LMFDB - Embedded newform 471.2.e.c.169.14

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:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			169.14
Character	$\chi$	$=$	471.169
Dual form			471.2.e.c.301.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.56656 q^{2} +(-0.500000 - 0.866025i) q^{3} +4.58726 q^{4} +(-1.76168 - 3.05133i) q^{5} +(-1.28328 - 2.22271i) q^{6} -0.0341584 q^{7} +6.64036 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+2.56656 q^{2} +(-0.500000 - 0.866025i) q^{3} +4.58726 q^{4} +(-1.76168 - 3.05133i) q^{5} +(-1.28328 - 2.22271i) q^{6} -0.0341584 q^{7} +6.64036 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.52148 - 7.83143i) q^{10} +(0.731999 + 1.26786i) q^{11} +(-2.29363 - 3.97268i) q^{12} +(0.617902 - 1.07024i) q^{13} -0.0876697 q^{14} +(-1.76168 + 3.05133i) q^{15} +7.86840 q^{16} +(1.48117 + 2.56546i) q^{17} +(-1.28328 + 2.22271i) q^{18} +(-0.941723 - 1.63111i) q^{19} +(-8.08130 - 13.9972i) q^{20} +(0.0170792 + 0.0295820i) q^{21} +(1.87872 + 3.25404i) q^{22} +0.478706 q^{23} +(-3.32018 - 5.75072i) q^{24} +(-3.70707 + 6.42083i) q^{25} +(1.58589 - 2.74684i) q^{26} +1.00000 q^{27} -0.156693 q^{28} +10.0289 q^{29} +(-4.52148 + 7.83143i) q^{30} +(-4.00867 + 6.94322i) q^{31} +6.91405 q^{32} +(0.731999 - 1.26786i) q^{33} +(3.80151 + 6.58441i) q^{34} +(0.0601763 + 0.104228i) q^{35} +(-2.29363 + 3.97268i) q^{36} +(-0.835107 + 1.44645i) q^{37} +(-2.41699 - 4.18635i) q^{38} -1.23580 q^{39} +(-11.6982 - 20.2619i) q^{40} +5.23877 q^{41} +(0.0438349 + 0.0759242i) q^{42} +(-4.18993 + 7.25717i) q^{43} +(3.35787 + 5.81600i) q^{44} +3.52337 q^{45} +1.22863 q^{46} +(3.43991 - 5.95809i) q^{47} +(-3.93420 - 6.81424i) q^{48} -6.99883 q^{49} +(-9.51443 + 16.4795i) q^{50} +(1.48117 - 2.56546i) q^{51} +(2.83448 - 4.90946i) q^{52} +(-5.10688 + 8.84538i) q^{53} +2.56656 q^{54} +(2.57910 - 4.46714i) q^{55} -0.226824 q^{56} +(-0.941723 + 1.63111i) q^{57} +25.7397 q^{58} -3.57175 q^{59} +(-8.08130 + 13.9972i) q^{60} +(6.93994 + 12.0203i) q^{61} +(-10.2885 + 17.8202i) q^{62} +(0.0170792 - 0.0295820i) q^{63} +2.00855 q^{64} -4.35420 q^{65} +(1.87872 - 3.25404i) q^{66} +5.26972 q^{67} +(6.79449 + 11.7684i) q^{68} +(-0.239353 - 0.414571i) q^{69} +(0.154446 + 0.267509i) q^{70} +(4.71288 - 8.16295i) q^{71} +(-3.32018 + 5.75072i) q^{72} +(-8.08545 - 14.0044i) q^{73} +(-2.14336 + 3.71240i) q^{74} +7.41413 q^{75} +(-4.31992 - 7.48232i) q^{76} +(-0.0250039 - 0.0433080i) q^{77} -3.17177 q^{78} -7.05177 q^{79} +(-13.8616 - 24.0091i) q^{80} +(-0.500000 - 0.866025i) q^{81} +13.4456 q^{82} +(0.106900 - 0.185157i) q^{83} +(0.0783466 + 0.135700i) q^{84} +(5.21870 - 9.03905i) q^{85} +(-10.7537 + 18.6260i) q^{86} +(-5.01443 - 8.68525i) q^{87} +(4.86074 + 8.41905i) q^{88} +(-9.20039 - 15.9355i) q^{89} +9.04296 q^{90} +(-0.0211065 + 0.0365576i) q^{91} +2.19595 q^{92} +8.01734 q^{93} +(8.82874 - 15.2918i) q^{94} +(-3.31804 + 5.74701i) q^{95} +(-3.45703 - 5.98774i) q^{96} +(5.60095 - 9.70114i) q^{97} -17.9630 q^{98} -1.46400 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) $ 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	2.56656			1.81484			0.907418	−	0.420230i	$-0.138051\pi$
$2$	2.56656			1.81484			0.907418	+	0.420230i	$0.138051\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	4.58726			2.29363
$5$	−1.76168	−	3.05133i	−0.787849	−	1.36460i	−0.927282	−	0.374364i	$-0.877861\pi$
$5$	−1.76168	−	3.05133i	−0.787849	−	1.36460i	0.139433	−	0.990232i	$-0.455472\pi$
$6$	−1.28328	−	2.22271i	−0.523898	−	0.907418i
$7$	−0.0341584			−0.0129107			−0.00645533	−	0.999979i	$-0.502055\pi$
$7$	−0.0341584			−0.0129107			−0.00645533	+	0.999979i	$0.502055\pi$
$8$	6.64036			2.34772
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−4.52148	−	7.83143i	−1.42982	−	2.47652i
$11$	0.731999	+	1.26786i	0.220706	+	0.382274i	0.955023	−	0.296533i	$-0.0958305\pi$
$11$	0.731999	+	1.26786i	0.220706	+	0.382274i	−0.734317	+	0.678807i	$0.762497\pi$
$12$	−2.29363	−	3.97268i	−0.662113	−	1.14681i
$13$	0.617902	−	1.07024i	0.171375	−	0.296831i	−0.767526	−	0.641018i	$-0.778512\pi$
$13$	0.617902	−	1.07024i	0.171375	−	0.296831i	0.938901	+	0.344188i	$0.111846\pi$
$14$	−0.0876697			−0.0234307
$15$	−1.76168	+	3.05133i	−0.454865	+	0.787849i
$16$	7.86840			1.96710
$17$	1.48117	+	2.56546i	0.359236	+	0.622214i	0.987833	−	0.155516i	$-0.0497041\pi$
$17$	1.48117	+	2.56546i	0.359236	+	0.622214i	−0.628598	+	0.777731i	$0.716371\pi$
$18$	−1.28328	+	2.22271i	−0.302473	+	0.523898i
$19$	−0.941723	−	1.63111i	−0.216046	−	0.374203i	0.737550	−	0.675293i	$-0.235983\pi$
$19$	−0.941723	−	1.63111i	−0.216046	−	0.374203i	−0.953596	+	0.301090i	$0.902649\pi$
$20$	−8.08130	−	13.9972i	−1.80703	−	3.12987i
$21$	0.0170792	+	0.0295820i	0.00372699	+	0.00645533i
$22$	1.87872	+	3.25404i	0.400545	+	0.693765i
$23$	0.478706			0.0998170			0.0499085	−	0.998754i	$-0.484107\pi$
$23$	0.478706			0.0998170			0.0499085	+	0.998754i	$0.484107\pi$
$24$	−3.32018	−	5.75072i	−0.677729	−	1.17386i
$25$	−3.70707	+	6.42083i	−0.741413	+	1.28417i
$26$	1.58589	−	2.74684i	0.311018	−	0.538699i
$27$	1.00000			0.192450
$28$	−0.156693			−0.0296122
$29$	10.0289			1.86231			0.931157	−	0.364619i	$-0.118801\pi$
$29$	10.0289			1.86231			0.931157	+	0.364619i	$0.118801\pi$
$30$	−4.52148	+	7.83143i	−0.825505	+	1.42982i
$31$	−4.00867	+	6.94322i	−0.719978	+	1.24704i	0.241029	+	0.970518i	$0.422515\pi$
$31$	−4.00867	+	6.94322i	−0.719978	+	1.24704i	−0.961008	+	0.276521i	$0.910818\pi$
$32$	6.91405			1.22224
$33$	0.731999	−	1.26786i	0.127425	−	0.220706i
$34$	3.80151	+	6.58441i	0.651954	+	1.12922i
$35$	0.0601763	+	0.104228i	0.0101717	+	0.0176178i
$36$	−2.29363	+	3.97268i	−0.382271	+	0.662113i
$37$	−0.835107	+	1.44645i	−0.137291	+	0.237794i	−0.926470	−	0.376368i	$-0.877173\pi$
$37$	−0.835107	+	1.44645i	−0.137291	+	0.237794i	0.789180	+	0.614163i	$0.210506\pi$
$38$	−2.41699	−	4.18635i	−0.392088	−	0.679116i
$39$	−1.23580			−0.197887
$40$	−11.6982	−	20.2619i	−1.84965	−	3.20369i
$41$	5.23877			0.818158			0.409079	−	0.912499i	$-0.365850\pi$
$41$	5.23877			0.818158			0.409079	+	0.912499i	$0.365850\pi$
$42$	0.0438349	+	0.0759242i	0.00676386	+	0.0117154i
$43$	−4.18993	+	7.25717i	−0.638958	+	1.10671i	0.346704	+	0.937975i	$0.387301\pi$
$43$	−4.18993	+	7.25717i	−0.638958	+	1.10671i	−0.985662	+	0.168733i	$0.946032\pi$
$44$	3.35787	+	5.81600i	0.506218	+	0.876795i
$45$	3.52337			0.525233
$46$	1.22863			0.181152
$47$	3.43991	−	5.95809i	0.501762	−	0.869077i	−0.498236	−	0.867041i	$-0.666019\pi$
$47$	3.43991	−	5.95809i	0.501762	−	0.869077i	0.999998	−	0.00203555i	$-0.000647936\pi$
$48$	−3.93420	−	6.81424i	−0.567853	−	0.983551i
$49$	−6.99883			−0.999833
$50$	−9.51443	+	16.4795i	−1.34554	+	2.33055i
$51$	1.48117	−	2.56546i	0.207405	−	0.359236i
$52$	2.83448	−	4.90946i	0.393071	−	0.680819i
$53$	−5.10688	+	8.84538i	−0.701484	+	1.21501i	0.266461	+	0.963846i	$0.414146\pi$
$53$	−5.10688	+	8.84538i	−0.701484	+	1.21501i	−0.967945	+	0.251161i	$0.919188\pi$
$54$	2.56656			0.349265
$55$	2.57910	−	4.46714i	0.347766	−	0.602349i
$56$	−0.226824			−0.0303106
$57$	−0.941723	+	1.63111i	−0.124734	+	0.216046i
$58$	25.7397			3.37979
$59$	−3.57175			−0.465003			−0.232501	−	0.972596i	$-0.574691\pi$
$59$	−3.57175			−0.465003			−0.232501	+	0.972596i	$0.574691\pi$
$60$	−8.08130	+	13.9972i	−1.04329	+	1.80703i
$61$	6.93994	+	12.0203i	0.888568	+	1.53905i	0.841568	+	0.540151i	$0.181633\pi$
$61$	6.93994	+	12.0203i	0.888568	+	1.53905i	0.0470000	+	0.998895i	$0.485034\pi$
$62$	−10.2885	+	17.8202i	−1.30664	+	2.26317i
$63$	0.0170792	−	0.0295820i	0.00215178	−	0.00372699i
$64$	2.00855			0.251069
$65$	−4.35420			−0.540072
$66$	1.87872	−	3.25404i	0.231255	−	0.400545i
$67$	5.26972			0.643799			0.321899	−	0.946774i	$-0.395679\pi$
$67$	5.26972			0.643799			0.321899	+	0.946774i	$0.395679\pi$
$68$	6.79449	+	11.7684i	0.823953	+	1.42713i
$69$	−0.239353	−	0.414571i	−0.0288147	−	0.0499085i
$70$	0.154446	+	0.267509i	0.0184599	+	0.0319734i
$71$	4.71288	−	8.16295i	0.559316	−	0.968764i	−0.438238	−	0.898859i	$-0.644397\pi$
$71$	4.71288	−	8.16295i	0.559316	−	0.968764i	0.997554	−	0.0699048i	$-0.0222695\pi$
$72$	−3.32018	+	5.75072i	−0.391287	+	0.677729i
$73$	−8.08545	−	14.0044i	−0.946330	−	1.63909i	−0.753066	−	0.657945i	$-0.771426\pi$
$73$	−8.08545	−	14.0044i	−0.946330	−	1.63909i	−0.193264	−	0.981147i	$-0.561907\pi$
