LMFDB - Embedded newform 1110.2.ba.a.619.13

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			619.13
Character	$\chi$	$=$	1110.619
Dual form			1110.2.ba.a.529.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.668714 - 2.13373i) q^{5} +1.00000i q^{6} +(2.13280 - 1.23137i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.668714 - 2.13373i) 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} +(-0.487744 - 2.18223i) 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} +(-2.18223 + 0.487744i) q^{20} +(1.23137 - 2.13280i) q^{21} +(0.226038 - 0.391509i) q^{22} -1.77585 q^{23} +(0.866025 - 0.500000i) q^{24} +(-4.10564 - 2.85372i) q^{25} +3.08804 q^{26} -1.00000i q^{27} +(-2.13280 - 1.23137i) q^{28} +8.36900i q^{29} +(2.13373 + 0.668714i) q^{30} +2.55531i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.391509 + 0.226038i) q^{33} +(1.05737 + 1.83142i) q^{34} +(-1.20119 - 5.37426i) q^{35} -1.00000 q^{36} +(0.0294493 - 6.08269i) q^{37} +2.98197i q^{38} +(-2.67433 - 1.54402i) q^{39} +(0.668714 - 2.13373i) 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} +(4.52421 - 2.12873i) q^{50} -2.11474i q^{51} +(-1.54402 + 2.67433i) q^{52} +(-8.26490 - 4.77175i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.302309 + 0.964609i) 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} +(-6.73881 + 1.50617i) q^{65} -0.452075i q^{66} +(8.26563 - 4.77217i) q^{67} -2.11474 q^{68} +(-1.53793 + 0.887924i) q^{69} +(5.25484 + 1.64687i) 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} +(2.18223 - 0.487744i) 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} +(-1.45444 - 6.50733i) 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} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	$ 36 q - 18 q^{2} - 18 q^{4} + 2 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} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 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} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) $ 36 * q - 18 * q^2 - 18 * q^4 + 2 * 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 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * 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 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * 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 $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

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

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
$5$	0.668714	−	2.13373i	0.299058	−	0.954235i
$5$	0.668714	−	2.13373i	0.299058	−	0.954235i
$6$			1.00000i			0.408248i
$7$	2.13280	−	1.23137i	0.806122	−	0.465415i	−0.0394853	−	0.999220i	$-0.512572\pi$
$7$	2.13280	−	1.23137i	0.806122	−	0.465415i	0.845607	+	0.533805i	$0.179239\pi$
$8$	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	$-0.307531\pi$
$13$	−1.54402	−	2.67433i	−0.428235	−	0.741724i	−0.996716	+	0.0809716i	$0.974198\pi$
$14$			2.46274i			0.658196i
$15$	−0.487744	−	2.18223i	−0.125935	−	0.563448i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.05737	−	1.83142i	0.256450	−	0.444185i	−0.708838	−	0.705371i	$-0.750780\pi$
$17$	1.05737	−	1.83142i	0.256450	−	0.444185i	0.965288	+	0.261186i	$0.0841137\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	2.58246	−	1.49098i	0.592457	−	0.342055i	−0.173611	−	0.984814i	$-0.555544\pi$
$19$	2.58246	−	1.49098i	0.592457	−	0.342055i	0.766068	+	0.642759i	$0.222210\pi$
$20$	−2.18223	+	0.487744i	−0.487960	+	0.109063i
$21$	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	$-0.559275\pi$
$23$	−1.77585			−0.370290			−0.185145	+	0.982711i	$0.559275\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−4.10564	−	2.85372i	−0.821128	−	0.570743i
$26$	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	$0.283281\pi$
$29$			8.36900i			1.55408i	−0.629448	+	0.777042i	$0.716719\pi$
$30$	2.13373	+	0.668714i	0.389565	+	0.122090i
$31$			2.55531i			0.458947i	0.973315	+	0.229473i	$0.0737004\pi$
$31$			2.55531i			0.458947i	−0.973315	+	0.229473i	$0.926300\pi$
$32$	−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
$35$	−1.20119	−	5.37426i	−0.203038	−	0.908416i
$36$	−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
$40$	0.668714	−	2.13373i	0.105733	−	0.337373i
$41$	−1.18271	−	2.04852i	−0.184709	−	0.319925i	0.758769	−	0.651359i	$-0.225801\pi$
$41$	−1.18271	−	2.04852i	−0.184709	−	0.319925i	−0.943478	+	0.331434i	$0.892468\pi$
$42$	1.23137	+	2.13280i	0.190005	+	0.329098i
$43$	−3.94663			−0.601856			−0.300928	−	0.953647i	$-0.597296\pi$
$43$	−3.94663			−0.601856			−0.300928	+	0.953647i	$0.597296\pi$
$44$	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
$50$	4.52421	−	2.12873i	0.639820	−	0.301048i
$51$		−	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	$-0.560854\pi$
$53$	−8.26490	−	4.77175i	−1.13527	−	0.655450i	−0.945255	+	0.326331i	$0.894187\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−0.302309	+	0.964609i	−0.0407634	+	0.130068i
$56$	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	0.307717	−	0.951478i	$-0.400435\pi$
$59$	−2.78387	−	1.60727i	−0.362429	−	0.209248i	−0.670146	+	0.742230i	$0.733768\pi$
$60$	−1.64599	+	1.51351i	−0.212496	+	0.195393i
$61$	7.10381	−	4.10139i	0.909550	−	0.525129i	0.0292637	−	0.999572i	$-0.490684\pi$
$61$	7.10381	−	4.10139i	0.909550	−	0.525129i	0.880286	+	0.474443i	$0.157350\pi$
$62$	−2.21296	−	1.27765i	−0.281046	−	0.162262i
$63$		−	2.46274i		−	0.310277i
$64$	1.00000			0.125000
$65$	−6.73881	+	1.50617i	−0.835846	+	0.186818i
$66$		−	0.452075i		−	0.0556466i
$67$	8.26563	−	4.77217i	1.00981	−	0.583013i	0.0986725	−	0.995120i	$-0.468540\pi$
$67$	8.26563	−	4.77217i	1.00981	−	0.583013i	0.911135	+	0.412107i	$0.135207\pi$
$68$	−2.11474			−0.256450
$69$	−1.53793	+	0.887924i	−0.185145	+	0.106893i
