LMFDB - Embedded newform 342.2.h.b.277.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(121,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("342.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.h (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:	$2.73088374913$
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			277.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	342.277
Dual form			342.2.h.b.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +2.00000 q^{5} +(-1.50000 + 0.866025i) q^{6} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +2.00000 q^{5} +(-1.50000 + 0.866025i) q^{6} +1.00000 q^{8} -3.00000 q^{9} +(-1.00000 - 1.73205i) q^{10} +(2.00000 - 3.46410i) q^{11} +(1.50000 + 0.866025i) q^{12} +(2.00000 - 3.46410i) q^{13} -3.46410i q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(1.50000 + 2.59808i) q^{18} +(-4.00000 + 1.73205i) q^{19} +(-1.00000 + 1.73205i) q^{20} -4.00000 q^{22} +(-4.00000 + 6.92820i) q^{23} -1.73205i q^{24} -1.00000 q^{25} -4.00000 q^{26} +5.19615i q^{27} +10.0000 q^{29} +(-3.00000 + 1.73205i) q^{30} +(-5.00000 - 8.66025i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-6.00000 - 3.46410i) q^{33} -3.00000 q^{34} +(1.50000 - 2.59808i) q^{36} -2.00000 q^{37} +(3.50000 + 2.59808i) q^{38} +(-6.00000 - 3.46410i) q^{39} +2.00000 q^{40} +1.00000 q^{41} +(-0.500000 - 0.866025i) q^{43} +(2.00000 + 3.46410i) q^{44} -6.00000 q^{45} +8.00000 q^{46} +2.00000 q^{47} +(-1.50000 + 0.866025i) q^{48} +(3.50000 + 6.06218i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-4.50000 - 2.59808i) q^{51} +(2.00000 + 3.46410i) q^{52} +(5.00000 + 8.66025i) q^{53} +(4.50000 - 2.59808i) q^{54} +(4.00000 - 6.92820i) q^{55} +(3.00000 + 6.92820i) q^{57} +(-5.00000 - 8.66025i) q^{58} +3.00000 q^{59} +(3.00000 + 1.73205i) q^{60} +2.00000 q^{61} +(-5.00000 + 8.66025i) q^{62} +1.00000 q^{64} +(4.00000 - 6.92820i) q^{65} +6.92820i q^{66} +(1.50000 - 2.59808i) q^{67} +(1.50000 + 2.59808i) q^{68} +(12.0000 + 6.92820i) q^{69} +(5.00000 - 8.66025i) q^{71} -3.00000 q^{72} +(-3.00000 + 5.19615i) q^{73} +(1.00000 + 1.73205i) q^{74} +1.73205i q^{75} +(0.500000 - 4.33013i) q^{76} +6.92820i q^{78} +(5.00000 + 8.66025i) q^{79} +(-1.00000 - 1.73205i) q^{80} +9.00000 q^{81} +(-0.500000 - 0.866025i) q^{82} +(-4.50000 + 7.79423i) q^{83} +(3.00000 - 5.19615i) q^{85} +(-0.500000 + 0.866025i) q^{86} -17.3205i q^{87} +(2.00000 - 3.46410i) q^{88} +(-3.00000 - 5.19615i) q^{89} +(3.00000 + 5.19615i) q^{90} +(-4.00000 - 6.92820i) q^{92} +(-15.0000 + 8.66025i) q^{93} +(-1.00000 - 1.73205i) q^{94} +(-8.00000 + 3.46410i) q^{95} +(1.50000 + 0.866025i) q^{96} +(7.00000 + 12.1244i) q^{97} +(3.50000 - 6.06218i) q^{98} +(-6.00000 + 10.3923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 4 q^{5} - 3 q^{6} + 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q - q^2 - q^4 + 4 * q^5 - 3 * q^6 + 2 * q^8 - 6 * q^9	$ 2 q - q^{2} - q^{4} + 4 q^{5} - 3 q^{6} + 2 q^{8} - 6 q^{9} - 2 q^{10} + 4 q^{11} + 3 q^{12} + 4 q^{13} - q^{16} + 3 q^{17} + 3 q^{18} - 8 q^{19} - 2 q^{20} - 8 q^{22} - 8 q^{23} - 2 q^{25} - 8 q^{26} + 20 q^{29} - 6 q^{30} - 10 q^{31} - q^{32} - 12 q^{33} - 6 q^{34} + 3 q^{36} - 4 q^{37} + 7 q^{38} - 12 q^{39} + 4 q^{40} + 2 q^{41} - q^{43} + 4 q^{44} - 12 q^{45} + 16 q^{46} + 4 q^{47} - 3 q^{48} + 7 q^{49} + q^{50} - 9 q^{51} + 4 q^{52} + 10 q^{53} + 9 q^{54} + 8 q^{55} + 6 q^{57} - 10 q^{58} + 6 q^{59} + 6 q^{60} + 4 q^{61} - 10 q^{62} + 2 q^{64} + 8 q^{65} + 3 q^{67} + 3 q^{68} + 24 q^{69} + 10 q^{71} - 6 q^{72} - 6 q^{73} + 2 q^{74} + q^{76} + 10 q^{79} - 2 q^{80} + 18 q^{81} - q^{82} - 9 q^{83} + 6 q^{85} - q^{86} + 4 q^{88} - 6 q^{89} + 6 q^{90} - 8 q^{92} - 30 q^{93} - 2 q^{94} - 16 q^{95} + 3 q^{96} + 14 q^{97} + 7 q^{98} - 12 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^4 + 4 * q^5 - 3 * q^6 + 2 * q^8 - 6 * q^9 - 2 * q^10 + 4 * q^11 + 3 * q^12 + 4 * q^13 - q^16 + 3 * q^17 + 3 * q^18 - 8 * q^19 - 2 * q^20 - 8 * q^22 - 8 * q^23 - 2 * q^25 - 8 * q^26 + 20 * q^29 - 6 * q^30 - 10 * q^31 - q^32 - 12 * q^33 - 6 * q^34 + 3 * q^36 - 4 * q^37 + 7 * q^38 - 12 * q^39 + 4 * q^40 + 2 * q^41 - q^43 + 4 * q^44 - 12 * q^45 + 16 * q^46 + 4 * q^47 - 3 * q^48 + 7 * q^49 + q^50 - 9 * q^51 + 4 * q^52 + 10 * q^53 + 9 * q^54 + 8 * q^55 + 6 * q^57 - 10 * q^58 + 6 * q^59 + 6 * q^60 + 4 * q^61 - 10 * q^62 + 2 * q^64 + 8 * q^65 + 3 * q^67 + 3 * q^68 + 24 * q^69 + 10 * q^71 - 6 * q^72 - 6 * q^73 + 2 * q^74 + q^76 + 10 * q^79 - 2 * q^80 + 18 * q^81 - q^82 - 9 * q^83 + 6 * q^85 - q^86 + 4 * q^88 - 6 * q^89 + 6 * q^90 - 8 * q^92 - 30 * q^93 - 2 * q^94 - 16 * q^95 + 3 * q^96 + 14 * q^97 + 7 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		−	1.73205i		−	1.00000i
$3$		−	1.73205i		−	1.00000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.00000			0.894427			0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000			0.894427			0.447214	+	0.894427i	$0.352416\pi$
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$7$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$8$	1.00000			0.353553
$9$	−3.00000			−1.00000
$10$	−1.00000	−	1.73205i	−0.316228	−	0.547723i
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	−0.389338	−	0.921095i	$-0.627296\pi$
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	0.992361	−	0.123371i	$-0.0393705\pi$
$12$	1.50000	+	0.866025i	0.433013	+	0.250000i
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$		0			0
$15$		−	3.46410i		−	0.894427i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	1.50000	+	2.59808i	0.353553	+	0.612372i
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$20$	−1.00000	+	1.73205i	−0.223607	+	0.387298i
$21$		0			0
$22$	−4.00000			−0.852803
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	0.0607377	+	0.998154i	$0.480655\pi$
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	−0.894795	+	0.446476i	$0.852679\pi$
$24$		−	1.73205i		−	0.353553i
$25$	−1.00000			−0.200000
$26$	−4.00000			−0.784465
$27$			5.19615i			1.00000i
$28$		0			0
$29$	10.0000			1.85695			0.928477	−	0.371391i	$-0.121119\pi$
$29$	10.0000			1.85695			0.928477	+	0.371391i	$0.121119\pi$
$30$	−3.00000	+	1.73205i	−0.547723	+	0.316228i
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.830014	−	0.557743i	$-0.811667\pi$
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.0680129	−	0.997684i	$-0.521666\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−6.00000	−	3.46410i	−1.04447	−	0.603023i
$34$	−3.00000			−0.514496
$35$		0			0
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	3.50000	+	2.59808i	0.567775	+	0.421464i
$39$	−6.00000	−	3.46410i	−0.960769	−	0.554700i
$40$	2.00000			0.316228
$41$	1.00000			0.156174			0.0780869	−	0.996947i	$-0.475119\pi$
$41$	1.00000			0.156174			0.0780869	+	0.996947i	$0.475119\pi$
$42$		0			0
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	0.825380	−	0.564578i	$-0.190961\pi$
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	−0.901629	+	0.432511i	$0.857628\pi$
$44$	2.00000	+	3.46410i	0.301511	+	0.522233i
$45$	−6.00000			−0.894427
$46$	8.00000			1.17954
$47$	2.00000			0.291730			0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000			0.291730			0.145865	+	0.989305i	$0.453403\pi$
$48$	−1.50000	+	0.866025i	−0.216506	+	0.125000i
$49$	3.50000	+	6.06218i	0.500000	+	0.866025i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−4.50000	−	2.59808i	−0.630126	−	0.363803i
$52$	2.00000	+	3.46410i	0.277350	+	0.480384i
$53$	5.00000	+	8.66025i	0.686803	+	1.18958i	0.972867	+	0.231367i	$0.0743197\pi$
$53$	5.00000	+	8.66025i	0.686803	+	1.18958i	−0.286064	+	0.958211i	$0.592347\pi$
$54$	4.50000	−	2.59808i	0.612372	−	0.353553i
$55$	4.00000	−	6.92820i	0.539360	−	0.934199i
$56$		0			0
$57$	3.00000	+	6.92820i	0.397360	+	0.917663i
$58$	−5.00000	−	8.66025i	−0.656532	−	1.13715i
$59$	3.00000			0.390567			0.195283	−	0.980747i	$-0.437437\pi$
$59$	3.00000			0.390567			0.195283	+	0.980747i	$0.437437\pi$
$60$	3.00000	+	1.73205i	0.387298	+	0.223607i
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$	−5.00000	+	8.66025i	−0.635001	+	1.09985i
$63$		0			0
$64$	1.00000			0.125000
$65$	4.00000	−	6.92820i	0.496139	−	0.859338i
