LMFDB - Embedded newform 672.2.cf.a.619.52

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(19,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 21, 0, 20]))

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

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

chi := DirichletCharacter("672.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.cf (of order $24$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$64$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			619.52
Character	$\chi$	$=$	672.619
Dual form			672.2.cf.a.355.52

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18697 - 0.768826i) q^{2} +(0.130526 - 0.991445i) q^{3} +(0.817812 - 1.82515i) q^{4} +(-0.534986 - 4.06362i) q^{5} +(-0.607318 - 1.27717i) q^{6} +(-2.42250 + 1.06373i) q^{7} +(-0.432504 - 2.79516i) q^{8} +(-0.965926 - 0.258819i) q^{9} +O(q^{10})$	\(q+(1.18697 - 0.768826i) q^{2} +(0.130526 - 0.991445i) q^{3} +(0.817812 - 1.82515i) q^{4} +(-0.534986 - 4.06362i) q^{5} +(-0.607318 - 1.27717i) q^{6} +(-2.42250 + 1.06373i) q^{7} +(-0.432504 - 2.79516i) q^{8} +(-0.965926 - 0.258819i) q^{9} +(-3.75923 - 4.41210i) q^{10} +(3.30637 + 4.30894i) q^{11} +(-1.70279 - 1.04905i) q^{12} +(2.93536 - 1.21586i) q^{13} +(-2.05762 + 3.12510i) q^{14} -4.09868 q^{15} +(-2.66237 - 2.98526i) q^{16} +(2.45514 - 4.25242i) q^{17} +(-1.34552 + 0.435418i) q^{18} +(-2.82426 + 3.68065i) q^{19} +(-7.85425 - 2.34685i) q^{20} +(0.738429 + 2.54061i) q^{21} +(7.23739 + 2.57258i) q^{22} +(-0.550501 + 2.05450i) q^{23} +(-2.82770 + 0.0639623i) q^{24} +(-11.3972 + 3.05386i) q^{25} +(2.54940 - 3.69998i) q^{26} +(-0.382683 + 0.923880i) q^{27} +(-0.0396792 + 5.29135i) q^{28} +(-2.03785 + 0.844105i) q^{29} +(-4.86503 + 3.15118i) q^{30} +(4.58762 - 7.94599i) q^{31} +(-5.45531 - 1.49653i) q^{32} +(4.70364 - 2.71565i) q^{33} +(-0.355192 - 6.93509i) q^{34} +(5.61859 + 9.27502i) q^{35} +(-1.26233 + 1.55130i) q^{36} +(-4.75180 + 0.625586i) q^{37} +(-0.522544 + 6.54021i) q^{38} +(-0.822322 - 3.06895i) q^{39} +(-11.1271 + 3.25291i) q^{40} +(6.91702 + 6.91702i) q^{41} +(2.82979 + 2.44792i) q^{42} +(1.52831 - 3.68968i) q^{43} +(10.5685 - 2.51072i) q^{44} +(-0.534986 + 4.06362i) q^{45} +(0.926122 + 2.86188i) q^{46} +(-3.26317 + 1.88399i) q^{47} +(-3.30723 + 2.24993i) q^{48} +(4.73696 - 5.15375i) q^{49} +(-11.1802 + 12.3873i) q^{50} +(-3.89558 - 2.98919i) q^{51} +(0.181431 - 6.35182i) q^{52} +(7.65851 - 5.87658i) q^{53} +(0.256068 + 1.39084i) q^{54} +(15.7410 - 15.7410i) q^{55} +(4.02103 + 6.31120i) q^{56} +(3.28052 + 3.28052i) q^{57} +(-1.76990 + 2.56868i) q^{58} +(2.25910 + 2.94411i) q^{59} +(-3.35195 + 7.48073i) q^{60} +(-1.57914 + 2.05797i) q^{61} +(-0.663704 - 12.9588i) q^{62} +(2.61526 - 0.400495i) q^{63} +(-7.62588 + 2.41784i) q^{64} +(-6.51118 - 11.2777i) q^{65} +(3.49524 - 6.83969i) q^{66} +(6.19933 + 0.816157i) q^{67} +(-5.75348 - 7.95868i) q^{68} +(1.96507 + 0.813958i) q^{69} +(13.8000 + 6.68948i) q^{70} +(7.30030 - 7.30030i) q^{71} +(-0.305674 + 2.81186i) q^{72} +(2.06358 - 0.552933i) q^{73} +(-5.15929 + 4.39586i) q^{74} +(1.54011 + 11.6983i) q^{75} +(4.40804 + 8.16480i) q^{76} +(-12.5932 - 6.92131i) q^{77} +(-3.33556 - 3.01054i) q^{78} +(-0.257056 - 0.445233i) q^{79} +(-10.7067 + 12.4159i) q^{80} +(0.866025 + 0.500000i) q^{81} +(13.5283 + 2.89233i) q^{82} +(-1.49166 - 3.60119i) q^{83} +(5.24091 + 0.730000i) q^{84} +(-18.5937 - 7.70176i) q^{85} +(-1.02265 - 5.55456i) q^{86} +(0.570891 + 2.13059i) q^{87} +(10.6142 - 11.1055i) q^{88} +(-3.20993 - 0.860098i) q^{89} +(2.48920 + 5.23472i) q^{90} +(-5.81754 + 6.06785i) q^{91} +(3.29957 + 2.68494i) q^{92} +(-7.27921 - 5.58553i) q^{93} +(-2.42484 + 4.74507i) q^{94} +(16.4677 + 9.50764i) q^{95} +(-2.19579 + 5.21330i) q^{96} -4.72140i q^{97} +(1.66031 - 9.75927i) q^{98} +(-2.07847 - 5.01787i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q + 64 q^{14} + 8 q^{16} - 8 q^{18} - 16 q^{22} - 16 q^{23} - 40 q^{28} + 48 q^{35} + 32 q^{43} + 8 q^{44} + 48 q^{50} - 72 q^{52} + 32 q^{53} + 32 q^{58} - 192 q^{59} - 48 q^{60} + 144 q^{64} - 144 q^{66} - 16 q^{67} - 72 q^{70} + 128 q^{71} + 32 q^{74} + 48 q^{78} - 72 q^{80} - 120 q^{82} + 88 q^{88} - 48 q^{91} + 128 q^{92} - 72 q^{94} - 120 q^{96} - 136 q^{98}+O(q^{100}) $ 512 * q + 64 * q^14 + 8 * q^16 - 8 * q^18 - 16 * q^22 - 16 * q^23 - 40 * q^28 + 48 * q^35 + 32 * q^43 + 8 * q^44 + 48 * q^50 - 72 * q^52 + 32 * q^53 + 32 * q^58 - 192 * q^59 - 48 * q^60 + 144 * q^64 - 144 * q^66 - 16 * q^67 - 72 * q^70 + 128 * q^71 + 32 * q^74 + 48 * q^78 - 72 * q^80 - 120 * q^82 + 88 * q^88 - 48 * q^91 + 128 * q^92 - 72 * q^94 - 120 * q^96 - 136 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.18697	−	0.768826i	0.839317	−	0.543642i
$2$	1.18697	−	0.768826i	0.839317	−	0.543642i
$3$	0.130526	−	0.991445i	0.0753593	−	0.572411i
$3$	0.130526	−	0.991445i	0.0753593	−	0.572411i
$4$	0.817812	−	1.82515i	0.408906	−	0.912576i
$5$	−0.534986	−	4.06362i	−0.239253	−	1.81731i	−0.516253	−	0.856436i	$-0.672674\pi$
$5$	−0.534986	−	4.06362i	−0.239253	−	1.81731i	0.277000	−	0.960870i	$-0.410660\pi$
$6$	−0.607318	−	1.27717i	−0.247936	−	0.521403i
$7$	−2.42250	+	1.06373i	−0.915617	+	0.402051i
$7$	−2.42250	+	1.06373i	−0.915617	+	0.402051i
$8$	−0.432504	−	2.79516i	−0.152913	−	0.988240i
$9$	−0.965926	−	0.258819i	−0.321975	−	0.0862730i
$10$	−3.75923	−	4.41210i	−1.18877	−	1.39523i
$11$	3.30637	+	4.30894i	0.996907	+	1.29919i	0.953902	+	0.300119i	$0.0970265\pi$
$11$	3.30637	+	4.30894i	0.996907	+	1.29919i	0.0430050	+	0.999075i	$0.486307\pi$
$12$	−1.70279	−	1.04905i	−0.491554	−	0.302833i
$13$	2.93536	−	1.21586i	0.814121	−	0.337220i	0.0635243	−	0.997980i	$-0.479766\pi$
$13$	2.93536	−	1.21586i	0.814121	−	0.337220i	0.750597	+	0.660760i	$0.229766\pi$
$14$	−2.05762	+	3.12510i	−0.549921	+	0.835217i
$15$	−4.09868			−1.05828
$16$	−2.66237	−	2.98526i	−0.665592	−	0.746316i
$17$	2.45514	−	4.25242i	0.595458	−	1.03136i	−0.398024	−	0.917375i	$-0.630304\pi$
$17$	2.45514	−	4.25242i	0.595458	−	1.03136i	0.993482	−	0.113989i	$-0.0363628\pi$
$18$	−1.34552	+	0.435418i	−0.317141	+	0.102629i
$19$	−2.82426	+	3.68065i	−0.647931	+	0.844400i	−0.995647	−	0.0931999i	$-0.970290\pi$
$19$	−2.82426	+	3.68065i	−0.647931	+	0.844400i	0.347717	+	0.937600i	$0.386957\pi$
$20$	−7.85425	−	2.34685i	−1.75626	−	0.524771i
$21$	0.738429	+	2.54061i	0.161138	+	0.554408i
$22$	7.23739	+	2.57258i	1.54302	+	0.548475i
$23$	−0.550501	+	2.05450i	−0.114787	+	0.428393i	−0.999271	−	0.0381789i	$-0.987844\pi$
$23$	−0.550501	+	2.05450i	−0.114787	+	0.428393i	0.884483	+	0.466572i	$0.154511\pi$
$24$	−2.82770	+	0.0639623i	−0.577203	+	0.0130562i
$25$	−11.3972	+	3.05386i	−2.27943	+	0.610772i
$26$	2.54940	−	3.69998i	0.499979	−	0.725625i
$27$	−0.382683	+	0.923880i	−0.0736475	+	0.177801i
$28$	−0.0396792	+	5.29135i	−0.00749866	+	0.999972i
$29$	−2.03785	+	0.844105i	−0.378419	+	0.156746i	−0.563782	−	0.825924i	$-0.690654\pi$
$29$	−2.03785	+	0.844105i	−0.378419	+	0.156746i	0.185363	+	0.982670i	$0.440654\pi$
$30$	−4.86503	+	3.15118i	−0.888229	+	0.575324i
$31$	4.58762	−	7.94599i	0.823961	−	1.42714i	−0.0787499	−	0.996894i	$-0.525093\pi$
$31$	4.58762	−	7.94599i	0.823961	−	1.42714i	0.902711	−	0.430248i	$-0.141574\pi$
$32$	−5.45531	−	1.49653i	−0.964371	−	0.264552i
$33$	4.70364	−	2.71565i	0.818799	−	0.472734i
$34$	−0.355192	−	6.93509i	−0.0609149	−	1.18936i
$35$	5.61859	+	9.27502i	0.949715	+	1.56776i
$36$	−1.26233	+	1.55130i	−0.210388	+	0.258550i
$37$	−4.75180	+	0.625586i	−0.781191	+	0.102846i	−0.510565	−	0.859839i	$-0.670564\pi$
$37$	−4.75180	+	0.625586i	−0.781191	+	0.102846i	−0.270626	+	0.962685i	$0.587231\pi$
$38$	−0.522544	+	6.54021i	−0.0847678	+	1.06096i
$39$	−0.822322	−	3.06895i	−0.131677	−	0.491425i
$40$	−11.1271	+	3.25291i	−1.75935	+	0.514330i
$41$	6.91702	+	6.91702i	1.08026	+	1.08026i	0.996485	+	0.0837713i	$0.0266965\pi$
$41$	6.91702	+	6.91702i	1.08026	+	1.08026i	0.0837713	+	0.996485i	$0.473303\pi$
$42$	2.82979	+	2.44792i	0.436646	+	0.377722i
$43$	1.52831	−	3.68968i	0.233066	−	0.562670i	−0.763469	−	0.645844i	$-0.776506\pi$
$43$	1.52831	−	3.68968i	0.233066	−	0.562670i	0.996535	+	0.0831737i	$0.0265056\pi$
$44$	10.5685	−	2.51072i	1.59326	−	0.378505i
$45$	−0.534986	+	4.06362i	−0.0797510	+	0.605769i
$46$	0.926122	+	2.86188i	0.136549	+	0.421961i
$47$	−3.26317	+	1.88399i	−0.475983	+	0.274809i	−0.718741	−	0.695278i	$-0.755281\pi$
$47$	−3.26317	+	1.88399i	−0.475983	+	0.274809i	0.242758	+	0.970087i	$0.421948\pi$
$48$	−3.30723	+	2.24993i	−0.477358	+	0.324750i
$49$	4.73696	−	5.15375i	0.676709	−	0.736250i
$50$	−11.1802	+	12.3873i	−1.58113	+	1.75183i
$51$	−3.89558	−	2.98919i	−0.545491	−	0.418570i
$52$	0.181431	−	6.35182i	0.0251600	−	0.880839i
$53$	7.65851	−	5.87658i	1.05198	−	0.807211i	0.0702551	−	0.997529i	$-0.477619\pi$
$53$	7.65851	−	5.87658i	1.05198	−	0.807211i	0.981722	+	0.190318i	$0.0609520\pi$
$54$	0.256068	+	1.39084i	0.0348464	+	0.189269i
$55$	15.7410	−	15.7410i	2.12252	−	2.12252i
$56$	4.02103	+	6.31120i	0.537333	+	0.843370i
$57$	3.28052	+	3.28052i	0.434516	+	0.434516i
$58$	−1.76990	+	2.56868i	−0.232400	+	0.337284i
$59$	2.25910	+	2.94411i	0.294110	+	0.383291i	0.916913	−	0.399087i	$-0.130673\pi$
$59$	2.25910	+	2.94411i	0.294110	+	0.383291i	−0.622803	+	0.782378i	$0.714006\pi$
$60$	−3.35195	+	7.48073i	−0.432735	+	0.965758i
$61$	−1.57914	+	2.05797i	−0.202188	+	0.263496i	−0.883431	−	0.468560i	$-0.844773\pi$
$61$	−1.57914	+	2.05797i	−0.202188	+	0.263496i	0.681244	+	0.732057i	$0.261439\pi$
$62$	−0.663704	−	12.9588i	−0.0842905	−	1.64576i
$63$	2.61526	−	0.400495i	0.329492	−	0.0504576i
