LMFDB - Embedded newform 126.2.f.b.43.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,2,Mod(43,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,1,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.00611506547$
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			43.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	126.43
Dual form			126.2.f.b.85.1

$q$-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 - 1.73205i) q^{5} +(1.50000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -2.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} -1.73205i q^{12} +(3.00000 + 5.19615i) q^{13} +(-0.500000 - 0.866025i) q^{14} -3.46410i q^{15} +(-0.500000 + 0.866025i) q^{16} -5.00000 q^{17} +3.00000 q^{18} -7.00000 q^{19} +(-1.00000 + 1.73205i) q^{20} +(1.50000 - 0.866025i) q^{21} +(0.500000 + 0.866025i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{25} +6.00000 q^{26} +5.19615i q^{27} -1.00000 q^{28} +(2.00000 - 3.46410i) q^{29} +(-3.00000 - 1.73205i) q^{30} +(3.00000 + 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 + 0.866025i) q^{33} +(-2.50000 + 4.33013i) q^{34} -2.00000 q^{35} +(1.50000 - 2.59808i) q^{36} +2.00000 q^{37} +(-3.50000 + 6.06218i) q^{38} +10.3923i q^{39} +(1.00000 + 1.73205i) q^{40} +(-1.50000 - 2.59808i) q^{41} -1.73205i q^{42} +(0.500000 - 0.866025i) q^{43} +1.00000 q^{44} +(3.00000 - 5.19615i) q^{45} -4.00000 q^{46} +(-1.50000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-7.50000 - 4.33013i) q^{51} +(3.00000 - 5.19615i) q^{52} +12.0000 q^{53} +(4.50000 + 2.59808i) q^{54} +2.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-10.5000 - 6.06218i) q^{57} +(-2.00000 - 3.46410i) q^{58} +(3.50000 + 6.06218i) q^{59} +(-3.00000 + 1.73205i) q^{60} +(6.00000 - 10.3923i) q^{61} +6.00000 q^{62} +3.00000 q^{63} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{65} +1.73205i q^{66} +(-6.50000 - 11.2583i) q^{67} +(2.50000 + 4.33013i) q^{68} -6.92820i q^{69} +(-1.00000 + 1.73205i) q^{70} -8.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} +1.00000 q^{73} +(1.00000 - 1.73205i) q^{74} +(1.50000 - 0.866025i) q^{75} +(3.50000 + 6.06218i) q^{76} +(0.500000 + 0.866025i) q^{77} +(9.00000 + 5.19615i) q^{78} +(3.00000 - 5.19615i) q^{79} +2.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} -3.00000 q^{82} +(-8.00000 + 13.8564i) q^{83} +(-1.50000 - 0.866025i) q^{84} +(5.00000 + 8.66025i) q^{85} +(-0.500000 - 0.866025i) q^{86} +(6.00000 - 3.46410i) q^{87} +(0.500000 - 0.866025i) q^{88} -6.00000 q^{89} +(-3.00000 - 5.19615i) q^{90} +6.00000 q^{91} +(-2.00000 + 3.46410i) q^{92} +10.3923i q^{93} +(7.00000 + 12.1244i) q^{95} +1.73205i q^{96} +(2.50000 - 4.33013i) q^{97} -1.00000 q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} - q^{4} - 2 q^{5} + 3 q^{6} + q^{7} - 2 q^{8} + 3 q^{9} - 4 q^{10} - q^{11} + 6 q^{13} - q^{14} - q^{16} - 10 q^{17} + 6 q^{18} - 14 q^{19} - 2 q^{20} + 3 q^{21} + q^{22} - 4 q^{23}+ \cdots - 6 q^{99}+O(q^{100}) $ 2 * q + q^2 + 3 * q^3 - q^4 - 2 * q^5 + 3 * q^6 + q^7 - 2 * q^8 + 3 * q^9 - 4 * q^10 - q^11 + 6 * q^13 - q^14 - q^16 - 10 * q^17 + 6 * q^18 - 14 * q^19 - 2 * q^20 + 3 * q^21 + q^22 - 4 * q^23 - 3 * q^24 + q^25 + 12 * q^26 - 2 * q^28 + 4 * q^29 - 6 * q^30 + 6 * q^31 + q^32 - 3 * q^33 - 5 * q^34 - 4 * q^35 + 3 * q^36 + 4 * q^37 - 7 * q^38 + 2 * q^40 - 3 * q^41 + q^43 + 2 * q^44 + 6 * q^45 - 8 * q^46 - 3 * q^48 - q^49 - q^50 - 15 * q^51 + 6 * q^52 + 24 * q^53 + 9 * q^54 + 4 * q^55 - q^56 - 21 * q^57 - 4 * q^58 + 7 * q^59 - 6 * q^60 + 12 * q^61 + 12 * q^62 + 6 * q^63 + 2 * q^64 + 12 * q^65 - 13 * q^67 + 5 * q^68 - 2 * q^70 - 16 * q^71 - 3 * q^72 + 2 * q^73 + 2 * q^74 + 3 * q^75 + 7 * q^76 + q^77 + 18 * q^78 + 6 * q^79 + 4 * q^80 - 9 * q^81 - 6 * q^82 - 16 * q^83 - 3 * q^84 + 10 * q^85 - q^86 + 12 * q^87 + q^88 - 12 * q^89 - 6 * q^90 + 12 * q^91 - 4 * q^92 + 14 * q^95 + 5 * q^97 - 2 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.50000	+	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	−	1.73205i	−0.447214	−	0.774597i	0.550990	−	0.834512i	$-0.314250\pi$
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$	1.50000	−	0.866025i	0.612372	−	0.353553i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−1.00000			−0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−2.00000			−0.632456
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$		−	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	$0.520500\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$		−	3.46410i		−	0.894427i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−5.00000			−1.21268			−0.606339	−	0.795206i	$-0.707363\pi$
$17$	−5.00000			−1.21268			−0.606339	+	0.795206i	$0.707363\pi$
$18$	3.00000			0.707107
$19$	−7.00000			−1.60591			−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−7.00000			−1.60591			−0.802955	+	0.596040i	$0.796740\pi$
$20$	−1.00000	+	1.73205i	−0.223607	+	0.387298i
$21$	1.50000	−	0.866025i	0.327327	−	0.188982i
$22$	0.500000	+	0.866025i	0.106600	+	0.184637i
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	6.00000			1.17670
$27$			5.19615i			1.00000i
$28$	−1.00000			−0.188982
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	−0.618389	−	0.785872i	$-0.712214\pi$
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	0.989780	+	0.142605i	$0.0455477\pi$
$30$	−3.00000	−	1.73205i	−0.547723	−	0.316228i
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.50000	+	0.866025i	−0.261116	+	0.150756i
$34$	−2.50000	+	4.33013i	−0.428746	+	0.742611i
$35$	−2.00000			−0.338062
$36$	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	$0.447432\pi$
$38$	−3.50000	+	6.06218i	−0.567775	+	0.983415i
$39$			10.3923i			1.66410i
$40$	1.00000	+	1.73205i	0.158114	+	0.273861i
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$		−	1.73205i		−	0.267261i
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	1.00000			0.150756
$45$	3.00000	−	5.19615i	0.447214	−	0.774597i
$46$	−4.00000			−0.589768
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	−1.50000	+	0.866025i	−0.216506	+	0.125000i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−7.50000	−	4.33013i	−1.05021	−	0.606339i
$52$	3.00000	−	5.19615i	0.416025	−	0.720577i
$53$	12.0000			1.64833			0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000			1.64833			0.824163	+	0.566352i	$0.191646\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$	2.00000			0.269680
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	−10.5000	−	6.06218i	−1.39076	−	0.802955i
$58$	−2.00000	−	3.46410i	−0.262613	−	0.454859i
$59$	3.50000	+	6.06218i	0.455661	+	0.789228i	0.998726	−	0.0504625i	$-0.0160695\pi$
$59$	3.50000	+	6.06218i	0.455661	+	0.789228i	−0.543065	+	0.839691i	$0.682736\pi$
$60$	−3.00000	+	1.73205i	−0.387298	+	0.223607i
$61$	6.00000	−	10.3923i	0.768221	−	1.33060i	−0.170305	−	0.985391i	$-0.554475\pi$
$61$	6.00000	−	10.3923i	0.768221	−	1.33060i	0.938527	−	0.345207i	$-0.112191\pi$
$62$	6.00000			0.762001
$63$	3.00000			0.377964
$64$	1.00000			0.125000
$65$	6.00000	−	10.3923i	0.744208	−	1.28901i
$66$			1.73205i			0.213201i
$67$	−6.50000	−	11.2583i	−0.794101	−	1.37542i	−0.923408	−	0.383819i	$-0.874609\pi$
$67$	−6.50000	−	11.2583i	−0.794101	−	1.37542i	0.129307	−	0.991605i	$-0.458725\pi$
$68$	2.50000	+	4.33013i	0.303170	+	0.525105i
$69$		−	6.92820i		−	0.834058i
$70$	−1.00000	+	1.73205i	−0.119523	+	0.207020i
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	1.00000			0.117041			0.0585206	−	0.998286i	$-0.481362\pi$
$73$	1.00000			0.117041			0.0585206	+	0.998286i	$0.481362\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	1.50000	−	0.866025i	0.173205	−	0.100000i
$76$	3.50000	+	6.06218i	0.401478	+	0.695379i
$77$	0.500000	+	0.866025i	0.0569803	+	0.0986928i
$78$	9.00000	+	5.19615i	1.01905	+	0.588348i
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	−0.646440	−	0.762964i	$-0.723743\pi$
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	0.983967	+	0.178352i	$0.0570765\pi$
$80$	2.00000			0.223607
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−3.00000			−0.331295
$83$	−8.00000	+	13.8564i	−0.878114	+	1.52094i	−0.0247060	+	0.999695i	$0.507865\pi$
$83$	−8.00000	+	13.8564i	−0.878114	+	1.52094i	−0.853408	+	0.521243i	$0.825468\pi$
$84$	−1.50000	−	0.866025i	−0.163663	−	0.0944911i
$85$	5.00000	+	8.66025i	0.542326	+	0.939336i
$86$	−0.500000	−	0.866025i	−0.0539164	−	0.0933859i
