999169	+	0.0407502i	$0.987025\pi$
$168$		−	15.5885i		−	1.20268i
$169$	−11.5000	+	19.9186i	−0.884615	+	1.53220i
$170$	3.00000			0.230089
$171$	−10.5000	−	7.79423i	−0.802955	−	0.596040i
$172$	−8.00000			−0.609994
$173$	7.00000	−	12.1244i	0.532200	−	0.921798i	−0.467093	−	0.884208i	$-0.654699\pi$
$173$	7.00000	−	12.1244i	0.532200	−	0.921798i	0.999293	−	0.0375896i	$-0.0119679\pi$
$174$	−7.50000	+	4.33013i	−0.568574	+	0.328266i
$175$	6.00000	+	10.3923i	0.453557	+	0.785584i
$176$	−3.00000			−0.226134
$177$	4.50000	+	2.59808i	0.338241	+	0.195283i
$178$	−0.500000	−	0.866025i	−0.0374766	−	0.0649113i
$179$	4.00000			0.298974			0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000			0.298974			0.149487	+	0.988764i	$0.452238\pi$
$180$	1.50000	−	2.59808i	0.111803	−	0.193649i
$181$	−5.50000	+	9.52628i	−0.408812	+	0.708083i	−0.994757	−	0.102268i	$-0.967390\pi$
$181$	−5.50000	+	9.52628i	−0.408812	+	0.708083i	0.585945	+	0.810351i	$0.300723\pi$
$182$	−9.00000	−	15.5885i	−0.667124	−	1.15549i
$183$	10.5000	+	6.06218i	0.776182	+	0.448129i
$184$	−12.0000	−	20.7846i	−0.884652	−	1.53226i
$185$	−2.00000			−0.147043
$186$		−	12.1244i		−	0.889001i
$187$	−4.50000	+	7.79423i	−0.329073	+	0.569970i
$188$	4.50000	+	7.79423i	0.328196	+	0.568453i
$189$	13.5000	−	7.79423i	0.981981	−	0.566947i
$190$	0.500000	−	4.33013i	0.0362738	−	0.314140i
$191$	4.50000	+	7.79423i	0.325609	+	0.563971i	0.981635	−	0.190767i	$-0.0610975\pi$
$191$	4.50000	+	7.79423i	0.325609	+	0.563971i	−0.656027	+	0.754738i	$0.727764\pi$
$192$	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	$0.709572\pi$
$194$	−1.00000	−	1.73205i	−0.0717958	−	0.124354i
$195$		−	10.3923i		−	0.744208i
$196$	−2.00000			−0.142857
$197$	−22.0000			−1.56744			−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000			−1.56744			−0.783718	+	0.621117i	$0.786679\pi$
$198$	−4.50000	−	7.79423i	−0.319801	−	0.553912i
$199$	8.50000	−	14.7224i	0.602549	−	1.04365i	−0.389885	−	0.920864i	$-0.627485\pi$
$199$	8.50000	−	14.7224i	0.602549	−	1.04365i	0.992434	−	0.122782i	$-0.0391815\pi$
$200$	−12.0000			−0.848528
$201$			6.92820i			0.488678i
$202$	−2.50000	+	4.33013i	−0.175899	+	0.304667i
$203$	7.50000	+	12.9904i	0.526397	+	0.911746i
$204$	4.50000	−	2.59808i	0.315063	−	0.181902i
$205$	1.00000			0.0698430
$206$	−3.50000	−	6.06218i	−0.243857	−	0.422372i
$207$	12.0000	−	20.7846i	0.834058	−	1.44463i
$208$	6.00000			0.416025
$209$	10.5000	+	7.79423i	0.726300	+	0.539138i
$210$	4.50000	+	2.59808i	0.310530	+	0.179284i
$211$	23.0000			1.58339			0.791693	−	0.610920i	$-0.209200\pi$
$211$	23.0000			1.58339			0.791693	+	0.610920i	$0.209200\pi$
$212$	−3.00000			−0.206041
$213$			25.9808i			1.78017i
$214$	−2.00000	+	3.46410i	−0.136717	+	0.236801i
$215$	4.00000	−	6.92820i	0.272798	−	0.472500i
$216$			15.5885i			1.06066i
$217$	−21.0000			−1.42557
$218$	1.00000			0.0677285
$219$			8.66025i			0.585206i
$220$	−1.50000	+	2.59808i	−0.101130	+	0.175162i
$221$	9.00000	−	15.5885i	0.605406	−	1.04859i
$222$	3.00000	−	1.73205i	0.201347	−	0.116248i
$223$	4.00000	−	6.92820i	0.267860	−	0.463947i	−0.700449	−	0.713702i	$-0.747017\pi$
$223$	4.00000	−	6.92820i	0.267860	−	0.463947i	0.968309	+	0.249756i	$0.0803503\pi$
$224$	7.50000	−	12.9904i	0.501115	−	0.867956i
$225$	−6.00000	−	10.3923i	−0.400000	−	0.692820i
$226$	7.50000	+	12.9904i	0.498893	+	0.864107i
$227$	10.5000	+	18.1865i	0.696909	+	1.20708i	0.969533	+	0.244962i	$0.0787754\pi$
$227$	10.5000	+	18.1865i	0.696909	+	1.20708i	−0.272623	+	0.962121i	$0.587891\pi$
$228$	−3.00000	−	6.92820i	−0.198680	−	0.458831i
$229$	−1.50000	+	2.59808i	−0.0991228	+	0.171686i	−0.911322	−	0.411695i	$-0.864937\pi$
$229$	−1.50000	+	2.59808i	−0.0991228	+	0.171686i	0.812199	+	0.583380i	$0.198270\pi$
$230$	8.00000			0.527504
$231$	−13.5000	+	7.79423i	−0.888235	+	0.512823i
$232$	−15.0000			−0.984798
$233$	0.500000	+	0.866025i	0.0327561	+	0.0567352i	0.881939	−	0.471364i	$-0.156238\pi$
$233$	0.500000	+	0.866025i	0.0327561	+	0.0567352i	−0.849183	+	0.528099i	$0.822905\pi$
$234$	9.00000	+	15.5885i	0.588348	+	1.01905i
$235$	−9.00000			−0.587095
$236$	1.50000	+	2.59808i	0.0976417	+	0.169120i
$237$	18.0000	−	10.3923i	1.16923	−	0.675053i
$238$	4.50000	+	7.79423i	0.291692	+	0.505225i
$239$	13.5000	−	23.3827i	0.873242	−	1.51250i	0.0146191	−	0.999893i	$-0.495346\pi$
$239$	13.5000	−	23.3827i	0.873242	−	1.51250i	0.858623	−	0.512607i	$-0.171320\pi$
$240$	−1.50000	+	0.866025i	−0.0968246	+	0.0559017i
$241$	15.0000			0.966235			0.483117	−	0.875556i	$-0.339504\pi$
$241$	15.0000			0.966235			0.483117	+	0.875556i	$0.339504\pi$
$242$	−1.00000	−	1.73205i	−0.0642824	−	0.111340i
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$	3.50000	+	6.06218i	0.224065	+	0.388091i
$245$	1.00000	−	1.73205i	0.0638877	−	0.110657i
$246$	−1.50000	+	0.866025i	−0.0956365	+	0.0552158i
$247$	−21.0000	−	15.5885i	−1.33620	−	0.991870i
$248$	10.5000	−	18.1865i	0.666751	−	1.15485i
$249$			1.73205i			0.109764i
$250$	4.50000	−	7.79423i	0.284605	−	0.492950i
$251$	−1.50000	+	2.59808i	−0.0946792	+	0.163989i	−0.909475	−	0.415759i	$-0.863516\pi$
$251$	−1.50000	+	2.59808i	−0.0946792	+	0.163989i	0.814795	+	0.579748i	$0.196849\pi$
$252$	9.00000			0.566947
$253$	−12.0000	+	20.7846i	−0.754434	+	1.30672i
$254$	3.50000	+	6.06218i	0.219610	+	0.380375i
$255$			5.19615i			0.325396i
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	0.895528	−	0.445005i	$-0.146798\pi$
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	−0.833150	+	0.553047i	$0.813465\pi$
$258$			13.8564i			0.862662i
$259$	−3.00000	−	5.19615i	−0.186411	−	0.322873i
$260$	3.00000	−	5.19615i	0.186052	−	0.322252i
$261$	−7.50000	−	12.9904i	−0.464238	−	0.804084i
$262$	−8.50000	+	14.7224i	−0.525132	+	0.909555i
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	0.212565	+	0.977147i	$0.431818\pi$
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	−0.952517	+	0.304487i	$0.901515\pi$
$264$		−	15.5885i		−	0.959403i
$265$	1.50000	−	2.59808i	0.0921443	−	0.159599i
$266$	12.0000	−	5.19615i	0.735767	−	0.318597i
$267$	1.50000	−	0.866025i	0.0917985	−	0.0529999i
$268$	−2.00000	+	3.46410i	−0.122169	+	0.211604i
$269$	−1.50000	−	2.59808i	−0.0914566	−	0.158408i	0.816668	−	0.577108i	$-0.195819\pi$
$269$	−1.50000	−	2.59808i	−0.0914566	−	0.158408i	−0.908124	+	0.418701i	$0.862486\pi$
$270$	−4.50000	−	2.59808i	−0.273861	−	0.158114i
$271$	7.50000	+	12.9904i	0.455593	+	0.789109i	0.998722	−	0.0505395i	$-0.0160941\pi$
$271$	7.50000	+	12.9904i	0.455593	+	0.789109i	−0.543130	+	0.839649i	$0.682761\pi$
$272$	−3.00000			−0.181902
$273$	27.0000	−	15.5885i	1.63411	−	0.943456i
$274$	1.50000	−	2.59808i	0.0906183	−	0.156956i
$275$	6.00000	+	10.3923i	0.361814	+	0.626680i