$70$	5.25484	+	1.64687i	0.628074	+	0.196839i
$71$	0.00323694	+	0.00560655i	0.000384154	+	0.000665375i	0.866217	−	0.499667i	$-0.166544\pi$
$71$	0.00323694	+	0.00560655i	0.000384154	+	0.000665375i	−0.865833	+	0.500333i	$0.833211\pi$
$72$	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	0.266773	−	0.963759i	$-0.414043\pi$
$79$	10.9751	−	6.33650i	1.23480	−	0.712912i	0.968027	+	0.250848i	$0.0807093\pi$
$80$	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	$-0.196872\pi$
$83$	6.55955	+	3.78716i	0.720005	+	0.415695i	−0.0947497	+	0.995501i	$0.530205\pi$
$84$	−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	0.895164	−	0.445737i	$-0.147059\pi$
$89$	9.02573	+	5.21101i	0.956726	+	0.552366i	0.0615619	+	0.998103i	$0.480392\pi$
$90$	2.18223	−	0.487744i	0.230027	−	0.0514127i
$91$	−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
$95$	−1.45444	−	6.50733i	−0.149222	−	0.667638i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	5.64069			0.572725			0.286363	−	0.958121i	$-0.407554\pi$
$97$	5.64069			0.572725			0.286363	+	0.958121i	$0.407554\pi$
$98$	−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	$-0.511076\pi$
$103$	−0.706172			−0.0695812			−0.0347906	+	0.999395i	$0.511076\pi$
$104$	−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	$-0.749098\pi$
$107$	−4.58807	+	2.64892i	−0.443545	+	0.256081i	0.261555	+	0.965189i	$0.415765\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	5.76779	+	3.33004i	0.552454	+	0.318960i	0.750111	−	0.661312i	$-0.230000\pi$
$109$	5.76779	+	3.33004i	0.552454	+	0.318960i	−0.197657	+	0.980271i	$0.563333\pi$
$110$	−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	0.369946	+	0.929053i	$0.379376\pi$
$113$	−6.58655	+	11.4082i	−0.619611	+	1.07320i	−0.989557	+	0.144144i	$0.953957\pi$
$114$	1.49098	+	2.58246i	0.139643	+	0.241870i
$115$	−1.18753	+	3.78919i	−0.110738	+	0.353344i
$116$	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
$120$	−0.487744	−	2.18223i	−0.0445247	−	0.199209i
$121$	−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	$-0.0335850\pi$
$127$	15.7823	+	9.11192i	1.40045	+	0.808552i	0.406014	+	0.913867i	$0.366918\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−3.41789	+	1.97332i	−0.300928	+	0.173741i
$130$	2.06502	−	6.58907i	0.181114	−	0.577899i
$131$	9.09771	+	5.25257i	0.794871	+	0.458919i	0.841674	−	0.539985i	$-0.181570\pi$
$131$	9.09771	+	5.25257i	0.794871	+	0.458919i	−0.0468037	+	0.998904i	$0.514904\pi$
$132$	0.391509	+	0.226038i	0.0340765	+	0.0196741i
$133$	3.67191	−	6.35994i	0.318395	−	0.551476i
$134$			9.54433i			0.824505i
$135$	−2.13373	−	0.668714i	−0.183643	−	0.0575538i
$136$	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	0.450168	+	0.892944i	$0.351364\pi$
$139$	−6.46352	+	11.1951i	−0.548228	+	0.949560i	−0.998396	+	0.0566155i	$0.981969\pi$
$140$	−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
$145$	17.8572	+	5.59647i	1.48296	+	0.464762i
$146$	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	$0.487972\pi$
$150$	2.85372	−	4.10564i	0.233005	−	0.335224i
$151$	−9.43397	−	16.3401i	−0.767726	−	1.32974i	−0.938793	−	0.344481i	$-0.888055\pi$
$151$	−9.43397	−	16.3401i	−0.767726	−	1.32974i	0.171067	−	0.985259i	$-0.445278\pi$
$152$	2.58246	−	1.49098i	0.209465	−	0.120935i
$153$	−1.05737	−	1.83142i	−0.0854834	−	0.148062i
$154$		−	1.11335i		−	0.0897159i
$155$	5.45235	+	1.70877i	0.437943	+	0.137252i
$156$			3.08804i			0.247241i
$157$	13.0389	+	7.52798i	1.04061	+	0.600799i	0.920007	−	0.391902i	$-0.128183\pi$
$157$	13.0389	+	7.52798i	1.04061	+	0.600799i	0.120607	+	0.992700i	$0.461516\pi$
$158$			12.6730i			1.00821i
$159$	−9.54349			−0.756848
$160$	−2.18223	+	0.487744i	−0.172520	+	0.0385595i
$161$	−3.78753	+	2.18673i	−0.298499	+	0.172338i
$162$	1.00000			0.0785674
$163$	8.68670	−	15.0458i	0.680395	−	1.17848i	−0.294465	−	0.955662i	$-0.595141\pi$
$163$	8.68670	−	15.0458i	0.680395	−	1.17848i	0.974860	−	0.222817i	$-0.0715252\pi$
$164$	−1.18271	+	2.04852i	−0.0923545	+	0.159963i
$165$	0.220497	+	0.986530i	0.0171657	+	0.0768013i
$166$	−6.55955	+	3.78716i	−0.509120	+	0.293941i
$167$	−1.65702	−	2.87004i	−0.128224	−	0.222090i	0.794765	−	0.606918i	$-0.207594\pi$
$167$	−1.65702	−	2.87004i	−0.128224	−	0.222090i	−0.922988	+	0.384828i	$0.874261\pi$
$168$	1.23137	−	2.13280i	0.0950024	−	0.164549i
$169$	1.73199	−	2.99990i	0.133230	−	0.230761i
$170$	4.61484	−	1.03145i	0.353942	−	0.0791087i
$171$		−	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	$-0.346992\pi$
$173$	−0.977227	−	0.564202i	−0.0742972	−	0.0428955i	−0.536688	+	0.843781i	$0.680325\pi$
$174$	−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	$-0.880740\pi$
$179$		−	9.79245i		−	0.731922i	0.930630	−	0.365961i	$-0.119260\pi$
$180$	−0.668714	+	2.13373i	−0.0498430	+	0.159039i
$181$	−6.70130	−	11.6070i	−0.498103	−	0.862740i	0.501894	−	0.864929i	$-0.332637\pi$
$181$	−6.70130	−	11.6070i	−0.498103	−	0.862740i	−0.999998	+	0.00218861i	$0.999303\pi$
$182$	6.58618	−	3.80253i	0.488200	−	0.281862i
$183$	4.10139	−	7.10381i	0.303183	−	0.525129i
$184$	−1.77585			−0.130917
$185$	−12.9592	−	4.13042i	−0.952776	−	0.303674i
$186$	−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
$190$	6.36273	+	1.99408i	0.461601	+	0.144666i
$191$		−	9.38260i		−	0.678901i	−0.940624	−	0.339451i	$-0.889759\pi$
$191$		−	9.38260i		−	0.678901i	0.940624	−	0.339451i	$-0.110241\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	12.5017			0.899890			0.449945	−	0.893056i	$-0.351444\pi$
$193$	12.5017			0.899890			0.449945	+	0.893056i	$0.351444\pi$
$194$	−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	$-0.355640\pi$
$197$	−1.70221	−	0.982774i	−0.121278	−	0.0700197i	−0.559412	+	0.828890i	$0.688973\pi$
$198$	−0.226038	−	0.391509i	−0.0160638	−	0.0278233i
$199$			12.7088i			0.900900i	0.892802	+	0.450450i	$0.148737\pi$