$87$	6.00000	−	3.46410i	0.643268	−	0.371391i
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$	−3.00000	−	5.19615i	−0.316228	−	0.547723i
$91$	6.00000			0.628971
$92$	−2.00000	+	3.46410i	−0.208514	+	0.361158i
$93$			10.3923i			1.07763i
$94$		0			0
$95$	7.00000	+	12.1244i	0.718185	+	1.24393i
$96$			1.73205i			0.176777i
$97$	2.50000	−	4.33013i	0.253837	−	0.439658i	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	2.50000	−	4.33013i	0.253837	−	0.439658i	0.964579	+	0.263795i	$0.0849741\pi$
$98$	−1.00000			−0.101015
$99$	−3.00000			−0.301511
$100$	−1.00000			−0.100000
$101$	2.00000	−	3.46410i	0.199007	−	0.344691i	−0.749199	−	0.662344i	$-0.769562\pi$
$101$	2.00000	−	3.46410i	0.199007	−	0.344691i	0.948207	+	0.317653i	$0.102895\pi$
$102$	−7.50000	+	4.33013i	−0.742611	+	0.428746i
$103$	−7.00000	−	12.1244i	−0.689730	−	1.19465i	−0.971925	−	0.235291i	$-0.924396\pi$
$103$	−7.00000	−	12.1244i	−0.689730	−	1.19465i	0.282194	−	0.959357i	$-0.408938\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$	−3.00000	−	1.73205i	−0.292770	−	0.169031i
$106$	6.00000	−	10.3923i	0.582772	−	1.00939i
$107$	3.00000			0.290021			0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000			0.290021			0.145010	+	0.989430i	$0.453678\pi$
$108$	4.50000	−	2.59808i	0.433013	−	0.250000i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	1.00000	−	1.73205i	0.0953463	−	0.165145i
$111$	3.00000	+	1.73205i	0.284747	+	0.164399i
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	5.00000	+	8.66025i	0.470360	+	0.814688i	0.999425	−	0.0338931i	$-0.0107906\pi$
$113$	5.00000	+	8.66025i	0.470360	+	0.814688i	−0.529065	+	0.848581i	$0.677457\pi$
$114$	−10.5000	+	6.06218i	−0.983415	+	0.567775i
$115$	−4.00000	+	6.92820i	−0.373002	+	0.646058i
$116$	−4.00000			−0.371391
$117$	−9.00000	+	15.5885i	−0.832050	+	1.44115i
$118$	7.00000			0.644402
$119$	−2.50000	+	4.33013i	−0.229175	+	0.396942i
$120$			3.46410i			0.316228i
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	−6.00000	−	10.3923i	−0.543214	−	0.940875i
$123$		−	5.19615i		−	0.468521i
$124$	3.00000	−	5.19615i	0.269408	−	0.466628i
$125$	−12.0000			−1.07331
$126$	1.50000	−	2.59808i	0.133631	−	0.231455i
$127$	−12.0000			−1.06483			−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000			−1.06483			−0.532414	+	0.846484i	$0.678715\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	1.50000	−	0.866025i	0.132068	−	0.0762493i
$130$	−6.00000	−	10.3923i	−0.526235	−	0.911465i
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	0.940072	−	0.340977i	$-0.110758\pi$
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	−0.765331	+	0.643637i	$0.777425\pi$
$132$	1.50000	+	0.866025i	0.130558	+	0.0753778i
$133$	−3.50000	+	6.06218i	−0.303488	+	0.525657i
$134$	−13.0000			−1.12303
$135$	9.00000	−	5.19615i	0.774597	−	0.447214i
$136$	5.00000			0.428746
$137$	9.50000	−	16.4545i	0.811640	−	1.40580i	−0.100076	−	0.994980i	$-0.531909\pi$
$137$	9.50000	−	16.4545i	0.811640	−	1.40580i	0.911716	−	0.410822i	$-0.134758\pi$
$138$	−6.00000	−	3.46410i	−0.510754	−	0.294884i
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	0.952355	−	0.304991i	$-0.0986536\pi$
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	−0.740308	+	0.672268i	$0.765320\pi$
$140$	1.00000	+	1.73205i	0.0845154	+	0.146385i
$141$		0			0
$142$	−4.00000	+	6.92820i	−0.335673	+	0.581402i
$143$	−6.00000			−0.501745
$144$	−3.00000			−0.250000
$145$	−8.00000			−0.664364
$146$	0.500000	−	0.866025i	0.0413803	−	0.0716728i
$147$		−	1.73205i		−	0.142857i
$148$	−1.00000	−	1.73205i	−0.0821995	−	0.142374i
$149$	12.0000	+	20.7846i	0.983078	+	1.70274i	0.650183	+	0.759778i	$0.274692\pi$
$149$	12.0000	+	20.7846i	0.983078	+	1.70274i	0.332896	+	0.942964i	$0.391974\pi$
$150$		−	1.73205i		−	0.141421i
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	−0.994540	−	0.104357i	$-0.966722\pi$
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	0.587646	+	0.809118i	$0.300055\pi$
$152$	7.00000			0.567775
$153$	−7.50000	−	12.9904i	−0.606339	−	1.05021i
$154$	1.00000			0.0805823
$155$	6.00000	−	10.3923i	0.481932	−	0.834730i
$156$	9.00000	−	5.19615i	0.720577	−	0.416025i
$157$	−1.00000	−	1.73205i	−0.0798087	−	0.138233i	0.823359	−	0.567521i	$-0.192098\pi$
$157$	−1.00000	−	1.73205i	−0.0798087	−	0.138233i	−0.903167	+	0.429289i	$0.858764\pi$
$158$	−3.00000	−	5.19615i	−0.238667	−	0.413384i
$159$	18.0000	+	10.3923i	1.42749	+	0.824163i
$160$	1.00000	−	1.73205i	0.0790569	−	0.136931i
$161$	−4.00000			−0.315244
$162$	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	$0.550070\pi$
$164$	−1.50000	+	2.59808i	−0.117130	+	0.202876i
$165$	3.00000	+	1.73205i	0.233550	+	0.134840i
$166$	8.00000	+	13.8564i	0.620920	+	1.07547i
$167$	−10.0000	−	17.3205i	−0.773823	−	1.34030i	−0.935454	−	0.353450i	$-0.885009\pi$
$167$	−10.0000	−	17.3205i	−0.773823	−	1.34030i	0.161630	−	0.986851i	$-0.448325\pi$
$168$	−1.50000	+	0.866025i	−0.115728	+	0.0668153i
$169$	−11.5000	+	19.9186i	−0.884615	+	1.53220i
$170$	10.0000			0.766965
$171$	−10.5000	−	18.1865i	−0.802955	−	1.39076i
$172$	−1.00000			−0.0762493
$173$	−1.00000	+	1.73205i	−0.0760286	+	0.131685i	−0.901533	−	0.432710i	$-0.857557\pi$
$173$	−1.00000	+	1.73205i	−0.0760286	+	0.131685i	0.825505	+	0.564396i	$0.190891\pi$
$174$		−	6.92820i		−	0.525226i
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	−0.500000	−	0.866025i	−0.0376889	−	0.0652791i
$177$			12.1244i			0.911322i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	24.0000			1.79384			0.896922	−	0.442189i	$-0.145798\pi$
$179$	24.0000			1.79384			0.896922	+	0.442189i	$0.145798\pi$
$180$	−6.00000			−0.447214
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$	3.00000	−	5.19615i	0.222375	−	0.385164i
$183$	18.0000	−	10.3923i	1.33060	−	0.768221i
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$	−2.00000	−	3.46410i	−0.147043	−	0.254686i
$186$	9.00000	+	5.19615i	0.659912	+	0.381000i
$187$	2.50000	−	4.33013i	0.182818	−	0.316650i
$188$		0			0
$189$	4.50000	+	2.59808i	0.327327	+	0.188982i
$190$	14.0000			1.01567
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$	1.50000	+	0.866025i	0.108253	+	0.0625000i
$193$	−8.50000	−	14.7224i	−0.611843	−	1.05974i	−0.990930	−	0.134382i	$-0.957095\pi$
$193$	−8.50000	−	14.7224i	−0.611843	−	1.05974i	0.379086	−	0.925361i	$-0.376238\pi$
$194$	−2.50000	−	4.33013i	−0.179490	−	0.310885i
$195$	18.0000	−	10.3923i	1.28901	−	0.744208i
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	10.0000			0.712470			0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000			0.712470			0.356235	+	0.934396i	$0.384060\pi$
$198$	−1.50000	+	2.59808i	−0.106600	+	0.184637i
$199$	14.0000			0.992434			0.496217	−	0.868199i	$-0.334722\pi$
$199$	14.0000			0.992434			0.496217	+	0.868199i	$0.334722\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$		−	22.5167i		−	1.58820i
$202$	−2.00000	−	3.46410i	−0.140720	−	0.243733i
$203$	−2.00000	−	3.46410i	−0.140372	−	0.243132i
$204$			8.66025i			0.606339i
$205$	−3.00000	+	5.19615i	−0.209529	+	0.362915i
$206$	−14.0000			−0.975426
$207$	6.00000	−	10.3923i	0.417029	−	0.722315i
$208$	−6.00000			−0.416025
$209$	3.50000	−	6.06218i	0.242100	−	0.419330i
$210$	−3.00000	+	1.73205i	−0.207020	+	0.119523i
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	0.998221	+	0.0596196i	$0.0189888\pi$
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	−0.447478	+	0.894295i	$0.647678\pi$
$212$	−6.00000	−	10.3923i	−0.412082	−	0.713746i
$213$	−12.0000	−	6.92820i	−0.822226	−	0.474713i
$214$	1.50000	−	2.59808i	0.102538	−	0.177601i
$215$	−2.00000			−0.136399
$216$		−	5.19615i		−	0.353553i
$217$	6.00000			0.407307
$218$	−1.00000	+	1.73205i	−0.0677285	+	0.117309i
$219$	1.50000	+	0.866025i	0.101361	+	0.0585206i
$220$	−1.00000	−	1.73205i	−0.0674200	−	0.116775i
$221$	−15.0000	−	25.9808i	−1.00901	−	1.74766i
$222$	3.00000	−	1.73205i	0.201347	−	0.116248i
$223$	2.00000	−	3.46410i	0.133930	−	0.231973i	−0.791258	−	0.611482i	$-0.790574\pi$
$223$	2.00000	−	3.46410i	0.133930	−	0.231973i	0.925188	+	0.379509i	$0.123907\pi$
$224$	1.00000			0.0668153
$225$	3.00000			0.200000
$226$	10.0000			0.665190
$227$	−1.50000	+	2.59808i	−0.0995585	+	0.172440i	−0.911502	−	0.411296i	$-0.865076\pi$
$227$	−1.50000	+	2.59808i	−0.0995585	+	0.172440i	0.811943	+	0.583736i	$0.198410\pi$
$228$			12.1244i			0.802955i
$229$	13.0000	+	22.5167i	0.859064	+	1.48794i	0.872823	+	0.488037i	$0.162287\pi$