$276$	12.0000	−	6.92820i	0.722315	−	0.417029i
$277$	2.50000	+	4.33013i	0.150210	+	0.260172i	0.931305	−	0.364241i	$-0.118672\pi$
$277$	2.50000	+	4.33013i	0.150210	+	0.260172i	−0.781094	+	0.624413i	$0.785338\pi$
$278$	−4.00000			−0.239904
$279$	21.0000			1.25724
$280$	4.50000	+	7.79423i	0.268926	+	0.465794i
$281$	−5.00000			−0.298275			−0.149137	−	0.988816i	$-0.547650\pi$
$281$	−5.00000			−0.298275			−0.149137	+	0.988816i	$0.547650\pi$
$282$	13.5000	−	7.79423i	0.803913	−	0.464140i
$283$	−5.00000			−0.297219			−0.148610	−	0.988896i	$-0.547480\pi$
$283$	−5.00000			−0.297219			−0.148610	+	0.988896i	$0.547480\pi$
$284$	−7.50000	+	12.9904i	−0.445043	+	0.770837i
$285$	7.50000	+	0.866025i	0.444262	+	0.0512989i
$286$	−9.00000	−	15.5885i	−0.532181	−	0.921765i
$287$	1.50000	+	2.59808i	0.0885422	+	0.153360i
$288$	−7.50000	+	12.9904i	−0.441942	+	0.765466i
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	2.50000	−	4.33013i	0.146805	−	0.254274i
$291$	3.00000	−	1.73205i	0.175863	−	0.101535i
$292$	−2.50000	+	4.33013i	−0.146301	+	0.253402i
$293$	12.5000	−	21.6506i	0.730258	−	1.26484i	−0.226515	−	0.974008i	$-0.572733\pi$
$293$	12.5000	−	21.6506i	0.730258	−	1.26484i	0.956773	−	0.290836i	$-0.0939334\pi$
$294$			3.46410i			0.202031i
$295$	−3.00000			−0.174667
$296$	6.00000			0.348743
$297$	13.5000	−	7.79423i	0.783349	−	0.452267i
$298$	1.50000	−	2.59808i	0.0868927	−	0.150503i
$299$	24.0000	−	41.5692i	1.38796	−	2.40401i
$300$		−	6.92820i		−	0.400000i
$301$	24.0000			1.38334
$302$	−19.0000			−1.09333
$303$	−7.50000	−	4.33013i	−0.430864	−	0.248759i
$304$	−0.500000	+	4.33013i	−0.0286770	+	0.248350i
$305$	−7.00000			−0.400819
$306$	−4.50000	−	7.79423i	−0.257248	−	0.445566i
$307$	−4.50000	−	7.79423i	−0.256829	−	0.444840i	0.708562	−	0.705649i	$-0.249344\pi$
$307$	−4.50000	−	7.79423i	−0.256829	−	0.444840i	−0.965391	+	0.260808i	$0.916011\pi$
$308$	−9.00000			−0.512823
$309$	10.5000	−	6.06218i	0.597324	−	0.344865i
$310$	3.50000	+	6.06218i	0.198787	+	0.344309i
$311$	3.50000	−	6.06218i	0.198467	−	0.343755i	−0.749565	−	0.661931i	$-0.769737\pi$
$311$	3.50000	−	6.06218i	0.198467	−	0.343755i	0.948031	+	0.318177i	$0.103070\pi$
$312$			31.1769i			1.76505i
$313$	−25.0000			−1.41308			−0.706542	−	0.707671i	$-0.749746\pi$
$313$	−25.0000			−1.41308			−0.706542	+	0.707671i	$0.749746\pi$
$314$	3.50000	−	6.06218i	0.197516	−	0.342108i
$315$	−4.50000	+	7.79423i	−0.253546	+	0.439155i
$316$	12.0000			0.675053
$317$	−21.0000			−1.17948			−0.589739	−	0.807594i	$-0.700769\pi$
$317$	−21.0000			−1.17948			−0.589739	+	0.807594i	$0.700769\pi$
$318$			5.19615i			0.291386i
$319$	7.50000	+	12.9904i	0.419919	+	0.727322i
$320$	−7.00000			−0.391312
$321$	−6.00000	−	3.46410i	−0.334887	−	0.193347i
$322$	12.0000	+	20.7846i	0.668734	+	1.15828i
$323$	10.5000	+	7.79423i	0.584236	+	0.433682i
$324$	−9.00000			−0.500000
$325$	−12.0000	−	20.7846i	−0.665640	−	1.15292i
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$			1.73205i			0.0957826i
$328$	−3.00000			−0.165647
$329$	−13.5000	−	23.3827i	−0.744279	−	1.28913i
$330$	4.50000	+	2.59808i	0.247717	+	0.143019i
$331$	−13.5000	−	23.3827i	−0.742027	−	1.28523i	−0.951571	−	0.307429i	$-0.900531\pi$
$331$	−13.5000	−	23.3827i	−0.742027	−	1.28523i	0.209544	−	0.977799i	$-0.432802\pi$
$332$	−0.500000	+	0.866025i	−0.0274411	+	0.0475293i
$333$	3.00000	+	5.19615i	0.164399	+	0.284747i
$334$	−12.0000			−0.656611
$335$	−2.00000	−	3.46410i	−0.109272	−	0.189264i
$336$	−4.50000	−	2.59808i	−0.245495	−	0.141737i
$337$	−13.0000			−0.708155			−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000			−0.708155			−0.354078	+	0.935216i	$0.615205\pi$
$338$	11.5000	+	19.9186i	0.625518	+	1.08343i
$339$	−22.5000	+	12.9904i	−1.22203	+	0.705541i
$340$	−1.50000	+	2.59808i	−0.0813489	+	0.140900i
$341$	−21.0000			−1.13721
$342$	−12.0000	+	5.19615i	−0.648886	+	0.280976i
$343$	−15.0000			−0.809924
$344$	−12.0000	+	20.7846i	−0.646997	+	1.12063i
$345$			13.8564i			0.746004i
$346$	−7.00000	−	12.1244i	−0.376322	−	0.651809i
$347$	−33.0000			−1.77153			−0.885766	−	0.464131i	$-0.846367\pi$
$347$	−33.0000			−1.77153			−0.885766	+	0.464131i	$0.846367\pi$
$348$		−	8.66025i		−	0.464238i
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	0.925147	−	0.379610i	$-0.123942\pi$
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	−0.791325	+	0.611396i	$0.790608\pi$
$350$	12.0000			0.641427
$351$	−27.0000	+	15.5885i	−1.44115	+	0.832050i
$352$	7.50000	−	12.9904i	0.399751	−	0.692390i
$353$	14.5000	+	25.1147i	0.771757	+	1.33672i	0.936599	+	0.350403i	$0.113955\pi$
$353$	14.5000	+	25.1147i	0.771757	+	1.33672i	−0.164842	+	0.986320i	$0.552711\pi$
$354$	4.50000	−	2.59808i	0.239172	−	0.138086i
$355$	−7.50000	−	12.9904i	−0.398059	−	0.689458i
$356$	1.00000			0.0529999
$357$	−13.5000	+	7.79423i	−0.714496	+	0.412514i
$358$	2.00000	−	3.46410i	0.105703	−	0.183083i
$359$	−8.50000	−	14.7224i	−0.448613	−	0.777020i	0.549683	−	0.835373i	$-0.314748\pi$
$359$	−8.50000	−	14.7224i	−0.448613	−	0.777020i	−0.998296	+	0.0583530i	$0.981415\pi$
$360$	−4.50000	−	7.79423i	−0.237171	−	0.410792i
$361$	13.0000	−	13.8564i	0.684211	−	0.729285i
$362$	5.50000	+	9.52628i	0.289074	+	0.500690i
$363$	3.00000	−	1.73205i	0.157459	−	0.0909091i
$364$	18.0000			0.943456
$365$	−2.50000	−	4.33013i	−0.130856	−	0.226649i
$366$	10.5000	−	6.06218i	0.548844	−	0.316875i
$367$	−31.0000			−1.61819			−0.809093	−	0.587680i	$-0.800041\pi$
$367$	−31.0000			−1.61819			−0.809093	+	0.587680i	$0.800041\pi$
$368$	−8.00000			−0.417029
$369$	−1.50000	−	2.59808i	−0.0780869	−	0.135250i
$370$	−1.00000	+	1.73205i	−0.0519875	+	0.0900450i
$371$	9.00000			0.467257
$372$	10.5000	+	6.06218i	0.544400	+	0.314309i
$373$	−11.5000	+	19.9186i	−0.595447	+	1.03135i	0.398036	+	0.917370i	$0.369692\pi$
$373$	−11.5000	+	19.9186i	−0.595447	+	1.03135i	−0.993484	+	0.113975i	$0.963641\pi$
$374$	4.50000	+	7.79423i	0.232689	+	0.403030i
$375$	13.5000	+	7.79423i	0.697137	+	0.402492i
$376$	27.0000			1.39242
$377$	−15.0000	−	25.9808i	−0.772539	−	1.33808i
$378$		−	15.5885i		−	0.801784i
$379$	12.0000			0.616399			0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000			0.616399			0.308199	+	0.951322i	$0.400274\pi$
$380$	3.50000	+	2.59808i	0.179546	+	0.133278i
$381$	−10.5000	+	6.06218i	−0.537931	+	0.310575i
$382$	9.00000			0.460480
$383$	19.0000			0.970855			0.485427	−	0.874277i	$-0.338664\pi$
$383$	19.0000			0.970855			0.485427	+	0.874277i	$0.338664\pi$
$384$	−4.50000	+	2.59808i	−0.229640	+	0.132583i
$385$	4.50000	−	7.79423i	0.229341	−	0.397231i
$386$	−8.50000	+	14.7224i	−0.432639	+	0.749352i
$387$	−24.0000			−1.21999
$388$	2.00000			0.101535
$389$	15.0000			0.760530			0.380265	−	0.924878i	$-0.375833\pi$
