LMFDB - Embedded newform 990.2.t.b.461.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(131,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.131"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			461.16
Character	$\chi$	$=$	990.461
Dual form			990.2.t.b.131.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(0.761656 + 1.55560i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.72801 + 0.118185i) q^{6} +(2.83014 + 1.63398i) q^{7} -1.00000 q^{8} +(-1.83976 + 2.36966i) q^{9} -1.00000i q^{10} +(-0.898862 - 3.19250i) q^{11} +(0.966358 - 1.43741i) q^{12} +(2.49573 - 1.44091i) q^{13} +(2.83014 - 1.63398i) q^{14} +(1.43741 + 0.966358i) q^{15} +(-0.500000 + 0.866025i) q^{16} +1.88020 q^{17} +(1.13231 + 2.77811i) q^{18} +4.33972i q^{19} +(-0.866025 - 0.500000i) q^{20} +(-0.386222 + 5.64708i) q^{21} +(-3.21422 - 0.817812i) q^{22} +(6.17351 - 3.56428i) q^{23} +(-0.761656 - 1.55560i) q^{24} +(0.500000 - 0.866025i) q^{25} -2.88183i q^{26} +(-5.08750 - 1.05706i) q^{27} -3.26796i q^{28} +(-0.688200 + 1.19200i) q^{29} +(1.55560 - 0.761656i) q^{30} +(1.78294 + 3.08815i) q^{31} +(0.500000 + 0.866025i) q^{32} +(4.28162 - 3.82985i) q^{33} +(0.940102 - 1.62830i) q^{34} +3.26796 q^{35} +(2.97206 + 0.408449i) q^{36} -7.24005 q^{37} +(3.75831 + 2.16986i) q^{38} +(4.14237 + 2.78488i) q^{39} +(-0.866025 + 0.500000i) q^{40} +(3.83291 + 6.63880i) q^{41} +(4.69740 + 3.15802i) q^{42} +(6.89392 + 3.98021i) q^{43} +(-2.31535 + 2.37469i) q^{44} +(-0.408449 + 2.97206i) q^{45} -7.12855i q^{46} +(-8.91993 - 5.14992i) q^{47} +(-1.72801 - 0.118185i) q^{48} +(1.83978 + 3.18659i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(1.43207 + 2.92484i) q^{51} +(-2.49573 - 1.44091i) q^{52} +3.25710i q^{53} +(-3.45919 + 3.87737i) q^{54} +(-2.37469 - 2.31535i) q^{55} +(-2.83014 - 1.63398i) q^{56} +(-6.75085 + 3.30537i) q^{57} +(0.688200 + 1.19200i) q^{58} +(-1.31366 + 0.758441i) q^{59} +(0.118185 - 1.72801i) q^{60} +(6.49131 + 3.74776i) q^{61} +3.56588 q^{62} +(-9.07874 + 3.70033i) q^{63} +1.00000 q^{64} +(1.44091 - 2.49573i) q^{65} +(-1.17594 - 5.62291i) q^{66} +(1.84864 + 3.20194i) q^{67} +(-0.940102 - 1.62830i) q^{68} +(10.2467 + 6.88873i) q^{69} +(1.63398 - 2.83014i) q^{70} -15.6364i q^{71} +(1.83976 - 2.36966i) q^{72} -11.3309i q^{73} +(-3.62003 + 6.27007i) q^{74} +(1.72801 + 0.118185i) q^{75} +(3.75831 - 2.16986i) q^{76} +(2.67258 - 10.5039i) q^{77} +(4.48296 - 2.19496i) q^{78} +(-11.3436 - 6.54921i) q^{79} +1.00000i q^{80} +(-2.23057 - 8.71921i) q^{81} +7.66582 q^{82} +(0.462740 - 0.801490i) q^{83} +(5.08362 - 2.48906i) q^{84} +(1.62830 - 0.940102i) q^{85} +(6.89392 - 3.98021i) q^{86} +(-2.37844 - 0.162669i) q^{87} +(0.898862 + 3.19250i) q^{88} +2.39265i q^{89} +(2.36966 + 1.83976i) q^{90} +9.41769 q^{91} +(-6.17351 - 3.56428i) q^{92} +(-3.44592 + 5.12564i) q^{93} +(-8.91993 + 5.14992i) q^{94} +(2.16986 + 3.75831i) q^{95} +(-0.966358 + 1.43741i) q^{96} +(-8.05367 + 13.9494i) q^{97} +3.67955 q^{98} +(9.21882 + 3.74343i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} - 48 q^{8} + 10 q^{9} - 12 q^{11} + 4 q^{12} - 24 q^{13} - 4 q^{15} - 24 q^{16} + 12 q^{17} + 8 q^{18} + 16 q^{21} - 6 q^{22} + 36 q^{23} + 2 q^{24} + 24 q^{25}+ \cdots - 44 q^{99}+O(q^{100}) $ 48 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 - 48 * q^8 + 10 * q^9 - 12 * q^11 + 4 * q^12 - 24 * q^13 - 4 * q^15 - 24 * q^16 + 12 * q^17 + 8 * q^18 + 16 * q^21 - 6 * q^22 + 36 * q^23 + 2 * q^24 + 24 * q^25 - 8 * q^27 - 8 * q^30 + 24 * q^32 + 12 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 + 40 * q^39 + 6 * q^41 + 8 * q^42 - 30 * q^43 + 6 * q^44 - 2 * q^48 + 24 * q^49 - 24 * q^50 - 22 * q^51 + 24 * q^52 - 22 * q^54 - 40 * q^57 - 54 * q^59 - 4 * q^60 + 38 * q^63 + 48 * q^64 - 12 * q^66 - 6 * q^67 - 6 * q^68 + 76 * q^69 - 10 * q^72 + 2 * q^75 - 6 * q^76 - 18 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 - 36 * q^83 - 8 * q^84 - 30 * q^86 + 44 * q^87 + 12 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 - 4 * q^96 + 6 * q^97 + 48 * q^98 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.761656	+	1.55560i	0.439742	+	0.898124i
$3$	0.761656	+	1.55560i	0.439742	+	0.898124i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	1.72801	+	0.118185i	0.705459	+	0.0482486i
$7$	2.83014	+	1.63398i	1.06969	+	0.617586i	0.928097	−	0.372339i	$-0.121444\pi$
$7$	2.83014	+	1.63398i	1.06969	+	0.617586i	0.141594	+	0.989925i	$0.454777\pi$
$8$	−1.00000			−0.353553
$9$	−1.83976	+	2.36966i	−0.613253	+	0.789886i
$10$		−	1.00000i		−	0.316228i
$11$	−0.898862	−	3.19250i	−0.271017	−	0.962575i
$11$	−0.898862	−	3.19250i	−0.271017	−	0.962575i
$12$	0.966358	−	1.43741i	0.278963	−	0.414945i
$13$	2.49573	−	1.44091i	0.692192	−	0.399637i	−0.112240	−	0.993681i	$-0.535803\pi$
$13$	2.49573	−	1.44091i	0.692192	−	0.399637i	0.804433	+	0.594044i	$0.202469\pi$
$14$	2.83014	−	1.63398i	0.756385	−	0.436699i
$15$	1.43741	+	0.966358i	0.371138	+	0.249513i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.88020			0.456016			0.228008	−	0.973659i	$-0.426779\pi$
$17$	1.88020			0.456016			0.228008	+	0.973659i	$0.426779\pi$
$18$	1.13231	+	2.77811i	0.266887	+	0.654806i
$19$			4.33972i			0.995600i	0.867292	+	0.497800i	$0.165859\pi$
$19$			4.33972i			0.995600i	−0.867292	+	0.497800i	$0.834141\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	−0.386222	+	5.64708i	−0.0842806	+	1.23229i
$22$	−3.21422	−	0.817812i	−0.685273	−	0.174358i
$23$	6.17351	−	3.56428i	1.28727	−	0.743203i	0.309099	−	0.951030i	$-0.399972\pi$
$23$	6.17351	−	3.56428i	1.28727	−	0.743203i	0.978166	+	0.207827i	$0.0666391\pi$
$24$	−0.761656	−	1.55560i	−0.155472	−	0.317535i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		−	2.88183i		−	0.565173i
$27$	−5.08750	−	1.05706i	−0.979089	−	0.203431i
$28$		−	3.26796i		−	0.617586i
$29$	−0.688200	+	1.19200i	−0.127796	+	0.221348i	−0.922822	−	0.385226i	$-0.874123\pi$
$29$	−0.688200	+	1.19200i	−0.127796	+	0.221348i	0.795027	+	0.606574i	$0.207457\pi$
$30$	1.55560	−	0.761656i	0.284012	−	0.139059i
$31$	1.78294	+	3.08815i	0.320226	+	0.554647i	0.980534	−	0.196347i	$-0.0629079\pi$
$31$	1.78294	+	3.08815i	0.320226	+	0.554647i	−0.660309	+	0.750994i	$0.729575\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	4.28162	−	3.82985i	0.745334	−	0.666692i
$34$	0.940102	−	1.62830i	0.161226	−	0.279252i
$35$	3.26796			0.552386
$36$	2.97206	+	0.408449i	0.495344	+	0.0680749i
$37$	−7.24005			−1.19026			−0.595129	−	0.803630i	$-0.702899\pi$
$37$	−7.24005			−1.19026			−0.595129	+	0.803630i	$0.702899\pi$
$38$	3.75831	+	2.16986i	0.609678	+	0.351998i
$39$	4.14237	+	2.78488i	0.663310	+	0.445937i
$40$	−0.866025	+	0.500000i	−0.136931	+	0.0790569i
$41$	3.83291	+	6.63880i	0.598600	+	1.03681i	0.993028	+	0.117879i	$0.0376095\pi$
$41$	3.83291	+	6.63880i	0.598600	+	1.03681i	−0.394428	+	0.918927i	$0.629057\pi$
$42$	4.69740	+	3.15802i	0.724825	+	0.487293i
$43$	6.89392	+	3.98021i	1.05131	+	0.606976i	0.923017	−	0.384760i	$-0.125716\pi$
$43$	6.89392	+	3.98021i	1.05131	+	0.606976i	0.128296	+	0.991736i	$0.459049\pi$
$44$	−2.31535	+	2.37469i	−0.349053	+	0.357997i
$45$	−0.408449	+	2.97206i	−0.0608880	+	0.443049i
$46$		−	7.12855i		−	1.05105i
$47$	−8.91993	−	5.14992i	−1.30111	−	0.751194i	−0.320512	−	0.947245i	$-0.603855\pi$
$47$	−8.91993	−	5.14992i	−1.30111	−	0.751194i	−0.980594	+	0.196051i	$0.937188\pi$
$48$	−1.72801	−	0.118185i	−0.249417	−	0.0170585i
$49$	1.83978	+	3.18659i	0.262825	+	0.455227i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	1.43207	+	2.92484i	0.200530	+	0.409559i
$52$	−2.49573	−	1.44091i	−0.346096	−	0.199819i
$53$			3.25710i			0.447398i	0.974658	+	0.223699i	$0.0718132\pi$
$53$			3.25710i			0.447398i	−0.974658	+	0.223699i	$0.928187\pi$
$54$	−3.45919	+	3.87737i	−0.470736	+	0.527644i
$55$	−2.37469	−	2.31535i	−0.320203	−	0.312202i
$56$	−2.83014	−	1.63398i	−0.378193	−	0.218350i
$57$	−6.75085	+	3.30537i	−0.894172	+	0.437807i
$58$	0.688200	+	1.19200i	0.0903651	+	0.156517i
$59$	−1.31366	+	0.758441i	−0.171024	+	0.0987406i	−0.583068	−	0.812423i	$-0.698148\pi$
$59$	−1.31366	+	0.758441i	−0.171024	+	0.0987406i	0.412045	+	0.911164i	$0.364815\pi$
$60$	0.118185	−	1.72801i	0.0152576	−	0.223086i
$61$	6.49131	+	3.74776i	0.831128	+	0.479852i	0.854239	−	0.519881i	$-0.174024\pi$
$61$	6.49131	+	3.74776i	0.831128	+	0.479852i	−0.0231111	+	0.999733i	$0.507357\pi$
$62$	3.56588			0.452868
$63$	−9.07874	+	3.70033i	−1.14381	+	0.466197i
$64$	1.00000			0.125000
$65$	1.44091	−	2.49573i	0.178723	−	0.309558i
$66$	−1.17594	−	5.62291i	−0.144748	−	0.692133i
$67$	1.84864	+	3.20194i	0.225847	+	0.391179i	0.956573	−	0.291492i	$-0.0941516\pi$
$67$	1.84864	+	3.20194i	0.225847	+	0.391179i	−0.730726	+	0.682671i	$0.760818\pi$
$68$	−0.940102	−	1.62830i	−0.114004	−	0.197461i
$69$	10.2467	+	6.88873i	1.23355	+	0.829306i
$70$	1.63398	−	2.83014i	0.195298	−	0.338266i
$71$		−	15.6364i		−	1.85570i	−0.372959	−	0.927848i	$-0.621657\pi$
$71$		−	15.6364i		−	1.85570i	0.372959	−	0.927848i	$-0.378343\pi$
