LMFDB - Embedded newform 570.2.q.c.349.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(49,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("570.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.q (of order $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 49 x^{16} - 8 x^{15} + 72 x^{13} + 2145 x^{12} - 648 x^{11} + 32 x^{10} - 7056 x^{9} + \cdots + 1024 $ x^20 - 49x^16 - 8x^15 + 72x^13 + 2145x^12 - 648x^11 + 32x^10 - 7056x^9 - 11968x^8 + 10368x^7 + 9344x^6 + 18176x^5 + 56320x^4 + 28160x^3 + 8192x^2 + 4096*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.7
Root			$0.0996880 - 0.372041i$ of defining polynomial
Character	$\chi$	$=$	570.349
Dual form			570.2.q.c.49.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.78590 + 1.34557i) q^{5} +(-0.500000 + 0.866025i) q^{6} +2.32136i q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.78590 + 1.34557i) q^{5} +(-0.500000 + 0.866025i) q^{6} +2.32136i q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.873846 + 2.05825i) q^{10} -2.85165 q^{11} +1.00000i q^{12} +(-5.20277 - 3.00382i) q^{13} +(1.16068 + 2.01036i) q^{14} +(0.873846 - 2.05825i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.79487 + 2.19097i) q^{17} -1.00000i q^{18} +(-2.63121 - 3.47516i) q^{19} +(0.272353 + 2.21942i) q^{20} +(-1.16068 - 2.01036i) q^{21} +(-2.46960 + 1.42582i) q^{22} +(4.36172 + 2.51824i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.37886 - 4.80612i) q^{25} -6.00764 q^{26} +1.00000i q^{27} +(2.01036 + 1.16068i) q^{28} +(-4.41039 + 7.63902i) q^{29} +(-0.272353 - 2.21942i) q^{30} -0.685205 q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.46960 - 1.42582i) q^{33} +(-2.19097 + 3.79487i) q^{34} +(-3.12356 - 4.14571i) q^{35} +(-0.500000 - 0.866025i) q^{36} +7.79872i q^{37} +(-4.01627 - 1.69397i) q^{38} +6.00764 q^{39} +(1.34557 + 1.78590i) q^{40} +(2.58128 + 4.47091i) q^{41} +(-2.01036 - 1.16068i) q^{42} +(-2.24057 + 1.29360i) q^{43} +(-1.42582 + 2.46960i) q^{44} +(0.272353 + 2.21942i) q^{45} +5.03648 q^{46} +(-6.83132 - 3.94406i) q^{47} +(0.866025 + 0.500000i) q^{48} +1.61129 q^{49} +(-1.20893 - 4.85165i) q^{50} +(2.19097 - 3.79487i) q^{51} +(-5.20277 + 3.00382i) q^{52} +(4.86905 + 2.81115i) q^{53} +(0.500000 + 0.866025i) q^{54} +(5.09275 - 3.83710i) q^{55} +2.32136 q^{56} +(4.01627 + 1.69397i) q^{57} +8.82078i q^{58} +(-0.724643 - 1.25512i) q^{59} +(-1.34557 - 1.78590i) q^{60} +(5.40264 - 9.35765i) q^{61} +(-0.593405 + 0.342602i) q^{62} +(2.01036 + 1.16068i) q^{63} -1.00000 q^{64} +(13.3335 - 1.63620i) q^{65} +(1.42582 - 2.46960i) q^{66} +(-5.89514 - 3.40356i) q^{67} +4.38194i q^{68} -5.03648 q^{69} +(-4.77794 - 2.02851i) q^{70} +(1.15149 + 1.99443i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(5.38195 - 3.10727i) q^{73} +(3.89936 + 6.75389i) q^{74} +(1.20893 + 4.85165i) q^{75} +(-4.32518 + 0.541114i) q^{76} -6.61970i q^{77} +(5.20277 - 3.00382i) q^{78} +(2.00683 + 3.47593i) q^{79} +(2.05825 + 0.873846i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.47091 + 2.58128i) q^{82} -12.2192i q^{83} -2.32136 q^{84} +(3.82914 - 9.01912i) q^{85} +(-1.29360 + 2.24057i) q^{86} -8.82078i q^{87} +2.85165i q^{88} +(-4.34444 + 7.52479i) q^{89} +(1.34557 + 1.78590i) q^{90} +(6.97295 - 12.0775i) q^{91} +(4.36172 - 2.51824i) q^{92} +(0.593405 - 0.342602i) q^{93} -7.88813 q^{94} +(9.37516 + 2.66579i) q^{95} +1.00000 q^{96} +(-5.79684 + 3.34681i) q^{97} +(1.39542 - 0.805646i) q^{98} +(-1.42582 + 2.46960i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) $ 20 * q + 10 * q^4 - 10 * q^6 + 10 * q^9	$ 20 q + 10 q^{4} - 10 q^{6} + 10 q^{9} - 2 q^{10} + 12 q^{11} + 10 q^{14} + 2 q^{15} - 10 q^{16} + 6 q^{19} - 10 q^{21} + 10 q^{24} + 14 q^{25} + 8 q^{29} + 40 q^{31} + 12 q^{34} + 2 q^{35} - 10 q^{36} + 2 q^{40} - 14 q^{41} + 6 q^{44} + 44 q^{46} - 8 q^{49} - 8 q^{50} - 12 q^{51} + 10 q^{54} + 20 q^{56} + 8 q^{59} - 2 q^{60} + 16 q^{61} - 20 q^{64} + 40 q^{65} - 6 q^{66} - 44 q^{69} + 8 q^{70} - 4 q^{71} + 26 q^{74} + 8 q^{75} + 8 q^{79} - 10 q^{81} - 20 q^{84} - 16 q^{85} - 20 q^{86} - 2 q^{89} + 2 q^{90} - 44 q^{91} - 32 q^{94} - 80 q^{95} + 20 q^{96} + 6 q^{99}+O(q^{100}) $ 20 * q + 10 * q^4 - 10 * q^6 + 10 * q^9 - 2 * q^10 + 12 * q^11 + 10 * q^14 + 2 * q^15 - 10 * q^16 + 6 * q^19 - 10 * q^21 + 10 * q^24 + 14 * q^25 + 8 * q^29 + 40 * q^31 + 12 * q^34 + 2 * q^35 - 10 * q^36 + 2 * q^40 - 14 * q^41 + 6 * q^44 + 44 * q^46 - 8 * q^49 - 8 * q^50 - 12 * q^51 + 10 * q^54 + 20 * q^56 + 8 * q^59 - 2 * q^60 + 16 * q^61 - 20 * q^64 + 40 * q^65 - 6 * q^66 - 44 * q^69 + 8 * q^70 - 4 * q^71 + 26 * q^74 + 8 * q^75 + 8 * q^79 - 10 * q^81 - 20 * q^84 - 16 * q^85 - 20 * q^86 - 2 * q^89 + 2 * q^90 - 44 * q^91 - 32 * q^94 - 80 * q^95 + 20 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.78590	+	1.34557i	−0.798678	+	0.601759i
$5$	−1.78590	+	1.34557i	−0.798678	+	0.601759i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$			2.32136i			0.877391i	0.898636	+	0.438696i	$0.144559\pi$
$7$			2.32136i			0.877391i	−0.898636	+	0.438696i	$0.855441\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.873846	+	2.05825i	−0.276334	+	0.650876i
$11$	−2.85165			−0.859804			−0.429902	−	0.902875i	$-0.641452\pi$
$11$	−2.85165			−0.859804			−0.429902	+	0.902875i	$0.641452\pi$
$12$			1.00000i			0.288675i
$13$	−5.20277	−	3.00382i	−1.44299	−	0.833110i	−0.444941	−	0.895560i	$-0.646776\pi$
$13$	−5.20277	−	3.00382i	−1.44299	−	0.833110i	−0.998048	+	0.0624492i	$0.980109\pi$
$14$	1.16068	+	2.01036i	0.310205	+	0.537290i
$15$	0.873846	−	2.05825i	0.225626	−	0.531438i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.79487	+	2.19097i	−0.920391	+	0.531388i	−0.883760	−	0.467941i	$-0.844996\pi$
$17$	−3.79487	+	2.19097i	−0.920391	+	0.531388i	−0.0366311	+	0.999329i	$0.511663\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−2.63121	−	3.47516i	−0.603641	−	0.797256i
$19$	−2.63121	−	3.47516i	−0.603641	−	0.797256i
$20$	0.272353	+	2.21942i	0.0608999	+	0.496277i
$21$	−1.16068	−	2.01036i	−0.253281	−	0.438696i
$22$	−2.46960	+	1.42582i	−0.526520	+	0.303987i
$23$	4.36172	+	2.51824i	0.909481	+	0.525089i	0.880264	−	0.474484i	$-0.157365\pi$
$23$	4.36172	+	2.51824i	0.909481	+	0.525089i	0.0292169	+	0.999573i	$0.490699\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	1.37886	−	4.80612i	0.275772	−	0.961223i
$26$	−6.00764			−1.17820
$27$			1.00000i			0.192450i
$28$	2.01036	+	1.16068i	0.379922	+	0.219348i
$29$	−4.41039	+	7.63902i	−0.818989	+	1.41853i	0.0874397	+	0.996170i	$0.472131\pi$
$29$	−4.41039	+	7.63902i	−0.818989	+	1.41853i	−0.906428	+	0.422360i	$0.861202\pi$
$30$	−0.272353	−	2.21942i	−0.0497246	−	0.405209i
$31$	−0.685205			−0.123066			−0.0615332	−	0.998105i	$-0.519599\pi$
$31$	−0.685205			−0.123066			−0.0615332	+	0.998105i	$0.519599\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	2.46960	−	1.42582i	0.429902	−	0.248204i
$34$	−2.19097	+	3.79487i	−0.375748	+	0.650815i
$35$	−3.12356	−	4.14571i	−0.527978	−	0.700753i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$			7.79872i			1.28210i	0.767499	+	0.641050i	$0.221501\pi$
$37$			7.79872i			1.28210i	−0.767499	+	0.641050i	$0.778499\pi$
$38$	−4.01627	−	1.69397i	−0.651526	−	0.274799i
$39$	6.00764			0.961993
$40$	1.34557	+	1.78590i	0.212754	+	0.282375i
$41$	2.58128	+	4.47091i	0.403128	+	0.698239i	0.994102	−	0.108452i	$-0.0345895\pi$
$41$	2.58128	+	4.47091i	0.403128	+	0.698239i	−0.590973	+	0.806691i	$0.701256\pi$
$42$	−2.01036	−	1.16068i	−0.310205	−	0.179097i
$43$	−2.24057	+	1.29360i	−0.341684	+	0.197271i	−0.661017	−	0.750371i	$-0.729875\pi$
$43$	−2.24057	+	1.29360i	−0.341684	+	0.197271i	0.319332	+	0.947643i	$0.396541\pi$
$44$	−1.42582	+	2.46960i	−0.214951	+	0.372306i
$45$	0.272353	+	2.21942i	0.0405999	+	0.330852i
$46$	5.03648			0.742588
$47$	−6.83132	−	3.94406i	−0.996450	−	0.575301i	−0.0892540	−	0.996009i	$-0.528448\pi$
$47$	−6.83132	−	3.94406i	−0.996450	−	0.575301i	−0.907196	+	0.420708i	$0.861782\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	1.61129			0.230184
$50$	−1.20893	−	4.85165i	−0.170968	−	0.686127i
$51$	2.19097	−	3.79487i	0.306797	−	0.531388i
$52$	−5.20277	+	3.00382i	−0.721495	+	0.416555i
$53$	4.86905	+	2.81115i	0.668815	+	0.386141i	0.795628	−	0.605786i	$-0.207141\pi$
$53$	4.86905	+	2.81115i	0.668815	+	0.386141i	−0.126812	+	0.991927i	$0.540475\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	5.09275	−	3.83710i	0.686706	−	0.517395i
$56$	2.32136			0.310205
$57$	4.01627	+	1.69397i	0.531968	+	0.224372i
$58$			8.82078i			1.15822i
$59$	−0.724643	−	1.25512i	−0.0943405	−	0.163403i	0.814993	−	0.579471i	$-0.196741\pi$
$59$	−0.724643	−	1.25512i	−0.0943405	−	0.163403i	−0.909333	+	0.416069i	$0.863408\pi$
$60$	−1.34557	−	1.78590i	−0.173713	−	0.230558i
$61$	5.40264	−	9.35765i	0.691737	−	1.19812i	−0.279531	−	0.960137i	$-0.590179\pi$
$61$	5.40264	−	9.35765i	0.691737	−	1.19812i	0.971268	−	0.237987i	$-0.0764876\pi$
$62$	−0.593405	+	0.342602i	−0.0753625	+	0.0435105i
