LMFDB - Embedded newform 471.2.e.b.301.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(169,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("471.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			301.4
Character	$\chi$	$=$	471.301
Dual form			471.2.e.b.169.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.685532 q^{2} +(0.500000 - 0.866025i) q^{3} -1.53005 q^{4} +(-0.295622 + 0.512033i) q^{5} +(-0.342766 + 0.593688i) q^{6} -1.98864 q^{7} +2.41996 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-0.685532 q^{2} +(0.500000 - 0.866025i) q^{3} -1.53005 q^{4} +(-0.295622 + 0.512033i) q^{5} +(-0.342766 + 0.593688i) q^{6} -1.98864 q^{7} +2.41996 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.202658 - 0.351015i) q^{10} +(0.0905346 - 0.156811i) q^{11} +(-0.765023 + 1.32506i) q^{12} +(0.547853 + 0.948910i) q^{13} +1.36327 q^{14} +(0.295622 + 0.512033i) q^{15} +1.40113 q^{16} +(-2.67424 + 4.63191i) q^{17} +(0.342766 + 0.593688i) q^{18} +(-2.51331 + 4.35318i) q^{19} +(0.452316 - 0.783433i) q^{20} +(-0.994318 + 1.72221i) q^{21} +(-0.0620644 + 0.107499i) q^{22} -3.48929 q^{23} +(1.20998 - 2.09575i) q^{24} +(2.32522 + 4.02739i) q^{25} +(-0.375571 - 0.650508i) q^{26} -1.00000 q^{27} +3.04271 q^{28} -4.94532 q^{29} +(-0.202658 - 0.351015i) q^{30} +(3.74771 + 6.49123i) q^{31} -5.80044 q^{32} +(-0.0905346 - 0.156811i) q^{33} +(1.83327 - 3.17532i) q^{34} +(0.587885 - 1.01825i) q^{35} +(0.765023 + 1.32506i) q^{36} +(2.38458 + 4.13022i) q^{37} +(1.72295 - 2.98424i) q^{38} +1.09571 q^{39} +(-0.715393 + 1.23910i) q^{40} +6.49564 q^{41} +(0.681637 - 1.18063i) q^{42} +(0.870301 + 1.50740i) q^{43} +(-0.138522 + 0.239927i) q^{44} +0.591244 q^{45} +2.39202 q^{46} +(-2.59427 - 4.49340i) q^{47} +(0.700567 - 1.21342i) q^{48} -3.04532 q^{49} +(-1.59401 - 2.76090i) q^{50} +(2.67424 + 4.63191i) q^{51} +(-0.838241 - 1.45188i) q^{52} +(1.27139 + 2.20210i) q^{53} +0.685532 q^{54} +(0.0535281 + 0.0927134i) q^{55} -4.81242 q^{56} +(2.51331 + 4.35318i) q^{57} +3.39017 q^{58} -9.94287 q^{59} +(-0.452316 - 0.783433i) q^{60} +(2.48663 - 4.30697i) q^{61} +(-2.56917 - 4.44994i) q^{62} +(0.994318 + 1.72221i) q^{63} +1.17412 q^{64} -0.647830 q^{65} +(0.0620644 + 0.107499i) q^{66} +1.85065 q^{67} +(4.09170 - 7.08704i) q^{68} +(-1.74465 + 3.02182i) q^{69} +(-0.403014 + 0.698041i) q^{70} +(-6.09127 - 10.5504i) q^{71} +(-1.20998 - 2.09575i) q^{72} +(-4.82332 + 8.35423i) q^{73} +(-1.63471 - 2.83140i) q^{74} +4.65043 q^{75} +(3.84548 - 6.66056i) q^{76} +(-0.180041 + 0.311839i) q^{77} -0.751142 q^{78} +5.82978 q^{79} +(-0.414206 + 0.717426i) q^{80} +(-0.500000 + 0.866025i) q^{81} -4.45297 q^{82} +(-1.34867 - 2.33597i) q^{83} +(1.52135 - 2.63506i) q^{84} +(-1.58113 - 2.73859i) q^{85} +(-0.596619 - 1.03337i) q^{86} +(-2.47266 + 4.28277i) q^{87} +(0.219090 - 0.379475i) q^{88} +(-6.46211 + 11.1927i) q^{89} -0.405317 q^{90} +(-1.08948 - 1.88704i) q^{91} +5.33878 q^{92} +7.49542 q^{93} +(1.77845 + 3.08037i) q^{94} +(-1.48598 - 2.57379i) q^{95} +(-2.90022 + 5.02333i) q^{96} +(-7.64453 - 13.2407i) q^{97} +2.08767 q^{98} -0.181069 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9}+O(q^{10}) $ 22 * q + 2 * q^2 + 11 * q^3 + 30 * q^4 - 4 * q^5 + q^6 + 4 * q^7 - 11 * q^9	\( 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9} - 5 q^{10} + 15 q^{12} + 3 q^{13} - 14 q^{14} + 4 q^{15} + 54 q^{16} - q^{17} - q^{18} - 22 q^{19} - 7 q^{20} + 2 q^{21} - 22 q^{22} - 10 q^{23} - 15 q^{25} - 10 q^{26} - 22 q^{27} - 38 q^{28} + 22 q^{29} + 5 q^{30} - 6 q^{31} + 32 q^{32} + 17 q^{34} - 11 q^{35} - 15 q^{36} + 8 q^{37} + 14 q^{38} + 6 q^{39} + 32 q^{40} - 7 q^{42} + q^{43} - 12 q^{44} + 8 q^{45} + 24 q^{46} + 7 q^{47} + 27 q^{48} + 22 q^{49} + 13 q^{50} + q^{51} + 17 q^{52} + 30 q^{53} - 2 q^{54} + 31 q^{55} - 82 q^{56} + 22 q^{57} - 90 q^{58} - 16 q^{59} + 7 q^{60} + 8 q^{61} - 28 q^{62} - 2 q^{63} - 32 q^{64} - 68 q^{65} + 22 q^{66} - 38 q^{67} - 8 q^{68} - 5 q^{69} + 43 q^{70} + 45 q^{71} - 4 q^{73} + 3 q^{74} - 30 q^{75} - 33 q^{76} + 21 q^{77} - 20 q^{78} + 26 q^{79} - 12 q^{80} - 11 q^{81} + 16 q^{82} + 8 q^{83} - 19 q^{84} - 28 q^{85} - 16 q^{86} + 11 q^{87} - 65 q^{88} + 15 q^{89} + 10 q^{90} - 3 q^{91} - 18 q^{92} - 12 q^{93} - 28 q^{94} - 5 q^{95} + 16 q^{96} - 35 q^{97} + 90 q^{98}+O(q^{100}) \) 22 * q + 2 * q^2 + 11 * q^3 + 30 * q^4 - 4 * q^5 + q^6 + 4 * q^7 - 11 * q^9 - 5 * q^10 + 15 * q^12 + 3 * q^13 - 14 * q^14 + 4 * q^15 + 54 * q^16 - q^17 - q^18 - 22 * q^19 - 7 * q^20 + 2 * q^21 - 22 * q^22 - 10 * q^23 - 15 * q^25 - 10 * q^26 - 22 * q^27 - 38 * q^28 + 22 * q^29 + 5 * q^30 - 6 * q^31 + 32 * q^32 + 17 * q^34 - 11 * q^35 - 15 * q^36 + 8 * q^37 + 14 * q^38 + 6 * q^39 + 32 * q^40 - 7 * q^42 + q^43 - 12 * q^44 + 8 * q^45 + 24 * q^46 + 7 * q^47 + 27 * q^48 + 22 * q^49 + 13 * q^50 + q^51 + 17 * q^52 + 30 * q^53 - 2 * q^54 + 31 * q^55 - 82 * q^56 + 22 * q^57 - 90 * q^58 - 16 * q^59 + 7 * q^60 + 8 * q^61 - 28 * q^62 - 2 * q^63 - 32 * q^64 - 68 * q^65 + 22 * q^66 - 38 * q^67 - 8 * q^68 - 5 * q^69 + 43 * q^70 + 45 * q^71 - 4 * q^73 + 3 * q^74 - 30 * q^75 - 33 * q^76 + 21 * q^77 - 20 * q^78 + 26 * q^79 - 12 * q^80 - 11 * q^81 + 16 * q^82 + 8 * q^83 - 19 * q^84 - 28 * q^85 - 16 * q^86 + 11 * q^87 - 65 * q^88 + 15 * q^89 + 10 * q^90 - 3 * q^91 - 18 * q^92 - 12 * q^93 - 28 * q^94 - 5 * q^95 + 16 * q^96 - 35 * q^97 + 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.685532			−0.484744			−0.242372	−	0.970183i	$-0.577925\pi$
$2$	−0.685532			−0.484744			−0.242372	+	0.970183i	$0.577925\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.53005			−0.765023
$5$	−0.295622	+	0.512033i	−0.132206	+	0.228988i	−0.924527	−	0.381117i	$-0.875539\pi$
$5$	−0.295622	+	0.512033i	−0.132206	+	0.228988i	0.792321	+	0.610105i	$0.208873\pi$
$6$	−0.342766	+	0.593688i	−0.139934	+	0.242372i
$7$	−1.98864			−0.751634			−0.375817	−	0.926694i	$-0.622638\pi$
$7$	−1.98864			−0.751634			−0.375817	+	0.926694i	$0.622638\pi$
$8$	2.41996			0.855585
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.202658	−	0.351015i	0.0640862	−	0.111001i
$11$	0.0905346	−	0.156811i	0.0272972	−	0.0472802i	−0.852054	−	0.523454i	$-0.824643\pi$
$11$	0.0905346	−	0.156811i	0.0272972	−	0.0472802i	0.879351	+	0.476174i	$0.157977\pi$
$12$	−0.765023	+	1.32506i	−0.220843	+	0.382512i
$13$	0.547853	+	0.948910i	0.151947	+	0.263180i	0.931943	−	0.362604i	$-0.118112\pi$
$13$	0.547853	+	0.948910i	0.151947	+	0.263180i	−0.779996	+	0.625784i	$0.784779\pi$
$14$	1.36327			0.364350
$15$	0.295622	+	0.512033i	0.0763293	+	0.132206i
$16$	1.40113			0.350284
$17$	−2.67424	+	4.63191i	−0.648597	+	1.12340i	0.334861	+	0.942268i	$0.391311\pi$
$17$	−2.67424	+	4.63191i	−0.648597	+	1.12340i	−0.983458	+	0.181136i	$0.942023\pi$
$18$	0.342766	+	0.593688i	0.0807907	+	0.139934i
$19$	−2.51331	+	4.35318i	−0.576592	+	0.998687i	0.419274	+	0.907860i	$0.362285\pi$
$19$	−2.51331	+	4.35318i	−0.576592	+	0.998687i	−0.995867	+	0.0908275i	$0.971049\pi$
$20$	0.452316	−	0.783433i	0.101141	−	0.175181i
$21$	−0.994318	+	1.72221i	−0.216978	+	0.375817i
$22$	−0.0620644	+	0.107499i	−0.0132322	+	0.0229188i
$23$	−3.48929			−0.727568			−0.363784	−	0.931483i	$-0.618515\pi$
$23$	−3.48929			−0.727568			−0.363784	+	0.931483i	$0.618515\pi$
$24$	1.20998	−	2.09575i	0.246986	−	0.427792i
$25$	2.32522	+	4.02739i	0.465043	+	0.805478i
$26$	−0.375571	−	0.650508i	−0.0736555	−	0.127575i
$27$	−1.00000			−0.192450
$28$	3.04271			0.575017
$29$	−4.94532			−0.918322			−0.459161	−	0.888353i	$-0.651850\pi$
$29$	−4.94532			−0.918322			−0.459161	+	0.888353i	$0.651850\pi$
$30$	−0.202658	−	0.351015i	−0.0370002	−	0.0640862i
$31$	3.74771	+	6.49123i	0.673109	+	1.16586i	0.977018	+	0.213158i	$0.0683748\pi$
$31$	3.74771	+	6.49123i	0.673109	+	1.16586i	−0.303909	+	0.952701i	$0.598292\pi$
$32$	−5.80044			−1.02538
$33$	−0.0905346	−	0.156811i	−0.0157601	−	0.0272972i
$34$	1.83327	−	3.17532i	0.314404	−	0.544563i
$35$	0.587885	−	1.01825i	0.0993707	−	0.172115i
$36$	0.765023	+	1.32506i	0.127504	+	0.220843i
$37$	2.38458	+	4.13022i	0.392023	+	0.679004i	0.992716	−	0.120476i	$-0.0384419\pi$
$37$	2.38458	+	4.13022i	0.392023	+	0.679004i	−0.600693	+	0.799480i	$0.705109\pi$
$38$	1.72295	−	2.98424i	0.279500	−	0.484108i
$39$	1.09571			0.175453
$40$	−0.715393	+	1.23910i	−0.113114	+	0.195919i
$41$	6.49564			1.01445			0.507224	−	0.861814i	$-0.330672\pi$
$41$	6.49564			1.01445			0.507224	+	0.861814i	$0.330672\pi$
$42$	0.681637	−	1.18063i	0.105179	−	0.182175i
$43$	0.870301	+	1.50740i	0.132720	+	0.229877i	0.924724	−	0.380638i	$-0.124296\pi$
$43$	0.870301	+	1.50740i	0.132720	+	0.229877i	−0.792004	+	0.610515i	$0.790962\pi$
$44$	−0.138522	+	0.239927i	−0.0208830	+	0.0361704i
$45$	0.591244			0.0881375
$46$	2.39202			0.352684
$47$	−2.59427	−	4.49340i	−0.378413	−	0.655430i	0.612419	−	0.790533i	$-0.290197\pi$
$47$	−2.59427	−	4.49340i	−0.378413	−	0.655430i	−0.990831	+	0.135104i	$0.956863\pi$
$48$	0.700567	−	1.21342i	0.101118	−	0.175142i