$229$	13.0000	+	22.5167i	0.859064	+	1.48794i	−0.0137585	+	0.999905i	$0.504380\pi$
$230$	4.00000	+	6.92820i	0.263752	+	0.456832i
$231$			1.73205i			0.113961i
$232$	−2.00000	+	3.46410i	−0.131306	+	0.227429i
$233$	−29.0000			−1.89985			−0.949927	−	0.312473i	$-0.898843\pi$
$233$	−29.0000			−1.89985			−0.949927	+	0.312473i	$0.898843\pi$
$234$	9.00000	+	15.5885i	0.588348	+	1.01905i
$235$		0			0
$236$	3.50000	−	6.06218i	0.227831	−	0.394614i
$237$	9.00000	−	5.19615i	0.584613	−	0.337526i
$238$	2.50000	+	4.33013i	0.162051	+	0.280680i
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	0.752536	−	0.658551i	$-0.228830\pi$
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	−0.946590	+	0.322440i	$0.895497\pi$
$240$	3.00000	+	1.73205i	0.193649	+	0.111803i
$241$	−11.5000	+	19.9186i	−0.740780	+	1.28307i	0.211360	+	0.977408i	$0.432211\pi$
$241$	−11.5000	+	19.9186i	−0.740780	+	1.28307i	−0.952141	+	0.305661i	$0.901123\pi$
$242$	10.0000			0.642824
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$	−12.0000			−0.768221
$245$	−1.00000	+	1.73205i	−0.0638877	+	0.110657i
$246$	−4.50000	−	2.59808i	−0.286910	−	0.165647i
$247$	−21.0000	−	36.3731i	−1.33620	−	2.31436i
$248$	−3.00000	−	5.19615i	−0.190500	−	0.329956i
$249$	−24.0000	+	13.8564i	−1.52094	+	0.878114i
$250$	−6.00000	+	10.3923i	−0.379473	+	0.657267i
$251$	3.00000			0.189358			0.0946792	−	0.995508i	$-0.469817\pi$
$251$	3.00000			0.189358			0.0946792	+	0.995508i	$0.469817\pi$
$252$	−1.50000	−	2.59808i	−0.0944911	−	0.163663i
$253$	4.00000			0.251478
$254$	−6.00000	+	10.3923i	−0.376473	+	0.652071i
$255$			17.3205i			1.08465i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	0.999325	−	0.0367485i	$-0.0117000\pi$
$257$	7.50000	+	12.9904i	0.467837	+	0.810318i	−0.531487	+	0.847066i	$0.678367\pi$
$258$		−	1.73205i		−	0.107833i
$259$	1.00000	−	1.73205i	0.0621370	−	0.107624i
$260$	−12.0000			−0.744208
$261$	12.0000			0.742781
$262$	4.00000			0.247121
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	0.442943	+	0.896550i	$0.353935\pi$
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	−0.997906	+	0.0646755i	$0.979399\pi$
$264$	1.50000	−	0.866025i	0.0923186	−	0.0533002i
$265$	−12.0000	−	20.7846i	−0.737154	−	1.27679i
$266$	3.50000	+	6.06218i	0.214599	+	0.371696i
$267$	−9.00000	−	5.19615i	−0.550791	−	0.317999i
$268$	−6.50000	+	11.2583i	−0.397051	+	0.687712i
$269$	20.0000			1.21942			0.609711	−	0.792624i	$-0.291286\pi$
$269$	20.0000			1.21942			0.609711	+	0.792624i	$0.291286\pi$
$270$		−	10.3923i		−	0.632456i
$271$	−6.00000			−0.364474			−0.182237	−	0.983255i	$-0.558334\pi$
$271$	−6.00000			−0.364474			−0.182237	+	0.983255i	$0.558334\pi$
$272$	2.50000	−	4.33013i	0.151585	−	0.262553i
$273$	9.00000	+	5.19615i	0.544705	+	0.314485i
$274$	−9.50000	−	16.4545i	−0.573916	−	0.994052i
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	−6.00000	+	3.46410i	−0.361158	+	0.208514i
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	−0.894503	−	0.447062i	$-0.852470\pi$
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	0.834419	+	0.551131i	$0.185804\pi$
$278$	5.00000			0.299880
$279$	−9.00000	+	15.5885i	−0.538816	+	0.933257i
$280$	2.00000			0.119523
$281$	−11.0000	+	19.0526i	−0.656205	+	1.13658i	0.325385	+	0.945582i	$0.394506\pi$
$281$	−11.0000	+	19.0526i	−0.656205	+	1.13658i	−0.981590	+	0.190999i	$0.938827\pi$
$282$		0			0
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$	4.00000	+	6.92820i	0.237356	+	0.411113i
$285$			24.2487i			1.43637i
$286$	−3.00000	+	5.19615i	−0.177394	+	0.307255i
$287$	−3.00000			−0.177084
$288$	−1.50000	+	2.59808i	−0.0883883	+	0.153093i
$289$	8.00000			0.470588
$290$	−4.00000	+	6.92820i	−0.234888	+	0.406838i
$291$	7.50000	−	4.33013i	0.439658	−	0.253837i
$292$	−0.500000	−	0.866025i	−0.0292603	−	0.0506803i
$293$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$293$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$294$	−1.50000	−	0.866025i	−0.0874818	−	0.0505076i
$295$	7.00000	−	12.1244i	0.407556	−	0.705907i
$296$	−2.00000			−0.116248
$297$	−4.50000	−	2.59808i	−0.261116	−	0.150756i
$298$	24.0000			1.39028
$299$	12.0000	−	20.7846i	0.693978	−	1.20201i
$300$	−1.50000	−	0.866025i	−0.0866025	−	0.0500000i
$301$	−0.500000	−	0.866025i	−0.0288195	−	0.0499169i
$302$	5.00000	+	8.66025i	0.287718	+	0.498342i
$303$	6.00000	−	3.46410i	0.344691	−	0.199007i
$304$	3.50000	−	6.06218i	0.200739	−	0.347690i
$305$	−24.0000			−1.37424
$306$	−15.0000			−0.857493
$307$	7.00000			0.399511			0.199756	−	0.979846i	$-0.435985\pi$
$307$	7.00000			0.399511			0.199756	+	0.979846i	$0.435985\pi$
$308$	0.500000	−	0.866025i	0.0284901	−	0.0493464i
$309$		−	24.2487i		−	1.37946i
$310$	−6.00000	−	10.3923i	−0.340777	−	0.590243i
$311$	−1.00000	−	1.73205i	−0.0567048	−	0.0982156i	0.836280	−	0.548303i	$-0.184726\pi$
$311$	−1.00000	−	1.73205i	−0.0567048	−	0.0982156i	−0.892984	+	0.450088i	$0.851393\pi$
$312$		−	10.3923i		−	0.588348i
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	−0.519300	−	0.854592i	$-0.673807\pi$
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	0.999748	+	0.0224310i	$0.00714060\pi$
$314$	−2.00000			−0.112867
$315$	−3.00000	−	5.19615i	−0.169031	−	0.292770i
$316$	−6.00000			−0.337526
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	−0.769395	−	0.638774i	$-0.779442\pi$
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	0.937892	+	0.346929i	$0.112775\pi$
$318$	18.0000	−	10.3923i	1.00939	−	0.582772i
$319$	2.00000	+	3.46410i	0.111979	+	0.193952i
$320$	−1.00000	−	1.73205i	−0.0559017	−	0.0968246i
$321$	4.50000	+	2.59808i	0.251166	+	0.145010i
$322$	−2.00000	+	3.46410i	−0.111456	+	0.193047i
$323$	35.0000			1.94745
$324$	9.00000			0.500000
$325$	6.00000			0.332820
$326$	−2.00000	+	3.46410i	−0.110770	+	0.191859i
$327$	−3.00000	−	1.73205i	−0.165900	−	0.0957826i
$328$	1.50000	+	2.59808i	0.0828236	+	0.143455i
$329$		0			0
$330$	3.00000	−	1.73205i	0.165145	−	0.0953463i
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	−0.954765	−	0.297361i	$-0.903893\pi$
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	0.734905	+	0.678170i	$0.237227\pi$
$332$	16.0000			0.878114
$333$	3.00000	+	5.19615i	0.164399	+	0.284747i
$334$	−20.0000			−1.09435
$335$	−13.0000	+	22.5167i	−0.710266	+	1.23022i
$336$			1.73205i			0.0944911i
$337$	4.50000	+	7.79423i	0.245131	+	0.424579i	0.962168	−	0.272456i	$-0.0878358\pi$
$337$	4.50000	+	7.79423i	0.245131	+	0.424579i	−0.717038	+	0.697034i	$0.754502\pi$
$338$	11.5000	+	19.9186i	0.625518	+	1.08343i
$339$			17.3205i			0.940721i
$340$	5.00000	−	8.66025i	0.271163	−	0.469668i
$341$	−6.00000			−0.324918
$342$	−21.0000			−1.13555
$343$	−1.00000			−0.0539949
$344$	−0.500000	+	0.866025i	−0.0269582	+	0.0466930i
$345$	−12.0000	+	6.92820i	−0.646058	+	0.373002i
$346$	1.00000	+	1.73205i	0.0537603	+	0.0931156i
$347$	1.50000	+	2.59808i	0.0805242	+	0.139472i	0.903475	−	0.428640i	$-0.141007\pi$
$347$	1.50000	+	2.59808i	0.0805242	+	0.139472i	−0.822951	+	0.568112i	$0.807674\pi$
$348$	−6.00000	−	3.46410i	−0.321634	−	0.185695i
$349$	7.00000	−	12.1244i	0.374701	−	0.649002i	−0.615581	−	0.788074i	$-0.711079\pi$
$349$	7.00000	−	12.1244i	0.374701	−	0.649002i	0.990282	+	0.139072i	$0.0444119\pi$
$350$	−1.00000			−0.0534522
$351$	−27.0000	+	15.5885i	−1.44115	+	0.832050i
$352$	−1.00000			−0.0533002
$353$	7.50000	−	12.9904i	0.399185	−	0.691408i	−0.594441	−	0.804139i	$-0.702627\pi$
$353$	7.50000	−	12.9904i	0.399185	−	0.691408i	0.993626	+	0.112731i	$0.0359599\pi$
$354$	10.5000	+	6.06218i	0.558069	+	0.322201i
$355$	8.00000	+	13.8564i	0.424596	+	0.735422i
$356$	3.00000	+	5.19615i	0.159000	+	0.275396i
$357$	−7.50000	+	4.33013i	−0.396942	+	0.229175i
$358$	12.0000	−	20.7846i	0.634220	−	1.09850i
$359$	2.00000			0.105556			0.0527780	−	0.998606i	$-0.483192\pi$
$359$	2.00000			0.105556			0.0527780	+	0.998606i	$0.483192\pi$
$360$	−3.00000	+	5.19615i	−0.158114	+	0.273861i
$361$	30.0000			1.57895
$362$		0			0
$363$			17.3205i			0.909091i
$364$	−3.00000	−	5.19615i	−0.157243	−	0.272352i
$365$	−1.00000	−	1.73205i	−0.0523424	−	0.0906597i
$366$		−	20.7846i		−	1.08643i
$367$	11.0000	−	19.0526i	0.574195	−	0.994535i	−0.421933	−	0.906627i	$-0.638648\pi$
$367$	11.0000	−	19.0526i	0.574195	−	0.994535i	0.996129	−	0.0879086i	$-0.0280183\pi$
$368$	4.00000			0.208514
$369$	4.50000	−	7.79423i	0.234261	−	0.405751i
$370$	−4.00000			−0.207950
$371$	6.00000	−	10.3923i	0.311504	−	0.539542i
