LMFDB - Embedded newform 966.2.l.c.47.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(47,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("966.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.6
Character	$\chi$	$=$	966.47
Dual form			966.2.l.c.185.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.319643 - 1.70230i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.224543 - 0.388920i) q^{5} +(-0.574332 + 1.63406i) q^{6} +(2.31951 - 1.27274i) q^{7} -1.00000i q^{8} +(-2.79566 + 1.08826i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.319643 - 1.70230i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.224543 - 0.388920i) q^{5} +(-0.574332 + 1.63406i) q^{6} +(2.31951 - 1.27274i) q^{7} -1.00000i q^{8} +(-2.79566 + 1.08826i) q^{9} +(-0.388920 + 0.224543i) q^{10} +(5.05716 - 2.91975i) q^{11} +(1.31441 - 1.12797i) q^{12} +0.135940i q^{13} +(-2.64513 - 0.0575322i) q^{14} +(-0.733832 - 0.257924i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.567334 - 0.982651i) q^{17} +(2.96524 + 0.455371i) q^{18} +(1.86799 + 1.07849i) q^{19} +0.449086 q^{20} +(-2.90800 - 3.54169i) q^{21} -5.83951 q^{22} +(0.866025 + 0.500000i) q^{23} +(-1.70230 + 0.319643i) q^{24} +(2.39916 + 4.15547i) q^{25} +(0.0679699 - 0.117727i) q^{26} +(2.74615 + 4.41120i) q^{27} +(2.26198 + 1.37239i) q^{28} -0.526964i q^{29} +(0.506555 + 0.590285i) q^{30} +(6.56452 - 3.79003i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-6.58678 - 7.67553i) q^{33} +1.13467i q^{34} +(0.0258369 - 1.18789i) q^{35} +(-2.34029 - 1.87698i) q^{36} +(4.20406 - 7.28165i) q^{37} +(-1.07849 - 1.86799i) q^{38} +(0.231411 - 0.0434522i) q^{39} +(-0.388920 - 0.224543i) q^{40} -2.16148 q^{41} +(0.747558 + 4.52119i) q^{42} -4.04738 q^{43} +(5.05716 + 2.91975i) q^{44} +(-0.204501 + 1.33165i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(0.140116 - 0.242688i) q^{47} +(1.63406 + 0.574332i) q^{48} +(3.76027 - 5.90426i) q^{49} -4.79832i q^{50} +(-1.49142 + 1.27987i) q^{51} +(-0.117727 + 0.0679699i) q^{52} +(-6.98356 + 4.03196i) q^{53} +(-0.172638 - 5.19328i) q^{54} -2.62244i q^{55} +(-1.27274 - 2.31951i) q^{56} +(1.23882 - 3.52462i) q^{57} +(-0.263482 + 0.456364i) q^{58} +(-2.03690 - 3.52802i) q^{59} +(-0.143547 - 0.764479i) q^{60} +(-6.63781 - 3.83234i) q^{61} -7.58006 q^{62} +(-5.09949 + 6.08236i) q^{63} -1.00000 q^{64} +(0.0528697 + 0.0305243i) q^{65} +(1.86656 + 9.94060i) q^{66} +(-1.86762 - 3.23481i) q^{67} +(0.567334 - 0.982651i) q^{68} +(0.574332 - 1.63406i) q^{69} +(-0.616319 + 1.01582i) q^{70} +14.4327i q^{71} +(1.08826 + 2.79566i) q^{72} +(-10.9281 + 6.30935i) q^{73} +(-7.28165 + 4.20406i) q^{74} +(6.30698 - 5.41236i) q^{75} +2.15697i q^{76} +(8.01406 - 13.2088i) q^{77} +(-0.222134 - 0.0780746i) q^{78} +(1.66943 - 2.89155i) q^{79} +(0.224543 + 0.388920i) q^{80} +(6.63140 - 6.08478i) q^{81} +(1.87190 + 1.08074i) q^{82} -4.63784 q^{83} +(1.61319 - 4.28924i) q^{84} -0.509563 q^{85} +(3.50513 + 2.02369i) q^{86} +(-0.897051 + 0.168440i) q^{87} +(-2.91975 - 5.05716i) q^{88} +(0.777291 - 1.34631i) q^{89} +(0.842926 - 1.05099i) q^{90} +(0.173016 + 0.315314i) q^{91} +1.00000i q^{92} +(-8.55007 - 9.96334i) q^{93} +(-0.242688 + 0.140116i) q^{94} +(0.838889 - 0.484333i) q^{95} +(-1.12797 - 1.31441i) q^{96} -0.916942i q^{97} +(-6.20862 + 3.23311i) q^{98} +(-10.9606 + 13.6661i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) $ 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9	$ 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) $ 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^12 - 36 * q^15 - 28 * q^16 + 8 * q^18 - 36 * q^19 + 34 * q^21 + 16 * q^22 - 46 * q^25 + 4 * q^28 - 6 * q^30 - 6 * q^31 + 30 * q^33 - 4 * q^36 - 8 * q^37 + 42 * q^39 - 6 * q^40 + 18 * q^42 + 64 * q^43 - 6 * q^45 - 28 * q^46 - 40 * q^49 - 24 * q^51 - 36 * q^52 - 60 * q^57 - 16 * q^58 - 18 * q^60 + 12 * q^61 + 36 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 34 * q^70 - 8 * q^72 - 102 * q^73 + 18 * q^75 - 16 * q^78 + 24 * q^79 + 54 * q^81 + 12 * q^82 - 4 * q^84 + 128 * q^85 + 102 * q^87 + 8 * q^88 + 68 * q^91 - 32 * q^93 + 6 * q^94 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.319643	−	1.70230i	−0.184546	−	0.982824i
$3$	−0.319643	−	1.70230i	−0.184546	−	0.982824i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.224543	−	0.388920i	0.100419	−	0.173930i	−0.811439	−	0.584438i	$-0.801315\pi$
$5$	0.224543	−	0.388920i	0.100419	−	0.173930i	0.911857	+	0.410508i	$0.134648\pi$
$6$	−0.574332	+	1.63406i	−0.234470	+	0.667101i
$7$	2.31951	−	1.27274i	0.876693	−	0.481050i
$7$	2.31951	−	1.27274i	0.876693	−	0.481050i
$8$		−	1.00000i		−	0.353553i
$9$	−2.79566	+	1.08826i	−0.931886	+	0.362752i
$10$	−0.388920	+	0.224543i	−0.122987	+	0.0710067i
$11$	5.05716	−	2.91975i	1.52479	−	0.880339i	0.525223	−	0.850965i	$-0.323982\pi$
$11$	5.05716	−	2.91975i	1.52479	−	0.880339i	0.999568	−	0.0293737i	$-0.00935130\pi$
$12$	1.31441	−	1.12797i	0.379439	−	0.325617i
$13$			0.135940i			0.0377029i	0.999822	+	0.0188515i	$0.00600096\pi$
$13$			0.135940i			0.0377029i	−0.999822	+	0.0188515i	$0.993999\pi$
$14$	−2.64513	−	0.0575322i	−0.706940	−	0.0153761i
$15$	−0.733832	−	0.257924i	−0.189474	−	0.0665957i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.567334	−	0.982651i	−0.137599	−	0.238328i	0.788988	−	0.614408i	$-0.210605\pi$
$17$	−0.567334	−	0.982651i	−0.137599	−	0.238328i	−0.926587	+	0.376080i	$0.877272\pi$
$18$	2.96524	+	0.455371i	0.698913	+	0.107332i
$19$	1.86799	+	1.07849i	0.428547	+	0.247422i	0.698727	−	0.715388i	$-0.253750\pi$
$19$	1.86799	+	1.07849i	0.428547	+	0.247422i	−0.270180	+	0.962810i	$0.587083\pi$
$20$	0.449086			0.100419
$21$	−2.90800	−	3.54169i	−0.634577	−	0.772859i
$22$	−5.83951			−1.24499
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i
$24$	−1.70230	+	0.319643i	−0.347481	+	0.0652468i
$25$	2.39916	+	4.15547i	0.479832	+	0.831094i
$26$	0.0679699	−	0.117727i	0.0133300	−	0.0230882i
$27$	2.74615	+	4.41120i	0.528497	+	0.848935i
$28$	2.26198	+	1.37239i	0.427474	+	0.259357i
$29$		−	0.526964i		−	0.0978548i	−0.998802	−	0.0489274i	$-0.984420\pi$
$29$		−	0.526964i		−	0.0978548i	0.998802	−	0.0489274i	$-0.0155803\pi$
$30$	0.506555	+	0.590285i	0.0924838	+	0.107771i
$31$	6.56452	−	3.79003i	1.17902	−	0.680710i	0.223235	−	0.974765i	$-0.428338\pi$
$31$	6.56452	−	3.79003i	1.17902	−	0.680710i	0.955788	+	0.294055i	$0.0950049\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−6.58678	−	7.67553i	−1.14661	−	1.33614i
$34$			1.13467i			0.194594i
$35$	0.0258369	−	1.18789i	0.00436723	−	0.200790i
$36$	−2.34029	−	1.87698i	−0.390048	−	0.312830i
$37$	4.20406	−	7.28165i	0.691144	−	1.19710i	−0.280320	−	0.959907i	$-0.590440\pi$
$37$	4.20406	−	7.28165i	0.691144	−	1.19710i	0.971463	−	0.237190i	$-0.0762262\pi$
$38$	−1.07849	−	1.86799i	−0.174954	−	0.303029i
$39$	0.231411	−	0.0434522i	0.0370553	−	0.00695792i
$40$	−0.388920	−	0.224543i	−0.0614936	−	0.0355033i
$41$	−2.16148			−0.337567			−0.168783	−	0.985653i	$-0.553984\pi$
$41$	−2.16148			−0.337567			−0.168783	+	0.985653i	$0.553984\pi$
$42$	0.747558	+	4.52119i	0.115351	+	0.697635i
$43$	−4.04738			−0.617220			−0.308610	−	0.951189i	$-0.599864\pi$
$43$	−4.04738			−0.617220			−0.308610	+	0.951189i	$0.599864\pi$
$44$	5.05716	+	2.91975i	0.762396	+	0.440169i
$45$	−0.204501	+	1.33165i	−0.0304851	+	0.198510i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	0.140116	−	0.242688i	0.0204381	−	0.0353997i	−0.855625	−	0.517595i	$-0.826827\pi$
$47$	0.140116	−	0.242688i	0.0204381	−	0.0353997i	0.876064	+	0.482196i	$0.160161\pi$
$48$	1.63406	+	0.574332i	0.235856	+	0.0828976i
$49$	3.76027	−	5.90426i	0.537182	−	0.843466i
$50$		−	4.79832i		−	0.678585i
$51$	−1.49142	+	1.27987i	−0.208841	+	0.179218i
$52$	−0.117727	+	0.0679699i	−0.0163258	+	0.00942573i
$53$	−6.98356	+	4.03196i	−0.959266	+	0.553832i	−0.895947	−	0.444161i	$-0.853502\pi$
$53$	−6.98356	+	4.03196i	−0.959266	+	0.553832i	−0.0633186	+	0.997993i	$0.520168\pi$
$54$	−0.172638	−	5.19328i	−0.0234931	−	0.706716i
$55$		−	2.62244i		−	0.353609i
$56$	−1.27274	−	2.31951i	−0.170077	−	0.309958i
$57$	1.23882	−	3.52462i	0.164085	−	0.466847i
$58$	−0.263482	+	0.456364i	−0.0345969	+	0.0599236i
$59$	−2.03690	−	3.52802i	−0.265182	−	0.459309i	0.702429	−	0.711753i	$-0.252099\pi$
$59$	−2.03690	−	3.52802i	−0.265182	−	0.459309i	−0.967611	+	0.252445i	$0.918765\pi$
$60$	−0.143547	−	0.764479i	−0.0185318	−	0.0986938i
$61$	−6.63781	−	3.83234i	−0.849885	−	0.490681i	0.0107270	−	0.999942i	$-0.496585\pi$
$61$	−6.63781	−	3.83234i	−0.849885	−	0.490681i	−0.860612	+	0.509261i	$0.829919\pi$
$62$	−7.58006			−0.962669
$63$	−5.09949	+	6.08236i	−0.642476	+	0.766306i
$64$	−1.00000			−0.125000
$65$	0.0528697	+	0.0305243i	0.00655767	+	0.00378608i
$66$	1.86656	+	9.94060i	0.229757	+	1.22360i
$67$	−1.86762	−	3.23481i	−0.228166	−	0.395195i	0.729099	−	0.684408i	$-0.239939\pi$
$67$	−1.86762	−	3.23481i	−0.228166	−	0.395195i	−0.957264	+	0.289214i	$0.906606\pi$
$68$	0.567334	−	0.982651i	0.0687994	−	0.119164i
$69$	0.574332	−	1.63406i	0.0691414	−	0.196717i
$70$	−0.616319	+	1.01582i	−0.0736643	+	0.121414i
