LMFDB - Embedded newform 370.2.r.e.347.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(23,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("370.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.r (of order $12$, degree $4$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			347.3
Root			$2.69978 - 0.355433i$ of defining polynomial
Character	$\chi$	$=$	370.347
Dual form			370.2.r.e.193.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.124844 - 0.465926i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.99671 - 1.00656i) q^{5} +(-0.341081 + 0.341081i) q^{6} +(-0.510450 + 1.90503i) q^{7} -1.00000i q^{8} +(2.39658 + 1.38366i) q^{9} +(1.22592 + 1.87006i) q^{10} +5.36697i q^{11} +(0.465926 - 0.124844i) q^{12} +(5.68547 - 3.28251i) q^{13} +(1.39458 - 1.39458i) q^{14} +(-0.718260 + 0.804654i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.89059 - 3.27460i) q^{17} +(-1.38366 - 2.39658i) q^{18} +(1.79370 - 6.69417i) q^{19} +(-0.126648 - 2.23248i) q^{20} +(0.823874 + 0.475664i) q^{21} +(2.68348 - 4.64793i) q^{22} +4.59101i q^{23} +(-0.465926 - 0.124844i) q^{24} +(2.97368 + 4.01961i) q^{25} -6.56502 q^{26} +(1.96713 - 1.96713i) q^{27} +(-1.90503 + 0.510450i) q^{28} +(-3.86934 + 3.86934i) q^{29} +(1.02436 - 0.337721i) q^{30} +(4.40372 + 4.40372i) q^{31} +(0.866025 - 0.500000i) q^{32} +(2.50061 + 0.670036i) q^{33} +(-3.27460 + 1.89059i) q^{34} +(2.93674 - 3.28998i) q^{35} +2.76733i q^{36} +(0.586988 - 6.05437i) q^{37} +(-4.90047 + 4.90047i) q^{38} +(-0.819606 - 3.05881i) q^{39} +(-1.00656 + 1.99671i) q^{40} +(3.09785 - 1.78854i) q^{41} +(-0.475664 - 0.823874i) q^{42} -3.24741i q^{43} +(-4.64793 + 2.68348i) q^{44} +(-3.39252 - 5.17507i) q^{45} +(2.29550 - 3.97593i) q^{46} +(2.56542 + 2.56542i) q^{47} +(0.341081 + 0.341081i) q^{48} +(2.69361 + 1.55516i) q^{49} +(-0.565478 - 4.96792i) q^{50} +(-1.28969 - 1.28969i) q^{51} +(5.68547 + 3.28251i) q^{52} +(1.62928 + 6.08055i) q^{53} +(-2.68715 + 0.720019i) q^{54} +(5.40217 - 10.7163i) q^{55} +(1.90503 + 0.510450i) q^{56} +(-2.89505 - 1.67146i) q^{57} +(5.28562 - 1.41628i) q^{58} +(-4.19024 + 1.12277i) q^{59} +(-1.05598 - 0.219704i) q^{60} +(-3.33371 + 12.4416i) q^{61} +(-1.61187 - 6.01559i) q^{62} +(-3.85925 + 3.85925i) q^{63} -1.00000 q^{64} +(-14.6563 + 0.831446i) q^{65} +(-1.83057 - 1.83057i) q^{66} +(4.86964 + 1.30482i) q^{67} +3.78118 q^{68} +(2.13907 + 0.573162i) q^{69} +(-4.18828 + 1.38084i) q^{70} +(3.00672 + 5.20780i) q^{71} +(1.38366 - 2.39658i) q^{72} +(-6.42799 - 6.42799i) q^{73} +(-3.53553 + 4.94975i) q^{74} +(2.24409 - 0.883688i) q^{75} +(6.69417 - 1.79370i) q^{76} +(-10.2242 - 2.73957i) q^{77} +(-0.819606 + 3.05881i) q^{78} +(-1.70817 + 6.37497i) q^{79} +(1.87006 - 1.22592i) q^{80} +(3.48004 + 6.02761i) q^{81} -3.57709 q^{82} +(-1.55206 - 5.79235i) q^{83} +0.951328i q^{84} +(-7.07103 + 4.63542i) q^{85} +(-1.62370 + 2.81234i) q^{86} +(1.31976 + 2.28589i) q^{87} +5.36697 q^{88} +(-4.07258 - 15.1991i) q^{89} +(0.350476 + 6.17800i) q^{90} +(3.35112 + 12.5065i) q^{91} +(-3.97593 + 2.29550i) q^{92} +(2.60158 - 1.50203i) q^{93} +(-0.939010 - 3.50443i) q^{94} +(-10.3196 + 11.5608i) q^{95} +(-0.124844 - 0.465926i) q^{96} -0.635573 q^{97} +(-1.55516 - 2.69361i) q^{98} +(-7.42608 + 12.8623i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{3} + 8 q^{4} - 8 q^{6} + 24 q^{9} - 4 q^{10} - 8 q^{12} + 12 q^{13} - 8 q^{16} - 16 q^{17} + 24 q^{19} + 12 q^{20} - 12 q^{21} + 8 q^{22} + 8 q^{24} + 16 q^{25} + 8 q^{26} - 16 q^{27} - 16 q^{29}+ \cdots - 8 q^{99}+O(q^{100}) $ 16 * q - 16 * q^3 + 8 * q^4 - 8 * q^6 + 24 * q^9 - 4 * q^10 - 8 * q^12 + 12 * q^13 - 8 * q^16 - 16 * q^17 + 24 * q^19 + 12 * q^20 - 12 * q^21 + 8 * q^22 + 8 * q^24 + 16 * q^25 + 8 * q^26 - 16 * q^27 - 16 * q^29 - 8 * q^30 + 24 * q^31 + 12 * q^33 - 8 * q^35 - 8 * q^40 - 36 * q^41 + 4 * q^42 + 20 * q^45 + 4 * q^46 + 32 * q^47 + 8 * q^48 - 24 * q^49 - 4 * q^50 - 16 * q^51 + 12 * q^52 + 24 * q^53 + 8 * q^54 - 12 * q^55 - 60 * q^57 + 8 * q^58 + 8 * q^59 - 12 * q^60 + 8 * q^61 + 12 * q^62 + 16 * q^63 - 16 * q^64 + 12 * q^65 - 24 * q^66 + 8 * q^67 - 32 * q^68 + 8 * q^69 - 20 * q^70 + 4 * q^71 - 48 * q^73 - 36 * q^75 + 24 * q^76 - 12 * q^77 - 20 * q^79 + 12 * q^80 + 16 * q^81 - 24 * q^82 - 48 * q^83 - 8 * q^85 + 8 * q^86 - 12 * q^87 + 16 * q^88 + 8 * q^89 + 4 * q^90 - 8 * q^91 + 12 * q^92 - 36 * q^93 + 28 * q^94 + 8 * q^95 + 16 * q^96 + 16 * q^97 - 8 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.124844	−	0.465926i	0.0720790	−	0.269002i	−0.920476	−	0.390799i	$-0.872199\pi$
$3$	0.124844	−	0.465926i	0.0720790	−	0.269002i	0.992555	+	0.121796i	$0.0388655\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.99671	−	1.00656i	−0.892955	−	0.450147i
$5$	−1.99671	−	1.00656i	−0.892955	−	0.450147i
$6$	−0.341081	+	0.341081i	−0.139246	+	0.139246i
$7$	−0.510450	+	1.90503i	−0.192932	+	0.720032i	0.799860	+	0.600186i	$0.204907\pi$
$7$	−0.510450	+	1.90503i	−0.192932	+	0.720032i	−0.992792	+	0.119846i	$0.961760\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.39658	+	1.38366i	0.798858	+	0.461221i
$10$	1.22592	+	1.87006i	0.387670	+	0.591365i
$11$			5.36697i			1.61820i	0.587670	+	0.809101i	$0.300045\pi$
$11$			5.36697i			1.61820i	−0.587670	+	0.809101i	$0.699955\pi$
$12$	0.465926	−	0.124844i	0.134501	−	0.0360395i
$13$	5.68547	−	3.28251i	1.57687	−	0.910404i	0.581573	−	0.813494i	$-0.302438\pi$
$13$	5.68547	−	3.28251i	1.57687	−	0.910404i	0.995293	−	0.0969097i	$-0.0308958\pi$
$14$	1.39458	−	1.39458i	0.372716	−	0.372716i
$15$	−0.718260	+	0.804654i	−0.185454	+	0.207761i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.89059	−	3.27460i	0.458535	−	0.794207i	−0.540348	−	0.841441i	$-0.681708\pi$
$17$	1.89059	−	3.27460i	0.458535	−	0.794207i	0.998884	+	0.0472348i	$0.0150409\pi$
$18$	−1.38366	−	2.39658i	−0.326133	−	0.564878i
$19$	1.79370	−	6.69417i	0.411503	−	1.53575i	−0.380237	−	0.924889i	$-0.624158\pi$
$19$	1.79370	−	6.69417i	0.411503	−	1.53575i	0.791739	−	0.610859i	$-0.209176\pi$
$20$	−0.126648	−	2.23248i	−0.0283193	−	0.499197i
$21$	0.823874	+	0.475664i	0.179784	+	0.103798i
$22$	2.68348	−	4.64793i	0.572121	−	0.990942i
$23$			4.59101i			0.957292i	0.878008	+	0.478646i	$0.158872\pi$
$23$			4.59101i			0.957292i	−0.878008	+	0.478646i	$0.841128\pi$
$24$	−0.465926	−	0.124844i	−0.0951067	−	0.0254838i
$25$	2.97368	+	4.01961i	0.594736	+	0.803921i
$26$	−6.56502			−1.28751
$27$	1.96713	−	1.96713i	0.378574	−	0.378574i
$28$	−1.90503	+	0.510450i	−0.360016	+	0.0964661i
$29$	−3.86934	+	3.86934i	−0.718519	+	0.718519i	−0.968302	−	0.249783i	$-0.919641\pi$
$29$	−3.86934	+	3.86934i	−0.718519	+	0.718519i	0.249783	+	0.968302i	$0.419641\pi$
$30$	1.02436	−	0.337721i	0.187021	−	0.0616592i
$31$	4.40372	+	4.40372i	0.790931	+	0.790931i	0.981646	−	0.190715i	$-0.0610805\pi$
$31$	4.40372	+	4.40372i	0.790931	+	0.790931i	−0.190715	+	0.981646i	$0.561081\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	2.50061	+	0.670036i	0.435300	+	0.116638i
$34$	−3.27460	+	1.89059i	−0.561589	+	0.324233i
$35$	2.93674	−	3.28998i	0.496400	−	0.556109i
$36$			2.76733i			0.461221i
$37$	0.586988	−	6.05437i	0.0965003	−	0.995333i
$37$	0.586988	−	6.05437i	0.0965003	−	0.995333i
$38$	−4.90047	+	4.90047i	−0.794962	+	0.794962i
$39$	−0.819606	−	3.05881i	−0.131242	−	0.489802i
$40$	−1.00656	+	1.99671i	−0.159151	+	0.315707i
$41$	3.09785	−	1.78854i	0.483803	−	0.279324i	−0.238197	−	0.971217i	$-0.576556\pi$
$41$	3.09785	−	1.78854i	0.483803	−	0.279324i	0.722000	+	0.691893i	$0.243223\pi$
$42$	−0.475664	−	0.823874i	−0.0733966	−	0.127127i
$43$		−	3.24741i		−	0.495225i	−0.968859	−	0.247612i	$-0.920354\pi$
$43$		−	3.24741i		−	0.495225i	0.968859	−	0.247612i	$-0.0796460\pi$
$44$	−4.64793	+	2.68348i	−0.700702	+	0.404550i
$45$	−3.39252	−	5.17507i	−0.505727	−	0.771453i
$46$	2.29550	−	3.97593i	0.338454	−	0.586219i
$47$	2.56542	+	2.56542i	0.374205	+	0.374205i	0.869006	−	0.494801i	$-0.164759\pi$
$47$	2.56542	+	2.56542i	0.374205	+	0.374205i	−0.494801	+	0.869006i	$0.664759\pi$
$48$	0.341081	+	0.341081i	0.0492309	+	0.0492309i
$49$	2.69361	+	1.55516i	0.384801	+	0.222165i
$50$	−0.565478	−	4.96792i	−0.0799706	−	0.702570i
$51$	−1.28969	−	1.28969i	−0.180593	−	0.180593i
$52$	5.68547	+	3.28251i	0.788433	+	0.455202i
$53$	1.62928	+	6.08055i	0.223798	+	0.835227i	0.982882	+	0.184234i	$0.0589805\pi$
$53$	1.62928	+	6.08055i	0.223798	+	0.835227i	−0.759084	+	0.650993i	$0.774353\pi$
$54$	−2.68715	+	0.720019i	−0.365674	+	0.0979821i
$55$	5.40217	−	10.7163i	0.728428	−	1.44498i
$56$	1.90503	+	0.510450i	0.254570	+	0.0682118i
$57$	−2.89505	−	1.67146i	−0.383459	−	0.221390i
$58$	5.28562	−	1.41628i	0.694036	−	0.185966i
$59$	−4.19024	+	1.12277i	−0.545522	+	0.146172i	−0.521047	−	0.853528i	$-0.674458\pi$
$59$	−4.19024	+	1.12277i	−0.545522	+	0.146172i	−0.0244756	+	0.999700i	$0.507792\pi$
$60$	−1.05598	−	0.219704i	−0.136327	−	0.0283637i
$61$	−3.33371	+	12.4416i	−0.426838	+	1.59298i	0.333039	+	0.942913i	$0.391926\pi$
$61$	−3.33371	+	12.4416i	−0.426838	+	1.59298i	−0.759877	+	0.650067i	$0.774741\pi$
$62$	−1.61187	−	6.01559i	−0.204708	−	0.763981i
$63$	−3.85925	+	3.85925i	−0.486220	+	0.486220i
$64$	−1.00000			−0.125000
$65$	−14.6563	+	0.831446i	−1.81789	+	0.103128i
$66$	−1.83057	−	1.83057i	−0.225328	−	0.225328i
$67$	4.86964	+	1.30482i	0.594921	+	0.159409i	0.543701	−	0.839279i	$-0.317022\pi$
