LMFDB - Embedded newform 1110.2.ba.b.529.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(529,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("1110.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.ba (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.6
Character	$\chi$	$=$	1110.529
Dual form			1110.2.ba.b.619.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.18223 - 0.487744i) q^{5} -1.00000i q^{6} +(-2.13280 - 1.23137i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.18223 - 0.487744i) q^{5} -1.00000i q^{6} +(-2.13280 - 1.23137i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(1.51351 + 1.64599i) q^{10} -0.452075 q^{11} +(0.866025 - 0.500000i) q^{12} +(1.54402 - 2.67433i) q^{13} -2.46274i q^{14} +(-2.13373 - 0.668714i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.05737 - 1.83142i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.58246 + 1.49098i) q^{19} +(-0.668714 + 2.13373i) q^{20} +(1.23137 + 2.13280i) q^{21} +(-0.226038 - 0.391509i) q^{22} +1.77585 q^{23} +(0.866025 + 0.500000i) q^{24} +(4.52421 - 2.12873i) q^{25} +3.08804 q^{26} -1.00000i q^{27} +(2.13280 - 1.23137i) q^{28} -8.36900i q^{29} +(-0.487744 - 2.18223i) q^{30} -2.55531i q^{31} +(0.500000 - 0.866025i) q^{32} +(0.391509 + 0.226038i) q^{33} +(1.05737 - 1.83142i) q^{34} +(-5.25484 - 1.64687i) q^{35} -1.00000 q^{36} +(-0.0294493 - 6.08269i) q^{37} +2.98197i q^{38} +(-2.67433 + 1.54402i) q^{39} +(-2.18223 + 0.487744i) q^{40} +(-1.18271 + 2.04852i) q^{41} +(-1.23137 + 2.13280i) q^{42} +3.94663 q^{43} +(0.226038 - 0.391509i) q^{44} +(1.51351 + 1.64599i) q^{45} +(0.887924 + 1.53793i) q^{46} +2.64363i q^{47} +1.00000i q^{48} +(-0.467447 - 0.809642i) q^{49} +(4.10564 + 2.85372i) q^{50} +2.11474i q^{51} +(1.54402 + 2.67433i) q^{52} +(8.26490 - 4.77175i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.986530 + 0.220497i) q^{55} +(2.13280 + 1.23137i) q^{56} +(-1.49098 - 2.58246i) q^{57} +(7.24777 - 4.18450i) q^{58} +(-2.78387 + 1.60727i) q^{59} +(1.64599 - 1.51351i) q^{60} +(7.10381 + 4.10139i) q^{61} +(2.21296 - 1.27765i) q^{62} -2.46274i q^{63} +1.00000 q^{64} +(2.06502 - 6.58907i) q^{65} +0.452075i q^{66} +(-8.26563 - 4.77217i) q^{67} +2.11474 q^{68} +(-1.53793 - 0.887924i) q^{69} +(-1.20119 - 5.37426i) q^{70} +(0.00323694 - 0.00560655i) q^{71} +(-0.500000 - 0.866025i) q^{72} -9.13122i q^{73} +(5.25304 - 3.06685i) q^{74} +(-4.98245 - 0.418570i) q^{75} +(-2.58246 + 1.49098i) q^{76} +(0.964186 + 0.556673i) q^{77} +(-2.67433 - 1.54402i) q^{78} +(10.9751 + 6.33650i) q^{79} +(-1.51351 - 1.64599i) q^{80} +(-0.500000 + 0.866025i) q^{81} -2.36543 q^{82} +(-6.55955 + 3.78716i) q^{83} -2.46274 q^{84} +(-3.20068 - 3.48085i) q^{85} +(1.97332 + 3.41789i) q^{86} +(-4.18450 + 7.24777i) q^{87} +0.452075 q^{88} +(9.02573 - 5.21101i) q^{89} +(-0.668714 + 2.13373i) q^{90} +(-6.58618 + 3.80253i) q^{91} +(-0.887924 + 1.53793i) q^{92} +(-1.27765 + 2.21296i) q^{93} +(-2.28945 + 1.32182i) q^{94} +(6.36273 + 1.99408i) q^{95} +(-0.866025 + 0.500000i) q^{96} -5.64069 q^{97} +(0.467447 - 0.809642i) q^{98} +(-0.226038 - 0.391509i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9	$ 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} + 14 q^{13} + 2 q^{15} - 18 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{20} + 2 q^{22} + 20 q^{23} - 2 q^{25} + 28 q^{26} - 2 q^{30} + 18 q^{32} + 6 q^{33} - 20 q^{35} - 36 q^{36} - 20 q^{37} + 6 q^{39} - 4 q^{40} + 10 q^{41} - 2 q^{44} + 2 q^{45} + 10 q^{46} + 10 q^{49} - 4 q^{50} + 14 q^{52} + 12 q^{53} + 40 q^{55} - 8 q^{57} - 30 q^{58} + 18 q^{59} - 4 q^{60} - 6 q^{61} + 12 q^{62} + 36 q^{64} - 32 q^{65} - 36 q^{67} + 12 q^{69} - 40 q^{70} - 24 q^{71} - 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} + 24 q^{77} + 6 q^{78} - 2 q^{80} - 18 q^{81} + 20 q^{82} - 36 q^{83} + 26 q^{85} + 10 q^{87} - 4 q^{88} - 2 q^{90} - 36 q^{91} - 10 q^{92} - 12 q^{93} + 12 q^{94} + 18 q^{95} - 52 q^{97} - 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 + 14 * q^13 + 2 * q^15 - 18 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^20 + 2 * q^22 + 20 * q^23 - 2 * q^25 + 28 * q^26 - 2 * q^30 + 18 * q^32 + 6 * q^33 - 20 * q^35 - 36 * q^36 - 20 * q^37 + 6 * q^39 - 4 * q^40 + 10 * q^41 - 2 * q^44 + 2 * q^45 + 10 * q^46 + 10 * q^49 - 4 * q^50 + 14 * q^52 + 12 * q^53 + 40 * q^55 - 8 * q^57 - 30 * q^58 + 18 * q^59 - 4 * q^60 - 6 * q^61 + 12 * q^62 + 36 * q^64 - 32 * q^65 - 36 * q^67 + 12 * q^69 - 40 * q^70 - 24 * q^71 - 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 + 24 * q^77 + 6 * q^78 - 2 * q^80 - 18 * q^81 + 20 * q^82 - 36 * q^83 + 26 * q^85 + 10 * q^87 - 4 * q^88 - 2 * q^90 - 36 * q^91 - 10 * q^92 - 12 * q^93 + 12 * q^94 + 18 * q^95 - 52 * q^97 - 10 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−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
$5$	2.18223	−	0.487744i	0.975921	−	0.218126i
$5$	2.18223	−	0.487744i	0.975921	−	0.218126i
$6$		−	1.00000i		−	0.408248i
$7$	−2.13280	−	1.23137i	−0.806122	−	0.465415i	0.0394853	−	0.999220i	$-0.487428\pi$
$7$	−2.13280	−	1.23137i	−0.806122	−	0.465415i	−0.845607	+	0.533805i	$0.820761\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.51351	+	1.64599i	0.478614	+	0.520508i
$11$	−0.452075			−0.136306			−0.0681529	−	0.997675i	$-0.521711\pi$
$11$	−0.452075			−0.136306			−0.0681529	+	0.997675i	$0.521711\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$	1.54402	−	2.67433i	0.428235	−	0.741724i	−0.568482	−	0.822696i	$-0.692469\pi$
$13$	1.54402	−	2.67433i	0.428235	−	0.741724i	0.996716	+	0.0809716i	$0.0258023\pi$
$14$		−	2.46274i		−	0.658196i
$15$	−2.13373	−	0.668714i	−0.550928	−	0.172661i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.05737	−	1.83142i	−0.256450	−	0.444185i	0.708838	−	0.705371i	$-0.249220\pi$
$17$	−1.05737	−	1.83142i	−0.256450	−	0.444185i	−0.965288	+	0.261186i	$0.915886\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	2.58246	+	1.49098i	0.592457	+	0.342055i	0.766068	−	0.642759i	$-0.222210\pi$
$19$	2.58246	+	1.49098i	0.592457	+	0.342055i	−0.173611	+	0.984814i	$0.555544\pi$
$20$	−0.668714	+	2.13373i	−0.149529	+	0.477117i
$21$	1.23137	+	2.13280i	0.268707	+	0.465415i
$22$	−0.226038	−	0.391509i	−0.0481914	−	0.0834699i
$23$	1.77585			0.370290			0.185145	−	0.982711i	$-0.440725\pi$
$23$	1.77585			0.370290			0.185145	+	0.982711i	$0.440725\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	4.52421	−	2.12873i	0.904843	−	0.425746i
$26$	3.08804			0.605615
$27$		−	1.00000i		−	0.192450i
$28$	2.13280	−	1.23137i	0.403061	−	0.232707i
$29$		−	8.36900i		−	1.55408i	−0.629448	−	0.777042i	$-0.716719\pi$
$29$		−	8.36900i		−	1.55408i	0.629448	−	0.777042i	$-0.283281\pi$
$30$	−0.487744	−	2.18223i	−0.0890494	−	0.398418i
$31$		−	2.55531i		−	0.458947i	−0.973315	−	0.229473i	$-0.926300\pi$
$31$		−	2.55531i		−	0.458947i	0.973315	−	0.229473i	$-0.0737004\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.391509	+	0.226038i	0.0681529	+	0.0393481i
$34$	1.05737	−	1.83142i	0.181338	−	0.314086i
$35$	−5.25484	−	1.64687i	−0.888230	−	0.278372i
$36$	−1.00000			−0.166667
$37$	−0.0294493	−	6.08269i	−0.00484144	−	0.999988i
$37$	−0.0294493	−	6.08269i	−0.00484144	−	0.999988i
$38$			2.98197i			0.483739i
$39$	−2.67433	+	1.54402i	−0.428235	+	0.247241i
$40$	−2.18223	+	0.487744i	−0.345040	+	0.0771190i
$41$	−1.18271	+	2.04852i	−0.184709	+	0.319925i	−0.943478	−	0.331434i	$-0.892468\pi$
$41$	−1.18271	+	2.04852i	−0.184709	+	0.319925i	0.758769	+	0.651359i	$0.225801\pi$
$42$	−1.23137	+	2.13280i	−0.190005	+	0.329098i
$43$	3.94663			0.601856			0.300928	−	0.953647i	$-0.402704\pi$
$43$	3.94663			0.601856			0.300928	+	0.953647i	$0.402704\pi$
$44$	0.226038	−	0.391509i	0.0340765	−	0.0590222i
$45$	1.51351	+	1.64599i	0.225621	+	0.245370i
$46$	0.887924	+	1.53793i	0.130917	+	0.226755i
$47$			2.64363i			0.385613i	0.981237	+	0.192807i	$0.0617590\pi$
$47$			2.64363i			0.385613i	−0.981237	+	0.192807i	$0.938241\pi$
$48$			1.00000i			0.144338i
$49$	−0.467447	−	0.809642i	−0.0667782	−	0.115663i
$50$	4.10564	+	2.85372i	0.580626	+	0.403577i
$51$			2.11474i			0.296123i
$52$	1.54402	+	2.67433i	0.214117	+	0.370862i
$53$	8.26490	−	4.77175i	1.13527	−	0.655450i	0.190017	−	0.981781i	$-0.439146\pi$
$53$	8.26490	−	4.77175i	1.13527	−	0.655450i	0.945255	+	0.326331i	$0.105813\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−0.986530	+	0.220497i	−0.133024	+	0.0297318i
$56$	2.13280	+	1.23137i	0.285007	+	0.164549i
$57$	−1.49098	−	2.58246i	−0.197486	−	0.342055i
$58$	7.24777	−	4.18450i	0.951679	−	0.549452i
$59$	−2.78387	+	1.60727i	−0.362429	+	0.209248i	−0.670146	−	0.742230i	$-0.733768\pi$
$59$	−2.78387	+	1.60727i	−0.362429	+	0.209248i	0.307717	+	0.951478i	$0.400435\pi$
$60$	1.64599	−	1.51351i	0.212496	−	0.195393i
$61$	7.10381	+	4.10139i	0.909550	+	0.525129i	0.880286	−	0.474443i	$-0.157350\pi$
$61$	7.10381	+	4.10139i	0.909550	+	0.525129i	0.0292637	+	0.999572i	$0.490684\pi$
$62$	2.21296	−	1.27765i	0.281046	−	0.162262i
$63$		−	2.46274i		−	0.310277i
$64$	1.00000			0.125000