$199$			12.7088i			0.900900i	−0.892802	+	0.450450i	$0.851263\pi$
$200$	−4.10564	−	2.85372i	−0.290313	−	0.201788i
$201$	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
$205$	−5.16190	+	1.15372i	−0.360523	+	0.0805795i
$206$	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
$210$	5.37426	−	1.20119i	0.370859	−	0.0828898i
$211$	−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
$215$	−2.63917	+	8.42107i	−0.179990	+	0.574312i
$216$		−	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
$220$	0.986530	−	0.220497i	0.0665118	−	0.0148659i
$221$	−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
$225$	−4.52421	+	2.12873i	−0.301614	+	0.141915i
$226$	−6.58655	−	11.4082i	−0.438131	−	0.758865i
$227$	10.0487	+	17.4048i	0.666953	+	1.15520i	0.978752	+	0.205048i	$0.0657351\pi$
$227$	10.0487	+	17.4048i	0.666953	+	1.15520i	−0.311799	+	0.950148i	$0.600932\pi$
$228$	−2.98197			−0.197486
$229$	2.81341	+	4.87296i	0.185915	+	0.322014i	0.943885	−	0.330276i	$-0.107142\pi$
$229$	2.81341	+	4.87296i	0.185915	+	0.322014i	−0.757969	+	0.652290i	$0.773808\pi$
$230$	−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
$235$	5.64081	+	1.76783i	0.367966	+	0.115321i
$236$			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	0.639204	−	0.769037i	$-0.279264\pi$
$239$	4.52658	+	2.61342i	0.292800	+	0.169048i	−0.346404	+	0.938085i	$0.612597\pi$
$240$	2.13373	+	0.668714i	0.137732	+	0.0431653i
$241$	−21.8978	+	12.6427i	−1.41056	+	0.814387i	−0.995441	−	0.0953804i	$-0.969593\pi$
$241$	−21.8978	+	12.6427i	−1.41056	+	0.814387i	−0.415119	+	0.909767i	$0.636260\pi$
$242$	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
$250$	−1.51674	−	11.0770i	−0.0959273	−	0.700570i
$251$			2.27414i			0.143542i	0.997421	+	0.0717712i	$0.0228652\pi$
$251$			2.27414i			0.143542i	−0.997421	+	0.0717712i	$0.977135\pi$
$252$	−2.13280	+	1.23137i	−0.134354	+	0.0775691i
$253$	0.802817			0.0504727
$254$	−15.7823	+	9.11192i	−0.990270	+	0.571733i
$255$	−4.51230	−	1.41416i	−0.282571	−	0.0885580i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.8758	+	18.8374i	−0.678413	+	1.17505i	0.297046	+	0.954863i	$0.403999\pi$
$257$	−10.8758	+	18.8374i	−0.678413	+	1.17505i	−0.975459	+	0.220182i	$0.929335\pi$
$258$		−	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	$-0.604903\pi$
$263$	5.41619	−	3.12704i	0.333977	−	0.192822i	0.657605	+	0.753363i	$0.271569\pi$
$264$	−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	−0.932174	−	0.362010i	$-0.882091\pi$
$271$	−2.51174	+	4.35046i	−0.152577	+	0.264272i	0.779597	+	0.626282i	$0.215424\pi$
$272$	1.05737	+	1.83142i	0.0641125	+	0.111046i
$273$	−7.60506			−0.460279
$274$	−13.4079	−	7.74103i	−0.809999	−	0.467653i
$275$	1.85606	+	1.29010i	0.111925	+	0.0777957i
$276$	1.53793	+	0.887924i	0.0925725	+	0.0534467i
$277$	14.3006	+	24.7694i	0.859242	+	1.48825i	0.872653	+	0.488341i	$0.162398\pi$
$277$	14.3006	+	24.7694i	0.859242	+	1.48825i	−0.0134110	+	0.999910i	$0.504269\pi$
$278$	−6.46352	−	11.1951i	−0.387656	−	0.671440i
$279$	2.21296	+	1.27765i	0.132487	+	0.0764912i
$280$	−1.20119	−	5.37426i	−0.0717847	−	0.321174i
$281$	−11.1812	−	6.45549i	−0.667017	−	0.385102i	0.127929	−	0.991783i	$-0.459167\pi$
$281$	−11.1812	−	6.45549i	−0.667017	−	0.385102i	−0.794945	+	0.606681i	$0.792500\pi$
$282$	−2.64363			−0.157426
$283$	−10.3736	−	17.9677i	−0.616648	−	1.06807i	−0.990093	−	0.140414i	$-0.955157\pi$
$283$	−10.3736	−	17.9677i	−0.616648	−	1.06807i	0.373444	−	0.927653i	$-0.378177\pi$
$284$	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	$-0.578253\pi$
$293$	8.12951	−	4.69358i	0.474931	−	0.274202i	0.718302	+	0.695732i	$0.244920\pi$
$294$	−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
$300$	2.12873	+	4.52421i	0.122902	+	0.261206i
$301$	−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
$305$	−4.00085	−	17.9003i	−0.229088	−	1.02497i
$306$	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	0.934517	−	0.355920i	$-0.115832\pi$
$311$	19.2848	+	11.1341i	1.09354	+	0.631355i	0.159023	+	0.987275i	$0.449166\pi$
$312$	−2.67433	−	1.54402i	−0.151404	−	0.0874130i
$313$	−8.32368	+	14.4170i	−0.470482	+	0.814899i	−0.999430	−	0.0337549i	$-0.989253\pi$
$313$	−8.32368	+	14.4170i	−0.470482	+	0.814899i	0.528948	+	0.848654i	$0.322587\pi$
$314$	−13.0389	+	7.52798i	−0.735825	+	0.424829i
$315$	−5.25484	−	1.64687i	−0.296077	−	0.0927907i
$316$	−10.9751	−	6.33650i	−0.617400	−	0.356456i
$317$	−2.95498	−	1.70606i	−0.165968	−	0.0958219i	0.414715	−	0.909951i	$-0.363881\pi$
$317$	−2.95498	−	1.70606i	−0.165968	−	0.0958219i	−0.580683	+	0.814129i	$0.697215\pi$
$318$	4.77175	−	8.26490i	0.267586	−	0.463473i
$319$		−	3.78342i		−	0.211831i
$320$	0.668714	−	2.13373i	0.0373823	−	0.119279i
$321$	−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
$330$	−0.964609	−	0.302309i	−0.0531000	−	0.0166416i
$331$	23.5466	+	13.5946i	1.29424	+	0.747229i	0.979403	−	0.201918i	$-0.0647173\pi$
$331$	23.5466	+	13.5946i	1.29424	+	0.747229i	0.314835	+	0.949146i	$0.398051\pi$
$332$		−	7.57432i		−	0.415695i
$333$	−5.25304	−	3.06685i	−0.287865	−	0.168062i
$334$	3.31403			0.181336
$335$	−4.65519	−	20.8279i	−0.254340	−	1.13795i
$336$	1.23137	+	2.13280i	0.0671768	+	0.116354i
$337$	−10.0266	+	5.78887i	−0.546185	+	0.315340i	−0.747582	−	0.664170i	$-0.768785\pi$
$337$	−10.0266	+	5.78887i	−0.546185	+	0.315340i	0.201397	+	0.979510i	$0.435452\pi$
$338$	1.73199	+	2.99990i	0.0942079	+	0.163173i
$339$			13.1731i			0.715465i
$340$	−1.41416	+	4.51230i	−0.0766935	+	0.244714i
$341$		−	1.15519i		−	0.0625571i
$342$	2.58246	+	1.49098i	0.139643	+	0.0806232i
$343$			19.5416i			1.05515i
$344$	−3.94663			−0.212788
$345$	0.866158	+	3.87530i	0.0466324	+	0.208639i
$346$	0.977227	−	0.564202i	0.0525360	−	0.0303317i
$347$	−18.7028			−1.00402			−0.502010	−	0.864862i	$-0.667406\pi$