$49$	−3.04532			−0.435046
$50$	−1.59401	−	2.76090i	−0.225427	−	0.390451i
$51$	2.67424	+	4.63191i	0.374468	+	0.648597i
$52$	−0.838241	−	1.45188i	−0.116243	−	0.201339i
$53$	1.27139	+	2.20210i	0.174638	+	0.302482i	0.940036	−	0.341075i	$-0.110791\pi$
$53$	1.27139	+	2.20210i	0.174638	+	0.302482i	−0.765398	+	0.643558i	$0.777458\pi$
$54$	0.685532			0.0932891
$55$	0.0535281	+	0.0927134i	0.00721773	+	0.0125015i
$56$	−4.81242			−0.643087
$57$	2.51331	+	4.35318i	0.332896	+	0.576592i
$58$	3.39017			0.445151
$59$	−9.94287			−1.29445			−0.647226	−	0.762299i	$-0.724071\pi$
$59$	−9.94287			−1.29445			−0.647226	+	0.762299i	$0.724071\pi$
$60$	−0.452316	−	0.783433i	−0.0583937	−	0.101141i
$61$	2.48663	−	4.30697i	0.318380	−	0.551451i	−0.661770	−	0.749707i	$-0.730195\pi$
$61$	2.48663	−	4.30697i	0.318380	−	0.551451i	0.980150	+	0.198256i	$0.0635278\pi$
$62$	−2.56917	−	4.44994i	−0.326286	−	0.565143i
$63$	0.994318	+	1.72221i	0.125272	+	0.216978i
$64$	1.17412			0.146765
$65$	−0.647830			−0.0803535
$66$	0.0620644	+	0.107499i	0.00763959	+	0.0132322i
$67$	1.85065			0.226093			0.113047	−	0.993590i	$-0.463939\pi$
$67$	1.85065			0.226093			0.113047	+	0.993590i	$0.463939\pi$
$68$	4.09170	−	7.08704i	0.496192	−	0.859430i
$69$	−1.74465	+	3.02182i	−0.210031	+	0.363784i
$70$	−0.403014	+	0.698041i	−0.0481694	+	0.0834318i
$71$	−6.09127	−	10.5504i	−0.722901	−	1.25210i	−0.959832	−	0.280575i	$-0.909475\pi$
$71$	−6.09127	−	10.5504i	−0.722901	−	1.25210i	0.236931	−	0.971526i	$-0.423858\pi$
$72$	−1.20998	−	2.09575i	−0.142597	−	0.246986i
$73$	−4.82332	+	8.35423i	−0.564527	+	0.977789i	0.432567	+	0.901602i	$0.357608\pi$
$73$	−4.82332	+	8.35423i	−0.564527	+	0.977789i	−0.997094	+	0.0761870i	$0.975725\pi$
$74$	−1.63471	−	2.83140i	−0.190031	−	0.329143i
$75$	4.65043			0.536985
$76$	3.84548	−	6.66056i	0.441106	−	0.764019i
$77$	−0.180041	+	0.311839i	−0.0205175	+	0.0355374i
$78$	−0.751142			−0.0850501
$79$	5.82978			0.655901			0.327951	−	0.944695i	$-0.393642\pi$
$79$	5.82978			0.655901			0.327951	+	0.944695i	$0.393642\pi$
$80$	−0.414206	+	0.717426i	−0.0463097	+	0.0802107i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.45297			−0.491748
$83$	−1.34867	−	2.33597i	−0.148036	−	0.256406i	0.782465	−	0.622694i	$-0.213962\pi$
$83$	−1.34867	−	2.33597i	−0.148036	−	0.256406i	−0.930502	+	0.366288i	$0.880629\pi$
$84$	1.52135	−	2.63506i	0.165993	−	0.287509i
$85$	−1.58113	−	2.73859i	−0.171497	−	0.297042i
$86$	−0.596619	−	1.03337i	−0.0643350	−	0.111432i
$87$	−2.47266	+	4.28277i	−0.265097	+	0.459161i
$88$	0.219090	−	0.379475i	0.0233551	−	0.0404522i
$89$	−6.46211	+	11.1927i	−0.684983	+	1.18643i	0.288459	+	0.957492i	$0.406857\pi$
$89$	−6.46211	+	11.1927i	−0.684983	+	1.18643i	−0.973442	+	0.228933i	$0.926476\pi$
$90$	−0.405317			−0.0427241
$91$	−1.08948	−	1.88704i	−0.114209	−	0.197815i
$92$	5.33878			0.556606
$93$	7.49542			0.777239
$94$	1.77845	+	3.08037i	0.183433	+	0.317716i
$95$	−1.48598	−	2.57379i	−0.152458	−	0.264065i
$96$	−2.90022	+	5.02333i	−0.296002	+	0.512691i
$97$	−7.64453	−	13.2407i	−0.776185	−	1.34439i	−0.934126	−	0.356943i	$-0.883819\pi$
$97$	−7.64453	−	13.2407i	−0.776185	−	1.34439i	0.157941	−	0.987448i	$-0.449514\pi$
$98$	2.08767			0.210886
$99$	−0.181069			−0.0181981
$100$	−3.55769	−	6.16209i	−0.355769	−	0.616209i
$101$	0.605854			0.0602848			0.0301424	−	0.999546i	$-0.490404\pi$
$101$	0.605854			0.0602848			0.0301424	+	0.999546i	$0.490404\pi$
$102$	−1.83327	−	3.17532i	−0.181521	−	0.314404i
$103$	−2.54452			−0.250719			−0.125359	−	0.992111i	$-0.540008\pi$
$103$	−2.54452			−0.250719			−0.125359	+	0.992111i	$0.540008\pi$
$104$	1.32578	+	2.29632i	0.130004	+	0.225173i
$105$	−0.587885	−	1.01825i	−0.0573717	−	0.0993707i
$106$	−0.871575	−	1.50961i	−0.0846549	−	0.146627i
$107$	−0.224047	−	0.388061i	−0.0216594	−	0.0375153i	0.854993	−	0.518640i	$-0.173562\pi$
$107$	−0.224047	−	0.388061i	−0.0216594	−	0.0375153i	−0.876652	+	0.481125i	$0.840228\pi$
$108$	1.53005			0.147229
$109$	2.44463	−	4.23422i	0.234153	−	0.405564i	−0.724873	−	0.688882i	$-0.758102\pi$
$109$	2.44463	−	4.23422i	0.234153	−	0.405564i	0.959026	+	0.283318i	$0.0914351\pi$
$110$	−0.0366952	−	0.0635579i	−0.00349875	−	0.00606001i
$111$	4.76917			0.452669
$112$	−2.78635			−0.263285
$113$	6.16196	−	10.6728i	0.579669	−	1.00402i	−0.415848	−	0.909434i	$-0.636515\pi$
$113$	6.16196	−	10.6728i	0.579669	−	1.00402i	0.995517	−	0.0945817i	$-0.0301514\pi$
$114$	−1.72295	−	2.98424i	−0.161369	−	0.279500i
$115$	1.03151	−	1.78663i	0.0961890	−	0.166604i
$116$	7.56656			0.702538
$117$	0.547853	−	0.948910i	0.0506491	−	0.0877267i
$118$	6.81615			0.627478
$119$	5.31808	−	9.21119i	0.487508	−	0.844389i
$120$	0.715393	+	1.23910i	0.0653062	+	0.113114i
$121$	5.48361	+	9.49789i	0.498510	+	0.863444i
$122$	−1.70466	+	2.95256i	−0.154333	+	0.267312i
$123$	3.24782	−	5.62539i	0.292846	−	0.507224i
$124$	−5.73417	−	9.93188i	−0.514944	−	0.891909i
$125$	−5.70576			−0.510339
$126$	−0.681637	−	1.18063i	−0.0607250	−	0.105179i
$127$	5.01838	+	8.69209i	0.445310	+	0.771299i	0.998074	−	0.0620390i	$-0.0197603\pi$
$127$	5.01838	+	8.69209i	0.445310	+	0.771299i	−0.552764	+	0.833338i	$0.686427\pi$
$128$	10.7960			0.954239
$129$	1.74060			0.153251
$130$	0.444108			0.0389509
$131$	−5.23597	−	9.06896i	−0.457469	−	0.792359i	0.541358	−	0.840792i	$-0.317910\pi$
$131$	−5.23597	−	9.06896i	−0.457469	−	0.792359i	−0.998826	+	0.0484333i	$0.984577\pi$
$132$	0.138522	+	0.239927i	0.0120568	+	0.0208830i
$133$	4.99806	−	8.65689i	0.433386	−	0.750647i
$134$	−1.26868			−0.109597
$135$	0.295622	−	0.512033i	0.0254431	−	0.0440687i
$136$	−6.47154	+	11.2090i	−0.554930	+	0.961167i
$137$	0.301018	−	0.521379i	0.0257177	−	0.0445444i	−0.852880	−	0.522107i	$-0.825146\pi$
$137$	0.301018	−	0.521379i	0.0257177	−	0.0445444i	0.878598	+	0.477562i	$0.158480\pi$
$138$	1.19601	−	2.07155i	0.101811	−	0.176342i
$139$	−2.99356	−	5.18499i	−0.253910	−	0.439785i	0.710689	−	0.703507i	$-0.248383\pi$
$139$	−2.99356	−	5.18499i	−0.253910	−	0.439785i	−0.964599	+	0.263721i	$0.915050\pi$
$140$	−0.899491	+	1.55796i	−0.0760209	+	0.131672i
$141$	−5.18853			−0.436953
$142$	4.17576	+	7.23263i	0.350422	+	0.606949i
$143$	0.198399			0.0165909
$144$	−0.700567	−	1.21342i	−0.0583806	−	0.101118i
$145$	1.46195	−	2.53216i	0.121408	−	0.210285i
$146$	3.30654	−	5.72709i	0.273651	−	0.473977i
$147$	−1.52266	+	2.63733i	−0.125587	+	0.217523i
$148$	−3.64852	−	6.31943i	−0.299907	−	0.519454i
$149$	8.35338			0.684335			0.342168	−	0.939639i	$-0.388839\pi$
$149$	8.35338			0.684335			0.342168	+	0.939639i	$0.388839\pi$
$150$	−3.18802			−0.260301
$151$	9.61211	−	16.6487i	0.782223	−	1.35485i	−0.148421	−	0.988924i	$-0.547419\pi$
$151$	9.61211	−	16.6487i	0.782223	−	1.35485i	0.930644	−	0.365925i	$-0.119247\pi$
$152$	−6.08210	+	10.5345i	−0.493323	+	0.854461i
$153$	5.34847			0.432398
$154$	0.123423	−	0.213776i	0.00994575	−	0.0172265i
$155$	−4.43163			−0.355957
$156$	−1.67648			−0.134226
$157$	−6.24016	+	10.8656i	−0.498019	+	0.867166i
$157$	−6.24016	+	10.8656i	−0.498019	+	0.867166i
$158$	−3.99650			−0.317944
$159$	2.54277			0.201655
$160$	1.71474	−	2.97001i	0.135562	−	0.234800i
$161$	6.93894			0.546865
$162$	0.342766	−	0.593688i	0.0269302	−	0.0466445i
$163$	−10.9088	+	18.8947i	−0.854446	+	1.47994i	0.0227121	+	0.999742i	$0.492770\pi$
$163$	−10.9088	+	18.8947i	−0.854446	+	1.47994i	−0.877158	+	0.480202i	$0.840563\pi$
$164$	−9.93863			−0.776076
$165$	0.107056			0.00833431
$166$	0.924559	+	1.60138i	0.0717597	+	0.124291i
$167$	−3.10725	+	5.38192i	−0.240446	+	0.416465i	−0.960842	−	0.277099i	$-0.910627\pi$
$167$	−3.10725	+	5.38192i	−0.240446	+	0.416465i	0.720395	+	0.693564i	$0.243960\pi$
$168$	−2.40621	+	4.16768i	−0.185643	+	0.321543i
$169$	5.89971	−	10.2186i	0.453824	−	0.786046i
$170$	1.08391	+	1.87739i	0.0831323	+	0.143989i
$171$	5.02661			0.384395
$172$	−1.33160	−	2.30640i	−0.101534	−	0.175861i
$173$	13.4951			1.02601			0.513007	−	0.858384i	$-0.328531\pi$
$173$	13.4951			1.02601			0.513007	+	0.858384i	$0.328531\pi$
$174$	1.69509	−	2.93597i	0.128504	−	0.222576i
$175$	−4.62401	−	8.00902i	−0.349542	−	0.605425i
$176$	0.126851	−	0.219713i	0.00956177	−	0.0165615i
$177$	−4.97143	+	8.61078i	−0.373676	+	0.647226i
$178$	4.42998	−	7.67296i	0.332041	−	0.575113i
$179$	2.00927	−	3.48016i	0.150180	−	0.260120i	−0.781113	−	0.624389i	$-0.785348\pi$
$179$	2.00927	−	3.48016i	0.150180	−	0.260120i	0.931294	+	0.364269i	$0.118681\pi$
$180$	−0.904631			−0.0674272
$181$	−5.60593	+	9.70976i	−0.416685	+	0.721720i	−0.995604	−	0.0936652i	$-0.970142\pi$
$181$	−5.60593	+	9.70976i	−0.416685	+	0.721720i	0.578918	+	0.815386i	$0.303475\pi$
$182$	0.746874	+	1.29362i	0.0553620	+	0.0958898i
$183$	−2.48663	−	4.30697i	−0.183817	−	0.318380i
$184$	−8.44394			−0.622496
$185$	−2.81974			−0.207312
$186$	−5.13835			−0.376762
$187$	0.484222	+	0.838697i	0.0354098	+	0.0613316i
$188$	3.96935	+	6.87511i	0.289494	+	0.501419i
$189$	1.98864			0.144652
$190$	1.01869	+	1.76441i	0.0739032	+	0.128004i
$191$	1.48550	−	2.57296i	0.107487	−	0.186173i	−0.807265	−	0.590190i	$-0.799053\pi$