$389$	15.0000			0.760530			0.380265	+	0.924878i	$0.375833\pi$
$390$	−9.00000	−	5.19615i	−0.455733	−	0.263117i
$391$	−12.0000	+	20.7846i	−0.606866	+	1.05112i
$392$	−3.00000	+	5.19615i	−0.151523	+	0.262445i
$393$	−25.5000	−	14.7224i	−1.28630	−	0.742648i
$394$	−11.0000	+	19.0526i	−0.554172	+	0.959854i
$395$	−6.00000	+	10.3923i	−0.301893	+	0.522894i
$396$	9.00000			0.452267
$397$	6.50000	+	11.2583i	0.326226	+	0.565039i	0.981760	−	0.190126i	$-0.0608897\pi$
$397$	6.50000	+	11.2583i	0.326226	+	0.565039i	−0.655534	+	0.755166i	$0.727556\pi$
$398$	−8.50000	−	14.7224i	−0.426067	−	0.737969i
$399$	9.00000	+	20.7846i	0.450564	+	1.04053i
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	−17.0000			−0.848939			−0.424470	−	0.905442i	$-0.639539\pi$
$401$	−17.0000			−0.848939			−0.424470	+	0.905442i	$0.639539\pi$
$402$	6.00000	+	3.46410i	0.299253	+	0.172774i
$403$	42.0000			2.09217
$404$	−2.50000	−	4.33013i	−0.124380	−	0.215432i
$405$	4.50000	−	7.79423i	0.223607	−	0.387298i
$406$	15.0000			0.744438
$407$	−3.00000	−	5.19615i	−0.148704	−	0.257564i
$408$		−	15.5885i		−	0.771744i
$409$	−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	$0.912855\pi$
$410$	0.500000	−	0.866025i	0.0246932	−	0.0427699i
$411$	4.50000	+	2.59808i	0.221969	+	0.128154i
$412$	7.00000			0.344865
$413$	−4.50000	−	7.79423i	−0.221431	−	0.383529i
$414$	−12.0000	−	20.7846i	−0.589768	−	1.02151i
$415$	−0.500000	−	0.866025i	−0.0245440	−	0.0425115i
$416$	−15.0000	+	25.9808i	−0.735436	+	1.27381i
$417$		−	6.92820i		−	0.339276i
$418$	12.0000	−	5.19615i	0.586939	−	0.254152i
$419$	11.5000	−	19.9186i	0.561812	−	0.973087i	−0.435527	−	0.900176i	$-0.643438\pi$
$419$	11.5000	−	19.9186i	0.561812	−	0.973087i	0.997338	−	0.0729107i	$-0.0232288\pi$
$420$	−4.50000	+	2.59808i	−0.219578	+	0.126773i
$421$	−1.00000	+	1.73205i	−0.0487370	+	0.0844150i	−0.889365	−	0.457198i	$-0.848853\pi$
$421$	−1.00000	+	1.73205i	−0.0487370	+	0.0844150i	0.840628	+	0.541613i	$0.182186\pi$
$422$	11.5000	−	19.9186i	0.559811	−	0.969622i
$423$	13.5000	+	23.3827i	0.656392	+	1.13691i
$424$	−4.50000	+	7.79423i	−0.218539	+	0.378521i
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$	22.5000	+	12.9904i	1.09013	+	0.629386i
$427$	−10.5000	−	18.1865i	−0.508131	−	0.880108i
$428$	−2.00000	−	3.46410i	−0.0966736	−	0.167444i
$429$	27.0000	−	15.5885i	1.30357	−	0.752618i
$430$	−4.00000	−	6.92820i	−0.192897	−	0.334108i
$431$	−13.5000	+	23.3827i	−0.650272	+	1.12630i	0.332785	+	0.943003i	$0.392012\pi$
$431$	−13.5000	+	23.3827i	−0.650272	+	1.12630i	−0.983057	+	0.183301i	$0.941322\pi$
$432$	4.50000	+	2.59808i	0.216506	+	0.125000i
$433$	14.5000	−	25.1147i	0.696826	−	1.20694i	−0.272736	−	0.962089i	$-0.587929\pi$
$433$	14.5000	−	25.1147i	0.696826	−	1.20694i	0.969561	−	0.244848i	$-0.0787382\pi$
$434$	−10.5000	+	18.1865i	−0.504016	+	0.872982i
$435$	7.50000	+	4.33013i	0.359597	+	0.207614i
$436$	−0.500000	+	0.866025i	−0.0239457	+	0.0414751i
$437$	28.0000	+	20.7846i	1.33942	+	0.994263i
$438$	7.50000	+	4.33013i	0.358364	+	0.206901i
$439$	−8.00000	+	13.8564i	−0.381819	+	0.661330i	−0.991322	−	0.131453i	$-0.958036\pi$
$439$	−8.00000	+	13.8564i	−0.381819	+	0.661330i	0.609503	+	0.792784i	$0.291369\pi$
$440$	4.50000	+	7.79423i	0.214529	+	0.371575i
$441$	−6.00000			−0.285714
$442$	−9.00000	−	15.5885i	−0.428086	−	0.741467i
$443$	9.00000			0.427603			0.213801	−	0.976877i	$-0.431415\pi$
$443$	9.00000			0.427603			0.213801	+	0.976877i	$0.431415\pi$
$444$			3.46410i			0.164399i
$445$	−0.500000	+	0.866025i	−0.0237023	+	0.0410535i
$446$	−4.00000	−	6.92820i	−0.189405	−	0.328060i
$447$	4.50000	+	2.59808i	0.212843	+	0.122885i
$448$	−10.5000	−	18.1865i	−0.496078	−	0.859233i
$449$	−10.0000			−0.471929			−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000			−0.471929			−0.235965	+	0.971762i	$0.575825\pi$
$450$	−12.0000			−0.565685
$451$	1.50000	+	2.59808i	0.0706322	+	0.122339i
$452$	−15.0000			−0.705541
$453$		−	32.9090i		−	1.54620i
$454$	21.0000			0.985579
$455$	−9.00000	+	15.5885i	−0.421927	+	0.730798i
$456$	−22.5000	−	2.59808i	−1.05366	−	0.121666i
$457$	−1.50000	−	2.59808i	−0.0701670	−	0.121533i	0.828807	−	0.559534i	$-0.189020\pi$
$457$	−1.50000	−	2.59808i	−0.0701670	−	0.121533i	−0.898974	+	0.438001i	$0.855687\pi$
$458$	1.50000	+	2.59808i	0.0700904	+	0.121400i
$459$	13.5000	−	7.79423i	0.630126	−	0.363803i
$460$	−4.00000	+	6.92820i	−0.186501	+	0.323029i
$461$	3.00000	−	5.19615i	0.139724	−	0.242009i	−0.787668	−	0.616100i	$-0.788712\pi$
$461$	3.00000	−	5.19615i	0.139724	−	0.242009i	0.927392	+	0.374091i	$0.122045\pi$
$462$			15.5885i			0.725241i
$463$	−2.50000	+	4.33013i	−0.116185	+	0.201238i	−0.918253	−	0.395995i	$-0.870400\pi$
$463$	−2.50000	+	4.33013i	−0.116185	+	0.201238i	0.802068	+	0.597233i	$0.203733\pi$
$464$	−2.50000	+	4.33013i	−0.116060	+	0.201021i
$465$	−10.5000	+	6.06218i	−0.486926	+	0.281127i
$466$	1.00000			0.0463241
$467$	8.00000			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$	−18.0000			−0.832050
$469$	6.00000	−	10.3923i	0.277054	−	0.479872i
$470$	−4.50000	+	7.79423i	−0.207570	+	0.359521i
$471$	10.5000	+	6.06218i	0.483814	+	0.279330i
$472$	9.00000			0.414259
$473$	24.0000			1.10352
$474$		−	20.7846i		−	0.954669i
$475$	16.0000	−	6.92820i	0.734130	−	0.317888i
$476$	−9.00000			−0.412514
$477$	−9.00000			−0.412082
$478$	−13.5000	−	23.3827i	−0.617476	−	1.06950i
$479$	1.00000			0.0456912			0.0228456	−	0.999739i	$-0.492727\pi$
$479$	1.00000			0.0456912			0.0228456	+	0.999739i	$0.492727\pi$
$480$		−	8.66025i		−	0.395285i
$481$	6.00000	+	10.3923i	0.273576	+	0.473848i
$482$	7.50000	−	12.9904i	0.341616	−	0.591696i
$483$	−36.0000	+	20.7846i	−1.63806	+	0.945732i
$484$	2.00000			0.0909091
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$			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	$0.241826\pi$
$488$	21.0000			0.950625
$489$	−6.00000	−	3.46410i	−0.271329	−	0.156652i
$490$	−1.00000	−	1.73205i	−0.0451754	−	0.0782461i
$491$	35.0000			1.57953			0.789764	−	0.613411i	$-0.210203\pi$
$491$	35.0000			1.57953			0.789764	+	0.613411i	$0.210203\pi$
$492$		−	1.73205i		−	0.0780869i
$493$	7.50000	+	12.9904i	0.337783	+	0.585057i
$494$	−24.0000	+	10.3923i	−1.07981	+	0.467572i
$495$	−4.50000	+	7.79423i	−0.202260	+	0.350325i
$496$	−3.50000	−	6.06218i	−0.157155	−	0.272200i
$497$	22.5000	−	38.9711i	1.00926	−	1.74809i
$498$	1.50000	+	0.866025i	0.0672166	+	0.0388075i
$499$	19.0000			0.850557			0.425278	−	0.905063i	$-0.360176\pi$
$499$	19.0000			0.850557			0.425278	+	0.905063i	$0.360176\pi$
$500$	4.50000	+	7.79423i	0.201246	+	0.348569i
$501$		−	20.7846i		−	0.928588i
$502$	1.50000	+	2.59808i	0.0669483	+	0.115958i