$71$			14.4327i			1.71285i	0.516271	+	0.856426i	$0.327320\pi$
$71$			14.4327i			1.71285i	−0.516271	+	0.856426i	$0.672680\pi$
$72$	1.08826	+	2.79566i	0.128252	+	0.329471i
$73$	−10.9281	+	6.30935i	−1.27904	+	0.738453i	−0.976672	−	0.214738i	$-0.931110\pi$
$73$	−10.9281	+	6.30935i	−1.27904	+	0.738453i	−0.302367	+	0.953192i	$0.597777\pi$
$74$	−7.28165	+	4.20406i	−0.846475	+	0.488713i
$75$	6.30698	−	5.41236i	0.728268	−	0.624965i
$76$			2.15697i			0.247422i
$77$	8.01406	−	13.2088i	0.913287	−	1.50529i
$78$	−0.222134	−	0.0780746i	−0.0251517	−	0.00884020i
$79$	1.66943	−	2.89155i	0.187826	−	0.325324i	−0.756699	−	0.653763i	$-0.773189\pi$
$79$	1.66943	−	2.89155i	0.187826	−	0.325324i	0.944525	+	0.328439i	$0.106523\pi$
$80$	0.224543	+	0.388920i	0.0251046	+	0.0434825i
$81$	6.63140	−	6.08478i	0.736822	−	0.676087i
$82$	1.87190	+	1.08074i	0.206716	+	0.119348i
$83$	−4.63784			−0.509069			−0.254534	−	0.967064i	$-0.581922\pi$
$83$	−4.63784			−0.509069			−0.254534	+	0.967064i	$0.581922\pi$
$84$	1.61319	−	4.28924i	0.176014	−	0.467995i
$85$	−0.509563			−0.0552699
$86$	3.50513	+	2.02369i	0.377968	+	0.218220i
$87$	−0.897051	+	0.168440i	−0.0961740	+	0.0180587i
$88$	−2.91975	−	5.05716i	−0.311247	−	0.539095i
$89$	0.777291	−	1.34631i	0.0823927	−	0.142708i	−0.821884	−	0.569654i	$-0.807077\pi$
$89$	0.777291	−	1.34631i	0.0823927	−	0.142708i	0.904277	+	0.426946i	$0.140410\pi$
$90$	0.842926	−	1.05099i	0.0888522	−	0.110784i
$91$	0.173016	+	0.315314i	0.0181370	+	0.0330539i
$92$			1.00000i			0.104257i
$93$	−8.55007	−	9.96334i	−0.886601	−	1.03315i
$94$	−0.242688	+	0.140116i	−0.0250314	+	0.0144519i
$95$	0.838889	−	0.484333i	0.0860682	−	0.0496915i
$96$	−1.12797	−	1.31441i	−0.115123	−	0.134152i
$97$		−	0.916942i		−	0.0931014i	−0.998916	−	0.0465507i	$-0.985177\pi$
$97$		−	0.916942i		−	0.0931014i	0.998916	−	0.0465507i	$-0.0148229\pi$
$98$	−6.20862	+	3.23311i	−0.627166	+	0.326593i
$99$	−10.9606	+	13.6661i	−1.10159	+	1.37350i
$100$	−2.39916	+	4.15547i	−0.239916	+	0.415547i
$101$	−1.04125	−	1.80350i	−0.103608	−	0.179455i	0.809560	−	0.587037i	$-0.199706\pi$
$101$	−1.04125	−	1.80350i	−0.103608	−	0.179455i	−0.913169	+	0.407582i	$0.866372\pi$
$102$	1.93155	−	0.362688i	0.191252	−	0.0359115i
$103$	−15.6122	−	9.01372i	−1.53832	−	0.888148i	−0.998937	−	0.0460866i	$-0.985325\pi$
$103$	−15.6122	−	9.01372i	−1.53832	−	0.888148i	−0.539381	−	0.842062i	$-0.681342\pi$
$104$	0.135940			0.0133300
$105$	−2.03040	+	0.335718i	−0.198147	+	0.0327627i
$106$	8.06392			0.783237
$107$	−5.23243	−	3.02094i	−0.505838	−	0.292046i	0.225283	−	0.974293i	$-0.427669\pi$
$107$	−5.23243	−	3.02094i	−0.505838	−	0.292046i	−0.731121	+	0.682248i	$0.761003\pi$
$108$	−2.44713	+	4.58383i	−0.235475	+	0.441080i
$109$	−0.00325052	−	0.00563007i	−0.000311344	−	0.000539263i	0.865870	−	0.500270i	$-0.166766\pi$
$109$	−0.00325052	−	0.00563007i	−0.000311344	−	0.000539263i	−0.866181	+	0.499730i	$0.833432\pi$
$110$	−1.31122	+	2.27110i	−0.125020	+	0.216541i
$111$	−13.7394	−	4.82905i	−1.30408	−	0.458354i
$112$	−0.0575322	+	2.64513i	−0.00543628	+	0.249941i
$113$			7.71606i			0.725866i	0.931815	+	0.362933i	$0.118225\pi$
$113$			7.71606i			0.725866i	−0.931815	+	0.362933i	$0.881775\pi$
$114$	−2.83516	+	2.43300i	−0.265537	+	0.227871i
$115$	0.388920	−	0.224543i	0.0362669	−	0.0209387i
$116$	0.456364	−	0.263482i	0.0423724	−	0.0244637i
$117$	−0.147937	−	0.380041i	−0.0136768	−	0.0351348i
$118$			4.07380i			0.375024i
$119$	−2.56660	−	1.55720i	−0.235280	−	0.142749i
$120$	−0.257924	+	0.733832i	−0.0235451	+	0.0669894i
$121$	11.5499	−	20.0050i	1.04999	−	1.81864i
$122$	3.83234	+	6.63781i	0.346964	+	0.600960i
$123$	0.690902	+	3.67949i	0.0622965	+	0.331768i
$124$	6.56452	+	3.79003i	0.589512	+	0.340355i
$125$	4.40029			0.393573
$126$	7.45747	−	2.71773i	0.664365	−	0.242115i
$127$	13.1852			1.17000			0.585001	−	0.811033i	$-0.301094\pi$
$127$	13.1852			1.17000			0.585001	+	0.811033i	$0.301094\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	1.29372	+	6.88986i	0.113905	+	0.606618i
$130$	−0.0305243	−	0.0528697i	−0.00267716	−	0.00463698i
$131$	−0.274946	+	0.476220i	−0.0240221	+	0.0416076i	−0.877787	−	0.479052i	$-0.840981\pi$
$131$	−0.274946	+	0.476220i	−0.0240221	+	0.0416076i	0.853764	+	0.520660i	$0.174314\pi$
$132$	3.35381	−	9.54209i	0.291912	−	0.830532i
$133$	5.70547	+	0.124095i	0.494727	+	0.0107604i
$134$			3.73523i			0.322675i
$135$	2.33223	−	0.0775294i	0.200726	−	0.00667267i
$136$	−0.982651	+	0.567334i	−0.0842617	+	0.0486485i
$137$	−7.70631	+	4.44924i	−0.658395	+	0.380124i	−0.791665	−	0.610955i	$-0.790786\pi$
$137$	−7.70631	+	4.44924i	−0.658395	+	0.380124i	0.133270	+	0.991080i	$0.457452\pi$
$138$	−1.31441	+	1.12797i	−0.111890	+	0.0960191i
$139$		−	1.61945i		−	0.137360i	−0.997639	−	0.0686799i	$-0.978121\pi$
$139$		−	1.61945i		−	0.137360i	0.997639	−	0.0686799i	$-0.0218787\pi$
$140$	1.04166	−	0.571569i	0.0880363	−	0.0483064i
$141$	−0.457916	−	0.160946i	−0.0385635	−	0.0135541i
$142$	7.21637	−	12.4991i	0.605584	−	1.04890i
$143$	0.396911	+	0.687470i	0.0331913	+	0.0574891i
$144$	0.455371	−	2.96524i	0.0379476	−	0.247103i
$145$	−0.204947	−	0.118326i	−0.0170199	−	0.00982644i
$146$	12.6187			1.04433
$147$	−11.2528	−	4.51386i	−0.928114	−	0.372297i
$148$	8.40813			0.691144
$149$	12.6506	+	7.30383i	1.03638	+	0.598353i	0.918805	−	0.394711i	$-0.129155\pi$
$149$	12.6506	+	7.30383i	1.03638	+	0.598353i	0.117573	+	0.993064i	$0.462489\pi$
$150$	−8.16819	+	1.53375i	−0.666930	+	0.125230i
$151$	1.61313	+	2.79402i	0.131275	+	0.227374i	0.924168	−	0.381986i	$-0.124760\pi$
$151$	1.61313	+	2.79402i	0.131275	+	0.227374i	−0.792894	+	0.609360i	$0.791426\pi$
$152$	1.07849	−	1.86799i	0.0874768	−	0.151514i
$153$	2.65545	+	2.12975i	0.214680	+	0.172180i
$154$	−13.5448	+	7.43216i	−1.09147	+	0.598901i
$155$		−	3.40410i		−	0.273424i
$156$	0.153336	+	0.178681i	0.0122767	+	0.0143060i
$157$	11.5583	−	6.67317i	0.922450	−	0.532577i	0.0380340	−	0.999276i	$-0.487890\pi$
$157$	11.5583	−	6.67317i	0.922450	−	0.532577i	0.884416	+	0.466700i	$0.154557\pi$
$158$	−2.89155	+	1.66943i	−0.230039	+	0.132813i
$159$	9.09585	+	10.5993i	0.721348	+	0.840582i
$160$		−	0.449086i		−	0.0355033i
$161$	2.64513	+	0.0575322i	0.208465	+	0.00453417i
$162$	−8.78535	+	1.95388i	−0.690242	+	0.153511i
$163$	1.47870	−	2.56118i	0.115821	−	0.200607i	−0.802287	−	0.596939i	$-0.796384\pi$
$163$	1.47870	−	2.56118i	0.115821	−	0.200607i	0.918108	+	0.396331i	$0.129717\pi$
$164$	−1.08074	−	1.87190i	−0.0843916	−	0.146171i
$165$	−4.46418	+	0.838243i	−0.347536	+	0.0652571i
$166$	4.01649	+	2.31892i	0.311740	+	0.179983i
$167$	−15.6005			−1.20720			−0.603600	−	0.797287i	$-0.706268\pi$
$167$	−15.6005			−1.20720			−0.603600	+	0.797287i	$0.706268\pi$
$168$	−3.54169	+	2.90800i	−0.273247	+	0.224357i
$169$	12.9815			0.998578
$170$	0.441295	+	0.254782i	0.0338457	+	0.0195409i
$171$	−6.39594	−	0.982223i	−0.489110	−	0.0751125i
$172$	−2.02369	−	3.50513i	−0.154305	−	0.267264i
$173$	5.16984	−	8.95443i	0.393056	−	0.680793i	−0.599795	−	0.800154i	$-0.704751\pi$
$173$	5.16984	−	8.95443i	0.393056	−	0.680793i	0.992851	+	0.119361i	$0.0380846\pi$
$174$	0.861089	+	0.302652i	0.0652790	+	0.0229440i
$175$	10.8537	+	6.58516i	0.820463	+	0.497791i
$176$			5.83951i			0.440169i
$177$	−5.35466	+	4.59512i	−0.402481	+	0.345391i
$178$	−1.34631	+	0.777291i	−0.100910	+	0.0582605i
$179$	4.14976	−	2.39587i	0.310168	−	0.179075i	−0.336834	−	0.941564i	$-0.609356\pi$
$179$	4.14976	−	2.39587i	0.310168	−	0.179075i	0.647002	+	0.762489i	$0.276023\pi$
$180$	−1.25549	+	0.488720i	−0.0935786	+	0.0364271i
$181$			11.6231i			0.863939i	0.901888	+	0.431970i	$0.142181\pi$
$181$			11.6231i			0.863939i	−0.901888	+	0.431970i	$0.857819\pi$
$182$	0.00782092	−	0.359578i	0.000579725	−	0.0266537i
$183$	−4.40207	+	12.5245i	−0.325411	+	0.925841i
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	−1.88798	−	3.27009i	−0.138807	−	0.240421i
$186$	2.42291	+	12.9035i	0.177656	+	0.946134i
$187$	−5.73820	−	3.31295i	−0.419619	−	0.242267i
$188$	0.280232			0.0204381
$189$	11.9840	+	6.73669i	0.871710	+	0.490022i
$190$	−0.968666			−0.0702744
$191$	21.4802	+	12.4016i	1.55425	+	0.897349i	0.997788	+	0.0664798i	$0.0211768\pi$
$191$	21.4802	+	12.4016i	1.55425	+	0.897349i	0.556467	+	0.830870i	$0.312157\pi$
$192$	0.319643	+	1.70230i	0.0230682	+	0.122853i
$193$	8.47497	+	14.6791i	0.610041	+	1.05662i	0.991233	+	0.132127i	$0.0421806\pi$
$193$	8.47497	+	14.6791i	0.610041	+	1.05662i	−0.381191	+	0.924496i	$0.624486\pi$
$194$	−0.458471	+	0.794095i	−0.0329163	+	0.0570127i
$195$	0.0350622	−	0.0997570i	0.00251085	−	0.00714374i
$196$	6.99338	+	0.304360i	0.499527	+	0.0217400i
$197$		−	12.4591i		−	0.887675i	−0.896107	−	0.443837i	$-0.853617\pi$
$197$		−	12.4591i		−	0.887675i	0.896107	−	0.443837i	$-0.146383\pi$
$198$	16.3253	−	6.35488i	1.16019	−	0.451622i
$199$	−17.7938	+	10.2732i	−1.26137	+	0.728251i	−0.973339	−	0.229371i	$-0.926333\pi$
$199$	−17.7938	+	10.2732i	−1.26137	+	0.728251i	−0.288028	+	0.957622i	$0.593000\pi$
$200$	4.15547	−	2.39916i	0.293836	−	0.169646i
$201$	−4.90964	+	4.21323i	−0.346300	+	0.297178i
$202$			2.08250i			0.146524i