$74$	−2.14336	+	3.71240i	−0.249160	+	0.431558i
$75$	7.41413			0.856110
$76$	−4.31992	−	7.48232i	−0.495529	−	0.858282i
$77$	−0.0250039	−	0.0433080i	−0.00284946	−	0.00493541i
$78$	−3.17177			−0.359133
$79$	−7.05177			−0.793386			−0.396693	−	0.917951i	$-0.629842\pi$
$79$	−7.05177			−0.793386			−0.396693	+	0.917951i	$0.629842\pi$
$80$	−13.8616	−	24.0091i	−1.54978	−	2.68430i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	13.4456			1.48482
$83$	0.106900	−	0.185157i	0.0117339	−	0.0203236i	−0.860099	−	0.510127i	$-0.829598\pi$
$83$	0.106900	−	0.185157i	0.0117339	−	0.0203236i	0.871833	+	0.489804i	$0.162932\pi$
$84$	0.0783466	+	0.135700i	0.00854832	+	0.0148061i
$85$	5.21870	−	9.03905i	0.566047	−	0.980423i
$86$	−10.7537	+	18.6260i	−1.15960	+	2.00849i
$87$	−5.01443	−	8.68525i	−0.537604	−	0.931157i
$88$	4.86074	+	8.41905i	0.518156	+	0.897473i
$89$	−9.20039	−	15.9355i	−0.975240	−	1.68916i	−0.679142	−	0.734007i	$-0.737648\pi$
$89$	−9.20039	−	15.9355i	−0.975240	−	1.68916i	−0.296098	−	0.955158i	$-0.595686\pi$
$90$	9.04296			0.953211
$91$	−0.0211065	+	0.0365576i	−0.00221257	+	0.00383228i
$92$	2.19595			0.228943
$93$	8.01734			0.831359
$94$	8.82874	−	15.2918i	0.910615	−	1.57723i
$95$	−3.31804	+	5.74701i	−0.340423	+	0.589631i
$96$	−3.45703	−	5.98774i	−0.352831	−	0.611122i
$97$	5.60095	−	9.70114i	0.568691	−	0.985001i	−0.428005	−	0.903776i	$-0.640783\pi$
$97$	5.60095	−	9.70114i	0.568691	−	0.985001i	0.996696	−	0.0812250i	$-0.0258832\pi$
$98$	−17.9630			−1.81453
$99$	−1.46400			−0.147137
$100$	−17.0053	+	29.4540i	−1.70053	+	2.94540i
$101$	0.786043			0.0782142			0.0391071	−	0.999235i	$-0.487549\pi$
$101$	0.786043			0.0782142			0.0391071	+	0.999235i	$0.487549\pi$
$102$	3.80151	−	6.58441i	0.376406	−	0.651954i
$103$	−15.9410			−1.57071			−0.785355	−	0.619045i	$-0.787520\pi$
$103$	−15.9410			−1.57071			−0.785355	+	0.619045i	$0.787520\pi$
$104$	4.10310	−	7.10677i	0.402342	−	0.696876i
$105$	0.0601763	−	0.104228i	0.00587261	−	0.0101717i
$106$	−13.1071	+	22.7022i	−1.27308	+	2.20504i
$107$	−1.00571	+	1.74194i	−0.0972256	+	0.168400i	−0.910535	−	0.413431i	$-0.864330\pi$
$107$	−1.00571	+	1.74194i	−0.0972256	+	0.168400i	0.813310	+	0.581831i	$0.197664\pi$
$108$	4.58726			0.441409
$109$	1.65371	+	2.86431i	0.158397	+	0.274351i	0.934291	−	0.356512i	$-0.116034\pi$
$109$	1.65371	+	2.86431i	0.158397	+	0.274351i	−0.775894	+	0.630863i	$0.782701\pi$
$110$	6.61944	−	11.4652i	0.631139	−	1.09316i
$111$	1.67021			0.158530
$112$	−0.268772			−0.0253966
$113$	2.34881	+	4.06825i	0.220957	+	0.382709i	0.955099	−	0.296287i	$-0.0957486\pi$
$113$	2.34881	+	4.06825i	0.220957	+	0.382709i	−0.734142	+	0.678996i	$0.762415\pi$
$114$	−2.41699	+	4.18635i	−0.226372	+	0.392088i
$115$	−0.843329	−	1.46069i	−0.0786408	−	0.136210i
$116$	46.0050			4.27145
$117$	0.617902	+	1.07024i	0.0571251	+	0.0989436i
$118$	−9.16714			−0.843904
$119$	−0.0505943	−	0.0876318i	−0.00463797	−	0.00803320i
$120$	−11.6982	+	20.2619i	−1.06790	+	1.84965i
$121$	4.42835	−	7.67013i	0.402578	−	0.697285i
$122$	17.8118	+	30.8510i	1.61261	+	2.79311i
$123$	−2.61938	−	4.53691i	−0.236182	−	0.409079i
$124$	−18.3888	+	31.8503i	−1.65136	+	2.86024i
$125$	8.50588			0.760789
$126$	0.0438349	−	0.0759242i	0.00390512	−	0.00676386i
$127$	−9.25316	+	16.0269i	−0.821085	+	1.42216i	0.0837897	+	0.996483i	$0.473298\pi$
$127$	−9.25316	+	16.0269i	−0.821085	+	1.42216i	−0.904875	+	0.425678i	$0.860036\pi$
$128$	−8.67302			−0.766594
$129$	8.37986			0.737805
$130$	−11.1753			−0.980141
$131$	6.58802	−	11.4108i	0.575598	−	0.996965i	−0.420378	−	0.907349i	$-0.638103\pi$
$131$	6.58802	−	11.4108i	0.575598	−	0.996965i	0.995976	−	0.0896161i	$-0.0285640\pi$
$132$	3.35787	−	5.81600i	0.292265	−	0.506218i
$133$	0.0321677	+	0.0557161i	0.00278929	+	0.00483120i
$134$	13.5251			1.16839
$135$	−1.76168	−	3.05133i	−0.151622	−	0.262616i
$136$	9.83548	+	17.0356i	0.843385	+	1.46079i
$137$	−0.680021	−	1.17783i	−0.0580981	−	0.100629i	0.835514	−	0.549470i	$-0.185170\pi$
$137$	−0.680021	−	1.17783i	−0.0580981	−	0.100629i	−0.893612	+	0.448841i	$0.851837\pi$
$138$	−0.614315	−	1.06402i	−0.0522939	−	0.0905758i
$139$	−5.65477	+	9.79434i	−0.479631	+	0.830745i	−0.999727	−	0.0233624i	$-0.992563\pi$
$139$	−5.65477	+	9.79434i	−0.479631	+	0.830745i	0.520096	+	0.854108i	$0.325896\pi$
$140$	0.276044	+	0.478122i	0.0233300	+	0.0404087i
$141$	−6.87981			−0.579385
$142$	12.0959	−	20.9507i	1.01507	−	1.75815i
$143$	1.80922			0.151294
$144$	−3.93420	+	6.81424i	−0.327850	+	0.567853i
$145$	−17.6677	−	30.6014i	−1.46722	−	2.54130i
$146$	−20.7518	−	35.9432i	−1.71743	−	2.97468i
$147$	3.49942	+	6.06117i	0.288627	+	0.499917i
$148$	−3.83085	+	6.63522i	−0.314894	+	0.545412i
$149$	11.0955			0.908981			0.454491	−	0.890752i	$-0.349821\pi$
$149$	11.0955			0.908981			0.454491	+	0.890752i	$0.349821\pi$
$150$	19.0289			1.55370
$151$	−9.46744	−	16.3981i	−0.770449	−	1.33446i	−0.937317	−	0.348478i	$-0.886699\pi$
$151$	−9.46744	−	16.3981i	−0.770449	−	1.33446i	0.166868	−	0.985979i	$-0.446635\pi$
$152$	−6.25338	−	10.8312i	−0.507216	−	0.878524i
$153$	−2.96233			−0.239490
$154$	−0.0641742	−	0.111153i	−0.00517130	−	0.00895696i
$155$	28.2481			2.26894
$156$	−5.66895			−0.453880
$157$	11.6786	+	4.53983i	0.932054	+	0.362318i
$157$	11.6786	+	4.53983i	0.932054	+	0.362318i
$158$	−18.0988			−1.43987
$159$	10.2138			0.810004
$160$	−12.1804	−	21.0970i	−0.962944	−	1.66787i
$161$	−0.0163518			−0.00128870
$162$	−1.28328	−	2.22271i	−0.100824	−	0.174633i
$163$	−3.96666	−	6.87045i	−0.310692	−	0.538135i	0.667820	−	0.744323i	$-0.267228\pi$
$163$	−3.96666	−	6.87045i	−0.310692	−	0.538135i	−0.978512	+	0.206188i	$0.933894\pi$
$164$	24.0316			1.87655
$165$	−5.15821			−0.401566
$166$	0.274367	−	0.475218i	0.0212950	−	0.0368840i
$167$	9.46095	+	16.3869i	0.732111	+	1.26805i	0.955979	+	0.293434i	$0.0947979\pi$
$167$	9.46095	+	16.3869i	0.732111	+	1.26805i	−0.223869	+	0.974619i	$0.571869\pi$
$168$	0.113412	+	0.196435i	0.00874992	+	0.0151553i
$169$	5.73639	+	9.93572i	0.441261	+	0.764286i
$170$	13.3941	−	23.1993i	1.02728	−	1.77931i
$171$	1.88345			0.144031
$172$	−19.2203	+	33.2905i	−1.46553	+	2.53838i
$173$	−5.41825			−0.411942			−0.205971	−	0.978558i	$-0.566035\pi$
$173$	−5.41825			−0.411942			−0.205971	+	0.978558i	$0.566035\pi$
$174$	−12.8699	−	22.2913i	−0.975662	−	1.68990i
$175$	0.126627	−	0.219325i	0.00957213	−	0.0165794i
$176$	5.75967	+	9.97603i	0.434151	+	0.751972i
$177$	1.78588	+	3.09323i	0.134235	+	0.232501i
$178$	−23.6134	−	40.8996i	−1.76990	−	3.06556i
$179$	−2.38983	−	4.13931i	−0.178625	−	0.309387i	0.762785	−	0.646652i	$-0.223831\pi$
$179$	−2.38983	−	4.13931i	−0.178625	−	0.309387i	−0.941410	+	0.337265i	$0.890498\pi$
$180$	16.1626			1.20469
$181$	−4.09827	−	7.09841i	−0.304622	−	0.527621i	0.672555	−	0.740047i	$-0.265197\pi$
$181$	−4.09827	−	7.09841i	−0.304622	−	0.527621i	−0.977177	+	0.212426i	$0.931863\pi$
$182$	−0.0541713	+	0.0938275i	−0.00401545	+	0.00695496i
$183$	6.93994	−	12.0203i	0.513015	−	0.888568i
$184$	3.17878			0.234343
$185$	5.88478			0.432657
$186$	20.5770			1.50878
$187$	−2.16843	+	3.75582i	−0.158571	+	0.274653i
$188$	15.7797	−	27.3313i	1.15085	−	1.99334i
$189$	−0.0341584			−0.00248466
$190$	−8.51596	+	14.7501i	−0.617812	+	1.07008i
$191$	2.66606	+	4.61775i	0.192909	+	0.334128i	0.946213	−	0.323544i	$-0.104874\pi$
$191$	2.66606	+	4.61775i	0.192909	+	0.334128i	−0.753304	+	0.657673i	$0.771541\pi$
$192$	−1.00428	−	1.73946i	−0.0724774	−	0.125535i
$193$	9.76374	−	16.9113i	0.702810	−	1.21730i	−0.264666	−	0.964340i	$-0.585262\pi$
$193$	9.76374	−	16.9113i	0.702810	−	1.21730i	0.967476	−	0.252962i	$-0.0814048\pi$
$194$	14.3752	−	24.8986i	1.03208	−	1.78762i
$195$	2.17710	+	3.77085i	0.155905	+	0.270036i
$196$	−32.1054			−2.29325
$197$	−6.20681	−	10.7505i	−0.442217	−	0.765942i	0.555637	−	0.831425i	$-0.312474\pi$
$197$	−6.20681	−	10.7505i	−0.442217	−	0.765942i	−0.997854	+	0.0654832i	$0.979141\pi$
$198$	−3.75745			−0.267030
$199$	11.3326	+	19.6286i	0.803346	+	1.39144i	0.917402	+	0.397962i	$0.130283\pi$
$199$	11.3326	+	19.6286i	0.803346	+	1.39144i	−0.114055	+	0.993474i	$0.536384\pi$
$200$	−24.6163	+	42.6366i	−1.74063	+	3.01486i
$201$	−2.63486	−	4.56371i	−0.185849	−	0.321899i
$202$	2.01743			0.141946
$203$	−0.342570			−0.0240437
$204$	6.79449	−	11.7684i	0.475709	−	0.823953i
$205$	−9.22906	−	15.9852i	−0.644585	−	1.11645i