$503$	−7.50000	+	12.9904i	−0.334408	+	0.579212i	−0.983371	−	0.181608i	$-0.941870\pi$
$503$	−7.50000	+	12.9904i	−0.334408	+	0.579212i	0.648963	+	0.760820i	$0.275203\pi$
$504$	13.5000	−	23.3827i	0.601338	−	1.04155i
$505$	5.00000			0.222497
$506$	12.0000	+	20.7846i	0.533465	+	0.923989i
$507$	−34.5000	+	19.9186i	−1.53220	+	0.884615i
$508$	−7.00000			−0.310575
$509$	19.0000	+	32.9090i	0.842160	+	1.45866i	0.888065	+	0.459718i	$0.152050\pi$
$509$	19.0000	+	32.9090i	0.842160	+	1.45866i	−0.0459045	+	0.998946i	$0.514617\pi$
$510$	4.50000	+	2.59808i	0.199263	+	0.115045i
$511$	7.50000	−	12.9904i	0.331780	−	0.574661i
$512$	11.0000			0.486136
$513$	−9.00000	−	20.7846i	−0.397360	−	0.917663i
$514$	2.00000			0.0882162
$515$	−3.50000	+	6.06218i	−0.154228	+	0.267131i
$516$	−12.0000	−	6.92820i	−0.528271	−	0.304997i
$517$	−13.5000	−	23.3827i	−0.593729	−	1.02837i
$518$	−6.00000			−0.263625
$519$	21.0000	−	12.1244i	0.921798	−	0.532200i
$520$	−9.00000	−	15.5885i	−0.394676	−	0.683599i
$521$	−2.00000			−0.0876216			−0.0438108	−	0.999040i	$-0.513950\pi$
$521$	−2.00000			−0.0876216			−0.0438108	+	0.999040i	$0.513950\pi$
$522$	−15.0000			−0.656532
$523$	−5.50000	+	9.52628i	−0.240498	+	0.416555i	−0.960856	−	0.277047i	$-0.910644\pi$
$523$	−5.50000	+	9.52628i	−0.240498	+	0.416555i	0.720358	+	0.693602i	$0.243977\pi$
$524$	−8.50000	−	14.7224i	−0.371324	−	0.643152i
$525$			20.7846i			0.907115i
$526$	12.0000	+	20.7846i	0.523225	+	0.906252i
$527$	−21.0000			−0.914774
$528$	−4.50000	−	2.59808i	−0.195837	−	0.113067i
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$	−1.50000	−	2.59808i	−0.0651558	−	0.112853i
$531$	4.50000	+	7.79423i	0.195283	+	0.338241i
$532$	−1.50000	+	12.9904i	−0.0650332	+	0.563204i
$533$	−3.00000	−	5.19615i	−0.129944	−	0.225070i
$534$		−	1.73205i		−	0.0749532i
$535$	4.00000			0.172935
$536$	6.00000	+	10.3923i	0.259161	+	0.448879i
$537$	6.00000	+	3.46410i	0.258919	+	0.149487i
$538$	−3.00000			−0.129339
$539$	6.00000			0.258438
$540$	4.50000	−	2.59808i	0.193649	−	0.111803i
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	−0.461625	−	0.887075i	$-0.652733\pi$
$541$	12.5000	−	21.6506i	0.537417	−	0.930834i	0.999042	−	0.0437584i	$-0.0139332\pi$
$542$	15.0000			0.644305
$543$	−16.5000	+	9.52628i	−0.708083	+	0.408812i
$544$	7.50000	−	12.9904i	0.321560	−	0.556958i
$545$	−0.500000	−	0.866025i	−0.0214176	−	0.0370965i
$546$		−	31.1769i		−	1.33425i
$547$	−11.0000			−0.470326			−0.235163	−	0.971956i	$-0.575562\pi$
$547$	−11.0000			−0.470326			−0.235163	+	0.971956i	$0.575562\pi$
$548$	1.50000	+	2.59808i	0.0640768	+	0.110984i
$549$	10.5000	+	18.1865i	0.448129	+	0.776182i
$550$	12.0000			0.511682
$551$	20.0000	−	8.66025i	0.852029	−	0.368939i
$552$		−	41.5692i		−	1.76930i
$553$	−36.0000			−1.53088
$554$	5.00000			0.212430
$555$	−3.00000	−	1.73205i	−0.127343	−	0.0735215i
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	4.50000	−	7.79423i	0.190671	−	0.330252i	−0.754802	−	0.655953i	$-0.772267\pi$
$557$	4.50000	−	7.79423i	0.190671	−	0.330252i	0.945473	+	0.325701i	$0.105600\pi$
$558$	10.5000	−	18.1865i	0.444500	−	0.769897i
$559$	−48.0000			−2.03018
$560$	3.00000			0.126773
$561$	−13.5000	+	7.79423i	−0.569970	+	0.329073i
$562$	−2.50000	+	4.33013i	−0.105456	+	0.182655i
$563$	−18.5000	+	32.0429i	−0.779682	+	1.35045i	0.152443	+	0.988312i	$0.451286\pi$
$563$	−18.5000	+	32.0429i	−0.779682	+	1.35045i	−0.932125	+	0.362137i	$0.882047\pi$
$564$			15.5885i			0.656392i
$565$	7.50000	−	12.9904i	0.315527	−	0.546509i
$566$	−2.50000	+	4.33013i	−0.105083	+	0.182009i
$567$	27.0000			1.13389
$568$	22.5000	+	38.9711i	0.944079	+	1.63519i
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	0.664897	−	0.746935i	$-0.268475\pi$
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	−0.979313	+	0.202350i	$0.935142\pi$
$570$	4.50000	−	6.06218i	0.188484	−	0.253917i
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	−0.595862	−	0.803087i	$-0.703189\pi$
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	0.993425	+	0.114488i	$0.0365228\pi$
$572$	18.0000			0.752618
$573$			15.5885i			0.651217i
$574$	3.00000			0.125218
$575$	16.0000	+	27.7128i	0.667246	+	1.15570i
$576$	10.5000	+	18.1865i	0.437500	+	0.757772i
$577$	30.0000			1.24892			0.624458	−	0.781058i	$-0.285320\pi$
$577$	30.0000			1.24892			0.624458	+	0.781058i	$0.285320\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$	−25.5000	−	14.7224i	−1.05974	−	0.611843i
$580$	2.50000	+	4.33013i	0.103807	+	0.179799i
$581$	1.50000	−	2.59808i	0.0622305	−	0.107786i
$582$		−	3.46410i		−	0.143592i
$583$	9.00000			0.372742
$584$	7.50000	+	12.9904i	0.310352	+	0.537546i
$585$	9.00000	−	15.5885i	0.372104	−	0.644503i
$586$	−12.5000	−	21.6506i	−0.516370	−	0.894379i
$587$	10.0000	−	17.3205i	0.412744	−	0.714894i	−0.582445	−	0.812870i	$-0.697904\pi$
$587$	10.0000	−	17.3205i	0.412744	−	0.714894i	0.995189	+	0.0979766i	$0.0312370\pi$
$588$	−3.00000	−	1.73205i	−0.123718	−	0.0714286i
$589$	−3.50000	+	30.3109i	−0.144215	+	1.24894i
$590$	−1.50000	+	2.59808i	−0.0617540	+	0.106961i
$591$	−33.0000	−	19.0526i	−1.35744	−	0.783718i
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	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	$0.107505\pi$
$594$		−	15.5885i		−	0.639602i
$595$	4.50000	−	7.79423i	0.184482	−	0.319532i
$596$	1.50000	+	2.59808i	0.0614424	+	0.106421i
$597$	25.5000	−	14.7224i	1.04365	−	0.602549i
$598$	−24.0000	−	41.5692i	−0.981433	−	1.69989i
$599$	−18.0000	−	31.1769i	−0.735460	−	1.27385i	−0.954521	−	0.298143i	$-0.903633\pi$
$599$	−18.0000	−	31.1769i	−0.735460	−	1.27385i	0.219061	−	0.975711i	$-0.429701\pi$
$600$	−18.0000	−	10.3923i	−0.734847	−	0.424264i
$601$	14.5000	+	25.1147i	0.591467	+	1.02445i	0.994035	+	0.109061i	$0.0347845\pi$
$601$	14.5000	+	25.1147i	0.591467	+	1.02445i	−0.402568	+	0.915390i	$0.631882\pi$
$602$	12.0000	−	20.7846i	0.489083	−	0.847117i
$603$	−6.00000	+	10.3923i	−0.244339	+	0.423207i
$604$	9.50000	−	16.4545i	0.386550	−	0.669523i
$605$	−1.00000	+	1.73205i	−0.0406558	+	0.0704179i
$606$	−7.50000	+	4.33013i	−0.304667	+	0.175899i
$607$	1.50000	−	2.59808i	0.0608831	−	0.105453i	−0.833977	−	0.551799i	$-0.813942\pi$
$607$	1.50000	−	2.59808i	0.0608831	−	0.105453i	0.894860	+	0.446346i	$0.147275\pi$
$608$	−17.5000	−	12.9904i	−0.709719	−	0.526830i
$609$			25.9808i			1.05279i
$610$	−3.50000	+	6.06218i	−0.141711	+	0.245450i
$611$	27.0000	+	46.7654i	1.09230	+	1.89192i
$612$	9.00000			0.363803
$613$	10.5000	+	18.1865i	0.424091	+	0.734547i	0.996335	−	0.0855362i	$-0.0272603\pi$
$613$	10.5000	+	18.1865i	0.424091	+	0.734547i	−0.572244	+	0.820083i	$0.693927\pi$
$614$	−9.00000			−0.363210
$615$	1.50000	+	0.866025i	0.0604858	+	0.0349215i