$72$	1.83976	−	2.36966i	0.216818	−	0.279267i
$73$		−	11.3309i		−	1.32618i	−0.748540	−	0.663090i	$-0.769245\pi$
$73$		−	11.3309i		−	1.32618i	0.748540	−	0.663090i	$-0.230755\pi$
$74$	−3.62003	+	6.27007i	−0.420819	+	0.728881i
$75$	1.72801	+	0.118185i	0.199534	+	0.0136468i
$76$	3.75831	−	2.16986i	0.431107	−	0.248900i
$77$	2.67258	−	10.5039i	0.304568	−	1.19703i
$78$	4.48296	−	2.19496i	0.507595	−	0.248530i
$79$	−11.3436	−	6.54921i	−1.27625	−	0.736843i	−0.300093	−	0.953910i	$-0.597018\pi$
$79$	−11.3436	−	6.54921i	−1.27625	−	0.736843i	−0.976157	+	0.217067i	$0.930351\pi$
$80$			1.00000i			0.111803i
$81$	−2.23057	−	8.71921i	−0.247841	−	0.968801i
$82$	7.66582			0.846548
$83$	0.462740	−	0.801490i	0.0507924	−	0.0879749i	−0.839511	−	0.543342i	$-0.817159\pi$
$83$	0.462740	−	0.801490i	0.0507924	−	0.0879749i	0.890304	+	0.455367i	$0.150492\pi$
$84$	5.08362	−	2.48906i	0.554669	−	0.271579i
$85$	1.62830	−	0.940102i	0.176614	−	0.101968i
$86$	6.89392	−	3.98021i	0.743390	−	0.429197i
$87$	−2.37844	−	0.162669i	−0.254995	−	0.0174400i
$88$	0.898862	+	3.19250i	0.0958190	+	0.340321i
$89$			2.39265i			0.253620i	0.991927	+	0.126810i	$0.0404739\pi$
$89$			2.39265i			0.253620i	−0.991927	+	0.126810i	$0.959526\pi$
$90$	2.36966	+	1.83976i	0.249784	+	0.193928i
$91$	9.41769			0.987242
$92$	−6.17351	−	3.56428i	−0.643633	−	0.371601i
$93$	−3.44592	+	5.12564i	−0.357325	+	0.531504i
$94$	−8.91993	+	5.14992i	−0.920021	+	0.531174i
$95$	2.16986	+	3.75831i	0.222623	+	0.385594i
$96$	−0.966358	+	1.43741i	−0.0986285	+	0.146705i
$97$	−8.05367	+	13.9494i	−0.817726	+	1.41634i	0.0896275	+	0.995975i	$0.471432\pi$
$97$	−8.05367	+	13.9494i	−0.817726	+	1.41634i	−0.907354	+	0.420368i	$0.861901\pi$
$98$	3.67955			0.371691
$99$	9.21882	+	3.74343i	0.926527	+	0.376229i
$100$	−1.00000			−0.100000
$101$	−1.81753	+	3.14805i	−0.180851	+	0.313243i	−0.942171	−	0.335134i	$-0.891218\pi$
$101$	−1.81753	+	3.14805i	−0.180851	+	0.313243i	0.761320	+	0.648377i	$0.224552\pi$
$102$	3.24902	+	0.222211i	0.321701	+	0.0220022i
$103$	1.93445	+	3.35057i	0.190607	+	0.330141i	0.945452	−	0.325763i	$-0.105621\pi$
$103$	1.93445	+	3.35057i	0.190607	+	0.330141i	−0.754845	+	0.655904i	$0.772288\pi$
$104$	−2.49573	+	1.44091i	−0.244727	+	0.141293i
$105$	2.48906	+	5.08362i	0.242907	+	0.496111i
$106$	2.82074	+	1.62855i	0.273974	+	0.158179i
$107$	7.19194			0.695271			0.347635	−	0.937630i	$-0.386985\pi$
$107$	7.19194			0.695271			0.347635	+	0.937630i	$0.386985\pi$
$108$	1.62831	+	4.93443i	0.156684	+	0.474816i
$109$		−	12.6752i		−	1.21406i	−0.794678	−	0.607031i	$-0.792360\pi$
$109$		−	12.6752i		−	1.21406i	0.794678	−	0.607031i	$-0.207640\pi$
$110$	−3.19250	+	0.898862i	−0.304393	+	0.0857031i
$111$	−5.51443	−	11.2626i	−0.523407	−	1.06900i
$112$	−2.83014	+	1.63398i	−0.267423	+	0.154397i
$113$	−2.95268	+	1.70473i	−0.277765	+	0.160368i	−0.632411	−	0.774633i	$-0.717935\pi$
$113$	−2.95268	+	1.70473i	−0.277765	+	0.160368i	0.354646	+	0.935001i	$0.384601\pi$
$114$	−0.512888	+	7.49909i	−0.0480363	+	0.702354i
$115$	3.56428	−	6.17351i	0.332370	−	0.575682i
$116$	1.37640			0.127796
$117$	−1.17708	+	8.56498i	−0.108821	+	0.791832i
$118$			1.51688i			0.139640i
$119$	5.32123	+	3.07221i	0.487796	+	0.281629i
$120$	−1.43741	−	0.966358i	−0.131217	−	0.0882160i
$121$	−9.38409	+	5.73923i	−0.853100	+	0.521748i
$122$	6.49131	−	3.74776i	0.587696	−	0.339306i
$123$	−7.40793	+	11.0189i	−0.667950	+	0.993545i
$124$	1.78294	−	3.08815i	0.160113	−	0.277324i
$125$		−	1.00000i		−	0.0894427i
$126$	−1.33480	+	9.71258i	−0.118913	+	0.865266i
$127$		−	6.58147i		−	0.584011i	−0.956417	−	0.292006i	$-0.905677\pi$
$127$		−	6.58147i		−	0.584011i	0.956417	−	0.292006i	$-0.0943226\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−0.940798	+	13.7557i	−0.0828326	+	1.21112i
$130$	−1.44091	−	2.49573i	−0.126376	−	0.218890i
$131$	−2.79118	−	4.83446i	−0.243866	−	0.422389i	0.717946	−	0.696099i	$-0.245083\pi$
$131$	−2.79118	−	4.83446i	−0.243866	−	0.422389i	−0.961812	+	0.273710i	$0.911749\pi$
$132$	−5.45756	−	1.79306i	−0.475019	−	0.156066i
$133$	−7.09101	+	12.2820i	−0.614868	+	1.06498i
$134$	3.69728			0.319397
$135$	−4.93443	+	1.62831i	−0.424688	+	0.140143i
$136$	−1.88020			−0.161226
$137$	−4.52136	−	2.61041i	−0.386286	−	0.223022i	0.294264	−	0.955724i	$-0.404926\pi$
$137$	−4.52136	−	2.61041i	−0.386286	−	0.223022i	−0.680549	+	0.732702i	$0.738259\pi$
$138$	11.0891	−	5.42950i	0.943971	−	0.462190i
$139$	−10.2061	+	5.89247i	−0.865666	+	0.499793i	−0.865906	−	0.500207i	$-0.833257\pi$
$139$	−10.2061	+	5.89247i	−0.865666	+	0.499793i	0.000239343		1.00000i	$0.499924\pi$
$140$	−1.63398	−	2.83014i	−0.138096	−	0.239190i
$141$	1.21728	−	17.7983i	0.102514	−	1.49889i
$142$	−13.5415	−	7.81819i	−1.13638	−	0.656088i
$143$	−6.84343	−	6.67245i	−0.572277	−	0.557978i
$144$	−1.13231	−	2.77811i	−0.0943588	−	0.231509i
$145$			1.37640i			0.114304i
$146$	−9.81284	−	5.66544i	−0.812116	−	0.468875i
$147$	−3.55577	+	5.28903i	−0.293275	+	0.436232i
$148$	3.62003	+	6.27007i	0.297564	+	0.515397i
$149$	1.35163	+	2.34110i	0.110730	+	0.191790i	0.916065	−	0.401030i	$-0.131348\pi$
$149$	1.35163	+	2.34110i	0.110730	+	0.191790i	−0.805335	+	0.592820i	$0.798014\pi$
$150$	0.966358	−	1.43741i	0.0789028	−	0.117364i
$151$	−9.07019	−	5.23668i	−0.738122	−	0.426155i	0.0832643	−	0.996527i	$-0.473465\pi$
$151$	−9.07019	−	5.23668i	−0.738122	−	0.426155i	−0.821386	+	0.570373i	$0.806799\pi$
$152$		−	4.33972i		−	0.351998i
$153$	−3.45912	+	4.45544i	−0.279653	+	0.360201i
$154$	−7.76038	−	7.56648i	−0.625349	−	0.609724i
$155$	3.08815	+	1.78294i	0.248046	+	0.143209i
$156$	0.340587	−	4.97984i	0.0272688	−	0.398706i
$157$	4.83418	+	8.37305i	0.385810	+	0.668242i	0.991881	−	0.127168i	$-0.0405888\pi$
$157$	4.83418	+	8.37305i	0.385810	+	0.668242i	−0.606072	+	0.795410i	$0.707255\pi$
$158$	−11.3436	+	6.54921i	−0.902445	+	0.521027i
$159$	−5.06674	+	2.48079i	−0.401819	+	0.196740i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	23.2958			1.83597
$162$	−8.66634	−	2.42787i	−0.680892	−	0.190752i
$163$	−20.0875			−1.57337			−0.786687	−	0.617352i	$-0.788206\pi$
$163$	−20.0875			−1.57337			−0.786687	+	0.617352i	$0.788206\pi$
$164$	3.83291	−	6.63880i	0.299300	−	0.518403i
$165$	1.79306	−	5.45756i	0.139590	−	0.424870i
$166$	−0.462740	−	0.801490i	−0.0359156	−	0.0622077i
$167$	−10.1839	−	17.6390i	−0.788052	−	1.36495i	−0.927159	−	0.374668i	$-0.877757\pi$
$167$	−10.1839	−	17.6390i	−0.788052	−	1.36495i	0.139107	−	0.990277i	$-0.455577\pi$
$168$	0.386222	−	5.64708i	0.0297977	−	0.435682i
$169$	−2.34754	+	4.06606i	−0.180580	+	0.312773i
$170$		−	1.88020i		−	0.144205i
$171$	−10.2837	−	7.98404i	−0.786410	−	0.610555i
$172$		−	7.96041i		−	0.606976i
$173$	6.26488	−	10.8511i	0.476310	−	0.824994i	−0.523321	−	0.852135i	$-0.675307\pi$
$173$	6.26488	−	10.8511i	0.476310	−	0.824994i	0.999632	+	0.0271419i	$0.00864058\pi$
$174$	−1.33010	+	1.97845i	−0.100834	+	0.149986i
$175$	2.83014	−	1.63398i	0.213938	−	0.123517i
$176$	3.21422	+	0.817812i	0.242281	+	0.0616449i
$177$	−2.18038	−	1.46585i	−0.163888	−	0.110180i
$178$	2.07209	+	1.19632i	0.155310	+	0.0896683i
$179$		−	22.5880i		−	1.68831i	−0.536103	−	0.844153i	$-0.680104\pi$
$179$		−	22.5880i		−	1.68831i	0.536103	−	0.844153i	$-0.319896\pi$
$180$	2.77811	−	1.13231i	0.207068	−	0.0843970i
$181$	−16.0655			−1.19414			−0.597069	−	0.802190i	$-0.703668\pi$
$181$	−16.0655			−1.19414			−0.597069	+	0.802190i	$0.703668\pi$
$182$	4.70884	−	8.15596i	0.349043	−	0.604560i
$183$	−0.885855	+	12.9524i	−0.0654843	+	0.957467i
$184$	−6.17351	+	3.56428i	−0.455117	+	0.262762i
$185$	−6.27007	+	3.62003i	−0.460985	+	0.266150i
$186$	2.71598	+	5.54708i	0.199145	+	0.406731i
$187$	−1.69004	−	6.00255i	−0.123588	−	0.438950i
$188$			10.2998i			0.751194i
$189$	−12.6711	−	11.3045i	−0.921686	−	0.822280i
$190$	4.33972			0.314836
$191$	1.49071	+	0.860659i	0.107864	+	0.0622751i	0.552961	−	0.833207i	$-0.313498\pi$
$191$	1.49071	+	0.860659i	0.107864	+	0.0622751i	−0.445098	+	0.895482i	$0.646831\pi$
$192$	0.761656	+	1.55560i	0.0549678	+	0.112265i
$193$	10.9926	−	6.34656i	0.791262	−	0.456836i	−0.0491444	−	0.998792i	$-0.515649\pi$
$193$	10.9926	−	6.34656i	0.791262	−	0.456836i	0.840407	+	0.541956i	$0.182316\pi$
$194$	8.05367	+	13.9494i	0.578220	+	1.00151i
$195$	4.97984	+	0.340587i	0.356613	+	0.0243900i
$196$	1.83978	−	3.18659i	0.131413	−	0.227613i
$197$	−0.626855			−0.0446615			−0.0223308	−	0.999751i	$-0.507109\pi$
$197$	−0.626855			−0.0446615			−0.0223308	+	0.999751i	$0.507109\pi$
$198$	7.85132	−	6.11202i	0.557969	−	0.434362i
$199$	−16.8127			−1.19182			−0.595909	−	0.803052i	$-0.703208\pi$
$199$	−16.8127			−1.19182			−0.595909	+	0.803052i	$0.703208\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−3.57290	+	5.31452i	−0.252013	+	0.374857i
$202$	1.81753	+	3.14805i	0.127881	+	0.221496i
$203$	−3.89540	+	2.24901i	−0.273403	+	0.157850i
$204$	1.81695	−	2.70263i	0.127212	−	0.189222i
$205$	6.63880	+	3.83291i	0.463674	+	0.267702i
$206$	3.86890			0.269559
$207$	−2.91165	+	21.1865i	−0.202374	+	1.47256i