$67$	4.86964	+	1.30482i	0.594921	+	0.159409i	0.0512200	+	0.998687i	$0.483689\pi$
$68$	3.78118			0.458535
$69$	2.13907	+	0.573162i	0.257514	+	0.0690006i
$70$	−4.18828	+	1.38084i	−0.500596	+	0.165042i
$71$	3.00672	+	5.20780i	0.356832	+	0.618052i	0.987430	−	0.158058i	$-0.0505234\pi$
$71$	3.00672	+	5.20780i	0.356832	+	0.618052i	−0.630597	+	0.776110i	$0.717190\pi$
$72$	1.38366	−	2.39658i	0.163066	−	0.282439i
$73$	−6.42799	−	6.42799i	−0.752340	−	0.752340i	0.222576	−	0.974915i	$-0.428553\pi$
$73$	−6.42799	−	6.42799i	−0.752340	−	0.752340i	−0.974915	+	0.222576i	$0.928553\pi$
$74$	−3.53553	+	4.94975i	−0.410997	+	0.575396i
$75$	2.24409	−	0.883688i	0.259125	−	0.102040i
$76$	6.69417	−	1.79370i	0.767874	−	0.205751i
$77$	−10.2242	−	2.73957i	−1.16516	−	0.312203i
$78$	−0.819606	+	3.05881i	−0.0928021	+	0.346342i
$79$	−1.70817	+	6.37497i	−0.192184	+	0.717240i	0.800794	+	0.598940i	$0.204411\pi$
$79$	−1.70817	+	6.37497i	−0.192184	+	0.717240i	−0.992978	+	0.118300i	$0.962255\pi$
$80$	1.87006	−	1.22592i	0.209079	−	0.137062i
$81$	3.48004	+	6.02761i	0.386671	+	0.669734i
$82$	−3.57709			−0.395023
$83$	−1.55206	−	5.79235i	−0.170360	−	0.635793i	−0.997296	−	0.0734962i	$-0.976584\pi$
$83$	−1.55206	−	5.79235i	−0.170360	−	0.635793i	0.826935	−	0.562297i	$-0.190082\pi$
$84$			0.951328i			0.103798i
$85$	−7.07103	+	4.63542i	−0.766961	+	0.502782i
$86$	−1.62370	+	2.81234i	−0.175088	+	0.303262i
$87$	1.31976	+	2.28589i	0.141493	+	0.245073i
$88$	5.36697			0.572121
$89$	−4.07258	−	15.1991i	−0.431692	−	1.61110i	−0.748861	−	0.662728i	$-0.769399\pi$
$89$	−4.07258	−	15.1991i	−0.431692	−	1.61110i	0.317168	−	0.948369i	$-0.397268\pi$
$90$	0.350476	+	6.17800i	0.0369435	+	0.651218i
$91$	3.35112	+	12.5065i	0.351292	+	1.31104i
$92$	−3.97593	+	2.29550i	−0.414519	+	0.239323i
$93$	2.60158	−	1.50203i	0.269772	−	0.155753i
$94$	−0.939010	−	3.50443i	−0.0968515	−	0.361455i
$95$	−10.3196	+	11.5608i	−1.05877	+	1.18612i
$96$	−0.124844	−	0.465926i	−0.0127419	−	0.0475534i
$97$	−0.635573			−0.0645326			−0.0322663	−	0.999479i	$-0.510272\pi$
$97$	−0.635573			−0.0645326			−0.0322663	+	0.999479i	$0.510272\pi$
$98$	−1.55516	−	2.69361i	−0.157095	−	0.272096i
$99$	−7.42608	+	12.8623i	−0.746349	+	1.29271i
$100$	−1.99424	+	4.58508i	−0.199424	+	0.458508i
$101$		−	16.1219i		−	1.60419i	−0.597194	−	0.802097i	$-0.703718\pi$
$101$		−	16.1219i		−	1.60419i	0.597194	−	0.802097i	$-0.296282\pi$
$102$	0.472059	+	1.76175i	0.0467408	+	0.174439i
$103$	−18.2655			−1.79975			−0.899875	−	0.436149i	$-0.856342\pi$
$103$	−18.2655			−1.79975			−0.899875	+	0.436149i	$0.856342\pi$
$104$	−3.28251	−	5.68547i	−0.321876	−	0.557506i
$105$	−1.16625	−	1.77904i	−0.113815	−	0.173617i
$106$	1.62928	−	6.08055i	0.158249	−	0.590595i
$107$	−0.321755	+	1.20081i	−0.0311052	+	0.116086i	−0.979733	−	0.200308i	$-0.935806\pi$
$107$	−0.321755	+	1.20081i	−0.0311052	+	0.116086i	0.948628	+	0.316395i	$0.102472\pi$
$108$	2.68715	+	0.720019i	0.258571	+	0.0692838i
$109$	−4.53766	+	1.21586i	−0.434629	+	0.116459i	−0.469498	−	0.882933i	$-0.655565\pi$
$109$	−4.53766	+	1.21586i	−0.434629	+	0.116459i	0.0348691	+	0.999392i	$0.488899\pi$
$110$	−10.0365	+	6.57947i	−0.956947	+	0.627328i
$111$	−2.74761	−	1.02935i	−0.260791	−	0.0977014i
$112$	−1.39458	−	1.39458i	−0.131775	−	0.131775i
$113$	0.952037	−	1.64898i	0.0895601	−	0.155123i	−0.817765	−	0.575552i	$-0.804787\pi$
$113$	0.952037	−	1.64898i	0.0895601	−	0.155123i	0.907325	+	0.420429i	$0.138121\pi$
$114$	1.67146	+	2.89505i	0.156547	+	0.271147i
$115$	4.62112	−	9.16690i	0.430922	−	0.854818i
$116$	−5.28562	−	1.41628i	−0.490757	−	0.131498i
$117$	18.1675			1.67959
$118$	4.19024	+	1.12277i	0.385742	+	0.103359i
$119$	5.27314	+	5.27314i	0.483388	+	0.483388i
$120$	0.804654	+	0.718260i	0.0734545	+	0.0655678i
$121$	−17.8043			−1.61857
$122$	9.10786	−	9.10786i	0.824587	−	0.824587i
$123$	−0.446580	−	1.66666i	−0.0402667	−	0.150278i
$124$	−1.61187	+	6.01559i	−0.144750	+	0.540216i
$125$	−1.89159	−	11.0192i	−0.169189	−	0.985584i
$126$	5.27183	−	1.41258i	0.469652	−	0.125843i
$127$	−1.24644	+	0.333984i	−0.110604	+	0.0296363i	−0.313697	−	0.949523i	$-0.601567\pi$
$127$	−1.24644	+	0.333984i	−0.110604	+	0.0296363i	0.203092	+	0.979160i	$0.434901\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−1.51305	−	0.405421i	−0.133217	−	0.0356953i
$130$	13.1084	+	6.60808i	1.14968	+	0.579567i
$131$	5.56678	−	1.49161i	0.486372	−	0.130323i	−0.00729635	−	0.999973i	$-0.502323\pi$
$131$	5.56678	−	1.49161i	0.486372	−	0.130323i	0.493668	+	0.869651i	$0.335656\pi$
$132$	0.670036	+	2.50061i	0.0583191	+	0.217650i
$133$	11.8370	+	6.83409i	1.02640	+	0.592590i
$134$	−3.56483	−	3.56483i	−0.307954	−	0.307954i
$135$	−5.90781	+	1.94775i	−0.508463	+	0.167635i
$136$	−3.27460	−	1.89059i	−0.280794	−	0.162117i
$137$	1.13890	+	1.13890i	0.0973027	+	0.0973027i	0.754082	−	0.656780i	$-0.228082\pi$
$137$	1.13890	+	1.13890i	0.0973027	+	0.0973027i	−0.656780	+	0.754082i	$0.728082\pi$
$138$	−1.56591	−	1.56591i	−0.133299	−	0.133299i
$139$	−5.21999	+	9.04129i	−0.442754	+	0.766872i	−0.997893	−	0.0648856i	$-0.979332\pi$
$139$	−5.21999	+	9.04129i	−0.442754	+	0.766872i	0.555139	+	0.831758i	$0.312665\pi$
$140$	4.31758	+	0.898302i	0.364902	+	0.0759204i
$141$	1.51558	−	0.875018i	0.127634	−	0.0736898i
$142$		−	6.01345i		−	0.504637i
$143$	17.6171	+	30.5137i	1.47322	+	2.55169i
$144$	−2.39658	+	1.38366i	−0.199715	+	0.115305i
$145$	11.6207	−	3.83122i	0.965044	−	0.318166i
$146$	2.35281	+	8.78080i	0.194720	+	0.726704i
$147$	1.06087	−	1.06087i	0.0874991	−	0.0874991i
$148$	5.53674	−	2.51884i	0.455117	−	0.207047i
$149$		−	19.7607i		−	1.61886i	−0.587218	−	0.809429i	$-0.699777\pi$
$149$		−	19.7607i		−	1.61886i	0.587218	−	0.809429i	$-0.300223\pi$
$150$	−2.38528	−	0.356747i	−0.194757	−	0.0291282i
$151$	−0.431688	+	0.249235i	−0.0351302	+	0.0202825i	−0.517462	−	0.855706i	$-0.673123\pi$
$151$	−0.431688	+	0.249235i	−0.0351302	+	0.0202825i	0.482332	+	0.875988i	$0.339790\pi$
$152$	−6.69417	−	1.79370i	−0.542969	−	0.145488i
$153$	9.06188	−	5.23188i	0.732610	−	0.422972i
$154$	7.48464	+	7.48464i	0.603130	+	0.603130i
$155$	−4.36033	−	13.2255i	−0.350230	−	1.06230i
$156$	2.23920	−	2.23920i	0.179280	−	0.179280i
$157$	−5.13368	+	1.37557i	−0.409712	+	0.109782i	−0.457788	−	0.889062i	$-0.651358\pi$
$157$	−5.13368	+	1.37557i	−0.409712	+	0.109782i	0.0480752	+	0.998844i	$0.484691\pi$
$158$	4.66680	−	4.66680i	0.371271	−	0.371271i
$159$	3.03649			0.240809
$160$	−2.23248	+	0.126648i	−0.176493	+	0.0100124i
$161$	−8.74600	−	2.34348i	−0.689281	−	0.184692i
$162$		−	6.96008i		−	0.546835i
$163$	7.10613	−	12.3082i	0.556595	−	0.964051i	−0.441183	−	0.897417i	$-0.645441\pi$
$163$	7.10613	−	12.3082i	0.556595	−	0.964051i	0.997778	−	0.0666334i	$-0.0212258\pi$
$164$	3.09785	+	1.78854i	0.241901	+	0.139662i
$165$	−4.31855	−	3.85487i	−0.336199	−	0.300102i
$166$	−1.55206	+	5.79235i	−0.120463	+	0.449574i
$167$	−5.30594	−	9.19015i	−0.410586	−	0.711155i	0.584368	−	0.811489i	$-0.301342\pi$
$167$	−5.30594	−	9.19015i	−0.410586	−	0.711155i	−0.994954	+	0.100333i	$0.968009\pi$
$168$	0.475664	−	0.823874i	0.0366983	−	0.0635633i
$169$	15.0497	−	26.0669i	1.15767	−	2.00514i
$170$	8.44140	−	0.478879i	0.647426	−	0.0367283i
$171$	13.5612	−	13.5612i	1.03705	−	1.03705i
$172$	2.81234	−	1.62370i	0.214439	−	0.123806i
$173$	−11.5831	+	3.10368i	−0.880646	+	0.235969i	−0.670686	−	0.741741i	$-0.734000\pi$
$173$	−11.5831	+	3.10368i	−0.880646	+	0.235969i	−0.209960	+	0.977710i	$0.567334\pi$
$174$		−	2.63952i		−	0.200102i
$175$	−9.17537	+	3.61313i	−0.693593	+	0.273127i
$176$	−4.64793	−	2.68348i	−0.350351	−	0.202275i
$177$			2.09251i			0.157283i
$178$	−4.07258	+	15.1991i	−0.305252	+	1.13922i
$179$	4.69109	−	4.69109i	0.350629	−	0.350629i	−0.509715	−	0.860343i	$-0.670249\pi$
$179$	4.69109	−	4.69109i	0.350629	−	0.350629i	0.860343	+	0.509715i	$0.170249\pi$
$180$	2.78548	−	5.52554i	0.207617	−	0.411850i
$181$	−3.44262	−	5.96279i	−0.255888	−	0.443211i	0.709248	−	0.704959i	$-0.249034\pi$
$181$	−3.44262	−	5.96279i	−0.255888	−	0.443211i	−0.965136	+	0.261748i	$0.915701\pi$
$182$	3.35112	−	12.5065i	0.248401	−	0.927046i
$183$	5.38066	+	3.10652i	0.397750	+	0.229641i
$184$	4.59101			0.338454
$185$	−7.26613	+	11.4980i	−0.534216	+	0.845348i
$186$	−3.00405			−0.220268
$187$	17.5747	+	10.1467i	1.28519	+	0.742002i
$188$	−0.939010	+	3.50443i	−0.0684843	+	0.255587i
$189$	2.74331	+	4.75155i	0.199546	+	0.345625i
$190$	14.7174	−	4.85220i	1.06771	−	0.352015i
$191$	−13.8143	+	13.8143i	−0.999568	+	0.999568i	−1.00000		0.000431752i	$-0.999863\pi$
$191$	−13.8143	+	13.8143i	−0.999568	+	0.999568i	0.000431752		1.00000i	$0.499863\pi$
$192$	−0.124844	+	0.465926i	−0.00900987	+	0.0336253i
$193$			5.84158i			0.420486i	0.977649	+	0.210243i	$0.0674255\pi$
$193$			5.84158i			0.420486i	−0.977649	+	0.210243i	$0.932574\pi$
$194$	0.550422	+	0.317786i	0.0395180	+	0.0228157i
$195$	−1.44236	+	6.93253i	−0.103290	+	0.496449i
$196$			3.11031i			0.222165i
$197$	2.58013	−	0.691344i	0.183827	−	0.0492562i	−0.165731	−	0.986171i	$-0.552998\pi$
$197$	2.58013	−	0.691344i	0.183827	−	0.0492562i	0.349558	+	0.936915i	$0.386332\pi$
$198$	12.8623	−	7.42608i	0.914087	−	0.527748i
$199$	9.22018	−	9.22018i	0.653601	−	0.653601i	−0.300257	−	0.953858i	$-0.597073\pi$
$199$	9.22018	−	9.22018i	0.653601	−	0.653601i	0.953858	+	0.300257i	$0.0970725\pi$