$63$	2.01036	+	1.16068i	0.253281	+	0.146232i
$64$	−1.00000			−0.125000
$65$	13.3335	−	1.63620i	1.65382	−	0.202945i
$66$	1.42582	−	2.46960i	0.175507	−	0.303987i
$67$	−5.89514	−	3.40356i	−0.720206	−	0.415811i	0.0946224	−	0.995513i	$-0.469836\pi$
$67$	−5.89514	−	3.40356i	−0.720206	−	0.415811i	−0.814829	+	0.579702i	$0.803169\pi$
$68$			4.38194i			0.531388i
$69$	−5.03648			−0.606321
$70$	−4.77794	−	2.02851i	−0.571073	−	0.242453i
$71$	1.15149	+	1.99443i	0.136656	+	0.236696i	0.926229	−	0.376961i	$-0.123031\pi$
$71$	1.15149	+	1.99443i	0.136656	+	0.236696i	−0.789573	+	0.613657i	$0.789698\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	5.38195	−	3.10727i	0.629909	−	0.363678i	−0.150808	−	0.988563i	$-0.548187\pi$
$73$	5.38195	−	3.10727i	0.629909	−	0.363678i	0.780717	+	0.624885i	$0.214854\pi$
$74$	3.89936	+	6.75389i	0.453291	+	0.785123i
$75$	1.20893	+	4.85165i	0.139595	+	0.560220i
$76$	−4.32518	+	0.541114i	−0.496132	+	0.0620700i
$77$		−	6.61970i		−	0.754385i
$78$	5.20277	−	3.00382i	0.589098	−	0.340116i
$79$	2.00683	+	3.47593i	0.225786	+	0.391072i	0.956555	−	0.291552i	$-0.0941718\pi$
$79$	2.00683	+	3.47593i	0.225786	+	0.391072i	−0.730769	+	0.682625i	$0.760838\pi$
$80$	2.05825	+	0.873846i	0.230119	+	0.0976989i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.47091	+	2.58128i	0.493729	+	0.285055i
$83$		−	12.2192i		−	1.34123i	−0.741806	−	0.670614i	$-0.766031\pi$
$83$		−	12.2192i		−	1.34123i	0.741806	−	0.670614i	$-0.233969\pi$
$84$	−2.32136			−0.253281
$85$	3.82914	−	9.01912i	0.415328	−	0.978261i
$86$	−1.29360	+	2.24057i	−0.139492	+	0.241607i
$87$		−	8.82078i		−	0.945687i
$88$			2.85165i			0.303987i
$89$	−4.34444	+	7.52479i	−0.460510	+	0.797626i	−0.998986	−	0.0450142i	$-0.985667\pi$
$89$	−4.34444	+	7.52479i	−0.460510	+	0.797626i	0.538477	+	0.842640i	$0.319000\pi$
$90$	1.34557	+	1.78590i	0.141836	+	0.188250i
$91$	6.97295	−	12.0775i	0.730964	−	1.26607i
$92$	4.36172	−	2.51824i	0.454740	−	0.262545i
$93$	0.593405	−	0.342602i	0.0615332	−	0.0355262i
$94$	−7.88813			−0.813598
$95$	9.37516	+	2.66579i	0.961871	+	0.273505i
$96$	1.00000			0.102062
$97$	−5.79684	+	3.34681i	−0.588580	+	0.339817i	−0.764536	−	0.644581i	$-0.777032\pi$
$97$	−5.79684	+	3.34681i	−0.588580	+	0.339817i	0.175956	+	0.984398i	$0.443698\pi$
$98$	1.39542	−	0.805646i	0.140959	−	0.0813825i
$99$	−1.42582	+	2.46960i	−0.143301	+	0.248204i
$100$	−3.47279	−	3.59719i	−0.347279	−	0.359719i
$101$	−7.02206	+	12.1626i	−0.698721	+	1.21022i	0.270189	+	0.962807i	$0.412914\pi$
$101$	−7.02206	+	12.1626i	−0.698721	+	1.21022i	−0.968910	+	0.247413i	$0.920419\pi$
$102$		−	4.38194i		−	0.433876i
$103$		−	14.0958i		−	1.38890i	−0.719542	−	0.694449i	$-0.755648\pi$
$103$		−	14.0958i		−	1.38890i	0.719542	−	0.694449i	$-0.244352\pi$
$104$	−3.00382	+	5.20277i	−0.294549	+	0.510174i
$105$	4.77794	+	2.02851i	0.466279	+	0.197962i
$106$	5.62229			0.546085
$107$			16.7729i			1.62150i	0.585395	+	0.810748i	$0.300940\pi$
$107$			16.7729i			1.62150i	−0.585395	+	0.810748i	$0.699060\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	4.45191	+	7.71093i	0.426416	+	0.738573i	0.996551	−	0.0829770i	$-0.0264428\pi$
$109$	4.45191	+	7.71093i	0.426416	+	0.738573i	−0.570136	+	0.821550i	$0.693109\pi$
$110$	2.49190	−	5.86941i	0.237593	−	0.559626i
$111$	−3.89936	−	6.75389i	−0.370111	−	0.641050i
$112$	2.01036	−	1.16068i	0.189961	−	0.109674i
$113$		−	11.8870i		−	1.11824i	−0.829087	−	0.559120i	$-0.811139\pi$
$113$		−	11.8870i		−	1.11824i	0.829087	−	0.559120i	$-0.188861\pi$
$114$	4.32518	−	0.541114i	0.405090	−	0.0506799i
$115$	−11.1781	+	1.37170i	−1.04236	+	0.127912i
$116$	4.41039	+	7.63902i	0.409494	+	0.709265i
$117$	−5.20277	+	3.00382i	−0.480997	+	0.277703i
$118$	−1.25512	−	0.724643i	−0.115543	−	0.0667088i
$119$	−5.08602	−	8.80925i	−0.466235	−	0.807543i
$120$	−2.05825	−	0.873846i	−0.187892	−	0.0797708i
$121$	−2.86810			−0.260737
$122$		−	10.8053i		−	0.978264i
$123$	−4.47091	−	2.58128i	−0.403128	−	0.232746i
$124$	−0.342602	+	0.593405i	−0.0307666	+	0.0532893i
$125$	4.00448	+	10.4386i	0.358172	+	0.933656i
$126$	2.32136			0.206803
$127$	7.72660	+	4.46095i	0.685625	+	0.395846i	0.801971	−	0.597363i	$-0.203785\pi$
$127$	7.72660	+	4.46095i	0.685625	+	0.395846i	−0.116346	+	0.993209i	$0.537118\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	1.29360	−	2.24057i	0.113895	−	0.197271i
$130$	10.7290	−	8.08373i	0.940999	−	0.708990i
$131$	0.0274319	+	0.0475134i	0.00239673	+	0.00415127i	0.867221	−	0.497923i	$-0.165904\pi$
$131$	0.0274319	+	0.0475134i	0.00239673	+	0.00415127i	−0.864825	+	0.502074i	$0.832570\pi$
$132$		−	2.85165i		−	0.248204i
$133$	8.06710	−	6.10798i	0.699506	−	0.529629i
$134$	−6.80712			−0.588046
$135$	−1.34557	−	1.78590i	−0.115809	−	0.153706i
$136$	2.19097	+	3.79487i	0.187874	+	0.325407i
$137$	15.5732	+	8.99119i	1.33051	+	0.768169i	0.985377	−	0.170386i	$-0.0545013\pi$
$137$	15.5732	+	8.99119i	1.33051	+	0.768169i	0.345131	+	0.938555i	$0.387835\pi$
$138$	−4.36172	+	2.51824i	−0.371294	+	0.214367i
$139$	−10.3327	+	17.8967i	−0.876405	+	1.51798i	−0.0211474	+	0.999776i	$0.506732\pi$
$139$	−10.3327	+	17.8967i	−0.876405	+	1.51798i	−0.855258	+	0.518202i	$0.826601\pi$
$140$	−5.15207	+	0.632228i	−0.435429	+	0.0534330i
$141$	7.88813			0.664300
$142$	1.99443	+	1.15149i	0.167369	+	0.0966306i
$143$	14.8365	+	8.56584i	1.24069	+	0.716312i
$144$	−1.00000			−0.0833333
$145$	−2.40236	−	19.5770i	−0.199505	−	1.62578i
$146$	3.10727	−	5.38195i	0.257159	−	0.445413i
$147$	−1.39542	+	0.805646i	−0.115092	+	0.0664485i
$148$	6.75389	+	3.89936i	0.555166	+	0.320525i
$149$	−1.92651	−	3.33682i	−0.157826	−	0.273363i	0.776258	−	0.630415i	$-0.217115\pi$
$149$	−1.92651	−	3.33682i	−0.157826	−	0.273363i	−0.934084	+	0.357052i	$0.883782\pi$
$150$	3.47279	+	3.59719i	0.283552	+	0.293709i
$151$	7.77324			0.632577			0.316289	−	0.948663i	$-0.397563\pi$
$151$	7.77324			0.632577			0.316289	+	0.948663i	$0.397563\pi$
$152$	−3.47516	+	2.63121i	−0.281873	+	0.213419i
$153$			4.38194i			0.354259i
$154$	−3.30985	−	5.73283i	−0.266715	−	0.461964i
$155$	1.22371	−	0.921994i	0.0982904	−	0.0740563i
$156$	3.00382	−	5.20277i	0.240498	−	0.416555i
$157$	16.6929	−	9.63765i	1.33224	−	0.769169i	0.346596	−	0.938014i	$-0.387337\pi$
$157$	16.6929	−	9.63765i	1.33224	−	0.769169i	0.985642	+	0.168846i	$0.0540040\pi$
$158$	3.47593	+	2.00683i	0.276530	+	0.159655i
$159$	−5.62229			−0.445877
$160$	2.21942	−	0.272353i	0.175461	−	0.0215314i
$161$	−5.84574	+	10.1251i	−0.460709	+	0.797971i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$		−	15.9168i		−	1.24670i	−0.781944	−	0.623348i	$-0.785772\pi$
$163$		−	15.9168i		−	1.24670i	0.781944	−	0.623348i	$-0.214228\pi$
$164$	5.16256			0.403128
$165$	−2.49190	+	5.86941i	−0.193994	+	0.456933i
$166$	−6.10958	−	10.5821i	−0.474196	−	0.821331i
$167$	−16.4675	−	9.50754i	−1.27430	−	0.735716i	−0.298503	−	0.954409i	$-0.596487\pi$
$167$	−16.4675	−	9.50754i	−1.27430	−	0.735716i	−0.975794	+	0.218693i	$0.929821\pi$
$168$	−2.01036	+	1.16068i	−0.155102	+	0.0895484i
$169$	11.5459	+	19.9981i	0.888146	+	1.53831i
$170$	−1.19343	−	9.72536i	−0.0915321	−	0.745901i
$171$	−4.32518	+	0.541114i	−0.330755	+	0.0413800i
$172$			2.58719i			0.197271i
$173$	−12.3792	+	7.14712i	−0.941172	+	0.543386i	−0.890327	−	0.455321i	$-0.849525\pi$
$173$	−12.3792	+	7.14712i	−0.941172	+	0.543386i	−0.0508444	+	0.998707i	$0.516191\pi$
$174$	−4.41039	−	7.63902i	−0.334351	−	0.579112i
$175$	11.1567	+	3.20083i	0.843369	+	0.241960i
$176$	1.42582	+	2.46960i	0.107476	+	0.186153i
$177$	1.25512	+	0.724643i	0.0943405	+	0.0544675i
$178$			8.68888i			0.651259i
$179$	−6.66682			−0.498301			−0.249151	−	0.968465i	$-0.580151\pi$
$179$	−6.66682			−0.498301			−0.249151	+	0.968465i	$0.580151\pi$
$180$	2.05825	+	0.873846i	0.153413	+	0.0651326i
$181$	−3.06793	+	5.31382i	−0.228038	+	0.394973i	−0.957226	−	0.289340i	$-0.906564\pi$
$181$	−3.06793	+	5.31382i	−0.228038	+	0.394973i	0.729189	+	0.684313i	$0.239898\pi$
$182$		−	13.9459i		−	1.03374i
$183$			10.8053i			0.798749i
$184$	2.51824	−	4.36172i	0.185647	−	0.321550i
$185$	−10.4937	−	13.9277i	−0.771516	−	1.02399i
$186$	0.342602	−	0.593405i	0.0251208	−	0.0435105i
$187$	10.8216	−	6.24787i	0.791356	−	0.456890i
$188$	−6.83132	+	3.94406i	−0.498225	+	0.287650i
$189$	−2.32136			−0.168854
$190$	9.45202	−	2.37893i	0.685722	−	0.172586i
$191$	−18.8448			−1.36356			−0.681780	−	0.731557i	$-0.738794\pi$
$191$	−18.8448			−1.36356			−0.681780	+	0.731557i	$0.738794\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−14.3105	+	8.26218i	−1.03009	+	0.594725i	−0.917012	−	0.398861i	$-0.869406\pi$
$193$	−14.3105	+	8.26218i	−1.03009	+	0.594725i	−0.113082	+	0.993586i	$0.536072\pi$
$194$	−3.34681	+	5.79684i	−0.240287	+	0.416189i
$195$	−10.7290	+	8.08373i	−0.768322	+	0.578888i
$196$	0.805646	−	1.39542i	0.0575461	−	0.0996728i
$197$			6.90254i			0.491786i	0.969297	+	0.245893i	$0.0790811\pi$
$197$			6.90254i			0.491786i	−0.969297	+	0.245893i	$0.920919\pi$
$198$			2.85165i			0.202658i