$616$	−13.5000	+	23.3827i	−0.543931	+	0.942115i
$617$	−11.0000	−	19.0526i	−0.442843	−	0.767027i	0.555056	−	0.831813i	$-0.312697\pi$
$617$	−11.0000	−	19.0526i	−0.442843	−	0.767027i	−0.997899	+	0.0647859i	$0.979364\pi$
$618$		−	12.1244i		−	0.487713i
$619$	−17.5000	−	30.3109i	−0.703384	−	1.21830i	−0.967271	−	0.253744i	$-0.918338\pi$
$619$	−17.5000	−	30.3109i	−0.703384	−	1.21830i	0.263887	−	0.964554i	$-0.414995\pi$
$620$	−7.00000			−0.281127
$621$	36.0000	−	20.7846i	1.44463	−	0.834058i
$622$	−3.50000	−	6.06218i	−0.140337	−	0.243071i
$623$	−3.00000			−0.120192
$624$	9.00000	+	5.19615i	0.360288	+	0.208013i
$625$	11.0000			0.440000
$626$	−12.5000	+	21.6506i	−0.499600	+	0.865333i
$627$	9.00000	+	20.7846i	0.359425	+	0.830057i
$628$	3.50000	+	6.06218i	0.139665	+	0.241907i
$629$	−3.00000	−	5.19615i	−0.119618	−	0.207184i
$630$	4.50000	+	7.79423i	0.179284	+	0.310530i
$631$	−21.5000	+	37.2391i	−0.855901	+	1.48246i	0.0199047	+	0.999802i	$0.493664\pi$
$631$	−21.5000	+	37.2391i	−0.855901	+	1.48246i	−0.875806	+	0.482663i	$0.839670\pi$
$632$	18.0000	−	31.1769i	0.716002	−	1.24015i
$633$	34.5000	+	19.9186i	1.37125	+	0.791693i
$634$	−10.5000	+	18.1865i	−0.417008	+	0.722280i
$635$	3.50000	−	6.06218i	0.138893	−	0.240570i
$636$	−4.50000	−	2.59808i	−0.178437	−	0.103020i
$637$	−12.0000			−0.475457
$638$	15.0000			0.593856
$639$	−22.5000	+	38.9711i	−0.890086	+	1.54167i
$640$	1.50000	−	2.59808i	0.0592927	−	0.102698i
$641$	−17.0000	+	29.4449i	−0.671460	+	1.16300i	0.306031	+	0.952022i	$0.400999\pi$
$641$	−17.0000	+	29.4449i	−0.671460	+	1.16300i	−0.977490	+	0.210981i	$0.932334\pi$
$642$	−6.00000	+	3.46410i	−0.236801	+	0.136717i
$643$	−1.00000			−0.0394362			−0.0197181	−	0.999806i	$-0.506277\pi$
$643$	−1.00000			−0.0394362			−0.0197181	+	0.999806i	$0.506277\pi$
$644$	−24.0000			−0.945732
$645$	12.0000	−	6.92820i	0.472500	−	0.272798i
$646$	12.0000	−	5.19615i	0.472134	−	0.204440i
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	−13.5000	+	23.3827i	−0.530330	+	0.918559i
$649$	−4.50000	−	7.79423i	−0.176640	−	0.305950i
$650$	−24.0000			−0.941357
$651$	−31.5000	−	18.1865i	−1.23458	−	0.712786i
$652$	−2.00000	−	3.46410i	−0.0783260	−	0.135665i
$653$	−9.50000	+	16.4545i	−0.371764	+	0.643914i	−0.989837	−	0.142207i	$-0.954580\pi$
$653$	−9.50000	+	16.4545i	−0.371764	+	0.643914i	0.618073	+	0.786121i	$0.287914\pi$
$654$	1.50000	+	0.866025i	0.0586546	+	0.0338643i
$655$	17.0000			0.664245
$656$	−0.500000	+	0.866025i	−0.0195217	+	0.0338126i
$657$	−7.50000	+	12.9904i	−0.292603	+	0.506803i
$658$	−27.0000			−1.05257
$659$	−31.0000			−1.20759			−0.603794	−	0.797140i	$-0.706345\pi$
$659$	−31.0000			−1.20759			−0.603794	+	0.797140i	$0.706345\pi$
$660$	−4.50000	+	2.59808i	−0.175162	+	0.101130i
$661$	−21.0000	−	36.3731i	−0.816805	−	1.41475i	−0.908024	−	0.418917i	$-0.862410\pi$
$661$	−21.0000	−	36.3731i	−0.816805	−	1.41475i	0.0912190	−	0.995831i	$-0.470924\pi$
$662$	−27.0000			−1.04938
$663$	27.0000	−	15.5885i	1.04859	−	0.605406i
$664$	1.50000	+	2.59808i	0.0582113	+	0.100825i
$665$	−10.5000	−	7.79423i	−0.407173	−	0.302247i
$666$	6.00000			0.232495
$667$	20.0000	+	34.6410i	0.774403	+	1.34131i
$668$	6.00000	−	10.3923i	0.232147	−	0.402090i
$669$	12.0000	−	6.92820i	0.463947	−	0.267860i
$670$	−4.00000			−0.154533
$671$	−10.5000	−	18.1865i	−0.405348	−	0.702083i
$672$	22.5000	−	12.9904i	0.867956	−	0.501115i
$673$	12.5000	+	21.6506i	0.481840	+	0.834571i	0.999783	−	0.0208444i	$-0.00663546\pi$
$673$	12.5000	+	21.6506i	0.481840	+	0.834571i	−0.517943	+	0.855415i	$0.673302\pi$
$674$	−6.50000	+	11.2583i	−0.250371	+	0.433655i
$675$		−	20.7846i		−	0.800000i
$676$	−23.0000			−0.884615
$677$	−3.50000	−	6.06218i	−0.134516	−	0.232988i	0.790897	−	0.611950i	$-0.209615\pi$
$677$	−3.50000	−	6.06218i	−0.134516	−	0.232988i	−0.925412	+	0.378962i	$0.876281\pi$
$678$			25.9808i			0.997785i
$679$	−6.00000			−0.230259
$680$	4.50000	+	7.79423i	0.172567	+	0.298895i
$681$			36.3731i			1.39382i
$682$	−10.5000	+	18.1865i	−0.402066	+	0.696398i
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$	1.50000	−	12.9904i	0.0573539	−	0.496700i
$685$	−3.00000			−0.114624
$686$	−7.50000	+	12.9904i	−0.286351	+	0.495975i
$687$	−4.50000	+	2.59808i	−0.171686	+	0.0991228i
$688$	4.00000	+	6.92820i	0.152499	+	0.264135i
$689$	−18.0000			−0.685745
$690$	12.0000	+	6.92820i	0.456832	+	0.263752i
$691$	6.50000	+	11.2583i	0.247272	+	0.428287i	0.962768	−	0.270330i	$-0.0871327\pi$
$691$	6.50000	+	11.2583i	0.247272	+	0.428287i	−0.715496	+	0.698617i	$0.753799\pi$
$692$	14.0000			0.532200
$693$	−27.0000			−1.02565
$694$	−16.5000	+	28.5788i	−0.626331	+	1.08484i
$695$	2.00000	+	3.46410i	0.0758643	+	0.131401i
$696$	−22.5000	−	12.9904i	−0.852860	−	0.492399i
$697$	1.50000	+	2.59808i	0.0568166	+	0.0984092i
$698$	5.00000			0.189253
$699$			1.73205i			0.0655122i
$700$	−6.00000	+	10.3923i	−0.226779	+	0.392792i
$701$	−19.5000	−	33.7750i	−0.736505	−	1.27566i	−0.954060	−	0.299616i	$-0.903142\pi$
$701$	−19.5000	−	33.7750i	−0.736505	−	1.27566i	0.217555	−	0.976048i	$-0.430192\pi$
$702$			31.1769i			1.17670i
$703$	−8.00000	+	3.46410i	−0.301726	+	0.130651i
$704$	−10.5000	−	18.1865i	−0.395734	−	0.685431i
$705$	−13.5000	−	7.79423i	−0.508439	−	0.293548i
$706$	29.0000			1.09143
$707$	7.50000	+	12.9904i	0.282067	+	0.488554i
$708$			5.19615i			0.195283i
$709$	11.0000			0.413114			0.206557	−	0.978435i	$-0.433774\pi$
$709$	11.0000			0.413114			0.206557	+	0.978435i	$0.433774\pi$
$710$	−15.0000			−0.562940
$711$	36.0000			1.35011
$712$	1.50000	−	2.59808i	0.0562149	−	0.0973670i
$713$	−56.0000			−2.09722
$714$			15.5885i			0.583383i
$715$	−9.00000	+	15.5885i	−0.336581	+	0.582975i
$716$	2.00000	+	3.46410i	0.0747435	+	0.129460i
$717$	40.5000	−	23.3827i	1.51250	−	0.873242i
$718$	−17.0000			−0.634434
$719$	−20.5000	−	35.5070i	−0.764521	−	1.32419i	−0.940499	−	0.339795i	$-0.889642\pi$
$719$	−20.5000	−	35.5070i	−0.764521	−	1.32419i	0.175978	−	0.984394i	$-0.443691\pi$
$720$	−3.00000			−0.111803
$721$	−21.0000			−0.782081
$722$	−5.50000	−	18.1865i	−0.204689	−	0.676833i
$723$	22.5000	+	12.9904i	0.836784	+	0.483117i
$724$	−11.0000			−0.408812
$725$	20.0000			0.742781
$726$		−	3.46410i		−	0.128565i
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	−0.930618	−	0.365991i	$-0.880730\pi$
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	0.782267	+	0.622944i	$0.214063\pi$
$728$	27.0000	−	46.7654i	1.00069	−	1.73324i
$729$	−27.0000			−1.00000
$730$	−5.00000			−0.185058
$731$	24.0000			0.887672
$732$			12.1244i			0.448129i
$733$	20.5000	−	35.5070i	0.757185	−	1.31148i	−0.187096	−	0.982342i	$-0.559908\pi$
$733$	20.5000	−	35.5070i	0.757185	−	1.31148i	0.944281	−	0.329141i	$-0.106759\pi$
