LMFDB - Embedded newform 399.2.ck.b.40.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [399,2,Mod(10,399)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("399.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(399, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 3, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	399.ck (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [84] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.18603104065$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			40.10
Character	$\chi$	$=$	399.40
Dual form			399.2.ck.b.10.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.849174 - 1.01201i) q^{2} +(0.173648 - 0.984808i) q^{3} +(0.0442365 + 0.250878i) q^{4} +(0.224052 + 0.0395064i) q^{5} +(-0.849174 - 1.01201i) q^{6} +(1.93362 + 1.80586i) q^{7} +(2.57963 + 1.48935i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(0.230240 - 0.193194i) q^{10} +3.09614 q^{11} +0.254748 q^{12} +(-0.305451 + 0.256304i) q^{13} +(3.46952 - 0.423342i) q^{14} +(0.0778124 - 0.213788i) q^{15} +(3.21902 - 1.17163i) q^{16} +(-1.37809 - 3.78627i) q^{17} +(-1.14409 + 0.660540i) q^{18} +(-3.93548 - 1.87404i) q^{19} +0.0579572i q^{20} +(2.11419 - 1.59066i) q^{21} +(2.62916 - 3.13332i) q^{22} +(-0.376899 + 0.316256i) q^{23} +(1.91467 - 2.28182i) q^{24} +(-4.64982 - 1.69240i) q^{25} +0.526765i q^{26} +(-0.500000 + 0.866025i) q^{27} +(-0.367513 + 0.564986i) q^{28} +(1.68689 - 0.297443i) q^{29} +(-0.150278 - 0.260289i) q^{30} +(-1.36285 + 2.36052i) q^{31} +(-0.489739 + 1.34555i) q^{32} +(0.537640 - 3.04911i) q^{33} +(-5.00197 - 1.82057i) q^{34} +(0.361887 + 0.480996i) q^{35} +(0.0442365 - 0.250878i) q^{36} +(-1.07552 - 0.620954i) q^{37} +(-5.23844 + 2.39134i) q^{38} +(0.199369 + 0.345318i) q^{39} +(0.519132 + 0.435604i) q^{40} +(3.24322 + 2.72139i) q^{41} +(0.185565 - 3.49032i) q^{42} +(-3.59164 + 1.30725i) q^{43} +(0.136963 + 0.776753i) q^{44} +(-0.197028 - 0.113754i) q^{45} +0.649980i q^{46} +(2.38769 - 6.56012i) q^{47} +(-0.594851 - 3.37357i) q^{48} +(0.477741 + 6.98368i) q^{49} +(-5.66123 + 3.26851i) q^{50} +(-3.96805 + 0.699675i) q^{51} +(-0.0778130 - 0.0652929i) q^{52} +(3.35773 - 0.592058i) q^{53} +(0.451836 + 1.24141i) q^{54} +(0.693696 + 0.122317i) q^{55} +(2.29846 + 7.53829i) q^{56} +(-2.52896 + 3.55026i) q^{57} +(1.13144 - 1.95972i) q^{58} +(-7.12781 + 2.59431i) q^{59} +(0.0570767 + 0.0100642i) q^{60} +(-5.10609 - 6.08520i) q^{61} +(1.23157 + 3.38371i) q^{62} +(-1.19936 - 2.35829i) q^{63} +(4.37144 + 7.57155i) q^{64} +(-0.0785625 + 0.0453581i) q^{65} +(-2.62916 - 3.13332i) q^{66} +(4.98026 + 5.93524i) q^{67} +(0.888929 - 0.513223i) q^{68} +(0.246003 + 0.426090i) q^{69} +(0.794076 + 0.0422175i) q^{70} +(0.0420089 + 0.115419i) q^{71} +(-1.91467 - 2.28182i) q^{72} +(-7.93156 - 1.39855i) q^{73} +(-1.54172 + 0.561139i) q^{74} +(-2.47412 + 4.28530i) q^{75} +(0.296063 - 1.07022i) q^{76} +(5.98675 + 5.59120i) q^{77} +(0.518763 + 0.0914718i) q^{78} +(-3.80954 - 10.4666i) q^{79} +(0.767513 - 0.135333i) q^{80} +(0.766044 + 0.642788i) q^{81} +(5.50812 - 0.971230i) q^{82} +(2.84448 - 1.64226i) q^{83} +(0.492584 + 0.460039i) q^{84} +(-0.159182 - 0.902764i) q^{85} +(-1.72698 + 4.74485i) q^{86} -1.71291i q^{87} +(7.98691 + 4.61125i) q^{88} +(1.03706 + 5.88145i) q^{89} +(-0.282431 + 0.102796i) q^{90} +(-1.05347 - 0.0560086i) q^{91} +(-0.0960142 - 0.0805655i) q^{92} +(2.08801 + 1.75204i) q^{93} +(-4.61132 - 7.98703i) q^{94} +(-0.807713 - 0.575359i) q^{95} +(1.24006 + 0.715951i) q^{96} +(-0.996683 + 5.65247i) q^{97} +(7.47321 + 5.44688i) q^{98} +(-2.90942 - 1.05894i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{7} - 12 q^{10} + 6 q^{11} - 96 q^{12} + 27 q^{13} + 9 q^{14} - 39 q^{19} + 6 q^{21} - 12 q^{22} - 6 q^{23} + 9 q^{24} + 18 q^{25} - 42 q^{27} + 45 q^{28} - 6 q^{29} + 18 q^{31} - 51 q^{32} + 12 q^{33}+ \cdots - 6 q^{99}+O(q^{100}) $ 84 * q - 6 * q^7 - 12 * q^10 + 6 * q^11 - 96 * q^12 + 27 * q^13 + 9 * q^14 - 39 * q^19 + 6 * q^21 - 12 * q^22 - 6 * q^23 + 9 * q^24 + 18 * q^25 - 42 * q^27 + 45 * q^28 - 6 * q^29 + 18 * q^31 - 51 * q^32 + 12 * q^33 + 6 * q^34 + 15 * q^35 + 18 * q^37 + 3 * q^38 + 18 * q^40 - 45 * q^41 + 15 * q^42 + 15 * q^43 - 36 * q^44 + 9 * q^45 - 24 * q^47 + 18 * q^49 - 27 * q^50 + 18 * q^51 - 84 * q^52 + 9 * q^53 - 30 * q^55 + 75 * q^56 - 6 * q^57 - 18 * q^58 + 24 * q^59 + 21 * q^61 - 45 * q^62 - 12 * q^63 + 84 * q^64 - 9 * q^65 + 12 * q^66 - 45 * q^67 + 12 * q^69 + 42 * q^70 + 42 * q^71 - 9 * q^72 - 72 * q^73 + 18 * q^74 + 57 * q^75 - 96 * q^76 - 51 * q^77 - 15 * q^78 - 42 * q^79 - 78 * q^80 + 24 * q^82 + 9 * q^84 - 48 * q^85 - 9 * q^86 + 108 * q^88 - 48 * q^89 - 21 * q^90 + 27 * q^91 + 6 * q^92 + 21 * q^93 + 30 * q^94 + 60 * q^95 - 21 * q^97 + 51 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{18}\right)$

Coefficient data

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

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

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

$2$	0.849174	−	1.01201i	0.600457	−	0.715596i	−0.377123	−	0.926163i	$-0.623087\pi$
$2$	0.849174	−	1.01201i	0.600457	−	0.715596i	0.977579	+	0.210567i	$0.0675310\pi$
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$4$	0.0442365	+	0.250878i	0.0221182	+	0.125439i
$5$	0.224052	+	0.0395064i	0.100199	+	0.0176678i	0.223523	−	0.974699i	$-0.428244\pi$
$5$	0.224052	+	0.0395064i	0.100199	+	0.0176678i	−0.123324	+	0.992366i	$0.539355\pi$
$6$	−0.849174	−	1.01201i	−0.346674	−	0.413150i
$7$	1.93362	+	1.80586i	0.730838	+	0.682551i
$7$	1.93362	+	1.80586i	0.730838	+	0.682551i
$8$	2.57963	+	1.48935i	0.912038	+	0.526565i
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$	0.230240	−	0.193194i	0.0728081	−	0.0610933i
$11$	3.09614			0.933523			0.466761	−	0.884383i	$-0.345421\pi$
$11$	3.09614			0.933523			0.466761	+	0.884383i	$0.345421\pi$
$12$	0.254748			0.0735393
$13$	−0.305451	+	0.256304i	−0.0847170	+	0.0710860i	−0.684163	−	0.729329i	$-0.739832\pi$
$13$	−0.305451	+	0.256304i	−0.0847170	+	0.0710860i	0.599446	+	0.800415i	$0.295388\pi$
$14$	3.46952	−	0.423342i	0.927267	−	0.113143i
$15$	0.0778124	−	0.213788i	0.0200911	−	0.0551997i
$16$	3.21902	−	1.17163i	0.804755	−	0.292907i
$17$	−1.37809	−	3.78627i	−0.334236	−	0.918306i	−0.986997	−	0.160741i	$-0.948611\pi$
$17$	−1.37809	−	3.78627i	−0.334236	−	0.918306i	0.652761	−	0.757564i	$-0.273611\pi$
$18$	−1.14409	+	0.660540i	−0.269664	+	0.155691i
$19$	−3.93548	−	1.87404i	−0.902860	−	0.429935i
$19$	−3.93548	−	1.87404i	−0.902860	−	0.429935i
$20$			0.0579572i			0.0129596i
$21$	2.11419	−	1.59066i	0.461355	−	0.347110i
$22$	2.62916	−	3.13332i	0.560540	−	0.668025i
$23$	−0.376899	+	0.316256i	−0.0785889	+	0.0659439i	−0.681236	−	0.732064i	$-0.738557\pi$
$23$	−0.376899	+	0.316256i	−0.0785889	+	0.0659439i	0.602647	+	0.798008i	$0.294113\pi$
$24$	1.91467	−	2.28182i	0.390831	−	0.465774i
$25$	−4.64982	−	1.69240i	−0.929965	−	0.338480i
$26$			0.526765i			0.103307i
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	−0.367513	+	0.564986i	−0.0694535	+	0.106772i
$29$	1.68689	−	0.297443i	0.313247	−	0.0552339i	−0.0148146	−	0.999890i	$-0.504716\pi$
$29$	1.68689	−	0.297443i	0.313247	−	0.0552339i	0.328061	+	0.944656i	$0.393605\pi$
$30$	−0.150278	−	0.260289i	−0.0274369	−	0.0475221i
$31$	−1.36285	+	2.36052i	−0.244775	+	0.423963i	−0.962068	−	0.272809i	$-0.912047\pi$
$31$	−1.36285	+	2.36052i	−0.244775	+	0.423963i	0.717293	+	0.696771i	$0.245381\pi$
$32$	−0.489739	+	1.34555i	−0.0865745	+	0.237861i
$33$	0.537640	−	3.04911i	0.0935911	−	0.530781i
$34$	−5.00197	−	1.82057i	−0.857830	−	0.312225i
$35$	0.361887	+	0.480996i	0.0611701	+	0.0813032i
$36$	0.0442365	−	0.250878i	0.00737275	−	0.0418129i
$37$	−1.07552	−	0.620954i	−0.176815	−	0.102084i	0.408980	−	0.912543i	$-0.365884\pi$
$37$	−1.07552	−	0.620954i	−0.176815	−	0.102084i	−0.585795	+	0.810459i	$0.699218\pi$
$38$	−5.23844	+	2.39134i	−0.849788	+	0.387926i
$39$	0.199369	+	0.345318i	0.0319246	+	0.0552951i
$40$	0.519132	+	0.435604i	0.0820820	+	0.0688750i
$41$	3.24322	+	2.72139i	0.506506	+	0.425009i	0.859898	−	0.510466i	$-0.170527\pi$
$41$	3.24322	+	2.72139i	0.506506	+	0.425009i	−0.353391	+	0.935476i	$0.614972\pi$
$42$	0.185565	−	3.49032i	0.0286333	−	0.538568i
$43$	−3.59164	+	1.30725i	−0.547721	+	0.199354i	−0.601033	−	0.799224i	$-0.705244\pi$
$43$	−3.59164	+	1.30725i	−0.547721	+	0.199354i	0.0533129	+	0.998578i	$0.483022\pi$
$44$	0.136963	+	0.776753i	0.0206479	+	0.117100i
$45$	−0.197028	−	0.113754i	−0.0293712	−	0.0169575i
$46$			0.649980i			0.0958344i
$47$	2.38769	−	6.56012i	0.348280	−	0.956891i	−0.634632	−	0.772815i	$-0.718848\pi$
$47$	2.38769	−	6.56012i	0.348280	−	0.956891i	0.982912	−	0.184077i	$-0.0589295\pi$
$48$	−0.594851	−	3.37357i	−0.0858593	−	0.486932i
$49$	0.477741	+	6.98368i	0.0682487	+	0.997668i
$50$	−5.66123	+	3.26851i	−0.800618	+	0.462237i
$51$	−3.96805	+	0.699675i	−0.555638	+	0.0979741i
$52$	−0.0778130	−	0.0652929i	−0.0107907	−	0.00905449i
$53$	3.35773	−	0.592058i	0.461220	−	0.0813255i	0.0617897	−	0.998089i	$-0.480319\pi$
$53$	3.35773	−	0.592058i	0.461220	−	0.0813255i	0.399430	+	0.916764i	$0.369208\pi$
$54$	0.451836	+	1.24141i	0.0614871	+	0.168934i
$55$	0.693696	+	0.122317i	0.0935380	+	0.0164933i
$56$	2.29846	+	7.53829i	0.307144	+	1.00735i
$57$	−2.52896	+	3.55026i	−0.334969	+	0.470244i
$58$	1.13144	−	1.95972i	0.148566	−	0.257324i
$59$	−7.12781	+	2.59431i	−0.927961	+	0.337750i	−0.761401	−	0.648281i	$-0.775488\pi$
$59$	−7.12781	+	2.59431i	−0.927961	+	0.337750i	−0.166560	+	0.986031i	$0.553266\pi$
$60$	0.0570767	+	0.0100642i	0.00736857	+	0.00129928i
$61$	−5.10609	−	6.08520i	−0.653768	−	0.779131i	0.332709	−	0.943030i	$-0.392037\pi$