$200$	4.01961	−	2.97368i	0.284229	−	0.210271i
$201$	1.21590	−	2.10599i	0.0857627	−	0.148545i
$202$	−8.06097	+	13.9620i	−0.567168	+	0.982364i
$203$	−5.39609	−	9.34631i	−0.378732	−	0.655982i
$204$	0.472059	−	1.76175i	0.0330508	−	0.123347i
$205$	−7.98578	+	0.453031i	−0.557751	+	0.0316411i
$206$	15.8184	+	9.13273i	1.10212	+	0.636307i
$207$	−6.35241	+	11.0027i	−0.441523	+	0.764741i
$208$			6.56502i			0.455202i
$209$	35.9274	+	9.62672i	2.48515	+	0.665894i
$210$	0.120484	+	2.12382i	0.00831417	+	0.146557i
$211$	24.7655			1.70493			0.852465	−	0.522784i	$-0.175107\pi$
$211$	24.7655			1.70493			0.852465	+	0.522784i	$0.175107\pi$
$212$	−4.45127	+	4.45127i	−0.305714	+	0.305714i
$213$	2.80182	−	0.750746i	0.191978	−	0.0514402i
$214$	0.879051	−	0.879051i	0.0600907	−	0.0600907i
$215$	−3.26871	+	6.48412i	−0.222924	+	0.442213i
$216$	−1.96713	−	1.96713i	−0.133846	−	0.133846i
$217$	−10.6371	+	6.14132i	−0.722092	+	0.416900i
$218$	4.53766	+	1.21586i	0.307329	+	0.0823487i
$219$	−3.79747	+	2.19247i	−0.256609	+	0.148153i
$220$	11.9816	−	0.679715i	0.807802	−	0.0458264i
$221$		−	24.8235i		−	1.66981i
$222$	1.86482	+	2.26525i	0.125159	+	0.152033i
$223$	−21.0409	+	21.0409i	−1.40900	+	1.40900i	−0.643846	+	0.765155i	$0.722662\pi$
$223$	−21.0409	+	21.0409i	−1.40900	+	1.40900i	−0.765155	+	0.643846i	$0.777338\pi$
$224$	0.510450	+	1.90503i	0.0341059	+	0.127285i
$225$	1.56486	+	13.7479i	0.104324	+	0.916524i
$226$	−1.64898	+	0.952037i	−0.109688	+	0.0633286i
$227$	−3.39712	−	5.88398i	−0.225475	−	0.390533i	0.730987	−	0.682391i	$-0.239060\pi$
$227$	−3.39712	−	5.88398i	−0.225475	−	0.390533i	−0.956462	+	0.291858i	$0.905727\pi$
$228$		−	3.34292i		−	0.221390i
$229$	−4.11181	+	2.37395i	−0.271716	+	0.156875i	−0.629667	−	0.776865i	$-0.716809\pi$
$229$	−4.11181	+	2.37395i	−0.271716	+	0.156875i	0.357951	+	0.933740i	$0.383475\pi$
$230$	−8.58546	+	5.62821i	−0.566108	+	0.371113i
$231$	−2.55287	+	4.42171i	−0.167967	+	0.290927i
$232$	3.86934	+	3.86934i	0.254035	+	0.254035i
$233$	−7.99123	−	7.99123i	−0.523523	−	0.523523i	0.395111	−	0.918634i	$-0.370706\pi$
$233$	−7.99123	−	7.99123i	−0.523523	−	0.523523i	−0.918634	+	0.395111i	$0.870706\pi$
$234$	−15.7336	−	9.08377i	−1.02853	−	0.593825i
$235$	−2.54015	−	7.70465i	−0.165701	−	0.502596i
$236$	−3.06747	−	3.06747i	−0.199675	−	0.199675i
$237$	2.75701	+	1.59176i	0.179087	+	0.103396i
$238$	−1.93010	−	7.20325i	−0.125110	−	0.466917i
$239$	−4.85485	+	1.30085i	−0.314034	+	0.0841453i	−0.412394	−	0.911006i	$-0.635307\pi$
$239$	−4.85485	+	1.30085i	−0.314034	+	0.0841453i	0.0983594	+	0.995151i	$0.468641\pi$
$240$	−0.337721	−	1.02436i	−0.0217998	−	0.0661220i
$241$	8.76657	+	2.34899i	0.564704	+	0.151312i	0.529867	−	0.848081i	$-0.322242\pi$
$241$	8.76657	+	2.34899i	0.564704	+	0.151312i	0.0348375	+	0.999393i	$0.488909\pi$
$242$	15.4190	+	8.90216i	0.991171	+	0.572253i
$243$	11.3043	−	3.02898i	0.725173	−	0.194309i
$244$	−12.4416	+	3.33371i	−0.796490	+	0.213419i
$245$	−3.81299	−	5.81647i	−0.243603	−	0.371601i
$246$	−0.446580	+	1.66666i	−0.0284729	+	0.106262i
$247$	−11.7757	−	43.9473i	−0.749267	−	2.79630i
$248$	4.40372	−	4.40372i	0.279636	−	0.279636i
$249$	−2.89257			−0.183309
$250$	−3.87141	+	10.4887i	−0.244850	+	0.663362i
$251$	7.96081	+	7.96081i	0.502482	+	0.502482i	0.912208	−	0.409726i	$-0.134376\pi$
$251$	7.96081	+	7.96081i	0.502482	+	0.502482i	−0.409726	+	0.912208i	$0.634376\pi$
$252$	−5.27183	−	1.41258i	−0.332094	−	0.0889844i
$253$	−24.6398			−1.54909
$254$	1.24644	+	0.333984i	0.0782089	+	0.0209560i
$255$	1.27698	+	3.87328i	0.0799679	+	0.242554i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−12.8468	+	22.2512i	−0.801359	+	1.38799i	0.117363	+	0.993089i	$0.462556\pi$
$257$	−12.8468	+	22.2512i	−0.801359	+	1.38799i	−0.918722	+	0.394905i	$0.870778\pi$
$258$	1.10763	+	1.10763i	0.0689580	+	0.0689580i
$259$	11.2341	+	4.20869i	0.698054	+	0.261515i
$260$	−8.04818	−	12.2770i	−0.499127	−	0.761385i
$261$	−14.6270	+	3.91930i	−0.905391	+	0.242599i
$262$	−5.56678	−	1.49161i	−0.343917	−	0.0921522i
$263$	4.11201	−	15.3462i	0.253557	−	0.946289i	−0.715330	−	0.698787i	$-0.753724\pi$
$263$	4.11201	−	15.3462i	0.253557	−	0.946289i	0.968887	−	0.247502i	$-0.0796097\pi$
$264$	0.670036	−	2.50061i	0.0412379	−	0.153902i
$265$	2.86724	−	13.7810i	0.176133	−	0.846562i
$266$	−6.83409	−	11.8370i	−0.419025	−	0.725772i
$267$	−7.59007			−0.464505
$268$	1.30482	+	4.86964i	0.0797044	+	0.297461i
$269$		−	14.0971i		−	0.859517i	−0.902944	−	0.429758i	$-0.858599\pi$
$269$		−	14.0971i		−	0.859517i	0.902944	−	0.429758i	$-0.141401\pi$
$270$	6.09019	+	1.26710i	0.370637	+	0.0771135i
$271$	13.6859	−	23.7046i	0.831357	−	1.43995i	−0.0656050	−	0.997846i	$-0.520898\pi$
$271$	13.6859	−	23.7046i	0.831357	−	1.43995i	0.896962	−	0.442107i	$-0.145769\pi$
$272$	1.89059	+	3.27460i	0.114634	+	0.198552i
$273$	6.24549			0.377994
$274$	−0.416866	−	1.55576i	−0.0251838	−	0.0939872i
$275$	−21.5731	+	15.9596i	−1.30091	+	0.962402i
$276$	0.573162	+	2.13907i	0.0345003	+	0.128757i
$277$	3.64275	−	2.10314i	0.218872	−	0.126366i	−0.386556	−	0.922266i	$-0.626335\pi$
$277$	3.64275	−	2.10314i	0.218872	−	0.126366i	0.605428	+	0.795900i	$0.293002\pi$
$278$	9.04129	−	5.21999i	0.542260	−	0.313074i
$279$	4.46058	+	16.6471i	0.267048	+	0.996636i
$280$	−3.28998	−	2.93674i	−0.196614	−	0.175504i
$281$	8.01768	+	29.9224i	0.478295	+	1.78502i	0.608522	+	0.793537i	$0.291763\pi$
$281$	8.01768	+	29.9224i	0.478295	+	1.78502i	−0.130227	+	0.991484i	$0.541571\pi$
$282$	−1.75004			−0.104213
$283$	−6.95899	−	12.0533i	−0.413669	−	0.716495i	0.581619	−	0.813461i	$-0.302420\pi$
$283$	−6.95899	−	12.0533i	−0.413669	−	0.716495i	−0.995288	+	0.0969660i	$0.969086\pi$
$284$	−3.00672	+	5.20780i	−0.178416	+	0.309026i
$285$	4.09815	+	6.25146i	0.242754	+	0.370304i
$286$		−	35.2342i		−	2.08344i
$287$	1.82593	+	6.81445i	0.107781	+	0.402244i
$288$	2.76733			0.163066
$289$	1.35134	+	2.34059i	0.0794906	+	0.137682i
$290$	−11.9794	−	2.49240i	−0.703455	−	0.146359i
$291$	−0.0793477	+	0.296130i	−0.00465145	+	0.0173594i
$292$	2.35281	−	8.78080i	0.137688	−	0.513857i
$293$	16.0083	+	4.28942i	0.935217	+	0.250591i	0.694078	−	0.719900i	$-0.255812\pi$
$293$	16.0083	+	4.28942i	0.935217	+	0.250591i	0.241139	+	0.970491i	$0.422479\pi$
$294$	−1.44918	+	0.388305i	−0.0845176	+	0.0226464i
$295$	9.49681	+	1.97588i	0.552926	+	0.115040i
$296$	−6.05437	−	0.586988i	−0.351903	−	0.0341180i
$297$	10.5575	+	10.5575i	0.612609	+	0.612609i
$298$	−9.88034	+	17.1132i	−0.572352	+	0.991344i
$299$	15.0700	+	26.1021i	0.871522	+	1.50952i
$300$	1.88734	+	1.50159i	0.108966	+	0.0866944i
$301$	6.18640	+	1.65764i	0.356578	+	0.0955448i
$302$	0.498470			0.0286837
$303$	−7.51163	−	2.01274i	−0.431532	−	0.115629i
$304$	4.90047	+	4.90047i	0.281061	+	0.281061i
$305$	19.1796	−	21.4866i	1.09822	−	1.23032i
$306$	−10.4638			−0.598173
$307$	−12.1318	+	12.1318i	−0.692398	+	0.692398i	−0.962759	−	0.270361i	$-0.912857\pi$
$307$	−12.1318	+	12.1318i	−0.692398	+	0.692398i	0.270361	+	0.962759i	$0.412857\pi$
$308$	−2.73957	−	10.2242i	−0.156101	−	0.582579i
$309$	−2.28034	+	8.51035i	−0.129724	+	0.484137i
$310$	−2.83661	+	13.6338i	−0.161109	+	0.774349i
$311$	−9.15508	+	2.45310i	−0.519137	+	0.139102i	−0.508867	−	0.860845i	$-0.669936\pi$
$311$	−9.15508	+	2.45310i	−0.519137	+	0.139102i	−0.0102695	+	0.999947i	$0.503269\pi$
$312$	−3.05881	+	0.819606i	−0.173171	+	0.0464010i
$313$	−15.1304	−	8.73552i	−0.855219	−	0.493761i	0.00718926	−	0.999974i	$-0.497712\pi$
$313$	−15.1304	−	8.73552i	−0.855219	−	0.493761i	−0.862408	+	0.506213i	$0.831045\pi$
$314$	5.13368	+	1.37557i	0.289710	+	0.0776277i
$315$	11.5904	−	3.82123i	0.653042	−	0.215302i
$316$	−6.37497	+	1.70817i	−0.358620	+	0.0960919i
$317$	−0.749376	−	2.79671i	−0.0420891	−	0.157079i	0.941683	−	0.336501i	$-0.109244\pi$
$317$	−0.749376	−	2.79671i	−0.0420891	−	0.157079i	−0.983772	+	0.179423i	$0.942577\pi$
$318$	−2.62968	−	1.51824i	−0.147465	−	0.0851389i
$319$	−20.7666	−	20.7666i	−1.16271	−	1.16271i
$320$	1.99671	+	1.00656i	0.111619	+	0.0562684i
$321$	0.519317	+	0.299828i	0.0289855	+	0.0167348i
$322$	6.40251	+	6.40251i	0.356798	+	0.356798i
$323$	−18.5296	−	18.5296i	−1.03101	−	1.03101i
$324$	−3.48004	+	6.02761i	−0.193336	+	0.334867i
$325$	30.1012	+	13.0922i	1.66971	+	0.726226i
$326$	−12.3082	+	7.10613i	−0.681687	+	0.393572i
$327$			2.26601i			0.125311i
$328$	−1.78854	−	3.09785i	−0.0987559	−	0.171050i
$329$	−6.19672	+	3.57768i	−0.341636	+	0.197244i
$330$	1.81254	+	5.49770i	0.0997769	+	0.302638i
$331$	−1.64693	−	6.14644i	−0.0905237	−	0.337839i	0.905779	−	0.423750i	$-0.139287\pi$
$331$	−1.64693	−	6.14644i	−0.0905237	−	0.337839i	−0.996303	+	0.0859112i	$0.972620\pi$
$332$	4.24030	−	4.24030i	0.232717	−	0.232717i
$333$	9.78398	−	13.6976i	0.536159	−	0.750622i
$334$			10.6119i			0.580656i
$335$	−8.40987	−	7.50692i	−0.459480	−	0.410147i
$336$	−0.823874	+	0.475664i	−0.0449460	+	0.0259496i
$337$	−5.91014	−	1.58362i	−0.321946	−	0.0862651i	0.0942269	−	0.995551i	$-0.469962\pi$
$337$	−5.91014	−	1.58362i	−0.321946	−	0.0862651i	−0.416172	+	0.909286i	$0.636629\pi$
$338$	−26.0669	+	15.0497i	−1.41785	+	0.818597i
$339$	−0.649444	−	0.649444i	−0.0352730	−	0.0352730i
$340$	−7.54991	−	3.80598i	−0.409451	−	0.206408i
$341$	−23.6346	+	23.6346i	−1.27989	+	1.27989i
$342$	−18.5250	+	4.96375i	−1.00172	+	0.268409i
$343$	−14.0996	+	14.0996i	−0.761307	+	0.761307i