$64$	−7.62588	+	2.41784i	−0.953235	+	0.302230i
$65$	−6.51118	−	11.2777i	−0.807613	−	1.39883i
$66$	3.49524	−	6.83969i	0.430234	−	0.841908i
$67$	6.19933	+	0.816157i	0.757369	+	0.0997095i	0.499314	−	0.866421i	$-0.333585\pi$
$67$	6.19933	+	0.816157i	0.757369	+	0.0997095i	0.258054	+	0.966130i	$0.416919\pi$
$68$	−5.75348	−	7.95868i	−0.697712	−	0.965132i
$69$	1.96507	+	0.813958i	0.236566	+	0.0979890i
$70$	13.8000	+	6.68948i	1.64941	+	0.799546i
$71$	7.30030	−	7.30030i	0.866386	−	0.866386i	−0.125684	−	0.992070i	$-0.540113\pi$
$71$	7.30030	−	7.30030i	0.866386	−	0.866386i	0.992070	+	0.125684i	$0.0401125\pi$
$72$	−0.305674	+	2.81186i	−0.0360241	+	0.331381i
$73$	2.06358	−	0.552933i	0.241523	−	0.0647160i	−0.136027	−	0.990705i	$-0.543433\pi$
$73$	2.06358	−	0.552933i	0.241523	−	0.0647160i	0.377550	+	0.925989i	$0.376767\pi$
$74$	−5.15929	+	4.39586i	−0.599755	+	0.511009i
$75$	1.54011	+	11.6983i	0.177836	+	1.35080i
$76$	4.40804	+	8.16480i	0.505637	+	0.936566i
$77$	−12.5932	−	6.92131i	−1.43513	−	0.788757i
$78$	−3.33556	−	3.01054i	−0.377678	−	0.340876i
$79$	−0.257056	−	0.445233i	−0.0289210	−	0.0500927i	0.851203	−	0.524837i	$-0.175874\pi$
$79$	−0.257056	−	0.445233i	−0.0289210	−	0.0500927i	−0.880124	+	0.474745i	$0.842540\pi$
$80$	−10.7067	+	12.4159i	−1.19704	+	1.38814i
$81$	0.866025	+	0.500000i	0.0962250	+	0.0555556i
$82$	13.5283	+	2.89233i	1.49395	+	0.319404i
$83$	−1.49166	−	3.60119i	−0.163731	−	0.395282i	0.820626	−	0.571465i	$-0.193625\pi$
$83$	−1.49166	−	3.60119i	−0.163731	−	0.395282i	−0.984357	+	0.176183i	$0.943625\pi$
$84$	5.24091	+	0.730000i	0.571830	+	0.0796495i
$85$	−18.5937	−	7.70176i	−2.01677	−	0.835373i
$86$	−1.02265	−	5.55456i	−0.110275	−	0.598963i
$87$	0.570891	+	2.13059i	0.0612059	+	0.228424i
$88$	10.6142	−	11.1055i	1.13147	−	1.18385i
$89$	−3.20993	−	0.860098i	−0.340252	−	0.0911702i	0.0846472	−	0.996411i	$-0.473024\pi$
$89$	−3.20993	−	0.860098i	−0.340252	−	0.0911702i	−0.424899	+	0.905241i	$0.639690\pi$
$90$	2.48920	+	5.23472i	0.262385	+	0.551788i
$91$	−5.81754	+	6.06785i	−0.609844	+	0.636083i
$92$	3.29957	+	2.68494i	0.344004	+	0.279925i
$93$	−7.27921	−	5.58553i	−0.754819	−	0.579193i
$94$	−2.42484	+	4.74507i	−0.250103	+	0.489416i
$95$	16.4677	+	9.50764i	1.68955	+	0.975463i
$96$	−2.19579	+	5.21330i	−0.224107	+	0.532080i
$97$		−	4.72140i		−	0.479386i	−0.970849	−	0.239693i	$-0.922953\pi$
$97$		−	4.72140i		−	0.479386i	0.970849	−	0.239693i	$-0.0770468\pi$
$98$	1.66031	−	9.75927i	0.167717	−	0.985835i
$99$	−2.07847	−	5.01787i	−0.208894	−	0.504315i
$100$	−3.74698	+	23.2991i	−0.374698	+	2.32991i
$101$	−3.30738	+	2.53784i	−0.329096	+	0.252524i	−0.760072	−	0.649839i	$-0.774836\pi$
$101$	−3.30738	+	2.53784i	−0.329096	+	0.252524i	0.430975	+	0.902364i	$0.358170\pi$
$102$	−6.92212	−	0.553057i	−0.685392	−	0.0547609i
$103$	3.56532	−	13.3060i	0.351301	−	1.31107i	−0.533774	−	0.845627i	$-0.679227\pi$
$103$	3.56532	−	13.3060i	0.351301	−	1.31107i	0.885076	−	0.465447i	$-0.154107\pi$
$104$	−4.66809	−	7.67893i	−0.457744	−	0.752981i
$105$	9.92904	−	4.35989i	0.968975	−	0.425481i
$106$	4.57238	−	12.8634i	0.444109	−	1.24941i
$107$	−9.56500	+	1.25926i	−0.924683	+	0.121737i	−0.577806	−	0.816174i	$-0.696091\pi$
$107$	−9.56500	+	1.25926i	−0.924683	+	0.121737i	−0.346877	+	0.937911i	$0.612758\pi$
$108$	1.37326	+	1.45402i	0.132142	+	0.139913i
$109$	14.5283	+	1.91268i	1.39156	+	0.183202i	0.788764	−	0.614696i	$-0.210721\pi$
$109$	14.5283	+	1.91268i	1.39156	+	0.183202i	0.602793	+	0.797898i	$0.294055\pi$
$110$	6.58207	−	30.7863i	0.627576	−	2.93536i
$111$			4.79280i			0.454913i
$112$	9.62508	+	4.39975i	0.909485	+	0.415738i
$113$		−	3.67339i		−	0.345564i	−0.984960	−	0.172782i	$-0.944724\pi$
$113$		−	3.67339i		−	0.345564i	0.984960	−	0.172782i	$-0.0552756\pi$
$114$	6.41605	+	1.37174i	0.600918	+	0.128475i
$115$	8.64321	+	1.13790i	0.805984	+	0.106110i
$116$	−0.125957	+	4.40971i	−0.0116948	+	0.409431i
$117$	−3.15003	+	0.414709i	−0.291220	+	0.0383398i
$118$	4.94500	+	1.75773i	0.455224	+	0.161812i
$119$	−1.42414	+	12.9131i	−0.130550	+	1.18374i
$120$	1.77270	+	11.4565i	0.161825	+	1.04583i
$121$	−4.78790	+	17.8687i	−0.435263	+	1.62442i
$122$	−0.292171	+	3.65684i	−0.0264519	+	0.331075i
$123$	7.76069	−	5.95499i	0.699758	−	0.536943i
$124$	−10.7508	−	14.8714i	−0.965454	−	1.33549i
$125$	10.6646	+	25.7465i	0.953867	+	2.30284i
$126$	2.79634	−	2.48606i	0.249118	−	0.221476i
$127$			8.85526i			0.785778i	0.919586	+	0.392889i	$0.128524\pi$
$127$			8.85526i			0.785778i	−0.919586	+	0.392889i	$0.871476\pi$
$128$	−7.19282	+	8.73289i	−0.635761	+	0.771886i
$129$	−3.45863	−	1.99684i	−0.304515	−	0.175812i
$130$	−16.3992	−	8.38036i	−1.43830	−	0.735006i
$131$	8.12045	+	6.23104i	0.709487	+	0.544408i	0.899257	−	0.437420i	$-0.144108\pi$
$131$	8.12045	+	6.23104i	0.709487	+	0.544408i	−0.189770	+	0.981829i	$0.560774\pi$
$132$	−1.10978	−	10.8058i	−0.0965939	−	0.940521i
$133$	2.92655	−	11.9206i	0.253764	−	1.03365i
$134$	7.98592	−	3.79745i	0.689879	−	0.328050i
$135$	3.95903	+	1.06082i	0.340739	+	0.0913006i
$136$	−12.9481	−	5.02332i	−1.11029	−	0.430746i
$137$	0.602821	+	2.24976i	0.0515025	+	0.192210i	0.986884	−	0.161430i	$-0.0516106\pi$
$137$	0.602821	+	2.24976i	0.0515025	+	0.192210i	−0.935382	+	0.353640i	$0.884944\pi$
$138$	2.95828	−	0.544650i	0.251825	−	0.0463637i
$139$	−2.76092	−	1.14361i	−0.234178	−	0.0969998i	0.262509	−	0.964930i	$-0.415450\pi$
$139$	−2.76092	−	1.14361i	−0.234178	−	0.0969998i	−0.496687	+	0.867930i	$0.665450\pi$
$140$	21.5233	−	2.66956i	1.81905	−	0.225619i
$141$	1.44195	+	3.48117i	0.121434	+	0.293167i
$142$	3.05260	−	14.2779i	0.256169	−	1.19818i
$143$	14.9444	+	8.62818i	1.24972	+	0.721525i
$144$	1.79901	+	3.57262i	0.149917	+	0.297718i
$145$	4.52034	+	7.82946i	0.375394	+	0.650201i
$146$	2.02430	−	2.24285i	0.167532	−	0.185619i
$147$	−4.49136	−	5.36914i	−0.370441	−	0.442839i
$148$	−2.74429	+	9.18437i	−0.225579	+	0.754951i
$149$	2.99638	+	22.7598i	0.245473	+	1.86455i	0.460112	+	0.887861i	$0.347809\pi$
$149$	2.99638	+	22.7598i	0.245473	+	1.86455i	−0.214638	+	0.976694i	$0.568857\pi$
$150$	10.8220	+	12.7015i	0.883613	+	1.03707i
$151$	−9.39341	+	2.51696i	−0.764425	+	0.204827i	−0.619907	−	0.784675i	$-0.712830\pi$
$151$	−9.39341	+	2.51696i	−0.764425	+	0.204827i	−0.144518	+	0.989502i	$0.546163\pi$
$152$	11.5095	+	6.30238i	0.933547	+	0.511191i
$153$	−3.47209	+	3.47209i	−0.280702	+	0.280702i
$154$	−20.2691	+	1.46657i	−1.63333	+	0.118179i
$155$	−34.7438	−	14.3914i	−2.79069	−	1.15594i
$156$	−6.27380	−	1.00896i	−0.502306	−	0.0807813i
$157$	−1.18854	−	0.156474i	−0.0948557	−	0.0124880i	0.0829489	−	0.996554i	$-0.473566\pi$
$157$	−1.18854	−	0.156474i	−0.0948557	−	0.0124880i	−0.177805	+	0.984066i	$0.556900\pi$
$158$	−0.647425	−	0.330849i	−0.0515064	−	0.0263209i
$159$	−4.82667	−	8.36004i	−0.382780	−	0.662994i
$160$	−3.16282	+	22.9689i	−0.250043	+	1.81585i
$161$	−0.851842	−	5.56260i	−0.0671345	−	0.438394i
$162$	1.41236	−	0.0723364i	0.110966	−	0.00568329i
$163$	−3.95817	+	5.15839i	−0.310028	+	0.404036i	−0.922215	−	0.386676i	$-0.873623\pi$
$163$	−3.95817	+	5.15839i	−0.310028	+	0.404036i	0.612188	+	0.790713i	$0.290290\pi$
$164$	18.2814	−	6.96779i	1.42754	−	0.544093i
$165$	−13.5517	−	17.6610i	−1.05500	−	1.37491i
$166$	−4.53925	−	3.12769i	−0.352314	−	0.242756i
$167$	14.8379	+	14.8379i	1.14819	+	1.14819i	0.986908	+	0.161286i	$0.0515641\pi$
$167$	14.8379	+	14.8379i	1.14819	+	1.14819i	0.161286	+	0.986908i	$0.448436\pi$
$168$	6.78206	−	3.16286i	0.523247	−	0.244020i
$169$	−2.05440	+	2.05440i	−0.158031	+	0.158031i
$170$	−27.9915	+	5.15354i	−2.14685	+	0.395258i
$171$	3.68065	−	2.82426i	0.281467	−	0.215977i
$172$	−5.48435	−	5.80687i	−0.418178	−	0.442770i
$173$	−10.2871	−	7.89360i	−0.782116	−	0.600139i	0.138610	−	0.990347i	$-0.455736\pi$
$173$	−10.2871	−	7.89360i	−0.782116	−	0.600139i	−0.920727	+	0.390208i	$0.872403\pi$
$174$	2.31569	+	2.09004i	0.175552	+	0.158446i
$175$	24.3611	−	19.5215i	1.84153	−	1.47568i
$176$	4.06057	−	21.3424i	0.306077	−	1.60874i
$177$	3.21380	−	1.85549i	0.241564	−	0.139467i
$178$	−4.47137	+	1.44696i	−0.335143	+	0.108455i
$179$	−3.19065	+	24.2354i	−0.238480	+	1.81144i	0.284042	+	0.958812i	$0.408324\pi$
$179$	−3.19065	+	24.2354i	−0.238480	+	1.81144i	−0.522523	+	0.852625i	$0.675009\pi$
$180$	6.97921	+	4.29971i	0.520200	+	0.320481i
$181$	6.73700	−	16.2645i	0.500757	−	1.20893i	−0.448315	−	0.893876i	$-0.647976\pi$
$181$	6.73700	−	16.2645i	0.500757	−	1.20893i	0.949072	−	0.315059i	$-0.102024\pi$
$182$	−2.24014	+	11.6750i	−0.166050	+	0.865412i
$183$	1.83425	+	1.83425i	0.135591	+	0.135591i
$184$	5.98075	+	0.650161i	0.440907	+	0.0479305i
$185$	5.08429	+	18.9748i	0.373804	+	1.39506i
$186$	−12.9345	−	1.03343i	−0.948406	−	0.0757749i
$187$	26.4410	−	3.48102i	1.93356	−	0.254558i
$188$	0.769915	+	7.49655i	0.0561518	+	0.546742i
$189$	−0.0557079	−	2.64516i	−0.00405215	−	0.192407i
$190$	26.8565	−	1.37550i	1.94837	−	0.0997890i
$191$	3.66510	−	2.11605i	0.265197	−	0.153112i	−0.361506	−	0.932370i	$-0.617737\pi$
$191$	3.66510	−	2.11605i	0.265197	−	0.153112i	0.626703	+	0.779258i	$0.284404\pi$
$192$	1.40178	+	7.87623i	0.101165	+	0.568418i
$193$	6.69153	−	11.5901i	0.481667	−	0.834272i	−0.518112	−	0.855313i	$-0.673365\pi$
$193$	6.69153	−	11.5901i	0.481667	−	0.834272i	0.999779	+	0.0210414i	$0.00669817\pi$
$194$	−3.62994	−	5.60418i	−0.260615	−	0.402357i
$195$	−12.0311	+	4.98344i	−0.861565	+	0.356872i
$196$	−5.53244	−	12.8605i	−0.395174	−	0.918606i
$197$	−0.136736	+	0.330109i	−0.00974202	+	0.0235193i	−0.928676	−	0.370893i	$-0.879052\pi$
$197$	−0.136736	+	0.330109i	−0.00974202	+	0.0235193i	0.918934	+	0.394412i	$0.129052\pi$
$198$	−6.32495	−	4.35809i	−0.449495	−	0.309716i