$206$	−40.9135			−2.85058
$207$	−0.239353	+	0.414571i	−0.0166362	+	0.0288147i
$208$	4.86191	−	8.42107i	0.337113	−	0.583896i
$209$	1.37868	−	2.38794i	0.0953653	−	0.165178i
$210$	0.154446	−	0.267509i	0.0106578	−	0.0184599i
$211$	2.95405			0.203365			0.101683	−	0.994817i	$-0.467577\pi$
$211$	2.95405			0.203365			0.101683	+	0.994817i	$0.467577\pi$
$212$	−23.4266	+	40.5760i	−1.60894	+	2.78677i
$213$	−9.42576			−0.645843
$214$	−2.58122	+	4.47080i	−0.176448	+	0.305618i
$215$	29.5253			2.01361
$216$	6.64036			0.451819
$217$	0.136930	−	0.237169i	0.00929539	−	0.0161001i
$218$	4.24435	+	7.35143i	0.287464	+	0.497902i
$219$	−8.08545	+	14.0044i	−0.546364	+	0.946330i
$220$	11.8310	−	20.4919i	0.797646	−	1.38156i
$221$	3.66087			0.246257
$222$	4.28671			0.287705
$223$	−6.49374	+	11.2475i	−0.434853	+	0.753188i	−0.997284	−	0.0736569i	$-0.976533\pi$
$223$	−6.49374	+	11.2475i	−0.434853	+	0.753188i	0.562431	+	0.826845i	$0.309866\pi$
$224$	−0.236173			−0.0157800
$225$	−3.70707	−	6.42083i	−0.247138	−	0.428055i
$226$	6.02836	+	10.4414i	0.401001	+	0.694554i
$227$	9.70792	+	16.8146i	0.644337	+	1.11602i	0.984454	+	0.175642i	$0.0562000\pi$
$227$	9.70792	+	16.8146i	0.644337	+	1.11602i	−0.340117	+	0.940383i	$0.610467\pi$
$228$	−4.31992	+	7.48232i	−0.286094	+	0.495529i
$229$	−12.1053	+	20.9670i	−0.799939	+	1.38554i	0.119716	+	0.992808i	$0.461802\pi$
$229$	−12.1053	+	20.9670i	−0.799939	+	1.38554i	−0.919655	+	0.392727i	$0.871532\pi$
$230$	−2.16446	−	3.74895i	−0.142720	−	0.247198i
$231$	−0.0250039	+	0.0433080i	−0.00164514	+	0.00284946i
$232$	66.5953			4.37219
$233$	−9.22305	−	15.9748i	−0.604222	−	1.04654i	−0.992174	−	0.124864i	$-0.960151\pi$
$233$	−9.22305	−	15.9748i	−0.604222	−	1.04654i	0.387951	−	0.921680i	$-0.373183\pi$
$234$	1.58589	+	2.74684i	0.103673	+	0.179566i
$235$	−24.2401			−1.58125
$236$	−16.3846			−1.06654
$237$	3.52589	+	6.10701i	0.229031	+	0.396693i
$238$	−0.129853	−	0.224913i	−0.00841715	−	0.0145789i
$239$	−17.1289			−1.10797			−0.553987	−	0.832525i	$-0.686894\pi$
$239$	−17.1289			−1.10797			−0.553987	+	0.832525i	$0.686894\pi$
$240$	−13.8616	+	24.0091i	−0.894766	+	1.54978i
$241$	−4.03197	−	6.98358i	−0.259722	−	0.449852i	0.706445	−	0.707768i	$-0.250298\pi$
$241$	−4.03197	−	6.98358i	−0.259722	−	0.449852i	−0.966167	+	0.257916i	$0.916964\pi$
$242$	11.3657	−	19.6859i	0.730612	−	1.26546i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	31.8353	+	55.1403i	2.03805	+	3.53000i
$245$	12.3297	+	21.3557i	0.787718	+	1.36437i
$246$	−6.72282	−	11.6443i	−0.428631	−	0.742411i
$247$	−2.32757			−0.148100
$248$	−26.6190	+	46.1055i	−1.69031	+	2.92770i
$249$	−0.213801			−0.0135491
$250$	21.8309			1.38071
$251$	−1.97516	+	3.42107i	−0.124671	+	0.215936i	−0.921604	−	0.388131i	$-0.873121\pi$
$251$	−1.97516	+	3.42107i	−0.124671	+	0.215936i	0.796933	+	0.604067i	$0.206454\pi$
$252$	0.0783466	−	0.135700i	0.00493537	−	0.00854832i
$253$	0.350412	+	0.606932i	0.0220302	+	0.0381575i
$254$	−23.7488	+	41.1342i	−1.49013	+	2.58099i
$255$	−10.4374			−0.653615
$256$	−26.2770			−1.64231
$257$	−3.68727	+	6.38654i	−0.230006	+	0.398381i	−0.957809	−	0.287404i	$-0.907208\pi$
$257$	−3.68727	+	6.38654i	−0.230006	+	0.398381i	0.727804	+	0.685785i	$0.240541\pi$
$258$	21.5074			1.33900
$259$	0.0285259	−	0.0494083i	0.00177251	−	0.00307008i
$260$	−19.9738			−1.23872
$261$	−5.01443	+	8.68525i	−0.310386	+	0.537604i
$262$	16.9086	−	29.2865i	1.04462	−	1.80933i
$263$	1.28078	−	2.21838i	0.0789765	−	0.136791i	−0.823832	−	0.566834i	$-0.808168\pi$
$263$	1.28078	−	2.21838i	0.0789765	−	0.136791i	0.902809	+	0.430043i	$0.141501\pi$
$264$	4.86074	−	8.41905i	0.299158	−	0.518156i
$265$	35.9869			2.21066
$266$	0.0825605	+	0.142999i	0.00506211	+	0.00876783i
$267$	−9.20039	+	15.9355i	−0.563055	+	0.975240i
$268$	24.1736			1.47663
$269$	17.9375			1.09367			0.546835	−	0.837240i	$-0.315832\pi$
$269$	17.9375			1.09367			0.546835	+	0.837240i	$0.315832\pi$
$270$	−4.52148	−	7.83143i	−0.275168	−	0.476606i
$271$	4.67110	−	8.09059i	0.283749	−	0.491468i	−0.688556	−	0.725183i	$-0.741755\pi$
$271$	4.67110	−	8.09059i	0.283749	−	0.491468i	0.972305	+	0.233715i	$0.0750883\pi$
$272$	11.6544	+	20.1860i	0.706653	+	1.22396i
$273$	0.0422131			0.00255485
$274$	−1.74532	−	3.02298i	−0.105439	−	0.182625i
$275$	−10.8543			−0.654538
$276$	−1.09797	−	1.90174i	−0.0660902	−	0.114472i
$277$	6.37662	−	11.0446i	0.383134	−	0.663608i	−0.608374	−	0.793650i	$-0.708178\pi$
$277$	6.37662	−	11.0446i	0.383134	−	0.663608i	0.991508	+	0.130042i	$0.0415113\pi$
$278$	−14.5133	+	25.1378i	−0.870451	+	1.50767i
$279$	−4.00867	−	6.94322i	−0.239993	−	0.415680i
$280$	0.399592	+	0.692114i	0.0238802	+	0.0413617i
$281$	−3.35657	+	5.81375i	−0.200236	+	0.346819i	−0.948604	−	0.316464i	$-0.897504\pi$
$281$	−3.35657	+	5.81375i	−0.200236	+	0.346819i	0.748368	+	0.663283i	$0.230838\pi$
$282$	−17.6575			−1.05149
$283$	6.27669	−	10.8715i	0.373111	−	0.646247i	−0.616932	−	0.787017i	$-0.711625\pi$
$283$	6.27669	−	10.8715i	0.373111	−	0.646247i	0.990042	+	0.140770i	$0.0449579\pi$
$284$	21.6192	−	37.4455i	1.28286	−	2.22198i
$285$	6.63607			0.393087
$286$	4.64347			0.274574
$287$	−0.178948			−0.0105630
$288$	−3.45703	+	5.98774i	−0.203707	+	0.352831i
$289$	4.11229	−	7.12270i	0.241899	−	0.418982i
$290$	−45.3453	−	78.5404i	−2.66277	−	4.61205i
$291$	−11.2019			−0.656668
$292$	−37.0900	−	64.2418i	−2.17053	−	3.75947i
$293$	−14.7507	−	25.5490i	−0.861745	−	1.49259i	−0.870243	−	0.492623i	$-0.836038\pi$
$293$	−14.7507	−	25.5490i	−0.861745	−	1.49259i	0.00849761	−	0.999964i	$-0.497295\pi$
$294$	8.98148	+	15.5564i	0.523811	+	0.907267i
$295$	6.29231	+	10.8986i	0.366352	+	0.634541i
$296$	−5.54541	+	9.60493i	−0.322320	+	0.558275i
$297$	0.731999	+	1.26786i	0.0424749	+	0.0735687i
$298$	28.4774			1.64965
$299$	0.295793	−	0.512329i	0.0171062	−	0.0296288i
$300$	34.0105			1.96360
$301$	0.143121	−	0.247893i	0.00824937	−	0.0142883i
$302$	−24.2988	−	42.0867i	−1.39824	−	2.42182i
$303$	−0.393021	−	0.680733i	−0.0225785	−	0.0391071i
$304$	−7.40985	−	12.8342i	−0.424984	−	0.736094i
$305$	24.4520	−	42.3521i	1.40012	−	2.42507i
$306$	−7.60302			−0.434636
$307$	−18.2639			−1.04238			−0.521188	−	0.853442i	$-0.674511\pi$
$307$	−18.2639			−1.04238			−0.521188	+	0.853442i	$0.674511\pi$
$308$	−0.114699	−	0.198665i	−0.00653560	−	0.0113200i
$309$	7.97049	+	13.8053i	0.453425	+	0.785355i
$310$	72.5005			4.11775
$311$	2.88977	+	5.00522i	0.163864	+	0.283820i	0.936251	−	0.351331i	$-0.114271\pi$
$311$	2.88977	+	5.00522i	0.163864	+	0.283820i	−0.772387	+	0.635152i	$0.780938\pi$
$312$	−8.20619			−0.464584
$313$	−4.97318			−0.281101			−0.140550	−	0.990074i	$-0.544887\pi$
$313$	−4.97318			−0.281101			−0.140550	+	0.990074i	$0.544887\pi$
$314$	29.9739	+	11.6518i	1.69153	+	0.657548i
$315$	−0.120353			−0.00678110
$316$	−32.3483			−1.81973
$317$	−10.8690	−	18.8257i	−0.610465	−	1.05736i	−0.991162	−	0.132657i	$-0.957649\pi$
$317$	−10.8690	−	18.8257i	−0.610465	−	1.05736i	0.380697	−	0.924700i	$-0.375684\pi$
$318$	26.2143			1.47002
$319$	7.34112	+	12.7152i	0.411024	+	0.711914i
$320$	−3.53844	−	6.12875i	−0.197805	−	0.342608i
$321$	2.01142			0.112266
$322$	−0.0419680			−0.00233878
$323$	2.78970	−	4.83190i	0.155223	−	0.268854i
$324$	−2.29363	−	3.97268i	−0.127424	−	0.220704i
$325$	4.58121	+	7.93489i	0.254120	+	0.440149i
$326$	−10.1807	−	17.6335i	−0.563856	−	0.976627i
$327$	1.65371	−	2.86431i	0.0914503	−	0.158397i
$328$	34.7873			1.92081
$329$	−0.117502	+	0.203519i	−0.00647807	+	0.0112204i
$330$	−13.2389			−0.728776
$331$	13.2357	+	22.9248i	0.727497	+	1.26006i	0.957938	+	0.286976i	$0.0926499\pi$
$331$	13.2357	+	22.9248i	0.727497	+	1.26006i	−0.230441	+	0.973086i	$0.574017\pi$
$332$	0.490380	−	0.849363i	0.0269131	−	0.0466148i
$333$	−0.835107	−	1.44645i	−0.0457636	−	0.0792648i
$334$	24.2822	+	42.0579i	1.32866	+	2.30131i
$335$	−9.28359	−	16.0796i	−0.507216	−	0.878525i
$336$	0.134386	+	0.232763i	0.00733136	+	0.0126983i
$337$	1.69382			0.0922682			0.0461341	−	0.998935i	$-0.485310\pi$
$337$	1.69382			0.0922682			0.0461341	+	0.998935i	$0.485310\pi$
$338$	14.7228	+	25.5007i	0.800816	+	1.38705i
$339$	2.34881	−	4.06825i	0.127570	−	0.220957i
$340$	23.9395	−	41.4644i	1.29830	−	2.24872i
$341$	−11.7374			−0.635614
$342$	4.83398			0.261392
$343$	0.478177			0.0258192
$344$	−27.8226	+	48.1902i	−1.50010	+	2.59824i
$345$	−0.843329	+	1.46069i	−0.0454033	+	0.0786408i