$61$	−5.10609	−	6.08520i	−0.653768	−	0.779131i	−0.986477	+	0.163899i	$0.947593\pi$
$62$	1.23157	+	3.38371i	0.156409	+	0.429731i
$63$	−1.19936	−	2.35829i	−0.151106	−	0.297116i
$64$	4.37144	+	7.57155i	0.546430	+	0.946444i
$65$	−0.0785625	+	0.0453581i	−0.00974448	+	0.00562598i
$66$	−2.62916	−	3.13332i	−0.323628	−	0.385685i
$67$	4.98026	+	5.93524i	0.608436	+	0.725105i	0.979036	−	0.203687i	$-0.0652925\pi$
$67$	4.98026	+	5.93524i	0.608436	+	0.725105i	−0.370600	+	0.928792i	$0.620848\pi$
$68$	0.888929	−	0.513223i	0.107798	−	0.0622375i
$69$	0.246003	+	0.426090i	0.0296153	+	0.0512953i
$70$	0.794076	+	0.0422175i	0.0949102	+	0.00504596i
$71$	0.0420089	+	0.115419i	0.00498554	+	0.0136977i	0.942160	−	0.335162i	$-0.108791\pi$
$71$	0.0420089	+	0.115419i	0.00498554	+	0.0136977i	−0.937175	+	0.348860i	$0.886569\pi$
$72$	−1.91467	−	2.28182i	−0.225646	−	0.268915i
$73$	−7.93156	−	1.39855i	−0.928319	−	0.163688i	−0.311008	−	0.950407i	$-0.600667\pi$
$73$	−7.93156	−	1.39855i	−0.928319	−	0.163688i	−0.617311	+	0.786720i	$0.711778\pi$
$74$	−1.54172	+	0.561139i	−0.179221	+	0.0652310i
$75$	−2.47412	+	4.28530i	−0.285687	+	0.494824i
$76$	0.296063	−	1.07022i	0.0339608	−	0.122763i
$77$	5.98675	+	5.59120i	0.682254	+	0.637177i
$78$	0.518763	+	0.0914718i	0.0587383	+	0.0103571i
$79$	−3.80954	−	10.4666i	−0.428607	−	1.17759i	−0.946659	−	0.322238i	$-0.895565\pi$
$79$	−3.80954	−	10.4666i	−0.428607	−	1.17759i	0.518052	−	0.855349i	$-0.326657\pi$
$80$	0.767513	−	0.135333i	0.0858106	−	0.0151307i
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$	5.50812	−	0.971230i	0.608270	−	0.107254i
$83$	2.84448	−	1.64226i	0.312222	−	0.180262i	−0.335698	−	0.941970i	$-0.608972\pi$
$83$	2.84448	−	1.64226i	0.312222	−	0.180262i	0.647921	+	0.761708i	$0.275639\pi$
$84$	0.492584	+	0.460039i	0.0537454	+	0.0501943i
$85$	−0.159182	−	0.902764i	−0.0172657	−	0.0979185i
$86$	−1.72698	+	4.74485i	−0.186225	+	0.511650i
$87$		−	1.71291i		−	0.183643i
$88$	7.98691	+	4.61125i	0.851408	+	0.491560i
$89$	1.03706	+	5.88145i	0.109928	+	0.623432i	0.989137	+	0.146996i	$0.0469605\pi$
$89$	1.03706	+	5.88145i	0.109928	+	0.623432i	−0.879209	+	0.476436i	$0.841928\pi$
$90$	−0.282431	+	0.102796i	−0.0297708	+	0.0108357i
$91$	−1.05347	−	0.0560086i	−0.110434	−	0.00587130i
$92$	−0.0960142	−	0.0805655i	−0.0100102	−	0.00839953i
$93$	2.08801	+	1.75204i	0.216516	+	0.181679i
$94$	−4.61132	−	7.98703i	−0.475621	−	0.823800i
$95$	−0.807713	−	0.575359i	−0.0828697	−	0.0590306i
$96$	1.24006	+	0.715951i	0.126563	+	0.0730714i
$97$	−0.996683	+	5.65247i	−0.101198	+	0.573922i	0.891473	+	0.453074i	$0.149673\pi$
$97$	−0.996683	+	5.65247i	−0.101198	+	0.573922i	−0.992671	+	0.120848i	$0.961439\pi$
$98$	7.47321	+	5.44688i	0.754908	+	0.550218i
$99$	−2.90942	−	1.05894i	−0.292408	−	0.106428i
$100$	0.218893	−	1.24140i	0.0218893	−	0.124140i
$101$	−0.861533	+	2.36704i	−0.0857258	+	0.235530i	−0.975147	−	0.221559i	$-0.928886\pi$
$101$	−0.861533	+	2.36704i	−0.0857258	+	0.235530i	0.889421	+	0.457088i	$0.151108\pi$
$102$	−2.66149	+	4.60984i	−0.263527	+	0.456442i
$103$	−8.34470	−	14.4535i	−0.822228	−	1.42414i	−0.904019	−	0.427491i	$-0.859397\pi$
$103$	−8.34470	−	14.4535i	−0.822228	−	1.42414i	0.0817914	−	0.996649i	$-0.473936\pi$
$104$	−1.16968	+	0.206246i	−0.114696	+	0.0202241i
$105$	0.536530	−	0.272865i	0.0523599	−	0.0266289i
$106$	2.25213	−	3.90080i	0.218746	−	0.378879i
$107$			10.0130i			0.967992i	0.875070	+	0.483996i	$0.160815\pi$
$107$			10.0130i			0.967992i	−0.875070	+	0.483996i	$0.839185\pi$
$108$	−0.239385	−	0.0871289i	−0.0230348	−	0.00838398i
$109$	−8.54338	+	10.1816i	−0.818308	+	0.975221i	−0.999967	−	0.00814052i	$-0.997409\pi$
$109$	−8.54338	+	10.1816i	−0.818308	+	0.975221i	0.181659	+	0.983362i	$0.441853\pi$
$110$	0.712855	−	0.598156i	0.0679680	−	0.0570320i
$111$	−0.798283	+	0.951357i	−0.0757697	+	0.0902988i
$112$	8.34014	+	3.54762i	0.788069	+	0.335219i
$113$			12.1923i			1.14696i	0.819220	+	0.573480i	$0.194407\pi$
$113$			12.1923i			1.14696i	−0.819220	+	0.573480i	$0.805593\pi$
$114$	1.44536	+	5.57411i	0.135370	+	0.522063i
$115$	−0.0969390	+	0.0559678i	−0.00903961	+	0.00521902i
$116$	0.149244	+	0.410044i	0.0138569	+	0.0380716i
$117$	0.374692	−	0.136377i	0.0346402	−	0.0126080i
$118$	−3.42729	+	9.41640i	−0.315508	+	0.866850i
$119$	4.17278	−	9.80983i	0.382518	−	0.899266i
$120$	0.519132	−	0.435604i	0.0473901	−	0.0397650i
$121$	−1.41389			−0.128536
$122$	−10.4942			−0.950102
$123$	3.24322	−	2.72139i	0.292432	−	0.245379i
$124$	−0.652490	−	0.237487i	−0.0585953	−	0.0213270i
$125$	−1.96008	−	1.13165i	−0.175315	−	0.101218i
$126$	−3.40507	−	0.788833i	−0.303348	−	0.0702749i
$127$	9.15001	+	10.9046i	0.811932	+	0.967623i	0.999894	−	0.0145532i	$-0.00463258\pi$
$127$	9.15001	+	10.9046i	0.811932	+	0.967623i	−0.187962	+	0.982176i	$0.560188\pi$
$128$	8.55427	+	1.50835i	0.756098	+	0.133320i
$129$	0.663709	+	3.76408i	0.0584363	+	0.331409i
$130$	−0.0208106	+	0.118023i	−0.00182521	+	0.0103513i
$131$	6.73904	−	8.03128i	0.588793	−	0.701696i	−0.386581	−	0.922256i	$-0.626344\pi$
$131$	6.73904	−	8.03128i	0.588793	−	0.701696i	0.975374	+	0.220560i	$0.0707883\pi$
$132$	0.788736			0.0686506
$133$	−4.22544	−	10.7306i	−0.366392	−	0.930461i
$134$	10.2356			0.884222
$135$	−0.146239	+	0.174281i	−0.0125863	+	0.0149997i
$136$	2.08412	−	11.8196i	0.178712	−	1.01353i
$137$	−2.57809	−	14.6211i	−0.220261	−	1.24916i	−0.871540	−	0.490324i	$-0.836878\pi$
$137$	−2.57809	−	14.6211i	−0.220261	−	1.24916i	0.651279	−	0.758838i	$-0.274233\pi$
$138$	0.640106	+	0.112868i	0.0544894	+	0.00960796i
$139$	−8.04272	−	9.58494i	−0.682175	−	0.812984i	0.308211	−	0.951318i	$-0.400270\pi$
$139$	−8.04272	−	9.58494i	−0.682175	−	0.812984i	−0.990386	+	0.138334i	$0.955825\pi$
$140$	−0.104663	+	0.112067i	−0.00884560	+	0.00947138i
$141$	−6.04584	−	3.49057i	−0.509151	−	0.293959i
$142$	0.152477	+	0.0554972i	0.0127956	+	0.00465722i
$143$	−0.945721	+	0.793554i	−0.0790852	+	0.0663604i
$144$	−3.42561			−0.285467
$145$	0.389701			0.0323629
$146$	−8.15061	+	6.83917i	−0.674549	+	0.566014i
$147$	6.96054	+	0.742220i	0.574096	+	0.0612173i
$148$	0.108206	−	0.297294i	0.00889448	−	0.0244374i
$149$	−16.6421	+	6.05721i	−1.36337	+	0.496226i	−0.917095	−	0.398669i	$-0.869472\pi$
$149$	−16.6421	+	6.05721i	−1.36337	+	0.496226i	−0.446276	+	0.894896i	$0.647250\pi$
$150$	2.23579	+	6.14279i	0.182552	+	0.501557i
$151$	3.38022	−	1.95157i	0.275079	−	0.158817i	−0.356115	−	0.934442i	$-0.615899\pi$
$151$	3.38022	−	1.95157i	0.275079	−	0.158817i	0.631193	+	0.775626i	$0.282565\pi$
$152$	−7.36097	−	10.6956i	−0.597054	−	0.867531i
$153$			4.02927i			0.325747i
$154$	10.7421	−	1.31073i	0.865625	−	0.105621i
$155$	−0.398604	+	0.475038i	−0.0320167	+	0.0381560i
$156$	−0.0778130	+	0.0652929i	−0.00623003	+	0.00522762i
$157$	10.0188	−	11.9399i	0.799586	−	0.952910i	−0.200052	−	0.979785i	$-0.564111\pi$
$157$	10.0188	−	11.9399i	0.799586	−	0.952910i	0.999639	+	0.0268753i	$0.00855569\pi$
$158$	−13.8272	−	5.03271i	−1.10004	−	0.400381i
$159$		−	3.40953i		−	0.270393i
$160$	−0.162885	+	0.282124i	−0.0128772	+	0.0223039i
$161$	−1.29989	−	0.0691095i	−0.102446	−	0.00544659i
$162$	1.30101	−	0.229403i	0.102217	−	0.0180236i
$163$	−1.05492	−	1.82717i	−0.0826274	−	0.143115i	0.821750	−	0.569848i	$-0.192998\pi$
$163$	−1.05492	−	1.82717i	−0.0826274	−	0.143115i	−0.904378	+	0.426733i	$0.859664\pi$
$164$	−0.539266	+	0.934037i	−0.0421096	+	0.0729360i
$165$	0.240918	−	0.661917i	0.0187555	−	0.0515302i
$166$	0.753480	−	4.27320i	0.0584814	−	0.331665i
$167$	−12.8128	−	4.66348i	−0.991486	−	0.360871i	−0.205190	−	0.978722i	$-0.565781\pi$
$167$	−12.8128	−	4.66348i	−0.991486	−	0.360871i	−0.786295	+	0.617851i	$0.788004\pi$
$168$	7.82289	−	0.954529i	0.603549	−	0.0736435i
$169$	−2.22982	+	12.6459i	−0.171524	+	0.972763i
$170$	−1.04878	−	0.605511i	−0.0804374	−	0.0464406i
$171$	3.05718	+	3.10704i	0.233788	+	0.237601i
$172$	−0.486842	−	0.843235i	−0.0371213	−	0.0642960i
$173$	9.78595	+	8.21139i	0.744012	+	0.624300i	0.933912	−	0.357503i	$-0.116372\pi$
$173$	9.78595	+	8.21139i	0.744012	+	0.624300i	−0.189900	+	0.981803i	$0.560816\pi$
$174$	−1.73347	−	1.45456i	−0.131414	−	0.110270i
$175$	−5.93474	−	11.6694i	−0.448624	−	0.882122i
$176$	9.96655	−	3.62753i	0.751257	−	0.273435i
$177$	1.31717	+	7.47002i	0.0990042	+	0.561481i
$178$	6.83271	+	3.94486i	0.512133	+	0.295680i
$179$		−	22.5186i		−	1.68312i	−0.540163	−	0.841560i	$-0.681637\pi$
$179$		−	22.5186i		−	1.68312i	0.540163	−	0.841560i	$-0.318363\pi$
$180$	0.0198225	−	0.0544619i	0.00147748	−	0.00405935i
$181$	2.00418	+	11.3663i	0.148969	+	0.844847i	0.964094	+	0.265561i	$0.0855572\pi$
$181$	2.00418	+	11.3663i	0.148969	+	0.844847i	−0.815125	+	0.579286i	$0.803332\pi$
$182$	−0.951264	+	1.01856i	−0.0705124	+	0.0755008i
$183$	−6.87942	+	3.97184i	−0.508541	+	0.293607i
$184$	−1.44328	+	0.254489i	−0.106400	+	0.0187612i
$185$	−0.216441	−	0.181616i	−0.0159131	−	0.0133527i
$186$	3.54616	−	0.625284i	0.260017	−	0.0458480i
$187$	−4.26677	−	11.7228i	−0.312017	−	0.857259i
$188$	1.75141	+	0.308821i	0.127735	+	0.0225231i
$189$	−2.53073	+	0.771631i	−0.184083	+	0.0561279i
$190$	−1.26816	+	0.328831i	−0.0920017	+	0.0238559i
$191$	13.5272	−	23.4298i	0.978795	−	1.69532i	0.311998	−	0.950083i	$-0.399002\pi$
$191$	13.5272	−	23.4298i	0.978795	−	1.69532i	0.666797	−	0.745239i	$-0.267665\pi$
$192$	8.21561	−	2.99024i	0.592911	−	0.215802i
$193$	10.2414	+	1.80583i	0.737190	+	0.129987i	0.529622	−	0.848234i	$-0.322334\pi$
$193$	10.2414	+	1.80583i	0.737190	+	0.129987i	0.207568	+	0.978220i	$0.433445\pi$
$194$	4.87398	+	5.80858i	0.349931	+	0.417032i
$195$	0.0310268	+	0.0852454i	0.00222187	+	0.00610455i