$344$	−3.24741			−0.175088
$345$	−3.69417	−	3.29754i	−0.198888	−	0.177533i
$346$	11.5831	+	3.10368i	0.622711	+	0.166855i
$347$			21.8691i			1.17400i	0.809588	+	0.586998i	$0.199690\pi$
$347$			21.8691i			1.17400i	−0.809588	+	0.586998i	$0.800310\pi$
$348$	−1.31976	+	2.28589i	−0.0707466	+	0.122537i
$349$	−10.6516	−	6.14968i	−0.570165	−	0.329185i	0.187050	−	0.982350i	$-0.440107\pi$
$349$	−10.6516	−	6.14968i	−0.570165	−	0.329185i	−0.757215	+	0.653166i	$0.773441\pi$
$350$	9.75267	+	1.45863i	0.521302	+	0.0779669i
$351$	4.72694	−	17.6412i	0.252305	−	0.941616i
$352$	2.68348	+	4.64793i	0.143030	+	0.247735i
$353$	12.1065	−	20.9691i	0.644365	−	1.11607i	−0.340082	−	0.940396i	$-0.610455\pi$
$353$	12.1065	−	20.9691i	0.644365	−	1.11607i	0.984448	−	0.175678i	$-0.0562117\pi$
$354$	1.04626	−	1.81217i	0.0556078	−	0.0963156i
$355$	−0.761591	−	13.4249i	−0.0404211	−	0.712519i
$356$	11.1265	−	11.1265i	0.589702	−	0.589702i
$357$	3.11522	−	1.79857i	0.164875	−	0.0951905i
$358$	−6.40815	+	1.71706i	−0.338681	+	0.0907494i
$359$		−	5.40490i		−	0.285260i	−0.989776	−	0.142630i	$-0.954444\pi$
$359$		−	5.40490i		−	0.285260i	0.989776	−	0.142630i	$-0.0455559\pi$
$360$	−5.17507	+	3.39252i	−0.272750	+	0.178802i
$361$	−25.1401	−	14.5146i	−1.32316	−	0.763928i
$362$			6.88524i			0.361880i
$363$	−2.22277	+	8.29549i	−0.116665	+	0.435401i
$364$	−9.15542	+	9.15542i	−0.479874	+	0.479874i
$365$	6.36466	+	19.3050i	0.333142	+	1.01047i
$366$	−3.10652	−	5.38066i	−0.162381	−	0.281251i
$367$	−6.87257	+	25.6488i	−0.358745	+	1.33886i	0.516960	+	0.856010i	$0.327064\pi$
$367$	−6.87257	+	25.6488i	−0.358745	+	1.33886i	−0.875705	+	0.482846i	$0.839603\pi$
$368$	−3.97593	−	2.29550i	−0.207260	−	0.119661i
$369$	9.89898			0.515320
$370$	12.0416	−	6.32447i	0.626015	−	0.328794i
$371$	−12.4153			−0.644569
$372$	2.60158	+	1.50203i	0.134886	+	0.0778764i
$373$	−3.01866	+	11.2658i	−0.156300	+	0.583321i	0.842690	+	0.538399i	$0.180971\pi$
$373$	−3.01866	+	11.2658i	−0.156300	+	0.583321i	−0.998991	+	0.0449219i	$0.985696\pi$
$374$	−10.1467	−	17.5747i	−0.524675	−	0.908764i
$375$	−5.37027	−	0.494338i	−0.277319	−	0.0255275i
$376$	2.56542	−	2.56542i	0.132302	−	0.132302i
$377$	−9.29789	+	34.7002i	−0.478865	+	1.78715i
$378$		−	5.48662i		−	0.282201i
$379$	19.3379	+	11.1647i	0.993321	+	0.573494i	0.906265	−	0.422709i	$-0.138921\pi$
$379$	19.3379	+	11.1647i	0.993321	+	0.573494i	0.0870560	+	0.996203i	$0.472254\pi$
$380$	−15.1718	−	3.15659i	−0.778295	−	0.161930i
$381$			0.622446i			0.0318889i
$382$	18.8707	−	5.05639i	0.965509	−	0.258707i
$383$	−14.5888	+	8.42285i	−0.745453	+	0.430388i	−0.824049	−	0.566519i	$-0.808290\pi$
$383$	−14.5888	+	8.42285i	−0.745453	+	0.430388i	0.0785955	+	0.996907i	$0.474956\pi$
$384$	0.341081	−	0.341081i	0.0174057	−	0.0174057i
$385$	17.6572	+	15.7614i	0.899895	+	0.803275i
$386$	2.92079	−	5.05896i	0.148664	−	0.257494i
$387$	4.49332	−	7.78266i	0.228408	−	0.395615i
$388$	−0.317786	−	0.550422i	−0.0161332	−	0.0279435i
$389$	3.32017	−	12.3910i	0.168339	−	0.628251i	−0.829251	−	0.558876i	$-0.811233\pi$
$389$	3.32017	−	12.3910i	0.168339	−	0.628251i	0.997591	−	0.0693748i	$-0.0221004\pi$
$390$	4.71539	−	5.28257i	0.238773	−	0.267493i
$391$	15.0337	+	8.67972i	0.760287	+	0.438952i
$392$	1.55516	−	2.69361i	0.0785473	−	0.136048i
$393$		−	2.77992i		−	0.140229i
$394$	−2.58013	−	0.691344i	−0.129985	−	0.0348294i
$395$	9.82749	−	11.0096i	0.494475	−	0.553952i
$396$	−14.8522			−0.746349
$397$	−4.74373	+	4.74373i	−0.238081	+	0.238081i	−0.816055	−	0.577974i	$-0.803843\pi$
$397$	−4.74373	+	4.74373i	−0.238081	+	0.238081i	0.577974	+	0.816055i	$0.303843\pi$
$398$	−12.5950	+	3.37482i	−0.631330	+	0.169164i
$399$	4.66196	−	4.66196i	0.233390	−	0.233390i
$400$	−4.96792	+	0.565478i	−0.248396	+	0.0282739i
$401$	−8.31260	−	8.31260i	−0.415112	−	0.415112i	0.468403	−	0.883515i	$-0.344829\pi$
$401$	−8.31260	−	8.31260i	−0.415112	−	0.415112i	−0.883515	+	0.468403i	$0.844829\pi$
$402$	−2.10599	+	1.21590i	−0.105037	+	0.0606434i
$403$	39.4924	+	10.5820i	1.96726	+	0.527125i
$404$	13.9620	−	8.06097i	0.694636	−	0.401048i
$405$	−0.881480	−	15.5382i	−0.0438011	−	0.772101i
$406$			10.7922i			0.535607i
$407$	32.4936	+	3.15035i	1.61065	+	0.156157i
$408$	−1.28969	+	1.28969i	−0.0638492	+	0.0638492i
$409$	−1.28183	−	4.78384i	−0.0633822	−	0.236545i	0.926966	−	0.375144i	$-0.122407\pi$
$409$	−1.28183	−	4.78384i	−0.0633822	−	0.236545i	−0.990349	+	0.138599i	$0.955740\pi$
$410$	7.14240	+	3.60055i	0.352738	+	0.177819i
$411$	0.672828	−	0.388457i	0.0331881	−	0.0191612i
$412$	−9.13273	−	15.8184i	−0.449937	−	0.779314i
$413$		−	8.55563i		−	0.420995i
$414$	11.0027	−	6.35241i	0.540753	−	0.312204i
$415$	−2.73134	+	13.1279i	−0.134076	+	0.644422i
$416$	3.28251	−	5.68547i	0.160938	−	0.278753i
$417$	3.56088	+	3.56088i	0.174377	+	0.174377i
$418$	−26.3007	−	26.3007i	−1.28641	−	1.28641i
$419$	−26.1044	−	15.0714i	−1.27528	−	0.736285i	−0.299306	−	0.954157i	$-0.596755\pi$
$419$	−26.1044	−	15.0714i	−1.27528	−	0.736285i	−0.975977	+	0.217872i	$0.930088\pi$
$420$	0.957568	−	1.89952i	0.0467245	−	0.0926873i
$421$	7.00494	+	7.00494i	0.341400	+	0.341400i	0.856893	−	0.515494i	$-0.172391\pi$
$421$	7.00494	+	7.00494i	0.341400	+	0.341400i	−0.515494	+	0.856893i	$0.672391\pi$
$422$	−21.4476	−	12.3828i	−1.04405	−	0.602784i
$423$	2.59855	+	9.69791i	0.126346	+	0.471529i
$424$	6.08055	−	1.62928i	0.295297	−	0.0791247i
$425$	18.7846	−	2.13817i	0.911187	−	0.103717i
$426$	−2.80182	−	0.750746i	−0.135749	−	0.0363737i
$427$	−21.9998	−	12.7016i	−1.06465	−	0.614674i
$428$	−1.20081	+	0.321755i	−0.0580432	+	0.0155526i
$429$	16.4165	−	4.39880i	0.792598	−	0.212376i
$430$	6.07284	−	3.98106i	0.292858	−	0.191984i
$431$	0.693145	−	2.58685i	0.0333876	−	0.124604i	−0.947221	−	0.320582i	$-0.896121\pi$
$431$	0.693145	−	2.58685i	0.0333876	−	0.124604i	0.980608	+	0.195978i	$0.0627881\pi$
$432$	0.720019	+	2.68715i	0.0346419	+	0.129285i
$433$	−17.8688	+	17.8688i	−0.858721	+	0.858721i	−0.991188	−	0.132466i	$-0.957710\pi$
$433$	−17.8688	+	17.8688i	−0.858721	+	0.858721i	0.132466	+	0.991188i	$0.457710\pi$
$434$	12.2826			0.589586
$435$	−0.334290	−	5.89267i	−0.0160280	−	0.282532i
$436$	−3.32180	−	3.32180i	−0.159085	−	0.159085i
$437$	30.7330	+	8.23488i	1.47016	+	0.393928i
$438$	4.38494			0.209520
$439$	−13.6742	−	3.66399i	−0.652633	−	0.174873i	−0.0827142	−	0.996573i	$-0.526359\pi$
$439$	−13.6742	−	3.66399i	−0.652633	−	0.174873i	−0.569919	+	0.821701i	$0.693026\pi$
$440$	−10.7163	−	5.40217i	−0.510878	−	0.257538i
$441$	4.30363	+	7.45410i	0.204935	+	0.354957i
$442$	−12.4118	+	21.4978i	−0.590367	+	1.02255i
$443$	−21.2048	−	21.2048i	−1.00747	−	1.00747i	−0.999972	−	0.00749634i	$-0.997614\pi$
$443$	−21.2048	−	21.2048i	−1.00747	−	1.00747i	−0.00749634	−	0.999972i	$-0.502386\pi$
$444$	−0.482362	−	2.89417i	−0.0228919	−	0.137351i
$445$	−7.16701	+	34.4474i	−0.339749	+	1.63296i
$446$	28.7424	−	7.70149i	1.36099	−	0.364676i
$447$	−9.20701	−	2.46701i	−0.435476	−	0.116686i
$448$	0.510450	−	1.90503i	0.0241165	−	0.0900041i
$449$	−2.30519	+	8.60310i	−0.108789	+	0.406006i	−0.998747	−	0.0500358i	$-0.984066\pi$
$449$	−2.30519	+	8.60310i	−0.108789	+	0.406006i	0.889959	+	0.456041i	$0.150733\pi$
$450$	5.51872	−	12.6884i	0.260155	−	0.598138i
$451$	9.59906	+	16.6261i	0.452002	+	0.782891i
$452$	1.90407			0.0895601
$453$	0.0622312	+	0.232250i	0.00292388	+	0.0109121i
$454$			6.79423i			0.318869i
$455$	5.89737	−	28.3450i	0.276473	−	1.32883i
$456$	−1.67146	+	2.89505i	−0.0782733	+	0.135573i
$457$	−10.9231	−	18.9193i	−0.510960	−	0.885008i	−0.999919	−	0.0127017i	$-0.995957\pi$
$457$	−10.9231	−	18.9193i	−0.510960	−	0.885008i	0.488960	−	0.872306i	$-0.337377\pi$
$458$	4.74790			0.221855
$459$	−2.72252	−	10.1606i	−0.127076	−	0.474255i
$460$	10.2493	−	0.581442i	0.477877	−	0.0271099i
$461$	−5.93578	−	22.1526i	−0.276457	−	1.03175i	−0.954859	−	0.297060i	$-0.903994\pi$
$461$	−5.93578	−	22.1526i	−0.276457	−	1.03175i	0.678402	−	0.734691i	$-0.262673\pi$
$462$	4.42171	−	2.55287i	0.205716	−	0.118770i
$463$	31.8878	−	18.4104i	1.48195	−	0.855605i	0.482161	−	0.876083i	$-0.339852\pi$
$463$	31.8878	−	18.4104i	1.48195	−	0.855605i	0.999790	+	0.0204776i	$0.00651867\pi$
$464$	−1.41628	−	5.28562i	−0.0657490	−	0.245379i
$465$	−6.70648	+	0.380457i	−0.311006	+	0.0176433i
$466$	2.92499	+	10.9162i	0.135498	+	0.505684i
$467$	5.17869			0.239641			0.119821	−	0.992796i	$-0.461768\pi$
$467$	5.17869			0.239641			0.119821	+	0.992796i	$0.461768\pi$
$468$	9.08377	+	15.7336i	0.419898	+	0.727284i
$469$	−4.97142	+	8.61075i	−0.229559	+	0.397608i
$470$	−1.65249	+	7.94249i	−0.0762237	+	0.366360i
$471$			2.56365i			0.118127i
$472$	1.12277	+	4.19024i	0.0516797	+	0.192871i
$473$	17.4287			0.801373
$474$	−1.59176	−	2.75701i	−0.0731119	−	0.126634i
$475$	32.2418	−	12.6964i	1.47936	−	0.582549i
$476$	−1.93010	+	7.20325i	−0.0884662	+	0.330160i
$477$	−4.50874	+	16.8269i	−0.206441	+	0.770449i
$478$	4.85485	+	1.30085i	0.222056	+	0.0594997i
$479$	18.9576	−	5.07969i	0.866197	−	0.232097i	0.201754	−	0.979436i	$-0.435336\pi$
$479$	18.9576	−	5.07969i	0.866197	−	0.232097i	0.664442	+	0.747339i	$0.268669\pi$
$480$	−0.219704	+	1.05598i	−0.0100281	+	0.0481987i
$481$	−16.5362	−	36.3488i	−0.753987	−	1.65736i
$482$	−6.41757	−	6.41757i	−0.292312	−	0.292312i
$483$	−2.18378	+	3.78241i	−0.0993653	+	0.172106i
$484$	−8.90216	−	15.4190i	−0.404644	−	0.700864i