$208$			2.88183i			0.199819i
$209$	13.8545	−	3.90081i	0.958339	−	0.269824i
$210$	5.64708	+	0.386222i	0.389685	+	0.0266519i
$211$	−10.0105	+	5.77955i	−0.689150	+	0.397881i	−0.803293	−	0.595584i	$-0.796921\pi$
$211$	−10.0105	+	5.77955i	−0.689150	+	0.397881i	0.114144	+	0.993464i	$0.463588\pi$
$212$	2.82074	−	1.62855i	0.193729	−	0.111849i
$213$	24.3239	−	11.9095i	1.66664	−	0.816028i
$214$	3.59597	−	6.22840i	0.245815	−	0.425765i
$215$	7.96041			0.542896
$216$	5.08750	+	1.05706i	0.346160	+	0.0719237i
$217$			11.6532i			0.791068i
$218$	−10.9770	−	6.33759i	−0.743459	−	0.429236i
$219$	17.6263	−	8.63024i	1.19107	−	0.583178i
$220$	−0.817812	+	3.21422i	−0.0551369	+	0.216702i
$221$	4.69249	−	2.70921i	0.315651	−	0.182241i
$222$	−12.5109	−	0.855662i	−0.839677	−	0.0574283i
$223$	−6.53996	+	11.3275i	−0.437948	+	0.758549i	−0.997531	−	0.0702259i	$-0.977628\pi$
$223$	−6.53996	+	11.3275i	−0.437948	+	0.758549i	0.559583	+	0.828774i	$0.310961\pi$
$224$			3.26796i			0.218350i
$225$	1.13231	+	2.77811i	0.0754870	+	0.185207i
$226$			3.40946i			0.226794i
$227$	−10.9195	+	18.9130i	−0.724749	+	1.25530i	0.234328	+	0.972158i	$0.424711\pi$
$227$	−10.9195	+	18.9130i	−0.724749	+	1.25530i	−0.959077	+	0.283145i	$0.908622\pi$
$228$	6.23796	+	4.19372i	0.413119	+	0.277736i
$229$	0.226279	+	0.391926i	0.0149529	+	0.0258992i	0.873405	−	0.486994i	$-0.161907\pi$
$229$	0.226279	+	0.391926i	0.0149529	+	0.0258992i	−0.858452	+	0.512894i	$0.828573\pi$
$230$	−3.56428	−	6.17351i	−0.235021	−	0.407069i
$231$	18.3754	−	3.84293i	1.20902	−	0.252846i
$232$	0.688200	−	1.19200i	0.0451826	−	0.0782585i
$233$	−28.9074			−1.89379			−0.946893	−	0.321549i	$-0.895796\pi$
$233$	−28.9074			−1.89379			−0.946893	+	0.321549i	$0.895796\pi$
$234$	6.82895	+	5.30187i	0.446422	+	0.346594i
$235$	−10.2998			−0.671888
$236$	1.31366	+	0.758441i	0.0855118	+	0.0493703i
$237$	1.54803	−	22.6342i	0.100555	−	1.47025i
$238$	5.32123	−	3.07221i	0.344924	−	0.199142i
$239$	−6.53619	−	11.3210i	−0.422791	−	0.732296i	0.573420	−	0.819261i	$-0.305616\pi$
$239$	−6.53619	−	11.3210i	−0.422791	−	0.732296i	−0.996211	+	0.0869659i	$0.972283\pi$
$240$	−1.55560	+	0.761656i	−0.100413	+	0.0491647i
$241$	20.5969	+	11.8916i	1.32676	+	0.766006i	0.984797	−	0.173707i	$-0.0555747\pi$
$241$	20.5969	+	11.8916i	1.32676	+	0.766006i	0.341964	+	0.939713i	$0.388908\pi$
$242$	0.278271	+	10.9965i	0.0178880	+	0.706880i
$243$	11.8646	−	10.1109i	0.761117	−	0.648615i
$244$		−	7.49552i		−	0.479852i
$245$	3.18659	+	1.83978i	0.203584	+	0.117539i
$246$	5.83872	+	11.9249i	0.372263	+	0.760305i
$247$	6.25316	+	10.8308i	0.397879	+	0.689146i
$248$	−1.78294	−	3.08815i	−0.113217	−	0.196097i
$249$	1.59924	+	0.109378i	0.101348	+	0.00693152i
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$		−	5.83695i		−	0.368425i	−0.982886	−	0.184212i	$-0.941027\pi$
$251$		−	5.83695i		−	0.368425i	0.982886	−	0.184212i	$-0.0589734\pi$
$252$	7.74395	+	6.01226i	0.487823	+	0.378737i
$253$	−16.9281	−	16.5051i	−1.06426	−	1.03767i
$254$	−5.69972	−	3.29074i	−0.357633	−	0.206479i
$255$	2.70263	+	1.81695i	0.169245	+	0.113782i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.461731	−	0.266581i	0.0288020	−	0.0166289i	−0.485530	−	0.874220i	$-0.661373\pi$
$257$	0.461731	−	0.266581i	0.0288020	−	0.0166289i	0.514332	+	0.857591i	$0.328040\pi$
$258$	11.4424	+	7.69261i	0.712372	+	0.478921i
$259$	−20.4903	−	11.8301i	−1.27321	−	0.735086i
$260$	−2.88183			−0.178723
$261$	−1.55851	−	3.82379i	−0.0964690	−	0.236687i
$262$	−5.58236			−0.344879
$263$	−1.99471	+	3.45494i	−0.122999	+	0.213041i	−0.920949	−	0.389683i	$-0.872585\pi$
$263$	−1.99471	+	3.45494i	−0.122999	+	0.213041i	0.797950	+	0.602724i	$0.205918\pi$
$264$	−4.28162	+	3.82985i	−0.263515	+	0.235711i
$265$	1.62855	+	2.82074i	0.100041	+	0.173276i
$266$	7.09101	+	12.2820i	0.434778	+	0.753057i
$267$	−3.72199	+	1.82238i	−0.227782	+	0.111528i
$268$	1.84864	−	3.20194i	0.112924	−	0.195590i
$269$			18.0847i			1.10265i	0.834292	+	0.551323i	$0.185877\pi$
$269$			18.0847i			1.10265i	−0.834292	+	0.551323i	$0.814123\pi$
$270$	−1.05706	+	5.08750i	−0.0643305	+	0.309615i
$271$		−	0.0590289i		−	0.00358575i	−0.999998	−	0.00179288i	$-0.999429\pi$
$271$		−	0.0590289i		−	0.00358575i	0.999998	−	0.00179288i	$-0.000570691\pi$
$272$	−0.940102	+	1.62830i	−0.0570020	+	0.0987304i
$273$	7.17304	+	14.6501i	0.434132	+	0.886666i
$274$	−4.52136	+	2.61041i	−0.273145	+	0.157700i
$275$	−3.21422	−	0.817812i	−0.193825	−	0.0493159i
$276$	0.842485	−	12.3182i	0.0507116	−	0.741471i
$277$	6.37510	+	3.68067i	0.383043	+	0.221150i	0.679141	−	0.734008i	$-0.262352\pi$
$277$	6.37510	+	3.68067i	0.383043	+	0.221150i	−0.296099	+	0.955157i	$0.595686\pi$
$278$			11.7849i			0.706814i
$279$	−10.5980	−	1.45648i	−0.634488	−	0.0871973i
$280$	−3.26796			−0.195298
$281$	11.7245	−	20.3075i	0.699428	−	1.21144i	−0.269237	−	0.963074i	$-0.586772\pi$
$281$	11.7245	−	20.3075i	0.699428	−	1.21144i	0.968665	−	0.248371i	$-0.0798951\pi$
$282$	−14.8051	−	9.95334i	−0.881632	−	0.592713i
$283$	−8.86343	+	5.11730i	−0.526876	+	0.304192i	−0.739743	−	0.672889i	$-0.765053\pi$
$283$	−8.86343	+	5.11730i	−0.526876	+	0.304192i	0.212867	+	0.977081i	$0.431720\pi$
$284$	−13.5415	+	7.81819i	−0.803540	+	0.463924i
$285$	−4.19372	+	6.23796i	−0.248415	+	0.369505i
$286$	−9.20023	+	2.59036i	−0.544021	+	0.153171i
$287$			25.0516i			1.47875i
$288$	−2.97206	−	0.408449i	−0.175131	−	0.0240681i
$289$	−13.4648			−0.792049
$290$	1.19200	+	0.688200i	0.0699965	+	0.0404125i
$291$	−27.8337	−	1.90364i	−1.63164	−	0.111593i
$292$	−9.81284	+	5.66544i	−0.574253	+	0.331545i
$293$	11.5431	+	19.9933i	0.674357	+	1.16802i	0.976656	+	0.214808i	$0.0689125\pi$
$293$	11.5431	+	19.9933i	0.674357	+	1.16802i	−0.302299	+	0.953213i	$0.597754\pi$
$294$	2.80255	+	5.72390i	0.163448	+	0.333825i
$295$	−0.758441	+	1.31366i	−0.0441581	+	0.0764841i
$296$	7.24005			0.420819
$297$	1.19830	+	17.1920i	0.0695324	+	0.997580i
$298$	2.70327			0.156596
$299$	10.2716	−	17.7910i	0.594023	−	1.02888i
$300$	−0.761656	−	1.55560i	−0.0439742	−	0.0898124i
$301$	13.0071	+	22.5290i	0.749719	+	1.29855i
$302$	−9.07019	+	5.23668i	−0.521931	+	0.301337i
$303$	−6.28143	−	0.429608i	−0.360859	−	0.0246803i
$304$	−3.75831	−	2.16986i	−0.215554	−	0.124450i
$305$	7.49552			0.429192
$306$	2.12896	+	5.22341i	0.121705	+	0.298602i
$307$			26.5900i			1.51757i	0.651339	+	0.758787i	$0.274207\pi$
$307$			26.5900i			1.51757i	−0.651339	+	0.758787i	$0.725793\pi$
$308$	−10.4330	+	2.93744i	−0.594473	+	0.167376i
$309$	−3.73874	+	5.56120i	−0.212690	+	0.316366i
$310$	3.08815	−	1.78294i	0.175395	−	0.101264i
$311$	17.4411	−	10.0696i	0.988992	−	0.570995i	0.0840190	−	0.996464i	$-0.473224\pi$
$311$	17.4411	−	10.0696i	0.988992	−	0.570995i	0.904973	+	0.425470i	$0.139891\pi$
$312$	−4.14237	−	2.78488i	−0.234516	−	0.157663i
$313$	14.9929	−	25.9684i	0.847446	−	1.46782i	−0.0360335	−	0.999351i	$-0.511472\pi$
$313$	14.9929	−	25.9684i	0.847446	−	1.46782i	0.883480	−	0.468469i	$-0.155194\pi$
$314$	9.66836			0.545617
$315$	−6.01226	+	7.74395i	−0.338752	+	0.436322i
$316$			13.0984i			0.736843i
$317$	−12.7330	−	7.35141i	−0.715157	−	0.412896i	0.0978106	−	0.995205i	$-0.468816\pi$
$317$	−12.7330	−	7.35141i	−0.715157	−	0.412896i	−0.812968	+	0.582309i	$0.802149\pi$
$318$	−0.384940	+	5.62832i	−0.0215863	+	0.315621i
$319$	4.42405	+	1.12564i	0.247699	+	0.0630236i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	5.47778	+	11.1878i	0.305740	+	0.624439i
$322$	11.6479	−	20.1748i	0.649112	−	1.12430i
$323$			8.15955i			0.454010i
$324$	−6.43577	+	6.29133i	−0.357543	+	0.349518i
$325$		−	2.88183i		−	0.159855i
$326$	−10.0438	+	17.3963i	−0.556272	+	0.963491i
$327$	19.7175	−	9.65414i	1.09038	−	0.533875i
$328$	−3.83291	−	6.63880i	−0.211637	−	0.366566i
$329$	−16.8297	−	29.1500i	−0.927854	−	1.60709i
$330$	−3.82985	−	4.28162i	−0.210826	−	0.235695i
$331$	6.84351	−	11.8533i	0.376153	−	0.651517i	−0.614346	−	0.789037i	$-0.710580\pi$
$331$	6.84351	−	11.8533i	0.376153	−	0.651517i	0.990499	+	0.137520i	$0.0439133\pi$
$332$	−0.925481			−0.0507924
$333$	13.3200	−	17.1565i	0.729929	−	0.940168i
$334$	−20.3677			−1.11447
$335$	3.20194	+	1.84864i	0.174941	+	0.101002i
$336$	−4.69740	−	3.15802i	−0.256264	−	0.172284i
$337$	−15.5359	+	8.96965i	−0.846294	+	0.488608i	−0.859399	−	0.511306i	$-0.829162\pi$
$337$	−15.5359	+	8.96965i	−0.846294	+	0.488608i	0.0131049	+	0.999914i	$0.495828\pi$
$338$	2.34754	+	4.06606i	0.127689	+	0.221164i
$339$	−4.90080	−	3.29476i	−0.266175	−	0.178947i
$340$	−1.62830	−	0.940102i	−0.0883072	−	0.0509842i
$341$	8.25628	−	8.46786i	0.447103	−	0.458560i
$342$	−12.0562	+	4.91388i	−0.651925	+	0.265712i
$343$		−	10.8511i		−	0.585903i
$344$	−6.89392	−	3.98021i	−0.371695	−	0.214598i
$345$	12.3182	+	0.842485i	0.663192	+	0.0453579i
$346$	−6.26488	−	10.8511i	−0.336802	−	0.583359i
$347$	9.69853	+	16.7983i	0.520644	+	0.901782i	0.999712	+	0.0240042i	$0.00764150\pi$
$347$	9.69853	+	16.7983i	0.520644	+	0.901782i	−0.479068	+	0.877778i	$0.659025\pi$
$348$	1.04834	+	2.14112i	0.0561971	+	0.114776i