$203$	−0.670687	−	1.22230i	−0.0470730	−	0.0857886i
$204$	−1.85411	−	0.651676i	−0.129814	−	0.0456264i
$205$	−0.485345	+	0.840642i	−0.0338980	+	0.0587130i
$206$	9.01372	+	15.6122i	0.628016	+	1.08776i
$207$	−2.96524	−	0.455371i	−0.206098	−	0.0316505i
$208$	−0.117727	−	0.0679699i	−0.00816292	−	0.00471287i
$209$	12.5957			0.871260
$210$	1.92624	+	0.724461i	0.132923	+	0.0499925i
$211$	−3.66807			−0.252521			−0.126260	−	0.991997i	$-0.540297\pi$
$211$	−3.66807			−0.252521			−0.126260	+	0.991997i	$0.540297\pi$
$212$	−6.98356	−	4.03196i	−0.479633	−	0.276916i
$213$	24.5689	−	4.61332i	1.68343	−	0.316100i
$214$	3.02094	+	5.23243i	0.206507	+	0.357681i
$215$	−0.908810	+	1.57411i	−0.0619803	+	0.107353i
$216$	4.41120	−	2.74615i	0.300144	−	0.186852i
$217$	10.4028	−	17.1459i	0.706187	−	1.16394i
$218$			0.00650105i			0.000440306i
$219$	14.2335	+	16.5862i	0.961811	+	1.12079i
$220$	2.27110	−	1.31122i	0.153117	−	0.0884024i
$221$	0.133581	−	0.0771233i	0.00898566	−	0.00518787i
$222$	9.48411	+	11.0518i	0.636532	+	0.741746i
$223$			6.09157i			0.407922i	0.978979	+	0.203961i	$0.0653816\pi$
$223$			6.09157i			0.407922i	−0.978979	+	0.203961i	$0.934618\pi$
$224$	1.37239	−	2.26198i	0.0916965	−	0.151135i
$225$	−11.2294	−	9.00636i	−0.748630	−	0.600424i
$226$	3.85803	−	6.68231i	0.256632	−	0.444500i
$227$	1.81603	+	3.14545i	0.120534	+	0.208771i	0.919978	−	0.391969i	$-0.128206\pi$
$227$	1.81603	+	3.14545i	0.120534	+	0.208771i	−0.799444	+	0.600740i	$0.794873\pi$
$228$	3.67182	−	0.689461i	0.243172	−	0.0456607i
$229$	17.3509	+	10.0175i	1.14658	+	0.661977i	0.948051	−	0.318118i	$-0.103051\pi$
$229$	17.3509	+	10.0175i	1.14658	+	0.661977i	0.198527	+	0.980095i	$0.436384\pi$
$230$	−0.449086			−0.0296118
$231$	−25.0471	−	9.42024i	−1.64798	−	0.619806i
$232$	−0.526964			−0.0345969
$233$	3.31734	+	1.91527i	0.217326	+	0.125473i	0.604712	−	0.796445i	$-0.293288\pi$
$233$	3.31734	+	1.91527i	0.217326	+	0.125473i	−0.387385	+	0.921918i	$0.626622\pi$
$234$	−0.0619031	+	0.403094i	−0.00404673	+	0.0263511i
$235$	−0.0629242	−	0.108988i	−0.00410472	−	0.00710959i
$236$	2.03690	−	3.52802i	0.132591	−	0.229654i
$237$	−5.45590	−	1.91762i	−0.354399	−	0.124563i
$238$	1.44414	+	2.63188i	0.0936094	+	0.170599i
$239$			19.3126i			1.24923i	0.780933	+	0.624615i	$0.214744\pi$
$239$			19.3126i			1.24923i	−0.780933	+	0.624615i	$0.785256\pi$
$240$	0.590285	−	0.506555i	0.0381027	−	0.0326980i
$241$	5.90863	−	3.41135i	0.380608	−	0.219744i	−0.297475	−	0.954730i	$-0.596144\pi$
$241$	5.90863	−	3.41135i	0.380608	−	0.219744i	0.678083	+	0.734985i	$0.262811\pi$
$242$	−20.0050	+	11.5499i	−1.28597	+	0.742457i
$243$	−12.4778	−	9.34368i	−0.800452	−	0.599397i
$244$		−	7.66469i		−	0.490681i
$245$	−1.45194	−	2.78820i	−0.0927611	−	0.178132i
$246$	1.24141	−	3.53198i	0.0791492	−	0.225191i
$247$	−0.146609	+	0.253935i	−0.00932853	+	0.0161575i
$248$	−3.79003	−	6.56452i	−0.240667	−	0.416848i
$249$	1.48245	+	7.89500i	0.0939466	+	0.500325i
$250$	−3.81076	−	2.20014i	−0.241014	−	0.139149i
$251$	11.3500			0.716404			0.358202	−	0.933644i	$-0.383390\pi$
$251$	11.3500			0.716404			0.358202	+	0.933644i	$0.383390\pi$
$252$	−7.81723	−	1.37511i	−0.492439	−	0.0866238i
$253$	5.83951			0.367127
$254$	−11.4188	−	6.59262i	−0.716477	−	0.413658i
$255$	0.162878	+	0.867430i	0.0101998	+	0.0543206i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.28917	−	10.8932i	0.392307	−	0.679496i	−0.600446	−	0.799665i	$-0.705010\pi$
$257$	6.28917	−	10.8932i	0.392307	−	0.679496i	0.992753	+	0.120169i	$0.0383436\pi$
$258$	2.32454	−	6.61365i	0.144719	−	0.411748i
$259$	0.483738	−	22.2406i	0.0300580	−	1.38196i
$260$			0.0610486i			0.00378608i
$261$	0.573472	+	1.47321i	0.0354970	+	0.0911895i
$262$	0.476220	−	0.274946i	0.0294210	−	0.0169862i
$263$	−22.1973	+	12.8156i	−1.36874	+	0.790245i	−0.990768	−	0.135571i	$-0.956713\pi$
$263$	−22.1973	+	12.8156i	−1.36874	+	0.790245i	−0.377976	+	0.925815i	$0.623380\pi$
$264$	−7.67553	+	6.58678i	−0.472396	+	0.405388i
$265$			3.62139i			0.222460i
$266$	−4.87903	−	2.96020i	−0.299153	−	0.181502i
$267$	−2.54028	−	0.892846i	−0.155462	−	0.0546413i
$268$	1.86762	−	3.23481i	0.114083	−	0.197597i
$269$	−9.98466	−	17.2939i	−0.608776	−	1.05443i	−0.991443	−	0.130544i	$-0.958328\pi$
$269$	−9.98466	−	17.2939i	−0.608776	−	1.05443i	0.382667	−	0.923886i	$-0.375006\pi$
$270$	−2.05853	−	1.09897i	−0.125278	−	0.0668813i
$271$	−12.6706	−	7.31538i	−0.769685	−	0.444378i	0.0630771	−	0.998009i	$-0.479909\pi$
$271$	−12.6706	−	7.31538i	−0.769685	−	0.444378i	−0.832762	+	0.553631i	$0.813242\pi$
$272$	1.13467			0.0687994
$273$	0.481456	−	0.395313i	0.0291391	−	0.0239254i
$274$	8.89849			0.537577
$275$	24.2659	+	14.0099i	1.46329	+	0.844830i
$276$	1.70230	−	0.319643i	0.102466	−	0.0192402i
$277$	11.9043	+	20.6189i	0.715261	+	1.23887i	0.962859	+	0.270005i	$0.0870253\pi$
$277$	11.9043	+	20.6189i	0.715261	+	1.23887i	−0.247598	+	0.968863i	$0.579641\pi$
$278$	−0.809725	+	1.40248i	−0.0485640	+	0.0841154i
$279$	−14.2276	+	17.7395i	−0.851786	+	1.06204i
$280$	−1.18789	−	0.0258369i	−0.0709899	−	0.00154405i
$281$			21.0827i			1.25769i	0.777531	+	0.628845i	$0.216472\pi$
$281$			21.0827i			1.25769i	−0.777531	+	0.628845i	$0.783528\pi$
$282$	0.316094	+	0.368342i	0.0188231	+	0.0219344i
$283$	21.2095	−	12.2453i	1.26077	−	0.727908i	0.287549	−	0.957766i	$-0.407159\pi$
$283$	21.2095	−	12.2453i	1.26077	−	0.727908i	0.973224	+	0.229858i	$0.0738261\pi$
$284$	−12.4991	+	7.21637i	−0.741686	+	0.428213i
$285$	−1.09263	−	1.27323i	−0.0647215	−	0.0754195i
$286$		−	0.793822i		−	0.0469397i
$287$	−5.01358	+	2.75100i	−0.295942	+	0.162386i
$288$	−1.87698	+	2.34029i	−0.110602	+	0.137903i
$289$	7.85626	−	13.6074i	0.462133	−	0.800438i
$290$	0.118326	+	0.204947i	0.00694834	+	0.0120349i
$291$	−1.56091	+	0.293094i	−0.0915023	+	0.0171815i
$292$	−10.9281	−	6.30935i	−0.639519	−	0.369227i
$293$	−19.8630			−1.16041			−0.580205	−	0.814471i	$-0.697027\pi$
$293$	−19.8630			−1.16041			−0.580205	+	0.814471i	$0.697027\pi$
$294$	7.48826	+	9.53551i	0.436724	+	0.556122i
$295$	−1.82949			−0.106517
$296$	−7.28165	−	4.20406i	−0.423237	−	0.244356i
$297$	26.7673	+	14.2900i	1.55320	+	0.829192i
$298$	−7.30383	−	12.6506i	−0.423099	−	0.732830i
$299$	−0.0679699	+	0.117727i	−0.00393080	+	0.00680835i
$300$	7.84073	+	2.75583i	0.452685	+	0.159108i
$301$	−9.38795	+	5.15126i	−0.541112	+	0.296914i
$302$		−	3.22626i		−	0.185650i
$303$	−2.73727	+	2.34900i	−0.157252	+	0.134947i
$304$	−1.86799	+	1.07849i	−0.107137	+	0.0618554i
$305$	−2.98095	+	1.72105i	−0.170689	+	0.0985471i
$306$	−1.23481	−	3.17214i	−0.0705894	−	0.181339i
$307$			28.3403i			1.61746i	0.588178	+	0.808732i	$0.299846\pi$
$307$			28.3403i			1.61746i	−0.588178	+	0.808732i	$0.700154\pi$
$308$	15.4462	+	0.335960i	0.880130	+	0.0191431i
$309$	−10.3537	+	29.4579i	−0.589003	+	1.67580i
$310$	−1.70205	+	2.94803i	−0.0966698	+	0.167437i
$311$	15.3800	+	26.6390i	0.872122	+	1.51056i	0.859797	+	0.510635i	$0.170590\pi$
$311$	15.3800	+	26.6390i	0.872122	+	1.51056i	0.0123245	+	0.999924i	$0.496077\pi$
$312$	−0.0434522	−	0.231411i	−0.00246000	−	0.0131010i
$313$	−9.42434	−	5.44115i	−0.532695	−	0.307552i	0.209418	−	0.977826i	$-0.432843\pi$
$313$	−9.42434	−	5.44115i	−0.532695	−	0.307552i	−0.742113	+	0.670274i	$0.766176\pi$
$314$	−13.3463			−0.753177
$315$	1.22050	+	3.34904i	0.0687671	+	0.188697i
$316$	3.33887			0.187826
$317$	26.0875	+	15.0616i	1.46522	+	0.845946i	0.999245	−	0.0388505i	$-0.0123696\pi$
$317$	26.0875	+	15.0616i	1.46522	+	0.845946i	0.465977	+	0.884797i	$0.345703\pi$
$318$	−2.57757	−	13.7272i	−0.144543	−	0.769784i
$319$	−1.53860	−	2.66494i	−0.0861453	−	0.149208i
$320$	−0.224543	+	0.388920i	−0.0125523	+	0.0217413i
$321$	−3.47005	+	9.87279i	−0.193679	+	0.551045i
$322$	−2.26198	−	1.37239i	−0.126055	−	0.0764801i
$323$		−	2.44745i		−	0.136180i
$324$	8.58527	+	2.70057i	0.476960	+	0.150031i
$325$	−0.564894	+	0.326142i	−0.0313347	+	0.0180911i
$326$	−2.56118	+	1.47870i	−0.141851	+	0.0818976i
$327$	−0.00854507	+	0.00733298i	−0.000472544	+	0.000405515i
$328$			2.16148i			0.119348i
$329$	0.0161224	−	0.741250i	0.000888856	−	0.0408664i
$330$	4.28521	+	1.50615i	0.235893	+	0.0829108i
$331$	−14.9477	+	25.8901i	−0.821597	+	1.42305i	0.0828949	+	0.996558i	$0.473583\pi$
$331$	−14.9477	+	25.8901i	−0.821597	+	1.42305i	−0.904492	+	0.426490i	$0.859750\pi$
$332$	−2.31892	−	4.01649i	−0.127267	−	0.220433i
$333$	−3.82882	+	24.9321i	−0.209818	+	1.36627i
$334$	13.5104	+	7.80023i	0.739256	+	0.426810i
$335$	−1.67744			−0.0916483
$336$	4.52119	−	0.747558i	0.246651	−	0.0407826i
$337$	−22.5450			−1.22810			−0.614051	−	0.789266i	$-0.710461\pi$
$337$	−22.5450			−1.22810			−0.614051	+	0.789266i	$0.710461\pi$
$338$	−11.2423	−	6.49076i	−0.611502	−	0.353051i
$339$	13.1351	−	2.46638i	0.713399	−	0.133956i
$340$	−0.254782	−	0.441295i	−0.0138175	−	0.0239326i
$341$	22.1319	−	38.3336i	1.19851	−	2.07588i
$342$	5.04793	+	4.04860i	0.272961	+	0.218923i
$343$	1.20741	−	18.4809i	0.0651943	−	0.997873i
$344$			4.04738i			0.218220i
$345$	−0.506555	−	0.590285i	−0.0272720	−	0.0317799i
$346$	−8.95443	+	5.16984i	−0.481393	+	0.277932i