$372$	9.00000	−	5.19615i	0.466628	−	0.269408i
$373$	−11.0000	−	19.0526i	−0.569558	−	0.986504i	−0.996610	−	0.0822766i	$-0.973781\pi$
$373$	−11.0000	−	19.0526i	−0.569558	−	0.986504i	0.427051	−	0.904227i	$-0.359552\pi$
$374$	−2.50000	−	4.33013i	−0.129272	−	0.223906i
$375$	−18.0000	−	10.3923i	−0.929516	−	0.536656i
$376$		0			0
$377$	24.0000			1.23606
$378$	4.50000	−	2.59808i	0.231455	−	0.133631i
$379$	−17.0000			−0.873231			−0.436616	−	0.899648i	$-0.643823\pi$
$379$	−17.0000			−0.873231			−0.436616	+	0.899648i	$0.643823\pi$
$380$	7.00000	−	12.1244i	0.359092	−	0.621966i
$381$	−18.0000	−	10.3923i	−0.922168	−	0.532414i
$382$	6.00000	+	10.3923i	0.306987	+	0.531717i
$383$	−2.00000	−	3.46410i	−0.102195	−	0.177007i	0.810394	−	0.585886i	$-0.199253\pi$
$383$	−2.00000	−	3.46410i	−0.102195	−	0.177007i	−0.912589	+	0.408879i	$0.865920\pi$
$384$	1.50000	−	0.866025i	0.0765466	−	0.0441942i
$385$	1.00000	−	1.73205i	0.0509647	−	0.0882735i
$386$	−17.0000			−0.865277
$387$	3.00000			0.152499
$388$	−5.00000			−0.253837
$389$	−4.00000	+	6.92820i	−0.202808	+	0.351274i	−0.949432	−	0.313972i	$-0.898340\pi$
$389$	−4.00000	+	6.92820i	−0.202808	+	0.351274i	0.746624	+	0.665246i	$0.231673\pi$
$390$		−	20.7846i		−	1.05247i
$391$	10.0000	+	17.3205i	0.505722	+	0.875936i
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$			6.92820i			0.349482i
$394$	5.00000	−	8.66025i	0.251896	−	0.436297i
$395$	−12.0000			−0.603786
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	18.0000			0.903394			0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000			0.903394			0.451697	+	0.892171i	$0.350819\pi$
$398$	7.00000	−	12.1244i	0.350878	−	0.607739i
$399$	−10.5000	+	6.06218i	−0.525657	+	0.303488i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−4.50000	−	7.79423i	−0.224719	−	0.389225i	0.731516	−	0.681824i	$-0.238813\pi$
$401$	−4.50000	−	7.79423i	−0.224719	−	0.389225i	−0.956235	+	0.292599i	$0.905480\pi$
$402$	−19.5000	−	11.2583i	−0.972572	−	0.561514i
$403$	−18.0000	+	31.1769i	−0.896644	+	1.55303i
$404$	−4.00000			−0.199007
$405$	18.0000			0.894427
$406$	−4.00000			−0.198517
$407$	−1.00000	+	1.73205i	−0.0495682	+	0.0858546i
$408$	7.50000	+	4.33013i	0.371305	+	0.214373i
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	0.697406	−	0.716677i	$-0.254338\pi$
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	−0.969363	+	0.245633i	$0.921004\pi$
$410$	3.00000	+	5.19615i	0.148159	+	0.256620i
$411$	28.5000	−	16.4545i	1.40580	−	0.811640i
$412$	−7.00000	+	12.1244i	−0.344865	+	0.597324i
$413$	7.00000			0.344447
$414$	−6.00000	−	10.3923i	−0.294884	−	0.510754i
$415$	32.0000			1.57082
$416$	−3.00000	+	5.19615i	−0.147087	+	0.254762i
$417$			8.66025i			0.424094i
$418$	−3.50000	−	6.06218i	−0.171191	−	0.296511i
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	0.974546	−	0.224189i	$-0.0719734\pi$
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	−0.681426	+	0.731887i	$0.738640\pi$
$420$			3.46410i			0.169031i
$421$	6.00000	−	10.3923i	0.292422	−	0.506490i	−0.681960	−	0.731390i	$-0.738872\pi$
$421$	6.00000	−	10.3923i	0.292422	−	0.506490i	0.974382	+	0.224900i	$0.0722054\pi$
$422$	16.0000			0.778868
$423$		0			0
$424$	−12.0000			−0.582772
$425$	−2.50000	+	4.33013i	−0.121268	+	0.210042i
$426$	−12.0000	+	6.92820i	−0.581402	+	0.335673i
$427$	−6.00000	−	10.3923i	−0.290360	−	0.502919i
$428$	−1.50000	−	2.59808i	−0.0725052	−	0.125583i
$429$	−9.00000	−	5.19615i	−0.434524	−	0.250873i
$430$	−1.00000	+	1.73205i	−0.0482243	+	0.0835269i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	−4.50000	−	2.59808i	−0.216506	−	0.125000i
$433$	−25.0000			−1.20142			−0.600712	−	0.799466i	$-0.705116\pi$
$433$	−25.0000			−1.20142			−0.600712	+	0.799466i	$0.705116\pi$
$434$	3.00000	−	5.19615i	0.144005	−	0.249423i
$435$	−12.0000	−	6.92820i	−0.575356	−	0.332182i
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	14.0000	+	24.2487i	0.669711	+	1.15997i
$438$	1.50000	−	0.866025i	0.0716728	−	0.0413803i
$439$	12.0000	−	20.7846i	0.572729	−	0.991995i	−0.423556	−	0.905870i	$-0.639218\pi$
$439$	12.0000	−	20.7846i	0.572729	−	0.991995i	0.996284	−	0.0861252i	$-0.0274485\pi$
$440$	−2.00000			−0.0953463
$441$	1.50000	−	2.59808i	0.0714286	−	0.123718i
$442$	−30.0000			−1.42695
$443$	−3.50000	+	6.06218i	−0.166290	+	0.288023i	−0.937113	−	0.349027i	$-0.886512\pi$
$443$	−3.50000	+	6.06218i	−0.166290	+	0.288023i	0.770823	+	0.637050i	$0.219845\pi$
$444$		−	3.46410i		−	0.164399i
$445$	6.00000	+	10.3923i	0.284427	+	0.492642i
$446$	−2.00000	−	3.46410i	−0.0947027	−	0.164030i
$447$			41.5692i			1.96616i
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	17.0000			0.802280			0.401140	−	0.916017i	$-0.368614\pi$
$449$	17.0000			0.802280			0.401140	+	0.916017i	$0.368614\pi$
$450$	1.50000	−	2.59808i	0.0707107	−	0.122474i
$451$	3.00000			0.141264
$452$	5.00000	−	8.66025i	0.235180	−	0.407344i
$453$	−15.0000	+	8.66025i	−0.704761	+	0.406894i
$454$	1.50000	+	2.59808i	0.0703985	+	0.121934i
$455$	−6.00000	−	10.3923i	−0.281284	−	0.487199i
$456$	10.5000	+	6.06218i	0.491708	+	0.283887i
$457$	−0.500000	+	0.866025i	−0.0233890	+	0.0405110i	−0.877483	−	0.479608i	$-0.840779\pi$
$457$	−0.500000	+	0.866025i	−0.0233890	+	0.0405110i	0.854094	+	0.520119i	$0.174112\pi$
$458$	26.0000			1.21490
$459$		−	25.9808i		−	1.21268i
$460$	8.00000			0.373002
$461$	−7.00000	+	12.1244i	−0.326023	+	0.564688i	−0.981719	−	0.190337i	$-0.939042\pi$
$461$	−7.00000	+	12.1244i	−0.326023	+	0.564688i	0.655696	+	0.755025i	$0.272375\pi$
$462$	1.50000	+	0.866025i	0.0697863	+	0.0402911i
$463$	4.00000	+	6.92820i	0.185896	+	0.321981i	0.943878	−	0.330294i	$-0.107148\pi$
$463$	4.00000	+	6.92820i	0.185896	+	0.321981i	−0.757982	+	0.652275i	$0.773815\pi$
$464$	2.00000	+	3.46410i	0.0928477	+	0.160817i
$465$	18.0000	−	10.3923i	0.834730	−	0.481932i
$466$	−14.5000	+	25.1147i	−0.671700	+	1.16342i
$467$	−13.0000			−0.601568			−0.300784	−	0.953692i	$-0.597248\pi$
$467$	−13.0000			−0.601568			−0.300784	+	0.953692i	$0.597248\pi$
$468$	18.0000			0.832050
$469$	−13.0000			−0.600284
$470$		0			0
$471$		−	3.46410i		−	0.159617i
$472$	−3.50000	−	6.06218i	−0.161101	−	0.279034i
$473$	0.500000	+	0.866025i	0.0229900	+	0.0398199i
$474$		−	10.3923i		−	0.477334i
$475$	−3.50000	+	6.06218i	−0.160591	+	0.278152i
$476$	5.00000			0.229175
$477$	18.0000	+	31.1769i	0.824163	+	1.42749i
$478$	−6.00000			−0.274434
$479$	10.0000	−	17.3205i	0.456912	−	0.791394i	−0.541884	−	0.840453i	$-0.682289\pi$
$479$	10.0000	−	17.3205i	0.456912	−	0.791394i	0.998796	+	0.0490589i	$0.0156222\pi$
$480$	3.00000	−	1.73205i	0.136931	−	0.0790569i
$481$	6.00000	+	10.3923i	0.273576	+	0.473848i
$482$	11.5000	+	19.9186i	0.523811	+	0.907267i
$483$	−6.00000	−	3.46410i	−0.273009	−	0.157622i
$484$	5.00000	−	8.66025i	0.227273	−	0.393648i
$485$	−10.0000			−0.454077
$486$			15.5885i			0.707107i
$487$	−10.0000			−0.453143			−0.226572	−	0.973995i	$-0.572752\pi$
$487$	−10.0000			−0.453143			−0.226572	+	0.973995i	$0.572752\pi$
$488$	−6.00000	+	10.3923i	−0.271607	+	0.470438i
$489$	−6.00000	−	3.46410i	−0.271329	−	0.156652i
$490$	1.00000	+	1.73205i	0.0451754	+	0.0782461i
$491$	−16.5000	−	28.5788i	−0.744635	−	1.28974i	−0.950365	−	0.311136i	$-0.899290\pi$
$491$	−16.5000	−	28.5788i	−0.744635	−	1.28974i	0.205731	−	0.978609i	$-0.434043\pi$
$492$	−4.50000	+	2.59808i	−0.202876	+	0.117130i
$493$	−10.0000	+	17.3205i	−0.450377	+	0.780076i
$494$	−42.0000			−1.88967
$495$	3.00000	+	5.19615i	0.134840	+	0.233550i
$496$	−6.00000			−0.269408
$497$	−4.00000	+	6.92820i	−0.179425	+	0.310772i
$498$			27.7128i			1.24184i
$499$	14.5000	+	25.1147i	0.649109	+	1.12429i	0.983336	+	0.181797i	$0.0581915\pi$
$499$	14.5000	+	25.1147i	0.649109	+	1.12429i	−0.334227	+	0.942493i	$0.608475\pi$
$500$	6.00000	+	10.3923i	0.268328	+	0.464758i
$501$		−	34.6410i		−	1.54765i
$502$	1.50000	−	2.59808i	0.0669483	−	0.115958i
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$	−3.00000			−0.133631
$505$	−8.00000			−0.355995
$506$	2.00000	−	3.46410i	0.0889108	−	0.153998i
$507$	−34.5000	+	19.9186i	−1.53220	+	0.884615i
$508$	6.00000	+	10.3923i	0.266207	+	0.461084i
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	−0.979322	−	0.202306i	$-0.935156\pi$
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	0.314459	−	0.949271i	$-0.398177\pi$
$510$	15.0000	+	8.66025i	0.664211	+	0.383482i
$511$	0.500000	−	0.866025i	0.0221187	−	0.0383107i
$512$	−1.00000			−0.0441942