$65$	2.06502	−	6.58907i	0.256134	−	0.817273i
$66$			0.452075i			0.0556466i
$67$	−8.26563	−	4.77217i	−1.00981	−	0.583013i	−0.0986725	−	0.995120i	$-0.531460\pi$
$67$	−8.26563	−	4.77217i	−1.00981	−	0.583013i	−0.911135	+	0.412107i	$0.864793\pi$
$68$	2.11474			0.256450
$69$	−1.53793	−	0.887924i	−0.185145	−	0.106893i
$70$	−1.20119	−	5.37426i	−0.143569	−	0.642347i
$71$	0.00323694	−	0.00560655i	0.000384154	−	0.000665375i	−0.865833	−	0.500333i	$-0.833211\pi$
$71$	0.00323694	−	0.00560655i	0.000384154	−	0.000665375i	0.866217	+	0.499667i	$0.166544\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$		−	9.13122i		−	1.06873i	−0.845254	−	0.534364i	$-0.820551\pi$
$73$		−	9.13122i		−	1.06873i	0.845254	−	0.534364i	$-0.179449\pi$
$74$	5.25304	−	3.06685i	0.610654	−	0.356514i
$75$	−4.98245	−	0.418570i	−0.575324	−	0.0483323i
$76$	−2.58246	+	1.49098i	−0.296228	+	0.171028i
$77$	0.964186	+	0.556673i	0.109879	+	0.0634388i
$78$	−2.67433	−	1.54402i	−0.302808	−	0.174826i
$79$	10.9751	+	6.33650i	1.23480	+	0.712912i	0.968027	−	0.250848i	$-0.0807093\pi$
$79$	10.9751	+	6.33650i	1.23480	+	0.712912i	0.266773	+	0.963759i	$0.414043\pi$
$80$	−1.51351	−	1.64599i	−0.169216	−	0.184027i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.36543			−0.261218
$83$	−6.55955	+	3.78716i	−0.720005	+	0.415695i	−0.814754	−	0.579806i	$-0.803128\pi$
$83$	−6.55955	+	3.78716i	−0.720005	+	0.415695i	0.0947497	+	0.995501i	$0.469795\pi$
$84$	−2.46274			−0.268707
$85$	−3.20068	−	3.48085i	−0.347163	−	0.377551i
$86$	1.97332	+	3.41789i	0.212788	+	0.368560i
$87$	−4.18450	+	7.24777i	−0.448626	+	0.777042i
$88$	0.452075			0.0481914
$89$	9.02573	−	5.21101i	0.956726	−	0.552366i	0.0615619	−	0.998103i	$-0.480392\pi$
$89$	9.02573	−	5.21101i	0.956726	−	0.552366i	0.895164	+	0.445737i	$0.147059\pi$
$90$	−0.668714	+	2.13373i	−0.0704887	+	0.224915i
$91$	−6.58618	+	3.80253i	−0.690419	+	0.398614i
$92$	−0.887924	+	1.53793i	−0.0925725	+	0.160340i
$93$	−1.27765	+	2.21296i	−0.132487	+	0.229473i
$94$	−2.28945	+	1.32182i	−0.236139	+	0.136335i
$95$	6.36273	+	1.99408i	0.652802	+	0.204589i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−5.64069			−0.572725			−0.286363	−	0.958121i	$-0.592446\pi$
$97$	−5.64069			−0.572725			−0.286363	+	0.958121i	$0.592446\pi$
$98$	0.467447	−	0.809642i	0.0472193	−	0.0817862i
$99$	−0.226038	−	0.391509i	−0.0227176	−	0.0393481i
$100$	−0.418570	+	4.98245i	−0.0418570	+	0.498245i
$101$	6.59186			0.655914			0.327957	−	0.944693i	$-0.393640\pi$
$101$	6.59186			0.655914			0.327957	+	0.944693i	$0.393640\pi$
$102$	−1.83142	+	1.05737i	−0.181338	+	0.104695i
$103$	0.706172			0.0695812			0.0347906	−	0.999395i	$-0.488924\pi$
$103$	0.706172			0.0695812			0.0347906	+	0.999395i	$0.488924\pi$
$104$	−1.54402	+	2.67433i	−0.151404	+	0.262239i
$105$	3.72739	+	4.05365i	0.363756	+	0.395596i
$106$	8.26490	+	4.77175i	0.802759	+	0.463473i
$107$	4.58807	+	2.64892i	0.443545	+	0.256081i	0.705100	−	0.709108i	$-0.250902\pi$
$107$	4.58807	+	2.64892i	0.443545	+	0.256081i	−0.261555	+	0.965189i	$0.584235\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	5.76779	−	3.33004i	0.552454	−	0.318960i	−0.197657	−	0.980271i	$-0.563333\pi$
$109$	5.76779	−	3.33004i	0.552454	−	0.318960i	0.750111	+	0.661312i	$0.230000\pi$
$110$	−0.684221	−	0.744112i	−0.0652379	−	0.0709483i
$111$	−3.01584	+	5.28249i	−0.286251	+	0.501392i
$112$			2.46274i			0.232707i
$113$	6.58655	+	11.4082i	0.619611	+	1.07320i	0.989557	+	0.144144i	$0.0460429\pi$
$113$	6.58655	+	11.4082i	0.619611	+	1.07320i	−0.369946	+	0.929053i	$0.620624\pi$
$114$	1.49098	−	2.58246i	0.139643	−	0.241870i
$115$	3.87530	−	0.866158i	0.361374	−	0.0807697i
$116$	7.24777	+	4.18450i	0.672938	+	0.388521i
$117$	3.08804			0.285490
$118$	−2.78387	−	1.60727i	−0.256276	−	0.147961i
$119$			5.20807i			0.477423i
$120$	2.13373	+	0.668714i	0.194782	+	0.0610450i
$121$	−10.7956			−0.981421
$122$			8.20278i			0.742644i
$123$	2.04852	−	1.18271i	0.184709	−	0.106642i
$124$	2.21296	+	1.27765i	0.198730	+	0.114737i
$125$	8.83457	−	6.85203i	0.790188	−	0.612864i
$126$	2.13280	−	1.23137i	0.190005	−	0.109699i
$127$	−15.7823	+	9.11192i	−1.40045	+	0.808552i	−0.994439	−	0.105315i	$-0.966415\pi$
$127$	−15.7823	+	9.11192i	−1.40045	+	0.808552i	−0.406014	+	0.913867i	$0.633082\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−3.41789	−	1.97332i	−0.300928	−	0.173741i
$130$	6.73881	−	1.50617i	0.591033	−	0.132100i
$131$	9.09771	−	5.25257i	0.794871	−	0.458919i	−0.0468037	−	0.998904i	$-0.514904\pi$
$131$	9.09771	−	5.25257i	0.794871	−	0.458919i	0.841674	+	0.539985i	$0.181570\pi$
$132$	−0.391509	+	0.226038i	−0.0340765	+	0.0196741i
$133$	−3.67191	−	6.35994i	−0.318395	−	0.551476i
$134$		−	9.54433i		−	0.824505i
$135$	−0.487744	−	2.18223i	−0.0419783	−	0.187816i
$136$	1.05737	+	1.83142i	0.0906688	+	0.157043i
$137$			15.4821i			1.32272i	0.750068	+	0.661361i	$0.230021\pi$
$137$			15.4821i			1.32272i	−0.750068	+	0.661361i	$0.769979\pi$
$138$		−	1.77585i		−	0.151170i
$139$	−6.46352	−	11.1951i	−0.548228	−	0.949560i	−0.998396	−	0.0566155i	$-0.981969\pi$
$139$	−6.46352	−	11.1951i	−0.548228	−	0.949560i	0.450168	−	0.892944i	$-0.351364\pi$
$140$	4.05365	−	3.72739i	0.342596	−	0.315022i
$141$	1.32182	−	2.28945i	0.111317	−	0.192807i
$142$	0.00647388			0.000543276
$143$	−0.698014	+	1.20900i	−0.0583709	+	0.101101i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−4.08193	−	18.2630i	−0.338986	−	1.51666i
$146$	7.90787	−	4.56561i	0.654460	−	0.377853i
$147$			0.934894i			0.0771088i
$148$	5.28249	+	3.01584i	0.434218	+	0.247901i
$149$	0.922279			0.0755560			0.0377780	−	0.999286i	$-0.487972\pi$
$149$	0.922279			0.0755560			0.0377780	+	0.999286i	$0.487972\pi$
$150$	−2.12873	−	4.52421i	−0.173810	−	0.369400i
$151$	−9.43397	+	16.3401i	−0.767726	+	1.32974i	0.171067	+	0.985259i	$0.445278\pi$
$151$	−9.43397	+	16.3401i	−0.767726	+	1.32974i	−0.938793	+	0.344481i	$0.888055\pi$
$152$	−2.58246	−	1.49098i	−0.209465	−	0.120935i
$153$	1.05737	−	1.83142i	0.0854834	−	0.148062i
$154$			1.11335i			0.0897159i
$155$	−1.24634	−	5.57626i	−0.100108	−	0.447896i
$156$		−	3.08804i		−	0.247241i
$157$	−13.0389	+	7.52798i	−1.04061	+	0.600799i	−0.920007	−	0.391902i	$-0.871817\pi$
$157$	−13.0389	+	7.52798i	−1.04061	+	0.600799i	−0.120607	+	0.992700i	$0.538484\pi$
$158$			12.6730i			1.00821i
$159$	−9.54349			−0.756848
$160$	0.668714	−	2.13373i	0.0528665	−	0.168686i
$161$	−3.78753	−	2.18673i	−0.298499	−	0.172338i
$162$	−1.00000			−0.0785674
$163$	−8.68670	−	15.0458i	−0.680395	−	1.17848i	−0.974860	−	0.222817i	$-0.928475\pi$
$163$	−8.68670	−	15.0458i	−0.680395	−	1.17848i	0.294465	−	0.955662i	$-0.404859\pi$
$164$	−1.18271	−	2.04852i	−0.0923545	−	0.159963i
$165$	0.964609	+	0.302309i	0.0750947	+	0.0235347i
$166$	−6.55955	−	3.78716i	−0.509120	−	0.293941i
$167$	1.65702	−	2.87004i	0.128224	−	0.222090i	−0.794765	−	0.606918i	$-0.792406\pi$
$167$	1.65702	−	2.87004i	0.128224	−	0.222090i	0.922988	+	0.384828i	$0.125739\pi$
$168$	−1.23137	−	2.13280i	−0.0950024	−	0.164549i
$169$	1.73199	+	2.99990i	0.133230	+	0.230761i
$170$	1.41416	−	4.51230i	0.108461	−	0.346077i
$171$			2.98197i			0.228037i
$172$	−1.97332	+	3.41789i	−0.150464	+	0.260611i
$173$	0.977227	−	0.564202i	0.0742972	−	0.0428955i	−0.462391	−	0.886676i	$-0.653008\pi$
$173$	0.977227	−	0.564202i	0.0742972	−	0.0428955i	0.536688	+	0.843781i	$0.319675\pi$
$174$	−8.36900			−0.634452
$175$	−12.2705	−	1.03083i	−0.927562	−	0.0779235i
$176$	0.226038	+	0.391509i	0.0170382	+	0.0295111i
$177$	3.21453			0.241619
$178$	9.02573	+	5.21101i	0.676507	+	0.390582i
$179$			9.79245i			0.731922i	0.930630	+	0.365961i	$0.119260\pi$
$179$			9.79245i			0.731922i	−0.930630	+	0.365961i	$0.880740\pi$
$180$	−2.18223	+	0.487744i	−0.162653	+	0.0363543i
$181$	−6.70130	+	11.6070i	−0.498103	+	0.862740i	−0.999998	−	0.00218861i	$-0.999303\pi$
$181$	−6.70130	+	11.6070i	−0.498103	+	0.862740i	0.501894	+	0.864929i	$0.332637\pi$
$182$	−6.58618	−	3.80253i	−0.488200	−	0.281862i
$183$	−4.10139	−	7.10381i	−0.303183	−	0.525129i
$184$	−1.77585			−0.130917
$185$	−3.03106	−	13.2594i	−0.222848	−	0.974853i
$186$	−2.55531			−0.187364
$187$	0.478011	+	0.827940i	0.0349556	+	0.0605450i
$188$	−2.28945	−	1.32182i	−0.166975	−	0.0964033i
$189$	−1.23137	+	2.13280i	−0.0895691	+	0.155138i
$190$	1.45444	+	6.50733i	0.105516	+	0.472091i
$191$			9.38260i			0.678901i	0.940624	+	0.339451i	$0.110241\pi$
$191$			9.38260i			0.678901i	−0.940624	+	0.339451i	$0.889759\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−12.5017			−0.899890			−0.449945	−	0.893056i	$-0.648556\pi$
$193$	−12.5017			−0.899890			−0.449945	+	0.893056i	$0.648556\pi$
$194$	−2.82034	−	4.88498i	−0.202489	−	0.350721i
$195$	−5.08289	+	4.67379i	−0.363993	+	0.334697i
$196$	0.934894			0.0667782
$197$	1.70221	−	0.982774i	0.121278	−	0.0700197i	−0.438134	−	0.898910i	$-0.644360\pi$
$197$	1.70221	−	0.982774i	0.121278	−	0.0700197i	0.559412	+	0.828890i	$0.311027\pi$
$198$	0.226038	−	0.391509i	0.0160638	−	0.0278233i
$199$		−	12.7088i		−	0.900900i	−0.892802	−	0.450450i	$-0.851263\pi$