$347$	26.1341	−	15.0885i	1.40295	−	0.809996i	0.408259	−	0.912866i	$-0.366136\pi$
$347$	26.1341	−	15.0885i	1.40295	−	0.809996i	0.994695	+	0.102870i	$0.0328027\pi$
$348$	−0.594399	−	0.692649i	−0.0318631	−	0.0371299i
$349$			26.1448i			1.39950i	0.714389	+	0.699749i	$0.246705\pi$
$349$			26.1448i			1.39950i	−0.714389	+	0.699749i	$0.753295\pi$
$350$	−6.10701	−	11.1298i	−0.326433	−	0.594911i
$351$	−0.599657	+	0.373311i	−0.0320073	+	0.0199259i
$352$	2.91975	−	5.05716i	0.155623	−	0.269548i
$353$	−8.21862	−	14.2351i	−0.437433	−	0.757656i	0.560058	−	0.828454i	$-0.310779\pi$
$353$	−8.21862	−	14.2351i	−0.437433	−	0.757656i	−0.997491	+	0.0707972i	$0.977446\pi$
$354$	6.93484	−	1.30216i	0.368582	−	0.0692091i
$355$	5.61317	+	3.24077i	0.297916	+	0.172002i
$356$	1.55458			0.0823927
$357$	−1.83044	+	4.86687i	−0.0968769	+	0.257582i
$358$	−4.79173			−0.253251
$359$	8.03320	+	4.63797i	0.423976	+	0.244783i	0.696777	−	0.717288i	$-0.254617\pi$
$359$	8.03320	+	4.63797i	0.423976	+	0.244783i	−0.272801	+	0.962071i	$0.587950\pi$
$360$	1.33165	+	0.204501i	0.0701839	+	0.0107781i
$361$	−7.17373	−	12.4253i	−0.377565	−	0.653962i
$362$	5.81156	−	10.0659i	0.305449	−	0.529053i
$363$	−37.7464	−	13.2670i	−1.98117	−	0.696335i
$364$	−0.186562	+	0.307493i	−0.00977851	+	0.0161170i
$365$			5.66687i			0.296618i
$366$	10.0746	−	8.64553i	0.526607	−	0.451909i
$367$	−27.8906	+	16.1027i	−1.45588	+	0.840552i	−0.998805	−	0.0488760i	$-0.984436\pi$
$367$	−27.8906	+	16.1027i	−1.45588	+	0.840552i	−0.457075	+	0.889428i	$0.651103\pi$
$368$	−0.866025	+	0.500000i	−0.0451447	+	0.0260643i
$369$	6.04276	−	2.35224i	0.314573	−	0.122453i
$370$			3.77597i			0.196303i
$371$	−11.0668	+	18.2404i	−0.574561	+	0.946996i
$372$	4.35347	−	12.3863i	0.225717	−	0.642197i
$373$	4.46099	−	7.72665i	0.230981	−	0.400071i	−0.727116	−	0.686515i	$-0.759140\pi$
$373$	4.46099	−	7.72665i	0.230981	−	0.400071i	0.958097	+	0.286444i	$0.0924731\pi$
$374$	3.31295	+	5.73820i	0.171309	+	0.296715i
$375$	−1.40652	−	7.49061i	−0.0726323	−	0.386813i
$376$	−0.242688	−	0.140116i	−0.0125157	−	0.00722594i
$377$	0.0716354			0.00368941
$378$	−7.01013	−	11.8262i	−0.360562	−	0.608272i
$379$	−14.9116			−0.765960			−0.382980	−	0.923757i	$-0.625102\pi$
$379$	−14.9116			−0.765960			−0.382980	+	0.923757i	$0.625102\pi$
$380$	0.838889	+	0.484333i	0.0430341	+	0.0248457i
$381$	−4.21457	−	22.4453i	−0.215919	−	1.14991i
$382$	−12.4016	−	21.4802i	−0.634522	−	1.09902i
$383$	12.4146	−	21.5028i	0.634359	−	1.09874i	−0.352292	−	0.935890i	$-0.614597\pi$
$383$	12.4146	−	21.5028i	0.634359	−	1.09874i	0.986651	−	0.162852i	$-0.0520692\pi$
$384$	0.574332	−	1.63406i	0.0293087	−	0.0833876i
$385$	−3.33768	−	6.08278i	−0.170104	−	0.310007i
$386$		−	16.9499i		−	0.862729i
$387$	11.3151	−	4.40459i	0.575178	−	0.223898i
$388$	0.794095	−	0.458471i	0.0403141	−	0.0232753i
$389$	−33.0553	+	19.0845i	−1.67597	+	0.967623i	−0.711787	+	0.702396i	$0.752114\pi$
$389$	−33.0553	+	19.0845i	−1.67597	+	0.967623i	−0.964186	+	0.265228i	$0.914553\pi$
$390$	−0.0802432	+	0.0688610i	−0.00406327	+	0.00348691i
$391$		−	1.13467i		−	0.0573826i
$392$	−5.90426	−	3.76027i	−0.298210	−	0.189922i
$393$	0.898555	+	0.315820i	0.0453261	+	0.0159310i
$394$	−6.22955	+	10.7899i	−0.313840	+	0.543587i
$395$	−0.749719	−	1.29855i	−0.0377225	−	0.0653372i
$396$	−17.3155	−	2.65914i	−0.870138	−	0.133627i
$397$	−20.0932	−	11.6008i	−1.00845	−	0.582229i	−0.0977132	−	0.995215i	$-0.531153\pi$
$397$	−20.0932	−	11.6008i	−1.00845	−	0.582229i	−0.910738	+	0.412985i	$0.864486\pi$
$398$	20.5465			1.02990
$399$	−1.61246	−	9.75209i	−0.0807241	−	0.488215i
$400$	−4.79832			−0.239916
$401$	−26.5444	−	15.3254i	−1.32556	−	0.765314i	−0.340953	−	0.940080i	$-0.610750\pi$
$401$	−26.5444	−	15.3254i	−1.32556	−	0.765314i	−0.984610	+	0.174766i	$0.944083\pi$
$402$	6.35849	−	1.19394i	0.317133	−	0.0595483i
$403$	0.515216	+	0.892381i	0.0256647	+	0.0444526i
$404$	1.04125	−	1.80350i	0.0518042	−	0.0897276i
$405$	−0.877458	−	3.94537i	−0.0436013	−	0.196047i
$406$	−0.0303174	+	1.39389i	−0.00150463	+	0.0691774i
$407$		−	49.0993i		−	2.43376i
$408$	1.27987	+	1.49142i	0.0633630	+	0.0738365i
$409$	30.4410	−	17.5751i	1.50521	−	0.869034i	0.505229	−	0.862986i	$-0.331408\pi$
$409$	30.4410	−	17.5751i	1.50521	−	0.869034i	0.999982	−	0.00604794i	$-0.00192513\pi$
$410$	0.840642	−	0.485345i	0.0415164	−	0.0239695i
$411$	10.0372	+	11.6963i	0.495099	+	0.576936i
$412$		−	18.0274i		−	0.888148i
$413$	−9.21486	−	5.59083i	−0.453434	−	0.275107i
$414$	2.34029	+	1.87698i	0.115019	+	0.0922486i
$415$	−1.04139	+	1.80375i	−0.0511200	+	0.0885424i
$416$	0.0679699	+	0.117727i	0.00333250	+	0.00577206i
$417$	−2.75679	+	0.517645i	−0.135001	+	0.0253492i
$418$	−10.9082	−	6.29783i	−0.533536	−	0.308037i
$419$	37.5996			1.83686			0.918430	−	0.395583i	$-0.129457\pi$
$419$	37.5996			1.83686			0.918430	+	0.395583i	$0.129457\pi$
$420$	−1.30594	−	1.59052i	−0.0637234	−	0.0776094i
$421$	−4.78864			−0.233384			−0.116692	−	0.993168i	$-0.537229\pi$
$421$	−4.78864			−0.233384			−0.116692	+	0.993168i	$0.537229\pi$
$422$	3.17665	+	1.83404i	0.154637	+	0.0892795i
$423$	−0.127610	+	0.830956i	−0.00620460	+	0.0404025i
$424$	4.03196	+	6.98356i	0.195809	+	0.339152i
$425$	2.72225	−	4.71508i	0.132049	−	0.228715i
$426$	−23.5839	−	8.28918i	−1.14264	−	0.401612i
$427$	−20.2741	−	0.440967i	−0.981131	−	0.0213399i
$428$		−	6.04189i		−	0.292046i
$429$	1.04341	−	0.895406i	0.0503763	−	0.0432306i
$430$	1.57411	−	0.908810i	0.0759101	−	0.0438267i
$431$	10.2896	−	5.94069i	0.495631	−	0.286153i	−0.231276	−	0.972888i	$-0.574290\pi$
$431$	10.2896	−	5.94069i	0.495631	−	0.286153i	0.726908	+	0.686735i	$0.240957\pi$
$432$	−5.19328	+	0.172638i	−0.249862	+	0.00830607i
$433$			3.59896i			0.172955i	0.996254	+	0.0864774i	$0.0275611\pi$
$433$			3.59896i			0.172955i	−0.996254	+	0.0864774i	$0.972439\pi$
$434$	−17.5820	+	9.64743i	−0.843965	+	0.463092i
$435$	−0.135917	+	0.386703i	−0.00651671	+	0.0185410i
$436$	0.00325052	−	0.00563007i	0.000155672	−	0.000269632i
$437$	1.07849	+	1.86799i	0.0515910	+	0.0893583i
$438$	−4.03347	−	21.4808i	−0.192727	−	1.02639i
$439$	12.9595	+	7.48214i	0.618521	+	0.357103i	0.776293	−	0.630372i	$-0.217098\pi$
$439$	12.9595	+	7.48214i	0.618521	+	0.357103i	−0.157772	+	0.987476i	$0.550431\pi$
$440$	−2.62244			−0.125020
$441$	−4.08708	+	20.5984i	−0.194623	+	0.980878i
$442$	−0.154247			−0.00733676
$443$	15.8538	+	9.15317i	0.753234	+	0.434880i	0.826861	−	0.562406i	$-0.190124\pi$
$443$	15.8538	+	9.15317i	0.753234	+	0.434880i	−0.0736269	+	0.997286i	$0.523457\pi$
$444$	−2.68760	−	14.3132i	−0.127548	−	0.679273i
$445$	−0.349070	−	0.604608i	−0.0165475	−	0.0286612i
$446$	3.04579	−	5.27546i	0.144222	−	0.249800i
$447$	8.38964	−	23.8698i	0.396816	−	1.12900i
$448$	−2.31951	+	1.27274i	−0.109587	+	0.0601312i
$449$		−	30.9006i		−	1.45829i	−0.684359	−	0.729145i	$-0.739918\pi$
$449$		−	30.9006i		−	1.45829i	0.684359	−	0.729145i	$-0.260082\pi$
$450$	5.22180	+	13.4145i	0.246158	+	0.632364i
$451$	−10.9310	+	6.31099i	−0.514718	+	0.297173i
$452$	−6.68231	+	3.85803i	−0.314309	+	0.181467i
$453$	4.24064	−	3.63912i	0.199243	−	0.170981i
$454$		−	3.63205i		−	0.170461i
$455$	0.161481	+	0.00351226i	0.00757036	+	0.000164657i
$456$	−3.52462	−	1.23882i	−0.165055	−	0.0580130i
$457$	2.03572	−	3.52597i	0.0952271	−	0.164938i	−0.814476	−	0.580197i	$-0.802976\pi$
$457$	2.03572	−	3.52597i	0.0952271	−	0.164938i	0.909703	+	0.415259i	$0.136309\pi$
$458$	−10.0175	−	17.3509i	−0.468089	−	0.810753i
$459$	2.77668	−	5.20113i	0.129604	−	0.242768i
$460$	0.388920	+	0.224543i	0.0181335	+	0.0104694i
$461$	26.9294			1.25423			0.627114	−	0.778928i	$-0.284236\pi$
$461$	26.9294			1.25423			0.627114	+	0.778928i	$0.284236\pi$
$462$	16.9813	+	20.6817i	0.790041	+	0.962200i
$463$	−4.45730			−0.207148			−0.103574	−	0.994622i	$-0.533028\pi$
$463$	−4.45730			−0.207148			−0.103574	+	0.994622i	$0.533028\pi$
$464$	0.456364	+	0.263482i	0.0211862	+	0.0122318i
$465$	−5.79480	+	1.08809i	−0.268727	+	0.0504592i
$466$	−1.91527	−	3.31734i	−0.0887230	−	0.153673i
$467$	18.0633	−	31.2865i	0.835870	−	1.44777i	−0.0574510	−	0.998348i	$-0.518297\pi$
$467$	18.0633	−	31.2865i	0.835870	−	1.44777i	0.893321	−	0.449420i	$-0.148369\pi$
$468$	0.255157	−	0.318138i	0.0117946	−	0.0147059i
$469$	−8.44902	−	5.12619i	−0.390140	−	0.236705i
$470$			0.125848i			0.00580495i
$471$	−15.0543	−	17.5426i	−0.693663	−	0.808321i
$472$	−3.52802	+	2.03690i	−0.162390	+	0.0937560i
$473$	−20.4683	+	11.8174i	−0.941131	+	0.543362i
$474$	3.76614	+	4.38866i	0.172985	+	0.201578i
$475$			10.3499i			0.474884i
$476$	0.0652800	−	3.00134i	0.00299210	−	0.137566i
$477$	15.1358	−	18.8719i	0.693022	−	0.864084i
$478$	9.65631	−	16.7252i	0.441669	−	0.764993i
$479$	−9.73047	−	16.8537i	−0.444596	−	0.770063i	0.553428	−	0.832897i	$-0.313320\pi$
$479$	−9.73047	−	16.8537i	−0.444596	−	0.770063i	−0.998024	+	0.0628338i	$0.979986\pi$
$480$	−0.764479	+	0.143547i	−0.0348935	+	0.00655199i
$481$	0.989867	+	0.571500i	0.0451340	+	0.0260581i
$482$	−6.82270			−0.310765
$483$	−0.747558	−	4.52119i	−0.0340151	−	0.205721i
$484$	23.0998			1.04999
$485$	−0.356617	−	0.205893i	−0.0161931	−	0.00934911i
$486$	6.13426	+	14.3308i	0.278256	+	0.650057i