$485$	1.26905	+	0.639742i	0.0576247	+	0.0290492i
$486$	−11.3043	−	3.02898i	−0.512774	−	0.137397i
$487$	−22.6191			−1.02497			−0.512484	−	0.858697i	$-0.671275\pi$
$487$	−22.6191			−1.02497			−0.512484	+	0.858697i	$0.671275\pi$
$488$	12.4416	+	3.33371i	0.563204	+	0.150910i
$489$	−4.84754	−	4.84754i	−0.219213	−	0.219213i
$490$	0.393915	+	6.94371i	0.0177953	+	0.313685i
$491$	5.38517			0.243029			0.121515	−	0.992590i	$-0.461225\pi$
$491$	5.38517			0.243029			0.121515	+	0.992590i	$0.461225\pi$
$492$	1.22008	−	1.22008i	0.0550054	−	0.0550054i
$493$	5.35520	+	19.9859i	0.241186	+	0.900119i
$494$	−11.7757	+	43.9473i	−0.529812	+	1.97728i
$495$	27.7744	−	18.2075i	1.24837	−	0.818368i
$496$	−6.01559	+	1.61187i	−0.270108	+	0.0723752i
$497$	−11.4558	+	3.06957i	−0.513862	+	0.137689i
$498$	2.50504	+	1.44629i	0.112254	+	0.0648096i
$499$	−14.7440	−	3.95063i	−0.660030	−	0.176855i	−0.0867707	−	0.996228i	$-0.527655\pi$
$499$	−14.7440	−	3.95063i	−0.660030	−	0.176855i	−0.573260	+	0.819374i	$0.694321\pi$
$500$	8.59707	−	7.14775i	0.384473	−	0.319657i
$501$	−4.94434	+	1.32483i	−0.220897	+	0.0591892i
$502$	−2.91386	−	10.8747i	−0.130052	−	0.485360i
$503$	−9.10341	−	5.25585i	−0.405901	−	0.234347i	0.283126	−	0.959083i	$-0.408629\pi$
$503$	−9.10341	−	5.25585i	−0.405901	−	0.234347i	−0.689027	+	0.724736i	$0.741962\pi$
$504$	3.85925	+	3.85925i	0.171905	+	0.171905i
$505$	−16.2277	+	32.1908i	−0.722123	+	1.43247i
$506$	21.3387	+	12.3199i	0.948620	+	0.547686i
$507$	−10.2664	−	10.2664i	−0.455945	−	0.455945i
$508$	−0.912460	−	0.912460i	−0.0404839	−	0.0404839i
$509$	−2.32973	+	4.03522i	−0.103264	+	0.178858i	−0.913027	−	0.407898i	$-0.866262\pi$
$509$	−2.32973	+	4.03522i	−0.103264	+	0.178858i	0.809764	+	0.586756i	$0.199595\pi$
$510$	0.830740	−	3.99285i	0.0367858	−	0.176806i
$511$	15.5267	−	8.96433i	0.686859	−	0.396558i
$512$			1.00000i			0.0441942i
$513$	−9.63986	−	16.6967i	−0.425610	−	0.737178i
$514$	22.2512	−	12.8468i	0.981460	−	0.566646i
$515$	36.4708	+	18.3853i	1.60709	+	0.810151i
$516$	−0.405421	−	1.51305i	−0.0178477	−	0.0666083i
$517$	−13.7685	+	13.7685i	−0.605539	+	0.605539i
$518$	−7.62469	−	9.26189i	−0.335010	−	0.406944i
$519$			5.78434i			0.253904i
$520$	0.831446	+	14.6563i	0.0364613	+	0.642719i
$521$	22.3164	−	12.8844i	0.977701	−	0.564476i	0.0761257	−	0.997098i	$-0.475745\pi$
$521$	22.3164	−	12.8844i	0.977701	−	0.564476i	0.901575	+	0.432622i	$0.142412\pi$
$522$	14.6270	+	3.91930i	0.640208	+	0.171543i
$523$	−5.19358	+	2.99852i	−0.227099	+	0.131116i	−0.609233	−	0.792991i	$-0.708523\pi$
$523$	−5.19358	+	2.99852i	−0.227099	+	0.131116i	0.382134	+	0.924107i	$0.375189\pi$
$524$	4.07516	+	4.07516i	0.178024	+	0.178024i
$525$	0.537955	+	4.72612i	0.0234783	+	0.206265i
$526$	−11.2342	+	11.2342i	−0.489835	+	0.489835i
$527$	22.7460	−	6.09478i	0.990832	−	0.265493i
$528$	−1.83057	+	1.83057i	−0.0796654	+	0.0796654i
$529$	1.92263			0.0835927
$530$	−9.37362	+	10.5011i	−0.407164	+	0.456139i
$531$	−11.5958	−	3.10707i	−0.503213	−	0.134835i
$532$			13.6682i			0.592590i
$533$	11.7418	−	20.3374i	0.508595	−	0.880912i
$534$	6.57319	+	3.79504i	0.284450	+	0.164227i
$535$	1.85113	−	2.07379i	0.0800315	−	0.0896579i
$536$	1.30482	−	4.86964i	0.0563595	−	0.210336i
$537$	−1.60004	−	2.77136i	−0.0690470	−	0.119593i
$538$	−7.04856	+	12.2085i	−0.303885	+	0.526344i
$539$	−8.34647	+	14.4565i	−0.359508	+	0.622686i
$540$	−4.64070	−	4.14244i	−0.199704	−	0.178262i
$541$	−2.57136	+	2.57136i	−0.110551	+	0.110551i	−0.760219	−	0.649667i	$-0.774908\pi$
$541$	−2.57136	+	2.57136i	−0.110551	+	0.110551i	0.649667	+	0.760219i	$0.274908\pi$
$542$	−23.7046	+	13.6859i	−1.01820	+	0.587858i
$543$	−3.20801	+	0.859584i	−0.137669	+	0.0368883i
$544$		−	3.78118i		−	0.162117i
$545$	10.2842	+	2.13970i	0.440528	+	0.0916548i
$546$	−5.40875	−	3.12274i	−0.231473	−	0.133641i
$547$		−	29.4642i		−	1.25980i	−0.776676	−	0.629900i	$-0.783096\pi$
$547$		−	29.4642i		−	1.25980i	0.776676	−	0.629900i	$-0.216904\pi$
$548$	−0.416866	+	1.55576i	−0.0178076	+	0.0664590i
$549$	−25.2044	+	25.2044i	−1.07570	+	1.07570i
$550$	26.6627	−	3.03490i	1.13690	−	0.129409i
$551$	18.9616	+	32.8425i	0.807792	+	1.39914i
$552$	0.573162	−	2.13907i	0.0243954	−	0.0910449i
$553$	−11.2726	−	6.50821i	−0.479358	−	0.276757i
$554$	−4.20628			−0.178708
$555$	4.45007	+	4.82093i	0.188895	+	0.204637i
$556$	−10.4400			−0.442754
$557$	5.16816	+	2.98384i	0.218982	+	0.126429i	0.605479	−	0.795861i	$-0.292982\pi$
$557$	5.16816	+	2.98384i	0.218982	+	0.126429i	−0.386497	+	0.922291i	$0.626315\pi$
$558$	4.46058	−	16.6471i	0.188831	−	0.704728i
$559$	−10.6596	−	18.4630i	−0.450855	−	0.780903i
$560$	1.38084	+	4.18828i	0.0583510	+	0.176987i
$561$	6.92172	−	6.92172i	0.292235	−	0.292235i
$562$	8.01768	−	29.9224i	0.338206	−	1.26220i
$563$			21.6691i			0.913243i	0.889661	+	0.456621i	$0.150941\pi$
$563$			21.6691i			0.913243i	−0.889661	+	0.456621i	$0.849059\pi$
$564$	1.51558	+	0.875018i	0.0638172	+	0.0368449i
$565$	−3.56073	+	2.33424i	−0.149801	+	0.0982023i
$566$			13.9180i			0.585016i
$567$	−13.2591	+	3.55278i	−0.556831	+	0.149203i
$568$	5.20780	−	3.00672i	0.218514	−	0.126159i
$569$	−11.7420	+	11.7420i	−0.492250	+	0.492250i	−0.909015	−	0.416764i	$-0.863164\pi$
$569$	−11.7420	+	11.7420i	−0.492250	+	0.492250i	0.416764	+	0.909015i	$0.363164\pi$
$570$	−0.423374	−	7.46300i	−0.0177332	−	0.312591i
$571$	1.51372	−	2.62184i	0.0633471	−	0.109720i	−0.832612	−	0.553856i	$-0.813156\pi$
$571$	1.51372	−	2.62184i	0.0633471	−	0.109720i	0.895960	+	0.444136i	$0.146489\pi$
$572$	−17.6171	+	30.5137i	−0.736608	+	1.27584i
$573$	4.71180	+	8.16108i	0.196838	+	0.340934i
$574$	1.82593	−	6.81445i	0.0762127	−	0.284430i
$575$	−18.4541	+	13.6522i	−0.769587	+	0.569335i
$576$	−2.39658	−	1.38366i	−0.0998573	−	0.0576526i
$577$	13.8637	−	24.0127i	0.577155	−	0.999662i	−0.418649	−	0.908148i	$-0.637496\pi$
$577$	13.8637	−	24.0127i	0.577155	−	0.999662i	0.995804	−	0.0915135i	$-0.0291705\pi$
$578$		−	2.70268i		−	0.112417i
$579$	2.72174	+	0.729289i	0.113112	+	0.0303082i
$580$	9.12827	+	8.14818i	0.379031	+	0.338335i
$581$	11.8268			0.490660
$582$	0.216782	−	0.216782i	0.00898591	−	0.00898591i
$583$	−32.6341	+	8.74428i	−1.35157	+	0.362151i
$584$	−6.42799	+	6.42799i	−0.265992	+	0.265992i
$585$	−36.2753	−	18.2867i	−1.49980	−	0.756062i
$586$	−11.7189	−	11.7189i	−0.484104	−	0.484104i
$587$	21.3879	−	12.3483i	0.882771	−	0.509668i	0.0112003	−	0.999937i	$-0.496435\pi$
$587$	21.3879	−	12.3483i	0.882771	−	0.509668i	0.871571	+	0.490269i	$0.163101\pi$
$588$	1.44918	+	0.388305i	0.0597630	+	0.0160134i
$589$	37.3782	−	21.5803i	1.54014	−	0.889201i
$590$	−7.23654	−	6.45956i	−0.297924	−	0.265936i
$591$		−	1.28846i		−	0.0530002i
$592$	4.94975	+	3.53553i	0.203433	+	0.145310i
$593$	−13.6561	+	13.6561i	−0.560788	+	0.560788i	−0.929531	−	0.368743i	$-0.879788\pi$
$593$	−13.6561	+	13.6561i	−0.560788	+	0.560788i	0.368743	+	0.929531i	$0.379788\pi$
$594$	−3.86432	−	14.4218i	−0.158555	−	0.591735i
$595$	−5.22119	−	15.8367i	−0.214048	−	0.649240i
$596$	17.1132	−	9.88034i	0.700986	−	0.404714i
$597$	−3.14483	−	5.44701i	−0.128709	−	0.222931i
$598$		−	30.1401i		−	1.23252i
$599$	13.3411	−	7.70246i	0.545101	−	0.314714i	−0.202043	−	0.979377i	$-0.564758\pi$
$599$	13.3411	−	7.70246i	0.545101	−	0.314714i	0.747144	+	0.664663i	$0.231425\pi$
$600$	−0.883688	−	2.24409i	−0.0360764	−	0.0916144i
$601$	−15.0549	+	26.0759i	−0.614103	+	1.06366i	0.376438	+	0.926442i	$0.377149\pi$
$601$	−15.0549	+	26.0759i	−0.614103	+	1.06366i	−0.990541	+	0.137216i	$0.956185\pi$
$602$	−4.52876	−	4.52876i	−0.184578	−	0.184578i
$603$	9.86504	+	9.86504i	0.401735	+	0.401735i
$604$	−0.431688	−	0.249235i	−0.0175651	−	0.0101412i
$605$	35.5500	+	17.9211i	1.44531	+	0.728596i
$606$	5.49890	+	5.49890i	0.223377	+	0.223377i
$607$	26.4558	+	15.2743i	1.07381	+	0.619964i	0.929219	−	0.369528i	$-0.120481\pi$
$607$	26.4558	+	15.2743i	1.07381	+	0.619964i	0.144589	+	0.989492i	$0.453814\pi$
$608$	−1.79370	−	6.69417i	−0.0727441	−	0.271484i
$609$	−5.02836	+	1.34734i	−0.203759	+	0.0545972i
$610$	−27.3533	+	9.01814i	−1.10750	+	0.365134i
$611$	23.0067	+	6.16462i	0.930750	+	0.249394i
$612$	9.06188	+	5.23188i	0.366305	+	0.211486i
$613$	16.8486	−	4.51456i	0.680507	−	0.182341i	0.0980240	−	0.995184i	$-0.468748\pi$
$613$	16.8486	−	4.51456i	0.680507	−	0.182341i	0.582483	+	0.812843i	$0.302081\pi$
$614$	16.5723	−	4.44054i	0.668805	−	0.179206i
$615$	−0.785901	+	3.77734i	−0.0316906	+	0.152317i
$616$	−2.73957	+	10.2242i	−0.110380	+	0.411945i
$617$	2.58283	+	9.63923i	0.103981	+	0.388061i	0.998228	−	0.0595130i	$-0.0189548\pi$
$617$	2.58283	+	9.63923i	0.103981	+	0.388061i	−0.894247	+	0.447574i	$0.852288\pi$
$618$	6.23001	−	6.23001i	0.250608	−	0.250608i
$619$	−0.193638			−0.00778297			−0.00389148	−	0.999992i	$-0.501239\pi$
$619$	−0.193638			−0.00778297			−0.00389148	+	0.999992i	$0.501239\pi$
$620$	9.27348	−	10.3889i	0.372432	−	0.417229i
$621$	9.03110	+	9.03110i	0.362406	+	0.362406i
$622$	9.15508	+	2.45310i	0.367085	+	0.0983602i
$623$	31.0335			1.24333
$624$	3.05881	+	0.819606i	0.122450	+	0.0328105i
$625$	−7.31447	+	23.9060i	−0.292579	+	0.956241i
$626$	8.73552	+	15.1304i	0.349142	+	0.604731i
$627$	8.97067	−	15.5377i	0.358254	−	0.620514i
$628$	−3.75812	−	3.75812i	−0.149965	−	0.149965i
$629$	−18.7159	−	13.3685i	−0.746251	−	0.533037i
$630$	−11.9482	−	2.48589i	−0.476026	−	0.0990404i