$196$	−1.73091	+	0.428788i	−0.123637	+	0.0306277i
$197$	11.2741	+	19.5274i	0.803248	+	1.39127i	0.917467	+	0.397811i	$0.130230\pi$
$197$	11.2741	+	19.5274i	0.803248	+	1.39127i	−0.114219	+	0.993456i	$0.536437\pi$
$198$	−3.54226	+	2.04513i	−0.251738	+	0.145341i
$199$	7.37066	+	8.78401i	0.522492	+	0.622682i	0.961168	−	0.275963i	$-0.0889968\pi$
$199$	7.37066	+	8.78401i	0.522492	+	0.622682i	−0.438676	+	0.898645i	$0.644552\pi$
$200$	−9.47426	−	11.2910i	−0.669931	−	0.798393i
$201$	6.70989	−	3.87395i	0.473279	−	0.273248i
$202$	1.66387	+	2.88191i	0.117070	+	0.202770i
$203$	3.79893	+	2.47114i	0.266633	+	0.173440i
$204$	−0.351065	−	0.964544i	−0.0245795	−	0.0675316i
$205$	0.619138	+	0.737860i	0.0432425	+	0.0515344i
$206$	−21.7131	−	3.82860i	−1.51282	−	0.266751i
$207$	0.462335	−	0.168276i	0.0321345	−	0.0116960i
$208$	−0.682961	+	1.18292i	−0.0473548	+	0.0820209i
$209$	−12.1848	−	5.80230i	−0.842840	−	0.401354i
$210$	0.179466	−	0.774681i	0.0123843	−	0.0534581i
$211$	−1.50390	−	0.265178i	−0.103533	−	0.0182556i	0.121642	−	0.992574i	$-0.461184\pi$
$211$	−1.50390	−	0.265178i	−0.103533	−	0.0182556i	−0.225174	+	0.974318i	$0.572295\pi$
$212$	0.297068	+	0.816188i	0.0204027	+	0.0560560i
$213$	0.120960	−	0.0213285i	0.00828804	−	0.00146140i
$214$	10.1332	+	8.50276i	0.692691	+	0.581237i
$215$	−0.856359	+	0.150999i	−0.0584032	+	0.0102981i
$216$	−2.57963	+	1.48935i	−0.175522	+	0.101338i
$217$	−6.89800	+	2.10323i	−0.468267	+	0.142777i
$218$	3.04903	+	17.2919i	0.206506	+	1.17116i
$219$	−2.75460	+	7.56821i	−0.186139	+	0.511412i
$220$			0.179444i			0.0120981i
$221$	1.39138	+	0.803312i	0.0935941	+	0.0540366i
$222$	0.284898	+	1.61573i	0.0191211	+	0.108441i
$223$	−7.12074	+	2.59174i	−0.476840	+	0.173555i	−0.569248	−	0.822166i	$-0.692766\pi$
$223$	−7.12074	+	2.59174i	−0.476840	+	0.173555i	0.0924085	+	0.995721i	$0.470543\pi$
$224$	−3.37684	+	1.71737i	−0.225624	+	0.114747i
$225$	3.79057	+	3.18067i	0.252705	+	0.212044i
$226$	12.3387	+	10.3534i	0.820760	+	0.688699i
$227$	0.900755	+	1.56015i	0.0597852	+	0.103551i	0.894369	−	0.447330i	$-0.147625\pi$
$227$	0.900755	+	1.56015i	0.0597852	+	0.103551i	−0.834584	+	0.550881i	$0.814292\pi$
$228$	−1.00255	−	0.477408i	−0.0663957	−	0.0316171i
$229$	−17.6494	−	10.1899i	−1.16630	−	0.673365i	−0.213496	−	0.976944i	$-0.568485\pi$
$229$	−17.6494	−	10.1899i	−1.16630	−	0.673365i	−0.952806	+	0.303579i	$0.901818\pi$
$230$	−0.0256784	+	0.145629i	−0.00169318	+	0.00960251i
$231$	6.54585	−	4.92490i	0.430685	−	0.324035i
$232$	4.79454	+	1.74507i	0.314777	+	0.114569i
$233$	3.95084	−	22.4063i	0.258828	−	1.46789i	−0.527223	−	0.849727i	$-0.676767\pi$
$233$	3.95084	−	22.4063i	0.258828	−	1.46789i	0.786052	−	0.618161i	$-0.212122\pi$
$234$	0.180164	−	0.494997i	0.0117777	−	0.0323590i
$235$	0.794132	−	1.37548i	0.0518034	−	0.0897262i
$236$	−0.966163	−	1.67344i	−0.0628919	−	0.108932i
$237$	−10.9691	+	1.93415i	−0.712522	+	0.125637i
$238$	−6.38419	−	12.5531i	−0.413826	−	0.813699i
$239$	8.01589	−	13.8839i	0.518505	−	0.898077i	−0.481264	−	0.876576i	$-0.659822\pi$
$239$	8.01589	−	13.8839i	0.518505	−	0.898077i	0.999769	−	0.0215011i	$-0.00684454\pi$
$240$		−	0.779354i		−	0.0503071i
$241$	26.3831	+	9.60268i	1.69949	+	0.618563i	0.995767	−	0.0919143i	$-0.0292986\pi$
$241$	26.3831	+	9.60268i	1.69949	+	0.618563i	0.703720	+	0.710477i	$0.251521\pi$
$242$	−1.20064	+	1.43087i	−0.0771800	+	0.0919796i
$243$	0.766044	−	0.642788i	0.0491418	−	0.0412348i
$244$	1.30077	−	1.55019i	0.0832730	−	0.0992409i
$245$	−0.168861	+	1.58358i	−0.0107881	+	0.101171i
$246$		−	5.59309i		−	0.356603i
$247$	1.68242	−	0.436250i	0.107050	−	0.0277579i
$248$	−7.03130	+	4.05952i	−0.446488	+	0.257780i
$249$	−1.12337	−	3.08644i	−0.0711909	−	0.195595i
$250$	−2.80969	+	1.02264i	−0.177700	+	0.0646776i
$251$	4.85965	−	13.3518i	0.306738	−	0.842756i	−0.686549	−	0.727083i	$-0.740875\pi$
$251$	4.85965	−	13.3518i	0.306738	−	0.842756i	0.993287	−	0.115673i	$-0.0369024\pi$
$252$	0.538586	−	0.405216i	0.0339277	−	0.0255262i
$253$	−1.16693	+	0.979174i	−0.0733645	+	0.0615601i
$254$	18.8054			1.17996
$255$	−0.916691			−0.0574054
$256$	−4.60434	+	3.86350i	−0.287771	+	0.241469i
$257$	23.7115	+	8.63027i	1.47908	+	0.538341i	0.950550	−	0.310572i	$-0.100521\pi$
$257$	23.7115	+	8.63027i	1.47908	+	0.538341i	0.528531	+	0.848914i	$0.322743\pi$
$258$	4.37288	+	2.52468i	0.272243	+	0.157180i
$259$	−0.958294	−	3.14293i	−0.0595455	−	0.195292i
$260$	−0.0148547	−	0.0177031i	−0.000921247	−	0.00109790i
$261$	−1.68689	−	0.297443i	−0.104416	−	0.0184113i
$262$	−2.40508	−	13.6399i	−0.148587	−	0.842676i
$263$	3.06558	−	17.3857i	0.189032	−	1.07205i	−0.731634	−	0.681698i	$-0.761242\pi$
$263$	3.06558	−	17.3857i	0.189032	−	1.07205i	0.920665	−	0.390353i	$-0.127647\pi$
$264$	5.92810	−	7.06484i	0.364850	−	0.434811i
$265$	0.775695			0.0476506
$266$	−14.4476	−	4.83597i	−0.885837	−	0.296512i
$267$	5.97218			0.365492
$268$	−1.26871	+	1.51199i	−0.0774988	+	0.0923595i
$269$	2.07674	−	11.7778i	0.126621	−	0.718104i	−0.853711	−	0.520748i	$-0.825653\pi$
$269$	2.07674	−	11.7778i	0.126621	−	0.718104i	0.980332	−	0.197357i	$-0.0632357\pi$
$270$	0.0521911	+	0.295990i	0.00317625	+	0.0180134i
$271$	22.2204	+	3.91805i	1.34979	+	0.238005i	0.801356	−	0.598188i	$-0.204113\pi$
$271$	22.2204	+	3.91805i	1.34979	+	0.238005i	0.548435	+	0.836193i	$0.315224\pi$
$272$	−8.87220	−	10.5735i	−0.537956	−	0.641111i
$273$	−0.238092	+	1.02774i	−0.0144100	+	0.0622019i
$274$	−16.9859	−	9.80679i	−1.02615	−	0.592450i
$275$	−14.3965	−	5.23991i	−0.868143	−	0.315978i
$276$	−0.0960142	+	0.0805655i	−0.00577938	+	0.00484947i
$277$	17.2354			1.03558			0.517789	−	0.855509i	$-0.326755\pi$
$277$	17.2354			1.03558			0.517789	+	0.855509i	$0.326755\pi$
$278$	−16.5297			−0.991385
$279$	2.08801	−	1.75204i	0.125006	−	0.104892i
$280$	0.217163	+	1.77977i	0.0129780	+	0.106362i
$281$	10.4708	−	28.7683i	0.624636	−	1.71617i	−0.0707091	−	0.997497i	$-0.522526\pi$
$281$	10.4708	−	28.7683i	0.624636	−	1.71617i	0.695345	−	0.718676i	$-0.255252\pi$
$282$	−8.66644	+	3.15433i	−0.516079	+	0.187837i
$283$	9.86308	+	27.0986i	0.586299	+	1.61084i	0.777214	+	0.629237i	$0.216632\pi$
$283$	9.86308	+	27.0986i	0.586299	+	1.61084i	−0.190915	+	0.981607i	$0.561145\pi$
$284$	−0.0270976	+	0.0156448i	−0.00160795	+	0.000928349i
$285$	−0.706876	+	0.695533i	−0.0418717	+	0.0411998i
$286$			1.63094i			0.0964396i
$287$	1.35670	+	11.1189i	0.0800837	+	0.656329i
$288$	0.920409	−	1.09690i	0.0542356	−	0.0646355i
$289$	0.586037	−	0.491743i	0.0344728	−	0.0289261i
$290$	0.330924	−	0.394379i	0.0194325	−	0.0231587i
$291$	5.39353	+	1.96308i	0.316174	+	0.115078i
$292$		−	2.05172i		−	0.120068i
$293$	−12.8237	+	22.2113i	−0.749168	+	1.29760i	0.199054	+	0.979989i	$0.436213\pi$
$293$	−12.8237	+	22.2113i	−0.749168	+	1.29760i	−0.948222	+	0.317609i	$0.897120\pi$
$294$	6.66184	−	6.41383i	0.388526	−	0.374062i
$295$	−1.69949	+	0.299666i	−0.0989481	+	0.0174472i
$296$	−1.84964	−	3.20367i	−0.107508	−	0.186209i
$297$	−1.54807	+	2.68134i	−0.0898283	+	0.155587i
$298$	−8.00206	+	21.9855i	−0.463547	+	1.27359i
$299$	0.0340667	−	0.193202i	0.00197013	−	0.0111731i
$300$	−1.18453	−	0.431135i	−0.0683890	−	0.0248916i
$301$	−9.30557	−	3.95828i	−0.536364	−	0.228152i
$302$	0.895394	−	5.07803i	0.0515241	−	0.292208i
$303$	2.18148	+	1.25948i	0.125323	+	0.0723551i
$304$	−14.8640	−	1.42167i	−0.852512	−	0.0815382i
$305$	−0.903625	−	1.56512i	−0.0517414	−	0.0896187i
$306$	4.07764	+	3.42155i	0.233103	+	0.195597i
$307$	9.70520	+	8.14363i	0.553905	+	0.464781i	0.876261	−	0.481837i	$-0.160030\pi$
$307$	9.70520	+	8.14363i	0.553905	+	0.464781i	−0.322356	+	0.946619i	$0.604475\pi$
$308$	−1.13787	+	1.74928i	−0.0648364	+	0.0996743i
$309$	−15.6829	+	5.70811i	−0.892170	+	0.324723i
$310$	0.142257	+	0.806780i	0.00807966	+	0.0458220i
$311$	19.0619	+	11.0054i	1.08090	+	0.624059i	0.931140	−	0.364663i	$-0.118816\pi$
$311$	19.0619	+	11.0054i	1.08090	+	0.624059i	0.149762	+	0.988722i	$0.452149\pi$
$312$			1.18772i			0.0672416i
$313$	−6.21482	+	17.0751i	−0.351283	+	0.965141i	0.630676	+	0.776046i	$0.282778\pi$
$313$	−6.21482	+	17.0751i	−0.351283	+	0.965141i	−0.981959	+	0.189095i	$0.939445\pi$
$314$	−3.57558	−	20.2781i	−0.201782	−	1.14436i
$315$	−0.175552	−	0.575761i	−0.00989125	−	0.0324405i
$316$	2.45732	−	1.41873i	0.138235	−	0.0798100i
$317$	−16.1601	+	2.84947i	−0.907643	+	0.160042i	−0.607933	−	0.793988i	$-0.708001\pi$
$317$	−16.1601	+	2.84947i	−0.907643	+	0.160042i	−0.299710	+	0.954030i	$0.596890\pi$
$318$	−3.45046	−	2.89528i	−0.193492	−	0.162359i
$319$	5.22284	−	0.920928i	0.292423	−	0.0515621i
$320$	0.680304	+	1.86912i	0.0380301	+	0.104487i
$321$	9.86086	+	1.73874i	0.550380	+	0.0970468i
$322$	−1.17377	+	1.25681i	−0.0654118	+	0.0700394i
$323$	−1.67219	+	17.4834i	−0.0930433	+	0.972801i
$324$	−0.127374	+	0.220618i	−0.00707633	+	0.0122566i
$325$	1.85406	−	0.674824i	0.102845	−	0.0374325i
$326$	−2.74491	−	0.484002i	−0.152027	−	0.0268064i
$327$	8.54338	+	10.1816i	0.472450	+	0.563044i
$328$	4.31322	+	11.8505i	0.238158	+	0.654333i
$329$	16.4635	−	8.37292i	0.907663	−	0.461614i
$330$	−0.465283	−	0.805894i	−0.0256130	−	0.0443630i
$331$	−11.6688	+	6.73696i	−0.641373	+	0.370297i	−0.785143	−	0.619314i	$-0.787411\pi$
$331$	−11.6688	+	6.73696i	−0.641373	+	0.370297i	0.143770	+	0.989611i	$0.454077\pi$
$332$	0.537837	+	0.640969i	0.0295176	+	0.0351777i
$333$	0.798283	+	0.951357i	0.0437456	+	0.0521340i
$334$	−15.5998	+	9.00654i	−0.853582	+	0.492816i
$335$	0.881356	+	1.52655i	0.0481536	+	0.0834045i
$336$	4.94197	−	7.59740i	0.269607	−	0.414472i
$337$	2.99442	+	8.22710i	0.163116	+	0.448159i	0.994143	−	0.108074i	$-0.0344684\pi$
$337$	2.99442	+	8.22710i	0.163116	+	0.448159i	−0.831026	+	0.556233i	$0.812246\pi$