$513$		−	36.3731i		−	1.60591i
$514$	15.0000			0.661622
$515$	−14.0000	+	24.2487i	−0.616914	+	1.06853i
$516$	−1.50000	−	0.866025i	−0.0660338	−	0.0381246i
$517$		0			0
$518$	−1.00000	−	1.73205i	−0.0439375	−	0.0761019i
$519$	−3.00000	+	1.73205i	−0.131685	+	0.0760286i
$520$	−6.00000	+	10.3923i	−0.263117	+	0.455733i
$521$	−9.00000			−0.394297			−0.197149	−	0.980374i	$-0.563168\pi$
$521$	−9.00000			−0.394297			−0.197149	+	0.980374i	$0.563168\pi$
$522$	6.00000	−	10.3923i	0.262613	−	0.454859i
$523$	−28.0000			−1.22435			−0.612177	−	0.790721i	$-0.709706\pi$
$523$	−28.0000			−1.22435			−0.612177	+	0.790721i	$0.709706\pi$
$524$	2.00000	−	3.46410i	0.0873704	−	0.151330i
$525$		−	1.73205i		−	0.0755929i
$526$	9.00000	+	15.5885i	0.392419	+	0.679689i
$527$	−15.0000	−	25.9808i	−0.653410	−	1.13174i
$528$		−	1.73205i		−	0.0753778i
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	−24.0000			−1.04249
$531$	−10.5000	+	18.1865i	−0.455661	+	0.789228i
$532$	7.00000			0.303488
$533$	9.00000	−	15.5885i	0.389833	−	0.675211i
$534$	−9.00000	+	5.19615i	−0.389468	+	0.224860i
$535$	−3.00000	−	5.19615i	−0.129701	−	0.224649i
$536$	6.50000	+	11.2583i	0.280757	+	0.486286i
$537$	36.0000	+	20.7846i	1.55351	+	0.896922i
$538$	10.0000	−	17.3205i	0.431131	−	0.746740i
$539$	1.00000			0.0430730
$540$	−9.00000	−	5.19615i	−0.387298	−	0.223607i
$541$	−24.0000			−1.03184			−0.515920	−	0.856637i	$-0.672550\pi$
$541$	−24.0000			−1.03184			−0.515920	+	0.856637i	$0.672550\pi$
$542$	−3.00000	+	5.19615i	−0.128861	+	0.223194i
$543$		0			0
$544$	−2.50000	−	4.33013i	−0.107187	−	0.185653i
$545$	2.00000	+	3.46410i	0.0856706	+	0.148386i
$546$	9.00000	−	5.19615i	0.385164	−	0.222375i
$547$	10.5000	−	18.1865i	0.448948	−	0.777600i	−0.549370	−	0.835579i	$-0.685132\pi$
$547$	10.5000	−	18.1865i	0.448948	−	0.777600i	0.998318	+	0.0579790i	$0.0184657\pi$
$548$	−19.0000			−0.811640
$549$	36.0000			1.53644
$550$	1.00000			0.0426401
$551$	−14.0000	+	24.2487i	−0.596420	+	1.03303i
$552$			6.92820i			0.294884i
$553$	−3.00000	−	5.19615i	−0.127573	−	0.220963i
$554$	1.00000	+	1.73205i	0.0424859	+	0.0735878i
$555$		−	6.92820i		−	0.294086i
$556$	2.50000	−	4.33013i	0.106024	−	0.183638i
$557$	−28.0000			−1.18640			−0.593199	−	0.805056i	$-0.702135\pi$
$557$	−28.0000			−1.18640			−0.593199	+	0.805056i	$0.702135\pi$
$558$	9.00000	+	15.5885i	0.381000	+	0.659912i
$559$	6.00000			0.253773
$560$	1.00000	−	1.73205i	0.0422577	−	0.0731925i
$561$	7.50000	−	4.33013i	0.316650	−	0.182818i
$562$	11.0000	+	19.0526i	0.464007	+	0.803684i
$563$	−15.5000	−	26.8468i	−0.653247	−	1.13146i	−0.982330	−	0.187156i	$-0.940073\pi$
$563$	−15.5000	−	26.8468i	−0.653247	−	1.13146i	0.329083	−	0.944301i	$-0.393260\pi$
$564$		0			0
$565$	10.0000	−	17.3205i	0.420703	−	0.728679i
$566$	−4.00000			−0.168133
$567$	4.50000	+	7.79423i	0.188982	+	0.327327i
$568$	8.00000			0.335673
$569$	7.50000	−	12.9904i	0.314416	−	0.544585i	−0.664897	−	0.746935i	$-0.731525\pi$
$569$	7.50000	−	12.9904i	0.314416	−	0.544585i	0.979313	+	0.202350i	$0.0648579\pi$
$570$	21.0000	+	12.1244i	0.879593	+	0.507833i
$571$	16.5000	+	28.5788i	0.690504	+	1.19599i	0.971673	+	0.236329i	$0.0759443\pi$
$571$	16.5000	+	28.5788i	0.690504	+	1.19599i	−0.281170	+	0.959658i	$0.590722\pi$
$572$	3.00000	+	5.19615i	0.125436	+	0.217262i
$573$	−18.0000	+	10.3923i	−0.751961	+	0.434145i
$574$	−1.50000	+	2.59808i	−0.0626088	+	0.108442i
$575$	−4.00000			−0.166812
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	−35.0000			−1.45707			−0.728535	−	0.685009i	$-0.759798\pi$
$577$	−35.0000			−1.45707			−0.728535	+	0.685009i	$0.759798\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$		−	29.4449i		−	1.22369i
$580$	4.00000	+	6.92820i	0.166091	+	0.287678i
$581$	8.00000	+	13.8564i	0.331896	+	0.574861i
$582$		−	8.66025i		−	0.358979i
$583$	−6.00000	+	10.3923i	−0.248495	+	0.430405i
$584$	−1.00000			−0.0413803
$585$	36.0000			1.48842
$586$		0			0
$587$	23.5000	−	40.7032i	0.969949	−	1.68000i	0.274263	−	0.961655i	$-0.411566\pi$
$587$	23.5000	−	40.7032i	0.969949	−	1.68000i	0.695686	−	0.718346i	$-0.255100\pi$
$588$	−1.50000	+	0.866025i	−0.0618590	+	0.0357143i
$589$	−21.0000	−	36.3731i	−0.865290	−	1.49873i
$590$	−7.00000	−	12.1244i	−0.288185	−	0.499152i
$591$	15.0000	+	8.66025i	0.617018	+	0.356235i
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	−6.00000			−0.246390			−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000			−0.246390			−0.123195	+	0.992382i	$0.539314\pi$
$594$	−4.50000	+	2.59808i	−0.184637	+	0.106600i
$595$	10.0000			0.409960
$596$	12.0000	−	20.7846i	0.491539	−	0.851371i
$597$	21.0000	+	12.1244i	0.859473	+	0.496217i
$598$	−12.0000	−	20.7846i	−0.490716	−	0.849946i
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	0.509631	−	0.860393i	$-0.329782\pi$
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	−0.999938	+	0.0111569i	$0.996449\pi$
$600$	−1.50000	+	0.866025i	−0.0612372	+	0.0353553i
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	−0.604601	−	0.796528i	$-0.706668\pi$
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	0.992114	+	0.125336i	$0.0400009\pi$
$602$	−1.00000			−0.0407570
$603$	19.5000	−	33.7750i	0.794101	−	1.37542i
$604$	10.0000			0.406894
$605$	10.0000	−	17.3205i	0.406558	−	0.704179i
$606$		−	6.92820i		−	0.281439i
$607$	12.0000	+	20.7846i	0.487065	+	0.843621i	0.999889	−	0.0148722i	$-0.00473415\pi$
$607$	12.0000	+	20.7846i	0.487065	+	0.843621i	−0.512824	+	0.858494i	$0.671401\pi$
$608$	−3.50000	−	6.06218i	−0.141944	−	0.245854i
$609$		−	6.92820i		−	0.280745i
$610$	−12.0000	+	20.7846i	−0.485866	+	0.841544i
$611$		0			0
$612$	−7.50000	+	12.9904i	−0.303170	+	0.525105i
$613$	42.0000			1.69636			0.848182	−	0.529705i	$-0.177697\pi$
$613$	42.0000			1.69636			0.848182	+	0.529705i	$0.177697\pi$
$614$	3.50000	−	6.06218i	0.141249	−	0.244650i
$615$	−9.00000	+	5.19615i	−0.362915	+	0.209529i
$616$	−0.500000	−	0.866025i	−0.0201456	−	0.0348932i
$617$	8.50000	+	14.7224i	0.342197	+	0.592703i	0.984840	−	0.173463i	$-0.0554956\pi$
$617$	8.50000	+	14.7224i	0.342197	+	0.592703i	−0.642643	+	0.766165i	$0.722162\pi$
$618$	−21.0000	−	12.1244i	−0.844744	−	0.487713i
$619$	−18.5000	+	32.0429i	−0.743578	+	1.28791i	0.207279	+	0.978282i	$0.433539\pi$
$619$	−18.5000	+	32.0429i	−0.743578	+	1.28791i	−0.950856	+	0.309633i	$0.899794\pi$
$620$	−12.0000			−0.481932
$621$	18.0000	−	10.3923i	0.722315	−	0.417029i
$622$	−2.00000			−0.0801927
$623$	−3.00000	+	5.19615i	−0.120192	+	0.208179i
$624$	−9.00000	−	5.19615i	−0.360288	−	0.208013i
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	−8.50000	−	14.7224i	−0.339728	−	0.588427i
$627$	10.5000	−	6.06218i	0.419330	−	0.242100i
$628$	−1.00000	+	1.73205i	−0.0399043	+	0.0691164i
$629$	−10.0000			−0.398726
$630$	−6.00000			−0.239046
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	−3.00000	+	5.19615i	−0.119334	+	0.206692i
$633$			27.7128i			1.10149i
$634$	−3.00000	−	5.19615i	−0.119145	−	0.206366i
$635$	12.0000	+	20.7846i	0.476205	+	0.824812i
$636$		−	20.7846i		−	0.824163i
$637$	3.00000	−	5.19615i	0.118864	−	0.205879i
$638$	4.00000			0.158362
$639$	−12.0000	−	20.7846i	−0.474713	−	0.822226i
$640$	−2.00000			−0.0790569
$641$	−0.500000	+	0.866025i	−0.0197488	+	0.0342059i	−0.875731	−	0.482800i	$-0.839620\pi$
$641$	−0.500000	+	0.866025i	−0.0197488	+	0.0342059i	0.855982	+	0.517005i	$0.172953\pi$
$642$	4.50000	−	2.59808i	0.177601	−	0.102538i
$643$	3.50000	+	6.06218i	0.138027	+	0.239069i	0.926750	−	0.375680i	$-0.122591\pi$
$643$	3.50000	+	6.06218i	0.138027	+	0.239069i	−0.788723	+	0.614749i	$0.789257\pi$
$644$	2.00000	+	3.46410i	0.0788110	+	0.136505i
$645$	−3.00000	−	1.73205i	−0.118125	−	0.0681994i
$646$	17.5000	−	30.3109i	0.688528	−	1.19257i
$647$	12.0000			0.471769			0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000			0.471769			0.235884	+	0.971781i	$0.424201\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	−7.00000			−0.274774
$650$	3.00000	−	5.19615i	0.117670	−	0.203810i
$651$	9.00000	+	5.19615i	0.352738	+	0.203653i
$652$	2.00000	+	3.46410i	0.0783260	+	0.135665i
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	0.918736	−	0.394872i	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$	−3.00000	+	1.73205i	−0.117309	+	0.0677285i
$655$	4.00000	−	6.92820i	0.156293	−	0.270707i
$656$	3.00000			0.117130
$657$	1.50000	+	2.59808i	0.0585206	+	0.101361i
$658$		0			0
$659$	−8.00000	+	13.8564i	−0.311636	+	0.539769i	−0.978717	−	0.205216i	$-0.934210\pi$