$349$	20.3082	+	11.7250i	1.08707	+	0.627623i	0.932796	−	0.360404i	$-0.117361\pi$
$349$	20.3082	+	11.7250i	1.08707	+	0.627623i	0.154279	+	0.988027i	$0.450695\pi$
$350$		−	3.26796i		−	0.174680i
$351$	−14.2202	+	4.69251i	−0.759017	+	0.250467i
$352$	2.31535	−	2.37469i	0.123409	−	0.126571i
$353$	9.72262	+	5.61336i	0.517483	+	0.298769i	0.735904	−	0.677086i	$-0.236757\pi$
$353$	9.72262	+	5.61336i	0.517483	+	0.298769i	−0.218421	+	0.975855i	$0.570091\pi$
$354$	−2.35965	+	1.15534i	−0.125414	+	0.0614057i
$355$	−7.81819	−	13.5415i	−0.414946	−	0.718708i
$356$	2.07209	−	1.19632i	0.109821	−	0.0634050i
$357$	−0.726176	+	10.6177i	−0.0384333	+	0.561946i
$358$	−19.5618	−	11.2940i	−1.03387	−	0.596906i
$359$	−5.59649			−0.295372			−0.147686	−	0.989034i	$-0.547182\pi$
$359$	−5.59649			−0.295372			−0.147686	+	0.989034i	$0.547182\pi$
$360$	0.408449	−	2.97206i	0.0215272	−	0.156642i
$361$	0.166851			0.00878161
$362$	−8.03274	+	13.9131i	−0.422191	+	0.731257i
$363$	−16.0754	−	10.2265i	−0.843739	−	0.536754i
$364$	−4.70884	−	8.15596i	−0.246811	−	0.427488i
$365$	−5.66544	−	9.81284i	−0.296543	−	0.513627i
$366$	10.7742	+	7.24336i	0.563174	+	0.378616i
$367$	−2.50320	+	4.33566i	−0.130666	+	0.226320i	−0.923933	−	0.382553i	$-0.875045\pi$
$367$	−2.50320	+	4.33566i	−0.130666	+	0.226320i	0.793268	+	0.608873i	$0.208378\pi$
$368$			7.12855i			0.371601i
$369$	−22.7833	−	3.13110i	−1.18605	−	0.162998i
$370$			7.24005i			0.376392i
$371$	−5.32204	+	9.21805i	−0.276307	+	0.478577i
$372$	6.16190	+	0.421432i	0.319479	+	0.0218503i
$373$	23.8159	−	13.7501i	1.23314	−	0.711953i	0.265456	−	0.964123i	$-0.414478\pi$
$373$	23.8159	−	13.7501i	1.23314	−	0.711953i	0.967683	+	0.252170i	$0.0811442\pi$
$374$	−6.04338	−	1.53765i	−0.312496	−	0.0795102i
$375$	1.55560	−	0.761656i	0.0803306	−	0.0393318i
$376$	8.91993	+	5.14992i	0.460010	+	0.265587i
$377$			3.96655i			0.204288i
$378$	−16.1255	+	5.32125i	−0.829407	+	0.273695i
$379$	33.0775			1.69908			0.849538	−	0.527527i	$-0.176881\pi$
$379$	33.0775			1.69908			0.849538	+	0.527527i	$0.176881\pi$
$380$	2.16986	−	3.75831i	0.111311	−	0.192797i
$381$	10.2381	−	5.01282i	0.524515	−	0.256815i
$382$	1.49071	−	0.860659i	0.0762711	−	0.0440352i
$383$	−27.2719	+	15.7454i	−1.39353	+	0.804555i	−0.993704	−	0.112036i	$-0.964263\pi$
$383$	−27.2719	+	15.7454i	−1.39353	+	0.804555i	−0.399826	+	0.916591i	$0.630929\pi$
$384$	1.72801	+	0.118185i	0.0881823	+	0.00603108i
$385$	−2.93744	−	10.4330i	−0.149706	−	0.531713i
$386$		−	12.6931i		−	0.646063i
$387$	−22.1149	+	9.01361i	−1.12416	+	0.458188i
$388$	16.1073			0.817726
$389$	33.1700	+	19.1507i	1.68179	+	0.970980i	0.960474	+	0.278371i	$0.0897943\pi$
$389$	33.1700	+	19.1507i	1.68179	+	0.970980i	0.721313	+	0.692609i	$0.243539\pi$
$390$	2.78488	−	4.14237i	0.141018	−	0.209757i
$391$	11.6074	−	6.70156i	0.587014	−	0.338913i
$392$	−1.83978	−	3.18659i	−0.0929228	−	0.160947i
$393$	5.39456	−	8.02415i	0.272119	−	0.404765i
$394$	−0.313427	+	0.542872i	−0.0157902	+	0.0273495i
$395$	−13.0984			−0.659053
$396$	−1.36750	−	9.85545i	−0.0687196	−	0.495255i
$397$	4.36717			0.219182			0.109591	−	0.993977i	$-0.465046\pi$
$397$	4.36717			0.219182			0.109591	+	0.993977i	$0.465046\pi$
$398$	−8.40633	+	14.5602i	−0.421371	+	0.729836i
$399$	−24.5067	−	1.67610i	−1.22687	−	0.0839097i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−9.63542	+	5.56301i	−0.481170	+	0.277804i	−0.720904	−	0.693035i	$-0.756273\pi$
$401$	−9.63542	+	5.56301i	−0.481170	+	0.277804i	0.239734	+	0.970839i	$0.422940\pi$
$402$	2.81606	+	5.75148i	0.140452	+	0.286858i
$403$	8.89950	+	5.13813i	0.443316	+	0.255948i
$404$	3.63506			0.180851
$405$	−6.29133	−	6.43577i	−0.312619	−	0.319796i
$406$			4.49802i			0.223233i
$407$	6.50781	+	23.1139i	0.322580	+	1.14571i
$408$	−1.43207	−	2.92484i	−0.0708980	−	0.144801i
$409$	4.54551	−	2.62435i	0.224761	−	0.129766i	−0.383392	−	0.923586i	$-0.625244\pi$
$409$	4.54551	−	2.62435i	0.224761	−	0.129766i	0.608153	+	0.793820i	$0.291911\pi$
$410$	6.63880	−	3.83291i	0.327867	−	0.189294i
$411$	0.617019	−	9.02164i	0.0304353	−	0.445005i
$412$	1.93445	−	3.35057i	0.0953035	−	0.165071i
$413$	−4.95710			−0.243923
$414$	16.8922	+	13.1148i	0.830208	+	0.644558i
$415$		−	0.925481i		−	0.0454301i
$416$	2.49573	+	1.44091i	0.122363	+	0.0706466i
$417$	−16.9398	−	11.3885i	−0.829546	−	0.557696i
$418$	3.54907	−	13.9488i	0.173591	−	0.682258i
$419$	15.2701	−	8.81620i	0.745994	−	0.430700i	−0.0782508	−	0.996934i	$-0.524933\pi$
$419$	15.2701	−	8.81620i	0.745994	−	0.430700i	0.824245	+	0.566234i	$0.191600\pi$
$420$	3.15802	−	4.69740i	0.154095	−	0.229210i
$421$	8.85232	−	15.3327i	0.431435	−	0.747268i	−0.565562	−	0.824706i	$-0.691341\pi$
$421$	8.85232	−	15.3327i	0.431435	−	0.747268i	0.996997	+	0.0774378i	$0.0246739\pi$
$422$			11.5591i			0.562688i
$423$	28.6141	−	11.6626i	1.39126	−	0.567054i
$424$		−	3.25710i		−	0.158179i
$425$	0.940102	−	1.62830i	0.0456016	−	0.0789843i
$426$	1.84798	−	27.0199i	0.0895348	−	1.30912i
$427$	12.2475	+	21.2133i	0.592699	+	1.02659i
$428$	−3.59597	−	6.22840i	−0.173818	−	0.301061i
$429$	5.16729	−	15.7277i	0.249479	−	0.759342i
$430$	3.98021	−	6.89392i	0.191943	−	0.332454i
$431$	34.6411			1.66860			0.834301	−	0.551310i	$-0.185872\pi$
$431$	34.6411			1.66860			0.834301	+	0.551310i	$0.185872\pi$
$432$	3.45919	−	3.87737i	0.166430	−	0.186550i
$433$	23.6691			1.13747			0.568733	−	0.822522i	$-0.307434\pi$
$433$	23.6691			1.13747			0.568733	+	0.822522i	$0.307434\pi$
$434$	10.0919	+	5.82658i	0.484428	+	0.279685i
$435$	−2.14112	+	1.04834i	−0.102659	+	0.0502642i
$436$	−10.9770	+	6.33759i	−0.525705	+	0.303516i
$437$	15.4679	+	26.7913i	0.739932	+	1.28160i
$438$	1.33914	−	19.5799i	0.0639864	−	0.935565i
$439$	30.7259	+	17.7396i	1.46647	+	0.846665i	0.999297	−	0.0375029i	$-0.0119403\pi$
$439$	30.7259	+	17.7396i	1.46647	+	0.846665i	0.467170	+	0.884168i	$0.345274\pi$
$440$	2.37469	+	2.31535i	0.113209	+	0.110380i
$441$	−10.9359	−	1.50291i	−0.520756	−	0.0715672i
$442$		−	5.41842i		−	0.257728i
$443$	−34.1454	−	19.7138i	−1.62230	−	0.936633i	−0.986304	−	0.164937i	$-0.947258\pi$
$443$	−34.1454	−	19.7138i	−1.62230	−	0.936633i	−0.635991	−	0.771696i	$-0.719409\pi$
$444$	−6.99648	+	10.4069i	−0.332038	+	0.493891i
$445$	1.19632	+	2.07209i	0.0567112	+	0.0982267i
$446$	6.53996	+	11.3275i	0.309676	+	0.536375i
$447$	−2.61232	+	3.88571i	−0.123559	+	0.183788i
$448$	2.83014	+	1.63398i	0.133711	+	0.0771983i
$449$		−	25.8480i		−	1.21984i	−0.792462	−	0.609921i	$-0.791201\pi$
$449$		−	25.8480i		−	1.21984i	0.792462	−	0.609921i	$-0.208799\pi$
$450$	2.97206	+	0.408449i	0.140104	+	0.0192545i
$451$	17.7491	−	18.2039i	0.835772	−	0.857189i
$452$	2.95268	+	1.70473i	0.138883	+	0.0801839i
$453$	1.23779	−	18.0981i	0.0581564	−	0.850323i
$454$	10.9195	+	18.9130i	0.512475	+	0.887633i
$455$	8.15596	−	4.70884i	0.382357	−	0.220754i
$456$	6.75085	−	3.30537i	0.316137	−	0.154788i
$457$	−11.7176	−	6.76513i	−0.548124	−	0.316460i	0.200241	−	0.979747i	$-0.435828\pi$
$457$	−11.7176	−	6.76513i	−0.548124	−	0.316460i	−0.748365	+	0.663287i	$0.769161\pi$
$458$	0.452557			0.0211466
$459$	−9.56553	−	1.98748i	−0.446481	−	0.0927678i
$460$	−7.12855			−0.332370
$461$	5.94147	−	10.2909i	0.276722	−	0.479296i	−0.693846	−	0.720123i	$-0.744085\pi$
$461$	5.94147	−	10.2909i	0.276722	−	0.479296i	0.970568	+	0.240827i	$0.0774186\pi$
$462$	5.85965	−	17.8351i	0.272616	−	0.829763i
$463$	−2.56020	−	4.43439i	−0.118982	−	0.206083i	0.800382	−	0.599490i	$-0.204630\pi$
$463$	−2.56020	−	4.43439i	−0.118982	−	0.206083i	−0.919365	+	0.393406i	$0.871297\pi$
$464$	−0.688200	−	1.19200i	−0.0319489	−	0.0553371i
$465$	−0.421432	+	6.16190i	−0.0195435	+	0.285751i
$466$	−14.4537	+	25.0345i	−0.669554	+	1.15970i
$467$		−	3.00206i		−	0.138919i	−0.997585	−	0.0694595i	$-0.977873\pi$
$467$		−	3.00206i		−	0.138919i	0.997585	−	0.0694595i	$-0.0221274\pi$
$468$	8.00603	−	3.26311i	0.370079	−	0.150837i
$469$			12.0826i			0.557921i
$470$	−5.14992	+	8.91993i	−0.237548	+	0.411446i
$471$	−9.34310	+	13.8974i	−0.430507	+	0.640359i
$472$	1.31366	−	0.758441i	0.0604660	−	0.0349101i
$473$	6.51012	−	25.5865i	0.299336	−	1.17647i
$474$	−18.8278	−	12.6578i	−0.864790	−	0.581390i
$475$	3.75831	+	2.16986i	0.172443	+	0.0995600i
$476$		−	6.14443i		−	0.281629i
$477$	−7.71823	−	5.99229i	−0.353393	−	0.274368i
$478$	−13.0724			−0.597917
$479$	−15.8657	+	27.4801i	−0.724921	+	1.25560i	0.234086	+	0.972216i	$0.424790\pi$
$479$	−15.8657	+	27.4801i	−0.724921	+	1.25560i	−0.959007	+	0.283384i	$0.908543\pi$
$480$	−0.118185	+	1.72801i	−0.00539436	+	0.0788727i
$481$	−18.0693	+	10.4323i	−0.823887	+	0.475671i
$482$	20.5969	−	11.8916i	0.938162	−	0.541648i
$483$	17.7434	+	36.2389i	0.807353	+	1.64893i
$484$	9.66237	+	5.25725i	0.439198	+	0.238966i
$485$			16.1073i			0.731397i
$486$	−2.82398	−	15.3305i	−0.128098	−	0.695407i
$487$	−21.3724			−0.968476			−0.484238	−	0.874936i	$-0.660903\pi$
$487$	−21.3724			−0.968476			−0.484238	+	0.874936i	$0.660903\pi$
$488$	−6.49131	−	3.74776i	−0.293848	−	0.169653i