$631$	−37.3679	+	10.0127i	−1.48759	+	0.398599i	−0.908924	−	0.416963i	$-0.863095\pi$
$631$	−37.3679	+	10.0127i	−1.48759	+	0.398599i	−0.578670	+	0.815562i	$0.696428\pi$
$632$	6.37497	+	1.70817i	0.253583	+	0.0679473i
$633$	3.09184	−	11.5389i	0.122890	−	0.458630i
$634$	−0.749376	+	2.79671i	−0.0297615	+	0.111071i
$635$	2.82496	+	0.587752i	0.112105	+	0.0233242i
$636$	1.51824	+	2.62968i	0.0602023	+	0.104273i
$637$	20.4193			0.809040
$638$	7.60111	+	28.3677i	0.300931	+	1.12309i
$639$			16.6412i			0.658315i
$640$	−1.22592	−	1.87006i	−0.0484587	−	0.0739206i
$641$	11.0406	−	19.1229i	0.436077	−	0.755308i	−0.561306	−	0.827609i	$-0.689701\pi$
$641$	11.0406	−	19.1229i	0.436077	−	0.755308i	0.997383	+	0.0723007i	$0.0230341\pi$
$642$	−0.299828	−	0.519317i	−0.0118333	−	0.0204958i
$643$	−27.4386			−1.08207			−0.541035	−	0.841000i	$-0.681968\pi$
$643$	−27.4386			−1.08207			−0.541035	+	0.841000i	$0.681968\pi$
$644$	−2.34348	−	8.74600i	−0.0923462	−	0.344641i
$645$	2.61304	+	2.33248i	0.102888	+	0.0918413i
$646$	6.78229	+	25.3119i	0.266846	+	0.995882i
$647$	7.14288	−	4.12394i	0.280816	−	0.162129i	−0.352977	−	0.935632i	$-0.614831\pi$
$647$	7.14288	−	4.12394i	0.280816	−	0.162129i	0.633793	+	0.773503i	$0.281497\pi$
$648$	6.02761	−	3.48004i	0.236787	−	0.136709i
$649$	−6.02587	−	22.4889i	−0.236536	−	0.882765i
$650$	−19.5222	−	26.3888i	−0.765726	−	1.03505i
$651$	1.53342	+	5.72280i	0.0600994	+	0.224294i
$652$	14.2123			0.556595
$653$	18.9161	+	32.7637i	0.740244	+	1.28214i	0.952384	+	0.304902i	$0.0986236\pi$
$653$	18.9161	+	32.7637i	0.740244	+	1.28214i	−0.212139	+	0.977239i	$0.568043\pi$
$654$	1.13300	−	1.96242i	0.0443040	−	0.0767367i
$655$	−12.6166	−	2.62497i	−0.492972	−	0.102566i
$656$			3.57709i			0.139662i
$657$	−6.51099	−	24.2993i	−0.254018	−	0.948008i
$658$	7.15536			0.278945
$659$	5.45357	+	9.44587i	0.212441	+	0.367959i	0.952478	−	0.304608i	$-0.0985253\pi$
$659$	5.45357	+	9.44587i	0.212441	+	0.367959i	−0.740037	+	0.672566i	$0.765192\pi$
$660$	1.17914	−	5.66741i	0.0458981	−	0.220604i
$661$	2.37617	−	8.86799i	0.0924223	−	0.344925i	−0.904194	−	0.427123i	$-0.859527\pi$
$661$	2.37617	−	8.86799i	0.0924223	−	0.344925i	0.996616	+	0.0821978i	$0.0261939\pi$
$662$	−1.64693	+	6.14644i	−0.0640099	+	0.238888i
$663$	−11.5659	−	3.09908i	−0.449183	−	0.120358i
$664$	−5.79235	+	1.55206i	−0.224787	+	0.0602315i
$665$	−16.7561	−	25.5603i	−0.649773	−	0.991185i
$666$	−15.3220	+	6.97045i	−0.593714	+	0.270100i
$667$	−17.7642	−	17.7642i	−0.687832	−	0.687832i
$668$	5.30594	−	9.19015i	0.205293	−	0.355578i
$669$	7.17665	+	12.4303i	0.277465	+	0.480584i
$670$	3.52971	+	10.7061i	0.136364	+	0.413613i
$671$	−66.7735	−	17.8919i	−2.57776	−	0.690709i
$672$	0.951328			0.0366983
$673$	32.9326	+	8.82427i	1.26946	+	0.340150i	0.829824	−	0.558026i	$-0.188441\pi$
$673$	32.9326	+	8.82427i	1.26946	+	0.340150i	0.439635	+	0.898176i	$0.355108\pi$
$674$	4.32652	+	4.32652i	0.166651	+	0.166651i
$675$	13.7567	+	2.05747i	0.529495	+	0.0791922i
$676$	30.0994			1.15767
$677$	−6.22348	+	6.22348i	−0.239188	+	0.239188i	−0.816514	−	0.577326i	$-0.804096\pi$
$677$	−6.22348	+	6.22348i	−0.239188	+	0.239188i	0.577326	+	0.816514i	$0.304096\pi$
$678$	0.237713	+	0.887157i	0.00912932	+	0.0340711i
$679$	0.324428	−	1.21078i	0.0124504	−	0.0464656i
$680$	4.63542	+	7.07103i	0.177760	+	0.271162i
$681$	−3.16561	+	0.848222i	−0.121306	+	0.0325039i
$682$	32.2855	−	8.65086i	1.23627	−	0.331259i
$683$	−3.63039	−	2.09601i	−0.138913	−	0.0802015i	0.428933	−	0.903336i	$-0.358890\pi$
$683$	−3.63039	−	2.09601i	−0.138913	−	0.0802015i	−0.567846	+	0.823135i	$0.692223\pi$
$684$	18.5250	+	4.96375i	0.708320	+	0.189794i
$685$	−1.12768	−	3.42042i	−0.0430864	−	0.130687i
$686$	19.2604	−	5.16081i	0.735366	−	0.197041i
$687$	0.592750	+	2.21217i	0.0226148	+	0.0843996i
$688$	2.81234	+	1.62370i	0.107219	+	0.0619031i
$689$	29.2227	+	29.2227i	1.11329	+	1.11329i
$690$	1.55048	+	4.70284i	0.0590258	+	0.179034i
$691$	−24.0071	−	13.8605i	−0.913273	−	0.527278i	−0.0317902	−	0.999495i	$-0.510121\pi$
$691$	−24.0071	−	13.8605i	−0.913273	−	0.527278i	−0.881483	+	0.472216i	$0.843454\pi$
$692$	−8.47941	−	8.47941i	−0.322339	−	0.322339i
$693$	−20.7125	−	20.7125i	−0.786801	−	0.786801i
$694$	10.9346	−	18.9392i	0.415070	−	0.718923i
$695$	19.5234	−	12.7986i	0.740564	−	0.485478i
$696$	2.28589	−	1.31976i	0.0866465	−	0.0500254i
$697$		−	13.5256i		−	0.512319i
$698$	6.14968	+	10.6516i	0.232769	+	0.403167i
$699$	−4.72098	+	2.72566i	−0.178564	+	0.103094i
$700$	−7.71675	−	6.13954i	−0.291666	−	0.232053i
$701$	−3.85344	−	14.3812i	−0.145542	−	0.543171i	−0.999731	−	0.0232075i	$-0.992612\pi$
$701$	−3.85344	−	14.3812i	−0.145542	−	0.543171i	0.854188	−	0.519964i	$-0.174055\pi$
$702$	−12.9142	+	12.9142i	−0.487416	+	0.487416i
$703$	−39.4761	−	14.7891i	−1.48887	−	0.557782i
$704$		−	5.36697i		−	0.202275i
$705$	−3.90692	+	0.221638i	−0.147143	+	0.00834739i
$706$	−20.9691	+	12.1065i	−0.789183	+	0.455635i
$707$	30.7127	+	8.22946i	1.15507	+	0.309501i
$708$	−1.81217	+	1.04626i	−0.0681054	+	0.0393207i
$709$	2.95851	+	2.95851i	0.111109	+	0.111109i	0.760476	−	0.649366i	$-0.224966\pi$
$709$	2.95851	+	2.95851i	0.111109	+	0.111109i	−0.649366	+	0.760476i	$0.724966\pi$
$710$	−6.05289	+	12.0071i	−0.227161	+	0.450618i
$711$	−12.9146	+	12.9146i	−0.484334	+	0.484334i
$712$	−15.1991	+	4.07258i	−0.569609	+	0.152626i
$713$	−20.2175	+	20.2175i	−0.757152	+	0.757152i
$714$	−3.59714			−0.134620
$715$	−4.46234	−	78.6596i	−0.166882	−	2.94170i
$716$	6.40815	+	1.71706i	0.239484	+	0.0641695i
$717$			2.42441i			0.0905411i
$718$	−2.70245	+	4.68078i	−0.100855	+	0.174685i
$719$	−7.90486	−	4.56388i	−0.294802	−	0.170204i	0.345304	−	0.938491i	$-0.387776\pi$
$719$	−7.90486	−	4.56388i	−0.294802	−	0.170204i	−0.640105	+	0.768287i	$0.721109\pi$
$720$	6.17800	−	0.350476i	0.230240	−	0.0130615i
$721$	9.32361	−	34.7962i	0.347229	−	1.29588i
$722$	14.5146	+	25.1401i	0.540179	+	0.935617i
$723$	2.18891	−	3.79131i	0.0814066	−	0.141000i
$724$	3.44262	−	5.96279i	0.127944	−	0.221605i
$725$	−27.0594	−	4.04705i	−1.00496	−	0.150304i
$726$	6.07272	−	6.07272i	0.225380	−	0.225380i
$727$	−21.8110	+	12.5926i	−0.808926	+	0.467034i	−0.846583	−	0.532257i	$-0.821344\pi$
$727$	−21.8110	+	12.5926i	−0.808926	+	0.467034i	0.0376568	+	0.999291i	$0.488011\pi$
$728$	12.5065	−	3.35112i	0.463523	−	0.124201i
$729$			15.2351i			0.564263i
$730$	4.14052	−	19.9009i	0.153248	−	0.736566i
$731$	−10.6340	−	6.13951i	−0.393311	−	0.227078i
$732$			6.21305i			0.229641i
$733$	6.32344	−	23.5994i	0.233562	−	0.871664i	−0.745230	−	0.666807i	$-0.767661\pi$
$733$	6.32344	−	23.5994i	0.233562	−	0.871664i	0.978792	−	0.204857i	$-0.0656728\pi$
$734$	18.7762	−	18.7762i	0.693043	−	0.693043i
$735$	−3.18607	+	1.05042i	−0.117520	+	0.0387453i
$736$	2.29550	+	3.97593i	0.0846134	+	0.146555i
$737$	−7.00291	+	26.1352i	−0.257955	+	0.962703i
$738$	−8.57277	−	4.94949i	−0.315568	−	0.182193i
$739$	−13.6836			−0.503358			−0.251679	−	0.967811i	$-0.580983\pi$
$739$	−13.6836			−0.503358			−0.251679	+	0.967811i	$0.580983\pi$
$740$	−13.5906	−	0.543665i	−0.499600	−	0.0199855i
$741$	−21.9463			−0.806219
$742$	10.7519	+	6.20763i	0.394716	+	0.227889i
$743$	7.50981	−	28.0270i	0.275508	−	1.02821i	−0.679992	−	0.733220i	$-0.738017\pi$
$743$	7.50981	−	28.0270i	0.275508	−	1.02821i	0.955500	−	0.294991i	$-0.0953166\pi$
$744$	−1.50203	−	2.60158i	−0.0550669	−	0.0953787i
$745$	−19.8903	+	39.4563i	−0.728723	+	1.44557i
$746$	8.24713	−	8.24713i	0.301949	−	0.301949i
$747$	4.29505	−	16.0293i	0.157148	−	0.586483i
$748$			20.2935i			0.742002i
$749$	−2.12333	−	1.22590i	−0.0775847	−	0.0447936i
$750$	4.40362	+	3.11324i	0.160797	+	0.113680i
$751$		−	8.25347i		−	0.301173i	−0.988597	−	0.150587i	$-0.951884\pi$
$751$		−	8.25347i		−	0.301173i	0.988597	−	0.150587i	$-0.0481163\pi$
$752$	−3.50443	+	0.939010i	−0.127793	+	0.0342422i
$753$	4.70301	−	2.71529i	0.171387	−	0.0989505i
$754$	25.4023	−	25.4023i	0.925097	−	0.925097i
$755$	1.11282	−	0.0631302i	0.0404998	−	0.00229754i
$756$	−2.74331	+	4.75155i	−0.0997732	+	0.172812i
$757$	3.62439	−	6.27763i	0.131731	−	0.228164i	−0.792613	−	0.609725i	$-0.791280\pi$
$757$	3.62439	−	6.27763i	0.131731	−	0.228164i	0.924344	+	0.381561i	$0.124613\pi$
$758$	−11.1647	−	19.3379i	−0.405522	−	0.702384i
$759$	−3.07614	+	11.4803i	−0.111657	+	0.416709i
$760$	11.5608	+	10.3196i	0.419356	+	0.374330i
$761$	30.3145	+	17.5021i	1.09890	+	0.634450i	0.935932	−	0.352181i	$-0.114560\pi$
$761$	30.3145	+	17.5021i	1.09890	+	0.634450i	0.162968	+	0.986631i	$0.447893\pi$
$762$	0.311223	−	0.539054i	0.0112744	−	0.0195279i
$763$		−	9.26501i		−	0.335416i
$764$	−18.8707	−	5.05639i	−0.682718	−	0.182934i
$765$	−23.3601	+	1.32521i	−0.844587	+	0.0479132i
$766$	16.8457			0.608660
$767$	−20.1380	+	20.1380i	−0.727140	+	0.727140i
$768$	−0.465926	+	0.124844i	−0.0168127	+	0.00450494i
$769$	−27.2577	+	27.2577i	−0.982937	+	0.982937i	−0.999857	−	0.0169197i	$-0.994614\pi$
$769$	−27.2577	+	27.2577i	−0.982937	+	0.982937i	0.0169197	+	0.999857i	$0.494614\pi$
$770$	−7.41091	−	22.4784i	−0.267071	−	0.810065i
$771$	8.76358	+	8.76358i	0.315613	+	0.315613i
$772$	−5.05896	+	2.92079i	−0.182076	+	0.105122i
$773$	4.13148	+	1.10703i	0.148599	+	0.0398170i	0.332352	−	0.943156i	$-0.392158\pi$
$773$	4.13148	+	1.10703i	0.148599	+	0.0398170i	−0.183753	+	0.982973i	$0.558825\pi$
$774$	−7.78266	+	4.49332i	−0.279742	+	0.161509i