$487$	1.17332	+	2.03224i	0.0531680	+	0.0920897i	0.891384	−	0.453248i	$-0.149735\pi$
$487$	1.17332	+	2.03224i	0.0531680	+	0.0920897i	−0.838216	+	0.545338i	$0.816401\pi$
$488$	−3.83234	+	6.63781i	−0.173482	+	0.300480i
$489$	−4.83256	−	1.69853i	−0.218536	−	0.0768101i
$490$	−0.136684	+	3.14063i	−0.00617474	+	0.141879i
$491$			41.1097i			1.85526i	0.373504	+	0.927628i	$0.378156\pi$
$491$			41.1097i			1.85526i	−0.373504	+	0.927628i	$0.621844\pi$
$492$	−2.84108	+	2.43808i	−0.128086	+	0.109917i
$493$	−0.517822	+	0.298965i	−0.0233215	+	0.0134647i
$494$	0.253935	−	0.146609i	0.0114251	−	0.00659626i
$495$	2.85388	+	7.33144i	0.128273	+	0.329524i
$496$			7.58006i			0.340355i
$497$	18.3691	+	33.4769i	0.823967	+	1.50164i
$498$	2.66366	−	7.57849i	0.119361	−	0.339600i
$499$	−20.3993	+	35.3327i	−0.913199	+	1.58171i	−0.103682	+	0.994611i	$0.533062\pi$
$499$	−20.3993	+	35.3327i	−0.913199	+	1.58171i	−0.809517	+	0.587096i	$0.800271\pi$
$500$	2.20014	+	3.81076i	0.0983934	+	0.170422i
$501$	4.98657	+	26.5567i	0.222784	+	1.18646i
$502$	−9.82936	−	5.67499i	−0.438706	−	0.253287i
$503$	−8.40003			−0.374539			−0.187269	−	0.982309i	$-0.559964\pi$
$503$	−8.40003			−0.374539			−0.187269	+	0.982309i	$0.559964\pi$
$504$	6.08236	+	5.09949i	0.270930	+	0.227150i
$505$	−0.935223			−0.0416169
$506$	−5.05716	−	2.91975i	−0.224818	−	0.129799i
$507$	−4.14945	−	22.0985i	−0.184283	−	0.981427i
$508$	6.59262	+	11.4188i	0.292500	+	0.506625i
$509$	−2.10840	+	3.65186i	−0.0934534	+	0.161866i	−0.908962	−	0.416879i	$-0.863124\pi$
$509$	−2.10840	+	3.65186i	−0.0934534	+	0.161866i	0.815509	+	0.578745i	$0.196457\pi$
$510$	0.292658	−	0.832655i	0.0129591	−	0.0368706i
$511$	−17.3177	+	28.5432i	−0.766091	+	1.26268i
$512$			1.00000i			0.0441942i
$513$	0.372377	+	11.2018i	0.0164408	+	0.494570i
$514$	−10.8932	+	6.28917i	−0.480476	+	0.277403i
$515$	−7.01123	+	4.04793i	−0.308952	+	0.178373i
$516$	−5.31994	+	4.56532i	−0.234197	+	0.200977i
$517$		−	1.63642i		−	0.0719696i
$518$	−11.5392	+	19.0190i	−0.507004	+	0.835648i
$519$	−16.8956	−	5.93841i	−0.741636	−	0.260667i
$520$	0.0305243	−	0.0528697i	0.00133858	−	0.00231849i
$521$	−15.1764	−	26.2863i	−0.664891	−	1.15162i	−0.979315	−	0.202342i	$-0.935145\pi$
$521$	−15.1764	−	26.2863i	−0.664891	−	1.15162i	0.314424	−	0.949283i	$-0.398189\pi$
$522$	0.239964	−	1.56257i	0.0105029	−	0.0683920i
$523$	2.15879	+	1.24638i	0.0943973	+	0.0545003i	0.546456	−	0.837488i	$-0.315977\pi$
$523$	2.15879	+	1.24638i	0.0943973	+	0.0545003i	−0.452058	+	0.891988i	$0.649310\pi$
$524$	−0.549892			−0.0240221
$525$	7.74061	−	20.5812i	0.337828	−	0.898236i
$526$	25.6312			1.11757
$527$	−7.44856	−	4.30043i	−0.324464	−	0.187330i
$528$	9.94060	−	1.86656i	0.432609	−	0.0812314i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	1.81069	−	3.13622i	0.0786516	−	0.136228i
$531$	9.53386	+	7.64645i	0.413734	+	0.331828i
$532$	2.74526	+	5.00313i	0.119022	+	0.216913i
$533$		−	0.293831i		−	0.0127272i
$534$	1.75352	+	2.04337i	0.0758823	+	0.0884251i
$535$	−2.34981	+	1.35666i	−0.101591	+	0.0586536i
$536$	−3.23481	+	1.86762i	−0.139722	+	0.0806687i
$537$	−5.40492	−	6.29832i	−0.233240	−	0.271793i
$538$			19.9693i			0.860939i
$539$	1.77731	−	40.8379i	0.0765542	−	1.75901i
$540$	1.23326	+	1.98100i	0.0530709	+	0.0852489i
$541$	−2.75316	+	4.76861i	−0.118368	+	0.205019i	−0.919121	−	0.393976i	$-0.871099\pi$
$541$	−2.75316	+	4.76861i	−0.118368	+	0.205019i	0.800753	+	0.598994i	$0.204433\pi$
$542$	7.31538	+	12.6706i	0.314223	+	0.544250i
$543$	19.7860	−	3.71524i	0.849100	−	0.159436i
$544$	−0.982651	−	0.567334i	−0.0421308	−	0.0243242i
$545$	−0.00291953			−0.000125059
$546$	−0.614610	+	0.101623i	−0.0263029	+	0.00434906i
$547$	−10.5601			−0.451515			−0.225758	−	0.974184i	$-0.572486\pi$
$547$	−10.5601			−0.451515			−0.225758	+	0.974184i	$0.572486\pi$
$548$	−7.70631	−	4.44924i	−0.329197	−	0.190062i
$549$	22.7276	+	3.49028i	0.969991	+	0.148961i
$550$	−14.0099	−	24.2659i	−0.597385	−	1.03470i
$551$	0.568324	−	0.984366i	0.0242114	−	0.0419354i
$552$	−1.63406	−	0.574332i	−0.0695501	−	0.0244452i
$553$	0.192093	−	8.83173i	0.00816861	−	0.375563i
$554$		−	23.8086i		−	1.01153i
$555$	−4.96319	+	4.25918i	−0.210676	+	0.180792i
$556$	1.40248	−	0.809725i	0.0594786	−	0.0343400i
$557$	7.07439	−	4.08440i	0.299751	−	0.173062i	−0.342580	−	0.939489i	$-0.611301\pi$
$557$	7.07439	−	4.08440i	0.299751	−	0.173062i	0.642331	+	0.766427i	$0.277967\pi$
$558$	21.1912	−	8.24905i	0.897097	−	0.349210i
$559$		−	0.550200i		−	0.0232710i
$560$	1.01582	+	0.616319i	0.0429263	+	0.0260442i
$561$	−3.80546	+	10.8271i	−0.160667	+	0.457121i
$562$	10.5414	−	18.2582i	0.444661	−	0.770175i
$563$	5.33908	+	9.24756i	0.225015	+	0.389738i	0.956324	−	0.292308i	$-0.0944234\pi$
$563$	5.33908	+	9.24756i	0.225015	+	0.389738i	−0.731309	+	0.682047i	$0.761090\pi$
$564$	−0.0895743	−	0.477040i	−0.00377176	−	0.0200870i
$565$	3.00093	+	1.73259i	0.126250	+	0.0728905i
$566$	−24.4906			−1.02942
$567$	7.63727	−	22.5538i	0.320735	−	0.947169i
$568$	14.4327			0.605584
$569$	−15.4740	−	8.93390i	−0.648702	−	0.374529i	0.139256	−	0.990256i	$-0.455529\pi$
$569$	−15.4740	−	8.93390i	−0.648702	−	0.374529i	−0.787959	+	0.615728i	$0.788862\pi$
$570$	0.309627	+	1.64896i	0.0129688	+	0.0690674i
$571$	−21.6291	−	37.4627i	−0.905149	−	1.56776i	−0.820718	−	0.571334i	$-0.806426\pi$
$571$	−21.6291	−	37.4627i	−0.905149	−	1.56776i	−0.0844308	−	0.996429i	$-0.526907\pi$
$572$	−0.396911	+	0.687470i	−0.0165957	+	0.0287445i
$573$	14.2453	−	40.5299i	0.595105	−	1.69316i
$574$	5.71739	+	0.124355i	0.238639	+	0.00519047i
$575$			4.79832i			0.200104i
$576$	2.79566	−	1.08826i	0.116486	−	0.0453440i
$577$	−10.2994	+	5.94633i	−0.428768	+	0.247549i	−0.698821	−	0.715296i	$-0.746292\pi$
$577$	−10.2994	+	5.94633i	−0.428768	+	0.247549i	0.270054	+	0.962845i	$0.412958\pi$
$578$	−13.6074	+	7.85626i	−0.565995	+	0.326778i
$579$	22.2792	−	19.1190i	0.925894	−	0.794559i
$580$		−	0.236652i		−	0.00982644i
$581$	−10.7575	+	5.90276i	−0.446297	+	0.244888i
$582$	1.49834	+	0.526629i	0.0621080	+	0.0218295i
$583$	−23.5446	+	40.7805i	−0.975120	+	1.68896i
$584$	6.30935	+	10.9281i	0.261083	+	0.452208i
$585$	−0.181024	−	0.0277998i	−0.00748441	−	0.00114938i
$586$	17.2019	+	9.93150i	0.710603	+	0.410267i
$587$	8.19977			0.338441			0.169220	−	0.985578i	$-0.445875\pi$
$587$	8.19977			0.338441			0.169220	+	0.985578i	$0.445875\pi$
$588$	−1.71727	−	12.0021i	−0.0708191	−	0.494959i
$589$	16.3500			0.673689
$590$	1.58438	+	0.914743i	0.0652279	+	0.0376594i
$591$	−21.2091	+	3.98246i	−0.872428	+	0.163817i
$592$	4.20406	+	7.28165i	0.172786	+	0.299274i
$593$	−10.3523	+	17.9307i	−0.425117	+	0.736325i	−0.996431	−	0.0844066i	$-0.973101\pi$
$593$	−10.3523	+	17.9307i	−0.425117	+	0.736325i	0.571314	+	0.820732i	$0.306434\pi$
$594$	−16.0362	−	25.7592i	−0.657972	−	1.05691i
$595$	−1.18194	+	0.648541i	−0.0484547	+	0.0265876i
$596$			14.6077i			0.598353i
$597$	23.1758	+	27.0066i	0.948522	+	1.10531i
$598$	0.117727	−	0.0679699i	0.00481423	−	0.00277950i
$599$	−19.4402	+	11.2238i	−0.794305	+	0.458592i	−0.841476	−	0.540295i	$-0.818313\pi$
$599$	−19.4402	+	11.2238i	−0.794305	+	0.458592i	0.0471709	+	0.998887i	$0.484979\pi$
$600$	−5.41236	−	6.30698i	−0.220959	−	0.257482i
$601$			29.1770i			1.19016i	0.803668	+	0.595078i	$0.202879\pi$
$601$			29.1770i			1.19016i	−0.803668	+	0.595078i	$0.797121\pi$
$602$	10.7058	+	0.232855i	0.436337	+	0.00949045i
$603$	8.74151	+	7.01096i	0.355982	+	0.285509i
$604$	−1.61313	+	2.79402i	−0.0656373	+	0.113687i
$605$	−5.18690	−	8.98397i	−0.210877	−	0.365250i
$606$	3.54505	−	0.665657i	0.144008	−	0.0270405i
$607$	−28.2734	−	16.3236i	−1.14758	−	0.662556i	−0.199284	−	0.979942i	$-0.563862\pi$
$607$	−28.2734	−	16.3236i	−1.14758	−	0.662556i	−0.948297	+	0.317386i	$0.897195\pi$
$608$	2.15697			0.0874768
$609$	−1.86634	+	1.53241i	−0.0756280	+	0.0620964i
$610$	3.44210			0.139367
$611$	0.0329910	+	0.0190474i	0.00133467	+	0.000770575i
$612$	−0.516695	+	3.36456i	−0.0208862	+	0.136004i
$613$	9.74991	+	16.8873i	0.393795	+	0.682073i	0.992947	−	0.118563i	$-0.0378286\pi$
$613$	9.74991	+	16.8873i	0.393795	+	0.682073i	−0.599152	+	0.800636i	$0.704495\pi$
$614$	14.1701	−	24.5434i	0.571860	−	0.990490i
$615$	1.58616	+	0.557498i	0.0639603	+	0.0224805i
$616$	−13.2088	−	8.01406i	−0.532200	−	0.322896i
$617$			9.27025i			0.373206i	0.982435	+	0.186603i	$0.0597479\pi$
$617$			9.27025i			0.373206i	−0.982435	+	0.186603i	$0.940252\pi$
$618$	23.6955	−	20.3344i	0.953174	−	0.817970i
$619$	32.0760	−	18.5191i	1.28924	−	0.744344i	0.310723	−	0.950500i	$-0.399429\pi$
$619$	32.0760	−	18.5191i	1.28924	−	0.744344i	0.978519	+	0.206156i	$0.0660955\pi$
$620$	2.94803	−	1.70205i	0.118396	−	0.0683559i
$621$	0.172638	+	5.19328i	0.00692774	+	0.208399i
$622$		−	30.7601i		−	1.23337i
$623$	0.0894386	−	4.11207i	0.00358328	−	0.164746i
$624$	−0.0780746	+	0.222134i	−0.00312548	+	0.00889246i
$625$	−11.0078	+	19.0660i	−0.440310	+	0.762639i
$626$	5.44115	+	9.42434i	0.217472	+	0.376672i
$627$	−4.02611	−	21.4416i	−0.160787	−	0.856295i
$628$	11.5583	+	6.67317i	0.461225	+	0.266288i
$629$	−9.54043			−0.380402