$489$	−15.2998	−	31.2480i	−0.691880	−	1.41309i
$490$	3.18659	−	1.83978i	0.143955	−	0.0831126i
$491$	14.5893	+	25.2694i	0.658406	+	1.14039i	0.981028	+	0.193865i	$0.0621025\pi$
$491$	14.5893	+	25.2694i	0.658406	+	1.14039i	−0.322622	+	0.946528i	$0.604564\pi$
$492$	13.2466	+	0.905982i	0.597205	+	0.0408448i
$493$	−1.29396	+	2.24120i	−0.0582769	+	0.100938i
$494$	12.5063			0.562686
$495$	9.85545	−	1.36750i	0.442970	−	0.0614646i
$496$	−3.56588			−0.160113
$497$	25.5495	−	44.2530i	1.14605	−	1.98502i
$498$	0.894346	−	1.33030i	0.0400766	−	0.0596120i
$499$	−19.2299	−	33.3072i	−0.860850	−	1.49104i	−0.871109	−	0.491089i	$-0.836599\pi$
$499$	−19.2299	−	33.3072i	−0.860850	−	1.49104i	0.0102592	−	0.999947i	$-0.496734\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	19.6825	−	29.2768i	0.879350	−	1.30799i
$502$	−5.05494	−	2.91847i	−0.225613	−	0.130258i
$503$	−37.0022			−1.64984			−0.824922	−	0.565246i	$-0.808781\pi$
$503$	−37.0022			−1.64984			−0.824922	+	0.565246i	$0.808781\pi$
$504$	9.07874	−	3.70033i	0.404399	−	0.164826i
$505$			3.63506i			0.161758i
$506$	−22.7579	+	6.40758i	−1.01171	+	0.284852i
$507$	−8.11316	−	0.554886i	−0.360318	−	0.0246433i
$508$	−5.69972	+	3.29074i	−0.252884	+	0.146003i
$509$	27.4788	−	15.8649i	1.21798	−	0.703199i	0.253491	−	0.967338i	$-0.418421\pi$
$509$	27.4788	−	15.8649i	1.21798	−	0.703199i	0.964485	+	0.264139i	$0.0850877\pi$
$510$	2.92484	−	1.43207i	0.129514	−	0.0634131i
$511$	18.5144	−	32.0679i	0.819030	−	1.41860i
$512$	−1.00000			−0.0441942
$513$	4.58733	−	22.0783i	0.202536	−	0.974781i
$514$		−	0.533162i		−	0.0235167i
$515$	3.35057	+	1.93445i	0.147644	+	0.0852420i
$516$	12.3832	−	6.06310i	0.545139	−	0.266913i
$517$	−8.42334	+	33.1059i	−0.370458	+	1.45600i
$518$	−20.4903	+	11.8301i	−0.900293	+	0.519785i
$519$	21.6516	+	1.48083i	0.950400	+	0.0650010i
$520$	−1.44091	+	2.49573i	−0.0631882	+	0.109445i
$521$			15.5516i			0.681329i	0.940185	+	0.340664i	$0.110652\pi$
$521$			15.5516i			0.681329i	−0.940185	+	0.340664i	$0.889348\pi$
$522$	−4.09075	−	0.562190i	−0.179047	−	0.0246064i
$523$		−	27.1075i		−	1.18533i	−0.805450	−	0.592664i	$-0.798076\pi$
$523$		−	27.1075i		−	1.18533i	0.805450	−	0.592664i	$-0.201924\pi$
$524$	−2.79118	+	4.83446i	−0.121933	+	0.211195i
$525$	4.69740	+	3.15802i	0.205011	+	0.137827i
$526$	1.99471	+	3.45494i	0.0869736	+	0.150643i
$527$	3.35229	+	5.80634i	0.146028	+	0.252928i
$528$	1.17594	+	5.62291i	0.0511763	+	0.244706i
$529$	13.9081	−	24.0896i	0.604701	−	1.04737i
$530$	3.25710			0.141480
$531$	0.619569	−	4.50827i	0.0268870	−	0.195642i
$532$	14.1820			0.614868
$533$	19.1319	+	11.0458i	0.828693	+	0.478446i
$534$	−0.282774	+	4.13453i	−0.0122368	+	0.178919i
$535$	6.22840	−	3.59597i	0.269277	−	0.155467i
$536$	−1.84864	−	3.20194i	−0.0798491	−	0.138303i
$537$	35.1378	−	17.2043i	1.51631	−	0.742420i
$538$	15.6618	+	9.04237i	0.675230	+	0.389844i
$539$	8.51947	−	8.73779i	0.366959	−	0.376363i
$540$	3.87737	+	3.45919i	0.166856	+	0.148860i
$541$			7.54485i			0.324379i	0.986760	+	0.162189i	$0.0518555\pi$
$541$			7.54485i			0.324379i	−0.986760	+	0.162189i	$0.948144\pi$
$542$	−0.0511206	−	0.0295145i	−0.00219582	−	0.00126776i
$543$	−12.2364	−	24.9914i	−0.525113	−	1.07248i
$544$	0.940102	+	1.62830i	0.0403065	+	0.0698130i
$545$	−6.33759	−	10.9770i	−0.271473	−	0.470205i
$546$	16.2739	+	1.11303i	0.696459	+	0.0476331i
$547$	32.5884	+	18.8149i	1.39338	+	0.804469i	0.993688	−	0.112180i	$-0.0357833\pi$
$547$	32.5884	+	18.8149i	1.39338	+	0.804469i	0.399693	+	0.916649i	$0.369117\pi$
$548$			5.22081i			0.223022i
$549$	−20.8234	+	8.48722i	−0.888720	+	0.362226i
$550$	−2.31535	+	2.37469i	−0.0987270	+	0.101257i
$551$	−5.17293	−	2.98659i	−0.220374	−	0.127233i
$552$	−10.2467	−	6.88873i	−0.436127	−	0.293204i
$553$	−21.4025	−	37.0703i	−0.910128	−	1.57639i
$554$	6.37510	−	3.68067i	0.270852	−	0.156377i
$555$	−10.4069	−	6.99648i	−0.441750	−	0.296984i
$556$	10.2061	+	5.89247i	0.432833	+	0.249896i
$557$	−16.4844			−0.698468			−0.349234	−	0.937036i	$-0.613558\pi$
$557$	−16.4844			−0.698468			−0.349234	+	0.937036i	$0.613558\pi$
$558$	−6.56037	+	8.44993i	−0.277723	+	0.357714i
$559$	22.9405			0.970281
$560$	−1.63398	+	2.83014i	−0.0690482	+	0.119595i
$561$	8.05031	−	7.20090i	0.339884	−	0.304022i
$562$	−11.7245	−	20.3075i	−0.494570	−	0.856621i
$563$	3.03905	+	5.26379i	0.128081	+	0.221842i	0.922933	−	0.384961i	$-0.125785\pi$
$563$	3.03905	+	5.26379i	0.128081	+	0.221842i	−0.794852	+	0.606803i	$0.792452\pi$
$564$	−16.0224	+	7.84494i	−0.674665	+	0.330332i
$565$	−1.70473	+	2.95268i	−0.0717186	+	0.124220i
$566$			10.2346i			0.430192i
$567$	7.93419	−	28.3212i	0.333205	−	1.18938i
$568$			15.6364i			0.656088i
$569$	8.67474	−	15.0251i	0.363664	−	0.629885i	−0.624897	−	0.780707i	$-0.714859\pi$
$569$	8.67474	−	15.0251i	0.363664	−	0.629885i	0.988561	+	0.150823i	$0.0481922\pi$
$570$	3.30537	+	6.75085i	0.138447	+	0.282762i
$571$	−3.31059	+	1.91137i	−0.138544	+	0.0799883i	−0.567670	−	0.823256i	$-0.692155\pi$
$571$	−3.31059	+	1.91137i	−0.138544	+	0.0799883i	0.429126	+	0.903245i	$0.358822\pi$
$572$	−2.35679	+	9.26281i	−0.0985425	+	0.387298i
$573$	−0.203433	+	2.97446i	−0.00849855	+	0.124260i
$574$	21.6953	+	12.5258i	0.905545	+	0.522817i
$575$		−	7.12855i		−	0.297281i
$576$	−1.83976	+	2.36966i	−0.0766567	+	0.0987358i
$577$	−23.5042			−0.978494			−0.489247	−	0.872145i	$-0.662728\pi$
$577$	−23.5042			−0.978494			−0.489247	+	0.872145i	$0.662728\pi$
$578$	−6.73242	+	11.6609i	−0.280032	+	0.485029i
$579$	18.2452	+	12.2661i	0.758247	+	0.509762i
$580$	1.19200	−	0.688200i	0.0494950	−	0.0285760i
$581$	2.61924	−	1.51222i	0.108664	−	0.0627373i
$582$	−15.5655	+	23.1529i	−0.645209	+	0.959718i
$583$	10.3983	−	2.92769i	0.430654	−	0.121252i
$584$			11.3309i			0.468875i
$585$	3.26311	+	8.00603i	0.134913	+	0.331008i
$586$	23.0863			0.953685
$587$	−8.03882	−	4.64121i	−0.331797	−	0.191563i	0.324841	−	0.945769i	$-0.394689\pi$
$587$	−8.03882	−	4.64121i	−0.331797	−	0.191563i	−0.656639	+	0.754205i	$0.728022\pi$
$588$	6.35832	+	0.434866i	0.262213	+	0.0179336i
$589$	−13.4017	+	7.73746i	−0.552207	+	0.318817i
$590$	0.758441	+	1.31366i	0.0312245	+	0.0540824i
$591$	−0.477448	−	0.975133i	−0.0196396	−	0.0401116i
$592$	3.62003	−	6.27007i	0.148782	−	0.257698i
$593$	−24.8486			−1.02041			−0.510205	−	0.860053i	$-0.670430\pi$
$593$	−24.8486			−1.02041			−0.510205	+	0.860053i	$0.670430\pi$
$594$	15.4878	+	7.55823i	0.635474	+	0.310118i
$595$	6.14443			0.251897
$596$	1.35163	−	2.34110i	0.0553651	−	0.0958951i
$597$	−12.8055	−	26.1537i	−0.524093	−	1.07040i
$598$	−10.2716	−	17.7910i	−0.420038	−	0.727527i
$599$	−25.6362	+	14.8011i	−1.04747	+	0.604755i	−0.921939	−	0.387336i	$-0.873396\pi$
$599$	−25.6362	+	14.8011i	−1.04747	+	0.604755i	−0.125527	+	0.992090i	$0.540062\pi$
$600$	−1.72801	−	0.118185i	−0.0705459	−	0.00482486i
$601$	2.39420	+	1.38229i	0.0976617	+	0.0563850i	0.548035	−	0.836455i	$-0.315376\pi$
$601$	2.39420	+	1.38229i	0.0976617	+	0.0563850i	−0.450374	+	0.892840i	$0.648709\pi$
$602$	26.0143			1.06026
$603$	−10.9886	−	1.51015i	−0.447489	−	0.0614981i
$604$			10.4734i			0.426155i
$605$	−5.25725	+	9.66237i	−0.213738	+	0.392831i
$606$	−3.51277	+	5.22508i	−0.142696	+	0.212254i
$607$	33.7561	−	19.4891i	1.37012	−	0.791039i	0.379176	−	0.925324i	$-0.376207\pi$
$607$	33.7561	−	19.4891i	1.37012	−	0.791039i	0.990943	+	0.134286i	$0.0428741\pi$
$608$	−3.75831	+	2.16986i	−0.152419	+	0.0879994i
$609$	−6.46551	−	4.34670i	−0.261996	−	0.176137i
$610$	3.74776	−	6.49131i	0.151742	−	0.262826i
$611$	−29.6824			−1.20082
$612$	5.58809	+	0.767968i	0.225885	+	0.0310432i
$613$			23.9844i			0.968722i	0.874868	+	0.484361i	$0.160948\pi$
$613$			23.9844i			0.968722i	−0.874868	+	0.484361i	$0.839052\pi$
$614$	23.0276	+	13.2950i	0.929320	+	0.536543i
$615$	−0.905982	+	13.2466i	−0.0365327	+	0.534156i
$616$	−2.67258	+	10.5039i	−0.107681	+	0.423215i
$617$	11.5361	−	6.66039i	0.464427	−	0.268137i	−0.249477	−	0.968381i	$-0.580259\pi$
$617$	11.5361	−	6.66039i	0.464427	−	0.268137i	0.713904	+	0.700244i	$0.246925\pi$
$618$	2.94677	+	6.01845i	0.118537	+	0.242097i
$619$	−13.4689	+	23.3289i	−0.541362	+	0.937666i	0.457465	+	0.889228i	$0.348758\pi$
$619$	−13.4689	+	23.3289i	−0.541362	+	0.937666i	−0.998826	+	0.0484380i	$0.984576\pi$
$620$		−	3.56588i		−	0.143209i
$621$	−35.1753	+	11.6075i	−1.41154	+	0.465792i
$622$		−	20.1392i		−	0.807508i
$623$	−3.90954	+	6.77152i	−0.156632	+	0.271295i
$624$	−4.48296	+	2.19496i	−0.179462	+	0.0878688i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−14.9929	−	25.9684i	−0.599235	−	1.03791i
$627$	16.6205	+	18.5810i	0.663758	+	0.742054i
$628$	4.83418	−	8.37305i	0.192905	−	0.334121i
$629$	−13.6128			−0.542777
$630$	3.70033	+	9.07874i	0.147425	+	0.361706i
$631$	34.3706			1.36827			0.684136	−	0.729354i	$-0.260179\pi$
$631$	34.3706			1.36827			0.684136	+	0.729354i	$0.260179\pi$
$632$	11.3436	+	6.54921i	0.451223	+	0.260513i
$633$	−16.6152	−	11.1702i	−0.660394	−	0.443977i
$634$	−12.7330	+	7.35141i	−0.505692	+	0.291962i