$347$	−18.7028			−1.00402			−0.502010	+	0.864862i	$0.667406\pi$
$348$	4.18450	−	7.24777i	0.224313	−	0.388521i
$349$	9.61263	−	16.6496i	0.514552	−	0.891231i	−0.485305	−	0.874345i	$-0.661291\pi$
$349$	9.61263	−	16.6496i	0.514552	−	0.891231i	0.999857	−	0.0168860i	$-0.00537524\pi$
$350$	7.02797	−	10.1111i	0.375661	−	0.540463i
$351$	−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	$-0.923340\pi$
$353$	−5.24212	+	9.07961i	−0.279010	+	0.483259i	0.692129	+	0.721774i	$0.256673\pi$
$354$	1.60727	−	2.78387i	0.0854253	−	0.147961i
$355$	0.0141275	−	0.00315760i	0.000749808	−	0.000167588i
$356$		−	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
$365$	−19.4836	−	6.10618i	−1.01982	−	0.319612i
$366$	4.10139	+	7.10381i	0.214383	+	0.371322i
$367$	−9.18534	+	5.30316i	−0.479471	+	0.276823i	−0.720196	−	0.693771i	$-0.755948\pi$
$367$	−9.18534	+	5.30316i	−0.479471	+	0.276823i	0.240725	+	0.970593i	$0.422615\pi$
$368$	0.887924	−	1.53793i	0.0462862	−	0.0801701i
$369$	−2.36543			−0.123139
$370$	10.0566	−	9.15775i	0.522819	−	0.476089i
$371$	−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	$-0.804630\pi$
$373$	−14.0490	+	8.11120i	−0.727430	+	0.419982i	0.0900510	+	0.995937i	$0.471297\pi$
$374$	−0.478011	−	0.827940i	−0.0247174	−	0.0428118i
$375$	−4.22495	+	10.3513i	−0.218176	+	0.534540i
$376$			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	−0.814928	−	0.579562i	$-0.803224\pi$
$379$	1.83877	−	3.18484i	0.0944511	−	0.163594i	0.909379	+	0.415968i	$0.136557\pi$
$380$	−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	$-0.211440\pi$
$383$	−2.74370	−	4.75222i	−0.140196	−	0.242827i	−0.927570	+	0.373648i	$0.878107\pi$
$384$			1.00000i			0.0510310i
$385$	0.543027	+	2.42957i	0.0276752	+	0.123822i
$386$	−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	0.292573	−	0.956243i	$-0.405488\pi$
$389$	24.9890	−	14.4274i	1.26699	−	0.731497i	0.974417	+	0.224746i	$0.0721551\pi$
$390$	−1.50617	−	6.73881i	−0.0762681	−	0.341233i
$391$	−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
$395$	−6.18117	−	27.6553i	−0.311009	−	1.39149i
$396$	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
$400$	4.52421	−	2.12873i	0.226211	−	0.106437i
$401$			20.0498i			1.00124i	0.865667	+	0.500620i	$0.166895\pi$
$401$			20.0498i			1.00124i	−0.865667	+	0.500620i	$0.833105\pi$
$402$	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
$405$	−2.18223	+	0.487744i	−0.108436	+	0.0242362i
$406$	−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	0.840873	−	0.541233i	$-0.182042\pi$
$409$	16.0291	+	9.25441i	0.792588	+	0.457601i	−0.0482847	+	0.998834i	$0.515375\pi$
$410$	1.58180	−	5.04720i	0.0781193	−	0.249263i
$411$	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	−0.250519	−	0.968112i	$-0.580601\pi$
$419$	14.5978	−	25.2842i	0.713150	−	1.23521i	0.963669	−	0.267100i	$-0.0860654\pi$
$420$	−1.64687	+	5.25484i	−0.0803591	+	0.256410i
$421$			26.4129i			1.28728i	0.765327	+	0.643642i	$0.222577\pi$
$421$			26.4129i			1.28728i	−0.765327	+	0.643642i	$0.777423\pi$
$422$	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
$425$	−9.56754	+	4.50172i	−0.464094	+	0.218365i
$426$	−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	−0.0109348	−	0.999940i	$-0.503481\pi$
$431$	17.6376	−	10.1831i	0.849571	−	0.490500i	0.860506	+	0.509440i	$0.170147\pi$
$432$	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
$435$	18.2630	−	4.08193i	0.875646	−	0.195713i
$436$		−	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	−0.246300	−	0.969194i	$-0.579215\pi$
$439$	9.84542	−	5.68426i	0.469896	−	0.271295i	0.716196	+	0.697899i	$0.245882\pi$
$440$	−0.302309	+	0.964609i	−0.0144120	+	0.0459859i
$441$	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	−0.149505	−	0.988761i	$-0.547768\pi$
$449$	13.3926	−	7.73221i	0.632035	−	0.364906i	0.781540	+	0.623855i	$0.214435\pi$
$450$	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	$-0.142313\pi$
$457$	1.63400	+	2.83018i	0.0764355	+	0.132390i	−0.825274	+	0.564732i	$0.808979\pi$
$458$	−5.62681			−0.262924
$459$	−1.83142	−	1.05737i	−0.0854834	−	0.0493538i
$460$	3.87530	−	0.866158i	0.180687	−	0.0403848i
$461$	27.4011	+	15.8201i	1.27620	+	0.736813i	0.976147	−	0.217110i	$-0.0696629\pi$
$461$	27.4011	+	15.8201i	1.27620	+	0.736813i	0.300051	+	0.953923i	$0.402996\pi$
$462$	−0.556673	−	0.964186i	−0.0258988	−	0.0448580i
$463$	−2.72366	−	4.71752i	−0.126579	−	0.219242i	0.795770	−	0.605599i	$-0.207067\pi$
$463$	−2.72366	−	4.71752i	−0.126579	−	0.219242i	−0.922349	+	0.386357i	$0.873733\pi$
$464$	−7.24777	−	4.18450i	−0.336469	−	0.194261i
$465$	5.57626	−	1.24634i	0.258593	−	0.0577974i
$466$	−14.0888	−	8.13416i	−0.652650	−	0.376808i
$467$	32.5303			1.50532			0.752662	−	0.658407i	$-0.228770\pi$
$467$	32.5303			1.50532			0.752662	+	0.658407i	$0.228770\pi$
$468$	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	0.451517	−	0.892262i	$-0.350883\pi$
$479$	−2.08893	−	1.20604i	−0.0954456	−	0.0551055i	−0.546963	+	0.837157i	$0.684216\pi$
$480$	−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
$485$	3.77201	−	12.0357i	0.171278	−	0.546514i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	−15.6442			−0.708907			−0.354453	−	0.935074i	$-0.615333\pi$
$487$	−15.6442			−0.708907			−0.354453	+	0.935074i	$0.615333\pi$
$488$	7.10381	−	4.10139i	0.321574	−	0.185661i
$489$		−	17.3734i		−	0.785653i
$490$	−2.04015	+	0.455989i	−0.0921646	+	0.0205995i
$491$	−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	0.222097	−	0.975025i	$-0.428710\pi$
$499$	26.3043	−	15.1868i	1.17754	−	0.679854i	0.955444	+	0.295171i	$0.0953766\pi$
$500$	10.3513	+	4.22495i	0.462925	+	0.188946i
$501$	−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	$-0.674036\pi$
$503$	10.7612	−	18.6389i	0.479817	−	0.831068i	0.999732	+	0.0231501i	$0.00736957\pi$
$504$		−	2.46274i		−	0.109699i