$199$	2.56565	−	0.687463i	0.181874	−	0.0487330i	−0.166733	−	0.986002i	$-0.553322\pi$
$199$	2.56565	−	0.687463i	0.181874	−	0.0487330i	0.348606	+	0.937269i	$0.386655\pi$
$200$	13.4654	+	30.5361i	0.952145	+	2.15923i
$201$	1.61835	−	6.03976i	0.114150	−	0.426012i
$202$	−1.97461	+	5.55515i	−0.138933	+	0.390859i
$203$	4.03878	−	4.21256i	0.283467	−	0.295664i
$204$	−8.64157	+	4.66544i	−0.605031	+	0.326646i
$205$	24.4076	−	31.8086i	1.70470	−	2.22161i
$206$	−5.99803	−	18.5349i	−0.417902	−	1.29139i
$207$	1.06349	−	1.84201i	0.0739174	−	0.128029i
$208$	−11.4447	−	5.52574i	−0.793545	−	0.383141i
$209$	−25.1978			−1.74297
$210$	8.43352	−	12.8088i	0.581968	−	0.883890i
$211$	−12.7092	+	5.26434i	−0.874941	+	0.362412i	−0.774533	−	0.632534i	$-0.782015\pi$
$211$	−12.7092	+	5.26434i	−0.874941	+	0.362412i	−0.100408	+	0.994946i	$0.532015\pi$
$212$	−4.46244	−	18.7839i	−0.306482	−	1.29008i
$213$	−6.28497	−	8.19073i	−0.430639	−	0.561219i
$214$	−10.3853	+	8.84853i	−0.709921	+	0.604873i
$215$	−15.8111	−	4.23656i	−1.07831	−	0.288931i
$216$	2.74791	+	0.670081i	0.186971	+	0.0455932i
$217$	−2.66111	+	24.1291i	−0.180648	+	1.63799i
$218$	18.7152	−	8.89942i	1.26755	−	0.602745i
$219$	−0.278852	−	2.11809i	−0.0188431	−	0.143127i
$220$	−15.8566	−	41.6030i	−1.06905	−	2.80487i
$221$	2.03633	−	15.4675i	0.136979	−	1.04046i
$222$	3.68483	+	5.68893i	0.247310	+	0.381816i
$223$	−7.76961			−0.520292			−0.260146	−	0.965569i	$-0.583771\pi$
$223$	−7.76961			−0.520292			−0.260146	+	0.965569i	$0.583771\pi$
$224$	14.8074	−	2.17762i	0.989358	−	0.145499i
$225$	11.7992			0.786614
$226$	−2.82420	−	4.36022i	−0.187863	−	0.290037i
$227$	−0.936577	+	7.11401i	−0.0621628	+	0.472173i	0.931844	+	0.362858i	$0.118199\pi$
$227$	−0.936577	+	7.11401i	−0.0621628	+	0.472173i	−0.994007	+	0.109315i	$0.965134\pi$
$228$	8.67031	−	3.30461i	0.574205	−	0.218853i
$229$	−2.76560	−	21.0068i	−0.182756	−	1.38817i	−0.799340	−	0.600879i	$-0.794817\pi$
$229$	−2.76560	−	21.0068i	−0.182756	−	1.38817i	0.616584	−	0.787289i	$-0.288516\pi$
$230$	11.1341	−	5.29447i	0.734162	−	0.349107i
$231$	−8.50584	+	11.5820i	−0.559643	+	0.762043i
$232$	3.24079	+	5.33104i	0.212768	+	0.350000i
$233$	3.14557	+	0.842853i	0.206073	+	0.0552172i	0.360379	−	0.932806i	$-0.382647\pi$
$233$	3.14557	+	0.842853i	0.206073	+	0.0552172i	−0.154306	+	0.988023i	$0.549314\pi$
$234$	−3.42016	+	2.91407i	−0.223583	+	0.190499i
$235$	9.40159	+	12.2524i	0.613292	+	0.799258i
$236$	7.22098	−	1.71547i	0.470046	−	0.111667i
$237$	−0.474977	+	0.196742i	−0.0308531	+	0.0127798i
$238$	8.23750	+	16.4224i	0.533958	+	1.06451i
$239$	2.25001			0.145541			0.0727705	−	0.997349i	$-0.476816\pi$
$239$	2.25001			0.145541			0.0727705	+	0.997349i	$0.476816\pi$
$240$	10.9122	+	12.2357i	0.704380	+	0.789808i
$241$	−10.2905	+	17.8237i	−0.662871	+	1.14813i	0.316987	+	0.948430i	$0.397329\pi$
$241$	−10.2905	+	17.8237i	−0.662871	+	1.14813i	−0.979858	+	0.199696i	$0.936005\pi$
$242$	8.05480	+	24.8907i	0.517782	+	1.60004i
$243$	0.608761	−	0.793353i	0.0390521	−	0.0508936i
$244$	2.46468	+	4.56520i	0.157785	+	0.292257i
$245$	−23.4771	−	16.4920i	−1.49990	−	1.05364i
$246$	4.63338	−	13.0350i	0.295414	−	0.831084i
$247$	−3.81505	+	14.2380i	−0.242746	+	0.905939i
$248$	−24.1945	−	9.38647i	−1.53635	−	0.596042i
$249$	−3.76508	+	1.00885i	−0.238602	+	0.0639333i
$250$	32.4532	+	22.3612i	2.05252	+	1.41425i
$251$	−0.662589	+	1.59963i	−0.0418222	+	0.100968i	−0.943410	−	0.331628i	$-0.892402\pi$
$251$	−0.662589	+	1.59963i	−0.0418222	+	0.100968i	0.901588	+	0.432596i	$0.142402\pi$
$252$	1.40783	−	5.10079i	0.0886850	−	0.321319i
$253$	−10.6729	+	4.42085i	−0.670998	+	0.277936i
$254$	6.80816	+	10.5110i	0.427182	+	0.659517i
$255$	−10.0628	+	17.4293i	−0.630159	+	1.09147i
$256$	−1.82361	+	15.8957i	−0.113975	+	0.993484i
$257$	4.19369	−	2.42123i	0.261595	−	0.151032i	−0.363467	−	0.931607i	$-0.618407\pi$
$257$	4.19369	−	2.42123i	0.261595	−	0.151032i	0.625062	+	0.780575i	$0.285074\pi$
$258$	−5.64052	+	0.288888i	−0.351163	+	0.0179854i
$259$	10.8458	−	6.57010i	0.673922	−	0.408246i
$260$	−25.9085	+	2.66087i	−1.60677	+	0.165020i
$261$	2.18688	−	0.287908i	0.135365	−	0.0178211i
$262$	14.4293	+	1.15286i	0.891448	+	0.0712242i
$263$	7.46251	+	27.8505i	0.460158	+	1.71733i	0.672463	+	0.740131i	$0.265236\pi$
$263$	7.46251	+	27.8505i	0.460158	+	1.71733i	−0.212305	+	0.977204i	$0.568097\pi$
$264$	−9.62503	−	11.9729i	−0.592380	−	0.736882i
$265$	−27.9774	−	27.9774i	−1.71864	−	1.71864i
$266$	−5.69114	−	16.3995i	−0.348946	−	1.00552i
$267$	−1.27172	+	3.07020i	−0.0778279	+	0.187893i
$268$	6.55950	−	10.6473i	0.400685	−	0.650385i
$269$	−0.800687	+	6.08182i	−0.0488187	+	0.370815i	0.949545	+	0.313631i	$0.101546\pi$
$269$	−0.800687	+	6.08182i	−0.0488187	+	0.370815i	−0.998364	+	0.0571840i	$0.981788\pi$
$270$	5.51484	−	1.78464i	0.335623	−	0.108610i
$271$	−11.8301	+	6.83012i	−0.718628	+	0.414900i	−0.814247	−	0.580518i	$-0.802850\pi$
$271$	−11.8301	+	6.83012i	−0.718628	+	0.414900i	0.0956195	+	0.995418i	$0.469517\pi$
$272$	−19.2311	+	3.99227i	−1.16606	+	0.242067i
$273$	5.25659	+	6.55978i	0.318144	+	0.397016i
$274$	2.44521	+	2.20694i	0.147720	+	0.133326i
$275$	−50.8421	−	39.0125i	−3.06589	−	2.35254i
$276$	3.09265	−	2.92088i	0.186156	−	0.175817i
$277$	−18.9963	+	14.5763i	−1.14137	+	0.875808i	−0.993571	−	0.113209i	$-0.963887\pi$
$277$	−18.9963	+	14.5763i	−1.14137	+	0.875808i	−0.147804	+	0.989017i	$0.547220\pi$
$278$	−4.15638	+	0.765233i	−0.249283	+	0.0458956i
$279$	−6.48788	+	6.48788i	−0.388419	+	0.388419i
$280$	23.4951	−	19.7164i	1.40410	−	1.17828i
$281$	1.85362	+	1.85362i	0.110578	+	0.110578i	0.760231	−	0.649653i	$-0.225086\pi$
$281$	1.85362	+	1.85362i	0.110578	+	0.110578i	−0.649653	+	0.760231i	$0.725086\pi$
$282$	4.38797	+	3.02345i	0.261300	+	0.180044i
$283$	13.7804	+	17.9590i	0.819159	+	1.06755i	0.996516	+	0.0834026i	$0.0265787\pi$
$283$	13.7804	+	17.9590i	0.819159	+	1.06755i	−0.177357	+	0.984147i	$0.556755\pi$
$284$	−7.35389	−	19.2944i	−0.436373	−	1.14491i
$285$	11.5758	−	15.0858i	0.685689	−	0.893608i
$286$	24.3722	−	1.24826i	1.44116	−	0.0738114i
$287$	−24.1143	−	9.39861i	−1.42342	−	0.554783i
$288$	4.88209	+	2.85748i	0.287680	+	0.168378i
$289$	−3.55539	−	6.15812i	−0.209141	−	0.362243i
$290$	11.3850	+	5.81800i	0.668551	+	0.341645i
$291$	−4.68101	−	0.616267i	−0.274406	−	0.0361262i
$292$	0.678429	−	4.21854i	0.0397020	−	0.246871i
$293$	10.1959	+	4.22328i	0.595651	+	0.246727i	0.660080	−	0.751196i	$-0.270523\pi$
$293$	10.1959	+	4.22328i	0.595651	+	0.246727i	−0.0644289	+	0.997922i	$0.520523\pi$
$294$	−9.45906	−	2.91995i	−0.551664	−	0.170295i
$295$	10.7552	−	10.7552i	0.626190	−	0.626190i
$296$	3.80379	+	13.0115i	0.221091	+	0.756277i
$297$	−5.24623	+	1.40572i	−0.304417	+	0.0815684i
$298$	21.0550	+	24.7116i	1.21968	+	1.43150i
$299$	0.882075	+	6.70002i	0.0510117	+	0.387472i
$300$	22.6107	+	6.75606i	1.30543	+	0.390061i
$301$	0.222479	+	10.5639i	0.0128235	+	0.608895i
$302$	−9.21463	+	10.2095i	−0.530242	+	0.587489i
$303$	2.08443	+	3.61034i	0.119747	+	0.207408i
$304$	18.5069	−	1.36807i	1.06145	−	0.0784643i
$305$	9.20763	+	5.31603i	0.527228	+	0.304395i
$306$	−1.45184	+	6.79071i	−0.0829964	+	0.388199i
$307$	−1.43187	−	3.45684i	−0.0817212	−	0.197293i	0.877737	−	0.479142i	$-0.159052\pi$
$307$	−1.43187	−	3.45684i	−0.0817212	−	0.197293i	−0.959459	+	0.281849i	$0.909052\pi$
$308$	−22.9313	+	17.3242i	−1.30663	+	0.987136i
$309$	−12.7267	−	5.27159i	−0.723999	−	0.299890i
$310$	−52.3044	+	9.62979i	−2.97069	+	0.546936i
$311$	−3.49372	−	13.0388i	−0.198111	−	0.739360i	−0.991440	−	0.130566i	$-0.958320\pi$
$311$	−3.49372	−	13.0388i	−0.198111	−	0.739360i	0.793329	−	0.608794i	$-0.208346\pi$
$312$	−8.22255	+	3.62586i	−0.465510	+	0.205274i
$313$	15.9660	+	4.27808i	0.902451	+	0.241811i	0.680069	−	0.733148i	$-0.261950\pi$
$313$	15.9660	+	4.27808i	0.902451	+	0.241811i	0.222383	+	0.974959i	$0.428617\pi$
$314$	−1.53106	+	0.728049i	−0.0864030	+	0.0410862i
$315$	−3.02659	−	10.4132i	−0.170529	−	0.586716i
$316$	−1.02284	+	0.105049i	−0.0575394	+	0.00590944i
$317$	7.52864	+	5.77693i	0.422851	+	0.324465i	0.798172	−	0.602430i	$-0.205801\pi$
$317$	7.52864	+	5.77693i	0.422851	+	0.324465i	−0.375321	+	0.926895i	$0.622467\pi$
$318$	−12.1566	−	6.21227i	−0.681705	−	0.348367i
$319$	−10.3751	−	5.99005i	−0.580892	−	0.335378i
$320$	13.9049	+	29.6952i	0.777309	+	1.66001i
$321$			9.64753i			0.538473i
$322$	−5.28778	−	5.94774i	−0.294677	−	0.331454i
$323$	8.71773	+	21.0465i	0.485068	+	1.17106i
$324$	1.62082	−	1.17172i	0.0900457	−	0.0650957i
$325$	−29.7417	+	22.8216i	−1.64977	+	1.26591i
$326$	−0.732339	+	9.16602i	−0.0405605	+	0.507659i
$327$	3.79264	−	14.1543i	0.209734	−	0.782736i
$328$	16.3426	−	22.3258i	0.902366	−	1.23274i
$329$	5.90097	−	8.03510i	0.325331	−	0.442989i
$330$	−29.6638	−	10.5442i	−1.63294	−	0.580438i
$331$	4.18040	−	0.550361i	0.229776	−	0.0302506i	−0.0147590	−	0.999891i	$-0.504698\pi$
$331$	4.18040	−	0.550361i	0.229776	−	0.0302506i	0.244535	+	0.969641i	$0.421365\pi$
$332$	−7.79262	−	0.222586i	−0.427676	−	0.0122160i
$333$	4.75180	+	0.625586i	0.260397	+	0.0342819i
$334$	29.0200	+	6.20444i	1.58790	+	0.339492i
$335$		−	25.6283i		−	1.40023i
$336$	5.61844	−	8.96845i	0.306511	−	0.489269i
$337$			8.26486i			0.450216i	0.974334	+	0.225108i	$0.0722735\pi$
$337$			8.26486i			0.450216i	−0.974334	+	0.225108i	$0.927727\pi$
$338$	−0.859041	+	4.01799i	−0.0467256	+	0.218550i
$339$	−3.64197	−	0.479474i	−0.197804	−	0.0260414i
$340$	−29.2630	+	27.6377i	−1.58701	+	1.49887i
$341$	49.4071	−	6.50457i	2.67555	−	0.352242i
$342$	2.19747	−	6.18211i	0.118825	−	0.334290i
$343$	−5.99308	+	17.5238i	−0.323596	+	0.946195i