$199$		−	12.7088i		−	0.900900i	0.892802	−	0.450450i	$-0.148737\pi$
$200$	−4.52421	+	2.12873i	−0.319910	+	0.150524i
$201$	4.77217	+	8.26563i	0.336603	+	0.583013i
$202$	3.29593	+	5.70872i	0.231901	+	0.401664i
$203$	−10.3054	+	17.8494i	−0.723294	+	1.25278i
$204$	−1.83142	−	1.05737i	−0.128225	−	0.0740308i
$205$	−1.58180	+	5.04720i	−0.110477	+	0.352512i
$206$	0.353086	+	0.611563i	0.0246007	+	0.0426096i
$207$	0.887924	+	1.53793i	0.0617150	+	0.106893i
$208$	−3.08804			−0.214117
$209$	−1.16747	−	0.674037i	−0.0807554	−	0.0466241i
$210$	−1.64687	+	5.25484i	−0.113645	+	0.362618i
$211$	−11.2817			−0.776662			−0.388331	−	0.921520i	$-0.626948\pi$
$211$	−11.2817			−0.776662			−0.388331	+	0.921520i	$0.626948\pi$
$212$			9.54349i			0.655450i
$213$	−0.00560655	+	0.00323694i	−0.000384154	+	0.000221792i
$214$			5.29785i			0.362153i
$215$	8.61245	−	1.92495i	0.587364	−	0.131280i
$216$			1.00000i			0.0680414i
$217$	−3.14653	+	5.44996i	−0.213601	+	0.369967i
$218$	5.76779	+	3.33004i	0.390644	+	0.225539i
$219$	−4.56561	+	7.90787i	−0.308515	+	0.534364i
$220$	0.302309	−	0.964609i	0.0203817	−	0.0650339i
$221$	−6.53042			−0.439283
$222$	−6.08269	+	0.0294493i	−0.408244	+	0.00197651i
$223$		−	13.9818i		−	0.936293i	−0.883651	−	0.468146i	$-0.844922\pi$
$223$		−	13.9818i		−	0.936293i	0.883651	−	0.468146i	$-0.155078\pi$
$224$	−2.13280	+	1.23137i	−0.142504	+	0.0822745i
$225$	4.10564	+	2.85372i	0.273709	+	0.190248i
$226$	−6.58655	+	11.4082i	−0.438131	+	0.758865i
$227$	−10.0487	+	17.4048i	−0.666953	+	1.15520i	0.311799	+	0.950148i	$0.399068\pi$
$227$	−10.0487	+	17.4048i	−0.666953	+	1.15520i	−0.978752	+	0.205048i	$0.934265\pi$
$228$	2.98197			0.197486
$229$	2.81341	−	4.87296i	0.185915	−	0.322014i	−0.757969	−	0.652290i	$-0.773808\pi$
$229$	2.81341	−	4.87296i	0.185915	−	0.322014i	0.943885	+	0.330276i	$0.107142\pi$
$230$	2.68777	+	2.92303i	0.177226	+	0.192739i
$231$	−0.556673	−	0.964186i	−0.0366264	−	0.0634388i
$232$			8.36900i			0.549452i
$233$			16.2683i			1.06577i	0.846187	+	0.532887i	$0.178893\pi$
$233$			16.2683i			1.06577i	−0.846187	+	0.532887i	$0.821107\pi$
$234$	1.54402	+	2.67433i	0.100936	+	0.174826i
$235$	1.28941	+	5.76900i	0.0841121	+	0.376328i
$236$		−	3.21453i		−	0.209248i
$237$	−6.33650	−	10.9751i	−0.411600	−	0.712912i
$238$	−4.51032	+	2.60403i	−0.292360	+	0.168794i
$239$	4.52658	−	2.61342i	0.292800	−	0.169048i	−0.346404	−	0.938085i	$-0.612597\pi$
$239$	4.52658	−	2.61342i	0.292800	−	0.169048i	0.639204	+	0.769037i	$0.279264\pi$
$240$	0.487744	+	2.18223i	0.0314837	+	0.140862i
$241$	−21.8978	−	12.6427i	−1.41056	−	0.814387i	−0.415119	−	0.909767i	$-0.636260\pi$
$241$	−21.8978	−	12.6427i	−1.41056	−	0.814387i	−0.995441	+	0.0953804i	$0.969593\pi$
$242$	−5.39781	−	9.34929i	−0.346985	−	0.600995i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−7.10381	+	4.10139i	−0.454775	+	0.262564i
$245$	−1.41497	−	1.53883i	−0.0903993	−	0.0983121i
$246$	2.04852	+	1.18271i	0.130609	+	0.0754071i
$247$	7.97475	−	4.60423i	0.507421	−	0.292960i
$248$			2.55531i			0.162262i
$249$	7.57432			0.480003
$250$	10.3513	+	4.22495i	0.654675	+	0.267209i
$251$		−	2.27414i		−	0.143542i	−0.997421	−	0.0717712i	$-0.977135\pi$
$251$		−	2.27414i		−	0.143542i	0.997421	−	0.0717712i	$-0.0228652\pi$
$252$	2.13280	+	1.23137i	0.134354	+	0.0775691i
$253$	−0.802817			−0.0504727
$254$	−15.7823	−	9.11192i	−0.990270	−	0.571733i
$255$	1.03145	+	4.61484i	0.0645920	+	0.288993i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.8758	+	18.8374i	0.678413	+	1.17505i	0.975459	+	0.220182i	$0.0706652\pi$
$257$	10.8758	+	18.8374i	0.678413	+	1.17505i	−0.297046	+	0.954863i	$0.596001\pi$
$258$		−	3.94663i		−	0.245707i
$259$	−7.42724	+	13.0094i	−0.461507	+	0.808366i
$260$	4.67379	+	5.08289i	0.289856	+	0.315228i
$261$	7.24777	−	4.18450i	0.448626	−	0.259014i
$262$	9.09771	+	5.25257i	0.562059	+	0.324505i
$263$	−5.41619	−	3.12704i	−0.333977	−	0.192822i	0.323629	−	0.946184i	$-0.395097\pi$
$263$	−5.41619	−	3.12704i	−0.333977	−	0.192822i	−0.657605	+	0.753363i	$0.728431\pi$
$264$	−0.391509	−	0.226038i	−0.0240957	−	0.0139117i
$265$	15.7085	−	14.4442i	0.964965	−	0.887299i
$266$	3.67191	−	6.35994i	0.225139	−	0.389953i
$267$	−10.4220			−0.637817
$268$	8.26563	−	4.77217i	0.504904	−	0.291506i
$269$	−7.07555			−0.431404			−0.215702	−	0.976459i	$-0.569204\pi$
$269$	−7.07555			−0.431404			−0.215702	+	0.976459i	$0.569204\pi$
$270$	1.64599	−	1.51351i	0.100172	−	0.0921093i
$271$	−2.51174	−	4.35046i	−0.152577	−	0.264272i	0.779597	−	0.626282i	$-0.215424\pi$
$271$	−2.51174	−	4.35046i	−0.152577	−	0.264272i	−0.932174	+	0.362010i	$0.882091\pi$
$272$	−1.05737	+	1.83142i	−0.0641125	+	0.111046i
$273$	7.60506			0.460279
$274$	−13.4079	+	7.74103i	−0.809999	+	0.467653i
$275$	−2.04528	+	0.962347i	−0.123335	+	0.0580317i
$276$	1.53793	−	0.887924i	0.0925725	−	0.0534467i
$277$	−14.3006	+	24.7694i	−0.859242	+	1.48825i	0.0134110	+	0.999910i	$0.495731\pi$
$277$	−14.3006	+	24.7694i	−0.859242	+	1.48825i	−0.872653	+	0.488341i	$0.837602\pi$
$278$	6.46352	−	11.1951i	0.387656	−	0.671440i
$279$	2.21296	−	1.27765i	0.132487	−	0.0764912i
$280$	5.25484	+	1.64687i	0.314037	+	0.0984194i
$281$	−11.1812	+	6.45549i	−0.667017	+	0.385102i	−0.794945	−	0.606681i	$-0.792500\pi$
$281$	−11.1812	+	6.45549i	−0.667017	+	0.385102i	0.127929	+	0.991783i	$0.459167\pi$
$282$	2.64363			0.157426
$283$	10.3736	−	17.9677i	0.616648	−	1.06807i	−0.373444	−	0.927653i	$-0.621823\pi$
$283$	10.3736	−	17.9677i	0.616648	−	1.06807i	0.990093	−	0.140414i	$-0.0448433\pi$
$284$	0.00323694	+	0.00560655i	0.000192077	+	0.000332687i
$285$	−4.51324	−	4.90829i	−0.267341	−	0.290742i
$286$	−1.39603			−0.0825489
$287$	5.04498	−	2.91272i	0.297796	−	0.171933i
$288$	1.00000			0.0589256
$289$	6.26393	−	10.8495i	0.368467	−	0.638203i
$290$	13.7753	−	12.6666i	0.808913	−	0.743807i
$291$	4.88498	+	2.82034i	0.286363	+	0.165332i
$292$	7.90787	+	4.56561i	0.462773	+	0.267182i
$293$	−8.12951	−	4.69358i	−0.474931	−	0.274202i	0.243371	−	0.969933i	$-0.421747\pi$
$293$	−8.12951	−	4.69358i	−0.474931	−	0.274202i	−0.718302	+	0.695732i	$0.755080\pi$
$294$	−0.809642	+	0.467447i	−0.0472193	+	0.0272621i
$295$	−5.29109	+	4.86523i	−0.308059	+	0.283265i
$296$	0.0294493	+	6.08269i	0.00171171	+	0.353549i
$297$			0.452075i			0.0262321i
$298$	0.461139	+	0.798717i	0.0267131	+	0.0462684i
$299$	2.74195	−	4.74919i	0.158571	−	0.274653i
$300$	2.85372	−	4.10564i	0.164759	−	0.237039i
$301$	−8.41738	−	4.85977i	−0.485170	−	0.280113i
$302$	−18.8679			−1.08573
$303$	−5.70872	−	3.29593i	−0.327957	−	0.189346i
$304$		−	2.98197i		−	0.171028i
$305$	17.5025	+	5.48531i	1.00219	+	0.314088i
$306$	2.11474			0.120892
$307$		−	2.11341i		−	0.120619i	−0.998180	−	0.0603095i	$-0.980791\pi$
$307$		−	2.11341i		−	0.120619i	0.998180	−	0.0603095i	$-0.0192088\pi$
$308$	−0.964186	+	0.556673i	−0.0549396	+	0.0317194i
$309$	−0.611563	−	0.353086i	−0.0347906	−	0.0200864i
$310$	4.20601	−	3.86749i	0.238886	−	0.219658i
$311$	19.2848	−	11.1341i	1.09354	−	0.631355i	0.159023	−	0.987275i	$-0.449166\pi$
$311$	19.2848	−	11.1341i	1.09354	−	0.631355i	0.934517	+	0.355920i	$0.115832\pi$
$312$	2.67433	−	1.54402i	0.151404	−	0.0874130i
$313$	8.32368	+	14.4170i	0.470482	+	0.814899i	0.999430	−	0.0337549i	$-0.0107466\pi$
$313$	8.32368	+	14.4170i	0.470482	+	0.814899i	−0.528948	+	0.848654i	$0.677413\pi$
$314$	−13.0389	−	7.52798i	−0.735825	−	0.424829i
$315$	−1.20119	−	5.37426i	−0.0676792	−	0.302805i
$316$	−10.9751	+	6.33650i	−0.617400	+	0.356456i
$317$	2.95498	−	1.70606i	0.165968	−	0.0958219i	−0.414715	−	0.909951i	$-0.636119\pi$
$317$	2.95498	−	1.70606i	0.165968	−	0.0958219i	0.580683	+	0.814129i	$0.302785\pi$
$318$	−4.77175	−	8.26490i	−0.267586	−	0.463473i
$319$			3.78342i			0.211831i
$320$	2.18223	−	0.487744i	0.121990	−	0.0272657i
$321$	−2.64892	−	4.58807i	−0.147848	−	0.256081i
$322$		−	4.37346i		−	0.243723i
$323$		−	6.30609i		−	0.350880i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	1.29256	−	15.3860i	0.0716985	−	0.853463i
$326$	8.68670	−	15.0458i	0.481112	−	0.833311i
$327$	−6.66007			−0.368303
$328$	1.18271	−	2.04852i	0.0653045	−	0.113111i
$329$	3.25529	−	5.63833i	0.179470	−	0.310851i
$330$	0.220497	+	0.986530i	0.0121380	+	0.0543067i
$331$	23.5466	−	13.5946i	1.29424	−	0.747229i	0.314835	−	0.949146i	$-0.398051\pi$
$331$	23.5466	−	13.5946i	1.29424	−	0.747229i	0.979403	+	0.201918i	$0.0647173\pi$
$332$		−	7.57432i		−	0.415695i
$333$	5.25304	−	3.06685i	0.287865	−	0.168062i
$334$	3.31403			0.181336
$335$	−20.3651	−	6.38243i	−1.11266	−	0.348709i
$336$	1.23137	−	2.13280i	0.0671768	−	0.116354i
$337$	10.0266	+	5.78887i	0.546185	+	0.315340i	0.747582	−	0.664170i	$-0.231215\pi$
$337$	10.0266	+	5.78887i	0.546185	+	0.315340i	−0.201397	+	0.979510i	$0.564548\pi$
$338$	−1.73199	+	2.99990i	−0.0942079	+	0.163173i
$339$		−	13.1731i		−	0.715465i
$340$	4.61484	−	1.03145i	0.250275	−	0.0559383i
$341$			1.15519i			0.0625571i
$342$	−2.58246	+	1.49098i	−0.139643	+	0.0806232i
$343$			19.5416i			1.05515i
$344$	−3.94663			−0.212788
$345$	−3.78919	−	1.18753i	−0.204003	−	0.0639347i
$346$	0.977227	+	0.564202i	0.0525360	+	0.0303317i