$346$	−13.9063			−0.747607
$347$	−8.73460	+	15.1288i	−0.468898	+	0.812155i	−0.999368	−	0.0355489i	$-0.988682\pi$
$347$	−8.73460	+	15.1288i	−0.468898	+	0.812155i	0.530470	+	0.847704i	$0.322015\pi$
$348$	−23.0025	−	39.8415i	−1.23306	−	2.13573i
$349$	−7.37963	−	12.7819i	−0.395023	−	0.684199i	0.598081	−	0.801435i	$-0.295930\pi$
$349$	−7.37963	−	12.7819i	−0.395023	−	0.684199i	−0.993104	+	0.117236i	$0.962597\pi$
$350$	0.324997	−	0.562912i	0.0173718	−	0.0300889i
$351$	0.617902	−	1.07024i	0.0329812	−	0.0571251i
$352$	5.06108	+	8.76605i	0.269756	+	0.467232i
$353$	−9.53940			−0.507731			−0.253865	−	0.967240i	$-0.581702\pi$
$353$	−9.53940			−0.507731			−0.253865	+	0.967240i	$0.581702\pi$
$354$	4.58357	+	7.93898i	0.243614	+	0.421952i
$355$	−33.2104			−1.76263
$356$	−42.2046	−	73.1004i	−2.23684	−	3.87432i
$357$	−0.0505943	+	0.0876318i	−0.00267773	+	0.00463797i
$358$	−6.13367	−	10.6238i	−0.324174	−	0.561486i
$359$	1.88064			0.0992564			0.0496282	−	0.998768i	$-0.484196\pi$
$359$	1.88064			0.0992564			0.0496282	+	0.998768i	$0.484196\pi$
$360$	23.3964			1.23310
$361$	7.72632	−	13.3824i	0.406648	−	0.704335i
$362$	−10.5185	−	18.2185i	−0.552839	−	0.957545i
$363$	−8.85671			−0.464857
$364$	−0.0968211	+	0.167699i	−0.00507481	+	0.00878982i
$365$	−28.4880	+	49.3427i	−1.49113	+	2.58271i
$366$	17.8118	−	30.8510i	0.931038	−	1.61261i
$367$	−18.3941	+	31.8596i	−0.960166	+	1.66306i	−0.238089	+	0.971243i	$0.576521\pi$
$367$	−18.3941	+	31.8596i	−0.960166	+	1.66306i	−0.722077	+	0.691813i	$0.756812\pi$
$368$	3.76665			0.196350
$369$	−2.61938	+	4.53691i	−0.136360	+	0.236182i
$370$	15.1037			0.785202
$371$	0.174443	−	0.302144i	0.00905662	−	0.0156865i
$372$	36.7776			1.90683
$373$	−7.46282			−0.386410			−0.193205	−	0.981158i	$-0.561888\pi$
$373$	−7.46282			−0.386410			−0.193205	+	0.981158i	$0.561888\pi$
$374$	−5.56541	+	9.63956i	−0.287780	+	0.498450i
$375$	−4.25294	−	7.36631i	−0.219621	−	0.380395i
$376$	22.8422	−	39.5639i	1.17800	−	2.04035i
$377$	6.19686	−	10.7333i	0.319155	−	0.552792i
$378$	−0.0876697			−0.00450924
$379$	34.7275			1.78383			0.891915	−	0.452203i	$-0.149362\pi$
$379$	34.7275			1.78383			0.891915	+	0.452203i	$0.149362\pi$
$380$	−15.2207	+	26.3630i	−0.780805	+	1.35239i
$381$	18.5063			0.948107
$382$	6.84261	+	11.8517i	0.350098	+	0.606388i
$383$	2.80909	+	4.86549i	0.143538	+	0.248615i	0.928827	−	0.370515i	$-0.120819\pi$
$383$	2.80909	+	4.86549i	0.143538	+	0.248615i	−0.785289	+	0.619130i	$0.787485\pi$
$384$	4.33651	+	7.51106i	0.221297	+	0.383297i
$385$	−0.0880980	+	0.152590i	−0.00448989	+	0.00777672i
$386$	25.0593	−	43.4040i	1.27548	−	2.20920i
$387$	−4.18993	−	7.25717i	−0.212986	−	0.368903i
$388$	25.6930	−	44.5016i	1.30437	−	2.25923i
$389$	16.8309			0.853361			0.426680	−	0.904402i	$-0.359683\pi$
$389$	16.8309			0.853361			0.426680	+	0.904402i	$0.359683\pi$
$390$	5.58767	+	9.67812i	0.282942	+	0.490071i
$391$	0.709043	+	1.22810i	0.0358578	+	0.0621076i
$392$	−46.4748			−2.34733
$393$	−13.1760			−0.664643
$394$	−15.9302	−	27.5919i	−0.802551	−	1.39006i
$395$	12.4230	+	21.5173i	0.625069	+	1.08265i
$396$	−6.71574			−0.337478
$397$	4.18026	−	7.24043i	0.209801	−	0.363387i	−0.741850	−	0.670565i	$-0.766052\pi$
$397$	4.18026	−	7.24043i	0.209801	−	0.363387i	0.951652	+	0.307179i	$0.0993849\pi$
$398$	29.0858	+	50.3782i	1.45794	+	2.52523i
$399$	0.0321677	−	0.0557161i	0.00161040	−	0.00278929i
$400$	−29.1687	+	50.5217i	−1.45843	+	2.52608i
$401$	12.8590	+	22.2725i	0.642149	+	1.11223i	0.984952	+	0.172827i	$0.0552902\pi$
$401$	12.8590	+	22.2725i	0.642149	+	1.11223i	−0.342804	+	0.939407i	$0.611377\pi$
$402$	−6.76254	−	11.7131i	−0.337285	−	0.584194i
$403$	4.95393	+	8.58047i	0.246773	+	0.427423i
$404$	3.60578			0.179394
$405$	−1.76168	+	3.05133i	−0.0875388	+	0.151622i
$406$	−0.879228			−0.0436353
$407$	−2.44519			−0.121204
$408$	9.83548	−	17.0356i	0.486929	−	0.843385i
$409$	1.55740	−	2.69749i	0.0770084	−	0.133383i	−0.824949	−	0.565206i	$-0.808796\pi$
$409$	1.55740	−	2.69749i	0.0770084	−	0.133383i	0.901958	+	0.431824i	$0.142130\pi$
$410$	−23.6870	−	41.0270i	−1.16982	−	2.02618i
$411$	−0.680021	+	1.17783i	−0.0335430	+	0.0580981i
$412$	−73.1253			−3.60263
$413$	0.122005			0.00600349
$414$	−0.614315	+	1.06402i	−0.0301919	+	0.0522939i
$415$	−0.753300			−0.0369780
$416$	4.27221	−	7.39968i	0.209462	−	0.362799i
$417$	11.3095			0.553830
$418$	3.53847	−	6.12881i	0.173072	−	0.299770i
$419$	−5.44277	+	9.42715i	−0.265897	+	0.460546i	−0.967798	−	0.251728i	$-0.919001\pi$
$419$	−5.44277	+	9.42715i	−0.265897	+	0.460546i	0.701902	+	0.712274i	$0.252335\pi$
$420$	0.276044	−	0.478122i	0.0134696	−	0.0233300i
$421$	8.21904	−	14.2358i	0.400571	−	0.693810i	−0.593224	−	0.805038i	$-0.702145\pi$
$421$	8.21904	−	14.2358i	0.400571	−	0.693810i	0.993795	+	0.111228i	$0.0354783\pi$
$422$	7.58176			0.369074
$423$	3.43991	+	5.95809i	0.167254	+	0.289692i
$424$	−33.9115	+	58.7365i	−1.64689	+	2.85250i
$425$	−21.9631			−1.06537
$426$	−24.1918			−1.17210
$427$	−0.237057	−	0.410595i	−0.0114720	−	0.0198701i
$428$	−4.61345	+	7.99072i	−0.222999	+	0.386246i
$429$	−0.904608	−	1.56683i	−0.0436749	−	0.0756471i
$430$	75.7787			3.65437
$431$	5.36805	+	9.29774i	0.258570	+	0.447857i	0.965859	−	0.259068i	$-0.0834154\pi$
$431$	5.36805	+	9.29774i	0.258570	+	0.447857i	−0.707289	+	0.706925i	$0.750082\pi$
$432$	7.86840			0.378569
$433$	−7.31778	−	12.6748i	−0.351670	−	0.609111i	0.634872	−	0.772617i	$-0.281053\pi$
$433$	−7.31778	−	12.6748i	−0.351670	−	0.609111i	−0.986542	+	0.163507i	$0.947719\pi$
$434$	0.351439	−	0.608710i	0.0168696	−	0.0292190i
$435$	−17.6677	+	30.6014i	−0.847101	+	1.46722i
$436$	7.58598	+	13.1393i	0.363303	+	0.629259i
$437$	−0.450808	−	0.780822i	−0.0215651	−	0.0373518i
$438$	−20.7518	+	35.9432i	−0.991561	+	1.71743i
$439$	−3.97272			−0.189607			−0.0948037	−	0.995496i	$-0.530222\pi$
$439$	−3.97272			−0.189607			−0.0948037	+	0.995496i	$0.530222\pi$
$440$	17.1262	−	29.6634i	0.816458	−	1.41415i
$441$	3.49942	−	6.06117i	0.166639	−	0.288627i
$442$	9.39585			0.446915
$443$	8.31514			0.395064			0.197532	−	0.980296i	$-0.436707\pi$
$443$	8.31514			0.395064			0.197532	+	0.980296i	$0.436707\pi$
$444$	7.66169			0.363608
$445$	−32.4164	+	56.1468i	−1.53668	+	2.66161i
$446$	−16.6666	+	28.8674i	−0.789187	+	1.36691i
$447$	−5.54776	−	9.60901i	−0.262400	−	0.454491i
$448$	−0.0686089			−0.00324147
$449$	−2.70527	−	4.68566i	−0.127669	−	0.221130i	0.795104	−	0.606473i	$-0.207416\pi$
$449$	−2.70527	−	4.68566i	−0.127669	−	0.221130i	−0.922773	+	0.385343i	$0.874083\pi$
$450$	−9.51443	−	16.4795i	−0.448514	−	0.776850i
$451$	3.83477	+	6.64202i	0.180572	+	0.312761i
$452$	10.7746	+	18.6621i	0.506793	+	0.877792i
$453$	−9.46744	+	16.3981i	−0.444819	+	0.770449i
$454$	24.9160	+	43.1558i	1.16937	+	2.02540i
$455$	0.148732			0.00697268
$456$	−6.25338	+	10.8312i	−0.292841	+	0.507216i
$457$	8.02556			0.375420			0.187710	−	0.982225i	$-0.439894\pi$
$457$	8.02556			0.375420			0.187710	+	0.982225i	$0.439894\pi$
$458$	−31.0690	+	53.8131i	−1.45176	+	2.51452i
$459$	1.48117	+	2.56546i	0.0691349	+	0.119745i
$460$	−3.86856	−	6.70055i	−0.180373	−	0.312415i
$461$	11.4926	+	19.9058i	0.535264	+	0.927104i	0.999151	+	0.0412093i	$0.0131211\pi$
$461$	11.4926	+	19.9058i	0.535264	+	0.927104i	−0.463887	+	0.885894i	$0.653546\pi$
$462$	−0.0641742	+	0.111153i	−0.00298565	+	0.00517130i
$463$	9.19124			0.427153			0.213576	−	0.976926i	$-0.431489\pi$
$463$	9.19124			0.427153			0.213576	+	0.976926i	$0.431489\pi$
$464$	78.9112			3.66336
$465$	−14.1240	−	24.4635i	−0.654986	−	1.13447i
$466$	−23.6716	−	41.0004i	−1.09656	−	1.89930i
$467$	18.5064			0.856373			0.428186	−	0.903690i	$-0.359153\pi$
$467$	18.5064			0.856373			0.428186	+	0.903690i	$0.359153\pi$
$468$	2.83448	+	4.90946i	0.131024	+	0.226940i
$469$	−0.180005			−0.00831186
$470$	−62.2138			−2.86971
$471$	−1.90769	−	12.3839i	−0.0879018	−	0.570619i
$472$	−23.7177			−1.09170
$473$	−12.2681			−0.564088
$474$	9.04941	+	15.6740i	0.415653	+	0.719933i
$475$	13.9641			0.640717
$476$	−0.232089	−	0.401990i	−0.0106378	−	0.0184252i
$477$	−5.10688	−	8.84538i	−0.233828	−	0.405002i
$478$	−43.9624			−2.01079
$479$	15.0393			0.687165			0.343583	−	0.939122i	$-0.388359\pi$
$479$	15.0393			0.687165			0.343583	+	0.939122i	$0.388359\pi$
$480$	−12.1804	+	21.0970i	−0.555956	+	0.962944i
$481$	1.03203	+	1.78753i	0.0470565	+	0.0815042i