$635$	−3.29074	−	5.69972i	−0.130589	−	0.226187i
$636$	4.68180	+	3.14753i	0.185645	+	0.124808i
$637$	9.18319	+	5.30192i	0.363851	+	0.210070i
$638$	3.18685	−	3.26852i	0.126169	−	0.129402i
$639$	37.0529	+	28.7672i	1.46579	+	1.13801i
$640$		−	1.00000i		−	0.0395285i
$641$	17.6637	+	10.1981i	0.697673	+	0.402802i	0.806480	−	0.591261i	$-0.201370\pi$
$641$	17.6637	+	10.1981i	0.697673	+	0.402802i	−0.108807	+	0.994063i	$0.534703\pi$
$642$	12.4278	+	0.849976i	0.490485	+	0.0335459i
$643$	−13.7828	−	23.8725i	−0.543539	−	0.941438i	−0.998697	−	0.0510272i	$-0.983750\pi$
$643$	−13.7828	−	23.8725i	−0.543539	−	0.941438i	0.455158	−	0.890411i	$-0.349583\pi$
$644$	−11.6479	−	20.1748i	−0.458992	−	0.794997i
$645$	6.06310	+	12.3832i	0.238734	+	0.487587i
$646$	7.06638	+	4.07978i	0.278023	+	0.160517i
$647$		−	41.7451i		−	1.64117i	−0.571525	−	0.820585i	$-0.693648\pi$
$647$		−	41.7451i		−	1.64117i	0.571525	−	0.820585i	$-0.306352\pi$
$648$	2.23057	+	8.71921i	0.0876250	+	0.342523i
$649$	3.60212	+	3.51212i	0.141395	+	0.137863i
$650$	−2.49573	−	1.44091i	−0.0978908	−	0.0565173i
$651$	−18.1276	+	8.87570i	−0.710477	+	0.347866i
$652$	10.0438	+	17.3963i	0.393344	+	0.681291i
$653$	−10.9169	+	6.30286i	−0.427210	+	0.246650i	−0.698157	−	0.715944i	$-0.745996\pi$
$653$	−10.9169	+	6.30286i	−0.427210	+	0.246650i	0.270947	+	0.962594i	$0.412663\pi$
$654$	1.49801	−	21.9029i	0.0585769	−	0.856471i
$655$	−4.83446	−	2.79118i	−0.188898	−	0.109060i
$656$	−7.66582			−0.299300
$657$	26.8503	+	20.8461i	1.04753	+	0.813284i
$658$	−33.6595			−1.31218
$659$	−2.55561	+	4.42644i	−0.0995523	+	0.172430i	−0.911499	−	0.411301i	$-0.865074\pi$
$659$	−2.55561	+	4.42644i	−0.0995523	+	0.172430i	0.811947	+	0.583731i	$0.198408\pi$
$660$	−5.62291	+	1.17594i	−0.218872	+	0.0457735i
$661$	16.2241	+	28.1010i	0.631045	+	1.09300i	0.987338	+	0.158628i	$0.0507070\pi$
$661$	16.2241	+	28.1010i	0.631045	+	1.09300i	−0.356293	+	0.934374i	$0.615960\pi$
$662$	−6.84351	−	11.8533i	−0.265981	−	0.460692i
$663$	7.78850	+	5.23613i	0.302480	+	0.203355i
$664$	−0.462740	+	0.801490i	−0.0179578	+	0.0311038i
$665$			14.1820i			0.549955i
$666$	−8.19795	−	20.1136i	−0.317664	−	0.779388i
$667$			9.81174i			0.379912i
$668$	−10.1839	+	17.6390i	−0.394026	+	0.682473i
$669$	−22.6023	−	1.54584i	−0.873855	−	0.0597658i
$670$	3.20194	−	1.84864i	0.123702	−	0.0714192i
$671$	6.12993	−	24.0922i	0.236643	−	0.930070i
$672$	−5.08362	+	2.48906i	−0.196105	+	0.0960176i
$673$	38.8482	+	22.4290i	1.49749	+	0.864574i	0.999996	−	0.00289542i	$-0.000921643\pi$
$673$	38.8482	+	22.4290i	1.49749	+	0.864574i	0.497490	+	0.867469i	$0.334255\pi$
$674$			17.9393i			0.690996i
$675$	−3.45919	+	3.87737i	−0.133144	+	0.149240i
$676$	4.69508			0.180580
$677$	9.57175	−	16.5788i	0.367872	−	0.637174i	−0.621360	−	0.783525i	$-0.713420\pi$
$677$	9.57175	−	16.5788i	0.367872	−	0.637174i	0.989233	+	0.146351i	$0.0467530\pi$
$678$	−5.30375	+	2.59684i	−0.203689	+	0.0997310i
$679$	−45.5859	+	26.3191i	−1.74943	+	1.01003i
$680$	−1.62830	+	0.940102i	−0.0624426	+	0.0360513i
$681$	−37.7379	−	2.58102i	−1.44612	−	0.0989049i
$682$	−3.20524	−	11.3841i	−0.122735	−	0.435919i
$683$			41.9745i			1.60611i	0.595906	+	0.803054i	$0.296793\pi$
$683$			41.9745i			1.60611i	−0.595906	+	0.803054i	$0.703207\pi$
$684$	−1.77255	+	12.8979i	−0.0677753	+	0.493164i
$685$	−5.22081			−0.199477
$686$	−9.39731	−	5.42554i	−0.358791	−	0.207148i
$687$	−0.437332	+	0.650511i	−0.0166853	+	0.0248185i
$688$	−6.89392	+	3.98021i	−0.262828	+	0.151744i
$689$	4.69321	+	8.12887i	0.178797	+	0.309685i
$690$	6.88873	−	10.2467i	0.262250	−	0.390084i
$691$	−11.6175	+	20.1221i	−0.441950	+	0.765480i	−0.997834	−	0.0657796i	$-0.979047\pi$
$691$	−11.6175	+	20.1221i	−0.441950	+	0.765480i	0.555884	+	0.831260i	$0.312380\pi$
$692$	−12.5298			−0.476310
$693$	19.9738	+	25.6578i	0.758743	+	0.974659i
$694$	19.3971			0.736302
$695$	−5.89247	+	10.2061i	−0.223514	+	0.387138i
$696$	2.37844	+	0.162669i	0.0901545	+	0.00616596i
$697$	7.20665	+	12.4823i	0.272971	+	0.472800i
$698$	20.3082	−	11.7250i	0.768678	−	0.443796i
$699$	−22.0175	−	44.9682i	−0.832778	−	1.70085i
$700$	−2.83014	−	1.63398i	−0.106969	−	0.0617586i
$701$	2.01452			0.0760872			0.0380436	−	0.999276i	$-0.487887\pi$
$701$	2.01452			0.0760872			0.0380436	+	0.999276i	$0.487887\pi$
$702$	−3.04626	+	14.6613i	−0.114974	+	0.553355i
$703$		−	31.4198i		−	1.18502i
$704$	−0.898862	−	3.19250i	−0.0338771	−	0.120322i
$705$	−7.84494	−	16.0224i	−0.295458	−	0.603439i
$706$	9.72262	−	5.61336i	0.365916	−	0.211262i
$707$	−10.2877	+	5.93961i	−0.386909	+	0.223382i
$708$	−0.179272	+	2.62119i	−0.00673745	+	0.0985104i
$709$	−10.3159	+	17.8676i	−0.387420	+	0.671032i	−0.992102	−	0.125436i	$-0.959967\pi$
$709$	−10.3159	+	17.8676i	−0.387420	+	0.671032i	0.604681	+	0.796468i	$0.293300\pi$
$710$	−15.6364			−0.586823
$711$	36.3888	−	14.8314i	1.36469	−	0.556221i
$712$		−	2.39265i		−	0.0896683i
$713$	22.0140	+	12.7098i	0.824431	+	0.475985i
$714$	8.83207	+	5.93771i	0.330532	+	0.222213i
$715$	−9.26281	−	2.35679i	−0.346410	−	0.0881391i
$716$	−19.5618	+	11.2940i	−0.731058	+	0.422076i
$717$	12.6326	−	18.7904i	0.471773	−	0.701740i
$718$	−2.79825	+	4.84670i	−0.104430	+	0.180877i
$719$		−	38.6759i		−	1.44237i	−0.692743	−	0.721185i	$-0.743598\pi$
$719$		−	38.6759i		−	1.44237i	0.692743	−	0.721185i	$-0.256402\pi$
$720$	−2.36966	−	1.83976i	−0.0883120	−	0.0685638i
$721$			12.6434i			0.470865i
$722$	0.0834253	−	0.144497i	0.00310477	−	0.00537762i
$723$	−2.81081	+	41.0977i	−0.104535	+	1.52844i
$724$	8.03274	+	13.9131i	0.298534	+	0.517077i
$725$	0.688200	+	1.19200i	0.0255591	+	0.0442697i
$726$	−16.8941	+	8.80841i	−0.627000	+	0.326911i
$727$	8.24260	−	14.2766i	0.305701	−	0.529490i	−0.671716	−	0.740809i	$-0.734443\pi$
$727$	8.24260	−	14.2766i	0.305701	−	0.529490i	0.977417	+	0.211319i	$0.0677759\pi$
$728$	−9.41769			−0.349043
$729$	24.7653	+	10.7556i	0.917232	+	0.398354i
$730$	−11.3309			−0.419375
$731$	12.9620	+	7.48360i	0.479416	+	0.276791i
$732$	11.6600	−	5.70901i	0.430966	−	0.211011i
$733$	−19.7637	+	11.4106i	−0.729989	+	0.421459i	−0.818418	−	0.574623i	$-0.805149\pi$
$733$	−19.7637	+	11.4106i	−0.729989	+	0.421459i	0.0884293	+	0.996082i	$0.471815\pi$
$734$	2.50320	+	4.33566i	0.0923946	+	0.160032i
$735$	−0.434866	+	6.35832i	−0.0160403	+	0.234530i
$736$	6.17351	+	3.56428i	0.227558	+	0.131381i
$737$	8.56052	−	8.77989i	0.315331	−	0.323411i
$738$	−14.1033	+	18.1654i	−0.519149	+	0.668677i
$739$		−	13.0567i		−	0.480299i	−0.970736	−	0.240149i	$-0.922804\pi$
$739$		−	13.0567i		−	0.480299i	0.970736	−	0.240149i	$-0.0771964\pi$
$740$	6.27007	+	3.62003i	0.230492	+	0.133075i
$741$	−12.0856	+	17.9767i	−0.443975	+	0.660391i
$742$	5.32204	+	9.21805i	0.195378	+	0.338405i
$743$	−5.08792	−	8.81253i	−0.186658	−	0.323300i	0.757476	−	0.652863i	$-0.226432\pi$
$743$	−5.08792	−	8.81253i	−0.186658	−	0.323300i	−0.944134	+	0.329562i	$0.893099\pi$
$744$	3.44592	−	5.12564i	0.126334	−	0.187915i
$745$	2.34110	+	1.35163i	0.0857712	+	0.0495200i
$746$		−	27.5002i		−	1.00685i
$747$	1.04793	+	2.57109i	0.0383416	+	0.0940711i
$748$	−4.35334	+	4.46489i	−0.159174	+	0.163253i
$749$	20.3542	+	11.7515i	0.743725	+	0.429390i
$750$	0.118185	−	1.72801i	0.00431549	−	0.0630982i
$751$	13.0380	+	22.5825i	0.475764	+	0.824047i	0.999615	−	0.0277630i	$-0.00883837\pi$
$751$	13.0380	+	22.5825i	0.475764	+	0.824047i	−0.523851	+	0.851810i	$0.675505\pi$
$752$	8.91993	−	5.14992i	0.325276	−	0.187798i
$753$	9.07993	−	4.44575i	0.330891	−	0.162012i
$754$	3.43513	+	1.98327i	0.125100	+	0.0722266i
$755$	−10.4734			−0.381164
$756$	−3.45442	+	16.6257i	−0.125636	+	0.604672i
$757$	15.5500			0.565176			0.282588	−	0.959241i	$-0.408807\pi$
$757$	15.5500			0.565176			0.282588	+	0.959241i	$0.408807\pi$
$758$	16.5387	−	28.6459i	0.600714	−	1.04047i
$759$	12.7819	−	38.9045i	0.463955	−	1.41214i
$760$	−2.16986	−	3.75831i	−0.0787091	−	0.136328i
$761$	14.8760	+	25.7659i	0.539253	+	0.934014i	0.998944	+	0.0459348i	$0.0146267\pi$
$761$	14.8760	+	25.7659i	0.539253	+	0.934014i	−0.459691	+	0.888079i	$0.652040\pi$
$762$	0.777829	−	11.3729i	0.0281778	−	0.411996i
$763$	20.7110	−	35.8725i	0.749788	−	1.29867i
$764$		−	1.72132i		−	0.0622751i
$765$	−0.767968	+	5.58809i	−0.0277659	+	0.202038i
$766$			31.4909i			1.13781i
$767$	−2.18569	+	3.78573i	−0.0789208	+	0.136695i
$768$	0.966358	−	1.43741i	0.0348704	−	0.0518681i
$769$	23.5942	−	13.6221i	0.850830	−	0.491227i	−0.0101010	−	0.999949i	$-0.503215\pi$
$769$	23.5942	−	13.6221i	0.850830	−	0.491227i	0.860931	+	0.508722i	$0.169882\pi$
$770$	−10.5039	−	2.67258i	−0.378535	−	0.0963130i
$771$	0.766373	+	0.515225i	0.0276002	+	0.0185554i
$772$	−10.9926	−	6.34656i	−0.395631	−	0.228418i
$773$			50.9522i			1.83262i	0.400466	+	0.916312i	$0.368848\pi$
$773$			50.9522i			1.83262i	−0.400466	+	0.916312i	$0.631152\pi$
$774$	−3.25142	+	23.6589i	−0.116870	+	0.850400i
$775$	3.56588			0.128090
$776$	8.05367	−	13.9494i	0.289110	−	0.500753i
$777$	2.79627	−	40.8851i	0.100316	−	1.46675i
$778$	33.1700	−	19.1507i	1.18920	−	0.686587i
$779$	−28.8105	+	16.6338i	−1.03224	+	0.595966i