$344$	−10.9743	−	2.67609i	−0.591692	−	0.144285i
$345$	2.25633	−	8.42074i	0.121477	−	0.453358i
$346$	−18.2794	−	1.46047i	−0.982704	−	0.0785153i
$347$	1.10607	−	0.848714i	0.0593767	−	0.0455613i	−0.578647	−	0.815578i	$-0.696419\pi$
$347$	1.10607	−	0.848714i	0.0593767	−	0.0455613i	0.638023	+	0.770017i	$0.279752\pi$
$348$	4.35554	+	0.700462i	0.233481	+	0.0375487i
$349$	13.3960	+	32.3407i	0.717069	+	1.73116i	0.681531	+	0.731789i	$0.261314\pi$
$349$	13.3960	+	32.3407i	0.717069	+	1.73116i	0.0355380	+	0.999368i	$0.488686\pi$
$350$	13.9074	−	41.9009i	0.743380	−	2.23970i
$351$			3.17721i			0.169587i
$352$	−11.5888	−	28.4547i	−0.617684	−	1.51664i
$353$	1.43561	+	0.828851i	0.0764099	+	0.0441153i	0.537718	−	0.843125i	$-0.319286\pi$
$353$	1.43561	+	0.828851i	0.0764099	+	0.0441153i	−0.461308	+	0.887240i	$0.652620\pi$
$354$	2.38815	−	4.67327i	0.126929	−	0.248381i
$355$	−33.5712	−	25.7601i	−1.78177	−	1.36720i
$356$	−4.19493	+	5.15521i	−0.222331	+	0.273226i
$357$	12.6167	+	3.09745i	0.667747	+	0.163934i
$358$	14.8456	+	31.2198i	0.784613	+	1.65002i
$359$	15.0639	+	4.03637i	0.795045	+	0.213032i	0.633407	−	0.773819i	$-0.281656\pi$
$359$	15.0639	+	4.03637i	0.795045	+	0.213032i	0.161637	+	0.986850i	$0.448322\pi$
$360$	11.5899	−	0.262161i	0.610840	−	0.0138171i
$361$	−0.653175	−	2.43768i	−0.0343776	−	0.128299i
$362$	−4.50798	−	24.4852i	−0.236934	−	1.28691i
$363$	17.0909	+	7.07927i	0.897037	+	0.371565i
$364$	6.31710	+	15.5803i	0.331106	+	0.816627i
$365$	−3.35089	−	8.08977i	−0.175394	−	0.423438i
$366$	3.58742	+	0.766985i	0.187518	+	0.0400910i
$367$	−20.6582	−	11.9270i	−1.07835	−	0.622587i	−0.147900	−	0.989002i	$-0.547252\pi$
$367$	−20.6582	−	11.9270i	−1.07835	−	0.622587i	−0.930451	+	0.366416i	$0.880585\pi$
$368$	7.59886	−	3.82644i	0.396118	−	0.199467i
$369$	−4.89107	−	8.47158i	−0.254619	−	0.441013i
$370$	20.6233	+	18.6137i	1.07215	+	0.967679i
$371$	−12.3016	+	22.3826i	−0.638668	+	1.16205i
$372$	−16.1475	+	8.71775i	−0.837208	+	0.451994i
$373$	−0.873830	−	6.63740i	−0.0452452	−	0.343671i	−0.999063	−	0.0432849i	$-0.986218\pi$
$373$	−0.873830	−	6.63740i	−0.0452452	−	0.343671i	0.953818	−	0.300386i	$-0.0971157\pi$
$374$	28.7085	−	24.4604i	1.48448	−	1.26482i
$375$	26.9183	−	7.21273i	1.39005	−	0.372464i
$376$	6.67741	+	8.30627i	0.344361	+	0.428363i
$377$	−4.95550	+	4.95550i	−0.255221	+	0.255221i
$378$	−2.09980	−	3.09691i	−0.108002	−	0.159288i
$379$	−29.6538	−	12.2830i	−1.52321	−	0.630936i	−0.544982	−	0.838448i	$-0.683463\pi$
$379$	−29.6538	−	12.2830i	−1.52321	−	0.630936i	−0.978233	+	0.207512i	$0.933463\pi$
$380$	30.8204	−	22.2806i	1.58105	−	1.14297i
$381$	8.77951	+	1.15584i	0.449788	+	0.0592157i
$382$	2.72350	−	5.32951i	0.139347	−	0.272682i
$383$	−4.31284	−	7.47005i	−0.220376	−	0.381702i	0.734546	−	0.678558i	$-0.237395\pi$
$383$	−4.31284	−	7.47005i	−0.220376	−	0.381702i	−0.954922	+	0.296857i	$0.904062\pi$
$384$	7.71933	+	8.27115i	0.393925	+	0.422085i
$385$	−21.3884	+	54.8768i	−1.09005	+	2.79678i
$386$	−0.968083	−	18.9017i	−0.0492741	−	0.962073i
$387$	−2.43120	+	3.16840i	−0.123585	+	0.161059i
$388$	−8.61729	−	3.86122i	−0.437476	−	0.196024i
$389$	−2.12145	−	2.76473i	−0.107562	−	0.140177i	0.736470	−	0.676470i	$-0.236491\pi$
$389$	−2.12145	−	2.76473i	−0.107562	−	0.140177i	−0.844032	+	0.536292i	$0.819824\pi$
$390$	−10.4492	+	15.1650i	−0.529115	+	0.767912i
$391$	7.38504	+	7.38504i	0.373478	+	0.373478i
$392$	−16.4543	−	11.0116i	−0.831070	−	0.556168i
$393$	7.23766	−	7.23766i	0.365092	−	0.365092i
$394$	0.0914951	+	0.496957i	0.00460945	+	0.0250363i
$395$	−1.67174	+	1.28277i	−0.0841143	+	0.0645431i
$396$	−10.8582	−	0.310149i	−0.545644	−	0.0155856i
$397$	−29.7574	−	22.8337i	−1.49348	−	1.14599i	−0.952331	−	0.305065i	$-0.901322\pi$
$397$	−29.7574	−	22.8337i	−1.49348	−	1.14599i	−0.541152	−	0.840925i	$-0.682012\pi$
$398$	2.51682	−	2.78854i	0.126157	−	0.139777i
$399$	−11.4366	−	4.45747i	−0.572548	−	0.223152i
$400$	39.4600	+	25.8931i	1.97300	+	1.29465i
$401$	30.9796	−	17.8861i	1.54705	−	0.893187i	0.548680	−	0.836032i	$-0.315131\pi$
$401$	30.9796	−	17.8861i	1.54705	−	0.893187i	0.998365	−	0.0571547i	$-0.0182028\pi$
$402$	−2.72259	−	8.41327i	−0.135790	−	0.419616i
$403$	3.80505	−	28.9022i	0.189543	−	1.43972i
$404$	1.92713	+	8.11194i	0.0958784	+	0.403584i
$405$	1.56850	−	3.78669i	0.0779393	−	0.188162i
$406$	1.55520	−	8.10532i	0.0771834	−	0.402260i
$407$	−18.4068	−	18.4068i	−0.912391	−	0.912391i
$408$	−6.67041	+	12.1816i	−0.330234	+	0.603080i
$409$	−7.88649	−	29.4328i	−0.389962	−	1.45536i	−0.830194	−	0.557474i	$-0.811771\pi$
$409$	−7.88649	−	29.4328i	−0.389962	−	1.45536i	0.440232	−	0.897884i	$-0.354896\pi$
$410$	4.51588	−	56.5212i	0.223024	−	2.79138i
$411$	2.30919	−	0.304011i	0.113904	−	0.0149958i
$412$	−21.3696	−	17.3890i	−1.05281	−	0.856695i
$413$	−8.60439	−	4.72904i	−0.423394	−	0.232701i
$414$	−0.153858	−	3.00406i	−0.00756169	−	0.147641i
$415$	−13.8359	+	7.98813i	−0.679175	+	0.392122i
$416$	−17.8329	+	2.24006i	−0.874328	+	0.109828i
$417$	−1.49420	+	2.58803i	−0.0731712	+	0.126736i
$418$	−29.9091	+	19.3727i	−1.46290	+	0.947550i
$419$	−34.5046	+	14.2923i	−1.68566	+	0.698224i	−0.999571	−	0.0292930i	$-0.990674\pi$
$419$	−34.5046	+	14.2923i	−1.68566	+	0.698224i	−0.686090	+	0.727517i	$0.740674\pi$
$420$	0.162632	−	21.6876i	0.00793565	−	1.05825i
$421$	−5.76454	+	13.9168i	−0.280947	+	0.678265i	−0.999858	−	0.0168364i	$-0.994641\pi$
$421$	−5.76454	+	13.9168i	−0.280947	+	0.678265i	0.718912	+	0.695101i	$0.244641\pi$
$422$	−11.0382	+	16.0198i	−0.537330	+	0.779833i
$423$	3.63960	−	0.975227i	0.176963	−	0.0474172i
$424$	−19.7384	−	18.8651i	−0.958579	−	0.916172i
$425$	−14.9953	+	55.9632i	−0.727379	+	2.71461i
$426$	−13.7573	−	4.89013i	−0.666545	−	0.236928i
$427$	1.63633	−	6.66520i	0.0791876	−	0.322552i
$428$	−5.52404	+	18.4874i	−0.267014	+	0.893623i
$429$	10.5050	−	13.6904i	0.507187	−	0.660978i
$430$	−22.0245	+	7.12728i	−1.06212	+	0.343708i
$431$	8.03762	−	13.9216i	0.387159	−	0.670578i	−0.604908	−	0.796296i	$-0.706790\pi$
$431$	8.03762	−	13.9216i	0.387159	−	0.670578i	0.992066	+	0.125717i	$0.0401233\pi$
$432$	3.77687	−	1.31730i	0.181715	−	0.0633784i
$433$	20.7900			0.999106			0.499553	−	0.866283i	$-0.333498\pi$
$433$	20.7900			0.999106			0.499553	+	0.866283i	$0.333498\pi$
$434$	15.3924	+	30.6865i	0.738860	+	1.47300i
$435$	8.35250	−	3.45972i	0.400472	−	0.165881i
$436$	15.3723	−	24.9521i	0.736202	−	1.19499i
$437$	−6.00714	−	7.82865i	−0.287360	−	0.374495i
$438$	−1.95944	−	2.29973i	−0.0936255	−	0.109885i
$439$	−15.4167	−	4.13088i	−0.735797	−	0.197156i	−0.128588	−	0.991698i	$-0.541044\pi$
$439$	−15.4167	−	4.13088i	−0.735797	−	0.197156i	−0.607209	+	0.794542i	$0.707711\pi$
$440$	−50.8068	−	37.1907i	−2.42212	−	1.77300i
$441$	−5.90945	+	3.75213i	−0.281402	+	0.178673i
$442$	−9.47474	−	19.9251i	−0.450667	−	0.947740i
$443$	2.27891	+	17.3101i	0.108274	+	0.822426i	0.956283	+	0.292443i	$0.0944682\pi$
$443$	2.27891	+	17.3101i	0.108274	+	0.822426i	−0.848009	+	0.529983i	$0.822198\pi$
$444$	8.74760	+	3.91961i	0.415143	+	0.186017i
$445$	−1.77784	+	13.5041i	−0.0842779	+	0.640154i
$446$	−9.22233	+	5.97348i	−0.436690	+	0.282853i
$447$	22.9562			1.08579
$448$	15.9017	−	13.9691i	0.751286	−	0.659977i
$449$	28.7885			1.35861			0.679306	−	0.733855i	$-0.262281\pi$
$449$	28.7885			1.35861			0.679306	+	0.733855i	$0.262281\pi$
$450$	14.0054	−	9.07155i	0.660219	−	0.427637i
$451$	−6.93482	+	52.6752i	−0.326548	+	2.48038i
$452$	−6.70450	−	3.00414i	−0.315353	−	0.141303i
$453$	1.26934	+	9.64158i	0.0596387	+	0.453001i
$454$	4.35774	+	9.16420i	0.204519	+	0.430097i
$455$	27.7697	+	20.3940i	1.30186	+	0.956088i
$456$	7.75076	−	10.5884i	0.362963	−	0.495849i
$457$	1.55644	+	0.417047i	0.0728072	+	0.0195086i	0.295039	−	0.955485i	$-0.404667\pi$
$457$	1.55644	+	0.417047i	0.0728072	+	0.0195086i	−0.222232	+	0.974994i	$0.571334\pi$
$458$	−19.4333	−	22.8083i	−0.908057	−	1.06576i
$459$	2.98919	+	3.89558i	0.139523	+	0.181830i
$460$	9.14537	−	14.8446i	0.426405	−	0.692133i
$461$	−24.0840	+	9.97590i	−1.12170	+	0.464624i	−0.864952	−	0.501854i	$-0.832651\pi$
$461$	−24.0840	+	9.97590i	−1.12170	+	0.464624i	−0.256749	+	0.966478i	$0.582651\pi$
$462$	−1.19162	+	20.2871i	−0.0554394	+	0.943841i
$463$	17.5865			0.817314			0.408657	−	0.912688i	$-0.365997\pi$
$463$	17.5865			0.817314			0.408657	+	0.912688i	$0.365997\pi$
$464$	7.94538	+	3.83620i	0.368855	+	0.178091i
$465$	−18.8032	+	32.5681i	−0.871978	+	1.51031i
$466$	4.38172	−	1.41795i	0.202979	−	0.0656854i
$467$	17.7876	−	23.1813i	0.823114	−	1.07270i	−0.173026	−	0.984917i	$-0.555354\pi$
$467$	17.7876	−	23.1813i	0.823114	−	1.07270i	0.996139	−	0.0877851i	$-0.0279789\pi$
$468$	−1.81922	+	6.08843i	−0.0840936	+	0.281438i
$469$	−15.8860	+	4.61726i	−0.733548	+	0.213205i
$470$	20.5794	+	7.31507i	0.949257	+	0.337419i
$471$	−0.310271	+	1.15795i	−0.0142965	+	0.0533553i
$472$	7.25221	−	7.58789i	0.333810	−	0.349261i
$473$	20.9518	−	5.61401i	0.963363	−	0.258132i
$474$	−0.412525	+	0.598702i	−0.0189479	+	0.0274993i
$475$	20.9484	−	50.5739i	0.961179	−	2.32049i
$476$	22.4037	+	13.1597i	1.02687	+	0.603175i
$477$	−8.91853	+	3.69417i	−0.408351	+	0.169145i
$478$	2.67070	−	1.72987i	0.122155	−	0.0791223i
$479$	20.5363	−	35.5700i	0.938329	−	1.62523i	0.169742	−	0.985488i	$-0.445706\pi$
$479$	20.5363	−	35.5700i	0.938329	−	1.62523i	0.768587	−	0.639745i	$-0.220960\pi$
$480$	22.3596	+	6.13381i	1.02057	+	0.279969i
$481$	−13.1876	+	7.61386i	−0.601303	+	0.347162i
$482$	1.48876	+	29.0679i	0.0678111	+	1.32401i
$483$	−5.62620	+	0.118489i	−0.256001	+	0.00539145i
$484$	28.6975	+	23.3519i	1.30443	+	1.06145i