$191$	1.48550	−	2.57296i	0.107487	−	0.186173i	0.914752	+	0.404017i	$0.132386\pi$
$192$	0.587059	−	1.01682i	0.0423673	−	0.0733823i
$193$	2.97960	+	5.16081i	0.214476	+	0.371483i	0.953110	−	0.302623i	$-0.0978623\pi$
$193$	2.97960	+	5.16081i	0.214476	+	0.371483i	−0.738634	+	0.674106i	$0.764529\pi$
$194$	5.24057	+	9.07693i	0.376251	+	0.651686i
$195$	−0.323915	+	0.561038i	−0.0231960	+	0.0401767i
$196$	4.65949			0.332820
$197$	−7.55021	+	13.0773i	−0.537930	+	0.931723i	0.461085	+	0.887356i	$0.347460\pi$
$197$	−7.55021	+	13.0773i	−0.537930	+	0.931723i	−0.999015	+	0.0443666i	$0.985873\pi$
$198$	0.124129			0.00882144
$199$	3.46155	−	5.99558i	0.245383	−	0.425015i	−0.716856	−	0.697221i	$-0.754420\pi$
$199$	3.46155	−	5.99558i	0.245383	−	0.425015i	0.962239	+	0.272206i	$0.0877531\pi$
$200$	5.62692	+	9.74612i	0.397884	+	0.689155i
$201$	0.925326	−	1.60271i	0.0652675	−	0.113047i
$202$	−0.415332			−0.0292227
$203$	9.83444			0.690242
$204$	−4.09170	−	7.08704i	−0.286477	−	0.496192i
$205$	−1.92025	+	3.32598i	−0.134116	+	0.232296i
$206$	1.74435			0.121534
$207$	1.74465	+	3.02182i	0.121261	+	0.210031i
$208$	0.767616	+	1.32955i	0.0532246	+	0.0921877i
$209$	0.455083	+	0.788226i	0.0314787	+	0.0545228i
$210$	0.403014	+	0.698041i	0.0278106	+	0.0481694i
$211$	−5.79437			−0.398901			−0.199451	−	0.979908i	$-0.563916\pi$
$211$	−5.79437			−0.398901			−0.199451	+	0.979908i	$0.563916\pi$
$212$	−1.94528	−	3.36932i	−0.133602	−	0.231406i
$213$	−12.1825			−0.834734
$214$	0.153591	+	0.266028i	0.0104993	+	0.0181853i
$215$	−1.02912			−0.0701854
$216$	−2.41996			−0.164657
$217$	−7.45284	−	12.9087i	−0.505932	−	0.876299i
$218$	−1.67587	+	2.90269i	−0.113504	+	0.196595i
$219$	4.82332	+	8.35423i	0.325930	+	0.564527i
$220$	−0.0819004	−	0.141856i	−0.00552173	−	0.00956391i
$221$	−5.86036			−0.394210
$222$	−3.26942			−0.219429
$223$	−6.56662	−	11.3737i	−0.439734	−	0.761641i	0.557935	−	0.829885i	$-0.311594\pi$
$223$	−6.56662	−	11.3737i	−0.439734	−	0.761641i	−0.997669	+	0.0682435i	$0.978261\pi$
$224$	11.5350			0.770712
$225$	2.32522	−	4.02739i	0.155014	−	0.268493i
$226$	−4.22422	+	7.31657i	−0.280991	+	0.486691i
$227$	−7.60672	+	13.1752i	−0.504876	+	0.874471i	0.495108	+	0.868831i	$0.335128\pi$
$227$	−7.60672	+	13.1752i	−0.504876	+	0.874471i	−0.999984	+	0.00563952i	$0.998205\pi$
$228$	−3.84548	−	6.66056i	−0.254673	−	0.441106i
$229$	14.7263	+	25.5067i	0.973141	+	1.68553i	0.685940	+	0.727658i	$0.259391\pi$
$229$	14.7263	+	25.5067i	0.973141	+	1.68553i	0.287201	+	0.957870i	$0.407275\pi$
$230$	−0.707134	+	1.22479i	−0.0466271	+	0.0807604i
$231$	0.180041	+	0.311839i	0.0118458	+	0.0205175i
$232$	−11.9675			−0.785702
$233$	−13.5125	+	23.4044i	−0.885235	+	1.53327i	−0.0397910	+	0.999208i	$0.512669\pi$
$233$	−13.5125	+	23.4044i	−0.885235	+	1.53327i	−0.845444	+	0.534064i	$0.820664\pi$
$234$	−0.375571	+	0.650508i	−0.0245518	+	0.0425250i
$235$	3.06769			0.200114
$236$	15.2130			0.990285
$237$	2.91489	−	5.04874i	0.189342	−	0.327951i
$238$	−3.64572	+	6.31456i	−0.236317	+	0.409312i
$239$	−11.3807			−0.736156			−0.368078	−	0.929795i	$-0.619984\pi$
$239$	−11.3807			−0.736156			−0.368078	+	0.929795i	$0.619984\pi$
$240$	0.414206	+	0.717426i	0.0267369	+	0.0463097i
$241$	−12.5201	+	21.6855i	−0.806492	+	1.39688i	0.108788	+	0.994065i	$0.465303\pi$
$241$	−12.5201	+	21.6855i	−0.806492	+	1.39688i	−0.915279	+	0.402819i	$0.868030\pi$
$242$	−3.75919	−	6.51110i	−0.241650	−	0.418549i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−3.80466	+	6.58986i	−0.243568	+	0.421872i
$245$	0.900265	−	1.55930i	0.0575158	−	0.0996203i
$246$	−2.22648	+	3.85638i	−0.141955	+	0.245874i
$247$	−5.50770			−0.350446
$248$	9.06931	+	15.7085i	0.575901	+	0.997491i
$249$	−2.69735			−0.170938
$250$	3.91148			0.247384
$251$	−1.77636	−	3.07675i	−0.112123	−	0.194203i	0.804503	−	0.593949i	$-0.202432\pi$
$251$	−1.77636	−	3.07675i	−0.112123	−	0.194203i	−0.916626	+	0.399746i	$0.869098\pi$
$252$	−1.52135	−	2.63506i	−0.0958362	−	0.165993i
$253$	−0.315902	+	0.547158i	−0.0198606	+	0.0343995i
$254$	−3.44026	−	5.95871i	−0.215861	−	0.373883i
$255$	−3.16225			−0.198028
$256$	−9.74922			−0.609326
$257$	4.41344	+	7.64431i	0.275303	+	0.476839i	0.970212	−	0.242259i	$-0.0778885\pi$
$257$	4.41344	+	7.64431i	0.275303	+	0.476839i	−0.694909	+	0.719098i	$0.744555\pi$
$258$	−1.19324			−0.0742877
$259$	−4.74207	−	8.21351i	−0.294658	−	0.510363i
$260$	0.991210			0.0614723
$261$	2.47266	+	4.28277i	0.153054	+	0.265097i
$262$	3.58942	+	6.21706i	0.221755	+	0.384091i
$263$	9.09873	+	15.7595i	0.561052	+	0.971770i	0.997405	+	0.0719948i	$0.0229365\pi$
$263$	9.09873	+	15.7595i	0.561052	+	0.971770i	−0.436353	+	0.899775i	$0.643730\pi$
$264$	−0.219090	−	0.379475i	−0.0134841	−	0.0233551i
$265$	−1.50340			−0.0923531
$266$	−3.42633	+	5.93457i	−0.210082	+	0.363872i
$267$	6.46211	+	11.1927i	0.395475	+	0.684983i
$268$	−2.83158			−0.172966
$269$	14.1282			0.861409			0.430705	−	0.902493i	$-0.358265\pi$
$269$	14.1282			0.861409			0.430705	+	0.902493i	$0.358265\pi$
$270$	−0.202658	+	0.351015i	−0.0123334	+	0.0213621i
$271$	2.82402	+	4.89135i	0.171547	+	0.297128i	0.938961	−	0.344024i	$-0.111790\pi$
$271$	2.82402	+	4.89135i	0.171547	+	0.297128i	−0.767414	+	0.641152i	$0.778457\pi$
$272$	−3.74696	+	6.48993i	−0.227193	+	0.393510i
$273$	−2.17896			−0.131877
$274$	−0.206358	+	0.357422i	−0.0124665	+	0.0215927i
$275$	0.842050			0.0507775
$276$	2.66939	−	4.62352i	0.160678	−	0.278303i
$277$	−6.43152	−	11.1397i	−0.386433	−	0.669321i	0.605534	−	0.795819i	$-0.292959\pi$
$277$	−6.43152	−	11.1397i	−0.386433	−	0.669321i	−0.991967	+	0.126498i	$0.959626\pi$
$278$	2.05218	+	3.55448i	0.123081	+	0.213183i
$279$	3.74771	−	6.49123i	0.224370	−	0.388620i
$280$	1.42266	−	2.46412i	0.0850201	−	0.147259i
$281$	4.83912	+	8.38159i	0.288677	+	0.500004i	0.973494	−	0.228711i	$-0.0734512\pi$
$281$	4.83912	+	8.38159i	0.288677	+	0.500004i	−0.684817	+	0.728715i	$0.740118\pi$
$282$	3.55690			0.211810
$283$	8.41371	+	14.5730i	0.500143	+	0.866273i	1.00000		0.000165084i	$5.25478e-5\pi$
$283$	8.41371	+	14.5730i	0.500143	+	0.866273i	−0.499857	+	0.866108i	$0.666614\pi$
$284$	9.31993	+	16.1426i	0.553036	+	0.957887i
$285$	−2.97196			−0.176044
$286$	−0.136009			−0.00804236
$287$	−12.9175			−0.762494
$288$	2.90022	+	5.02333i	0.170897	+	0.296002i
$289$	−5.80307	−	10.0512i	−0.341357	−	0.591248i
$290$	−1.00221	+	1.73588i	−0.0588518	+	0.101934i
$291$	−15.2891			−0.896261
$292$	7.37990	−	12.7824i	0.431876	−	0.748031i
$293$	14.8252	−	25.6780i	0.866097	−	1.50012i	0.000142243	−	1.00000i	$-0.499955\pi$
$293$	14.8252	−	25.6780i	0.866097	−	1.50012i	0.865954	−	0.500123i	$-0.166712\pi$
$294$	1.04383	−	1.80797i	0.0608776	−	0.105443i
$295$	2.93933	−	5.09107i	0.171135	−	0.296414i
$296$	5.77060	+	9.99497i	0.335409	+	0.580946i
$297$	−0.0905346	+	0.156811i	−0.00525335	+	0.00909907i
$298$	−5.72650			−0.331728
$299$	−1.91162	−	3.31102i	−0.110552	−	0.191481i
$300$	−7.11537			−0.410806
$301$	−1.73071	−	2.99768i	−0.0997566	−	0.172783i
$302$	−6.58941	+	11.4132i	−0.379178	+	0.656755i
$303$	0.302927	−	0.524685i	0.0174027	−	0.0301424i
$304$	−3.52148	+	6.09938i	−0.201971	+	0.349824i
$305$	1.47020	+	2.54647i	0.0841837	+	0.145810i
$306$	−3.66655			−0.209603
$307$	2.98155			0.170166			0.0850830	−	0.996374i	$-0.472884\pi$
$307$	2.98155			0.170166			0.0850830	+	0.996374i	$0.472884\pi$
$308$	0.275470	−	0.477129i	0.0156964	−	0.0271869i
$309$	−1.27226	+	2.20362i	−0.0723762	+	0.125359i
$310$	3.03802			0.172548
$311$	6.76973	−	11.7255i	0.383876	−	0.664893i	−0.607736	−	0.794139i	$-0.707922\pi$
$311$	6.76973	−	11.7255i	0.383876	−	0.664893i	0.991613	+	0.129246i	$0.0412555\pi$
$312$	2.65157			0.150115
$313$	8.47960			0.479295			0.239648	−	0.970860i	$-0.422968\pi$
$313$	8.47960			0.479295			0.239648	+	0.970860i	$0.422968\pi$
$314$	4.27783	−	7.44869i	0.241412	−	0.420354i
$315$	−1.17577			−0.0662471
$316$	−8.91983			−0.501780
$317$	−3.17994	+	5.50781i	−0.178603	+	0.309349i	−0.941402	−	0.337286i	$-0.890491\pi$
$317$	−3.17994	+	5.50781i	−0.178603	+	0.309349i	0.762799	+	0.646635i	$0.223824\pi$
$318$	−1.74315			−0.0977510
$319$	−0.447722	+	0.775478i	−0.0250676	+	0.0434184i
$320$	−0.347095	+	0.601186i	−0.0194032	+	0.0336073i
$321$	−0.448094			−0.0250102
$322$	−4.75686			−0.265090
$323$	−13.4424	−	23.2828i	−0.747952	−	1.29549i
$324$	0.765023	−	1.32506i	0.0425013	−	0.0736144i
$325$	−2.54775	+	4.41284i	−0.141324	+	0.244780i
$326$	7.47835	−	12.9529i	0.414188	−	0.717394i
$327$	−2.44463	−	4.23422i	−0.135188	−	0.234153i
$328$	15.7192			0.867946
$329$	5.15905	+	8.93574i	0.284428	+	0.492643i
$330$	−0.0733904			−0.00404001
$331$	10.4800	−	18.1520i	0.576035	−	0.997723i	−0.419893	−	0.907574i	$-0.637932\pi$
$331$	10.4800	−	18.1520i	0.576035	−	0.997723i	0.995928	−	0.0901490i	$-0.0287343\pi$
$332$	2.06353	+	3.57415i	0.113251	+	0.196157i
$333$	2.38458	−	4.13022i	0.130674	−	0.226335i
$334$	2.13012	−	3.68948i	0.116555	−	0.201879i
$335$	−0.547094	+	0.947594i	−0.0298909	+	0.0517726i