$482$	−10.3483	−	17.9238i	−0.471353	−	0.816408i
$483$	0.00817591	+	0.0141611i	0.000372017	+	0.000644352i
$484$	20.3140	−	35.1849i	0.923363	−	1.59931i
$485$	−39.4685			−1.79217
$486$	−1.28328	+	2.22271i	−0.0582109	+	0.100824i
$487$	−6.25606			−0.283489			−0.141745	−	0.989903i	$-0.545271\pi$
$487$	−6.25606			−0.283489			−0.141745	+	0.989903i	$0.545271\pi$
$488$	46.0837	+	79.8193i	2.08611	+	3.61325i
$489$	−3.96666	+	6.87045i	−0.179378	+	0.310692i
$490$	31.6451	+	54.8109i	1.42958	+	2.47610i
$491$	−11.9284	−	20.6605i	−0.538319	−	0.932396i	−0.998995	−	0.0448272i	$-0.985726\pi$
$491$	−11.9284	−	20.6605i	−0.538319	−	0.932396i	0.460676	−	0.887568i	$-0.347607\pi$
$492$	−12.0158	−	20.8119i	−0.541713	−	0.938275i
$493$	14.8544	+	25.7286i	0.669009	+	1.15876i
$494$	−5.97386			−0.268777
$495$	2.57910	+	4.46714i	0.115922	+	0.200783i
$496$	−31.5418	+	54.6321i	−1.41627	+	2.45305i
$497$	−0.160984	+	0.278833i	−0.00722114	+	0.0125074i
$498$	−0.548734			−0.0245894
$499$	−18.8210			−0.842543			−0.421272	−	0.906934i	$-0.638416\pi$
$499$	−18.8210			−0.842543			−0.421272	+	0.906934i	$0.638416\pi$
$500$	39.0187			1.74497
$501$	9.46095	−	16.3869i	0.422684	−	0.732111i
$502$	−5.06937	+	8.78040i	−0.226257	+	0.391889i
$503$	−33.3170			−1.48553			−0.742766	−	0.669551i	$-0.766486\pi$
$503$	−33.3170			−1.48553			−0.742766	+	0.669551i	$0.766486\pi$
$504$	0.113412	−	0.196435i	0.00505177	−	0.00874992i
$505$	−1.38476	−	2.39847i	−0.0616210	−	0.106731i
$506$	0.899356	+	1.55773i	0.0399812	+	0.0692495i
$507$	5.73639	−	9.93572i	0.254762	−	0.441261i
$508$	−42.4466	+	73.5197i	−1.88326	+	3.26191i
$509$	13.5131	+	23.4053i	0.598956	+	1.03742i	0.992975	+	0.118320i	$0.0377510\pi$
$509$	13.5131	+	23.4053i	0.598956	+	1.03742i	−0.394019	+	0.919102i	$0.628916\pi$
$510$	−26.7883			−1.18620
$511$	0.276186	+	0.478368i	0.0122177	+	0.0211617i
$512$	−50.0955			−2.21393
$513$	−0.941723	−	1.63111i	−0.0415781	−	0.0720153i
$514$	−9.46362	+	16.3915i	−0.417422	+	0.722997i
$515$	28.0830	+	48.6411i	1.23748	+	2.14338i
$516$	38.4405			1.69225
$517$	10.0720			0.442967
$518$	0.0732135	−	0.126810i	0.00321682	−	0.00557169i
$519$	2.70913	+	4.69234i	0.118917	+	0.205971i
$520$	−28.9134			−1.26794
$521$	−18.6811	+	32.3566i	−0.818433	+	1.41757i	0.0884029	+	0.996085i	$0.471824\pi$
$521$	−18.6811	+	32.3566i	−0.818433	+	1.41757i	−0.906836	+	0.421483i	$0.861510\pi$
$522$	−12.8699	+	22.2913i	−0.563299	+	0.975662i
$523$	20.4314	−	35.3883i	0.893404	−	1.54742i	0.0576359	−	0.998338i	$-0.481644\pi$
$523$	20.4314	−	35.3883i	0.893404	−	1.54742i	0.835768	−	0.549083i	$-0.185023\pi$
$524$	30.2209	−	52.3442i	1.32021	−	2.28667i
$525$	−0.253255			−0.0110529
$526$	3.28721	−	5.69362i	0.143329	−	0.248254i
$527$	−23.7500			−1.03457
$528$	5.75967	−	9.97603i	0.250657	−	0.434151i
$529$	−22.7708			−0.990037
$530$	92.3627			4.01198
$531$	1.78588	−	3.09323i	0.0775005	−	0.134235i
$532$	0.147562	+	0.255584i	0.00639760	+	0.0110810i
$533$	3.23705	−	5.60673i	0.140212	−	0.242854i
$534$	−23.6134	+	40.8996i	−1.02185	+	1.76990i
$535$	7.08697			0.306397
$536$	34.9928			1.51146
$537$	−2.38983	+	4.13931i	−0.103129	+	0.178625i
$538$	46.0378			1.98483
$539$	−5.12314	−	8.87354i	−0.220669	−	0.382210i
$540$	−8.08130	−	13.9972i	−0.347764	−	0.602344i
$541$	2.61719	+	4.53311i	0.112522	+	0.194894i	0.916786	−	0.399378i	$-0.130774\pi$
$541$	2.61719	+	4.53311i	0.112522	+	0.194894i	−0.804265	+	0.594271i	$0.797440\pi$
$542$	11.9887	−	20.7650i	0.514958	−	0.891934i
$543$	−4.09827	+	7.09841i	−0.175874	+	0.304622i
$544$	10.2409	+	17.7377i	0.439073	+	0.760497i
$545$	5.82663	−	10.0920i	0.249585	−	0.432294i
$546$	0.108343			0.00463664
$547$	−3.89581	−	6.74774i	−0.166573	−	0.288512i	0.770640	−	0.637271i	$-0.219937\pi$
$547$	−3.89581	−	6.74774i	−0.166573	−	0.288512i	−0.937213	+	0.348758i	$0.886603\pi$
$548$	−3.11943	−	5.40301i	−0.133255	−	0.230805i
$549$	−13.8799			−0.592379
$550$	−27.8582			−1.18788
$551$	−9.44441	−	16.3582i	−0.402345	−	0.696883i
$552$	−1.58939	−	2.75290i	−0.0676489	−	0.117171i
$553$	0.240877			0.0102431
$554$	16.3660	−	28.3468i	0.695326	−	1.20434i
$555$	−2.94239	−	5.09637i	−0.124897	−	0.216329i
$556$	−25.9399	+	44.9292i	−1.10010	+	1.90542i
$557$	11.2336	−	19.4571i	0.475981	−	0.824424i	−0.523640	−	0.851940i	$-0.675426\pi$
$557$	11.2336	−	19.4571i	0.475981	−	0.824424i	0.999621	+	0.0275156i	$0.00875959\pi$
$558$	−10.2885	−	17.8202i	−0.435547	−	0.754390i
$559$	5.17793	+	8.96844i	0.219003	+	0.379325i
$560$	0.473491	+	0.820111i	0.0200087	+	0.0346560i
$561$	4.33685			0.183102
$562$	−8.61485	+	14.9214i	−0.363396	+	0.629420i
$563$	−22.1599			−0.933927			−0.466964	−	0.884276i	$-0.654652\pi$
$563$	−22.1599			−0.933927			−0.466964	+	0.884276i	$0.654652\pi$
$564$	−31.5595			−1.32889
$565$	8.27571	−	14.3340i	0.348162	−	0.603034i
$566$	16.1095	−	27.9025i	0.677134	−	1.17283i
$567$	0.0170792	+	0.0295820i	0.000717259	+	0.00124233i
$568$	31.2952	−	54.2049i	1.31312	−	2.27439i
$569$	4.74077			0.198743			0.0993716	−	0.995050i	$-0.468317\pi$
$569$	4.74077			0.198743			0.0993716	+	0.995050i	$0.468317\pi$
$570$	17.0319			0.713388
$571$	−15.1994	+	26.3262i	−0.636076	+	1.10172i	0.350210	+	0.936671i	$0.386110\pi$
$571$	−15.1994	+	26.3262i	−0.636076	+	1.10172i	−0.986286	+	0.165045i	$0.947223\pi$
$572$	8.29934			0.347013
$573$	2.66606	−	4.61775i	0.111376	−	0.192909i
$574$	−0.459281			−0.0191700
$575$	−1.77459	+	3.07369i	−0.0740057	+	0.128182i
$576$	−1.00428	+	1.73946i	−0.0418449	+	0.0724774i
$577$	−18.3026	+	31.7010i	−0.761946	+	1.31973i	0.179899	+	0.983685i	$0.442423\pi$
$577$	−18.3026	+	31.7010i	−0.761946	+	1.31973i	−0.941846	+	0.336045i	$0.890911\pi$
$578$	10.5545	−	18.2809i	0.439008	−	0.760384i
$579$	−19.5275			−0.811535
$580$	−81.0463	−	140.376i	−3.36526	−	5.82881i
$581$	−0.00365155	+	0.00632467i	−0.000151492	+	0.000262391i
$582$	−28.7504			−1.19174
$583$	−14.9529			−0.619287
$584$	−53.6903	−	92.9943i	−2.22172	−	3.84813i
$585$	2.17710	−	3.77085i	0.0900120	−	0.155905i
$586$	−37.8586	−	65.5731i	−1.56393	−	2.70880i
$587$	−8.19529			−0.338256			−0.169128	−	0.985594i	$-0.554095\pi$
$587$	−8.19529			−0.338256			−0.169128	+	0.985594i	$0.554095\pi$
$588$	16.0527	+	27.8041i	0.662003	+	1.14662i
$589$	15.1002			0.622194
$590$	16.1496	+	27.9719i	0.664869	+	1.15159i
$591$	−6.20681	+	10.7505i	−0.255314	+	0.442217i
$592$	−6.57096	+	11.3812i	−0.270065	+	0.467766i
$593$	−2.49042	−	4.31353i	−0.102269	−	0.177135i	0.810350	−	0.585946i	$-0.199277\pi$
$593$	−2.49042	−	4.31353i	−0.102269	−	0.177135i	−0.912619	+	0.408811i	$0.865944\pi$
$594$	1.87872	+	3.25404i	0.0770850	+	0.133515i
$595$	−0.178262	+	0.308759i	−0.00730804	+	0.0126579i
$596$	50.8980			2.08486
$597$	11.3326	−	19.6286i	0.463812	−	0.803346i
$598$	0.759173	−	1.31493i	0.0310449	−	0.0537713i
$599$	2.82843			0.115567			0.0577833	−	0.998329i	$-0.481597\pi$
$599$	2.82843			0.115567			0.0577833	+	0.998329i	$0.481597\pi$
$600$	49.2325			2.00991
$601$	19.0703			0.777893			0.388946	−	0.921260i	$-0.372839\pi$
$601$	19.0703			0.777893			0.388946	+	0.921260i	$0.372839\pi$
$602$	0.367330	−	0.636234i	0.0149712	−	0.0259310i
$603$	−2.63486	+	4.56371i	−0.107300	+	0.185849i
$604$	−43.4296	−	75.2222i	−1.76712	−	3.06075i
$605$	−31.2055			−1.26868
$606$	−1.00871	−	1.74715i	−0.0409762	−	0.0709729i
$607$	17.1360	+	29.6804i	0.695527	+	1.20469i	0.970003	+	0.243094i	$0.0781624\pi$
$607$	17.1360	+	29.6804i	0.695527	+	1.20469i	−0.274476	+	0.961594i	$0.588504\pi$
$608$	−6.51112	−	11.2776i	−0.264061	−	0.457367i
$609$	0.171285	+	0.296674i	0.00694081	+	0.0120218i
$610$	62.7576	−	108.699i	2.54098	−	4.40111i
$611$	−4.25105	−	7.36304i	−0.171979	−	0.297877i
$612$	−13.5890			−0.549302
$613$	8.78421	−	15.2147i	0.354791	−	0.614516i	−0.632291	−	0.774731i	$-0.717885\pi$
$613$	8.78421	−	15.2147i	0.354791	−	0.614516i	0.987082	+	0.160215i	$0.0512187\pi$
$614$	−46.8755			−1.89174
$615$	−9.22906	+	15.9852i	−0.372151	+	0.644585i
$616$	−0.166035	−	0.287581i	−0.00668974	−	0.0115870i
$617$	9.62298	+	16.6675i	0.387407	+	0.671008i	0.992100	−	0.125450i	$-0.0400376\pi$
$617$	9.62298	+	16.6675i	0.387407	+	0.671008i	−0.604693	+	0.796459i	$0.706704\pi$
$618$	20.4568	+	35.4322i	0.822892	+	1.42529i
$619$	8.65952	−	14.9987i	0.348055	−	0.602849i	−0.637849	−	0.770162i	$-0.720175\pi$
$619$	8.65952	−	14.9987i	0.348055	−	0.602849i	0.985904	+	0.167312i	$0.0535088\pi$
$620$	129.581			5.20410