$630$	0.617542	−	3.51061i	0.0246035	−	0.139866i
$631$	31.4919			1.25367			0.626836	−	0.779152i	$-0.284350\pi$
$631$	31.4919			1.25367			0.626836	+	0.779152i	$0.284350\pi$
$632$	−2.89155	−	1.66943i	−0.115019	−	0.0664065i
$633$	1.17247	+	6.24417i	0.0466016	+	0.248183i
$634$	−15.0616	−	26.0875i	−0.598174	−	1.03607i
$635$	2.96065	−	5.12800i	0.117490	−	0.203498i
$636$	−4.63136	+	13.1769i	−0.183646	+	0.522498i
$637$	0.802625	+	0.511171i	0.0318012	+	0.0202533i
$638$			3.07721i			0.121828i
$639$	−15.7065	−	40.3490i	−0.621340	−	1.59618i
$640$	0.388920	−	0.224543i	0.0153734	−	0.00887583i
$641$	9.94529	−	5.74191i	0.392815	−	0.226792i	−0.290564	−	0.956856i	$-0.593843\pi$
$641$	9.94529	−	5.74191i	0.392815	−	0.226792i	0.683379	+	0.730064i	$0.260510\pi$
$642$	7.94154	−	6.81506i	0.313428	−	0.268969i
$643$			2.48514i			0.0980044i	0.998799	+	0.0490022i	$0.0156041\pi$
$643$			2.48514i			0.0980044i	−0.998799	+	0.0490022i	$0.984396\pi$
$644$	1.27274	+	2.31951i	0.0501529	+	0.0914016i
$645$	2.97010	+	1.04392i	0.116947	+	0.0411042i
$646$	−1.22372	+	2.11955i	−0.0481468	+	0.0833927i
$647$	5.90973	+	10.2360i	0.232335	+	0.402417i	0.958495	−	0.285109i	$-0.0920300\pi$
$647$	5.90973	+	10.2360i	0.232335	+	0.402417i	−0.726160	+	0.687526i	$0.758697\pi$
$648$	−6.08478	−	6.63140i	−0.239033	−	0.260506i
$649$	−20.6019	−	11.8945i	−0.808694	−	0.466900i
$650$	0.652283			0.0255847
$651$	−32.5127	−	12.2281i	−1.27427	−	0.479256i
$652$	2.95740			0.115821
$653$	8.40410	+	4.85211i	0.328878	+	0.189878i	0.655343	−	0.755332i	$-0.272524\pi$
$653$	8.40410	+	4.85211i	0.328878	+	0.189878i	−0.326465	+	0.945209i	$0.605857\pi$
$654$	0.0110667	−	0.00207801i	0.000432744	−	8.12567e-5i
$655$	0.123474	+	0.213864i	0.00482454	+	0.00835635i
$656$	1.08074	−	1.87190i	0.0421958	−	0.0730853i
$657$	23.6851	−	29.5314i	0.924042	−	1.15213i
$658$	−0.384587	+	0.633880i	−0.0149928	+	0.0247112i
$659$			14.8509i			0.578509i	0.957252	+	0.289255i	$0.0934074\pi$
$659$			14.8509i			0.578509i	−0.957252	+	0.289255i	$0.906593\pi$
$660$	−2.95803	−	3.44697i	−0.115141	−	0.134173i
$661$	−25.8839	+	14.9441i	−1.00677	+	0.581257i	−0.910244	−	0.414073i	$-0.864106\pi$
$661$	−25.8839	+	14.9441i	−1.00677	+	0.581257i	−0.0965238	+	0.995331i	$0.530772\pi$
$662$	25.8901	−	14.9477i	1.00625	−	0.580957i
$663$	−0.173985	−	0.202744i	−0.00675703	−	0.00787392i
$664$			4.63784i			0.179983i
$665$	1.32938	−	2.19110i	0.0515513	−	0.0849673i
$666$	15.7819	−	19.6774i	0.611536	−	0.762485i
$667$	0.263482	−	0.456364i	0.0102021	−	0.0176705i
$668$	−7.80023	−	13.5104i	−0.301800	−	0.522733i
$669$	10.3697	−	1.94713i	0.400915	−	0.0752803i
$670$	1.45271	+	0.838720i	0.0561229	+	0.0324026i
$671$	−44.7580			−1.72786
$672$	−4.28924	−	1.61319i	−0.165461	−	0.0622302i
$673$	30.2594			1.16641			0.583207	−	0.812324i	$-0.301798\pi$
$673$	30.2594			1.16641			0.583207	+	0.812324i	$0.301798\pi$
$674$	19.5245	+	11.2725i	0.752056	+	0.434200i
$675$	−11.7421	+	21.9947i	−0.451955	+	0.846577i
$676$	6.49076	+	11.2423i	0.249645	+	0.432397i
$677$	6.58769	−	11.4102i	0.253185	−	0.438530i	−0.711216	−	0.702974i	$-0.751855\pi$
$677$	6.58769	−	11.4102i	0.253185	−	0.438530i	0.964401	+	0.264444i	$0.0851884\pi$
$678$	−12.6085	−	4.43158i	−0.484226	−	0.170194i
$679$	−1.16703	−	2.12686i	−0.0447864	−	0.0816213i
$680$			0.509563i			0.0195409i
$681$	4.77403	−	4.09685i	0.182941	−	0.156991i
$682$	−38.3336	+	22.1319i	−1.46787	+	0.847474i
$683$	−8.15691	+	4.70939i	−0.312115	+	0.180200i	−0.647873	−	0.761749i	$-0.724341\pi$
$683$	−8.15691	+	4.70939i	−0.312115	+	0.180200i	0.335757	+	0.941949i	$0.391008\pi$
$684$	−2.34734	−	6.03016i	−0.0897528	−	0.230569i
$685$			3.99618i			0.152686i
$686$	−10.2861	+	15.4012i	−0.392724	+	0.588020i
$687$	11.5068	−	32.7384i	0.439011	−	1.24905i
$688$	2.02369	−	3.50513i	0.0771525	−	0.133632i
$689$	−0.548104	−	0.949344i	−0.0208811	−	0.0361671i
$690$	0.143547	+	0.764479i	0.00546474	+	0.0291032i
$691$	−23.4166	−	13.5196i	−0.890809	−	0.514309i	−0.0166017	−	0.999862i	$-0.505285\pi$
$691$	−23.4166	−	13.5196i	−0.890809	−	0.514309i	−0.874207	+	0.485554i	$0.838618\pi$
$692$	10.3397			0.393056
$693$	−8.02996	+	45.6488i	−0.305033	+	1.73405i
$694$	−30.1771			−1.14551
$695$	−0.629835	−	0.363636i	−0.0238910	−	0.0137935i
$696$	0.168440	+	0.897051i	0.00638471	+	0.0340026i
$697$	1.22628	+	2.12398i	0.0464487	+	0.0804515i
$698$	13.0724	−	22.6420i	0.494797	−	0.857013i
$699$	2.20000	−	6.25931i	0.0832115	−	0.236749i
$700$	−0.276058	+	12.6922i	−0.0104340	+	0.479719i
$701$		−	31.5488i		−	1.19158i	−0.803139	−	0.595792i	$-0.796838\pi$
$701$		−	31.5488i		−	1.19158i	0.803139	−	0.595792i	$-0.203162\pi$
$702$	0.705974	−	0.0234684i	0.0266453	−	0.000885759i
$703$	15.7063	−	9.06805i	0.592375	−	0.342008i
$704$	−5.05716	+	2.91975i	−0.190599	+	0.110042i
$705$	−0.165417	+	0.141953i	−0.00622996	+	0.00534626i
$706$			16.4372i			0.618624i
$707$	−4.71058	−	2.85800i	−0.177160	−	0.107486i
$708$	−6.65683	−	2.33971i	−0.250179	−	0.0879318i
$709$	−9.50528	+	16.4636i	−0.356978	+	0.618304i	−0.987454	−	0.157904i	$-0.949526\pi$
$709$	−9.50528	+	16.4636i	−0.356978	+	0.618304i	0.630476	+	0.776209i	$0.282860\pi$
$710$	−3.24077	−	5.61317i	−0.121624	−	0.210659i
$711$	−1.52042	+	9.90054i	−0.0570204	+	0.371299i
$712$	−1.34631	−	0.777291i	−0.0504550	−	0.0291302i
$713$	7.58006			0.283875
$714$	4.01864	−	3.29961i	0.150394	−	0.123485i
$715$	0.356494			0.0133321
$716$	4.14976	+	2.39587i	0.155084	+	0.0895377i
$717$	32.8759	−	6.17314i	1.22777	−	0.230540i
$718$	−4.63797	−	8.03320i	−0.173088	−	0.299796i
$719$	−15.9134	+	27.5629i	−0.593472	+	1.02792i	0.400289	+	0.916389i	$0.368910\pi$
$719$	−15.9134	+	27.5629i	−0.593472	+	1.02792i	−0.993761	+	0.111534i	$0.964424\pi$
$720$	−1.05099	−	0.842926i	−0.0391680	−	0.0314140i
$721$	−47.6849	−	1.03716i	−1.77588	−	0.0386258i
$722$			14.3475i			0.533957i
$723$	−7.69579	−	8.96785i	−0.286210	−	0.333518i
$724$	−10.0659	+	5.81156i	−0.374097	+	0.215985i
$725$	2.18978	−	1.26427i	0.0813265	−	0.0469539i
$726$	26.0559	+	30.3627i	0.967025	+	1.12687i
$727$			51.0731i			1.89420i	0.320944	+	0.947098i	$0.396000\pi$
$727$			51.0731i			1.89420i	−0.320944	+	0.947098i	$0.604000\pi$
$728$	0.315314	−	0.173016i	0.0116863	−	0.00641240i
$729$	−11.9173	+	24.2276i	−0.441382	+	0.897319i
$730$	2.83344	−	4.90766i	0.104870	−	0.181641i
$731$	2.29622	+	3.97716i	0.0849286	+	0.147101i
$732$	−13.0476	+	2.44996i	−0.482253	+	0.0905532i
$733$	−21.1556	−	12.2142i	−0.781400	−	0.451142i	0.0555262	−	0.998457i	$-0.482316\pi$
$733$	−21.1556	−	12.2142i	−0.781400	−	0.451142i	−0.836926	+	0.547316i	$0.815650\pi$
$734$	32.2053			1.18872
$735$	−4.28226	+	3.36287i	−0.157954	+	0.124041i
$736$	1.00000			0.0368605
$737$	−18.8897	−	10.9060i	−0.695810	−	0.401726i
$738$	−6.40930	−	0.984275i	−0.235930	−	0.0362317i
$739$	9.01089	+	15.6073i	0.331471	+	0.574124i	0.982800	−	0.184671i	$-0.0591218\pi$
$739$	9.01089	+	15.6073i	0.331471	+	0.574124i	−0.651330	+	0.758795i	$0.725788\pi$
$740$	1.88798	−	3.27009i	0.0694037	−	0.120211i
$741$	0.479136	+	0.168405i	0.0176015	+	0.00618650i
$742$	18.7044	−	10.2633i	0.686659	−	0.376776i
$743$			3.95737i			0.145182i	0.997362	+	0.0725908i	$0.0231267\pi$
$743$			3.95737i			0.145182i	−0.997362	+	0.0725908i	$0.976873\pi$
$744$	−9.96334	+	8.55007i	−0.365274	+	0.313461i
$745$	5.68120	−	3.28004i	0.208143	−	0.120172i
$746$	−7.72665	+	4.46099i	−0.282893	+	0.163328i
$747$	12.9658	−	5.04716i	0.474394	−	0.184666i
$748$		−	6.62590i		−	0.242267i
$749$	−15.9815	−	0.347603i	−0.583953	−	0.0127011i
$750$	−2.52722	+	7.19032i	−0.0922812	+	0.262553i
$751$	−8.82071	+	15.2779i	−0.321872	+	0.557499i	−0.980874	−	0.194642i	$-0.937645\pi$
$751$	−8.82071	+	15.2779i	−0.321872	+	0.557499i	0.659002	+	0.752141i	$0.270979\pi$
$752$	0.140116	+	0.242688i	0.00510951	+	0.00884994i
$753$	−3.62794	−	19.3211i	−0.132209	−	0.704099i
$754$	−0.0620381	−	0.0358177i	−0.00225929	−	0.00130440i
$755$	1.44887			0.0527297
$756$	0.157869	+	13.7468i	0.00574165	+	0.499967i
$757$	32.8802			1.19505			0.597526	−	0.801850i	$-0.296151\pi$
$757$	32.8802			1.19505			0.597526	+	0.801850i	$0.296151\pi$
$758$	12.9139	+	7.45582i	0.469053	+	0.270808i
$759$	−1.86656	−	9.94060i	−0.0677517	−	0.360821i
$760$	−0.484333	−	0.838889i	−0.0175686	−	0.0304297i
$761$	−22.0958	+	38.2710i	−0.800972	+	1.38732i	0.118005	+	0.993013i	$0.462350\pi$
$761$	−22.0958	+	38.2710i	−0.800972	+	1.38732i	−0.918977	+	0.394311i	$0.870983\pi$
$762$	−7.57270	+	21.5454i	−0.274330	+	0.780509i
$763$	−0.0147052	−	0.00892195i	−0.000532365	−	0.000322996i
$764$			24.8032i			0.897349i
$765$	1.42456	−	0.554535i	0.0515052	−	0.0200493i
$766$	−21.5028	+	12.4146i	−0.776928	+	0.448559i
$767$	0.479598	−	0.276896i	0.0173173	−	0.00999814i
$768$	−1.31441	+	1.12797i	−0.0474298	+	0.0407021i
$769$		−	42.7778i		−	1.54261i	−0.636467	−	0.771304i	$-0.719605\pi$
$769$		−	42.7778i		−	1.54261i	0.636467	−	0.771304i	$-0.280395\pi$
$770$	−0.150875	+	6.93668i	−0.00543715	+	0.249981i
$771$	−20.5537	−	7.22414i	−0.740224	−	0.260171i
$772$	−8.47497	+	14.6791i	−0.305021	+	0.528311i
$773$	1.38682	+	2.40204i	0.0498805	+	0.0863955i	0.889888	−	0.456180i	$-0.150783\pi$