$659$	−8.00000	+	13.8564i	−0.311636	+	0.539769i	0.667081	+	0.744985i	$0.267544\pi$
$660$		−	3.46410i		−	0.134840i
$661$	−14.0000	−	24.2487i	−0.544537	−	0.943166i	−0.998636	−	0.0522143i	$-0.983372\pi$
$661$	−14.0000	−	24.2487i	−0.544537	−	0.943166i	0.454099	−	0.890951i	$-0.349961\pi$
$662$	4.00000	+	6.92820i	0.155464	+	0.269272i
$663$		−	51.9615i		−	2.01802i
$664$	8.00000	−	13.8564i	0.310460	−	0.537733i
$665$	14.0000			0.542897
$666$	6.00000			0.232495
$667$	−16.0000			−0.619522
$668$	−10.0000	+	17.3205i	−0.386912	+	0.670151i
$669$	6.00000	−	3.46410i	0.231973	−	0.133930i
$670$	13.0000	+	22.5167i	0.502234	+	0.869894i
$671$	6.00000	+	10.3923i	0.231627	+	0.401190i
$672$	1.50000	+	0.866025i	0.0578638	+	0.0334077i
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	−0.968818	−	0.247774i	$-0.920301\pi$
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	0.698988	+	0.715134i	$0.253634\pi$
$674$	9.00000			0.346667
$675$	4.50000	+	2.59808i	0.173205	+	0.100000i
$676$	23.0000			0.884615
$677$	−15.0000	+	25.9808i	−0.576497	+	0.998522i	0.419380	+	0.907811i	$0.362247\pi$
$677$	−15.0000	+	25.9808i	−0.576497	+	0.998522i	−0.995877	+	0.0907112i	$0.971086\pi$
$678$	15.0000	+	8.66025i	0.576072	+	0.332595i
$679$	−2.50000	−	4.33013i	−0.0959412	−	0.166175i
$680$	−5.00000	−	8.66025i	−0.191741	−	0.332106i
$681$	−4.50000	+	2.59808i	−0.172440	+	0.0995585i
$682$	−3.00000	+	5.19615i	−0.114876	+	0.198971i
$683$	39.0000			1.49229			0.746147	−	0.665782i	$-0.231902\pi$
$683$	39.0000			1.49229			0.746147	+	0.665782i	$0.231902\pi$
$684$	−10.5000	+	18.1865i	−0.401478	+	0.695379i
$685$	−38.0000			−1.45191
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$			45.0333i			1.71813i
$688$	0.500000	+	0.866025i	0.0190623	+	0.0330169i
$689$	36.0000	+	62.3538i	1.37149	+	2.37549i
$690$			13.8564i			0.527504i
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	0.382791	+	0.923835i	$0.374963\pi$
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	−0.991460	+	0.130410i	$0.958371\pi$
$692$	2.00000			0.0760286
$693$	−1.50000	+	2.59808i	−0.0569803	+	0.0986928i
$694$	3.00000			0.113878
$695$	5.00000	−	8.66025i	0.189661	−	0.328502i
$696$	−6.00000	+	3.46410i	−0.227429	+	0.131306i
$697$	7.50000	+	12.9904i	0.284083	+	0.492046i
$698$	−7.00000	−	12.1244i	−0.264954	−	0.458914i
$699$	−43.5000	−	25.1147i	−1.64532	−	0.949927i
$700$	−0.500000	+	0.866025i	−0.0188982	+	0.0327327i
$701$	8.00000			0.302156			0.151078	−	0.988522i	$-0.451726\pi$
$701$	8.00000			0.302156			0.151078	+	0.988522i	$0.451726\pi$
$702$			31.1769i			1.17670i
$703$	−14.0000			−0.528020
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$		0			0
$706$	−7.50000	−	12.9904i	−0.282266	−	0.488899i
$707$	−2.00000	−	3.46410i	−0.0752177	−	0.130281i
$708$	10.5000	−	6.06218i	0.394614	−	0.227831i
$709$	2.00000	−	3.46410i	0.0751116	−	0.130097i	−0.826023	−	0.563636i	$-0.809402\pi$
$709$	2.00000	−	3.46410i	0.0751116	−	0.130097i	0.901135	+	0.433539i	$0.142735\pi$
$710$	16.0000			0.600469
$711$	18.0000			0.675053
$712$	6.00000			0.224860
$713$	12.0000	−	20.7846i	0.449404	−	0.778390i
$714$			8.66025i			0.324102i
$715$	6.00000	+	10.3923i	0.224387	+	0.388650i
$716$	−12.0000	−	20.7846i	−0.448461	−	0.776757i
$717$		−	10.3923i		−	0.388108i
$718$	1.00000	−	1.73205i	0.0373197	−	0.0646396i
$719$	6.00000			0.223762			0.111881	−	0.993722i	$-0.464312\pi$
$719$	6.00000			0.223762			0.111881	+	0.993722i	$0.464312\pi$
$720$	3.00000	+	5.19615i	0.111803	+	0.193649i
$721$	−14.0000			−0.521387
$722$	15.0000	−	25.9808i	0.558242	−	0.966904i
$723$	−34.5000	+	19.9186i	−1.28307	+	0.740780i
$724$		0			0
$725$	−2.00000	−	3.46410i	−0.0742781	−	0.128654i
$726$	15.0000	+	8.66025i	0.556702	+	0.321412i
$727$	7.00000	−	12.1244i	0.259616	−	0.449667i	−0.706523	−	0.707690i	$-0.749737\pi$
$727$	7.00000	−	12.1244i	0.259616	−	0.449667i	0.966139	+	0.258022i	$0.0830708\pi$
$728$	−6.00000			−0.222375
$729$	−27.0000			−1.00000
$730$	−2.00000			−0.0740233
$731$	−2.50000	+	4.33013i	−0.0924658	+	0.160156i
$732$	−18.0000	−	10.3923i	−0.665299	−	0.384111i
$733$	9.00000	+	15.5885i	0.332423	+	0.575773i	0.982986	−	0.183679i	$-0.0588007\pi$
$733$	9.00000	+	15.5885i	0.332423	+	0.575773i	−0.650564	+	0.759452i	$0.725467\pi$
$734$	−11.0000	−	19.0526i	−0.406017	−	0.703243i
$735$	−3.00000	+	1.73205i	−0.110657	+	0.0638877i
$736$	2.00000	−	3.46410i	0.0737210	−	0.127688i
$737$	13.0000			0.478861
$738$	−4.50000	−	7.79423i	−0.165647	−	0.286910i
$739$	−33.0000			−1.21392			−0.606962	−	0.794731i	$-0.707612\pi$
$739$	−33.0000			−1.21392			−0.606962	+	0.794731i	$0.707612\pi$
$740$	−2.00000	+	3.46410i	−0.0735215	+	0.127343i
$741$		−	72.7461i		−	2.67240i
$742$	−6.00000	−	10.3923i	−0.220267	−	0.381514i
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	0.915794	−	0.401648i	$-0.131563\pi$
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	−0.805735	+	0.592277i	$0.798229\pi$
$744$		−	10.3923i		−	0.381000i
$745$	24.0000	−	41.5692i	0.879292	−	1.52298i
$746$	−22.0000			−0.805477
$747$	−48.0000			−1.75623
$748$	−5.00000			−0.182818
$749$	1.50000	−	2.59808i	0.0548088	−	0.0949316i
$750$	−18.0000	+	10.3923i	−0.657267	+	0.379473i
$751$	9.00000	+	15.5885i	0.328415	+	0.568831i	0.982197	−	0.187851i	$-0.0601523\pi$
$751$	9.00000	+	15.5885i	0.328415	+	0.568831i	−0.653783	+	0.756682i	$0.726819\pi$
$752$		0			0
$753$	4.50000	+	2.59808i	0.163989	+	0.0946792i
$754$	12.0000	−	20.7846i	0.437014	−	0.756931i
$755$	20.0000			0.727875
$756$		−	5.19615i		−	0.188982i
$757$	−48.0000			−1.74459			−0.872295	−	0.488980i	$-0.837369\pi$
$757$	−48.0000			−1.74459			−0.872295	+	0.488980i	$0.837369\pi$
$758$	−8.50000	+	14.7224i	−0.308734	+	0.534743i
$759$	6.00000	+	3.46410i	0.217786	+	0.125739i
$760$	−7.00000	−	12.1244i	−0.253917	−	0.439797i
$761$	−5.00000	−	8.66025i	−0.181250	−	0.313934i	0.761057	−	0.648686i	$-0.224681\pi$
$761$	−5.00000	−	8.66025i	−0.181250	−	0.313934i	−0.942306	+	0.334752i	$0.891348\pi$
$762$	−18.0000	+	10.3923i	−0.652071	+	0.376473i
$763$	−1.00000	+	1.73205i	−0.0362024	+	0.0627044i
$764$	12.0000			0.434145
$765$	−15.0000	+	25.9808i	−0.542326	+	0.939336i
$766$	−4.00000			−0.144526
$767$	−21.0000	+	36.3731i	−0.758266	+	1.31336i
$768$		−	1.73205i		−	0.0625000i
$769$	−11.0000	−	19.0526i	−0.396670	−	0.687053i	0.596643	−	0.802507i	$-0.296501\pi$
$769$	−11.0000	−	19.0526i	−0.396670	−	0.687053i	−0.993313	+	0.115454i	$0.963168\pi$
$770$	−1.00000	−	1.73205i	−0.0360375	−	0.0624188i
$771$			25.9808i			0.935674i
$772$	−8.50000	+	14.7224i	−0.305922	+	0.529872i
$773$	−52.0000			−1.87031			−0.935155	−	0.354239i	$-0.884740\pi$
$773$	−52.0000			−1.87031			−0.935155	+	0.354239i	$0.884740\pi$
$774$	1.50000	−	2.59808i	0.0539164	−	0.0933859i
$775$	6.00000			0.215526
$776$	−2.50000	+	4.33013i	−0.0897448	+	0.155443i
$777$	3.00000	−	1.73205i	0.107624	−	0.0621370i
$778$	4.00000	+	6.92820i	0.143407	+	0.248388i
$779$	10.5000	+	18.1865i	0.376202	+	0.651600i
$780$	−18.0000	−	10.3923i	−0.644503	−	0.372104i
$781$	4.00000	−	6.92820i	0.143131	−	0.247911i
$782$	20.0000			0.715199
$783$	18.0000	+	10.3923i	0.643268	+	0.371391i
$784$	1.00000			0.0357143
$785$	−2.00000	+	3.46410i	−0.0713831	+	0.123639i
$786$	6.00000	+	3.46410i	0.214013	+	0.123560i
$787$	6.00000	+	10.3923i	0.213877	+	0.370446i	0.952925	−	0.303207i	$-0.0980575\pi$
$787$	6.00000	+	10.3923i	0.213877	+	0.370446i	−0.739048	+	0.673653i	$0.764724\pi$
$788$	−5.00000	−	8.66025i	−0.178118	−	0.308509i
$789$	−27.0000	+	15.5885i	−0.961225	+	0.554964i
$790$	−6.00000	+	10.3923i	−0.213470	+	0.369742i
$791$	10.0000			0.355559
$792$	3.00000			0.106600
$793$	72.0000			2.55679
$794$	9.00000	−	15.5885i	0.319398	−	0.553214i
$795$		−	41.5692i		−	1.47431i
$796$	−7.00000	−	12.1244i	−0.248108	−	0.429736i
$797$	6.00000	+	10.3923i	0.212531	+	0.368114i	0.952506	−	0.304520i	$-0.0984960\pi$
$797$	6.00000	+	10.3923i	0.212531	+	0.368114i	−0.739975	+	0.672634i	$0.765163\pi$
$798$			12.1244i			0.429198i
$799$		0			0
$800$	1.00000			0.0353553
$801$	−9.00000	−	15.5885i	−0.317999	−	0.550791i
$802$	−9.00000			−0.317801
$803$	−0.500000	+	0.866025i	−0.0176446	+	0.0305614i
$804$	−19.5000	+	11.2583i	−0.687712	+	0.397051i
$805$	4.00000	+	6.92820i	0.140981	+	0.244187i
$806$	18.0000	+	31.1769i	0.634023	+	1.09816i
$807$	30.0000	+	17.3205i	1.05605	+	0.609711i
$808$	−2.00000	+	3.46410i	−0.0703598	+	0.121867i