$505$	4.40807	−	14.0653i	0.196156	−	0.625896i
$506$	−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	−0.636620	−	0.771178i	$-0.719668\pi$
$509$	7.88620	−	13.6593i	0.349550	−	0.605438i	0.986169	+	0.165740i	$0.0530013\pi$
$510$	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
$515$	−0.472227	+	1.50678i	−0.0208088	+	0.0663968i
$516$	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
$520$	−6.73881	+	1.50617i	−0.295516	+	0.0660501i
$521$	−10.0002	−	17.3208i	−0.438115	−	0.758837i	0.559429	−	0.828878i	$-0.311020\pi$
$521$	−10.0002	−	17.3208i	−0.438115	−	0.758837i	−0.997544	+	0.0700410i	$0.977687\pi$
$522$	−7.24777	+	4.18450i	−0.317226	+	0.183151i
$523$	12.9129	+	22.3658i	0.564643	+	0.977990i	0.997083	+	0.0763270i	$0.0243193\pi$
$523$	12.9129	+	22.3658i	0.564643	+	0.977990i	−0.432440	+	0.901663i	$0.642347\pi$
$524$		−	10.5051i		−	0.458919i
$525$	−11.1420	+	5.24252i	−0.486276	+	0.228802i
$526$			6.25408i			0.272691i
$527$	4.67984	+	2.70191i	0.203857	+	0.117697i
$528$		−	0.452075i		−	0.0196741i
$529$	−19.8464			−0.862885
$530$	−4.65478	−	20.8260i	−0.202191	−	0.904626i
$531$	−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
$535$	2.58399	+	11.5611i	0.111716	+	0.499830i
$536$	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
$540$	0.487744	+	2.18223i	0.0209891	+	0.0939080i
$541$		−	18.3497i		−	0.788917i	−0.918914	−	0.394459i	$-0.870932\pi$
$541$		−	18.3497i		−	0.788917i	0.918914	−	0.394459i	$-0.129068\pi$
$542$	−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	$-0.364331\pi$
$547$	19.3385			0.826856			0.413428	+	0.910537i	$0.364331\pi$
$548$	13.4079	−	7.74103i	0.572755	−	0.330681i
$549$		−	8.20278i		−	0.350086i
$550$	−2.04528	+	0.962347i	−0.0872112	+	0.0410346i
$551$	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
$555$	−13.2882	+	2.90253i	−0.564051	+	0.123205i
$556$	12.9270			0.548228
$557$	−2.23202	+	3.86597i	−0.0945736	+	0.163806i	−0.909431	−	0.415856i	$-0.863482\pi$
$557$	−2.23202	+	3.86597i	−0.0945736	+	0.163806i	0.814857	+	0.579662i	$0.196815\pi$
$558$	−2.21296	+	1.27765i	−0.0936821	+	0.0540874i
$559$	6.09369	+	10.5546i	0.257736	+	0.446411i
$560$	5.25484	+	1.64687i	0.222058	+	0.0695930i
$561$			0.956023i			0.0403633i
$562$	11.1812	−	6.45549i	0.471652	−	0.272308i
$563$	−36.4158			−1.53474			−0.767371	−	0.641203i	$-0.778436\pi$
$563$	−36.4158			−1.53474			−0.767371	+	0.641203i	$0.778436\pi$
$564$	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	$0.134153\pi$
$569$			19.5165i			0.818175i	−0.912495	+	0.409087i	$0.865847\pi$
$570$	6.50733	−	1.45444i	0.272562	−	0.0609196i
$571$	11.5820	−	20.0607i	0.484693	−	0.839512i	−0.515153	−	0.857098i	$-0.672265\pi$
$571$	11.5820	−	20.0607i	0.484693	−	0.839512i	0.999845	+	0.0175863i	$0.00559817\pi$
$572$	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
$575$	7.29100	+	5.06777i	0.304056	+	0.211341i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	1.50983	−	2.61511i	0.0628552	−	0.108868i	−0.832885	−	0.553446i	$-0.813313\pi$
$577$	1.50983	−	2.61511i	0.0628552	−	0.108868i	0.895741	+	0.444577i	$0.146646\pi$
$578$	−12.5279			−0.521091
$579$	10.8268	−	6.25084i	0.449945	−	0.259776i
$580$	−4.08193	−	18.2630i	−0.169493	−	0.758332i
$581$	18.6536			0.773882
$582$			5.64069i			0.233814i
$583$	3.73636	+	2.15719i	0.154744	+	0.0893416i
$584$		−	9.13122i		−	0.377853i
$585$	−2.06502	+	6.58907i	−0.0853780	+	0.272424i
$586$			9.38715i			0.387780i
$587$	−14.4633	−	25.0511i	−0.596963	−	1.03397i	−0.993267	−	0.115851i	$-0.963040\pi$
$587$	−14.4633	−	25.0511i	−0.596963	−	1.03397i	0.396303	−	0.918120i	$-0.370293\pi$
$588$	0.809642	−	0.467447i	0.0333891	−	0.0192772i
$589$	3.80992	+	6.59898i	0.156985	+	0.271906i
$590$	−1.56787	−	7.01484i	−0.0645481	−	0.288796i
$591$	−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
$595$	−11.1126	−	3.48271i	−0.455573	−	0.142777i
$596$	−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	0.790617	−	0.612311i	$-0.209760\pi$
$599$	−3.30328	−	5.72145i	−0.134968	−	0.233772i	−0.925585	+	0.378539i	$0.876427\pi$
$600$	−4.98245	−	0.418570i	−0.203408	−	0.0170881i
$601$	−7.30388	+	12.6507i	−0.297932	+	0.516033i	−0.975663	−	0.219277i	$-0.929630\pi$
$601$	−7.30388	+	12.6507i	−0.297932	+	0.516033i	0.677731	+	0.735310i	$0.262963\pi$
$602$		−	9.71955i		−	0.396139i
$603$		−	9.54433i		−	0.388675i
$604$	−9.43397	+	16.3401i	−0.383863	+	0.664870i
$605$	−7.21919	+	23.0350i	−0.293502	+	0.936506i
$606$			6.59186i			0.267776i
$607$	13.5413	−	23.4542i	0.549624	−	0.951976i	−0.448676	−	0.893694i	$-0.648104\pi$
$607$	13.5413	−	23.4542i	0.549624	−	0.951976i	0.998300	−	0.0582820i	$-0.0185622\pi$
$608$	−2.58246	−	1.49098i	−0.104733	−	0.0604674i
$609$	17.8494	+	10.3054i	0.723294	+	0.417594i
$610$	17.5025	+	5.48531i	0.708657	+	0.222094i
$611$	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	$-0.295833\pi$
$613$	5.04052	+	2.91015i	0.203585	+	0.117540i	−0.394742	+	0.918792i	$0.629166\pi$
$614$	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	$-0.538532\pi$
$617$	−25.8535	−	14.9265i	−1.04082	−	0.600920i	−0.920067	+	0.391762i	$0.871866\pi$
$618$		−	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	$0.233460\pi$
$620$	−1.24634	−	5.57626i	−0.0500540	−	0.223948i
$621$			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
$625$	8.71260	+	23.4327i	0.348504	+	0.937307i
$626$	−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	0.989386	−	0.145309i	$-0.0464175\pi$
$631$	34.1186	+	19.6984i	1.35824	+	0.784179i	0.368852	+	0.929488i	$0.379751\pi$
$632$	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	−0.413562	−	0.910476i	$-0.635716\pi$
$641$	14.7278	−	25.5093i	0.581714	−	1.00756i	0.995276	−	0.0970827i	$-0.0309511\pi$
$642$	−2.64892	−	4.58807i	−0.104545	−	0.181077i
$643$	−22.3938			−0.883124			−0.441562	−	0.897231i	$-0.645575\pi$