$199$	3.26514	−	5.65540i	0.231460	−	0.400900i	−0.726778	−	0.686872i	$-0.758983\pi$
$199$	3.26514	−	5.65540i	0.231460	−	0.400900i	0.958238	+	0.285972i	$0.0923164\pi$
$200$	−4.80612	−	1.37886i	−0.339844	−	0.0975001i
$201$	6.80712			0.480137
$202$			14.0441i			0.988141i
$203$	−17.7329	−	10.2381i	−1.24461	−	0.718573i
$204$	−2.19097	−	3.79487i	−0.153398	−	0.265694i
$205$	−10.6258	−	4.51128i	−0.742141	−	0.315082i
$206$	−7.04788	−	12.2073i	−0.491049	−	0.850522i
$207$	4.36172	−	2.51824i	0.303160	−	0.175030i
$208$			6.00764i			0.416555i
$209$	7.50328	+	9.90993i	0.519013	+	0.685484i
$210$	5.15207	−	0.632228i	0.355527	−	0.0436279i
$211$	−11.1943	−	19.3891i	−0.770648	−	1.33480i	−0.937208	−	0.348771i	$-0.886599\pi$
$211$	−11.1943	−	19.3891i	−0.770648	−	1.33480i	0.166560	−	0.986031i	$-0.446734\pi$
$212$	4.86905	−	2.81115i	0.334408	−	0.193070i
$213$	−1.99443	−	1.15149i	−0.136656	−	0.0788986i
$214$	8.38645	+	14.5258i	0.573286	+	0.992960i
$215$	2.26081	−	5.32509i	0.154186	−	0.363168i
$216$	1.00000			0.0680414
$217$		−	1.59061i		−	0.107977i
$218$	7.71093	+	4.45191i	0.522250	+	0.301521i
$219$	−3.10727	+	5.38195i	−0.209970	+	0.363678i
$220$	−0.776654	−	6.32900i	−0.0523620	−	0.426701i
$221$	26.3251			1.77082
$222$	−6.75389	−	3.89936i	−0.453291	−	0.261708i
$223$	1.62511	−	0.938256i	0.108825	−	0.0628302i	−0.444600	−	0.895729i	$-0.646654\pi$
$223$	1.62511	−	0.938256i	0.108825	−	0.0628302i	0.553425	+	0.832899i	$0.313321\pi$
$224$	1.16068	−	2.01036i	0.0775512	−	0.134323i
$225$	−3.47279	−	3.59719i	−0.231519	−	0.239812i
$226$	−5.94352	−	10.2945i	−0.395357	−	0.684779i
$227$		−	20.3703i		−	1.35203i	−0.736890	−	0.676013i	$-0.763706\pi$
$227$		−	20.3703i		−	1.35203i	0.736890	−	0.676013i	$-0.236294\pi$
$228$	3.47516	−	2.63121i	0.230148	−	0.174256i
$229$	−10.7813			−0.712449			−0.356224	−	0.934400i	$-0.615936\pi$
$229$	−10.7813			−0.712449			−0.356224	+	0.934400i	$0.615936\pi$
$230$	−8.99463	+	6.77695i	−0.593089	+	0.446859i
$231$	3.30985	+	5.73283i	0.217772	+	0.377192i
$232$	7.63902	+	4.41039i	0.501526	+	0.289556i
$233$	−11.7576	+	6.78823i	−0.770263	+	0.444711i	−0.832968	−	0.553321i	$-0.813360\pi$
$233$	−11.7576	+	6.78823i	−0.770263	+	0.444711i	0.0627056	+	0.998032i	$0.480027\pi$
$234$	−3.00382	+	5.20277i	−0.196366	+	0.340116i
$235$	17.5071	−	2.14835i	1.14203	−	0.140143i
$236$	−1.44929			−0.0943405
$237$	−3.47593	−	2.00683i	−0.225786	−	0.130357i
$238$	−8.80925	−	5.08602i	−0.571019	−	0.329678i
$239$	2.08081			0.134596			0.0672981	−	0.997733i	$-0.478562\pi$
$239$	2.08081			0.134596			0.0672981	+	0.997733i	$0.478562\pi$
$240$	−2.21942	+	0.272353i	−0.143263	+	0.0175803i
$241$	−8.51317	+	14.7453i	−0.548382	+	0.949825i	0.450004	+	0.893027i	$0.351423\pi$
$241$	−8.51317	+	14.7453i	−0.548382	+	0.949825i	−0.998386	+	0.0567985i	$0.981911\pi$
$242$	−2.48385	+	1.43405i	−0.159668	+	0.0921843i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−5.40264	−	9.35765i	−0.345869	−	0.599062i
$245$	−2.87760	+	2.16811i	−0.183843	+	0.138516i
$246$	−5.16256			−0.329153
$247$	3.25082	+	25.9842i	0.206845	+	1.65333i
$248$			0.685205i			0.0435105i
$249$	6.10958	+	10.5821i	0.387179	+	0.670614i
$250$	8.68728	+	7.03784i	0.549432	+	0.445112i
$251$	9.62571	−	16.6722i	0.607569	−	1.05234i	−0.384070	−	0.923304i	$-0.625478\pi$
$251$	9.62571	−	16.6722i	0.607569	−	1.05234i	0.991640	−	0.129037i	$-0.0411886\pi$
$252$	2.01036	−	1.16068i	0.126641	−	0.0731159i
$253$	−12.4381	−	7.18113i	−0.781976	−	0.451474i
$254$	8.92191			0.559810
$255$	1.19343	+	9.72536i	0.0747356	+	0.609026i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	15.3212	+	8.84568i	0.955708	+	0.551779i	0.894850	−	0.446368i	$-0.147283\pi$
$257$	15.3212	+	8.84568i	0.955708	+	0.551779i	0.0608589	+	0.998146i	$0.480616\pi$
$258$		−	2.58719i		−	0.161072i
$259$	−18.1036			−1.12490
$260$	5.24975	−	12.3652i	0.325576	−	0.766859i
$261$	4.41039	+	7.63902i	0.272996	+	0.472843i
$262$	0.0475134	+	0.0274319i	0.00293539	+	0.00169475i
$263$	−9.98291	+	5.76364i	−0.615573	+	0.355401i	−0.775143	−	0.631785i	$-0.782322\pi$
$263$	−9.98291	+	5.76364i	−0.615573	+	0.355401i	0.159570	+	0.987187i	$0.448989\pi$
$264$	−1.42582	−	2.46960i	−0.0877534	−	0.151993i
$265$	−12.4782	+	1.53125i	−0.766532	+	0.0940637i
$266$	3.93232	−	9.32321i	0.241106	−	0.571643i
$267$		−	8.68888i		−	0.531751i
$268$	−5.89514	+	3.40356i	−0.360103	+	0.207906i
$269$	10.2776	+	17.8013i	0.626635	+	1.08536i	0.988222	+	0.153025i	$0.0489016\pi$
$269$	10.2776	+	17.8013i	0.626635	+	1.08536i	−0.361587	+	0.932338i	$0.617765\pi$
$270$	−2.05825	−	0.873846i	−0.125261	−	0.0531805i
$271$	12.9912	+	22.5014i	0.789159	+	1.36686i	0.926483	+	0.376337i	$0.122816\pi$
$271$	12.9912	+	22.5014i	0.789159	+	1.36686i	−0.137324	+	0.990526i	$0.543850\pi$
$272$	3.79487	+	2.19097i	0.230098	+	0.132847i
$273$			13.9459i			0.844044i
$274$	17.9824			1.08636
$275$	−3.93202	+	13.7053i	−0.237110	+	0.826464i
$276$	−2.51824	+	4.36172i	−0.151580	+	0.262545i
$277$		−	4.14296i		−	0.248926i	−0.992224	−	0.124463i	$-0.960279\pi$
$277$		−	4.14296i		−	0.248926i	0.992224	−	0.124463i	$-0.0397208\pi$
$278$			20.6653i			1.23942i
$279$	−0.342602	+	0.593405i	−0.0205111	+	0.0355262i
$280$	−4.14571	+	3.12356i	−0.247754	+	0.186668i
$281$	−4.29844	+	7.44511i	−0.256423	+	0.444138i	−0.965281	−	0.261213i	$-0.915877\pi$
$281$	−4.29844	+	7.44511i	−0.256423	+	0.444138i	0.708858	+	0.705351i	$0.249211\pi$
$282$	6.83132	−	3.94406i	0.406799	−	0.234866i
$283$	12.4490	−	7.18742i	0.740015	−	0.427248i	−0.0820596	−	0.996627i	$-0.526150\pi$
$283$	12.4490	−	7.18742i	0.740015	−	0.427248i	0.822075	+	0.569379i	$0.192816\pi$
$284$	2.30297			0.136656
$285$	−9.45202	+	2.37893i	−0.559889	+	0.140916i
$286$	17.1317			1.01302
$287$	−10.3786	+	5.99208i	−0.612628	+	0.353701i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	1.10069	−	1.90644i	0.0647462	−	0.112144i
$290$	−11.8690	−	15.7530i	−0.696972	−	0.925048i
$291$	3.34681	−	5.79684i	0.196193	−	0.339817i
$292$		−	6.21454i		−	0.363678i
$293$			8.47490i			0.495109i	0.968874	+	0.247554i	$0.0796269\pi$
$293$			8.47490i			0.495109i	−0.968874	+	0.247554i	$0.920373\pi$
$294$	−0.805646	+	1.39542i	−0.0469862	+	0.0813825i
$295$	2.98299	+	1.26645i	0.173677	+	0.0737357i
$296$	7.79872			0.453291
$297$		−	2.85165i		−	0.165469i
$298$	−3.33682	−	1.92651i	−0.193297	−	0.111600i
$299$	−15.1287	−	26.2037i	−0.874914	−	1.51540i
$300$	4.80612	+	1.37886i	0.277481	+	0.0796085i
$301$	−3.00290	−	5.20118i	−0.173084	−	0.299791i
$302$	6.73182	−	3.88662i	0.387373	−	0.223650i
$303$		−	14.0441i		−	0.806814i
$304$	−1.69397	+	4.01627i	−0.0971560	+	0.230349i
$305$	2.94285	+	23.9814i	0.168507	+	1.37317i
$306$	2.19097	+	3.79487i	0.125249	+	0.216938i
$307$	−18.6780	+	10.7838i	−1.06601	+	0.615462i	−0.927089	−	0.374841i	$-0.877697\pi$
$307$	−18.6780	+	10.7838i	−1.06601	+	0.615462i	−0.138922	+	0.990303i	$0.544364\pi$
$308$	−5.73283	−	3.30985i	−0.326658	−	0.188596i
$309$	7.04788	+	12.2073i	0.400940	+	0.694449i
$310$	0.598763	−	1.41032i	0.0340074	−	0.0801009i
$311$	6.25433			0.354650			0.177325	−	0.984152i	$-0.443256\pi$
$311$	6.25433			0.354650			0.177325	+	0.984152i	$0.443256\pi$
$312$		−	6.00764i		−	0.340116i
$313$	−15.3732	−	8.87575i	−0.868947	−	0.501687i	−0.00194901	−	0.999998i	$-0.500620\pi$
$313$	−15.3732	−	8.87575i	−0.868947	−	0.501687i	−0.866998	+	0.498311i	$0.833954\pi$
$314$	9.63765	−	16.6929i	0.543884	−	0.942035i
$315$	−5.15207	+	0.632228i	−0.290286	+	0.0356220i
$316$	4.01365			0.225786
$317$	−0.640437	−	0.369757i	−0.0359705	−	0.0207676i	0.481907	−	0.876222i	$-0.339944\pi$
$317$	−0.640437	−	0.369757i	−0.0359705	−	0.0207676i	−0.517877	+	0.855455i	$0.673278\pi$
$318$	−4.86905	+	2.81115i	−0.273043	+	0.157641i
$319$	12.5769	−	21.7838i	0.704170	−	1.21966i
$320$	1.78590	−	1.34557i	0.0998347	−	0.0752199i
$321$	−8.38645	−	14.5258i	−0.468086	−	0.810748i
$322$			11.6915i			0.651540i
$323$	17.5991	+	7.42288i	0.979238	+	0.413020i
$324$	−1.00000			−0.0555556
$325$	−21.6106	+	20.8633i	−1.19874	+	1.15729i
$326$	−7.95838	−	13.7843i	−0.440774	−	0.763442i
$327$	−7.71093	−	4.45191i	−0.426416	−	0.246191i
$328$	4.47091	−	2.58128i	0.246865	−	0.142527i
$329$	9.15559	−	15.8579i	0.504764	−	0.874277i
$330$	0.776654	+	6.32900i	0.0427534	+	0.348400i
$331$	−4.54461			−0.249794			−0.124897	−	0.992170i	$-0.539860\pi$
$331$	−4.54461			−0.249794			−0.124897	+	0.992170i	$0.539860\pi$
$332$	−10.5821	−	6.10958i	−0.580769	−	0.335307i
$333$	6.75389	+	3.89936i	0.370111	+	0.213683i
$334$	−19.0151			−1.04046
$335$	15.1079	−	1.85394i	0.825431	−	0.101291i
$336$	−1.16068	+	2.01036i	−0.0633203	+	0.109674i
$337$	−17.9486	+	10.3626i	−0.977722	+	0.564488i	−0.901582	−	0.432609i	$-0.857593\pi$
$337$	−17.9486	+	10.3626i	−0.977722	+	0.564488i	−0.0761405	+	0.997097i	$0.524260\pi$
$338$	19.9981	+	11.5459i	1.08775	+	0.628014i
$339$	5.94352	+	10.2945i	0.322808	+	0.559120i
$340$	−5.89622	−	7.82569i	−0.319767	−	0.424408i
$341$	1.95396			0.105813
$342$	−3.47516	+	2.63121i	−0.187915	+	0.142279i
$343$			19.9899i			1.07935i