$66$			6.92820i			0.852803i
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	−0.759733	−	0.650236i	$-0.774670\pi$
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	0.942987	+	0.332830i	$0.108004\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	12.0000	+	6.92820i	1.44463	+	0.834058i
$70$		0			0
$71$	5.00000	−	8.66025i	0.593391	−	1.02778i	−0.400381	−	0.916349i	$-0.631122\pi$
$71$	5.00000	−	8.66025i	0.593391	−	1.02778i	0.993772	−	0.111434i	$-0.0355445\pi$
$72$	−3.00000			−0.353553
$73$	−3.00000	+	5.19615i	−0.351123	+	0.608164i	−0.986447	−	0.164083i	$-0.947534\pi$
$73$	−3.00000	+	5.19615i	−0.351123	+	0.608164i	0.635323	+	0.772246i	$0.280867\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$			1.73205i			0.200000i
$76$	0.500000	−	4.33013i	0.0573539	−	0.496700i
$77$		0			0
$78$			6.92820i			0.784465i
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$	−1.00000	−	1.73205i	−0.111803	−	0.193649i
$81$	9.00000			1.00000
$82$	−0.500000	−	0.866025i	−0.0552158	−	0.0956365i
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	−0.999976	−	0.00698436i	$-0.997777\pi$
$83$	−4.50000	+	7.79423i	−0.493939	+	0.855528i	0.506036	+	0.862512i	$0.331110\pi$
$84$		0			0
$85$	3.00000	−	5.19615i	0.325396	−	0.563602i
$86$	−0.500000	+	0.866025i	−0.0539164	+	0.0933859i
$87$		−	17.3205i		−	1.85695i
$88$	2.00000	−	3.46410i	0.213201	−	0.369274i
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$	3.00000	+	5.19615i	0.316228	+	0.547723i
$91$		0			0
$92$	−4.00000	−	6.92820i	−0.417029	−	0.722315i
$93$	−15.0000	+	8.66025i	−1.55543	+	0.898027i
$94$	−1.00000	−	1.73205i	−0.103142	−	0.178647i
$95$	−8.00000	+	3.46410i	−0.820783	+	0.355409i
$96$	1.50000	+	0.866025i	0.153093	+	0.0883883i
$97$	7.00000	+	12.1244i	0.710742	+	1.23104i	0.964579	+	0.263795i	$0.0849741\pi$
$97$	7.00000	+	12.1244i	0.710742	+	1.23104i	−0.253837	+	0.967247i	$0.581693\pi$
$98$	3.50000	−	6.06218i	0.353553	−	0.612372i
$99$	−6.00000	+	10.3923i	−0.603023	+	1.04447i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	8.00000			0.796030			0.398015	−	0.917379i	$-0.369699\pi$
$101$	8.00000			0.796030			0.398015	+	0.917379i	$0.369699\pi$
$102$			5.19615i			0.514496i
$103$	3.00000	+	5.19615i	0.295599	+	0.511992i	0.975124	−	0.221660i	$-0.0711475\pi$
$103$	3.00000	+	5.19615i	0.295599	+	0.511992i	−0.679525	+	0.733652i	$0.737814\pi$
$104$	2.00000	−	3.46410i	0.196116	−	0.339683i
$105$		0			0
$106$	5.00000	−	8.66025i	0.485643	−	0.841158i
$107$	17.0000			1.64345			0.821726	−	0.569883i	$-0.193011\pi$
$107$	17.0000			1.64345			0.821726	+	0.569883i	$0.193011\pi$
$108$	−4.50000	−	2.59808i	−0.433013	−	0.250000i
$109$	3.00000	−	5.19615i	0.287348	−	0.497701i	−0.685828	−	0.727764i	$-0.740560\pi$
$109$	3.00000	−	5.19615i	0.287348	−	0.497701i	0.973176	+	0.230063i	$0.0738931\pi$
$110$	−8.00000			−0.762770
$111$			3.46410i			0.328798i
$112$		0			0
$113$	0.500000	+	0.866025i	0.0470360	+	0.0814688i	0.888585	−	0.458712i	$-0.151689\pi$
$113$	0.500000	+	0.866025i	0.0470360	+	0.0814688i	−0.841549	+	0.540181i	$0.818356\pi$
$114$	4.50000	−	6.06218i	0.421464	−	0.567775i
$115$	−8.00000	+	13.8564i	−0.746004	+	1.29212i
$116$	−5.00000	+	8.66025i	−0.464238	+	0.804084i
$117$	−6.00000	+	10.3923i	−0.554700	+	0.960769i
$118$	−1.50000	−	2.59808i	−0.138086	−	0.239172i
$119$		0			0
$120$		−	3.46410i		−	0.316228i
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	−1.00000	−	1.73205i	−0.0905357	−	0.156813i
$123$		−	1.73205i		−	0.156174i
$124$	10.0000			0.898027
$125$	−12.0000			−1.07331
$126$		0			0
$127$	−6.00000	−	10.3923i	−0.532414	−	0.922168i	−0.999284	−	0.0378419i	$-0.987952\pi$
$127$	−6.00000	−	10.3923i	−0.532414	−	0.922168i	0.466870	−	0.884326i	$-0.345382\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−1.50000	+	0.866025i	−0.132068	+	0.0762493i
$130$	−8.00000			−0.701646
$131$	−9.00000			−0.786334			−0.393167	−	0.919467i	$-0.628621\pi$
$131$	−9.00000			−0.786334			−0.393167	+	0.919467i	$0.628621\pi$
$132$	6.00000	−	3.46410i	0.522233	−	0.301511i
$133$		0			0
$134$	−3.00000			−0.259161
$135$			10.3923i			0.894427i
$136$	1.50000	−	2.59808i	0.128624	−	0.222783i
$137$	−14.0000			−1.19610			−0.598050	−	0.801459i	$-0.704058\pi$
$137$	−14.0000			−1.19610			−0.598050	+	0.801459i	$0.704058\pi$
$138$		−	13.8564i		−	1.17954i
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	0.491033	+	0.871141i	$0.336619\pi$
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	−0.999947	+	0.0103230i	$0.996714\pi$
$140$		0			0
$141$		−	3.46410i		−	0.291730i
$142$	−10.0000			−0.839181
$143$	−8.00000	−	13.8564i	−0.668994	−	1.15873i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	20.0000			1.66091
$146$	6.00000			0.496564
$147$	10.5000	−	6.06218i	0.866025	−	0.500000i
$148$	1.00000	−	1.73205i	0.0821995	−	0.142374i
$149$	12.0000			0.983078			0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000			0.983078			0.491539	+	0.870855i	$0.336434\pi$
$150$	1.50000	−	0.866025i	0.122474	−	0.0707107i
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	0.0964061	+	0.995342i	$0.469265\pi$
$151$	−10.0000	+	17.3205i	−0.813788	+	1.40952i	−0.910195	+	0.414181i	$0.864068\pi$
$152$	−4.00000	+	1.73205i	−0.324443	+	0.140488i
$153$	−4.50000	+	7.79423i	−0.363803	+	0.630126i
$154$		0			0
$155$	−10.0000	−	17.3205i	−0.803219	−	1.39122i
$156$	6.00000	−	3.46410i	0.480384	−	0.277350i
$157$	−14.0000			−1.11732			−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000			−1.11732			−0.558661	+	0.829396i	$0.688685\pi$
$158$	5.00000	−	8.66025i	0.397779	−	0.688973i
$159$	15.0000	−	8.66025i	1.18958	−	0.686803i
$160$	−1.00000	+	1.73205i	−0.0790569	+	0.136931i
$161$		0			0
$162$	−4.50000	−	7.79423i	−0.353553	−	0.612372i
$163$	11.0000			0.861586			0.430793	−	0.902451i	$-0.358234\pi$
$163$	11.0000			0.861586			0.430793	+	0.902451i	$0.358234\pi$
$164$	−0.500000	+	0.866025i	−0.0390434	+	0.0676252i
$165$	−12.0000	−	6.92820i	−0.934199	−	0.539360i
$166$	9.00000			0.698535
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	−0.958440	−	0.285295i	$-0.907908\pi$
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	0.726293	+	0.687386i	$0.241242\pi$
$168$		0			0
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$	−6.00000			−0.460179
$171$	12.0000	−	5.19615i	0.917663	−	0.397360i
$172$	1.00000			0.0762493
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$	−15.0000	+	8.66025i	−1.13715	+	0.656532i
$175$		0			0
$176$	−4.00000			−0.301511
$177$		−	5.19615i		−	0.390567i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	15.0000			1.12115			0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000			1.12115			0.560576	+	0.828103i	$0.310580\pi$
$180$	3.00000	−	5.19615i	0.223607	−	0.387298i
$181$	7.00000	+	12.1244i	0.520306	+	0.901196i	0.999721	+	0.0236082i	$0.00751541\pi$
$181$	7.00000	+	12.1244i	0.520306	+	0.901196i	−0.479415	+	0.877588i	$0.659151\pi$
$182$		0			0
$183$		−	3.46410i		−	0.256074i
$184$	−4.00000	+	6.92820i	−0.294884	+	0.510754i
$185$	−4.00000			−0.294086
$186$	15.0000	+	8.66025i	1.09985	+	0.635001i
$187$	−6.00000	−	10.3923i	−0.438763	−	0.759961i
$188$	−1.00000	+	1.73205i	−0.0729325	+	0.126323i
$189$		0			0
$190$	7.00000	+	5.19615i	0.507833	+	0.376969i
$191$	−2.00000	+	3.46410i	−0.144715	+	0.250654i	−0.929267	−	0.369410i	$-0.879560\pi$
$191$	−2.00000	+	3.46410i	−0.144715	+	0.250654i	0.784552	+	0.620063i	$0.212893\pi$
$192$		−	1.73205i		−	0.125000i
$193$	−3.00000			−0.215945			−0.107972	−	0.994154i	$-0.534436\pi$
$193$	−3.00000			−0.215945			−0.107972	+	0.994154i	$0.534436\pi$
$194$	7.00000	−	12.1244i	0.502571	−	0.870478i
$195$	−12.0000	−	6.92820i	−0.859338	−	0.496139i
$196$	−7.00000			−0.500000
$197$	−16.0000			−1.13995			−0.569976	−	0.821661i	$-0.693048\pi$
$197$	−16.0000			−1.13995			−0.569976	+	0.821661i	$0.693048\pi$
$198$	12.0000			0.852803
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	−0.965272	−	0.261245i	$-0.915867\pi$
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	0.256391	−	0.966573i	$-0.417466\pi$
$200$	−1.00000			−0.0707107
$201$	−4.50000	−	2.59808i	−0.317406	−	0.183254i
$202$	−4.00000	−	6.92820i	−0.281439	−	0.487467i
$203$		0			0
$204$	4.50000	−	2.59808i	0.315063	−	0.181902i