$773$	1.38682	+	2.40204i	0.0498805	+	0.0863955i	−0.840007	+	0.542575i	$0.817449\pi$
$774$	−12.0014	−	1.84306i	−0.431383	−	0.0662474i
$775$	31.4987	+	18.1858i	1.13147	+	0.653253i
$776$	−0.916942			−0.0329163
$777$	−38.0147	+	6.28556i	−1.36377	+	0.225493i
$778$	38.1690			1.36843
$779$	−4.03763	−	2.33113i	−0.144663	−	0.0835213i
$780$	0.103923	−	0.0195138i	0.00372105	−	0.000698704i
$781$	42.1400	+	72.9887i	1.50789	+	2.61174i
$782$	−0.567334	+	0.982651i	−0.0202878	+	0.0351395i
$783$	2.32454	−	1.44712i	0.0830724	−	0.0517160i
$784$	3.23311	+	6.20862i	0.115468	+	0.221737i
$785$		−	5.99365i		−	0.213922i
$786$	−0.620261	−	0.722786i	−0.0221240	−	0.0257809i
$787$	11.6746	−	6.74036i	0.416156	−	0.240268i	−0.277275	−	0.960790i	$-0.589431\pi$
$787$	11.6746	−	6.74036i	0.416156	−	0.240268i	0.693431	+	0.720523i	$0.256098\pi$
$788$	10.7899	−	6.22955i	0.384374	−	0.221919i
$789$	28.9112	+	33.6901i	1.02927	+	1.19940i
$790$			1.49944i			0.0533476i
$791$	9.82053	+	17.8975i	0.349178	+	0.636362i
$792$	13.6661	+	10.9606i	0.485604	+	0.389470i
$793$	0.520968	−	0.902344i	0.0185001	−	0.0320432i
$794$	11.6008	+	20.0932i	0.411698	+	0.713082i
$795$	6.16470	−	1.15755i	0.218639	−	0.0410541i
$796$	−17.7938	−	10.2732i	−0.630684	−	0.364125i
$797$	40.8059			1.44542			0.722710	−	0.691151i	$-0.242896\pi$
$797$	40.8059			1.44542			0.722710	+	0.691151i	$0.242896\pi$
$798$	−3.47961	+	9.25179i	−0.123177	+	0.327510i
$799$	−0.317971			−0.0112490
$800$	4.15547	+	2.39916i	0.146918	+	0.0848232i
$801$	−0.707912	+	4.60971i	−0.0250128	+	0.162876i
$802$	15.3254	+	26.5444i	0.541159	+	0.937315i
$803$	−36.8435	+	63.8148i	−1.30018	+	2.25197i
$804$	−6.10358	−	2.14526i	−0.215257	−	0.0756576i
$805$	0.616319	−	1.01582i	0.0217224	−	0.0358030i
$806$		−	1.03043i		−	0.0362954i
$807$	−26.2480	+	22.5248i	−0.923972	+	0.792910i
$808$	−1.80350	+	1.04125i	−0.0634470	+	0.0366311i
$809$	−6.07024	+	3.50466i	−0.213418	+	0.123217i	−0.602899	−	0.797817i	$-0.705988\pi$
$809$	−6.07024	+	3.50466i	−0.213418	+	0.123217i	0.389481	+	0.921035i	$0.372655\pi$
$810$	−1.21279	+	3.85552i	−0.0426129	+	0.135469i
$811$		−	33.0837i		−	1.16173i	−0.814001	−	0.580864i	$-0.802715\pi$
$811$		−	33.0837i		−	1.16173i	0.814001	−	0.580864i	$-0.197285\pi$
$812$	0.723199	−	1.19198i	0.0253793	−	0.0418304i
$813$	−8.40291	+	23.9075i	−0.294703	+	0.838473i
$814$	−24.5497	+	42.5212i	−0.860465	+	1.49037i
$815$	−0.664063	−	1.15019i	−0.0232611	−	0.0402894i
$816$	−0.362688	−	1.93155i	−0.0126966	−	0.0676177i
$817$	−7.56048	−	4.36505i	−0.264508	−	0.152714i
$818$	−35.1502			−1.22900
$819$	−0.826836	−	0.693225i	−0.0288920	−	0.0242232i
$820$	−0.970690			−0.0338980
$821$	37.9611	+	21.9169i	1.32485	+	0.764903i	0.984498	−	0.175394i	$-0.0561200\pi$
$821$	37.9611	+	21.9169i	1.32485	+	0.764903i	0.340353	+	0.940298i	$0.389453\pi$
$822$	−2.84434	−	15.1479i	−0.0992076	−	0.528344i
$823$	0.429824	+	0.744477i	0.0149827	+	0.0259509i	0.873420	−	0.486968i	$-0.161897\pi$
$823$	0.429824	+	0.744477i	0.0149827	+	0.0259509i	−0.858437	+	0.512919i	$0.828564\pi$
$824$	−9.01372	+	15.6122i	−0.314008	+	0.543878i
$825$	16.0927	−	45.7860i	0.560275	−	1.59406i
$826$	5.18488	+	9.44923i	0.180405	+	0.328781i
$827$			21.8101i			0.758413i	0.925312	+	0.379206i	$0.123803\pi$
$827$			21.8101i			0.758413i	−0.925312	+	0.379206i	$0.876197\pi$
$828$	−1.08826	−	2.79566i	−0.0378195	−	0.0971558i
$829$	10.3344	−	5.96655i	0.358927	−	0.207227i	−0.309683	−	0.950840i	$-0.600223\pi$
$829$	10.3344	−	5.96655i	0.358927	−	0.207227i	0.668610	+	0.743613i	$0.266890\pi$
$830$	1.80375	−	1.04139i	0.0626089	−	0.0361473i
$831$	31.2944	−	26.8554i	1.08559	−	0.931603i
$832$		−	0.135940i		−	0.00471287i
$833$	−7.93516	−	0.345347i	−0.274937	−	0.0119656i
$834$	2.64627	+	0.930101i	0.0916329	+	0.0322068i
$835$	−3.50297	+	6.06732i	−0.121225	+	0.209968i
$836$	6.29783	+	10.9082i	0.217815	+	0.377267i
$837$	34.7457	+	18.5494i	1.20099	+	0.641161i
$838$	−32.5622	−	18.7998i	−1.12484	−	0.649428i
$839$	40.0065			1.38118			0.690588	−	0.723248i	$-0.257352\pi$
$839$	40.0065			1.38118			0.690588	+	0.723248i	$0.257352\pi$
$840$	0.335718	+	2.03040i	0.0115834	+	0.0700555i
$841$	28.7223			0.990424
$842$	4.14708	+	2.39432i	0.142918	+	0.0825137i
$843$	35.8892	−	6.73894i	1.23609	−	0.232101i
$844$	−1.83404	−	3.17665i	−0.0631302	−	0.109345i
$845$	2.91491	−	5.04877i	0.100276	−	0.173683i
$846$	0.525991	−	0.655824i	0.0180840	−	0.0225477i
$847$	1.32898	−	61.1019i	0.0456644	−	2.09949i
$848$		−	8.06392i		−	0.276916i
$849$	−27.6247	−	32.1908i	−0.948076	−	1.10479i
$850$	−4.71508	+	2.72225i	−0.161726	+	0.0933725i
$851$	7.28165	−	4.20406i	0.249612	−	0.144113i
$852$	16.2797	+	18.9706i	0.557733	+	0.649922i
$853$			28.6329i			0.980371i	0.871618	+	0.490185i	$0.163071\pi$
$853$			28.6329i			0.980371i	−0.871618	+	0.490185i	$0.836929\pi$
$854$	17.3374	+	10.5189i	0.593273	+	0.359950i
$855$	−1.81817	+	2.26695i	−0.0621800	+	0.0775282i
$856$	−3.02094	+	5.23243i	−0.103254	+	0.178841i
$857$	−25.4346	−	44.0540i	−0.868828	−	1.50485i	−0.863195	−	0.504870i	$-0.831540\pi$
$857$	−25.4346	−	44.0540i	−0.868828	−	1.50485i	−0.00563280	−	0.999984i	$-0.501793\pi$
$858$	−1.35132	+	0.253739i	−0.0461334	+	0.00866252i
$859$	−3.81054	−	2.20001i	−0.130014	−	0.0750635i	0.433582	−	0.901114i	$-0.357249\pi$
$859$	−3.81054	−	2.20001i	−0.130014	−	0.0750635i	−0.563596	+	0.826050i	$0.690583\pi$
$860$	−1.81762			−0.0619803
$861$	6.28558	+	7.65529i	0.214212	+	0.260891i
$862$	−11.8814			−0.404681
$863$	9.96762	+	5.75481i	0.339302	+	0.195896i	0.659963	−	0.751298i	$-0.270572\pi$
$863$	9.96762	+	5.75481i	0.339302	+	0.195896i	−0.320661	+	0.947194i	$0.603905\pi$
$864$	4.58383	+	2.44713i	0.155945	+	0.0832531i
$865$	−2.32170	−	4.02131i	−0.0789402	−	0.136728i
$866$	1.79948	−	3.11679i	0.0611488	−	0.105913i
$867$	−25.6752	−	9.02420i	−0.871975	−	0.306478i
$868$	20.0502	+	0.436098i	0.680549	+	0.0148021i
$869$		−	19.4973i		−	0.661402i
$870$	0.311059	−	0.266936i	0.0105459	−	0.00904998i
$871$	0.439739	−	0.253884i	0.0149000	−	0.00860251i
$872$	−0.00563007	+	0.00325052i	−0.000190658	+	0.000110077i
$873$	0.997868	+	2.56346i	0.0337727	+	0.0867598i
$874$		−	2.15697i		−	0.0729607i
$875$	10.2065	−	5.60041i	0.345043	−	0.189329i
$876$	−7.24732	+	20.6197i	−0.244864	+	0.696674i
$877$	23.2017	−	40.1864i	0.783464	−	1.35700i	−0.146448	−	0.989218i	$-0.546784\pi$
$877$	23.2017	−	40.1864i	0.783464	−	1.35700i	0.929912	−	0.367782i	$-0.119883\pi$
$878$	−7.48214	−	12.9595i	−0.252510	−	0.437360i
$879$	6.34907	+	33.8128i	0.214149	+	1.14048i
$880$	2.27110	+	1.31122i	0.0765587	+	0.0442012i
$881$	−13.7483			−0.463191			−0.231595	−	0.972812i	$-0.574395\pi$
$881$	−13.7483			−0.463191			−0.231595	+	0.972812i	$0.574395\pi$
$882$	13.8387	−	15.7952i	0.465975	−	0.531853i
$883$	−16.9987			−0.572053			−0.286026	−	0.958222i	$-0.592335\pi$
$883$	−16.9987			−0.572053			−0.286026	+	0.958222i	$0.592335\pi$
$884$	0.133581	+	0.0771233i	0.00449283	+	0.00259394i
$885$	0.584782	+	3.11434i	0.0196572	+	0.104687i
$886$	−9.15317	−	15.8538i	−0.307507	−	0.532617i
$887$	−12.6512	+	21.9125i	−0.424786	+	0.735751i	−0.996400	−	0.0847713i	$-0.972984\pi$
$887$	−12.6512	+	21.9125i	−0.424786	+	0.735751i	0.571614	+	0.820522i	$0.306317\pi$
$888$	−4.82905	+	13.7394i	−0.162052	+	0.461063i
$889$	30.5833	−	16.7814i	1.02573	−	0.562829i
$890$			0.698141i			0.0234017i
$891$	15.7700	−	50.1338i	0.528314	−	1.67954i
$892$	−5.27546	+	3.04579i	−0.176635	+	0.101980i
$893$	0.523472	−	0.302227i	0.0175173	−	0.0101136i
$894$	−19.2005	+	16.4770i	−0.642161	+	0.551073i
$895$		−	2.15190i		−	0.0719300i
$896$	2.64513	+	0.0575322i	0.0883674	+	0.00192202i
$897$	0.222134	+	0.0780746i	0.00741682	+	0.00260683i
$898$	−15.4503	+	26.7607i	−0.515584	+	0.893017i
$899$	−1.99721	−	3.45927i	−0.0666107	−	0.115373i
$900$	2.18502	−	14.2282i	0.0728339	−	0.474272i
$901$	7.92402	+	4.57494i	0.263987	+	0.152413i
$902$	12.6220			0.420266
$903$	11.7698	+	14.3346i	0.391674	+	0.477024i
$904$	7.71606			0.256632
$905$	4.52046	+	2.60989i	0.150265	+	0.0867556i
$906$	−5.49206	+	1.03125i	−0.182462	+	0.0342610i
$907$	−20.6824	−	35.8230i	−0.686748	−	1.18948i	−0.972884	−	0.231294i	$-0.925704\pi$
$907$	−20.6824	−	35.8230i	−0.686748	−	1.18948i	0.286136	−	0.958189i	$-0.407629\pi$
$908$	−1.81603	+	3.14545i	−0.0602670	+	0.104385i
$909$	4.87366	+	3.90882i	0.161649	+	0.129647i
$910$	−0.138091	−	0.0837824i	−0.00457766	−	0.00277736i
$911$		−	9.60530i		−	0.318238i	−0.987259	−	0.159119i	$-0.949135\pi$
$911$		−	9.60530i		−	0.318238i	0.987259	−	0.159119i	$-0.0508653\pi$
$912$	2.43300	+	2.83516i	0.0805647	+	0.0938814i
$913$	−23.4543	+	13.5413i	−0.776224	+	0.448153i
$914$	−3.52597	+	2.03572i	−0.116629	+	0.0673357i
$915$	3.88258	+	4.52435i	0.128354	+	0.149570i
$916$			20.0351i			0.661977i
$917$	−0.0316365	+	1.45453i	−0.00104473	+	0.0480329i
$918$	−5.00524	+	3.11597i	−0.165198	+	0.102842i
$919$	−15.7906	+	27.3501i	−0.520884	+	0.902198i	0.478821	+	0.877913i	$0.341064\pi$
$919$	−15.7906	+	27.3501i	−0.520884	+	0.902198i	−0.999705	+	0.0242852i	$0.992269\pi$
$920$	−0.224543	−	0.388920i	−0.00740296	−	0.0128223i
$921$	48.2436	−	9.05876i	1.58968	−	0.298496i