$338$	10.9042	+	12.9952i	0.593113	+	0.706844i
$339$	12.0071	+	2.11718i	0.652137	+	0.114989i
$340$	0.219442	−	0.0798702i	0.0119009	−	0.00433157i
$341$	−4.21958	+	7.30852i	−0.228503	+	0.395779i
$342$	5.74041	−	0.455468i	0.310406	−	0.0246289i
$343$	−11.6878	+	14.3665i	−0.631081	+	0.775717i
$344$	−11.2121	−	1.97699i	−0.604515	−	0.106592i
$345$	0.0382842	+	0.105185i	0.00206115	+	0.00566297i
$346$	16.6199	−	2.93054i	0.893494	−	0.157547i
$347$	−14.9375	−	12.5341i	−0.801889	−	0.672865i	0.146768	−	0.989171i	$-0.453113\pi$
$347$	−14.9375	−	12.5341i	−0.801889	−	0.672865i	−0.948657	+	0.316306i	$0.897557\pi$
$348$	0.429730	−	0.0757730i	0.0230360	−	0.00406186i
$349$	−7.94338	+	4.58611i	−0.425199	+	0.245489i	−0.697299	−	0.716780i	$-0.745615\pi$
$349$	−7.94338	+	4.58611i	−0.425199	+	0.245489i	0.272100	+	0.962269i	$0.412282\pi$
$350$	−16.8491	−	3.90334i	−0.900623	−	0.208642i
$351$	−0.0692402	−	0.392681i	−0.00369577	−	0.0209597i
$352$	−1.51630	+	4.16601i	−0.0808192	+	0.222049i
$353$			18.1880i			0.968049i	0.875054	+	0.484025i	$0.160826\pi$
$353$			18.1880i			0.968049i	−0.875054	+	0.484025i	$0.839174\pi$
$354$	8.67820	+	5.01036i	0.461241	+	0.266298i
$355$	0.00485241	+	0.0275194i	0.000257539	+	0.00146058i
$356$	−1.42965	+	0.520349i	−0.0757712	+	0.0275785i
$357$	−8.93620	−	5.81284i	−0.472954	−	0.307648i
$358$	−22.7890	−	19.1222i	−1.20444	−	1.01064i
$359$	−14.5748	−	12.2297i	−0.769231	−	0.645461i	0.171281	−	0.985222i	$-0.445209\pi$
$359$	−14.5748	−	12.2297i	−0.769231	−	0.645461i	−0.940512	+	0.339761i	$0.889654\pi$
$360$	−0.338839	−	0.586887i	−0.0178584	−	0.0309317i
$361$	11.9759	+	14.7505i	0.630312	+	0.776342i
$362$	13.2046	+	7.62368i	0.694019	+	0.400692i
$363$	−0.245520	+	1.39241i	−0.0128864	+	0.0730826i
$364$	−0.0325507	−	0.266771i	−0.00170612	−	0.0139826i
$365$	−1.72183	−	0.626694i	−0.0901246	−	0.0328027i
$366$	−1.82230	+	10.3348i	−0.0952533	+	0.540208i
$367$	1.06075	−	2.91438i	0.0553706	−	0.152129i	−0.908924	−	0.416963i	$-0.863095\pi$
$367$	1.06075	−	2.91438i	0.0553706	−	0.152129i	0.964294	+	0.264833i	$0.0853169\pi$
$368$	−0.842711	+	1.45962i	−0.0439294	+	0.0760879i
$369$	−2.11686	−	3.66652i	−0.110200	−	0.190871i
$370$	−0.367593	+	0.0648165i	−0.0191102	+	0.00336965i
$371$	7.56173	+	4.91878i	0.392586	+	0.255370i
$372$	−0.347183	+	0.601338i	−0.0180006	+	0.0311779i
$373$			9.58791i			0.496443i	0.968703	+	0.248222i	$0.0798461\pi$
$373$			9.58791i			0.496443i	−0.968703	+	0.248222i	$0.920154\pi$
$374$	−15.4868	−	5.63674i	−0.800804	−	0.291469i
$375$	−1.45482	+	1.73379i	−0.0751268	+	0.0895327i
$376$	15.9297	−	13.3666i	0.821510	−	0.689329i
$377$	−0.439025	+	0.523210i	−0.0226110	+	0.0269467i
$378$	−1.36813	+	3.21636i	−0.0703692	+	0.165432i
$379$			14.5327i			0.746496i	0.927732	+	0.373248i	$0.121756\pi$
$379$			14.5327i			0.746496i	−0.927732	+	0.373248i	$0.878244\pi$
$380$	0.108614	−	0.228089i	0.00557179	−	0.0117007i
$381$	12.3278	−	7.11745i	0.631571	−	0.364638i
$382$	−12.2242	−	33.5856i	−0.625443	−	1.71839i
$383$	−5.85643	+	2.13156i	−0.299249	+	0.108918i	−0.487281	−	0.873245i	$-0.662011\pi$
$383$	−5.85643	+	2.13156i	−0.299249	+	0.108918i	0.188032	+	0.982163i	$0.439789\pi$
$384$	2.97087	−	8.16239i	0.151606	−	0.416535i
$385$	1.12045	+	1.48923i	0.0571036	+	0.0758984i
$386$	10.5242	−	8.83087i	0.535669	−	0.449479i
$387$	3.82215			0.194291
$388$	−1.46217			−0.0742303
$389$	7.18650	−	6.03019i	0.364370	−	0.305743i	−0.442160	−	0.896936i	$-0.645788\pi$
$389$	7.18650	−	6.03019i	0.364370	−	0.305743i	0.806530	+	0.591194i	$0.201343\pi$
$390$	0.112616	+	0.0409888i	0.00570253	+	0.00207555i
$391$	1.71683	+	0.991213i	0.0868239	+	0.0501278i
$392$	−9.16875	+	18.7268i	−0.463092	+	0.945848i
$393$	−6.73904	−	8.03128i	−0.339940	−	0.405124i
$394$	29.3355	+	5.17264i	1.47790	+	0.260594i
$395$	−0.440036	−	2.49557i	−0.0221406	−	0.125566i
$396$	0.136963	−	0.776753i	0.00688263	−	0.0390333i
$397$	−14.8442	+	17.6906i	−0.745008	+	0.887866i	−0.996802	−	0.0799150i	$-0.974535\pi$
$397$	−14.8442	+	17.6906i	−0.745008	+	0.887866i	0.251794	+	0.967781i	$0.418980\pi$
$398$	15.1484			0.759323
$399$	−11.3013	+	2.29790i	−0.565773	+	0.115039i
$400$	−16.9507			−0.847537
$401$	−9.30774	+	11.0925i	−0.464807	+	0.553935i	−0.946625	−	0.322336i	$-0.895532\pi$
$401$	−9.30774	+	11.0925i	−0.464807	+	0.553935i	0.481819	+	0.876271i	$0.339976\pi$
$402$	1.77739	−	10.0801i	0.0886484	−	0.502750i
$403$	−0.188728	−	1.07033i	−0.00940120	−	0.0533169i
$404$	−0.631949	−	0.111430i	−0.0314406	−	0.00554383i
$405$	0.146239	+	0.174281i	0.00726669	+	0.00866011i
$406$	5.72676	−	1.74611i	0.284214	−	0.0866582i
$407$	−3.32998	−	1.92256i	−0.165061	−	0.0952979i
$408$	−11.2782	−	4.10492i	−0.558353	−	0.203224i
$409$	−7.89237	+	6.62249i	−0.390253	+	0.327461i	−0.816712	−	0.577046i	$-0.804205\pi$
$409$	−7.89237	+	6.62249i	−0.390253	+	0.327461i	0.426459	+	0.904507i	$0.359761\pi$
$410$	1.27247			0.0628430
$411$	−14.8466			−0.732330
$412$	3.25691	−	2.73287i	0.160456	−	0.134639i
$413$	−18.4674	−	7.85542i	−0.908721	−	0.386540i
$414$	0.222306	−	0.610782i	0.0109258	−	0.0300183i
$415$	0.702191	−	0.255577i	0.0344692	−	0.0125458i
$416$	−0.195278	−	0.536522i	−0.00957428	−	0.0263051i
$417$	−10.8359	+	6.25613i	−0.530638	+	0.306364i
$418$	−16.2190	+	7.40392i	−0.793296	+	0.362138i
$419$			6.08954i			0.297493i	0.988875	+	0.148747i	$0.0475239\pi$
$419$			6.08954i			0.297493i	−0.988875	+	0.148747i	$0.952476\pi$
$420$	0.0921899	+	0.122533i	0.00449841	+	0.00597898i
$421$	11.2721	−	13.4335i	0.549367	−	0.654711i	−0.417893	−	0.908496i	$-0.637231\pi$
$421$	11.2721	−	13.4335i	0.549367	−	0.654711i	0.967261	+	0.253786i	$0.0816758\pi$
$422$	−1.54543	+	1.29677i	−0.0752305	+	0.0631259i
$423$	−4.48738	+	5.34786i	−0.218184	+	0.260022i
$424$	9.54349	+	3.47355i	0.463473	+	0.168690i
$425$			19.9378i			0.967124i
$426$	0.0811314	−	0.140524i	0.00393083	−	0.00680840i
$427$	1.11580	−	20.9873i	0.0539975	−	1.01565i
$428$	−2.51203	+	0.442939i	−0.121424	+	0.0214103i
$429$	0.617276	+	1.06915i	0.0298024	+	0.0516192i
$430$	−0.574385	+	0.994865i	−0.0276993	+	0.0479766i
$431$	6.76299	−	18.5812i	0.325762	−	0.895023i	−0.663410	−	0.748256i	$-0.730891\pi$
$431$	6.76299	−	18.5812i	0.325762	−	0.895023i	0.989171	−	0.146766i	$-0.0468865\pi$
$432$	−0.594851	+	3.37357i	−0.0286198	+	0.162311i
$433$	−19.4482	−	7.07858i	−0.934623	−	0.340175i	−0.170582	−	0.985343i	$-0.554565\pi$
$433$	−19.4482	−	7.07858i	−0.934623	−	0.340175i	−0.764040	+	0.645169i	$0.776787\pi$
$434$	−3.72912	+	8.76683i	−0.179003	+	0.420821i
$435$	0.0676708	−	0.383780i	0.00324457	−	0.0184008i
$436$	−2.93227	−	1.69294i	−0.140430	−	0.0810773i
$437$	2.07595	−	0.538293i	0.0993064	−	0.0257500i
$438$	5.31993	+	9.21439i	0.254196	+	0.440281i
$439$	2.34716	+	1.96950i	0.112024	+	0.0939990i	0.697079	−	0.716994i	$-0.254483\pi$
$439$	2.34716	+	1.96950i	0.112024	+	0.0939990i	−0.585055	+	0.810993i	$0.698927\pi$
$440$	1.60731	+	1.34869i	0.0766254	+	0.0642963i
$441$	1.93963	−	6.72591i	0.0923633	−	0.320281i
$442$	1.99448	−	0.725930i	0.0948676	−	0.0345290i
$443$	0.884466	+	5.01606i	0.0420223	+	0.238320i	0.998583	−	0.0532123i	$-0.0169460\pi$
$443$	0.884466	+	5.01606i	0.0420223	+	0.238320i	−0.956561	+	0.291532i	$0.905835\pi$
$444$	−0.273987	−	0.158187i	−0.0130029	−	0.00750721i
$445$			1.35872i			0.0644095i
$446$	−3.42389	+	9.40706i	−0.162126	+	0.445437i
$447$	3.07533	+	17.4411i	0.145458	+	0.824933i
$448$	−5.22048	+	22.5347i	−0.246644	+	1.06466i
$449$	5.12847	−	2.96092i	0.242027	−	0.139735i	−0.374081	−	0.927396i	$-0.622042\pi$
$449$	5.12847	−	2.96092i	0.242027	−	0.139735i	0.616108	+	0.787662i	$0.288708\pi$
$450$	6.43771	−	1.13514i	0.303477	−	0.0535111i
$451$	10.0415	+	8.42581i	0.472835	+	0.396756i
$452$	−3.05879	+	0.539347i	−0.143873	+	0.0253687i
$453$	−1.33495	−	3.66776i	−0.0627216	−	0.172326i
$454$	2.34378	+	0.413272i	0.109999	+	0.0193958i
$455$	−0.233820	−	0.0541678i	−0.0109617	−	0.00253943i
$456$	−11.8114	+	5.39186i	−0.553118	+	0.252497i
$457$	−1.11779	+	1.93608i	−0.0522882	+	0.0905659i	−0.890985	−	0.454033i	$-0.849985\pi$
$457$	−1.11779	+	1.93608i	−0.0522882	+	0.0905659i	0.838697	+	0.544599i	$0.183318\pi$
$458$	−25.2996	+	9.20829i	−1.18217	+	0.430275i
$459$	3.96805	+	0.699675i	0.185213	+	0.0326580i
$460$	−0.0183293	−	0.0218440i	−0.000854608	−	0.00101848i
$461$	1.25034	+	3.43528i	0.0582341	+	0.159997i	0.965398	−	0.260780i	$-0.0839797\pi$
$461$	1.25034	+	3.43528i	0.0582341	+	0.159997i	−0.907164	+	0.420777i	$0.861758\pi$
$462$	0.574536	−	10.8065i	0.0267298	−	0.502765i
$463$	−3.70098	−	6.41029i	−0.171999	−	0.297911i	0.767120	−	0.641504i	$-0.221689\pi$
$463$	−3.70098	−	6.41029i	−0.171999	−	0.297911i	−0.939119	+	0.343593i	$0.888356\pi$
$464$	5.08162	−	2.93388i	0.235908	−	0.136202i
$465$	0.398604	+	0.475038i	0.0184848	+	0.0220294i
$466$	−19.3204	−	23.0251i	−0.895000	−	1.06662i
$467$	−10.0312	+	5.79154i	−0.464190	+	0.268000i	−0.713805	−	0.700345i	$-0.753030\pi$
$467$	−10.0312	+	5.79154i	−0.464190	+	0.268000i	0.249614	+	0.968345i	$0.419696\pi$
$468$	0.0507889	+	0.0879689i	0.00234772	+	0.00406636i
$469$	−1.08831	+	20.4701i	−0.0502533	+	0.945223i
$470$	−0.717635	−	1.97168i	−0.0331020	−	0.0909470i
$471$	−10.0188	−	11.9399i	−0.461641	−	0.550163i
$472$	−22.2510	−	3.92344i	−1.02418	−	0.180591i
$473$	−11.1202	+	4.04744i	−0.511310	+	0.186101i
$474$	−7.35732	+	12.7433i	−0.337933	+	0.585317i
$475$	15.1276	+	15.3744i	0.694104	+	0.705424i
$476$	2.64566	+	0.612904i	0.121263	+	0.0280924i
$477$	−3.35773	−	0.592058i	−0.153740	−	0.0271085i
$478$	−7.24374	−	19.9020i	−0.331321	−	0.910296i
$479$	−24.9985	+	4.40792i	−1.14221	+	0.201403i	−0.712573	−	0.701598i	$-0.752470\pi$