$485$	−19.1860	+	2.52588i	−0.871191	+	0.114694i
$486$	0.112633	−	1.40972i	0.00510912	−	0.0639463i
$487$	−8.25506	−	30.8083i	−0.374073	−	1.39606i	−0.854695	−	0.519131i	$-0.826256\pi$
$487$	−8.25506	−	30.8083i	−0.374073	−	1.39606i	0.480622	−	0.876928i	$-0.340411\pi$
$488$	6.43535	+	3.52387i	0.291315	+	0.159518i
$489$	4.59761	+	4.59761i	0.207911	+	0.207911i
$490$	−40.5462	−	1.52580i	−1.83169	−	0.0689288i
$491$	2.40771	−	5.81273i	0.108659	−	0.262325i	−0.860192	−	0.509970i	$-0.829657\pi$
$491$	2.40771	−	5.81273i	0.108659	−	0.262325i	0.968851	+	0.247645i	$0.0796566\pi$
$492$	−4.52198	−	19.0345i	−0.203866	−	0.858142i
$493$	−1.41371	+	10.7382i	−0.0636703	+	0.483624i
$494$	6.41815	+	19.8332i	0.288766	+	0.892337i
$495$	−19.2787	+	11.1306i	−0.866515	+	0.500283i
$496$	−35.9348	+	7.45988i	−1.61352	+	0.334959i
$497$	−9.91941	+	25.4505i	−0.444946	+	1.14161i
$498$	−3.69342	+	4.09218i	−0.165506	+	0.183375i
$499$	22.6524	+	17.3818i	1.01406	+	0.778115i	0.975244	−	0.221131i	$-0.0709749\pi$
$499$	22.6524	+	17.3818i	1.01406	+	0.778115i	0.0388156	+	0.999246i	$0.487642\pi$
$500$	55.7130	+	1.59137i	2.49156	+	0.0711680i
$501$	16.6477	−	12.7743i	0.743766	−	0.570711i
$502$	0.443363	+	2.40813i	0.0197883	+	0.107480i
$503$	18.5201	−	18.5201i	0.825772	−	0.825772i	−0.161156	−	0.986929i	$-0.551522\pi$
$503$	18.5201	−	18.5201i	0.825772	−	0.825772i	0.986929	+	0.161156i	$0.0515224\pi$
$504$	−2.25056	−	7.13687i	−0.100248	−	0.317902i
$505$	12.0822	+	12.0822i	0.537651	+	0.537651i
$506$	−9.26955	+	13.4530i	−0.412082	+	0.598059i
$507$	1.76867	+	2.30497i	0.0785494	+	0.102368i
$508$	16.1622	+	7.24194i	0.717082	+	0.321309i
$509$	−17.0375	+	22.2037i	−0.755173	+	0.984161i	0.244721	+	0.969594i	$0.421304\pi$
$509$	−17.0375	+	22.2037i	−0.755173	+	0.984161i	−0.999894	+	0.0145671i	$0.995363\pi$
$510$	1.45582	+	28.4247i	0.0644647	+	1.25867i
$511$	−4.41083	+	3.53456i	−0.195124	+	0.156360i
$512$	10.0565	+	20.2699i	0.444438	+	0.895809i
$513$	−2.31968	−	4.01780i	−0.102416	−	0.177390i
$514$	3.11629	−	6.09815i	0.137454	−	0.268978i
$515$	−55.9777	−	7.36961i	−2.46667	−	0.324744i
$516$	−6.47304	+	4.67948i	−0.284960	+	0.206003i
$517$	−18.9073	−	7.83165i	−0.831541	−	0.344435i
$518$	7.82236	−	16.1370i	0.343695	−	0.709021i
$519$	−9.16881	+	9.16881i	−0.402466	+	0.402466i
$520$	−28.7069	+	23.0775i	−1.25888	+	1.01201i
$521$	−1.22379	+	0.327913i	−0.0536152	+	0.0143661i	−0.285527	−	0.958371i	$-0.592169\pi$
$521$	−1.22379	+	0.327913i	−0.0536152	+	0.0143661i	0.231912	+	0.972737i	$0.425502\pi$
$522$	2.37442	−	2.02307i	0.103925	−	0.0885474i
$523$	−1.63609	−	12.4274i	−0.0715414	−	0.543411i	−0.989259	−	0.146177i	$-0.953303\pi$
$523$	−1.63609	−	12.4274i	−0.0715414	−	0.543411i	0.917717	−	0.397235i	$-0.130030\pi$
$524$	18.0136	−	9.72524i	0.786928	−	0.424849i
$525$	−16.1747	−	26.7007i	−0.705921	−	1.16532i
$526$	30.2700	+	27.3204i	1.31983	+	1.19123i
$527$	−22.5265	−	39.0170i	−0.981269	−	1.69961i
$528$	−20.6298	−	6.81156i	−0.897795	−	0.296435i
$529$	16.0007	+	9.23799i	0.695681	+	0.401652i
$530$	−54.7182	−	11.6987i	−2.37681	−	0.508158i
$531$	−1.42013	−	3.42849i	−0.0616283	−	0.148784i
$532$	−19.3636	−	15.0902i	−0.839517	−	0.654244i
$533$	28.7141	+	11.8938i	1.24374	+	0.515176i
$534$	0.850955	+	4.62198i	0.0368244	+	0.200013i
$535$	10.2343	+	38.1948i	0.442466	+	1.65131i
$536$	−0.399945	−	17.6811i	−0.0172750	−	0.763709i
$537$	23.6116	+	6.32670i	1.01891	+	0.273017i
$538$	3.72547	+	7.83455i	0.160616	+	0.337771i
$539$	37.8693	+	3.37111i	1.63115	+	0.145204i
$540$	5.17389	−	6.35828i	0.222649	−	0.273617i
$541$	−29.0275	−	22.2736i	−1.24799	−	0.957617i	−0.248053	−	0.968746i	$-0.579791\pi$
$541$	−29.0275	−	22.2736i	−1.24799	−	0.957617i	−0.999938	+	0.0111292i	$0.996457\pi$
$542$	−8.79085	+	17.2025i	−0.377599	+	0.738909i
$543$	−15.2460	−	8.80231i	−0.654271	−	0.377743i
$544$	−19.7574	+	19.5241i	−0.847092	+	0.837088i
$545$		−	60.0607i		−	2.57272i
$546$	11.2828	+	3.74488i	0.482858	+	0.160266i
$547$	−2.64533	−	6.38638i	−0.113106	−	0.273062i	0.857183	−	0.515013i	$-0.172213\pi$
$547$	−2.64533	−	6.38638i	−0.113106	−	0.273062i	−0.970289	+	0.241951i	$0.922213\pi$
$548$	4.59915	+	0.739639i	0.196466	+	0.0315958i
$549$	2.05797	−	1.57914i	0.0878321	−	0.0673960i
$550$	−90.3421	−	7.21808i	−3.85220	−	0.307780i
$551$	2.64857	−	9.88459i	0.112833	−	0.421098i
$552$	1.42524	−	5.84473i	0.0606624	−	0.248768i
$553$	1.09632	+	0.805138i	0.0466204	+	0.0342380i
$554$	−11.3414	+	31.9066i	−0.481849	+	1.35558i
$555$	19.4761	−	2.56408i	0.826715	−	0.108839i
$556$	−4.34518	+	4.10384i	−0.184277	+	0.174042i
$557$	17.5905	+	2.31583i	0.745332	+	0.0981249i	0.493621	−	0.869677i	$-0.335673\pi$
$557$	17.5905	+	2.31583i	0.745332	+	0.0981249i	0.251712	+	0.967802i	$0.419007\pi$
$558$	−2.71289	+	12.6890i	−0.114846	+	0.537168i
$559$		−	12.6887i		−	0.536676i
$560$	12.7296	−	41.4665i	0.537926	−	1.75228i
$561$		−	26.6692i		−	1.12597i
$562$	3.62531	+	0.775086i	0.152924	+	0.0326950i
$563$	2.45350	+	0.323010i	0.103403	+	0.0136132i	0.182050	−	0.983289i	$-0.441727\pi$
$563$	2.45350	+	0.323010i	0.103403	+	0.0136132i	−0.0786472	+	0.996903i	$0.525060\pi$
$564$	7.53291	+	0.215167i	0.317193	+	0.00906018i
$565$	−14.9273	+	1.96521i	−0.627995	+	0.0826771i
$566$	30.1643	+	10.7221i	1.26790	+	0.450683i
$567$	−2.62981	−	0.290032i	−0.110441	−	0.0121802i
$568$	−23.5630	−	17.2481i	−0.988679	−	0.723715i
$569$	3.77256	−	14.0794i	0.158154	−	0.590239i	−0.840660	−	0.541563i	$-0.817833\pi$
$569$	3.77256	−	14.0794i	0.158154	−	0.590239i	0.998815	−	0.0486767i	$-0.0155004\pi$
$570$	2.14174	−	26.8062i	0.0897077	−	1.12279i
$571$	3.03599	−	2.32960i	0.127052	−	0.0974906i	−0.543281	−	0.839551i	$-0.682818\pi$
$571$	3.03599	−	2.32960i	0.127052	−	0.0974906i	0.670333	+	0.742061i	$0.266151\pi$
$572$	27.9695	−	20.2197i	1.16946	−	0.845427i
$573$	−1.61955	−	3.90994i	−0.0676577	−	0.163340i
$574$	−35.8489	+	7.38378i	−1.49630	+	0.308193i
$575$		−	25.0966i		−	1.04660i
$576$	7.99182	−	0.361733i	0.332992	−	0.0150722i
$577$	−16.4075	−	9.47290i	−0.683055	−	0.394362i	0.117950	−	0.993020i	$-0.462368\pi$
$577$	−16.4075	−	9.47290i	−0.683055	−	0.394362i	−0.801005	+	0.598657i	$0.795701\pi$
$578$	−8.95469	−	4.57605i	−0.372466	−	0.190339i
$579$	−10.6175	−	8.14709i	−0.441248	−	0.338582i
$580$	17.9868	−	1.84729i	0.746859	−	0.0767044i
$581$	7.44423	+	7.13715i	0.308839	+	0.296099i
$582$	−6.03004	+	2.86739i	−0.249953	+	0.118857i
$583$	50.6437	+	13.5699i	2.09745	+	0.562009i
$584$	−2.43804	−	5.52888i	−0.100887	−	0.228787i
$585$	3.37044	+	12.5786i	0.139350	+	0.520063i
$586$	15.3492	−	2.82595i	0.634071	−	0.116739i
$587$	18.9024	+	7.82965i	0.780187	+	0.323164i	0.736991	−	0.675903i	$-0.236246\pi$
$587$	18.9024	+	7.82965i	0.780187	+	0.323164i	0.0431961	+	0.999067i	$0.486246\pi$
$588$	−13.4726	+	3.80648i	−0.555600	+	0.156977i
$589$	16.2898	+	39.3270i	0.671209	+	1.62044i
$590$	4.49725	−	21.0350i	0.185149	−	0.865996i
$591$	0.309438	+	0.178654i	0.0127286	+	0.00734884i
$592$	14.5186	+	12.5198i	0.596710	+	0.514562i
$593$	−21.8124	−	37.7802i	−0.895728	−	1.55145i	−0.832901	−	0.553421i	$-0.813322\pi$
$593$	−21.8124	−	37.7802i	−0.895728	−	1.55145i	−0.0628262	−	0.998024i	$-0.520011\pi$
$594$	−5.14638	+	5.70200i	−0.211159	+	0.233956i
$595$	53.2357	−	1.12116i	2.18245	−	0.0459630i
$596$	43.9906	+	13.1444i	1.80192	+	0.538415i
$597$	−0.346698	−	2.63343i	−0.0141894	−	0.107779i
$598$	6.19815	+	7.27459i	0.253461	+	0.297480i
$599$	−5.50280	+	1.47447i	−0.224838	+	0.0602453i	−0.369479	−	0.929239i	$-0.620464\pi$
$599$	−5.50280	+	1.47447i	−0.224838	+	0.0602453i	0.144641	+	0.989484i	$0.453797\pi$
$600$	32.0325	−	9.36440i	1.30772	−	0.382300i
$601$	−21.8762	+	21.8762i	−0.892349	+	0.892349i	−0.994744	−	0.102395i	$-0.967350\pi$
$601$	−21.8762	+	21.8762i	−0.892349	+	0.892349i	0.102395	+	0.994744i	$0.467350\pi$
$602$	8.38591	+	12.3681i	0.341784	+	0.504085i
$603$	−5.77685	−	2.39285i	−0.235252	−	0.0974445i
$604$	−3.08821	+	19.2028i	−0.125658	+	0.781352i
$605$	75.1730	+	9.89671i	3.05622	+	0.402358i
$606$	5.24988	+	2.68281i	0.213262	+	0.108982i
$607$	−1.64254	−	2.84497i	−0.0666688	−	0.115474i	0.830764	−	0.556624i	$-0.187904\pi$
$607$	−1.64254	−	2.84497i	−0.0666688	−	0.115474i	−0.897433	+	0.441151i	$0.854570\pi$
$608$	20.9154	−	15.8525i	0.848233	−	0.642904i
$609$	−3.64935	−	4.55408i	−0.147879	−	0.184541i
$610$	15.0163	−	0.769085i	0.607993	−	0.0311393i
$611$	−7.28790	+	9.49777i	−0.294837	+	0.384239i
$612$	3.49758	+	9.17661i	0.141381	+	0.370942i
$613$	22.7741	+	29.6798i	0.919837	+	1.19876i	0.979684	+	0.200548i	$0.0642721\pi$
$613$	22.7741	+	29.6798i	0.919837	+	1.19876i	−0.0598467	+	0.998208i	$0.519061\pi$
$614$	−4.35731	−	3.00232i	−0.175847	−	0.121164i
$615$	−28.3507	−	28.3507i	−1.14321	−	1.14321i
$616$	−13.8996	+	38.1935i	−0.560030	+	1.53886i
$617$	8.13093	−	8.13093i	0.327339	−	0.327339i	−0.524235	−	0.851574i	$-0.675649\pi$
$617$	8.13093	−	8.13093i	0.327339	−	0.327339i	0.851574	+	0.524235i	$0.175649\pi$
$618$	−19.1593	+	3.52742i	−0.770698	+	0.141894i
$619$	−28.0732	+	21.5413i	−1.12836	+	0.865817i	−0.992174	−	0.124866i	$-0.960150\pi$
$619$	−28.0732	+	21.5413i	−1.12836	+	0.865817i	−0.136182	+	0.990684i	$0.543483\pi$
$620$	−54.6803	+	51.6433i	−2.19601	+	2.07405i
$621$	−1.68744	−	1.29482i	−0.0677147	−	0.0519593i
$622$	−14.1715	−	12.7906i	−0.568225	−	0.512856i
$623$	8.69095	−	1.33091i	0.348195	−	0.0533217i
$624$	−6.97229	+	10.6255i	−0.279115	+	0.425361i
$625$	47.8266	−	27.6127i	1.91306	−	1.10451i
$626$	22.2403	−	7.19712i	0.888902	−	0.287655i
$627$	−3.28897	+	24.9822i	−0.131349	+	0.997693i
$628$	−1.25759	+	2.04130i	−0.0501833	+	0.0814567i
$629$	−9.00606	+	21.7426i	−0.359095	+	0.866932i