$336$	−1.39317	+	2.41305i	−0.0760038	+	0.131643i
$337$	−2.63357			−0.143460			−0.0717298	−	0.997424i	$-0.522852\pi$
$337$	−2.63357			−0.143460			−0.0717298	+	0.997424i	$0.522852\pi$
$338$	−4.04444	+	7.00518i	−0.219989	+	0.381031i
$339$	−6.16196	−	10.6728i	−0.334672	−	0.579669i
$340$	2.41920	+	4.19017i	0.131199	+	0.227244i
$341$	1.35719			0.0734960
$342$	−3.44590			−0.186333
$343$	19.9765			1.07863
$344$	2.10609	+	3.64786i	0.113553	+	0.196679i
$345$	−1.03151	−	1.78663i	−0.0555348	−	0.0961890i
$346$	−9.25133			−0.497354
$347$	−3.09400	−	5.35897i	−0.166095	−	0.287685i	0.770949	−	0.636897i	$-0.219782\pi$
$347$	−3.09400	−	5.35897i	−0.166095	−	0.287685i	−0.937044	+	0.349213i	$0.886449\pi$
$348$	3.78328	−	6.55284i	0.202805	−	0.351269i
$349$	14.9150	−	25.8335i	0.798379	−	1.38283i	−0.122292	−	0.992494i	$-0.539024\pi$
$349$	14.9150	−	25.8335i	0.798379	−	1.38283i	0.920671	−	0.390339i	$-0.127642\pi$
$350$	3.16990	+	5.49044i	0.169439	+	0.293476i
$351$	−0.547853	−	0.948910i	−0.0292422	−	0.0506491i
$352$	−0.525141	+	0.909570i	−0.0279901	+	0.0484803i
$353$	−30.6761			−1.63272			−0.816362	−	0.577540i	$-0.804013\pi$
$353$	−30.6761			−1.63272			−0.816362	+	0.577540i	$0.804013\pi$
$354$	3.40808	−	5.90296i	0.181137	−	0.313739i
$355$	7.20286			0.382288
$356$	9.88733	−	17.1254i	0.524028	−	0.907643i
$357$	−5.31808	−	9.21119i	−0.281463	−	0.487508i
$358$	−1.37742	+	2.38576i	−0.0727990	+	0.126091i
$359$	35.8732			1.89332			0.946658	−	0.322239i	$-0.104435\pi$
$359$	35.8732			1.89332			0.946658	+	0.322239i	$0.104435\pi$
$360$	1.43079			0.0754091
$361$	−3.13343	−	5.42725i	−0.164917	−	0.285645i
$362$	3.84304	−	6.65635i	0.201986	−	0.349850i
$363$	10.9672			0.575629
$364$	1.66696	+	2.88725i	0.0873723	+	0.151333i
$365$	−2.85176	−	4.93939i	−0.149268	−	0.258540i
$366$	1.70466	+	2.95256i	0.0891041	+	0.154333i
$367$	−8.24032	−	14.2727i	−0.430141	−	0.745027i	0.566744	−	0.823894i	$-0.308203\pi$
$367$	−8.24032	−	14.2727i	−0.430141	−	0.745027i	−0.996885	+	0.0788674i	$0.974870\pi$
$368$	−4.88897			−0.254855
$369$	−3.24782	−	5.62539i	−0.169075	−	0.292846i
$370$	1.93302			0.100493
$371$	−2.52832	−	4.37919i	−0.131264	−	0.227356i
$372$	−11.4683			−0.594606
$373$	−21.8203			−1.12981			−0.564906	−	0.825155i	$-0.691088\pi$
$373$	−21.8203			−1.12981			−0.564906	+	0.825155i	$0.691088\pi$
$374$	−0.331949	−	0.574953i	−0.0171647	−	0.0297301i
$375$	−2.85288	+	4.94133i	−0.147322	+	0.255169i
$376$	−6.27802	−	10.8738i	−0.323764	−	0.560776i
$377$	−2.70931	−	4.69266i	−0.139536	−	0.241684i
$378$	−1.36327			−0.0701192
$379$	13.4235			0.689517			0.344758	−	0.938691i	$-0.387961\pi$
$379$	13.4235			0.689517			0.344758	+	0.938691i	$0.387961\pi$
$380$	2.27362	+	3.93802i	0.116634	+	0.202016i
$381$	10.0368			0.514199
$382$	−1.01836	+	1.76385i	−0.0521037	+	0.0902462i
$383$	9.54562	−	16.5335i	0.487759	−	0.844823i	−0.512142	−	0.858901i	$-0.671148\pi$
$383$	9.54562	−	16.5335i	0.487759	−	0.844823i	0.999901	+	0.0140780i	$0.00448133\pi$
$384$	5.39799	−	9.34960i	0.275465	−	0.477120i
$385$	−0.106448	−	0.184373i	−0.00542509	−	0.00939653i
$386$	−2.04261	−	3.53790i	−0.103966	−	0.180074i
$387$	0.870301	−	1.50740i	0.0442399	−	0.0766257i
$388$	11.6965	+	20.2589i	0.593799	+	1.02849i
$389$	3.14148			0.159279			0.0796397	−	0.996824i	$-0.474623\pi$
$389$	3.14148			0.159279			0.0796397	+	0.996824i	$0.474623\pi$
$390$	0.222054	−	0.384609i	0.0112441	−	0.0194754i
$391$	9.33119	−	16.1621i	0.471899	−	0.817352i
$392$	−7.36956			−0.372219
$393$	−10.4719			−0.528239
$394$	5.17591	−	8.96494i	0.260759	−	0.451647i
$395$	−1.72341	+	2.98504i	−0.0867142	+	0.150193i
$396$	0.277044			0.0139220
$397$	−13.7048	−	23.7375i	−0.687825	−	1.19135i	−0.972540	−	0.232736i	$-0.925232\pi$
$397$	−13.7048	−	23.7375i	−0.687825	−	1.19135i	0.284715	−	0.958612i	$-0.408101\pi$
$398$	−2.37300	+	4.11016i	−0.118948	+	0.206024i
$399$	−4.99806	−	8.65689i	−0.250216	−	0.433386i
$400$	3.25794	+	5.64291i	0.162897	+	0.282146i
$401$	1.24249	−	2.15206i	0.0620472	−	0.107469i	−0.833333	−	0.552771i	$-0.813570\pi$
$401$	1.24249	−	2.15206i	0.0620472	−	0.107469i	0.895380	+	0.445302i	$0.146904\pi$
$402$	−0.634340	+	1.09871i	−0.0316380	+	0.0547987i
$403$	−4.10639	+	7.11248i	−0.204554	+	0.354298i
$404$	−0.926985			−0.0461192
$405$	−0.295622	−	0.512033i	−0.0146896	−	0.0254431i
$406$	−6.74182			−0.334591
$407$	0.863550			0.0428046
$408$	6.47154	+	11.2090i	0.320389	+	0.554930i
$409$	16.2849	+	28.2063i	0.805238	+	1.39471i	0.916130	+	0.400881i	$0.131296\pi$
$409$	16.2849	+	28.2063i	0.805238	+	1.39471i	−0.110892	+	0.993832i	$0.535371\pi$
$410$	1.31640	−	2.28006i	0.0650121	−	0.112604i
$411$	−0.301018	−	0.521379i	−0.0148481	−	0.0257177i
$412$	3.89323			0.191806
$413$	19.7728			0.972954
$414$	−1.19601	−	2.07155i	−0.0587807	−	0.101811i
$415$	1.59479			0.0782853
$416$	−3.17779	−	5.50409i	−0.155804	−	0.269860i
$417$	−5.98711			−0.293190
$418$	−0.311974	−	0.540354i	−0.0152591	−	0.0264296i
$419$	−10.8030	−	18.7114i	−0.527762	−	0.914111i	−0.999476	−	0.0323595i	$-0.989698\pi$
$419$	−10.8030	−	18.7114i	−0.527762	−	0.914111i	0.471714	−	0.881752i	$-0.343635\pi$
$420$	0.899491	+	1.55796i	0.0438907	+	0.0760209i
$421$	19.8594	+	34.3975i	0.967888	+	1.67643i	0.701646	+	0.712526i	$0.252449\pi$
$421$	19.8594	+	34.3975i	0.967888	+	1.67643i	0.266243	+	0.963906i	$0.414218\pi$
$422$	3.97223			0.193365
$423$	−2.59427	+	4.49340i	−0.126138	+	0.218477i
$424$	3.07670	+	5.32900i	0.149418	+	0.258799i
$425$	−24.8727			−1.20650
$426$	8.35152			0.404633
$427$	−4.94500	+	8.56499i	−0.239305	+	0.414489i
$428$	0.342802	+	0.593751i	0.0165700	+	0.0287000i
$429$	0.0991994	−	0.171818i	0.00478939	−	0.00829547i
$430$	0.705495			0.0340220
$431$	7.38181	−	12.7857i	0.355569	−	0.615864i	−0.631646	−	0.775257i	$-0.717620\pi$
$431$	7.38181	−	12.7857i	0.355569	−	0.615864i	0.987215	+	0.159393i	$0.0509537\pi$
$432$	−1.40113			−0.0674121
$433$	−8.25178	+	14.2925i	−0.396555	+	0.686854i	−0.993298	−	0.115578i	$-0.963128\pi$
$433$	−8.25178	+	14.2925i	−0.396555	+	0.686854i	0.596743	+	0.802432i	$0.296461\pi$
$434$	5.10916	+	8.84932i	0.245247	+	0.424781i
$435$	−1.46195	−	2.53216i	−0.0700949	−	0.121408i
$436$	−3.74039	+	6.47854i	−0.179132	+	0.310266i
$437$	8.76966	−	15.1895i	0.419510	−	0.726613i
$438$	−3.30654	−	5.72709i	−0.157992	−	0.273651i
$439$	−2.01532			−0.0961859			−0.0480930	−	0.998843i	$-0.515314\pi$
$439$	−2.01532			−0.0961859			−0.0480930	+	0.998843i	$0.515314\pi$
$440$	0.129536	+	0.224362i	0.00617537	+	0.0106961i
$441$	1.52266	+	2.63733i	0.0725077	+	0.125587i
$442$	4.01746			0.191091
$443$	−30.9706			−1.47146			−0.735730	−	0.677275i	$-0.763161\pi$
$443$	−30.9706			−1.47146			−0.735730	+	0.677275i	$0.763161\pi$
$444$	−7.29705			−0.346303
$445$	−3.82069	−	6.61763i	−0.181118	−	0.313706i
$446$	4.50163	+	7.79705i	0.213158	+	0.369201i
$447$	4.17669	−	7.23424i	0.197551	−	0.342168i
$448$	−2.33489			−0.110313
$449$	3.65567	−	6.33181i	0.172522	−	0.298817i	−0.766779	−	0.641911i	$-0.778142\pi$
$449$	3.65567	−	6.33181i	0.172522	−	0.298817i	0.939301	+	0.343094i	$0.111475\pi$
$450$	−1.59401	+	2.76090i	−0.0751423	+	0.130150i
$451$	0.588080	−	1.01858i	0.0276916	−	0.0479633i
$452$	−9.42809	+	16.3299i	−0.443460	+	0.768095i
$453$	−9.61211	−	16.6487i	−0.451617	−	0.782223i
$454$	5.21465	−	9.03204i	0.244736	−	0.423895i
$455$	1.28830			0.0603964
$456$	6.08210	+	10.5345i	0.284820	+	0.493323i
$457$	−28.5275			−1.33446			−0.667229	−	0.744853i	$-0.732520\pi$
$457$	−28.5275			−1.33446			−0.667229	+	0.744853i	$0.732520\pi$
$458$	−10.0953	−	17.4856i	−0.471724	−	0.817050i
$459$	2.67424	−	4.63191i	0.124823	−	0.216199i
$460$	−1.57826	+	2.73363i	−0.0735868	+	0.127456i
$461$	−10.9099	+	18.8965i	−0.508124	+	0.880097i	0.491831	+	0.870690i	$0.336328\pi$
$461$	−10.9099	+	18.8965i	−0.508124	+	0.880097i	−0.999956	+	0.00940663i	$0.997006\pi$
$462$	−0.123423	−	0.213776i	−0.00574218	−	0.00994575i
$463$	19.8383			0.921965			0.460982	−	0.887409i	$-0.347497\pi$
$463$	19.8383			0.921965			0.460982	+	0.887409i	$0.347497\pi$
$464$	−6.92905			−0.321673
$465$	−2.21581	+	3.83790i	−0.102756	+	0.177978i
$466$	9.26327	−	16.0444i	0.429112	−	0.743245i
$467$	14.3212			0.662707			0.331353	−	0.943507i	$-0.392495\pi$
$467$	14.3212			0.662707			0.331353	+	0.943507i	$0.392495\pi$
$468$	−0.838241	+	1.45188i	−0.0387477	+	0.0671130i
$469$	−3.68028			−0.169939
$470$	−2.10300			−0.0970041
$471$	6.28977	+	10.8369i	0.289817	+	0.499339i
$472$	−24.0613			−1.10751
$473$	0.315169			0.0144915
$474$	−1.99825	+	3.46107i	−0.0917826	+	0.158972i
$475$	−23.3759			−1.07256
$476$	−8.13691	+	14.0935i	−0.372955	+	0.645977i
$477$	1.27139	−	2.20210i	0.0582128	−	0.100827i
$478$	7.80183			0.356848
$479$	23.4968			1.07360			0.536799	−	0.843710i	$-0.319633\pi$
$479$	23.4968			1.07360			0.536799	+	0.843710i	$0.319633\pi$
$480$	−1.71474	−	2.97001i	−0.0782667	−	0.135562i
$481$	−2.61281	+	4.52551i	−0.119134	+	0.206346i
$482$	8.58294	−	14.8661i	0.390942	−	0.677132i
$483$	3.46947	−	6.00930i	0.157866	−	0.273432i