$621$	0.478706			0.0192098
$622$	7.41678	+	12.8462i	0.297386	+	0.515087i
$623$	0.314271	+	0.544333i	0.0125910	+	0.0218082i
$624$	−9.72381			−0.389264
$625$	3.55065	+	6.14990i	0.142026	+	0.245996i
$626$	−12.7640			−0.510151
$627$	−2.75736			−0.110118
$628$	53.5728	+	20.8254i	2.13779	+	0.831023i
$629$	−4.94773			−0.197279
$630$	−0.308893			−0.0123066
$631$	−8.20614	−	14.2135i	−0.326681	−	0.565829i	0.655170	−	0.755482i	$-0.272597\pi$
$631$	−8.20614	−	14.2135i	−0.326681	−	0.565829i	−0.981851	+	0.189653i	$0.939264\pi$
$632$	−46.8263			−1.86265
$633$	−1.47702	−	2.55828i	−0.0587064	−	0.101683i
$634$	−27.8961	−	48.3174i	−1.10789	−	1.91893i
$635$	65.2046			2.58757
$636$	46.8532			1.85785
$637$	−4.32460	+	7.49042i	−0.171347	+	0.296781i
$638$	18.8415	+	32.6344i	0.745941	+	1.29201i
$639$	4.71288	+	8.16295i	0.186439	+	0.322921i
$640$	15.2791	+	26.4642i	0.603961	+	1.04609i
$641$	8.16411	−	14.1407i	0.322463	−	0.558522i	−0.658533	−	0.752552i	$-0.728823\pi$
$641$	8.16411	−	14.1407i	0.322463	−	0.558522i	0.980996	+	0.194030i	$0.0621559\pi$
$642$	5.16244			0.203745
$643$	6.90759	−	11.9643i	0.272409	−	0.471826i	−0.697069	−	0.717004i	$-0.745513\pi$
$643$	6.90759	−	11.9643i	0.272409	−	0.471826i	0.969478	+	0.245178i	$0.0788463\pi$
$644$	−0.0750099			−0.00295581
$645$	−14.7627	−	25.5697i	−0.581279	−	1.00681i
$646$	7.15994	−	12.4014i	0.281704	−	0.487926i
$647$	−18.5076	−	32.0561i	−0.727610	−	1.26026i	−0.957891	−	0.287133i	$-0.907298\pi$
$647$	−18.5076	−	32.0561i	−0.727610	−	1.26026i	0.230281	−	0.973124i	$-0.426035\pi$
$648$	−3.32018	−	5.75072i	−0.130429	−	0.225910i
$649$	−2.61452	−	4.52848i	−0.102629	−	0.177759i
$650$	11.7580	+	20.3654i	0.461186	+	0.798797i
$651$	−0.273859			−0.0107334
$652$	−18.1961	−	31.5165i	−0.712613	−	1.23428i
$653$	−0.836771	+	1.44933i	−0.0327454	+	0.0567166i	−0.881934	−	0.471374i	$-0.843758\pi$
$653$	−0.836771	+	1.44933i	−0.0327454	+	0.0567166i	0.849188	+	0.528090i	$0.177092\pi$
$654$	4.24435	−	7.35143i	0.165967	−	0.287464i
$655$	−46.4241			−1.81394
$656$	41.2207			1.60940
$657$	16.1709			0.630887
$658$	−0.301576	+	0.522344i	−0.0117566	+	0.0203631i
$659$	12.3769	−	21.4373i	0.482134	−	0.835080i	−0.517656	−	0.855589i	$-0.673195\pi$
$659$	12.3769	−	21.4373i	0.482134	−	0.835080i	0.999790	+	0.0205087i	$0.00652857\pi$
$660$	−23.6620			−0.921043
$661$	−8.74662	+	15.1496i	−0.340204	+	0.589251i	−0.984470	−	0.175550i	$-0.943830\pi$
$661$	−8.74662	+	15.1496i	−0.340204	+	0.589251i	0.644266	+	0.764801i	$0.277163\pi$
$662$	33.9702	+	58.8380i	1.32029	+	2.28681i
$663$	−1.83043	−	3.17040i	−0.0710881	−	0.123128i
$664$	0.709858	−	1.22951i	0.0275478	−	0.0477142i
$665$	0.113339	−	0.196308i	0.00439509	−	0.00761252i
$666$	−2.14336	−	3.71240i	−0.0830533	−	0.143853i
$667$	4.80087			0.185891
$668$	43.3998	+	75.1707i	1.67919	+	2.90844i
$669$	12.9875			0.502125
$670$	−23.8269	−	41.2694i	−0.920514	−	1.59438i
$671$	−10.1601	+	17.5977i	−0.392225	+	0.679353i
$672$	0.118086	+	0.204532i	0.00455528	+	0.00788998i
$673$	49.4679			1.90685			0.953424	−	0.301632i	$-0.0975315\pi$
$673$	49.4679			1.90685			0.953424	+	0.301632i	$0.0975315\pi$
$674$	4.34730			0.167452
$675$	−3.70707	+	6.42083i	−0.142685	+	0.247138i
$676$	26.3143	+	45.5777i	1.01209	+	1.75299i
$677$	28.4276			1.09256			0.546281	−	0.837602i	$-0.316043\pi$
$677$	28.4276			1.09256			0.546281	+	0.837602i	$0.316043\pi$
$678$	6.02836	−	10.4414i	0.231518	−	0.401001i
$679$	−0.191320	+	0.331375i	−0.00734217	+	0.0127170i
$680$	34.6540	−	60.0225i	1.32892	−	2.30176i
$681$	9.70792	−	16.8146i	0.372008	−	0.644337i
$682$	−30.1247			−1.15354
$683$	−11.8352	+	20.4991i	−0.452860	+	0.784376i	−0.998562	−	0.0536029i	$-0.982929\pi$
$683$	−11.8352	+	20.4991i	−0.452860	+	0.784376i	0.545703	+	0.837979i	$0.316263\pi$
$684$	8.63984			0.330353
$685$	−2.39597	+	4.14993i	−0.0915451	+	0.158561i
$686$	1.22727			0.0468575
$687$	24.2106			0.923690
$688$	−32.9680	+	57.1023i	−1.25690	+	2.17701i
$689$	6.31111	+	10.9312i	0.240434	+	0.416444i
$690$	−2.16446	+	3.74895i	−0.0823995	+	0.142720i
$691$	−11.4200	+	19.7800i	−0.434437	+	0.752467i	−0.997249	−	0.0741178i	$-0.976386\pi$
$691$	−11.4200	+	19.7800i	−0.434437	+	0.752467i	0.562813	+	0.826584i	$0.309719\pi$
$692$	−24.8549			−0.944842
$693$	0.0500078			0.00189964
$694$	−22.4179	+	38.8290i	−0.850972	+	1.47393i
$695$	39.8477			1.51151
$696$	−33.2976	−	57.6732i	−1.26214	−	2.18610i
$697$	7.75949	+	13.4398i	0.293912	+	0.509070i
$698$	−18.9403	−	32.8056i	−0.716901	−	1.24171i
$699$	−9.22305	+	15.9748i	−0.348848	+	0.604222i
$700$	0.580872	−	1.00610i	0.0219549	−	0.0380270i
$701$	−20.8793	−	36.1641i	−0.788601	−	1.36590i	−0.926824	−	0.375496i	$-0.877472\pi$
$701$	−20.8793	−	36.1641i	−0.788601	−	1.36590i	0.138223	−	0.990401i	$-0.455861\pi$
$702$	1.58589	−	2.74684i	0.0598554	−	0.103673i
$703$	3.14575			0.118644
$704$	1.47026	+	2.54656i	0.0554125	+	0.0959772i
$705$	12.1201	+	20.9926i	0.456468	+	0.790625i
$706$	−24.4835			−0.921448
$707$	−0.0268499			−0.00100980
$708$	8.19228	+	14.1894i	0.307885	+	0.533272i
$709$	17.8623	+	30.9384i	0.670833	+	1.16192i	0.977668	+	0.210155i	$0.0673968\pi$
$709$	17.8623	+	30.9384i	0.670833	+	1.16192i	−0.306835	+	0.951763i	$0.599270\pi$
$710$	−85.2368			−3.19888
$711$	3.52589	−	6.10701i	0.132231	−	0.229031i
$712$	−61.0939	−	105.818i	−2.28959	−	3.96569i
$713$	−1.91897	+	3.32376i	−0.0718661	+	0.124476i
$714$	−0.129853	+	0.224913i	−0.00485964	+	0.00841715i
$715$	−3.18727	−	5.52051i	−0.119197	−	0.206455i
$716$	−10.9628	−	18.9881i	−0.409698	−	0.709618i
$717$	8.56444	+	14.8340i	0.319845	+	0.553987i
$718$	4.82679			0.180134
$719$	23.1468	−	40.0914i	0.863229	−	1.49516i	−0.00556616	−	0.999985i	$-0.501772\pi$
$719$	23.1468	−	40.0914i	0.863229	−	1.49516i	0.868795	−	0.495172i	$-0.164895\pi$
$720$	27.7233			1.03319
$721$	0.544518			0.0202789
$722$	19.8301	−	34.3467i	0.738000	−	1.27825i
$723$	−4.03197	+	6.98358i	−0.149951	+	0.259722i
$724$	−18.7998	−	32.5622i	−0.698690	−	1.21017i
$725$	−37.1777	+	64.3936i	−1.38074	+	2.39152i
$726$	−22.7313			−0.843638
$727$	−36.1660			−1.34132			−0.670662	−	0.741763i	$-0.733990\pi$
$727$	−36.1660			−1.34132			−0.670662	+	0.741763i	$0.733990\pi$
$728$	−0.140155	+	0.242756i	−0.00519449	+	0.00899713i
$729$	1.00000			0.0370370
$730$	−73.1164	+	126.641i	−2.70616	+	4.68720i
$731$	−24.8239			−0.918146
$732$	31.8353	−	55.1403i	1.17667	−	2.03805i
$733$	7.54768	−	13.0730i	0.278780	−	0.482861i	−0.692302	−	0.721608i	$-0.743403\pi$
$733$	7.54768	−	13.0730i	0.278780	−	0.482861i	0.971082	+	0.238747i	$0.0767366\pi$
$734$	−47.2097	+	81.7697i	−1.74254	+	3.01817i
$735$	12.3297	−	21.3557i	0.454789	−	0.787718i
$736$	3.30980			0.122001
$737$	3.85743	+	6.68127i	0.142090	+	0.246108i
$738$	−6.72282	+	11.6443i	−0.247470	+	0.428631i
$739$	33.7182			1.24035			0.620173	−	0.784465i	$-0.287063\pi$
$739$	33.7182			1.24035			0.620173	+	0.784465i	$0.287063\pi$
$740$	26.9950			0.992355
$741$	1.16379	+	2.01574i	0.0427527	+	0.0740499i
$742$	0.447719	−	0.775472i	0.0164363	−	0.0284685i
$743$	−15.7116	−	27.2133i	−0.576404	−	0.998360i	−0.995888	−	0.0905976i	$-0.971122\pi$
$743$	−15.7116	−	27.2133i	−0.576404	−	0.998360i	0.419484	−	0.907763i	$-0.362211\pi$
$744$	53.2380			1.95180
$745$	−19.5468	−	33.8561i	−0.716140	−	1.24039i
$746$	−19.1538			−0.701271
$747$	0.106900	+	0.185157i	0.00391128	+	0.00677454i
$748$	−9.94712	+	17.2289i	−0.363703	+	0.629952i
$749$	0.0343534	−	0.0595018i	0.00125525	−	0.00217415i
$750$	−10.9154	−	18.9061i	−0.398576	−	0.690354i
$751$	−3.03615	−	5.25876i	−0.110791	−	0.191895i	0.805299	−	0.592869i	$-0.202005\pi$
$751$	−3.03615	−	5.25876i	−0.110791	−	0.191895i	−0.916089	+	0.400974i	$0.868672\pi$
$752$	27.0666	−	46.8807i	0.987016	−	1.70956i
$753$	3.95031			0.143957
$754$	15.9046	−	27.5477i	0.579213	−	1.00323i
$755$	−33.3573	+	57.7765i	−1.21400	+	2.10270i
$756$	−0.156693			−0.00569888
$757$	23.3737			0.849531			0.424765	−	0.905303i	$-0.360357\pi$
$757$	23.3737			0.849531			0.424765	+	0.905303i	$0.360357\pi$
$758$	89.1303			3.23736
$759$	0.350412	−	0.606932i	0.0127192	−	0.0220302i
$760$	−22.0330	+	38.1622i	−0.799219	+	1.38429i
$761$	−13.9076	−	24.0886i	−0.504149	−	0.873212i	−0.999988	−	0.00479763i	$-0.998473\pi$
$761$	−13.9076	−	24.0886i	−0.504149	−	0.873212i	0.495839	−	0.868414i	$-0.334860\pi$
$762$	47.4977			1.72066
$763$	−0.0564880	−	0.0978401i	−0.00204500	−	0.00354205i