$643$	−22.3938			−0.883124			−0.441562	+	0.897231i	$0.645575\pi$
$644$	3.78753	+	2.18673i	0.149249	+	0.0861692i
$645$	1.92495	+	8.61245i	0.0757947	+	0.339115i
$646$	5.46124	+	3.15305i	0.214869	+	0.124055i
$647$	10.8449	+	18.7839i	0.426356	+	0.738471i	0.996546	−	0.0830421i	$-0.0264636\pi$
$647$	10.8449	+	18.7839i	0.426356	+	0.738471i	−0.570190	+	0.821513i	$0.693130\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	1.25852	+	0.726606i	0.0494012	+	0.0285218i
$650$	−12.6784	−	8.81240i	−0.497288	−	0.345651i
$651$	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	$-0.173026\pi$
$653$	−0.510467	−	0.884155i	−0.0199761	−	0.0345996i	−0.875841	+	0.482600i	$0.839692\pi$
$654$	−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	−0.953718	−	0.300701i	$-0.902779\pi$
$659$	−18.9266	−	32.7818i	−0.737274	−	1.27700i	0.216444	−	0.976295i	$-0.430554\pi$
$660$	0.744112	−	0.684221i	0.0289645	−	0.0266333i
$661$	−23.1502	+	13.3658i	−0.900437	+	0.519868i	−0.877342	−	0.479866i	$-0.840685\pi$
$661$	−23.1502	+	13.3658i	−0.900437	+	0.519868i	−0.0230953	+	0.999733i	$0.507352\pi$
$662$	−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
$670$	20.3651	+	6.38243i	0.786771	+	0.246575i
$671$	−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	$-0.624360\pi$
$673$	5.95454	−	3.43786i	0.229531	−	0.132520i	0.610356	+	0.792128i	$0.291027\pi$
$674$		−	11.5777i		−	0.445958i
$675$	−2.85372	+	4.10564i	−0.109840	+	0.158026i
$676$	−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	0.221544	+	0.975150i	$0.428890\pi$
$683$	−19.1756	+	33.2131i	−0.733733	+	1.27086i	−0.955277	+	0.295713i	$0.904443\pi$
$684$	−2.58246	+	1.49098i	−0.0987428	+	0.0570092i
$685$	33.0346	+	10.3531i	1.26219	+	0.395571i
$686$	−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
$690$	−3.78919	−	1.18753i	−0.144252	−	0.0452087i
$691$	2.58576	−	4.47867i	0.0983669	−	0.170376i	−0.812642	−	0.582763i	$-0.801971\pi$
$691$	2.58576	−	4.47867i	0.0983669	−	0.170376i	0.911009	+	0.412387i	$0.135305\pi$
$692$			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
$700$	5.24252	+	11.1420i	0.198149	+	0.421127i
$701$	−9.82218	−	5.67084i	−0.370979	−	0.214185i	0.302907	−	0.953020i	$-0.402043\pi$
$701$	−9.82218	−	5.67084i	−0.370979	−	0.214185i	−0.673886	+	0.738835i	$0.735376\pi$
$702$		−	3.08804i		−	0.116551i
$703$	−8.99314	−	15.7522i	−0.339183	−	0.594106i
$704$	−0.452075			−0.0170382
$705$	5.76900	−	1.28941i	0.217273	−	0.0485621i
$706$	−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	$0.119518\pi$
$709$			19.5292i			0.733434i	−0.930332	+	0.366717i	$0.880482\pi$
$710$	−0.00432918	+	0.0138135i	−0.000162471	+	0.000518413i
$711$		−	12.6730i		−	0.475275i
$712$	9.02573	+	5.21101i	0.338254	+	0.195291i
$713$		−	4.53784i		−	0.169943i
$714$	5.20807			0.194907
$715$	3.04645	−	0.680904i	0.113931	−	0.0254644i
$716$	−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	−0.877223	−	0.480084i	$-0.840606\pi$
$719$	−0.612617	+	1.06108i	−0.0228468	+	0.0395718i	0.854376	+	0.519655i	$0.173940\pi$
$720$	2.18223	−	0.487744i	0.0813267	−	0.0181771i
$721$	−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
$725$	23.8828	−	34.3601i	0.886984	−	1.27610i
$726$		−	10.7956i		−	0.400663i
$727$	3.71182	+	6.42905i	0.137664	+	0.238440i	0.926612	−	0.376019i	$-0.122707\pi$
$727$	3.71182	+	6.42905i	0.137664	+	0.238440i	−0.788948	+	0.614460i	$0.789374\pi$
$728$	−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	$-0.755071\pi$
$733$	−12.8570	+	7.42300i	−0.474885	+	0.274175i	0.243398	+	0.969927i	$0.421738\pi$
$734$		−	10.6063i		−	0.391486i
$735$	1.99482	+	0.625177i	0.0735799	+	0.0230600i
$736$	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	$0.561263\pi$
$740$	2.90253	+	13.2882i	0.106699	+	0.488483i
$741$	−9.20845			−0.338281
$742$	11.7516	−	20.3543i	0.431414	−	0.747231i
$743$	44.2189	−	25.5298i	1.62223	−	0.936597i	0.635913	−	0.771761i	$-0.280624\pi$
$743$	44.2189	−	25.5298i	1.62223	−	0.936597i	0.986321	−	0.164836i	$-0.0527095\pi$
$744$	1.27765	+	2.21296i	0.0468411	+	0.0811311i
$745$	0.616741	−	1.96790i	0.0225956	−	0.0720982i
$746$		−	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
$755$	−41.1741	+	9.20272i	−1.49848	+	0.334921i
$756$	−1.23137	+	2.13280i	−0.0447846	+	0.0775691i
$757$	15.0203	−	26.0160i	0.545924	−	0.945567i	−0.452625	−	0.891701i	$-0.649512\pi$
$757$	15.0203	−	26.0160i	0.545924	−	0.945567i	0.998548	−	0.0538661i	$-0.0171544\pi$
$758$	1.83877	+	3.18484i	0.0667870	+	0.115679i
$759$	0.695260	−	0.401409i	0.0252363	−	0.0145702i
$760$	−1.45444	−	6.50733i	−0.0527579	−	0.236046i
$761$	−4.46887	+	7.74032i	−0.161997	+	0.280586i	−0.935585	−	0.353103i	$-0.885127\pi$
$761$	−4.46887	+	7.74032i	−0.161997	+	0.280586i	0.773588	+	0.633689i	$0.218460\pi$
$762$	−9.11192	+	15.7823i	−0.330090	+	0.571733i
$763$	16.4021			0.593794
$764$	−8.12557	+	4.69130i	−0.293973	+	0.169725i
$765$	−4.61484	+	1.03145i	−0.166850	+	0.0372922i
$766$	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	$0.145414\pi$
$769$			24.4645i			0.882214i	−0.897455	+	0.441107i	$0.854586\pi$
$770$	−2.37558	−	0.744510i	−0.0856101	−	0.0268303i
$771$			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	$-0.882234\pi$
$773$	−30.1761	+	17.4222i	−1.08536	+	0.626633i	−0.153023	+	0.988223i	$0.548901\pi$
$774$	−1.97332	−	3.41789i	−0.0709294	−	0.122853i
$775$	7.29213	−	10.4912i	0.261941	−	0.376854i
$776$	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
$780$	6.58907	+	2.06502i	0.235926	+	0.0739396i
$781$	−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
$790$	27.0408	+	8.47461i	0.962069	+	0.301513i
$791$			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
$795$	−6.38187	+	20.3633i	−0.226342	+	0.722211i
$796$	11.0061	−	6.35438i	0.390101	−	0.225225i
$797$	−9.39958	+	16.2806i	−0.332950	+	0.576687i	−0.983089	−	0.183129i	$-0.941377\pi$