$484$	−8.39017	−	14.5322i	−0.381371	−	0.660555i
$485$	9.03957			0.410466
$486$	−0.342766	−	0.593688i	−0.0155482	−	0.0269302i
$487$	1.11030			0.0503125			0.0251563	−	0.999684i	$-0.491992\pi$
$487$	1.11030			0.0503125			0.0251563	+	0.999684i	$0.491992\pi$
$488$	6.01754	−	10.4227i	0.272401	−	0.471813i
$489$	10.9088	+	18.8947i	0.493315	+	0.854446i
$490$	−0.617160	+	1.06895i	−0.0278805	+	0.0482904i
$491$	9.43185	−	16.3364i	0.425654	−	0.737254i	−0.570828	−	0.821070i	$-0.693378\pi$
$491$	9.43185	−	16.3364i	0.425654	−	0.737254i	0.996481	+	0.0838164i	$0.0267109\pi$
$492$	−4.96931	+	8.60710i	−0.224034	+	0.388038i
$493$	13.2249	−	22.9063i	0.595622	−	1.03165i
$494$	3.77570			0.169877
$495$	0.0535281	−	0.0927134i	0.00240591	−	0.00416716i
$496$	5.25105	+	9.09508i	0.235779	+	0.408381i
$497$	12.1133	+	20.9809i	0.543357	+	0.941122i
$498$	1.84912			0.0828610
$499$	6.79203			0.304053			0.152026	−	0.988376i	$-0.451420\pi$
$499$	6.79203			0.304053			0.152026	+	0.988376i	$0.451420\pi$
$500$	8.73008			0.390421
$501$	3.10725	+	5.38192i	0.138822	+	0.240446i
$502$	1.21775	+	2.10921i	0.0543510	+	0.0941386i
$503$	−15.2512			−0.680017			−0.340008	−	0.940422i	$-0.610430\pi$
$503$	−15.2512			−0.680017			−0.340008	+	0.940422i	$0.610430\pi$
$504$	2.40621	+	4.16768i	0.107181	+	0.185643i
$505$	−0.179104	+	0.310217i	−0.00797002	+	0.0138045i
$506$	0.216561	−	0.375094i	0.00962730	−	0.0166750i
$507$	−5.89971	−	10.2186i	−0.262015	−	0.453824i
$508$	−7.67836	−	13.2993i	−0.340672	−	0.590061i
$509$	−5.99929	+	10.3911i	−0.265914	+	0.460576i	−0.967803	−	0.251710i	$-0.919007\pi$
$509$	−5.99929	+	10.3911i	−0.265914	+	0.460576i	0.701889	+	0.712287i	$0.252340\pi$
$510$	2.16782			0.0959929
$511$	9.59183	−	16.6135i	0.424318	−	0.734939i
$512$	−14.9086			−0.658872
$513$	2.51331	−	4.35318i	0.110965	−	0.192197i
$514$	−3.02556	−	5.24042i	−0.133452	−	0.231145i
$515$	0.752215	−	1.30288i	0.0331466	−	0.0574115i
$516$	−2.66320			−0.117241
$517$	−0.939483			−0.0413184
$518$	3.25084	+	5.63062i	0.142834	+	0.247395i
$519$	6.74756	−	11.6871i	0.296185	−	0.513007i
$520$	−1.56772			−0.0687492
$521$	4.56978	+	7.91510i	0.200206	+	0.346767i	0.948595	−	0.316494i	$-0.102506\pi$
$521$	4.56978	+	7.91510i	0.200206	+	0.346767i	−0.748389	+	0.663260i	$0.769172\pi$
$522$	−1.69509	−	2.93597i	−0.0741919	−	0.128504i
$523$	0.927346	+	1.60621i	0.0405500	+	0.0702346i	0.885588	−	0.464471i	$-0.153756\pi$
$523$	0.927346	+	1.60621i	0.0405500	+	0.0702346i	−0.845038	+	0.534706i	$0.820422\pi$
$524$	8.01127	+	13.8759i	0.349974	+	0.606173i
$525$	−9.24802			−0.403617
$526$	−6.23747	−	10.8036i	−0.271967	−	0.471060i
$527$	−40.0891			−1.74631
$528$	−0.126851	−	0.219713i	−0.00552049	−	0.00956177i
$529$	−10.8248			−0.470645
$530$	1.03063			0.0447676
$531$	4.97143	+	8.61078i	0.215742	+	0.373676i
$532$	−7.64726	+	13.2454i	−0.331551	+	0.574262i
$533$	3.55866	+	6.16377i	0.154143	+	0.266983i
$534$	−4.42998	−	7.67296i	−0.191704	−	0.332041i
$535$	0.264933			0.0114541
$536$	4.47850			0.193442
$537$	−2.00927	−	3.48016i	−0.0867066	−	0.150180i
$538$	−9.68531			−0.417563
$539$	−0.275707	+	0.477539i	−0.0118755	+	0.0205691i
$540$	−0.452316	+	0.783433i	−0.0194646	+	0.0337136i
$541$	9.49089	−	16.4387i	0.408045	−	0.706755i	−0.586625	−	0.809858i	$-0.699544\pi$
$541$	9.49089	−	16.4387i	0.408045	−	0.706755i	0.994671	+	0.103103i	$0.0328772\pi$
$542$	−1.93596	−	3.35318i	−0.0831565	−	0.144031i
$543$	5.60593	+	9.70976i	0.240573	+	0.416685i
$544$	15.5117	−	26.8671i	0.665060	−	1.15192i
$545$	1.44537	+	2.50346i	0.0619129	+	0.107236i
$546$	1.49375			0.0639265
$547$	9.32423	−	16.1500i	0.398675	−	0.690526i	−0.594888	−	0.803809i	$-0.702803\pi$
$547$	9.32423	−	16.1500i	0.398675	−	0.690526i	0.993563	+	0.113283i	$0.0361368\pi$
$548$	−0.460572	+	0.797734i	−0.0196747	+	0.0340775i
$549$	−4.97326			−0.212253
$550$	−0.577252			−0.0246141
$551$	12.4291	−	21.5278i	0.529497	−	0.917117i
$552$	−4.22197	+	7.31267i	−0.179699	+	0.311248i
$553$	−11.5933			−0.492998
$554$	4.40901	+	7.63663i	0.187321	+	0.324449i
$555$	−1.40987	+	2.44197i	−0.0598457	+	0.103656i
$556$	4.58028	+	7.93328i	0.194247	+	0.336446i
$557$	3.18619	+	5.51864i	0.135003	+	0.233832i	0.925599	−	0.378506i	$-0.123562\pi$
$557$	3.18619	+	5.51864i	0.135003	+	0.233832i	−0.790596	+	0.612339i	$0.790229\pi$
$558$	−2.56917	+	4.44994i	−0.108762	+	0.188381i
$559$	−0.953594	+	1.65167i	−0.0403327	+	0.0698583i
$560$	0.823706	−	1.42670i	0.0348079	−	0.0602891i
$561$	0.968444			0.0408877
$562$	−3.31737	−	5.74585i	−0.139935	−	0.242374i
$563$	9.27270			0.390798			0.195399	−	0.980724i	$-0.437400\pi$
$563$	9.27270			0.390798			0.195399	+	0.980724i	$0.437400\pi$
$564$	7.93869			0.334279
$565$	3.64323	+	6.31025i	0.153272	+	0.265474i
$566$	−5.76786	−	9.99023i	−0.242441	−	0.419921i
$567$	0.994318	−	1.72221i	0.0417575	−	0.0723260i
$568$	−14.7406	−	25.5315i	−0.618503	−	1.07128i
$569$	17.6701			0.740768			0.370384	−	0.928879i	$-0.379226\pi$
$569$	17.6701			0.740768			0.370384	+	0.928879i	$0.379226\pi$
$570$	2.03737			0.0853361
$571$	−11.7389	−	20.3324i	−0.491258	−	0.850884i	0.508691	−	0.860949i	$-0.330130\pi$
$571$	−11.7389	−	20.3324i	−0.491258	−	0.850884i	−0.999949	+	0.0100649i	$0.996796\pi$
$572$	−0.303559			−0.0126925
$573$	−1.48550	−	2.57296i	−0.0620576	−	0.107487i
$574$	8.85533			0.369614
$575$	−8.11336	−	14.0527i	−0.338350	−	0.586040i
$576$	−0.587059	−	1.01682i	−0.0244608	−	0.0423673i
$577$	19.0131	+	32.9317i	0.791526	+	1.37096i	0.925022	+	0.379914i	$0.124046\pi$
$577$	19.0131	+	32.9317i	0.791526	+	1.37096i	−0.133496	+	0.991049i	$0.542620\pi$
$578$	3.97819	+	6.89043i	0.165471	+	0.286604i
$579$	5.95919			0.247656
$580$	−2.23684	+	3.87433i	−0.0928799	+	0.160873i
$581$	2.68202	+	4.64540i	0.111269	+	0.192724i
$582$	10.4811			0.434457
$583$	0.460418			0.0190686
$584$	−11.6722	+	20.2169i	−0.483000	+	0.836581i
$585$	0.323915	+	0.561038i	0.0133922	+	0.0231960i
$586$	−10.1631	+	17.6031i	−0.419835	+	0.727176i
$587$	−1.08572			−0.0448124			−0.0224062	−	0.999749i	$-0.507133\pi$
$587$	−1.08572			−0.0448124			−0.0224062	+	0.999749i	$0.507133\pi$
$588$	2.32974	−	4.03523i	0.0960770	−	0.166410i
$589$	−37.6766			−1.55244
$590$	−2.01501	+	3.49009i	−0.0829565	+	0.143685i
$591$	7.55021	+	13.0773i	0.310574	+	0.537930i
$592$	3.34112	+	5.78699i	0.137319	+	0.237844i
$593$	−15.8785	+	27.5024i	−0.652053	+	1.12939i	0.330571	+	0.943781i	$0.392759\pi$
$593$	−15.8785	+	27.5024i	−0.652053	+	1.12939i	−0.982624	+	0.185607i	$0.940575\pi$
$594$	0.0620644	−	0.107499i	0.00254653	−	0.00441072i
$595$	3.14429	+	5.44606i	0.128903	+	0.223267i
$596$	−12.7811			−0.523532
$597$	−3.46155	−	5.99558i	−0.141672	−	0.245383i
$598$	1.31048	+	2.26981i	0.0535894	+	0.0928195i
$599$	36.2616			1.48161			0.740803	−	0.671722i	$-0.234445\pi$
$599$	36.2616			1.48161			0.740803	+	0.671722i	$0.234445\pi$
$600$	11.2538			0.459436
$601$	32.1521			1.31151			0.655755	−	0.754973i	$-0.272350\pi$
$601$	32.1521			1.31151			0.655755	+	0.754973i	$0.272350\pi$
$602$	1.18646	+	2.05501i	0.0483564	+	0.0837558i
$603$	−0.925326	−	1.60271i	−0.0376822	−	0.0652675i
$604$	−14.7070	+	25.4732i	−0.598419	+	1.03649i
$605$	−6.48430			−0.263624
$606$	−0.207666	+	0.359688i	−0.00843586	+	0.0146113i
$607$	3.96939	−	6.87518i	0.161112	−	0.279055i	−0.774155	−	0.632995i	$-0.781825\pi$
$607$	3.96939	−	6.87518i	0.161112	−	0.279055i	0.935268	+	0.353941i	$0.115158\pi$
$608$	14.5783	−	25.2503i	0.591228	−	1.02404i
$609$	4.91722	−	8.51687i	0.199256	−	0.345121i
$610$	−1.00787	−	1.74569i	−0.0408075	−	0.0706807i
$611$	2.84255	−	4.92345i	0.114997	−	0.199181i
$612$	−8.18341			−0.330795
$613$	6.97443	+	12.0801i	0.281695	+	0.487909i	0.971802	−	0.235797i	$-0.0757702\pi$
$613$	6.97443	+	12.0801i	0.281695	+	0.487909i	−0.690108	+	0.723707i	$0.742437\pi$
$614$	−2.04395			−0.0824870
$615$	1.92025	+	3.32598i	0.0774321	+	0.134116i
$616$	−0.435691	+	0.754638i	−0.0175545	+	0.0304052i
$617$	−11.2040	+	19.4059i	−0.451056	+	0.781252i	−0.998452	−	0.0556220i	$-0.982286\pi$
$617$	−11.2040	+	19.4059i	−0.451056	+	0.781252i	0.547396	+	0.836874i	$0.315619\pi$
$618$	0.872173	−	1.51065i	0.0350840	−	0.0607672i
$619$	10.8292	+	18.7568i	0.435263	+	0.753898i	0.997317	−	0.0732024i	$-0.0233219\pi$
$619$	10.8292	+	18.7568i	0.435263	+	0.753898i	−0.562054	+	0.827101i	$0.689989\pi$
$620$	6.78059			0.272315
$621$	3.48929			0.140021
$622$	−4.64087	+	8.03822i	−0.186082	+	0.322303i
$623$	12.8508	−	22.2582i	0.514856	−	0.891758i
$624$	1.53523			0.0614585
$625$	−9.93933	+	17.2154i	−0.397573	+	0.688617i
$626$	−5.81303			−0.232336
$627$	0.910165			0.0363485
$628$	9.54774	−	16.6248i	0.380996	−	0.663402i
$629$	−25.5078			−1.01706
$630$	0.806028			0.0321129
$631$	−8.43252	+	14.6055i	−0.335693	+	0.581438i	−0.983618	−	0.180267i	$-0.942304\pi$
$631$	−8.43252	+	14.6055i	−0.335693	+	0.581438i	0.647925	+	0.761704i	$0.275637\pi$
$632$	14.1078			0.561179
$633$	−2.89719	+	5.01808i	−0.115153	+	0.199451i
$634$	2.17995	−	3.77578i	0.0865768	−	0.149955i
$635$	−5.93418			−0.235491