$764$	12.2299	+	21.1828i	0.442462	+	0.766366i
$765$	5.21870	+	9.03905i	0.188682	+	0.326808i
$766$	7.20972	+	12.4876i	0.260498	+	0.451196i
$767$	−2.20700	+	3.82263i	−0.0796900	+	0.138027i
$768$	13.1385	+	22.7565i	0.474094	+	0.821156i
$769$	−15.1497			−0.546311			−0.273155	−	0.961970i	$-0.588067\pi$
$769$	−15.1497			−0.546311			−0.273155	+	0.961970i	$0.588067\pi$
$770$	−0.226109	+	0.391633i	−0.00814841	+	0.0141135i
$771$	7.37454			0.265588
$772$	44.7888	−	77.5765i	1.61198	−	2.79204i
$773$	26.1456	+	45.2854i	0.940390	+	1.62880i	0.764728	+	0.644353i	$0.222873\pi$
$773$	26.1456	+	45.2854i	0.940390	+	1.62880i	0.175662	+	0.984450i	$0.443793\pi$
$774$	−10.7537	−	18.6260i	−0.386535	−	0.669498i
$775$	−29.7208	−	51.4780i	−1.06760	−	1.84914i
$776$	37.1924	−	64.4191i	1.33513	−	2.31251i
$777$	−0.0570518			−0.00204672
$778$	43.1976			1.54871
$779$	−4.93346	−	8.54501i	−0.176760	−	0.306157i
$780$	9.98691	+	17.2978i	0.357589	+	0.619362i
$781$	13.7993			0.493778
$782$	1.81980	+	3.15199i	0.0650761	+	0.112715i
$783$	10.0289			0.358402
$784$	−55.0697			−1.96677
$785$	−6.72151	−	43.6330i	−0.239901	−	1.55733i
$786$	−33.8172			−1.20622
$787$	8.42074			0.300167			0.150084	−	0.988673i	$-0.452046\pi$
$787$	8.42074			0.300167			0.150084	+	0.988673i	$0.452046\pi$
$788$	−28.4722	−	49.3153i	−1.01428	−	1.75679i
$789$	−2.56157			−0.0911942
$790$	31.8844	+	55.2255i	1.13440	+	1.96483i
$791$	−0.0802314	−	0.138965i	−0.00285270	−	0.00494102i
$792$	−9.72148			−0.345438
$793$	17.1528			0.609115
$794$	10.7289	−	18.5830i	0.380755	−	0.659487i
$795$	−17.9934	−	31.1655i	−0.638161	−	1.10533i
$796$	51.9855	+	90.0416i	1.84258	+	3.19144i
$797$	−8.34091	−	14.4469i	−0.295450	−	0.511734i	0.679639	−	0.733546i	$-0.262136\pi$
$797$	−8.34091	−	14.4469i	−0.295450	−	0.511734i	−0.975089	+	0.221812i	$0.928803\pi$
$798$	0.0825605	−	0.142999i	0.00292261	−	0.00506211i
$799$	20.3803			0.721003
$800$	−25.6308	+	44.3939i	−0.906187	+	1.56956i
$801$	18.4008			0.650160
$802$	33.0035	+	57.1637i	1.16539	+	2.01852i
$803$	11.8371	−	20.5024i	0.417722	−	0.723515i
$804$	−12.0868	−	20.9349i	−0.426268	−	0.738317i
$805$	0.0288067	+	0.0498947i	0.00101530	+	0.00175856i
$806$	12.7146	+	22.0223i	0.447852	+	0.775703i
$807$	−8.96876	−	15.5344i	−0.315715	−	0.546835i
$808$	5.21961			0.183625
$809$	−13.9023	−	24.0795i	−0.488780	−	0.846591i	0.511137	−	0.859499i	$-0.329224\pi$
$809$	−13.9023	−	24.0795i	−0.488780	−	0.846591i	−0.999917	+	0.0129082i	$0.995891\pi$
$810$	−4.52148	+	7.83143i	−0.158869	+	0.275168i
$811$	4.95598	−	8.58400i	0.174028	−	0.301425i	−0.765797	−	0.643083i	$-0.777655\pi$
$811$	4.95598	−	8.58400i	0.174028	−	0.301425i	0.939824	+	0.341658i	$0.110988\pi$
$812$	−1.57146			−0.0551473
$813$	−9.34221			−0.327645
$814$	−6.27574			−0.219964
$815$	−13.9760	+	24.2071i	−0.489558	+	0.847939i
$816$	11.6544	−	20.1860i	0.407986	−	0.706653i
$817$	15.7830			0.552177
$818$	3.99717	−	6.92329i	0.139758	−	0.242067i
$819$	−0.0211065	−	0.0365576i	−0.000737522	−	0.00127743i
$820$	−42.3360	−	73.3282i	−1.47844	−	2.56073i
$821$	9.89266	−	17.1346i	0.345256	−	0.598001i	−0.640144	−	0.768255i	$-0.721125\pi$
$821$	9.89266	−	17.1346i	0.345256	−	0.598001i	0.985400	+	0.170254i	$0.0544587\pi$
$822$	−1.74532	+	3.02298i	−0.0608750	+	0.105439i
$823$	−21.7584	−	37.6867i	−0.758450	−	1.31367i	−0.943641	−	0.330972i	$-0.892623\pi$
$823$	−21.7584	−	37.6867i	−0.758450	−	1.31367i	0.185190	−	0.982703i	$-0.440710\pi$
$824$	−105.854			−3.68759
$825$	5.42714	+	9.40008i	0.188949	+	0.327269i
$826$	0.313135			0.0108953
$827$	8.17607	+	14.1614i	0.284310	+	0.492439i	0.972442	−	0.233147i	$-0.0749023\pi$
$827$	8.17607	+	14.1614i	0.284310	+	0.492439i	−0.688132	+	0.725586i	$0.741569\pi$
$828$	−1.09797	+	1.90174i	−0.0381572	+	0.0660902i
$829$	22.7495	+	39.4033i	0.790123	+	1.36853i	0.925890	+	0.377792i	$0.123317\pi$
$829$	22.7495	+	39.4033i	0.790123	+	1.36853i	−0.135768	+	0.990741i	$0.543350\pi$
$830$	−1.93339			−0.0671091
$831$	−12.7532			−0.442405
$832$	1.24109	−	2.14963i	0.0430270	−	0.0745250i
$833$	−10.3664	−	17.9552i	−0.359176	−	0.622111i
$834$	29.0267			1.00511
$835$	33.3344	−	57.7369i	1.15359	−	1.99807i
$836$	6.32436	−	10.9541i	0.218733	−	0.378856i
$837$	−4.00867	+	6.94322i	−0.138560	+	0.239993i
$838$	−13.9692	+	24.1954i	−0.482559	+	0.835816i
$839$	−25.5737			−0.882903			−0.441452	−	0.897285i	$-0.645536\pi$
$839$	−25.5737			−0.882903			−0.441452	+	0.897285i	$0.645536\pi$
$840$	0.399592	−	0.692114i	0.0137872	−	0.0238802i
$841$	71.5781			2.46821
$842$	21.0947	−	36.5371i	0.726971	−	1.25915i
$843$	6.71314			0.231213
$844$	13.5510			0.466444
$845$	20.2114	−	35.0072i	0.695294	−	1.20429i
$846$	8.82874	+	15.2918i	0.303538	+	0.525744i
$847$	−0.151265	+	0.261999i	−0.00519754	+	0.00900241i
$848$	−40.1830	+	69.5990i	−1.37989	+	2.39004i
$849$	−12.5534			−0.430831
$850$	−56.3698			−1.93347
$851$	−0.399770	+	0.692422i	−0.0137039	+	0.0237359i
$852$	−43.2384			−1.48132
$853$	2.08749	+	3.61563i	0.0714741	+	0.123797i	0.899548	−	0.436823i	$-0.143896\pi$
$853$	2.08749	+	3.61563i	0.0714741	+	0.123797i	−0.828073	+	0.560620i	$0.810563\pi$
$854$	−0.608423	−	1.05382i	−0.0208198	−	0.0360609i
$855$	−3.31804	−	5.74701i	−0.113474	−	0.196544i
$856$	−6.67827	+	11.5671i	−0.228259	+	0.395356i
$857$	25.8639	−	44.7976i	0.883494	−	1.53026i	0.0360629	−	0.999350i	$-0.488518\pi$
$857$	25.8639	−	44.7976i	0.883494	−	1.53026i	0.847431	−	0.530906i	$-0.178148\pi$
$858$	−2.32174	−	4.02136i	−0.0792628	−	0.137287i
$859$	16.0786	−	27.8490i	0.548596	−	0.950196i	−0.449775	−	0.893142i	$-0.648496\pi$
$859$	16.0786	−	27.8490i	0.548596	−	0.950196i	0.998371	−	0.0570541i	$-0.0181707\pi$
$860$	135.440			4.61847
$861$	0.0894739	+	0.154973i	0.00304926	+	0.00528148i
$862$	13.7775	+	23.8633i	0.469262	+	0.812786i
$863$	35.2697			1.20060			0.600298	−	0.799777i	$-0.295049\pi$
$863$	35.2697			1.20060			0.600298	+	0.799777i	$0.295049\pi$
$864$	6.91405			0.235221
$865$	9.54525	+	16.5329i	0.324548	+	0.562134i
$866$	−18.7816	−	32.5306i	−0.638224	−	1.10544i
$867$	−8.22458			−0.279321
$868$	0.628132	−	1.08796i	0.0213202	−	0.0369276i
$869$	−5.16189	−	8.94066i	−0.175105	−	0.303291i
$870$	−45.3453	+	78.5404i	−1.53735	+	2.66277i
$871$	3.25617	−	5.63986i	0.110331	−	0.191099i
$872$	10.9812	+	19.0200i	0.371871	+	0.644100i
$873$	5.60095	+	9.70114i	0.189564	+	0.328334i
$874$	−1.15703	−	2.00403i	−0.0391371	−	0.0677874i
$875$	−0.290547			−0.00982229
$876$	−37.0900	+	64.2418i	−1.25316	+	2.17053i
$877$	−41.2381			−1.39251			−0.696256	−	0.717793i	$-0.745152\pi$
$877$	−41.2381			−1.39251			−0.696256	+	0.717793i	$0.745152\pi$
$878$	−10.1962			−0.344106
$879$	−14.7507	+	25.5490i	−0.497529	+	0.861745i
$880$	20.2934	−	35.1493i	0.684091	−	1.18488i
$881$	−17.6309	−	30.5376i	−0.594000	−	1.02884i	−0.993687	−	0.112187i	$-0.964215\pi$
$881$	−17.6309	−	30.5376i	−0.594000	−	1.02884i	0.399687	−	0.916652i	$-0.369119\pi$
$882$	8.98148	−	15.5564i	0.302422	−	0.523811i
$883$	−5.52517			−0.185937			−0.0929683	−	0.995669i	$-0.529636\pi$
$883$	−5.52517			−0.185937			−0.0929683	+	0.995669i	$0.529636\pi$
$884$	16.7933			0.564821
$885$	6.29231	−	10.8986i	0.211514	−	0.366352i
$886$	21.3413			0.716976
$887$	29.0363	−	50.2924i	0.974944	−	1.68865i	0.294825	−	0.955551i	$-0.404739\pi$
$887$	29.0363	−	50.2924i	0.974944	−	1.68865i	0.680119	−	0.733102i	$-0.261928\pi$
$888$	11.0908			0.372183
$889$	0.316073	−	0.547454i	0.0106007	−	0.0183610i
$890$	−83.1988	+	144.104i	−2.78883	+	4.83039i
$891$	0.731999	−	1.26786i	0.0245229	−	0.0424749i
$892$	−29.7885	+	51.5951i	−0.997391	+	1.72753i
$893$	−12.9577			−0.433614
$894$	−14.2387	−	24.6621i	−0.476213	−	0.824826i
$895$	−8.42027	+	14.5843i	−0.281459	+	0.487501i
$896$	0.296256			0.00989723
$897$	−0.591587			−0.0197525
$898$	−6.94324	−	12.0261i	−0.231699	−	0.401315i
$899$	−40.2024	+	69.6326i	−1.34083	+	2.32238i
$900$	−17.0053	−	29.4540i	−0.566842	−	0.981799i
$901$	−30.2566			−1.00799
$902$	9.84219	+	17.0472i	0.327709	+	0.567609i
$903$	−0.286242			−0.00952555
$904$	15.5969	+	27.0147i	0.518746	+	0.898494i
$905$	−14.4397	+	25.0103i	−0.479993	+	0.831371i
$906$	−24.2988	+	42.0867i	−0.807273	+	1.39824i
$907$	−26.0509	−	45.1215i	−0.865005	−	1.49823i	−0.867042	−	0.498235i	$-0.833982\pi$
$907$	−26.0509	−	45.1215i	−0.865005	−	1.49823i	0.00203635	−	0.999998i	$-0.499352\pi$
$908$	44.5327	+	77.1329i	1.47787	+	2.55975i