$775$	−4.60597	+	30.7964i	−0.165451	+	1.10624i
$776$			0.635573i			0.0228157i
$777$	3.36345	−	4.70883i	0.120663	−	0.168928i
$778$	−9.07087	+	9.07087i	−0.325206	+	0.325206i
$779$	−6.41622	−	23.9457i	−0.229885	−	0.857942i
$780$	−6.72493	+	2.21714i	−0.240791	+	0.0793865i
$781$	−27.9501	+	16.1370i	−1.00013	+	0.577427i
$782$	−8.67972	−	15.0337i	−0.310386	−	0.537604i
$783$			15.2230i			0.544025i
$784$	−2.69361	+	1.55516i	−0.0962004	+	0.0555413i
$785$	11.6350	+	2.42075i	0.415273	+	0.0864003i
$786$	−1.38996	+	2.40749i	−0.0495783	+	0.0858722i
$787$	−25.5115	−	25.5115i	−0.909388	−	0.909388i	0.0868345	−	0.996223i	$-0.472325\pi$
$787$	−25.5115	−	25.5115i	−0.909388	−	0.909388i	−0.996223	+	0.0868345i	$0.972325\pi$
$788$	1.88879	+	1.88879i	0.0672852	+	0.0672852i
$789$	−6.63684	−	3.83178i	−0.236278	−	0.136415i
$790$	−14.0156	+	4.62082i	−0.498654	+	0.164402i
$791$	2.65538	+	2.65538i	0.0944143	+	0.0944143i
$792$	12.8623	+	7.42608i	0.457043	+	0.263874i
$793$	21.8859	+	81.6791i	0.777190	+	2.90051i
$794$	6.48006	−	1.73633i	0.229969	−	0.0616199i
$795$	−6.06298	−	3.05641i	−0.215032	−	0.108400i
$796$	12.5950	+	3.37482i	0.446418	+	0.119617i
$797$	3.02143	+	1.74443i	0.107025	+	0.0617907i	0.552557	−	0.833475i	$-0.313652\pi$
$797$	3.02143	+	1.74443i	0.107025	+	0.0617907i	−0.445532	+	0.895266i	$0.646986\pi$
$798$	−6.36835	+	1.70640i	−0.225437	+	0.0604057i
$799$	13.2509	−	3.55056i	0.468783	−	0.125610i
$800$	4.58508	+	1.99424i	0.162107	+	0.0705071i
$801$	11.2701	−	42.0608i	0.398211	−	1.48614i
$802$	3.04262	+	11.3552i	0.107439	+	0.400967i
$803$	34.4988	−	34.4988i	1.21744	−	1.21744i
$804$	2.43179			0.0857627
$805$	15.1043	+	13.4826i	0.532358	+	0.475200i
$806$	−28.9105	−	28.9105i	−1.01833	−	1.01833i
$807$	−6.56821	−	1.75995i	−0.231212	−	0.0619531i
$808$	−16.1219			−0.567168
$809$	−14.5067	−	3.88706i	−0.510028	−	0.136662i	−0.00537798	−	0.999986i	$-0.501712\pi$
$809$	−14.5067	−	3.88706i	−0.510028	−	0.136662i	−0.504650	+	0.863324i	$0.668379\pi$
$810$	−7.00573	+	13.8972i	−0.246156	+	0.488299i
$811$	9.36658	+	16.2234i	0.328905	+	0.569680i	0.982295	−	0.187341i	$-0.0599870\pi$
$811$	9.36658	+	16.2234i	0.328905	+	0.569680i	−0.653390	+	0.757022i	$0.726654\pi$
$812$	5.39609	−	9.34631i	0.189366	−	0.327991i
$813$	−9.33599	−	9.33599i	−0.327427	−	0.327427i
$814$	−26.5651	−	18.9751i	−0.931107	−	0.665077i
$815$	−26.5778	+	17.4231i	−0.930978	+	0.610304i
$816$	1.76175	−	0.472059i	0.0616736	−	0.0165254i
$817$	−21.7387	−	5.82487i	−0.760541	−	0.203786i
$818$	−1.28183	+	4.78384i	−0.0448180	+	0.167263i
$819$	−9.27363	+	34.6097i	−0.324047	+	1.20936i
$820$	−4.38522	−	6.68937i	−0.153139	−	0.233603i
$821$	−17.2447	−	29.8687i	−0.601845	−	1.04243i	−0.992542	−	0.121906i	$-0.961099\pi$
$821$	−17.2447	−	29.8687i	−0.601845	−	1.04243i	0.390697	−	0.920519i	$-0.372234\pi$
$822$	−0.776914			−0.0270980
$823$	0.110082	+	0.410832i	0.00383722	+	0.0143207i	0.967818	−	0.251652i	$-0.0809737\pi$
$823$	0.110082	+	0.410832i	0.00383722	+	0.0143207i	−0.963981	+	0.265972i	$0.914307\pi$
$824$			18.2655i			0.636307i
$825$	4.74272	+	12.0439i	0.165120	+	0.419316i
$826$	−4.27782	+	7.40939i	−0.148844	+	0.257806i
$827$	−21.9872	−	38.0829i	−0.764570	−	1.32427i	−0.940474	−	0.339866i	$-0.889618\pi$
$827$	−21.9872	−	38.0829i	−0.764570	−	1.32427i	0.175904	−	0.984407i	$-0.443715\pi$
$828$	−12.7048			−0.441523
$829$	12.9861	+	48.4649i	0.451027	+	1.68326i	0.699513	+	0.714620i	$0.253400\pi$
$829$	12.9861	+	48.4649i	0.451027	+	1.68326i	−0.248486	+	0.968635i	$0.579933\pi$
$830$	8.92935	−	10.0034i	0.309942	−	0.347223i
$831$	−0.525131	−	1.95982i	−0.0182166	−	0.0679853i
$832$	−5.68547	+	3.28251i	−0.197108	+	0.113801i
$833$	10.1850	−	5.88033i	0.352890	−	0.203741i
$834$	−1.30337	−	4.86426i	−0.0451321	−	0.168435i
$835$	1.34397	+	23.6908i	0.0465101	+	0.819853i
$836$	9.62672	+	35.9274i	0.332947	+	1.24257i
$837$	17.3253			0.598852
$838$	15.0714	+	26.1044i	0.520632	+	0.901761i
$839$	−27.7780	+	48.1130i	−0.959004	+	1.66104i	−0.234079	+	0.972218i	$0.575207\pi$
$839$	−27.7780	+	48.1130i	−0.959004	+	1.66104i	−0.724926	+	0.688827i	$0.758126\pi$
$840$	−1.77904	+	1.16625i	−0.0613827	+	0.0402395i
$841$		−	0.943618i		−	0.0325385i
$842$	−2.56398	−	9.56892i	−0.0883607	−	0.329767i
$843$	14.9426			0.514650
$844$	12.3828	+	21.4476i	0.426233	+	0.738257i
$845$	−56.2877	+	36.8995i	−1.93636	+	1.26938i
$846$	2.59855	−	9.69791i	0.0893399	−	0.333421i
$847$	9.08822	−	33.9177i	0.312275	−	1.16543i
$848$	−6.08055	−	1.62928i	−0.208807	−	0.0559496i
$849$	−6.48474	+	1.73758i	−0.222556	+	0.0596337i
$850$	−17.3370	−	7.54059i	−0.594655	−	0.258640i
$851$	27.7957	+	2.69487i	0.952824	+	0.0923789i
$852$	2.05108	+	2.05108i	0.0702687	+	0.0702687i
$853$	−9.86858	+	17.0929i	−0.337894	+	0.585249i	−0.984036	−	0.177967i	$-0.943048\pi$
$853$	−9.86858	+	17.0929i	−0.337894	+	0.585249i	0.646143	+	0.763217i	$0.276381\pi$
$854$	12.7016	+	21.9998i	0.434640	+	0.752819i
$855$	−40.7279	+	13.4276i	−1.39287	+	0.459215i
$856$	1.20081	+	0.321755i	0.0410427	+	0.0109974i
$857$	2.19062			0.0748301			0.0374150	−	0.999300i	$-0.488088\pi$
$857$	2.19062			0.0748301			0.0374150	+	0.999300i	$0.488088\pi$
$858$	−16.4165	−	4.39880i	−0.560451	−	0.150172i
$859$	−23.7052	−	23.7052i	−0.808810	−	0.808810i	0.175644	−	0.984454i	$-0.443799\pi$
$859$	−23.7052	−	23.7052i	−0.808810	−	0.808810i	−0.984454	+	0.175644i	$0.943799\pi$
$860$	−7.24977	+	0.411277i	−0.247215	+	0.0140244i
$861$	3.40299			0.115973
$862$	−1.89371	+	1.89371i	−0.0645000	+	0.0645000i
$863$	4.45538	+	16.6277i	0.151663	+	0.566013i	0.999368	+	0.0355458i	$0.0113170\pi$
$863$	4.45538	+	16.6277i	0.151663	+	0.566013i	−0.847705	+	0.530468i	$0.822016\pi$
$864$	0.720019	−	2.68715i	0.0244955	−	0.0914186i
$865$	26.2521	+	5.46193i	0.892598	+	0.185711i
$866$	24.4093	−	6.54045i	0.829461	−	0.222253i
$867$	1.25925	−	0.337415i	0.0427663	−	0.0114592i
$868$	−10.6371	−	6.14132i	−0.361046	−	0.208450i
$869$	−34.2142	−	9.16768i	−1.16064	−	0.310992i
$870$	−2.65683	+	5.27035i	−0.0900751	+	0.178682i
$871$	31.9693	−	8.56614i	1.08324	−	0.290253i
$872$	1.21586	+	4.53766i	0.0411743	+	0.153665i
$873$	−1.52320	−	0.879419i	−0.0515525	−	0.0297638i
$874$	−22.4981	−	22.4981i	−0.761010	−	0.761010i
$875$	21.9574	+	2.02120i	0.742294	+	0.0683289i
$876$	−3.79747	−	2.19247i	−0.128305	−	0.0740766i
$877$	−1.32377	−	1.32377i	−0.0447005	−	0.0447005i	0.684403	−	0.729104i	$-0.260063\pi$
$877$	−1.32377	−	1.32377i	−0.0447005	−	0.0447005i	−0.729104	+	0.684403i	$0.760063\pi$
$878$	10.0102	+	10.0102i	0.337828	+	0.337828i
$879$	3.99710	−	6.92319i	0.134819	−	0.233513i
$880$	6.57947	+	10.0365i	0.221794	+	0.338332i
$881$	8.51804	−	4.91789i	0.286980	−	0.165688i	−0.349599	−	0.936899i	$-0.613682\pi$
$881$	8.51804	−	4.91789i	0.286980	−	0.165688i	0.636579	+	0.771211i	$0.280349\pi$
$882$		−	8.60725i		−	0.289821i
$883$	−13.8030	−	23.9076i	−0.464510	−	0.804554i	0.534670	−	0.845061i	$-0.320436\pi$
$883$	−13.8030	−	23.9076i	−0.464510	−	0.804554i	−0.999179	+	0.0405070i	$0.987103\pi$
$884$	21.4978	−	12.4118i	0.723049	−	0.417452i
$885$	2.10624	−	4.17813i	0.0708003	−	0.140446i
$886$	7.76148	+	28.9662i	0.260752	+	0.973140i
$887$	20.9681	−	20.9681i	0.704041	−	0.704041i	−0.261235	−	0.965275i	$-0.584130\pi$
$887$	20.9681	−	20.9681i	0.704041	−	0.704041i	0.965275	+	0.261235i	$0.0841296\pi$
$888$	−1.02935	+	2.74761i	−0.0345427	+	0.0922037i
$889$		−	2.54499i		−	0.0853563i
$890$	23.4305	−	26.2488i	0.785392	−	0.879861i
$891$	−32.3500	+	18.6773i	−1.08376	+	0.625712i
$892$	−28.7424	−	7.70149i	−0.962366	−	0.257865i
$893$	21.7750	−	12.5718i	0.728672	−	0.420699i
$894$	6.74000	+	6.74000i	0.225419	+	0.225419i
$895$	−14.0886	+	4.64488i	−0.470930	+	0.155261i
$896$	−1.39458	+	1.39458i	−0.0465895	+	0.0465895i
$897$	14.0430	−	3.76282i	0.468883	−	0.125637i
$898$	6.29791	−	6.29791i	0.210164	−	0.210164i
$899$	−34.0790			−1.13660
$900$	−11.1236	+	8.22914i	−0.370786	+	0.274305i
$901$	22.9916	+	6.16059i	0.765962	+	0.205239i
$902$		−	19.1981i		−	0.639227i
$903$	1.54467	−	2.67546i	0.0514036	−	0.0890336i
$904$	−1.64898	−	0.952037i	−0.0548441	−	0.0316643i
$905$	0.872002	+	15.3711i	0.0289863	+	0.510954i
$906$	0.0622312	−	0.232250i	0.00206749	−	0.00771599i
$907$	3.98843	+	6.90816i	0.132434	+	0.229382i	0.924614	−	0.380905i	$-0.124388\pi$
$907$	3.98843	+	6.90816i	0.132434	+	0.229382i	−0.792181	+	0.610287i	$0.791054\pi$
$908$	3.39712	−	5.88398i	0.112737	−	0.195267i
$909$	22.3074	−	38.6375i	0.739888	−	1.28152i
$910$	−19.2798	+	21.5988i	−0.639118	+	0.715993i
$911$	19.2508	−	19.2508i	0.637809	−	0.637809i	−0.312206	−	0.950015i	$-0.601068\pi$
$911$	19.2508	−	19.2508i	0.637809	−	0.637809i	0.950015	+	0.312206i	$0.101068\pi$
$912$	2.89505	−	1.67146i	0.0958648	−	0.0553476i
$913$	31.0874	−	8.32983i	1.02884	−	0.275677i
$914$			21.8461i			0.722606i
$915$	−7.61669	−	11.6188i	−0.251800	−	0.384104i
$916$	−4.11181	−	2.37395i	−0.135858	−	0.0784376i
$917$			11.3663i			0.375347i
$918$	−2.72252	+	10.1606i	−0.0898566	+	0.335349i
$919$	4.89008	−	4.89008i	0.161309	−	0.161309i	−0.621838	−	0.783146i	$-0.713614\pi$
$919$	4.89008	−	4.89008i	0.161309	−	0.161309i	0.783146	+	0.621838i	$0.213614\pi$
$920$	−9.16690	−	4.62112i	−0.302224	−	0.152354i
$921$	4.13793	+	7.16710i	0.136349	+	0.236164i
$922$	−5.93578	+	22.1526i	−0.195484	+	0.729558i
$923$	34.1893	+	19.7392i	1.12535	+	0.649723i
$924$	−5.10575			−0.167967