$734$	−15.5000	+	26.8468i	−0.572115	+	0.990933i
$735$	3.00000	−	1.73205i	0.110657	−	0.0638877i
$736$	20.0000	−	34.6410i	0.737210	−	1.27688i
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$	−3.00000			−0.110432
$739$	−22.5000	−	38.9711i	−0.827676	−	1.43358i	−0.899857	−	0.436185i	$-0.856329\pi$
$739$	−22.5000	−	38.9711i	−0.827676	−	1.43358i	0.0721811	−	0.997392i	$-0.477004\pi$
$740$	−1.00000	−	1.73205i	−0.0367607	−	0.0636715i
$741$	−18.0000	−	41.5692i	−0.661247	−	1.52708i
$742$	4.50000	−	7.79423i	0.165200	−	0.286135i
$743$	−21.0000			−0.770415			−0.385208	−	0.922830i	$-0.625870\pi$
$743$	−21.0000			−0.770415			−0.385208	+	0.922830i	$0.625870\pi$
$744$	31.5000	−	18.1865i	1.15485	−	0.666751i
$745$	−3.00000			−0.109911
$746$	11.5000	+	19.9186i	0.421045	+	0.729271i
$747$	−1.50000	+	2.59808i	−0.0548821	+	0.0950586i
$748$	−9.00000			−0.329073
$749$	6.00000	+	10.3923i	0.219235	+	0.379727i
$750$	13.5000	−	7.79423i	0.492950	−	0.284605i
$751$	−20.0000	−	34.6410i	−0.729810	−	1.26407i	−0.956963	−	0.290209i	$-0.906275\pi$
$751$	−20.0000	−	34.6410i	−0.729810	−	1.26407i	0.227153	−	0.973859i	$-0.427058\pi$
$752$	4.50000	−	7.79423i	0.164098	−	0.284226i
$753$	−4.50000	+	2.59808i	−0.163989	+	0.0946792i
$754$	−30.0000			−1.09254
$755$	9.50000	+	16.4545i	0.345740	+	0.598840i
$756$	13.5000	+	7.79423i	0.490990	+	0.283473i
$757$	6.50000	+	11.2583i	0.236247	+	0.409191i	0.959634	−	0.281251i	$-0.0907494\pi$
$757$	6.50000	+	11.2583i	0.236247	+	0.409191i	−0.723388	+	0.690442i	$0.757416\pi$
$758$	6.00000	−	10.3923i	0.217930	−	0.377466i
$759$	−36.0000	+	20.7846i	−1.30672	+	0.754434i
$760$	12.0000	−	5.19615i	0.435286	−	0.188484i
$761$	8.50000	−	14.7224i	0.308125	−	0.533688i	−0.669827	−	0.742517i	$-0.733632\pi$
$761$	8.50000	−	14.7224i	0.308125	−	0.533688i	0.977952	+	0.208829i	$0.0669652\pi$
$762$			12.1244i			0.439219i
$763$	1.50000	−	2.59808i	0.0543036	−	0.0940567i
$764$	−4.50000	+	7.79423i	−0.162804	+	0.281985i
$765$	−4.50000	+	7.79423i	−0.162698	+	0.281801i
$766$	9.50000	−	16.4545i	0.343249	−	0.594525i
$767$	9.00000	+	15.5885i	0.324971	+	0.562867i
$768$			29.4449i			1.06250i
$769$	21.0000	+	36.3731i	0.757279	+	1.31165i	0.944233	+	0.329278i	$0.106805\pi$
$769$	21.0000	+	36.3731i	0.757279	+	1.31165i	−0.186954	+	0.982369i	$0.559861\pi$
$770$	−4.50000	−	7.79423i	−0.162169	−	0.280885i
$771$			3.46410i			0.124757i
$772$	−8.50000	−	14.7224i	−0.305922	−	0.529872i
$773$	22.5000	−	38.9711i	0.809269	−	1.40169i	−0.104102	−	0.994567i	$-0.533197\pi$
$773$	22.5000	−	38.9711i	0.809269	−	1.40169i	0.913371	−	0.407128i	$-0.133470\pi$
$774$	−12.0000	+	20.7846i	−0.431331	+	0.747087i
$775$	−14.0000	+	24.2487i	−0.502895	+	0.871039i
$776$	3.00000	−	5.19615i	0.107694	−	0.186531i
$777$		−	10.3923i		−	0.372822i
$778$	7.50000	−	12.9904i	0.268888	−	0.465728i
$779$	4.00000	−	1.73205i	0.143315	−	0.0620572i
$780$	9.00000	−	5.19615i	0.322252	−	0.186052i
$781$	22.5000	−	38.9711i	0.805113	−	1.39450i
$782$	12.0000	+	20.7846i	0.429119	+	0.743256i
$783$		−	25.9808i		−	0.928477i
$784$	1.00000	+	1.73205i	0.0357143	+	0.0618590i
$785$	−7.00000			−0.249841
$786$	−25.5000	+	14.7224i	−0.909555	+	0.525132i
$787$	−8.50000	+	14.7224i	−0.302992	+	0.524798i	−0.976812	−	0.214097i	$-0.931319\pi$
$787$	−8.50000	+	14.7224i	−0.302992	+	0.524798i	0.673820	+	0.738896i	$0.264652\pi$
$788$	−11.0000	−	19.0526i	−0.391859	−	0.678719i
$789$	−36.0000	+	20.7846i	−1.28163	+	0.739952i
$790$	6.00000	+	10.3923i	0.213470	+	0.369742i
$791$	45.0000			1.60002
$792$	13.5000	−	23.3827i	0.479702	−	0.830868i
$793$	21.0000	+	36.3731i	0.745732	+	1.29165i
$794$	13.0000			0.461353
$795$	4.50000	−	2.59808i	0.159599	−	0.0921443i
$796$	17.0000			0.602549
$797$	−7.50000	+	12.9904i	−0.265664	+	0.460143i	−0.967737	−	0.251961i	$-0.918924\pi$
$797$	−7.50000	+	12.9904i	−0.265664	+	0.460143i	0.702074	+	0.712104i	$0.252258\pi$
$798$	22.5000	+	2.59808i	0.796491	+	0.0919709i
$799$	−13.5000	−	23.3827i	−0.477596	−	0.827220i
$800$	−10.0000	−	17.3205i	−0.353553	−	0.612372i
$801$	3.00000			0.106000
$802$	−8.50000	+	14.7224i	−0.300145	+	0.519867i
$803$	7.50000	−	12.9904i	0.264669	−	0.458421i
$804$	−6.00000	+	3.46410i	−0.211604	+	0.122169i
$805$	12.0000	−	20.7846i	0.422944	−	0.732561i
$806$	21.0000	−	36.3731i	0.739693	−	1.28119i
$807$		−	5.19615i		−	0.182913i
$808$	−15.0000			−0.527698
$809$	22.0000			0.773479			0.386739	−	0.922189i	$-0.373601\pi$
$809$	22.0000			0.773479			0.386739	+	0.922189i	$0.373601\pi$
$810$	−4.50000	−	7.79423i	−0.158114	−	0.273861i
$811$	−11.5000	+	19.9186i	−0.403820	+	0.699436i	−0.994183	−	0.107701i	$-0.965651\pi$
$811$	−11.5000	+	19.9186i	−0.403820	+	0.699436i	0.590364	+	0.807137i	$0.298984\pi$
$812$	−7.50000	+	12.9904i	−0.263198	+	0.455873i
$813$			25.9808i			0.911185i
$814$	−6.00000			−0.210300
$815$	4.00000			0.140114
$816$	−4.50000	−	2.59808i	−0.157532	−	0.0909509i
$817$	4.00000	−	34.6410i	0.139942	−	1.21194i
$818$	−10.0000			−0.349642
$819$	54.0000			1.88691
$820$	0.500000	+	0.866025i	0.0174608	+	0.0302429i
$821$	3.00000			0.104701			0.0523504	−	0.998629i	$-0.483329\pi$
$821$	3.00000			0.104701			0.0523504	+	0.998629i	$0.483329\pi$
$822$	4.50000	−	2.59808i	0.156956	−	0.0906183i
$823$	28.0000	+	48.4974i	0.976019	+	1.69051i	0.676532	+	0.736413i	$0.263482\pi$
$823$	28.0000	+	48.4974i	0.976019	+	1.69051i	0.299487	+	0.954100i	$0.403185\pi$
$824$	10.5000	−	18.1865i	0.365785	−	0.633558i
$825$			20.7846i			0.723627i
$826$	−9.00000			−0.313150
$827$	−3.50000	+	6.06218i	−0.121707	+	0.210803i	−0.920441	−	0.390882i	$-0.872170\pi$
$827$	−3.50000	+	6.06218i	−0.121707	+	0.210803i	0.798734	+	0.601684i	$0.205503\pi$
$828$	24.0000			0.834058
$829$	2.00000			0.0694629			0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000			0.0694629			0.0347314	+	0.999397i	$0.488942\pi$
$830$	−1.00000			−0.0347105
$831$			8.66025i			0.300421i
$832$	21.0000	+	36.3731i	0.728044	+	1.26101i
$833$	6.00000			0.207888
$834$	−6.00000	−	3.46410i	−0.207763	−	0.119952i
$835$	6.00000	+	10.3923i	0.207639	+	0.359641i
$836$	−1.50000	+	12.9904i	−0.0518786	+	0.449282i
$837$	31.5000	+	18.1865i	1.08880	+	0.628619i
$838$	−11.5000	−	19.9186i	−0.397261	−	0.688076i
$839$	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
$841$	−4.00000			−0.137931
$842$	1.00000	+	1.73205i	0.0344623	+	0.0596904i
$843$	−7.50000	−	4.33013i	−0.258314	−	0.149137i
$844$	11.5000	+	19.9186i	0.395846	+	0.685626i
$845$	11.5000	−	19.9186i	0.395612	−	0.685220i
$846$	27.0000			0.928279
$847$	−6.00000			−0.206162
$848$	1.50000	+	2.59808i	0.0515102	+	0.0892183i
$849$	−7.50000	−	4.33013i	−0.257399	−	0.148610i
$850$	12.0000			0.411597
$851$	−8.00000	−	13.8564i	−0.274236	−	0.474991i
$852$	−22.5000	+	12.9904i	−0.770837	+	0.445043i