$344$	1.29360	+	2.24057i	0.0697460	+	0.120804i
$345$	8.99463	−	6.77695i	0.484255	−	0.364859i
$346$	−7.14712	+	12.3792i	−0.384232	+	0.665509i
$347$	−10.7406	+	6.20108i	−0.576585	+	0.332891i	−0.759775	−	0.650186i	$-0.774691\pi$
$347$	−10.7406	+	6.20108i	−0.576585	+	0.332891i	0.183190	+	0.983077i	$0.441358\pi$
$348$	−7.63902	−	4.41039i	−0.409494	−	0.236422i
$349$	14.4163			0.771684			0.385842	−	0.922565i	$-0.373911\pi$
$349$	14.4163			0.771684			0.385842	+	0.922565i	$0.373911\pi$
$350$	11.2624	−	2.80636i	0.602002	−	0.150006i
$351$	3.00382	−	5.20277i	0.160332	−	0.277703i
$352$	2.46960	+	1.42582i	0.131630	+	0.0759967i
$353$		−	35.6707i		−	1.89856i	−0.314430	−	0.949281i	$-0.601813\pi$
$353$		−	35.6707i		−	1.89856i	0.314430	−	0.949281i	$-0.398187\pi$
$354$	1.44929			0.0770287
$355$	−4.74009	−	2.01244i	−0.251578	−	0.106809i
$356$	4.34444	+	7.52479i	0.230255	+	0.398813i
$357$	8.80925	+	5.08602i	0.466235	+	0.269181i
$358$	−5.77363	+	3.33341i	−0.305146	+	0.176176i
$359$	1.15286	+	1.99682i	0.0608457	+	0.105388i	0.894844	−	0.446380i	$-0.147287\pi$
$359$	1.15286	+	1.99682i	0.0608457	+	0.105388i	−0.833998	+	0.551768i	$0.813954\pi$
$360$	2.21942	−	0.272353i	0.116974	−	0.0143542i
$361$	−5.15348	+	18.2877i	−0.271236	+	0.962513i
$362$			6.13587i			0.322494i
$363$	2.48385	−	1.43405i	0.130368	−	0.0752682i
$364$	−6.97295	−	12.0775i	−0.365482	−	0.633033i
$365$	−5.43054	+	12.7911i	−0.284248	+	0.669515i
$366$	5.40264	+	9.35765i	0.282400	+	0.489132i
$367$	9.47038	+	5.46773i	0.494350	+	0.285413i	0.726377	−	0.687296i	$-0.241203\pi$
$367$	9.47038	+	5.46773i	0.494350	+	0.285413i	−0.232027	+	0.972709i	$0.574536\pi$
$368$		−	5.03648i		−	0.262545i
$369$	5.16256			0.268752
$370$	−16.0517	−	6.81487i	−0.834489	−	0.354288i
$371$	−6.52568	+	11.3028i	−0.338796	+	0.586813i
$372$		−	0.685205i		−	0.0355262i
$373$		−	23.3847i		−	1.21082i	−0.795915	−	0.605408i	$-0.793010\pi$
$373$		−	23.3847i		−	1.21082i	0.795915	−	0.605408i	$-0.206990\pi$
$374$	6.24787	−	10.8216i	0.323070	−	0.559573i
$375$	−8.68728	−	7.03784i	−0.448609	−	0.363433i
$376$	−3.94406	+	6.83132i	−0.203400	+	0.352298i
$377$	45.8925	−	26.4960i	2.36358	−	1.36462i
$378$	−2.01036	+	1.16068i	−0.103402	+	0.0596989i
$379$	−23.2493			−1.19424			−0.597118	−	0.802154i	$-0.703687\pi$
$379$	−23.2493			−1.19424			−0.597118	+	0.802154i	$0.703687\pi$
$380$	6.99622	−	6.78623i	0.358899	−	0.348126i
$381$	−8.92191			−0.457083
$382$	−16.3200	+	9.42238i	−0.835006	+	0.482091i
$383$	−17.9351	+	10.3548i	−0.916441	+	0.529107i	−0.882498	−	0.470317i	$-0.844140\pi$
$383$	−17.9351	+	10.3548i	−0.916441	+	0.529107i	−0.0339428	+	0.999424i	$0.510806\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	8.90730	+	11.8221i	0.453958	+	0.602510i
$386$	−8.26218	+	14.3105i	−0.420534	+	0.728386i
$387$			2.58719i			0.131514i
$388$			6.69361i			0.339817i
$389$	18.1887	−	31.5037i	0.922203	−	1.59730i	0.126203	−	0.992004i	$-0.459721\pi$
$389$	18.1887	−	31.5037i	0.922203	−	1.59730i	0.795999	−	0.605297i	$-0.206946\pi$
$390$	−5.24975	+	12.3652i	−0.265832	+	0.626138i
$391$	−22.0695			−1.11610
$392$		−	1.61129i		−	0.0813825i
$393$	−0.0475134	−	0.0274319i	−0.00239673	−	0.00138376i
$394$	3.45127	+	5.97778i	0.173873	+	0.301156i
$395$	−8.26110	−	3.50731i	−0.415661	−	0.176472i
$396$	1.42582	+	2.46960i	0.0716504	+	0.124102i
$397$	−28.6128	+	16.5196i	−1.43604	+	0.829096i	−0.997571	−	0.0696530i	$-0.977811\pi$
$397$	−28.6128	+	16.5196i	−1.43604	+	0.829096i	−0.438464	+	0.898749i	$0.644477\pi$
$398$		−	6.53029i		−	0.327334i
$399$	−3.93232	+	9.32321i	−0.196862	+	0.466745i
$400$	−4.85165	+	1.20893i	−0.242582	+	0.0604465i
$401$	−10.5982	−	18.3566i	−0.529249	−	0.916685i	−0.999418	−	0.0341092i	$-0.989141\pi$
$401$	−10.5982	−	18.3566i	−0.529249	−	0.916685i	0.470170	−	0.882576i	$-0.344193\pi$
$402$	5.89514	−	3.40356i	0.294023	−	0.169754i
$403$	3.56496	+	2.05823i	0.177583	+	0.102528i
$404$	7.02206	+	12.1626i	0.349361	+	0.605110i
$405$	2.05825	+	0.873846i	0.102275	+	0.0434217i
$406$	−20.4762			−1.01622
$407$		−	22.2392i		−	1.10236i
$408$	−3.79487	−	2.19097i	−0.187874	−	0.108469i
$409$	−5.26086	+	9.11207i	−0.260133	+	0.450563i	−0.966277	−	0.257505i	$-0.917100\pi$
$409$	−5.26086	+	9.11207i	−0.260133	+	0.450563i	0.706144	+	0.708068i	$0.250433\pi$
$410$	−11.4579	+	1.40604i	−0.565865	+	0.0694392i
$411$	−17.9824			−0.887005
$412$	−12.2073	−	7.04788i	−0.601410	−	0.347224i
$413$	2.91358	−	1.68216i	0.143368	−	0.0827735i
$414$	2.51824	−	4.36172i	0.123765	−	0.214367i
$415$	16.4418	+	21.8222i	0.807096	+	1.07121i
$416$	3.00382	+	5.20277i	0.147275	+	0.255087i
$417$		−	20.6653i		−	1.01199i
$418$	11.4530	+	4.83061i	0.560185	+	0.236273i
$419$	−26.3874			−1.28911			−0.644555	−	0.764558i	$-0.722957\pi$
$419$	−26.3874			−1.28911			−0.644555	+	0.764558i	$0.722957\pi$
$420$	4.14571	−	3.12356i	0.202290	−	0.152414i
$421$	−4.24202	−	7.34740i	−0.206743	−	0.358090i	0.743943	−	0.668243i	$-0.232953\pi$
$421$	−4.24202	−	7.34740i	−0.206743	−	0.358090i	−0.950687	+	0.310152i	$0.899620\pi$
$422$	−19.3891	−	11.1943i	−0.943847	−	0.544931i
$423$	−6.83132	+	3.94406i	−0.332150	+	0.191767i
$424$	2.81115	−	4.86905i	0.136521	−	0.236462i
$425$	5.29745	+	21.2596i	0.256964	+	1.03124i
$426$	−2.30297			−0.111579
$427$	21.7225	+	12.5415i	1.05122	+	0.606924i
$428$	14.5258	+	8.38645i	0.702129	+	0.405374i
$429$	−17.1317			−0.827126
$430$	−0.704628	−	5.74206i	−0.0339802	−	0.276907i
$431$	9.83833	−	17.0405i	0.473896	−	0.820811i	−0.525658	−	0.850696i	$-0.676181\pi$
$431$	9.83833	−	17.0405i	0.473896	−	0.820811i	0.999553	+	0.0298849i	$0.00951409\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	12.0899	+	6.98010i	0.581003	+	0.335442i	0.761532	−	0.648127i	$-0.224448\pi$
$433$	12.0899	+	6.98010i	0.581003	+	0.335442i	−0.180529	+	0.983570i	$0.557781\pi$
$434$	−0.795303	−	1.37751i	−0.0381758	−	0.0661224i
$435$	11.8690	+	15.7530i	0.569075	+	0.755299i
$436$	8.90382			0.426416
$437$	−2.72531	−	21.7837i	−0.130369	−	1.04205i
$438$			6.21454i			0.296942i
$439$	10.2610	+	17.7725i	0.489729	+	0.848236i	0.999930	−	0.0118193i	$-0.00376230\pi$
$439$	10.2610	+	17.7725i	0.489729	+	0.848236i	−0.510201	+	0.860055i	$0.670429\pi$
$440$	−3.83710	−	5.09275i	−0.182927	−	0.242787i
$441$	0.805646	−	1.39542i	0.0383641	−	0.0664485i
$442$	22.7982	−	13.1626i	1.08440	−	0.626079i
$443$	20.4256	+	11.7927i	0.970450	+	0.560290i	0.899374	−	0.437181i	$-0.144023\pi$
$443$	20.4256	+	11.7927i	0.970450	+	0.560290i	0.0710768	+	0.997471i	$0.477356\pi$
$444$	−7.79872			−0.370111
$445$	−2.36644	−	19.2843i	−0.112180	−	0.914162i
$446$	0.938256	−	1.62511i	0.0444277	−	0.0769510i
$447$	3.33682	+	1.92651i	0.157826	+	0.0911209i
$448$		−	2.32136i		−	0.109674i
$449$	−28.2500			−1.33320			−0.666601	−	0.745415i	$-0.732251\pi$
$449$	−28.2500			−1.33320			−0.666601	+	0.745415i	$0.732251\pi$
$450$	−4.80612	−	1.37886i	−0.226562	−	0.0650001i
$451$	−7.36090	−	12.7495i	−0.346611	−	0.600349i
$452$	−10.2945	−	5.94352i	−0.484212	−	0.279560i
$453$	−6.73182	+	3.88662i	−0.316289	+	0.182609i
$454$	−10.1852	−	17.6412i	−0.478013	−	0.827943i
$455$	3.79820	+	30.9518i	0.178063	+	1.45104i
$456$	1.69397	−	4.01627i	0.0793275	−	0.188079i
$457$			31.6784i			1.48185i	0.671587	+	0.740926i	$0.265613\pi$
$457$			31.6784i			1.48185i	−0.671587	+	0.740926i	$0.734387\pi$
$458$	−9.33688	+	5.39065i	−0.436284	+	0.251889i
$459$	−2.19097	−	3.79487i	−0.102266	−	0.177129i
$460$	−4.40110	+	10.3663i	−0.205203	+	0.483333i
$461$	0.595751	+	1.03187i	0.0277469	+	0.0480590i	0.879565	−	0.475778i	$-0.157833\pi$
$461$	0.595751	+	1.03187i	0.0277469	+	0.0480590i	−0.851819	+	0.523837i	$0.824500\pi$
$462$	5.73283	+	3.30985i	0.266715	+	0.153988i
$463$		−	19.8469i		−	0.922366i	−0.887305	−	0.461183i	$-0.847425\pi$
$463$		−	19.8469i		−	0.922366i	0.887305	−	0.461183i	$-0.152575\pi$
$464$	8.82078			0.409494
$465$	−0.598763	+	1.41032i	−0.0277670	+	0.0654021i
$466$	−6.78823	+	11.7576i	−0.314458	+	0.544658i
$467$		−	14.2451i		−	0.659184i	−0.944123	−	0.329592i	$-0.893089\pi$
$467$		−	14.2451i		−	0.659184i	0.944123	−	0.329592i	$-0.106911\pi$
$468$			6.00764i			0.277703i
$469$	7.90089	−	13.6847i	0.364829	−	0.631903i
$470$	14.0874	−	10.6141i	0.649803	−	0.489590i
$471$	−9.63765	+	16.6929i	−0.444080	+	0.769169i
$472$	−1.25512	+	0.724643i	−0.0577715	+	0.0333544i
$473$	6.38933	−	3.68888i	0.293782	−	0.169615i
$474$	−4.01365			−0.184353
$475$	−20.3301	+	7.85413i	−0.932809	+	0.360372i
$476$	−10.1720			−0.466235
$477$	4.86905	−	2.81115i	0.222938	−	0.128714i
$478$	1.80203	−	1.04040i	0.0824231	−	0.0475870i
$479$	14.3482	−	24.8519i	0.655588	−	1.13551i	−0.326159	−	0.945315i	$-0.605754\pi$
$479$	14.3482	−	24.8519i	0.655588	−	1.13551i	0.981746	−	0.190196i	$-0.0609123\pi$
$480$	−1.78590	+	1.34557i	−0.0815147	+	0.0614168i
$481$	23.4260	−	40.5749i	1.06813	−	1.85006i
$482$			17.0263i			0.775529i
$483$		−	11.6915i		−	0.531980i
$484$	−1.43405	+	2.48385i	−0.0651842	+	0.112902i
$485$	5.84918	−	13.7771i	0.265598	−	0.625587i
$486$	1.00000			0.0453609