$780$	−2.19496	−	4.48296i	−0.0785922	−	0.160516i
$781$	−49.9191	+	14.0549i	−1.78625	+	0.502925i
$782$		−	13.4031i		−	0.479295i
$783$	4.76123	−	5.33682i	0.170152	−	0.190722i
$784$	−3.67955			−0.131413
$785$	8.37305	+	4.83418i	0.298847	+	0.172539i
$786$	−4.25184	−	8.68390i	−0.151658	−	0.309744i
$787$	−3.16619	+	1.82800i	−0.112863	+	0.0651612i	−0.555369	−	0.831604i	$-0.687423\pi$
$787$	−3.16619	+	1.82800i	−0.112863	+	0.0651612i	0.442506	+	0.896765i	$0.354090\pi$
$788$	0.313427	+	0.542872i	0.0111654	+	0.0193390i
$789$	−6.89378	−	0.471488i	−0.245425	−	0.0167854i
$790$	−6.54921	+	11.3436i	−0.233010	+	0.403586i
$791$	−11.1420			−0.396164
$792$	−9.21882	−	3.74343i	−0.327577	−	0.133017i
$793$	21.6008			0.767067
$794$	2.18358	−	3.78208i	0.0774925	−	0.134221i
$795$	−3.14753	+	4.68180i	−0.111631	+	0.166046i
$796$	8.40633	+	14.5602i	0.297954	+	0.516072i
$797$	1.24075	−	0.716346i	0.0439495	−	0.0253743i	−0.477864	−	0.878434i	$-0.658589\pi$
$797$	1.24075	−	0.716346i	0.0439495	−	0.0253743i	0.521814	+	0.853059i	$0.325256\pi$
$798$	−13.7049	+	20.3854i	−0.485148	+	0.721635i
$799$	−16.7713	−	9.68290i	−0.593325	−	0.342557i
$800$	1.00000			0.0353553
$801$	−5.66976	−	4.40190i	−0.200331	−	0.155533i
$802$			11.1260i			0.392874i
$803$	−36.1738	+	10.1849i	−1.27655	+	0.359417i
$804$	6.38896	+	0.436962i	0.225321	+	0.0154105i
$805$	20.1748	−	11.6479i	0.711067	−	0.410535i
$806$	8.89950	−	5.13813i	0.313472	−	0.180983i
$807$	−28.1325	+	13.7744i	−0.990313	+	0.484880i
$808$	1.81753	−	3.14805i	0.0639405	−	0.110748i
$809$	−47.3250			−1.66386			−0.831929	−	0.554882i	$-0.812763\pi$
$809$	−47.3250			−1.66386			−0.831929	+	0.554882i	$0.812763\pi$
$810$	−8.71921	+	2.23057i	−0.306362	+	0.0783742i
$811$		−	19.8112i		−	0.695664i	−0.937557	−	0.347832i	$-0.886918\pi$
$811$		−	19.8112i		−	0.695664i	0.937557	−	0.347832i	$-0.113082\pi$
$812$	3.89540	+	2.24901i	0.136702	+	0.0789248i
$813$	0.0918252	−	0.0449598i	0.00322045	−	0.00157681i
$814$	23.2711	+	5.92100i	0.815651	+	0.207531i
$815$	−17.3963	+	10.0438i	−0.609365	+	0.351817i
$816$	−3.24902	−	0.222211i	−0.113738	−	0.00777894i
$817$	−17.2730	+	29.9177i	−0.604305	+	1.04669i
$818$		−	5.24870i		−	0.183517i
$819$	−17.3263	+	22.3167i	−0.605429	+	0.779809i
$820$		−	7.66582i		−	0.267702i
$821$	−10.8369	+	18.7700i	−0.378210	+	0.655079i	−0.990802	−	0.135321i	$-0.956794\pi$
$821$	−10.8369	+	18.7700i	−0.378210	+	0.655079i	0.612592	+	0.790399i	$0.290127\pi$
$822$	−7.50446	−	5.04517i	−0.261748	−	0.175971i
$823$	20.1692	+	34.9340i	0.703053	+	1.21772i	0.967390	+	0.253293i	$0.0815136\pi$
$823$	20.1692	+	34.9340i	0.703053	+	1.21772i	−0.264337	+	0.964430i	$0.585153\pi$
$824$	−1.93445	−	3.35057i	−0.0673898	−	0.116722i
$825$	−1.17594	−	5.62291i	−0.0409410	−	0.195765i
$826$	−2.47855	+	4.29298i	−0.0862399	+	0.149372i
$827$	−38.9841			−1.35561			−0.677805	−	0.735242i	$-0.737069\pi$
$827$	−38.9841			−1.35561			−0.677805	+	0.735242i	$0.737069\pi$
$828$	19.8039	−	8.07169i	0.688233	−	0.280511i
$829$	28.1575			0.977952			0.488976	−	0.872297i	$-0.337371\pi$
$829$	28.1575			0.977952			0.488976	+	0.872297i	$0.337371\pi$
$830$	−0.801490	−	0.462740i	−0.0278201	−	0.0160620i
$831$	−0.869996	+	12.7205i	−0.0301798	+	0.441269i
$832$	2.49573	−	1.44091i	0.0865240	−	0.0499547i
$833$	3.45915	+	5.99143i	0.119853	+	0.207591i
$834$	−18.3326	+	8.97607i	−0.634806	+	0.310816i
$835$	−17.6390	−	10.1839i	−0.610422	−	0.352427i
$836$	−10.3055	−	10.0480i	−0.356422	−	0.347517i
$837$	−5.80636	−	17.5956i	−0.200697	−	0.608193i
$838$		−	17.6324i		−	0.609101i
$839$	−2.08528	−	1.20394i	−0.0719918	−	0.0415645i	0.463572	−	0.886059i	$-0.346568\pi$
$839$	−2.08528	−	1.20394i	−0.0719918	−	0.0415645i	−0.535564	+	0.844495i	$0.679901\pi$
$840$	−2.48906	−	5.08362i	−0.0858808	−	0.175402i
$841$	13.5528	+	23.4741i	0.467337	+	0.809451i
$842$	−8.85232	−	15.3327i	−0.305071	−	0.528398i
$843$	40.5204	+	2.77132i	1.39560	+	0.0954494i
$844$	10.0105	+	5.77955i	0.344575	+	0.198940i
$845$			4.69508i			0.161516i
$846$	4.20696	−	30.6118i	0.144638	−	1.05246i
$847$	−35.9360	+	0.909380i	−1.23478	+	0.0312467i
$848$	−2.82074	−	1.62855i	−0.0968645	−	0.0559247i
$849$	−14.7113	−	9.89029i	−0.504892	−	0.339434i
$850$	−0.940102	−	1.62830i	−0.0322452	−	0.0558504i
$851$	−44.6965	+	25.8055i	−1.53218	+	0.884603i
$852$	−22.4759	−	15.1103i	−0.770012	−	0.517671i
$853$	0.00677959	+	0.00391420i	0.000232129	+	0.000134020i	0.500116	−	0.865958i	$-0.333291\pi$
$853$	0.00677959	+	0.00391420i	0.000232129	+	0.000134020i	−0.499884	+	0.866092i	$0.666624\pi$
$854$	24.4951			0.838204
$855$	−12.8979	−	1.77255i	−0.441100	−	0.0606201i
$856$	−7.19194			−0.245815
$857$	−6.78272	+	11.7480i	−0.231693	+	0.401304i	−0.958307	−	0.285742i	$-0.907760\pi$
$857$	−6.78272	+	11.7480i	−0.231693	+	0.401304i	0.726613	+	0.687047i	$0.241093\pi$
$858$	−11.0370	−	12.3389i	−0.376796	−	0.421242i
$859$	−4.78235	−	8.28327i	−0.163172	−	0.282622i	0.772833	−	0.634610i	$-0.218839\pi$
$859$	−4.78235	−	8.28327i	−0.163172	−	0.282622i	−0.936004	+	0.351988i	$0.885506\pi$
$860$	−3.98021	−	6.89392i	−0.135724	−	0.235081i
$861$	−38.9702	+	19.0807i	−1.32810	+	0.650268i
$862$	17.3205	−	30.0000i	0.589940	−	1.02181i
$863$		−	4.90873i		−	0.167095i	−0.996504	−	0.0835476i	$-0.973375\pi$
$863$		−	4.90873i		−	0.167095i	0.996504	−	0.0835476i	$-0.0266251\pi$
$864$	−1.62831	−	4.93443i	−0.0553962	−	0.167873i
$865$		−	12.5298i		−	0.426025i
$866$	11.8346	−	20.4981i	0.402155	−	0.696553i
$867$	−10.2556	−	20.9458i	−0.348298	−	0.711358i
$868$	10.0919	−	5.82658i	0.342543	−	0.197767i
$869$	−10.7120	+	42.1011i	−0.363381	+	1.42818i
$870$	−0.162669	+	2.37844i	−0.00551501	+	0.0806366i
$871$	9.22744	+	5.32746i	0.312660	+	0.180514i
$872$			12.6752i			0.429236i
$873$	−18.2384	−	44.7479i	−0.617277	−	1.51449i
$874$	30.9359			1.04642
$875$	1.63398	−	2.83014i	0.0552386	−	0.0956760i
$876$	−16.2872	−	10.9497i	−0.550292	−	0.369956i
$877$	33.7633	−	19.4933i	1.14011	−	0.658241i	0.193650	−	0.981071i	$-0.437968\pi$
$877$	33.7633	−	19.4933i	1.14011	−	0.658241i	0.946457	+	0.322830i	$0.104634\pi$
$878$	30.7259	−	17.7396i	1.03695	−	0.598682i
$879$	−22.3096	+	33.1845i	−0.752484	+	1.11928i
$880$	3.19250	−	0.898862i	0.107619	−	0.0303006i
$881$		−	31.1989i		−	1.05112i	−0.850758	−	0.525558i	$-0.823857\pi$
$881$		−	31.1989i		−	1.05112i	0.850758	−	0.525558i	$-0.176143\pi$
$882$	−6.76949	+	8.71929i	−0.227941	+	0.293594i
$883$	−15.2943			−0.514693			−0.257347	−	0.966319i	$-0.582848\pi$
$883$	−15.2943			−0.514693			−0.257347	+	0.966319i	$0.582848\pi$
$884$	−4.69249	−	2.70921i	−0.157825	−	0.0911206i
$885$	−2.62119	−	0.179272i	−0.0881104	−	0.00602616i
$886$	−34.1454	+	19.7138i	−1.14714	+	0.662299i
$887$	12.7148	+	22.0226i	0.426921	+	0.739448i	0.996598	−	0.0824205i	$-0.0262651\pi$
$887$	12.7148	+	22.0226i	0.426921	+	0.739448i	−0.569677	+	0.821869i	$0.692932\pi$
$888$	5.51443	+	11.2626i	0.185052	+	0.377948i
$889$	10.7540	−	18.6265i	0.360677	−	0.624712i
$890$	2.39265			0.0802017
$891$	−25.8311	+	14.9584i	−0.865374	+	0.501127i
$892$	13.0799			0.437948
$893$	22.3492	−	38.7100i	0.747888	−	1.29538i
$894$	2.05896	+	4.20519i	0.0688620	+	0.140643i
$895$	−11.2940	−	19.5618i	−0.377517	−	0.653878i
$896$	2.83014	−	1.63398i	0.0945482	−	0.0545874i
$897$	35.4990	+	2.42789i	1.18528	+	0.0810651i
$898$	−22.3850	−	12.9240i	−0.746998	−	0.431280i
$899$	−4.90808			−0.163694
$900$	1.83976	−	2.36966i	0.0613253	−	0.0789886i
$901$			6.12402i			0.204021i
$902$	−6.89051	−	24.4731i	−0.229429	−	0.814866i
$903$	−25.1391	+	37.3933i	−0.836577	+	1.24437i
$904$	2.95268	−	1.70473i	0.0982048	−	0.0566986i
$905$	−13.9131	+	8.03274i	−0.462487	+	0.267017i
$906$	−15.0545	−	10.1210i	−0.500153	−	0.336248i
$907$	10.7067	−	18.5446i	0.355511	−	0.615763i	−0.631694	−	0.775218i	$-0.717640\pi$
$907$	10.7067	−	18.5446i	0.355511	−	0.615763i	0.987205	+	0.159454i	$0.0509735\pi$
$908$	21.8389			0.724749
$909$	−4.11600	−	10.0986i	−0.136519	−	0.334949i
$910$		−	9.41769i		−	0.312193i
$911$	16.9252	+	9.77174i	0.560755	+	0.323752i	0.753449	−	0.657507i	$-0.228389\pi$
$911$	16.9252	+	9.77174i	0.560755	+	0.323752i	−0.192693	+	0.981259i	$0.561722\pi$
$912$	0.512888	−	7.49909i	0.0169834	−	0.248320i
$913$	−2.97469	−	0.756869i	−0.0984480	−	0.0250487i
$914$	−11.7176	+	6.76513i	−0.387582	+	0.223771i
$915$	5.70901	+	11.6600i	0.188734	+	0.385468i
$916$	0.226279	−	0.391926i	0.00747646	−	0.0129496i
$917$		−	18.2429i		−	0.602434i
$918$	−6.50398	+	7.29025i	−0.214663	+	0.240614i
$919$			4.69659i			0.154926i	0.996995	+	0.0774632i	$0.0246820\pi$
$919$			4.69659i			0.154926i	−0.996995	+	0.0774632i	$0.975318\pi$
$920$	−3.56428	+	6.17351i	−0.117511	+	0.203534i
$921$	−41.3634	+	20.2525i	−1.36297	+	0.667341i
$922$	−5.94147	−	10.2909i	−0.195672	−	0.338914i
$923$	−22.5307	−	39.0242i	−0.741606	−	1.28450i
$924$	−12.5158	−	13.9921i	−0.411740	−	0.460308i
$925$	−3.62003	+	6.27007i	−0.119026	+	0.206159i
$926$	−5.12039			−0.168266
$927$	−11.4986	−	1.58025i	−0.377664	−	0.0519022i
$928$	−1.37640			−0.0451826