$630$	−11.5984	−	10.0332i	−0.462091	−	0.399734i
$631$	4.68719	+	4.68719i	0.186594	+	0.186594i	0.794222	−	0.607628i	$-0.207879\pi$
$631$	4.68719	+	4.68719i	0.186594	+	0.186594i	−0.607628	+	0.794222i	$0.707879\pi$
$632$	−1.13332	+	0.911078i	−0.0450811	+	0.0362407i
$633$	3.56042	+	13.2877i	0.141514	+	0.528137i
$634$	13.3778	+	1.06884i	0.531299	+	0.0424493i
$635$	35.9844	−	4.73744i	1.42800	−	0.188000i
$636$	−19.2057	+	1.97247i	−0.761554	+	0.0782136i
$637$	7.63842	−	20.8876i	0.302645	−	0.827597i
$638$	−16.9202	+	0.866597i	−0.669879	+	0.0343089i
$639$	−8.94101	+	5.16209i	−0.353701	+	0.204209i
$640$	39.3352	+	24.5569i	1.55486	+	0.970697i
$641$	13.4563	−	23.3069i	0.531491	−	0.920569i	−0.467834	−	0.883816i	$-0.654965\pi$
$641$	13.4563	−	23.3069i	0.531491	−	0.920569i	0.999324	−	0.0367523i	$-0.0117012\pi$
$642$	7.41728	+	11.4514i	0.292737	+	0.451949i
$643$	2.35758	−	0.976543i	0.0929740	−	0.0385111i	−0.335712	−	0.941965i	$-0.608977\pi$
$643$	2.35758	−	0.976543i	0.0929740	−	0.0385111i	0.428686	+	0.903454i	$0.358977\pi$
$644$	−10.8492	−	2.99442i	−0.427520	−	0.117997i
$645$	−6.26408	+	15.1228i	−0.246648	+	0.595460i
$646$	26.5288	+	18.2792i	1.04376	+	0.719185i
$647$	−8.04402	+	2.15539i	−0.316243	+	0.0847371i	−0.413449	−	0.910527i	$-0.635676\pi$
$647$	−8.04402	+	2.15539i	−0.316243	+	0.0847371i	0.0972061	+	0.995264i	$0.469009\pi$
$648$	1.02302	−	2.63693i	0.0401881	−	0.103589i
$649$	−5.21660	+	19.4686i	−0.204770	+	0.764211i
$650$	−17.7567	+	49.9548i	−0.696476	+	1.95939i
$651$	23.5753	+	5.78783i	0.923990	+	0.226843i
$652$	6.17781	+	11.4429i	0.241942	+	0.448137i
$653$	−7.49536	+	9.76815i	−0.293316	+	0.382257i	−0.916645	−	0.399703i	$-0.869113\pi$
$653$	−7.49536	+	9.76815i	−0.293316	+	0.382257i	0.623328	+	0.781960i	$0.285780\pi$
$654$	−6.38046	−	19.7167i	−0.249496	−	0.770984i
$655$	20.9763	−	36.3319i	0.819610	−	1.41961i
$656$	2.23349	−	39.0648i	0.0872030	−	1.52522i
$657$	−2.13637			−0.0833477
$658$	0.826695	−	14.0743i	0.0322279	−	0.548672i
$659$	7.48579	−	3.10072i	0.291605	−	0.120787i	−0.232085	−	0.972695i	$-0.574555\pi$
$659$	7.48579	−	3.10072i	0.291605	−	0.120787i	0.523690	+	0.851909i	$0.324555\pi$
$660$	−43.3168	+	10.2906i	−1.68610	+	0.400563i
$661$	−15.7874	−	20.5746i	−0.614059	−	0.800258i	0.378030	−	0.925793i	$-0.376602\pi$
$661$	−15.7874	−	20.5746i	−0.614059	−	0.800258i	−0.992089	+	0.125536i	$0.959935\pi$
$662$	4.53890	−	3.86727i	0.176409	−	0.150306i
$663$	−15.0694	−	4.03782i	−0.585246	−	0.156816i
$664$	−9.42077	+	5.72697i	−0.365597	+	0.222250i
$665$	−50.0065	−	5.51504i	−1.93917	−	0.213864i
$666$	6.12123	−	2.91075i	0.237193	−	0.112789i
$667$	−0.612374	−	4.65144i	−0.0237112	−	0.180104i
$668$	39.2161	−	14.9469i	1.51732	−	0.578311i
$669$	−1.01414	+	7.70314i	−0.0392088	+	0.297821i
$670$	−19.7037	−	30.4202i	−0.761222	−	1.17523i
$671$	−14.0889			−0.543895
$672$	−0.226246	−	14.9649i	−0.00872763	−	0.577284i
$673$	18.0036			0.693986			0.346993	−	0.937868i	$-0.387203\pi$
$673$	18.0036			0.693986			0.346993	+	0.937868i	$0.387203\pi$
$674$	6.35425	+	9.81018i	0.244756	+	0.377874i
$675$	1.54011	−	11.6983i	0.0592787	−	0.450267i
$676$	2.06948	+	5.42970i	0.0795953	+	0.208835i
$677$	1.73511	+	13.1795i	0.0666858	+	0.506529i	0.991894	+	0.127069i	$0.0405570\pi$
$677$	1.73511	+	13.1795i	0.0666858	+	0.506529i	−0.925208	+	0.379460i	$0.876110\pi$
$678$	−4.69155	+	2.23092i	−0.180178	+	0.0856778i
$679$	5.02229	+	11.4376i	0.192738	+	0.438934i
$680$	−13.4858	+	55.3034i	−0.517158	+	2.12079i
$681$	6.93090	+	1.85713i	0.265593	+	0.0711653i
$682$	53.6441	−	45.7063i	2.05414	−	1.75018i
$683$	29.3910	+	38.3030i	1.12461	+	1.46562i	0.866273	+	0.499571i	$0.166509\pi$
$683$	29.3910	+	38.3030i	1.12461	+	1.46562i	0.258341	+	0.966054i	$0.416824\pi$
$684$	−2.14463	−	9.02747i	−0.0820021	−	0.345174i
$685$	8.81966	−	3.65322i	0.336982	−	0.139582i
$686$	6.35912	+	25.4079i	0.242792	+	0.970078i
$687$	−21.1881			−0.808375
$688$	−15.0836	+	5.26085i	−0.575057	+	0.200568i
$689$	15.3353	−	26.5616i	0.584230	−	1.01192i
$690$	−3.79588	−	11.7299i	−0.144507	−	0.446551i
$691$	−8.52652	+	11.1120i	−0.324364	+	0.422720i	−0.926863	−	0.375400i	$-0.877505\pi$
$691$	−8.52652	+	11.1120i	−0.324364	+	0.422720i	0.602499	+	0.798120i	$0.294172\pi$
$692$	−22.8200	+	12.3201i	−0.867485	+	0.468341i
$693$	10.3727	+	9.94483i	0.394027	+	0.377773i
$694$	0.660357	−	1.85777i	0.0250668	−	0.0705201i
$695$	−3.17014	+	11.8311i	−0.120250	+	0.448781i
$696$	5.70844	−	2.51722i	0.216378	−	0.0954151i
$697$	46.3963	−	12.4318i	1.75738	−	0.470890i
$698$	40.7650	+	28.0884i	1.54298	+	1.06316i
$699$	1.24622	−	3.00865i	0.0471365	−	0.113797i
$700$	−15.7068	−	60.4276i	−0.593662	−	2.28395i
$701$	−29.0077	+	12.0154i	−1.09561	+	0.453815i	−0.855959	−	0.517044i	$-0.827032\pi$
$701$	−29.0077	+	12.0154i	−1.09561	+	0.453815i	−0.239648	+	0.970860i	$0.577032\pi$
$702$	2.44272	+	3.77126i	0.0921945	+	0.142337i
$703$	11.1178	−	19.2565i	0.419315	−	0.726274i
$704$	−35.6323	−	24.8652i	−1.34294	−	0.937142i
$705$	13.3747	−	7.72190i	0.503721	−	0.290824i
$706$	2.34128	−	0.119912i	0.0881151	−	0.00451296i
$707$	5.31253	−	9.66605i	0.199798	−	0.363529i
$708$	−0.758265	−	7.38311i	−0.0284973	−	0.277474i
$709$	−22.4482	+	2.95537i	−0.843061	+	0.110991i	−0.539672	−	0.841876i	$-0.681452\pi$
$709$	−22.4482	+	2.95537i	−0.843061	+	0.110991i	−0.303389	+	0.952867i	$0.598118\pi$
$710$	−59.6532	−	4.76612i	−2.23874	−	0.178869i
$711$	0.133062	+	0.496593i	0.00499021	+	0.0186237i
$712$	−1.01581	+	9.34427i	−0.0380689	+	0.350191i
$713$	13.7995	+	13.7995i	0.516797	+	0.516797i
$714$	17.3571	−	6.02347i	0.649573	−	0.225423i
$715$	27.0666	−	65.3445i	1.01223	−	2.44375i
$716$	41.6239	+	25.6434i	1.55556	+	0.958339i
$717$	0.293685	−	2.23076i	0.0109679	−	0.0833093i
$718$	20.9838	−	6.79049i	0.783108	−	0.253419i
$719$	−20.1536	+	11.6357i	−0.751603	+	0.433938i	−0.826273	−	0.563270i	$-0.809543\pi$
$719$	−20.1536	+	11.6357i	−0.751603	+	0.433938i	0.0746700	+	0.997208i	$0.476210\pi$
$720$	13.5553	−	9.22177i	0.505176	−	0.343675i
$721$	5.51695	+	36.0261i	0.205462	+	1.34168i
$722$	−2.64946	−	2.39129i	−0.0986026	−	0.0889945i
$723$	16.3280	+	12.5289i	0.607246	+	0.465956i
$724$	−24.1757	−	25.5974i	−0.898482	−	0.951320i
$725$	20.6479	−	15.8437i	0.766845	−	0.588421i
$726$	25.7291	−	4.73700i	0.954897	−	0.175807i
$727$	−17.4915	+	17.4915i	−0.648724	+	0.648724i	−0.952685	−	0.303960i	$-0.901691\pi$
$727$	−17.4915	+	17.4915i	−0.648724	+	0.648724i	0.303960	+	0.952685i	$0.401691\pi$
$728$	19.4767	+	13.6366i	0.721856	+	0.505406i
$729$	−0.707107	−	0.707107i	−0.0261891	−	0.0261891i
$730$	−10.1971	−	7.02609i	−0.377410	−	0.260047i
$731$	−11.9378	−	15.5577i	−0.441537	−	0.575422i
$732$	4.84785	−	1.84771i	0.179182	−	0.0682934i
$733$	3.77262	−	4.91657i	0.139345	−	0.181598i	−0.718468	−	0.695560i	$-0.755156\pi$
$733$	3.77262	−	4.91657i	0.139345	−	0.181598i	0.857813	+	0.513962i	$0.171823\pi$
$734$	−33.6906	+	1.72552i	−1.24354	+	0.0636901i
$735$	−19.4153	+	21.1236i	−0.716145	+	0.779156i
$736$	6.07778	−	10.3841i	0.224030	−	0.382762i
$737$	16.9805	+	29.4110i	0.625484	+	1.08337i
$738$	−12.3187	−	6.29516i	−0.453459	−	0.231728i
$739$	0.134692	+	0.0177326i	0.00495474	+	0.000652304i	0.133003	−	0.991116i	$-0.457538\pi$
$739$	0.134692	+	0.0177326i	0.00495474	+	0.000652304i	−0.128048	+	0.991768i	$0.540871\pi$
$740$	38.7899	+	6.23823i	1.42595	+	0.229322i
$741$	13.6182	+	5.64083i	0.500276	+	0.207221i
$742$	2.60661	+	36.0253i	0.0956917	+	1.32253i
$743$	−16.8406	+	16.8406i	−0.617822	+	0.617822i	−0.944972	−	0.327150i	$-0.893912\pi$
$743$	−16.8406	+	16.8406i	−0.617822	+	0.617822i	0.327150	+	0.944972i	$0.393912\pi$
$744$	−12.4642	+	22.7623i	−0.456959	+	0.834508i
$745$	90.8841	−	24.3523i	3.32974	−	0.892200i
$746$	−6.14022	−	7.20659i	−0.224809	−	0.263852i
$747$	0.508778	+	3.86455i	0.0186152	+	0.141397i
$748$	15.2704	−	51.1057i	0.558340	−	1.86861i
$749$	21.8317	−	13.2251i	0.797711	−	0.483235i
$750$	26.4059	−	29.2568i	0.964208	−	1.06831i
$751$	1.33389	+	2.31037i	0.0486743	+	0.0843064i	0.889336	−	0.457254i	$-0.151167\pi$
$751$	1.33389	+	2.31037i	0.0486743	+	0.0843064i	−0.840662	+	0.541561i	$0.817834\pi$
$752$	14.3120	+	4.72555i	0.521905	+	0.172323i
$753$	1.49946	+	0.865714i	0.0546434	+	0.0315484i
$754$	−2.07213	+	9.69196i	−0.0754624	+	0.352960i
$755$	15.2533	+	36.8247i	0.555125	+	1.34019i
$756$	−4.87339	−	2.06157i	−0.177243	−	0.0749787i
$757$	28.4174	+	11.7709i	1.03285	+	0.427819i	0.833739	−	0.552158i	$-0.186196\pi$
$757$	28.4174	+	11.7709i	1.03285	+	0.427819i	0.199108	+	0.979978i	$0.436196\pi$
$758$	−44.6418	+	8.21903i	−1.62146	+	0.298528i
$759$	2.98994	+	11.1586i	0.108528	+	0.405031i
$760$	19.4530	−	50.1421i	0.705636	−	1.81884i
$761$	31.5323	+	8.44904i	1.14304	+	0.306278i	0.780174	−	0.625562i	$-0.215130\pi$
$761$	31.5323	+	8.44904i	1.14304	+	0.306278i	0.362869	+	0.931840i	$0.381797\pi$
$762$	11.3097	−	5.37796i	0.409707	−	0.194823i
$763$	−37.2293	+	10.8207i	−1.34779	+	0.391735i
$764$	−0.864745	−	8.41989i	−0.0312854	−	0.304621i
$765$	15.9668	+	12.2517i	0.577280	+	0.442962i
$766$	−10.8624	−	5.55093i	−0.392474	−	0.200563i
$767$	10.2109	+	5.89527i	0.368694	+	0.212866i
$768$	15.5217	+	3.88281i	0.560092	+	0.140109i
$769$			26.5087i			0.955929i	0.878379	+	0.477965i	$0.158625\pi$
$769$			26.5087i			0.955929i	−0.878379	+	0.477965i	$0.841375\pi$
$770$	16.8032	+	81.5812i	0.605547	+	2.93998i
$771$	−1.85313	−	4.47384i	−0.0667387	−	0.161122i
$772$	−15.6812	−	21.6916i	−0.564380	−	0.780697i
$773$	21.5110	−	16.5060i	0.773698	−	0.593679i	−0.144637	−	0.989485i	$-0.546201\pi$
$773$	21.5110	−	16.5060i	0.773698	−	0.593679i	0.918334	+	0.395806i	$0.129535\pi$