$922$	−23.3215	−	13.4647i	−0.768054	−	0.443436i
$923$	−1.96198			−0.0645795
$924$	−4.36537	−	26.4015i	−0.143610	−	0.868546i
$925$	40.3449			1.32653
$926$	3.86013	+	2.22865i	0.126852	+	0.0732379i
$927$	53.4557	+	8.20917i	1.75571	+	0.269625i
$928$	−0.263482	−	0.456364i	−0.00864922	−	0.0149809i
$929$	−24.3986	+	42.2596i	−0.800492	+	1.38649i	0.118800	+	0.992918i	$0.462095\pi$
$929$	−24.3986	+	42.2596i	−0.800492	+	1.38649i	−0.919292	+	0.393575i	$0.871238\pi$
$930$	5.56249	+	1.95508i	0.182401	+	0.0641096i
$931$	13.3918	−	6.97372i	0.438900	−	0.228555i
$932$			3.83053i			0.125473i
$933$	40.4315	−	34.6964i	1.32367	−	1.13591i
$934$	−31.2865	+	18.0633i	−1.02373	+	0.591049i
$935$	−2.57694	+	1.48780i	−0.0842750	+	0.0486562i
$936$	−0.380041	+	0.147937i	−0.0124220	+	0.00483549i
$937$		−	60.4177i		−	1.97376i	−0.161456	−	0.986880i	$-0.551619\pi$
$937$		−	60.4177i		−	1.97376i	0.161456	−	0.986880i	$-0.448381\pi$
$938$	4.75397	+	8.66392i	0.155223	+	0.282887i
$939$	−6.25004	+	17.7823i	−0.203963	+	0.580303i
$940$	0.0629242	−	0.108988i	0.00205236	−	0.00355479i
$941$	−20.0502	−	34.7280i	−0.653618	−	1.13210i	−0.982238	−	0.187638i	$-0.939917\pi$
$941$	−20.0502	−	34.7280i	−0.653618	−	1.13210i	0.328620	−	0.944462i	$-0.393416\pi$
$942$	4.26606	+	22.7195i	0.138996	+	0.740240i
$943$	−1.87190	−	1.08074i	−0.0609574	−	0.0351937i
$944$	4.07380			0.132591
$945$	5.31096	−	3.14815i	0.172766	−	0.102409i
$946$	23.6347			0.768430
$947$	33.7894	+	19.5083i	1.09801	+	0.633935i	0.935697	−	0.352804i	$-0.114772\pi$
$947$	33.7894	+	19.5083i	1.09801	+	0.633935i	0.162311	+	0.986740i	$0.448105\pi$
$948$	−1.06725	−	5.68376i	−0.0346625	−	0.184600i
$949$	−0.857692	−	1.48557i	−0.0278418	−	0.0482235i
$950$	5.17493	−	8.96324i	0.167897	−	0.290806i
$951$	17.3008	−	49.2232i	0.561016	−	1.59617i
$952$	−1.55720	+	2.56660i	−0.0504693	+	0.0831839i
$953$			7.98134i			0.258541i	0.991609	+	0.129270i	$0.0412635\pi$
$953$			7.98134i			0.258541i	−0.991609	+	0.129270i	$0.958736\pi$
$954$	−22.5440	+	8.77561i	−0.729887	+	0.284121i
$955$	9.64646	−	5.56939i	0.312152	−	0.180221i
$956$	−16.7252	+	9.65631i	−0.540932	+	0.312307i
$957$	−4.04473	+	3.47100i	−0.130748	+	0.112201i
$958$			19.4609i			0.628754i
$959$	−12.2122	+	20.1282i	−0.394351	+	0.649973i
$960$	0.733832	+	0.257924i	0.0236843	+	0.00832447i
$961$	13.2287	−	22.9127i	0.426731	−	0.739120i
$962$	−0.571500	−	0.989867i	−0.0184259	−	0.0319146i
$963$	17.9156	+	2.75130i	0.577323	+	0.0886594i
$964$	5.90863	+	3.41135i	0.190304	+	0.109872i
$965$	7.61197			0.245038
$966$	−1.61319	+	4.28924i	−0.0519036	+	0.138004i
$967$	−5.64420			−0.181505			−0.0907527	−	0.995873i	$-0.528927\pi$
$967$	−5.64420			−0.181505			−0.0907527	+	0.995873i	$0.528927\pi$
$968$	−20.0050	−	11.5499i	−0.642986	−	0.371228i
$969$	−4.16629	+	0.782309i	−0.133841	+	0.0251314i
$970$	0.205893	+	0.356617i	0.00661082	+	0.0114503i
$971$	−13.2521	+	22.9533i	−0.425279	+	0.736606i	−0.996446	−	0.0842283i	$-0.973157\pi$
$971$	−13.2521	+	22.9533i	−0.425279	+	0.736606i	0.571167	+	0.820834i	$0.306491\pi$
$972$	1.85296	−	15.4779i	0.0594336	−	0.496455i
$973$	−2.06114	−	3.75633i	−0.0660770	−	0.120422i
$974$		−	2.34663i		−	0.0751909i
$975$	0.735755	+	0.857371i	0.0235630	+	0.0274578i
$976$	6.63781	−	3.83234i	0.212471	−	0.122670i
$977$	50.4402	−	29.1217i	1.61373	−	0.931685i	0.625229	−	0.780441i	$-0.285006\pi$
$977$	50.4402	−	29.1217i	1.61373	−	0.931685i	0.988497	−	0.151243i	$-0.0483277\pi$
$978$	3.33585	+	3.88725i	0.106669	+	0.124300i
$979$		−	9.07800i		−	0.290134i
$980$	1.68868	−	2.65152i	0.0539431	−	0.0846997i
$981$	0.0152143	+	0.0122023i	0.000485756	+	0.000389591i
$982$	20.5549	−	35.6021i	0.655932	−	1.13611i
$983$	11.9240	+	20.6529i	0.380315	+	0.658725i	0.991107	−	0.133066i	$-0.0424822\pi$
$983$	11.9240	+	20.6529i	0.380315	+	0.658725i	−0.610792	+	0.791791i	$0.709149\pi$
$984$	3.67949	−	0.690902i	0.117298	−	0.0220251i
$985$	−4.84559	−	2.79760i	−0.154393	−	0.0891390i
$986$	0.597929			0.0190419
$987$	−1.26698	+	0.209490i	−0.0403286	+	0.00666814i
$988$	−0.293219			−0.00932853
$989$	−3.50513	−	2.02369i	−0.111457	−	0.0643496i
$990$	1.19418	−	7.77615i	0.0379536	−	0.247142i
$991$	−7.83284	−	13.5669i	−0.248818	−	0.430966i	0.714380	−	0.699758i	$-0.246709\pi$
$991$	−7.83284	−	13.5669i	−0.248818	−	0.430966i	−0.963198	+	0.268792i	$0.913376\pi$
$992$	3.79003	−	6.56452i	0.120334	−	0.208424i
$993$	48.8506	+	17.1698i	1.55023	+	0.544868i
$994$	0.830348	−	38.1764i	0.0263370	−	1.21088i
$995$			9.22713i			0.292520i
$996$	−6.09604	+	5.23134i	−0.193161	+	0.165761i
$997$	−30.6048	+	17.6697i	−0.969265	+	0.559605i	−0.899012	−	0.437924i	$-0.855714\pi$
$997$	−30.6048	+	17.6697i	−0.969265	+	0.559605i	−0.0702526	+	0.997529i	$0.522381\pi$
$998$	35.3327	−	20.3993i	1.11844	−	0.645729i
$999$	43.6658	−	1.45157i	1.38152	−	0.0459255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.c.47.6	✓	56
3.2	odd	2	inner	966.2.l.c.47.25	yes	56
7.3	odd	6	inner	966.2.l.c.185.25	yes	56
21.17	even	6	inner	966.2.l.c.185.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.c.47.6	✓	56	1.1	even	1	trivial
966.2.l.c.47.25	yes	56	3.2	odd	2	inner
966.2.l.c.185.6	yes	56	21.17	even	6	inner
966.2.l.c.185.25	yes	56	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.319643 - 1.70230i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.224543 - 0.388920i) q^{5} +(-0.574332 + 1.63406i) q^{6} +(2.31951 - 1.27274i) q^{7} -1.00000i q^{8} +(-2.79566 + 1.08826i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.319643 - 1.70230i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.224543 - 0.388920i) q^{5} +(-0.574332 + 1.63406i) q^{6} +(2.31951 - 1.27274i) q^{7} -1.00000i q^{8} +(-2.79566 + 1.08826i) q^{9} +(-0.388920 + 0.224543i) q^{10} +(5.05716 - 2.91975i) q^{11} +(1.31441 - 1.12797i) q^{12} +0.135940i q^{13} +(-2.64513 - 0.0575322i) q^{14} +(-0.733832 - 0.257924i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.567334 - 0.982651i) q^{17} +(2.96524 + 0.455371i) q^{18} +(1.86799 + 1.07849i) q^{19} +0.449086 q^{20} +(-2.90800 - 3.54169i) q^{21} -5.83951 q^{22} +(0.866025 + 0.500000i) q^{23} +(-1.70230 + 0.319643i) q^{24} +(2.39916 + 4.15547i) q^{25} +(0.0679699 - 0.117727i) q^{26} +(2.74615 + 4.41120i) q^{27} +(2.26198 + 1.37239i) q^{28} -0.526964i q^{29} +(0.506555 + 0.590285i) q^{30} +(6.56452 - 3.79003i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-6.58678 - 7.67553i) q^{33} +1.13467i q^{34} +(0.0258369 - 1.18789i) q^{35} +(-2.34029 - 1.87698i) q^{36} +(4.20406 - 7.28165i) q^{37} +(-1.07849 - 1.86799i) q^{38} +(0.231411 - 0.0434522i) q^{39} +(-0.388920 - 0.224543i) q^{40} -2.16148 q^{41} +(0.747558 + 4.52119i) q^{42} -4.04738 q^{43} +(5.05716 + 2.91975i) q^{44} +(-0.204501 + 1.33165i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(0.140116 - 0.242688i) q^{47} +(1.63406 + 0.574332i) q^{48} +(3.76027 - 5.90426i) q^{49} -4.79832i q^{50} +(-1.49142 + 1.27987i) q^{51} +(-0.117727 + 0.0679699i) q^{52} +(-6.98356 + 4.03196i) q^{53} +(-0.172638 - 5.19328i) q^{54} -2.62244i q^{55} +(-1.27274 - 2.31951i) q^{56} +(1.23882 - 3.52462i) q^{57} +(-0.263482 + 0.456364i) q^{58} +(-2.03690 - 3.52802i) q^{59} +(-0.143547 - 0.764479i) q^{60} +(-6.63781 - 3.83234i) q^{61} -7.58006 q^{62} +(-5.09949 + 6.08236i) q^{63} -1.00000 q^{64} +(0.0528697 + 0.0305243i) q^{65} +(1.86656 + 9.94060i) q^{66} +(-1.86762 - 3.23481i) q^{67} +(0.567334 - 0.982651i) q^{68} +(0.574332 - 1.63406i) q^{69} +(-0.616319 + 1.01582i) q^{70} +14.4327i q^{71} +(1.08826 + 2.79566i) q^{72} +(-10.9281 + 6.30935i) q^{73} +(-7.28165 + 4.20406i) q^{74} +(6.30698 - 5.41236i) q^{75} +2.15697i q^{76} +(8.01406 - 13.2088i) q^{77} +(-0.222134 - 0.0780746i) q^{78} +(1.66943 - 2.89155i) q^{79} +(0.224543 + 0.388920i) q^{80} +(6.63140 - 6.08478i) q^{81} +(1.87190 + 1.08074i) q^{82} -4.63784 q^{83} +(1.61319 - 4.28924i) q^{84} -0.509563 q^{85} +(3.50513 + 2.02369i) q^{86} +(-0.897051 + 0.168440i) q^{87} +(-2.91975 - 5.05716i) q^{88} +(0.777291 - 1.34631i) q^{89} +(0.842926 - 1.05099i) q^{90} +(0.173016 + 0.315314i) q^{91} +1.00000i q^{92} +(-8.55007 - 9.96334i) q^{93} +(-0.242688 + 0.140116i) q^{94} +(0.838889 - 0.484333i) q^{95} +(-1.12797 - 1.31441i) q^{96} -0.916942i q^{97} +(-6.20862 + 3.23311i) q^{98} +(-10.9606 + 13.6661i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) \) 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9	\( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) \) 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^12 - 36 * q^15 - 28 * q^16 + 8 * q^18 - 36 * q^19 + 34 * q^21 + 16 * q^22 - 46 * q^25 + 4 * q^28 - 6 * q^30 - 6 * q^31 + 30 * q^33 - 4 * q^36 - 8 * q^37 + 42 * q^39 - 6 * q^40 + 18 * q^42 + 64 * q^43 - 6 * q^45 - 28 * q^46 - 40 * q^49 - 24 * q^51 - 36 * q^52 - 60 * q^57 - 16 * q^58 - 18 * q^60 + 12 * q^61 + 36 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 34 * q^70 - 8 * q^72 - 102 * q^73 + 18 * q^75 - 16 * q^78 + 24 * q^79 + 54 * q^81 + 12 * q^82 - 4 * q^84 + 128 * q^85 + 102 * q^87 + 8 * q^88 + 68 * q^91 - 32 * q^93 + 6 * q^94 - 112 * q^99

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