$479$	−24.9985	+	4.40792i	−1.14221	+	0.201403i	−0.429639	+	0.903001i	$0.641359\pi$
$480$	0.249554	+	0.209400i	0.0113905	+	0.00955778i
$481$	0.487673	−	0.0859900i	0.0222360	−	0.00392080i
$482$	32.1218	−	18.5456i	1.46311	−	0.844727i
$483$	−0.293783	+	1.26814i	−0.0133676	+	0.0577025i
$484$	−0.0625456	−	0.354714i	−0.00284298	−	0.0161233i
$485$	−0.446617	+	1.22707i	−0.0202798	+	0.0557184i
$486$		−	1.32108i		−	0.0599254i
$487$	24.3818	+	14.0768i	1.10484	+	0.637881i	0.937489	−	0.348015i	$-0.113144\pi$
$487$	24.3818	+	14.0768i	1.10484	+	0.637881i	0.167354	+	0.985897i	$0.446478\pi$
$488$	−4.10883	−	23.3024i	−0.185998	−	1.05485i
$489$	−1.98259	+	0.721605i	−0.0896560	+	0.0326321i
$490$	1.45920	+	1.51562i	0.0659199	+	0.0684688i
$491$	11.4777	+	9.63096i	0.517983	+	0.434639i	0.863928	−	0.503616i	$-0.167997\pi$
$491$	11.4777	+	9.63096i	0.517983	+	0.434639i	−0.345945	+	0.938255i	$0.612442\pi$
$492$	0.826204	+	0.693267i	0.0372481	+	0.0312549i
$493$	−3.45088	−	5.97710i	−0.155420	−	0.269195i
$494$	0.987180	−	2.07307i	0.0444153	−	0.0932719i
$495$	−0.610026	−	0.352199i	−0.0274186	−	0.0158302i
$496$	−1.62138	+	9.19532i	−0.0728022	+	0.412882i
$497$	−0.127201	+	0.299038i	−0.00570573	+	0.0134137i
$498$	−4.07744	−	1.48407i	−0.182714	−	0.0665026i
$499$	4.21577	−	23.9088i	0.188724	−	1.07031i	−0.732353	−	0.680925i	$-0.761578\pi$
$499$	4.21577	−	23.9088i	0.188724	−	1.07031i	0.921077	−	0.389381i	$-0.127311\pi$
$500$	0.197199	−	0.541800i	0.00881902	−	0.0242300i
$501$	−6.81756	+	11.8084i	−0.304586	+	0.527558i
$502$	−9.38539	−	16.2560i	−0.418890	−	0.725539i
$503$	40.9239	−	7.21598i	1.82471	−	0.321745i	0.846979	−	0.531627i	$-0.178419\pi$
$503$	40.9239	−	7.21598i	1.82471	−	0.321745i	0.977727	+	0.209882i	$0.0673081\pi$
$504$	0.418402	−	7.86979i	0.0186371	−	0.350548i
$505$	−0.286541	+	0.496304i	−0.0127509	+	0.0220852i
$506$			2.01243i			0.0894636i
$507$	12.0666	+	4.39188i	0.535897	+	0.195050i
$508$	−2.33094	+	2.77791i	−0.103419	+	0.123250i
$509$	−2.22833	+	1.86979i	−0.0987689	+	0.0828769i	−0.690835	−	0.723012i	$-0.742757\pi$
$509$	−2.22833	+	1.86979i	−0.0987689	+	0.0828769i	0.592066	+	0.805889i	$0.298312\pi$
$510$	−0.778430	+	0.927696i	−0.0344694	+	0.0410791i
$511$	−12.8110	−	17.0275i	−0.566726	−	0.753254i
$512$			25.3129i			1.11868i
$513$	3.59071	−	2.47120i	0.158534	−	0.109106i
$514$	28.8690	−	16.6676i	1.27336	−	0.735174i
$515$	−1.29864	−	3.56799i	−0.0572250	−	0.157224i
$516$	−0.914963	+	0.333019i	−0.0402790	+	0.0146604i
$517$	7.39262	−	20.3111i	0.325127	−	0.893280i
$518$	−3.99442	−	1.69910i	−0.175505	−	0.0746540i
$519$	9.78595	−	8.21139i	0.429555	−	0.360440i
$520$	−0.270217			−0.0118498
$521$	27.9349			1.22385			0.611925	−	0.790916i	$-0.290395\pi$
$521$	27.9349			1.22385			0.611925	+	0.790916i	$0.290395\pi$
$522$	−1.73347	+	1.45456i	−0.0758721	+	0.0636642i
$523$	28.5415	+	10.3883i	1.24803	+	0.454247i	0.879737	−	0.475461i	$-0.157719\pi$
$523$	28.5415	+	10.3883i	1.24803	+	0.454247i	0.368297	+	0.929708i	$0.379941\pi$
$524$	2.31298	+	1.33540i	0.101043	+	0.0583372i
$525$	−12.5227	+	3.81821i	−0.546533	+	0.166640i
$526$	−14.9913	−	17.8659i	−0.653650	−	0.778990i
$527$	10.8157	+	1.90710i	0.471140	+	0.0830747i
$528$	−1.84174	−	10.4450i	−0.0801516	−	0.454562i
$529$	−3.95187	+	22.4122i	−0.171821	+	0.974443i
$530$	0.658700	−	0.785008i	0.0286121	−	0.0340986i
$531$	7.58525			0.329172
$532$	2.50515	−	1.53475i	0.108612	−	0.0665399i
$533$	−1.68815			−0.0731219
$534$	5.07142	−	6.04388i	0.219462	−	0.261544i
$535$	−0.395577	+	2.24343i	−0.0171023	+	0.0969918i
$536$	4.00758	+	22.7281i	0.173101	+	0.981704i
$537$	−22.1765	−	3.91032i	−0.956987	−	0.168743i
$538$	−10.1557	−	12.1031i	−0.437842	−	0.521800i
$539$	1.47915	+	21.6225i	0.0637117	+	0.931346i
$540$	−0.0501924	−	0.0289786i	−0.00215994	−	0.00124704i
$541$	−39.8633	−	14.5091i	−1.71386	−	0.623793i	−0.716577	−	0.697508i	$-0.754292\pi$
$541$	−39.8633	−	14.5091i	−1.71386	−	0.623793i	−0.997279	+	0.0737148i	$0.976515\pi$
$542$	22.8340	−	19.1600i	0.980806	−	0.822994i
$543$	11.5416			0.495297
$544$	5.76951			0.247366
$545$	−2.31640	+	1.94369i	−0.0992236	+	0.0832585i
$546$	0.837902	+	1.11368i	0.0358589	+	0.0476613i
$547$	14.3108	−	39.3186i	0.611886	−	1.68114i	−0.114131	−	0.993466i	$-0.536408\pi$
$547$	14.3108	−	39.3186i	0.611886	−	1.68114i	0.726017	−	0.687677i	$-0.241369\pi$
$548$	3.55405	−	1.29357i	0.151822	−	0.0552585i
$549$	2.71690	+	7.46461i	0.115954	+	0.318582i
$550$	−17.5280	+	10.1198i	−0.747395	+	0.431509i
$551$	−7.19612	−	1.99071i	−0.306565	−	0.0848072i
$552$			1.46554i			0.0623776i
$553$	11.5351	−	27.1179i	0.490521	−	1.15317i
$554$	14.6359	−	17.4424i	0.621819	−	0.741055i
$555$	−0.216441	+	0.181616i	−0.00918742	+	0.00770916i
$556$	2.04886	−	2.44174i	0.0868912	−	0.103553i
$557$	37.4655	+	13.6363i	1.58746	+	0.577789i	0.976810	−	0.214109i	$-0.0686849\pi$
$557$	37.4655	+	13.6363i	1.58746	+	0.577789i	0.610653	+	0.791899i	$0.290907\pi$
$558$		−	3.60086i		−	0.152437i
$559$	0.762019	−	1.31985i	0.0322299	−	0.0558239i
$560$	1.72847	+	1.12434i	0.0730412	+	0.0475120i
$561$	−12.2857	+	2.16629i	−0.518701	+	0.0914610i
$562$	−20.2222	−	35.0258i	−0.853020	−	1.47747i
$563$	−19.7814	+	34.2623i	−0.833685	+	1.44399i	0.0614110	+	0.998113i	$0.480440\pi$
$563$	−19.7814	+	34.2623i	−0.833685	+	1.44399i	−0.895096	+	0.445873i	$0.852893\pi$
$564$	0.608258	−	1.67117i	0.0256123	−	0.0703692i
$565$	−0.481675	+	2.73172i	−0.0202642	+	0.114924i
$566$	35.7994	+	13.0299i	1.50476	+	0.547688i
$567$	0.320451	+	2.62627i	0.0134577	+	0.110293i
$568$	−0.0635312	+	0.360304i	−0.00266571	+	0.0151180i
$569$	25.0580	+	14.4672i	1.05049	+	0.606498i	0.922785	−	0.385315i	$-0.125907\pi$
$569$	25.0580	+	14.4672i	1.05049	+	0.606498i	0.127700	+	0.991813i	$0.459240\pi$
$570$	0.103623	+	1.30599i	0.00434028	+	0.0547019i
$571$	−11.4584	−	19.8465i	−0.479519	−	0.830552i	0.520205	−	0.854042i	$-0.325856\pi$
$571$	−11.4584	−	19.8465i	−0.479519	−	0.830552i	−0.999724	+	0.0234898i	$0.992522\pi$
$572$	−0.240920	−	0.202156i	−0.0100734	−	0.00845258i
$573$	−20.7249	−	17.3902i	−0.865795	−	0.726488i
$574$	12.4045	+	8.06891i	0.517754	+	0.336790i
$575$	2.28775	−	0.832671i	0.0954056	−	0.0347248i
$576$	−1.51818	−	8.61005i	−0.0632577	−	0.358752i
$577$	6.05025	+	3.49312i	0.251875	+	0.145420i	0.620623	−	0.784109i	$-0.286880\pi$
$577$	6.05025	+	3.49312i	0.251875	+	0.145420i	−0.368747	+	0.929530i	$0.620213\pi$
$578$		−	1.01065i		−	0.0420374i
$579$	3.55679	−	9.77220i	0.147815	−	0.406119i
$580$	0.0172390	+	0.0977671i	0.000715810	+	0.00405956i
$581$	8.46583	+	1.96123i	0.351222	+	0.0813656i
$582$	6.56669	−	3.79128i	0.272198	−	0.157154i
$583$	10.3960	−	1.83310i	0.430559	−	0.0759192i
$584$	−18.3776	−	15.4206i	−0.760469	−	0.638110i
$585$	0.0893380	−	0.0157527i	0.00369367	−	0.000651294i
$586$	11.5884	+	31.8389i	0.478713	+	1.31525i
$587$	−11.9252	−	2.10273i	−0.492204	−	0.0867888i	−0.0779632	−	0.996956i	$-0.524842\pi$
$587$	−11.9252	−	2.10273i	−0.492204	−	0.0867888i	−0.414241	+	0.910167i	$0.635953\pi$
$588$	0.121703	+	1.77908i	0.00501896	+	0.0733679i
$589$	9.78718	−	6.73575i	0.403274	−	0.277542i
$590$	−1.13990	+	1.97436i	−0.0469289	+	0.0812832i
$591$	21.1884	−	7.71196i	0.871575	−	0.317228i
$592$	−4.18966	−	0.738750i	−0.172194	−	0.0303624i
$593$	25.9737	+	30.9542i	1.06661	+	1.27114i	0.960946	+	0.276736i	$0.0892526\pi$
$593$	25.9737	+	30.9542i	1.06661	+	1.27114i	0.105665	+	0.994402i	$0.466303\pi$
$594$	1.39895	+	3.84358i	0.0573996	+	0.157704i
$595$	1.32247	−	2.03306i	0.0542159	−	0.0833473i
$596$	−2.25580	−	3.90717i	−0.0924014	−	0.160044i
$597$	9.93047	−	5.73336i	0.406427	−	0.234651i
$598$	−0.166593	−	0.198537i	−0.00681248	−	0.00811880i
$599$	−16.6618	−	19.8568i	−0.680783	−	0.811326i	0.309425	−	0.950924i	$-0.399863\pi$
$599$	−16.6618	−	19.8568i	−0.680783	−	0.811326i	−0.990208	+	0.139598i	$0.955419\pi$
$600$	−12.7646	+	7.36967i	−0.521114	+	0.300865i
$601$	−22.0985	−	38.2757i	−0.901416	−	1.56130i	−0.825657	−	0.564173i	$-0.809195\pi$
$601$	−22.0985	−	38.2757i	−0.901416	−	1.56130i	−0.0757594	−	0.997126i	$-0.524138\pi$
$602$	−11.9079	+	6.05602i	−0.485328	+	0.246825i
$603$	−2.64994	−	7.28065i	−0.107914	−	0.296491i
$604$	0.639135	+	0.761691i	0.0260060	+	0.0309928i
$605$	−0.316785	−	0.0558577i	−0.0128791	−	0.00227094i
$606$	3.12705	−	1.13815i	0.127028	−	0.0462344i
$607$	18.9948	−	32.8999i	0.770974	−	1.33537i	−0.166056	−	0.986116i	$-0.553103\pi$
$607$	18.9948	−	32.8999i	0.770974	−	1.33537i	0.937030	−	0.349249i	$-0.113563\pi$
$608$	4.44897	−	4.37758i	0.180430	−	0.177534i
$609$	3.09327	−	3.31211i	0.125346	−	0.134213i
$610$	−2.35125	−	0.414589i	−0.0951993	−	0.0167862i
$611$	0.952063	+	2.61577i	0.0385163	+	0.105823i
$612$	−1.01085	+	0.178241i	−0.0408613	+	0.00720495i
$613$	−3.03889	−	2.54993i	−0.122740	−	0.102991i	0.579352	−	0.815078i	$-0.303306\pi$
$613$	−3.03889	−	2.54993i	−0.122740	−	0.102991i	−0.702091	+	0.712087i	$0.747750\pi$
$614$	16.4828	−	2.90636i	0.665192	−	0.117291i
$615$	0.834162	−	0.481604i	0.0336367	−	0.0194201i
$616$	7.11636	+	23.3396i	0.286726	+	0.940380i
$617$	−0.977637	−	5.54446i	−0.0393582	−	0.223211i	0.958784	−	0.284135i	$-0.0917065\pi$
$617$	−0.977637	−	5.54446i	−0.0393582	−	0.223211i	−0.998142	+	0.0609238i	$0.980595\pi$
$618$	−7.54087	+	20.7184i	−0.303338	+	0.833416i
$619$		−	3.75310i		−	0.150850i	−0.997151	−	0.0754249i	$-0.975969\pi$
$619$		−	3.75310i		−	0.150850i	0.997151	−	0.0754249i	$-0.0240313\pi$
$620$	−0.136809	−	0.0789869i	−0.00549439	−	0.00317219i
$621$	−0.0854361	−	0.484532i	−0.00342843	−	0.0194436i
$622$	27.3244	−	9.94527i	1.09561	−	0.398769i
$623$	−8.61580	+	13.2452i	−0.345185	+	0.530660i
$624$	1.04636	+	0.877997i	0.0418878	+	0.0351480i
$625$	18.5584	+	15.5724i	0.742336	+	0.622894i