$853$	7.00000	−	12.1244i	0.239675	−	0.415130i	−0.720946	−	0.692992i	$-0.756292\pi$
$853$	7.00000	−	12.1244i	0.239675	−	0.415130i	0.960621	+	0.277862i	$0.0896256\pi$
$854$	−21.0000			−0.718605
$855$	10.5000	+	7.79423i	0.359092	+	0.266557i
$856$	−12.0000			−0.410152
$857$	−3.00000	+	5.19615i	−0.102478	+	0.177497i	−0.912705	−	0.408619i	$-0.866010\pi$
$857$	−3.00000	+	5.19615i	−0.102478	+	0.177497i	0.810227	+	0.586116i	$0.199344\pi$
$858$		−	31.1769i		−	1.06436i
$859$	−10.0000	−	17.3205i	−0.341196	−	0.590968i	0.643459	−	0.765480i	$-0.277499\pi$
$859$	−10.0000	−	17.3205i	−0.341196	−	0.590968i	−0.984655	+	0.174512i	$0.944165\pi$
$860$	8.00000			0.272798
$861$			5.19615i			0.177084i
$862$	13.5000	+	23.3827i	0.459812	+	0.796417i
$863$	−32.0000			−1.08929			−0.544646	−	0.838666i	$-0.683336\pi$
$863$	−32.0000			−1.08929			−0.544646	+	0.838666i	$0.683336\pi$
$864$	−22.5000	+	12.9904i	−0.765466	+	0.441942i
$865$	−7.00000	+	12.1244i	−0.238007	+	0.412240i
$866$	−14.5000	−	25.1147i	−0.492730	−	0.853433i
$867$	12.0000	−	6.92820i	0.407541	−	0.235294i
$868$	−10.5000	−	18.1865i	−0.356393	−	0.617291i
$869$	−36.0000			−1.22122
$870$	7.50000	−	4.33013i	0.254274	−	0.146805i
$871$	−12.0000	+	20.7846i	−0.406604	+	0.704260i
$872$	1.50000	+	2.59808i	0.0507964	+	0.0879820i
$873$	6.00000			0.203069
$874$	32.0000	−	13.8564i	1.08242	−	0.468700i
$875$	−13.5000	−	23.3827i	−0.456383	−	0.790479i
$876$	−7.50000	+	4.33013i	−0.253402	+	0.146301i
$877$	−13.0000			−0.438979			−0.219489	−	0.975615i	$-0.570439\pi$
$877$	−13.0000			−0.438979			−0.219489	+	0.975615i	$0.570439\pi$
$878$	8.00000	+	13.8564i	0.269987	+	0.467631i
$879$	37.5000	−	21.6506i	1.26484	−	0.730258i
$880$	3.00000			0.101130
$881$	−10.0000			−0.336909			−0.168454	−	0.985709i	$-0.553878\pi$
$881$	−10.0000			−0.336909			−0.168454	+	0.985709i	$0.553878\pi$
$882$	−3.00000	+	5.19615i	−0.101015	+	0.174964i
$883$	22.5000	−	38.9711i	0.757185	−	1.31148i	−0.187095	−	0.982342i	$-0.559907\pi$
$883$	22.5000	−	38.9711i	0.757185	−	1.31148i	0.944281	−	0.329142i	$-0.106759\pi$
$884$	18.0000			0.605406
$885$	−4.50000	−	2.59808i	−0.151266	−	0.0873334i
$886$	4.50000	−	7.79423i	0.151180	−	0.261852i
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	0.925332	−	0.379157i	$-0.123786\pi$
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	−0.791026	+	0.611783i	$0.790453\pi$
$888$	9.00000	+	5.19615i	0.302020	+	0.174371i
$889$	21.0000			0.704317
$890$	0.500000	+	0.866025i	0.0167600	+	0.0290292i
$891$	27.0000			0.904534
$892$	8.00000			0.267860
$893$	−36.0000	+	15.5885i	−1.20469	+	0.521648i
$894$	4.50000	−	2.59808i	0.150503	−	0.0868927i
$895$	−4.00000			−0.133705
$896$	9.00000			0.300669
$897$	72.0000	−	41.5692i	2.40401	−	1.38796i
$898$	−5.00000	+	8.66025i	−0.166852	+	0.288996i
$899$	−17.5000	+	30.3109i	−0.583658	+	1.01092i
$900$	6.00000	−	10.3923i	0.200000	−	0.346410i
$901$	9.00000			0.299833
$902$	3.00000			0.0998891
$903$	36.0000	+	20.7846i	1.19800	+	0.691669i
$904$	−22.5000	+	38.9711i	−0.748339	+	1.29616i
$905$	5.50000	−	9.52628i	0.182826	−	0.316664i
$906$	−28.5000	−	16.4545i	−0.946849	−	0.546664i
$907$	−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
$909$	−7.50000	−	12.9904i	−0.248759	−	0.430864i
$910$	9.00000	+	15.5885i	0.298347	+	0.516752i
$911$	−3.50000	−	6.06218i	−0.115960	−	0.200849i	0.802203	−	0.597051i	$-0.203661\pi$
$911$	−3.50000	−	6.06218i	−0.115960	−	0.200849i	−0.918163	+	0.396202i	$0.870328\pi$
$912$	−4.50000	+	6.06218i	−0.149010	+	0.200739i
$913$	1.50000	−	2.59808i	0.0496428	−	0.0859838i
$914$	−3.00000			−0.0992312
$915$	−10.5000	−	6.06218i	−0.347119	−	0.200409i
$916$	−3.00000			−0.0991228
$917$	25.5000	+	44.1673i	0.842084	+	1.45853i
$918$		−	15.5885i		−	0.514496i
$919$	−28.0000			−0.923635			−0.461817	−	0.886975i	$-0.652802\pi$
$919$	−28.0000			−0.923635			−0.461817	+	0.886975i	$0.652802\pi$
$920$	12.0000	+	20.7846i	0.395628	+	0.685248i
$921$		−	15.5885i		−	0.513657i
$922$	−3.00000	−	5.19615i	−0.0987997	−	0.171126i
$923$	−45.0000	+	77.9423i	−1.48119	+	2.56550i
$924$	−13.5000	−	7.79423i	−0.444117	−	0.256411i
$925$	−8.00000			−0.263038
$926$	2.50000	+	4.33013i	0.0821551	+	0.142297i
$927$	21.0000			0.689730
$928$	−12.5000	−	21.6506i	−0.410333	−	0.710717i
$929$	−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	$0.860516\pi$
$930$			12.1244i			0.397573i
$931$	1.00000	−	8.66025i	0.0327737	−	0.283828i
$932$	−0.500000	+	0.866025i	−0.0163780	+	0.0283676i
$933$	10.5000	−	6.06218i	0.343755	−	0.198467i
$934$	4.00000	−	6.92820i	0.130884	−	0.226698i
$935$	4.50000	−	7.79423i	0.147166	−	0.254899i
$936$	−27.0000	+	46.7654i	−0.882523	+	1.52857i
$937$	−23.5000	+	40.7032i	−0.767712	+	1.32972i	0.171089	+	0.985255i	$0.445271\pi$
$937$	−23.5000	+	40.7032i	−0.767712	+	1.32972i	−0.938801	+	0.344460i	$0.888062\pi$
$938$	−6.00000	−	10.3923i	−0.195907	−	0.339321i
$939$	−37.5000	−	21.6506i	−1.22377	−	0.706542i
$940$	−4.50000	−	7.79423i	−0.146774	−	0.254220i
$941$	19.0000	+	32.9090i	0.619382	+	1.07280i	0.989599	+	0.143856i	$0.0459502\pi$
$941$	19.0000	+	32.9090i	0.619382	+	1.07280i	−0.370216	+	0.928946i	$0.620716\pi$
$942$	10.5000	−	6.06218i	0.342108	−	0.197516i
$943$	4.00000	+	6.92820i	0.130258	+	0.225613i
$944$	1.50000	−	2.59808i	0.0488208	−	0.0845602i
$945$	−13.5000	+	7.79423i	−0.439155	+	0.253546i
$946$	12.0000	−	20.7846i	0.390154	−	0.675766i
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	−0.831699	−	0.555227i	$-0.812631\pi$
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	0.896690	+	0.442659i	$0.145965\pi$
$948$	18.0000	+	10.3923i	0.584613	+	0.337526i
$949$	−15.0000	+	25.9808i	−0.486921	+	0.843371i
$950$	2.00000	−	17.3205i	0.0648886	−	0.561951i
$951$	−31.5000	−	18.1865i	−1.02146	−	0.589739i
$952$	−13.5000	+	23.3827i	−0.437538	+	0.757837i
$953$	−15.5000	−	26.8468i	−0.502094	−	0.869653i	−0.999997	−	0.00241992i	$-0.999230\pi$
$953$	−15.5000	−	26.8468i	−0.502094	−	0.869653i	0.497903	−	0.867233i	$-0.334104\pi$
$954$	−4.50000	+	7.79423i	−0.145693	+	0.252347i
$955$	−4.50000	−	7.79423i	−0.145617	−	0.252215i
$956$	27.0000			0.873242
$957$			25.9808i			0.839839i
$958$	0.500000	−	0.866025i	0.0161543	−	0.0279800i
$959$	−4.50000	−	7.79423i	−0.145313	−	0.251689i
$960$	−10.5000	−	6.06218i	−0.338886	−	0.195656i
$961$	−9.00000	−	15.5885i	−0.290323	−	0.502853i
$962$	12.0000			0.386896
$963$	−6.00000	−	10.3923i	−0.193347	−	0.334887i
$964$	7.50000	+	12.9904i	0.241559	+	0.418392i
$965$	17.0000			0.547249
$966$			41.5692i			1.33747i
$967$	7.00000			0.225105			0.112552	−	0.993646i	$-0.464097\pi$
$967$	7.00000			0.225105			0.112552	+	0.993646i	$0.464097\pi$
$968$	3.00000	−	5.19615i	0.0964237	−	0.167011i