$347$	18.7028			1.00402			0.502010	−	0.864862i	$-0.332594\pi$
$347$	18.7028			1.00402			0.502010	+	0.864862i	$0.332594\pi$
$348$	−4.18450	−	7.24777i	−0.224313	−	0.388521i
$349$	9.61263	+	16.6496i	0.514552	+	0.891231i	0.999857	+	0.0168860i	$0.00537524\pi$
$349$	9.61263	+	16.6496i	0.514552	+	0.891231i	−0.485305	+	0.874345i	$0.661291\pi$
$350$	−5.24252	−	11.1420i	−0.280225	−	0.595564i
$351$	−2.67433	−	1.54402i	−0.142745	−	0.0824138i
$352$	−0.226038	+	0.391509i	−0.0120478	+	0.0208675i
$353$	5.24212	+	9.07961i	0.279010	+	0.483259i	0.971139	−	0.238515i	$-0.0766605\pi$
$353$	5.24212	+	9.07961i	0.279010	+	0.483259i	−0.692129	+	0.721774i	$0.743327\pi$
$354$	1.60727	+	2.78387i	0.0854253	+	0.147961i
$355$	0.00432918	−	0.0138135i	0.000229769	−	0.000733147i
$356$			10.4220i			0.552366i
$357$	2.60403	−	4.51032i	0.137820	−	0.238711i
$358$	−8.48051	+	4.89623i	−0.448209	+	0.258774i
$359$	−6.92393			−0.365431			−0.182716	−	0.983166i	$-0.558489\pi$
$359$	−6.92393			−0.365431			−0.182716	+	0.983166i	$0.558489\pi$
$360$	−1.51351	−	1.64599i	−0.0797690	−	0.0867513i
$361$	−5.05393	−	8.75367i	−0.265996	−	0.460719i
$362$	−13.4026			−0.704425
$363$	9.34929	+	5.39781i	0.490710	+	0.283312i
$364$		−	7.60506i		−	0.398614i
$365$	−4.45369	−	19.9264i	−0.233117	−	1.04299i
$366$	4.10139	−	7.10381i	0.214383	−	0.371322i
$367$	9.18534	+	5.30316i	0.479471	+	0.276823i	0.720196	−	0.693771i	$-0.244052\pi$
$367$	9.18534	+	5.30316i	0.479471	+	0.276823i	−0.240725	+	0.970593i	$0.577385\pi$
$368$	−0.887924	−	1.53793i	−0.0462862	−	0.0801701i
$369$	−2.36543			−0.123139
$370$	9.96748	−	9.25469i	0.518185	−	0.481129i
$371$	−23.5032			−1.22022
$372$	−1.27765	−	2.21296i	−0.0662433	−	0.114737i
$373$	14.0490	+	8.11120i	0.727430	+	0.419982i	0.817481	−	0.575955i	$-0.195370\pi$
$373$	14.0490	+	8.11120i	0.727430	+	0.419982i	−0.0900510	+	0.995937i	$0.528703\pi$
$374$	−0.478011	+	0.827940i	−0.0247174	+	0.0428118i
$375$	−11.0770	+	1.51674i	−0.572013	+	0.0783243i
$376$		−	2.64363i		−	0.136335i
$377$	−22.3814	−	12.9219i	−1.15270	−	0.665513i
$378$	−2.46274			−0.126670
$379$	1.83877	+	3.18484i	0.0944511	+	0.163594i	0.909379	−	0.415968i	$-0.136557\pi$
$379$	1.83877	+	3.18484i	0.0944511	+	0.163594i	−0.814928	+	0.579562i	$0.803224\pi$
$380$	−4.90829	+	4.51324i	−0.251790	+	0.231524i
$381$	18.2238			0.933635
$382$	−8.12557	+	4.69130i	−0.415740	+	0.240028i
$383$	2.74370	−	4.75222i	0.140196	−	0.242827i	−0.787374	−	0.616475i	$-0.788560\pi$
$383$	2.74370	−	4.75222i	0.140196	−	0.242827i	0.927570	+	0.373648i	$0.121893\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	2.37558	+	0.744510i	0.121071	+	0.0379437i
$386$	−6.25084	−	10.8268i	−0.318159	−	0.551068i
$387$	1.97332	+	3.41789i	0.100309	+	0.173741i
$388$	2.82034	−	4.88498i	0.143181	−	0.247997i
$389$	24.9890	+	14.4274i	1.26699	+	0.731497i	0.974417	−	0.224746i	$-0.0721551\pi$
$389$	24.9890	+	14.4274i	1.26699	+	0.731497i	0.292573	+	0.956243i	$0.405488\pi$
$390$	−6.58907	−	2.06502i	−0.333650	−	0.104566i
$391$	−1.87773	−	3.25232i	−0.0949609	−	0.164477i
$392$	0.467447	+	0.809642i	0.0236096	+	0.0408931i
$393$	−10.5051			−0.529914
$394$	1.70221	+	0.982774i	0.0857563	+	0.0495114i
$395$	27.0408	+	8.47461i	1.36057	+	0.426404i
$396$	0.452075			0.0227176
$397$			13.9468i			0.699970i	0.936755	+	0.349985i	$0.113813\pi$
$397$			13.9468i			0.699970i	−0.936755	+	0.349985i	$0.886187\pi$
$398$	11.0061	−	6.35438i	0.551687	−	0.318516i
$399$			7.34382i			0.367651i
$400$	−4.10564	−	2.85372i	−0.205282	−	0.142686i
$401$		−	20.0498i		−	1.00124i	−0.865667	−	0.500620i	$-0.833105\pi$
$401$		−	20.0498i		−	1.00124i	0.865667	−	0.500620i	$-0.166895\pi$
$402$	−4.77217	+	8.26563i	−0.238014	+	0.412252i
$403$	−6.83373	−	3.94545i	−0.340412	−	0.196537i
$404$	−3.29593	+	5.70872i	−0.163979	+	0.284019i
$405$	−0.668714	+	2.13373i	−0.0332287	+	0.106026i
$406$	−20.6107			−1.02289
$407$	0.0133133	+	2.74983i	0.000659916	+	0.136304i
$408$		−	2.11474i		−	0.104695i
$409$	16.0291	−	9.25441i	0.792588	−	0.457601i	−0.0482847	−	0.998834i	$-0.515375\pi$
$409$	16.0291	−	9.25441i	0.792588	−	0.457601i	0.840873	+	0.541233i	$0.182042\pi$
$410$	−5.16190	+	1.15372i	−0.254928	+	0.0569783i
$411$	7.74103	−	13.4079i	0.381837	−	0.661361i
$412$	−0.353086	+	0.611563i	−0.0173953	+	0.0301295i
$413$	7.91658			0.389549
$414$	−0.887924	+	1.53793i	−0.0436391	+	0.0755851i
$415$	−12.4673	+	11.4638i	−0.611994	+	0.562737i
$416$	−1.54402	−	2.67433i	−0.0757019	−	0.131120i
$417$			12.9270i			0.633040i
$418$		−	1.34807i		−	0.0659365i
$419$	14.5978	+	25.2842i	0.713150	+	1.23521i	0.963669	+	0.267100i	$0.0860654\pi$
$419$	14.5978	+	25.2842i	0.713150	+	1.23521i	−0.250519	+	0.968112i	$0.580601\pi$
$420$	−5.37426	+	1.20119i	−0.262237	+	0.0586119i
$421$		−	26.4129i		−	1.28728i	−0.765327	−	0.643642i	$-0.777423\pi$
$421$		−	26.4129i		−	1.28728i	0.765327	−	0.643642i	$-0.222577\pi$
$422$	−5.64084	−	9.77021i	−0.274592	−	0.475607i
$423$	−2.28945	+	1.32182i	−0.111317	+	0.0642689i
$424$	−8.26490	+	4.77175i	−0.401379	+	0.231736i
$425$	−8.68237	−	6.03487i	−0.421157	−	0.292734i
$426$	−0.00560655	−	0.00323694i	−0.000271638	−	0.000156830i
$427$	−10.1007	−	17.4949i	−0.488806	−	0.846636i
$428$	−4.58807	+	2.64892i	−0.221773	+	0.128041i
$429$	1.20900	−	0.698014i	0.0583709	−	0.0337005i
$430$	5.97327	+	6.49612i	0.288057	+	0.313271i
$431$	17.6376	+	10.1831i	0.849571	+	0.490500i	0.860506	−	0.509440i	$-0.170147\pi$
$431$	17.6376	+	10.1831i	0.849571	+	0.490500i	−0.0109348	+	0.999940i	$0.503481\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$			33.1108i			1.59120i	0.605820	+	0.795602i	$0.292845\pi$
$433$			33.1108i			1.59120i	−0.605820	+	0.795602i	$0.707155\pi$
$434$	−6.29307			−0.302077
$435$	−5.59647	+	17.8572i	−0.268330	+	0.856188i
$436$			6.66007i			0.318960i
$437$	4.58606	+	2.64776i	0.219381	+	0.126660i
$438$	−9.13122			−0.436307
$439$	9.84542	+	5.68426i	0.469896	+	0.271295i	0.716196	−	0.697899i	$-0.245882\pi$
$439$	9.84542	+	5.68426i	0.469896	+	0.271295i	−0.246300	+	0.969194i	$0.579215\pi$
$440$	0.986530	−	0.220497i	0.0470310	−	0.0105118i
$441$	0.467447	−	0.809642i	0.0222594	−	0.0385544i
$442$	−3.26521	−	5.65551i	−0.155310	−	0.269005i
$443$		−	3.67208i		−	0.174466i	−0.996188	−	0.0872328i	$-0.972198\pi$
$443$		−	3.67208i		−	0.174466i	0.996188	−	0.0872328i	$-0.0278024\pi$
$444$	−3.06685	−	5.25304i	−0.145546	−	0.249298i
$445$	17.1545	−	15.7738i	0.813203	−	0.747752i
$446$	12.1086	−	6.99092i	0.573360	−	0.331029i
$447$	−0.798717	−	0.461139i	−0.0377780	−	0.0218111i
$448$	−2.13280	−	1.23137i	−0.100765	−	0.0581768i
$449$	13.3926	+	7.73221i	0.632035	+	0.364906i	0.781540	−	0.623855i	$-0.214435\pi$
$449$	13.3926	+	7.73221i	0.632035	+	0.364906i	−0.149505	+	0.988761i	$0.547768\pi$
$450$	−0.418570	+	4.98245i	−0.0197316	+	0.234875i
$451$	0.534676	−	0.926086i	0.0251769	−	0.0436077i
$452$	−13.1731			−0.619611
$453$	16.3401	−	9.43397i	0.767726	−	0.443247i
$454$	−20.0973			−0.943214
$455$	−12.5179	+	11.5103i	−0.586846	+	0.539613i
$456$	1.49098	+	2.58246i	0.0698217	+	0.120935i
$457$	−1.63400	+	2.83018i	−0.0764355	+	0.132390i	−0.901710	−	0.432342i	$-0.857687\pi$
$457$	−1.63400	+	2.83018i	−0.0764355	+	0.132390i	0.825274	+	0.564732i	$0.191021\pi$
$458$	5.62681			0.262924
$459$	−1.83142	+	1.05737i	−0.0854834	+	0.0493538i
$460$	−1.18753	+	3.78919i	−0.0553691	+	0.176672i
$461$	27.4011	−	15.8201i	1.27620	−	0.736813i	0.300051	−	0.953923i	$-0.402996\pi$
$461$	27.4011	−	15.8201i	1.27620	−	0.736813i	0.976147	+	0.217110i	$0.0696629\pi$
$462$	0.556673	−	0.964186i	0.0258988	−	0.0448580i
$463$	2.72366	−	4.71752i	0.126579	−	0.219242i	−0.795770	−	0.605599i	$-0.792933\pi$
$463$	2.72366	−	4.71752i	0.126579	−	0.219242i	0.922349	+	0.386357i	$0.126267\pi$
$464$	−7.24777	+	4.18450i	−0.336469	+	0.194261i
$465$	−1.70877	+	5.45235i	−0.0792424	+	0.252847i
$466$	−14.0888	+	8.13416i	−0.652650	+	0.376808i
$467$	−32.5303			−1.50532			−0.752662	−	0.658407i	$-0.771230\pi$
$467$	−32.5303			−1.50532			−0.752662	+	0.658407i	$0.771230\pi$
$468$	−1.54402	+	2.67433i	−0.0713725	+	0.123621i
$469$	11.7526	+	20.3561i	0.542686	+	0.939959i
$470$	−4.35139	+	4.00116i	−0.200715	+	0.184560i
$471$	15.0560			0.693742
$472$	2.78387	−	1.60727i	0.128138	−	0.0739805i
$473$	−1.78418			−0.0820365
$474$	6.33650	−	10.9751i	0.291045	−	0.504105i
$475$	14.8575	+	1.24816i	0.681709	+	0.0572696i
$476$	−4.51032	−	2.60403i	−0.206730	−	0.119356i
$477$	8.26490	+	4.77175i	0.378424	+	0.218483i
$478$	4.52658	+	2.61342i	0.207041	+	0.119535i
$479$	−2.08893	+	1.20604i	−0.0954456	+	0.0551055i	−0.546963	−	0.837157i	$-0.684216\pi$
$479$	−2.08893	+	1.20604i	−0.0954456	+	0.0551055i	0.451517	+	0.892262i	$0.350883\pi$
$480$	−1.64599	+	1.51351i	−0.0751288	+	0.0690820i
$481$	−16.3126	−	9.31305i	−0.743789	−	0.424639i
$482$		−	25.2854i		−	1.15172i
$483$	2.18673	+	3.78753i	0.0994996	+	0.172338i
$484$	5.39781	−	9.34929i	0.245355	−	0.424968i
$485$	−12.3093	+	2.75121i	−0.558934	+	0.124926i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	15.6442			0.708907			0.354453	−	0.935074i	$-0.384667\pi$