$925$	26.0817	−	15.6443i	0.857562	−	0.514381i
$926$	−36.8209			−1.21001
$927$	−43.7746	−	25.2733i	−1.43774	−	0.830082i
$928$	−1.41628	+	5.28562i	−0.0464916	+	0.173509i
$929$	1.19241	+	2.06531i	0.0391216	+	0.0677606i	0.884923	−	0.465737i	$-0.154211\pi$
$929$	1.19241	+	2.06531i	0.0391216	+	0.0677606i	−0.845802	+	0.533498i	$0.820877\pi$
$930$	5.99821	+	3.02375i	0.196689	+	0.0991528i
$931$	15.2420	−	15.2420i	0.499537	−	0.499537i
$932$	2.92499	−	10.9162i	0.0958114	−	0.357573i
$933$			4.57184i			0.149675i
$934$	−4.48488	−	2.58935i	−0.146750	−	0.0847260i
$935$	−24.8782	−	37.9500i	−0.813603	−	1.24110i
$936$		−	18.1675i		−	0.593825i
$937$	56.6567	−	15.1811i	1.85089	−	0.495945i	0.851306	−	0.524670i	$-0.175811\pi$
$937$	56.6567	−	15.1811i	1.85089	−	0.495945i	0.999587	+	0.0287247i	$0.00914461\pi$
$938$	8.61075	−	4.97142i	0.281151	−	0.162323i
$939$	−5.95905	+	5.95905i	−0.194466	+	0.194466i
$940$	5.40234	−	6.05216i	0.176205	−	0.197400i
$941$	−12.6032	+	21.8293i	−0.410852	+	0.711616i	−0.994983	−	0.100043i	$-0.968102\pi$
$941$	−12.6032	+	21.8293i	−0.410852	+	0.711616i	0.584131	+	0.811659i	$0.301435\pi$
$942$	1.28182	−	2.22018i	0.0417641	−	0.0723375i
$943$	8.21123	+	14.2223i	0.267394	+	0.463141i
$944$	1.12277	−	4.19024i	0.0365431	−	0.136381i
$945$	−0.694869	−	12.2488i	−0.0226041	−	0.398452i
$946$	−15.0937	−	8.71436i	−0.490739	−	0.283328i
$947$	−13.2377	+	22.9283i	−0.430167	+	0.745071i	−0.996887	−	0.0788395i	$-0.974879\pi$
$947$	−13.2377	+	22.9283i	−0.430167	+	0.745071i	0.566721	+	0.823910i	$0.308212\pi$
$948$			3.18352i			0.103396i
$949$	−57.6461	−	15.4462i	−1.87127	−	0.501406i
$950$	−34.2704	−	5.12554i	−1.11188	−	0.166295i
$951$	−1.39661			−0.0452883
$952$	5.27314	−	5.27314i	0.170904	−	0.170904i
$953$	1.65020	−	0.442171i	0.0534554	−	0.0143233i	−0.231992	−	0.972718i	$-0.574524\pi$
$953$	1.65020	−	0.442171i	0.0534554	−	0.0143233i	0.285448	+	0.958394i	$0.407858\pi$
$954$	12.3181	−	12.3181i	0.398814	−	0.398814i
$955$	41.4880	−	13.6782i	1.34252	−	0.442617i
$956$	−3.55400	−	3.55400i	−0.114945	−	0.114945i
$957$	−12.2683	+	7.08311i	−0.396578	+	0.228964i
$958$	−18.9576	−	5.07969i	−0.612494	−	0.164117i
$959$	−2.75098	+	1.58828i	−0.0888339	+	0.0512883i
$960$	0.718260	−	0.804654i	0.0231817	−	0.0259701i
$961$			7.78544i			0.251143i
$962$	−3.85359	+	39.7471i	−0.124245	+	1.28150i
$963$	−2.43262	+	2.43262i	−0.0783902	+	0.0783902i
$964$	2.34899	+	8.76657i	0.0756560	+	0.282352i
$965$	5.87989	−	11.6639i	0.189281	−	0.375475i
$966$	3.78241	−	2.18378i	0.121697	−	0.0702619i
$967$	−2.34589	−	4.06319i	−0.0754386	−	0.130664i	0.825838	−	0.563907i	$-0.190702\pi$
$967$	−2.34589	−	4.06319i	−0.0754386	−	0.130664i	−0.901277	+	0.433243i	$0.857369\pi$
$968$			17.8043i			0.572253i
$969$	−10.9467	+	6.32009i	−0.351659	+	0.203031i
$970$	−0.779161	−	1.18856i	−0.0250174	−	0.0381623i
$971$	−5.76350	+	9.98268i	−0.184960	+	0.320359i	−0.943563	−	0.331193i	$-0.892549\pi$
$971$	−5.76350	+	9.98268i	−0.184960	+	0.320359i	0.758603	+	0.651553i	$0.225882\pi$
$972$	8.27534	+	8.27534i	0.265432	+	0.265432i
$973$	−14.5594	−	14.5594i	−0.466751	−	0.466751i
$974$	19.5887	+	11.3095i	0.627663	+	0.362381i
$975$	9.85797	−	12.3904i	0.315708	−	0.396811i
$976$	−9.10786	−	9.10786i	−0.291536	−	0.291536i
$977$	9.81837	+	5.66864i	0.314117	+	0.181356i	0.648767	−	0.760987i	$-0.275285\pi$
$977$	9.81837	+	5.66864i	0.314117	+	0.181356i	−0.334650	+	0.942342i	$0.608618\pi$
$978$	1.77432	+	6.62186i	0.0567365	+	0.211744i
$979$	81.5728	−	21.8574i	2.60708	−	0.698565i
$980$	3.13071	−	6.21038i	0.100007	−	0.198383i
$981$	−12.5572	−	3.36469i	−0.400921	−	0.107426i
$982$	−4.66370	−	2.69259i	−0.148825	−	0.0859239i
$983$	−26.9488	+	7.22092i	−0.859534	+	0.230311i	−0.661557	−	0.749895i	$-0.730104\pi$
$983$	−26.9488	+	7.22092i	−0.859534	+	0.230311i	−0.197977	+	0.980207i	$0.563437\pi$
$984$	−1.66666	+	0.446580i	−0.0531311	+	0.0142364i
$985$	−5.84764	−	1.21664i	−0.186321	−	0.0387654i
$986$	5.35520	−	19.9859i	0.170544	−	0.636480i
$987$	0.893306	+	3.33387i	0.0284343	+	0.106118i
$988$	32.1717	−	32.1717i	1.02352	−	1.02352i
$989$	14.9089			0.474075
$990$	−33.1571	+	1.88099i	−1.05380	+	0.0597819i
$991$	33.7108	+	33.7108i	1.07086	+	1.07086i	0.997290	+	0.0735670i	$0.0234383\pi$
$991$	33.7108	+	33.7108i	1.07086	+	1.07086i	0.0735670	+	0.997290i	$0.476562\pi$
$992$	6.01559	+	1.61187i	0.190995	+	0.0511770i
$993$	−3.06940			−0.0974043
$994$	11.4558	+	3.06957i	0.363355	+	0.0973608i
$995$	−27.6906	+	9.12934i	−0.877852	+	0.289420i
$996$	−1.44629	−	2.50504i	−0.0458273	−	0.0793753i
$997$	−1.22477	+	2.12136i	−0.0387888	+	0.0671841i	−0.884768	−	0.466032i	$-0.845683\pi$
$997$	−1.22477	+	2.12136i	−0.0387888	+	0.0671841i	0.845979	+	0.533216i	$0.179017\pi$
$998$	10.7933	+	10.7933i	0.341657	+	0.341657i
$999$	−10.7550	−	13.0644i	−0.340275	−	0.413340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.r.e.347.3	yes	16
5.3	odd	4		370.2.q.e.273.3	yes	16
37.8	odd	12		370.2.q.e.267.3	✓	16
185.8	even	12	inner	370.2.r.e.193.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.e.267.3	✓	16	37.8	odd	12
370.2.q.e.273.3	yes	16	5.3	odd	4
370.2.r.e.193.3	yes	16	185.8	even	12	inner
370.2.r.e.347.3	yes	16	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.r (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.124844 - 0.465926i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.99671 - 1.00656i) q^{5} +(-0.341081 + 0.341081i) q^{6} +(-0.510450 + 1.90503i) q^{7} -1.00000i q^{8} +(2.39658 + 1.38366i) q^{9} +(1.22592 + 1.87006i) q^{10} +5.36697i q^{11} +(0.465926 - 0.124844i) q^{12} +(5.68547 - 3.28251i) q^{13} +(1.39458 - 1.39458i) q^{14} +(-0.718260 + 0.804654i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.89059 - 3.27460i) q^{17} +(-1.38366 - 2.39658i) q^{18} +(1.79370 - 6.69417i) q^{19} +(-0.126648 - 2.23248i) q^{20} +(0.823874 + 0.475664i) q^{21} +(2.68348 - 4.64793i) q^{22} +4.59101i q^{23} +(-0.465926 - 0.124844i) q^{24} +(2.97368 + 4.01961i) q^{25} -6.56502 q^{26} +(1.96713 - 1.96713i) q^{27} +(-1.90503 + 0.510450i) q^{28} +(-3.86934 + 3.86934i) q^{29} +(1.02436 - 0.337721i) q^{30} +(4.40372 + 4.40372i) q^{31} +(0.866025 - 0.500000i) q^{32} +(2.50061 + 0.670036i) q^{33} +(-3.27460 + 1.89059i) q^{34} +(2.93674 - 3.28998i) q^{35} +2.76733i q^{36} +(0.586988 - 6.05437i) q^{37} +(-4.90047 + 4.90047i) q^{38} +(-0.819606 - 3.05881i) q^{39} +(-1.00656 + 1.99671i) q^{40} +(3.09785 - 1.78854i) q^{41} +(-0.475664 - 0.823874i) q^{42} -3.24741i q^{43} +(-4.64793 + 2.68348i) q^{44} +(-3.39252 - 5.17507i) q^{45} +(2.29550 - 3.97593i) q^{46} +(2.56542 + 2.56542i) q^{47} +(0.341081 + 0.341081i) q^{48} +(2.69361 + 1.55516i) q^{49} +(-0.565478 - 4.96792i) q^{50} +(-1.28969 - 1.28969i) q^{51} +(5.68547 + 3.28251i) q^{52} +(1.62928 + 6.08055i) q^{53} +(-2.68715 + 0.720019i) q^{54} +(5.40217 - 10.7163i) q^{55} +(1.90503 + 0.510450i) q^{56} +(-2.89505 - 1.67146i) q^{57} +(5.28562 - 1.41628i) q^{58} +(-4.19024 + 1.12277i) q^{59} +(-1.05598 - 0.219704i) q^{60} +(-3.33371 + 12.4416i) q^{61} +(-1.61187 - 6.01559i) q^{62} +(-3.85925 + 3.85925i) q^{63} -1.00000 q^{64} +(-14.6563 + 0.831446i) q^{65} +(-1.83057 - 1.83057i) q^{66} +(4.86964 + 1.30482i) q^{67} +3.78118 q^{68} +(2.13907 + 0.573162i) q^{69} +(-4.18828 + 1.38084i) q^{70} +(3.00672 + 5.20780i) q^{71} +(1.38366 - 2.39658i) q^{72} +(-6.42799 - 6.42799i) q^{73} +(-3.53553 + 4.94975i) q^{74} +(2.24409 - 0.883688i) q^{75} +(6.69417 - 1.79370i) q^{76} +(-10.2242 - 2.73957i) q^{77} +(-0.819606 + 3.05881i) q^{78} +(-1.70817 + 6.37497i) q^{79} +(1.87006 - 1.22592i) q^{80} +(3.48004 + 6.02761i) q^{81} -3.57709 q^{82} +(-1.55206 - 5.79235i) q^{83} +0.951328i q^{84} +(-7.07103 + 4.63542i) q^{85} +(-1.62370 + 2.81234i) q^{86} +(1.31976 + 2.28589i) q^{87} +5.36697 q^{88} +(-4.07258 - 15.1991i) q^{89} +(0.350476 + 6.17800i) q^{90} +(3.35112 + 12.5065i) q^{91} +(-3.97593 + 2.29550i) q^{92} +(2.60158 - 1.50203i) q^{93} +(-0.939010 - 3.50443i) q^{94} +(-10.3196 + 11.5608i) q^{95} +(-0.124844 - 0.465926i) q^{96} -0.635573 q^{97} +(-1.55516 - 2.69361i) q^{98} +(-7.42608 + 12.8623i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{3} + 8 q^{4} - 8 q^{6} + 24 q^{9} - 4 q^{10} - 8 q^{12} + 12 q^{13} - 8 q^{16} - 16 q^{17} + 24 q^{19} + 12 q^{20} - 12 q^{21} + 8 q^{22} + 8 q^{24} + 16 q^{25} + 8 q^{26} - 16 q^{27} - 16 q^{29}+ \cdots - 8 q^{99}+O(q^{100}) \) 16 * q - 16 * q^3 + 8 * q^4 - 8 * q^6 + 24 * q^9 - 4 * q^10 - 8 * q^12 + 12 * q^13 - 8 * q^16 - 16 * q^17 + 24 * q^19 + 12 * q^20 - 12 * q^21 + 8 * q^22 + 8 * q^24 + 16 * q^25 + 8 * q^26 - 16 * q^27 - 16 * q^29 - 8 * q^30 + 24 * q^31 + 12 * q^33 - 8 * q^35 - 8 * q^40 - 36 * q^41 + 4 * q^42 + 20 * q^45 + 4 * q^46 + 32 * q^47 + 8 * q^48 - 24 * q^49 - 4 * q^50 - 16 * q^51 + 12 * q^52 + 24 * q^53 + 8 * q^54 - 12 * q^55 - 60 * q^57 + 8 * q^58 + 8 * q^59 - 12 * q^60 + 8 * q^61 + 12 * q^62 + 16 * q^63 - 16 * q^64 + 12 * q^65 - 24 * q^66 + 8 * q^67 - 32 * q^68 + 8 * q^69 - 20 * q^70 + 4 * q^71 - 48 * q^73 - 36 * q^75 + 24 * q^76 - 12 * q^77 - 20 * q^79 + 12 * q^80 + 16 * q^81 - 24 * q^82 - 48 * q^83 - 8 * q^85 + 8 * q^86 - 12 * q^87 + 16 * q^88 + 8 * q^89 + 4 * q^90 - 8 * q^91 + 12 * q^92 - 36 * q^93 + 28 * q^94 + 8 * q^95 + 16 * q^96 + 16 * q^97 - 8 * q^98 - 8 * q^99

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