$636$	−3.89056			−0.154271
$637$	−1.66839	−	2.88974i	−0.0661040	−	0.114496i
$638$	0.306928	−	0.531615i	0.0121514	−	0.0210468i
$639$	−6.09127	+	10.5504i	−0.240967	+	0.417367i
$640$	−3.19153	+	5.52790i	−0.126156	+	0.218509i
$641$	−8.44391	−	14.6253i	−0.333514	−	0.577664i	0.649684	−	0.760204i	$-0.274901\pi$
$641$	−8.44391	−	14.6253i	−0.333514	−	0.577664i	−0.983198	+	0.182541i	$0.941568\pi$
$642$	0.307183			0.0121235
$643$	14.9181	+	25.8389i	0.588312	+	1.01899i	0.994454	+	0.105177i	$0.0335408\pi$
$643$	14.9181	+	25.8389i	0.588312	+	1.01899i	−0.406141	+	0.913810i	$0.633126\pi$
$644$	−10.6169			−0.418364
$645$	−0.514560	+	0.891244i	−0.0202608	+	0.0350927i
$646$	9.21516	+	15.9611i	0.362566	+	0.627982i
$647$	−22.6508	+	39.2324i	−0.890495	+	1.54238i	−0.0512124	+	0.998688i	$0.516309\pi$
$647$	−22.6508	+	39.2324i	−0.890495	+	1.54238i	−0.839283	+	0.543695i	$0.817025\pi$
$648$	−1.20998	+	2.09575i	−0.0475325	+	0.0823287i
$649$	−0.900174	+	1.55915i	−0.0353349	+	0.0612019i
$650$	1.74657	−	3.02514i	0.0685060	−	0.118656i
$651$	−14.9057			−0.584199
$652$	16.6910	−	28.9097i	0.653671	−	1.13219i
$653$	−3.21195	−	5.56325i	−0.125693	−	0.217707i	0.796311	−	0.604888i	$-0.206782\pi$
$653$	−3.21195	−	5.56325i	−0.125693	−	0.217707i	−0.922004	+	0.387181i	$0.873449\pi$
$654$	1.67587	+	2.90269i	0.0655316	+	0.113504i
$655$	6.19147			0.241921
$656$	9.10126			0.355344
$657$	9.64664			0.376351
$658$	−3.53669	−	6.12573i	−0.137875	−	0.238806i
$659$	−21.7671	−	37.7017i	−0.847926	−	1.46865i	−0.883056	−	0.469268i	$-0.844518\pi$
$659$	−21.7671	−	37.7017i	−0.847926	−	1.46865i	0.0351294	−	0.999383i	$-0.488816\pi$
$660$	−0.163801			−0.00637594
$661$	−13.2846	−	23.0096i	−0.516711	−	0.894970i	−0.999812	−	0.0194053i	$-0.993823\pi$
$661$	−13.2846	−	23.0096i	−0.516711	−	0.894970i	0.483100	−	0.875565i	$-0.339511\pi$
$662$	−7.18440	+	12.4438i	−0.279230	+	0.483640i
$663$	−2.93018	+	5.07522i	−0.113799	+	0.197105i
$664$	−3.26374	−	5.65296i	−0.126658	−	0.219377i
$665$	2.95507	+	5.11833i	0.114593	+	0.198480i
$666$	−1.63471	+	2.83140i	−0.0633437	+	0.109714i
$667$	17.2557			0.668142
$668$	4.75424	−	8.23458i	0.183947	−	0.318606i
$669$	−13.1332			−0.507761
$670$	0.375050	−	0.649606i	0.0144895	−	0.0250965i
$671$	−0.450252	−	0.779859i	−0.0173818	−	0.0301061i
$672$	5.76748	−	9.98958i	0.222486	−	0.385356i
$673$	36.1561			1.39371			0.696857	−	0.717210i	$-0.254581\pi$
$673$	36.1561			1.39371			0.696857	+	0.717210i	$0.254581\pi$
$674$	1.80539			0.0695412
$675$	−2.32522	−	4.02739i	−0.0894976	−	0.155014i
$676$	−9.02683	+	15.6349i	−0.347186	+	0.601344i
$677$	22.4956			0.864574			0.432287	−	0.901736i	$-0.357707\pi$
$677$	22.4956			0.864574			0.432287	+	0.901736i	$0.357707\pi$
$678$	4.22422	+	7.31657i	0.162230	+	0.280991i
$679$	15.2022	+	26.3310i	0.583407	+	1.01049i
$680$	−3.82626	−	6.62728i	−0.146730	−	0.254145i
$681$	7.60672	+	13.1752i	0.291490	+	0.504876i
$682$	−0.930397			−0.0356267
$683$	−14.3221	−	24.8065i	−0.548018	−	0.949196i	−0.998410	−	0.0563647i	$-0.982049\pi$
$683$	−14.3221	−	24.8065i	−0.548018	−	0.949196i	0.450392	−	0.892831i	$-0.351284\pi$
$684$	−7.69095			−0.294071
$685$	0.177975	+	0.308262i	0.00680009	+	0.0117781i
$686$	−13.6945			−0.522859
$687$	29.4526			1.12369
$688$	1.21941	+	2.11208i	0.0464895	+	0.0805221i
$689$	−1.39307	+	2.41286i	−0.0530716	+	0.0919227i
$690$	0.707134	+	1.22479i	0.0269201	+	0.0466271i
$691$	−5.00995	−	8.67749i	−0.190587	−	0.330107i	0.754858	−	0.655889i	$-0.227706\pi$
$691$	−5.00995	−	8.67749i	−0.190587	−	0.330107i	−0.945445	+	0.325782i	$0.894373\pi$
$692$	−20.6481			−0.784925
$693$	0.360081			0.0136783
$694$	2.12104	+	3.67374i	0.0805135	+	0.139453i
$695$	3.53985			0.134274
$696$	−5.98373	+	10.3641i	−0.226813	+	0.392851i
$697$	−17.3709	+	30.0872i	−0.657968	+	1.13963i
$698$	−10.2247	+	17.7097i	−0.387010	+	0.670320i
$699$	13.5125	+	23.4044i	0.511091	+	0.885235i
$700$	7.07495	+	12.2542i	0.267408	+	0.463164i
$701$	21.4926	−	37.2263i	0.811765	−	1.40602i	−0.0998619	−	0.995001i	$-0.531840\pi$
$701$	21.4926	−	37.2263i	0.811765	−	1.40602i	0.911627	−	0.411018i	$-0.134827\pi$
$702$	0.375571	+	0.650508i	0.0141750	+	0.0245518i
$703$	−23.9728			−0.904150
$704$	0.106298	−	0.184114i	0.00400627	−	0.00693906i
$705$	1.53384	−	2.65670i	0.0577679	−	0.100057i
$706$	21.0294			0.791453
$707$	−1.20482			−0.0453121
$708$	7.60652	−	13.1749i	0.285871	−	0.495143i
$709$	14.7802	−	25.6000i	0.555082	−	0.961429i	−0.442816	−	0.896613i	$-0.646020\pi$
$709$	14.7802	−	25.6000i	0.555082	−	0.961429i	0.997897	−	0.0648167i	$-0.0206463\pi$
$710$	−4.93779			−0.185312
$711$	−2.91489	−	5.04874i	−0.109317	−	0.189342i
$712$	−15.6381	+	27.0859i	−0.586061	+	1.01509i
$713$	−13.0769	−	22.6498i	−0.489732	−	0.848241i
$714$	3.64572	+	6.31456i	0.136437	+	0.236317i
$715$	−0.0586511	+	0.101587i	−0.00219343	+	0.00379913i
$716$	−3.07428	+	5.32481i	−0.114891	+	0.198998i
$717$	−5.69035	+	9.85598i	−0.212510	+	0.368078i
$718$	−24.5922			−0.917774
$719$	0.351749	+	0.609247i	0.0131180	+	0.0227211i	0.872510	−	0.488596i	$-0.162491\pi$
$719$	0.351749	+	0.609247i	0.0131180	+	0.0227211i	−0.859392	+	0.511318i	$0.829158\pi$
$720$	0.828412			0.0308731
$721$	5.06012			0.188449
$722$	2.14806	+	3.72055i	0.0799426	+	0.138465i
$723$	12.5201	+	21.6855i	0.465628	+	0.806492i
$724$	8.57733	−	14.8564i	0.318774	−	0.552133i
$725$	−11.4989	−	19.9167i	−0.427059	−	0.739689i
$726$	−7.51837			−0.279033
$727$	−36.4655			−1.35243			−0.676215	−	0.736704i	$-0.736381\pi$
$727$	−36.4655			−1.35243			−0.676215	+	0.736704i	$0.736381\pi$
$728$	−2.63650	−	4.56655i	−0.0977152	−	0.169248i
$729$	1.00000			0.0370370
$730$	1.95497	+	3.38611i	0.0723567	+	0.125326i
$731$	−9.30956			−0.344326
$732$	3.80466	+	6.58986i	0.140624	+	0.243568i
$733$	−14.6608	−	25.3933i	−0.541509	−	0.937922i	−0.998818	−	0.0486136i	$-0.984520\pi$
$733$	−14.6608	−	25.3933i	−0.541509	−	0.937922i	0.457308	−	0.889308i	$-0.348814\pi$
$734$	5.64900	+	9.78436i	0.208509	+	0.361147i
$735$	−0.900265	−	1.55930i	−0.0332068	−	0.0575158i
$736$	20.2394			0.746035
$737$	0.167548	−	0.290202i	0.00617171	−	0.0106897i
$738$	2.22648	+	3.85638i	0.0819580	+	0.141955i
$739$	−2.73404			−0.100573			−0.0502867	−	0.998735i	$-0.516013\pi$
$739$	−2.73404			−0.100573			−0.0502867	+	0.998735i	$0.516013\pi$
$740$	4.31434			0.158598
$741$	−2.75385	+	4.76980i	−0.101165	+	0.175223i
$742$	1.73325	+	3.00207i	0.0636295	+	0.110210i
$743$	−14.0214	+	24.2858i	−0.514397	+	0.890961i	0.485464	+	0.874257i	$0.338651\pi$
$743$	−14.0214	+	24.2858i	−0.514397	+	0.890961i	−0.999860	+	0.0167044i	$0.994683\pi$
$744$	18.1386			0.664994
$745$	−2.46944	+	4.27720i	−0.0904734	+	0.156705i
$746$	14.9585			0.547670
$747$	−1.34867	+	2.33597i	−0.0493454	+	0.0854688i
$748$	−0.740882	−	1.28325i	−0.0270893	−	0.0469201i
$749$	0.445548	+	0.771712i	0.0162800	+	0.0281978i
$750$	1.95574	−	3.38744i	0.0714135	−	0.123692i
$751$	4.70165	−	8.14349i	0.171566	−	0.297160i	−0.767402	−	0.641166i	$-0.778451\pi$
$751$	4.70165	−	8.14349i	0.171566	−	0.297160i	0.938967	+	0.344006i	$0.111784\pi$
$752$	−3.63491	−	6.29586i	−0.132552	−	0.229586i
$753$	−3.55272			−0.129468
$754$	1.85732	+	3.21697i	0.0676395	+	0.117155i
$755$	5.68311	+	9.84343i	0.206829	+	0.358239i
$756$	−3.04271			−0.110662
$757$	−5.49527			−0.199729			−0.0998645	−	0.995001i	$-0.531841\pi$
$757$	−5.49527			−0.199729			−0.0998645	+	0.995001i	$0.531841\pi$
$758$	−9.20221			−0.334239
$759$	0.315902	+	0.547158i	0.0114665	+	0.0198606i
$760$	−3.59601	−	6.22847i	−0.130441	−	0.225930i
$761$	−10.3720	+	17.9648i	−0.375983	+	0.651222i	−0.990474	−	0.137702i	$-0.956028\pi$
$761$	−10.3720	+	17.9648i	−0.375983	+	0.651222i	0.614490	+	0.788924i	$0.289362\pi$
$762$	−6.88052			−0.249255
$763$	−4.86147	+	8.42032i	−0.175997	+	0.304836i
$764$	−2.27288	+	3.93675i	−0.0822300	+	0.142427i
$765$	−1.58113	+	2.73859i	−0.0571658	+	0.0990140i
$766$	−6.54383	+	11.3342i	−0.236438	+	0.409523i
$767$	−5.44723	−	9.43489i	−0.196688	−	0.340674i
$768$	−4.87461	+	8.44308i	−0.175897	+	0.304663i
$769$	39.6200			1.42873			0.714366	−	0.699772i	$-0.246715\pi$
$769$	39.6200			1.42873			0.714366	+	0.699772i	$0.246715\pi$
$770$	0.0729734	+	0.126394i	0.00262978	+	0.00455491i
$771$	8.82689			0.317893
$772$	−4.55892	−	7.89628i	−0.164079	−	0.284193i
$773$	−17.1924	+	29.7781i	−0.618367	+	1.07104i	0.371417	+	0.928466i	$0.378872\pi$
$773$	−17.1924	+	29.7781i	−0.618367	+	1.07104i	−0.989784	+	0.142577i	$0.954461\pi$
$774$	−0.596619	+	1.03337i	−0.0214450	+	0.0371439i
$775$	−17.4285	+	30.1870i	−0.626049	+	1.08435i
$776$	−18.4995	−	32.0420i	−0.664092	−	1.15024i
$777$	−9.48415			−0.340242
$778$	−2.15359			−0.0772098
$779$	−16.3255	+	28.2767i	−0.584923	+	1.01312i
$780$	0.495605	−	0.858413i	0.0177455	−	0.0307361i
$781$	−2.20588			−0.0789328
$782$	−6.39683	+	11.0796i	−0.228750	+	0.396207i
$783$	4.94532			0.176731
$784$	−4.26691			−0.152389
$785$	−3.71879	−	6.40727i	−0.132729	−	0.228685i
$786$	7.17885			0.256061
$787$	21.6244			0.770828			0.385414	−	0.922744i	$-0.374059\pi$