$487$	15.6442			0.708907			0.354453	+	0.935074i	$0.384667\pi$
$488$	−7.10381	−	4.10139i	−0.321574	−	0.185661i
$489$			17.3734i			0.785653i
$490$	0.625177	−	1.99482i	0.0282426	−	0.0901166i
$491$	−20.4625			−0.923459			−0.461730	−	0.887021i	$-0.652771\pi$
$491$	−20.4625			−0.923459			−0.461730	+	0.887021i	$0.652771\pi$
$492$			2.36543i			0.106642i
$493$	−15.3272	+	8.84914i	−0.690301	+	0.398545i
$494$	7.97475	+	4.60423i	0.358801	+	0.207154i
$495$	−0.684221	−	0.744112i	−0.0307534	−	0.0334453i
$496$	−2.21296	+	1.27765i	−0.0993649	+	0.0573684i
$497$	−0.0138075	+	0.00797176i	−0.000619351	+	0.000357582i
$498$	3.78716	+	6.55955i	0.169707	+	0.293941i
$499$	26.3043	+	15.1868i	1.17754	+	0.679854i	0.955444	−	0.295171i	$-0.0953766\pi$
$499$	26.3043	+	15.1868i	1.17754	+	0.679854i	0.222097	+	0.975025i	$0.428710\pi$
$500$	1.51674	+	11.0770i	0.0678308	+	0.495378i
$501$	−2.87004	+	1.65702i	−0.128224	+	0.0740300i
$502$	1.96946	−	1.13707i	0.0879015	−	0.0507499i
$503$	−10.7612	−	18.6389i	−0.479817	−	0.831068i	0.519915	−	0.854218i	$-0.325964\pi$
$503$	−10.7612	−	18.6389i	−0.479817	−	0.831068i	−0.999732	+	0.0231501i	$0.992630\pi$
$504$			2.46274i			0.109699i
$505$	14.3849	−	3.21514i	0.640120	−	0.143072i
$506$	−0.401409	−	0.695260i	−0.0178448	−	0.0309081i
$507$		−	3.46398i		−	0.153841i
$508$		−	18.2238i		−	0.808552i
$509$	7.88620	+	13.6593i	0.349550	+	0.605438i	0.986169	−	0.165740i	$-0.0530013\pi$
$509$	7.88620	+	13.6593i	0.349550	+	0.605438i	−0.636620	+	0.771178i	$0.719668\pi$
$510$	−3.48085	+	3.20068i	−0.154134	+	0.141729i
$511$	−11.2439	+	19.4751i	−0.497402	+	0.861526i
$512$	−1.00000			−0.0441942
$513$	1.49098	−	2.58246i	0.0658286	−	0.114018i
$514$	−10.8758	+	18.8374i	−0.479710	+	0.830883i
$515$	1.54103	−	0.344431i	0.0679057	−	0.0151774i
$516$	3.41789	−	1.97332i	0.150464	−	0.0868705i
$517$		−	1.19512i		−	0.0525613i
$518$	−14.9801	+	0.0725261i	−0.658188	+	0.00318661i
$519$	−1.12840			−0.0495314
$520$	−2.06502	+	6.58907i	−0.0905571	+	0.288950i
$521$	−10.0002	+	17.3208i	−0.438115	+	0.758837i	−0.997544	−	0.0700410i	$-0.977687\pi$
$521$	−10.0002	+	17.3208i	−0.438115	+	0.758837i	0.559429	+	0.828878i	$0.311020\pi$
$522$	7.24777	+	4.18450i	0.317226	+	0.183151i
$523$	−12.9129	+	22.3658i	−0.564643	+	0.977990i	0.432440	+	0.901663i	$0.357653\pi$
$523$	−12.9129	+	22.3658i	−0.564643	+	0.977990i	−0.997083	+	0.0763270i	$0.975681\pi$
$524$			10.5051i			0.458919i
$525$	10.1111	+	7.02797i	0.441287	+	0.306726i
$526$		−	6.25408i		−	0.272691i
$527$	−4.67984	+	2.70191i	−0.203857	+	0.117697i
$528$		−	0.452075i		−	0.0196741i
$529$	−19.8464			−0.862885
$530$	20.3633	+	6.38187i	0.884524	+	0.277211i
$531$	−2.78387	−	1.60727i	−0.120810	−	0.0697495i
$532$	7.34382			0.318395
$533$	3.65228	+	6.32593i	0.158198	+	0.274006i
$534$	−5.21101	−	9.02573i	−0.225502	−	0.390582i
$535$	11.3042	+	3.54275i	0.488723	+	0.153166i
$536$	8.26563	+	4.77217i	0.357021	+	0.206126i
$537$	4.89623	−	8.48051i	0.211288	−	0.365961i
$538$	−3.53778	−	6.12761i	−0.152524	−	0.264180i
$539$	0.211321	+	0.366019i	0.00910225	+	0.0157656i
$540$	2.13373	+	0.668714i	0.0918213	+	0.0287769i
$541$			18.3497i			0.788917i	0.918914	+	0.394459i	$0.129068\pi$
$541$			18.3497i			0.788917i	−0.918914	+	0.394459i	$0.870932\pi$
$542$	2.51174	−	4.35046i	0.107888	−	0.186868i
$543$	11.6070	−	6.70130i	0.498103	−	0.287580i
$544$	−2.11474			−0.0906688
$545$	10.9624	−	10.0801i	0.469578	−	0.431784i
$546$	3.80253	+	6.58618i	0.162733	+	0.281862i
$547$	−19.3385			−0.826856			−0.413428	−	0.910537i	$-0.635669\pi$
$547$	−19.3385			−0.826856			−0.413428	+	0.910537i	$0.635669\pi$
$548$	−13.4079	−	7.74103i	−0.572755	−	0.330681i
$549$			8.20278i			0.350086i
$550$	−1.85606	−	1.29010i	−0.0791427	−	0.0550098i
$551$	12.4780	−	21.6126i	0.531583	−	0.920728i
$552$	1.53793	+	0.887924i	0.0654586	+	0.0377926i
$553$	−15.6052	−	27.0290i	−0.663599	−	1.14939i
$554$	−28.6013			−1.21515
$555$	−4.00475	+	12.9985i	−0.169992	+	0.551757i
$556$	12.9270			0.548228
$557$	2.23202	+	3.86597i	0.0945736	+	0.163806i	0.909431	−	0.415856i	$-0.136518\pi$
$557$	2.23202	+	3.86597i	0.0945736	+	0.163806i	−0.814857	+	0.579662i	$0.803185\pi$
$558$	2.21296	+	1.27765i	0.0936821	+	0.0540874i
$559$	6.09369	−	10.5546i	0.257736	−	0.446411i
$560$	1.20119	+	5.37426i	0.0507594	+	0.227104i
$561$		−	0.956023i		−	0.0403633i
$562$	−11.1812	−	6.45549i	−0.471652	−	0.272308i
$563$	36.4158			1.53474			0.767371	−	0.641203i	$-0.221564\pi$
$563$	36.4158			1.53474			0.767371	+	0.641203i	$0.221564\pi$
$564$	1.32182	+	2.28945i	0.0556585	+	0.0964033i
$565$	19.9376	+	21.6828i	0.838783	+	0.912203i
$566$	20.7473			0.872073
$567$	2.13280	−	1.23137i	0.0895691	−	0.0517128i
$568$	−0.00323694	+	0.00560655i	−0.000135819	+	0.000235246i
$569$		−	19.5165i		−	0.818175i	−0.912495	−	0.409087i	$-0.865847\pi$
$569$		−	19.5165i		−	0.818175i	0.912495	−	0.409087i	$-0.134153\pi$
$570$	1.99408	−	6.36273i	0.0835230	−	0.266505i
$571$	11.5820	+	20.0607i	0.484693	+	0.839512i	0.999845	−	0.0175863i	$-0.00559817\pi$
$571$	11.5820	+	20.0607i	0.484693	+	0.839512i	−0.515153	+	0.857098i	$0.672265\pi$
$572$	−0.698014	−	1.20900i	−0.0291854	−	0.0505507i
$573$	4.69130	−	8.12557i	0.195982	−	0.339451i
$574$	5.04498	+	2.91272i	0.210574	+	0.121575i
$575$	8.03431	−	3.78030i	0.335054	−	0.157650i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−1.50983	−	2.61511i	−0.0628552	−	0.108868i	0.832885	−	0.553446i	$-0.186687\pi$
$577$	−1.50983	−	2.61511i	−0.0628552	−	0.108868i	−0.895741	+	0.444577i	$0.853354\pi$
$578$	12.5279			0.521091
$579$	10.8268	+	6.25084i	0.449945	+	0.259776i
$580$	17.8572	+	5.59647i	0.741481	+	0.232381i
$581$	18.6536			0.773882
$582$			5.64069i			0.233814i
$583$	−3.73636	+	2.15719i	−0.154744	+	0.0893416i
$584$			9.13122i			0.377853i
$585$	6.73881	−	1.50617i	0.278615	−	0.0622726i
$586$		−	9.38715i		−	0.387780i
$587$	14.4633	−	25.0511i	0.596963	−	1.03397i	−0.396303	−	0.918120i	$-0.629707\pi$
$587$	14.4633	−	25.0511i	0.596963	−	1.03397i	0.993267	−	0.115851i	$-0.0369596\pi$
$588$	−0.809642	−	0.467447i	−0.0333891	−	0.0192772i
$589$	3.80992	−	6.59898i	0.156985	−	0.271906i
$590$	−6.85896	−	2.14961i	−0.282379	−	0.0884979i
$591$	−1.96555			−0.0808518
$592$	−5.25304	+	3.06685i	−0.215899	+	0.126047i
$593$		−	45.1760i		−	1.85516i	−0.373630	−	0.927578i	$-0.621887\pi$
$593$		−	45.1760i		−	1.85516i	0.373630	−	0.927578i	$-0.378113\pi$
$594$	−0.391509	+	0.226038i	−0.0160638	+	0.00927444i
$595$	2.54020	+	11.3652i	0.104138	+	0.465927i
$596$	−0.461139	+	0.798717i	−0.0188890	+	0.0327167i
$597$	−6.35438	+	11.0061i	−0.260068	+	0.450450i
$598$	5.48390			0.224253
$599$	−3.30328	+	5.72145i	−0.134968	+	0.233772i	−0.925585	−	0.378539i	$-0.876427\pi$
$599$	−3.30328	+	5.72145i	−0.134968	+	0.233772i	0.790617	+	0.612311i	$0.209760\pi$
$600$	4.98245	+	0.418570i	0.203408	+	0.0170881i
$601$	−7.30388	−	12.6507i	−0.297932	−	0.516033i	0.677731	−	0.735310i	$-0.262963\pi$
$601$	−7.30388	−	12.6507i	−0.297932	−	0.516033i	−0.975663	+	0.219277i	$0.929630\pi$
$602$		−	9.71955i		−	0.396139i
$603$		−	9.54433i		−	0.388675i
$604$	−9.43397	−	16.3401i	−0.383863	−	0.664870i
$605$	−23.5585	+	5.26550i	−0.957789	+	0.214073i
$606$		−	6.59186i		−	0.267776i
$607$	−13.5413	−	23.4542i	−0.549624	−	0.951976i	−0.998300	−	0.0582820i	$-0.981438\pi$
$607$	−13.5413	−	23.4542i	−0.549624	−	0.951976i	0.448676	−	0.893694i	$-0.351896\pi$
$608$	2.58246	−	1.49098i	0.104733	−	0.0604674i
$609$	17.8494	−	10.3054i	0.723294	−	0.417594i
$610$	4.00085	+	17.9003i	0.161990	+	0.724762i
$611$	7.06993	+	4.08183i	0.286019	+	0.165133i
$612$	1.05737	+	1.83142i	0.0427417	+	0.0740308i
$613$	−5.04052	+	2.91015i	−0.203585	+	0.117540i	−0.598326	−	0.801252i	$-0.704167\pi$
$613$	−5.04052	+	2.91015i	−0.203585	+	0.117540i	0.394742	+	0.918792i	$0.370834\pi$
$614$	1.83027	−	1.05671i	0.0738637	−	0.0426452i
$615$	3.89347	−	3.58010i	0.157000	−	0.144364i
$616$	−0.964186	−	0.556673i	−0.0388481	−	0.0224290i
$617$	25.8535	−	14.9265i	1.04082	−	0.600920i	0.120758	−	0.992682i	$-0.461468\pi$
$617$	25.8535	−	14.9265i	1.04082	−	0.600920i	0.920067	+	0.391762i	$0.128134\pi$
$618$		−	0.706172i		−	0.0284064i
$619$	36.9652			1.48576			0.742878	−	0.669427i	$-0.233460\pi$
$619$	36.9652			1.48576			0.742878	+	0.669427i	$0.233460\pi$
$620$	5.45235	+	1.70877i	0.218972	+	0.0686259i
$621$		−	1.77585i		−	0.0712623i
$622$	19.2848	+	11.1341i	0.773249	+	0.446436i
$623$	−25.6668			−1.02832
$624$	2.67433	+	1.54402i	0.107059	+	0.0618104i
$625$	15.9370	−	19.2617i	0.637480	−	0.770467i
$626$	−8.32368	+	14.4170i	−0.332681	+	0.576221i
$627$	0.674037	+	1.16747i	0.0269185	+	0.0466241i
$628$		−	15.0560i		−	0.600799i
$629$	−11.1088	+	6.48559i	−0.442938	+	0.258598i
$630$	4.05365	−	3.72739i	0.161501	−	0.148503i
$631$	34.1186	−	19.6984i	1.35824	−	0.784179i	0.368852	−	0.929488i	$-0.379751\pi$
$631$	34.1186	−	19.6984i	1.35824	−	0.784179i	0.989386	+	0.145309i	$0.0464175\pi$
$632$	−10.9751	−	6.33650i	−0.436568	−	0.252052i
$633$	9.77021	+	5.64084i	0.388331	+	0.224203i
$634$	2.95498	+	1.70606i	0.117357	+	0.0677563i