$205$	2.00000			0.139686
$206$	3.00000	−	5.19615i	0.209020	−	0.362033i
$207$	12.0000	−	20.7846i	0.834058	−	1.44463i
$208$	−4.00000			−0.277350
$209$	−2.00000	+	17.3205i	−0.138343	+	1.19808i
$210$		0			0
$211$	−12.0000			−0.826114			−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$	−10.0000			−0.686803
$213$	−15.0000	−	8.66025i	−1.02778	−	0.593391i
$214$	−8.50000	−	14.7224i	−0.581048	−	1.00640i
$215$	−1.00000	−	1.73205i	−0.0681994	−	0.118125i
$216$			5.19615i			0.353553i
$217$		0			0
$218$	−6.00000			−0.406371
$219$	9.00000	+	5.19615i	0.608164	+	0.351123i
$220$	4.00000	+	6.92820i	0.269680	+	0.467099i
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$	3.00000	−	1.73205i	0.201347	−	0.116248i
$223$	−7.00000	−	12.1244i	−0.468755	−	0.811907i	0.530607	−	0.847618i	$-0.321964\pi$
$223$	−7.00000	−	12.1244i	−0.468755	−	0.811907i	−0.999362	+	0.0357107i	$0.988630\pi$
$224$		0			0
$225$	3.00000			0.200000
$226$	0.500000	−	0.866025i	0.0332595	−	0.0576072i
$227$	−8.00000	+	13.8564i	−0.530979	+	0.919682i	0.468368	+	0.883534i	$0.344842\pi$
$227$	−8.00000	+	13.8564i	−0.530979	+	0.919682i	−0.999346	+	0.0361484i	$0.988491\pi$
$228$	−7.50000	−	0.866025i	−0.496700	−	0.0573539i
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	0.924510	−	0.381157i	$-0.124474\pi$
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	−0.792347	+	0.610071i	$0.791141\pi$
$230$	16.0000			1.05501
$231$		0			0
$232$	10.0000			0.656532
$233$	−1.50000	+	2.59808i	−0.0982683	+	0.170206i	−0.910968	−	0.412477i	$-0.864664\pi$
$233$	−1.50000	+	2.59808i	−0.0982683	+	0.170206i	0.812700	+	0.582683i	$0.197997\pi$
$234$	12.0000			0.784465
$235$	4.00000			0.260931
$236$	−1.50000	+	2.59808i	−0.0976417	+	0.169120i
$237$	15.0000	−	8.66025i	0.974355	−	0.562544i
$238$		0			0
$239$	6.00000	+	10.3923i	0.388108	+	0.672222i	0.992195	−	0.124696i	$-0.0397955\pi$
$239$	6.00000	+	10.3923i	0.388108	+	0.672222i	−0.604087	+	0.796918i	$0.706462\pi$
$240$	−3.00000	+	1.73205i	−0.193649	+	0.111803i
$241$	1.00000			0.0644157			0.0322078	−	0.999481i	$-0.489746\pi$
$241$	1.00000			0.0644157			0.0322078	+	0.999481i	$0.489746\pi$
$242$	−2.50000	+	4.33013i	−0.160706	+	0.278351i
$243$		−	15.5885i		−	1.00000i
$244$	−1.00000	+	1.73205i	−0.0640184	+	0.110883i
$245$	7.00000	+	12.1244i	0.447214	+	0.774597i
$246$	−1.50000	+	0.866025i	−0.0956365	+	0.0552158i
$247$	−2.00000	+	17.3205i	−0.127257	+	1.10208i
$248$	−5.00000	−	8.66025i	−0.317500	−	0.549927i
$249$	13.5000	+	7.79423i	0.855528	+	0.493939i
$250$	6.00000	+	10.3923i	0.379473	+	0.657267i
$251$	−8.50000	−	14.7224i	−0.536515	−	0.929272i	−0.999088	−	0.0426905i	$-0.986407\pi$
$251$	−8.50000	−	14.7224i	−0.536515	−	0.929272i	0.462573	−	0.886581i	$-0.346926\pi$
$252$		0			0
$253$	16.0000	+	27.7128i	1.00591	+	1.74229i
$254$	−6.00000	+	10.3923i	−0.376473	+	0.652071i
$255$	−9.00000	−	5.19615i	−0.563602	−	0.325396i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.500000	−	0.866025i	0.0311891	−	0.0540212i	−0.850010	−	0.526767i	$-0.823404\pi$
$257$	0.500000	−	0.866025i	0.0311891	−	0.0540212i	0.881199	+	0.472746i	$0.156737\pi$
$258$	1.50000	+	0.866025i	0.0933859	+	0.0539164i
$259$		0			0
$260$	4.00000	+	6.92820i	0.248069	+	0.429669i
$261$	−30.0000			−1.85695
$262$	4.50000	+	7.79423i	0.278011	+	0.481529i
$263$	3.00000	+	5.19615i	0.184988	+	0.320408i	0.943572	−	0.331166i	$-0.107442\pi$
$263$	3.00000	+	5.19615i	0.184988	+	0.320408i	−0.758585	+	0.651575i	$0.774109\pi$
$264$	−6.00000	−	3.46410i	−0.369274	−	0.213201i
$265$	10.0000	+	17.3205i	0.614295	+	1.06399i
$266$		0			0
$267$	−9.00000	+	5.19615i	−0.550791	+	0.317999i
$268$	1.50000	+	2.59808i	0.0916271	+	0.158703i
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	−0.449622	−	0.893219i	$-0.648441\pi$
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	0.998361	−	0.0572259i	$-0.0182255\pi$
$270$	9.00000	−	5.19615i	0.547723	−	0.316228i
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	−0.384201	−	0.923249i	$-0.625523\pi$
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	0.991658	−	0.128897i	$-0.0411435\pi$
$272$	−3.00000			−0.181902
$273$		0			0
$274$	7.00000	+	12.1244i	0.422885	+	0.732459i
$275$	−2.00000	+	3.46410i	−0.120605	+	0.208893i
$276$	−12.0000	+	6.92820i	−0.722315	+	0.417029i
$277$	−14.0000	+	24.2487i	−0.841178	+	1.45696i	0.0477206	+	0.998861i	$0.484804\pi$
$277$	−14.0000	+	24.2487i	−0.841178	+	1.45696i	−0.888899	+	0.458103i	$0.848529\pi$
$278$	12.0000			0.719712
$279$	15.0000	+	25.9808i	0.898027	+	1.55543i
$280$		0			0
$281$	31.0000			1.84930			0.924652	−	0.380812i	$-0.124356\pi$
$281$	31.0000			1.84930			0.924652	+	0.380812i	$0.124356\pi$
$282$	−3.00000	+	1.73205i	−0.178647	+	0.103142i
$283$	−21.0000			−1.24832			−0.624160	−	0.781296i	$-0.714559\pi$
$283$	−21.0000			−1.24832			−0.624160	+	0.781296i	$0.714559\pi$
$284$	5.00000	+	8.66025i	0.296695	+	0.513892i
$285$	6.00000	+	13.8564i	0.355409	+	0.820783i
$286$	−8.00000	+	13.8564i	−0.473050	+	0.819346i
$287$		0			0
$288$	1.50000	−	2.59808i	0.0883883	−	0.153093i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−10.0000	−	17.3205i	−0.587220	−	1.01710i
$291$	21.0000	−	12.1244i	1.23104	−	0.710742i
$292$	−3.00000	−	5.19615i	−0.175562	−	0.304082i
$293$	−12.0000	−	20.7846i	−0.701047	−	1.21425i	−0.968099	−	0.250568i	$-0.919383\pi$
$293$	−12.0000	−	20.7846i	−0.701047	−	1.21425i	0.267052	−	0.963682i	$-0.413951\pi$
$294$	−10.5000	−	6.06218i	−0.612372	−	0.353553i
$295$	6.00000			0.349334
$296$	−2.00000			−0.116248
$297$	18.0000	+	10.3923i	1.04447	+	0.603023i
$298$	−6.00000	−	10.3923i	−0.347571	−	0.602010i
$299$	16.0000	+	27.7128i	0.925304	+	1.60267i
$300$	−1.50000	−	0.866025i	−0.0866025	−	0.0500000i
$301$		0			0
$302$	20.0000			1.15087
$303$		−	13.8564i		−	0.796030i
$304$	3.50000	+	2.59808i	0.200739	+	0.149010i
$305$	4.00000			0.229039
$306$	9.00000			0.514496
$307$	−10.5000	+	18.1865i	−0.599267	+	1.03796i	0.393663	+	0.919255i	$0.371208\pi$
$307$	−10.5000	+	18.1865i	−0.599267	+	1.03796i	−0.992930	+	0.118705i	$0.962126\pi$
$308$		0			0
$309$	9.00000	−	5.19615i	0.511992	−	0.295599i
$310$	−10.0000	+	17.3205i	−0.567962	+	0.983739i
$311$	−8.00000	−	13.8564i	−0.453638	−	0.785725i	0.544970	−	0.838455i	$-0.316541\pi$
$311$	−8.00000	−	13.8564i	−0.453638	−	0.785725i	−0.998609	+	0.0527306i	$0.983208\pi$
$312$	−6.00000	−	3.46410i	−0.339683	−	0.196116i
$313$	29.0000			1.63918			0.819588	−	0.572953i	$-0.194202\pi$
$313$	29.0000			1.63918			0.819588	+	0.572953i	$0.194202\pi$
$314$	7.00000	+	12.1244i	0.395033	+	0.684217i
$315$		0			0
$316$	−10.0000			−0.562544
$317$	−24.0000			−1.34797			−0.673987	−	0.738743i	$-0.735420\pi$
$317$	−24.0000			−1.34797			−0.673987	+	0.738743i	$0.735420\pi$
$318$	−15.0000	−	8.66025i	−0.841158	−	0.485643i
$319$	20.0000	−	34.6410i	1.11979	−	1.93952i
$320$	2.00000			0.111803
$321$		−	29.4449i		−	1.64345i
$322$		0			0
$323$	−1.50000	+	12.9904i	−0.0834622	+	0.722804i
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−2.00000	+	3.46410i	−0.110940	+	0.192154i
$326$	−5.50000	−	9.52628i	−0.304617	−	0.527612i
$327$	−9.00000	−	5.19615i	−0.497701	−	0.287348i
$328$	1.00000			0.0552158
$329$		0			0
$330$			13.8564i			0.762770i
$331$	12.5000	−	21.6506i	0.687062	−	1.19003i	−0.285722	−	0.958313i	$-0.592233\pi$
$331$	12.5000	−	21.6506i	0.687062	−	1.19003i	0.972784	−	0.231714i	$-0.0744333\pi$
$332$	−4.50000	−	7.79423i	−0.246970	−	0.427764i
$333$	6.00000			0.328798
$334$	6.00000			0.328305
$335$	3.00000	−	5.19615i	0.163908	−	0.283896i
$336$		0			0
$337$	−14.0000			−0.762629			−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000			−0.762629			−0.381314	+	0.924445i	$0.624528\pi$
$338$	−1.50000	+	2.59808i	−0.0815892	+	0.141317i
$339$	1.50000	−	0.866025i	0.0814688	−	0.0470360i
$340$	3.00000	+	5.19615i	0.162698	+	0.281801i
$341$	−40.0000			−2.16612
$342$	−10.5000	−	7.79423i	−0.567775	−	0.421464i
$343$		0			0
$344$	−0.500000	−	0.866025i	−0.0269582	−	0.0466930i
$345$	24.0000	+	13.8564i	1.29212	+	0.746004i
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	16.0000			0.858925			0.429463	−	0.903085i	$-0.358703\pi$
$347$	16.0000			0.858925			0.429463	+	0.903085i	$0.358703\pi$
$348$	15.0000	+	8.66025i	0.804084	+	0.464238i