$487$		−	19.6433i		−	0.890122i	−0.895500	−	0.445061i	$-0.853182\pi$
$487$		−	19.6433i		−	0.890122i	0.895500	−	0.445061i	$-0.146818\pi$
$488$	−9.35765	−	5.40264i	−0.423601	−	0.244566i
$489$	7.95838	+	13.7843i	0.359890	+	0.623348i
$490$	−1.40802	+	3.31644i	−0.0636079	+	0.149822i
$491$	4.99544	+	8.65235i	0.225441	+	0.390475i	0.956452	−	0.291891i	$-0.0942844\pi$
$491$	4.99544	+	8.65235i	0.225441	+	0.390475i	−0.731011	+	0.682366i	$0.760951\pi$
$492$	−4.47091	+	2.58128i	−0.201564	+	0.116373i
$493$		−	38.6521i		−	1.74080i
$494$	15.8074	+	20.8775i	0.711207	+	0.939324i
$495$	−0.776654	−	6.32900i	−0.0349080	−	0.284468i
$496$	0.342602	+	0.593405i	0.0153833	+	0.0266446i
$497$	−4.62980	+	2.67301i	−0.207675	+	0.119901i
$498$	10.5821	+	6.10958i	0.474196	+	0.273777i
$499$	−7.18085	−	12.4376i	−0.321459	−	0.556784i	0.659330	−	0.751854i	$-0.270840\pi$
$499$	−7.18085	−	12.4376i	−0.321459	−	0.556784i	−0.980789	+	0.195070i	$0.937507\pi$
$500$	11.0423	+	1.75131i	0.493828	+	0.0783210i
$501$	19.0151			0.849531
$502$		−	19.2514i		−	0.859233i
$503$	7.26003	+	4.19158i	0.323709	+	0.186893i	0.653044	−	0.757320i	$-0.273491\pi$
$503$	7.26003	+	4.19158i	0.323709	+	0.186893i	−0.329336	+	0.944213i	$0.606825\pi$
$504$	1.16068	−	2.01036i	0.0517008	−	0.0895484i
$505$	−3.82495	−	31.1698i	−0.170208	−	1.38704i
$506$	−14.3623			−0.638480
$507$	−19.9981	−	11.5459i	−0.888146	−	0.512771i
$508$	7.72660	−	4.46095i	0.342812	−	0.197923i
$509$	5.67635	−	9.83173i	0.251600	−	0.435784i	−0.712367	−	0.701808i	$-0.752377\pi$
$509$	5.67635	−	9.83173i	0.251600	−	0.435784i	0.963966	+	0.266024i	$0.0857100\pi$
$510$	5.89622	+	7.82569i	0.261089	+	0.346527i
$511$	7.21308	+	12.4934i	0.319088	+	0.552677i
$512$			1.00000i			0.0441942i
$513$	3.47516	−	2.63121i	0.153432	−	0.116171i
$514$	17.6914			0.780333
$515$	18.9669	+	25.1736i	0.835781	+	1.10928i
$516$	−1.29360	−	2.24057i	−0.0569474	−	0.0986357i
$517$	19.4805	+	11.2471i	0.856752	+	0.494646i
$518$	−15.6782	+	9.05181i	−0.688860	+	0.397714i
$519$	7.14712	−	12.3792i	0.313724	−	0.543386i
$520$	−1.63620	−	13.3335i	−0.0717520	−	0.584712i
$521$	−29.3742			−1.28691			−0.643453	−	0.765485i	$-0.722499\pi$
$521$	−29.3742			−1.28691			−0.643453	+	0.765485i	$0.722499\pi$
$522$	7.63902	+	4.41039i	0.334351	+	0.193037i
$523$	35.2243	+	20.3368i	1.54025	+	0.889265i	0.998822	+	0.0485186i	$0.0154500\pi$
$523$	35.2243	+	20.3368i	1.54025	+	0.889265i	0.541429	+	0.840746i	$0.317883\pi$
$524$	0.0548638			0.00239673
$525$	−11.2624	+	2.80636i	−0.491532	+	0.122480i
$526$	−5.76364	+	9.98291i	−0.251307	+	0.435276i
$527$	2.60026	−	1.50126i	0.113269	−	0.0653960i
$528$	−2.46960	−	1.42582i	−0.107476	−	0.0620510i
$529$	1.18305	+	2.04911i	0.0514371	+	0.0890917i
$530$	−10.0408	+	7.56521i	−0.436146	+	0.328612i
$531$	−1.44929			−0.0628937
$532$	−1.25612	−	10.0403i	−0.0544597	−	0.435302i
$533$		−	31.0148i		−	1.34340i
$534$	−4.34444	−	7.52479i	−0.188002	−	0.325630i
$535$	−22.5692	−	29.9547i	−0.975750	−	1.29505i
$536$	−3.40356	+	5.89514i	−0.147011	+	0.254631i
$537$	5.77363	−	3.33341i	0.249151	−	0.143847i
$538$	17.8013	+	10.2776i	0.767468	+	0.443098i
$539$	−4.59484			−0.197914
$540$	−2.21942	+	0.272353i	−0.0955086	+	0.0117202i
$541$	−12.6792	+	21.9610i	−0.545122	+	0.944179i	0.453478	+	0.891268i	$0.350183\pi$
$541$	−12.6792	+	21.9610i	−0.545122	+	0.944179i	−0.998599	+	0.0529108i	$0.983150\pi$
$542$	22.5014	+	12.9912i	0.966518	+	0.558019i
$543$		−	6.13587i		−	0.263315i
$544$	4.38194			0.187874
$545$	−18.3263	−	7.78056i	−0.785012	−	0.333283i
$546$	6.97295	+	12.0775i	0.298415	+	0.516870i
$547$	27.8110	+	16.0567i	1.18911	+	0.686535i	0.958105	−	0.286417i	$-0.0924641\pi$
$547$	27.8110	+	16.0567i	1.18911	+	0.686535i	0.231009	+	0.972952i	$0.425797\pi$
$548$	15.5732	−	8.99119i	0.665254	−	0.384085i
$549$	−5.40264	−	9.35765i	−0.230579	−	0.399375i
$550$	3.44744	+	13.8352i	0.146999	+	0.589935i
$551$	38.1515	−	4.77304i	1.62531	−	0.203338i
$552$			5.03648i			0.214367i
$553$	−8.06887	+	4.65857i	−0.343123	+	0.198102i
$554$	−2.07148	−	3.58791i	−0.0880087	−	0.152435i
$555$	16.0517	+	6.81487i	0.681357	+	0.289275i
$556$	10.3327	+	17.8967i	0.438203	+	0.758989i
$557$	−6.90306	−	3.98549i	−0.292492	−	0.168870i	0.346573	−	0.938023i	$-0.387345\pi$
$557$	−6.90306	−	3.98549i	−0.292492	−	0.168870i	−0.639065	+	0.769153i	$0.720679\pi$
$558$			0.685205i			0.0290070i
$559$	15.5429			0.657396
$560$	−2.02851	+	4.77794i	−0.0857202	+	0.201905i
$561$	−6.24787	+	10.8216i	−0.263785	+	0.456890i
$562$			8.59688i			0.362637i
$563$			13.8459i			0.583537i	0.956489	+	0.291768i	$0.0942436\pi$
$563$			13.8459i			0.583537i	−0.956489	+	0.291768i	$0.905756\pi$
$564$	3.94406	−	6.83132i	0.166075	−	0.287650i
$565$	15.9949	+	21.2290i	0.672911	+	0.893113i
$566$	7.18742	−	12.4490i	0.302110	−	0.523270i
$567$	2.01036	−	1.16068i	0.0844270	−	0.0487440i
$568$	1.99443	−	1.15149i	0.0836846	−	0.0483153i
$569$	28.6171			1.19969			0.599845	−	0.800117i	$-0.295229\pi$
$569$	28.6171			1.19969			0.599845	+	0.800117i	$0.295229\pi$
$570$	−6.99622	+	6.78623i	−0.293040	+	0.284244i
$571$	18.2331			0.763033			0.381517	−	0.924362i	$-0.375402\pi$
$571$	18.2331			0.763033			0.381517	+	0.924362i	$0.375402\pi$
$572$	14.8365	−	8.56584i	0.620344	−	0.358156i
$573$	16.3200	−	9.42238i	0.681780	−	0.393626i
$574$	−5.99208	+	10.3786i	−0.250105	+	0.433194i
$575$	18.1171	−	17.4906i	0.755537	−	0.729409i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$			37.3878i			1.55647i	0.627970	+	0.778237i	$0.283886\pi$
$577$			37.3878i			1.55647i	−0.627970	+	0.778237i	$0.716114\pi$
$578$		−	2.20137i		−	0.0915650i
$579$	8.26218	−	14.3105i	0.343365	−	0.594725i
$580$	−18.1554	−	7.70800i	−0.753860	−	0.320057i
$581$	28.3651			1.17678
$582$		−	6.69361i		−	0.277459i
$583$	−13.8848	−	8.01640i	−0.575050	−	0.332005i
$584$	−3.10727	−	5.38195i	−0.128580	−	0.222707i
$585$	5.24975	−	12.3652i	0.217051	−	0.511240i
$586$	4.23745	+	7.33948i	0.175047	+	0.303191i
$587$	1.52408	−	0.879926i	0.0629053	−	0.0363184i	−0.468217	−	0.883613i	$-0.655104\pi$
$587$	1.52408	−	0.879926i	0.0629053	−	0.0363184i	0.531123	+	0.847295i	$0.321770\pi$
$588$			1.61129i			0.0664485i
$589$	1.80292	+	2.38120i	0.0742879	+	0.0981155i
$590$	3.21657	−	0.394717i	0.132424	−	0.0162502i
$591$	−3.45127	−	5.97778i	−0.141966	−	0.245893i
$592$	6.75389	−	3.89936i	0.277583	−	0.160263i
$593$	9.65263	+	5.57295i	0.396386	+	0.228854i	0.684923	−	0.728615i	$-0.259836\pi$
$593$	9.65263	+	5.57295i	0.396386	+	0.228854i	−0.288537	+	0.957469i	$0.593169\pi$
$594$	−1.42582	−	2.46960i	−0.0585023	−	0.101329i
$595$	20.9366	+	8.88880i	0.858318	+	0.364405i
$596$	−3.85302			−0.157826
$597$			6.53029i			0.267267i
$598$	−26.2037	−	15.1287i	−1.07155	−	0.618658i
$599$	19.0286	−	32.9586i	0.777489	−	1.34665i	−0.155896	−	0.987774i	$-0.549826\pi$
$599$	19.0286	−	32.9586i	0.777489	−	1.34665i	0.933385	−	0.358877i	$-0.116840\pi$
$600$	4.85165	−	1.20893i	0.198068	−	0.0493543i
$601$	34.4084			1.40355			0.701775	−	0.712399i	$-0.252391\pi$
$601$	34.4084			1.40355			0.701775	+	0.712399i	$0.252391\pi$
$602$	−5.20118	−	3.00290i	−0.211984	−	0.122389i
$603$	−5.89514	+	3.40356i	−0.240069	+	0.138604i
$604$	3.88662	−	6.73182i	0.158144	−	0.273914i
$605$	5.12214	−	3.85925i	0.208245	−	0.156901i
$606$	−7.02206	−	12.1626i	−0.285252	−	0.494071i
$607$			16.1885i			0.657071i	0.944492	+	0.328536i	$0.106555\pi$
$607$			16.1885i			0.657071i	−0.944492	+	0.328536i	$0.893445\pi$
$608$	0.541114	+	4.32518i	0.0219451	+	0.175409i
$609$	20.4762			0.829737
$610$	14.5393	+	19.2971i	0.588679	+	0.781318i
$611$	23.6945	+	41.0401i	0.958578	+	1.66031i
$612$	3.79487	+	2.19097i	0.153398	+	0.0885647i
$613$	16.7637	−	9.67851i	0.677078	−	0.390911i	−0.121675	−	0.992570i	$-0.538827\pi$
$613$	16.7637	−	9.67851i	0.677078	−	0.390911i	0.798753	+	0.601659i	$0.205493\pi$
$614$	−10.7838	+	18.6780i	−0.435197	+	0.753784i
$615$	11.4579	−	1.40604i	0.462027	−	0.0566969i
$616$	−6.61970			−0.266715
$617$	7.58517	+	4.37930i	0.305367	+	0.176304i	0.644852	−	0.764308i	$-0.276919\pi$
$617$	7.58517	+	4.37930i	0.305367	+	0.176304i	−0.339484	+	0.940612i	$0.610253\pi$
$618$	12.2073	+	7.04788i	0.491049	+	0.283507i
$619$	36.5640			1.46963			0.734815	−	0.678268i	$-0.237269\pi$
$619$	36.5640			1.46963			0.734815	+	0.678268i	$0.237269\pi$
$620$	−0.186617	−	1.52076i	−0.00749473	−	0.0610750i
$621$	−2.51824	+	4.36172i	−0.101053	+	0.175030i
$622$	5.41641	−	3.12716i	0.217178	−	0.125388i
$623$	−17.4677	−	10.0850i	−0.699830	−	0.404047i
$624$	−3.00382	−	5.20277i	−0.120249	−	0.208278i
$625$	−21.1975	−	13.2539i	−0.847900	−	0.530157i
$626$	−17.7515			−0.709492
$627$	−11.4530	−	4.83061i	−0.457389	−	0.192916i
$628$		−	19.2753i		−	0.769169i
$629$	−17.0867	−	29.5951i	−0.681293	−	1.18003i
$630$	−4.14571	+	3.12356i	−0.165169	+	0.124446i
$631$	12.0437	−	20.8604i	0.479453	−	0.830437i	−0.520269	−	0.854002i	$-0.674168\pi$
$631$	12.0437	−	20.8604i	0.479453	−	0.830437i	0.999722	+	0.0235650i	$0.00750166\pi$
$632$	3.47593	−	2.00683i	0.138265	−	0.0798273i