$635$	−29.9963	+	27.5820i	−1.19037	+	1.09456i
$636$	4.77175	−	8.26490i	0.189212	−	0.327725i
$637$	−2.88699			−0.114387
$638$	−3.27654	+	1.89171i	−0.129719	+	0.0748935i
$639$	0.00647388			0.000256103
$640$	1.51351	+	1.64599i	0.0598268	+	0.0650635i
$641$	14.7278	+	25.5093i	0.581714	+	1.00756i	0.995276	+	0.0970827i	$0.0309511\pi$
$641$	14.7278	+	25.5093i	0.581714	+	1.00756i	−0.413562	+	0.910476i	$0.635716\pi$
$642$	2.64892	−	4.58807i	0.104545	−	0.181077i
$643$	22.3938			0.883124			0.441562	−	0.897231i	$-0.354425\pi$
$643$	22.3938			0.883124			0.441562	+	0.897231i	$0.354425\pi$
$644$	3.78753	−	2.18673i	0.149249	−	0.0861692i
$645$	−8.42107	−	2.63917i	−0.331579	−	0.103917i
$646$	5.46124	−	3.15305i	0.214869	−	0.124055i
$647$	−10.8449	+	18.7839i	−0.426356	+	0.738471i	−0.996546	−	0.0830421i	$-0.973536\pi$
$647$	−10.8449	+	18.7839i	−0.426356	+	0.738471i	0.570190	+	0.821513i	$0.306870\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	1.25852	−	0.726606i	0.0494012	−	0.0285218i
$650$	13.9710	−	6.57362i	0.547987	−	0.257839i
$651$	5.44996	−	3.14653i	0.213601	−	0.123322i
$652$	17.3734			0.680395
$653$	0.510467	−	0.884155i	0.0199761	−	0.0345996i	−0.855865	−	0.517200i	$-0.826974\pi$
$653$	0.510467	−	0.884155i	0.0199761	−	0.0345996i	0.875841	+	0.482600i	$0.160308\pi$
$654$	−3.33004	−	5.76779i	−0.130215	−	0.225539i
$655$	17.2914	−	15.8996i	0.675629	−	0.621250i
$656$	2.36543			0.0923545
$657$	7.90787	−	4.56561i	0.308515	−	0.178121i
$658$	6.51059			0.253809
$659$	−18.9266	+	32.7818i	−0.737274	+	1.27700i	0.216444	+	0.976295i	$0.430554\pi$
$659$	−18.9266	+	32.7818i	−0.737274	+	1.27700i	−0.953718	+	0.300701i	$0.902779\pi$
$660$	−0.744112	+	0.684221i	−0.0289645	+	0.0266333i
$661$	−23.1502	−	13.3658i	−0.900437	−	0.519868i	−0.0230953	−	0.999733i	$-0.507352\pi$
$661$	−23.1502	−	13.3658i	−0.900437	−	0.519868i	−0.877342	+	0.479866i	$0.840685\pi$
$662$	23.5466	+	13.5946i	0.915164	+	0.528370i
$663$	5.65551	+	3.26521i	0.219642	+	0.126810i
$664$	6.55955	−	3.78716i	0.254560	−	0.146970i
$665$	−11.1150	−	12.0879i	−0.431019	−	0.468747i
$666$	5.28249	+	3.01584i	0.204692	+	0.116861i
$667$		−	14.8621i		−	0.575462i
$668$	1.65702	+	2.87004i	0.0641119	+	0.111045i
$669$	−6.99092	+	12.1086i	−0.270284	+	0.468146i
$670$	−4.65519	−	20.8279i	−0.179846	−	0.804651i
$671$	−3.21146	−	1.85414i	−0.123977	−	0.0715781i
$672$	2.46274			0.0950024
$673$	−5.95454	−	3.43786i	−0.229531	−	0.132520i	0.380825	−	0.924647i	$-0.375640\pi$
$673$	−5.95454	−	3.43786i	−0.229531	−	0.132520i	−0.610356	+	0.792128i	$0.708973\pi$
$674$			11.5777i			0.445958i
$675$	−2.12873	−	4.52421i	−0.0819349	−	0.174137i
$676$	−3.46398			−0.133230
$677$			32.9788i			1.26748i	0.773547	+	0.633739i	$0.218481\pi$
$677$			32.9788i			1.26748i	−0.773547	+	0.633739i	$0.781519\pi$
$678$	11.4082	−	6.58655i	0.438131	−	0.252955i
$679$	12.0305	+	6.94578i	0.461686	+	0.266555i
$680$	3.20068	+	3.48085i	0.122741	+	0.133484i
$681$	17.4048	−	10.0487i	0.666953	−	0.385065i
$682$	−1.00043	+	0.577596i	−0.0383083	+	0.0221173i
$683$	19.1756	+	33.2131i	0.733733	+	1.27086i	0.955277	+	0.295713i	$0.0955571\pi$
$683$	19.1756	+	33.2131i	0.733733	+	1.27086i	−0.221544	+	0.975150i	$0.571110\pi$
$684$	−2.58246	−	1.49098i	−0.0987428	−	0.0570092i
$685$	7.55128	+	33.7853i	0.288519	+	1.29087i
$686$	−16.9235	+	9.77080i	−0.646143	+	0.373051i
$687$	−4.87296	+	2.81341i	−0.185915	+	0.107338i
$688$	−1.97332	−	3.41789i	−0.0752320	−	0.130306i
$689$		−	29.4707i		−	1.12275i
$690$	−0.866158	−	3.87530i	−0.0329741	−	0.147530i
$691$	2.58576	+	4.47867i	0.0983669	+	0.170376i	0.911009	−	0.412387i	$-0.135305\pi$
$691$	2.58576	+	4.47867i	0.0983669	+	0.170376i	−0.812642	+	0.582763i	$0.801971\pi$
$692$			1.12840i			0.0428955i
$693$			1.11335i			0.0422925i
$694$	9.35142	+	16.1971i	0.354975	+	0.614835i
$695$	−19.5652	−	21.2778i	−0.742151	−	0.807112i
$696$	4.18450	−	7.24777i	0.158613	−	0.274726i
$697$	5.00227			0.189475
$698$	−9.61263	+	16.6496i	−0.363844	+	0.630195i
$699$	8.13416	−	14.0888i	0.307662	−	0.532887i
$700$	7.02797	−	10.1111i	0.265632	−	0.382165i
$701$	−9.82218	+	5.67084i	−0.370979	+	0.214185i	−0.673886	−	0.738835i	$-0.735376\pi$
$701$	−9.82218	+	5.67084i	−0.370979	+	0.214185i	0.302907	+	0.953020i	$0.402043\pi$
$702$		−	3.08804i		−	0.116551i
$703$	8.99314	−	15.7522i	0.339183	−	0.594106i
$704$	−0.452075			−0.0170382
$705$	1.76783	−	5.64081i	0.0665805	−	0.212445i
$706$	−5.24212	+	9.07961i	−0.197290	+	0.341716i
$707$	−14.0591	−	8.11703i	−0.528747	−	0.305272i
$708$	−1.60727	+	2.78387i	−0.0604048	+	0.104624i
$709$		−	19.5292i		−	0.733434i	−0.930332	−	0.366717i	$-0.880482\pi$
$709$		−	19.5292i		−	0.733434i	0.930332	−	0.366717i	$-0.119518\pi$
$710$	0.0141275	−	0.00315760i	0.000530195	−	0.000118502i
$711$			12.6730i			0.475275i
$712$	−9.02573	+	5.21101i	−0.338254	+	0.195291i
$713$		−	4.53784i		−	0.169943i
$714$	5.20807			0.194907
$715$	−0.933544	+	2.97875i	−0.0349126	+	0.111399i
$716$	−8.48051	−	4.89623i	−0.316932	−	0.182981i
$717$	−5.22684			−0.195200
$718$	−3.46197	−	5.99630i	−0.129199	−	0.223780i
$719$	−0.612617	−	1.06108i	−0.0228468	−	0.0395718i	0.854376	−	0.519655i	$-0.173940\pi$
$719$	−0.612617	−	1.06108i	−0.0228468	−	0.0395718i	−0.877223	+	0.480084i	$0.840606\pi$
$720$	0.668714	−	2.13373i	0.0249215	−	0.0795196i
$721$	−1.50612	−	0.869560i	−0.0560909	−	0.0323841i
$722$	5.05393	−	8.75367i	0.188088	−	0.325778i
$723$	12.6427	+	21.8978i	0.470187	+	0.814387i
$724$	−6.70130	−	11.6070i	−0.249052	−	0.431370i
$725$	−17.8154	−	37.8631i	−0.661646	−	1.40620i
$726$			10.7956i			0.400663i
$727$	−3.71182	+	6.42905i	−0.137664	+	0.238440i	−0.926612	−	0.376019i	$-0.877293\pi$
$727$	−3.71182	+	6.42905i	−0.137664	+	0.238440i	0.788948	+	0.614460i	$0.210626\pi$
$728$	6.58618	−	3.80253i	0.244100	−	0.140931i
$729$	−1.00000			−0.0370370
$730$	15.0299	−	13.8202i	0.556282	−	0.511509i
$731$	−4.17306	−	7.22795i	−0.154346	−	0.267335i
$732$	8.20278			0.303183
$733$	12.8570	+	7.42300i	0.474885	+	0.274175i	0.718282	−	0.695752i	$-0.244929\pi$
$733$	12.8570	+	7.42300i	0.474885	+	0.274175i	−0.243398	+	0.969927i	$0.578262\pi$
$734$			10.6063i			0.391486i
$735$	0.455989	+	2.04015i	0.0168194	+	0.0752520i
$736$	0.887924	−	1.53793i	0.0327293	−	0.0566888i
$737$	3.73669	+	2.15738i	0.137643	+	0.0794681i
$738$	−1.18271	−	2.04852i	−0.0435363	−	0.0754071i
$739$	−10.3995			−0.382552			−0.191276	−	0.981536i	$-0.561263\pi$
$739$	−10.3995			−0.382552			−0.191276	+	0.981536i	$0.561263\pi$
$740$	12.9985	+	4.00475i	0.477836	+	0.147217i
$741$	−9.20845			−0.338281
$742$	−11.7516	−	20.3543i	−0.431414	−	0.747231i
$743$	−44.2189	−	25.5298i	−1.62223	−	0.936597i	−0.986321	−	0.164836i	$-0.947290\pi$
$743$	−44.2189	−	25.5298i	−1.62223	−	0.936597i	−0.635913	−	0.771761i	$-0.719376\pi$
$744$	1.27765	−	2.21296i	0.0468411	−	0.0811311i
$745$	2.01262	−	0.449835i	0.0737367	−	0.0164807i
$746$			16.2224i			0.593944i
$747$	−6.55955	−	3.78716i	−0.240002	−	0.138565i
$748$	−0.956023			−0.0349556
$749$	−6.52362	−	11.2992i	−0.238368	−	0.412865i
$750$	−6.85203	−	8.83457i	−0.250201	−	0.322593i
$751$	−51.8267			−1.89118			−0.945591	−	0.325357i	$-0.894516\pi$
$751$	−51.8267			−1.89118			−0.945591	+	0.325357i	$0.894516\pi$
$752$	2.28945	−	1.32182i	0.0834877	−	0.0482017i
$753$	−1.13707	+	1.96946i	−0.0414371	+	0.0717712i
$754$		−	25.8439i		−	0.941178i
$755$	−12.6173	+	40.2592i	−0.459189	+	1.46518i
$756$	−1.23137	−	2.13280i	−0.0447846	−	0.0775691i
$757$	−15.0203	−	26.0160i	−0.545924	−	0.945567i	−0.998548	−	0.0538661i	$-0.982846\pi$
$757$	−15.0203	−	26.0160i	−0.545924	−	0.945567i	0.452625	−	0.891701i	$-0.350488\pi$
$758$	−1.83877	+	3.18484i	−0.0667870	+	0.115679i
$759$	0.695260	+	0.401409i	0.0252363	+	0.0145702i
$760$	−6.36273	−	1.99408i	−0.230800	−	0.0723331i
$761$	−4.46887	−	7.74032i	−0.161997	−	0.280586i	0.773588	−	0.633689i	$-0.218460\pi$
$761$	−4.46887	−	7.74032i	−0.161997	−	0.280586i	−0.935585	+	0.353103i	$0.885127\pi$
$762$	9.11192	+	15.7823i	0.330090	+	0.571733i
$763$	−16.4021			−0.593794
$764$	−8.12557	−	4.69130i	−0.293973	−	0.169725i
$765$	1.41416	−	4.51230i	0.0511290	−	0.163142i
$766$	5.48739			0.198267
$767$			9.92663i			0.358430i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$		−	24.4645i		−	0.882214i	−0.897455	−	0.441107i	$-0.854586\pi$
$769$		−	24.4645i		−	0.882214i	0.897455	−	0.441107i	$-0.145414\pi$
$770$	0.543027	+	2.42957i	0.0195693	+	0.0875557i
$771$		−	21.7516i		−	0.783364i
$772$	6.25084	−	10.8268i	0.224973	−	0.389664i
$773$	30.1761	+	17.4222i	1.08536	+	0.626633i	0.932337	−	0.361590i	$-0.117766\pi$
$773$	30.1761	+	17.4222i	1.08536	+	0.626633i	0.153023	+	0.988223i	$0.451099\pi$
$774$	−1.97332	+	3.41789i	−0.0709294	+	0.122853i
$775$	−5.43957	−	11.5608i	−0.195395	−	0.415275i
$776$	5.64069			0.202489
$777$	12.9369	−	7.55286i	0.464108	−	0.270957i
$778$			28.8548i			1.03449i
$779$	−6.10863	+	3.52682i	−0.218864	+	0.126361i
$780$	−1.50617	−	6.73881i	−0.0539297	−	0.241288i
$781$	−0.00146334	+	0.00253458i	−5.23625e−5	+	9.06945e-5i
$782$	1.87773	−	3.25232i	0.0671475	−	0.116303i
$783$	−8.36900			−0.299084