$774$	−0.449819	+	5.62997i	−0.0161684	+	0.202365i
$775$	−28.0199	+	104.572i	−1.00651	+	3.75633i
$776$	−13.1971	+	2.04203i	−0.473748	+	0.0733045i
$777$	−5.09824	−	11.6105i	−0.182898	−	0.416526i
$778$	−4.64371	−	1.65063i	−0.166485	−	0.0591781i
$779$	−44.9946	+	5.92365i	−1.61210	+	0.212237i
$780$	−0.743630	+	26.0341i	−0.0266262	+	0.932171i
$781$	55.5940	+	7.31909i	1.98931	+	0.261898i
$782$	14.4437	+	3.08803i	0.516504	+	0.110428i
$783$		−	2.20575i		−	0.0788271i
$784$	−27.9969	−	0.419913i	−0.999888	−	0.0149969i
$785$			4.91348i			0.175370i
$786$	3.02641	−	14.1554i	0.107948	−	0.504907i
$787$	−31.5497	−	4.15360i	−1.12463	−	0.148060i	−0.454811	−	0.890588i	$-0.650293\pi$
$787$	−31.5497	−	4.15360i	−1.12463	−	0.148060i	−0.669815	+	0.742528i	$0.733626\pi$
$788$	0.490676	+	0.519531i	0.0174796	+	0.0185075i
$789$	28.5863	−	3.76345i	1.01770	−	0.133983i
$790$	−0.998082	+	2.80789i	−0.0355101	+	0.0999002i
$791$	3.90749	+	8.89877i	0.138934	+	0.316404i
$792$	−13.1268	+	7.97991i	−0.466441	+	0.283554i
$793$	−2.13312	+	7.96090i	−0.0757492	+	0.282700i
$794$	−52.8764	−	4.22468i	−1.87651	−	0.149928i
$795$	−31.3898	+	24.0863i	−1.11328	+	0.854252i
$796$	0.843492	−	5.24491i	0.0298968	−	0.185901i
$797$	−0.552028	−	1.33271i	−0.0195538	−	0.0472072i	0.913801	−	0.406162i	$-0.133133\pi$
$797$	−0.552028	−	1.33271i	−0.0195538	−	0.0472072i	−0.933355	+	0.358955i	$0.883133\pi$
$798$	−17.0020	+	3.50189i	−0.601864	+	0.123966i
$799$			18.5019i			0.654549i
$800$	66.7453	+	0.396465i	2.35980	+	0.0140171i
$801$	2.87794	+	1.66158i	0.101687	+	0.0587091i
$802$	23.0206	−	45.0482i	0.812887	−	1.59071i
$803$	9.20549	+	7.06362i	0.324855	+	0.249270i
$804$	−9.69999	−	7.89313i	−0.342092	−	0.278369i
$805$	−22.1486	+	6.43747i	−0.780634	+	0.226891i
$806$	−17.7043	−	37.2316i	−0.623608	−	1.31143i
$807$	5.92528	+	1.58767i	0.208580	+	0.0558887i
$808$	8.52413	+	8.14703i	0.299878	+	0.286612i
$809$	−6.15724	−	22.9791i	−0.216477	−	0.807904i	−0.985641	−	0.168853i	$-0.945994\pi$
$809$	−6.15724	−	22.9791i	−0.216477	−	0.807904i	0.769164	−	0.639051i	$-0.220673\pi$
$810$	−1.04954	−	5.70060i	−0.0368771	−	0.200299i
$811$	9.15243	+	3.79106i	0.321385	+	0.133122i	0.537543	−	0.843236i	$-0.319353\pi$
$811$	9.15243	+	3.79106i	0.321385	+	0.133122i	−0.216158	+	0.976358i	$0.569353\pi$
$812$	−4.38560	−	10.8165i	−0.153904	−	0.379584i
$813$	5.22754	+	12.6204i	0.183338	+	0.442617i
$814$	−36.0000	−	7.69675i	−1.26180	−	0.269771i
$815$	23.0793	+	13.3248i	0.808432	+	0.466749i
$816$	1.44796	+	19.5877i	0.0506888	+	0.685705i
$817$	9.26406	+	16.0458i	0.324108	+	0.561372i
$818$	−31.9898	−	28.8726i	−1.11850	−	1.00951i
$819$	7.18978	−	4.35540i	0.251231	−	0.152190i
$820$	−38.0948	−	70.5611i	−1.33033	−	2.46410i
$821$	−3.38388	−	25.7031i	−0.118098	−	0.897044i	−0.943238	−	0.332116i	$-0.892237\pi$
$821$	−3.38388	−	25.7031i	−0.118098	−	0.897044i	0.825140	−	0.564928i	$-0.191096\pi$
$822$	2.50722	−	2.13622i	0.0874494	−	0.0745093i
$823$	−38.6537	+	10.3572i	−1.34738	+	0.361031i	−0.859169	−	0.511692i	$-0.829019\pi$
$823$	−38.6537	+	10.3572i	−1.34738	+	0.361031i	−0.488216	+	0.872723i	$0.662352\pi$
$824$	−38.7343	−	4.21077i	−1.34937	−	0.146689i
$825$	−45.3150	+	45.3150i	−1.57767	+	1.57767i
$826$	−13.8490	+	1.00204i	−0.481868	+	0.0348655i
$827$	−43.7034	−	18.1026i	−1.51972	−	0.629488i	−0.542182	−	0.840261i	$-0.682402\pi$
$827$	−43.7034	−	18.1026i	−1.51972	−	0.629488i	−0.977535	+	0.210773i	$0.932402\pi$
$828$	−2.49222	−	3.44745i	−0.0866108	−	0.119807i
$829$	−8.55337	−	1.12607i	−0.297071	−	0.0391101i	−0.0194823	−	0.999810i	$-0.506202\pi$
$829$	−8.55337	−	1.12607i	−0.297071	−	0.0391101i	−0.277588	+	0.960700i	$0.589535\pi$
$830$	−10.2813	+	20.1191i	−0.356869	+	0.698343i
$831$	11.9721	+	20.7363i	0.415309	+	0.719336i
$832$	−19.4449	+	16.3693i	−0.674131	+	0.567502i
$833$	−10.2860	−	32.7967i	−0.356390	−	1.13634i
$834$	0.216170	+	4.22070i	0.00748535	+	0.146151i
$835$	52.3576	−	68.2338i	1.81191	−	2.36133i
$836$	−20.6070	+	45.9898i	−0.712709	+	1.59059i
$837$	5.58553	+	7.27921i	0.193064	+	0.251606i
$838$	−29.9678	+	43.4926i	−1.03522	+	1.50243i
$839$	−12.0657	−	12.0657i	−0.416553	−	0.416553i	0.467461	−	0.884014i	$-0.345169\pi$
$839$	−12.0657	−	12.0657i	−0.416553	−	0.416553i	−0.884014	+	0.467461i	$0.845169\pi$
$840$	−16.4810	−	25.8676i	−0.568647	−	0.892518i
$841$	−17.0658	+	17.0658i	−0.588475	+	0.588475i
$842$	3.85727	+	20.9508i	0.132930	+	0.722014i
$843$	2.07971	−	1.59582i	0.0716289	−	0.0549628i
$844$	−0.785545	+	27.5016i	−0.0270396	+	0.946643i
$845$	9.44736	+	7.24922i	0.324999	+	0.249381i
$846$	3.57033	−	3.95579i	0.122750	−	0.136003i
$847$	−7.40875	−	48.3798i	−0.254568	−	1.66235i
$848$	−37.9329	−	7.21706i	−1.30262	−	0.247835i
$849$	19.6040	−	11.3184i	0.672808	−	0.388446i
$850$	25.2270	+	77.9556i	0.865278	+	2.67386i
$851$	1.33061	−	10.1070i	0.0456126	−	0.346462i
$852$	−20.0893	+	4.77255i	−0.688246	+	0.163505i
$853$	−11.4542	+	27.6529i	−0.392185	+	0.946818i	0.597279	+	0.802034i	$0.296249\pi$
$853$	−11.4542	+	27.6529i	−0.392185	+	0.946818i	−0.989463	+	0.144784i	$0.953751\pi$
$854$	−3.18210	−	9.16947i	−0.108889	−	0.313773i
$855$	−13.4458	−	13.4458i	−0.459838	−	0.459838i
$856$	7.65673	+	26.1911i	0.261702	+	0.895193i
$857$	−2.91599	−	10.8826i	−0.0996084	−	0.371743i	0.898069	−	0.439854i	$-0.144970\pi$
$857$	−2.91599	−	10.8826i	−0.0996084	−	0.371743i	−0.997678	+	0.0681102i	$0.978303\pi$
$858$	1.94363	−	24.3267i	0.0663545	−	0.830498i
$859$	−6.15789	+	0.810701i	−0.210104	+	0.0276608i	−0.234844	−	0.972033i	$-0.575458\pi$
$859$	−6.15789	+	0.810701i	−0.210104	+	0.0276608i	0.0247392	+	0.999694i	$0.492124\pi$
$860$	−20.6629	+	25.3929i	−0.704598	+	0.865891i
$861$	−12.4657	+	22.6812i	−0.424832	+	0.772973i
$862$	−1.16283	−	22.7041i	−0.0396060	−	0.773304i
$863$	3.84789	−	2.22158i	0.130984	−	0.0756235i	−0.433076	−	0.901357i	$-0.642572\pi$
$863$	3.84789	−	2.22158i	0.130984	−	0.0756235i	0.564060	+	0.825734i	$0.309239\pi$
$864$	3.47027	−	4.46735i	0.118061	−	0.151982i
$865$	−26.5731	+	46.0260i	−0.903513	+	1.56493i
$866$	24.6772	−	15.9839i	0.838566	−	0.543156i
$867$	−6.56951	+	2.72118i	−0.223112	+	0.0924162i
$868$	41.8630	+	24.5900i	1.42092	+	0.834639i
$869$	1.06856	−	2.57974i	0.0362485	−	0.0875117i
$870$	7.25427	−	10.5282i	0.245943	−	0.356940i
$871$	19.1896	−	5.14183i	0.650214	−	0.174224i
$872$	−0.937280	−	41.4362i	−0.0317403	−	1.40321i
$873$	−1.22199	+	4.56053i	−0.0413581	+	0.154350i
$874$	−13.1492	−	4.67396i	−0.444778	−	0.158099i
$875$	−53.2221	−	51.0266i	−1.79924	−	1.72502i
$876$	−4.09389	−	1.22325i	−0.138320	−	0.0413299i
$877$	24.7230	−	32.2196i	0.834836	−	1.08798i	−0.160063	−	0.987107i	$-0.551170\pi$
$877$	24.7230	−	32.2196i	0.834836	−	1.08798i	0.994899	−	0.100873i	$-0.0321636\pi$
$878$	−21.4751	+	6.94948i	−0.724749	+	0.234534i
$879$	5.51798	−	9.55742i	0.186117	−	0.322364i
$880$	−88.8995	−	5.08274i	−2.99680	−	0.171339i
$881$	−2.26533			−0.0763209			−0.0381604	−	0.999272i	$-0.512150\pi$
$881$	−2.26533			−0.0763209			−0.0381604	+	0.999272i	$0.512150\pi$
$882$	−4.12962	+	8.99701i	−0.139052	+	0.302945i
$883$	−5.64390	+	2.33778i	−0.189932	+	0.0786725i	−0.475623	−	0.879649i	$-0.657777\pi$
$883$	−5.64390	+	2.33778i	−0.189932	+	0.0786725i	0.285690	+	0.958322i	$0.407777\pi$
$884$	−26.5652	−	16.3661i	−0.893484	−	0.550452i
$885$	−9.25933	−	12.0670i	−0.311249	−	0.405628i
$886$	16.0134	+	18.7945i	0.537982	+	0.631413i
$887$	21.9614	+	5.88454i	0.737392	+	0.197584i	0.607919	−	0.793999i	$-0.292005\pi$
$887$	21.9614	+	5.88454i	0.737392	+	0.197584i	0.129473	+	0.991583i	$0.458671\pi$
$888$	13.3967	−	2.07291i	0.449563	−	0.0695622i
$889$	−9.41959	−	21.4518i	−0.315923	−	0.719471i
$890$	8.27203	+	17.3958i	0.277279	+	0.583109i
$891$	0.708927	+	5.38483i	0.0237499	+	0.180399i
$892$	−6.35408	+	14.1807i	−0.212750	+	0.474806i
$893$	2.28174	−	17.3315i	0.0763554	−	0.579977i
$894$	27.2484	−	17.6493i	0.911322	−	0.590282i
$895$	100.190			3.34899
$896$	8.13514	−	28.8066i	0.271776	−	0.962361i
$897$	6.75784			0.225638
$898$	34.1712	−	22.1333i	1.14031	−	0.738599i
$899$	−2.64163	+	20.0652i	−0.0881033	+	0.669211i
$900$	9.64954	−	21.5354i	0.321651	−	0.717846i
$901$	−6.18701	−	46.9950i	−0.206119	−	1.56563i
$902$	32.2666	+	67.8557i	1.07436	+	2.25935i
$903$	10.5026	+	1.15829i	0.349505	+	0.0385456i
$904$	−10.2677	+	1.58876i	−0.341500	+	0.0528413i
$905$	−69.6971	−	18.6753i	−2.31681	−	0.620788i
$906$	8.91937	+	10.4684i	0.296326	+	0.347789i
$907$	−26.4499	−	34.4702i	−0.878255	−	1.14456i	−0.988584	−	0.150669i	$-0.951857\pi$
$907$	−26.4499	−	34.4702i	−0.878255	−	1.14456i	0.110329	−	0.993895i	$-0.464810\pi$
$908$	12.2182	+	7.52732i	0.405475	+	0.249803i
$909$	3.85152	−	1.59535i	0.127747	−	0.0529145i
$910$	48.6414	+	2.85710i	1.61245	+	0.0947120i
$911$	−4.75078			−0.157400			−0.0787001	−	0.996898i	$-0.525077\pi$
$911$	−4.75078			−0.157400			−0.0787001	+	0.996898i	$0.525077\pi$
$912$	1.05927	−	18.5272i	0.0350760	−	0.613497i
$913$	10.5853	−	18.3343i	0.350323	−	0.606778i
$914$	2.16809	−	0.701609i	0.0717141	−	0.0232072i
$915$	6.47239	−	8.43498i	0.213971	−	0.278852i
$916$	−40.6024	−	12.1320i	−1.34154	−	0.400852i
$917$	−26.2999	−	6.45671i	−0.868499	−	0.213219i
$918$	6.54311	+	2.32579i	0.215955	+	0.0767625i
$919$	−12.1663	+	45.4053i	−0.401330	+	1.49778i	0.409396	+	0.912357i	$0.365739\pi$
$919$	−12.1663	+	45.4053i	−0.401330	+	1.49778i	−0.810726	+	0.585426i	$0.800927\pi$
$920$	−0.557610	−	24.6513i	−0.0183838	−	0.812731i
$921$	−3.61417	+	0.968413i	−0.119091	+	0.0319103i
$922$	−20.9173	+	30.3575i	−0.688874	+	0.999771i
$923$	12.5528	−	30.3052i	0.413181	−	0.997507i
$924$	14.1828	+	24.9964i	0.466581	+	0.822321i