$809$	−43.0000			−1.51180			−0.755900	−	0.654687i	$-0.772800\pi$
$809$	−43.0000			−1.51180			−0.755900	+	0.654687i	$0.772800\pi$
$810$	9.00000	−	15.5885i	0.316228	−	0.547723i
$811$	31.0000			1.08856			0.544279	−	0.838905i	$-0.316803\pi$
$811$	31.0000			1.08856			0.544279	+	0.838905i	$0.316803\pi$
$812$	−2.00000	+	3.46410i	−0.0701862	+	0.121566i
$813$	−9.00000	−	5.19615i	−0.315644	−	0.182237i
$814$	1.00000	+	1.73205i	0.0350500	+	0.0607083i
$815$	4.00000	+	6.92820i	0.140114	+	0.242684i
$816$	7.50000	−	4.33013i	0.262553	−	0.151585i
$817$	−3.50000	+	6.06218i	−0.122449	+	0.212089i
$818$	−11.0000			−0.384606
$819$	9.00000	+	15.5885i	0.314485	+	0.544705i
$820$	6.00000			0.209529
$821$	−23.0000	+	39.8372i	−0.802706	+	1.39033i	0.115124	+	0.993351i	$0.463274\pi$
$821$	−23.0000	+	39.8372i	−0.802706	+	1.39033i	−0.917829	+	0.396976i	$0.870060\pi$
$822$		−	32.9090i		−	1.14783i
$823$	−17.0000	−	29.4449i	−0.592583	−	1.02638i	−0.993883	−	0.110437i	$-0.964775\pi$
$823$	−17.0000	−	29.4449i	−0.592583	−	1.02638i	0.401300	−	0.915947i	$-0.368558\pi$
$824$	7.00000	+	12.1244i	0.243857	+	0.422372i
$825$			1.73205i			0.0603023i
$826$	3.50000	−	6.06218i	0.121781	−	0.210930i
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$	−12.0000			−0.417029
$829$	4.00000			0.138926			0.0694629	−	0.997585i	$-0.477871\pi$
$829$	4.00000			0.138926			0.0694629	+	0.997585i	$0.477871\pi$
$830$	16.0000	−	27.7128i	0.555368	−	0.961926i
$831$	−3.00000	+	1.73205i	−0.104069	+	0.0600842i
$832$	3.00000	+	5.19615i	0.104006	+	0.180144i
$833$	2.50000	+	4.33013i	0.0866199	+	0.150030i
$834$	7.50000	+	4.33013i	0.259704	+	0.149940i
$835$	−20.0000	+	34.6410i	−0.692129	+	1.19880i
$836$	−7.00000			−0.242100
$837$	−27.0000	+	15.5885i	−0.933257	+	0.538816i
$838$	12.0000			0.414533
$839$	10.0000	−	17.3205i	0.345238	−	0.597970i	−0.640159	−	0.768243i	$-0.721131\pi$
$839$	10.0000	−	17.3205i	0.345238	−	0.597970i	0.985397	+	0.170272i	$0.0544647\pi$
$840$	3.00000	+	1.73205i	0.103510	+	0.0597614i
$841$	6.50000	+	11.2583i	0.224138	+	0.388218i
$842$	−6.00000	−	10.3923i	−0.206774	−	0.358142i
$843$	−33.0000	+	19.0526i	−1.13658	+	0.656205i
$844$	8.00000	−	13.8564i	0.275371	−	0.476957i
$845$	46.0000			1.58245
$846$		0			0
$847$	10.0000			0.343604
$848$	−6.00000	+	10.3923i	−0.206041	+	0.356873i
$849$		−	6.92820i		−	0.237775i
$850$	2.50000	+	4.33013i	0.0857493	+	0.148522i
$851$	−4.00000	−	6.92820i	−0.137118	−	0.237496i
$852$			13.8564i			0.474713i
$853$	−22.0000	+	38.1051i	−0.753266	+	1.30469i	0.192966	+	0.981205i	$0.438189\pi$
$853$	−22.0000	+	38.1051i	−0.753266	+	1.30469i	−0.946232	+	0.323489i	$0.895144\pi$
$854$	−12.0000			−0.410632
$855$	−21.0000	+	36.3731i	−0.718185	+	1.24393i
$856$	−3.00000			−0.102538
$857$	−15.0000	+	25.9808i	−0.512390	+	0.887486i	0.487507	+	0.873119i	$0.337907\pi$
$857$	−15.0000	+	25.9808i	−0.512390	+	0.887486i	−0.999897	+	0.0143666i	$0.995427\pi$
$858$	−9.00000	+	5.19615i	−0.307255	+	0.177394i
$859$	−14.5000	−	25.1147i	−0.494734	−	0.856904i	0.505248	−	0.862974i	$-0.331401\pi$
$859$	−14.5000	−	25.1147i	−0.494734	−	0.856904i	−0.999982	+	0.00607046i	$0.998068\pi$
$860$	1.00000	+	1.73205i	0.0340997	+	0.0590624i
$861$	−4.50000	−	2.59808i	−0.153360	−	0.0885422i
$862$		0			0
$863$	38.0000			1.29354			0.646768	−	0.762687i	$-0.276120\pi$
$863$	38.0000			1.29354			0.646768	+	0.762687i	$0.276120\pi$
$864$	−4.50000	+	2.59808i	−0.153093	+	0.0883883i
$865$	4.00000			0.136004
$866$	−12.5000	+	21.6506i	−0.424767	+	0.735719i
$867$	12.0000	+	6.92820i	0.407541	+	0.235294i
$868$	−3.00000	−	5.19615i	−0.101827	−	0.176369i
$869$	3.00000	+	5.19615i	0.101768	+	0.176267i
$870$	−12.0000	+	6.92820i	−0.406838	+	0.234888i
$871$	39.0000	−	67.5500i	1.32146	−	2.28884i
$872$	2.00000			0.0677285
$873$	15.0000			0.507673
$874$	28.0000			0.947114
$875$	−6.00000	+	10.3923i	−0.202837	+	0.351324i
$876$		−	1.73205i		−	0.0585206i
$877$	−8.00000	−	13.8564i	−0.270141	−	0.467898i	0.698757	−	0.715359i	$-0.253737\pi$
$877$	−8.00000	−	13.8564i	−0.270141	−	0.467898i	−0.968898	+	0.247462i	$0.920404\pi$
$878$	−12.0000	−	20.7846i	−0.404980	−	0.701447i
$879$		0			0
$880$	−1.00000	+	1.73205i	−0.0337100	+	0.0583874i
$881$	42.0000			1.41502			0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000			1.41502			0.707508	+	0.706705i	$0.249819\pi$
$882$	−1.50000	−	2.59808i	−0.0505076	−	0.0874818i
$883$	53.0000			1.78359			0.891796	−	0.452438i	$-0.149446\pi$
$883$	53.0000			1.78359			0.891796	+	0.452438i	$0.149446\pi$
$884$	−15.0000	+	25.9808i	−0.504505	+	0.873828i
$885$	21.0000	−	12.1244i	0.705907	−	0.407556i
$886$	3.50000	+	6.06218i	0.117585	+	0.203663i
$887$	3.00000	+	5.19615i	0.100730	+	0.174470i	0.911986	−	0.410222i	$-0.134549\pi$
$887$	3.00000	+	5.19615i	0.100730	+	0.174470i	−0.811256	+	0.584692i	$0.801215\pi$
$888$	−3.00000	−	1.73205i	−0.100673	−	0.0581238i
$889$	−6.00000	+	10.3923i	−0.201234	+	0.348547i
$890$	12.0000			0.402241
$891$	−4.50000	−	7.79423i	−0.150756	−	0.261116i
$892$	−4.00000			−0.133930
$893$		0			0
$894$	36.0000	+	20.7846i	1.20402	+	0.695141i
$895$	−24.0000	−	41.5692i	−0.802232	−	1.38951i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$	36.0000	−	20.7846i	1.20201	−	0.693978i
$898$	8.50000	−	14.7224i	0.283649	−	0.491294i
$899$	24.0000			0.800445
$900$	−1.50000	−	2.59808i	−0.0500000	−	0.0866025i
$901$	−60.0000			−1.99889
$902$	1.50000	−	2.59808i	0.0499445	−	0.0865065i
$903$		−	1.73205i		−	0.0576390i
$904$	−5.00000	−	8.66025i	−0.166298	−	0.288036i
$905$		0			0
$906$			17.3205i			0.575435i
$907$	13.5000	−	23.3827i	0.448260	−	0.776409i	−0.550013	−	0.835156i	$-0.685377\pi$
$907$	13.5000	−	23.3827i	0.448260	−	0.776409i	0.998273	+	0.0587469i	$0.0187105\pi$
$908$	3.00000			0.0995585
$909$	12.0000			0.398015
$910$	−12.0000			−0.397796
$911$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$911$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$912$	10.5000	−	6.06218i	0.347690	−	0.200739i
$913$	−8.00000	−	13.8564i	−0.264761	−	0.458580i
$914$	0.500000	+	0.866025i	0.0165385	+	0.0286456i
$915$	−36.0000	−	20.7846i	−1.19012	−	0.687118i
$916$	13.0000	−	22.5167i	0.429532	−	0.743971i
$917$	4.00000			0.132092
$918$	−22.5000	−	12.9904i	−0.742611	−	0.428746i
$919$	16.0000			0.527791			0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000			0.527791			0.263896	+	0.964551i	$0.414993\pi$
$920$	4.00000	−	6.92820i	0.131876	−	0.228416i
$921$	10.5000	+	6.06218i	0.345987	+	0.199756i
$922$	7.00000	+	12.1244i	0.230533	+	0.399294i
$923$	−24.0000	−	41.5692i	−0.789970	−	1.36827i
$924$	1.50000	−	0.866025i	0.0493464	−	0.0284901i
$925$	1.00000	−	1.73205i	0.0328798	−	0.0569495i
$926$	8.00000			0.262896
$927$	21.0000	−	36.3731i	0.689730	−	1.19465i
$928$	4.00000			0.131306
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	−0.679770	−	0.733426i	$-0.737920\pi$
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	0.975050	+	0.221985i	$0.0712536\pi$
$930$		−	20.7846i		−	0.681554i
$931$	3.50000	+	6.06218i	0.114708	+	0.198680i
$932$	14.5000	+	25.1147i	0.474963	+	0.822661i
$933$		−	3.46410i		−	0.113410i
$934$	−6.50000	+	11.2583i	−0.212686	+	0.368384i
$935$	−10.0000			−0.327035
$936$	9.00000	−	15.5885i	0.294174	−	0.509525i
$937$	2.00000			0.0653372			0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000			0.0653372			0.0326686	+	0.999466i	$0.489599\pi$
$938$	−6.50000	+	11.2583i	−0.212233	+	0.367598i
$939$	25.5000	−	14.7224i	0.832161	−	0.480448i
$940$		0			0
$941$	−10.0000	−	17.3205i	−0.325991	−	0.564632i	0.655722	−	0.755003i	$-0.272364\pi$
$941$	−10.0000	−	17.3205i	−0.325991	−	0.564632i	−0.981712	+	0.190370i	$0.939031\pi$
$942$	−3.00000	−	1.73205i	−0.0977453	−	0.0564333i
$943$	−6.00000	+	10.3923i	−0.195387	+	0.338420i
$944$	−7.00000			−0.227831
$945$		−	10.3923i		−	0.338062i
$946$	1.00000			0.0325128
$947$	18.5000	−	32.0429i	0.601169	−	1.04126i	−0.391475	−	0.920189i	$-0.628035\pi$
$947$	18.5000	−	32.0429i	0.601169	−	1.04126i	0.992644	−	0.121067i	$-0.0386316\pi$
$948$	−9.00000	−	5.19615i	−0.292306	−	0.168763i
$949$	3.00000	+	5.19615i	0.0973841	+	0.168674i
$950$	3.50000	+	6.06218i	0.113555	+	0.196683i
$951$	9.00000	−	5.19615i	0.291845	−	0.168497i
$952$	2.50000	−	4.33013i	0.0810255	−	0.140340i
$953$	−35.0000			−1.13376			−0.566881	−	0.823800i	$-0.691850\pi$
$953$	−35.0000			−1.13376			−0.566881	+	0.823800i	$0.691850\pi$
$954$	36.0000			1.16554
$955$	24.0000			0.776622
$956$	−3.00000	+	5.19615i	−0.0970269	+	0.168056i