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	−0.968253	−	0.249973i	$-0.919578\pi$
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	0.700609	+	0.713545i	$0.252912\pi$
$350$		0			0
$351$	18.0000	+	10.3923i	0.960769	+	0.554700i
$352$	2.00000	+	3.46410i	0.106600	+	0.184637i
$353$	15.0000	−	25.9808i	0.798369	−	1.38282i	−0.122308	−	0.992492i	$-0.539030\pi$
$353$	15.0000	−	25.9808i	0.798369	−	1.38282i	0.920677	−	0.390324i	$-0.127637\pi$
$354$	−4.50000	+	2.59808i	−0.239172	+	0.138086i
$355$	10.0000	−	17.3205i	0.530745	−	0.919277i
$356$	6.00000			0.317999
$357$		0			0
$358$	−7.50000	−	12.9904i	−0.396387	−	0.686563i
$359$	−15.0000	+	25.9808i	−0.791670	+	1.37121i	0.133263	+	0.991081i	$0.457455\pi$
$359$	−15.0000	+	25.9808i	−0.791670	+	1.37121i	−0.924932	+	0.380131i	$0.875879\pi$
$360$	−6.00000			−0.316228
$361$	13.0000	−	13.8564i	0.684211	−	0.729285i
$362$	7.00000	−	12.1244i	0.367912	−	0.637242i
$363$	−7.50000	+	4.33013i	−0.393648	+	0.227273i
$364$		0			0
$365$	−6.00000	+	10.3923i	−0.314054	+	0.543958i
$366$	−3.00000	+	1.73205i	−0.156813	+	0.0905357i
$367$	22.0000			1.14839			0.574195	−	0.818718i	$-0.305315\pi$
$367$	22.0000			1.14839			0.574195	+	0.818718i	$0.305315\pi$
$368$	8.00000			0.417029
$369$	−3.00000			−0.156174
$370$	2.00000	+	3.46410i	0.103975	+	0.180090i
$371$		0			0
$372$		−	17.3205i		−	0.898027i
$373$	−10.0000	−	17.3205i	−0.517780	−	0.896822i	−0.999787	−	0.0206542i	$-0.993425\pi$
$373$	−10.0000	−	17.3205i	−0.517780	−	0.896822i	0.482006	−	0.876168i	$-0.339908\pi$
$374$	−6.00000	+	10.3923i	−0.310253	+	0.537373i
$375$			20.7846i			1.07331i
$376$	2.00000			0.103142
$377$	20.0000	−	34.6410i	1.03005	−	1.78410i
$378$		0			0
$379$	−27.0000			−1.38690			−0.693448	−	0.720506i	$-0.743909\pi$
$379$	−27.0000			−1.38690			−0.693448	+	0.720506i	$0.743909\pi$
$380$	1.00000	−	8.66025i	0.0512989	−	0.444262i
$381$	−18.0000	+	10.3923i	−0.922168	+	0.532414i
$382$	4.00000			0.204658
$383$	−14.0000			−0.715367			−0.357683	−	0.933843i	$-0.616433\pi$
$383$	−14.0000			−0.715367			−0.357683	+	0.933843i	$0.616433\pi$
$384$	−1.50000	+	0.866025i	−0.0765466	+	0.0441942i
$385$		0			0
$386$	1.50000	+	2.59808i	0.0763480	+	0.132239i
$387$	1.50000	+	2.59808i	0.0762493	+	0.132068i
$388$	−14.0000			−0.710742
$389$		0			0			−	1.00000i	$-0.5\pi$
$389$		0			0				1.00000i	$0.5\pi$
$390$			13.8564i			0.701646i
$391$	12.0000	+	20.7846i	0.606866	+	1.05112i
$392$	3.50000	+	6.06218i	0.176777	+	0.306186i
$393$			15.5885i			0.786334i
$394$	8.00000	+	13.8564i	0.403034	+	0.698076i
$395$	10.0000	+	17.3205i	0.503155	+	0.871489i
$396$	−6.00000	−	10.3923i	−0.301511	−	0.522233i
$397$	−1.00000	+	1.73205i	−0.0501886	+	0.0869291i	−0.890028	−	0.455905i	$-0.849316\pi$
$397$	−1.00000	+	1.73205i	−0.0501886	+	0.0869291i	0.839840	+	0.542834i	$0.182649\pi$
$398$	−10.0000	+	17.3205i	−0.501255	+	0.868199i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	10.0000			0.499376			0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000			0.499376			0.249688	+	0.968326i	$0.419672\pi$
$402$			5.19615i			0.259161i
$403$	−40.0000			−1.99254
$404$	−4.00000	+	6.92820i	−0.199007	+	0.344691i
$405$	18.0000			0.894427
$406$		0			0
$407$	−4.00000	+	6.92820i	−0.198273	+	0.343418i
$408$	−4.50000	−	2.59808i	−0.222783	−	0.128624i
$409$	5.50000	−	9.52628i	0.271957	−	0.471044i	−0.697406	−	0.716677i	$-0.745662\pi$
$409$	5.50000	−	9.52628i	0.271957	−	0.471044i	0.969363	+	0.245633i	$0.0789957\pi$
$410$	−1.00000	−	1.73205i	−0.0493865	−	0.0855399i
$411$			24.2487i			1.19610i
$412$	−6.00000			−0.295599
$413$		0			0
$414$	−24.0000			−1.17954
$415$	−9.00000	+	15.5885i	−0.441793	+	0.765207i
$416$	2.00000	+	3.46410i	0.0980581	+	0.169842i
$417$	18.0000	+	10.3923i	0.881464	+	0.508913i
$418$	16.0000	−	6.92820i	0.782586	−	0.338869i
$419$	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	$0.738640\pi$
$420$		0			0
$421$	−16.0000	−	27.7128i	−0.779792	−	1.35064i	−0.932061	−	0.362301i	$-0.881991\pi$
$421$	−16.0000	−	27.7128i	−0.779792	−	1.35064i	0.152269	−	0.988339i	$-0.451342\pi$
$422$	6.00000	+	10.3923i	0.292075	+	0.505889i
$423$	−6.00000			−0.291730
$424$	5.00000	+	8.66025i	0.242821	+	0.420579i
$425$	−1.50000	+	2.59808i	−0.0727607	+	0.126025i
$426$			17.3205i			0.839181i
$427$		0			0
$428$	−8.50000	+	14.7224i	−0.410863	+	0.711636i
$429$	−24.0000	+	13.8564i	−1.15873	+	0.668994i
$430$	−1.00000	+	1.73205i	−0.0482243	+	0.0835269i
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	0.973574	−	0.228373i	$-0.0733406\pi$
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	−0.684564	+	0.728953i	$0.740007\pi$
$432$	4.50000	−	2.59808i	0.216506	−	0.125000i
$433$	−8.50000	−	14.7224i	−0.408484	−	0.707515i	0.586236	−	0.810140i	$-0.300609\pi$
$433$	−8.50000	−	14.7224i	−0.408484	−	0.707515i	−0.994720	+	0.102625i	$0.967276\pi$
$434$		0			0
$435$		−	34.6410i		−	1.66091i
$436$	3.00000	+	5.19615i	0.143674	+	0.248851i
$437$	4.00000	−	34.6410i	0.191346	−	1.65710i
$438$		−	10.3923i		−	0.496564i
$439$	−7.00000	−	12.1244i	−0.334092	−	0.578664i	0.649218	−	0.760602i	$-0.275096\pi$
$439$	−7.00000	−	12.1244i	−0.334092	−	0.578664i	−0.983310	+	0.181938i	$0.941763\pi$
$440$	4.00000	−	6.92820i	0.190693	−	0.330289i
$441$	−10.5000	−	18.1865i	−0.500000	−	0.866025i
$442$	−6.00000	+	10.3923i	−0.285391	+	0.494312i
$443$	16.0000			0.760183			0.380091	−	0.924949i	$-0.375893\pi$
$443$	16.0000			0.760183			0.380091	+	0.924949i	$0.375893\pi$
$444$	−3.00000	−	1.73205i	−0.142374	−	0.0821995i
$445$	−6.00000	−	10.3923i	−0.284427	−	0.492642i
$446$	−7.00000	+	12.1244i	−0.331460	+	0.574105i
$447$		−	20.7846i		−	0.983078i
$448$		0			0
$449$	−14.0000			−0.660701			−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000			−0.660701			−0.330350	+	0.943858i	$0.607167\pi$
$450$	−1.50000	−	2.59808i	−0.0707107	−	0.122474i
$451$	2.00000	−	3.46410i	0.0941763	−	0.163118i
$452$	−1.00000			−0.0470360
$453$	30.0000	+	17.3205i	1.40952	+	0.813788i
$454$	16.0000			0.750917
$455$		0			0
$456$	3.00000	+	6.92820i	0.140488	+	0.324443i
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	0.958950	+	0.283577i	$0.0915211\pi$
$458$	2.00000	−	3.46410i	0.0934539	−	0.161867i
$459$	13.5000	+	7.79423i	0.630126	+	0.363803i
$460$	−8.00000	−	13.8564i	−0.373002	−	0.646058i
$461$	−16.0000	−	27.7128i	−0.745194	−	1.29071i	−0.950104	−	0.311933i	$-0.899023\pi$
$461$	−16.0000	−	27.7128i	−0.745194	−	1.29071i	0.204910	−	0.978781i	$-0.434310\pi$
$462$		0			0
$463$	−5.00000	−	8.66025i	−0.232370	−	0.402476i	0.726135	−	0.687552i	$-0.241315\pi$
$463$	−5.00000	−	8.66025i	−0.232370	−	0.402476i	−0.958505	+	0.285076i	$0.907981\pi$
$464$	−5.00000	−	8.66025i	−0.232119	−	0.402042i
$465$	−30.0000	+	17.3205i	−1.39122	+	0.803219i
$466$	3.00000			0.138972
$467$	13.0000			0.601568			0.300784	−	0.953692i	$-0.402752\pi$
$467$	13.0000			0.601568			0.300784	+	0.953692i	$0.402752\pi$
$468$	−6.00000	−	10.3923i	−0.277350	−	0.480384i
$469$		0			0
$470$	−2.00000	−	3.46410i	−0.0922531	−	0.159787i
$471$			24.2487i			1.11732i
$472$	3.00000			0.138086
$473$	−4.00000			−0.183920
$474$	−15.0000	−	8.66025i	−0.688973	−	0.397779i
$475$	4.00000	−	1.73205i	0.183533	−	0.0794719i
$476$		0			0
$477$	−15.0000	−	25.9808i	−0.686803	−	1.18958i
$478$	6.00000	−	10.3923i	0.274434	−	0.475333i
$479$	−8.00000			−0.365529			−0.182765	−	0.983157i	$-0.558505\pi$
$479$	−8.00000			−0.365529			−0.182765	+	0.983157i	$0.558505\pi$
$480$	3.00000	+	1.73205i	0.136931	+	0.0790569i
$481$	−4.00000	+	6.92820i	−0.182384	+	0.315899i
$482$	−0.500000	−	0.866025i	−0.0227744	−	0.0394464i
$483$		0			0
$484$	5.00000			0.227273
$485$	14.0000	+	24.2487i	0.635707	+	1.10108i
$486$	−13.5000	+	7.79423i	−0.612372	+	0.353553i
$487$	−20.0000			−0.906287			−0.453143	−	0.891438i	$-0.649697\pi$
$487$	−20.0000			−0.906287			−0.453143	+	0.891438i	$0.649697\pi$
$488$	2.00000			0.0905357
$489$		−	19.0526i		−	0.861586i
$490$	7.00000	−	12.1244i	0.316228	−	0.547723i
$491$	−13.0000			−0.586682			−0.293341	−	0.956008i	$-0.594767\pi$
$491$	−13.0000			−0.586682			−0.293341	+	0.956008i	$0.594767\pi$
$492$	1.50000	+	0.866025i	0.0676252	+	0.0390434i
$493$	15.0000	−	25.9808i	0.675566	−	1.17011i