$797$	−9.39958	+	16.2806i	−0.332950	+	0.576687i	0.650139	+	0.759816i	$0.274711\pi$
$798$	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
$805$	2.13313	+	9.54387i	0.0751828	+	0.336377i
$806$			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	−0.774066	−	0.633104i	$-0.781780\pi$
$809$	−17.4303	+	10.0634i	−0.612815	+	0.353809i	0.161251	+	0.986913i	$0.448447\pi$
$810$	0.668714	−	2.13373i	0.0234962	−	0.0749718i
$811$	−5.19642	−	9.00046i	−0.182471	−	0.316049i	0.760251	−	0.649630i	$-0.225076\pi$
$811$	−5.19642	−	9.00046i	−0.182471	−	0.316049i	−0.942721	+	0.333581i	$0.891743\pi$
$812$	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	−0.932122	−	0.362146i	$-0.882044\pi$
$821$	−22.3405	−	38.6948i	−0.779688	−	1.35046i	0.152433	−	0.988314i	$-0.451289\pi$
$822$	−15.4821			−0.539999
$823$	−26.1020	−	15.0700i	−0.909858	−	0.525307i	−0.0294727	−	0.999566i	$-0.509383\pi$
$823$	−26.1020	−	15.0700i	−0.909858	−	0.525307i	−0.880386	+	0.474259i	$0.842716\pi$
$824$	−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	$-0.328061\pi$
$827$	−13.9643	−	24.1869i	−0.485586	−	0.841060i	−0.999863	+	0.0165641i	$0.994727\pi$
$828$	1.77585			0.0617150
$829$	32.1434	+	18.5580i	1.11639	+	0.644546i	0.940476	−	0.339861i	$-0.110380\pi$
$829$	32.1434	+	18.5580i	1.11639	+	0.644546i	0.175910	+	0.984406i	$0.443713\pi$
$830$	3.69433	+	16.5289i	0.128232	+	0.573726i
$831$	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
$835$	−7.23196	+	1.61640i	−0.250272	+	0.0559377i
$836$	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	−0.783908	−	0.620877i	$-0.786777\pi$
$839$	4.22147	−	7.31179i	0.145741	−	0.252431i	0.929649	+	0.368446i	$0.120110\pi$
$840$	−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	$-0.900321\pi$
$853$	−6.10114	+	10.5675i	−0.208899	+	0.361824i	0.742469	+	0.669880i	$0.233655\pi$
$854$	10.1007	+	17.4949i	0.345638	+	0.598662i
$855$	−6.36273	−	1.99408i	−0.217601	−	0.0681963i
$856$	−4.58807	+	2.64892i	−0.156817	+	0.0905383i
$857$	−28.1230			−0.960663			−0.480331	−	0.877087i	$-0.659484\pi$
$857$	−28.1230			−0.960663			−0.480331	+	0.877087i	$0.659484\pi$
$858$	−1.20900	+	0.698014i	−0.0412745	+	0.0238298i
$859$		−	3.92512i		−	0.133923i	−0.997756	−	0.0669616i	$-0.978669\pi$
$859$		−	3.92512i		−	0.133923i	0.997756	−	0.0669616i	$-0.0213305\pi$
$860$	8.61245	−	1.92495i	0.293682	−	0.0656401i
$861$	−5.82545			−0.198531
$862$			20.3661i			0.693672i
$863$	49.8149	+	28.7607i	1.69572	+	0.979025i	0.949731	+	0.313067i	$0.101356\pi$
$863$	49.8149	+	28.7607i	1.69572	+	0.979025i	0.745989	+	0.665958i	$0.231977\pi$
$864$	−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
$870$	−5.59647	+	17.8572i	−0.189738	+	0.605417i
$871$	−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
$875$	−10.4050	+	25.4926i	−0.351752	+	0.861809i
$876$	−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	0.775496	−	0.631352i	$-0.217500\pi$
$881$	−4.71995	−	8.17519i	−0.159019	−	0.275429i	−0.934515	+	0.355923i	$0.884166\pi$
$882$	−0.934894			−0.0314795
$883$	−14.3072	−	24.7808i	−0.481476	−	0.833940i	0.518298	−	0.855200i	$-0.326566\pi$
$883$	−14.3072	−	24.7808i	−0.481476	−	0.833940i	−0.999774	+	0.0212597i	$0.993232\pi$
$884$	3.26521	+	5.65551i	0.109821	+	0.190215i
$885$	−2.14961	+	6.85896i	−0.0722582	+	0.230562i
$886$	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
$890$	5.08327	+	22.7432i	0.170392	+	0.762353i
$891$	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
$895$	−20.8945	−	6.54835i	−0.698426	−	0.218887i
$896$			2.46274i			0.0822745i
$897$	4.74919	+	2.74195i	0.158571	+	0.0915510i
$898$			15.4644i			0.516054i
$899$	−21.3854			−0.713242
$900$	4.10564	+	2.85372i	0.136855	+	0.0951239i
$901$	−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
$905$	−29.2475	+	6.53703i	−0.972219	+	0.217298i
$906$	16.3401	−	9.43397i	0.542864	−	0.313423i
$907$	9.16742	+	15.8784i	0.304399	+	0.527235i	0.977127	−	0.212655i	$-0.0682110\pi$
$907$	9.16742	+	15.8784i	0.304399	+	0.527235i	−0.672728	+	0.739890i	$0.734878\pi$
$908$	10.0487	−	17.4048i	0.333476	−	0.577598i
$909$	3.29593	−	5.70872i	0.109319	−	0.189346i
$910$	−3.70932	−	16.5960i	−0.122963	−	0.550151i
$911$			31.0919i			1.03012i	0.857154	+	0.515060i	$0.172230\pi$
$911$			31.0919i			1.03012i	−0.857154	+	0.515060i	$0.827770\pi$
$912$	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	$-0.975532\pi$
$919$		−	4.65598i		−	0.153587i	0.997047	−	0.0767934i	$-0.0244682\pi$
$920$	−1.18753	+	3.78919i	−0.0391519	+	0.124926i
$921$	−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
$925$	−17.4792	+	24.8893i	−0.574712	+	0.818356i
$926$	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	0.995604	−	0.0936586i	$-0.0298562\pi$
$929$	12.7005	+	21.9980i	0.416691	+	0.721731i	−0.578913	+	0.815389i	$0.696523\pi$
$930$	−1.70877	+	5.45235i	−0.0560328	+	0.178790i
$931$			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	$-0.442549\pi$
$937$	−17.8365	−	10.2979i	−0.582692	−	0.336417i	−0.762202	+	0.647339i	$0.775882\pi$
$938$	11.7526	+	20.3561i	0.383737	+	0.664651i
$939$			16.6474i			0.543266i
$940$	−1.28941	−	5.76900i	−0.0420560	−	0.188164i
$941$	2.99808	−	5.19283i	0.0977348	−	0.169282i	−0.813012	−	0.582247i	$-0.802174\pi$
$941$	2.99808	−	5.19283i	0.0977348	−	0.169282i	0.910747	+	0.412965i	$0.135507\pi$
$942$	−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
$945$	−5.37426	+	1.20119i	−0.174825	+	0.0390746i
$946$	−0.892088	+	1.54514i	−0.0290043	+	0.0502369i
$947$	0.385031	−	0.666893i	0.0125118	−	0.0216711i	−0.859702	−	0.510796i	$-0.829351\pi$
$947$	0.385031	−	0.666893i	0.0125118	−	0.0216711i	0.872214	+	0.489125i	$0.162684\pi$
$948$	−12.6730			−0.411600
$949$	−24.4199	+	14.0988i	−0.792702	+	0.457667i
$950$	8.50969	−	12.2429i	0.276091	−	0.397212i