$633$	19.3891	+	11.1943i	0.770648	+	0.444934i
$634$	−0.739513			−0.0293698
$635$	−19.8015	+	2.42991i	−0.785797	+	0.0964279i
$636$	−2.81115	+	4.86905i	−0.111469	+	0.193070i
$637$	−8.38318	−	4.84003i	−0.332154	−	0.191769i
$638$		−	25.1538i		−	0.995847i
$639$	2.30297			0.0911042
$640$	0.873846	−	2.05825i	0.0345418	−	0.0813595i
$641$	−12.7503	−	22.0841i	−0.503605	−	0.872270i	−0.999991	−	0.00416788i	$-0.998673\pi$
$641$	−12.7503	−	22.0841i	−0.503605	−	0.872270i	0.496386	−	0.868102i	$-0.334660\pi$
$642$	−14.5258	−	8.38645i	−0.573286	−	0.330987i
$643$	−8.09885	+	4.67587i	−0.319387	+	0.184398i	−0.651119	−	0.758975i	$-0.725700\pi$
$643$	−8.09885	+	4.67587i	−0.319387	+	0.184398i	0.331732	+	0.943374i	$0.392367\pi$
$644$	5.84574	+	10.1251i	0.230354	+	0.398985i
$645$	0.704628	+	5.74206i	0.0277447	+	0.226094i
$646$	18.9527	−	2.37113i	0.745683	−	0.0932907i
$647$			2.93501i			0.115387i	0.998334	+	0.0576935i	$0.0183746\pi$
$647$			2.93501i			0.115387i	−0.998334	+	0.0576935i	$0.981625\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	2.06643	+	3.57916i	0.0811144	+	0.140494i
$650$	−8.28370	+	28.8734i	−0.324914	+	1.13251i
$651$	0.795303	+	1.37751i	0.0311704	+	0.0539887i
$652$	−13.7843	−	7.95838i	−0.539835	−	0.311674i
$653$			13.5336i			0.529613i	0.964302	+	0.264806i	$0.0853080\pi$
$653$			13.5336i			0.529613i	−0.964302	+	0.264806i	$0.914692\pi$
$654$	−8.90382			−0.348167
$655$	−0.112923	−	0.0479425i	−0.00441228	−	0.00187327i
$656$	2.58128	−	4.47091i	0.100782	−	0.174560i
$657$		−	6.21454i		−	0.242452i
$658$		−	18.3112i		−	0.713844i
$659$	−11.2236	+	19.4399i	−0.437210	+	0.757270i	−0.997473	−	0.0710447i	$-0.977367\pi$
$659$	−11.2236	+	19.4399i	−0.437210	+	0.757270i	0.560263	+	0.828315i	$0.310700\pi$
$660$	3.83710	+	5.09275i	0.149359	+	0.198235i
$661$	−4.81389	+	8.33791i	−0.187239	+	0.324307i	−0.944329	−	0.329004i	$-0.893287\pi$
$661$	−4.81389	+	8.33791i	−0.187239	+	0.324307i	0.757090	+	0.653311i	$0.226620\pi$
$662$	−3.93574	+	2.27230i	−0.152967	+	0.0883156i
$663$	−22.7982	+	13.1626i	−0.885410	+	0.511191i
$664$	−12.2192			−0.474196
$665$	−6.18826	+	21.7631i	−0.239971	+	0.843937i
$666$	7.79872			0.302194
$667$	−38.4737	+	22.2128i	−1.48971	+	0.860084i
$668$	−16.4675	+	9.50754i	−0.637148	+	0.367858i
$669$	−0.938256	+	1.62511i	−0.0362751	+	0.0628302i
$670$	12.1568	−	9.15949i	0.469659	−	0.353862i
$671$	−15.4064	+	26.6847i	−0.594758	+	1.03015i
$672$			2.32136i			0.0895484i
$673$		−	3.35484i		−	0.129320i	−0.997907	−	0.0646598i	$-0.979404\pi$
$673$		−	3.35484i		−	0.129320i	0.997907	−	0.0646598i	$-0.0205962\pi$
$674$	−10.3626	+	17.9486i	−0.399153	+	0.691354i
$675$	4.80612	+	1.37886i	0.184987	+	0.0530724i
$676$	23.0918			0.888146
$677$			18.6287i			0.715958i	0.933730	+	0.357979i	$0.116534\pi$
$677$			18.6287i			0.715958i	−0.933730	+	0.357979i	$0.883466\pi$
$678$	10.2945	+	5.94352i	0.395357	+	0.228260i
$679$	−7.76914	−	13.4565i	−0.298152	−	0.516415i
$680$	−9.01912	−	3.82914i	−0.345868	−	0.146841i
$681$	10.1852	+	17.6412i	0.390296	+	0.676013i
$682$	1.69218	−	0.976981i	0.0647970	−	0.0374105i
$683$		−	22.3842i		−	0.856506i	−0.903659	−	0.428253i	$-0.859129\pi$
$683$		−	22.3842i		−	0.856506i	0.903659	−	0.428253i	$-0.140871\pi$
$684$	−1.69397	+	4.01627i	−0.0647707	+	0.153566i
$685$	−39.9104	+	4.89755i	−1.52490	+	0.187126i
$686$	9.99495	+	17.3118i	0.381609	+	0.660966i
$687$	9.33688	−	5.39065i	0.356224	−	0.205666i
$688$	2.24057	+	1.29360i	0.0854211	+	0.0493179i
$689$	−16.8884	−	29.2515i	−0.643396	−	1.11439i
$690$	4.40110	−	10.3663i	0.167547	−	0.394639i
$691$	−43.1700			−1.64226			−0.821132	−	0.570738i	$-0.806657\pi$
$691$	−43.1700			−1.64226			−0.821132	+	0.570738i	$0.806657\pi$
$692$			14.2942i			0.543386i
$693$	−5.73283	−	3.30985i	−0.217772	−	0.125731i
$694$	−6.20108	+	10.7406i	−0.235390	+	0.407707i
$695$	−5.62826	−	45.8651i	−0.213492	−	1.73976i
$696$	−8.82078			−0.334351
$697$	−19.5912	−	11.3110i	−0.742071	−	0.428435i
$698$	12.4848	−	7.20813i	0.472558	−	0.272832i
$699$	6.78823	−	11.7576i	0.256754	−	0.444711i
$700$	8.35036	−	8.06159i	0.315614	−	0.304699i
$701$	−14.1571	−	24.5208i	−0.534705	−	0.926137i	−0.999178	−	0.0405493i	$-0.987089\pi$
$701$	−14.1571	−	24.5208i	−0.534705	−	0.926137i	0.464472	−	0.885588i	$-0.346244\pi$
$702$		−	6.00764i		−	0.226744i
$703$	27.1018	−	20.5200i	1.02216	−	0.773928i
$704$	2.85165			0.107476
$705$	−14.0874	+	10.6141i	−0.530562	+	0.399749i
$706$	−17.8354	−	30.8918i	−0.671243	−	1.16263i
$707$	−28.2337	−	16.3007i	−1.06184	−	0.613052i
$708$	1.25512	−	0.724643i	0.0471702	−	0.0272338i
$709$	8.52409	−	14.7642i	0.320129	−	0.554480i	−0.660385	−	0.750927i	$-0.729607\pi$
$709$	8.52409	−	14.7642i	0.320129	−	0.554480i	0.980514	+	0.196447i	$0.0629404\pi$
$710$	−5.11126	+	0.627221i	−0.191822	+	0.0235392i
$711$	4.01365			0.150524
$712$	7.52479	+	4.34444i	0.282003	+	0.162815i
$713$	−2.98867	−	1.72551i	−0.111927	−	0.0646208i
$714$	10.1720			0.380679
$715$	−38.0224	+	4.66586i	−1.42196	+	0.174493i
$716$	−3.33341	+	5.77363i	−0.124575	+	0.215771i
$717$	−1.80203	+	1.04040i	−0.0672981	+	0.0388546i
$718$	1.99682	+	1.15286i	0.0745205	+	0.0430244i
$719$	−1.65729	−	2.87050i	−0.0618063	−	0.107052i	0.833467	−	0.552570i	$-0.186353\pi$
$719$	−1.65729	−	2.87050i	−0.0618063	−	0.107052i	−0.895273	+	0.445518i	$0.853019\pi$
$720$	1.78590	−	1.34557i	0.0665565	−	0.0501466i
$721$	32.7213			1.21861
$722$	4.68083	+	18.4144i	0.174202	+	0.685313i
$723$		−	17.0263i		−	0.633217i
$724$	3.06793	+	5.31382i	0.114019	+	0.197486i
$725$	30.6327	+	31.7300i	1.13767	+	1.17842i
$726$	1.43405	−	2.48385i	0.0532226	−	0.0921843i
$727$	−29.7663	+	17.1856i	−1.10397	+	0.637379i	−0.937261	−	0.348627i	$-0.886648\pi$
$727$	−29.7663	+	17.1856i	−1.10397	+	0.637379i	−0.166711	+	0.986006i	$0.553315\pi$
$728$	−12.0775	−	6.97295i	−0.447622	−	0.258435i
$729$	−1.00000			−0.0370370
$730$	1.69255	+	13.7927i	0.0626439	+	0.510489i
$731$	5.66845	−	9.81805i	0.209655	−	0.363134i
$732$	9.35765	+	5.40264i	0.345869	+	0.199687i
$733$			39.0068i			1.44075i	0.693585	+	0.720375i	$0.256030\pi$
$733$			39.0068i			1.44075i	−0.693585	+	0.720375i	$0.743970\pi$
$734$	10.9355			0.403635
$735$	1.40802	−	3.31644i	0.0519356	−	0.122329i
$736$	−2.51824	−	4.36172i	−0.0928235	−	0.160775i
$737$	16.8109	+	9.70576i	0.619236	+	0.357516i
$738$	4.47091	−	2.58128i	0.164576	−	0.0950182i
$739$	−4.19339	−	7.26316i	−0.154256	−	0.267180i	0.778532	−	0.627605i	$-0.215965\pi$
$739$	−4.19339	−	7.26316i	−0.154256	−	0.267180i	−0.932788	+	0.360426i	$0.882631\pi$
$740$	−17.3086	+	2.12400i	−0.636278	+	0.0780798i
$741$	−15.8074	−	20.8775i	−0.580698	−	0.766955i
$742$			13.0514i			0.479131i
$743$	−1.64985	+	0.952540i	−0.0605270	+	0.0349453i	−0.529958	−	0.848024i	$-0.677792\pi$
$743$	−1.64985	+	0.952540i	−0.0605270	+	0.0349453i	0.469431	+	0.882969i	$0.344459\pi$
$744$	−0.342602	−	0.593405i	−0.0125604	−	0.0217553i
$745$	7.93049	+	3.36695i	0.290551	+	0.123355i
$746$	−11.6924	−	20.2518i	−0.428088	−	0.741470i
$747$	−10.5821	−	6.10958i	−0.387179	−	0.223538i
$748$		−	12.4957i		−	0.456890i
$749$	−38.9359			−1.42269
$750$	−11.0423	−	1.75131i	−0.403209	−	0.0639488i
$751$	−5.63534	+	9.76069i	−0.205636	+	0.356173i	−0.950335	−	0.311228i	$-0.899260\pi$
$751$	−5.63534	+	9.76069i	−0.205636	+	0.356173i	0.744699	+	0.667401i	$0.232593\pi$
$752$			7.88813i			0.287650i
$753$			19.2514i			0.701561i
$754$	26.4960	−	45.8925i	0.964929	−	1.67131i
$755$	−13.8822	+	10.4595i	−0.505225	+	0.380659i
$756$	−1.16068	+	2.01036i	−0.0422135	+	0.0731159i
$757$	38.7692	−	22.3834i	1.40909	−	0.813540i	0.413792	−	0.910372i	$-0.364204\pi$
$757$	38.7692	−	22.3834i	1.40909	−	0.813540i	0.995301	+	0.0968318i	$0.0308709\pi$
$758$	−20.1345	+	11.6246i	−0.731317	+	0.422226i
$759$	14.3623			0.521317
$760$	2.66579	−	9.37516i	0.0966985	−	0.340073i
$761$	−33.7181			−1.22228			−0.611139	−	0.791523i	$-0.709289\pi$
$761$	−33.7181			−1.22228			−0.611139	+	0.791523i	$0.709289\pi$
$762$	−7.72660	+	4.46095i	−0.279905	+	0.161603i
$763$	−17.8998	+	10.3345i	−0.648018	+	0.374133i
$764$	−9.42238	+	16.3200i	−0.340890	+	0.590439i
$765$	−5.89622	−	7.82569i	−0.213178	−	0.282938i
$766$	−10.3548	+	17.9351i	−0.374135	+	0.648021i
$767$			8.70680i			0.314384i
$768$		−	1.00000i		−	0.0360844i
$769$	16.2178	−	28.0901i	0.584830	−	1.01296i	−0.410066	−	0.912056i	$-0.634494\pi$
$769$	16.2178	−	28.0901i	0.584830	−	1.01296i	0.994897	−	0.100900i	$-0.0321723\pi$
$770$	13.6250	+	5.78460i	0.491011	+	0.208462i
$771$	−17.6914			−0.637139
$772$			16.5244i			0.594725i
$773$	35.2122	+	20.3298i	1.26649	+	0.731211i	0.974323	−	0.225155i	$-0.0722888\pi$
$773$	35.2122	+	20.3298i	1.26649	+	0.731211i	0.292172	+	0.956366i	$0.405622\pi$
$774$	1.29360	+	2.24057i	0.0464973	+	0.0805358i
$775$	−0.944801	+	3.29317i	−0.0339383	+	0.118294i
$776$	3.34681	+	5.79684i	0.120143	+	0.208094i
$777$	15.6782	−	9.05181i	0.562452	−	0.324732i
$778$		−	36.3774i		−	1.30419i
$779$	8.74524	−	20.7343i	0.313331	−	0.742882i
$780$	1.63620	+	13.3335i	0.0585853	+	0.477415i