$494$	16.0000	−	6.92820i	0.719874	−	0.311715i
$495$	−12.0000	+	20.7846i	−0.539360	+	0.934199i
$496$	−5.00000	+	8.66025i	−0.224507	+	0.388857i
$497$		0			0
$498$		−	15.5885i		−	0.698535i
$499$	19.0000			0.850557			0.425278	−	0.905063i	$-0.360176\pi$
$499$	19.0000			0.850557			0.425278	+	0.905063i	$0.360176\pi$
$500$	6.00000	−	10.3923i	0.268328	−	0.464758i
$501$	9.00000	+	5.19615i	0.402090	+	0.232147i
$502$	−8.50000	+	14.7224i	−0.379374	+	0.657094i
$503$	3.00000	+	5.19615i	0.133763	+	0.231685i	0.925124	−	0.379664i	$-0.123960\pi$
$503$	3.00000	+	5.19615i	0.133763	+	0.231685i	−0.791361	+	0.611349i	$0.790627\pi$
$504$		0			0
$505$	16.0000			0.711991
$506$	16.0000	−	27.7128i	0.711287	−	1.23198i
$507$	−4.50000	+	2.59808i	−0.199852	+	0.115385i
$508$	12.0000			0.532414
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	0.314459	+	0.949271i	$0.398177\pi$
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	−0.979322	+	0.202306i	$0.935156\pi$
$510$			10.3923i			0.460179i
$511$		0			0
$512$	1.00000			0.0441942
$513$	−9.00000	−	20.7846i	−0.397360	−	0.917663i
$514$	−1.00000			−0.0441081
$515$	6.00000	+	10.3923i	0.264392	+	0.457940i
$516$		−	1.73205i		−	0.0762493i
$517$	4.00000	−	6.92820i	0.175920	−	0.304702i
$518$		0			0
$519$	−9.00000	+	5.19615i	−0.395056	+	0.228086i
$520$	4.00000	−	6.92820i	0.175412	−	0.303822i
$521$	2.00000			0.0876216			0.0438108	−	0.999040i	$-0.486050\pi$
$521$	2.00000			0.0876216			0.0438108	+	0.999040i	$0.486050\pi$
$522$	15.0000	+	25.9808i	0.656532	+	1.13715i
$523$	−22.0000	−	38.1051i	−0.961993	−	1.66622i	−0.717486	−	0.696573i	$-0.754707\pi$
$523$	−22.0000	−	38.1051i	−0.961993	−	1.66622i	−0.244507	−	0.969648i	$-0.578626\pi$
$524$	4.50000	−	7.79423i	0.196583	−	0.340492i
$525$		0			0
$526$	3.00000	−	5.19615i	0.130806	−	0.226563i
$527$	−30.0000			−1.30682
$528$			6.92820i			0.301511i
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$	10.0000	−	17.3205i	0.434372	−	0.752355i
$531$	−9.00000			−0.390567
$532$		0			0
$533$	2.00000	−	3.46410i	0.0866296	−	0.150047i
$534$	9.00000	+	5.19615i	0.389468	+	0.224860i
$535$	34.0000			1.46995
$536$	1.50000	−	2.59808i	0.0647901	−	0.112220i
$537$		−	25.9808i		−	1.12115i
$538$	−18.0000			−0.776035
$539$	28.0000			1.20605
$540$	−9.00000	−	5.19615i	−0.387298	−	0.223607i
$541$	−10.0000	−	17.3205i	−0.429934	−	0.744667i	0.566933	−	0.823764i	$-0.308130\pi$
$541$	−10.0000	−	17.3205i	−0.429934	−	0.744667i	−0.996867	+	0.0790969i	$0.974796\pi$
$542$	−20.0000			−0.859074
$543$	21.0000	−	12.1244i	0.901196	−	0.520306i
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$	6.00000	−	10.3923i	0.257012	−	0.445157i
$546$		0			0
$547$	13.0000			0.555840			0.277920	−	0.960604i	$-0.410355\pi$
$547$	13.0000			0.555840			0.277920	+	0.960604i	$0.410355\pi$
$548$	7.00000	−	12.1244i	0.299025	−	0.517927i
$549$	−6.00000			−0.256074
$550$	4.00000			0.170561
$551$	−40.0000	+	17.3205i	−1.70406	+	0.737878i
$552$	12.0000	+	6.92820i	0.510754	+	0.294884i
$553$		0			0
$554$	28.0000			1.18961
$555$			6.92820i			0.294086i
$556$	−6.00000	−	10.3923i	−0.254457	−	0.440732i
$557$	−11.0000	−	19.0526i	−0.466085	−	0.807283i	0.533165	−	0.846011i	$-0.321003\pi$
$557$	−11.0000	−	19.0526i	−0.466085	−	0.807283i	−0.999250	+	0.0387286i	$0.987669\pi$
$558$	15.0000	−	25.9808i	0.635001	−	1.09985i
$559$	−4.00000			−0.169182
$560$		0			0
$561$	−18.0000	+	10.3923i	−0.759961	+	0.438763i
$562$	−15.5000	−	26.8468i	−0.653828	−	1.13246i
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	0.943560	+	0.331202i	$0.107454\pi$
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	−0.184950	+	0.982748i	$0.559212\pi$
$564$	3.00000	+	1.73205i	0.126323	+	0.0729325i
$565$	1.00000	+	1.73205i	0.0420703	+	0.0728679i
$566$	10.5000	+	18.1865i	0.441348	+	0.764437i
$567$		0			0
$568$	5.00000	−	8.66025i	0.209795	−	0.363376i
$569$	−12.5000	+	21.6506i	−0.524027	+	0.907642i	0.475581	+	0.879672i	$0.342238\pi$
$569$	−12.5000	+	21.6506i	−0.524027	+	0.907642i	−0.999609	+	0.0279702i	$0.991096\pi$
$570$	9.00000	−	12.1244i	0.376969	−	0.507833i
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	16.0000			0.668994
$573$	6.00000	+	3.46410i	0.250654	+	0.144715i
$574$		0			0
$575$	4.00000	−	6.92820i	0.166812	−	0.288926i
$576$	−3.00000			−0.125000
$577$	23.0000			0.957503			0.478751	−	0.877951i	$-0.341090\pi$
$577$	23.0000			0.957503			0.478751	+	0.877951i	$0.341090\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$			5.19615i			0.215945i
$580$	−10.0000	+	17.3205i	−0.415227	+	0.719195i
$581$		0			0
$582$	−21.0000	−	12.1244i	−0.870478	−	0.502571i
$583$	40.0000			1.65663
$584$	−3.00000	+	5.19615i	−0.124141	+	0.215018i
$585$	−12.0000	+	20.7846i	−0.496139	+	0.859338i
$586$	−12.0000	+	20.7846i	−0.495715	+	0.858604i
$587$	7.50000	+	12.9904i	0.309558	+	0.536170i	0.978266	−	0.207355i	$-0.0664855\pi$
$587$	7.50000	+	12.9904i	0.309558	+	0.536170i	−0.668708	+	0.743525i	$0.733152\pi$
$588$			12.1244i			0.500000i
$589$	35.0000	+	25.9808i	1.44215	+	1.07052i
$590$	−3.00000	−	5.19615i	−0.123508	−	0.213922i
$591$			27.7128i			1.13995i
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	2.50000	+	4.33013i	0.102663	+	0.177817i	0.912781	−	0.408450i	$-0.133930\pi$
$593$	2.50000	+	4.33013i	0.102663	+	0.177817i	−0.810118	+	0.586267i	$0.800597\pi$
$594$		−	20.7846i		−	0.852803i
$595$		0			0
$596$	−6.00000	+	10.3923i	−0.245770	+	0.425685i
$597$	−30.0000	+	17.3205i	−1.22782	+	0.708881i
$598$	16.0000	−	27.7128i	0.654289	−	1.13326i
$599$	3.00000	−	5.19615i	0.122577	−	0.212309i	−0.798206	−	0.602384i	$-0.794218\pi$
$599$	3.00000	−	5.19615i	0.122577	−	0.212309i	0.920783	+	0.390075i	$0.127551\pi$
$600$			1.73205i			0.0707107i
$601$	8.50000	−	14.7224i	0.346722	−	0.600541i	−0.638943	−	0.769254i	$-0.720628\pi$
$601$	8.50000	−	14.7224i	0.346722	−	0.600541i	0.985665	+	0.168714i	$0.0539613\pi$
$602$		0			0
$603$	−4.50000	+	7.79423i	−0.183254	+	0.317406i
$604$	−10.0000	−	17.3205i	−0.406894	−	0.704761i
$605$	−5.00000	−	8.66025i	−0.203279	−	0.352089i
$606$	−12.0000	+	6.92820i	−0.487467	+	0.281439i
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	0.998154	−	0.0607380i	$-0.0193454\pi$
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	−0.551678	+	0.834058i	$0.686012\pi$
$608$	0.500000	−	4.33013i	0.0202777	−	0.175610i
$609$		0			0
$610$	−2.00000	−	3.46410i	−0.0809776	−	0.140257i
$611$	4.00000	−	6.92820i	0.161823	−	0.280285i
$612$	−4.50000	−	7.79423i	−0.181902	−	0.315063i
$613$	−8.00000	+	13.8564i	−0.323117	+	0.559655i	−0.981129	−	0.193352i	$-0.938064\pi$
$613$	−8.00000	+	13.8564i	−0.323117	+	0.559655i	0.658012	+	0.753007i	$0.271397\pi$
$614$	21.0000			0.847491
$615$		−	3.46410i		−	0.139686i
$616$		0			0
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	0.455211	+	0.890384i	$0.349564\pi$
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	−0.998700	+	0.0509678i	$0.983769\pi$
$618$	−9.00000	−	5.19615i	−0.362033	−	0.209020i
$619$	5.50000	−	9.52628i	0.221064	−	0.382893i	−0.734068	−	0.679076i	$-0.762380\pi$
$619$	5.50000	−	9.52628i	0.221064	−	0.382893i	0.955131	+	0.296183i	$0.0957138\pi$
$620$	20.0000			0.803219
$621$	−36.0000	−	20.7846i	−1.44463	−	0.834058i
$622$	−8.00000	+	13.8564i	−0.320771	+	0.555591i
$623$		0			0
$624$			6.92820i			0.277350i
$625$	−19.0000			−0.760000
$626$	−14.5000	−	25.1147i	−0.579537	−	1.00379i
$627$	30.0000	+	3.46410i	1.19808	+	0.138343i
$628$	7.00000	−	12.1244i	0.279330	−	0.483814i
$629$	−3.00000	+	5.19615i	−0.119618	+	0.207184i
$630$		0			0
$631$	−4.00000	−	6.92820i	−0.159237	−	0.275807i	0.775356	−	0.631524i	$-0.217570\pi$
$631$	−4.00000	−	6.92820i	−0.159237	−	0.275807i	−0.934594	+	0.355716i	$0.884237\pi$
$632$	5.00000	+	8.66025i	0.198889	+	0.344486i
$633$			20.7846i			0.826114i
$634$	12.0000	+	20.7846i	0.476581	+	0.825462i
$635$	−12.0000	−	20.7846i	−0.476205	−	0.824812i
$636$			17.3205i			0.686803i
$637$	28.0000			1.10940
$638$	−40.0000			−1.58362
$639$	−15.0000	+	25.9808i	−0.593391	+	1.02778i
$640$	−1.00000	−	1.73205i	−0.0395285	−	0.0684653i
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	0.631721	−	0.775196i	$-0.282349\pi$
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	−0.987200	+	0.159489i	$0.949015\pi$