$626$	12.0026	+	20.7892i	0.479721	+	0.830902i
$627$	−7.83002	+	10.9921i	−0.312701	+	0.438983i
$628$	3.43866	+	1.98531i	0.137217	+	0.0792224i
$629$	−0.868932	+	4.92796i	−0.0346466	+	0.196490i
$630$	−0.731748	−	0.311261i	−0.0291535	−	0.0124010i
$631$	46.6209	+	16.9686i	1.85595	+	0.675510i	0.981819	+	0.189820i	$0.0607903\pi$
$631$	46.6209	+	16.9686i	1.85595	+	0.675510i	0.874131	+	0.485691i	$0.161432\pi$
$632$	5.76127	−	32.6738i	0.229171	−	1.29969i
$633$	−0.522299	+	1.43500i	−0.0207595	+	0.0570363i
$634$	−10.8391	+	18.7738i	−0.430475	+	0.745604i
$635$	1.61928	+	2.80467i	0.0642590	+	0.111300i
$636$	0.855374	−	0.150826i	0.0339178	−	0.00598062i
$637$	−1.93587	−	2.01073i	−0.0767020	−	0.0796679i
$638$	3.50312	−	6.06757i	0.138690	−	0.240218i
$639$		−	0.122826i		−	0.00485892i
$640$	1.85701	+	0.675896i	0.0734047	+	0.0267171i
$641$	6.06564	−	7.22875i	0.239578	−	0.285518i	−0.632836	−	0.774286i	$-0.718109\pi$
$641$	6.06564	−	7.22875i	0.239578	−	0.285518i	0.872414	+	0.488768i	$0.162554\pi$
$642$	10.1332	−	8.50276i	0.399926	−	0.335577i
$643$	27.5750	−	32.8626i	1.08745	−	1.29598i	0.135149	−	0.990825i	$-0.456849\pi$
$643$	27.5750	−	32.8626i	1.08745	−	1.29598i	0.952304	−	0.305151i	$-0.0987068\pi$
$644$	−0.0401646	−	0.329171i	−0.00158271	−	0.0129712i
$645$			0.869570i			0.0342393i
$646$	16.2733	+	16.5387i	0.640264	+	0.650706i
$647$	−12.6636	+	7.31135i	−0.497859	+	0.287439i	−0.727829	−	0.685759i	$-0.759470\pi$
$647$	−12.6636	+	7.31135i	−0.497859	+	0.287439i	0.229970	+	0.973198i	$0.426137\pi$
$648$	1.01878	+	2.79906i	0.0400213	+	0.109958i
$649$	−22.0687	+	8.03236i	−0.866273	+	0.315298i
$650$	0.891496	−	2.44937i	0.0349674	−	0.0960721i
$651$	0.873454	+	7.15843i	0.0342333	+	0.280561i
$652$	0.411730	−	0.345482i	0.0161246	−	0.0135301i
$653$	26.2960			1.02904			0.514521	−	0.857478i	$-0.327970\pi$
$653$	26.2960			1.02904			0.514521	+	0.857478i	$0.327970\pi$
$654$	17.5587			0.686598
$655$	1.82718	−	1.53319i	0.0713939	−	0.0599066i
$656$	13.6284	+	4.96035i	0.532102	+	0.193669i
$657$	6.97490	+	4.02696i	0.272117	+	0.157107i
$658$	5.50695	−	23.7712i	0.214683	−	0.926700i
$659$	−27.5080	−	32.7828i	−1.07156	−	1.27704i	−0.959004	−	0.283392i	$-0.908540\pi$
$659$	−27.5080	−	32.7828i	−1.07156	−	1.27704i	−0.112557	−	0.993645i	$-0.535904\pi$
$660$	0.176718	+	0.0311601i	0.00687872	+	0.00121290i
$661$	−6.08182	−	34.4917i	−0.236555	−	1.34157i	−0.839313	−	0.543648i	$-0.817042\pi$
$661$	−6.08182	−	34.4917i	−0.236555	−	1.34157i	0.602758	−	0.797924i	$-0.294069\pi$
$662$	−3.09096	+	17.5297i	−0.120134	+	0.681311i
$663$	1.03272	−	1.23074i	0.0401074	−	0.0477982i
$664$	9.78362			0.379678
$665$	−0.522790	−	2.57114i	−0.0202729	−	0.0997045i
$666$	1.64066			0.0635743
$667$	−0.541717	+	0.645594i	−0.0209754	+	0.0249975i
$668$	0.603169	−	3.42074i	0.0233373	−	0.132353i
$669$	1.31586	+	7.46261i	0.0508740	+	0.288521i
$670$	2.29331	+	0.404372i	0.0885981	+	0.0156222i
$671$	−15.8092	−	18.8407i	−0.610307	−	0.727336i
$672$	1.10490	+	3.62375i	0.0426224	+	0.139789i
$673$	−13.3721	−	7.72040i	−0.515457	−	0.297599i	0.219617	−	0.975586i	$-0.429519\pi$
$673$	−13.3721	−	7.72040i	−0.515457	−	0.297599i	−0.735074	+	0.677987i	$0.762853\pi$
$674$	10.8687	+	3.95587i	0.418645	+	0.152374i
$675$	3.79057	−	3.18067i	0.145899	−	0.122424i
$676$	−3.27122			−0.125816
$677$	−12.6658			−0.486788			−0.243394	−	0.969928i	$-0.578261\pi$
$677$	−12.6658			−0.486788			−0.243394	+	0.969928i	$0.578261\pi$
$678$	12.3387	−	10.3534i	0.473866	−	0.397621i
$679$	−12.1348	+	9.12984i	−0.465690	+	0.350371i
$680$	0.933902	−	2.56588i	0.0358135	−	0.0983969i
$681$	1.69287	−	0.616153i	0.0648708	−	0.0236110i
$682$	3.81311	+	10.4764i	0.146012	+	0.401164i
$683$	−9.81627	+	5.66742i	−0.375609	+	0.216858i	−0.675906	−	0.736988i	$-0.736248\pi$
$683$	−9.81627	+	5.66742i	−0.375609	+	0.216858i	0.300297	+	0.953846i	$0.402914\pi$
$684$	−0.644247	+	0.904421i	−0.0246334	+	0.0345814i
$685$		−	3.37773i		−	0.129056i
$686$	4.61401	+	24.0277i	0.176164	+	0.917383i
$687$	−13.0998	+	15.6118i	−0.499790	+	0.595626i
$688$	−10.0300	+	8.41613i	−0.382389	+	0.320862i
$689$	−0.873876	+	1.04144i	−0.0332920	+	0.0396759i
$690$	0.138958	+	0.0505765i	0.00529003	+	0.00192541i
$691$			15.2820i			0.581353i	0.956821	+	0.290677i	$0.0938803\pi$
$691$			15.2820i			0.581353i	−0.956821	+	0.290677i	$0.906120\pi$
$692$	−1.62716	+	2.81832i	−0.0618552	+	0.107136i
$693$	−3.71340	−	7.30160i	−0.141061	−	0.277365i
$694$	−25.3691	+	4.47326i	−0.963000	+	0.169803i
$695$	−1.42332	−	2.46526i	−0.0539896	−	0.0935127i
$696$	2.55112	−	4.41867i	0.0967000	−	0.167489i
$697$	5.83446	−	16.0300i	0.220996	−	0.607181i
$698$	−2.10414	+	11.9331i	−0.0796427	+	0.451676i
$699$	−21.3799	−	7.78164i	−0.808661	−	0.294329i
$700$	2.66505	−	2.00511i	0.100730	−	0.0757859i
$701$	−1.12240	+	6.36547i	−0.0423926	+	0.240420i	−0.998640	−	0.0521394i	$-0.983396\pi$
$701$	−1.12240	+	6.36547i	−0.0423926	+	0.240420i	0.956247	+	0.292560i	$0.0945071\pi$
$702$	−0.456192	−	0.263383i	−0.0172179	−	0.00994074i
$703$	3.06900	+	4.45933i	0.115750	+	0.168187i
$704$	13.5346	+	23.4426i	0.510104	+	0.883527i
$705$	−1.21668	−	1.02092i	−0.0458228	−	0.0384499i
$706$	18.4064	+	15.4448i	0.692733	+	0.581272i
$707$	−5.94042	+	3.02114i	−0.223413	+	0.113622i
$708$	−1.81579	+	0.660894i	−0.0682417	+	0.0248379i
$709$	3.84958	+	21.8320i	0.144574	+	0.819919i	0.967708	+	0.252073i	$0.0811122\pi$
$709$	3.84958	+	21.8320i	0.144574	+	0.819919i	−0.823134	+	0.567847i	$0.807777\pi$
$710$	0.0319703	+	0.0184581i	0.00119982	+	0.000692719i
$711$			11.1383i			0.417721i
$712$	−6.08432	+	16.7165i	−0.228019	+	0.626478i
$713$	−0.232873	−	1.32069i	−0.00872116	−	0.0494602i
$714$	−13.4710	+	4.10738i	−0.504140	+	0.153715i
$715$	−0.243241	+	0.140435i	−0.00909670	+	0.00525198i
$716$	5.64942	−	0.996145i	0.211129	−	0.0372277i
$717$	−12.2811	−	10.3050i	−0.458645	−	0.384848i
$718$	−24.7532	+	4.36465i	−0.923779	+	0.162887i
$719$	−2.44823	−	6.72647i	−0.0913037	−	0.250855i	0.885632	−	0.464387i	$-0.153725\pi$
$719$	−2.44823	−	6.72647i	−0.0913037	−	0.250855i	−0.976936	+	0.213532i	$0.931503\pi$
$720$	−0.767513	−	0.135333i	−0.0286035	−	0.00504358i
$721$	9.96545	−	43.0168i	0.371133	−	1.60203i
$722$	25.0972	+	0.406017i	0.934022	+	0.0151104i
$723$	14.0382	−	24.3148i	0.522085	−	0.904278i
$724$	−2.76288	+	1.00561i	−0.102682	+	0.0373730i
$725$	−8.34711	−	1.47182i	−0.310004	−	0.0546621i
$726$	1.20064	+	1.43087i	0.0445599	+	0.0531044i
$727$	−0.299919	−	0.824019i	−0.0111234	−	0.0305612i	0.934007	−	0.357256i	$-0.116287\pi$
$727$	−0.299919	−	0.824019i	−0.0111234	−	0.0305612i	−0.945130	+	0.326694i	$0.894065\pi$
$728$	−2.63416	−	1.71348i	−0.0976285	−	0.0635056i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−2.09635	+	1.21033i	−0.0775894	+	0.0447962i
$731$	9.89922	+	11.7974i	0.366136	+	0.436344i
$732$	−1.30077	−	1.55019i	−0.0480777	−	0.0572967i
$733$	−16.3055	+	9.41398i	−0.602257	+	0.347713i	−0.769929	−	0.638130i	$-0.779708\pi$
$733$	−16.3055	+	9.41398i	−0.602257	+	0.347713i	0.167672	+	0.985843i	$0.446375\pi$
$734$	−2.04861	−	3.54830i	−0.0756156	−	0.130970i
$735$	1.53020	+	0.441281i	0.0564422	+	0.0162769i
$736$	−0.240955	−	0.662019i	−0.00888172	−	0.0244023i
$737$	15.4196	+	18.3764i	0.567988	+	0.676902i
$738$	−5.50812	−	0.971230i	−0.202757	−	0.0357515i
$739$	−24.2985	+	8.84392i	−0.893833	+	0.325329i	−0.747779	−	0.663948i	$-0.768880\pi$
$739$	−24.2985	+	8.84392i	−0.893833	+	0.325329i	−0.146054	+	0.989277i	$0.546657\pi$
$740$	0.0359887	−	0.0623343i	0.00132297	−	0.00229146i
$741$	−0.137473	−	1.73262i	−0.00505019	−	0.0636492i
$742$	11.3991	−	3.47562i	0.418472	−	0.127594i
$743$	−49.9244	−	8.80302i	−1.83155	−	0.322951i	−0.851905	−	0.523697i	$-0.824552\pi$
$743$	−49.9244	−	8.80302i	−1.83155	−	0.322951i	−0.979643	+	0.200746i	$0.935664\pi$
$744$	2.77688	+	7.62940i	0.101805	+	0.279708i
$745$	−3.96798	+	0.699662i	−0.145376	+	0.0256336i
$746$	9.70302	+	8.14180i	0.355253	+	0.298092i
$747$	−3.23463	+	0.570352i	−0.118349	+	0.0208681i
$748$	2.75225	−	1.58901i	0.100632	−	0.0581001i
$749$	−18.0820	+	19.3613i	−0.660704	+	0.707445i
$750$	0.519209	+	2.94458i	0.0189588	+	0.107521i
$751$	−12.0186	+	33.0208i	−0.438565	+	1.20495i	0.501861	+	0.864948i	$0.332649\pi$
$751$	−12.0186	+	33.0208i	−0.438565	+	1.20495i	−0.940426	+	0.339999i	$0.889573\pi$
$752$		−	23.9146i		−	0.872076i
$753$	−12.3051	−	7.10433i	−0.448421	−	0.258896i
$754$	0.156683	+	0.888593i	0.00570605	+	0.0323606i
$755$	0.834444	−	0.303713i	0.0303685	−	0.0110532i
$756$	−0.305535	−	0.600769i	−0.0111122	−	0.0218497i
$757$	−37.0397	−	31.0800i	−1.34623	−	1.12962i	−0.979977	−	0.199109i	$-0.936195\pi$
$757$	−37.0397	−	31.0800i	−1.34623	−	1.12962i	−0.366255	−	0.930514i	$-0.619360\pi$
$758$	14.7072	+	12.3408i	0.534190	+	0.448239i
$759$	0.761662	+	1.31924i	0.0276466	+	0.0478853i
$760$	−1.22669	−	2.68718i	−0.0444968	−	0.0974744i
$761$	−22.1530	−	12.7900i	−0.803045	−	0.463638i	0.0414898	−	0.999139i	$-0.486790\pi$
$761$	−22.1530	−	12.7900i	−0.803045	−	0.463638i	−0.844535	+	0.535501i	$0.820123\pi$
$762$	3.26553	−	18.5197i	0.118298	−	0.670899i
$763$	−34.9062	+	4.25917i	−1.26369	+	0.154192i
$764$	6.47641	+	2.35722i	0.234308	+	0.0852813i
$765$	−0.159182	+	0.902764i	−0.00575522	+	0.0326395i
$766$	−2.81597	+	7.73681i	−0.101745	+	0.279542i
$767$	1.51227	−	2.61932i	0.0546048	−	0.0945782i
$768$	3.00527	+	5.20528i	0.108443	+	0.187829i
$769$	42.0827	−	7.42031i	1.51754	−	0.267583i	0.648074	−	0.761577i	$-0.275575\pi$
$769$	42.0827	−	7.42031i	1.51754	−	0.267583i	0.869465	+	0.493994i	$0.164463\pi$
$770$	2.45857	+	0.130712i	0.0886008	+	0.00471052i
$771$	12.6166	−	21.8526i	0.454376	−	0.787003i
$772$			2.64921i			0.0953473i