$909$	−0.393021	+	0.680733i	−0.0130357	+	0.0225785i
$910$	0.381731			0.0126543
$911$	22.6093	−	39.1605i	0.749080	−	1.29745i	−0.199184	−	0.979962i	$-0.563829\pi$
$911$	22.6093	−	39.1605i	0.749080	−	1.29745i	0.948264	−	0.317483i	$-0.102838\pi$
$912$	−7.40985	+	12.8342i	−0.245365	+	0.424984i
$913$	0.313004			0.0103589
$914$	20.5981			0.681325
$915$	−48.9040			−1.61671
$916$	−55.5300	+	96.1808i	−1.83476	+	3.17790i
$917$	−0.225036	+	0.389774i	−0.00743135	+	0.0128715i
$918$	3.80151	+	6.58441i	0.125469	+	0.217318i
$919$	33.9430			1.11968			0.559838	−	0.828602i	$-0.310863\pi$
$919$	33.9430			1.11968			0.559838	+	0.828602i	$0.310863\pi$
$920$	−5.60001	−	9.69949i	−0.184627	−	0.319783i
$921$	9.13195	+	15.8170i	0.300908	+	0.521188i
$922$	29.4965	+	51.0894i	0.971415	+	1.68254i
$923$	−5.82420	−	10.0878i	−0.191706	−	0.332044i
$924$	−0.114699	+	0.198665i	−0.00377333	+	0.00653560i
$925$	−6.19159	−	10.7241i	−0.203578	−	0.352608i
$926$	23.5899			0.775212
$927$	7.97049	−	13.8053i	0.261785	−	0.453425i
$928$	69.3401			2.27620
$929$	28.2339	−	48.9026i	0.926325	−	1.60444i	0.136908	−	0.990584i	$-0.456284\pi$
$929$	28.2339	−	48.9026i	0.926325	−	1.60444i	0.789417	−	0.613858i	$-0.210383\pi$
$930$	−36.2502	−	62.7872i	−1.18869	−	2.05887i
$931$	6.59096	+	11.4159i	0.216010	+	0.374140i
$932$	−42.3085	−	73.2805i	−1.38586	−	2.40038i
$933$	2.88977	−	5.00522i	0.0946067	−	0.163864i
$934$	47.4978			1.55418
$935$	15.2803			0.499720
$936$	4.10310	+	7.10677i	0.134114	+	0.232292i
$937$	17.3897	+	30.1198i	0.568096	+	0.983972i	0.996754	+	0.0805047i	$0.0256532\pi$
$937$	17.3897	+	30.1198i	0.568096	+	0.983972i	−0.428658	+	0.903467i	$0.641013\pi$
$938$	−0.461995			−0.0150847
$939$	2.48659	+	4.30690i	0.0811468	+	0.140550i
$940$	−111.196			−3.62680
$941$	−1.83840			−0.0599300			−0.0299650	−	0.999551i	$-0.509540\pi$
$941$	−1.83840			−0.0599300			−0.0299650	+	0.999551i	$0.509540\pi$
$942$	−4.89622	−	31.7841i	−0.159527	−	1.03558i
$943$	2.50783			0.0816661
$944$	−28.1040			−0.914708
$945$	0.0601763	+	0.104228i	0.00195754	+	0.00339055i
$946$	−31.4869			−1.02373
$947$	−16.3207	−	28.2683i	−0.530352	−	0.918597i	−0.999373	−	0.0354098i	$-0.988726\pi$
$947$	−16.3207	−	28.2683i	−0.530352	−	0.918597i	0.469021	−	0.883187i	$-0.344607\pi$
$948$	16.1741	+	28.0144i	0.525312	+	0.909866i
$949$	−19.9841			−0.648710
$950$	35.8398			1.16280
$951$	−10.8690	+	18.8257i	−0.352452	+	0.610465i
$952$	−0.335964	−	0.581907i	−0.0108887	−	0.0188597i
$953$	−2.06428	−	3.57544i	−0.0668686	−	0.115820i	0.830653	−	0.556791i	$-0.187967\pi$
$953$	−2.06428	−	3.57544i	−0.0668686	−	0.115820i	−0.897521	+	0.440971i	$0.854634\pi$
$954$	−13.1071	−	22.7022i	−0.424360	−	0.735012i
$955$	9.39351	−	16.2700i	0.303967	−	0.526486i
$956$	−78.5745			−2.54128
$957$	7.34112	−	12.7152i	0.237305	−	0.411024i
$958$	38.5995			1.24709
$959$	0.0232284	+	0.0402328i	0.000750085	+	0.00129919i
$960$	−3.53844	+	6.12875i	−0.114203	+	0.197805i
$961$	−16.6389	−	28.8194i	−0.536738	−	0.929657i
$962$	2.64877	+	4.58780i	0.0853997	+	0.147917i
$963$	−1.00571	−	1.74194i	−0.0324085	−	0.0561332i
$964$	−18.4957	−	32.0355i	−0.595706	−	1.03179i
$965$	−68.8026			−2.21483
$966$	0.0209840	+	0.0363453i	0.000675149	+	0.00116939i
$967$	−3.12539	+	5.41334i	−0.100506	+	0.174081i	−0.911893	−	0.410428i	$-0.865379\pi$
$967$	−3.12539	+	5.41334i	−0.100506	+	0.174081i	0.811387	+	0.584509i	$0.198713\pi$
$968$	29.4059	−	50.9325i	0.945140	−	1.63703i
$969$	−5.57939			−0.179236
$970$	−101.298			−3.25250
$971$	7.85805			0.252177			0.126088	−	0.992019i	$-0.459758\pi$
$971$	7.85805			0.252177			0.126088	+	0.992019i	$0.459758\pi$
$972$	−2.29363	+	3.97268i	−0.0735682	+	0.127424i
$973$	0.193158	−	0.334559i	0.00619235	−	0.0107255i
$974$	−16.0566			−0.514486
$975$	4.58121	−	7.93489i	0.146716	−	0.254120i
$976$	54.6063	+	94.5808i	1.74790	+	3.02746i
$977$	4.21051	+	7.29282i	0.134706	+	0.233318i	0.925485	−	0.378784i	$-0.123658\pi$
$977$	4.21051	+	7.29282i	0.134706	+	0.233318i	−0.790779	+	0.612102i	$0.790324\pi$
$978$	−10.1807	+	17.6335i	−0.325542	+	0.563856i
$979$	13.4694	−	23.3296i	0.430483	−	0.745618i
$980$	56.5597	+	97.9642i	1.80673	+	3.12935i
$981$	−3.30742			−0.105598
$982$	−30.6149	−	53.0265i	−0.976960	−	1.69214i
$983$	−33.8826			−1.08069			−0.540343	−	0.841445i	$-0.681705\pi$
$983$	−33.8826			−1.08069			−0.540343	+	0.841445i	$0.681705\pi$
$984$	−17.3937	−	30.1267i	−0.554489	−	0.960404i
$985$	−21.8689	+	37.8780i	−0.696800	+	1.20689i
$986$	38.1248	+	66.0342i	1.21414	+	2.10296i
$987$	0.235003			0.00748023
$988$	−10.6772			−0.339686
$989$	−2.00574	+	3.47405i	−0.0637789	+	0.110468i
$990$	6.61944	+	11.4652i	0.210380	+	0.364388i
$991$	58.9885			1.87383			0.936915	−	0.349556i	$-0.113668\pi$
$991$	58.9885			1.87383			0.936915	+	0.349556i	$0.113668\pi$
$992$	−27.7162	+	48.0058i	−0.879989	+	1.52419i
$993$	13.2357	−	22.9248i	0.420021	−	0.727497i
$994$	−0.413177	+	0.715643i	−0.0131052	+	0.0226988i
$995$	39.9289	−	69.1589i	1.26583	−	2.19249i
$996$	−0.980760			−0.0310766
$997$	23.6753	−	41.0069i	0.749805	−	1.29870i	−0.198111	−	0.980180i	$-0.563481\pi$
$997$	23.6753	−	41.0069i	0.749805	−	1.29870i	0.947916	−	0.318521i	$-0.103186\pi$
$998$	−48.3053			−1.52908
$999$	−0.835107	+	1.44645i	−0.0264216	+	0.0457636i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.e.c.169.14	✓	28
157.144	even	3	inner	471.2.e.c.301.14	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.e.c.169.14	✓	28	1.1	even	1	trivial
471.2.e.c.301.14	yes	28	157.144	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.56656 q^{2} +(-0.500000 - 0.866025i) q^{3} +4.58726 q^{4} +(-1.76168 - 3.05133i) q^{5} +(-1.28328 - 2.22271i) q^{6} -0.0341584 q^{7} +6.64036 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+2.56656 q^{2} +(-0.500000 - 0.866025i) q^{3} +4.58726 q^{4} +(-1.76168 - 3.05133i) q^{5} +(-1.28328 - 2.22271i) q^{6} -0.0341584 q^{7} +6.64036 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.52148 - 7.83143i) q^{10} +(0.731999 + 1.26786i) q^{11} +(-2.29363 - 3.97268i) q^{12} +(0.617902 - 1.07024i) q^{13} -0.0876697 q^{14} +(-1.76168 + 3.05133i) q^{15} +7.86840 q^{16} +(1.48117 + 2.56546i) q^{17} +(-1.28328 + 2.22271i) q^{18} +(-0.941723 - 1.63111i) q^{19} +(-8.08130 - 13.9972i) q^{20} +(0.0170792 + 0.0295820i) q^{21} +(1.87872 + 3.25404i) q^{22} +0.478706 q^{23} +(-3.32018 - 5.75072i) q^{24} +(-3.70707 + 6.42083i) q^{25} +(1.58589 - 2.74684i) q^{26} +1.00000 q^{27} -0.156693 q^{28} +10.0289 q^{29} +(-4.52148 + 7.83143i) q^{30} +(-4.00867 + 6.94322i) q^{31} +6.91405 q^{32} +(0.731999 - 1.26786i) q^{33} +(3.80151 + 6.58441i) q^{34} +(0.0601763 + 0.104228i) q^{35} +(-2.29363 + 3.97268i) q^{36} +(-0.835107 + 1.44645i) q^{37} +(-2.41699 - 4.18635i) q^{38} -1.23580 q^{39} +(-11.6982 - 20.2619i) q^{40} +5.23877 q^{41} +(0.0438349 + 0.0759242i) q^{42} +(-4.18993 + 7.25717i) q^{43} +(3.35787 + 5.81600i) q^{44} +3.52337 q^{45} +1.22863 q^{46} +(3.43991 - 5.95809i) q^{47} +(-3.93420 - 6.81424i) q^{48} -6.99883 q^{49} +(-9.51443 + 16.4795i) q^{50} +(1.48117 - 2.56546i) q^{51} +(2.83448 - 4.90946i) q^{52} +(-5.10688 + 8.84538i) q^{53} +2.56656 q^{54} +(2.57910 - 4.46714i) q^{55} -0.226824 q^{56} +(-0.941723 + 1.63111i) q^{57} +25.7397 q^{58} -3.57175 q^{59} +(-8.08130 + 13.9972i) q^{60} +(6.93994 + 12.0203i) q^{61} +(-10.2885 + 17.8202i) q^{62} +(0.0170792 - 0.0295820i) q^{63} +2.00855 q^{64} -4.35420 q^{65} +(1.87872 - 3.25404i) q^{66} +5.26972 q^{67} +(6.79449 + 11.7684i) q^{68} +(-0.239353 - 0.414571i) q^{69} +(0.154446 + 0.267509i) q^{70} +(4.71288 - 8.16295i) q^{71} +(-3.32018 + 5.75072i) q^{72} +(-8.08545 - 14.0044i) q^{73} +(-2.14336 + 3.71240i) q^{74} +7.41413 q^{75} +(-4.31992 - 7.48232i) q^{76} +(-0.0250039 - 0.0433080i) q^{77} -3.17177 q^{78} -7.05177 q^{79} +(-13.8616 - 24.0091i) q^{80} +(-0.500000 - 0.866025i) q^{81} +13.4456 q^{82} +(0.106900 - 0.185157i) q^{83} +(0.0783466 + 0.135700i) q^{84} +(5.21870 - 9.03905i) q^{85} +(-10.7537 + 18.6260i) q^{86} +(-5.01443 - 8.68525i) q^{87} +(4.86074 + 8.41905i) q^{88} +(-9.20039 - 15.9355i) q^{89} +9.04296 q^{90} +(-0.0211065 + 0.0365576i) q^{91} +2.19595 q^{92} +8.01734 q^{93} +(8.82874 - 15.2918i) q^{94} +(-3.31804 + 5.74701i) q^{95} +(-3.45703 - 5.98774i) q^{96} +(5.60095 - 9.70114i) q^{97} -17.9630 q^{98} -1.46400 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more