$969$	9.00000	+	20.7846i	0.289122	+	0.667698i
$970$	1.00000	+	1.73205i	0.0321081	+	0.0556128i
$971$	1.50000	+	2.59808i	0.0481373	+	0.0833762i	0.889090	−	0.457732i	$-0.151338\pi$
$971$	1.50000	+	2.59808i	0.0481373	+	0.0833762i	−0.840953	+	0.541108i	$0.818005\pi$
$972$	−13.5000	−	7.79423i	−0.433013	−	0.250000i
$973$	−6.00000	+	10.3923i	−0.192351	+	0.333162i
$974$	16.0000	−	27.7128i	0.512673	−	0.887976i
$975$		−	41.5692i		−	1.33128i
$976$	3.50000	−	6.06218i	0.112032	−	0.194046i
$977$	22.5000	−	38.9711i	0.719839	−	1.24680i	−0.241225	−	0.970469i	$-0.577549\pi$
$977$	22.5000	−	38.9711i	0.719839	−	1.24680i	0.961063	−	0.276328i	$-0.0891176\pi$
$978$	−6.00000	+	3.46410i	−0.191859	+	0.110770i
$979$	−3.00000			−0.0958804
$980$	2.00000			0.0638877
$981$	−1.50000	+	2.59808i	−0.0478913	+	0.0829502i
$982$	17.5000	−	30.3109i	0.558447	−	0.967259i
$983$	20.0000	−	34.6410i	0.637901	−	1.10488i	−0.347992	−	0.937498i	$-0.613136\pi$
$983$	20.0000	−	34.6410i	0.637901	−	1.10488i	0.985893	−	0.167379i	$-0.0535304\pi$
$984$	−4.50000	−	2.59808i	−0.143455	−	0.0828236i
$985$	22.0000			0.700978
$986$	15.0000			0.477697
$987$		−	46.7654i		−	1.48856i
$988$	3.00000	−	25.9808i	0.0954427	−	0.826558i
$989$	64.0000			2.03508
$990$	4.50000	+	7.79423i	0.143019	+	0.247717i
$991$	−6.50000	−	11.2583i	−0.206479	−	0.357633i	0.744124	−	0.668042i	$-0.232867\pi$
$991$	−6.50000	−	11.2583i	−0.206479	−	0.357633i	−0.950603	+	0.310409i	$0.899534\pi$
$992$	35.0000			1.11125
$993$		−	46.7654i		−	1.48405i
$994$	−22.5000	−	38.9711i	−0.713657	−	1.23609i
$995$	−8.50000	+	14.7224i	−0.269468	+	0.466732i
$996$	−1.50000	+	0.866025i	−0.0475293	+	0.0274411i
$997$	−25.0000			−0.791758			−0.395879	−	0.918303i	$-0.629560\pi$
$997$	−25.0000			−0.791758			−0.395879	+	0.918303i	$0.629560\pi$
$998$	9.50000	−	16.4545i	0.300717	−	0.520858i
$999$			10.3923i			0.328798i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 - 0.866025i) q^{6} +(-1.50000 - 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 - 0.866025i) q^{6} +(-1.50000 - 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-1.50000 - 2.59808i) q^{11} +1.73205i q^{12} +(3.00000 + 5.19615i) q^{13} -3.00000 q^{14} +(-1.50000 - 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +3.00000 q^{18} +(-4.00000 + 1.73205i) q^{19} +(-0.500000 - 0.866025i) q^{20} -5.19615i q^{21} -3.00000 q^{22} +(-4.00000 - 6.92820i) q^{23} +(4.50000 + 2.59808i) q^{24} -4.00000 q^{25} +6.00000 q^{26} +5.19615i q^{27} +(1.50000 - 2.59808i) q^{28} -5.00000 q^{29} +(-1.50000 + 0.866025i) q^{30} +(3.50000 - 6.06218i) q^{31} +(2.50000 + 4.33013i) q^{32} -5.19615i q^{33} -3.00000 q^{34} +(1.50000 + 2.59808i) q^{35} +(-1.50000 + 2.59808i) q^{36} +2.00000 q^{37} +(-0.500000 + 4.33013i) q^{38} +10.3923i q^{39} -3.00000 q^{40} -1.00000 q^{41} +(-4.50000 - 2.59808i) q^{42} +(-4.00000 + 6.92820i) q^{43} +(1.50000 - 2.59808i) q^{44} +(-1.50000 - 2.59808i) q^{45} -8.00000 q^{46} +9.00000 q^{47} +(1.50000 - 0.866025i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(-2.00000 + 3.46410i) q^{50} -5.19615i q^{51} +(-3.00000 + 5.19615i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(4.50000 + 2.59808i) q^{54} +(1.50000 + 2.59808i) q^{55} +(-4.50000 - 7.79423i) q^{56} +(-7.50000 - 0.866025i) q^{57} +(-2.50000 + 4.33013i) q^{58} +3.00000 q^{59} -1.73205i q^{60} +7.00000 q^{61} +(-3.50000 - 6.06218i) q^{62} +(4.50000 - 7.79423i) q^{63} +7.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} +(-4.50000 - 2.59808i) q^{66} +(2.00000 + 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} -13.8564i q^{69} +3.00000 q^{70} +(7.50000 + 12.9904i) q^{71} +(4.50000 + 7.79423i) q^{72} +(2.50000 + 4.33013i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-6.00000 - 3.46410i) q^{75} +(-3.50000 - 2.59808i) q^{76} +(-4.50000 + 7.79423i) q^{77} +(9.00000 + 5.19615i) q^{78} +(6.00000 - 10.3923i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-0.500000 + 0.866025i) q^{82} +(0.500000 + 0.866025i) q^{83} +(4.50000 - 2.59808i) q^{84} +(1.50000 + 2.59808i) q^{85} +(4.00000 + 6.92820i) q^{86} +(-7.50000 - 4.33013i) q^{87} +(-4.50000 - 7.79423i) q^{88} +(0.500000 - 0.866025i) q^{89} -3.00000 q^{90} +(9.00000 - 15.5885i) q^{91} +(4.00000 - 6.92820i) q^{92} +(10.5000 - 6.06218i) q^{93} +(4.50000 - 7.79423i) q^{94} +(4.00000 - 1.73205i) q^{95} +8.66025i q^{96} +(1.00000 - 1.73205i) q^{97} +(1.00000 + 1.73205i) q^{98} +(4.50000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} + q^{4} - 2 q^{5} + 3 q^{6} - 3 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + q^2 + 3 * q^3 + q^4 - 2 * q^5 + 3 * q^6 - 3 * q^7 + 6 * q^8 + 3 * q^9	\( 2 q + q^{2} + 3 q^{3} + q^{4} - 2 q^{5} + 3 q^{6} - 3 q^{7} + 6 q^{8} + 3 q^{9} - q^{10} - 3 q^{11} + 6 q^{13} - 6 q^{14} - 3 q^{15} + q^{16} - 3 q^{17} + 6 q^{18} - 8 q^{19} - q^{20} - 6 q^{22} - 8 q^{23} + 9 q^{24} - 8 q^{25} + 12 q^{26} + 3 q^{28} - 10 q^{29} - 3 q^{30} + 7 q^{31} + 5 q^{32} - 6 q^{34} + 3 q^{35} - 3 q^{36} + 4 q^{37} - q^{38} - 6 q^{40} - 2 q^{41} - 9 q^{42} - 8 q^{43} + 3 q^{44} - 3 q^{45} - 16 q^{46} + 18 q^{47} + 3 q^{48} - 2 q^{49} - 4 q^{50} - 6 q^{52} - 3 q^{53} + 9 q^{54} + 3 q^{55} - 9 q^{56} - 15 q^{57} - 5 q^{58} + 6 q^{59} + 14 q^{61} - 7 q^{62} + 9 q^{63} + 14 q^{64} - 6 q^{65} - 9 q^{66} + 4 q^{67} + 3 q^{68} + 6 q^{70} + 15 q^{71} + 9 q^{72} + 5 q^{73} + 2 q^{74} - 12 q^{75} - 7 q^{76} - 9 q^{77} + 18 q^{78} + 12 q^{79} - q^{80} - 9 q^{81} - q^{82} + q^{83} + 9 q^{84} + 3 q^{85} + 8 q^{86} - 15 q^{87} - 9 q^{88} + q^{89} - 6 q^{90} + 18 q^{91} + 8 q^{92} + 21 q^{93} + 9 q^{94} + 8 q^{95} + 2 q^{97} + 2 q^{98} + 9 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 + q^4 - 2 * q^5 + 3 * q^6 - 3 * q^7 + 6 * q^8 + 3 * q^9 - q^10 - 3 * q^11 + 6 * q^13 - 6 * q^14 - 3 * q^15 + q^16 - 3 * q^17 + 6 * q^18 - 8 * q^19 - q^20 - 6 * q^22 - 8 * q^23 + 9 * q^24 - 8 * q^25 + 12 * q^26 + 3 * q^28 - 10 * q^29 - 3 * q^30 + 7 * q^31 + 5 * q^32 - 6 * q^34 + 3 * q^35 - 3 * q^36 + 4 * q^37 - q^38 - 6 * q^40 - 2 * q^41 - 9 * q^42 - 8 * q^43 + 3 * q^44 - 3 * q^45 - 16 * q^46 + 18 * q^47 + 3 * q^48 - 2 * q^49 - 4 * q^50 - 6 * q^52 - 3 * q^53 + 9 * q^54 + 3 * q^55 - 9 * q^56 - 15 * q^57 - 5 * q^58 + 6 * q^59 + 14 * q^61 - 7 * q^62 + 9 * q^63 + 14 * q^64 - 6 * q^65 - 9 * q^66 + 4 * q^67 + 3 * q^68 + 6 * q^70 + 15 * q^71 + 9 * q^72 + 5 * q^73 + 2 * q^74 - 12 * q^75 - 7 * q^76 - 9 * q^77 + 18 * q^78 + 12 * q^79 - q^80 - 9 * q^81 - q^82 + q^83 + 9 * q^84 + 3 * q^85 + 8 * q^86 - 15 * q^87 - 9 * q^88 + q^89 - 6 * q^90 + 18 * q^91 + 8 * q^92 + 21 * q^93 + 9 * q^94 + 8 * q^95 + 2 * q^97 + 2 * q^98 + 9 * q^99

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