$773$	−37.9893	−	13.8270i	−1.36638	−	0.497322i	−0.448359	−	0.893853i	$-0.647992\pi$
$773$	−37.9893	−	13.8270i	−1.36638	−	0.497322i	−0.918021	+	0.396532i	$0.870214\pi$
$774$	3.24567	−	3.86804i	0.116663	−	0.139034i
$775$	10.3320	−	8.66954i	0.371135	−	0.311419i
$776$	−10.9896	+	13.0969i	−0.394503	+	0.470151i
$777$	−3.26159	+	0.397971i	−0.117009	+	0.0142771i
$778$		−	12.3935i		−	0.444327i
$779$	−7.66363	−	16.7879i	−0.274578	−	0.601489i
$780$	−0.0200136	+	0.0115549i	−0.000716603	+	0.000413731i
$781$	0.130066	+	0.357353i	0.00465412	+	0.0127871i
$782$	2.46100	−	0.895732i	0.0880053	−	0.0320313i
$783$	−0.585849	+	1.60961i	−0.0209365	+	0.0575227i
$784$	9.72012	+	21.9209i	0.347147	+	0.782888i
$785$	2.71643	−	2.27936i	0.0969535	−	0.0813537i
$786$	−13.8503			−0.494025
$787$	−26.2807			−0.936807			−0.468404	−	0.883515i	$-0.655171\pi$
$787$	−26.2807			−0.936807			−0.468404	+	0.883515i	$0.655171\pi$
$788$	−4.40025	+	3.69225i	−0.156752	+	0.131531i
$789$	−16.5893	−	6.03801i	−0.590594	−	0.214959i
$790$	−2.89919	−	1.67385i	−0.103149	−	0.0595529i
$791$	−22.0177	+	23.5753i	−0.782858	+	0.838242i
$792$	−5.92810	−	7.06484i	−0.210646	−	0.251038i
$793$	3.11933	+	0.550021i	0.110771	+	0.0195318i
$794$	5.29771	+	30.0448i	0.188009	+	1.06625i
$795$	0.134698	−	0.763911i	0.00477725	−	0.0270931i
$796$	−1.87766	+	2.23771i	−0.0665519	+	0.0793135i
$797$	47.3868			1.67853			0.839264	−	0.543724i	$-0.182986\pi$
$797$	47.3868			1.67853			0.839264	+	0.543724i	$0.182986\pi$
$798$	−7.27129	+	13.3883i	−0.257401	+	0.473941i
$799$	−28.1288			−0.995126
$800$	4.55440	−	5.42773i	0.161022	−	0.191899i
$801$	1.03706	−	5.88145i	0.0366427	−	0.207811i
$802$	3.32182	+	18.8390i	0.117298	+	0.665228i
$803$	−24.5572	−	4.33011i	−0.866606	−	0.152806i
$804$	1.26871	+	1.51199i	0.0447439	+	0.0533238i
$805$	−0.288513	−	0.0668381i	−0.0101687	−	0.00235573i
$806$	−1.24344	−	0.717902i	−0.0437984	−	0.0252870i
$807$	−11.2382	−	4.09038i	−0.395605	−	0.143988i
$808$	−5.74780	+	4.82297i	−0.202207	+	0.169672i
$809$	27.1101			0.953141			0.476570	−	0.879136i	$-0.341880\pi$
$809$	27.1101			0.953141			0.476570	+	0.879136i	$0.341880\pi$
$810$	0.300556			0.0105605
$811$	15.9715	−	13.4017i	0.560835	−	0.470596i	−0.317755	−	0.948173i	$-0.602929\pi$
$811$	15.9715	−	13.4017i	0.560835	−	0.470596i	0.878590	+	0.477576i	$0.158485\pi$
$812$	−0.451902	+	1.06238i	−0.0158586	+	0.0372823i
$813$	7.71705	−	21.2024i	0.270649	−	0.743602i
$814$	−4.77337	+	1.73737i	−0.167307	+	0.0608947i
$815$	−0.164171	−	0.451056i	−0.00575066	−	0.0157998i
$816$	−11.9535	+	6.90134i	−0.418455	+	0.241595i
$817$	16.5847	+	1.58624i	0.580224	+	0.0554954i
$818$			13.6108i			0.475889i
$819$	0.970786	+	0.412940i	0.0339220	+	0.0144293i
$820$	−0.157724	+	0.187968i	−0.00550796	+	0.00656413i
$821$	−29.4199	+	24.6862i	−1.02676	+	0.861555i	−0.990462	−	0.137786i	$-0.956001\pi$
$821$	−29.4199	+	24.6862i	−1.02676	+	0.861555i	−0.0362995	+	0.999341i	$0.511557\pi$
$822$	−12.6074	+	15.0249i	−0.439732	+	0.524053i
$823$	2.58602	+	0.941234i	0.0901429	+	0.0328093i	0.386698	−	0.922206i	$-0.373616\pi$
$823$	2.58602	+	0.941234i	0.0901429	+	0.0328093i	−0.296555	+	0.955016i	$0.595838\pi$
$824$		−	49.7128i		−	1.73183i
$825$	−7.66023	+	13.2679i	−0.266695	+	0.461929i
$826$	−23.6318	+	12.0185i	−0.822254	+	0.418177i
$827$	7.50382	−	1.32313i	0.260934	−	0.0460096i	−0.0416508	−	0.999132i	$-0.513262\pi$
$827$	7.50382	−	1.32313i	0.260934	−	0.0460096i	0.302584	+	0.953123i	$0.402151\pi$
$828$	0.0626688	+	0.108546i	0.00217789	+	0.00377222i
$829$	−10.5220	+	18.2246i	−0.365443	+	0.632965i	−0.988847	−	0.148934i	$-0.952416\pi$
$829$	−10.5220	+	18.2246i	−0.365443	+	0.632965i	0.623405	+	0.781899i	$0.285749\pi$
$830$	0.337637	−	0.927650i	0.0117196	−	0.0321992i
$831$	2.99290	−	16.9736i	0.103823	−	0.588808i
$832$	−3.27588	−	1.19232i	−0.113571	−	0.0413364i
$833$	25.7837	−	11.4330i	0.893353	−	0.396130i
$834$	−2.87035	+	16.2786i	−0.0993921	+	0.563680i
$835$	−2.68650	−	1.55105i	−0.0929700	−	0.0536763i
$836$	0.916655	−	3.31357i	0.0317032	−	0.114602i
$837$	−1.36285	−	2.36052i	−0.0471069	−	0.0815916i
$838$	6.16265	+	5.17108i	0.212885	+	0.178632i
$839$	−13.8915	−	11.6564i	−0.479589	−	0.402423i	0.370689	−	0.928757i	$-0.379122\pi$
$839$	−13.8915	−	11.6564i	−0.479589	−	0.402423i	−0.850278	+	0.526334i	$0.823566\pi$
$840$	1.79044	+	0.0951899i	0.0617761	+	0.00328436i
$841$	−24.4940	+	8.91508i	−0.844620	+	0.307416i
$842$	−4.02287	−	22.8148i	−0.138637	−	0.786251i
$843$	−26.5130	−	15.3073i	−0.913157	−	0.527211i
$844$		−	0.389025i		−	0.0133908i
$845$	−0.999189	+	2.74525i	−0.0343731	+	0.0944394i
$846$	1.60149	+	9.08252i	0.0550605	+	0.312263i
$847$	−2.73392	−	2.55329i	−0.0939387	−	0.0877321i
$848$	10.1149	−	5.83985i	0.347348	−	0.200541i
$849$	28.3996	−	5.00762i	0.974672	−	0.171861i
$850$	20.1771	+	16.9306i	0.692070	+	0.580716i
$851$	0.601744	−	0.106104i	0.0206275	−	0.00363719i
$852$	0.0107017	+	0.0294026i	0.000366634	+	0.00100732i
$853$	−32.6619	−	5.75917i	−1.11832	−	0.197190i	−0.416218	−	0.909265i	$-0.636645\pi$
$853$	−32.6619	−	5.75917i	−1.11832	−	0.197190i	−0.702104	+	0.712075i	$0.747756\pi$
$854$	−20.2918	−	18.9511i	−0.694371	−	0.648493i
$855$	0.562218	+	0.816915i	0.0192275	+	0.0279379i
$856$	−14.9128	+	25.8298i	−0.509711	+	0.882845i
$857$	−18.1907	+	6.62086i	−0.621381	+	0.226164i	−0.633476	−	0.773763i	$-0.718372\pi$
$857$	−18.1907	+	6.62086i	−0.621381	+	0.226164i	0.0120945	+	0.999927i	$0.496150\pi$
$858$	1.60616	+	0.283210i	0.0548335	+	0.00966863i
$859$	23.4089	+	27.8976i	0.798701	+	0.951855i	0.999615	−	0.0277538i	$-0.00883544\pi$
$859$	23.4089	+	27.8976i	0.798701	+	0.951855i	−0.200913	+	0.979609i	$0.564391\pi$
$860$	−0.0757646	−	0.208162i	−0.00258355	−	0.00709825i
$861$	11.1856	+	0.594689i	0.381204	+	0.0202669i
$862$	−13.0613	−	22.6228i	−0.444869	−	0.770536i
$863$	19.5389	−	11.2808i	0.665112	−	0.384002i	−0.129110	−	0.991630i	$-0.541212\pi$
$863$	19.5389	−	11.2808i	0.665112	−	0.384002i	0.794222	+	0.607628i	$0.207879\pi$
$864$	−0.920409	−	1.09690i	−0.0313129	−	0.0373173i
$865$	1.86816	+	2.22638i	0.0635192	+	0.0756993i
$866$	−23.6785	+	13.6708i	−0.804628	+	0.464552i
$867$	−0.382508	−	0.662524i	−0.0129907	−	0.0225005i
$868$	−0.832797	−	1.63751i	−0.0282670	−	0.0555808i
$869$	−11.7949	−	32.4062i	−0.400114	−	1.09930i
$870$	−0.330924	−	0.394379i	−0.0112194	−	0.0133707i
$871$	−3.04245	−	0.536467i	−0.103090	−	0.0181775i
$872$	−37.2028	+	13.5407i	−1.25984	+	0.458546i
$873$	2.86984	−	4.97070i	0.0971292	−	0.168233i
$874$	1.21809	−	2.55798i	0.0412025	−	0.0865250i
$875$	−1.74644	−	5.72781i	−0.0590403	−	0.193635i
$876$	−2.02055	−	0.356277i	−0.0682679	−	0.0120375i
$877$	6.57947	+	18.0770i	0.222173	+	0.610415i	0.999833	−	0.0182696i	$-0.00581571\pi$
$877$	6.57947	+	18.0770i	0.222173	+	0.610415i	−0.777660	+	0.628685i	$0.783593\pi$
$878$	3.98629	−	0.702890i	0.134531	−	0.0237214i
$879$	19.6470	+	16.4858i	0.662678	+	0.556053i
$880$	2.37633	−	0.419012i	0.0801061	−	0.0141249i
$881$	0.0778003	−	0.0449180i	0.00262116	−	0.00151333i	−0.498689	−	0.866781i	$-0.666185\pi$
$881$	0.0778003	−	0.0449180i	0.00262116	−	0.00151333i	0.501310	+	0.865268i	$0.332852\pi$
$882$	−5.15958	−	7.67438i	−0.173732	−	0.258410i
$883$	5.77820	+	32.7698i	0.194452	+	1.10279i	0.913197	+	0.407518i	$0.133605\pi$
$883$	5.77820	+	32.7698i	0.194452	+	1.10279i	−0.718746	+	0.695273i	$0.755283\pi$
$884$	−0.139983	+	0.384601i	−0.00470815	+	0.0129355i
$885$			1.72571i			0.0580090i
$886$	5.82735	+	3.36442i	0.195774	+	0.113030i
$887$	1.59788	+	9.06204i	0.0536517	+	0.304274i	0.999811	−	0.0194267i	$-0.00618411\pi$
$887$	1.59788	+	9.06204i	0.0536517	+	0.304274i	−0.946160	+	0.323700i	$0.895073\pi$
$888$	−3.47618	+	1.26523i	−0.116653	+	0.0424582i
$889$	−1.99950	+	37.6089i	−0.0670610	+	1.26136i
$890$	1.37503	+	1.15379i	0.0460912	+	0.0386751i
$891$	2.37178	+	1.99016i	0.0794578	+	0.0666730i
$892$	−0.965205	−	1.67178i	−0.0323174	−	0.0559755i
$893$	−21.6906	+	21.3426i	−0.725849	+	0.714201i
$894$	20.2619	+	11.6982i	0.677660	+	0.391247i
$895$	0.889629	−	5.04534i	0.0297370	−	0.168647i
$896$	13.8168	+	18.3644i	0.461587	+	0.613511i
$897$	−0.184351	−	0.0670982i	−0.00615529	−	0.00224034i
$898$	1.35849	−	7.70438i	0.0453334	−	0.257098i
$899$	−1.59685	+	4.38730i	−0.0532579	+	0.146325i
$900$	−0.630276	+	1.09167i	−0.0210092	+	0.0363890i
$901$	−6.86895	−	11.8974i	−0.228838	−	0.396359i
$902$	17.0539	−	3.00707i	0.567834	−	0.100124i
$903$	−5.51404	+	8.47685i	−0.183496	+	0.282092i
$904$	−18.1587	+	31.4518i	−0.603949	+	1.04607i
$905$			2.62581i			0.0872847i
$906$	−4.84540	−	1.76358i	−0.160978	−	0.0585911i
$907$	−1.11049	+	1.32343i	−0.0368732	+	0.0439437i	−0.784166	−	0.620551i	$-0.786909\pi$
$907$	−1.11049	+	1.32343i	−0.0368732	+	0.0439437i	0.747293	+	0.664495i	$0.231353\pi$
$908$	−0.351561	+	0.294995i	−0.0116670	+	0.00978975i
$909$	1.61915	−	1.92963i	0.0537039	−	0.0640018i
$910$	−0.253372	+	0.190630i	−0.00839920	+	0.00631931i
$911$		−	2.62040i		−	0.0868178i	−0.999057	−	0.0434089i	$-0.986178\pi$
$911$		−	2.62040i		−	0.0868178i	0.999057	−	0.0434089i	$-0.0138218\pi$
$912$	−3.98118	+	14.3914i	−0.131830	+	0.476546i
$913$	8.80693	−	5.08468i	0.291467	−	0.168278i
$914$	1.01012	+	2.77528i	0.0334118	+	0.0917981i
$915$	−1.69826	+	0.618116i	−0.0561427	+	0.0204343i
$916$	1.77566	−	4.87859i	0.0586695	−	0.161193i
$917$	27.5341	−	3.35964i	0.909256	−	0.110945i
$918$	4.07764	−	3.42155i	0.134582	−	0.112928i
$919$	−38.1974			−1.26001			−0.630007	−	0.776589i	$-0.716948\pi$
$919$	−38.1974			−1.26001			−0.630007	+	0.776589i	$0.716948\pi$
$920$	−0.333423			−0.0109926
$921$	9.70520	−	8.14363i	0.319797	−	0.268342i
$922$	4.53828	+	1.65180i	0.149460	+	0.0543991i
$923$	−0.0424140	−	0.0244877i	−0.00139607	−	0.000806023i