$784$	−0.467447	+	0.809642i	−0.0166945	+	0.0289158i
$785$	−24.7820	+	22.7874i	−0.884507	+	0.813316i
$786$	−5.25257	−	9.09771i	−0.187353	−	0.324505i
$787$		−	35.5191i		−	1.26612i	−0.774103	−	0.633059i	$-0.781799\pi$
$787$		−	35.5191i		−	1.26612i	0.774103	−	0.633059i	$-0.218201\pi$
$788$			1.96555i			0.0700197i
$789$	3.12704	+	5.41619i	0.111326	+	0.192822i
$790$	6.18117	+	27.6553i	0.219916	+	0.983933i
$791$		−	32.4420i		−	1.15350i
$792$	0.226038	+	0.391509i	0.00803190	+	0.0139117i
$793$	21.9369	−	12.6653i	0.779002	−	0.449757i
$794$	−12.0783	+	6.97341i	−0.428643	+	0.247477i
$795$	−20.8260	+	4.65478i	−0.738624	+	0.165088i
$796$	11.0061	+	6.35438i	0.390101	+	0.225225i
$797$	9.39958	+	16.2806i	0.332950	+	0.576687i	0.983089	−	0.183129i	$-0.0586225\pi$
$797$	9.39958	+	16.2806i	0.332950	+	0.576687i	−0.650139	+	0.759816i	$0.725289\pi$
$798$	−6.35994	+	3.67191i	−0.225139	+	0.129984i
$799$	4.84160	−	2.79530i	0.171283	−	0.0988906i
$800$	0.418570	−	4.98245i	0.0147987	−	0.176156i
$801$	9.02573	+	5.21101i	0.318909	+	0.184122i
$802$	17.3636	−	10.0249i	0.613132	−	0.353992i
$803$			4.12800i			0.145674i
$804$	−9.54433			−0.336603
$805$	−9.33180	−	2.92459i	−0.328903	−	0.103078i
$806$		−	7.89091i		−	0.277945i
$807$	6.12761	+	3.53778i	0.215702	+	0.124536i
$808$	−6.59186			−0.231901
$809$	−17.4303	−	10.0634i	−0.612815	−	0.353809i	0.161251	−	0.986913i	$-0.448447\pi$
$809$	−17.4303	−	10.0634i	−0.612815	−	0.353809i	−0.774066	+	0.633104i	$0.781780\pi$
$810$	−2.18223	+	0.487744i	−0.0766756	+	0.0171376i
$811$	−5.19642	+	9.00046i	−0.182471	+	0.316049i	−0.942721	−	0.333581i	$-0.891743\pi$
$811$	−5.19642	+	9.00046i	−0.182471	+	0.316049i	0.760251	+	0.649630i	$0.225076\pi$
$812$	−10.3054	−	17.8494i	−0.361647	−	0.626391i
$813$			5.02348i			0.176181i
$814$	−2.37477	+	1.38645i	−0.0832356	+	0.0485949i
$815$	−26.2948	−	28.5965i	−0.921068	−	1.00169i
$816$	1.83142	−	1.05737i	0.0641125	−	0.0370154i
$817$	10.1920	+	5.88437i	0.356574	+	0.205868i
$818$	16.0291	+	9.25441i	0.560445	+	0.323573i
$819$	−6.58618	−	3.80253i	−0.230140	−	0.132871i
$820$	−3.58010	−	3.89347i	−0.125023	−	0.135966i
$821$	−22.3405	+	38.6948i	−0.779688	+	1.35046i	0.152433	+	0.988314i	$0.451289\pi$
$821$	−22.3405	+	38.6948i	−0.779688	+	1.35046i	−0.932122	+	0.362146i	$0.882044\pi$
$822$	15.4821			0.539999
$823$	26.1020	−	15.0700i	0.909858	−	0.525307i	0.0294727	−	0.999566i	$-0.490617\pi$
$823$	26.1020	−	15.0700i	0.909858	−	0.525307i	0.880386	+	0.474259i	$0.157284\pi$
$824$	−0.706172			−0.0246007
$825$	2.25244	+	0.189225i	0.0784200	+	0.00658798i
$826$	3.95829	+	6.85596i	0.137726	+	0.238549i
$827$	13.9643	−	24.1869i	0.485586	−	0.841060i	−0.514276	−	0.857625i	$-0.671939\pi$
$827$	13.9643	−	24.1869i	0.485586	−	0.841060i	0.999863	+	0.0165641i	$0.00527277\pi$
$828$	−1.77585			−0.0617150
$829$	32.1434	−	18.5580i	1.11639	−	0.644546i	0.175910	−	0.984406i	$-0.443713\pi$
$829$	32.1434	−	18.5580i	1.11639	−	0.644546i	0.940476	+	0.339861i	$0.110380\pi$
$830$	−16.1616	−	5.06506i	−0.560977	−	0.175811i
$831$	24.7694	−	14.3006i	0.859242	−	0.496084i
$832$	1.54402	−	2.67433i	0.0535293	−	0.0927155i
$833$	−0.988530	+	1.71218i	−0.0342505	+	0.0593237i
$834$	−11.1951	+	6.46352i	−0.387656	+	0.223813i
$835$	2.21614	−	7.07126i	0.0766927	−	0.244711i
$836$	1.16747	−	0.674037i	0.0403777	−	0.0233121i
$837$	−2.55531			−0.0883244
$838$	−14.5978	+	25.2842i	−0.504273	+	0.873427i
$839$	4.22147	+	7.31179i	0.145741	+	0.252431i	0.929649	−	0.368446i	$-0.120110\pi$
$839$	4.22147	+	7.31179i	0.145741	+	0.252431i	−0.783908	+	0.620877i	$0.786777\pi$
$840$	−3.72739	−	4.05365i	−0.128607	−	0.139864i
$841$	−41.0402			−1.41518
$842$	22.8742	−	13.2064i	0.788297	−	0.455124i
$843$	12.9110			0.444678
$844$	5.64084	−	9.77021i	0.194166	−	0.336305i
$845$	5.24277	+	5.70168i	0.180357	+	0.196144i
$846$	−2.28945	−	1.32182i	−0.0787130	−	0.0454450i
$847$	23.0249	+	13.2934i	0.791145	+	0.456768i
$848$	−8.26490	−	4.77175i	−0.283818	−	0.163862i
$849$	−17.9677	+	10.3736i	−0.616648	+	0.356022i
$850$	0.885168	−	10.5366i	0.0303610	−	0.361402i
$851$	−0.0522975	−	10.8019i	−0.00179274	−	0.370286i
$852$		−	0.00647388i		−	0.000221792i
$853$	6.10114	+	10.5675i	0.208899	+	0.361824i	0.951368	−	0.308057i	$-0.0996787\pi$
$853$	6.10114	+	10.5675i	0.208899	+	0.361824i	−0.742469	+	0.669880i	$0.766345\pi$
$854$	10.1007	−	17.4949i	0.345638	−	0.598662i
$855$	1.45444	+	6.50733i	0.0497406	+	0.222546i
$856$	−4.58807	−	2.64892i	−0.156817	−	0.0905383i
$857$	28.1230			0.960663			0.480331	−	0.877087i	$-0.340516\pi$
$857$	28.1230			0.960663			0.480331	+	0.877087i	$0.340516\pi$
$858$	1.20900	+	0.698014i	0.0412745	+	0.0238298i
$859$			3.92512i			0.133923i	0.997756	+	0.0669616i	$0.0213305\pi$
$859$			3.92512i			0.133923i	−0.997756	+	0.0669616i	$0.978669\pi$
$860$	−2.63917	+	8.42107i	−0.0899950	+	0.287156i
$861$	−5.82545			−0.198531
$862$			20.3661i			0.693672i
$863$	−49.8149	+	28.7607i	−1.69572	+	0.979025i	−0.745989	+	0.665958i	$0.768023\pi$
$863$	−49.8149	+	28.7607i	−1.69572	+	0.979025i	−0.949731	+	0.313067i	$0.898644\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	1.85734	−	1.70785i	0.0631515	−	0.0580687i
$866$	−28.6748	+	16.5554i	−0.974410	+	0.562576i
$867$	−10.8495	+	6.26393i	−0.368467	+	0.212734i
$868$	−3.14653	−	5.44996i	−0.106800	−	0.184984i
$869$	−4.96159	−	2.86457i	−0.168310	−	0.0971740i
$870$	−18.2630	+	4.08193i	−0.619175	+	0.138390i
$871$	−25.5246	+	14.7367i	−0.864870	+	0.499333i
$872$	−5.76779	+	3.33004i	−0.195322	+	0.112769i
$873$	−2.82034	−	4.88498i	−0.0954542	−	0.165332i
$874$			5.29552i			0.179124i
$875$	−27.2798	+	3.73535i	−0.922224	+	0.126278i
$876$	−4.56561	−	7.90787i	−0.154258	−	0.267182i
$877$		−	15.1386i		−	0.511194i	−0.966783	−	0.255597i	$-0.917728\pi$
$877$		−	15.1386i		−	0.511194i	0.966783	−	0.255597i	$-0.0822720\pi$
$878$			11.3685i			0.383669i
$879$	4.69358	+	8.12951i	0.158310	+	0.274202i
$880$	0.684221	+	0.744112i	0.0230651	+	0.0250840i
$881$	−4.71995	+	8.17519i	−0.159019	+	0.275429i	−0.934515	−	0.355923i	$-0.884166\pi$
$881$	−4.71995	+	8.17519i	−0.159019	+	0.275429i	0.775496	+	0.631352i	$0.217500\pi$
$882$	0.934894			0.0314795
$883$	14.3072	−	24.7808i	0.481476	−	0.833940i	−0.518298	−	0.855200i	$-0.673434\pi$
$883$	14.3072	−	24.7808i	0.481476	−	0.833940i	0.999774	+	0.0212597i	$0.00676768\pi$
$884$	3.26521	−	5.65551i	0.109821	−	0.190215i
$885$	7.01484	−	1.56787i	0.235801	−	0.0527033i
$886$	3.18011	−	1.83604i	0.106838	−	0.0616829i
$887$		−	17.5826i		−	0.590365i	−0.955441	−	0.295182i	$-0.904620\pi$
$887$		−	17.5826i		−	0.590365i	0.955441	−	0.295182i	$-0.0953804\pi$
$888$	3.01584	−	5.28249i	0.101205	−	0.177269i
$889$	44.8806			1.50525
$890$	22.2378	+	6.96935i	0.745413	+	0.233613i
$891$	0.226038	−	0.391509i	0.00757255	−	0.0131160i
$892$	12.1086	+	6.99092i	0.405427	+	0.234073i
$893$	−3.94161	+	6.82707i	−0.131901	+	0.228459i
$894$		−	0.922279i		−	0.0308456i
$895$	4.77621	+	21.3693i	0.159651	+	0.714298i
$896$		−	2.46274i		−	0.0822745i
$897$	−4.74919	+	2.74195i	−0.158571	+	0.0915510i
$898$			15.4644i			0.516054i
$899$	−21.3854			−0.713242
$900$	−4.52421	+	2.12873i	−0.150807	+	0.0709577i
$901$	−17.4781	−	10.0910i	−0.582281	−	0.336180i
$902$	1.06935			0.0356055
$903$	4.85977	+	8.41738i	0.161723	+	0.280113i
$904$	−6.58655	−	11.4082i	−0.219066	−	0.379433i
$905$	−8.96250	+	28.5976i	−0.297924	+	0.950615i
$906$	16.3401	+	9.43397i	0.542864	+	0.313423i
$907$	−9.16742	+	15.8784i	−0.304399	+	0.527235i	−0.977127	−	0.212655i	$-0.931789\pi$
$907$	−9.16742	+	15.8784i	−0.304399	+	0.527235i	0.672728	+	0.739890i	$0.265122\pi$
$908$	−10.0487	−	17.4048i	−0.333476	−	0.577598i
$909$	3.29593	+	5.70872i	0.109319	+	0.189346i
$910$	−16.2272	−	5.08561i	−0.537926	−	0.168586i
$911$		−	31.0919i		−	1.03012i	−0.857154	−	0.515060i	$-0.827770\pi$
$911$		−	31.0919i		−	1.03012i	0.857154	−	0.515060i	$-0.172230\pi$
$912$	−1.49098	+	2.58246i	−0.0493714	+	0.0855138i
$913$	2.96541	−	1.71208i	0.0981408	−	0.0566616i
$914$	−3.26801			−0.108096
$915$	−12.4150	−	13.5017i	−0.410427	−	0.446352i
$916$	2.81341	+	4.87296i	0.0929576	+	0.161007i
$917$	−25.8714			−0.854351
$918$	−1.83142	−	1.05737i	−0.0604459	−	0.0348984i
$919$			4.65598i			0.153587i	0.997047	+	0.0767934i	$0.0244682\pi$
$919$			4.65598i			0.153587i	−0.997047	+	0.0767934i	$0.975532\pi$
$920$	−3.87530	+	0.866158i	−0.127765	+	0.0285564i
$921$	−1.05671	+	1.83027i	−0.0348197	+	0.0603095i
$922$	27.4011	+	15.8201i	0.902408	+	0.521006i
$923$	−0.00999582	−	0.0173133i	−0.000329016	−	0.000569873i
$924$	1.11335			0.0366264
$925$	−13.0817	−	27.4567i	−0.430122	−	0.902771i
$926$	5.44733			0.179010
$927$	0.353086	+	0.611563i	0.0115969	+	0.0200864i
$928$	−7.24777	−	4.18450i	−0.237920	−	0.137363i
$929$	12.7005	−	21.9980i	0.416691	−	0.721731i	−0.578913	−	0.815389i	$-0.696523\pi$
$929$	12.7005	−	21.9980i	0.416691	−	0.721731i	0.995604	+	0.0936586i	$0.0298562\pi$
$930$	−5.57626	+	1.24634i	−0.182853	+	0.0408689i
$931$		−	2.78782i		−	0.0913673i
$932$	−14.0888	−	8.13416i	−0.461493	−	0.266443i
$933$	−22.2681			−0.729026