$642$	−25.5000	+	14.7224i	−1.00640	+	0.581048i
$643$	−32.0000			−1.26196			−0.630978	−	0.775800i	$-0.717346\pi$
$643$	−32.0000			−1.26196			−0.630978	+	0.775800i	$0.717346\pi$
$644$		0			0
$645$	−3.00000	+	1.73205i	−0.118125	+	0.0681994i
$646$	12.0000	−	5.19615i	0.472134	−	0.204440i
$647$	32.0000			1.25805			0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000			1.25805			0.629025	+	0.777385i	$0.283454\pi$
$648$	9.00000			0.353553
$649$	6.00000	−	10.3923i	0.235521	−	0.407934i
$650$	4.00000			0.156893
$651$		0			0
$652$	−5.50000	+	9.52628i	−0.215397	+	0.373078i
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	0.986634	−	0.162951i	$-0.0521013\pi$
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	−0.634437	+	0.772975i	$0.718768\pi$
$654$			10.3923i			0.406371i
$655$	−18.0000			−0.703318
$656$	−0.500000	−	0.866025i	−0.0195217	−	0.0338126i
$657$	9.00000	−	15.5885i	0.351123	−	0.608164i
$658$		0			0
$659$	44.0000			1.71400			0.856998	−	0.515319i	$-0.172327\pi$
$659$	44.0000			1.71400			0.856998	+	0.515319i	$0.172327\pi$
$660$	12.0000	−	6.92820i	0.467099	−	0.269680i
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	−0.697174	−	0.716902i	$-0.745559\pi$
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	0.969442	+	0.245319i	$0.0788928\pi$
$662$	−25.0000			−0.971653
$663$	−18.0000	+	10.3923i	−0.699062	+	0.403604i
$664$	−4.50000	+	7.79423i	−0.174634	+	0.302475i
$665$		0			0
$666$	−3.00000	−	5.19615i	−0.116248	−	0.201347i
$667$	−40.0000	+	69.2820i	−1.54881	+	2.68261i
$668$	−3.00000	−	5.19615i	−0.116073	−	0.201045i
$669$	−21.0000	+	12.1244i	−0.811907	+	0.468755i
$670$	−6.00000			−0.231800
$671$	4.00000	−	6.92820i	0.154418	−	0.267460i
$672$		0			0
$673$	−13.0000	+	22.5167i	−0.501113	+	0.867953i	0.498886	+	0.866668i	$0.333743\pi$
$673$	−13.0000	+	22.5167i	−0.501113	+	0.867953i	−0.999999	+	0.00128586i	$0.999591\pi$
$674$	7.00000	+	12.1244i	0.269630	+	0.467013i
$675$		−	5.19615i		−	0.200000i
$676$	3.00000			0.115385
$677$	7.00000	−	12.1244i	0.269032	−	0.465977i	−0.699580	−	0.714554i	$-0.746630\pi$
$677$	7.00000	−	12.1244i	0.269032	−	0.465977i	0.968612	+	0.248577i	$0.0799630\pi$
$678$	−1.50000	−	0.866025i	−0.0576072	−	0.0332595i
$679$		0			0
$680$	3.00000	−	5.19615i	0.115045	−	0.199263i
$681$	24.0000	+	13.8564i	0.919682	+	0.530979i
$682$	20.0000	+	34.6410i	0.765840	+	1.32647i
$683$	−23.0000			−0.880071			−0.440035	−	0.897980i	$-0.645034\pi$
$683$	−23.0000			−0.880071			−0.440035	+	0.897980i	$0.645034\pi$
$684$	−1.50000	+	12.9904i	−0.0573539	+	0.496700i
$685$	−28.0000			−1.06983
$686$		0			0
$687$	6.00000	−	3.46410i	0.228914	−	0.132164i
$688$	−0.500000	+	0.866025i	−0.0190623	+	0.0330169i
$689$	40.0000			1.52388
$690$		−	27.7128i		−	1.05501i
$691$	−18.0000	+	31.1769i	−0.684752	+	1.18603i	0.288762	+	0.957401i	$0.406756\pi$
$691$	−18.0000	+	31.1769i	−0.684752	+	1.18603i	−0.973515	+	0.228625i	$0.926577\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−8.00000	−	13.8564i	−0.303676	−	0.525982i
$695$	−12.0000	+	20.7846i	−0.455186	+	0.788405i
$696$		−	17.3205i		−	0.656532i
$697$	1.50000	−	2.59808i	0.0568166	−	0.0984092i
$698$	10.0000			0.378506
$699$	4.50000	+	2.59808i	0.170206	+	0.0982683i
$700$		0			0
$701$	−25.0000	+	43.3013i	−0.944237	+	1.63547i	−0.186965	+	0.982367i	$0.559865\pi$
$701$	−25.0000	+	43.3013i	−0.944237	+	1.63547i	−0.757272	+	0.653100i	$0.773468\pi$
$702$		−	20.7846i		−	0.784465i
$703$	8.00000	−	3.46410i	0.301726	−	0.130651i
$704$	2.00000	−	3.46410i	0.0753778	−	0.130558i
$705$		−	6.92820i		−	0.260931i
$706$	−30.0000			−1.12906
$707$		0			0
$708$	4.50000	+	2.59808i	0.169120	+	0.0976417i
$709$		0			0			−	1.00000i	$-0.5\pi$
$709$		0			0				1.00000i	$0.5\pi$
$710$	−20.0000			−0.750587
$711$	−15.0000	−	25.9808i	−0.562544	−	0.974355i
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$	80.0000			2.99602
$714$		0			0
$715$	−16.0000	−	27.7128i	−0.598366	−	1.03640i
$716$	−7.50000	+	12.9904i	−0.280288	+	0.485473i
$717$	18.0000	−	10.3923i	0.672222	−	0.388108i
$718$	30.0000			1.11959
$719$	16.0000	−	27.7128i	0.596699	−	1.03351i	−0.396605	−	0.917989i	$-0.629812\pi$
$719$	16.0000	−	27.7128i	0.596699	−	1.03351i	0.993305	−	0.115524i	$-0.0368548\pi$
$720$	3.00000	+	5.19615i	0.111803	+	0.193649i
$721$		0			0
$722$	−18.5000	−	4.33013i	−0.688499	−	0.161151i
$723$		−	1.73205i		−	0.0644157i
$724$	−14.0000			−0.520306
$725$	−10.0000			−0.371391
$726$	7.50000	+	4.33013i	0.278351	+	0.160706i
$727$	1.00000	+	1.73205i	0.0370879	+	0.0642382i	0.883974	−	0.467537i	$-0.154858\pi$
$727$	1.00000	+	1.73205i	0.0370879	+	0.0642382i	−0.846886	+	0.531775i	$0.821525\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	12.0000			0.444140
$731$	−3.00000			−0.110959
$732$	3.00000	+	1.73205i	0.110883	+	0.0640184i
$733$	6.00000	+	10.3923i	0.221615	+	0.383849i	0.955299	−	0.295643i	$-0.0955338\pi$
$733$	6.00000	+	10.3923i	0.221615	+	0.383849i	−0.733683	+	0.679491i	$0.762200\pi$
$734$	−11.0000	−	19.0526i	−0.406017	−	0.703243i
$735$	21.0000	−	12.1244i	0.774597	−	0.447214i
$736$	−4.00000	−	6.92820i	−0.147442	−	0.255377i
$737$	−6.00000	−	10.3923i	−0.221013	−	0.382805i
$738$	1.50000	+	2.59808i	0.0552158	+	0.0956365i
$739$	18.5000	−	32.0429i	0.680534	−	1.17872i	−0.294285	−	0.955718i	$-0.595081\pi$
$739$	18.5000	−	32.0429i	0.680534	−	1.17872i	0.974818	−	0.223001i	$-0.0715853\pi$
$740$	2.00000	−	3.46410i	0.0735215	−	0.127343i
$741$	30.0000	+	3.46410i	1.10208	+	0.127257i
$742$		0			0
$743$	−28.0000			−1.02722			−0.513610	−	0.858024i	$-0.671692\pi$
$743$	−28.0000			−1.02722			−0.513610	+	0.858024i	$0.671692\pi$
$744$	−15.0000	+	8.66025i	−0.549927	+	0.317500i
$745$	24.0000			0.879292
$746$	−10.0000	+	17.3205i	−0.366126	+	0.634149i
$747$	13.5000	−	23.3827i	0.493939	−	0.855528i
$748$	12.0000			0.438763
$749$		0			0
$750$	18.0000	−	10.3923i	0.657267	−	0.379473i
$751$	−7.00000	+	12.1244i	−0.255434	+	0.442424i	−0.965013	−	0.262201i	$-0.915552\pi$
$751$	−7.00000	+	12.1244i	−0.255434	+	0.442424i	0.709580	+	0.704625i	$0.248885\pi$
$752$	−1.00000	−	1.73205i	−0.0364662	−	0.0631614i
$753$	−25.5000	+	14.7224i	−0.929272	+	0.536515i
$754$	−40.0000			−1.45671
$755$	−20.0000	+	34.6410i	−0.727875	+	1.26072i
$756$		0			0
$757$	−26.0000	+	45.0333i	−0.944986	+	1.63676i	−0.189207	+	0.981937i	$0.560592\pi$
$757$	−26.0000	+	45.0333i	−0.944986	+	1.63676i	−0.755779	+	0.654827i	$0.772742\pi$
$758$	13.5000	+	23.3827i	0.490342	+	0.849297i
$759$	48.0000	−	27.7128i	1.74229	−	1.00591i
$760$	−8.00000	+	3.46410i	−0.290191	+	0.125656i
$761$	7.50000	+	12.9904i	0.271875	+	0.470901i	0.969342	−	0.245716i	$-0.0790230\pi$
$761$	7.50000	+	12.9904i	0.271875	+	0.470901i	−0.697467	+	0.716617i	$0.745690\pi$
$762$	18.0000	+	10.3923i	0.652071	+	0.376473i
$763$		0			0
$764$	−2.00000	−	3.46410i	−0.0723575	−	0.125327i
$765$	−9.00000	+	15.5885i	−0.325396	+	0.563602i
$766$	7.00000	+	12.1244i	0.252920	+	0.438071i
$767$	6.00000	−	10.3923i	0.216647	−	0.375244i
$768$	1.50000	+	0.866025i	0.0541266	+	0.0312500i
$769$	−17.0000	+	29.4449i	−0.613036	+	1.06181i	0.377690	+	0.925932i	$0.376718\pi$
$769$	−17.0000	+	29.4449i	−0.613036	+	1.06181i	−0.990726	+	0.135877i	$0.956615\pi$
$770$		0			0
$771$	−1.50000	−	0.866025i	−0.0540212	−	0.0311891i
$772$	1.50000	−	2.59808i	0.0539862	−	0.0935068i
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	0.657542	−	0.753418i	$-0.271596\pi$
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	−0.981250	+	0.192740i	$0.938263\pi$
$774$	1.50000	−	2.59808i	0.0539164	−	0.0933859i
$775$	5.00000	+	8.66025i	0.179605	+	0.311086i
$776$	7.00000	+	12.1244i	0.251285	+	0.435239i
$777$		0			0
$778$		0			0
$779$	−4.00000	+	1.73205i	−0.143315	+	0.0620572i
$780$	12.0000	−	6.92820i	0.429669	−	0.248069i
$781$	−20.0000	−	34.6410i	−0.715656	−	1.23955i
$782$	12.0000	−	20.7846i	0.429119	−	0.743256i
$783$			51.9615i			1.85695i
$784$	3.50000	−	6.06218i	0.125000	−	0.216506i
$785$	−28.0000			−0.999363
$786$	13.5000	−	7.79423i	0.481529	−	0.278011i
$787$	26.5000	+	45.8993i	0.944623	+	1.63614i	0.756504	+	0.653989i	$0.226906\pi$
$787$	26.5000	+	45.8993i	0.944623	+	1.63614i	0.188119	+	0.982146i	$0.439761\pi$
$788$	8.00000	−	13.8564i	0.284988	−	0.493614i
$789$	9.00000	−	5.19615i	0.320408	−	0.184988i