$787$	21.6244			0.770828			0.385414	+	0.922744i	$0.374059\pi$
$788$	11.5522	−	20.0089i	0.411529	−	0.712789i
$789$	18.1975			0.647847
$790$	1.18145	−	2.04634i	0.0420342	−	0.0728054i
$791$	−12.2539	+	21.2244i	−0.435699	+	0.754652i
$792$	−0.438180			−0.0155701
$793$	5.44923			0.193508
$794$	9.39509	+	16.2728i	0.333419	+	0.577499i
$795$	−0.751700	+	1.30198i	−0.0266600	+	0.0461765i
$796$	−5.29633	+	9.17351i	−0.187723	+	0.325146i
$797$	−0.711741	+	1.23277i	−0.0252111	+	0.0436670i	−0.878356	−	0.478008i	$-0.841359\pi$
$797$	−0.711741	+	1.23277i	−0.0252111	+	0.0436670i	0.853145	+	0.521675i	$0.174692\pi$
$798$	3.42633	+	5.93457i	0.121291	+	0.210082i
$799$	27.7507			0.981750
$800$	−13.4873	−	23.3606i	−0.476847	−	0.825923i
$801$	12.9242			0.456655
$802$	−0.851769	+	1.47531i	−0.0300770	+	0.0520949i
$803$	0.873355	+	1.51269i	0.0308200	+	0.0533818i
$804$	−1.41579	+	2.45222i	−0.0499311	+	0.0864832i
$805$	−2.05130	+	3.55296i	−0.0722989	+	0.125225i
$806$	2.81506	−	4.87583i	0.0991563	−	0.171744i
$807$	7.06408	−	12.2353i	0.248667	−	0.430705i
$808$	1.46614			0.0515787
$809$	−21.9603	+	38.0363i	−0.772081	+	1.33728i	0.164339	+	0.986404i	$0.447451\pi$
$809$	−21.9603	+	38.0363i	−0.772081	+	1.33728i	−0.936420	+	0.350880i	$0.885882\pi$
$810$	0.202658	+	0.351015i	0.00712069	+	0.0123334i
$811$	14.4836	+	25.0863i	0.508587	+	0.880899i	0.999951	+	0.00994421i	$0.00316539\pi$
$811$	14.4836	+	25.0863i	0.508587	+	0.880899i	−0.491363	+	0.870955i	$0.663501\pi$
$812$	−15.0471			−0.528051
$813$	5.64805			0.198086
$814$	−0.591991			−0.0207493
$815$	−6.44979	−	11.1714i	−0.225926	−	0.391316i
$816$	3.74696	+	6.48993i	0.131170	+	0.227193i
$817$	−8.74933			−0.306100
$818$	−11.1638	−	19.3363i	−0.390334	−	0.676079i
$819$	−1.08948	+	1.88704i	−0.0380696	+	0.0659384i
$820$	2.93808	−	5.08890i	0.102602	−	0.177712i
$821$	−5.50448	−	9.53403i	−0.192108	−	0.332740i	0.753841	−	0.657057i	$-0.228199\pi$
$821$	−5.50448	−	9.53403i	−0.192108	−	0.332740i	−0.945948	+	0.324317i	$0.894866\pi$
$822$	0.206358	+	0.357422i	0.00719755	+	0.0124665i
$823$	−18.7499	+	32.4757i	−0.653579	+	1.13203i	0.328669	+	0.944445i	$0.393400\pi$
$823$	−18.7499	+	32.4757i	−0.653579	+	1.13203i	−0.982248	+	0.187587i	$0.939933\pi$
$824$	−6.15762			−0.214511
$825$	0.421025	−	0.729237i	0.0146582	−	0.0253888i
$826$	−13.5549			−0.471634
$827$	−2.16791	+	3.75493i	−0.0753856	+	0.130572i	−0.901254	−	0.433291i	$-0.857352\pi$
$827$	−2.16791	+	3.75493i	−0.0753856	+	0.130572i	0.825868	+	0.563863i	$0.190685\pi$
$828$	−2.66939	−	4.62352i	−0.0927677	−	0.160678i
$829$	4.91476	−	8.51262i	0.170697	−	0.295656i	−0.767967	−	0.640490i	$-0.778731\pi$
$829$	4.91476	−	8.51262i	0.170697	−	0.295656i	0.938664	+	0.344834i	$0.112065\pi$
$830$	−1.09328			−0.0379483
$831$	−12.8630			−0.446214
$832$	0.643244	+	1.11413i	0.0223005	+	0.0386256i
$833$	8.14391	−	14.1057i	0.282170	−	0.488732i
$834$	4.10435			0.142122
$835$	−1.83715	−	3.18203i	−0.0635770	−	0.110119i
$836$	−0.696298	−	1.20602i	−0.0240820	−	0.0417112i
$837$	−3.74771	−	6.49123i	−0.129540	−	0.224370i
$838$	7.40582	+	12.8273i	0.255830	+	0.443110i
$839$	−14.7713			−0.509961			−0.254980	−	0.966946i	$-0.582069\pi$
$839$	−14.7713			−0.509961			−0.254980	+	0.966946i	$0.582069\pi$
$840$	−1.42266	−	2.46412i	−0.0490864	−	0.0850201i
$841$	−4.54384			−0.156684
$842$	−13.6143	−	23.5806i	−0.469178	−	0.812641i
$843$	9.67823			0.333336
$844$	8.86566			0.305169
$845$	3.48817	+	6.04169i	0.119997	+	0.207840i
$846$	1.77845	−	3.08037i	0.0611444	−	0.105905i
$847$	−10.9049	−	18.8878i	−0.374697	−	0.648994i
$848$	1.78138	+	3.08544i	0.0611729	+	0.105955i
$849$	16.8274			0.577515
$850$	17.0510			0.584845
$851$	−8.32051	−	14.4116i	−0.285224	−	0.494022i
$852$	18.6399			0.638591
$853$	−4.56911	+	7.91393i	−0.156443	+	0.270968i	−0.933584	−	0.358360i	$-0.883336\pi$
$853$	−4.56911	+	7.91393i	−0.156443	+	0.270968i	0.777140	+	0.629327i	$0.216669\pi$
$854$	3.38995	−	5.87157i	0.116002	−	0.200921i
$855$	−1.48598	+	2.57379i	−0.0508194	+	0.0880218i
$856$	−0.542185	−	0.939091i	−0.0185315	−	0.0320975i
$857$	14.4362	+	25.0042i	0.493131	+	0.854128i	0.999969	−	0.00791372i	$-0.00251904\pi$
$857$	14.4362	+	25.0042i	0.493131	+	0.854128i	−0.506838	+	0.862041i	$0.669186\pi$
$858$	−0.0680043	+	0.117787i	−0.00232163	+	0.00402118i
$859$	5.68442	+	9.84570i	0.193950	+	0.335931i	0.946556	−	0.322540i	$-0.104537\pi$
$859$	5.68442	+	9.84570i	0.193950	+	0.335931i	−0.752606	+	0.658471i	$0.771203\pi$
$860$	1.57460			0.0536935
$861$	−6.45873	+	11.1869i	−0.220113	+	0.381247i
$862$	−5.06046	+	8.76498i	−0.172360	+	0.298536i
$863$	5.91901			0.201485			0.100743	−	0.994913i	$-0.467878\pi$
$863$	5.91901			0.201485			0.100743	+	0.994913i	$0.467878\pi$
$864$	5.80044			0.197335
$865$	−3.98945	+	6.90994i	−0.135645	+	0.234945i
$866$	5.65686	−	9.79797i	0.192228	−	0.332949i
$867$	−11.6061			−0.394165
$868$	11.4032	+	19.7509i	0.387049	+	0.670389i
$869$	0.527797	−	0.914171i	0.0179043	−	0.0310111i
$870$	1.00221	+	1.73588i	0.0339781	+	0.0588518i
$871$	1.01389	+	1.75610i	0.0343542	+	0.0595033i
$872$	5.91589	−	10.2466i	0.200337	−	0.346995i
$873$	−7.64453	+	13.2407i	−0.258728	+	0.448130i
$874$	−6.01188	+	10.4129i	−0.203355	+	0.352221i
$875$	11.3467			0.383588
$876$	−7.37990	−	12.7824i	−0.249344	−	0.431876i
$877$	17.5293			0.591921			0.295961	−	0.955200i	$-0.404360\pi$
$877$	17.5293			0.591921			0.295961	+	0.955200i	$0.404360\pi$
$878$	1.38157			0.0466256
$879$	−14.8252	−	25.6780i	−0.500041	−	0.866097i
$880$	0.0750000	+	0.129904i	0.00252825	+	0.00437906i
$881$	23.1894	−	40.1653i	0.781271	−	1.35320i	−0.149930	−	0.988697i	$-0.547905\pi$
$881$	23.1894	−	40.1653i	0.781271	−	1.35320i	0.931201	−	0.364505i	$-0.118762\pi$
$882$	−1.04383	−	1.80797i	−0.0351477	−	0.0608776i
$883$	−28.6150			−0.962973			−0.481486	−	0.876454i	$-0.659903\pi$
$883$	−28.6150			−0.962973			−0.481486	+	0.876454i	$0.659903\pi$
$884$	8.96662			0.301580
$885$	−2.93933	−	5.09107i	−0.0988046	−	0.171135i
$886$	21.2314			0.713281
$887$	−3.41901	−	5.92189i	−0.114799	−	0.198838i	0.802900	−	0.596113i	$-0.203289\pi$
$887$	−3.41901	−	5.92189i	−0.114799	−	0.198838i	−0.917699	+	0.397276i	$0.869956\pi$
$888$	11.5412			0.387297
$889$	−9.97974	−	17.2854i	−0.334710	−	0.579734i
$890$	2.61920	+	4.53659i	0.0877959	+	0.152067i
$891$	0.0905346	+	0.156811i	0.00303302	+	0.00525335i
$892$	10.0472	+	17.4023i	0.336406	+	0.582673i
$893$	26.0807			0.872759
$894$	−2.86325	+	4.95930i	−0.0957615	+	0.165864i
$895$	1.18797	+	2.05763i	0.0397095	+	0.0687789i
$896$	−21.4693			−0.717239
$897$	−3.82324			−0.127654
$898$	−2.50608	+	4.34066i	−0.0836290	+	0.144850i
$899$	−18.5336	−	32.1012i	−0.618131	−	1.07063i
$900$	−3.55769	+	6.16209i	−0.118590	+	0.205403i
$901$	−13.5999			−0.453080
$902$	−0.403148	+	0.698272i	−0.0134233	+	0.0232499i
$903$	−3.46142			−0.115189
$904$	14.9117	−	25.8278i	0.495956	−	0.859020i
$905$	−3.31447	−	5.74084i	−0.110177	−	0.190832i
$906$	6.58941	+	11.4132i	0.218918	+	0.379178i
$907$	22.0464	−	38.1855i	0.732038	−	1.26793i	−0.223972	−	0.974595i	$-0.571903\pi$
$907$	22.0464	−	38.1855i	0.732038	−	1.26793i	0.956011	−	0.293332i	$-0.0947641\pi$
$908$	11.6386	−	20.1587i	0.386242	−	0.668990i
$909$	−0.302927	−	0.524685i	−0.0100475	−	0.0174027i
$910$	−0.883170			−0.0292768
$911$	−10.4393	−	18.0814i	−0.345869	−	0.599063i	0.639642	−	0.768673i	$-0.279083\pi$
$911$	−10.4393	−	18.0814i	−0.345869	−	0.599063i	−0.985511	+	0.169610i	$0.945749\pi$
$912$	3.52148	+	6.09938i	0.116608	+	0.201971i
$913$	−0.488407			−0.0161639
$914$	19.5565			0.646871
$915$	2.94041			0.0972069
$916$	−22.5319	−	39.0264i	−0.744475	−	1.28947i
$917$	10.4124	+	18.0349i	0.343849	+	0.595564i
$918$	−1.83327	+	3.17532i	−0.0605070	+	0.104801i
$919$	−20.5096			−0.676549			−0.338275	−	0.941047i	$-0.609843\pi$
$919$	−20.5096			−0.676549			−0.338275	+	0.941047i	$0.609843\pi$
$920$	2.49622	−	4.32357i	0.0822978	−	0.142544i
$921$	1.49078	−	2.58210i	0.0491227	−	0.0850830i
$922$	7.47908	−	12.9541i	0.246310	−	0.426622i
$923$	6.67425	−	11.5601i	0.219686	−	0.380507i
$924$	−0.275470	−	0.477129i	−0.00906231	−	0.0156964i
$925$	−11.0893	+	19.2073i	−0.364615	+	0.631532i
$926$	−13.5998			−0.446917
$927$	1.27226	+	2.20362i	0.0417864	+	0.0723762i
$928$	28.6850			0.941632
$929$	4.59258	+	7.95458i	0.150678	+	0.260981i	0.931477	−	0.363801i	$-0.118521\pi$
$929$	4.59258	+	7.95458i	0.150678	+	0.260981i	−0.780799	+	0.624782i	$0.785188\pi$
$930$	1.51901	−	2.63100i	0.0498103	−	0.0862740i
$931$	7.65383	−	13.2568i	0.250844	−	0.434475i
$932$	20.6748	−	35.8098i	0.677225	−	1.17299i
$933$	−6.76973	−	11.7255i	−0.221631	−	0.383876i
$934$	−9.81765			−0.321243
$935$	−0.572587			−0.0187256
$936$	1.32578	−	2.29632i	0.0433346	−	0.0750577i
$937$	7.40026	−	12.8176i	0.241756	−	0.418733i	−0.719459	−	0.694535i	$-0.755610\pi$
$937$	7.40026	−	12.8176i	0.241756	−	0.418733i	0.961215	+	0.275802i	$0.0889433\pi$
$938$	2.52295			0.0823771
$939$	4.23980	−	7.34355i	0.138361	−	0.239648i
$940$	−4.69371			−0.153092