$925$	52.2466	−	21.6412i	1.71786	−	0.711560i
$926$	20.8747	−	13.5210i	0.685986	−	0.444327i
$927$	−6.88767	+	11.9298i	−0.226221	+	0.391826i
$928$	12.3803	−	1.55515i	0.406404	−	0.0510502i
$929$	−34.4034	+	19.8628i	−1.12874	+	0.651678i	−0.943618	−	0.331037i	$-0.892601\pi$
$929$	−34.4034	+	19.8628i	−1.12874	+	0.651678i	−0.185122	+	0.982715i	$0.559268\pi$
$930$	2.72031	+	53.1139i	0.0892026	+	1.74167i
$931$	5.59073	+	31.9907i	0.183229	+	1.04845i
$932$	4.11082	−	5.05185i	0.134654	−	0.165479i
$933$	−13.3832	+	1.76194i	−0.438147	+	0.0576832i
$934$	3.29106	−	41.1912i	0.107687	−	1.34782i
$935$	−28.2911	−	105.584i	−0.925219	−	3.45296i
$936$	2.52158	+	8.62547i	0.0824204	+	0.281932i
$937$	−19.5085	−	19.5085i	−0.637315	−	0.637315i	0.312577	−	0.949892i	$-0.398808\pi$
$937$	−19.5085	−	19.5085i	−0.637315	−	0.637315i	−0.949892	+	0.312577i	$0.898808\pi$
$938$	−15.3064	+	17.6942i	−0.499772	+	0.577735i
$939$	6.32546	−	15.2710i	0.206423	−	0.498350i
$940$	30.0512	−	7.13919i	0.980163	−	0.232855i
$941$	−4.06185	+	30.8528i	−0.132412	+	1.00577i	0.788234	+	0.615375i	$0.210996\pi$
$941$	−4.06185	+	30.8528i	−0.132412	+	1.00577i	−0.920647	+	0.390397i	$0.872338\pi$
$942$	0.521976	+	1.61300i	0.0170069	+	0.0525542i
$943$	−18.0188	+	10.4032i	−0.586774	+	0.338774i
$944$	2.77441	−	14.5823i	0.0902994	−	0.474614i
$945$	−10.7191	+	1.64150i	−0.348694	+	0.0533980i
$946$	20.5530	−	22.7719i	0.668235	−	0.740380i
$947$	1.38026	+	1.05911i	0.0448525	+	0.0344165i	0.630944	−	0.775828i	$-0.282668\pi$
$947$	1.38026	+	1.05911i	0.0448525	+	0.0344165i	−0.586092	+	0.810245i	$0.699334\pi$
$948$	−0.0293578	+	1.02780i	−0.000953498	+	0.0333815i
$949$	5.38504	−	4.13208i	0.174806	−	0.134133i
$950$	−14.0174	−	76.1356i	−0.454783	−	2.47016i
$951$	6.71019	−	6.71019i	0.217593	−	0.217593i
$952$	36.7101	−	1.60427i	1.18978	−	0.0519946i
$953$	−42.3239	−	42.3239i	−1.37101	−	1.37101i	−0.858954	−	0.512053i	$-0.828885\pi$
$953$	−42.3239	−	42.3239i	−1.37101	−	1.37101i	−0.512053	−	0.858954i	$-0.671115\pi$
$954$	−7.74588	+	11.2417i	−0.250782	+	0.363963i
$955$	−10.5596	−	13.7615i	−0.341700	−	0.445312i
$956$	1.84008	−	4.10661i	0.0595126	−	0.132817i
$957$	−7.29302	+	9.50445i	−0.235750	+	0.307235i
$958$	−2.97105	−	58.0095i	−0.0959903	−	1.87420i
$959$	−3.85346	−	4.80879i	−0.124435	−	0.155284i
$960$	31.2561	−	9.90997i	1.00879	−	0.319843i
$961$	−26.5925	−	46.0596i	−0.857823	−	1.48579i
$962$	−9.79959	+	19.1764i	−0.315951	+	0.618273i
$963$	9.56500	+	1.25926i	0.308228	+	0.0405790i
$964$	24.1153	+	33.3582i	0.776701	+	1.07440i
$965$	−50.6775	−	20.9913i	−1.63137	−	0.675734i
$966$	−6.58705	+	4.46621i	−0.211935	+	0.143698i
$967$	−4.36971	+	4.36971i	−0.140520	+	0.140520i	−0.773868	−	0.633347i	$-0.781680\pi$
$967$	−4.36971	+	4.36971i	−0.140520	+	0.140520i	0.633347	+	0.773868i	$0.281680\pi$
$968$	52.0167	+	5.65467i	1.67188	+	0.181748i
$969$	22.0043	−	5.89604i	0.706880	−	0.189408i
$970$	−20.8313	+	17.7489i	−0.668853	+	0.569881i
$971$	7.93031	+	60.2367i	0.254496	+	1.93309i	0.348056	+	0.937474i	$0.386842\pi$
$971$	7.93031	+	60.2367i	0.254496	+	1.93309i	−0.0935597	+	0.995614i	$0.529825\pi$
$972$	−0.950139	−	1.75990i	−0.0304757	−	0.0564487i
$973$	7.90480	−	0.166477i	0.253416	−	0.00533702i
$974$	−33.4848	−	30.2219i	−1.07292	−	0.968374i
$975$	18.7443	+	32.4660i	0.600297	+	1.03975i
$976$	10.3478	−	0.764934i	0.331226	−	0.0244849i
$977$	41.8851	+	24.1824i	1.34002	+	0.773662i	0.986810	−	0.161881i	$-0.0517561\pi$
$977$	41.8851	+	24.1824i	1.34002	+	0.773662i	0.353212	+	0.935543i	$0.385089\pi$
$978$	8.99201	+	1.92248i	0.287533	+	0.0614741i
$979$	−6.90709	−	16.6752i	−0.220751	−	0.532941i
$980$	−49.3004	+	29.3619i	−1.57484	+	0.937932i
$981$	−13.5382	−	5.60771i	−0.432241	−	0.179040i
$982$	−1.61109	−	8.75067i	−0.0514120	−	0.279245i
$983$	12.7316	+	47.5149i	0.406074	+	1.51549i	0.802066	+	0.597235i	$0.203734\pi$
$983$	12.7316	+	47.5149i	0.406074	+	1.51549i	−0.395992	+	0.918254i	$0.629599\pi$
$984$	−20.0017	−	19.1168i	−0.637631	−	0.609423i
$985$	1.41459	+	0.379039i	0.0450726	+	0.0120772i
$986$	6.57777	+	13.8328i	0.209479	+	0.440527i
$987$	−7.19613	−	6.89927i	−0.229055	−	0.219606i
$988$	22.8664	+	18.6070i	0.727479	+	0.591968i
$989$	6.73910	+	5.17109i	0.214291	+	0.164431i
$990$	−14.3259	+	28.0337i	−0.455306	+	0.890970i
$991$	−28.3011	−	16.3396i	−0.899014	−	0.519046i	−0.0221337	−	0.999755i	$-0.507046\pi$
$991$	−28.3011	−	16.3396i	−0.899014	−	0.519046i	−0.876880	+	0.480709i	$0.840379\pi$
$992$	−36.9183	+	36.4823i	−1.17216	+	1.15831i
$993$		−	4.21648i		−	0.133806i
$994$	7.79293	+	37.8354i	0.247177	+	1.20006i
$995$	−4.16617	−	10.0580i	−0.132077	−	0.318861i
$996$	−1.23782	+	7.69690i	−0.0392219	+	0.243886i
$997$	−0.0339786	+	0.0260727i	−0.00107611	+	0.000825731i	−0.609299	−	0.792940i	$-0.708549\pi$
$997$	−0.0339786	+	0.0260727i	−0.00107611	+	0.000825731i	0.608223	+	0.793766i	$0.291883\pi$
$998$	40.2513	+	3.21597i	1.27413	+	0.101800i
$999$	1.24047	−	4.62949i	0.0392467	−	0.146471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.cf.a.619.52	yes	512
7.5	odd	6	inner	672.2.cf.a.523.12	yes	512
32.3	odd	8	inner	672.2.cf.a.451.12	yes	512
224.131	even	24	inner	672.2.cf.a.355.52	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.cf.a.355.52	✓	512	224.131	even	24	inner
672.2.cf.a.451.12	yes	512	32.3	odd	8	inner
672.2.cf.a.523.12	yes	512	7.5	odd	6	inner
672.2.cf.a.619.52	yes	512	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.cf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18697 - 0.768826i) q^{2} +(0.130526 - 0.991445i) q^{3} +(0.817812 - 1.82515i) q^{4} +(-0.534986 - 4.06362i) q^{5} +(-0.607318 - 1.27717i) q^{6} +(-2.42250 + 1.06373i) q^{7} +(-0.432504 - 2.79516i) q^{8} +(-0.965926 - 0.258819i) q^{9} +O(q^{10})\)	\(q+(1.18697 - 0.768826i) q^{2} +(0.130526 - 0.991445i) q^{3} +(0.817812 - 1.82515i) q^{4} +(-0.534986 - 4.06362i) q^{5} +(-0.607318 - 1.27717i) q^{6} +(-2.42250 + 1.06373i) q^{7} +(-0.432504 - 2.79516i) q^{8} +(-0.965926 - 0.258819i) q^{9} +(-3.75923 - 4.41210i) q^{10} +(3.30637 + 4.30894i) q^{11} +(-1.70279 - 1.04905i) q^{12} +(2.93536 - 1.21586i) q^{13} +(-2.05762 + 3.12510i) q^{14} -4.09868 q^{15} +(-2.66237 - 2.98526i) q^{16} +(2.45514 - 4.25242i) q^{17} +(-1.34552 + 0.435418i) q^{18} +(-2.82426 + 3.68065i) q^{19} +(-7.85425 - 2.34685i) q^{20} +(0.738429 + 2.54061i) q^{21} +(7.23739 + 2.57258i) q^{22} +(-0.550501 + 2.05450i) q^{23} +(-2.82770 + 0.0639623i) q^{24} +(-11.3972 + 3.05386i) q^{25} +(2.54940 - 3.69998i) q^{26} +(-0.382683 + 0.923880i) q^{27} +(-0.0396792 + 5.29135i) q^{28} +(-2.03785 + 0.844105i) q^{29} +(-4.86503 + 3.15118i) q^{30} +(4.58762 - 7.94599i) q^{31} +(-5.45531 - 1.49653i) q^{32} +(4.70364 - 2.71565i) q^{33} +(-0.355192 - 6.93509i) q^{34} +(5.61859 + 9.27502i) q^{35} +(-1.26233 + 1.55130i) q^{36} +(-4.75180 + 0.625586i) q^{37} +(-0.522544 + 6.54021i) q^{38} +(-0.822322 - 3.06895i) q^{39} +(-11.1271 + 3.25291i) q^{40} +(6.91702 + 6.91702i) q^{41} +(2.82979 + 2.44792i) q^{42} +(1.52831 - 3.68968i) q^{43} +(10.5685 - 2.51072i) q^{44} +(-0.534986 + 4.06362i) q^{45} +(0.926122 + 2.86188i) q^{46} +(-3.26317 + 1.88399i) q^{47} +(-3.30723 + 2.24993i) q^{48} +(4.73696 - 5.15375i) q^{49} +(-11.1802 + 12.3873i) q^{50} +(-3.89558 - 2.98919i) q^{51} +(0.181431 - 6.35182i) q^{52} +(7.65851 - 5.87658i) q^{53} +(0.256068 + 1.39084i) q^{54} +(15.7410 - 15.7410i) q^{55} +(4.02103 + 6.31120i) q^{56} +(3.28052 + 3.28052i) q^{57} +(-1.76990 + 2.56868i) q^{58} +(2.25910 + 2.94411i) q^{59} +(-3.35195 + 7.48073i) q^{60} +(-1.57914 + 2.05797i) q^{61} +(-0.663704 - 12.9588i) q^{62} +(2.61526 - 0.400495i) q^{63} +(-7.62588 + 2.41784i) q^{64} +(-6.51118 - 11.2777i) q^{65} +(3.49524 - 6.83969i) q^{66} +(6.19933 + 0.816157i) q^{67} +(-5.75348 - 7.95868i) q^{68} +(1.96507 + 0.813958i) q^{69} +(13.8000 + 6.68948i) q^{70} +(7.30030 - 7.30030i) q^{71} +(-0.305674 + 2.81186i) q^{72} +(2.06358 - 0.552933i) q^{73} +(-5.15929 + 4.39586i) q^{74} +(1.54011 + 11.6983i) q^{75} +(4.40804 + 8.16480i) q^{76} +(-12.5932 - 6.92131i) q^{77} +(-3.33556 - 3.01054i) q^{78} +(-0.257056 - 0.445233i) q^{79} +(-10.7067 + 12.4159i) q^{80} +(0.866025 + 0.500000i) q^{81} +(13.5283 + 2.89233i) q^{82} +(-1.49166 - 3.60119i) q^{83} +(5.24091 + 0.730000i) q^{84} +(-18.5937 - 7.70176i) q^{85} +(-1.02265 - 5.55456i) q^{86} +(0.570891 + 2.13059i) q^{87} +(10.6142 - 11.1055i) q^{88} +(-3.20993 - 0.860098i) q^{89} +(2.48920 + 5.23472i) q^{90} +(-5.81754 + 6.06785i) q^{91} +(3.29957 + 2.68494i) q^{92} +(-7.27921 - 5.58553i) q^{93} +(-2.42484 + 4.74507i) q^{94} +(16.4677 + 9.50764i) q^{95} +(-2.19579 + 5.21330i) q^{96} -4.72140i q^{97} +(1.66031 - 9.75927i) q^{98} +(-2.07847 - 5.01787i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q + 64 q^{14} + 8 q^{16} - 8 q^{18} - 16 q^{22} - 16 q^{23} - 40 q^{28} + 48 q^{35} + 32 q^{43} + 8 q^{44} + 48 q^{50} - 72 q^{52} + 32 q^{53} + 32 q^{58} - 192 q^{59} - 48 q^{60} + 144 q^{64} - 144 q^{66} - 16 q^{67} - 72 q^{70} + 128 q^{71} + 32 q^{74} + 48 q^{78} - 72 q^{80} - 120 q^{82} + 88 q^{88} - 48 q^{91} + 128 q^{92} - 72 q^{94} - 120 q^{96} - 136 q^{98}+O(q^{100}) \) 512 * q + 64 * q^14 + 8 * q^16 - 8 * q^18 - 16 * q^22 - 16 * q^23 - 40 * q^28 + 48 * q^35 + 32 * q^43 + 8 * q^44 + 48 * q^50 - 72 * q^52 + 32 * q^53 + 32 * q^58 - 192 * q^59 - 48 * q^60 + 144 * q^64 - 144 * q^66 - 16 * q^67 - 72 * q^70 + 128 * q^71 + 32 * q^74 + 48 * q^78 - 72 * q^80 - 120 * q^82 + 88 * q^88 - 48 * q^91 + 128 * q^92 - 72 * q^94 - 120 * q^96 - 136 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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