$924$	1.52511	+	1.42435i	0.0501725	+	0.0468575i
$925$	3.95010	+	4.70754i	0.129878	+	0.154783i
$926$	−9.63002	−	1.69803i	−0.316462	−	0.0558008i
$927$	2.89809	+	16.4359i	0.0951856	+	0.539824i
$928$	−0.425910	+	2.41545i	−0.0139812	+	0.0792912i
$929$	19.0821	−	22.7411i	0.626063	−	0.746113i	−0.356037	−	0.934472i	$-0.615872\pi$
$929$	19.0821	−	22.7411i	0.626063	−	0.746113i	0.982100	+	0.188359i	$0.0603169\pi$
$930$	0.819226			0.0268635
$931$	11.2076	−	28.3794i	0.367313	−	0.930097i
$932$	5.79602			0.189855
$933$	14.1483	−	16.8613i	0.463194	−	0.552013i
$934$	−2.65719	+	15.0697i	−0.0869461	+	0.493096i
$935$	−0.492849	−	2.79509i	−0.0161179	−	0.0914091i
$936$	1.16968	+	0.206246i	0.0382321	+	0.00674136i
$937$	24.6810	+	29.4136i	0.806292	+	0.960902i	0.999796	−	0.0201977i	$-0.00642955\pi$
$937$	24.6810	+	29.4136i	0.806292	+	0.960902i	−0.193504	+	0.981100i	$0.561985\pi$
$938$	19.7917	+	18.4841i	0.646223	+	0.603526i
$939$	15.7365	+	9.08547i	0.513541	+	0.296493i
$940$	0.380206	+	0.138384i	0.0124009	+	0.00451358i
$941$	30.8002	−	25.8444i	1.00406	−	0.842504i	0.0165159	−	0.999864i	$-0.494743\pi$
$941$	30.8002	−	25.8444i	1.00406	−	0.842504i	0.987541	+	0.157360i	$0.0502981\pi$
$942$	−20.5910			−0.670890
$943$	−2.08302			−0.0678326
$944$	−19.9050	+	16.7023i	−0.647852	+	0.543612i
$945$	−0.597498	+	0.0729053i	−0.0194366	+	0.00237161i
$946$	−5.34699	+	14.6907i	−0.173846	+	0.477637i
$947$	−33.0769	+	12.0390i	−1.07486	+	0.391216i	−0.817991	−	0.575232i	$-0.804912\pi$
$947$	−33.0769	+	12.0390i	−1.07486	+	0.391216i	−0.256865	+	0.966447i	$0.582690\pi$
$948$	−0.970471	−	2.66635i	−0.0315194	−	0.0865990i
$949$	2.78116	−	1.60570i	0.0902802	−	0.0521233i
$950$	28.4049	−	2.25377i	0.921578	−	0.0731218i
$951$			16.4094i			0.532112i
$952$	25.3745	−	19.0910i	0.822393	−	0.618744i
$953$	−11.9056	+	14.1886i	−0.385661	+	0.459613i	−0.923593	−	0.383375i	$-0.874762\pi$
$953$	−11.9056	+	14.1886i	−0.385661	+	0.459613i	0.537931	+	0.842989i	$0.319206\pi$
$954$	−3.45046	+	2.89528i	−0.111713	+	0.0937382i
$955$	3.95642	−	4.71508i	0.128027	−	0.152576i
$956$	3.83776	+	1.39683i	0.124122	+	0.0451767i
$957$		−	5.30341i		−	0.171435i
$958$	−16.7673	+	29.0418i	−0.541726	+	0.938297i
$959$	21.4186	−	32.9272i	0.691642	−	1.06327i
$960$	1.95886	−	0.345399i	0.0632218	−	0.0111477i
$961$	11.7853	+	20.4127i	0.380171	+	0.658475i
$962$	0.327097	−	0.566549i	0.0105460	−	0.0182663i
$963$	3.42464	−	9.40913i	0.110358	−	0.303205i
$964$	−1.24200	+	7.04373i	−0.0400021	+	0.226863i
$965$	2.22326	+	0.809199i	0.0715691	+	0.0260490i
$966$	1.03390	+	1.37418i	0.0332650	+	0.0442137i
$967$	−4.71640	+	26.7480i	−0.151669	+	0.860159i	0.810099	+	0.586293i	$0.199413\pi$
$967$	−4.71640	+	26.7480i	−0.151669	+	0.860159i	−0.961768	+	0.273865i	$0.911698\pi$
$968$	−3.64732	−	2.10578i	−0.117229	−	0.0676823i
$969$	16.9274	+	4.68274i	0.543786	+	0.150431i
$970$	0.862547	+	1.49398i	0.0276947	+	0.0479687i
$971$	9.33947	+	7.83675i	0.299718	+	0.251493i	0.780227	−	0.625497i	$-0.215104\pi$
$971$	9.33947	+	7.83675i	0.299718	+	0.251493i	−0.480509	+	0.876990i	$0.659548\pi$
$972$	0.195148	+	0.163749i	0.00625938	+	0.00525224i
$973$	1.75753	−	33.0576i	0.0563438	−	1.05978i
$974$	34.9502	−	12.7208i	1.11988	−	0.407601i
$975$	−0.342617	−	1.94308i	−0.0109725	−	0.0622283i
$976$	−23.5662	−	13.6060i	−0.754336	−	0.435516i
$977$			28.4410i			0.909909i	0.890515	+	0.454955i	$0.150345\pi$
$977$			28.4410i			0.909909i	−0.890515	+	0.454955i	$0.849655\pi$
$978$	−0.953298	+	2.61917i	−0.0304831	+	0.0837517i
$979$	3.21088	+	18.2098i	0.102620	+	0.581988i
$980$	−0.404754	+	0.0276885i	−0.0129294	+	0.000884477i
$981$	11.5105	−	6.64557i	0.367501	−	0.212177i
$982$	19.4932	−	3.43717i	0.622053	−	0.109685i
$983$	1.79440	+	1.50568i	0.0572325	+	0.0480237i	0.670955	−	0.741498i	$-0.265884\pi$
$983$	1.79440	+	1.50568i	0.0572325	+	0.0480237i	−0.613723	+	0.789522i	$0.710329\pi$
$984$	12.4194	−	2.18988i	0.395917	−	0.0698108i
$985$	1.75453	+	4.82054i	0.0559041	+	0.153595i
$986$	−8.97926	−	1.58329i	−0.285958	−	0.0504221i
$987$	−5.38685	−	17.6673i	−0.171465	−	0.562358i
$988$	0.183870	+	0.402783i	0.00584967	+	0.0128142i
$989$	0.940261	−	1.62858i	0.0298986	−	0.0517859i
$990$	−0.874446	+	0.318272i	−0.0277917	+	0.0101154i
$991$	−37.0482	−	6.53260i	−1.17688	−	0.207515i	−0.449197	−	0.893433i	$-0.648290\pi$
$991$	−37.0482	−	6.53260i	−1.17688	−	0.207515i	−0.727679	+	0.685918i	$0.759401\pi$
$992$	−2.50876	−	2.98982i	−0.0796531	−	0.0949269i
$993$	4.60835	+	12.6613i	0.146242	+	0.401796i
$994$	0.194612	+	0.382663i	0.00617273	+	0.0121373i
$995$	1.30439	+	2.25926i	0.0413518	+	0.0716234i
$996$	0.724625	−	0.418363i	0.0229606	−	0.0132563i
$997$	−17.7474	−	21.1505i	−0.562065	−	0.669843i	0.407917	−	0.913019i	$-0.366255\pi$
$997$	−17.7474	−	21.1505i	−0.562065	−	0.669843i	−0.969982	+	0.243176i	$0.921811\pi$
$998$	−20.6159	−	24.5691i	−0.652586	−	0.777722i
$999$	1.07552	−	0.620954i	0.0340281	−	0.0196461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.ck.b.40.10	yes	84
7.3	odd	6		399.2.cd.b.325.10	yes	84
19.10	odd	18		399.2.cd.b.124.10	✓	84
133.10	even	18	inner	399.2.ck.b.10.10	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.cd.b.124.10	✓	84	19.10	odd	18
399.2.cd.b.325.10	yes	84	7.3	odd	6
399.2.ck.b.10.10	yes	84	133.10	even	18	inner
399.2.ck.b.40.10	yes	84	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	399.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.849174 - 1.01201i) q^{2} +(0.173648 - 0.984808i) q^{3} +(0.0442365 + 0.250878i) q^{4} +(0.224052 + 0.0395064i) q^{5} +(-0.849174 - 1.01201i) q^{6} +(1.93362 + 1.80586i) q^{7} +(2.57963 + 1.48935i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(0.230240 - 0.193194i) q^{10} +3.09614 q^{11} +0.254748 q^{12} +(-0.305451 + 0.256304i) q^{13} +(3.46952 - 0.423342i) q^{14} +(0.0778124 - 0.213788i) q^{15} +(3.21902 - 1.17163i) q^{16} +(-1.37809 - 3.78627i) q^{17} +(-1.14409 + 0.660540i) q^{18} +(-3.93548 - 1.87404i) q^{19} +0.0579572i q^{20} +(2.11419 - 1.59066i) q^{21} +(2.62916 - 3.13332i) q^{22} +(-0.376899 + 0.316256i) q^{23} +(1.91467 - 2.28182i) q^{24} +(-4.64982 - 1.69240i) q^{25} +0.526765i q^{26} +(-0.500000 + 0.866025i) q^{27} +(-0.367513 + 0.564986i) q^{28} +(1.68689 - 0.297443i) q^{29} +(-0.150278 - 0.260289i) q^{30} +(-1.36285 + 2.36052i) q^{31} +(-0.489739 + 1.34555i) q^{32} +(0.537640 - 3.04911i) q^{33} +(-5.00197 - 1.82057i) q^{34} +(0.361887 + 0.480996i) q^{35} +(0.0442365 - 0.250878i) q^{36} +(-1.07552 - 0.620954i) q^{37} +(-5.23844 + 2.39134i) q^{38} +(0.199369 + 0.345318i) q^{39} +(0.519132 + 0.435604i) q^{40} +(3.24322 + 2.72139i) q^{41} +(0.185565 - 3.49032i) q^{42} +(-3.59164 + 1.30725i) q^{43} +(0.136963 + 0.776753i) q^{44} +(-0.197028 - 0.113754i) q^{45} +0.649980i q^{46} +(2.38769 - 6.56012i) q^{47} +(-0.594851 - 3.37357i) q^{48} +(0.477741 + 6.98368i) q^{49} +(-5.66123 + 3.26851i) q^{50} +(-3.96805 + 0.699675i) q^{51} +(-0.0778130 - 0.0652929i) q^{52} +(3.35773 - 0.592058i) q^{53} +(0.451836 + 1.24141i) q^{54} +(0.693696 + 0.122317i) q^{55} +(2.29846 + 7.53829i) q^{56} +(-2.52896 + 3.55026i) q^{57} +(1.13144 - 1.95972i) q^{58} +(-7.12781 + 2.59431i) q^{59} +(0.0570767 + 0.0100642i) q^{60} +(-5.10609 - 6.08520i) q^{61} +(1.23157 + 3.38371i) q^{62} +(-1.19936 - 2.35829i) q^{63} +(4.37144 + 7.57155i) q^{64} +(-0.0785625 + 0.0453581i) q^{65} +(-2.62916 - 3.13332i) q^{66} +(4.98026 + 5.93524i) q^{67} +(0.888929 - 0.513223i) q^{68} +(0.246003 + 0.426090i) q^{69} +(0.794076 + 0.0422175i) q^{70} +(0.0420089 + 0.115419i) q^{71} +(-1.91467 - 2.28182i) q^{72} +(-7.93156 - 1.39855i) q^{73} +(-1.54172 + 0.561139i) q^{74} +(-2.47412 + 4.28530i) q^{75} +(0.296063 - 1.07022i) q^{76} +(5.98675 + 5.59120i) q^{77} +(0.518763 + 0.0914718i) q^{78} +(-3.80954 - 10.4666i) q^{79} +(0.767513 - 0.135333i) q^{80} +(0.766044 + 0.642788i) q^{81} +(5.50812 - 0.971230i) q^{82} +(2.84448 - 1.64226i) q^{83} +(0.492584 + 0.460039i) q^{84} +(-0.159182 - 0.902764i) q^{85} +(-1.72698 + 4.74485i) q^{86} -1.71291i q^{87} +(7.98691 + 4.61125i) q^{88} +(1.03706 + 5.88145i) q^{89} +(-0.282431 + 0.102796i) q^{90} +(-1.05347 - 0.0560086i) q^{91} +(-0.0960142 - 0.0805655i) q^{92} +(2.08801 + 1.75204i) q^{93} +(-4.61132 - 7.98703i) q^{94} +(-0.807713 - 0.575359i) q^{95} +(1.24006 + 0.715951i) q^{96} +(-0.996683 + 5.65247i) q^{97} +(7.47321 + 5.44688i) q^{98} +(-2.90942 - 1.05894i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{7} - 12 q^{10} + 6 q^{11} - 96 q^{12} + 27 q^{13} + 9 q^{14} - 39 q^{19} + 6 q^{21} - 12 q^{22} - 6 q^{23} + 9 q^{24} + 18 q^{25} - 42 q^{27} + 45 q^{28} - 6 q^{29} + 18 q^{31} - 51 q^{32} + 12 q^{33}+ \cdots - 6 q^{99}+O(q^{100}) \) 84 * q - 6 * q^7 - 12 * q^10 + 6 * q^11 - 96 * q^12 + 27 * q^13 + 9 * q^14 - 39 * q^19 + 6 * q^21 - 12 * q^22 - 6 * q^23 + 9 * q^24 + 18 * q^25 - 42 * q^27 + 45 * q^28 - 6 * q^29 + 18 * q^31 - 51 * q^32 + 12 * q^33 + 6 * q^34 + 15 * q^35 + 18 * q^37 + 3 * q^38 + 18 * q^40 - 45 * q^41 + 15 * q^42 + 15 * q^43 - 36 * q^44 + 9 * q^45 - 24 * q^47 + 18 * q^49 - 27 * q^50 + 18 * q^51 - 84 * q^52 + 9 * q^53 - 30 * q^55 + 75 * q^56 - 6 * q^57 - 18 * q^58 + 24 * q^59 + 21 * q^61 - 45 * q^62 - 12 * q^63 + 84 * q^64 - 9 * q^65 + 12 * q^66 - 45 * q^67 + 12 * q^69 + 42 * q^70 + 42 * q^71 - 9 * q^72 - 72 * q^73 + 18 * q^74 + 57 * q^75 - 96 * q^76 - 51 * q^77 - 15 * q^78 - 42 * q^79 - 78 * q^80 + 24 * q^82 + 9 * q^84 - 48 * q^85 - 9 * q^86 + 108 * q^88 - 48 * q^89 - 21 * q^90 + 27 * q^91 + 6 * q^92 + 21 * q^93 + 30 * q^94 + 60 * q^95 - 21 * q^97 + 51 * q^98 - 6 * q^99

Introduction

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