$941$	−0.195440			−0.00637118			−0.00318559	−	0.999995i	$-0.501014\pi$
$941$	−0.195440			−0.00637118			−0.00318559	+	0.999995i	$0.501014\pi$
$942$	−4.31184	−	7.42905i	−0.140487	−	0.242052i
$943$	−22.6652			−0.738080
$944$	−13.9313			−0.453425
$945$	−0.587885	+	1.01825i	−0.0191239	+	0.0331236i
$946$	−0.216059			−0.00702467
$947$	−18.6159	+	32.2437i	−0.604935	+	1.04778i	0.387127	+	0.922026i	$0.373468\pi$
$947$	−18.6159	+	32.2437i	−0.604935	+	1.04778i	−0.992062	+	0.125752i	$0.959866\pi$
$948$	−4.45992	+	7.72480i	−0.144851	+	0.250890i
$949$	−10.5699			−0.343113
$950$	16.0249			0.519918
$951$	3.17994	+	5.50781i	0.103116	+	0.178603i
$952$	12.8695	−	22.2907i	0.417104	−	0.722446i
$953$	25.2785	−	43.7836i	0.818850	−	1.41829i	−0.0876810	−	0.996149i	$-0.527946\pi$
$953$	25.2785	−	43.7836i	0.818850	−	1.41829i	0.906530	−	0.422140i	$-0.138721\pi$
$954$	−0.871575	+	1.50961i	−0.0282183	+	0.0488755i
$955$	0.878293	+	1.52125i	0.0284209	+	0.0492264i
$956$	17.4130			0.563177
$957$	0.447722	+	0.775478i	0.0144728	+	0.0250676i
$958$	−16.1078			−0.520421
$959$	−0.598616	+	1.03683i	−0.0193303	+	0.0334811i
$960$	0.347095	+	0.601186i	0.0112024	+	0.0194032i
$961$	−12.5907	+	21.8077i	−0.406151	+	0.703474i
$962$	1.79116	−	3.10238i	0.0577493	−	0.100025i
$963$	−0.224047	+	0.388061i	−0.00721982	+	0.0125051i
$964$	19.1564	−	33.1798i	0.616985	−	1.06865i
$965$	−3.52334			−0.113420
$966$	−2.37843	+	4.11956i	−0.0765248	+	0.132545i
$967$	5.22487	+	9.04974i	0.168021	+	0.291020i	0.937724	−	0.347382i	$-0.112929\pi$
$967$	5.22487	+	9.04974i	0.168021	+	0.291020i	−0.769703	+	0.638402i	$0.779596\pi$
$968$	13.2701	+	22.9845i	0.426517	+	0.738750i
$969$	−26.8847			−0.863661
$970$	−6.19691			−0.198971
$971$	46.3976			1.48897			0.744485	−	0.667639i	$-0.232695\pi$
$971$	46.3976			1.48897			0.744485	+	0.667639i	$0.232695\pi$
$972$	−0.765023	−	1.32506i	−0.0245381	−	0.0425013i
$973$	5.95310	+	10.3111i	0.190847	+	0.330558i
$974$	−0.761146			−0.0243887
$975$	2.54775	+	4.41284i	0.0815934	+	0.141324i
$976$	3.48410	−	6.03464i	0.111523	−	0.193164i
$977$	−17.1151	+	29.6442i	−0.547560	+	0.948402i	0.450881	+	0.892584i	$0.351110\pi$
$977$	−17.1151	+	29.6442i	−0.547560	+	0.948402i	−0.998441	+	0.0558177i	$0.982223\pi$
$978$	−7.47835	−	12.9529i	−0.239131	−	0.414188i
$979$	1.17009	+	2.02666i	0.0373962	+	0.0647722i
$980$	−1.37745	+	2.38581i	−0.0440009	+	0.0762118i
$981$	−4.88925			−0.156102
$982$	−6.46583	+	11.1992i	−0.206333	+	0.357379i
$983$	17.4499			0.556565			0.278282	−	0.960499i	$-0.410235\pi$
$983$	17.4499			0.556565			0.278282	+	0.960499i	$0.410235\pi$
$984$	7.85959	−	13.6132i	0.250554	−	0.433973i
$985$	−4.46402	−	7.73191i	−0.142235	−	0.246359i
$986$	−9.06612	+	15.7030i	−0.288724	+	0.500085i
$987$	10.3181			0.328429
$988$	8.42703			0.268099
$989$	−3.03673	−	5.25978i	−0.0965625	−	0.167251i
$990$	−0.0366952	+	0.0635579i	−0.00116625	+	0.00202000i
$991$	30.7424			0.976564			0.488282	−	0.872686i	$-0.337624\pi$
$991$	30.7424			0.976564			0.488282	+	0.872686i	$0.337624\pi$
$992$	−21.7384	−	37.6520i	−0.690194	−	1.19545i
$993$	−10.4800	−	18.1520i	−0.332574	−	0.576035i
$994$	−8.30407	−	14.3831i	−0.263389	−	0.456203i
$995$	2.04662	+	3.54485i	0.0648822	+	0.112379i
$996$	4.12707			0.130771
$997$	−8.48607	−	14.6983i	−0.268757	−	0.465500i	0.699784	−	0.714354i	$-0.253279\pi$
$997$	−8.48607	−	14.6983i	−0.268757	−	0.465500i	−0.968541	+	0.248854i	$0.919946\pi$
$998$	−4.65615			−0.147388
$999$	−2.38458	−	4.13022i	−0.0754449	−	0.130674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.e.b.301.4	yes	22
157.12	even	3	inner	471.2.e.b.169.4	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.e.b.169.4	✓	22	157.12	even	3	inner
471.2.e.b.301.4	yes	22	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.685532 q^{2} +(0.500000 - 0.866025i) q^{3} -1.53005 q^{4} +(-0.295622 + 0.512033i) q^{5} +(-0.342766 + 0.593688i) q^{6} -1.98864 q^{7} +2.41996 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-0.685532 q^{2} +(0.500000 - 0.866025i) q^{3} -1.53005 q^{4} +(-0.295622 + 0.512033i) q^{5} +(-0.342766 + 0.593688i) q^{6} -1.98864 q^{7} +2.41996 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.202658 - 0.351015i) q^{10} +(0.0905346 - 0.156811i) q^{11} +(-0.765023 + 1.32506i) q^{12} +(0.547853 + 0.948910i) q^{13} +1.36327 q^{14} +(0.295622 + 0.512033i) q^{15} +1.40113 q^{16} +(-2.67424 + 4.63191i) q^{17} +(0.342766 + 0.593688i) q^{18} +(-2.51331 + 4.35318i) q^{19} +(0.452316 - 0.783433i) q^{20} +(-0.994318 + 1.72221i) q^{21} +(-0.0620644 + 0.107499i) q^{22} -3.48929 q^{23} +(1.20998 - 2.09575i) q^{24} +(2.32522 + 4.02739i) q^{25} +(-0.375571 - 0.650508i) q^{26} -1.00000 q^{27} +3.04271 q^{28} -4.94532 q^{29} +(-0.202658 - 0.351015i) q^{30} +(3.74771 + 6.49123i) q^{31} -5.80044 q^{32} +(-0.0905346 - 0.156811i) q^{33} +(1.83327 - 3.17532i) q^{34} +(0.587885 - 1.01825i) q^{35} +(0.765023 + 1.32506i) q^{36} +(2.38458 + 4.13022i) q^{37} +(1.72295 - 2.98424i) q^{38} +1.09571 q^{39} +(-0.715393 + 1.23910i) q^{40} +6.49564 q^{41} +(0.681637 - 1.18063i) q^{42} +(0.870301 + 1.50740i) q^{43} +(-0.138522 + 0.239927i) q^{44} +0.591244 q^{45} +2.39202 q^{46} +(-2.59427 - 4.49340i) q^{47} +(0.700567 - 1.21342i) q^{48} -3.04532 q^{49} +(-1.59401 - 2.76090i) q^{50} +(2.67424 + 4.63191i) q^{51} +(-0.838241 - 1.45188i) q^{52} +(1.27139 + 2.20210i) q^{53} +0.685532 q^{54} +(0.0535281 + 0.0927134i) q^{55} -4.81242 q^{56} +(2.51331 + 4.35318i) q^{57} +3.39017 q^{58} -9.94287 q^{59} +(-0.452316 - 0.783433i) q^{60} +(2.48663 - 4.30697i) q^{61} +(-2.56917 - 4.44994i) q^{62} +(0.994318 + 1.72221i) q^{63} +1.17412 q^{64} -0.647830 q^{65} +(0.0620644 + 0.107499i) q^{66} +1.85065 q^{67} +(4.09170 - 7.08704i) q^{68} +(-1.74465 + 3.02182i) q^{69} +(-0.403014 + 0.698041i) q^{70} +(-6.09127 - 10.5504i) q^{71} +(-1.20998 - 2.09575i) q^{72} +(-4.82332 + 8.35423i) q^{73} +(-1.63471 - 2.83140i) q^{74} +4.65043 q^{75} +(3.84548 - 6.66056i) q^{76} +(-0.180041 + 0.311839i) q^{77} -0.751142 q^{78} +5.82978 q^{79} +(-0.414206 + 0.717426i) q^{80} +(-0.500000 + 0.866025i) q^{81} -4.45297 q^{82} +(-1.34867 - 2.33597i) q^{83} +(1.52135 - 2.63506i) q^{84} +(-1.58113 - 2.73859i) q^{85} +(-0.596619 - 1.03337i) q^{86} +(-2.47266 + 4.28277i) q^{87} +(0.219090 - 0.379475i) q^{88} +(-6.46211 + 11.1927i) q^{89} -0.405317 q^{90} +(-1.08948 - 1.88704i) q^{91} +5.33878 q^{92} +7.49542 q^{93} +(1.77845 + 3.08037i) q^{94} +(-1.48598 - 2.57379i) q^{95} +(-2.90022 + 5.02333i) q^{96} +(-7.64453 - 13.2407i) q^{97} +2.08767 q^{98} -0.181069 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9}+O(q^{10}) \) 22 * q + 2 * q^2 + 11 * q^3 + 30 * q^4 - 4 * q^5 + q^6 + 4 * q^7 - 11 * q^9	\( 22 q + 2 q^{2} + 11 q^{3} + 30 q^{4} - 4 q^{5} + q^{6} + 4 q^{7} - 11 q^{9} - 5 q^{10} + 15 q^{12} + 3 q^{13} - 14 q^{14} + 4 q^{15} + 54 q^{16} - q^{17} - q^{18} - 22 q^{19} - 7 q^{20} + 2 q^{21} - 22 q^{22} - 10 q^{23} - 15 q^{25} - 10 q^{26} - 22 q^{27} - 38 q^{28} + 22 q^{29} + 5 q^{30} - 6 q^{31} + 32 q^{32} + 17 q^{34} - 11 q^{35} - 15 q^{36} + 8 q^{37} + 14 q^{38} + 6 q^{39} + 32 q^{40} - 7 q^{42} + q^{43} - 12 q^{44} + 8 q^{45} + 24 q^{46} + 7 q^{47} + 27 q^{48} + 22 q^{49} + 13 q^{50} + q^{51} + 17 q^{52} + 30 q^{53} - 2 q^{54} + 31 q^{55} - 82 q^{56} + 22 q^{57} - 90 q^{58} - 16 q^{59} + 7 q^{60} + 8 q^{61} - 28 q^{62} - 2 q^{63} - 32 q^{64} - 68 q^{65} + 22 q^{66} - 38 q^{67} - 8 q^{68} - 5 q^{69} + 43 q^{70} + 45 q^{71} - 4 q^{73} + 3 q^{74} - 30 q^{75} - 33 q^{76} + 21 q^{77} - 20 q^{78} + 26 q^{79} - 12 q^{80} - 11 q^{81} + 16 q^{82} + 8 q^{83} - 19 q^{84} - 28 q^{85} - 16 q^{86} + 11 q^{87} - 65 q^{88} + 15 q^{89} + 10 q^{90} - 3 q^{91} - 18 q^{92} - 12 q^{93} - 28 q^{94} - 5 q^{95} + 16 q^{96} - 35 q^{97} + 90 q^{98}+O(q^{100}) \) 22 * q + 2 * q^2 + 11 * q^3 + 30 * q^4 - 4 * q^5 + q^6 + 4 * q^7 - 11 * q^9 - 5 * q^10 + 15 * q^12 + 3 * q^13 - 14 * q^14 + 4 * q^15 + 54 * q^16 - q^17 - q^18 - 22 * q^19 - 7 * q^20 + 2 * q^21 - 22 * q^22 - 10 * q^23 - 15 * q^25 - 10 * q^26 - 22 * q^27 - 38 * q^28 + 22 * q^29 + 5 * q^30 - 6 * q^31 + 32 * q^32 + 17 * q^34 - 11 * q^35 - 15 * q^36 + 8 * q^37 + 14 * q^38 + 6 * q^39 + 32 * q^40 - 7 * q^42 + q^43 - 12 * q^44 + 8 * q^45 + 24 * q^46 + 7 * q^47 + 27 * q^48 + 22 * q^49 + 13 * q^50 + q^51 + 17 * q^52 + 30 * q^53 - 2 * q^54 + 31 * q^55 - 82 * q^56 + 22 * q^57 - 90 * q^58 - 16 * q^59 + 7 * q^60 + 8 * q^61 - 28 * q^62 - 2 * q^63 - 32 * q^64 - 68 * q^65 + 22 * q^66 - 38 * q^67 - 8 * q^68 - 5 * q^69 + 43 * q^70 + 45 * q^71 - 4 * q^73 + 3 * q^74 - 30 * q^75 - 33 * q^76 + 21 * q^77 - 20 * q^78 + 26 * q^79 - 12 * q^80 - 11 * q^81 + 16 * q^82 + 8 * q^83 - 19 * q^84 - 28 * q^85 - 16 * q^86 + 11 * q^87 - 65 * q^88 + 15 * q^89 + 10 * q^90 - 3 * q^91 - 18 * q^92 - 12 * q^93 - 28 * q^94 - 5 * q^95 + 16 * q^96 - 35 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

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Database

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