$951$	−3.41212			−0.110646
$952$		−	5.20807i		−	0.168794i
$953$	−41.0658	−	23.7093i	−1.33025	−	0.768021i	−0.344913	−	0.938635i	$-0.612092\pi$
$953$	−41.0658	−	23.7093i	−1.33025	−	0.768021i	−0.985338	+	0.170614i	$0.945425\pi$
$954$		−	9.54349i		−	0.308982i
$955$	−20.0200	−	6.27428i	−0.647831	−	0.203031i
$956$		−	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
$960$	−0.487744	−	2.18223i	−0.0157419	−	0.0704310i
$961$	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
$965$	8.36005	−	26.6753i	0.269119	−	0.858707i
$966$	−2.18673	−	3.78753i	−0.0703569	−	0.121862i
$967$	13.9911	+	24.2333i	0.449923	+	0.779290i	0.998381	−	0.0568884i	$-0.0181179\pi$
$967$	13.9911	+	24.2333i	0.449923	+	0.779290i	−0.548457	+	0.836179i	$0.684785\pi$
$968$	−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	−0.902449	−	0.430797i	$-0.858233\pi$
$971$	−2.43501	+	4.21757i	−0.0781433	+	0.135348i	0.824306	+	0.566145i	$0.191566\pi$
$972$			1.00000i			0.0320750i
$973$			31.8360i			1.02061i
$974$	7.82210	−	13.5483i	0.250636	−	0.434115i
$975$	6.57362	+	13.9710i	0.210524	+	0.447429i
$976$			8.20278i			0.262564i
$977$	−4.47908	+	7.75800i	−0.143299	+	0.248200i	−0.928737	−	0.370740i	$-0.879104\pi$
$977$	−4.47908	+	7.75800i	−0.143299	+	0.248200i	0.785438	+	0.618940i	$0.212438\pi$
$978$	15.0458	+	8.68670i	0.481112	+	0.277770i
$979$	−4.08031	−	2.35577i	−0.130407	−	0.0752907i
$980$	0.625177	−	1.99482i	0.0199705	−	0.0637220i
$981$	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	$-0.374113\pi$
$983$	−6.93809	−	4.00571i	−0.221291	−	0.127762i	−0.606548	+	0.795047i	$0.707446\pi$
$984$	−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
$990$	−0.986530	+	0.220497i	−0.0313540	+	0.00700785i
$991$			13.7352i			0.436312i	0.975914	+	0.218156i	$0.0700041\pi$
$991$			13.7352i			0.436312i	−0.975914	+	0.218156i	$0.929996\pi$
$992$	2.21296	−	1.27765i	0.0702616	−	0.0405656i
$993$	27.1893			0.862825
$994$	−0.0138075	+	0.00797176i	−0.000437947	+	0.000252849i
$995$	27.1171	+	8.49853i	0.859671	+	0.269422i
$996$	−3.78716	−	6.55955i	−0.120001	−	0.207847i
$997$	−14.1059	+	24.4321i	−0.446738	+	0.773774i	−0.998172	−	0.0604454i	$-0.980748\pi$
$997$	−14.1059	+	24.4321i	−0.446738	+	0.773774i	0.551433	+	0.834219i	$0.314081\pi$
$998$			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.a.619.13	yes	36
5.4	even	2		1110.2.ba.b.619.6	yes	36
37.11	even	6		1110.2.ba.b.529.6	yes	36
185.159	even	6	inner	1110.2.ba.a.529.13	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.ba.a.529.13	✓	36	185.159	even	6	inner
1110.2.ba.a.619.13	yes	36	1.1	even	1	trivial
1110.2.ba.b.529.6	yes	36	37.11	even	6
1110.2.ba.b.619.6	yes	36	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.668714 - 2.13373i) q^{5} +1.00000i q^{6} +(2.13280 - 1.23137i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.668714 - 2.13373i) 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} +(-0.487744 - 2.18223i) 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} +(-2.18223 + 0.487744i) q^{20} +(1.23137 - 2.13280i) q^{21} +(0.226038 - 0.391509i) q^{22} -1.77585 q^{23} +(0.866025 - 0.500000i) q^{24} +(-4.10564 - 2.85372i) q^{25} +3.08804 q^{26} -1.00000i q^{27} +(-2.13280 - 1.23137i) q^{28} +8.36900i q^{29} +(2.13373 + 0.668714i) q^{30} +2.55531i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.391509 + 0.226038i) q^{33} +(1.05737 + 1.83142i) q^{34} +(-1.20119 - 5.37426i) q^{35} -1.00000 q^{36} +(0.0294493 - 6.08269i) q^{37} +2.98197i q^{38} +(-2.67433 - 1.54402i) q^{39} +(0.668714 - 2.13373i) 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} +(4.52421 - 2.12873i) q^{50} -2.11474i q^{51} +(-1.54402 + 2.67433i) q^{52} +(-8.26490 - 4.77175i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.302309 + 0.964609i) 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} +(-6.73881 + 1.50617i) q^{65} -0.452075i q^{66} +(8.26563 - 4.77217i) q^{67} -2.11474 q^{68} +(-1.53793 + 0.887924i) q^{69} +(5.25484 + 1.64687i) 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} +(2.18223 - 0.487744i) 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} +(-1.45444 - 6.50733i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9}+O(q^{10}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * q^5 + 36 * q^8 + 18 * q^9	\( 36 q - 18 q^{2} - 18 q^{4} + 2 q^{5} + 36 q^{8} + 18 q^{9} + 2 q^{10} + 4 q^{11} - 14 q^{13} - 2 q^{15} - 18 q^{16} + 18 q^{18} + 6 q^{19} - 4 q^{20} - 2 q^{22} - 20 q^{23} + 4 q^{25} + 28 q^{26} - 2 q^{30} - 18 q^{32} - 6 q^{33} - 40 q^{35} - 36 q^{36} + 20 q^{37} + 6 q^{39} + 2 q^{40} + 10 q^{41} - 2 q^{44} - 2 q^{45} + 10 q^{46} + 10 q^{49} - 2 q^{50} - 14 q^{52} - 12 q^{53} + 56 q^{55} + 8 q^{57} + 30 q^{58} + 18 q^{59} + 4 q^{60} - 6 q^{61} - 12 q^{62} + 36 q^{64} + 40 q^{65} + 36 q^{67} + 12 q^{69} + 20 q^{70} - 24 q^{71} + 18 q^{72} - 34 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{77} - 6 q^{78} + 2 q^{80} - 18 q^{81} - 20 q^{82} + 36 q^{83} + 26 q^{85} - 10 q^{87} + 4 q^{88} + 4 q^{90} - 36 q^{91} + 10 q^{92} + 12 q^{93} + 12 q^{94} - 30 q^{95} + 52 q^{97} + 10 q^{98} + 2 q^{99}+O(q^{100}) \) 36 * q - 18 * q^2 - 18 * q^4 + 2 * 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 - 4 * q^20 - 2 * q^22 - 20 * q^23 + 4 * q^25 + 28 * q^26 - 2 * q^30 - 18 * q^32 - 6 * q^33 - 40 * q^35 - 36 * q^36 + 20 * q^37 + 6 * q^39 + 2 * q^40 + 10 * q^41 - 2 * q^44 - 2 * q^45 + 10 * q^46 + 10 * q^49 - 2 * q^50 - 14 * q^52 - 12 * q^53 + 56 * q^55 + 8 * q^57 + 30 * q^58 + 18 * q^59 + 4 * q^60 - 6 * q^61 - 12 * q^62 + 36 * q^64 + 40 * q^65 + 36 * q^67 + 12 * q^69 + 20 * 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 + 4 * q^90 - 36 * q^91 + 10 * q^92 + 12 * q^93 + 12 * q^94 - 30 * q^95 + 52 * q^97 + 10 * q^98 + 2 * q^99

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