$934$	−16.2652	−	28.1721i	−0.532212	−	0.921819i
$935$	1.44695	+	1.57360i	0.0473203	+	0.0514624i
$936$	−3.08804			−0.100936
$937$	17.8365	−	10.2979i	0.582692	−	0.336417i	−0.179511	−	0.983756i	$-0.557451\pi$
$937$	17.8365	−	10.2979i	0.582692	−	0.336417i	0.762202	+	0.647339i	$0.224118\pi$
$938$	−11.7526	+	20.3561i	−0.383737	+	0.664651i
$939$		−	16.6474i		−	0.543266i
$940$	−5.64081	−	1.76783i	−0.183983	−	0.0576604i
$941$	2.99808	+	5.19283i	0.0977348	+	0.169282i	0.910747	−	0.412965i	$-0.135507\pi$
$941$	2.99808	+	5.19283i	0.0977348	+	0.169282i	−0.813012	+	0.582247i	$0.802174\pi$
$942$	7.52798	+	13.0389i	0.245275	+	0.424829i
$943$	−2.10032	+	3.63786i	−0.0683959	+	0.118465i
$944$	2.78387	+	1.60727i	0.0906072	+	0.0523121i
$945$	−1.64687	+	5.25484i	−0.0535727	+	0.170940i
$946$	−0.892088	−	1.54514i	−0.0290043	−	0.0502369i
$947$	−0.385031	−	0.666893i	−0.0125118	−	0.0216711i	0.859702	−	0.510796i	$-0.170649\pi$
$947$	−0.385031	−	0.666893i	−0.0125118	−	0.0216711i	−0.872214	+	0.489125i	$0.837316\pi$
$948$	12.6730			0.411600
$949$	−24.4199	−	14.0988i	−0.792702	−	0.457667i
$950$	6.34781	+	13.4911i	0.205950	+	0.437708i
$951$	−3.41212			−0.110646
$952$		−	5.20807i		−	0.168794i
$953$	41.0658	−	23.7093i	1.33025	−	0.768021i	0.344913	−	0.938635i	$-0.387908\pi$
$953$	41.0658	−	23.7093i	1.33025	−	0.768021i	0.985338	+	0.170614i	$0.0545752\pi$
$954$			9.54349i			0.308982i
$955$	4.57630	+	20.4750i	0.148086	+	0.662554i
$956$			5.22684i			0.169048i
$957$	1.89171	−	3.27654i	0.0611503	−	0.105915i
$958$	−2.08893	−	1.20604i	−0.0674902	−	0.0389655i
$959$	19.0642	−	33.0201i	0.615614	−	1.06628i
$960$	−2.13373	−	0.668714i	−0.0688660	−	0.0215827i
$961$	24.4704			0.789368
$962$	−0.0909408	−	18.7836i	−0.00293205	−	0.605608i
$963$			5.29785i			0.170721i
$964$	21.8978	−	12.6427i	0.705280	−	0.407193i
$965$	−27.2815	+	6.09761i	−0.878222	+	0.196289i
$966$	−2.18673	+	3.78753i	−0.0703569	+	0.121862i
$967$	−13.9911	+	24.2333i	−0.449923	+	0.779290i	−0.998381	−	0.0568884i	$-0.981882\pi$
$967$	−13.9911	+	24.2333i	−0.449923	+	0.779290i	0.548457	+	0.836179i	$0.315215\pi$
$968$	10.7956			0.346985
$969$	−3.15305	+	5.46124i	−0.101290	+	0.175440i
$970$	−8.53724	−	9.28452i	−0.274114	−	0.298108i
$971$	−2.43501	−	4.21757i	−0.0781433	−	0.135348i	0.824306	−	0.566145i	$-0.191566\pi$
$971$	−2.43501	−	4.21757i	−0.0781433	−	0.135348i	−0.902449	+	0.430797i	$0.858233\pi$
$972$			1.00000i			0.0320750i
$973$			31.8360i			1.02061i
$974$	7.82210	+	13.5483i	0.250636	+	0.434115i
$975$	−8.81240	+	12.6784i	−0.282223	+	0.406034i
$976$		−	8.20278i		−	0.262564i
$977$	4.47908	+	7.75800i	0.143299	+	0.248200i	0.928737	−	0.370740i	$-0.120896\pi$
$977$	4.47908	+	7.75800i	0.143299	+	0.248200i	−0.785438	+	0.618940i	$0.787562\pi$
$978$	−15.0458	+	8.68670i	−0.481112	+	0.277770i
$979$	−4.08031	+	2.35577i	−0.130407	+	0.0752907i
$980$	2.04015	−	0.455989i	0.0651702	−	0.0145660i
$981$	5.76779	+	3.33004i	0.184151	+	0.106320i
$982$	−10.2312	−	17.7210i	−0.326492	−	0.565501i
$983$	6.93809	−	4.00571i	0.221291	−	0.127762i	−0.385257	−	0.922809i	$-0.625887\pi$
$983$	6.93809	−	4.00571i	0.221291	−	0.127762i	0.606548	+	0.795047i	$0.292554\pi$
$984$	−2.04852	+	1.18271i	−0.0653045	+	0.0377036i
$985$	3.23527	−	2.97488i	0.103084	−	0.0947875i
$986$	−15.3272	−	8.84914i	−0.488116	−	0.281814i
$987$	−5.63833	+	3.25529i	−0.179470	+	0.103617i
$988$			9.20845i			0.292960i
$989$	7.00862			0.222861
$990$	0.302309	−	0.964609i	0.00960802	−	0.0306573i
$991$		−	13.7352i		−	0.436312i	−0.975914	−	0.218156i	$-0.929996\pi$
$991$		−	13.7352i		−	0.436312i	0.975914	−	0.218156i	$-0.0700041\pi$
$992$	−2.21296	−	1.27765i	−0.0702616	−	0.0405656i
$993$	−27.1893			−0.862825
$994$	−0.0138075	−	0.00797176i	−0.000437947	−	0.000252849i
$995$	−6.19862	−	27.7334i	−0.196509	−	0.879207i
$996$	−3.78716	+	6.55955i	−0.120001	+	0.207847i
$997$	14.1059	+	24.4321i	0.446738	+	0.773774i	0.998172	−	0.0604454i	$-0.0192521\pi$
$997$	14.1059	+	24.4321i	0.446738	+	0.773774i	−0.551433	+	0.834219i	$0.685919\pi$
$998$			30.3736i			0.961458i
$999$	−6.08269	+	0.0294493i	−0.192448	+	0.000931735i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.ba.b.529.6	yes	36
5.4	even	2		1110.2.ba.a.529.13	✓	36
37.27	even	6		1110.2.ba.a.619.13	yes	36
185.64	even	6	inner	1110.2.ba.b.619.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.13	✓	36	5.4	even	2
1110.2.ba.a.619.13	yes	36	37.27	even	6
1110.2.ba.b.529.6	yes	36	1.1	even	1	trivial
1110.2.ba.b.619.6	yes	36	185.64	even	6	inner

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.18223 - 0.487744i) q^{5} -1.00000i q^{6} +(-2.13280 - 1.23137i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.18223 - 0.487744i) q^{5} -1.00000i q^{6} +(-2.13280 - 1.23137i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(1.51351 + 1.64599i) q^{10} -0.452075 q^{11} +(0.866025 - 0.500000i) q^{12} +(1.54402 - 2.67433i) q^{13} -2.46274i q^{14} +(-2.13373 - 0.668714i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.05737 - 1.83142i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.58246 + 1.49098i) q^{19} +(-0.668714 + 2.13373i) q^{20} +(1.23137 + 2.13280i) q^{21} +(-0.226038 - 0.391509i) q^{22} +1.77585 q^{23} +(0.866025 + 0.500000i) q^{24} +(4.52421 - 2.12873i) q^{25} +3.08804 q^{26} -1.00000i q^{27} +(2.13280 - 1.23137i) q^{28} -8.36900i q^{29} +(-0.487744 - 2.18223i) q^{30} -2.55531i q^{31} +(0.500000 - 0.866025i) q^{32} +(0.391509 + 0.226038i) q^{33} +(1.05737 - 1.83142i) q^{34} +(-5.25484 - 1.64687i) q^{35} -1.00000 q^{36} +(-0.0294493 - 6.08269i) q^{37} +2.98197i q^{38} +(-2.67433 + 1.54402i) q^{39} +(-2.18223 + 0.487744i) q^{40} +(-1.18271 + 2.04852i) q^{41} +(-1.23137 + 2.13280i) q^{42} +3.94663 q^{43} +(0.226038 - 0.391509i) q^{44} +(1.51351 + 1.64599i) q^{45} +(0.887924 + 1.53793i) q^{46} +2.64363i q^{47} +1.00000i q^{48} +(-0.467447 - 0.809642i) q^{49} +(4.10564 + 2.85372i) q^{50} +2.11474i q^{51} +(1.54402 + 2.67433i) q^{52} +(8.26490 - 4.77175i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-0.986530 + 0.220497i) q^{55} +(2.13280 + 1.23137i) q^{56} +(-1.49098 - 2.58246i) q^{57} +(7.24777 - 4.18450i) q^{58} +(-2.78387 + 1.60727i) q^{59} +(1.64599 - 1.51351i) q^{60} +(7.10381 + 4.10139i) q^{61} +(2.21296 - 1.27765i) q^{62} -2.46274i q^{63} +1.00000 q^{64} +(2.06502 - 6.58907i) q^{65} +0.452075i q^{66} +(-8.26563 - 4.77217i) q^{67} +2.11474 q^{68} +(-1.53793 - 0.887924i) q^{69} +(-1.20119 - 5.37426i) q^{70} +(0.00323694 - 0.00560655i) q^{71} +(-0.500000 - 0.866025i) q^{72} -9.13122i q^{73} +(5.25304 - 3.06685i) q^{74} +(-4.98245 - 0.418570i) q^{75} +(-2.58246 + 1.49098i) q^{76} +(0.964186 + 0.556673i) q^{77} +(-2.67433 - 1.54402i) q^{78} +(10.9751 + 6.33650i) q^{79} +(-1.51351 - 1.64599i) q^{80} +(-0.500000 + 0.866025i) q^{81} -2.36543 q^{82} +(-6.55955 + 3.78716i) q^{83} -2.46274 q^{84} +(-3.20068 - 3.48085i) q^{85} +(1.97332 + 3.41789i) q^{86} +(-4.18450 + 7.24777i) q^{87} +0.452075 q^{88} +(9.02573 - 5.21101i) q^{89} +(-0.668714 + 2.13373i) q^{90} +(-6.58618 + 3.80253i) q^{91} +(-0.887924 + 1.53793i) q^{92} +(-1.27765 + 2.21296i) q^{93} +(-2.28945 + 1.32182i) q^{94} +(6.36273 + 1.99408i) q^{95} +(-0.866025 + 0.500000i) q^{96} -5.64069 q^{97} +(0.467447 - 0.809642i) q^{98} +(-0.226038 - 0.391509i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9	\( 36 q + 18 q^{2} - 18 q^{4} + 4 q^{5} - 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} + 14 q^{13} + 2 q^{15} - 18 q^{16} - 18 q^{18} + 6 q^{19} - 2 q^{20} + 2 q^{22} + 20 q^{23} - 2 q^{25} + 28 q^{26} - 2 q^{30} + 18 q^{32} + 6 q^{33} - 20 q^{35} - 36 q^{36} - 20 q^{37} + 6 q^{39} - 4 q^{40} + 10 q^{41} - 2 q^{44} + 2 q^{45} + 10 q^{46} + 10 q^{49} - 4 q^{50} + 14 q^{52} + 12 q^{53} + 40 q^{55} - 8 q^{57} - 30 q^{58} + 18 q^{59} - 4 q^{60} - 6 q^{61} + 12 q^{62} + 36 q^{64} - 32 q^{65} - 36 q^{67} + 12 q^{69} - 40 q^{70} - 24 q^{71} - 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} + 24 q^{77} + 6 q^{78} - 2 q^{80} - 18 q^{81} + 20 q^{82} - 36 q^{83} + 26 q^{85} + 10 q^{87} - 4 q^{88} - 2 q^{90} - 36 q^{91} - 10 q^{92} - 12 q^{93} + 12 q^{94} + 18 q^{95} - 52 q^{97} - 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q + 18 * q^2 - 18 * q^4 + 4 * q^5 - 36 * q^8 + 18 * q^9 + 2 * q^10 + 4 * q^11 + 14 * q^13 + 2 * q^15 - 18 * q^16 - 18 * q^18 + 6 * q^19 - 2 * q^20 + 2 * q^22 + 20 * q^23 - 2 * q^25 + 28 * q^26 - 2 * q^30 + 18 * q^32 + 6 * q^33 - 20 * q^35 - 36 * q^36 - 20 * q^37 + 6 * q^39 - 4 * q^40 + 10 * q^41 - 2 * q^44 + 2 * q^45 + 10 * q^46 + 10 * q^49 - 4 * q^50 + 14 * q^52 + 12 * q^53 + 40 * q^55 - 8 * q^57 - 30 * q^58 + 18 * q^59 - 4 * q^60 - 6 * q^61 + 12 * q^62 + 36 * q^64 - 32 * q^65 - 36 * q^67 + 12 * q^69 - 40 * q^70 - 24 * q^71 - 18 * q^72 - 34 * q^74 + 8 * q^75 - 6 * q^76 + 24 * q^77 + 6 * q^78 - 2 * q^80 - 18 * q^81 + 20 * q^82 - 36 * q^83 + 26 * q^85 + 10 * q^87 - 4 * q^88 - 2 * q^90 - 36 * q^91 - 10 * q^92 - 12 * q^93 + 12 * q^94 + 18 * q^95 - 52 * q^97 - 10 * q^98 + 2 * q^99

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