$781$	−3.28363	−	5.68742i	−0.117498	−	0.203512i
$782$	−19.1128	+	11.0348i	−0.683471	+	0.394602i
$783$	−7.63902	−	4.41039i	−0.272996	−	0.157614i
$784$	−0.805646	−	1.39542i	−0.0287731	−	0.0498364i
$785$	−16.8436	+	39.6734i	−0.601175	+	1.41600i
$786$	−0.0548638			−0.00195693
$787$		−	33.0432i		−	1.17786i	−0.808183	−	0.588931i	$-0.799549\pi$
$787$		−	33.0432i		−	1.17786i	0.808183	−	0.588931i	$-0.200451\pi$
$788$	5.97778	+	3.45127i	0.212949	+	0.122946i
$789$	5.76364	−	9.98291i	0.205191	−	0.355401i
$790$	−8.90798	+	1.09313i	−0.316932	+	0.0388918i
$791$	27.5941			0.981133
$792$	2.46960	+	1.42582i	0.0877534	+	0.0506645i
$793$	−56.2174	+	32.4571i	−1.99634	+	1.15259i
$794$	−16.5196	+	28.6128i	−0.586259	+	1.01543i
$795$	10.0408	−	7.56521i	0.356112	−	0.268310i
$796$	−3.26514	−	5.65540i	−0.115730	−	0.200450i
$797$			25.1288i			0.890109i	0.895504	+	0.445054i	$0.146816\pi$
$797$			25.1288i			0.890109i	−0.895504	+	0.445054i	$0.853184\pi$
$798$	1.25612	+	10.0403i	0.0444661	+	0.355423i
$799$	34.5653			1.22283
$800$	−3.59719	+	3.47279i	−0.127180	+	0.122782i
$801$	4.34444	+	7.52479i	0.153503	+	0.265875i
$802$	−18.3566	−	10.5982i	−0.648194	−	0.374235i
$803$	−15.3474	+	8.86083i	−0.541599	+	0.312692i
$804$	3.40356	−	5.89514i	0.120034	−	0.207906i
$805$	−3.18420	−	25.9483i	−0.112228	−	0.914557i
$806$	4.11647			0.144996
$807$	−17.8013	−	10.2776i	−0.626635	−	0.361788i
$808$	12.1626	+	7.02206i	0.427878	+	0.247035i
$809$	22.9578			0.807152			0.403576	−	0.914946i	$-0.367767\pi$
$809$	22.9578			0.807152			0.403576	+	0.914946i	$0.367767\pi$
$810$	2.21942	−	0.272353i	0.0779825	−	0.00956950i
$811$	−27.0425	+	46.8390i	−0.949590	+	1.64474i	−0.203301	+	0.979116i	$0.565167\pi$
$811$	−27.0425	+	46.8390i	−0.949590	+	1.64474i	−0.746289	+	0.665622i	$0.768166\pi$
$812$	−17.7329	+	10.2381i	−0.622303	+	0.359287i
$813$	−22.5014	−	12.9912i	−0.789159	−	0.455621i
$814$	−11.1196	−	19.2597i	−0.389742	−	0.675052i
$815$	21.4172	+	28.4257i	0.750211	+	0.995708i
$816$	−4.38194			−0.153398
$817$	10.3909	+	4.38263i	0.363531	+	0.153329i
$818$			10.5217i			0.367883i
$819$	−6.97295	−	12.0775i	−0.243655	−	0.422022i
$820$	−9.21980	+	6.94661i	−0.321970	+	0.242586i
$821$	5.40068	−	9.35426i	0.188485	−	0.326466i	−0.756260	−	0.654271i	$-0.772976\pi$
$821$	5.40068	−	9.35426i	0.188485	−	0.326466i	0.944745	+	0.327805i	$0.106309\pi$
$822$	−15.5732	+	8.99119i	−0.543178	+	0.313604i
$823$	29.3326	+	16.9352i	1.02247	+	0.590324i	0.914819	−	0.403865i	$-0.132333\pi$
$823$	29.3326	+	16.9352i	1.02247	+	0.590324i	0.107652	+	0.994189i	$0.465667\pi$
$824$	−14.0958			−0.491049
$825$	−3.44744	−	13.8352i	−0.120025	−	0.481680i
$826$	1.68216	−	2.91358i	0.0585297	−	0.101376i
$827$	−14.8973	−	8.60097i	−0.518030	−	0.299085i	0.218098	−	0.975927i	$-0.430015\pi$
$827$	−14.8973	−	8.60097i	−0.518030	−	0.299085i	−0.736128	+	0.676842i	$0.763348\pi$
$828$		−	5.03648i		−	0.175030i
$829$	−15.3463			−0.532998			−0.266499	−	0.963835i	$-0.585867\pi$
$829$	−15.3463			−0.532998			−0.266499	+	0.963835i	$0.585867\pi$
$830$	25.1501	+	10.6777i	0.872973	+	0.370627i
$831$	2.07148	+	3.58791i	0.0718588	+	0.124463i
$832$	5.20277	+	3.00382i	0.180374	+	0.104139i
$833$	−6.11464	+	3.53029i	−0.211860	+	0.122317i
$834$	−10.3327	−	17.8967i	−0.357791	−	0.619712i
$835$	42.2024	−	5.17881i	1.46048	−	0.179220i
$836$	12.3339	−	1.54307i	0.426577	−	0.0533680i
$837$		−	0.685205i		−	0.0236841i
$838$	−22.8522	+	13.1937i	−0.789415	+	0.455769i
$839$	22.5501	+	39.0579i	0.778516	+	1.34843i	0.932797	+	0.360402i	$0.117361\pi$
$839$	22.5501	+	39.0579i	0.778516	+	1.34843i	−0.154281	+	0.988027i	$0.549306\pi$
$840$	2.02851	−	4.77794i	0.0699902	−	0.164855i
$841$	−24.4030	−	42.2673i	−0.841484	−	1.45749i
$842$	−7.34740	−	4.24202i	−0.253208	−	0.146190i
$843$		−	8.59688i		−	0.296092i
$844$	−22.3886			−0.770648
$845$	−47.5287	−	20.1787i	−1.63504	−	0.694167i
$846$	−3.94406	+	6.83132i	−0.135600	+	0.234866i
$847$		−	6.65790i		−	0.228768i
$848$		−	5.62229i		−	0.193070i
$849$	−7.18742	+	12.4490i	−0.246672	+	0.427248i
$850$	15.2175	+	15.7626i	0.521957	+	0.540654i
$851$	−19.6390	+	34.0158i	−0.673217	+	1.16605i
$852$	−1.99443	+	1.15149i	−0.0683282	+	0.0394493i
$853$	−11.3790	+	6.56967i	−0.389609	+	0.224941i	−0.681991	−	0.731361i	$-0.738886\pi$
$853$	−11.3790	+	6.56967i	−0.389609	+	0.224941i	0.292381	+	0.956302i	$0.405552\pi$
$854$	25.0829			0.858320
$855$	6.99622	−	6.78623i	0.239266	−	0.232084i
$856$	16.7729			0.573286
$857$	−19.8940	+	11.4858i	−0.679566	+	0.392348i	−0.799692	−	0.600411i	$-0.795004\pi$
$857$	−19.8940	+	11.4858i	−0.679566	+	0.392348i	0.120125	+	0.992759i	$0.461670\pi$
$858$	−14.8365	+	8.56584i	−0.506509	+	0.292433i
$859$	−11.2488	+	19.4834i	−0.383803	+	0.664766i	−0.991602	−	0.129325i	$-0.958719\pi$
$859$	−11.2488	+	19.4834i	−0.383803	+	0.664766i	0.607800	+	0.794090i	$0.292052\pi$
$860$	−3.48126	−	4.62046i	−0.118710	−	0.157556i
$861$	5.99208	−	10.3786i	0.204209	−	0.353701i
$862$		−	19.6767i		−	0.670190i
$863$			24.1235i			0.821175i	0.911821	+	0.410587i	$0.134676\pi$
$863$			24.1235i			0.821175i	−0.911821	+	0.410587i	$0.865324\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	12.4910	−	29.4211i	0.424706	−	1.00035i
$866$	13.9602			0.474387
$867$			2.20137i			0.0747625i
$868$	−1.37751	−	0.795303i	−0.0467556	−	0.0269943i
$869$	−5.72276	−	9.91212i	−0.194131	−	0.336246i
$870$	18.1554	+	7.70800i	0.615525	+	0.261326i
$871$	20.4474	+	35.4159i	0.692833	+	1.20002i
$872$	7.71093	−	4.45191i	0.261125	−	0.150761i
$873$			6.69361i			0.226544i
$874$	−13.2520	−	17.5026i	−0.448256	−	0.592033i
$875$	−24.2317	+	9.29584i	−0.819181	+	0.314257i
$876$	3.10727	+	5.38195i	0.104985	+	0.181839i
$877$	−1.11105	+	0.641465i	−0.0375175	+	0.0216607i	−0.518641	−	0.854992i	$-0.673562\pi$
$877$	−1.11105	+	0.641465i	−0.0375175	+	0.0216607i	0.481124	+	0.876653i	$0.340229\pi$
$878$	17.7725	+	10.2610i	0.599793	+	0.346291i
$879$	−4.23745	−	7.33948i	−0.142926	−	0.247554i
$880$	−5.86941	−	2.49190i	−0.197858	−	0.0840019i
$881$	−18.1444			−0.611301			−0.305650	−	0.952144i	$-0.598874\pi$
$881$	−18.1444			−0.611301			−0.305650	+	0.952144i	$0.598874\pi$
$882$		−	1.61129i		−	0.0542550i
$883$	39.6706	+	22.9039i	1.33502	+	0.770776i	0.986065	−	0.166362i	$-0.0532021\pi$
$883$	39.6706	+	22.9039i	1.33502	+	0.770776i	0.348958	+	0.937138i	$0.386535\pi$
$884$	13.1626	−	22.7982i	0.442705	−	0.766787i
$885$	−3.21657	+	0.394717i	−0.108124	+	0.0132683i
$886$	23.5855			0.792369
$887$	−50.4856	−	29.1479i	−1.69514	−	0.978689i	−0.950243	−	0.311509i	$-0.899166\pi$
$887$	−50.4856	−	29.1479i	−1.69514	−	0.978689i	−0.744896	−	0.667180i	$-0.767501\pi$
$888$	−6.75389	+	3.89936i	−0.226646	+	0.130854i
$889$	−10.3555	+	17.9362i	−0.347312	+	0.601561i
$890$	−11.6915	−	15.5174i	−0.391901	−	0.520146i
$891$	1.42582	+	2.46960i	0.0477669	+	0.0827347i
$892$		−	1.87651i		−	0.0628302i
$893$	4.26837	+	34.1176i	0.142836	+	1.14170i
$894$	3.85302			0.128864
$895$	11.9063	−	8.97070i	0.397982	−	0.299857i
$896$	−1.16068	−	2.01036i	−0.0387756	−	0.0671613i
$897$	26.2037	+	15.1287i	0.874914	+	0.505132i
$898$	−24.4653	+	14.1250i	−0.816416	+	0.471358i
$899$	3.02202	−	5.23429i	0.100790	−	0.174573i
$900$	−4.85165	+	1.20893i	−0.161722	+	0.0402977i
$901$	−24.6365			−0.820762
$902$	−12.7495	−	7.36090i	−0.424511	−	0.245091i
$903$	5.20118	+	3.00290i	0.173084	+	0.0999303i
$904$	−11.8870			−0.395357
$905$	−1.67112	−	13.6181i	−0.0555499	−	0.452680i
$906$	−3.88662	+	6.73182i	−0.129124	+	0.223650i
$907$	−27.2008	+	15.7044i	−0.903187	+	0.521455i	−0.878233	−	0.478233i	$-0.841277\pi$
$907$	−27.2008	+	15.7044i	−0.903187	+	0.521455i	−0.0249542	+	0.999689i	$0.507944\pi$
$908$	−17.6412	−	10.1852i	−0.585444	−	0.338006i
$909$	7.02206	+	12.1626i	0.232907	+	0.403407i
$910$	18.7652	+	24.9060i	0.622062	+	0.825624i
$911$	19.8665			0.658206			0.329103	−	0.944294i	$-0.393254\pi$
$911$	19.8665			0.658206			0.329103	+	0.944294i	$0.393254\pi$
$912$	−0.541114	−	4.32518i	−0.0179181	−	0.143221i
$913$			34.8448i			1.15319i
$914$	15.8392	+	27.4343i	0.523914	+	0.907445i
$915$	−14.5393	−	19.2971i	−0.480655	−	0.637943i
$916$	−5.39065	+	9.33688i	−0.178112	+	0.308499i
$917$	−0.110296	+	0.0636793i	−0.00364228	+	0.00210287i
$918$	−3.79487	−	2.19097i	−0.125249	−	0.0723127i
$919$	40.8314			1.34690			0.673451	−	0.739231i	$-0.264811\pi$
$919$	40.8314			1.34690			0.673451	+	0.739231i	$0.264811\pi$
$920$	1.37170	+	11.1781i	0.0452235	+	0.368530i
$921$	10.7838	−	18.6780i	0.355337	−	0.615462i
$922$	1.03187	+	0.595751i	0.0339828	+	0.0196200i
$923$		−	13.8354i		−	0.455399i
$924$	6.61970			0.217772
$925$	37.4815	+	10.7533i	1.23238	+	0.353568i
$926$	−9.92347	−	17.1880i	−0.326106	−	0.564831i
$927$	−12.2073	−	7.04788i	−0.400940	−	0.231483i
$928$	7.63902	−	4.41039i	0.250763	−	0.144778i
$929$	10.3109	+	17.8591i	0.338291	+	0.585937i	0.984111	−	0.177553i	$-0.0568180\pi$
$929$	10.3109	+	17.8591i	0.338291	+	0.585937i	−0.645821	+	0.763489i	$0.723485\pi$
$930$	0.186617	+	1.52076i	0.00611942	+	0.0498676i