$957$			6.92820i			0.223957i
$958$	−10.0000	−	17.3205i	−0.323085	−	0.559600i
$959$	−9.50000	−	16.4545i	−0.306771	−	0.531343i
$960$		−	3.46410i		−	0.111803i
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	12.0000			0.386896
$963$	4.50000	+	7.79423i	0.145010	+	0.251166i
$964$	23.0000			0.740780
$965$	−17.0000	+	29.4449i	−0.547249	+	0.947864i
$966$	−6.00000	+	3.46410i	−0.193047	+	0.111456i
$967$	−7.00000	−	12.1244i	−0.225105	−	0.389893i	0.731246	−	0.682114i	$-0.238939\pi$
$967$	−7.00000	−	12.1244i	−0.225105	−	0.389893i	−0.956351	+	0.292221i	$0.905606\pi$
$968$	−5.00000	−	8.66025i	−0.160706	−	0.278351i
$969$	52.5000	+	30.3109i	1.68654	+	0.973726i
$970$	−5.00000	+	8.66025i	−0.160540	+	0.278064i
$971$	−12.0000			−0.385098			−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000			−0.385098			−0.192549	+	0.981287i	$0.561675\pi$
$972$	13.5000	+	7.79423i	0.433013	+	0.250000i
$973$	5.00000			0.160293
$974$	−5.00000	+	8.66025i	−0.160210	+	0.277492i
$975$	9.00000	+	5.19615i	0.288231	+	0.166410i
$976$	6.00000	+	10.3923i	0.192055	+	0.332650i
$977$	7.50000	+	12.9904i	0.239946	+	0.415599i	0.960699	−	0.277594i	$-0.0895368\pi$
$977$	7.50000	+	12.9904i	0.239946	+	0.415599i	−0.720752	+	0.693193i	$0.756204\pi$
$978$	−6.00000	+	3.46410i	−0.191859	+	0.110770i
$979$	3.00000	−	5.19615i	0.0958804	−	0.166070i
$980$	2.00000			0.0638877
$981$	−3.00000	−	5.19615i	−0.0957826	−	0.165900i
$982$	−33.0000			−1.05307
$983$	30.0000	−	51.9615i	0.956851	−	1.65732i	0.226778	−	0.973946i	$-0.427181\pi$
$983$	30.0000	−	51.9615i	0.956851	−	1.65732i	0.730073	−	0.683369i	$-0.239486\pi$
$984$			5.19615i			0.165647i
$985$	−10.0000	−	17.3205i	−0.318626	−	0.551877i
$986$	10.0000	+	17.3205i	0.318465	+	0.551597i
$987$		0			0
$988$	−21.0000	+	36.3731i	−0.668099	+	1.15718i
$989$	−4.00000			−0.127193
$990$	6.00000			0.190693
$991$	−28.0000			−0.889449			−0.444725	−	0.895667i	$-0.646698\pi$
$991$	−28.0000			−0.889449			−0.444725	+	0.895667i	$0.646698\pi$
$992$	−3.00000	+	5.19615i	−0.0952501	+	0.164978i
$993$	−12.0000	+	6.92820i	−0.380808	+	0.219860i
$994$	4.00000	+	6.92820i	0.126872	+	0.219749i
$995$	−14.0000	−	24.2487i	−0.443830	−	0.768736i
$996$	24.0000	+	13.8564i	0.760469	+	0.439057i
$997$	−1.00000	+	1.73205i	−0.0316703	+	0.0548546i	−0.881426	−	0.472322i	$-0.843416\pi$
$997$	−1.00000	+	1.73205i	−0.0316703	+	0.0548546i	0.849756	+	0.527176i	$0.176749\pi$
$998$	29.0000			0.917979
$999$			10.3923i			0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.f.b.43.1	✓	2
3.2	odd	2		378.2.f.b.127.1		2
4.3	odd	2		1008.2.r.a.673.1		2
7.2	even	3		882.2.e.a.655.1		2
7.3	odd	6		882.2.h.g.79.1		2
7.4	even	3		882.2.h.h.79.1		2
7.5	odd	6		882.2.e.e.655.1		2
7.6	odd	2		882.2.f.f.295.1		2
9.2	odd	6		1134.2.a.f.1.1		1
9.4	even	3	inner	126.2.f.b.85.1	yes	2
9.5	odd	6		378.2.f.b.253.1		2
9.7	even	3		1134.2.a.c.1.1		1
12.11	even	2		3024.2.r.c.2017.1		2
21.2	odd	6		2646.2.e.i.2125.1		2
21.5	even	6		2646.2.e.h.2125.1		2
21.11	odd	6		2646.2.h.b.667.1		2
21.17	even	6		2646.2.h.c.667.1		2
21.20	even	2		2646.2.f.b.883.1		2
36.7	odd	6		9072.2.a.t.1.1		1
36.11	even	6		9072.2.a.f.1.1		1
36.23	even	6		3024.2.r.c.1009.1		2
36.31	odd	6		1008.2.r.a.337.1		2
63.4	even	3		882.2.e.a.373.1		2
63.5	even	6		2646.2.h.c.361.1		2
63.13	odd	6		882.2.f.f.589.1		2
63.20	even	6		7938.2.a.bb.1.1		1
63.23	odd	6		2646.2.h.b.361.1		2
63.31	odd	6		882.2.e.e.373.1		2
63.32	odd	6		2646.2.e.i.1549.1		2
63.34	odd	6		7938.2.a.e.1.1		1
63.40	odd	6		882.2.h.g.67.1		2
63.41	even	6		2646.2.f.b.1765.1		2
63.58	even	3		882.2.h.h.67.1		2
63.59	even	6		2646.2.e.h.1549.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.b.43.1	✓	2	1.1	even	1	trivial
126.2.f.b.85.1	yes	2	9.4	even	3	inner
378.2.f.b.127.1		2	3.2	odd	2
378.2.f.b.253.1		2	9.5	odd	6
882.2.e.a.373.1		2	63.4	even	3
882.2.e.a.655.1		2	7.2	even	3
882.2.e.e.373.1		2	63.31	odd	6
882.2.e.e.655.1		2	7.5	odd	6
882.2.f.f.295.1		2	7.6	odd	2
882.2.f.f.589.1		2	63.13	odd	6
882.2.h.g.67.1		2	63.40	odd	6
882.2.h.g.79.1		2	7.3	odd	6
882.2.h.h.67.1		2	63.58	even	3
882.2.h.h.79.1		2	7.4	even	3
1008.2.r.a.337.1		2	36.31	odd	6
1008.2.r.a.673.1		2	4.3	odd	2
1134.2.a.c.1.1		1	9.7	even	3
1134.2.a.f.1.1		1	9.2	odd	6
2646.2.e.h.1549.1		2	63.59	even	6
2646.2.e.h.2125.1		2	21.5	even	6
2646.2.e.i.1549.1		2	63.32	odd	6
2646.2.e.i.2125.1		2	21.2	odd	6
2646.2.f.b.883.1		2	21.20	even	2
2646.2.f.b.1765.1		2	63.41	even	6
2646.2.h.b.361.1		2	63.23	odd	6
2646.2.h.b.667.1		2	21.11	odd	6
2646.2.h.c.361.1		2	63.5	even	6
2646.2.h.c.667.1		2	21.17	even	6
3024.2.r.c.1009.1		2	36.23	even	6
3024.2.r.c.2017.1		2	12.11	even	2
7938.2.a.e.1.1		1	63.34	odd	6
7938.2.a.bb.1.1		1	63.20	even	6
9072.2.a.f.1.1		1	36.11	even	6
9072.2.a.t.1.1		1	36.7	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.f (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 - 1.73205i) q^{5} +(1.50000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} -2.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} -1.73205i q^{12} +(3.00000 + 5.19615i) q^{13} +(-0.500000 - 0.866025i) q^{14} -3.46410i q^{15} +(-0.500000 + 0.866025i) q^{16} -5.00000 q^{17} +3.00000 q^{18} -7.00000 q^{19} +(-1.00000 + 1.73205i) q^{20} +(1.50000 - 0.866025i) q^{21} +(0.500000 + 0.866025i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{25} +6.00000 q^{26} +5.19615i q^{27} -1.00000 q^{28} +(2.00000 - 3.46410i) q^{29} +(-3.00000 - 1.73205i) q^{30} +(3.00000 + 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 + 0.866025i) q^{33} +(-2.50000 + 4.33013i) q^{34} -2.00000 q^{35} +(1.50000 - 2.59808i) q^{36} +2.00000 q^{37} +(-3.50000 + 6.06218i) q^{38} +10.3923i q^{39} +(1.00000 + 1.73205i) q^{40} +(-1.50000 - 2.59808i) q^{41} -1.73205i q^{42} +(0.500000 - 0.866025i) q^{43} +1.00000 q^{44} +(3.00000 - 5.19615i) q^{45} -4.00000 q^{46} +(-1.50000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-7.50000 - 4.33013i) q^{51} +(3.00000 - 5.19615i) q^{52} +12.0000 q^{53} +(4.50000 + 2.59808i) q^{54} +2.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-10.5000 - 6.06218i) q^{57} +(-2.00000 - 3.46410i) q^{58} +(3.50000 + 6.06218i) q^{59} +(-3.00000 + 1.73205i) q^{60} +(6.00000 - 10.3923i) q^{61} +6.00000 q^{62} +3.00000 q^{63} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{65} +1.73205i q^{66} +(-6.50000 - 11.2583i) q^{67} +(2.50000 + 4.33013i) q^{68} -6.92820i q^{69} +(-1.00000 + 1.73205i) q^{70} -8.00000 q^{71} +(-1.50000 - 2.59808i) q^{72} +1.00000 q^{73} +(1.00000 - 1.73205i) q^{74} +(1.50000 - 0.866025i) q^{75} +(3.50000 + 6.06218i) q^{76} +(0.500000 + 0.866025i) q^{77} +(9.00000 + 5.19615i) q^{78} +(3.00000 - 5.19615i) q^{79} +2.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} -3.00000 q^{82} +(-8.00000 + 13.8564i) q^{83} +(-1.50000 - 0.866025i) q^{84} +(5.00000 + 8.66025i) q^{85} +(-0.500000 - 0.866025i) q^{86} +(6.00000 - 3.46410i) q^{87} +(0.500000 - 0.866025i) q^{88} -6.00000 q^{89} +(-3.00000 - 5.19615i) q^{90} +6.00000 q^{91} +(-2.00000 + 3.46410i) q^{92} +10.3923i q^{93} +(7.00000 + 12.1244i) q^{95} +1.73205i q^{96} +(2.50000 - 4.33013i) q^{97} -1.00000 q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} - q^{4} - 2 q^{5} + 3 q^{6} + q^{7} - 2 q^{8} + 3 q^{9} - 4 q^{10} - q^{11} + 6 q^{13} - q^{14} - q^{16} - 10 q^{17} + 6 q^{18} - 14 q^{19} - 2 q^{20} + 3 q^{21} + q^{22} - 4 q^{23}+ \cdots - 6 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 - q^4 - 2 * q^5 + 3 * q^6 + q^7 - 2 * q^8 + 3 * q^9 - 4 * q^10 - q^11 + 6 * q^13 - q^14 - q^16 - 10 * q^17 + 6 * q^18 - 14 * q^19 - 2 * q^20 + 3 * q^21 + q^22 - 4 * q^23 - 3 * q^24 + q^25 + 12 * q^26 - 2 * q^28 + 4 * q^29 - 6 * q^30 + 6 * q^31 + q^32 - 3 * q^33 - 5 * q^34 - 4 * q^35 + 3 * q^36 + 4 * q^37 - 7 * q^38 + 2 * q^40 - 3 * q^41 + q^43 + 2 * q^44 + 6 * q^45 - 8 * q^46 - 3 * q^48 - q^49 - q^50 - 15 * q^51 + 6 * q^52 + 24 * q^53 + 9 * q^54 + 4 * q^55 - q^56 - 21 * q^57 - 4 * q^58 + 7 * q^59 - 6 * q^60 + 12 * q^61 + 12 * q^62 + 6 * q^63 + 2 * q^64 + 12 * q^65 - 13 * q^67 + 5 * q^68 - 2 * q^70 - 16 * q^71 - 3 * q^72 + 2 * q^73 + 2 * q^74 + 3 * q^75 + 7 * q^76 + q^77 + 18 * q^78 + 6 * q^79 + 4 * q^80 - 9 * q^81 - 6 * q^82 - 16 * q^83 - 3 * q^84 + 10 * q^85 - q^86 + 12 * q^87 + q^88 - 12 * q^89 - 6 * q^90 + 12 * q^91 - 4 * q^92 + 14 * q^95 + 5 * q^97 - 2 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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