$790$	10.0000	−	17.3205i	0.355784	−	0.616236i
$791$		0			0
$792$	−6.00000	+	10.3923i	−0.213201	+	0.369274i
$793$	4.00000	−	6.92820i	0.142044	−	0.246028i
$794$	2.00000			0.0709773
$795$	30.0000	−	17.3205i	1.06399	−	0.614295i
$796$	20.0000			0.708881
$797$	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	$0.765163\pi$
$798$		0			0
$799$	3.00000	−	5.19615i	0.106132	−	0.183827i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	9.00000	+	15.5885i	0.317999	+	0.550791i
$802$	−5.00000	−	8.66025i	−0.176556	−	0.305804i
$803$	12.0000	+	20.7846i	0.423471	+	0.733473i
$804$	4.50000	−	2.59808i	0.158703	−	0.0916271i
$805$		0			0
$806$	20.0000	+	34.6410i	0.704470	+	1.22018i
$807$	−27.0000	−	15.5885i	−0.950445	−	0.548740i
$808$	8.00000			0.281439
$809$	−39.0000			−1.37117			−0.685583	−	0.727994i	$-0.740453\pi$
$809$	−39.0000			−1.37117			−0.685583	+	0.727994i	$0.740453\pi$
$810$	−9.00000	−	15.5885i	−0.316228	−	0.547723i
$811$	16.5000	+	28.5788i	0.579393	+	1.00354i	0.995549	+	0.0942453i	$0.0300438\pi$
$811$	16.5000	+	28.5788i	0.579393	+	1.00354i	−0.416156	+	0.909293i	$0.636623\pi$
$812$		0			0
$813$	−30.0000	−	17.3205i	−1.05215	−	0.607457i
$814$	8.00000			0.280400
$815$	22.0000			0.770626
$816$			5.19615i			0.181902i
$817$	3.50000	+	2.59808i	0.122449	+	0.0908952i
$818$	−11.0000			−0.384606
$819$		0			0
$820$	−1.00000	+	1.73205i	−0.0349215	+	0.0604858i
$821$	18.0000			0.628204			0.314102	−	0.949389i	$-0.398297\pi$
$821$	18.0000			0.628204			0.314102	+	0.949389i	$0.398297\pi$
$822$	21.0000	−	12.1244i	0.732459	−	0.422885i
$823$	−22.0000	+	38.1051i	−0.766872	+	1.32826i	0.172379	+	0.985031i	$0.444854\pi$
$823$	−22.0000	+	38.1051i	−0.766872	+	1.32826i	−0.939251	+	0.343230i	$0.888479\pi$
$824$	3.00000	+	5.19615i	0.104510	+	0.181017i
$825$	6.00000	+	3.46410i	0.208893	+	0.120605i
$826$		0			0
$827$	18.5000	+	32.0429i	0.643308	+	1.11424i	0.984690	+	0.174317i	$0.0557719\pi$
$827$	18.5000	+	32.0429i	0.643308	+	1.11424i	−0.341381	+	0.939925i	$0.610895\pi$
$828$	12.0000	+	20.7846i	0.417029	+	0.722315i
$829$	−54.0000			−1.87550			−0.937749	−	0.347314i	$-0.887094\pi$
$829$	−54.0000			−1.87550			−0.937749	+	0.347314i	$0.887094\pi$
$830$	18.0000			0.624789
$831$	42.0000	+	24.2487i	1.45696	+	0.841178i
$832$	2.00000	−	3.46410i	0.0693375	−	0.120096i
$833$	21.0000			0.727607
$834$		−	20.7846i		−	0.719712i
$835$	−6.00000	+	10.3923i	−0.207639	+	0.359641i
$836$	−14.0000	−	10.3923i	−0.484200	−	0.359425i
$837$	45.0000	−	25.9808i	1.55543	−	0.898027i
$838$	6.00000	−	10.3923i	0.207267	−	0.358996i
$839$	−1.00000	−	1.73205i	−0.0345238	−	0.0597970i	0.848247	−	0.529600i	$-0.177658\pi$
$839$	−1.00000	−	1.73205i	−0.0345238	−	0.0597970i	−0.882771	+	0.469803i	$0.844325\pi$
$840$		0			0
$841$	71.0000			2.44828
$842$	−16.0000	+	27.7128i	−0.551396	+	0.955047i
$843$		−	53.6936i		−	1.84930i
$844$	6.00000	−	10.3923i	0.206529	−	0.357718i
$845$	−3.00000	−	5.19615i	−0.103203	−	0.178753i
$846$	3.00000	+	5.19615i	0.103142	+	0.178647i
$847$		0			0
$848$	5.00000	−	8.66025i	0.171701	−	0.297394i
$849$			36.3731i			1.24832i
$850$	3.00000			0.102899
$851$	8.00000	−	13.8564i	0.274236	−	0.474991i
$852$	15.0000	−	8.66025i	0.513892	−	0.296695i
$853$	−21.0000	−	36.3731i	−0.719026	−	1.24539i	−0.961386	−	0.275204i	$-0.911255\pi$
$853$	−21.0000	−	36.3731i	−0.719026	−	1.24539i	0.242360	−	0.970186i	$-0.422079\pi$
$854$		0			0
$855$	24.0000	−	10.3923i	0.820783	−	0.355409i
$856$	17.0000			0.581048
$857$	−22.5000	−	38.9711i	−0.768585	−	1.33123i	−0.938330	−	0.345741i	$-0.887628\pi$
$857$	−22.5000	−	38.9711i	−0.768585	−	1.33123i	0.169745	−	0.985488i	$-0.445706\pi$
$858$	24.0000	+	13.8564i	0.819346	+	0.473050i
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	−0.898126	−	0.439738i	$-0.855071\pi$
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	0.829887	+	0.557931i	$0.188405\pi$
$860$	2.00000			0.0681994
$861$		0			0
$862$	6.00000	−	10.3923i	0.204361	−	0.353963i
$863$	30.0000			1.02121			0.510606	−	0.859815i	$-0.329421\pi$
$863$	30.0000			1.02121			0.510606	+	0.859815i	$0.329421\pi$
$864$	−4.50000	−	2.59808i	−0.153093	−	0.0883883i
$865$	−6.00000	−	10.3923i	−0.204006	−	0.353349i
$866$	−8.50000	+	14.7224i	−0.288842	+	0.500289i
$867$	12.0000	−	6.92820i	0.407541	−	0.235294i
$868$		0			0
$869$	40.0000			1.35691
$870$	−30.0000	+	17.3205i	−1.01710	+	0.587220i
$871$	−6.00000	−	10.3923i	−0.203302	−	0.352130i
$872$	3.00000	−	5.19615i	0.101593	−	0.175964i
$873$	−21.0000	−	36.3731i	−0.710742	−	1.23104i
$874$	−32.0000	+	13.8564i	−1.08242	+	0.468700i
$875$		0			0
$876$	−9.00000	+	5.19615i	−0.304082	+	0.175562i
$877$	−32.0000			−1.08056			−0.540282	−	0.841484i	$-0.681682\pi$
$877$	−32.0000			−1.08056			−0.540282	+	0.841484i	$0.681682\pi$
$878$	−7.00000	+	12.1244i	−0.236239	+	0.409177i
$879$	−36.0000	+	20.7846i	−1.21425	+	0.701047i
$880$	−8.00000			−0.269680
$881$	−9.00000			−0.303218			−0.151609	−	0.988441i	$-0.548445\pi$
$881$	−9.00000			−0.303218			−0.151609	+	0.988441i	$0.548445\pi$
$882$	−10.5000	+	18.1865i	−0.353553	+	0.612372i
$883$	17.5000	+	30.3109i	0.588922	+	1.02004i	0.994374	+	0.105926i	$0.0337808\pi$
$883$	17.5000	+	30.3109i	0.588922	+	1.02004i	−0.405452	+	0.914116i	$0.632886\pi$
$884$	12.0000			0.403604
$885$		−	10.3923i		−	0.349334i
$886$	−8.00000	−	13.8564i	−0.268765	−	0.465515i
$887$	−26.0000	+	45.0333i	−0.872995	+	1.51207i	−0.0141108	+	0.999900i	$0.504492\pi$
$887$	−26.0000	+	45.0333i	−0.872995	+	1.51207i	−0.858884	+	0.512170i	$0.828842\pi$
$888$			3.46410i			0.116248i
$889$		0			0
$890$	−6.00000	+	10.3923i	−0.201120	+	0.348351i
$891$	18.0000	−	31.1769i	0.603023	−	1.04447i
$892$	14.0000			0.468755
$893$	−8.00000	+	3.46410i	−0.267710	+	0.115922i
$894$	−18.0000	+	10.3923i	−0.602010	+	0.347571i
$895$	30.0000			1.00279
$896$		0			0
$897$	48.0000	−	27.7128i	1.60267	−	0.925304i
$898$	7.00000	+	12.1244i	0.233593	+	0.404595i
$899$	−50.0000	−	86.6025i	−1.66759	−	2.88836i
$900$	−1.50000	+	2.59808i	−0.0500000	+	0.0866025i
$901$	30.0000			0.999445
$902$	−4.00000			−0.133185
$903$		0			0
$904$	0.500000	+	0.866025i	0.0166298	+	0.0288036i
$905$	14.0000	+	24.2487i	0.465376	+	0.806054i
$906$		−	34.6410i		−	1.15087i
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	0.689698	−	0.724097i	$-0.257743\pi$
$907$	−8.50000	−	14.7224i	−0.282238	−	0.488850i	−0.971936	+	0.235247i	$0.924410\pi$
$908$	−8.00000	−	13.8564i	−0.265489	−	0.459841i
$909$	−24.0000			−0.796030
$910$		0			0
$911$	12.0000	−	20.7846i	0.397578	−	0.688625i	−0.595849	−	0.803097i	$-0.703184\pi$
$911$	12.0000	−	20.7846i	0.397578	−	0.688625i	0.993426	+	0.114472i	$0.0365176\pi$
$912$	4.50000	−	6.06218i	0.149010	−	0.200739i
$913$	18.0000	+	31.1769i	0.595713	+	1.03181i
$914$	−10.0000			−0.330771
$915$		−	6.92820i		−	0.229039i
$916$	−4.00000			−0.132164
$917$		0			0
$918$		−	15.5885i		−	0.514496i
$919$	8.00000			0.263896			0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000			0.263896			0.131948	+	0.991257i	$0.457877\pi$
$920$	−8.00000	+	13.8564i	−0.263752	+	0.456832i
$921$	31.5000	+	18.1865i	1.03796	+	0.599267i
$922$	−16.0000	+	27.7128i	−0.526932	+	0.912673i
$923$	−20.0000	−	34.6410i	−0.658308	−	1.14022i
$924$		0			0
$925$	2.00000			0.0657596
$926$	−5.00000	+	8.66025i	−0.164310	+	0.284594i
$927$	−9.00000	−	15.5885i	−0.295599	−	0.511992i
$928$	−5.00000	+	8.66025i	−0.164133	+	0.284287i
$929$	−14.5000	−	25.1147i	−0.475730	−	0.823988i	0.523884	−	0.851790i	$-0.324483\pi$
$929$	−14.5000	−	25.1147i	−0.475730	−	0.823988i	−0.999613	+	0.0278019i	$0.991149\pi$
$930$	30.0000	+	17.3205i	0.983739	+	0.567962i
$931$	−24.5000	−	18.1865i	−0.802955	−	0.596040i
$932$	−1.50000	−	2.59808i	−0.0491341	−	0.0851028i
$933$	−24.0000	+	13.8564i	−0.785725	+	0.453638i
$934$	−6.50000	−	11.2583i	−0.212686	−	0.368384i
$935$	−12.0000	−	20.7846i	−0.392442	−	0.679729i
$936$	−6.00000	+	10.3923i	−0.196116	+	0.339683i
$937$	−5.50000	−	9.52628i	−0.179677	−	0.311210i	0.762093	−	0.647468i	$-0.224172\pi$
$937$	−5.50000	−	9.52628i	−0.179677	−	0.311210i	−0.941770	+	0.336258i	$0.890839\pi$
$938$		0			0
$939$		−	50.2295i		−	1.63918i
$940$	−2.00000	+	3.46410i	−0.0652328	+	0.112987i
$941$	16.0000	−	27.7128i	0.521585	−	0.903412i	−0.478100	−	0.878306i	$-0.658674\pi$