$931$	−4.23964	−	5.59950i	−0.138949	−	0.183516i
$932$			13.5765i			0.444711i
$933$	−5.41641	+	3.12716i	−0.177325	+	0.102379i
$934$	−7.12255	−	12.3366i	−0.233057	−	0.403666i
$935$	−10.9193	+	25.7194i	−0.357101	+	0.841113i
$936$	3.00382	+	5.20277i	0.0981830	+	0.170058i
$937$	−11.5342	−	6.65926i	−0.376805	−	0.217548i	0.299622	−	0.954058i	$-0.403139\pi$
$937$	−11.5342	−	6.65926i	−0.376805	−	0.217548i	−0.676427	+	0.736509i	$0.736473\pi$
$938$		−	15.8018i		−	0.515946i
$939$	17.7515			0.579298
$940$	6.89300	−	16.2357i	0.224825	−	0.529551i
$941$	2.77725	−	4.81033i	0.0905356	−	0.156812i	−0.817201	−	0.576353i	$-0.804475\pi$
$941$	2.77725	−	4.81033i	0.0905356	−	0.156812i	0.907737	+	0.419540i	$0.137809\pi$
$942$			19.2753i			0.628023i
$943$			26.0011i			0.846713i
$944$	−0.724643	+	1.25512i	−0.0235851	+	0.0408506i
$945$	4.14571	−	3.12356i	0.134860	−	0.101609i
$946$	3.68888	−	6.38933i	0.119936	−	0.207735i
$947$	1.05045	−	0.606477i	0.0341350	−	0.0197079i	−0.482835	−	0.875711i	$-0.660393\pi$
$947$	1.05045	−	0.606477i	0.0341350	−	0.0197079i	0.516970	+	0.856003i	$0.327060\pi$
$948$	−3.47593	+	2.00683i	−0.112893	+	0.0651787i
$949$	−37.3347			−1.21194
$950$	−13.6793	+	16.9669i	−0.443815	+	0.550480i
$951$	0.739513			0.0239804
$952$	−8.80925	+	5.08602i	−0.285510	+	0.164839i
$953$	5.12855	−	2.96097i	0.166130	−	0.0959153i	−0.414630	−	0.909990i	$-0.636089\pi$
$953$	5.12855	−	2.96097i	0.166130	−	0.0959153i	0.580760	+	0.814075i	$0.302756\pi$
$954$	2.81115	−	4.86905i	0.0910142	−	0.157641i
$955$	33.6548	−	25.3570i	1.08904	−	0.820534i
$956$	1.04040	−	1.80203i	0.0336491	−	0.0582819i
$957$			25.1538i			0.813105i
$958$		−	28.6965i		−	0.927141i
$959$	−20.8718	+	36.1510i	−0.673985	+	1.16738i
$960$	−0.873846	+	2.05825i	−0.0282032	+	0.0664297i
$961$	−30.5305			−0.984855
$962$		−	46.8519i		−	1.51057i
$963$	14.5258	+	8.38645i	0.468086	+	0.270249i
$964$	8.51317	+	14.7453i	0.274191	+	0.474913i
$965$	14.4397	−	34.0113i	0.464832	−	1.09486i
$966$	−5.84574	−	10.1251i	−0.188084	−	0.325770i
$967$	38.8853	−	22.4505i	1.25047	−	0.721958i	0.279265	−	0.960214i	$-0.409909\pi$
$967$	38.8853	−	22.4505i	1.25047	−	0.721958i	0.971202	+	0.238256i	$0.0765758\pi$
$968$			2.86810i			0.0921843i
$969$	−18.9527	+	2.37113i	−0.608848	+	0.0761715i
$970$	−1.82302	−	14.8559i	−0.0585337	−	0.476995i
$971$	−3.97050	−	6.87710i	−0.127419	−	0.220697i	0.795257	−	0.606273i	$-0.207336\pi$
$971$	−3.97050	−	6.87710i	−0.127419	−	0.220697i	−0.922676	+	0.385576i	$0.874003\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	−41.5447	−	23.9858i	−1.33186	−	0.768950i
$974$	−9.82164	−	17.0116i	−0.314706	−	0.545086i
$975$	8.28370	−	28.8734i	0.265291	−	0.924690i
$976$	−10.8053			−0.345869
$977$		−	25.2607i		−	0.808162i	−0.914723	−	0.404081i	$-0.867591\pi$
$977$		−	25.2607i		−	0.808162i	0.914723	−	0.404081i	$-0.132409\pi$
$978$	13.7843	+	7.95838i	0.440774	+	0.254481i
$979$	12.3888	−	21.4581i	0.395948	−	0.685802i
$980$	0.438840	+	3.57613i	0.0140182	+	0.114235i
$981$	8.90382			0.284277
$982$	8.65235	+	4.99544i	0.276108	+	0.159411i
$983$	−9.18945	+	5.30553i	−0.293098	+	0.169220i	−0.639338	−	0.768926i	$-0.720792\pi$
$983$	−9.18945	+	5.30553i	−0.293098	+	0.169220i	0.346240	+	0.938146i	$0.387458\pi$
$984$	−2.58128	+	4.47091i	−0.0822882	+	0.142527i
$985$	−9.28788	−	12.3272i	−0.295937	−	0.392778i
$986$	−19.3260	−	33.4737i	−0.615467	−	1.06602i
$987$			18.3112i			0.582851i
$988$	24.1283	+	10.1768i	0.767625	+	0.323767i
$989$	−13.0303			−0.414340
$990$	−3.83710	−	5.09275i	−0.121951	−	0.161858i
$991$	10.6138	+	18.3837i	0.337159	+	0.583976i	0.983897	−	0.178736i	$-0.0572007\pi$
$991$	10.6138	+	18.3837i	0.337159	+	0.583976i	−0.646738	+	0.762712i	$0.723867\pi$
$992$	0.593405	+	0.342602i	0.0188406	+	0.0108776i
$993$	3.93574	−	2.27230i	0.124897	−	0.0721093i
$994$	−2.67301	+	4.62980i	−0.0847829	+	0.146848i
$995$	1.77854	+	14.4935i	0.0563836	+	0.459473i
$996$	12.2192			0.387179
$997$	34.4427	+	19.8855i	1.09081	+	0.629780i	0.933792	−	0.357816i	$-0.116478\pi$
$997$	34.4427	+	19.8855i	1.09081	+	0.629780i	0.157019	+	0.987596i	$0.449812\pi$
$998$	−12.4376	−	7.18085i	−0.393705	−	0.227306i
$999$	−7.79872			−0.246740

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.q.c.349.7	yes	20
3.2	odd	2		1710.2.t.c.919.4		20
5.4	even	2	inner	570.2.q.c.349.5	yes	20
15.14	odd	2		1710.2.t.c.919.6		20
19.11	even	3	inner	570.2.q.c.49.5	✓	20
57.11	odd	6		1710.2.t.c.1189.6		20
95.49	even	6	inner	570.2.q.c.49.7	yes	20
285.239	odd	6		1710.2.t.c.1189.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.q.c.49.5	✓	20	19.11	even	3	inner
570.2.q.c.49.7	yes	20	95.49	even	6	inner
570.2.q.c.349.5	yes	20	5.4	even	2	inner
570.2.q.c.349.7	yes	20	1.1	even	1	trivial
1710.2.t.c.919.4		20	3.2	odd	2
1710.2.t.c.919.6		20	15.14	odd	2
1710.2.t.c.1189.4		20	285.239	odd	6
1710.2.t.c.1189.6		20	57.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.78590 + 1.34557i) q^{5} +(-0.500000 + 0.866025i) q^{6} +2.32136i q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.78590 + 1.34557i) q^{5} +(-0.500000 + 0.866025i) q^{6} +2.32136i q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.873846 + 2.05825i) q^{10} -2.85165 q^{11} +1.00000i q^{12} +(-5.20277 - 3.00382i) q^{13} +(1.16068 + 2.01036i) q^{14} +(0.873846 - 2.05825i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.79487 + 2.19097i) q^{17} -1.00000i q^{18} +(-2.63121 - 3.47516i) q^{19} +(0.272353 + 2.21942i) q^{20} +(-1.16068 - 2.01036i) q^{21} +(-2.46960 + 1.42582i) q^{22} +(4.36172 + 2.51824i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.37886 - 4.80612i) q^{25} -6.00764 q^{26} +1.00000i q^{27} +(2.01036 + 1.16068i) q^{28} +(-4.41039 + 7.63902i) q^{29} +(-0.272353 - 2.21942i) q^{30} -0.685205 q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.46960 - 1.42582i) q^{33} +(-2.19097 + 3.79487i) q^{34} +(-3.12356 - 4.14571i) q^{35} +(-0.500000 - 0.866025i) q^{36} +7.79872i q^{37} +(-4.01627 - 1.69397i) q^{38} +6.00764 q^{39} +(1.34557 + 1.78590i) q^{40} +(2.58128 + 4.47091i) q^{41} +(-2.01036 - 1.16068i) q^{42} +(-2.24057 + 1.29360i) q^{43} +(-1.42582 + 2.46960i) q^{44} +(0.272353 + 2.21942i) q^{45} +5.03648 q^{46} +(-6.83132 - 3.94406i) q^{47} +(0.866025 + 0.500000i) q^{48} +1.61129 q^{49} +(-1.20893 - 4.85165i) q^{50} +(2.19097 - 3.79487i) q^{51} +(-5.20277 + 3.00382i) q^{52} +(4.86905 + 2.81115i) q^{53} +(0.500000 + 0.866025i) q^{54} +(5.09275 - 3.83710i) q^{55} +2.32136 q^{56} +(4.01627 + 1.69397i) q^{57} +8.82078i q^{58} +(-0.724643 - 1.25512i) q^{59} +(-1.34557 - 1.78590i) q^{60} +(5.40264 - 9.35765i) q^{61} +(-0.593405 + 0.342602i) q^{62} +(2.01036 + 1.16068i) q^{63} -1.00000 q^{64} +(13.3335 - 1.63620i) q^{65} +(1.42582 - 2.46960i) q^{66} +(-5.89514 - 3.40356i) q^{67} +4.38194i q^{68} -5.03648 q^{69} +(-4.77794 - 2.02851i) q^{70} +(1.15149 + 1.99443i) q^{71} +(-0.866025 - 0.500000i) q^{72} +(5.38195 - 3.10727i) q^{73} +(3.89936 + 6.75389i) q^{74} +(1.20893 + 4.85165i) q^{75} +(-4.32518 + 0.541114i) q^{76} -6.61970i q^{77} +(5.20277 - 3.00382i) q^{78} +(2.00683 + 3.47593i) q^{79} +(2.05825 + 0.873846i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.47091 + 2.58128i) q^{82} -12.2192i q^{83} -2.32136 q^{84} +(3.82914 - 9.01912i) q^{85} +(-1.29360 + 2.24057i) q^{86} -8.82078i q^{87} +2.85165i q^{88} +(-4.34444 + 7.52479i) q^{89} +(1.34557 + 1.78590i) q^{90} +(6.97295 - 12.0775i) q^{91} +(4.36172 - 2.51824i) q^{92} +(0.593405 - 0.342602i) q^{93} -7.88813 q^{94} +(9.37516 + 2.66579i) q^{95} +1.00000 q^{96} +(-5.79684 + 3.34681i) q^{97} +(1.39542 - 0.805646i) q^{98} +(-1.42582 + 2.46960i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{4} - 10 q^{6} + 10 q^{9}+O(q^{10}) \) 20 * q + 10 * q^4 - 10 * q^6 + 10 * q^9	\( 20 q + 10 q^{4} - 10 q^{6} + 10 q^{9} - 2 q^{10} + 12 q^{11} + 10 q^{14} + 2 q^{15} - 10 q^{16} + 6 q^{19} - 10 q^{21} + 10 q^{24} + 14 q^{25} + 8 q^{29} + 40 q^{31} + 12 q^{34} + 2 q^{35} - 10 q^{36} + 2 q^{40} - 14 q^{41} + 6 q^{44} + 44 q^{46} - 8 q^{49} - 8 q^{50} - 12 q^{51} + 10 q^{54} + 20 q^{56} + 8 q^{59} - 2 q^{60} + 16 q^{61} - 20 q^{64} + 40 q^{65} - 6 q^{66} - 44 q^{69} + 8 q^{70} - 4 q^{71} + 26 q^{74} + 8 q^{75} + 8 q^{79} - 10 q^{81} - 20 q^{84} - 16 q^{85} - 20 q^{86} - 2 q^{89} + 2 q^{90} - 44 q^{91} - 32 q^{94} - 80 q^{95} + 20 q^{96} + 6 q^{99}+O(q^{100}) \) 20 * q + 10 * q^4 - 10 * q^6 + 10 * q^9 - 2 * q^10 + 12 * q^11 + 10 * q^14 + 2 * q^15 - 10 * q^16 + 6 * q^19 - 10 * q^21 + 10 * q^24 + 14 * q^25 + 8 * q^29 + 40 * q^31 + 12 * q^34 + 2 * q^35 - 10 * q^36 + 2 * q^40 - 14 * q^41 + 6 * q^44 + 44 * q^46 - 8 * q^49 - 8 * q^50 - 12 * q^51 + 10 * q^54 + 20 * q^56 + 8 * q^59 - 2 * q^60 + 16 * q^61 - 20 * q^64 + 40 * q^65 - 6 * q^66 - 44 * q^69 + 8 * q^70 - 4 * q^71 + 26 * q^74 + 8 * q^75 + 8 * q^79 - 10 * q^81 - 20 * q^84 - 16 * q^85 - 20 * q^86 - 2 * q^89 + 2 * q^90 - 44 * q^91 - 32 * q^94 - 80 * q^95 + 20 * q^96 + 6 * q^99

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