$929$	−12.9688	−	7.48755i	−0.425493	−	0.245659i	0.271932	−	0.962317i	$-0.412338\pi$
$929$	−12.9688	−	7.48755i	−0.425493	−	0.245659i	−0.697425	+	0.716658i	$0.745671\pi$
$930$	5.12564	+	3.44592i	0.168076	+	0.112996i
$931$	−13.8289	+	7.98411i	−0.453223	+	0.261669i
$932$	14.4537	+	25.0345i	0.473446	+	0.820033i
$933$	28.9483	+	19.4617i	0.947726	+	0.637147i
$934$	−2.59986	−	1.50103i	−0.0850701	−	0.0491153i
$935$	−4.46489	−	4.35334i	−0.146018	−	0.142369i
$936$	1.17708	−	8.56498i	0.0384741	−	0.279955i
$937$			10.3961i			0.339626i	0.985476	+	0.169813i	$0.0543164\pi$
$937$			10.3961i			0.339626i	−0.985476	+	0.169813i	$0.945684\pi$
$938$	10.4638	+	6.04128i	0.341655	+	0.197255i
$939$	51.8157	+	3.54385i	1.69094	+	0.115649i
$940$	5.14992	+	8.91993i	0.167972	+	0.290936i
$941$	25.8519	+	44.7768i	0.842748	+	1.45968i	0.887562	+	0.460687i	$0.152397\pi$
$941$	25.8519	+	44.7768i	0.842748	+	1.45968i	−0.0448143	+	0.998995i	$0.514270\pi$
$942$	7.36397	+	15.0401i	0.239931	+	0.490032i
$943$	47.3250	+	27.3231i	1.54111	+	0.889763i
$944$		−	1.51688i		−	0.0493703i
$945$	−16.6257	−	3.45442i	−0.540835	−	0.112372i
$946$	−18.9035	−	18.4312i	−0.614605	−	0.599249i
$947$	−9.41189	−	5.43396i	−0.305845	−	0.176580i	0.339220	−	0.940707i	$-0.389837\pi$
$947$	−9.41189	−	5.43396i	−0.305845	−	0.176580i	−0.645066	+	0.764127i	$0.723170\pi$
$948$	−20.3758	+	9.97649i	−0.661777	+	0.324021i
$949$	−16.3268	−	28.2789i	−0.529991	−	0.917972i
$950$	3.75831	−	2.16986i	0.121936	−	0.0703995i
$951$	1.73765	−	25.4067i	0.0563470	−	0.823868i
$952$	−5.32123	−	3.07221i	−0.172462	−	0.0995710i
$953$	−49.8541			−1.61493			−0.807467	−	0.589913i	$-0.799162\pi$
$953$	−49.8541			−1.61493			−0.807467	+	0.589913i	$0.799162\pi$
$954$	−9.04859	+	3.68804i	−0.292959	+	0.119405i
$955$	1.72132			0.0557006
$956$	−6.53619	+	11.3210i	−0.211396	+	0.366148i
$957$	1.61857	+	7.73938i	0.0523208	+	0.250179i
$958$	15.8657	+	27.4801i	0.512597	+	0.887843i
$959$	−8.53070	−	14.7756i	−0.275471	−	0.477129i
$960$	1.43741	+	0.966358i	0.0463923	+	0.0311891i
$961$	9.14224	−	15.8348i	0.294911	−	0.510801i
$962$			20.8646i			0.672701i
$963$	−13.2314	+	17.0424i	−0.426377	+	0.549185i
$964$		−	23.7832i		−	0.766006i
$965$	6.34656	−	10.9926i	0.204303	−	0.353863i
$966$	40.2555	+	2.75321i	1.29520	+	0.0885829i
$967$	33.1745	−	19.1533i	1.06682	−	0.615928i	0.139509	−	0.990221i	$-0.455448\pi$
$967$	33.1745	−	19.1533i	1.06682	−	0.615928i	0.927311	+	0.374292i	$0.122114\pi$
$968$	9.38409	−	5.73923i	0.301616	−	0.184466i
$969$	−12.6930	+	6.21477i	−0.407757	+	0.199647i
$970$	13.9494	+	8.05367i	0.447887	+	0.258588i
$971$			26.2790i			0.843333i	0.906751	+	0.421667i	$0.138555\pi$
$971$			26.2790i			0.843333i	−0.906751	+	0.421667i	$0.861445\pi$
$972$	−14.6886	−	5.21963i	−0.471138	−	0.167420i
$973$	−38.5127			−1.23466
$974$	−10.6862	+	18.5090i	−0.342408	+	0.593068i
$975$	4.48296	−	2.19496i	0.143570	−	0.0702950i
$976$	−6.49131	+	3.74776i	−0.207782	+	0.119963i
$977$	−29.5918	+	17.0848i	−0.946725	+	0.546592i	−0.892062	−	0.451913i	$-0.850742\pi$
$977$	−29.5918	+	17.0848i	−0.946725	+	0.546592i	−0.0546627	+	0.998505i	$0.517408\pi$
$978$	−34.7115	−	2.37403i	−1.10995	−	0.0759132i
$979$	7.63853	−	2.15066i	0.244128	−	0.0687354i
$980$		−	3.67955i		−	0.117539i
$981$	30.0359	+	23.3193i	0.958972	+	0.744528i
$982$	29.1786			0.931127
$983$	−4.41072	−	2.54653i	−0.140680	−	0.0812217i	0.428008	−	0.903775i	$-0.359216\pi$
$983$	−4.41072	−	2.54653i	−0.140680	−	0.0812217i	−0.568688	+	0.822553i	$0.692549\pi$
$984$	7.40793	−	11.0189i	0.236156	−	0.351271i
$985$	−0.542872	+	0.313427i	−0.0172973	+	0.00998663i
$986$	1.29396	+	2.24120i	0.0412080	+	0.0713743i
$987$	32.5271	−	48.3825i	1.03535	−	1.54003i
$988$	6.25316	−	10.8308i	0.198939	−	0.344573i
$989$	56.7462			1.80442
$990$	3.74343	−	9.21882i	0.118974	−	0.292993i
$991$	51.0722			1.62236			0.811181	−	0.584795i	$-0.198825\pi$
$991$	51.0722			1.62236			0.811181	+	0.584795i	$0.198825\pi$
$992$	−1.78294	+	3.08815i	−0.0566085	+	0.0980487i
$993$	23.6514	+	1.61759i	0.750553	+	0.0513328i
$994$	−25.5495	−	44.2530i	−0.810381	−	1.40362i
$995$	−14.5602	+	8.40633i	−0.461589	+	0.266499i
$996$	−0.704898	−	1.43967i	−0.0223356	−	0.0456178i
$997$	2.51845	+	1.45403i	0.0797600	+	0.0460495i	0.539350	−	0.842082i	$-0.318670\pi$
$997$	2.51845	+	1.45403i	0.0797600	+	0.0460495i	−0.459590	+	0.888131i	$0.652003\pi$
$998$	−38.4599			−1.21743
$999$	36.8337	+	7.65316i	1.16537	+	0.242135i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.t.b.461.16	yes	48
3.2	odd	2		2970.2.t.a.791.11		48
9.4	even	3		2970.2.t.b.2771.11		48
9.5	odd	6		990.2.t.a.131.16	✓	48
11.10	odd	2		990.2.t.a.461.16	yes	48
33.32	even	2		2970.2.t.b.791.11		48
99.32	even	6	inner	990.2.t.b.131.16	yes	48
99.76	odd	6		2970.2.t.a.2771.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.16	✓	48	9.5	odd	6
990.2.t.a.461.16	yes	48	11.10	odd	2
990.2.t.b.131.16	yes	48	99.32	even	6	inner
990.2.t.b.461.16	yes	48	1.1	even	1	trivial
2970.2.t.a.791.11		48	3.2	odd	2
2970.2.t.a.2771.11		48	99.76	odd	6
2970.2.t.b.791.11		48	33.32	even	2
2970.2.t.b.2771.11		48	9.4	even	3

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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.761656 + 1.55560i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.72801 + 0.118185i) q^{6} +(2.83014 + 1.63398i) q^{7} -1.00000 q^{8} +(-1.83976 + 2.36966i) q^{9} -1.00000i q^{10} +(-0.898862 - 3.19250i) q^{11} +(0.966358 - 1.43741i) q^{12} +(2.49573 - 1.44091i) q^{13} +(2.83014 - 1.63398i) q^{14} +(1.43741 + 0.966358i) q^{15} +(-0.500000 + 0.866025i) q^{16} +1.88020 q^{17} +(1.13231 + 2.77811i) q^{18} +4.33972i q^{19} +(-0.866025 - 0.500000i) q^{20} +(-0.386222 + 5.64708i) q^{21} +(-3.21422 - 0.817812i) q^{22} +(6.17351 - 3.56428i) q^{23} +(-0.761656 - 1.55560i) q^{24} +(0.500000 - 0.866025i) q^{25} -2.88183i q^{26} +(-5.08750 - 1.05706i) q^{27} -3.26796i q^{28} +(-0.688200 + 1.19200i) q^{29} +(1.55560 - 0.761656i) q^{30} +(1.78294 + 3.08815i) q^{31} +(0.500000 + 0.866025i) q^{32} +(4.28162 - 3.82985i) q^{33} +(0.940102 - 1.62830i) q^{34} +3.26796 q^{35} +(2.97206 + 0.408449i) q^{36} -7.24005 q^{37} +(3.75831 + 2.16986i) q^{38} +(4.14237 + 2.78488i) q^{39} +(-0.866025 + 0.500000i) q^{40} +(3.83291 + 6.63880i) q^{41} +(4.69740 + 3.15802i) q^{42} +(6.89392 + 3.98021i) q^{43} +(-2.31535 + 2.37469i) q^{44} +(-0.408449 + 2.97206i) q^{45} -7.12855i q^{46} +(-8.91993 - 5.14992i) q^{47} +(-1.72801 - 0.118185i) q^{48} +(1.83978 + 3.18659i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(1.43207 + 2.92484i) q^{51} +(-2.49573 - 1.44091i) q^{52} +3.25710i q^{53} +(-3.45919 + 3.87737i) q^{54} +(-2.37469 - 2.31535i) q^{55} +(-2.83014 - 1.63398i) q^{56} +(-6.75085 + 3.30537i) q^{57} +(0.688200 + 1.19200i) q^{58} +(-1.31366 + 0.758441i) q^{59} +(0.118185 - 1.72801i) q^{60} +(6.49131 + 3.74776i) q^{61} +3.56588 q^{62} +(-9.07874 + 3.70033i) q^{63} +1.00000 q^{64} +(1.44091 - 2.49573i) q^{65} +(-1.17594 - 5.62291i) q^{66} +(1.84864 + 3.20194i) q^{67} +(-0.940102 - 1.62830i) q^{68} +(10.2467 + 6.88873i) q^{69} +(1.63398 - 2.83014i) q^{70} -15.6364i q^{71} +(1.83976 - 2.36966i) q^{72} -11.3309i q^{73} +(-3.62003 + 6.27007i) q^{74} +(1.72801 + 0.118185i) q^{75} +(3.75831 - 2.16986i) q^{76} +(2.67258 - 10.5039i) q^{77} +(4.48296 - 2.19496i) q^{78} +(-11.3436 - 6.54921i) q^{79} +1.00000i q^{80} +(-2.23057 - 8.71921i) q^{81} +7.66582 q^{82} +(0.462740 - 0.801490i) q^{83} +(5.08362 - 2.48906i) q^{84} +(1.62830 - 0.940102i) q^{85} +(6.89392 - 3.98021i) q^{86} +(-2.37844 - 0.162669i) q^{87} +(0.898862 + 3.19250i) q^{88} +2.39265i q^{89} +(2.36966 + 1.83976i) q^{90} +9.41769 q^{91} +(-6.17351 - 3.56428i) q^{92} +(-3.44592 + 5.12564i) q^{93} +(-8.91993 + 5.14992i) q^{94} +(2.16986 + 3.75831i) q^{95} +(-0.966358 + 1.43741i) q^{96} +(-8.05367 + 13.9494i) q^{97} +3.67955 q^{98} +(9.21882 + 3.74343i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} - 48 q^{8} + 10 q^{9} - 12 q^{11} + 4 q^{12} - 24 q^{13} - 4 q^{15} - 24 q^{16} + 12 q^{17} + 8 q^{18} + 16 q^{21} - 6 q^{22} + 36 q^{23} + 2 q^{24} + 24 q^{25}+ \cdots - 44 q^{99}+O(q^{100}) \) 48 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 - 48 * q^8 + 10 * q^9 - 12 * q^11 + 4 * q^12 - 24 * q^13 - 4 * q^15 - 24 * q^16 + 12 * q^17 + 8 * q^18 + 16 * q^21 - 6 * q^22 + 36 * q^23 + 2 * q^24 + 24 * q^25 - 8 * q^27 - 8 * q^30 + 24 * q^32 + 12 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 + 40 * q^39 + 6 * q^41 + 8 * q^42 - 30 * q^43 + 6 * q^44 - 2 * q^48 + 24 * q^49 - 24 * q^50 - 22 * q^51 + 24 * q^52 - 22 * q^54 - 40 * q^57 - 54 * q^59 - 4 * q^60 + 38 * q^63 + 48 * q^64 - 12 * q^66 - 6 * q^67 - 6 * q^68 + 76 * q^69 - 10 * q^72 + 2 * q^75 - 6 * q^76 - 18 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 - 36 * q^83 - 8 * q^84 - 30 * q^86 + 44 * q^87 + 12 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 - 4 * q^96 + 6 * q^97 + 48 * q^98 - 44 * q^99

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