$941$	16.0000	−	27.7128i	0.521585	−	0.903412i	0.999685	−	0.0251063i	$-0.00799243\pi$
$942$	21.0000	−	12.1244i	0.684217	−	0.395033i
$943$	−4.00000	+	6.92820i	−0.130258	+	0.225613i
$944$	−1.50000	−	2.59808i	−0.0488208	−	0.0845602i
$945$		0			0
$946$	2.00000	+	3.46410i	0.0650256	+	0.112628i
$947$	−16.5000	−	28.5788i	−0.536178	−	0.928687i	−0.999105	−	0.0422912i	$-0.986534\pi$
$947$	−16.5000	−	28.5788i	−0.536178	−	0.928687i	0.462927	−	0.886396i	$-0.346799\pi$
$948$			17.3205i			0.562544i
$949$	12.0000	+	20.7846i	0.389536	+	0.674697i
$950$	−3.50000	−	2.59808i	−0.113555	−	0.0842927i
$951$			41.5692i			1.34797i
$952$		0			0
$953$	−13.0000	+	22.5167i	−0.421111	+	0.729386i	−0.996048	−	0.0888114i	$-0.971693\pi$
$953$	−13.0000	+	22.5167i	−0.421111	+	0.729386i	0.574937	+	0.818198i	$0.305026\pi$
$954$	−15.0000	+	25.9808i	−0.485643	+	0.841158i
$955$	−4.00000	+	6.92820i	−0.129437	+	0.224191i
$956$	−12.0000			−0.388108
$957$	−60.0000	−	34.6410i	−1.93952	−	1.11979i
$958$	4.00000	+	6.92820i	0.129234	+	0.223840i
$959$		0			0
$960$		−	3.46410i		−	0.111803i
$961$	−34.5000	+	59.7558i	−1.11290	+	1.92760i
$962$	8.00000			0.257930
$963$	−51.0000			−1.64345
$964$	−0.500000	+	0.866025i	−0.0161039	+	0.0278928i
$965$	−6.00000			−0.193147
$966$		0			0
$967$	18.0000			0.578841			0.289420	−	0.957202i	$-0.406537\pi$
$967$	18.0000			0.578841			0.289420	+	0.957202i	$0.406537\pi$
$968$	−2.50000	−	4.33013i	−0.0803530	−	0.139176i
$969$	22.5000	+	2.59808i	0.722804	+	0.0834622i
$970$	14.0000	−	24.2487i	0.449513	−	0.778579i
$971$	12.5000	−	21.6506i	0.401144	−	0.694802i	−0.592720	−	0.805408i	$-0.701946\pi$
$971$	12.5000	−	21.6506i	0.401144	−	0.694802i	0.993864	+	0.110607i	$0.0352793\pi$
$972$	13.5000	+	7.79423i	0.433013	+	0.250000i
$973$		0			0
$974$	10.0000	+	17.3205i	0.320421	+	0.554985i
$975$	6.00000	+	3.46410i	0.192154	+	0.110940i
$976$	−1.00000	−	1.73205i	−0.0320092	−	0.0554416i
$977$	−14.5000	−	25.1147i	−0.463896	−	0.803492i	0.535255	−	0.844691i	$-0.320216\pi$
$977$	−14.5000	−	25.1147i	−0.463896	−	0.803492i	−0.999151	+	0.0411990i	$0.986882\pi$
$978$	−16.5000	+	9.52628i	−0.527612	+	0.304617i
$979$	−24.0000			−0.767043
$980$	−14.0000			−0.447214
$981$	−9.00000	+	15.5885i	−0.287348	+	0.497701i
$982$	6.50000	+	11.2583i	0.207423	+	0.359268i
$983$	−9.00000	−	15.5885i	−0.287055	−	0.497195i	0.686050	−	0.727554i	$-0.259343\pi$
$983$	−9.00000	−	15.5885i	−0.287055	−	0.497195i	−0.973106	+	0.230360i	$0.926010\pi$
$984$		−	1.73205i		−	0.0552158i
$985$	−32.0000			−1.01960
$986$	−30.0000			−0.955395
$987$		0			0
$988$	−14.0000	−	10.3923i	−0.445399	−	0.330623i
$989$	8.00000			0.254385
$990$	24.0000			0.762770
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	−0.795474	−	0.605988i	$-0.792778\pi$
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	0.922538	+	0.385906i	$0.126111\pi$
$992$	10.0000			0.317500
$993$	−37.5000	−	21.6506i	−1.19003	−	0.687062i
$994$		0			0
$995$	−20.0000	−	34.6410i	−0.634043	−	1.09819i
$996$	−13.5000	+	7.79423i	−0.427764	+	0.246970i
$997$	10.0000			0.316703			0.158352	−	0.987383i	$-0.449382\pi$
$997$	10.0000			0.316703			0.158352	+	0.987383i	$0.449382\pi$
$998$	−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	342.2.h.b.277.1	yes	2
3.2	odd	2		1026.2.h.b.505.1		2
9.4	even	3		342.2.f.d.49.1	yes	2
9.5	odd	6		1026.2.f.c.847.1		2
19.7	even	3		342.2.f.d.7.1	✓	2
57.26	odd	6		1026.2.f.c.235.1		2
171.121	even	3	inner	342.2.h.b.121.1	yes	2
171.140	odd	6		1026.2.h.b.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.d.7.1	✓	2	19.7	even	3
342.2.f.d.49.1	yes	2	9.4	even	3
342.2.h.b.121.1	yes	2	171.121	even	3	inner
342.2.h.b.277.1	yes	2	1.1	even	1	trivial
1026.2.f.c.235.1		2	57.26	odd	6
1026.2.f.c.847.1		2	9.5	odd	6
1026.2.h.b.505.1		2	3.2	odd	2
1026.2.h.b.577.1		2	171.140	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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +2.00000 q^{5} +(-1.50000 + 0.866025i) q^{6} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +2.00000 q^{5} +(-1.50000 + 0.866025i) q^{6} +1.00000 q^{8} -3.00000 q^{9} +(-1.00000 - 1.73205i) q^{10} +(2.00000 - 3.46410i) q^{11} +(1.50000 + 0.866025i) q^{12} +(2.00000 - 3.46410i) q^{13} -3.46410i q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(1.50000 + 2.59808i) q^{18} +(-4.00000 + 1.73205i) q^{19} +(-1.00000 + 1.73205i) q^{20} -4.00000 q^{22} +(-4.00000 + 6.92820i) q^{23} -1.73205i q^{24} -1.00000 q^{25} -4.00000 q^{26} +5.19615i q^{27} +10.0000 q^{29} +(-3.00000 + 1.73205i) q^{30} +(-5.00000 - 8.66025i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-6.00000 - 3.46410i) q^{33} -3.00000 q^{34} +(1.50000 - 2.59808i) q^{36} -2.00000 q^{37} +(3.50000 + 2.59808i) q^{38} +(-6.00000 - 3.46410i) q^{39} +2.00000 q^{40} +1.00000 q^{41} +(-0.500000 - 0.866025i) q^{43} +(2.00000 + 3.46410i) q^{44} -6.00000 q^{45} +8.00000 q^{46} +2.00000 q^{47} +(-1.50000 + 0.866025i) q^{48} +(3.50000 + 6.06218i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-4.50000 - 2.59808i) q^{51} +(2.00000 + 3.46410i) q^{52} +(5.00000 + 8.66025i) q^{53} +(4.50000 - 2.59808i) q^{54} +(4.00000 - 6.92820i) q^{55} +(3.00000 + 6.92820i) q^{57} +(-5.00000 - 8.66025i) q^{58} +3.00000 q^{59} +(3.00000 + 1.73205i) q^{60} +2.00000 q^{61} +(-5.00000 + 8.66025i) q^{62} +1.00000 q^{64} +(4.00000 - 6.92820i) q^{65} +6.92820i q^{66} +(1.50000 - 2.59808i) q^{67} +(1.50000 + 2.59808i) q^{68} +(12.0000 + 6.92820i) q^{69} +(5.00000 - 8.66025i) q^{71} -3.00000 q^{72} +(-3.00000 + 5.19615i) q^{73} +(1.00000 + 1.73205i) q^{74} +1.73205i q^{75} +(0.500000 - 4.33013i) q^{76} +6.92820i q^{78} +(5.00000 + 8.66025i) q^{79} +(-1.00000 - 1.73205i) q^{80} +9.00000 q^{81} +(-0.500000 - 0.866025i) q^{82} +(-4.50000 + 7.79423i) q^{83} +(3.00000 - 5.19615i) q^{85} +(-0.500000 + 0.866025i) q^{86} -17.3205i q^{87} +(2.00000 - 3.46410i) q^{88} +(-3.00000 - 5.19615i) q^{89} +(3.00000 + 5.19615i) q^{90} +(-4.00000 - 6.92820i) q^{92} +(-15.0000 + 8.66025i) q^{93} +(-1.00000 - 1.73205i) q^{94} +(-8.00000 + 3.46410i) q^{95} +(1.50000 + 0.866025i) q^{96} +(7.00000 + 12.1244i) q^{97} +(3.50000 - 6.06218i) q^{98} +(-6.00000 + 10.3923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 4 q^{5} - 3 q^{6} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q - q^2 - q^4 + 4 * q^5 - 3 * q^6 + 2 * q^8 - 6 * q^9	\( 2 q - q^{2} - q^{4} + 4 q^{5} - 3 q^{6} + 2 q^{8} - 6 q^{9} - 2 q^{10} + 4 q^{11} + 3 q^{12} + 4 q^{13} - q^{16} + 3 q^{17} + 3 q^{18} - 8 q^{19} - 2 q^{20} - 8 q^{22} - 8 q^{23} - 2 q^{25} - 8 q^{26} + 20 q^{29} - 6 q^{30} - 10 q^{31} - q^{32} - 12 q^{33} - 6 q^{34} + 3 q^{36} - 4 q^{37} + 7 q^{38} - 12 q^{39} + 4 q^{40} + 2 q^{41} - q^{43} + 4 q^{44} - 12 q^{45} + 16 q^{46} + 4 q^{47} - 3 q^{48} + 7 q^{49} + q^{50} - 9 q^{51} + 4 q^{52} + 10 q^{53} + 9 q^{54} + 8 q^{55} + 6 q^{57} - 10 q^{58} + 6 q^{59} + 6 q^{60} + 4 q^{61} - 10 q^{62} + 2 q^{64} + 8 q^{65} + 3 q^{67} + 3 q^{68} + 24 q^{69} + 10 q^{71} - 6 q^{72} - 6 q^{73} + 2 q^{74} + q^{76} + 10 q^{79} - 2 q^{80} + 18 q^{81} - q^{82} - 9 q^{83} + 6 q^{85} - q^{86} + 4 q^{88} - 6 q^{89} + 6 q^{90} - 8 q^{92} - 30 q^{93} - 2 q^{94} - 16 q^{95} + 3 q^{96} + 14 q^{97} + 7 q^{98} - 12 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^4 + 4 * q^5 - 3 * q^6 + 2 * q^8 - 6 * q^9 - 2 * q^10 + 4 * q^11 + 3 * q^12 + 4 * q^13 - q^16 + 3 * q^17 + 3 * q^18 - 8 * q^19 - 2 * q^20 - 8 * q^22 - 8 * q^23 - 2 * q^25 - 8 * q^26 + 20 * q^29 - 6 * q^30 - 10 * q^31 - q^32 - 12 * q^33 - 6 * q^34 + 3 * q^36 - 4 * q^37 + 7 * q^38 - 12 * q^39 + 4 * q^40 + 2 * q^41 - q^43 + 4 * q^44 - 12 * q^45 + 16 * q^46 + 4 * q^47 - 3 * q^48 + 7 * q^49 + q^50 - 9 * q^51 + 4 * q^52 + 10 * q^53 + 9 * q^54 + 8 * q^55 + 6 * q^57 - 10 * q^58 + 6 * q^59 + 6 * q^60 + 4 * q^61 - 10 * q^62 + 2 * q^64 + 8 * q^65 + 3 * q^67 + 3 * q^68 + 24 * q^69 + 10 * q^71 - 6 * q^72 - 6 * q^73 + 2 * q^74 + q^76 + 10 * q^79 - 2 * q^80 + 18 * q^81 - q^82 - 9 * q^83 + 6 * q^85 - q^86 + 4 * q^88 - 6 * q^89 + 6 * q^90 - 8 * q^92 - 30 * q^93 - 2 * q^94 - 16 * q^95 + 3 * q^96 + 14 * q^97 + 7 * q^98 - 12 * q^99

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